example/notebook/Harmonic (Sn_Zn).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Electron capture via Sn_Zn in CZTS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook demonstrates some of the basic features of `CarrierCapture`, a set of codes to compute carrier capture and recombination rates in semiconducting compounds.\n",
    "\n",
    "This notebook was last updated 10-Mar-2020 for version 0.2 of `CarrierCapture`.\n",
    "\n",
    "See more in [J. Mater. Chem. A 7, 2686 (2019)](https://pubs.rsc.org/en/content/articlelanding/2019/ta/c8ta10130b).\n",
    "\n",
    "## Overview\n",
    "In this notebook, we will:\n",
    "\n",
    "1. Find a best fit for the energy calculations of the deferomed structures (potential) to generate potential energy surfaces (PES). Solve the 1D Schrödinger equation for each PES to obtain their phonon (nuclear) wavefunctions.\n",
    "2. Constructe configuration coordinate (conf_coord) to calculate the wavefunction overlap between each PES, which forms part of the temperature-dependent capture coefficient.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VERSION = v\"1.4.1\"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "v\"1.4.1\""
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using CarrierCapture\n",
    "using Plots, LaTeXStrings\n",
    "using DataFrames\n",
    "@show VERSION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Potentials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The domain of PES (`Q`) is defined. Make sure all relevent wave functions are in the domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-25.0:0.020006668889629875:35.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Qmin = -25\n",
    "Qmax = 35\n",
    "NQ = 3000\n",
    "Q = range(Qmin, stop=Qmax, length=NQ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find a best fit for the energy calculations of the deferomed structures (potential) to generate potential energy surfaces (PES). \n",
    "Here we using [spline interpolation](https://en.wikipedia.org/wiki/Spline_interpolation) to find their best fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Potential fitting: SnII+e+h\n",
      "========harmonic=========\n",
      "\n",
      "Potential fitting: SnIII+h\n",
      "========harmonic=========\n",
      "\n",
      "Potential fitting: SnII\n",
      "========harmonic=========\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\"Fitting completed\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pot1\n",
    "nev = 30\n",
    "name = \"SnII+e+h\"\n",
    "\n",
    "pot1 = Potential(); pot1.name = name\n",
    "pot1.Q0 = 0; pot1.E0 = 1.46\n",
    "pot1.nev = nev\n",
    "pot1.func_type = \"harmonic\"\n",
    "params = Dict()\n",
    "params[\"hw\"] = 0.0288945775003\n",
    "pot1.Q = Q\n",
    "pot1.params = params\n",
    "fit_pot!(pot1)\n",
    "# pot1.func = x -> harmonic(x, 0.0288945775003; E₀ = pot1.E0, Q₀ = pot1.Q0)\n",
    "# pot1.Q = Q\n",
    "# pot1.E = pot1.func.(Q)\n",
    "\n",
    "\n",
    "# pot2\n",
    "nev = 40\n",
    "name = \"SnIII+h\"\n",
    "\n",
    "pot2 = Potential(); pot2.name = name\n",
    "pot2.Q0 = 1.90291674728; pot2.E0 = 0.585005\n",
    "pot2.nev = nev\n",
    "pot2.func_type = \"harmonic\"\n",
    "params = Dict()\n",
    "params[\"hw\"] = 0.0281812646475\n",
    "pot2.Q = Q\n",
    "pot2.params = params\n",
    "fit_pot!(pot2)\n",
    "# pot2.func = x -> harmonic(x, 0.1281812646475; E₀ = pot2.E0, Q₀ = pot2.Q0)\n",
    "# pot2.Q = Q\n",
    "# pot2.E = pot2.func.(Q)\n",
    "\n",
    "\n",
    "# pot3\n",
    "nev = 30\n",
    "hw = 0.0288945775003\n",
    "name = \"SnII\"\n",
    "\n",
    "pot3 = Potential(); pot3.name = name\n",
    "pot3.Q0 = 0; pot3.E0 = 0\n",
    "pot3.nev = nev\n",
    "pot3.func_type = \"harmonic\"\n",
    "params = Dict()\n",
    "params[\"hw\"] = 0.0288945775003\n",
    "pot3.Q = Q\n",
    "pot3.params = params\n",
    "fit_pot!(pot3)\n",
    "# pot3.func = x -> harmonic(x, 0.0288945775003; E₀ = pot3.E0, Q₀ = pot3.Q0)\n",
    "# pot3.Q = Q\n",
    "# pot3.E = pot3.func.(Q)\n",
    "\"Fitting completed\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is solving the 1D Schrödinger equation for each PES to obtain their phonon (nuclear) wavefunctions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Schrödinger equation solved\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "solve_pot!(pot1)\n",
    "solve_pot!(pot2)\n",
    "solve_pot!(pot3)\n",
    "\"Schrödinger equation solved\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Capture barriers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The classic energy barrier to capture an electron or a hole can be calculated using `find_crossing` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Electron capture barrier: 0.2244086500961966 eV\n",
      "Hole capture barrier: 0.03233164063109362 eV\n"
     ]
    }
   ],
   "source": [
    "Qx, Ex = find_crossing(pot1, pot2)\n",
    "println(\"Electron capture barrier: $(Ex-pot1.E0) eV\")\n",
    "Qx, Ex = find_crossing(pot2, pot3)\n",
    "println(\"Hole capture barrier: $(Ex-pot2.E0) eV\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Potentials and associated wave functions "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the potential energy surfaces and associated wave functions can help you to understand what is happening. Make sure you calculated an enough number of state (`nev`) to describe the carrier-cature behavior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "  925.131,380.824 927.99,380.779 930.848,380.684 933.707,380.54 936.566,380.347 939.424,380.104 942.283,379.812 945.141,379.47 948,379.079 950.859,378.639 \n",
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       "  982.303,370.535 985.162,369.502 988.02,368.42 990.879,367.288 993.737,366.107 996.596,364.876 999.454,363.597 1002.31,362.267 1005.17,360.889 1008.03,359.46 \n",
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       "  1611.19,-1046.42 1614.05,-1058.32 1616.91,-1070.27 1619.77,-1082.26 1622.63,-1094.31 1625.48,-1106.41 1628.34,-1118.55 1631.2,-1130.74 1634.06,-1142.99 1636.92,-1155.28 \n",
       "  1639.78,-1167.62 1642.64,-1180.01 1645.49,-1192.46 1648.35,-1204.95 1651.21,-1217.49 1654.07,-1230.08 1656.93,-1242.71 1659.79,-1255.4 1662.65,-1268.14 1665.5,-1280.93 \n",
       "  1668.36,-1293.76 1671.22,-1306.65 1674.08,-1319.58 1676.94,-1332.57 1679.8,-1345.6 1682.66,-1358.68 1685.51,-1371.82 1688.37,-1385 1691.23,-1398.23 1694.09,-1411.51 \n",
       "  1696.95,-1424.84 1699.81,-1438.22 1702.67,-1451.65 1705.52,-1465.13 1708.38,-1478.65 1711.24,-1492.23 1714.1,-1505.86 1716.96,-1519.53 1719.82,-1533.26 1722.68,-1547.03 \n",
       "  1725.53,-1560.86 1728.39,-1574.73 1731.25,-1588.65 1734.11,-1602.62 1736.97,-1616.65 1739.83,-1630.72 1742.69,-1644.84 1745.54,-1659.01 1748.4,-1673.23 1751.26,-1687.49 \n",
       "  1754.12,-1701.81 1756.98,-1716.18 1759.84,-1730.6 1762.7,-1745.06 1765.56,-1759.58 1768.41,-1774.14 1771.27,-1788.75 1774.13,-1803.42 1776.99,-1818.13 1779.85,-1832.89 \n",
       "  1782.71,-1847.71 1785.57,-1862.57 1788.42,-1877.48 1791.28,-1892.44 1794.14,-1907.45 1797,-1922.5 1799.86,-1937.61 1802.72,-1952.77 1805.58,-1967.98 1808.43,-1983.23 \n",
       "  1811.29,-1998.54 1814.15,-2013.89 1817.01,-2029.3 1819.87,-2044.75 1822.73,-2060.25 1825.59,-2075.81 1828.44,-2091.41 1831.3,-2107.06 1834.16,-2122.76 1837.02,-2138.51 \n",
       "  1839.88,-2154.31 1842.74,-2170.16 1845.6,-2186.05 1848.45,-2202 1851.31,-2218 1854.17,-2234.05 1857.03,-2250.14 1859.89,-2266.29 1862.75,-2282.48 1865.61,-2298.72 \n",
       "  1868.46,-2315.02 1871.32,-2331.36 1874.18,-2347.75 1877.04,-2364.19 1879.9,-2380.68 1882.76,-2397.22 1885.62,-2413.81 1888.47,-2430.45 1891.33,-2447.14 1894.19,-2463.88 \n",
       "  1897.05,-2480.66 1899.91,-2497.5 1902.77,-2514.39 1905.63,-2531.32 1908.48,-2548.31 1911.34,-2565.34 1914.2,-2582.42 1917.06,-2599.56 1919.92,-2616.74 1922.78,-2633.97 \n",
       "  1925.64,-2651.25 1928.49,-2668.58 1931.35,-2685.96 1934.21,-2703.39 1937.07,-2720.87 1939.93,-2738.4 1942.79,-2755.97 1945.65,-2773.6 1948.5,-2791.28 1951.36,-2809 \n",
       "  1954.22,-2826.78 1957.08,-2844.6 1959.94,-2862.47 1962.8,-2880.4 1965.66,-2898.37 1968.51,-2916.39 1971.37,-2934.46 1974.23,-2952.58 1977.09,-2970.75 1979.95,-2988.97 \n",
       "  1982.81,-3007.24 1985.67,-3025.56 1988.52,-3043.93 1991.38,-3062.34 1994.24,-3080.81 1997.1,-3099.32 1999.96,-3117.89 2002.82,-3136.5 2005.68,-3155.17 2008.53,-3173.88 \n",
       "  2011.39,-3192.64 2014.25,-3211.45 2017.11,-3230.31 2019.97,-3249.23 2022.83,-3268.19 2025.69,-3287.19 2028.54,-3306.25 2031.4,-3325.36 2034.26,-3344.52 2037.12,-3363.73 \n",
