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srikumarks/exploring-measurements.ipynb

Created April 15, 2023 09:25
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Trying to understand what "measurement" means in quantum mechanics.
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exploring-measurements.ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "fed75000",
"metadata": {},
"source": [
"# Exploring measurement\n",
"\n",
"(Srikumar K. S., 15 Apr 2023)\n",
"\n",
"The goal of this exploratory notebook is to examine measurement as a process of\n",
"interaction between a high dimensional system and a qubit being measured."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "33e17d3a-418a-4c7a-a9a2-745a9e08ebb1",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"MersenneTwister(1234)"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Random, LinearAlgebra\n",
"rng = MersenneTwister(1234)"
]
},
{
"cell_type": "markdown",
"id": "fffc7288-54dd-4d5a-b09d-f4a6b5c33f4b",
"metadata": {},
"source": [
"\n",
"$$\n",
"\\newcommand{\\ket}[1]{\\left|{#1}\\right\\rangle}\n",
"\\newcommand{\\bra}[1]{\\left\\langle{#1}\\right|}\n",
"\\newcommand{\\braket}[1]{\\left\\langle{#1}\\right\\rangle}\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"id": "b24e2c32",
"metadata": {},
"source": [
"## Approach\n",
"\n",
"The idea is to see how a qubit in a random superposition of its two possibilities evolves when \"measured\" by a random observer that can distinguish between the two qubit states. Towards this, we need the ability to construct a random state, a random observable and a random observer. In this exploration, we're not initially concerned with the nature of the distribution when creating random states/observables and observers. We'll get to that later on ... if necessary.\n",
"\n",
"## Random states\n",
"\n",
"We can make any N-dimensional random vector with complex components such that $\\sum_{i}|c_i|^2 = 1$ where $c_i$ are the amplitudes of the basis states that make up the random state vector. Note that the constraint implies $|c_i|^2 \\leq 1$ for all $i$."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "4d495dfd-43e6-4ebd-9241-5958da11c9c2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4-element Vector{ComplexF64}:\n",
" 0.13894291414503196 + 0.4080544353672953im\n",
" 0.10130724069115052 - 0.06104772848254118im\n",
" 0.44969950485897653 + 0.5416517697082908im\n",
" -0.4579406055551145 - 0.30801068114907093im"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function random_state(rng, N)\n",
" @assert N >= 2\n",
" z = zeros(Complex, N)\n",
" for i in 1:N\n",
" a = 2.0 * (rand(rng, Float64) - 0.5)\n",
" b = 2.0 * (rand(rng, Float64) - 0.5)\n",
" z[i] = a+b*im\n",
" end\n",
" return z / sqrt(sum(abs2, z))\n",
"end\n",
"\n",
"random_state(rng, 4)"
]
},
{
"cell_type": "markdown",
"id": "1f111eee",
"metadata": {},
"source": [
"## Random density matrix\n",
"\n",
"A random density matrix must meet the criterion that its eigenvalues must be real and they must sum to unity."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "573165b7",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4×4 Matrix{ComplexF64}:\n",
" 0.0981778-3.46945e-18im … -0.011408+0.0348368im\n",
" -0.0607316-0.00682211im 0.0594336-0.180245im\n",
" 0.00579272-0.0772894im -0.00395489+0.00300028im\n",
" -0.011408-0.0348368im 0.191688-8.90799e-18im"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"function random_ρ(rng, N; noise_floor=1e-10/N, bias=ones(Float64,N))\n",
" m = 2.0 * (rand(rng, Float64, (N,N)) + im * rand(rng, Float64, (N,N)) .- (0.5 + im*0.5))\n",
" m = 0.5*(m+m')\n",
" e = eigen(m)\n",
" eva = abs2.(e.values)\n",
" evam = maximum(eva)\n",
" ev = (eva .+ noise_floor * evam) .* bias\n",
" ev /= sum(ev)\n",
" e.vectors * Diagonal(ev) * inv(e.vectors)\n",
"end\n",
"\n",
"random_ρ(rng, 4)"
]
},
{
"cell_type": "markdown",
"id": "987b9bef",
"metadata": {},
"source": [
"## Random observers\n",
"\n",
"What is a random observer? Let's focus on observers for single qubits. A single qubit can be either in the $\\ket{0}$ state or in the $\\ket{1}$ state or in general in a superposition of the form $\\ket{q} = q_0\\ket{0}+q_1\\ket{1}$ where $|q_0|^2 + |q_1|^2 = 1$. Let's consider an \"ideal observer\" represented by a unitary operator $\\Omega$ and with $n$ dimensional internal state $\\ket{\\omega}$ which behaves like this -\n",
"\n",
"$$\\Omega\\ket{\\omega}\\ket{0} = \\ket{\\omega_0}\\ket{0}$$\n",
"and\n",
"$$\\Omega\\ket{\\omega}\\ket{1} = \\ket{\\omega_1}\\ket{1}$$\n",
"\n",
"Therefore such an $\\Omega$ will transform an arbitrary $\\ket{q}$ according to --\n",
"\n",
"$$\\Omega\\ket{\\omega}\\ket{q} = q_0\\ket{\\omega_0}\\ket{0} + q_1\\ket{\\omega_1}\\ket{1}$$\n",
"\n",
"Such an $\\Omega$ can be thought of as a combination of $\\Omega_0$ and $\\Omega_1$ where --\n",
"\n",
"$$\\Omega_0\\ket{\\omega}\\ket{q} = q_0\\ket{\\omega_0}\\ket{0} + q_1\\ket{\\omega}\\ket{1}$$\n",
"and\n",
"$$\\Omega_1\\ket{\\omega}\\ket{q} = q_0\\ket{\\omega}\\ket{0} + q_1\\ket{\\omega_1}\\ket{1}$$\n",
"\n",
"and we can write -\n",
"\n",
"$$\\Omega = \\Omega_1\\Omega_0 = \\Omega_0\\Omega_1$$\n",
"\n",
"We can therefore pick $\\Omega_0$ and $\\Omega_1$ to be unitary transformations due to random commuting observables $H_0$ and $H_1$.\n",
"\n",
"The combined observable (a self adjoint matrix) can therefore be written as --\n",
"\n",
"$$H = \\begin{bmatrix}\n",
"H_0 & \\mathbb{0} \\\\\n",
"\\mathbb{0} & H_1\n",
"\\end{bmatrix}$$"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "7e3630af",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Eigen{ComplexF64, ComplexF64, Matrix{ComplexF64}, Vector{ComplexF64}}\n",
"values:\n",
"4-element Vector{ComplexF64}:\n",
" -1.0000000000000004 + 2.511783216587311e-18im\n",
" -0.8508733840007167 - 9.308839331308716e-17im\n",
" -0.4816167585468012 - 3.077092716616459e-17im\n",
" -1.157401475209869e-16 - 1.7430340815480004e-17im\n",
"vectors:\n",
"4×4 Matrix{ComplexF64}:\n",
" 0.645644+0.0im -0.140488+0.620761im … -0.144119-0.257587im\n",
" 0.134682+0.435929im 0.666776+0.0im -0.133027-0.275052im\n",
" 0.288964+0.0572762im 0.313974-0.137567im 0.830699+0.0im\n",
" 0.535022+0.0440478im -0.144123-0.109784im -0.0465203+0.356796im"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"function random_observable(rng, N; minmax=(-1.0,1.0))\n",
" m = 2.0 * (rand(rng, Float64, (N,N)) + im * rand(rng, Float64, (N,N)) .- (0.5 + im*0.5))\n",
" m = 0.5*(m+m')\n",
" e = eigen(m)\n",
" emin = minimum(real.(e.values))\n",
" emax = maximum(real.(e.values))\n",
" ev = minmax[1] .+ (e.values .- emin) * (minmax[2] / (emax - emin))\n",
" e.vectors * Diagonal(ev) * inv(e.vectors)\n",
"end\n",
"\n",
"eigen(random_observable(rng, 4))"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "a4060de9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4×4 Matrix{Complex}:\n",
" -0.788404-5.55112e-17im 0.175255-0.368929im … 0+0im\n",
" 0.175255+0.368929im -0.211596+2.87947e-17im 0+0im\n",
" 0+0im 0+0im -0.499198-0.0166176im\n",
" 0+0im 0+0im -0.477093-1.19695e-18im"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"function random_observer(rng, n; minmax=(-1.0,1.0))\n",
" H0 = random_observable(rng, n; minmax)\n",
" H1 = random_observable(rng, n; minmax)\n",
" Z = zeros(Complex, (n,n))\n",
" H = vcat(hcat(H0, Z), hcat(Z, H1))\n",
"end\n",
"\n",
"random_observer(rng, 2)"
]
},
{
"cell_type": "markdown",
"id": "9fdd5928",
"metadata": {},
"source": [
"## Utilities\n",
"\n",
"We need some utilities like ability to make pure state vectors, take scalar products, tensor products and such."
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "b51b4716",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"rot (generic function with 1 method)"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"function pure_state(N, m)\n",
" z = zeros(Complex, N)\n",
" m = mod(m, N)\n",
" z[m+1] = 1.0 + 0im\n",
" return z\n",
"end\n",
"\n",
"function bra(state)\n",
" state'\n",
"end\n",
"\n",
"function braket(state1, state2)\n",
" bra(state1) * state2\n",
"end\n",
"\n",
"function ketbra(state1, state2)\n",
" state1 * bra(state2)\n",
"end\n",
"\n",
"function ρ(probs)\n",
" aprobs = abs.(probs)\n",
" nprobs = aprobs / sum(aprobs)\n",
" return Diagonal{Complex,Vector{Complex}}(nprobs)\n",
"end\n",
"\n",
"# The purity of the state represented by a sensity matrix is\n",
"# the trace of its square. The purity will be 1 if it represents\n",
"# a pure state and less than 1 if the state is a mixed state.\n",
"function purity(density)\n",
" tr(density * density)\n",
"end\n",
"\n",
"# We extend that notion of purity of a density matrix to that\n",
"# of a state, relative of the chosen set of basis states as well.\n",
"# Straightforward extension ... and I'm not even sure I'll be using it.\n",
"function spurity(state)\n",
" s = state .* conj.(state)\n",
" sum(abs2, s)\n",
"end\n",
"\n",
"# Tensor product of states is just the kron operator.\n",
"⊗ = kron\n",
"\n",
"# Exepectation of an operator given the density matrix.\n",
"function E(densityop, op)\n",
" tr(densityop * op)\n",
"end\n",
"\n",
"# Pauli matrices and identity matrices.\n",
"σx = Complex.([0 1; 1 0])\n",
"σy = Complex.([0 (-im); (im) 0])\n",
"σz = Complex.([1 0; 0 -1])\n",
"Ik(k) = Diagonal(ones(Complex, k))\n",
"I = Ik(2)\n",
"\n",
"# Pauli rotation. Computes e^{iPa}\n",
"# Assumes that pauli * pauli = I, i.e. pauli is its own inverse.\n",
"function rot(pauli, alpha)\n",
" id = Ik(size(pauli)[1])\n",
" cos(alpha) * id + im * sin(alpha) * pauli\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "dc2216d0",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2-element Vector{Complex}:\n",
" 1.0 + 0.0im\n",
" 0 + 0im"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"4×4 Diagonal{Complex, Vector{Complex}}:\n",
" 1+0im ⋅ ⋅ ⋅ \n",
" ⋅ 1+0im ⋅ ⋅ \n",
" ⋅ ⋅ 1+0im ⋅ \n",
" ⋅ ⋅ ⋅ 1+0im"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"4×4 Matrix{ComplexF64}:\n",
" 0.809017+0.0im 0.0+0.0im … 0.0+0.0im\n",
" 0.0+0.0im 0.809017+0.0im 0.0+0.587785im\n",
" 0.0+0.587785im 0.0+0.0im 0.0+0.0im\n",
" 0.0+0.0im 0.0+0.587785im 0.809017+0.0im"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"display(pure_state(2,0))\n",
"display(Ik(4))\n",
"display(rot(kron(σx,I), pi/5))"
]
},
{
"cell_type": "markdown",
"id": "221b0d6f",
"metadata": {},
"source": [
"## Evolution due to a random observable\n",
"\n",
"We take a random observable $H$ and evolve a random state $\\ket{r}$ over time\n",
"using the unitary operation $\\ket{r(t)} = e^{i2\\pi Ht}\\ket{r}$. Then we compare the result state to the\n",
"original random state as a function of time using the dot product of the two\n",
"states $\\braket{r(t)|r}$. We use $2\\pi$ as a convenience so the H makes sense as a spectrum."
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "23104103",
"metadata": {},
"outputs": [
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" 421.148,650.281 421.351,644.307 421.555,638.708 421.759,633.495 421.963,628.677 422.166,624.262 422.37,620.258 422.574,616.672 422.778,613.508 422.981,610.773 \n",
" 423.185,608.47 423.389,606.602 423.593,605.173 423.796,604.184 424,603.637 424.204,603.531 424.408,603.867 424.611,604.645 424.815,605.863 425.019,607.518 \n",
" 425.223,609.61 425.426,612.134 425.63,615.088 425.834,618.468 426.038,622.269 426.241,626.487 426.445,631.116 426.649,636.151 426.853,641.587 427.056,647.417 \n",
" 427.26,653.634 427.464,660.232 427.668,667.203 427.871,674.541 428.075,682.237 428.279,690.284 428.483,698.673 428.687,707.395 428.89,716.443 429.094,725.807 \n",
" 429.298,735.478 429.502,745.446 429.705,755.701 429.909,766.234 430.113,777.034 430.317,788.091 430.52,799.394 430.724,810.931 430.928,822.692 431.132,834.665 \n",
" 431.335,846.838 431.539,859.198 431.743,871.733 431.947,884.429 432.15,897.275 432.354,910.256 432.558,923.358 432.762,936.566 432.965,949.867 433.169,963.245 \n",
" 433.373,976.684 433.577,990.169 433.78,1003.68 433.984,1017.21 434.188,1030.74 434.392,1044.24 434.595,1057.7 434.799,1071.11 435.003,1084.44 435.207,1097.68 \n",
" 435.41,1110.8 435.614,1123.79 435.818,1136.63 436.022,1149.3 436.225,1161.77 436.429,1174.03 436.633,1186.06 436.837,1197.83 437.041,1209.33 437.244,1220.52 \n",
" 437.448,1231.4 437.652,1241.94 437.856,1252.12 438.059,1261.92 438.263,1271.31 438.467,1280.28 438.671,1288.81 438.874,1296.87 439.078,1304.44 439.282,1311.51 \n",
" 439.486,1318.05 439.689,1324.05 439.893,1329.49 440.097,1334.34 440.301,1338.6 440.504,1342.24 440.708,1345.25 440.912,1347.61 441.116,1349.32 441.319,1350.35 \n",
" 441.523,1350.7 441.727,1350.35 441.931,1349.29 442.134,1347.51 442.338,1345.01 442.542,1341.79 442.746,1337.82 442.949,1333.12 443.153,1327.67 443.357,1321.48 \n",
" 443.561,1314.55 443.764,1306.87 443.968,1298.46 444.172,1289.32 444.376,1279.44 444.579,1268.85 444.783,1257.55 444.987,1245.56 445.191,1232.88 445.395,1219.53 \n",
" 445.598,1205.52 445.802,1190.88 446.006,1175.62 446.21,1159.77 446.413,1143.34 446.617,1126.37 446.821,1108.87 447.025,1090.87 447.228,1072.41 447.432,1053.5 \n",
" 447.636,1034.2 447.84,1014.51 448.043,994.485 448.247,974.153 448.451,953.55 448.655,932.713 448.858,911.68 449.062,890.489 449.266,869.18 449.47,847.791 \n",
" 449.673,826.365 449.877,804.941 450.081,783.562 450.285,762.268 450.488,741.101 450.692,720.103 450.896,699.317 451.1,678.782 451.303,658.541 451.507,638.635 \n",
" 451.711,619.104 451.915,599.988 452.118,581.326 452.322,563.157 452.526,545.517 452.73,528.443 452.933,511.971 453.137,496.135 453.341,480.967 453.545,466.498 \n",
" 453.749,452.759 453.952,439.777 454.156,427.579 454.36,416.19 454.564,405.632 454.767,395.927 454.971,387.093 455.175,379.148 455.379,372.105 455.582,365.978 \n",
" 455.786,360.776 455.99,356.509 456.194,353.181 456.397,350.797 456.601,349.357 456.805,348.86 457.009,349.303 457.212,350.679 457.416,352.981 457.62,356.197 \n",
" 457.824,360.315 458.027,365.319 458.231,371.193 458.435,377.915 458.639,385.464 458.842,393.815 459.046,402.944 459.25,412.82 459.454,423.415 459.657,434.695 \n",
" 459.861,446.627 460.065,459.176 460.269,472.304 460.472,485.973 460.676,500.141 460.88,514.769 461.084,529.812 461.287,545.228 461.491,560.972 461.695,576.998 \n",
" 461.899,593.259 462.103,609.709 462.306,626.301 462.51,642.987 462.714,659.718 462.918,676.447 463.121,693.125 463.325,709.705 463.529,726.14 463.733,742.382 \n",
" 463.936,758.385 464.14,774.103 464.344,789.49 464.548,804.503 464.751,819.1 464.955,833.237 465.159,846.874 465.363,859.973 465.566,872.496 465.77,884.406 \n",
" 465.974,895.669 466.178,906.254 466.381,916.128 466.585,925.264 466.789,933.635 466.993,941.217 467.196,947.986 467.4,953.923 467.604,959.011 467.808,963.233 \n",
" 468.011,966.577 468.215,969.032 468.419,970.589 468.623,971.243 468.826,970.99 469.03,969.829 469.234,967.762 469.438,964.793 469.641,960.927 469.845,956.175 \n",
" 470.049,950.546 470.253,944.054 470.457,936.714 470.66,928.546 470.864,919.568 471.068,909.803 471.272,899.275 471.475,888.01 471.679,876.036 471.883,863.383 \n",
" 472.087,850.083 472.29,836.168 472.494,821.673 472.698,806.635 472.902,791.09 473.105,775.078 473.309,758.638 473.513,741.81 473.717,724.636 473.92,707.158 \n",
" 474.124,689.42 474.328,671.465 474.532,653.336 474.735,635.077 474.939,616.734 475.143,598.349 475.347,579.968 475.55,561.634 475.754,543.391 475.958,525.283 \n",
" 476.162,507.351 476.365,489.639 476.569,472.187 476.773,455.037 476.977,438.227 477.18,421.796 477.384,405.782 477.588,390.22 477.792,375.147 477.995,360.595 \n",
" 478.199,346.596 478.403,333.181 478.607,320.379 478.811,308.218 479.014,296.722 479.218,285.916 479.422,275.823 479.626,266.462 479.829,257.852 480.033,250.01 \n",
" 480.237,242.95 480.441,236.685 480.644,231.227 480.848,226.584 481.052,222.764 481.256,219.771 481.459,217.61 481.663,216.281 481.867,215.785 482.071,216.12 \n",
" 482.274,217.281 482.478,219.262 482.682,222.058 482.886,225.657 483.089,230.051 483.293,235.227 483.497,241.171 483.701,247.868 483.904,255.302 484.108,263.455 \n",
" 484.312,272.308 484.516,281.841 484.719,292.033 484.923,302.861 485.127,314.303 485.331,326.334 485.534,338.929 485.738,352.062 485.942,365.708 486.146,379.84 \n",
" 486.349,394.429 486.553,409.449 486.757,424.872 486.961,440.668 487.165,456.809 487.368,473.266 487.572,490.012 487.776,507.016 487.98,524.25 488.183,541.685 \n",
" 488.387,559.293 488.591,577.046 488.795,594.916 488.998,612.874 489.202,630.895 489.406,648.951 489.61,667.016 489.813,685.065 490.017,703.071 490.221,721.011 \n",
" 490.425,738.861 490.628,756.598 490.832,774.198 491.036,791.64 491.24,808.904 491.443,825.967 491.647,842.812 491.851,859.419 492.055,875.769 492.258,891.847 \n",
" 492.462,907.634 492.666,923.116 492.87,938.276 493.073,953.102 493.277,967.58 493.481,981.696 493.685,995.439 493.888,1008.8 494.092,1021.76 494.296,1034.32 \n",
" 494.5,1046.47 494.704,1058.19 494.907,1069.48 495.111,1080.34 495.315,1090.75 495.519,1100.71 495.722,1110.22 495.926,1119.27 496.13,1127.85 496.334,1135.96 \n",
" 496.537,1143.6 496.741,1150.77 496.945,1157.46 497.149,1163.68 497.352,1169.41 497.556,1174.66 497.76,1179.43 497.964,1183.71 498.167,1187.52 498.371,1190.84 \n",
" 498.575,1193.68 498.779,1196.04 498.982,1197.92 499.186,1199.33 499.39,1200.26 499.594,1200.72 499.797,1200.71 500.001,1200.24 500.205,1199.3 500.409,1197.91 \n",
" 500.612,1196.06 500.816,1193.76 501.02,1191.02 501.224,1187.83 501.427,1184.22 501.631,1180.18 501.835,1175.72 502.039,1170.84 502.242,1165.56 502.446,1159.88 \n",
" 502.65,1153.81 502.854,1147.36 503.058,1140.54 503.261,1133.36 503.465,1125.83 503.669,1117.95 503.873,1109.75 504.076,1101.23 504.28,1092.41 504.484,1083.29 \n",
" 504.688,1073.9 504.891,1064.24 505.095,1054.33 505.299,1044.19 505.503,1033.84 505.706,1023.28 505.91,1012.54 506.114,1001.63 506.318,990.575 506.521,979.39 \n",
" 506.725,968.095 506.929,956.711 507.133,945.256 507.336,933.753 507.54,922.222 507.744,910.684 507.948,899.162 508.151,887.679 508.355,876.256 508.559,864.918 \n",
" 508.763,853.686 508.966,842.585 509.17,831.638 509.374,820.869 509.578,810.301 509.781,799.958 509.985,789.864 510.189,780.043 510.393,770.517 510.596,761.31 \n",
" 510.8,752.445 511.004,743.945 511.208,735.83 511.412,728.124 511.615,720.847 511.819,714.019 512.023,707.66 512.227,701.79 512.43,696.426 512.634,691.587 \n",
" 512.838,687.287 513.042,683.543 513.245,680.369 513.449,677.778 513.653,675.782 513.857,674.393 514.06,673.618 514.264,673.467 514.468,673.947 514.672,675.062 \n",
" 514.875,676.816 515.079,679.213 515.283,682.251 515.487,685.931 515.69,690.25 515.894,695.203 516.098,700.785 516.302,706.989 516.505,713.805 516.709,721.222 \n",
" 516.913,729.228 517.117,737.808 517.32,746.947 517.524,756.626 517.728,766.826 517.932,777.527 518.135,788.705 518.339,800.337 518.543,812.396 518.747,824.856 \n",
" 518.95,837.689 519.154,850.863 519.358,864.348 519.562,878.111 519.766,892.119 519.969,906.336 520.173,920.727 520.377,935.255 520.581,949.882 520.784,964.57 \n",
" 520.988,979.279 521.192,993.97 521.396,1008.6 521.599,1023.14 521.803,1037.53 522.007,1051.74 522.211,1065.73 522.414,1079.46 522.618,1092.88 522.822,1105.96 \n",
" 523.026,1118.65 523.229,1130.92 523.433,1142.73 523.637,1154.03 523.841,1164.79 524.044,1174.97 524.248,1184.55 524.452,1193.47 524.656,1201.72 524.859,1209.26 \n",
" 525.063,1216.05 525.267,1222.07 525.471,1227.3 525.674,1231.7 525.878,1235.25 526.082,1237.94 526.286,1239.74 526.489,1240.63 526.693,1240.6 526.897,1239.64 \n",
" 527.101,1237.73 527.304,1234.87 527.508,1231.04 527.712,1226.25 527.916,1220.49 528.12,1213.77 528.323,1206.08 528.527,1197.44 528.731,1187.85 528.935,1177.31 \n",
" 529.138,1165.85 529.342,1153.47 529.546,1140.2 529.75,1126.06 529.953,1111.06 530.157,1095.23 530.361,1078.6 530.565,1061.19 530.768,1043.04 530.972,1024.18 \n",
" 531.176,1004.64 531.38,984.461 531.583,963.679 531.787,942.333 531.991,920.466 532.195,898.119 532.398,875.336 532.602,852.163 532.806,828.645 533.01,804.831 \n",
" 533.213,780.768 533.417,756.504 533.621,732.09 533.825,707.575 534.028,683.01 534.232,658.444 534.436,633.929 534.64,609.514 534.843,585.251 535.047,561.19 \n",
" 535.251,537.379 535.455,513.868 535.658,490.705 535.862,467.938 536.066,445.614 536.27,423.777 536.474,402.472 536.677,381.742 536.881,361.629 537.085,342.172 \n",
" 537.289,323.411 537.492,305.381 537.696,288.118 537.9,271.655 538.104,256.023 538.307,241.251 538.511,227.366 538.715,214.392 538.919,202.353 539.122,191.267 \n",
" 539.326,181.154 539.53,172.028 539.734,163.903 539.937,156.789 540.141,150.694 540.345,145.625 540.549,141.585 540.752,138.573 540.956,136.59 541.16,135.63 \n",
" 541.364,135.688 541.567,136.755 541.771,138.819 541.975,141.868 542.179,145.885 542.382,150.853 542.586,156.752 542.79,163.56 542.994,171.253 543.197,179.805 \n",
" 543.401,189.189 543.605,199.376 543.809,210.333 544.012,222.03 544.216,234.431 544.42,247.502 544.624,261.205 544.828,275.504 545.031,290.36 545.235,305.732 \n",
" 545.439,321.581 545.643,337.865 545.846,354.543 546.05,371.572 546.254,388.91 546.458,406.515 546.661,424.344 546.865,442.353 547.069,460.5 547.273,478.743 \n",
" 547.476,497.04 547.68,515.348 547.884,533.627 548.088,551.837 548.291,569.937 548.495,587.888 548.699,605.653 548.903,623.195 549.106,640.477 549.31,657.466 \n",
" 549.514,674.127 549.718,690.428 549.921,706.339 550.125,721.831 550.329,736.875 550.533,751.446 550.736,765.518 550.94,779.069 551.144,792.077 551.348,804.523 \n",
" 551.551,816.388 551.755,827.657 551.959,838.314 552.163,848.348 552.366,857.746 552.57,866.501 552.774,874.604 552.978,882.05 553.182,888.834 553.385,894.954 \n",
" 553.589,900.41 553.793,905.203 553.997,909.334 554.2,912.808 554.404,915.632 554.608,917.811 554.812,919.354 555.015,920.271 555.219,920.574 555.423,920.275 \n",
" 555.627,919.387 555.83,917.925 556.034,915.905 556.238,913.344 556.442,910.26 556.645,906.672 556.849,902.598 557.053,898.06 557.257,893.077 557.46,887.673 \n",
" 557.664,881.867 557.868,875.684 558.072,869.146 558.275,862.276 558.479,855.097 558.683,847.634 558.887,839.911 559.09,831.95 559.294,823.777 559.498,815.414 \n",
" 559.702,806.887 559.905,798.217 560.109,789.43 560.313,780.548 560.517,771.594 560.72,762.591 560.924,753.561 561.128,744.526 561.332,735.507 561.536,726.525 \n",
" 561.739,717.601 561.943,708.754 562.147,700.005 562.351,691.371 562.554,682.871 562.758,674.523 562.962,666.343 563.166,658.348 563.369,650.555 563.573,642.977 \n",
" 563.777,635.63 563.981,628.527 564.184,621.681 564.388,615.106 564.592,608.813 564.796,602.814 564.999,597.119 565.203,591.739 565.407,586.684 565.611,581.961 \n",
" 565.814,577.58 566.018,573.549 566.222,569.876 566.426,566.566 566.629,563.627 566.833,561.064 567.037,558.883 567.241,557.09 567.444,555.687 567.648,554.68 \n",
" 567.852,554.073 568.056,553.868 568.259,554.069 568.463,554.679 568.667,555.698 568.871,557.13 569.074,558.976 569.278,561.237 569.482,563.914 569.686,567.007 \n",
" 569.89,570.516 570.093,574.442 570.297,578.784 570.501,583.54 570.705,588.711 570.908,594.293 571.112,600.287 571.316,606.688 571.52,613.495 571.723,620.705 \n",
" 571.927,628.314 572.131,636.319 572.335,644.715 572.538,653.497 572.742,662.662 572.946,672.203 573.15,682.114 573.353,692.389 573.557,703.021 573.761,714.003 \n",
" 573.965,725.325 574.168,736.981 574.372,748.96 574.576,761.252 574.78,773.848 574.983,786.736 575.187,799.905 575.391,813.342 575.595,827.035 575.798,840.969 \n",
" 576.002,855.131 576.206,869.505 576.41,884.076 576.613,898.828 576.817,913.742 577.021,928.802 577.225,943.99 577.429,959.285 577.632,974.668 577.836,990.12 \n",
" 578.04,1005.62 578.244,1021.14 578.447,1036.67 578.651,1052.17 578.855,1067.63 579.059,1083.03 579.262,1098.33 579.466,1113.51 579.67,1128.56 579.874,1143.43 \n",
" 580.077,1158.11 580.281,1172.57 580.485,1186.79 580.689,1200.73 580.892,1214.37 581.096,1227.68 581.3,1240.65 581.504,1253.23 581.707,1265.4 581.911,1277.14 \n",
" 582.115,1288.42 582.319,1299.21 582.522,1309.5 582.726,1319.24 582.93,1328.43 583.134,1337.03 583.337,1345.03 583.541,1352.39 583.745,1359.11 583.949,1365.15 \n",
" 584.152,1370.5 584.356,1375.14 584.56,1379.05 584.764,1382.22 584.967,1384.63 585.171,1386.26 585.375,1387.11 585.579,1387.16 585.783,1386.41 585.986,1384.84 \n",
" 586.19,1382.45 586.394,1379.24 586.598,1375.2 586.801,1370.33 587.005,1364.63 587.209,1358.1 587.413,1350.75 587.616,1342.59 587.82,1333.61 588.024,1323.83 \n",
" 588.228,1313.27 588.431,1301.93 588.635,1289.83 588.839,1276.98 589.043,1263.41 589.246,1249.14 589.45,1234.18 589.654,1218.57 589.858,1202.33 590.061,1185.48 \n",
" 590.265,1168.05 590.469,1150.08 590.673,1131.6 590.876,1112.64 591.08,1093.24 591.284,1073.42 591.488,1053.24 591.691,1032.73 591.895,1011.92 592.099,990.864 \n",
" 592.303,969.598 592.506,948.163 592.71,926.605 592.914,904.966 593.118,883.289 593.321,861.621 593.525,840.004 593.729,818.484 593.933,797.106 594.137,775.914 \n",
" 594.34,754.952 594.544,734.265 594.748,713.896 594.952,693.887 595.155,674.283 595.359,655.122 595.563,636.448 595.767,618.297 595.97,600.711 596.174,583.724 \n",
" 596.378,567.373 596.582,551.693 596.785,536.715 596.989,522.472 597.193,508.992 597.397,496.303 597.6,484.43 597.804,473.396 598.008,463.225 598.212,453.933 \n",
" 598.415,445.54 598.619,438.06 598.823,431.504 599.027,425.885 599.23,421.209 599.434,417.482 599.638,414.708 599.842,412.886 600.045,412.015 600.249,412.091 \n",
" 600.453,413.107 600.657,415.054 600.86,417.921 601.064,421.693 601.268,426.354 601.472,431.885 601.675,438.267 601.879,445.475 602.083,453.485 602.287,462.269 \n",
" 602.491,471.798 602.694,482.041 602.898,492.964 603.102,504.532 603.306,516.71 603.509,529.459 603.713,542.739 603.917,556.509 604.121,570.728 604.324,585.351 \n",
" 604.528,600.335 604.732,615.635 604.936,631.203 605.139,646.994 605.343,662.961 605.547,679.055 605.751,695.23 605.954,711.436 606.158,727.627 606.362,743.754 \n",
" 606.566,759.77 606.769,775.627 606.973,791.279 607.177,806.681 607.381,821.786 607.584,836.551 607.788,850.933 607.992,864.888 608.196,878.377 608.399,891.36 \n",
" 608.603,903.799 608.807,915.656 609.011,926.899 609.214,937.492 609.418,947.406 609.622,956.61 609.826,965.077 610.029,972.782 610.233,979.702 610.437,985.816 \n",
" 610.641,991.105 610.845,995.552 611.048,999.142 611.252,1001.87 611.456,1003.71 611.66,1004.67 611.863,1004.74 612.067,1003.92 612.271,1002.21 612.475,999.604 \n",
" 612.678,996.116 612.882,991.748 613.086,986.511 613.29,980.416 613.493,973.477 613.697,965.709 613.901,957.13 614.105,947.761 614.308,937.622 614.512,926.738 \n",
" 614.716,915.134 614.92,902.838 615.123,889.879 615.327,876.286 615.531,862.093 615.735,847.333 615.938,832.039 616.142,816.249 616.346,799.999 616.55,783.326 \n",
" 616.753,766.27 616.957,748.87 617.161,731.167 617.365,713.2 617.568,695.012 617.772,676.642 617.976,658.134 618.18,639.528 618.383,620.867 618.587,602.191 \n",
