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genkuroki/Si function.ipynb

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Si function
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Si function.ipynb
{
"cells": [
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# plot sine integral function\n\nusing QuadGK\nusing Plots; gr(); ENV[\"PLOTS_TEST\"] = \"true\"\nSi(x) = quadgk(t->sin(t)/t, eps(), x)[1]\n@show g = (2/π)*Si(π)\nx = eps():0.01:7π\nplot(size=(500,300))\nplot!(title=\"(2/pi)Si(x)\", titlefontsize=10, legend=:topright)\nplot!(x, (2/π).*Si.(x), label=\"\", xlims=(0,7π), ylims=(0.8, 1.25))\nplot!([0, 7π], [1, 1], label=\"y = 1/2\", ls=:dot)\nplot!([0, π], [g, g], label=\"y = (2/pi)Si(pi) = 1.17898\", ls=:dashdot)\nplot!([π, π], [0, g], label=\"x = pi\", ls=:dash)",
"execution_count": 2,
"outputs": [
{
"output_type": "stream",
"text": "g = (2 / π) * Si(π) = 1.1789797444721672\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 2,
"data": {
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style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:12; text-anchor:middle;\" transform=\"rotate(0, 240.414, 290.007)\" x=\"240.414\" y=\"290.007\">10</text>\n</g>\n<g clip-path=\"url(#clip0700)\">\n<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:12; text-anchor:middle;\" transform=\"rotate(0, 340.446, 290.007)\" x=\"340.446\" y=\"290.007\">15</text>\n</g>\n<g clip-path=\"url(#clip0700)\">\n<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:12; text-anchor:middle;\" transform=\"rotate(0, 440.479, 290.007)\" x=\"440.479\" y=\"290.007\">20</text>\n</g>\n<g clip-path=\"url(#clip0700)\">\n<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:12; text-anchor:end;\" transform=\"rotate(0, 35.3485, 281.207)\" x=\"35.3485\" y=\"281.207\">0.8</text>\n</g>\n<g clip-path=\"url(#clip0700)\">\n<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:12; text-anchor:end;\" transform=\"rotate(0, 35.3485, 226.716)\" x=\"35.3485\" y=\"226.716\">0.9</text>\n</g>\n<g clip-path=\"url(#clip0700)\">\n<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:12; text-anchor:end;\" transform=\"rotate(0, 35.3485, 172.224)\" x=\"35.3485\" y=\"172.224\">1.0</text>\n</g>\n<g clip-path=\"url(#clip0700)\">\n<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:12; text-anchor:end;\" transform=\"rotate(0, 35.3485, 117.733)\" x=\"35.3485\" y=\"117.733\">1.1</text>\n</g>\n<g clip-path=\"url(#clip0700)\">\n<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:12; text-anchor:end;\" transform=\"rotate(0, 35.3485, 63.2417)\" x=\"35.3485\" y=\"63.2417\">1.2</text>\n</g>\n<g clip-path=\"url(#clip0700)\">\n<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:15; text-anchor:middle;\" transform=\"rotate(0, 260.332, 13.2)\" x=\"260.332\" y=\"13.2\">(2/pi)Si(x)</text>\n</g>\n<polyline clip-path=\"url(#clip0702)\" style=\"stroke:#009af9; stroke-width:1; stroke-opacity:1; fill:none\" points=\"\n 40.3485,712.638 40.5486,709.169 40.7486,705.7 40.9487,702.231 41.1488,698.763 41.3488,695.295 41.5489,691.828 41.749,688.361 41.949,684.895 42.1491,681.43 \n 42.3492,677.967 42.5492,674.504 42.7493,671.043 42.9494,667.583 43.1494,664.124 43.3495,660.667 43.5496,657.212 43.7496,653.759 43.9497,650.307 44.1497,646.858 \n 44.3498,643.411 44.5499,639.966 44.7499,636.524 44.95,633.084 45.1501,629.647 45.3501,626.213 45.5502,622.781 45.7503,619.352 45.9503,615.927 46.1504,612.505 \n 46.3505,609.086 46.5505,605.67 46.7506,602.258 46.9507,598.85 47.1507,595.446 47.3508,592.045 47.5509,588.648 47.7509,585.256 47.951,581.868 48.1511,578.484 \n 48.3511,575.104 48.5512,571.729 48.7512,568.359 48.9513,564.993 49.1514,561.633 49.3514,558.277 49.5515,554.926 49.7516,551.581 49.9516,548.241 50.1517,544.906 \n 50.3518,541.577 50.5518,538.254 50.7519,534.936 50.952,531.624 51.152,528.319 51.3521,525.019 51.5522,521.725 51.7522,518.438 51.9523,515.157 52.1524,511.882 \n 52.3524,508.614 52.5525,505.353 52.7526,502.099 52.9526,498.851 53.1527,495.61 53.3528,492.377 53.5528,489.151 53.7529,485.932 53.9529,482.72 54.153,479.516 \n 54.3531,476.32 54.5531,473.131 54.7532,469.95 54.9533,466.777 55.1533,463.612 55.3534,460.455 55.5535,457.307 