Time series

A time series is a sequence of observations \[\begin{aligned} (y_1, y_2, \ldots, y_N) , \end{aligned}\] that were taken at some set of times \[\begin{aligned} t_1 < t_2 < \cdots < t_N . \end{aligned}\]

The thing about time

Many statistical methods assume independence of observations.

A discrete, noisy oscillator

Suppose we have regular, noisy observations from a discrete, noisy oscillator.

The system itself does \[\begin{aligned} x_{t+1} - x_t &= \alpha y_t + \Normal(0, \sigma_{xy}) \\ y_{t+1} - y_t &= - \beta x_t + \Normal(0, \sigma_{xy}) \end{aligned}\] but we only get to observe \[\begin{aligned} X_t &= x_t + \Normal(0, \sigma_\epsilon) \\ Y_t &= y_t + \Normal(0, \sigma_\epsilon) . \end{aligned}\]

Some data

data/osc_data.csv

head(
     osc_data <- read.csv("data/osc_data.csv", header=TRUE)
)

##           X          Y
## 1 3.0294511  0.1077934
## 2 2.1624268  0.7287783
## 3 3.4787385 -0.2474969
## 4 0.8519628  0.1390850
## 5 2.8182162 -1.1920302
## 6 3.8786329 -0.1581520

Our model-building plan

0. Write down a model.

1. Simulate from the model.

2. Check the simulations kinda look like the real data.

3. Write a method to fit the model.

4. Check the method correctly infers the true parameters of simulated data.

5. Fit the model to the real data.

6. Check that posterior predictive simulations look like the real data.

7. Celebrate!

Exercise:

1. Suppose \(\alpha = \beta = 0.1\) and \(\sigma_\epsilon = 1\) and \(\sigma_{xy} = 0.01\). How well do you think we can estimate \(\alpha\) and \(\beta\)? (Play around with them, to see how much they change the data.)

2. What if \(\sigma_{\epsilon} = 10\)?

plot(xy, type='l', col='red', xlab='x', ylab='y')
points(XY, col=rainbow(N))
legend("topright", lty=c(1, NA), pch=c(NA,1), col=c("red","black"),
       legend=c("xy", "XY"))

A Stan block

osc_block <- "
data {
    int N;
    vector[N] X;
    vector[N] Y;
}
parameters {
    real alpha;
    real beta;
    real<lower=0> sigma_xy;
    real<lower=0> sigma_eps;
    vector[N] x;
    vector[N] y;
}
model {
    x[1] ~ normal(0, 5);
    y[1] ~ normal(0, 5);
    x[2:N] ~ normal(x[1:(N-1)] + alpha * y[1:(N-1)], sigma_xy);
    y[2:N] ~ normal(y[1:(N-1)] - beta * x[1:(N-1)], sigma_xy);
    X ~ normal(x, sigma_eps);
    Y ~ normal(y, sigma_eps);
    alpha ~ normal(0, 1);
    beta ~ normal(0, 1);
    sigma_xy ~ normal(0, 1);
    sigma_eps ~ normal(0, 1);
}
"
osc_model <- stan_model(model_code=osc_block)

osc_fit <- sampling(osc_model,
                    data=list(N=N,
                              X=XY[,1],
                              Y=XY[,2]),
                    iter=1000, chains=3,
                    control=list(max_treedepth=14))

## Warning: There were 3 chains where the estimated Bayesian Fraction of Missing Information was low. See
## http://mc-stan.org/misc/warnings.html#bfmi-low

## Warning: Examine the pairs() plot to diagnose sampling problems

## Warning: The largest R-hat is 1.96, indicating chains have not mixed.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#r-hat

## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess

## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#tail-ess

How’d we do?

cbind(truth=c(true_osc$alpha, true_osc$beta, true_osc$sigma_xy, true_osc$sigma_eps),
      rstan::summary(osc_fit, pars=c("alpha", "beta", "sigma_xy", "sigma_eps"))$summary)

##           truth       mean      se_mean           sd        2.5%        25%        50%        75%      97.5%       n_eff     Rhat
## alpha      0.10 0.09950010 6.169861e-05 0.0018347714 0.096044115 0.09820606 0.09951923 0.10067989 0.10316309  884.327461 1.000051
## beta       0.05 0.05011448 3.090389e-05 0.0009264783 0.048325695 0.04951725 0.05009466 0.05075242 0.05192722  898.760907 1.000292
## sigma_xy   0.01 0.02062393 4.212708e-03 0.0065187639 0.009178815 0.01614820 0.01977550 0.02630435 0.03244747    2.394461 2.132853
## sigma_eps  1.00 0.99985662 6.835608e-04 0.0233698082 0.957753401 0.98408138 0.99918806 1.01575953 1.04698140 1168.842337 1.006658

Here is a density plot of 100 estimated trajectories (of x and y) from the Stan fit, with the true values in red.

A noisier oscillator

Let’s try that again, with more noise.

Here’s what this looks like.

true_osc2 <- list(alpha=.1,
                 beta=.05,
                 sigma_xy=2.0,
                 sigma_eps=4.0)
xy2 <- matrix(nrow=N, ncol=2)
xy2[1,] <- c(3,0)
for (k in 1:(N-1)) {
    xy2[k+1,] <- (xy2[k,] 
                + c(true_osc2$alpha * xy2[k,2],
                    (-1) * true_osc2$beta * xy2[k,1])
                + rnorm(2, 0, true_osc2$sigma_xy))
}
XY2 <- xy2 + rnorm(N*2, 0, true_osc2$sigma_eps)

osc_fit2 <- sampling(osc_model,
                    data=list(N=N,
                              X=XY2[,1],
                              Y=XY2[,2]),
                    iter=1000, chains=3,
                    control=list(max_treedepth=12))

## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess

How’d we do?

cbind(truth=c(true_osc2$alpha, true_osc2$beta, true_osc2$sigma_xy, true_osc2$sigma_eps),
      rstan::summary(osc_fit2, pars=c("alpha", "beta", "sigma_xy", "sigma_eps"))$summary)

##           truth       mean      se_mean          sd       2.5%        25%        50%       75%      97.5%     n_eff      Rhat
## alpha      0.10 0.10123799 3.935719e-05 0.001642870 0.09801558 0.10010042 0.10127181 0.1023376 0.10451309 1742.4410 0.9997534
## beta       0.05 0.05141579 3.018645e-05 0.001181041 0.04909184 0.05061257 0.05142453 0.0522106 0.05373877 1530.7559 1.0006137
## sigma_xy   2.00 2.07727845 1.256498e-02 0.142052935 1.81357843 1.97775757 2.07045167 2.1710405 2.36771597  127.8135 1.0202276
## sigma_eps  4.00 3.88583351 4.596211e-03 0.121267863 3.65422247 3.79886698 3.88400777 3.9680865 4.12732245  696.1319 1.0011903

Here is a density plot of 100 estimated trajectories (of x and y) from the Stan fit, with the true values in red.

Fit the model, again

real_fit <- sampling(osc_model,
                    data=list(N=nrow(osc_data),
                              X=osc_data[,1],
                              Y=osc_data[,2]),
                    iter=1000, chains=3,
                    control=list(max_treedepth=14))

## Warning: There were 3 chains where the estimated Bayesian Fraction of Missing Information was low. See
## http://mc-stan.org/misc/warnings.html#bfmi-low

## Warning: Examine the pairs() plot to diagnose sampling problems

## Warning: The largest R-hat is 2.3, indicating chains have not mixed.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#r-hat

## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess

## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#tail-ess

Check for convergence

rstan::summary(real_fit)$summary

##                    mean      se_mean           sd          2.5%           25%           50%           75%         97.5%       n_eff      Rhat
## alpha      1.008104e-01 6.418202e-05 1.772977e-03  9.736394e-02  9.962001e-02  1.008142e-01  1.019818e-01  1.043653e-01  763.096364 1.0013730
## beta       4.928773e-02 3.214881e-05 8.725226e-04  4.753006e-02  4.872654e-02  4.927210e-02  4.984254e-02  5.105128e-02  736.586090 1.0006042
## sigma_xy   1.645999e-02 3.389622e-03 7.502791e-03  6.211528e-03  1.129008e-02  1.447433e-02  2.096380e-02  3.385537e-02    4.899403 2.2999149
## sigma_eps  1.042205e+00 5.971120e-04 2.503574e-02  9.938256e-01  1.025483e+00  1.042920e+00  1.058784e+00  1.091258e+00 1757.960833 0.9993080
## x[1]       3.107086e+00 3.518795e-03 1.360745e-01  2.840554e+00  3.016827e+00  3.106453e+00  3.192883e+00  3.380660e+00 1495.427984 1.0007943
## x[2]       3.099409e+00 3.506638e-03 1.354533e-01  2.833730e+00  3.012462e+00  3.094816e+00  3.185125e+00  3.379834e+00 1492.096743 1.0012713
## x[3]       3.075726e+00 3.494210e-03 1.331047e-01  2.818874e+00  2.987542e+00  3.072988e+00  3.161315e+00  3.352671e+00 1451.070481 1.0018495
## x[4]       3.036724e+00 3.533753e-03 1.324260e-01  2.782878e+00  2.950806e+00  3.033343e+00  3.121177e+00  3.310836e+00 1404.346102 1.0029472
## x[5]       2.982827e+00 3.514757e-03 1.314889e-01  2.737742e+00  2.894701e+00  2.979902e+00  3.069057e+00  3.255201e+00 1399.547303 1.0033595
## x[6]       2.913907e+00 3.616998e-03 1.312431e-01  2.670807e+00  2.823704e+00  2.911142e+00  2.999143e+00  3.184095e+00 1316.608320 1.0044145
## x[7]       2.830164e+00 3.685223e-03 1.315823e-01  2.578404e+00  2.741398e+00  2.828441e+00  2.914813e+00  3.099346e+00 1274.874981 1.0049492
## x[8]       2.729832e+00 3.760844e-03 1.307744e-01  2.478021e+00  2.641777e+00  2.728533e+00  2.815765e+00  2.995845e+00 1209.135534 1.0057213
## x[9]       2.618192e+00 3.787475e-03 1.291662e-01  2.366196e+00  2.533631e+00  2.615702e+00  2.700148e+00  2.882476e+00 1163.049564 1.0063610
## x[10]      2.492177e+00 3.815261e-03 1.289472e-01  2.236825e+00  2.406810e+00  2.490684e+00  2.575140e+00  2.749641e+00 1142.287991 1.0065553
## x[11]      2.352717e+00 4.006726e-03 1.288760e-01  2.092560e+00  2.267632e+00  2.355709e+00  2.438343e+00  2.605885e+00 1034.581238 1.0069255
## x[12]      2.201063e+00 3.948860e-03 1.286762e-01  1.933400e+00  2.115999e+00  2.202531e+00  2.286072e+00  2.448990e+00 1061.824452 1.0072516
## x[13]      2.038720e+00 3.981464e-03 1.299064e-01  1.766290e+00  1.951793e+00  2.040601e+00  2.124752e+00  2.286363e+00 1064.572953 1.0071480
## x[14]      1.864565e+00 3.903805e-03 1.305053e-01  1.592583e+00  1.778774e+00  1.865998e+00  1.947292e+00  2.116231e+00 1117.583276 1.0070097
## x[15]      1.680345e+00 3.909602e-03 1.298446e-01  1.414329e+00  1.594920e+00  1.685766e+00  1.764759e+00  1.929487e+00 1103.018437 1.0069442
## x[16]      1.487391e+00 3.833383e-03 1.298002e-01  1.214490e+00  1.402540e+00  1.489379e+00  1.573531e+00  1.737385e+00 1146.532015 1.0067759
## x[17]      1.285047e+00 3.841861e-03 1.301201e-01  1.013213e+00  1.202769e+00  1.285604e+00  1.371424e+00  1.535560e+00 1147.111371 1.0067345
## x[18]      1.075949e+00 3.699505e-03 1.280564e-01  8.133037e-01  9.940031e-01  1.076503e+00  1.161291e+00  1.325640e+00 1198.161969 1.0068995
## x[19]      8.606423e-01 3.680938e-03 1.279648e-01  6.000902e-01  7.785523e-01  8.610872e-01  9.463143e-01  1.114348e+00 1208.549031 1.0071411
## x[20]      6.407060e-01 3.607135e-03 1.279770e-01  3.793225e-01  5.579321e-01  6.420767e-01  7.238907e-01  8.902760e-01 1258.749178 1.0068350
## x[21]      4.161159e-01 3.607167e-03 1.284946e-01  1.525855e-01  3.345841e-01  4.160163e-01  5.025594e-01  6.695655e-01 1268.927964 1.0057863
## x[22]      1.888027e-01 3.573736e-03 1.288059e-01 -7.255504e-02  1.051527e-01  1.903539e-01  2.729899e-01  4.387171e-01 1299.052683 1.0047782
## x[23]     -4.136401e-02 3.508199e-03 1.285330e-01 -3.016729e-01 -1.253114e-01 -3.811313e-02  4.376542e-02  2.041607e-01 1342.335564 1.0044477
## x[24]     -2.707266e-01 3.435747e-03 1.281554e-01 -5.288703e-01 -3.512253e-01 -2.701873e-01 -1.850773e-01 -2.195330e-02 1391.334402 1.0038327
## x[25]     -5.010298e-01 3.360184e-03 1.277836e-01 -7.521077e-01 -5.815825e-01 -4.994760e-01 -4.178094e-01 -2.568108e-01 1446.186188 1.0032905
## x[26]     -7.291316e-01 3.331367e-03 1.268865e-01 -9.774206e-01 -8.120411e-01 -7.275615e-01 -6.453805e-01 -4.844382e-01 1450.726318 1.0020903
## x[27]     -9.547300e-01 3.336190e-03 1.267762e-01 -1.203520e+00 -1.037522e+00 -9.517874e-01 -8.725357e-01 -7.152408e-01 1444.021662 1.0018606
## x[28]     -1.178093e+00 3.271618e-03 1.258812e-01 -1.428054e+00 -1.257883e+00 -1.177543e+00 -1.095211e+00 -9.327244e-01 1480.459257 1.0011758
## x[29]     -1.394674e+00 3.278969e-03 1.250214e-01 -1.642283e+00 -1.474202e+00 -1.394159e+00 -1.312830e+00 -1.150445e+00 1453.765881 1.0004930
## x[30]     -1.605554e+00 3.279691e-03 1.248425e-01 -1.848101e+00 -1.681984e+00 -1.605745e+00 -1.526267e+00 -1.349696e+00 1448.967822 1.0000689
## x[31]     -1.810541e+00 3.246824e-03 1.243952e-01 -2.058875e+00 -1.887601e+00 -1.810585e+00 -1.731352e+00 -1.560644e+00 1467.877808 1.0002406
## x[32]     -2.008076e+00 3.243757e-03 1.237519e-01 -2.256711e+00 -2.083049e+00 -2.007729e+00 -1.927442e+00 -1.761827e+00 1455.482942 0.9999995
## x[33]     -2.196650e+00 3.259884e-03 1.234480e-01 -2.451780e+00 -2.273221e+00 -2.199531e+00 -2.117927e+00 -1.944540e+00 1434.048932 1.0001364
## x[34]     -2.374978e+00 3.266874e-03 1.234816e-01 -2.624927e+00 -2.450896e+00 -2.380508e+00 -2.296221e+00 -2.123379e+00 1428.694865 1.0001877
## x[35]     -2.542592e+00 3.258095e-03 1.223090e-01 -2.784191e+00 -2.622365e+00 -2.545099e+00 -2.466141e+00 -2.291253e+00 1409.255473 1.0006688
## x[36]     -2.698349e+00 3.314509e-03 1.227551e-01 -2.942628e+00 -2.776742e+00 -2.702069e+00 -2.619649e+00 -2.440504e+00 1371.641648 1.0017190
## x[37]     -2.842240e+00 3.323292e-03 1.226264e-01 -3.089776e+00 -2.920383e+00 -2.844499e+00 -2.763700e+00 -2.590874e+00 1361.541047 1.0024289
## x[38]     -2.972313e+00 3.319980e-03 1.225102e-01 -3.216498e+00 -3.052462e+00 -2.974285e+00 -2.891904e+00 -2.722025e+00 1361.675951 1.0032167
## x[39]     -3.088648e+00 3.322522e-03 1.211976e-01 -3.327409e+00 -3.168715e+00 -3.092144e+00 -3.006250e+00 -2.834577e+00 1330.615567 1.0036677
## x[40]     -3.190102e+00 3.341883e-03 1.204628e-01 -3.427839e+00 -3.270617e+00 -3.193010e+00 -3.112783e+00 -2.937673e+00 1299.342633 1.0042275
## x[41]     -3.275426e+00 3.398007e-03 1.200574e-01 -3.513592e+00 -3.357461e+00 -3.276240e+00 -3.196446e+00 -3.023635e+00 1248.328845 1.0059035
## x[42]     -3.345854e+00 3.377740e-03 1.190428e-01 -3.577851e+00 -3.426166e+00 -3.346479e+00 -3.269986e+00 -3.096288e+00 1242.091830 1.0075592
## x[43]     -3.400687e+00 3.395084e-03 1.175585e-01 -3.626347e+00 -3.479624e+00 -3.402835e+00 -3.324838e+00 -3.152226e+00 1198.965753 1.0070330
## x[44]     -3.438709e+00 3.398376e-03 1.176337e-01 -3.668662e+00 -3.517302e+00 -3.438866e+00 -3.363859e+00 -3.192882e+00 1198.177322 1.0070339
## x[45]     -3.458892e+00 3.376880e-03 1.160433e-01 -3.688268e+00 -3.533545e+00 -3.461232e+00 -3.386962e+00 -3.216139e+00 1180.888556 1.0085579
## x[46]     -3.462994e+00 3.422885e-03 1.164319e-01 -3.693618e+00 -3.539710e+00 -3.468087e+00 -3.389404e+00 -3.217129e+00 1157.068559 1.0102230
## x[47]     -3.449817e+00 3.421111e-03 1.158118e-01 -3.673132e+00 -3.523804e+00 -3.452919e+00 -3.375654e+00 -3.205112e+00 1145.964753 1.0101101
## x[48]     -3.418930e+00 3.465740e-03 1.159961e-01 -3.641577e+00 -3.494342e+00 -3.421317e+00 -3.343556e+00 -3.180209e+00 1120.198261 1.0116693
## x[49]     -3.370122e+00 4.072503e-03 1.154472e-01 -3.599567e+00 -3.444761e+00 -3.372830e+00 -3.296335e+00 -3.128221e+00  803.607034 1.0124322
## x[50]     -3.304602e+00 4.547237e-03 1.153372e-01 -3.528926e+00 -3.382966e+00 -3.304901e+00 -3.230678e+00 -3.075652e+00  643.345042 1.0134322
## x[51]     -3.222743e+00 4.422869e-03 1.154610e-01 -3.442701e+00 -3.301143e+00 -3.225742e+00 -3.149620e+00 -2.986594e+00  681.494220 1.0130406
## x[52]     -3.124382e+00 4.373259e-03 1.154529e-01 -3.350938e+00 -3.203054e+00 -3.127726e+00 -3.047962e+00 -2.889313e+00  696.946188 1.0130260
## x[53]     -3.009632e+00 5.194350e-03 1.158121e-01 -3.233266e+00 -3.087891e+00 -3.014140e+00 -2.935981e+00 -2.769968e+00  497.102140 1.0136084
## x[54]     -2.879086e+00 5.909255e-03 1.163064e-01 -3.101680e+00 -2.958282e+00 -2.882477e+00 -2.807401e+00 -2.636406e+00  387.384088 1.0138487
## x[55]     -2.733645e+00 5.742419e-03 1.173090e-01 -2.954602e+00 -2.816437e+00 -2.734745e+00 -2.661039e+00 -2.489414e+00  417.323520 1.0139051
## x[56]     -2.573788e+00 5.715162e-03 1.170010e-01 -2.784191e+00 -2.655290e+00 -2.574437e+00 -2.498632e+00 -2.332794e+00  419.103976 1.0150813
## x[57]     -2.400393e+00 5.243605e-03 1.184042e-01 -2.626187e+00 -2.483121e+00 -2.403786e+00 -2.325048e+00 -2.163591e+00  509.887231 1.0146859
## x[58]     -2.213018e+00 5.459016e-03 1.188045e-01 -2.440795e+00 -2.293985e+00 -2.217014e+00 -2.138058e+00 -1.966480e+00  473.627725 1.0159885
## x[59]     -2.014140e+00 6.199096e-03 1.201831e-01 -2.241771e+00 -2.094992e+00 -2.018598e+00 -1.937508e+00 -1.775896e+00  375.863719 1.0166631
## x[60]     -1.803929e+00 6.467070e-03 1.208003e-01 -2.026342e+00 -1.886624e+00 -1.809118e+00 -1.726520e+00 -1.557960e+00  348.915830 1.0169822
## x[61]     -1.583981e+00 6.652214e-03 1.206641e-01 -1.807094e+00 -1.665247e+00 -1.590749e+00 -1.503847e+00 -1.331903e+00  329.020966 1.0173802
## x[62]     -1.354932e+00 6.805562e-03 1.206682e-01 -1.577871e+00 -1.434948e+00 -1.363267e+00 -1.274868e+00 -1.103851e+00  314.382057 1.0182762
## x[63]     -1.117028e+00 6.635981e-03 1.211649e-01 -1.345842e+00 -1.196380e+00 -1.124025e+00 -1.035596e+00 -8.635488e-01  333.382906 1.0184248
## x[64]     -8.743018e-01 6.504662e-03 1.209368e-01 -1.101165e+00 -9.543113e-01 -8.806096e-01 -7.944539e-01 -6.220666e-01  345.674388 1.0175791
## x[65]     -6.250269e-01 6.710707e-03 1.205897e-01 -8.553717e-01 -7.038142e-01 -6.272940e-01 -5.471323e-01 -3.723694e-01  322.911523 1.0189369
## x[66]     -3.713147e-01 6.578959e-03 1.207959e-01 -6.059667e-01 -4.513916e-01 -3.760486e-01 -2.896541e-01 -1.236782e-01  337.124370 1.0193988
## x[67]     -1.150254e-01 6.488347e-03 1.196641e-01 -3.413537e-01 -1.928703e-01 -1.207383e-01 -3.588632e-02  1.333665e-01  340.141624 1.0187500
## x[68]      1.418907e-01 6.015114e-03 1.187043e-01 -7.749672e-02  6.492932e-02  1.380560e-01  2.198914e-01  3.765781e-01  389.444266 1.0166977
## x[69]      4.001241e-01 5.966522e-03 1.178052e-01  1.759389e-01  3.226213e-01  3.979848e-01  4.798569e-01  6.390633e-01  389.839789 1.0160031
## x[70]      6.587438e-01 6.174715e-03 1.158736e-01  4.372101e-01  5.820656e-01  6.574084e-01  7.343170e-01  8.868001e-01  352.155909 1.0167034
## x[71]      9.159577e-01 5.882611e-03 1.150265e-01  6.986744e-01  8.410457e-01  9.133879e-01  9.922954e-01  1.138718e+00  382.344784 1.0165878
## x[72]      1.168428e+00 5.834325e-03 1.151478e-01  9.483616e-01  1.091366e+00  1.167662e+00  1.241123e+00  1.398355e+00  389.520158 1.0155071
## x[73]      1.416196e+00 5.592763e-03 1.153128e-01  1.196829e+00  1.338584e+00  1.416040e+00  1.490748e+00  1.637473e+00  425.110549 1.0135895
## x[74]      1.658377e+00 5.513928e-03 1.144339e-01  1.440995e+00  1.581331e+00  1.657951e+00  1.732773e+00  1.896837e+00  430.712395 1.0141774
## x[75]      1.892844e+00 5.233208e-03 1.138426e-01  1.679562e+00  1.816700e+00  1.892706e+00  1.965637e+00  2.121542e+00  473.231332 1.0126454
## x[76]      2.119628e+00 4.561828e-03 1.144637e-01  1.908009e+00  2.043553e+00  2.119556e+00  2.191345e+00  2.350635e+00  629.590456 1.0113525
## x[77]      2.336907e+00 4.166900e-03 1.150591e-01  2.120370e+00  2.262908e+00  2.336550e+00  2.409135e+00  2.563545e+00  762.458227 1.0090135
## x[78]      2.543804e+00 4.153781e-03 1.151705e-01  2.321875e+00  2.469300e+00  2.541817e+00  2.616550e+00  2.776252e+00  768.767932 1.0076016
## x[79]      2.738007e+00 4.086482e-03 1.158000e-01  2.513825e+00  2.665869e+00  2.737737e+00  2.810981e+00  2.968791e+00  803.004757 1.0065564
## x[80]      2.920189e+00 3.941620e-03 1.156308e-01  2.694598e+00  2.846439e+00  2.918295e+00  2.993918e+00  3.157675e+00  860.592859 1.0055681
## x[81]      3.089053e+00 3.922276e-03 1.153028e-01  2.871864e+00  3.013042e+00  3.089750e+00  3.163147e+00  3.326290e+00  864.178171 1.0047857
## x[82]      3.244705e+00 4.081179e-03 1.156348e-01  3.017778e+00  3.168846e+00  3.245964e+00  3.320875e+00  3.476527e+00  802.797536 1.0049060
## x[83]      3.383770e+00 4.072482e-03 1.155108e-01  3.161109e+00  3.309131e+00  3.385163e+00  3.459007e+00  3.608920e+00  804.501108 1.0046015
## x[84]      3.507352e+00 4.155261e-03 1.140792e-01  3.269500e+00  3.432100e+00  3.509777e+00  3.582168e+00  3.726992e+00  753.730802 1.0059073
## x[85]      3.614401e+00 4.192579e-03 1.137560e-01  3.380675e+00  3.540034e+00  3.617940e+00  3.686089e+00  3.826588e+00  736.182886 1.0064982
## x[86]      3.704265e+00 4.103614e-03 1.129801e-01  3.480533e+00  3.630859e+00  3.707075e+00  3.779376e+00  3.917700e+00  758.003092 1.0073490
## x[87]      3.777073e+00 4.269336e-03 1.128644e-01  3.553507e+00  3.705104e+00  3.780603e+00  3.852978e+00  3.988580e+00  698.865013 1.0083800
## x[88]      3.829804e+00 4.320258e-03 1.136196e-01  3.596584e+00  3.757849e+00  3.833148e+00  3.905029e+00  4.043266e+00  691.651621 1.0081146
## x[89]      3.863536e+00 4.341957e-03 1.125439e-01  3.636987e+00  3.792680e+00  3.867169e+00  3.939216e+00  4.071728e+00  671.851152 1.0086975
## x[90]      3.877811e+00 4.368120e-03 1.134003e-01  3.644876e+00  3.802096e+00  3.881274e+00  3.955407e+00  4.088576e+00  673.968394 1.0094596
## x[91]      3.872834e+00 4.479453e-03 1.135262e-01  3.635777e+00  3.797277e+00  3.878610e+00  3.952081e+00  4.081509e+00  642.305780 1.0103429
## x[92]      3.847858e+00 4.674667e-03 1.140438e-01  3.613058e+00  3.772090e+00  3.853501e+00  3.928685e+00  4.055780e+00  595.171868 1.0126513
## x[93]      3.803248e+00 4.799147e-03 1.137045e-01  3.574289e+00  3.726440e+00  3.808935e+00  3.883462e+00  4.012989e+00  561.341858 1.0158119
## x[94]      3.740637e+00 5.038732e-03 1.148535e-01  3.505460e+00  3.665306e+00  3.746342e+00  3.820175e+00  3.947820e+00  519.571989 1.0179873
## x[95]      3.660242e+00 5.458539e-03 1.148469e-01  3.423627e+00  3.583043e+00  3.665821e+00  3.739645e+00  3.868431e+00  442.675764 1.0194158
## x[96]      3.560075e+00 6.010636e-03 1.147531e-01  3.325353e+00  3.481858e+00  3.565954e+00  3.642812e+00  3.765329e+00  364.491790 1.0220130
## x[97]      3.441412e+00 7.612175e-03 1.144771e-01  3.202793e+00  3.362016e+00  3.447205e+00  3.522464e+00  3.649686e+00  226.162182 1.0263403
## x[98]      3.305144e+00 9.123154e-03 1.156268e-01  3.065319e+00  3.228588e+00  3.312047e+00  3.386207e+00  3.515019e+00  160.630135 1.0300048
## x[99]      3.151702e+00 1.001681e-02 1.161899e-01  2.903328e+00  3.075260e+00  3.156896e+00  3.232356e+00  3.356724e+00  134.548203 1.0341432
## x[100]     2.983248e+00 1.049301e-02 1.165331e-01  2.738038e+00  2.908530e+00  2.988726e+00  3.064004e+00  3.189028e+00  123.338425 1.0364681
## x[101]     2.798631e+00 1.061893e-02 1.172399e-01  2.544447e+00  2.724194e+00  2.806041e+00  2.879640e+00  3.010944e+00  121.895978 1.0372512
## x[102]     2.598984e+00 1.136097e-02 1.182609e-01  2.347546e+00  2.525373e+00  2.607583e+00  2.679562e+00  2.804108e+00  108.355557 1.0380779
## x[103]     2.385899e+00 1.200685e-02 1.186866e-01  2.121012e+00  2.314104e+00  2.391763e+00  2.467257e+00  2.591656e+00   97.711398 1.0397820
## x[104]     2.160510e+00 1.138711e-02 1.190279e-01  1.901924e+00  2.089639e+00  2.170498e+00  2.242019e+00  2.371221e+00  109.262287 1.0388268
## x[105]     1.923594e+00 1.094693e-02 1.199324e-01  1.659093e+00  1.850429e+00  1.933330e+00  2.004338e+00  2.140916e+00  120.029543 1.0383099
## x[106]     1.675495e+00 1.072250e-02 1.197082e-01  1.407028e+00  1.603459e+00  1.683016e+00  1.755972e+00  1.895099e+00  124.639503 1.0378504
## x[107]     1.418043e+00 1.103360e-02 1.205362e-01  1.160723e+00  1.343876e+00  1.424101e+00  1.497781e+00  1.640147e+00  119.343836 1.0360263
## x[108]     1.151777e+00 1.068651e-02 1.226288e-01  8.942739e-01  1.080069e+00  1.158411e+00  1.231533e+00  1.374859e+00  131.677841 1.0336884
## x[109]     8.802600e-01 9.838345e-03 1.218589e-01  6.150593e-01  8.094569e-01  8.839971e-01  9.632207e-01  1.103021e+00  153.416004 1.0308656
## x[110]     6.012662e-01 9.484394e-03 1.228772e-01  3.395512e-01  5.283356e-01  6.064835e-01  6.867821e-01  8.292199e-01  167.850700 1.0301627
## x[111]     3.186477e-01 8.663384e-03 1.224011e-01  5.532965e-02  2.467068e-01  3.219935e-01  4.021359e-01  5.502542e-01  199.616200 1.0275232
## x[112]     3.356782e-02 6.964609e-03 1.219505e-01 -2.260072e-01 -3.783147e-02  3.784393e-02  1.136497e-01  2.629625e-01  306.601022 1.0234642
## x[113]    -2.537224e-01 6.930590e-03 1.212053e-01 -5.196643e-01 -3.257692e-01 -2.502552e-01 -1.733009e-01 -2.520060e-02  305.846208 1.0223295
## x[114]    -5.398960e-01 5.386016e-03 1.211106e-01 -7.975461e-01 -6.105361e-01 -5.347249e-01 -4.633862e-01 -3.075371e-01  505.625354 1.0183629
## x[115]    -8.254069e-01 5.088822e-03 1.210543e-01 -1.088607e+00 -8.969042e-01 -8.202150e-01 -7.474807e-01 -5.971276e-01  565.882325 1.0154346
## x[116]    -1.107841e+00 4.253911e-03 1.205856e-01 -1.371273e+00 -1.180322e+00 -1.101568e+00 -1.030982e+00 -8.787510e-01  803.552245 1.0115527
## x[117]    -1.387152e+00 4.298681e-03 1.209746e-01 -1.645309e+00 -1.458749e+00 -1.382899e+00 -1.310698e+00 -1.154029e+00  791.987200 1.0114593
## x[118]    -1.659683e+00 4.097882e-03 1.206633e-01 -1.918955e+00 -1.732341e+00 -1.656731e+00 -1.586309e+00 -1.429017e+00  867.024765 1.0077749
## x[119]    -1.926054e+00 4.001794e-03 1.206563e-01 -2.182905e+00 -1.998103e+00 -1.924119e+00 -1.849449e+00 -1.695842e+00  909.054890 1.0054601
## x[120]    -2.184861e+00 3.781866e-03 1.195436e-01 -2.434193e+00 -2.255910e+00 -2.183953e+00 -2.108923e+00 -1.946695e+00  999.172590 1.0040296
## x[121]    -2.434047e+00 3.643315e-03 1.194586e-01 -2.689339e+00 -2.507463e+00 -2.434246e+00 -2.357915e+00 -2.196530e+00 1075.081214 1.0031979
## x[122]    -2.672291e+00 3.545455e-03 1.194797e-01 -2.920250e+00 -2.745440e+00 -2.674800e+00 -2.593776e+00 -2.426957e+00 1135.649101 1.0021887
## x[123]    -2.898697e+00 3.481427e-03 1.187005e-01 -3.135875e+00 -2.974900e+00 -2.902587e+00 -2.821135e+00 -2.651615e+00 1162.494083 1.0014734
## x[124]    -3.111957e+00 3.403166e-03 1.194094e-01 -3.351161e+00 -3.189136e+00 -3.114090e+00 -3.037524e+00 -2.865330e+00 1231.149800 1.0014964
## x[125]    -3.311073e+00 3.383704e-03 1.188080e-01 -3.542888e+00 -3.389298e+00 -3.315764e+00 -3.233095e+00 -3.067837e+00 1232.840124 1.0026224
## x[126]    -3.495201e+00 3.393261e-03 1.186890e-01 -3.724078e+00 -3.576196e+00 -3.499684e+00 -3.417549e+00 -3.247735e+00 1223.450546 1.0037630
## x[127]    -3.662575e+00 3.414966e-03 1.193338e-01 -3.896952e+00 -3.742204e+00 -3.667125e+00 -3.584170e+00 -3.422083e+00 1221.109345 1.0051333
## x[128]    -3.812688e+00 3.488323e-03 1.187377e-01 -4.034079e+00 -3.891326e+00 -3.814716e+00 -3.735627e+00 -3.568957e+00 1158.627644 1.0068697
## x[129]    -3.945087e+00 3.556694e-03 1.194675e-01 -4.172972e+00 -4.024090e+00 -3.946903e+00 -3.868693e+00 -3.704316e+00 1128.253070 1.0087282
## x[130]    -4.058570e+00 3.513011e-03 1.185430e-01 -4.279079e+00 -4.138024e+00 -4.059675e+00 -3.983809e+00 -3.814793e+00 1138.656205 1.0099346
## x[131]    -4.152439e+00 3.506999e-03 1.186641e-01 -4.365938e+00 -4.232347e+00 -4.154868e+00 -4.078391e+00 -3.906381e+00 1144.899315 1.0118430
## x[132]    -4.226127e+00 3.633861e-03 1.189572e-01 -4.447629e+00 -4.308657e+00 -4.227298e+00 -4.152100e+00 -3.983894e+00 1071.629958 1.0136754
## x[133]    -4.280149e+00 3.704521e-03 1.188786e-01 -4.501458e+00 -4.360495e+00 -4.283774e+00 -4.202378e+00 -4.038653e+00 1029.776944 1.0156896
## x[134]    -4.312635e+00 4.417823e-03 1.197792e-01 -4.535861e+00 -4.392270e+00 -4.317752e+00 -4.232666e+00 -4.075918e+00  735.099320 1.0171476
## x[135]    -4.325061e+00 4.796954e-03 1.186446e-01 -4.546412e+00 -4.399930e+00 -4.329341e+00 -4.245037e+00 -4.087537e+00  611.737699 1.0182437
## x[136]    -4.315632e+00 4.958058e-03 1.187125e-01 -4.534013e+00 -4.392239e+00 -4.321462e+00 -4.238941e+00 -4.074525e+00  573.283939 1.0203014
## x[137]    -4.285613e+00 5.393564e-03 1.186058e-01 -4.505377e+00 -4.367251e+00 -4.291643e+00 -4.206995e+00 -4.051532e+00  483.570845 1.0203660
## x[138]    -4.234002e+00 6.118156e-03 1.192381e-01 -4.454914e+00 -4.316075e+00 -4.239479e+00 -4.153332e+00 -3.996782e+00  379.829602 1.0211041
## x[139]    -4.161545e+00 6.529283e-03 1.193692e-01 -4.383988e+00 -4.242371e+00 -4.167304e+00 -4.083720e+00 -3.925443e+00  334.236070 1.0215855
## x[140]    -4.068795e+00 6.504697e-03 1.203484e-01 -4.294457e+00 -4.149809e+00 -4.076246e+00 -3.991013e+00 -3.832770e+00  342.315773 1.0212910
## x[141]    -3.955189e+00 6.647949e-03 1.197230e-01 -4.174549e+00 -4.033589e+00 -3.961010e+00 -3.876126e+00 -3.715294e+00  324.324486 1.0210185
## x[142]    -3.822574e+00 6.195525e-03 1.200899e-01 -4.036492e+00 -3.902536e+00 -3.828577e+00 -3.745592e+00 -3.580832e+00  375.713497 1.0193134
## x[143]    -3.669275e+00 6.195440e-03 1.193870e-01 -3.883746e+00 -3.749117e+00 -3.676785e+00 -3.595114e+00 -3.428700e+00  371.338019 1.0188819
## x[144]    -3.498099e+00 5.635718e-03 1.181566e-01 -3.715728e+00 -3.579581e+00 -3.506660e+00 -3.423965e+00 -3.261483e+00  439.559443 1.0169498
## x[145]    -3.308657e+00 4.731716e-03 1.164468e-01 -3.522972e+00 -3.388970e+00 -3.315295e+00 -3.233727e+00 -3.075516e+00  605.644671 1.0146222
## x[146]    -3.103102e+00 3.973769e-03 1.148208e-01 -3.318985e+00 -3.179246e+00 -3.107053e+00 -3.030631e+00 -2.869536e+00  834.903488 1.0121290
## x[147]    -2.880589e+00 3.857249e-03 1.141239e-01 -3.098570e+00 -2.955978e+00 -2.884551e+00 -2.810687e+00 -2.649075e+00  875.382908 1.0099739
## x[148]    -2.642583e+00 3.620494e-03 1.132294e-01 -2.860292e+00 -2.714419e+00 -2.646296e+00 -2.573406e+00 -2.414058e+00  978.098535 1.0078421
## x[149]    -2.391024e+00 3.474277e-03 1.128798e-01 -2.605636e+00 -2.463707e+00 -2.394812e+00 -2.323171e+00 -2.169721e+00 1055.609280 1.0065007
## x[150]    -2.126230e+00 3.419329e-03 1.114345e-01 -2.348164e+00 -2.195500e+00 -2.128855e+00 -2.057122e+00 -1.901566e+00 1062.081473 1.0059800
## x[151]    -1.849214e+00 3.432268e-03 1.109380e-01 -2.068033e+00 -1.917001e+00 -1.851287e+00 -1.778016e+00 -1.622645e+00 1044.715239 1.0057173
## x[152]    -1.561980e+00 3.395212e-03 1.106320e-01 -1.781782e+00 -1.633436e+00 -1.564535e+00 -1.491461e+00 -1.343134e+00 1061.763738 1.0059005
## x[153]    -1.265127e+00 3.411523e-03 1.096057e-01 -1.490156e+00 -1.335913e+00 -1.264828e+00 -1.195326e+00 -1.054222e+00 1032.215019 1.0081154
## x[154]    -9.617241e-01 3.546893e-03 1.104850e-01 -1.186032e+00 -1.029140e+00 -9.609216e-01 -8.937756e-01 -7.458345e-01  970.309803 1.0113827
## x[155]    -6.517853e-01 3.989809e-03 1.110160e-01 -8.813647e-01 -7.224001e-01 -6.481760e-01 -5.817975e-01 -4.322402e-01  774.223972 1.0169439
## x[156]    -3.363499e-01 4.588726e-03 1.103208e-01 -5.671530e-01 -4.065511e-01 -3.328146e-01 -2.686032e-01 -1.220593e-01  578.003107 1.0197963
## x[157]    -1.862521e-02 6.675158e-03 1.117281e-01 -2.559809e-01 -8.719610e-02 -1.503448e-02  5.233082e-02  1.905362e-01  280.157371 1.0271398
## x[158]     3.013841e-01 8.286426e-03 1.131347e-01  5.280858e-02  2.334317e-01  3.049591e-01  3.735384e-01  5.142132e-01  186.404676 1.0329272
## x[159]     6.214737e-01 9.522874e-03 1.131689e-01  3.785182e-01  5.539803e-01  6.289201e-01  6.965734e-01  8.240677e-01  141.227062 1.0376443
## x[160]     9.401256e-01 1.079513e-02 1.140461e-01  6.939071e-01  8.717754e-01  9.456007e-01  1.015156e+00  1.148494e+00  111.610401 1.0421678
## x[161]     1.256020e+00 1.239204e-02 1.147092e-01  1.004347e+00  1.185696e+00  1.260551e+00  1.332624e+00  1.462087e+00   85.686167 1.0479848
## x[162]     1.568507e+00 1.335780e-02 1.160096e-01  1.311062e+00  1.496286e+00  1.574911e+00  