{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lateral Stability\n",
    "\n",
    "Lateral motions refer to the aircraft response in roll. In a static sense, there is no such concept as \"roll stiffness\" because there is no aerodynamic roll angle (the aircraft doesn't know if the wind vector is rotated about its own axis).\n",
    "\n",
    "```{epigraph}\n",
    "\"*...the concept of roll stability, in the static sense, does not exist. At the most one could say that an airplane possesses neutral static stability in roll.*\"\n",
    "\n",
    "-- Aerodynamics, Aeronautics and Flight Mechanics, page 545 {cite}`MacCormick:1995wq`\n",
    "```\n",
    "\n",
    "$$C_{\\ell} = C_{\\ell_\\beta}\\cdot\\beta + C_{\\ell_P}\\cdot P + C_{\\ell_{\\delta_a}}\\cdot\\delta_a$$\n",
    "\n",
    "Some (mostly online, but that's what you guys will find when searching) texts refer to the derivative $C_{\\ell_\\beta}$ as *roll stiffness*, and I can see *why*, but it's incorrect. This derivative is *dihedral effect*, and is an example of a **cross-coupling**, which will be talked about further in [cross-couplings](cross-couplings).\n",
    "\n",
    "The second term is the roll damping - again, this is always restorative and hence negative.\n",
    "\n",
    "## Roll damping\n",
    "\n",
    "The parameter $C_{\\ell_{P}}$ or $C_{\\ell_\\bar{p}}$ is known as roll damping, and refers to the rate of change of rolling moment with roll rate. Since both $\\ell$ and $P$ are defined as a right-handed rotation, the stability condition for both of these is a **negative derivative**.\n",
    "\n",
    "```{margin} Derivative signs\n",
    "The **direct** derivatives *i.e., NOT cross-couplings* are all negative for stability *except* $C_{n_\\beta}$. It's the only one that's positive for stability.\n",
    "```\n",
    "\n",
    "Roll damping is always restorative - consider a positive roll rate, $P$, and the contribution due the aircraft wings:\n",
    "- Starboard wing down $=$ upwash$\\,\\therefore\\alpha\\uparrow\\,\\therefore C_L\\uparrow\\,\\therefore C_\\ell=f(y\\cdot C_L)\\downarrow$ \n",
    "- Port wing up $=$ downwash$\\,\\therefore\\,\\alpha\\downarrow\\,\\therefore C_L\\downarrow\\,\\therefore C_\\ell=f(-y\\cdot C_L)\\downarrow$ \n",
    "- Hence an increase in roll rate $P$ causes a decrease in rolling moment $L$\n",
    "- A negative roll rate similarly causes an increase in rolling moment\n",
    "- $\\therefore C_{\\ell_P}<0$\n",
    "\n",
    "The contribution from the wings to roll damping is only part of the aerodynamic roll damping - similar contributions can be found from both the horizontal and vertical stabilisers, and a viscous component can be considered from the different surfaces including the fuselage.\n",
    "\n",
    "The wing contribution is by far the largest, though, due to the greater moment arm that increases both the angle of attack change, and the moment produced by the lift increase/decrease.\n",
    "\n",
    "### Numerical Estimates\n",
    "\n",
    "An estimate can be considered of the roll damping based upon the wing contribution. In a simplified model of the aerodynamics, a strip model of the wing can be utilised. Consider a section of the wing at location $y$, a wing _element_ of span $\\text{d}y$\n",
    "\n",
    "```{margin}\n",
    "Just for the hell of it, that is a 2412 section which is really present on the Cessna 172.\n",
    "```\n",
    "```{figure} ../Images/RollDamping.png\n",
    "---\n",
    "height: 600px\n",
    "name: RollDamping\n",
    "---\n",
    "Upwash and Downwash on wings due to positive roll rate\n",
    "```\n",
    "The vertical velocity, positive in the sense of an *upwash* is $P\\cdot y$.\n",
    "\n",
    "The change in effective angle of attack, $\\alpha^\\prime$, is therefore\n",
    "\n",
    "$$\\alpha^\\prime=\\tan^{-1}\\frac{y\\,P}{V_{\\infty}}$$\n",
    "\n",
    "Which, subject to the small angle approximation (expand the bit of code below if you're interested about small angles) is\n",
    "\n",
    "$$\\alpha^\\prime\\simeq\\frac{y\\,P}{V_{\\infty}}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "hide-input",
     "hide-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "mode": "lines",
         "name": "$\\theta - \\sin\\theta$",
         "type": "scatter",
         "x": [
          0.1,
          0.14994994994994995,
          0.1998998998998999,
          0.24984984984984984,
          0.29979979979979976,
          0.3497497497497497,
          0.39969969969969965,
          0.4496496496496496,
          0.49959959959959954,
          0.5495495495495495,
          0.5994994994994994,
          0.6494494494494494,
          0.6993993993993993,
          0.7493493493493493,
          0.7992992992992992,
          0.8492492492492492,
          0.8991991991991991,
          0.949149149149149,
          0.999099099099099,
          1.049049049049049,
          1.098998998998999,
          1.148948948948949,
          1.198898898898899,
          1.2488488488488487,
          1.2987987987987988,
          1.3487487487487488,
          1.3986986986986987,
          1.4486486486486485,
          1.4985985985985986,
          1.5485485485485486,
          1.5984984984984985,
          1.6484484484484483,
          1.6983983983983983,
          1.7483483483483484,
          1.7982982982982982,
          1.848248248248248,
          1.8981981981981981,
          1.9481481481481482,
          1.998098098098098,
          2.048048048048048,
          2.097997997997998,
          2.147947947947948,
          2.197897897897898,
          2.2478478478478476,
          2.2977977977977977,
          2.3477477477477477,
          2.3976976976976974,
          2.4476476476476474,
          2.4975975975975975,
          2.5475475475475475,
          2.5974974974974976,
          2.647447447447447,
          2.6973973973973973,
          2.7473473473473473,
          2.797297297297297,
          2.847247247247247,
          2.897197197197197,
          2.947147147147147,
          2.997097097097097,
          3.0470470470470468,
          3.096996996996997,
          3.146946946946947,
          3.1968968968968965,
          3.2468468468468465,
          3.2967967967967966,
          3.3467467467467467,
          3.3966966966966967,
          3.4466466466466463,
          3.4965965965965964,
          3.5465465465465464,
          3.596496496496496,
          3.646446446446446,
          3.696396396396396,
          3.7463463463463462,
          3.7962962962962963,
          3.846246246246246,
          3.896196196196196,
          3.946146146146146,
          3.9960960960960956,
          4.046046046046046,
          4.095995995995995,
          4.145945945945945,
          4.195895895895895,
          4.245845845845845,
          4.2957957957957955,
          4.345745745745745,
          4.395695695695695,
          4.445645645645645,
          4.495595595595595,
          4.5455455455455445,
          4.595495495495495,
          4.645445445445445,
          4.695395395395394,
          4.745345345345345,
          4.795295295295294,
          4.845245245245245,
          4.895195195195194,
          4.945145145145144,
          4.9950950950950945,
          5.045045045045044,
          5.094994994994995,
          5.144944944944944,
          5.194894894894894,
          5.244844844844844,
          5.294794794794794,
          5.344744744744744,
          5.394694694694694,
          5.444644644644644,
          5.494594594594593,
          5.544544544544544,
          5.594494494494493,
          5.644444444444444,
          5.6943943943943935,
          5.744344344344343,
          5.794294294294294,
          5.844244244244243,
          5.894194194194194,
          5.944144144144143,
          5.994094094094093,
          6.0440440440440435,
          6.093993993993993,
          6.143943943943943,
          6.193893893893893,
          6.243843843843843,
          6.2937937937937924,
          6.343743743743743,
          6.393693693693693,
          6.443643643643643,
          6.493593593593593,
          6.543543543543542,
          6.593493493493493,
          6.643443443443442,
          6.693393393393393,
          6.7433433433433425,
          6.793293293293292,
          6.843243243243243,
          6.893193193193192,
          6.943143143143142,
          6.993093093093092,
          7.043043043043042,
          7.092992992992992,
          7.142942942942942,
          7.192892892892892,
          7.242842842842842,
          7.292792792792792,
          7.342742742742741,
          7.392692692692692,
          7.4426426426426415,
          7.492592592592592,
          7.542542542542542,
          7.592492492492491,
          7.642442442442442,
          7.692392392392391,
          7.742342342342341,
          7.7922922922922915,
          7.842242242242241,
          7.892192192192191,
          7.942142142142141,
          7.992092092092091,
          8.042042042042041,
          8.091991991991991,
          8.14194194194194,
          8.19189189189189,
          8.241841841841842,
          8.291791791791791,
          8.34174174174174,
          8.39169169169169,
          8.44164164164164,
          8.491591591591591,
          8.541541541541541,
          8.59149149149149,
          8.64144144144144,
          8.69139139139139,
          8.74134134134134,
          8.79129129129129,
          8.84124124124124,
          8.89119119119119,
          8.94114114114114,
          8.99109109109109,
          9.04104104104104,
          9.09099099099099,
          9.14094094094094,
          9.19089089089089,
          9.24084084084084,
          9.290790790790789,
          9.34074074074074,
          9.39069069069069,
          9.44064064064064,
          9.490590590590589,
          9.540540540540539,
          9.59049049049049,
          9.64044044044044,
          9.69039039039039,
          9.740340340340339,
          9.790290290290288,
          9.84024024024024,
          9.89019019019019,
          9.940140140140139,
          9.990090090090089,
          10.040040040040038,
          10.08998998998999,
          10.13993993993994,
          10.189889889889889,
          10.239839839839838,
          10.289789789789788,
          10.339739739739738,
          10.389689689689689,
          10.439639639639639,
          10.489589589589588,
          10.539539539539538,
          10.589489489489488,
          10.639439439439439,
          10.689389389389389,
          10.739339339339338,
          10.789289289289288,
          10.839239239239237,
          10.889189189189187,
          10.939139139139138,
          10.989089089089088,
          11.039039039039038,
          11.088988988988987,
          11.138938938938937,
          11.188888888888888,
          11.238838838838838,
          11.288788788788787,
          11.338738738738737,
          11.388688688688687,
          11.438638638638638,
          11.488588588588588,
          11.538538538538537,
          11.588488488488487,
          11.638438438438437,
          11.688388388388388,
          11.738338338338338,
          11.788288288288287,
          11.838238238238237,
          11.888188188188186,
          11.938138138138136,
          11.988088088088087,
          12.038038038038037,
          12.087987987987987,
          12.137937937937936,
          12.187887887887886,
          12.237837837837837,
          12.287787787787787,
          12.337737737737736,
          12.387687687687686,
          12.437637637637636,
          12.487587587587585,
          12.537537537537537,
          12.587487487487486,
          12.637437437437436,
          12.687387387387385,
          12.737337337337335,
          12.787287287287286,
          12.837237237237236,
          12.887187187187186,
          12.937137137137135,
          12.987087087087085,
          13.037037037037036,
          13.086986986986986,
          13.136936936936936,
          13.186886886886885,
          13.236836836836835,
          13.286786786786786,
          13.336736736736736,
          13.386686686686685,
          13.436636636636635,
          13.486586586586585,
          13.536536536536534,
          13.586486486486486,
          13.636436436436435,
          13.686386386386385,
          13.736336336336334,
          13.786286286286284,
          13.836236236236235,
          13.886186186186185,
          13.936136136136135,
          13.986086086086084,
          14.036036036036034,
          14.085985985985984,
          14.135935935935935,
          14.185885885885885,
          14.235835835835834,
          14.285785785785784,
          14.335735735735733,
          14.385685685685685,
          14.435635635635634,
          14.485585585585584,
          14.535535535535534,
          14.585485485485483,
          14.635435435435435,
          14.685385385385384,
          14.735335335335334,
          14.785285285285283,
          14.835235235235233,
          14.885185185185184,
          14.935135135135134,
          14.985085085085084,
          15.035035035035033,
          15.084984984984983,
          15.134934934934932,
          15.184884884884884,
          15.234834834834833,
          15.284784784784783,
          15.334734734734733,
          15.384684684684682,
          15.434634634634634,
          15.484584584584583,
          15.534534534534533,
          15.584484484484483,
          15.634434434434432,
          15.684384384384382,
          15.734334334334333,
          15.784284284284283,
          15.834234234234232,
          15.884184184184182,
          15.934134134134132,
          15.984084084084083,
          16.034034034034033,
          16.083983983983984,
          16.133933933933935,
          16.183883883883883,
          16.233833833833835,
          16.283783783783782,
          16.333733733733734,
          16.383683683683685,
          16.433633633633633,
          16.483583583583584,
          16.533533533533532,
          16.583483483483484,
          16.633433433433435,
          16.683383383383383,
          16.733333333333334,
          16.783283283283282,
          16.833233233233234,
          16.883183183183185,
          16.933133133133133,
          16.983083083083084,
          17.033033033033032,
          17.082982982982983,
          17.13293293293293,
          17.182882882882883,
          17.232832832832834,
          17.282782782782782,
          17.332732732732733,
          17.38268268268268,
          17.432632632632632,
          17.482582582582584,
          17.53253253253253,
          17.582482482482483,
          17.63243243243243,
          17.682382382382382,
          17.732332332332334,
          17.78228228228228,
          17.832232232232233,
          17.88218218218218,
          17.932132132132132,
          17.982082082082083,
          18.03203203203203,
          18.081981981981983,
          18.13193193193193,
          18.181881881881882,
          18.231831831831833,
          18.28178178178178,
          18.331731731731733,
          18.38168168168168,
          18.43163163163163,
          18.48158158158158,
          18.53153153153153,
          18.581481481481482,
          18.63143143143143,
          18.68138138138138,
          18.73133133133133,
          18.78128128128128,
          18.831231231231232,
          18.88118118118118,
          18.93113113113113,
          18.98108108108108,
          19.03103103103103,
          19.080980980980982,
          19.13093093093093,
          19.18088088088088,
          19.23083083083083,
          19.28078078078078,
          19.330730730730732,
          19.38068068068068,
          19.43063063063063,
          19.48058058058058,
          19.53053053053053,
          19.58048048048048,
          19.63043043043043,
          19.68038038038038,
          19.73033033033033,
          19.78028028028028,
          19.83023023023023,
          19.88018018018018,
          19.93013013013013,
          19.98008008008008,
          20.03003003003003,
          20.07997997997998,
          20.12992992992993,
          20.17987987987988,
          20.22982982982983,
          20.27977977977978,
          20.329729729729728,
          20.37967967967968,
          20.42962962962963,
          20.47957957957958,
          20.52952952952953,
          20.579479479479478,
          20.62942942942943,
          20.67937937937938,
          20.729329329329328,
          20.77927927927928,
          20.829229229229227,
          20.87917917917918,
          20.92912912912913,
          20.979079079079078,
          21.02902902902903,
          21.078978978978977,
          21.12892892892893,
          21.17887887887888,
          21.228828828828828,
          21.27877877877878,
          21.328728728728727,
          21.37867867867868,
          21.42862862862863,
          21.478578578578578,
          21.52852852852853,
          21.578478478478477,
          21.62842842842843,
          21.678378378378376,
          21.728328328328328,
          21.77827827827828,
          21.828228228228227,
          21.878178178178178,
          21.928128128128126,
          21.978078078078077,
          22.02802802802803,
          22.077977977977977,
          22.127927927927928,
          22.177877877877876,
          22.227827827827827,
          22.27777777777778,
          22.327727727727726,
          22.377677677677678,
          22.427627627627626,
          22.477577577577577,
          22.52752752752753,
          22.577477477477476,
          22.627427427427428,
          22.677377377377375,
          22.727327327327327,
          22.77727727727728,
          22.827227227227226,
          22.877177177177177,
          22.927127127127125,
          22.977077077077077,
          23.027027027027028,
          23.076976976976976,
          23.126926926926927,
          23.176876876876875,
          23.226826826826827,
          23.276776776776778,
          23.326726726726726,
          23.376676676676677,
          23.426626626626625,
          23.476576576576576,
          23.526526526526524,
          23.576476476476476,
          23.626426426426427,
          23.676376376376375,
          23.726326326326326,
          23.776276276276274,
          23.826226226226225,
          23.876176176176177,
          23.926126126126125,
          23.976076076076076,
          24.026026026026024,
          24.075975975975975,
          24.125925925925927,
          24.175875875875874,
          24.225825825825826,
          24.275775775775774,
          24.325725725725725,
          24.375675675675677,
          24.425625625625624,
          24.475575575575576,
          24.525525525525524,
          24.575475475475475,
          24.625425425425426,
          24.675375375375374,
          24.725325325325326,
          24.775275275275273,
          24.825225225225225,
          24.875175175175173,
          24.925125125125124,
          24.975075075075075,
          25.025025025025023,
          25.074974974974975,
          25.124924924924922,
          25.174874874874874,
          25.224824824824825,
          25.274774774774773,
          25.324724724724724,
          25.374674674674672,
          25.424624624624624,
          25.474574574574575,
          25.524524524524523,
          25.574474474474474,
          25.624424424424422,
          25.674374374374374,
          25.724324324324325,
          25.774274274274273,
          25.824224224224224,
          25.874174174174172,
          25.924124124124123,
          25.974074074074075,
          26.024024024024023,
          26.073973973973974,
          26.123923923923922,
          26.173873873873873,
          26.223823823823825,
          26.273773773773772,
          26.323723723723724,
          26.37367367367367,
          26.423623623623623,
          26.473573573573574,
          26.523523523523522,
          26.573473473473474,
          26.62342342342342,
          26.673373373373373,
          26.72332332332332,
          26.773273273273272,
          26.823223223223223,
          26.87317317317317,
          26.923123123123123,
          26.97307307307307,
          27.023023023023022,
          27.072972972972973,
          27.12292292292292,
          27.172872872872873,
          27.22282282282282,
          27.272772772772772,
          27.322722722722723,
          27.37267267267267,
          27.422622622622622,
          27.47257257257257,
          27.52252252252252,
          27.572472472472473,
          27.62242242242242,
          27.672372372372372,
          27.72232232232232,
          27.77227227227227,
          27.822222222222223,
          27.87217217217217,
          27.922122122122122,
          27.97207207207207,
          28.02202202202202,
          28.07197197197197,
          28.12192192192192,
          28.171871871871872,
          28.22182182182182,
          28.27177177177177,
          28.32172172172172,
          28.37167167167167,
          28.42162162162162,
          28.47157157157157,
          28.52152152152152,
          28.57147147147147,
          28.62142142142142,
          28.67137137137137,
          28.72132132132132,
          28.77127127127127,
          28.82122122122122,
          28.87117117117117,
          28.92112112112112,
          28.97107107107107,
          29.02102102102102,
          29.07097097097097,
          29.12092092092092,
          29.17087087087087,
          29.22082082082082,
          29.27077077077077,
          29.32072072072072,
          29.37067067067067,
          29.42062062062062,
          29.47057057057057,
          29.52052052052052,
          29.570470470470468,
          29.62042042042042,
          29.67037037037037,
          29.72032032032032,
          29.77027027027027,
          29.820220220220218,
          29.87017017017017,
          29.920120120120117,
          29.97007007007007,
          30.02002002002002,
          30.069969969969968,
          30.11991991991992,
          30.169869869869867,
          30.21981981981982,
          30.26976976976977,
          30.319719719719718,
          30.36966966966967,
          30.419619619619617,
          30.46956956956957,
          30.51951951951952,
          30.569469469469468,
          30.61941941941942,
          30.669369369369367,
          30.719319319319318,
          30.76926926926927,
          30.819219219219217,
          30.86916916916917,
          30.919119119119117,
          30.969069069069068,
          31.01901901901902,
          31.068968968968967,
          31.11891891891892,
          31.168868868868866,
          31.218818818818818,
          31.268768768768766,
          31.318718718718717,
          31.36866866866867,
          31.418618618618616,
          31.468568568568568,
          31.518518518518515,
          31.568468468468467,
          31.61841841841842,
          31.668368368368366,
          31.718318318318317,
          31.768268268268265,
          31.818218218218217,
          31.868168168168168,
          31.918118118118116,
          31.968068068068067,
          32.01801801801801,
          32.06796796796797,
          32.117917917917914,
          32.16786786786787,
          32.21781781781782,
          32.267767767767765,
          32.31771771771771,
          32.36766766766767,
          32.417617617617616,
          32.46756756756756,
          32.51751751751752,
          32.567467467467466,
          32.617417417417414,
          32.66736736736737,
          32.71731731731732,
          32.767267267267265,
          32.81721721721721,
          32.86716716716717,
          32.917117117117115,
          32.96706706706706,
          33.01701701701702,
          33.066966966966966,
          33.116916916916914,
          33.16686686686687,
          33.21681681681682,
          33.266766766766764,
          33.31671671671671,
          33.36666666666667,
          33.416616616616615,
          33.46656656656656,
          33.51651651651652,
          33.566466466466466,
          33.61641641641641,
          33.66636636636637,
          33.716316316316316,
          33.766266266266264,
          33.81621621621621,
          33.86616616616617,
          33.916116116116115,
          33.96606606606606,
          34.01601601601602,
          34.065965965965965,
          34.11591591591591,
          34.16586586586586,
          34.215815815815816,
          34.265765765765764,
          34.31571571571571,
          34.36566566566567,
          34.415615615615614,
          34.46556556556556,
          34.51551551551552,
          34.565465465465465,
          34.61541541541541,
          34.66536536536536,
          34.715315315315316,
          34.76526526526526,
          34.81521521521521,
          34.865165165165166,
          34.915115115115114,
          34.96506506506506,
          35.01501501501502,
          35.064964964964965,
          35.11491491491491,
          35.16486486486486,
          35.214814814814815,
          35.26476476476476,
          35.31471471471471,
          35.364664664664666,
          35.414614614614614,
          35.46456456456456,
          35.51451451451451,
          35.564464464464464,
          35.61441441441441,
          35.66436436436436,
          35.714314314314315,
          35.76426426426426,
          35.81421421421421,
          35.864164164164166,
          35.91411411411411,
          35.96406406406406,
          36.01401401401401,
          36.063963963963964,
          36.11391391391391,
          36.16386386386386,
          36.213813813813815,
          36.26376376376376,
          36.31371371371371,
          36.363663663663665,
          36.41361361361361,
          36.46356356356356,
          36.51351351351351,
          36.563463463463464,
          36.61341341341341,
          36.66336336336336,
          36.713313313313314,
          36.76326326326326,
          36.81321321321321,
          36.86316316316316,
          36.91311311311311,
          36.96306306306306,
          37.01301301301301,
          37.06296296296296,
          37.11291291291291,
          37.16286286286286,
          37.212812812812814,
          37.26276276276276,
          37.31271271271271,
          37.36266266266266,
          37.41261261261261,
          37.46256256256256,
          37.51251251251251,
          37.56246246246246,
          37.61241241241241,
          37.66236236236236,
          37.712312312312314,
          37.76226226226226,
          37.81221221221221,
          37.86216216216216,
          37.91211211211211,
          37.96206206206206,
          38.01201201201201,
          38.06196196196196,
          38.11191191191191,
          38.16186186186186,
          38.21181181181181,
          38.26176176176176,
          38.31171171171171,
          38.36166166166166,
          38.41161161161161,
          38.46156156156156,
          38.51151151151151,
          38.56146146146146,
          38.61141141141141,
          38.66136136136136,
          38.711311311311306,
          38.76126126126126,
          38.81121121121121,
          38.86116116116116,
          38.91111111111111,
          38.96106106106106,
          39.01101101101101,
          39.06096096096096,
          39.11091091091091,
          39.16086086086086,
          39.210810810810806,
          39.26076076076076,
          39.31071071071071,
          39.360660660660656,
          39.41061061061061,
          39.46056056056056,
          39.51051051051051,
          39.56046046046046,
          39.61041041041041,
          39.66036036036036,
          39.710310310310305,
          39.76026026026026,
          39.81021021021021,
          39.860160160160156,
          39.91011011011011,
          39.96006006006006,
          40.01001001001001,
          40.05995995995996,
          40.10990990990991,
          40.15985985985986,
          40.209809809809805,
          40.25975975975976,
          40.30970970970971,
          40.359659659659656,
          40.40960960960961,
          40.45955955955956,
          40.509509509509506,
          40.559459459459454,
          40.60940940940941,
          40.65935935935936,
          40.709309309309305,
          40.75925925925926,
          40.80920920920921,
          40.859159159159155,
          40.90910910910911,
          40.95905905905906,
          41.009009009009006,
          41.058958958958954,
          41.10890890890891,
          41.158858858858856,
          41.208808808808804,
          41.25875875875876,
          41.30870870870871,
          41.358658658658655,
          41.40860860860861,
          41.45855855855856,
          41.508508508508505,
          41.55845845845845,
          41.60840840840841,
          41.658358358358356,
          41.708308308308304,
          41.75825825825826,
          41.80820820820821,
          41.858158158158155,
          41.9081081081081,
          41.95805805805806,
          42.008008008008005,
          42.05795795795795,
          42.10790790790791,
          42.157857857857856,
          42.207807807807804,
          42.25775775775776,
          42.307707707707706,
          42.357657657657654,
          42.4076076076076,
          42.45755755755756,
          42.507507507507505,
          42.55745745745745,
          42.60740740740741,
          42.657357357357355,
          42.7073073073073,
          42.75725725725726,
          42.807207207207206,
          42.857157157157154,
          42.9071071071071,
          42.95705705705706,
          43.007007007007005,
          43.05695695695695,
          43.10690690690691,
          43.156856856856855,
          43.2068068068068,
          43.25675675675675,
          43.306706706706706,
          43.356656656656654,
          43.4066066066066,
          43.456556556556556,
          43.506506506506504,
          43.55645645645645,
          43.60640640640641,
          43.656356356356355,
          43.7063063063063,
          43.75625625625625,
          43.806206206206205,
          43.85615615615615,
          43.9061061061061,
          43.956056056056056,
          44.006006006006004,
          44.05595595595595,
          44.10590590590591,
          44.155855855855854,
          44.2058058058058,
          44.25575575575575,
          44.305705705705705,
          44.35565565565565,
          44.4056056056056,
          44.455555555555556,
          44.5055055055055,
          44.55545545545545,
          44.605405405405406,
          44.655355355355354,
          44.7053053053053,
          44.75525525525525,
          44.805205205205205,
          44.85515515515515,
          44.9051051051051,
          44.955055055055055,
          45.005005005005,
          45.05495495495495,
          45.1049049049049,
          45.154854854854854,
          45.2048048048048,
          45.25475475475475,
          45.304704704704704,
          45.35465465465465,
          45.4046046046046,
          45.454554554554555,
          45.5045045045045,
          45.55445445445445,
          45.6044044044044,
          45.65435435435435,
          45.7043043043043,
          45.75425425425425,
          45.804204204204204,
          45.85415415415415,
          45.9041041041041,
          45.954054054054055,
          46.004004004004,
          46.05395395395395,
          46.1039039039039,
          46.15385385385385,
          46.2038038038038,
          46.25375375375375,
          46.303703703703704,
          46.35365365365365,
          46.4036036036036,
          46.453553553553554,
          46.5035035035035,
          46.55345345345345,
          46.6034034034034,
          46.65335335335335,
          46.7033033033033,
          46.75325325325325,
          46.8032032032032,
          46.85315315315315,
          46.9031031031031,
          46.95305305305305,
          47.003003003003,
          47.05295295295295,
          47.1029029029029,
          47.15285285285285,
          47.2028028028028,
          47.25275275275275,
          47.3027027027027,
          47.35265265265265,
          47.4026026026026,
          47.45255255255255,
          47.5025025025025,
          47.55245245245245,
          47.6024024024024,
          47.65235235235235,
          47.7023023023023,
          47.75225225225225,
          47.8022022022022,
          47.85215215215215,
          47.9021021021021,
          47.952052052052046,
          48.002002002002,
          48.05195195195195,
          48.1019019019019,
          48.15185185185185,
          48.2018018018018,
          48.25175175175175,
          48.301701701701695,
          48.35165165165165,
          48.4016016016016,
          48.451551551551546,
          48.5015015015015,
          48.55145145145145,
          48.6014014014014,
          48.65135135135135,
          48.7013013013013,
          48.75125125125125,
          48.801201201201195,
          48.85115115115115,
          48.9011011011011,
          48.951051051051046,
          49.001001001001,
          49.05095095095095,
          49.100900900900896,
          49.15085085085085,
          49.2008008008008,
          49.25075075075075,
          49.300700700700695,
          49.35065065065065,
          49.4006006006006,
          49.450550550550545,
          49.5005005005005,
          49.55045045045045,
          49.600400400400396,
          49.650350350350344,
          49.7003003003003,
          49.75025025025025,
          49.800200200200194,
          49.85015015015015,
          49.9001001001001,
          49.950050050050045,
          50
         ],
         "y": [
          5.076958800933835e-05,
          0.00011415540577553646,
          0.00020287533727882784,
          0.0003169294769271526,
          0.0004563179460632927,
          0.0006210408930030778,
          0.000811098493045201,
          0.0010264909483808198,
          0.0012672184882218033,
          0.0015332813687146474,
          0.0018246798729557585,
          0.002141414311000001,
          0.0024834850198943263,
          0.002850892363618697,
          0.003243636733124101,
          0.0036617185463106803,
          0.004105138248079807,
          0.004573896310254869,
          0.005067993231645552,
          0.005587429538046736,
          0.006132205782201855,
          0.006702322543810799,
          0.007297780429569336,
          0.007918580073151705,
          0.008564722135182253,
          0.009236207303272735,
          0.009933036292023523,
          0.010655209842997504,
          0.011402728724752636,
          0.012175593732817206,
          0.012973805689719875,
          0.013797365444954277,
          0.014646273875043957,
          0.015520531883460033,
          0.016420140400685658,
          0.017345100384205867,
          0.01829541281846794,
          0.0192710787150014,
          0.0202720991122417,
          0.021298475075690784,
          0.022350207697827654,
          0.023427298098179894,
          0.02452974742324104,
          0.025657556846558675,
          0.026810727568690133,
          0.02798926081718129,
          0.02919315784664786,
          0.030422419938733413,
          0.031677048402056825,
          0.03295704457233814,
          0.03426240981228049,
          0.035593145511676236,
          0.036949253087324586,
          0.03833073398308909,
          0.03973758966987807,
          0.041169821645655594,
          0.04262743143543787,
          0.04411042059131746,
          0.04561879069243233,
          0.04715254334501673,
          0.04871168018234461,
          0.050296202864780246,
          0.05190611307978687,
          0.053541412541898314,
          0.05520210299271774,
          0.056888186200976264,
          0.058599663962481445,
          0.06033653810013985,
          0.06209881046398947,
          0.06388648293115129,
          0.06569955740587381,
          0.06753803581950873,
          0.06940192013056447,
          0.07129121232464956,
          0.07320591441453612,
          0.07514602844010508,
          0.07711155646837764,
          0.07910250059354486,
          0.08111886293695542,
          0.08316064564710483,
          0.0852278508996452,
          0.08732048089741386,
          0.08943853787042245,
          0.09158202407582854,
          0.09375094179803894,
          0.09594529334856872,
          0.09816508106621766,
          0.10041030731691308,
          0.10268097449384683,
          0.10497708501737597,
          0.10729864133510361,
          0.10964564592188632,
          0.11201810127973968,
          0.1144160099379685,
          0.11683937445310655,
          0.11928819740895888,
          0.12176248141654455,
          0.12426222911418819,
          0.12678744316744678,
          0.129338126269152,
          0.13191428113946577,
          0.13451591052577858,
          0.1371430172028283,
          0.13979560397258511,
          0.14247367366439911,
          0.1451772291349012,
          0.14790627326804318,
          0.15066080897510675,
          0.15344083919471213,
          0.15624636689282698,
          0.15907739506276067,
          0.16193392672518778,
          0.1648159649281286,
          0.1677235127470143,
          0.17065657328461167,
          0.1736151496710886,
          0.17659924506402216,
          0.17960886264838033,
          0.1826440056365446,
          0.18570467726829235,
          0.1887908808108594,
          0.19190261955888224,
          0.19503989683448605,
          0.19820271598717676,
          0.2013910803939921,
          0.20460499345935682,
          0.20784445861524495,
          0.2111094793210616,
          0.21440005906372828,
          0.21771620135762954,
          0.22105790974470868,
          0.2244251877943907,
          0.22781803910362844,
          0.23123646729690012,
          0.23468047602626546,
          0.2381500689712806,
          0.24164524983910163,
          0.24516602236443527,
          0.24871239030955997,
          0.25228435746435823,
          0.25588192764630313,
          0.25950510470045607,
          0.26315389249952204,
          0.26682829494380206,
          0.27052831596124804,
          0.27425395950743875,
          0.2780052295656222,
          0.28178213014670367,
          0.28558466528923315,
          0.2894128390595016,
          0.29326665555144277,
          0.29714611888668624,
          0.301051233214609,
          0.3049820027122822,
          0.3089384315845224,
          0.3129205240638806,
          0.31692828441065246,
          0.32096171691290826,
          0.32502082588648223,
          0.32910561567500307,
          0.33321609064988295,