55.7535,454.166 55.9536,451.034 56.1537,447.911 \n 56.3537,444.796 56.5538,441.689 56.7539,438.592 56.9539,435.503 57.154,432.423 57.3541,429.353 57.5541,426.291 57.7542,423.239 57.9543,420.196 58.1543,417.162 \n 58.3544,414.138 58.5544,411.124 58.7545,408.119 58.9546,405.124 59.1546,402.139 59.3547,399.163 59.5548,396.198 59.7548,393.243 59.9549,390.298 60.155,387.363 \n 60.355,384.439 60.5551,381.525 60.7552,378.622 60.9552,375.729 61.1553,372.847 61.3554,369.976 61.5554,367.115 61.7555,364.266 61.9556,361.428 62.1556,358.6 \n 62.3557,355.784 62.5558,352.979 62.7558,350.186 62.9559,347.403 63.1559,344.633 63.356,341.873 63.5561,339.126 63.7561,336.39 63.9562,333.666 64.1563,330.954 \n 64.3563,328.253 64.5564,325.565 64.7565,322.888 64.9565,320.224 65.1566,317.572 65.3567,314.932 65.5567,312.305 65.7568,309.69 65.9569,307.087 66.1569,304.497 \n 66.357,301.92 66.5571,299.355 66.7571,296.802 66.9572,294.263 67.1573,291.736 67.3573,289.223 67.5574,286.722 67.7574,284.234 67.9575,281.759 68.1576,279.298 \n 68.3576,276.849 68.5577,274.414 68.7578,271.992 68.9578,269.584 69.1579,267.188 69.358,264.807 69.558,262.439 69.7581,260.084 69.9582,257.743 70.1582,255.415 \n 70.3583,253.102 70.5584,250.802 70.7584,248.515 70.9585,246.243 71.1586,243.984 71.3586,241.74 71.5587,239.509 71.7588,237.293 71.9588,235.09 72.1589,232.902 \n 72.3589,230.727 72.559,228.567 72.7591,226.421 72.9591,224.29 73.1592,222.172 73.3593,220.069 73.5593,217.981 73.7594,215.906 73.9595,213.847 74.1595,211.801 \n 74.3596,209.77 74.5597,207.754 74.7597,205.752 74.9598,203.765 75.1599,201.793 75.3599,199.835 75.56,197.891 75.7601,195.963 75.9601,194.049 76.1602,192.15 \n 76.3603,190.266 76.5603,188.397 76.7604,186.542 76.9604,184.702 77.1605,182.877 77.3606,181.067 77.5606,179.272 77.7607,177.492 77.9608,175.727 78.1608,173.977 \n 78.3609,172.241 78.561,170.521 78.761,168.816 78.9611,167.126 79.1612,165.45 79.3612,163.79 79.5613,162.145 79.7614,160.515 79.9614,158.9 80.1615,157.301 \n 80.3616,155.716 80.5616,154.146 80.7617,152.592 80.9618,151.052 81.1618,149.528 81.3619,148.019 81.5619,146.525 81.762,145.046 81.9621,143.582 82.1621,142.133 \n 82.3622,140.7 82.5623,139.281 82.7623,137.878 82.9624,136.49 83.1625,135.117 83.3625,133.759 83.5626,132.416 83.7627,131.089 83.9627,129.776 84.1628,128.479 \n 84.3629,127.196 84.5629,125.929 84.763,124.677 84.9631,123.439 85.1631,122.217 85.3632,121.01 85.5633,119.818 85.7633,118.641 85.9634,117.479 86.1635,116.332 \n 86.3635,115.199 86.5636,114.082 86.7636,112.98 86.9637,111.892 87.1638,110.82 87.3638,109.762 87.5639,108.719 87.764,107.691 87.964,106.678 88.1641,105.68 \n 88.3642,104.696 88.5642,103.727 88.7643,102.773 88.9644,101.833 89.1644,100.908 89.3645,99.9978 89.5646,99.1021 89.7646,98.2209 89.9647,97.3543 90.1648,96.5021 \n 90.3648,95.6644 90.5649,94.8412 90.765,94.0324 90.965,93.2379 91.1651,92.4578 91.3651,91.692 91.5652,90.9404 91.7653,90.2031 91.9653,89.48 92.1654,88.771 \n 92.3655,88.0762 92.5655,87.3954 92.7656,86.7287 92.9657,86.076 93.1657,85.4372 93.3658,84.8123 93.5659,84.2013 93.7659,83.6042 93.966,83.0208 94.1661,82.4512 \n 94.3661,81.8952 94.5662,81.3529 94.7663,80.8242 94.9663,80.3091 95.1664,79.8075 95.3665,79.3193 95.5665,78.8446 95.7666,78.3832 95.9666,77.9351 96.1667,77.5003 \n 96.3668,77.0786 96.5668,76.6702 96.7669,76.2748 96.967,75.8925 97.167,75.5232 97.3671,75.1668 97.5672,74.8234 97.7672,74.4927 97.9673,74.1748 98.1674,73.8697 \n 98.3674,73.5771 98.5675,73.2972 98.7676,73.0299 98.9676,72.775 99.1677,72.5326 99.3678,72.3025 99.5678,72.0847 99.7679,71.8791 99.968,71.6858 100.168,71.5045 \n 100.368,71.3353 100.568,71.1782 100.768,71.0329 100.968,70.8995 101.168,70.7779 101.368,70.668 101.568,70.5698 101.769,70.4832 101.969,70.4081 102.169,70.3445 \n 102.369,70.2923 102.569,70.2514 102.769,70.2218 102.969,70.2034 103.169,70.1961 103.369,70.1998 103.569,70.2146 103.769,70.2402 103.969,70.2767 104.169,70.324 \n 104.369,70.3819 104.569,70.4505 104.77,70.5296 104.97,70.6193 105.17,70.7193 105.37,70.8296 105.57,70.9502 105.77,71.081 105.97,71.2219 106.17,71.3728 \n 106.37,71.5337 106.57,71.7044 106.77,71.885 106.97,72.0753 107.17,72.2752 107.37,72.4847 107.57,72.7037 