       "  2039.98,-3382.98 2042.84,-3402.29 2045.7,-3421.64 2048.55,-3441.05 2051.41,-3460.5 2054.27,-3480 2057.13,-3499.56 2059.99,-3519.16 2062.85,-3538.81 2065.71,-3558.51 \n",
       "  2068.56,-3578.26 2071.42,-3598.06 2074.28,-3617.91 2077.14,-3637.81 2080,-3657.76 2082.86,-3677.75 2085.72,-3697.8 2088.58,-3717.9 2091.43,-3738.04 2094.29,-3758.24 \n",
       "  2097.15,-3778.48 2100.01,-3798.77 2102.87,-3819.12 2105.73,-3839.51 2108.59,-3859.95 2111.44,-3880.44 2114.3,-3900.98 2117.16,-3921.57 2120.02,-3942.21 2122.88,-3962.9 \n",
       "  2125.74,-3983.64 2128.6,-4004.42 2131.45,-4025.26 2134.31,-4046.15 2137.17,-4067.08 2140.03,-4088.07 2142.89,-4109.1 2145.75,-4130.18 2148.61,-4151.32 2151.46,-4172.5 \n",
       "  2154.32,-4193.73 2157.18,-4215.01 2160.04,-4236.34 2162.9,-4257.72 2165.76,-4279.15 2168.62,-4300.63 2171.47,-4322.16 2174.33,-4343.74 2177.19,-4365.36 2180.05,-4387.04 \n",
       "  2182.91,-4408.76 2185.77,-4430.54 2188.63,-4452.36 2191.48,-4474.24 2194.34,-4496.16 2197.2,-4518.13 2200.06,-4540.15 2202.92,-4562.23 2205.78,-4584.35 2208.64,-4606.52 \n",
       "  2211.49,-4628.74 2214.35,-4651.01 2217.21,-4673.32 2220.07,-4695.69 2222.93,-4718.11 2225.79,-4740.57 2228.65,-4763.09 2231.5,-4785.66 2234.36,-4808.27 2237.22,-4830.93 \n",
       "  2240.08,-4853.65 2242.94,-4876.41 2245.8,-4899.22 2248.66,-4922.08 2251.51,-4944.99 2254.37,-4967.95 2257.23,-4990.96 2260.09,-5014.02 2262.95,-5037.13 2265.81,-5060.29 \n",
       "  2268.67,-5083.5 2271.52,-5106.75 2274.38,-5130.06 2277.24,-5153.41 2280.1,-5176.82 2282.96,-5200.27 2285.82,-5223.78 2288.68,-5247.33 2291.53,-5270.93 2294.39,-5294.58 \n",
       "  2297.25,-5318.28 2300.11,-5342.03 2302.97,-5365.83 2305.83,-5389.68 2308.69,-5413.58 2311.54,-5437.53 2314.4,-5461.53 2317.26,-5485.57 2320.12,-5509.67 2322.98,-5533.82 \n",
       "  2325.84,-5558.01 2328.7,-5582.25 2331.55,-5606.55 2334.41,-5630.89 2337.27,-5655.28 2340.13,-5679.73 2342.99,-5704.22 2345.85,-5728.76 2348.71,-5753.35 2351.56,-5777.99 \n",
       "  2354.42,-5802.68 2357.28,-5827.41 2360.14,-5852.2 2363,-5877.04 2365.86,-5901.92 2368.72,-5926.86 2371.57,-5951.84 2374.43,-5976.88 2377.29,-6001.96 2380.15,-6027.1 \n",
       "  2383.01,-6052.28 2385.87,-6077.51 2388.73,-6102.79 2391.59,-6128.12 2394.44,-6153.5 2397.3,-6178.93 2400.16,-6204.41 2403.02,-6229.94 2405.88,-6255.52 2408.74,-6281.14 \n",
       "  2411.6,-6306.82 2414.45,-6332.55 2417.31,-6358.32 2420.17,-6384.15 2423.03,-6410.02 2425.89,-6435.94 2428.75,-6461.92 2431.61,-6487.94 2434.46,-6514.01 2437.32,-6540.13 \n",
       "  2440.18,-6566.3 2443.04,-6592.52 2445.9,-6618.79 2448.76,-6645.11 2451.62,-6671.48 2454.47,-6697.89 2457.33,-6724.36 2460.19,-6750.88 2463.05,-6777.44 2465.91,-6804.06 \n",
       "  2468.77,-6830.72 2471.63,-6857.43 2474.48,-6884.2 2477.34,-6911.01 2480.2,-6937.87 2483.06,-6964.78 2485.92,-6991.74 2488.78,-7018.75 2491.64,-7045.81 2494.49,-7072.92 \n",
       "  2497.35,-7100.08 2500.21,-7127.29 2503.07,-7154.54 2505.93,-7181.85 2508.79,-7209.2 2511.65,-7236.61 2514.5,-7264.06 2517.36,-7291.57 2520.22,-7319.12 2523.08,-7346.72 \n",
       "  2525.94,-7374.37 2528.8,-7402.08 2531.66,-7429.83 2534.51,-7457.63 2537.37,-7485.48 2540.23,-7513.37 2543.09,-7541.32 2545.95,-7569.32 2548.81,-7597.37 2551.67,-7625.46 \n",
       "  2554.52,-7653.61 2557.38,-7681.8 2560.24,-7710.05 2563.1,-7738.34 2565.96,-7766.69 2568.82,-7795.08 2571.68,-7823.52 2574.53,-7852.01 2577.39,-7880.55 2580.25,-7909.14 \n",
       "  2583.11,-7937.78 2585.97,-7966.47 2588.83,-7995.21 2591.69,-8024 2594.54,-8052.84 2597.4,-8081.72 2600.26,-8110.66 2603.12,-8139.64 2605.98,-8168.68 2608.84,-8197.76 \n",
       "  2611.7,-8226.89 2614.55,-8256.08 2617.41,-8285.31 2620.27,-8314.59 2623.13,-8343.92 2625.99,-8373.3 2628.85,-8402.73 2631.71,-8432.21 2634.56,-8461.74 2637.42,-8491.32 \n",
       "  2640.28,-8520.95 2643.14,-8550.62 2646,-8580.35 2648.86,-8610.12 2651.72,-8639.95 2654.57,-8669.82 2657.43,-8699.75 2660.29,-8729.72 2663.15,-8759.74 2666.01,-8789.81 \n",
       "  2668.87,-8819.93 2671.73,-8850.11 2674.58,-8880.33 2677.44,-8910.59 2680.3,-8940.91 2683.16,-8971.28 2686.02,-9001.7 2688.88,-9032.17 2691.74,-9062.68 2694.59,-9093.25 \n",
       "  2697.45,-9123.86 2700.31,-9154.53 2703.17,-9185.24 2706.03,-9216 2708.89,-9246.82 2711.75,-9277.68 2714.61,-9308.59 2717.46,-9339.55 2720.32,-9370.56 2723.18,-9401.62 \n",
       "  2726.04,-9432.73 2728.9,-9463.89 2731.76,-9495.09 2734.62,-9526.35 2737.47,-9557.66 2740.33,-9589.01 2743.19,-9620.42 2746.05,-9651.87 2748.91,-9683.38 2751.77,-9714.93 \n",
       "  2754.63,-9746.53 2757.48,-9778.19 2760.34,-9809.89 2763.2,-9841.64 2766.06,-9873.44 2768.92,-9905.29 2771.78,-9937.19 2774.64,-9969.14 2777.49,-10001.1 2780.35,-10033.2 \n",
       "  2783.21,-10065.3 2786.07,-10097.4 2788.93,-10129.6 2791.79,-10161.9 2794.65,-10194.2 2797.5,-10226.5 2800.36,-10258.9 2803.22,-10291.3 2806.08,-10323.8 2808.94,-10356.4 \n",
       "  2811.8,-10389 2814.66,-10421.6 2817.51,-10454.3 2820.37,-10487 2823.23,-10519.8 2826.09,-10552.7 2828.95,-10585.5 2831.81,-10618.5 2834.67,-10651.5 2837.52,-10684.5 \n",
       "  2840.38,-10717.6 2843.24,-10750.7 2846.1,-10783.9 2848.96,-10817.1 2851.82,-10850.4 2854.68,-10883.7 2857.53,-10917.1 2860.39,-10950.6 2863.25,-10984 2866.11,-11017.6 \n",
       "  2868.97,-11051.1 2871.83,-11084.8 2874.69,-11118.4 2877.54,-11152.2 2880.4,-11185.9 2883.26,-11219.8 2886.12,-11253.6 2888.98,-11287.6 2891.84,-11321.5 2894.7,-11355.6 \n",
       "  2897.55,-11389.6 2900.41,-11423.8 2903.27,-11457.9 2906.13,-11492.1 2908.99,-11526.4 2911.85,-11560.7 2914.71,-11595.1 2917.56,-11629.5 2920.42,-11664 2923.28,-11698.5 \n",
       "  2926.14,-11733.1 2929,-11767.7 2931.86,-11802.4 2934.72,-11837.1 2937.57,-11871.8 2940.43,-11906.6 2943.29,-11941.5 2946.15,-11976.4 2949.01,-12011.4 2951.87,-12046.4 \n",
       "  2954.73,-12081.4 2957.58,-12116.6 2960.44,-12151.7 2963.3,-12186.9 2966.16,-12222.2 2969.02,-12257.5 2971.88,-12292.8 2974.74,-12328.2 2977.59,-12363.7 2980.45,-12399.2 \n",
       "  2983.31,-12434.8 2986.17,-12470.4 2989.03,-12506 2991.89,-12541.7 2994.75,-12577.5 2997.6,-12613.3 3000.46,-12649.1 3003.32,-12685 3006.18,-12721 3009.04,-12757 \n",
       "  3011.9,-12793 3014.76,-12829.1 3017.61,-12865.3 3020.47,-12901.5 3023.33,-12937.7 3026.19,-12974 3029.05,-13010.3 3031.91,-13046.7 3034.77,-13083.2 3037.63,-13119.7 \n",
       "  3040.48,-13156.2 3043.34,-13192.8 3046.2,-13229.4 3049.06,-13266.1 3051.92,-13302.9 3054.78,-13339.7 3057.64,-13376.5 3060.49,-13413.4 3063.35,-13450.3 3066.21,-13487.3 \n",
       "  3069.07,-13524.3 3071.93,-13561.4 3074.79,-13598.6 3077.65,-13635.7 3080.5,-13673 3083.36,-13710.2 3086.22,-13747.6 3089.08,-13785 3091.94,-13822.4 3094.8,-13859.9 \n",
       "  3097.66,-13897.4 3100.51,-13935 3103.37,-13972.6 3106.23,-14010.3 3109.09,-14048 3111.95,-14085.8 3114.81,-14123.6 3117.67,-14161.5 3120.52,-14199.4 3123.38,-14237.4 \n",
       "  3126.24,-14275.4 3129.1,-14313.5 3131.96,-14351.6 3134.82,-14389.8 3137.68,-14428 3140.53,-14466.3 3143.39,-14504.6 3146.25,-14542.9 3149.11,-14581.4 3151.97,-14619.8 \n",
       "  3154.83,-14658.4 3157.69,-14696.9 3160.54,-14735.5 3163.4,-14774.2 3166.26,-14812.9 3169.12,-14851.7 3171.98,-14890.5 3174.84,-14929.4 3177.7,-14968.3 3180.55,-15007.2 \n",
       "  3183.41,-15046.2 3186.27,-15085.3 3189.13,-15124.4 3191.99,-15163.6 3194.85,-15202.8 3197.71,-15242 3200.56,-15281.3 3203.42,-15320.7 3206.28,-15360.1 3209.14,-15399.6 \n",
       "  3212,-15439.1 3214.86,-15478.6 3217.72,-15518.2 3220.57,-15557.9 3223.43,-15597.6 3226.29,-15637.3 3229.15,-15677.1 3232.01,-15717 3234.87,-15756.9 3237.73,-15796.8 \n",
       "  3240.58,-15836.8 3243.44,-15876.9 3246.3,-15917 3249.16,-15957.1 3252.02,-15997.3 3254.88,-16037.5 3257.74,-16077.8 3260.59,-16118.2 3263.45,-16158.6 3266.31,-16199 \n",
       "  3269.17,-16239.5 3272.03,-16280.1 3274.89,-16320.6 3277.75,-16361.3 3280.6,-16402 3283.46,-16442.7 3286.32,-16483.5 3289.18,-16524.3 3292.04,-16565.2 3294.9,-16606.2 \n",
       "  3297.76,-16647.2 3300.61,-16688.2 3303.47,-16729.3 3306.33,-16770.4 3309.19,-16811.6 3312.05,-16852.8 3314.91,-16894.1 3317.77,-16935.4 3320.62,-16976.8 3323.48,-17018.3 \n",
       "  3326.34,-17059.7 3329.2,-17101.3 3332.06,-17142.8 3334.92,-17184.5 3337.78,-17226.1 3340.64,-17267.9 3343.49,-17309.6 3346.35,-17351.5 3349.21,-17393.3 3352.07,-17435.3 \n",
       "  3354.93,-17477.2 3357.79,-17519.3 3360.65,-17561.3 3363.5,-17603.5 3366.36,-17645.6 3369.22,-17687.9 3372.08,-17730.1 3374.94,-17772.4 3377.8,-17814.8 3380.66,-17857.2 \n",