          0.33735225521032847,
          0.34151411378338953,
          0.3457016708239298,
          0.34991493081461766,
          0.35415389826601407,
          0.358418577716524,
          0.36270897373238803,
          0.3670250909077685,
          0.3713669338647219,
          0.3757345072531706,
          0.3801278157509705,
          0.3845468640639204,
          0.3889916569257169,
          0.39346219909803865,
          0.3979584953705197,
          0.4024805505607237,
          0.4070283695142629,
          0.4116019571047007,
          0.41620131823359735,
          0.4208264578305928,
          0.42547738085327425,
          0.43015409228732876,
          0.43485659714650055,
          0.439584900472567,
          0.44433900733540105,
          0.4491189228329487,
          0.453924652091307,
          0.45875620026464947,
          0.46361357253527186,
          0.46849677411365304,
          0.4734058102383818,
          0.4783406861762351,
          0.4833014072221554,
          0.48828797869932783,
          0.49330040595905916,
          0.4983386943809378,
          0.5034028493727778,
          0.5084928763705984,
          0.5136087808387164,
          0.5187505682697241,
          0.5239182441844538,
          0.5291118141320676,
          0.5343312836900538,
          0.5395766584641899,
          0.5448479440886023,
          0.5501451462258081,
          0.5554682705666333,
          0.5608173228303024,
          0.5661923087644799,
          0.5715932341451596,
          0.5770201047768291,
          0.5824729264923746,
          0.5879517051531231,
          0.5934564466488996,
          0.5989871568979935,
          0.6045438418471852,
          0.6101265074717586,
          0.6157351597755416,
          0.6213698047908752,
          0.627030448578668,
          0.6327170972283803,
          0.6384297568580789,
          0.6441684336144061,
          0.6499331336726207,
          0.6557238632366243,
          0.6615406285389308,
          0.6673834358407494,
          0.6732522914319135,
          0.6791472016309893,
          0.6850681727852338,
          0.6910152112706205,
          0.6969883234918379,
          0.7029875158823585,
          0.7090127949043945,
          0.7150641670489525,
          0.7211416388358465,
          0.7272452168136823,
          0.7333749075599117,
          0.739530717680832,
          0.7457126538115841,
          0.7519207226162071,
          0.7581549307876365,
          0.7644152850477045,
          0.7707017921471665,
          0.7770144588657533,
          0.7833532920121181,
          0.7897182984239162,
          0.7961094849677903,
          0.8025268585394112,
          0.8089704260634264,
          0.8154401944935878,
          0.821936170812664,
          0.8284583620325555,
          0.8350067751941921,
          0.8415814173676635,
          0.8481822956521917,
          0.8548094171761214,
          0.8614627890969704,
          0.8681424186014561,
          0.8748483129054845,
          0.8815804792541749,
          0.8883389249219008,
          0.895123657212277,
          0.9019346834581865,
          0.9087720110218314,
          0.9156356472946732,
          0.9225255996975567,
          0.9294418756806261,
          0.9363844827234249,
          0.9433534283348373,
          0.9503487200531864,
          0.9573703654461999,
          0.9644183721110375,
          0.9714927476743163,
          0.9785934997921488,
          0.9857206361501105,
          0.9928741644633015,
          1.0000540924763721,
          1.0072604279635027,
          1.0144931787284417,
          1.0217523526045433,
          1.0290379574547595,
          1.0363500011716764,
          1.0436884916775082,
          1.0510534369241784,
          1.058444844893257,
          1.0658627235960312,
          1.0733070810735201,
          1.0807779253965013,
          1.0882752646654814,
          1.0957991070107889,
          1.1033494605925456,
          1.1109263336007034,
          1.118529734255037,
          1.1261596708052495,
          1.1338161515308525,
          1.1414991847412947,
          1.1492087787760188,
          1.1569449420043039,
          1.1647076828254754,
          1.172497009668814,
          1.1803129309936562,
          1.1881554552893032,
          1.1960245910751872,
          1.2039203469007362,
          1.2118427313455407,
          1.2197917530192834,
          1.2277674205617566,
          1.2357697426429397,
          1.2437987279630172,
          1.2518543852523094,
          1.2599367232714571,
          1.268045750811249,
          1.2761814766927855,
          1.2843439097674918,
          1.2925330589170347,
          1.3007489330534603,
          1.3089915411191695,
          1.317260892086916,
          1.3255569949599015,
          1.3338798587716734,
          1.3422294925863223,
          1.3506059054983164,
          1.3590091066326615,
          1.3674391051448755,
          1.3758959102210266,
          1.3843795310776708,
          1.3928899769620455,
          1.4014272571519129,
          1.4099913809557096,
          1.4185823577124899,
          1.4272001967920198,
          1.4358449075947348,
          1.444516499551798,
          1.4532149821251354,
          1.4619403648074158,
          1.4706926571221066,
          1.4794718686234907,
          1.488278008896706,
          1.4971110875577203,
          1.5059711142534495,
          1.5148580986616387,
          1.5237720504910524,
          1.532712979481341,
          1.541680895403209,
          1.5506758080583034,
          1.5596977272793404,
          1.568746662930091,
          1.5778226249054152,
          1.5869256231312796,
          1.5960556675647415,
          1.6052127681940933,
          1.614396935038718,
          1.6236081781492904,
          1.6328465076076486,
          1.6421119335269594,
          1.6514044660515912,
          1.660724115357278,
          1.670070891651085,
          1.679444805171406,
          1.6888458661880414,
          1.6982740850021951,
          1.7077294719465144,
          1.7172120373851063,
          1.7267217917135584,
          1.7362587453589953,
          1.7458229087800394,
          1.7554142924669442,
          1.7650329069415,
          1.7746787627571288,
          1.7843518704989205,
          1.7940522407836155,
          1.8037798842596795,
          1.8135348116072858,
          1.8233170335383373,
          1.8331265607965725,
          1.842963404157497,
          1.8528275744284755,
          1.862719082448697,
          1.872637939089301,
          1.8825841552532585,
          1.8925577418755641,
          1.9025587099231536,
          1.9125870703949406,
          1.9226428343219064,
          1.9327260127670356,
          1.9428366168254692,
          1.9529746576243765,
          1.9631401463231255,
          1.9733330941132037,
          1.983553512218356,
          1.9938014118945036,
          2.004076804429801,
          2.0143797011447537,
          2.02471011339211,
          2.0350680525569786,
          2.045453530056849,
          2.055866557341583,
          2.0663071458934987,
          2.07677530722733,
          2.087271052890307,
          2.0977943944621846,
          2.1083453435552424,
          2.118923911814342,
          2.12953011091693,
          2.1401639525731095,
          2.1508254485256155,
          2.1615146105498964,
          2.172231450454107,
          2.1829759800791297,
          2.1937482112986615,
          2.2045481560191855,
          2.2153758261800447,
          2.226231233753444,
          2.237114390744476,
          2.2480253091911893,
          2.258964001164547,
          2.2699304787685612,
          2.2809247541402358,
          2.291946839449621,
          2.3029967468998818,
          2.3140744887272597,
          2.325180077201189,
          2.3363135246242557,
          2.3474748433322534,
          2.358664045694204,
          2.3698811441124468,
          2.3811261510225794,
          2.3923990788935616,
          2.403699940227722,
          2.4150287475607635,
          2.4263855134618386,
          2.437770250533567,
          2.449182971412062,
          2.4606236887669697,
          2.4720924153014594,
          2.483589163752357,
          2.4951139468900596,
          2.5066667775186686,
          2.5182476684759205,
          2.529856632633316,
          2.541493682896132,
          2.5531588322033656,
          2.5648520935279007,
          2.5765734798764495,
          2.5883230042896104,
          2.600100679841939,
          2.611906519641894,
          2.623740536831983,
          2.63560274458867,
          2.647493156122558,
          2.6594117846782557,
          2.671358643534563,
          2.683333746004407,
          2.6953371054349264,
          2.707368735207482,
          2.71942864873768,
          2.7315168594754446,
          2.7436333809050395,
          2.755778226545051,
          2.7679514099485445,
          2.7801529447029303,
          2.7923828444301475,
          2.804641122786647,
          2.8169277934633743,
          2.829242870185894,
          2.8415863667143757,
          2.853958296843616,
          2.8663586744031253,
          2.878787513257094,
          2.8912448273045057,
          2.903730630479107,
          2.9162449367495014,
          2.928787760119109,
          2.941359114626302,
          2.9539590143443513,
          2.9665874733815047,
          2.97924450588103,
          2.9919301260212414,
          3.0046443480155114,
          3.0173871861123547,
          3.0301586545954264,
          3.0429587677835923,
          3.055787540030926,
          3.068644985726777,
          3.0815311192958035,
          3.0944459551979926,
          3.1073895079287186,
          3.1203617920187723,
          3.1333628220343983,
          3.1463926125773396,
          3.159451178284863,
          3.1725385338297745,
          3.1856546939205574,
          3.198799673301246,
          3.21197348675165,
          3.2251761490872424,
          3.238407675159269,
          3.2516680798547677,
          3.2649573780966454,
          3.2782755848436413,
          3.2916227150904365,
          3.3049987838676547,
          3.3184038062419328,
          3.3318377973159197,
          3.3453007722283346,
          3.358792746154022,
          3.37231373430398,
          3.3858637519253763,
          3.39944281430163,
          3.4130509367524167,
          3.426688134633745,
          3.440354423337941,
          3.4540498182937625,
          3.4677743349663537,
          3.481527988857381,
          3.4953107955049787,
          3.50912277048385,
          3.5229639294053205,
          3.5368342879173,
          3.550733861704411,
          3.5646626664879846,
          3.5786207180260967,
          3.592608032113661,
          3.606624624582392,
          3.620670511300893,
          3.634745708174732,
          3.6488502311463855,
          3.662984096195374,
          3.6771473193382747,
          3.691339916628716,
          3.7055619041575283,
          3.7198132980526517,
          3.7340941144793,
          3.7484043696398905,
          3.7627440797742127,
          3.777113261159358,
          3.791511930109817,
          3.8059401029775333,
          3.820397796151901,
          3.8348850260598546,
          3.8494018091658804,
          3.863948161972082,
          3.8785241010182157,
          3.8931296428817084,
          3.9077648041777517,
          3.92242960155931,
          3.937124051717179,
          3.9518481713800133,
          3.9666019773143915,
          3.981385486324868,
          3.996198715253955,
          4.011041680982272,
          4.0259144004284755,
          4.040816890549405,
          4.0557491683400535,
          4.070711250833651,
          4.085703155101732,
          4.100724898254085,
          4.115776497438923,
          4.1308579698428485,
          4.145969332690909,
          4.161110603246657,
          4.176281798812205,
          4.191482936728254,
          4.206714034374153,
          4.22197510916791,
          4.2372661785662835,
          4.252587260064809,
          4.267938371197866,
          4.2833195295386775,
          4.298730752699406,
          4.31417205833116,
          4.329643464124082,
          4.345144987807367,
          4.360676647149324,
          4.376238459957412,
          4.391830444078291,
          4.407452617397867,
          4.423104997841373,
          4.4387876033733615,
          4.454500451997785,
          4.470243561758049,
          4.486016950737035,
          4.501820637057192,
          4.5176546388805265,
          4.533518974408702,
          4.549413661883066,
          4.565338719584704,
          4.581294165834469,
          4.59728001899307,
          4.613296297461083,
          4.6293430196790375,
          4.6454202041274195,
          4.6615278693267586,
          4.677666033837673,
          4.693834716260908,
          4.710033935237382,
          4.726263709448266,
          4.742524057614996,
          4.758814998499345,
          4.775136550903471,
          4.791488733670002,
          4.80787156568196,
          4.824285065862988,
          4.840729253177302,
          4.85720414662973,
          4.8737097652658194,
          4.89024612817182,
          4.906813254474835,
          4.9234111633427595,
          4.940039873984398,
          4.956699405649542,
          4.973389777628941,
          4.990111009254391,
          5.006863119898832,
          5.02364612897638,
          5.040460055942256,
          5.057304920293089,
          5.074180741566723,
          5.091087539342436,
          5.108025333240848,
          5.12499414292414,
          5.141993988095997,
          5.159024888501681,
          5.1760868639280835,
          5.19317993420382,
          5.21030411919921,
          5.227459438826407,
          5.244645913039391,
          5.261863561834096,
          5.279112405248395,
          5.296392463362124,
          5.313703756297314,
          5.331046304218001,
          5.348420127330498,
          5.365825245883292,
          5.383261680167204,
          5.4007294505153824,
          5.41822857730339,
          5.435759080949267,
          5.4533209819135475,
          5.470914300699352,
          5.488539057852402,
          5.506195273961148,
          5.523882969656752,
          5.541602165613211,
          5.5593528825473415,
          5.577135141218871,
          5.59494896243053,
          5.612794367028042,
          5.630671375900248,
          5.648580009979132,
          5.666520290239809,
          5.684492237700765,
          5.7024958734236915,
          5.720531218513715,
          5.738598294119403,
          5.7566971214327785,
          5.77482772168944,
          5.792990116168547,
          5.811184326193008,
          5.829410373129362,
          5.847668278388025,
          5.865958063423154,
          5.884279749732932,
          5.902633358859379,
          5.921018912388649,
          5.939436431950878,
          5.957885939220438,
          5.97636745591581,
          5.9948810037998355,
          6.013426604679588,
          6.032004280406567,
          6.050614052876761,
          6.069255944030571,
          6.087929975853023,
          6.106636170373771,
          6.125374549667119,
          6.144145135852162,
          6.162947951092796,
          6.1817830175977955,
          6.200650357620835,
          6.219549993460602,
          6.238481947460903,
          6.257446242010599,
          6.276442899543714,
          6.295471942539605,
          6.314533393522895,
          6.33362727506355,
          6.352753609777029,
          6.371912420324251,
          6.391103729411703,
          6.41032755979151,
          6.4295839342615055,
          6.448872875665232,
          6.46819440689206,
          6.487548550877285,
          6.506935330602108,
          6.526354769093756,
          6.545806889425538,
          6.565291714716884,
          6.584809268133443,
          6.604359572887152,
          6.623942652236263,
          6.643558529485406,
          6.663207227985758,
          6.6828887711349285,
          6.702603182377229,
          6.722350485203547,
          6.742130703151536,
          6.761943859805705,
          6.781789978797321,
          6.801669083804658,
          6.821581198552964,
          6.8415263468145735,
          6.861504552408924,
          6.881515839202658,
          6.901560231109735,
          6.921637752091368,
          6.941748426156237,
          6.96189227736049,
          6.9820693298077625,
          7.002279607649366,
          7.022523135084245,
          7.042799936359118,
          7.063110035768502,
          7.0834534576548,
          7.103830226408345,
          7.124240366467564,
          7.144683902318873,
          7.165160858496969,
          7.185671259584668,
          7.206215130213161,
          7.226792495061997,
          7.247403378859124,
          7.2680478063810785,
          7.288725802452924,
          7.309437391948396,
          7.330182599789984,
          7.350961450948901,
          7.371773970445298,
          7.392620183348251,
          7.4135001147758395,
          7.434413789895225,
          7.455361233922736,
          7.47634247212392,
          7.497357529813642,
          7.5184064323561115,
          7.539489205165002,
          7.56060587370353,
          7.5817564634844805,
          7.602941000070268,
          7.624159509073134,
          7.64541201615508,
          7.6666985470279805,
          7.688019127453703,
          7.7093737832441445,
          7.730762540261321,
          7.752185424417387,
          7.773642461674823,
          7.795133678046409,
          7.816659099595323,
          7.8382187524352815,
          7.8598126627304925,
          7.881440856695832,
          7.903103360596921,
          7.924800200750131,
          7.946531403522686,
          7.968296995332777,
          7.990097002649643,
          8.011931451993547,
          8.03380036993597,
          8.055703783099656,
          8.077641718158612,
          8.09961420183831,
          8.121621260915688,
          8.143662922219251,
          8.165739212629102,
          8.187850159077104,
          8.209995788546887,
          8.232176128073974,
          8.254391204745849,
          8.276641045701991,
          8.298925678134022,
          8.321245129285721,
          8.343599426453194,
          8.36598859698482,
          8.388412668281463,
          8.410871667796489,
          8.43336562303584,
          8.455894561558145,
          8.478458510974757,
          8.501057498949885,
          8.523691553200665,
          8.546360701497187,
          8.569064971662637,
          8.591804391573373,
          8.614578989158987,
          8.63738879240239,
          8.660233829339886,
          8.683114128061279,
          8.706029716709935,
          8.728980623482897,
          8.751966876630924,
          8.774988504458598,
          8.798045535324402,
          8.821137997640797,
          8.844265919874324,
          8.867429330545718,
          8.890628258229873,
          8.913862731556069,
          8.937132779208,
          8.960438429923775,
          8.983779712496192,
          9.00715665577263,
          9.030569288655252,
          9.054017640101053,
          9.077501739121933,
          9.101021614784836,
          9.124577296211779,
          9.148168812579955,
          9.171796193121796,
          9.195459467125188,
          9.219158663933323,
          9.242893812945056,
          9.266664943614748,
          9.290472085452528,
          9.3143152680243,
          9.338194520951863,
          9.362109873912964,
          9.386061356641425,
          9.410048998927211,
          9.434072830616518,
          9.458132881611862,
          9.482229181872194,
          9.50636176141295,
          9.53053065030619,
          9.554735878680633,
          9.578977476721775,
          9.603255474672014,
          9.627569902830631,
          9.651920791554026,
          9.676308171255727,
          9.700732072406463,
          9.725192525534302,
          9.749689561224741,
          9.774223210120777,
          9.798793502922969,
          9.823400470389622,
          9.848044143336832,
          9.87272455263849,
          9.897441729226557,
          9.922195704091003,
          9.946986508279952,
          9.971814172899839,
          9.996678729115361,
          10.02158020814973,
          10.046518641284658,
          10.071494059860479,
          10.096506495276298,
          10.12155597898998,
          10.146642542518343,
          10.171766217437234,
          10.196927035381568,
          10.2221250280455,
          10.247360227182451,
          10.272632664605256,
          10.297942372186277,
          10.3232893818574,
          10.348673725610263,
          10.37409543549627,
          10.399554543626708,
          10.425051082172825,
          10.450585083365983,
          10.476156579497736,
          10.501765602919848,
          10.527412186044543,
          10.553096361344464,
          10.578818161352876,
          10.604577618663669,
          10.630374765931556,
          10.656209635872095,
          10.682082261261842,
          10.707992674938426,
          10.733940909800651,
          10.75992699880859,
          10.78595097498373,
          10.812012871408996,
          10.838112721228947,
          10.864250557649791,
          10.890426413939549,
          10.916640323428117,
          10.94289231950739,
          10.96918243563139,
          10.995510705316287,
          11.021877162140617,
          11.048281839745298,
          11.074724771833736,
          11.101205992171979,
          11.127725534588826,
          11.154283432975873,
          11.180879721287623,
          11.207514433541677,
          11.234187603818738,
          11.260899266262763,
          11.28764945508109,
          11.31443820454449,
          11.341265548987314,
          11.36813152280763,
          11.395036160467214,
          11.421979496491783,
          11.448961565471038,
          11.475982402058797,
          11.503042040973083,
          11.53014051699624,
          11.557277864975077,
          11.584454119820874,
          11.611669316509637,
          11.638923490082101,
          11.66621667564387,
          11.69354890836551,
          11.720920223482725,
          11.748330656296377,
          11.775780242172669,
          11.803269016543192,
          11.830797014905112,
          11.858364272821222,
          11.885970825920058,
          11.91361670989608,
          11.941301960509684,
          11.969026613587356,
          11.996790705021805,
          12.024594270772086,
          12.052437346863677,
          12.080319969388547,
          12.10824217450545,
          12.1362039984398,
          12.164205477484002,
          12.192246647997358,
          12.220327546406386,
          12.24844820920484,
          12.276608672953783,
          12.304808974281729,
          12.333049149884877,
          12.36132923652703,
          12.38964927103989,
          12.418009290323024,
          12.446409331344105,
          12.47484943113897,
          12.503329626811738,
          12.531849955534947,
          12.560410454549634,
          12.58901116116555,
          12.61765211276112,
          12.646333346783761,
          12.67505490074979,
          12.703816812244737,
          12.732619118923333,
          12.761461858509659,
          12.790345068797357,
          12.819268787649587,
          12.848233052999305,
          12.877237902849329,
          12.906283375272357,
          12.93536950841127,
          12.9644963404792,
          12.993663909759508,
          13.022872254606114,
          13.052121413443476,
          13.081411424766806,
          13.110742327142134,
          13.14011415920644,
          13.169526959667833,
          13.19898076730557,
          13.22847562097033,
          13.25801155958416,
          13.287588622140781,
          13.317206847705574,
          13.346866275415806,
          13.376566944480677,
          13.406308894181503,
          13.436092163871818,
          13.46591679297752,
          13.495782820996972,
          13.52569028750116,
          13.55563923213379,
          13.585629694611468,
          13.615661714723768,
          13.64573533233339,
          13.675850587376303,
          13.706007519861874,
          13.736206169872961,
          13.766446577566093,
          13.796728783171563,
          13.827052826993599,
          13.857418749410424,
          13.887826590874495,
          13.91827639191256
         ]
        },
        {
         "mode": "lines",
         "name": "$1-\\cos\\theta$",
         "type": "scatter",
         "x": [
          0.1,
          0.14994994994994995,
          0.1998998998998999,
          0.24984984984984984,
          0.29979979979979976,
          0.3497497497497497,
          0.39969969969969965,
          0.4496496496496496,
          0.49959959959959954,
          0.5495495495495495,
          0.5994994994994994,
          0.6494494494494494,
          0.6993993993993993,
          0.7493493493493493,
          0.7992992992992992,
          0.8492492492492492,
          0.8991991991991991,
          0.949149149149149,
          0.999099099099099,
          1.049049049049049,
          1.098998998998999,
          1.148948948948949,
          1.198898898898899,
          1.2488488488488487,
          1.2987987987987988,
          1.3487487487487488,
          1.3986986986986987,
          1.4486486486486485,
          1.4985985985985986,
          1.5485485485485486,
          1.5984984984984985,
          1.6484484484484483,
          1.6983983983983983,
          1.7483483483483484,
          1.7982982982982982,
          1.848248248248248,
          1.8981981981981981,
          1.9481481481481482,
          1.998098098098098,
          2.048048048048048,
          2.097997997997998,
          2.147947947947948,
          2.197897897897898,
          2.2478478478478476,
          2.2977977977977977,
          2.3477477477477477,
          2.3976976976976974,
          2.4476476476476474,
          2.4975975975975975,
          2.5475475475475475,
          2.5974974974974976,
          2.647447447447447,
          2.6973973973973973,
          2.7473473473473473,
          2.797297297297297,
          2.847247247247247,
          2.897197197197197,
          2.947147147147147,
          2.997097097097097,
          3.0470470470470468,
          3.096996996996997,
          3.146946946946947,
          3.1968968968968965,
          3.2468468468468465,
          3.2967967967967966,
          3.3467467467467467,
          3.3966966966966967,
          3.4466466466466463,
          3.4965965965965964,
          3.5465465465465464,
          3.596496496496496,
          3.646446446446446,
          3.696396396396396,
          3.7463463463463462,
          3.7962962962962963,
          3.846246246246246,
          3.896196196196196,
          3.946146146146146,
          3.9960960960960956,
          4.046046046046046,
          4.095995995995995,
          4.145945945945945,
          4.195895895895895,
          4.245845845845845,
          4.2957957957957955,
          4.345745745745745,
          4.395695695695695,
          4.445645645645645,
          4.495595595595595,
          4.5455455455455445,
          4.595495495495495,
          4.645445445445445,
          4.695395395395394,
          4.745345345345345,
          4.795295295295294,
          4.845245245245245,
          4.895195195195194,
          4.945145145145144,
          4.9950950950950945,
          5.045045045045044,
          5.094994994994995,
          5.144944944944944,
          5.194894894894894,
          5.244844844844844,
          5.294794794794794,
          5.344744744744744,
          5.394694694694694,
          5.444644644644644,
          5.494594594594593,
          5.544544544544544,
          5.594494494494493,
          5.644444444444444,
          5.6943943943943935,
          5.744344344344343,
          5.794294294294294,
          5.844244244244243,
          5.894194194194194,
          5.944144144144143,
          5.994094094094093,
          6.0440440440440435,
          6.093993993993993,
          6.143943943943943,
          6.193893893893893,
          6.243843843843843,
          6.2937937937937924,
          6.343743743743743,
          6.393693693693693,
          6.443643643643643,
          6.493593593593593,
          6.543543543543542,
          6.593493493493493,
          6.643443443443442,
          6.693393393393393,
          6.7433433433433425,
          6.793293293293292,
          6.843243243243243,
          6.893193193193192,
          6.943143143143142,
          6.993093093093092,
          7.043043043043042,
          7.092992992992992,
          7.142942942942942,
          7.192892892892892,
          7.242842842842842,
          7.292792792792792,
          7.342742742742741,
          7.392692692692692,
          7.4426426426426415,
          7.492592592592592,
          7.542542542542542,
          7.592492492492491,
          7.642442442442442,
          7.692392392392391,
          7.742342342342341,
          7.7922922922922915,
          7.842242242242241,
          7.892192192192191,
          7.942142142142141,
          7.992092092092091,
          8.042042042042041,
          8.091991991991991,
          8.14194194194194,
          8.19189189189189,
          8.241841841841842,
          8.291791791791791,
          8.34174174174174,
          8.39169169169169,
          8.44164164164164,
          8.491591591591591,
          8.541541541541541,
          8.59149149149149,
          8.64144144144144,
          8.69139139139139,
          8.74134134134134,
          8.79129129129129,
          8.84124124124124,
          8.89119119119119,
          8.94114114114114,
          8.99109109109109,
          9.04104104104104,
          9.09099099099099,
          9.14094094094094,
          9.19089089089089,
          9.24084084084084,
          9.290790790790789,
          9.34074074074074,
          9.39069069069069,
          9.44064064064064,
          9.490590590590589,
          9.540540540540539,
          9.59049049049049,
          9.64044044044044,
          9.69039039039039,
          9.740340340340339,
          9.790290290290288,
          9.84024024024024,
          9.89019019019019,
          9.940140140140139,
          9.990090090090089,
          10.040040040040038,
          10.08998998998999,
          10.13993993993994,
          10.189889889889889,
          10.239839839839838,
          10.289789789789788,
          10.339739739739738,
          10.389689689689689,
          10.439639639639639,
          10.489589589589588,
          10.539539539539538,
          10.589489489489488,
          10.639439439439439,
          10.689389389389389,
          10.739339339339338,
          10.789289289289288,
          10.839239239239237,
          10.889189189189187,
          10.939139139139138,
          10.989089089089088,
          11.039039039039038,
          11.088988988988987,
          11.138938938938937,
          11.188888888888888,
          11.238838838838838,
          11.288788788788787,
          11.338738738738737,
          11.388688688688687,
          11.438638638638638,
          11.488588588588588,
          11.538538538538537,
          11.588488488488487,
          11.638438438438437,
          11.688388388388388,
          11.738338338338338,
          11.788288288288287,
          11.838238238238237,
          11.888188188188186,
          11.938138138138136,
          11.988088088088087,
          12.038038038038037,
          12.087987987987987,
          12.137937937937936,
          12.187887887887886,
          12.237837837837837,
          12.287787787787787,
          12.337737737737736,
          12.387687687687686,
          12.437637637637636,
          12.487587587587585,
          12.537537537537537,
          12.587487487487486,
          12.637437437437436,
          12.687387387387385,
          12.737337337337335,
          12.787287287287286,
          12.837237237237236,
          12.887187187187186,
          12.937137137137135,
          12.987087087087085,
          13.037037037037036,
          13.086986986986986,
          13.136936936936936,
          13.186886886886885,
          13.236836836836835,
          13.286786786786786,
          13.336736736736736,
          13.386686686686685,
          13.436636636636635,
          13.486586586586585,
          13.536536536536534,
          13.586486486486486,
          13.636436436436435,
          13.686386386386385,
          13.736336336336334,
          13.786286286286284,
          13.836236236236235,
          13.886186186186185,
          13.936136136136135,
          13.986086086086084,
          14.036036036036034,
          14.085985985985984,
          14.135935935935935,
          14.185885885885885,
          14.235835835835834,
          14.285785785785784,
          14.335735735735733,
          14.385685685685685,
          14.435635635635634,
          14.485585585585584,
          14.535535535535534,
          14.585485485485483,
          14.635435435435435,
          14.685385385385384,
          14.735335335335334,
          14.785285285285283,
          14.835235235235233,
          14.885185185185184,
          14.935135135135134,
          14.985085085085084,
          15.035035035035033,
          15.084984984984983,
          15.134934934934932,
          15.184884884884884,
          15.234834834834833,
          15.284784784784783,
          15.334734734734733,
          15.384684684684682,
          15.434634634634634,
          15.484584584584583,
          15.534534534534533,
          15.584484484484483,
          15.634434434434432,
          15.684384384384382,
          15.734334334334333,
          15.784284284284283,
          15.834234234234232,
          15.884184184184182,
          15.934134134134132,
          15.984084084084083,
          16.034034034034033,
          16.083983983983984,
          16.133933933933935,
          16.183883883883883,
          16.233833833833835,
          16.283783783783782,
          16.333733733733734,
          16.383683683683685,
          16.433633633633633,
          16.483583583583584,
          16.533533533533532,
          16.583483483483484,
          16.633433433433435,
          16.683383383383383,
          16.733333333333334,
          16.783283283283282,
          16.833233233233234,
          16.883183183183185,
          16.933133133133133,
          16.983083083083084,
          17.033033033033032,
          17.082982982982983,
          17.13293293293293,
          17.182882882882883,
          17.232832832832834,
          17.282782782782782,
          17.332732732732733,
          17.38268268268268,
          17.432632632632632,
          17.482582582582584,
          17.53253253253253,
          17.582482482482483,
          17.63243243243243,
          17.682382382382382,
          17.732332332332334,
          17.78228228228228,
          17.832232232232233,
          17.88218218218218,
          17.932132132132132,
          17.982082082082083,
          18.03203203203203,
          18.081981981981983,
          18.13193193193193,
          18.181881881881882,
          18.231831831831833,
          18.28178178178178,
          18.331731731731733,
          18.38168168168168,
          18.43163163163163,
          18.48158158158158,
          18.53153153153153,
          18.581481481481482,
          18.63143143143143,
          18.68138138138138,
          18.73133133133133,
          18.78128128128128,
          18.831231231231232,
          18.88118118118118,
          18.93113113113113,
          18.98108108108108,
          19.03103103103103,
          19.080980980980982,
          19.13093093093093,
          19.18088088088088,
          19.23083083083083,
          19.28078078078078,
          19.330730730730732,
          19.38068068068068,
          19.43063063063063,
          19.48058058058058,
          19.53053053053053,
          19.58048048048048,
          19.63043043043043,
          19.68038038038038,
          19.73033033033033,
          19.78028028028028,
          19.83023023023023,
          19.88018018018018,
          19.93013013013013,
          19.98008008008008,
          20.03003003003003,
          20.07997997997998,
          20.12992992992993,
          20.17987987987988,
          20.22982982982983,
          20.27977977977978,
          20.329729729729728,
          20.37967967967968,
          20.42962962962963,
          20.47957957957958,
          20.52952952952953,
          20.579479479479478,
          20.62942942942943,
          20.67937937937938,
          20.729329329329328,
          20.77927927927928,
          20.829229229229227,
          20.87917917917918,
          20.92912912912913,
          20.979079079079078,
          21.02902902902903,
          21.078978978978977,
          21.12892892892893,
          21.17887887887888,
          21.228828828828828,
          21.27877877877878,
          21.328728728728727,
          21.37867867867868,
          21.42862862862863,
          21.478578578578578,
          21.52852852852853,
          21.578478478478477,
          21.62842842842843,
          21.678378378378376,
          21.728328328328328,
          21.77827827827828,
          21.828228228228227,
          21.878178178178178,
          21.928128128128126,
          21.978078078078077,
          22.02802802802803,
          22.077977977977977,
          22.127927927927928,
          22.177877877877876,
          22.227827827827827,
          22.27777777777778,
          22.327727727727726,
          22.377677677677678,
          22.427627627627626,
          22.477577577577577,
          22.52752752752753,
          22.577477477477476,
          22.627427427427428,
          22.677377377377375,
          22.727327327327327,
          22.77727727727728,
          22.827227227227226,
          22.877177177177177,
          22.927127127127125,
          22.977077077077077,
          23.027027027027028,
          23.076976976976976,
          23.126926926926927,
          23.176876876876875,
          23.226826826826827,
          23.276776776776778,
          23.326726726726726,
          23.376676676676677,
          23.426626626626625,
          23.476576576576576,
          23.526526526526524,
