gtsam/python/gtsam/examples/RangeISAMExample_plaza2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "GTSAM Copyright 2010-2022, Georgia Tech Research Corporation,\n",
    "Atlanta, Georgia 30332-0415\n",
    "All Rights Reserved\n",
    "\n",
    "Authors: Frank Dellaert, et al. (see THANKS for the full author list)\n",
    "\n",
    "See LICENSE for the license information\n",
    "\n",
    "A 2D Range SLAM example, with iSAM and smart range factors\n",
    "\n",
    "Author: Frank Dellaert"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data is second UWB ranging dataset, B2 or \"plaza 2\", from\n",
    "\n",
    "> \"Navigating with Ranging Radios: Five Data Sets with Ground Truth\", by Joseph Djugash, Bradley Hamner, and Stephan Roth, available at https://www.ri.cmu.edu/pub_files/2009/9/Final_5datasetsRangingRadios.pdf\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pylint: disable=invalid-name, E1101\n",
    "\n",
    "from gtsam import Point2, Pose2\n",
    "import plotly.express as px\n",
    "import numpy as np\n",
    "import gtsam\n",
    "import math\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from gtsam.utils import plot\n",
    "from numpy.random import default_rng\n",
    "\n",
    "rng = default_rng()\n",
    "\n",
    "NM = gtsam.noiseModel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Read 4090 odometry entries.\n"
     ]
    }
   ],
   "source": [
    "# load the odometry\n",
    "# DR: Odometry Input (delta distance traveled and delta heading change)\n",
    "#    Time (sec)  Delta Distance Traveled (m) Delta Heading (rad)\n",
    "odometry = {}\n",
    "data_file = gtsam.findExampleDataFile(\"Plaza2_DR.txt\")\n",
    "for row in np.loadtxt(data_file):\n",
    "    t, distance_traveled, delta_heading = row\n",
    "    odometry[t] = Pose2(distance_traveled, 0, delta_heading)\n",
    "M = len(odometry)\n",
    "print(f\"Read {M} odometry entries.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Read 1816 range triples.\n"
     ]
    }
   ],
   "source": [
    "# load the ranges from TD\n",
    "#    Time (sec)  Sender / Antenna ID Receiver Node ID  Range (m)\n",
    "triples = []\n",
    "data_file = gtsam.findExampleDataFile(\"Plaza2_TD.txt\")\n",
    "for row in np.loadtxt(data_file):\n",
    "    t, sender, receiver, _range = row\n",
    "    triples.append((t, int(receiver), _range))\n",
    "K = len(triples)\n",
    "print(f\"Read {K} range triples.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# parameters\n",
    "minK = 150  # minimum number of range measurements to process initially\n",
    "incK = 25  # minimum number of range measurements to process after\n",
    "robust = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set Noise parameters\n",
    "priorSigmas = gtsam.Point3(1, 1, math.pi)\n",
    "odoSigmas = gtsam.Point3(0.05, 0.01, 0.1)\n",
    "sigmaR = 100        # range standard deviation\n",
    "\n",
    "priorNoise = NM.Diagonal.Sigmas(priorSigmas)  # prior\n",
    "looseNoise = NM.Isotropic.Sigma(2, 1000)     # loose LM prior\n",
    "odoNoise = NM.Diagonal.Sigmas(odoSigmas)     # odometry\n",
    "gaussian = NM.Isotropic.Sigma(1, sigmaR)     # non-robust\n",
    "tukey = NM.Robust.Create(NM.mEstimator.Tukey.Create(15), gaussian)  # robust\n",
    "rangeNoise = tukey if robust else gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ": cliques: 0, variables: 0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Initialize iSAM\n",
    "isam = gtsam.ISAM2()\n",
    "print(isam)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NonlinearFactorGraph: size: 1\n",
      "\n",
      "Factor 0: PriorFactor on 0\n",
      "  prior mean:  (-34.208649, 45.300764, 1.12050365)\n",
      "  noise model: diagonal sigmas[1; 1; 3.14159265];\n",
      "\n",
      " Values with 1 values:\n",
      "Value 0: (gtsam::Pose2)\n",
      "(-34.208649, 45.300764, 1.12050365)\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Add prior on first pose\n",
    "pose0 = Pose2(-34.2086489999201, 45.3007639991120, math.pi - 2.021089)\n",
    "newFactors = gtsam.NonlinearFactorGraph()\n",
    "newFactors.addPriorPose2(0, pose0, priorNoise)\n",
    "initial = gtsam.Values()\n",
    "initial.insert(0, pose0)\n",
    "print(newFactors, initial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding landmark L1\n",
      "Adding landmark L6\n",
      "Adding landmark L0\n",
      "Adding landmark L5\n",
      "Initializing at time 151\n"
     ]
    }
   ],
   "source": [
    "# set some loop variables\n",
    "i = 1  # step counter\n",
    "k = 0  # range measurement counter\n",
    "initialized = False\n",
    "lastPose = pose0\n",
    "countK = 0\n",
    "\n",
    "initializedLandmarks = set()\n",
    "\n",
    "# Loop over odometry\n",
    "for t, relative_pose in odometry.items():\n",
    "    # add odometry factor\n",
    "    newFactors.add(gtsam.BetweenFactorPose2(i - 1, i, relative_pose,\n",
    "                                            odoNoise))\n",
    "\n",
    "    # predict pose and add as initial estimate\n",
    "    predictedPose = lastPose.compose(relative_pose)\n",
    "    lastPose = predictedPose\n",
    "    initial.insert(i, predictedPose)\n",
    "\n",
    "    # Check if there are range factors to be added\n",
    "    while (k < K) and (triples[k][0] <= t):\n",
    "        j = triples[k][1]\n",
    "        landmark_key = gtsam.symbol('L', j)\n",
    "        _range = triples[k][2]\n",
    "        newFactors.add(gtsam.RangeFactor2D(\n",
    "            i, landmark_key, _range, rangeNoise))\n",
    "        if landmark_key not in initializedLandmarks:\n",
    "            p = rng.normal(loc=0, scale=100, size=(2,))\n",
    "            initial.insert(landmark_key, p)\n",
    "            print(f\"Adding landmark L{j}\")\n",
    "            initializedLandmarks.add(landmark_key)\n",
    "            # We also add a very loose prior on the landmark in case there is only\n",
    "            # one sighting, which cannot fully determine the landmark.\n",
    "            newFactors.add(gtsam.PriorFactorPoint2(\n",
    "                landmark_key, Point2(0, 0), looseNoise))\n",
    "        k = k + 1\n",
    "        countK = countK + 1\n",
    "\n",
    "    # Check whether to update iSAM 2\n",
    "    if (k > minK) and (countK > incK):\n",
    "        if not initialized:  # Do a full optimize for first minK ranges\n",
    "            print(f\"Initializing at time {k}\")\n",
    "            batchOptimizer = gtsam.LevenbergMarquardtOptimizer(\n",
    "                newFactors, initial)\n",
    "            initial = batchOptimizer.optimize()\n",
    "            initialized = True\n",
    "\n",
    "        isam.update(newFactors, initial)\n",
    "        result = isam.calculateEstimate()\n",
    "        lastPose = result.atPose2(i)\n",
    "        newFactors = gtsam.NonlinearFactorGraph()\n",
    "        initial = gtsam.Values()\n",
    "        countK = 0\n",
    "\n",
    "    i += 1\n",
    "\n",
    "finalResult = isam.calculateEstimate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5476377146882523136: [-35.97329685  26.31658086]\n",
      "5476377146882523137: [-75.1003452   21.01144091]\n",
      "5476377146882523141: [ -1.03876425 -12.13811931]\n",
      "5476377146882523142: [-36.08926944  72.3500464 ]\n"
     ]
    }
   ],
   "source": [
    "# Print optimized landmarks:\n",
    "for j in [0,1,5,6]:\n",
    "    landmark_key = gtsam.symbol('L', j)\n",
    "    p = finalResult.atPoint2(landmark_key)\n",
    "    print(f\"{landmark_key}: {p}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4090, 2)\n"
     ]
    }
   ],
   "source": [
    "# plot positions\n",
    "poses = gtsam.utilities.allPose2s(finalResult)\n",
    "landmarks = gtsam.utilities.extractPoint2(finalResult)\n",
    "positions = np.array([poses.atPose2(key).translation()\n",
    "                     for key in poses.keys()])\n",
    "print(positions.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "hovertemplate": "x=%{x}<br>y=%{y}<extra></extra>",
         "legendgroup": "",
         "marker": {
          "color": "#636efa",
          "symbol": "circle"
         },
         "mode": "markers",
         "name": "",
         "showlegend": false,
         "type": "scattergl",
         "x": [
          -34.20850096446654,
          -34.208238954743685,
          -34.20792902100424,
          -34.20760757184568,
          -34.20738361846996,
          -34.20720176000561,
          -34.20683416597183,
          -34.20650648822083,
          -34.20608935588558,
          -34.20572966544402,
          -34.20539047307245,
          -34.204978189129015,
          -34.204550257854706,
          -34.20419937583317,
          -34.203851648593165,
          -34.20343169052313,
          -34.203042274235045,
          -34.20264363032312,
          -34.2023726490794,
          -34.202098140666784,
          -34.20181134675162,
          -34.20148933862536,
          -34.20121738216338,
          -34.2009080994932,
          -34.20063643983228,
          -34.20034481742374,
          -34.2000696237222,
          -34.19983311428898,
          -34.19961392234484,
          -34.19937365514169,
          -34.199189402854074,
          -34.19900317603461,
          -34.19880114105563,
          -34.19861066740314,
          -34.19837645150039,
          -34.19816029290118,
          -34.19797297627397,
          -34.19781332693034,
          -34.197621612689275,
          -34.19741383124952,
          -34.19727147453903,
          -34.19707929682523,
          -34.196825570993276,
          -34.19668981102975,
          -34.1965642221961,
          -34.196420248329694,
          -34.196235418026966,
          -34.196100527762006,
          -34.19595528348216,
          -34.19577717294135,
          -34.19561281660328,
          -34.19541564722681,
          -34.19522091075678,
          -34.19506867319604,
          -34.19491322906737,
          -34.19475617348167,
          -34.19456738946074,
          -34.19441257759611,
          -34.194305608523415,
          -34.19413890108838,
          -34.19402563257533,
          -34.193871851019416,
          -34.19370503405217,
          -34.19358027267171,
          -34.19344531751981,
          -34.19329006230464,
          -34.19314564970173,
          -34.19281770202517,
          -34.19237269478954,
          -34.19196721038553,
          -34.191578273729284,
          -34.19110684869285,
          -34.19059806524432,
          -34.19014443601172,
          -34.18971520292186,
          -34.18923602362348,
          -34.18869913427268,
          -34.18833003245038,
          -34.18794166622675,
          -34.18751483624891,
          -34.187190230565314,
          -34.18680050834423,
          -34.18632317786081,
          -34.185942639398604,
          -34.18557941319778,
          -34.185093513453985,
          -34.18464292833133,
          -34.184145833297634,
          -34.1835690413308,
          -34.183009218187,
          -34.18245641784577,
          -34.18194165756511,
          -34.181411245583405,
          -34.180842191387,
          -34.18031070625432,
          -34.17977878608106,
          -34.179274141905964,
          -34.178791235572014,
          -34.17844353743938,
          -34.178133542359454,
          -34.17772043770016,
          -34.17732671873731,
          -34.17705071666225,
          -34.17674574279609,
          -34.17648907354066,
          -34.17609695070887,
          -34.175650899786554,
          -34.17532133596385,
          -34.1749278740639,
          -34.1745363562516,
          -34.17415109707245,
          -34.17368635309034,
          -34.173255122177345,
          -34.172899756560206,
          -34.17251040591449,
          -34.172086874520765,
          -34.171630360950736,
          -34.17117119532719,
          -34.17084558026226,
          -34.170524084280146,
          -34.170110063374906,
          -34.16967258385827,
          -34.16930042973883,
          -34.168970613859635,
          -34.16856304460919,
          -34.16811576085387,
          -34.16768676123481,
          -34.16736099295385,
          -34.167124898097356,
          -34.16672691923807,
          -34.16629949645637,
          -34.166020544017336,
          -34.16567348824885,
          -34.165206629486555,
          -34.1649102522274,
          -34.16442554900806,
          -34.16411656055334,
          -34.163835743037595,
          -34.163667960830786,
          -34.163287829216934,
          -34.16288151302674,
          -34.16269395430048,
          -34.16238991455418,
          -34.162026429660955,
          -34.161650280510415,
          -34.16120406524903,
          -34.16081468768969,
          -34.16051969428689,
          -34.16009094929095,
          -34.15946914274596,
          -34.159176862117704,
          -34.15888727213249,
          -34.15848397635331,
          -34.15805064953907,
          -34.15768222447644,
          -34.15741075690409,
          -34.157199236984766,
          -34.15702885116569,
          -34.156646530479655,
          -34.15631433417576,
          -34.15610539694631,
          -34.155873450868484,
          -34.155492955086224,
          -34.15500939848627,
          -34.15434250697164,
          -34.15403249529436,
          -34.15373559707832,
          -34.153195077612814,
          -34.15237223406272,
          -34.151197823002306,
          -34.150389061340434,
          -34.14972355532398,
          -34.14876182425223,
          -34.147753205875084,
          -34.1468315985221,
          -34.14592332052173,
          -34.14499865748368,
          -34.14413081753902,
          -34.14326697595306,
          -34.14235363131009,
          -34.141504566972635,
          -34.140670341648466,
          -34.13977560684852,
          -34.138843663846956,
          -34.13797352118324,
          -34.13704209938618,
          -34.136104337300594,
          -34.13535680475344,
          -34.13475717277114,
          -34.13405664376714,
          -34.13324167350189,
          -34.13239793097516,
          -34.13162108183035,
          -34.13104483686513,
          -34.130370325655754,
          -34.129575170192076,
          -34.12883978107497,
          -34.12818004157837,
          -34.12769342542458,
          -34.12707652242479,
          -34.12625640229815,
          -34.12573308632649,
          -34.1251498038307,
          -34.124445847032156,
          -34.12353836877944,
          -34.122053316887815,
          -34.1211257367895,
          -34.119724360218534,
          -34.11843319269593,
          -34.11718493708246,
          -34.11338507210205,
          -34.10590214862871,
          -34.09282073690137,
          -34.07236785491298,
          -34.04366888084793,
          -34.007605138373535,
          -33.96775324384806,
          -33.92893317560639,
          -33.89642176487315,
          -33.87043613439064,
          -33.85153191238244,
          -33.83740516873628,
          -33.82726615508978,
          -33.820250147386204,
          -33.81406643483115,
          -33.806553260040644,
          -33.79553734291343,
          -33.77741136696219,
          -33.751353316306194,
          -33.71687278795068,
          -33.673404994787944,
          -33.62118686393082,
          -33.56068922257415,
          -33.49143699335243,
          -33.412834311016205,
          -33.3237099791763,
          -33.22310971008737,
          -33.11154866410422,
          -32.990842000614734,
          -32.86212511539496,
          -32.72309606849177,
          -32.57062017013406,
          -32.40851697353658,
          -32.23720250997644,
          -32.05784746076087,
          -31.866728622723116,
          -31.666281580501536,
          -31.45888722393481,
          -31.236188791114166,
          -31.006924763292396,
          -30.77239936272471,
          -30.52223313580673,
          -30.2651984576044,
          -30.000474598875655,
          -29.731386707719196,
          -29.452770053026384,
          -29.16946897839721,
          -28.89232263981253,
          -28.60861583098035,
          -28.320690784708873,
          -28.03548898720037,
          -27.750887893729637,
          -27.462116131387482,
          -27.179759975432518,
          -26.903824475123297,
          -26.631328055718043,
          -26.36043103504407,
          -26.096833531141332,
          -25.850422454635652,
          -25.602392293361373,
          -25.35759661816489,
          -25.14796974324249,
          -24.936472171543887,
          -24.729593124054873,
          -24.537083022661065,
          -24.353155730789634,
          -24.178930832936064,
          -24.00913393888203,
          -23.839729121837294,
          -23.687506229039517,
          -23.537568073364582,
          -23.385293532067568,
          -23.247396754879265,
          -23.113088745898345,
          -22.97788261894402,
          -22.85033600215608,
          -22.7302817180564,
          -22.614875683411867,
          -22.501606043047857,
          -22.39296302095069,
          -22.291124620939094,
          -22.1931172182229,
          -22.10259642363014,
          -22.01442660431957,
          -21.930835891539587,
          -21.854838952711773,
          -21.785225767526434,
          -21.71575024868301,
          -21.648654064018306,
          -21.584573001491112,
          -21.520141220887233,
          -21.45177011272198,
          -21.384492813439486,
          -21.318955993291997,
          -21.25214802678836,
          -21.183657070739866,
          -21.119719849680337,
          -21.054127260365053,
          -20.983247893375697,
          -20.91436578568897,
          -20.84846061043535,
          -20.77885808389792,
          -20.70787520393427,
          -20.64043121965617,
          -20.567976117179327,
          -20.49802638852945,
          -20.425461212722524,
          -20.35479298424054,
          -20.282674033670123,
          -20.20903252554625,
          -20.137397231124215,
          -20.064022256051153,
          -19.989043931523284,
          -19.90910114815038,
          -19.83232039990529,
          -19.753511678281324,
          -19.669105733913366,
          -19.583314519263745,
          -19.494616842451236,
          -19.40443270134451,
          -19.310538831842955,
          -19.213843720805905,
          -19.115886189028437,
          -19.01472079114958,
          -18.911519476095137,
          -18.806724464509383,
          -18.699383897195215,
          -18.587828190276884,
          -18.475139327437294,
          -18.358508133023715,
          -18.23250049997659,
          -18.107209041615686,
          -17.97898633278654,
          -17.839883042643052,
          -17.69648363507199,
          -17.551859605023964,
          -17.39543380713658,
          -17.234970818650286,
          -17.070046627768086,
          -16.896655854204827,
          -16.72189078956723,
          -16.53903862823957,
          -16.345578366064313,
          -16.15040970857468,
          -15.949004036301039,
          -15.73409882318099,
          -15.520776286461096,
          -15.301925922368234,
          -15.070678004620648,
          -14.843307150651425,
          -14.613679045242476,
          -14.375157473101241,
          -14.139389072791404,
          -13.904988476433443,
          -13.661150612368795,
          -13.41707736541694,
          -13.180820011095541,
          -12.940189575595827,
          -12.700155724224805,
          -12.46287048059889,
          -12.225978074095101,
          -11.983676868668432,
          -11.741119724603255,
          -11.498800839246972,
          -11.257118257374717,
          -11.01223198786857,
          -10.771316621036691,
          -10.531816609803048,
          -10.289242645492118,
          -10.051094210070056,
          -9.813321328273139,
          -9.572194435045677,
          -9.335290205071642,
          -9.103435364388192,
          -8.870725952526021,
          -8.643668752575262,
          -8.425262228892867,
          -8.180860199005918,
          -7.957839554013466,
          -7.742057345061757,
          -7.528013744629356,
          -7.314109479110836,
          -7.103808525252691,
          -6.898801427447551,
          -6.693570821226059,
          -6.493186831966468,
          -6.296214106306464,
          -6.099657869405394,
          -5.908827113614065,
          -5.715615709860129,
          -5.521984170694302,
          -5.332461478571686,
          -5.143684708007091,
          -4.953569959626599,
          -4.772259464875152,
          -4.599443535946358,
          -4.422658612841595,
          -4.25775388602834,
          -4.1065418176812125,
          -3.954217993435107,
          -3.8120387751928058,
          -3.684418011623918,
          -3.560233442270346,
          -3.4467609954925646,
          -3.347455125665888,
          -3.256983334164835,
          -3.1818452917066,
          -3.119373397337299,
          -3.0677831078079105,
          -3.031257649766328,
          -3.0084601096112937,
          -2.999507935999349,
          -3.0054698298286207,
          -3.0281236342209943,
          -3.0700352925929155,
          -3.128581122683889,
          -3.204051529859299,
          -3.29715812617134,
          -3.410492761151179,
          -3.548730766585928,
          -3.7148238763535497,
          -3.892215883500358,
          -4.08410985314791,
          -4.303713350962656,
          -4.53199807872445,
          -4.769603912150116,
          -5.039499581466397,
          -5.317875891463045,
          -5.594221969919161,
          -5.890632592115414,
          -6.198945169797842,
          -6.511674328245961,
          -6.833766739908534,
          -7.159226307604196,
          -7.485880834688631,
          -7.8213576057842005,
          -8.155947721189817,
          -8.490831353136372,
          -8.82915319130515,
          -9.167136649612592,
          -9.50351549191835,
          -9.844389215804224,
          -10.179525657340298,
          -10.515272701348366,
          -10.853513119276752,
          -11.186384006918765,
          -11.51885458278919,
          -11.853887739779578,
          -12.186218771001966,
          -12.518838054018211,
          -12.85379646413921,
          -13.192524168500752,
          -13.531297475935212,
          -13.87278381731817,
          -14.216843064780582,
          -14.565137202540603,
          -14.916964860695987,
          -15.276638133253954,
          -15.649521404743567,
          -16.023504645043484,
          -16.399218438899965,
          -16.787539834221676,
          -17.17487956619213,
          -17.55780193233755,
          -17.953415497509326,
          -18.36193162941352,
          -18.753242349393854,
          -19.1547288146283,
          -19.57488363759125,
          -19.97196405956268,
          -20.382959986893194,
          -20.808590477926927,
          -21.214446333859488,
          -21.63333896306491,
          -22.063312427305817,
          -22.469330277045458,
          -22.883562574578935,
          -23.30562305116361,
          -23.69693990260586,
          -24.089484082222096,
          -24.508476133226807,
          -24.91173666527541,
          -25.300314654764954,
          -25.714811859707304,
          -26.12548731270093,
          -26.513524431697025,
          -26.921808472447154,
          -27.335390292031736,
          -27.730896380438267,
          -28.135096223390125,
          -28.54305955816263,
          -28.936817600015,
          -29.33587430829889,
          -29.735739337632634,
          -30.131784852729698,
          -30.531510034799926,
          -30.931020949816958,
          -31.328154826694753,
          -31.73203776645058,
          -32.134486553878176,
          -32.54050706752538,
          -32.949192934150325,
          -33.36421956031278,
          -33.7768751678339,
          -34.18940158319885,
          -34.6021492023042,
          -35.01047415651771,
          -35.41171781082104,
          -35.813119692813984,
          -36.215050467039944,
          -36.621893345222226,
          -37.03717132871312,
          -37.46002493725777,
          -37.883741357496945,
          -38.30719995932858,
          -38.72938025987588,
          -39.14924357296815,
          -39.57802315670335,
          -40.01043348825386,
          -40.439590791865776,
          -40.85750222093139,
          -41.27182723776138,
          -41.68831190734649,
          -42.104015239877675,
          -42.52170843545669,
          -42.93599499431075,
          -43.354357210777145,
          -43.7750624616118,
          -44.180848445444646,
          -44.58812097321755,
          -45.007713562651716,
          -45.417312323038956,
          -45.82621709698976,
          -46.24179036897837,
          -46.659494896046056,
          -47.0695288423755,
          -47.476973756636134,
          -47.88445074356961,
          -48.28357380372633,
          -48.67844143188854,
          -49.08561638451694,
          -49.48706722067271,
          -49.877482019089115,
          -50.279156256808044,
          -50.676273600636236,
          -51.053999874666324,
          -51.447405905939775,
          -51.835994120984935,
          -52.21242997655724,
          -52.60506604706158,
          -52.998686597981106,
          -53.37501814955399,
          -53.768167517412685,
          -54.159168318936786,
          -54.53551172277161,
          -54.92985669052983,
          -55.31894439666703,
          -55.69133528047126,
          -56.07482392120389,
          -56.444863159140716,
          -56.81320710027343,
          -57.19053508956895,
          -57.56215251701041,
          -57.93099347502464,
          -58.30172428484685,
          -58.664305554440965,
          -59.025359706567336,
          -59.39829137353854,
          -59.7582141542276,
          -60.124530748974514,
          -60.4908578766057,
          -60.83505696904816,
          -61.18130885226007,
          -61.52499966132512,
          -61.83836490363596,
          -62.158196325612444,
          -62.47435398172692,
          -62.76534189619135,
          -63.05109916028611,
          -63.32856523564792,
          -63.59049106119492,
          -63.83443997198932,
          -64.07088373841837,
          -64.29533435273933,
          -64.50526421490805,
          -64.7052822956055,
          -64.88974984865094,
          -65.06757453538047,
          -65.23988864735162,
          -65.39869442920023,
          -65.54776860045122,
          -65.68685907210161,
          -65.81838416625914,
          -65.9438257267132,
          -66.0586877840251,
          -66.16983067614979,
          -66.2802816919717,
          -66.3794524945481,
          -66.47116560935949,
          -66.5580783084223,
          -66.63414777564289,
          -66.7028493866808,
          -66.76637121729858,
          -66.81648907329419,
          -66.85396394868584,
          -66.88622644304414,
          -66.9069131925393,
          -66.91060786059475,
          -66.89911095628779,
          -66.87390242235816,
          -66.83644811340965,
          -66.7854338571656,
          -66.71980373895558,
          -66.6393075249817,
          -66.54347632615395,
          -66.43556800084674,
          -66.31751313422161,
          -66.1879628899378,
          -66.0492213591998,
          -65.90249473180852,
          -65.74234707643778,
          -65.56934163451142,
          -65.38876145051714,
          -65.20278639422463,
          -65.00492563650491,
          -64.80032711231964,
          -64.60508760719165,
          -64.39640405531888,
          -64.17347324859307,
          -63.96347278695096,
          -63.74783369003469,
          -63.50827319197837,
          -63.27817201058187,
          -63.049125731267196,
          -62.79906825605081,
          -62.55571846530885,
          -62.314009308642575,
          -62.06057816611769,
          -61.812002866040984,
          -61.568008672865844,
          -61.31977697955609,
          -61.07544160626518,
          -60.83338909845368,
          -60.58843697818208,
          -60.342020309956226,
          -60.0982834257727,
          -59.854435946413936,
          -59.614697844411104,
          -59.37731347930396,
          -59.1442368134974,
          -58.907917683733785,
          -58.67663687502402,
          -58.44415651110442,
          -58.2105060936788,
          -57.98171333830625,
          -57.75986034582937,
          -57.53099620873651,
          -57.31742354180103,
          -57.11094708789625,
          -56.89404473721648,
          -56.686883256420124,
          -56.47789349938912,
          -56.25906193982285,
          -56.04874031747729,
          -55.838189439977356,
          -55.60030507722978,
          -55.389217653260076,
          -55.18088735036473,
          -54.964419297405115,
          -54.74251225436768,
          -54.526641540244455,
          -54.309039392756404,
          -54.08466206621436,
          -53.864323502833976,
          -53.64917961946586,
          -53.42760336382845,
          -53.20497730544819,
          -52.98581775877011,
          -52.76052182351032,
          -52.53402751945837,
          -52.3150187111637,
          -52.09446139112003,
          -51.875301855406015,
          -51.66458491630855,
          -51.44880184949696,
          -51.23583887481144,
          -51.024251639441495,
          -50.8071041651678,
          -50.584758876264836,
          -50.35673439549038,
          -50.1297573599387,
          -49.89796426630089,
          -49.6561733825751,
          -49.408897775010146,
          -49.158956206097,
          -48.907045966962926,
          -48.65259274481218,
          -48.39660932186194,
          -48.14165349692995,
          -47.89462459547674,
          -47.649591173534326,
          -47.40018989835032,
          -47.153616860328476,
          -46.910162188884115,
          -46.66125059392396,
          -46.41004047357298,
          -46.160765219588185,
          -45.91311081595627,
          -45.66671801274094,
          -45.40747481662267,
          -45.15426593717196,
          -44.909388930303805,
          -44.647962917352636,
          -44.38667975642351,
          -44.146999413931816,
          -43.889502030617585,
          -43.61894147724354,
          -43.365040674727965,
          -43.10397341963339,
          -42.82173856681402,
          -42.54942670163961,
          -42.29427549203657,
          -42.01245170382104,
          -41.72086995614185,
          -41.44495855163145,
          -41.14649300925449,
          -40.83513244019241,
          -40.53309408854726,
          -40.217082860406435,
          -39.899885571661386,
          -39.58322762333115,
          -39.25927891824996,
          -38.929237385790294,
          -38.60501927350662,
          -38.26979751771763,
          -37.9385310519133,
          -37.61768400267112,
          -37.277203470340076,
          -36.93210187510192,
          -36.5989670409393,
          -36.2605671033598,
          -35.917965476399594,
          -35.58097928977165,
          -35.25319314601881,
          -34.92046457703637,
          -34.60122646328586,
          -34.29598638239527,
          -33.98750709553549,
          -33.68152469734872,
          -33.39455183864643,
          -33.105969452117364,
          -32.81664183529315,
          -32.54062425940163,
          -32.26072655522608,
          -31.99050060497156,
          -31.72877191156155,
          -31.468227199983055,
          -31.21843403205665,
          -30.977134869050094,
          -30.744551200538588,
          -30.520450877430214,
          -30.306724802221535,
          -30.101948932135542,
          -29.90258558513699,
          -29.711945872526478,
          -29.52797590846506,
          -29.350878727858255,
          -29.18247502170537,
          -29.01909000846517,
