This one is a quick one and based on some work that I have already done. Given the ongoing controversy about President Trump potentially using publically held funds to strong arm a foreign entity for personal and political gain, I figured it was time to do some state-space modeling on approval polls. This will be a quick one just because I want an answer.
The Data
I am going to get some approval polling data from fivethirtyeight. I sincerely appreciate that they put this data out for others to use. Do I wish it had some weights and more data cooked into it? Absolutely. Do I have the resources to do something better? No, I do not. But anyways, thanks fivethirtyeight!
suppressPackageStartupMessages(library(tidyverse))
theme_set(theme_minimal())
dat <- read_csv("https://projects.fivethirtyeight.com/polls-page/president_approval_polls.csv")Multiple Polls on Multiple Days?
In order to build the data for Stan, it is necessary to make some wide data frame. Additionally, I need to calculate some standard errors. Just a reminder for those at home, the standard error for a binomial distribution is:
\[SE = \sqrt\frac{p(1-p)}{n}\]
I’m also going to use some of the new pivot_* functions from {tidyr}. They are great! These tools bring back some of the functionality that was missing when {tidyr} emerged from {reshape2}.
library(lubridate)
dat_range <- crossing(seq(min(mdy(dat$end_date)),
max(mdy("11/1/2019")),
"1 day") %>%
enframe(name = NULL) %>%
set_names("date_range"), pollster = unique(dat$pollster))
formatted_data <- dat %>%
mutate(my_end = lubridate::mdy(end_date)) %>%
select(my_end, yes, sample_size, pollster) %>%
mutate(polling_var = sqrt(.5 * (1-.5)/sample_size)*100) %>%
right_join(dat_range, by = c("my_end" = "date_range", "pollster"))
formatted_data[is.na(formatted_data)] <- -9
sigma <- formatted_data %>%
select(my_end, pollster, polling_var) %>%
pivot_wider(names_from = pollster,
values_from = polling_var,
values_fn = list(polling_var = max)) %>%
select(-my_end) %>%
as.matrix()
y <- formatted_data %>%
select(my_end, pollster, yes) %>%
pivot_wider(names_from = pollster,
values_from = yes,
values_fn = list(yes = max)) %>%
select(-my_end) %>%
as.matrix()Our Model
This is the same model from this blog post courtsey of James Savage and Peter Ellis.
// Base Syntax from James Savage at https://github.com/khakieconomics/stanecon_short_course/blob/80263f84ebe95be3247e591515ea1ead84f26e3f/03-fun_time_series_models.Rmd
//and modification inspired by Peter Ellis at https://github.com/ellisp/ozfedelect/blob/master/model-2pp/model-2pp.R
data {
int polls; // number of polls
int T; // number of days
matrix[T, polls] Y; // polls
matrix[T, polls] sigma; // polls standard deviations
real inflator; // amount by which to multiply the standard error of polls
real initial_prior;
real random_walk_sd;
real mu_sigma;
}
parameters {
vector[T] mu; // the mean of the polls
real<lower = 0> tau; // the standard deviation of the random effects
matrix[T, polls] shrunken_polls;
}
model {
// prior on initial difference
mu[1] ~ normal(initial_prior, mu_sigma);
tau ~ student_t(4, 0, 5);
// state model
for(t in 2:T) {
mu[t] ~ normal(mu[t-1], random_walk_sd);
}
// measurement model
for(t in 1:T) {
for(p in 1:polls) {
if(Y[t, p] != -9) {
Y[t,p]~ normal(shrunken_polls[t, p], sigma[t,p] * inflator);
shrunken_polls[t, p] ~ normal(mu[t], tau);
} else {
shrunken_polls[t, p] ~ normal(0, 1);
}
}
}
}
Prep the Data
Now we can put the data in the proper format for Stan. I’m also going to supply the 2016 voteshare as the initial prior. This is probably a favourable place to start.
library(rstan)
rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())
approval_data <- list(
T = nrow(y),
polls = ncol(sigma),
Y = y,
sigma = sigma,
initial_prior = 46, # 2016 Election Results
random_walk_sd = 0.2,
mu_sigma = 1,
inflator =sqrt(2)
)Run the Model
Now we can run the model. Caution, this takes a good while to run…oh how I miss having a cluster….
trump_model <- sampling(sstrump,
data = approval_data,
iter = 1000,
refresh = 0,
chains = 2,
control = list(adapt_delta = .95,
max_treedepth = 15))Did It Converge?
I’m just going to look quickly at some of the Rhat values. I see that some of my ESS are a little lower than I would like. This isn’t completely surprising given the sparsity of data (57 different polls).
print(trump_model, pars = "mu")