          23.576476476476476,
          23.626426426426427,
          23.676376376376375,
          23.726326326326326,
          23.776276276276274,
          23.826226226226225,
          23.876176176176177,
          23.926126126126125,
          23.976076076076076,
          24.026026026026024,
          24.075975975975975,
          24.125925925925927,
          24.175875875875874,
          24.225825825825826,
          24.275775775775774,
          24.325725725725725,
          24.375675675675677,
          24.425625625625624,
          24.475575575575576,
          24.525525525525524,
          24.575475475475475,
          24.625425425425426,
          24.675375375375374,
          24.725325325325326,
          24.775275275275273,
          24.825225225225225,
          24.875175175175173,
          24.925125125125124,
          24.975075075075075,
          25.025025025025023,
          25.074974974974975,
          25.124924924924922,
          25.174874874874874,
          25.224824824824825,
          25.274774774774773,
          25.324724724724724,
          25.374674674674672,
          25.424624624624624,
          25.474574574574575,
          25.524524524524523,
          25.574474474474474,
          25.624424424424422,
          25.674374374374374,
          25.724324324324325,
          25.774274274274273,
          25.824224224224224,
          25.874174174174172,
          25.924124124124123,
          25.974074074074075,
          26.024024024024023,
          26.073973973973974,
          26.123923923923922,
          26.173873873873873,
          26.223823823823825,
          26.273773773773772,
          26.323723723723724,
          26.37367367367367,
          26.423623623623623,
          26.473573573573574,
          26.523523523523522,
          26.573473473473474,
          26.62342342342342,
          26.673373373373373,
          26.72332332332332,
          26.773273273273272,
          26.823223223223223,
          26.87317317317317,
          26.923123123123123,
          26.97307307307307,
          27.023023023023022,
          27.072972972972973,
          27.12292292292292,
          27.172872872872873,
          27.22282282282282,
          27.272772772772772,
          27.322722722722723,
          27.37267267267267,
          27.422622622622622,
          27.47257257257257,
          27.52252252252252,
          27.572472472472473,
          27.62242242242242,
          27.672372372372372,
          27.72232232232232,
          27.77227227227227,
          27.822222222222223,
          27.87217217217217,
          27.922122122122122,
          27.97207207207207,
          28.02202202202202,
          28.07197197197197,
          28.12192192192192,
          28.171871871871872,
          28.22182182182182,
          28.27177177177177,
          28.32172172172172,
          28.37167167167167,
          28.42162162162162,
          28.47157157157157,
          28.52152152152152,
          28.57147147147147,
          28.62142142142142,
          28.67137137137137,
          28.72132132132132,
          28.77127127127127,
          28.82122122122122,
          28.87117117117117,
          28.92112112112112,
          28.97107107107107,
          29.02102102102102,
          29.07097097097097,
          29.12092092092092,
          29.17087087087087,
          29.22082082082082,
          29.27077077077077,
          29.32072072072072,
          29.37067067067067,
          29.42062062062062,
          29.47057057057057,
          29.52052052052052,
          29.570470470470468,
          29.62042042042042,
          29.67037037037037,
          29.72032032032032,
          29.77027027027027,
          29.820220220220218,
          29.87017017017017,
          29.920120120120117,
          29.97007007007007,
          30.02002002002002,
          30.069969969969968,
          30.11991991991992,
          30.169869869869867,
          30.21981981981982,
          30.26976976976977,
          30.319719719719718,
          30.36966966966967,
          30.419619619619617,
          30.46956956956957,
          30.51951951951952,
          30.569469469469468,
          30.61941941941942,
          30.669369369369367,
          30.719319319319318,
          30.76926926926927,
          30.819219219219217,
          30.86916916916917,
          30.919119119119117,
          30.969069069069068,
          31.01901901901902,
          31.068968968968967,
          31.11891891891892,
          31.168868868868866,
          31.218818818818818,
          31.268768768768766,
          31.318718718718717,
          31.36866866866867,
          31.418618618618616,
          31.468568568568568,
          31.518518518518515,
          31.568468468468467,
          31.61841841841842,
          31.668368368368366,
          31.718318318318317,
          31.768268268268265,
          31.818218218218217,
          31.868168168168168,
          31.918118118118116,
          31.968068068068067,
          32.01801801801801,
          32.06796796796797,
          32.117917917917914,
          32.16786786786787,
          32.21781781781782,
          32.267767767767765,
          32.31771771771771,
          32.36766766766767,
          32.417617617617616,
          32.46756756756756,
          32.51751751751752,
          32.567467467467466,
          32.617417417417414,
          32.66736736736737,
          32.71731731731732,
          32.767267267267265,
          32.81721721721721,
          32.86716716716717,
          32.917117117117115,
          32.96706706706706,
          33.01701701701702,
          33.066966966966966,
          33.116916916916914,
          33.16686686686687,
          33.21681681681682,
          33.266766766766764,
          33.31671671671671,
          33.36666666666667,
          33.416616616616615,
          33.46656656656656,
          33.51651651651652,
          33.566466466466466,
          33.61641641641641,
          33.66636636636637,
          33.716316316316316,
          33.766266266266264,
          33.81621621621621,
          33.86616616616617,
          33.916116116116115,
          33.96606606606606,
          34.01601601601602,
          34.065965965965965,
          34.11591591591591,
          34.16586586586586,
          34.215815815815816,
          34.265765765765764,
          34.31571571571571,
          34.36566566566567,
          34.415615615615614,
          34.46556556556556,
          34.51551551551552,
          34.565465465465465,
          34.61541541541541,
          34.66536536536536,
          34.715315315315316,
          34.76526526526526,
          34.81521521521521,
          34.865165165165166,
          34.915115115115114,
          34.96506506506506,
          35.01501501501502,
          35.064964964964965,
          35.11491491491491,
          35.16486486486486,
          35.214814814814815,
          35.26476476476476,
          35.31471471471471,
          35.364664664664666,
          35.414614614614614,
          35.46456456456456,
          35.51451451451451,
          35.564464464464464,
          35.61441441441441,
          35.66436436436436,
          35.714314314314315,
          35.76426426426426,
          35.81421421421421,
          35.864164164164166,
          35.91411411411411,
          35.96406406406406,
          36.01401401401401,
          36.063963963963964,
          36.11391391391391,
          36.16386386386386,
          36.213813813813815,
          36.26376376376376,
          36.31371371371371,
          36.363663663663665,
          36.41361361361361,
          36.46356356356356,
          36.51351351351351,
          36.563463463463464,
          36.61341341341341,
          36.66336336336336,
          36.713313313313314,
          36.76326326326326,
          36.81321321321321,
          36.86316316316316,
          36.91311311311311,
          36.96306306306306,
          37.01301301301301,
          37.06296296296296,
          37.11291291291291,
          37.16286286286286,
          37.212812812812814,
          37.26276276276276,
          37.31271271271271,
          37.36266266266266,
          37.41261261261261,
          37.46256256256256,
          37.51251251251251,
          37.56246246246246,
          37.61241241241241,
          37.66236236236236,
          37.712312312312314,
          37.76226226226226,
          37.81221221221221,
          37.86216216216216,
          37.91211211211211,
          37.96206206206206,
          38.01201201201201,
          38.06196196196196,
          38.11191191191191,
          38.16186186186186,
          38.21181181181181,
          38.26176176176176,
          38.31171171171171,
          38.36166166166166,
          38.41161161161161,
          38.46156156156156,
          38.51151151151151,
          38.56146146146146,
          38.61141141141141,
          38.66136136136136,
          38.711311311311306,
          38.76126126126126,
          38.81121121121121,
          38.86116116116116,
          38.91111111111111,
          38.96106106106106,
          39.01101101101101,
          39.06096096096096,
          39.11091091091091,
          39.16086086086086,
          39.210810810810806,
          39.26076076076076,
          39.31071071071071,
          39.360660660660656,
          39.41061061061061,
          39.46056056056056,
          39.51051051051051,
          39.56046046046046,
          39.61041041041041,
          39.66036036036036,
          39.710310310310305,
          39.76026026026026,
          39.81021021021021,
          39.860160160160156,
          39.91011011011011,
          39.96006006006006,
          40.01001001001001,
          40.05995995995996,
          40.10990990990991,
          40.15985985985986,
          40.209809809809805,
          40.25975975975976,
          40.30970970970971,
          40.359659659659656,
          40.40960960960961,
          40.45955955955956,
          40.509509509509506,
          40.559459459459454,
          40.60940940940941,
          40.65935935935936,
          40.709309309309305,
          40.75925925925926,
          40.80920920920921,
          40.859159159159155,
          40.90910910910911,
          40.95905905905906,
          41.009009009009006,
          41.058958958958954,
          41.10890890890891,
          41.158858858858856,
          41.208808808808804,
          41.25875875875876,
          41.30870870870871,
          41.358658658658655,
          41.40860860860861,
          41.45855855855856,
          41.508508508508505,
          41.55845845845845,
          41.60840840840841,
          41.658358358358356,
          41.708308308308304,
          41.75825825825826,
          41.80820820820821,
          41.858158158158155,
          41.9081081081081,
          41.95805805805806,
          42.008008008008005,
          42.05795795795795,
          42.10790790790791,
          42.157857857857856,
          42.207807807807804,
          42.25775775775776,
          42.307707707707706,
          42.357657657657654,
          42.4076076076076,
          42.45755755755756,
          42.507507507507505,
          42.55745745745745,
          42.60740740740741,
          42.657357357357355,
          42.7073073073073,
          42.75725725725726,
          42.807207207207206,
          42.857157157157154,
          42.9071071071071,
          42.95705705705706,
          43.007007007007005,
          43.05695695695695,
          43.10690690690691,
          43.156856856856855,
          43.2068068068068,
          43.25675675675675,
          43.306706706706706,
          43.356656656656654,
          43.4066066066066,
          43.456556556556556,
          43.506506506506504,
          43.55645645645645,
          43.60640640640641,
          43.656356356356355,
          43.7063063063063,
          43.75625625625625,
          43.806206206206205,
          43.85615615615615,
          43.9061061061061,
          43.956056056056056,
          44.006006006006004,
          44.05595595595595,
          44.10590590590591,
          44.155855855855854,
          44.2058058058058,
          44.25575575575575,
          44.305705705705705,
          44.35565565565565,
          44.4056056056056,
          44.455555555555556,
          44.5055055055055,
          44.55545545545545,
          44.605405405405406,
          44.655355355355354,
          44.7053053053053,
          44.75525525525525,
          44.805205205205205,
          44.85515515515515,
          44.9051051051051,
          44.955055055055055,
          45.005005005005,
          45.05495495495495,
          45.1049049049049,
          45.154854854854854,
          45.2048048048048,
          45.25475475475475,
          45.304704704704704,
          45.35465465465465,
          45.4046046046046,
          45.454554554554555,
          45.5045045045045,
          45.55445445445445,
          45.6044044044044,
          45.65435435435435,
          45.7043043043043,
          45.75425425425425,
          45.804204204204204,
          45.85415415415415,
          45.9041041041041,
          45.954054054054055,
          46.004004004004,
          46.05395395395395,
          46.1039039039039,
          46.15385385385385,
          46.2038038038038,
          46.25375375375375,
          46.303703703703704,
          46.35365365365365,
          46.4036036036036,
          46.453553553553554,
          46.5035035035035,
          46.55345345345345,
          46.6034034034034,
          46.65335335335335,
          46.7033033033033,
          46.75325325325325,
          46.8032032032032,
          46.85315315315315,
          46.9031031031031,
          46.95305305305305,
          47.003003003003,
          47.05295295295295,
          47.1029029029029,
          47.15285285285285,
          47.2028028028028,
          47.25275275275275,
          47.3027027027027,
          47.35265265265265,
          47.4026026026026,
          47.45255255255255,
          47.5025025025025,
          47.55245245245245,
          47.6024024024024,
          47.65235235235235,
          47.7023023023023,
          47.75225225225225,
          47.8022022022022,
          47.85215215215215,
          47.9021021021021,
          47.952052052052046,
          48.002002002002,
          48.05195195195195,
          48.1019019019019,
          48.15185185185185,
          48.2018018018018,
          48.25175175175175,
          48.301701701701695,
          48.35165165165165,
          48.4016016016016,
          48.451551551551546,
          48.5015015015015,
          48.55145145145145,
          48.6014014014014,
          48.65135135135135,
          48.7013013013013,
          48.75125125125125,
          48.801201201201195,
          48.85115115115115,
          48.9011011011011,
          48.951051051051046,
          49.001001001001,
          49.05095095095095,
          49.100900900900896,
          49.15085085085085,
          49.2008008008008,
          49.25075075075075,
          49.300700700700695,
          49.35065065065065,
          49.4006006006006,
          49.450550550550545,
          49.5005005005005,
          49.55045045045045,
          49.600400400400396,
          49.650350350350344,
          49.7003003003003,
          49.75025025025025,
          49.800200200200194,
          49.85015015015015,
          49.9001001001001,
          49.950050050050045,
          50
         ],
         "y": [
          0.0001523089032103942,
          0.0003424669210139892,
          0.0006086282343902852,
          0.0009507938547829841,
          0.0013689650824703838,
          0.0018631435066105459,
          0.002433331005189174,
          0.0030795297450922554,
          0.0038017421821036203,
          0.004599971060927341,
          0.005474219415223869,
          0.006424490567637712,
          0.007450788129783321,
          0.008553116002377978,
          0.00973147837515523,
          0.010985879727014158,
          0.012316324825982503,
          0.013722818729293488,
          0.01520536678345417,
          0.016763974624249795,
          0.01839864817680634,
          0.020109393655689006,
          0.02189621756489228,
          0.02375912669796596,
          0.025698128138021605,
          0.02771322925784161,
          0.02980443771991322,
          0.031971761476542876,
          0.0342152087698733,
          0.03653478813201428,
          0.03893050838507613,
          0.04140237864128362,
          0.04395040830307026,
          0.046574607063108654,
          0.0492749849044657,
          0.052051552100660425,
          0.05490431921574676,
          0.0578332971044545,
          0.060838496912266296,
          0.06391993007550834,
          0.06707760832146603,
          0.07031154366851344,
          0.07362174842621202,
          0.07700823519540091,
          0.08047101686833444,
          0.08401010662882218,
          0.08762551795231627,
          0.09131726460605684,
          0.09508536064919804,
          0.09892982043292545,
          0.10285065860060971,
          0.10684789008792948,
          0.110921530123008,
          0.11507159422657486,
          0.11929809821207474,
          0.1236010581858566,
          0.12798049054731025,
          0.13243641198897194,
          0.1369688394967552,
          0.14157779035006196,
          0.14626328212196324,
          0.151025332679349,
          0.15586396018309204,
          0.1607791830882366,
          0.1657710201441679,
          0.17083949039475038,
          0.17598461317856953,
          0.18120640812903108,
          0.1865048951746417,
          0.19188009453911373,
          0.1973320267415732,
          0.20286071259678182,
          0.20846617321529448,
          0.21414843000369788,
          0.2199075046647514,
          0.22574341919763133,
          0.23165619589816622,
          0.23764585735894184,
          0.2437124264696424,
          0.24985592641714977,
          0.2560763806858461,
          0.26237381305777385,
          0.2687482476128883,
          0.27519970872930155,
          0.2817282210834401,
          0.28833380965035,
          0.29501649970391575,
          0.3017763168170491,
          0.30861328686197953,
          0.3155274360104939,
          0.3225187907341544,
          0.32958737780454345,
          0.3367332242935661,
          0.34395635757365534,
          0.3512568053180246,
          0.3586345955009793,
          0.3660897563981079,
          0.3736223165866216,
          0.38123230494556215,
          0.3889197506561025,
          0.3966846832018277,
          0.40452713236898524,
          0.4124471282467828,
          0.42044470122767785,
          0.4285198820076366,
          0.4366727015864629,
          0.4449031912680516,
          0.45321138266069,
          0.46159730767738394,
          0.47006099853613137,
          0.47860248776022113,
          0.4872218081785789,
          0.49591899292602765,
          0.504694075443617,
          0.5135470894789557,
          0.522478069086526,
          0.5314870486279657,
          0.5405740627724654,
          0.5497391464970132,
          0.5589823350867862,
          0.5683036641354684,
          0.5777031695455698,
          0.5871808875287945,
          0.5967368546063327,
          0.6063711076092911,
          0.6160836836789567,
          0.6258746202671772,
          0.6357439551367541,
          0.6456917263617402,
          0.655717972327838,
          0.6658227317327481,
          0.6760060435865515,
          0.6862679472120525,
          0.6966084822452023,
          0.7070276886354007,
          0.7175256066459493,
          0.728102276854383,
          0.7387577401528826,
          0.7494920377486588,
          0.7603052111643359,
          0.7711973022383546,
          0.78216835312535,
          0.7932184062966056,
          0.8043475045403925,
          0.8155556909624297,
          0.8268430089862302,
          0.8382095023536225,
          0.849655215125048,
          0.8611801916800546,
          0.8727844767177241,
          0.8844681152570366,
          0.8962311526373617,
          0.9080736345188741,
          0.9199956068829938,
          0.9319971160328082,
          0.9440782085935095,
          0.9562389315129002,
          0.9684793320617687,
          0.9807994578343698,
          0.993199356748929,
          1.005679077048006,
          1.0182386672990282,
          1.0308781763947616,
          1.0435976535537284,
          1.0563971483207273,
          1.0692767105672587,
          1.0822363904920869,
          1.0952762386216361,
          1.1083963058105253,
          1.1215966432420288,
          1.1348773024286285,
          1.1482383352124133,
          1.161679793765671,
          1.1752017305913527,
          1.1888041985235462,
          1.2024872507280708,
          1.216250940702891,
          1.2300953222787288,
          1.2440204496194953,
          1.2580263772228877,
          1.2721131599208724,
          1.2862808528802208,
          1.3005295116030808,
          1.314859191927471,
          1.329269950027815,
          1.3437618424155453,
          1.3583349259395885,
          1.3729892577869627,
          1.3877248954832806,
          1.4025418968933925,
          1.4174403202218466,
          1.4324202240135397,
          1.4474816671542319,
          1.4626247088711686,
          1.4778494087336151,
          1.493155826653439,
          1.5085440228857323,
          1.524014058029355,
          1.539565993027576,
          1.5551998891686023,
          1.5709158080862362,
          1.5867138117604596,
          1.602593962518029,
          1.6185563230331008,
          1.6346009563278245,
          1.650727925772984,
          1.6669372950886114,
          1.683229128344612,
          1.6996034899613748,
          1.7160604447104395,
          1.7326000577150897,
          1.7492223944510528,
          1.7659275207470644,
          1.7827155027855999,
          1.7995864071034702,
          1.8165403005925012,
          1.8335772505001604,
          1.850697324430269,
          1.867900590343647,
          1.8851871165587744,
          1.9025569717524795,
          1.9200102249605964,
          1.9375469455786827,
          1.955167203362687,
          1.9728710684296273,
          1.9906586112583229,
          2.0085299026900363,
          2.0264850139292236,
          2.0445240165442558,
          2.0626469824680456,
          2.080853983998848,
          2.0991450938009564,
          2.1175203849054145,
          2.1359799307107106,
          2.154523804983589,
          2.1731520818597296,
          2.1918648358444774,
          2.2106621418136316,
          2.229544075014149,
          2.2485107110649416,
          2.2675621259575895,
          2.286698396057121,
          2.3059195981027596,
          2.325225809208747,
          2.344617106865037,
          2.3640935689381326,
          2.3836552736718533,
          2.40330229968809,
          2.4230347259876375,
          2.442852631950983,
          2.4627560973390774,
          2.4827452022941516,
          2.502820027340537,
          2.5229806533854644,
          2.5432271617198925,
          2.5635596340192817,
          2.583978152344524,
          2.6044827991426334,
          2.625073657247696,
          2.64575080988166,
          2.666514340655158,
          2.6873643335684116,
          2.708300873012034,
          2.7293240437679134,
          2.7504339310100354,
          2.771630620305421,
          2.7929141976149237,
          2.8142847492941403,
          2.8357423620942797,
          2.857287123163078,
          2.87891912004563,
          2.9006384406853303,
          2.922445173424744,
          2.944339407006512,
          2.966321230574313,
          2.9883907336736617,
          3.0105480062529626,
          3.0327931386643017,
          3.055126221664482,
          3.0775473464158773,
          3.1000566044874196,
          3.122654087855513,
          3.1453398889049557,
          3.168114100429984,
          3.1909768156351213,
          3.2139281281361947,
          3.2369681319612784,
          3.2600969215516957,
          3.283314591762961,
          3.3066212378657798,
          3.3300169555470336,
          3.3535018409107455,
          3.377075990479124,
          3.400739501193522,
          3.424492470415445,
          3.448334995927608,
          3.4722671759348747,
          3.4962891090653647,
          3.520400894371406,
          3.544602631330622,
          3.5688944198469326,
          3.5932763602516062,
          3.6177485533043314,
          3.642311100194225,
          3.666964102540933,
          3.691707662395648,
          3.7165418822422422,
          3.741466864998285,
          3.766482714016138,
          3.7915895330840708,
          3.8167874264272754,
          3.842076498709072,
          3.8674568550319197,
          3.892928600938536,
          3.918491842413078,
          3.9441466858821697,
          3.9698932382160783,
          3.9957316067298327,
          4.021661899184362,
          4.04768422378763,
          4.0737986891957645,
          4.10000540451426,
          4.1263044792990655,
          4.152696023557823,
          4.179180147750968,
          4.205756962792963,
          4.232426580053417,
          4.259189111358315,
          4.286044668991231,
          4.3129933656944495,
          4.340035314670255,
          4.3671706295820725,
          4.394399424555745,
          4.421721814180687,
          4.449137913511188,
          4.476647838067574,
          4.5042517038375145,
          4.531949627277204,
          4.559741725312671,
          4.5876281153410154,
          4.615608915231642,
          4.643684243327591,
          4.671854218446754,
          4.700118959883218,
          4.728478587408484,
          4.7569332212728535,
          4.785482982206619,
          4.814127991421486,
          4.842868370611804,
          4.871704241955927,
          4.90063572811755,
          4.929662952246981,
          4.958786037982573,
          4.988005109452013,
          5.0173202912736565,
          5.046731708557959,
          5.076239486908799,
          5.10584375242482,
          5.135544631700874,
          5.165342251829387,
          5.195236740401719,
          5.225228225509622,
          5.255316835746585,
          5.285502700209316,
          5.315785948499071,
          5.346166710723211,
          5.376645117496489,
          5.407221299942611,
          5.437895389695633,
          5.468667518901406,
          5.49953782021906,
          5.530506426822456,
          5.561573472401722,
          5.592739091164626,
          5.624003417838163,
          5.655366587670025,
          5.686828736430086,
          5.718390000411934,
          5.750050516434395,
          5.781810421843022,
          5.813669854511707,
          5.845628952844144,
          5.877687855775394,
          5.909846702773504,
          5.942105633840984,
          5.974464789516438,
          6.006924310876111,
          6.039484339535512,
          6.072145017650941,
          6.104906487921185,
          6.1377688935890635,
          6.17073237844303,
          6.203797086818877,
          6.236963163601287,
          6.270230754225523,
          6.303600004679034,
          6.33707106150318,
          6.370644071794828,
          6.404319183208059,
          6.438096543955833,
          6.471976302811703,
          6.505958609111483,
          6.5400436127549675,
          6.574231464207646,
          6.608522314502416,
          6.642916315241322,
          6.677413618597286,
          6.712014377315849,
          6.746718744716946,
          6.781526874696629,
          6.816438921728913,
          6.851455040867477,
          6.886575387747462,
          6.921800118587311,
          6.957129390190582,
          6.992563359947685,
          7.0281021858377795,
          7.063746026430566,
          7.099495040888129,
          7.135349388966854,
          7.171309231019138,
          7.207374727995427,
          7.243546041445985,
          7.279823333522763,
          7.316206766981417,
          7.35269650518304,
          7.389292712096241,
          7.425995552298938,
          7.462805190980343,
          7.499721793942935,
          7.536745527604323,
          7.57387655899928,
          7.611115055781675,
          7.64846118622647,
          7.685915119231672,
          7.723477024320363,
          7.761147071642692,
          7.79892543197791,
          7.836812276736343,
          7.874807777961491,
          7.912912108332012,
          7.951125441163846,
          7.98944795041219,
          8.027879810673682,
          8.066421197188353,
          8.105072285841839,
          8.143833253167438,
          8.182704276348183,
          8.22168553321906,
          8.26077720226905,
          8.299979462643318,
          8.339292494145365,
          8.378716477239182,
          8.418251593051458,
          8.457898023373717,
          8.497655950664546,
          8.537525558051795,
          8.57750702933478,
          8.617600548986552,
          8.657806302156104,
          8.698124474670585,
          8.738555253037658,
          8.779098824447678,
          8.819755376776033,
          8.860525098585406,
          8.901408179128074,
          8.94240480834827,
          8.98351517688446,
          9.024739476071694,
          9.06607789794396,
          9.107530635236573,
          9.149097881388457,
          9.190779830544662,
          9.23257667755864,
          9.274488617994688,
          9.316515848130434,
          9.358658564959141,
          9.400916966192254,
          9.443291250261792,
          9.485781616322853,
          9.528388264256055,
          9.571111394670078,
          9.61395120890407,
          9.656907909030272,
          9.699981697856455,
          9.743172778928527,
          9.786481356533013,
          9.829907635699676,
          9.87345182220404,
          9.917114122570043,
          9.960894744072565,
          10.004793894740079,
          10.048811783357284,
          10.092948619467698,
          10.137204613376374,
          10.181579976152484,
          10.226074919632074,
          10.270689656420709,
          10.31542439989616,
          10.360279364211143,
          10.405254764296078,
          10.450350815861775,
          10.495567735402208,
          10.540905740197298,
          10.586365048315653,
          10.63194587861746,
          10.677648450757166,
          10.723472985186396,
          10.76941970315673,
          10.815488826722602,
          10.86168057874415,
          10.907995182890067,
          10.95443286364052,
          11.000993846290042,
          11.04767835695046,
          11.094486622553857,
          11.141418870855466,
          11.188475330436667,
          11.23565623070796,
          11.282961801911968,
          11.330392275126417,
          11.377947882267206,
          11.425628856091375,
          11.47343543020022,
          11.521367839042348,
          11.569426317916715,
          11.617611102975774,
          11.66592243122857,
          11.71436054054387,
          11.762925669653287,
          11.811618058154478,
          11.860437946514274,
          11.909385576071896,
          11.958461189042167,
          12.007665028518714,
          12.056997338477213,
          12.106458363778632,
          12.156048350172535,
          12.20576754430032,
          12.255616193698566,
          12.305594546802325,
          12.35570285294843,
          12.405941362378925,
          12.456310326244365,
          12.506809996607215,
          12.557440626445269,
          12.60820246965502,
          12.659095781055196,
          12.710120816390086,
          12.761277832333102,
          12.812567086490237,
          12.863988837403554,
          12.915543344554717,
          12.967230868368526,
          13.019051670216516,
          13.071006012420474,
          13.123094158256032,
          13.175316371956336,
          13.227672918715584,
          13.280164064692784,
          13.33279007701532,
          13.385551223782677,
          13.43844777407016,
          13.491479997932576,
          13.544648166407978,
          13.597952551521452,
          13.651393426288852,
          13.704971064720672,
          13.758685741825715,
          13.812537733615107,
          13.866527317105998,
          13.92065477032551,
          13.974920372314639,
          14.029324403132106,
          14.083867143858336,
          14.138548876599405,
          14.19336988449098,
          14.248330451702332,
          14.30343086344035,
          14.35867140595359,
          14.414052366536259,
          14.469574033532353,
          14.525236696339732,
          14.581040645414218,
          14.636986172273728,
          14.693073569502483,
          14.74930313075509,
          14.805675150760822,
          14.8621899253278,
          14.918847751347233,
          14.97564892679769,
          15.032593750749395,
          15.089682523368458,
          15.146915545921352,
          15.204293120779091,
          15.261815551421726,
          15.319483142442664,
          15.377296199553165,
          15.435255029586667,
          15.493359940503352,
          15.551611241394575,
          15.610009242487408,
          15.668554255149111,
          15.727246591891763,
          15.786086566376792,
          15.845074493419546,
          15.904210688994013,
          15.963495470237381,
          16.02292915545473,
          16.08251206412375,
          16.142244516899478,
          16.202126835618973,
          16.26215934330615,
          16.322342364176567,
          16.382676223642186,
          16.443161248316287,
          16.503797766018323,
          16.56458610577876,
          16.62552659784407,
          16.686619573681636,
          16.747865365984698,
          16.80926430867746,
          16.87081673691991,
          16.932522987113117,
          16.994383396904077,
          17.056398305191,
          17.118568052128285,
          17.180892979131784,
          17.243373428883956,
          17.306009745339,
          17.368802273728214,
          17.431751360565183,
          17.494857353651064,
          17.558120602079956,
          17.62154145624418,
          17.685120267839714,
          17.748857389871546,
          17.812753176659168,
          17.876807983841946,
          17.94102216838469,
          18.00539608858314,
          18.069930104069496,
          18.13462457581799,
          18.199479866150558,
          18.26449633874239,
          18.329674358627635,
          18.395014292205087,
          18.46051650724392,
          18.526181372889432,
          18.592009259668842,
          18.658000539497042,
          18.72415558568255,
          18.790474772933365,
          18.85695847736273,
          18.923607076495312,
          18.990420949272973,
          19.057400476060888,
          19.124546038653502,
          19.191858020280684,
          19.259336805613756,
          19.326982780771644,
          19.394796333327065,
          19.46277785231273,
          19.530927728227503,
          19.599246353042787,
          19.667734120208692,
          19.73639142466049,
          19.805218662824885,
          19.87421623262647,
          19.943384533494132,
          20.012723966367542,
          20.08223493370365,
          20.151917839483243,
          20.221773089217486,
          20.29180108995456,
          20.36200225028628,
          20.43237698035484,
          20.502925691859435,
          20.573648798063118,
          20.64454671379952,
          20.715619855479705,
          20.78686864109901,
          20.858293490244,
          20.92989482409939,
          21.001673065454955,
          21.07362863871266,
          21.14576196989366,
          21.21807348664529,
          21.29056361824844,
          21.363232795624487,
          21.436081451342627,
          21.50911001962709,
          21.582318936364448,
          21.655708639110934,
          21.729279567099784,
          21.803032161248698,
          21.876966864167276,
          21.951084120164435,
          22.025384375256078,
          22.099868077172566,
          22.174535675366332,
          22.249387621019615,
          22.324424367052103,
          22.399646368128682,
          22.475054080667203,
          22.550647962846387,
          22.626428474613608,
          22.70239607769284,
          22.778551235592634,
          22.854894413614147,
          22.93142607885908,
          23.008146700237894,
          23.085056748477907,
          23.16215669613143,
          23.239447017584062,
          23.316928189062942,
          23.394600688645067,
          23.472464996265646,
          23.550521593726533,
          23.628770964704717,
          23.70721359476076,
          23.78584997134743,
          23.864680583818217,
          23.943705923436124,
          24.022926483382207,
          24.10234275876443,
          24.181955246626504,
          24.26176444595656,
          24.34177085769626,
          24.421974984749614,
          24.502377331992005,
          24.582978406279295,
          24.66377871645684,
          24.74477877336876,
          24.825979089866994,
          24.90738018082074,
          24.988982563125596,
          25.070786755713037,
          25.152793279559777,
          25.235002657697294,
          25.317415415221316,
          25.400032079301383,
          25.482853179190514,
          25.565879246234964,
          25.64911081388373,
          25.732548417698727,
          25.81619259536429,
          25.900043886697315,
          25.984102833657108,
          26.06836998035547,
          26.152845873066795,
          26.237531060238183,
          26.322426092499633,
          26.407531522674354,
          26.49284790578903,
          26.57837579908423,
          26.66411576202486,
          26.75006835631067,
          26.836234145886745,
          26.922613696954212,
          27.009207577980916,
          27.0960163597121,
          27.183040615181298,
          27.270280919721166,
          27.357737850974395,
          27.445411988904755,
          27.533303915808183,
          27.621414216323824,
          27.70974347744528,
          27.798292288531883,
          27.887061241320012,
          27.97605092993443,
          28.065261950899824,
          28.15469490315229,
          28.244350388050954,
          28.334229009389546,
          28.42433137340828,
          28.514658088805522,
          28.605209766749738,
          28.6959870208914,
          28.786990467375002,