107.77,72.9321 107.971,73.1698 108.171,73.4168 \n 108.371,73.673 108.571,73.9382 108.771,74.2125 108.971,74.4957 109.171,74.7878 109.371,75.0887 109.571,75.3982 109.771,75.7164 109.971,76.0431 110.171,76.3782 \n 110.371,76.7217 110.571,77.0736 110.771,77.4336 110.972,77.8017 111.172,78.1779 111.372,78.562 111.572,78.954 111.772,79.3538 111.972,79.7614 112.172,80.1765 \n 112.372,80.5992 112.572,81.0293 112.772,81.4668 112.972,81.9116 113.172,82.3636 113.372,82.8227 113.572,83.2889 113.772,83.762 113.973,84.242 114.173,84.7287 \n 114.373,85.2222 114.573,85.7222 114.773,86.2288 114.973,86.7418 115.173,87.2612 115.373,87.7868 115.573,88.3186 115.773,88.8565 115.973,89.4004 116.173,89.9503 \n 116.373,90.5059 116.573,91.0674 116.773,91.6345 116.973,92.2071 117.174,92.7853 117.374,93.3689 117.574,93.9577 117.774,94.5519 117.974,95.1511 118.174,95.7555 \n 118.374,96.3648 118.574,96.979 118.774,97.598 118.974,98.2217 119.174,98.85 119.374,99.4829 119.574,100.12 119.774,100.762 119.974,101.408 120.175,102.058 \n 120.375,102.712 120.575,103.371 120.775,104.033 120.975,104.699 121.175,105.369 121.375,106.043 121.575,106.72 121.775,107.401 121.975,108.085 122.175,108.772 \n 122.375,109.463 122.575,110.157 122.775,110.854 122.975,111.554 123.176,112.257 123.376,112.963 123.576,113.671 123.776,114.382 123.976,115.096 124.176,115.812 \n 124.376,116.531 124.576,117.252 124.776,117.976 124.976,118.701 125.176,119.429 125.376,120.158 125.576,120.89 125.776,121.623 125.976,122.358 126.176,123.095 \n 126.377,123.833 126.577,124.573 126.777,125.314 126.977,126.057 127.177,126.801 127.377,127.546 127.577,128.292 127.777,129.039 127.977,129.788 128.177,130.537 \n 128.377,131.287 128.577,132.037 128.777,132.788 128.977,133.54 129.177,134.292 129.378,135.045 129.578,135.798 129.778,136.551 129.978,137.305 130.178,138.059 \n 130.378,138.812 130.578,139.566 130.778,140.319 130.978,141.072 131.178,141.825 131.378,142.578 131.578,143.33 131.778,144.082 131.978,144.833 132.178,145.583 \n 132.379,146.333 132.579,147.082 132.779,147.83 132.979,148.577 133.179,149.323 133.379,150.069 133.579,150.813 133.779,151.555 133.979,152.297 134.179,153.037 \n 134.379,153.776 134.579,154.513 134.779,155.249 134.979,155.983 135.179,156.715 135.38,157.446 135.58,158.175 135.78,158.902 135.98,159.627 136.18,160.35 \n 136.38,161.071 136.58,161.79 136.78,162.507 136.98,163.221 137.18,163.933 137.38,164.643 137.58,165.35 137.78,166.055 137.98,166.757 138.18,167.457 \n 138.38,168.154 138.581,168.848 138.781,169.539 138.981,170.228 139.181,170.913 139.381,171.596 139.581,172.275 139.781,172.952 139.981,173.625 140.181,174.296 \n 140.381,174.963 140.581,175.626 140.781,176.286 140.981,176.943 141.181,177.597 141.381,178.247 141.582,178.893 141.782,179.536 141.982,180.175 142.182,180.81 \n 142.382,181.442 142.582,182.07 142.782,182.694 142.982,183.314 143.182,183.93 143.382,184.542 143.582,185.15 143.782,185.754 143.982,186.354 144.182,186.95 \n 144.382,187.541 144.583,188.129 144.783,188.711 144.983,189.29 145.183,189.864 145.383,190.434 145.583,190.999 145.783,191.56 145.983,192.116 146.183,192.668 \n 146.383,193.215 146.583,193.758 146.783,194.295 146.983,194.828 147.183,195.357 147.383,195.88 147.583,196.399 147.784,196.912 147.984,197.421 148.184,197.925 \n 148.384,198.424 148.584,198.918 148.784,199.407 148.984,199.891 149.184,200.369 149.384,200.843 149.584,201.312 149.784,201.775 149.984,202.233 150.184,202.686 \n 150.384,203.133 150.584,203.576 150.785,204.013 150.985,204.445 151.185,204.871 151.385,205.292 151.585,205.708 151.785,206.118 151.985,206.523 152.185,206.922 \n 152.385,207.316 152.585,207.704 152.785,208.087 152.985,208.464 153.185,208.836 153.385,209.202 153.585,209.562 153.786,209.917 153.986,210.266 154.186,210.61 \n 154.386,210.948 154.586,211.28 154.786,211.607 154.986,211.928 155.186,212.243 155.386,212.553 155.586,212.856 155.786,213.154 155.986,213.447 156.186,213.733 \n 156.386,214.014 156.586,214.289 156.786,214.558 156.987,214.822 157.187,215.079 157.387,215.331 157.587,215.577 157.787,215.817 157.987,216.052 158.187,216.28 \n 158.387,216.503 158.587,216.72 158.787,216.931 158.987,217.136 159.187,217.336 159.387,217.529 