Inference for Stan model: a643d45063962397b14f15d26d605751.
2 chains, each with iter=1000; warmup=500; thin=1;
post-warmup draws per chain=500, total post-warmup draws=1000.
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
mu[1] 46.59 0.03 0.52 45.55 46.24 46.58 46.96 47.56 310 1.01
mu[2] 46.62 0.03 0.50 45.65 46.27 46.63 46.98 47.57 283 1.01
mu[3] 46.65 0.03 0.50 45.68 46.33 46.66 47.00 47.57 267 1.01
mu[4] 46.67 0.03 0.48 45.73 46.37 46.67 46.99 47.59 222 1.01
mu[5] 46.68 0.03 0.47 45.75 46.37 46.69 47.01 47.58 213 1.01
mu[6] 46.69 0.03 0.47 45.75 46.38 46.71 47.02 47.56 255 1.01
mu[7] 46.71 0.03 0.46 45.75 46.39 46.73 47.07 47.57 233 1.01
mu[8] 46.75 0.03 0.44 45.82 46.47 46.76 47.07 47.54 199 1.01
mu[9] 46.75 0.03 0.43 45.82 46.44 46.77 47.06 47.52 168 1.02
mu[10] 46.73 0.04 0.43 45.85 46.46 46.74 47.03 47.53 140 1.01
mu[11] 46.69 0.04 0.42 45.83 46.42 46.69 46.98 47.50 128 1.01
mu[12] 46.64 0.03 0.41 45.82 46.37 46.63 46.93 47.39 153 1.02
mu[13] 46.63 0.04 0.41 45.79 46.36 46.63 46.91 47.40 119 1.02
mu[14] 46.61 0.04 0.41 45.75 46.34 46.62 46.89 47.39 119 1.02
mu[15] 46.60 0.04 0.41 45.75 46.34 46.62 46.88 47.37 129 1.02
mu[16] 46.57 0.04 0.41 45.75 46.32 46.58 46.85 47.37 117 1.01
mu[17] 46.53 0.04 0.41 45.71 46.26 46.53 46.82 47.30 86 1.02
mu[18] 46.48 0.04 0.42 45.68 46.21 46.49 46.79 47.24 94 1.02
mu[19] 46.42 0.04 0.42 45.62 46.16 46.43 46.70 47.22 92 1.02
mu[20] 46.35 0.04 0.41 45.54 46.08 46.34 46.63 47.15 90 1.01
mu[21] 46.28 0.04 0.43 45.45 45.99 46.28 46.57 47.07 94 1.01
mu[22] 46.23 0.04 0.42 45.42 45.94 46.24 46.50 47.05 125 1.01
mu[23] 46.19 0.04 0.42 45.36 45.91 46.20 46.46 47.01 134 1.01
mu[24] 46.14 0.03 0.42 45.39 45.85 46.14 46.42 46.94 163 1.01
mu[25] 46.08 0.03 0.41 45.28 45.79 46.08 46.36 46.87 156 1.01
mu[26] 46.00 0.03 0.40 45.26 45.72 46.00 46.26 46.81 141 1.01
mu[27] 45.91 0.04 0.40 45.12 45.63 45.90 46.18 46.70 129 1.01
mu[28] 45.84 0.03 0.40 45.08 45.57 45.83 46.11 46.65 146 1.01
mu[29] 45.80 0.03 0.41 45.02 45.52 45.81 46.08 46.58 152 1.00
mu[30] 45.80 0.03 0.39 45.07 45.52 45.80 46.06 46.59 145 1.01
mu[31] 45.78 0.03 0.38 45.05 45.52 45.78 46.05 46.50 149 1.01
mu[32] 45.80 0.03 0.40 45.05 45.53 45.80 46.08 46.61 162 1.00
mu[33] 45.82 0.03 0.41 45.03 45.55 45.81 46.09 46.61 171 1.00
mu[34] 45.82 0.03 0.42 44.99 45.54 45.83 46.11 46.62 180 1.00
mu[35] 45.84 0.03 0.42 45.04 45.57 45.84 46.11 46.61 162 1.01
mu[36] 45.86 0.03 0.43 45.02 45.58 45.88 46.14 46.70 177 1.00
mu[37] 45.87 0.03 0.42 45.08 45.60 45.88 46.15 46.71 160 1.01
mu[38] 45.86 0.04 0.42 44.98 45.60 45.87 46.12 46.67 137 1.01
mu[39] 45.85 0.03 0.42 45.00 45.59 45.87 46.11 46.62 181 1.01
mu[40] 45.81 0.03 0.42 44.95 45.54 45.83 46.10 46.60 170 1.01
mu[41] 45.76 0.04 0.43 44.93 45.48 45.78 46.04 46.57 138 1.02
mu[42] 45.72 0.04 0.42 44.86 45.45 45.73 45.99 46.51 126 1.02
mu[43] 45.70 0.03 0.42 44.83 45.42 45.73 45.98 46.51 159 1.02
mu[44] 45.65 0.03 0.42 44.76 45.38 45.67 45.92 46.46 168 1.01
mu[45] 45.57 0.03 0.42 44.71 45.29 45.58 45.86 46.37 172 1.01
mu[46] 45.48 0.03 0.42 44.62 45.19 45.49 45.76 46.28 176 1.01
mu[47] 45.38 0.03 0.42 44.55 45.09 45.38 45.66 46.17 174 1.01
mu[48] 45.26 0.03 0.42 44.43 44.97 45.27 45.55 46.07 182 1.01
mu[49] 45.13 0.03 0.41 44.32 44.84 45.13 45.42 45.91 191 1.00
mu[50] 44.98 0.03 0.41 44.18 44.70 44.98 45.29 45.76 201 1.00
mu[51] 44.88 0.03 0.41 44.06 44.61 44.90 45.16 45.66 210 1.00
mu[52] 44.76 0.03 0.41 43.94 44.49 44.77 45.05 45.58 228 1.00
mu[53] 44.65 0.03 0.41 43.84 44.39 44.67 44.93 45.41 223 1.00
mu[54] 44.56 0.03 0.41 43.72 44.30 44.56 44.85 45.34 222 1.00
mu[55] 44.43 0.03 0.41 43.62 44.15 44.45 44.70 45.22 239 1.00
mu[56] 44.29 0.03 0.41 43.49 44.02 44.29 44.57 45.07 235 1.00
mu[57] 44.19 0.03 0.40 43.41 43.92 44.21 44.45 44.95 234 1.00
mu[58] 44.05 0.03 0.41 43.22 43.77 44.04 44.32 44.85 248 1.00
mu[59] 43.88 0.03 0.40 43.13 43.61 43.87 44.15 44.68 244 1.00
mu[60] 43.73 0.03 0.40 42.99 43.46 43.72 44.00 44.55 254 1.00
mu[61] 43.57 0.02 0.39 42.83 43.30 43.57 43.84 44.34 270 1.00
mu[62] 43.42 0.02 0.40 42.66 43.14 43.42 43.70 44.20 267 1.00
mu[63] 43.26 0.02 0.40 42.44 42.99 43.27 43.54 44.02 274 1.00
mu[64] 43.11 0.03 0.41 42.25 42.83 43.10 43.40 43.88 270 1.00
mu[65] 42.97 0.02 0.40 42.17 42.70 42.96 43.23 43.70 283 1.00
mu[66] 42.88 0.02 0.40 42.10 42.60 42.88 43.16 43.66 283 1.00
mu[67] 42.82 0.02 0.40 42.05 42.54 42.82 43.10 43.57 264 1.00
mu[68] 42.82 0.02 0.39 42.06 42.55 42.82 43.10 43.55 278 1.00