          -28.861102358688207,
          -28.708252894134002,
          -28.557369426591453,
          -28.409309883669305,
          -28.268708922244162,
          -28.126963558263956,
          -27.984308901106722,
          -27.85100925439488,
          -27.71529717169798,
          -27.576840023148723,
          -27.44251871424342,
          -27.313256895515355,
          -27.180729339362657,
          -27.04782848835487,
          -26.92002153360609,
          -26.790315116923516,
          -26.660100898820513,
          -26.53355776255497,
          -26.405116036858658,
          -26.276057964785224,
          -26.148177020639906,
          -26.02033937766196,
          -25.88848134437824,
          -25.755681789181292,
          -25.624872901363535,
          -25.490242505278097,
          -25.355470932101024,
          -25.22236384459584,
          -25.088800442352564,
          -24.95535322982862,
          -24.82351898930916,
          -24.689119954604983,
          -24.558511466905593,
          -24.425997464165782,
          -24.290544088167824,
          -24.157214348218936,
          -24.021861518407203,
          -23.885871920684064,
          -23.7523139250111,
          -23.619343365392247,
          -23.486278389618853,
          -23.35571588003516,
          -23.227448808905987,
          -23.09791383972981,
          -22.973946373338865,
          -22.853558225518288,
          -22.732734754033817,
          -22.615414309116364,
          -22.50516554436355,
          -22.397252798556945,
          -22.29470452337946,
          -22.194411644474002,
          -22.095695812618867,
          -22.005828463686132,
          -21.918981677629155,
          -21.832796787388066,
          -21.748707256505124,
          -21.6700995782513,
          -21.588476863832106,
          -21.502785620624614,
          -21.42035927917382,
          -21.33895745261171,
          -21.25746798767443,
          -21.173432789420303,
          -21.093717056254025,
          -21.01421380814389,
          -20.92910815212903,
          -20.845431538646466,
          -20.763570632347665,
          -20.683981750056073,
          -20.605257257783588,
          -20.527823423418333,
          -20.450680999068584,
          -20.37330676600147,
          -20.297762528648224,
          -20.22249251447037,
          -20.149339684754093,
          -20.07675386335212,
          -20.001966877314885,
          -19.930592511200402,
          -19.85838426092376,
          -19.784511919787423,
          -19.71074907849777,
          -19.641326428023383,
          -19.57203711207824,
          -19.499837444978393,
          -19.419880274945527,
          -19.3467494212837,
          -19.270347377065946,
          -19.18931053505767,
          -19.105591213435552,
          -19.01875416637844,
          -18.92788485237338,
          -18.8336186850511,
          -18.73710595657461,
          -18.634141549797043,
          -18.525922295281873,
          -18.413488281084675,
          -18.296599974487968,
          -18.171392414075658,
          -18.040355925748102,
          -17.910027118057833,
          -17.77338992847017,
          -17.629885914394755,
          -17.487061658089928,
          -17.339625102593942,
          -17.18249906920041,
          -17.027878626052093,
          -16.873170781463866,
          -16.706255793779288,
          -16.540318732606554,
          -16.376606673490276,
          -16.2001022273604,
          -16.023159396344724,
          -15.850571060076042,
          -15.664271270944365,
          -15.475896287314427,
          -15.298426651813514,
          -15.091561042812065,
          -14.892259901334407,
          -14.705024033893125,
          -14.512483072769651,
          -14.305026564216309,
          -14.10519411144605,
          -13.903524572486049,
          -13.692464657487488,
          -13.483742809265246,
          -13.274246955139253,
          -13.059759920135956,
          -12.84455403674611,
          -12.627799045360609,
          -12.409685667361273,
          -12.1924413750488,
          -11.970868912787585,
          -11.7464236450359,
          -11.522442826727415,
          -11.295977029960582,
          -11.067532313046188,
          -10.839099112981014,
          -10.61717452483189,
          -10.388719073544767,
          -10.16158941914945,
          -9.937843429918663,
          -9.708727087611281,
          -9.480656932105369,
          -9.253151528476407,
          -9.026050056669934,
          -8.799426062753268,
          -8.577421694627647,
          -8.356533192411291,
          -8.134179831465978,
          -7.912744714117008,
          -7.694252414226817,
          -7.476803140464561,
          -7.259360915045362,
          -7.045289914935967,
          -6.835186557510802,
          -6.6243444886204585,
          -6.419611856274912,
          -6.2210353157285665,
          -6.02486892025979,
          -5.83073140440032,
          -5.640612261893859,
          -5.4562844787822256,
          -5.269901658356259,
          -5.084882915776098,
          -4.898135437540016,
          -4.714547937466565,
          -4.533587236559559,
          -4.3288310694700245,
          -4.143397569531199,
          -3.967343203614429,
          -3.7935401456925155,
          -3.619734248375605,
          -3.450697890446953,
          -3.2925389530276097,
          -3.1389235386498022,
          -2.990376432907575,
          -2.8535680191276174,
          -2.7222266067770535,
          -2.6005019413857395,
          -2.497352417612733,
          -2.4000035272737996,
          -2.3089878530450045,
          -2.2337449494523565,
          -2.1701904299675587,
          -2.1159681678033944,
          -2.074625610913162,
          -2.045475535555629,
          -2.029161475575345,
          -2.026358986910275,
          -2.0371416488528715,
          -2.0618610307693253,
          -2.100938228557439,
          -2.155907372425467,
          -2.2255863659585926,
          -2.3095800842277896,
          -2.407399203609409,
          -2.5225881586497594,
          -2.6630509837274308,
          -2.8185007212722084,
          -2.986035983338265,
          -3.183263172760066,
          -3.397533865505796,
          -3.619823420106108,
          -3.8637291704136136,
          -4.124021877019453,
          -4.390613092861507,
          -4.6773400070370545,
          -4.975224485938064,
          -5.27345518278105,
          -5.587907304664719,
          -5.911992859510572,
          -6.230762785194832,
          -6.55513967648047,
          -6.886529345227692,
          -7.206733306233928,
          -7.5352635724096775,
          -7.869206688399662,
          -8.189496714942116,
          -8.513422442809402,
          -8.83988899464593,
          -9.152968752423135,
          -9.466355174354861,
          -9.780120593229137,
          -10.087283830882374,
          -10.391203247701847,
          -10.695466047400185,
          -10.997952737530179,
          -11.2968763513574,
          -11.59695340044311,
          -11.89762892723237,
          -12.199047458639765,
          -12.503552294087825,
          -12.810250490063101,
          -13.123043937553804,
          -13.436433210200024,
          -13.751874414867586,
          -14.071036938215897,
          -14.390312532211357,
          -14.712179025001948,
          -15.03737136375139,
          -15.36352784876661,
          -15.695121715030757,
          -16.026625347948894,
          -16.355412133457943,
          -16.69674625962069,
          -17.033640657897166,
          -17.369267607448105,
          -17.704054002405943,
          -18.054108663868952,
          -18.40259955279605,
          -18.736412744667824,
          -19.091415333251987,
          -19.449470775356403,
          -19.79053783368905,
          -20.142884001997782,
          -20.511361012524375,
          -20.864014383527227,
          -21.220138142465128,
          -21.592449615714653,
          -21.95105644301703,
          -22.306083533920376,
          -22.67429333385156,
          -23.037392076997108,
          -23.393195909901355,
          -23.75368144445266,
          -24.12053574396884,
          -24.482355018737177,
          -24.84277917128603,
          -25.20546346341832,
          -25.57296965523862,
          -25.933788732782507,
          -26.295052429160425,
          -26.66664627437255,
          -27.035480756971413,
          -27.399127734923916,
          -27.769060923278527,
          -28.146037446226607,
          -28.51169084023298,
          -28.87468841939414,
          -29.24624414963434,
          -29.604713050167096,
          -29.962627439354968,
          -30.32445985346866,
          -30.681273837093627,
          -31.03950346961145,
          -31.39679867260935,
          -31.748219274989207,
          -32.10410935222879,
          -32.46541736589728,
          -32.821335797797595,
          -33.1796506882653,
          -33.54110010763142,
          -33.89853684918133,
          -34.25586492273972,
          -34.61612883746897,
          -34.97040605630931,
          -35.31793899655061,
          -35.672835745619764,
          -36.01812177167872,
          -36.36670621473768,
          -36.72506259706506,
          -37.08436397400378,
          -37.44385573591024,
          -37.816975636283104,
          -38.18916070593347,
          -38.55455601119412,
          -38.92460038130979,
          -39.299503653654085,
          -39.66411577470547,
          -40.03225720112146,
          -40.40549389662069,
          -40.76736290191831,
          -41.12269769746697,
          -41.482852300709595,
          -41.84225629509178,
          -42.1938791629395,
          -42.55609226584854,
          -42.91934939165613,
          -43.27528231397707,
          -43.636636751629936,
          -43.99890114014338,
          -44.34786787571027,
          -44.701227001123364,
          -45.05899890206312,
          -45.412497155596654,
          -45.761181757254725,
          -46.11438109125427,
          -46.468353171673265,
          -46.820220999222904,
          -47.16840113637365,
          -47.51786808464334,
          -47.86888628608643,
          -48.21737330898203,
          -48.56310893062025,
          -48.91521831222494,
          -49.272464591852795,
          -49.62173762377014,
          -49.96970628222811,
          -50.32443776675892,
          -50.67498731428199,
          -51.012205085006684,
          -51.35865074123352,
          -51.706623319588275,
          -52.043596672557385,
          -52.38645600411932,
          -52.73627141639067,
          -53.07957442147244,
          -53.41971349747408,
          -53.77095151892777,
          -54.114957890414765,
          -54.45019496610639,
          -54.79856140679166,
          -55.146660878574004,
          -55.48081222853083,
          -55.81990923461163,
          -56.16331143241947,
          -56.494210845184845,
          -56.82777955894273,
          -57.166836628774895,
          -57.49731944828853,
          -57.82638527590838,
          -58.15808213867223,
          -58.48476491883403,
          -58.803442229655566,
          -59.122058537933945,
          -59.444892148310636,
          -59.762422052013186,
          -60.08008914024777,
          -60.40578938497902,
          -60.72188398200776,
          -61.02658827196787,
          -61.33811740634257,
          -61.64817223693242,
          -61.94016895889685,
          -62.23021658249741,
          -62.52097652742526,
          -62.79630336970065,
          -63.06227947815229,
          -63.33040216818478,
          -63.57961685109977,
          -63.824155271857705,
          -64.06078522539734,
          -64.27601863921969,
          -64.48611394439426,
          -64.68291275551678,
          -64.8688910556516,
          -65.05883481493532,
          -65.2295824985437,
          -65.39107094542109,
          -65.55888416912086,
          -65.71953239347093,
          -65.87235787735521,
          -66.02122733852457,
          -66.16097797595631,
          -66.3001078504453,
          -66.43607181753445,
          -66.5649978184758,
          -66.68447963809102,
          -66.80496996462325,
          -66.91749658058505,
          -67.01499682792995,
          -67.10451054468302,
          -67.18398164698797,
          -67.24855957610923,
          -67.30529088716048,
          -67.3489588700816,
          -67.37678516450451,
          -67.39878145401124,
          -67.41350821822829,
          -67.41462716887222,
          -67.4014549685066,
          -67.37738092142811,
          -67.34327272135867,
          -67.29916608466613,
          -67.24443754844559,
          -67.17819032906456,
          -67.09504772459013,
          -67.00028290392237,
          -66.89428747725327,
          -66.77724842495371,
          -66.64867135313715,
          -66.50926243576065,
          -66.36805672868711,
          -66.21853389972787,
          -66.06400771932115,
          -65.90164156157225,
          -65.734632794016,
          -65.56657721606501,
          -65.39037351954278,
          -65.21468008734657,
          -65.03688644861485,
          -64.85251657624295,
          -64.66359622923198,
          -64.47857172903966,
          -64.28603113159828,
          -64.08911541569569,
          -63.89806627292407,
          -63.702733993316485,
          -63.50088321116002,
          -63.29755695886102,
          -63.09161931112981,
          -62.87983162884179,
          -62.6671544312839,
          -62.451920772708206,
          -62.2337393737835,
          -62.0166704822151,
          -61.792339473587255,
          -61.56352323841773,
          -61.33568055930336,
          -61.1016579322237,
          -60.862786281664306,
          -60.62418752885767,
          -60.383963344211935,
          -60.141195225475855,
          -59.901914270296935,
          -59.660478242705985,
          -59.42293859390448,
          -59.18513332557597,
          -58.941345177919416,
          -58.7002959173493,
          -58.46433951249894,
          -58.22189301364764,
          -57.986011878624765,
          -57.75913529554494,
          -57.52218633547478,
          -57.29423931936483,
          -57.0698705213643,
          -56.837254235681065,
          -56.611813590205564,
          -56.388279414302474,
          -56.15604413982848,
          -55.93087161005591,
          -55.71582916372175,
          -55.48567875695876,
          -55.254269686957365,
          -55.03334941884798,
          -54.80055829621406,
          -54.56311277320943,
          -54.33762906335555,
          -54.10600016746531,
          -53.869014087005894,
          -53.63889286127345,
          -53.40369522408548,
          -53.16219284132628,
          -52.931527826394884,
          -52.703625976211065,
          -52.47509795814298,
          -52.25330743116507,
          -52.03453983917092,
          -51.82054456648979,
          -51.602559678881605,
          -51.384751277985615,
          -51.162011385075836,
          -50.93741702373425,
          -50.71615399273452,
          -50.48993478386764,
          -50.25605295810436,
          -50.021506529335404,
          -49.788406338011605,
          -49.54634219897052,
          -49.30882398784405,
          -49.078007785005084,
          -48.843338943819056,
          -48.61757268965913,
          -48.39566728328335,
          -48.160147679826615,
          -47.91391012701571,
          -47.681482808142384,
          -47.445264365310344,
          -47.19521380793525,
          -46.94829331667921,
          -46.705173200194736,
          -46.45590249097712,
          -46.19414798768018,
          -45.938591625021985,
          -45.69135464833386,
          -45.436556691036294,
          -45.1700352242094,
          -44.9193464817555,
          -44.66370427821693,
          -44.38462162809643,
          -44.10928850903636,
          -43.84475633329836,
          -43.56101912259667,
          -43.26916780925776,
          -43.00215538749537,
          -42.730103248848714,
          -42.43255454426534,
          -42.14271369274558,
          -41.85100933746453,
          -41.53016148815435,
          -41.210831215664115,
          -40.88815509054743,
          -40.5510344005366,
          -40.21464673634862,
          -39.873850051081675,
          -39.521198215048955,
          -39.17320252466675,
          -38.81390435094139,
          -38.45129600828928,
          -38.0975338708504,
          -37.73035353362482,
          -37.35950643773611,
          -36.99679419638933,
          -36.632887522917756,
          -36.26406605379358,
          -35.91209689382184,
          -35.565609465375076,
          -35.21445744958684,
          -34.89036309066244,
          -34.57407088684302,
          -34.24588188342661,
          -33.94459584976613,
          -33.647373976645035,
          -33.34684672071522,
          -33.0639932380401,
          -32.78837738725645,
          -32.5060827451208,
          -32.233616178662146,
          -31.974568655034858,
          -31.715857675406586,
          -31.461831254485197,
          -31.22039968696241,
          -30.987933228162344,
          -30.760172487308616,
          -30.53458248163382,
          -30.314936479045173,
          -30.104151305456135,
          -29.899127412438165,
          -29.697353012702013,
          -29.5040090923272,
          -29.31373973405169,
          -29.123571697693556,
          -28.941167377881264,
          -28.76558256105084,
          -28.587589482188562,
          -28.420649669863987,
          -28.264423190323043,
          -28.103857859423396,
          -27.95094691330261,
          -27.807944638035227,
          -27.660012091095293,
          -27.515775067245535,
          -27.37740325508359,
          -27.236327458306935,
          -27.09665204951298,
          -26.959008262330904,
          -26.818546998844113,
          -26.67694543511828,
          -26.53794803076415,
          -26.39265680223,
          -26.244917938631552,
          -26.099260537815184,
          -25.947248918197815,
          -25.795964651986313,
          -25.645215501942417,
          -25.491078797437968,
          -25.335977085982055,
          -25.181077948821404,
          -25.029432783995343,
          -24.87271441809661,
          -24.71553012384757,
          -24.560659198297937,
          -24.40528157733817,
          -24.25222422438953,
          -24.099913260358807,
          -23.95199826779356,
          -23.80705387831147,
          -23.66389650129534,
          -23.50860153926942,
          -23.377205840182665,
          -23.247375051793995,
          -23.11994141914694,
          -23.000168906362543,
          -22.885095003156678,
          -22.77561164838907,
          -22.671021165335954,
          -22.570048134501,
          -22.475925129539053,
          -22.3871268371147,
          -22.297129381391294,
          -22.208194495110913,
          -22.124045343718752,
          -22.032814062121165,
          -21.938671705458578,
          -21.84945388620275,
          -21.75913901266592,
          -21.66291869108665,
          -21.571842556129557,
          -21.47889433693878,
          -21.377522783740005,
          -21.279676525653205,
          -21.187195966730886,
          -21.092740410870768,
          -21.00013433181636,
          -20.910009128995,
          -20.81803034627194,
          -20.725254572870437,
          -20.635908500377614,
          -20.549458520919444,
          -20.462560882591013,
          -20.375027708946895,
          -20.29179943034236,
          -20.207735550713927,
          -20.123140092350056,
          -20.0422695909282,
          -19.963284652474147,
          -19.882417677939628,
          -19.80006098860956,
          -19.7164917979833,
          -19.629668419272896,
          -19.537748434389247,
          -19.44329916286591,
          -19.343888268147293,
          -19.239331412049115,
          -19.132778184945618,
          -19.019851930988047,
          -18.899693634244414,
          -18.7740222361764,
          -18.64098764588919,
          -18.498694309792743,
          -18.35070991187078,
          -18.201133407197233,
          -18.042508094909714,
          -17.880072443923964,
          -17.714131263705024,
          -17.534272578123293,
          -17.352049855298723,
          -17.166474852006907,
          -16.971031804739926,
          -16.77285335055818,
          -16.57108523614885,
          -16.362789926429176,
          -16.1568502058274,
          -15.945924725414416,
          -15.727011384518159,
          -15.52087926321072,
          -15.308608777976925,
          -15.081023749659833,
          -14.867190488523567,
          -14.65261469516981,
          -14.422873334341448,
          -14.19775737997882,
          -13.97538784029993,
          -13.74029848216648,
          -13.514067712925359,
          -13.305662879590912,
          -13.090133036188979,
          -12.8749084736165,
          -12.66460687077586,
          -12.447283591667928,
          -12.226123652789182,
          -12.008635692779118,
          -11.786103363661667,
          -11.563554636491423,
          -11.336508136336477,
          -11.105139193387451,
          -10.87310897973837,
          -10.641936490991498,
          -10.41504853696415,
          -10.187361287970107,
          -9.959962900483445,
          -9.734518728442552,
          -9.512464440594053,
          -9.289723557559512,
          -9.06962063046247,
          -8.850349641018138,
          -8.629493815200412,
          -8.408026328287127,
          -8.190105732462012,
          -7.977462748886694,
          -7.764403192292031,
          -7.555317194741051,
          -7.353277302203586,
          -7.154073892218664,
          -6.959369532699178,
          -6.772135414139355,
          -6.588362759891173,
          -6.407471870227311,
          -6.230809235740635,
          -6.0514239953809925,
          -5.873849213501359,
          -5.704583332793421,
          -5.517992193649563,
          -5.351842156381033,
          -5.195978546597032,
          -5.0444182955658725,
          -4.89452980585661,
          -4.75265711854504,
          -4.616714693316472,
          -4.478987911620376,
          -4.347586387492915,
          -4.221261991556717,
          -4.094105073197255,
          -3.973620987203808,
          -3.8582581195654524,
          -3.743854038062321,
          -3.6406250204203503,
          -3.543159820531951,
          -3.451697622539284,
          -3.373083583306613,
          -3.302958184860286,
          -3.238454729469617,
          -3.1840381544859695,
          -3.138262606993281,
          -3.101446047905101,
          -3.075092558166955,
          -3.057787655905119,
          -3.051154313913769,
          -3.057541909161938,
          -3.0777058046686556,
          -3.11226177300754,
          -3.1633028148244224,
          -3.2269528478740774,
          -3.3055484962963204,
          -3.411798257575102,
          -3.5327781800075804,
          -3.6598205132349197,
          -3.8042761382970274,
          -3.9637921100409432,
          -4.1343610580237,
          -4.321488710941954,
          -4.5254183007263,
          -4.743492198481461,
          -4.976546490154955,
          -5.217377413034586,
          -5.463944656267498,
          -5.725466210792774,
          -5.9942265008430455,
          -6.266880248401289,
          -6.547174852306351,
          -6.830449296321783,
          -7.140692472535568,
          -7.4244805791327595,
          -7.712915267119155,
          -7.99947758519533,
          -8.287869958446791,
          -8.580775449727524,
          -8.870859696915527,
          -9.158148441959966,
          -9.44699351667771,
          -9.732155623590316,
          -10.014872063053648,
          -10.29775979865664,
          -10.5749857424261,
          -10.852780150019186,
          -11.13579070510385,
          -11.414735024671282,
          -11.691983571243979,
          -12.001988427141596,
          -12.284375625399804,
          -12.56870016424334,
          -12.853058122056988,
          -13.137900260390332,
          -13.42979842600842,
          -13.719020086320706,
          -14.009281632255217,
          -14.301011028445044,
          -14.592116426583539,
          -14.890971598247424,
          -15.184707720545834,
          -15.481093409437367,
          -15.785987358772202,
          -16.092112434469538,
          -16.39191902946486,
          -16.69850670541692,
          -17.0161434213426,
          -17.32450689834855,
          -17.639360481835368,
          -17.952300054487637,
          -18.27492426202884,
          -18.60534648107577,
          -18.923198927697737,
          -19.25420879463818,
          -19.595659059684134,
          -19.922765883100173,
          -20.253464392487235,
          -20.601756971249607,
          -20.942552896658825,
          -21.278023387366545,
          -21.630659974387093,
          -21.981249616001126,
          -22.32017323749989,
          -22.668377046161826,
          -23.05463993470257,
          -23.399669839059996,
          -23.744378497142918,
          -24.093191328550297,
          -24.44436936299327,
          -24.795515704871704,
          -25.14414383087788,
          -25.496241874938153,
          -25.849278367345228,
          -26.20207562252542,
          -26.55782194511243,
          -26.9148884183778,
          -27.273738204083404,
          -27.62996812180062,
          -27.988628487833694,
          -28.343905979595174,
          -28.69105165873182,
          -29.037582666102935,
          -29.38635666555043,
          -29.723594788931088,
          -30.056689528810995,
          -30.398340778637635,
          -30.732889562974144,
          -31.064289829857046,
          -31.399693377691765,
          -31.73114349509177,
          -32.06073470265107,
          -32.39085993270465,
          -32.726477933935236,
          -33.06476388178211,
          -33.39372387206702,
          -33.72672082897999,
          -34.065249854126584,
          -34.39760966485348,
          -34.73058887095751,
          -35.06296182746248,
          -35.38255055373931,
          -35.70814463524432,
          -36.039025349592656,
          -36.35972932359205,
          -36.68348309060314,
          -37.015753113562184,
          -37.34542599091974,
          -37.67911904288027,
          -38.020693570149206,
          -38.36066205243361,
          -38.70234003793076,
          -39.0451492945628,
          -39.39470491993342,
          -39.74042583403011,
          -40.08281748005475,
          -40.43186199005066,
          -40.78057224431363,
          -41.12203865389018,
          -41.46267864179745,
          -41.808416009280755,
          -42.1509228039912,
          -42.49332936056103,
          -42.8435430598219,
          -43.18692325830212,
          -43.52734250106671,
          -43.8776940098036,
          -44.21698436032345,
          -44.556835639299806,
          -44.89983918658318,
          -45.242047277374795,
          -45.5826423524521,
          -45.92626112623457,
          -46.26649535067602,
          -46.60896010384153,
          -46.949825362626704,
          -47.28504508563118,
          -47.62134759487119,
          -47.95862599059289,
          -48.29311570298762,
          -48.62734834939975,
          -48.96608905881075,
          -49.30823556860031,
          -49.64709563386687,
          -49.98457430475821,
          -50.32742155888007,
          -50.66680723085256,
          -50.992571879080906,
          -51.32806674987615,
          -51.6678732874057,
          -51.99491914646086,
          -52.33010756345978,
          -52.67357247262765,
          -53.010980957968805,
          -53.346069446378266,
          -53.693569866543896,
          -54.037595073463436,
          -54.373086426955794,
          -54.72237993359764,
          -55.07397645239609,
          -55.412614130024785,
          -55.75677926690112,
          -56.106190350043306,
          -56.43909434686085,
          -56.77630047366981,
          -57.11950997288579,
          -57.455225540470664,
          -57.78897197103224,
          -58.126435303607316,
          -58.45929014889902,
          -58.78439546632375,
          -59.11397571401777,
          -59.45000916190445,
          -59.77746170812227,
          -60.108321017355244,
          -60.440039735420875,
          -60.751897208358145,
          -61.05539281208393,
          -61.35354119299772,
          -61.643599581934104,
          -61.912007900310435,
          -62.18193003148963,
          -62.44967261244594,
          -62.69734117106019,
          -62.94625825298737,
          -63.1885117669288,
          -63.44629136317529,
          -63.71321495812481,
          -63.96855143572826,
          -64.21750078899412,
          -64.45998084573628,
          -64.69048974510206,
          -64.9097276652017,
          -65.13231715848787,
          -65.33119631774655,
          -65.52088910011457,
          -65.70062746247886,
          -65.8565819388565,
          -66.00708425595732,
          -66.15325504641662,
          -66.28385190357783,
          -66.40717356075399,
          -66.52631527291177,
          -66.62958093381904,
          -66.72924851871147,
          -66.82707187290991,
          -66.91117047812757,
          -66.98971235880302,
          -67.06456025223856,
          -67.1300129744069,
          -67.1889735503678,
          -67.23783511245693,
          -67.27488175592373,
          -67.30723066911459,
          -67.32866615617212,
          -67.33249111606224,
          -67.32121765826327,
          -67.29769196841443,
          -67.26372753216401,
          -67.21770276411456,
          -67.15775947255702,
          -67.08362594093559,
          -66.99374450078747,
          -66.88971886776457,
          -66.7747525958143,
          -66.64499872374087,
          -66.5047908956285,
          -66.35542672806882,
          -66.19544669942078,
          -66.02707019249198,
          -65.8507498384762,
          -65.66671210846613,
          -65.4831662845677,
          -65.29471575998292,
          -65.09597657589894,
          -64.90250498287553,
          -64.70670321752343,
          -64.49651569008526,
          -64.28647349591253,
          -64.0832888223937,
          -63.8636405810657,
          -63.6391231646599,
          -63.4189590613997,
          -63.19149285289527,
          -62.95389538462015,
          -62.71839446630718,
          -62.478440369530034,
          -62.23445317242666,
          -61.98963337497661,
          -61.740036658029396,
          -61.49076695590796,
          -61.241328126844905,
          -60.98683623445296,
          -60.73310879462256,
          -60.477894447425896,
          -60.220686607194,
          -59.96636730543988,
          -59.714213309905475,
          -59.4590148414393,
          -59.20951404769694,
          -58.96006911126184,
          -58.70508896088304,
          -58.45649206354154,
          -58.20666486943769,
          -57.951979833842046,
          -57.70589026616218,
          -57.464689786537754,
          -57.21669082657974,
          -56.980934676128975,
          -56.745921029818305,
          -56.50802576386077,
          -56.276750829476114,
          -56.04317179109562,
          -55.80867142570943,
          -55.57667262122025,
          -55.341456448501326,
          -55.10434011192988,
          -54.877842723637585,
          -54.643498335668696,
          -54.403127624811034,
          -54.168984336643426,
          -53.93372568497106,
          -53.69061024371152,
          -53.45504493834885,
          -53.21811788454279,
          -52.972977071567044,
          -52.72832673016044,
          -52.47843122474741,
          -52.22517971900285,
          -51.97870037637053,
          -51.73492669184909,