       "  3383.51,-17899.7 3386.37,-17942.2 3389.23,-17984.8 3392.09,-18027.4 3394.95,-18070.1 3397.81,-18112.8 3400.67,-18155.5 3403.52,-18198.4 3406.38,-18241.2 3409.24,-18284.1 \n",
       "  3412.1,-18327.1 3414.96,-18370.1 3417.82,-18413.2 3420.68,-18456.3 3423.53,-18499.4 3426.39,-18542.6 3429.25,-18585.9 3432.11,-18629.2 3434.97,-18672.6 3437.83,-18716 \n",
       "  3440.69,-18759.4 3443.54,-18802.9 3446.4,-18846.5 3449.26,-18890.1 3452.12,-18933.7 3454.98,-18977.4 3457.84,-19021.2 3460.7,-19065 3463.55,-19108.8 3466.41,-19152.7 \n",
       "  3469.27,-19196.7 3472.13,-19240.7 3474.99,-19284.7 3477.85,-19328.8 3480.71,-19373 3483.56,-19417.2 3486.42,-19461.4 3489.28,-19505.7 3492.14,-19550.1 3495,-19594.5 \n",
       "  3497.86,-19638.9 3500.72,-19683.4 3503.57,-19727.9 3506.43,-19772.5 3509.29,-19817.2 3512.15,-19861.9 3515.01,-19906.6 3517.87,-19951.4 3520.73,-19996.2 3523.58,-20041.1 \n",
       "  3526.44,-20086 3529.3,-20131 3532.16,-20176.1 3535.02,-20221.2 3537.88,-20266.3 3540.74,-20311.5 3543.59,-20356.7 3546.45,-20402 3549.31,-20447.3 3552.17,-20492.7 \n",
       "  3555.03,-20538.1 3557.89,-20583.6 3560.75,-20629.1 3563.6,-20674.7 3566.46,-20720.3 3569.32,-20766 3572.18,-20811.7 3575.04,-20857.5 3577.9,-20903.4 3580.76,-20949.2 \n",
       "  3583.61,-20995.2 3586.47,-21041.1 3589.33,-21087.1 3592.19,-21133.2 3595.05,-21179.3 3597.91,-21225.5 3600.77,-21271.7 3603.62,-21318 3606.48,-21364.3 3609.34,-21410.7 \n",
       "  3612.2,-21457.1 3615.06,-21503.6 3617.92,-21550.1 3620.78,-21596.7 3623.63,-21643.3 3626.49,-21689.9 3629.35,-21736.7 3632.21,-21783.4 3635.07,-21830.2 3637.93,-21877.1 \n",
       "  3640.79,-21924 3643.64,-21971 3646.5,-22018 3649.36,-22065 3652.22,-22112.2 3655.08,-22159.3 3657.94,-22206.5 3660.8,-22253.8 3663.66,-22301.1 3666.51,-22348.4 \n",
       "  3669.37,-22395.9 3672.23,-22443.3 3675.09,-22490.8 3677.95,-22538.4 3680.81,-22586 3683.67,-22633.6 3686.52,-22681.3 3689.38,-22729.1 3692.24,-22776.9 3695.1,-22824.7 \n",
       "  3697.96,-22872.6 3700.82,-22920.6 3703.68,-22968.6 3706.53,-23016.6 3709.39,-23064.7 3712.25,-23112.9 3715.11,-23161.1 3717.97,-23209.3 3720.83,-23257.6 3723.69,-23306 \n",
       "  3726.54,-23354.3 3729.4,-23402.8 3732.26,-23451.3 3735.12,-23499.8 3737.98,-23548.4 3740.84,-23597.1 3743.7,-23645.7 3746.55,-23694.5 3749.41,-23743.3 3752.27,-23792.1 \n",
       "  3755.13,-23841 3757.99,-23889.9 3760.85,-23938.9 3763.71,-23988 3766.56,-24037 3769.42,-24086.2 3772.28,-24135.4 3775.14,-24184.6 3778,-24233.9 3780.86,-24283.2 \n",
       "  3783.72,-24332.6 3786.57,-24382 3789.43,-24431.5 3792.29,-24481 3795.15,-24530.6 3798.01,-24580.2 3800.87,-24629.9 3803.73,-24679.6 3806.58,-24729.4 3809.44,-24779.3 \n",
       "  3812.3,-24829.1 3815.16,-24879.1 3818.02,-24929 3820.88,-24979 3823.74,-25029.1 3826.59,-25079.2 3829.45,-25129.4 3832.31,-25179.6 3835.17,-25229.9 3838.03,-25280.2 \n",
       "  3840.89,-25330.6 3843.75,-25381 3846.6,-25431.5 3849.46,-25482 3852.32,-25532.6 3855.18,-25583.2 3858.04,-25633.9 3860.9,-25684.6 3863.76,-25735.3 3866.61,-25786.1 \n",
       "  3869.47,-25837 3872.33,-25887.9 3875.19,-25938.9 3878.05,-25989.9 3880.91,-26041 3883.77,-26092.1 3886.62,-26143.2 3889.48,-26194.4 3892.34,-26245.7 3895.2,-26297 \n",
       "  3898.06,-26348.4 3900.92,-26399.8 3903.78,-26451.2 3906.63,-26502.7 3909.49,-26554.3 3912.35,-26605.9 3915.21,-26657.5 3918.07,-26709.2 3920.93,-26761 3923.79,-26812.8 \n",
       "  3926.64,-26864.6 3929.5,-26916.5 3932.36,-26968.5 3935.22,-27020.5 3938.08,-27072.5 3940.94,-27124.6 3943.8,-27176.8 3946.65,-27229 3949.51,-27281.2 3952.37,-27333.5 \n",
       "  3955.23,-27385.9 3958.09,-27438.3 3960.95,-27490.7 3963.81,-27543.2 3966.66,-27595.7 3969.52,-27648.3 3972.38,-27701 3975.24,-27753.7 3978.1,-27806.4 3980.96,-27859.2 \n",
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       "  -18.2016,-3315.26 -15.343,-3295.33 -12.4844,-3275.45 -9.62582,-3255.61 -6.76723,-3235.83 -3.90865,-3216.09 -1.05007,-3196.4 1.80852,-3176.75 4.6671,-3157.15 7.52569,-3137.6 \n",
       "  10.3843,-3118.09 13.2429,-3098.64 16.1014,-3079.22 18.96,-3059.86 21.8186,-3040.54 24.6772,-3021.27 27.5358,-3002.05 30.3944,-2982.87 33.2529,-2963.75 36.1115,-2944.66 \n",
       "  38.9701,-2925.63 41.8287,-2906.64 44.6873,-2887.7 47.5459,-2868.8 50.4045,-2849.96 53.263,-2831.16 56.1216,-2812.4 58.9802,-2793.7 61.8388,-2775.04 64.6974,-2756.43 \n",
       "  67.556,-2737.86 70.4145,-2719.34 73.2731,-2700.87 76.1317,-2682.45 78.9903,-2664.07 81.8489,-2645.74 84.7075,-2627.45 87.566,-2609.22 90.4246,-2591.03 93.2832,-2572.89 \n",
       "  96.1418,-2554.79 99.0004,-2536.74 101.859,-2518.74 104.718,-2500.79 107.576,-2482.88 110.435,-2465.02 113.293,-2447.2 116.152,-2429.44 119.01,-2411.72 121.869,-2394.04 \n",
       "  124.728,-2376.42 127.586,-2358.84 130.445,-2341.31 133.303,-2323.82 136.162,-2306.39 139.021,-2288.99 141.879,-2271.65 144.738,-2254.35 147.596,-2237.1 150.455,-2219.9 \n",
       "  153.313,-2202.74 156.172,-2185.64 159.031,-2168.57 161.889,-2151.56 164.748,-2134.59 167.606,-2117.67 170.465,-2100.79 173.324,-2083.97 176.182,-2067.19 179.041,-2050.45 \n",
       "  181.899,-2033.77 184.758,-2017.13 187.616,-2000.54 190.475,-1983.99 193.334,-1967.49 196.192,-1951.04 199.051,-1934.64 201.909,-1918.28 204.768,-1901.97 207.627,-1885.71 \n",
       "  210.485,-1869.49 213.344,-1853.32 216.202,-1837.2 219.061,-1821.12 221.92,-1805.09 224.778,-1789.11 227.637,-1773.18 230.495,-1757.29 233.354,-1741.45 236.212,-1725.65 \n",
       "  239.071,-1709.91 241.93,-1694.21 244.788,-1678.55 247.647,-1662.95 250.505,-1647.39 253.364,-1631.88 256.223,-1616.41 259.081,-1601 261.94,-1585.62 264.798,-1570.3 \n",
       "  267.657,-1555.02 270.515,-1539.79 273.374,-1524.61 276.233,-1509.48 279.091,-1494.39 281.95,-1479.34 284.808,-1464.35 287.667,-1449.4 290.526,-1434.5 293.384,-1419.65 \n",
       "  296.243,-1404.84 299.101,-1390.08 301.96,-1375.36 304.818,-1360.7 307.677,-1346.08 310.536,-1331.51 313.394,-1316.98 316.253,-1302.5 319.111,-1288.07 321.97,-1273.69 \n",
       "  324.829,-1259.35 327.687,-1245.06 330.546,-1230.82 333.404,-1216.62 336.263,-1202.47 339.121,-1188.37 341.98,-1174.31 344.839,-1160.3 347.697,-1146.34 350.556,-1132.43 \n",
       "  353.414,-1118.56 356.273,-1104.74 359.132,-1090.97 361.99,-1077.24 364.849,-1063.56 367.707,-1049.93 370.566,-1036.34 373.424,-1022.8 376.283,-1009.31 379.142,-995.866 \n",
       "  382,-982.468 384.859,-969.117 387.717,-955.813 390.576,-942.556 393.435,-929.346 396.293,-916.183 399.152,-903.067 402.01,-889.998 404.869,-876.976 407.727,-864.001 \n",
       "  410.586,-851.073 413.445,-838.192 416.303,-825.358 419.162,-812.571 422.02,-799.831 424.879,-787.137 427.738,-774.491 430.596,-761.892 433.455,-749.34 436.313,-736.834 \n",
       "  439.172,-724.376 442.031,-711.965 444.889,-699.6 447.748,-687.283 450.606,-675.013 453.465,-662.789 456.323,-650.613 459.182,-638.483 462.041,-626.401 464.899,-614.365 \n",
       "  467.758,-602.377 470.616,-590.435 473.475,-578.541 476.334,-566.693 479.192,-554.893 482.051,-543.139 484.909,-531.432 487.768,-519.773 490.626,-508.16 493.485,-496.594 \n",
       "  496.344,-485.075 499.202,-473.604 502.061,-462.179 504.919,-450.801 507.778,-439.47 510.637,-428.186 513.495,-416.949 516.354,-405.76 519.212,-394.617 522.071,-383.521 \n",
       "  524.929,-372.472 527.788,-361.47 530.647,-350.515 533.505,-339.607 536.364,-328.746 539.222,-317.932 542.081,-307.164 544.94,-296.444 547.798,-285.771 550.657,-275.145 \n",
       "  553.515,-264.566 556.374,-254.034 559.232,-243.548 562.091,-233.11 564.95,-222.719 567.808,-212.374 570.667,-202.077 573.525,-191.827 576.384,-181.623 579.243,-171.467 \n",
       "  582.101,-161.358 584.96,-151.295 587.818,-141.28 590.677,-131.311 593.535,-121.39 596.394,-111.515 599.253,-101.688 602.111,-91.9069 604.97,-82.1733 607.828,-72.4867 \n",
       "  610.687,-62.847 613.546,-53.2544 616.404,-43.7087 619.263,-34.2099 622.121,-24.7582 624.98,-15.3534 627.838,-5.99566 630.697,3.31515 633.556,12.579 636.414,21.7958 \n",
       "  639.273,30.9657 642.131,40.0886 644.99,49.1645 647.849,58.1935 650.707,67.1754 653.566,76.1104 656.424,84.9984 659.283,93.8395 662.141,102.634 665,111.381 \n",
       "  667.859,120.081 670.717,128.734 673.576,137.34 676.434,145.899 679.293,154.411 682.152,162.877 685.01,171.295 687.869,179.666 690.727,187.99 693.586,196.268 \n",
       "  696.445,204.498 699.303,212.681 702.162,220.818 705.02,228.907 707.879,236.95 710.737,244.945 713.596,252.893 716.455,260.795 719.313,268.649 722.172,276.457 \n",