mu[69] 42.86 0.02 0.41 42.10 42.58 42.85 43.13 43.67 291 1.00
mu[70] 42.89 0.02 0.41 42.13 42.62 42.89 43.17 43.73 271 1.00
mu[71] 42.92 0.03 0.41 42.11 42.64 42.91 43.20 43.74 248 1.00
mu[72] 42.94 0.03 0.41 42.12 42.67 42.95 43.22 43.76 264 1.01
mu[73] 43.01 0.03 0.41 42.23 42.74 43.01 43.29 43.80 256 1.01
mu[74] 43.06 0.03 0.41 42.25 42.80 43.05 43.33 43.90 243 1.01
mu[75] 43.13 0.03 0.41 42.36 42.87 43.12 43.41 43.96 212 1.01
mu[76] 43.22 0.03 0.41 42.44 42.95 43.23 43.50 44.03 208 1.02
mu[77] 43.31 0.03 0.42 42.47 43.03 43.31 43.60 44.12 199 1.01
mu[78] 43.41 0.03 0.41 42.59 43.13 43.42 43.70 44.21 188 1.01
mu[79] 43.49 0.03 0.42 42.62 43.23 43.49 43.78 44.33 187 1.01
mu[80] 43.55 0.03 0.43 42.69 43.27 43.56 43.83 44.41 196 1.01
mu[81] 43.58 0.03 0.42 42.75 43.31 43.59 43.87 44.42 193 1.02
mu[82] 43.66 0.03 0.42 42.83 43.38 43.66 43.93 44.49 202 1.01
mu[83] 43.70 0.03 0.43 42.85 43.39 43.71 43.99 44.54 197 1.01
mu[84] 43.75 0.03 0.42 42.94 43.47 43.75 44.04 44.55 184 1.01
mu[85] 43.80 0.03 0.41 42.99 43.51 43.81 44.09 44.55 175 1.01
mu[86] 43.80 0.03 0.41 43.00 43.53 43.80 44.09 44.58 174 1.01
mu[87] 43.76 0.03 0.41 42.92 43.49 43.74 44.04 44.56 151 1.01
mu[88] 43.77 0.03 0.40 42.94 43.50 43.76 44.04 44.54 135 1.01
mu[89] 43.76 0.04 0.40 42.97 43.50 43.74 44.02 44.50 132 1.02
mu[90] 43.76 0.03 0.41 42.95 43.50 43.75 44.04 44.57 152 1.01
mu[91] 43.76 0.04 0.41 42.94 43.49 43.76 44.04 44.55 134 1.01
mu[92] 43.78 0.03 0.41 42.98 43.51 43.78 44.04 44.60 144 1.01
mu[93] 43.78 0.04 0.40 42.99 43.51 43.76 44.05 44.57 128 1.02
mu[94] 43.74 0.04 0.40 42.89 43.47 43.73 44.01 44.51 118 1.03
mu[95] 43.72 0.03 0.41 42.94 43.46 43.71 44.00 44.54 139 1.02
mu[96] 43.70 0.04 0.41 42.92 43.44 43.69 43.99 44.49 109 1.03
mu[97] 43.70 0.04 0.41 42.95 43.41 43.67 43.97 44.53 112 1.03
mu[98] 43.70 0.04 0.41 42.94 43.41 43.69 44.00 44.51 128 1.02
mu[99] 43.70 0.03 0.41 42.91 43.43 43.70 43.98 44.51 151 1.03
mu[100] 43.69 0.03 0.41 42.89 43.40 43.68 43.97 44.46 154 1.02
mu[101] 43.65 0.03 0.41 42.83 43.37 43.64 43.92 44.47 176 1.02
mu[102] 43.57 0.03 0.42 42.76 43.30 43.56 43.83 44.40 182 1.02
mu[103] 43.48 0.03 0.42 42.64 43.20 43.48 43.76 44.30 179 1.02
mu[104] 43.38 0.03 0.43 42.52 43.08 43.37 43.65 44.25 154 1.02
mu[105] 43.27 0.03 0.43 42.41 43.00 43.27 43.56 44.11 166 1.02
mu[106] 43.16 0.03 0.43 42.32 42.87 43.16 43.44 44.00 159 1.02
mu[107] 43.03 0.03 0.43 42.16 42.72 43.02 43.33 43.89 162 1.02
mu[108] 42.88 0.03 0.42 42.09 42.60 42.87 43.15 43.71 149 1.02
mu[109] 42.76 0.04 0.42 42.00 42.48 42.75 43.06 43.57 140 1.02
mu[110] 42.63 0.03 0.42 41.87 42.35 42.62 42.91 43.46 157 1.01
mu[111] 42.45 0.04 0.43 41.66 42.14 42.45 42.75 43.31 146 1.02
mu[112] 42.27 0.04 0.43 41.46 41.98 42.25 42.55 43.10 140 1.02
mu[113] 42.11 0.03 0.42 41.34 41.81 42.11 42.40 42.95 150 1.02
mu[114] 41.94 0.03 0.42 41.16 41.64 41.94 42.22 42.78 152 1.02
mu[115] 41.80 0.04 0.41 41.02 41.51 41.80 42.06 42.65 129 1.02
mu[116] 41.67 0.04 0.41 40.83 41.39 41.69 41.96 42.50 107 1.03
mu[117] 41.57 0.04 0.42 40.74 41.29 41.58 41.87 42.33 98 1.03
mu[118] 41.53 0.04 0.42 40.70 41.25 41.54 41.83 42.36 137 1.02
mu[119] 41.52 0.04 0.42 40.70 41.22 41.53 41.83 42.33 145 1.02
mu[120] 41.48 0.04 0.43 40.65 41.19 41.49 41.80 42.31 136 1.02
mu[121] 41.47 0.04 0.43 40.59 41.18 41.47 41.78 42.31 105 1.02
mu[122] 41.46 0.04 0.43 40.61 41.17 41.46 41.72 42.27 147 1.02
mu[123] 41.46 0.04 0.44 40.62 41.16 41.48 41.77 42.31 143 1.02
mu[124] 41.45 0.04 0.44 40.60 41.16 41.46 41.77 42.28 142 1.02
mu[125] 41.47 0.04 0.45 40.62 41.15 41.48 41.76 42.36 162 1.01
mu[126] 41.50 0.03 0.45 40.58 41.19 41.51 41.79 42.40 167 1.01
mu[127] 41.52 0.04 0.44 40.67 41.21 41.53 41.82 42.35 153 1.02
mu[128] 41.53 0.03 0.43 40.71 41.25 41.52 41.83 42.39 161 1.02
mu[129] 41.51 0.03 0.44 40.70 41.21 41.51 41.82 42.36 168 1.02
mu[130] 41.49 0.03 0.43 40.68 41.19 41.48 41.79 42.33 191 1.01
mu[131] 41.43 0.03 0.43 40.58 41.12 41.43 41.74 42.24 183 1.02
mu[132] 41.36 0.03 0.44 40.47 41.05 41.36 41.67 42.20 172 1.02
mu[133] 41.30 0.03 0.46 40.46 40.99 41.29 41.60 42.17 200 1.02
mu[134] 41.26 0.03 0.46 40.39 40.95 41.26 41.58 42.17 205 1.02
mu[135] 41.23 0.03 0.46 40.37 40.93 41.21 41.52 42.14 200 1.03
mu[136] 41.16 0.03 0.44 40.33 40.88 41.16 41.45 42.04 199 1.03
mu[137] 41.16 0.03 0.45 40.26 40.86 41.16 41.45 42.05 204 1.03
mu[138] 41.14 0.03 0.44 40.32 40.83 41.15 41.46 41.96 211 1.03