1.645556e+00  1.782421e+00   75.425542 1.0525145
## x[163]     1.875528e+00 1.345901e-02 1.163028e-01  1.623468e+00  1.801922e+00  1.881462e+00  1.955111e+00  2.087026e+00   74.671353 1.0545919
## x[164]     2.174290e+00 1.388788e-02 1.174724e-01  1.918469e+00  2.103948e+00  2.180567e+00  2.254189e+00  2.394133e+00   71.548388 1.0539452
## x[165]     2.463901e+00 1.441538e-02 1.173833e-01  2.218403e+00  2.394266e+00  2.467724e+00  2.544646e+00  2.671648e+00   66.307200 1.0565908
## x[166]     2.743221e+00 1.449569e-02 1.173096e-01  2.489919e+00  2.671265e+00  2.750691e+00  2.827302e+00  2.953644e+00   65.492207 1.0565983
## x[167]     3.009088e+00 1.438283e-02 1.168407e-01  2.765503e+00  2.935453e+00  3.015765e+00  3.092375e+00  3.221213e+00   65.993322 1.0557145
## x[168]     3.260998e+00 1.528588e-02 1.177470e-01  3.009425e+00  3.185863e+00  3.266808e+00  3.343852e+00  3.471567e+00   59.336042 1.0580768
## x[169]     3.499573e+00 1.529868e-02 1.184231e-01  3.243374e+00  3.425125e+00  3.506271e+00  3.583014e+00  3.711725e+00   59.918987 1.0547629
## x[170]     3.721068e+00 1.546224e-02 1.190786e-01  3.462268e+00  3.646270e+00  3.728675e+00  3.804967e+00  3.937881e+00   59.309271 1.0567787
## x[171]     3.924169e+00 1.603083e-02 1.198533e-01  3.662763e+00  3.849123e+00  3.930406e+00  4.012213e+00  4.138825e+00   55.896989 1.0608819
## x[172]     4.110022e+00 1.620695e-02 1.199419e-01  3.851981e+00  4.033411e+00  4.116041e+00  4.200110e+00  4.324224e+00   54.769596 1.0604747
## x[173]     4.275121e+00 1.697783e-02 1.192197e-01  4.022353e+00  4.201335e+00  4.278408e+00  4.363885e+00  4.489723e+00   49.309601 1.0639418
## x[174]     4.419977e+00 1.765511e-02 1.204384e-01  4.162921e+00  4.344613e+00  4.423380e+00  4.509326e+00  4.637030e+00   46.535990 1.0675789
## x[175]     4.543569e+00 1.828178e-02 1.203056e-01  4.280228e+00  4.469327e+00  4.549222e+00  4.634116e+00  4.759484e+00   43.304700 1.0712675
## x[176]     4.645556e+00 1.806455e-02 1.200983e-01  4.383026e+00  4.570428e+00  4.651640e+00  4.734466e+00  4.859341e+00   44.199670 1.0729395
## x[177]     4.725743e+00 1.722787e-02 1.196572e-01  4.468658e+00  4.647216e+00  4.731781e+00  4.810734e+00  4.936950e+00   48.240774 1.0684639
## x[178]     4.782921e+00 1.676451e-02 1.201819e-01  4.526676e+00  4.703315e+00  4.789456e+00  4.868157e+00  5.002395e+00   51.392077 1.0637969
## x[179]     4.816731e+00 1.558466e-02 1.202920e-01  4.556055e+00  4.743344e+00  4.822127e+00  4.898817e+00  5.033555e+00   59.577013 1.0568239
## x[180]     4.826257e+00 1.478880e-02 1.196795e-01  4.571896e+00  4.751379e+00  4.831907e+00  4.910053e+00  5.040003e+00   65.489741 1.0547506
## x[181]     4.811687e+00 1.455082e-02 1.180634e-01  4.557388e+00  4.739299e+00  4.818897e+00  4.893566e+00  5.014287e+00   65.834819 1.0527297
## x[182]     4.772631e+00 1.378216e-02 1.164268e-01  4.524225e+00  4.698371e+00  4.781534e+00  4.851971e+00  4.980881e+00   71.362721 1.0521914
## x[183]     4.709812e+00 1.293267e-02 1.165006e-01  4.459434e+00  4.637131e+00  4.716093e+00  4.789401e+00  4.914645e+00   81.148491 1.0477096
## x[184]     4.623207e+00 1.253156e-02 1.157405e-01  4.374804e+00  4.551454e+00  4.629563e+00  4.701349e+00  4.826164e+00   85.302241 1.0455231
## x[185]     4.512517e+00 1.237635e-02 1.147804e-01  4.266798e+00  4.441137e+00  4.515560e+00  4.589421e+00  4.717834e+00   86.010296 1.0457501
## x[186]     4.377819e+00 1.246134e-02 1.139626e-01  4.134006e+00  4.304529e+00  4.380846e+00  4.458293e+00  4.581779e+00   83.636380 1.0463692
## x[187]     4.220775e+00 1.339501e-02 1.130313e-01  3.982786e+00  4.147217e+00  4.226095e+00  4.298595e+00  4.431135e+00   71.205157 1.0459976
## x[188]     4.043098e+00 1.250510e-02 1.121334e-01  3.812608e+00  3.969975e+00  4.047248e+00  4.118916e+00  4.248616e+00   80.407366 1.0425601
## x[189]     3.843270e+00 1.233372e-02 1.101627e-01  3.621897e+00  3.772263e+00  3.845190e+00  3.917916e+00  4.048460e+00   79.777516 1.0430761
## x[190]     3.622601e+00 1.231384e-02 1.087558e-01  3.406791e+00  3.551904e+00  3.623226e+00  3.695678e+00  3.822972e+00   78.004159 1.0431948
## x[191]     3.383822e+00 1.115779e-02 1.067887e-01  3.170092e+00  3.312619e+00  3.385159e+00  3.456960e+00  3.583129e+00   91.599755 1.0391070
## x[192]     3.127556e+00 9.834906e-03 1.059593e-01  2.914257e+00  3.056780e+00  3.129872e+00  3.197531e+00  3.320659e+00  116.074856 1.0349541
## x[193]     2.853660e+00 8.545106e-03 1.054958e-01  2.640722e+00  2.784185e+00  2.856006e+00  2.924063e+00  3.047862e+00  152.417600 1.0302251
## x[194]     2.565039e+00 7.392684e-03 1.045586e-01  2.359455e+00  2.497707e+00  2.568419e+00  2.634462e+00  2.763736e+00  200.039071 1.0265022
## x[195]     2.261884e+00 5.568754e-03 1.038108e-01  2.053175e+00  2.194229e+00  2.265070e+00  2.330840e+00  2.458886e+00  347.511141 1.0198959
## x[196]     1.945384e+00 4.390329e-03 1.038220e-01  1.739062e+00  1.879087e+00  1.944318e+00  2.015041e+00  2.142327e+00  559.222803 1.0164519
## x[197]     1.618203e+00 3.774061e-03 1.039569e-01  1.406011e+00  1.553500e+00  1.617313e+00  1.689841e+00  1.816516e+00  758.733428 1.0132713
## x[198]     1.279979e+00 3.694980e-03 1.028504e-01  1.072533e+00  1.214501e+00  1.278268e+00  1.348850e+00  1.478519e+00  774.796697 1.0104818
## x[199]     9.344224e-01 3.402168e-03 1.036545e-01  7.254217e-01  8.694115e-01  9.313024e-01  1.002973e+00  1.136117e+00  928.250231 1.0073299
## x[200]     5.813859e-01 3.348036e-03 1.028802e-01  3.743998e-01  5.146892e-01  5.809141e-01  6.504069e-01  7.819986e-01  944.242040 1.0054369
## x[201]     2.235607e-01 3.324858e-03 1.028958e-01  2.279355e-02  1.575411e-01  2.216341e-01  2.920970e-01  4.323654e-01  957.744054 1.0030507
## x[202]    -1.379769e-01 3.262540e-03 1.032347e-01 -3.415843e-01 -2.035290e-01 -1.378935e-01 -7.064236e-02  6.887573e-02 1001.242963 1.0020566
## x[203]    -5.011753e-01 3.218975e-03 1.030987e-01 -6.956495e-01 -5.652627e-01 -5.031820e-01 -4.318567e-01 -2.869480e-01 1025.819564 1.0012887
## x[204]    -8.642172e-01 3.190868e-03 1.033670e-01 -1.068865e+00 -9.303291e-01 -8.654367e-01 -7.975582e-01 -6.493155e-01 1049.412500 1.0013681
## x[205]    -1.223949e+00 3.145297e-03 1.033682e-01 -1.430394e+00 -1.291522e+00 -1.226478e+00 -1.158480e+00 -1.014469e+00 1080.067402 1.0013888
## x[206]    -1.580616e+00 3.177054e-03 1.051352e-01 -1.787857e+00 -1.647038e+00 -1.583592e+00 -1.515224e+00 -1.369955e+00 1095.083157 1.0013368
## x[207]    -1.931064e+00 3.212971e-03 1.058877e-01 -2.141652e+00 -1.998947e+00 -1.931577e+00 -1.865156e+00 -1.723487e+00 1086.118434 1.0022356
## x[208]    -2.274329e+00 3.256657e-03 1.063228e-01 -2.483362e+00 -2.339063e+00 -2.275093e+00 -2.208136e+00 -2.062763e+00 1065.881839 1.0033614
## x[209]    -2.609010e+00 3.303827e-03 1.072579e-01 -2.824998e+00 -2.674467e+00 -2.611784e+00 -2.542529e+00 -2.391494e+00 1053.959847 1.0051766
## x[210]    -2.931833e+00 3.410401e-03 1.091923e-01 -3.142745e+00 -3.001627e+00 -2.933666e+00 -2.862572e+00 -2.718642e+00 1025.115512 1.0066113
## x[211]    -3.242372e+00 3.483884e-03 1.103616e-01 -3.457308e+00 -3.313017e+00 -3.244374e+00 -3.174283e+00 -3.026213e+00 1003.479603 1.0068319
## x[212]    -3.537430e+00 3.652976e-03 1.111536e-01 -3.754664e+00 -3.610253e+00 -3.539970e+00 -3.465612e+00 -3.328906e+00  925.877115 1.0082581
## x[213]    -3.817320e+00 3.717103e-03 1.110269e-01 -4.031192e+00 -3.887896e+00 -3.819090e+00 -3.744800e+00 -3.591544e+00  892.169207 1.0078566
## x[214]    -4.079315e+00 3.795067e-03 1.115286e-01 -4.298415e+00 -4.151142e+00 -4.081508e+00 -4.007919e+00 -3.856668e+00  863.641399 1.0086131
## x[215]    -4.323241e+00 3.781920e-03 1.118956e-01 -4.542457e+00 -4.394039e+00 -4.325327e+00 -4.251308e+00 -4.111274e+00  875.388820 1.0093350
## x[216]    -4.547793e+00 3.648064e-03 1.121568e-01 -4.777231e+00 -4.618331e+00 -4.551846e+00 -4.471056e+00 -4.335489e+00  945.205114 1.0093845
## x[217]    -4.750046e+00 3.661264e-03 1.120319e-01 -4.980329e+00 -4.823018e+00 -4.751741e+00 -4.673820e+00 -4.534136e+00  936.313751 1.0089351
## x[218]    -4.929794e+00 3.610351e-03 1.119329e-01 -5.157720e+00 -5.002247e+00 -4.931218e+00 -4.854883e+00 -4.713698e+00  961.206099 1.0082864
## x[219]    -5.087744e+00 3.539651e-03 1.123731e-01 -5.321321e+00 -5.158816e+00 -5.089477e+00 -5.011911e+00 -4.868710e+00 1007.868103 1.0080422
## x[220]    -5.219858e+00 3.527150e-03 1.125689e-01 -5.449067e+00 -5.293436e+00 -5.223674e+00 -5.145097e+00 -5.003143e+00 1018.565260 1.0086131
## x[221]    -5.326782e+00 3.492342e-03 1.129664e-01 -5.553292e+00 -5.400348e+00 -5.328846e+00 -5.250930e+00 -5.105803e+00 1046.321027 1.0078217
## x[222]    -5.407665e+00 3.545514e-03 1.131097e-01 -5.624154e+00 -5.481427e+00 -5.410933e+00 -5.333651e+00 -5.184234e+00 1017.750259 1.0082344
## x[223]    -5.462667e+00 3.609116e-03 1.127441e-01 -5.684945e+00 -5.536952e+00 -5.466197e+00 -5.386938e+00 -5.239429e+00  975.856235 1.0082062
## x[224]    -5.490539e+00 3.490333e-03 1.128804e-01 -5.722912e+00 -5.563602e+00 -5.493192e+00 -5.414198e+00 -5.271775e+00 1045.932325 1.0060464
## x[225]    -5.491762e+00 3.465708e-03 1.134132e-01 -5.720448e+00 -5.563691e+00 -5.494625e+00 -5.415763e+00 -5.275893e+00 1070.885263 1.0056443
## x[226]    -5.465237e+00 3.460175e-03 1.140681e-01 -5.696563e+00 -5.537277e+00 -5.466564e+00 -5.388322e+00 -5.249525e+00 1086.756631 1.0056895
## x[227]    -5.412213e+00 3.495640e-03 1.142977e-01 -5.647444e+00 -5.482225e+00 -5.412970e+00 -5.337102e+00 -5.190773e+00 1069.107448 1.0048663
## x[228]    -5.333206e+00 3.395891e-03 1.137250e-01 -5.566289e+00 -5.404624e+00 -5.334015e+00 -5.260018e+00 -5.115137e+00 1121.514057 1.0059658
## x[229]    -5.226334e+00 3.411651e-03 1.141343e-01 -5.465068e+00 -5.299759e+00 -5.226535e+00 -5.152641e+00 -5.008422e+00 1119.187696 1.0057752
## x[230]    -5.092412e+00 3.447568e-03 1.144719e-01 -5.328132e+00 -5.162239e+00 -5.094481e+00 -5.017111e+00 -4.872338e+00 1102.483383 1.0044414
## x[231]    -4.933292e+00 3.356264e-03 1.136333e-01 -5.169914e+00 -5.006629e+00 -4.934652e+00 -4.859211e+00 -4.716952e+00 1146.302839 1.0040204
## x[232]    -4.748865e+00 3.315794e-03 1.132452e-01 -4.981906e+00 -4.822046e+00 -4.749790e+00 -4.675193e+00 -4.533688e+00 1166.444683 1.0036127
## x[233]    -4.540207e+00 3.211226e-03 1.124683e-01 -4.770972e+00 -4.612249e+00 -4.542023e+00 -4.464878e+00 -4.323930e+00 1226.643522 1.0038143
## x[234]    -4.307412e+00 3.167018e-03 1.116933e-01 -4.539151e+00 -4.379084e+00 -4.307257e+00 -4.233389e+00 -4.093559e+00 1243.807738 1.0028323
## x[235]    -4.053385e+00 3.320520e-03 1.119740e-01 -4.284561e+00 -4.125564e+00 -4.052806e+00 -3.982025e+00 -3.836504e+00 1137.161534 1.0033855
## x[236]    -3.778844e+00 3.694046e-03 1.117792e-01 -4.008768e+00 -3.851216e+00 -3.778837e+00 -3.706317e+00 -3.562594e+00  915.624793 1.0054988
## x[237]    -3.482675e+00 3.771884e-03 1.104488e-01 -3.713684e+00 -3.555153e+00 -3.480047e+00 -3.411835e+00 -3.274250e+00  857.443751 1.0076048
## x[238]    -3.168069e+00 3.796052e-03 1.104071e-01 -3.402548e+00 -3.239023e+00 -3.166247e+00 -3.096848e+00 -2.955425e+00  845.920984 1.0112961
## x[239]    -2.836355e+00 3.967595e-03 1.100112e-01 -3.071715e+00 -2.904979e+00 -2.834366e+00 -2.761040e+00 -2.625317e+00  768.810414 1.0143071
## x[240]    -2.490351e+00 4.324288e-03 1.107164e-01 -2.729356e+00 -2.559453e+00 -2.487526e+00 -2.417121e+00 -2.282982e+00  655.532663 1.0191765
## x[241]    -2.128657e+00 4.440215e-03 1.113916e-01 -2.371244e+00 -2.197968e+00 -2.124556e+00 -2.054835e+00 -1.919674e+00  629.356218 1.0198036
## x[242]    -1.754200e+00 5.290911e-03 1.103509e-01 -1.986467e+00 -1.823395e+00 -1.750344e+00 -1.684633e+00 -1.548648e+00  435.001763 1.0244713
## x[243]    -1.368562e+00 5.559466e-03 1.099769e-01 -1.599944e+00 -1.438300e+00 -1.363037e+00 -1.297551e+00 -1.164909e+00  391.324146 1.0237292
## x[244]    -9.744688e-01 5.681751e-03 1.091409e-01 -1.195506e+00 -1.042678e+00 -9.697252e-01 -9.052305e-01 -7.701544e-01  368.986471 1.0241798
## x[245]    -5.726887e-01 5.753882e-03 1.080473e-01 -7.917112e-01 -6.407976e-01 -5.677372e-01 -5.030092e-01 -3.714166e-01  352.619401 1.0235618
## x[246]    -1.663613e-01 6.442221e-03 1.079059e-01 -3.860373e-01 -2.355486e-01 -1.621289e-01 -9.415709e-02  3.419284e-02  280.555508 1.0229383
## x[247]     2.423197e-01 6.596093e-03 1.066834e-01  2.376526e-02  1.751099e-01  2.460383e-01  3.110192e-01  4.442045e-01  261.589385 1.0233754
## x[248]     6.524904e-01 6.759089e-03 1.065344e-01  4.279035e-01  5.861726e-01  6.579342e-01  7.219312e-01  8.558115e-01  248.429518 1.0244714
## x[249]     1.061338e+00 6.607794e-03 1.054834e-01  8.381582e-01  9.973469e-01  1.065636e+00  1.132174e+00  1.257955e+00  254.832678 1.0254780
## x[250]     1.467412e+00 6.459184e-03 1.053751e-01  1.244382e+00  1.401487e+00  1.471448e+00  1.536388e+00  1.667029e+00  266.146255 1.0234512
## x[251]     1.868506e+00 5.904417e-03 1.054254e-01  1.655498e+00  1.803338e+00  1.872938e+00  1.937198e+00  2.070653e+00  318.813169 1.0220470
## x[252]     2.262806e+00 5.796601e-03 1.052206e-01  2.051911e+00  2.200061e+00  2.266306e+00  2.330221e+00  2.466883e+00  329.499497 1.0204524
## x[253]     2.647080e+00 5.374496e-03 1.061799e-01  2.428501e+00  2.580847e+00  2.652673e+00  2.715921e+00  2.858529e+00  390.309112 1.0197286
## x[254]     3.020287e+00 4.622168e-03 1.066492e-01  2.805514e+00  2.954540e+00  3.024356e+00  3.090227e+00  3.230966e+00  532.382429 1.0184008
## x[255]     3.380984e+00 3.946216e-03 1.064348e-01  3.166710e+00  3.313456e+00  3.383694e+00  3.453478e+00  3.586774e+00  727.454095 1.0179257
## x[256]     3.727208e+00 3.776570e-03 1.067202e-01  3.506703e+00  3.662182e+00  3.730374e+00  3.798605e+00  3.929658e+00  798.542262 1.0162488
## x[257]     4.056749e+00 3.515194e-03 1.059893e-01  3.842310e+00  3.991260e+00  4.057825e+00  4.127961e+00  4.262986e+00  909.129279 1.0138749
## x[258]     4.367617e+00 3.289739e-03 1.075099e-01  4.149946e+00  4.298129e+00  4.368330e+00  4.441502e+00  4.577033e+00 1068.006309 1.0121028
## x[259]     4.660595e+00 3.188143e-03 1.082299e-01  4.444531e+00  4.590275e+00  4.663021e+00  4.733217e+00  4.871412e+00 1152.440714 1.0086219
## x[260]     4.930955e+00 3.154092e-03 1.084927e-01  4.720844e+00  4.860157e+00  4.932889e+00  5.005672e+00  5.143490e+00 1183.185247 1.0064258
## x[261]     5.178254e+00 3.164903e-03 1.088718e-01  4.968165e+00  5.107480e+00  5.180731e+00  5.250581e+00  5.384286e+00 1183.342380 1.0048922
## x[262]     5.400534e+00 3.162616e-03 1.088066e-01  5.184038e+00  5.328065e+00  5.404573e+00  5.471590e+00  5.610018e+00 1183.634326 1.0042343
## x[263]     5.596715e+00 3.231269e-03 1.089785e-01  5.380921e+00  5.524390e+00  5.601263e+00  5.666875e+00  5.809496e+00 1137.458041 1.0034067
## x[264]     5.767211e+00 3.321289e-03 1.106488e-01  5.549556e+00  5.693789e+00  5.771024e+00  5.837773e+00  5.989876e+00 1109.890000 1.0025296
## x[265]     5.909758e+00 3.414679e-03 1.118409e-01  5.688044e+00  5.836993e+00  5.913513e+00  5.979233e+00  6.133345e+00 1072.757458 1.0027240
## x[266]     6.022895e+00 3.493128e-03 1.126992e-01  5.801589e+00  5.947317e+00  6.024024e+00  6.092291e+00  6.259693e+00 1040.909787 1.0032421
## x[267]     6.106813e+00 3.577388e-03 1.133229e-01  5.888600e+00  6.032121e+00  6.106372e+00  6.176230e+00  6.338641e+00 1003.467206 1.0037976
## x[268]     6.161520e+00 3.736042e-03 1.132474e-01  5.940062e+00  6.086522e+00  6.158405e+00  6.229354e+00  6.399142e+00  918.824784 1.0049633
## x[269]     6.184321e+00 3.877932e-03 1.137848e-01  5.971244e+00  6.109816e+00  6.181707e+00  6.253668e+00  6.423265e+00  860.930445 1.0068886
## x[270]     6.176918e+00 4.038935e-03 1.156599e-01  5.954772e+00  6.101888e+00  6.177273e+00  6.244669e+00  6.429971e+00  820.034311 1.0085971
## x[271]     6.138729e+00 4.109709e-03 1.168639e-01  5.922445e+00  6.063796e+00  6.136186e+00  6.206104e+00  6.402980e+00  808.608715 1.0090302
## x[272]     6.068970e+00 3.958030e-03 1.170589e-01  5.848068e+00  5.995054e+00  6.065425e+00  6.136856e+00  6.322563e+00  874.683228 1.0085913
## x[273]     5.968183e+00 3.940742e-03 1.162672e-01  5.750973e+00  5.895197e+00  5.965683e+00  6.034080e+00  6.232103e+00  870.479004 1.0083572
## x[274]     5.836929e+00 4.541010e-03 1.172048e-01  5.608167e+00  5.761032e+00  5.833365e+00  5.904020e+00  6.097548e+00  666.171729 1.0086062
## x[275]     5.677313e+00 4.507081e-03 1.171754e-01  5.445687e+00  5.601566e+00  5.673088e+00  5.744708e+00  5.935932e+00  675.899384 1.0093256
## x[276]     5.489006e+00 4.303113e-03 1.181696e-01  5.263658e+00  5.411841e+00  5.485927e+00  5.555263e+00  5.748617e+00  754.129897 1.0098189
## x[277]     5.272936e+00 5.813339e-03 1.180932e-01  5.043651e+00  5.194772e+00  5.269503e+00  5.340762e+00  5.528826e+00  412.665664 1.0123852
## x[278]     5.029512e+00 6.894765e-03 1.183239e-01  4.803050e+00  4.951904e+00  5.024894e+00  5.094823e+00  5.290469e+00  294.514172 1.0143140
## x[279]     4.759560e+00 7.334706e-03 1.195375e-01  4.532641e+00  4.680603e+00  4.754121e+00  4.826425e+00  5.008833e+00  265.609106 1.0155529
## x[280]     4.464244e+00 7.648315e-03 1.194187e-01  4.236385e+00  4.387562e+00  4.457989e+00  4.533188e+00  4.732813e+00  243.788297 1.0186564
## x[281]     4.145438e+00 7.835063e-03 1.179923e-01  3.929711e+00  4.069766e+00  4.137905e+00  4.214105e+00  4.408972e+00  226.789261 1.0193511
## x[282]     3.805994e+00 9.147309e-03 1.181233e-01  3.582291e+00  3.729651e+00  3.797559e+00  3.877266e+00  4.064155e+00  166.757085 1.0236192
## x[283]     3.445505e+00 9.723490e-03 1.174984e-01  3.234078e+00  3.367771e+00  3.435720e+00  3.515210e+00  3.708311e+00  146.022472 1.0267426
## x[284]     3.065739e+00 9.994503e-03 1.178235e-01  2.854529e+00  2.987597e+00  3.055160e+00  3.137015e+00  3.323606e+00  138.976503 1.0306018
## x[285]     2.669939e+00 1.132578e-02 1.174807e-01  2.455910e+00  2.591734e+00  2.659013e+00  2.741863e+00  2.924800e+00  107.596256 1.0376277
## x[286]     2.258652e+00 1.304791e-02 1.167595e-01  2.049741e+00  2.181575e+00  2.246365e+00  2.329377e+00  2.513820e+00   80.075928 1.0445098
## x[287]     1.834343e+00 1.443260e-02 1.163251e-01  1.627608e+00  1.757802e+00  1.825486e+00  1.901642e+00  2.086818e+00   64.961703 1.0515420
## x[288]     1.398645e+00 1.541194e-02 1.168618e-01  1.188049e+00  1.320657e+00  1.387528e+00  1.465631e+00  1.660430e+00   57.495052 1.0579489
## x[289]     9.527517e-01 1.558720e-02 1.165103e-01  7.417503e-01  8.760869e-01  9.411506e-01  1.022067e+00  1.207316e+00   55.871786 1.0605438
## x[290]     5.002624e-01 1.572402e-02 1.168738e-01  2.815701e-01  4.233926e-01  4.907076e-01  5.696510e-01  7.508522e-01   55.246818 1.0614760
## x[291]     4.261557e-02 1.604421e-02 1.169449e-01 -1.663741e-01 -3.377847e-02  3.148075e-02  1.117658e-01  2.980727e-01   53.128313 1.0654986
## x[292]    -4.174459e-01 1.622492e-02 1.163141e-01 -6.232208e-01 -4.942394e-01 -4.259026e-01 -3.493901e-01 -1.518143e-01   51.392549 1.0684645
## x[293]    -8.778214e-01 1.641283e-02 1.166683e-01 -1.083932e+00 -9.542114e-01 -8.837564e-01 -8.100185e-01 -6.133404e-01   50.528806 1.0694718
## x[294]    -1.337306e+00 1.607625e-02 1.158884e-01 -1.547622e+00 -1.414056e+00 -1.344799e+00 -1.269388e+00 -1.078254e+00   51.964993 1.0701793
## x[295]    -1.791812e+00 1.595399e-02 1.155606e-01 -2.005680e+00 -1.869239e+00 -1.798649e+00 -1.722338e+00 -1.539158e+00   52.466348 1.0708466
## x[296]    -2.238665e+00 1.684645e-02 1.154244e-01 -2.451128e+00 -2.314627e+00 -2.247805e+00 -2.166554e+00 -1.992026e+00   46.943837 1.0775415
## x[297]    -2.677439e+00 1.611789e-02 1.149366e-01 -2.884874e+00 -2.753609e+00 -2.684503e+00 -2.607399e+00 -2.430038e+00   50.851108 1.0722014
## x[298]    -3.104517e+00 1.577842e-02 1.160164e-01 -3.309274e+00 -3.180981e+00 -3.110779e+00 -3.032642e+00 -2.858091e+00   54.064393 1.0689593
## x[299]    -3.519625e+00 1.445102e-02 1.156350e-01 -3.729021e+00 -3.597653e+00 -3.526590e+00 -3.449128e+00 -3.276863e+00   64.029697 1.0643797
## x[300]    -3.920006e+00 1.372938e-02 1.150801e-01 -4.131517e+00 -3.997894e+00 -3.927018e+00 -3.851386e+00 -3.677002e+00   70.258397 1.0582845
## x[301]    -4.300599e+00 1.352628e-02 1.156811e-01 -4.510654e+00 -4.381257e+00 -4.307685e+00 -4.230191e+00 -4.052049e+00   73.142277 1.0561936
## x[302]    -4.662539e+00 1.310242e-02 1.148054e-01 -4.877974e+00 -4.741234e+00 -4.668527e+00 -4.591461e+00 -4.420777e+00   76.775291 1.0531238
## x[303]    -5.003366e+00 1.241487e-02 1.149591e-01 -5.219714e+00 -5.080134e+00 -5.008520e+00 -4.933424e+00 -4.752818e+00   85.743695 1.0476345
## x[304]    -5.321365e+00 1.112112e-02 1.140523e-01 -5.537557e+00 -5.396700e+00 -5.325476e+00 -5.251833e+00 -5.072409e+00  105.174622 1.0435059
## x[305]    -5.612523e+00 1.068519e-02 1.138093e-01 -5.831398e+00 -5.687069e+00 -5.616207e+00 -5.541636e+00 -5.373136e+00  113.446486 1.0412325
## x[306]    -5.877021e+00 1.053326e-02 1.149965e-01 -6.097709e+00 -5.950162e+00 -5.881934e+00 -5.808229e+00 -5.636785e+00  119.191076 1.0386093
## x[307]    -6.113551e+00 1.023034e-02 1.151308e-01 -6.332963e+00 -6.188289e+00 -6.117148e+00 -6.043731e+00 -5.876143e+00  126.649180 1.0377048
## x[308]    -6.321657e+00 9.806772e-03 1.150190e-01 -6.542930e+00 -6.394340e+00 -6.325890e+00 -6.249676e+00 -6.086421e+00  137.558463 1.0351967
## x[309]    -6.499081e+00 8.738803e-03 1.148001e-01 -6.717628e+00 -6.572218e+00 -6.502202e+00 -6.428680e+00 -6.263693e+00  172.576005 1.0319760
## x[310]    -6.644728e+00 7.299926e-03 1.147109e-01 -6.868244e+00 -6.718924e+00 -6.649650e+00 -6.569502e+00 -6.412002e+00  246.929335 1.0265357
## x[311]    -6.757155e+00 5.881936e-03 1.146697e-01 -6.983359e+00 -6.830946e+00 -6.762642e+00 -6.682725e+00 -6.522231e+00  380.063816 1.0234470
## x[312]    -6.836626e+00 5.346696e-03 1.151764e-01 -7.068371e+00 -6.909495e+00 -6.841629e+00 -6.762330e+00 -6.602044e+00  464.040898 1.0196418
## x[313]    -6.881595e+00 5.139530e-03 1.165068e-01 -7.118859e+00 -6.955100e+00 -6.887041e+00 -6.805189e+00 -6.643641e+00  513.872591 1.0187281
## x[314]    -6.892668e+00 4.695670e-03 1.170381e-01 -7.131948e+00 -6.965833e+00 -6.896792e+00 -6.817424e+00 -6.656018e+00  621.239980 1.0171084
## x[315]    -6.870160e+00 4.157214e-03 1.173251e-01 -7.110784e+00 -6.941896e+00 -6.872302e+00 -6.799548e+00 -6.636402e+00  796.484763 1.0142361
## x[316]    -6.812673e+00 3.981218e-03 1.169367e-01 -7.053145e+00 -6.882980e+00 -6.816506e+00 -6.739435e+00 -6.575891e+00  862.720039 1.0116458
## x[317]    -6.720498e+00 3.974846e-03 1.167007e-01 -6.958652e+00 -6.792396e+00 -6.724243e+00 -6.647121e+00 -6.490303e+00  861.998283 1.0110402
## x[318]    -6.594754e+00 3.869929e-03 1.172146e-01 -6.834065e+00 -6.667765e+00 -6.598183e+00 -6.521754e+00 -6.361092e+00  917.397604 1.0094633
## x[319]    -6.435484e+00 3.741608e-03 1.175163e-01 -6.672340e+00 -6.508938e+00 -6.436751e+00 -6.365288e+00 -6.206980e+00  986.459727 1.0087896
## x[320]    -6.243553e+00 3.679539e-03 1.177080e-01 -6.478065e+00 -6.316488e+00 -6.244160e+00 -6.173759e+00 -6.006274e+00 1023.351904 1.0068346
## x[321]    -6.018713e+00 3.664925e-03 1.169813e-01 -6.258315e+00 -6.090234e+00 -6.020058e+00 -5.947479e+00 -5.791121e+00 1018.832712 1.0055474
## x[322]    -5.763642e+00 3.521487e-03 1.161779e-01 -6.002000e+00 -5.836327e+00 -5.765031e+00 -5.693185e+00 -5.537636e+00 1088.415981 1.0037284
## x[323]    -5.477030e+00 3.503130e-03 1.154390e-01 -5.715878e+00 -5.548386e+00 -5.477593e+00 -5.407582e+00 -5.251569e+00 1085.906721 1.0037067
## x[324]    -5.162025e+00 3.503102e-03 1.150554e-01 -5.397050e+00 -5.232810e+00 -5.160663e+00 -5.090670e+00 -4.935950e+00 1078.718324 1.0028481
## x[325]    -4.820037e+00 3.391434e-03 1.149480e-01 -5.045110e+00 -4.892341e+00 -4.818445e+00 -4.750560e+00 -4.598164e+00 1148.778236 1.0016272
## x[326]    -4.451603e+00 3.342472e-03 1.145880e-01 -4.680654e+00 -4.520973e+00 -4.450200e+00 -4.381446e+00 -4.230112e+00 1175.283640 1.0004448
## x[327]    -4.058920e+00 3.269634e-03 1.138721e-01 -4.288781e+00 -4.128933e+00 -4.059509e+00 -3.988757e+00 -3.831218e+00 1212.931442 0.9995988
## x[328]    -3.644532e+00 3.185590e-03 1.131535e-01 -3.871989e+00 -3.715986e+00 -3.643074e+00 -3.573462e+00 -3.423362e+00 1261.700810 0.9992411
## x[329]    -3.208581e+00 3.123263e-03 1.126001e-01 -3.434400e+00 -3.277196e+00 -3.207381e+00 -3.137578e+00 -2.988492e+00 1299.751560 0.9989636
## x[330]    -2.756066e+00 3.155337e-03 1.125493e-01 -2.983001e+00 -2.824097e+00 -2.754496e+00 -2.686882e+00 -2.538726e+00 1272.312849 0.9986156
## x[331]    -2.285781e+00 3.117223e-03 1.117446e-01 -2.504419e+00 -2.356441e+00 -2.285603e+00 -2.214451e+00 -2.065755e+00 1285.041626 0.9987444
## x[332]    -1.801956e+00 3.090594e-03 1.103638e-01 -2.020490e+00 -1.871539e+00 -1.802653e+00 -1.731296e+00 -1.586746e+00 1275.174556 0.9987622
## x[333]    -1.307150e+00 3.048270e-03 1.094757e-01 -1.532433e+00 -1.374312e+00 -1.308329e+00 -1.234960e+00 -1.088267e+00 1289.818831 0.9985292
## x[334]    -8.034942e-01 3.128521e-03 1.100413e-01 -1.023744e+00 -8.703054e-01 -8.027466e-01 -7.342167e-01 -5.880716e-01 1237.181743 0.9986783
## x[335]    -2.925545e-01 3.069953e-03 1.092745e-01 -5.126201e-01 -3.624614e-01 -2.907760e-01 -2.222250e-01 -7.832659e-02 1266.993436 0.9986801
## x[336]     2.229973e-01 3.051310e-03 1.089758e-01  4.975602e-03  1.553230e-01  2.241039e-01  2.905923e-01  4.412999e-01 1275.520504 0.9990455
## x[337]     7.413591e-01 3.055229e-03 1.079071e-01  5.258865e-01  6.716209e-01  7.440917e-01  8.099996e-01  9.526916e-01 1247.419949 0.9989745
## x[338]     1.257926e+00 3.057800e-03 1.081936e-01  1.043222e+00  1.187093e+00  1.258880e+00  1.326706e+00  1.471182e+00 1251.944149 0.9986653
## x[339]     1.771030e+00 3.041184e-03 1.079379e-01  1.563003e+00  1.701655e+00  1.775232e+00  1.843302e+00  1.982339e+00 1259.687048 0.9989853
## x[340]     2.278440e+00 3.045119e-03 1.085508e-01  2.064147e+00  2.207979e+00  2.283426e+00  2.349916e+00  2.497342e+00 1270.742210 0.9998851
## x[341]     2.776146e+00 3.141924e-03 1.096609e-01  2.563523e+00  2.705018e+00  2.776443e+00  2.847966e+00  2.992139e+00 1218.182947 1.0005020
## x[342]     3.262480e+00 3.123456e-03 1.092777e-01  3.046431e+00  3.191927e+00  3.262822e+00  3.335457e+00  3.485637e+00 1224.030047 1.0002398
## x[343]     3.735228e+00 3.105010e-03 1.095157e-01  3.519495e+00  3.665002e+00  3.734375e+00  3.806947e+00  3.953264e+00 1244.017949 1.0013097
## x[344]     4.192350e+00 3.137910e-03 1.100429e-01  3.979954e+00  4.120366e+00  4.189942e+00  4.263863e+00  4.412383e+00 1229.825170 1.0012355
## x[345]     4.631083e+00 3.190630e-03 1.109318e-01  4.421163e+00  4.557290e+00  4.627296e+00  4.700033e+00  4.853625e+00 1208.813074 1.0026152
## x[346]     5.049918e+00 3.296135e-03 1.101385e-01  4.841401e+00  4.976444e+00  5.046418e+00  5.121938e+00  5.274905e+00 1116.525463 1.0035321
## x[347]     5.444512e+00 3.499077e-03 1.109715e-01  5.237081e+00  5.372157e+00  5.439475e+00  5.516037e+00  5.665801e+00 1005.809720 1.0034321
## x[348]     5.813858e+00 3.352796e-03 1.122908e-01  5.598293e+00  5.739957e+00  5.809118e+00  5.884808e+00  6.045620e+00 1121.694222 1.0036418
## x[349]     6.156067e+00 3.157387e-03 1.126565e-01  5.936804e+00  6.083064e+00  6.151140e+00  6.226809e+00  6.386368e+00 1273.083307 1.0039618
## x[350]     6.470006e+00 3.230717e-03 1.136467e-01  6.255319e+00  6.398386e+00  6.463457e+00  6.538762e+00  6.705440e+00 1237.415370 1.0054587
## x[351]     6.753327e+00 3.200656e-03 1.143382e-01  6.543926e+00  6.678935e+00  6.747472e+00  6.824480e+00  6.979737e+00 1276.158608 1.0045596
## x[352]     7.004351e+00 3.087000e-03 1.153412e-01  6.790907e+00  6.929604e+00  6.999426e+00  7.074166e+00  7.241613e+00 1396.033676 1.0047039
## x[353]     7.221469e+00 3.046035e-03 1.156972e-01  7.002702e+00  7.145104e+00  7.216950e+00  7.294880e+00  7.460651e+00 1442.698720 1.0049254
## x[354]     7.403426e+00 3.050302e-03 1.162142e-01  7.182251e+00  7.331257e+00  7.396693e+00  7.479583e+00  7.642153e+00 1451.552044 1.0043999
## x[355]     7.549977e+00 3.070696e-03 1.166950e-01  7.327653e+00  7.475629e+00  7.542880e+00  7.622719e+00  7.790683e+00 1444.210348 1.0052808
## x[356]     7.658895e+00 3.251255e-03 1.172557e-01  7.437595e+00  7.582764e+00  7.654012e+00  7.732515e+00  7.901733e+00 1300.665275 1.0047965
## x[357]     7.731213e+00 3.218503e-03 1.166499e-01  7.506842e+00  7.656879e+00  7.724318e+00  7.809442e+00  7.973385e+00 1313.593907 1.0041153
## x[358]     7.767299e+00 3.401744e-03 1.174489e-01  7.540258e+00  7.691649e+00  7.764115e+00  7.841198e+00  8.010455e+00 1192.050404 1.0047009
## x[359]     7.763528e+00 3.518322e-03 1.173162e-01  7.542698e+00  7.687842e+00  7.761091e+00  7.838155e+00  8.008302e+00 1111.847278 1.0069145
## x[360]     7.720206e+00 3.521250e-03 1.170422e-01  7.496415e+00  7.645012e+00  7.716545e+00  7.796045e+00  7.960368e+00 1104.819992 1.0082026
## x[361]     7.638924e+00 3.529863e-03 1.165871e-01  7.413871e+00  7.563188e+00  7.635512e+00  7.714371e+00  7.876145e+00 1090.900658 1.0068213
## x[362]     7.519430e+00 3.554782e-03 1.162355e-01  7.286610e+00  7.443572e+00  7.516519e+00  7.595117e+00  7.754478e+00 1069.181361 1.0073360
## x[363]     7.360665e+00 3.302361e-03 1.176030e-01  7.126939e+00  7.285758e+00  7.356924e+00  7.435945e+00  7.607829e+00 1268.200396 1.0063940
## x[364]     7.164657e+00 3.365343e-03 1.169751e-01  6.939796e+00  7.086496e+00  7.161117e+00  7.239545e+00  7.407132e+00 1208.170015 1.0058773
## x[365]     6.933147e+00 3.275570e-03 1.167157e-01  6.706671e+00  6.855965e+00  6.930216e+00  7.008468e+00  7.177593e+00 1269.651206 1.0060237
## x[366]     6.664250e+00 3.268871e-03 1.155429e-01  6.439316e+00  6.589853e+00  6.659616e+00  6.738270e+00  6.903459e+00 1249.370169 1.0046821
## x[367]     6.361609e+00 3.311317e-03 1.149867e-01  6.139223e+00  6.287544e+00  6.356536e+00  6.435088e+00  6.601855e+00 1205.850948 1.0044975
## x[368]     6.025762e+00 3.316764e-03 1.141091e-01  5.809159e+00  5.952615e+00  6.021455e+00  6.100278e+00  6.255468e+00 1183.618884 1.0049880
## x[369]     5.657734e+00 3.363969e-03 1.141559e-01  5.444326e+00  5.586756e+00  5.652962e+00  5.732003e+00  5.893234e+00 1151.576678 1.0049374
## x[370]     5.259756e+00 3.368831e-03 1.143870e-01  5.045481e+00  5.186878e+00  5.258311e+00  5.332414e+00  5.498392e+00 1152.908948 1.0045036
## x[371]     4.833813e+00 3.378410e-03 1.156017e-01  4.609785e+00  4.759156e+00  4.831789e+00  4.905494e+00  5.072127e+00 1170.857382 1.0036726
## x[372]     4.381429e+00 3.356856e-03 1.158034e-01  4.165226e+00  4.306103e+00  4.378570e+00  4.454136e+00  4.630619e+00 1190.082238 1.0032769
## x[373]     3.904941e+00 3.337959e-03 1.159105e-01  3.689603e+00  3.829171e+00  3.905183e+00  3.975702e+00  4.150244e+00 1205.823075 1.0018427
## x[374]     3.406037e+00 3.279039e-03 1.147092e-01  3.188384e+00  3.331098e+00  3.404444e+00  3.475556e+00  3.649866e+00 1223.780649 1.0012273
## x[375]     2.887632e+00 3.295824e-03 1.148005e-01  2.665666e+00  2.816361e+00  2.885275e+00  2.956922e+00  3.128424e+00 1213.276093 1.0011340
## x[376]     2.352047e+00 3.248585e-03 1.146267e-01  2.134563e+00  2.277722e+00  2.350060e+00  2.420018e+00  2.592810e+00 1245.039403 1.0008641
## x[377]     1.802082e+00 3.234428e-03 1.138310e-01  1.581687e+00  1.726854e+00  1.802871e+00  1.870863e+00  2.035388e+00 1238.585185 1.0008231
## x[378]     1.240909e+00 3.166817e-03 1.127445e-01  1.013022e+00  1.168047e+00  1.242544e+00  1.308783e+00  1.480572e+00 1267.491647 1.0003655
## x[379]     6.702700e-01 3.088630e-03 1.122780e-01  4.431329e-01  5.996632e-01  6.734133e-01  7.391387e-01  9.011403e-01 1321.470110 1.0000982
## x[380]     9.397518e-02 2.995651e-03 1.120640e-01 -1.392907e-01  2.305709e-02  9.873575e-02  1.616425e-01  3.205598e-01 1399.425256 1.0000455
## x[381]    -4.853512e-01 2.929326e-03 1.121388e-01 -7.170974e-01 -5.560942e-01 -4.815936e-01 -4.178100e-01 -2.568759e-01 1465.468204 0.9996966
## x[382]    -1.065546e+00 2.926931e-03 1.122987e-01 -1.302796e+00 -1.136082e+00 -1.063130e+00 -9.971400e-01 -8.396689e-01 1472.056153 0.9999911
## x[383]    -1.644139e+00 2.898313e-03 1.124660e-01 -1.876807e+00 -1.715903e+00 -1.642656e+00 -1.576972e+00 -1.424602e+00 1505.747225 0.9996846
## x[384]    -2.216453e+00 2.916002e-03 1.121174e-01 -2.447416e+00 -2.287509e+00 -2.214617e+00 -2.146699e+00 -2.001581e+00 1478.326996 0.9996535
## x[385]    -2.780388e+00 2.908887e-03 1.119499e-01 -3.003618e+00 -2.851539e+00 -2.780978e+00 -2.709897e+00 -2.562262e+00 1481.131013 0.9995992
## x[386]    -3.334173e+00 2.896953e-03 1.125485e-01 -3.565941e+00 -3.406293e+00 -3.335517e+00 -3.264247e+00 -3.112220e+00 1509.372507 0.9997783
## x[387]    -3.874189e+00 2.941984e-03 1.137134e-01 -4.107089e+00 -3.943653e+00 -3.874183e+00 -3.800946e+00 -3.649255e+00 1493.973895 0.9999214
## x[388]    -4.398223e+00 3.027802e-03 1.149010e-01 -4.634785e+00 -4.470046e+00 -4.400627e+00 -4.323947e+00 -4.174864e+00 1440.100750 1.0001959
## x[389]    -4.903557e+00 3.117821e-03 1.149942e-01 -5.147294e+00 -4.974171e+00 -4.905217e+00 -4.828057e+00 -4.687112e+00 1360.345831 1.0009048
## x[390]    -5.385753e+00 3.124924e-03 1.154522e-01 -5.626475e+00 -5.456097e+00 -5.384728e+00 -5.310493e+00 -5.165750e+00 1364.977205 1.0007158
## x[391]    -5.843920e+00 3.127001e-03 1.160876e-01 -6.082365e+00 -5.915665e+00 -5.843804e+00 -5.766687e+00 -5.617356e+00 1378.210275 1.0010506
## x[392]    -6.276345e+00 3.146841e-03 1.172110e-01 -6.522017e+00 -6.347834e+00 -6.274573e+00 -6.197262e+00 -6.052251e+00 1387.352354 1.0014718
## x[393]    -6.678894e+00 3.222057e-03 1.182665e-01 -6.925621e+00 -6.753397e+00 -6.678371e+00 -6.599654e+00 -6.452589e+00 1347.278490 1.0020753
## x[394]    -7.049540e+00 3.220892e-03 1.184742e-01 -7.286741e+00 -7.124762e+00 -7.049496e+00 -6.969761e+00 -6.811657e+00 1352.991474 1.0023873
## x[395]    -7.386829e+00 3.269297e-03 1.194000e-01 -7.626321e+00 -7.461315e+00 -7.388424e+00 -7.307523e+00 -7.160939e+00 1333.828719 1.0026328
## x[396]    -7.689791e+00 3.314383e-03 1.201195e-01 -7.922083e+00 -7.762933e+00 -7.687120e+00 -7.610737e+00 -7.462309e+00 1313.475283 1.0034696
## x[397]    -7.955200e+00 3.321908e-03 1.211750e-01 -8.193371e+00 -8.033512e+00 -7.951717e+00 -7.874214e+00 -7.723554e+00 1330.609402 1.0039442
## x[398]    -8.182300e+00 3.317027e-03 1.215109e-01 -8.417312e+00 -8.259968e+00 -8.181792e+00 -8.098902e+00 -7.949198e+00 1341.937190 1.0039285
## x[399]    -8.369663e+00 3.349557e-03 1.219879e-01 -8.607843e+00 -8.450804e+00 -8.369274e+00 -8.284886e+00 -8.144350e+00 1326.350702 1.0032244
## x[400]    -8.516789e+00 3.316549e-03 1.238682e-01 -8.759999e+00 -8.598165e+00 -8.516050e+00 -8.432300e+00 -8.281663e+00 1394.912678 1.0027220
## x[401]    -8.621245e+00 3.287312e-03 1.233581e-01 -8.856693e+00 -8.704793e+00 -8.620697e+00 -8.537865e+00 -8.378060e+00 1408.164209 1.0020591
## x[402]    -8.683153e+00 3.305185e-03 1.232017e-01 -8.924356e+00 -8.765363e+00 -8.684283e+00 -8.599705e+00 -8.441032e+00 1389.446249 1.0020861
## x[403]    -8.700959e+00 3.308786e-03 1.232607e-01 -8.942292e+00 -8.784741e+00 -8.699620e+00 -8.620719e+00 -8.461803e+00 1387.751916 1.0013920
## x[404]    -8.675520e+00 3.357079e-03 1.227255e-01 -8.918365e+00 -8.762279e+00 -8.676158e+00 -8.594953e+00 -8.437617e+00 1336.431305 1.0005361
## x[405]    -8.606654e+00 3.370378e-03 1.229451e-01 -8.842011e+00 -8.690147e+00 -8.606357e+00 -8.529566e+00 -8.373387e+00 1330.654812 1.0014859
## x[406]    -8.495157e+00 3.444256e-03 1.233012e-01 -8.738118e+00 -8.579679e+00 -8.496210e+00 -8.416514e+00 -8.256863e+00 1281.574805 1.0019084
## x[407]    -8.340174e+00 3.656355e-03 1.233335e-01 -8.584327e+00 -8.425393e+00 -8.339536e+00 -8.262830e+00 -8.095315e+00 1137.798920 1.0026588
## x[408]    -8.143302e+00 3.835782e-03 1.233419e-01 -8.383854e+00 -8.228387e+00 -8.143419e+00 -8.064931e+00 -7.896241e+00 1033.982642 1.0037443
## x[409]    -7.903890e+00 4.148874e-03 1.225094e-01 -8.137734e+00 -7.987829e+00 -7.906325e+00 -7.825630e+00 -7.646970e+00  871.923949 1.0059963
## x[410]    -7.624021e+00 4.808337e-03 1.215021e-01 -7.849921e+00 -7.707536e+00 -7.626278e+00 -7.546012e+00 -7.371061e+00  638.525376 1.0090457
## x[411]    -7.304917e+00 5.617372e-03 1.216108e-01 -7.535771e+00 -7.386503e+00 -7.307300e+00 -7.228618e+00 -7.055630e+00  468.681912 1.0120293
## x[412]    -6.948942e+00 6.156286e-03 1.222374e-01 -7.177619e+00 -7.032251e+00 -6.951938e+00 -6.869646e+00 -6.692525e+00  394.248973 1.0146982
## x[413]    -6.555599e+00 7.627116e-03 1.233392e-01 -6.788286e+00 -6.638977e+00 -6.561707e+00 -6.475390e+00 -6.294335e+00  261.505799 1.0215625
## x[414]    -6.128157e+00 1.000079e-02 1.246712e-01 -6.363058e+00 -6.211641e+00 -6.137858e+00 -6.046529e+00 -5.853477e+00  155.404511 1.0277449
## x[415]    -5.668585e+00 1.096098e-02 1.240233e-01 -5.901829e+00 -5.752090e+00 -5.678139e+00 -5.588514e+00 -5.418079e+00  128.028894 1.0324438
## x[416]    -5.178857e+00 1.223262e-02 1.241015e-01 -5.406964e+00 -5.262937e+00 -5.188124e+00 -5.102463e+00 -4.920974e+00  102.923657 1.0378255
## x[417]    -4.662248e+00 1.230253e-02 1.234201e-01 -4.891298e+00 -4.744427e+00 -4.669098e+00 -4.586835e+00 -4.407575e+00  100.642790 1.0373089
## x[418]    -4.119312e+00 1.206668e-02 1.232639e-01 -4.345033e+00 -4.199179e+00 -4.125916e+00 -4.043476e+00 -3.857887e+00  104.350841 1.0375626
## x[419]    -3.552609e+00 1.217649e-02 1.232594e-01 -3.781705e+00 -3.635572e+00 -3.557389e+00 -3.477499e+00 -3.287222e+00  102.469707 1.0383430
## x[420]    -2.964897e+00 1.285937e-02 1.231590e-01 -3.185309e+00 -3.048189e+00 -2.968867e+00 -2.893457e+00 -2.692144e+00   91.726138 1.0401627
## x[421]    -2.359511e+00 1.393179e-02 1.231682e-01 -2.585778e+00 -2.440859e+00 -2.361565e+00 -2.287715e+00 -2.093484e+00   78.159753 1.0448103
## x[422]    -1.739842e+00 1.442688e-02 1.223098e-01 -1.969417e+00 -1.821718e+00 -1.742478e+00 -1.666315e+00 -1.478392e+00   71.874930 1.0470220
## x[423]    -1.108108e+00 1.479896e-02 1.208151e-01 -1.335587e+00 -1.187307e+00 -1.111367e+00 -1.034948e+00 -8.452304e-01   66.646917 1.0507291
## x[424]    -4.672445e-01 1.529881e-02 1.205659e-01 -7.026934e-01 -5.471301e-01 -4.714609e-01 -3.943439e-01 -2.135237e-01   62.105982 1.0534996
## x[425]     1.782016e-01 1.540061e-02 1.196463e-01 -5.134066e-02  9.663404e-02  1.737438e-01  2.521495e-01  4.357497e-01   60.356296 1.0528529
## x[426]     8.259805e-01 1.467642e-02 1.189320e-01  5.964760e-01  7.484116e-01  8.232964e-01  8.989349e-01  1.076895e+00   65.668499 1.0510984
## x[427]     1.473385e+00 1.464617e-02 1.199908e-01  1.241065e+00  1.396569e+00  1.470731e+00  1.548710e+00  1.718301e+00   67.119346 1.0488175
## x[428]     2.115868e+00 1.372444e-02 1.202010e-01  1.878508e+00  2.038055e+00  2.111664e+00  2.191597e+00  2.355955e+00   76.705556 1.0430865
## x[429]     2.751201e+00 1.261850e-02 1.204914e-01  2.518916e+00  2.672245e+00  2.747970e+00  2.828567e+00  2.997051e+00   91.179359 1.0378739
## x[430]     3.376474e+00 1.172373e-02 1.211371e-01  3.137909e+00  3.296796e+00  3.374248e+00  3.454554e+00  3.621330e+00  106.763421 1.0331408
## x[431]     3.987331e+00 1.051286e-02 1.211735e-01  3.747435e+00  3.907838e+00  3.982058e+00  4.065856e+00  4.243862e+00  132.853547 1.0296318
## x[432]     4.581689e+00 8.783302e-03 1.220265e-01  4.349090e+00  4.497515e+00  4.576846e+00  4.655256e+00  4.833247e+00  193.015593 1.0232676
## x[433]     5.156462e+00 5.677925e-03 1.225169e-01  4.919499e+00  5.073115e+00  5.153197e+00  5.231691e+00  5.413068e+00  465.600000 1.0193513
## x[434]     5.708140e+00 3.977918e-03 1.227806e-01  5.473822e+00  5.623463e+00  5.703436e+00  5.786019e+00  5.954124e+00  952.681347 1.0156567
## x[435]     6.233952e+00 3.791443e-03 1.233540e-01  5.997794e+00  6.148372e+00  6.230161e+00  6.313584e+00  6.482690e+00 1058.515580 1.0103984
## x[436]     6.731845e+00 3.635790e-03 1.233758e-01  6.492363e+00  6.646539e+00  6.729110e+00  6.811170e+00  6.975071e+00 1151.495425 1.0068428
## x[437]     7.198258e+00 3.556488e-03 1.244500e-01  6.950923e+00  7.111850e+00  7.197032e+00  7.280249e+00  7.443439e+00 1224.466569 1.0039450
## x[438]     7.632343e+00 3.523742e-03 1.259695e-01  7.385927e+00  7.545275e+00  7.629740e+00  7.713726e+00  7.884746e+00 1277.975226 1.0020370
## x[439]     8.030111e+00 3.478467e-03 1.266322e-01  7.784478e+00  7.943685e+00  8.026036e+00  8.114650e+00  8.285823e+00 1325.295232 1.0004111
## x[440]     8.390910e+00 3.499498e-03 1.269833e-01  8.152407e+00  8.304044e+00  8.389246e+00  8.473708e+00  8.645969e+00 1316.684010 0.9997585
## x[441]     8.712509e+00 3.505421e-03 1.275227e-01  8.471871e+00  8.626846e+00  8.712543e+00  8.798259e+00  8.967278e+00 1323.410717 0.9997270
## x[442]     8.992745e+00 3.509218e-03 1.278684e-01  8.746043e+00  8.906073e+00  8.992518e+00  9.076650e+00  9.247787e+00 1327.718822 1.0000329
## x[443]     9.228878e+00 3.597966e-03 1.290481e-01  8.975936e+00  9.141626e+00  9.230190e+00  9.316212e+00  9.484726e+00 1286.438897 1.0009945
## x[444]     9.420870e+00 3.691434e-03 1.302529e-01  9.163871e+00  9.335455e+00  9.423357e+00  9.509283e+00  9.678103e+00 1245.043814 1.0024429
## x[445]     9.569291e+00 3.718901e-03 1.310493e-01  9.313740e+00  9.482535e+00  9.571309e+00  9.656647e+00  9.831239e+00 1241.767654 1.0028808
## x[446]     9.671050e+00 3.748740e-03 1.318004e-01  9.414303e+00  9.584668e+00  9.672298e+00  9.757582e+00  9.930433e+00 1236.125568 1.0026916
## x[447]     9.725373e+00 3.762002e-03 1.315475e-01  9.465763e+00  9.639302e+00  9.727981e+00  9.809800e+00  9.985170e+00 1222.719563 1.0038217
## x[448]     9.731843e+00 3.799577e-03 1.314221e-01  9.474973e+00  9.647583e+00  9.733222e+00  9.817000e+00  9.987902e+00 1196.372017 1.0032171
## x[449]     9.690450e+00 3.849991e-03 1.318233e-01  9.431430e+00  9.607661e+00  9.692021e+00  9.774109e+00  9.947740e+00 1172.370043 1.0031142
## x[450]     9.600686e+00 3.907522e-03 1.324732e-01  9.348396e+00  9.517777e+00  9.601196e+00  9.684909e+00  9.858002e+00 1149.352198 1.0029685
## x[451]     9.464319e+00 3.885293e-03 1.322681e-01  9.209322e+00  9.380121e+00  9.465206e+00  9.547108e+00  9.728877e+00 1158.943842 1.0024139
## x[452]     9.279684e+00 3.828766e-03 1.312722e-01  9.023622e+00  9.195733e+00  9.281359e+00  9.360678e+00  9.536112e+00 1175.513730 1.0019094
## x[453]     9.048716e+00 3.863424e-03 1.322195e-01  8.787403e+00  8.965333e+00  9.047582e+00  9.133174e+00  9.307244e+00 1171.241248 1.0017956
## x[454]     8.772212e+00 3.849773e-03 1.318863e-01  8.518741e+00  8.688797e+00  8.771197e+00  8.855841e+00  9.036320e+00 1173.625012 1.0015094
## x[455]     8.450752e+00 3.852215e-03 1.316660e-01  8.194947e+00  8.370956e+00  8.450741e+00  8.533408e+00  8.718968e+00 1168.224465 1.0014340
## x[456]     8.087258e+00 3.928451e-03 1.323964e-01  7.831196e+00  8.002355e+00  8.086898e+00  8.169468e+00  8.350910e+00 1135.820193 1.0018968
## x[457]     7.680513e+00 4.027772e-03 1.330549e-01  7.421317e+00  7.594453e+00  7.680120e+00  7.766605e+00  7.947999e+00 1091.269172 1.0029968
## x[458]     7.233379e+00 4.120465e-03 1.337536e-01  6.976160e+00  7.144346e+00  7.232872e+00  7.316569e+00  7.505893e+00 1053.703275 1.0048322
## x[459]     6.748509e+00 4.156681e-03 1.335401e-01  6.494178e+00  6.658598e+00  6.745553e+00  6.830297e+00  7.026451e+00 1032.118813 1.0067063
## x[460]     6.227730e+00 4.285474e-03 1.342369e-01  5.972661e+00  6.140098e+00  6.223764e+00  6.308771e+00  6.507441e+00  981.173635 1.0087980
## x[461]     5.674094e+00 4.886368e-03 1.343010e-01  5.426248e+00  5.585909e+00  5.667144e+00  5.754627e+00  5.954166e+00  755.416186 1.0124573
## x[462]     5.089112e+00 5.073560e-03 1.349115e-01  4.838235e+00  4.996914e+00  5.084239e+00  5.169917e+00  5.375195e+00  707.086608 1.0141085
## x[463]     4.475685e+00 5.626625e-03 1.355683e-01  4.226454e+00  4.384113e+00  4.469815e+00  4.559935e+00  4.770121e+00  580.524719 1.0179287
## x[464]     3.835408e+00 6.112094e-03 1.365521e-01  3.582031e+00  3.744082e+00  3.833226e+00  3.920549e+00  4.124963e+00  499.133649 1.0182057
## x[465]     3.171763e+00 5.869884e-03 1.362615e-01  2.917532e+00  3.082955e+00  3.169619e+00  3.257042e+00  3.459966e+00  538.873893 1.0169718
## x[466]     2.488558e+00 5.699138e-03 1.364801e-01  2.229652e+00  2.399832e+00  2.484904e+00  2.578571e+00  2.772867e+00  573.482985 1.0164242
## x[467]     1.789823e+00 5.618466e-03 1.367032e-01  1.528323e+00  1.701075e+00  1.787862e+00  1.878875e+00  2.083486e+00  591.999897 1.0154945
## x[468]     1.078293e+00 5.144933e-03 1.367702e-01  8.196371e-01  9.885070e-01  1.073192e+00  1.167399e+00  1.363545e+00  706.681594 1.0130781
## x[469]     3.573081e-01 4.797977e-03 1.365551e-01  9.695701e-02  2.679132e-01  3.552911e-01  4.504474e-01  6.441128e-01  810.027095 1.0114966
## x[470]    -3.690431e-01 4.944179e-03 1.371302e-01 -6.338826e-01 -4.604687e-01 -3.695389e-01 -2.753032e-01 -8.448730e-02  769.267856 1.0106868
## x[471]    -1.097563e+00 4.712990e-03 1.383230e-01 -1.364271e+00 -1.188829e+00 -1.098616e+00 -1.002019e+00 -8.095474e-01  861.382479 1.0090281
## x[472]    -1.824523e+00 4.435824e-03 1.388886e-01 -2.097287e+00 -1.917476e+00 -1.824635e+00 -1.730626e+00 -1.535116e+00  980.357407 1.0066817
## x[473]    -2.547193e+00 4.416873e-03 1.395109e-01 -2.812518e+00 -2.638905e+00 -2.546658e+00 -2.454946e+00 -2.261137e+00  997.669332 1.0037957
## x[474]    -3.259106e+00 4.425182e-03 1.409051e-01 -3.521071e+00 -3.352581e+00 -3.259144e+00 -3.165490e+00 -2.973988e+00 1013.891025 1.0029079
## x[475]    -3.958688e+00 4.353588e-03 1.425012e-01 -4.222477e+00 -4.054469e+00 -3.959394e+00 -3.864893e+00 -3.666560e+00 1071.377565 1.0018914
## x[476]    -4.643580e+00 4.306546e-03 1.443231e-01 -4.915975e+00 -4.739649e+00 -4.644702e+00 -4.546382e+00 -4.343907e+00 1123.087882 1.0004042
## x[477]    -5.308662e+00 4.311509e-03 1.455407e-01 -5.587731e+00 -5.405676e+00 -5.308515e+00 -5.212761e+00 -5.007832e+00 1139.490179 0.9993205
## x[478]    -5.950439e+00 4.291533e-03 1.463217e-01 -6.227515e+00 -6.048209e+00 -5.951246e+00 -5.853409e+00 -5.648543e+00 1162.498121 0.9991445
## x[479]    -6.566070e+00 4.292382e-03 1.474437e-01 -6.853928e+00 -6.661407e+00 -6.565911e+00 -6.467829e+00 -6.265844e+00 1179.927932 0.9987867
## x[480]    -7.152985e+00 4.266923e-03 1.475876e-01 -7.441500e+00 -7.244697e+00 -7.156681e+00 -7.058163e+00 -6.853830e+00 1196.382564 0.9992688
## x[481]    -7.706444e+00 4.256337e-03 1.492153e-01 -7.992773e+00 -7.797942e+00 -7.709184e+00 -7.609120e+00 -7.402098e+00 1229.007238 0.9997936
## x[482]    -8.224735e+00 4.278004e-03 1.508620e-01 -8.520274e+00 -8.320564e+00 -8.228255e+00 -8.125844e+00 -7.918394e+00 1243.591233 1.0011210
## x[483]    -8.704882e+00 4.292504e-03 1.512550e-01 -9.002939e+00 -8.800583e+00 -8.705838e+00 -8.606169e+00 -8.413751e+00 1241.646471 1.0022736
## x[484]    -9.145151e+00 4.333342e-03 1.535079e-01 -9.435574e+00 -9.244206e+00 -9.146814e+00 -9.042565e+00 -8.845798e+00 1254.919136 1.0047187
## x[485]    -9.542677e+00 4.440846e-03 1.548903e-01 -9.839756e+00 -9.644090e+00 -9.544055e+00 -9.436323e+00 -9.244363e+00 1216.513086 1.0074160
## x[486]    -9.893573e+00 4.586041e-03 1.563851e-01 -1.020787e+01 -9.996800e+00 -9.895041e+00 -9.785607e+00 -9.599747e+00 1162.826893 1.0107597
## x[487]    -1.019713e+01 6.020604e-03 1.573139e-01 -1.051665e+01 -1.030255e+01 -1.019652e+01 -1.009104e+01 -9.896646e+00  682.737888 1.0144879
## x[488]    -1.045210e+01 7.453259e-03 1.584918e-01 -1.078437e+01 -1.055429e+01 -1.045022e+01 -1.034308e+01 -1.015091e+01  452.190232 1.0181886
## x[489]    -1.065684e+01 8.794895e-03 1.595561e-01 -1.099107e+01 -1.076244e+01 -1.065477e+01 -1.054715e+01 -1.035811e+01  329.128592 1.0223764
## x[490]    -1.080967e+01 1.124789e-02 1.609675e-01 -1.114423e+01 -1.091368e+01 -1.080389e+01 -1.070095e+01 -1.051769e+01  204.802177 1.0261243
## x[491]    -1.091010e+01 1.471725e-02 1.621301e-01 -1.124487e+01 -1.101652e+01 -1.089971e+01 -1.079600e+01 -1.061442e+01  121.359559 1.0326745
## x[492]    -1.095692e+01 1.689538e-02 1.645350e-01 -1.130484e+01 -1.106308e+01 -1.094945e+01 -1.084481e+01 -1.064802e+01   94.837587 1.0379963
## x[493]    -1.094948e+01 1.908670e-02 1.671364e-01 -1.130669e+01 -1.105909e+01 -1.093826e+01 -1.083385e+01 -1.064127e+01   76.679752 1.0441397
## x[494]    -1.088643e+01 2.036827e-02 1.703155e-01 -1.125768e+01 -1.099444e+01 -1.087729e+01 -1.076842e+01 -1.057406e+01   69.919781 1.0469032
## x[495]    -1.076981e+01 2.188336e-02 1.732178e-01 -1.115691e+01 -1.087730e+01 -1.075893e+01 -1.065110e+01 -1.045384e+01   62.655188 1.0495675
## x[496]    -1.059828e+01 2.277898e-02 1.763568e-01 -1.098647e+01 -1.070773e+01 -1.058891e+01 -1.047506e+01 -1.028422e+01   59.939840 1.0514049
## x[497]    -1.037237e+01 2.328498e-02 1.793829e-01 -1.076285e+01 -1.048396e+01 -1.036447e+01 -1.024654e+01 -1.004542e+01   59.348603 1.0518917
## x[498]    -1.009314e+01 2.391875e-02 1.821107e-01 -1.048795e+01 -1.020931e+01 -1.008097e+01 -9.968112e+00 -9.775829e+00   57.968762 1.0520850
## x[499]    -9.762641e+00 2.405826e-02 1.852469e-01 -1.015857e+01 -9.879171e+00 -9.749857e+00 -9.636169e+00 -9.440142e+00   59.288937 1.0520104
## x[500]    -9.381692e+00 2.427796e-02 1.878648e-01 -9.786759e+00 -9.501653e+00 -9.369078e+00 -9.247873e+00 -9.051319e+00   59.877888 1.0516335
## y[1]      -8.028952e-02 2.712245e-03 1.045584e-01 -2.821688e-01 -1.468174e-01 -8.116283e-02 -1.285474e-02  1.272166e-01 1486.141032 1.0040569
## y[2]      -2.343128e-01 2.746586e-03 1.036648e-01 -4.483135e-01 -2.983349e-01 -2.317127e-01 -1.710385e-01 -2.588402e-02 1424.546471 1.0043821
## y[3]      -3.867754e-01 2.644408e-03 1.032755e-01 -6.010008e-01 -4.529284e-01 -3.838813e-01 -3.201670e-01 -1.813913e-01 1525.239312 1.0042339
## y[4]      -5.388088e-01 2.614333e-03 1.020454e-01 -7.436933e-01 -6.013860e-01 -5.361319e-01 -4.753763e-01 -3.439896e-01 1523.577986 1.0045631
## y[5]      -6.890225e-01 2.663079e-03 1.007086e-01 -8.930561e-01 -7.499544e-01 -6.860306e-01 -6.262901e-01 -4.955949e-01 1430.094816 1.0055764
## y[6]      -8.365733e-01 2.976901e-03 9.994328e-02 -1.036273e+00 -8.976006e-01 -8.317431e-01 -7.719500e-01 -6.502872e-01 1127.141450 1.0065643
## y[7]      -9.807169e-01 2.779551e-03 9.870132e-02 -1.179853e+00 -1.044638e+00 -9.778306e-01 -9.187273e-01 -7.956790e-01 1260.946478 1.0078008
## y[8]      -1.121171e+00 2.857492e-03 9.902496e-02 -1.323584e+00 -1.182084e+00 -1.119135e+00 -1.057999e+00 -9.332989e-01 1200.934265 1.0083111
## y[9]      -1.256020e+00 2.790007e-03 9.913956e-02 -1.458670e+00 -1.316730e+00 -1.253414e+00 -1.190787e+00 -1.070047e+00 1262.651625 1.0085251
## y[10]     -1.385334e+00 2.772103e-03 9.769181e-02 -1.585609e+00 -1.447196e+00 -1.383551e+00 -1.319571e+00 -1.201030e+00 1241.931165 1.0091987
## y[11]     -1.507314e+00 2.769883e-03 9.676475e-02 -1.705486e+00 -1.568805e+00 -1.505068e+00 -1.441372e+00 -1.319586e+00 1220.426493 1.0083191
## y[12]     -1.622935e+00 2.799470e-03 9.724671e-02 -1.826363e+00 -1.684752e+00 -1.622916e+00 -1.556683e+00 -1.438781e+00 1206.696904 1.0073839
## y[13]     -1.731395e+00 2.800182e-03 9.664157e-02 -1.924544e+00 -1.795414e+00 -1.730722e+00 -1.667117e+00 -1.544493e+00 1191.120100 1.0063011
## y[14]     -1.831370e+00 2.778665e-03 9.571165e-02 -2.019029e+00 -1.894843e+00 -1.830235e+00 -1.766918e+00 -1.645337e+00 1186.471585 1.0043559
## y[15]     -1.922562e+00 2.747177e-03 9.586263e-02 -2.114661e+00 -1.985861e+00 -1.922033e+00 -1.857490e+00 -1.731079e+00 1217.658144 1.0021534
## y[16]     -2.005800e+00 2.627436e-03 9.519647e-02 -2.196985e+00 -2.068832e+00 -2.004749e+00 -1.942253e+00 -1.817165e+00 1312.735994 1.0019234
## y[17]     -2.079742e+00 2.638639e-03 9.451880e-02 -2.264492e+00 -2.145036e+00 -2.074922e+00 -2.016592e+00 -1.897935e+00 1283.147237 1.0019004
## y[18]     -2.143362e+00 2.624817e-03 9.357686e-02 -2.329590e+00 -2.207452e+00 -2.140242e+00 -2.081471e+00 -1.969267e+00 1270.980874 1.0017497
## y[19]     -2.196376e+00 2.605826e-03 9.244571e-02 -2.381426e+00 -2.260310e+00 -2.190450e+00 -2.134725e+00 -2.022010e+00 1258.585048 1.0013600
## y[20]     -2.237995e+00 2.558678e-03 9.187868e-02 -2.425497e+00 -2.300440e+00 -2.236046e+00 -2.176682e+00 -2.064165e+00 1289.431097 1.0014357
## y[21]     -2.268886e+00 2.586458e-03 9.170412e-02 -2.460353e+00 -2.330267e+00 -2.265416e+00 -2.207320e+00 -2.096378e+00 1257.090941 1.0009244
## y[22]     -2.289601e+00 2.587441e-03 9.111718e-02 -2.476475e+00 -2.348926e+00 -2.285708e+00 -2.227811e+00 -2.112239e+00 1240.108032 1.0009921
## y[23]     -2.299010e+00 2.619313e-03 9.030504e-02 -2.485753e+00 -2.357831e+00 -2.298280e+00 -2.237566e+00 -2.125195e+00 1188.637035 1.0014451
## y[24]     -2.297113e+00 2.636224e-03 9.027921e-02 -2.480406e+00 -2.354635e+00 -2.298000e+00 -2.234455e+00 -2.127417e+00 1172.764482 1.0010578
## y[25]     -2.282925e+00 2.641589e-03 9.064950e-02 -2.469042e+00 -2.341387e+00 -2.281363e+00 -2.220999e+00 -2.111699e+00 1177.606663 1.0008796
## y[26]     -2.257955e+00 2.611750e-03 9.001613e-02 -2.444526e+00 -2.318122e+00 -2.257072e+00 -2.197043e+00 -2.089453e+00 1187.893569 1.0013092
## y[27]     -2.222603e+00 2.621107e-03 8.970730e-02 -2.411056e+00 -2.281667e+00 -2.220385e+00 -2.160515e+00 -2.051321e+00 1171.348019 1.0021600
## y[28]     -2.174852e+00 2.609771e-03 8.943654e-02 -2.357853e+00 -2.231681e+00 -2.174214e+00 -2.113292e+00 -2.005976e+00 1174.424720 1.0026962
## y[29]     -2.117467e+00 2.577654e-03 8.949473e-02 -2.297811e+00 -2.174529e+00 -2.116192e+00 -2.057226e+00 -1.944799e+00 1205.439830 1.0035833
## y[30]     -2.049173e+00 2.602873e-03 8.903099e-02 -2.226895e+00 -2.106182e+00 -2.049235e+00 -1.988661e+00 -1.871635e+00 1169.974825 1.0048820
## y[31]     -1.969785e+00 2.637157e-03 8.772493e-02 -2.144895e+00 -2.026820e+00 -1.969263e+00 -1.912666e+00 -1.793121e+00 1106.557701 1.0043128
## y[32]     -1.880461e+00 2.573370e-03 8.720271e-02 -2.051836e+00 -1.937775e+00 -1.880498e+00 -1.821672e+00 -1.707481e+00 1148.299906 1.0050237
## y[33]     -1.780336e+00 2.564325e-03 8.733358e-02 -1.955516e+00 -1.836028e+00 -1.778543e+00 -1.722840e+00 -1.610122e+00 1159.888800 1.0053947
## y[34]     -1.672679e+00 2.513640e-03 8.676256e-02 -1.841839e+00 -1.727725e+00 -1.672130e+00 -1.617581e+00 -1.501246e+00 1191.402388 1.0059648
## y[35]     -1.556016e+00 2.586071e-03 8.589982e-02 -1.729099e+00 -1.609450e+00 -1.555338e+00 -1.502575e+00 -1.384350e+00 1103.325271 1.0069407
## y[36]     -1.431066e+00 2.642561e-03 8.590884e-02 -1.605547e+00 -1.486606e+00 -1.430403e+00 -1.376893e+00 -1.259605e+00 1056.879640 1.0057440
## y[37]     -1.297837e+00 2.596785e-03 8.599122e-02 -1.474536e+00 -1.353318e+00 -1.299124e+00 -1.240228e+00 -1.130216e+00 1096.570034 1.0053983
## y[38]     -1.157985e+00 2.526222e-03 8.565974e-02 -1.327357e+00 -1.214520e+00 -1.156434e+00 -1.102373e+00 -9.908641e-01 1149.768723 1.0051804
## y[39]     -1.012354e+00 2.511756e-03 8.560023e-02 -1.181826e+00 -1.067845e+00 -1.012702e+00 -9.573349e-01 -8.485370e-01 1161.435396 1.0055385
## y[40]     -8.610242e-01 2.407035e-03 8.618296e-02 -1.030906e+00 -9.161857e-01 -8.617772e-01 -8.022905e-01 -6.937872e-01 1281.970403 1.0051720
## y[41]     -7.047815e-01 2.389036e-03 8.651254e-02 -8.734298e-01 -7.607453e-01 -7.038594e-01 -6.471652e-01 -5.450351e-01 1311.331902 1.0046386
## y[42]     -5.437716e-01 2.389535e-03 8.626352e-02 -7.188319e-01 -5.977301e-01 -5.432994e-01 -4.865472e-01 -3.786112e-01 1303.249105 1.0047054
## y[43]     -3.786983e-01 2.438197e-03 8.636186e-02 -5.584574e-01 -4.331222e-01 -3.782023e-01 -3.204711e-01 -2.205710e-01 1254.602841 1.0057401
## y[44]     -2.099060e-01 2.446553e-03 8.666470e-02 -3.898638e-01 -2.638837e-01 -2.080900e-01 -1.529357e-01 -4.317460e-02 1254.801745 1.0066402
## y[45]     -3.997962e-02 2.449917e-03 8.697949e-02 -2.238686e-01 -9.746207e-02 -3.893303e-02  1.498752e-02  1.262724e-01 1260.465486 1.0073233
## y[46]      1.311387e-01 2.405336e-03 8.594914e-02 -4.770967e-02  7.331992e-02  1.338138e-01  1.881212e-01  2.957405e-01 1276.825125 1.0069205
## y[47]      3.037636e-01 2.378131e-03 8.630314e-02  1.288932e-01  2.474009e-01  3.038435e-01  3.588635e-01  4.753080e-01 1316.987705 1.0041349
## y[48]      4.741429e-01 2.393049e-03 8.620634e-02  3.063323e-01  4.179086e-01  4.750840e-01  5.284537e-01  6.396584e-01 1297.702657 1.0033913
## y[49]      6.427668e-01 2.370861e-03 8.696523e-02  4.704174e-01  5.858676e-01  6.425769e-01  6.994916e-01  8.093121e-01 1345.485734 1.0023823
## y[50]      8.094201e-01 2.381977e-03 8.664532e-02  6.416044e-01  7.531160e-01  8.102556e-01  8.663543e-01  9.776044e-01 1323.167919 1.0022755
## y[51]      9.740272e-01 2.386289e-03 8.626352e-02  8.063276e-01  9.160859e-01  9.746148e-01  1.030778e+00  1.143497e+00 1306.797032 1.0013116
## y[52]      1.134929e+00 2.474575e-03 8.605668e-02  9.642721e-01  1.080128e+00  1.134410e+00  1.191560e+00  1.307076e+00 1209.394267 1.0009196
## y[53]      1.290313e+00 2.468756e-03 8.634153e-02  1.120224e+00  1.235978e+00  1.291506e+00  1.345613e+00  1.462500e+00 1223.160065 1.0008287
## y[54]      1.439772e+00 2.466480e-03 8.648536e-02  1.275167e+00  1.381404e+00  1.441514e+00  1.494345e+00  1.614439e+00 1229.504416 1.0008211
## y[55]      1.582739e+00 2.454352e-03 8.638441e-02  1.411751e+00  1.524326e+00  1.582633e+00  1.638102e+00  1.760104e+00 1238.787982 1.0007665
## y[56]      1.718705e+00 2.491794e-03 8.706465e-02  1.540663e+00  1.661764e+00  1.718367e+00  1.773569e+00  1.891517e+00 1220.842066 1.0008445
## y[57]      1.846654e+00 2.498545e-03 8.660383e-02  1.674182e+00  1.791464e+00  1.849186e+00  1.902473e+00  2.018730e+00 1201.434148 1.0008863
## y[58]      1.964357e+00 2.539950e-03 8.683988e-02  1.791163e+00  1.911190e+00  1.966287e+00  2.020628e+00  2.132874e+00 1168.928493 1.0005200
## y[59]      2.073451e+00 2.546004e-03 8.655813e-02  1.902251e+00  2.020311e+00  2.074293e+00  2.128564e+00  2.243153e+00 1155.839960 1.0004473
## y[60]      2.172681e+00 2.591509e-03 8.632840e-02  1.998128e+00  2.117698e+00  2.172366e+00  2.227495e+00  2.338546e+00 1109.690604 1.0004784
## y[61]      2.262223e+00 2.574739e-03 8.628077e-02  2.093906e+00  2.207238e+00  2.262509e+00  2.316531e+00  2.436147e+00 1122.953385 0.9999433
## y[62]      2.340015e+00 2.633495e-03 8.636443e-02  2.173566e+00  2.284694e+00  2.339024e+00  2.393426e+00  2.513024e+00 1075.486508 1.0004273
## y[63]      2.407360e+00 2.636460e-03 8.629017e-02  2.238205e+00  2.353876e+00  2.407571e+00  2.461416e+00  2.575126e+00 1071.224062 1.0004761
## y[64]      2.462459e+00 2.636766e-03 8.616700e-02  2.293365e+00  2.405692e+00  2.463473e+00  2.516253e+00  2.625959e+00 1067.920301 1.0005022
## y[65]      2.504793e+00 2.682477e-03 8.664875e-02  2.327028e+00  2.450585e+00  2.504273e+00  2.561971e+00  2.669392e+00 1043.403860 1.0013456
## y[66]      2.535893e+00 2.650428e-03 8.690369e-02  2.359715e+00  2.480793e+00  2.534411e+00  2.595420e+00  2.706364e+00 1075.089312 1.0016921
## y[67]      2.553700e+00 2.667041e-03 8.732138e-02  2.381629e+00  2.499576e+00  2.553307e+00  2.614910e+00  2.720312e+00 1071.968013 1.0028360
## y[68]      2.559914e+00 2.977802e-03 8.762142e-02  2.393651e+00  2.504053e+00  2.559063e+00  2.618191e+00  2.728032e+00  865.822355 1.0040119
## y[69]      2.552566e+00 2.667851e-03 8.788238e-02  2.379758e+00  2.496585e+00  2.552502e+00  2.613587e+00  2.726041e+00 1085.126697 1.0050826
## y[70]      2.532514e+00 3.242334e-03 8.835084e-02  2.361588e+00  2.476197e+00  2.532736e+00  2.595086e+00  2.698802e+00  742.516090 1.0076933
## y[71]      2.499205e+00 3.883035e-03 8.818447e-02  2.323015e+00  2.441680e+00  2.499319e+00  2.558438e+00  2.663684e+00  515.752742 1.0090618
## y[72]      2.453684e+00 4.831146e-03 8.843748e-02  2.274834e+00  2.398669e+00  2.454656e+00  2.513531e+00  2.619920e+00  335.098432 1.0136541
## y[73]      2.395992e+00 5.054979e-03 8.844759e-02  2.216236e+00  2.340676e+00  2.396093e+00  2.458489e+00  2.566487e+00  306.149340 1.0160798
## y[74]      2.326629e+00 5.390615e-03 8.694135e-02  2.146844e+00  2.271508e+00  2.326168e+00  2.386887e+00  2.494553e+00  260.121422 1.0176054
## y[75]      2.244947e+00 5.580560e-03 8.655053e-02  2.065229e+00  2.191962e+00  2.246264e+00  2.302119e+00  2.414395e+00  240.538127 1.0191556
## y[76]      2.152724e+00 5.503782e-03 8.647463e-02  1.970484e+00  2.101114e+00  2.152557e+00  2.209544e+00  2.321189e+00  246.862467 1.0193402
## y[77]      2.047753e+00 6.259273e-03 8.590139e-02  1.864167e+00  1.995978e+00  2.048095e+00  2.103218e+00  2.210250e+00  188.344320 1.0227869
## y[78]      1.932830e+00 6.219009e-03 8.556959e-02  1.748153e+00  1.880055e+00  1.932792e+00  1.988573e+00  2.099331e+00  189.320018 1.0245910
## y[79]      1.807727e+00 6.187246e-03 8.438872e-02  1.625667e+00  1.755931e+00  1.809902e+00  1.864056e+00  1.970794e+00  186.026149 1.0266854
## y[80]      1.672296e+00 6.377438e-03 8.467240e-02  1.497307e+00  1.617902e+00  1.674288e+00  1.731673e+00  1.831811e+00  176.275192 1.0286330
## y[81]      1.528652e+00 7.726447e-03 8.565975e-02  1.344449e+00  1.474995e+00  1.530809e+00  1.586016e+00  1.688518e+00  122.911897 1.0319554
## y[82]      1.376577e+00 8.236639e-03 8.586309e-02  1.195868e+00  1.325135e+00  1.380536e+00  1.434381e+00  1.537655e+00  108.670815 1.0340832
## y[83]      1.215887e+00 8.566930e-03 8.487882e-02  1.040034e+00  1.164806e+00  1.218339e+00  1.273435e+00  1.374405e+00   98.163095 1.0371735
## y[84]      1.049315e+00 9.406495e-03 8.497905e-02  8.616887e-01  9.982603e-01  1.053404e+00  1.105953e+00  1.202071e+00   81.614645 1.0412397
## y[85]      8.768573e-01 8.721626e-03 8.531535e-02  6.885125e-01  8.248406e-01  8.819785e-01  9.345581e-01  1.030394e+00   95.688445 1.0367622
## y[86]      6.991434e-01 8.857024e-03 8.377126e-02  5.182318e-01  6.482942e-01  7.058082e-01  7.558754e-01  8.455442e-01   89.457015 1.0395588
## y[87]      5.164007e-01 9.034631e-03 8.495438e-02  3.325470e-01  4.644009e-01  5.209963e-01  5.745146e-01  6.720898e-01   88.420032 1.0401338
## y[88]      3.305546e-01 8.744408e-03 8.504507e-02  1.431435e-01  2.780291e-01  3.357309e-01  3.882744e-01  4.891122e-01   94.588315 1.0382995
## y[89]      1.420037e-01 8.495504e-03 8.509067e-02 -4.455142e-02  9.096393e-02  1.463425e-01  1.982902e-01  2.970438e-01  100.319550 1.0373233
## y[90]     -4.807308e-02 7.918233e-03 8.471495e-02 -2.381257e-01 -9.616313e-02 -4.581534e-02  7.697901e-03  1.123103e-01  114.462583 1.0348411
## y[91]     -2.385769e-01 7.332072e-03 8.471258e-02 -4.242983e-01 -2.891590e-01 -2.341155e-01 -1.829763e-01 -7.842832e-02  133.488055 1.0329696
## y[92]     -4.295366e-01 7.324140e-03 8.422289e-02 -6.113646e-01 -4.803925e-01 -4.268129e-01 -3.747775e-01 -2.692387e-01  132.235178 1.0322050
## y[93]     -6.189228e-01 6.758913e-03 8.437110e-02 -7.979185e-01 -6.690185e-01 -6.158793e-01 -5.629810e-01 -4.628989e-01  155.823748 1.0306530
## y[94]     -8.067646e-01 6.122979e-03 8.568913e-02 -9.896617e-01 -8.583468e-01 -8.041978e-01 -7.514091e-01 -6.471528e-01  195.851080 1.0288893
## y[95]     -9.911209e-01 5.646236e-03 8.519617e-02 -1.173300e+00 -1.041363e+00 -9.884751e-01 -9.352836e-01 -8.359225e-01  227.678513 1.0279195
## y[96]     -1.171267e+00 5.205263e-03 8.628986e-02 -1.357987e+00 -1.224253e+00 -1.167170e+00 -1.114248e+00 -1.016792e+00  274.811079 1.0235461
## y[97]     -1.346031e+00 5.077731e-03 8.720142e-02 -1.540450e+00 -1.399418e+00 -1.342911e+00 -1.288524e+00 -1.185885e+00  294.922455 1.0203753
## y[98]     -1.515573e+00 4.500293e-03 8.783745e-02 -1.714197e+00 -1.569608e+00 -1.511432e+00 -1.457275e+00 -1.352801e+00  380.958604 1.0172520
## y[99]     -1.678588e+00 4.450997e-03 8.772728e-02 -1.875417e+00 -1.730609e+00 -1.674685e+00 -1.620526e+00 -1.521136e+00  388.467444 1.0157849
## y[100]    -1.832719e+00 3.961756e-03 8.783765e-02 -2.022575e+00 -1.886988e+00 -1.831182e+00 -1.774326e+00 -1.672242e+00  491.570715 1.0107920
## y[101]    -1.978981e+00 3.533552e-03 8.842924e-02 -2.173486e+00 -2.031787e+00 -1.976223e+00 -1.919614e+00 -1.816633e+00  626.280485 1.0075148
## y[102]    -2.115595e+00 2.991367e-03 8.847259e-02 -2.309310e+00 -2.171108e+00 -2.114612e+00 -2.058718e+00 -1.948815e+00  874.738353 1.0037211
## y[103]    -2.243192e+00 2.872223e-03 8.858800e-02 -2.426783e+00 -2.297672e+00 -2.240598e+00 -2.185664e+00 -2.073387e+00  951.290941 1.0012838
## y[104]    -2.360213e+00 2.833263e-03 8.857247e-02 -2.546509e+00 -2.414919e+00 -2.358959e+00 -2.301907e+00 -2.194636e+00  977.290382 1.0005460
## y[105]    -2.466130e+00 2.794281e-03 8.863313e-02 -2.650907e+00 -2.521109e+00 -2.466166e+00 -2.408951e+00 -2.294058e+00 1006.125303 1.0003069
## y[106]    -2.561310e+00 2.798549e-03 8.865782e-02 -2.747414e+00 -2.616024e+00 -2.560152e+00 -2.503602e+00 -2.386438e+00 1003.617854 1.0005869
## y[107]    -2.643610e+00 2.735869e-03 8.794221e-02 -2.828639e+00 -2.699241e+00 -2.642124e+00 -2.586247e+00 -2.473984e+00 1033.246990 1.0007637
## y[108]    -2.712750e+00 2.754792e-03 8.771077e-02 -2.886834e+00 -2.770780e+00 -2.710885e+00 -2.656513e+00 -2.540491e+00 1013.743847 1.0014145
## y[109]    -2.769241e+00 2.724521e-03 8.839131e-02 -2.945009e+00 -2.828789e+00 -2.766107e+00 -2.713043e+00 -2.597819e+00 1052.540047 1.0016883
## y[110]    -2.812150e+00 2.751502e-03 8.910984e-02 -2.990239e+00 -2.872010e+00 -2.810884e+00 -2.754079e+00 -2.635379e+00 1048.846169 1.0026494
## y[111]    -2.840763e+00 2.807638e-03 8.876045e-02 -3.014736e+00 -2.898759e+00 -2.839676e+00 -2.784582e+00 -2.656714e+00  999.439852 1.0037692
## y[112]    -2.857158e+00 2.833499e-03 8.918372e-02 -3.031359e+00 -2.915324e+00 -2.856127e+00 -2.802262e+00 -2.673489e+00  990.660988 1.0046945
## y[113]    -2.858443e+00 3.012047e-03 8.990870e-02 -3.037827e+00 -2.915945e+00 -2.857835e+00 -2.802246e+00 -2.669845e+00  891.004531 1.0068387
## y[114]    -2.845754e+00 2.951998e-03 8.987622e-02 -3.024851e+00 -2.903033e+00 -2.845716e+00 -2.788672e+00 -2.665179e+00  926.952406 1.0090155
## y[115]    -2.818651e+00 2.983789e-03 8.994542e-02 -2.995480e+00 -2.875410e+00 -2.820998e+00 -2.761027e+00 -2.633008e+00  908.703097 1.0111650
## y[116]    -2.778496e+00 2.966193e-03 9.004719e-02 -2.955359e+00 -2.835524e+00 -2.781286e+00 -2.721754e+00 -2.589951e+00  921.597764 1.0117522
## y[117]    -2.723589e+00 3.096939e-03 8.836632e-02 -2.892067e+00 -2.781026e+00 -2.725910e+00 -2.666927e+00 -2.529666e+00  814.156911 1.0150324
## y[118]    -2.654816e+00 4.220963e-03 8.766978e-02 -2.820614e+00 -2.713720e+00 -2.658918e+00 -2.597993e+00 -2.467605e+00  431.396504 1.0188888
## y[119]    -2.573605e+00 4.550191e-03 8.825640e-02 -2.737823e+00 -2.633319e+00 -2.578209e+00 -2.516574e+00 -2.386207e+00  376.212432 1.0195873
## y[120]    -2.479531e+00 4.602000e-03 8.901160e-02 -2.640954e+00 -2.538728e+00 -2.485923e+00 -2.424314e+00 -2.286032e+00  374.110505 1.0195510
## y[121]    -2.372314e+00 5.098703e-03 8.802050e-02 -2.536447e+00 -2.431822e+00 -2.376582e+00 -2.316850e+00 -2.184485e+00  298.021960 1.0208268
## y[122]    -2.253638e+00 5.071716e-03 8.812247e-02 -2.415163e+00 -2.312689e+00 -2.257911e+00 -2.199067e+00 -2.061308e+00  301.900282 1.0209161
## y[123]    -2.122997e+00 4.615478e-03 8.755239e-02 -2.277929e+00 -2.181651e+00 -2.130499e+00 -2.068197e+00 -1.934253e+00  359.834319 1.0218898
## y[124]    -1.981302e+00 4.886824e-03 8.717234e-02 -2.136893e+00 -2.039964e+00 -1.986665e+00 -1.925354e+00 -1.794663e+00  318.202792 1.0223458
## y[125]    -1.829264e+00 4.081289e-03 8.669431e-02 -1.987002e+00 -1.886339e+00 -1.833994e+00 -1.775544e+00 -1.641644e+00  451.217952 1.0210545
## y[126]    -1.668016e+00 4.786055e-03 8.607074e-02 -1.822724e+00 -1.725263e+00 -1.674655e+00 -1.616453e+00 -1.483321e+00  323.411731 1.0186120
## y[127]    -1.497204e+00 4.454753e-03 8.559689e-02 -1.655386e+00 -1.555442e+00 -1.502545e+00 -1.447544e+00 -1.313627e+00  369.205936 1.0174608
## y[128]    -1.319378e+00 2.834193e-03 8.566636e-02 -1.474930e+00 -1.375751e+00 -1.323065e+00 -1.269265e+00 -1.139973e+00  913.612278 1.0135998
## y[129]    -1.133810e+00 2.757816e-03 8.524234e-02 -1.291449e+00 -1.188780e+00 -1.136068e+00 -1.082788e+00 -9.536427e-01  955.388543 1.0108453
## y[130]    -9.421559e-01 2.699129e-03 8.384548e-02 -1.093255e+00 -9.981242e-01 -9.444861e-01 -8.937078e-01 -7.657388e-01  964.966172 1.0078239
## y[131]    -7.448392e-01 2.576688e-03 8.325682e-02 -8.984353e-01 -7.979662e-01 -7.469616e-01 -6.943103e-01 -5.732214e-01 1044.037384 1.0058115
## y[132]    -5.430138e-01 2.463654e-03 8.206665e-02 -6.999997e-01 -5.950428e-01 -5.451802e-01 -4.914671e-01 -3.777262e-01 1109.619542 1.0037517
## y[133]    -3.371382e-01 2.478217e-03 8.231254e-02 -4.969069e-01 -3.896555e-01 -3.378016e-01 -2.845928e-01 -1.744861e-01 1103.197794 1.0021469
## y[134]    -1.288300e-01 2.419926e-03 8.284394e-02 -2.925421e-01 -1.797978e-01 -1.310140e-01 -7.700328e-02  3.325413e-02 1171.972372 1.0006998
## y[135]     8.136194e-02 2.466297e-03 8.274294e-02 -8.331002e-02  2.791122e-02  8.087808e-02  1.337649e-01  2.438362e-01 1125.566878 1.0007498
## y[136]     2.920019e-01 2.480706e-03 8.304418e-02  1.274109e-01  2.403000e-01  2.925435e-01  3.436891e-01  4.482178e-01 1120.644378 1.0007771
## y[137]     5.034996e-01 2.546383e-03 8.383369e-02  3.337499e-01  4.525500e-01  5.041882e-01  5.534464e-01  6.683896e-01 1083.901085 1.0004384
## y[138]     7.125731e-01 2.603203e-03 8.299776e-02  5.390401e-01  6.595640e-01  7.143979e-01  7.635895e-01  8.749887e-01 1016.521751 1.0018765
## y[139]     9.186940e-01 2.641060e-03 8.398575e-02  7.497643e-01  8.679142e-01  9.211004e-01  9.718094e-01  1.084187e+00 1011.241418 1.0029137
## y[140]     1.121591e+00 2.634669e-03 8.376719e-02  9.546999e-01  1.069064e+00  1.125215e+00  1.174945e+00  1.283053e+00 1010.870672 1.0054787
## y[141]     1.319279e+00 2.844169e-03 8.431522e-02  1.145589e+00  1.266596e+00  1.323361e+00  1.373236e+00  1.481927e+00  878.822286 1.0112247
## y[142]     1.512706e+00 2.925372e-03 8.523853e-02  1.339533e+00  1.459939e+00  1.515181e+00  1.566834e+00  1.677221e+00  849.004148 1.0121099
## y[143]     1.699526e+00 3.033267e-03 8.587882e-02  1.524378e+00  1.645722e+00  1.704890e+00  1.754602e+00  1.866348e+00  801.587082 1.0178123
## y[144]     1.878957e+00 3.150098e-03 8.653561e-02  1.704118e+00  1.823970e+00  1.882513e+00  1.934685e+00  2.043298e+00  754.642880 1.0218963
## y[145]     2.048596e+00 4.433420e-03 8.716923e-02  1.864551e+00  1.992145e+00  2.052808e+00  2.106632e+00  2.213489e+00  386.588359 1.0299236
## y[146]     2.209440e+00 7.168961e-03 8.861273e-02  2.017386e+00  2.153819e+00  2.213426e+00  2.268803e+00  2.373162e+00  152.784657 1.0374756
## y[147]     2.360987e+00 8.604481e-03 8.880883e-02  2.176738e+00  2.304854e+00  2.364063e+00  2.420723e+00  2.524714e+00  106.527802 1.0447955
## y[148]     2.501952e+00 9.078841e-03 9.078814e-02  2.307705e+00  2.447112e+00  2.506774e+00  2.562249e+00  2.668276e+00   99.999406 1.0481371
## y[149]     2.631427e+00 9.267907e-03 9.143171e-02  2.432628e+00  2.574881e+00  2.638431e+00  2.691102e+00  2.796404e+00   97.326341 1.0536092
## y[150]     2.748313e+00 9.794128e-03 9.340405e-02  2.548531e+00  2.688765e+00  2.756460e+00  2.811759e+00  2.919652e+00   90.949392 1.0557721
## y[151]     2.852445e+00 9.999712e-03 9.418954e-02  2.656836e+00  2.790979e+00  2.861783e+00  2.915128e+00  3.027878e+00   88.721808 1.0572744
## y[152]     2.943264e+00 1.009500e-02 9.477485e-02  2.750328e+00  2.883122e+00  2.952703e+00  3.007425e+00  3.114603e+00   88.140151 1.0567967
## y[153]     3.019396e+00 1.069421e-02 9.568172e-02  2.819427e+00  2.959821e+00  3.028243e+00  3.084040e+00  3.190227e+00   80.049840 1.0603109
## y[154]     3.081639e+00 1.104470e-02 9.545916e-02  2.877946e+00  3.019508e+00  3.090439e+00  3.146814e+00  3.259073e+00   74.701207 1.0613217
## y[155]     3.128833e+00 1.099866e-02 9.486203e-02  2.929633e+00  3.065009e+00  3.137963e+00  3.193120e+00  3.307677e+00   74.388403 1.0598814
## y[156]     3.160863e+00 1.120944e-02 9.408444e-02  2.964516e+00  3.098741e+00  3.170223e+00  3.225321e+00  3.335204e+00   70.447912 1.0598942
## y[157]     3.178365e+00 1.019402e-02 9.373529e-02  2.981102e+00  3.118277e+00  3.184391e+00  3.242934e+00  3.351735e+00   84.550288 1.0506483
## y[158]     3.179128e+00 9.306459e-03 9.266596e-02  2.989754e+00  3.119564e+00  3.184246e+00  3.240870e+00  3.348365e+00   99.145170 1.0481667
## y[159]     3.164860e+00 8.732248e-03 9.218541e-02  2.976913e+00  3.105965e+00  3.171054e+00  3.227850e+00  3.337791e+00  111.448000 1.0408570
## y[160]     3.135460e+00 8.015462e-03 9.125826e-02  2.947184e+00  3.076084e+00  3.140858e+00  3.198276e+00  3.303595e+00  129.624546 1.0340180
## y[161]     3.090430e+00 6.436526e-03 9.036037e-02  2.900773e+00  3.032348e+00  3.095432e+00  3.151053e+00  3.256168e+00  197.084727 1.0282593
## y[162]     3.028994e+00 6.074553e-03 8.854862e-02  2.838584e+00  2.972896e+00  3.031572e+00  3.088923e+00  3.188466e+00  212.488280 1.0273693
## y[163]     2.951971e+00 5.224073e-03 8.669782e-02  2.768102e+00  2.895067e+00  2.955182e+00  3.010508e+00  3.115666e+00  275.421557 1.0243327
## y[164]     2.859688e+00 4.866900e-03 8.584893e-02  2.674634e+00  2.803806e+00  2.862958e+00  2.916282e+00  3.022976e+00  311.146487 1.0206763
## y[165]     2.752570e+00 4.156951e-03 8.429315e-02  2.573977e+00  2.697474e+00  2.755419e+00  2.809411e+00  2.911257e+00  411.182668 1.0182527
## y[166]     2.630472e+00 3.466194e-03 