       "  725.03,284.217 727.889,291.931 730.748,299.598 733.606,307.217 736.465,314.79 739.323,322.316 742.182,329.794 745.04,337.226 747.899,344.611 750.758,351.948 \n",
       "  753.616,359.239 756.475,366.483 759.333,373.68 762.192,380.83 765.051,387.933 767.909,394.988 770.768,401.997 773.626,408.959 776.485,415.874 779.343,422.742 \n",
       "  782.202,429.563 785.061,436.337 787.919,443.064 790.778,449.744 793.636,456.378 796.495,462.964 799.354,469.503 802.212,475.995 805.071,482.44 807.929,488.838 \n",
       "  810.788,495.19 813.646,501.494 816.505,507.751 819.364,513.961 822.222,520.125 825.081,526.241 827.939,532.31 830.798,538.333 833.657,544.308 836.515,550.237 \n",
       "  839.374,556.118 842.232,561.953 845.091,567.74 847.949,573.481 850.808,579.174 853.667,584.821 856.525,590.42 859.384,595.973 862.242,601.479 865.101,606.937 \n",
       "  867.96,612.349 870.818,617.714 873.677,623.031 876.535,628.302 879.394,633.526 882.252,638.703 885.111,643.832 887.97,648.915 890.828,653.951 893.687,658.94 \n",
       "  896.545,663.882 899.404,668.777 902.263,673.625 905.121,678.426 907.98,683.18 910.838,687.887 913.697,692.547 916.556,697.16 919.414,701.726 922.273,706.245 \n",
       "  925.131,710.717 927.99,715.142 930.848,719.521 933.707,723.852 936.566,728.136 939.424,732.373 942.283,736.564 945.141,740.707 948,744.803 950.859,748.852 \n",
       "  953.717,752.855 956.576,756.81 959.434,760.719 962.293,764.58 965.151,768.395 968.01,772.162 970.869,775.882 973.727,779.556 976.586,783.183 979.444,786.762 \n",
       "  982.303,790.295 985.162,793.78 988.02,797.219 990.879,800.611 993.737,803.955 996.596,807.253 999.454,810.504 1002.31,813.707 1005.17,816.864 1008.03,819.974 \n",
       "  1010.89,823.037 1013.75,826.053 1016.61,829.021 1019.46,831.943 1022.32,834.818 1025.18,837.646 1028.04,840.427 1030.9,843.161 1033.76,845.848 1036.62,848.488 \n",
       "  1039.47,851.081 1042.33,853.627 1045.19,856.126 1048.05,858.578 1050.91,860.983 1053.77,863.342 1056.63,865.653 1059.48,867.917 1062.34,870.134 1065.2,872.304 \n",
       "  1068.06,874.428 1070.92,876.504 1073.78,878.533 1076.64,880.516 1079.49,882.451 1082.35,884.339 1085.21,886.181 1088.07,887.975 1090.93,889.723 1093.79,891.423 \n",
       "  1096.65,893.077 1099.5,894.683 1102.36,896.243 1105.22,897.755 1108.08,899.221 1110.94,900.639 1113.8,902.011 1116.66,903.336 1119.51,904.613 1122.37,905.844 \n",
       "  1125.23,907.028 1128.09,908.164 1130.95,909.254 1133.81,910.297 1136.67,911.293 1139.53,912.242 1142.38,913.143 1145.24,913.998 1148.1,914.806 1150.96,915.567 \n",
       "  1153.82,916.281 1156.68,916.948 1159.54,917.568 1162.39,918.141 1165.25,918.667 1168.11,919.146 1170.97,919.578 1173.83,919.963 1176.69,920.301 1179.55,920.592 \n",
       "  1182.4,920.837 1185.26,921.034 1188.12,921.184 1190.98,921.287 1193.84,921.343 1196.7,921.353 1199.56,921.315 1202.41,921.23 1205.27,921.099 1208.13,920.92 \n",
       "  1210.99,920.694 1213.85,920.422 1216.71,920.102 1219.57,919.736 1222.42,919.322 1225.28,918.862 1228.14,918.354 1231,917.8 1233.86,917.198 1236.72,916.55 \n",
       "  1239.58,915.855 1242.43,915.112 1245.29,914.323 1248.15,913.487 1251.01,912.603 1253.87,911.673 1256.73,910.696 1259.59,909.672 1262.44,908.6 1265.3,907.482 \n",
       "  1268.16,906.317 1271.02,905.105 1273.88,903.846 1276.74,902.54 1279.6,901.187 1282.45,899.787 1285.31,898.34 1288.17,896.846 1291.03,895.305 1293.89,893.717 \n",
       "  1296.75,892.082 1299.61,890.4 1302.46,888.671 1305.32,886.895 1308.18,885.072 1311.04,883.202 1313.9,881.285 1316.76,879.322 1319.62,877.311 1322.47,875.253 \n",
       "  1325.33,873.149 1328.19,870.997 1331.05,868.798 1333.91,866.553 1336.77,864.26 1339.63,861.92 1342.48,859.534 1345.34,857.1 1348.2,854.62 1351.06,852.092 \n",
       "  1353.92,849.518 1356.78,846.896 1359.64,844.228 1362.49,841.512 1365.35,838.75 1368.21,835.941 1371.07,833.084 1373.93,830.181 1376.79,827.231 1379.65,824.233 \n",
       "  1382.5,821.189 1385.36,818.098 1388.22,814.96 1391.08,811.774 1393.94,808.542 1396.8,805.263 1399.66,801.937 1402.51,798.564 1405.37,795.144 1408.23,791.677 \n",
       "  1411.09,788.163 1413.95,784.602 1416.81,780.994 1419.67,777.339 1422.52,773.637 1425.38,769.888 1428.24,766.092 1431.1,762.249 1433.96,758.359 1436.82,754.422 \n",
       "  1439.68,750.439 1442.54,746.408 1445.39,742.33 1448.25,738.205 1451.11,734.034 1453.97,729.815 1456.83,725.549 1459.69,721.237 1462.55,716.877 1465.4,712.47 \n",
       "  1468.26,708.017 1471.12,703.516 1473.98,698.969 1476.84,694.374 1479.7,689.733 1482.56,685.044 1485.41,680.309 1488.27,675.526 1491.13,670.697 1493.99,665.821 \n",
       "  1496.85,660.897 1499.71,655.927 1502.57,650.91 1505.42,645.845 1508.28,640.734 1511.14,635.576 1514,630.371 1516.86,625.118 1519.72,619.819 1522.58,614.473 \n",
       "  1525.43,609.08 1528.29,603.64 1531.15,598.153 1534.01,592.619 1536.87,587.038 1539.73,581.41 1542.59,575.735 1545.44,570.013 1548.3,564.244 1551.16,558.428 \n",
       "  1554.02,552.565 1556.88,546.655 1559.74,540.698 1562.6,534.694 1565.45,528.644 1568.31,522.546 1571.17,516.401 1574.03,510.209 1576.89,503.971 1579.75,497.685 \n",
       "  1582.61,491.352 1585.46,484.972 1588.32,478.546 1591.18,472.072 1594.04,465.552 1596.9,458.984 1599.76,452.37 1602.62,445.708 1605.47,439 1608.33,432.244 \n",
       "  1611.19,425.442 1614.05,418.592 1616.91,411.696 1619.77,404.752 1622.63,397.762 1625.48,390.725 1628.34,383.64 1631.2,376.509 1634.06,369.331 1636.92,362.106 \n",
       "  1639.78,354.833 1642.64,347.514 1645.49,340.148 1648.35,332.735 1651.21,325.275 1654.07,317.768 1656.93,310.213 1659.79,302.612 1662.65,294.964 1665.5,287.269 \n",
       "  1668.36,279.527 1671.22,271.738 1674.08,263.902 1676.94,256.019 1679.8,248.09 1682.66,240.113 1685.51,232.089 1688.37,224.018 1691.23,215.9 1694.09,207.735 \n",
       "  1696.95,199.524 1699.81,191.265 1702.67,182.959 1705.52,174.606 1708.38,166.207 1711.24,157.76 1714.1,149.266 1716.96,140.726 1719.82,132.138 1722.68,123.504 \n",
       "  1725.53,114.822 1728.39,106.093 1731.25,97.318 1734.11,88.4955 1736.97,79.626 1739.83,70.7096 1742.69,61.7462 1745.54,52.7358 1748.4,43.6784 1751.26,34.5741 \n",
       "  1754.12,25.4227 1756.98,16.2244 1759.84,6.97915 1762.7,-2.3131 1765.56,-11.6523 1768.41,-21.0386 1771.27,-30.4717 1774.13,-39.9519 1776.99,-49.479 1779.85,-59.0532 \n",
       "  1782.71,-68.6743 1785.57,-78.3423 1788.42,-88.0574 1791.28,-97.8194 1794.14,-107.628 1797,-117.484 1799.86,-127.387 1802.72,-137.337 1805.58,-147.334 1808.43,-157.378 \n",
       "  1811.29,-167.469 1814.15,-177.607 1817.01,-187.792 1819.87,-198.024 1822.73,-208.302 1825.59,-218.628 1828.44,-229.001 1831.3,-239.42 1834.16,-249.887 1837.02,-260.401 \n",
       "  1839.88,-270.962 1842.74,-281.569 1845.6,-292.224 1848.45,-302.925 1851.31,-313.674 1854.17,-324.469 1857.03,-335.312 1859.89,-346.201 1862.75,-357.138 1865.61,-368.121 \n",
       "  1868.46,-379.152 1871.32,-390.229 1874.18,-401.354 1877.04,-412.525 1879.9,-423.743 1882.76,-435.009 1885.62,-446.321 1888.47,-457.68 1891.33,-469.086 1894.19,-480.54 \n",
       "  1897.05,-492.04 1899.91,-503.587 1902.77,-515.181 1905.63,-526.822 1908.48,-538.51 1911.34,-550.245 1914.2,-562.027 1917.06,-573.856 1919.92,-585.732 1922.78,-597.655 \n",
       "  1925.64,-609.625 1928.49,-621.642 1931.35,-633.706 1934.21,-645.817 1937.07,-657.975 1939.93,-670.18 1942.79,-682.432 1945.65,-694.731 1948.5,-707.076 1951.36,-719.469 \n",
       "  1954.22,-731.909 1957.08,-744.396 1959.94,-756.929 1962.8,-769.51 1965.66,-782.138 1968.51,-794.812 1971.37,-807.534 1974.23,-820.302 1977.09,-833.118 1979.95,-845.981 \n",
       "  1982.81,-858.89 1985.67,-871.847 1988.52,-884.85 1991.38,-897.901 1994.24,-910.998 1997.1,-924.142 1999.96,-937.334 2002.82,-950.572 2005.68,-963.857 2008.53,-977.19 \n",
       "  2011.39,-990.569 2014.25,-1004 2017.11,-1017.47 2019.97,-1030.99 2022.83,-1044.56 2025.69,-1058.17 2028.54,-1071.83 2031.4,-1085.54 2034.26,-1099.29 2037.12,-1113.1 \n",
       "  2039.98,-1126.95 2042.84,-1140.84 2045.7,-1154.78 2048.55,-1168.77 2051.41,-1182.81 2054.27,-1196.9 2057.13,-1211.03 2059.99,-1225.2 2062.85,-1239.43 2065.71,-1253.7 \n",
       "  2068.56,-1268.02 2071.42,-1282.39 2074.28,-1296.8 2077.14,-1311.26 2080,-1325.77 2082.86,-1340.32 2085.72,-1354.92 2088.58,-1369.57 2091.43,-1384.26 2094.29,-1399 \n",
       "  2097.15,-1413.79 2100.01,-1428.63 2102.87,-1443.51 2105.73,-1458.44 2108.59,-1473.42 2111.44,-1488.44 2114.3,-1503.51 2117.16,-1518.63 2120.02,-1533.79 2122.88,-1549 \n",