          28.87822072485112,
          28.96967841448867,
          29.061364159986937,
          29.15327858758814,
          29.245422326089464,
          29.337796006855903,
          29.430400263832418,
          29.523235733556746,
          29.616303055172004,
          29.709602870439443,
          29.803135823751248,
          29.896902562143442,
          29.990903735308887,
          30.085139995610355,
          30.17961199809352,
          30.274320400500372,
          30.369265863282386,
          30.46444904961385,
          30.559870625405438,
          30.655531259317648,
          30.751431622774465,
          30.847572389977003,
          30.943954237917342,
          31.04057784639234,
          31.137443898017597,
          31.234553078241532,
          31.3319060753594,
          31.429503580527516,
          31.527346287777686,
          31.62543489403133,
          31.72377009911415,
          31.822352605770593,
          31.92118311967852,
          32.02026234946387,
          32.119591006715545,
          32.219169806000316,
          32.318999464877805,
          32.419080703915526,
          32.51941424670417,
          32.62000081987281,
          32.72084115310434,
          32.82193597915082,
          32.923286033849145,
          33.02489205613669,
          33.12675478806706,
          33.22887497482589,
          33.33125336474687,
          33.43389070932773,
          33.53678776324644,
          33.639945284377404,
          33.74336403380795,
          33.8470447758545,
          33.9509882780794,
          34.055195311307564,
          34.15966664964296,
          34.26440307048576,
          34.36940535454928,
          34.47467428587691,
          34.58021065185932,
          34.68601524325198,
          34.79208885419229,
          34.898432282217215,
          35.00504632828083,
          35.11193179677225,
          35.219089495533154,
          35.32652023587609,
          35.43422483260223,
          35.54220410401981,
          35.65045887196219,
          35.758989961806535,
          35.86779820249212,
          35.97688442653904,
          36.08624947006703,
          36.1958941728144,
          36.30581937815683,
          36.416025933126726,
          36.526514688432364,
          36.63728649847727,
          36.74834222137969,
          36.8596827189923,
          36.97130885692189,
          37.08322150454917,
          37.19542153504903,
          37.30790982541032,
          37.42068725645637,
          37.53375471286528,
          37.64711308319042,
          37.760763259881166,
          37.87470613930367,
          37.98894262176167,
          38.10347361151771,
          38.21830001681421,
          38.33342274989489,
          38.448842727026204,
          38.564560868518925,
          38.680578098749855,
          38.796895346183895,
          38.91351354339595,
          39.030433627093046,
          39.14765653813681,
          39.26518322156579,
          39.383014626618255,
          39.50115170675477,
          39.6195954196812,
          39.73834672737187,
          39.85740659609256,
          39.97677599642408,
          40.096455903285715,
          40.21644729595889,
          40.33675115811105,
          40.45736847781959,
          40.57830024759612,
          40.69954746441062,
          40.82111112971612,
          40.94299224947316,
          41.0651918341746,
          41.18771089887079,
          41.310550463194446,
          41.43371155138604,
          41.55719519231941,
          41.68100241952721,
          41.80513427122683,
          41.92959179034629,
          42.054376024550486,
          42.17948802626756,
          42.304928852715236,
          42.43069956592774,
          42.556801232782455,
          42.683234925027165,
          42.81000171930714,
          42.93710269719262,
          43.064538945206465,
          43.19231155485182,
          43.32042162264024,
          43.448870250119754,
          43.5776585439033,
          43.706787615697166,
          43.836258582330004,
          43.966072565781346,
          44.09623069321115,
          44.22673409698899,
          44.357583914723556,
          44.48878128929241,
          44.62032736887202,
          44.75222330696788,
          44.8844702624448,
          45.01706939955757,
          45.15002188798171,
          45.28332890284443,
          45.41699162475595,
          45.551011239840754,
          45.68538893976946,
          45.82012592179039,
          45.95522338876197,
          46.09068254918479,
          46.22650461723426,
          46.36269081279331,
          46.499242361485464,
          46.63616049470794,
          46.77344644966518,
          46.911101469402475,
          47.04912680283999,
          47.18752370480676,
          47.326293436075204,
          47.46543726339578,
          47.604956459531714,
          47.744852303294344,
          47.8851260795783,
          48.02577907939726,
          48.16681259991971,
          48.308227944505255,
          48.45002642274081,
          48.59220935047732,
          48.73477804986673,
          48.877733849399036,
          49.02107808393981,
          49.164812094767846,
          49.30893722961317,
          49.45345484269526,
          49.59836629476147,
          49.74367295312603,
          49.8893761917089,
          50.03547739107519,
          50.181977938474866,
          50.32887922788254,
          50.47618266003781,
          50.62388964248551,
          50.772001589616835,
          50.920519922710184,
          51.06944606997256,
          51.218781466581284,
          51.36852755472601,
          51.518685783650945,
          51.66925760969746,
          51.82024449634702,
          51.971647914264395,
          52.12346934134106,
          52.27571026273928,
          52.42837217093612,
          52.5814565657679,
          52.734964954475124,
          52.88889885174761,
          53.04325977976991,
          53.198049268267155,
          53.353268854551274,
          53.508920083567304,
          53.66500450794045,
          53.821523688023085,
          53.978479191942455,
          54.13587259564834,
          54.293705482961485,
          54.45197944562216,
          54.61069608333907,
          54.76985700383864,
          54.92946382291488,
          55.08951816447928,
          55.25002166061127,
          55.41097595160917,
          55.57238268604122
         ]
        },
        {
         "mode": "lines",
         "name": "$\\theta-\\tan\\theta$",
         "type": "scatter",
         "x": [
          0.1,
          0.14994994994994995,
          0.1998998998998999,
          0.24984984984984984,
          0.29979979979979976,
          0.3497497497497497,
          0.39969969969969965,
          0.4496496496496496,
          0.49959959959959954,
          0.5495495495495495,
          0.5994994994994994,
          0.6494494494494494,
          0.6993993993993993,
          0.7493493493493493,
          0.7992992992992992,
          0.8492492492492492,
          0.8991991991991991,
          0.949149149149149,
          0.999099099099099,
          1.049049049049049,
          1.098998998998999,
          1.148948948948949,
          1.198898898898899,
          1.2488488488488487,
          1.2987987987987988,
          1.3487487487487488,
          1.3986986986986987,
          1.4486486486486485,
          1.4985985985985986,
          1.5485485485485486,
          1.5984984984984985,
          1.6484484484484483,
          1.6983983983983983,
          1.7483483483483484,
          1.7982982982982982,
          1.848248248248248,
          1.8981981981981981,
          1.9481481481481482,
          1.998098098098098,
          2.048048048048048,
          2.097997997997998,
          2.147947947947948,
          2.197897897897898,
          2.2478478478478476,
          2.2977977977977977,
          2.3477477477477477,
          2.3976976976976974,
          2.4476476476476474,
          2.4975975975975975,
          2.5475475475475475,
          2.5974974974974976,
          2.647447447447447,
          2.6973973973973973,
          2.7473473473473473,
          2.797297297297297,
          2.847247247247247,
          2.897197197197197,
          2.947147147147147,
          2.997097097097097,
          3.0470470470470468,
          3.096996996996997,
          3.146946946946947,
          3.1968968968968965,
          3.2468468468468465,
          3.2967967967967966,
          3.3467467467467467,
          3.3966966966966967,
          3.4466466466466463,
          3.4965965965965964,
          3.5465465465465464,
          3.596496496496496,
          3.646446446446446,
          3.696396396396396,
          3.7463463463463462,
          3.7962962962962963,
          3.846246246246246,
          3.896196196196196,
          3.946146146146146,
          3.9960960960960956,
          4.046046046046046,
          4.095995995995995,
          4.145945945945945,
          4.195895895895895,
          4.245845845845845,
          4.2957957957957955,
          4.345745745745745,
          4.395695695695695,
          4.445645645645645,
          4.495595595595595,
          4.5455455455455445,
          4.595495495495495,
          4.645445445445445,
          4.695395395395394,
          4.745345345345345,
          4.795295295295294,
          4.845245245245245,
          4.895195195195194,
          4.945145145145144,
          4.9950950950950945,
          5.045045045045044,
          5.094994994994995,
          5.144944944944944,
          5.194894894894894,
          5.244844844844844,
          5.294794794794794,
          5.344744744744744,
          5.394694694694694,
          5.444644644644644,
          5.494594594594593,
          5.544544544544544,
          5.594494494494493,
          5.644444444444444,
          5.6943943943943935,
          5.744344344344343,
          5.794294294294294,
          5.844244244244243,
          5.894194194194194,
          5.944144144144143,
          5.994094094094093,
          6.0440440440440435,
          6.093993993993993,
          6.143943943943943,
          6.193893893893893,
          6.243843843843843,
          6.2937937937937924,
          6.343743743743743,
          6.393693693693693,
          6.443643643643643,
          6.493593593593593,
          6.543543543543542,
          6.593493493493493,
          6.643443443443442,
          6.693393393393393,
          6.7433433433433425,
          6.793293293293292,
          6.843243243243243,
          6.893193193193192,
          6.943143143143142,
          6.993093093093092,
          7.043043043043042,
          7.092992992992992,
          7.142942942942942,
          7.192892892892892,
          7.242842842842842,
          7.292792792792792,
          7.342742742742741,
          7.392692692692692,
          7.4426426426426415,
          7.492592592592592,
          7.542542542542542,
          7.592492492492491,
          7.642442442442442,
          7.692392392392391,
          7.742342342342341,
          7.7922922922922915,
          7.842242242242241,
          7.892192192192191,
          7.942142142142141,
          7.992092092092091,
          8.042042042042041,
          8.091991991991991,
          8.14194194194194,
          8.19189189189189,
          8.241841841841842,
          8.291791791791791,
          8.34174174174174,
          8.39169169169169,
          8.44164164164164,
          8.491591591591591,
          8.541541541541541,
          8.59149149149149,
          8.64144144144144,
          8.69139139139139,
          8.74134134134134,
          8.79129129129129,
          8.84124124124124,
          8.89119119119119,
          8.94114114114114,
          8.99109109109109,
          9.04104104104104,
          9.09099099099099,
          9.14094094094094,
          9.19089089089089,
          9.24084084084084,
          9.290790790790789,
          9.34074074074074,
          9.39069069069069,
          9.44064064064064,
          9.490590590590589,
          9.540540540540539,
          9.59049049049049,
          9.64044044044044,
          9.69039039039039,
          9.740340340340339,
          9.790290290290288,
          9.84024024024024,
          9.89019019019019,
          9.940140140140139,
          9.990090090090089,
          10.040040040040038,
          10.08998998998999,
          10.13993993993994,
          10.189889889889889,
          10.239839839839838,
          10.289789789789788,
          10.339739739739738,
          10.389689689689689,
          10.439639639639639,
          10.489589589589588,
          10.539539539539538,
          10.589489489489488,
          10.639439439439439,
          10.689389389389389,
          10.739339339339338,
          10.789289289289288,
          10.839239239239237,
          10.889189189189187,
          10.939139139139138,
          10.989089089089088,
          11.039039039039038,
          11.088988988988987,
          11.138938938938937,
          11.188888888888888,
          11.238838838838838,
          11.288788788788787,
          11.338738738738737,
          11.388688688688687,
          11.438638638638638,
          11.488588588588588,
          11.538538538538537,
          11.588488488488487,
          11.638438438438437,
          11.688388388388388,
          11.738338338338338,
          11.788288288288287,
          11.838238238238237,
          11.888188188188186,
          11.938138138138136,
          11.988088088088087,
          12.038038038038037,
          12.087987987987987,
          12.137937937937936,
          12.187887887887886,
          12.237837837837837,
          12.287787787787787,
          12.337737737737736,
          12.387687687687686,
          12.437637637637636,
          12.487587587587585,
          12.537537537537537,
          12.587487487487486,
          12.637437437437436,
          12.687387387387385,
          12.737337337337335,
          12.787287287287286,
          12.837237237237236,
          12.887187187187186,
          12.937137137137135,
          12.987087087087085,
          13.037037037037036,
          13.086986986986986,
          13.136936936936936,
          13.186886886886885,
          13.236836836836835,
          13.286786786786786,
          13.336736736736736,
          13.386686686686685,
          13.436636636636635,
          13.486586586586585,
          13.536536536536534,
          13.586486486486486,
          13.636436436436435,
          13.686386386386385,
          13.736336336336334,
          13.786286286286284,
          13.836236236236235,
          13.886186186186185,
          13.936136136136135,
          13.986086086086084,
          14.036036036036034,
          14.085985985985984,
          14.135935935935935,
          14.185885885885885,
          14.235835835835834,
          14.285785785785784,
          14.335735735735733,
          14.385685685685685,
          14.435635635635634,
          14.485585585585584,
          14.535535535535534,
          14.585485485485483,
          14.635435435435435,
          14.685385385385384,
          14.735335335335334,
          14.785285285285283,
          14.835235235235233,
          14.885185185185184,
          14.935135135135134,
          14.985085085085084,
          15.035035035035033,
          15.084984984984983,
          15.134934934934932,
          15.184884884884884,
          15.234834834834833,
          15.284784784784783,
          15.334734734734733,
          15.384684684684682,
          15.434634634634634,
          15.484584584584583,
          15.534534534534533,
          15.584484484484483,
          15.634434434434432,
          15.684384384384382,
          15.734334334334333,
          15.784284284284283,
          15.834234234234232,
          15.884184184184182,
          15.934134134134132,
          15.984084084084083,
          16.034034034034033,
          16.083983983983984,
          16.133933933933935,
          16.183883883883883,
          16.233833833833835,
          16.283783783783782,
          16.333733733733734,
          16.383683683683685,
          16.433633633633633,
          16.483583583583584,
          16.533533533533532,
          16.583483483483484,
          16.633433433433435,
          16.683383383383383,
          16.733333333333334,
          16.783283283283282,
          16.833233233233234,
          16.883183183183185,
          16.933133133133133,
          16.983083083083084,
          17.033033033033032,
          17.082982982982983,
          17.13293293293293,
          17.182882882882883,
          17.232832832832834,
          17.282782782782782,
          17.332732732732733,
          17.38268268268268,
          17.432632632632632,
          17.482582582582584,
          17.53253253253253,
          17.582482482482483,
          17.63243243243243,
          17.682382382382382,
          17.732332332332334,
          17.78228228228228,
          17.832232232232233,
          17.88218218218218,
          17.932132132132132,
          17.982082082082083,
          18.03203203203203,
          18.081981981981983,
          18.13193193193193,
          18.181881881881882,
          18.231831831831833,
          18.28178178178178,
          18.331731731731733,
          18.38168168168168,
          18.43163163163163,
          18.48158158158158,
          18.53153153153153,
          18.581481481481482,
          18.63143143143143,
          18.68138138138138,
          18.73133133133133,
          18.78128128128128,
          18.831231231231232,
          18.88118118118118,
          18.93113113113113,
          18.98108108108108,
          19.03103103103103,
          19.080980980980982,
          19.13093093093093,
          19.18088088088088,
          19.23083083083083,
          19.28078078078078,
          19.330730730730732,
          19.38068068068068,
          19.43063063063063,
          19.48058058058058,
          19.53053053053053,
          19.58048048048048,
          19.63043043043043,
          19.68038038038038,
          19.73033033033033,
          19.78028028028028,
          19.83023023023023,
          19.88018018018018,
          19.93013013013013,
          19.98008008008008,
          20.03003003003003,
          20.07997997997998,
          20.12992992992993,
          20.17987987987988,
          20.22982982982983,
          20.27977977977978,
          20.329729729729728,
          20.37967967967968,
          20.42962962962963,
          20.47957957957958,
          20.52952952952953,
          20.579479479479478,
          20.62942942942943,
          20.67937937937938,
          20.729329329329328,
          20.77927927927928,
          20.829229229229227,
          20.87917917917918,
          20.92912912912913,
          20.979079079079078,
          21.02902902902903,
          21.078978978978977,
          21.12892892892893,
          21.17887887887888,
          21.228828828828828,
          21.27877877877878,
          21.328728728728727,
          21.37867867867868,
          21.42862862862863,
          21.478578578578578,
          21.52852852852853,
          21.578478478478477,
          21.62842842842843,
          21.678378378378376,
          21.728328328328328,
          21.77827827827828,
          21.828228228228227,
          21.878178178178178,
          21.928128128128126,
          21.978078078078077,
          22.02802802802803,
          22.077977977977977,
          22.127927927927928,
          22.177877877877876,
          22.227827827827827,
          22.27777777777778,
          22.327727727727726,
          22.377677677677678,
          22.427627627627626,
          22.477577577577577,
          22.52752752752753,
          22.577477477477476,
          22.627427427427428,
          22.677377377377375,
          22.727327327327327,
          22.77727727727728,
          22.827227227227226,
          22.877177177177177,
          22.927127127127125,
          22.977077077077077,
          23.027027027027028,
          23.076976976976976,
          23.126926926926927,
          23.176876876876875,
          23.226826826826827,
          23.276776776776778,
          23.326726726726726,
          23.376676676676677,
          23.426626626626625,
          23.476576576576576,
          23.526526526526524,
          23.576476476476476,
          23.626426426426427,
          23.676376376376375,
          23.726326326326326,
          23.776276276276274,
          23.826226226226225,
          23.876176176176177,
          23.926126126126125,
          23.976076076076076,
          24.026026026026024,
          24.075975975975975,
          24.125925925925927,
          24.175875875875874,
          24.225825825825826,
          24.275775775775774,
          24.325725725725725,
          24.375675675675677,
          24.425625625625624,
          24.475575575575576,
          24.525525525525524,
          24.575475475475475,
          24.625425425425426,
          24.675375375375374,
          24.725325325325326,
          24.775275275275273,
          24.825225225225225,
          24.875175175175173,
          24.925125125125124,
          24.975075075075075,
          25.025025025025023,
          25.074974974974975,
          25.124924924924922,
          25.174874874874874,
          25.224824824824825,
          25.274774774774773,
          25.324724724724724,
          25.374674674674672,
          25.424624624624624,
          25.474574574574575,
          25.524524524524523,
          25.574474474474474,
          25.624424424424422,
          25.674374374374374,
          25.724324324324325,
          25.774274274274273,
          25.824224224224224,
          25.874174174174172,
          25.924124124124123,
          25.974074074074075,
          26.024024024024023,
          26.073973973973974,
          26.123923923923922,
          26.173873873873873,
          26.223823823823825,
          26.273773773773772,
          26.323723723723724,
          26.37367367367367,
          26.423623623623623,
          26.473573573573574,
          26.523523523523522,
          26.573473473473474,
          26.62342342342342,
          26.673373373373373,
          26.72332332332332,
          26.773273273273272,
          26.823223223223223,
          26.87317317317317,
          26.923123123123123,
          26.97307307307307,
          27.023023023023022,
          27.072972972972973,
          27.12292292292292,
          27.172872872872873,
          27.22282282282282,
          27.272772772772772,
          27.322722722722723,
          27.37267267267267,
          27.422622622622622,
          27.47257257257257,
          27.52252252252252,
          27.572472472472473,
          27.62242242242242,
          27.672372372372372,
          27.72232232232232,
          27.77227227227227,
          27.822222222222223,
          27.87217217217217,
          27.922122122122122,
          27.97207207207207,
          28.02202202202202,
          28.07197197197197,
          28.12192192192192,
          28.171871871871872,
          28.22182182182182,
          28.27177177177177,
          28.32172172172172,
          28.37167167167167,
          28.42162162162162,
          28.47157157157157,
          28.52152152152152,
          28.57147147147147,
          28.62142142142142,
          28.67137137137137,
          28.72132132132132,
          28.77127127127127,
          28.82122122122122,
          28.87117117117117,
          28.92112112112112,
          28.97107107107107,
          29.02102102102102,
          29.07097097097097,
          29.12092092092092,
          29.17087087087087,
          29.22082082082082,
          29.27077077077077,
          29.32072072072072,
          29.37067067067067,
          29.42062062062062,
          29.47057057057057,
          29.52052052052052,
          29.570470470470468,
          29.62042042042042,
          29.67037037037037,
          29.72032032032032,
          29.77027027027027,
          29.820220220220218,
          29.87017017017017,
          29.920120120120117,
          29.97007007007007,
          30.02002002002002,
          30.069969969969968,
          30.11991991991992,
          30.169869869869867,
          30.21981981981982,
          30.26976976976977,
          30.319719719719718,
          30.36966966966967,
          30.419619619619617,
          30.46956956956957,
          30.51951951951952,
          30.569469469469468,
          30.61941941941942,
          30.669369369369367,
          30.719319319319318,
          30.76926926926927,
          30.819219219219217,
          30.86916916916917,
          30.919119119119117,
          30.969069069069068,
          31.01901901901902,
          31.068968968968967,
          31.11891891891892,
          31.168868868868866,
          31.218818818818818,
          31.268768768768766,
          31.318718718718717,
          31.36866866866867,
          31.418618618618616,
          31.468568568568568,
          31.518518518518515,
          31.568468468468467,
          31.61841841841842,
          31.668368368368366,
          31.718318318318317,
          31.768268268268265,
          31.818218218218217,
          31.868168168168168,
          31.918118118118116,
          31.968068068068067,
          32.01801801801801,
          32.06796796796797,
          32.117917917917914,
          32.16786786786787,
          32.21781781781782,
          32.267767767767765,
          32.31771771771771,
          32.36766766766767,
          32.417617617617616,
          32.46756756756756,
          32.51751751751752,
          32.567467467467466,
          32.617417417417414,
          32.66736736736737,
          32.71731731731732,
          32.767267267267265,
          32.81721721721721,
          32.86716716716717,
          32.917117117117115,
          32.96706706706706,
          33.01701701701702,
          33.066966966966966,
          33.116916916916914,
          33.16686686686687,
          33.21681681681682,
          33.266766766766764,
          33.31671671671671,
          33.36666666666667,
          33.416616616616615,
          33.46656656656656,
          33.51651651651652,
          33.566466466466466,
          33.61641641641641,
          33.66636636636637,
          33.716316316316316,
          33.766266266266264,
          33.81621621621621,
          33.86616616616617,
          33.916116116116115,
          33.96606606606606,
          34.01601601601602,
          34.065965965965965,
          34.11591591591591,
          34.16586586586586,
          34.215815815815816,
          34.265765765765764,
          34.31571571571571,
          34.36566566566567,
          34.415615615615614,
          34.46556556556556,
          34.51551551551552,
          34.565465465465465,
          34.61541541541541,
          34.66536536536536,
          34.715315315315316,
          34.76526526526526,
          34.81521521521521,
          34.865165165165166,
          34.915115115115114,
          34.96506506506506,
          35.01501501501502,
          35.064964964964965,
          35.11491491491491,
          35.16486486486486,
          35.214814814814815,
          35.26476476476476,
          35.31471471471471,
          35.364664664664666,
          35.414614614614614,
          35.46456456456456,
          35.51451451451451,
          35.564464464464464,
          35.61441441441441,
          35.66436436436436,
          35.714314314314315,
          35.76426426426426,
          35.81421421421421,
          35.864164164164166,
          35.91411411411411,
          35.96406406406406,
          36.01401401401401,
          36.063963963963964,
          36.11391391391391,
          36.16386386386386,
          36.213813813813815,
          36.26376376376376,
          36.31371371371371,
          36.363663663663665,
          36.41361361361361,
          36.46356356356356,
          36.51351351351351,
          36.563463463463464,
          36.61341341341341,
          36.66336336336336,
          36.713313313313314,
          36.76326326326326,
          36.81321321321321,
          36.86316316316316,
          36.91311311311311,
          36.96306306306306,
          37.01301301301301,
          37.06296296296296,
          37.11291291291291,
          37.16286286286286,
          37.212812812812814,
          37.26276276276276,
          37.31271271271271,
          37.36266266266266,
          37.41261261261261,
          37.46256256256256,
          37.51251251251251,
          37.56246246246246,
          37.61241241241241,
          37.66236236236236,
          37.712312312312314,
          37.76226226226226,
          37.81221221221221,
          37.86216216216216,
          37.91211211211211,
          37.96206206206206,
          38.01201201201201,
          38.06196196196196,
          38.11191191191191,
          38.16186186186186,
          38.21181181181181,
          38.26176176176176,
          38.31171171171171,
          38.36166166166166,
          38.41161161161161,
          38.46156156156156,
          38.51151151151151,
          38.56146146146146,
          38.61141141141141,
          38.66136136136136,
          38.711311311311306,
          38.76126126126126,
          38.81121121121121,
          38.86116116116116,
          38.91111111111111,
          38.96106106106106,
          39.01101101101101,
          39.06096096096096,
          39.11091091091091,
          39.16086086086086,
          39.210810810810806,
          39.26076076076076,
          39.31071071071071,
          39.360660660660656,
          39.41061061061061,
          39.46056056056056,
          39.51051051051051,
          39.56046046046046,
          39.61041041041041,
          39.66036036036036,
          39.710310310310305,
          39.76026026026026,
          39.81021021021021,
          39.860160160160156,
          39.91011011011011,
          39.96006006006006,
          40.01001001001001,
          40.05995995995996,
          40.10990990990991,
          40.15985985985986,
          40.209809809809805,
          40.25975975975976,
          40.30970970970971,
          40.359659659659656,
          40.40960960960961,
          40.45955955955956,
          40.509509509509506,
          40.559459459459454,
          40.60940940940941,
          40.65935935935936,
          40.709309309309305,
          40.75925925925926,
          40.80920920920921,
          40.859159159159155,
          40.90910910910911,
          40.95905905905906,
          41.009009009009006,
          41.058958958958954,
          41.10890890890891,
          41.158858858858856,
          41.208808808808804,
          41.25875875875876,
          41.30870870870871,
          41.358658658658655,
          41.40860860860861,
          41.45855855855856,
          41.508508508508505,
          41.55845845845845,
          41.60840840840841,
          41.658358358358356,
          41.708308308308304,
          41.75825825825826,
          41.80820820820821,
          41.858158158158155,
          41.9081081081081,
          41.95805805805806,
          42.008008008008005,
          42.05795795795795,
          42.10790790790791,
          42.157857857857856,
          42.207807807807804,
          42.25775775775776,
          42.307707707707706,
          42.357657657657654,
          42.4076076076076,
          42.45755755755756,
          42.507507507507505,
          42.55745745745745,
          42.60740740740741,
          42.657357357357355,
          42.7073073073073,
          42.75725725725726,
          42.807207207207206,
          42.857157157157154,
          42.9071071071071,
          42.95705705705706,
          43.007007007007005,
          43.05695695695695,
          43.10690690690691,
          43.156856856856855,
          43.2068068068068,
          43.25675675675675,
          43.306706706706706,
          43.356656656656654,
          43.4066066066066,
          43.456556556556556,
          43.506506506506504,
          43.55645645645645,
          43.60640640640641,
          43.656356356356355,
          43.7063063063063,
          43.75625625625625,
          43.806206206206205,
          43.85615615615615,
          43.9061061061061,
          43.956056056056056,
          44.006006006006004,
          44.05595595595595,
          44.10590590590591,
          44.155855855855854,
          44.2058058058058,
          44.25575575575575,
          44.305705705705705,
          44.35565565565565,
          44.4056056056056,
          44.455555555555556,
          44.5055055055055,
          44.55545545545545,
          44.605405405405406,
          44.655355355355354,
          44.7053053053053,
          44.75525525525525,
          44.805205205205205,
          44.85515515515515,
          44.9051051051051,
          44.955055055055055,
          45.005005005005,
          45.05495495495495,
          45.1049049049049,
          45.154854854854854,
          45.2048048048048,
          45.25475475475475,
          45.304704704704704,
          45.35465465465465,
          45.4046046046046,
          45.454554554554555,
          45.5045045045045,
          45.55445445445445,
          45.6044044044044,
          45.65435435435435,
          45.7043043043043,
          45.75425425425425,
          45.804204204204204,
          45.85415415415415,
          45.9041041041041,
          45.954054054054055,
          46.004004004004,
          46.05395395395395,
          46.1039039039039,
          46.15385385385385,
          46.2038038038038,
          46.25375375375375,
          46.303703703703704,
          46.35365365365365,
          46.4036036036036,
          46.453553553553554,
          46.5035035035035,
          46.55345345345345,
          46.6034034034034,
          46.65335335335335,
          46.7033033033033,
          46.75325325325325,
          46.8032032032032,
          46.85315315315315,
          46.9031031031031,
          46.95305305305305,
          47.003003003003,
          47.05295295295295,
          47.1029029029029,
          47.15285285285285,
          47.2028028028028,
          47.25275275275275,
          47.3027027027027,
          47.35265265265265,
          47.4026026026026,
          47.45255255255255,
          47.5025025025025,
          47.55245245245245,
          47.6024024024024,
          47.65235235235235,
          47.7023023023023,
          47.75225225225225,
          47.8022022022022,
          47.85215215215215,
          47.9021021021021,
          47.952052052052046,
          48.002002002002,
          48.05195195195195,
          48.1019019019019,
          48.15185185185185,
          48.2018018018018,
          48.25175175175175,
          48.301701701701695,
          48.35165165165165,
          48.4016016016016,
          48.451551551551546,
          48.5015015015015,
          48.55145145145145,
          48.6014014014014,
          48.65135135135135,
          48.7013013013013,
          48.75125125125125,
          48.801201201201195,
          48.85115115115115,
          48.9011011011011,
          48.951051051051046,
          49.001001001001,
          49.05095095095095,
          49.100900900900896,
          49.15085085085085,
          49.2008008008008,
          49.25075075075075,
          49.300700700700695,
          49.35065065065065,
          49.4006006006006,
          49.450550550550545,
          49.5005005005005,
          49.55045045045045,
          49.600400400400396,
          49.650350350350344,
          49.7003003003003,
          49.75025025025025,
          49.800200200200194,
          49.85015015015015,
          49.9001001001001,
          49.950050050050045,
          50
         ],
         "y": [
          -0.00010153916055210504,
          -0.00022831073334717597,
          -0.00040575042759396975,
          -0.000633858351161624,
          -0.0009126346427494265,
          -0.0012420794718884455,
          -0.0016221930388135442,
          -0.002052975574716978,
          -0.0025344273414887107,
          -0.00306654863187034,
          -0.0036493397693991153,
          -0.004282801108491393,
          -0.004966933034225532,
          -0.0057017359626666255,
          -0.006487210340562804,
          -0.007323356645548832,
          -0.008210175386029136,
          -0.009147667101266096,
          -0.01013583236131272,
          -0.011174671767058922,
          -0.012264185950173876,
          -0.013404375573226393,
          -0.014595241329533076,
          -0.015836783943255602,
          -0.01712900416940416,
          -0.01847190279380049,
          -0.019865480633081124,
          -0.021309738534772027,
          -0.022804677377152267,
          -0.024350298069390357,
          -0.025946601551458122,
          -0.027593588794218533,
          -0.029291260799312036,
          -0.03103961859925645,
          -0.03283866325742019,
          -0.03468839586799998,
          -0.03658881755609619,
          -0.038539929477541555,
          -0.04054173281915261,
          -0.042594228798555275,
          -0.04469741866421412,
          -0.04685130369548374,
          -0.049055885202570086,
          -0.0513111645265746,
          -0.05361714303941794,
          -0.055973822143965825,
          -0.058381203273912864,
          -0.06083928789381582,
          -0.06334807749919154,
          -0.06590757361635871,
          -0.06851777780260782,
          -0.07117869164604129,
          -0.07389031676571459,
          -0.07665265481157772,
          -0.0794657074644546,
          -0.08232947643612502,
          -0.0852439634692641,
          -0.0882091703374171,
          -0.09122509884511136,
          -0.0942917508277381,
          -0.09740912815170326,
          -0.10057723271426337,
          -0.10379606644362607,
          -0.1070656312989692,
          -0.11038592927039906,
          -0.11375696237896055,
          -0.11717873267665843,
          -0.1206512422464545,
          -0.12417449320227601,
          -0.12774848768901284,
          -0.1313732278825143,
          -0.13504871598966212,
          -0.13877495424822264,
          -0.14255194492703832,
          -0.14637969032587925,
          -0.15025819277552227,
          -0.15418745463781242,
          -0.15816747830550762,
          -0.16219826620244135,
          -0.1662798207833874,
          -0.17041214453423326,
          -0.1745952399718233,
          -0.17882910964406679,
          -0.18311375612995212,
          -0.1874491820394008,
          -0.19183539001350391,