8.327420e-02  2.457386e+00  2.578214e+00  2.631987e+00  2.687911e+00  2.792374e+00  577.185074 1.0170096
## y[167]     2.495484e+00 3.031220e-03 8.115295e-02  2.329961e+00  2.443758e+00  2.496065e+00  2.550509e+00  2.651164e+00  716.759886 1.0148048
## y[168]     2.346518e+00 3.169856e-03 8.023672e-02  2.181253e+00  2.296388e+00  2.346063e+00  2.399684e+00  2.501323e+00  640.718542 1.0131070
## y[169]     2.185877e+00 2.839827e-03 7.904270e-02  2.027144e+00  2.136102e+00  2.185092e+00  2.234695e+00  2.339480e+00  774.710869 1.0103366
## y[170]     2.013452e+00 2.774050e-03 7.821666e-02  1.861746e+00  1.963138e+00  2.012909e+00  2.065573e+00  2.159584e+00  795.004854 1.0081942
## y[171]     1.830312e+00 2.533095e-03 7.798318e-02  1.677727e+00  1.782085e+00  1.830050e+00  1.881275e+00  1.981023e+00  947.761197 1.0065904
## y[172]     1.636066e+00 2.430190e-03 7.664598e-02  1.484642e+00  1.588035e+00  1.636064e+00  1.686861e+00  1.784428e+00  994.714072 1.0050931
## y[173]     1.432866e+00 2.370172e-03 7.549805e-02  1.280536e+00  1.384778e+00  1.431751e+00  1.482651e+00  1.576842e+00 1014.639446 1.0039074
## y[174]     1.222496e+00 2.259532e-03 7.480761e-02  1.074455e+00  1.176443e+00  1.222097e+00  1.273023e+00  1.369192e+00 1096.111469 1.0019018
## y[175]     1.004500e+00 2.197655e-03 7.401945e-02  8.615815e-01  9.573634e-01  1.003572e+00  1.054955e+00  1.149197e+00 1134.417397 1.0003828
## y[176]     7.805876e-01 2.149675e-03 7.367577e-02  6.333392e-01  7.335025e-01  7.784741e-01  8.291817e-01  9.260014e-01 1174.637343 1.0000939
## y[177]     5.514157e-01 2.093524e-03 7.292097e-02  4.106440e-01  5.029054e-01  5.506105e-01  5.988256e-01  6.934208e-01 1213.245898 1.0001844
## y[178]     3.186043e-01 2.080292e-03 7.297764e-02  1.789382e-01  2.707489e-01  3.178732e-01  3.656294e-01  4.625728e-01 1230.640618 1.0005314
## y[179]     8.252563e-02 2.122787e-03 7.274628e-02 -6.242651e-02  3.721618e-02  8.132241e-02  1.286125e-01  2.290148e-01 1174.380614 1.0018388
## y[180]    -1.564454e-01 2.166684e-03 7.366758e-02 -3.008679e-01 -2.000652e-01 -1.574414e-01 -1.109336e-01 -1.008429e-02 1156.009890 1.0025629
## y[181]    -3.952991e-01 2.202401e-03 7.470441e-02 -5.428763e-01 -4.423013e-01 -3.972702e-01 -3.459654e-01 -2.375553e-01 1150.534613 1.0030232
## y[182]    -6.333550e-01 2.331909e-03 7.523348e-02 -7.794127e-01 -6.802345e-01 -6.365783e-01 -5.843738e-01 -4.796714e-01 1040.875969 1.0037876
## y[183]    -8.708890e-01 2.376477e-03 7.623726e-02 -1.017521e+00 -9.186789e-01 -8.719763e-01 -8.233294e-01 -7.134839e-01 1029.122857 1.0024480
## y[184]    -1.104315e+00 2.398032e-03 7.642776e-02 -1.249225e+00 -1.152433e+00 -1.106848e+00 -1.056027e+00 -9.430101e-01 1015.762601 1.0012779
## y[185]    -1.334361e+00 2.498849e-03 7.684065e-02 -1.480749e+00 -1.384070e+00 -1.334080e+00 -1.287012e+00 -1.173804e+00  945.588583 1.0013721
## y[186]    -1.556959e+00 2.561950e-03 7.820278e-02 -1.705921e+00 -1.609818e+00 -1.557461e+00 -1.508317e+00 -1.391007e+00  931.757689 1.0037821
## y[187]    -1.774624e+00 2.650035e-03 7.894735e-02 -1.922886e+00 -1.828114e+00 -1.773136e+00 -1.725383e+00 -1.608427e+00  887.506890 1.0045722
## y[188]    -1.984873e+00 2.683211e-03 7.920364e-02 -2.134645e+00 -2.039065e+00 -1.984589e+00 -1.935121e+00 -1.821427e+00  871.326173 1.0056226
## y[189]    -2.185948e+00 2.766361e-03 8.090178e-02 -2.339937e+00 -2.240364e+00 -2.184489e+00 -2.135782e+00 -2.026876e+00  855.260441 1.0069713
## y[190]    -2.376799e+00 2.956043e-03 8.273423e-02 -2.533832e+00 -2.432387e+00 -2.376120e+00 -2.326264e+00 -2.209470e+00  783.337317 1.0080236
## y[191]    -2.555703e+00 3.079077e-03 8.422323e-02 -2.721272e+00 -2.612021e+00 -2.556799e+00 -2.504773e+00 -2.386334e+00  748.208791 1.0093592
## y[192]    -2.723593e+00 3.191550e-03 8.600590e-02 -2.889449e+00 -2.779803e+00 -2.725498e+00 -2.671638e+00 -2.546290e+00  726.194876 1.0103646
## y[193]    -2.877890e+00 3.311150e-03 8.741493e-02 -3.042672e+00 -2.936815e+00 -2.879837e+00 -2.824793e+00 -2.701289e+00  696.969033 1.0136754
## y[194]    -3.019858e+00 3.337765e-03 8.790675e-02 -3.183659e+00 -3.078330e+00 -3.023947e+00 -2.963445e+00 -2.845454e+00  693.637889 1.0135882
## y[195]    -3.148131e+00 3.401230e-03 8.894943e-02 -3.315454e+00 -3.206553e+00 -3.151921e+00 -3.089960e+00 -2.972070e+00  683.934260 1.0136254
## y[196]    -3.261410e+00 3.468349e-03 8.941879e-02 -3.431319e+00 -3.320391e+00 -3.263081e+00 -3.202038e+00 -3.079563e+00  664.678830 1.0144513
## y[197]    -3.358540e+00 3.400546e-03 9.014272e-02 -3.534570e+00 -3.418593e+00 -3.360187e+00 -3.300860e+00 -3.180636e+00  702.690138 1.0154065
## y[198]    -3.440185e+00 3.385315e-03 9.090308e-02 -3.612172e+00 -3.501532e+00 -3.438875e+00 -3.380049e+00 -3.256210e+00  721.039619 1.0151834
## y[199]    -3.504701e+00 3.481839e-03 9.133545e-02 -3.686146e+00 -3.564888e+00 -3.505246e+00 -3.443209e+00 -3.320980e+00  688.115540 1.0148856
## y[200]    -3.551780e+00 3.964455e-03 9.177369e-02 -3.730272e+00 -3.611801e+00 -3.554663e+00 -3.489527e+00 -3.368185e+00  535.882307 1.0162051
## y[201]    -3.581789e+00 3.643765e-03 9.198360e-02 -3.763306e+00 -3.642809e+00 -3.579999e+00 -3.520757e+00 -3.404356e+00  637.265081 1.0145685
## y[202]    -3.595291e+00 3.623521e-03 9.293988e-02 -3.780215e+00 -3.657411e+00 -3.594497e+00 -3.536191e+00 -3.407460e+00  657.873828 1.0125367
## y[203]    -3.590761e+00 3.601068e-03 9.291685e-02 -3.774140e+00 -3.651265e+00 -3.590443e+00 -3.531678e+00 -3.403265e+00  665.773098 1.0122828
## y[204]    -3.568201e+00 3.501617e-03 9.206738e-02 -3.751098e+00 -3.628773e+00 -3.567615e+00 -3.508823e+00 -3.383316e+00  691.312172 1.0114010
## y[205]    -3.527889e+00 3.332952e-03 9.173184e-02 -3.704482e+00 -3.587351e+00 -3.526990e+00 -3.466176e+00 -3.346242e+00  757.499018 1.0115336
## y[206]    -3.470004e+00 3.197040e-03 8.997479e-02 -3.641188e+00 -3.527872e+00 -3.470753e+00 -3.410218e+00 -3.299481e+00  792.036953 1.0088466
## y[207]    -3.393476e+00 3.147645e-03 8.959696e-02 -3.566592e+00 -3.451906e+00 -3.391685e+00 -3.336046e+00 -3.220108e+00  810.242357 1.0093863
## y[208]    -3.300244e+00 3.097624e-03 8.886776e-02 -3.477718e+00 -3.360092e+00 -3.298125e+00 -3.242122e+00 -3.127708e+00  823.059085 1.0080411
## y[209]    -3.190520e+00 3.049136e-03 8.786783e-02 -3.366341e+00 -3.251972e+00 -3.185997e+00 -3.134418e+00 -3.022186e+00  830.436202 1.0067107
## y[210]    -3.064240e+00 3.102136e-03 8.656967e-02 -3.230431e+00 -3.121796e+00 -3.062335e+00 -3.008240e+00 -2.902289e+00  778.770899 1.0062826
## y[211]    -2.921780e+00 3.065529e-03 8.536303e-02 -3.083148e+00 -2.979669e+00 -2.922352e+00 -2.865536e+00 -2.761675e+00  775.405427 1.0052852
## y[212]    -2.764046e+00 2.977844e-03 8.441968e-02 -2.923678e+00 -2.821545e+00 -2.764504e+00 -2.707797e+00 -2.602424e+00  803.680613 1.0055252
## y[213]    -2.590767e+00 3.011558e-03 8.244793e-02 -2.746504e+00 -2.647575e+00 -2.589537e+00 -2.535514e+00 -2.431187e+00  749.509524 1.0055218
## y[214]    -2.405051e+00 2.906768e-03 8.099007e-02 -2.559260e+00 -2.461137e+00 -2.402788e+00 -2.353007e+00 -2.251926e+00  776.323763 1.0052897
## y[215]    -2.205552e+00 2.847868e-03 8.041363e-02 -2.363611e+00 -2.257517e+00 -2.203938e+00 -2.152679e+00 -2.054524e+00  797.295851 1.0052423
## y[216]    -1.993728e+00 2.782855e-03 7.900187e-02 -2.148676e+00 -2.043758e+00 -1.995310e+00 -1.942226e+00 -1.846168e+00  805.922954 1.0048459
## y[217]    -1.769602e+00 2.809792e-03 7.851686e-02 -1.926029e+00 -1.819971e+00 -1.770585e+00 -1.719187e+00 -1.622136e+00  780.867669 1.0071838
## y[218]    -1.537296e+00 2.819721e-03 7.829188e-02 -1.693253e+00 -1.586091e+00 -1.540331e+00 -1.486745e+00 -1.385631e+00  770.941236 1.0078317
## y[219]    -1.295555e+00 2.777462e-03 7.777609e-02 -1.449557e+00 -1.346360e+00 -1.296969e+00 -1.244989e+00 -1.140819e+00  784.144245 1.0085818
## y[220]    -1.045538e+00 2.883714e-03 7.733979e-02 -1.197116e+00 -1.098046e+00 -1.046338e+00 -9.967999e-01 -8.898727e-01  719.285915 1.0095621
## y[221]    -7.895896e-01 2.789852e-03 7.602062e-02 -9.359281e-01 -8.393663e-01 -7.909856e-01 -7.415793e-01 -6.379510e-01  742.506866 1.0095780
## y[222]    -5.281961e-01 2.776385e-03 7.523605e-02 -6.693134e-01 -5.772717e-01 -5.279350e-01 -4.814696e-01 -3.784755e-01  734.332049 1.0094039
## y[223]    -2.636940e-01 2.669856e-03 7.532482e-02 -4.096357e-01 -3.128452e-01 -2.637679e-01 -2.164158e-01 -1.093719e-01  795.977315 1.0091657
## y[224]     4.278161e-03 2.499355e-03 7.562931e-02 -1.394366e-01 -4.396453e-02  4.105219e-03  5.218637e-02  1.590097e-01  915.639407 1.0068154
## y[225]     2.756188e-01 2.493359e-03 7.601740e-02  1.333464e-01  2.277318e-01  2.750516e-01  3.244976e-01  4.257077e-01  929.515164 1.0096189
## y[226]     5.452249e-01 2.428538e-03 7.582570e-02  3.963234e-01  4.952381e-01  5.443624e-01  5.925489e-01  6.952084e-01  974.861363 1.0083286
## y[227]     8.135546e-01 2.441265e-03 7.759736e-02  6.646625e-01  7.632823e-01  8.138140e-01  8.631837e-01  9.673210e-01 1010.332017 1.0076239
## y[228]     1.079739e+00 2.424354e-03 7.862454e-02  9.268228e-01  1.029769e+00  1.079758e+00  1.130272e+00  1.237385e+00 1051.778447 1.0060035
## y[229]     1.341581e+00 2.526422e-03 8.005001e-02  1.187063e+00  1.290277e+00  1.341879e+00  1.394515e+00  1.504372e+00 1003.947819 1.0051028
## y[230]     1.598380e+00 2.558853e-03 8.070096e-02  1.439052e+00  1.548036e+00  1.598524e+00  1.652135e+00  1.758588e+00  994.642120 1.0050897
## y[231]     1.847750e+00 2.557379e-03 8.103732e-02  1.687881e+00  1.798378e+00  1.846780e+00  1.901943e+00  2.012213e+00 1004.106537 1.0043836
## y[232]     2.090110e+00 2.645381e-03 8.201765e-02  1.924254e+00  2.039028e+00  2.089022e+00  2.143356e+00  2.254122e+00  961.254302 1.0052424
## y[233]     2.323293e+00 2.725265e-03 8.320457e-02  2.157242e+00  2.269488e+00  2.323433e+00  2.375429e+00  2.489336e+00  932.131020 1.0048467
## y[234]     2.547385e+00 2.791773e-03 8.372168e-02  2.375499e+00  2.494870e+00  2.548251e+00  2.600198e+00  2.718470e+00  899.323329 1.0059672
## y[235]     2.758939e+00 2.846487e-03 8.447943e-02  2.591252e+00  2.705573e+00  2.757959e+00  2.813531e+00  2.936665e+00  880.812538 1.0056627
## y[236]     2.958066e+00 2.915407e-03 8.540657e-02  2.791079e+00  2.903306e+00  2.956988e+00  3.011857e+00  3.134065e+00  858.191160 1.0044157
## y[237]     3.143380e+00 2.917232e-03 8.729180e-02  2.972745e+00  3.087000e+00  3.142339e+00  3.200474e+00  3.319380e+00  895.375075 1.0029660
## y[238]     3.314562e+00 2.913645e-03 8.811943e-02  3.146016e+00  3.257792e+00  3.313588e+00  3.372165e+00  3.489159e+00  914.682191 1.0024057
## y[239]     3.469873e+00 3.003409e-03 8.906602e-02  3.300166e+00  3.412721e+00  3.468346e+00  3.526434e+00  3.644839e+00  879.417821 1.0017756
## y[240]     3.608763e+00 3.033325e-03 9.006322e-02  3.437146e+00  3.551065e+00  3.606703e+00  3.668276e+00  3.795920e+00  881.570734 1.0010936
## y[241]     3.731651e+00 3.113431e-03 9.140047e-02  3.549823e+00  3.671547e+00  3.729111e+00  3.791314e+00  3.917354e+00  861.823547 1.0009201
## y[242]     3.837688e+00 3.149530e-03 9.192312e-02  3.662839e+00  3.778957e+00  3.835465e+00  3.897136e+00  4.022721e+00  851.839896 1.0008162
## y[243]     3.924145e+00 3.181737e-03 9.243993e-02  3.752098e+00  3.862400e+00  3.920324e+00  3.986739e+00  4.117571e+00  844.093559 1.0015161
## y[244]     3.992559e+00 3.199585e-03 9.306398e-02  3.819675e+00  3.929352e+00  3.989293e+00  4.055094e+00  4.185227e+00  846.010677 1.0018769
## y[245]     4.041730e+00 3.277470e-03 9.423067e-02  3.868925e+00  3.980009e+00  4.039114e+00  4.105557e+00  4.228818e+00  826.622353 1.0031993
## y[246]     4.070529e+00 3.197010e-03 9.449639e-02  3.893399e+00  4.010022e+00  4.067071e+00  4.132196e+00  4.256758e+00  873.659920 1.0039377
## y[247]     4.078410e+00 3.111170e-03 9.343806e-02  3.901782e+00  4.018144e+00  4.074226e+00  4.139179e+00  4.262808e+00  901.986679 1.0028163
## y[248]     4.067127e+00 3.152416e-03 9.343116e-02  3.894188e+00  4.004703e+00  4.062315e+00  4.129793e+00  4.259136e+00  878.408129 1.0036541
## y[249]     4.035500e+00 3.129617e-03 9.341914e-02  3.859308e+00  3.972398e+00  4.032001e+00  4.096537e+00  4.224785e+00  891.023966 1.0032734
## y[250]     3.983889e+00 3.076418e-03 9.291987e-02  3.810716e+00  3.921494e+00  3.978215e+00  4.044735e+00  4.172659e+00  912.276743 1.0050615
## y[251]     3.913417e+00 3.161943e-03 9.251181e-02  3.741659e+00  3.849795e+00  3.908373e+00  3.973449e+00  4.101789e+00  856.024868 1.0068355
## y[252]     3.822225e+00 3.133547e-03 9.163132e-02  3.654620e+00  3.759921e+00  3.818111e+00  3.881352e+00  4.006676e+00  855.097000 1.0074973
## y[253]     3.711233e+00 3.159197e-03 9.047455e-02  3.545343e+00  3.650594e+00  3.708933e+00  3.769916e+00  3.897965e+00  820.161723 1.0086889
## y[254]     3.582331e+00 3.334555e-03 9.035138e-02  3.409170e+00  3.520146e+00  3.578433e+00  3.640987e+00  3.768085e+00  734.165482 1.0117251
## y[255]     3.434238e+00 3.549525e-03 8.945696e-02  3.268815e+00  3.373448e+00  3.432085e+00  3.490794e+00  3.615906e+00  635.166673 1.0147842
## y[256]     3.269847e+00 4.657859e-03 8.915212e-02  3.101527e+00  3.207986e+00  3.266210e+00  3.325165e+00  3.449759e+00  366.345317 1.0214987
## y[257]     3.087780e+00 5.856064e-03 8.800059e-02  2.920296e+00  3.030354e+00  3.085271e+00  3.141478e+00  3.274282e+00  225.818488 1.0243578
## y[258]     2.889271e+00 6.897767e-03 8.704813e-02  2.725208e+00  2.831169e+00  2.886274e+00  2.943395e+00  3.076866e+00  159.258225 1.0293378
## y[259]     2.674765e+00 7.235544e-03 8.640519e-02  2.510490e+00  2.617391e+00  2.669489e+00  2.728639e+00  2.856027e+00  142.605809 1.0330809
## y[260]     2.445011e+00 8.229207e-03 8.534515e-02  2.283304e+00  2.390887e+00  2.439958e+00  2.497781e+00  2.624672e+00  107.557766 1.0361509
## y[261]     2.201796e+00 8.481361e-03 8.508440e-02  2.044594e+00  2.147512e+00  2.197636e+00  2.253155e+00  2.376769e+00  100.639580 1.0371675
## y[262]     1.945763e+00 8.436938e-03 8.342077e-02  1.789134e+00  1.894286e+00  1.942688e+00  1.997138e+00  2.125355e+00   97.763920 1.0353949
## y[263]     1.679215e+00 7.940148e-03 8.132350e-02  1.529569e+00  1.625979e+00  1.676240e+00  1.729379e+00  1.850422e+00  104.899880 1.0361148
## y[264]     1.403419e+00 7.617592e-03 8.053740e-02  1.254002e+00  1.349175e+00  1.398173e+00  1.452237e+00  1.571762e+00  111.778902 1.0342621
## y[265]     1.118267e+00 6.327089e-03 7.909433e-02  9.677912e-01  1.065789e+00  1.116650e+00  1.165205e+00  1.282974e+00  156.272562 1.0300566
## y[266]     8.264624e-01 6.205498e-03 7.921427e-02  6.735077e-01  7.745165e-01  8.242611e-01  8.733343e-01  9.967547e-01  162.949725 1.0297331
## y[267]     5.286116e-01 5.293394e-03 7.846612e-02  3.720734e-01  4.764165e-01  5.263692e-01  5.767553e-01  6.885892e-01  219.733323 1.0260696
## y[268]     2.267676e-01 4.597094e-03 7.818563e-02  7.433831e-02  1.744562e-01  2.233650e-01  2.759852e-01  3.842966e-01  289.259161 1.0229490
## y[269]    -7.868025e-02 3.832446e-03 7.802317e-02 -2.300906e-01 -1.272273e-01 -8.061498e-02 -3.011292e-02  7.592265e-02  414.471899 1.0181361
## y[270]    -3.846246e-01 3.265971e-03 7.861182e-02 -5.388156e-01 -4.328786e-01 -3.888128e-01 -3.355266e-01 -2.205865e-01  579.363406 1.0137670
## y[271]    -6.896342e-01 2.684983e-03 7.955054e-02 -8.467482e-01 -7.387304e-01 -6.926850e-01 -6.398289e-01 -5.269827e-01  877.815126 1.0120291
## y[272]    -9.929700e-01 2.928045e-03 7.911019e-02 -1.153698e+00 -1.041818e+00 -9.953932e-01 -9.445085e-01 -8.295979e-01  729.977081 1.0110434
## y[273]    -1.292619e+00 2.632217e-03 7.935494e-02 -1.446275e+00 -1.343038e+00 -1.294462e+00 -1.241847e+00 -1.132003e+00  908.876032 1.0092932
## y[274]    -1.586653e+00 2.452053e-03 7.935138e-02 -1.741865e+00 -1.636919e+00 -1.587364e+00 -1.537087e+00 -1.425840e+00 1047.246839 1.0089147
## y[275]    -1.874110e+00 2.471071e-03 7.977519e-02 -2.034114e+00 -1.924011e+00 -1.873561e+00 -1.824357e+00 -1.716212e+00 1042.234082 1.0082864
## y[276]    -2.154346e+00 2.515018e-03 8.155571e-02 -2.316042e+00 -2.204824e+00 -2.154631e+00 -2.100797e+00 -1.995125e+00 1051.541877 1.0075101
## y[277]    -2.423343e+00 2.549466e-03 8.258110e-02 -2.589851e+00 -2.474990e+00 -2.424454e+00 -2.372184e+00 -2.261569e+00 1049.210819 1.0086175
## y[278]    -2.683881e+00 2.506590e-03 8.342067e-02 -2.855056e+00 -2.736971e+00 -2.685941e+00 -2.630290e+00 -2.516928e+00 1107.594186 1.0056297
## y[279]    -2.931513e+00 2.614713e-03 8.468333e-02 -3.104355e+00 -2.985793e+00 -2.933574e+00 -2.877172e+00 -2.760465e+00 1048.932918 1.0056221
## y[280]    -3.165252e+00 2.717081e-03 8.610460e-02 -3.333168e+00 -3.220494e+00 -3.166495e+00 -3.110132e+00 -2.995846e+00 1004.263446 1.0059044
## y[281]    -3.384104e+00 2.775099e-03 8.655343e-02 -3.557290e+00 -3.435733e+00 -3.383612e+00 -3.328703e+00 -3.208706e+00  972.773004 1.0065670
## y[282]    -3.588545e+00 2.774081e-03 8.708337e-02 -3.758383e+00 -3.644190e+00 -3.589141e+00 -3.534525e+00 -3.418755e+00  985.444348 1.0051714
## y[283]    -3.776384e+00 2.892284e-03 8.936703e-02 -3.951630e+00 -3.833953e+00 -3.776818e+00 -3.720750e+00 -3.591916e+00  954.712707 1.0045400
## y[284]    -3.945328e+00 2.905206e-03 9.049282e-02 -4.125426e+00 -4.004775e+00 -3.943852e+00 -3.888255e+00 -3.762925e+00  970.229248 1.0030412
## y[285]    -4.096409e+00 2.926192e-03 9.152374e-02 -4.278802e+00 -4.157207e+00 -4.094488e+00 -4.036747e+00 -3.912732e+00  978.277442 1.0028596
## y[286]    -4.226857e+00 2.952044e-03 9.223778e-02 -4.408288e+00 -4.284576e+00 -4.227832e+00 -4.166247e+00 -4.046413e+00  976.274636 1.0039229
## y[287]    -4.336834e+00 2.944635e-03 9.355382e-02 -4.521468e+00 -4.394962e+00 -4.336108e+00 -4.275074e+00 -4.154531e+00 1009.392816 1.0026777
## y[288]    -4.426842e+00 2.950540e-03 9.385343e-02 -4.611002e+00 -4.487575e+00 -4.427738e+00 -4.365123e+00 -4.243266e+00 1011.805998 1.0023750
## y[289]    -4.495714e+00 2.939132e-03 9.471282e-02 -4.677294e+00 -4.557061e+00 -4.496714e+00 -4.433091e+00 -4.312229e+00 1038.434846 1.0012540
## y[290]    -4.542548e+00 3.003190e-03 9.538480e-02 -4.726683e+00 -4.603999e+00 -4.540972e+00 -4.479663e+00 -4.354226e+00 1008.771161 1.0011640
## y[291]    -4.567459e+00 3.055822e-03 9.698637e-02 -4.753887e+00 -4.631251e+00 -4.566351e+00 -4.503217e+00 -4.372017e+00 1007.314674 1.0005770
## y[292]    -4.570434e+00 3.055231e-03 9.717406e-02 -4.757026e+00 -4.634235e+00 -4.568885e+00 -4.508070e+00 -4.383188e+00 1011.608689 1.0004323
## y[293]    -4.549551e+00 3.059110e-03 9.707642e-02 -4.741670e+00 -4.613912e+00 -4.546126e+00 -4.487408e+00 -4.362807e+00 1007.018332 1.0002585
## y[294]    -4.506036e+00 3.151220e-03 9.799217e-02 -4.701257e+00 -4.571760e+00 -4.502678e+00 -4.443463e+00 -4.315308e+00  966.997525 1.0001956
## y[295]    -4.439418e+00 3.223259e-03 9.730564e-02 -4.635171e+00 -4.502131e+00 -4.435616e+00 -4.375985e+00 -4.246922e+00  911.350831 1.0010502
## y[296]    -4.350508e+00 3.287988e-03 9.645085e-02 -4.545487e+00 -4.412589e+00 -4.345859e+00 -4.287984e+00 -4.166341e+00  860.501455 1.0019512
## y[297]    -4.239850e+00 3.522366e-03 9.543519e-02 -4.432335e+00 -4.303008e+00 -4.235451e+00 -4.177416e+00 -4.053746e+00  734.087995 1.0042828
## y[298]    -4.107143e+00 3.613640e-03 9.454863e-02 -4.294579e+00 -4.168101e+00 -4.105262e+00 -4.046705e+00 -3.924646e+00  684.574635 1.0064030
## y[299]    -3.953084e+00 3.667875e-03 9.326154e-02 -4.140919e+00 -4.013324e+00 -3.953300e+00 -3.894365e+00 -3.767247e+00  646.511352 1.0071898
## y[300]    -3.777729e+00 3.402945e-03 9.253044e-02 -3.961593e+00 -3.836593e+00 -3.777488e+00 -3.718608e+00 -3.592539e+00  739.365636 1.0079788
## y[301]    -3.583753e+00 3.275398e-03 9.154780e-02 -3.769138e+00 -3.641269e+00 -3.583050e+00 -3.524332e+00 -3.403478e+00  781.209831 1.0101032
## y[302]    -3.370145e+00 2.916788e-03 8.892980e-02 -3.548995e+00 -3.425406e+00 -3.371357e+00 -3.311857e+00 -3.196827e+00  929.575864 1.0099879
## y[303]    -3.138624e+00 2.781359e-03 8.797284e-02 -3.322748e+00 -3.196204e+00 -3.139135e+00 -3.081502e+00 -2.970226e+00 1000.421599 1.0103516
## y[304]    -2.889691e+00 2.809036e-03 8.615940e-02 -3.070016e+00 -2.943286e+00 -2.888501e+00 -2.832421e+00 -2.726042e+00  940.785496 1.0101967
## y[305]    -2.624810e+00 2.877931e-03 8.543028e-02 -2.800276e+00 -2.679764e+00 -2.622258e+00 -2.568289e+00 -2.460294e+00  881.176208 1.0099237
## y[306]    -2.345976e+00 2.633106e-03 8.357659e-02 -2.517515e+00 -2.397185e+00 -2.346300e+00 -2.290576e+00 -2.190188e+00 1007.470987 1.0099711
## y[307]    -2.054071e+00 2.600402e-03 8.268591e-02 -2.225958e+00 -2.103423e+00 -2.052659e+00 -2.000031e+00 -1.901352e+00 1011.071556 1.0083212
## y[308]    -1.751138e+00 2.721319e-03 8.132620e-02 -1.921625e+00 -1.799453e+00 -1.748720e+00 -1.698338e+00 -1.600612e+00  893.104017 1.0098519
## y[309]    -1.436937e+00 2.375947e-03 8.119941e-02 -1.608701e+00 -1.485609e+00 -1.431680e+00 -1.385260e+00 -1.287717e+00 1167.971943 1.0095067
## y[310]    -1.113661e+00 2.406173e-03 7.933799e-02 -1.285584e+00 -1.163169e+00 -1.109794e+00 -1.063461e+00 -9.651237e-01 1087.197748 1.0093374
## y[311]    -7.834359e-01 2.186904e-03 7.814697e-02 -9.531278e-01 -8.303961e-01 -7.812427e-01 -7.319075e-01 -6.350021e-01 1276.922860 1.0074769
## y[312]    -4.483936e-01 2.176405e-03 7.813462e-02 -6.175978e-01 -4.957768e-01 -4.461894e-01 -3.954959e-01 -2.993423e-01 1288.865366 1.0065994
## y[313]    -1.094756e-01 2.211499e-03 7.882035e-02 -2.784695e-01 -1.558156e-01 -1.077821e-01 -5.837827e-02  3.951832e-02 1270.290881 1.0054980
## y[314]     2.310033e-01 2.447374e-03 7.871608e-02  6.541947e-02  1.834067e-01  2.323093e-01  2.819627e-01  3.792587e-01 1034.489669 1.0059751
## y[315]     5.714881e-01 2.859809e-03 8.035347e-02  4.004185e-01  5.213617e-01  5.732692e-01  6.218086e-01  7.237597e-01  789.469406 1.0069785
## y[316]     9.126836e-01 2.401119e-03 7.979573e-02  7.469489e-01  8.617224e-01  9.132425e-01  9.646516e-01  1.062027e+00 1104.414229 1.0056266
## y[317]     1.250392e+00 2.410394e-03 8.079653e-02  1.090004e+00  1.198393e+00  1.253740e+00  1.303152e+00  1.407712e+00 1123.594096 1.0048323
## y[318]     1.583501e+00 2.698471e-03 8.229129e-02  1.420274e+00  1.530928e+00  1.584090e+00  1.638695e+00  1.746364e+00  929.976927 1.0056589
## y[319]     1.910430e+00 2.770462e-03 8.319100e-02  1.740072e+00  1.858203e+00  1.911221e+00  1.962604e+00  2.076383e+00  901.671728 1.0043176
## y[320]     2.229293e+00 3.105914e-03 8.465233e-02  2.050470e+00  2.177840e+00  2.231656e+00  2.282311e+00  2.396776e+00  742.846451 1.0063105
## y[321]     2.538728e+00 2.723769e-03 8.539084e-02  2.358963e+00  2.488222e+00  2.540492e+00  2.592888e+00  2.705741e+00  982.838060 1.0057061
## y[322]     2.836860e+00 2.702181e-03 8.682275e-02  2.651803e+00  2.784123e+00  2.839411e+00  2.892162e+00  3.002100e+00 1032.376831 1.0057979
## y[323]     3.122394e+00 2.870239e-03 8.867290e-02  2.936641e+00  3.067848e+00  3.124848e+00  3.179253e+00  3.294317e+00  954.433451 1.0054678
## y[324]     3.393439e+00 3.227840e-03 8.988810e-02  3.203570e+00  3.339117e+00  3.394510e+00  3.451878e+00  3.564405e+00  775.497495 1.0059382
## y[325]     3.650040e+00 3.076025e-03 9.191524e-02  3.462087e+00  3.592168e+00  3.651906e+00  3.710990e+00  3.827133e+00  892.884780 1.0035667
## y[326]     3.890482e+00 3.038827e-03 9.351643e-02  3.703375e+00  3.831551e+00  3.892062e+00  3.951787e+00  4.068188e+00  947.030164 1.0034506
## y[327]     4.112236e+00 2.991607e-03 9.447758e-02  3.923187e+00  4.050144e+00  4.114017e+00  4.176643e+00  4.300901e+00  997.351899 1.0019507
## y[328]     4.314565e+00 3.097053e-03 9.497740e-02  4.124843e+00  4.250907e+00  4.318308e+00  4.377150e+00  4.497222e+00  940.466376 1.0010930
## y[329]     4.496583e+00 3.112245e-03 9.646483e-02  4.299677e+00  4.431037e+00  4.499883e+00  4.560588e+00  4.682595e+00  960.705744 0.9998287
## y[330]     4.656609e+00 3.145062e-03 9.751739e-02  4.463196e+00  4.592518e+00  4.660208e+00  4.721278e+00  4.849147e+00  961.403777 0.9994120
## y[331]     4.794769e+00 3.160078e-03 9.796300e-02  4.605637e+00  4.731158e+00  4.797874e+00  4.858170e+00  4.981070e+00  961.011045 0.9994221
## y[332]     4.909291e+00 3.222944e-03 9.916968e-02  4.721486e+00  4.843423e+00  4.910403e+00  4.973006e+00  5.095421e+00  946.786865 0.9988405
## y[333]     5.000799e+00 3.231026e-03 9.962796e-02  4.806607e+00  4.936619e+00  5.002507e+00  5.065466e+00  5.194423e+00  950.783274 0.9986729
## y[334]     