diff --git a/23323049_vatsal/assignment_1/assignment 1.ipynb b/23323049_vatsal/assignment_1/assignment 1.ipynb new file mode 100644 index 0000000..a276518 --- /dev/null +++ b/23323049_vatsal/assignment_1/assignment 1.ipynb @@ -0,0 +1,569 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "2243fc84", + "metadata": {}, + "source": [ + "# 1.a) Deriving the Poisson Distribution from the Binomial Distribution\n", + "\n", + "### The Binomial Distribution\n", + "\n", + "\n", + "$\\ P(X = k) = \\binom{n}{k} \\cdot p^k \\cdot (1 - p)^{n-k} \\$\n", + "\n", + "\n", + "### Conditions for the Poisson Distribution\n", + "\n", + "The Poisson distribution arises as a limiting case of the binomial distribution under certain conditions:\n", + "\n", + "1. The number of trials \\$ n \\$, is large.\n", + "2. The probability of success \\$ p \\$ is small.\n", + "3. The product \\$ n \\cdot p \\$ remains constant.\n", + "\n", + "Substitute \\$ p = \\frac{\\lambda}{n} \\$ into the binomial PMF:\n", + "\n", + "\\$ P(X = x) = \\binom{n}{x} \\cdot \\left(\\frac{\\lambda}{n}\\right)^x \\cdot \\left(1 - \\frac{\\lambda}{n}\\right)^{n-x} \\$\n", + "\n", + "As \\$ n \\$ becomes large, we can rewrite the binomial coefficient and apply limits:\n", + "\n", + "\\$ P(X = x) = \\lim_{n \\to \\infty} \\frac{n!}{x!(n-x)!} \\cdot \\left(\\frac{\\lambda}{n}\\right)^x \\cdot \\left(1 - \\frac{\\lambda}{n}\\right)^{n-x} \\$\n", + "\n", + "\n", + "\\$ P(X = k) = \\lim_{n \\to \\infty} \\frac{n!}{x!(n-x)!} \\cdot \\frac{\\lambda^x}{n^x} \\cdot \\left(1 - \\frac{\\lambda}{n}\\right)^{n} \\cdot \\left(1 - \\frac{\\lambda}{n}\\right)^{-x} \\$\n", + "As \\$ n \\to \\infty \\$:\n", + "\n", + "- \\$ \\left(1 - \\frac{\\lambda}{n}\\right)^{n} \\to e^{-\\lambda} \\$\n", + "- \\$ \\left(1 - \\frac{\\lambda}{n}\\right)^{-k} \\to 1 \\$\n", + "- \\$ \\frac{n!}{(n-x)!n^x} = \\frac{(n) (n-1)...(n-x+1)}{n^x}\\approx 1 \\$ for large \\$ n \\$\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\\$ P(X = k) = \\frac{e^{-\\lambda} \\cdot \\lambda^k}{k!} \\$\n", + "\n", + "which is the PMF of the Poisson distribution with parameter \\$ \\lambda \\$.\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "07fb074e", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "\n", + "# 1.b) Graph" + ] + }, + { + "cell_type": "markdown", + "id": "fab61340", + "metadata": {}, + "source": [ + "### binomial distribution and poisson distribution" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "93d5979e", + "metadata": {}, + "outputs": [], + "source": [ + "n=20\n", + "p=0.23\n", + "lambdaa=n*p\n", + "from scipy.stats import binom\n", + "dist= binom(n,p)\n", + "r_val=[range(21)]\n", + "prob=[binom.pmf(r,n,p) for r in r_val]" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "8c21ea7d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([5.36802467e-03, 3.20687188e-02, 9.10001957e-02, 1.63091260e-01,\n", + " 2.07041177e-01, 1.97899099e-01, 1.47781795e-01, 8.82852281e-02,\n", + " 4.28527325e-02, 1.70668891e-02, 5.60769214e-03, 1.52274993e-03,\n", + " 3.41135537e-04, 6.27062325e-05, 9.36521654e-06, 1.11896094e-06,\n", + " 1.04448464e-07, 7.34091574e-09, 3.65456844e-10, 1.14907825e-11,\n", + " 1.71615583e-13])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "prob[0]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "aaa44537", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.bar(r_val[0],prob[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "7ca3b1d2", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import poisson\n", + "r_val=[range(21)]\n", + "prob_pos=[poisson.pmf(r,n*p) for r in r_val]" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "01d8a9fe", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[array([1.00518357e-02, 4.62384444e-02, 1.06348422e-01, 1.63067581e-01,\n", + " 1.87527718e-01, 1.72525500e-01, 1.32269550e-01, 8.69199902e-02,\n", + " 4.99789944e-02, 2.55448193e-02, 1.17506169e-02, 4.91389434e-03,\n", + " 1.88365950e-03, 6.66525668e-04, 2.19001291e-04, 6.71603959e-05,\n", + " 1.93086138e-05, 5.22468374e-06, 1.33519696e-06, 3.23258210e-07,\n", + " 7.43493883e-08])]" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "prob_pos" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "bf615c52", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.bar(r_val[0],prob_pos[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "60ef6d64", + "metadata": {}, + "outputs": [], + "source": [ + "n2=3*10**5\n", + "p2=10**(-6)\n", + "r_vals=[range(0,n2+1,100)]\n", + "binomial_dist=[binom.pmf(r,n2,p2) for r in r_vals]" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "2c132512", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n = 3 * 10**5\n", + "p = 10**-6\n", + "lambda_poisson = n * p\n", + "\n", + "k_values = np.arange(0, 10)\n", + "\n", + "binomial_pmf = binom.pmf(k_values, n, p)\n", + "\n", + "poisson_pmf = poisson.pmf(k_values, lambda_poisson)\n", + "\n", + "plt.figure(figsize=(10, 6))\n", + "\n", + "# Binomial Distribution Plot\n", + "plt.plot(k_values, binomial_pmf, 'bo', ms=10, label='Binomial PMF')\n", + "plt.vlines(k_values, 0, binomial_pmf, colors='b',lw=3)\n", + "\n", + "# Poisson Distribution Plot\n", + "plt.plot(k_values, poisson_pmf, 'ro', label='Poisson PMF (λ=0.3)')\n", + "plt.vlines(k_values, 0, poisson_pmf, colors='r', lw=5, alpha=0.5)\n", + "\n", + "plt.xlabel('k')\n", + "plt.ylabel('Probability')\n", + "plt.title('Binomial vs Poisson Distribution')\n", + "plt.legend()\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "4f8befa1", + "metadata": {}, + "source": [ + "# 2. Cov(W,Z)\n", + "$$W= XY+X^2Y+XY^2= XY(1+X+Y)$$\n", + "$$Z=XY^3+X^3Y = XY(X^2+Y^2)$$\n", + "$$Cov(W,Z)=E[WZ]-E[W]E[Z]$$\n", + "\\$X$~$N(0,1)\\$\n", + "\n", + "\\$Y$~$N(0,1)\\$\n", + "\n", + "$X^2$~$\\chi^2(1)$\n", + "\n", + "$Y^2$~$\\chi^2(1)$\n", + "\n", + "$X^2+Y^2$~$\\chi^2(2)$\n", + "\n", + "\\$1+X+Y$~$N(1,2)\\$\n", + "\n", + "$E[W]=E[XY]+E[X^2Y]+E[XY^2]=0$\n", + "\n", + "$E[Z]=E[XY ^\n", + "3\n", + " ]+E[X ^\n", + "3\n", + " Y]=0$\n", + " \n", + " $E[WZ]=E[(XY+X ^\n", + "2\n", + " Y+XY ^\n", + "2\n", + " )(XY ^\n", + "3\n", + " +X ^\n", + "3\n", + " Y)]$\n", + " \n", + "Expanding this, we get\n", + "\n", + " \n", + "$WZ=XY⋅XY ^3 +XY⋅X ^3 Y+X ^2 Y⋅XY ^3 +X ^2 Y⋅X ^3 Y+XY ^2 ⋅XY ^3 +XY ^2 ⋅X ^3 Y=X ^2 Y ^4 +X ^4 Y ^2 +X ^3 Y ^4 +X ^5 Y ^2 +X ^3 Y^5 +X ^5 Y ^3$\n", + " \n", + " Using the moments of the standard normal distribution $E[X^ k ]:$\n", + " \n", + " $E[X^ 2 ]=1$\n", + " \n", + " $E[X ^4 ]=3$\n", + " \n", + " $E[X ^k]=0$ for odd k\n", + " \n", + " $E[X ^2 Y ^4 ]=E[X ^2 ]E[Y ^4 ]=1⋅3=3$\n", + "\n", + " $E[X ^4 Y ^2 ]=E[X ^4 ]E[Y ^2]=3⋅1=3$\n", + " \n", + " $E[WZ]=E[X ^2Y ^4]+E[X ^4Y ^2]=3+3=6$\n", + " \n", + "$Cov(W,Z)=6$" + ] + }, + { + "cell_type": "markdown", + "id": "213947cc", + "metadata": {}, + "source": [ + "# 3. WLLN statement using chebychev's inequality\n", + "This proof uses the assumption of finite variance \n", + "$Var(X_{i})=\\sigma ^2$\n", + "The independence of the random variables implies no correlation between them, and we have that\n", + "$$Var( \\bar X ) =Var(\\frac{1}{n}(X_{1}+X_{2}+ ... +X_{n})=\\frac{\\sigma ^2}{n}$$\n", + "Similarly, we have sample mean = $\\mu$\n", + "\n", + "Using Chebyshev's inequality on \n", + "$\\bar X_{n}$ :\n", + "$P( |{\\bar X_{n}-\\mu}|\\ge\\epsilon)\\le\\frac{\\sigma^2}{n\\epsilon^2}$\n", + "\n", + "$lim_{n->\\infty}P( |{\\bar X_{n}-\\mu}|\\ge \\epsilon)=0$ because probability can not be negative" + ] + }, + { + "cell_type": "markdown", + "id": "b2812f1f", + "metadata": {}, + "source": [ + "# 4.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "4b05b1d0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Digit probabilities:\n", + "P(X=1) = 0.07692307692307693\n", + "P(X=2) = 0.11538461538461539\n", + "P(X=3) = 0.11538461538461539\n", + "P(X=4) = 0.07692307692307693\n", + "P(X=5) = 0.11538461538461539\n", + "P(X=6) = 0.0\n", + "P(X=7) = 0.15384615384615385\n", + "P(X=8) = 0.34615384615384615\n", + "mean=4.384615384615384\n", + "std=2.5279502654084594\n", + "Experimental mean (mu): 3.25043952\n", + "Experimental standard deviation (sigma): 0.024686891950377227\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\Laptop Solution\\anaconda3\\Lib\\site-packages\\seaborn\\_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.\n", + " with pd.option_context('mode.use_inf_as_na', True):\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "\n", + "\n", + "enrollment_number = '23323049'\n", + "digits = [int(d) for d in enrollment_number]\n", + "sum_digits = sum(digits)\n", + "probabilities = [d / sum_digits for d in digits]\n", + "\n", + "\n", + "print(\"Digit probabilities:\")\n", + "s=0\n", + "m=0\n", + "for i, prob in enumerate(probabilities):\n", + " s=s+i*prob\n", + " m=m+i**2*prob\n", + " print(f\"P(X={i+1}) = {prob}\")\n", + "print(f\"mean={s}\") \n", + "print(f'std={np.sqrt(m-s**2)}')\n", + "means = []\n", + "for _ in range(10000):\n", + " sample = np.random.choice(digits, size=10000)\n", + " means.append(np.mean(sample))\n", + "exp_mu = np.mean(means)\n", + "exp_sigma = np.std(means)\n", + "print(f\"Experimental mean (mu): {exp_mu}\")\n", + "print(f\"Experimental standard deviation (sigma): {exp_sigma}\")\n", + " \n", + "sns.histplot(means, kde=True)\n", + "plt.xlabel('Sample Means')\n", + "plt.ylabel('Frequency')\n", + "plt.title('Histogram of Sample Means (10,000 repetitions)')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "afdafa1a", + "metadata": {}, + "source": [ + "the resultant graph can be approximated by a normal distribution which largelty conforms the central limit theorem." + ] + }, + { + "cell_type": "markdown", + "id": "7015d272", + "metadata": {}, + "source": [ + "# 5. joint pdf\n", + "$$P_{x}(x)=_{y}\\int P(x,y)dy $$\n", + "\n", + "$$= \\int_{0}^{\\epsilon^{-x}} 1.dy = e^{-x}$$\n", + "\n", + "$$P_{y}(y)=_{x}\\int P(x,y)dx $$\n", + "\n", + "$$= \\int_{0}^{-lny} 1.dy = -ln y$$\n", + "\n", + "$p(x)p(y)\\ne p(x,y)$\n", + "\n", + "$=>$ X and Y are not independent\n", + "\n", + "$ p(y|x)=\\frac{p(x,y)}{p(x)} =- \\frac{1}{lny} $ given $0\\le x<\\infty , 0\\le y\\le e^{-x}$" + ] + }, + { + "cell_type": "markdown", + "id": "66938780", + "metadata": {}, + "source": [ + "# 6. \n", + "for \n", + "$\\alpha =0.05$\n", + "if test static $\\\\in$ [$-Z_{\\alpha/2},Z_{\\alpha/2}$] then we cannot reject null hypothesis\n", + "\n", + "$Z_{\\alpha/2} = 1.96$\n", + "\n", + "$z = \\frac{\\bar X-p_{0}}{\\sqrt{{\\frac{p_{0}(1-p_{0})}{{n}}}}} = 28.27$\n", + "we can reject null hypothesis" + ] + }, + { + "cell_type": "markdown", + "id": "e1dc3813", + "metadata": {}, + "source": [ + "# 7.\n", + "$$f(X,Y) = \\frac{1}{2\\pi(1-\\rho^2)^{1/2}} exp\\left(\\frac{-1}{2(1-\\rho^2)} (x^2 - 2\\rho xy + y^2) \\right)$$\n", + "\n", + "on comparing the given function with general bivariate normal pdf function we get $ \\mu_{1}=\\mu_{2}=0$ and $ \\sigma_{1}=\\sigma_{2}=1$\n", + "\n", + "$$ Cov(X,Y)= \\rho\\sigma_{1}\\sigma_{2}=\\rho = corr(X,Y)$$" + ] + }, + { + "cell_type": "markdown", + "id": "bcc9acdd", + "metadata": {}, + "source": [ + "$E(X ^2 )=Var(X)+(E(X)) ^2 =1+0=1,$\n", + "$E(Y ^2 )=Var(Y)+(E(Y)) ^2 =1+0=1.$\n", + "\n", + "\n", + "$E(X ^2 Y ^2 )=E(X ^2 )E(Y ^2 )+2(Cov(X,Y)) ^2 .$\n", + " \n", + "$E(X ^2 Y ^2 )=1+2ρ ^2 $\n", + "\n", + "$Cov(X ^2 ,Y ^2 )=E[X ^2 Y 2 ]−E[X ^2 ]E[Y ^2 ]=(1+2ρ ^2 )−1=2ρ ^2$\n", + "\n", + "For the variance, since \n", + "$E[X ^\n", + "4\n", + " ]=3 $ for a standard normal distribution, we have:\n", + "\n", + "$Var(X ^2 )=E[X ^4 ]−(E[X^ 2 ]) ^2 =3−1 ^2 =2$\n", + "\n", + "$Var(Y ^2 )=E[Y ^4 ]−(E[Y^2 ]) ^2 =3−1 ^2 =2$\n", + "\n", + "$Corr(X ^2 ,Y ^2 )= \\frac{ Cov(X ^2 ,Y ^2 )}{\\sqrt{Var(X ^2 )Var(Y ^2 )}} = \\rho^2$\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dcc09155", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/23323049_vatsal/assignment_2/.ipynb_checkpoints/assignment 2-checkpoint.ipynb b/23323049_vatsal/assignment_2/.ipynb_checkpoints/assignment 2-checkpoint.ipynb new file mode 100644 index 0000000..6bbe56f --- /dev/null +++ b/23323049_vatsal/assignment_2/.ipynb_checkpoints/assignment 2-checkpoint.ipynb @@ -0,0 +1,520 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "e6d7f127", + "metadata": {}, + "source": [ + "# 1.\n", + "## part1\n", + "The prior distribution of \n", + "𝜃\n", + "θ is given by:\n", + "$θ∼N(5,9)$\n", + "This means the prior mean \n", + "$\\mu=5$ and $\\sigma =9$\n", + "\n", + "The noise model tells us that the received value x given θ is normally distributed:\n", + "\n", + "$x∣θ∼N(θ,4)$\n", + "This means the likelihood mean is θ and the likelihood variance is $\\sigma^2=4$\n", + "\n", + "If the prior distribution of \n", + "θ is:\n", + "\n", + "$\\theta $~$ N(\\mu_0,{\\sigma_0}^2)$\n", + "\n", + "The probability density function (pdf) of the prior is:\n", + "\n", + "$p(\\theta)$=$ \\frac{1}{\\sqrt{2\\pi\\sigma_0^2}} exp $(-$\\frac{(\\theta - \\mu_0)^2}{2 \\sigma_0^2}$) \n", + "\n", + "$x∣θ$~$ N(\\theta,{\\sigma_x}^2)$\n", + "\n", + "$p(x|\\theta)$=$ \\frac{1}{\\sqrt{2\\pi\\sigma_x^2}} exp $(-$\\frac{(x-\\theta )^2}{2 \\sigma_x^2}$) \n", + "\n", + "$p(\\theta|x) \\propto p(x|\\theta)p(\\theta) \\propto exp(-\\frac{(x-\\theta )^2}{2 \\sigma_x^2} -\\frac{(\\theta - \\mu_0)^2}{2 \\sigma_0^2})$ \n", + "\n", + "$-\\frac{(x-\\theta )^2}{2 \\sigma_x^2} -\\frac{(\\theta - \\mu_0)^2}{2 \\sigma_0^2}=$\n", + "$-\\frac{1}{2} \\left( \\theta^2 \\left( \\frac{1}{\\sigma_x^2} + \\frac{1}{\\sigma_0^2} \\right) - 2 \\theta \\left( \\frac{x}{\\sigma_x^2} + \\frac{\\mu_0}{\\sigma_0^2} \\right) + \\text{const} \\right)$\n", + "\n", + "$=-\\frac{1}{2} \\left( \\left( \\theta^2 \\left( \\frac{1}{\\sigma_x^2} + \\frac{1}{\\sigma_0^2} \\right) - 2\\theta \\left( \\frac{x}{\\sigma_x^2} + \\frac{\\mu_0}{\\sigma_0^2} \\right) + \\left( \\frac{x}{\\sigma_x^2} + \\frac{\\mu_0}{\\sigma_0^2} \\right)^2 \\left( \\frac{1}{\\sigma_x^2} + \\frac{1}{\\sigma_0^2} \\right)^{-1} \\right) - \\left( \\frac{x}{\\sigma_x^2} + \\frac{\\mu_0}{\\sigma_0^2} \\right)^2 \\left( \\frac{1}{\\sigma_x^2} + \\frac{1}{\\sigma_0^2} \\right)^{-1} + \\text{constant terms} \\right)$\n", + "\n", + "$p(\\theta \\mid x) \\propto \\exp \\left( -\\frac{1}{2} \\left( \\frac{\\left( \\theta - \\left( \\frac{x}{\\sigma_x^2} + \\frac{\\mu_0}{\\sigma_0^2} \\right) \\left( \\frac{1}{\\sigma_x^2} + \\frac{1}{\\sigma_0^2} \\right)^{-1} \\right)^2}{\\left( \\frac{1}{\\sigma_x^2} + \\frac{1}{\\sigma_0^2} \\right)^{-1}} \\right) \\right)\n", + "$\n", + "\n", + "$\\sigma_n^2 = \\left( \\frac{1}{9} + \\frac{1}{4} \\right)^{-1} = \\left( \\frac{4 + 9}{36} \\right)^{-1} = \\left( \\frac{36}{13} \\right) \n", + "$\n", + "\n", + "$\\mu_n = \\frac{\\frac{1}{9} \\cdot 5 + \\frac{1}{4} \\cdot 6}{\\frac{1}{9} + \\frac{1}{4}} = \\frac{74}{13}\n", + "$" + ] + }, + { + "cell_type": "markdown", + "id": "1f304853", + "metadata": {}, + "source": [ + "## part 2\n", + "$$\\mu_{post} =\n", + "\\frac{\\frac{1}{\\sigma_{prior}^2}\\mu_{prior}+\\frac{n}{\\sigma_{likelihood}^2}\\bar x}\n", + "{\\frac{1}{\\sigma_{prior}^2}+\\frac{n}{\\sigma_{likelihood}^2}}$$\n", + "\n", + "$$σ_{post}^2 =\\frac{1}{\\sigma_{prior}^2}+\\frac{n}{\\sigma_{likelihood}^2}$$\n", + "\n", + " $\\theta|\\bar x$~$N(\\mu_{post},σ_{post}^2)$" + ] + }, + { + "cell_type": "markdown", + "id": "ba67a3df", + "metadata": {}, + "source": [ + "## part 3\n", + "The posterior variance \n", + "$\\sigma_{post}^2$ decreases, meaning our estimate of $θ$ becomes more precise.\n", + "\n", + "The posterior mean $\\mu_{post}$will move closer to the sample mean $\\bar x$ as $n$ increases." + ] + }, + { + "cell_type": "markdown", + "id": "fac39d71", + "metadata": {}, + "source": [ + "## part 4 \n", + "### subpart 1\n", + "The prior distribution of IQ in the general population:\n", + "$IQ∼N(100,152)$\n", + "This means the prior mean \n", + " $= 100$ and the prior variance $= 152$\n", + " \n", + "The likelihood of the test score given the true IQ:\n", + "$X∣IQ∼N(IQ,100)$\n", + "This means the test score mean is \n", + "IQ and the test score variance $100$\n", + "$$E[x]=\\mu_{post}=\\frac{a\\mu_{0}+bX}{a+b}\n", + "$$\n", + "$$=\\frac{\\frac{100}{152}+\\frac{80}{100}}{\\frac{1}{152}+\\frac{1}{100}}=87.9$$" + ] + }, + { + "cell_type": "markdown", + "id": "1c44192c", + "metadata": {}, + "source": [ + "### subpart 2\n", + "$$E[x]=\\mu_{post}=\\frac{a\\mu_{0}+bX}{a+b}\n", + "$$\n", + "$$=\\frac{\\frac{100}{152}+\\frac{150}{100}}{\\frac{1}{152}+\\frac{1}{100}}=130.16$$" + ] + }, + { + "cell_type": "markdown", + "id": "324764ca", + "metadata": {}, + "source": [ + "# 2.\n", + "The pdf of a normal distribution is:\n", + "$f(x \\mid \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp\\left( -\\frac{(x - \\mu)^2}{2\\sigma^2} \\right)$\n", + "\n", + "For a dataset $x_{1},x_{2},...,x_{n}$, the likelihood function is:\n", + "$L(\\mu, \\sigma^2) = \\prod_{i=1}^{n} f(x_i \\mid \\mu, \\sigma^2)$\n", + "\n", + "Log-Likelihood Function:\n", + "$\\log L(\\mu, \\sigma^2) = \\sum_{i=1}^{n} \\log f(x_i \\mid \\mu, \\sigma^2) = \\sum_{i=1}^{n} \\left[ -\\frac{1}{2} \\log(2\\pi\\sigma^2) - \\frac{(x_i - \\mu)^2}{2\\sigma^2} \\right] = -\\frac{n}{2} \\log(2\\pi\\sigma^2) - \\frac{1}{2\\sigma^2} \\sum_{i=1}^{n} (x_i - \\mu)^2$\n", + "\n", + "$\\frac{\\partial \\log L(\\mu, \\sigma^2)}{\\partial \\mu} = \\frac{1}{\\sigma^2} \\sum_{i=1}^{n} (x_i - \\mu) = 0 \\implies \\hat{\\mu} = \\frac{1}{n} \\sum_{i=1}^{n} x_i$\n", + "\n", + "$\\frac{\\partial \\log L(\\mu, \\sigma^2)}{\\partial \\sigma^2} = -\\frac{n}{2\\sigma^2} + \\frac{1}{2\\sigma^4} \\sum_{i=1}^{n} (x_i - \\mu)^2 = 0 \\implies \\hat{\\sigma}^2 = \\frac{1}{n} \\sum_{i=1}^{n} (x_i - \\hat{\\mu})^2$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "b9b99962", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MLE estimate of mean : 4.909486585019609\n", + "MLE estimate of standard deviation : 1.9740663173380517\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "\n", + "np.random.seed(0) \n", + "true_mu = 5\n", + "true_sigma = 2\n", + "data = np.random.normal(true_mu, true_sigma, 1000)\n", + "\n", + "def mle_gaussian(data):\n", + " n = len(data)\n", + " mu_mle = np.mean(data)\n", + " sigma_mle = np.sqrt(np.sum((data - mu_mle) ** 2) / n)\n", + " return mu_mle, sigma_mle\n", + "\n", + "# Calculate MLE estimates\n", + "mu_mle, sigma_mle = mle_gaussian(data)\n", + "\n", + "print(f\"MLE estimate of mean : {mu_mle}\")\n", + "print(f\"MLE estimate of standard deviation : {sigma_mle}\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "b36c1b1d", + "metadata": {}, + "source": [ + "# 3.\n", + "$P(y \\mid X, w) = \\prod_{i=1}^{N} \\sigma(x_i^T w)^{y_i} (1 - \\sigma(x_i^T w))^{1 - y_i}$\n", + "\n", + "let the prior be $P(w) = \\mathcal{N}(w \\mid 0, \\tau^2 I) \\propto \\exp \\left( -\\frac{1}{2\\tau^2} w^T w \\right)\n", + "$ \n", + "\n", + "$P(w \\mid X, y) \\propto P(y \\mid X, w) P(w)$\n", + "\n", + "$\\log P(w \\mid X, y) = \\sum_{i=1}^{N} \\left[ y_i \\log \\sigma(x_i^T w) + (1 - y_i) \\log (1 - \\sigma(x_i^T w)) \\right] - \\frac{1}{2\\tau^2} w^T w\n", + "$\n", + "\n", + "The MAP estimate of \n", + "𝑤 is the value that maximizes the log-posterior.\n", + "$w_{map}=argmax(\\sum_{i=1}^{N} \\left[ y_i \\log \\sigma(x_i^T w) + (1 - y_i) \\log (1 - \\sigma(x_i^T w)) \\right] - \\frac{1}{2\\tau^2} w^T w)$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "7a01f881", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.optimize import minimize\n", + "from scipy.special import expit\n", + "\n", + "def log_posterior(w, X, y, tau):\n", + " \n", + " # Log-likelihood part\n", + " z = X.dot(w)\n", + " log_likelihood = y.dot(np.log(expit(z))) + (1 - y).dot(np.log(1 - expit(z)))\n", + " #log prior part\n", + " log_prior = -0.5 * np.sum(w**2) / tau**2\n", + " return -(log_likelihood + log_prior)\n", + "\n", + "def map_estimate(X, y, tau):\n", + " \n", + " initial_w = np.zeros(X.shape[1])\n", + " \n", + " # Minimize the negative log-posterior\n", + " result = minimize(log_posterior, initial_w, args=(X, y, tau), method='L-BFGS-B')\n", + " \n", + " return result.x" + ] + }, + { + "cell_type": "markdown", + "id": "dba2f9df", + "metadata": {}, + "source": [ + "# 4. VC dimension\n", + "constant function = 1\n", + "\n", + "Linear Function in d Dimensions = d+1\n", + "\n", + "Axis-Aligned Rectangle in 2-Dimensions = 4\n", + "\n", + "Intervals = 2" + ] + }, + { + "cell_type": "markdown", + "id": "e1d1d0e9", + "metadata": {}, + "source": [ + "# 5. KL divergence" + ] + }, + { + "cell_type": "markdown", + "id": "3d49d328", + "metadata": {}, + "source": [ + "## part 1\n", + "$D_{kl}(p(x)||q(x))=\\int_{-\\infty}^{\\infty} p(x)ln\\frac{p(x)}{q(x)}dx$\n", + "\n", + "$p(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma_1} \\exp\\left( -\\frac{(x - \\mu_1)^2}{2\\sigma_1^2} \\right)$\n", + "\n", + "$q(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma_2} \\exp\\left( -\\frac{(x - \\mu_2)^2}{2\\sigma_2^2} \\right)$\n", + "\n", + "$D_{KL}(p \\parallel q) = \\int_{-\\infty}^{\\infty} \\frac{1}{\\sqrt{2\\pi}\\sigma_1} \\exp\\left( -\\frac{(x-\\mu_1)^2}{2\\sigma_1^2} \\right) \\log \\left( \\frac{\\sqrt{2\\pi}\\sigma_2}{\\sqrt{2\\pi}\\sigma_1} \\exp\\left(\\frac{(-\\frac{(x-\\mu_1)^2}{2\\sigma_1^2})}{(-\\frac{(x-\\mu_2)^2}{2\\sigma_2^2})} \\right) \\right) dx\n", + "$\n", + "\n", + "simplifying\n", + "$\\log \\left( \\frac{\\sqrt{2\\pi}\\sigma_2}{\\sqrt{2\\pi}\\sigma_1} \\exp\\left(\\frac{(-\\frac{(x-\\mu_1)^2}{2\\sigma_1^2})}{(-\\frac{(x-\\mu_2)^2}{2\\sigma_2^2})} \\right) \\right) dx = \\log\\left(\\frac{\\sigma_1}{\\sigma_2}\\right) + \\frac{2\\sigma_2^2}{\\sigma_1^2} (x - \\mu_2)^2 - \\frac{2\\sigma_1^2}{\\sigma_2^2} (x - \\mu_1)^2\n", + "$\n", + "\n", + "$\\begin{aligned}\n", + "& \\int_{-\\infty}^{\\infty} \\frac{1}{\\sqrt{2\\pi}\\sigma_1} \\exp\\left( -\\frac{(x-\\mu_1)^2}{2\\sigma_1^2} \\right) \\log\\left(\\frac{\\sigma_1}{\\sigma_2}\\right) dx \\\\\n", + "& = \\log\\left(\\frac{\\sigma_1}{\\sigma_2}\\right) \\int_{-\\infty}^{\\infty} \\frac{1}{\\sqrt{2\\pi}\\sigma_1} \\exp\\left( -\\frac{(x-\\mu_1)^2}{2\\sigma_1^2} \\right) dx \\\\\n", + "& = \\log\\left(\\frac{\\sigma_1}{\\sigma_2}\\right) \\\\\n", + "& \\int_{-\\infty}^{\\infty} \\frac{1}{2\\pi\\sigma_1}\\exp\\left( -\\frac{(x-\\mu_1)^2}{2\\sigma_1^2} \\right) \\left(\\frac{(x-\\mu_2)^2}{2\\sigma_2^2}\\right) dx \\\\\n", + "& = \\frac{\\sigma_1^2 + (\\mu_1 - \\mu_2)^2}{2\\sigma_2^2} \\\\\n", + "& \\int_{-\\infty}^{\\infty} \\frac{1}{2\\pi\\sigma_1} \\exp\\left( -\\frac{(x-\\mu_1)^2}{2\\sigma_1^2} \\right) \\left(\\frac{(x-\\mu_1)^2}{2\\sigma_1^2}\\right) dx \\\\\n", + "& = \\frac{1}{2}\n", + "\\end{aligned}\n", + "$\n", + "\n", + "$D_{KL}(N(\\mu_1, \\sigma_1^2) \\parallel N(\\mu_2, \\sigma_2^2)) = \\log\\left(\\frac{\\sigma_1}{\\sigma_2}\\right) + \\frac{2\\sigma_2^2}{\\sigma_1^2} + \\left(\\frac{\\mu_1 - \\mu_2}{\\sigma_2}\\right)^2 - \\frac{1}{2}\n", + "$" + ] + }, + { + "cell_type": "markdown", + "id": "d75fa21f", + "metadata": {}, + "source": [ + "## part 2" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "8af9679b", + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "df=pd.read_csv('data_KL.csv')\n", + "\n", + "df['ln(p/q)'] = np.log(df['P'] / df['Q'])\n", + "kl = np.sum(df['P']*df['ln(p/q)'])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "e47885fd", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
Unnamed: 0PQln(p/q)
007.888609e-311.486720e-07-53.593195
117.888609e-292.438962e-07-49.483025
223.904861e-273.961301e-07-46.066052
331.275588e-256.369829e-07-43.054697
443.093301e-241.014086e-06-40.331280
\n", + "
" + ], + "text/plain": [ + " Unnamed: 0 P Q ln(p/q)\n", + "0 0 7.888609e-31 1.486720e-07 -53.593195\n", + "1 1 7.888609e-29 2.438962e-07 -49.483025\n", + "2 2 3.904861e-27 3.961301e-07 -46.066052\n", + "3 3 1.275588e-25 6.369829e-07 -43.054697\n", + "4 4 3.093301e-24 1.014086e-06 -40.331280" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "e4158996", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.31815510041414485" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "kl" + ] + }, + { + "cell_type": "markdown", + "id": "0c90c6de", + "metadata": {}, + "source": [ + "## part 3\n", + "KL Divergence represrnt the divergence not the distance between the two distributions and also it is not symmetric.\n", + "one way of finding the distance could be taking the absolute difference between p($x_{i}$) and q($x_{i}$) and then taking the maximum and minimum of them" + ] + }, + { + "cell_type": "markdown", + "id": "f25bd905", + "metadata": {}, + "source": [ + "# 6. mixture of gaussians\n", + "## part 1\n", + "we can use the EM algorithm for mixture of gaussians" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "e7e4d152", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of D1: [5.93675083e+03 2.49829361e+00]\n", + "Mean of D2: [2072.63804569 2.52201437]\n", + "Variance of D1: [1.59305645e+06 1.63133898e+01]\n", + "Variance of D2: [1.6079402e+06 1.5969658e+01]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from sklearn.mixture import GaussianMixture\n", + "\n", + "mixed_data = pd.read_csv('data_open.csv')\n", + "\n", + "num_components = 2\n", + "\n", + "gmm = GaussianMixture(n_components=num_components)\n", + "\n", + "gmm.fit(mixed_data)\n", + "\n", + "means = gmm.means_\n", + "covariances = gmm.covariances_\n", + "\n", + "mean_D1 = means[0]\n", + "mean_D2 = means[1]\n", + "variance_D1 = np.diag(covariances[0])\n", + "variance_D2 = np.diag(covariances[1])\n", + "\n", + "print(\"Mean of D1:\", mean_D1)\n", + "print(\"Mean of D2:\", mean_D2)\n", + "print(\"Variance of D1:\", variance_D1)\n", + "print(\"Variance of D2:\", variance_D2)\n" + ] + }, + { + "cell_type": "markdown", + "id": "b389d356", + "metadata": {}, + "source": [ + "## part 2\n", + "Fit GMM: Use the EM algorithm to fit a GMM to the mixed dataset. \n", + "\n", + "Extract Parameters: After fitting the GMM, you can obtain the means, variances, and mixing coefficients of the Gaussian components.\n", + "\n", + "Identify Components: Identify which Gaussian components correspond to D1 and D2 by comparing their means and variances.\n", + "\n", + "Estimate Ratio: We can use the mixing coefficients of these components to estimate the ratio of data points taken from each distribution. The mixing coefficient represents the proportion of data points assigned to each component by the GMM.\n", + "\n", + "Ratio Calculation: The ratio of data points taken from D1 and D2 can be estimated as the ratio of the mixing coefficients of the corresponding Gaussian components." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "30c7dafa", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/23323049_vatsal/assignment_2/assignment 2.ipynb b/23323049_vatsal/assignment_2/assignment 2.ipynb new file mode 100644 index 0000000..6bbe56f --- /dev/null +++ b/23323049_vatsal/assignment_2/assignment 2.ipynb @@ -0,0 +1,520 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "e6d7f127", + "metadata": {}, + "source": [ + "# 1.\n", + "## part1\n", + "The prior distribution of \n", + "𝜃\n", + "θ is given by:\n", + "$θ∼N(5,9)$\n", + "This means the prior mean \n", + "$\\mu=5$ and $\\sigma =9$\n", + "\n", + "The noise model tells us that the received value x given θ is normally distributed:\n", + "\n", + "$x∣θ∼N(θ,4)$\n", + "This means the likelihood mean is θ and the likelihood variance is $\\sigma^2=4$\n", + "\n", + "If the prior distribution of \n", + "θ is:\n", + "\n", + "$\\theta $~$ N(\\mu_0,{\\sigma_0}^2)$\n", + "\n", + "The probability density function (pdf) of the prior is:\n", + "\n", + "$p(\\theta)$=$ \\frac{1}{\\sqrt{2\\pi\\sigma_0^2}} exp $(-$\\frac{(\\theta - \\mu_0)^2}{2 \\sigma_0^2}$) \n", + "\n", + "$x∣θ$~$ N(\\theta,{\\sigma_x}^2)$\n", + "\n", + "$p(x|\\theta)$=$ \\frac{1}{\\sqrt{2\\pi\\sigma_x^2}} exp $(-$\\frac{(x-\\theta )^2}{2 \\sigma_x^2}$) \n", + "\n", + "$p(\\theta|x) \\propto p(x|\\theta)p(\\theta) \\propto exp(-\\frac{(x-\\theta )^2}{2 \\sigma_x^2} -\\frac{(\\theta - \\mu_0)^2}{2 \\sigma_0^2})$ \n", + "\n", + "$-\\frac{(x-\\theta )^2}{2 \\sigma_x^2} -\\frac{(\\theta - \\mu_0)^2}{2 \\sigma_0^2}=$\n", + "$-\\frac{1}{2} \\left( \\theta^2 \\left( \\frac{1}{\\sigma_x^2} + \\frac{1}{\\sigma_0^2} \\right) - 2 \\theta \\left( \\frac{x}{\\sigma_x^2} + \\frac{\\mu_0}{\\sigma_0^2} \\right) + \\text{const} \\right)$\n", + "\n", + "$=-\\frac{1}{2} \\left( \\left( \\theta^2 \\left( \\frac{1}{\\sigma_x^2} + \\frac{1}{\\sigma_0^2} \\right) - 2\\theta \\left( \\frac{x}{\\sigma_x^2} + \\frac{\\mu_0}{\\sigma_0^2} \\right) + \\left( \\frac{x}{\\sigma_x^2} + \\frac{\\mu_0}{\\sigma_0^2} \\right)^2 \\left( \\frac{1}{\\sigma_x^2} + \\frac{1}{\\sigma_0^2} \\right)^{-1} \\right) - \\left( \\frac{x}{\\sigma_x^2} + \\frac{\\mu_0}{\\sigma_0^2} \\right)^2 \\left( \\frac{1}{\\sigma_x^2} + \\frac{1}{\\sigma_0^2} \\right)^{-1} + \\text{constant terms} \\right)$\n", + "\n", + "$p(\\theta \\mid x) \\propto \\exp \\left( -\\frac{1}{2} \\left( \\frac{\\left( \\theta - \\left( \\frac{x}{\\sigma_x^2} + \\frac{\\mu_0}{\\sigma_0^2} \\right) \\left( \\frac{1}{\\sigma_x^2} + \\frac{1}{\\sigma_0^2} \\right)^{-1} \\right)^2}{\\left( \\frac{1}{\\sigma_x^2} + \\frac{1}{\\sigma_0^2} \\right)^{-1}} \\right) \\right)\n", + "$\n", + "\n", + "$\\sigma_n^2 = \\left( \\frac{1}{9} + \\frac{1}{4} \\right)^{-1} = \\left( \\frac{4 + 9}{36} \\right)^{-1} = \\left( \\frac{36}{13} \\right) \n", + "$\n", + "\n", + "$\\mu_n = \\frac{\\frac{1}{9} \\cdot 5 + \\frac{1}{4} \\cdot 6}{\\frac{1}{9} + \\frac{1}{4}} = \\frac{74}{13}\n", + "$" + ] + }, + { + "cell_type": "markdown", + "id": "1f304853", + "metadata": {}, + "source": [ + "## part 2\n", + "$$\\mu_{post} =\n", + "\\frac{\\frac{1}{\\sigma_{prior}^2}\\mu_{prior}+\\frac{n}{\\sigma_{likelihood}^2}\\bar x}\n", + "{\\frac{1}{\\sigma_{prior}^2}+\\frac{n}{\\sigma_{likelihood}^2}}$$\n", + "\n", + "$$σ_{post}^2 =\\frac{1}{\\sigma_{prior}^2}+\\frac{n}{\\sigma_{likelihood}^2}$$\n", + "\n", + " $\\theta|\\bar x$~$N(\\mu_{post},σ_{post}^2)$" + ] + }, + { + "cell_type": "markdown", + "id": "ba67a3df", + "metadata": {}, + "source": [ + "## part 3\n", + "The posterior variance \n", + "$\\sigma_{post}^2$ decreases, meaning our estimate of $θ$ becomes more precise.