mu[139] 41.13 0.03 0.44 40.26 40.82 41.14 41.43 41.95 204 1.03
mu[140] 41.11 0.03 0.44 40.16 40.83 41.11 41.42 41.89 204 1.03
mu[141] 41.11 0.03 0.42 40.26 40.84 41.13 41.41 41.86 204 1.03
mu[142] 41.13 0.03 0.42 40.28 40.84 41.15 41.43 41.89 206 1.03
mu[143] 41.16 0.03 0.43 40.29 40.86 41.17 41.48 41.92 204 1.03
mu[144] 41.18 0.03 0.43 40.36 40.88 41.20 41.51 41.99 203 1.03
mu[145] 41.19 0.03 0.42 40.36 40.91 41.20 41.47 42.03 210 1.03
mu[146] 41.16 0.03 0.41 40.38 40.87 41.16 41.45 41.93 220 1.02
mu[147] 41.13 0.03 0.41 40.31 40.84 41.13 41.41 41.91 237 1.01
mu[148] 41.11 0.02 0.40 40.34 40.86 41.11 41.38 41.90 258 1.02
mu[149] 41.17 0.02 0.39 40.43 40.89 41.16 41.43 41.94 255 1.01
mu[150] 41.21 0.03 0.39 40.48 40.95 41.21 41.46 41.99 235 1.01
mu[151] 41.27 0.02 0.38 40.55 41.01 41.26 41.53 42.01 257 1.01
mu[152] 41.29 0.02 0.38 40.57 41.01 41.27 41.55 42.04 247 1.01
mu[153] 41.22 0.02 0.39 40.45 40.96 41.22 41.49 41.98 250 1.01
mu[154] 41.17 0.02 0.38 40.41 40.92 41.17 41.42 41.95 255 1.00
mu[155] 41.13 0.03 0.38 40.38 40.87 41.13 41.39 41.88 225 1.00
mu[156] 41.10 0.02 0.39 40.31 40.83 41.09 41.37 41.85 246 1.00
mu[157] 41.09 0.02 0.38 40.36 40.84 41.08 41.36 41.86 240 1.00
mu[158] 41.05 0.02 0.39 40.30 40.80 41.04 41.32 41.83 244 1.00
mu[159] 41.00 0.03 0.40 40.25 40.74 40.98 41.27 41.78 215 1.00
mu[160] 40.95 0.03 0.40 40.19 40.66 40.95 41.23 41.74 234 1.00
mu[161] 40.91 0.03 0.41 40.16 40.64 40.90 41.17 41.73 248 1.00
mu[162] 40.88 0.03 0.41 40.10 40.60 40.87 41.15 41.72 241 1.00
mu[163] 40.89 0.03 0.41 40.08 40.64 40.90 41.16 41.71 245 1.00
mu[164] 40.91 0.03 0.42 40.12 40.63 40.90 41.17 41.76 249 1.00
mu[165] 40.92 0.03 0.42 40.07 40.65 40.92 41.20 41.74 243 1.00
mu[166] 40.96 0.03 0.43 40.10 40.66 40.95 41.23 41.82 247 1.01
mu[167] 40.94 0.03 0.43 40.12 40.66 40.95 41.22 41.80 239 1.01
mu[168] 40.94 0.03 0.42 40.18 40.63 40.94 41.23 41.81 217 1.01
mu[169] 40.94 0.03 0.42 40.17 40.66 40.95 41.23 41.75 217 1.02
mu[170] 40.90 0.03 0.41 40.09 40.63 40.88 41.19 41.69 212 1.02
mu[171] 40.86 0.03 0.41 40.06 40.58 40.85 41.17 41.67 212 1.02
mu[172] 40.84 0.03 0.42 40.03 40.53 40.84 41.15 41.66 227 1.02
mu[173] 40.78 0.03 0.42 40.02 40.47 40.80 41.06 41.61 209 1.02
mu[174] 40.71 0.03 0.43 39.91 40.40 40.71 40.99 41.55 215 1.02
mu[175] 40.64 0.03 0.43 39.82 40.36 40.63 40.91 41.48 213 1.02
mu[176] 40.55 0.03 0.43 39.68 40.25 40.54 40.85 41.39 217 1.02
mu[177] 40.42 0.03 0.42 39.61 40.14 40.42 40.70 41.23 210 1.02
mu[178] 40.30 0.03 0.42 39.47 40.01 40.29 40.60 41.14 215 1.01
mu[179] 40.19 0.03 0.43 39.34 39.92 40.19 40.46 41.04 205 1.01
mu[180] 40.09 0.03 0.42 39.26 39.81 40.08 40.36 40.96 221 1.01
mu[181] 40.00 0.03 0.43 39.22 39.69 39.98 40.28 40.88 209 1.01
mu[182] 39.91 0.03 0.43 39.11 39.62 39.89 40.22 40.81 205 1.01
mu[183] 39.81 0.03 0.43 38.97 39.52 39.81 40.08 40.65 216 1.01
mu[184] 39.71 0.03 0.42 38.88 39.42 39.72 39.99 40.56 239 1.01
mu[185] 39.59 0.03 0.43 38.76 39.30 39.59 39.88 40.41 228 1.00
mu[186] 39.47 0.03 0.42 38.63 39.21 39.46 39.76 40.27 233 1.00
mu[187] 39.38 0.03 0.41 38.58 39.11 39.38 39.67 40.22 234 1.00
mu[188] 39.29 0.03 0.41 38.48 39.03 39.28 39.55 40.07 242 1.00
mu[189] 39.20 0.02 0.40 38.43 38.92 39.20 39.47 39.97 264 1.00
mu[190] 39.10 0.02 0.41 38.33 38.81 39.10 39.38 39.88 284 1.00
mu[191] 39.01 0.02 0.40 38.27 38.74 39.00 39.29 39.82 290 1.00
mu[192] 38.92 0.02 0.40 38.12 38.66 38.91 39.19 39.69 301 1.00
mu[193] 38.87 0.02 0.40 38.10 38.60 38.87 39.16 39.65 286 1.00
mu[194] 38.84 0.02 0.40 38.04 38.58 38.86 39.10 39.64 318 1.00
mu[195] 38.80 0.02 0.41 37.99 38.52 38.82 39.06 39.60 344 1.00
mu[196] 38.77 0.02 0.40 38.00 38.52 38.76 39.04 39.55 337 1.00
mu[197] 38.78 0.02 0.39 38.02 38.52 38.79 39.03 39.50 324 1.00
mu[198] 38.79 0.02 0.38 38.04 38.55 38.80 39.06 39.49 343 1.00
mu[199] 38.80 0.02 0.38 38.08 38.55 38.81 39.06 39.57 329 1.00
mu[200] 38.80 0.02 0.39 38.03 38.54 38.79 39.05 39.57 344 1.00
mu[201] 38.82 0.02 0.39 38.05 38.56 38.81 39.08 39.60 343 1.00
mu[202] 38.78 0.02 0.38 38.00 38.53 38.79 39.03 39.54 356 1.00
mu[203] 38.76 0.02 0.38 37.97 38.52 38.77 39.02 39.45 252 1.00
mu[204] 38.74 0.02 0.38 38.00 38.48 38.74 38.99 39.48 320 1.00
mu[205] 38.73 0.02 0.38 38.02 38.47 38.73 38.99 39.49 311 1.00
mu[206] 38.68 0.02 0.38 37.97 38.42 38.67 38.93 39.44 278 1.00
mu[207] 38.64 0.02 0.38 37.85 38.40 38.65 38.89 39.41 272 1.00
mu[208] 38.62 0.02 0.39 37.86 38.38 38.62 38.88 39.40 245 1.00