159.587,217.717 159.787,217.899 159.988,218.075 160.188,218.245 \n 160.388,218.41 160.588,218.569 160.788,218.721 160.988,218.868 161.188,219.01 161.388,219.145 161.588,219.275 161.788,219.398 161.988,219.516 162.188,219.629 \n 162.388,219.735 162.588,219.836 162.788,219.931 162.989,220.02 163.189,220.103 163.389,220.181 163.589,220.253 163.789,220.32 163.989,220.38 164.189,220.435 \n 164.389,220.485 164.589,220.528 164.789,220.566 164.989,220.599 165.189,220.626 165.389,220.647 165.589,220.662 165.789,220.672 165.989,220.677 166.19,220.676 \n 166.39,220.669 166.59,220.657 166.79,220.64 166.99,220.617 167.19,220.589 167.39,220.555 167.59,220.516 167.79,220.471 167.99,220.421 168.19,220.366 \n 168.39,220.306 168.59,220.24 168.79,220.169 168.99,220.092 169.191,220.011 169.391,219.924 169.591,219.832 169.791,219.735 169.991,219.633 170.191,219.526 \n 170.391,219.414 170.591,219.296 170.791,219.174 170.991,219.047 171.191,218.914 171.391,218.777 171.591,218.635 171.791,218.488 171.991,218.336 172.192,218.18 \n 172.392,218.018 172.592,217.852 172.792,217.681 172.992,217.506 173.192,217.326 173.392,217.141 173.592,216.952 173.792,216.758 173.992,216.559 174.192,216.356 \n 174.392,216.149 174.592,215.937 174.792,215.721 174.992,215.5 175.192,215.275 175.393,215.046 175.593,214.813 175.793,214.575 175.993,214.333 176.193,214.087 \n 176.393,213.837 176.593,213.583 176.793,213.325 176.993,213.063 177.193,212.797 177.393,212.527 177.593,212.253 177.793,211.975 177.993,211.694 178.193,211.409 \n 178.394,211.12 178.594,210.827 178.794,210.531 178.994,210.231 179.194,209.927 179.394,209.621 179.594,209.31 179.794,208.996 179.994,208.679 180.194,208.358 \n 180.394,208.034 180.594,207.707 180.794,207.377 180.994,207.043 181.194,206.706 181.395,206.366 181.595,206.023 181.795,205.678 181.995,205.329 182.195,204.977 \n 182.395,204.622 182.595,204.264 182.795,203.904 182.995,203.541 183.195,203.175 183.395,202.807 183.595,202.435 183.795,202.062 183.995,201.685 184.195,201.307 \n 184.395,200.925 184.596,200.542 184.796,200.156 184.996,199.768 185.196,199.377 185.396,198.984 185.596,198.59 185.796,198.192 185.996,197.793 186.196,197.392 \n 186.396,196.989 186.596,196.584 186.796,196.177 186.996,195.768 187.196,195.357 187.396,194.945 187.597,194.531 187.797,194.115 187.997,193.698 188.197,193.279 \n 188.397,192.858 188.597,192.436 188.797,192.012 188.997,191.588 189.197,191.161 189.397,190.734 189.597,190.305 189.797,189.875 189.997,189.444 190.197,189.012 \n 190.397,188.578 190.598,188.144 190.798,187.709 190.998,187.272 191.198,186.835 191.398,186.397 191.598,185.958 191.798,185.519 191.998,185.079 192.198,184.638 \n 192.398,184.196 192.598,183.754 192.798,183.311 192.998,182.868 193.198,182.425 193.398,181.981 193.598,181.537 193.799,181.092 193.999,180.648 194.199,180.203 \n 194.399,179.757 194.599,179.312 194.799,178.867 194.999,178.422 195.199,177.976 195.399,177.531 195.599,177.086 195.799,176.641 195.999,176.196 196.199,175.752 \n 196.399,175.307 196.599,174.863 196.8,174.42 197,173.977 197.2,173.534 197.4,173.092 197.6,172.65 197.8,172.209 198,171.769 198.2,171.329 \n 198.4,170.89 198.6,170.452 198.8,170.014 199,169.578 199.2,169.142 199.4,168.707 199.6,168.273 199.801,167.84 200.001,167.409 200.201,166.978 \n 200.401,166.548 200.601,166.12 200.801,165.693 201.001,165.267 201.201,164.842 201.401,164.419 201.601,163.997 201.801,163.576 202.001,163.157 202.201,162.739 \n 202.401,162.323 202.601,161.908 202.801,161.495 203.002,161.084 203.202,160.674 203.402,160.266 203.602,159.86 203.802,159.456 204.002,159.053 204.202,158.652 \n 204.402,158.253 204.602,157.856 204.802,157.461 205.002,157.068 205.202,156.677 205.402,156.288 205.602,155.901 205.802,155.516 206.003,155.134 206.203,154.753 \n 206.403,154.375 206.603,153.999 206.803,153.626 207.003,153.254 207.203,152.885 207.403,152.519 207.603,152.155 207.803,151.793 208.003,151.434 208.203,151.077 \n 208.403,150.723 208.603,150.371 208.803,150.022 209.004,149.675 209.204,149.332 209.404,148.991 209.604,148.652 209.804,148.317 210.004,147.984 210.204,147.654 \n 210.404,147.326 210.604,147.002 210.804,146.68 211.004,146.361 211.204,146.046 211.404,145.733 