          -0.19627238272429737,
          -0.2007601628749699,
          -0.20529873319972738,
          -0.20988809646384762,
          -0.21452825546375365,
          -0.2192192130267987,
          -0.22396097201160978,
          -0.22875353530781425,
          -0.23359690583615186,
          -0.23849108654847,
          -0.24343608042774065,
          -0.2484318904880484,
          -0.2534785197746314,
          -0.2585759713638611,
          -0.26372424836321173,
          -0.26892335391135874,
          -0.27417329117807654,
          -0.2794740633643731,
          -0.28482567370236506,
          -0.29022812545537086,
          -0.2956814219179142,
          -0.30118556641565697,
          -0.3067405623055117,
          -0.31234641297557914,
          -0.318003121845149,
          -0.32371069236478583,
          -0.32946912801623357,
          -0.3352784323124773,
          -0.34113860879777724,
          -0.3470496610476218,
          -0.3530115926687511,
          -0.359024407299208,
          -0.36508810860824314,
          -0.3712027002964741,
          -0.3773681860957399,
          -0.3835845697692466,
          -0.3898518551114135,
          -0.3961700459480695,
          -0.40253914613631375,
          -0.40895915956460854,
          -0.4154300901527076,
          -0.42195194185178364,
          -0.428524718644308,
          -0.43514842454417685,
          -0.44182306359658013,
          -0.4485486398781626,
          -0.4553251574969284,
          -0.4621526205923386,
          -0.46903103333515855,
          -0.4759603999276935,
          -0.4829407246035893,
          -0.48997201162795906,
          -0.4970542652974024,
          -0.5041874899399228,
          -0.5113716899150138,
          -0.518606869613652,
          -0.5258930334582577,
          -0.5332301859028173,
          -0.5406183314327967,
          -0.5480574745651186,
          -0.5555476198483328,
          -0.5630887718624296,
          -0.5706809352190236,
          -0.5783241145612098,
          -0.5860183145637198,
          -0.5937635399327948,
          -0.6015597954063167,
          -0.6094070857537379,
          -0.6173054157761452,
          -0.6252547903061668,
          -0.6332552142081502,
          -0.6413066923780442,
          -0.6494092297434302,
          -0.6575628312635993,
          -0.6657675019294387,
          -0.6740232467635616,
          -0.6823300708203044,
          -0.6906879791856361,
          -0.6990969769773234,
          -0.7075570693447768,
          -0.7160682614691883,
          -0.7246305585635046,
          -0.7332439658724422,
          -0.7419084886724379,
          -0.7506241322717485,
          -0.7593909020104477,
          -0.7682088032603545,
          -0.777077841425168,
          -0.7859980219403699,
          -0.7949693502733144,
          -0.8039918319232308,
          -0.8130654724211437,
          -0.8221902773300281,
          -0.8313662522447208,
          -0.840593402791943,
          -0.8498717346303607,
          -0.8592012534505631,
          -0.8685819649750792,
          -0.8780138749583486,
          -0.8874969891868626,
          -0.8970313134790422,
          -0.906616853685269,
          -0.9162536156879703,
          -0.9259416054015905,
          -0.9356808287725831,
          -0.9454712917794711,
          -0.9553130004327963,
          -0.9652059607752173,
          -0.9751501788814173,
          -0.9851456608582544,
          -0.9951924128446121,
          -1.0052904410115384,
          -1.0154397515622426,
          -1.0256403507320357,
          -1.035892244788394,
          -1.0461954400310285,
          -1.0565499427917977,
          -1.0669557594347492,
          -1.0774128963561906,
          -1.0879213599846587,
          -1.0984811567809014,
          -1.1090922932379719,
          -1.1197547758811832,
          -1.1304686112681146,
          -1.1412338059887048,
          -1.1520503666651547,
          -1.162918299952039,
          -1.1738376125362704,
          -1.184808311137122,
          -1.1958304025062407,
          -1.206903893427685,
          -1.2180287907179086,
          -1.2292051012257725,
          -1.2404328318326285,
          -1.251711989452221,
          -1.263042581030824,
          -1.274424613547117,
          -1.2858580940123654,
          -1.2973430294702955,
          -1.3088794269971906,
          -1.3204672937018633,
          -1.3321066367256698,
          -1.343797463242631,
          -1.3555397804592557,
          -1.3673335956147137,
          -1.3791789159807828,
          -1.3910757488619503,
          -1.4030241015952387,
          -1.4150239815504677,
          -1.4270753961300748,
          -1.4391783527691933,
          -1.4513328589357606,
          -1.4635389221303554,
          -1.4757965498863839,
          -1.4881057497700179,
          -1.5004665293801969,
          -1.5128788963486552,
          -1.525342858339996,
          -1.5378584230516392,
          -1.5504255982138309,
          -1.5630443915897734,
          -1.57571481097547,
          -1.5884368641998905,
          -1.6012105591249086,
          -1.614035903645377,
          -1.6269129056890628,
          -1.639841573216752,
          -1.6528219142221727,
          -1.6658539367321514,
          -1.67893764880646,
          -1.6920730585380055,
          -1.7052601740526807,
          -1.7184990035095267,
          -1.7317895551006854,
          -1.7451318370513658,
          -1.758525857619982,
          -1.7719716250980753,
          -1.7854691478103897,
          -1.7990184341148332,
          -1.8126194924025378,
          -1.826272331097907,
          -1.8399769586585264,
          -1.853733383575323,
          -1.8675416143724712,
          -1.8814016596074952,
          -1.8953135278712028,
          -1.9092772277877603,
          -1.9232927680147085,
          -1.9373601572430053,
          -1.9514794041969454,
          -1.965650517634309,
          -1.9798735063462944,
          -1.9941483791575683,
          -2.0084751449262694,
          -2.0228538125440716,
          -2.037284390936157,
          -2.051766889061207,
          -2.066301315911549,
          -2.0808876805130407,
          -2.095525991925123,
          -2.1102162592409317,
          -2.124958491587171,
          -2.1397526981242745,
          -2.154598888046316,
          -2.1694970705811087,
          -2.184447254990145,
          -2.1994494505686886,
          -2.2145036666458062,
          -2.2296099125843254,
          -2.2447681977808367,
          -2.2599785316658245,
          -2.2752409237036204,
          -2.290555383392376,
          -2.305921920264211,
          -2.321340543885097,
          -2.3368112638549894,
          -2.3523340898077607,
          -2.3679090314113265,
          -2.3835360983675042,
          -2.399215300412221,
          -2.41494664731541,
          -2.430730148881085,
          -2.446565814947358,
          -2.462453655386445,
          -2.4783936801046558,
          -2.4943858990425376,
          -2.5104303221747206,
          -2.526526959510104,
          -2.5426758210918052,
          -2.558876916997123,
          -2.5751302573377397,
          -2.591435852259501,
          -2.6077937119426595,
          -2.624203846601778,
          -2.640666266485728,
          -2.657180981877864,
          -2.6737480030958394,
          -2.690367340491803,
          -2.707039004452353,
          -2.723763005398566,
          -2.7405393537859384,
          -2.757368060104588,
          -2.7742491348791596,
          -2.7911825886688297,
          -2.808168432067394,
          -2.8252066757032814,
          -2.8422973302395187,
          -2.859440406373827,
          -2.876635914838619,
          -2.8938838664010187,
          -2.9111842718628633,
          -2.9285371420608,
          -2.9459424878662257,
          -2.963400320185379,
          -2.9809106499593128,
          -2.9984734881639135,
          -3.0160888458100383,
          -3.033756733943358,
          -3.0514771636445457,
          -3.0692501460292085,
          -3.087075692247958,
          -3.1049538134863863,
          -3.1228845209651612,
          -3.1408678259399685,
          -3.158903739701615,
          -3.176992273576012,
          -3.1951334389241905,
          -3.2133272471424195,
          -3.231573709662033,
          -3.2498728379496833,
          -3.2682246435072337,
          -3.2866291378718215,
          -3.3050863326158564,
          -3.3235962393470957,
          -3.3421588697086166,
          -3.3607742353789,
          -3.3794423480718283,
          -3.398163219536663,
          -3.416936861558164,
          -3.4357632859565883,
          -3.4546425045876292,
          -3.473574529342579,
          -3.492559372148258,
          -3.511597044967093,
          -3.530687559797125,
          -3.5498309286720064,
          -3.5690271636611253,
          -3.588276276869473,
          -3.607578280437862,
          -3.626933186542833,
          -3.6463410073966482,
          -3.6658017552474407,
          -3.6853154423791628,
          -3.7048820811116143,
          -3.7245016838005096,
          -3.74417426283752,
          -3.76389983065016,
          -3.7836783997020103,
          -3.803509982492642,
          -3.823394591557636,
          -3.8433322394686846,
          -3.8633229388335044,
          -3.883366702295985,
          -3.903463542536139,
          -3.9236134722701923,
          -3.943816504250502,
          -3.9640726512657682,
          -3.9843819261408875,
          -4.0047443417370685,
          -4.025159910951822,
          -4.0456286467190825,
          -4.066150562009102,
          -4.0867256698285646,
          -4.107353983220586,
          -4.128035515264786,
          -4.148770279077288,
          -4.169558287810716,
          -4.190399554654297,
          -4.211294092833829,
          -4.232241915611738,
          -4.253243036287105,
          -4.274297468195694,
          -4.295405224709996,
          -4.3165663192392145,
          -4.337780765229414,
          -4.3590485761634055,
          -4.380369765560834,
          -4.401744346978216,
          -4.423172334009013,
          -4.444653740283595,
          -4.466188579469277,
          -4.487776865270404,
          -4.509418611428321,
          -4.531113831721484,
          -4.5528625399653695,
          -4.574664750012617,
          -4.596520475753054,
          -4.618429731113613,
          -4.640392530058516,
          -4.662408886589193,
          -4.6844788147444385,
          -4.706602328600233,
          -4.7287794422700244,
          -4.751010169904595,
          -4.773294525692121,
          -4.795632523858271,
          -4.818024178666177,
          -4.840469504416475,
          -4.862968515447364,
          -4.885521226134599,
          -4.908127650891574,
          -4.930787804169321,
          -4.953501700456566,
          -4.976269354279691,
          -4.999090780202907,
          -5.021965992828176,
          -5.044895006795216,
          -5.0678778367817126,
          -5.090914497503123,
          -5.114005003712891,
          -5.137149370202404,
          -5.160347611800976,
          -5.183599743376034,
          -5.206905779832997,
          -5.230265736115401,
          -5.253679627204868,
          -5.277147468121236,
          -5.300669273922516,
          -5.3242450597049515,
          -5.3478748406030245,
          -5.371558631789541,
          -5.3952964484756505,
          -5.41908830591087,
          -5.442934219383103,
          -5.466834204218726,
          -5.490788275782543,
          -5.514796449477951,
          -5.538858740746839,
          -5.562975165069684,
          -5.587145737965618,
          -5.611370474992423,
          -5.635649391746538,
          -5.659982503863187,
          -5.684369827016309,
          -5.708811376918729,
          -5.733307169322021,
          -5.757857220016697,
          -5.782461544832166,
          -5.8071201596367885,
          -5.831833080337937,
          -5.856600322881969,
          -5.881421903254362,
          -5.90629783747965,
          -5.931228141621514,
          -5.95621283178283,
          -5.981251924105717,
          -6.006345434771475,
          -6.0314933800007475,
          -6.0566957760534965,
          -6.081952639229061,
          -6.107263985866162,
          -6.132629832343003,
          -6.158050195077223,
          -6.183525090526051,
          -6.209054535186207,
          -6.23463854559404,
          -6.260277138325546,
          -6.285970329996397,
          -6.311718137261979,
          -6.337520576817454,
          -6.363377665397715,
          -6.389289419777593,
          -6.415255856771697,
          -6.441276993234607,
          -6.467352846060846,
          -6.493483432184946,
          -6.519668768581445,
          -6.54590887226498,
          -6.57220376029026,
          -6.598553449752241,
          -6.6249579577859805,
          -6.651417301566835,
          -6.677931498310398,
          -6.704500565272606,
          -6.731124519749769,
          -6.757803379078576,
          -6.784537160636146,
          -6.811325881840112,
          -6.838169560148585,
          -6.865068213060324,
          -6.892021858114622,
          -6.9190305128914416,
          -6.9460941950114625,
          -6.973212922136051,
          -7.000386711967391,
          -7.02761558224848,
          -7.0548995507631345,
          -7.082238635336141,
          -7.109632853833162,
          -7.137082224160903,
          -7.164586764267064,
          -7.192146492140406,
          -7.2197614258108915,
          -7.247431583349533,
          -7.275156982868605,
          -7.302937642521639,
          -7.330773580503398,
          -7.358664815050059,
          -7.3866113644390845,
          -7.414613246989424,
          -7.4426704810614615,
          -7.470783085057127,
          -7.498951077419829,
          -7.52717447663466,
          -7.555453301228278,
          -7.583787569769061,
          -7.6121773008671445,
          -7.640622513174386,
          -7.669123225384494,
          -7.697679456233029,
          -7.726291224497441,
          -7.754958548997198,
          -7.7836814485937085,
          -7.812459942190439,
          -7.84129404873297,
          -7.870183787208984,
          -7.899129176648373,
          -7.928130236123219,
          -7.957186984747963,
          -7.986299441679277,
          -8.01546762611622,
          -8.044691557300306,
          -8.073971254515428,
          -8.103306737088092,
          -8.132698024387272,
          -8.162145135824552,
          -8.191648090854198,
          -8.22120690897316,
          -8.250821609721088,
          -8.280492212680473,
          -8.310218737476593,
          -8.340001203777668,
          -8.3698396312948,
          -8.39973403978208,
          -8.429684449036632,
          -8.459690878898646,
          -8.48975334925143,
          -8.519871880021498,
          -8.550046491178554,
          -8.58027720273556,
          -8.6105640347488,
          -8.64090700731795,
          -8.671306140586065,
          -8.701761454739716,
          -8.73227297000892,
          -8.762840706667262,
          -8.793464685032012,
          -8.824144925464005,
          -8.85488144836786,
          -8.885674274191913,
          -8.916523423428337,
          -8.94742891661313,
          -8.978390774326254,
          -9.009409017191567,
          -9.040483665877002,
          -9.071614741094491,
          -9.102802263600122,
          -9.134046254194137,
          -9.16534673372098,
          -9.19670372306938,
          -9.228117243172349,
          -9.259587315007334,
          -9.291113959596107,
          -9.322697198004962,
          -9.354337051344713,
          -9.386033540770786,
          -9.41778668748313,
          -9.449596512726464,
          -9.481463037790238,
          -9.513386284008627,
          -9.545366272760683,
          -9.57740302547032,
          -9.609496563606392,
          -9.641646908682802,
          -9.673854082258424,
          -9.706118105937275,
          -9.73843900136853,
          -9.770816790246545,
          -9.803251494310922,
          -9.835743135346647,
          -9.868291735184027,
          -9.900897315698723,
          -9.93355989881205,
          -9.966279506490663,
          -9.999056160746878,
          -10.03188988363872,
          -10.06478069726978,
          -10.097728623789523,
          -10.130733685393073,
          -10.16379590432155,
          -10.196915302861912,
          -10.230091903347079,
          -10.263325728156069,
          -10.296616799713895,
          -10.329965140491753,
          -10.36337077300702,
          -10.396833719823286,
          -10.430354003550548,
          -10.463931646845019,
          -10.497566672409446,
          -10.531259102992967,
          -10.565008961391321,
          -10.59881627044677,
          -10.632681053048271,
          -10.666603332131471,
          -10.70058313067873,
          -10.734620471719262,
          -10.768715378329137,
          -10.802867873631408,
          -10.837077980796026,
          -10.87134572304009,
          -10.905671123627686,
          -10.94005420587017,
          -10.97449499312608,
          -11.008993508801193,
          -11.043549776348675,
          -11.078163819269125,
          -11.11283566111044,
          -11.147565325468252,
          -11.182352835985586,
          -11.217198216353202,
          -11.252101490309519,
          -11.287062681640709,
          -11.322081814180756,
          -11.357158911811519,
          -11.392293998462815,
          -11.427487098112412,
          -11.462738234786151,
          -11.498047432558007,
          -11.533414715550123,
          -11.56884010793282,
          -11.604323633924825,
          -11.639865317793117,
          -11.675465183853179,
          -11.711123256468914,
          -11.74683956005279,
          -11.7826141190659,
          -11.818446958017976,
          -11.854338101467508,
          -11.89028757402171,
          -11.926295400336747,
          -11.962361605117628,
          -11.998486213118358,
          -12.034669249142011,
          -12.070910738040737,
          -12.10721070471585,
          -12.1435691741179,
          -12.17998617124676,
          -12.216461721151633,
          -12.25299584893113,
          -12.2895885797334,
          -12.326239938756093,
          -12.36294995124649,
          -12.399718642501547,
          -12.436546037867982,
          -12.473432162742272,
          -12.51037704257084,
          -12.547380702850003,
          -12.584443169126084,
          -12.621564466995435,
          -12.658744622104656,
          -12.695983660150429,
          -12.733281606879746,
          -12.77063848808995,
          -12.808054329628751,
          -12.845529157394326,
          -12.883062997335404,
          -12.920655875451303,
          -12.958307817791976,
          -12.996018850458144,
          -13.033788999601354,
          -13.071618291423881,
          -13.109506752179112,
          -13.147454408171305,
          -13.185461285755846,
          -13.223527411339248,
          -13.261652811379202,
          -13.299837512384702,
          -13.338081540916058,
          -13.376384923585011,
          -13.41474768705478,
          -13.453169858040093,
          -13.491651463307361,
          -13.530192529674585,
          -13.568793084011634,
          -13.607453153240112,
          -13.646172764333524,
          -13.684951944317447,
          -13.723790720269308,
          -13.762689119318791,
          -13.801647168647706,
          -13.840664895490054,
          -13.879742327132256,
          -13.918879490913044,
          -13.958076414223594,
          -13.997333124507708,
          -14.036649649261653,
          -14.076026016034518,
          -14.115462252427994,
          -14.154958386096677,
          -14.194514444748036,
          -14.23413045614248,
          -14.273806448093444,
          -14.313542448467494,
          -14.353338485184375,
          -14.393194586217078,
          -14.433110779591896,
          -14.473087093388564,
          -14.51312355574022,
          -14.55322019483363,
          -14.593377038909106,
          -14.63359411626071,
          -14.673871455236226,
          -14.714209084237309,
          -14.754607031719507,
          -14.795065326192388,
          -14.835583996219562,
          -14.876163070418801,
          -14.916802577462049,
          -14.957502546075583,
          -14.99826300504005,
          -15.039083983190526,
          -15.079965509416596,
          -15.120907612662435,
          -15.161910321926959,
          -15.202973666263734,
          -15.244097674781203,
          -15.285282376642739,
          -15.326527801066604,
          -15.367833977326207,
          -15.40920093475006,
          -15.450628702721875,
          -15.49211731068065,
          -15.533666788120772,
          -15.575277164592105,
          -15.61694846969993,
          -15.658680733105221,
          -15.70047398452461,
          -15.742328253730504,
          -15.784243570551126,
          -15.826219964870644,
          -15.868257466629169,
          -15.91035610582295,
          -15.952515912504397,
          -15.99473691678212,
          -16.037019148821052,
          -16.07936263884257,
          -16.121767417124435,
          -16.164233514001115,
          -16.206760959863555,
          -16.249349785159588,
          -16.2920000203937,
          -16.334711696127375,
          -16.37748484297902,
          -16.420319491624078,
          -16.463215672795155,
          -16.506173417282053,
          -16.549192755931884,
          -16.59227371964915,
          -16.635416339395768,
          -16.67862064619124,
          -16.721886671112742,
          -16.76521444529506,
          -16.808603999930863,
          -16.852055366270648,
          -16.895568575622928,
          -16.939143659354233,
          -16.982780648889243,
          -17.026479575710827,
          -17.0702404713602,
          -17.114063367436955,
          -17.157948295599144,
          -17.20189528756339,
          -17.245904375105003,
          -17.289975590057935,
          -17.334108964315035,
          -17.378304529828043,
          -17.422562318607664,
          -17.466882362723723,
          -17.511264694305158,
          -17.555709345540215,
          -17.600216348676472,
          -17.64478573602089,
          -17.689417539940006,
          -17.734111792859906,
          -17.778868527266443,
          -17.82368777570518,
          -17.868569570781595,
          -17.913513945161075,
          -17.958520931569126,
          -18.00359056279135,
          -18.04872287167358,
          -18.093917891121983,
          -18.139175654103106,
          -18.184496193644012,
          -18.229879542832368,
          -18.27532573481648,
          -18.32083480280543,
          -18.366406780069234,
          -18.412041699938765,
          -18.457739595805972,
          -18.503500501123973,
          -18.54932444940709,
          -18.595211474230915,
          -18.64116160923256,
          -18.68717488811055,
          -18.733251344625064,
          -18.779391012597902,
          -18.825593925912738,
          -18.87186011851505,
          -18.918189624412342,
          -18.964582477674146,
          -19.011038712432164,
          -19.057558362880368,
          -19.10414146327506,
          -19.150788047934984,
          -19.197498151241444,
          -19.244271807638324,
          -19.29110905163234,
          -19.33800991779293,
          -19.384974440752476,
          -19.43200265520645,
          -19.479094595913367,
          -19.52625029769493,
          -19.573469795436235,
          -19.620753124085713,
          -19.668100318655306,
          -19.715511414220614,
          -19.762986445920863,
          -19.810525448959115,
          -19.8581284586023,
          -19.905795510181353,
          -19.95352663909132,
          -20.0013218807914,
          -20.049181270805125,
          -20.09710484472037,
          -20.145092638189517,
          -20.193144686929543,
          -20.24126102672214,
          -20.289441693413735,
          -20.33768672291565,
          -20.385996151204257,
          -20.434370014320972,
          -20.482808348372412,
          -20.531311189530488,
          -20.5798785740325,
          -20.628510538181278,
          -20.67720711834523,
          -20.725968350958446,
          -20.774794272520896,
          -20.82368491959837,
          -20.87264032882275,
          -20.92166053689197,
          -20.97074558057024,
          -21.01989549668805,
          -21.069110322142347,
          -21.11839009389661,
          -21.167734848980917,
          -21.21714462449219,
          -21.26661945759408,
          -21.316159385517246,
          -21.365764445559428,
          -21.415434675085507,
          -21.465170111527623,
          -21.51497079238534,
          -21.564836755225677,
          -21.61476803768325,
          -21.664764677460393,
          -21.714826712327195,
          -21.76495418012175,
          -21.815147118750094,
          -21.865405566186443,
          -21.91572956047322,
          -21.966119139721265,
          -22.01657434210978,
          -22.067095205886602,
          -22.117681769368254,
          -22.168334070940002,
          -22.219052149056054,
          -22.269836042239596,
          -22.32068578908295,
          -22.37160142824762,
          -22.42258299846461,
          -22.473630538534177,
          -22.524744087326226,
          -22.575923683780402,
          -22.62716936690606,
          -22.678481175782466,
          -22.72985914955893,
          -22.78130332745489,
          -22.832813748760017,
          -22.884390452834303,
          -22.93603347910829,
          -22.987742867083018,
          -23.039518656330273,
          -23.09136088649263,
          -23.143269597283652,
          -23.195244828487873,
          -23.247286619961034,
          -23.299395011630093,
          -23.351570043493496,
          -23.40381175562109,
          -23.456120188154415,
          -23.508495381306723,
          -23.560937375363185,
          -23.613446210680834,
          -23.666021927688895,
          -23.71866456688875,
          -23.771374168854166,
          -23.824150774231313,
          -23.87699442373895,
          -23.92990515816849,
          -23.98288301838422,
          -24.035928045323303,
          -24.08904027999593,
          -24.14221976348553,
          -24.195466536948768,
          -24.248780641615742,
          -24.302162118790054,
          -24.35561100984899,
          -24.40912735624358,
          -24.462711199498763,
          -24.516362581213492,
          -24.570081543060894,
          -24.623868126788313,
          -24.677722374217513,
          -24.73164432724474,
          -24.78563402784091,
          -24.839691518051644,
          -24.893816839997537,
          -24.948010035874137,
          -25.002271147952055,
          -25.056600218577312,
          -25.110997290171223,
          -25.16546240523061,
          -25.219995606327966,
          -25.274596936111504,
          -25.329266437305392,
          -25.38400415270974,
          -25.438810125200874,
          -25.49368439773137,
          -25.548627013330172,
          -25.6036380151028,
          -25.65871744623142,
          -25.713865349974974,
          -25.7690817696693,
          -25.82436674872736,
          -25.87972033063921,
          -25.935142558972263,
          -25.99063347737135,
          -26.046193129558894,
          -26.10182155933497,
          -26.15751881057754,
          -26.21328492724251,
          -26.26911995336385,
          -26.32502393305381,
          -26.38099691050298,
          -26.437038929980456,
          -26.49315003583389,
          -26.549330272489836,
          -26.605579684453595,
          -26.661898316309628,
          -26.718286212721477,
          -26.77474341843199
         ]
        }
       ],
       "layout": {
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "Percentage error in small angle approximations",
         "x": 0.5
        },
        "xaxis": {
         "title": {
          "text": "$\\frac{\\theta}{\\circ}$"
         }
        },
        "yaxis": {
         "title": {
          "text": "Percentage Error"
         }
        }
       }
      },
      "text/html": [
       "<div>\n",
       "        \n",
       "        \n",
       "            <div id=\"cc809769-87fe-43a8-bdf7-e0e36e2f2897\" class=\"plotly-graph-div\" style=\"height:525px; width:100%;\"></div>\n",
       "            <script type=\"text/javascript\">\n",
       "                require([\"plotly\"], function(Plotly) {\n",
       "                    window.PLOTLYENV=window.PLOTLYENV || {};\n",
       "                    \n",
       "                if (document.getElementById(\"cc809769-87fe-43a8-bdf7-e0e36e2f2897\")) {\n",
       "                    Plotly.newPlot(\n",
       "                        'cc809769-87fe-43a8-bdf7-e0e36e2f2897',\n",
       "                        [{\"mode\": \"lines\", \"name\": \"$\\\\theta - \\\\sin\\\\theta$\", \"type\": \"scatter\", \"x\": [0.1, 0.14994994994994995, 0.1998998998998999, 0.24984984984984984, 0.29979979979979976, 0.3497497497497497, 0.39969969969969965, 0.4496496496496496, 0.49959959959959954, 0.5495495495495495, 0.5994994994994994, 0.6494494494494494, 0.6993993993993993, 0.7493493493493493, 0.7992992992992992, 0.8492492492492492, 0.8991991991991991, 0.949149149149149, 0.999099099099099, 1.049049049049049, 1.098998998998999, 1.148948948948949, 1.198898898898899, 1.2488488488488487, 1.2987987987987988, 1.3487487487487488, 1.3986986986986987, 1.4486486486486485, 1.4985985985985986, 1.5485485485485486, 1.5984984984984985, 1.6484484484484483, 1.6983983983983983, 1.7483483483483484, 1.7982982982982982, 1.848248248248248, 1.8981981981981981, 1.9481481481481482, 1.998098098098098, 2.048048048048048, 2.097997997997998, 2.147947947947948, 2.197897897897898, 2.2478478478478476, 2.2977977977977977, 2.3477477477477477, 2.3976976976976974, 2.4476476476476474, 2.4975975975975975, 2.5475475475475475, 2.5974974974974976, 2.647447447447447, 2.6973973973973973, 2.7473473473473473, 2.797297297297297, 2.847247247247247, 2.897197197197197, 2.947147147147147, 2.997097097097097, 3.0470470470470468, 3.096996996996997, 3.146946946946947, 3.1968968968968965, 3.2468468468468465, 3.2967967967967966, 3.3467467467467467, 3.3966966966966967, 3.4466466466466463, 3.4965965965965964, 3.5465465465465464, 3.596496496496496, 3.646446446446446, 3.696396396396396, 3.7463463463463462, 3.7962962962962963, 3.846246246246246, 3.896196196196196, 3.946146146146146, 3.9960960960960956, 4.046046046046046, 4.095995995995995, 4.145945945945945, 4.195895895895895, 4.245845845845845, 4.2957957957957955, 4.345745745745745, 4.395695695695695, 4.445645645645645, 4.495595595595595, 4.5455455455455445, 4.595495495495495, 4.645445445445445, 4.695395395395394, 4.745345345345345, 4.795295295295294, 4.845245245245245, 4.895195195195194, 4.945145145145144, 4.9950950950950945, 5.045045045045044, 5.094994994994995, 5.144944944944944, 5.194894894894894, 5.244844844844844, 5.294794794794794, 5.344744744744744, 5.394694694694694, 5.444644644644644, 5.494594594594593, 5.544544544544544, 5.594494494494493, 5.644444444444444, 5.6943943943943935, 5.744344344344343, 5.794294294294294, 5.844244244244243, 5.894194194194194, 5.944144144144143, 5.994094094094093, 6.0440440440440435, 6.093993993993993, 6.143943943943943, 6.193893893893893, 6.243843843843843, 6.2937937937937924, 6.343743743743743, 6.393693693693693, 6.443643643643643, 6.493593593593593, 6.543543543543542, 6.593493493493493, 6.643443443443442, 6.693393393393393, 6.7433433433433425, 6.793293293293292, 6.843243243243243, 6.893193193193192, 6.943143143143142, 6.993093093093092, 7.043043043043042, 7.092992992992992, 7.142942942942942, 7.192892892892892, 7.242842842842842, 7.292792792792792, 7.342742742742741, 7.392692692692692, 7.4426426426426415, 7.492592592592592, 7.542542542542542, 7.592492492492491, 7.642442442442442, 7.692392392392391, 7.742342342342341, 7.7922922922922915, 7.842242242242241, 7.892192192192191, 7.942142142142141, 7.992092092092091, 8.042042042042041, 8.091991991991991, 8.14194194194194, 8.19189189189189, 8.241841841841842, 8.291791791791791, 8.34174174174174, 8.39169169169169, 8.44164164164164, 8.491591591591591, 8.541541541541541, 8.59149149149149, 8.64144144144144, 8.69139139139139, 8.74134134134134, 8.79129129129129, 8.84124124124124, 8.89119119119119, 8.94114114114114, 8.99109109109109, 9.04104104104104, 9.09099099099099, 9.14094094094094, 9.19089089089089, 9.24084084084084, 9.290790790790789, 9.34074074074074, 9.39069069069069, 9.44064064064064, 9.490590590590589, 9.540540540540539, 9.59049049049049, 9.64044044044044, 9.69039039039039, 9.740340340340339, 9.790290290290288, 9.84024024024024, 9.89019019019019, 9.940140140140139, 9.990090090090089, 10.040040040040038, 10.08998998998999, 10.13993993993994, 10.189889889889889, 10.239839839839838, 10.289789789789788, 10.339739739739738, 10.389689689689689, 10.439639639639639, 10.489589589589588, 10.539539539539538, 10.589489489489488, 10.639439439439439, 10.689389389389389, 10.739339339339338, 10.789289289289288, 10.839239239239237, 10.889189189189187, 10.939139139139138, 10.989089089089088, 11.039039039039038, 11.088988988988987, 11.138938938938937, 11.188888888888888, 11.238838838838838, 11.288788788788787, 11.338738738738737, 11.388688688688687, 11.438638638638638, 11.488588588588588, 11.538538538538537, 11.588488488488487, 11.638438438438437, 11.688388388388388, 11.738338338338338, 11.788288288288287, 11.838238238238237, 11.888188188188186, 11.938138138138136, 11.988088088088087, 12.038038038038037, 12.087987987987987, 12.137937937937936, 12.187887887887886, 12.237837837837837, 12.287787787787787, 12.337737737737736, 12.387687687687686, 12.437637637637636, 12.487587587587585, 12.537537537537537, 12.587487487487486, 12.637437437437436, 12.687387387387385, 12.737337337337335, 12.787287287287286, 12.837237237237236, 12.887187187187186, 12.937137137137135, 12.987087087087085, 13.037037037037036, 13.086986986986986, 13.136936936936936, 13.186886886886885, 13.236836836836835, 13.286786786786786, 13.336736736736736, 13.386686686686685, 13.436636636636635, 13.486586586586585, 13.536536536536534, 13.586486486486486, 13.636436436436435, 13.686386386386385, 13.736336336336334, 13.786286286286284, 13.836236236236235, 13.886186186186185, 13.936136136136135, 13.986086086086084, 14.036036036036034, 14.085985985985984, 14.135935935935935, 14.185885885885885, 14.235835835835834, 14.285785785785784, 14.335735735735733, 14.385685685685685, 14.435635635635634, 14.485585585585584, 14.535535535535534, 14.585485485485483, 14.635435435435435, 14.685385385385384, 14.735335335335334, 14.785285285285283, 14.835235235235233, 14.885185185185184, 14.935135135135134, 14.985085085085084, 15.035035035035033, 15.084984984984983, 15.134934934934932, 15.184884884884884, 15.234834834834833, 15.284784784784783, 15.334734734734733, 15.384684684684682, 15.434634634634634, 15.484584584584583, 15.534534534534533, 15.584484484484483, 15.634434434434432, 15.684384384384382, 15.734334334334333, 15.784284284284283, 15.834234234234232, 15.884184184184182, 15.934134134134132, 15.984084084084083, 16.034034034034033, 16.083983983983984, 16.133933933933935, 16.183883883883883, 16.233833833833835, 16.283783783783782, 16.333733733733734, 16.383683683683685, 16.433633633633633, 16.483583583583584, 16.533533533533532, 16.583483483483484, 16.633433433433435, 16.683383383383383, 16.733333333333334, 16.783283283283282, 16.833233233233234, 16.883183183183185, 16.933133133133133, 16.983083083083084, 17.033033033033032, 17.082982982982983, 17.13293293293293, 17.182882882882883, 17.232832832832834, 17.282782782782782, 17.332732732732733, 17.38268268268268, 17.432632632632632, 17.482582582582584, 17.53253253253253, 17.582482482482483, 17.63243243243243, 17.682382382382382, 17.732332332332334, 17.78228228228228, 17.832232232232233, 17.88218218218218, 17.932132132132132, 17.982082082082083, 18.03203203203203, 18.081981981981983, 18.13193193193193, 18.181881881881882, 18.231831831831833, 18.28178178178178, 18.331731731731733, 18.38168168168168, 18.43163163163163, 18.48158158158158, 18.53153153153153, 18.581481481481482, 18.63143143143143, 18.68138138138138, 18.73133133133133, 18.78128128128128, 18.831231231231232, 18.88118118118118, 18.93113113113113, 18.98108108108108, 19.03103103103103, 19.080980980980982, 19.13093093093093, 19.18088088088088, 19.23083083083083, 19.28078078078078, 19.330730730730732, 19.38068068068068, 19.43063063063063, 19.48058058058058, 19.53053053053053, 19.58048048048048, 19.63043043043043, 19.68038038038038, 19.73033033033033, 19.78028028028028, 19.83023023023023, 19.88018018018018, 19.93013013013013, 19.98008008008008, 20.03003003003003, 20.07997997997998, 20.12992992992993, 20.17987987987988, 20.22982982982983, 20.27977977977978, 20.329729729729728, 20.37967967967968, 20.42962962962963, 20.47957957957958, 20.52952952952953, 20.579479479479478, 20.62942942942943, 20.67937937937938, 20.729329329329328, 20.77927927927928, 20.829229229229227, 20.87917917917918, 20.92912912912913, 20.979079079079078, 21.02902902902903, 21.078978978978977, 21.12892892892893, 21.17887887887888, 21.228828828828828, 21.27877877877878, 21.328728728728727, 21.37867867867868, 21.42862862862863, 21.478578578578578, 21.52852852852853, 21.578478478478477, 21.62842842842843, 21.678378378378376, 21.728328328328328, 21.77827827827828, 21.828228228228227, 21.878178178178178, 21.928128128128126, 21.978078078078077, 22.02802802802803, 22.077977977977977, 22.127927927927928, 22.177877877877876, 22.227827827827827, 22.27777777777778, 22.327727727727726, 22.377677677677678, 22.427627627627626, 22.477577577577577, 22.52752752752753, 22.577477477477476, 22.627427427427428, 22.677377377377375, 22.727327327327327, 22.77727727727728, 22.827227227227226, 22.877177177177177, 22.927127127127125, 22.977077077077077, 23.027027027027028, 23.076976976976976, 23.126926926926927, 23.176876876876875, 23.226826826826827, 23.276776776776778, 23.326726726726726, 23.376676676676677, 23.426626626626625, 23.476576576576576, 23.526526526526524, 23.576476476476476, 23.626426426426427, 23.676376376376375, 23.726326326326326, 23.776276276276274, 23.826226226226225, 23.876176176176177, 23.926126126126125, 23.976076076076076, 24.026026026026024, 24.075975975975975, 24.125925925925927, 24.175875875875874, 24.225825825825826, 24.275775775775774, 24.325725725725725, 24.375675675675677, 24.425625625625624, 24.475575575575576, 24.525525525525524, 24.575475475475475, 