mu[209] 38.55 0.02 0.39 37.77 38.28 38.56 38.83 39.29 255 1.00
mu[210] 38.51 0.03 0.40 37.74 38.24 38.52 38.77 39.25 222 1.00
mu[211] 38.49 0.02 0.39 37.74 38.22 38.48 38.74 39.24 241 1.00
mu[212] 38.50 0.02 0.38 37.76 38.25 38.52 38.76 39.23 245 1.00
mu[213] 38.52 0.02 0.38 37.73 38.27 38.54 38.79 39.26 259 1.00
mu[214] 38.55 0.02 0.39 37.76 38.28 38.56 38.82 39.26 258 1.01
mu[215] 38.60 0.03 0.40 37.74 38.35 38.60 38.87 39.36 234 1.00
mu[216] 38.65 0.03 0.41 37.84 38.39 38.64 38.93 39.41 250 1.01
mu[217] 38.71 0.02 0.41 37.90 38.46 38.72 38.99 39.48 299 1.01
mu[218] 38.80 0.02 0.40 37.98 38.53 38.81 39.06 39.54 270 1.01
mu[219] 38.90 0.02 0.40 38.10 38.63 38.90 39.14 39.67 255 1.01
mu[220] 38.97 0.03 0.39 38.15 38.69 38.98 39.25 39.71 235 1.01
mu[221] 39.05 0.03 0.40 38.28 38.77 39.06 39.31 39.84 210 1.01
mu[222] 39.17 0.03 0.41 38.37 38.89 39.17 39.42 39.99 243 1.01
mu[223] 39.28 0.03 0.42 38.49 38.99 39.27 39.55 40.07 208 1.01
mu[224] 39.42 0.03 0.42 38.65 39.15 39.42 39.67 40.29 203 1.00
mu[225] 39.56 0.03 0.41 38.75 39.28 39.55 39.83 40.40 165 1.01
mu[226] 39.70 0.03 0.41 38.89 39.42 39.70 39.98 40.49 198 1.01
mu[227] 39.81 0.03 0.41 39.01 39.55 39.81 40.09 40.65 191 1.00
mu[228] 39.90 0.03 0.41 39.13 39.63 39.90 40.17 40.70 198 1.00
mu[229] 39.98 0.03 0.40 39.22 39.72 39.98 40.25 40.76 184 1.01
mu[230] 40.02 0.03 0.39 39.24 39.76 40.04 40.29 40.76 144 1.01
mu[231] 40.04 0.03 0.39 39.28 39.76 40.05 40.31 40.76 167 1.01
mu[232] 40.04 0.03 0.39 39.26 39.78 40.04 40.31 40.78 168 1.01
mu[233] 40.04 0.03 0.38 39.27 39.78 40.06 40.32 40.76 171 1.01
mu[234] 40.03 0.03 0.39 39.24 39.76 40.05 40.32 40.76 197 1.00
mu[235] 40.07 0.03 0.39 39.27 39.80 40.08 40.33 40.80 209 1.00
mu[236] 40.10 0.03 0.38 39.32 39.83 40.13 40.35 40.79 202 1.01
mu[237] 40.10 0.03 0.38 39.36 39.86 40.11 40.36 40.86 229 1.01
mu[238] 40.14 0.02 0.36 39.40 39.90 40.16 40.37 40.89 252 1.01
mu[239] 40.17 0.02 0.37 39.40 39.93 40.17 40.41 40.90 263 1.01
mu[240] 40.19 0.02 0.36 39.45 39.95 40.19 40.42 40.88 242 1.01
mu[241] 40.21 0.02 0.36 39.50 39.97 40.23 40.44 40.91 257 1.01
mu[242] 40.21 0.02 0.36 39.49 39.98 40.21 40.44 40.91 303 1.01
mu[243] 40.19 0.02 0.36 39.48 39.96 40.19 40.42 40.89 334 1.01
mu[244] 40.12 0.02 0.37 39.39 39.87 40.11 40.37 40.84 290 1.00
mu[245] 40.05 0.02 0.38 39.33 39.79 40.05 40.30 40.79 328 1.00
mu[246] 40.00 0.02 0.38 39.28 39.74 40.01 40.27 40.73 335 1.00
mu[247] 39.94 0.02 0.39 39.22 39.68 39.92 40.20 40.72 305 1.00
mu[248] 39.87 0.02 0.38 39.16 39.62 39.86 40.12 40.63 306 1.01
mu[249] 39.83 0.02 0.37 39.13 39.58 39.83 40.08 40.54 314 1.01
mu[250] 39.81 0.02 0.38 39.08 39.55 39.81 40.08 40.55 330 1.01
mu[251] 39.79 0.02 0.40 39.00 39.53 39.79 40.05 40.56 327 1.00
mu[252] 39.77 0.02 0.40 39.01 39.50 39.78 40.05 40.52 325 1.01
mu[253] 39.77 0.02 0.40 38.97 39.50 39.78 40.03 40.54 300 1.01
mu[254] 39.74 0.02 0.39 38.96 39.47 39.75 40.01 40.45 288 1.01
mu[255] 39.74 0.02 0.40 38.98 39.46 39.74 39.99 40.52 270 1.01
mu[256] 39.71 0.02 0.40 38.95 39.44 39.71 39.97 40.55 286 1.00
mu[257] 39.66 0.02 0.41 38.92 39.38 39.66 39.94 40.51 279 1.00
mu[258] 39.61 0.02 0.41 38.85 39.32 39.61 39.89 40.40 290 1.00
mu[259] 39.54 0.02 0.42 38.77 39.23 39.54 39.83 40.40 299 1.00
mu[260] 39.50 0.02 0.42 38.71 39.23 39.49 39.78 40.30 288 1.00
mu[261] 39.48 0.02 0.40 38.71 39.21 39.46 39.75 40.25 264 1.00
mu[262] 39.45 0.02 0.39 38.72 39.17 39.44 39.71 40.22 277 1.00
mu[263] 39.43 0.02 0.39 38.68 39.15 39.44 39.70 40.17 255 1.00
mu[264] 39.40 0.02 0.39 38.64 39.12 39.40 39.67 40.13 299 1.00
mu[265] 39.35 0.02 0.39 38.62 39.08 39.34 39.62 40.11 327 1.00
mu[266] 39.31 0.02 0.38 38.56 39.04 39.31 39.58 40.07 307 1.00
mu[267] 39.26 0.02 0.37 38.50 39.02 39.26 39.51 39.98 327 1.00
mu[268] 39.20 0.02 0.36 38.50 38.95 39.20 39.45 39.92 341 1.00
mu[269] 39.11 0.02 0.37 38.39 38.86 39.11 39.36 39.83 330 1.01
mu[270] 39.02 0.02 0.37 38.29 38.75 39.00 39.28 39.78 310 1.00
mu[271] 38.97 0.02 0.38 38.24 38.70 38.97 39.23 39.68 315 1.00
mu[272] 38.93 0.02 0.38 38.16 38.67 38.94 39.17 39.65 302 1.01
mu[273] 38.90 0.02 0.38 38.17 38.63 38.91 39.17 39.66 290 1.01
mu[274] 38.89 0.02 0.38 38.15 38.63 38.90 39.15 39.63 295 1.01
mu[275] 38.91 0.02 0.39 38.14 38.63 38.91 39.16 39.68 311 1.01
mu[276] 38.92 0.02 0.38 38.20 38.65 38.91 39.16 39.66 313 1.00
mu[277] 38.92 0.02 0.38 38.21 38.67 38.90 39.16 39.70 330 1.00