" 618.791,583.542 618.995,564.962 619.199,546.489 619.402,528.166 619.606,510.03 619.81,492.12 620.014,474.474 620.217,457.129 620.421,440.121 620.625,423.485 \n",
" 620.829,407.253 621.032,391.46 621.236,376.135 621.44,361.309 621.644,347.01 621.847,333.265 622.051,320.099 622.255,307.537 622.459,295.601 622.662,284.311 \n",
" 622.866,273.687 623.07,263.746 623.274,254.505 623.477,245.977 623.681,238.174 623.885,231.108 624.089,224.788 624.292,219.221 624.496,214.413 624.7,210.367 \n",
" 624.904,207.088 625.107,204.574 625.311,202.827 625.515,201.843 625.719,201.62 625.922,202.151 626.126,203.431 626.33,205.451 626.534,208.202 626.737,211.674 \n",
" 626.941,215.854 627.145,220.731 627.349,226.291 627.553,232.517 627.756,239.394 627.96,246.906 628.164,255.034 628.368,263.76 628.571,273.065 628.775,282.928 \n",
" 628.979,293.329 629.183,304.246 629.386,315.659 629.59,327.545 629.794,339.881 629.998,352.646 630.201,365.815 630.405,379.365 630.609,393.274 630.813,407.518 \n",
" 631.016,422.073 631.22,436.916 631.424,452.023 631.628,467.372 631.831,482.938 632.035,498.699 632.239,514.632 632.443,530.715 632.646,546.925 632.85,563.24 \n",
" 633.054,579.639 633.258,596.1 633.461,612.603 633.665,629.126 633.869,645.651 634.073,662.156 634.276,678.624 634.48,695.034 634.684,711.369 634.888,727.612 \n",
" 635.091,743.744 635.295,759.748 635.499,775.609 635.703,791.31 635.907,806.835 636.11,822.17 636.314,837.3 636.518,852.211 636.722,866.888 636.925,881.32 \n",
" 637.129,895.491 637.333,909.391 637.537,923.007 637.74,936.327 637.944,949.34 638.148,962.035 638.352,974.401 638.555,986.428 638.759,998.106 638.963,1009.43 \n",
" 639.167,1020.38 639.37,1030.95 639.574,1041.14 639.778,1050.94 639.982,1060.33 640.185,1069.31 640.389,1077.88 640.593,1086.02 640.797,1093.73 641,1101 \n",
" 641.204,1107.83 641.408,1114.21 641.612,1120.13 641.815,1125.6 642.019,1130.59 642.223,1135.12 642.427,1139.17 642.63,1142.75 642.834,1145.84 643.038,1148.45 \n",
" 643.242,1150.58 643.445,1152.21 643.649,1153.36 643.853,1154.01 644.057,1154.18 644.261,1153.85 644.464,1153.03 644.668,1151.72 644.872,1149.92 645.076,1147.64 \n",
" 645.279,1144.88 645.483,1141.64 645.687,1137.93 645.891,1133.75 646.094,1129.11 646.298,1124.01 646.502,1118.47 646.706,1112.49 646.909,1106.08 647.113,1099.25 \n",
" 647.317,1092.01 647.521,1084.38 647.724,1076.37 647.928,1067.98 648.132,1059.24 648.336,1050.17 648.539,1040.76 648.743,1031.06 648.947,1021.06 649.151,1010.8 \n",
" 649.354,1000.28 649.558,989.542 649.762,978.592 649.966,967.457 650.169,956.159 650.373,944.721 650.577,933.169 650.781,921.526 650.984,909.818 651.188,898.072 \n",
" 651.392,886.313 651.596,874.568 651.799,862.865 652.003,851.232 652.207,839.696 652.411,828.285 652.615,817.028 652.818,805.953 653.022,795.089 653.226,784.464 \n",
" 653.43,774.105 653.633,764.042 653.837,754.302 654.041,744.912 654.245,735.9 654.448,727.291 654.652,719.113 654.856,711.389 655.06,704.144 655.263,697.403 \n",
" 655.467,691.188 655.671,685.52 655.875,680.421 656.078,675.91 656.282,672.006 656.486,668.725 656.69,666.084 656.893,664.097 657.097,662.777 657.301,662.136 \n",
" 657.505,662.182 657.708,662.925 657.912,664.372 658.116,666.526 658.32,669.391 658.523,672.968 658.727,677.257 658.931,682.255 659.135,687.958 659.338,694.359 \n",
" 659.542,701.451 659.746,709.224 659.95,717.665 660.154,726.76 660.357,736.495 660.561,746.85 660.765,757.808 660.969,769.345 661.172,781.44 661.376,794.067 \n",
" 661.58,807.199 661.784,820.809 661.987,834.866 662.191,849.338 662.395,864.194 662.599,879.398 662.802,894.915 663.006,910.708 663.21,926.738 663.414,942.968 \n",
" 663.617,959.355 663.821,975.86 664.025,992.44 664.229,1009.05 664.432,1025.66 664.636,1042.21 664.84,1058.66 665.044,1074.97 665.247,1091.09 665.451,1106.98 \n",
" 665.655,1122.6 665.859,1137.9 666.062,1152.84 666.266,1167.38 666.47,1181.46 666.674,1195.06 666.877,1208.13 667.081,1220.63 667.285,1232.52 667.489,1243.77 \n",
" 667.692,1254.33 667.896,1264.17 668.1,1273.27 668.304,1281.58 668.508,1289.07 668.711,1295.73 668.915,1301.52 669.119,1306.42 669.323,1310.4 669.526,1313.45 \n",
" 669.73,1315.55 669.934,1316.68 670.138,1316.82 670.341,1315.97 670.545,1314.12 670.749,1311.26 670.953,1307.39 671.156,1302.51 671.36,1296.61 671.564,1289.7 \n",
" 671.768,1281.78 671.971,1272.87 672.175,1262.98 672.379,1252.11 672.583,1240.29 672.786,1227.53 672.99,1213.86 673.194,1199.29 673.398,1183.85 673.601,1167.57 \n",
" 673.805,1150.48 674.009,1132.6 674.213,1113.98 674.416,1094.65 674.62,1074.64 674.824,1053.99 675.028,1032.75 675.231,1010.95 675.435,988.645 675.639,965.871 \n",
" 675.843,942.675 676.046,919.105 676.25,895.207 676.454,871.031 676.658,846.626 676.862,822.041 677.065,797.325 677.269,772.53 677.473,747.705 677.677,722.901 \n",
" 677.88,698.168 678.084,673.556 678.288,649.114 678.492,624.892 678.695,600.939 678.899,577.301 679.103,554.026 679.307,531.159 679.51,508.746 679.714,486.829 \n",
" 679.918,465.45 680.122,444.651 680.325,424.47 680.529,404.945 680.733,386.112 680.937,368.004 681.14,350.654 681.344,334.091 681.548,318.344 681.752,303.439 \n",
" 681.955,289.399 682.159,276.247 682.363,264.001 682.567,252.679 682.77,242.295 682.974,232.862 683.178,224.39 683.382,216.887 683.585,210.358 683.789,204.807 \n",
" 683.993,200.234 684.197,196.637 684.4,194.014 684.604,192.357 684.808,191.659 685.012,191.908 685.216,193.093 685.419,195.199 685.623,198.208 685.827,202.102 \n",
" 686.031,206.861 686.234,212.462 686.438,218.881 686.642,226.092 686.846,234.068 687.049,242.779 687.253,252.196 687.457,262.287 687.661,273.02 687.864,284.36 \n",
" 688.068,296.272 688.272,308.722 688.476,321.672 688.679,335.085 688.883,348.923 689.087,363.149 689.291,377.723 689.494,392.607 689.698,407.762 689.902,423.148 \n",
" 690.106,438.727 690.309,454.459 690.513,470.307 690.717,486.232 690.921,502.196 691.124,518.162 691.328,534.093 691.532,549.954 691.736,565.709 691.939,581.323 \n",
" 692.143,596.764 692.347,612 692.551,626.999 692.754,641.73 692.958,656.166 693.162,670.278 693.366,684.04 693.57,697.427 693.773,710.415 693.977,722.982 \n",
" 694.181,735.108 694.385,746.773 694.588,757.959 694.792,768.65 694.996,778.83 695.2,788.488 695.403,797.61 695.607,806.186 695.811,814.209 696.015,821.67 \n",
" 696.218,828.563 696.422,834.884 696.626,840.631 696.83,845.802 697.033,850.396 697.237,854.414 697.441,857.86 697.645,860.737 697.848,863.05 698.052,864.805 \n",
" 698.256,866.009 698.46,866.671 698.663,866.799 698.867,866.406 699.071,865.501 699.275,864.096 699.478,862.206 699.682,859.843 699.886,857.023 700.09,853.76 \n",
" 700.293,850.069 700.497,845.968 700.701,841.474 700.905,836.602 701.108,831.371 701.312,825.799 701.516,819.904 701.72,813.705 701.924,807.22 702.127,800.467 \n",
" 702.331,793.467 702.535,786.237 702.739,778.797 702.942,771.165 703.146,763.362 703.35,755.404 703.554,747.311 703.757,739.102 703.961,730.794 704.165,722.407 \n",
" 704.369,713.957 704.572,705.462 704.776,696.941 704.98,688.409 705.184,679.885 705.387,671.383 705.591,662.921 705.795,654.514 705.999,646.179 706.202,637.929 \n",
" 706.406,629.78 706.61,621.747 706.814,613.844 707.017,606.085 707.221,598.482 707.425,591.051 707.629,583.803 707.832,576.751 708.036,569.907 708.24,563.284 \n",
" 708.444,556.893 708.647,550.746 708.851,544.853 709.055,539.227 709.259,533.877 709.462,528.814 709.666,524.047 709.87,519.588 710.074,515.446 710.278,511.63 \n",
" 710.481,508.149 710.685,505.013 710.889,502.23 711.093,499.809 711.296,497.758 711.5,496.085 711.704,494.799 711.908,493.906 712.111,493.415 712.315,493.332 \n",
" 712.519,493.664 712.723,494.417 712.926,495.599 713.13,497.215 713.334,499.27 713.538,501.77 713.741,504.721 713.945,508.125 714.149,511.988 714.353,516.313 \n",
" 714.556,521.103 714.76,526.361 714.964,532.09 715.168,538.29 715.371,544.963 715.575,552.11 715.779,559.73 715.983,567.823 716.186,576.387 716.39,585.419 \n",
" 716.594,594.918 716.798,604.878 717.001,615.296 717.205,626.167 717.409,637.484 717.613,649.24 717.816,661.427 718.02,674.037 718.224,687.059 718.428,700.483 \n",
" 718.632,714.298 718.835,728.49 719.039,743.046 719.243,757.951 719.447,773.19 719.65,788.746 719.854,804.601 720.058,820.737 720.262,837.135 720.465,853.774 \n",
" 720.669,870.631 720.873,887.686 721.077,904.914 721.28,922.291 721.484,939.793 721.688,957.393 721.892,975.065 722.095,992.781 722.299,1010.51 722.503,1028.23 \n",
" 722.707,1045.91 722.91,1063.51 723.114,1081.02 723.318,1098.39 723.522,1115.59 723.725,1132.6 723.929,1149.38 724.133,1165.9 724.337,1182.12 724.54,1198.03 \n",
" 724.744,1213.57 724.948,1228.73 725.152,1243.47 725.355,1257.76 725.559,1271.57 725.763,1284.86 725.967,1297.61 726.17,1309.79 726.374,1321.36 726.578,1332.31 \n",
" 726.782,1342.61 726.986,1352.22 727.189,1361.13 727.393,1369.3 727.597,1376.73 727.801,1383.38 728.004,1389.24 728.208,1394.29 728.412,1398.51 728.616,1401.88 \n",
" 728.819,1404.4 729.023,1406.05 729.227,1406.82 729.431,1406.7 729.634,1405.69 729.838,1403.78 730.042,1400.98 730.246,1397.26 730.449,1392.65 730.653,1387.15 \n",
" 730.857,1380.75 731.061,1373.46 731.264,1365.31 731.468,1356.29 731.672,1346.42 731.876,1335.72 732.079,1324.2 732.283,1311.89 732.487,1298.81 732.691,1284.97 \n",
" 732.894,1270.41 733.098,1255.15 733.302,1239.23 733.506,1222.67 733.709,1205.5 733.913,1187.76 734.117,1169.49 734.321,1150.73 734.524,1131.5 734.728,1111.86 \n",
" 734.932,1091.83 735.136,1071.47 735.34,1050.82 735.543,1029.93 735.747,1008.82 735.951,987.562 736.155,966.188 736.358,944.748 736.562,923.289 736.766,901.857 \n",
" 736.97,880.5 737.173,859.263 737.377,838.194 737.581,817.339 737.785,796.744 737.988,776.455 738.192,756.515 738.396,736.968 738.6,717.859 738.803,699.228 \n",
" 739.007,681.116 739.211,663.563 739.415,646.607 739.618,630.284 739.822,614.629 740.026,599.677 740.23,585.457 740.433,572.001 740.637,559.335 740.841,547.486 \n",
" 741.045,536.477 741.248,526.329 741.452,517.062 741.656,508.693 741.86,501.236 742.063,494.703 742.267,489.105 742.471,484.447 742.675,480.737 742.879,477.975 \n",
" 743.082,476.162 743.286,475.295 743.49,475.369 743.694,476.376 743.897,478.307 744.101,481.149 744.305,484.887 744.509,489.505 744.712,494.982 744.916,501.297 \n",
" 745.12,508.426 745.324,516.343 745.527,525.02 745.731,534.427 745.935,544.531 746.139,555.301 746.342,566.699 746.546,578.689 746.75,591.233 746.954,604.29 \n",
" 747.157,617.819 747.361,631.778 747.565,646.124 747.769,660.812 747.972,675.798 748.176,691.035 748.38,706.477 748.584,722.078 748.787,737.79 748.991,753.566 \n",
" 749.195,769.359 749.399,785.122 749.602,800.807 749.806,816.37 750.01,831.762 750.214,846.939 750.417,861.857 750.621,876.471 750.825,890.738 751.029,904.617 \n",
" 751.233,918.066 751.436,931.047 751.64,943.521 751.844,955.452 752.048,966.805 752.251,977.547 752.455,987.646 752.659,997.073 752.863,1005.8 753.066,1013.8 \n",
" 753.27,1021.05 753.474,1027.53 753.678,1033.22 753.881,1038.09 754.085,1042.15 754.289,1045.37 754.493,1047.74 754.696,1049.25 754.9,1049.9 755.104,1049.68 \n",
" 755.308,1048.6 755.511,1046.64 755.715,1043.82 755.919,1040.15 756.123,1035.61 756.326,1030.23 756.53,1024.02 756.734,1016.99 756.938,1009.16 757.141,1000.54 \n",
" 757.345,991.145 757.549,981.007 757.753,970.145 757.956,958.583 758.16,946.346 758.364,933.463 758.568,919.962 758.771,905.873 758.975,891.228 759.179,876.058 \n",
" 759.383,860.398 759.587,844.282 759.79,827.746 759.994,810.825 760.198,793.556 760.402,775.976 760.605,758.123 760.809,740.035 761.013,721.751 761.217,703.308 \n",
" 761.42,684.745 761.624,666.1 761.828,647.411 762.032,628.717 762.235,610.055 762.439,591.462 762.643,572.974 762.847,554.628 763.05,536.459 763.254,518.501 \n",
" 763.458,500.789 763.662,483.355 763.865,466.23 764.069,449.446 764.273,433.032 764.477,417.018 764.68,401.43 764.884,386.294 765.088,371.636 765.292,357.479 \n",
" 765.495,343.845 765.699,330.755 765.903,318.228 766.107,306.284 766.31,294.937 766.514,284.205 766.718,274.099 766.922,264.634 767.125,255.819 767.329,247.664 \n",
" 767.533,240.177 767.737,233.366 767.941,227.235 768.144,221.788 768.348,217.028 768.552,212.956 768.756,209.573 768.959,206.877 769.163,204.866 769.367,203.536 \n",
" 769.571,202.883 769.774,202.9 769.978,203.582 770.182,204.921 770.386,206.907 770.589,209.531 770.793,212.783 770.997,216.651 771.201,221.124 771.404,226.188 \n",
" 771.608,231.831 771.812,238.038 772.016,244.795 772.219,252.087 772.423,259.898 772.627,268.212 772.831,277.013 773.034,286.284 773.238,296.009 773.442,306.17 \n",
" 773.646,316.75 773.849,327.731 774.053,339.095 774.257,350.824 774.461,362.901 774.664,375.308 774.868,388.027 775.072,401.039 775.276,414.326 775.479,427.872 \n",
" 775.683,441.657 775.887,455.664 776.091,469.875 776.295,484.274 776.498,498.841 776.702,513.561 776.906,528.415 777.11,543.387 777.313,558.46 777.517,573.616 \n",
" 777.721,588.841 777.925,604.116 778.128,619.426 778.332,634.754 778.536,650.085 778.74,665.402 778.943,680.691 779.147,695.934 779.351,711.118 779.555,726.226 \n",
" 779.758,741.243 779.962,756.154 780.166,770.944 780.37,785.599 780.573,800.103 780.777,814.442 780.981,828.6 781.185,842.565 781.388,856.32 781.592,869.852 \n",
" 781.796,883.147 782,896.191 782.203,908.969 782.407,921.467 782.611,933.673 782.815,945.571 783.018,957.149 783.222,968.394 783.426,979.292 783.63,989.83 \n",
" 783.833,999.995 784.037,1009.78 784.241,1019.16 784.445,1028.13 784.649,1036.68 784.852,1044.8 785.056,1052.48 785.26,1059.7 785.464,1066.46 785.667,1072.74 \n",
" 785.871,1078.54 786.075,1083.85 786.279,1088.65 786.482,1092.95 786.686,1096.73 786.89,1099.99 787.094,1102.72 787.297,1104.92 787.501,1106.58 787.705,1107.69 \n",
" 787.909,1108.27 788.112,1108.3 788.316,1107.78 788.52,1106.72 788.724,1105.11 788.927,1102.96 789.131,1100.27 789.335,1097.04 789.539,1093.28 789.742,1089 \n",
" 789.946,1084.2 790.15,1078.88 790.354,1073.07 790.557,1066.77 790.761,1059.99 790.965,1052.74 791.169,1045.04 791.372,1036.91 791.576,1028.36 791.78,1019.41 \n",
" 791.984,1010.08 792.187,1000.38 792.391,990.338 792.595,979.978 792.799,969.322 793.003,958.392 793.206,947.214 793.41,935.814 793.614,924.218 793.818,912.455 \n",
" 794.021,900.553 794.225,888.541 794.429,876.448 794.633,864.306 794.836,852.145 795.04,839.996 795.244,827.892 795.448,815.865 795.651,803.947 795.855,792.172 \n",
" 796.059,780.57 796.263,769.177 796.466,758.023 796.67,747.142 796.874,736.566 797.078,726.327 797.281,716.456 797.485,706.984 797.689,697.942 797.893,689.359 \n",
" 798.096,681.264 798.3,673.686 798.504,666.651 798.708,660.184 798.911,654.312 799.115,649.057 799.319,644.442 799.523,640.488 799.726,637.213 799.93,634.637 \n",
" 800.134,632.775 800.338,631.641 800.541,631.249 800.745,631.61 800.949,632.733 801.153,634.624 801.357,637.291 801.56,640.735 801.764,644.959 801.968,649.961 \n",
" 802.172,655.739 802.375,662.288 802.579,669.602 802.783,677.67 802.987,686.482 803.19,696.025 803.394,706.284 803.598,717.24 803.802,728.876 804.005,741.168 \n",
" 804.209,754.094 804.413,767.629 804.617,781.744 804.82,796.413 805.024,811.602 805.228,827.281 805.432,843.414 805.635,859.966 805.839,876.901 806.043,894.179 \n",
" 806.247,911.76 806.45,929.605 806.654,947.67 806.858,965.913 807.062,984.289 807.265,1002.76 807.469,1021.26 807.673,1039.77 807.877,1058.23 808.08,1076.59 \n",
" 808.284,1094.82 808.488,1112.85 808.692,1130.65 808.895,1148.16 809.099,1165.35 809.303,1182.17 809.507,1198.56 809.711,1214.5 809.914,1229.93 810.118,1244.8 \n",
" 810.322,1259.09 810.526,1272.75 810.729,1285.73 810.933,1298.01 811.137,1309.55 811.341,1320.31 811.544,1330.25 811.748,1339.36 811.952,1347.59 812.156,1354.93 \n",
" 812.359,1361.35 812.563,1366.82 812.767,1371.32 812.971,1374.84 813.174,1377.36 813.378,1378.86 813.582,1379.34 813.786,1378.79 813.989,1377.2 814.193,1374.56 \n",
" 814.397,1370.88 814.601,1366.16 814.804,1360.4 815.008,1353.6 815.212,1345.78 815.416,1336.95 815.619,1327.12 815.823,1316.3 816.027,1304.53 816.231,1291.8 \n",
" 816.434,1278.16 816.638,1263.63 816.842,1248.23 817.046,1231.99 817.249,1214.95 817.453,1197.13 817.657,1178.58 817.861,1159.33 818.065,1139.42 818.268,1118.88 \n",
" 818.472,1097.77 818.676,1076.13 818.88,1053.99 819.083,1031.41 819.287,1008.43 819.491,985.092 819.695,961.452 819.898,937.555 820.102,913.45 820.306,889.186 \n",
" 820.51,864.812 820.713,840.378 820.917,815.932 821.121,791.524 821.325,767.203 821.528,743.016 821.732,719.011 821.936,695.236 822.14,671.737 822.343,648.558 \n",
" 822.547,625.745 822.751,603.339 822.955,581.383 823.158,559.918 823.362,538.983 823.566,518.614 823.77,498.848 823.973,479.719 824.177,461.26 824.381,443.501 \n",
" 824.585,426.47 824.788,410.195 824.992,394.7 825.196,380.007 825.4,366.138 825.604,353.11 825.807,340.94 826.011,329.642 826.215,319.228 826.419,309.707 \n",
" 826.622,301.086 826.826,293.372 827.03,286.566 827.234,280.67 827.437,275.683 827.641,271.601 827.845,268.418 828.049,266.127 828.252,264.719 828.456,264.181 \n",
" 828.66,264.501 828.864,265.664 829.067,267.651 829.271,270.445 829.475,274.025 829.679,278.369 829.882,283.454 830.086,289.255 830.29,295.746 830.494,302.899 \n",
" 830.697,310.686 830.901,319.078 831.105,328.044 831.309,337.552 831.512,347.571 831.716,358.068 831.92,369.01 832.124,380.362 832.327,392.091 832.531,404.162 \n",
" 832.735,416.541 832.939,429.192 833.142,442.082 833.346,455.174 833.55,468.436 833.754,481.833 833.958,495.33 834.161,508.894 834.365,522.493 834.569,536.094 \n",
" 834.773,549.665 834.976,563.176 835.18,576.595 835.384,589.893 835.588,603.043 835.791,616.016 835.995,628.785 836.199,641.326 836.403,653.613 836.606,665.623 \n",
" 836.81,677.335 837.014,688.726 837.218,699.778 837.421,710.471 837.625,720.787 837.829,730.712 838.033,740.229 838.236,749.326 838.44,757.989 838.644,766.207 \n",
" 838.848,773.972 839.051,781.273 839.255,788.103 839.459,794.457 839.663,800.328 839.866,805.714 840.07,810.61 840.274,815.016 840.478,818.931 840.681,822.354 \n",
" 840.885,825.288 841.089,827.735 841.293,829.698 841.496,831.181 841.7,832.19 841.904,832.73 842.108,832.807 842.312,832.429 842.515,831.605 842.719,830.342 \n",
" 842.923,828.651 843.127,826.54 843.33,824.02 843.534,821.103 843.738,817.799 843.942,814.121 844.145,810.08 844.349,805.688 844.553,800.959 844.757,795.905 \n",
" 844.96,790.539 845.164,784.876 845.368,778.928 845.572,772.71 845.775,766.235 845.979,759.517 846.183,752.57 846.387,745.409 846.59,738.047 846.794,730.499 \n",
" 846.998,722.779 847.202,714.9 847.405,706.878 847.609,698.726 847.813,690.459 848.017,682.09 848.22,673.635 848.424,665.105 848.628,656.517 848.832,647.883 \n",
" 849.035,639.218 849.239,630.535 849.443,621.848 849.647,613.172 849.85,604.52 850.054,595.905 850.258,587.342 850.462,578.845 850.666,570.426 850.869,562.1 \n",
" 851.073,553.881 851.277,545.782 851.481,537.817 851.684,530.001 851.888,522.346 852.092,514.866 852.296,507.576 852.499,500.489 852.703,493.619 852.907,486.981 \n",
" 853.111,480.587 853.314,474.452 853.518,468.59 853.722,463.015 853.926,457.739 854.129,452.778 854.333,448.145 854.537,443.854 854.741,439.917 854.944,436.349 \n",
" 855.148,433.163 855.352,430.371 855.556,427.987 855.759,426.023 855.963,424.492 856.167,423.406 856.371,422.776 856.574,422.615 856.778,422.932 856.982,423.739 \n",
" 857.186,425.046 857.389,426.862 857.593,429.196 857.797,432.058 858.001,435.454 858.204,439.392 858.408,443.878 858.612,448.918 858.816,454.517 859.02,460.679 \n",
" 859.223,467.407 859.427,474.703 859.631,482.569 859.835,491.004 860.038,500.008 860.242,509.58 860.446,519.716 860.65,530.412 860.853,541.662 861.057,553.462 \n",
" 861.261,565.802 861.465,578.674 861.668,592.068 861.872,605.972 862.076,620.375 862.28,635.261 862.483,650.616 862.687,666.423 862.891,682.665 863.095,699.323 \n",
" 863.298,716.376 863.502,733.802 863.706,751.579 863.91,769.684 864.113,788.09 864.317,806.772 864.521,825.702 864.725,844.852 864.928,864.193 865.132,883.693 \n",
" 865.336,903.322 865.54,923.047 865.743,942.836 865.947,962.655 866.151,982.469 866.355,1002.24 866.558,1021.94 866.762,1041.53 866.966,1060.97 867.17,1080.23 \n",
" 867.374,1099.27 867.577,1118.05 867.781,1136.53 867.985,1154.69 868.189,1172.47 868.392,1189.86 868.596,1206.8 868.8,1223.27 869.004,1239.22 869.207,1254.64 \n",
" 869.411,1269.47 869.615,1283.69 869.819,1297.27 870.022,1310.18 870.226,1322.39 870.43,1333.86 870.634,1344.58 870.837,1354.51 871.041,1363.63 871.245,1371.93 \n",
" 871.449,1379.37 871.652,1385.94 871.856,1391.63 872.06,1396.41 872.264,1400.27 872.467,1403.21 872.671,1405.2 872.875,1406.25 873.079,1406.35 873.282,1405.49 \n",
" 873.486,1403.68 873.69,1400.91 873.894,1397.19 874.097,1392.52 874.301,1386.91 874.505,1380.38 874.709,1372.92 874.912,1364.57 875.116,1355.32 875.32,1345.21 \n",
" 875.524,1334.25 875.728,1322.47 875.931,1309.89 876.135,1296.54 876.339,1282.44 876.543,1267.63 876.746,1252.14 876.95,1236 877.154,1219.26 877.358,1201.94 \n",
" 877.561,1184.09 877.765,1165.74 877.969,1146.95 878.173,1127.74 878.376,1108.17 878.58,1088.28 878.784,1068.12 878.988,1047.73 879.191,1027.16 879.395,1006.46 \n",
" 879.599,985.666 879.803,964.84 880.006,944.025 880.21,923.269 880.414,902.621 880.618,882.129 880.821,861.84 881.025,841.8 881.229,822.056 881.433,802.654 \n",
" 881.636,783.638 881.84,765.052 882.044,746.938 882.248,729.336 882.451,712.288 882.655,695.831 882.859,680.002 883.063,664.835 883.266,650.365 883.47,636.622 \n",
" 883.674,623.636 883.878,611.434 884.082,600.042 884.285,589.482 884.489,579.776 884.693,570.942 884.897,562.996 885.1,555.953 885.304,549.822 885.508,544.615 \n",
" 885.712,540.336 885.915,536.99 886.119,534.579 886.323,533.101 886.527,532.553 886.73,532.93 886.934,534.222 887.138,536.419 887.342,539.508 887.545,543.472 \n",
" 887.749,548.295 887.953,553.957 888.157,560.434 888.36,567.702 888.564,575.736 888.768,584.506 888.972,593.982 889.175,604.133 889.379,614.923 889.583,626.319 \n",
" 889.787,638.283 889.99,650.777 890.194,663.76 890.398,677.193 890.602,691.034 890.805,705.239 891.009,719.766 891.213,734.57 891.417,749.605 891.62,764.828 \n",
" 891.824,780.192 892.028,795.651 892.232,811.16 892.436,826.673 892.639,842.144 892.843,857.528 893.047,872.78 893.251,887.855 893.454,902.71 893.658,917.303 \n",
" 893.862,931.59 894.066,945.532 894.269,959.088 894.473,972.219 894.677,984.888 894.881,997.058 895.084,1008.7 895.288,1019.77 895.492,1030.25 895.696,1040.09 \n",
" 895.899,1049.29 896.103,1057.8 896.307,1065.61 896.511,1072.69 896.714,1079.03 896.918,1084.6 897.122,1089.39 897.326,1093.38 897.529,1096.57 897.733,1098.94 \n",
" 897.937,1100.48 898.141,1101.19 898.344,1101.07 898.548,1100.11 898.752,1098.32 898.956,1095.7 899.159,1092.24 899.363,1087.97 899.567,1082.89 899.771,1077 \n",
" 899.975,1070.32 900.178,1062.87 900.382,1054.66 900.586,1045.71 900.79,1036.04 900.993,1025.67 901.197,1014.61 901.401,1002.91 901.605,990.571 901.808,977.631 \n",
" 902.012,964.115 902.216,950.052 902.42,935.471 902.623,920.403 902.827,904.878 903.031,888.93 903.235,872.59 903.438,855.892 903.642,838.869 903.846,821.555 \n",
" 904.05,803.984 904.253,786.191 904.457,768.21 904.661,750.076 904.865,731.823 905.068,713.485 905.272,695.096 905.476,676.69 905.68,658.3 905.883,639.958 \n",
" 906.087,621.698 906.291,603.551 906.495,585.548 906.698,567.718 906.902,550.092 907.106,532.699 907.31,515.565 907.513,498.718 907.717,482.184 907.921,465.988 \n",
" 908.125,450.153 908.329,434.702 908.532,419.658 908.736,405.04 908.94,390.868 909.144,377.161 909.347,363.935 909.551,351.207 909.755,338.992 909.959,327.302 \n",
" 910.162,316.152 910.366,305.552 910.57,295.513 910.774,286.043 910.977,277.151 911.181,268.844 911.385,261.127 911.589,254.006 911.792,247.485 911.996,241.565 \n",
" 912.2,236.25 912.404,231.539 912.607,227.433 912.811,223.932 913.015,221.032 913.219,218.733 913.422,217.03 913.626,215.92 913.83,215.398 914.034,215.458 \n",
" 914.237,216.095 914.441,217.302 914.645,219.072 914.849,221.396 915.052,224.267 915.256,227.677 915.46,231.615 915.664,236.073 915.867,241.041 916.071,246.508 \n",
" 916.275,252.464 916.479,258.897 916.683,265.798 916.886,273.154 917.09,280.953 917.294,289.184 917.498,297.835 917.701,306.894 917.905,316.347 918.109,326.183 \n",
" 918.313,336.389 918.516,346.951 918.72,357.856 918.924,369.092 919.128,380.645 919.331,392.501 919.535,404.646 919.739,417.068 919.943,429.751 920.146,442.683 \n",
" 920.35,455.848 920.554,469.232 920.758,482.821 920.961,496.6 921.165,510.555 921.369,524.669 921.573,538.928 921.776,553.317 921.98,567.82 922.184,582.421 \n",
" 922.388,597.104 922.591,611.853 922.795,626.652 922.999,641.484 923.203,656.333 923.406,671.181 923.61,686.011 923.814,700.806 924.018,715.549 924.221,730.222 \n",
" 924.425,744.807 924.629,759.286 924.833,773.64 925.037,787.852 925.24,801.904 925.444,815.776 925.648,829.45 925.852,842.907 926.055,856.13 926.259,869.099 \n",
" 926.463,881.796 926.667,894.202 926.87,906.299 927.074,918.068 927.278,929.492 927.482,940.553 927.685,951.233 927.889,961.515 928.093,971.382 928.297,980.817 \n",
" 928.5,989.804 928.704,998.328 928.908,1006.37 929.112,1013.92 929.315,1020.97 929.519,1027.49 929.723,1033.48 929.927,1038.93 930.13,1043.82 930.334,1048.15 \n",
" 930.538,1051.9 930.742,1055.07 930.945,1057.64 931.149,1059.63 931.353,1061.01 931.557,1061.78 931.76,1061.95 931.964,1061.51 932.168,1060.46 932.372,1058.8 \n",
" 932.575,1056.54 932.779,1053.67 932.983,1050.21 933.187,1046.15 933.391,1041.52 933.594,1036.31 933.798,1030.53 934.002,1024.21 934.206,1017.35 934.409,1009.97 \n",
" 934.613,1002.09 934.817,993.711 935.021,984.869 935.224,975.579 935.428,965.862 935.632,955.743 935.836,945.246 936.039,934.396 936.243,923.22 936.447,911.746 \n",
" 936.651,900.003 936.854,888.023 937.058,875.834 937.262,863.47 937.466,850.964 937.669,838.348 937.873,825.658 938.077,812.928 938.281,800.193 938.484,787.49 \n",
" 938.688,774.855 938.892,762.324 939.096,749.933 939.299,737.72 939.503,725.721 939.707,713.973 939.911,702.511 940.114,691.373 940.318,680.593 940.522,670.207 \n",
" 940.726,660.249 940.929,650.752 941.133,641.75 941.337,633.274 941.541,625.355 941.745,618.023 941.948,611.307 942.152,605.233 942.356,599.828 942.56,595.115 \n",
" 942.763,591.118 942.967,587.857 943.171,585.353 943.375,583.622 943.578,582.679 943.782,582.54 943.986,583.215 944.19,584.715 944.393,587.047 944.597,590.216 \n",
" 944.801,594.226 945.005,599.077 945.208,604.77 945.412,611.299 945.616,618.661 945.82,626.847 946.023,635.846 946.227,645.647 946.431,656.235 946.635,667.593 \n",
" 946.838,679.703 947.042,692.542 947.246,706.088 947.45,720.315 947.653,735.197 947.857,750.703 948.061,766.803 948.265,783.464 948.468,800.65 948.672,818.326 \n",
" 948.876,836.454 949.08,854.994 949.283,873.905 949.487,893.145 949.691,912.67 949.895,932.438 950.099,952.401 950.302,972.514 950.506,992.731 950.71,1013 \n",
" 950.914,1033.28 951.117,1053.52 951.321,1073.67 951.525,1093.68 951.729,1113.51 951.932,1133.1 952.136,1152.41 952.34,1171.39 952.544,1189.99 952.747,1208.17 \n",