       "  2125.74,-1564.26 2128.6,-1579.57 2131.45,-1594.92 2134.31,-1610.32 2137.17,-1625.77 2140.03,-1641.26 2142.89,-1656.8 2145.75,-1672.39 2148.61,-1688.02 2151.46,-1703.7 \n",
       "  2154.32,-1719.43 2157.18,-1735.21 2160.04,-1751.03 2162.9,-1766.9 2165.76,-1782.81 2168.62,-1798.78 2171.47,-1814.79 2174.33,-1830.84 2177.19,-1846.95 2180.05,-1863.1 \n",
       "  2182.91,-1879.3 2185.77,-1895.54 2188.63,-1911.83 2191.48,-1928.17 2194.34,-1944.56 2197.2,-1960.99 2200.06,-1977.47 2202.92,-1994 2205.78,-2010.57 2208.64,-2027.19 \n",
       "  2211.49,-2043.86 2214.35,-2060.57 2217.21,-2077.33 2220.07,-2094.14 2222.93,-2111 2225.79,-2127.9 2228.65,-2144.85 2231.5,-2161.85 2234.36,-2178.89 2237.22,-2195.98 \n",
       "  2240.08,-2213.12 2242.94,-2230.3 2245.8,-2247.54 2248.66,-2264.81 2251.51,-2282.14 2254.37,-2299.51 2257.23,-2316.93 2260.09,-2334.4 2262.95,-2351.91 2265.81,-2369.47 \n",
       "  2268.67,-2387.08 2271.52,-2404.73 2274.38,-2422.43 2277.24,-2440.18 2280.1,-2457.98 2282.96,-2475.82 2285.82,-2493.71 2288.68,-2511.64 2291.53,-2529.63 2294.39,-2547.66 \n",
       "  2297.25,-2565.73 2300.11,-2583.86 2302.97,-2602.03 2305.83,-2620.25 2308.69,-2638.51 2311.54,-2656.82 2314.4,-2675.18 2317.26,-2693.59 2320.12,-2712.04 2322.98,-2730.54 \n",
       "  2325.84,-2749.09 2328.7,-2767.68 2331.55,-2786.32 2334.41,-2805.01 2337.27,-2823.75 2340.13,-2842.53 2342.99,-2861.36 2345.85,-2880.23 2348.71,-2899.15 2351.56,-2918.12 \n",
       "  2354.42,-2937.14 2357.28,-2956.2 2360.14,-2975.31 2363,-2994.47 2365.86,-3013.68 2368.72,-3032.93 2371.57,-3052.23 2374.43,-3071.57 2377.29,-3090.96 2380.15,-3110.4 \n",
       "  2383.01,-3129.89 2385.87,-3149.42 2388.73,-3169 2391.59,-3188.63 2394.44,-3208.31 2397.3,-3228.03 2400.16,-3247.79 2403.02,-3267.61 2405.88,-3287.47 2408.74,-3307.38 \n",
       "  2411.6,-3327.34 2414.45,-3347.34 2417.31,-3367.39 2420.17,-3387.49 2423.03,-3407.63 2425.89,-3427.82 2428.75,-3448.06 2431.61,-3468.35 2434.46,-3488.68 2437.32,-3509.06 \n",
       "  2440.18,-3529.48 2443.04,-3549.96 2445.9,-3570.48 2448.76,-3591.04 2451.62,-3611.66 2454.47,-3632.32 2457.33,-3653.02 2460.19,-3673.78 2463.05,-3694.58 2465.91,-3715.43 \n",
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       "  2840.38,-6852.78 2843.24,-6879.83 2846.1,-6906.92 2848.96,-6934.07 2851.82,-6961.26 2854.68,-6988.5 2857.53,-7015.78 2860.39,-7043.11 2863.25,-7070.49 2866.11,-7097.92 \n",
       "  2868.97,-7125.39 2871.83,-7152.91 2874.69,-7180.47 2877.54,-7208.09 2880.4,-7235.75 2883.26,-7263.46 2886.12,-7291.21 2888.98,-7319.01 2891.84,-7346.86 2894.7,-7374.76 \n",
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       "  2983.31,-8262.81 2986.17,-8292.21 2989.03,-8321.66 2991.89,-8351.15 2994.75,-8380.69 2997.6,-8410.27 3000.46,-8439.91 3003.32,-8469.59 3006.18,-8499.32 3009.04,-8529.09 \n",
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       "  3040.48,-8859.71 3043.34,-8890.05 3046.2,-8920.43 3049.06,-8950.86 3051.92,-8981.34 3054.78,-9011.87 3057.64,-9042.44 3060.49,-9073.06 3063.35,-9103.73 3066.21,-9134.44 \n",
       "  3069.07,-9165.2 3071.93,-9196.01 3074.79,-9226.87 3077.65,-9257.77 3080.5,-9288.72 3083.36,-9319.71 3086.22,-9350.76 3089.08,-9381.85 3091.94,-9412.98 3094.8,-9444.17 \n",
       "  3097.66,-9475.4 3100.51,-9506.68 3103.37,-9538 3106.23,-9569.37 3109.09,-9600.79 3111.95,-9632.26 3114.81,-9663.77 3117.67,-9695.33 3120.52,-9726.93 3123.38,-9758.59 \n",
       "  3126.24,-9790.29 3129.1,-9822.04 3131.96,-9853.83 3134.82,-9885.67 3137.68,-9917.56 3140.53,-9949.5 3143.39,-9981.48 3146.25,-10013.5 3149.11,-10045.6 3151.97,-10077.7 \n",
       "  3154.83,-10109.9 3157.69,-10142.1 3160.54,-10174.4 3163.4,-10206.7 3166.26,-10239 3169.12,-10271.4 3171.98,-10303.9 3174.84,-10336.4 3177.7,-10368.9 3180.55,-10401.5 \n",
       "  3183.41,-10434.2 3186.27,-10466.9 3189.13,-10499.6 3191.99,-10532.4 3194.85,-10565.2 3197.71,-10598.1 3200.56,-10631 3203.42,-10664 3206.28,-10697 3209.14,-10730 \n",
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       "  3240.58,-11096.8 3243.44,-11130.5 3246.3,-11164.1 3249.16,-11197.9 3252.02,-11231.6 3254.88,-11265.4 3257.74,-11299.3 3260.59,-11333.2 3263.45,-11367.2 3266.31,-11401.2 \n",
       "  3269.17,-11435.2 3272.03,-11469.3 3274.89,-11503.4 3277.75,-11537.6 3280.6,-11571.9 3283.46,-11606.2 3286.32,-11640.5 3289.18,-11674.9 3292.04,-11709.3 3294.9,-11743.8 \n",
       "  3297.76,-11778.3 3300.61,-11812.9 3303.47,-11847.5 3306.33,-11882.1 3309.19,-11916.8 3312.05,-11951.6 3314.91,-11986.4 3317.77,-12021.2 3320.62,-12056.1 3323.48,-12091.1 \n",
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       "  3354.93,-12478.5 3357.79,-12514 3360.65,-12549.6 3363.5,-12585.2 3366.36,-12620.8 3369.22,-12656.5 3372.08,-12692.3 3374.94,-12728.1 3377.8,-12763.9 3380.66,-12799.8 \n",
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       "  3440.69,-13564.1 3443.54,-13601.1 3446.4,-13638 3449.26,-13675 3452.12,-13712.1 3454.98,-13749.2 3457.84,-13786.3 3460.7,-13823.5 3463.55,-13860.8 3466.41,-13898.1 \n",
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       "  3869.47,-19626.4 3872.33,-19670.3 3875.19,-19714.3 3878.05,-19758.4 3880.91,-19802.5 3883.77,-19846.6 3886.62,-19890.8 3889.48,-19935.1 3892.34,-19979.4 3895.2,-20023.7 \n",
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       "  3955.23,-20965.6 3958.09,-21011 3960.95,-21056.4 3963.81,-21101.9 3966.66,-21147.4 3969.52,-21193 3972.38,-21238.6 3975.24,-21284.2 3978.1,-21329.9 3980.96,-21375.7 \n",
       "  3983.82,-21421.5 3986.68,-21467.3 3989.53,-21513.2 3992.39,-21559.1 3995.25,-21605.1 3998.11,-21651.1 4000.97,-21697.2 4003.83,-21743.3 4006.69,-21789.5 4009.54,-21835.7 \n",
       "  4012.4,-21882 4015.26,-21928.3 4018.12,-21974.7 4020.98,-22021.1 4023.84,-22067.5 4026.7,-22114 4029.55,-22160.6 4032.41,-22207.1 4035.27,-22253.8 4038.13,-22300.5 \n",
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       "  4098.16,-23291.7 4101.02,-23339.5 4103.88,-23387.2 4106.74,-23435 4109.59,-23482.9 4112.45,-23530.8 4115.31,-23578.8 4118.17,-23626.8 4121.03,-23674.8 4123.89,-23722.9 \n",
       "  4126.75,-23771.1 4129.6,-23819.2 4132.46,-23867.5 4135.32,-23915.8 4138.18,-23964.1 4141.04,-24012.5 4143.9,-24060.9 4146.76,-24109.4 4149.61,-24157.9 4152.47,-24206.4 \n",
       "  4155.33,-24255.1 4158.19,-24303.7 4161.05,-24352.4 4163.91,-24401.2 4166.77,-24450 4169.62,-24498.8 4172.48,-24547.7 4175.34,-24596.7 4178.2,-24645.7 4181.06,-24694.7 \n",
       "  4183.92,-24743.8 4186.78,-24792.9 4189.63,-24842.1 4192.49,-24891.3 4195.35,-24940.6 4198.21,-24989.9 4201.07,-25039.2 4203.93,-25088.7 4206.79,-25138.1 4209.64,-25187.6 \n",
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       "  4326.85,-27257.8 4329.71,-27309.2 4332.56,-27360.8 4335.42,-27412.3 4338.28,-27464 4341.14,-27515.6 4344,-27567.3 4346.86,-27619.1 4349.72,-27670.9 4352.57,-27722.8 \n",
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       "  4441.19,-29353.5 4444.05,-29406.9 4446.91,-29460.3 4449.77,-29513.7 4452.62,-29567.2 4455.48,-29620.8 4458.34,-29674.4 4461.2,-29728 4464.06,-29781.7 4466.92,-29835.4 \n",
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       "  4526.95,-30974.7 4529.81,-31029.4 4532.66,-31084.3 4535.52,-31139.1 4538.38,-31194 4541.24,-31249 4544.1,-31304 4546.96,-31359 4549.82,-31414.1 4552.67,-31469.3 \n",
       "  4555.53,-31524.5 4558.39,-31579.7 4561.25,-31635 4564.11,-31690.3 4566.97,-31745.7 4569.83,-31801.1 4572.68,-31856.6 4575.54,-31912.1 4578.4,-31967.7 4581.26,-32023.3 \n",
       "  4584.12,-32078.9 4586.98,-32134.6 4589.84,-32190.4 4592.69,-32246.2 4595.55,-32302 4598.41,-32357.9 4601.27,-32413.9 4604.13,-32469.9 4606.99,-32525.9 4609.85,-32582 \n",
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       "  4669.88,-33770.5 4672.74,-33827.7 4675.59,-33884.8 4678.45,-33942 4681.31,-33999.3 4684.17,-34056.6 4687.03,-34113.9 4689.89,-34171.3 4692.75,-34228.8 4695.6,-34286.3 \n",
       "  4698.46,-34343.8 4701.32,-34401.4 4704.18,-34459 4707.04,-34516.7 4709.9,-34574.4 4712.76,-34632.2 4715.61,-34690 4718.47,-34747.9 4721.33,-34805.8 4724.19,-34863.8 \n",
       "  4727.05,-34921.8 4729.91,-34979.8 4732.77,-35037.9 4735.62,-35096.1 4738.48,-35154.3 4741.34,-35212.5 4744.2,-35270.8 4747.06,-35329.2 4749.92,-35387.5 4752.78,-35446 \n",
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       "  267.657,-18.782 270.515,-7.4686 273.374,3.79545 276.233,15.0101 279.091,26.1754 281.95,37.2913 284.808,48.3578 287.667,59.3749 290.526,70.3427 293.384,81.261 \n",
       "  296.243,92.13 299.101,102.95 301.96,113.72 304.818,124.441 307.677,135.112 310.536,145.734 313.394,156.307 316.253,166.83 319.111,177.304 321.97,187.728 \n",