mu[278] 38.92 0.02 0.38 38.17 38.67 38.90 39.19 39.64 321 1.01
mu[279] 38.91 0.02 0.39 38.11 38.66 38.89 39.17 39.66 350 1.01
mu[280] 38.93 0.02 0.39 38.17 38.67 38.93 39.20 39.71 330 1.01
mu[281] 38.96 0.02 0.38 38.21 38.70 38.96 39.24 39.68 337 1.01
mu[282] 38.99 0.02 0.38 38.22 38.73 39.00 39.25 39.75 315 1.01
mu[283] 39.02 0.02 0.38 38.27 38.76 39.01 39.29 39.78 336 1.01
mu[284] 39.03 0.02 0.37 38.33 38.77 39.04 39.30 39.78 362 1.01
mu[285] 39.07 0.02 0.39 38.36 38.79 39.07 39.33 39.84 350 1.00
mu[286] 39.08 0.02 0.39 38.35 38.80 39.09 39.36 39.80 325 1.00
mu[287] 39.11 0.02 0.39 38.40 38.84 39.10 39.37 39.88 339 1.01
mu[288] 39.16 0.02 0.38 38.39 38.90 39.15 39.41 39.92 374 1.00
mu[289] 39.21 0.02 0.37 38.49 38.95 39.20 39.45 39.97 387 1.00
mu[290] 39.25 0.02 0.37 38.59 38.99 39.24 39.48 40.01 382 1.00
mu[291] 39.28 0.02 0.37 38.56 39.03 39.28 39.52 40.03 399 1.00
mu[292] 39.31 0.02 0.38 38.60 39.06 39.31 39.56 40.07 420 1.00
mu[293] 39.35 0.02 0.38 38.57 39.09 39.37 39.60 40.10 418 1.00
mu[294] 39.40 0.02 0.38 38.63 39.14 39.41 39.64 40.18 377 1.00
mu[295] 39.44 0.02 0.38 38.71 39.20 39.45 39.69 40.20 388 1.00
mu[296] 39.45 0.02 0.37 38.72 39.21 39.44 39.71 40.22 374 1.00
mu[297] 39.46 0.02 0.38 38.72 39.21 39.45 39.73 40.15 356 1.00
mu[298] 39.47 0.02 0.39 38.67 39.20 39.47 39.73 40.20 347 1.00
mu[299] 39.46 0.02 0.40 38.69 39.19 39.46 39.71 40.26 345 1.00
mu[300] 39.43 0.02 0.41 38.58 39.17 39.43 39.72 40.21 312 1.00
mu[301] 39.42 0.02 0.41 38.57 39.18 39.42 39.71 40.23 296 1.00
mu[302] 39.41 0.02 0.41 38.53 39.15 39.42 39.69 40.17 309 1.00
mu[303] 39.39 0.02 0.41 38.56 39.12 39.40 39.67 40.19 309 1.00
mu[304] 39.39 0.02 0.41 38.58 39.10 39.40 39.66 40.20 301 1.00
mu[305] 39.36 0.02 0.42 38.53 39.08 39.37 39.64 40.17 322 1.00
mu[306] 39.35 0.02 0.42 38.49 39.08 39.36 39.63 40.19 328 1.00
mu[307] 39.33 0.02 0.42 38.50 39.06 39.35 39.62 40.12 307 1.00
mu[308] 39.32 0.02 0.42 38.49 39.04 39.32 39.61 40.12 324 1.00
mu[309] 39.31 0.02 0.42 38.48 39.02 39.30 39.58 40.17 308 1.00
mu[310] 39.27 0.02 0.42 38.45 39.00 39.27 39.56 40.09 304 1.00
mu[311] 39.24 0.02 0.41 38.43 38.95 39.24 39.51 40.04 313 1.00
mu[312] 39.18 0.02 0.41 38.40 38.89 39.16 39.47 39.95 299 1.00
mu[313] 39.13 0.02 0.41 38.34 38.84 39.12 39.42 39.90 290 1.01
mu[314] 39.06 0.02 0.41 38.31 38.79 39.03 39.33 39.86 305 1.00
mu[315] 39.01 0.02 0.39 38.29 38.74 39.00 39.28 39.78 326 1.00
mu[316] 38.99 0.02 0.38 38.25 38.74 38.98 39.22 39.77 308 1.00
mu[317] 38.92 0.02 0.38 38.16 38.67 38.91 39.15 39.69 282 1.01
mu[318] 38.87 0.02 0.37 38.17 38.61 38.87 39.11 39.66 299 1.01
mu[319] 38.84 0.02 0.38 38.10 38.58 38.81 39.08 39.59 282 1.01
mu[320] 38.77 0.03 0.39 38.06 38.50 38.76 39.03 39.55 236 1.01
mu[321] 38.70 0.03 0.39 37.95 38.44 38.69 38.96 39.45 227 1.01
mu[322] 38.69 0.03 0.39 37.97 38.42 38.69 38.94 39.44 240 1.00
mu[323] 38.68 0.03 0.39 37.95 38.42 38.67 38.93 39.47 210 1.00
mu[324] 38.70 0.02 0.37 37.97 38.45 38.69 38.93 39.41 236 1.00
mu[325] 38.71 0.03 0.37 37.98 38.47 38.71 38.94 39.42 209 1.00
mu[326] 38.74 0.03 0.37 38.01 38.48 38.76 38.99 39.46 207 1.00
mu[327] 38.77 0.03 0.36 38.07 38.54 38.78 39.03 39.46 197 1.00
mu[328] 38.83 0.02 0.37 38.10 38.58 38.83 39.08 39.53 228 1.00
mu[329] 38.89 0.02 0.38 38.12 38.63 38.88 39.16 39.65 258 1.00
mu[330] 38.97 0.02 0.39 38.20 38.72 38.98 39.24 39.74 253 1.00
mu[331] 39.09 0.02 0.39 38.30 38.83 39.09 39.35 39.91 272 1.00
mu[332] 39.19 0.02 0.40 38.42 38.92 39.19 39.44 39.99 269 1.00
mu[333] 39.27 0.02 0.39 38.53 39.01 39.23 39.53 40.07 265 1.00
mu[334] 39.39 0.02 0.40 38.61 39.13 39.40 39.67 40.19 291 1.00
mu[335] 39.51 0.02 0.41 38.73 39.24 39.50 39.80 40.30 313 1.00
mu[336] 39.63 0.02 0.41 38.83 39.34 39.64 39.91 40.41 319 1.00
mu[337] 39.76 0.02 0.42 38.89 39.48 39.77 40.04 40.56 319 1.00
mu[338] 39.89 0.02 0.42 39.05 39.59 39.91 40.16 40.67 327 1.00
mu[339] 40.01 0.02 0.42 39.15 39.72 40.04 40.30 40.78 320 1.00
mu[340] 40.13 0.02 0.41 39.27 39.86 40.14 40.42 40.90 303 1.00
mu[341] 40.28 0.02 0.42 39.40 40.01 40.30 40.56 41.04 286 1.01
mu[342] 40.43 0.03 0.42 39.56 40.15 40.45 40.73 41.20 270 1.01
mu[343] 40.60 0.03 0.44 39.71 40.30 40.63 40.90 41.43 251 1.01
mu[344] 40.76 0.03 0.44 39.87 40.47 40.78 41.06 41.57 257 1.01
mu[345] 40.92 0.03 0.44 40.02 40.64 40.93 41.21 41.75 246 1.01
mu[346] 41.08 0.03 0.43 40.22 40.80 41.08 41.37 41.89 235 1.01
mu[347] 41.20 0.03 0.43 40.33 40.93 41.20 41.48 42.06 223 1.01