" 952.951,1225.88 953.155,1243.07 953.359,1259.71 953.562,1275.74 953.766,1291.14 953.97,1305.85 954.174,1319.84 954.377,1333.08 954.581,1345.53 954.785,1357.16 \n",
" 954.989,1367.93 955.192,1377.82 955.396,1386.79 955.6,1394.83 955.804,1401.91 956.007,1408.01 956.211,1413.12 956.415,1417.21 956.619,1420.28 956.822,1422.31 \n",
" 957.026,1423.29 957.23,1423.22 957.434,1422.1 957.637,1419.92 957.841,1416.68 958.045,1412.4 958.249,1407.08 958.453,1400.72 958.656,1393.33 958.86,1384.94 \n",
" 959.064,1375.56 959.268,1365.2 959.471,1353.89 959.675,1341.65 959.879,1328.51 960.083,1314.49 960.286,1299.63 960.49,1283.95 960.694,1267.48 960.898,1250.27 \n",
" 961.101,1232.35 961.305,1213.75 961.509,1194.52 961.713,1174.69 961.916,1154.32 962.12,1133.43 962.324,1112.08 962.528,1090.32 962.731,1068.17 962.935,1045.7 \n",
" 963.139,1022.95 963.343,999.968 963.546,976.795 963.75,953.483 963.954,930.079 964.158,906.629 964.361,883.181 964.565,859.781 964.769,836.475 964.973,813.31 \n",
" 965.176,790.328 965.38,767.575 965.584,745.094 965.788,722.925 965.991,701.111 966.195,679.69 966.399,658.701 966.603,638.18 966.807,618.164 967.01,598.685 \n",
" 967.214,579.776 967.418,561.468 967.622,543.788 967.825,526.765 968.029,510.422 968.233,494.784 968.437,479.87 968.64,465.702 968.844,452.295 969.048,439.665 \n",
" 969.252,427.826 969.455,416.787 969.659,406.56 969.863,397.15 970.067,388.563 970.27,380.802 970.474,373.868 970.678,367.76 970.882,362.476 971.085,358.01 \n",
" 971.289,354.358 971.493,351.509 971.697,349.455 971.9,348.184 972.104,347.682 972.308,347.934 972.512,348.925 972.715,350.636 972.919,353.048 973.123,356.141 \n",
" 973.327,359.893 973.53,364.281 973.734,369.282 973.938,374.871 974.142,381.021 974.345,387.708 974.549,394.902 974.753,402.577 974.957,410.704 975.161,419.254 \n",
" 975.364,428.198 975.568,437.506 975.772,447.149 975.976,457.096 976.179,467.318 976.383,477.785 976.587,488.466 976.791,499.332 976.994,510.354 977.198,521.502 \n",
" 977.402,532.747 977.606,544.062 977.809,555.417 978.013,566.787 978.217,578.143 978.421,589.46 978.624,600.713 978.828,611.876 979.032,622.926 979.236,633.84 \n",
" 979.439,644.595 979.643,655.17 979.847,665.545 980.051,675.699 980.254,685.614 980.458,695.273 980.662,704.658 980.866,713.754 981.069,722.546 981.273,731.021 \n",
" 981.477,739.164 981.681,746.965 981.884,754.413 982.088,761.497 982.292,768.208 982.496,774.538 982.7,780.481 982.903,786.029 983.107,791.177 983.311,795.921 \n",
" 983.515,800.256 983.718,804.181 983.922,807.692 984.126,810.787 984.33,813.468 984.533,815.732 984.737,817.581 984.941,819.016 985.145,820.039 985.348,820.653 \n",
" 985.552,820.859 985.756,820.662 985.96,820.066 986.163,819.075 986.367,817.694 986.571,815.928 986.775,813.783 986.978,811.265 987.182,808.38 987.386,805.136 \n",
" 987.59,801.539 987.793,797.596 987.997,793.315 988.201,788.704 988.405,783.772 988.608,778.525 988.812,772.974 989.016,767.127 989.22,760.993 989.423,754.58 \n",
" 989.627,747.9 989.831,740.961 990.035,733.773 990.238,726.346 990.442,718.69 990.646,710.817 990.85,702.736 991.054,694.459 991.257,685.997 991.461,677.361 \n",
" 991.665,668.563 991.869,659.614 992.072,650.528 992.276,641.316 992.48,631.99 992.684,622.565 992.887,613.052 993.091,603.466 993.295,593.821 993.499,584.13 \n",
" 993.702,574.408 993.906,564.67 994.11,554.93 994.314,545.205 994.517,535.509 994.721,525.86 994.925,516.272 995.129,506.763 995.332,497.35 995.536,488.049 \n",
" 995.74,478.879 995.944,469.857 996.147,461 996.351,452.328 996.555,443.858 996.759,435.608 996.962,427.599 997.166,419.848 997.37,412.375 997.574,405.198 \n",
" 997.777,398.337 997.981,391.811 998.185,385.638 998.389,379.837 998.592,374.428 998.796,369.43 999,364.859 999.204,360.735 999.408,357.076 999.611,353.899 \n",
" 999.815,351.22 1000.02,349.058 1000.22,347.427 1000.43,346.343 1000.63,345.821 1000.83,345.876 1001.04,346.52 1001.24,347.767 1001.45,349.628 1001.65,352.114 \n",
" 1001.85,355.235 1002.06,359 1002.26,363.417 1002.46,368.492 1002.67,374.231 1002.87,380.639 1003.08,387.718 1003.28,395.47 1003.48,403.896 1003.69,412.994 \n",
" 1003.89,422.763 1004.09,433.199 1004.3,444.296 1004.5,456.048 1004.71,468.446 1004.91,481.48 1005.11,495.141 1005.32,509.413 1005.52,524.283 1005.72,539.736 \n",
" 1005.93,555.753 1006.13,572.316 1006.34,589.403 1006.54,606.994 1006.74,625.064 1006.95,643.588 1007.15,662.54 1007.35,681.892 1007.56,701.615 1007.76,721.679 \n",
" 1007.97,742.052 1008.17,762.701 1008.37,783.593 1008.58,804.692 1008.78,825.962 1008.98,847.367 1009.19,868.869 1009.39,890.43 1009.6,912.01 1009.8,933.57 \n",
" 1010,955.07 1010.21,976.47 1010.41,997.728 1010.61,1018.8 1010.82,1039.66 1011.02,1060.24 1011.23,1080.53 1011.43,1100.47 1011.63,1120.02 1011.84,1139.14 \n",
" 1012.04,1157.8 1012.24,1175.96 1012.45,1193.58 1012.65,1210.61 1012.86,1227.04 1013.06,1242.81 1013.26,1257.9 1013.47,1272.28 1013.67,1285.9 1013.87,1298.76 \n",
" 1014.08,1310.8 1014.28,1322.02 1014.49,1332.38 1014.69,1341.87 1014.89,1350.45 1015.1,1358.12 1015.3,1364.85 1015.5,1370.63 1015.71,1375.45 1015.91,1379.29 \n",
" 1016.12,1382.16 1016.32,1384.03 1016.52,1384.92 1016.73,1384.81 1016.93,1383.71 1017.13,1381.62 1017.34,1378.55 1017.54,1374.5 1017.75,1369.49 1017.95,1363.53 \n",
" 1018.15,1356.62 1018.36,1348.8 1018.56,1340.08 1018.76,1330.48 1018.97,1320.03 1019.17,1308.74 1019.38,1296.66 1019.58,1283.8 1019.78,1270.21 1019.99,1255.91 \n",
" 1020.19,1240.94 1020.39,1225.34 1020.6,1209.14 1020.8,1192.39 1021.01,1175.14 1021.21,1157.41 1021.41,1139.25 1021.62,1120.72 1021.82,1101.86 1022.02,1082.7 \n",
" 1022.23,1063.31 1022.43,1043.73 1022.64,1024 1022.84,1004.18 1023.04,984.312 1023.25,964.448 1023.45,944.637 1023.65,924.926 1023.86,905.365 1024.06,885.999 \n",
" 1024.27,866.878 1024.47,848.046 1024.67,829.55 1024.88,811.433 1025.08,793.74 1025.28,776.511 1025.49,759.789 1025.69,743.612 1025.9,728.019 1026.1,713.044 \n",
" 1026.3,698.723 1026.51,685.087 1026.71,672.169 1026.91,659.995 1027.12,648.593 1027.32,637.987 1027.53,628.198 1027.73,619.248 1027.93,611.153 1028.14,603.928 \n",
" 1028.34,597.587 1028.54,592.14 1028.75,587.594 1028.95,583.956 1029.16,581.227 1029.36,579.41 1029.56,578.501 1029.77,578.497 1029.97,579.39 1030.17,581.172 \n",
" 1030.38,583.832 1030.58,587.355 1030.79,591.725 1030.99,596.924 1031.19,602.932 1031.4,609.727 1031.6,617.282 1031.8,625.573 1032.01,634.571 1032.21,644.246 \n",
" 1032.42,654.566 1032.62,665.497 1032.82,677.005 1033.03,689.054 1033.23,701.606 1033.43,714.623 1033.64,728.064 1033.84,741.89 1034.05,756.058 1034.25,770.527 \n",
" 1034.45,785.254 1034.66,800.196 1034.86,815.309 1035.06,830.549 1035.27,845.873 1035.47,861.236 1035.68,876.596 1035.88,891.908 1036.08,907.129 1036.29,922.217 \n",
" 1036.49,937.13 1036.69,951.826 1036.9,966.265 1037.1,980.407 1037.31,994.213 1037.51,1007.65 1037.71,1020.67 1037.92,1033.25 1038.12,1045.35 1038.32,1056.94 \n",
" 1038.53,1067.99 1038.73,1078.47 1038.94,1088.35 1039.14,1097.61 1039.34,1106.22 1039.55,1114.16 1039.75,1121.41 1039.95,1127.94 1040.16,1133.75 1040.36,1138.82 \n",
" 1040.57,1143.13 1040.77,1146.68 1040.97,1149.45 1041.18,1151.44 1041.38,1152.64 1041.59,1153.06 1041.79,1152.67 1041.99,1151.5 1042.2,1149.54 1042.4,1146.79 \n",
" 1042.6,1143.26 1042.81,1138.95 1043.01,1133.89 1043.22,1128.07 1043.42,1121.51 1043.62,1114.23 1043.83,1106.24 1044.03,1097.55 1044.23,1088.19 1044.44,1078.18 \n",
" 1044.64,1067.53 1044.85,1056.26 1045.05,1044.41 1045.25,1032 1045.46,1019.04 1045.66,1005.57 1045.86,991.613 1046.07,977.194 1046.27,962.344 1046.48,947.089 \n",
" 1046.68,931.459 1046.88,915.483 1047.09,899.191 1047.29,882.612 1047.49,865.776 1047.7,848.714 1047.9,831.455 1048.11,814.029 1048.31,796.465 1048.51,778.794 \n",
" 1048.72,761.045 1048.92,743.247 1049.12,725.428 1049.33,707.616 1049.53,689.839 1049.74,672.125 1049.94,654.5 1050.14,636.99 1050.35,619.62 1050.55,602.415 \n",
" 1050.75,585.399 1050.96,568.594 1051.16,552.025 1051.37,535.711 1051.57,519.674 1051.77,503.933 1051.98,488.509 1052.18,473.418 1052.38,458.679 1052.59,444.308 \n",
" 1052.79,430.321 1053,416.732 1053.2,403.556 1053.4,390.805 1053.61,378.492 1053.81,366.629 1054.01,355.225 1054.22,344.291 1054.42,333.836 1054.63,323.867 \n",
" 1054.83,314.393 1055.03,305.42 1055.24,296.954 1055.44,289.001 1055.64,281.565 1055.85,274.65 1056.05,268.259 1056.26,262.396 1056.46,257.063 1056.66,252.26 \n",
" 1056.87,247.99 1057.07,244.252 1057.27,241.048 1057.48,238.376 1057.68,236.235 1057.89,234.625 1058.09,233.544 1058.29,232.988 1058.5,232.957 1058.7,233.447 \n",
" 1058.9,234.454 1059.11,235.975 1059.31,238.007 1059.52,240.544 1059.72,243.582 1059.92,247.116 1060.13,251.14 1060.33,255.649 1060.53,260.638 1060.74,266.098 \n",
" 1060.94,272.025 1061.15,278.41 1061.35,285.247 1061.55,292.528 1061.76,300.244 1061.96,308.387 1062.16,316.949 1062.37,325.92 1062.57,335.29 1062.78,345.051 \n",
" 1062.98,355.19 1063.18,365.698 1063.39,376.563 1063.59,387.773 1063.79,399.316 1064,411.18 1064.2,423.352 1064.41,435.817 1064.61,448.562 1064.81,461.572 \n",
" 1065.02,474.833 1065.22,488.327 1065.42,502.041 1065.63,515.956 1065.83,530.055 1066.04,544.322 1066.24,558.737 1066.44,573.283 1066.65,587.94 1066.85,602.688 \n",
" 1067.05,617.508 1067.26,632.378 1067.46,647.279 1067.67,662.189 1067.87,677.086 1068.07,691.947 1068.28,706.752 1068.48,721.476 1068.68,736.097 1068.89,750.593 \n",
" 1069.09,764.939 1069.3,779.112 1069.5,793.088 1069.7,806.845 1069.91,820.357 1070.11,833.603 1070.31,846.558 1070.52,859.199 1070.72,871.502 1070.93,883.446 \n",
" 1071.13,895.008 1071.33,906.164 1071.54,916.895 1071.74,927.179 1071.94,936.994 1072.15,946.322 1072.35,955.143 1072.56,963.438 1072.76,971.191 1072.96,978.383 \n",
" 1073.17,985 1073.37,991.027 1073.57,996.449 1073.78,1001.26 1073.98,1005.43 1074.19,1008.97 1074.39,1011.87 1074.59,1014.1 1074.8,1015.68 1075,1016.59 \n",
" 1075.2,1016.84 1075.41,1016.41 1075.61,1015.31 1075.82,1013.55 1076.02,1011.11 1076.22,1008.02 1076.43,1004.27 1076.63,999.873 1076.83,994.839 1077.04,989.178 \n",
" 1077.24,982.904 1077.45,976.031 1077.65,968.575 1077.85,960.555 1078.06,951.988 1078.26,942.898 1078.46,933.305 1078.67,923.235 1078.87,912.713 1079.08,901.766 \n",
" 1079.28,890.423 1079.48,878.713 1079.69,866.667 1079.89,854.317 1080.09,841.697 1080.3,828.842 1080.5,815.786 1080.71,802.566 1080.91,789.22 1081.11,775.784 \n",
" 1081.32,762.298 1081.52,748.801 1081.72,735.331 1081.93,721.929 1082.13,708.635 1082.34,695.489 1082.54,682.531 1082.74,669.801 1082.95,657.339 1083.15,645.185 \n",
" 1083.36,633.377 1083.56,621.955 1083.76,610.956 1083.97,600.418 1084.17,590.377 1084.37,580.868 1084.58,571.926 1084.78,563.583 1084.99,555.872 1085.19,548.823 \n",
" 1085.39,542.465 1085.6,536.826 1085.8,531.931 1086,527.804 1086.21,524.468 1086.41,521.942 1086.62,520.245 1086.82,519.394 1087.02,519.402 1087.23,520.282 \n",
" 1087.43,522.043 1087.63,524.693 1087.84,528.237 1088.04,532.678 1088.25,538.018 1088.45,544.253 1088.65,551.38 1088.86,559.392 1089.06,568.282 1089.26,578.036 \n",
" 1089.47,588.642 1089.67,600.084 1089.88,612.344 1090.08,625.401 1090.28,639.233 1090.49,653.814 1090.69,669.117 1090.89,685.115 1091.1,701.774 1091.3,719.064 \n",
" 1091.51,736.948 1091.71,755.39 1091.91,774.353 1092.12,793.796 1092.32,813.678 1092.52,833.957 1092.73,854.588 1092.93,875.527 1093.14,896.728 1093.34,918.144 \n",
" 1093.54,939.727 1093.75,961.429 1093.95,983.201 1094.15,1004.99 1094.36,1026.76 1094.56,1048.45 1094.77,1070 1094.97,1091.38 1095.17,1112.54 1095.38,1133.42 \n",
" 1095.58,1153.97 1095.78,1174.16 1095.99,1193.92 1096.19,1213.22 1096.4,1232.01 1096.6,1250.25 1096.8,1267.89 1097.01,1284.89 1097.21,1301.22 1097.41,1316.83 \n",
" 1097.62,1331.69 1097.82,1345.77 1098.03,1359.02 1098.23,1371.43 1098.43,1382.96 1098.64,1393.58 1098.84,1403.27 1099.04,1412.01 1099.25,1419.77 1099.45,1426.55 \n",
" 1099.66,1432.32 1099.86,1437.07 1100.06,1440.79 1100.27,1443.48 1100.47,1445.12 1100.67,1445.72 1100.88,1445.27 1101.08,1443.77 1101.29,1441.24 1101.49,1437.67 \n",
" 1101.69,1433.07 1101.9,1427.47 1102.1,1420.86 1102.3,1413.27 1102.51,1404.72 1102.71,1395.22 1102.92,1384.79 1103.12,1373.48 1103.32,1361.29 1103.53,1348.26 \n",
" 1103.73,1334.41 1103.93,1319.79 1104.14,1304.42 1104.34,1288.33 1104.55,1271.57 1104.75,1254.18 1104.95,1236.18 1105.16,1217.63 1105.36,1198.56 1105.56,1179.01 \n",
" 1105.77,1159.03 1105.97,1138.66 1106.18,1117.94 1106.38,1096.92 1106.58,1075.64 1106.79,1054.15 1106.99,1032.49 1107.19,1010.7 1107.4,988.837 1107.6,966.935 \n",
" 1107.81,945.04 1108.01,923.195 1108.21,901.443 1108.42,879.826 1108.62,858.384 1108.82,837.157 1109.03,816.185 1109.23,795.505 1109.44,775.153 1109.64,755.167 \n",
" 1109.84,735.578 1110.05,716.421 1110.25,697.726 1110.45,679.524 1110.66,661.842 1110.86,644.707 1111.07,628.144 1111.27,612.175 1111.47,596.823 1111.68,582.107 \n",
" 1111.88,568.046 1112.08,554.654 1112.29,541.946 1112.49,529.935 1112.7,518.632 1112.9,508.045 1113.1,498.181 1113.31,489.045 1113.51,480.641 1113.71,472.971 \n",
" 1113.92,466.035 1114.12,459.83 1114.33,454.354 1114.53,449.602 1114.73,445.567 1114.94,442.241 1115.14,439.615 1115.34,437.678 1115.55,436.418 1115.75,435.82 \n",
" 1115.96,435.872 1116.16,436.556 1116.36,437.856 1116.57,439.753 1116.77,442.23 1116.97,445.265 1117.18,448.839 1117.38,452.93 1117.59,457.516 1117.79,462.574 \n",
" 1117.99,468.082 1118.2,474.015 1118.4,480.35 1118.6,487.062 1118.81,494.127 1119.01,501.52 1119.22,509.217 1119.42,517.191 1119.62,525.419 1119.83,533.876 \n",
" 1120.03,542.536 1120.23,551.375 1120.44,560.369 1120.64,569.495 1120.85,578.727 1121.05,588.043 1121.25,597.42 1121.46,606.835 1121.66,616.267 1121.86,625.693 \n",
" 1122.07,635.093 1122.27,644.447 1122.48,653.735 1122.68,662.937 1122.88,672.035 1123.09,681.012 1123.29,689.849 1123.5,698.53 1123.7,707.04 1123.9,715.363 \n",
" 1124.11,723.485 1124.31,731.392 1124.51,739.07 1124.72,746.508 1124.92,753.693 1125.13,760.614 1125.33,767.261 1125.53,773.623 1125.74,779.692 1125.94,785.459 \n",
" 1126.14,790.916 1126.35,796.055 1126.55,800.87 1126.76,805.353 1126.96,809.5 1127.16,813.305 1127.37,816.762 1127.57,819.869 1127.77,822.62 1127.98,825.013 \n",
" 1128.18,827.045 1128.39,828.712 1128.59,830.013 1128.79,830.945 1129,831.508 1129.2,831.701 1129.4,831.522 1129.61,830.971 1129.81,830.048 1130.02,828.754 \n",
" 1130.22,827.089 1130.42,825.054 1130.63,822.651 1130.83,819.88 1131.03,816.744 1131.24,813.245 1131.44,809.385 1131.65,805.168 1131.85,800.596 1132.05,795.673 \n",
" 1132.26,790.403 1132.46,784.791 1132.66,778.84 1132.87,772.556 1133.07,765.944 1133.28,759.011 1133.48,751.762 1133.68,744.203 1133.89,736.343 1134.09,728.189 \n",
" 1134.29,719.748 1134.5,711.03 1134.7,702.043 1134.91,692.798 1135.11,683.304 1135.31,673.572 1135.52,663.614 1135.72,653.44 1135.92,643.065 1136.13,632.501 \n",
" 1136.33,621.761 1136.54,610.86 1136.74,599.812 1136.94,588.634 1137.15,577.342 1137.35,565.952 1137.55,554.481 1137.76,542.948 1137.96,531.371 1138.17,519.769 \n",
" 1138.37,508.163 1138.57,496.572 1138.78,485.017 1138.98,473.519 1139.18,462.101 1139.39,450.784 1139.59,439.591 1139.8,428.545 1140,417.67 1140.2,406.99 \n",
" 1140.41,396.527 1140.61,386.307 1140.81,376.354 1141.02,366.691 1141.22,357.345 1141.43,348.339 1141.63,339.699 1141.83,331.447 1142.04,323.609 1142.24,316.208 \n",
" 1142.44,309.269 1142.65,302.815 1142.85,296.868 1143.06,291.451 1143.26,286.587 1143.46,282.295 1143.67,278.598 1143.87,275.514 1144.07,273.062 1144.28,271.261 \n",
" 1144.48,270.128 1144.69,269.678 1144.89,269.927 1145.09,270.888 1145.3,272.574 1145.5,274.997 1145.7,278.165 1145.91,282.088 1146.11,286.772 1146.32,292.223 \n",
" 1146.52,298.445 1146.72,305.44 1146.93,313.209 1147.13,321.751 1147.33,331.064 1147.54,341.142 1147.74,351.98 1147.95,363.57 1148.15,375.902 1148.35,388.965 \n",
" 1148.56,402.745 1148.76,417.228 1148.96,432.396 1149.17,448.23 1149.37,464.711 1149.58,481.817 1149.78,499.522 1149.98,517.803 1150.19,536.631 1150.39,555.978 \n",
" 1150.59,575.814 1150.8,596.107 1151,616.824 1151.21,637.93 1151.41,659.39 1151.61,681.166 1151.82,703.22 1152.02,725.512 1152.22,748.004 1152.43,770.654 \n",
" 1152.63,793.419 1152.84,816.257 1153.04,839.126 1153.24,861.981 1153.45,884.778 1153.65,907.474 1153.85,930.024 1154.06,952.383 1154.26,974.508 1154.47,996.353 \n",
" 1154.67,1017.88 1154.87,1039.03 1155.08,1059.78 1155.28,1080.07 1155.48,1099.88 1155.69,1119.15 1155.89,1137.84 1156.1,1155.93 1156.3,1173.36 1156.5,1190.11 \n",
" 1156.71,1206.15 1156.91,1221.42 1157.11,1235.92 1157.32,1249.6 1157.52,1262.44 1157.73,1274.41 1157.93,1285.5 1158.13,1295.66 1158.34,1304.9 1158.54,1313.18 \n",
" 1158.74,1320.5 1158.95,1326.84 1159.15,1332.18 1159.36,1336.53 1159.56,1339.87 1159.76,1342.2 1159.97,1343.52 1160.17,1343.84 1160.37,1343.14 1160.58,1341.45 \n",
" 1160.78,1338.76 1160.99,1335.09 1161.19,1330.46 1161.39,1324.87 1161.6,1318.35 1161.8,1310.91 1162,1302.59 1162.21,1293.4 1162.41,1283.37 1162.62,1272.52 \n",
" 1162.82,1260.9 1163.02,1248.53 1163.23,1235.45 1163.43,1221.69 1163.63,1207.3 1163.84,1192.31 1164.04,1176.76 1164.25,1160.69 1164.45,1144.15 1164.65,1127.19 \n",
" 1164.86,1109.84 1165.06,1092.16 1165.27,1074.19 1165.47,1055.97 1165.67,1037.57 1165.88,1019.02 1166.08,1000.38 1166.28,981.691 1166.49,963.004 1166.69,944.367 \n",
" 1166.9,925.829 1167.1,907.438 1167.3,889.24 1167.51,871.283 1167.71,853.611 1167.91,836.269 1168.12,819.301 1168.32,802.75 1168.53,786.656 1168.73,771.059 \n",
" 1168.93,755.998 1169.14,741.508 1169.34,727.625 1169.54,714.382 1169.75,701.809 1169.95,689.937 1170.16,678.793 1170.36,668.401 1170.56,658.784 1170.77,649.964 \n",
" 1170.97,641.959 1171.17,634.786 1171.38,628.457 1171.58,622.985 1171.79,618.379 1171.99,614.645 1172.19,611.789 1172.4,609.812 1172.6,608.714 1172.8,608.493 \n",
" 1173.01,609.143 1173.21,610.656 1173.42,613.024 1173.62,616.234 1173.82,620.273 1174.03,625.124 1174.23,630.769 1174.43,637.187 1174.64,644.357 1174.84,652.253 \n",
" 1175.05,660.852 1175.25,670.123 1175.45,680.039 1175.66,690.569 1175.86,701.68 1176.06,713.339 1176.27,725.51 1176.47,738.158 1176.68,751.246 1176.88,764.736 \n",
" 1177.08,778.59 1177.29,792.767 1177.49,807.227 1177.69,821.931 1177.9,836.837 1178.1,851.905 1178.31,867.092 1178.51,882.358 1178.71,897.661 1178.92,912.961 \n",
" 1179.12,928.216 1179.32,943.386 1179.53,958.433 1179.73,973.315 1179.94,987.995 1180.14,1002.44 1180.34,1016.6 1180.55,1030.45 1180.75,1043.95 1180.95,1057.08 \n",
" 1181.16,1069.78 1181.36,1082.05 1181.57,1093.84 1181.77,1105.12 1181.97,1115.88 1182.18,1126.08 1182.38,1135.7 1182.58,1144.72 1182.79,1153.11 1182.99,1160.87 \n",
" 1183.2,1167.96 1183.4,1174.38 1183.6,1180.11 1183.81,1185.14 1184.01,1189.46 1184.21,1193.06 1184.42,1195.92 1184.62,1198.06 1184.83,1199.46 1185.03,1200.12 \n",
" 1185.23,1200.04 1185.44,1199.22 1185.64,1197.67 1185.84,1195.39 1186.05,1192.38 1186.25,1188.65 1186.46,1184.22 1186.66,1179.08 1186.86,1173.26 1187.07,1166.76 \n",
" 1187.27,1159.61 1187.47,1151.8 1187.68,1143.37 1187.88,1134.33 1188.09,1124.69 1188.29,1114.48 1188.49,1103.71 1188.7,1092.41 1188.9,1080.59 1189.1,1068.28 \n",
" 1189.31,1055.51 1189.51,1042.29 1189.72,1028.65 1189.92,1014.61 1190.12,1000.2 1190.33,985.439 1190.53,970.355 1190.73,954.971 1190.94,939.314 1191.14,923.408 \n",
" 1191.35,907.277 1191.55,890.948 1191.75,874.444 1191.96,857.79 1192.16,841.011 1192.36,824.13 1192.57,807.173 1192.77,790.161 1192.98,773.119 1193.18,756.069 \n",
" 1193.38,739.033 1193.59,722.034 1193.79,705.093 1193.99,688.231 1194.2,671.468 1194.4,654.825 1194.61,638.32 1194.81,621.973 1195.01,605.802 1195.22,589.825 \n",
" 1195.42,574.058 1195.62,558.52 1195.83,543.225 1196.03,528.19 1196.24,513.43 1196.44,498.958 1196.64,484.79 1196.85,470.938 1197.05,457.415 1197.25,444.234 \n",
" 1197.46,431.406 1197.66,418.944 1197.87,406.857 1198.07,395.158 1198.27,383.854 1198.48,372.957 1198.68,362.475 1198.88,352.417 1199.09,342.792 1199.29,333.607 \n",
" 1199.5,324.87 1199.7,316.588 1199.9,308.768 1200.11,301.417 1200.31,294.54 1200.51,288.144 1200.72,282.233 1200.92,276.813 1201.13,271.889 1201.33,267.465 \n",
" 1201.53,263.544 1201.74,260.132 1201.94,257.23 1202.14,254.843 1202.35,252.972 1202.55,251.62 1202.76,250.788 1202.96,250.479 1203.16,250.693 1203.37,251.43 \n",
" 1203.57,252.692 1203.77,254.477 1203.98,256.784 1204.18,259.614 1204.39,262.962 1204.59,266.828 1204.79,271.209 1205,276.1 1205.2,281.498 1205.4,287.398 \n",
" 1205.61,293.794 1205.81,300.682 1206.02,308.053 1206.22,315.901 1206.42,324.217 1206.63,332.994 1206.83,342.22 1207.04,351.886 1207.24,361.981 1207.44,372.492 \n",
" 1207.65,383.407 1207.85,394.713 1208.05,406.395 1208.26,418.439 1208.46,430.827 1208.67,443.543 1208.87,456.57 1209.07,469.89 1209.28,483.483 1209.48,497.329 \n",
" 1209.68,511.407 1209.89,525.696 1210.09,540.174 1210.3,554.818 1210.5,569.604 1210.7,584.509 1210.91,599.506 1211.11,614.571 1211.31,629.679 1211.52,644.801 \n",
" 1211.72,659.912 1211.93,674.985 1212.13,689.991 1212.33,704.903 1212.54,719.693 1212.74,734.332 1212.94,748.793 1213.15,763.046 1213.35,777.063 1213.56,790.816 \n",
" 1213.76,804.277 1213.96,817.418 1214.17,830.211 1214.37,842.629 1214.57,854.646 1214.78,866.235 1214.98,877.371 1215.19,888.029 1215.39,898.184 1215.59,907.813 \n",
" 1215.8,916.895 1216,925.407 1216.2,933.33 1216.41,940.643 1216.61,947.33 1216.82,953.374 1217.02,958.759 1217.22,963.471 1217.43,967.497 1217.63,970.828 \n",
" 1217.83,973.453 1218.04,975.364 1218.24,976.556 1218.45,977.024 1218.65,976.766 1218.85,975.78 1219.06,974.068 1219.26,971.632 1219.46,968.477 1219.67,964.609 \n",
" 1219.87,960.038 1220.08,954.772 1220.28,948.825 1220.48,942.21 1220.69,934.943 1220.89,927.042 1221.09,918.527 1221.3,909.418 1221.5,899.739 1221.71,889.515 \n",
" 1221.91,878.772 1222.11,867.539 1222.32,855.844 1222.52,843.719 1222.72,831.197 1222.93,818.311 1223.13,805.097 1223.34,791.592 1223.54,777.832 1223.74,763.856 \n",
" 1223.95,749.704 1224.15,735.416 1224.35,721.033 1224.56,706.597 1224.76,692.15 1224.97,677.734 1225.17,663.393 1225.37,649.169 1225.58,635.106 1225.78,621.247 \n",
" 1225.98,607.634 1226.19,594.311 1226.39,581.319 1226.6,568.7 1226.8,556.495 1227,544.745 1227.21,533.489 1227.41,522.765 1227.61,512.611 1227.82,503.062 \n",
" 1228.02,494.154 1228.23,485.92 1228.43,478.391 1228.63,471.599 1228.84,465.57 1229.04,460.333 1229.24,455.912 1229.45,452.329 1229.65,449.605 1229.86,447.76 \n",
" 1230.06,446.809 1230.26,446.766 1230.47,447.645 1230.67,449.453 1230.87,452.2 1231.08,455.888 1231.28,460.521 1231.49,466.1 1231.69,472.62 1231.89,480.078 \n",
" 1232.1,488.465 1232.3,497.773 1232.5,507.989 1232.71,519.098 1232.91,531.082 1233.12,543.924 1233.32,557.6 1233.52,572.087 1233.73,587.36 1233.93,603.388 \n",
" 1234.13,620.143 1234.34,637.592 1234.54,655.701 1234.75,674.433 1234.95,693.751 1235.15,713.616 1235.36,733.986 1235.56,754.82 1235.76,776.074 1235.97,797.703 \n",
" 1236.17,819.661 1236.38,841.901 1236.58,864.376 1236.78,887.038 1236.99,909.837 1237.19,932.724 1237.39,955.649 1237.6,978.563 1237.8,1001.42 1238.01,1024.16 \n",
" 1238.21,1046.74 1238.41,1069.11 1238.62,1091.22 1238.82,1113.03 1239.02,1134.48 1239.23,1155.52 1239.43,1176.13 1239.64,1196.24 1239.84,1215.81 1240.04,1234.81 \n",
" 1240.25,1253.19 1240.45,1270.92 1240.65,1287.95 1240.86,1304.25 1241.06,1319.79 1241.27,1334.53 1241.47,1348.44 1241.67,1361.5 1241.88,1373.68 1242.08,1384.96 \n",
" 1242.28,1395.3 1242.49,1404.71 1242.69,1413.15 1242.9,1420.61 1243.1,1427.09 1243.3,1432.56 1243.51,1437.03 1243.71,1440.48 1243.91,1442.92 1244.12,1444.33 \n",
" 1244.32,1444.74 1244.53,1444.13 1244.73,1442.52 1244.93,1439.92 1245.14,1436.33 1245.34,1431.77 1245.54,1426.25 1245.75,1419.79 1245.95,1412.41 1246.16,1404.14 \n",
" 1246.36,1394.99 1246.56,1384.99 1246.77,1374.16 1246.97,1362.55 1247.17,1350.16 1247.38,1337.05 1247.58,1323.23 1247.79,1308.75 1247.99,1293.64 1248.19,1277.93 \n",
" 1248.4,1261.66 1248.6,1244.87 1248.81,1227.6 1249.01,1209.9 1249.21,1191.78 1249.42,1173.31 1249.62,1154.52 1249.82,1135.45 1250.03,1116.14 1250.23,1096.63 \n",
" 1250.44,1076.97 1250.64,1057.19 1250.84,1037.33 1251.05,1017.44 1251.25,997.554 1251.45,977.709 1251.66,957.944 1251.86,938.298 1252.07,918.805 1252.27,899.503 \n",
" 1252.47,880.425 1252.68,861.605 1252.88,843.074 1253.08,824.865 1253.29,807.006 1253.49,789.527 1253.7,772.454 1253.9,755.814 1254.1,739.629 1254.31,723.923 \n",
" 1254.51,708.718 1254.71,694.032 1254.92,679.885 1255.12,666.292 1255.33,653.268 1255.53,640.828 1255.73,628.982 1255.94,617.741 1256.14,607.114 1256.34,597.108 \n",
" 1256.55,587.728 1256.75,578.979 1256.96,570.862 1257.16,563.381 1257.36,556.533 1257.57,550.317 1257.77,544.731 1257.97,539.77 1258.18,535.429 1258.38,531.7 \n",
" 1258.59,528.575 1258.79,526.047 1258.99,524.104 1259.2,522.736 1259.4,521.929 1259.6,521.672 1259.81,521.951 1260.01,522.751 1260.22,524.056 1260.42,525.851 \n",
" 1260.62,528.118 1260.83,530.842 1261.03,534.004 1261.23,537.586 1261.44,541.57 1261.64,545.937 1261.85,550.667 1262.05,555.742 1262.25,561.143 1262.46,566.849 \n",
" 1262.66,572.841 1262.86,579.099 1263.07,585.604 1263.27,592.336 1263.48,599.275 1263.68,606.402 1263.88,613.699 1264.09,621.145 1264.29,628.722 1264.49,636.411 \n",
" 1264.7,644.195 1264.9,652.055 1265.11,659.972 1265.31,667.931 1265.51,675.914 1265.72,683.903 1265.92,691.884 1266.12,699.839 1266.33,707.754 1266.53,715.612 \n",
" 1266.74,723.4 1266.94,731.102 1267.14,738.705 1267.35,746.194 1267.55,753.558 1267.75,760.782 1267.96,767.853 1268.16,774.761 1268.37,781.492 1268.57,788.036 \n",
" 1268.77,794.381 1268.98,800.516 1269.18,806.431 1269.38,812.115 1269.59,817.558 1269.79,822.751 1270,827.685 1270.2,832.35 1270.4,836.737 1270.61,840.837 \n",
" 1270.81,844.643 1271.01,848.147 1271.22,851.339 1271.42,854.214 1271.63,856.763 1271.83,858.979 1272.03,860.856 1272.24,862.387 1272.44,863.565 1272.64,864.385 \n",
" 1272.85,864.84 1273.05,864.926 1273.26,864.636 1273.46,863.967 1273.66,862.913 1273.87,861.469 1274.07,859.634 1274.27,857.401 1274.48,854.77 1274.68,851.736 \n",
" 1274.89,848.298 1275.09,844.453 1275.29,840.201 1275.5,835.541 1275.7,830.471 1275.9,824.993 1276.11,819.108 1276.31,812.816 1276.52,806.12 1276.72,799.023 \n",
" 1276.92,791.528 1277.13,783.639 1277.33,775.361 1277.53,766.7 1277.74,757.662 1277.94,748.254 1278.15,738.485 1278.35,728.364 1278.55,717.899 1278.76,707.103 \n",
" 1278.96,695.986 1279.16,684.561 1279.37,672.841 1279.57,660.84 1279.78,648.574 1279.98,636.059 1280.18,623.312 1280.39,610.35 1280.59,597.193 1280.79,583.859 \n",
" 1281,570.371 1281.2,556.749 1281.41,543.015 1281.61,529.193 1281.81,515.307 1282.02,501.38 1282.22,487.439 1282.42,473.509 1282.63,459.617 1282.83,445.79 \n",
" 1283.04,432.056 1283.24,418.443 1283.44,404.98 1283.65,391.696 1283.85,378.62 1284.05,365.781 1284.26,353.21 1284.46,340.937 1284.67,328.99 1284.87,317.401 \n",