211.604,145.423 211.804,145.116 212.004,144.812 212.205,144.511 \n 212.405,144.214 212.605,143.919 212.805,143.627 213.005,143.339 213.205,143.054 213.405,142.771 213.605,142.492 213.805,142.217 214.005,141.944 214.205,141.675 \n 214.405,141.409 214.605,141.146 214.805,140.887 215.005,140.631 215.206,140.378 215.406,140.129 215.606,139.883 215.806,139.64 216.006,139.401 216.206,139.165 \n 216.406,138.933 216.606,138.704 216.806,138.479 217.006,138.257 217.206,138.038 217.406,137.824 217.606,137.612 217.806,137.404 218.006,137.2 218.207,137 \n 218.407,136.802 218.607,136.609 218.807,136.419 219.007,136.233 219.207,136.05 219.407,135.871 219.607,135.696 219.807,135.524 220.007,135.356 220.207,135.192 \n 220.407,135.031 220.607,134.874 220.807,134.721 221.007,134.571 221.207,134.425 221.408,134.283 221.608,134.145 221.808,134.01 222.008,133.879 222.208,133.752 \n 222.408,133.628 222.608,133.508 222.808,133.392 223.008,133.28 223.208,133.171 223.408,133.067 223.608,132.966 223.808,132.868 224.008,132.775 224.208,132.685 \n 224.409,132.599 224.609,132.517 224.809,132.439 225.009,132.364 225.209,132.293 225.409,132.226 225.609,132.163 225.809,132.103 226.009,132.048 226.209,131.995 \n 226.409,131.947 226.609,131.903 226.809,131.862 227.009,131.825 227.209,131.791 227.41,131.762 227.61,131.736 227.81,131.714 228.01,131.695 228.21,131.681 \n 228.41,131.67 228.61,131.663 228.81,131.659 229.01,131.659 229.21,131.663 229.41,131.67 229.61,131.681 229.81,131.696 230.01,131.714 230.21,131.736 \n 230.41,131.762 230.611,131.791 230.811,131.824 231.011,131.861 231.211,131.901 231.411,131.944 231.611,131.991 231.811,132.042 232.011,132.096 232.211,132.154 \n 232.411,132.215 232.611,132.28 232.811,132.348 233.011,132.42 233.211,132.495 233.411,132.574 233.612,132.656 233.812,132.741 234.012,132.83 234.212,132.922 \n 234.412,133.017 234.612,133.116 234.812,133.218 235.012,133.324 235.212,133.433 235.412,133.545 235.612,133.66 235.812,133.779 236.012,133.9 236.212,134.025 \n 236.412,134.153 236.613,134.285 236.813,134.419 237.013,134.557 237.213,134.697 237.413,134.841 237.613,134.988 237.813,135.138 238.013,135.291 238.213,135.447 \n 238.413,135.605 238.613,135.767 238.813,135.932 239.013,136.1 239.213,136.27 239.413,136.444 239.613,136.62 239.814,136.799 240.014,136.981 240.214,137.165 \n 240.414,137.353 240.614,137.543 240.814,137.735 241.014,137.931 241.214,138.129 241.414,138.33 241.614,138.533 241.814,138.739 242.014,138.947 242.214,139.158 \n 242.414,139.372 242.614,139.588 242.815,139.806 243.015,140.027 243.215,140.25 243.415,140.476 243.615,140.703 243.815,140.934 244.015,141.166 244.215,141.401 \n 244.415,141.638 244.615,141.877 244.815,142.118 245.015,142.362 245.215,142.607 245.415,142.855 245.615,143.104 245.816,143.356 246.016,143.61 246.216,143.865 \n 246.416,144.123 246.616,144.382 246.816,144.644 247.016,144.907 247.216,145.172 247.416,145.439 247.616,145.708 247.816,145.978 248.016,146.25 248.216,146.524 \n 248.416,146.799 248.616,147.076 248.816,147.354 249.017,147.634 249.217,147.916 249.417,148.199 249.617,148.483 249.817,148.769 250.017,149.057 250.217,149.345 \n 250.417,149.635 250.617,149.927 250.817,150.219 251.017,150.513 251.217,150.808 251.417,151.104 251.617,151.401 251.817,151.7 252.018,151.999 252.218,152.3 \n 252.418,152.601 252.618,152.904 252.818,153.207 253.018,153.511 253.218,153.817 253.418,154.123 253.618,154.43 253.818,154.737 254.018,155.046 254.218,155.355 \n 254.418,155.665 254.618,155.975 254.818,156.286 255.019,156.598 255.219,156.91 255.419,157.223 255.619,157.536 255.819,157.85 256.019,158.164 256.219,158.478 \n 256.419,158.793 256.619,159.109 256.819,159.424 257.019,159.74 257.219,160.056 257.419,160.372 257.619,160.689 257.819,161.005 258.019,161.322 258.22,161.639 \n 258.42,161.955 258.62,162.272 258.82,162.589 259.02,162.906 259.22,163.222 259.42,163.539 259.62,163.855 259.82,164.172 260.02,164.488 260.22,164.803 \n 260.42,165.119 260.62,165.434 260.82,165.749 261.02,166.064 261.221,166.378 261.421,166.691 261.621,167.005 261.821,167.317 262.021,167.63 262.221,167.941 \n 262.421,168.252 262.621,168.563 262.821,168.873 263.021,169.182 263.221,169.491 263.421,169.798 