          -51.495159189060026,
          -51.25994896995887,
          -51.02679480745267,
          -50.7949423064563,
          -50.56273688923523,
          -50.322646298805935,
          -50.0518369270235,
          -49.80940060456466,
          -49.56274912715791,
          -49.30633051674411,
          -49.048153248661066,
          -48.788574214159524,
          -48.528002933079165,
          -48.26586732939847,
          -48.0063101472052,
          -47.76030630870287,
          -47.52441189578046,
          -47.291128619127235,
          -47.05883153043223,
          -46.82799772148867,
          -46.59482025492095,
          -46.365585376495105,
          -46.11109902775143,
          -45.87727287335853,
          -45.642914140177105,
          -45.40265378491914,
          -45.152736261013686,
          -44.897224738899496,
          -44.65296719519171,
          -44.40939803456398,
          -44.15264580641331,
          -43.90177598054978,
          -43.663467940761436,
          -43.409574537718164,
          -43.149188443721904,
          -42.91191714832933,
          -42.672110917469624,
          -42.423003772869414,
          -42.17677983247791,
          -41.929123357104196,
          -41.67955502117077,
          -41.413873554753664,
          -41.14334513864083,
          -40.86956510701395,
          -40.5741653030368,
          -40.26044947653966,
          -39.94043634888155,
          -39.610520471411476,
          -39.277888904030334,
          -38.93790784879036,
          -38.59248930617415,
          -38.2485112170478,
          -37.89317134392239,
          -37.53036248814005,
          -37.174427806825406,
          -36.85794224453516,
          -36.53845093440649,
          -36.21348196170747,
          -35.89285402641411,
          -35.582396884716175,
          -35.260874017508556,
          -34.95264533947338,
          -34.657933152357934,
          -34.364936308225865,
          -34.06839631466887,
          -33.75798183397996,
          -33.453822376036925,
          -33.15327496730229,
          -32.85245477930143,
          -32.55264967900641,
          -32.25956613718065,
          -31.968360034488466,
          -31.678558658588116,
          -31.395253608918217,
          -31.12487086303531,
          -30.86073486042292,
          -30.596911207466043,
          -30.35094700172187,
          -30.107916916846243,
          -29.86662969238843,
          -29.64140287514268,
          -29.42465730060835,
          -29.20873141950385,
          -29.003208174876242,
          -28.801047166518092,
          -28.598559421673098,
          -28.408279489559504,
          -28.226271545182716,
          -28.04055186945441,
          -27.87096283596155,
          -27.71148765551883,
          -27.546167521352587,
          -27.39230417727304,
          -27.24877580876583,
          -27.09783215893978,
          -26.954937921799782,
          -26.818949965758552,
          -26.681676601821323,
          -26.547398310076627,
          -26.416396387906435,
          -26.285743836643963,
          -26.154399525411,
          -26.028216440474537,
          -25.89718916840326,
          -25.76383098390717,
          -25.63069841007004,
          -25.496061982526225,
          -25.359107458747367,
          -25.224247495385317,
          -25.089574969004996,
          -24.95285873066305,
          -24.819494799318345,
          -24.684718566617278,
          -24.554116616503265,
          -24.419019357854157,
          -24.284172149282224,
          -24.148707793931205,
          -24.01186473981563,
          -23.876342746496064,
          -23.738868073052906,
          -23.601694397583806,
          -23.46532239616867,
          -23.32692643656262,
          -23.18872086142345,
          -23.05105840492789,
          -22.91885948279839,
          -22.785663621276885,
          -22.654800919142524,
          -22.532057954698,
          -22.411929968003665,
          -22.29671530099123,
          -22.186545449912806,
          -22.07959033186948,
          -21.979140273166,
          -21.88559955764864,
          -21.793155405157744,
          -21.701638186393176,
          -21.617775345367917,
          -21.53450567338066,
          -21.44536929480654,
          -21.36241397007175,
          -21.284528674198466,
          -21.205495079814423,
          -21.127556831766018,
          -21.054384220246313,
          -20.97955361232512,
          -20.90073577389424,
          -20.82357507949722,
          -20.74731866628342,
          -20.6711798956272,
          -20.593662158870323,
          -20.515250902662043,
          -20.435299164524103,
          -20.35293541021248,
          -20.268813027999187,
          -20.185173336563242,
          -20.10105356746033,
          -20.0118211480889,
          -19.92464043858409,
          -19.836792297259407,
          -19.747523545570328,
          -19.6571131930019,
          -19.570821403242952,
          -19.486117255630514,
          -19.40006239938822,
          -19.31576568805221,
          -19.230069952903875,
          -19.143307897505597,
          -19.054961879789328,
          -18.965652637571274,
          -18.873872155913173,
          -18.778858428906904,
          -18.68578786711409,
          -18.58738025704817,
          -18.483825961339633,
          -18.381112187414274,
          -18.2740657788208,
          -18.162325042151902,
          -18.04407412307408,
          -17.919854667959843,
          -17.792509316116345,
          -17.66184175675464,
          -17.523915424889008,
          -17.380889757343244,
          -17.23131569457251,
          -17.07543853247107,
          -16.912602931612362,
          -16.742816293028714,
          -16.57246049417901,
          -16.3943147157906,
          -16.212966686173175,
          -16.032686508658802,
          -15.847141521277802,
          -15.651425656594203,
          -15.464992511939615,
          -15.278464908435609,
          -15.072448379880425,
          -14.8761217062947,
          -14.685520947858995,
          -14.480019650318107,
          -14.27821657976232,
          -14.081162336099894,
          -13.878548719850825,
          -13.676114825254635,
          -13.479426329362635,
          -13.281653292041767,
          -13.081932356207679,
          -12.883715506200103,
          -12.679829250555638,
          -12.474074208665568,
          -12.264738759020902,
          -12.052432689037936,
          -11.836503537782825,
          -11.621061684740479,
          -11.401713923807238,
          -11.180083391260311,
          -10.958317772071153,
          -10.731046098698549,
          -10.505790343847037,
          -10.278488349239959,
          -10.047943367741272,
          -9.817561506108019,
          -9.587572898564792,
          -9.35766954806178,
          -9.126937303434898,
          -8.900387525863927,
          -8.67631977764867,
          -8.448014145550228,
          -8.220877478765015,
          -7.998791010097954,
          -7.773894684448212,
          -7.541617244165808,
          -7.320168571875958,
          -7.098763267260314,
          -6.8729716888569605,
          -6.652353600687759,
          -6.43479038495738,
          -6.217797107537136,
          -5.998216552350932,
          -5.776678779729985,
          -5.560223461091686,
          -5.345274024557623,
          -5.127561761243892,
          -4.917491843645876,
          -4.715461570545477,
          -4.505065395882604,
          -4.307361113708217,
          -4.124523779496649,
          -3.9355579397707596,
          -3.7491507672574134,
          -3.5787963356111887,
          -3.406589393198464,
          -3.24175832452202,
          -3.086619820093648,
          -2.930549832146983,
          -2.795652688582039,
          -2.6676514831264004,
          -2.5401125480067064,
          -2.4299029546326705,
          -2.333505659562151,
          -2.2450534950716903,
          -2.17204735922884,
          -2.1128176477362017,
          -2.064530519347138,
          -2.030370074393183,
          -2.010393138338829,
          -2.004138709737753,
          -2.012870078493015,
          -2.0370841526207615,
          -2.0763602872947198,
          -2.131686324194107,
          -2.2055013778985,
          -2.2978840990695226,
          -2.4069163471706303,
          -2.5364879960175424,
          -2.68534378683897,
          -2.848188644199925,
          -3.037611048174019,
          -3.2441099854616016,
          -3.4647746970836804,
          -3.703799504275772,
          -3.9553835254678953,
          -4.218520760246446,
          -4.495366437253349,
          -4.785639833248068,
          -5.08484574406934,
          -5.386986180057311,
          -5.702574899155793,
          -6.024555013090089,
          -6.348233572480257,
          -6.676596928656058,
          -7.002112491822304,
          -7.323535097965916,
          -7.64907641442559,
          -7.974162122243784,
          -8.29329386687016,
          -8.614724092092834,
          -8.967351104418675,
          -9.281004572916306,
          -9.595351486147798,
          -9.906920463817347,
          -10.215609104682294,
          -10.522452460283825,
          -10.822021762894998,
          -11.12167338367002,
          -11.419731886306183,
          -11.71402587006081,
          -12.009303977815186,
          -12.3039125702886,
          -12.59794267786584,
          -12.890491044518715,
          -13.183914504029614,
          -13.481320566748892,
          -13.77774003043691,
          -14.076319692672689,
          -15.135851789820482,
          -15.448746547073267,
          -15.7701082496401,
          -16.09652425161251,
          -16.419857209306667,
          -16.74923535317632,
          -17.087754028882582,
          -17.418509385474984,
          -17.749829044650806,
          -18.081905985797718,
          -18.43035359220856,
          -18.774654053643356,
          -19.111139682495992,
          -19.46983396195551,
          -19.826603384066924,
          -20.169733909783766,
          -20.52679978792883,
          -20.892862525450653,
          -21.24183538689616,
          -21.599351761140987,
          -21.969785438463287,
          -22.3253797601872,
          -22.684291974552025,
          -23.052360362425834,
          -23.41196124967644,
          -23.770153047626177,
          -24.133781319508433,
          -24.50390460074309,
          -24.872779437632673,
          -25.240713528172346,
          -25.613006170135684,
          -25.986125133400538,
          -26.356572373107657,
          -26.732719884490372,
          -27.110898722633916,
          -27.488921639221125,
          -27.867802714125826,
          -28.250522161210075,
          -28.627673559074477,
          -28.999630763154563,
          -29.374260600789675,
          -29.747133847477823,
          -30.108627139695123,
          -30.4738748947489,
          -30.845345249687618,
          -31.20496502543251,
          -31.56838718343814,
          -31.934373093137385,
          -32.29625825293812,
          -32.655795528669486,
          -33.023786562502075,
          -33.394066451795176,
          -33.75437144700971,
          -34.12279959224543,
          -34.49565203273659,
          -34.86116745868966,
          -35.22769623168896,
          -35.58748552490108,
          -35.93626152603457,
          -36.29294327802148,
          -36.64582261485386,
          -36.995657073893845,
          -37.35707992209258,
          -37.719757995762386,
          -38.08279784436257,
          -38.45545006209987,
          -38.82825938742799,
          -39.19826192510871,
          -39.57148727374065,
          -39.94837305387175,
          -40.3131466176835,
          -40.68148435156973,
          -41.053580633180246,
          -41.41471059380327,
          -41.771110999942785,
          -42.13160233797795,
          -42.48929319127417,
          -42.83258211303702,
          -43.17156392946248,
          -43.50777876759926,
          -43.83621764122727,
          -44.17080271291086,
          -44.52739005309362,
          -44.84879118581973,
          -45.172689735288515,
          -45.49298321643188,
          -45.81118501611773,
          -46.13863714923011,
          -46.46773403246215,
          -46.795166887960754,
          -47.1257062847864,
          -47.44813465160126,
          -47.76764993598219,
          -48.086771459399884,
          -48.40222941032584,
          -48.71907808757432,
          -49.03399471655375,
          -49.34354732591616,
          -49.64813474894097,
          -49.94981490289839,
          -50.251862128363726,
          -50.55493943284664,
          -50.85796949254924,
          -51.15180674861884,
          -51.44529451950592,
          -51.74712457823629,
          -52.04292433028553,
          -52.33742608542614,
          -52.64444297727034,
          -52.95310408136931,
          -53.25735769920424,
          -53.559259930307086,
          -53.868186045975776,
          -54.176431125540695,
          -54.478829869137414,
          -54.78500535792089,
          -55.095673466036885,
          -55.40471352965616,
          -55.714435944882986,
          -56.02605195190667,
          -56.33613734445318,
          -56.64287796102448,
          -56.94404246659396,
          -57.2454612627552,
          -57.547812439847576,
          -57.84562457342142,
          -58.13879443261982,
          -58.433761921080084,
          -58.72899131468643,
          -59.01665140201153,
          -59.30114472694361,
          -59.590252232730855,
          -59.87847927387634,
          -60.162801188955875,
          -60.44947893580497,
          -60.738067632631044,
          -61.01861847533337,
          -61.29090609295296,
          -61.55798266103622,
          -61.823011438212895,
          -62.08601868209725,
          -62.332524119480766,
          -62.585320398106404,
          -62.835515300168986,
          -63.07422177960659,
          -63.31370164822563,
          -63.54605428117169,
          -63.7728317320232,
          -63.998742709320645,
          -64.2148619436213,
          -64.4281100223949,
          -64.63494551952286,
          -64.8312054221813,
          -65.02270635297941,
          -65.21286313376582,
          -65.38030932523728,
          -65.55025723287066,
          -65.7186392970733,
          -65.87307562484358,
          -66.02658267148043,
          -66.16997682946553,
          -66.30036537860236,
          -66.42860486157353,
          -66.54586257112908,
          -66.65080224457779,
          -66.75524537867345,
          -66.84978197627228,
          -66.93204206142951,
          -67.00986209234982,
          -67.07818786683039,
          -67.13766003323333,
          -67.18855777233131,
          -67.22686182700441,
          -67.2561763081435,
          -67.28037100105091,
          -67.29232540801087,
          -67.28902093918421,
          -67.27309618532365,
          -67.24619829938165,
          -67.20977023756896,
          -67.16182994888243,
          -67.10232748696933,
          -67.0303655676146,
          -66.94613023023517,
          -66.85302319135522,
          -66.75040284348367,
          -66.63711735946971,
          -66.514289986404,
          -66.38405686478657,
          -66.24356107069106,
          -66.09319796269615,
          -65.93253183883319,
          -65.76682167290186,
          -65.60006941227343,
          -65.42529806307405,
          -65.24472705747665,
          -65.06968890862828,
          -64.88883274173362,
          -64.69673994010479,
          -64.50796366224124,
          -64.32312159258277,
          -64.12314018644014,
          -63.92081827337502,
          -63.72362476919724,
          -63.518495215160286,
          -63.30621814697917,
          -63.09775156198335,
          -62.88512388334975,
          -62.66755489876957,
          -62.45221622175098,
          -62.23244384909481,
          -62.01294574095953,
          -61.797165848834396,
          -61.57844859793764,
          -61.35676750292627,
          -61.13764904108875,
          -60.913958948083966,
          -60.68835770839192,
          -60.4639032078944,
          -60.240140380911946,
          -60.01428124793145,
          -59.79349400741151,
          -59.568453565516144,
          -59.34337280034526,
          -59.12099930516383,
          -58.89234417074142,
          -58.66546206150973,
          -58.443926654764425,
          -58.22197563076419,
          -57.99691914914282,
          -57.7858573920524,
          -57.56798673677686,
          -57.347636867085846,
          -57.13459913937889,
          -56.912562430064085,
          -56.687429448579756,
          -56.468789942761816,
          -56.245386985762075,
          -56.018754601727956,
          -55.799065418774035,
          -55.5855183332723,
          -55.36229348495816,
          -55.14053947443615,
          -54.9222949185408,
          -54.70282645857301,
          -54.480597882969064,
          -54.26499998226399,
          -54.05146625314503,
          -53.833881587790664,
          -53.61799894792032,
          -53.40159086033317,
          -53.180210132692544,
          -52.962174855186966,
          -52.747858101984505,
          -52.5351623575907,
          -52.328901860940086,
          -52.12870463886185,
          -51.924782676423575,
          -51.72756685644262,
          -51.53106038072766,
          -51.3286602838826,
          -51.123117717595456,
          -50.91323763770998,
          -50.70543784235384,
          -50.49438155851113,
          -50.27510822028462,
          -50.050909480063616,
          -49.823669528226226,
          -49.59422691319602,
          -49.36440612388891,
          -49.134583903761175,
          -48.90276059387876,
          -48.6776976551374,
          -48.45875150493637,
          -48.237037244812875,
          -48.01299505200677,
          -47.78735522324146,
          -47.56730557931867,
          -47.34259502952261,
          -47.11120550652267,
          -46.88007594379417,
          -46.64671633762666,
          -46.416150078136745,
          -46.172300421953395,
          -45.92810876478263,
          -45.68903856733507,
          -45.446385626242474,
          -45.18985324628705,
          -44.94372691322733,
          -44.70192897308499,
          -44.4388573852421,
          -44.17362366263393,
          -43.92040723303416,
          -43.65516753542635,
          -43.37830386078054,
          -43.12025807725942,
          -42.86759601270207,
          -42.58731737506445,
          -42.30107905713094,
          -42.022423625323306,
          -41.719980538226665,
          -41.41304072763449,
          -41.11286088896048,
          -40.795923494360935,
          -40.48217486048098,
          -40.16624475184209,
          -39.83954074672723,
          -39.51433138503104,
          -39.19059499041351,
          -38.855692630079304,
          -38.52375773208069,
          -38.19461421504617,
          -37.84480949933679,
          -37.49163018486492,
          -37.144637803730156,
          -36.7925621307796,
          -36.43533341187442,
          -36.086511974681386,
          -35.74411094330811,
          -35.3974239198621,
          -35.070615321269564,
          -34.75612404371996,
          -34.433828009503436,
          -34.119296782661245,
          -33.82917333821225,
          -33.53119170654072,
          -33.23896565819366,
          -32.96298573650396,
          -32.68880755570047,
          -32.411180307255314,
          -32.14730907317692,
          -31.89148736574123,
          -31.63406399894263,
          -31.382816104159236,
          -31.14260470511524,
          -30.908738528997826,
          -30.679175267360588,
          -30.453972229323984,
          -30.239954435773935,
          -30.034953451987597,
          -29.83544699147934,
          -29.63870010592736,
          -29.45051392019687,
          -29.26484764906907,
          -29.080832426982415,
          -28.904547605644584,
          -28.733812127457593,
          -28.560948097803262,
          -28.398201418249936,
          -28.244219460857213,
          -28.085503298428566,
          -27.93239840355711,
          -27.788020578850716,
          -27.6382945306535,
          -27.489944406321268,
          -27.347831741300396,
          -27.204421570626206,
          -27.05296883779879,
          -26.898753759572028,
          -26.743990246723495,
          -26.58693748758553,
          -26.434903402143977,
          -26.27864859898281,
          -26.118987136725572,
          -25.960688848867633,
          -25.80263384082788,
          -25.641587531545945,
          -25.490634425886167,
          -25.345428899364343,
          -25.198233210221513,
          -25.054022176188564,
          -24.90948308823688,
          -24.768150125688518,
          -24.622367149289303,
          -24.47454313616094,
          -24.32689585944346,
          -24.177551516639706,
          -24.02368924149357,
          -23.864973243607917,
          -23.70908548011217,
          -23.55665080355543,
          -23.40380073678331,
          -23.255790164156334,
          -23.112005237974362,
          -22.974921510501254,
          -22.836658156324113,
          -22.701933896202043,
          -22.57860038025221,
          -22.460292385077597,
          -22.34604813811691,
          -22.235431708965255,
          -22.12778442554132,
          -22.02883321507727,
          -21.934526113250715,
          -21.841440296149116,
          -21.750985679990453,
          -21.667079661963893,
          -21.5867976110394,
          -21.508110597429436,
          -21.437055558110558,
          -21.36902699900956,
          -21.298175186937353,
          -21.230834669316433,
          -21.167569360273735,
          -21.099309576083893,
          -21.030590119263348,
          -20.963200368387593,
          -20.890956437634305,
          -20.8155983053334,
          -20.738588165632944,
          -20.660873903780818,
          -20.58267998099796,
          -20.502745508009546,
          -20.421955384431214,
          -20.34330220580916,
          -20.265145814853938,
          -20.18118020561016,
          -20.102040809730145,
          -20.026286139676,
          -19.94960758496676,
          -19.87154028788423,
          -19.796544460529947,
          -19.722975346652813,
          -19.646816421842942,
          -19.568828146982252,
          -19.485389574699816,
          -19.396748886114946,
          -19.300280064223347,
          -19.196228108034806,
          -19.088681697785233,
          -18.973792366598712,
          -18.855078107823672,
          -18.73464300770831,
          -18.60742735561582,
          -18.47426458226979,
          -18.3356953708922,
          -18.192468238461107,
          -18.05014620355314,
          -17.900311344850667,
          -17.748259627428386,
          -17.59985239845478,
          -17.44749018124793,
          -17.289831861687734,
          -17.13476711030833,
          -16.978987429061053,
          -16.815182750249186,
          -16.649125894399738,
          -16.484893876493732,
          -16.31141786509426,
          -16.13937011537734,
          -15.966794840397359,
          -15.78756663352844,
          -15.60156817702558,
          -15.42305278717738,
          -15.242249598749698,
          -15.043921348952347,
          -14.860129157670553,
          -14.670611824815383,
          -14.465757156182125,
          -14.264695572567078,
          -14.063136254561105,
          -13.855595937981844,
          -13.646791011708268,
          -13.442235373770762,
          -13.233586255091215,
          -13.022735948499761,
          -12.812340887866805,
          -12.599936269082722,
          -12.3875157182114,
          -12.174185056595656,
          -11.961061223735184,
          -11.743969719285408,
          -11.530653431910961,
          -11.314437774434387,
          -11.10220201621013,
          -10.891674418989599,
          -10.678543557240541,
          -10.469547248740419,
          -10.2624515237825,
          -10.051378919587437,
          -9.841779070441515,
          -9.634490779696469,
          -9.427093585360735,
          -9.218670150847851,
          -9.015585082397052,
          -8.813825543884338,
          -8.607017514119331,
          -8.401703878797997,
          -8.20298074403046,
          -8.004702741756736,
          -7.801652168700154,
          -7.610108952407171,
          -7.42142288803849,
          -7.2264885692473735,
          -7.039059526496087,
          -6.8538488835666485,
          -6.667048806111803,
          -6.480069200058203,
          -6.290853721787352,
          -6.098503309303771,
          -5.9105502171822195,
          -5.7192761035844,
          -5.529391050315129,
          -5.346962338968414,
          -5.156469172134299,
          -4.973915853484037,
          -4.797752869141554,
          -4.6190817736512875,
          -4.447224680955508,
          -4.283957503658762,
          -4.125194422673401,
          -3.970335520706842,
          -3.823632292155835,
          -3.6807675216413864,
          -3.547546651900776,
          -3.423187895815954,
          -3.3027916263417385,
          -3.192411461611369,
          -3.091623219459845,
          -2.9974353690905984,
          -2.9142283907573603,
          -2.842398311146486,
          -2.78200160182335,
          -2.7332929856987773,
          -2.697585945913979,
          -2.6758406562339077,
          -2.6692647170003116,
          -2.6794013408390134,
          -2.7068345307342736,
          -2.750243888382191,
          -2.8140204735141774,
          -2.9019989163318414,
          -3.0102149280354915,
          -3.136163434944975,
          -3.292116164523131,
          -3.4732407107632817,
          -3.6673367794577665,
          -3.8855819480982174,
          -4.121239444135406,
          -4.367886537153666,
          -4.6310590045092255,
          -4.909107602324732,
          -5.198241707007494,
          -5.493338337837971,
          -5.801065701760351,
          -6.11715304648553,
          -6.436004558689778,
          -6.761900661809447,
          -7.08484882685639,
          -7.406039134764869,
          -7.729457535360628,
          -8.053267053009991,
          -8.37159367129153,
          -8.68936576889038,
          -9.004949568297512,
          -9.31682047245802,
          -9.62696774417688,
          -9.93245417582924,
          -10.235487151275668,
          -10.536757563008043,
          -10.831021603735033,
          -11.126865921930344,
          -11.422013064881448,
          -11.711720823201341,
          -12.003050423904435,
          -12.296803887576305,
          -12.589869543335947,
          -12.882519007259162,
          -13.206824304862469,
          -13.506153041046147,
          -13.804482252710493,
          -14.104526524025465,
          -14.407232207829418,
          -14.713380061745976,
          -15.025173389468257,
          -15.339392391657894,
          -15.657636340223394,
          -15.985835400864142,
          -16.315854623638366,
          -16.645196662538208,
          -16.98721157759249,
          -17.32813326129069,
          -17.670578183215763,
          -18.012771106910797,
          -18.372457112967986,
          -18.728236276014083,
          -19.07590688798593,
          -19.448794833792853,
          -19.819856423742173,
          -20.17754088957126,
          -20.55025241238078,
          -20.93166781440896,
          -21.29683990132369,
          -21.674990368027238,
          -22.06002927686083,
          -22.43131262677279,
          -22.81070485571307,
          -23.193418361000578,
          -23.565429945496376,
          -23.940763282180978,
          -24.326808498268797,
          -24.70813635926141,
          -25.085573837306793,
          -25.471415865390853,
          -25.85905754259594,
          -26.24067967699594,
          -26.62835577756132,
          -27.023276222597836,
          -27.41673543567052,
          -27.810942640593055,
          -28.21092489010343,
          -28.603232087112556,
          -28.99032235059943,
          -29.38285130277187,
          -29.7640527462422,
          -30.138842298441205,
          -30.524940716961034,
          -30.9031609071591,
          -31.275535933580933,
          -31.653674064251156,
          -32.031825364270404,
          -32.40078807806816,
          -32.77565139090284,
          -33.15572092407154,
          -33.524616131218615,
          -33.89788555388855,
          -34.31205031475888,
          -34.67917302969318,
          -35.047490717617805,
          -35.40843109635998,
          -35.765511114477306,
          -36.12346065001754,
          -36.47838098507164,
          -36.83849735418127,
          -37.20493953280114,
          -37.566328907076304,
          -37.93701170042838,
          -38.31494730759715,
          -38.6832600789177,
          -39.04813864890323,
          -39.42307988909404,
          -39.788370226073305,
          -40.14692481413972,
          -40.514965166964416,
          -40.876722858299054,
          -41.22342213010617,
          -41.574186828760354,
          -41.93368443234105,
          -42.28015563616246,
          -42.63314166434982,
          -42.98871329167694,
          -43.336115226771106,
          -43.682257706749766,
          -44.03144549426208,
          -44.37217780132779,
          -44.714603335792184,
          -45.056444297411836,
          -45.39785578436033,
          -45.73739926610399,
          -46.07722256707363,
          -46.41392265976048,
          -46.7536884124984,
          -47.08837036597805,
          -47.41816538407625,
          -47.74972236062895,
          -48.07810458489749,
          -48.406582657969295,
          -48.735465316936306,
          -49.06695767124381,
          -49.39895970424358,
          -49.73018564900906,
          -50.06126296328641,
          -50.39551242883402,
          -50.72834905185715,
          -51.05150893735426,
          -51.38114781399141,
          -51.717259812594975,
          -52.07301299189745,
          -52.39875053442496,
          -52.733819938449834,
          -53.06355532999838,
          -53.38589277702482,
          -53.716245957876666,
          -54.04869301317649,
          -54.37178924855617,
          -54.69642329062652,
          -55.02574949580002,
          -55.34834129208912,
          -55.669145147422846,
          -55.98960028704136,
          -56.3076972647037,
          -56.621269058949764,
          -56.93013001812104,
          -57.24022509237409,
          -57.55092377293988,
          -57.85341381392597,
          -58.15499335547893,
          -58.49317394099913,
          -58.795631088408726,
          -59.091024596135846,
          -59.39217311527495,
          -59.69419299884416,
          -59.99299964095694,
          -60.29196990099787,
          -60.59386658038928,
          -60.88848406793987,
          -61.17521208756635,
          -61.4546765742016,
          -61.735882797629706,
          -62.00895634729002,
          -62.26878311208972,
          -62.535928099095486,
          -62.79467599850539,
          -63.04577366907901,
          -63.29258615431078,
          -63.532465026755965,
          -63.76603160470231,
          -64.01143698884582,
          -64.2470503431708,
          -64.47776937000921,
          -64.69985146036979,
          -64.91011890076263,
          -65.11988179054424,
          -65.3067541269102,
          -65.49349294740588,
          -65.67787352151993,
          -65.84831801820904,
          -66.00543237013562,
          -66.15149592500164,
          -66.28718826595971,
          -66.42162106870808,
          -66.5449400884666,
          -66.65912764232849,
          -66.77431064903143,
          -66.87844686027412,
          -66.97074860087946,
          -67.0581201025096,