" 1285.07,306.199 1285.28,295.413 1285.48,285.073 1285.68,275.207 1285.89,265.845 1286.09,257.013 1286.3,248.741 1286.5,241.053 1286.7,233.978 1286.91,227.538 \n",
" 1287.11,221.76 1287.31,216.665 1287.52,212.277 1287.72,208.615 1287.93,205.701 1288.13,203.552 1288.33,202.186 1288.54,201.617 1288.74,201.861 1288.95,202.93 \n",
" 1289.15,204.834 1289.35,207.584 1289.56,211.185 1289.76,215.645 1289.96,220.967 1290.17,227.153 1290.37,234.203 1290.58,242.114 1290.78,250.885 1290.98,260.507 \n",
" 1291.19,270.974 1291.39,282.276 1291.59,294.401 1291.8,307.335 1292,321.063 1292.21,335.565 1292.41,350.824 1292.61,366.816 1292.82,383.518 1293.02,400.905 \n",
" 1293.22,418.95 1293.43,437.622 1293.63,456.893 1293.84,476.728 1294.04,497.093 1294.24,517.954 1294.45,539.273 1294.65,561.012 1294.85,583.131 1295.06,605.588 \n",
" 1295.26,628.343 1295.47,651.352 1295.67,674.571 1295.87,697.955 1296.08,721.459 1296.28,745.038 1296.48,768.644 1296.69,792.231 1296.89,815.752 1297.1,839.16 \n",
" 1297.3,862.408 1297.5,885.449 1297.71,908.237 1297.91,930.724 1298.11,952.866 1298.32,974.618 1298.52,995.934 1298.73,1016.77 1298.93,1037.09 1299.13,1056.84 \n",
" 1299.34,1076 1299.54,1094.51 1299.74,1112.34 1299.95,1129.46 1300.15,1145.83 1300.36,1161.42 1300.56,1176.2 1300.76,1190.14 1300.97,1203.21 1301.17,1215.39 \n",
" 1301.37,1226.65 1301.58,1236.98 1301.78,1246.36 1301.99,1254.77 1302.19,1262.2 1302.39,1268.64 1302.6,1274.08 1302.8,1278.51 1303,1281.94 1303.21,1284.35 \n",
" 1303.41,1285.75 1303.62,1286.15 1303.82,1285.55 1304.02,1283.96 1304.23,1281.39 1304.43,1277.85 1304.63,1273.37 1304.84,1267.96 1305.04,1261.64 1305.25,1254.44 \n",
" 1305.45,1246.37 1305.65,1237.47 1305.86,1227.77 1306.06,1217.3 1306.26,1206.08 1306.47,1194.17 1306.67,1181.58 1306.88,1168.37 1307.08,1154.57 1307.28,1140.22 \n",
" 1307.49,1125.36 1307.69,1110.04 1307.89,1094.31 1308.1,1078.2 1308.3,1061.76 1308.51,1045.04 1308.71,1028.09 1308.91,1010.96 1309.12,993.686 1309.32,976.322 \n",
" 1309.52,958.917 1309.73,941.518 1309.93,924.171 1310.14,906.925 1310.34,889.826 1310.54,872.919 1310.75,856.249 1310.95,839.862 1311.15,823.799 1311.36,808.103 \n",
" 1311.56,792.815 1311.77,777.974 1311.97,763.618 1312.17,749.784 1312.38,736.507 1312.58,723.819 1312.78,711.752 1312.99,700.336 1313.19,689.598 1313.4,679.564 \n",
" 1313.6,670.257 1313.8,661.699 1314.01,653.908 1314.21,646.902 1314.41,640.696 1314.62,635.303 1314.82,630.732 1315.03,626.992 1315.23,624.089 1315.43,622.026 \n",
" 1315.64,620.804 1315.84,620.422 1316.04,620.878 1316.25,622.165 1316.45,624.276 1316.66,627.201 1316.86,630.929 1317.06,635.445 1317.27,640.734 1317.47,646.778 \n",
" 1317.67,653.556 1317.88,661.049 1318.08,669.231 1318.29,678.08 1318.49,687.567 1318.69,697.667 1318.9,708.348 1319.1,719.581 1319.3,731.334 1319.51,743.575 \n",
" 1319.71,756.269 1319.92,769.381 1320.12,782.877 1320.32,796.72 1320.53,810.874 1320.73,825.301 1320.93,839.963 1321.14,854.823 1321.34,869.842 1321.55,884.983 \n",
" 1321.75,900.207 1321.95,915.477 1322.16,930.754 1322.36,946.001 1322.56,961.181 1322.77,976.258 1322.97,991.195 1323.18,1005.96 1323.38,1020.51 1323.58,1034.82 \n",
" 1323.79,1048.86 1323.99,1062.58 1324.19,1075.97 1324.4,1088.99 1324.6,1101.62 1324.81,1113.82 1325.01,1125.57 1325.21,1136.85 1325.42,1147.62 1325.62,1157.88 \n",
" 1325.82,1167.6 1326.03,1176.76 1326.23,1185.34 1326.44,1193.32 1326.64,1200.7 1326.84,1207.45 1327.05,1213.57 1327.25,1219.05 1327.45,1223.87 1327.66,1228.03 \n",
" 1327.86,1231.52 1328.07,1234.34 1328.27,1236.49 1328.47,1237.96 1328.68,1238.76 1328.88,1238.88 1329.08,1238.32 1329.29,1237.1 1329.49,1235.21 1329.7,1232.66 \n",
" 1329.9,1229.46 1330.1,1225.62 1330.31,1221.14 1330.51,1216.03 1330.72,1210.31 1330.92,1203.99 1331.12,1197.09 1331.33,1189.6 1331.53,1181.56 1331.73,1172.97 \n",
" 1331.94,1163.85 1332.14,1154.22 1332.35,1144.1 1332.55,1133.49 1332.75,1122.42 1332.96,1110.91 1333.16,1098.98 1333.36,1086.64 1333.57,1073.91 1333.77,1060.82 \n",
" 1333.98,1047.38 1334.18,1033.61 1334.38,1019.53 1334.59,1005.17 1334.79,990.531 1334.99,975.648 1335.2,960.535 1335.4,945.212 1335.61,929.699 1335.81,914.016 \n",
" 1336.01,898.18 1336.22,882.213 1336.42,866.132 1336.62,849.956 1336.83,833.704 1337.03,817.395 1337.24,801.046 1337.44,784.675 1337.64,768.3 1337.85,751.938 \n",
" 1338.05,735.607 1338.25,719.323 1338.46,703.103 1338.66,686.964 1338.87,670.922 1339.07,654.993 1339.27,639.193 1339.48,623.537 1339.68,608.04 1339.88,592.718 \n",
" 1340.09,577.586 1340.29,562.658 1340.5,547.949 1340.7,533.474 1340.9,519.245 1341.11,505.278 1341.31,491.587 1341.51,478.184 1341.72,465.083 1341.92,452.298 \n",
" 1342.13,439.841 1342.33,427.726 1342.53,415.966 1342.74,404.572 1342.94,393.558 1343.14,382.935 1343.35,372.715 1343.55,362.911 1343.76,353.534 1343.96,344.595 \n",
" 1344.16,336.105 1344.37,328.075 1344.57,320.515 1344.77,313.436 1344.98,306.848 1345.18,300.76 1345.39,295.18 1345.59,290.119 1345.79,285.584 1346,281.583 \n",
" 1346.2,278.123 1346.4,275.212 1346.61,272.854 1346.81,271.057 1347.02,269.825 1347.22,269.162 1347.42,269.073 1347.63,269.56 1347.83,270.626 1348.03,272.271 \n",
" 1348.24,274.498 1348.44,277.305 1348.65,280.691 1348.85,284.655 1349.05,289.193 1349.26,294.303 1349.46,299.979 1349.66,306.214 1349.87,313.004 1350.07,320.338 \n",
" 1350.28,328.21 1350.48,336.608 1350.68,345.521 1350.89,354.937 1351.09,364.844 1351.29,375.225 1351.5,386.067 1351.7,397.352 1351.91,409.062 1352.11,421.179 \n",
" 1352.31,433.683 1352.52,446.552 1352.72,459.765 1352.92,473.3 1353.13,487.13 1353.33,501.233 1353.54,515.582 1353.74,530.15 1353.94,544.91 1354.15,559.834 \n",
" 1354.35,574.891 1354.55,590.054 1354.76,605.291 1354.96,620.571 1355.17,635.863 1355.37,651.136 1355.57,666.356 1355.78,681.493 1355.98,696.512 1356.18,711.381 \n",
" 1356.39,726.068 1356.59,740.539 1356.8,754.762 1357,768.705 1357.2,782.335 1357.41,795.62 1357.61,808.529 1357.81,821.032 1358.02,833.098 1358.22,844.699 \n",
" 1358.43,855.804 1358.63,866.387 1358.83,876.421 1359.04,885.88 1359.24,894.741 1359.44,902.979 1359.65,910.573 1359.85,917.502 1360.06,923.748 1360.26,929.293 \n",
" 1360.46,934.121 1360.67,938.218 1360.87,941.572 1361.07,944.172 1361.28,946.009 1361.48,947.076 1361.69,947.368 1361.89,946.882 1362.09,945.617 1362.3,943.575 \n",
" 1362.5,940.757 1362.7,937.17 1362.91,932.82 1363.11,927.717 1363.32,921.872 1363.52,915.298 1363.72,908.01 1363.93,900.027 1364.13,891.367 1364.33,882.051 \n",
" 1364.54,872.104 1364.74,861.55 1364.95,850.416 1365.15,838.732 1365.35,826.527 1365.56,813.833 1365.76,800.685 1365.96,787.118 1366.17,773.167 1366.37,758.872 \n",
" 1366.58,744.271 1366.78,729.405 1366.98,714.315 1367.19,699.042 1367.39,683.631 1367.59,668.124 1367.8,652.567 1368,637.004 1368.21,621.48 1368.41,606.041 \n",
" 1368.61,590.732 1368.82,575.599 1369.02,560.687 1369.22,546.041 1369.43,531.706 1369.63,517.726 1369.84,504.145 1370.04,491.006 1370.24,478.349 1370.45,466.218 \n",
" 1370.65,454.65 1370.85,443.686 1371.06,433.361 1371.26,423.713 1371.47,414.774 1371.67,406.579 1371.87,399.157 1372.08,392.537 1372.28,386.748 1372.49,381.813 \n",
" 1372.69,377.756 1372.89,374.598 1373.1,372.356 1373.3,371.049 1373.5,370.689 1373.71,371.288 1373.91,372.855 1374.12,375.397 1374.32,378.919 1374.52,383.422 \n",
" 1374.73,388.906 1374.93,395.366 1375.13,402.799 1375.34,411.194 1375.54,420.542 1375.75,430.83 1375.95,442.041 1376.15,454.159 1376.36,467.162 1376.56,481.028 \n",
" 1376.76,495.733 1376.97,511.249 1377.17,527.547 1377.38,544.597 1377.58,562.365 1377.78,580.816 1377.99,599.914 1378.19,619.621 1378.39,639.896 1378.6,660.699 \n",
" 1378.8,681.986 1379.01,703.715 1379.21,725.84 1379.41,748.315 1379.62,771.093 1379.82,794.127 1380.02,817.369 1380.23,840.77 1380.43,864.281 1380.64,887.853 \n",
" 1380.84,911.437 1381.04,934.983 1381.25,958.442 1381.45,981.765 1381.65,1004.9 1381.86,1027.81 1382.06,1050.44 1382.27,1072.74 1382.47,1094.67 1382.67,1116.19 \n",
" 1382.88,1137.24 1383.08,1157.8 1383.28,1177.81 1383.49,1197.24 1383.69,1216.05 1383.9,1234.2 1384.1,1251.67 1384.3,1268.41 1384.51,1284.39 1384.71,1299.59 \n",
" 1384.91,1313.99 1385.12,1327.54 1385.32,1340.24 1385.53,1352.06 1385.73,1362.98 1385.93,1372.99 1386.14,1382.07 1386.34,1390.2 1386.54,1397.39 1386.75,1403.62 \n",
" 1386.95,1408.89 1387.16,1413.19 1387.36,1416.52 1387.56,1418.89 1387.77,1420.3 1387.97,1420.75 1388.17,1420.25 1388.38,1418.82 1388.58,1416.45 1388.79,1413.18 \n",
" 1388.99,1409.01 1389.19,1403.97 1389.4,1398.06 1389.6,1391.32 1389.8,1383.76 1390.01,1375.41 1390.21,1366.3 1390.42,1356.45 1390.62,1345.9 1390.82,1334.66 \n",
" 1391.03,1322.78 1391.23,1310.28 1391.43,1297.2 1391.64,1283.57 1391.84,1269.43 1392.05,1254.8 1392.25,1239.73 1392.45,1224.26 1392.66,1208.41 1392.86,1192.22 \n",
" 1393.06,1175.74 1393.27,1159 1393.47,1142.03 1393.68,1124.88 1393.88,1107.57 1394.08,1090.15 1394.29,1072.65 1394.49,1055.1 1394.69,1037.54 1394.9,1020.01 \n",
" 1395.1,1002.53 1395.31,985.141 1395.51,967.874 1395.71,950.76 1395.92,933.828 1396.12,917.106 1396.32,900.622 1396.53,884.403 1396.73,868.475 1396.94,852.861 \n",
" 1397.14,837.585 1397.34,822.669 1397.55,808.133 1397.75,793.996 1397.95,780.277 1398.16,766.992 1398.36,754.157 1398.57,741.785 1398.77,729.889 1398.97,718.482 \n",
" 1399.18,707.572 1399.38,697.168 1399.58,687.279 1399.79,677.911 1399.99,669.068 1400.2,660.755 1400.4,652.974 1400.6,645.726 1400.81,639.013 1401.01,632.833 \n",
" 1401.21,627.185 1401.42,622.066 1401.62,617.472 1401.83,613.399 1402.03,609.841 1402.23,606.792 1402.44,604.244 1402.64,602.191 1402.84,600.623 1403.05,599.53 \n",
" 1403.25,598.904 1403.46,598.733 1403.66,599.007 1403.86,599.714 1404.07,600.842 1404.27,602.378 1404.47,604.311 1404.68,606.627 1404.88,609.312 1405.09,612.353 \n",
" 1405.29,615.737 1405.49,619.449 1405.7,623.475 1405.9,627.8 1406.1,632.411 1406.31,637.293 1406.51,642.431 1406.72,647.811 1406.92,653.418 1407.12,659.238 \n",
" 1407.33,665.256 1407.53,671.457 1407.73,677.828 1407.94,684.354 1408.14,691.02 1408.35,697.812 1408.55,704.717 1408.75,711.719 1408.96,718.806 1409.16,725.963 \n",
" 1409.36,733.175 1409.57,740.431 1409.77,747.715 1409.98,755.015 1410.18,762.316 1410.38,769.605 1410.59,776.87 1410.79,784.096 1410.99,791.271 1411.2,798.381 \n",
" 1411.4,805.412 1411.61,812.353 1411.81,819.19 1412.01,825.909 1412.22,832.498 1412.42,838.944 1412.62,845.234 1412.83,851.354 1413.03,857.293 1413.24,863.036 \n",
" 1413.44,868.572 1413.64,873.887 1413.85,878.969 1414.05,883.805 1414.26,888.382 1414.46,892.688 1414.66,896.71 1414.87,900.435 1415.07,903.853 1415.27,906.95 \n",
" 1415.48,909.714 1415.68,912.135 1415.89,914.199 1416.09,915.897 1416.29,917.216 1416.5,918.147 1416.7,918.678 1416.9,918.8 1417.11,918.502 1417.31,917.777 \n",
" 1417.52,916.614 1417.72,915.005 1417.92,912.943 1418.13,910.421 1418.33,907.431 1418.53,903.968 1418.74,900.027 1418.94,895.603 1419.15,890.692 1419.35,885.291 \n",
" 1419.55,879.399 1419.76,873.013 1419.96,866.134 1420.16,858.761 1420.37,850.898 1420.57,842.545 1420.78,833.708 1420.98,824.389 1421.18,814.597 1421.39,804.336 \n",
" 1421.59,793.616 1421.79,782.445 1422,770.834 1422.2,758.794 1422.41,746.339 1422.61,733.482 1422.81,720.238 1423.02,706.624 1423.22,692.658 1423.42,678.357 \n",
" 1423.63,663.743 1423.83,648.835 1424.04,633.658 1424.24,618.232 1424.44,602.585 1424.65,586.739 1424.85,570.724 1425.05,554.565 1425.26,538.291 1425.46,521.932 \n",
" 1425.67,505.517 1425.87,489.079 1426.07,472.647 1426.28,456.255 1426.48,439.936 1426.68,423.723 1426.89,407.65 1427.09,391.75 1427.3,376.06 1427.5,360.612 \n",
" 1427.7,345.443 1427.91,330.586 1428.11,316.078 1428.31,301.951 1428.52,288.242 1428.72,274.984 1428.93,262.21 1429.13,249.955 1429.33,238.249 1429.54,227.126 \n",
" 1429.74,216.617 1429.94,206.751 1430.15,197.558 1430.35,189.065 1430.56,181.3 1430.76,174.289 1430.96,168.056 1431.17,162.623 1431.37,158.013 1431.57,154.245 \n",
" 1431.78,151.337 1431.98,149.306 1432.19,148.167 1432.39,147.933 1432.59,148.613 1432.8,150.218 1433,152.755 1433.2,156.228 1433.41,160.64 1433.61,165.993 \n",
" 1433.82,172.284 1434.02,179.51 1434.22,187.666 1434.43,196.743 1434.63,206.731 1434.83,217.618 1435.04,229.39 1435.24,242.03 1435.45,255.519 1435.65,269.836 \n",
" 1435.85,284.958 1436.06,300.86 1436.26,317.516 1436.46,334.896 1436.67,352.969 1436.87,371.703 1437.08,391.064 1437.28,411.014 1437.48,431.518 1437.69,452.536 \n",
" 1437.89,474.026 1438.09,495.948 1438.3,518.258 1438.5,540.913 1438.71,563.866 1438.91,587.072 1439.11,610.485 1439.32,634.056 1439.52,657.738 1439.72,681.483 \n",
" 1439.93,705.241 1440.13,728.964 1440.34,752.604 1440.54,776.11 1440.74,799.436 1440.95,822.531 1441.15,845.35 1441.35,867.845 1441.56,889.969 1441.76,911.677 \n",
" 1441.97,932.924 1442.17,953.667 1442.37,973.864 1442.58,993.474 1442.78,1012.46 1442.98,1030.78 1443.19,1048.39 1443.39,1065.28 1443.6,1081.39 1443.8,1096.71 \n",
" 1444,1111.19 1444.21,1124.83 1444.41,1137.58 1444.61,1149.44 1444.82,1160.37 1445.02,1170.36 1445.23,1179.4 1445.43,1187.48 1445.63,1194.57 1445.84,1200.68 \n",
" 1446.04,1205.8 1446.24,1209.93 1446.45,1213.06 1446.65,1215.2 1446.86,1216.35 1447.06,1216.53 1447.26,1215.73 1447.47,1213.97 1447.67,1211.27 1447.87,1207.64 \n",
" 1448.08,1203.1 1448.28,1197.68 1448.49,1191.39 1448.69,1184.26 1448.89,1176.32 1449.1,1167.6 1449.3,1158.13 1449.5,1147.94 1449.71,1137.07 1449.91,1125.55 \n",
" 1450.12,1113.43 1450.32,1100.74 1450.52,1087.52 1450.73,1073.81 1450.93,1059.66 1451.13,1045.11 1451.34,1030.2 1451.54,1014.99 1451.75,999.504 1451.95,983.802 \n",
" 1452.15,967.927 1452.36,951.924 1452.56,935.841 1452.76,919.724 1452.97,903.618 1453.17,887.569 1453.38,871.623 1453.58,855.824 1453.78,840.215 1453.99,824.841 \n",
" 1454.19,809.743 1454.4,794.962 1454.6,780.537 1454.8,766.509 1455.01,752.914 1455.21,739.787 1455.41,727.164 1455.62,715.076 1455.82,703.556 1456.03,692.632 \n",
" 1456.23,682.332 1456.43,672.681 1456.64,663.704 1456.84,655.421 1457.04,647.853 1457.25,641.017 1457.45,634.929 1457.66,629.603 1457.86,625.048 1458.06,621.276 \n",
" 1458.27,618.292 1458.47,616.102 1458.67,614.709 1458.88,614.113 1459.08,614.313 1459.29,615.305 1459.49,617.084 1459.69,619.642 1459.9,622.97 1460.1,627.057 \n",
" 1460.3,631.888 1460.51,637.451 1460.71,643.726 1460.92,650.697 1461.12,658.342 1461.32,666.642 1461.53,675.571 1461.73,685.106 1461.93,695.222 1462.14,705.89 \n",
" 1462.34,717.084 1462.55,728.775 1462.75,740.931 1462.95,753.522 1463.16,766.517 1463.36,779.883 1463.56,793.588 1463.77,807.597 1463.97,821.878 1464.18,836.395 \n",
" 1464.38,851.115 1464.58,866.004 1464.79,881.026 1464.99,896.148 1465.19,911.335 1465.4,926.553 1465.6,941.769 1465.81,956.949 1466.01,972.06 1466.21,987.071 \n",
" 1466.42,1001.95 1466.62,1016.66 1466.82,1031.18 1467.03,1045.48 1467.23,1059.52 1467.44,1073.29 1467.64,1086.75 1467.84,1099.87 1468.05,1112.64 1468.25,1125.03 \n",
" 1468.45,1137.01 1468.66,1148.57 1468.86,1159.68 1469.07,1170.33 1469.27,1180.5 1469.47,1190.17 1469.68,1199.32 1469.88,1207.95 1470.08,1216.03 1470.29,1223.56 \n",
" 1470.49,1230.52 1470.7,1236.91 1470.9,1242.72 1471.1,1247.94 1471.31,1252.57 1471.51,1256.59 1471.71,1260.01 1471.92,1262.83 1472.12,1265.04 1472.33,1266.64 \n",
" 1472.53,1267.63 1472.73,1268.02 1472.94,1267.81 1473.14,1266.99 1473.34,1265.58 1473.55,1263.58 1473.75,1260.99 1473.96,1257.83 1474.16,1254.1 1474.36,1249.8 \n",
" 1474.57,1244.95 1474.77,1239.55 1474.97,1233.62 1475.18,1227.16 1475.38,1220.19 1475.59,1212.71 1475.79,1204.75 1475.99,1196.3 1476.2,1187.39 1476.4,1178.03 \n",
" 1476.6,1168.22 1476.81,1157.98 1477.01,1147.34 1477.22,1136.29 1477.42,1124.85 1477.62,1113.04 1477.83,1100.88 1478.03,1088.37 1478.23,1075.53 1478.44,1062.38 \n",
" 1478.64,1048.93 1478.85,1035.19 1479.05,1021.18 1479.25,1006.92 1479.46,992.419 1479.66,977.694 1479.86,962.759 1480.07,947.63 1480.27,932.323 1480.48,916.853 \n",
" 1480.68,901.235 1480.88,885.485 1481.09,869.619 1481.29,853.652 1481.49,837.6 1481.7,821.479 1481.9,805.305 1482.11,789.094 1482.31,772.862 1482.51,756.625 \n",
" 1482.72,740.401 1482.92,724.204 1483.12,708.053 1483.33,691.963 1483.53,675.951 1483.74,660.035 1483.94,644.23 1484.14,628.556 1484.35,613.028 1484.55,597.664 \n",
" 1484.75,582.481 1484.96,567.497 1485.16,552.73 1485.37,538.196 1485.57,523.915 1485.77,509.902 1485.98,496.177 1486.18,482.756 1486.38,469.657 1486.59,456.898 \n",
" 1486.79,444.496 1487,432.469 1487.2,420.833 1487.4,409.605 1487.61,398.803 1487.81,388.442 1488.01,378.539 1488.22,369.109 1488.42,360.168 1488.63,351.732 \n",
" 1488.83,343.813 1489.03,336.427 1489.24,329.587 1489.44,323.306 1489.64,317.596 1489.85,312.469 1490.05,307.934 1490.26,304.003 1490.46,300.685 1490.66,297.987 \n",
" 1490.87,295.917 1491.07,294.481 1491.27,293.686 1491.48,293.535 1491.68,294.031 1491.89,295.176 1492.09,296.972 1492.29,299.419 1492.5,302.514 1492.7,306.255 \n",
" 1492.9,310.638 1493.11,315.657 1493.31,321.306 1493.52,327.578 1493.72,334.462 1493.92,341.947 1494.13,350.022 1494.33,358.673 1494.53,367.886 1494.74,377.643 \n",
" 1494.94,387.928 1495.15,398.721 1495.35,410.001 1495.55,421.748 1495.76,433.939 1495.96,446.549 1496.17,459.552 1496.37,472.923 1496.57,486.633 1496.78,500.654 \n",
" 1496.98,514.957 1497.18,529.509 1497.39,544.28 1497.59,559.236 1497.8,574.345 1498,589.573 1498.2,604.885 1498.41,620.245 1498.61,635.618 1498.81,650.968 \n",
" 1499.02,666.259 1499.22,681.453 1499.43,696.515 1499.63,711.407 1499.83,726.092 1500.04,740.535 1500.24,754.699 1500.44,768.549 1500.65,782.048 1500.85,795.162 \n",
" 1501.06,807.857 1501.26,820.099 1501.46,831.856 1501.67,843.096 1501.87,853.79 1502.07,863.907 1502.28,873.419 1502.48,882.299 1502.69,890.523 1502.89,898.066 \n",
" 1503.09,904.906 1503.3,911.023 1503.5,916.397 1503.7,921.011 1503.91,924.851 1504.11,927.902 1504.32,930.154 1504.52,931.598 1504.72,932.225 1504.93,932.031 \n",
" 1505.13,931.014 1505.33,929.171 1505.54,926.506 1505.74,923.02 1505.95,918.721 1506.15,913.617 1506.35,907.716 1506.56,901.034 1506.76,893.582 1506.96,885.38 \n",
" 1507.17,876.446 1507.37,866.8 1507.58,856.467 1507.78,845.471 1507.98,833.839 1508.19,821.602 1508.39,808.788 1508.59,795.433 1508.8,781.569 1509,767.232 \n",
" 1509.21,752.461 1509.41,737.294 1509.61,721.771 1509.82,705.934 1510.02,689.826 1510.22,673.489 1510.43,656.969 1510.63,640.311 1510.84,623.56 1511.04,606.763 \n",
" 1511.24,589.967 1511.45,573.22 1511.65,556.567 1511.85,540.058 1512.06,523.738 1512.26,507.655 1512.47,491.855 1512.67,476.385 1512.87,461.29 1513.08,446.615 \n",
" 1513.28,432.404 1513.48,418.7 1513.69,405.544 1513.89,392.978 1514.1,381.04 1514.3,369.768 1514.5,359.198 1514.71,349.366 1514.91,340.304 1515.11,332.043 \n",
" 1515.32,324.611 1515.52,318.037 1515.73,312.345 1515.93,307.557 1516.13,303.695 1516.34,300.777 1516.54,298.818 1516.74,297.832 1516.95,297.831 1517.15,298.822 \n",
" 1517.36,300.812 1517.56,303.805 1517.76,307.802 1517.97,312.802 1518.17,318.8 1518.37,325.791 1518.58,333.766 1518.78,342.713 1518.99,352.618 1519.19,363.466 \n",
" 1519.39,375.238 1519.6,387.914 1519.8,401.47 1520,415.881 1520.21,431.121 1520.41,447.159 1520.62,463.965 1520.82,481.506 1521.02,499.747 1521.23,518.652 \n",
" 1521.43,538.182 1521.63,558.298 1521.84,578.959 1522.04,600.124 1522.25,621.748 1522.45,643.789 1522.65,666.199 1522.86,688.935 1523.06,711.949 1523.26,735.194 \n",
" 1523.47,758.623 1523.67,782.188 1523.88,805.841 1524.08,829.535 1524.28,853.221 1524.49,876.853 1524.69,900.382 1524.89,923.762 1525.1,946.947 1525.3,969.892 \n",
" 1525.51,992.551 1525.71,1014.88 1525.91,1036.84 1526.12,1058.39 1526.32,1079.48 1526.52,1100.08 1526.73,1120.15 1526.93,1139.65 1527.14,1158.55 1527.34,1176.82 \n",
" 1527.54,1194.42 1527.75,1211.33 1527.95,1227.52 1528.15,1242.96 1528.36,1257.62 1528.56,1271.5 1528.77,1284.56 1528.97,1296.79 1529.17,1308.17 1529.38,1318.7 \n",
" 1529.58,1328.35 1529.78,1337.12 1529.99,1345 1530.19,1351.99 1530.4,1358.08 1530.6,1363.27 1530.8,1367.57 1531.01,1370.97 1531.21,1373.48 1531.41,1375.1 \n",
" 1531.62,1375.86 1531.82,1375.75 1532.03,1374.79 1532.23,1372.99 1532.43,1370.36 1532.64,1366.94 1532.84,1362.72 1533.04,1357.74 1533.25,1352.02 1533.45,1345.57 \n",
" 1533.66,1338.42 1533.86,1330.6 1534.06,1322.14 1534.27,1313.05 1534.47,1303.37 1534.67,1293.13 1534.88,1282.36 1535.08,1271.08 1535.29,1259.33 1535.49,1247.14 \n",
" 1535.69,1234.53 1535.9,1221.55 1536.1,1208.22 1536.3,1194.58 1536.51,1180.65 1536.71,1166.47 1536.92,1152.07 1537.12,1137.49 1537.32,1122.75 1537.53,1107.88 \n",
" 1537.73,1092.92 1537.94,1077.9 1538.14,1062.84 1538.34,1047.77 1538.55,1032.73 1538.75,1017.74 1538.95,1002.82 1539.16,988.003 1539.36,973.316 1539.57,958.781 \n",
" 1539.77,944.422 1539.97,930.261 1540.18,916.319 1540.38,902.618 1540.58,889.176 1540.79,876.012 1540.99,863.144 1541.2,850.588 1541.4,838.36 1541.6,826.474 \n",
" 1541.81,814.943 1542.01,803.779 1542.21,792.995 1542.42,782.6 1542.62,772.604 1542.83,763.015 1543.03,753.84 1543.23,745.086 1543.44,736.758 1543.64,728.861 \n",
" 1543.84,721.399 1544.05,714.374 1544.25,707.789 1544.46,701.645 1544.66,695.942 1544.86,690.681 1545.07,685.86 1545.27,681.478 1545.47,677.532 1545.68,674.021 \n",
" 1545.88,670.94 1546.09,668.285 1546.29,666.053 1546.49,664.239 1546.7,662.836 1546.9,661.839 1547.1,661.243 1547.31,661.04 1547.51,661.223 1547.72,661.786 \n",
" 1547.92,662.721 1548.12,664.02 1548.33,665.675 1548.53,667.678 1548.73,670.019 1548.94,672.691 1549.14,675.684 1549.35,678.99 1549.55,682.597 1549.75,686.499 \n",
" 1549.96,690.683 1550.16,695.141 1550.36,699.862 1550.57,704.836 1550.77,710.053 1550.98,715.502 1551.18,721.172 1551.38,727.052 1551.59,733.131 1551.79,739.398 \n",
" 1551.99,745.841 1552.2,752.449 1552.4,759.209 1552.61,766.109 1552.81,773.138 1553.01,780.282 1553.22,787.528 1553.42,794.864 1553.62,802.277 1553.83,809.752 \n",
" 1554.03,817.276 1554.24,824.834 1554.44,832.414 1554.64,839.999 1554.85,847.575 1555.05,855.127 1555.25,862.64 1555.46,870.097 1555.66,877.484 1555.87,884.784 \n",
" 1556.07,891.981 1556.27,899.057 1556.48,905.998 1556.68,912.784 1556.88,919.401 1557.09,925.829 1557.29,932.053 1557.5,938.054 1557.7,943.815 1557.9,949.318 \n",
" 1558.11,954.546 1558.31,959.482 1558.51,964.108 1558.72,968.406 1558.92,972.359 1559.13,975.951 1559.33,979.165 1559.53,981.983 1559.74,984.39 1559.94,986.371 \n",
" 1560.14,987.908 1560.35,988.988 1560.55,989.597 1560.76,989.719 1560.96,989.343 1561.16,988.455 1561.37,987.043 1561.57,985.097 1561.77,982.606 1561.98,979.56 \n",
" 1562.18,975.952 1562.39,971.774 1562.59,967.02 1562.79,961.683 1563,955.76 1563.2,949.248 1563.4,942.145 1563.61,934.451 1563.81,926.165 1564.02,917.291 \n",
" 1564.22,907.83 1564.42,897.789 1564.63,887.173 1564.83,875.99 1565.03,864.249 1565.24,851.96 1565.44,839.135 1565.65,825.788 1565.85,811.934 1566.05,797.588 \n",
" 1566.26,782.769 1566.46,767.496 1566.66,751.789 1566.87,735.671 1567.07,719.166 1567.28,702.298 1567.48,685.093 1567.68,667.579 1567.89,649.785 1568.09,631.74 \n",
" 1568.29,613.476 1568.5,595.025 1568.7,576.42 1568.91,557.695 1569.11,538.886 1569.31,520.027 1569.52,501.157 1569.72,482.311 1569.92,463.528 1570.13,444.846 \n",
" 1570.33,426.305 1570.54,407.942 1570.74,389.797 1570.94,371.909 1571.15,354.318 1571.35,337.063 1571.55,320.183 1571.76,303.717 1571.96,287.703 1572.17,272.178 \n",
" 1572.37,257.181 1572.57,242.747 1572.78,228.912 1572.98,215.711 1573.18,203.178 1573.39,191.344 1573.59,180.243 1573.8,169.902 1574,160.352 1574.2,151.62 \n",
" 1574.41,143.729 1574.61,136.706 1574.81,130.571 1575.02,125.345 1575.22,121.046 1575.43,117.691 1575.63,115.294 1575.83,113.867 1576.04,113.42 1576.24,113.961 \n",
" 1576.44,115.496 1576.65,118.028 1576.85,121.559 1577.06,126.087 1577.26,131.609 1577.46,138.119 1577.67,145.609 1577.87,154.067 1578.07,163.483 1578.28,173.839 \n",
" 1578.48,185.119 1578.69,197.304 1578.89,210.371 1579.09,224.296 1579.3,239.054 1579.5,254.615 1579.71,270.95 1579.91,288.027 1580.11,305.811 1580.32,324.267 \n",
" 1580.52,343.358 1580.72,363.043 1580.93,383.284 1581.13,404.036 1581.34,425.259 1581.54,446.906 1581.74,468.932 1581.95,491.291 1582.15,513.936 1582.35,536.818 \n",
" 1582.56,559.888 1582.76,583.098 1582.97,606.398 1583.17,629.738 1583.37,653.069 1583.58,676.34 1583.78,699.503 1583.98,722.507 1584.19,745.305 1584.39,767.847 \n",
" 1584.6,790.086 1584.8,811.976 1585,833.471 1585.21,854.525 1585.41,875.096 1585.61,895.142 1585.82,914.62 1586.02,933.493 1586.23,951.722 1586.43,969.271 \n",
" 1586.63,986.106 1586.84,1002.2 1587.04,1017.51 1587.24,1032.02 1587.45,1045.7 1587.65,1058.52 1587.86,1070.47 1588.06,1081.52 1588.26,1091.66 1588.47,1100.87 \n",
" 1588.67,1109.14 1588.87,1116.47 1589.08,1122.84 1589.28,1128.25 1589.49,1132.69 1589.69,1136.17 1589.89,1138.7 1590.1,1140.26 1590.3,1140.88 1590.5,1140.57 \n",
" 1590.71,1139.32 1590.91,1137.17 1591.12,1134.13 1591.32,1130.21 1591.52,1125.43 1591.73,1119.83 1591.93,1113.42 1592.13,1106.24 1592.34,1098.31 1592.54,1089.66 \n",
" 1592.75,1080.33 1592.95,1070.35 1593.15,1059.75 1593.36,1048.58 1593.56,1036.86 1593.76,1024.65 1593.97,1011.98 1594.17,998.884 1594.38,985.415 1594.58,971.613 \n",
" 1594.78,957.519 1594.99,943.179 1595.19,928.636 1595.39,913.935 1595.6,899.118 1595.8,884.231 1596.01,869.317 1596.21,854.42 1596.41,839.584 1596.62,824.85 \n",
" 1596.82,810.262 1597.02,795.86 1597.23,781.684 1597.43,767.776 1597.64,754.172 1597.84,740.91 1598.04,728.026 1598.25,715.556 1598.45,703.531 1598.65,691.985 \n",
" 1598.86,680.948 1599.06,670.448 1599.27,660.513 1599.47,651.167 1599.67,642.435 1599.88,634.338 1600.08,626.896 1600.28,620.126 1600.49,614.046 1600.69,608.669 \n",
" 1600.9,604.007 1601.1,600.071 1601.3,596.869 1601.51,594.407 1601.71,592.69 1601.91,591.72 1602.12,591.497 1602.32,592.02 1602.53,593.286 1602.73,595.29 \n",
" 1602.93,598.025 1603.14,601.482 1603.34,605.652 1603.54,610.521 1603.75,616.076 1603.95,622.303 1604.16,629.185 1604.36,636.704 1604.56,644.839 1604.77,653.572 \n",
" 1604.97,662.88 1605.17,672.74 1605.38,683.128 1605.58,694.02 1605.79,705.389 1605.99,717.209 1606.19,729.452 1606.4,742.091 1606.6,755.097 1606.8,768.442 \n",
" 1607.01,782.094 1607.21,796.026 1607.42,810.207 1607.62,824.606 1607.82,839.194 1608.03,853.94 1608.23,868.815 1608.43,883.788 1608.64,898.829 1608.84,913.909 \n",
" 1609.05,928.998 1609.25,944.068 1609.45,959.09 1609.66,974.037 1609.86,988.88 1610.06,1003.59 1610.27,1018.15 1610.47,1032.53 1610.68,1046.7 1610.88,1060.64 \n",
" 1611.08,1074.33 1611.29,1087.74 1611.49,1100.86 1611.69,1113.66 1611.9,1126.13 1612.1,1138.23 1612.31,1149.97 1612.51,1161.31 1612.71,1172.25 1612.92,1182.77 \n",
" 1613.12,1192.85 1613.32,1202.49 1613.53,1211.66 1613.73,1220.36 1613.94,1228.58 1614.14,1236.31 1614.34,1243.54 1614.55,1250.26 1614.75,1256.46 1614.95,1262.14 \n",
" 1615.16,1267.3 1615.36,1271.93 1615.57,1276.02 1615.77,1279.57 1615.97,1282.59 1616.18,1285.06 1616.38,1286.99 1616.58,1288.38 1616.79,1289.23 1616.99,1289.53 \n",
" 1617.2,1289.3 1617.4,1288.53 1617.6,1287.22 1617.81,1285.38 1618.01,1283.02 1618.21,1280.13 1618.42,1276.72 1618.62,1272.79 1618.83,1268.36 1619.03,1263.42 \n",