5.067310e+00 3.181508e-03 9.864663e-02  4.875900e+00  5.000346e+00  5.066002e+00  5.129621e+00  5.261180e+00  961.387266 0.9986340
## y[335]     5.108992e+00 3.146108e-03 9.848185e-02  4.919960e+00  5.042503e+00  5.110581e+00  5.169866e+00  5.302350e+00  979.862539 0.9988800
## y[336]     5.125581e+00 3.150082e-03 9.850588e-02  4.942356e+00  5.060756e+00  5.125842e+00  5.185836e+00  5.323854e+00  977.868973 0.9995924
## y[337]     5.115860e+00 3.127795e-03 9.779646e-02  4.932476e+00  5.053627e+00  5.114468e+00  5.177329e+00  5.312792e+00  977.619281 0.9996685
## y[338]     5.079927e+00 3.073659e-03 9.725189e-02  4.891974e+00  5.018985e+00  5.077350e+00  5.141607e+00  5.275593e+00 1001.116658 0.9996400
## y[339]     5.018272e+00 3.074974e-03 9.637687e-02  4.827064e+00  4.956770e+00  5.016666e+00  5.078973e+00  5.217063e+00  982.342214 0.9995555
## y[340]     4.930947e+00 2.962680e-03 9.469175e-02  4.739783e+00  4.870849e+00  4.930063e+00  4.990893e+00  5.118523e+00 1021.538872 0.9996625
## y[341]     4.819222e+00 2.920531e-03 9.385996e-02  4.632077e+00  4.758844e+00  4.819152e+00  4.880186e+00  5.004653e+00 1032.849910 0.9993850
## y[342]     4.682580e+00 2.904710e-03 9.301845e-02  4.498317e+00  4.620667e+00  4.683395e+00  4.744120e+00  4.867193e+00 1025.493155 0.9994141
## y[343]     4.523053e+00 2.869663e-03 9.048316e-02  4.349308e+00  4.461650e+00  4.522407e+00  4.579395e+00  4.708512e+00  994.200319 0.9995805
## y[344]     4.339093e+00 2.848818e-03 8.995496e-02  4.160848e+00  4.279752e+00  4.338230e+00  4.397338e+00  4.521313e+00  997.059015 0.9996413
## y[345]     4.131544e+00 2.771152e-03 8.789801e-02  3.957066e+00  4.072820e+00  4.128577e+00  4.188724e+00  4.310646e+00 1006.091111 0.9995451
## y[346]     3.902809e+00 2.752047e-03 8.684268e-02  3.730854e+00  3.845489e+00  3.901387e+00  3.958903e+00  4.080215e+00  995.760080 0.9996293
## y[347]     3.654239e+00 2.674796e-03 8.539892e-02  3.489202e+00  3.595988e+00  3.652931e+00  3.707866e+00  3.824685e+00 1019.350432 0.9993740
## y[348]     3.386453e+00 2.618704e-03 8.410186e-02  3.224515e+00  3.330372e+00  3.384538e+00  3.440357e+00  3.562637e+00 1031.426954 0.9992240
## y[349]     3.099710e+00 2.502460e-03 8.295612e-02  2.943293e+00  3.045038e+00  3.097528e+00  3.152947e+00  3.267468e+00 1098.911164 0.9994185
## y[350]     2.795297e+00 2.422587e-03 8.161962e-02  2.641081e+00  2.742734e+00  2.793684e+00  2.846486e+00  2.957392e+00 1135.090189 0.9992554
## y[351]     2.476194e+00 2.368675e-03 7.993092e-02  2.319387e+00  2.423082e+00  2.476357e+00  2.527657e+00  2.630515e+00 1138.724497 0.9992733
## y[352]     2.143191e+00 2.314486e-03 7.984299e-02  1.984510e+00  2.093828e+00  2.144181e+00  2.193513e+00  2.300552e+00 1190.048386 0.9991043
## y[353]     1.797375e+00 2.309247e-03 7.960220e-02  1.633282e+00  1.746217e+00  1.798378e+00  1.848170e+00  1.957967e+00 1188.253731 0.9996905
## y[354]     1.441189e+00 2.250734e-03 7.956828e-02  1.281311e+00  1.392160e+00  1.441536e+00  1.490691e+00  1.605293e+00 1249.774376 1.0003455
## y[355]     1.077051e+00 2.213035e-03 7.946480e-02  9.175347e-01  1.027305e+00  1.076028e+00  1.126950e+00  1.242983e+00 1289.356489 1.0009189
## y[356]     7.044758e-01 2.238405e-03 8.049325e-02  5.395854e-01  6.541327e-01  7.050594e-01  7.564843e-01  8.712432e-01 1293.127907 1.0011367
## y[357]     3.263560e-01 2.264843e-03 7.995933e-02  1.699820e-01  2.763030e-01  3.267581e-01  3.751326e-01  4.866269e-01 1246.413202 1.0017961
## y[358]    -5.528774e-02 2.279794e-03 7.943761e-02 -2.135955e-01 -1.053237e-01 -5.650635e-02 -4.972929e-03  1.052394e-01 1214.118848 1.0028932
## y[359]    -4.383245e-01 2.307808e-03 8.013067e-02 -5.957088e-01 -4.897889e-01 -4.378573e-01 -3.892226e-01 -2.738260e-01 1205.585869 1.0029793
## y[360]    -8.214875e-01 2.297943e-03 8.041839e-02 -9.860286e-01 -8.732345e-01 -8.210508e-01 -7.714153e-01 -6.547914e-01 1224.706912 1.0045243
## y[361]    -1.202480e+00 2.414656e-03 8.197858e-02 -1.361113e+00 -1.255625e+00 -1.201435e+00 -1.150097e+00 -1.038068e+00 1152.630799 1.0053361
## y[362]    -1.578978e+00 2.496539e-03 8.428261e-02 -1.744494e+00 -1.634621e+00 -1.580116e+00 -1.525008e+00 -1.405248e+00 1139.722523 1.0049235
## y[363]    -1.949667e+00 2.564254e-03 8.485989e-02 -2.120195e+00 -2.005316e+00 -1.950401e+00 -1.896847e+00 -1.770633e+00 1095.173172 1.0049358
## y[364]    -2.312416e+00 2.573788e-03 8.520833e-02 -2.478315e+00 -2.367470e+00 -2.314984e+00 -2.259366e+00 -2.139895e+00 1096.020515 1.0045484
## y[365]    -2.665394e+00 2.632341e-03 8.702493e-02 -2.841114e+00 -2.719517e+00 -2.666282e+00 -2.608503e+00 -2.489947e+00 1092.956678 1.0046476
## y[366]    -3.006599e+00 2.701366e-03 8.888529e-02 -3.181493e+00 -3.062970e+00 -3.007412e+00 -2.949235e+00 -2.827417e+00 1082.662016 1.0027840
## y[367]    -3.335927e+00 2.822922e-03 9.131365e-02 -3.519979e+00 -3.393835e+00 -3.337004e+00 -3.279655e+00 -3.151302e+00 1046.341712 1.0030189
## y[368]    -3.649543e+00 2.922833e-03 9.350967e-02 -3.831627e+00 -3.707886e+00 -3.650736e+00 -3.589233e+00 -3.460200e+00 1023.540531 1.0030729
## y[369]    -3.946281e+00 2.970631e-03 9.456613e-02 -4.130541e+00 -4.005399e+00 -3.947655e+00 -3.883057e+00 -3.752599e+00 1013.383571 1.0024142
## y[370]    -4.225897e+00 3.076150e-03 9.644217e-02 -4.418856e+00 -4.287587e+00 -4.227029e+00 -4.160960e+00 -4.026043e+00  982.921962 1.0026780
## y[371]    -4.486150e+00 3.201737e-03 9.762853e-02 -4.676806e+00 -4.547941e+00 -4.484755e+00 -4.422651e+00 -4.285476e+00  929.784398 1.0030413
## y[372]    -4.725117e+00 3.441677e-03 9.871193e-02 -4.919400e+00 -4.787873e+00 -4.725747e+00 -4.659434e+00 -4.534377e+00  822.619521 1.0027885
## y[373]    -4.943139e+00 3.489179e-03 9.987507e-02 -5.141348e+00 -5.005664e+00 -4.941850e+00 -4.877491e+00 -4.747881e+00  819.346716 1.0038160
## y[374]    -5.136930e+00 3.447071e-03 1.020553e-01 -5.337511e+00 -5.202900e+00 -5.136487e+00 -5.066926e+00 -4.936776e+00  876.538302 1.0040348
## y[375]    -5.305318e+00 3.432422e-03 1.025380e-01 -5.511843e+00 -5.371489e+00 -5.305439e+00 -5.236479e+00 -5.098832e+00  892.418012 1.0039720
## y[376]    -5.448177e+00 3.594847e-03 1.025300e-01 -5.653727e+00 -5.512979e+00 -5.448540e+00 -5.379575e+00 -5.252290e+00  813.469059 1.0038555
## y[377]    -5.564362e+00 3.534028e-03 1.035055e-01 -5.777012e+00 -5.632972e+00 -5.563712e+00 -5.493000e+00 -5.366568e+00  857.801352 1.0031652
## y[378]    -5.652631e+00 3.555832e-03 1.040068e-01 -5.864573e+00 -5.721069e+00 -5.649779e+00 -5.580679e+00 -5.455097e+00  855.542207 1.0025876
## y[379]    -5.713105e+00 3.545448e-03 1.029446e-01 -5.922910e+00 -5.780254e+00 -5.712461e+00 -5.642785e+00 -5.519249e+00  843.073150 1.0024361
## y[380]    -5.744965e+00 3.501119e-03 1.027043e-01 -5.949978e+00 -5.811370e+00 -5.745672e+00 -5.674847e+00 -5.544202e+00  860.524441 1.0017757
## y[381]    -5.750407e+00 3.520170e-03 1.025563e-01 -5.957194e+00 -5.816911e+00 -5.752749e+00 -5.679701e+00 -5.549648e+00  848.784932 1.0017842
## y[382]    -5.726830e+00 3.458954e-03 1.024739e-01 -5.929979e+00 -5.795315e+00 -5.729031e+00 -5.658356e+00 -5.524666e+00  877.681311 1.0020302
## y[383]    -5.674396e+00 3.457866e-03 1.017597e-01 -5.875495e+00 -5.743028e+00 -5.675824e+00 -5.607003e+00 -5.479405e+00  866.034905 1.0018393
## y[384]    -5.593816e+00 3.469249e-03 1.012423e-01 -5.789389e+00 -5.664338e+00 -5.593857e+00 -5.525129e+00 -5.394231e+00  851.634113 1.0016927
## y[385]    -5.484184e+00 3.427049e-03 1.001007e-01 -5.679685e+00 -5.552281e+00 -5.483842e+00 -5.417620e+00 -5.287241e+00  853.165683 1.0014834
## y[386]    -5.347955e+00 3.353321e-03 9.889380e-02 -5.536239e+00 -5.414401e+00 -5.349878e+00 -5.277283e+00 -5.156342e+00  869.736544 1.0016583
## y[387]    -5.184093e+00 3.281752e-03 9.798315e-02 -5.368427e+00 -5.248386e+00 -5.186667e+00 -5.114060e+00 -4.995175e+00  891.438469 1.0014262
## y[388]    -4.993477e+00 3.219342e-03 9.600417e-02 -5.178820e+00 -5.058658e+00 -4.996439e+00 -4.923999e+00 -4.809656e+00  889.295272 1.0008157
## y[389]    -4.776421e+00 3.134618e-03 9.445882e-02 -4.957537e+00 -4.839062e+00 -4.778035e+00 -4.708175e+00 -4.587602e+00  908.062567 1.0002382
## y[390]    -4.534217e+00 3.110511e-03 9.274768e-02 -4.715858e+00 -4.596098e+00 -4.534425e+00 -4.471437e+00 -4.351503e+00  889.083375 1.0000281
## y[391]    -4.267137e+00 3.003877e-03 9.060036e-02 -4.442671e+00 -4.326695e+00 -4.268698e+00 -4.208721e+00 -4.084574e+00  909.694478 1.0005704
## y[392]    -3.978024e+00 2.911849e-03 8.931069e-02 -4.149169e+00 -4.039496e+00 -3.980912e+00 -3.918976e+00 -3.796180e+00  940.738845 1.0004528
## y[393]    -3.668089e+00 2.794563e-03 8.781898e-02 -3.835724e+00 -3.726942e+00 -3.670885e+00 -3.608701e+00 -3.488132e+00  987.527009 0.9993475
## y[394]    -3.337165e+00 2.897767e-03 8.740176e-02 -3.505278e+00 -3.394440e+00 -3.339478e+00 -3.277012e+00 -3.165117e+00  909.732161 0.9994845
## y[395]    -2.988033e+00 2.934387e-03 8.603430e-02 -3.160163e+00 -3.043924e+00 -2.990726e+00 -2.931023e+00 -2.812765e+00  859.624126 1.0009418
## y[396]    -2.622875e+00 2.884806e-03 8.598433e-02 -2.786984e+00 -2.679502e+00 -2.624740e+00 -2.564885e+00 -2.441768e+00  888.393218 1.0019067
## y[397]    -2.241828e+00 3.106617e-03 8.648257e-02 -2.408231e+00 -2.298273e+00 -2.245200e+00 -2.185739e+00 -2.056621e+00  774.964154 1.0033886
## y[398]    -1.847672e+00 3.217304e-03 8.564102e-02 -2.012239e+00 -1.903889e+00 -1.851366e+00 -1.793186e+00 -1.665413e+00  708.564681 1.0057547
## y[399]    -1.442817e+00 3.376911e-03 8.435290e-02 -1.605292e+00 -1.498648e+00 -1.445666e+00 -1.390154e+00 -1.269467e+00  623.965647 1.0089942
## y[400]    -1.028743e+00 4.915697e-03 8.395957e-02 -1.185455e+00 -1.084720e+00 -1.030657e+00 -9.745091e-01 -8.494059e-01  291.722636 1.0134851
## y[401]    -6.071918e-01 5.752743e-03 8.367896e-02 -7.586022e-01 -6.638121e-01 -6.082171e-01 -5.547161e-01 -4.342753e-01  211.583895 1.0186186
## y[402]    -1.797642e-01 6.285178e-03 8.418444e-02 -3.346228e-01 -2.368321e-01 -1.823757e-01 -1.277296e-01 -2.076448e-03  179.402489 1.0205797
## y[403]     2.502415e-01 7.103647e-03 8.492696e-02  9.725453e-02  1.938584e-01  2.463425e-01  2.988640e-01  4.422438e-01  142.931646 1.0265186
## y[404]     6.811199e-01 7.880983e-03 8.595009e-02  5.264200e-01  6.237609e-01  6.775833e-01  7.296707e-01  8.691428e-01  118.941059 1.0313360
## y[405]     1.110784e+00 9.025066e-03 8.729733e-02  9.485938e-01  1.052339e+00  1.107619e+00  1.161447e+00  1.301545e+00   93.562358 1.0373001
## y[406]     1.536543e+00 9.466521e-03 8.891674e-02  1.372932e+00  1.476884e+00  1.532972e+00  1.587374e+00  1.733120e+00   88.223903 1.0396647
## y[407]     1.955464e+00 9.407422e-03 9.035274e-02  1.789516e+00  1.895009e+00  1.952034e+00  2.008983e+00  2.145350e+00   92.244694 1.0396175
## y[408]     2.368123e+00 9.722857e-03 9.209045e-02  2.197017e+00  2.307504e+00  2.364534e+00  2.425414e+00  2.574636e+00   89.710118 1.0402600
## y[409]     2.769602e+00 8.545864e-03 9.381781e-02  2.595542e+00  2.707421e+00  2.765767e+00  2.828588e+00  2.971743e+00  120.519862 1.0359939
## y[410]     3.159182e+00 7.512891e-03 9.598263e-02  2.977916e+00  3.095744e+00  3.156578e+00  3.218643e+00  3.360178e+00  163.219147 1.0339700
## y[411]     3.535272e+00 7.146690e-03 9.811382e-02  3.351698e+00  3.468566e+00  3.532742e+00  3.597351e+00  3.742204e+00  188.473558 1.0321268
## y[412]     3.894086e+00 6.110943e-03 9.881790e-02  3.706956e+00  3.825485e+00  3.892861e+00  3.955203e+00  4.094547e+00  261.489787 1.0253192
## y[413]     4.236148e+00 5.492759e-03 9.967192e-02  4.048798e+00  4.169533e+00  4.235381e+00  4.298556e+00  4.442375e+00  329.279391 1.0210553
## y[414]     4.559023e+00 5.294724e-03 1.016634e-01  4.364482e+00  4.492436e+00  4.556801e+00  4.622219e+00  4.770064e+00  368.674357 1.0184891
## y[415]     4.860305e+00 4.867810e-03 1.039651e-01  4.661690e+00  4.792243e+00  4.857521e+00  4.927083e+00  5.074530e+00  456.150518 1.0154967
## y[416]     5.139089e+00 4.658332e-03 1.062045e-01  4.935900e+00  5.069681e+00  5.134848e+00  5.207992e+00  5.350182e+00  519.786776 1.0124768
## y[417]     5.393974e+00 4.246610e-03 1.069284e-01  5.192508e+00  5.322473e+00  5.390939e+00  5.465397e+00  5.609704e+00  634.018368 1.0099693
## y[418]     5.624145e+00 4.120102e-03 1.083335e-01  5.416532e+00  5.551723e+00  5.621594e+00  5.695560e+00  5.843560e+00  691.368043 1.0087189
## y[419]     5.826963e+00 3.952973e-03 1.091550e-01  5.612007e+00  5.754229e+00  5.823943e+00  5.899896e+00  6.046015e+00  762.499798 1.0069452
## y[420]     6.002265e+00 4.012161e-03 1.098815e-01  5.791949e+00  5.930774e+00  5.999115e+00  6.075629e+00  6.218095e+00  750.053973 1.0054887
## y[421]     6.148301e+00 3.993665e-03 1.108949e-01  5.934406e+00  6.076521e+00  6.145040e+00  6.221989e+00  6.369799e+00  771.045037 1.0039836
## y[422]     6.264756e+00 3.994247e-03 1.111196e-01  6.053878e+00  6.192360e+00  6.262225e+00  6.338180e+00  6.478649e+00  773.947668 1.0032768
## y[423]     6.349592e+00 4.017854e-03 1.119683e-01  6.137167e+00  6.270774e+00  6.348176e+00  6.424125e+00  6.559832e+00  776.608173 1.0027930
## y[424]     6.404256e+00 4.046807e-03 1.130682e-01  6.186553e+00  6.327251e+00  6.405073e+00  6.477912e+00  6.621241e+00  780.649446 1.0025844
## y[425]     6.426672e+00 4.064030e-03 1.143399e-01  6.207460e+00  6.348745e+00  6.430245e+00  6.503495e+00  6.642318e+00  791.556027 1.0027582
## y[426]     6.418248e+00 4.011210e-03 1.134371e-01  6.197878e+00  6.338762e+00  6.420429e+00  6.495925e+00  6.635155e+00  799.760122 1.0028237
## y[427]     6.377492e+00 4.206891e-03 1.132740e-01  6.161432e+00  6.298768e+00  6.378868e+00  6.453606e+00  6.594346e+00  725.000376 1.0044282
## y[428]     6.304964e+00 4.448201e-03 1.134409e-01  6.085611e+00  6.226983e+00  6.305479e+00  6.383527e+00  6.526933e+00  650.385296 1.0062234
## y[429]     6.201733e+00 4.488192e-03 1.119080e-01  5.989972e+00  6.124687e+00  6.202438e+00  6.273728e+00  6.416096e+00  621.698290 1.0079158
## y[430]     6.066981e+00 4.373181e-03 1.103700e-01  5.863310e+00  5.991235e+00  6.066542e+00  6.142503e+00  6.279820e+00  636.953012 1.0088633
## y[431]     5.900815e+00 4.398704e-03 1.093857e-01  5.694640e+00  5.826583e+00  5.898748e+00  5.976868e+00  6.111978e+00  618.402644 1.0113764
## y[432]     5.705179e+00 4.479190e-03 1.082796e-01  5.497385e+00  5.630568e+00  5.704876e+00  5.779241e+00  5.916005e+00  584.378249 1.0147648
## y[433]     5.479844e+00 4.864867e-03 1.065408e-01  5.274151e+00  5.404086e+00  5.478556e+00  5.553221e+00  5.683033e+00  479.611458 1.0180825
## y[434]     5.227311e+00 5.259103e-03 1.047307e-01  5.023076e+00  5.153752e+00  5.228149e+00  5.300579e+00  5.428755e+00  396.574482 1.0187830
## y[435]     4.947219e+00 5.243706e-03 1.033155e-01  4.743973e+00  4.876176e+00  4.949237e+00  5.019929e+00  5.142924e+00  388.198807 1.0193816
## y[436]     4.641311e+00 5.329090e-03 1.012480e-01  4.444935e+00  4.573224e+00  4.641893e+00  4.711073e+00  4.835824e+00  360.966770 1.0197675
## y[437]     4.311883e+00 5.333475e-03 9.870979e-02  4.116608e+00  4.245045e+00  4.312724e+00  4.377868e+00  4.499452e+00  342.531029 1.0201661
## y[438]     3.959220e+00 4.983291e-03 9.740336e-02  3.760744e+00  3.895847e+00  3.960687e+00  4.024352e+00  4.145359e+00  382.045743 1.0196169
## y[439]     3.585462e+00 4.926613e-03 9.543840e-02  3.395494e+00  3.522112e+00  3.585790e+00  3.651104e+00  3.763518e+00  375.274756 1.0192705
## y[440]     3.191514e+00 4.983666e-03 9.391914e-02  3.002386e+00  3.129062e+00  3.193139e+00  3.254574e+00  3.368839e+00  355.148852 1.0206188
## y[441]     2.780424e+00 4.558833e-03 9.227227e-02  2.591287e+00  2.718003e+00  2.781976e+00  2.840788e+00  2.958610e+00  409.670816 1.0180632
## y[442]     2.353004e+00 3.759379e-03 9.057009e-02  2.171927e+00  2.294664e+00  2.354781e+00  2.414365e+00  2.528469e+00  580.413394 1.0178511
## y[443]     1.911952e+00 3.369510e-03 8.980939e-02  1.729571e+00  1.855769e+00  1.913732e+00  1.972046e+00  2.083840e+00  710.411676 1.0148330
## y[444]     1.458741e+00 3.506719e-03 8.937890e-02  1.272254e+00  1.401393e+00  1.459070e+00  1.518207e+00  1.633713e+00  649.632849 1.0132825
## y[445]     9.962201e-01 3.200403e-03 8.883746e-02  8.193446e-01  9.402720e-01  9.962616e-01  1.054301e+00  1.174026e+00  770.518248 1.0084622
## y[446]     5.273803e-01 3.047959e-03 8.847065e-02  3.540446e-01  4.739508e-01  5.291694e-01  5.841959e-01  7.086240e-01  842.520110 1.0051878
## y[447]     5.416667e-02 2.741791e-03 8.793312e-02 -1.214640e-01 -6.245639e-04  5.361996e-02  1.085742e-01  2.401325e-01 1028.575643 1.0023952
## y[448]    -4.228654e-01 2.784628e-03 8.863098e-02 -5.953635e-01 -4.799413e-01 -4.228971e-01 -3.674979e-01 -2.402698e-01 1013.063465 1.0011560
## y[449]    -9.008027e-01 2.855885e-03 8.941860e-02 -1.073698e+00 -9.588185e-01 -9.002725e-01 -8.429370e-01 -7.191225e-01  980.334517 1.0016877
## y[450]    -1.376839e+00 2.887791e-03 9.118403e-02 -1.551257e+00 -1.437732e+00 -1.376006e+00 -1.320480e+00 -1.188734e+00  997.025115 1.0016678
## y[451]    -1.847323e+00 2.990113e-03 9.266786e-02 -2.024175e+00 -1.907928e+00 -1.846684e+00 -1.789096e+00 -1.660113e+00  960.468360 1.0027964
## y[452]    -2.311222e+00 3.146390e-03 9.486792e-02 -2.494747e+00 -2.376028e+00 -2.311872e+00 -2.249335e+00 -2.118444e+00  909.104191 1.0052257
## y[453]    -2.766113e+00 3.243680e-03 9.822917e-02 -2.960232e+00 -2.831727e+00 -2.766634e+00 -2.700490e+00 -2.564385e+00  917.075233 1.0060756
## y[454]    -3.210540e+00 3.447149e-03 9.987821e-02 -3.407449e+00 -3.277440e+00 -3.212219e+00 -3.141619e+00 -3.014932e+00  839.501321 1.0067071
## y[455]    -3.641060e+00 3.739860e-03 1.022705e-01 -3.844110e+00 -3.709919e+00 -3.642755e+00 -3.572772e+00 -3.437761e+00  747.808384 1.0070483
## y[456]    -4.056659e+00 3.826134e-03 1.050628e-01 -4.261241e+00 -4.126515e+00 -4.056752e+00 -3.986340e+00 -3.846213e+00  754.011214 1.0068102
## y[457]    -4.454876e+00 3.949441e-03 1.071114e-01 -4.670636e+00 -4.527977e+00 -4.454144e+00 -4.384588e+00 -4.239130e+00  735.528725 1.0073121
## y[458]    -4.832803e+00 3.905643e-03 1.098238e-01 -5.053881e+00 -4.905366e+00 -4.834457e+00 -4.760589e+00 -4.609039e+00  790.693344 1.0068546
## y[459]    -5.189760e+00 4.091328e-03 1.123848e-01 -5.412417e+00 -5.267421e+00 -5.189949e+00 -5.114766e+00 -4.965419e+00  754.547811 1.0064053
## y[460]    -5.522686e+00 4.151819e-03 1.143665e-01 -5.750082e+00 -5.599014e+00 -5.524833e+00 -5.445897e+00 -5.302318e+00  758.788482 1.0061487
## y[461]    -5.830355e+00 4.140265e-03 1.165163e-01 -6.060412e+00 -5.908798e+00 -5.831488e+00 -5.749774e+00 -5.612259e+00  791.985230 1.0061448
## y[462]    -6.111627e+00 4.227695e-03 1.182391e-01 -6.347994e+00 -6.193135e+00 -6.113457e+00 -6.029490e+00 -5.890181e+00  782.195168 1.0053889
## y[463]    -6.363701e+00 4.281035e-03 1.208457e-01 -6.605979e+00 -6.448349e+00 -6.365228e+00 -6.279880e+00 -6.133689e+00  796.828684 1.0041120
## y[464]    -6.585301e+00 4.375620e-03 1.227318e-01 -6.827150e+00 -6.670164e+00 -6.587145e+00 -6.502069e+00 -6.348801e+00  786.746566 1.0038903
## y[465]    -6.776585e+00 4.433967e-03 1.249581e-01 -7.016463e+00 -6.859945e+00 -6.777465e+00 -6.691749e+00 -6.534118e+00  794.226140 1.0042691
## y[466]    -6.933474e+00 4.449263e-03 1.253247e-01 -7.174360e+00 -7.017355e+00 -6.933477e+00 -6.845140e+00 -6.693225e+00  793.408914 1.0048983
## y[467]    -7.058167e+00 4.448885e-03 1.267681e-01 -7.298388e+00 -7.144289e+00 -7.058059e+00 -6.970004e+00 -6.814751e+00  811.927872 1.0054895
## y[468]    -7.148503e+00 4.701793e-03 1.275485e-01 -7.395328e+00 -7.235054e+00 -7.148226e+00 -7.059913e+00 -6.903078e+00  735.908700 1.0067951
## y[469]    -7.203065e+00 4.746165e-03 1.284625e-01 -7.450075e+00 -7.290497e+00 -7.204399e+00 -7.114375e+00 -6.954225e+00  732.600800 1.0073201
## y[470]    -7.222251e+00 4.860699e-03 1.289746e-01 -7.469777e+00 -7.309870e+00 -7.222770e+00 -7.132559e+00 -6.968480e+00  704.062468 1.0079039
## y[471]    -7.205458e+00 4.939153e-03 1.291424e-01 -7.451073e+00 -7.294983e+00 -7.205049e+00 -7.115843e+00 -6.956635e+00  683.648377 1.0088174
## y[472]    -7.152725e+00 5.116782e-03 1.287974e-01 -7.396721e+00 -7.238997e+00 -7.154062e+00 -7.064208e+00 -6.902479e+00  633.607739 1.0102346
## y[473]    -7.063638e+00 5.109104e-03 1.285744e-01 -7.309599e+00 -7.149090e+00 -7.066419e+00 -6.974622e+00 -6.813683e+00  633.315088 1.0117999
## y[474]    -6.939609e+00 5.072703e-03 1.280409e-01 -7.182877e+00 -7.025804e+00 -6.943019e+00 -6.852746e+00 -6.687342e+00  637.116279 1.0139467
## y[475]    -6.780082e+00 5.101713e-03 1.265345e-01 -7.019233e+00 -6.865063e+00 -6.783606e+00 -6.689945e+00 -6.535809e+00  615.157026 1.0161737
## y[476]    -6.586308e+00 5.018348e-03 1.260869e-01 -6.827976e+00 -6.668311e+00 -6.588328e+00 -6.495693e+00 -6.348280e+00  631.274929 1.0173788
## y[477]    -6.358720e+00 5.062233e-03 1.254378e-01 -6.599556e+00 -6.446642e+00 -6.360449e+00 -6.270301e+00 -6.111585e+00  614.005663 1.0194451
## y[478]    -6.097861e+00 5.177291e-03 1.248060e-01 -6.340382e+00 -6.184891e+00 -6.099733e+00 -6.008370e+00 -5.856970e+00  581.120010 1.0205616
## y[479]    -5.807420e+00 6.346724e-03 1.236832e-01 -6.047333e+00 -5.892090e+00 -5.808799e+00 -5.717356e+00 -5.564618e+00  379.771301 1.0233113
## y[480]    -5.485599e+00 6.941260e-03 1.223207e-01 -5.715324e+00 -5.569651e+00 -5.486057e+00 -5.400375e+00 -5.247698e+00  310.543965 1.0259090
## y[481]    -5.134626e+00 6.211190e-03 1.220467e-01 -5.368179e+00 -5.217010e+00 -5.137084e+00 -5.047134e+00 -4.896191e+00  386.102496 1.0261405
## y[482]    -4.756559e+00 6.936383e-03 1.207648e-01 -4.992201e+00 -4.838935e+00 -4.756404e+00 -4.674230e+00 -4.523734e+00  303.119794 1.0271572
## y[483]    -4.352650e+00 7.762525e-03 1.201470e-01 -4.586513e+00 -4.431323e+00 -4.350643e+00 -4.273792e+00 -4.122384e+00  239.563239 1.0271613
## y[484]    -3.924970e+00 7.553823e-03 1.198639e-01 -4.158287e+00 -4.001420e+00 -3.924386e+00 -3.845390e+00 -3.696061e+00  251.792810 1.0280054
## y[485]    -3.475698e+00 7.682934e-03 1.199829e-01 -3.716767e+00 -3.549982e+00 -3.474881e+00 -3.399593e+00 -3.248470e+00  243.884625 1.0285204
## y[486]    -3.007049e+00 8.894048e-03 1.199193e-01 -3.247619e+00 -3.084112e+00 -3.004828e+00 -2.926411e+00 -2.778266e+00  181.794003 1.0308584
## y[487]    -2.520288e+00 8.124840e-03 1.200852e-01 -2.760269e+00 -2.596629e+00 -2.518742e+00 -2.441069e+00 -2.291026e+00  218.448578 1.0292001
## y[488]    -2.019114e+00 8.060611e-03 1.206091e-01 -2.259215e+00 -2.095846e+00 -2.016106e+00 -1.940047e+00 -1.791119e+00  223.884651 1.0286428
## y[489]    -1.504946e+00 7.700196e-03 1.212717e-01 -1.748904e+00 -1.579346e+00 -1.503272e+00 -1.423361e+00 -1.270798e+00  248.036169 1.0273398
## y[490]    -9.794153e-01 6.056667e-03 1.226861e-01 -1.225863e+00 -1.055123e+00 -9.766534e-01 -8.977862e-01 -7.439109e-01  410.320904 1.0218263
## y[491]    -4.464521e-01 5.341470e-03 1.230739e-01 -6.915370e-01 -5.248580e-01 -4.433708e-01 -3.638398e-01 -2.151261e-01  530.897487 1.0191144
## y[492]     9.188079e-02 3.957601e-03 1.239158e-01 -1.501190e-01  1.398457e-02  9.465974e-02  1.738274e-01  3.267843e-01  980.369146 1.0132733
## y[493]     6.325283e-01 3.796911e-03 1.262945e-01  3.775100e-01  5.539319e-01  6.352488e-01  7.196832e-01  8.717249e-01 1106.389099 1.0099505
## y[494]     1.173381e+00 3.681869e-03 1.282797e-01  9.113382e-01  1.090559e+00  1.176296e+00  1.261647e+00  1.418311e+00 1213.889571 1.0059965
## y[495]     1.711463e+00 3.624300e-03 1.308725e-01  1.452508e+00  1.627420e+00  1.712799e+00  1.799680e+00  1.958630e+00 1303.912502 1.0029627
## y[496]     2.243650e+00 3.684176e-03 1.340014e-01  1.977415e+00  2.157301e+00  2.244522e+00  2.333275e+00  2.509759e+00 1322.933931 1.0007402
## y[497]     2.767775e+00 3.750595e-03 1.361182e-01  2.505948e+00  2.677826e+00  2.770351e+00  2.856928e+00  3.033508e+00 1317.139976 0.9998065
## y[498]     3.278941e+00 3.887059e-03 1.389878e-01  3.010931e+00  3.189030e+00  3.279934e+00  3.370113e+00  3.554967e+00 1278.529731 0.9998958
## y[499]     3.777621e+00 4.042767e-03 1.399243e-01  3.506428e+00  3.688005e+00  3.777031e+00  3.870539e+00  4.053012e+00 1197.923392 1.0008993
## y[500]     4.258251e+00 4.201316e-03 1.429225e-01  3.976754e+00  4.164305e+00  4.257375e+00  4.353300e+00  4.547949e+00 1157.258676 1.0020165
## lp__       3.154266e+03 2.042118e+02 4.474804e+02  2.340477e+03  2.815106e+03  3.176430e+03  3.427675e+03  4.028442e+03    4.801602 2.3592771