       "  324.829,198.103 327.687,208.429 330.546,218.705 333.404,228.932 336.263,239.11 339.121,249.238 341.98,259.317 344.839,269.346 347.697,279.326 350.556,289.257 \n",
       "  353.414,299.138 356.273,308.97 359.132,318.753 361.99,328.486 364.849,338.169 367.707,347.804 370.566,357.389 373.424,366.924 376.283,376.41 379.142,385.847 \n",
       "  382,395.235 384.859,404.573 387.717,413.861 390.576,423.1 393.435,432.29 396.293,441.431 399.152,450.522 402.01,459.564 404.869,468.556 407.727,477.499 \n",
       "  410.586,486.392 413.445,495.237 416.303,504.031 419.162,512.777 422.02,521.473 424.879,530.119 427.738,538.716 430.596,547.264 433.455,555.763 436.313,564.212 \n",
       "  439.172,572.612 442.031,580.962 444.889,589.263 447.748,597.514 450.606,605.716 453.465,613.869 456.323,621.973 459.182,630.026 462.041,638.031 464.899,645.986 \n",
       "  467.758,653.892 470.616,661.749 473.475,669.556 476.334,677.313 479.192,685.022 482.051,692.68 484.909,700.29 487.768,707.85 490.626,715.361 493.485,722.822 \n",
       "  496.344,730.234 499.202,737.597 502.061,744.91 504.919,752.174 507.778,759.388 510.637,766.553 513.495,773.669 516.354,780.735 519.212,787.752 522.071,794.72 \n",
       "  524.929,801.638 527.788,808.506 530.647,815.326 533.505,822.096 536.364,828.816 539.222,835.487 542.081,842.109 544.94,848.682 547.798,855.205 550.657,861.678 \n",
       "  553.515,868.103 556.374,874.477 559.232,880.803 562.091,887.079 564.95,893.306 567.808,899.483 570.667,905.611 573.525,911.69 576.384,917.719 579.243,923.698 \n",
       "  582.101,929.629 584.96,935.51 587.818,941.341 590.677,947.124 593.535,952.857 596.394,958.54 599.253,964.174 602.111,969.759 604.97,975.294 607.828,980.78 \n",
       "  610.687,986.217 613.546,991.604 616.404,996.942 619.263,1002.23 622.121,1007.47 624.98,1012.66 627.838,1017.8 630.697,1022.89 633.556,1027.93 636.414,1032.92 \n",
       "  639.273,1037.87 642.131,1042.76 644.99,1047.6 647.849,1052.4 650.707,1057.14 653.566,1061.84 656.424,1066.48 659.283,1071.08 662.141,1075.63 665,1080.13 \n",
       "  667.859,1084.58 670.717,1088.98 673.576,1093.33 676.434,1097.63 679.293,1101.88 682.152,1106.08 685.01,1110.23 687.869,1114.34 690.727,1118.39 693.586,1122.39 \n",
       "  696.445,1126.35 699.303,1130.25 702.162,1134.11 705.02,1137.92 707.879,1141.67 710.737,1145.38 713.596,1149.04 716.455,1152.65 719.313,1156.21 722.172,1159.72 \n",
       "  725.03,1163.18 727.889,1166.59 730.748,1169.96 733.606,1173.27 736.465,1176.53 739.323,1179.75 742.182,1182.91 745.04,1186.03 747.899,1189.09 750.758,1192.11 \n",
       "  753.616,1195.08 756.475,1197.99 759.333,1200.86 762.192,1203.68 765.051,1206.45 767.909,1209.17 770.768,1211.84 773.626,1214.46 776.485,1217.04 779.343,1219.56 \n",
       "  782.202,1222.03 785.061,1224.46 787.919,1226.83 790.778,1229.16 793.636,1231.43 796.495,1233.66 799.354,1235.84 802.212,1237.96 805.071,1240.04 807.929,1242.07 \n",
       "  810.788,1244.05 813.646,1245.98 816.505,1247.86 819.364,1249.69 822.222,1251.48 825.081,1253.21 827.939,1254.89 830.798,1256.53 833.657,1258.11 836.515,1259.64 \n",
       "  839.374,1261.13 842.232,1262.57 845.091,1263.95 847.949,1265.29 850.808,1266.58 853.667,1267.82 856.525,1269.01 859.384,1270.15 862.242,1271.24 865.101,1272.28 \n",
       "  867.96,1273.27 870.818,1274.21 873.677,1275.11 876.535,1275.95 879.394,1276.74 882.252,1277.49 885.111,1278.18 887.97,1278.83 890.828,1279.43 893.687,1279.98 \n",
       "  896.545,1280.47 899.404,1280.92 902.263,1281.32 905.121,1281.67 907.98,1281.97 910.838,1282.22 913.697,1282.42 916.556,1282.58 919.414,1282.68 922.273,1282.73 \n",
       "  925.131,1282.74 927.99,1282.69 930.848,1282.6 933.707,1282.45 936.566,1282.26 939.424,1282.02 942.283,1281.72 945.141,1281.38 948,1280.99 950.859,1280.55 \n",
       "  953.717,1280.06 956.576,1279.52 959.434,1278.93 962.293,1278.3 965.151,1277.61 968.01,1276.87 970.869,1276.09 973.727,1275.25 976.586,1274.37 979.444,1273.43 \n",
       "  982.303,1272.45 985.162,1271.41 988.02,1270.33 990.879,1269.2 993.737,1268.02 996.596,1266.79 999.454,1265.51 1002.31,1264.18 1005.17,1262.8 1008.03,1261.37 \n",
       "  1010.89,1259.9 1013.75,1258.37 1016.61,1256.79 1019.46,1255.17 1022.32,1253.49 1025.18,1251.77 1028.04,1249.99 1030.9,1248.17 1033.76,1246.3 1036.62,1244.38 \n",
       "  1039.47,1242.4 1042.33,1240.38 1045.19,1238.31 1048.05,1236.19 1050.91,1234.03 1053.77,1231.81 1056.63,1229.54 1059.48,1227.22 1062.34,1224.86 1065.2,1222.44 \n",
       "  1068.06,1219.98 1070.92,1217.46 1073.78,1214.9 1076.64,1212.28 1079.49,1209.62 1082.35,1206.91 1085.21,1204.15 1088.07,1201.34 1090.93,1198.48 1093.79,1195.57 \n",
       "  1096.65,1192.61 1099.5,1189.6 1102.36,1186.54 1105.22,1183.43 1108.08,1180.28 1110.94,1177.07 1113.8,1173.82 1116.66,1170.51 1119.51,1167.16 1122.37,1163.75 \n",
       "  1125.23,1160.3 1128.09,1156.8 1130.95,1153.25 1133.81,1149.65 1136.67,1146 1139.53,1142.3 1142.38,1138.55 1145.24,1134.75 1148.1,1130.9 1150.96,1127 \n",
       "  1153.82,1123.06 1156.68,1119.06 1159.54,1115.01 1162.39,1110.92 1165.25,1106.78 1168.11,1102.58 1170.97,1098.34 1173.83,1094.05 1176.69,1089.7 1179.55,1085.31 \n",
       "  1182.4,1080.87 1185.26,1076.38 1188.12,1071.84 1190.98,1067.25 1193.84,1062.62 1196.7,1057.93 1199.56,1053.19 1202.41,1048.41 1205.27,1043.57 1208.13,1038.68 \n",
       "  1210.99,1033.75 1213.85,1028.77 1216.71,1023.73 1219.57,1018.65 1222.42,1013.52 1225.28,1008.34 1228.14,1003.11 1231,997.826 1233.86,992.497 1236.72,987.118 \n",
       "  1239.58,981.69 1242.43,976.212 1245.29,970.685 1248.15,965.108 1251.01,959.482 1253.87,953.807 1256.73,948.083 1259.59,942.309 1262.44,936.485 1265.3,930.612 \n",
       "  1268.16,924.69 1271.02,918.719 1273.88,912.698 1276.74,906.627 1279.6,900.508 1282.45,894.339 1285.31,888.12 1288.17,881.852 1291.03,875.535 1293.89,869.168 \n",
       "  1296.75,862.752 1299.61,856.287 1302.46,849.772 1305.32,843.208 1308.18,836.594 1311.04,829.932 1313.9,823.219 1316.76,816.457 1319.62,809.646 1322.47,802.786 \n",
       "  1325.33,795.876 1328.19,788.917 1331.05,781.908 1333.91,774.85 1336.77,767.743 1339.63,760.586 1342.48,753.38 1345.34,746.124 1348.2,738.819 1351.06,731.465 \n",
       "  1353.92,724.061 1356.78,716.608 1359.64,709.105 1362.49,701.553 1365.35,693.952 1368.21,686.301 1371.07,678.601 1373.93,670.852 1376.79,663.053 1379.65,655.205 \n",
       "  1382.5,647.307 1385.36,639.36 1388.22,631.364 1391.08,623.318 1393.94,615.223 1396.8,607.079 1399.66,598.885 1402.51,590.641 1405.37,582.349 1408.23,574.007 \n",
       "  1411.09,565.615 1413.95,557.174 1416.81,548.684 1419.67,540.145 1422.52,531.556 1425.38,522.917 1428.24,514.229 1431.1,505.492 1433.96,496.706 1436.82,487.87 \n",
       "  1439.68,478.984 1442.54,470.05 1445.39,461.066 1448.25,452.032 1451.11,442.949 1453.97,433.817 1456.83,424.636 1459.69,415.405 1462.55,406.124 1465.4,396.794 \n",
       "  1468.26,387.415 1471.12,377.987 1473.98,368.509 1476.84,358.981 1479.7,349.405 1482.56,339.779 1485.41,330.103 1488.27,320.378 1491.13,310.604 1493.99,300.78 \n",
       "  1496.85,290.907 1499.71,280.985 1502.57,271.013 1505.42,260.992 1508.28,250.921 1511.14,240.801 1514,230.632 1516.86,220.413 1519.72,210.145 1522.58,199.828 \n",
       "  1525.43,189.461 1528.29,179.045 1531.15,168.579 1534.01,158.064 1536.87,147.5 1539.73,136.886 1542.59,126.223 1545.44,115.51 1548.3,104.748 1551.16,93.9367 \n",
       "  1554.02,83.0759 1556.88,72.1658 1559.74,61.2063 1562.6,50.1974 1565.45,39.1391 1568.31,28.0315 1571.17,16.8744 1574.03,5.66799 1576.89,-5.58783 1579.75,-16.893 \n",
       "  1582.61,-28.2476 1585.46,-39.6516 1588.32,-51.105 1591.18,-62.6077 1594.04,-74.1598 1596.9,-85.7614 1599.76,-97.4123 1602.62,-109.113 1605.47,-120.862 1608.33,-132.661 \n",
       "  1611.19,-144.51 1614.05,-156.408 1616.91,-168.355 1619.77,-180.351 1622.63,-192.397 1625.48,-204.493 1628.34,-216.638 1631.2,-228.832 1634.06,-241.075 1636.92,-253.368 \n",
       "  1639.78,-265.71 1642.64,-278.102 1645.49,-290.543 1648.35,-303.034 1651.21,-315.574 1654.07,-328.163 1656.93,-340.801 1659.79,-353.489 1662.65,-366.227 1665.5,-379.014 \n",
       "  1668.36,-391.85 1671.22,-404.735 1674.08,-417.67 1676.94,-430.655 1679.8,-443.688 1682.66,-456.771 1685.51,-469.904 1688.37,-483.086 1691.23,-496.317 1694.09,-509.598 \n",
       "  1696.95,-522.928 1699.81,-536.307 1702.67,-549.736 1705.52,-563.214 1708.38,-576.741 1711.24,-590.318 1714.1,-603.945 1716.96,-617.62 1719.82,-631.346 1722.68,-645.12 \n",