" 1619.23,1257.98 1619.44,1252.05 1619.64,1245.63 1619.85,1238.74 1620.05,1231.38 1620.25,1223.55 1620.46,1215.27 1620.66,1206.54 1620.86,1197.37 1621.07,1187.77 \n",
" 1621.27,1177.75 1621.48,1167.32 1621.68,1156.49 1621.88,1145.27 1622.09,1133.66 1622.29,1121.68 1622.49,1109.35 1622.7,1096.66 1622.9,1083.64 1623.11,1070.29 \n",
" 1623.31,1056.63 1623.51,1042.67 1623.72,1028.42 1623.92,1013.9 1624.12,999.116 1624.33,984.086 1624.53,968.825 1624.74,953.346 1624.94,937.667 1625.14,921.801 \n",
" 1625.35,905.765 1625.55,889.577 1625.75,873.252 1625.96,856.809 1626.16,840.265 1626.37,823.639 1626.57,806.948 1626.77,790.213 1626.98,773.453 1627.18,756.687 \n",
" 1627.38,739.936 1627.59,723.221 1627.79,706.563 1628,689.982 1628.2,673.501 1628.4,657.141 1628.61,640.924 1628.81,624.874 1629.01,609.011 1629.22,593.36 \n",
" 1629.42,577.942 1629.63,562.781 1629.83,547.9 1630.03,533.321 1630.24,519.067 1630.44,505.161 1630.64,491.625 1630.85,478.482 1631.05,465.754 1631.26,453.462 \n",
" 1631.46,441.628 1631.66,430.273 1631.87,419.417 1632.07,409.081 1632.27,399.283 1632.48,390.042 1632.68,381.375 1632.89,373.301 1633.09,365.835 1633.29,358.993 \n",
" 1633.5,352.788 1633.7,347.235 1633.9,342.345 1634.11,338.13 1634.31,334.599 1634.52,331.761 1634.72,329.624 1634.92,328.194 1635.13,327.474 1635.33,327.47 \n",
" 1635.53,328.181 1635.74,329.61 1635.94,331.753 1636.15,334.609 1636.35,338.174 1636.55,342.441 1636.76,347.402 1636.96,353.049 1637.16,359.37 1637.37,366.354 \n",
" 1637.57,373.986 1637.78,382.251 1637.98,391.13 1638.18,400.606 1638.39,410.658 1638.59,421.264 1638.79,432.399 1639,444.04 1639.2,456.16 1639.41,468.731 \n",
" 1639.61,481.723 1639.81,495.107 1640.02,508.851 1640.22,522.922 1640.42,537.285 1640.63,551.907 1640.83,566.751 1641.04,581.781 1641.24,596.96 1641.44,612.248 \n",
" 1641.65,627.608 1641.85,643 1642.05,658.385 1642.26,673.722 1642.46,688.973 1642.67,704.096 1642.87,719.052 1643.07,733.801 1643.28,748.303 1643.48,762.518 \n",
" 1643.68,776.408 1643.89,789.935 1644.09,803.06 1644.3,815.747 1644.5,827.96 1644.7,839.664 1644.91,850.825 1645.11,861.41 1645.31,871.389 1645.52,880.73 \n",
" 1645.72,889.406 1645.93,897.39 1646.13,904.657 1646.33,911.182 1646.54,916.945 1646.74,921.926 1646.94,926.107 1647.15,929.472 1647.35,932.007 1647.56,933.702 \n",
" 1647.76,934.547 1647.96,934.534 1648.17,933.66 1648.37,931.921 1648.57,929.318 1648.78,925.852 1648.98,921.529 1649.19,916.354 1649.39,910.338 1649.59,903.492 \n",
" 1649.8,895.829 1650,887.367 1650.2,878.122 1650.41,868.117 1650.61,857.373 1650.82,845.916 1651.02,833.772 1651.22,820.972 1651.43,807.545 1651.63,793.524 \n",
" 1651.83,778.944 1652.04,763.842 1652.24,748.255 1652.45,732.222 1652.65,715.784 1652.85,698.984 1653.06,681.864 1653.26,664.47 1653.46,646.845 1653.67,629.037 \n",
" 1653.87,611.091 1654.08,593.056 1654.28,574.98 1654.48,556.91 1654.69,538.894 1654.89,520.982 1655.09,503.222 1655.3,485.662 1655.5,468.349 1655.71,451.332 \n",
" 1655.91,434.657 1656.11,418.37 1656.32,402.516 1656.52,387.14 1656.72,372.285 1656.93,357.994 1657.13,344.306 1657.34,331.261 1657.54,318.897 1657.74,307.25 \n",
" 1657.95,296.354 1658.15,286.243 1658.35,276.946 1658.56,268.492 1658.76,260.909 1658.97,254.22 1659.17,248.448 1659.37,243.613 1659.58,239.732 1659.78,236.822 \n",
" 1659.98,234.894 1660.19,233.959 1660.39,234.026 1660.6,235.101 1660.8,237.185 1661,240.281 1661.21,244.386 1661.41,249.496 1661.62,255.604 1661.82,262.701 \n",
" 1662.02,270.776 1662.23,279.815 1662.43,289.801 1662.63,300.717 1662.84,312.541 1663.04,325.252 1663.25,338.823 1663.45,353.229 1663.65,368.44 1663.86,384.426 \n",
" 1664.06,401.155 1664.26,418.592 1664.47,436.703 1664.67,455.45 1664.88,474.795 1665.08,494.699 1665.28,515.12 1665.49,536.018 1665.69,557.349 1665.89,579.071 \n",
" 1666.1,601.139 1666.3,623.508 1666.51,646.134 1666.71,668.971 1666.91,691.974 1667.12,715.097 1667.32,738.295 1667.52,761.522 1667.73,784.733 1667.93,807.883 \n",
" 1668.14,830.928 1668.34,853.825 1668.54,876.531 1668.75,899.002 1668.95,921.199 1669.15,943.082 1669.36,964.609 1669.56,985.745 1669.77,1006.45 1669.97,1026.7 \n",
" 1670.17,1046.44 1670.38,1065.66 1670.58,1084.31 1670.78,1102.37 1670.99,1119.82 1671.19,1136.62 1671.4,1152.76 1671.6,1168.2 1671.8,1182.93 1672.01,1196.94 \n",
" 1672.21,1210.19 1672.41,1222.69 1672.62,1234.41 1672.82,1245.34 1673.03,1255.48 1673.23,1264.82 1673.43,1273.35 1673.64,1281.07 1673.84,1287.97 1674.04,1294.07 \n",
" 1674.25,1299.35 1674.45,1303.82 1674.66,1307.48 1674.86,1310.35 1675.06,1312.44 1675.27,1313.74 1675.47,1314.28 1675.67,1314.06 1675.88,1313.1 1676.08,1311.42 \n",
" 1676.29,1309.03 1676.49,1305.95 1676.69,1302.2 1676.9,1297.8 1677.1,1292.77 1677.3,1287.13 1677.51,1280.9 1677.71,1274.11 1677.92,1266.79 1678.12,1258.95 \n",
" 1678.32,1250.62 1678.53,1241.83 1678.73,1232.61 1678.93,1222.97 1679.14,1212.95 1679.34,1202.58 1679.55,1191.87 1679.75,1180.86 1679.95,1169.58 1680.16,1158.04 \n",
" 1680.36,1146.28 1680.56,1134.33 1680.77,1122.2 1680.97,1109.93 1681.18,1097.54 1681.38,1085.05 1681.58,1072.49 1681.79,1059.89 1681.99,1047.26 1682.19,1034.63 \n",
" 1682.4,1022.02 1682.6,1009.46 1682.81,996.959 1683.01,984.544 1683.21,972.233 1683.42,960.046 1683.62,947.999 1683.82,936.111 1684.03,924.399 1684.23,912.878 \n",
" 1684.44,901.563 1684.64,890.469 1684.84,879.611 1685.05,868.999 1685.25,858.649 1685.45,848.569 1685.66,838.773 1685.86,829.269 1686.07,820.067 1686.27,811.176 \n",
" 1686.47,802.605 1686.68,794.36 1686.88,786.449 1687.08,778.879 1687.29,771.654 1687.49,764.78 1687.7,758.262 1687.9,752.105 1688.1,746.311 1688.31,740.884 \n",
" 1688.51,735.826 1688.71,731.141 1688.92,726.83 1689.12,722.893 1689.33,719.334 1689.53,716.151 1689.73,713.346 1689.94,710.918 1690.14,708.867 1690.34,707.192 \n",
" 1690.55,705.893 1690.75,704.968 1690.96,704.415 1691.16,704.232 1691.36,704.417 1691.57,704.968 1691.77,705.881 1691.97,707.153 1692.18,708.781 1692.38,710.761 \n",
" 1692.59,713.088 1692.79,715.758 1692.99,718.766 1693.2,722.108 1693.4,725.776 1693.6,729.766 1693.81,734.071 1694.01,738.684 1694.22,743.598 1694.42,748.806 \n",
" 1694.62,754.299 1694.83,760.068 1695.03,766.106 1695.23,772.401 1695.44,778.946 1695.64,785.728 1695.85,792.737 1696.05,799.962 1696.25,807.39 1696.46,815.009 \n",
" 1696.66,822.805 1696.86,830.766 1697.07,838.877 1697.27,847.123 1697.48,855.488 1697.68,863.957 1697.88,872.514 1698.09,881.14 1698.29,889.82 1698.49,898.534 \n",
" 1698.7,907.264 1698.9,915.99 1699.11,924.695 1699.31,933.356 1699.51,941.955 1699.72,950.47 1699.92,958.879 1700.12,967.162 1700.33,975.296 1700.53,983.259 \n",
" 1700.74,991.029 1700.94,998.584 1701.14,1005.9 1701.35,1012.96 1701.55,1019.73 1701.75,1026.19 1701.96,1032.33 1702.16,1038.11 1702.37,1043.52 1702.57,1048.53 \n",
" 1702.77,1053.13 1702.98,1057.28 1703.18,1060.98 1703.39,1064.19 1703.59,1066.9 1703.79,1069.09 1704,1070.75 1704.2,1071.84 1704.4,1072.36 1704.61,1072.29 \n",
" 1704.81,1071.62 1705.02,1070.32 1705.22,1068.4 1705.42,1065.83 1705.63,1062.6 1705.83,1058.71 1706.03,1054.15 1706.24,1048.9 1706.44,1042.98 1706.65,1036.36 \n",
" 1706.85,1029.05 1707.05,1021.05 1707.26,1012.36 1707.46,1002.98 1707.66,992.917 1707.87,982.174 1708.07,970.759 1708.28,958.681 1708.48,945.952 1708.68,932.583 \n",
" 1708.89,918.59 1709.09,903.987 1709.29,888.793 1709.5,873.028 1709.7,856.711 1709.91,839.867 1710.11,822.518 1710.31,804.692 1710.52,786.416 1710.72,767.718 \n",
" 1710.92,748.63 1711.13,729.182 1711.33,709.408 1711.54,689.343 1711.74,669.023 1711.94,648.483 1712.15,627.762 1712.35,606.899 1712.55,585.932 1712.76,564.904 \n",
" 1712.96,543.854 1713.17,522.826 1713.37,501.859 1713.57,480.999 1713.78,460.287 1713.98,439.766 1714.18,419.48 1714.39,399.472 1714.59,379.784 1714.8,360.46 \n",
" 1715,341.542 1715.2,323.071 1715.41,305.089 1715.61,287.637 1715.81,270.753 1716.02,254.478 1716.22,238.847 1716.43,223.899 1716.63,209.667 1716.83,196.187 \n",
" 1717.04,183.489 1717.24,171.606 1717.44,160.566 1717.65,150.397 1717.85,141.124 1718.06,132.771 1718.26,125.36 1718.46,118.91 1718.67,113.438 1718.87,108.961 \n",
" 1719.07,105.49 1719.28,103.037 1719.48,101.611 1719.69,101.216 1719.89,101.858 1720.09,103.537 1720.3,106.251 1720.5,109.998 1720.7,114.772 1720.91,120.563 \n",
" 1721.11,127.361 1721.32,135.153 1721.52,143.923 1721.72,153.653 1721.93,164.322 1722.13,175.907 1722.33,188.385 1722.54,201.728 1722.74,215.906 1722.95,230.89 \n",
" 1723.15,246.645 1723.35,263.136 1723.56,280.328 1723.76,298.181 1723.96,316.657 1724.17,335.712 1724.37,355.305 1724.58,375.392 1724.78,395.927 1724.98,416.864 \n",
" 1725.19,438.156 1725.39,459.755 1725.59,481.612 1725.8,503.679 1726,525.906 1726.21,548.243 1726.41,570.641 1726.61,593.049 1726.82,615.417 1727.02,637.697 \n",
" 1727.22,659.839 1727.43,681.795 1727.63,703.516 1727.84,724.955 1728.04,746.067 1728.24,766.807 1728.45,787.129 1728.65,806.991 1728.85,826.352 1729.06,845.172 \n",
" 1729.26,863.412 1729.47,881.035 1729.67,898.007 1729.87,914.295 1730.08,929.866 1730.28,944.693 1730.48,958.748 1730.69,972.005 1730.89,984.443 1731.1,996.04 \n",
" 1731.3,1006.78 1731.5,1016.64 1731.71,1025.62 1731.91,1033.7 1732.11,1040.86 1732.32,1047.12 1732.52,1052.45 1732.73,1056.87 1732.93,1060.37 1733.13,1062.95 \n",
" 1733.34,1064.62 1733.54,1065.39 1733.74,1065.26 1733.95,1064.26 1734.15,1062.4 1734.36,1059.68 1734.56,1056.14 1734.76,1051.78 1734.97,1046.65 1735.17,1040.75 \n",
" 1735.37,1034.12 1735.58,1026.78 1735.78,1018.77 1735.99,1010.12 1736.19,1000.85 1736.39,991.006 1736.6,980.62 1736.8,969.729 1737,958.369 1737.21,946.581 \n",
" 1737.41,934.402 1737.62,921.873 1737.82,909.033 1738.02,895.924 1738.23,882.587 1738.43,869.063 1738.63,855.394 1738.84,841.621 1739.04,827.784 1739.25,813.927 \n",
" 1739.45,800.088 1739.65,786.308 1739.86,772.628 1740.06,759.085 1740.26,745.719 1740.47,732.567 1740.67,719.665 1740.88,707.049 1741.08,694.752 1741.28,682.81 \n",
" 1741.49,671.252 1741.69,660.111 1741.89,649.415 1742.1,639.192 1742.3,629.468 1742.51,620.268 1742.71,611.616 1742.91,603.532 1743.12,596.036 1743.32,589.148 \n",
" 1743.52,582.882 1743.73,577.255 1743.93,572.278 1744.14,567.963 1744.34,564.32 1744.54,561.355 1744.75,559.076 1744.95,557.486 1745.16,556.588 1745.36,556.382 \n",
" 1745.56,556.868 1745.77,558.043 1745.97,559.903 1746.17,562.443 1746.38,565.655 1746.58,569.53 1746.79,574.059 1746.99,579.23 1747.19,585.03 1747.4,591.445 \n",
" 1747.6,598.46 1747.8,606.059 1748.01,614.223 1748.21,622.936 1748.42,632.177 1748.62,641.925 1748.82,652.161 1749.03,662.861 1749.23,674.005 1749.43,685.567 \n",
" 1749.64,697.525 1749.84,709.855 1750.05,722.532 1750.25,735.531 1750.45,748.828 1750.66,762.396 1750.86,776.21 1751.06,790.245 1751.27,804.475 1751.47,818.875 \n",
" 1751.68,833.419 1751.88,848.082 1752.08,862.839 1752.29,877.664 1752.49,892.533 1752.69,907.423 1752.9,922.308 1753.1,937.166 1753.31,951.973 1753.51,966.707 \n",
" 1753.71,981.346 1753.92,995.868 1754.12,1010.25 1754.32,1024.48 1754.53,1038.52 1754.73,1052.37 1754.94,1066.01 1755.14,1079.4 1755.34,1092.55 1755.55,1105.43 \n",
" 1755.75,1118.02 1755.95,1130.32 1756.16,1142.29 1756.36,1153.94 1756.57,1165.25 1756.77,1176.2 1756.97,1186.78 1757.18,1196.98 1757.38,1206.79 1757.58,1216.19 \n",
" 1757.79,1225.19 1757.99,1233.76 1758.2,1241.9 1758.4,1249.61 1758.6,1256.86 1758.81,1263.66 1759.01,1270 1759.21,1275.87 1759.42,1281.27 1759.62,1286.19 \n",
" 1759.83,1290.62 1760.03,1294.56 1760.23,1298.01 1760.44,1300.96 1760.64,1303.41 1760.84,1305.36 1761.05,1306.8 1761.25,1307.73 1761.46,1308.14 1761.66,1308.05 \n",
" 1761.86,1307.43 1762.07,1306.31 1762.27,1304.66 1762.47,1302.5 1762.68,1299.82 1762.88,1296.63 1763.09,1292.92 1763.29,1288.7 1763.49,1283.96 1763.7,1278.71 \n",
" 1763.9,1272.96 1764.1,1266.7 1764.31,1259.94 1764.51,1252.68 1764.72,1244.93 1764.92,1236.69 1765.12,1227.97 1765.33,1218.76 1765.53,1209.09 1765.73,1198.96 \n",
" 1765.94,1188.37 1766.14,1177.33 1766.35,1165.85 1766.55,1153.94 1766.75,1141.61 1766.96,1128.87 1767.16,1115.74 1767.36,1102.22 1767.57,1088.33 1767.77,1074.08 \n",
" 1767.98,1059.49 1768.18,1044.56 1768.38,1029.32 1768.59,1013.79 1768.79,997.975 1768.99,981.899 1769.2,965.581 1769.4,949.038 1769.61,932.292 1769.81,915.364 \n",
" 1770.01,898.275 1770.22,881.047 1770.42,863.704 1770.62,846.268 1770.83,828.764 1771.03,811.216 1771.24,793.65 1771.44,776.092 1771.64,758.566 1771.85,741.101 \n",
" 1772.05,723.723 1772.25,706.458 1772.46,689.336 1772.66,672.383 1772.87,655.627 1773.07,639.096 1773.27,622.818 1773.48,606.822 1773.68,591.134 1773.88,575.784 \n",
" 1774.09,560.798 1774.29,546.203 1774.5,532.027 1774.7,518.296 1774.9,505.035 1775.11,492.271 1775.31,480.027 1775.51,468.329 1775.72,457.198 1775.92,446.657 \n",
" 1776.13,436.728 1776.33,427.43 1776.53,418.784 1776.74,410.807 1776.94,403.515 1777.14,396.925 1777.35,391.051 1777.55,385.905 1777.76,381.499 1777.96,377.842 \n",
" 1778.16,374.943 1778.37,372.809 1778.57,371.444 1778.77,370.851 1778.98,371.033 1779.18,371.988 1779.39,373.715 1779.59,376.21 1779.79,379.467 1780,383.479 \n",
" 1780.2,388.236 1780.4,393.727 1780.61,399.938 1780.81,406.856 1781.02,414.462 1781.22,422.739 1781.42,431.666 1781.63,441.221 1781.83,451.38 1782.03,462.118 \n",
" 1782.24,473.408 1782.44,485.22 1782.65,497.524 1782.85,510.29 1783.05,523.484 1783.26,537.071 1783.46,551.016 1783.66,565.282 1783.87,579.832 1784.07,594.626 \n",
" 1784.28,609.626 1784.48,624.79 1784.68,640.077 1784.89,655.446 1785.09,670.855 1785.3,686.261 1785.5,701.621 1785.7,716.892 1785.91,732.032 1786.11,746.998 \n",
" 1786.31,761.747 1786.52,776.237 1786.72,790.425 1786.93,804.272 1787.13,817.735 1787.33,830.776 1787.54,843.355 1787.74,855.435 1787.94,866.979 1788.15,877.951 \n",
" 1788.35,888.317 1788.56,898.045 1788.76,907.104 1788.96,915.463 1789.17,923.096 1789.37,929.976 1789.57,936.08 1789.78,941.384 1789.98,945.87 1790.19,949.519 \n",
" 1790.39,952.316 1790.59,954.247 1790.8,955.301 1791,955.469 1791.2,954.744 1791.41,953.123 1791.61,950.603 1791.82,947.186 1792.02,942.875 1792.22,937.674 \n",
" 1792.43,931.592 1792.63,924.64 1792.83,916.831 1793.04,908.178 1793.24,898.701 1793.45,888.418 1793.65,877.353 1793.85,865.528 1794.06,852.971 1794.26,839.71 \n",
" 1794.46,825.775 1794.67,811.2 1794.87,796.017 1795.08,780.264 1795.28,763.977 1795.48,747.197 1795.69,729.963 1795.89,712.318 1796.09,694.305 1796.3,675.969 \n",
" 1796.5,657.354 1796.71,638.507 1796.91,619.475 1797.11,600.306 1797.32,581.048 1797.52,561.749 1797.72,542.458 1797.93,523.225 1798.13,504.097 1798.34,485.124 \n",
" 1798.54,466.354 1798.74,447.835 1798.95,429.614 1799.15,411.739 1799.35,394.255 1799.56,377.207 1799.76,360.64 1799.97,344.596 1800.17,329.117 1800.37,314.243 \n",
" 1800.58,300.013 1800.78,286.464 1800.98,273.632 1801.19,261.551 1801.39,250.252 1801.6,239.765 1801.8,230.118 1802,221.338 1802.21,213.447 1802.41,206.468 \n",
" 1802.61,200.42 1802.82,195.32 1803.02,191.182 1803.23,188.019 1803.43,185.841 1803.63,184.655 1803.84,184.467 1804.04,185.279 1804.24,187.093 1804.45,189.905 \n",
" 1804.65,193.711 1804.86,198.506 1805.06,204.279 1805.26,211.019 1805.47,218.714 1805.67,227.347 1805.87,236.9 1806.08,247.353 1806.28,258.685 1806.49,270.871 \n",
" 1806.69,283.887 1806.89,297.704 1807.1,312.293 1807.3,327.624 1807.5,343.664 1807.71,360.379 1807.91,377.735 1808.12,395.695 1808.32,414.222 1808.52,433.277 \n",
" 1808.73,452.821 1808.93,472.815 1809.13,493.217 1809.34,513.986 1809.54,535.08 1809.75,556.458 1809.95,578.076 1810.15,599.893 1810.36,621.866 1810.56,643.952 \n",
" 1810.76,666.11 1810.97,688.296 1811.17,710.471 1811.38,732.593 1811.58,754.621 1811.78,776.516 1811.99,798.238 1812.19,819.751 1812.39,841.016 1812.6,861.997 \n",
" 1812.8,882.66 1813.01,902.971 1813.21,922.897 1813.41,942.407 1813.62,961.471 1813.82,980.06 1814.02,998.148 1814.23,1015.71 1814.43,1032.72 1814.64,1049.15 \n",
" 1814.84,1065 1815.04,1080.22 1815.25,1094.82 1815.45,1108.77 1815.65,1122.06 1815.86,1134.67 1816.06,1146.6 1816.27,1157.83 1816.47,1168.37 1816.67,1178.19 \n",
" 1816.88,1187.3 1817.08,1195.7 1817.28,1203.38 1817.49,1210.34 1817.69,1216.58 1817.9,1222.12 1818.1,1226.94 1818.3,1231.07 1818.51,1234.49 1818.71,1237.24 \n",
" 1818.91,1239.3 1819.12,1240.7 1819.32,1241.44 1819.53,1241.55 1819.73,1241.02 1819.93,1239.88 1820.14,1238.14 1820.34,1235.82 1820.54,1232.94 1820.75,1229.51 \n",
" 1820.95,1225.56 1821.16,1221.09 1821.36,1216.13 1821.56,1210.71 1821.77,1204.83 1821.97,1198.53 1822.17,1191.81 1822.38,1184.71 1822.58,1177.25 1822.79,1169.44 \n",
" 1822.99,1161.3 1823.19,1152.87 1823.4,1144.15 1823.6,1135.17 1823.8,1125.95 1824.01,1116.52 1824.21,1106.89 1824.42,1097.08 1824.62,1087.12 1824.82,1077.02 \n",
" 1825.03,1066.8 1825.23,1056.49 1825.43,1046.1 1825.64,1035.65 1825.84,1025.15 1826.05,1014.64 1826.25,1004.11 1826.45,993.599 1826.66,983.112 1826.86,972.669 \n",
" 1827.07,962.284 1827.27,951.972 1827.47,941.75 1827.68,931.63 1827.88,921.628 1828.08,911.755 1828.29,902.026 1828.49,892.453 1828.7,883.048 1828.9,873.823 \n",
" 1829.1,864.79 1829.31,855.96 1829.51,847.343 1829.71,838.95 1829.92,830.79 1830.12,822.874 1830.33,815.211 1830.53,807.81 1830.73,800.679 1830.94,793.828 \n",
" 1831.14,787.263 1831.34,780.994 1831.55,775.028 1831.75,769.371 1831.96,764.032 1832.16,759.017 1832.36,754.332 1832.57,749.983 1832.77,745.977 1832.97,742.319 \n",
" 1833.18,739.015 1833.38,736.069 1833.59,733.487 1833.79,731.273 1833.99,729.431 1834.2,727.965 1834.4,726.878 1834.6,726.173 1834.81,725.854 1835.01,725.922 \n",
" 1835.22,726.379 1835.42,727.227 1835.62,728.468 1835.83,730.1 1836.03,732.125 1836.23,734.541 1836.44,737.348 1836.64,740.544 1836.85,744.127 1837.05,748.093 \n",
" 1837.25,752.44 1837.46,757.163 1837.66,762.257 1837.86,767.717 1838.07,773.536 1838.27,779.707 1838.48,786.222 1838.68,793.073 1838.88,800.249 1839.09,807.742 \n",
" 1839.29,815.539 1839.49,823.628 1839.7,831.997 1839.9,840.633 1840.11,849.52 1840.31,858.643 1840.51,867.986 1840.72,877.531 1840.92,887.262 1841.12,897.159 \n",
" 1841.33,907.202 1841.53,917.371 1841.74,927.646 1841.94,938.003 1842.14,948.421 1842.35,958.877 1842.55,969.345 1842.75,979.803 1842.96,990.224 1843.16,1000.58 \n",
" 1843.37,1010.85 1843.57,1021.01 1843.77,1031.02 1843.98,1040.87 1844.18,1050.52 1844.38,1059.94 1844.59,1069.11 1844.79,1078.01 1845,1086.59 1845.2,1094.84 \n",
" 1845.4,1102.72 1845.61,1110.22 1845.81,1117.29 1846.01,1123.92 1846.22,1130.08 1846.42,1135.74 1846.63,1140.88 1846.83,1145.47 1847.03,1149.49 1847.24,1152.92 \n",
" 1847.44,1155.73 1847.64,1157.9 1847.85,1159.42 1848.05,1160.26 1848.26,1160.4 1848.46,1159.84 1848.66,1158.55 1848.87,1156.53 1849.07,1153.75 1849.27,1150.21 \n",
" 1849.48,1145.91 1849.68,1140.82 1849.89,1134.96 1850.09,1128.31 1850.29,1120.87 1850.5,1112.64 1850.7,1103.62 1850.9,1093.83 1851.11,1083.25 1851.31,1071.91 \n",
" 1851.52,1059.81 1851.72,1046.96 1851.92,1033.37 1852.13,1019.06 1852.33,1004.05 1852.53,988.357 1852.74,972 1852.94,955.002 1853.15,937.389 1853.35,919.187 \n",
" 1853.55,900.425 1853.76,881.131 1853.96,861.339 1854.16,841.08 1854.37,820.39 1854.57,799.304 1854.78,777.861 1854.98,756.098 1855.18,734.056 1855.39,711.776 \n",
" 1855.59,689.299 1855.79,666.669 1856,643.929 1856.2,621.124 1856.41,598.299 1856.61,575.499 1856.81,552.771 1857.02,530.16 1857.22,507.712 1857.42,485.474 \n",
" 1857.63,463.493 1857.83,441.813 1858.04,420.481 1858.24,399.541 1858.44,379.039 1858.65,359.017 1858.85,339.52 1859.05,320.589 1859.26,302.264 1859.46,284.587 \n",
" 1859.67,267.594 1859.87,251.324 1860.07,235.812 1860.28,221.093 1860.48,207.197 1860.68,194.156 1860.89,181.998 1861.09,170.751 1861.3,160.438 1861.5,151.083 \n",
" 1861.7,142.705 1861.91,135.322 1862.11,128.951 1862.31,123.605 1862.52,119.294 1862.72,116.028 1862.93,113.813 1863.13,112.651 1863.33,112.545 1863.54,113.493 \n",
" 1863.74,115.491 1863.94,118.533 1864.15,122.609 1864.35,127.71 1864.56,133.82 1864.76,140.924 1864.96,149.003 1865.17,158.036 1865.37,168 1865.57,178.87 \n",
" 1865.78,190.619 1865.98,203.216 1866.19,216.63 1866.39,230.828 1866.59,245.774 1866.8,261.432 1867,277.762 1867.2,294.725 1867.41,312.279 1867.61,330.381 \n",
" 1867.82,348.987 1868.02,368.051 1868.22,387.529 1868.43,407.372 1868.63,427.534 1868.84,447.966 1869.04,468.619 1869.24,489.445 1869.45,510.394 1869.65,531.418 \n",
" 1869.85,552.467 1870.06,573.492 1870.26,594.445 1870.47,615.277 1870.67,635.942 1870.87,656.393 1871.08,676.584 1871.28,696.469 1871.48,716.005 1871.69,735.15 \n",
" 1871.89,753.861 1872.1,772.1 1872.3,789.827 1872.5,807.005 1872.71,823.6 1872.91,839.579 1873.11,854.908 1873.32,869.56 1873.52,883.506 1873.73,896.72 \n",
" 1873.93,909.179 1874.13,920.862 1874.34,931.75 1874.54,941.825 1874.74,951.074 1874.95,959.483 1875.15,967.042 1875.36,973.744 1875.56,979.583 1875.76,984.557 \n",
" 1875.97,988.663 1876.17,991.905 1876.37,994.284 1876.58,995.808 1876.78,996.484 1876.99,996.323 1877.19,995.337 1877.39,993.539 1877.6,990.948 1877.8,987.581 \n",
" 1878,983.457 1878.21,978.6 1878.41,973.033 1878.62,966.781 1878.82,959.87 1879.02,952.33 1879.23,944.19 1879.43,935.481 1879.63,926.234 1879.84,916.483 \n",
" 1880.04,906.263 1880.25,895.608 1880.45,884.553 1880.65,873.136 1880.86,861.394 1881.06,849.363 1881.26,837.081 1881.47,824.587 1881.67,811.919 1881.88,799.114 \n",
" 1882.08,786.212 1882.28,773.249 1882.49,760.263 1882.69,747.292 1882.89,734.373 1883.1,721.541 1883.3,708.833 1883.51,696.283 1883.71,683.925 1883.91,671.793 \n",
" 1884.12,659.919 1884.32,648.334 1884.52,637.068 1884.73,626.15 1884.93,615.608 1885.14,605.468 1885.34,595.756 1885.54,586.496 1885.75,577.709 1885.95,569.418 \n",
" 1886.15,561.641 1886.36,554.397 1886.56,547.702 1886.77,541.571 1886.97,536.019 1887.17,531.057 1887.38,526.696 1887.58,522.944 1887.78,519.809 1887.99,517.298 \n",
" 1888.19,515.414 1888.4,514.162 1888.6,513.541 1888.8,513.554 1889.01,514.198 1889.21,515.47 1889.41,517.368 1889.62,519.886 1889.82,523.017 1890.03,526.755 \n",
" 1890.23,531.09 1890.43,536.012 1890.64,541.512 1890.84,547.576 1891.04,554.193 1891.25,561.348 1891.45,569.027 1891.66,577.215 1891.86,585.896 1892.06,595.053 \n",
" 1892.27,604.669 1892.47,614.726 1892.67,625.206 1892.88,636.09 1893.08,647.359 1893.29,658.993 1893.49,670.973 1893.69,683.278 1893.9,695.889 1894.1,708.784 \n",
" 1894.3,721.943 1894.51,735.346 1894.71,748.972 1894.92,762.801 1895.12,776.811 1895.32,790.983 1895.53,805.296 1895.73,819.729 1895.93,834.263 1896.14,848.878 \n",
" 1896.34,863.554 1896.55,878.272 1896.75,893.012 1896.95,907.756 1897.16,922.485 1897.36,937.181 1897.56,951.826 1897.77,966.401 1897.97,980.89 1898.18,995.276 \n",
" 1898.38,1009.54 1898.58,1023.67 1898.79,1037.65 1898.99,1051.45 1899.19,1065.08 1899.4,1078.5 1899.6,1091.71 1899.81,1104.7 1900.01,1117.44 1900.21,1129.92 \n",
" 1900.42,1142.13 1900.62,1154.06 1900.82,1165.7 1901.03,1177.02 1901.23,1188.03 1901.44,1198.69 1901.64,1209.02 1901.84,1218.98 1902.05,1228.58 1902.25,1237.79 \n",
" 1902.45,1246.61 1902.66,1255.03 1902.86,1263.04 1903.07,1270.62 1903.27,1277.77 1903.47,1284.47 1903.68,1290.72 1903.88,1296.51 1904.08,1301.82 1904.29,1306.66 \n",
" 1904.49,1311 1904.7,1314.85 1904.9,1318.19 1905.1,1321.02 1905.31,1323.33 1905.51,1325.11 1905.71,1326.35 1905.92,1327.06 1906.12,1327.22 1906.33,1326.83 \n",
" 1906.53,1325.89 1906.73,1324.38 1906.94,1322.32 1907.14,1319.68 1907.34,1316.48 1907.55,1312.71 1907.75,1308.36 1907.96,1303.44 1908.16,1297.96 1908.36,1291.9 \n",
" 1908.57,1285.27 1908.77,1278.07 1908.97,1270.32 1909.18,1262 1909.38,1253.13 1909.59,1243.71 1909.79,1233.76 1909.99,1223.27 1910.2,1212.25 1910.4,1200.73 \n",
" 1910.61,1188.7 1910.81,1176.18 1911.01,1163.19 1911.22,1149.73 1911.42,1135.82 1911.62,1121.48 1911.83,1106.72 1912.03,1091.57 1912.24,1076.04 1912.44,1060.16 \n",
" 1912.64,1043.93 1912.85,1027.4 1913.05,1010.57 1913.25,993.474 1913.46,976.138 1913.66,958.586 1913.87,940.845 1914.07,922.943 1914.27,904.907 1914.48,886.767 \n",
" 1914.68,868.553 1914.88,850.294 1915.09,832.021 1915.29,813.766 1915.5,795.56 1915.7,777.436 1915.9,759.425 1916.11,741.56 1916.31,723.874 1916.51,706.4 \n",
" 1916.72,689.169 1916.92,672.216 1917.13,655.572 1917.33,639.269 1917.53,623.339 1917.74,607.814 1917.94,592.725 1918.14,578.101 1918.35,563.973 1918.55,550.369 \n",
" 1918.76,537.316 1918.96,524.843 1919.16,512.975 1919.37,501.737 1919.57,491.153 1919.77,481.244 1919.98,472.032 1920.18,463.537 1920.39,455.777 1920.59,448.768 \n",
" 1920.79,442.526 1921,437.063 1921.2,432.391 1921.4,428.52 1921.61,425.458 1921.81,423.211 1922.02,421.783 1922.22,421.176 1922.42,421.39 1922.63,422.424 \n",
" 1922.83,424.273 1923.03,426.932 1923.24,430.392 1923.44,434.644 1923.65,439.676 1923.85,445.473 1924.05,452.02 1924.26,459.299 1924.46,467.288 1924.66,475.967 \n",
" 1924.87,485.312 1925.07,495.296 1925.28,505.893 1925.48,517.073 1925.68,528.806 1925.89,541.058 1926.09,553.795 1926.29,566.984 1926.5,580.585 1926.7,594.562 \n",
" 1926.91,608.876 1927.11,623.485 1927.31,638.349 1927.52,653.425 1927.72,668.67 1927.92,684.041 1928.13,699.494 1928.33,714.983 1928.54,730.465 1928.74,745.894 \n",
" 1928.94,761.224 1929.15,776.411 1929.35,791.411 1929.55,806.177 1929.76,820.667 1929.96,834.836 1930.17,848.641 1930.37,862.041 1930.57,874.995 1930.78,887.461 \n",
" 1930.98,899.401 1931.18,910.778 1931.39,921.554 1931.59,931.695 1931.8,941.168 1932,949.94 1932.2,957.983 1932.41,965.267 1932.61,971.767 1932.81,977.459 \n",
" 1933.02,982.32 1933.22,986.331 1933.43,989.475 1933.63,991.735 1933.83,993.1 1934.04,993.557 1934.24,993.1 1934.44,991.723 1934.65,989.421 1934.85,986.195 \n",
" 1935.06,982.045 1935.26,976.977 1935.46,970.996 1935.67,964.112 1935.87,956.336 1936.07,947.682 1936.28,938.167 1936.48,927.809 1936.69,916.629 1936.89,904.65 \n",
" 1937.09,891.898 1937.3,878.401 1937.5,864.187 1937.7,849.288 1937.91,833.738 1938.11,817.572 1938.32,800.826 1938.52,783.539 1938.72,765.752 1938.93,747.505 \n",
" 1939.13,728.841 1939.33,709.803 1939.54,690.437 1939.74,670.789 1939.95,650.904 1940.15,630.83 1940.35,610.614 1940.56,590.306 1940.76,569.952 1940.96,549.602 \n",
" 1941.17,529.304 1941.37,509.107 1941.58,489.059 1941.78,469.208 1941.98,449.601 1942.19,430.285 1942.39,411.306 1942.59,392.709 1942.8,374.538 1943,356.837 \n",
" 1943.21,339.648 1943.41,323.01 1943.61,306.963 1943.82,291.545 1944.02,276.793 1944.22,262.739 1944.43,249.418 1944.63,236.86 1944.84,225.094 1945.04,214.146 \n",
" 1945.24,204.042 1945.45,194.805 1945.65,186.455 1945.85,179.01 1946.06,172.488 1946.26,166.901 1946.47,162.262 1946.67,158.58 1946.87,155.863 1947.08,154.115 \n",
" 1947.28,153.34 1947.48,153.536 1947.69,154.704 1947.89,156.837 1948.1,159.931 1948.3,163.977 1948.5,168.963 1948.71,174.878 1948.91,181.706 1949.11,189.431 \n",
" 1949.32,198.035 1949.52,207.497 1949.73,217.794 1949.93,228.903 1950.13,240.799 1950.34,253.454 1950.54,266.839 1950.75,280.926 1950.95,295.682 1951.15,311.076 \n",