24.625425425425426, 24.675375375375374, 24.725325325325326, 24.775275275275273, 24.825225225225225, 24.875175175175173, 24.925125125125124, 24.975075075075075, 25.025025025025023, 25.074974974974975, 25.124924924924922, 25.174874874874874, 25.224824824824825, 25.274774774774773, 25.324724724724724, 25.374674674674672, 25.424624624624624, 25.474574574574575, 25.524524524524523, 25.574474474474474, 25.624424424424422, 25.674374374374374, 25.724324324324325, 25.774274274274273, 25.824224224224224, 25.874174174174172, 25.924124124124123, 25.974074074074075, 26.024024024024023, 26.073973973973974, 26.123923923923922, 26.173873873873873, 26.223823823823825, 26.273773773773772, 26.323723723723724, 26.37367367367367, 26.423623623623623, 26.473573573573574, 26.523523523523522, 26.573473473473474, 26.62342342342342, 26.673373373373373, 26.72332332332332, 26.773273273273272, 26.823223223223223, 26.87317317317317, 26.923123123123123, 26.97307307307307, 27.023023023023022, 27.072972972972973, 27.12292292292292, 27.172872872872873, 27.22282282282282, 27.272772772772772, 27.322722722722723, 27.37267267267267, 27.422622622622622, 27.47257257257257, 27.52252252252252, 27.572472472472473, 27.62242242242242, 27.672372372372372, 27.72232232232232, 27.77227227227227, 27.822222222222223, 27.87217217217217, 27.922122122122122, 27.97207207207207, 28.02202202202202, 28.07197197197197, 28.12192192192192, 28.171871871871872, 28.22182182182182, 28.27177177177177, 28.32172172172172, 28.37167167167167, 28.42162162162162, 28.47157157157157, 28.52152152152152, 28.57147147147147, 28.62142142142142, 28.67137137137137, 28.72132132132132, 28.77127127127127, 28.82122122122122, 28.87117117117117, 28.92112112112112, 28.97107107107107, 29.02102102102102, 29.07097097097097, 29.12092092092092, 29.17087087087087, 29.22082082082082, 29.27077077077077, 29.32072072072072, 29.37067067067067, 29.42062062062062, 29.47057057057057, 29.52052052052052, 29.570470470470468, 29.62042042042042, 29.67037037037037, 29.72032032032032, 29.77027027027027, 29.820220220220218, 29.87017017017017, 29.920120120120117, 29.97007007007007, 30.02002002002002, 30.069969969969968, 30.11991991991992, 30.169869869869867, 30.21981981981982, 30.26976976976977, 30.319719719719718, 30.36966966966967, 30.419619619619617, 30.46956956956957, 30.51951951951952, 30.569469469469468, 30.61941941941942, 30.669369369369367, 30.719319319319318, 30.76926926926927, 30.819219219219217, 30.86916916916917, 30.919119119119117, 30.969069069069068, 31.01901901901902, 31.068968968968967, 31.11891891891892, 31.168868868868866, 31.218818818818818, 31.268768768768766, 31.318718718718717, 31.36866866866867, 31.418618618618616, 31.468568568568568, 31.518518518518515, 31.568468468468467, 31.61841841841842, 31.668368368368366, 31.718318318318317, 31.768268268268265, 31.818218218218217, 31.868168168168168, 31.918118118118116, 31.968068068068067, 32.01801801801801, 32.06796796796797, 32.117917917917914, 32.16786786786787, 32.21781781781782, 32.267767767767765, 32.31771771771771, 32.36766766766767, 32.417617617617616, 32.46756756756756, 32.51751751751752, 32.567467467467466, 32.617417417417414, 32.66736736736737, 32.71731731731732, 32.767267267267265, 32.81721721721721, 32.86716716716717, 32.917117117117115, 32.96706706706706, 33.01701701701702, 33.066966966966966, 33.116916916916914, 33.16686686686687, 33.21681681681682, 33.266766766766764, 33.31671671671671, 33.36666666666667, 33.416616616616615, 33.46656656656656, 33.51651651651652, 33.566466466466466, 33.61641641641641, 33.66636636636637, 33.716316316316316, 33.766266266266264, 33.81621621621621, 33.86616616616617, 33.916116116116115, 33.96606606606606, 34.01601601601602, 34.065965965965965, 34.11591591591591, 34.16586586586586, 34.215815815815816, 34.265765765765764, 34.31571571571571, 34.36566566566567, 34.415615615615614, 34.46556556556556, 34.51551551551552, 34.565465465465465, 34.61541541541541, 34.66536536536536, 34.715315315315316, 34.76526526526526, 34.81521521521521, 34.865165165165166, 34.915115115115114, 34.96506506506506, 35.01501501501502, 35.064964964964965, 35.11491491491491, 35.16486486486486, 35.214814814814815, 35.26476476476476, 35.31471471471471, 35.364664664664666, 35.414614614614614, 35.46456456456456, 35.51451451451451, 35.564464464464464, 35.61441441441441, 35.66436436436436, 35.714314314314315, 35.76426426426426, 35.81421421421421, 35.864164164164166, 35.91411411411411, 35.96406406406406, 36.01401401401401, 36.063963963963964, 36.11391391391391, 36.16386386386386, 36.213813813813815, 36.26376376376376, 36.31371371371371, 36.363663663663665, 36.41361361361361, 36.46356356356356, 36.51351351351351, 36.563463463463464, 36.61341341341341, 36.66336336336336, 36.713313313313314, 36.76326326326326, 36.81321321321321, 36.86316316316316, 36.91311311311311, 36.96306306306306, 37.01301301301301, 37.06296296296296, 37.11291291291291, 37.16286286286286, 37.212812812812814, 37.26276276276276, 37.31271271271271, 37.36266266266266, 37.41261261261261, 37.46256256256256, 37.51251251251251, 37.56246246246246, 37.61241241241241, 37.66236236236236, 37.712312312312314, 37.76226226226226, 37.81221221221221, 37.86216216216216, 37.91211211211211, 37.96206206206206, 38.01201201201201, 38.06196196196196, 38.11191191191191, 38.16186186186186, 38.21181181181181, 38.26176176176176, 38.31171171171171, 38.36166166166166, 38.41161161161161, 38.46156156156156, 38.51151151151151, 38.56146146146146, 38.61141141141141, 38.66136136136136, 38.711311311311306, 38.76126126126126, 38.81121121121121, 38.86116116116116, 38.91111111111111, 38.96106106106106, 39.01101101101101, 39.06096096096096, 39.11091091091091, 39.16086086086086, 39.210810810810806, 39.26076076076076, 39.31071071071071, 39.360660660660656, 39.41061061061061, 39.46056056056056, 39.51051051051051, 39.56046046046046, 39.61041041041041, 39.66036036036036, 39.710310310310305, 39.76026026026026, 39.81021021021021, 39.860160160160156, 39.91011011011011, 39.96006006006006, 40.01001001001001, 40.05995995995996, 40.10990990990991, 40.15985985985986, 40.209809809809805, 40.25975975975976, 40.30970970970971, 40.359659659659656, 40.40960960960961, 40.45955955955956, 40.509509509509506, 40.559459459459454, 40.60940940940941, 40.65935935935936, 40.709309309309305, 40.75925925925926, 40.80920920920921, 40.859159159159155, 40.90910910910911, 40.95905905905906, 41.009009009009006, 41.058958958958954, 41.10890890890891, 41.158858858858856, 41.208808808808804, 41.25875875875876, 41.30870870870871, 41.358658658658655, 41.40860860860861, 41.45855855855856, 41.508508508508505, 41.55845845845845, 41.60840840840841, 41.658358358358356, 41.708308308308304, 41.75825825825826, 41.80820820820821, 41.858158158158155, 41.9081081081081, 41.95805805805806, 42.008008008008005, 42.05795795795795, 42.10790790790791, 42.157857857857856, 42.207807807807804, 42.25775775775776, 42.307707707707706, 42.357657657657654, 42.4076076076076, 42.45755755755756, 42.507507507507505, 42.55745745745745, 42.60740740740741, 42.657357357357355, 42.7073073073073, 42.75725725725726, 42.807207207207206, 42.857157157157154, 42.9071071071071, 42.95705705705706, 43.007007007007005, 43.05695695695695, 43.10690690690691, 43.156856856856855, 43.2068068068068, 43.25675675675675, 43.306706706706706, 43.356656656656654, 43.4066066066066, 43.456556556556556, 43.506506506506504, 43.55645645645645, 43.60640640640641, 43.656356356356355, 43.7063063063063, 43.75625625625625, 43.806206206206205, 43.85615615615615, 43.9061061061061, 43.956056056056056, 44.006006006006004, 44.05595595595595, 44.10590590590591, 44.155855855855854, 44.2058058058058, 44.25575575575575, 44.305705705705705, 44.35565565565565, 44.4056056056056, 44.455555555555556, 44.5055055055055, 44.55545545545545, 44.605405405405406, 44.655355355355354, 44.7053053053053, 44.75525525525525, 44.805205205205205, 44.85515515515515, 44.9051051051051, 44.955055055055055, 45.005005005005, 45.05495495495495, 45.1049049049049, 45.154854854854854, 45.2048048048048, 45.25475475475475, 45.304704704704704, 45.35465465465465, 45.4046046046046, 45.454554554554555, 45.5045045045045, 45.55445445445445, 45.6044044044044, 45.65435435435435, 45.7043043043043, 45.75425425425425, 45.804204204204204, 45.85415415415415, 45.9041041041041, 45.954054054054055, 46.004004004004, 46.05395395395395, 46.1039039039039, 46.15385385385385, 46.2038038038038, 46.25375375375375, 46.303703703703704, 46.35365365365365, 46.4036036036036, 46.453553553553554, 46.5035035035035, 46.55345345345345, 46.6034034034034, 46.65335335335335, 46.7033033033033, 46.75325325325325, 46.8032032032032, 46.85315315315315, 46.9031031031031, 46.95305305305305, 47.003003003003, 47.05295295295295, 47.1029029029029, 47.15285285285285, 47.2028028028028, 47.25275275275275, 47.3027027027027, 47.35265265265265, 47.4026026026026, 47.45255255255255, 47.5025025025025, 47.55245245245245, 47.6024024024024, 47.65235235235235, 47.7023023023023, 47.75225225225225, 47.8022022022022, 47.85215215215215, 47.9021021021021, 47.952052052052046, 48.002002002002, 48.05195195195195, 48.1019019019019, 48.15185185185185, 48.2018018018018, 48.25175175175175, 48.301701701701695, 48.35165165165165, 48.4016016016016, 48.451551551551546, 48.5015015015015, 48.55145145145145, 48.6014014014014, 48.65135135135135, 48.7013013013013, 48.75125125125125, 48.801201201201195, 48.85115115115115, 48.9011011011011, 48.951051051051046, 49.001001001001, 49.05095095095095, 49.100900900900896, 49.15085085085085, 49.2008008008008, 49.25075075075075, 49.300700700700695, 49.35065065065065, 49.4006006006006, 49.450550550550545, 49.5005005005005, 49.55045045045045, 49.600400400400396, 49.650350350350344, 49.7003003003003, 49.75025025025025, 49.800200200200194, 49.85015015015015, 49.9001001001001, 49.950050050050045, 50.0], \"y\": [5.076958800933835e-05, 0.00011415540577553646, 0.00020287533727882784, 0.0003169294769271526, 0.0004563179460632927, 0.0006210408930030778, 0.000811098493045201, 0.0010264909483808198, 0.0012672184882218033, 0.0015332813687146474, 0.0018246798729557585, 0.002141414311000001, 0.0024834850198943263, 0.002850892363618697, 0.003243636733124101, 0.0036617185463106803, 0.004105138248079807, 0.004573896310254869, 0.005067993231645552, 0.005587429538046736, 0.006132205782201855, 0.006702322543810799, 0.007297780429569336, 0.007918580073151705, 0.008564722135182253, 0.009236207303272735, 0.009933036292023523, 0.010655209842997504, 0.011402728724752636, 0.012175593732817206, 0.012973805689719875, 0.013797365444954277, 0.014646273875043957, 0.015520531883460033, 0.016420140400685658, 0.017345100384205867, 0.01829541281846794, 0.0192710787150014, 0.0202720991122417, 0.021298475075690784, 0.022350207697827654, 0.023427298098179894, 0.02452974742324104, 0.025657556846558675, 0.026810727568690133, 0.02798926081718129, 0.02919315784664786, 0.030422419938733413, 0.031677048402056825, 0.03295704457233814, 0.03426240981228049, 0.035593145511676236, 0.036949253087324586, 0.03833073398308909, 0.03973758966987807, 0.041169821645655594, 0.04262743143543787, 0.04411042059131746, 0.04561879069243233, 0.04715254334501673, 0.04871168018234461, 0.050296202864780246, 0.05190611307978687, 0.053541412541898314, 0.05520210299271774, 0.056888186200976264, 0.058599663962481445, 0.06033653810013985, 0.06209881046398947, 0.06388648293115129, 0.06569955740587381, 0.06753803581950873, 0.06940192013056447, 0.07129121232464956, 0.07320591441453612, 0.07514602844010508, 0.07711155646837764, 0.07910250059354486, 0.08111886293695542, 0.08316064564710483, 0.0852278508996452, 0.08732048089741386, 0.08943853787042245, 0.09158202407582854, 0.09375094179803894, 0.09594529334856872, 0.09816508106621766, 0.10041030731691308, 0.10268097449384683, 0.10497708501737597, 0.10729864133510361, 0.10964564592188632, 0.11201810127973968, 0.1144160099379685, 0.11683937445310655, 0.11928819740895888, 0.12176248141654455, 0.12426222911418819, 0.12678744316744678, 0.129338126269152, 0.13191428113946577, 0.13451591052577858, 0.1371430172028283, 0.13979560397258511, 0.14247367366439911, 0.1451772291349012, 0.14790627326804318, 0.15066080897510675, 0.15344083919471213, 0.15624636689282698, 0.15907739506276067, 0.16193392672518778, 0.1648159649281286, 0.1677235127470143, 0.17065657328461167, 0.1736151496710886, 0.17659924506402216, 0.17960886264838033, 0.1826440056365446, 0.18570467726829235, 0.1887908808108594, 0.19190261955888224, 0.19503989683448605, 0.19820271598717676, 0.2013910803939921, 0.20460499345935682, 0.20784445861524495, 0.2111094793210616, 0.21440005906372828, 0.21771620135762954, 0.22105790974470868, 0.2244251877943907, 0.22781803910362844, 0.23123646729690012, 0.23468047602626546, 0.2381500689712806, 0.24164524983910163, 0.24516602236443527, 0.24871239030955997, 0.25228435746435823, 0.25588192764630313, 0.25950510470045607, 0.26315389249952204, 0.26682829494380206, 0.27052831596124804, 0.27425395950743875, 0.2780052295656222, 0.28178213014670367, 0.28558466528923315, 0.2894128390595016, 0.29326665555144277, 0.29714611888668624, 0.301051233214609, 0.3049820027122822, 0.3089384315845224, 0.3129205240638806, 0.31692828441065246, 0.32096171691290826, 0.32502082588648223, 0.32910561567500307, 0.33321609064988295, 0.33735225521032847, 0.34151411378338953, 0.3457016708239298, 0.34991493081461766, 0.35415389826601407, 0.358418577716524, 0.36270897373238803, 0.3670250909077685, 0.3713669338647219, 0.3757345072531706, 0.3801278157509705, 0.3845468640639204, 0.3889916569257169, 0.39346219909803865, 0.3979584953705197, 0.4024805505607237, 0.4070283695142629, 0.4116019571047007, 0.41620131823359735, 0.4208264578305928, 0.42547738085327425, 0.43015409228732876, 0.43485659714650055, 0.439584900472567, 0.44433900733540105, 0.4491189228329487, 0.453924652091307, 0.45875620026464947, 0.46361357253527186, 0.46849677411365304, 0.4734058102383818, 0.4783406861762351, 0.4833014072221554, 0.48828797869932783, 0.49330040595905916, 0.4983386943809378, 0.5034028493727778, 0.5084928763705984, 0.5136087808387164, 0.5187505682697241, 0.5239182441844538, 0.5291118141320676, 0.5343312836900538, 0.5395766584641899, 0.5448479440886023, 0.5501451462258081, 0.5554682705666333, 0.5608173228303024, 0.5661923087644799, 0.5715932341451596, 0.5770201047768291, 0.5824729264923746, 0.5879517051531231, 0.5934564466488996, 0.5989871568979935, 0.6045438418471852, 0.6101265074717586, 0.6157351597755416, 0.6213698047908752, 0.627030448578668, 0.6327170972283803, 0.6384297568580789, 0.6441684336144061, 0.6499331336726207, 0.6557238632366243, 0.6615406285389308, 0.6673834358407494, 0.6732522914319135, 0.6791472016309893, 0.6850681727852338, 0.6910152112706205, 0.6969883234918379, 0.7029875158823585, 0.7090127949043945, 0.7150641670489525, 0.7211416388358465, 0.7272452168136823, 0.7333749075599117, 0.739530717680832, 0.7457126538115841, 0.7519207226162071, 0.7581549307876365, 0.7644152850477045, 0.7707017921471665, 0.7770144588657533, 0.7833532920121181, 0.7897182984239162, 0.7961094849677903, 0.8025268585394112, 0.8089704260634264, 0.8154401944935878, 0.821936170812664, 0.8284583620325555, 0.8350067751941921, 0.8415814173676635, 0.8481822956521917, 0.8548094171761214, 0.8614627890969704, 0.8681424186014561, 0.8748483129054845, 0.8815804792541749, 0.8883389249219008, 0.895123657212277, 0.9019346834581865, 0.9087720110218314, 0.9156356472946732, 0.9225255996975567, 0.9294418756806261, 0.9363844827234249, 0.9433534283348373, 0.9503487200531864, 0.9573703654461999, 0.9644183721110375, 0.9714927476743163, 0.9785934997921488, 0.9857206361501105, 0.9928741644633015, 1.0000540924763721, 1.0072604279635027, 1.0144931787284417, 1.0217523526045433, 1.0290379574547595, 1.0363500011716764, 1.0436884916775082, 1.0510534369241784, 1.058444844893257, 1.0658627235960312, 1.0733070810735201, 1.0807779253965013, 1.0882752646654814, 1.0957991070107889, 1.1033494605925456, 1.1109263336007034, 1.118529734255037, 1.1261596708052495, 1.1338161515308525, 1.1414991847412947, 1.1492087787760188, 1.1569449420043039, 1.1647076828254754, 1.172497009668814, 1.1803129309936562, 1.1881554552893032, 1.1960245910751872, 1.2039203469007362, 1.2118427313455407, 1.2197917530192834, 1.2277674205617566, 1.2357697426429397, 1.2437987279630172, 1.2518543852523094, 1.2599367232714571, 1.268045750811249, 1.2761814766927855, 1.2843439097674918, 1.2925330589170347, 1.3007489330534603, 1.3089915411191695, 1.317260892086916, 1.3255569949599015, 1.3338798587716734, 1.3422294925863223, 1.3506059054983164, 1.3590091066326615, 1.3674391051448755, 1.3758959102210266, 1.3843795310776708, 1.3928899769620455, 1.4014272571519129, 1.4099913809557096, 1.4185823577124899, 1.4272001967920198, 1.4358449075947348, 1.444516499551798, 1.4532149821251354, 1.4619403648074158, 1.4706926571221066, 1.4794718686234907, 1.488278008896706, 1.4971110875577203, 1.5059711142534495, 1.5148580986616387, 1.5237720504910524, 1.532712979481341, 1.541680895403209, 1.5506758080583034, 1.5596977272793404, 1.568746662930091, 1.5778226249054152, 1.5869256231312796, 1.5960556675647415, 1.6052127681940933, 1.614396935038718, 1.6236081781492904, 1.6328465076076486, 1.6421119335269594, 1.6514044660515912, 1.660724115357278, 1.670070891651085, 1.679444805171406, 1.6888458661880414, 1.6982740850021951, 1.7077294719465144, 1.7172120373851063, 1.7267217917135584, 1.7362587453589953, 1.7458229087800394, 1.7554142924669442, 1.7650329069415, 1.7746787627571288, 1.7843518704989205, 1.7940522407836155, 1.8037798842596795, 1.8135348116072858, 1.8233170335383373, 1.8331265607965725, 1.842963404157497, 1.8528275744284755, 1.862719082448697, 1.872637939089301, 1.8825841552532585, 1.8925577418755641, 1.9025587099231536, 1.9125870703949406, 1.9226428343219064, 1.9327260127670356, 1.9428366168254692, 1.9529746576243765, 1.9631401463231255, 1.9733330941132037, 1.983553512218356, 1.9938014118945036, 2.004076804429801, 2.0143797011447537, 2.02471011339211, 2.0350680525569786, 2.045453530056849, 2.055866557341583, 2.0663071458934987, 2.07677530722733, 2.087271052890307, 2.0977943944621846, 2.1083453435552424, 2.118923911814342, 2.12953011091693, 2.1401639525731095, 2.1508254485256155, 2.1615146105498964, 2.172231450454107, 2.1829759800791297, 2.1937482112986615, 2.2045481560191855, 2.2153758261800447, 2.226231233753444, 2.237114390744476, 2.2480253091911893, 2.258964001164547, 2.2699304787685612, 2.2809247541402358, 2.291946839449621, 2.3029967468998818, 2.3140744887272597, 2.325180077201189, 2.3363135246242557, 2.3474748433322534, 2.358664045694204, 2.3698811441124468, 2.3811261510225794, 2.3923990788935616, 2.403699940227722, 2.4150287475607635, 2.4263855134618386, 2.437770250533567, 2.449182971412062, 2.4606236887669697, 2.4720924153014594, 2.483589163752357, 2.4951139468900596, 2.5066667775186686, 2.5182476684759205, 2.529856632633316, 2.541493682896132, 2.5531588322033656, 2.5648520935279007, 2.5765734798764495, 2.5883230042896104, 2.600100679841939, 2.611906519641894, 2.623740536831983, 2.63560274458867, 2.647493156122558, 2.6594117846782557, 2.671358643534563, 2.683333746004407, 2.6953371054349264, 2.707368735207482, 2.71942864873768, 2.7315168594754446, 2.7436333809050395, 2.755778226545051, 2.7679514099485445, 2.7801529447029303, 2.7923828444301475, 2.804641122786647, 2.8169277934633743, 2.829242870185894, 2.8415863667143757, 2.853958296843616, 2.8663586744031253, 2.878787513257094, 2.8912448273045057, 2.903730630479107, 2.9162449367495014, 2.928787760119109, 2.941359114626302, 2.9539590143443513, 2.9665874733815047, 2.97924450588103, 2.9919301260212414, 3.0046443480155114, 3.0173871861123547, 3.0301586545954264, 3.0429587677835923, 3.055787540030926, 3.068644985726777, 3.0815311192958035, 3.0944459551979926, 3.1073895079287186, 3.1203617920187723, 3.1333628220343983, 3.1463926125773396, 3.159451178284863, 3.1725385338297745, 3.1856546939205574, 3.198799673301246, 3.21197348675165, 3.2251761490872424, 3.238407675159269, 3.2516680798547677, 3.2649573780966454, 3.2782755848436413, 3.2916227150904365, 3.3049987838676547, 3.3184038062419328, 3.3318377973159197, 3.3453007722283346, 3.358792746154022, 3.37231373430398, 3.3858637519253763, 3.39944281430163, 3.4130509367524167, 3.426688134633745, 3.440354423337941, 3.4540498182937625, 3.4677743349663537, 3.481527988857381, 3.4953107955049787, 3.50912277048385, 3.5229639294053205, 3.5368342879173, 3.550733861704411, 3.5646626664879846, 3.5786207180260967, 3.592608032113661, 3.606624624582392, 3.620670511300893, 3.634745708174732, 3.6488502311463855, 3.662984096195374, 3.6771473193382747, 3.691339916628716, 3.7055619041575283, 3.7198132980526517, 3.7340941144793, 3.7484043696398905, 3.7627440797742127, 3.777113261159358, 3.791511930109817, 3.8059401029775333, 3.820397796151901, 3.8348850260598546, 3.8494018091658804, 3.863948161972082, 3.8785241010182157, 3.8931296428817084, 3.9077648041777517, 3.92242960155931, 3.937124051717179, 3.9518481713800133, 3.9666019773143915, 3.981385486324868, 3.996198715253955, 4.011041680982272, 4.0259144004284755, 4.040816890549405, 4.0557491683400535, 4.070711250833651, 4.085703155101732, 4.100724898254085, 4.115776497438923, 4.1308579698428485, 4.145969332690909, 4.161110603246657, 4.176281798812205, 4.191482936728254, 4.206714034374153, 4.22197510916791, 4.2372661785662835, 4.252587260064809, 4.267938371197866, 4.2833195295386775, 4.298730752699406, 4.31417205833116, 4.329643464124082, 4.345144987807367, 4.360676647149324, 4.376238459957412, 4.391830444078291, 4.407452617397867, 4.423104997841373, 4.4387876033733615, 4.454500451997785, 4.470243561758049, 4.486016950737035, 4.501820637057192, 4.5176546388805265, 4.533518974408702, 4.549413661883066, 4.565338719584704, 4.581294165834469, 4.59728001899307, 4.613296297461083, 4.6293430196790375, 4.6454202041274195, 4.6615278693267586, 4.677666033837673, 4.693834716260908, 4.710033935237382, 4.726263709448266, 4.742524057614996, 4.758814998499345, 4.775136550903471, 4.791488733670002, 4.80787156568196, 4.824285065862988, 4.840729253177302, 4.85720414662973, 4.8737097652658194, 4.89024612817182, 4.906813254474835, 4.9234111633427595, 4.940039873984398, 4.956699405649542, 4.973389777628941, 4.990111009254391, 5.006863119898832, 5.02364612897638, 5.040460055942256, 5.057304920293089, 5.074180741566723, 5.091087539342436, 5.108025333240848, 5.12499414292414, 5.141993988095997, 5.159024888501681, 5.1760868639280835, 5.19317993420382, 5.21030411919921, 5.227459438826407, 5.244645913039391, 5.261863561834096, 5.279112405248395, 5.296392463362124, 5.313703756297314, 5.331046304218001, 5.348420127330498, 5.365825245883292, 5.383261680167204, 5.4007294505153824, 5.41822857730339, 5.435759080949267, 5.4533209819135475, 5.470914300699352, 5.488539057852402, 5.506195273961148, 5.523882969656752, 5.541602165613211, 5.5593528825473415, 5.577135141218871, 5.59494896243053, 5.612794367028042, 5.630671375900248, 5.648580009979132, 5.666520290239809, 5.684492237700765, 5.7024958734236915, 5.720531218513715, 5.738598294119403, 5.7566971214327785, 5.77482772168944, 5.792990116168547, 5.811184326193008, 5.829410373129362, 5.847668278388025, 5.865958063423154, 5.884279749732932, 5.902633358859379, 5.921018912388649, 5.939436431950878, 5.957885939220438, 5.97636745591581, 5.9948810037998355, 6.013426604679588, 6.032004280406567, 6.050614052876761, 6.069255944030571, 6.087929975853023, 6.106636170373771, 6.125374549667119, 6.144145135852162, 6.162947951092796, 6.1817830175977955, 6.200650357620835, 6.219549993460602, 6.238481947460903, 6.257446242010599, 6.276442899543714, 6.295471942539605, 6.314533393522895, 6.33362727506355, 6.352753609777029, 6.371912420324251, 6.391103729411703, 6.41032755979151, 6.4295839342615055, 6.448872875665232, 6.46819440689206, 6.487548550877285, 6.506935330602108, 6.526354769093756, 6.545806889425538, 6.565291714716884, 6.584809268133443, 6.604359572887152, 6.623942652236263, 6.643558529485406, 6.663207227985758, 6.6828887711349285, 6.702603182377229, 6.722350485203547, 6.742130703151536, 6.761943859805705, 6.781789978797321, 6.801669083804658, 6.821581198552964, 6.8415263468145735, 6.861504552408924, 6.881515839202658, 6.901560231109735, 6.921637752091368, 6.941748426156237, 6.96189227736049, 6.9820693298077625, 7.002279607649366, 7.022523135084245, 7.042799936359118, 7.063110035768502, 7.0834534576548, 7.103830226408345, 7.124240366467564, 7.144683902318873, 7.165160858496969, 7.185671259584668, 7.206215130213161, 7.226792495061997, 7.247403378859124, 7.2680478063810785, 7.288725802452924, 7.309437391948396, 7.330182599789984, 7.350961450948901, 7.371773970445298, 7.392620183348251, 7.4135001147758395, 7.434413789895225, 7.455361233922736, 7.47634247212392, 7.497357529813642, 7.5184064323561115, 7.539489205165002, 7.56060587370353, 7.5817564634844805, 7.602941000070268, 7.624159509073134, 7.64541201615508, 7.6666985470279805, 7.688019127453703, 7.7093737832441445, 7.730762540261321, 7.752185424417387, 7.773642461674823, 7.795133678046409, 7.816659099595323, 7.8382187524352815, 7.8598126627304925, 7.881440856695832, 7.903103360596921, 7.924800200750131, 7.946531403522686, 7.968296995332777, 7.990097002649643, 8.011931451993547, 8.03380036993597, 8.055703783099656, 8.077641718158612, 8.09961420183831, 8.121621260915688, 8.143662922219251, 8.165739212629102, 8.187850159077104, 8.209995788546887, 8.232176128073974, 8.254391204745849, 8.276641045701991, 8.298925678134022, 8.321245129285721, 8.343599426453194, 8.36598859698482, 8.388412668281463, 8.410871667796489, 8.43336562303584, 8.455894561558145, 8.478458510974757, 8.501057498949885, 8.523691553200665, 8.546360701497187, 8.569064971662637, 8.591804391573373, 8.614578989158987, 8.63738879240239, 8.660233829339886, 8.683114128061279, 8.706029716709935, 8.728980623482897, 8.751966876630924, 8.774988504458598, 8.798045535324402, 8.821137997640797, 8.844265919874324, 8.867429330545718, 8.890628258229873, 8.913862731556069, 8.937132779208, 8.960438429923775, 8.983779712496192, 9.00715665577263, 9.030569288655252, 9.054017640101053, 9.077501739121933, 9.101021614784836, 9.124577296211779, 9.148168812579955, 9.171796193121796, 9.195459467125188, 9.219158663933323, 9.242893812945056, 9.266664943614748, 9.290472085452528, 9.3143152680243, 9.338194520951863, 9.362109873912964, 9.386061356641425, 9.410048998927211, 9.434072830616518, 9.458132881611862, 9.482229181872194, 9.50636176141295, 9.53053065030619, 9.554735878680633, 9.578977476721775, 9.603255474672014, 9.627569902830631, 9.651920791554026, 9.676308171255727, 9.700732072406463, 9.725192525534302, 9.749689561224741, 9.774223210120777, 9.798793502922969, 9.823400470389622, 9.848044143336832, 9.87272455263849, 9.897441729226557, 9.922195704091003, 9.946986508279952, 9.971814172899839, 9.996678729115361, 10.02158020814973, 10.046518641284658, 10.071494059860479, 10.096506495276298, 10.12155597898998, 10.146642542518343, 10.171766217437234, 10.196927035381568, 10.2221250280455, 10.247360227182451, 10.272632664605256, 10.297942372186277, 10.3232893818574, 10.348673725610263, 10.37409543549627, 10.399554543626708, 10.425051082172825, 10.450585083365983, 10.476156579497736, 10.501765602919848, 10.527412186044543, 10.553096361344464, 10.578818161352876, 10.604577618663669, 10.630374765931556, 10.656209635872095, 10.682082261261842, 10.707992674938426, 10.733940909800651, 10.75992699880859, 10.78595097498373, 10.812012871408996, 10.838112721228947, 10.864250557649791, 10.890426413939549, 10.916640323428117, 10.94289231950739, 10.96918243563139, 10.995510705316287, 11.021877162140617, 11.048281839745298, 11.074724771833736, 11.101205992171979, 11.127725534588826, 11.154283432975873, 11.180879721287623, 11.207514433541677, 11.234187603818738, 11.260899266262763, 11.28764945508109, 11.31443820454449, 11.341265548987314, 11.36813152280763, 11.395036160467214, 11.421979496491783, 11.448961565471038, 11.475982402058797, 11.503042040973083, 11.53014051699624, 11.557277864975077, 11.584454119820874, 11.611669316509637, 11.638923490082101, 11.66621667564387, 11.69354890836551, 11.720920223482725, 11.748330656296377, 11.775780242172669, 11.803269016543192, 11.830797014905112, 11.858364272821222, 11.885970825920058, 11.91361670989608, 11.941301960509684, 11.969026613587356, 11.996790705021805, 12.024594270772086, 12.052437346863677, 12.080319969388547, 12.10824217450545, 12.1362039984398, 12.164205477484002, 12.192246647997358, 12.220327546406386, 12.24844820920484, 12.276608672953783, 12.304808974281729, 12.333049149884877, 12.36132923652703, 12.38964927103989, 12.418009290323024, 12.446409331344105, 12.47484943113897, 12.503329626811738, 12.531849955534947, 12.560410454549634, 12.58901116116555, 12.61765211276112, 12.646333346783761, 12.67505490074979, 12.703816812244737, 12.732619118923333, 12.761461858509659, 12.790345068797357, 12.819268787649587, 12.848233052999305, 12.877237902849329, 12.906283375272357, 12.93536950841127, 12.9644963404792, 12.993663909759508, 13.022872254606114, 13.052121413443476, 13.081411424766806, 13.110742327142134, 13.14011415920644, 13.169526959667833, 13.19898076730557, 13.22847562097033, 13.25801155958416, 13.287588622140781, 13.317206847705574, 13.346866275415806, 13.376566944480677, 13.406308894181503, 13.436092163871818, 13.46591679297752, 13.495782820996972, 13.52569028750116, 13.55563923213379, 13.585629694611468, 13.615661714723768, 13.64573533233339, 13.675850587376303, 13.706007519861874, 13.736206169872961, 13.766446577566093, 13.796728783171563, 13.827052826993599, 13.857418749410424, 13.887826590874495, 13.91827639191256]}, {\"mode\": \"lines\", \"name\": \"$1-\\\\cos\\\\theta$\", \"type\": \"scatter\", \"x\": [0.1, 0.14994994994994995, 0.1998998998998999, 0.24984984984984984, 0.29979979979979976, 0.3497497497497497, 0.39969969969969965, 0.4496496496496496, 0.49959959959959954, 0.5495495495495495, 0.5994994994994994, 0.6494494494494494, 0.6993993993993993, 0.7493493493493493, 0.7992992992992992, 0.8492492492492492, 0.8991991991991991, 0.949149149149149, 0.999099099099099, 1.049049049049049, 1.098998998998999, 1.148948948948949, 1.198898898898899, 1.2488488488488487, 1.2987987987987988, 1.3487487487487488, 1.3986986986986987, 1.4486486486486485, 1.4985985985985986, 1.5485485485485486, 1.5984984984984985, 1.6484484484484483, 1.6983983983983983, 1.7483483483483484, 1.7982982982982982, 1.848248248248248, 1.8981981981981981, 1.9481481481481482, 1.998098098098098, 2.048048048048048, 2.097997997997998, 2.147947947947948, 2.197897897897898, 2.2478478478478476, 2.2977977977977977, 2.3477477477477477, 2.3976976976976974, 2.4476476476476474, 2.4975975975975975, 2.5475475475475475, 2.5974974974974976, 2.647447447447447, 2.6973973973973973, 2.7473473473473473, 2.797297297297297, 2.847247247247247, 2.897197197197197, 2.947147147147147, 2.997097097097097, 3.0470470470470468, 3.096996996996997, 3.146946946946947, 3.1968968968968965, 3.2468468468468465, 3.2967967967967966, 3.3467467467467467, 3.3966966966966967, 3.4466466466466463, 3.4965965965965964, 3.5465465465465464, 3.596496496496496, 3.646446446446446, 3.696396396396396, 3.7463463463463462, 3.7962962962962963, 3.846246246246246, 3.896196196196196, 3.946146146146146, 3.9960960960960956, 4.046046046046046, 4.095995995995995, 4.145945945945945, 4.195895895895895, 4.245845845845845, 4.2957957957957955, 4.345745745745745, 4.395695695695695, 4.445645645645645, 4.495595595595595, 4.5455455455455445, 4.595495495495495, 4.645445445445445, 4.695395395395394, 4.745345345345345, 4.795295295295294, 4.845245245245245, 4.895195195195194, 4.945145145145144, 4.9950950950950945, 5.045045045045044, 5.094994994994995, 5.144944944944944, 5.194894894894894, 5.244844844844844, 5.294794794794794, 5.344744744744744, 5.394694694694694, 5.444644644644644, 5.494594594594593, 5.544544544544544, 5.594494494494493, 5.644444444444444, 5.6943943943943935, 5.744344344344343, 5.794294294294294, 5.844244244244243, 5.894194194194194, 5.944144144144143, 5.994094094094093, 6.0440440440440435, 6.093993993993993, 6.143943943943943, 6.193893893893893, 6.243843843843843, 6.2937937937937924, 6.343743743743743, 6.393693693693693, 6.443643643643643, 6.493593593593593, 6.543543543543542, 6.593493493493493, 6.643443443443442, 6.693393393393393, 6.7433433433433425, 6.793293293293292, 6.843243243243243, 6.893193193193192, 6.943143143143142, 6.993093093093092, 7.043043043043042, 7.092992992992992, 7.142942942942942, 7.192892892892892, 7.242842842842842, 7.292792792792792, 7.342742742742741, 7.392692692692692, 7.4426426426426415, 7.492592592592592, 7.542542542542542, 7.592492492492491, 7.642442442442442, 7.692392392392391, 7.742342342342341, 7.7922922922922915, 7.842242242242241, 7.892192192192191, 7.942142142142141, 7.992092092092091, 8.042042042042041, 8.091991991991991, 8.14194194194194, 8.19189189189189, 8.241841841841842, 8.291791791791791, 8.34174174174174, 8.39169169169169, 8.44164164164164, 8.491591591591591, 8.541541541541541, 8.59149149149149, 8.64144144144144, 8.69139139139139, 8.74134134134134, 8.79129129129129, 8.84124124124124, 8.89119119119119, 8.94114114114114, 8.99109109109109, 9.04104104104104, 9.09099099099099, 9.14094094094094, 9.19089089089089, 9.24084084084084, 9.290790790790789, 9.34074074074074, 9.39069069069069, 9.44064064064064, 9.490590590590589, 9.540540540540539, 9.59049049049049, 9.64044044044044, 9.69039039039039, 9.740340340340339, 9.790290290290288, 9.84024024024024, 9.89019019019019, 9.940140140140139, 9.990090090090089, 10.040040040040038, 10.08998998998999, 10.13993993993994, 10.189889889889889, 10.239839839839838, 10.289789789789788, 10.339739739739738, 10.389689689689689, 10.439639639639639, 10.489589589589588, 10.539539539539538, 10.589489489489488, 10.639439439439439, 10.689389389389389, 10.739339339339338, 10.789289289289288, 10.839239239239237, 10.889189189189187, 10.939139139139138, 10.989089089089088, 11.039039039039038, 11.088988988988987, 11.138938938938937, 11.188888888888888, 11.238838838838838, 11.288788788788787, 11.338738738738737, 11.388688688688687, 11.438638638638638, 11.488588588588588, 11.538538538538537, 11.588488488488487, 11.638438438438437, 11.688388388388388, 11.738338338338338, 11.788288288288287, 11.838238238238237, 11.888188188188186, 11.938138138138136, 11.988088088088087, 12.038038038038037, 12.087987987987987, 12.137937937937936, 12.187887887887886, 12.237837837837837, 12.287787787787787, 12.337737737737736, 12.387687687687686, 12.437637637637636, 12.487587587587585, 12.537537537537537, 12.587487487487486, 12.637437437437436, 12.687387387387385, 12.737337337337335, 12.787287287287286, 12.837237237237236, 12.887187187187186, 12.937137137137135, 12.987087087087085, 13.037037037037036, 13.086986986986986, 13.136936936936936, 13.186886886886885, 13.236836836836835, 13.286786786786786, 13.336736736736736, 13.386686686686685, 13.436636636636635, 13.486586586586585, 13.536536536536534, 13.586486486486486, 13.636436436436435, 13.686386386386385, 13.736336336336334, 13.786286286286284, 13.836236236236235, 13.886186186186185, 13.936136136136135, 13.986086086086084, 14.036036036036034, 14.085985985985984, 14.135935935935935, 14.185885885885885, 14.235835835835834, 14.285785785785784, 14.335735735735733, 14.385685685685685, 14.435635635635634, 14.485585585585584, 14.535535535535534, 14.585485485485483, 14.635435435435435, 14.685385385385384, 14.735335335335334, 14.785285285285283, 14.835235235235233, 14.885185185185184, 14.935135135135134, 14.985085085085084, 15.035035035035033, 15.084984984984983, 15.134934934934932, 15.184884884884884, 15.234834834834833, 15.284784784784783, 15.334734734734733, 15.384684684684682, 15.434634634634634, 15.484584584584583, 15.534534534534533, 15.584484484484483, 15.634434434434432, 15.684384384384382, 15.734334334334333, 15.784284284284283, 15.834234234234232, 15.884184184184182, 15.934134134134132, 15.984084084084083, 16.034034034034033, 16.083983983983984, 16.133933933933935, 16.183883883883883, 16.233833833833835, 16.283783783783782, 16.333733733733734, 16.383683683683685, 16.433633633633633, 16.483583583583584, 16.533533533533532, 16.583483483483484, 16.633433433433435, 16.683383383383383, 16.733333333333334, 16.783283283283282, 16.833233233233234, 16.883183183183185, 16.933133133133133, 16.983083083083084, 17.033033033033032, 17.082982982982983, 17.13293293293293, 17.182882882882883, 17.232832832832834, 17.282782782782782, 17.332732732732733, 17.38268268268268, 17.432632632632632, 17.482582582582584, 17.53253253253253, 17.582482482482483, 17.63243243243243, 17.682382382382382, 17.732332332332334, 17.78228228228228, 17.832232232232233, 17.88218218218218, 17.932132132132132, 17.982082082082083, 18.03203203203203, 18.081981981981983, 18.13193193193193, 18.181881881881882, 18.231831831831833, 18.28178178178178, 18.331731731731733, 18.38168168168168, 18.43163163163163, 18.48158158158158, 18.53153153153153, 18.581481481481482, 18.63143143143143, 18.68138138138138, 18.73133133133133, 18.78128128128128, 18.831231231231232, 18.88118118118118, 18.93113113113113, 18.98108108108108, 19.03103103103103, 19.080980980980982, 19.13093093093093, 19.18088088088088, 19.23083083083083, 19.28078078078078, 19.330730730730732, 19.38068068068068, 19.43063063063063, 19.48058058058058, 19.53053053053053, 19.58048048048048, 19.63043043043043, 19.68038038038038, 19.73033033033033, 19.78028028028028, 19.83023023023023, 19.88018018018018, 19.93013013013013, 19.98008008008008, 20.03003003003003, 20.07997997997998, 20.12992992992993, 20.17987987987988, 20.22982982982983, 20.27977977977978, 20.329729729729728, 20.37967967967968, 20.42962962962963, 20.47957957957958, 20.52952952952953, 20.579479479479478, 20.62942942942943, 20.67937937937938, 20.729329329329328, 20.77927927927928, 20.829229229229227, 20.87917917917918, 20.92912912912913, 20.979079079079078, 21.02902902902903, 21.078978978978977, 21.12892892892893, 21.17887887887888, 21.228828828828828, 21.27877877877878, 21.328728728728727, 21.37867867867868, 21.42862862862863, 21.478578578578578, 21.52852852852853, 21.578478478478477, 21.62842842842843, 21.678378378378376, 21.728328328328328, 21.77827827827828, 21.828228228228227, 21.878178178178178, 21.928128128128126, 21.978078078078077, 22.02802802802803, 22.077977977977977, 22.127927927927928, 22.177877877877876, 22.227827827827827, 22.27777777777778, 22.327727727727726, 22.377677677677678, 22.427627627627626, 22.477577577577577, 22.52752752752753, 22.577477477477476, 22.627427427427428, 22.677377377377375, 22.727327327327327, 22.77727727727728, 22.827227227227226, 22.877177177177177, 22.927127127127125, 22.977077077077077, 23.027027027027028, 23.076976976976976, 23.126926926926927, 23.176876876876875, 23.226826826826827, 23.276776776776778, 23.326726726726726, 23.376676676676677, 