          -67.13291211280782,
          -67.19976263984901,
          -67.2577201728544,
          -67.30180824980346,
          -67.33745312389016,
          -67.36778895840271,
          -67.38511135378526,
          -67.38654074476754,
          -67.37602965781693,
          -67.35486159496755,
          -67.32253305632219,
          -67.27822350802018,
          -67.2214423833344,
          -67.15138090897804,
          -67.06713408138613,
          -66.97115496015253,
          -66.86398241166371,
          -66.74260535983153,
          -66.6124286904359,
          -66.47603631568566,
          -66.3223538863303,
          -66.16347486178844,
          -66.00119848845848,
          -65.83522823405262,
          -65.67165984607001,
          -65.50577920561427,
          -65.32982397618471,
          -65.15726721485673,
          -64.9839874745163,
          -64.80122020292747,
          -64.61961921010575,
          -64.43955916572844,
          -64.25791070889484,
          -64.06429147947685,
          -63.86949330469262,
          -63.67349152816083,
          -63.47230699031968,
          -63.26594689905641,
          -63.0585791504768,
          -62.84804847784432,
          -62.63558106177187,
          -62.42359538938827,
          -62.20750638047554,
          -61.99064999614591,
          -61.77627137593541,
          -61.5591030115546,
          -61.3393009777562,
          -61.119650829716875,
          -60.895726935657365,
          -60.668349275660866,
          -60.440341380750475,
          -60.21114195590213,
          -59.9799352263799,
          -59.72910276464591,
          -59.498188999257664,
          -59.26975687989393,
          -59.04510407064621,
          -58.818231079100684,
          -58.5988116024957,
          -58.38759521545623,
          -58.175723036610236,
          -57.967848630035796,
          -57.77784702640796,
          -57.582916018358446,
          -57.38763405398029,
          -57.2043625573086,
          -57.01231722463997,
          -56.81442331127769,
          -56.62234054540864,
          -56.42458477237226,
          -56.224255895006415,
          -56.02328811809464,
          -55.81992462558698,
          -55.62008498502751,
          -55.41666243639262,
          -55.203566020502805,
          -54.99347717623862,
          -54.7827257372063,
          -54.563907961629525,
          -54.34541200182019,
          -54.12995911009073,
          -53.90694176591345,
          -53.68048133160258,
          -53.45608410949461,
          -53.22444569531539,
          -52.988828306748424,
          -52.759969627072124,
          -52.5307230438456,
          -52.30249765484058,
          -52.08318313925874,
          -51.8617495682587,
          -51.64291895230069,
          -51.42674271864286,
          -51.205374836573014,
          -50.978822865355845,
          -50.74893558123603,
          -50.520451718492126,
          -50.286235222182874,
          -50.04404205777941,
          -49.79841125314252,
          -49.55133029598883,
          -49.301142538041006,
          -49.05171706351374,
          -48.80262570546493,
          -48.55795012537514,
          -48.320503554169306,
          -48.08122853844462,
          -47.83923244013082,
          -47.597854027344184,
          -47.36296859969274,
          -47.119848164271716,
          -46.87179152215019,
          -46.62784398461014,
          -46.3865185398944,
          -46.13758662508226,
          -45.882506913206186,
          -45.638350768579734,
          -45.40202584931485,
          -45.15286767081181,
          -44.910602981557574,
          -44.68683528605533,
          -44.44814233486934,
          -44.197869411745884,
          -43.958137197320205,
          -43.7175201928318,
          -43.4659316411832,
          -43.20799095845028,
          -42.958669988965056,
          -42.714975562290384,
          -42.45226502704055,
          -42.18397429266377,
          -41.92212531907494,
          -41.64374813716246,
          -41.35245730080967,
          -41.06432149035486,
          -40.761467928484095,
          -40.454594322204976,
          -40.150273450651085,
          -39.8354963456903,
          -39.51103483054273,
          -39.18926132755797,
          -38.859115427458796,
          -38.52251769893648,
          -38.19902540483133,
          -37.86218669225267,
          -37.50934723842243,
          -37.16581799944193,
          -36.82223660091939,
          -36.47303888228664,
          -36.123074121166894,
          -35.782204882836574,
          -35.442409260937794,
          -35.102056320517846,
          -34.78629987780564,
          -34.471883439756084,
          -34.14746347121026,
          -33.84605388489217,
          -33.553708101905876,
          -33.250563454522336,
          -32.96460424785478,
          -32.68641759692767,
          -32.40952811630079,
          -32.13647907841946,
          -31.875496718347694,
          -31.62040906978592,
          -31.3692731568516,
          -31.128653885588243,
          -30.895484754384583,
          -30.673021061602277,
          -30.4564499076067,
          -30.243102858337505,
          -30.037110492090004,
          -29.840072342414665,
          -29.646596192747868,
          -29.45520323757677,
          -29.27322605585274,
          -29.092874082076392,
          -28.911547352606625,
          -28.736870940234013,
          -28.569567648391725,
          -28.404831342714697,
          -28.246515067547016,
          -28.097330488214077,
          -27.946981831102516,
          -27.797469042688693,
          -27.65824620050871,
          -27.518667348820248,
          -27.377270208336014,
          -27.243466225191476,
          -27.108572634055996,
          -26.970365830634698,
          -26.836377997977227,
          -26.70039720608668,
          -26.56266711343642,
          -26.426854755029865,
          -26.290415675286066,
          -26.149065128213227,
          -26.008000462419282,
          -25.868400980166317,
          -25.72419946234665,
          -25.583747645422825,
          -25.44457752090553,
          -25.304002733636057,
          -25.16402169134971,
          -25.024850126056847,
          -24.886710853992444,
          -24.75077367734998,
          -24.612215773194514,
          -24.475219884022657,
          -24.33902673184721,
          -24.20212450543729,
          -24.068034805090296,
          -23.934360297636253,
          -23.80302587282976,
          -23.671934351942323,
          -23.541636228121696,
          -23.41150044334196,
          -23.28447644210979,
          -23.148561389650993,
          -23.025401165750644,
          -22.90954852775124,
          -22.796729788349747,
          -22.684810104200672,
          -22.57605822622979,
          -22.46792378791558,
          -22.361120401782223,
          -22.261551301205262,
          -22.16353455580876,
          -22.064981855155263,
          -21.966975526131932,
          -21.87150168248146,
          -21.772723029819876,
          -21.66942948268381,
          -21.57520608187572,
          -21.484674383312882,
          -21.39262706670191,
          -21.30338594612345,
          -21.220403163730513,
          -21.136668215983228,
          -21.050642316748583,
          -20.971266422092764,
          -20.893704719430318,
          -20.819095103855986,
          -20.744356394558064,
          -20.668110426183997,
          -20.593575790907362,
          -20.51913769651664,
          -20.44398529835246,
          -20.37019633369734,
          -20.298325499929867,
          -20.222271214700026,
          -20.14286692746316,
          -20.068865753641326,
          -19.994722344735,
          -19.921408639803634,
          -19.848279216226192,
          -19.77733712660915,
          -19.708843692405654,
          -19.639876490727172,
          -19.571363877498232,
          -19.500457183976046,
          -19.42755711057401,
          -19.353821194607914,
          -19.277222947707447,
          -19.198696655644017,
          -19.117528511903302,
          -19.032573119760347,
          -18.948416948005327,
          -18.8617110322628,
          -18.76787339255267,
          -18.671976260282626,
          -18.572269788069963,
          -18.465027304774082,
          -18.35302653550974,
          -18.23322606697562,
          -18.109198924002346,
          -17.97901877700008,
          -17.8424357393355,
          -17.699650572565574,
          -17.546991433374593,
          -17.388572184205284,
          -17.22651462273087,
          -17.05426537516221,
          -16.875136298756033,
          -16.696253347316734,
          -16.505823524083787,
          -16.312044657667926,
          -16.121715044231273,
          -15.918228961012252,
          -15.713662817862469,
          -15.520349065238337,
          -15.314117388062634,
          -15.101981873349454,
          -14.901015296769765,
          -14.692722931406239,
          -14.47507862921057,
          -14.264177112491339,
          -14.051834892143809,
          -13.828488818514472,
          -13.610171729805234,
          -13.392998744052473,
          -13.14431326671235,
          -12.919627335562577,
          -12.694532034725631,
          -12.46382295349791,
          -12.231529775858943,
          -12.002729134096949,
          -11.770840032936897,
          -11.545372404882938,
          -11.319961015720121,
          -11.094155532004333,
          -10.870343496667056,
          -10.649476851254931,
          -10.432298095911957,
          -10.216307836805138,
          -10.001517123035553,
          -9.790703986991717,
          -9.580788044014426,
          -9.370481683762973,
          -9.16321502127577,
          -8.961535107073983,
          -8.759009779363042,
          -8.557318526251073,
          -8.355886338897776,
          -8.153905396308813,
          -7.951682623975034,
          -7.75027452716869,
          -7.5512766894352366,
          -7.350702686380873,
          -7.154769967425929,
          -6.960011268123255,
          -6.766274518296466,
          -6.572764187927147,
          -6.37801869391982,
          -6.186990444418874,
          -5.9952547142450285,
          -5.8024834919889425,
          -5.610113250581571,
          -5.421421402540372,
          -5.230705688924124,
          -5.046683022305792,
          -4.872716593779623,
          -4.6951301980288855,
          -4.511179217587073,
          -4.332158443315197,
          -4.158427781620778,
          -3.9781560199225248,
          -3.804624532867186,
          -3.6385278102201566,
          -3.4657404385840342,
          -3.2985543996196376,
          -3.143760131127154,
          -2.990897550279068,
          -2.853284988059845,
          -2.728124024093954,
          -2.6083346915128622,
          -2.4995781005502993,
          -2.401952119700064,
          -2.3136789494691223,
          -2.238971619951746,
          -2.178121549782583,
          -2.1308086498294294,
          -2.0989279496834654,
          -2.0811384019076833,
          -2.0791462567281584,
          -2.0941115217407553,
          -2.127357150261988,
          -2.1812564930478997,
          -2.255843138179999,
          -2.351285321542093,
          -2.470949885461389,
          -2.619418061092849,
          -2.7877105289187534,
          -2.975052188900128,
          -3.186661968551388,
          -3.4111859653665855,
          -3.653318850390739,
          -3.9126615935363556,
          -4.1800908551126845,
          -4.467339948394169,
          -4.76213772483465,
          -5.057079131423051,
          -5.366431454037695,
          -5.686629453715802,
          -6.000219054441521,
          -6.315818757227649,
          -6.636045568944125,
          -6.948817367054708,
          -7.261130271977808,
          -7.577241231467479,
          -7.888166201756551,
          -8.197871795054352,
          -8.50808823068634,
          -8.812478521149504,
          -9.115105767042023,
          -9.414291744215312,
          -9.711444317474582,
          -10.007502270019703,
          -10.299487170473892,
          -10.592538344186792,
          -10.891153498312034,
          -11.187520981503875,
          -11.482022983094124,
          -11.780385466250532,
          -12.081554951147046,
          -12.381652289882577,
          -12.682140856885521,
          -12.990862659199513,
          -13.299742955942214,
          -13.611617440190054,
          -13.934305403208066,
          -14.256927111462618,
          -14.586113170885733,
          -14.917746982119734,
          -15.251391235544043,
          -15.594129593187766,
          -15.940412518175888,
          -16.28431813443251,
          -16.642108913478406,
          -16.995968507434565,
          -17.341447380945205,
          -17.68624308935871,
          -18.046967535864507,
          -18.40739677468867,
          -18.75423808809474,
          -19.122883537464627,
          -19.494562086443743,
          -19.850467709603112,
          -20.217375693444236,
          -20.600471912205226,
          -20.964774255638137,
          -21.334574125398436,
          -21.71635453927342,
          -22.08321685900946,
          -22.451794632413858,
          -22.830192417191082,
          -23.197398613331025,
          -23.56588574348082,
          -23.9411828469809,
          -24.317713222784892,
          -24.691862653126957,
          -25.067342381426663,
          -25.446518281020253,
          -25.823575223588996,
          -26.2028494895185,
          -26.583118605135837,
          -26.966954059517665,
          -27.35077087822334,
          -27.734676910582905,
          -28.118658584974153,
          -28.49849501805635,
          -28.87466346669121,
          -29.25502327108787,
          -29.62282677381422,
          -29.98810194848637,
          -30.36409863788679,
          -30.729381056802502,
          -31.093416129346256,
          -31.462290431553313,
          -31.82712487808434,
          -32.183114856408764,
          -32.54546634304612,
          -32.91461519520696,
          -33.27211085075718,
          -33.634882201375724,
          -34.00379296069003,
          -34.365538004602506,
          -34.729305012827695,
          -35.09053582815073,
          -35.442051401313115,
          -35.80147397332604,
          -36.156478428285936,
          -36.509943348927166,
          -36.87540585234159,
          -37.23901072209325,
          -37.60450716369108,
          -37.98091776311527,
          -38.35826093083761,
          -38.72586756756725,
          -39.099598938468134,
          -39.47442917873935,
          -39.83691641541903,
          -40.204012329161955,
          -40.574518240633275,
          -40.93284919279329,
          -41.286376866942405,
          -41.64670181348839,
          -42.002212553600565,
          -42.3507670717366,
          -42.710882038521,
          -43.06959132588439,
          -43.421435885960044,
          -43.7807719502002,
          -44.13042410569125,
          -44.47974523087207,
          -44.83083555170508,
          -45.17975029971333,
          -45.526137563452274,
          -45.875589050399924,
          -46.22206441573103,
          -46.569064381392046,
          -46.91316488006124,
          -47.252871500956985,
          -47.59460254898223,
          -47.93472843239765,
          -48.27245989973975,
          -48.61316785031234,
          -48.95780558244229,
          -49.30319506797552,
          -49.64442423993319,
          -49.98381841805986,
          -50.32604717784858,
          -50.66631640577856,
          -50.99451219306471,
          -51.32925243718483,
          -51.66956924331703,
          -51.998736515246826,
          -52.3287767677094,
          -52.667858253196044,
          -53.01000201520464,
          -53.36753357541763,
          -53.73099880724471,
          -54.095482201916454,
          -54.451681350020955,
          -54.80973824207325,
          -55.17013669730103,
          -55.524106384949896,
          -55.8756427780986,
          -56.22684818609178,
          -56.568173790368725,
          -56.89164961503797,
          -57.210054830820965,
          -57.527142887254534,
          -57.84681566068695,
          -58.1570298021242,
          -58.463839291949,
          -58.77464051965263,
          -59.080840617557335,
          -59.379611364919995,
          -59.676143211914265,
          -59.95963755435715,
          -60.239955016541984,
          -60.52007216423825,
          -60.80366715994708,
          -61.08194029433051,
          -61.35281209135889,
          -61.61752644560808,
          -61.88090988763418,
          -62.17169681900389,
          -62.41810160592986,
          -62.67171699605905,
          -62.92700286480446,
          -63.171093429782275,
          -63.40996922133053,
          -63.648671884466815,
          -63.881023424434204,
          -64.11161156677625,
          -64.33274081599845,
          -64.5484139784681,
          -64.76538019545904,
          -64.9762134188021,
          -65.20740470348781,
          -65.40373475442904,
          -65.59756447844596,
          -65.80873944884215,
          -65.99163835726283,
          -66.1642621214959,
          -66.32658432151234,
          -66.48021806007075,
          -66.62097019240412,
          -66.74939135202578,
          -66.87171558534783,
          -66.97876032382108,
          -67.07211215897057,
          -67.15447761613395,
          -67.22104224477765,
          -67.2741529478326,
          -67.31308135995369,
          -67.33853409042516,
          -67.35370455384614,
          -67.35460539923463,
          -67.33965814033566,
          -67.30902899364848,
          -67.26404469862514,
          -67.2078001782688,
          -67.13824374251357,
          -67.05358555831275,
          -66.95710528627973,
          -66.84693482330073,
          -66.72309386440044,
          -66.58992031612112,
          -66.44468496860021,
          -66.29607605628406,
          -66.14247628542849,
          -65.98439382705837,
          -65.82077959233854,
          -65.65819730422088,
          -65.49709534143815,
          -65.32840960359943,
          -65.16012022721834,
          -64.99283673717963,
          -64.81902387014065,
          -64.64236745794976,
          -64.46675564704715,
          -64.28902454181636,
          -64.10627233332251,
          -63.9245189968719,
          -63.739895374679506,
          -63.552789948909144,
          -63.36255950167904,
          -63.171640173338844,
          -62.977289859578626,
          -62.78089205260735,
          -62.58559801107137,
          -62.385988271432005,
          -62.18664524096537,
          -61.98937501139463,
          -61.78934089875508,
          -61.585390276013854,
          -61.38256301127122,
          -61.174410387424665,
          -60.961679105118876,
          -60.74845623489055,
          -60.533814350995335,
          -60.31690206841151,
          -60.10096530121553,
          -59.882987962738184,
          -59.66207909539635,
          -59.44231655656435,
          -59.21722167022417,
          -58.98802951173427,
          -58.76205771207255,
          -58.53723530877152,
          -58.30593089017669,
          -58.08199102346705,
          -57.86537305766054,
          -57.63728994130255,
          -57.417093154127556,
          -57.19783982644442,
          -56.96809559375092,
          -56.745401588101466,
          -56.527400212898556,
          -56.302759666354554,
          -56.08121448281064,
          -55.86963629564599,
          -55.65688287615789,
          -55.43401671720818,
          -55.21534072806675,
          -54.99965622634113,
          -54.77522794277379,
          -54.550565532425885,
          -54.33252560499146,
          -54.10737652938803,
          -53.87845931182021,
          -53.65398134783925,
          -53.423887931321886,
          -53.18849279457918,
          -52.96138067614139,
          -52.73633495991684,
          -52.511767140085105,
          -52.293945992345314,
          -52.07486610261543,
          -51.86308025501084,
          -51.64710141416969,
          -51.4285046739303,
          -51.207936041427956,
          -50.98112666724028,
          -50.75759524732726,
          -50.530524647357275,
          -50.29611717891968,
          -50.05853979565974,
          -49.82148790953997,
          -49.579964240667685,
          -49.337494641666325,
          -49.099491975439534,
          -48.86009979050132,
          -48.63134517445355,
          -48.40446603377749,
          -48.15076643023613,
          -47.91352750034972,
          -47.68602777604388,
          -47.4606470698996,
          -47.22363976674354,
          -46.98960292127097,
          -46.75719495268253,
          -46.526941675163066,
          -46.28666461660954,
          -46.049829381604496,
          -45.818999186174935,
          -45.590109752221245,
          -45.34974987102058,
          -45.11066667581404,
          -44.882333624532365,
          -44.64177533187349,
          -44.38690967518651,
          -44.13745327703394,
          -43.89167800014418,
          -43.6346765855797,
          -43.37106746872596,
          -43.120170567487335,
          -42.87514780108498,
          -42.61189937175488,
          -42.3444472783157,
          -42.08199659401624,
          -41.80345028441472,
          -41.514048526503196,
          -41.22651686968583,
          -40.92555981169007,
          -40.620679684726795,
          -40.31489772743544,
          -39.99940914928018,
          -39.672597049306184,
          -39.34823267667472,
          -39.01389573865975,
          -38.67111447699712,
          -38.3417180772891,
          -37.99869991142855,
          -37.64066093269598,
          -37.29183094018727,
          -36.944293079592875,
          -36.59102497377393,
          -36.240332036105386,
          -35.903320575532284,
          -35.56515687007894,
          -35.23029923900151,
          -34.92269420854079,
          -34.614763213636685,
          -34.29892708616655,
          -34.01210940746176,
          -33.72535284716105,
          -33.43346597443473,
          -33.16069412386568,
          -32.893568944678464,
          -32.618449071051465,
          -32.351954603625344,
          -32.09740388948943,
          -31.843371052113444,
          -31.591763948974286,
          -31.34816043213504,
          -31.111338409549965,
          -30.884495494391107,
          -30.660592507642257,
          -30.43986832898685,
          -30.232311921187634,
          -30.034832536263558,
          -29.836882422200684,
          -29.647805933322292,
          -29.464161681522267,
          -29.278335121264682,
          -29.09703501070668,
          -28.92426903504328,
          -28.752792917301697,
          -28.57969357253216,
          -28.419568014755612,
          -28.264885833516104,
          -28.105049263851885,
          -27.953223004070953,
          -27.809238189289864,
          -27.658637193310675,
          -27.51092928949594,
          -27.368130468550394,
          -27.22228630232354,
          -27.078306792113878,
          -26.93666850605959,
          -26.793280175586176,
          -26.647893986261852,
          -26.506868769852076,
          -26.362206492738075,
          -26.213789442975205,
          -26.065900168254448,
          -25.917723340433536,
          -25.76644333607956,
          -25.617643956734327,
          -25.469910724251086,
          -25.32087796709313,
          -25.175205130333048,
          -25.02923169482956,
          -24.88858201198964,
          -24.744508251223348,
          -24.599890378823794,
          -24.45614000552284,
          -24.31174841617279,
          -24.169613655949668,
          -24.025554899223497,
          -23.88392619934849,
          -23.744495502265423,
          -23.603328354286806,
          -23.46321450382037,
          -23.326411948354405,
          -23.195045748240727,
          -23.06177641883814,
          -22.93121302256855,
          -22.80615728391779,
          -22.68289856818865,
          -22.56415621191781,
          -22.447976935762057,
          -22.333911497446024,
          -22.22793228306158,
          -22.124055858807413,
          -22.01852245969138,
          -21.91624251358265,
          -21.819172107053053,
          -21.71383450795761,
          -21.60779321331262,
          -21.51057160389064,
          -21.413535363175278,
          -21.313846004326333,
          -21.221748340988928,
          -21.132012972374937,
          -21.034140729436047,
          -20.940020427879332,
          -20.84880348241341,
          -20.757562254644483,
          -20.666031727970818,
          -20.574703883397184,
          -20.482314164119668,
          -20.38841150430447,
          -20.29335029544132,
          -20.200865709932508,
          -20.11118814062886,
          -20.017291769726018,
          -19.925399536618944,
          -19.836184497930848,
          -19.74708590869075,
          -19.655944044723206,
          -19.569553194373647,
          -19.48507098397482,
          -19.398711486551836,
          -19.311303325113908,
          -19.218866146453074,
          -19.122777395645734,
          -19.023391537244862,
          -18.921415244909824,
          -18.815847394177677,
          -18.706022277471703,
          -18.59663693758805,
          -18.481433923823037,
          -18.360150135271645,
          -18.23514641089734,
          -18.11650148987277,
          -17.998273267605136,
          -17.873623826276784,
          -17.744163833825844,
          -17.611702852220468,
          -17.475956962954065,
          -17.333844386239388,
          -17.185815383871923,
          -17.036862941336874,
          -16.88543948550195,
          -16.71508023090852,
          -16.539657270708158,
          -16.361528991185704,
          -16.175309519380576,
          -15.992975878334086,
          -15.809859644432564,
          -15.613581896340465,
          -15.425261356390541,
          -15.24047317195969,
          -15.035840578274309,
          -14.84650269721174,
          -14.670204811131125,
          -14.475004061424876,
          -14.277627277337423,
          -14.085006727846713,
          -13.883696292373584,
          -13.6760943845444,
          -13.475113325042148,
          -13.273863511387828,
          -13.06761417066516,
          -12.85571265687709,
          -12.642648543091907,
          -12.426046847370069,
          -12.206646246010985,
          -11.989051906594568,
          -11.767208718892018,
          -11.548567712995542,
          -11.327059003885726,
          -11.108289901515315,
          -10.89483712861106,
          -10.651596952608092,
          -10.402437268413932,
          -10.154654641580422,
          -9.903982397230568,
          -9.655577505284743,
          -9.410451765981142,
          -9.167145777093761,
          -8.922410420456462,
          -8.677950678765317,
          -8.442878178667304,
          -8.224549091238233,
          -8.012244108645312,
          -7.803377836943842,
          -7.5992916658262235,
          -7.3905951917552155,
          -7.180661574635478,
          -6.978917859540822,
          -6.775344940328747,
          -6.5707139938575985,
          -6.369800614404133,
          -6.16294179079084,
          -5.955294821820569,
          -5.7494593187793015,
          -5.53920160205076,
          -5.327561320334729,
          -5.127665088135819,
          -4.923495928887167,
          -4.716923102821366,
          -4.522760306960668,
          -4.324679740492083,
          -4.1349298904023835,
          -3.9574413344576356,
          -3.779892597270801,
          -3.603220899922884,
          -3.435553303622606,
          -3.272291094171636,
          -3.1088952667081533,
          -2.9554104392099503,
          -2.8056806730677,
          -2.661758505747535,
          -2.528416841861101,
          -2.397186683423948,
          -2.27517888973646,
          -2.164584053072101,
          -2.0615658461716873,
          -1.9662971884350573,
          -1.880455250454103,
          -1.8062125159846574,
          -1.7416060408752518,
          -1.6883575246470086,
          -1.6464221118954492,
          -1.6161019349254333,
          -1.598952334573434,
          -1.5962239149252784,
          -1.6088778091433145,
          -1.6365442606316238,
          -1.6817466445111175,
          -1.7471709239700712,
          -1.8304379054912938,
          -1.9293634624295373,
          -2.0557765917490776,
          -2.2106226245532574,
          -2.379448232045034,
          -2.5642431789587876,
          -2.770485432445319,
          -2.984658334705341,
          -3.2125196137460006,
          -3.4560509928231054,
          -3.7074353443265613,
          -3.9715840351858427,
          -4.261318533939599,
          -4.524814887744411,
          -4.801974158007338,
          -5.086049453114505,
          -5.3717500378122764,
          -5.661918145237242,
          -5.951433251046758,
          -6.239212786650746,
          -6.528322701353272,
          -6.816435192112626,
          -7.093688572207026,
          -7.380497893714439,
          -7.669322202948817,
          -7.957540775263811,
          -8.240558247756539,
          -8.526147085033289,
          -8.8094926928902,
          -9.088670509354857,
          -9.370651659488038,
          -9.64811978897924,
          -9.92364255285066,
          -10.204372674559558,
          -10.482359883396267,
          -10.759157124840334,
          -11.041214801482244,
          -11.323874997705309,
          -11.607346828275382,
          -11.892572715090681,
          -12.179160979136796,
          -12.47143522716537,
          -12.764556620481914,
          -13.057292124639014,
          -13.353928227169805,
          -13.654242722158928,
          -13.957140782146217,
          -14.264127794442901,
          -14.573264478042214,
          -14.887181306730454,
          -15.20907860518733,
          -15.526499329387255,
          -15.849211824472095,
          -16.1837218211788,
          -16.51242832777449,
          -16.844908402576852,
          -17.17604128776223,
          -17.52185730380651,
          -17.86363848644997,
          -18.195146483620313,
          -18.546750146028806,
          -18.89652427529972,
          -19.233422785718236,
          -19.58001510150497,
          -19.93962503028559,
          -20.288186067872886,
          -20.63609329753014,
          -20.995772633526173,
          -21.348988875525382,
          -21.69659190603601,
          -22.05360912650614,
          -22.407707415262625,
          -22.75424121571816,
          -23.108273307268206,
          -23.456800500960327,
          -23.81209383041351,
          -24.16824531704238,
          -24.52007929669434,
          -24.875864462154343,
          -25.234450167280023,
          -25.59249566257504,
          -25.94840914936964,
          -26.312619561636854,
          -26.67225056181053,
          -27.03042670043228,
          -27.393002228059295,
          -27.750145402605973,
          -28.056119222177905,
          -28.406556474352666,
          -28.755716255364483,
          -29.09454159159732,
          -29.43946894773987,
          -29.7860694420215,
          -30.12272349580964,
          -30.47029680231665,
          -30.813465404750218,
          -31.14857999508093,
          -31.489246573379937,
          -31.83343464508342,
          -32.180106428740125,
          -32.5181274336786,
          -32.859070374984235,
          -33.2098595497299,
          -33.553603501315536,
          -33.89825888738154,
          -34.237887134155855,
          -34.56665357821295,
          -34.899538291821145,
          -35.22762919113327,
          -35.55176383432408,
          -35.87623956047461,
          -36.201292388560894,
          -36.5207841866333,
          -36.84531761093447,