" 1951.36,327.074 1951.56,343.642 1951.76,360.744 1951.97,378.345 1952.17,396.408 1952.38,414.895 1952.58,433.769 1952.78,452.992 1952.99,472.526 1953.19,492.331 \n",
" 1953.39,512.37 1953.6,532.603 1953.8,552.992 1954.01,573.498 1954.21,594.085 1954.41,614.713 1954.62,635.347 1954.82,655.949 1955.02,676.483 1955.23,696.915 \n",
" 1955.43,717.21 1955.64,737.334 1955.84,757.254 1956.04,776.94 1956.25,796.36 1956.45,815.485 1956.65,834.286 1956.86,852.737 1957.06,870.811 1957.27,888.484 \n",
" 1957.47,905.732 1957.67,922.533 1957.88,938.867 1958.08,954.714 1958.28,970.056 1958.49,984.877 1958.69,999.161 1958.9,1012.9 1959.1,1026.07 1959.3,1038.66 \n",
" 1959.51,1050.68 1959.71,1062.1 1959.91,1072.92 1960.12,1083.14 1960.32,1092.76 1960.53,1101.75 1960.73,1110.14 1960.93,1117.91 1961.14,1125.07 1961.34,1131.62 \n",
" 1961.54,1137.56 1961.75,1142.89 1961.95,1147.62 1962.16,1151.76 1962.36,1155.31 1962.56,1158.29 1962.77,1160.69 1962.97,1162.52 1963.17,1163.81 1963.38,1164.55 \n",
" 1963.58,1164.77 1963.79,1164.46 1963.99,1163.65 1964.19,1162.35 1964.4,1160.57 1964.6,1158.32 1964.8,1155.62 1965.01,1152.49 1965.21,1148.93 1965.42,1144.97 \n",
" 1965.62,1140.61 1965.82,1135.88 1966.03,1130.79 1966.23,1125.35 1966.43,1119.59 1966.64,1113.51 1966.84,1107.13 1967.05,1100.48 1967.25,1093.55 1967.45,1086.38 \n",
" 1967.66,1078.98 1967.86,1071.35 1968.06,1063.53 1968.27,1055.51 1968.47,1047.33 1968.68,1038.99 1968.88,1030.5 1969.08,1021.89 1969.29,1013.17 1969.49,1004.36 \n",
" 1969.69,995.459 1969.9,986.493 1970.1,977.474 1970.31,968.416 1970.51,959.333 1970.71,950.24 1970.92,941.15 1971.12,932.077 1971.32,923.034 1971.53,914.035 \n",
" 1971.73,905.094 1971.94,896.224 1972.14,887.437 1972.34,878.748 1972.55,870.17 1972.75,861.714 1972.95,853.395 1973.16,845.226 1973.36,837.218 1973.57,829.385 \n",
" 1973.77,821.739 1973.97,814.294 1974.18,807.061 1974.38,800.053 1974.58,793.282 1974.79,786.76 1974.99,780.5 1975.2,774.514 1975.4,768.813 1975.6,763.408 \n",
" 1975.81,758.312 1976.01,753.536 1976.21,749.09 1976.42,744.986 1976.62,741.233 1976.83,737.843 1977.03,734.825 1977.23,732.188 1977.44,729.942 1977.64,728.096 \n",
" 1977.84,726.657 1978.05,725.634 1978.25,725.034 1978.46,724.863 1978.66,725.127 1978.86,725.833 1979.07,726.985 1979.27,728.587 1979.47,730.642 1979.68,733.154 \n",
" 1979.88,736.123 1980.09,739.552 1980.29,743.439 1980.49,747.785 1980.7,752.587 1980.9,757.843 1981.1,763.549 1981.31,769.701 1981.51,776.292 1981.72,783.316 \n",
" 1981.92,790.765 1982.12,798.63 1982.33,806.901 1982.53,815.566 1982.73,824.613 1982.94,834.029 1983.14,843.799 1983.35,853.907 1983.55,864.337 1983.75,875.069 \n",
" 1983.96,886.085 1984.16,897.365 1984.36,908.887 1984.57,920.629 1984.77,932.567 1984.98,944.678 1985.18,956.935 1985.38,969.313 1985.59,981.784 1985.79,994.32 \n",
" 1985.99,1006.89 1986.2,1019.47 1986.4,1032.03 1986.61,1044.53 1986.81,1056.95 1987.01,1069.25 1987.22,1081.41 1987.42,1093.38 1987.62,1105.14 1987.83,1116.65 \n",
" 1988.03,1127.88 1988.24,1138.8 1988.44,1149.38 1988.64,1159.58 1988.85,1169.37 1989.05,1178.72 1989.25,1187.59 1989.46,1195.96 1989.66,1203.8 1989.87,1211.08 \n",
" 1990.07,1217.76 1990.27,1223.82 1990.48,1229.23 1990.68,1233.97 1990.88,1238.02 1991.09,1241.34 1991.29,1243.92 1991.5,1245.74 1991.7,1246.78 1991.9,1247.02 \n",
" 1992.11,1246.44 1992.31,1245.03 1992.52,1242.79 1992.72,1239.68 1992.92,1235.72 1993.13,1230.89 1993.33,1225.19 1993.53,1218.61 1993.74,1211.16 1993.94,1202.84 \n",
" 1994.15,1193.64 1994.35,1183.58 1994.55,1172.66 1994.76,1160.89 1994.96,1148.28 1995.16,1134.86 1995.37,1120.63 1995.57,1105.62 1995.78,1089.83 1995.98,1073.31 \n",
" 1996.18,1056.06 1996.39,1038.13 1996.59,1019.53 1996.79,1000.29 1997,980.453 1997.2,960.047 1997.41,939.109 1997.61,917.675 1997.81,895.784 1998.02,873.476 \n",
" 1998.22,850.792 1998.42,827.775 1998.63,804.468 1998.83,780.915 1999.04,757.163 1999.24,733.257 1999.44,709.245 1999.65,685.175 1999.85,661.093 2000.05,637.049 \n",
" 2000.26,613.091 2000.46,589.268 2000.67,565.627 2000.87,542.218 2001.07,519.089 2001.28,496.287 2001.48,473.859 2001.68,451.852 2001.89,430.31 2002.09,409.28 \n",
" 2002.3,388.803 2002.5,368.923 2002.7,349.681 2002.91,331.116 2003.11,313.267 2003.31,296.17 2003.52,279.86 2003.72,264.369 2003.93,249.73 2004.13,235.972 \n",
" 2004.33,223.121 2004.54,211.202 2004.74,200.239 2004.94,190.251 2005.15,181.257 2005.35,173.273 2005.56,166.313 2005.76,160.386 2005.96,155.502 2006.17,151.666 \n",
" 2006.37,148.882 2006.57,147.151 2006.78,146.471 2006.98,146.839 2007.19,148.246 2007.39,150.685 2007.59,154.143 2007.8,158.607 2008,164.06 2008.2,170.483 \n",
" 2008.41,177.855 2008.61,186.153 2008.82,195.352 2009.02,205.423 2009.22,216.337 2009.43,228.064 2009.63,240.568 2009.83,253.816 2010.04,267.77 2010.24,282.393 \n",
" 2010.45,297.644 2010.65,313.483 2010.85,329.867 2011.06,346.753 2011.26,364.097 2011.46,381.853 2011.67,399.975 2011.87,418.418 2012.08,437.134 2012.28,456.075 \n",
" 2012.48,475.194 2012.69,494.445 2012.89,513.778 2013.09,533.146 2013.3,552.503 2013.5,571.802 2013.71,590.996 2013.91,610.04 2014.11,628.889 2014.32,647.499 \n",
" 2014.52,665.828 2014.72,683.834 2014.93,701.475 2015.13,718.713 2015.34,735.51 2015.54,751.83 2015.74,767.638 2015.95,782.9 2016.15,797.586 2016.35,811.665 \n",
" 2016.56,825.11 2016.76,837.896 2016.97,849.998 2017.17,861.395 2017.37,872.066 2017.58,881.996 2017.78,891.167 2017.98,899.566 2018.19,907.183 2018.39,914.008 \n",
" 2018.6,920.035 2018.8,925.259 2019,929.677 2019.21,933.289 2019.41,936.097 2019.61,938.104 2019.82,939.317 2020.02,939.743 2020.23,939.392 2020.43,938.276 \n",
" 2020.63,936.409 2020.84,933.806 2021.04,930.484 2021.24,926.462 2021.45,921.761 2021.65,916.402 2021.86,910.409 2022.06,903.808 2022.26,896.623 2022.47,888.882 \n",
" 2022.67,880.615 2022.87,871.849 2023.08,862.616 2023.28,852.946 2023.49,842.872 2023.69,832.425 2023.89,821.64 2024.1,810.55 2024.3,799.188 2024.5,787.589 \n",
" 2024.71,775.786 2024.91,763.816 2025.12,751.711 2025.32,739.506 2025.52,727.235 2025.73,714.932 2025.93,702.63 2026.13,690.363 2026.34,678.163 2026.54,666.061 \n",
" 2026.75,654.089 2026.95,642.277 2027.15,630.656 2027.36,619.254 2027.56,608.098 2027.76,597.217 2027.97,586.635 2028.17,576.378 2028.38,566.469 2028.58,556.932 \n",
" 2028.78,547.788 2028.99,539.057 2029.19,530.758 2029.39,522.91 2029.6,515.528 2029.8,508.628 2030.01,502.225 2030.21,496.332 2030.41,490.959 2030.62,486.117 \n",
" 2030.82,481.815 2031.02,478.062 2031.23,474.863 2031.43,472.225 2031.64,470.15 2031.84,468.643 2032.04,467.706 2032.25,467.337 2032.45,467.539 2032.65,468.309 \n",
" 2032.86,469.644 2033.06,471.542 2033.27,473.998 2033.47,477.006 2033.67,480.561 2033.88,484.656 2034.08,489.283 2034.29,494.433 2034.49,500.097 2034.69,506.265 \n",
" 2034.9,512.927 2035.1,520.072 2035.3,527.688 2035.51,535.762 2035.71,544.283 2035.92,553.237 2036.12,562.611 2036.32,572.391 2036.53,582.563 2036.73,593.113 \n",
" 2036.93,604.025 2037.14,615.286 2037.34,626.879 2037.55,638.79 2037.75,651.004 2037.95,663.505 2038.16,676.277 2038.36,689.304 2038.56,702.572 2038.77,716.063 \n",
" 2038.97,729.763 2039.18,743.656 2039.38,757.725 2039.58,771.955 2039.79,786.33 2039.99,800.834 2040.19,815.451 2040.4,830.166 2040.6,844.963 2040.81,859.826 \n",
" 2041.01,874.739 2041.21,889.686 2041.42,904.653 2041.62,919.622 2041.82,934.579 2042.03,949.507 2042.23,964.392 2042.44,979.217 2042.64,993.967 2042.84,1008.63 \n",
" 2043.05,1023.18 2043.25,1037.61 2043.45,1051.9 2043.66,1066.04 2043.86,1080 2044.07,1093.78 2044.27,1107.36 2044.47,1120.73 2044.68,1133.85 2044.88,1146.73 \n",
" 2045.08,1159.35 2045.29,1171.68 2045.49,1183.72 2045.7,1195.44 2045.9,1206.83 2046.1,1217.88 2046.31,1228.57 2046.51,1238.88 2046.71,1248.8 2046.92,1258.31 \n",
" 2047.12,1267.4 2047.33,1276.05 2047.53,1284.25 2047.73,1291.98 2047.94,1299.23 2048.14,1305.98 2048.34,1312.23 2048.55,1317.95 2048.75,1323.13 2048.96,1327.77 \n",
" 2049.16,1331.85 2049.36,1335.35 2049.57,1338.27 2049.77,1340.6 2049.97,1342.32 2050.18,1343.43 2050.38,1343.93 2050.59,1343.79 2050.79,1343.02 2050.99,1341.61 \n",
" 2051.2,1339.55 2051.4,1336.85 2051.6,1333.49 2051.81,1329.48 2052.01,1324.81 2052.22,1319.5 2052.42,1313.52 2052.62,1306.9 2052.83,1299.63 2053.03,1291.72 \n",
" 2053.23,1283.18 2053.44,1274 2053.64,1264.21 2053.85,1253.81 2054.05,1242.82 2054.25,1231.23 2054.46,1219.08 2054.66,1206.37 2054.86,1193.13 2055.07,1179.36 \n",
" 2055.27,1165.09 2055.48,1150.34 2055.68,1135.14 2055.88,1119.49 2056.09,1103.44 2056.29,1087 2056.49,1070.2 2056.7,1053.07 2056.9,1035.64 2057.11,1017.93 \n",
" 2057.31,999.988 2057.51,981.832 2057.72,963.499 2057.92,945.021 2058.12,926.433 2058.33,907.77 2058.53,889.066 2058.74,870.358 2058.94,851.683 2059.14,833.075 \n",
" 2059.35,814.572 2059.55,796.211 2059.75,778.028 2059.96,760.061 2060.16,742.347 2060.37,724.921 2060.57,707.819 2060.77,691.079 2060.98,674.734 2061.18,658.82 \n",
" 2061.38,643.371 2061.59,628.418 2061.79,613.996 2062,600.134 2062.2,586.863 2062.4,574.213 2062.61,562.209 2062.81,550.88 2063.01,540.248 2063.22,530.339 \n",
" 2063.42,521.174 2063.63,512.772 2063.83,505.152 2064.03,498.33 2064.24,492.321 2064.44,487.137 2064.64,482.79 2064.85,479.288 2065.05,476.636 2065.26,474.841 \n",
" 2065.46,473.903 2065.66,473.824 2065.87,474.601 2066.07,476.229 2066.27,478.703 2066.48,482.013 2066.68,486.149 2066.89,491.098 2067.09,496.845 2067.29,503.371 \n",
" 2067.5,510.658 2067.7,518.684 2067.9,527.425 2068.11,536.856 2068.31,546.949 2068.52,557.675 2068.72,569.003 2068.92,580.9 2069.13,593.331 2069.33,606.26 \n",
" 2069.53,619.65 2069.74,633.462 2069.94,647.655 2070.15,662.189 2070.35,677.02 2070.55,692.106 2070.76,707.401 2070.96,722.862 2071.16,738.442 2071.37,754.096 \n",
" 2071.57,769.777 2071.78,785.439 2071.98,801.034 2072.18,816.517 2072.39,831.839 2072.59,846.956 2072.79,861.821 2073,876.39 2073.2,890.616 2073.41,904.457 \n",
" 2073.61,917.869 2073.81,930.81 2074.02,943.24 2074.22,955.118 2074.42,966.408 2074.63,977.071 2074.83,987.074 2075.04,996.382 2075.24,1004.96 2075.44,1012.79 \n",
" 2075.65,1019.83 2075.85,1026.06 2076.06,1031.46 2076.26,1036.01 2076.46,1039.67 2076.67,1042.45 2076.87,1044.33 2077.07,1045.28 2077.28,1045.31 2077.48,1044.4 \n",
" 2077.69,1042.55 2077.89,1039.76 2078.09,1036.03 2078.3,1031.35 2078.5,1025.75 2078.7,1019.21 2078.91,1011.76 2079.11,1003.4 2079.32,994.155 2079.52,984.035 \n",
" 2079.72,973.061 2079.93,961.256 2080.13,948.644 2080.33,935.249 2080.54,921.101 2080.74,906.23 2080.95,890.667 2081.15,874.446 2081.35,857.603 2081.56,840.174 \n",
" 2081.76,822.198 2081.96,803.716 2082.17,784.768 2082.37,765.397 2082.58,745.646 2082.78,725.559 2082.98,705.183 2083.19,684.562 2083.39,663.743 2083.59,642.774 \n",
" 2083.8,621.701 2084,600.572 2084.21,579.434 2084.41,558.335 2084.61,537.323 2084.82,516.443 2085.02,495.743 2085.22,475.269 2085.43,455.065 2085.63,435.178 \n",
" 2085.84,415.649 2086.04,396.522 2086.24,377.838 2086.45,359.638 2086.65,341.961 2086.85,324.844 2087.06,308.323 2087.26,292.433 2087.47,277.208 2087.67,262.678 \n",
" 2087.87,248.872 2088.08,235.819 2088.28,223.543 2088.48,212.07 2088.69,201.419 2088.89,191.612 2089.1,182.665 2089.3,174.595 2089.5,167.414 2089.71,161.135 \n",
" 2089.91,155.765 2090.11,151.313 2090.32,147.783 2090.52,145.177 2090.73,143.498 2090.93,142.742 2091.13,142.907 2091.34,143.988 2091.54,145.976 2091.74,148.862 \n",
" 2091.95,152.636 2092.15,157.284 2092.36,162.791 2092.56,169.14 2092.76,176.314 2092.97,184.292 2093.17,193.053 2093.37,202.575 2093.58,212.832 2093.78,223.8 \n",
" 2093.99,235.452 2094.19,247.761 2094.39,260.697 2094.6,274.231 2094.8,288.332 2095,302.969 2095.21,318.111 2095.41,333.723 2095.62,349.775 2095.82,366.231 \n",
" 2096.02,383.058 2096.23,400.223 2096.43,417.692 2096.63,435.429 2096.84,453.402 2097.04,471.575 2097.25,489.916 2097.45,508.391 2097.65,526.966 2097.86,545.61 \n",
" 2098.06,564.289 2098.26,582.972 2098.47,601.627 2098.67,620.226 2098.88,638.737 2099.08,657.132 2099.28,675.383 2099.49,693.463 2099.69,711.345 2099.89,729.004 \n",
" 2100.1,746.417 2100.3,763.558 2100.51,780.407 2100.71,796.942 2100.91,813.143 2101.12,828.99 2101.32,844.467 2101.52,859.556 2101.73,874.241 2101.93,888.507 \n",
" 2102.14,902.343 2102.34,915.734 2102.54,928.669 2102.75,941.139 2102.95,953.135 2103.15,964.647 2103.36,975.67 2103.56,986.197 2103.77,996.222 2103.97,1005.74 \n",
" 2104.17,1014.76 2104.38,1023.26 2104.58,1031.25 2104.78,1038.72 2104.99,1045.69 2105.19,1052.14 2105.4,1058.09 2105.6,1063.52 2105.8,1068.46 2106.01,1072.89 \n",
" 2106.21,1076.83 2106.41,1080.27 2106.62,1083.24 2106.82,1085.72 2107.03,1087.73 2107.23,1089.27 2107.43,1090.35 2107.64,1090.99 2107.84,1091.18 2108.04,1090.93 \n",
" 2108.25,1090.26 2108.45,1089.18 2108.66,1087.68 2108.86,1085.79 2109.06,1083.51 2109.27,1080.85 2109.47,1077.82 2109.67,1074.44 2109.88,1070.71 2110.08,1066.64 \n",
" 2110.29,1062.25 2110.49,1057.54 2110.69,1052.53 2110.9,1047.22 2111.1,1041.64 2111.3,1035.78 2111.51,1029.67 2111.71,1023.31 2111.92,1016.72 2112.12,1009.9 \n",
" 2112.32,1002.88 2112.53,995.659 2112.73,988.254 2112.93,980.677 2113.14,972.941 2113.34,965.059 2113.55,957.045 2113.75,948.911 2113.95,940.672 2114.16,932.342 \n",
" 2114.36,923.934 2114.56,915.462 2114.77,906.942 2114.97,898.388 2115.18,889.815 2115.38,881.237 2115.58,872.671 2115.79,864.132 2115.99,855.634 2116.2,847.196 \n",
" 2116.4,838.831 2116.6,830.558 2116.81,822.391 2117.01,814.348 2117.21,806.445 2117.42,798.699 2117.62,791.128 2117.83,783.747 2118.03,776.574 2118.23,769.625 \n",
" 2118.44,762.919 2118.64,756.471 2118.84,750.298 2119.05,744.418 2119.25,738.846 2119.46,733.599 2119.66,728.693 2119.86,724.144 2120.07,719.968 2120.27,716.179 \n",
" 2120.47,712.792 2120.68,709.821 2120.88,707.28 2121.09,705.183 2121.29,703.541 2121.49,702.367 2121.7,701.671 2121.9,701.465 2122.1,701.758 2122.31,702.558 \n",
" 2122.51,703.873 2122.72,705.711 2122.92,708.077 2123.12,710.976 2123.33,714.411 2123.53,718.386 2123.73,722.901 2123.94,727.958 2124.14,733.554 2124.35,739.688 \n",
" 2124.55,746.357 2124.75,753.555 2124.96,761.276 2125.16,769.512 2125.36,778.255 2125.57,787.494 2125.77,797.217 2125.98,807.411 2126.18,818.062 2126.38,829.153 \n",
" 2126.59,840.667 2126.79,852.586 2126.99,864.889 2127.2,877.554 2127.4,890.559 2127.61,903.879 2127.81,917.49 2128.01,931.364 2128.22,945.474 2128.42,959.791 \n",
" 2128.62,974.285 2128.83,988.925 2129.03,1003.68 2129.24,1018.51 2129.44,1033.4 2129.64,1048.29 2129.85,1063.17 2130.05,1077.98 2130.25,1092.71 2130.46,1107.3 \n",
" 2130.66,1121.72 2130.87,1135.94 2131.07,1149.92 2131.27,1163.62 2131.48,1177.01 2131.68,1190.04 2131.88,1202.68 2132.09,1214.89 2132.29,1226.65 2132.5,1237.9 \n",
" 2132.7,1248.62 2132.9,1258.77 2133.11,1268.32 2133.31,1277.24 2133.51,1285.49 2133.72,1293.05 2133.92,1299.89 2134.13,1305.98 2134.33,1311.29 2134.53,1315.79 \n",
" 2134.74,1319.48 2134.94,1322.32 2135.14,1324.29 2135.35,1325.38 2135.55,1325.57 2135.76,1324.86 2135.96,1323.21 2136.16,1320.64 2136.37,1317.12 2136.57,1312.66 \n",
" 2136.77,1307.24 2136.98,1300.88 2137.18,1293.57 2137.39,1285.31 2137.59,1276.11 2137.79,1265.98 2138,1254.92 2138.2,1242.96 2138.4,1230.11 2138.61,1216.38 \n",
" 2138.81,1201.79 2139.02,1186.37 2139.22,1170.14 2139.42,1153.12 2139.63,1135.35 2139.83,1116.84 2140.03,1097.65 2140.24,1077.79 2140.44,1057.3 2140.65,1036.23 \n",
" 2140.85,1014.6 2141.05,992.47 2141.26,969.869 2141.46,946.844 2141.66,923.439 2141.87,899.7 2142.07,875.672 2142.28,851.404 2142.48,826.943 2142.68,802.339 \n",
" 2142.89,777.64 2143.09,752.896 2143.29,728.157 2143.5,703.473 2143.7,678.894 2143.91,654.471 2144.11,630.251 2144.31,606.286 2144.52,582.623 2144.72,559.31 \n",
" 2144.92,536.395 2145.13,513.925 2145.33,491.943 2145.54,470.496 2145.74,449.625 2145.94,429.372 2146.15,409.778 2146.35,390.88 2146.55,372.715 2146.76,355.319 \n",
" 2146.96,338.725 2147.17,322.963 2147.37,308.063 2147.57,294.051 2147.78,280.954 2147.98,268.792 2148.18,257.587 2148.39,247.355 2148.59,238.114 2148.8,229.875 \n",
" 2149,222.649 2149.2,216.445 2149.41,211.267 2149.61,207.119 2149.81,204.002 2150.02,201.913 2150.22,200.848 2150.43,200.801 2150.63,201.761 2150.83,203.717 \n",
" 2151.04,206.655 2151.24,210.558 2151.44,215.408 2151.65,221.183 2151.85,227.861 2152.06,235.416 2152.26,243.822 2152.46,253.048 2152.67,263.065 2152.87,273.839 \n",
" 2153.07,285.336 2153.28,297.521 2153.48,310.355 2153.69,323.802 2153.89,337.82 2154.09,352.369 2154.3,367.406 2154.5,382.89 2154.7,398.777 2154.91,415.023 \n",
" 2155.11,431.582 2155.32,448.411 2155.52,465.463 2155.72,482.694 2155.93,500.057 2156.13,517.509 2156.33,535.003 2156.54,552.496 2156.74,569.942 2156.95,587.298 \n",
" 2157.15,604.522 2157.35,621.571 2157.56,638.403 2157.76,654.979 2157.97,671.26 2158.17,687.208 2158.37,702.785 2158.58,717.957 2158.78,732.69 2158.98,746.952 \n",
" 2159.19,760.711 2159.39,773.94 2159.6,786.61 2159.8,798.696 2160,810.175 2160.21,821.025 2160.41,831.225 2160.61,840.758 2160.82,849.608 2161.02,857.761 \n",
" 2161.23,865.204 2161.43,871.928 2161.63,877.924 2161.84,883.187 2162.04,887.712 2162.24,891.498 2162.45,894.543 2162.65,896.85 2162.86,898.423 2163.06,899.267 \n",
" 2163.26,899.388 2163.47,898.797 2163.67,897.504 2163.87,895.522 2164.08,892.863 2164.28,889.545 2164.49,885.583 2164.69,880.997 2164.89,875.806 2165.1,870.032 \n",
" 2165.3,863.695 2165.5,856.82 2165.71,849.431 2165.91,841.554 2166.12,833.214 2166.32,824.438 2166.52,815.254 2166.73,805.69 2166.93,795.775 2167.13,785.538 \n",
" 2167.34,775.008 2167.54,764.216 2167.75,753.192 2167.95,741.966 2168.15,730.567 2168.36,719.026 2168.56,707.373 2168.76,695.639 2168.97,683.851 2169.17,672.041 \n",
" 2169.38,660.237 2169.58,648.466 2169.78,636.758 2169.99,625.139 2170.19,613.637 2170.39,602.277 2170.6,591.085 2170.8,580.086 2171.01,569.302 2171.21,558.758 \n",
" 2171.41,548.476 2171.62,538.476 2171.82,528.78 2172.02,519.406 2172.23,510.372 2172.43,501.698 2172.64,493.399 2172.84,485.49 2173.04,477.986 2173.25,470.901 \n",
" 2173.45,464.247 2173.65,458.036 2173.86,452.278 2174.06,446.984 2174.27,442.161 2174.47,437.817 2174.67,433.96 2174.88,430.595 2175.08,427.727 2175.28,425.36 \n",
" 2175.49,423.498 2175.69,422.142 2175.9,421.295 2176.1,420.958 2176.3,421.13 2176.51,421.812 2176.71,423.001 2176.91,424.696 2177.12,426.895 2177.32,429.594 \n",
" 2177.53,432.79 2177.73,436.478 2177.93,440.654 2178.14,445.312 2178.34,450.446 2178.54,456.051 2178.75,462.12 2178.95,468.646 2179.16,475.622 2179.36,483.039 \n",
" 2179.56,490.89 2179.77,499.167 2179.97,507.86 2180.17,516.961 2180.38,526.461 2180.58,536.35 2180.79,546.618 2180.99,557.255 2181.19,568.252 2181.4,579.597 \n",
" 2181.6,591.28 2181.8,603.289 2182.01,615.615 2182.21,628.244 2182.42,641.166 2182.62,654.369 2182.82,667.84 2183.03,681.567 2183.23,695.538 2183.43,709.739 \n",
" 2183.64,724.157 2183.84,738.779 2184.05,753.591 2184.25,768.58 2184.45,783.729 2184.66,799.026 2184.86,814.455 2185.06,830.001 2185.27,845.648 2185.47,861.38 \n",
" 2185.68,877.181 2185.88,893.035 2186.08,908.924 2186.29,924.832 2186.49,940.74 2186.69,956.631 2186.9,972.486 2187.1,988.288 2187.31,1004.02 2187.51,1019.65 \n",
" 2187.71,1035.18 2187.92,1050.57 2188.12,1065.81 2188.32,1080.88 2188.53,1095.76 2188.73,1110.43 2188.94,1124.86 2189.14,1139.04 2189.34,1152.94 2189.55,1166.54 \n",
" 2189.75,1179.83 2189.95,1192.78 2190.16,1205.37 2190.36,1217.57 2190.57,1229.37 2190.77,1240.75 2190.97,1251.69 2191.18,1262.16 2191.38,1272.15 2191.58,1281.63 \n",
" 2191.79,1290.59 2191.99,1299.01 2192.2,1306.86 2192.4,1314.14 2192.6,1320.83 2192.81,1326.9 2193.01,1332.35 2193.21,1337.15 2193.42,1341.3 2193.62,1344.78 \n",
" 2193.83,1347.58 2194.03,1349.69 2194.23,1351.09 2194.44,1351.79 2194.64,1351.76 2194.84,1351.02 2195.05,1349.54 2195.25,1347.33 2195.46,1344.39 2195.66,1340.71 \n",
" 2195.86,1336.29 2196.07,1331.14 2196.27,1325.26 2196.47,1318.66 2196.68,1311.33 2196.88,1303.3 2197.09,1294.56 2197.29,1285.13 2197.49,1275.02 2197.7,1264.26 \n",
" 2197.9,1252.84 2198.1,1240.79 2198.31,1228.14 2198.51,1214.89 2198.72,1201.08 2198.92,1186.72 2199.12,1171.84 2199.33,1156.47 2199.53,1140.64 2199.74,1124.37 \n",
" 2199.94,1107.69 2200.14,1090.65 2200.35,1073.26 2200.55,1055.56 2200.75,1037.59 2200.96,1019.39 2201.16,1000.98 2201.37,982.415 2201.57,963.726 2201.77,944.951 \n",
" 2201.98,926.131 2202.18,907.305 2202.38,888.513 2202.59,869.796 2202.79,851.194 2203,832.748 2203.2,814.497 2203.4,796.482 2203.61,778.743 2203.81,761.319 \n",
" 2204.01,744.25 2204.22,727.573 2204.42,711.326 2204.63,695.546 2204.83,680.269 2205.03,665.529 2205.24,651.361 2205.44,637.796 2205.64,624.866 2205.85,612.601 \n",
" 2206.05,601.028 2206.26,590.174 2206.46,580.063 2206.66,570.72 2206.87,562.164 2207.07,554.415 2207.27,547.491 2207.48,541.407 2207.68,536.176 2207.89,531.808 \n",
" 2208.09,528.313 2208.29,525.697 2208.5,523.964 2208.7,523.117 2208.9,523.155 2209.11,524.075 2209.31,525.872 2209.52,528.539 2209.72,532.067 2209.92,536.443 \n",
" 2210.13,541.653 2210.33,547.681 2210.53,554.507 2210.74,562.112 2210.94,570.471 2211.15,579.56 2211.35,589.351 2211.55,599.815 2211.76,610.922 2211.96,622.638 \n",
" 2212.16,634.929 2212.37,647.758 2212.57,661.088 2212.78,674.879 2212.98,689.091 2213.18,703.682 2213.39,718.609 2213.59,733.828 2213.79,749.294 2214,764.961 \n",
" 2214.2,780.783 2214.41,796.713 2214.61,812.704 2214.81,828.709 2215.02,844.679 2215.22,860.566 2215.42,876.324 2215.63,891.905 2215.83,907.261 2216.04,922.347 \n",
" 2216.24,937.117 2216.44,951.524 2216.65,965.527 2216.85,979.08 2217.05,992.142 2217.26,1004.67 2217.46,1016.63 2217.67,1027.98 2217.87,1038.68 2218.07,1048.71 \n",
" 2218.28,1058.02 2218.48,1066.58 2218.68,1074.37 2218.89,1081.36 2219.09,1087.52 2219.3,1092.84 2219.5,1097.28 2219.7,1100.84 2219.91,1103.49 2220.11,1105.22 \n",
" 2220.31,1106.02 2220.52,1105.89 2220.72,1104.8 2220.93,1102.77 2221.13,1099.79 2221.33,1095.86 2221.54,1090.98 2221.74,1085.16 2221.94,1078.41 2222.15,1070.74 \n",
" 2222.35,1062.16 2222.56,1052.68 2222.76,1042.33 2222.96,1031.12 2223.17,1019.08 2223.37,1006.23 2223.57,992.59 2223.78,978.198 2223.98,963.08 2224.19,947.268 \n",
" 2224.39,930.794 2224.59,913.695 2224.8,896.007 2225,877.767 2225.2,859.015 2225.41,839.79 2225.61,820.135 2225.82,800.092 2226.02,779.704 2226.22,759.014 \n",
" 2226.43,738.067 2226.63,716.909 2226.83,695.584 2227.04,674.139 2227.24,652.618 2227.45,631.067 2227.65,609.532 2227.85,588.058 2228.06,566.691 2228.26,545.473 \n",
" 2228.46,524.451 2228.67,503.665 2228.87,483.16 2229.08,462.976 2229.28,443.154 2229.48,423.733 2229.69,404.752 2229.89,386.248 2230.09,368.255 2230.3,350.809 \n",
" 2230.5,333.941 2230.71,317.684 2230.91,302.066 2231.11,287.116 2231.32,272.858 2231.52,259.319 2231.72,246.519 2231.93,234.48 2232.13,223.221 2232.34,212.758 \n",
" 2232.54,203.106 2232.74,194.277 2232.95,186.284 2233.15,179.135 2233.35,172.837 2233.56,167.395 2233.76,162.812 2233.97,159.091 2234.17,156.23 2234.37,154.227 \n",
" 2234.58,153.078 2234.78,152.777 2234.98,153.316 2235.19,154.687 2235.39,156.877 2235.6,159.875 2235.8,163.667 2236,168.237 2236.21,173.569 2236.41,179.643 \n",
" 2236.61,186.442 2236.82,193.944 2237.02,202.127 2237.23,210.97 2237.43,220.447 2237.63,230.536 2237.84,241.21 2238.04,252.443 2238.24,264.21 2238.45,276.482 \n",
" 2238.65,289.231 2238.86,302.431 2239.06,316.051 2239.26,330.065 2239.47,344.442 2239.67,359.153 2239.87,374.17 2240.08,389.464 2240.28,405.005 2240.49,420.765 \n",
" 2240.69,436.715 2240.89,452.827 2241.1,469.073 2241.3,485.426 2241.51,501.858 2241.71,518.342 2241.91,534.853 2242.12,551.365 2242.32,567.852 2242.52,584.291 \n",
" 2242.73,600.659 2242.93,616.931 2243.14,633.086 2243.34,649.103 2243.54,664.96 2243.75,680.638 2243.95,696.117 2244.15,711.38 2244.36,726.409 2244.56,741.187 \n",
" 2244.77,755.698 2244.97,769.927 2245.17,783.86 2245.38,797.483 2245.58,810.785 2245.78,823.752 2245.99,836.374 2246.19,848.641 2246.4,860.543 2246.6,872.071 \n",
" 2246.8,883.217 2247.01,893.973 2247.21,904.333 2247.41,914.291 2247.62,923.841 2247.82,932.978 2248.03,941.699 2248.23,949.998 2248.43,957.874 2248.64,965.323 \n",
" 2248.84,972.344 2249.04,978.934 2249.25,985.092 2249.45,990.818 2249.66,996.112 2249.86,1000.97 2250.06,1005.4 2250.27,1009.4 2250.47,1012.97 2250.67,1016.11 \n",
" 2250.88,1018.82 2251.08,1021.11 2251.29,1022.97 2251.49,1024.42 2251.69,1025.45 2251.9,1026.07 2252.1,1026.29 2252.3,1026.09 2252.51,1025.5 2252.71,1024.51 \n",
" 2252.92,1023.14 2253.12,1021.38 2253.32,1019.24 2253.53,1016.73 2253.73,1013.85 2253.93,1010.61 2254.14,1007.02 2254.34,1003.08 2254.55,998.812 2254.75,994.212 \n",
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]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function random_evolution(rng, n, T, dt)\n",
" H = random_observable(rng, n)\n",
" r = random_state(rng, n)\n",
" r0 = r\n",
" evolve = exp(im * 2 * pi * dt * H)\n",
" result = []\n",
" for t in 0:dt:T\n",
" push!(result, braket(r, r0))\n",
" r = evolve * r\n",
" end\n",
" \n",
" return real.(result), imag.(result)\n",
"end\n",
"\n",
"using Plots\n",
"plot(random_evolution(rng, 4, 100, 0.01)[1])"
]
},
{
"cell_type": "markdown",
"id": "0bb1f98e",
"metadata": {},
"source": [
"That is kind of what you'd expect - a superposition of oscillations at a number of different frequencies."
]
},
{
"cell_type": "markdown",
"id": "f491b616",
"metadata": {},
"source": [
"## Using an observer\n",
"\n",
"Now what happens to the states if we evolve a random state similarly using an\n",
"observer. We'll try to look at the observation process as a series of small unitary\n",
"transformations and keep track of how the two states of the original measured qubit\n",
"evolve when considered along with the n states of the observer."
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "2d71dea6",
"metadata": {},
"outputs": [
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},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function evolve_observer(rng, n, T, dt)\n",
" H = random_observer(rng, n)\n",
" w = random_state(rng, n)\n",
" q = random_state(rng, 2)\n",
" r = kron(q,w)\n",
" r0 = r\n",
" result = []\n",
" evolve = exp(im * 2 * pi * H * dt)\n",
" for t in 0:dt:T\n",
" costate_0 = r[1:n]\n",
" costate_1 = r[n+1:end]\n",
" costate_0 /= sqrt(sum(abs2, costate_0))\n",
" costate_1 /= sqrt(sum(abs2, costate_1))\n",
" push!(result, braket(costate_0, costate_1))\n",
" r = evolve * r\n",
" end\n",
" return abs.(result)\n",
"end\n",
"\n",
"evols = evolve_observer.(rng, 2 .^ (4:8), 10, 0.1)\n",
"plot(evols)\n"
]
},
{
"cell_type": "markdown",
"id": "d5b7b64a",
"metadata": {},
"source": [
"That looks interesting to me. While initially there is some correlation between the two parts of the\n",
"state vector $r_{1\\ldots n}$ and $r_{(n+1)\\ldots 2n}$, it rapidly declines to near 0 and lingers around 0 forever, the larger $n$ gets. For small $n$, we essentially have a small coherent superposition, but the superpositions get complex for observers with larger n. Let's split the plots into a series and see it more clearly."