23.426626626626625, 23.476576576576576, 23.526526526526524, 23.576476476476476, 23.626426426426427, 23.676376376376375, 23.726326326326326, 23.776276276276274, 23.826226226226225, 23.876176176176177, 23.926126126126125, 23.976076076076076, 24.026026026026024, 24.075975975975975, 24.125925925925927, 24.175875875875874, 24.225825825825826, 24.275775775775774, 24.325725725725725, 24.375675675675677, 24.425625625625624, 24.475575575575576, 24.525525525525524, 24.575475475475475, 24.625425425425426, 24.675375375375374, 24.725325325325326, 24.775275275275273, 24.825225225225225, 24.875175175175173, 24.925125125125124, 24.975075075075075, 25.025025025025023, 25.074974974974975, 25.124924924924922, 25.174874874874874, 25.224824824824825, 25.274774774774773, 25.324724724724724, 25.374674674674672, 25.424624624624624, 25.474574574574575, 25.524524524524523, 25.574474474474474, 25.624424424424422, 25.674374374374374, 25.724324324324325, 25.774274274274273, 25.824224224224224, 25.874174174174172, 25.924124124124123, 25.974074074074075, 26.024024024024023, 26.073973973973974, 26.123923923923922, 26.173873873873873, 26.223823823823825, 26.273773773773772, 26.323723723723724, 26.37367367367367, 26.423623623623623, 26.473573573573574, 26.523523523523522, 26.573473473473474, 26.62342342342342, 26.673373373373373, 26.72332332332332, 26.773273273273272, 26.823223223223223, 26.87317317317317, 26.923123123123123, 26.97307307307307, 27.023023023023022, 27.072972972972973, 27.12292292292292, 27.172872872872873, 27.22282282282282, 27.272772772772772, 27.322722722722723, 27.37267267267267, 27.422622622622622, 27.47257257257257, 27.52252252252252, 27.572472472472473, 27.62242242242242, 27.672372372372372, 27.72232232232232, 27.77227227227227, 27.822222222222223, 27.87217217217217, 27.922122122122122, 27.97207207207207, 28.02202202202202, 28.07197197197197, 28.12192192192192, 28.171871871871872, 28.22182182182182, 28.27177177177177, 28.32172172172172, 28.37167167167167, 28.42162162162162, 28.47157157157157, 28.52152152152152, 28.57147147147147, 28.62142142142142, 28.67137137137137, 28.72132132132132, 28.77127127127127, 28.82122122122122, 28.87117117117117, 28.92112112112112, 28.97107107107107, 29.02102102102102, 29.07097097097097, 29.12092092092092, 29.17087087087087, 29.22082082082082, 29.27077077077077, 29.32072072072072, 29.37067067067067, 29.42062062062062, 29.47057057057057, 29.52052052052052, 29.570470470470468, 29.62042042042042, 29.67037037037037, 29.72032032032032, 29.77027027027027, 29.820220220220218, 29.87017017017017, 29.920120120120117, 29.97007007007007, 30.02002002002002, 30.069969969969968, 30.11991991991992, 30.169869869869867, 30.21981981981982, 30.26976976976977, 30.319719719719718, 30.36966966966967, 30.419619619619617, 30.46956956956957, 30.51951951951952, 30.569469469469468, 30.61941941941942, 30.669369369369367, 30.719319319319318, 30.76926926926927, 30.819219219219217, 30.86916916916917, 30.919119119119117, 30.969069069069068, 31.01901901901902, 31.068968968968967, 31.11891891891892, 31.168868868868866, 31.218818818818818, 31.268768768768766, 31.318718718718717, 31.36866866866867, 31.418618618618616, 31.468568568568568, 31.518518518518515, 31.568468468468467, 31.61841841841842, 31.668368368368366, 31.718318318318317, 31.768268268268265, 31.818218218218217, 31.868168168168168, 31.918118118118116, 31.968068068068067, 32.01801801801801, 32.06796796796797, 32.117917917917914, 32.16786786786787, 32.21781781781782, 32.267767767767765, 32.31771771771771, 32.36766766766767, 32.417617617617616, 32.46756756756756, 32.51751751751752, 32.567467467467466, 32.617417417417414, 32.66736736736737, 32.71731731731732, 32.767267267267265, 32.81721721721721, 32.86716716716717, 32.917117117117115, 32.96706706706706, 33.01701701701702, 33.066966966966966, 33.116916916916914, 33.16686686686687, 33.21681681681682, 33.266766766766764, 33.31671671671671, 33.36666666666667, 33.416616616616615, 33.46656656656656, 33.51651651651652, 33.566466466466466, 33.61641641641641, 33.66636636636637, 33.716316316316316, 33.766266266266264, 33.81621621621621, 33.86616616616617, 33.916116116116115, 33.96606606606606, 34.01601601601602, 34.065965965965965, 34.11591591591591, 34.16586586586586, 34.215815815815816, 34.265765765765764, 34.31571571571571, 34.36566566566567, 34.415615615615614, 34.46556556556556, 34.51551551551552, 34.565465465465465, 34.61541541541541, 34.66536536536536, 34.715315315315316, 34.76526526526526, 34.81521521521521, 34.865165165165166, 34.915115115115114, 34.96506506506506, 35.01501501501502, 35.064964964964965, 35.11491491491491, 35.16486486486486, 35.214814814814815, 35.26476476476476, 35.31471471471471, 35.364664664664666, 35.414614614614614, 35.46456456456456, 35.51451451451451, 35.564464464464464, 35.61441441441441, 35.66436436436436, 35.714314314314315, 35.76426426426426, 35.81421421421421, 35.864164164164166, 35.91411411411411, 35.96406406406406, 36.01401401401401, 36.063963963963964, 36.11391391391391, 36.16386386386386, 36.213813813813815, 36.26376376376376, 36.31371371371371, 36.363663663663665, 36.41361361361361, 36.46356356356356, 36.51351351351351, 36.563463463463464, 36.61341341341341, 36.66336336336336, 36.713313313313314, 36.76326326326326, 36.81321321321321, 36.86316316316316, 36.91311311311311, 36.96306306306306, 37.01301301301301, 37.06296296296296, 37.11291291291291, 37.16286286286286, 37.212812812812814, 37.26276276276276, 37.31271271271271, 37.36266266266266, 37.41261261261261, 37.46256256256256, 37.51251251251251, 37.56246246246246, 37.61241241241241, 37.66236236236236, 37.712312312312314, 37.76226226226226, 37.81221221221221, 37.86216216216216, 37.91211211211211, 37.96206206206206, 38.01201201201201, 38.06196196196196, 38.11191191191191, 38.16186186186186, 38.21181181181181, 38.26176176176176, 38.31171171171171, 38.36166166166166, 38.41161161161161, 38.46156156156156, 38.51151151151151, 38.56146146146146, 38.61141141141141, 38.66136136136136, 38.711311311311306, 38.76126126126126, 38.81121121121121, 38.86116116116116, 38.91111111111111, 38.96106106106106, 39.01101101101101, 39.06096096096096, 39.11091091091091, 39.16086086086086, 39.210810810810806, 39.26076076076076, 39.31071071071071, 39.360660660660656, 39.41061061061061, 39.46056056056056, 39.51051051051051, 39.56046046046046, 39.61041041041041, 39.66036036036036, 39.710310310310305, 39.76026026026026, 39.81021021021021, 39.860160160160156, 39.91011011011011, 39.96006006006006, 40.01001001001001, 40.05995995995996, 40.10990990990991, 40.15985985985986, 40.209809809809805, 40.25975975975976, 40.30970970970971, 40.359659659659656, 40.40960960960961, 40.45955955955956, 40.509509509509506, 40.559459459459454, 40.60940940940941, 40.65935935935936, 40.709309309309305, 40.75925925925926, 40.80920920920921, 40.859159159159155, 40.90910910910911, 40.95905905905906, 41.009009009009006, 41.058958958958954, 41.10890890890891, 41.158858858858856, 41.208808808808804, 41.25875875875876, 41.30870870870871, 41.358658658658655, 41.40860860860861, 41.45855855855856, 41.508508508508505, 41.55845845845845, 41.60840840840841, 41.658358358358356, 41.708308308308304, 41.75825825825826, 41.80820820820821, 41.858158158158155, 41.9081081081081, 41.95805805805806, 42.008008008008005, 42.05795795795795, 42.10790790790791, 42.157857857857856, 42.207807807807804, 42.25775775775776, 42.307707707707706, 42.357657657657654, 42.4076076076076, 42.45755755755756, 42.507507507507505, 42.55745745745745, 42.60740740740741, 42.657357357357355, 42.7073073073073, 42.75725725725726, 42.807207207207206, 42.857157157157154, 42.9071071071071, 42.95705705705706, 43.007007007007005, 43.05695695695695, 43.10690690690691, 43.156856856856855, 43.2068068068068, 43.25675675675675, 43.306706706706706, 43.356656656656654, 43.4066066066066, 43.456556556556556, 43.506506506506504, 43.55645645645645, 43.60640640640641, 43.656356356356355, 43.7063063063063, 43.75625625625625, 43.806206206206205, 43.85615615615615, 43.9061061061061, 43.956056056056056, 44.006006006006004, 44.05595595595595, 44.10590590590591, 44.155855855855854, 44.2058058058058, 44.25575575575575, 44.305705705705705, 44.35565565565565, 44.4056056056056, 44.455555555555556, 44.5055055055055, 44.55545545545545, 44.605405405405406, 44.655355355355354, 44.7053053053053, 44.75525525525525, 44.805205205205205, 44.85515515515515, 44.9051051051051, 44.955055055055055, 45.005005005005, 45.05495495495495, 45.1049049049049, 45.154854854854854, 45.2048048048048, 45.25475475475475, 45.304704704704704, 45.35465465465465, 45.4046046046046, 45.454554554554555, 45.5045045045045, 45.55445445445445, 45.6044044044044, 45.65435435435435, 45.7043043043043, 45.75425425425425, 45.804204204204204, 45.85415415415415, 45.9041041041041, 45.954054054054055, 46.004004004004, 46.05395395395395, 46.1039039039039, 46.15385385385385, 46.2038038038038, 46.25375375375375, 46.303703703703704, 46.35365365365365, 46.4036036036036, 46.453553553553554, 46.5035035035035, 46.55345345345345, 46.6034034034034, 46.65335335335335, 46.7033033033033, 46.75325325325325, 46.8032032032032, 46.85315315315315, 46.9031031031031, 46.95305305305305, 47.003003003003, 47.05295295295295, 47.1029029029029, 47.15285285285285, 47.2028028028028, 47.25275275275275, 47.3027027027027, 47.35265265265265, 47.4026026026026, 47.45255255255255, 47.5025025025025, 47.55245245245245, 47.6024024024024, 47.65235235235235, 47.7023023023023, 47.75225225225225, 47.8022022022022, 47.85215215215215, 47.9021021021021, 47.952052052052046, 48.002002002002, 48.05195195195195, 48.1019019019019, 48.15185185185185, 48.2018018018018, 48.25175175175175, 48.301701701701695, 48.35165165165165, 48.4016016016016, 48.451551551551546, 48.5015015015015, 48.55145145145145, 48.6014014014014, 48.65135135135135, 48.7013013013013, 48.75125125125125, 48.801201201201195, 48.85115115115115, 48.9011011011011, 48.951051051051046, 49.001001001001, 49.05095095095095, 49.100900900900896, 49.15085085085085, 49.2008008008008, 49.25075075075075, 49.300700700700695, 49.35065065065065, 49.4006006006006, 49.450550550550545, 49.5005005005005, 49.55045045045045, 49.600400400400396, 49.650350350350344, 49.7003003003003, 49.75025025025025, 49.800200200200194, 49.85015015015015, 49.9001001001001, 49.950050050050045, 50.0], \"y\": [0.0001523089032103942, 0.0003424669210139892, 0.0006086282343902852, 0.0009507938547829841, 0.0013689650824703838, 0.0018631435066105459, 0.002433331005189174, 0.0030795297450922554, 0.0038017421821036203, 0.004599971060927341, 0.005474219415223869, 0.006424490567637712, 0.007450788129783321, 0.008553116002377978, 0.00973147837515523, 0.010985879727014158, 0.012316324825982503, 0.013722818729293488, 0.01520536678345417, 0.016763974624249795, 0.01839864817680634, 0.020109393655689006, 0.02189621756489228, 0.02375912669796596, 0.025698128138021605, 0.02771322925784161, 0.02980443771991322, 0.031971761476542876, 0.0342152087698733, 0.03653478813201428, 0.03893050838507613, 0.04140237864128362, 0.04395040830307026, 0.046574607063108654, 0.0492749849044657, 0.052051552100660425, 0.05490431921574676, 0.0578332971044545, 0.060838496912266296, 0.06391993007550834, 0.06707760832146603, 0.07031154366851344, 0.07362174842621202, 0.07700823519540091, 0.08047101686833444, 0.08401010662882218, 0.08762551795231627, 0.09131726460605684, 0.09508536064919804, 0.09892982043292545, 0.10285065860060971, 0.10684789008792948, 0.110921530123008, 0.11507159422657486, 0.11929809821207474, 0.1236010581858566, 0.12798049054731025, 0.13243641198897194, 0.1369688394967552, 0.14157779035006196, 0.14626328212196324, 0.151025332679349, 0.15586396018309204, 0.1607791830882366, 0.1657710201441679, 0.17083949039475038, 0.17598461317856953, 0.18120640812903108, 0.1865048951746417, 0.19188009453911373, 0.1973320267415732, 0.20286071259678182, 0.20846617321529448, 0.21414843000369788, 0.2199075046647514, 0.22574341919763133, 0.23165619589816622, 0.23764585735894184, 0.2437124264696424, 0.24985592641714977, 0.2560763806858461, 0.26237381305777385, 0.2687482476128883, 0.27519970872930155, 0.2817282210834401, 0.28833380965035, 0.29501649970391575, 0.3017763168170491, 0.30861328686197953, 0.3155274360104939, 0.3225187907341544, 0.32958737780454345, 0.3367332242935661, 0.34395635757365534, 0.3512568053180246, 0.3586345955009793, 0.3660897563981079, 0.3736223165866216, 0.38123230494556215, 0.3889197506561025, 0.3966846832018277, 0.40452713236898524, 0.4124471282467828, 0.42044470122767785, 0.4285198820076366, 0.4366727015864629, 0.4449031912680516, 0.45321138266069, 0.46159730767738394, 0.47006099853613137, 0.47860248776022113, 0.4872218081785789, 0.49591899292602765, 0.504694075443617, 0.5135470894789557, 0.522478069086526, 0.5314870486279657, 0.5405740627724654, 0.5497391464970132, 0.5589823350867862, 0.5683036641354684, 0.5777031695455698, 0.5871808875287945, 0.5967368546063327, 0.6063711076092911, 0.6160836836789567, 0.6258746202671772, 0.6357439551367541, 0.6456917263617402, 0.655717972327838, 0.6658227317327481, 0.6760060435865515, 0.6862679472120525, 0.6966084822452023, 0.7070276886354007, 0.7175256066459493, 0.728102276854383, 0.7387577401528826, 0.7494920377486588, 0.7603052111643359, 0.7711973022383546, 0.78216835312535, 0.7932184062966056, 0.8043475045403925, 0.8155556909624297, 0.8268430089862302, 0.8382095023536225, 0.849655215125048, 0.8611801916800546, 0.8727844767177241, 0.8844681152570366, 0.8962311526373617, 0.9080736345188741, 0.9199956068829938, 0.9319971160328082, 0.9440782085935095, 0.9562389315129002, 0.9684793320617687, 0.9807994578343698, 0.993199356748929, 1.005679077048006, 1.0182386672990282, 1.0308781763947616, 1.0435976535537284, 1.0563971483207273, 1.0692767105672587, 1.0822363904920869, 1.0952762386216361, 1.1083963058105253, 1.1215966432420288, 1.1348773024286285, 1.1482383352124133, 1.161679793765671, 1.1752017305913527, 1.1888041985235462, 1.2024872507280708, 1.216250940702891, 1.2300953222787288, 1.2440204496194953, 1.2580263772228877, 1.2721131599208724, 1.2862808528802208, 1.3005295116030808, 1.314859191927471, 1.329269950027815, 1.3437618424155453, 1.3583349259395885, 1.3729892577869627, 1.3877248954832806, 1.4025418968933925, 1.4174403202218466, 1.4324202240135397, 1.4474816671542319, 1.4626247088711686, 1.4778494087336151, 1.493155826653439, 1.5085440228857323, 1.524014058029355, 1.539565993027576, 1.5551998891686023, 1.5709158080862362, 1.5867138117604596, 1.602593962518029, 1.6185563230331008, 1.6346009563278245, 1.650727925772984, 1.6669372950886114, 1.683229128344612, 1.6996034899613748, 1.7160604447104395, 1.7326000577150897, 1.7492223944510528, 1.7659275207470644, 1.7827155027855999, 1.7995864071034702, 1.8165403005925012, 1.8335772505001604, 1.850697324430269, 1.867900590343647, 1.8851871165587744, 1.9025569717524795, 1.9200102249605964, 1.9375469455786827, 1.955167203362687, 1.9728710684296273, 1.9906586112583229, 2.0085299026900363, 2.0264850139292236, 2.0445240165442558, 2.0626469824680456, 2.080853983998848, 2.0991450938009564, 2.1175203849054145, 2.1359799307107106, 2.154523804983589, 2.1731520818597296, 2.1918648358444774, 2.2106621418136316, 2.229544075014149, 2.2485107110649416, 2.2675621259575895, 2.286698396057121, 2.3059195981027596, 2.325225809208747, 2.344617106865037, 2.3640935689381326, 2.3836552736718533, 2.40330229968809, 2.4230347259876375, 2.442852631950983, 2.4627560973390774, 2.4827452022941516, 2.502820027340537, 2.5229806533854644, 2.5432271617198925, 2.5635596340192817, 2.583978152344524, 2.6044827991426334, 2.625073657247696, 2.64575080988166, 2.666514340655158, 2.6873643335684116, 2.708300873012034, 2.7293240437679134, 2.7504339310100354, 2.771630620305421, 2.7929141976149237, 2.8142847492941403, 2.8357423620942797, 2.857287123163078, 2.87891912004563, 2.9006384406853303, 2.922445173424744, 2.944339407006512, 2.966321230574313, 2.9883907336736617, 3.0105480062529626, 3.0327931386643017, 3.055126221664482, 3.0775473464158773, 3.1000566044874196, 3.122654087855513, 3.1453398889049557, 3.168114100429984, 3.1909768156351213, 3.2139281281361947, 3.2369681319612784, 3.2600969215516957, 3.283314591762961, 3.3066212378657798, 3.3300169555470336, 3.3535018409107455, 3.377075990479124, 3.400739501193522, 3.424492470415445, 3.448334995927608, 3.4722671759348747, 3.4962891090653647, 3.520400894371406, 3.544602631330622, 3.5688944198469326, 3.5932763602516062, 3.6177485533043314, 3.642311100194225, 3.666964102540933, 3.691707662395648, 3.7165418822422422, 3.741466864998285, 3.766482714016138, 3.7915895330840708, 3.8167874264272754, 3.842076498709072, 3.8674568550319197, 3.892928600938536, 3.918491842413078, 3.9441466858821697, 3.9698932382160783, 3.9957316067298327, 4.021661899184362, 4.04768422378763, 4.0737986891957645, 4.10000540451426, 4.1263044792990655, 4.152696023557823, 4.179180147750968, 4.205756962792963, 4.232426580053417, 4.259189111358315, 4.286044668991231, 4.3129933656944495, 4.340035314670255, 4.3671706295820725, 4.394399424555745, 4.421721814180687, 4.449137913511188, 4.476647838067574, 4.5042517038375145, 4.531949627277204, 4.559741725312671, 4.5876281153410154, 4.615608915231642, 4.643684243327591, 4.671854218446754, 4.700118959883218, 4.728478587408484, 4.7569332212728535, 4.785482982206619, 4.814127991421486, 4.842868370611804, 4.871704241955927, 4.90063572811755, 4.929662952246981, 4.958786037982573, 4.988005109452013, 5.0173202912736565, 5.046731708557959, 5.076239486908799, 5.10584375242482, 5.135544631700874, 5.165342251829387, 5.195236740401719, 5.225228225509622, 5.255316835746585, 5.285502700209316, 5.315785948499071, 5.346166710723211, 5.376645117496489, 5.407221299942611, 5.437895389695633, 5.468667518901406, 5.49953782021906, 5.530506426822456, 5.561573472401722, 5.592739091164626, 5.624003417838163, 5.655366587670025, 5.686828736430086, 5.718390000411934, 5.750050516434395, 5.781810421843022, 5.813669854511707, 5.845628952844144, 5.877687855775394, 5.909846702773504, 5.942105633840984, 5.974464789516438, 6.006924310876111, 6.039484339535512, 6.072145017650941, 6.104906487921185, 6.1377688935890635, 6.17073237844303, 6.203797086818877, 6.236963163601287, 6.270230754225523, 6.303600004679034, 6.33707106150318, 6.370644071794828, 6.404319183208059, 6.438096543955833, 6.471976302811703, 6.505958609111483, 6.5400436127549675, 6.574231464207646, 6.608522314502416, 6.642916315241322, 6.677413618597286, 6.712014377315849, 6.746718744716946, 6.781526874696629, 6.816438921728913, 6.851455040867477, 6.886575387747462, 6.921800118587311, 6.957129390190582, 6.992563359947685, 7.0281021858377795, 7.063746026430566, 7.099495040888129, 7.135349388966854, 7.171309231019138, 7.207374727995427, 7.243546041445985, 7.279823333522763, 7.316206766981417, 7.35269650518304, 7.389292712096241, 7.425995552298938, 7.462805190980343, 7.499721793942935, 7.536745527604323, 7.57387655899928, 7.611115055781675, 7.64846118622647, 7.685915119231672, 7.723477024320363, 7.761147071642692, 7.79892543197791, 7.836812276736343, 7.874807777961491, 7.912912108332012, 7.951125441163846, 7.98944795041219, 8.027879810673682, 8.066421197188353, 8.105072285841839, 8.143833253167438, 8.182704276348183, 8.22168553321906, 8.26077720226905, 8.299979462643318, 8.339292494145365, 8.378716477239182, 8.418251593051458, 8.457898023373717, 8.497655950664546, 8.537525558051795, 8.57750702933478, 8.617600548986552, 8.657806302156104, 8.698124474670585, 8.738555253037658, 8.779098824447678, 8.819755376776033, 8.860525098585406, 8.901408179128074, 8.94240480834827, 8.98351517688446, 9.024739476071694, 9.06607789794396, 9.107530635236573, 9.149097881388457, 9.190779830544662, 9.23257667755864, 9.274488617994688, 9.316515848130434, 9.358658564959141, 9.400916966192254, 9.443291250261792, 9.485781616322853, 9.528388264256055, 9.571111394670078, 9.61395120890407, 9.656907909030272, 9.699981697856455, 9.743172778928527, 9.786481356533013, 9.829907635699676, 9.87345182220404, 9.917114122570043, 9.960894744072565, 10.004793894740079, 10.048811783357284, 10.092948619467698, 10.137204613376374, 10.181579976152484, 10.226074919632074, 10.270689656420709, 10.31542439989616, 10.360279364211143, 10.405254764296078, 10.450350815861775, 10.495567735402208, 10.540905740197298, 10.586365048315653, 10.63194587861746, 10.677648450757166, 10.723472985186396, 10.76941970315673, 10.815488826722602, 10.86168057874415, 10.907995182890067, 10.95443286364052, 11.000993846290042, 11.04767835695046, 11.094486622553857, 11.141418870855466, 11.188475330436667, 11.23565623070796, 11.282961801911968, 11.330392275126417, 11.377947882267206, 11.425628856091375, 11.47343543020022, 11.521367839042348, 11.569426317916715, 11.617611102975774, 11.66592243122857, 11.71436054054387, 11.762925669653287, 11.811618058154478, 11.860437946514274, 11.909385576071896, 11.958461189042167, 12.007665028518714, 12.056997338477213, 12.106458363778632, 12.156048350172535, 12.20576754430032, 12.255616193698566, 12.305594546802325, 12.35570285294843, 12.405941362378925, 12.456310326244365, 12.506809996607215, 12.557440626445269, 12.60820246965502, 12.659095781055196, 12.710120816390086, 12.761277832333102, 12.812567086490237, 12.863988837403554, 12.915543344554717, 12.967230868368526, 13.019051670216516, 13.071006012420474, 13.123094158256032, 13.175316371956336, 13.227672918715584, 13.280164064692784, 13.33279007701532, 13.385551223782677, 13.43844777407016, 13.491479997932576, 13.544648166407978, 13.597952551521452, 13.651393426288852, 13.704971064720672, 13.758685741825715, 13.812537733615107, 13.866527317105998, 13.92065477032551, 13.974920372314639, 14.029324403132106, 14.083867143858336, 14.138548876599405, 14.19336988449098, 14.248330451702332, 14.30343086344035, 14.35867140595359, 14.414052366536259, 14.469574033532353, 14.525236696339732, 14.581040645414218, 14.636986172273728, 14.693073569502483, 14.74930313075509, 14.805675150760822, 14.8621899253278, 14.918847751347233, 14.97564892679769, 15.032593750749395, 15.089682523368458, 15.146915545921352, 15.204293120779091, 15.261815551421726, 15.319483142442664, 15.377296199553165, 15.435255029586667, 15.493359940503352, 15.551611241394575, 15.610009242487408, 15.668554255149111, 15.727246591891763, 15.786086566376792, 15.845074493419546, 15.904210688994013, 15.963495470237381, 16.02292915545473, 16.08251206412375, 16.142244516899478, 16.202126835618973, 16.26215934330615, 16.322342364176567, 16.382676223642186, 16.443161248316287, 16.503797766018323, 16.56458610577876, 16.62552659784407, 16.686619573681636, 16.747865365984698, 16.80926430867746, 16.87081673691991, 16.932522987113117, 16.994383396904077, 17.056398305191, 17.118568052128285, 17.180892979131784, 17.243373428883956, 17.306009745339, 17.368802273728214, 17.431751360565183, 17.494857353651064, 17.558120602079956, 17.62154145624418, 17.685120267839714, 17.748857389871546, 17.812753176659168, 17.876807983841946, 17.94102216838469, 18.00539608858314, 18.069930104069496, 18.13462457581799, 18.199479866150558, 18.26449633874239, 18.329674358627635, 18.395014292205087, 18.46051650724392, 18.526181372889432, 18.592009259668842, 18.658000539497042, 18.72415558568255, 18.790474772933365, 18.85695847736273, 18.923607076495312, 18.990420949272973, 19.057400476060888, 19.124546038653502, 19.191858020280684, 19.259336805613756, 19.326982780771644, 19.394796333327065, 19.46277785231273, 19.530927728227503, 19.599246353042787, 19.667734120208692, 19.73639142466049, 19.805218662824885, 19.87421623262647, 19.943384533494132, 20.012723966367542, 20.08223493370365, 20.151917839483243, 20.221773089217486, 20.29180108995456, 20.36200225028628, 20.43237698035484, 20.502925691859435, 20.573648798063118, 20.64454671379952, 20.715619855479705, 20.78686864109901, 20.858293490244, 20.92989482409939, 21.001673065454955, 21.07362863871266, 21.14576196989366, 21.21807348664529, 21.29056361824844, 21.363232795624487, 21.436081451342627, 21.50911001962709, 21.582318936364448, 21.655708639110934, 21.729279567099784, 21.803032161248698, 21.876966864167276, 21.951084120164435, 22.025384375256078, 22.099868077172566, 22.174535675366332, 22.249387621019615, 22.324424367052103, 22.399646368128682, 22.475054080667203, 22.550647962846387, 22.626428474613608, 22.70239607769284, 22.778551235592634, 22.854894413614147, 22.93142607885908, 23.008146700237894, 23.085056748477907, 23.16215669613143, 23.239447017584062, 23.316928189062942, 23.394600688645067, 23.472464996265646, 23.550521593726533, 23.628770964704717, 23.70721359476076, 23.78584997134743, 23.864680583818217, 23.943705923436124, 24.022926483382207, 24.10234275876443, 24.181955246626504, 24.26176444595656, 24.34177085769626, 24.421974984749614, 24.502377331992005, 24.582978406279295, 24.66377871645684, 24.74477877336876, 24.825979089866994, 24.90738018082074, 24.988982563125596, 25.070786755713037, 25.152793279559777, 25.235002657697294, 25.317415415221316, 25.400032079301383, 25.482853179190514, 25.565879246234964, 25.64911081388373, 25.732548417698727, 25.81619259536429, 25.900043886697315, 25.984102833657108, 26.06836998035547, 26.152845873066795, 26.237531060238183, 26.322426092499633, 26.407531522674354, 26.49284790578903, 26.57837579908423, 26.66411576202486, 26.75006835631067, 26.836234145886745, 26.922613696954212, 27.009207577980916, 27.0960163597121, 27.183040615181298, 27.270280919721166, 27.357737850974395, 27.445411988904755, 27.533303915808183, 27.621414216323824, 27.70974347744528, 27.798292288531883, 27.887061241320012, 27.97605092993443, 28.065261950899824, 28.15469490315229, 28.244350388050954, 28.334229009389546, 28.42433137340828, 28.514658088805522, 28.605209766749738, 28.6959870208914, 28.786990467375002, 28.87822072485112, 28.96967841448867, 29.061364159986937, 29.15327858758814, 29.245422326089464, 29.337796006855903, 29.430400263832418, 29.523235733556746, 29.616303055172004, 29.709602870439443, 29.803135823751248, 29.896902562143442, 29.990903735308887, 30.085139995610355, 30.17961199809352, 30.274320400500372, 30.369265863282386, 30.46444904961385, 30.559870625405438, 30.655531259317648, 30.751431622774465, 30.847572389977003, 30.943954237917342, 31.04057784639234, 31.137443898017597, 31.234553078241532, 31.3319060753594, 31.429503580527516, 31.527346287777686, 31.62543489403133, 31.72377009911415, 31.822352605770593, 31.92118311967852, 32.02026234946387, 32.119591006715545, 32.219169806000316, 32.318999464877805, 32.419080703915526, 32.51941424670417, 32.62000081987281, 32.72084115310434, 32.82193597915082, 32.923286033849145, 33.02489205613669, 33.12675478806706, 33.22887497482589, 33.33125336474687, 33.43389070932773, 33.53678776324644, 33.639945284377404, 33.74336403380795, 33.8470447758545, 33.9509882780794, 34.055195311307564, 34.15966664964296, 34.26440307048576, 34.36940535454928, 34.47467428587691, 34.58021065185932, 34.68601524325198, 34.79208885419229, 34.898432282217215, 35.00504632828083, 35.11193179677225, 35.219089495533154, 35.32652023587609, 35.43422483260223, 35.54220410401981, 35.65045887196219, 35.758989961806535, 35.86779820249212, 35.97688442653904, 36.08624947006703, 36.1958941728144, 36.30581937815683, 36.416025933126726, 36.526514688432364, 36.63728649847727, 36.74834222137969, 36.8596827189923, 36.97130885692189, 37.08322150454917, 37.19542153504903, 37.30790982541032, 37.42068725645637, 37.53375471286528, 37.64711308319042, 37.760763259881166, 37.87470613930367, 37.98894262176167, 38.10347361151771, 38.21830001681421, 38.33342274989489, 38.448842727026204, 38.564560868518925, 38.680578098749855, 38.796895346183895, 38.91351354339595, 39.030433627093046, 39.14765653813681, 39.26518322156579, 39.383014626618255, 39.50115170675477, 39.6195954196812, 39.73834672737187, 39.85740659609256, 39.97677599642408, 40.096455903285715, 40.21644729595889, 40.33675115811105, 40.45736847781959, 40.57830024759612, 40.69954746441062, 40.82111112971612, 40.94299224947316, 41.0651918341746, 41.18771089887079, 41.310550463194446, 41.43371155138604, 41.55719519231941, 41.68100241952721, 41.80513427122683, 41.92959179034629, 42.054376024550486, 42.17948802626756, 42.304928852715236, 42.43069956592774, 42.556801232782455, 42.683234925027165, 42.81000171930714, 42.93710269719262, 43.064538945206465, 43.19231155485182, 43.32042162264024, 43.448870250119754, 43.5776585439033, 43.706787615697166, 43.836258582330004, 43.966072565781346, 44.09623069321115, 44.22673409698899, 44.357583914723556, 44.48878128929241, 44.62032736887202, 44.75222330696788, 44.8844702624448, 45.01706939955757, 45.15002188798171, 45.28332890284443, 45.41699162475595, 45.551011239840754, 45.68538893976946, 45.82012592179039, 45.95522338876197, 46.09068254918479, 46.22650461723426, 46.36269081279331, 46.499242361485464, 46.63616049470794, 46.77344644966518, 46.911101469402475, 47.04912680283999, 47.18752370480676, 47.326293436075204, 47.46543726339578, 47.604956459531714, 47.744852303294344, 47.8851260795783, 48.02577907939726, 48.16681259991971, 48.308227944505255, 48.45002642274081, 48.59220935047732, 48.73477804986673, 48.877733849399036, 49.02107808393981, 49.164812094767846, 49.30893722961317, 49.45345484269526, 49.59836629476147, 49.74367295312603, 49.8893761917089, 50.03547739107519, 50.181977938474866, 50.32887922788254, 50.47618266003781, 50.62388964248551, 50.772001589616835, 50.920519922710184, 51.06944606997256, 51.218781466581284, 51.36852755472601, 51.518685783650945, 51.66925760969746, 51.82024449634702, 51.971647914264395, 52.12346934134106, 52.27571026273928, 52.42837217093612, 52.5814565657679, 52.734964954475124, 52.88889885174761, 53.04325977976991, 53.198049268267155, 53.353268854551274, 53.508920083567304, 53.66500450794045, 53.821523688023085, 53.978479191942455, 54.13587259564834, 54.293705482961485, 54.45197944562216, 54.61069608333907, 54.76985700383864, 54.92946382291488, 55.08951816447928, 55.25002166061127, 55.41097595160917, 55.57238268604122]}, {\"mode\": \"lines\", \"name\": \"$\\\\theta-\\\\tan\\\\theta$\", \"type\": \"scatter\", \"x\": [0.1, 0.14994994994994995, 0.1998998998998999, 0.24984984984984984, 0.29979979979979976, 0.3497497497497497, 0.39969969969969965, 0.4496496496496496, 0.49959959959959954, 0.5495495495495495, 0.5994994994994994, 0.6494494494494494, 0.6993993993993993, 0.7493493493493493, 0.7992992992992992, 0.8492492492492492, 0.8991991991991991, 0.949149149149149, 0.999099099099099, 1.049049049049049, 1.098998998998999, 1.148948948948949, 1.198898898898899, 1.2488488488488487, 1.2987987987987988, 1.3487487487487488, 1.3986986986986987, 1.4486486486486485, 1.4985985985985986, 1.5485485485485486, 1.5984984984984985, 1.6484484484484483, 1.6983983983983983, 1.7483483483483484, 1.7982982982982982, 1.848248248248248, 1.8981981981981981, 1.9481481481481482, 1.998098098098098, 2.048048048048048, 2.097997997997998, 2.147947947947948, 2.197897897897898, 2.2478478478478476, 2.2977977977977977, 2.3477477477477477, 2.3976976976976974, 2.4476476476476474, 2.4975975975975975, 2.5475475475475475, 2.5974974974974976, 2.647447447447447, 2.6973973973973973, 2.7473473473473473, 2.797297297297297, 2.847247247247247, 2.897197197197197, 2.947147147147147, 2.997097097097097, 3.0470470470470468, 3.096996996996997, 3.146946946946947, 3.1968968968968965, 3.2468468468468465, 3.2967967967967966, 3.3467467467467467, 3.3966966966966967, 3.4466466466466463, 3.4965965965965964, 3.5465465465465464, 3.596496496496496, 3.646446446446446, 3.696396396396396, 3.7463463463463462, 3.7962962962962963, 3.846246246246246, 3.896196196196196, 3.946146146146146, 3.9960960960960956, 4.046046046046046, 4.095995995995995, 4.145945945945945, 4.195895895895895, 4.245845845845845, 4.2957957957957955, 4.345745745745745, 4.395695695695695, 4.445645645645645, 4.495595595595595, 4.5455455455455445, 4.595495495495495, 4.645445445445445, 4.695395395395394, 4.745345345345345, 4.795295295295294, 4.845245245245245, 4.895195195195194, 4.945145145145144, 4.9950950950950945, 5.045045045045044, 5.094994994994995, 5.144944944944944, 5.194894894894894, 5.244844844844844, 5.294794794794794, 5.344744744744744, 5.394694694694694, 5.444644644644644, 5.494594594594593, 5.544544544544544, 5.594494494494493, 5.644444444444444, 5.6943943943943935, 5.744344344344343, 5.794294294294294, 5.844244244244243, 5.894194194194194, 5.944144144144143, 5.994094094094093, 6.0440440440440435, 6.093993993993993, 6.143943943943943, 6.193893893893893, 6.243843843843843, 6.2937937937937924, 6.343743743743743, 6.393693693693693, 6.443643643643643, 6.493593593593593, 6.543543543543542, 6.593493493493493, 6.643443443443442, 6.693393393393393, 6.7433433433433425, 6.793293293293292, 6.843243243243243, 6.893193193193192, 6.943143143143142, 6.993093093093092, 7.043043043043042, 7.092992992992992, 7.142942942942942, 7.192892892892892, 7.242842842842842, 7.292792792792792, 7.342742742742741, 7.392692692692692, 7.4426426426426415, 7.492592592592592, 7.542542542542542, 7.592492492492491, 7.642442442442442, 7.692392392392391, 7.742342342342341, 7.7922922922922915, 7.842242242242241, 7.892192192192191, 7.942142142142141, 7.992092092092091, 8.042042042042041, 8.091991991991991, 8.14194194194194, 8.19189189189189, 8.241841841841842, 8.291791791791791, 8.34174174174174, 8.39169169169169, 8.44164164164164, 8.491591591591591, 8.541541541541541, 8.59149149149149, 8.64144144144144, 8.69139139139139, 8.74134134134134, 8.79129129129129, 8.84124124124124, 8.89119119119119, 8.94114114114114, 8.99109109109109, 9.04104104104104, 9.09099099099099, 9.14094094094094, 9.19089089089089, 9.24084084084084, 9.290790790790789, 9.34074074074074, 9.39069069069069, 9.44064064064064, 9.490590590590589, 9.540540540540539, 9.59049049049049, 9.64044044044044, 9.69039039039039, 9.740340340340339, 9.790290290290288, 9.84024024024024, 9.89019019019019, 9.940140140140139, 9.990090090090089, 10.040040040040038, 10.08998998998999, 10.13993993993994, 10.189889889889889, 10.239839839839838, 10.289789789789788, 10.339739739739738, 10.389689689689689, 10.439639639639639, 10.489589589589588, 10.539539539539538, 10.589489489489488, 10.639439439439439, 10.689389389389389, 10.739339339339338, 10.789289289289288, 10.839239239239237, 10.889189189189187, 10.939139139139138, 10.989089089089088, 11.039039039039038, 11.088988988988987, 11.138938938938937, 11.188888888888888, 11.238838838838838, 11.288788788788787, 11.338738738738737, 11.388688688688687, 11.438638638638638, 11.488588588588588, 11.538538538538537, 11.588488488488487, 11.638438438438437, 11.688388388388388, 11.738338338338338, 11.788288288288287, 11.838238238238237, 11.888188188188186, 11.938138138138136, 11.988088088088087, 12.038038038038037, 12.087987987987987, 12.137937937937936, 12.187887887887886, 12.237837837837837, 12.287787787787787, 12.337737737737736, 12.387687687687686, 12.437637637637636, 12.487587587587585, 12.537537537537537, 12.587487487487486, 12.637437437437436, 12.687387387387385, 12.737337337337335, 12.787287287287286, 12.837237237237236, 12.887187187187186, 12.937137137137135, 12.987087087087085, 13.037037037037036, 13.086986986986986, 13.136936936936936, 13.186886886886885, 13.236836836836835, 13.286786786786786, 13.336736736736736, 13.386686686686685, 13.436636636636635, 13.486586586586585, 13.536536536536534, 13.586486486486486, 13.636436436436435, 13.686386386386385, 13.736336336336334, 13.786286286286284, 13.836236236236235, 13.886186186186185, 13.936136136136135, 13.986086086086084, 14.036036036036034, 14.085985985985984, 14.135935935935935, 14.185885885885885, 14.235835835835834, 14.285785785785784, 14.335735735735733, 14.385685685685685, 14.435635635635634, 14.485585585585584, 14.535535535535534, 14.585485485485483, 14.635435435435435, 14.685385385385384, 14.735335335335334, 14.785285285285283, 14.835235235235233, 14.885185185185184, 14.935135135135134, 14.985085085085084, 15.035035035035033, 15.084984984984983, 15.134934934934932, 15.184884884884884, 15.234834834834833, 15.284784784784783, 15.334734734734733, 15.384684684684682, 15.434634634634634, 15.484584584584583, 15.534534534534533, 15.584484484484483, 15.634434434434432, 15.684384384384382, 15.734334334334333, 15.784284284284283, 15.834234234234232, 15.884184184184182, 15.934134134134132, 15.984084084084083, 16.034034034034033, 16.083983983983984, 16.133933933933935, 16.183883883883883, 16.233833833833835, 16.283783783783782, 16.333733733733734, 16.383683683683685, 16.433633633633633, 16.483583583583584, 16.533533533533532, 16.583483483483484, 16.633433433433435, 16.683383383383383, 16.733333333333334, 16.783283283283282, 16.833233233233234, 16.883183183183185, 16.933133133133133, 16.983083083083084, 17.033033033033032, 17.082982982982983, 17.13293293293293, 17.182882882882883, 17.232832832832834, 17.282782782782782, 17.332732732732733, 17.38268268268268, 17.432632632632632, 17.482582582582584, 17.53253253253253, 17.582482482482483, 17.63243243243243, 17.682382382382382, 17.732332332332334, 17.78228228228228, 17.832232232232233, 17.88218218218218, 17.932132132132132, 17.982082082082083, 18.03203203203203, 18.081981981981983, 18.13193193193193, 18.181881881881882, 18.231831831831833, 18.28178178178178, 18.331731731731733, 18.38168168168168, 18.43163163163163, 18.48158158158158, 18.53153153153153, 18.581481481481482, 18.63143143143143, 18.68138138138138, 18.73133133133133, 18.78128128128128, 18.831231231231232, 18.88118118118118, 18.93113113113113, 18.98108108108108, 19.03103103103103, 19.080980980980982, 19.13093093093093, 19.18088088088088, 19.23083083083083, 19.28078078078078, 19.330730730730732, 19.38068068068068, 19.43063063063063, 19.48058058058058, 19.53053053053053, 19.58048048048048, 19.63043043043043, 19.68038038038038, 19.73033033033033, 19.78028028028028, 19.83023023023023, 19.88018018018018, 19.93013013013013, 19.98008008008008, 20.03003003003003, 20.07997997997998, 20.12992992992993, 20.17987987987988, 20.22982982982983, 20.27977977977978, 20.329729729729728, 20.37967967967968, 20.42962962962963, 20.47957957957958, 20.52952952952953, 20.579479479479478, 20.62942942942943, 20.67937937937938, 20.729329329329328, 20.77927927927928, 20.829229229229227, 20.87917917917918, 20.92912912912913, 20.979079079079078, 21.02902902902903, 21.078978978978977, 21.12892892892893, 21.17887887887888, 21.228828828828828, 21.27877877877878, 21.328728728728727, 21.37867867867868, 21.42862862862863, 21.478578578578578, 21.52852852852853, 21.578478478478477, 21.62842842842843, 21.678378378378376, 21.728328328328328, 21.77827827827828, 21.828228228228227, 21.878178178178178, 21.928128128128126, 21.978078078078077, 22.02802802802803, 22.077977977977977, 22.127927927927928, 22.177877877877876, 22.227827827827827, 22.27777777777778, 22.327727727727726, 22.377677677677678, 22.427627627627626, 22.477577577577577, 