       "  1725.53,-658.944 1728.39,-672.817 1731.25,-686.74 1734.11,-700.712 1736.97,-714.733 1739.83,-728.804 1742.69,-742.924 1745.54,-757.094 1748.4,-771.313 1751.26,-785.581 \n",
       "  1754.12,-799.899 1756.98,-814.266 1759.84,-828.683 1762.7,-843.148 1765.56,-857.664 1768.41,-872.228 1771.27,-886.842 1774.13,-901.506 1776.99,-916.219 1779.85,-930.981 \n",
       "  1782.71,-945.792 1785.57,-960.653 1788.42,-975.564 1791.28,-990.524 1794.14,-1005.53 1797,-1020.59 1799.86,-1035.7 1802.72,-1050.86 1805.58,-1066.06 1808.43,-1081.32 \n",
       "  1811.29,-1096.62 1814.15,-1111.98 1817.01,-1127.38 1819.87,-1142.84 1822.73,-1158.34 1825.59,-1173.89 1828.44,-1189.49 1831.3,-1205.15 1834.16,-1220.85 1837.02,-1236.6 \n",
       "  1839.88,-1252.4 1842.74,-1268.24 1845.6,-1284.14 1848.45,-1300.09 1851.31,-1316.09 1854.17,-1332.13 1857.03,-1348.23 1859.89,-1364.37 1862.75,-1380.57 1865.61,-1396.81 \n",
       "  1868.46,-1413.1 1871.32,-1429.45 1874.18,-1445.84 1877.04,-1462.28 1879.9,-1478.77 1882.76,-1495.31 1885.62,-1511.9 1888.47,-1528.54 1891.33,-1545.23 1894.19,-1561.97 \n",
       "  1897.05,-1578.75 1899.91,-1595.59 1902.77,-1612.47 1905.63,-1629.41 1908.48,-1646.39 1911.34,-1663.43 1914.2,-1680.51 1917.06,-1697.64 1919.92,-1714.83 1922.78,-1732.06 \n",
       "  1925.64,-1749.34 1928.49,-1766.67 1931.35,-1784.05 1934.21,-1801.48 1937.07,-1818.96 1939.93,-1836.48 1942.79,-1854.06 1945.65,-1871.69 1948.5,-1889.36 1951.36,-1907.09 \n",
       "  1954.22,-1924.86 1957.08,-1942.69 1959.94,-1960.56 1962.8,-1978.48 1965.66,-1996.46 1968.51,-2014.48 1971.37,-2032.55 1974.23,-2050.67 1977.09,-2068.84 1979.95,-2087.06 \n",
       "  1982.81,-2105.33 1985.67,-2123.65 1988.52,-2142.01 1991.38,-2160.43 1994.24,-2178.9 1997.1,-2197.41 1999.96,-2215.98 2002.82,-2234.59 2005.68,-2253.25 2008.53,-2271.97 \n",
       "  2011.39,-2290.73 2014.25,-2309.54 2017.11,-2328.4 2019.97,-2347.31 2022.83,-2366.27 2025.69,-2385.28 2028.54,-2404.34 2031.4,-2423.45 2034.26,-2442.61 2037.12,-2461.81 \n",
       "  2039.98,-2481.07 2042.84,-2500.38 2045.7,-2519.73 2048.55,-2539.14 2051.41,-2558.59 2054.27,-2578.09 2057.13,-2597.64 2059.99,-2617.25 2062.85,-2636.9 2065.71,-2656.6 \n",
       "  2068.56,-2676.35 2071.42,-2696.15 2074.28,-2716 2077.14,-2735.9 2080,-2755.84 2082.86,-2775.84 2085.72,-2795.89 2088.58,-2815.98 2091.43,-2836.13 2094.29,-2856.32 \n",
       "  2097.15,-2876.57 2100.01,-2896.86 2102.87,-2917.2 2105.73,-2937.6 2108.59,-2958.04 2111.44,-2978.53 2114.3,-2999.07 2117.16,-3019.66 2120.02,-3040.3 2122.88,-3060.99 \n",
       "  2125.74,-3081.72 2128.6,-3102.51 2131.45,-3123.35 2134.31,-3144.23 2137.17,-3165.17 2140.03,-3186.15 2142.89,-3207.19 2145.75,-3228.27 2148.61,-3249.4 2151.46,-3270.59 \n",
       "  2154.32,-3291.82 2157.18,-3313.1 2160.04,-3334.43 2162.9,-3355.81 2165.76,-3377.24 2168.62,-3398.72 2171.47,-3420.25 2174.33,-3441.82 2177.19,-3463.45 2180.05,-3485.13 \n",
       "  2182.91,-3506.85 2185.77,-3528.63 2188.63,-3550.45 2191.48,-3572.32 2194.34,-3594.25 2197.2,-3616.22 2200.06,-3638.24 2202.92,-3660.31 2205.78,-3682.43 2208.64,-3704.6 \n",
       "  2211.49,-3726.82 2214.35,-3749.09 2217.21,-3771.41 2220.07,-3793.78 2222.93,-3816.2 2225.79,-3838.66 2228.65,-3861.18 2231.5,-3883.74 2234.36,-3906.36 2237.22,-3929.02 \n",
       "  2240.08,-3951.73 2242.94,-3974.5 2245.8,-3997.31 2248.66,-4020.17 2251.51,-4043.08 2254.37,-4066.04 2257.23,-4089.05 2260.09,-4112.11 2262.95,-4135.22 2265.81,-4158.38 \n",
       "  2268.67,-4181.58 2271.52,-4204.84 2274.38,-4228.15 2277.24,-4251.5 2280.1,-4274.91 2282.96,-4298.36 2285.82,-4321.86 2288.68,-4345.42 2291.53,-4369.02 2294.39,-4392.67 \n",
       "  2297.25,-4416.37 2300.11,-4440.12 2302.97,-4463.92 2305.83,-4487.77 2308.69,-4511.67 2311.54,-4535.62 2314.4,-4559.61 2317.26,-4583.66 2320.12,-4607.76 2322.98,-4631.9 \n",
       "  2325.84,-4656.1 2328.7,-4680.34 2331.55,-4704.64 2334.41,-4728.98 2337.27,-4753.37 2340.13,-4777.81 2342.99,-4802.3 2345.85,-4826.84 2348.71,-4851.43 2351.56,-4876.07 \n",
       "  2354.42,-4900.76 2357.28,-4925.5 2360.14,-4950.29 2363,-4975.13 2365.86,-5000.01 2368.72,-5024.95 2371.57,-5049.93 2374.43,-5074.97 2377.29,-5100.05 2380.15,-5125.18 \n",
       "  2383.01,-5150.37 2385.87,-5175.6 2388.73,-5200.88 2391.59,-5226.21 2394.44,-5251.59 2397.3,-5277.02 2400.16,-5302.5 2403.02,-5328.03 2405.88,-5353.6 2408.74,-5379.23 \n",
       "  2411.6,-5404.91 2414.45,-5430.63 2417.31,-5456.41 2420.17,-5482.23 2423.03,-5508.11 2425.89,-5534.03 2428.75,-5560 2431.61,-5586.03 2434.46,-5612.1 2437.32,-5638.22 \n",
       "  2440.18,-5664.39 2443.04,-5690.61 2445.9,-5716.88 2448.76,-5743.2 2451.62,-5769.56 2454.47,-5795.98 2457.33,-5822.45 2460.19,-5848.96 2463.05,-5875.53 2465.91,-5902.14 \n",
       "  2468.77,-5928.81 2471.63,-5955.52 2474.48,-5982.28 2477.34,-6009.1 2480.2,-6035.96 2483.06,-6062.87 2485.92,-6089.83 2488.78,-6116.84 2491.64,-6143.9 2494.49,-6171.01 \n",
       "  2497.35,-6198.17 2500.21,-6225.37 2503.07,-6252.63 2505.93,-6279.94 2508.79,-6307.29 2511.65,-6334.7 2514.5,-6362.15 2517.36,-6389.65 2520.22,-6417.21 2523.08,-6444.81 \n",
       "  2525.94,-6472.46 2528.8,-6500.16 2531.66,-6527.91 2534.51,-6555.71 2537.37,-6583.56 2540.23,-6611.46 2543.09,-6639.41 2545.95,-6667.41 2548.81,-6695.45 2551.67,-6723.55 \n",
       "  2554.52,-6751.7 2557.38,-6779.89 2560.24,-6808.14 2563.1,-6836.43 2565.96,-6864.77 2568.82,-6893.17 2571.68,-6921.61 2574.53,-6950.1 2577.39,-6978.64 2580.25,-7007.23 \n",
       "  2583.11,-7035.87 2585.97,-7064.56 2588.83,-7093.3 2591.69,-7122.09 2594.54,-7150.92 2597.4,-7179.81 2600.26,-7208.74 2603.12,-7237.73 2605.98,-7266.76 2608.84,-7295.85 \n",
       "  2611.7,-7324.98 2614.55,-7354.17 2617.41,-7383.4 2620.27,-7412.68 2623.13,-7442.01 2625.99,-7471.39 2628.85,-7500.82 2631.71,-7530.3 2634.56,-7559.83 2637.42,-7589.41 \n",
       "  2640.28,-7619.03 2643.14,-7648.71 2646,-7678.44 2648.86,-7708.21 2651.72,-7738.04 2654.57,-7767.91 2657.43,-7797.83 2660.29,-7827.81 2663.15,-7857.83 2666.01,-7887.9 \n",
       "  2668.87,-7918.02 2671.73,-7948.19 2674.58,-7978.41 2677.44,-8008.68 2680.3,-8039 2683.16,-8069.37 2686.02,-8099.79 2688.88,-8130.25 2691.74,-8160.77 2694.59,-8191.33 \n",
       "  2697.45,-8221.95 2700.31,-8252.61 2703.17,-8283.33 2706.03,-8314.09 2708.89,-8344.9 2711.75,-8375.77 2714.61,-8406.68 2717.46,-8437.64 2720.32,-8468.65 2723.18,-8499.71 \n",
       "  2726.04,-8530.82 2728.9,-8561.97 2731.76,-8593.18 2734.62,-8624.44 2737.47,-8655.75 2740.33,-8687.1 2743.19,-8718.51 2746.05,-8749.96 2748.91,-8781.46 2751.77,-8813.02 \n",
       "  2754.63,-8844.62 2757.48,-8876.27 2760.34,-8907.97 2763.2,-8939.73 2766.06,-8971.53 2768.92,-9003.38 2771.78,-9035.27 2774.64,-9067.22 2777.49,-9099.22 2780.35,-9131.27 \n",
       "  2783.21,-9163.36 2786.07,-9195.51 2788.93,-9227.71 2791.79,-9259.95 2794.65,-9292.24 2797.5,-9324.59 2800.36,-9356.98 2803.22,-9389.42 2806.08,-9421.91 2808.94,-9454.46 \n",
       "  2811.8,-9487.05 2814.66,-9519.69 2817.51,-9552.38 2820.37,-9585.11 2823.23,-9617.9 2826.09,-9650.74 2828.95,-9683.63 2831.81,-9716.56 2834.67,-9749.55 2837.52,-9782.58 \n",
       "  2840.38,-9815.67 2843.24,-9848.8 2846.1,-9881.98 2848.96,-9915.22 2851.82,-9948.5 2854.68,-9981.83 2857.53,-10015.2 2860.39,-10048.6 2863.25,-10082.1 2866.11,-10115.6 \n",
       "  2868.97,-10149.2 2871.83,-10182.9 2874.69,-10216.5 2877.54,-10250.3 2880.4,-10284 2883.26,-10317.9 2886.12,-10351.7 2888.98,-10385.7 2891.84,-10419.6 2894.7,-10453.7 \n",
       "  2897.55,-10487.7 2900.41,-10521.8 2903.27,-10556 2906.13,-10590.2 2908.99,-10624.5 2911.85,-10658.8 2914.71,-10693.2 2917.56,-10727.6 2920.42,-10762.1 2923.28,-10796.6 \n",
       "  2926.14,-10831.2 2929,-10865.8 2931.86,-10900.4 2934.72,-10935.2 2937.57,-10969.9 2940.43,-11004.7 2943.29,-11039.6 2946.15,-11074.5 2949.01,-11109.5 2951.87,-11144.5 \n",
       "  2954.73,-11179.5 2957.58,-11214.6 2960.44,-11249.8 2963.3,-11285 2966.16,-11320.3 2969.02,-11355.6 2971.88,-11390.9 2974.74,-11426.3 2977.59,-11461.8 2980.45,-11497.3 \n",
       "  2983.31,-11532.8 2986.17,-11568.5 2989.03,-11604.1 2991.89,-11639.8 2994.75,-11675.6 2997.6,-11711.4 3000.46,-11747.2 3003.32,-11783.1 3006.18,-11819.1 3009.04,-11855.1 \n",
       "  3011.9,-11891.1 3014.76,-11927.2 3017.61,-11963.3 3020.47,-11999.5 3023.33,-12035.8 3026.19,-12072.1 3029.05,-12108.4 3031.91,-12144.8 3034.77,-12181.3 3037.63,-12217.7 \n",
       "  3040.48,-12254.3 3043.34,-12290.9 3046.2,-12327.5 3049.06,-12364.2 3051.92,-12400.9 3054.78,-12437.7 3057.64,-12474.6 3060.49,-12511.5 3063.35,-12548.4 3066.21,-12585.4 \n",
       "  3069.07,-12622.4 3071.93,-12659.5 3074.79,-12696.6 3077.65,-12733.8 3080.5,-12771.1 3083.36,-12808.3 3086.22,-12845.7 3089.08,-12883 3091.94,-12920.5 3094.8,-12958 \n",