Posterior predictive sampling

sim_data <- function (x0, y0, alpha, beta, sigma_xy, sigma_eps, N) {
    xy <- matrix(nrow=N, ncol=2)
    xy[1,] <- c(x0, y0)
    for (k in 1:(N-1)) {
        xy[k+1,] <- (xy[k,] 
                    + c(alpha * xy[k,2],
                        (-1) * beta * xy[k,1])
                    + rnorm(2, 0, sigma_xy))
    }
    XY <- xy + rnorm(N*2, 0, sigma_eps)
    return(XY)
}

Real data in red:

Note: this is an autoregressive model with measurement error, and it’s (now) possible to fit this model in brms, using a multivariate model, ar() terms for the “autoregressive” part, and mi() terms for the measurement error:

(ar_fit <- brm( mvbf(
        Y | mi() ~ 0 + X + ar(),
        X | mi() ~ 0 + Y + ar(),
        rescor=FALSE
    ),
    data=osc_data, chains=2
))

## Compiling Stan program...

## Start sampling

##  Family: MV(gaussian, gaussian) 
##   Links: mu = identity; sigma = identity
##          mu = identity; sigma = identity 
## Formula: Y | mi() ~ 0 + X + ar() 
##          X | mi() ~ 0 + Y + ar() 
##    Data: osc_data (Number of observations: 500) 
##   Draws: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup draws = 2000
## 
## Correlation Structures:
##         Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## ar_Y[1]     0.91      0.02     0.87     0.95 1.00     2744     1401
## ar_X[1]     0.95      0.01     0.92     0.98 1.00     2727     1543
## 
## Population-Level Effects: 
##     Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Y_X     0.02      0.04    -0.06     0.09 1.00     2400     1605
## X_Y     0.02      0.05    -0.07     0.12 1.00     2391     1481
## 
## Family Specific Parameters: 
##         Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma_Y     1.44      0.05     1.36     1.53 1.00     2681     1461
## sigma_X     1.58      0.05     1.48     1.68 1.00     2170     1631
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

ar_fit

##  Family: MV(gaussian, gaussian) 
##   Links: mu = identity; sigma = identity
##          mu = identity; sigma = identity 
## Formula: Y | mi() ~ 0 + X + ar() 
##          X | mi() ~ 0 + Y + ar() 
##    Data: osc_data (Number of observations: 500) 
##   Draws: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup draws = 2000
## 
## Correlation Structures:
##         Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## ar_Y[1]     0.91      0.02     0.87     0.95 1.00     2744     1401
## ar_X[1]     0.95      0.01     0.92     0.98 1.00     2727     1543
## 
## Population-Level Effects: 
##     Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Y_X     0.02      0.04    -0.06     0.09 1.00     2400     1605
## X_Y     0.02      0.05    -0.07     0.12 1.00     2391     1481
## 
## Family Specific Parameters: 
##         Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma_Y     1.44      0.05     1.36     1.53 1.00     2681     1461
## sigma_X     1.58      0.05     1.48     1.68 1.00     2170     1631
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).