22.52752752752753, 22.577477477477476, 22.627427427427428, 22.677377377377375, 22.727327327327327, 22.77727727727728, 22.827227227227226, 22.877177177177177, 22.927127127127125, 22.977077077077077, 23.027027027027028, 23.076976976976976, 23.126926926926927, 23.176876876876875, 23.226826826826827, 23.276776776776778, 23.326726726726726, 23.376676676676677, 23.426626626626625, 23.476576576576576, 23.526526526526524, 23.576476476476476, 23.626426426426427, 23.676376376376375, 23.726326326326326, 23.776276276276274, 23.826226226226225, 23.876176176176177, 23.926126126126125, 23.976076076076076, 24.026026026026024, 24.075975975975975, 24.125925925925927, 24.175875875875874, 24.225825825825826, 24.275775775775774, 24.325725725725725, 24.375675675675677, 24.425625625625624, 24.475575575575576, 24.525525525525524, 24.575475475475475, 24.625425425425426, 24.675375375375374, 24.725325325325326, 24.775275275275273, 24.825225225225225, 24.875175175175173, 24.925125125125124, 24.975075075075075, 25.025025025025023, 25.074974974974975, 25.124924924924922, 25.174874874874874, 25.224824824824825, 25.274774774774773, 25.324724724724724, 25.374674674674672, 25.424624624624624, 25.474574574574575, 25.524524524524523, 25.574474474474474, 25.624424424424422, 25.674374374374374, 25.724324324324325, 25.774274274274273, 25.824224224224224, 25.874174174174172, 25.924124124124123, 25.974074074074075, 26.024024024024023, 26.073973973973974, 26.123923923923922, 26.173873873873873, 26.223823823823825, 26.273773773773772, 26.323723723723724, 26.37367367367367, 26.423623623623623, 26.473573573573574, 26.523523523523522, 26.573473473473474, 26.62342342342342, 26.673373373373373, 26.72332332332332, 26.773273273273272, 26.823223223223223, 26.87317317317317, 26.923123123123123, 26.97307307307307, 27.023023023023022, 27.072972972972973, 27.12292292292292, 27.172872872872873, 27.22282282282282, 27.272772772772772, 27.322722722722723, 27.37267267267267, 27.422622622622622, 27.47257257257257, 27.52252252252252, 27.572472472472473, 27.62242242242242, 27.672372372372372, 27.72232232232232, 27.77227227227227, 27.822222222222223, 27.87217217217217, 27.922122122122122, 27.97207207207207, 28.02202202202202, 28.07197197197197, 28.12192192192192, 28.171871871871872, 28.22182182182182, 28.27177177177177, 28.32172172172172, 28.37167167167167, 28.42162162162162, 28.47157157157157, 28.52152152152152, 28.57147147147147, 28.62142142142142, 28.67137137137137, 28.72132132132132, 28.77127127127127, 28.82122122122122, 28.87117117117117, 28.92112112112112, 28.97107107107107, 29.02102102102102, 29.07097097097097, 29.12092092092092, 29.17087087087087, 29.22082082082082, 29.27077077077077, 29.32072072072072, 29.37067067067067, 29.42062062062062, 29.47057057057057, 29.52052052052052, 29.570470470470468, 29.62042042042042, 29.67037037037037, 29.72032032032032, 29.77027027027027, 29.820220220220218, 29.87017017017017, 29.920120120120117, 29.97007007007007, 30.02002002002002, 30.069969969969968, 30.11991991991992, 30.169869869869867, 30.21981981981982, 30.26976976976977, 30.319719719719718, 30.36966966966967, 30.419619619619617, 30.46956956956957, 30.51951951951952, 30.569469469469468, 30.61941941941942, 30.669369369369367, 30.719319319319318, 30.76926926926927, 30.819219219219217, 30.86916916916917, 30.919119119119117, 30.969069069069068, 31.01901901901902, 31.068968968968967, 31.11891891891892, 31.168868868868866, 31.218818818818818, 31.268768768768766, 31.318718718718717, 31.36866866866867, 31.418618618618616, 31.468568568568568, 31.518518518518515, 31.568468468468467, 31.61841841841842, 31.668368368368366, 31.718318318318317, 31.768268268268265, 31.818218218218217, 31.868168168168168, 31.918118118118116, 31.968068068068067, 32.01801801801801, 32.06796796796797, 32.117917917917914, 32.16786786786787, 32.21781781781782, 32.267767767767765, 32.31771771771771, 32.36766766766767, 32.417617617617616, 32.46756756756756, 32.51751751751752, 32.567467467467466, 32.617417417417414, 32.66736736736737, 32.71731731731732, 32.767267267267265, 32.81721721721721, 32.86716716716717, 32.917117117117115, 32.96706706706706, 33.01701701701702, 33.066966966966966, 33.116916916916914, 33.16686686686687, 33.21681681681682, 33.266766766766764, 33.31671671671671, 33.36666666666667, 33.416616616616615, 33.46656656656656, 33.51651651651652, 33.566466466466466, 33.61641641641641, 33.66636636636637, 33.716316316316316, 33.766266266266264, 33.81621621621621, 33.86616616616617, 33.916116116116115, 33.96606606606606, 34.01601601601602, 34.065965965965965, 34.11591591591591, 34.16586586586586, 34.215815815815816, 34.265765765765764, 34.31571571571571, 34.36566566566567, 34.415615615615614, 34.46556556556556, 34.51551551551552, 34.565465465465465, 34.61541541541541, 34.66536536536536, 34.715315315315316, 34.76526526526526, 34.81521521521521, 34.865165165165166, 34.915115115115114, 34.96506506506506, 35.01501501501502, 35.064964964964965, 35.11491491491491, 35.16486486486486, 35.214814814814815, 35.26476476476476, 35.31471471471471, 35.364664664664666, 35.414614614614614, 35.46456456456456, 35.51451451451451, 35.564464464464464, 35.61441441441441, 35.66436436436436, 35.714314314314315, 35.76426426426426, 35.81421421421421, 35.864164164164166, 35.91411411411411, 35.96406406406406, 36.01401401401401, 36.063963963963964, 36.11391391391391, 36.16386386386386, 36.213813813813815, 36.26376376376376, 36.31371371371371, 36.363663663663665, 36.41361361361361, 36.46356356356356, 36.51351351351351, 36.563463463463464, 36.61341341341341, 36.66336336336336, 36.713313313313314, 36.76326326326326, 36.81321321321321, 36.86316316316316, 36.91311311311311, 36.96306306306306, 37.01301301301301, 37.06296296296296, 37.11291291291291, 37.16286286286286, 37.212812812812814, 37.26276276276276, 37.31271271271271, 37.36266266266266, 37.41261261261261, 37.46256256256256, 37.51251251251251, 37.56246246246246, 37.61241241241241, 37.66236236236236, 37.712312312312314, 37.76226226226226, 37.81221221221221, 37.86216216216216, 37.91211211211211, 37.96206206206206, 38.01201201201201, 38.06196196196196, 38.11191191191191, 38.16186186186186, 38.21181181181181, 38.26176176176176, 38.31171171171171, 38.36166166166166, 38.41161161161161, 38.46156156156156, 38.51151151151151, 38.56146146146146, 38.61141141141141, 38.66136136136136, 38.711311311311306, 38.76126126126126, 38.81121121121121, 38.86116116116116, 38.91111111111111, 38.96106106106106, 39.01101101101101, 39.06096096096096, 39.11091091091091, 39.16086086086086, 39.210810810810806, 39.26076076076076, 39.31071071071071, 39.360660660660656, 39.41061061061061, 39.46056056056056, 39.51051051051051, 39.56046046046046, 39.61041041041041, 39.66036036036036, 39.710310310310305, 39.76026026026026, 39.81021021021021, 39.860160160160156, 39.91011011011011, 39.96006006006006, 40.01001001001001, 40.05995995995996, 40.10990990990991, 40.15985985985986, 40.209809809809805, 40.25975975975976, 40.30970970970971, 40.359659659659656, 40.40960960960961, 40.45955955955956, 40.509509509509506, 40.559459459459454, 40.60940940940941, 40.65935935935936, 40.709309309309305, 40.75925925925926, 40.80920920920921, 40.859159159159155, 40.90910910910911, 40.95905905905906, 41.009009009009006, 41.058958958958954, 41.10890890890891, 41.158858858858856, 41.208808808808804, 41.25875875875876, 41.30870870870871, 41.358658658658655, 41.40860860860861, 41.45855855855856, 41.508508508508505, 41.55845845845845, 41.60840840840841, 41.658358358358356, 41.708308308308304, 41.75825825825826, 41.80820820820821, 41.858158158158155, 41.9081081081081, 41.95805805805806, 42.008008008008005, 42.05795795795795, 42.10790790790791, 42.157857857857856, 42.207807807807804, 42.25775775775776, 42.307707707707706, 42.357657657657654, 42.4076076076076, 42.45755755755756, 42.507507507507505, 42.55745745745745, 42.60740740740741, 42.657357357357355, 42.7073073073073, 42.75725725725726, 42.807207207207206, 42.857157157157154, 42.9071071071071, 42.95705705705706, 43.007007007007005, 43.05695695695695, 43.10690690690691, 43.156856856856855, 43.2068068068068, 43.25675675675675, 43.306706706706706, 43.356656656656654, 43.4066066066066, 43.456556556556556, 43.506506506506504, 43.55645645645645, 43.60640640640641, 43.656356356356355, 43.7063063063063, 43.75625625625625, 43.806206206206205, 43.85615615615615, 43.9061061061061, 43.956056056056056, 44.006006006006004, 44.05595595595595, 44.10590590590591, 44.155855855855854, 44.2058058058058, 44.25575575575575, 44.305705705705705, 44.35565565565565, 44.4056056056056, 44.455555555555556, 44.5055055055055, 44.55545545545545, 44.605405405405406, 44.655355355355354, 44.7053053053053, 44.75525525525525, 44.805205205205205, 44.85515515515515, 44.9051051051051, 44.955055055055055, 45.005005005005, 45.05495495495495, 45.1049049049049, 45.154854854854854, 45.2048048048048, 45.25475475475475, 45.304704704704704, 45.35465465465465, 45.4046046046046, 45.454554554554555, 45.5045045045045, 45.55445445445445, 45.6044044044044, 45.65435435435435, 45.7043043043043, 45.75425425425425, 45.804204204204204, 45.85415415415415, 45.9041041041041, 45.954054054054055, 46.004004004004, 46.05395395395395, 46.1039039039039, 46.15385385385385, 46.2038038038038, 46.25375375375375, 46.303703703703704, 46.35365365365365, 46.4036036036036, 46.453553553553554, 46.5035035035035, 46.55345345345345, 46.6034034034034, 46.65335335335335, 46.7033033033033, 46.75325325325325, 46.8032032032032, 46.85315315315315, 46.9031031031031, 46.95305305305305, 47.003003003003, 47.05295295295295, 47.1029029029029, 47.15285285285285, 47.2028028028028, 47.25275275275275, 47.3027027027027, 47.35265265265265, 47.4026026026026, 47.45255255255255, 47.5025025025025, 47.55245245245245, 47.6024024024024, 47.65235235235235, 47.7023023023023, 47.75225225225225, 47.8022022022022, 47.85215215215215, 47.9021021021021, 47.952052052052046, 48.002002002002, 48.05195195195195, 48.1019019019019, 48.15185185185185, 48.2018018018018, 48.25175175175175, 48.301701701701695, 48.35165165165165, 48.4016016016016, 48.451551551551546, 48.5015015015015, 48.55145145145145, 48.6014014014014, 48.65135135135135, 48.7013013013013, 48.75125125125125, 48.801201201201195, 48.85115115115115, 48.9011011011011, 48.951051051051046, 49.001001001001, 49.05095095095095, 49.100900900900896, 49.15085085085085, 49.2008008008008, 49.25075075075075, 49.300700700700695, 49.35065065065065, 49.4006006006006, 49.450550550550545, 49.5005005005005, 49.55045045045045, 49.600400400400396, 49.650350350350344, 49.7003003003003, 49.75025025025025, 49.800200200200194, 49.85015015015015, 49.9001001001001, 49.950050050050045, 50.0], \"y\": [-0.00010153916055210504, -0.00022831073334717597, -0.00040575042759396975, -0.000633858351161624, -0.0009126346427494265, -0.0012420794718884455, -0.0016221930388135442, -0.002052975574716978, -0.0025344273414887107, -0.00306654863187034, -0.0036493397693991153, -0.004282801108491393, -0.004966933034225532, -0.0057017359626666255, -0.006487210340562804, -0.007323356645548832, -0.008210175386029136, -0.009147667101266096, -0.01013583236131272, -0.011174671767058922, -0.012264185950173876, -0.013404375573226393, -0.014595241329533076, -0.015836783943255602, -0.01712900416940416, -0.01847190279380049, -0.019865480633081124, -0.021309738534772027, -0.022804677377152267, -0.024350298069390357, -0.025946601551458122, -0.027593588794218533, -0.029291260799312036, -0.03103961859925645, -0.03283866325742019, -0.03468839586799998, -0.03658881755609619, -0.038539929477541555, -0.04054173281915261, -0.042594228798555275, -0.04469741866421412, -0.04685130369548374, -0.049055885202570086, -0.0513111645265746, -0.05361714303941794, -0.055973822143965825, -0.058381203273912864, -0.06083928789381582, -0.06334807749919154, -0.06590757361635871, -0.06851777780260782, -0.07117869164604129, -0.07389031676571459, -0.07665265481157772, -0.0794657074644546, -0.08232947643612502, -0.0852439634692641, -0.0882091703374171, -0.09122509884511136, -0.0942917508277381, -0.09740912815170326, -0.10057723271426337, -0.10379606644362607, -0.1070656312989692, -0.11038592927039906, -0.11375696237896055, -0.11717873267665843, -0.1206512422464545, -0.12417449320227601, -0.12774848768901284, -0.1313732278825143, -0.13504871598966212, -0.13877495424822264, -0.14255194492703832, -0.14637969032587925, -0.15025819277552227, -0.15418745463781242, -0.15816747830550762, -0.16219826620244135, -0.1662798207833874, -0.17041214453423326, -0.1745952399718233, -0.17882910964406679, -0.18311375612995212, -0.1874491820394008, -0.19183539001350391, -0.19627238272429737, -0.2007601628749699, -0.20529873319972738, -0.20988809646384762, -0.21452825546375365, -0.2192192130267987, -0.22396097201160978, -0.22875353530781425, -0.23359690583615186, -0.23849108654847, -0.24343608042774065, -0.2484318904880484, -0.2534785197746314, -0.2585759713638611, -0.26372424836321173, -0.26892335391135874, -0.27417329117807654, -0.2794740633643731, -0.28482567370236506, -0.29022812545537086, -0.2956814219179142, -0.30118556641565697, -0.3067405623055117, -0.31234641297557914, -0.318003121845149, -0.32371069236478583, -0.32946912801623357, -0.3352784323124773, -0.34113860879777724, -0.3470496610476218, -0.3530115926687511, -0.359024407299208, -0.36508810860824314, -0.3712027002964741, -0.3773681860957399, -0.3835845697692466, -0.3898518551114135, -0.3961700459480695, -0.40253914613631375, -0.40895915956460854, -0.4154300901527076, -0.42195194185178364, -0.428524718644308, -0.43514842454417685, -0.44182306359658013, -0.4485486398781626, -0.4553251574969284, -0.4621526205923386, -0.46903103333515855, -0.4759603999276935, -0.4829407246035893, -0.48997201162795906, -0.4970542652974024, -0.5041874899399228, -0.5113716899150138, -0.518606869613652, -0.5258930334582577, -0.5332301859028173, -0.5406183314327967, -0.5480574745651186, -0.5555476198483328, -0.5630887718624296, -0.5706809352190236, -0.5783241145612098, -0.5860183145637198, -0.5937635399327948, -0.6015597954063167, -0.6094070857537379, -0.6173054157761452, -0.6252547903061668, -0.6332552142081502, -0.6413066923780442, -0.6494092297434302, -0.6575628312635993, -0.6657675019294387, -0.6740232467635616, -0.6823300708203044, -0.6906879791856361, -0.6990969769773234, -0.7075570693447768, -0.7160682614691883, -0.7246305585635046, -0.7332439658724422, -0.7419084886724379, -0.7506241322717485, -0.7593909020104477, -0.7682088032603545, -0.777077841425168, -0.7859980219403699, -0.7949693502733144, -0.8039918319232308, -0.8130654724211437, -0.8221902773300281, -0.8313662522447208, -0.840593402791943, -0.8498717346303607, -0.8592012534505631, -0.8685819649750792, -0.8780138749583486, -0.8874969891868626, -0.8970313134790422, -0.906616853685269, -0.9162536156879703, -0.9259416054015905, -0.9356808287725831, -0.9454712917794711, -0.9553130004327963, -0.9652059607752173, -0.9751501788814173, -0.9851456608582544, -0.9951924128446121, -1.0052904410115384, -1.0154397515622426, -1.0256403507320357, -1.035892244788394, -1.0461954400310285, -1.0565499427917977, -1.0669557594347492, -1.0774128963561906, -1.0879213599846587, -1.0984811567809014, -1.1090922932379719, -1.1197547758811832, -1.1304686112681146, -1.1412338059887048, -1.1520503666651547, -1.162918299952039, -1.1738376125362704, -1.184808311137122, -1.1958304025062407, -1.206903893427685, -1.2180287907179086, -1.2292051012257725, -1.2404328318326285, -1.251711989452221, -1.263042581030824, -1.274424613547117, -1.2858580940123654, -1.2973430294702955, -1.3088794269971906, -1.3204672937018633, -1.3321066367256698, -1.343797463242631, -1.3555397804592557, -1.3673335956147137, -1.3791789159807828, -1.3910757488619503, -1.4030241015952387, -1.4150239815504677, -1.4270753961300748, -1.4391783527691933, -1.4513328589357606, -1.4635389221303554, -1.4757965498863839, -1.4881057497700179, -1.5004665293801969, -1.5128788963486552, -1.525342858339996, -1.5378584230516392, -1.5504255982138309, -1.5630443915897734, -1.57571481097547, -1.5884368641998905, -1.6012105591249086, -1.614035903645377, -1.6269129056890628, -1.639841573216752, -1.6528219142221727, -1.6658539367321514, -1.67893764880646, -1.6920730585380055, -1.7052601740526807, -1.7184990035095267, -1.7317895551006854, -1.7451318370513658, -1.758525857619982, -1.7719716250980753, -1.7854691478103897, -1.7990184341148332, -1.8126194924025378, -1.826272331097907, -1.8399769586585264, -1.853733383575323, -1.8675416143724712, -1.8814016596074952, -1.8953135278712028, -1.9092772277877603, -1.9232927680147085, -1.9373601572430053, -1.9514794041969454, -1.965650517634309, -1.9798735063462944, -1.9941483791575683, -2.0084751449262694, -2.0228538125440716, -2.037284390936157, -2.051766889061207, -2.066301315911549, -2.0808876805130407, -2.095525991925123, -2.1102162592409317, -2.124958491587171, -2.1397526981242745, -2.154598888046316, -2.1694970705811087, -2.184447254990145, -2.1994494505686886, -2.2145036666458062, -2.2296099125843254, -2.2447681977808367, -2.2599785316658245, -2.2752409237036204, -2.290555383392376, -2.305921920264211, -2.321340543885097, -2.3368112638549894, -2.3523340898077607, -2.3679090314113265, -2.3835360983675042, -2.399215300412221, -2.41494664731541, -2.430730148881085, -2.446565814947358, -2.462453655386445, -2.4783936801046558, -2.4943858990425376, -2.5104303221747206, -2.526526959510104, -2.5426758210918052, -2.558876916997123, -2.5751302573377397, -2.591435852259501, -2.6077937119426595, -2.624203846601778, -2.640666266485728, -2.657180981877864, -2.6737480030958394, -2.690367340491803, -2.707039004452353, -2.723763005398566, -2.7405393537859384, -2.757368060104588, -2.7742491348791596, -2.7911825886688297, -2.808168432067394, -2.8252066757032814, -2.8422973302395187, -2.859440406373827, -2.876635914838619, -2.8938838664010187, -2.9111842718628633, -2.9285371420608, -2.9459424878662257, -2.963400320185379, -2.9809106499593128, -2.9984734881639135, -3.0160888458100383, -3.033756733943358, -3.0514771636445457, -3.0692501460292085, -3.087075692247958, -3.1049538134863863, -3.1228845209651612, -3.1408678259399685, -3.158903739701615, -3.176992273576012, -3.1951334389241905, -3.2133272471424195, -3.231573709662033, -3.2498728379496833, -3.2682246435072337, -3.2866291378718215, -3.3050863326158564, -3.3235962393470957, -3.3421588697086166, -3.3607742353789, -3.3794423480718283, -3.398163219536663, -3.416936861558164, -3.4357632859565883, -3.4546425045876292, -3.473574529342579, -3.492559372148258, -3.511597044967093, -3.530687559797125, -3.5498309286720064, -3.5690271636611253, -3.588276276869473, -3.607578280437862, -3.626933186542833, -3.6463410073966482, -3.6658017552474407, -3.6853154423791628, -3.7048820811116143, -3.7245016838005096, -3.74417426283752, -3.76389983065016, -3.7836783997020103, -3.803509982492642, -3.823394591557636, -3.8433322394686846, -3.8633229388335044, -3.883366702295985, -3.903463542536139, -3.9236134722701923, -3.943816504250502, -3.9640726512657682, -3.9843819261408875, -4.0047443417370685, -4.025159910951822, -4.0456286467190825, -4.066150562009102, -4.0867256698285646, -4.107353983220586, -4.128035515264786, -4.148770279077288, -4.169558287810716, -4.190399554654297, -4.211294092833829, -4.232241915611738, -4.253243036287105, -4.274297468195694, -4.295405224709996, -4.3165663192392145, -4.337780765229414, -4.3590485761634055, -4.380369765560834, -4.401744346978216, -4.423172334009013, -4.444653740283595, -4.466188579469277, -4.487776865270404, -4.509418611428321, -4.531113831721484, -4.5528625399653695, -4.574664750012617, -4.596520475753054, -4.618429731113613, -4.640392530058516, -4.662408886589193, -4.6844788147444385, -4.706602328600233, -4.7287794422700244, -4.751010169904595, -4.773294525692121, -4.795632523858271, -4.818024178666177, -4.840469504416475, -4.862968515447364, -4.885521226134599, -4.908127650891574, -4.930787804169321, -4.953501700456566, -4.976269354279691, -4.999090780202907, -5.021965992828176, -5.044895006795216, -5.0678778367817126, -5.090914497503123, -5.114005003712891, -5.137149370202404, -5.160347611800976, -5.183599743376034, -5.206905779832997, -5.230265736115401, -5.253679627204868, -5.277147468121236, -5.300669273922516, -5.3242450597049515, -5.3478748406030245, -5.371558631789541, -5.3952964484756505, -5.41908830591087, -5.442934219383103, -5.466834204218726, -5.490788275782543, -5.514796449477951, -5.538858740746839, -5.562975165069684, -5.587145737965618, -5.611370474992423, -5.635649391746538, -5.659982503863187, -5.684369827016309, -5.708811376918729, -5.733307169322021, -5.757857220016697, -5.782461544832166, -5.8071201596367885, -5.831833080337937, -5.856600322881969, -5.881421903254362, -5.90629783747965, -5.931228141621514, -5.95621283178283, -5.981251924105717, -6.006345434771475, -6.0314933800007475, -6.0566957760534965, -6.081952639229061, -6.107263985866162, -6.132629832343003, -6.158050195077223, -6.183525090526051, -6.209054535186207, -6.23463854559404, -6.260277138325546, -6.285970329996397, -6.311718137261979, -6.337520576817454, -6.363377665397715, -6.389289419777593, -6.415255856771697, -6.441276993234607, -6.467352846060846, -6.493483432184946, -6.519668768581445, -6.54590887226498, -6.57220376029026, -6.598553449752241, -6.6249579577859805, -6.651417301566835, -6.677931498310398, -6.704500565272606, -6.731124519749769, -6.757803379078576, -6.784537160636146, -6.811325881840112, -6.838169560148585, -6.865068213060324, -6.892021858114622, -6.9190305128914416, -6.9460941950114625, -6.973212922136051, -7.000386711967391, -7.02761558224848, -7.0548995507631345, -7.082238635336141, -7.109632853833162, -7.137082224160903, -7.164586764267064, -7.192146492140406, -7.2197614258108915, -7.247431583349533, -7.275156982868605, -7.302937642521639, -7.330773580503398, -7.358664815050059, -7.3866113644390845, -7.414613246989424, -7.4426704810614615, -7.470783085057127, -7.498951077419829, -7.52717447663466, -7.555453301228278, -7.583787569769061, -7.6121773008671445, -7.640622513174386, -7.669123225384494, -7.697679456233029, -7.726291224497441, -7.754958548997198, -7.7836814485937085, -7.812459942190439, -7.84129404873297, -7.870183787208984, -7.899129176648373, -7.928130236123219, -7.957186984747963, -7.986299441679277, -8.01546762611622, -8.044691557300306, -8.073971254515428, -8.103306737088092, -8.132698024387272, -8.162145135824552, -8.191648090854198, -8.22120690897316, -8.250821609721088, -8.280492212680473, -8.310218737476593, -8.340001203777668, -8.3698396312948, -8.39973403978208, -8.429684449036632, -8.459690878898646, -8.48975334925143, -8.519871880021498, -8.550046491178554, -8.58027720273556, -8.6105640347488, -8.64090700731795, -8.671306140586065, -8.701761454739716, -8.73227297000892, -8.762840706667262, -8.793464685032012, -8.824144925464005, -8.85488144836786, -8.885674274191913, -8.916523423428337, -8.94742891661313, -8.978390774326254, -9.009409017191567, -9.040483665877002, -9.071614741094491, -9.102802263600122, -9.134046254194137, -9.16534673372098, -9.19670372306938, -9.228117243172349, -9.259587315007334, -9.291113959596107, -9.322697198004962, -9.354337051344713, -9.386033540770786, -9.41778668748313, -9.449596512726464, -9.481463037790238, -9.513386284008627, -9.545366272760683, -9.57740302547032, -9.609496563606392, -9.641646908682802, -9.673854082258424, -9.706118105937275, -9.73843900136853, -9.770816790246545, -9.803251494310922, -9.835743135346647, -9.868291735184027, -9.900897315698723, -9.93355989881205, -9.966279506490663, -9.999056160746878, -10.03188988363872, -10.06478069726978, -10.097728623789523, -10.130733685393073, -10.16379590432155, -10.196915302861912, -10.230091903347079, -10.263325728156069, -10.296616799713895, -10.329965140491753, -10.36337077300702, -10.396833719823286, -10.430354003550548, -10.463931646845019, -10.497566672409446, -10.531259102992967, -10.565008961391321, -10.59881627044677, -10.632681053048271, -10.666603332131471, -10.70058313067873, -10.734620471719262, -10.768715378329137, -10.802867873631408, -10.837077980796026, -10.87134572304009, -10.905671123627686, -10.94005420587017, -10.97449499312608, -11.008993508801193, -11.043549776348675, -11.078163819269125, -11.11283566111044, -11.147565325468252, -11.182352835985586, -11.217198216353202, -11.252101490309519, -11.287062681640709, -11.322081814180756, -11.357158911811519, -11.392293998462815, -11.427487098112412, -11.462738234786151, -11.498047432558007, -11.533414715550123, -11.56884010793282, -11.604323633924825, -11.639865317793117, -11.675465183853179, -11.711123256468914, -11.74683956005279, -11.7826141190659, -11.818446958017976, -11.854338101467508, -11.89028757402171, -11.926295400336747, -11.962361605117628, -11.998486213118358, -12.034669249142011, -12.070910738040737, -12.10721070471585, -12.1435691741179, -12.17998617124676, -12.216461721151633, -12.25299584893113, -12.2895885797334, -12.326239938756093, -12.36294995124649, -12.399718642501547, -12.436546037867982, -12.473432162742272, -12.51037704257084, -12.547380702850003, -12.584443169126084, -12.621564466995435, -12.658744622104656, -12.695983660150429, -12.733281606879746, -12.77063848808995, -12.808054329628751, -12.845529157394326, -12.883062997335404, -12.920655875451303, -12.958307817791976, -12.996018850458144, -13.033788999601354, -13.071618291423881, -13.109506752179112, -13.147454408171305, -13.185461285755846, -13.223527411339248, -13.261652811379202, -13.299837512384702, -13.338081540916058, -13.376384923585011, -13.41474768705478, -13.453169858040093, -13.491651463307361, -13.530192529674585, -13.568793084011634, -13.607453153240112, -13.646172764333524, -13.684951944317447, -13.723790720269308, -13.762689119318791, -13.801647168647706, -13.840664895490054, -13.879742327132256, -13.918879490913044, -13.958076414223594, -13.997333124507708, -14.036649649261653, -14.076026016034518, -14.115462252427994, -14.154958386096677, -14.194514444748036, -14.23413045614248, -14.273806448093444, -14.313542448467494, -14.353338485184375, -14.393194586217078, -14.433110779591896, -14.473087093388564, -14.51312355574022, -14.55322019483363, -14.593377038909106, -14.63359411626071, -14.673871455236226, -14.714209084237309, -14.754607031719507, -14.795065326192388, -14.835583996219562, -14.876163070418801, -14.916802577462049, -14.957502546075583, -14.99826300504005, -15.039083983190526, -15.079965509416596, -15.120907612662435, -15.161910321926959, -15.202973666263734, -15.244097674781203, -15.285282376642739, -15.326527801066604, -15.367833977326207, -15.40920093475006, -15.450628702721875, -15.49211731068065, -15.533666788120772, -15.575277164592105, -15.61694846969993, -15.658680733105221, -15.70047398452461, -15.742328253730504, -15.784243570551126, -15.826219964870644, -15.868257466629169, -15.91035610582295, -15.952515912504397, -15.99473691678212, -16.037019148821052, -16.07936263884257, -16.121767417124435, -16.164233514001115, -16.206760959863555, -16.249349785159588, -16.2920000203937, -16.334711696127375, -16.37748484297902, -16.420319491624078, -16.463215672795155, -16.506173417282053, -16.549192755931884, -16.59227371964915, -16.635416339395768, -16.67862064619124, -16.721886671112742, -16.76521444529506, -16.808603999930863, -16.852055366270648, -16.895568575622928, -16.939143659354233, -16.982780648889243, -17.026479575710827, -17.0702404713602, -17.114063367436955, -17.157948295599144, -17.20189528756339, -17.245904375105003, -17.289975590057935, -17.334108964315035, -17.378304529828043, -17.422562318607664, -17.466882362723723, -17.511264694305158, -17.555709345540215, -17.600216348676472, -17.64478573602089, -17.689417539940006, -17.734111792859906, -17.778868527266443, -17.82368777570518, -17.868569570781595, -17.913513945161075, -17.958520931569126, -18.00359056279135, -18.04872287167358, -18.093917891121983, -18.139175654103106, -18.184496193644012, -18.229879542832368, -18.27532573481648, -18.32083480280543, -18.366406780069234, -18.412041699938765, -18.457739595805972, -18.503500501123973, -18.54932444940709, -18.595211474230915, -18.64116160923256, -18.68717488811055, -18.733251344625064, -18.779391012597902, -18.825593925912738, -18.87186011851505, -18.918189624412342, -18.964582477674146, -19.011038712432164, -19.057558362880368, -19.10414146327506, -19.150788047934984, -19.197498151241444, -19.244271807638324, -19.29110905163234, -19.33800991779293, -19.384974440752476, -19.43200265520645, -19.479094595913367, -19.52625029769493, -19.573469795436235, -19.620753124085713, -19.668100318655306, -19.715511414220614, -19.762986445920863, -19.810525448959115, -19.8581284586023, -19.905795510181353, -19.95352663909132, -20.0013218807914, -20.049181270805125, -20.09710484472037, -20.145092638189517, -20.193144686929543, -20.24126102672214, -20.289441693413735, -20.33768672291565, -20.385996151204257, -20.434370014320972, -20.482808348372412, -20.531311189530488, -20.5798785740325, -20.628510538181278, -20.67720711834523, -20.725968350958446, -20.774794272520896, -20.82368491959837, -20.87264032882275, -20.92166053689197, -20.97074558057024, -21.01989549668805, -21.069110322142347, -21.11839009389661, -21.167734848980917, -21.21714462449219, -21.26661945759408, -21.316159385517246, -21.365764445559428, -21.415434675085507, -21.465170111527623, -21.51497079238534, -21.564836755225677, -21.61476803768325, -21.664764677460393, -21.714826712327195, -21.76495418012175, -21.815147118750094, -21.865405566186443, -21.91572956047322, -21.966119139721265, -22.01657434210978, -22.067095205886602, -22.117681769368254, -22.168334070940002, -22.219052149056054, -22.269836042239596, -22.32068578908295, -22.37160142824762, -22.42258299846461, -22.473630538534177, -22.524744087326226, -22.575923683780402, -22.62716936690606, -22.678481175782466, -22.72985914955893, -22.78130332745489, -22.832813748760017, -22.884390452834303, -22.93603347910829, -22.987742867083018, -23.039518656330273, -23.09136088649263, -23.143269597283652, -23.195244828487873, -23.247286619961034, -23.299395011630093, -23.351570043493496, -23.40381175562109, -23.456120188154415, -23.508495381306723, -23.560937375363185, -23.613446210680834, -23.666021927688895, -23.71866456688875, -23.771374168854166, -23.824150774231313, -23.87699442373895, -23.92990515816849, -23.98288301838422, -24.035928045323303, -24.08904027999593, -24.14221976348553, -24.195466536948768, -24.248780641615742, -24.302162118790054, -24.35561100984899, -24.40912735624358, -24.462711199498763, -24.516362581213492, -24.570081543060894, -24.623868126788313, -24.677722374217513, -24.73164432724474, -24.78563402784091, -24.839691518051644, -24.893816839997537, -24.948010035874137, -25.002271147952055, -25.056600218577312, -25.110997290171223, -25.16546240523061, -25.219995606327966, -25.274596936111504, -25.329266437305392, -25.38400415270974, -25.438810125200874, -25.49368439773137, -25.548627013330172, -25.6036380151028, -25.65871744623142, -25.713865349974974, -25.7690817696693, -25.82436674872736, -25.87972033063921, -25.935142558972263, -25.99063347737135, -26.046193129558894, -26.10182155933497, -26.15751881057754, -26.21328492724251, -26.26911995336385, -26.32502393305381, -26.38099691050298, -26.437038929980456, -26.49315003583389, -26.549330272489836, -26.605579684453595, -26.661898316309628, -26.718286212721477, -26.77474341843199]}],\n",
       "                        {\"template\": {\"data\": {\"bar\": [{\"error_x\": {\"color\": \"#2a3f5f\"}, \"error_y\": {\"color\": \"#2a3f5f\"}, \"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"bar\"}], \"barpolar\": [{\"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"barpolar\"}], \"carpet\": [{\"aaxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"baxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"type\": \"carpet\"}], \"choropleth\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"choropleth\"}], \"contour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"contour\"}], \"contourcarpet\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"contourcarpet\"}], \"heatmap\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmap\"}], \"heatmapgl\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmapgl\"}], \"histogram\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"histogram\"}], \"histogram2d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2d\"}], \"histogram2dcontour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2dcontour\"}], \"mesh3d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"mesh3d\"}], \"parcoords\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"parcoords\"}], \"pie\": [{\"automargin\": true, \"type\": \"pie\"}], \"scatter\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter\"}], \"scatter3d\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter3d\"}], \"scattercarpet\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattercarpet\"}], \"scattergeo\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergeo\"}], \"scattergl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergl\"}], \"scattermapbox\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattermapbox\"}], \"scatterpolar\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolar\"}], \"scatterpolargl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolargl\"}], \"scatterternary\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterternary\"}], \"surface\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"surface\"}], \"table\": [{\"cells\": {\"fill\": {\"color\": \"#EBF0F8\"}, \"line\": {\"color\": \"white\"}}, \"header\": {\"fill\": {\"color\": \"#C8D4E3\"}, \"line\": {\"color\": \"white\"}}, \"type\": \"table\"}]}, \"layout\": {\"annotationdefaults\": {\"arrowcolor\": \"#2a3f5f\", \"arrowhead\": 0, \"arrowwidth\": 1}, \"coloraxis\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"colorscale\": {\"diverging\": [[0, \"#8e0152\"], [0.1, \"#c51b7d\"], [0.2, \"#de77ae\"], [0.3, \"#f1b6da\"], [0.4, \"#fde0ef\"], [0.5, \"#f7f7f7\"], [0.6, \"#e6f5d0\"], [0.7, \"#b8e186\"], [0.8, \"#7fbc41\"], [0.9, \"#4d9221\"], [1, \"#276419\"]], \"sequential\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"sequentialminus\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"title\": {\"text\": \"Percentage error in small angle approximations\", \"x\": 0.5}, \"xaxis\": {\"title\": {\"text\": \"$\\\\frac{\\\\theta}{\\\\circ}$\"}}, \"yaxis\": {\"title\": {\"text\": \"Percentage Error\"}}},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('cc809769-87fe-43a8-bdf7-e0e36e2f2897');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import plotly.graph_objects as go\n",
    "# What about the small angle assumption?\n",
    "\n",
    "# We often use the small angle assumption in aerodynamics, but have you over looked at its validity?\n",
    "# You also may not have seen the arctangent small angle assumption\n",
    "\n",
    "angle = np.linspace(.1, 50, 1000)\n",
    "rangle = np.radians(angle)\n",
    "sin = np.sin(rangle)\n",
    "cos = np.cos(rangle)\n",
    "tan = np.tan(rangle)\n",
    "\n",
    "sin_error = (rangle - sin)/sin*100\n",
    "cos_error = (1 - cos)/cos*100\n",
    "tan_error = (rangle - tan)/tan*100\n",
    "\n",
    "fig = go.Figure()\n",
    "\n",
    "\n",
    "fig.add_trace(go.Scatter(x=angle, y=sin_error,\n",
    "    mode='lines', name='$\\\\theta - \\\\sin\\\\theta$'))\n",
    "fig.add_trace(go.Scatter(x=angle, y=cos_error,\n",
    "    mode='lines', name='$1-\\\\cos\\\\theta$'))\n",
    "fig.add_trace(go.Scatter(x=angle, y=tan_error,\n",
    "    mode='lines', name='$\\\\theta-\\\\tan\\\\theta$'))\n",
    "\n",
    "fig.update_layout(\n",
    "    title='Percentage error in small angle approximations', title_x=0.5,\n",
    "    xaxis_title=\"$\\\\frac{\\\\theta}{\\circ}$\",\n",
    "    yaxis_title=\"Percentage Error\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The change in the lift produced at the wing element is\n",
    "\n",
    "$$dC_L^\\prime = a_w\\cdot\\alpha^\\prime\\simeq a_w\\frac{y\\,P}{V_\\infty}$$\n",
    "\n",
    "The change in the elemental lift, $dL_{lift}$\n",
    "```{margin} $dL_{lift}$??\n",
    "This isn't standard nomenclature, but included here to make it *really* clear that this is lift and not rolling moment.\n",
    "```\n",
    "$$dL_{lift}=a_w\\frac{y\\,P}{V_\\infty}q_\\infty\\,c$$\n",
    "\n",
    "which gives a contribution to the rolling moment, $dL$ recalling that $L$ is positive starboard down, so the lift above produces a negative rolling moment\n",
    "\n",
    "$$dL = -y\\cdot a_w\\frac{y\\,P}{V_\\infty}q_\\infty\\,c$$\n",
    "\n",
    "which is integrated from wingtip to wingtip to give the total rolling moment, $L$, assuming a constant chord\n",
    "\n",
    "$$L=\\int^{\\frac{b}{2}}_{-\\frac{b}{2}}dL\\,\\text{d}y=-\\int^{\\frac{b}{2}}_{-\\frac{b}{2}}a_w\\,y^2\\frac{P}{V_\\infty}q_\\infty\\,c\\,\\text{d}y=-a_w\\frac{b^3}{12}\\frac{P}{V_\\infty}q_\\infty\\,c$$\n",
    "\n",
    "The above expression is only valid for a rectangular wing, else the chord needs to be represented as a function of the span - this is covered well in McCormick's textbook but is an exercise in algebra and calculus that we don't need here.\n",
    "\n",
    "From the definition of the rolling moment coefficient, noting that for a rectangular wing, $S=b\\,c$\n",
    "\n",
    "$$C_\\ell=-a_w\\frac{b\\,P}{12\\,V_\\infty}=-\\frac{a_w}{6}\\bar{p}$$\n",
    "\n",
    "and hence the roll damping is \n",
    "\n",
    "$$C_{\\ell_\\bar{p}}=\\frac{\\partial C_\\ell}{\\partial\\bar{p}}=-\\frac{a_w}{6}$$\n",
    "\n",
    "For a tapered wing, with $\\lambda=\\frac{c_t}{c_0}$ [(recall $\\lambda$ definition)](wing-parameters), McCormick gives:\n",
    "\n",
    "$$C_{\\ell_\\bar{p}}=\\frac{\\partial C_\\ell}{\\partial\\bar{p}}=-\\frac{a_w}{12}\\frac{1+3\\lambda}{1+\\lambda}$$\n",
    "\n",
    "Substitution of $\\lambda=1$ for the rectangular wing into the above confirms the result found.\n",
    "\n",
    "It can be observed that for this estimate the roll damping derivative is proportional the main wing lift curve slope, and inversely proportional to the taper ratio. Since\n",
    "\n",
    "$$\\frac{\\partial C_\\ell}{\\partial P} = \\frac{\\partial C_\\ell}{\\partial\\bar{p}}\\frac{\\partial\\bar{p}}{\\partial P}=\\frac{\\partial C_\\ell}{\\partial\\bar{p}}\\frac{b}{2\\,V_\\infty}$$\n",
    "\n",
    "you can further see that the roll damping is proportional to the wingspan, which makes sense due to the greater moment arm. You will also see that the roll damping is inversely proportional to the flightspeed which, again, makes sense - with a greater $V_\\infty$, the change in sectional angle of attack due to a given $P$ is smaller."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}