          -37.165586545365954,
          -37.475087034752455,
          -37.781226759500434,
          -38.07977000686565,
          -38.36833329366603,
          -38.64527235782367,
          -38.95212376368915,
          -39.22191254840864,
          -39.476727235435135,
          -39.72943703874776,
          -39.978926081087,
          -40.21587167988429,
          -40.44927422439422,
          -40.67779494125739,
          -40.89732908766,
          -41.10698439454845,
          -41.31169356236648,
          -41.50934421279334,
          -41.70070147597102,
          -41.885089193801406,
          -42.0623696183549,
          -42.23242790307994,
          -42.3975268493152,
          -42.554139770735866,
          -42.706005443434805,
          -42.85119877794946,
          -42.99326441183154,
          -43.13043244029614,
          -43.26536152526621,
          -43.396386244919455,
          -43.525692046003925,
          -43.645579472730375,
          -43.76058152027081,
          -43.87314104004291,
          -43.97967154488688,
          -44.08086289472793,
          -44.14137311119168,
          -44.23687926633128,
          -44.32673352167267,
          -44.411268496572475,
          -44.488690502888126,
          -44.563273244780454,
          -44.63163749042488,
          -44.69691641427846,
          -44.76166908041577,
          -44.82416156640577,
          -44.88329338084764,
          -44.938867626121535,
          -44.991684912561816,
          -45.04115679053738,
          -45.084374913991404,
          -45.12328908023327,
          -45.158615138261865,
          -45.18908164182476,
          -45.21715773717338,
          -45.241843955700894,
          -45.26225978074167,
          -45.2812397669999,
          -45.29912954405049,
          -45.31495342648793,
          -45.32909914608487,
          -45.34129563765416,
          -45.35123159378307,
          -45.36002550833295,
          -45.367429663092,
          -45.373450790889294,
          -45.37892491568039,
          -45.38348451296948,
          -45.38709576122565,
          -45.38987259486149,
          -45.39201223749755,
          -45.39378837231216,
          -45.39522130842233,
          -45.39638158814507,
          -45.39745662734854,
          -45.39852915472637,
          -45.39959623986342,
          -45.40060689908244,
          -45.4009172382536,
          -45.40117706279354,
          -45.40140460923213,
          -45.40163051313254,
          -45.4018254182305,
          -45.40199439764787,
          -45.40215732635067,
          -45.40230463500697,
          -45.402431118078326,
          -45.40253451824544,
          -45.40347533642653,
          -45.4045009196911,
          -45.40552077161054,
          -45.406543967452464,
          -45.40756378700323,
          -45.40413971615596,
          -45.405139804092926,
          -45.40612640666854,
          -45.4071109824521,
          -45.40809951205476,
          -45.40833313628159,
          -45.40847880006112,
          -45.40862585447327,
          -45.40876694322939,
          -45.40890264220816,
          -45.40903780334378,
          -45.409165907549266,
          -45.40928989672995,
          -45.40941046317816,
          -45.40952603744997,
          -45.409900894210814,
          -45.41028605882007,
          -45.41065411389173,
          -45.41100188576985,
          -45.41133135166681,
          -45.4116413057063,
          -45.411932882404905,
          -45.41220387265481,
          -45.41245398582146,
          -45.41268703353797,
          -45.412762329630134,
          -45.41281787658448,
          -45.412867679042265,
          -45.41291217928194,
          -45.41295127054923,
          -45.41298450778652,
          -45.41301281485027,
          -45.4130352475178,
          -45.41305221925071,
          -45.41306374612866,
          -45.41309799695799,
          -45.413099614007116,
          -45.41306145129848,
          -45.41298698123988,
          -45.41287818974583,
          -45.41273854380772,
          -45.4125637350658,
          -45.41235486001969,
          -45.412116954526766,
          -45.411841286248574,
          -45.41177303123894,
          -45.411730072958946,
          -45.4116850162911,
          -45.411637649842746,
          -45.41158623264187,
          -45.4115310064707,
          -45.41147140268202,
          -45.411400723873406,
          -45.41133185972873,
          -45.41126062736721,
          -45.41124040327362,
          -45.41122029569904,
          -45.411202513724646,
          -45.41118365673517,
          -45.41116019455542,
          -45.411136594624296,
          -45.411114116089095,
          -45.41108971761326
         ],
         "xaxis": "x",
         "y": [
          45.30065635922624,
          45.30124205437229,
          45.30193400755794,
          45.30265046529222,
          45.303148779253284,
          45.30355241309474,
          45.30436763201242,
          45.30509261653337,
          45.30601404203569,
          45.306807104326325,
          45.30755378323268,
          45.3084595882965,
          45.30939829386062,
          45.310166602457215,
          45.31092652284556,
          45.31184263146779,
          45.31269093838768,
          45.3135576272191,
          45.31414556023766,
          45.31474025871411,
          45.315360652914144,
          45.31605557841787,
          45.31664194012994,
          45.31730697535071,
          45.317890613009425,
          45.31851538132313,
          45.319104667384806,
          45.319609469309746,
          45.32007727141195,
          45.320588366136754,
          45.32098028619176,
          45.32137490542775,
          45.3218027568607,
          45.322205865337594,
          45.322700240070716,
          45.323155095223285,
          45.32354950746685,
          45.32388409129931,
          45.32428643617517,
          45.324720620555965,
          45.325017845529025,
          45.32541910711946,
          45.32594672200731,
          45.32622930094886,
          45.32648902428704,
          45.32678770395347,
          45.3271690999394,
          45.327448012220245,
          45.32774646010955,
          45.32811341332325,
          45.32845006239287,
          45.328854892378736,
          45.32925256389109,
          45.32956418507035,
          45.3298872080439,
          45.330206948208186,
          45.33058368137483,
          45.330898532790556,
          45.33111427854165,
          45.33145221325836,
          45.331679937477944,
          45.331990641078995,
          45.33232540056891,
          45.33257673594378,
          45.33284641602727,
          45.33315718987583,
          45.33344664049978,
          45.3341012148372,
          45.33498707332209,
          45.33579373852934,
          45.33656718067833,
          45.337500908131304,
          45.33850912961951,
          45.339404503757684,
          45.34025240597607,
          45.34119504699709,
          45.34225198723166,
          45.342975385452,
          45.34373765087828,
          45.34457141712823,
          45.34520671973865,
          45.3459652914809,
          45.3468944913872,
          45.34763544710913,
          45.34834020280647,
          45.34927992179219,
          45.350152851503346,
          45.35111122525774,
          45.35222320834729,
          45.353302302900545,
          45.35436280634842,
          45.355351858982594,
          45.35636600921168,
          45.357455718978656,
          45.35846858023884,
          45.359484076225094,
          45.36044248198346,
          45.36136159825707,
          45.36201903786664,
          45.362607731819615,
          45.36338685277333,
          45.3641318443685,
          45.36464971564687,
          45.365223329150176,
          45.365707271298,
          45.36644051487314,
          45.36727776004473,
          45.36789140847082,
          45.36862781694657,
          45.36935732697808,
          45.37007171229736,
          45.37093491702046,
          45.37173675951087,
          45.37239239138229,
          45.37311424419294,
          45.373893642577876,
          45.3747371400346,
          45.37557952956787,
          45.37617997045989,
          45.37676707820621,
          45.37752752882974,
          45.378324959843155,
          45.379006673860545,
          45.379605142930025,
          45.38034676039454,
          45.381162078651684,
          45.38194037878425,
          45.382527586665006,
          45.38295425868896,
          45.383675463602145,
          45.384443316479214,
          45.38494781921849,
          45.385568689166135,
          45.38640871629172,
          45.38693699116032,
          45.38780653396654,
          45.38835553836785,
          45.38885891735504,
          45.389154530847094,
          45.3898332667208,
          45.39055161538907,
          45.39088370020398,
          45.39142454130535,
          45.39206677437021,
          45.39272727527996,
          45.39351633320761,
          45.39419795561232,
          45.39471870690721,
          45.395467328939716,
          45.3965562787684,
          45.397069915703106,
          45.397574952630535,
          45.398274735105915,
          45.39902863728136,
          45.39967158075588,
          45.40013911515351,
          45.40050842848147,
          45.400799460712484,
          45.40146284138777,
          45.402032107932655,
          45.402394761819686,
          45.40278992019668,
          45.403446170751124,
          45.4042712768712,
          45.40541550236088,
          45.40594147911467,
          45.40645103491125,
          45.40736818440101,
          45.40877140195812,
          45.41076173057873,
          45.41213695009949,
          45.413260271751,
          45.41488591444327,
          45.41659224102789,
          45.41814194246695,
          45.41967431722273,
          45.42122421702902,
          45.42268026571465,
          45.42412747733741,
          45.4256593487682,
          45.427073589205904,
          45.42846906335461,
          45.42995491671941,
          45.431508868967576,
          45.43294949070756,
          45.43449795571096,
          45.436045896077744,
          45.43728591240688,
          45.43830163804861,
          45.439456093556636,
          45.44079735860992,
          45.44215224015999,
          45.44343120932357,
          45.444375003035816,
          45.445473560628116,
          45.44677225297314,
          45.44797609993086,
          45.44904543456109,
          45.44984120341096,
          45.45083794348416,
          45.452172561035646,
          45.45301431712992,
          45.45396179300497,
          45.45509309570998,
          45.45656097111738,
          45.458946085778955,
          45.460441648941014,
          45.462685237721104,
          45.46475459325952,
          45.466758441210935,
          45.472838358761976,
          45.484788098251514,
          45.50565315221926,
          45.53818408883597,
          45.5837903752552,
          45.64111097475223,
          45.704187093594705,
          45.76522474138874,
          45.815936438604616,
          45.856251405721544,
          45.88558165611295,
          45.907505296726434,
          45.923163721268345,
          45.93400337920274,
          45.94351507725153,
          45.955115010582595,
          45.972050141859455,
          45.999918103421045,
          46.03983971828734,
          46.09248763925718,
          46.158414662017144,
          46.23703736619839,
          46.327072657177446,
          46.42859592850699,
          46.541639647834934,
          46.667231187151486,
          46.8061285382561,
          46.957309432679715,
          47.118302808644636,
          47.28683927792054,
          47.463314218233265,
          47.64834611054478,
          47.83566798625701,
          48.023172248939865,
          48.20956769266305,
          48.39662784137522,
          48.57955770996967,
          48.75555971609832,
          48.92948050858245,
          49.093625856117846,
          49.24649494120659,
          49.393815701230196,
          49.52991360445883,
          49.65438721604678,
          49.76523014549145,
          49.8657542055838,
          49.95354106003255,
          50.02452950595315,
          50.081488363030104,
          50.125347509952476,
          50.153806861592756,
          50.16461030378974,
          50.15624106610237,
          50.12911427774848,
          50.083836488523914,
          50.02017330276769,
          49.93702726391105,
          49.836609476753964,
          49.723397604679526,
          49.58920810115112,
          49.43606536365915,
          49.28353242203603,
          49.10416673639415,
          48.90626942969818,
          48.70003420605666,
          48.478655587866776,
          48.25004021935163,
          48.00576350908627,
          47.74332031709656,
          47.48982967303377,
          47.22313318201167,
          46.93662462568459,
          46.659443183046186,
          46.37493857465736,
          46.07180596975934,
          45.76914529901862,
          45.464300795957406,
          45.15069647264574,
          44.82778404522427,
          44.504214552495256,
          44.175672589939694,
          43.84039272948602,
          43.50903893858218,
          43.174720354105986,
          42.826041969874936,
          42.48349316746876,
          42.139016908716485,
          41.786461125674016,
          41.41556209947847,
          41.064403391404404,
          40.70602954504817,
          40.32807491275439,
          39.959394441926364,
          39.59687493350447,
          39.2248773385048,
          38.84348071036869,
          38.48260607577791,
          38.11372693814414,
          37.73017677472638,
          37.359222962492275,
          36.99840874913466,
          36.624498682198684,
          36.256436845624044,
          35.89994905495483,
          35.532620226739965,
          35.167989300368006,
          34.80099922747861,
          34.44037918294277,
          34.07418353586902,
          33.70399761498599,
          33.34426143382196,
          32.98334220062625,
          32.62887100293793,
          32.2600001708878,
          31.91429267155726,
          31.567862840036128,
          31.20477116469836,
          30.852135211188124,
          30.5041019515858,
          30.15437616855528,
          29.795493418235086,
          29.439773034543396,
          29.092867442925655,
          28.74074003409194,
          28.389689200180523,
          28.04108618783154,
          27.694376883639453,
          27.343390182357584,
          26.99807895619347,
          26.654587155780035,
          26.298581014537678,
          25.96005462606094,
          25.62522181335514,
          25.276650295123694,
          24.933256141845575,
          24.600249322179046,
          24.25324649044085,
          23.912317605463883,
          23.578091177360236,
          23.238691252751593,
          22.913128686706337,
          22.587558377602974,
          22.260670840822804,
          21.945386829709058,
          21.632131528260782,
          21.309847674618073,
          21.00083876508177,
          20.692869915956067,
          20.374059350389338,
          20.069267127553385,
          19.76556702024636,
          19.45555588051149,
          19.152908458260175,
          18.853670810727607,
          18.54332865279199,
          18.233151029185514,
          17.931059701218214,
          17.621971149590077,
          17.314731946458686,
          17.01364025257034,
          16.714380610703095,
          16.411528787587354,
          16.109089073258097,
          15.805912897581694,
          15.502517862735598,
          15.194229158304234,
          14.887743611100595,
          14.580535534255668,
          14.267081270570092,
          13.957935779247167,
          13.645837748807345,
          13.329297699110638,
          13.017084780374136,
          12.708165383851261,
          12.391605224475741,
          12.076588495210615,
          11.771657252356125,
          11.428856918233718,
          11.115085510666857,
          10.811547455719008,
          10.508092171074775,
          10.202100623559728,
          9.902107827661291,
          9.606825690276896,
          9.310224501023288,
          9.016231326587475,
          8.724466119535888,
          8.429646961681588,
          8.141380509861708,
          7.847680658910126,
          7.548387398439552,
          7.2557844820569155,
          6.958131601985776,
          6.648654056656934,
          6.342844172003127,
          6.0429672685303055,
          5.724886961082017,
          5.414892843547536,
          5.1155752002257335,
          4.793823666094012,
          4.475778975369742,
          4.167811483842318,
          3.8436931817113065,
          3.5206956344703415,
          3.205702010388127,
          2.88152243930825,
          2.570958053977248,
          2.260990016202482,
          1.9440542354900103,
          1.6457803016981958,
          1.344874972001644,
          1.0359357387089771,
          0.7431647760945245,
          0.4470713207390033,
          0.14182208713334643,
          -0.14927943330410953,
          -0.44086000184198426,
          -0.7319241037042714,
          -1.01638476911375,
          -1.293997171603349,
          -1.5693275790496173,
          -1.815731952007402,
          -2.0444292003357356,
          -2.274251979854682,
          -2.481389733636101,
          -2.6646039940176514,
          -2.838972470329237,
          -2.9884123218117042,
          -3.11023864851491,
          -3.21472992012814,
          -3.2974032758040073,
          -3.355915431645531,
          -3.3913835382922035,
          -3.4048123854802816,
          -3.39803858859178,
          -3.3710280857549937,
          -3.325108369200027,
          -3.2611074439519006,
          -3.1802804961620454,
          -3.084287327127412,
          -2.974114920253723,
          -2.8483406607594324,
          -2.7114471000777796,
          -2.5612456990820673,
          -2.3972975979451885,
          -2.2240683506681793,
          -2.0399820767784145,
          -1.8454583819492636,
          -1.6462925311363519,
          -1.4426765317417052,
          -1.2355122652243018,
          -1.0266833604456562,
          -0.8203287147004672,
          -0.6151670102511687,
          -0.41186524360498994,
          -0.21142850065476018,
          -0.014788827337959793,
          0.17912239878214273,
          0.3695248181338274,
          0.5497528631733597,
          0.7202484735149064,
          0.8870487712695617,
          1.044087887633294,
          1.1923079643531156,
          1.3375689256931582,
          1.478910789980186,
          1.6021343359196878,
          1.7198753508456497,
          1.8343477615511954,
          1.935784009373079,
          2.034653048186079,
          2.1293593031519724,
          2.209958860284805,
          2.285664476839112,
          2.3577403536442203,
          2.422468884831358,
          2.4857085427293923,
          2.545101229466147,
          2.5939810802864383,
          2.63730522737304,
          2.6793949775599177,
          2.716254932991565,
          2.750329503332266,
          2.7847351056235126,
          2.8149824253505944,
          2.840858525848436,
          2.866832856374559,
          2.89238014379388,
          2.9184729701399044,
          2.9480580670122456,
          2.979556576918602,
          3.0146754054240814,
          3.054826423352543,
          3.096675035659461,
          3.139990556703625,
          3.184667815612314,
          3.2292327942258465,
          3.2743714193132347,
          3.32226300056172,
          3.371700814595118,
          3.424566973691934,
          3.4830876993069837,
          3.5485035527291973,
          3.619961418131344,
          3.6975441393227633,
          3.781726261926542,
          3.8735972866285193,
          3.9715187448803877,
          4.077521685436444,
          4.190621417091774,
          4.311281690122221,
          4.437588575041153,
          4.569883254801034,
          4.7074473641466374,
          4.8516013531248126,
          5.002459568735386,
          5.157973202353776,
          5.32030188422588,
          5.489787275327103,
          5.664176150901903,
          5.841915989421802,
          6.025743569696181,
          6.215099677021708,
          6.4056394329494495,
          6.599747195124951,
          6.796871578543679,
          7.000876578665662,
          7.210515601989129,
          7.414008863247476,
          7.619599845586016,
          7.833515395655514,
          8.04457660123133,
          8.25985916135352,
          8.481300158080627,
          8.703533225016418,
          8.922489518320095,
          9.142777567531969,
          9.366623691436404,
          9.591344715497799,
          9.819215722954493,
          10.057646146450304,
          10.29427445882235,
          10.526748962602603,
          10.7706706591195,
          11.015257917073688,
          11.253385326295108,
          11.506395584240968,
          11.758353643179158,
          12.005630872525707,
          12.267258033357656,
          12.530909801550804,
          12.786219345300823,
          13.057092854792527,
          13.32675583986419,
          13.587365823600374,
          13.862357481099695,
          14.134623496051223,
          14.394828503880833,
          14.66369232146545,
          14.921908316794884,
          15.18178455458598,
          15.44913444616254,
          15.710475691890215,
          15.966310648688792,
          16.220032134403954,
          16.464998920790475,
          16.71058892492495,
          16.964207762201045,
          17.209136022293695,
          17.461327162857966,
          17.716838938047527,
          17.960616386513582,
          18.210827985277778,
          18.46779453122991,
          18.71105572938212,
          18.97297690737294,
          19.241911854540295,
          19.500014477003784,
          19.767568083880867,
          20.039002069566862,
          20.306012026346778,
          20.564985494761704,
          20.83235000158009,
          21.09764463708101,
          21.35937942682989,
          21.6232834573419,
          21.876158423324846,
          22.128987388840248,
          22.384981603051383,
          22.63557889065227,
          22.886990330602675,
          23.1340420780325,
          23.381549899588997,
          23.63432836002035,
          23.884484257210527,
          24.141551206805165,
          24.410597473604646,
          24.668300827657163,
          24.941057687774595,
          25.235389680352345,
          25.52246640034228,
          25.820733265212404,
          26.146261319287532,
          26.459876076891092,
          26.758775995034405,
          27.083479341448516,
          27.416728140297526,
          27.737446902315366,
          28.074198688632993,
          28.424149427074962,
          28.76398193325348,
          29.105992458154173,
          29.455341264256788,
          29.804127060503248,
          30.15726674063583,
          30.5131652108559,
          30.873861402715676,
          31.24506793191564,
          31.61839907168172,
          31.987082870538966,
          32.36529463382383,
          32.74973439340146,
          33.129260166990576,
          33.507090698883566,
          33.89352452630285,
          34.274803994394475,
          34.62557077132737,
          34.97840526938305,
          35.3422523640149,
          35.67228967036853,
          36.00004151381821,
          36.351047157615085,
          36.67870026120099,
          36.99436114487999,
          37.3308200786596,
          37.65797535807802,
          37.98028943410984,
          38.319243502578786,
          38.65300220649891,
          38.980404389671115,
          39.31352333739406,
          39.6443216231381,
          39.9735661614373,
          40.30608505693576,
          40.64112651950941,
          40.97431678441473,
          41.3094050207714,
          41.639694499983264,
          41.970172151397996,
          42.298154479387556,
          42.63252777091632,
          42.961975135376704,
          43.29487399499332,
          43.63078203673385,
          43.960324113806855,
          44.280587363603054,
          44.61022584117488,
          44.91814656157118,
          45.21551535146278,
          45.52393224649588,
          45.816086558073636,
          46.105626265729946,
          46.40708217324153,
          46.695976393416366,
          46.980681696970024,
          47.302051147569,
          47.59138340375597,
          47.8763230782806,
          48.16904590905884,
          48.46962976416081,
          48.76150376781474,
          49.051398520258836,
          49.347994812593775,
          49.6389114935602,
          49.923916276300005,
          50.21596991028357,
          50.50779320964663,
          50.790358821381034,
          51.07948178153422,
          51.37078619788843,
          51.65129645766725,
          51.93142224600338,
          52.209249332542704,
          52.474303990615155,
          52.74191204645305,
          53.004554558054494,
          53.26258271656714,
          53.52397070358046,
          53.786443744982456,
          54.05305086160046,
          54.316936240388834,
          54.58382060666164,
          54.85971421690486,
          55.139833110999646,
          55.422915124787856,
          55.7068940366129,
          55.9926321361938,
          56.28063917988319,
          56.56640100698341,
          56.845524203622524,
          57.1221086914137,
          57.40251863786673,
          57.68043863229484,
          57.95409464108825,
          58.2316791416228,
          58.51290285072393,
          58.794513578866905,
          59.07724275831911,
          59.358543609297875,
          59.65469311588764,
          59.94482815433133,
          60.22598664665075,
          60.52269524291083,
          60.819740480228326,
          61.09034466522357,
          61.37502407232589,
          61.66738107404477,
          61.92984680065179,
          62.18397791345223,
          62.44359295123307,
          62.680022794538566,
          62.88649249020206,
          63.105048476809586,
          63.317588877884944,
          63.502937534715095,
          63.686564391128805,
          63.86294009574444,
          64.0186306609059,
          64.16673301835688,
          64.30334395151725,
          64.42663562399538,
          64.53651397526073,
          64.63161466900597,
          64.70816300520418,
          64.77281153676934,
          64.82311159398937,
          64.86002769221417,
          64.8892987824187,
          64.9063208822544,
          64.90763321466169,
          64.89550866877087,
          64.8720369381132,
          64.83709216836066,
          64.78896813125499,
          64.72646694884126,
          64.65180600879873,
          64.56676316067332,
          64.46485226581336,
          64.34873269231545,
          64.22535653966474,
          64.0865173517071,
          63.93315970541152,
          63.77116117350705,
          63.59061669908269,
          63.3980218639613,
          63.19137370472949,
          62.96576109058118,
          62.728687979886935,
          62.477231154300924,
          62.21413222611236,
          61.94292872182762,
          61.66377917267032,
          61.377245128534945,
          61.08228224831478,
          60.786882322751936,
          60.48741490343282,
          60.18441305967586,
          59.883376067533106,
          59.58182549475365,
          59.27927534524969,
          58.971913215094816,
          58.656278852646786,
          58.33845528784237,
          58.030759945024286,
          57.71592718520604,
          57.39280002548415,
          57.08655392095955,
          56.77130031276584,
          56.4490628529945,
          56.13098410273622,
          55.822499964849065,
          55.50558258918016,
          55.19053868704912,
          54.88597372525349,
          54.570850756057624,
          54.253975835514126,
          53.94573842453985,
          53.63051043994362,
          53.31091129134796,
          52.993804550829,
          52.67858715138811,
          52.35427618518613,
          52.029122339850936,
          51.709388406735044,
          51.37997236972773,
          51.05126997517338,
          50.72869087137583,
          50.40673533921882,
          50.087407082488724,
          49.76918964500379,
          49.44359393141434,
          49.12774868708828,
          48.80936249396381,
          48.482471009638466,
          48.16154030687558,
          47.83975326351295,
          47.51791137988673,
          47.198017846154094,
          46.87762889692828,
          46.55362901235234,
          46.23150805396997,
          45.91080859581661,
          45.58201851787454,
          45.258302837766585,
          44.93505012540116,
          44.605107474019384,
          44.277477323798685,
          43.955016245727585,
          43.62820678836799,
          43.30942836303323,
          42.98600470233816,
          42.65115161151966,
          42.32784807714479,
          42.001137866568904,
          41.66248222985032,
          41.315973962492706,
          40.9869940930252,
          40.64246110903902,
          40.284759235795846,
          39.93720250367378,
          39.58972856230055,
          39.2391737060455,
          38.881433406578324,
          38.53986266002814,
          38.196382868875865,
          37.844457631283646,
          37.50221303275838,
          37.15913681583543,
          36.81304313884099,
          36.465684266328594,
          36.12490782074833,
          35.78431103636534,
          35.43850879148098,
          35.09626933188624,
          34.74763222137042,
          34.40528131864121,
          34.060431499684526,
          33.709413402553835,
          33.374583192523616,
          33.03659172933373,
          32.69472681307677,
          32.352871024716386,
          32.02382317548636,
          31.692640813105342,
          31.351825875548375,
          30.981931236957166,
          30.649926729282427,
          30.308778463062776,
          29.958820918627342,
          29.612163221650928,
          29.27205607700253,
          28.928528663361543,
          28.587289296537417,
          28.252425888312267,
          27.913438454958953,
          27.575693933844544,
          27.243387472339872,
          26.920450503404965,
          26.593324956162824,
          26.268851354846873,
          25.961662584533766,
          25.648983227043615,
          25.330841804496647,
          25.024094124192995,
          24.716810376168564,
          24.397226452860163,
          24.09106675332628,
          23.792899362983363,
          23.47963434262606,
          23.178586035797643,
          22.89036554768616,
          22.588507931956737,
          22.29472900096752,
          22.016067916560125,
          21.72151298888659,
          21.424651910482837,
          21.14884867245253,
          20.831723694209558,
          20.52882144534976,
          20.251926737154022,
          19.969856166318113,
          19.674857734782908,
          19.394901622127772,
          19.115589157764912,
          18.825826774014903,
          18.540882879612287,
          18.25670131857264,
          17.966870319203498,
          17.679928870075006,
          17.395216912925186,
          17.111623677846932,
          16.83327633895371,
          16.553289938794,
          16.272858561236113,
          15.99475508423096,
          15.714673362984552,
          15.434100350148046,
          15.153104332282986,
          14.878737149287456,
          14.59569361776559,
          14.314400851082752,
          14.037187911041322,
          13.752669178415237,