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "7f9770cb",
"metadata": {},
"outputs": [
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" 218.488,330.787 220.205,323.846 221.922,326.208 223.639,334.356 225.356,338.409 227.073,327.711 228.79,305.793 230.508,284.434 232.225,272.659 233.942,275.301 \n",
" 235.659,293.316 237.376,324.097 239.093,361.574 240.81,387.374 242.527,365.319 244.244,339.707 245.961,324.717 247.679,321.495 249.396,328.033 251.113,340.594 \n",
" 252.83,354.872 254.547,367.211 256.264,375.861 257.981,381.539 259.698,386.037 261.415,390.264 263.132,393.835 264.85,395.593 266.567,394.573 268.284,390.92 \n",
" 270.001,385.004 271.718,376.713 273.435,365.998 275.152,353.559 276.869,341.097 278.586,331.081 280.303,326.189 282.021,328.619 283.738,339.458 285.455,358.296 \n",
" 287.172,383.159 288.889,403.707 290.606,377.384 292.323,354.833 294.04,339.327 295.757,332.15 297.474,332.996 299.191,340.159 300.909,350.963 302.626,362.267 \n",
" 304.343,370.927 306.06,374.608 307.777,373.254 309.494,368.805 311.211,363.111 312.928,357.408 314.645,352.846 316.362,350.836 318.08,352.942 319.797,360.178 \n",
" 321.514,370.813 323.231,373.597 324.948,354.523 326.665,322.564 328.382,287.897 330.099,256.814 331.816,234.007 333.533,222.577 335.251,223.64 336.968,236.183 \n",
" 338.685,257.368 340.402,283.299 342.119,310.169 343.836,335.517 345.553,358.992 347.27,381.767 348.987,401.484 350.704,383.137 352.421,358.793 354.139,336.627 \n",
" 355.856,318.659 357.573,305.613 359.29,296.72 361.007,290.143 362.724,284.119 364.441,278.146 366.158,273.166 367.875,270.519 369.592,270.545 371.31,271.779 \n",
" 373.027,271.32 374.744,266.659 376.461,257.831 378.178,247.625 379.895,239.78 381.612,237.235 383.329,241.437 385.046,252.468 386.763,269.566 388.481,291.614 \n",
" 390.198,317.185 391.915,343.631 393.632,363.793 395.349,363.567 397.066,346.615 398.783,329.427 400.5,319.811 402.217,320.588 403.934,331.803 405.651,351.429 \n",
" 407.369,376.133 409.086,402.263 410.803,388.61 412.52,366.961 414.237,348.666 415.954,333.768 417.671,323.049 419.388,318.271 421.105,321.441 422.822,333.708 \n",
" 424.54,354.553 426.257,381.572 427.974,404.21 429.691,377.239 431.408,356.097 433.125,343.784 434.842,341.135 436.559,346.991 438.276,358.488 439.993,371.47 \n",
" 441.711,380.713 443.428,382.096 445.145,378.101 446.862,373.422 448.579,369.986 450.296,368.378 452.013,368.953 453.73,371.81 455.447,376.405 457.164,381.369 \n",
" 458.881,384.684 460.599,384.1 462.316,377.696 464.033,364.724 465.75,346.133 467.467,324.534 469.184,303.844 470.901,288.602 472.618,283.027 474.335,289.988 \n",
" 476.052,310.138 477.77,341.276 479.487,376.551 481.204,380.861 482.921,350.073 484.638,325.189 486.355,313.285 488.072,315.339 489.789,328.643 491.506,346.935 \n",
" 493.223,360.18 494.941,359.608 496.658,350.212 498.375,340.746 500.092,333.757 501.809,328.711 503.526,325.554 505.243,325.928 506.96,332.12 508.677,345.381 \n",
" 510.394,364.864 512.112,386.107 513.829,388.267 515.546,368.853 517.263,350.829 518.98,338.529 520.697,332.294 522.414,330.712 524.131,331.351 525.848,331.762 \n",
" 527.565,330.714 529.282,328.783 531,327.654 532.717,328.902 534.434,333.295 536.151,340.791 537.868,350.992 539.585,363.623 541.302,378.515 543.019,393.946 \n",
" 544.736,393.281 546.453,376.547 548.171,361.436 549.888,352.606 551.605,352.357 553.322,360.107 555.039,369.052 556.756,363.716 558.473,342.632 560.19,319.004 \n",
" 561.907,301.427 563.624,294.293 565.342,298.977 567.059,314.206 568.776,336.562 570.493,361.168 572.21,381.809 573.927,389.325 575.644,384.488 577.361,379.251 \n",
" 579.078,374.799 580.795,368.525 582.512,360.024 584.23,351.522 585.947,345.494 587.664,343.235 589.381,344.488 591.098,347.525 592.815,349.643 594.532,348.42 \n",
" 596.249,343.249 597.966,335.375 599.683,326.633 601.401,318.775 603.118,313.566 604.835,312.878 606.552,318.384 608.269,330.853 609.986,348.877 611.703,365.332 \n",
" 613.42,362.778 615.137,340.37 616.854,314.676 618.572,294.545 620.289,284.062 622.006,284.594 623.723,295.15 625.44,312.658 627.157,332.431 628.874,348.936 \n",
" 630.591,357.673 632.308,358.409 634.025,354.109 635.742,346.122 637.46,334.476 639.177,320.487 640.894,306.906 642.611,296.386 644.328,290.195 646.045,287.709 \n",
" 647.762,286.848 649.479,285.548 651.196,283.523 652.913,282.702 654.631,285.844 656.348,294.644 658.065,308.353 659.782,322.867 661.499,330.728 663.216,325.944 \n",
" 664.933,311.249 666.65,293.68 668.367,277.877 670.084,265.503 671.802,256.356 673.519,249.329 675.236,243.183 676.953,237.164 678.67,231.414 680.387,227.008 \n",
" 682.104,225.589 683.821,228.743 685.538,237.361 687.255,251.244 688.972,269.049 690.69,288.6 692.407,307.5 694.124,323.91 695.841,337.2 697.558,347.971 \n",
" 699.275,357.209 700.992,364.982 702.709,369.325 704.426,366.797 706.143,356.443 707.861,340.727 709.578,322.355 711.295,303.352 713.012,285.409 714.729,270.108 \n",
" 716.446,258.88 718.163,252.774 719.88,252.158 721.597,256.527 723.314,264.57 725.032,274.602 726.749,285.214 728.466,295.788 730.183,306.413 731.9,317.257 \n",
" 733.617,327.953 735.334,337.538 737.051,344.959 738.768,349.559 740.485,350.892 742.203,348.354 743.92,341.833 745.637,332.706 747.354,323.514 749.071,316.824 \n",
" 750.788,314.348 752.505,316.574 754.222,322.71 755.939,330.788 757.656,337.935 759.373,341.374 761.091,340.546 762.808,338.204 764.525,338.659 766.242,345.585 \n",
" 767.959,360.995 769.676,384.918 771.393,400.109 773.11,366.343 774.827,333.511 776.544,305.648 778.262,285.816 779.979,275.554 781.696,274.712 783.413,281.662 \n",
" 785.13,293.722 786.847,307.571 788.564,319.604 790.281,326.601 791.998,327.145 793.715,322.473 795.433,315.09 797.15,306.983 798.867,299.323 800.584,293.069 \n",
" 802.301,289.392 804.018,289.389 805.735,293.17 807.452,298.797 809.169,301.959 810.886,298.077 812.603,286.538 814.321,271.574 816.038,258.764 817.755,252.277 \n",
" 819.472,254.089 821.189,263.988 822.906,279.817 824.623,297.886 826.34,313.811 828.057,324.335 829.774,329.476 831.492,331.882 833.209,333.166 834.926,331.789 \n",
" 836.643,325.068 838.36,313.381 840.077,300.793 841.794,292.063 843.511,290.378 845.228,296.59 846.945,309.333 848.663,325.767 850.38,342.887 852.097,359.086 \n",
" 853.814,374.99 855.531,392.423 857.248,401.532 858.965,379.235 860.682,355.774 862.399,334.031 864.116,316.06 865.833,303.016 867.551,295.062 869.268,291.607 \n",
" 870.985,291.766 872.702,294.847 874.419,300.682 876.136,309.689 877.853,322.631 879.57,340.14 881.287,362.081 883.004,386.157 884.722,391.012 886.439,367.389 \n",
" 888.156,344.573 889.873,327.504 891.59,317.466 893.307,313.62 895.024,313.426 896.741,314.075 898.458,314.637 900.175,316.987 901.893,324.336 903.61,338.971 \n",
" 905.327,360.727 907.044,384.418 908.761,382.441 910.478,357.499 912.195,335.3 913.912,321.506 915.629,317.759 917.346,323.4 919.063,335.97 920.781,351.947 \n",
" 922.498,367.736 924.215,380.541 925.932,387.678 927.649,384.632 929.366,372.075 931.083,355.228 932.8,338.174 934.517,324.213 936.234,315.596 937.952,312.742 \n",
" 939.669,313.464 941.386,312.925 943.103,306.034 944.82,291.95 946.537,274.896 948.254,260.645 949.971,253.909 951.688,257.514 953.405,272.256 955.123,296.969 \n",
" 956.84,328.614 958.557,361.499 960.274,378.752 961.991,361.207 963.708,336.751 965.425,317.831 967.142,306.934 968.859,304.417 970.576,309.806 972.294,322.13 \n",
" 974.011,339.797 975.728,359.92 977.445,376.255 979.162,377.939 980.879,368.714 982.596,362.186 984.313,364.174 986.03,375.982 987.747,395.761 989.464,390.726 \n",
" 991.182,362.759 992.899,336.12 994.616,314.157 996.333,298.382 998.05,288.759 999.767,284.292 1001.48,283.949 1003.2,287.399 1004.92,295.086 1006.64,307.668 \n",
" 1008.35,325.338 1010.07,347.455 1011.79,372.499 1013.5,396.836 1015.22,387.973 1016.94,365.729 1018.66,347.643 1020.37,335.916 1022.09,331.787 1023.81,335.526 \n",
" 1025.52,345.999 1027.24,359.856 1028.96,369.657 1030.67,366.08 1032.39,352.468 1034.11,337.905 1035.83,326.762 1037.54,320.23 1039.26,317.958 1040.98,319.079 \n",
" 1042.69,322.968 1044.41,329.524 1046.13,338.694 1047.85,349.364 1049.56,357.876 1051.28,358.2 1053,348.453 1054.71,333.61 1056.43,318.586 1058.15,305.759 \n",
" 1059.87,295.858 1061.58,289.159 1063.3,286.43 1065.02,289.168 1066.73,299.011 1068.45,316.738 1070.17,341.405 1071.89,369.717 1073.6,392.096 1075.32,382.792 \n",
" 1077.04,368.495 1078.75,363.807 1080.47,366.9 1082.19,364.122 1083.9,341.645 1085.62,307.491 1087.34,273.218 1089.06,247.03 1090.77,234.598 1092.49,238.935 \n",
" 1094.21,260.112 1095.92,295.279 1097.64,338.923 1099.36,380.966 1101.08,376.575 1102.79,346.624 1104.51,327.754 1106.23,323.621 1107.94,333.499 1109.66,353.961 \n",
" 1111.38,377.273 1113.1,378.206 1114.81,353.051 1116.53,326.689 1118.25,306.488 1119.96,295.723 1121.68,296.351 1123.4,308.923 1125.12,331.757 1126.83,358.224 \n",
" 1128.55,366.047 1130.27,341.302 1131.98,309.874 1133.7,284.988 1135.42,271.261 1137.13,269.651 1138.85,278.321 1140.57,293.157 1142.29,308.505 1144,318.622 \n",
" 1145.72,320.408 1147.44,315.14 1149.15,305.992 1150.87,295.104 1152.59,283.405 1154.31,271.544 1156.02,260.523 1157.74,251.826 1159.46,247.304 1161.17,248.929 \n",
" 1162.89,258.45 1164.61,276.936 1166.33,304.304 1168.04,338.868 1169.76,375.748 1171.48,382.591 1173.19,349.137 1174.91,317.711 1176.63,294.736 1178.35,281.64 \n",
" 1180.06,277.545 1181.78,279.767 1183.5,284.729 1185.21,289.465 1186.93,293.005 1188.65,296.429 1190.36,301.444 1192.08,308.961 1193.8,318.642 1195.52,329.25 \n",
" 1197.23,339.022 1198.95,345.325 1200.67,344.288 1202.38,333.485 1204.1,315.267 1205.82,294.812 1207.54,277.311 1209.25,266.9 1210.97,266.124 1212.69,275.529 \n",
" 1214.4,293.506 1216.12,316.334 1217.84,338.23 1219.56,351.847 1221.27,353.324 1222.99,348.461 1224.71,345.055 1226.42,346.743 1228.14,354.126 1229.86,366.135 \n",
" 1231.58,380.084 1233.29,388.503 1235.01,381.183 1236.73,367.221 1238.44,354.518 1240.16,345.449 1241.88,340.59 1243.59,339.6 1245.31,341.688 1247.03,346.015 \n",
" 1248.75,351.903 1250.46,358.778 1252.18,366.034 1253.9,372.989 1255.61,378.644 1257.33,380.574 1259.05,375.07 1260.77,361.971 1262.48,344.731 1264.2,327.18 \n",
" 1265.92,312.789 1267.63,304.291 1269.35,303.157 1271.07,309.162 1272.79,320.159 1274.5,332.001 1276.22,339.058 1277.94,337.232 1279.65,327.941 1281.37,315.958 \n",
" 1283.09,305.236 1284.81,297.993 1286.52,294.932 1288.24,295.275 1289.96,296.874 1291.67,297.046 1293.39,294.294 1295.11,289.629 1296.82,285.896 1298.54,285.843 \n",
" 1300.26,290.473 1301.98,297.943 1303.69,302.98 1305.41,298.677 1307.13,282.453 1308.84,258.778 1310.56,234.682 1312.28,216.12 1314,207.103 1315.71,209.616 \n",
" 1317.43,223.681 1319.15,247.605 1320.86,278.453 1322.58,312.681 1324.3,346.719 1326.02,377.003 1327.73,394.237 1329.45,382.656 1331.17,368.916 1332.88,360.509 \n",
" 1334.6,357.993 1336.32,360.898 1338.04,367.709 1339.75,374.529 1341.47,373.517 1343.19,360.814 1344.9,341.859 1346.62,322.1 1348.34,305.292 1350.05,294.347 \n",
" 1351.77,291.339 1353.49,297.149 1355.21,311.039 1356.92,330.279 1358.64,349.571 1360.36,360.714 1362.07,359.015 1363.79,351.976 1365.51,348.293 1367.23,351.399 \n",
" 1368.94,361.127 1370.66,374.862 1372.38,386.375 1374.09,384.035 1375.81,371.21 1377.53,357.217 1379.25,344.422 1380.96,333.19 1382.68,323.763 1384.4,316.639 \n",
" 1386.11,312.349 1387.83,311.13 1389.55,312.875 1391.27,317.402 1392.98,324.787 1394.7,335.385 1396.42,349.367 1398.13,365.827 1399.85,380.668 1401.57,382.094 \n",
" 1403.28,368.416 1405,351.656 1406.72,335.706 1408.44,320.212 1410.15,303.849 1411.87,286.388 1413.59,269.631 1415.3,256.8 1417.02,251.203 1418.74,255.043 \n",
" 1420.46,268.71 1422.17,290.619 1423.89,317.538 1425.61,345.311 1427.32,369.809 1429.04,387.924 1430.76,398.22 1432.48,399.29 1434.19,392.339 1435.91,382.172 \n",
" 1437.63,371.989 1439.34,364.199 1441.06,359.861 1442.78,358.266 1444.5,357.367 1446.21,355.409 1447.93,352.645 1449.65,350.936 1451.36,351.793 1453.08,354.88 \n",
" 1454.8,357.65 1456.51,356.845 1458.23,351.914 1459.95,345.747 1461.67,341.626 1463.38,341.168 1465.1,344.072 1466.82,348.786 1468.53,353.872 1470.25,359.463 \n",
" 1471.97,367.205 1473.69,377.89 1475.4,384.947 1477.12,372.222 1478.84,346.911 1480.55,319.514 1482.27,295.142 1483.99,276.925 1485.71,266.31 1487.42,263.016 \n",
" 1489.14,265.347 1490.86,270.877 1492.57,277.369 1494.29,283.509 1496.01,289.116 1497.73,294.797 1499.44,301.424 1501.16,309.717 1502.88,319.844 1504.59,330.923 \n",
" 1506.31,340.595 1508.03,345.619 1509.74,344.724 1511.46,340.797 1513.18,338.39 1514.9,340.682 1516.61,348.662 1518.33,361.255 1520.05,375.396 1521.76,385.25 \n",
" 1523.48,384.667 1525.2,379.08 1526.92,375.854 1528.63,376.924 1530.35,380.659 1532.07,381.408 1533.78,373.061 1535.5,357.639 1537.22,339.826 1538.94,322.874 \n",
" 1540.65,309.145 1542.37,300.377 1544.09,297.538 1545.8,300.583 1547.52,308.334 1549.24,318.663 1550.96,329.097 1552.67,337.68 1554.39,343.242 1556.11,344.346 \n",
" 1557.82,338.641 1559.54,325.308 1561.26,307.273 1562.97,289.569 1564.69,276.968 1566.41,272.533 1568.13,276.708 1569.84,286.854 1571.56,297.657 1573.28,303.511 \n",
" 1574.99,302.823 1576.71,299.151 1578.43,296.837 1580.15,297.274 1581.86,298.632 1583.58,297.949 1585.3,294.093 1587.01,288.941 1588.73,285.785 1590.45,287.327 \n",
" 1592.17,294.907 1593.88,308.525 1595.6,326.919 1597.32,347.214 1599.03,363.826 1600.75,368.89 1602.47,363.22 1604.19,356.579 1605.9,353.528 1607.62,352.062 \n",
" 1609.34,346.897 1611.05,336.029 1612.77,323.727 1614.49,316.032 1616.2,317.069 1617.92,327.968 1619.64,346.693 1621.36,367.548 1623.07,378.014 1624.79,369.19 \n",
" 1626.51,355.752 1628.22,346.729 1629.94,343.806 1631.66,346.238 1633.38,351.827 1635.09,355.649 1636.81,349.566 1638.53,330.288 1640.24,303.263 1641.96,275.63 \n",
" 1643.68,253.378 1645.4,240.973 1647.11,240.944 1648.83,253.599 1650.55,277.102 1652.26,307.938 1653.98,341.537 1655.7,372.221 1657.42,387.301 1659.13,376.217 \n",
" 1660.85,362.642 1662.57,354.102 1664.28,350.602 1666,350.813 1667.72,353.098 1669.43,355.869 1671.15,357.839 1672.87,358.327 1674.59,357.491 1676.3,356.23 \n",
" 1678.02,355.71 1679.74,356.845 1681.45,359.922 1683.17,364.425 1684.89,369.207 1686.61,373.169 1688.32,376.159 1690.04,378.776 1691.76,380.41 1693.47,377.69 \n",
" 1695.19,368.322 1696.91,355.099 1698.63,342.613 1700.34,334.835 1702.06,334.391 1703.78,341.732 1705.49,353.569 1707.21,360.027 1708.93,350.287 1710.65,330.394 \n",
" 1712.36,311.849 1714.08,301.51 1715.8,302.651 1717.51,315.802 1719.23,339.235 1720.95,369.662 1722.66,402.823 1724.38,378.523 1726.1,346.913 1727.82,317.527 \n",
" 1729.53,290.006 1731.25,264.566 1732.97,242.803 1734.68,227.334 1736.4,220.582 1738.12,223.387 1739.84,233.981 1741.55,247.663 1743.27,257.889 1744.99,259.765 \n",
" 1746.7,253.953 1748.42,245.739 1750.14,240.575 1751.86,241.554 1753.57,249.303 1755.29,262.721 1757.01,279.743 1758.72,297.901 1760.44,314.724 1762.16,328.18 \n",
" 1763.88,337.28 1765.59,342.437 1767.31,344.857 1769.03,345.373 1770.74,343.928 1772.46,339.991 1774.18,333.353 1775.89,324.673 1777.61,315.603 1779.33,308.575 \n",
" 1781.05,306.321 1782.76,311.157 1784.48,324.147 1786.2,344.133 1787.91,365.411 1789.63,370.657 1791.35,351.416 1793.07,326.449 1794.78,305.084 1796.5,289.969 \n",
" 1798.22,281.425 1799.93,279.069 1801.65,282.83 1803.37,293.247 1805.09,310.953 1806.8,335.809 1808.52,366.282 1810.24,399.093 1811.95,383.577 1813.67,356.503 \n",
" 1815.39,337.484 1817.11,328.351 1818.82,329.237 1820.54,338.739 1822.26,354.347 1823.97,373.045 1825.69,391.92 1827.41,406.143 1829.12,393.28 1830.84,383.568 \n",
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" 235.659,1475.95 237.376,1482.16 239.093,1493.46 240.81,1507.46 242.527,1521.62 244.244,1533.92 245.961,1542.96 247.679,1545.56 249.396,1540.98 251.113,1535.11 \n",
" 252.83,1529.68 254.547,1525.17 256.264,1521.61 257.981,1518.78 259.698,1516.88 261.415,1516.59 263.132,1518.46 264.85,1521.79 266.567,1523.64 268.284,1520.64 \n",
" 270.001,1513.89 271.718,1507.67 273.435,1505.36 275.152,1508.61 276.869,1517.36 278.586,1530.04 280.303,1542.58 282.021,1539.19 283.738,1527.95 285.455,1519.51 \n",
" 287.172,1515.23 288.889,1515.15 290.606,1518.78 292.323,1525.36 294.04,1533.82 295.757,1541.52 297.474,1540.09 299.191,1531.11 300.909,1521.75 302.626,1514.02 \n",
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" 321.514,1541.05 323.231,1538.38 324.948,1533.99 326.665,1528.38 328.382,1521.88 330.099,1515.07 331.816,1508.84 333.533,1504.23 335.251,1502.14 336.968,1503.01 \n",
" 338.685,1506.56 340.402,1511.62 342.119,1516.11 343.836,1517.71 345.553,1515.55 347.27,1510.97 348.987,1505.86 350.704,1501.44 352.421,1498.23 354.139,1496.5 \n",
" 355.856,1496.57 357.573,1498.89 359.29,1503.97 361.007,1511.94 362.724,1521.59 364.441,1527.95 366.158,1522.92 367.875,1509.62 369.592,1495.57 371.31,1484.78 \n",
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" 424.54,1486.32 426.257,1488.69 427.974,1492.18 429.691,1496.01 431.408,1499.61 433.125,1502.69 434.842,1505.02 436.559,1506.57 438.276,1507.76 439.993,1509.39 \n",
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" 458.881,1532.64 460.599,1525.67 462.316,1520.83 464.033,1519.25 465.75,1520.74 467.467,1523.94 469.184,1526.75 470.901,1527.54 472.618,1526.58 474.335,1525.03 \n",
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" 561.907,1534 563.624,1542.69 565.342,1539.32 567.059,1524.62 568.776,1509.66 570.493,1497.31 572.21,1488.99 573.927,1485.19 575.644,1485.47 577.361,1488.72 \n",
" 579.078,1493.47 580.795,1498.38 582.512,1502.45 584.23,1504.85 585.947,1504.59 587.664,1501.19 589.381,1495.65 591.098,1490.24 592.815,1487.38 594.532,1488.6 \n",
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" 802.301,1535.47 804.018,1532.95 805.735,1528.1 807.452,1521.81 809.169,1514.62 810.886,1507.05 812.603,1499.78 814.321,1493.6 816.038,1489.32 817.755,1487.64 \n",
" 819.472,1488.93 821.189,1493.1 822.906,1499.45 824.623,1506.76 826.34,1513.45 828.057,1518.25 829.774,1521.03 831.492,1522.76 833.209,1524.25 834.926,1525.26 \n",
" 836.643,1524.97 838.36,1523.15 840.077,1520.42 841.794,1517.04 843.511,1512.01 845.228,1504.07 846.945,1493.41 848.663,1482.05 850.38,1472.71 852.097,1467.77 \n",
" 853.814,1468.59 855.531,1475.19 857.248,1486.24 858.965,1499.2 860.682,1510.82 862.399,1517.9 864.116,1519.38 865.833,1517.26 867.551,1513.9 869.268,1510.57 \n",
" 870.985,1508.13 872.702,1507.31 874.419,1508.09 876.136,1508.78 877.853,1506.19 879.57,1498.34 881.287,1486.8 883.004,1474.95 884.722,1465.85 886.439,1461.58 \n",
" 888.156,1463.15 889.873,1470.66 891.59,1483.37 893.307,1500.03 895.024,1518.99 896.741,1537.9 898.458,1541.32 900.175,1525.35 901.893,1510.4 903.61,1498.22 \n",
" 905.327,1489.19 907.044,1483.39 908.761,1480.81 910.478,1481.45 912.195,1485.3 913.912,1492.21 915.629,1501.63 917.346,1512.06 919.063,1519.81 920.781,1519.03 \n",
" 922.498,1509.44 924.215,1496.75 925.932,1485.26 927.649,1477.38 929.366,1474.39 931.083,1476.7 932.8,1483.95 934.517,1494.99 936.234,1508 937.952,1520.38 \n",
" 939.669,1528.23 941.386,1527.41 943.103,1519.63 944.82,1508.68 946.537,1496.32 948.254,1483.91 949.971,1473.27 951.688,1466.3 953.405,1464.43 955.123,1468.03 \n",
" 956.84,1476.29 958.557,1487.35 960.274,1498.67 961.991,1507.54 963.708,1511.63 965.425,1510.24 967.142,1505.13 968.859,1499.52 970.576,1496.67 972.294,1499.24 \n",
" 974.011,1508.74 975.728,1525.07 977.445,1545.98 979.162,1533.07 980.879,1511.26 982.596,1494.7 984.313,1486.14 986.03,1486.74 987.747,1495.83 989.464,1510.95 \n",
" 991.182,1527.55 992.899,1535.1 994.616,1526.91 996.333,1517.43 998.05,1512.11 999.767,1510.62 1001.48,1510.23 1003.2,1507.52 1004.92,1501.24 1006.64,1493.29 \n",
" 1008.35,1486.6 1010.07,1483.48 1011.79,1485.27 1013.5,1492.34 1015.22,1504.2 1016.94,1519.5 1018.66,1535.37 1020.37,1539.67 1022.09,1527.5 1023.81,1515.99 \n",
" 1025.52,1509.04 1027.24,1507.53 1028.96,1511.2 1030.67,1518.94 1032.39,1529 1034.11,1539.32 1035.83,1546.82 1037.54,1545.12 1039.26,1541.6 1040.98,1540.34 \n",
" 1042.69,1541.02 1044.41,1542.38 1046.13,1542.45 1047.85,1540.23 1049.56,1536.95 1051.28,1534.07 1053,1532.27 1054.71,1531.2 1056.43,1529.26 1058.15,1524.45 \n",
" 1059.87,1516.23 1061.58,1505.65 1063.3,1494.12 1065.02,1482.99 1066.73,1473.58 1068.45,1467.25 1070.17,1465.33 1071.89,1468.86 1073.6,1478.11 1075.32,1492.12 \n",
" 1077.04,1507.92 1078.75,1518.75 1080.47,1516.52 1082.19,1506.25 1083.9,1497.4 1085.62,1494.22 1087.34,1497.78 1089.06,1507.35 1090.77,1520.88 1092.49,1534.78 \n",
" 1094.21,1539.79 1095.92,1531.85 1097.64,1523.91 1099.36,1519.56 1101.08,1518.9 1102.79,1520.93 1104.51,1524.22 1106.23,1527.44 1107.94,1529.91 1109.66,1531.76 \n",
" 1111.38,1533.3 1113.1,1534.37 1114.81,1534.33 1116.53,1533.07 1118.25,1531.59 1119.96,1531.21 1121.68,1532.93 1123.4,1536.96 1125.12,1542.39 1126.83,1545.32 \n",
" 1128.55,1541.43 1130.27,1536.73 1131.98,1534.62 1133.7,1536.1 1135.42,1540.53 1137.13,1542.76 1138.85,1535.8 1140.57,1525.76 1142.29,1517.01 1144,1511.58 \n",
" 1145.72,1510.44 1147.44,1513.55 1149.15,1519.82 1150.87,1526.95 1152.59,1531.27 1154.31,1530.04 1156.02,1525.54 1157.74,1521.14 1159.46,1518.2 1161.17,1516.72 \n",
" 1162.89,1516.12 1164.61,1515.79 1166.33,1515.46 1168.04,1515.14 1169.76,1514.79 1171.48,1513.88 1173.19,1511.47 1174.91,1506.73 1176.63,1499.8 1178.35,1491.91 \n",
" 1180.06,1484.95 1181.78,1480.86 1183.5,1481.2 1185.21,1486.74 1186.93,1496.82 1188.65,1508.47 1190.36,1514.88 1192.08,1509.83 1193.8,1498.11 1195.52,1487.47 \n",
" 1197.23,1481.95 1198.95,1482.81 1200.67,1489.23 1202.38,1498.73 1204.1,1507.62 1205.82,1512.35 1207.54,1512.46 1209.25,1510.91 1210.97,1510.46 1212.69,1512.08 \n",
" 1214.4,1515.32 1216.12,1518.95 1217.84,1521.18 1219.56,1520.25 1221.27,1515.96 1222.99,1510.1 1224.71,1505.18 1226.42,1503.4 1228.14,1506.07 1229.86,1513.18 \n",
" 1231.58,1522.35 1233.29,1526.75 1235.01,1520.21 1236.73,1508.99 1238.44,1500.18 1240.16,1497.1 1241.88,1500.67 1243.59,1509.91 1245.31,1521.9 1247.03,1531.51 \n",
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" 287.172,2069.17 288.889,2065.57 290.606,2065.94 292.323,2069.48 294.04,2074.98 295.757,2081.16 297.474,2087.03 299.191,2092.06 300.909,2096.09 302.626,2099.09 \n",
" 304.343,2101 306.06,2101.82 307.777,2101.76 309.494,2101.4 311.211,2101.62 312.928,2103.33 314.645,2107.01 316.362,2111.88 318.08,2113.26 319.797,2107.9 \n",
" 321.514,2101.8 323.231,2098.34 324.948,2098.99 326.665,2104.08 328.382,2112.68 330.099,2117.18 331.816,2107.21 333.533,2098.49 335.251,2093.3 336.968,2092.11 \n",
" 338.685,2093.95 340.402,2096.1 342.119,2095.16 343.836,2090.37 345.553,2084.16 347.27,2078.87 348.987,2075.61 350.704,2074.6 352.421,2075.61 354.139,2078.34 \n",
" 355.856,2082.56 357.573,2088.1 359.29,2094.76 361.007,2102.15 362.724,2109.74 364.441,2116.93 366.158,2119.5 367.875,2114.44 369.592,2110.65 371.31,2108.06 \n",
" 373.027,2106.44 374.744,2105.43 376.461,2104.41 378.178,2102.68 379.895,2099.94 381.612,2096.58 383.329,2093.5 385.046,2091.46 386.763,2090.84 388.481,2091.46 \n",
" 390.198,2092.7 391.915,2093.9 393.632,2094.72 395.349,2095.22 397.066,2095.33 398.783,2094.38 400.5,2091.45 402.217,2086.47 403.934,2080.52 405.651,2075.21 \n",
" 407.369,2071.98 409.086,2071.82 410.803,2075.09 412.52,2081.5 414.237,2090.08 415.954,2099.22 417.671,2106.49 419.388,2109.18 421.105,2108.5 422.822,2108.49 \n",
" 424.54,2110.9 426.257,2115.32 427.974,2117.01 429.691,2111.37 431.408,2105.05 433.125,2099.74 434.842,2095.74 436.559,2092.95 438.276,2091.36 439.993,2091.3 \n",
" 441.711,2093.34 443.428,2097.77 445.145,2103.78 446.862,2107.55 448.579,2103.62 450.296,2095.62 452.013,2088.75 453.73,2085.56 455.447,2087.15 457.164,2093.53 \n",
" 458.881,2103.61 460.599,2114.72 462.316,2112.19 464.033,2102.47 465.75,2095.85 467.467,2093.6 469.184,2095.64 470.901,2100.73 472.618,2106.3 474.335,2108.34 \n",
" 476.052,2105.99 477.77,2103.21 479.487,2101.91 481.204,2100.95 482.921,2097.57 484.638,2090.91 486.355,2083.09 488.072,2076.88 489.789,2074.32 491.506,2076.32 \n",
" 493.223,2082.43 494.941,2090.43 496.658,2095.7 498.375,2093.8 500.092,2087.3 501.809,2081.32 503.526,2078.39 505.243,2079.05 506.96,2082.68 508.677,2088.14 \n",
" 510.394,2094.36 512.112,2100.69 513.829,2106.83 515.546,2111.55 517.263,2110.87 518.98,2105.07 520.697,2098.45 522.414,2093.13 524.131,2090.2 525.848,2090.23 \n",
" 527.565,2093.34 529.282,2099.27 531,2107.38 532.717,2116.63 534.434,2115.78 536.151,2107.24 537.868,2100.74 539.585,2097.34 541.302,2097.39 543.019,2100 \n",
" 544.736,2101.75 546.453,2097.43 548.171,2087.4 549.888,2075.86 551.605,2066 553.322,2059.87 555.039,2058.6 556.756,2062.36 558.473,2070.4 560.19,2081.13 \n",
" 561.907,2092.11 563.624,2099.89 565.342,2101.29 567.059,2098.27 568.776,2095.05 570.493,2093.45 572.21,2093.68 573.927,2095.34 575.644,2097.9 577.361,2100.82 \n",
" 579.078,2103.75 580.795,2106.71 582.512,2110.01 584.23,2113.42 585.947,2113.3 587.664,2107.09 589.381,2098.55 591.098,2090.14 592.815,2083.45 594.532,2079.59 \n",
" 596.249,2079.05 597.966,2081.61 599.683,2086.46 601.401,2092.38 603.118,2098.08 604.835,2102.44 606.552,2104.81 608.269,2105.13 609.986,2103.87 611.703,2101.71 \n",
" 613.42,2099.23 615.137,2096.72 616.854,2094.07 618.572,2090.87 620.289,2086.71 622.006,2081.63 623.723,2076.26 625.44,2071.57 627.157,2068.65 628.874,2068.34 \n",
" 630.591,2071.09 632.308,2076.72 634.025,2084.32 635.742,2091.95 637.46,2096.44 639.177,2095.35 640.894,2090.58 642.611,2085.66 644.328,2082.64 646.045,2082.26 \n",
" 647.762,2084.46 649.479,2088.54 651.196,2093.34 652.913,2097.4 654.631,2099.48 656.348,2099.56 658.065,2098.89 659.782,2098.76 661.499,2099.81 663.216,2101.94 \n",
" 664.933,2104.63 666.65,2107.25 668.367,2109.66 670.084,2112.39 671.802,2116.13 673.519,2120.4 675.236,2115.52 676.953,2109.9 678.67,2105.68 680.387,2103.92 \n",
" 682.104,2105.14 683.821,2108.83 685.538,2112.26 687.255,2109.76 688.972,2103.07 690.69,2096.5 692.407,2091.7 694.124,2089.05 695.841,2088.18 697.558,2088.26 \n",
" 699.275,2088.39 700.992,2088.03 702.709,2087.19 704.426,2086.24 706.143,2085.55 707.861,2085.28 709.578,2085.23 711.295,2084.97 713.012,2084.15 714.729,2082.74 \n",
" 716.446,2081.04 718.163,2079.33 719.88,2077.54 721.597,2075.25 723.314,2072.16 725.032,2068.55 726.749,2065.32 728.466,2063.62 730.183,2064.35 731.9,2067.88 \n",
" 733.617,2074.01 735.334,2081.99 737.051,2090.82 738.768,2099.34 740.485,2106.38 742.203,2110.7 743.92,2111.57 745.637,2109.95 747.354,2106.92 749.071,2102.67 \n",
" 750.788,2097.59 752.505,2092.62 754.222,2089.04 755.939,2087.96 757.656,2089.84 759.373,2093.97 761.091,2097.75 762.808,2097.17 764.525,2091.52 766.242,2084.25 \n",
" 767.959,2078.18 769.676,2074.51 771.393,2073.36 773.11,2074.32 774.827,2076.95 776.544,2080.88 778.262,2085.66 779.979,2090.25 781.696,2093.19 783.413,2093.82 \n",
" 785.13,2093.44 786.847,2094.32 788.564,2098.07 790.281,2105.17 791.998,2115.06 793.715,2115.71 795.433,2103.93 797.15,2093.29 798.867,2085.03 800.584,2079.89 \n",
" 802.301,2078.08 804.018,2079.24 805.735,2082.52 807.452,2086.69 809.169,2090.59 810.886,2093.58 812.603,2095.8 814.321,2097.65 816.038,2099.11 817.755,2099.75 \n",
" 819.472,2099.54 821.189,2099.27 822.906,2099.93 824.623,2101.8 826.34,2103.77 828.057,2103.57 829.774,2100.19 831.492,2095.41 833.209,2091.34 834.926,2089.15 \n",
" 836.643,2089.13 838.36,2090.95 840.077,2093.97 841.794,2097.6 843.511,2101.57 845.228,2105.9 846.945,2110.63 848.663,2115.7 850.38,2120.43 852.097,2116.6 \n",
" 853.814,2111.82 855.531,2107.22 857.248,2102.68 858.965,2098.07 860.682,2093.17 862.399,2087.68 864.116,2081.3 865.833,2074.11 867.551,2066.87 869.268,2060.83 \n",