\n", + "\n", + "The posterior mean $\\mu_{post}$will move closer to the sample mean $\\bar x$ as $n$ increases." + ] + }, + { + "cell_type": "markdown", + "id": "fac39d71", + "metadata": {}, + "source": [ + "## part 4 \n", + "### subpart 1\n", + "The prior distribution of IQ in the general population:\n", + "$IQ∼N(100,152)$\n", + "This means the prior mean \n", + " $= 100$ and the prior variance $= 152$\n", + " \n", + "The likelihood of the test score given the true IQ:\n", + "$X∣IQ∼N(IQ,100)$\n", + "This means the test score mean is \n", + "IQ and the test score variance $100$\n", + "$$E[x]=\\mu_{post}=\\frac{a\\mu_{0}+bX}{a+b}\n", + "$$\n", + "$$=\\frac{\\frac{100}{152}+\\frac{80}{100}}{\\frac{1}{152}+\\frac{1}{100}}=87.9$$" + ] + }, + { + "cell_type": "markdown", + "id": "1c44192c", + "metadata": {}, + "source": [ + "### subpart 2\n", + "$$E[x]=\\mu_{post}=\\frac{a\\mu_{0}+bX}{a+b}\n", + "$$\n", + "$$=\\frac{\\frac{100}{152}+\\frac{150}{100}}{\\frac{1}{152}+\\frac{1}{100}}=130.16$$" + ] + }, + { + "cell_type": "markdown", + "id": "324764ca", + "metadata": {}, + "source": [ + "# 2.\n", + "The pdf of a normal distribution is:\n", + "$f(x \\mid \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp\\left( -\\frac{(x - \\mu)^2}{2\\sigma^2} \\right)$\n", + "\n", + "For a dataset $x_{1},x_{2},...,x_{n}$, the likelihood function is:\n", + "$L(\\mu, \\sigma^2) = \\prod_{i=1}^{n} f(x_i \\mid \\mu, \\sigma^2)$\n", + "\n", + "Log-Likelihood Function:\n", + "$\\log L(\\mu, \\sigma^2) = \\sum_{i=1}^{n} \\log f(x_i \\mid \\mu, \\sigma^2) = \\sum_{i=1}^{n} \\left[ -\\frac{1}{2} \\log(2\\pi\\sigma^2) - \\frac{(x_i - \\mu)^2}{2\\sigma^2} \\right] = -\\frac{n}{2} \\log(2\\pi\\sigma^2) - \\frac{1}{2\\sigma^2} \\sum_{i=1}^{n} (x_i - \\mu)^2$\n", + "\n", + "$\\frac{\\partial \\log L(\\mu, \\sigma^2)}{\\partial \\mu} = \\frac{1}{\\sigma^2} \\sum_{i=1}^{n} (x_i - \\mu) = 0 \\implies \\hat{\\mu} = \\frac{1}{n} \\sum_{i=1}^{n} x_i$\n", + "\n", + "$\\frac{\\partial \\log L(\\mu, \\sigma^2)}{\\partial \\sigma^2} = -\\frac{n}{2\\sigma^2} + \\frac{1}{2\\sigma^4} \\sum_{i=1}^{n} (x_i - \\mu)^2 = 0 \\implies \\hat{\\sigma}^2 = \\frac{1}{n} \\sum_{i=1}^{n} (x_i - \\hat{\\mu})^2$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "b9b99962", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MLE estimate of mean : 4.909486585019609\n", + "MLE estimate of standard deviation : 1.9740663173380517\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "\n", + "np.random.seed(0) \n", + "true_mu = 5\n", + "true_sigma = 2\n", + "data = np.random.normal(true_mu, true_sigma, 1000)\n", + "\n", + "def mle_gaussian(data):\n", + " n = len(data)\n", + " mu_mle = np.mean(data)\n", + " sigma_mle = np.sqrt(np.sum((data - mu_mle) ** 2) / n)\n", + " return mu_mle, sigma_mle\n", + "\n", + "# Calculate MLE estimates\n", + "mu_mle, sigma_mle = mle_gaussian(data)\n", + "\n", + "print(f\"MLE estimate of mean : {mu_mle}\")\n", + "print(f\"MLE estimate of standard deviation : {sigma_mle}\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "b36c1b1d", + "metadata": {}, + "source": [ + "# 3.\n", + "$P(y \\mid X, w) = \\prod_{i=1}^{N} \\sigma(x_i^T w)^{y_i} (1 - \\sigma(x_i^T w))^{1 - y_i}$\n", + "\n", + "let the prior be $P(w) = \\mathcal{N}(w \\mid 0, \\tau^2 I) \\propto \\exp \\left( -\\frac{1}{2\\tau^2} w^T w \\right)\n", + "$ \n", + "\n", + "$P(w \\mid X, y) \\propto P(y \\mid X, w) P(w)$\n", + "\n", + "$\\log P(w \\mid X, y) = \\sum_{i=1}^{N} \\left[ y_i \\log \\sigma(x_i^T w) + (1 - y_i) \\log (1 - \\sigma(x_i^T w)) \\right] - \\frac{1}{2\\tau^2} w^T w\n", + "$\n", + "\n", + "The MAP estimate of \n", + "𝑤 is the value that maximizes the log-posterior.\n", + "$w_{map}=argmax(\\sum_{i=1}^{N} \\left[ y_i \\log \\sigma(x_i^T w) + (1 - y_i) \\log (1 - \\sigma(x_i^T w)) \\right] - \\frac{1}{2\\tau^2} w^T w)$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "7a01f881", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.optimize import minimize\n", + "from scipy.special import expit\n", + "\n", + "def log_posterior(w, X, y, tau):\n", + " \n", + " # Log-likelihood part\n", + " z = X.dot(w)\n", + " log_likelihood = y.dot(np.log(expit(z))) + (1 - y).dot(np.log(1 - expit(z)))\n", + " #log prior part\n", + " log_prior = -0.5 * np.sum(w**2) / tau**2\n", + " return -(log_likelihood + log_prior)\n", + "\n", + "def map_estimate(X, y, tau):\n", + " \n", + " initial_w = np.zeros(X.shape[1])\n", + " \n", + " # Minimize the negative log-posterior\n", + " result = minimize(log_posterior, initial_w, args=(X, y, tau), method='L-BFGS-B')\n", + " \n", + " return result.x" + ] + }, + { + "cell_type": "markdown", + "id": "dba2f9df", + "metadata": {}, + "source": [ + "# 4. VC dimension\n", + "constant function = 1\n", + "\n", + "Linear Function in d Dimensions = d+1\n", + "\n", + "Axis-Aligned Rectangle in 2-Dimensions = 4\n", + "\n", + "Intervals = 2" + ] + }, + { + "cell_type": "markdown", + "id": "e1d1d0e9", + "metadata": {}, + "source": [ + "# 5. KL divergence" + ] + }, + { + "cell_type": "markdown", + "id": "3d49d328", + "metadata": {}, + "source": [ + "## part 1\n", + "$D_{kl}(p(x)||q(x))=\\int_{-\\infty}^{\\infty} p(x)ln\\frac{p(x)}{q(x)}dx$\n", + "\n", + "$p(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma_1} \\exp\\left( -\\frac{(x - \\mu_1)^2}{2\\sigma_1^2} \\right)$\n", + "\n", + "$q(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma_2} \\exp\\left( -\\frac{(x - \\mu_2)^2}{2\\sigma_2^2} \\right)$\n", + "\n", + "$D_{KL}(p \\parallel q) = \\int_{-\\infty}^{\\infty} \\frac{1}{\\sqrt{2\\pi}\\sigma_1} \\exp\\left( -\\frac{(x-\\mu_1)^2}{2\\sigma_1^2} \\right) \\log \\left( \\frac{\\sqrt{2\\pi}\\sigma_2}{\\sqrt{2\\pi}\\sigma_1} \\exp\\left(\\frac{(-\\frac{(x-\\mu_1)^2}{2\\sigma_1^2})}{(-\\frac{(x-\\mu_2)^2}{2\\sigma_2^2})} \\right) \\right) dx\n", + "$\n", + "\n", + "simplifying\n", + "$\\log \\left( \\frac{\\sqrt{2\\pi}\\sigma_2}{\\sqrt{2\\pi}\\sigma_1} \\exp\\left(\\frac{(-\\frac{(x-\\mu_1)^2}{2\\sigma_1^2})}{(-\\frac{(x-\\mu_2)^2}{2\\sigma_2^2})} \\right) \\right) dx = \\log\\left(\\frac{\\sigma_1}{\\sigma_2}\\right) + \\frac{2\\sigma_2^2}{\\sigma_1^2} (x - \\mu_2)^2 - \\frac{2\\sigma_1^2}{\\sigma_2^2} (x - \\mu_1)^2\n", + "$\n", + "\n", + "$\\begin{aligned}\n", + "& \\int_{-\\infty}^{\\infty} \\frac{1}{\\sqrt{2\\pi}\\sigma_1} \\exp\\left( -\\frac{(x-\\mu_1)^2}{2\\sigma_1^2} \\right) \\log\\left(\\frac{\\sigma_1}{\\sigma_2}\\right) dx \\\\\n", + "& = \\log\\left(\\frac{\\sigma_1}{\\sigma_2}\\right) \\int_{-\\infty}^{\\infty} \\frac{1}{\\sqrt{2\\pi}\\sigma_1} \\exp\\left( -\\frac{(x-\\mu_1)^2}{2\\sigma_1^2} \\right) dx \\\\\n", + "& = \\log\\left(\\frac{\\sigma_1}{\\sigma_2}\\right) \\\\\n", + "& \\int_{-\\infty}^{\\infty} \\frac{1}{2\\pi\\sigma_1}\\exp\\left( -\\frac{(x-\\mu_1)^2}{2\\sigma_1^2} \\right) \\left(\\frac{(x-\\mu_2)^2}{2\\sigma_2^2}\\right) dx \\\\\n", + "& = \\frac{\\sigma_1^2 + (\\mu_1 - \\mu_2)^2}{2\\sigma_2^2} \\\\\n", + "& \\int_{-\\infty}^{\\infty} \\frac{1}{2\\pi\\sigma_1} \\exp\\left( -\\frac{(x-\\mu_1)^2}{2\\sigma_1^2} \\right) \\left(\\frac{(x-\\mu_1)^2}{2\\sigma_1^2}\\right) dx \\\\\n", + "& = \\frac{1}{2}\n", + "\\end{aligned}\n", + "$\n", + "\n", + "$D_{KL}(N(\\mu_1, \\sigma_1^2) \\parallel N(\\mu_2, \\sigma_2^2)) = \\log\\left(\\frac{\\sigma_1}{\\sigma_2}\\right) + \\frac{2\\sigma_2^2}{\\sigma_1^2} + \\left(\\frac{\\mu_1 - \\mu_2}{\\sigma_2}\\right)^2 - \\frac{1}{2}\n", + "$" + ] + }, + { + "cell_type": "markdown", + "id": "d75fa21f", + "metadata": {}, + "source": [ + "## part 2" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "8af9679b", + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "df=pd.read_csv('data_KL.csv')\n", + "\n", + "df['ln(p/q)'] = np.log(df['P'] / df['Q'])\n", + "kl = np.sum(df['P']*df['ln(p/q)'])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "e47885fd", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
Unnamed: 0PQln(p/q)
007.888609e-311.486720e-07-53.593195
117.888609e-292.438962e-07-49.483025
223.904861e-273.961301e-07-46.066052
331.275588e-256.369829e-07-43.054697
443.093301e-241.014086e-06-40.331280
\n", + "
" + ], + "text/plain": [ + " Unnamed: 0 P Q ln(p/q)\n", + "0 0 7.888609e-31 1.486720e-07 -53.593195\n", + "1 1 7.888609e-29 2.438962e-07 -49.483025\n", + "2 2 3.904861e-27 3.961301e-07 -46.066052\n", + "3 3 1.275588e-25 6.369829e-07 -43.054697\n", + "4 4 3.093301e-24 1.014086e-06 -40.331280" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "e4158996", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.31815510041414485" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "kl" + ] + }, + { + "cell_type": "markdown", + "id": "0c90c6de", + "metadata": {}, + "source": [ + "## part 3\n", + "KL Divergence represrnt the divergence not the distance between the two distributions and also it is not symmetric.\n", + "one way of finding the distance could be taking the absolute difference between p($x_{i}$) and q($x_{i}$) and then taking the maximum and minimum of them" + ] + }, + { + "cell_type": "markdown", + "id": "f25bd905", + "metadata": {}, + "source": [ + "# 6. mixture of gaussians\n", + "## part 1\n", + "we can use the EM algorithm for mixture of gaussians" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "e7e4d152", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of D1: [5.93675083e+03 2.49829361e+00]\n", + "Mean of D2: [2072.63804569 2.52201437]\n", + "Variance of D1: [1.59305645e+06 1.63133898e+01]\n", + "Variance of D2: [1.6079402e+06 1.5969658e+01]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from sklearn.mixture import GaussianMixture\n", + "\n", + "mixed_data = pd.read_csv('data_open.csv')\n", + "\n", + "num_components = 2\n", + "\n", + "gmm = GaussianMixture(n_components=num_components)\n", + "\n", + "gmm.fit(mixed_data)\n", + "\n", + "means = gmm.means_\n", + "covariances = gmm.covariances_\n", + "\n", + "mean_D1 = means[0]\n", + "mean_D2 = means[1]\n", + "variance_D1 = np.diag(covariances[0])\n", + "variance_D2 = np.diag(covariances[1])\n", + "\n", + "print(\"Mean of D1:\", mean_D1)\n", + "print(\"Mean of D2:\", mean_D2)\n", + "print(\"Variance of D1:\", variance_D1)\n", + "print(\"Variance of D2:\", variance_D2)\n" + ] + }, + { + "cell_type": "markdown", + "id": "b389d356", + "metadata": {}, + "source": [ + "## part 2\n", + "Fit GMM: Use the EM algorithm to fit a GMM to the mixed dataset. \n", + "\n", + "Extract Parameters: After fitting the GMM, you can obtain the means, variances, and mixing coefficients of the Gaussian components.\n", + "\n", + "Identify Components: Identify which Gaussian components correspond to D1 and D2 by comparing their means and variances.\n", + "\n", + "Estimate Ratio: We can use the mixing coefficients of these components to estimate the ratio of data points taken from each distribution. The mixing coefficient represents the proportion of data points assigned to each component by the GMM.\n", + "\n", + "Ratio Calculation: The ratio of data points taken from D1 and D2 can be estimated as the ratio of the mixing coefficients of the corresponding Gaussian components." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "30c7dafa", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/23323049_vatsal/assignment_2/data_KL.csv b/23323049_vatsal/assignment_2/data_KL.csv new file mode 100644 index 0000000..f621176 --- /dev/null +++ b/23323049_vatsal/assignment_2/data_KL.csv @@ -0,0 +1,101 @@ +,P,Q +0,7.88860905221016e-31,1.486720385427983e-07 +1,7.88860905221004e-29,2.438962174264809e-07 +2,3.904861480844006e-27,3.9613014109573e-07 +3,1.275588083742379e-25,6.369828909339788e-07 +4,3.093301103075289e-24,1.0140858004452227e-06 +5,5.939138117904556e-23,1.5983750467744769e-06 +6,9.403635353348723e-22,2.4942485897551474e-06 +7,1.2627738903068471e-20,3.853521931013182e-06 +8,1.4679746474817013e-19,5.894310227640482e-06 +9,1.5005963063146228e-18,8.92617094530064e-06 +10,1.365542638746319e-17,1.3383030414223315e-05 +11,1.117262158974263e-16,1.986555877348687e-05 +12,8.286361012392394e-16,2.919470967694707e-05 +13,5.6092289930040604e-15,4.2478051932228865e-05 +14,3.4857351599382385e-14,6.119022884726562e-05 +15,1.998488158364584e-13,8.726832061302681e-05 +16,1.061696834131184e-12,0.0001232219890119193 +17,5.2460314157070536e-12,0.0001722569947872011 +18,2.4190033750204664e-11,0.0002384089597700325 +19,1.0439909302719975e-10,0.00032668209694045915 +20,4.2281632676015655e-10,0.00044318510074393025 +21,1.6107288638482235e-09,0.0005952535905862057 +22,5.783980920182251e-09,0.0007915456218645029 +23,1.9615239642357194e-08,0.001042094091741784 +24,6.293222718589578e-08,0.0013582977188518668 +25,1.91313970645124e-07,0.0017528310758975296 +26,5.518672230147828e-07,0.0022394543410145357 +27,1.5125249815960546e-06,0.0028327054331262276 +28,3.943368702018315e-06,0.0035474613621840857 +29,9.790432639493707e-06,0.004398362173931372 +30,2.317069058013514e-05,0.0053990998132866916 +31,5.232091421320849e-05,0.006561585320241969 +32,0.00011281697127223027,0.007895020453786327 +33,0.000232471334742778,0.009404913245650147 +34,0.00045810527728723993,0.011092089963997388 +35,0.0008638556657416476,0.012951767151755816 +36,0.00155973939647798,0.01497275533232727 +37,0.002697927604718676,0.017136869240940846 +38,0.004472879976244128,0.019418616870780607 +39,0.007110732269926539,0.02178523046171507 +40,0.01084386671163798,0.024197086622871247 +41,0.01586907323654335,0.026608540573093736 +42,0.02229226954657284,0.02896917224186394 +43,0.030068642644214553,0.031225411623752156 +44,0.03895255978909616,0.03332247980439818 +45,0.04847429662643073,0.0352065532950506 +46,0.05795839814029768,0.036827035597983955 +47,0.06659049999098023,0.03813880388193751 +48,0.07352701040670744,0.03910429229886631 +49,0.07802866410507721,0.039695277995131034 +50,0.07958923738717877,0.039894251404101355 +51,0.07802866410507721,0.039695277995131034 +52,0.07352701040670744,0.03910429229886631 +53,0.06659049999098024,0.03813880388193751 +54,0.05795839814029768,0.036827035597983955 +55,0.048474296626430734,0.0352065532950506 +56,0.03895255978909616,0.03332247980439818 +57,0.030068642644214504,0.031225411623752156 +58,0.022292269546572777,0.02896917224186394 +59,0.01586907323654335,0.026608540573093736 +60,0.010843866711637961,0.024197086622871247 +61,0.007110732269926539,0.02178523046171507 +62,0.004472879976244128,0.019418616870780607 +63,0.002697927604718676,0.017136869240940846 +64,0.00155973939647798,0.01497275533232727 +65,0.0008638556657416476,0.012951767151755816 +66,0.00045810527728723993,0.011092089963997388 +67,0.00023247133474277795,0.009404913245650147 +68,0.00011281697127223027,0.007895020453786327 +69,5.232091421320849e-05,0.006561585320241969 +70,2.3170690580135137e-05,0.0053990998132866916 +71,9.790432639493707e-06,0.004398362173931372 +72,3.943368702018315e-06,0.0035474613621840857 +73,1.5125249815960546e-06,0.0028327054331262276 +74,5.518672230147828e-07,0.0022394543410145357 +75,1.91313970645124e-07,0.0017528310758975296 +76,6.293222718589578e-08,0.0013582977188518668 +77,1.961523964235719e-08,0.001042094091741784 +78,5.78398092018225e-09,0.0007915456218645029 +79,1.6107288638482239e-09,0.0005952535905862057 +80,4.2281632676015655e-10,0.00044318510074393025 +81,1.0439909302719976e-10,0.00032668209694045915 +82,2.4190033750204664e-11,0.0002384089597700325 +83,5.2460314157070536e-12,0.0001722569947872011 +84,1.061696834131184e-12,0.0001232219890119193 +85,1.9984881583645844e-13,8.726832061302681e-05 +86,3.4857351599382385e-14,6.119022884726562e-05 +87,5.609228993004061e-15,4.2478051932228865e-05 +88,8.2863610123923925e-16,2.919470967694707e-05 +89,1.117262158974263e-16,1.986555877348687e-05 +90,1.3655426387463192e-17,1.3383030414223315e-05 +91,1.5005963063146224e-18,8.92617094530064e-06 +92,1.4679746474817013e-19,5.894310227640482e-06 +93,1.2627738903068471e-20,3.853521931013182e-06 +94,9.403635353348723e-22,2.4942485897551474e-06 +95,5.939138117904558e-23,1.5983750467744769e-06 +96,3.093301103075289e-24,1.0140858004452227e-06 +97,1.2755880837423788e-25,6.369828909339788e-07 +98,3.904861480844006e-27,3.9613014109573e-07 +99,7.888609052210037e-29,2.438962174264809e-07 diff --git a/23323049_vatsal/assignment_2/data_open.csv b/23323049_vatsal/assignment_2/data_open.csv new file mode 100644 index 0000000..758df09 --- /dev/null +++ b/23323049_vatsal/assignment_2/data_open.csv @@ -0,0 +1,8001 @@ +,data +0,5.242409064737171 +1,1.5677360608794515 +2,-5.809161571554837 +3,-3.2231270533908565 +4,8.075653178740438 +5,8.49078129185581 +6,0.5133242523171647 +7,5.422983584086264 +8,6.087403516168843 +9,-4.188569384569602 +10,6.20854371500797 +11,-1.586595061840926 +12,1.1077902987661634 +13,4.103752448016364 +14,10.653689221671835 +15,7.631957507254828 +16,0.4247231100353259 +17,2.5339947468398805 +18,-1.1861318179224927 +19,5.684853169226132 +20,1.3923776889636903 +21,2.382084479475592 +22,3.5792740096929334 +23,0.9923935300980397 +24,6.924337426002784 +25,-5.649405744821586 +26,7.15558731840432 +27,1.5117737155102733 +28,-3.2696797357824416 +29,4.305265862335088 +30,8.402610939064381 +31,0.38570318678997484 +32,10.908606968574622 +33,2.8082675049919428 +34,4.803961497145239 +35,0.08013191022010656 +36,3.4460825663994754 +37,-4.363577915544254 +38,2.691977230716098 +39,2.911180949452228 +40,5.382290130786188 +41,1.4318395070168919 +42,4.642841708370146 +43,6.277127737382148 +44,7.046906093150713 +45,0.18701292317875662 +46,4.935923343838247 +47,3.465131424658645 +48,4.087216961074889 +49,7.072794151143383 +50,6.617893915312073 +51,5.929677578678684 +52,5.001185026291678 +53,3.916315142077032 +54,-3.347044403210839 +55,1.218372732239246 +56,1.465652687939301 +57,7.793465655090935 +58,4.837863477259029 +59,3.270137104795232 +60,3.6553325561241317 +61,3.1431568387530735 +62,0.7332726498967755 +63,1.564517289145407 +64,4.382176099534969 +65,2.8707516963807884 +66,-2.675199017057384 +67,5.497283429517307 +68,-1.0984813608183195 +69,3.53960439611266 +70,-6.3822030784951735 +71,6.251784451486587 +72,1.6623984008545252 +73,-4.295498461048329 +74,8.679062612059502 +75,6.324716817129817 +76,4.528463855602141 +77,0.5252737143400855 +78,5.85115906519871 +79,-0.6878415300032077 +80,5.336031885002961 +81,7.713289397583935 +82,5.496592877070581 +83,2.455864484013352 +84,7.767018251623552 +85,5.379044547658823 +86,4.162397123430973 +87,8.347844117976987 +88,-2.7796541602438967 +89,-7.753693675715147 +90,6.936946250861469 +91,5.100764031661544 +92,3.387107575147651 +93,3.9596229848874653 +94,3.6960657523793143 +95,-2.776741706473857 +96,-1.1493473192657138 +97,6.358532019532134 +98,-2.6826378937495745 +99,6.662061241605729 +100,2.9586364351451073 +101,6.916242876237959 +102,5.482983823276855 +103,2.4337955323296545 +104,3.098397812272081 +105,4.104766757947843 +106,4.167834508633921 +107,3.5821341263178597 +108,-3.064240491562944 +109,5.5109071092436315 +110,-2.499350825520608 +111,3.100700231467118 +112,-0.8995379094375537 +113,5.576619969432219 +114,8.315952359369518 +115,9.372606038392195 +116,2.2697959672577532 +117,-0.5318388592527202 +118,-4.000986085722222 +119,4.384795492040935 +120,-1.267874234191452 +121,7.695471379553684 +122,2.9762298453299993 +123,2.176111030846786 +124,7.310276711269087 +125,1.7739237869956601 +126,5.764816393295877 +127,-1.4975073048219838 +128,-2.014539857651291 +129,-0.3774098601178155 +130,8.44545211047004 +131,-0.7207623872163307 +132,5.253241861700542 +133,5.16400340188178 +134,6.985034116145107 +135,-0.046737643405116124 +136,2.148571454841124 +137,7.102175948123378 +138,7.204583270532084 +139,5.663569194505756 +140,8.872148353493303 +141,-0.21282147534303836 +142,-3.029119694667892 +143,3.1338298515608756 +144,0.3564588212863137 +145,-1.2001218478813482 +146,3.7755526233115044 +147,6.458381603019503 +148,3.639467029572709 +149,2.320986329583138 +150,5.481320978014295 +151,4.075615349080646 +152,-0.8932332678015231 +153,-5.063882748707875 +154,8.322946818350205 +155,6.464817684140486 +156,9.934270210408512 +157,1.8919790238614298 +158,-2.605975699326787 +159,7.239918980096887 +160,-3.0929044082849777 +161,6.127777585958039 +162,2.065876729860724 +163,-3.3844358281445728 +164,3.956732032782681 +165,-5.35858918640705 +166,2.0197319669451854 +167,-0.9964737562275263 +168,-2.136010444598822 +169,5.402215304318416 +170,-7.9407401838704015 +171,5.026002216339679 +172,3.6106518116595776 +173,5.273406607522347 +174,6.038268829030087 +175,3.558262909342586 +176,2.978417510295043 +177,-3.5217553102369643 +178,1.6877880993262966 +179,0.7534071901872403 +180,8.344928934895174 +181,-4.4584802107584025 +182,4.117895671946632 +183,-3.040873694809729 +184,-5.035561884528305 +185,3.733750753380705 +186,0.453790316556387 +187,6.629656472125946 +188,-4.097183836275427 +189,-5.29788945629532 +190,-2.797652296503885 +191,0.5595813798991252 +192,5.120811143170857 +193,3.3910596278207623 +194,3.0084591911426246 +195,3.768475568946255 +196,3.096585678246755 +197,8.802797234108318 +198,8.420949015523355 +199,5.866196462327688 +200,6.761057087527178 +201,4.622407138293899 +202,4.0376869421334876 +203,-2.642952090100599 +204,5.087863517689416 +205,-3.8366385948575408 +206,3.6679506429814492 +207,6.34744673341463 +208,7.241647374276005 +209,0.3371528836815166 +210,3.5428450743395246 +211,0.28732721115970683 +212,1.9313204154421757 +213,5.067931306361231 +214,3.8111004775808555 +215,-6.822618216952494 +216,8.899332890417378 +217,2.7170559377358554 +218,6.508345665516647 +219,0.6211203768256047 +220,2.6777676089740496 +221,9.03229155238748 +222,6.284139735476087 +223,-7.411448327017139 +224,5.147593597482745 +225,-5.775637808586447 +226,7.166116796636068 +227,-2.427935528537344 +228,4.783138574987892 +229,4.248690314524849 +230,6.29386813045724 +231,8.255873623103088 +232,3.922961125961373 +233,-2.0681732436932485 +234,4.925524148962208 +235,4.767427008715394 +236,6.465374015681768 +237,5.955790822857006 +238,5.552744272229563 +239,5.636447531605678 +240,5.65525035806667 +241,2.5105856092010406 +242,0.7148648789434843 +243,-0.2738561825088329 +244,5.2374277789048795 +245,4.38584750993402 +246,8.761123049942011 +247,1.9485863733240907 +248,-0.6167895607015528 +249,-2.4178626986866605 +250,8.483695859346039 +251,-5.792002691841504 +252,3.004538141092862 +253,5.684093634219064 +254,5.495749868327033 +255,-2.6591551008106724 +256,3.8135713859208824 +257,0.12551624349025095 +258,-4.968657291398925 +259,3.47429704461828 +260,6.724215328133677 +261,-5.184018972906207 +262,4.525995011056746 +263,-0.5744159914481447 +264,-1.0549018374145844 +265,7.062729500052591 +266,7.482617442732474 +267,6.918386923088372 +268,5.680113160412952 +269,-1.5530067928992997 +270,-1.116074286596746 +271,-5.284337116993051 +272,-1.9207882685093258 +273,0.8586469126321918 +274,-2.5403398764378124 +275,4.2265868141197585 +276,-9.257914054923297 +277,6.869238982264922 +278,0.1592134475553351 +279,0.7535305709833894 +280,-1.294915842507104 +281,3.414475488128605 +282,5.813901669432234 +283,4.993787908094609 +284,4.548037241861532 +285,6.620626370185487 +286,6.7429072285035785 +287,5.598042691607996 +288,-8.990790288441579 +289,1.3170745248863005 +290,5.8839887461474 +291,4.705059322973322 +292,4.69820570692693 +293,8.121786831068535 +294,-1.2502688136887568 +295,-2.889267694303905 +296,2.680992210685313 +297,-1.1627881438236578 +298,2.615202697589787 +299,-1.7916670426233283 +300,2.969041233069632 +301,5.205201387564098 +302,6.522050688650084 +303,0.8591837238023695 +304,-9.391093069472793 +305,4.6978613737949875 +306,-4.751661360893496 +307,4.363770820172429 +308,-1.39874807031875 +309,2.953812678692835 +310,-5.975209232275665 +311,5.158259624613944 +312,4.777290706854574 +313,0.4631479145678062 +314,-1.9128509394888897 +315,-1.1921962712497238 +316,3.089670967744806 +317,0.02699107975693163 +318,2.188927880087672 +319,-8.27956595017402 +320,1.1452283452335064 +321,0.5352140871480072 +322,4.579463595194043 +323,5.267673017599565 +324,4.2656241635489165 +325,1.2743942298797242 +326,-5.060989276463313 +327,7.594472982027975 +328,6.550219135996868 +329,5.3435558716757035 +330,0.3968945002936848 +331,7.009913065102845 +332,4.937984646079172 +333,6.049978204701823 +334,-3.115953236234903 +335,7.552266534395391 +336,4.424869822387048 +337,4.722917238336361 +338,6.376263718505493 +339,2.6169699534025375 +340,7.612986378107345 +341,3.2647443447181344 +342,-0.27366029897752236 +343,4.288046268884099 +344,3.139897005894654 +345,8.304544946323459 +346,-4.808283415912383 +347,5.1177874948050786 +348,3.8416834635671213 +349,0.4073602880223295 +350,6.704318969790596 +351,4.275027308740484 +352,0.7898599298897292 +353,6.437251932081625 +354,3.6697155592239854 +355,4.905654080361202 +356,5.038597733721062 +357,-0.5511301283020695 +358,1.6913960119828486 +359,3.6673950810419065 +360,5.75073922369588 +361,4.595571831417916 +362,3.1935224952213215 +363,5.61997498889655 +364,3.755176342934689 +365,4.411445597704945 +366,9.05824501957615 +367,0.9111737475493825 +368,-5.598114353551734 +369,1.1301162603839827 +370,-7.538985587317896 +371,2.2065494113946236 +372,-1.5017404106199956 +373,-1.4955039338839249 +374,4.349055155208555 +375,0.7825981909576559 +376,-1.431625949256745 +377,5.216669948542745 +378,4.425092860179529 +379,-4.281307978760256 +380,5.029765488917892 +381,1.1648389648057873 +382,7.537700285692162 +383,3.932005065473325 +384,3.825145681056516 +385,-3.237313566424465 +386,0.5809983393365514 +387,5.339872231408968 +388,7.416198523673728 +389,4.022559313283184 +390,8.519486620238023 +391,5.30092283053434 +392,4.0177541073538725 +393,3.1389412482554704 +394,2.815867222982468 +395,0.5458158598642049 +396,-1.7762716326419443 +397,1.7446486239896237 +398,1.798247364693604 +399,-2.9645136786357247 +400,-3.5665344155561622 +401,5.912402314757928 +402,4.640695369396886 +403,-1.344721725122235 +404,2.269721327963776 +405,-4.071927760090637 +406,2.8522649574281895 +407,8.214975174745586 +408,3.599788471875398 +409,-0.9956717648465321 +410,-2.6156556514746856 +411,7.949148606034537 +412,4.9519236258067885 +413,0.9664716509052463 +414,-0.8346251955778934 +415,4.096883250112151 +416,-1.8161431904730427 +417,-6.794090749603845 +418,8.1501747729533 +419,0.43766296154546275 +420,2.9847344979667305 +421,-1.719778918149403 +422,3.0773929517750482 +423,2.6975458992927037 +424,4.734317939635958 +425,-1.0569396235380664 +426,2.890018726238895 +427,-5.17700173485538 +428,-1.3453691749742187 +429,-1.7201029064369422 +430,2.529763166226857 +431,3.0735505584751657 +432,3.996153529923779 +433,6.922841673229919 +434,0.72842237840457 +435,3.614133878264892 +436,5.187825707691079 +437,-2.287029352179871 +438,6.786053383928779 +439,-3.761561017620826 +440,4.486119992654625 +441,1.0161584706763014 +442,6.768814291286725 +443,4.000498364075099 +444,5.805817462680396 +445,5.314585687099873 +446,3.4586972957909565 +447,4.906522138899044 +448,4.061675132251863 +449,4.922056688402887 +450,-1.5092280647848357 +451,4.061752435890899 +452,6.310300727433985 +453,5.47387046335843 +454,0.6676713079126602 +455,3.9612008816111652 +456,-0.79863139244367 +457,-8.020013345906591 +458,5.0351392247303455 +459,-5.067740211037565 +460,0.889497062503446 +461,4.765510533246667 +462,4.273447986847541 +463,2.4356112826483183 +464,7.905972522937044 +465,4.615395677564295 +466,-1.9288177746359623 +467,-3.4731860031001096 +468,1.2133837579023072 +469,-6.117817381047931 +470,5.094973960736897 +471,10.99237180819912 +472,6.684812697236 +473,6.268585584414565 +474,6.772396747802102 +475,2.127223516375836 +476,7.588863527203042 +477,5.420593212471162 +478,7.212259588500878 +479,5.738706183139445 +480,-4.4367145987054775 +481,-1.3656030269940573 +482,4.880834678903672 +483,-5.330950545269139 +484,-1.9688069620480897 +485,1.3300346479813276 +486,-2.8448329791415308 +487,-1.8041525369913447 +488,-3.2075628082457173 +489,-1.4648045669483682 +490,-11.188953798371177 +491,-1.6935234579665017 +492,4.746266594032853 +493,-2.1158455791987607 +494,2.7133247952096347 +495,5.713065732818079 +496,1.4076948935449283 +497,-1.0562092563172534 +498,0.5943548704198758 +499,0.09811128775061295 +500,-0.2996545804650639 +501,5.218126447249175 +502,0.34204941686687995 +503,3.57382260089805 +504,6.624642905263954 +505,-5.546205838288771 +506,3.285223391422963 +507,-0.5994443604215076 +508,7.015622964594588 +509,0.013948665730705365 +510,0.9967524543012405 +511,4.20350465924024 +512,-5.427227012360862 +513,6.3392028726994605 +514,7.423765556421367 +515,-5.262526527965737 +516,-0.18310251817987647 +517,2.2730230843980155 +518,-2.0849772883068987 +519,7.101399774744385 +520,8.455455813094225 +521,4.672304745475431 +522,2.5266168442199555 +523,2.743603727064832 +524,5.065687105059479 +525,1.439620201133998 +526,-3.988538131158084 +527,4.732886776671404 +528,-1.843209202868243 +529,6.644367992725896 +530,0.1859759457499397 +531,7.907246553559579 +532,0.906083459698451 +533,6.030452201556409 +534,5.253046747658343 +535,4.038110062065705 +536,4.0498752269104346 +537,1.7682509743894297 +538,-4.5345832966936355 +539,3.6946230837497054 +540,4.409123894252753 +541,6.533905139623475 +542,-0.820522066193386 +543,-5.941102894401722 +544,6.259280017092523 +545,4.050528725744186 +546,0.5022360670429357 +547,1.0557825678865829 +548,7.515397430067751 +549,-1.9305326254098623 +550,4.783876142048603 +551,8.384358683399201 +552,9.225424473537583 +553,6.234923553546951 +554,5.3513297917422475 +555,8.659735825838185 +556,-4.4296925342755555 +557,7.342182158374531 +558,-2.6625859595865555 +559,6.32203054776771 +560,0.6614784013447732 +561,2.9449986475030894 +562,4.1516651701509 +563,2.7012952557801984 +564,3.6653297712149495 +565,-3.9899263630945763 +566,-5.2849526346559585 +567,-4.176321922859656 +568,-2.495095237343155 +569,3.7829464992766137 +570,2.121840631656411 +571,1.6893841807469188 +572,-1.2178609261288131 +573,2.94131549219798 +574,-1.484193781542562 +575,1.7822907979718374 +576,-4.583137987657568 +577,5.320116789997664 +578,-1.9358514757837448 +579,-4.289549868551048 +580,4.514811530766382 +581,4.674584106612034 +582,6.985707344790705 +583,4.904562196625412 +584,0.7235378761137372 +585,6.767542395694897 +586,5.563000570339259 +587,-0.7318486582159258 +588,1.9029217644144283 +589,5.258202648030712 +590,4.500394115274509 +591,5.335210720342312 +592,0.05042402722112357 +593,-2.3224966294075817 +594,7.475440966917017 +595,2.2067068318662852 +596,2.3356932259555405 +597,4.954400589201145 +598,1.0224812289684744 +599,4.822797578089545 +600,5.253890326541446 +601,2.687009993110919 +602,7.51337648845519 +603,5.988552044214598 +604,1.1190932204828057 +605,-2.2217918982586444 +606,-1.574982531597708 +607,-4.343760196910884 +608,4.398391812972506 +609,5.842768820645142 +610,6.69150506491342 +611,-12.751983877281557 +612,12.099190115157995 +613,4.250747836535061 +614,-1.2672870306105046 +615,0.6339822021809017 +616,7.7598636639339365 +617,4.029168203284867 +618,5.230520361228311 +619,2.417118812103363 +620,1.8896025030265649 +621,-1.981402429210698 +622,-2.281868215988543 +623,-1.129157615976335 +624,-4.452150799860013 +625,5.8192798165017585 +626,6.284017513624307 +627,-4.468329221988465 +628,4.165123347187532 +629,3.783267015597529 +630,-0.09374719223185742 +631,5.883895913659826 +632,5.878027192924832 +633,5.9009830595768715 +634,4.165505913683836 +635,6.369708567691868 +636,6.095444067474669 +637,3.395189224705128 +638,6.647456395634724 +639,-1.0412618892074759 +640,7.673395472786552 +641,-7.756969687209361 +642,-0.060299002021857284 +643,3.443305525557112 +644,11.251533138224294 +645,3.2443171539810023 +646,-3.6875185469833154 +647,-5.464848745738634 +648,5.392360949145045 +649,3.6374730450235218 +650,-3.94370054814615 +651,-2.3154465796846186 +652,9.078646565714834 +653,4.377164124151419 +654,3.9425237347322764 +655,-1.188073929432339 +656,4.3827674083570525 +657,3.250350473313831 +658,4.047782624458617 +659,3.9126073478047583 +660,-1.9210143967893931 +661,3.7747597249617497 +662,4.808428388142286 +663,6.5949098710628995 +664,3.2185436256136857 +665,1.268086812077221 +666,4.6260578444201546 +667,4.302454603710344 +668,6.361168642197259 +669,-1.8429176734979629 +670,-6.947572122129879 +671,6.17482970234699 +672,6.221513089279261 +673,2.611705236181417 +674,-1.5065034052984698 +675,3.255459468767283 +676,-0.7651409227358514 +677,3.611865958830779 +678,6.190449654180798 +679,0.25746907162631444 +680,2.5400917014885303 +681,3.8996325451368326 +682,5.797479019432605 +683,3.6137345545309105 +684,-0.5795293560380411 +685,4.839308163916062 +686,5.674307339278542 +687,4.3166457469456345 +688,5.659798484425597 +689,0.13519101274874232 +690,5.215236609466374 +691,0.005488985676841196 +692,2.679646129369883 +693,2.848049986049967 +694,-4.067473272835838 +695,5.8713757888801394 +696,8.215917733458614 +697,5.861399116051215 +698,4.168197808829848 +699,4.299366442935733 +700,-2.730903504882805 +701,-0.3544848298850122 +702,0.8360620996890308 +703,7.651551209406762 +704,-1.1856370413555977 +705,6.197874578680522 +706,7.720311801710795 +707,-4.884458888292519 +708,7.72659867479336 +709,6.474302765768826 +710,-0.37275370819692133 +711,5.390667966230281 +712,8.062592322884711 +713,-9.109686648333707 +714,-0.8516401569947146 +715,4.64818962954236 +716,2.388286833499949 +717,4.194568703242949 +718,2.117854273458785 +719,-1.5720120946805631 +720,-2.7978864840586133 +721,-3.9688726156851573 +722,4.138056602841328 +723,-1.4549263516773028 +724,2.1799558747223515 +725,0.2835539041492292 +726,5.707117972454939 +727,6.870874544614711 +728,3.375464587271595 +729,-8.378410670071187 +730,0.2771523773846542 +731,7.075333908075532 +732,6.010390824735483 +733,-0.198329316132904 +734,-2.51438756875298 +735,9.764471937257229 +736,0.23584979849309234 +737,-4.084286344972537 +738,3.164582527679932 +739,2.455198518538958 +740,4.880909537368695 +741,7.019165642195144 +742,-2.480377191332358 +743,2.113360441457276 +744,6.199718461675989 +745,6.1664706511276535 +746,1.7033615618278917 +747,6.893118318888453 +748,4.975956332537316 +749,7.8592339904335216 +750,4.305246025600557 +751,0.5860117761121436 +752,-4.468591514444271 +753,4.244006419113471 +754,6.7019551864698945 +755,7.849831200169331 +756,3.0671135527352016 +757,-1.4963263436061476 +758,6.9120182482897325 +759,4.285255461135551 +760,-1.9008592279366017 +761,4.702695708284344 +762,1.922992015096897 +763,3.7331278175608245 +764,-6.692365149638966 +765,7.361123256529302 +766,7.530441578623444 +767,5.330689556307798 +768,3.3019317266976103 +769,7.655691267500915 +770,5.916037022672498 +771,1.2548464689981846 +772,2.472333827263346 +773,4.278330508154717 +774,3.682214129734305 +775,3.039230570679784 +776,5.995076908308267 +777,-2.216417073910555 +778,5.500477245968256 +779,4.23774403381077 +780,-7.055265110988654 +781,5.584906533726528 +782,3.0779118651204405 +783,8.399077218181596 +784,8.195845912914363 +785,3.8883534697624462 +786,4.712967401783413 +787,5.8889782941845885 +788,1.8124136181502646 +789,12.044694570139066 +790,2.1770211265847927 +791,7.695478062470247 +792,-4.609925888877797 +793,4.081946297778044 +794,3.6492870782320663 +795,-5.83010374527988 +796,4.900107906236284 +797,3.741576252243924 +798,7.968036659738765 +799,-0.5510119624752574 +800,-4.77719285027884 +801,7.696747736647008 +802,4.838396326820585 +803,5.254388347480887 +804,4.635000622869605 +805,5.634393095626772 +806,9.322375731162873 +807,6.660136755497651 +808,7.510962585775868 +809,5.3869336912701185 +810,9.775286920092014 +811,1.362946338714292 +812,6.027529246470634 +813,-2.8538750918945754 +814,-0.15997876075201817 +815,6.286917023424439 +816,6.10972376432333 +817,3.0052009994369135 +818,7.638731286983441 +819,-5.728931906510165 +820,6.672940536603212 +821,2.304771963854399 +822,3.8606726827950313 +823,1.9893885470302002 +824,4.90352013374597 +825,-0.47311583771351157 +826,-11.736391496174873 +827,5.696873608416696 +828,-0.8801925764110566 +829,3.2689523271457963 +830,4.831099162317846 +831,3.045398633412758 +832,6.95314848244285 +833,4.603152137044944 +834,4.377704373364106 +835,4.347140858817411 +836,3.0724547159266073 +837,-1.5085204077252743 +838,6.416788410377208 +839,6.195243200914846 +840,0.01037594306566551 +841,-2.6993455157957897 +842,0.8059888536107814 +843,5.555471314656259 +844,2.6192883415845856 +845,4.12491616286953 +846,0.975149185417513 +847,2.2179650530089674 +848,1.6106548494802162 +849,6.163922186718549 +850,3.7427814207080043 +851,-1.3893393753999999 +852,-3.4743979744413567 +853,8.232164846627233 +854,6.682687916264261 +855,4.28693327322866 +856,2.4298404363779476 +857,3.6056703880793215 +858,-1.9680056482603272 +859,-1.5991728413171593 +860,-3.2937442086174094 +861,-4.003974688134747 +862,3.975343706464306 +863,-3.6112285800728263 +864,6.4794679937855 +865,8.39554730293824 +866,-0.9979455896405897 +867,8.60593720986528 +868,-3.8822042991122463 +869,-2.0092652044679653 +870,5.300734732692026 +871,-2.2834319375200893 +872,5.837440751115019 +873,7.130282772851492 +874,-3.7293357005367342 +875,-3.689089132884636 +876,-0.7364823824434233 +877,-4.043554939744139 +878,1.9305764535812282 +879,5.311465795802848 +880,-4.520906019340436 +881,6.5021491280509 +882,-7.792995605116059 +883,2.9954756017963744 +884,3.727804607423823 +885,-1.592816803130258 +886,2.9805427005732548 +887,2.1532738951800114 +888,-4.1170092536376535 +889,-1.098783628797254 +890,1.7055454583529839 +891,6.418166452269077 +892,7.014390324300995 +893,-0.9101634768608444 +894,5.228329571321052 +895,3.42696602525388 +896,2.096455130776678 +897,5.626663599943323 +898,7.909577180728602 +899,8.780746315909344 +900,5.948716487950302 +901,2.705308464444845 +902,3.9752885573955568 +903,4.662063026213083 +904,7.0217739097069565 +905,-2.8845646187112717 +906,1.5066299927261109 +907,2.582820328617825 +908,5.870776025642095 +909,-1.9789925402033535 +910,7.932276975606415 +911,5.332976528409866 +912,3.928805603788508 +913,9.397219943428087 +914,5.0678159327088155 +915,4.006614485370969 +916,5.27058864584073 +917,4.083990307654747 +918,1.3154517986105967 +919,2.052724260368489 +920,8.706416916785798 +921,4.182950883300854 +922,4.373398814028002 +923,4.7150270618164605 +924,-2.2887965231134926 +925,-1.5542173980860599 +926,-3.6464223938207816 +927,1.8917699101526169 +928,5.916304328875033 +929,7.3535362696778455 +930,5.752075822581313 +931,7.575552403911319 +932,-1.0228909122093186 +933,-2.0325091110174958 +934,5.431647170502307 +935,-0.616004783516896 +936,-5.130108031395986 +937,8.376226292186487 +938,3.909683068590927 +939,4.346035857670349 +940,1.902848008004871 +941,5.879248367126162 +942,7.708146430486294 +943,10.851486960494842 +944,6.416464145567832 +945,6.0836828620331715 +946,3.0216283345622545 +947,2.9389647451569187 +948,-6.527471554511419 +949,-1.1642128152143976 +950,4.360490234646221 +951,1.346701858829073 +952,6.468330539039387 +953,6.5210858393172755 +954,-1.8520229246719513 +955,0.4662806973167486 +956,1.7776944907894057 +957,10.72550159604181 +958,-2.821845111613743 +959,1.2109715105000207 +960,3.690721751636853 +961,-4.426222890937337 +962,-0.8524682284237788 +963,5.829150555518971 +964,1.9818256958772908 +965,7.07432288435389 +966,3.9458662684966894 +967,2.9523305599614758 +968,6.8748315061751395 +969,8.161404264159401 +970,-1.6377489475670266 +971,-3.0032221869527036 +972,5.113852893874669 +973,-1.8161293336431465 +974,7.426127764645715 +975,-0.7645108355929005 +976,8.372602732826575 +977,5.601405592902985 +978,-1.329498854431334 +979,4.852229547852224 +980,5.588000386695685 +981,-6.217332583372499 +982,-4.563844977474777 +983,7.492659609145262 +984,3.0582020956589426 +985,4.8579386968180716 +986,-4.109104595585397 +987,2.170714908599479 +988,7.918883162142323 +989,0.5621833618926394 +990,-1.9304824005271217 +991,6.382899799968543 +992,2.9639772373493316 +993,4.595262681651405 +994,1.9939292891856208 +995,11.053728942815145 +996,-0.3150162436719191 +997,3.8055450030416598 +998,-4.559624813835187 +999,3.5808841775269924 +1000,5.414832801734577 +1001,0.9135446108026483 +1002,-2.015363677134844 +1003,7.712406144698779 +1004,2.626368949739828 +1005,3.902238661077125 +1006,-8.334520425951066 +1007,-3.3651227982831036 +1008,5.515686626624187 +1009,1.079037305273118 +1010,-0.8377054956897079 +1011,-5.293064657306829 +1012,-3.382253410193929 +1013,-4.420554519226272 +1014,-6.596862288079336 +1015,-4.4169173952805725 +1016,4.1614577841529234 +1017,2.59198551155561 +1018,1.6853758092522875 +1019,6.447663808393414 +1020,-4.271869142379941 +1021,-0.4645869718993386 +1022,-3.2529456255525027 +1023,-7.139896737908488 +1024,1.721048717268041 +1025,1.755854299633899 +1026,6.527850754266421 +1027,5.352355832425711 +1028,-0.36113288822812234 +1029,-6.2269966535792785 +1030,1.0374800257010002 +1031,5.50702422776475 +1032,-2.2397827198230758 +1033,-0.8527137508574333 +1034,1.484847686720361 +1035,4.913183801948555 +1036,4.808854712966914 +1037,-5.69132311293628 +1038,3.4998649971705875 +1039,1.438860967164349 +1040,4.9983871006550835 +1041,3.887608433215239 +1042,2.60050322706167 +1043,3.3085828891484006 +1044,1.3081322910129414 +1045,-0.6680048203075905 +1046,7.775977373901799 +1047,-3.599208000353349 +1048,0.6763657469871881 +1049,3.9424328976162606 +1050,8.137031442926663 +1051,5.593958804880499 +1052,3.4905587448017377 +1053,3.495153356294174 +1054,-4.065019717707837 +1055,-1.4836452118183816 +1056,3.911226529759386 +1057,3.515062482284352 +1058,1.643803801575902 +1059,-2.559510605057584 +1060,-1.102601890965864 +1061,2.2199652845901476 +1062,5.535703112576843 +1063,-0.4568789345317169 +1064,0.7195812090055314 +1065,5.56426024823574 +1066,3.2358785392589655 +1067,-3.847444703980555 +1068,5.527737894704357 +1069,2.7636914780517023 +1070,6.893764775898196 +1071,4.742199223749693 +1072,-0.8866490313573981 +1073,2.480684247327662 +1074,6.353485201200577 +1075,7.049073395762021 +1076,1.5751210015759864 +1077,3.5524547183387805 +1078,3.9838110411737695 +1079,-0.6920713695748973 +1080,1.7076352668548136 +1081,-3.630135989926977 +1082,3.6972836192566896 +1083,5.6990672251786805 +1084,-3.515226024709693 +1085,0.7061664227215207 +1086,-6.615098762641594 +1087,6.418105559072432 +1088,10.194116123252691 +1089,5.285472868706431 +1090,5.414415913088709 +1091,-4.031314539087335 +1092,4.334756887378096 +1093,5.898723755382036 +1094,7.458861573095975 +1095,1.4204379429383371 +1096,5.09544060320438 +1097,-3.7127124374507425 +1098,5.331942738843488 +1099,4.004445669418812 +1100,0.4861260098901371 +1101,1.7407033912961163 +1102,7.1429578721752325 +1103,8.844359724898943 +1104,-1.7648106908723682 +1105,-2.347960220603505 +1106,5.998886048092684 +1107,6.273060558839261 +1108,5.29086095349352 +1109,4.78232095920575 +1110,6.160891540434236 +1111,8.010217544180199 +1112,-3.372852829275122 +1113,-1.073877779618248 +1114,7.7680334365900325 +1115,3.9653224262732634 +1116,0.7314583744167935 +1117,6.471128160444448 +1118,5.053375463684857 +1119,5.813450224951461 +1120,8.656869429584622 +1121,4.186123897184403 +1122,7.057911033040279 +1123,3.0116613386753914 +1124,4.903760268644596 +1125,4.132906120191891 +1126,4.566717210678861 +1127,6.431444213218741 +1128,1.8543612123330755 +1129,4.325896215875399 +1130,2.412361643190513 +1131,-4.063534792428525 +1132,2.6356917536394064 +1133,-3.4093717776297283 +1134,4.299693663688236 +1135,5.080988508682874 +1136,5.444092920689291 +1137,8.652802365614537 +1138,-4.518504636373969 +1139,5.3213002215351715 +1140,4.702140080646027 +1141,4.881736938919988 +1142,1.425639270498904 +1143,6.363638947970863 +1144,-0.17345536977726095 +1145,4.286961349304465 +1146,5.684919138796496 +1147,3.7488072878036744 +1148,4.2645648826772415 +1149,2.3725884638818466 +1150,-4.086661686787366 +1151,-6.5890350477361865 +1152,6.0343317708936 +1153,1.8183544408981294 +1154,1.5886909476809334 +1155,0.9168389223880486 +1156,-3.902187317705464 +1157,-5.419305832074407 +1158,4.35462274870395 +1159,2.007577533384666 +1160,2.4870494197684283 +1161,8.022574983084043 +1162,6.668276077756367 +1163,-13.581416266862608 +1164,-0.1305859620496834 +1165,-4.311720814504098 +1166,4.436669244953114 +1167,0.15029151542314842 +1168,3.144037481352518 +1169,-2.893979308529326 +1170,6.640266252616131 +1171,4.484222723634947 +1172,9.322099520604153 +1173,-5.609805070916336 +1174,8.649110019374394 +1175,4.785143712114974 +1176,-1.60961510834116 +1177,5.642455485724089 +1178,7.910576535720728 +1179,5.513741173282799 +1180,4.506893577386185 +1181,4.354800591608838 +1182,-0.4535750423960639 +1183,-8.118696671512966 +1184,1.5309428241571956 +1185,1.7077219150773677 +1186,-5.675481356494355 +1187,4.762452633949115 +1188,5.866190515302936 +1189,5.113694816832049 +1190,5.808722539528786 +1191,6.189313803559905 +1192,5.768244553082733 +1193,1.8287876587920442 +1194,3.75690274213976 +1195,4.389103290986704 +1196,3.600764971912242 +1197,7.48696842213565 +1198,3.8908333774754733 +1199,2.883206776290011 +1200,0.6957962697993465 +1201,3.691485602177213 +1202,5.950434294284686 +1203,4.099390879810792 +1204,-0.8188876873951103 +1205,3.3529837888387233 +1206,8.299276555390303 +1207,8.471654584272018 +1208,-1.0320692591986969 +1209,8.097779758312697 +1210,6.2474566217924785 +1211,6.092583924436517 +1212,4.894742733357355 +1213,2.760384796935982 +1214,6.703427783109175 +1215,-5.194204345659675 +1216,3.858683625201601 +1217,-3.638669173826469 +1218,1.53925394339951 +1219,5.984602501045281 +1220,0.13804679641445544 +1221,0.26146222396875457 +1222,-1.135465093536543 +1223,4.146795057082263 +1224,3.7783927475831884 +1225,-3.5341995788891274 +1226,6.565065147577165 +1227,6.603930874397351 +1228,4.8951463509683615 +1229,3.8776074880179756 +1230,1.8225559225998955 +1231,2.036329420772783 +1232,4.7890909820197 +1233,2.120425497557169 +1234,-3.1589846155758066 +1235,5.138833054133063 +1236,-0.4112486319353234 +1237,4.304779733780377 +1238,6.727889780116365 +1239,7.855164082877964 +1240,1.6518190335921508 +1241,2.9371398464836416 +1242,5.128512772019171 +1243,6.908479311410851 +1244,7.515826920821023 +1245,6.391013862592716 +1246,2.4450144710298436 +1247,-0.598900956526986 +1248,-4.580445308735302 +1249,-4.88729265393836 +1250,7.5412192662983895 +1251,2.7943242619186885 +1252,4.136464037718883 +1253,-0.15649845999338688 +1254,3.3163792532865837 +1255,-3.370198459061457 +1256,4.25799023509093 +1257,6.0753521830803425 +1258,-4.924463975676923 +1259,2.388963627673562 +1260,-0.8037839415647535 +1261,2.2253616172855324 +1262,5.005035753033727 +1263,1.4338153112713077 +1264,-4.184552790605382 +1265,4.540028655163089 +1266,5.850536442936796 +1267,0.30114013091413216 +1268,0.5748451906884211 +1269,6.077246399025627 +1270,4.171945237408793 +1271,4.679524135663302 +1272,0.0036943305569539695 +1273,4.65946845906404 +1274,-8.461447816522687 +1275,5.634703865818595 +1276,-0.41278679707664556 +1277,7.3462946497343005 +1278,5.452539451547604 +1279,6.87107736323457 +1280,-5.5313696460871675 +1281,-3.6651779439143644 +1282,4.550679456951688 +1283,8.930268258421096 +1284,-4.323316197487832 +1285,8.370833012406028 +1286,3.225346507170099 +1287,0.27477551660067073 +1288,2.7034318273945295 +1289,5.245467087446265 +1290,4.701269178147679 +1291,6.988924378267226 +1292,-5.891964085567006 +1293,-2.6264142505865107 +1294,4.044619022863136 +1295,-0.20767524764268308 +1296,6.434932271872307 +1297,6.214766330125344 +1298,-0.26591546376085295 +1299,0.896664286670356 +1300,2.6553045049743025 +1301,7.315450009411993 +1302,2.636522477871396 +1303,6.689398590839493 +1304,6.826242164075684 +1305,-7.785947908564047 +1306,1.2642057647582798 +1307,0.21031535063662787 +1308,4.3405100856415535 +1309,1.8926490359736474 +1310,4.857345782096694 +1311,5.4690509330240715 +1312,-2.2589046986678234 +1313,5.563117454226875 +1314,-1.4216692624291734 +1315,2.757974585180639 +1316,-5.188461905621228 +1317,-1.4386124014921637 +1318,8.737546067371873 +1319,0.18951918782042446 +1320,3.3517356113360433 +1321,6.413955955678198 +1322,1.9779986205487357 +1323,5.367257242478309 +1324,-5.800420728469791 +1325,-0.6687977760027719 +1326,-1.039528923006002 +1327,-4.410975913661917 +1328,3.0810874588780495 +1329,1.1719573228358675 +1330,3.116533133811722 +1331,6.097046385714667 +1332,5.609949229498416 +1333,-2.9263439544142122 +1334,7.9184713140842105 +1335,3.219345514974187 +1336,4.853224813617509 +1337,2.1104777931454177 +1338,5.234046901678384 +1339,1.8482613059077417 +1340,1.2683679643902181 +1341,4.443527628632924 +1342,5.68437828978002 +1343,2.4222362103384385 +1344,4.139798178755234 +1345,-2.4617456827217596 +1346,1.6336737604926013 +1347,0.8887044835275342 +1348,5.850724480846263 +1349,0.28905060709451474 +1350,5.0622901108169795 +1351,5.247208230537129 +1352,4.121608348032901 +1353,5.776986858325358 +1354,7.565469469432489 +1355,2.168537296207705 +1356,-7.7476248419969735 +1357,5.503997811650209 +1358,0.771680484861891 +1359,8.350016325237524 +1360,1.5416281733844324 +1361,5.356724346827059 +1362,5.811285517897074 +1363,5.900276690566657 +1364,-2.813542337409686 +1365,-7.672712962189642 +1366,0.11769586385419614 +1367,2.6541308597584217 +1368,-1.1632264348617827 +1369,9.518701163064069 +1370,0.07533977562971285 +1371,4.891363483964604 +1372,2.26504086691043 +1373,4.441773856934329 +1374,-4.815330565452386 +1375,6.321890612870629 +1376,4.636824366915145 +1377,4.9951956207306 +1378,3.6248704278259227 +1379,5.312616631267386 +1380,8.975099161797397 +1381,-2.509753703687308 +1382,-3.2489933882907573 +1383,-2.539679714128143 +1384,4.610613720021297 +1385,2.2743717822345233 +1386,-1.7534547062552464 +1387,3.8390330162854234 +1388,9.375872623045012 +1389,1.1017647876528947 +1390,7.007308424597349 +1391,-3.241346234308816 +1392,4.131623459550213 +1393,5.1069107469368715 +1394,4.989646643608096 +1395,-6.825734483429047 +1396,1.6108767754535176 +1397,-4.952926179996867 +1398,-0.18764275727882604 +1399,6.897180596617855 +1400,-2.5797606706428855 +1401,7.728629898186698 +1402,-2.4920940928189674 +1403,8.314627179063317 +1404,1.6409615334381782 +1405,4.580288020612876 +1406,-4.469284243685494 +1407,-4.101677526646353 +1408,6.173938382593635 +1409,8.617115406289903 +1410,-0.6636370804797027 +1411,5.077258216865364 +1412,6.712121664763431 +1413,2.2404034542386833 +1414,4.029756787563171 +1415,4.907335266830256 +1416,2.0755571488769484 +1417,3.0552937481865046 +1418,1.3467972878973415 +1419,5.849248801477379 +1420,0.29682041656238745 +1421,2.689098608211202 +1422,6.779465308889119 +1423,4.317372139913004 +1424,-5.7541351924390725 +1425,3.5873001798874684 +1426,6.539452963353801 +1427,-1.977729780459891 +1428,5.552952481021882 +1429,-3.39620061602093 +1430,2.7323913267888353 +1431,1.4469336001935176 +1432,-5.468693631214123 +1433,1.0187879532108315 +1434,0.5099708619137951 +1435,0.8774003967786528 +1436,3.1713910833070242 +1437,1.5291738021713484 +1438,4.377720961692995 +1439,2.369448177315436 +1440,9.292324810000505 +1441,4.508352998058996 +1442,-2.671790189360726 +1443,3.3643900502476836 +1444,2.3184638808219464 +1445,2.4220729823318736 +1446,1.6178267390259329 +1447,-5.180842967911908 +1448,7.203865888466106 +1449,-6.222638065362672 +1450,6.187780098875188 +1451,-2.214508789671049 +1452,-1.0906665988176747 +1453,-2.4223131268824423 +1454,-3.2648230845996973 +1455,4.0645198721643006 +1456,-4.31932730882835 +1457,-4.133705056048721 +1458,2.1703765622745936 +1459,-0.7280806913427618 +1460,5.7146505925069215 +1461,1.171324191716749 +1462,2.3314294800823507 +1463,0.6558612260712646 +1464,7.484511696637555 +1465,4.834641502501322 +1466,3.915759723700857 +1467,-4.2967183505187165 +1468,0.04983799666504525 +1469,5.986103205961594 +1470,-1.196908821730044 +1471,4.152546672587899 +1472,5.807463911307134 +1473,7.49085989438522 +1474,-0.8539372307627696 +1475,1.9569566627109687 +1476,5.95199014183499 +1477,3.242907407216278 +1478,3.5200619885605127 +1479,-6.883881119074051 +1480,2.130063343577738 +1481,4.794381245613308 +1482,4.651785466071816 +1483,4.190556721287585 +1484,5.304085597260705 +1485,-2.2104824559824636 +1486,3.6877736656685105 +1487,8.418415445298203 +1488,6.612096498721032 +1489,1.4986956054997866 +1490,1.0600322393954644 +1491,8.983286720869426 +1492,2.995936996220903 +1493,5.877081861338837 +1494,2.994092230998381 +1495,4.831820511018899 +1496,7.338943489393227 +1497,-2.00610228921618 +1498,-0.14693268640566876 +1499,7.671400661127979 +1500,3.5160896331461564 +1501,-2.8236479827928633 +1502,7.950986635063499 +1503,0.03319180581251135 +1504,0.9712044027228609 +1505,4.039771375679604 +1506,4.739526228470288 +1507,-3.4936608930650275 +1508,-0.8088003709819815 +1509,6.9403889995729315 +1510,6.862512189539172 +1511,4.838761406359567 +1512,3.8215715101402967 +1513,4.283873410960384 +1514,8.482432344879896 +1515,-2.0164175284410857 +1516,2.4452947937710143 +1517,-4.782722394866798 +1518,-1.6080240720313983 +1519,4.48092142754945 +1520,6.0338369106278575 +1521,-3.9155622151168505 +1522,3.189360390352218 +1523,-1.1819678713694244 +1524,4.163498860316532 +1525,6.124262866276184 +1526,-0.033598993207311294 +1527,2.0543457404060805 +1528,6.183564843636722 +1529,9.217495053091739 +1530,4.805716590396978 +1531,5.064254223644353 +1532,2.1911733549430563 +1533,-3.173248839129686 +1534,2.15960474318175 +1535,-2.3408197036870018 +1536,4.115467285906728 +1537,2.2710712759752973 +1538,-2.831864555592239 +1539,5.822592144077547 +1540,-2.6720152886949164 +1541,5.260717468817331 +1542,2.333095767744646 +1543,-1.722831419605003 +1544,4.261252112436609 +1545,4.116360879371562 +1546,0.9643552834705198 +1547,2.650756011006102 +1548,4.181514898894723 +1549,7.4813476361648545 +1550,-1.8681399861987096 +1551,-6.303989425982515 +1552,5.654215437917252 +1553,-1.7113638335118915 +1554,1.36504711905522 +1555,2.2342186275563893 +1556,3.9833592091723258 +1557,6.158926900678819 +1558,-0.966339958298529 +1559,1.9460305442116816 +1560,2.97039132284836 +1561,7.307166068312982 +1562,1.3274786866372703 +1563,2.194182851739237 +1564,-3.010208611967237 +1565,3.880846036850075 +1566,-2.5246824570207167 +1567,5.2537264326398105 +1568,4.949316053457516 +1569,3.405477681609063 +1570,4.840712513508348 +1571,3.372932612863023 +1572,2.7339392321610316 +1573,-0.20660709121845935 +1574,-1.5237277310750146 +1575,5.653813168651464 +1576,7.124872230861402 +1577,6.557800650863329 +1578,7.211660372468106 +1579,4.167467205430746 +1580,4.491056605245811 +1581,-6.500211334800373 +1582,-6.910744104229446 +1583,5.031916995161636 +1584,4.495771649889585 +1585,-0.30924797629544837 +1586,3.134708197067102 +1587,-3.0276391983385977 +1588,4.996948699662821 +1589,3.2012378192885635 +1590,2.6424474689747908 +1591,3.333063053316157 +1592,6.677212722426857 +1593,3.098657361149726 +1594,1.192079450538615 +1595,0.4429012489410206 +1596,4.570762591246543 +1597,-0.17632820237664104 +1598,-0.10707058445986063 +1599,-0.19509747207786793 +1600,3.343518165300612 +1601,2.032343144633984 +1602,4.953830968621776 +1603,0.8728842532831608 +1604,-0.5210635321088635 +1605,-0.7449970479965499 +1606,-4.911358888492302 +1607,-2.1027756578534293 +1608,7.252981740157488 +1609,1.036321053482211 +1610,3.628679715338235 +1611,-6.486179886290468 +1612,3.3165935040332073 +1613,-5.102135336396497 +1614,7.309672383057207 +1615,2.666353421960811 +1616,0.45696377324932086 +1617,4.975975098286707 +1618,7.442782728833879 +1619,5.63378130786372 +1620,4.7738519637382 +1621,1.1727448829619231 +1622,2.83112422956342 +1623,4.881960857388913 +1624,8.780467159172094 +1625,8.240556586542857 +1626,6.493399664659151 +1627,0.4550042258396141 +1628,-0.3479640001224183 +1629,7.5021527953815275 +1630,-2.1970916190992096 +1631,3.745854773535016 +1632,0.7637022910818015 +1633,6.978646167364903 +1634,1.8339490742796736 +1635,-5.030282316350051 +1636,3.553915689783733 +1637,2.3177223538956726 +1638,5.760612106237147 +1639,2.642706180814959 +1640,-2.1471632272270442 +1641,2.4794292202646093 +1642,3.318202689822131 +1643,-0.3115425453995449 +1644,4.455543414365252 +1645,6.345935977779044 +1646,-2.8103099483309215 +1647,4.576413564935117 +1648,4.650999222281472 +1649,-4.142923052634014 +1650,-1.7963773208970724 +1651,6.608440426174807 +1652,3.6826093439558156 +1653,0.5392712985010433 +1654,-2.2350375095908275 +1655,2.4037063391494007 +1656,0.23525262731004257 +1657,4.007782091551056 +1658,6.066062763621199 +1659,5.287669450544546 +1660,-7.071714355018255 +1661,0.7820991537024113 +1662,6.677533493135758 +1663,-5.903439460494055 +1664,0.48695762660869074 +1665,6.697872778226022 +1666,6.525673805998983 +1667,0.3389759339322088 +1668,3.2559380119313093 +1669,5.142128191396159 +1670,0.7247014704016267 +1671,4.24035709991691 +1672,4.581816843496926 +1673,1.8055937035467498 +1674,3.810078868992119 +1675,2.9652608917462873 +1676,6.258770844273297 +1677,3.2623564635351037 +1678,3.6203955333523936 +1679,7.41981549361374 +1680,5.181030500672612 +1681,3.796223283554453 +1682,-1.377652506785716 +1683,9.180173682197823 +1684,3.7554140828045206 +1685,2.3837371544580632 +1686,-0.6275766369687367 +1687,7.3266021687496945 +1688,3.8297848217368378 +1689,2.553108318079844 +1690,5.575605777067073 +1691,11.11774996467138 +1692,4.501638817888049 +1693,5.8202564223779 +1694,8.006849815831593 +1695,-3.7992349349522168 +1696,-1.3322323407161527 +1697,5.638990544866613 +1698,2.8110612295856674 +1699,7.994211713359091 +1700,4.463027512934056 +1701,4.628217999938471 +1702,9.58709792704847 +1703,5.909468627268657 +1704,6.237372769625538 +1705,5.627193264232657 +1706,5.676162037465503 +1707,-1.477789441437246 +1708,0.5523755486973436 +1709,3.9631549307451763 +1710,6.550593246884335 +1711,0.10994248187608105 +1712,0.6511041729368565 +1713,0.6694595711833455 +1714,5.841953372640671 +1715,3.4844272054143106 +1716,6.625760482498584 +1717,1.5067709125898423 +1718,5.393816414214575 +1719,2.414776306163034 +1720,7.1837149418478905 +1721,-4.071810527614349 +1722,9.380334138457554 +1723,4.375707640389877 +1724,8.52612326341806 +1725,5.813726329034468 +1726,-7.450602499793526 +1727,0.32663309436805377 +1728,5.6707983078299815 +1729,4.40053649911641 +1730,1.1816506392441894 +1731,4.684319266648326 +1732,7.898375088613109 +1733,8.790931169602628 +1734,-1.0823848580290139 +1735,3.4408086882472184 +1736,3.9562065693557615 +1737,-9.300532904171774 +1738,6.285203894011059 +1739,6.287893211143522 +1740,8.60351122637962 +1741,0.4930747558132857 +1742,7.92971976269087 +1743,5.635485454793379 +1744,4.2507493674989085 +1745,3.3964704385705233 +1746,2.2987080441218644 +1747,3.4893479622771055 +1748,3.9569307545112054 +1749,-4.211432747371924 +1750,2.7011932530155884 +1751,2.6983377038165695 +1752,-3.170797288812414 +1753,-2.7746397634820847 +1754,7.109164352141986 +1755,7.446023996820563 +1756,1.9466809498282214 +1757,4.90368369906024 +1758,5.182264787857909 +1759,3.989728881461545 +1760,0.02282777905920188 +1761,2.452526969792216 +1762,6.590552541879592 +1763,-5.290614322189467 +1764,4.278970007715574 +1765,4.06738059065073 +1766,6.037190930578543 +1767,5.097162821119969 +1768,-4.3125868436186074 +1769,-12.511651829919051 +1770,5.076821670013793 +1771,4.638015675963 +1772,0.13816925176189143 +1773,0.5870615065073664 +1774,-3.9704204125556917 +1775,-2.669518302328014 +1776,4.964819904328773 +1777,4.1728053558040505 +1778,1.571710534798433 +1779,-1.5800458404775994 +1780,2.080436604300848 +1781,-2.5877912710161866 +1782,4.860151933595585 +1783,5.335138570889264 +1784,5.654912923652004 +1785,3.0055492630502347 +1786,-1.1052697839211554 +1787,2.0602169272194795 +1788,6.355126705257514 +1789,8.395019293677562 +1790,7.000501520129335 +1791,5.579984708344195 +1792,3.389322329487416 +1793,-2.2458430798881235 +1794,5.667555393462939 +1795,7.017807250517411 +1796,2.668820656942412 +1797,-0.5659433533875907 +1798,3.3951985376696294 +1799,9.351117132818572 +1800,3.8590301636612767 +1801,-3.0538670710540523 +1802,6.425038953514802 +1803,3.812306656969176 +1804,-1.3331900616868544 +1805,8.352753277850066 +1806,4.163284009369756 +1807,-4.770034006438676 +1808,7.664924141992101 +1809,-1.5522592025146857 +1810,7.566957841553449 +1811,-0.5309595853001908 +1812,-2.553775227682591 +1813,2.3836541236869753 +1814,6.569217437711386 +1815,9.484157669611358 +1816,7.030670555223427 +1817,4.908192951942921 +1818,4.863982790562629 +1819,8.457965392775913 +1820,-4.853669547294866 +1821,4.657077604102501 +1822,-4.042828015173064 +1823,7.97960220492201 +1824,-8.206316017502786 +1825,4.158793809368439 +1826,2.869313230724694 +1827,4.846672025170333 +1828,3.199318375307205 +1829,5.271926870375753 +1830,1.5076219613920077 +1831,2.594496755097506 +1832,5.4560323721922925 +1833,-4.757553354622118 +1834,3.172695852216487 +1835,3.9105451587933975 +1836,-1.908389468847864 +1837,-0.3848027951263598 +1838,-1.872281836331938 +1839,3.964432931315008 +1840,1.9651577817642345 +1841,4.228786446206263 +1842,5.404100752622587 +1843,1.1687379292503945 +1844,-1.333747643780019 +1845,0.8423168723949298 +1846,1.6699013242492269 +1847,5.5781544601947255 +1848,7.48589893107617 +1849,4.4374120879603876 +1850,0.2261950486754856 +1851,10.127757690371322 +1852,5.4689097765018255 +1853,4.566808027774289 +1854,-2.6452661932282147 +1855,1.9205585027808914 +1856,6.797633485056792 +1857,-0.25665943097927696 +1858,5.916088144319707 +1859,2.3184130579781685 +1860,-3.6319028370858013 +1861,10.029698607055728 +1862,4.743300675320475 +1863,-2.505182142240774 +1864,3.4831243750999534 +1865,4.76072914263245 +1866,4.487973235556317 +1867,4.496527766451058 +1868,-1.8832436267569954 +1869,7.6356595815679045 +1870,3.557467100950999 +1871,3.632596698818088 +1872,0.2822887461709143 +1873,4.202690668017714 +1874,1.2202112143768338 +1875,0.7412036223641943 +1876,-2.425754276112048 +1877,2.421916592213661 +1878,3.511650209835845 +1879,4.175714423006704 +1880,6.0882029567144915 +1881,-2.682121360942635 +1882,2.542145444197761 +1883,-0.09167472186279708 +1884,2.202993325544979 +1885,5.551824514659548 +1886,6.049004233069969 +1887,5.955729951412383 +1888,5.921758986073602 +1889,5.507405997497051 +1890,3.521451726700425 +1891,1.45073492336317 +1892,4.2303160117818 +1893,1.0816336623504272 +1894,-5.376618456596508 +1895,1.988711329471645 +1896,-1.4109745246268617 +1897,5.745728807418877 +1898,7.284237175409476 +1899,2.3252052555576115 +1900,2.826345153005884 +1901,5.63458533619359 +1902,6.758831029813351 +1903,4.757585151926715 +1904,2.331549159421548 +1905,4.085929679178303 +1906,4.8318987007992344 +1907,6.040739693140087 +1908,-0.6346910069914508 +1909,4.886228365017568 +1910,-1.6547292529116073 +1911,4.251973362183344 +1912,2.4593895982662133 +1913,7.108527700318344 +1914,1.8308968674330224 +1915,7.768584770174739 +1916,0.7002576421635915 +1917,4.346766360636073 +1918,0.6790108068764436 +1919,-6.760152998955748 +1920,3.9839127033760047 +1921,2.0533643217169697 +1922,4.390170638027542 +1923,-0.24537094925722214 +1924,7.461521683475331 +1925,4.879254938456621 +1926,6.414049624579878 +1927,-4.038316847592861 +1928,5.460679927620518 +1929,-1.7922408571596524 +1930,5.979536703162847 +1931,3.931576896142232 +1932,-4.35274346981215 +1933,5.973943798431593 +1934,4.013421968992268 +1935,2.0338757925991495 +1936,4.637281602590999 +1937,8.059277488112585 +1938,1.8715565738992073 +1939,6.389030245137313 +1940,-1.9788873041673722 +1941,7.232675231459948 +1942,6.588099500723524 +1943,4.763862222889316 +1944,6.915615620929355 +1945,-1.8641933880821588 +1946,-6.404392807433875 +1947,-2.213871900941364 +1948,4.254473029659541 +1949,4.770258329821157 +1950,6.451404200752251 +1951,-3.1618089540814864 +1952,-6.83074261614983 +1953,-1.6563321274297091 +1954,-2.796026436027149 +1955,-4.663354283565308 +1956,0.31417220922037237 +1957,4.976391326363267 +1958,4.442959876771991 +1959,4.0515604484003624 +1960,-6.8461413501797095 +1961,5.104088091650218 +1962,5.67531543598 +1963,3.678073474259133 +1964,4.465517389158089 +1965,0.852029999794361 +1966,-4.872805650866616 +1967,4.1607828578491155 +1968,-3.5499983085025173 +1969,1.2652026266219232 +1970,1.754784823772888 +1971,5.8173970773529495 +1972,6.233549089988273 +1973,-0.5420845099530782 +1974,-0.5228423716171446 +1975,-4.352261139217063 +1976,1.5266190713605194 +1977,-7.667861210350159 +1978,-5.111444959468385 +1979,4.632464790664216 +1980,-1.0882238205065908 +1981,-4.408105841978501 +1982,-8.545285973623644 +1983,3.1844207208418522 +1984,1.6390624384489745 +1985,-3.1109625473283917 +1986,-0.5865255988064724 +1987,4.423089868337878 +1988,8.137247523991407 +1989,3.8165392654006984 +1990,7.303407732972177 +1991,-4.215963182365922 +1992,4.553598832292182 +1993,-3.6980932824507473 +1994,4.596882494384471 +1995,4.631806924721708 +1996,4.421967333873264 +1997,-6.2124988695878764 +1998,6.879997187163699 +1999,3.302457565390095 +2000,2.3838476414804046 +2001,5.934800353768829 +2002,1.737419523934388 +2003,9.011189995385589 +2004,2.862551527188769 +2005,3.394733663511087 +2006,5.4554060499056565 +2007,-1.2164659884243996 +2008,2.6428890039938624 +2009,5.461222803737254 +2010,2.41961534667118 +2011,2.290523028640117 +2012,-9.15594329128699 +2013,6.387912896914077 +2014,1.7983326157874413 +2015,4.166490596239327 +2016,4.808366455476401 +2017,1.4423141776739672 +2018,-5.621580065126527 +2019,-6.120115690059437 +2020,4.198772558979363 +2021,0.7578640966172234 +2022,6.095491084087563 +2023,2.9268467781959218 +2024,-11.925543433501774 +2025,-4.068270350670563 +2026,6.9512092017992435 +2027,-0.31716816493478384 +2028,-1.9677342253728138 +2029,2.192104281536395 +2030,6.14285447217439 +2031,1.5485519974534845 +2032,7.014820410624396 +2033,3.084703985151249 +2034,2.7437681231759776 +2035,2.8936226409828887 +2036,4.348748395718055 +2037,1.8027573919208324 +2038,0.7035680288295441 +2039,6.390911183787432 +2040,4.68377733728687 +2041,4.405669052268987 +2042,4.57042231217415 +2043,-5.781581867014252 +2044,2.450220271132671 +2045,3.371142311268621 +2046,5.060543115547405 +2047,5.041606012114107 +2048,4.283819529670995 +2049,-0.3051391134296135 +2050,2.8629770181904655 +2051,-3.7298293200035646 +2052,1.6372773971528036 +2053,3.415425917764344 +2054,4.625888281743101 +2055,-10.50159664642867 +2056,5.968866185336991 +2057,3.08476942338715 +2058,7.0972670603916725 +2059,3.5056291751257316 +2060,3.187234065978009 +2061,3.137079770305319 +2062,5.737185917842739 +2063,-8.23969117743359 +2064,1.8494511273249803 +2065,3.1859076649598554 +2066,3.5404021151696705 +2067,6.763066933372327 +2068,3.4951744185759166 +2069,5.544509183810285 +2070,-6.953500939071413 +2071,7.676569138139827 +2072,3.9125325268368645 +2073,5.556014734374537 +2074,5.946861520995243 +2075,5.855219782852248 +2076,-0.12468550515143888 +2077,0.9140296016126852 +2078,2.058735737932589 +2079,-0.49985066104201875 +2080,-4.947575374331079 +2081,-1.2068647891571238 +2082,3.322839609718652 +2083,4.025275091951224 +2084,0.07681745956907658 +2085,5.180957826396244 +2086,2.1764752558788967 +2087,5.056396162504989 +2088,5.790874144824131 +2089,1.9220598039944976 +2090,3.7883129802146103 +2091,3.208849209673001 +2092,8.792081677321478 +2093,5.329820814819031 +2094,-3.334173090131421 +2095,-0.893985754859081 +2096,3.7810095173561553 +2097,-3.6822137398540504 +2098,1.1632334703212162 +2099,4.830031223145606 +2100,9.292148609515632 +2101,6.071000627691623 +2102,-0.6349710625425224 +2103,5.448254844339366 +2104,6.780987585470294 +2105,1.9879094663575518 +2106,4.683457966858145 +2107,4.669960872149055 +2108,-3.948915835792244 +2109,-0.05049639035833438 +2110,3.043957939039988 +2111,3.760427718923723 +2112,2.8624456667757494 +2113,8.005945851828324 +2114,0.44502256470984025 +2115,5.9928555108638015 +2116,7.104100759523806 +2117,5.202516798057143 +2118,2.7625301969261575 +2119,-1.9133523767912917 +2120,-2.3293588477285265 +2121,0.5397524071533661 +2122,-5.640402902743821 +2123,5.336884541891873 +2124,3.5407696345680337 +2125,8.155809818746308 +2126,-1.5136969589904599 +2127,3.8323094311089716 +2128,1.5287101979139697 +2129,6.857152402250614 +2130,-1.8116862670271046 +2131,9.564261588110893 +2132,4.942324413631052 +2133,5.719957236628672 +2134,3.7409488195624467 +2135,6.9881868589774 +2136,-6.410415074673943 +2137,1.7963616092863173 +2138,-7.168067285104524 +2139,6.1112447006262745 +2140,-2.5057198790366755 +2141,5.784880560990447 +2142,3.268457478442488 +2143,4.813038516324998 +2144,4.516478469229184 +2145,0.9708582447099751 +2146,-2.732520662160366 +2147,-1.7976113849030362 +2148,-1.9976670229858364 +2149,5.1454085775162755 +2150,5.867542272514061 +2151,3.663833446594471 +2152,6.15401639077678 +2153,4.266085580072933 +2154,-3.4359401915215866 +2155,6.931550925756614 +2156,2.1858530135538223 +2157,-1.5645114813254788 +2158,3.887184186426528 +2159,4.4775117677317855 +2160,3.7570473147611745 +2161,9.140268321304596 +2162,3.568370364802489 +2163,1.4902334652658011 +2164,3.9791206655097784 +2165,0.9164438435943285 +2166,4.026737102163235 +2167,6.292146903142224 +2168,-6.951291203180509 +2169,5.674565012474665 +2170,5.476393931558573 +2171,-0.5979108486014346 +2172,5.78952912186533 +2173,3.1217910136978095 +2174,8.565975802980091 +2175,-2.972952487318901 +2176,4.393091223850749 +2177,1.3129482609912273 +2178,6.973302781345295 +2179,-1.8598851000885985 +2180,4.025788913365286 +2181,-2.146828994301917 +2182,-2.3679537249525193 +2183,6.006052095892234 +2184,1.8022451381770797 +2185,-1.2263257338590112 +2186,9.120580805612605 +2187,-0.9551259225650137 +2188,4.184317205053007 +2189,0.6508491788872164 +2190,3.163794215475028 +2191,-3.7602180912475194 +2192,5.207295945055029 +2193,3.4476531106819572 +2194,6.037518981399472 +2195,4.229152676078189 +2196,3.54996534905772 +2197,2.689064586324733 +2198,5.136175997328509 +2199,7.219818844338805 +2200,2.805217823588597 +2201,0.4163888972616569 +2202,2.9212642946799128 +2203,-5.349503493079187 +2204,-0.01741799689331392 +2205,7.158779108340484 +2206,-1.3917766616474223 +2207,7.1386910082074415 +2208,-1.1247068258835073 +2209,0.3199414886161325 +2210,6.356791531052423 +2211,10.279830093070446 +2212,3.9740759465585636 +2213,-1.4216273013846659 +2214,-1.2048097924147807 +2215,-2.245803603884939 +2216,-3.2131969799421287 +2217,5.807491920676171 +2218,1.333534496757495 +2219,6.481129814200159 +2220,-8.33841429600427 +2221,8.184234020650239 +2222,6.725884303778807 +2223,1.8258532227770148 +2224,-3.518024308197035 +2225,-1.1638335170989929 +2226,2.590849425360317 +2227,2.8211943168596916 +2228,5.806567214479399 +2229,2.975040325788275 +2230,5.101508865813907 +2231,-1.4160817345317733 +2232,2.290818727950931 +2233,2.549332890771166 +2234,0.23744494871831484 +2235,5.461982455861151 +2236,2.4763911216887573 +2237,-0.09216320592727328 +2238,-1.305812835113853 +2239,7.55877794857145 +2240,4.964865126944986 +2241,-4.054764017518147 +2242,-0.8924990776492214 +2243,5.6530701139842 +2244,-2.1628919489692247 +2245,-3.266739459318655 +2246,-2.9836356339517978 +2247,-4.919368764248724 +2248,2.660878143363426 +2249,2.7618433962469866 +2250,8.049691026046323 +2251,0.5417527513830025 +2252,4.170516776761887 +2253,7.696219410735682 +2254,6.034280510600736 +2255,-4.630327774699216 +2256,2.032164037353001 +2257,-7.299104515892516 +2258,7.1364601652954365 +2259,4.715755532684168 +2260,4.1071780325848115 +2261,5.3815101826457665 +2262,7.87052991463891 +2263,5.8054855942968375 +2264,4.78519911584521 +2265,3.8268192375754557 +2266,-1.3327618554659386 +2267,4.462133681806259 +2268,-2.8929613866852177 +2269,2.6511138520055475 +2270,1.6669728501950225 +2271,5.615575551142705 +2272,3.629931594100741 +2273,7.26919447810057 +2274,-4.8070419644796685 +2275,2.689845215293584 +2276,-3.3343461740823237 +2277,1.7352961255121782 +2278,4.962604458178321 +2279,7.531190774533357 +2280,-1.6583199014243002 +2281,6.967069095054654 +2282,3.617319266742123 +2283,0.9888371568133636 +2284,4.6848027943538595 +2285,2.464641790391042 +2286,4.193614814776595 +2287,-2.640998098214213 +2288,5.0449974654207965 +2289,0.4737395073778421 +2290,9.230785840753244 +2291,-0.40488998998429865 +2292,4.478744963507854 +2293,1.6470166098037893 +2294,4.338961865484339 +2295,2.586958925691813 +2296,4.034964767264102 +2297,8.442039402984172 +2298,5.29567024493631 +2299,2.264672667473531 +2300,-0.2756791110905441 +2301,5.105949566093361 +2302,-1.9674006470491405 +2303,2.1877380617581643 +2304,1.935141997189922 +2305,3.5572650471269625 +2306,5.940026304738 +2307,5.589652234323482 +2308,-0.2515369460482199 +2309,6.167833334189937 +2310,3.953084515551697 +2311,3.521211767167505 +2312,9.968329676974228 +2313,6.064449034032597 +2314,5.116348269818814 +2315,3.850833005233462 +2316,0.8506026872906065 +2317,4.257698657254112 +2318,1.8059513498831494 +2319,4.464448155280856 +2320,3.7233092344141268 +2321,1.8815406150754244 +2322,6.610351711512625 +2323,1.811830659140972 +2324,5.261907251622256 +2325,-2.8413276369333893 +2326,3.1798307002473933 +2327,3.958739580803706 +2328,5.204275842269705 +2329,3.426937510114644 +2330,-5.190665524021619 +2331,3.776758282066183 +2332,8.47139018029889 +2333,2.15376028094485 +2334,4.728197576716088 +2335,6.782007154962017 +2336,-1.710450906792574 +2337,3.558811678133596 +2338,5.170570228875574 +2339,5.325305904335442 +2340,-8.577904282843672 +2341,4.386396117354438 +2342,6.457627491530692 +2343,2.5667619208883448 +2344,7.350441950794635 +2345,1.6888069151615648 +2346,6.5880062367032295 +2347,3.8516204152632096 +2348,-3.0282355304440958 +2349,2.1639058610287756 +2350,0.5853880000258819 +2351,2.1531205238906193 +2352,1.813437309821019 +2353,4.11390068968503 +2354,2.0834699894162063 +2355,3.223960489245083 +2356,-1.848072077002161 +2357,6.922464730439272 +2358,-1.8818531898211832 +2359,7.274097892562639 +2360,1.843464643493852 +2361,-4.072843988940476 +2362,0.6991439228155365 +2363,5.362573991940451 +2364,0.08116250442622733 +2365,4.031267471406211 +2366,2.493298586116052 +2367,-2.0968785632722975 +2368,-1.6565381585311942 +2369,2.3078351500605816 +2370,5.8223676986715605 +2371,7.020231725294918 +2372,-0.3145250108681717 +2373,0.1793398064162747 +2374,7.68406790987941 +2375,-4.737168801298016 +2376,0.4770463085343606 +2377,4.29696497742177 +2378,0.7403238684647889 +2379,-3.8862229473727545 +2380,5.495553208066025 +2381,1.0491756802548562 +2382,2.1888410073436257 +2383,6.225470388882103 +2384,3.543938914319031 +2385,3.4317738005020653 +2386,7.003021452116933 +2387,7.258000109558559 +2388,4.647110396152762 +2389,-7.485943678065109 +2390,2.518469550110288 +2391,-6.517176437467804 +2392,-0.16124634206100985 +2393,-0.335787728988608 +2394,8.729365038949284 +2395,-3.898093865849102 +2396,3.3421934483563347 +2397,-0.9262236558483644 +2398,3.1123103091187896 +2399,3.0738014983597086 +2400,6.037859845094641 +2401,4.585791138523463 +2402,-3.1468042793918896 +2403,3.0581846286922962 +2404,3.55663462236089 +2405,3.6015718524814986 +2406,1.7328325023403703 +2407,-1.835178656234765 +2408,-1.6426813667577913 +2409,-7.235242813186912 +2410,4.536724872905263 +2411,1.5688551859673727 +2412,7.3208909433075195 +2413,-3.3176638384730355 +2414,4.205437992684078 +2415,5.755698457020155 +2416,4.103832855268209 +2417,3.3974921250000536 +2418,-5.125236065979318 +2419,5.708418881554653 +2420,5.365045719707885 +2421,1.7128084303001565 +2422,-2.949763984366234 +2423,3.179464348331 +2424,3.6478387901088314 +2425,3.9175336734443382 +2426,1.209266064410892 +2427,5.803875815062927 +2428,5.312488222734625 +2429,-2.9267697765612573 +2430,8.064271831639703 +2431,5.445192812297957 +2432,3.7670726690220824 +2433,4.74946686682945 +2434,3.7458383384473426 +2435,6.289113257528558 +2436,1.9740258787797313 +2437,4.7577941325139905 +2438,8.600604317593152 +2439,9.11930709622413 +2440,0.982987658117275 +2441,-2.472173571034547 +2442,-4.7380533883406555 +2443,-2.3341343953768043 +2444,1.5475204242497003 +2445,-8.311153948625659 +2446,4.020687479949246 +2447,3.4086486591716882 +2448,-0.988413017770404 +2449,9.720370862683488 +2450,5.474399383111333 +2451,3.682747855581741 +2452,6.562210905938311 +2453,5.147104859063212 +2454,4.026741423611375 +2455,-2.327887430361799 +2456,5.64024730926703 +2457,0.9219774959573936 +2458,3.222480492462726 +2459,-1.0774276717022042 +2460,-4.829116444671064 +2461,5.0622190705088865 +2462,-2.17971253909899 +2463,-4.099755388007667 +2464,0.8083007650769136 +2465,-2.5678332984517374 +2466,0.6029436842123097 +2467,1.8454108769664468 +2468,6.121968133958113 +2469,2.93196546319838 +2470,-1.4575981424720186 +2471,0.806965709443592 +2472,8.823257856200913 +2473,1.5541927376229712 +2474,-5.560534893143031 +2475,-0.5160688191318624 +2476,0.4152539282506096 +2477,8.823860569142816 +2478,2.5785159737522036 +2479,3.3035801619873943 +2480,-2.6065471473372166 +2481,3.2338772529334943 +2482,0.47149243194036305 +2483,4.072402993729162 +2484,4.917269832860378 +2485,1.9142858439739334 +2486,5.0999327004720705 +2487,6.426758439543793 +2488,-0.5283780399636502 +2489,4.130335751205789 +2490,-0.0033814264377237013 +2491,-0.1540747301366835 +2492,3.594684544706843 +2493,5.217227605343498 +2494,7.557838355751947 +2495,-1.7634504916580154 +2496,1.3122033051183482 +2497,-2.8029632319453834 +2498,-1.6105418768825408 +2499,-4.257886942123852 +2500,1.123177792921466 +2501,0.24203891824334636 +2502,3.7461474366066057 +2503,7.513557365119135 +2504,1.2802373528538287 +2505,3.138389847420496 +2506,6.079442469814428 +2507,5.913239373973133 +2508,4.1446059119597845 +2509,4.350719300312689 +2510,-0.8388019195153542 +2511,3.1105975578549523 +2512,2.8594629024720963 +2513,5.397794983308599 +2514,1.4630587117320666 +2515,5.58849565174578 +2516,7.753367033018332 +2517,10.288419598718363 +2518,7.526220632684517 +2519,0.1942190604375382 +2520,2.689301217593294 +2521,7.155919437612588 +2522,-9.105834546914137 +2523,1.9455098591496163 +2524,0.030803365457061787 +2525,4.608890995811614 +2526,2.6465797451030753 +2527,3.004738855552924 +2528,4.174953475699791 +2529,6.641458743562293 +2530,3.5172832713208 +2531,-1.1007754771608167 +2532,0.5742651311079365 +2533,1.9185353397940141 +2534,2.6002095802975074 +2535,2.841422908043897 +2536,4.096083269978757 +2537,4.991193126063482 +2538,1.9434105403494628 +2539,-2.394021071973998 +2540,0.9197792990734919 +2541,-6.23747288219533 +2542,4.302405107076133 +2543,5.30735109903281 +2544,-2.6150657058165767 +2545,4.60945096690532 +2546,-7.369764301852484 +2547,6.861035838635786 +2548,5.134312119523401 +2549,4.49802903350502 +2550,8.401072452590103 +2551,-0.12805892273699587 +2552,-1.2841881590520576 +2553,-2.6164825911306786 +2554,1.0158597533721399 +2555,5.504824202442908 +2556,5.2021596567495285 +2557,-3.1337886926756444 +2558,2.6064920090083175 +2559,3.967759467004436 +2560,2.937974478108114 +2561,2.7829843646246215 +2562,-2.78662168588814 +2563,1.066751829065026 +2564,4.430879851426388 +2565,5.588270053186567 +2566,3.8412282751161793 +2567,2.6637723644044597 +2568,5.483622545426772 +2569,-4.27005283105389 +2570,-3.4806757716833254 +2571,-3.172987131189435 +2572,-2.211742701077308 +2573,4.549965373235333 +2574,1.7884912815308782 +2575,-3.340368976266025 +2576,5.081882610836099 +2577,1.1671692909428737 +2578,5.256177562315251 +2579,1.3884102272033212 +2580,6.099534803853813 +2581,6.887228982626052 +2582,6.071115879138983 +2583,5.8795391781944515 +2584,-0.9210168420260322 +2585,5.789307292998563 +2586,3.7244819394400865 +2587,3.8170472511175877 +2588,5.313784335605022 +2589,5.258588728842057 +2590,5.557316825653832 +2591,4.480757166955673 +2592,5.823852731329932 +2593,1.9101108322320544 +2594,0.6233178549753152 +2595,5.263093471711592 +2596,0.23799444096899747 +2597,3.6008601975215524 +2598,-2.4232843941898308 +2599,4.633608811131614 +2600,5.599448619809463 +2601,-8.407428827093142 +2602,2.8937732637187263 +2603,0.0002477456684461414 +2604,4.814752147763833 +2605,1.914382765526455 +2606,8.404698621515498 +2607,3.4946298412054304 +2608,6.155226820545445 +2609,4.978045529716339 +2610,2.9435184664203105 +2611,-0.0996550313318847 +2612,-2.0452832133450984 +2613,5.4876952725191765 +2614,7.010380331973319 +2615,5.364862820075215 +2616,0.2190559906680124 +2617,-3.087443627011298 +2618,-1.1704328695479254 +2619,2.9111167809980536 +2620,-5.082131434357062 +2621,5.014121071137224 +2622,3.304201594588218 +2623,0.6669371907616953 +2624,6.306424684269553 +2625,1.7494414931591975 +2626,5.490201117046903 +2627,7.781622153828513 +2628,6.711122721858421 +2629,6.347015278343646 +2630,1.9006438120467188 +2631,-0.9072557039112202 +2632,4.557846199866051 +2633,6.0605629199771816 +2634,2.660780571262749 +2635,1.4392376617346954 +2636,-0.5716425879632813 +2637,-4.97680246463315 +2638,-3.642362435038099 +2639,6.24655904627442 +2640,5.313946325471783 +2641,-5.842097061648124 +2642,-0.9297028834048695 +2643,7.75710988822849 +2644,-2.7752224330806152 +2645,-0.35943364868641137 +2646,3.4158057828657036 +2647,-1.764458147533291 +2648,3.1114763087188404 +2649,1.405457248683908 +2650,3.184854086746541 +2651,-0.42047157880333774 +2652,4.692392155544087 +2653,5.254594269470754 +2654,-2.8862256122779133 +2655,-1.287953029944584 +2656,3.4908195215135347 +2657,2.5592685856135953 +2658,5.609572798959902 +2659,0.09861282667222676 +2660,0.1130366441215237 +2661,-0.243503909528084 +2662,-2.234618837527453 +2663,8.498468784663384 +2664,6.487479335965041 +2665,2.421194405260175 +2666,5.850699999180569 +2667,1.3683617879273626 +2668,-3.488805870210143 +2669,-0.2740029230000789 +2670,0.8468700316871712 +2671,0.6891496322087168 +2672,-3.912212856853909 +2673,7.7978664387718855 +2674,7.0325718825651276 +2675,4.895621105667689 +2676,3.0880777671580653 +2677,-1.9558780254302162 +2678,4.968603965418006 +2679,1.354003190871098 +2680,7.034692291200907 +2681,4.203497293040566 +2682,-2.362798528460427 +2683,1.0815182096326996 +2684,0.5089010112628348 +2685,5.654212581808647 +2686,6.253541954120832 +2687,-0.036514942638785186 +2688,0.8518566890089908 +2689,5.3027502790444005 +2690,0.5763921802739277 +2691,2.779010363041776 +2692,2.161809257062384 +2693,-1.77859072264198 +2694,7.167401137208214 +2695,0.4958082630625816 +2696,6.067149501990615 +2697,8.330872540785943 +2698,-4.109170815760753 +2699,-4.731832232363897 +2700,-7.342307823916548 +2701,8.74900980888254 +2702,1.3054007815953932 +2703,7.090720531951295 +2704,3.8690131822189757 +2705,5.436705428815933 +2706,5.124158546749295 +2707,5.384435422411182 +2708,5.339991723875409 +2709,6.498818964389841 +2710,2.4598459763537743 +2711,5.5653076220791595 +2712,3.131463650072142 +2713,-3.816464085555678 +2714,-0.24294959237690655 +2715,2.1871134966466035 +2716,3.5244535398223378 +2717,3.403222907409159 +2718,4.3198021837528255 +2719,0.6030687116486071 +2720,4.612243685982832 +2721,4.851577709192668 +2722,3.0362025555409597 +2723,-0.960693817261778 +2724,-1.8312559999363516 +2725,4.945684275829485 +2726,6.228643009759511 +2727,2.077333095971436 +2728,-4.404328406981736 +2729,9.112439969322953 +2730,2.992812772304387 +2731,3.2523333016079174 +2732,2.1937345837409876 +2733,7.4306961904149835 +2734,-0.019817289789155607 +2735,7.836920376101772 +2736,3.736462580999946 +2737,4.65016106498464 +2738,4.643585193754248 +2739,4.022060247428234 +2740,3.265471261402215 +2741,6.255806076116678 +2742,0.7167319452377287 +2743,7.468632036373743 +2744,2.419637369754422 +2745,2.0113206890585493 +2746,8.392277012196528 +2747,5.924952789525633 +2748,2.7225166773338354 +2749,-0.1896790483233046 +2750,5.230081325536689 +2751,2.931692814612565 +2752,-4.428939736165018 +2753,-0.7016990528424715 +2754,7.12607860988367 +2755,4.0754532367061485 +2756,-1.636558162105671 +2757,-1.0034208097842965 +2758,4.883773251060262 +2759,1.1766766106532893 +2760,4.400241578255971 +2761,-5.617140845086543 +2762,4.355967872141696 +2763,3.0291432632065245 +2764,-1.5903467090529713 +2765,4.3301107051105685 +2766,7.477216291220334 +2767,7.268533498909665 +2768,1.4019826479325304 +2769,-5.212943514739233 +2770,-0.6163953305635685 +2771,3.742365721856589 +2772,-5.912595123823642 +2773,7.053216693144803 +2774,2.271088055303815 +2775,4.477534155416625 +2776,0.5898491056023021 +2777,-5.82575549701791 +2778,-4.654141084251662 +2779,1.393721674218734 +2780,3.8933902189222818 +2781,5.53714594662511 +2782,2.896406410560674 +2783,-3.19953304868826 +2784,2.194873720356474 +2785,-1.3266677861820781 +2786,3.342635445088916 +2787,5.114034189374115 +2788,8.008608320704129 +2789,3.2808869962542477 +2790,0.21603410206124168 +2791,1.8370132431760973 +2792,4.512732085994971 +2793,4.901208401526307 +2794,0.32253570983169144 +2795,2.6559995788272484 +2796,6.854436754014692 +2797,7.550236012373417 +2798,5.523926381183106 +2799,-0.8370945363803968 +2800,4.797086333362316 +2801,4.678291735564238 +2802,-1.319994647522579 +2803,9.37131714710241 +2804,-2.514748603761485 +2805,2.2946879686829122 +2806,6.938048743348923 +2807,6.980728717279231 +2808,5.89008608953734 +2809,-5.944574590615882 +2810,4.577562734291074 +2811,5.995938010650141 +2812,7.49518930213441 +2813,-0.5374604094202482 +2814,-4.054163595782699 +2815,4.721222963684977 +2816,3.546299150703329 +2817,-0.06886720546452203 +2818,-1.2189340137600748 +2819,-3.6132049118163434 +2820,3.140851797493453 +2821,-6.982649490303432 +2822,7.252572333844309 +2823,4.571116329589266 +2824,1.7225701139885958 +2825,-4.015587515936037 +2826,-2.1375758864697403 +2827,2.8865625013496183 +2828,6.61001708235228 +2829,-2.528768638266213 +2830,5.15732266722997 +2831,0.3147490242932682 +2832,5.561917481128408 +2833,0.7049847816102278 +2834,9.408923093229665 +2835,1.9383605286669445 +2836,2.246006247928661 +2837,8.507220419652294 +2838,6.8736665155292185 +2839,8.236423493119045 +2840,-8.291289613394069 +2841,1.5761638631263817 +2842,5.9518853696155265 +2843,-5.101603195832645 +2844,6.291291228217003 +2845,7.6206695111977405 +2846,7.4067384314780105 +2847,8.586453450817608 +2848,1.9225907599410144 +2849,0.6172470469618102 +2850,-2.6867082736970134 +2851,3.9537036333704174 +2852,1.0186226951370863 +2853,8.38184889912894 +2854,4.624469671858907 +2855,-2.7525904788473934 +2856,2.424004875313987 +2857,6.510716231487347 +2858,5.988479413931266 +2859,6.805448791761711 +2860,2.359658032246853 +2861,-0.3248841030574559 +2862,-0.8735000359998901 +2863,6.119235136302944 +2864,-2.915180067208313 +2865,1.2622383904577779 +2866,-3.645797155758732 +2867,1.8568324730651302 +2868,5.118528740344176 +2869,4.723369220135606 +2870,5.480103767846564 +2871,4.601101809936872 +2872,1.8656955527801835 +2873,7.303580001825166 +2874,-5.253206128059618 +2875,3.313603201077525 +2876,9.116003062362669 +2877,4.27542029461336 +2878,6.7642424714489655 +2879,1.2336868145810853 +2880,2.8544698861003646 +2881,0.488279249354153 +2882,5.619010891739597 +2883,-1.0337204034540182 +2884,4.712605011118266 +2885,3.530080293298037 +2886,5.520769393848353 +2887,1.1921325771816305 +2888,6.54190823582236 +2889,-3.133847272223258 +2890,3.3467861091143982 +2891,-1.2829256474559818 +2892,6.662215577717376 +2893,6.605538681078331 +2894,8.568860433811901 +2895,5.597018650017483 +2896,2.3178743177639656 +2897,0.8738789012203234 +2898,-3.4105633579307297 +2899,4.5697604480512455 +2900,6.221417520572441 +2901,0.551172603819152 +2902,6.003975336555499 +2903,6.746310573710782 +2904,5.093291348485834 +2905,-2.976972436314386 +2906,4.098994709195875 +2907,-3.945813344160859 +2908,5.562917214719786 +2909,-0.20565497480589612 +2910,-1.274278475528292 +2911,0.8117891398982331 +2912,4.53251169160528 +2913,3.874211135517715 +2914,0.4672731572986845 +2915,3.9928091691236967 +2916,-2.5561322230385772 +2917,7.917642784992784 +2918,6.5591074371196925 +2919,5.2385621101393465 +2920,4.984616262754963 +2921,3.6408832317286244 +2922,-5.3115629784911755 +2923,-0.1995036268593181 +2924,0.6890583282078345 +2925,-4.270556202663576 +2926,4.1087889776122 +2927,0.42149044739041813 +2928,2.5364969485512114 +2929,2.4853431493425724 +2930,3.939408627952628 +2931,-2.955638603238302 +2932,6.287982807228082 +2933,-2.6734391522158805 +2934,7.180171072116989 +2935,3.09159292640907 +2936,0.5029806073848265 +2937,6.752268153297325 +2938,5.218951998360743 +2939,3.611048115099288 +2940,4.524359092121965 +2941,-7.0684843483823485 +2942,4.830783275986673 +2943,7.02379102818118 +2944,4.67025658884085 +2945,2.180124509007439 +2946,4.218806167814726 +2947,1.9861356082131998 +2948,4.458702941382748 +2949,-0.20781682159779225 +2950,0.18135787091844474 +2951,4.026580568174911 +2952,-3.935851581939808 +2953,3.044260830510167 +2954,2.101894639865502 +2955,4.844688984524076 +2956,6.567720314988654 +2957,-6.514118354291116 +2958,-5.13534735665267 +2959,7.839592194641092 +2960,-0.9103648831985508 +2961,1.1904751884333094 +2962,3.864614047535193 +2963,3.366159165513043 +2964,-3.1807671739743313 +2965,1.957123717653638 +2966,2.755435588394127 +2967,-2.2324640568470233 +2968,8.189068916061766 +2969,6.714226884999235 +2970,5.206811887126534 +2971,-2.6777446005837735 +2972,10.14039269625792 +2973,8.286675840312515 +2974,0.7757677498819057 +2975,7.896348174230796 +2976,5.3501629187861 +2977,5.186814960451769 +2978,-3.8427363274003716 +2979,5.062512195792714 +2980,-0.5211327768784609 +2981,8.28735170610705 +2982,3.3065106018654253 +2983,7.014601658879426 +2984,-0.3437918037091787 +2985,5.385727197510992 +2986,-0.36526796358678476 +2987,5.199672313869944 +2988,0.32273725575142553 +2989,-0.497859916341718 +2990,4.639003605381146 +2991,7.348079826322643 +2992,3.6230408338172673 +2993,8.088538460088044 +2994,5.777525280577659 +2995,1.6650342583782711 +2996,0.2280413015786444 +2997,-3.6137751769741215 +2998,5.435015281073731 +2999,6.006414872657955 +3000,6.2566730045275945 +3001,-0.3995850489268598 +3002,4.001988237396469 +3003,2.703250987632293 +3004,1.724373216020127 +3005,0.5319446661030767 +3006,-5.271835549913084 +3007,-2.522764136515233 +3008,3.1014331268461786 +3009,-1.3884556887221795 +3010,1.3137313507025232 +3011,-6.929220513448409 +3012,8.008298926981814 +3013,5.706125267745429 +3014,1.3927386215443955 +3015,7.309782987449502 +3016,5.718491924596098 +3017,3.232748651168704 +3018,3.060731041471372 +3019,-3.936895445268196 +3020,2.239056399407549 +3021,-1.7816735114758084 +3022,7.6442829387671285 +3023,6.024207568932712 +3024,3.805217713150295 +3025,8.865524207398234 +3026,-1.1176165322459217 +3027,5.701983165711134 +3028,8.615942547249606 +3029,5.454809291709837 +3030,6.928051961997254 +3031,0.1523993390690965 +3032,3.944831702360227 +3033,-1.9903096893368897 +3034,6.187261465613036 +3035,8.845404586668886 +3036,0.7595431291693666 +3037,-2.990407688608089 +3038,2.6142205995191494 +3039,3.757727917212311 +3040,5.533005046369195 +3041,4.5480044232229435 +3042,-1.1619229083277614 +3043,-1.951315511429441 +3044,-0.23638963759635012 +3045,-8.172576360622587 +3046,6.099640119195278 +3047,-0.9492604727163885 +3048,5.399252783841867 +3049,-0.5374569188420939 +3050,4.573402138051307 +3051,8.992050213037048 +3052,4.314241832193872 +3053,2.643013418151115 +3054,-5.236684086155077 +3055,5.5542033318440325 +3056,8.610333157014978 +3057,-0.35675004326232124 +3058,5.104332209363783 +3059,5.2693164366442256 +3060,3.6046242408763867 +3061,2.117356693474986 +3062,6.5448090759594635 +3063,5.476994230039066 +3064,-3.4777513004740466 +3065,1.6891591090215654 +3066,0.9454840392646632 +3067,1.792846114596606 +3068,-0.8159175081973857 +3069,1.4983299082256945 +3070,3.1387127383614195 +3071,6.146835578914884 +3072,4.823168233767564 +3073,2.180610425313213 +3074,5.528677397595352 +3075,4.458662294562279 +3076,2.9044681405425763 +3077,-8.470608227659504 +3078,3.566637650486669 +3079,1.9132674499607982 +3080,4.444712386054924 +3081,0.13275446646950156 +3082,4.720954385427904 +3083,1.610321264383816 +3084,1.7704722965971982 +3085,3.167820806042438 +3086,0.6913375509154456 +3087,-4.0389456919397215 +3088,1.7124915447357099 +3089,-1.8645436469392167 +3090,2.0203117047411983 +3091,-3.9274742963195086 +3092,5.048139301369626 +3093,-2.8331069389403076 +3094,5.866842538188148 +3095,-3.313032148965207 +3096,0.9915445319999837 +3097,1.064883706995239 +3098,5.429431407870813 +3099,8.45513127393409 +3100,2.458152765297171 +3101,-1.3286117052489592 +3102,3.966168991017634 +3103,5.265535041087739 +3104,3.6406486380820997 +3105,-11.137719989160558 +3106,0.8509164752673728 +3107,-0.388986572921593 +3108,3.909360060864293 +3109,-0.2234940149887511 +3110,6.524231210306171 +3111,0.36181952669450806 +3112,4.485885918615059 +3113,5.538071489010603 +3114,-9.488362550305396 +3115,3.3507647870974164 +3116,5.704175169584834 +3117,7.316172521723507 +3118,6.445231635285284 +3119,0.2926977272084408 +3120,0.9503831550865811 +3121,-8.571470224036556 +3122,-2.0612842654373176 +3123,2.8103363097246383 +3124,3.699131067220553 +3125,5.957566157528537 +3126,2.4125714039592876 +3127,4.525327560687374 +3128,-0.08339976245338807 +3129,1.6887564352590572 +3130,-3.300755096059724 +3131,4.370898657056392 +3132,6.181161279913234 +3133,3.759666358708492 +3134,-1.9452427934067502 +3135,-0.06210910018689581 +3136,2.8822187610224037 +3137,1.034532373388704 +3138,5.019880603343746 +3139,1.0218870024410294 +3140,1.715182590790685 +3141,5.082297726868938 +3142,2.719325353175307 +3143,2.7524452109456763 +3144,7.050148271710953 +3145,-6.046398258756216 +3146,3.142295298082473 +3147,7.076221945572501 +3148,5.636832621027757 +3149,6.945014713635752 +3150,2.887659662042809 +3151,7.0386455622868835 +3152,0.5810353945498283 +3153,1.7137320664689575 +3154,4.581006541727902 +3155,3.0548117690324554 +3156,5.2785650189045645 +3157,-1.2099440982119951 +3158,2.1691258590254154 +3159,1.4686075493815087 +3160,4.897006049864474 +3161,5.408920054398877 +3162,2.9768402544424672 +3163,-2.276336417848642 +3164,4.913337296661249 +3165,4.632314288418843 +3166,2.91253691984674 +3167,1.002235234689354 +3168,-0.5932833079532767 +3169,7.96819448983026 +3170,-1.1350146259922567 +3171,1.1234751634871258 +3172,4.884892682626126 +3173,9.18658498966731 +3174,4.32814458996013 +3175,7.155369927789797 +3176,4.935883820180865 +3177,3.0536351287259182 +3178,-2.0622015749209135 +3179,4.687781005948511 +3180,7.2178077424835365 +3181,1.5330706903505342 +3182,-1.1234499254087873 +3183,7.102303816491286 +3184,8.735895347679046 +3185,-1.2130991507158049 +3186,2.192435294530225 +3187,5.62292380136211 +3188,4.093161459122647 +3189,9.367924833385732 +3190,5.490395287619276 +3191,-0.9464221685116114 +3192,-1.7111976095684918 +3193,0.7447459310846275 +3194,-7.005737555518859 +3195,-4.235631903443941 +3196,-3.771593468406315 +3197,4.427170666727854 +3198,-0.1372779691764512 +3199,5.345086100260354 +3200,5.113287236075775 +3201,5.337811430230684 +3202,1.4328895713018162 +3203,5.205004807501198 +3204,7.783750851727565 +3205,2.232913553953719 +3206,3.7395855266043037 +3207,5.604165496611523 +3208,7.013810908330526 +3209,-1.8656663000948377 +3210,5.258610082669211 +3211,5.35391903894243 +3212,2.7647761726207154 +3213,-1.9758086040898568 +3214,7.009781693120017 +3215,-7.36123216972188 +3216,4.094221401810315 +3217,0.5674170804636468 +3218,5.3756722396900125 +3219,10.472562462203662 +3220,-1.4935968840086824 +3221,-7.7724911677755655 +3222,0.44743075498356194 +3223,3.2165825074197234 +3224,5.049092481782235 +3225,7.184080421608245 +3226,-5.369810885290306 +3227,2.8290454223025834 +3228,2.8118516346761826 +3229,1.6812044752577853 +3230,1.0967628935588114 +3231,7.382226053532332 +3232,5.821476516070235 +3233,3.53323861605804 +3234,4.107072171658713 +3235,-9.308925558148879 +3236,4.427299106527943 +3237,1.6819543930163339 +3238,7.044236119707923 +3239,2.455844423874394 +3240,-3.7953860163219835 +3241,4.323976642231904 +3242,3.1125819120913096 +3243,-1.4289159239112854 +3244,2.213415022997795 +3245,1.743651911941536 +3246,-0.7098513716272395 +3247,-7.992193048006794 +3248,4.230803246419918 +3249,6.9398341090948685 +3250,5.821965432097028 +3251,5.732523236433492 +3252,5.262583639487503 +3253,3.496864169745625 +3254,2.5562827736274665 +3255,8.465193065715559 +3256,3.5837000172517994 +3257,-2.662044399015308 +3258,-1.84786386710504 +3259,0.9286871047639167 +3260,3.9474427803574166 +3261,4.237692544388515 +3262,5.643994246002525 +3263,3.747801493135284 +3264,6.7143536566964706 +3265,2.9501214675143252 +3266,8.967605889058804 +3267,4.2458697173716375 +3268,2.6010713174352884 +3269,4.629638506481081 +3270,-3.453039568675478 +3271,0.9409079649744955 +3272,4.540450138454961 +3273,3.9078421166761474 +3274,0.5365462897045916 +3275,4.531842795796751 +3276,3.984876676045692 +3277,6.767164278569283 +3278,2.816624169174892 +3279,3.5888057576404817 +3280,3.9381108877783424 +3281,1.8719919262387263 +3282,4.6412491838700785 +3283,4.1404781518961995 +3284,5.718971345202158 +3285,-0.35876903733526866 +3286,-4.672477582045317 +3287,-2.2984229869850274 +3288,-1.3921947977918094 +3289,6.433123761802289 +3290,9.899489859402987 +3291,3.3038704653665905 +3292,-5.567599282325775 +3293,1.7167127770211958 +3294,5.165145353991933 +3295,3.3069130024785673 +3296,3.11668742907099 +3297,-1.9036155132681278 +3298,6.380767975914548 +3299,-8.246064964349891 +3300,-2.1479130210148107 +3301,-0.2510184681277474 +3302,-5.230417987504522 +3303,3.9062791942238007 +3304,5.498718751358423 +3305,5.603646232894717 +3306,7.907826874057187 +3307,2.287700235654414 +3308,8.03198844427079 +3309,1.0677551314558855 +3310,4.553248518575074 +3311,1.3852733392322938 +3312,-0.6326145120086814 +3313,6.612054521679646 +3314,6.120126162671243 +3315,9.435752575778118 +3316,-2.0486076584213357 +3317,4.775133989980032 +3318,3.2462261415394105 +3319,-2.9090556014886664 +3320,-5.733740052921391 +3321,3.0419183020196146 +3322,0.27823854594714204 +3323,5.644051676206339 +3324,-7.768719007351993 +3325,4.957384710891229 +3326,0.4638221113518277 +3327,6.55498643051919 +3328,0.5723962597172434 +3329,-9.302355730951259 +3330,1.759543425046794 +3331,6.1335492793654325 +3332,6.505663879715243 +3333,5.8372376528881835 +3334,6.895103386083315 +3335,2.627608745845908 +3336,3.2266995722473233 +3337,7.3935876463216825 +3338,3.5558115590520836 +3339,3.937261318941322 +3340,-4.9589023051896355 +3341,-8.092386197268679 +3342,2.9754413818507373 +3343,4.5681885037124355 +3344,4.059477361284004 +3345,7.095271700493168 +3346,6.401423116430395 +3347,0.8512152019029591 +3348,-0.6503977277993199 +3349,6.131029863917519 +3350,2.5903948280043343 +3351,-0.29851164364787364 +3352,5.644599754531306 +3353,-0.5994864695110351 +3354,3.9344654628827325 +3355,0.6003811015840794 +3356,1.8106533276784895 +3357,-10.167591477153989 +3358,0.9861270271047483 +3359,-0.8221765043107108 +3360,5.614169539158767 +3361,-4.710640352072619 +3362,-0.4188034977155766 +3363,-0.06103992252487167 +3364,4.970778921256699 +3365,5.7270619784573364 +3366,8.594220788635809 +3367,4.279531985003229 +3368,3.5632661270633332 +3369,4.390110240234773 +3370,-1.3249461557739106 +3371,-4.113980004235646 +3372,-0.827531061911837 +3373,8.140479172271633 +3374,4.805646092825754 +3375,5.594723512048692 +3376,-8.122075480676651 +3377,5.023815226422954 +3378,4.316773162448428 +3379,4.428726400160746 +3380,4.561829076621591 +3381,5.3391369052369155 +3382,-0.1524936415635819 +3383,7.9797191357033235 +3384,0.9904473532440081 +3385,5.975525413801769 +3386,3.509867800888167 +3387,3.4749453305692453 +3388,5.736517605648584 +3389,-4.628250741254846 +3390,-4.082835418554305 +3391,1.402623468316495 +3392,3.1058687224730344 +3393,6.705514880942543 +3394,-5.91259258070241 +3395,4.848393742241569 +3396,8.952236610465192 +3397,0.4244399442734881 +3398,5.409683422520979 +3399,-0.26667300037162595 +3400,4.531000958098637 +3401,-8.496156343909956 +3402,5.275606653461861 +3403,2.922677483845263 +3404,-1.1264484048892134 +3405,-0.3909225639147974 +3406,-10.333455903043154 +3407,2.5579151978907206 +3408,3.584225986450045 +3409,3.7516755016608423 +3410,6.800034024132633 +3411,4.276404335564255 +3412,-6.910107580590706 +3413,3.3933819053711947 +3414,7.644992548706288 +3415,3.9038982982222588 +3416,0.13062350160495712 +3417,-8.738170912856447 +3418,7.195279127328775 +3419,1.4251512621679225 +3420,3.17055755529673 +3421,-2.6768259795210394 +3422,-5.593145555572158 +3423,6.326213449254265 +3424,3.0221476793104265 +3425,5.569647243692858 +3426,7.918592918735206 +3427,5.521335501470097 +3428,4.050707238188927 +3429,1.7914643695961776 +3430,6.672793056250377 +3431,3.6519859509270978 +3432,5.799958453411498 +3433,5.931693216167563 +3434,4.032688117492661 +3435,2.61639889243776 +3436,-1.2733999902281727 +3437,5.448832405712712 +3438,1.5937919890796006 +3439,-1.6211753265392679 +3440,10.778983845660214 +3441,-4.420709913130815 +3442,3.7967523834650936 +3443,1.9158804222987091 +3444,-0.6106428014103259 +3445,6.6263110594466506 +3446,3.341890566808343 +3447,5.6626799707642785 +3448,-1.3574797432392884 +3449,4.41242247961784 +3450,3.3239521785225867 +3451,3.744933425478383 +3452,2.571721675063996 +3453,3.797183773931102 +3454,-4.553412831039574 +3455,4.350241431002125 +3456,1.2139496015105045 +3457,0.4509570807972304 +3458,4.156102226993671 +3459,5.441344563756853 +3460,1.3253499579992334 +3461,4.3230253562648295 +3462,4.702750882999953 +3463,-2.227777105503838 +3464,4.6981583540539384 +3465,6.807964403560311 +3466,5.755961395991805 +3467,3.773786799572625 +3468,-1.2422504227097253 +3469,3.6043553878669217 +3470,5.158305363986611 +3471,4.983840722280293 +3472,1.0549770454796157 +3473,4.181490143660709 +3474,6.0194763688694 +3475,2.0319395870063244 +3476,4.8222392401147065 +3477,5.2639555809673855 +3478,-6.374539480124131 +3479,6.673564431925241 +3480,6.114496068739367 +3481,0.07439371680733381 +3482,6.088278513921762 +3483,1.10890381656797 +3484,7.357665092614829 +3485,1.2277662551805082 +3486,3.795695598385491 +3487,-3.8299407433338994 +3488,-6.902426720276944 +3489,4.513833732780464 +3490,0.27037451947441477 +3491,6.3017672288485755 +3492,7.972582772680821 +3493,4.68456301033197 +3494,-0.14133738248738897 +3495,4.824924511884256 +3496,-1.6281182376878147 +3497,5.491567477419956 +3498,-0.4988184231882848 +3499,-0.5798279933822644 +3500,4.058960615759652 +3501,0.8537644436598972 +3502,7.903524986319084 +3503,-7.518661601126605 +3504,6.138416866097203 +3505,2.6608580311171774 +3506,-3.3294390569758425 +3507,2.8336858855896128 +3508,5.429501248696946 +3509,-0.9875512249902346 +3510,5.173676037931418 +3511,6.125877617505976 +3512,-1.2355866945490137 +3513,3.5833802444908045 +3514,3.036730504330742 +3515,5.566074917651115 +3516,5.211495811254541 +3517,3.7703089026030074 +3518,0.7888445409906281 +3519,6.008239509727881 +3520,3.8306848087946186 +3521,-3.646753326580677 +3522,5.566071514200737 +3523,-2.3220330927070614 +3524,5.9385895323160085 +3525,0.28261470735214084 +3526,5.278728538857885 +3527,7.7147119151042505 +3528,4.445870779041565 +3529,3.8663400493083158 +3530,-2.2467193329938993 +3531,-5.137832679000832 +3532,0.8387789042088377 +3533,0.1234599732278092 +3534,5.071031141146216 +3535,5.200677125910106 +3536,-1.4475749795684842 +3537,5.0073989908981575 +3538,0.7263475358806765 +3539,7.985461450631465 +3540,-0.9537629891965286 +3541,5.43738315381532 +3542,8.265898824169865 +3543,3.5446015763946592 +3544,6.568241941181504 +3545,4.984683182019338 +3546,-3.054770753136549 +3547,-7.608582127645075 +3548,3.3171684398383197 +3549,5.294913917925596 +3550,5.222437467012003 +3551,-1.1621171788992644 +3552,5.76466294227535 +3553,5.557420434356556 +3554,6.4125529452310905 +3555,3.2106484376808764 +3556,0.007113238384559623 +3557,3.3056045924212727 +3558,-6.009427766059843 +3559,6.616983632638316 +3560,3.198894959309585 +3561,3.4979791668885936 +3562,1.7468770865649994 +3563,2.5308498865791074 +3564,-1.3596030189535766 +3565,0.008748076528212911 +3566,-1.4996458651898756 +3567,-2.7405487830316275 +3568,-0.12732446536851885 +3569,5.555064028984133 +3570,-2.307400994313744 +3571,2.7081170508966075 +3572,1.466796175486844 +3573,4.802163123667523 +3574,4.997745097621954 +3575,4.291861499828582 +3576,-3.2096632051897003 +3577,4.199883645314004 +3578,-6.421009486932599 +3579,-1.9246725021832896 +3580,5.829544713925407 +3581,2.018166799404288 +3582,4.669168563730535 +3583,6.302446201754849 +3584,2.4339455040362767 +3585,8.201838427632895 +3586,-0.05507456803614175 +3587,5.671736853488129 +3588,0.5089733545773675 +3589,-2.3635266048564576 +3590,7.41539165239719 +3591,-2.464103954447874 +3592,7.272197560819142 +3593,5.7721199277347095 +3594,3.972848511551873 +3595,-11.540214806698625 +3596,-2.4834685143543243 +3597,6.106369700701265 +3598,6.740278317548239 +3599,4.329455955132821 +3600,5.6683989469863345 +3601,4.340435522017229 +3602,1.6085685058874004 +3603,6.350938727549173 +3604,1.831129216901585 +3605,4.869205685211868 +3606,4.0557428878262645 +3607,-2.9026665876193234 +3608,5.067220897396312 +3609,5.617075216533811 +3610,6.397922106366596 +3611,-3.0675780075702024 +3612,5.276425172381462 +3613,5.147446163526397 +3614,-1.6680361835029565 +3615,6.064746152734372 +3616,2.565586565054918 +3617,9.076114293380709 +3618,4.714360927597272 +3619,7.024222423505064 +3620,4.621301569542594 +3621,7.010377448370415 +3622,3.707102491860962 +3623,4.678604384113972 +3624,1.7854685800351366 +3625,0.797721108056549 +3626,0.05525566013845573 +3627,3.470492567769286 +3628,1.3646772748252405 +3629,4.548573437185859 +3630,4.919195771061901 +3631,4.815105344582393 +3632,3.7223594639915927 +3633,-4.539962249865884 +3634,7.157724290465149 +3635,3.2985414999623694 +3636,8.20444355946542 +3637,4.459939548005801 +3638,-5.572829386929818 +3639,3.2879202297880825 +3640,-5.915143296617711 +3641,0.8301448514998678 +3642,3.8162160943179346 +3643,6.132802909148158 +3644,1.3500594004005544 +3645,0.6778013480818835 +3646,2.65385644213388 +3647,3.6814338656953045 +3648,-2.398218982598905 +3649,-3.1525155655996455 +3650,0.1354462831054629 +3651,-1.233174202027659 +3652,11.178505879819813 +3653,-3.3015438660855834 +3654,4.113197671504874 +3655,6.764605372857156 +3656,5.214439489829465 +3657,7.594195023634855 +3658,5.781193715700605 +3659,-0.6739580824840813 +3660,6.8403490948566565 +3661,-6.377699334346324 +3662,2.482158857509185 +3663,-1.3099247784908452 +3664,3.6316724308631594 +3665,3.346362890517991 +3666,9.3793418313617 +3667,5.946870172450201 +3668,5.586135878897426 +3669,3.543380814837348 +3670,2.568110431253348 +3671,-0.3322282098414508 +3672,5.313139358023825 +3673,0.3188746333214601 +3674,7.170426884717089 +3675,3.609324764802947 +3676,3.8397615088832886 +3677,4.774883523159862 +3678,5.02857557996738 +3679,5.4086596096925685 +3680,-6.3005858193050575 +3681,4.3173444484916255 +3682,-0.33187243144579537 +3683,-3.544433102449146 +3684,0.4923337706887419 +3685,5.750302545774469 +3686,7.822977421664039 +3687,2.1444650136729275 +3688,1.3400334499963065 +3689,4.720707380540865 +3690,5.341211881647823 +3691,-1.6842507506317923 +3692,-4.304506902399834 +3693,5.718336127365226 +3694,-5.3766645631100545 +3695,4.5321977616018465 +3696,-0.40768004624660226 +3697,-5.33596259918425 +3698,0.09131625580477498 +3699,-5.4696493414808005 +3700,3.2766096414280628 +3701,0.5502414181707642 +3702,4.481287436938458 +3703,5.956698339192172 +3704,6.871587568871598 +3705,0.21827072030435568 +3706,-3.474863929964134 +3707,-3.4310271266643477 +3708,0.36423183491805833 +3709,4.276603544176314 +3710,2.916646981594268 +3711,5.34006023789478 +3712,4.067010350968992 +3713,-3.3226468936961693 +3714,0.6591187349372429 +3715,-0.9154603414463196 +3716,5.318287815644922 +3717,7.111531737058275 +3718,-0.8383965134548814 +3719,0.6258489266142063 +3720,2.579158545873463 +3721,3.355703031493404 +3722,3.416003238488806 +3723,5.782109953746712 +3724,1.2673277109224772 +3725,3.264217605322531 +3726,7.028181584872318 +3727,2.6305613246903214 +3728,4.013410892777718 +3729,3.459117361003564 +3730,-5.464873694186454 +3731,-1.755041876585305 +3732,4.716724964570102 +3733,8.90814408766925 +3734,2.779106957604079 +3735,3.6858109655137565 +3736,4.9064222283614765 +3737,-3.195948731739494 +3738,3.967621963464764 +3739,-4.297228274945994 +3740,5.699249334758685 +3741,4.5332302372392315 +3742,0.3918306540816244 +3743,4.603071830041534 +3744,8.106672628060593 +3745,4.514472085426336 +3746,3.806089672337122 +3747,5.196792630365548 +3748,5.459633077092706 +3749,3.551408924092467 +3750,5.808919262046395 +3751,3.9330922817170992 +3752,-4.08191047288409 +3753,3.621790354659696 +3754,-7.806633335422003 +3755,1.9204064102100051 +3756,3.1886255323774826 +3757,9.460660388295725 +3758,6.222648584031315 +3759,5.687971638014658 +3760,5.151054992824413 +3761,1.0762919159021531 +3762,-5.635347960663625 +3763,8.299028418645086 +3764,3.8609299803854267 +3765,4.831553734407099 +3766,-3.8262702566782583 +3767,3.350494404577071 +3768,-5.869041060516688 +3769,4.355475011100628 +3770,0.8842694937111755 +3771,-1.1541890917039361 +3772,-1.5743955999221593 +3773,2.984853471479171 +3774,8.758724954661698 +3775,2.757214375610562 +3776,-7.124969553977912 +3777,3.717645513040048 +3778,4.120911130976771 +3779,-3.629220612364385 +3780,3.257248070448154 +3781,8.122544872112123 +3782,5.321629997866693 +3783,8.353432529174817 +3784,0.9788897792974306 +3785,2.349495581001414 +3786,4.919423598510929 +3787,0.27241061421748725 +3788,5.021567537816224 +3789,3.3590899412323925 +3790,0.17943535237596678 +3791,3.2944700061986714 +3792,-6.695931195741568 +3793,4.161974939392294 +3794,5.139952123686177 +3795,4.7760857917937125 +3796,-2.852977093498036 +3797,5.720118491336192 +3798,8.646566473937286 +3799,2.6281957034530845 +3800,7.155393454566221 +3801,-5.309368928609153 +3802,-1.929665769859313 +3803,6.4361387910998955 +3804,2.2469753370933114 +3805,9.335242419608896 +3806,-3.529014131059062 +3807,-8.177029184289628 +3808,0.11236586966259803 +3809,7.596199681644004 +3810,-3.3602442714313563 +3811,9.31725842307052 +3812,3.012783522432776 +3813,6.583198125247717 +3814,6.749035002537029 +3815,8.182623177554735 +3816,2.6270918686947398 +3817,4.74236496895549 +3818,-2.643040673691499 +3819,7.293412926113774 +3820,5.099923193832186 +3821,-1.4378197567805695 +3822,7.7929493351761066 +3823,5.101927667277352 +3824,-1.5903102957492805 +3825,-2.6480645973831365 +3826,3.5247640116170698 +3827,3.4848150215643416 +3828,-1.8600081033201221 +3829,7.087853107816567 +3830,-8.242517604721249 +3831,4.761773601281225 +3832,5.919357521717765 +3833,3.0436250113750702 +3834,0.8370939167647273 +3835,3.4593554022725423 +3836,4.334950549926355 +3837,6.230561760333986 +3838,-1.059566298255465 +3839,2.979095874950969 +3840,3.9809119450869255 +3841,9.936043758092923 +3842,-2.628957509730392 +3843,7.850524400716445 +3844,-6.991454086048193 +3845,6.304138504675894 +3846,3.00153819529678 +3847,1.9592812603664462 +3848,4.773010363544987 +3849,5.779154740757141 +3850,5.114940540883284 +3851,-6.951153143390786 +3852,2.0298936112050407 +3853,0.07279807011775521 +3854,-4.631584326477051 +3855,-0.4657573470678222 +3856,5.840854441808063 +3857,2.5400862554343937 +3858,4.295402487617507 +3859,-2.176897490699923 +3860,6.550836765880033 +3861,0.7065605072169487 +3862,5.639060437558621 +3863,2.561884965162496 +3864,4.026826837628201 +3865,8.831850357264486 +3866,3.860900486963552 +3867,6.661488399850638 +3868,-2.7226174759234225 +3869,6.4127511473623295 +3870,-2.9689499370708017 +3871,0.9289776573901933 +3872,4.556108054587724 +3873,5.990076725629726 +3874,5.2001458122592235 +3875,1.314461016846783 +3876,0.08223263776225724 +3877,1.6104921598229778 +3878,4.155147204677695 +3879,8.088138184296437 +3880,0.6813581638741459 +3881,-4.9564217382721605 +3882,-9.496057644458272 +3883,7.975347195689535 +3884,-3.0005482264009324 +3885,7.00152385022912 +3886,-2.019044087374487 +3887,-5.6580216985629495 +3888,1.523674538770806 +3889,3.656380555304618 +3890,3.002385992226934 +3891,5.15596106478353 +3892,3.6576847215571267 +3893,3.5653803023714126 +3894,5.7292731226946785 +3895,8.619652842976453 +3896,4.187933802836586 +3897,4.703295723280938 +3898,4.670297725778724 +3899,-4.62710297922953 +3900,5.312266671109616 +3901,-1.6937740863629025 +3902,-3.3162744303396483 +3903,4.534294065584814 +3904,5.201349817251212 +3905,1.6396625931682371 +3906,4.924862008211685 +3907,3.379431247979513 +3908,7.824039061979821 +3909,5.414577405211131 +3910,6.334460582646321 +3911,1.8460851163774539 +3912,5.687072036014255 +3913,-0.5335315950472974 +3914,6.00354532066013 +3915,-1.6450721083645552 +3916,-3.0726796884517316 +3917,-2.934699613268698 +3918,-3.566265816449654 +3919,5.37436827378824 +3920,5.705678126694264 +3921,7.700645531252732 +3922,-0.7491410382932816 +3923,6.968366212386812 +3924,7.222871220689164 +3925,-2.3638826915005238 +3926,5.625828947202473 +3927,-0.34594535420640843 +3928,7.972882788643846 +3929,1.6398678523616783 +3930,-0.0963848295806546 +3931,3.1110759420595406 +3932,4.974762151252292 +3933,5.3830547388545735 +3934,5.348854103393728 +3935,5.139748337215554 +3936,5.127318210294799 +3937,3.4615871567592675 +3938,6.738880613149378 +3939,6.009922235506536 +3940,-5.2862007605502965 +3941,0.18305019442646475 +3942,9.323630668802057 +3943,4.617647237533193 +3944,0.2877059006899859 +3945,0.9527445534324046 +3946,1.1099829657892955 +3947,11.531547389316447 +3948,3.154324664200022 +3949,7.787797759875439 +3950,-5.466914823346372 +3951,1.6652508036720963 +3952,-0.5532836534015287 +3953,4.621337606550354 +3954,7.288103010583124 +3955,2.2995521086470125 +3956,3.6817368024414368 +3957,6.764551272850101 +3958,6.085759540239835 +3959,3.194027593601273 +3960,5.221148642650907 +3961,4.471742443374683 +3962,5.3477485688715 +3963,7.634377049718032 +3964,6.664776767012249 +3965,8.532744682207122 +3966,-1.3477188958089223 +3967,3.7003823995019776 +3968,8.418261104415928 +3969,5.282474898703682 +3970,2.9435181960358836 +3971,4.944159615863474 +3972,-3.886767638224403 +3973,-1.628718282883466 +3974,4.448388231906561 +3975,6.902355020094548 +3976,5.11426029080858 +3977,8.003017757904114 +3978,-5.954832521349586 +3979,5.461509921453452 +3980,6.543949469945323 +3981,3.4889196090458734 +3982,0.14208233864501957 +3983,7.157304876639502 +3984,4.111544139355718 +3985,2.5567451949133564 +3986,5.135128136755284 +3987,0.7535334423097018 +3988,1.1774076918619532 +3989,-0.6201107617337774 +3990,-3.3553758016472046 +3991,-4.678632047947258 +3992,-9.272847970016967 +3993,-0.1323438575226636 +3994,5.4629263875378316 +3995,-0.9693571529449196 +3996,3.2742170874415866 +3997,2.008905728369474 +3998,6.41941997062566 +3999,-0.9625380267148004 +4000,4.970897215801954 +4001,9.736260179079572 +4002,5.499884885521976 +4003,2.16526046060597 +4004,-3.6721137472182726 +4005,4.962135174394586 +4006,-6.744549185837891 +4007,7.604328288024966 +4008,5.6760329998228976 +4009,10.041175377057792 +4010,7.856719922464635 +4011,4.463812914157565 +4012,-4.199971922268241 +4013,6.514906449668699 +4014,-7.276103859743677 +4015,7.671196403546379 +4016,4.3771854744165966 +4017,5.2969053368511885 +4018,4.8688767778119795 +4019,-2.6085180943361514 +4020,7.431062727220301 +4021,-9.95554101148785 +4022,4.860522745645386 +4023,7.626571190515406 +4024,1.8497152058397535 +4025,-3.1673150647807455 +4026,6.784843098388834 +4027,1.8572830708389438 +4028,6.556967773962193 +4029,-3.149273580538618 +4030,5.796834442383266 +4031,7.214120577076608 +4032,4.877007814261069 +4033,-3.3180337478309383 +4034,0.5651653692101387 +4035,4.157890847830622 +4036,5.03949791608564 +4037,2.083825653195647 +4038,2.7623592230458764 +4039,5.666656004300581 +4040,3.7911736010907946 +4041,2.4950820263233906 +4042,7.060735267280674 +4043,1.5896835668397902 +4044,1.0553224887271762 +4045,5.024543378566287 +4046,2.6405847274078758 +4047,3.3057132497264243 +4048,-7.148635742309766 +4049,6.561214085236004 +4050,0.6425223334290515 +4051,2.58434539594086 +4052,5.628698876278459 +4053,4.049761883004829 +4054,4.4637051075299 +4055,0.9024169728420305 +4056,5.079761225770974 +4057,7.443118567219427 +4058,8.94761389488702 +4059,-1.2718612535942102 +4060,4.881764084796553 +4061,-1.4863876630172406 +4062,8.23736322773654 +4063,-3.1934788647018255 +4064,6.246565447247642 +4065,4.0163282532731 +4066,2.9529765082942316 +4067,-10.498828640424486 +4068,1.448643734336787 +4069,0.13368028219494152 +4070,-1.9767982731671063 +4071,0.646433570555842 +4072,-2.3225779859427496 +4073,4.949486973902718 +4074,6.3214828378149654 +4075,4.342865275408493 +4076,7.647179571844051 +4077,5.886222857011829 +4078,3.592316791093422 +4079,5.401435619025098 +4080,3.2153528085679173 +4081,0.9467193385526601 +4082,0.28094010949006604 +4083,4.408990128469534 +4084,3.50949541287478 +4085,5.001489195187447 +4086,-1.0308282844891754 +4087,-0.10155988268328138 +4088,5.5125361373237 +4089,-1.0685591472649352 +4090,4.274670716631085 +4091,6.524774107043941 +4092,6.970584050522375 +4093,0.2501328380376304 +4094,5.8727654733349395 +4095,7.077811457077444 +4096,-2.2347373986788766 +4097,4.231099573268062 +4098,7.870703749125566 +4099,3.726807259546515 +4100,-1.0576743320067168 +4101,5.174957242482133 +4102,1.3353785901534412 +4103,-6.244065401586494 +4104,-1.3444624999863306 +4105,4.944037302753487 +4106,-1.0885391934992281 +4107,3.980534855409288 +4108,4.507015026875948 +4109,0.6609348616882215 +4110,-3.4276170895746265 +4111,2.2842973224134924 +4112,-5.3820243788270234 +4113,5.564138456565629 +4114,2.6626884380269797 +4115,5.922168611305363 +4116,6.7849139512656516 +4117,1.7910378873062718 +4118,1.254877673637036 +4119,6.17056475690981 +4120,-0.9470690279126063 +4121,3.728519946633143 +4122,7.575844378090695 +4123,1.2167844965425751 +4124,3.4268944690271077 +4125,5.332200471828567 +4126,2.5996835509314202 +4127,5.3204569574101965 +4128,1.5365241808095713 +4129,-4.4667337045376945 +4130,1.8572163403064141 +4131,2.2640137039978034 +4132,1.388383221797565 +4133,4.13941462215019 +4134,7.362033216937328 +4135,3.322104462385012 +4136,4.703835197350114 +4137,1.3621092101686656 +4138,-3.613763277035654 +4139,4.728218105970499 +4140,-3.6773994133626204 +4141,-0.19321890450633408 +4142,3.732292308544576 +4143,7.365627763468112 +4144,4.819824529180166 +4145,5.747526247945866 +4146,-5.971767466470184 +4147,6.074558003035214 +4148,3.5542429582826314 +4149,6.2950435358716526 +4150,5.24997836582211 +4151,6.335874165866588 +4152,2.9935283479606376 +4153,2.697407704128158 +4154,2.523774559419255 +4155,3.0770258062257696 +4156,1.3556630671836172 +4157,5.310487100703289 +4158,1.312083972895719 +4159,-0.6514193990941968 +4160,2.9293474275041302 +4161,-4.030742818185322 +4162,2.9340002240789986 +4163,4.872678994016928 +4164,4.634229240994885 +4165,6.4986155111889765 +4166,0.5981865540698186 +4167,6.7154601913000596 +4168,-1.6586768406964825 +4169,2.7179862572672704 +4170,6.694343853364646 +4171,4.290403100345653 +4172,2.3329911343945047 +4173,5.821617456216047 +4174,3.4276889985397747 +4175,6.277170927905601 +4176,-2.8890543012120693 +4177,2.0228763715330844 +4178,-5.421424627701834 +4179,2.0173304044837 +4180,5.4204361744357055 +4181,-3.058630692709255 +4182,1.1667816484937785 +4183,5.484498344598336 +4184,-3.955241248703333 +4185,8.92861634884718 +4186,3.8672287041505813 +4187,6.333417126603945 +4188,0.48219813001672235 +4189,1.04129509589522 +4190,2.296418427692746 +4191,7.072959364112131 +4192,2.541234270011649 +4193,4.387659500486214 +4194,4.8228509577095195 +4195,3.9588630982676833 +4196,6.9914468481888505 +4197,-1.2460719721779696 +4198,-1.5547933621048333 +4199,2.235811758898513 +4200,3.9523076606210386 +4201,3.3199921114647415 +4202,0.7532712405164909 +4203,3.5291017783999714 +4204,0.40065604985716824 +4205,3.724997632901727 +4206,-1.3596047422601845 +4207,5.366540776475209 +4208,0.9550466149622482 +4209,4.304104198494473 +4210,6.698030843450425 +4211,6.863375318425836 +4212,4.2451094438622565 +4213,7.546328838105316 +4214,3.3149120565193395 +4215,4.541821879694392 +4216,5.549290160931297 +4217,5.254972460672556 +4218,3.165507439924876 +4219,-1.0357640651083393 +4220,-2.9226400071591465 +4221,-1.2034226333755422 +4222,2.0769031021256197 +4223,-0.36326351138942375 +4224,-3.9642907096409123 +4225,5.031227418465347 +4226,4.7539067815606 +4227,5.198700039656777 +4228,-3.683597814478263 +4229,4.779082702572065 +4230,-0.8086717248880818 +4231,6.609848313340778 +4232,-8.427438506845386 +4233,3.571573959005752 +4234,4.105961917923571 +4235,6.283420490350565 +4236,6.87735967611069 +4237,-0.7343217079294027 +4238,2.6895989601715264 +4239,3.1815002937949353 +4240,-3.0555048653493686 +4241,-3.8952824372207044 +4242,6.37430357175023 +4243,7.030696093911729 +4244,4.595052872529386 +4245,-4.697622197520114 +4246,6.1168081084154755 +4247,-4.966597352006023 +4248,3.151208362969153 +4249,8.36872392267574 +4250,2.976485927959549 +4251,-5.588005409548258 +4252,2.2410943524141147 +4253,5.79880388024606 +4254,2.5542149623043295 +4255,2.887298247528814 +4256,9.841208987733916 +4257,7.154788082182684 +4258,8.430101750871478 +4259,5.075368335943187 +4260,-2.9209858011380874 +4261,6.089176058960545 +4262,0.7200406509436251 +4263,-1.9092643363379234 +4264,1.6171970371223807 +4265,0.78538856367824 +4266,-5.006316498206284 +4267,1.7911671083236649 +4268,4.983769234895013 +4269,4.939263698665928 +4270,5.5946003118585725 +4271,-3.317809162338548 +4272,-1.5929592711698572 +4273,4.809384118541895 +4274,0.09565954362921984 +4275,1.072268865533815 +4276,6.825915832275551 +4277,7.076946567686793 +4278,5.641997870665314 +4279,-2.7388960131639215 +4280,5.096455389806583 +4281,1.59561293915004 +4282,4.815920193182441 +4283,1.398720546996542 +4284,4.112648813381088 +4285,6.401678922531711 +4286,-2.9187767100533124 +4287,-1.9777798560947562 +4288,2.8396699128319143 +4289,-4.96314562383024 +4290,2.810162839149948 +4291,4.9565057708523 +4292,1.417285379096154 +4293,4.292494729796477 +4294,1.8148589770664532 +4295,1.962687685783392 +4296,4.499856440889597 +4297,-0.6977852415792095 +4298,6.939483005506899 +4299,2.0410165177500827 +4300,-4.882909352650003 +4301,4.1618229500158845 +4302,8.922338508515129 +4303,-4.82492391368296 +4304,4.018587745199934 +4305,7.794420187380286 +4306,0.1883526349826985 +4307,-3.8142617111251784 +4308,-0.9820782271415958 +4309,7.046153641187331 +4310,5.135270129571869 +4311,-0.440109452403294 +4312,3.3510266854215067 +4313,1.2664565151816445 +4314,7.810288702041559 +4315,-1.0745893625079839 +4316,5.4019445031844455 +4317,6.563257558328547 +4318,8.46077295330827 +4319,-0.11004002663809143 +4320,2.009219414047816 +4321,1.789506866210206 +4322,7.042932528590205 +4323,4.213506102433868 +4324,1.3910653294072155 +4325,1.383953775559339 +4326,2.882076043381556 +4327,4.442447389656413 +4328,0.9272598613081374 +4329,-2.8908695507879885 +4330,4.768186584385922 +4331,4.724386005756479 +4332,-0.5731614636217438 +4333,2.2056040099658363 +4334,4.070713373604478 +4335,5.775608966634452 +4336,2.003804749077135 +4337,4.828229047782158 +4338,1.900614698897226 +4339,6.661452539225765 +4340,-1.9108731684623814 +4341,5.113017467371173 +4342,-0.14859771653714704 +4343,7.6949917884548675 +4344,3.7952368382237305 +4345,5.449554658761555 +4346,-4.224097687549259 +4347,1.141578981359186 +4348,-2.265953485958279 +4349,-7.1452057605422 +4350,2.163349399453561 +4351,-2.786488965018132 +4352,-0.18483532311481632 +4353,-10.321936689019745 +4354,-1.6252359193786172 +4355,-3.543198978363906 +4356,2.5597215746905477 +4357,6.020440957857499 +4358,-2.14496888389354 +4359,0.15535357044990777 +4360,5.894941467452869 +4361,6.885788429372006 +4362,5.9674543461334 +4363,4.131838040193933 +4364,-0.07259286183249553 +4365,1.6551619246299327 +4366,2.700859890195215 +4367,4.425171568947887 +4368,5.7473038858977405 +4369,3.17644983048993 +4370,4.216363739321206 +4371,5.015590367869684 +4372,1.0586876839749089 +4373,6.3019496795487315 +4374,6.317917644726467 +4375,-5.1849359230772185 +4376,-3.673442836141436 +4377,-1.6767328705466074 +4378,10.021774845214324 +4379,6.339353593147068 +4380,-0.2483613270116205 +4381,7.418536611542433 +4382,6.071775843997818 +4383,-1.1633399645095817 +4384,-0.976426956140158 +4385,4.844516418543072 +4386,7.971897573882013 +4387,4.599179587737778 +4388,0.5445716683327433 +4389,2.0537156149874543 +4390,4.318527415074125 +4391,1.4445349558584988 +4392,3.8599195762712206 +4393,5.697801172322023 +4394,1.3629232998740648 +4395,8.505970997503539 +4396,-0.09195215042260452 +4397,-2.3454121986868732 +4398,-0.6497753263046063 +4399,-4.2579456571594525 +4400,0.18095166219125414 +4401,4.105337845552997 +4402,-0.8638628061653856 +4403,-2.447891571241531 +4404,4.2444222924118735 +4405,0.1064840136157523 +4406,2.092713009706196 +4407,-2.27640431956767 +4408,-0.6973516634026502 +4409,5.2396593889270315 +4410,-1.3509584146466276 +4411,6.837250340692831 +4412,-4.226344814071309 +4413,6.904075297585259 +4414,4.298938524070957 +4415,5.29714032795486 +4416,6.128125364460978 +4417,-0.719446601278358 +4418,-6.0115582632059885 +4419,4.634114775884665 +4420,-0.7086649355838256 +4421,6.177716620070706 +4422,7.827499043982664 +4423,5.816953018610998 +4424,-0.1523415818309728 +4425,9.796650569773801 +4426,-0.574265372975457 +4427,-1.324942605840028 +4428,6.297841446383651 +4429,-3.8190486759392344 +4430,-1.9025140939576493 +4431,0.24461923520834514 +4432,3.689839320809889 +4433,-1.3078141410220379 +4434,2.674257081172014 +4435,4.079478352860724 +4436,1.8575058325187708 +4437,7.780107343001735 +4438,6.251071534342714 +4439,8.631775315037869 +4440,5.063694852298579 +4441,3.157541282184124 +4442,4.160504921566012 +4443,2.5945153818968354 +4444,1.3389764219214613 +4445,8.601534467995588 +4446,-1.3655663097321178 +4447,-1.5820572414201404 +4448,4.31192117783395 +4449,1.4375068176034342 +4450,-2.2382380404188993 +4451,4.9966317510642355 +4452,-0.026619548146915188 +4453,3.313232178804693 +4454,2.88775726803874 +4455,5.658189113357355 +4456,5.343302781926173 +4457,1.45038746354435 +4458,5.139994723695492 +4459,1.1168972983752514 +4460,-0.3150276073114839 +4461,1.9347903299435427 +4462,-5.112788616523116 +4463,-4.469764283524802 +4464,1.5829793358267108 +4465,0.3325560172862276 +4466,-1.4683908899877434 +4467,-1.486122203832151 +4468,4.541583457983734 +4469,1.2562609217365939 +4470,1.916167969230993 +4471,2.532488591942916 +4472,2.9174103495574633 +4473,4.685874743115385 +4474,-0.2505014225316432 +4475,6.917624253033027 +4476,4.753740270908692 +4477,4.159276512391916 +4478,10.730567381651582 +4479,6.502973133354013 +4480,-1.334654119243702 +4481,-0.9170920757874796 +4482,3.010341932818191 +4483,-0.07845754412037742 +4484,-1.8322345330454646 +4485,-0.1688324391821805 +4486,4.432009483436356 +4487,4.673931057238607 +4488,8.399699982265442 +4489,5.652832696576959 +4490,6.658952995905377 +4491,5.974435963030853 +4492,3.2950389178145656 +4493,2.865451016824523 +4494,4.236802229349508 +4495,4.867742827029121 +4496,4.961219198313318 +4497,-4.016390423513608 +4498,3.419986379962795 +4499,3.431201344258214 +4500,3.081940687873227 +4501,1.98265774277737 +4502,-1.251779999841984 +4503,-1.584714930919961 +4504,2.2733570777421286 +4505,-3.296934592956212 +4506,5.675572546380055 +4507,1.7808745667013364 +4508,4.694245081193143 +4509,2.122455644492282 +4510,4.529101239639578 +4511,7.591550772660079 +4512,0.8507558962540903 +4513,9.124334353931348 +4514,4.282991853024318 +4515,5.424811249570597 +4516,-8.376482330264963 +4517,6.2347537822579175 +4518,-3.1410818766986255 +4519,2.0965663523414184 +4520,2.302451663682496 +4521,4.596060520234277 +4522,6.29890655442005 +4523,3.3918351903228077 +4524,6.9282627715464224 +4525,7.01124386072094 +4526,6.593494551562705 +4527,4.147603376934197 +4528,4.523412096145096 +4529,-2.600268569603592 +4530,0.7810572095948293 +4531,0.5199180448994731 +4532,5.494168157761578 +4533,3.1828524324081355 +4534,-4.8521761192208555 +4535,0.9907052225969869 +4536,-0.28899921543191365 +4537,3.3570782703544273 +4538,2.4351423668196257 +4539,8.590238409958195 +4540,4.781740948465341 +4541,6.671695645809399 +4542,6.266156301418521 +4543,7.67426567648448 +4544,1.4488209146706463 +4545,8.050826158646395 +4546,-7.351384856873985 +4547,5.204985518625875 +4548,3.787482986272992 +4549,3.418729839314772 +4550,4.116009122563242 +4551,1.623209994464604 +4552,7.4318498789339635 +4553,1.7447210313188362 +4554,2.0238310107150035 +4555,4.744962578861565 +4556,3.280076822738872 +4557,-2.117282200700888 +4558,4.501934758869646 +4559,2.3381516405357625 +4560,7.470786616155719 +4561,-0.8318835361998032 +4562,7.807966809957138 +4563,-2.412790650140592 +4564,-1.5617169827527093 +4565,-3.432776658695519 +4566,5.994351412237398 +4567,-2.388443952624839 +4568,4.5413386273432 +4569,5.5816635956811025 +4570,5.703496648960533 +4571,5.559237070608069 +4572,2.5059977630144097 +4573,0.9155379159697469 +4574,-4.480474093874841 +4575,4.786707603349091 +4576,5.5250021901735265 +4577,-2.9121328642462583 +4578,2.4221652176918846 +4579,-3.1882040389176165 +4580,-4.408347770228983 +4581,1.5645810232534307 +4582,3.3060865605637213 +4583,6.198518306930694 +4584,5.825292151608014 +4585,-5.688974176151918 +4586,4.098639580480765 +4587,-2.2209962310074767 +4588,2.0097318864340723 +4589,4.57911862751455 +4590,2.13797825598253 +4591,-2.089709920128478 +4592,5.897669224203032 +4593,7.754518456719447 +4594,0.8828222238898084 +4595,7.38638226886251 +4596,4.856624241658147 +4597,-3.522468030909242 +4598,7.269763926374785 +4599,-1.6895583014487734 +4600,4.442252942810719 +4601,4.319557355397883 +4602,3.0168634857077183 +4603,6.1268689357112445 +4604,-0.39719393038081 +4605,2.6472420080249206 +4606,2.8456566011319224 +4607,8.535570763861038 +4608,1.948684284822315 +4609,2.778611514308001 +4610,-2.944351818736127 +4611,-3.35793383365281 +4612,2.9075833581946138 +4613,5.376011267876593 +4614,-10.25153230574877 +4615,0.0020015333278279273 +4616,-0.7820923589767229 +4617,4.5546085318754645 +4618,6.948232431192436 +4619,4.241757948171525 +4620,2.377278654136363 +4621,4.354492013583198 +4622,3.827437296412914 +4623,-3.597206181495006 +4624,7.781043997078847 +4625,4.655396255030283 +4626,-0.7444789402159733 +4627,2.540126216810969 +4628,-4.44725378095651 +4629,6.724293463598766 +4630,0.219010596265685 +4631,4.644485273719484 +4632,3.925856546744269 +4633,-0.21983133550180708 +4634,5.345202225427445 +4635,-2.6938835307314535 +4636,-1.6595697736941586 +4637,3.533166215439306 +4638,0.18213340079267937 +4639,2.772484750822498 +4640,5.52378549052486 +4641,2.854110164204417 +4642,5.413699635975096 +4643,-2.321327751135087 +4644,-0.1876129310569021 +4645,2.748353888914829 +4646,2.683674683746304 +4647,5.55675313338672 +4648,-4.623279705526187 +4649,5.959991103732057 +4650,10.341668108081803 +4651,7.456543005847033 +4652,3.862138512999615 +4653,1.0602574254945472 +4654,-2.153355181406039 +4655,1.1298019255521858 +4656,1.7916062313270704 +4657,0.9958370198746452 +4658,4.273858849976241 +4659,-1.1425196420760186 +4660,1.5840820108202376 +4661,5.939095908270438 +4662,1.0978700408525577 +4663,8.944128743735467 +4664,4.363174102775347 +4665,5.988056225593089 +4666,4.0827797929577665 +4667,3.435183608519724 +4668,1.4048482046070068 +4669,1.0977068733729856 +4670,5.289987888090687 +4671,4.224223442051409 +4672,-6.269371474854779 +4673,5.2705837802314095 +4674,3.6957286256027846 +4675,0.762077191252437 +4676,0.23193675260205074 +4677,5.879351717283063 +4678,3.438979412403957 +4679,3.9910445325079507 +4680,5.4035939375139685 +4681,2.8411066634458515 +4682,4.749604826883212 +4683,6.827135779620563 +4684,6.10164956009176 +4685,3.0645325069203 +4686,6.141455528623242 +4687,2.648870588753131 +4688,9.593235311899265 +4689,-3.9873625298185997 +4690,0.5372389543212165 +4691,6.929843641565796 +4692,2.9381219623279344 +4693,3.854391214913966 +4694,5.113993312838541 +4695,-3.4526215255375523 +4696,0.6903293928136153 +4697,6.313110460160793 +4698,-2.9779571821399844 +4699,4.3815366529001665 +4700,6.386719514608291 +4701,4.059703480871226 +4702,-3.44863093382098 +4703,0.4614339569926116 +4704,0.5523117833228202 +4705,1.3958654957873686 +4706,4.655019964169494 +4707,6.880195954960262 +4708,-4.134615550041916 +4709,-1.8374540524342082 +4710,2.5715966571239073 +4711,0.6318367360505794 +4712,6.062503230078636 +4713,1.219281237789889 +4714,-2.52660060505454 +4715,-3.0640225393135703 +4716,-1.6839802307619685 +4717,-0.7978820646852992 +4718,-6.5360796889907276 +4719,1.7343320401132596 +4720,3.634332592101175 +4721,-8.278939271944644 +4722,4.898814335312745 +4723,-10.295126541721471 +4724,5.7436911743198 +4725,3.1284311115889274 +4726,-1.437311850433456 +4727,-3.220439567438444 +4728,5.640990705347354 +4729,6.847574062180179 +4730,2.1394220989134802 +4731,4.918082433424809 +4732,4.2244435710979475 +4733,3.697766567594055 +4734,4.860379867487964 +4735,-3.655752050471074 +4736,1.6564205301893005 +4737,4.475352247340128 +4738,5.414997779746955 +4739,2.576926930292919 +4740,4.969523576056961 +4741,-4.045685743028703 +4742,-1.5251970751260522 +4743,0.005503218655829775 +4744,3.7642910174022752 +4745,-1.4701657267123585 +4746,0.4400348610160242 +4747,-5.675051156264058 +4748,2.28782621255195 +4749,3.9287683671634976 +4750,2.934348960771463 +4751,1.8704451914668256 +4752,4.831158853904178 +4753,2.04238015416443 +4754,2.6364988541932446 +4755,-3.785581671739578 +4756,5.556994601935823 +4757,4.957989342146 +4758,2.515295128902413 +4759,0.19780331138536988 +4760,1.8118259199773423 +4761,6.500871179076843 +4762,6.313322295307788 +4763,4.8950281424614275 +4764,-2.4057583817341994 +4765,-1.988141111222964 +4766,4.30420352003921 +4767,2.898100191243478 +4768,2.7619126824612996 +4769,-11.01550566141855 +4770,4.940552070708077 +4771,5.873335369378856 +4772,8.554374774045444 +4773,0.14105903596429514 +4774,4.37332270471128 +4775,6.009873540177821 +4776,4.311465994284966 +4777,5.929433895392505 +4778,5.645259418658264 +4779,7.409021927668214 +4780,6.726035520786239 +4781,6.582874594932145 +4782,5.4284279584166955 +4783,-4.361748847478462 +4784,5.942813734411591 +4785,3.3916179111072355 +4786,7.891624840461404 +4787,2.095992412908537 +4788,12.149445037823472 +4789,3.8180716731172755 +4790,-11.10182040585989 +4791,2.1221617527163428 +4792,8.192612273547969 +4793,-7.962320664607995 +4794,-3.6040726544698467 +4795,7.364921955600682 +4796,5.3459117446244155 +4797,-1.1649887942131951 +4798,5.522381742047375 +4799,4.424917165677077 +4800,8.937999334703793 +4801,7.262454715853403 +4802,6.504668154423462 +4803,-2.3673610840913075 +4804,3.289623987203191 +4805,-4.418063645978714 +4806,3.311440466855897 +4807,-2.310434868931421 +4808,-1.4025594536245787 +4809,0.6620241043691313 +4810,-1.2557254263453783 +4811,0.08335763393801238 +4812,2.088173900013518 +4813,8.03418244257474 +4814,4.170026815337027 +4815,5.999124651906416 +4816,-3.444223310701491 +4817,-3.992610371549984 +4818,4.638659079823493 +4819,-2.8916746358419245 +4820,8.287260353758263 +4821,4.595595734648451 +4822,1.069714178835695 +4823,0.8576720084241565 +4824,3.2211469922546696 +4825,1.38394290283146 +4826,1.1973603707132765 +4827,4.081691720611662 +4828,-0.7203433620303968 +4829,3.8612331045309576 +4830,4.333731338866464 +4831,-3.3640652245133547 +4832,7.414614397466061 +4833,1.0301779754962617 +4834,3.201903180434175 +4835,4.902592185921275 +4836,3.7705064709997123 +4837,0.9329799006866362 +4838,3.704007372593294 +4839,-3.460350505925799 +4840,0.8486728557758 +4841,4.8635830728526805 +4842,1.8976939744680417 +4843,3.009861635167894 +4844,-8.44314056698044 +4845,5.995734542523619 +4846,8.072572378003478 +4847,8.222093978040716 +4848,-8.996415798529732 +4849,-0.6052226421388436 +4850,4.397164915407676 +4851,6.491813561196826 +4852,4.082968849332828 +4853,3.955799734190685 +4854,3.74057276698443 +4855,1.243003943226856 +4856,3.122131457809745 +4857,7.453509595599392 +4858,5.981982749887501 +4859,3.9145377199240894 +4860,4.7721927398530175 +4861,0.8819717683485433 +4862,4.885978869831336 +4863,4.521728393027035 +4864,-1.0859349956308424 +4865,-1.55108308419634 +4866,-9.284804497632374 +4867,3.816667819013009 +4868,5.381743976023154 +4869,-8.283016854043945 +4870,-1.1358062143046874 +4871,6.964169570208997 +4872,5.286489893390761 +4873,4.459194349259732 +4874,-0.18016408398760642 +4875,5.537659497529885 +4876,6.623488951421697 +4877,-2.5230325157331044 +4878,-6.746905461074112 +4879,5.777042391220435 +4880,-2.6167920724825917 +4881,-2.8055570691211846 +4882,-2.284797700534045 +4883,4.953638901978164 +4884,5.4961785720403675 +4885,-0.3946831931914131 +4886,5.013364384946895 +4887,4.437380815383864 +4888,-0.16420943856321912 +4889,3.5198229673902066 +4890,5.634692504349536 +4891,-9.494781124791222 +4892,5.727236676005175 +4893,5.884825617817754 +4894,2.5904389538211894 +4895,1.9111864407960613 +4896,6.846515033210567 +4897,5.331421773730374 +4898,-6.517617854803611 +4899,-0.9901415428619441 +4900,5.526264863603937 +4901,-3.509824046775743 +4902,-3.6432850080943386 +4903,4.594458176304414 +4904,-2.7690512177689066 +4905,0.036534494627998695 +4906,5.1240265218142005 +4907,6.021358472274429 +4908,-2.5626200168638147 +4909,6.97142070754354 +4910,-3.8540443780393563 +4911,3.0091314876002317 +4912,3.8955468865230323 +4913,2.0342755467116493 +4914,5.880514665317723 +4915,-0.49801553378497126 +4916,0.26158223100554673 +4917,3.1499837173458034 +4918,1.5773720652666212 +4919,-1.1628576002633277 +4920,6.060546435992443 +4921,1.4179418306408649 +4922,4.615959751981716 +4923,7.566262658181968 +4924,9.439717313009107 +4925,5.743534591188379 +4926,6.206827398766697 +4927,4.691942769142206 +4928,4.8160950269894585 +4929,2.7234529895458617 +4930,0.10133628319642686 +4931,6.473865381528492 +4932,0.2124405250659814 +4933,4.781701606447368 +4934,5.3184129997091745 +4935,-1.7283803338148565 +4936,4.488452982167822 +4937,0.8062677703886644 +4938,1.3570104465206465 +4939,-6.771373698173244 +4940,5.245865810708924 +4941,0.614314366497304 +4942,8.122517541439517 +4943,-2.0881899692469386 +4944,3.186342629791641 +4945,4.532139144706132 +4946,-5.438766074299777 +4947,5.522073822737795 +4948,-8.21004236205292 +4949,-2.4520689157324065 +4950,-2.9787641074139337 +4951,-2.5644212944716895 +4952,-2.634317158999018 +4953,-6.342977212545 +4954,-5.216061663286918 +4955,7.651219161743734 +4956,-2.937065351985503 +4957,-9.241616769584438 +4958,10.200859755479925 +4959,6.207839238508156 +4960,7.108391636417294 +4961,1.0334110840933333 +4962,-3.404851605558287 +4963,5.079659178510592 +4964,2.092809802766186 +4965,-0.9662742796362404 +4966,2.4115754838066623 +4967,4.492003984675898 +4968,0.28426951326206823 +4969,5.650994233069595 +4970,-0.05402593980475809 +4971,2.5664296348168074 +4972,-0.6889464733723161 +4973,7.3783462567277525 +4974,-7.0170087392879115 +4975,2.500625689801672 +4976,3.1224747384828806 +4977,-3.136500507565665 +4978,-5.57974168471489 +4979,8.6906278948806 +4980,6.369061448835144 +4981,6.97883314422778 +4982,2.3407737344293382 +4983,-5.636720248793545 +4984,6.457426867434574 +4985,0.32409157893050106 +4986,-1.2861350669357203 +4987,7.989858900459417 +4988,4.20708758901903 +4989,-1.6082444905335933 +4990,1.8982066986115353 +4991,-3.547322394158778 +4992,2.5984186690595634 +4993,6.6317936488447256 +4994,-4.097248384118585 +4995,4.1876973016337 +4996,3.377279141014795 +4997,5.4937682857798755 +4998,2.910793445616358 +4999,-4.021532082194688 +5000,9.500957172504107 +5001,2.1144594701649257 +5002,3.2717009662923355 +5003,1.5087018735894029 +5004,2.051902708266722 +5005,1.067844177472079 +5006,-4.461357904340182 +5007,5.613154041012434 +5008,-3.45749831983761 +5009,3.47703016199259 +5010,6.2359888502570655 +5011,3.796632514966231 +5012,5.69465272717636 +5013,4.326783451476745 +5014,-9.46313937432023 +5015,2.462046685511479 +5016,1.74708692941268 +5017,-1.1164099309213735 +5018,4.705204412955606 +5019,3.0789633723227507 +5020,2.423058279136792 +5021,-2.7354863718227542 +5022,5.4679295269529335 +5023,1.0822904205399333 +5024,4.658847912430482 +5025,9.6141723662987 +5026,-2.9015536791344467 +5027,-0.01857180241570167 +5028,5.820173977856746 +5029,-5.226637701216287 +5030,0.002088568102320215 +5031,0.9828916707726574 +5032,-0.1259044610091997 +5033,-0.14481355471586513 +5034,-3.645633451137628 +5035,1.296983059841889 +5036,5.7741919921243 +5037,2.394571248330566 +5038,-3.2951184123627795 +5039,6.748197670542229 +5040,4.622432112617067 +5041,-1.8277129178541938 +5042,6.304510397684031 +5043,5.396468038249906 +5044,2.5218725686424484 +5045,3.1112032309449833 +5046,-2.64970245611513 +5047,1.1881006704871826 +5048,-4.234249656958444 +5049,6.874264357349361 +5050,6.772074545957548 +5051,2.654308003084639 +5052,-0.7740397480168302 +5053,5.531087419100175 +5054,8.207640817526533 +5055,3.8560612947482715 +5056,6.051709589845555 +5057,5.365107638659485 +5058,5.411799474941711 +5059,3.684632621159197 +5060,3.897475170587577 +5061,2.9498163907037425 +5062,7.164706064740361 +5063,5.668242917649176 +5064,1.3400845771069427 +5065,5.031506287555373 +5066,2.1538347923273244 +5067,2.2255127147192706 +5068,0.8884016549647509 +5069,-5.137258242398461 +5070,2.168715304285196 +5071,2.0886728565134627 +5072,-5.552035255330589 +5073,2.0211582117910885 +5074,-0.9265609935096956 +5075,6.610860074242707 +5076,7.013832454853642 +5077,-5.839791037695427 +5078,-4.165233554885948 +5079,4.721266105174911 +5080,6.5820325128397466 +5081,6.709314942084809 +5082,0.00707216984120901 +5083,3.079666695253106 +5084,8.507704110962438 +5085,6.022012421530488 +5086,4.498904696109512 +5087,5.302765908114759 +5088,3.1757387236849626 +5089,8.398991061901 +5090,5.254798864890953 +5091,5.072462341392406 +5092,2.7768010392026086 +5093,0.6086922697090325 +5094,6.578338646070986 +5095,2.052261634901884 +5096,0.12185617090818834 +5097,6.198270958915463 +5098,1.5959832613248877 +5099,1.383420110094876 +5100,4.413324863407544 +5101,6.964856665418306 +5102,0.47718879799461433 +5103,1.0829573933312666 +5104,3.709376669220199 +5105,3.5134445813810866 +5106,2.90870191923162 +5107,-6.191171090954847 +5108,4.242944715812028 +5109,5.826960820880697 +5110,3.107663101336062 +5111,6.819504457314199 +5112,8.051799790702022 +5113,7.39653373585457 +5114,7.49166749691808 +5115,1.8672150306115516 +5116,2.0021639138974634 +5117,-0.5714742252378335 +5118,2.163735008531179 +5119,0.12833904295445664 +5120,-1.4732225383367734 +5121,6.618481857035093 +5122,1.7307202862835651 +5123,-2.11836243493547 +5124,4.769322661476669 +5125,-2.4466530135550566 +5126,8.049381570115118 +5127,3.6135592364086144 +5128,2.275750536348994 +5129,6.025543286176869 +5130,5.464815567731621 +5131,5.626263107300497 +5132,-2.2556709654407108 +5133,6.547291360768077 +5134,8.367741223189073 +5135,-0.5747303148024328 +5136,2.9370345135947313 +5137,2.563685007661215 +5138,0.4649525764578744 +5139,-4.545896897593546 +5140,2.817292974567692 +5141,-2.437698686423354 +5142,3.9144350070134726 +5143,3.5424569803208454 +5144,6.093254166255168 +5145,3.5333000387934543 +5146,6.857835072691675 +5147,5.201903661606839 +5148,-6.1096274079470625 +5149,0.49489847927198233 +5150,-5.359330240749247 +5151,8.027643942298303 +5152,-2.482188888056411 +5153,4.956618981868374 +5154,-4.233180718337637 +5155,7.649486219155416 +5156,2.8796956418267623 +5157,2.042553619061948 +5158,0.4158668544318332 +5159,-2.6295172051637534 +5160,5.140050864228929 +5161,-2.0929594338096993 +5162,-3.266598738068137 +5163,5.58770689587516 +5164,-4.355457002574084 +5165,2.62281821957163 +5166,-2.882699677115947 +5167,5.517552818187472 +5168,1.370101236518513 +5169,7.376255668584568 +5170,3.32811775368564 +5171,4.185455629547837 +5172,-0.24600047485129053 +5173,5.351975013949696 +5174,-1.0399212930721922 +5175,4.976636233048764 +5176,-6.477931873569389 +5177,6.913864343583011 +5178,7.593252521755337 +5179,7.377833564252349 +5180,-3.442193981750504 +5181,3.517382928925987 +5182,-2.100962404100039 +5183,7.15155743353558 +5184,4.10737205953852 +5185,1.3895063739640188 +5186,-4.576098901724922 +5187,-3.0016117915258063 +5188,4.3901245387716825 +5189,7.457624371292447 +5190,4.7078237152263105 +5191,5.354031060604952 +5192,-4.664215287061964 +5193,4.6103546862765485 +5194,3.64948361512902 +5195,5.518910474127318 +5196,2.491880321267482 +5197,5.894575791594881 +5198,6.9627005610606325 +5199,-7.74984123663707 +5200,3.176119326008616 +5201,5.7330924200338345 +5202,1.4378978626564818 +5203,4.8656800999463785 +5204,4.308441648800411 +5205,6.452202485163159 +5206,5.677865355737879 +5207,0.9020834944279918 +5208,6.575455288526678 +5209,-0.39443510652390634 +5210,3.876034767034924 +5211,4.6224096170406 +5212,4.549394202861818 +5213,5.886042146771971 +5214,-11.773511463386312 +5215,4.24602053440924 +5216,1.577143765147109 +5217,3.168852466852079 +5218,5.253590196045371 +5219,4.970345971226503 +5220,4.3339499114282924 +5221,-0.14604893781329983 +5222,4.676793438201983 +5223,6.052483735223051 +5224,4.58323728654829 +5225,7.384746366274883 +5226,-2.4647620870260583 +5227,5.911164195811059 +5228,5.975502201377391 +5229,6.471143225983365 +5230,0.448720936115053 +5231,8.679412556717757 +5232,6.434024541155914 +5233,-7.551039436713416 +5234,-6.265586447422283 +5235,-2.600226774394993 +5236,5.589401265267952 +5237,5.315040948289009 +5238,6.227251812829207 +5239,-2.4153254833347346 +5240,1.8445618178676344 +5241,9.351580018335161 +5242,-2.335759222445755 +5243,7.294157291727705 +5244,-0.8184740274914405 +5245,6.50863521381237 +5246,-1.514043362460051 +5247,5.024581595228039 +5248,7.882013093902291 +5249,-4.847414162155276 +5250,4.791252653418349 +5251,2.6935186460424947 +5252,3.5510151446374745 +5253,5.857313316657975 +5254,4.346522508770969 +5255,5.468498628276325 +5256,-0.218987730877291 +5257,-0.6996033833141354 +5258,3.0329938102541063 +5259,7.282001966829911 +5260,5.971093160914327 +5261,6.062153057839629 +5262,3.015672056102046 +5263,1.0028783884645875 +5264,7.921014670256406 +5265,3.8505011402820744 +5266,3.3642420033157863 +5267,4.373941028778376 +5268,3.632217655146342 +5269,5.7056245614423124 +5270,4.825991358753131 +5271,1.4146778736817942 +5272,-3.2709773596092373 +5273,-2.876101762184877 +5274,-1.7614049476792928 +5275,6.222925663061601 +5276,6.939257677054945 +5277,3.0813526984416244 +5278,6.5704390933781545 +5279,7.41501810695061 +5280,2.838568840841289 +5281,-5.016273318665313 +5282,5.057805275546413 +5283,-2.3617827183075275 +5284,3.689460504832903 +5285,-7.0467696996408264 +5286,7.544235065341258 +5287,-0.46682928134616125 +5288,-0.054840802655515775 +5289,5.100863917292426 +5290,6.916267844642092 +5291,1.9552508694634638 +5292,3.574397915990989 +5293,-6.3774392900600505 +5294,5.141603949699296 +5295,6.662505739792868 +5296,5.718573894212334 +5297,-1.2121464345422555 +5298,0.3846031800507097 +5299,3.419491214519276 +5300,0.5444437508066784 +5301,-4.980175806521802 +5302,2.979009676925338 +5303,-0.4773528685913467 +5304,3.348923843593112 +5305,2.448508665655988 +5306,3.2732145153969237 +5307,-4.181272053656391 +5308,0.6315848406059554 +5309,6.1195599008397465 +5310,3.4850892432965983 +5311,-0.265395483116962 +5312,-2.9010614842996985 +5313,1.6763139744599953 +5314,-0.8892782637310834 +5315,-2.98712029208854 +5316,6.216003243559055 +5317,-10.778028579851002 +5318,10.65927671860647 +5319,-1.3339620398069696 +5320,4.585047979375337 +5321,2.918674771434742 +5322,5.567252429874 +5323,2.3891416935592944 +5324,2.634017721329349 +5325,-3.004547118332114 +5326,6.520470926084725 +5327,1.3898894491098013 +5328,-5.194054575983651 +5329,0.7452441854224698 +5330,-0.4450590490705615 +5331,4.639790002690959 +5332,-2.98197216763785 +5333,-0.0005864913487073564 +5334,4.07706666690353 +5335,5.171075120075583 +5336,3.0397808233918897 +5337,1.9637184777282606 +5338,4.37811095034344 +5339,-1.26568854145209 +5340,4.836749204579006 +5341,8.007882475809598 +5342,-4.39295831588269 +5343,4.927556921471465 +5344,5.495348499229414 +5345,2.930876857062232 +5346,2.975250960056683 +5347,4.648015921651582 +5348,2.9982656165438186 +5349,4.290197708877923 +5350,3.5777979943770273 +5351,4.052328577568843 +5352,9.531717302480956 +5353,-3.503000016750114 +5354,7.046384655332032 +5355,5.280932787571267 +5356,5.097331773921873 +5357,2.0271585626570685 +5358,0.5739759133463442 +5359,3.5676124125944986 +5360,4.029471435173953 +5361,4.44578404843422 +5362,7.347568138226233 +5363,-0.8355313487890287 +5364,4.363435531262392 +5365,8.048730632609711 +5366,6.286785638347173 +5367,3.7444091438495137 +5368,5.12557892964101 +5369,5.436586825063101 +5370,4.729631471103684 +5371,8.296164806087425 +5372,0.07493228313366444 +5373,-1.9630409434601483 +5374,-5.573618153603987 +5375,6.833544065093408 +5376,5.498926612436488 +5377,0.5364771502672547 +5378,4.413131194420063 +5379,-1.699472891909143 +5380,2.3806312651460977 +5381,6.35048304112033 +5382,-5.059699178360956 +5383,5.1995992339166515 +5384,4.509357460507901 +5385,6.995059771654828 +5386,6.5788858726261665 +5387,2.273967202418291 +5388,3.68053141069037 +5389,3.448811071495644 +5390,3.1374812892040174 +5391,2.758806160458373 +5392,-1.5395893699125098 +5393,6.7208172327277005 +5394,3.268316208460341 +5395,7.119746373000886 +5396,0.8959879273911947 +5397,3.400123256052934 +5398,0.9003621027692933 +5399,2.6211570937202784 +5400,5.112775299807887 +5401,6.9449846720261315 +5402,-0.10420636460473902 +5403,6.0669304983576176 +5404,-2.7566718832040715 +5405,4.643981618483343 +5406,4.332428105334772 +5407,4.4384181085888486 +5408,6.061449647774478 +5409,3.9485949850154656 +5410,0.4517014575387628 +5411,2.892301659605149 +5412,3.813279812720609 +5413,9.464505316748307 +5414,0.3321812910995044 +5415,6.647209402670083 +5416,5.856250583768239 +5417,3.6078100595769724 +5418,1.1276223986475205 +5419,3.4602608861823647 +5420,3.756776019213172 +5421,0.7573037635764102 +5422,1.1655965697842967 +5423,4.111231178660887 +5424,2.868857901548034 +5425,-2.3632835923912974 +5426,8.038057589583763 +5427,-4.2629581824708875 +5428,4.009411760557628 +5429,-7.1467200537335795 +5430,-2.857071369791641 +5431,1.442690699002497 +5432,3.958007684905585 +5433,2.779391042574281 +5434,-0.3905207566773004 +5435,-1.937580083470664 +5436,-0.1398953746792833 +5437,-0.35596726592660216 +5438,5.948589660001835 +5439,3.8710042247098713 +5440,6.789957914748627 +5441,6.628693687496937 +5442,6.829824278726226 +5443,5.6520533520938665 +5444,3.3864396817812548 +5445,6.110741474180071 +5446,7.8243778241810835 +5447,4.31918612573466 +5448,4.896675666494421 +5449,3.392828974666187 +5450,4.640806210080871 +5451,-4.947186565561385 +5452,-5.730169408301639 +5453,3.4952133677669743 +5454,1.4735930221296427 +5455,-3.0382327503876803 +5456,1.3112686370472237 +5457,6.346443561770377 +5458,1.2068954534932588 +5459,5.681505939429487 +5460,3.82980692679466 +5461,2.8281361027547787 +5462,5.731173069623981 +5463,2.530181795419803 +5464,5.148220897068477 +5465,5.299432428105772 +5466,-1.8531955306682522 +5467,-3.8006817921865603 +5468,1.3915179210755257 +5469,-0.1545096756485678 +5470,-4.6930005510472075 +5471,5.997910358356284 +5472,2.650740917135566 +5473,2.2772767771928866 +5474,0.7650028324214624 +5475,5.221439519903117 +5476,-1.8663945438792038 +5477,4.253765058522179 +5478,3.9899769988541047 +5479,4.825324101834687 +5480,2.1393637072276888 +5481,3.9249503138066064 +5482,8.45301706700561 +5483,4.003916620734752 +5484,6.0331593114487365 +5485,0.7436122457655143 +5486,1.835091383574323 +5487,5.0778103477410275 +5488,3.584856133923218 +5489,-2.5522046569466457 +5490,1.990869954710836 +5491,-0.9967563577185364 +5492,2.093506689931766 +5493,0.12870299775418564 +5494,-3.073197045095564 +5495,-2.1092235836764397 +5496,5.642113867335502 +5497,2.6454587376707877 +5498,-2.3448811533207934 +5499,-1.12878691608509 +5500,4.725770632469139 +5501,-0.9763158695975123 +5502,2.3823579083796322 +5503,-0.14934173348875798 +5504,6.457945313094571 +5505,-5.669879859331723 +5506,4.738257969352624 +5507,0.9011061734231741 +5508,7.627774496566088 +5509,7.2180494653638325 +5510,1.1433277738020298 +5511,5.711791391907843 +5512,-6.833260665572138 +5513,4.4202610016099335 +5514,8.016305390261063 +5515,1.494234583142505 +5516,-1.7520240962136797 +5517,7.276186845205022 +5518,1.8984530232264074 +5519,7.105833039632099 +5520,5.845362549875144 +5521,-9.661235242027544 +5522,5.057106657050662 +5523,6.675631340913701 +5524,-1.2966671754322612 +5525,8.503260711363827 +5526,0.4404940487307994 +5527,4.811519970095391 +5528,0.6193441712038245 +5529,-4.57812828064225 +5530,2.787569701337196 +5531,4.7601539219105655 +5532,2.167056214744583 +5533,5.756740303695345 +5534,3.63303479911637 +5535,6.751509755111858 +5536,-4.963508497133206 +5537,6.73979962457528 +5538,1.1961840786980202 +5539,3.8979983415780204 +5540,-3.742607352468185 +5541,3.4490283107066615 +5542,-1.839221028813691 +5543,-0.5340748094070512 +5544,-1.6864820301116368 +5545,6.1700699872655544 +5546,7.224665053130007 +5547,5.503859938142142 +5548,-0.4323691321336378 +5549,3.237182857164915 +5550,5.435033316763164 +5551,3.1518277852859047 +5552,-8.362600036282293 +5553,4.029984085778275 +5554,9.842610965204663 +5555,6.074477459764186 +5556,4.159745099886619 +5557,5.375253627684863 +5558,1.2103674988051334 +5559,1.63741809959985 +5560,-2.292229969822068 +5561,2.4299770785181933 +5562,5.875921142644088 +5563,-0.23712753556063296 +5564,7.332853660086994 +5565,-1.4433589497270485 +5566,4.661332093454673 +5567,3.931128773757293 +5568,-0.5988791626084968 +5569,5.912690640979614 +5570,4.478453027874732 +5571,1.1029112921778315 +5572,-1.6220469991051143 +5573,-3.0715963260359005 +5574,1.377301555749027 +5575,8.680789283524867 +5576,6.2282993575551036 +5577,0.0753566053652967 +5578,0.5030315472320293 +5579,5.660620684707676 +5580,4.864615694604672 +5581,-0.7761411322103677 +5582,6.541135602910338 +5583,2.2818620827555054 +5584,1.2028742566357926 +5585,4.6803051655006165 +5586,6.212592891527257 +5587,6.174048916576032 +5588,6.431504593413422 +5589,6.545287838868285 +5590,5.342392550033357 +5591,-3.2683730806335314 +5592,7.855373100078228 +5593,-2.960860313526539 +5594,2.8577579617767825 +5595,4.0356896510694265 +5596,1.4977205459498804 +5597,-2.006155227700671 +5598,3.8732803143687335 +5599,2.763827795356428 +5600,5.54985934585939 +5601,7.2959026465893295 +5602,5.7686449356317295 +5603,8.313075045285721 +5604,5.402991391392426 +5605,-0.9043964238225191 +5606,2.9224640443166043 +5607,5.078637101370413 +5608,5.540703969385447 +5609,4.882655860336023 +5610,2.313399116961235 +5611,0.46098775833178607 +5612,-1.6285948416266367 +5613,8.887902003000283 +5614,2.5459019733547796 +5615,3.227754232703988 +5616,3.161843020901232 +5617,7.597230188126687 +5618,1.8883412934853812 +5619,7.197194367518437 +5620,-0.12777335846276533 +5621,1.1421200951274026 +5622,-0.3099811060306951 +5623,4.229979034899722 +5624,7.391485794991398 +5625,-4.904737774495724 +5626,4.102685419612022 +5627,4.018947540873479 +5628,4.537110209275228 +5629,-2.052676209878999 +5630,-3.0756922974645184 +5631,-0.761193759413014 +5632,2.9600690169816684 +5633,-2.4543145498422856 +5634,-3.043962879224241 +5635,1.025501591393475 +5636,1.3878066399106899 +5637,-1.8507693919566557 +5638,1.1427518205373228 +5639,-2.9396139559885732 +5640,3.4856007873633 +5641,0.20398392905872426 +5642,5.876989325583598 +5643,1.7380043937277527 +5644,3.109605831836396 +5645,-2.8311975209894844 +5646,0.7663534906878102 +5647,2.6737865259562703 +5648,-0.08160724463900218 +5649,6.413932512002518 +5650,0.6177244229761367 +5651,-0.4096562889145232 +5652,-3.4394799828634186 +5653,7.123234291195117 +5654,1.7783140650202225 +5655,1.959949019856 +5656,6.978324181778325 +5657,-3.0686834410522 +5658,-0.08241774782327208 +5659,2.6788749411388815 +5660,-2.287839624705585 +5661,6.194511119760736 +5662,0.889371537793866 +5663,6.717697418056446 +5664,4.6029576399593255 +5665,1.9718828850925205 +5666,3.287375460318431 +5667,0.20341299889804185 +5668,-1.771000346492004 +5669,-7.363878096906133 +5670,4.9240077967893185 +5671,3.4706384330280455 +5672,3.50039454714444 +5673,2.3941006005176506 +5674,3.338405458237499 +5675,9.873694096075008 +5676,-4.184668410989229 +5677,1.6202320467746718 +5678,6.586648596512379 +5679,4.741255708289633 +5680,5.57028161172129 +5681,5.093583595784778 +5682,6.375026761466495 +5683,-0.7552217271940143 +5684,7.8754741866569 +5685,0.8978353772517197 +5686,-4.291442328731767 +5687,0.2840522128099261 +5688,9.770428381479986 +5689,1.7028672721991795 +5690,-0.3428983467518929 +5691,6.191121130786717 +5692,-1.5544117558358062 +5693,6.693339844799989 +5694,0.6665320376954867 +5695,5.65038981982618 +5696,-4.152886850520385 +5697,2.31080036381415 +5698,-0.6836017720722681 +5699,-0.3232425815749556 +5700,-7.426142779470688 +5701,0.23742124183236823 +5702,4.670172973205815 +5703,6.266236477996971 +5704,6.101886694344514 +5705,5.788054897901772 +5706,-0.09533773576391091 +5707,2.2544645835385246 +5708,6.7492719910161325 +5709,3.1485558857139573 +5710,2.679386959231159 +5711,1.2682159956682333 +5712,6.858496184596994 +5713,-6.963667998044183 +5714,5.532922364640034 +5715,0.0454159505624412 +5716,6.603359891221074 +5717,-1.2546467632608274 +5718,-4.0229579709755185 +5719,3.9488167722554364 +5720,5.243055186941116 +5721,6.818274075623055 +5722,3.165381037706668 +5723,3.505577765528433 +5724,2.877932596267618 +5725,6.782961340420324 +5726,2.695019683396308 +5727,6.456804559383379 +5728,5.222263227071768 +5729,3.7012286888354087 +5730,-2.0105622303804775 +5731,9.895361693735808 +5732,4.3419378106592745 +5733,5.629978503496565 +5734,7.294216257252881 +5735,0.6659313650514962 +5736,2.4493164218193297 +5737,6.527876856143223 +5738,1.8904482239408726 +5739,1.8178015067552586 +5740,-0.7402368118044129 +5741,1.5494540950744442 +5742,2.884234396222675 +5743,4.709015068641453 +5744,7.290855212321904 +5745,1.2388668760299597 +5746,0.9406831053867097 +5747,-2.263739189347451 +5748,0.628165615580928 +5749,-5.280332568297767 +5750,-1.661316899477561 +5751,8.026753934737274 +5752,7.750640367191919 +5753,3.467819210738545 +5754,-5.772037380613137 +5755,3.050646821569996 +5756,8.303242532202557 +5757,4.836842355285718 +5758,1.95418974485885 +5759,-5.237536935623247 +5760,8.115979721771446 +5761,3.4381189079094154 +5762,5.707811171482956 +5763,5.371393225629279 +5764,-2.636242786297186 +5765,6.450352137026255 +5766,-2.655311317952659 +5767,1.2292573934999882 +5768,-5.806331685495772 +5769,4.238656314403757 +5770,4.750499953892213 +5771,4.467785271231352 +5772,-2.6369490753485834 +5773,7.063927009043143 +5774,2.2837685251417223 +5775,3.7083625430252956 +5776,-8.78194316544501 +5777,-4.822706517165513 +5778,6.371901648934955 +5779,-1.3314652459361493 +5780,3.7053794270543716 +5781,3.1341162096744486 +5782,-1.0432530769443034 +5783,4.832551896065231 +5784,6.454231087205203 +5785,7.740104978270729 +5786,5.8672996761016485 +5787,-0.5223095301657193 +5788,1.9952625756372715 +5789,-4.703287989424365 +5790,0.18096538250131008 +5791,5.217467066085387 +5792,-0.8370872989724935 +5793,-7.462259458409795 +5794,3.3476087717893126 +5795,0.14748115180159313 +5796,1.4643641356332415 +5797,4.340886557489171 +5798,4.7268190663992575 +5799,6.1162977020291445 +5800,-1.1826711071539098 +5801,-1.3427362439502517 +5802,-0.5894764273474934 +5803,8.597362835912534 +5804,1.2393917464973288 +5805,-1.6876611453355337 +5806,-9.929152971797263 +5807,3.342342090242285 +5808,3.479351859301361 +5809,-1.6326463535513187 +5810,-1.1346809784089964 +5811,4.565281148684251 +5812,-6.008349066045974 +5813,-1.0060290641864296 +5814,3.6778092348978464 +5815,7.812805759049257 +5816,5.25719405608862 +5817,-3.3509574177417982 +5818,1.8085415529280042 +5819,4.77306040735844 +5820,1.7810419320974198 +5821,-3.780952324909268 +5822,2.9395112758942967 +5823,6.322634682698553 +5824,7.992803527533441 +5825,3.755761018280549 +5826,-2.15320841309278 +5827,3.123275432850318 +5828,2.3839551421089644 +5829,3.2220966980226846 +5830,-1.7836744317870559 +5831,3.5360517744200326 +5832,4.4999434852257565 +5833,3.680530636965199 +5834,8.235758111298912 +5835,3.429155493440897 +5836,-2.1098673012695053 +5837,4.944372709720386 +5838,5.433869217571554 +5839,-4.262068743659202 +5840,2.5157780352885872 +5841,6.792589055323265 +5842,-4.528026725453455 +5843,3.488793910174789 +5844,7.411215189391987 +5845,6.781791214715643 +5846,5.487764024751463 +5847,-6.097940435749995 +5848,8.862328828885097 +5849,1.136197933930434 +5850,5.232493807772071 +5851,4.717175063804153 +5852,2.2386305185632636 +5853,4.211693531070922 +5854,6.8135396399629045 +5855,7.212860586998614 +5856,3.2901705954283518 +5857,-2.5142327034422896 +5858,5.869691741282973 +5859,3.137166902510928 +5860,-0.28654690450675163 +5861,4.63546342053953 +5862,3.0365280526038645 +5863,4.331423073689314 +5864,4.199122451923676 +5865,6.905080271770131 +5866,6.597848846338488 +5867,3.320364979339051 +5868,-1.2018165544036379 +5869,-1.6887970759914914 +5870,2.388604817761505 +5871,5.552091004990596 +5872,6.69924316856822 +5873,8.334520418023844 +5874,1.6018751423034332 +5875,5.783993184823138 +5876,6.187039117985973 +5877,-7.563619944569729 +5878,1.7573110794213924 +5879,6.098866000622463 +5880,0.9610948109329943 +5881,2.282388417930839 +5882,8.84752158225193 +5883,1.1070425406486717 +5884,0.6288388967282214 +5885,5.4291189635029955 +5886,-11.228544803539824 +5887,-2.9878655407672614 +5888,6.904910745800756 +5889,6.07872307178131 +5890,2.0886087676017513 +5891,8.026692050591612 +5892,0.8821231849716735 +5893,6.070494996463016 +5894,4.509830631363653 +5895,-3.3008810939291586 +5896,5.821559023251572 +5897,5.184074091463146 +5898,3.9950593925365663 +5899,3.992435201805283 +5900,4.708265318778923 +5901,3.1167504194334406 +5902,-1.7737270037838875 +5903,-1.8323385285935985 +5904,6.842888813934238 +5905,5.096000913787729 +5906,2.9852384607086018 +5907,10.169141512116102 +5908,6.307737030453541 +5909,3.234941233795964 +5910,3.569902076322247 +5911,7.366718824367219 +5912,-1.7012602286241139 +5913,5.274341521357151 +5914,3.4714030896366426 +5915,7.264978262382398 +5916,6.236032622580945 +5917,8.919626751678829 +5918,-2.003647052611844 +5919,1.9720150692453462 +5920,5.7616630441157675 +5921,1.056712921843302 +5922,6.214578076753163 +5923,-2.3456774157479465 +5924,-0.3021565233505501 +5925,-1.4600429773933044 +5926,9.960829172801937 +5927,4.194421360092384 +5928,-1.8471086302434392 +5929,3.270806099534592 +5930,5.147259522990643 +5931,4.32326295524783 +5932,-3.8546408976704574 +5933,1.8528924434407141 +5934,2.5048283670041984 +5935,5.626027384611136 +5936,1.5167903856510123 +5937,-1.809282035135078 +5938,-2.3554984142660764 +5939,-2.058434333971161 +5940,-0.2173759044470467 +5941,1.5416577700470673 +5942,4.152215482088172 +5943,5.530574406945821 +5944,-4.818418261979427 +5945,-0.834964875602248 +5946,6.271816734079678 +5947,-0.46818424487609067 +5948,4.9002461116252745 +5949,2.6339023900172753 +5950,3.767635417009293 +5951,2.428889890638834 +5952,6.741011908077361 +5953,1.2603176234843696 +5954,0.9064749869888987 +5955,-8.361853806413926 +5956,-0.676257459389279 +5957,3.0604228479271276 +5958,6.707970048481275 +5959,3.532492005767237 +5960,3.9105472879747563 +5961,5.523849026572535 +5962,5.000561057299452 +5963,-4.239602923752116 +5964,-3.589039779132127 +5965,-1.5855935682014866 +5966,1.612050362968334 +5967,2.8389685343221194 +5968,3.1439894357667506 +5969,4.581591954441166 +5970,2.249854660715516 +5971,1.4369388566473804 +5972,5.6140621054068935 +5973,4.285823170978327 +5974,-0.6024516324490311 +5975,5.1485008199519 +5976,3.6165796381637048 +5977,2.976577105228494 +5978,7.638165013632095 +5979,4.154163326457141 +5980,5.103053333500977 +5981,11.201861643702772 +5982,1.9598395935295494 +5983,2.6321855650257353 +5984,-1.9435099629378276 +5985,9.965160884140698 +5986,4.060028803691281 +5987,4.878362244083865 +5988,-1.8288632586887503 +5989,2.1540964472541253 +5990,8.909016739813822 +5991,5.8112646481038555 +5992,6.885725263788768 +5993,7.442616767027063 +5994,8.186202646395486 +5995,1.267092913457681 +5996,-6.569142536750483 +5997,5.1910903888444615 +5998,5.0005194876785595 +5999,3.214710671279863 +6000,-1.6288017223675157 +6001,3.814789108963 +6002,-1.540340195828931 +6003,0.4286180952497951 +6004,6.205131965531583 +6005,10.580006894481713 +6006,6.022432897194891 +6007,-5.239825373974932 +6008,8.18598048198304 +6009,0.15985582504115103 +6010,3.7556668173463064 +6011,5.451686439977718 +6012,1.989775090616435 +6013,6.695618908587263 +6014,6.168562744259313 +6015,3.5844531051411916 +6016,-8.116620008216852 +6017,5.540517761404413 +6018,1.7378432197841063 +6019,1.2457430522047095 +6020,3.533024018187721 +6021,0.580479365535965 +6022,0.9144486367927691 +6023,-0.06138508062231408 +6024,1.3541151991357914 +6025,7.448981088532101 +6026,3.4860253556081915 +6027,-3.8599814636935097 +6028,-3.224997904628381 +6029,6.372991836676008 +6030,5.914624489721448 +6031,-4.073449280491909 +6032,4.663593679358516 +6033,6.267745087811037 +6034,3.258227825696313 +6035,3.8857100819635146 +6036,-2.3030501978541498 +6037,4.35778888853563 +6038,5.611147160207986 +6039,1.195839662499602 +6040,3.8978325111499936 +6041,-3.1176278815344225 +6042,8.487457540312167 +6043,-9.296365230438862 +6044,5.888593765663588 +6045,5.693510569664966 +6046,5.574470807495788 +6047,3.863779013681171 +6048,3.6727330226734196 +6049,3.250341901035835 +6050,3.482514498937742 +6051,8.085025317848944 +6052,7.811536172083381 +6053,3.8670812143252573 +6054,-2.7252201929282873 +6055,4.738095107258784 +6056,6.05972342995563 +6057,6.29831733177213 +6058,-2.628629581919495 +6059,-0.9450787938717095 +6060,3.509130114821177 +6061,-4.9810347048296535 +6062,6.473583186633998 +6063,-1.8224163874949522 +6064,-8.506823182784183 +6065,-7.748232682766566 +6066,4.277281932368678 +6067,-1.3748760372341202 +6068,3.3457016753413362 +6069,5.592984779725747 +6070,1.2006050247382654 +6071,3.764363730429144 +6072,6.261844689261164 +6073,6.243424099020706 +6074,5.925070281739162 +6075,5.519533517133652 +6076,-0.4286999335272292 +6077,4.812850316932362 +6078,4.822792671966045 +6079,-3.616853004117733 +6080,1.591547843157635 +6081,1.230157179078056 +6082,1.4457606697308707 +6083,7.159181465457637 +6084,-2.152891902292702 +6085,5.645814870932265 +6086,-1.3135112191060954 +6087,5.179770885668348 +6088,4.603726726455155 +6089,-0.7906455356055168 +6090,2.3694380638557515 +6091,-10.026909296477204 +6092,7.89168039063893 +6093,6.264307315738004 +6094,4.077645593186199 +6095,6.360864822675567 +6096,-2.950703810159958 +6097,1.9244085161698297 +6098,1.5150135549352195 +6099,-0.22810850063023003 +6100,-0.5969457079504858 +6101,4.703313798638609 +6102,7.401114399232162 +6103,4.740641209441891 +6104,-2.8814699221978617 +6105,-5.927660891680687 +6106,1.723778230269816 +6107,2.931639994277826 +6108,-3.012224645249205 +6109,0.4415009815976975 +6110,5.066488435933593 +6111,5.588811533962436 +6112,-6.6480275901656904 +6113,3.723867280624984 +6114,3.3640274458497084 +6115,4.79169873736965 +6116,1.9515388524677346 +6117,2.2981457073250815 +6118,5.966309444128806 +6119,4.2488837776368715 +6120,6.054699648719728 +6121,2.932718282937686 +6122,1.586414682584607 +6123,4.597825018966203 +6124,6.8165381844256006 +6125,1.7466795739238816 +6126,2.907444644779866 +6127,4.045518264972544 +6128,3.0603254031087896 +6129,1.1410043353876207 +6130,-0.9023476005183529 +6131,2.288412515807241 +6132,6.203704654786472 +6133,6.698176709006274 +6134,7.54532877387717 +6135,2.2655831919058644 +6136,7.857945443053129 +6137,-6.592715482791209 +6138,-0.79573051129127 +6139,2.0966871211266658 +6140,2.5795395796253566 +6141,3.092646621249248 +6142,7.7788449926776675 +6143,3.5400056561645608 +6144,-6.625668254137904 +6145,-3.7436542690892627 +6146,3.937855717402422 +6147,5.212674743329267 +6148,3.46854732145293 +6149,5.086640468480098 +6150,2.0477746743388003 +6151,6.333670609941649 +6152,5.447265823035346 +6153,4.124539459748389 +6154,6.928575951675362 +6155,7.08506821901168 +6156,3.1108171057536325 +6157,-2.838384451569186 +6158,7.712469902115177 +6159,4.542782709520098 +6160,2.7340645137676933 +6161,1.4451731128312868 +6162,2.458604646009838 +6163,2.4673746734400135 +6164,4.122675238404673 +6165,7.976863962596768 +6166,1.4177080815777385 +6167,7.607813669337977 +6168,4.74621399418198 +6169,5.60057680351727 +6170,-4.365375784282438 +6171,1.8564466450499855 +6172,-0.6870469000683853 +6173,-1.0520431669446833 +6174,-6.188091101655755 +6175,-4.336761863553485 +6176,3.609485589886494 +6177,-1.1962315679743214 +6178,-2.94662121325513 +6179,5.440456589038622 +6180,-3.011730677728156 +6181,4.244872183136769 +6182,-3.159889975723755 +6183,5.522660353230769 +6184,5.078054573948814 +6185,8.674049346101254 +6186,6.967134549505549 +6187,6.894180425819853 +6188,5.763664553423332 +6189,7.31315307424617 +6190,1.7972509814130524 +6191,3.9951858378377496 +6192,4.991081131282719 +6193,2.3850662190570713 +6194,5.733768706463881 +6195,-4.421715149064113 +6196,5.752430219608436 +6197,3.6070446713693647 +6198,2.6339882515149498 +6199,6.145994459069094 +6200,6.037838497756571 +6201,-4.920635649327662 +6202,3.4872678685230376 +6203,0.25131637889475855 +6204,5.658718791671829 +6205,5.843611723022495 +6206,4.616335336781695 +6207,3.9180789906865243 +6208,3.6846702920094687 +6209,-0.28524967077610197 +6210,3.5275516113253227 +6211,1.577226621987192 +6212,4.326864241597943 +6213,-3.48445870068422 +6214,-0.39489212685419683 +6215,4.42192625706387 +6216,-1.3195366673140339 +6217,0.9251561803544048 +6218,1.0709668752148274 +6219,3.9074121225916514 +6220,-0.48631290222190743 +6221,1.4229240044605622 +6222,8.537577774794912 +6223,5.488237805349856 +6224,7.248215623651609 +6225,0.4478099838702228 +6226,-4.494749064285642 +6227,5.1520927676051995 +6228,7.960869482265911 +6229,2.3442251407823966 +6230,7.47254244019765 +6231,4.881486136763299 +6232,4.961983475242343 +6233,5.79954686550428 +6234,1.9863661974358442 +6235,0.07996496162363119 +6236,-2.955269723311849 +6237,1.7271087547461461 +6238,-4.010571974410019 +6239,1.5447974162347227 +6240,6.198994995328579 +6241,-6.109691330774047 +6242,5.287514280639839 +6243,3.6222762861643707 +6244,-3.116854242909119 +6245,2.144208029266041 +6246,0.48663386876092657 +6247,8.029431364589353 +6248,-4.031216227366781 +6249,1.4117138417705626 +6250,5.828327084842143 +6251,2.1728192352392073 +6252,6.598946820508909 +6253,5.577730902629844 +6254,-8.336691355826316 +6255,-1.669262907776586 +6256,-3.8642450933769714 +6257,6.626629954395065 +6258,0.8628987116462918 +6259,1.3938267580569197 +6260,-3.6057642626540067 +6261,-0.167372355474666 +6262,3.817113176058403 +6263,-6.448149205654937 +6264,0.5076544308786612 +6265,4.652745516352351 +6266,10.145764870862234 +6267,-0.6720804752428948 +6268,3.0629275189750453 +6269,-1.0305058937027751 +6270,7.700870809390654 +6271,1.5878454089624983 +6272,5.272771169058917 +6273,-1.9335875116478392 +6274,1.7000308614310806 +6275,-0.812664494173629 +6276,4.721520876795435 +6277,3.870513958671821 +6278,7.893243978297555 +6279,5.33139853471053 +6280,1.460144681713577 +6281,-0.38281827064983653 +6282,5.06292133359893 +6283,-1.2004779619196038 +6284,-0.9781493829571211 +6285,-8.767127750661993 +6286,-6.186689386332776 +6287,-1.8973455600635272 +6288,4.801560800954753 +6289,0.047450722858627295 +6290,2.8678916623509965 +6291,5.332639483509223 +6292,4.826487182948927 +6293,7.911546689360808 +6294,4.9301757741538665 +6295,3.8316109380898293 +6296,5.827291637961876 +6297,4.1636770617373156 +6298,7.147083485702576 +6299,6.467365064207715 +6300,2.7993851763696638 +6301,6.111663583197161 +6302,6.367128928504646 +6303,6.92072151897136 +6304,-1.3471420822719302 +6305,1.9398762655165136 +6306,-2.645654983358535 +6307,-1.778702729215678 +6308,8.137588248876499 +6309,7.358429828296643 +6310,5.376534473820363 +6311,5.972713321537612 +6312,5.984219864664776 +6313,4.923464488493964 +6314,6.968564845328796 +6315,2.11097242303496 +6316,6.784692781143841 +6317,1.5162740862245905 +6318,2.4188102453709 +6319,5.407323939816199 +6320,1.2492075844576234 +6321,3.7630685518833866 +6322,3.775148008034873 +6323,4.410032195682395 +6324,3.5689835995626464 +6325,2.837645003232084 +6326,3.8495067816825945 +6327,-1.1043362598696096 +6328,3.8730687284434335 +6329,-5.726246314900106 +6330,5.9925760808795125 +6331,-3.821791677818716 +6332,3.491994830581684 +6333,1.342273533016129 +6334,3.8119926368840824 +6335,6.205347653276972 +6336,2.836874137421895 +6337,-3.940457469742228 +6338,5.757131027940343 +6339,7.480979101515199 +6340,-2.694056259426979 +6341,3.7705940914979523 +6342,-1.955181681490937 +6343,4.73732900205024 +6344,-4.252059962442076 +6345,0.5101229656433371 +6346,4.763082569484342 +6347,3.760128433888825 +6348,1.2267391424724006 +6349,4.933891635724682 +6350,3.6381663759443708 +6351,2.9739750466046995 +6352,4.628790695286147 +6353,6.771823249162251 +6354,-2.636472342388679 +6355,3.8578691289773728 +6356,-5.106436341427089 +6357,2.4939138057768253 +6358,7.148468883778529 +6359,3.5108907451105336 +6360,-4.451491796702749 +6361,5.924703735124007 +6362,-4.989775523470034 +6363,2.1335928317149833 +6364,-6.232836156472646 +6365,-0.3872850616243977 +6366,4.060970914806871 +6367,7.1897329905522485 +6368,4.4236141848085255 +6369,-5.93987772889935 +6370,-0.34000820874953874 +6371,-3.9977497729115985 +6372,2.8505917912037044 +6373,4.828846698378658 +6374,-0.7954948046155391 +6375,2.841091341758605 +6376,0.054429026775495604 +6377,7.122320466511892 +6378,4.543529559245729 +6379,6.048689035782765 +6380,4.238772967120944 +6381,4.547710195770045 +6382,5.663628757203935 +6383,4.195534050261791 +6384,-2.2209187847312406 +6385,5.816659556373197 +6386,1.8481198186374717 +6387,3.018748929654058 +6388,-6.594978943949655 +6389,5.727388864782845 +6390,3.322373777714538 +6391,6.447214015326324 +6392,-5.944767187357209 +6393,-6.8491912479756065 +6394,6.24829853831019 +6395,4.753742207364095 +6396,4.017118352843668 +6397,-0.14897532547835052 +6398,4.888058929357417 +6399,7.527634168566136 +6400,-1.0712957364545248 +6401,4.643972279588956 +6402,7.565294971920057 +6403,5.175120798037753 +6404,1.8277874434436814 +6405,-2.329387207233079 +6406,5.6052627327264615 +6407,5.508794954719492 +6408,3.327019235392336 +6409,5.536100544310196 +6410,5.466722587518996 +6411,3.493705589656596 +6412,-5.343800759830142 +6413,-0.6545400903915644 +6414,4.208400530127173 +6415,3.3102695488957288 +6416,3.4427357054355134 +6417,1.071775333508078 +6418,-1.7295298707558093 +6419,4.944917718169891 +6420,5.842955497654796 +6421,6.206417924078397 +6422,2.939444837545798 +6423,7.352097889720886 +6424,-3.405125227831914 +6425,5.724783503888196 +6426,-6.936232583841579 +6427,2.8356813587251173 +6428,5.932012143110067 +6429,4.067024169231409 +6430,3.152253759796268 +6431,7.905780488915772 +6432,6.241723301550059 +6433,8.490539021154538 +6434,5.38990143641541 +6435,5.901999036665078 +6436,5.913877109278518 +6437,5.85973551635247 +6438,0.5248159919903704 +6439,1.4406185881756335 +6440,5.237904874645453 +6441,4.315309521725316 +6442,4.34661630589394 +6443,7.1938242598989115 +6444,6.0255984740007165 +6445,1.9899076847017012 +6446,5.871654888990876 +6447,4.272510314806437 +6448,-0.6863057192139842 +6449,5.5622249123087855 +6450,5.329926168533716 +6451,5.480845692539999 +6452,2.755379298319731 +6453,3.9463505565654255 +6454,6.720946850618161 +6455,1.686679644316183 +6456,4.8662802718680425 +6457,5.222002781107454 +6458,9.378388276708904 +6459,5.579613995587977 +6460,6.124897649835441 +6461,2.268319459880635 +6462,-3.878538534823625 +6463,1.629305324481352 +6464,8.208896106335235 +6465,6.032916255709965 +6466,8.081168143619449 +6467,5.871777996609986 +6468,-3.2957273231995656 +6469,-0.14122775019946232 +6470,7.646932410116986 +6471,6.888825967034361 +6472,4.342368322008118 +6473,3.932618508191211 +6474,3.9409939567403716 +6475,8.459532376416131 +6476,4.417121774629457 +6477,-6.934489357475354 +6478,6.968012896034233 +6479,1.8684389459204933 +6480,2.986468094264172 +6481,3.878991752332571 +6482,4.523224918795731 +6483,-0.25640076766909337 +6484,-1.3118472950768196 +6485,4.503821823494782 +6486,6.189745721731199 +6487,1.47866611584613 +6488,-6.298881163821992 +6489,1.4052674624191064 +6490,5.593521529204448 +6491,6.187984310461473 +6492,2.545209209096281 +6493,-0.4649521968673452 +6494,4.128126574228039 +6495,6.547404734426538 +6496,-0.4784288421943097 +6497,4.579840620336567 +6498,-0.5900421957850256 +6499,5.163179900035856 +6500,6.381905589977534 +6501,-3.640942430208868 +6502,-7.73076496310616 +6503,-0.3419724301131679 +6504,4.107423743025337 +6505,6.482858841387573 +6506,3.403972749394151 +6507,4.174180747673683 +6508,-6.6174819359361265 +6509,5.589076089504081 +6510,-1.408953749668594 +6511,5.237197094398485 +6512,2.7482488092815776 +6513,6.034411796813989 +6514,2.4232112404449957 +6515,-2.678814298447737 +6516,6.663807024161811 +6517,7.078815973628866 +6518,6.3617365765662335 +6519,5.6354495111513465 +6520,6.521819345773336 +6521,5.717806628408421 +6522,5.29170018192745 +6523,5.436705114561688 +6524,-0.3277813690521936 +6525,-6.991040530370285 +6526,2.7704330991996047 +6527,-2.5277385603786793 +6528,5.795866135605364 +6529,5.830386364147438 +6530,5.78496150935654 +6531,1.070144154851391 +6532,4.597792495088255 +6533,7.04841703038154 +6534,9.507660468359953 +6535,7.850299777237095 +6536,6.165281736026441 +6537,-3.090029467124046 +6538,6.935468615367704 +6539,3.451346809607445 +6540,1.5273292625415427 +6541,5.664973455844113 +6542,-3.62354206822787 +6543,1.5424923301891322 +6544,8.102938957195118 +6545,5.660056636230498 +6546,3.046383823490459 +6547,7.208441623559073 +6548,3.444929241961753 +6549,4.790888715844373 +6550,4.344336016835442 +6551,3.7769055414025656 +6552,-2.4054923889316964 +6553,-1.3146331534996267 +6554,5.3562525614933785 +6555,4.688446502660722 +6556,5.323017946102781 +6557,-3.6292814499530612 +6558,-1.4857987919677735 +6559,2.644455388124733 +6560,7.928594047036454 +6561,2.5913967955105655 +6562,-2.6330988720913338 +6563,3.395104065666592 +6564,4.132413345469005 +6565,2.5085736587397656 +6566,3.8641957035221526 +6567,0.4343830899053025 +6568,4.340374276409639 +6569,5.222159568379192 +6570,9.179328427377637 +6571,3.640451961457299 +6572,6.645494119575139 +6573,-1.1599804597527237 +6574,4.284834063397376 +6575,0.2430546518115233 +6576,4.3235629528184685 +6577,5.354536434026245 +6578,5.59284119898995 +6579,4.690387305686723 +6580,5.776038205180215 +6581,-3.731127235582938 +6582,-7.161681709414476 +6583,5.2502369350274325 +6584,1.8325080088649945 +6585,0.8775101931178674 +6586,-5.663024498930598 +6587,3.2934087396037617 +6588,5.287942136797399 +6589,-1.9288566342731914 +6590,7.175252524963337 +6591,1.4670159844226531 +6592,3.199546984841195 +6593,1.5236446413092684 +6594,7.630051253770419 +6595,1.6585802976443085 +6596,-4.713512809669222 +6597,3.3918952455047364 +6598,6.8982101578810555 +6599,3.6742501322487304 +6600,6.580590868489787 +6601,8.297059470841182 +6602,3.266419177899264 +6603,-3.2807492750094736 +6604,0.8942159205878185 +6605,3.9529045171864583 +6606,0.969323405254802 +6607,5.546737234239845 +6608,2.3624525407555907 +6609,0.7597607214599649 +6610,4.5871415731520395 +6611,7.651454172773864 +6612,6.349264415150406 +6613,5.548546752748652 +6614,8.727880964678043 +6615,3.69925377446233 +6616,3.9471550452978 +6617,-1.0825475122743768 +6618,-3.1634891988892986 +6619,9.725882938843927 +6620,7.251157656811989 +6621,2.603655868004324 +6622,1.5349484387272698 +6623,5.195030535410575 +6624,5.078251966370045 +6625,0.7075952204406554 +6626,-3.894361368532785 +6627,3.683587865471897 +6628,0.11408516993827861 +6629,-0.8035659949492509 +6630,3.6801744756974273 +6631,-0.19302751128839532 +6632,-0.8981613967970413 +6633,5.246267504395266 +6634,-6.482895208510185 +6635,8.070487575713344 +6636,4.366515219055607 +6637,1.0200259442920943 +6638,6.746060374075982 +6639,5.039028261954503 +6640,4.937987846805312 +6641,5.950141579246566 +6642,2.088200647245615 +6643,-13.162814267431662 +6644,5.368950924483589 +6645,9.250399731132891 +6646,5.402903673717476 +6647,6.026503605596265 +6648,-8.021330703174502 +6649,-4.13347549873901 +6650,6.790385318300321 +6651,1.5503756338641672 +6652,4.749083644263936 +6653,7.535850693197472 +6654,5.285696253556779 +6655,-1.884346070036567 +6656,-3.5787088765238577 +6657,3.483917636861105 +6658,-4.119911854064225 +6659,-8.767259421643914 +6660,2.495571487026788 +6661,4.012876855708622 +6662,-4.003997271132282 +6663,0.7032341998303987 +6664,0.6249326016930122 +6665,-2.083096030722205 +6666,6.281536758956231 +6667,7.969442786523591 +6668,-3.853654905249365 +6669,6.773513308532012 +6670,6.807021683704657 +6671,6.4787854943469325 +6672,4.744711453894478 +6673,1.5509270172387588 +6674,3.171668181051902 +6675,2.1567747491287257 +6676,4.721917717436058 +6677,-7.673744362678695 +6678,6.04343165048278 +6679,5.369533315231003 +6680,3.610471491721662 +6681,0.3939488188326395 +6682,-9.502730384756543 +6683,0.010682385920153534 +6684,4.114170150783842 +6685,-5.694749544315842 +6686,2.7800941970137805 +6687,6.17852473069606 +6688,2.362229214568842 +6689,5.148404628377214 +6690,10.535180205406988 +6691,-7.316218634865712 +6692,-2.4609001594850195 +6693,5.865406258551455 +6694,6.825157906502396 +6695,6.0550881725739245 +6696,-3.151935549903809 +6697,5.5333181562713785 +6698,3.6858309060914043 +6699,2.7054676644571893 +6700,-3.0624903114995097 +6701,5.414732859520438 +6702,-12.432459559474836 +6703,0.05282964215484039 +6704,-0.7186831961915424 +6705,6.477607997905459 +6706,1.5614212951766815 +6707,-4.850415386482323 +6708,5.626651788881978 +6709,-3.933234717284884 +6710,6.0180413085490585 +6711,-7.578004017023828 +6712,4.343998257687909 +6713,1.9891210771272254 +6714,1.9600638489621893 +6715,5.802198446128069 +6716,4.365382812092214 +6717,-4.973266054089018 +6718,0.8531283428566777 +6719,0.43257722241698743 +6720,2.7939632169252024 +6721,0.7662911601210539 +6722,4.930702077746358 +6723,4.790736613413184 +6724,4.4043661136996395 +6725,-1.951785097780107 +6726,3.268167604225889 +6727,3.3718061058893873 +6728,1.11646309993163 +6729,-3.8809564270767223 +6730,8.946593266150478 +6731,-5.57959835433535 +6732,3.678597151331764 +6733,0.5096296732679619 +6734,4.395485003003873 +6735,-0.16604475069286995 +6736,8.260449590392998 +6737,-6.625549488066095 +6738,1.9179006971801178 +6739,-4.714128833949016 +6740,5.962247514460594 +6741,5.424906710166722 +6742,9.340877663765777 +6743,5.526742814900707 +6744,7.148453478254206 +6745,8.579455903298669 +6746,-6.3545221374082566 +6747,2.5120094654616247 +6748,4.464867741857904 +6749,1.599951653966186 +6750,4.634671485986208 +6751,-2.078034175856477 +6752,-3.7701939451939155 +6753,3.7709235470802698 +6754,6.029103679657816 +6755,7.618188085164018 +6756,-1.3600615018898237 +6757,-0.8137985373762759 +6758,-6.761454565845327 +6759,-4.904394472316503 +6760,-7.399541648784355 +6761,8.177187385867661 +6762,1.2750072498346996 +6763,-0.503166069634053 +6764,-7.922093758226476 +6765,0.7308055966027821 +6766,-1.6210530381353145 +6767,8.539426561701944 +6768,4.476583700010144 +6769,8.76652784830248 +6770,4.080135316175994 +6771,5.365631669900673 +6772,-3.955332055221023 +6773,-3.842108532159728 +6774,2.578734381585133 +6775,2.557913756960382 +6776,7.7767717348065 +6777,3.2200171373258124 +6778,3.478105704986601 +6779,3.56514980935624 +6780,2.171101798140894 +6781,4.264326892247929 +6782,3.108869577507587 +6783,6.1473422141173515 +6784,-3.066174270797742 +6785,4.507875748567022 +6786,5.318840311947507 +6787,5.672857982771379 +6788,5.279041385698271 +6789,5.030912037655054 +6790,6.592367482182724 +6791,3.008938283656051 +6792,5.870681606390691 +6793,6.259500050966196 +6794,5.07871226684646 +6795,2.6950228850421567 +6796,3.4458601672257463 +6797,0.5623714150971175 +6798,5.572921088884291 +6799,3.7993231240661762 +6800,4.2382792259232165 +6801,-1.2782013915578323 +6802,3.5427896207240526 +6803,4.135349116831402 +6804,2.685559378753453 +6805,4.167870415075156 +6806,3.975205186984745 +6807,4.510401094737903 +6808,7.213181810604742 +6809,4.20295462024741 +6810,6.049507067388898 +6811,-1.4237462169567796 +6812,1.3652520605238787 +6813,3.8933361265730966 +6814,4.955103606588637 +6815,-3.0557382657480208 +6816,2.331073608723186 +6817,6.685440618532885 +6818,-4.999492230640538 +6819,-4.188958341382415 +6820,2.2019747734214627 +6821,-3.252464455305971 +6822,4.4984073632699175 +6823,1.7066957233307432 +6824,0.567415362716881 +6825,6.86112534091703 +6826,7.143422885815493 +6827,-0.41316192486709796 +6828,-7.0989285639974185 +6829,4.624110608834148 +6830,5.871102165190944 +6831,-8.614240197206255 +6832,2.112927445925213 +6833,9.240984554385406 +6834,5.665913867419977 +6835,1.8078419196116151 +6836,5.884294865939216 +6837,8.231876656859196 +6838,3.684097400284969 +6839,-5.9795993213974485 +6840,2.801604927633077 +6841,3.6857219503741376 +6842,5.90136369810755 +6843,4.424484186485252 +6844,4.504600089629436 +6845,4.739084887330709 +6846,-1.2716815059071591 +6847,4.612659862997217 +6848,1.0386815058055459 +6849,8.517304704610643 +6850,3.1115437709422644 +6851,-2.396906442644026 +6852,6.1839853878688436 +6853,4.361458620482511 +6854,7.394029774078465 +6855,2.7102103391027996 +6856,5.870317645933513 +6857,1.5316575572985092 +6858,3.9887493986463736 +6859,2.5007776657723313 +6860,3.6742556429015742 +6861,2.6142889847854187 +6862,5.6961782407592585 +6863,-0.5138073758417717 +6864,7.931474781946488 +6865,0.14457152153251837 +6866,2.321669010211297 +6867,5.910853212868884 +6868,-8.234146779257477 +6869,-4.716722484533869 +6870,5.901445313531134 +6871,-2.58928271410596 +6872,6.598140438587614 +6873,0.17353587826228944 +6874,-4.095578880397891 +6875,5.010291957460459 +6876,5.0240074248744335 +6877,3.962636921827838 +6878,-3.4114085524939326 +6879,2.4096556168749803 +6880,1.832312272150485 +6881,6.724532398670812 +6882,3.231626923606261 +6883,7.88135180983941 +6884,1.784072787061401 +6885,6.7395196518885685 +6886,6.62124794173482 +6887,5.479536027055417 +6888,4.186274501815227 +6889,2.6476058412013868 +6890,2.722880214921371 +6891,5.115819638259684 +6892,1.703363774601593 +6893,-2.979077942131179 +6894,6.648481502610576 +6895,4.4575209841175685 +6896,0.7765769256933313 +6897,2.926260942099636 +6898,-3.8504679929083574 +6899,-2.154192494224855 +6900,-3.157350907553372 +6901,6.148805480858918 +6902,-9.127716270907774 +6903,2.356952063295076 +6904,3.747654600349512 +6905,4.101415746295379 +6906,-0.6932612887035218 +6907,3.7720000796961966 +6908,-0.8994117812425104 +6909,0.4092578329924517 +6910,4.345693039567429 +6911,6.4210664223632055 +6912,-3.215046213462046 +6913,-0.6387907715810696 +6914,1.3470345071195875 +6915,1.4271552235346716 +6916,4.108352903627276 +6917,2.8596846845777586 +6918,6.869090873491696 +6919,7.558287535745182 +6920,1.0184937102732476 +6921,6.152667766162019 +6922,4.193729122005649 +6923,3.773452987630193 +6924,1.9189186949394004 +6925,4.818726614122956 +6926,-2.1442086158175466 +6927,-2.5695738480176766 +6928,4.056057646708295 +6929,6.734939908128799 +6930,9.621936200135275 +6931,-4.126282257529374 +6932,3.5793673320707255 +6933,4.931106635589113 +6934,3.1276244819558086 +6935,2.8784949562861937 +6936,6.656769371541793 +6937,9.729183599658644 +6938,1.752165902353303 +6939,3.8969721514192854 +6940,-0.3556378712025576 +6941,-6.649658847852623 +6942,-0.7488630406470443 +6943,-3.895026033145772 +6944,2.231925657752669 +6945,-3.5150800464139795 +6946,-4.265878704535522 +6947,6.644690487747326 +6948,1.0282857898356612 +6949,3.162445460144877 +6950,2.0051796757672595 +6951,-3.4459159698609296 +6952,-6.618252604056567 +6953,3.0345849492238814 +6954,7.146627502352967 +6955,3.5815367802619393 +6956,8.033203570362693 +6957,-0.4679216367714127 +6958,5.941046562704955 +6959,5.491076834427245 +6960,5.655729427133409 +6961,-0.759998677532307 +6962,0.5891024967524782 +6963,5.792502567216379 +6964,3.5471787339192216 +6965,3.999745646052115 +6966,-1.6751782984952888 +6967,3.880630232487233 +6968,5.141798355336651 +6969,-1.2601187916589984 +6970,-3.1986478624556014 +6971,3.622094636408693 +6972,3.6584352206223816 +6973,-0.6783084889311803 +6974,1.1811693800812975 +6975,6.04707584972124 +6976,5.112112046222534 +6977,3.5929298544200163 +6978,6.335861430262234 +6979,3.1251749744566064 +6980,4.1054066407820216 +6981,5.752466270413157 +6982,-1.2422573956667764 +6983,2.537036825605407 +6984,6.324629198001331 +6985,4.470047906460908 +6986,-0.15683082619555508 +6987,-6.617557056795583 +6988,4.751123469786434 +6989,1.3069753579717696 +6990,-8.068036455851454 +6991,6.423709589172352 +6992,-3.5018664017166468 +6993,4.585732600892802 +6994,13.12197172902388 +6995,5.207201493735711 +6996,6.059840866345893 +6997,5.779626513970028 +6998,-2.8140664257516903 +6999,5.306803312065629 +7000,-3.304706032593397 +7001,7.1231458532423 +7002,-4.363592779847754 +7003,1.8885663575905631 +7004,-4.353647868305092 +7005,-11.374572076921599 +7006,1.8460782164753398 +7007,3.907880492703701 +7008,3.1287362176948585 +7009,3.48771673479324 +7010,3.3792664315198713 +7011,4.3242255975855635 +7012,6.191527907493501 +7013,3.3224411084438064 +7014,6.819502304992728 +7015,-1.3833486895146605 +7016,1.2017826403588898 +7017,-1.5124760313873522 +7018,3.7046932850128673 +7019,4.151523744058046 +7020,-0.009640706201651606 +7021,-0.33059602907557367 +7022,3.7803608600519496 +7023,6.931950289188309 +7024,-9.100611415275782 +7025,5.731834638044297 +7026,6.163659274834565 +7027,4.560883267244594 +7028,4.420370484338033 +7029,7.765147271719228 +7030,6.864992850346019 +7031,0.6660178329223931 +7032,10.04647318112734 +7033,-8.342548523415847 +7034,1.0945837972482049 +7035,-3.985933758236275 +7036,4.75317328816951 +7037,5.160689491189772 +7038,7.018147233148051 +7039,-5.535096642502435 +7040,1.1170510184591689 +7041,1.6954745029521883 +7042,-0.47552691854811013 +7043,3.342357047952981 +7044,3.9651279531576153 +7045,-6.02992075230745 +7046,3.3419323440675743 +7047,-0.19179164248257136 +7048,7.676158795243101 +7049,4.4610944840122135 +7050,-4.849558962634852 +7051,6.402083587175215 +7052,4.731327528917492 +7053,4.555277176522664 +7054,-11.896595305198481 +7055,7.398075200670943 +7056,-1.871289761628349 +7057,3.2057946251595424 +7058,5.687539404315723 +7059,4.8628281363373915 +7060,4.775040221944085 +7061,-1.2597970959277354 +7062,2.565188996658201 +7063,-1.628544890412081 +7064,2.233108276528365 +7065,1.625961106554473 +7066,1.2711399996477684 +7067,3.363880314840506 +7068,6.309975707724558 +7069,6.622074592876776 +7070,0.03630637666378409 +7071,5.002216989989114 +7072,-0.6570830495182931 +7073,4.230882113586722 +7074,6.258241429304221 +7075,5.163594672764253 +7076,-8.370714573145591 +7077,8.577603046758803 +7078,4.204557333826348 +7079,4.997766508448484 +7080,3.0071005370506816 +7081,0.6285643076163971 +7082,-4.586709242723244 +7083,1.4377355442838917 +7084,4.825257595287917 +7085,-4.9267771587919835 +7086,2.1446889558235482 +7087,4.549137934122003 +7088,7.549851528872998 +7089,7.813094905697327 +7090,7.92172989074383 +7091,4.25393642337292 +7092,4.448775186641216 +7093,4.24385682966544 +7094,4.735834506119383 +7095,3.7566972081837724 +7096,0.9347577057358004 +7097,-8.465874857233597 +7098,6.381173921114555 +7099,6.667866989241839 +7100,1.022967873817747 +7101,4.778249452144329 +7102,-3.8198328777221793 +7103,4.193081372381408 +7104,1.896738141850847 +7105,3.9508191453837203 +7106,5.0982480829472845 +7107,7.057468924506655 +7108,-6.612274758212836 +7109,2.09226904920823 +7110,-0.5779190074223187 +7111,2.135249502176577 +7112,-1.5394946709753443 +7113,-5.78085363175395 +7114,5.174947048004851 +7115,-0.8443722117584236 +7116,-5.48542336586604 +7117,3.940688847401153 +7118,0.5259401185002195 +7119,7.22258902379683 +7120,9.118770612843367 +7121,4.156550097682075 +7122,2.2792424325432092 +7123,7.076026689505419 +7124,8.24729943021374 +7125,-2.1540590167232176 +7126,-1.1343269357459675 +7127,6.83148029087973 +7128,4.979162563779128 +7129,-1.4524181660621058 +7130,7.311996220888129 +7131,4.295493390952238 +7132,8.912039312748487 +7133,-3.8828265289663197 +7134,-7.666280647170457 +7135,6.273829526933602 +7136,9.892237851560399 +7137,-2.7704233728616927 +7138,0.8989662356773059 +7139,-4.396153865296037 +7140,-1.789075041836461 +7141,4.3159392530389695 +7142,-1.5649593540521898 +7143,0.2515234648146081 +7144,1.76639879471123 +7145,4.846994006186022 +7146,-1.6300809441197104 +7147,0.4721208194987674 +7148,2.4611990757158475 +7149,2.1878514544811525 +7150,-2.125554849302594 +7151,4.064765758841766 +7152,3.6484541631811456 +7153,5.814198915817638 +7154,3.911613921512523 +7155,4.793006495052502 +7156,3.2493167625551758 +7157,-1.9519911355639818 +7158,4.2540189880538 +7159,-4.092246173979196 +7160,-1.1400523193538907 +7161,-1.2875349514134635 +7162,1.0440232047901787 +7163,-6.214791345348556 +7164,5.15572764140325 +7165,7.730314131224022 +7166,-4.176339623694668 +7167,-1.391116002916637 +7168,5.5448090115318465 +7169,-1.0036792880190766 +7170,-0.4132238920672229 +7171,1.3478593922420539 +7172,8.376436775361292 +7173,4.70833011591832 +7174,5.217201141636188 +7175,-4.891898931587207 +7176,-8.129383292651365 +7177,-2.065280114803448 +7178,3.4971246978257664 +7179,1.7445714150908587 +7180,4.122407770841747 +7181,3.5017839592206594 +7182,0.640208442171619 +7183,6.761478208099087 +7184,6.659757888017434 +7185,4.170385064839596 +7186,-8.475062702045783 +7187,-0.5657748280935934 +7188,-4.533567201910425 +7189,-0.6273586865785002 +7190,8.31972012040017 +7191,7.6137973569450175 +7192,7.335125801980205 +7193,1.0826539702153437 +7194,6.309601764483758 +7195,5.056215383644452 +7196,0.01615656779773855 +7197,2.6547058913512607 +7198,7.663334520172205 +7199,2.3006404039290236 +7200,3.7144468319485715 +7201,0.8351439619114466 +7202,4.8910215249148 +7203,0.10715578296424955 +7204,4.598446859688512 +7205,2.500074778389396 +7206,4.733694867691137 +7207,4.147280124348735 +7208,-4.668996259719124 +7209,-5.599074137740873 +7210,1.3213006475624005 +7211,5.762567474649926 +7212,5.408249343652432 +7213,-0.23341064335696593 +7214,6.383893546997727 +7215,5.123289436805724 +7216,-1.126809854924362 +7217,3.054719621031146 +7218,7.570498038900087 +7219,3.3293332144421717 +7220,6.016186630836196 +7221,6.09841936070494 +7222,1.6108061780058691 +7223,4.59672399808603 +7224,9.36812166965889 +7225,0.8421539685488515 +7226,5.000488341587077 +7227,6.5939421971611765 +7228,-1.5963375051040671 +7229,-4.195118441904987 +7230,3.7229811026224926 +7231,6.6363242419106365 +7232,1.4296881067718032 +7233,5.565358322142982 +7234,8.326105038235443 +7235,7.9100563608925905 +7236,-4.534211817440225 +7237,9.511681679899581 +7238,2.996135577433253 +7239,-3.159945936336926 +7240,-1.2327943828923777 +7241,-3.570052400807519 +7242,6.378747996360211 +7243,-6.699332540840285 +7244,-0.41660355027189233 +7245,2.7616975545494444 +7246,1.4101639979054055 +7247,5.241116427476905 +7248,0.690530489191044 +7249,6.735183562102266 +7250,0.7109577396121979 +7251,7.705879198356182 +7252,0.5958231073111279 +7253,2.121029787349889 +7254,9.23055168954766 +7255,-4.4427327375860655 +7256,7.212235490685561 +7257,-4.941688323135752 +7258,2.0661846179977332 +7259,0.752111229787458 +7260,6.466653816460382 +7261,6.104253512275607 +7262,-0.7282094419313507 +7263,1.6794910786488981 +7264,-2.4182781056041187 +7265,-1.7512475148278488 +7266,4.97552536987101 +7267,-1.8874729889568442 +7268,7.159558769167289 +7269,3.429471427783652 +7270,4.115442768238448 +7271,7.393830174754461 +7272,7.242678970358504 +7273,1.3211856809499523 +7274,6.1848251137961014 +7275,8.122393173567023 +7276,-1.351717398473443 +7277,2.2277547413614265 +7278,4.3593041785438755 +7279,-2.770122014367441 +7280,5.339866872400053 +7281,-6.834490703200393 +7282,0.5314302246770387 +7283,5.230215206510541 +7284,6.1033640178329565 +7285,7.562074501407281 +7286,3.486109991161205 +7287,0.852129993673227 +7288,1.6983546374560838 +7289,1.7447736793888313 +7290,4.475815933730971 +7291,-1.8789376487330287 +7292,-8.853908847737593 +7293,5.625159987011495 +7294,-3.3351713089335018 +7295,1.3815636412197339 +7296,4.613772375431673 +7297,5.418692494948229 +7298,4.976434527350356 +7299,7.214138912604828 +7300,-1.9025315126581632 +7301,4.062601587409582 +7302,3.769722092405919 +7303,4.47718443127241 +7304,8.396922462650313 +7305,-0.7260502691868679 +7306,4.422673698864385 +7307,1.4803999430338823 +7308,2.574829193317988 +7309,-1.73081760352875 +7310,7.509863129510037 +7311,2.313636098988157 +7312,-2.7857546706447547 +7313,-3.4876147957714076 +7314,-1.8201218110609891 +7315,3.6392454752192736 +7316,6.52492436350177 +7317,4.822123741132941 +7318,2.8041160366495745 +7319,6.107716720987546 +7320,1.9763806704477536 +7321,-2.3471544699778484 +7322,-2.1664106453482765 +7323,-0.3040558309134518 +7324,-3.0296944352294988 +7325,6.629643021882023 +7326,3.885789892806318 +7327,4.860803915379633 +7328,-5.534937615394367 +7329,4.0507017973639705 +7330,-3.6279060530831835 +7331,6.975856071951275 +7332,3.8314844091490468 +7333,0.8602105102361489 +7334,5.749081247938475 +7335,-2.9914765087953263 +7336,8.12631780195961 +7337,6.078973084300856 +7338,1.8373988633595046 +7339,3.9313458012881703 +7340,5.085317744028979 +7341,4.669763994796473 +7342,-2.299144619334144 +7343,-7.192708745741116 +7344,6.36705385807398 +7345,-3.7943531198769587 +7346,5.396638523742443 +7347,9.630788919204246 +7348,6.409210815651171 +7349,6.703230729064078 +7350,4.620927750181098 +7351,-0.6350784370705578 +7352,0.766510938830252 +7353,2.103488981117711 +7354,3.1712335752938734 +7355,6.744138578275488 +7356,3.269365450583244 +7357,3.997001121011119 +7358,9.507389743617194 +7359,4.694358454658412 +7360,-2.3990960263175425 +7361,3.063330950449778 +7362,1.7866786235315726 +7363,-3.8785514284120604 +7364,2.947067313364579 +7365,0.7545324479496214 +7366,4.45324048355117 +7367,3.676196197867395 +7368,6.141830117267942 +7369,-1.2162537307162984 +7370,3.1210473650449577 +7371,4.874530566073408 +7372,-4.103726950543332 +7373,-2.3419123245635425 +7374,7.943922396075745 +7375,3.0070016232813748 +7376,-1.8553482464915674 +7377,6.874141319488922 +7378,-9.942102729542983 +7379,2.3300497640351616 +7380,-2.654357998508046 +7381,-3.6732540432728364 +7382,4.9991941153751345 +7383,5.288548067865706 +7384,6.294997961391321 +7385,6.174552454206048 +7386,6.114754498895663 +7387,-4.848411479741129 +7388,7.048264680938356 +7389,-1.0185818843467944 +7390,8.129328368165641 +7391,5.47904004641753 +7392,0.051517853312945075 +7393,5.105370000895203 +7394,5.088452760744348 +7395,10.560053003673286 +7396,3.4335336774527905 +7397,0.914611861831741 +7398,8.181245174996459 +7399,5.245715898625999 +7400,6.001570095634668 +7401,5.9754422109344425 +7402,2.24358268892757 +7403,-0.09995146981043847 +7404,7.763406668202727 +7405,1.1298153395328179 +7406,4.5981980321592655 +7407,0.693845783512596 +7408,-9.986250529264945 +7409,3.489916176285486 +7410,6.381724139528506 +7411,-1.612487121908747 +7412,6.901735538848095 +7413,2.054742656506974 +7414,4.998983657463115 +7415,4.706451335994752 +7416,-3.5809556566641385 +7417,3.667509899722597 +7418,-6.394185981563129 +7419,-3.3778312559409853 +7420,4.284419307219781 +7421,0.9210940993699315 +7422,0.49621565970224685 +7423,4.845407421450916 +7424,4.772197817999912 +7425,3.275119328044758 +7426,4.986153641479943 +7427,-0.14791733330328863 +7428,-6.596612171973076 +7429,4.480385154721056 +7430,2.862555785612275 +7431,2.9646850694077798 +7432,5.940572273852509 +7433,8.685288363914196 +7434,-1.2006917908658907 +7435,4.017282415197801 +7436,-4.988166517420703 +7437,7.353738312563089 +7438,6.3195312592432105 +7439,4.015984873289023 +7440,0.8363692813360956 +7441,8.299625977382995 +7442,0.7161320010945847 +7443,6.30223625011508 +7444,-3.7153849841845634 +7445,4.380251033867576 +7446,-0.1802753916282857 +7447,-0.24810187130602887 +7448,4.761927980765101 +7449,2.535703378879135 +7450,7.495710259861363 +7451,-2.11902953635163 +7452,6.9996929515368835 +7453,6.633603881488448 +7454,2.3480800895182887 +7455,8.317490946747327 +7456,4.614590394019659 +7457,-4.3713599832662435 +7458,5.656500595575656 +7459,0.07237277482508107 +7460,4.73570665815125 +7461,0.7400529827333787 +7462,5.366074457042278 +7463,-1.5746746053216043 +7464,4.336799978111982 +7465,6.487275113341685 +7466,3.907145659720504 +7467,3.64463478879084 +7468,4.608576021046625 +7469,7.0609349503522285 +7470,4.788628935813708 +7471,-0.32896760122608865 +7472,-3.0975145613991657 +7473,-3.3954419621486376 +7474,4.338230455359625 +7475,6.386254249255774 +7476,3.047041063244346 +7477,-0.2113643515931088 +7478,4.160041042773772 +7479,0.019885925093222255 +7480,5.733583710171598 +7481,1.0275825615768566 +7482,5.233005420970474 +7483,5.092556188513462 +7484,6.229726539879475 +7485,1.9143533997412816 +7486,3.728225716885524 +7487,4.910735984396091 +7488,3.5876161388926113 +7489,7.226819272865249 +7490,3.8966563818208124 +7491,3.608306487805995 +7492,-0.02305944873244533 +7493,-6.254964541424597 +7494,5.587332576129118 +7495,10.452087530460878 +7496,5.093469073819476 +7497,6.442591793069242 +7498,1.3218860535505434 +7499,3.9814402744694384 +7500,-0.818195001033252 +7501,0.6496220433081011 +7502,4.106723842121558 +7503,1.3045948411266226 +7504,8.595459304276236 +7505,2.0452762039115444 +7506,5.874075863824143 +7507,-7.020295837683105 +7508,0.8159663179502283 +7509,-9.450516822685836 +7510,-9.695569972682346 +7511,7.240704146617565 +7512,0.8160869786842432 +7513,8.25135698667531 +7514,-1.1010046628019474 +7515,2.473515343593073 +7516,-0.6226227136899962 +7517,1.5642219659455894 +7518,-4.550348772496289 +7519,1.8626909812511423 +7520,3.2099094823407563 +7521,7.7952417423061195 +7522,-0.6837443317280947 +7523,-3.6282691113663743 +7524,4.3138093640462145 +7525,5.122691829710275 +7526,6.286182415410631 +7527,2.843886430094731 +7528,4.564000949937566 +7529,3.890786498021427 +7530,3.977114215998981 +7531,2.920983819343358 +7532,5.353807531847418 +7533,8.886980560387752 +7534,-0.0019327452708055826 +7535,5.216201583174423 +7536,6.7124681840666405 +7537,1.7609270917108941 +7538,3.6378822017398154 +7539,5.737606463151101 +7540,6.026283520217915 +7541,9.231683844353391 +7542,7.840946974133768 +7543,5.503867670328274 +7544,2.5770257251131716 +7545,5.2206662438515785 +7546,2.213790862557118 +7547,-0.24505780697751894 +7548,6.446067963493791 +7549,6.671561996158971 +7550,0.9864572840817507 +7551,7.074403015193757 +7552,4.69110913611282 +7553,2.511111822125638 +7554,5.506928876156218 +7555,6.794816044425164 +7556,1.5989825361872527 +7557,4.572746138112366 +7558,4.0295394513017815 +7559,-2.1328822437862422 +7560,-0.6888253269036162 +7561,1.3998758322743434 +7562,5.81806281297555 +7563,6.400152281498577 +7564,-0.669592023396829 +7565,4.092279252400819 +7566,-9.541962155156007 +7567,5.359327675523804 +7568,5.318301561081111 +7569,2.454430900473206 +7570,3.4287876604778154 +7571,2.7355858473708006 +7572,-1.7214111288466882 +7573,2.4279444523697147 +7574,3.743805365485714 +7575,4.850094785788944 +7576,7.350625694043962 +7577,8.455158776357194 +7578,0.15338189971935454 +7579,1.9192757604586796 +7580,3.3329856575179315 +7581,6.8495493632440185 +7582,4.949744119600131 +7583,5.689222933610292 +7584,-0.9043551924178833 +7585,-0.8882302471018906 +7586,3.801766137656241 +7587,-2.044892071484442 +7588,4.327931789278071 +7589,-6.511245204568615 +7590,6.4070285081197 +7591,6.936840887450652 +7592,-6.5080966642999325 +7593,1.1853369380090966 +7594,4.899071694438274 +7595,4.225260790826341 +7596,3.870431886060923 +7597,-5.286332382375209 +7598,-4.6551645290491175 +7599,-0.867173995379537 +7600,6.2890763172807915 +7601,-5.962565601174222 +7602,-0.1018772735175128 +7603,8.04325674182364 +7604,1.7989287238759277 +7605,-1.7449684875405027 +7606,1.2390991441834083 +7607,-5.976676029521319 +7608,-0.2285455538228742 +7609,5.487815004695171 +7610,3.954939728066016 +7611,1.2775951033662942 +7612,7.135282341484502 +7613,-1.7009489609885002 +7614,2.154641826976243 +7615,3.8380718462190693 +7616,4.4234138498182425 +7617,5.580765390846377 +7618,5.3904453888488195 +7619,3.9613993174921154 +7620,4.008099361525017 +7621,4.8127873644877175 +7622,4.192322342847889 +7623,-5.448951857529598 +7624,0.785529403437994 +7625,6.69525589961418 +7626,0.5851878728384134 +7627,5.527683614700694 +7628,7.845981405329267 +7629,-2.075110245103559 +7630,4.537308783521532 +7631,4.406332057027209 +7632,4.137475900926018 +7633,3.1572222312980696 +7634,-6.11509141870688 +7635,3.198718585768864 +7636,2.0324771582717758 +7637,-1.2568165872620924 +7638,5.062298471186313 +7639,0.062239009831074006 +7640,5.239598320832831 +7641,5.87803918973527 +7642,7.200859872628451 +7643,3.076366158924171 +7644,6.472933026338194 +7645,2.3663205688497544 +7646,2.5124169650614525 +7647,3.1284333495995247 +7648,1.8989285571120458 +7649,-7.619754088165439 +7650,4.009842926068777 +7651,4.0781515901941905 +7652,-2.915231033170175 +7653,-1.1493488399603256 +7654,6.041147776863728 +7655,5.424005305630814 +7656,6.294951820646531 +7657,7.276283249584914 +7658,6.456693867465706 +7659,6.6231728070475855 +7660,2.557664289514088 +7661,5.326447454428248 +7662,3.5204480284334254 +7663,4.4862387388853815 +7664,3.0602831930206187 +7665,6.484669046932399 +7666,2.4890231688893536 +7667,7.830303969490577 +7668,4.665007635347767 +7669,3.4543115378675577 +7670,4.82409896799451 +7671,1.669947173341872 +7672,-2.621075249954887 +7673,5.724874631020079 +7674,1.9171896933971448 +7675,-2.960991234014809 +7676,-0.91454160054278 +7677,-2.9208040789374334 +7678,6.292436305620272 +7679,5.448733936176476 +7680,4.669124818889449 +7681,5.2304821566321245 +7682,2.9593902916360006 +7683,-1.138019667788753 +7684,-2.6729478431994793 +7685,5.363682046410198 +7686,2.985681378334788 +7687,-6.820399958888976 +7688,7.840544695615301 +7689,0.06471527412001166 +7690,-5.789743643315164 +7691,3.1837136135937962 +7692,5.206221796880842 +7693,-1.335643543025579 +7694,5.665609270122818 +7695,-0.06780423778346582 +7696,4.911580895798257 +7697,7.61664781266845 +7698,0.9411748807260536 +7699,1.024708434149241 +7700,-7.2157780145313515 +7701,4.361777651012735 +7702,3.1118276246169345 +7703,13.339165990020227 +7704,-3.7955982235581223 +7705,7.220330121429605 +7706,8.250792361579915 +7707,6.474691071090418 +7708,-1.2376344025702357 +7709,7.938112259018425 +7710,2.6775551302272294 +7711,9.941801780546813 +7712,5.684149207004115 +7713,1.6250909263198505 +7714,4.268649986952238 +7715,-2.0317304263672415 +7716,-0.9641410273440734 +7717,0.9602302863449647 +7718,-1.402169875949574 +7719,-2.248166190925146 +7720,6.348899161100666 +7721,7.3393988863468875 +7722,4.677588351748947 +7723,1.9860466760285183 +7724,5.820092328944626 +7725,3.0322222392149905 +7726,4.473119615199547 +7727,-2.4759551789291767 +7728,-0.757736506857111 +7729,5.105041323953681 +7730,-2.0509708004945217 +7731,-3.2888175447669497 +7732,-4.138510622207986 +7733,-1.9379359998679053 +7734,1.3611493073861354 +7735,-6.100992459217071 +7736,2.6266777147899805 +7737,4.910914150374996 +7738,-3.932254187777237 +7739,7.114895551735712 +7740,3.3913978763509407 +7741,2.4002144473371203 +7742,1.8770912931310182 +7743,0.9649661122374545 +7744,3.9078520769313894 +7745,3.765508383977986 +7746,1.351621332071519 +7747,-2.2951712397177917 +7748,-1.3374204604375541 +7749,-1.8507643823253834 +7750,7.071267272884269 +7751,4.073119201505694 +7752,1.0838095677208834 +7753,2.443538890772431 +7754,6.326210206008048 +7755,-0.5838821023598937 +7756,-4.905692880036092 +7757,0.04259187273699671 +7758,5.15939500274966 +7759,6.410080041752568 +7760,2.0964163502031017 +7761,3.9046298224772484 +7762,2.0441556111682764 +7763,4.2658207045328425 +7764,6.1510271079782015 +7765,6.662048180363253 +7766,6.613307308054586 +7767,0.7179793223092188 +7768,-2.7469243474647898 +7769,2.1780948336401114 +7770,-7.101576367531277 +7771,6.70026764063617 +7772,4.509322458795823 +7773,2.6482771419518474 +7774,4.606753852987993 +7775,5.418001095956453 +7776,-0.0886718368332519 +7777,7.119409766413725 +7778,3.3016320916747106 +7779,-2.8761545559640602 +7780,6.689736462536498 +7781,-2.2343392228480448 +7782,6.1048704929792095 +7783,-0.8559517167680881 +7784,3.529313601887199 +7785,-1.1980015186704176 +7786,7.904925334258977 +7787,4.65866072271795 +7788,4.167283657125098 +7789,1.048852579889338 +7790,-3.713534274968277 +7791,1.3674587523584152 +7792,7.519498060169633 +7793,-2.5062477846498443 +7794,5.875058612407388 +7795,-5.342318012535437 +7796,3.0938726091063704 +7797,2.0799913209332246 +7798,5.376799442364328 +7799,3.4459816076785534 +7800,4.7282595065299455 +7801,3.3298608280703297 +7802,3.254585227330765 +7803,1.370651837459767 +7804,4.945944053245948 +7805,6.9377392117070045 +7806,-4.809944394892481 +7807,-6.579687359466957 +7808,4.724576660040722 +7809,0.8139486225315394 +7810,3.5182942779051807 +7811,7.687869944431186 +7812,1.1319203120377825 +7813,-0.8936208301048637 +7814,2.7483611877175913 +7815,-2.210638644013872 +7816,-2.652214807829499 +7817,5.650315711748345 +7818,2.8888343828939287 +7819,2.052763618954894 +7820,-6.540513884330567 +7821,-1.453789531592424 +7822,-1.5325817294725685 +7823,1.951747091882248 +7824,7.38799364046263 +7825,4.023461513567881 +7826,-0.7788112761843218 +7827,1.907426836782788 +7828,4.336958998390602 +7829,2.5547979748248006 +7830,-3.8833880435242336 +7831,5.232301406302019 +7832,-3.934271059567106 +7833,7.105735797706615 +7834,-7.5998414095809235 +7835,-1.733890757106212 +7836,4.682757889156954 +7837,5.601309437350186 +7838,4.231165549219874 +7839,4.269340163892667 +7840,8.0303718450739 +7841,3.00805180553766 +7842,4.543240614934523 +7843,7.600320140891667 +7844,6.9625392087527445 +7845,-0.5724314978261064 +7846,3.3195508687334474 +7847,3.021392298447794 +7848,-0.7969870712918139 +7849,6.800088760167539 +7850,-3.081712374655967 +7851,7.113819170884816 +7852,6.707964457357411 +7853,-4.274442241969993 +7854,6.019274000064455 +7855,5.443510328588399 +7856,-4.3665927784419125 +7857,3.905483868506818 +7858,6.2377427375471 +7859,-1.0218733202587984 +7860,2.4886791769808743 +7861,-6.143049308653919 +7862,0.25093909348716537 +7863,4.769854485885161 +7864,7.646849650650897 +7865,3.136412603855442 +7866,-10.445063138327328 +7867,3.16897604039319 +7868,1.3314219816012676 +7869,0.1399654824943476 +7870,3.7311704885639827 +7871,1.9605363457676437 +7872,2.3103181780503315 +7873,5.32773041900114 +7874,7.218927938875805 +7875,-3.276893507890049 +7876,-7.481777162487126 +7877,7.619129292835856 +7878,5.841061674884895 +7879,4.7381693045370765 +7880,5.948869122910181 +7881,5.4523624623109415 +7882,-3.382343319521037 +7883,5.6217575503041415 +7884,5.042703822181978 +7885,3.2675849242315333 +7886,2.171433849183428 +7887,-3.340202337294686 +7888,2.078822207016341 +7889,2.99569224134625 +7890,0.8861957222157736 +7891,1.654188768316424 +7892,3.5524280464853595 +7893,-5.6158583752498865 +7894,6.219445355664143 +7895,1.633052730719447 +7896,5.392460355817006 +7897,-2.6941627184397365 +7898,3.279981095965385 +7899,8.113676877407826 +7900,0.7800472176721311 +7901,5.8731836744763255 +7902,0.5669319270156434 +7903,-0.5463145673602963 +7904,0.45576821884733787 +7905,1.552311980015369 +7906,2.137644071235188 +7907,3.2458824625532072 +7908,6.9729375480811715 +7909,5.405366103350801 +7910,1.9354230849364271 +7911,6.811133883978693 +7912,-5.786441441461293 +7913,6.838532892491 +7914,5.089112870597326 +7915,5.124673027101479 +7916,6.130470660512758 +7917,4.641627258069403 +7918,-2.291562142413446 +7919,3.493339562006799 +7920,3.52582046854526 +7921,-1.2705901180106254 +7922,-2.4800404307095913 +7923,6.078972733682507 +7924,1.9745078875834408 +7925,0.514812287651636 +7926,6.7727850089469435 +7927,7.322199421867866 +7928,-0.6110474603062418 +7929,2.7313371336508605 +7930,7.499039180145244 +7931,7.289150535841895 +7932,1.151864665580766 +7933,-3.195787785617175 +7934,2.7438661519437075 +7935,2.712943919299541 +7936,3.3908108896912803 +7937,1.08112481236977 +7938,4.724981004524254 +7939,-0.13325168441042656 +7940,1.3187005482578598 +7941,11.21330924656328 +7942,1.8841369154546221 +7943,4.675310559900688 +7944,4.555043773868653 +7945,4.173749134507289 +7946,0.3037974401676283 +7947,-7.312157961334269 +7948,-4.422057791156276 +7949,2.554321971497783 +7950,5.151331802558963 +7951,5.368108473298509 +7952,5.747144959948442 +7953,5.3772656156584455 +7954,1.431532498959364 +7955,2.6189907702535806 +7956,5.426521043271636 +7957,6.099016903393312 +7958,-7.182364383691413 +7959,4.149436217175703 +7960,0.40170978008109826 +7961,5.082049123273754 +7962,3.0606552566079746 +7963,5.005938119058792 +7964,5.605955183481356 +7965,4.268490793958572 +7966,1.6680720647616267 +7967,-2.474851827514643 +7968,4.59465604824448 +7969,4.5088466633973034 +7970,7.048431360257193 +7971,7.832997053999818 +7972,0.5366620941498261 +7973,7.084110436920657 +7974,7.242057693986602 +7975,7.1151316481986395 +7976,2.840092697110526 +7977,3.6054219117935076 +7978,3.5917108437715513 +7979,-2.3453465480242155 +7980,10.28268848414609 +7981,1.8750875421876922 +7982,-2.792860488092499 +7983,2.5267013631788395 +7984,7.259821287859238 +7985,3.0020749625127463 +7986,4.290289238213979 +7987,-1.5692297317156345 +7988,2.411424781294878 +7989,1.5922160182857885 +7990,3.785020706390924 +7991,0.13450169744077564 +7992,7.4039009261135735 +7993,3.7441384628596324 +7994,4.748197434285619 +7995,10.475467099026911 +7996,5.479538126822994 +7997,4.3477536134189165 +7998,2.279800010468329 +7999,2.4603698288491076