          13.469130969104476,
          13.186252551954205,
          12.899769263558902,
          12.608741436899221,
          12.320483607054424,
          12.033333952864483,
          11.743212867818992,
          11.452400836491277,
          11.163832061493704,
          10.87428313586358,
          10.581298211797025,
          10.289585233925095,
          10.003460194212307,
          9.714023874585337,
          9.431185913029365,
          9.152679304249583,
          8.876103763020335,
          8.60106861338303,
          8.330234351226155,
          8.062399392062407,
          7.789153086387231,
          7.518843322043353,
          7.244486191065995,
          6.972379311833277,
          6.702715121419891,
          6.397657078386688,
          6.119546934832735,
          5.850730903770537,
          5.5778769180651375,
          5.295731491782003,
          5.010585368516014,
          4.732149618759102,
          4.446223579405364,
          4.154052964445426,
          3.8707771410600462,
          3.578668000483556,
          3.283248346031772,
          3.009831509551147,
          2.7294772185752003,
          2.439359255974464,
          2.165069821066807,
          1.8922510554894079,
          1.611875081193677,
          1.3398181623517504,
          1.06716635467668,
          0.7930661827227454,
          0.5213396865892294,
          0.24900753508883527,
          -0.02927115132790787,
          -0.30631210960349814,
          -0.5903008760638585,
          -0.8740797373657807,
          -1.1557809442866598,
          -1.43457206073578,
          -1.7109215467472685,
          -1.9875241679544764,
          -2.243214593134427,
          -2.4798193150215364,
          -2.716157479213643,
          -2.9366919052011538,
          -3.1346932650920354,
          -3.323224561917978,
          -3.4968741879849956,
          -3.6479032785146766,
          -3.782963066035635,
          -3.8967752603163106,
          -3.986063585407675,
          -4.05570221046406,
          -4.102947137383738,
          -4.125668714420832,
          -4.126023698323803,
          -4.106316079237101,
          -4.069879750356919,
          -4.013507029812954,
          -3.9388505583439106,
          -3.8521203595204794,
          -3.748246727545021,
          -3.628567392124721,
          -3.4997206517553705,
          -3.356917373552429,
          -3.2018029807575537,
          -3.037824888284141,
          -2.8652333256444793,
          -2.684198629368167,
          -2.4974028485933752,
          -2.306800582453958,
          -2.1105985560625293,
          -1.9120259660815933,
          -1.7137098506786699,
          -1.5177394157354076,
          -1.3267271944641734,
          -1.138814197084552,
          -0.9579866704342876,
          -0.781498247925053,
          -0.6072680113377534,
          -0.4379243557395881,
          -0.2726371571455989,
          -0.11020970900653274,
          0.04568686663126684,
          0.19655028292906002,
          0.33990140254323953,
          0.4746665422254469,
          0.6091185402850376,
          0.7351145318647105,
          0.8559473234029513,
          0.9709084656969998,
          1.0877879580709697,
          1.1983330275124655,
          1.2949339891721148,
          1.3926104580928997,
          1.4861922949559723,
          1.5718667115192695,
          1.6556812775728242,
          1.737533576764661,
          1.8103433203707366,
          1.8768386752259385,
          1.94169337644323,
          2.0008644539328135,
          2.058011016547057,
          2.113376084090168,
          2.161917395027421,
          2.206327915063,
          2.2470241984415624,
          2.2844376943959053,
          2.3167971720485934,
          2.3463759940634703,
          2.3732528454295974,
          2.3977015645263875,
          2.419424716496846,
          2.4391257210056154,
          2.4581661721343564,
          2.4760834025730842,
          2.4948209717097534,
          2.5152157292469712,
          2.537726956003219,
          2.563045175832419,
          2.5923259488744463,
          2.6235803001400018,
          2.6547104375531503,
          2.6882468672845015,
          2.722868273296302,
          2.7577078965335047,
          2.7947002260250353,
          2.833303583593914,
          2.8722764445081204,
          2.913744128947523,
          2.9582002371524707,
          3.0043149595698164,
          3.054572368166239,
          3.109635545671697,
          3.169127382480864,
          3.233982551457134,
          3.305067027519865,
          3.381649352350055,
          3.462579502841436,
          3.548881480285042,
          3.6387510749962053,
          3.73422127659939,
          3.837246845655587,
          3.9438950955057437,
          4.055148513043715,
          4.175796563345039,
          4.299857145929124,
          4.427920028760938,
          4.564200864570259,
          4.706662589097586,
          4.845795057310785,
          4.990574450932911,
          5.141452335010133,
          5.2924638623179305,
          5.445462298161452,
          5.6047012143928665,
          5.7656655200045765,
          5.923161432890435,
          6.086715257279508,
          6.253030729176701,
          6.418953847168114,
          6.591517594838,
          6.767784638605135,
          6.939741504314393,
          7.117000458113039,
          7.300423866865699,
          7.485421635925301,
          7.672668670726102,
          7.867973639907908,
          8.064928215884052,
          8.261454641495268,
          8.456323783215645,
          8.653707009385208,
          8.853109363506482,
          9.052095269379818,
          9.251010569352694,
          9.455883497431737,
          9.664548108832998,
          9.86867958138228,
          10.072192968002337,
          10.283140091676069,
          10.493257173499961,
          10.697821767737025,
          10.911771274136825,
          11.127694008643468,
          11.338431291874018,
          11.555933018342088,
          11.77915157388375,
          11.999906705493894,
          12.22073278204977,
          12.450875494394165,
          12.677462465857127,
          12.89944884663247,
          13.131417460797836,
          13.365342006427221,
          13.59036767840702,
          13.819426994262399,
          14.052295347324945,
          14.27679261328338,
          14.505431181488275,
          14.74058925982937,
          14.96915917570018,
          15.197299561430436,
          15.424908144460323,
          15.64782793185962,
          15.86418333806608,
          16.081449408336358,
          16.302276766260317,
          16.520593847042477,
          16.73952000038133,
          16.966763792036904,
          17.187508805665516,
          17.402097786691098,
          17.62437166898507,
          17.849784911959865,
          18.067067204532794,
          18.288807239623967,
          18.519673597989403,
          18.741453074728906,
          18.960201003842627,
          19.187528970108,
          19.40603607314136,
          19.6295802469014,
          19.851471769792692,
          20.063892902360426,
          20.28284044547063,
          20.49506265498528,
          20.70484641453179,
          20.931845452406186,
          21.14380278638029,
          21.351556856093342,
          21.573710934054002,
          21.797372150281266,
          22.025143555702744,
          22.26162635728783,
          22.49555917009494,
          22.74108251568682,
          22.997379529708848,
          23.259893410872117,
          23.521739121800756,
          23.803526124778454,
          24.085909301716974,
          24.364358564513505,
          24.66952019053571,
          24.984296990340198,
          25.288991394864112,
          25.621334529400418,
          25.94923672774287,
          26.231807525533302,
          26.528803991800288,
          26.83558524180938,
          27.13251200071202,
          27.43363846792482,
          27.745063153098563,
          28.050495350322393,
          28.352985451389543,
          28.657802793457517,
          28.965318681392027,
          29.290414036766883,
          29.613305450592385,
          29.935893118228776,
          30.261392835932636,
          30.590872510173433,
          30.923368052022465,
          31.244988057728378,
          31.575803204180385,
          31.911151803658623,
          32.25018089339783,
          32.59480910699614,
          32.937627402566825,
          33.28794588439994,
          33.6279347381299,
          33.96190557936996,
          34.294610113578194,
          34.627339545147244,
          34.95052864881934,
          35.281680386612635,
          35.6130857622301,
          35.9290746696189,
          36.24852163663968,
          36.57422177102859,
          36.899631083515544,
          37.22588313597998,
          37.559215504866344,
          37.892777877735455,
          38.22551890017168,
          38.560538554247486,
          38.89158251079862,
          39.23302529975385,
          39.57820606213428,
          39.91884227485884,
          40.26306141062812,
          40.60937815640735,
          40.951666628629305,
          41.29318404025987,
          41.63657129801098,
          41.975595254807295,
          42.31734029198733,
          42.65353646987068,
          42.98831713780912,
          43.32888139048449,
          43.6655586896088,
          43.99368605046921,
          44.33142138232008,
          44.66215604052806,
          44.98490126596221,
          45.320020446725124,
          45.6423555683974,
          45.957346640807316,
          46.28348996674704,
          46.60040390395959,
          46.911337690664304,
          47.23368236810229,
          47.548562973696995,
          47.84594364853935,
          48.161893501649466,
          48.47966621412509,
          48.78104052066766,
          49.09550960412552,
          49.41365828497713,
          49.71392945487082,
          50.01885034497675,
          50.32869305739655,
          50.62525095914379,
          50.92564264333343,
          51.23246453113018,
          51.524620784434596,
          51.81150141540853,
          52.10062067544182,
          52.380974291115784,
          52.65774195484237,
          52.92921084593508,
          53.204554760149584,
          53.4783903496776,
          53.75658240531161,
          54.0366105377843,
          54.31404765242369,
          54.59787519797507,
          54.88992129520901,
          55.18350011196275,
          55.47300473071834,
          55.77115199960749,
          56.06407678115986,
          56.34957599191736,
          56.640500017847735,
          56.918919577569525,
          57.18651191609925,
          57.464796277014536,
          57.7489816803978,
          58.01228352171607,
          58.27448447590476,
          58.549261764877976,
          58.81966354190635,
          59.0810190597338,
          59.34550804391031,
          59.621904510986425,
          59.89243981498452,
          60.15054633062333,
          60.4146359330284,
          60.690927131716464,
          60.95117336000782,
          61.211926574230255,
          61.49175187232582,
          61.75862622972725,
          62.002538063312464,
          62.25130083747442,
          62.494978305394376,
          62.70413113581055,
          62.90684831747295,
          63.11819867225374,
          63.30876360557971,
          63.48255241562824,
          63.65652732608937,
          63.81188357849256,
          63.952223161903035,
          64.08384835040273,
          64.20228694366901,
          64.3058778678585,
          64.39431052265087,
          64.46181476053984,
          64.5138221164496,
          64.55037676437557,
          64.57202236022114,
          64.58122002040913,
          64.57357281798858,
          64.54846525516317,
          64.5066277721625,
          64.44855207527613,
          64.37828463181846,
          64.29050019600527,
          64.1837097623907,
          64.06820377617622,
          63.9359705388783,
          63.78154042851915,
          63.62139498865959,
          63.443128478639025,
          63.246074115359114,
          63.044716788422015,
          62.830994017778295,
          62.59475675268386,
          62.35145991094609,
          62.102827126482275,
          61.836469170239184,
          61.56052117465298,
          61.28350782294512,
          61.00211248774538,
          60.71319822773284,
          60.415230565970255,
          60.11068377896734,
          59.80297097306492,
          59.487662636397125,
          59.166261821624495,
          58.84489002582075,
          58.51493489560721,
          58.17376645681918,
          57.83577562934087,
          57.50159619448542,
          57.150206968316674,
          56.8098775057813,
          56.480478255854734,
          56.1337826236115,
          55.79212702638441,
          55.46529845716434,
          55.122389420158356,
          54.78620751035339,
          54.45562989734567,
          54.112611391115095,
          53.77183859158204,
          53.4346064857942,
          53.08624326957375,
          52.73705271285156,
          52.396702556113986,
          52.04201990757297,
          51.68831138692674,
          51.341335793576874,
          50.98392454616007,
          50.63082960851566,
          50.2845751874734,
          49.935157892616516,
          49.585502316420516,
          49.23450291787667,
          48.89043106822508,
          48.53718118140634,
          48.183106174437874,
          47.83290180765036,
          47.48342297947092,
          47.13267354616005,
          46.779444550330155,
          46.4290543350682,
          46.079316639733236,
          45.72484143705796,
          45.33074088809445,
          44.97905968459101,
          44.61934566425871,
          44.25404515186802,
          43.89440567514032,
          43.52880276659065,
          43.16432513341936,
          42.80109993962998,
          42.426443112120424,
          42.05458400887959,
          41.68869886475714,
          41.30406811282386,
          40.91732412143384,
          40.55184686255979,
          40.162958205166085,
          39.77007580965446,
          39.39551996242697,
          39.011968802918155,
          38.61155593306669,
          38.237991349744036,
          37.862498253284045,
          37.47087662406409,
          37.09438850324539,
          36.725218789343096,
          36.34145903615912,
          35.962788171007944,
          35.59742720821883,
          35.22314046889542,
          34.845470615037904,
          34.47077348983268,
          34.10078165992983,
          33.720052942159576,
          33.34048087728195,
          32.970353952554824,
          32.59422500184866,
          32.21704072487308,
          31.8485029905479,
          31.48400049576467,
          31.112191483180407,
          30.739825730803798,
          30.37312850259972,
          29.99985756267379,
          29.617963798496188,
          29.2467291159945,
          28.875955840739014,
          28.502309183512967,
          28.135940856742728,
          27.766807861272547,
          27.39749678995351,
          27.034658109848234,
          26.677225788696784,
          26.318530075613232,
          25.967085718463615,
          25.627262362385075,
          25.277091515812,
          24.93020802031985,
          24.58994780320747,
          24.23465416028736,
          23.88850758412448,
          23.548554735994852,
          23.202723948728426,
          22.86842250365915,
          22.538816273231063,
          22.205466008741364,
          21.883740759053744,
          21.559288904454927,
          21.224337741051304,
          20.91460446251487,
          20.59968776191551,
          20.264677799873517,
          19.954420542202634,
          19.642669745042046,
          19.314741441083697,
          18.998021408460353,
          18.688882635627362,
          18.36340240744392,
          18.052109997714656,
          17.76556782272875,
          17.47181725701148,
          17.182570274630805,
          16.904251916910184,
          16.62114939379875,
          16.33708929371887,
          16.059215464919923,
          15.775224779471078,
          15.492091854500226,
          15.202113729578942,
          14.903877747934894,
          14.602521465534105,
          14.301146836855489,
          14.004371042662179,
          13.704510927008922,
          13.404502075527272,
          13.106773714107563,
          12.810173788665038,
          12.50792605386516,
          12.204309055755756,
          11.901595980951306,
          11.597353718742553,
          11.29308072858805,
          10.994020537350567,
          10.699498462628563,
          10.400942490118092,
          10.107273838156436,
          9.819291714596416,
          9.53246740519458,
          9.246960777908608,
          8.967798298246185,
          8.687201947034684,
          8.406735056830456,
          8.129034611020845,
          7.84208767826444,
          7.552771676692099,
          7.270788312748914,
          6.948883786893604,
          6.647360760685175,
          6.352150079582912,
          6.054043535841086,
          5.747904281550427,
          5.450203041801112,
          5.153571962327716,
          4.845539280114005,
          4.547248750200525,
          4.254694092048906,
          3.950410623554936,
          3.653454874272269,
          3.361836168080324,
          3.0649956197929056,
          2.784864028950497,
          2.5030941040493673,
          2.2184336888929423,
          1.9506677645006707,
          1.6831380259049515,
          1.4099914836804952,
          1.148007225055149,
          0.8825854868148396,
          0.6091438528935407,
          0.3329631741793019,
          0.047078976871867295,
          -0.2352447315031835,
          -0.508756199989569,
          -0.7853828673457621,
          -1.0603026857941362,
          -1.338679442750711,
          -1.6007652894089202,
          -1.847553644318416,
          -2.1040329713990307,
          -2.3418535145622625,
          -2.5538629993803976,
          -2.765133911770426,
          -2.9701720576168875,
          -3.1595598230605817,
          -3.3382909620172394,
          -3.504147407326207,
          -3.6539679529776756,
          -3.78939863520616,
          -3.907272219931894,
          -4.0066095925570115,
          -4.091204898540712,
          -4.158262119894641,
          -4.206623367713327,
          -4.236058617552424,
          -4.246644353929049,
          -4.239034035612159,
          -4.213506574398528,
          -4.171128279359379,
          -4.113710327681287,
          -4.0419241443501,
          -3.9559111690968516,
          -3.857513719772755,
          -3.748090036784706,
          -3.626855195420487,
          -3.496670562598065,
          -3.3563265848874084,
          -3.205151737412957,
          -3.0488316854022117,
          -2.8854476964654956,
          -2.7128724275487377,
          -2.5379062116092443,
          -2.3614629685122734,
          -2.163055172621855,
          -1.982818367233269,
          -1.8038731289925154,
          -1.6272554952898974,
          -1.4532546008280691,
          -1.278990090742027,
          -1.1098506009116396,
          -0.942136755407772,
          -0.776576723408273,
          -0.6158370508830519,
          -0.4544020997355928,
          -0.29942973559885255,
          -0.1454188060245573,
          0.007936003205972264,
          0.15565305258712397,
          0.29457625258933406,
          0.4314142580302064,
          0.5683430981854892,
          0.694846679137476,
          0.8188379360171041,
          0.9358809833941538,
          1.0527320108236529,
          1.1671660272613753,
          1.2671443883084748,
          1.3640722172091344,
          1.4577010292601715,
          1.542415850180607,
          1.6223748629558545,
          1.699971255890312,
          1.7685763797422365,
          1.8275838981024881,
          1.8824069707097382,
          1.9315755100308414,
          1.9761177832561962,
          2.0184224135107582,
          2.058772295444945,
          2.090048449146628,
          2.118414284995719,
          2.1433218020241127,
          2.164499847176934,
          2.183624398856786,
          2.201745563914696,
          2.2191163862191376,
          2.2356112568211453,
          2.252205190590705,
          2.2696734386851425,
          2.2861436871219065,
          2.3028388082520315,
          2.320156656784082,
          2.3385900642083643,
          2.3592713493285324,
          2.381709319584404,
          2.4070750850405918,
          2.433536714213401,
          2.460323180625303,
          2.488334737445989,
          2.517470701544321,
          2.546629802554478,
          2.5761035809681236,
          2.605801430812296,
          2.6346378618305946,
          2.664230743227441,
          2.694549804929435,
          2.7258159022823096,
          2.759238603216797,
          2.7944993759776464,
          2.8341113639860507,
          2.878222183433039,
          2.9265506539557307,
          2.9817570389312267,
          3.0424355076743477,
          3.10706981078607,
          3.176268493362981,
          3.2518366092586892,
          3.3306555083175096,
          3.4167003836949985,
          3.5103863409690583,
          3.608075276617331,
          3.712465197951945,
          3.824986779880386,
          3.9414953622228603,
          4.063337721981724,
          4.189228453085594,
          4.32305494845731,
          4.4601335086936915,
          4.599612768708412,
          4.745724565432593,
          4.894244097721296,
          5.041885910037444,
          5.191764910987589,
          5.346624945272,
          5.502136993699961,
          5.66031023985374,
          5.827040420228186,
          5.993915138638752,
          6.163019081791028,
          6.340004190690086,
          6.51480791576448,
          6.693052797442919,
          6.876344788889039,
          7.061744999846965,
          7.249530507137674,
          7.442401885917925,
          7.6363173798228825,
          7.833347531175167,
          8.031939902077687,
          8.231630218605986,
          8.437204769860044,
          8.646940742133532,
          8.857529835015656,
          9.07108788216632,
          9.290443494699435,
          9.513642844314555,
          9.734015257909563,
          9.952667334600143,
          10.176895422656376,
          10.399408406976416,
          10.612948927801359,
          10.835322750369697,
          11.060327826084288,
          11.278301473239495,
          11.503489875629574,
          11.73523294520646,
          11.963468785348505,
          12.191789007678494,
          12.429478131732653,
          12.665443031503617,
          12.89579158070827,
          13.136067873538982,
          13.377967392787282,
          13.609060380777938,
          13.842656718036658,
          14.079282585095763,
          14.303025116185163,
          14.531193772188637,
          14.76343373257601,
          14.988364717265448,
          15.210401108907472,
          15.432194824916941,
          15.648898221378381,
          15.859666504257781,
          16.07159243459752,
          16.28587704705328,
          16.492741049637687,
          16.70271477593439,
          16.916959488029352,
          17.120388676395603,
          17.321872086130636,
          17.52598437352893,
          17.73069132213282,
          17.923541381424986,
          18.12415877679045,
          18.33055247009981,
          18.527339344950683,
          18.728619393999544,
          18.93229651117788,
          19.159708602880198,
          19.4082784942946,
          19.657013882891285,
          19.913688153069966,
          20.1810237350667,
          20.44925984654765,
          20.71943223986166,
          21.013255340780542,
          21.296880996082397,
          21.587008717105277,
          21.87669543522121,
          22.14614390357882,
          22.429699716773424,
          22.72867919352653,
          23.015124808272496,
          23.309689131058693,
          23.62072737599991,
          23.917317997509155,
          24.22728923897416,
          24.549557830741826,
          24.859284779918198,
          25.198737878170633,
          25.55124425892161,
          25.891361522185825,
          26.253819551000504,
          26.613487891441043,
          26.953390314574257,
          27.310638571378494,
          27.675098879004985,
          28.02257609685884,
          28.372024437456844,
          28.722782278393833,
          29.056779778170263,
          29.391639482158382,
          29.733978619258064,
          30.06954199813284,
          30.405578557387145,
          30.74290460478035,
          31.076644811849285,
          31.415921869142643,
          31.75168566214963,
          32.07880615187477,
          32.40706885545298,
          32.73851460197841,
          33.0676807176834,
          33.39832381666462,
          33.722583165076074,
          34.047658623891216,
          34.379238402257826,
          34.69422166225884,
          35.000045231143986,
          35.31662744158378,
          35.626168566857515,
          35.92233434856951,
          36.23308218134385,
          36.54449892409094,
          36.84456016976044,
          37.1509961306791,
          37.46708218572251,
          37.778666332331575,
          38.09528208590343,
          38.41604525917596,
          38.73530274120566,
          39.055625712890404,
          39.37255657030364,
          39.68694055810615,
          40.00704721386262,
          40.32652264170847,
          40.648259894550165,
          40.97597427139211,
          41.301638338918146,
          41.62584438215976,
          41.956297836934525,
          42.284245628285845,
          42.613262425546324,
          42.95240079702139,
          43.28646993462193,
          43.625021677518454,
          43.97328896243987,
          44.312702543278725,
          44.64813124991473,
          44.99439254626033,
          45.3277421467613,
          45.66063501705099,
          45.99941329622676,
          46.3335422645042,
          46.67401168335572,
          47.01662165443693,
          47.35177127067828,
          47.68824468473037,
          48.02732167165485,
          48.34825278519832,
          48.67520754566773,
          49.009570294261664,
          49.330733779477306,
          49.64803478144664,
          49.97272288173262,
          50.28626181294306,
          50.59636292421281,
          50.91164452188793,
          51.217231473830275,
          51.523743506303816,
          51.83079606383554,
          52.12537571031702,
          52.41455454927051,
          52.69755428166409,
          52.97307848949289,
          53.244803055412994,
          53.51315808323412,
          53.77889165725008,
          54.0491643707451,
          54.35163494380637,
          54.62137644655208,
          54.893989465334805,
          55.17536679309078,
          55.45710389409889,
          55.74015307895498,
          56.0220228048467,
          56.303164609917786,
          56.58000819492296,
          56.841236795067466,
          57.09245391592853,
          57.339838256342624,
          57.58516029644259,
          57.82775634694091,
          58.070779490401414,
          58.308651526869305,
          58.57167097058137,
          58.81437714424254,
          59.060321005464154,
          59.31221678831944,
          59.57476904619701,
          59.84574422526881,
          60.10556921586334,
          60.36630394592955,
          60.64091672994618,
          60.911254785589264,
          61.16707885205474,
          61.434349921802685,
          61.70112616186897,
          61.93388386434675,
          62.15830832844092,
          62.38125936047842,
          62.590587097629445,
          62.787725268168,
          62.97481626703805,
          63.16308213907139,
          63.34120860191085,
          63.50523215150407,
          63.665414522459955,
          63.81702987323637,
          63.95334470163948,
          64.07447428964709,
          64.17894658610709,
          64.26765538233062,
          64.33715010727487,
          64.38424431844649,
          64.41170181037019,
          64.42031773573312,
          64.40931520031016,
          64.38339297026431,
          64.34336667198134,
          64.28737658398609,
          64.21855403422586,
          64.14121152797942,
          64.04995761227521,
          63.94846791151717,
          63.838660338765,
          63.71870140813576,
          63.58564694001701,
          63.43286502924833,
          63.26756956130647,
          63.089021454444065,
          62.89696735199743,
          62.69109830514015,
          62.475849872656646,
          62.24723760717158,
          62.00403832883274,
          61.74744926263506,
          61.48441603100128,
          61.21147438509104,
          60.92554547200103,
          60.64556168698664,
          60.35556131366098,
          60.05528774603434,
          59.761106324338954,
          59.45953567556409,
          59.14674387373742,
          58.83877987674616,
          58.52537351931939,
          58.19696747819619,
          57.87673206832023,
          57.55904407515568,
          57.219522834317935,
          56.89825560150076,
          56.583692262369006,
          56.247382950278954,
          55.925194275975464,
          55.61661738404746,
          55.287665670641275,
          54.97358775518657,
          54.667044557843184,
          54.34926065592826,
          54.033403777056186,
          53.72032698465734,
          53.39942408763453,
          53.07425797607542,
          52.76026576865347,
          52.43499851719745,
          52.1044872768535,
          51.77589236535425,
          51.44234818902297,
          51.10348480799015,
          50.77061054705971,
          50.43943035416799,
          50.105447993078876,
          49.775680140952204,
          49.437693937288984,
          49.109475016229915,
          48.774063273912645,
          48.44174250821862,
          48.11031287371997,
          47.780591614667,
          47.455178389408125,
          47.12345403343129,
          46.79250829325339,
          46.463096924711756,
          46.1302104268118,
          45.79628426756038,
          45.46087308387347,
          45.12707494978503,
          44.78291080964345,
          44.435197543313826,
          44.095601761189705,
          43.74644247020221,
          43.398053080714256,
          43.05685402972333,
          42.707021234983905,
          42.35524805506865,
          42.009044387462,
          41.65243165458508,
          41.276103231129696,
          40.9187023488142,
          40.5627451827555,
          40.18094692538712,
          39.81602462825786,
          39.4544890754482,
          39.075386646568006,
          38.70226880539241,
          38.3415785656529,
          37.97676501433701,
          37.60772571361131,
          37.250223049724525,
          36.88744324348057,
          36.52416454726091,
          36.1573556895985,
          35.79788148487995,
          35.437265081393555,
          35.07271719105067,
          34.70233914650486,
          34.334966911426164,
          33.96279699298524,
          33.57711933124139,
          33.20363930786742,
          32.83230262301181,
          32.460658625022646,
          32.08325053537434,
          31.71958169915117,
          31.357203914839488,
          30.990154777772926,
          30.631982239623195,
          30.275221666848807,
          29.915767642342555,
          29.55390361714718,
          29.197115634246998,
          28.838005033417023,
          28.47869388507307,
          28.13208967675225,
          27.77559158249143,
          27.421637809516504,