263.621,170.105 263.821,170.412 264.021,170.717 264.222,171.022 \n 264.422,171.325 264.622,171.628 264.822,171.93 265.022,172.231 265.222,172.531 265.422,172.83 265.622,173.128 265.822,173.425 266.022,173.72 266.222,174.015 \n 266.422,174.309 266.622,174.601 266.822,174.892 267.022,175.182 267.222,175.47 267.423,175.758 267.623,176.044 267.823,176.328 268.023,176.612 268.223,176.893 \n 268.423,177.174 268.623,177.453 268.823,177.73 269.023,178.007 269.223,178.281 269.423,178.554 269.623,178.826 269.823,179.095 270.023,179.364 270.223,179.63 \n 270.424,179.895 270.624,180.158 270.824,180.42 271.024,180.68 271.224,180.938 271.424,181.194 271.624,181.448 271.824,181.701 272.024,181.952 272.224,182.201 \n 272.424,182.448 272.624,182.693 272.824,182.936 273.024,183.177 273.224,183.417 273.425,183.654 273.625,183.889 273.825,184.122 274.025,184.353 274.225,184.582 \n 274.425,184.809 274.625,185.034 274.825,185.257 275.025,185.478 275.225,185.696 275.425,185.912 275.625,186.126 275.825,186.338 276.025,186.548 276.225,186.755 \n 276.425,186.96 276.626,187.163 276.826,187.363 277.026,187.561 277.226,187.757 277.426,187.95 277.626,188.141 277.826,188.33 278.026,188.516 278.226,188.7 \n 278.426,188.882 278.626,189.061 278.826,189.237 279.026,189.411 279.226,189.583 279.426,189.752 279.627,189.918 279.827,190.082 280.027,190.244 280.227,190.403 \n 280.427,190.559 280.627,190.713 280.827,190.864 281.027,191.013 281.227,191.159 281.427,191.302 281.627,191.443 281.827,191.582 282.027,191.717 282.227,191.85 \n 282.427,191.98 282.628,192.108 282.828,192.233 283.028,192.355 283.228,192.474 283.428,192.591 283.628,192.705 283.828,192.817 284.028,192.925 284.228,193.031 \n 284.428,193.135 284.628,193.235 284.828,193.333 285.028,193.428 285.228,193.52 285.428,193.61 285.628,193.696 285.829,193.78 286.029,193.862 286.229,193.94 \n 286.429,194.016 286.629,194.088 286.829,194.158 287.029,194.226 287.229,194.29 287.429,194.352 287.629,194.411 287.829,194.467 288.029,194.52 288.229,194.571 \n 288.429,194.619 288.629,194.663 288.83,194.706 289.03,194.745 289.23,194.781 289.43,194.815 289.63,194.846 289.83,194.874 290.03,194.9 290.23,194.922 \n 290.43,194.942 290.63,194.959 290.83,194.973 291.03,194.985 291.23,194.993 291.43,194.999 291.63,195.003 291.831,195.003 292.031,195.001 292.231,194.995 \n 292.431,194.988 292.631,194.977 292.831,194.964 293.031,194.947 293.231,194.929 293.431,194.907 293.631,194.883 293.831,194.856 294.031,194.826 294.231,194.794 \n 294.431,194.759 294.631,194.721 294.832,194.681 295.032,194.638 295.232,194.592 295.432,194.543 295.632,194.492 295.832,194.439 296.032,194.383 296.232,194.324 \n 296.432,194.262 296.632,194.198 296.832,194.132 297.032,194.062 297.232,193.991 297.432,193.916 297.632,193.84 297.832,193.76 298.033,193.678 298.233,193.594 \n 298.433,193.507 298.633,193.418 298.833,193.326 299.033,193.232 299.233,193.135 299.433,193.036 299.633,192.935 299.833,192.831 300.033,192.725 300.233,192.616 \n 300.433,192.505 300.633,192.392 300.833,192.276 301.034,192.158 301.234,192.038 301.434,191.916 301.634,191.791 301.834,191.664 302.034,191.535 302.234,191.403 \n 302.434,191.27 302.634,191.134 302.834,190.996 303.034,190.856 303.234,190.714 303.434,190.569 303.634,190.423 303.834,190.275 304.035,190.124 304.235,189.971 \n 304.435,189.817 304.635,189.66 304.835,189.502 305.035,189.341 305.235,189.179 305.435,189.014 305.635,188.848 305.835,188.68 306.035,188.51 306.235,188.338 \n 306.435,188.164 306.635,187.988 306.835,187.811 307.035,187.632 307.236,187.451 307.436,187.269 307.636,187.084 307.836,186.898 308.036,186.711 308.236,186.522 \n 308.436,186.331 308.636,186.138 308.836,185.944 309.036,185.749 309.236,185.551 309.436,185.353 309.636,185.153 309.836,184.951 310.036,184.748 310.237,184.544 \n 310.437,184.338 310.637,184.131 310.837,183.922 311.037,183.712 311.237,183.501 311.437,183.288 311.637,183.075 311.837,182.86 312.037,182.643 312.237,182.426 \n 312.437,182.207 312.637,181.988 312.837,181.767 313.037,181.545 313.238,181.322 313.438,181.098 313.638,180.873 313.838,180.647 314.038,180.42 314.238,180.192 \n 314.438,179.963 314.638,179.733 314.838,179.502 315.038,179.27 315.238,179.038 