mu[348] 41.30 0.03 0.44 40.45 41.01 41.31 41.60 42.12 202 1.01
mu[349] 41.39 0.03 0.43 40.54 41.09 41.40 41.67 42.18 208 1.01
mu[350] 41.43 0.03 0.44 40.53 41.13 41.41 41.72 42.28 191 1.01
mu[351] 41.47 0.03 0.43 40.57 41.17 41.47 41.75 42.31 197 1.01
mu[352] 41.52 0.03 0.42 40.67 41.25 41.52 41.81 42.35 185 1.01
mu[353] 41.56 0.03 0.42 40.69 41.28 41.57 41.86 42.33 163 1.01
mu[354] 41.61 0.03 0.41 40.79 41.34 41.63 41.88 42.40 164 1.01
mu[355] 41.66 0.03 0.40 40.82 41.41 41.68 41.93 42.45 163 1.01
mu[356] 41.67 0.03 0.41 40.87 41.39 41.68 41.94 42.50 164 1.01
mu[357] 41.67 0.03 0.41 40.86 41.42 41.66 41.92 42.49 174 1.01
mu[358] 41.67 0.03 0.41 40.88 41.41 41.66 41.95 42.50 189 1.01
mu[359] 41.66 0.03 0.41 40.87 41.39 41.67 41.91 42.52 171 1.01
mu[360] 41.68 0.03 0.41 40.86 41.40 41.69 41.95 42.49 212 1.01
mu[361] 41.70 0.03 0.40 40.91 41.44 41.71 41.98 42.50 198 1.01
mu[362] 41.71 0.03 0.40 40.91 41.45 41.72 41.99 42.51 188 1.01
mu[363] 41.73 0.03 0.41 40.95 41.45 41.73 42.01 42.49 180 1.02
mu[364] 41.74 0.03 0.41 40.90 41.46 41.75 42.02 42.54 178 1.02
mu[365] 41.78 0.03 0.42 40.97 41.49 41.80 42.06 42.60 188 1.02
mu[366] 41.88 0.03 0.42 41.06 41.60 41.88 42.15 42.75 192 1.02
mu[367] 41.99 0.03 0.42 41.17 41.71 41.98 42.25 42.82 197 1.02
mu[368] 42.09 0.03 0.42 41.28 41.84 42.10 42.37 42.93 203 1.02
mu[369] 42.21 0.03 0.43 41.33 41.94 42.21 42.51 43.03 183 1.03
mu[370] 42.32 0.03 0.43 41.46 42.04 42.31 42.61 43.13 190 1.03
mu[371] 42.44 0.03 0.44 41.57 42.15 42.45 42.72 43.30 158 1.04
mu[372] 42.56 0.03 0.42 41.67 42.30 42.57 42.84 43.33 170 1.03
mu[373] 42.70 0.03 0.43 41.77 42.44 42.71 43.00 43.43 173 1.03
mu[374] 42.85 0.03 0.43 41.93 42.59 42.87 43.16 43.58 196 1.03
mu[375] 42.99 0.03 0.42 42.14 42.70 43.02 43.30 43.79 187 1.02
mu[376] 43.10 0.03 0.43 42.26 42.82 43.11 43.40 43.91 167 1.03
mu[377] 43.18 0.04 0.42 42.36 42.90 43.18 43.48 44.01 138 1.03
mu[378] 43.26 0.04 0.42 42.42 42.99 43.28 43.52 44.08 128 1.03
mu[379] 43.36 0.04 0.43 42.53 43.07 43.36 43.64 44.22 116 1.03
mu[380] 43.43 0.04 0.42 42.59 43.15 43.43 43.71 44.25 101 1.03
mu[381] 43.50 0.05 0.42 42.64 43.22 43.51 43.77 44.31 77 1.03
mu[382] 43.53 0.04 0.43 42.68 43.25 43.54 43.81 44.37 92 1.03
mu[383] 43.57 0.04 0.42 42.72 43.28 43.59 43.86 44.40 109 1.03
mu[384] 43.57 0.04 0.42 42.76 43.29 43.57 43.85 44.41 120 1.03
mu[385] 43.56 0.04 0.42 42.76 43.26 43.56 43.84 44.40 127 1.02
mu[386] 43.53 0.03 0.42 42.72 43.27 43.54 43.79 44.36 211 1.02
mu[387] 43.50 0.03 0.42 42.67 43.22 43.51 43.77 44.32 206 1.01
mu[388] 43.46 0.03 0.42 42.61 43.17 43.45 43.74 44.26 250 1.01
mu[389] 43.43 0.03 0.42 42.64 43.14 43.42 43.72 44.23 273 1.00
mu[390] 43.40 0.02 0.41 42.63 43.12 43.40 43.69 44.21 287 1.00
mu[391] 43.38 0.02 0.41 42.55 43.09 43.39 43.66 44.16 307 1.00
mu[392] 43.35 0.02 0.41 42.56 43.07 43.35 43.65 44.14 328 1.00
mu[393] 43.32 0.02 0.41 42.58 43.03 43.31 43.57 44.16 334 1.00
mu[394] 43.31 0.02 0.39 42.62 43.02 43.29 43.58 44.10 323 1.00
mu[395] 43.32 0.02 0.38 42.66 43.07 43.31 43.56 44.09 307 1.00
mu[396] 43.36 0.02 0.38 42.61 43.11 43.35 43.60 44.05 327 1.00
mu[397] 43.38 0.02 0.39 42.62 43.13 43.37 43.63 44.18 327 1.00
mu[398] 43.38 0.02 0.39 42.61 43.13 43.38 43.62 44.15 358 1.00
mu[399] 43.39 0.02 0.39 42.61 43.13 43.39 43.64 44.18 362 1.00
mu[400] 43.43 0.02 0.39 42.66 43.17 43.44 43.69 44.19 312 1.00
mu[401] 43.46 0.02 0.38 42.71 43.20 43.48 43.71 44.22 288 1.00
mu[402] 43.45 0.02 0.39 42.71 43.19 43.44 43.71 44.23 304 1.00
mu[403] 43.43 0.02 0.38 42.69 43.16 43.43 43.68 44.19 291 1.01
mu[404] 43.37 0.03 0.39 42.61 43.09 43.37 43.62 44.10 216 1.01
mu[405] 43.31 0.03 0.40 42.53 43.04 43.32 43.56 44.07 229 1.01
mu[406] 43.27 0.03 0.40 42.45 43.02 43.29 43.52 44.07 205 1.02
mu[407] 43.24 0.03 0.40 42.47 42.98 43.25 43.49 44.07 155 1.02
mu[408] 43.21 0.03 0.40 42.43 42.95 43.23 43.47 43.98 176 1.03
mu[409] 43.19 0.03 0.40 42.43 42.94 43.20 43.47 43.98 138 1.03
mu[410] 43.17 0.03 0.40 42.40 42.91 43.16 43.45 43.93 178 1.03
mu[411] 43.12 0.05 0.40 42.35 42.85 43.13 43.39 43.90 68 1.04
mu[412] 43.06 0.04 0.40 42.26 42.79 43.06 43.34 43.83 126 1.03
mu[413] 43.02 0.03 0.41 42.23 42.73 43.02 43.29 43.84 162 1.02
mu[414] 43.00 0.03 0.40 42.23 42.73 42.99 43.28 43.73 146 1.03
mu[415] 43.00 0.03 0.40 42.24 42.73 43.01 43.27 43.81 180 1.02
mu[416] 42.99 0.03 0.40 42.19 42.72 42.98 43.26 43.77 129 1.02
mu[417] 42.97 0.03 0.40 42.19 42.70 42.96 43.27 43.73 237 1.01