          27.090678679335795,
          26.75922066017794,
          26.43484794550527,
          26.11289662642745,
          25.79380377776938,
          25.47813120634998,
          25.164360541699196,
          24.847550507204833,
          24.534393432863162,
          24.220401011247223,
          23.90615233246471,
          23.589665253530022,
          23.273895528473595,
          22.971481724084825,
          22.665888937391326,
          22.3620898886782,
          22.069296232048632,
          21.77440371495339,
          21.466856629222264,
          21.17859792836629,
          20.8934541543908,
          20.58147048470993,
          20.285748877176808,
          20.001366350635404,
          19.69549193285993,
          19.395772270006105,
          19.102822298479825,
          18.79866540471908,
          18.49086458184024,
          18.18718747554513,
          17.87562827174696,
          17.561654080135373,
          17.25428736220401,
          16.943385909834873,
          16.635600645459125,
          16.328601752378894,
          16.022285516326736,
          15.713355480669735,
          15.406459366001444,
          15.098179998114757,
          14.788261722135921,
          14.480811970868182,
          14.168821267560622,
          13.861490918040086,
          13.552445228312457,
          13.241443743478781,
          12.931410145368236,
          12.621438580723158,
          12.308900177709276,
          11.991856791088074,
          11.677526845036505,
          11.368176690497656,
          11.05392183631032,
          10.741464037040421,
          10.439526008169324,
          10.136818386414463,
          9.82423644278,
          9.531400298275525,
          9.238686371846137,
          8.941403335004782,
          8.65284802362914,
          8.370242659390138,
          8.090755133450198,
          7.810471819959358,
          7.5290850443663935,
          7.255905312909552,
          6.981271089469676,
          6.696914938425842,
          6.4181863050356345,
          6.146481325295194,
          5.85483052076996,
          5.570950955358325,
          5.297348884398934,
          5.001466191033476,
          4.702468465076711,
          4.418485385786011,
          4.116906583262891,
          3.8174808038538623,
          3.5235553830862942,
          3.2118632499177506,
          2.9281086942201098,
          2.6440876629142287,
          2.344325939053991,
          2.0635779600180695,
          1.787671719069037,
          1.4993269583573747,
          1.2207628985657388,
          0.9454794304059446,
          0.6640958804600767,
          0.3877002089322421,
          0.11448444930974705,
          -0.16578620518746093,
          -0.44750527714441424,
          -0.7258070032432261,
          -1.0046909442100316,
          -1.2832724040354047,
          -1.5631608335006302,
          -1.839274903874311,
          -2.10599621587619,
          -2.3694675277233017,
          -2.62343893987978,
          -2.858403956492617,
          -3.090102958119805,
          -3.3069641079040974,
          -3.507229477288608,
          -3.6938382521769215,
          -3.8629814663577817,
          -4.01420132205265,
          -4.1466584356736265,
          -4.259877706509005,
          -4.352527189824512,
          -4.422964230685253,
          -4.473565063110901,
          -4.502183007140632,
          -4.507021577830109,
          -4.489283337148372,
          -4.45174440211488,
          -4.397050804131656,
          -4.323598131913655,
          -4.231769913016596,
          -4.124768055855302,
          -4.000782801956151,
          -3.848806574422038,
          -3.7008431642453847,
          -3.542712038947353,
          -3.378535522961384,
          -3.2077932292354094,
          -3.030690460174938,
          -2.8519001098794727,
          -2.666681213026716,
          -2.477801972577572,
          -2.288094039386811,
          -2.0954870850756433,
          -1.902136836077668,
          -1.7092534902537027,
          -1.5183759989546781,
          -1.32893877896922,
          -1.1404759348918994,
          -0.9554250517824684,
          -0.770610521851054,
          -0.1285582442863698,
          0.043080907309530216,
          0.211280767432397,
          0.37327933021129,
          0.5247876104488909,
          0.6714241109417203,
          0.8148578400793581,
          0.9457752361654689,
          1.0699833089646602,
          1.1874050240947238,
          1.3062525644859002,
          1.4148382096503505,
          1.5101383386416976,
          1.6047030472306796,
          1.6933293187395781,
          1.7742607545942723,
          1.8534355266406306,
          1.9285556499646628,
          1.9949586429074053,
          2.057049811045084,
          2.117137136923471,
          2.1715376262881505,
          2.224645268626372,
          2.2751400325408344,
          2.3194737710752404,
          2.3609646532785145,
          2.3993493477777537,
          2.434847778227501,
          2.4667596720468703,
          2.496246389384398,
          2.524205932018945,
          2.5508374102446174,
          2.5768897875550767,
          2.603334615586056,
          2.627617746830503,
          2.651458920424354,
          2.675565875821827,
          2.699632969712007,
          2.724885295219408,
          2.7514870422184745,
          2.7805366985599824,
          2.8100202298576566,
          2.839351985580052,
          2.870126952080361,
          2.902052472474704,
          2.934071944572666,
          2.9667649677538774,
          2.999161281092309,
          3.033247502509151,
          3.069458790047973,
          3.109101654141103,
          3.1521991926926627,
          3.1984060810843857,
          3.2513735416748735,
          3.3096335977130296,
          3.3721912004533228,
          3.442704234125669,
          3.518800508446662,
          3.598955450020016,
          3.6852691404136575,
          3.776690115407541,
          3.873897199025853,
          3.9809590777696595,
          4.093369901196933,
          4.21073543806722,
          4.337228720660737,
          4.467472306282675,
          4.600399174940791,
          4.7378920080515625,
          4.8818043434231715,
          5.025019052801778,
          5.174247070572004,
          5.328205564256003,
          5.479368840755798,
          5.631256669496028,
          5.788513887931863,
          5.948897262006386,
          6.10670218711256,
          6.26844904483016,
          6.432903803230794,
          6.596779259376989,
          6.7669267608152985,
          6.951513019733041,
          7.121582061617247,
          7.296303722578637,
          7.471446604902217,
          7.648390856797305,
          7.8329936775282905,
          8.020794966136831,
          8.209632808845917,
          8.401417620202345,
          8.590646064052626,
          8.783114896662422,
          8.978829742472467,
          9.175300105333713,
          9.375093784722608,
          9.576483388082313,
          9.776822687641996,
          9.974478826265862,
          10.16913283903571,
          10.363268687008691,
          10.55903746225986,
          10.75563130245319,
          10.945306668273254,
          11.135763190050596,
          11.332323488480347,
          11.525328914372237,
          11.720578016653537,
          11.926693929229051,
          12.135399727870412,
          12.342714717150432,
          12.55003234180756,
          12.761801265083607,
          12.97256146778967,
          13.179128127067901,
          13.387694609538476,
          13.597709724968675,
          13.80361797596977,
          14.006064805723163,
          14.207421030004635,
          14.406475207674958,
          14.601841720278095,
          14.793749819797004,
          14.987798478702754,
          15.181954233018319,
          15.372252885129878,
          15.558553037905114,
          15.745354404116084,
          15.931025015334148,
          16.112133567599226,
          16.29169380601665,
          16.474231645900765,
          16.65673077203514,
          16.838598653819968,
          17.024090442972696,
          17.215763953323627,
          17.40575160280916,
          17.593940114722514,
          17.78483760605761,
          17.981528288357495,
          18.182422671778454,
          18.374776814112163,
          18.581111160182836,
          18.79362259697671,
          19.002776113219582,
          19.21626970605701,
          19.43112870827955,
          19.65102080898132,
          19.878853568831616,
          20.10312546864239,
          20.33456798064165,
          20.571455677987018,
          20.805307917268557,
          21.045403500637494,
          21.298626572310877,
          21.53535576431192,
          21.787166760774234,
          22.04704548994729,
          22.30130520146322,
          22.574917940685502,
          22.846884374467052,
          23.11244824903883,
          23.394736111510714,
          23.676559415391722,
          23.953561991223374,
          24.250244848173462,
          24.540664243181794,
          24.833706554567964,
          25.156073221083844,
          25.473212534749933,
          25.796484527816077,
          26.13727266230354,
          26.460167230968434,
          26.77512580126815,
          27.108708116478457,
          27.438704853826536,
          27.759939243778156,
          28.097005722458324,
          28.43352407824126,
          28.759042039978237,
          29.089389232226157,
          29.420449816116722,
          29.74983119488025,
          30.08212078675594,
          30.411269707900978,
          30.742944489098743,
          31.079775794747977,
          31.415306515442328,
          31.741820418039623,
          32.07149075857679,
          32.40361086995983,
          32.73287821237294,
          33.05788248022835,
          33.377945876076446,
          33.703491287061006,
          34.02881086933761,
          34.336350875136155,
          34.63920540415571,
          34.95101710678149,
          35.252506576967846,
          35.54453913345566,
          35.85123718330825,
          36.1556024863718,
          36.44855841864565,
          36.750834738479114,
          37.06178859755466,
          37.36669465341993,
          37.67828627342124,
          37.99722984607634,
          38.3128101331543,
          38.63145517761055,
          38.94999809789752,
          39.262558010339916,
          39.579606480905696,
          39.900656383320424,
          40.21583267579129,
          40.53472068673256,
          40.85465562257616,
          41.171871203786324,
          41.486037357245635,
          41.80341437120019,
          42.115184424916826,
          42.432267817800195,
          42.74869006613391,
          43.06151791935443,
          43.3820080676286,
          43.70140529186662,
          44.013298163509596,
          44.328170401408954,
          44.64674426514315,
          44.947785521041396,
          45.25663632901949,
          45.56604597424447,
          45.86151513692612,
          46.1652166857148,
          46.47234999090252,
          46.76795480259499,
          47.06580954138513,
          47.369754222452364,
          47.66790276213002,
          47.955036340077136,
          48.25304046096536,
          48.55028755018086,
          48.84124349388114,
          49.13120357369446,
          49.425155662794786,
          49.71207103834986,
          49.997415742459815,
          50.28675152243265,
          50.57106337226466,
          50.851292024285996,
          51.13648119935449,
          51.417560945870974,
          51.69166214349666,
          51.96406627724454,
          52.22926991177055,
          52.48582986037931,
          52.745453668301394,
          52.99701452760204,
          53.24552141987308,
          53.4978257580014,
          53.7494697455108,
          54.00373136573797,
          54.255545635500454,
          54.50935013800976,
          54.770800669626155,
          55.036105044860285,
          55.30578103475355,
          55.57712629270071,
          55.84841517886736,
          56.121305819378854,
          56.396127182219146,
          56.66480154268678,
          56.92590628816359,
          57.18698185333048,
          57.44827129411211,
          57.71011908320546,
          57.963999775378376,
          58.218160972638955,
          58.47851432665823,
          58.73886674078835,
          59.0018961803807,
          59.25945908560965,
          59.52850899544941,
          59.7983985531829,
          60.06082253745904,
          60.325324743604384,
          60.603310869586814,
          60.87044228018748,
          61.12857127677023,
          61.40259509282569,
          61.67108245307185,
          61.91466944388023,
          62.15701613438367,
          62.39918205440036,
          62.61468586808511,
          62.814890921539984,
          63.02869703724511,
          63.23373607245903,
          63.41827901302412,
          63.60299309694622,
          63.775328972893604,
          63.92889207470187,
          64.07696865776536,
          64.21234997683516,
          64.33590342676878,
          64.44841181662521,
          64.54345291530073,
          64.61930888948838,
          64.6804588488602,
          64.72498316710659,
          64.75503192542301,
          64.77423687634494,
          64.77803140213041,
          64.76324698744891,
          64.7316474879003,
          64.68467452846008,
          64.6238135747295,
          64.54563229844479,
          64.44741475264918,
          64.3356181562903,
          64.20980251223435,
          64.05914493782261,
          63.89264825264366,
          63.72007165595962,
          63.522447573320285,
          63.31200360543133,
          63.09432787491209,
          62.85875514113911,
          62.60149057913376,
          62.33823598972425,
          62.06428886562031,
          61.77172285159672,
          61.47355105704766,
          61.17496468507821,
          60.87045058716934,
          60.55938185071553,
          60.24397081513541,
          59.93095284858972,
          59.61728220176726,
          59.299333939218656,
          58.97707926350325,
          58.65792783521924,
          58.33271154277494,
          58.0012539725055,
          57.67455351559774,
          57.35069668912867,
          57.0110033390398,
          56.682707863948245,
          56.36397335195614,
          56.03032003075439,
          55.70119001727611,
          55.386535174913206,
          55.05762540355066,
          54.73099797658368,
          54.413186029836865,
          54.08440679283176,
          53.73343743190345,
          53.37357244061748,
          53.004494568369005,
          52.62954228046007,
          52.26446093215443,
          51.8915976868798,
          51.510535483981364,
          51.13531867866375,
          50.75821421464184,
          50.37417727794913,
          50.014487343204124,
          49.669224905922185,
          49.321863973983824,
          48.97802674707963,
          48.62923138335952,
          48.28707355315305,
          47.93763151574009,
          47.5872907197428,
          47.24000687906527,
          46.893839862634835,
          46.53587658051037,
          46.163590570402484,
          45.79241563967316,
          45.42317540460844,
          45.04551180986331,
          44.66978917424429,
          44.29262343794187,
          43.91757027134529,
          43.531587538619334,
          43.14696794743754,
          42.78206108151733,
          42.41824049184275,
          42.060184243998044,
          41.70452003079957,
          41.33805206358612,
          40.9766109893554,
          40.61983341924642,
          40.24887535369847,
          39.87223229958563,
          39.519149902919985,
          39.18455634113386,
          38.860337834576384,
          38.55863130316872,
          38.25385652507213,
          37.934972214089946,
          37.63300200201469,
          37.3396025668475,
          37.03070272139799,
          36.7277037174502,
          36.43124540575485,
          36.10315588004389,
          35.76046113590517,
          35.41316425324658,
          35.07222237259091,
          34.731873722071725,
          34.387032236592475,
          34.036139478930146,
          33.69462576680907,
          33.35530418497045,
          32.99712842178764,
          32.65920215189999,
          32.333351840655396,
          32.0051779050895,
          31.672771298385804,
          31.345114919508905,
          31.023647925277686,
          30.69561782251355,
          30.372857957424703,
          30.04455318675462,
          29.716530650772686,
          29.376775009459283,
          29.032727437247416,
          28.694625437234627,
          28.349447040615075,
          28.011036457098466,
          27.678311777443966,
          27.340469359712845,
          27.009506139351178,
          26.681481223625706,
          26.35123343731874,
          26.030749965565633,
          25.703695028905464,
          25.3729809368927,
          25.05138638577504,
          24.72510824817708,
          24.39159632548782,
          24.06553639184264,
          23.740206121656943,
          23.40739769660998,
          23.081261657381123,
          22.763948496106984,
          22.434754638579886,
          22.11865931239052,
          21.807961662977746,
          21.4905386192929,
          21.164729629764402,
          20.862205917135583,
          20.557598524940502,
          20.22856773223279,
          19.92575997577919,
          19.6153881903489,
          19.286986859541866,
          18.97106000671142,
          18.65889334937452,
          18.33971068441129,
          18.018534079578565,
          17.705214573794848,
          17.385735385576314,
          17.068365578110665,
          16.757617040072198,
          16.4496460625785,
          16.145614271502176,
          15.843183457518938,
          15.539724258363853,
          15.23081033491441,
          14.928168044593754,
          14.619350352711118,
          14.312415204065331,
          14.004900876356503,
          13.691505397129548,
          13.382761226417156,
          13.072808436633192,
          12.75617255762379,
          12.440687864840086,
          12.126135942931526,
          11.807694599494935,
          11.481563043217621,
          11.160286642289627,
          10.843404375716958,
          10.519724274272413,
          10.197474213686554,
          9.885910478792159,
          9.576727165359841,
          9.255507127598605,
          8.954497568968769,
          8.656825556729501,
          8.35151396705426,
          8.061474395638424,
          7.7724433786617295,
          7.479411741392958,
          7.188095097181444,
          6.89573277042006,
          6.601306178114268,
          6.311113766360433,
          6.012875205586886,
          5.711826949516217,
          5.418867168237042,
          5.11094740753219,
          4.812014104697031,
          4.518557033966874,
          4.21565271665293,
          3.9175057084956775,
          3.6254461948470915,
          3.331545966540914,
          3.0376112132400044,
          2.7496280170382965,
          2.458511058356632,
          2.1776750685582287,
          1.9023324270350852,
          1.6219873136478071,
          1.3515619052253622,
          1.085310220601021,
          0.8132238274266218,
          0.542831482048225,
          0.27315570468110895,
          0.0028421577680153853,
          -0.27049276703125885,
          -0.5463268248329006,
          -0.8262004551646298,
          -1.107879395286346,
          -1.3916557107149121,
          -1.6774387069881023,
          -1.9574536540348448,
          -2.2414835550731893,
          -2.526726733690335,
          -2.796098289993876,
          -3.0485159716884143,
          -3.3022453823800215,
          -3.545904518964392,
          -3.7680426080445755,
          -3.9822654167228353,
          -4.182143455408361,
          -4.362342772072077,
          -4.525006759792942,
          -4.667669520894381,
          -4.786895394067779,
          -4.882482773350822,
          -4.9567380382589485,
          -5.00760632093183,
          -5.033904877646841,
          -5.035950736923687,
          -5.015924590660966,
          -4.977009753510907,
          -4.918364667515823,
          -4.840335445178749,
          -4.7456233965048025,
          -4.633561589034956,
          -4.505079616704708,
          -4.36172030627776,
          -4.204324694798168,
          -4.036262663020632,
          -3.8583288185661546,
          -3.6709480583204877,
          -3.480061577759506,
          -3.282265203079415,
          -3.079398118769766,
          -2.87609039202851,
          -2.6689610642012136,
          -2.4603357019972623,
          -2.2549151712934425,
          -2.0555541820113747,
          -1.8414780652124227,
          -1.651346634081261,
          -1.4682549265943972,
          -1.2889642340245302,
          -1.113857587858442,
          -0.9438890907116492,
          -0.7775191634099369,
          -0.6157830205941762,
          -0.4605198406816952,
          -0.30980998000948873,
          -0.1681397575337732,
          -0.03536969681095837,
          0.0949241979294292,
          0.21648296179149223,
          0.33224419728985344,
          0.44184639524177516,
          0.5530670602380464,
          0.6552431131693358,
          0.7450458870719152,
          0.8349279146221444,
          0.9197564848703558,
          0.9981466064915008,
          1.0757093210853481,
          1.1498858268519423,
          1.2157172484173244,
          1.277918760588237,
          1.3369809429183377,
          1.3913095375182345,
          1.4445619806903216,
          1.4930199416312082,
          1.5353990216939157,
          1.57393914736842,
          1.6094500826339255,
          1.640371474278643,
          1.6681913617370199,
          1.6941189600356357,
          1.7183310280475588,
          1.7415256307133822,
          1.7652994469640837,
          1.7876405491265939,
          1.8093238050473628,
          1.8308054348159348,
          1.8520438795362315,
          1.8748257790396303,
          1.8996520904616516,
          1.9262057756298006,
          1.952449525353578,
          1.979242520411555,
          2.008259301776948,
          2.0384574799230704,
          2.069874562285853,
          2.1033989223984486,
          2.139669610737211,
          2.178847733484213,
          2.2224087485069375,
          2.2704188602062985,
          2.321978765945034,
          2.3805472836395496,
          2.451333063077684,
          2.5204186862095352,
          2.596175004887099,
          2.6769282243746972,
          2.7612674531780805,
          2.850935968758286,
          2.944825825949513,
          3.0466485157760412,
          3.1548488331499427,
          3.2655988413770833,
          3.3841870985236198,
          3.5110067392985895,
          3.6403081450036745,
          3.772111482310876,
          3.91300797460865,
          4.053585243976242,
          4.196203948618943,
          4.346386942022684,
          4.4964075473362435,
          4.6438185147866395,
          4.797364815007405,
          4.957656078701385,
          5.113551060641826,
          5.277450170411978,
          5.447738805582302,
          5.61868728094935,
          5.792274115754509,
          5.970106560387088,
          6.1457914048665065,
          6.3240470581112325,
          6.5038232997804295,
          6.684811613747742,
          6.867542189719006,
          7.0527788657473085,
          7.23832605270834,
          7.4271045363039025,
          7.61488157945303,
          7.803947766682915,
          7.997218280776169,
          8.191109069136724,
          8.386710094937602,
          8.584029781015781,
          8.784563043070957,
          8.98616378095811,
          9.186300524490916,
          9.384675712138709,
          9.58578425900947,
          9.785127603053741,
          9.977131089883029,
          10.17423205860926,
          10.375199026198787,
          10.589069677872354,
          10.787897957613902,
          10.9944989318322,
          11.199313719525836,
          11.40220889785868,
          11.611422327244709,
          11.822203056455006,
          12.028078159659541,
          12.236382887514369,
          12.448917898577703,
          12.656943496096835,
          12.86293268568178,
          13.068496729897587,
          13.273911901456566,
          13.476843235127044,
          13.677405638669933,
          13.880626236854065,
          14.083914035531546,
          14.281469296468464,
          14.477584788810997,
          14.696795871184278,
          14.891196227875946,
          15.082311130722983,
          15.276633135204207,
          15.472227614634006,
          15.667924286693639,
          15.866672791542968,
          16.0723923531363,
          16.277184547378898,
          16.48010689593563,
          16.683861003762978,
          16.89619857368472,
          17.108556511388578,
          17.315968162417718,
          17.539772148344706,
          17.765361978006677,
          17.990712281871108,
          18.21992972308881,
          18.451895868100554,
          18.68826151201862,
          18.9436482275444,
          19.19867073009613,
          19.463662386025156,
          19.730008903195234,
          19.9952377679208,
          20.276325961206325,
          20.541583971021918,
          20.819617418066056,
          21.104824436489302,
          21.38463648974693,
          21.66152259805987,
          21.932805429587546,
          22.199802235368654,
          22.482130779534508,
          22.761252586310977,
          23.03887936669711,
          23.334516634642657,
          23.61941361492147,
          23.911167285421456,
          24.228285841106565,
          24.53476624296535,
          24.855426896910537,
          25.18760203848001,
          25.49634142742295,
          25.802876757165475,
          26.12767599834626,
          26.448340980539754,
          26.758791512708367,
          27.084390931040822,
          27.40786261649449,
          27.731069968144634,
          28.05683599811312,
          28.3814308398038,
          28.702588021869904,
          29.024447450977327,
          29.342072286186745,
          29.65736677249564,
          29.980166530694827,
          30.29936164656833,
          30.609351396683735,
          30.942218991646982,
          31.274985758940357,
          31.59873538561554,
          31.917679388804146,
          32.22637499903647,
          32.53261266046398,
          32.84957140299829,
          33.1537604937998,
          33.45175328611491,
          33.75321001672992,
          34.04505669586066,
          34.3315081975387,
          34.61734665505737,
          34.91373649998367,
          35.20612154712153,
          35.4972385862957,
          35.79638421038561,
          36.10143582856517,
          36.40616431502931,
          36.7166564837261,
          37.03092016042375,
          37.34524010017537,
          37.66244537940462,
          37.98099835555076,
          38.29525213913023,
          38.613917564197976,
          38.93655431141074,
          39.25684937883945,
          39.58090054663728,
          39.908278426885154,
          40.2359741012518,
          40.56312289221807,
          40.89323347893464,
          41.252771217355594,
          41.583297146888995,
          41.90962386932896,
          42.22992667364179,
          42.55172726340942,
          42.86374484428655,
          43.163666724218984,
          43.4657626112107,
          43.76206757207292,
          44.03554399500987,
          44.3155751391994,
          44.59400240126925,
          44.85395319498643,
          45.12284975288024,
          45.39909856508403,
          45.66769236792282,
          45.94006227356499,
          46.21462418755764,
          46.4915005790355,
          46.77438105175335,
          47.04990057016058,
          47.32688896385801,
          47.6175106516778,
          47.90280342864727,
          48.18506541471182,
          48.47461299275151,
          48.761709218167425,
          49.043855530041554,
          49.333408220082184,
          49.624954836179626,
          49.907927570110175,
          50.196870979637715,
          50.49018285919311,
          50.77470018970976,
          51.05728309383378,
          51.33949904509417,
          51.61068049658557,
          51.88334215765688,
          52.153806801541364,
          52.42080888823905,
          52.692224989140016,
          52.96637536516427,
          53.24359290174978,
          53.51893086188829,
          53.799865792365004,
          54.088940690466885,
          54.38145622363204,
          54.67559382248205,
          54.972990652781654,
          55.26971689965987,
          55.567887137864005,
          55.861405261790225,
          56.146119876549264,
          56.43012315788755,
          56.71446933117696,
          56.996859523816624,
          57.26842312183835,
          57.544300551709576,
          57.825632761545144,
          58.10239128015138,
          58.375800451310475,
          58.65452129529378,
          58.93909611047069,
          59.21085667673081,
          59.47113500778839,
          59.740987264165724,
          60.00288489650001,
          60.2411062117452,
          60.489616959428595,
          60.74440561630401,
          60.97948612363302,
          61.20377689502732,
          61.42669067933879,
          61.644217562591095,
          61.84154689449571,
          62.02494818540991,
          62.216494455226645,
          62.40301496814696,
          62.5729062602609,
          62.739733953662665,
          62.90127769126194,
          63.0479087832785,
          63.188862066127065,
          63.32009926727753,
          63.43892000765799,
          63.548062032563706,
          63.64495326883894,
          63.723300638418195,
          63.78756769276339,
          63.83887868470011,
          63.87464820900632,
          63.90015377300029,
          63.91353245152039,
          63.91048662090791,
          63.891427781412744,
          63.85912787946155,
          63.813384867752916,
          63.75416329934468,
          63.67813296736693,
          63.584576370320185,
          63.482783152394894,
          63.36265994441006,
          63.22093511317302,
          63.07142173192214,
          62.90890336399922,
          62.72142432038193,
          62.52867142173112,
          62.323333738872115,
          62.09941765674898,
          61.85980415567179,
          61.61067513099217,
          61.347178835717614,
          61.06974311268001,
          60.78741520466235,
          60.497830705641256,
          60.20279873773858,
          59.89873348432303,
          59.585043621096226,
          59.266936513389,
          58.948489803259854,
          58.621791337080595,
          58.28971966682808,
          57.962389710684064,
          57.62597298102287,
          57.27909752193891,
          56.936167214092045,
          56.599916639903,
          56.26025818730859,
          55.923789485388916,
          55.601350547949295,
          55.27176884837666,
          54.93680527794924,
          54.62045518974739,
          54.296942341618085,
          53.96884906228317,
          53.65506611243988,
          53.33251378359047,
          53.00009929624337,
          52.676468408131186,
          52.34445179465412,
          52.00681219218575,
          51.67495333296684,
          51.34402544088789,
          51.001131750417386,
          50.66352177516216,
          50.328657755750555,
          49.984471850724496,
          49.649447251285785,
          49.319524842901195,
          48.98736591985296,
          48.6577174415375,
          48.32583472324404,
          47.993326969072214,