315.438,178.805 315.638,178.571 315.838,178.336 316.038,178.101 316.238,177.864 \n 316.439,177.627 316.639,177.39 316.839,177.152 317.039,176.913 317.239,176.674 317.439,176.434 317.639,176.193 317.839,175.952 318.039,175.711 318.239,175.469 \n 318.439,175.226 318.639,174.984 318.839,174.74 319.039,174.497 319.239,174.253 319.44,174.009 319.64,173.764 319.84,173.52 320.04,173.275 320.24,173.029 \n 320.44,172.784 320.64,172.538 320.84,172.293 321.04,172.047 321.24,171.801 321.44,171.555 321.64,171.309 321.84,171.063 322.04,170.817 322.24,170.571 \n 322.441,170.325 322.641,170.08 322.841,169.834 323.041,169.588 323.241,169.343 323.441,169.098 323.641,168.853 323.841,168.608 324.041,168.363 324.241,168.119 \n 324.441,167.875 324.641,167.631 324.841,167.388 325.041,167.145 325.241,166.903 325.441,166.66 325.642,166.419 325.842,166.178 326.042,165.937 326.242,165.697 \n 326.442,165.457 326.642,165.218 326.842,164.979 327.042,164.742 327.242,164.504 327.442,164.268 327.642,164.032 327.842,163.796 328.042,163.562 328.242,163.328 \n 328.442,163.095 328.643,162.863 328.843,162.631 329.043,162.401 329.243,162.171 329.443,161.942 329.643,161.714 329.843,161.487 330.043,161.261 330.243,161.036 \n 330.443,160.812 330.643,160.589 330.843,160.367 331.043,160.145 331.243,159.925 331.443,159.706 331.644,159.489 331.844,159.272 332.044,159.056 332.244,158.842 \n 332.444,158.629 332.644,158.417 332.844,158.206 333.044,157.996 333.244,157.788 333.444,157.581 333.644,157.376 333.844,157.171 334.044,156.968 334.244,156.766 \n 334.444,156.566 334.644,156.367 334.845,156.17 335.045,155.974 335.245,155.779 335.445,155.586 335.645,155.394 335.845,155.204 336.045,155.016 336.245,154.829 \n 336.445,154.643 336.645,154.459 336.845,154.277 337.045,154.096 337.245,153.917 337.445,153.739 337.645,153.563 337.846,153.389 338.046,153.216 338.246,153.046 \n 338.446,152.876 338.646,152.709 338.846,152.543 339.046,152.379 339.246,152.217 339.446,152.057 339.646,151.898 339.846,151.741 340.046,151.586 340.246,151.433 \n 340.446,151.282 340.646,151.132 340.847,150.985 341.047,150.839 341.247,150.695 341.447,150.553 341.647,150.413 341.847,150.275 342.047,150.139 342.247,150.005 \n 342.447,149.873 342.647,149.743 342.847,149.614 343.047,149.488 343.247,149.364 343.447,149.242 343.647,149.121 343.847,149.003 344.048,148.887 344.248,148.773 \n 344.448,148.661 344.648,148.551 344.848,148.443 345.048,148.337 345.248,148.233 345.448,148.132 345.648,148.032 345.848,147.935 346.048,147.84 346.248,147.746 \n 346.448,147.655 346.648,147.567 346.848,147.48 347.049,147.395 347.249,147.313 347.449,147.233 347.649,147.154 347.849,147.079 348.049,147.005 348.249,146.933 \n 348.449,146.864 348.649,146.797 348.849,146.732 349.049,146.669 349.249,146.608 349.449,146.55 349.649,146.494 349.849,146.44 350.05,146.388 350.25,146.338 \n 350.45,146.291 350.65,146.246 350.85,146.203 351.05,146.162 351.25,146.124 351.45,146.088 351.65,146.054 351.85,146.022 352.05,145.993 352.25,145.965 \n 352.45,145.94 352.65,145.917 352.85,145.897 353.05,145.878 353.251,145.862 353.451,145.848 353.651,145.836 353.851,145.827 354.051,145.82 354.251,145.815 \n 354.451,145.812 354.651,145.811 354.851,145.813 355.051,145.816 355.251,145.822 355.451,145.831 355.651,145.841 355.851,145.853 356.051,145.868 356.252,145.885 \n 356.452,145.904 356.652,145.925 356.852,145.949 357.052,145.974 357.252,146.002 357.452,146.032 357.652,146.064 357.852,146.098 358.052,146.135 358.252,146.173 \n 358.452,146.214 358.652,146.256 358.852,146.301 359.052,146.348 359.253,146.397 359.453,146.448 359.653,146.501 359.853,146.557 360.053,146.614 360.253,146.673 \n 360.453,146.735 360.653,146.798 360.853,146.864 361.053,146.931 361.253,147.001 361.453,147.072 361.653,147.146 361.853,147.221 362.053,147.298 362.253,147.378 \n 362.454,147.459 362.654,147.543 362.854,147.628 363.054,147.715 363.254,147.804 363.454,147.895 363.654,147.988 363.854,148.082 364.054,148.179 364.254,148.277 \n 364.454,148.378 364.654,148.48 364.854,148.584 365.054,148.689 365.254,148.797 365.455,148.906 365.655,149.017 365.855,149.13 366.055,149.244 366.255,149.36 \n 366.455,149.478 366.655,149.598 366.855,149.719 367.055,149.842 