" 870.985,2057.43 872.702,2057.76 874.419,2062.17 876.136,2070.01 877.853,2079.37 879.57,2086.94 881.287,2089.1 883.004,2085.71 884.722,2080.26 886.439,2075.45 \n",
" 888.156,2072.11 889.873,2069.98 891.59,2068.47 893.307,2067.09 895.024,2065.62 896.741,2064.16 898.458,2063.09 900.175,2063.05 901.893,2064.86 903.61,2069.19 \n",
" 905.327,2076.21 907.044,2085.14 908.761,2093.47 910.478,2096.55 912.195,2092.25 913.912,2085.09 915.629,2079.33 917.346,2076.77 919.063,2077.63 920.781,2081.18 \n",
" 922.498,2086.11 924.215,2090.97 925.932,2094.65 927.649,2096.64 929.366,2097.04 931.083,2096.34 932.8,2095.23 934.517,2094.56 936.234,2095.06 937.952,2096.98 \n",
" 939.669,2099.67 941.386,2101.39 943.103,2100.25 944.82,2096.59 946.537,2092.5 948.254,2089.78 949.971,2089.17 951.688,2090.11 953.405,2090.47 955.123,2087.44 \n",
" 956.84,2080.27 958.557,2071.09 960.274,2062.74 961.991,2057.46 963.708,2056.66 965.425,2060.79 967.142,2069.34 968.859,2080.86 970.576,2093 972.294,2101.94 \n",
" 974.011,2103.13 975.728,2099.07 977.445,2095.46 979.162,2094.48 980.879,2096.27 982.596,2099.96 984.313,2103.57 986.03,2103.99 987.747,2099.79 989.464,2093.09 \n",
" 991.182,2086.12 992.899,2080.09 994.616,2075.69 996.333,2073.39 998.05,2073.54 999.767,2076.37 1001.48,2081.79 1003.2,2089.18 1004.92,2097.08 1006.64,2102.7 \n",
" 1008.35,2102.94 1010.07,2099.12 1011.79,2094.92 1013.5,2092.08 1015.22,2090.88 1016.94,2091.13 1018.66,2092.61 1020.37,2095.22 1022.09,2098.62 1023.81,2101.8 \n",
" 1025.52,2103.05 1027.24,2101.58 1028.96,2098.89 1030.67,2097.02 1032.39,2097.12 1034.11,2099.29 1035.83,2102.59 1037.54,2105.01 1039.26,2104.14 1040.98,2099.77 \n",
" 1042.69,2093.51 1044.41,2086.5 1046.13,2079.26 1047.85,2072.22 1049.56,2065.88 1051.28,2060.9 1053,2057.91 1054.71,2057.41 1056.43,2059.58 1058.15,2064.17 \n",
" 1059.87,2070.45 1061.58,2077.3 1063.3,2083.43 1065.02,2087.81 1066.73,2090.19 1068.45,2091.2 1070.17,2091.82 1071.89,2092.89 1073.6,2095.1 1075.32,2098.92 \n",
" 1077.04,2104.39 1078.75,2110.17 1080.47,2111 1082.19,2104.71 1083.9,2097.21 1085.62,2091.55 1087.34,2089.05 1089.06,2090.16 1090.77,2094.55 1092.49,2101.27 \n",
" 1094.21,2108.8 1095.92,2114.99 1097.64,2116.1 1099.36,2113.94 1101.08,2112.22 1102.79,2109.83 1104.51,2105.2 1106.23,2098.75 1107.94,2091.94 1109.66,2086.05 \n",
" 1111.38,2081.94 1113.1,2079.97 1114.81,2080.04 1116.53,2081.74 1118.25,2084.47 1119.96,2087.6 1121.68,2090.48 1123.4,2092.5 1125.12,2093.23 1126.83,2092.73 \n",
" 1128.55,2091.66 1130.27,2091.01 1131.98,2091.75 1133.7,2094.5 1135.42,2099.34 1137.13,2105.78 1138.85,2112.76 1140.57,2117.55 1142.29,2114.64 1144,2110.2 \n",
" 1145.72,2106.08 1147.44,2101.7 1149.15,2096.95 1150.87,2092.69 1152.59,2090.21 1154.31,2090.55 1156.02,2094.14 1157.74,2100.62 1159.46,2108.78 1161.17,2115.14 \n",
" 1162.89,2111.57 1164.61,2105.03 1166.33,2100.08 1168.04,2097.23 1169.76,2096.17 1171.48,2096.25 1173.19,2096.97 1174.91,2098.23 1176.63,2100.15 1178.35,2102.34 \n",
" 1180.06,2102.89 1181.78,2099.47 1183.5,2092.74 1185.21,2085.41 1186.93,2079.82 1188.65,2077.36 1190.36,2078.42 1192.08,2082.32 1193.8,2087.6 1195.52,2092.6 \n",
" 1197.23,2096.52 1198.95,2099.95 1200.67,2104.1 1202.38,2109.55 1204.1,2115.78 1205.82,2118.67 1207.54,2114.36 1209.25,2111.36 1210.97,2110.72 1212.69,2112.21 \n",
" 1214.4,2115 1216.12,2117.65 1217.84,2117.88 1219.56,2116.46 1221.27,2115.29 1222.99,2114.25 1224.71,2112.62 1226.42,2110.15 1228.14,2107.2 1229.86,2104.25 \n",
" 1231.58,2101.61 1233.29,2099.52 1235.01,2098.21 1236.73,2097.92 1238.44,2098.57 1240.16,2099.21 1241.88,2097.86 1243.59,2093.27 1245.31,2086.59 1247.03,2080.2 \n",
" 1248.75,2076.19 1250.46,2075.85 1252.18,2079.44 1253.9,2086.12 1255.61,2094.11 1257.33,2101.21 1259.05,2105.98 1260.77,2109.49 1262.48,2113.89 1264.2,2116.03 \n",
" 1265.92,2107.8 1267.63,2096.75 1269.35,2086.28 1271.07,2078.34 1272.79,2074.25 1274.5,2074.56 1276.22,2079.08 1277.94,2086.99 1279.65,2097.11 1281.37,2108.17 \n",
" 1283.09,2119.02 1284.81,2113.74 1286.52,2105.33 1288.24,2098.63 1289.96,2093.7 1291.67,2090.52 1293.39,2089.03 1295.11,2089.07 1296.82,2090.4 1298.54,2092.68 \n",
" 1300.26,2095.44 1301.98,2098.13 1303.69,2100.13 1305.41,2100.99 1307.13,2100.74 1308.84,2100.05 1310.56,2099.85 1312.28,2100.99 1314,2104.02 1315.71,2109.05 \n",
" 1317.43,2115.72 1319.15,2119.09 1320.86,2111.91 1322.58,2106.01 1324.3,2102.55 1326.02,2102.06 1327.73,2104.42 1329.45,2108.8 1331.17,2113.73 1332.88,2117.02 \n",
" 1334.6,2116.67 1336.32,2114.21 1338.04,2109.42 1339.75,2101.92 1341.47,2092.83 1343.19,2083.93 1344.9,2076.9 1346.62,2073.02 1348.34,2072.88 1350.05,2076.36 \n",
" 1351.77,2082.8 1353.49,2091.2 1355.21,2100.49 1356.92,2109.68 1358.64,2117.54 1360.36,2116.61 1362.07,2111.58 1363.79,2107.6 1365.51,2103.68 1367.23,2098.31 \n",
" 1368.94,2090.94 1370.66,2082.43 1372.38,2074.33 1374.09,2068.2 1375.81,2065.25 1377.53,2066.06 1379.25,2070.57 1380.96,2078.02 1382.68,2086.96 1384.4,2095.11 \n",
" 1386.11,2099.25 1387.83,2097.79 1389.55,2093.64 1391.27,2090.18 1392.98,2089.16 1394.7,2091.2 1396.42,2096.11 1398.13,2102.79 1399.85,2107.9 1401.57,2105.81 \n",
" 1403.28,2098.72 1405,2091.93 1406.72,2087.81 1408.44,2087.32 1410.15,2090.49 1411.87,2096.59 1413.59,2104.12 1415.3,2110.08 1417.02,2109.12 1418.74,2102.66 \n",
" 1420.46,2095.05 1422.17,2087.55 1423.89,2080.75 1425.61,2075.35 1427.32,2072.17 1429.04,2071.8 1430.76,2074.4 1432.48,2079.62 1434.19,2086.73 1435.91,2094.82 \n",
" 1437.63,2102.92 1439.34,2110.04 1441.06,2114.7 1442.78,2114.81 1444.5,2112.16 1446.21,2108.6 1447.93,2103.86 1449.65,2097.96 1451.36,2091.79 1453.08,2086.54 \n",
" 1454.8,2083.13 1456.51,2081.74 1458.23,2081.8 1459.95,2082.49 1461.67,2083.56 1463.38,2085.8 1465.1,2090.44 1466.82,2098.24 1468.53,2108.8 1470.25,2119.16 \n",
" 1471.97,2110.31 1473.69,2102.3 1475.4,2099.1 1477.12,2101.42 1478.84,2108.42 1480.55,2115.02 1482.27,2107.96 1483.99,2098.38 1485.71,2092.28 1487.42,2091.26 \n",
" 1489.14,2095.44 1490.86,2103.67 1492.57,2113.72 1494.29,2116.23 1496.01,2108.29 1497.73,2102.18 1499.44,2098.12 1501.16,2094.92 1502.88,2091.64 1504.59,2088.67 \n",
" 1506.31,2087.27 1508.03,2088.35 1509.74,2091.43 1511.46,2093.78 1513.18,2091.61 1514.9,2084.81 1516.61,2077.01 1518.33,2071.52 1520.05,2070.17 1521.76,2073.5 \n",
" 1523.48,2080.91 1525.2,2090.9 1526.92,2100.86 1528.63,2105.95 1530.35,2102.62 1532.07,2096.11 1533.78,2090.47 1535.5,2086.77 1537.22,2085.09 1538.94,2085.08 \n",
" 1540.65,2086.1 1542.37,2087.34 1544.09,2088.13 1545.8,2088.33 1547.52,2088.39 1549.24,2088.98 1550.96,2090.37 1552.67,2092.17 1554.39,2093.53 1556.11,2093.81 \n",
" 1557.82,2093.27 1559.54,2092.92 1561.26,2093.57 1562.97,2095.31 1564.69,2097.29 1566.41,2098.22 1568.13,2097.49 1569.84,2096.01 1571.56,2095.33 1573.28,2096.57 \n",
" 1574.99,2100.11 1576.71,2105.64 1578.43,2112.34 1580.15,2119.2 1581.86,2117.48 1583.58,2112.93 1585.3,2110.2 1587.01,2109.21 1588.73,2109.67 1590.45,2111.17 \n",
" 1592.17,2113.16 1593.88,2114.28 1595.6,2112.62 1597.32,2108.61 1599.03,2103.84 1600.75,2099.35 1602.47,2095.7 1604.19,2093.24 1605.9,2092.21 1607.62,2092.78 \n",
" 1609.34,2095.06 1611.05,2098.83 1612.77,2103.19 1614.49,2105.95 1616.2,2104.69 1617.92,2100.37 1619.64,2095.66 1621.36,2092.07 1623.07,2090.07 1624.79,2089.54 \n",
" 1626.51,2090.01 1628.22,2090.8 1629.94,2091.08 1631.66,2090.1 1633.38,2087.82 1635.09,2085.12 1636.81,2083.26 1638.53,2083.24 1640.24,2085.31 1641.96,2088.89 \n",
" 1643.68,2092.89 1645.4,2096.32 1647.11,2098.81 1648.83,2100.2 1650.55,2099.51 1652.26,2095.63 1653.98,2089.37 1655.7,2082.88 1657.42,2078.09 1659.13,2076.09 \n",
" 1660.85,2076.99 1662.57,2080.17 1664.28,2084.66 1666,2089.51 1667.72,2093.5 1669.43,2094.76 1671.15,2091.96 1672.87,2086.52 1674.59,2081.52 1676.3,2079.61 \n",
" 1678.02,2082.27 1679.74,2089.59 1681.45,2100.2 1683.17,2110.34 1684.89,2109.49 1686.61,2101.34 1688.32,2094.87 1690.04,2091.17 1691.76,2089.35 1693.47,2088.38 \n",
" 1695.19,2088.33 1696.91,2090.38 1698.63,2095.81 1700.34,2104.94 1702.06,2115.67 1703.78,2109.47 1705.49,2096.67 1707.21,2086.4 1708.93,2080.54 1710.65,2079.76 \n",
" 1712.36,2083.63 1714.08,2090.76 1715.8,2099.13 1717.51,2106.5 1719.23,2110.99 1720.95,2112.53 1722.66,2112.93 1724.38,2112.8 1726.1,2111.49 1727.82,2109.24 \n",
" 1729.53,2107.04 1731.25,2105.71 1732.97,2105.69 1734.68,2107.28 1736.4,2110.67 1738.12,2115.83 1739.84,2120.39 1741.55,2113.41 1743.27,2107.14 1744.99,2102.82 \n",
" 1746.7,2101.32 1748.42,2102.81 1750.14,2106.44 1751.86,2109.59 1753.57,2108.42 1755.29,2103.82 1757.01,2099.27 1758.72,2096.48 1760.44,2096 1762.16,2097.72 \n",
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" 252.83,3828.55 254.547,3829.67 256.264,3828.72 257.981,3826.81 259.698,3825.03 261.415,3823.84 263.132,3823.41 264.85,3823.7 266.567,3824.62 268.284,3826.02 \n",
" 270.001,3827.7 271.718,3829.43 273.435,3830.78 275.152,3831.18 276.869,3830.52 278.586,3829.38 280.303,3828.22 282.021,3827.2 283.738,3826.35 285.455,3825.68 \n",
" 287.172,3825.23 288.889,3825.01 290.606,3824.92 292.323,3824.7 294.04,3824.01 295.757,3822.67 297.474,3820.84 299.191,3818.88 300.909,3817.17 302.626,3816.01 \n",
" 304.343,3815.59 306.06,3815.97 307.777,3817.14 309.494,3819 311.211,3821.34 312.928,3823.86 314.645,3826.08 316.362,3827.39 318.08,3827.39 319.797,3826.52 \n",
" 321.514,3825.59 323.231,3825.09 324.948,3825.21 326.665,3825.88 328.382,3826.76 330.099,3827.44 331.816,3827.65 333.533,3827.56 335.251,3827.63 336.968,3828.26 \n",
" 338.685,3829.61 340.402,3831.42 342.119,3832.24 343.836,3830.3 345.553,3827.27 347.27,3824.23 348.987,3821.59 350.704,3819.5 352.421,3817.99 354.139,3817 \n",
" 355.856,3816.44 357.573,3816.27 359.29,3816.57 361.007,3817.43 362.724,3818.97 364.441,3821.24 366.158,3824.1 367.875,3827.13 369.592,3829.28 371.31,3829.03 \n",
" 373.027,3826.95 374.744,3824.71 376.461,3823.07 378.178,3822.24 379.895,3822.17 381.612,3822.67 383.329,3823.52 385.046,3824.54 386.763,3825.65 388.481,3826.81 \n",
" 390.198,3827.96 391.915,3828.94 393.632,3829.58 395.349,3829.87 397.066,3829.99 398.783,3830.19 400.5,3830.62 402.217,3831.23 403.934,3831.91 405.651,3832.47 \n",
" 407.369,3832.75 409.086,3832.6 410.803,3831.96 412.52,3830.91 414.237,3829.61 415.954,3828.22 417.671,3826.85 419.388,3825.54 421.105,3824.3 422.822,3823.16 \n",
" 424.54,3822.22 426.257,3821.58 427.974,3821.38 429.691,3821.62 431.408,3822.19 433.125,3822.81 434.842,3823.11 436.559,3822.75 438.276,3821.68 439.993,3820.06 \n",
" 441.711,3818.12 443.428,3816.07 445.145,3814.11 446.862,3812.49 448.579,3811.52 450.296,3811.53 452.013,3812.78 453.73,3815.39 455.447,3819.31 457.164,3824.25 \n",
" 458.881,3829.44 460.599,3831.23 462.316,3826.91 464.033,3822.11 465.75,3818.24 467.467,3815.72 469.184,3814.71 470.901,3815.19 472.618,3817 474.335,3819.83 \n",
" 476.052,3823.25 477.77,3826.79 479.487,3830 481.204,3832.56 482.921,3834.06 484.638,3833.27 486.355,3831.45 488.072,3829.35 489.789,3827.3 491.506,3825.64 \n",
" 493.223,3824.69 494.941,3824.55 496.658,3825.08 498.375,3825.9 500.092,3826.46 501.809,3826.43 503.526,3825.93 505.243,3825.38 506.96,3825.07 508.677,3825.04 \n",
" 510.394,3825.08 512.112,3824.95 513.829,3824.52 515.546,3823.84 517.263,3823.07 518.98,3822.35 520.697,3821.69 522.414,3821.07 524.131,3820.38 525.848,3819.57 \n",
" 527.565,3818.63 529.282,3817.6 531,3816.62 532.717,3815.82 534.434,3815.31 536.151,3815.22 537.868,3815.63 539.585,3816.66 541.302,3818.43 543.019,3821.01 \n",
" 544.736,3824.28 546.453,3827.72 548.171,3829.65 549.888,3828.19 551.605,3825.34 553.322,3823.06 555.039,3822.03 556.756,3822.37 558.473,3823.81 560.19,3825.82 \n",
" 561.907,3827.75 563.624,3829 565.342,3829.4 567.059,3829.24 568.776,3828.89 570.493,3828.68 572.21,3828.93 573.927,3829.96 575.644,3831.93 577.361,3834.61 \n",
" 579.078,3832.45 580.795,3829.24 582.512,3826.69 584.23,3825.3 585.947,3825.31 587.664,3826.66 589.381,3828.98 591.098,3831.62 592.815,3833.31 594.532,3832.47 \n",
" 596.249,3830.91 597.966,3829.07 599.683,3826.54 601.401,3823.25 603.118,3819.67 604.835,3816.44 606.552,3814.17 608.269,3813.32 609.986,3814.12 611.703,3816.55 \n",
" 613.42,3820.35 615.137,3825.07 616.854,3830.01 618.572,3833.06 620.289,3830.26 622.006,3827.26 623.723,3825.38 625.44,3824.69 627.157,3825.02 628.874,3826.06 \n",
" 630.591,3827.44 632.308,3828.83 634.025,3829.93 635.742,3830.51 637.46,3830.54 639.177,3830.17 640.894,3829.61 642.611,3828.95 644.328,3828.22 646.045,3827.48 \n",
" 647.762,3826.88 649.479,3826.6 651.196,3826.89 652.913,3827.87 654.631,3829.57 656.348,3831.65 658.065,3832.43 659.782,3830.17 661.499,3827.02 663.216,3824.03 \n",
" 664.933,3821.64 666.65,3820.08 668.367,3819.44 670.084,3819.69 671.802,3820.64 673.519,3822.01 675.236,3823.51 676.953,3824.87 678.67,3825.97 680.387,3826.84 \n",
" 682.104,3827.56 683.821,3828.23 685.538,3828.85 687.255,3829.39 688.972,3829.8 690.69,3830.06 692.407,3830.14 694.124,3830.07 695.841,3829.86 697.558,3829.6 \n",
" 699.275,3829.34 700.992,3829.19 702.709,3829.15 704.426,3829.1 706.143,3828.73 707.861,3827.69 709.578,3825.96 711.295,3823.94 713.012,3822.17 714.729,3821.12 \n",
" 716.446,3821.17 718.163,3822.46 719.88,3824.86 721.597,3827.92 723.314,3830.64 725.032,3830.86 726.749,3828.66 728.466,3826.13 730.183,3823.85 731.9,3821.87 \n",
" 733.617,3820.23 735.334,3819.15 737.051,3818.95 738.768,3819.9 740.485,3822.01 742.203,3824.94 743.92,3827.83 745.637,3829.05 747.354,3827.81 749.071,3825.78 \n",
" 750.788,3824.21 752.505,3823.5 754.222,3823.59 755.939,3824.26 757.656,3825.19 759.373,3826.02 761.091,3826.47 762.808,3826.52 764.525,3826.43 766.242,3826.59 \n",
" 767.959,3827.21 769.676,3828.25 771.393,3829.32 773.11,3829.92 774.827,3829.94 776.544,3829.9 778.262,3830.31 779.979,3831.28 781.696,3832.19 783.413,3831.71 \n",
" 785.13,3829.94 786.847,3827.94 788.564,3826.24 790.281,3824.99 791.998,3824.26 793.715,3824.12 795.433,3824.68 797.15,3826.01 798.867,3828.08 800.584,3830.56 \n",
" 802.301,3832.08 804.018,3830.54 805.735,3827.81 807.452,3825.36 809.169,3823.64 810.886,3822.83 812.603,3822.93 814.321,3823.83 816.038,3825.3 817.755,3827.09 \n",
" 819.472,3828.89 821.189,3830.44 822.906,3831.49 824.623,3831.83 826.34,3831.41 828.057,3830.44 829.774,3829.22 831.492,3828.02 833.209,3827.09 834.926,3826.62 \n",
" 836.643,3826.74 838.36,3827.53 840.077,3829 841.794,3831.09 843.511,3833.45 845.228,3833.16 846.945,3830.35 848.663,3827.57 850.38,3825.24 852.097,3823.55 \n",
" 853.814,3822.55 855.531,3822.17 857.248,3822.29 858.965,3822.78 860.682,3823.52 862.399,3824.44 864.116,3825.48 865.833,3826.55 867.551,3827.59 869.268,3828.55 \n",
" 870.985,3829.37 872.702,3830 874.419,3830.4 876.136,3830.55 877.853,3830.57 879.57,3830.59 881.287,3830.69 883.004,3830.85 884.722,3830.96 886.439,3830.87 \n",
" 888.156,3830.55 889.873,3830.02 891.59,3829.44 893.307,3829 895.024,3828.93 896.741,3829.39 898.458,3830.42 900.175,3831.81 901.893,3832.74 903.61,3832.06 \n",
" 905.327,3830.6 907.044,3829.37 908.761,3828.64 910.478,3828.27 912.195,3827.87 913.912,3827.1 915.629,3826.04 917.346,3825.1 919.063,3824.69 920.781,3825.04 \n",
" 922.498,3826.14 924.215,3827.72 925.932,3829.23 927.649,3829.96 929.366,3829.62 931.083,3828.73 932.8,3827.86 934.517,3827.24 936.234,3826.83 937.952,3826.56 \n",
" 939.669,3826.36 941.386,3826.26 943.103,3826.3 944.82,3826.51 946.537,3826.86 948.254,3827.25 949.971,3827.55 951.688,3827.61 953.405,3827.3 955.123,3826.63 \n",
" 956.84,3825.72 958.557,3824.74 960.274,3823.83 961.991,3823.03 963.708,3822.37 965.425,3821.85 967.142,3821.56 968.859,3821.59 970.576,3822.05 972.294,3822.98 \n",
" 974.011,3824.39 975.728,3826.29 977.445,3828.69 979.162,3831.25 980.879,3831.4 982.596,3827.69 984.313,3822.88 986.03,3818.16 987.747,3814.24 989.464,3811.73 \n",
" 991.182,3811.01 992.899,3812.24 994.616,3815.29 996.333,3819.83 998.05,3825.35 999.767,3831.28 1001.48,3833.2 1003.2,3827.96 1004.92,3823.58 1006.64,3820.42 \n",
" 1008.35,3818.68 1010.07,3818.44 1011.79,3819.63 1013.5,3822.07 1015.22,3825.48 1016.94,3829.46 1018.66,3833.49 1020.37,3832.72 1022.09,3829.44 1023.81,3827.01 \n",
" 1025.52,3825.73 1027.24,3825.7 1028.96,3826.8 1030.67,3828.63 1032.39,3830.3 1034.11,3830.4 1035.83,3829.04 1037.54,3827.68 1039.26,3827.14 1040.98,3827.62 \n",
" 1042.69,3828.92 1044.41,3830.3 1046.13,3830.42 1047.85,3828.88 1049.56,3826.8 1051.28,3824.96 1053,3823.66 1054.71,3822.96 1056.43,3822.83 1058.15,3823.18 \n",
" 1059.87,3823.81 1061.58,3824.38 1063.3,3824.44 1065.02,3823.68 1066.73,3822.21 1068.45,3820.52 1070.17,3819.14 1071.89,3818.46 1073.6,3818.67 1075.32,3819.75 \n",
" 1077.04,3821.45 1078.75,3823.36 1080.47,3825.02 1082.19,3826.16 1083.9,3826.93 1085.62,3827.73 1087.34,3828.89 1089.06,3830.3 1090.77,3831.32 1092.49,3830.99 \n",
" 1094.21,3829.61 1095.92,3828.19 1097.64,3827.25 1099.36,3826.95 1101.08,3827.32 1102.79,3828.22 1104.51,3829.42 1106.23,3830.45 1107.94,3830.58 1109.66,3829.61 \n",
" 1111.38,3828.19 1113.1,3826.98 1114.81,3826.3 1116.53,3826.26 1118.25,3826.73 1119.96,3827.39 1121.68,3827.81 1123.4,3827.66 1125.12,3826.97 1126.83,3825.97 \n",
" 1128.55,3824.92 1130.27,3823.97 1131.98,3823.22 1133.7,3822.77 1135.42,3822.74 1137.13,3823.25 1138.85,3824.4 1140.57,3826.17 1142.29,3828.33 1144,3830.08 \n",
" 1145.72,3829.92 1147.44,3827.83 1149.15,3825.34 1150.87,3823.28 1152.59,3822.03 1154.31,3821.71 1156.02,3822.26 1157.74,3823.46 1159.46,3824.95 1161.17,3826.27 \n",
" 1162.89,3826.94 1164.61,3826.87 1166.33,3826.45 1168.04,3826.21 1169.76,3826.51 1171.48,3827.42 1173.19,3828.82 1174.91,3830.37 1176.63,3831.55 1178.35,3831.84 \n",
" 1180.06,3831.38 1181.78,3830.7 1183.5,3830.01 1185.21,3829.28 1186.93,3828.41 1188.65,3827.45 1190.36,3826.54 1192.08,3825.89 1193.8,3825.75 1195.52,3826.29 \n",
" 1197.23,3827.53 1198.95,3829.18 1200.67,3830.25 1202.38,3829.46 1204.1,3827.38 1205.82,3825.34 1207.54,3824.12 1209.25,3824.07 1210.97,3825.26 1212.69,3827.44 \n",
" 1214.4,3829.97 1216.12,3831.16 1217.84,3829.49 1219.56,3826.83 1221.27,3824.49 1222.99,3822.89 1224.71,3822.14 1226.42,3822.22 1228.14,3823.03 1229.86,3824.45 \n",
" 1231.58,3826.38 1233.29,3828.68 1235.01,3831.17 1236.73,3833.26 1238.44,3833.03 1240.16,3831.45 1241.88,3830.29 1243.59,3829.85 1245.31,3829.91 1247.03,3829.88 \n",
" 1248.75,3829.05 1250.46,3827.49 1252.18,3825.81 1253.9,3824.6 1255.61,3824.18 1257.33,3824.64 1259.05,3825.81 1260.77,3827.3 1262.48,3828.58 1264.2,3829.2 \n",
" 1265.92,3829.2 1267.63,3829.04 1269.35,3829.01 1271.07,3829.04 1272.79,3828.74 1274.5,3827.8 1276.22,3826.35 1277.94,3824.74 1279.65,3823.24 1281.37,3821.95 \n",
" 1283.09,3820.8 1284.81,3819.68 1286.52,3818.61 1288.24,3817.79 1289.96,3817.52 1291.67,3818.12 1293.39,3819.74 1295.11,3822.32 1296.82,3825.59 1298.54,3829 \n",
" 1300.26,3831.62 1301.98,3831.91 1303.69,3830.85 1305.41,3830.18 1307.13,3830.06 1308.84,3829.8 1310.56,3828.66 1312.28,3826.81 1314,3825.03 1315.71,3823.97 \n",
" 1317.43,3824.02 1319.15,3825.28 1320.86,3827.49 1322.58,3829.97 1324.3,3831.1 1326.02,3829.76 1327.73,3827.74 1329.45,3826.26 1331.17,3825.61 1332.88,3825.79 \n",
" 1334.6,3826.65 1336.32,3828.01 1338.04,3829.64 1339.75,3830.75 1341.47,3829.86 1343.19,3827.13 1344.9,3823.83 1346.62,3820.74 1348.34,3818.27 1350.05,3816.61 \n",
" 1351.77,3815.67 1353.49,3815.23 1355.21,3815.11 1356.92,3815.28 1358.64,3815.98 1360.36,3817.47 1362.07,3819.96 1363.79,3823.38 1365.51,3827.42 1367.23,3831.59 \n",
" 1368.94,3834.65 1370.66,3832.29 1372.38,3830.87 1374.09,3830.92 1375.81,3832.28 1377.53,3833.59 1379.25,3831.35 1380.96,3828.07 1382.68,3825.1 1384.4,3822.92 \n",
" 1386.11,3821.8 1387.83,3821.75 1389.55,3822.55 1391.27,3823.87 1392.98,3825.29 1394.7,3826.55 1396.42,3827.59 1398.13,3828.58 1399.85,3829.71 1401.57,3831.04 \n",
" 1403.28,3832.5 1405,3833.87 1406.72,3834.6 1408.44,3834.08 1410.15,3833.52 1411.87,3833.11 1413.59,3832.57 1415.3,3831.6 1417.02,3830.08 1418.74,3828.09 \n",
" 1420.46,3825.83 1422.17,3823.54 1423.89,3821.46 1425.61,3819.83 1427.32,3818.86 1429.04,3818.65 1430.76,3819.19 1432.48,3820.34 1434.19,3821.84 1435.91,3823.27 \n",
" 1437.63,3824.16 1439.34,3824.17 1441.06,3823.46 1442.78,3822.51 1444.5,3821.83 1446.21,3821.8 1447.93,3822.58 1449.65,3824.14 1451.36,3826.28 1453.08,3828.57 \n",
" 1454.8,3830.26 1456.51,3830.37 1458.23,3828.87 1459.95,3826.56 1461.67,3823.76 1463.38,3820.58 1465.1,3817.23 1466.82,3814.08 1468.53,3811.53 1470.25,3809.97 \n",
" 1471.97,3809.61 1473.69,3810.48 1475.4,3812.37 1477.12,3814.76 1478.84,3816.85 1480.55,3817.7 1482.27,3816.93 1483.99,3815.02 1485.71,3812.91 1487.42,3811.37 \n",
" 1489.14,3810.81 1490.86,3811.34 1492.57,3812.81 1494.29,3814.88 1496.01,3817.13 1497.73,3819.12 1499.44,3820.55 1501.16,3821.37 1502.88,3821.75 1504.59,3821.97 \n",
" 1506.31,3822.3 1508.03,3822.91 1509.74,3823.85 1511.46,3825.05 1513.18,3826.34 1514.9,3827.41 1516.61,3827.96 1518.33,3827.89 1520.05,3827.32 1521.76,3826.48 \n",
" 1523.48,3825.56 1525.2,3824.7 1526.92,3824.05 1528.63,3823.8 1530.35,3824.14 1532.07,3825.19 1533.78,3826.96 1535.5,3829.31 1537.22,3831.7 1538.94,3832.43 \n",
" 1540.65,3830.74 1542.37,3828.91 1544.09,3827.87 1545.8,3827.82 1547.52,3828.5 1549.24,3828.86 1550.96,3827.6 1552.67,3824.88 1554.39,3821.89 1556.11,3819.54 \n",
" 1557.82,3818.4 1559.54,3818.7 1561.26,3820.29 1562.97,3822.65 1564.69,3824.86 1566.41,3825.87 1568.13,3825.54 1569.84,3824.86 1571.56,3824.7 1573.28,3825.26 \n",
" 1574.99,3826.13 1576.71,3826.55 1578.43,3826.08 1580.15,3825.14 1581.86,3824.45 1583.58,3824.44 1585.3,3825.13 1587.01,3826.27 1588.73,3827.42 1590.45,3828.19 \n",
" 1592.17,3828.34 1593.88,3827.86 1595.6,3826.84 1597.32,3825.5 1599.03,3824.2 1600.75,3823.39 1602.47,3823.48 1604.19,3824.67 1605.9,3826.97 1607.62,3830 \n",
" 1609.34,3832.45 1611.05,3830.93 1612.77,3827.9 1614.49,3825.45 1616.2,3824.09 1617.92,3823.88 1619.64,3824.63 1621.36,3825.76 1623.07,3826.42 1624.79,3825.9 \n",
" 1626.51,3824.4 1628.22,3822.65 1629.94,3821.21 1631.66,3820.31 1633.38,3819.96 1635.09,3820.05 1636.81,3820.43 1638.53,3821.07 1640.24,3821.98 1641.96,3823.16 \n",
" 1643.68,3824.43 1645.4,3825.31 1647.11,3825.18 1648.83,3823.86 1650.55,3821.87 1652.26,3819.87 1653.98,3818.31 1655.7,3817.39 1657.42,3817.1 1659.13,3817.25 \n",
" 1660.85,3817.61 1662.57,3817.94 1664.28,3818.08 1666,3818.04 1667.72,3817.91 1669.43,3817.85 1671.15,3818.04 1672.87,3818.58 1674.59,3819.53 1676.3,3820.85 \n",
" 1678.02,3822.48 1679.74,3824.35 1681.45,3826.42 1683.17,3828.71 1684.89,3831.22 1686.61,3833.93 1688.32,3833.89 1690.04,3831.33 1691.76,3829.28 1693.47,3828.01 \n",
" 1695.19,3827.72 1696.91,3828.46 1698.63,3830.06 1700.34,3832.08 1702.06,3833.41 1703.78,3832.67 1705.49,3831.7 1707.21,3831.62 1708.93,3832.64 1710.65,3834.54 \n",
" 1712.36,3833.12 1714.08,3830.17 1715.8,3827.31 1717.51,3824.84 1719.23,3822.82 1720.95,3821.19 1722.66,3819.88 1724.38,3818.92 1726.1,3818.5 1727.82,3818.82 \n",
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},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tsteps = 0:0.1:100\n",
"evols = evolve_observer.(rng, 2 .^ (4:10), tsteps[end], tsteps[2]-tsteps[1])\n",
"plot(tsteps, [evols...], layout=(length(evols),1), size=(500,1000))"
]
},
{
"cell_type": "markdown",
"id": "fa69042c-405a-4afe-b2a8-8119af855187",
"metadata": {},
"source": [
"Let's now zoom in to the first few \"seconds\" to see what happens there."
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "e7a36d51-0716-4f73-8ed7-0a08dabb4e5b",
"metadata": {},
"outputs": [
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},
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"source": [
"zoom=1:30\n",
"plot(tsteps[zoom], [e[zoom] for e in evols], layout=(length(evols),1), size=(500,1000))"
]
},
{
"cell_type": "markdown",
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"## Observations\n",
"\n",
"The dot products of the two co-states goes to zero after about a time of $1$\n",
"for larger $n$.\n",
"\n",
"The dot product of the co-states represents the internal states taken on by the\n",
"observer for each of the two states of the qubit - i.e. the\n",
"two possibilities starting with $\\ket{\\omega}\\ket{0}$ and\n",
"$\\ket{\\omega}\\ket{1}$.\n",
"\n",
"I interpret the dot product of the co-states going to 0 as $n$ becomes larger,\n",
"as the states evolving in their own \"worlds\" and not crossing each other.\n",
"If they did cross, it would mean that at some point in the future of the\n",
"observer the qubit and the observer would become separable."
]
},
{
"cell_type": "markdown",
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"source": [
"## Analysis\n",
"\n",
"Given the observer $H = \\begin{bmatrix} H_0 & 0 \\\\ 0 & H_1 \\end{bmatrix}$, and $H_0$ and $H_1$ are both self adjoint (i.e. $H_0 = H_0^\\dagger$ and $H_1 = H_1^\\dagger$), we have --\n",
"\n",
"$$ e^{iHt} = \\begin{bmatrix} e^{iH_0t} & 0 \\\\ 0 & e^{iH_1t} \\end{bmatrix} $$\n",
"\n",
"If we notate the combined state vector of the observer+qubit system as $\\ket{\\Psi} = \\ket{q} \\otimes \\ket{psi} = \\begin{bmatrix}q_0\\ket{\\psi} \\\\ q_1\\ket{\\psi}\\end{bmatrix}$ where $\\ket{q} = q_0\\ket{0} + q_1\\ket{1}$ (implying $|q_0|^2 + |q_1|^2 = 1$), The evolution of the joint state can be written --\n",
"\n",
"$$e^{iHt}\\ket{\\Psi} = \\begin{bmatrix}q_0e^{iH_0t}\\ket{\\psi} \\\\ q_1e^{iH_1t}\\ket{\\psi}\\end{bmatrix} = \\begin{bmatrix} q_0\\ket{\\psi_0(t)} \\\\ q_1\\ket{\\psi_1(t)}\\end{bmatrix}$$\n",
"\n",
"So if we're examining the inner product of the two co-state vectors, we get -\n",
"\n",
"$$ \\alpha = \\braket{\\psi\\left|e^{-iH_1t}e^{iH_0t}\\right|\\psi} = \\braket{\\psi\\left|e^{i(H_0-H_1)t}\\right|\\psi} = \\braket{\\psi\\left|e^{i\\Delta Ht}\\right|\\psi}$$ \n",
"\n",
"If $H_0$ and $H_1$ are very close to each other, then $\\Delta H$ ends up being small -- i.e. its eigenvalues end up small relative to the eigenvalues of $H_0$ and $H_1$ and the inner product becomes close to $1.0$. Therefore for $H$ to actually represent an observer, it must be able to differentiate between the two qubit states and therefore $\\Delta H$ itself must have random eigen values comparable in magnitude to both $H_0$ and $H_1$. \n",
"\n",
"If we then consider $\\ket{\\psi}$ in an eigen basis $\\ket{\\phi_k}$ of $\\Delta H$ with $\\braket{\\phi_i|\\phi_j} = \\delta_{ij}$ and $\\Delta H \\ket{\\phi_k} = 2\\pi f_k\\ket{\\phi_k}$, then taking $\\ket{\\psi} = \\sum_k{\\beta_k\\ket{\\phi_k}}$, we see that -\n",
"\n",
"$$ \\alpha = \\sum_k{|\\beta_k|^2e^{i(2\\pi f_kt)}} $$"
]
},
{
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"So if a) $\\ket{\\psi}$ is mixed enough in that basis and b) the \"frequencies\" $f_k$ are different enough, then for $t \\gtrapprox 0$, we see that $\\alpha \\approx 1$ and as $t$ increases, all sorts of frequencies will get mixed up and $\\alpha \\to 0$ with larger dimensions $n \\gg 1$. So the behaviour of the observer relative to the qubit states must also not have degenerate eigenvalues, or at least have sufficient number of different eigenvalues (\"frequencies\"). If we start out in a pure state of the observer system in that eigen basis though, we'll get $\\alpha = 1$. The interval during which $\\alpha \\sim 1$ (say $\\alpha > 0.5$) can then be called the \"coherence interval\" of the observer, beyond which you get \"decoherence\".\n",
"\n",
"So this is what we're seeing in the trend plot in the previous section using a random observer starting out at a random state.\n",
"\n",
"All these points correlate well with the mental model of \"observer\" that I started with, so I'm wondering whether all this should've been \"obvious\" from the get go :) I'm still irked by not being able to see why the Born rule has to hold based on this model of an observer, but that problem remains unsolved for now."
]
},
{
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