       "  3097.66,-12995.5 3100.51,-13033.1 3103.37,-13070.7 3106.23,-13108.4 3109.09,-13146.1 3111.95,-13183.9 3114.81,-13221.7 3117.67,-13259.6 3120.52,-13297.5 3123.38,-13335.5 \n",
       "  3126.24,-13373.5 3129.1,-13411.6 3131.96,-13449.7 3134.82,-13487.9 3137.68,-13526.1 3140.53,-13564.3 3143.39,-13602.7 3146.25,-13641 3149.11,-13679.5 3151.97,-13717.9 \n",
       "  3154.83,-13756.4 3157.69,-13795 3160.54,-13833.6 3163.4,-13872.3 3166.26,-13911 3169.12,-13949.8 3171.98,-13988.6 3174.84,-14027.4 3177.7,-14066.4 3180.55,-14105.3 \n",
       "  3183.41,-14144.3 3186.27,-14183.4 3189.13,-14222.5 3191.99,-14261.7 3194.85,-14300.9 3197.71,-14340.1 3200.56,-14379.4 3203.42,-14418.8 3206.28,-14458.2 3209.14,-14497.6 \n",
       "  3212,-14537.1 3214.86,-14576.7 3217.72,-14616.3 3220.57,-14656 3223.43,-14695.7 3226.29,-14735.4 3229.15,-14775.2 3232.01,-14815.1 3234.87,-14855 3237.73,-14894.9 \n",
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       "  3326.34,-16157.8 3329.2,-16199.3 3332.06,-16240.9 3334.92,-16282.6 3337.78,-16324.2 3340.64,-16366 3343.49,-16407.7 3346.35,-16449.6 3349.21,-16491.4 3352.07,-16533.4 \n",
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       "  3440.69,-17857.5 3443.54,-17901 3446.4,-17944.6 3449.26,-17988.2 3452.12,-18031.8 3454.98,-18075.5 3457.84,-18119.3 3460.7,-18163.1 3463.55,-18206.9 3466.41,-18250.8 \n",
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       "  3555.03,-19636.2 3557.89,-19681.7 3560.75,-19727.2 3563.6,-19772.8 3566.46,-19818.4 3569.32,-19864.1 3572.18,-19909.8 3575.04,-19955.6 3577.9,-20001.4 3580.76,-20047.3 \n",
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       "  3612.2,-20555.2 3615.06,-20601.7 3617.92,-20648.2 3620.78,-20694.8 3623.63,-20741.4 3626.49,-20788 3629.35,-20834.7 3632.21,-20881.5 3635.07,-20928.3 3637.93,-20975.2 \n",
       "  3640.79,-21022.1 3643.64,-21069.1 3646.5,-21116.1 3649.36,-21163.1 3652.22,-21210.2 3655.08,-21257.4 3657.94,-21304.6 3660.8,-21351.9 3663.66,-21399.2 3666.51,-21446.5 \n",
       "  3669.37,-21493.9 3672.23,-21541.4 3675.09,-21588.9 3677.95,-21636.5 3680.81,-21684.1 3683.67,-21731.7 3686.52,-21779.4 3689.38,-21827.2 3692.24,-21875 3695.1,-21922.8 \n",
       "  3697.96,-21970.7 3700.82,-22018.7 3703.68,-22066.7 3706.53,-22114.7 3709.39,-22162.8 3712.25,-22211 3715.11,-22259.2 3717.97,-22307.4 3720.83,-22355.7 3723.69,-22404 \n",
       "  3726.54,-22452.4 3729.4,-22500.9 3732.26,-22549.4 3735.12,-22597.9 3737.98,-22646.5 3740.84,-22695.1 3743.7,-22743.8 3746.55,-22792.6 3749.41,-22841.4 3752.27,-22890.2 \n",
       "  3755.13,-22939.1 3757.99,-22988 3760.85,-23037 3763.71,-23086 3766.56,-23135.1 3769.42,-23184.3 3772.28,-23233.5 3775.14,-23282.7 3778,-23332 3780.86,-23381.3 \n",
       "  3783.72,-23430.7 3786.57,-23480.1 3789.43,-23529.6 3792.29,-23579.1 3795.15,-23628.7 3798.01,-23678.3 3800.87,-23728 3803.73,-23777.7 3806.58,-23827.5 3809.44,-23877.3 \n",
       "  3812.3,-23927.2 3815.16,-23977.1 3818.02,-24027.1 3820.88,-24077.1 3823.74,-24127.2 3826.59,-24177.3 3829.45,-24227.5 3832.31,-24277.7 3835.17,-24328 3838.03,-24378.3 \n",
       "  3840.89,-24428.7 3843.75,-24479.1 3846.6,-24529.6 3849.46,-24580.1 3852.32,-24630.7 3855.18,-24681.3 3858.04,-24731.9 3860.9,-24782.7 3863.76,-24833.4 3866.61,-24884.2 \n",
       "  3869.47,-24935.1 3872.33,-24986 3875.19,-25037 3878.05,-25088 3880.91,-25139 3883.77,-25190.2 3886.62,-25241.3 3889.48,-25292.5 3892.34,-25343.8 3895.2,-25395.1 \n",
       "  3898.06,-25446.4 3900.92,-25497.8 3903.78,-25549.3 3906.63,-25600.8 3909.49,-25652.4 3912.35,-25704 3915.21,-25755.6 3918.07,-25807.3 3920.93,-25859.1 3923.79,-25910.9 \n",
       "  3926.64,-25962.7 3929.5,-26014.6 3932.36,-26066.6 3935.22,-26118.6 3938.08,-26170.6 3940.94,-26222.7 3943.8,-26274.9 3946.65,-26327.1 3949.51,-26379.3 3952.37,-26431.6 \n",
       "  3955.23,-26484 3958.09,-26536.3 3960.95,-26588.8 3963.81,-26641.3 3966.66,-26693.8 3969.52,-26746.4 3972.38,-26799.1 3975.24,-26851.7 3978.1,-26904.5 3980.96,-26957.3 \n",
       "  3983.82,-27010.1 3986.68,-27063 3989.53,-27115.9 3992.39,-27168.9 3995.25,-27222 3998.11,-27275 4000.97,-27328.2 4003.83,-27381.4 4006.69,-27434.6 4009.54,-27487.9 \n",
       "  4012.4,-27541.2 4015.26,-27594.6 4018.12,-27648 4020.98,-27701.5 4023.84,-27755 4026.7,-27808.6 4029.55,-27862.2 4032.41,-27915.9 4035.27,-27969.7 4038.13,-28023.4 \n",
       "  4040.99,-28077.3 4043.85,-28131.1 4046.71,-28185.1 4049.56,-28239 4052.42,-28293.1 4055.28,-28347.1 4058.14,-28401.3 4061,-28455.4 4063.86,-28509.6 4066.72,-28563.9 \n",
       "  4069.57,-28618.2 4072.43,-28672.6 4075.29,-28727 4078.15,-28781.5 4081.01,-28836 4083.87,-28890.6 4086.73,-28945.2 4089.58,-28999.9 4092.44,-29054.6 4095.3,-29109.3 \n",
       "  4098.16,-29164.2 4101.02,-29219 4103.88,-29273.9 4106.74,-29328.9 4109.59,-29383.9 4112.45,-29439 4115.31,-29494.1 4118.17,-29549.2 4121.03,-29604.4 4123.89,-29659.7 \n",
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       "  4298.26,-33123.9 4301.12,-33182.2 4303.98,-33240.5 4306.84,-33299 4309.7,-33357.4 4312.55,-33416 4315.41,-33474.5 4318.27,-33533.1 4321.13,-33591.8 4323.99,-33650.5 \n",
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       "  4384.02,-34895 4386.88,-34954.8 4389.74,-35014.6 4392.59,-35074.5 4395.45,-35134.5 4398.31,-35194.5 4401.17,-35254.5 4404.03,-35314.6 4406.89,-35374.7 4409.75,-35434.9 \n",
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       "  4927.15,-47144 4930.01,-47213.2 4932.87,-47282.5 4935.73,-47351.7 4938.58,-47421.1 4941.44,-47490.5 4944.3,-47559.9 4947.16,-47629.4 4950.02,-47698.9 4952.88,-47768.5 \n",
       "  4955.74,-47838.1 4958.59,-47907.8 4961.45,-47977.5 4964.31,-48047.3 4967.17,-48117.1 4970.03,-48187 4972.89,-48256.9 4975.75,-48326.9 4978.6,-48396.9 4981.46,-48467 \n",
       "  4984.32,-48537.1 4987.18,-48607.3 4990.04,-48677.5 4992.9,-48747.8 4995.76,-48818.1 4998.61,-48888.5 5001.47,-48958.9 5004.33,-49029.4 5007.19,-49099.9 5010.05,-49170.5 \n",
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       "  5041.49,-49950 5044.35,-50021.1 5047.21,-50092.3 5050.07,-50163.6 5052.93,-50234.9 5055.79,-50306.3 5058.64,-50377.7 5061.5,-50449.1 5064.36,-50520.6 5067.22,-50592.2 \n",
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       "  5470.28,-61176 5473.14,-61254.5 5476,-61333.1 5478.86,-61411.8 5481.71,-61490.5 5484.57,-61569.3 5487.43,-61648.1 5490.29,-61727 5493.15,-61805.9 5496.01,-61884.8 \n",
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      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt = plot()\n",
    "Plotter.plot_pot!(pot1; lplt_wf = false, plt = plt, color = \"#b2182b\")\n",
    "Plotter.plot_pot!(pot2; lplt_wf = false, plt = plt, color = \"#2166ac\")\n",
    "Plotter.plot_pot!(pot3; lplt_wf = false, plt = plt, color = \"#b2182b\")\n",
    "xlims!((-5, 10))\n",
    "ylims!((-0.2, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Capture coefficient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define parameters for calculating capture coefficient (e.g. temperature and Volume of the supercell)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.0:7.97979797979798:800.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Tmin = 10\n",
    "Tmax = 800\n",
    "NT = 100\n",
    "Volume = 1.28463E-21\n",
    "cut_off = 0.25\n",
    "σ = 0.0075\n",
    "temperature = range(Tmin, stop=Tmax, length=NT)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Constructe configuration coordinate (`conf_coord`) to calculate the wavefunction overlap between each PES, which forms part of the temperature-dependent capture coefficient.\n",
    "The capture coefficient is given as a function of temperature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Electron capture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.0:7.97979797979798:800.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W = 0.205 # e-ph coupling\n",
    "g = 1 # degeneracy\n",
    "\n",
    "# build a configuration coordinate for the electron capture\n",
    "cc_e = conf_coord(pot1, pot2)\n",
    "cc_e.W = W\n",
    "cc_e.g = g\n",
    "calc_overlap!(cc_e; cut_off = cut_off, σ = σ)\n",
    "calc_capt_coeff!(cc_e, Volume, temperature)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "invTmin = 1\n",
    "invTmax = 13\n",
    "\n",
    "plt = plot()\n",
    "\n",
    "Plotter.plot_cc!(cc_e; plt=plt, label=\"electron capture\")\n",
    "\n",
    "xlims!(invTmin, invTmax)\n",
    "ylims!(1E-12, 1E-6)"
   ]
  }
 ],
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