          47.66618385550341,
          47.33024882085921,
          46.996015374056576,
          46.6625747941048,
          46.3288997901906,
          45.99449743748959,
          45.65820973178802,
          45.32367401442467,
          44.98701469094136,
          44.65087242754459,
          44.3128161997339,
          43.97490572725108,
          43.60540030037656,
          43.2693660002701,
          42.9533266225585,
          42.63806078501144,
          42.32052615358233,
          42.0095836811218,
          41.693147034220765,
          41.37030589200015,
          41.056625342652836,
          40.74007253894454,
          40.40955698480483,
          40.07238619335842,
          39.73983985942109,
          39.39260096861668,
          39.029058991457305,
          38.68573293410243,
          38.33982956594653,
          37.9793949940433,
          37.63018870182943,
          37.29310655753665,
          36.95160633019749,
          36.60880867832948,
          36.293045043930555,
          35.97320318330131,
          35.65843250820487,
          35.34143487093785,
          35.023269264007865,
          34.71491328954702,
          34.404730125534805,
          34.08880522075607,
          33.77287508607854,
          33.464978895564755,
          33.13532789499079,
          32.79521185152687,
          32.470538905825705,
          32.142421903556844,
          31.816023894313595,
          31.489715051373466,
          31.162633798062817,
          30.844728987655056,
          30.520512393006193,
          30.200186095790748,
          29.874214475069444,
          29.546783390008734,
          29.22024519972762,
          28.88660565295937,
          28.556615940743562,
          28.225122145310184,
          27.887892089126876,
          27.55833359518771,
          27.225281584961564,
          26.880269079369786,
          26.546483679129313,
          26.211752975406316,
          25.872264985783026,
          25.54079640197197,
          25.206617009471472,
          24.87929742152391,
          24.54970022173698,
          24.21830077512884,
          23.89078380024956,
          23.55858934148418,
          23.229282320037715,
          22.90869003444346,
          22.582503646843886,
          22.259829266745648,
          21.951962768662916,
          21.636761446826245,
          21.325235204922894,
          21.027892349667027,
          20.71510396184291,
          20.400388442243187,
          20.10406009212683,
          19.788973839438082,
          19.465898738205222,
          19.16521682464404,
          18.853977589852196,
          18.533844973163838,
          18.225560236998408,
          17.916390066821002,
          17.593149552008764,
          17.279735159101676,
          16.96738557844563,
          16.61353796299852,
          16.300786009462797,
          15.993030516912416,
          15.681375942368238,
          15.370879265711897,
          15.064397930064088,
          14.749228817483711,
          14.439039644775507,
          14.124585889320837,
          13.804131998714254,
          13.481147050734426,
          13.157733911860888,
          12.834151570500785,
          12.505922526550986,
          12.175900497336459,
          11.84838349465872,
          11.519249127080254,
          11.185757644129255,
          10.852782421353982,
          10.525000382206137,
          10.192836056464515,
          9.866128307061684,
          9.542051026352523,
          9.217309348473334,
          8.895321172734855,
          8.578402333638502,
          8.26170217041076,
          7.939481330769564,
          7.627377744402807,
          7.3177884251394145,
          7.010961355341202,
          6.70668843031132,
          6.403785089924659,
          6.10947597925163,
          5.814662071230183,
          5.519360755593465,
          5.225755566271759,
          4.941538545824498,
          4.654884637718361,
          4.38037694029395,
          4.120549845484478,
          3.8539538181153965,
          3.579046402777778,
          3.313308735996936,
          3.0528396543980385,
          2.7771352753989516,
          2.50866923525166,
          2.2483543666163492,
          1.9711689430605315,
          1.6920598186618878,
          1.418285367364076,
          1.1352485535177619,
          0.8652150394627393,
          0.5996267110920918,
          0.3251281950151414,
          0.053165143872573595,
          -0.2163908265782503,
          -0.4892134221579513,
          -0.754967675341181,
          -1.016081762235151,
          -1.2804261208534857,
          -1.5432177157655607,
          -1.8140142664177707,
          -2.0899060194822106,
          -2.36329393983016,
          -2.6378118023299026,
          -2.915525029592267,
          -3.1890168242133385,
          -3.454539702908877,
          -3.7163576609103215,
          -3.975675678123687,
          -4.2169925406172375,
          -4.442689768247701,
          -4.658572553725139,
          -4.852573105338675,
          -5.030485206627612,
          -5.190462235832259,
          -5.3259049753047725,
          -5.443858062965672,
          -5.538424480407576,
          -5.609667089114421,
          -5.66232695645199,
          -5.694878036607654,
          -5.704945724777047,
          -5.694117560591922,
          -5.664957132654981,
          -5.619711295630675,
          -5.556593805077401,
          -5.475222126440451,
          -5.379112331432588,
          -5.267802947825157,
          -5.141050971444225,
          -5.0015617749878665,
          -4.8494632509374025,
          -4.687618016712599,
          -4.517439685474579,
          -4.338229332376084,
          -4.153840410571848,
          -3.9630722745112554,
          -3.762739198445909,
          -3.559114993832612,
          -3.354593878788111,
          -3.1470325361190508,
          -2.9382350311469287,
          -2.7327155931539,
          -2.5306624485787,
          -2.328507542270429,
          -2.132728645912017,
          -1.9398885568742124,
          -1.7454978122007605,
          -1.5582439754376392,
          -1.3742513527750697,
          -1.1958249393208156,
          -1.0243365165770353,
          -0.8596568349141067,
          -0.7045010362854772,
          -0.5612043749577209,
          -0.4213395870413378,
          -0.29265799824540595,
          -0.1747140709160461,
          -0.06427383575028402,
          0.04523888440500598,
          0.1470176048847739,
          0.2335592457807787,
          0.31806725376161676,
          0.39725495085779616,
          0.4688920850625567,
          0.5378993094566618,
          0.6042473556930033,
          0.6626326850149867,
          0.7166694726914491,
          0.7682639322389797,
          0.8145747696512449,
          0.8593962881678019,
          0.902068632543713,
          0.9396647149657125,
          0.9750302682532217,
          1.0078196208749777,
          1.0370968429022625,
          1.0632475635657515,
          1.0885355014874818,
          1.1129560030203436,
          1.1368010358379101,
          1.1616439975988324,
          1.185384436834196,
          1.2084431698441171,
          1.231475823346499,
          1.254762415104005,
          1.279003680873743,
          1.304490645361735,
          1.3321634619381912,
          1.3605681174269533,
          1.3892327278655954,
          1.4186765175872023,
          1.449830915578756,
          1.481366538781976,
          1.5139104799467373,
          1.5476033220878807,
          1.583263999062211,
          1.6211933233438354,
          1.6631383793633245,
          1.7085112718607305,
          1.7566245083624843,
          1.8106609482744596,
          1.8701071709030277,
          1.9325622125965751,
          2.000600405276433,
          2.073073719730457,
          2.1487545459062662,
          2.229233110974539,
          2.314248791055779,
          2.404061883807194,
          2.503093932077756,
          2.605972973079022,
          2.713395029001061,
          2.8296484655673715,
          2.9507293024997834,
          3.073381872513424,
          3.202339794245352,
          3.337032920952903,
          3.4721955709684758,
          3.6149854181753436,
          3.7636729912526707,
          3.910178150042658,
          4.058923070848974,
          4.21475164808327,
          4.3719460968550985,
          4.529731913673303,
          4.699013206401141,
          4.872421310561653,
          5.046968437777668,
          5.229006277495889,
          5.409705435527416,
          5.593652208359495,
          5.782655045033461,
          5.973170236368014,
          6.165235802080729,
          6.362082629896817,
          6.559839729215012,
          6.758378728278356,
          6.955605431440671,
          7.152684060701755,
          7.354195314330586,
          7.556177350072287,
          7.757156526317015,
          7.961187881364418,
          8.169003680971045,
          8.377459379121646,
          8.581252383706312,
          8.781756769247409,
          8.98448890738033,
          9.185323285345376,
          9.377647316277997,
          9.574631679098811,
          9.77453789199406,
          9.968845107737579,
          10.165648840966393,
          10.369614482872768,
          10.576969644898908,
          10.796436682491988,
          11.021275163606756,
          11.246864619549918,
          11.468880277362299,
          11.693590573508914,
          11.92143585618974,
          12.146513612658033,
          12.371844212598857,
          12.598693790863255,
          12.822096235578423,
          13.035439877280268,
          13.247246640349253,
          13.460973546419812,
          13.67818491273366,
          13.889488252801932,
          14.09869730671219,
          14.310534066599072,
          14.517203507884803,
          14.719377674133092,
          14.91959255573849,
          15.11129102371526,
          15.302603365919937,
          15.497272166423574,
          15.698383337483369,
          15.900379833012433,
          16.10047374125098,
          16.301025074430772,
          16.509151973958257,
          16.746694732657037,
          16.953910521678782,
          17.177209192109522,
          17.41215293423783,
          17.64433768572708,
          17.877133390770577,
          18.119552844386924,
          18.364348477256137,
          18.615503268685643,
          18.86396729684635,
          19.119776393134917,
          19.387481743891833,
          19.65799693723779,
          19.97138913535241,
          20.252628616256146,
          20.53972116370472,
          20.864599743802877,
          21.167491705195776,
          21.479459035401458,
          21.794086367754364,
          22.11399182898066,
          22.431454120196182,
          22.750859270112684,
          23.08280638027464,
          23.40683337366142,
          23.752317076511204,
          24.111574288181092,
          24.463440793015387,
          24.83238042227069,
          25.195968103920862,
          25.539312503153802,
          25.893310860662872,
          26.24369925261043,
          26.582267823747525,
          26.934328990924996,
          27.28588487239649,
          27.621442569502996,
          27.960117425471747,
          28.303818723395178,
          28.635159948539933,
          28.96563663478973,
          29.302293916387427,
          29.63502560679554,
          29.971363294207848,
          30.29806216363941,
          30.627519894388662,
          30.96068694316108,
          31.294987541140635,
          31.623092608346326,
          31.944797115786923,
          32.27409768959656,
          32.592069090265866,
          32.89812328844543,
          33.2033668790907,
          33.50553426591979,
          33.80315270375641,
          34.10199116335442,
          34.40374116129653,
          34.70037769128913,
          34.99930901872234,
          35.3027502455714,
          35.61019483415942,
          35.91778870110349,
          36.23177032401961,
          36.549318572671865,
          36.86447146895361,
          37.18297074853924,
          37.50051483488108,
          37.812978772462074,
          38.12853715955711,
          38.44735728290711,
          38.761536901895255,
          39.07845222453753,
          39.398809727184464,
          39.71473270566849,
          40.029760352806896,
          40.34504792610765,
          40.656417875372846,
          40.968938220175374,
          41.28462245556623,
          41.595517406598056,
          41.9094211795519,
          42.22432579850013,
          42.533473369050185,
          42.8382291810717,
          43.149608904374205,
          43.451222239978314,
          43.7461698096567,
          44.055228739426425,
          44.3520907788295,
          44.64503373770526,
          44.950728556177175,
          45.24935317712527,
          45.54098436312996,
          45.842943558877685,
          46.14755303458895,
          46.443326146505704,
          46.73854919902926,
          47.04786138192352,
          47.35185725399669,
          47.6496011629088,
          47.95643597017896,
          48.26021279372815,
          48.5526815219461,
          48.85167784575071,
          49.15353998314599,
          49.44431352175967,
          49.73911939311548,
          50.03882848645932,
          50.32720195041783,
          50.61033855379421,
          50.89366193587728,
          51.167884941565404,
          51.442476792158224,
          51.70740478669174,
          51.97455183959459,
          52.2424372398762,
          52.50955159749591,
          52.7824441181921,
          53.051639281404725,
          53.324425481435284,
          53.60486635010587,
          53.88963555239475,
          54.17262292819129,
          54.4593666694105,
          54.746556348026466,
          55.0305015067513,
          55.31720677899201,
          55.59453917403792,
          55.86299504245453,
          56.15888068132426,
          56.43126106967637,
          56.689559026047526,
          56.94065230347727,
          57.20232586978722,
          57.46099179998578,
          57.716605912095446,
          57.9667704481623,
          58.22562514258538,
          58.48279049995408,
          58.73193463906139,
          58.97679471021057,
          59.231726255130766,
          59.48618960316225,
          59.72657914780032,
          59.97475629090222,
          60.23213442959812,
          60.47564590161082,
          60.7049426999666,
          60.93445010429704,
          61.16012701900658,
          61.3628146677447,
          61.550008156074576,
          61.74411336584359,
          61.93120147403796,
          62.101802479904414,
          62.270331330755454,
          62.43413388237453,
          62.58517546562002,
          62.73057604318588,
          62.8658714391403,
          62.989543574071305,
          63.103099285653244,
          63.20404152139367,
          63.28437587397921,
          63.34853626378916,
          63.39811140601858,
          63.43054360930116,
          63.45097372267109,
          63.4567870942156,
          63.4447036226012,
          63.415166511477636,
          63.37023820702246,
          63.31125332955198,
          63.23868736126066,
          63.14754852230307,
          63.03907964589805,
          62.92303318853251,
          62.78694141392481,
          62.63013965343733,
          62.47033102323899,
          62.291344581506586,
          62.09359031103882,
          61.89338210735949,
          61.68071930303039,
          61.44532632829423,
          61.203398502780615,
          60.956911902839714,
          60.69511980115445,
          60.42411300080536,
          60.151264974959936,
          59.874515231224194,
          59.597389428236895,
          59.31315620970049,
          59.021405078511236,
          58.73348260878832,
          58.44388700203228,
          58.14274849214298,
          57.845826988627806,
          57.547992367501905,
          57.23870777395376,
          56.928117561617285,
          56.62382853069168,
          56.31482853049869,
          55.990849826911465,
          55.683937631249485,
          55.379659002614254,
          55.05940881942585,
          54.7478383274686,
          54.446228891852904,
          54.12854095685096,
          53.81675817839018,
          53.51092358754183,
          53.191921350580614,
          52.874242507329065,
          52.560490915928355,
          52.23665547370583,
          51.9077213338404,
          51.586335427714964,
          51.25869299864215,
          50.92217315579611,
          50.58992709820675,
          50.25454632426013,
          49.91197629794347,
          49.57380078223236,
          49.237340611949016,
          48.898109266487566,
          48.561150029770815,
          48.217675361077035,
          47.8814988613294,
          47.538440549060454,
          47.193064510530945,
          46.84970730673195,
          46.50781183219243,
          46.16979702769043,
          45.82343644077698,
          45.479765835147404,
          45.13888378364644,
          44.79218792981562,
          44.44490713561993,
          44.0988326524609,
          43.75639413298596,
          43.405006335112816,
          43.055527911170955,
          42.7086224383385,
          42.35636752516571,
          42.01094060050921,
          41.66224869226204,
          41.30453120325186,
          40.955322427633995,
          40.606122509777826,
          40.23671831132266,
          39.87349021139226,
          39.5275216361299,
          39.15532054602195,
          38.7817917199122,
          38.42861344698394,
          38.061284715268485,
          37.68275186248695,
          37.327194044766365,
          36.97288601560147,
          36.59687620499849,
          36.23856852027886,
          35.88109543832795,
          35.51698266869542,
          35.151454114699064,
          34.794316267355306,
          34.437446570826715,
          34.0771206780121,
          33.71134847630277,
          33.35259399364076,
          33.003896861735065,
          32.640723827922415,
          32.28507059277639,
          31.936035330965904,
          31.586702433075484,
          31.22925195912165,
          30.88262143045321,
          30.53913232170126,
          30.188714527696792,
          29.840928928588454,
          29.48492688340245,
          29.125366374489975,
          28.76159707627873,
          28.402096387015956,
          28.04029167738964,
          27.677618347007837,
          27.324717705275482,
          26.96516969116016,
          26.60742238152953,
          26.25813582849179,
          25.940644512843257,
          25.64412781515667,
          25.348022830332283,
          25.054248705830318,
          24.762940172729472,
          24.474128236011488,
          24.183142438830497,
          23.889583459808744,
          23.60377062481296,
          23.31867446763228,
          23.00573403717028,
          22.69543862677699,
          22.38831817031561,
          22.07397291674327,
          21.77221620303394,
          21.474625655377526,
          21.159855111507262,
          20.860472983457548,
          20.57213799635636,
          20.259065357779058,
          19.974570675468115,
          19.717712944410955,
          19.440432089622206,
          19.16813345630301,
          18.908419499224287,
          18.64000437675221,
          18.36595897269595,
          18.101705674415747,
          17.836092414791384,
          17.56766658637108,
          17.29630341598981,
          17.025696047063235,
          16.75357804943685,
          16.481298915640618,
          16.21239540766006,
          15.937971120749795,
          15.666811668372599,
          15.391689270983614,
          15.117745913680936,
          14.848566220763917,
          14.540019487081059,
          14.222796660348196,
          13.903347266645358,
          13.579127085268404,
          13.257103352453145,
          12.937332081227593,
          12.61581250883567,
          12.287693670984922,
          11.954463566316953,
          11.631394681600423,
          11.329342568479117,
          11.031985211164129,
          10.737523628601888,
          10.45177322208383,
          10.159690898535434,
          9.86528611566276,
          9.585463943766001,
          9.302510829422065,
          9.018771681351822,
          8.740721821328417,
          8.451412847625747,
          8.16055976991773,
          7.940739885595652,
          7.649689547274853,
          7.355041201225335,
          7.073086663607159,
          6.781403498982336,
          6.480975198189406,
          6.193000995912802,
          5.894118683471748,
          5.604056865569893,
          5.33068637775697,
          5.0487330235721695,
          4.759880363605886,
          4.478298131655137,
          4.196421392600951,
          3.905844195969257,
          3.622675096119216,
          3.3335103833622286,
          3.0471742784361973,
          2.7719845417630884,
          2.487867692040898,
          2.2085807352402806,
          1.9386381623244573,
          1.6696997892504515,
          1.4008923722223003,
          1.1325338854488094,
          0.8698931640746329,
          0.6058550815292704,
          0.34178591209782944,
          0.07667844538865048,
          -0.19026593451683016,
          -0.4554406244379945,
          -0.7270459916318173,
          -0.9993729438317401,
          -1.2657127999327225,
          -1.5359056209694093,
          -1.80910351197689,
          -2.0707859508561195,
          -2.3171929634210486,
          -2.57303096028214,
          -2.8298091729269363,
          -3.06656586192069,
          -3.2899355731611752,
          -3.5058629323482395,
          -3.7002218758350507,
          -3.8799659060810683,
          -4.044154401469258,
          -4.188005818183804,
          -4.3152184885170035,
          -4.431354366367503,
          -4.514703010052084,
          -4.582047960812328,
          -4.631528872229713,
          -4.660910020821575,
          -4.6708403048030105,
          -4.662449926632847,
          -4.637595003710751,
          -4.596236011176684,
          -4.537947385026952,
          -4.376888542703274,
          -4.288209726394857,
          -4.18429492589649,
          -4.066784639944364,
          -3.9387904539825316,
          -3.799571967547997,
          -3.653433657150335,
          -3.501583167393676,
          -3.3401169800524984,
          -3.1744481619690124,
          -3.0052437357619475,
          -2.829155463434466,
          -2.6527959456576737,
          -2.475772365932245,
          -2.2955140655935677,
          -2.1163822744969565,
          -1.9392996466493302,
          -1.7651734640595305,
          -1.5942498473022266,
          -1.4247547430679854,
          -1.2604125493983682,
          -1.1006254540448448,
          -0.9428929999493842,
          -0.7885739354253732,
          -0.6394382491121076,
          -0.49422949338813715,
          -0.3547025436789347,
          -0.2220377492865131,
          -0.09497282596831103,
          0.021735167796699595,
          0.13285858280024343,
          0.24087676995385654,
          0.33923224114094186,
          0.4329200110885978,
          0.5201430763632404,
          0.6076261201085276,
          0.6879757431943925,
          0.7578119823986187,
          0.8269555418893362,
          0.8913029716133205,
          0.9503621390414663,
          1.0076633251910367,
          1.0619069384761641,
          1.1108600056309395,
          1.154451832954652,
          1.1949563456065757,
          1.2306989835976558,
          1.2636346948814599,
          1.2938187560504752,
          1.3188102651418132,
          1.3400979295708186,
          1.3587029727938362,
          1.3736961944225057,
          1.3874170183239944,
          1.4002813212691323,
          1.413864282540611,
          1.428639923213225,
          1.4439159929580396,
          1.4588185530447295,
          1.4716824922168787,
          1.4835117408193126,
          1.4944732530514964,
          1.505037309620955,
          1.5159365970329328,
          1.5279182777271618,
          1.5710227590004497,
          1.585487163567568,
          1.601561593277515,
          1.6191296376214352,
          1.6392118118171357,
          1.661332817227168,
          1.683818426776412,
          1.7097134479140736,
          1.7383053758480917,
          1.7712132265080818,
          1.8082864177801734,
          1.8495958259515872,
          1.8971048618132835,
          1.9495414443591164,
          2.0089977824310385,
          2.0774488692880864,
          2.152719910738682,
          2.238964543324992,
          2.334237456808289,
          2.4368837415056133,
          2.548951046986737,
          2.6712010864801186,
          2.804199387424994,
          2.9489350548037434,
          3.104840352919012,
          3.2696446307951232,
          3.449537370291477,
          3.6422762528119206,
          3.844964818735719,
          4.064028170637739,
          4.296194383137763,
          4.536128453129303,
          4.780515740575605,
          5.068595331826337,
          5.339755000188887,
          5.614200312412775,
          5.903984607704475,
          6.204051350614986,
          6.502448630503951,
          6.810922050815234,
          7.129056537553518,
          7.449288520433644,
          7.773967266604292,
          8.107895570113833,
          8.446125235123965,
          8.788662654274459,
          9.13733022137939,
          9.492647484169803,
          9.849955649461563,
          10.21254506524584,
          10.577595066343726,
          10.945159109465557,
          11.317011962849532,
          11.695576288011447,
          12.073581835360525,
          12.45651816101892,
          12.83768461737093,
          13.225855182239112,
          13.6045467550301,
          13.982960369263015,
          14.37046998740073,
          14.753653591504062,
          15.128301092639678,
          15.48333670659692,
          15.866854354862518,
          16.245350633101292,
          16.624730674923363,
          17.001686838803085,
          17.37919471421535,
          17.740406988155204,
          18.101336461510847,
          18.468215679311406,
          18.82581382576176,
          19.18161067675971,
          19.535407199454607,
          19.884345087594586,
          20.228653998324123,
          20.548386356183464,
          20.865869997294162,
          21.16885830062872,
          21.444246808429096,
          21.723230991549734,
          21.981530352651177,
          22.224328239948395,
          22.46410538987838,
          22.682047779183893,
          22.87564032840609,
          23.07241333225752,
          23.249333466160344,
          23.402534058412485,
          23.554669446076673,
          23.689115788959498,
          23.803609375044548,
          23.914176643879845,
          24.00819998804275,
          24.090429572476623,
          24.15856535870222,
          24.21198547003588,
          24.258824715173773,
          24.299506484657044,
          24.333927203988285,
          24.36638965023104,
          24.3987771413772,
          24.4317546647794,
          24.463807479798007,
          24.47374998174773,
          24.482187505217095,
          24.489667268472083,
          24.497212999751582,
          24.50380722017657,
          24.50955393584218,
          24.515152386071996,
          24.520318624688684,
          24.5248045628062,
          24.52850286369933,
          24.562741464181546,
          24.600868556033113,
          24.639572183517366,
          24.678999202340567,
          24.71910268613251,
          24.752167541806834,
          24.79364139014063,
          24.835708363767267,
          24.87896621837055,
          24.9232279506598,
          24.934048566691608,
          24.94107921159258,
          24.948355187402903,
          24.955586820345676,
          24.962806447321853,
          24.97021256670934,
          24.977547770122076,
          24.98494706269543,
          24.99242952739627,
          24.99994437339902,
          25.02540271299319,
          25.052916655074828,
          25.08056116530959,
          25.108168293242098,
          25.135808603887792,
          25.163485883998344,
          25.19115746111873,
          25.218876122759994,
          25.24661949756898,
          25.274470489049747,
          25.284313636520654,
          25.292359845297213,
          25.30049146549067,
          25.308518479646892,
          25.316455103602966,
          25.32458102322264,
          25.332738211605577,
          25.340816196491332,
          25.349086424508247,
          25.357295176651835,
          25.403074324577638,
          25.45374928722011,
          25.504408168173335,
          25.55487276861665,
          25.605032335771533,
          25.655136174273608,
          25.705378138595986,
          25.755388975120873,
          25.80516652331133,
          25.855482764168823,
          25.866115316851094,
          25.872209004406198,
          25.87815187371181,
          25.88382182578971,
          25.889485629453922,
          25.895124265033186,
          25.900828708697823,
          25.907149898069797,
          25.912957769240567,
          25.91864769467925,
          25.920183502332854,
          25.921636104878875,
          25.922860010393627,
          25.92409529747196,
          25.925571771507055,
          25.92699075098118,
          25.928285237895963,
          25.929639765365053
         ],
         "yaxis": "y"
        },
        {
         "mode": "markers",
         "showlegend": false,
         "type": "scatter",
         "x": [
          -35.97329684506414,
          -75.10034519689322,
          -1.038764248227812,
          -36.0892694400111
         ],
         "y": [
          26.316580859038513,
          21.011440906439965,
          -12.138119313965529,
          72.35004639855165
         ]
        }
       ],
       "layout": {
        "legend": {
         "tracegroupgap": 0
        },
        "margin": {
         "b": 0,
         "l": 0,
         "r": 0,
         "t": 0
        },
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "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": {
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "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
          },
          "autotypenumbers": "strict",
          "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
          }
         }
        },
        "xaxis": {
         "anchor": "y",
         "domain": [
          0,
          1
         ],
         "title": {
          "text": "x"
         }
        },
        "yaxis": {
         "anchor": "x",
         "domain": [
          0,
          1
         ],
         "scaleanchor": "x",
         "scaleratio": 1,
         "title": {
          "text": "y"
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = px.scatter(x=positions[:,0],y=positions[:,1])\n",
    "fig.add_scatter(x=landmarks[:,0], y=landmarks[:,1], mode=\"markers\", showlegend= False)\n",
    "fig.update_layout(margin=dict(l=0, r=0, t=0, b=0))\n",
    "fig.update_yaxes(scaleanchor = \"x\", scaleratio = 1)\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-35.97329685,  26.31658086],\n",
       "       [-75.1003452 ,  21.01144091],\n",
       "       [ -1.03876425, -12.13811931],\n",
       "       [-36.08926944,  72.3500464 ]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "landmarks"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "341996cd3f3db7b5e0d1eaea072c5502d80452314e72e6b77c40445f6e9ba101"
  },
  "kernelspec": {
   "display_name": "Python 3.8.12 ('nbdev')",
   "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": "3.8.12"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}