367.255,149.967 367.455,150.093 367.655,150.221 367.855,150.35 368.055,150.481 368.255,150.614 \n 368.456,150.748 368.656,150.884 368.856,151.021 369.056,151.16 369.256,151.3 369.456,151.442 369.656,151.585 369.856,151.73 370.056,151.876 370.256,152.024 \n 370.456,152.173 370.656,152.323 370.856,152.475 371.056,152.628 371.256,152.782 371.456,152.938 371.657,153.095 371.857,153.253 372.057,153.413 372.257,153.574 \n 372.457,153.736 372.657,153.899 372.857,154.063 373.057,154.229 373.257,154.396 373.457,154.564 373.657,154.733 373.857,154.903 374.057,155.074 374.257,155.247 \n 374.457,155.42 374.658,155.594 374.858,155.77 375.058,155.946 375.258,156.124 375.458,156.302 375.658,156.481 375.858,156.662 376.058,156.843 376.258,157.025 \n 376.458,157.207 376.658,157.391 376.858,157.576 377.058,157.761 377.258,157.947 377.458,158.134 377.659,158.322 377.859,158.51 378.059,158.699 378.259,158.889 \n 378.459,159.079 378.659,159.27 378.859,159.462 379.059,159.654 379.259,159.847 379.459,160.04 379.659,160.234 379.859,160.429 380.059,160.624 380.259,160.819 \n 380.459,161.015 380.659,161.212 380.86,161.408 381.06,161.606 381.26,161.803 381.46,162.001 381.66,162.2 381.86,162.398 382.06,162.597 382.26,162.797 \n 382.46,162.996 382.66,163.196 382.86,163.396 383.06,163.596 383.26,163.796 383.46,163.997 383.66,164.197 383.861,164.398 384.061,164.599 384.261,164.8 \n 384.461,165.001 384.661,165.202 384.861,165.403 385.061,165.604 385.261,165.806 385.461,166.007 385.661,166.208 385.861,166.408 386.061,166.609 386.261,166.81 \n 386.461,167.011 386.661,167.211 386.862,167.411 387.062,167.611 387.262,167.811 387.462,168.011 387.662,168.21 387.862,168.409 388.062,168.608 388.262,168.806 \n 388.462,169.004 388.662,169.202 388.862,169.399 389.062,169.596 389.262,169.793 389.462,169.989 389.662,170.184 389.862,170.38 390.063,170.574 390.263,170.769 \n 390.463,170.962 390.663,171.155 390.863,171.348 391.063,171.54 391.263,171.731 391.463,171.922 391.663,172.112 391.863,172.302 392.063,172.49 392.263,172.678 \n 392.463,172.866 392.663,173.052 392.863,173.238 393.064,173.424 393.264,173.608 393.464,173.791 393.664,173.974 393.864,174.156 394.064,174.337 394.264,174.517 \n 394.464,174.697 394.664,174.875 394.864,175.053 395.064,175.229 395.264,175.405 395.464,175.579 395.664,175.753 395.864,175.926 396.065,176.097 396.265,176.268 \n 396.465,176.437 396.665,176.606 396.865,176.773 397.065,176.94 397.265,177.105 397.465,177.269 397.665,177.432 397.865,177.593 398.065,177.754 398.265,177.913 \n 398.465,178.072 398.665,178.229 398.865,178.384 399.065,178.539 399.266,178.692 399.466,178.844 399.666,178.995 399.866,179.144 400.066,179.292 400.266,179.439 \n 400.466,179.584 400.666,179.728 400.866,179.871 401.066,180.012 401.266,180.152 401.466,180.291 401.666,180.428 401.866,180.564 402.066,180.698 402.267,180.831 \n 402.467,180.962 402.667,181.092 402.867,181.22 403.067,181.347 403.267,181.472 403.467,181.596 403.667,181.718 403.867,181.839 404.067,181.958 404.267,182.076 \n 404.467,182.192 404.667,182.307 404.867,182.42 405.067,182.531 405.268,182.641 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417.872,186.024 418.072,186.019 418.272,186.013 \n 418.472,186.004 418.672,185.994 418.872,185.982 419.072,185.968 419.272,185.953 419.472,185.935 419.672,185.916 419.872,185.895 420.072,185.872 420.272,185.847 \n 420.472,185.821 420.673,185.793 420.873,185.763 421.073,185.731 421.273,185.697 421.473,185.662 421.673,185.625 421.873,185.586 422.073,185.545 422.273,185.503 \n 422.473,185.459 422.673,185.413 422.873,185.365 423.073,185.316 423.273,185.265 423.473,185.212 423.674,185.158 423.874,185.101 424.074,185.044 424.274,184.984 \n 424.474,184.923 424.674,184.86 424.874,184.795 425.074,184.729 425.274,184.661 425.474,184.592 425.674,184.521 425.874,184.448 426.074,184.374 426.274,184.298 \n 426.474,184.221 426.674,184.142 426.875,184.061 427.075,183.979 427.275,183.895 427.475,183.81 427.675,183.723 427.875,183.635 428.075,183.545 428.275,183.454 \n 428.475,183.361 428.675,183.267 428.875,183.171 429.075,183.074 429.275,182.975 429.475,182.875 429.675,182.774 429.876,182.671 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