mu[418] 42.95 0.02 0.40 42.15 42.68 42.97 43.22 43.70 272 1.01
mu[419] 42.93 0.03 0.40 42.13 42.65 42.93 43.21 43.70 250 1.01
mu[420] 42.92 0.02 0.40 42.15 42.65 42.93 43.19 43.71 258 1.01
mu[421] 42.91 0.02 0.39 42.16 42.66 42.92 43.16 43.68 249 1.01
mu[422] 42.90 0.02 0.38 42.20 42.63 42.89 43.17 43.62 253 1.01
mu[423] 42.88 0.02 0.37 42.22 42.60 42.88 43.14 43.62 255 1.01
mu[424] 42.90 0.02 0.38 42.17 42.63 42.90 43.15 43.64 244 1.02
mu[425] 42.87 0.02 0.39 42.10 42.61 42.88 43.13 43.64 264 1.01
mu[426] 42.85 0.02 0.40 42.09 42.57 42.85 43.14 43.61 276 1.01
mu[427] 42.84 0.02 0.39 42.09 42.57 42.83 43.11 43.61 282 1.01
mu[428] 42.83 0.02 0.39 42.11 42.56 42.84 43.07 43.56 299 1.00
mu[429] 42.85 0.02 0.39 42.14 42.59 42.84 43.10 43.64 268 1.00
mu[430] 42.86 0.02 0.39 42.16 42.60 42.85 43.14 43.63 276 1.01
mu[431] 42.88 0.02 0.38 42.13 42.62 42.88 43.14 43.63 250 1.01
mu[432] 42.89 0.02 0.38 42.18 42.63 42.90 43.15 43.65 281 1.01
mu[433] 42.91 0.02 0.39 42.19 42.64 42.92 43.17 43.69 269 1.01
mu[434] 42.93 0.02 0.39 42.18 42.64 42.93 43.19 43.75 284 1.01
mu[435] 42.97 0.02 0.39 42.20 42.70 42.96 43.23 43.73 316 1.00
mu[436] 43.00 0.02 0.39 42.24 42.73 43.00 43.26 43.77 268 1.01
mu[437] 43.01 0.02 0.39 42.19 42.74 43.01 43.28 43.76 276 1.01
mu[438] 43.00 0.02 0.39 42.22 42.76 43.01 43.26 43.75 296 1.01
mu[439] 43.00 0.02 0.39 42.19 42.75 43.02 43.26 43.75 290 1.01
mu[440] 43.01 0.02 0.39 42.24 42.74 43.02 43.28 43.77 244 1.01
mu[441] 43.04 0.03 0.40 42.26 42.80 43.05 43.29 43.81 242 1.01
mu[442] 43.08 0.03 0.39 42.31 42.83 43.08 43.33 43.86 236 1.01
mu[443] 43.12 0.03 0.40 42.37 42.85 43.11 43.39 43.92 245 1.01
mu[444] 43.15 0.02 0.40 42.41 42.86 43.14 43.41 43.96 261 1.01
mu[445] 43.20 0.03 0.39 42.44 42.91 43.20 43.46 43.96 237 1.01
mu[446] 43.21 0.03 0.39 42.48 42.94 43.20 43.46 43.97 231 1.01
mu[447] 43.22 0.03 0.40 42.49 42.94 43.21 43.48 44.00 209 1.00
mu[448] 43.23 0.03 0.40 42.46 42.97 43.24 43.50 44.03 188 1.01
mu[449] 43.25 0.03 0.41 42.46 42.98 43.26 43.52 44.05 181 1.01
mu[450] 43.25 0.03 0.41 42.45 42.97 43.25 43.53 44.05 185 1.01
mu[451] 43.29 0.03 0.40 42.55 43.01 43.29 43.56 44.13 168 1.01
mu[452] 43.36 0.03 0.40 42.64 43.06 43.36 43.63 44.17 181 1.01
mu[453] 43.39 0.03 0.41 42.59 43.12 43.39 43.67 44.21 167 1.01
mu[454] 43.41 0.03 0.41 42.62 43.13 43.41 43.70 44.22 194 1.01
mu[455] 43.46 0.03 0.42 42.63 43.18 43.46 43.73 44.29 169 1.01
mu[456] 43.51 0.03 0.42 42.68 43.24 43.51 43.79 44.38 180 1.01
mu[457] 43.57 0.03 0.41 42.72 43.30 43.56 43.83 44.39 169 1.01
mu[458] 43.63 0.03 0.41 42.87 43.36 43.62 43.90 44.38 186 1.01
mu[459] 43.69 0.03 0.40 42.90 43.43 43.68 43.94 44.49 170 1.01
mu[460] 43.74 0.03 0.40 42.95 43.49 43.73 44.00 44.50 194 1.00
mu[461] 43.78 0.03 0.40 43.03 43.52 43.77 44.05 44.60 176 1.00
mu[462] 43.83 0.03 0.40 43.07 43.56 43.83 44.08 44.64 185 1.00
mu[463] 43.91 0.03 0.40 43.08 43.63 43.91 44.16 44.71 182 1.00
mu[464] 44.00 0.03 0.40 43.21 43.74 44.01 44.25 44.84 164 1.00
mu[465] 44.09 0.03 0.40 43.31 43.82 44.09 44.35 44.91 165 1.00
mu[466] 44.16 0.03 0.39 43.39 43.89 44.16 44.43 44.95 168 1.00
mu[467] 44.22 0.03 0.41 43.41 43.94 44.22 44.51 44.99 179 1.00
mu[468] 44.24 0.03 0.41 43.43 43.96 44.26 44.52 45.01 174 1.00
mu[469] 44.25 0.03 0.40 43.44 43.99 44.25 44.53 45.00 179 1.00
mu[470] 44.26 0.03 0.40 43.41 43.98 44.26 44.55 45.01 176 1.00
mu[471] 44.29 0.03 0.40 43.44 44.03 44.30 44.57 45.10 180 1.00
mu[472] 44.34 0.03 0.40 43.52 44.09 44.34 44.60 45.14 186 1.00
mu[473] 44.38 0.03 0.40 43.52 44.11 44.39 44.65 45.14 193 1.00
mu[474] 44.40 0.03 0.40 43.59 44.12 44.42 44.67 45.20 190 1.00
mu[475] 44.39 0.03 0.41 43.57 44.11 44.42 44.68 45.15 178 1.01
mu[476] 44.39 0.03 0.40 43.55 44.12 44.39 44.68 45.14 177 1.01
mu[477] 44.37 0.03 0.40 43.54 44.10 44.40 44.66 45.08 175 1.01
mu[478] 44.36 0.03 0.39 43.55 44.09 44.37 44.64 45.07 225 1.00
mu[479] 44.35 0.02 0.38 43.62 44.07 44.37 44.61 45.08 269 1.00
mu[480] 44.31 0.03 0.38 43.59 44.06 44.32 44.56 45.05 208 1.00
mu[481] 44.29 0.03 0.40 43.53 44.02 44.29 44.55 45.06 247 1.00
mu[482] 44.26 0.03 0.41 43.44 43.97 44.28 44.53 45.08 214 1.00
mu[483] 44.25 0.03 0.41 43.48 43.98 44.27 44.54 45.08 196 1.00
mu[484] 44.24 0.03 0.40 43.49 43.96 44.25 44.50 45.01 187 1.00
mu[485] 44.27 0.03 0.40 43.48 44.00 44.27 44.54 45.07 172 1.00
mu[486] 44.28 0.03 0.40 43.50 44.03 44.27 44.54 45.07 161 1.00
mu[487] 44.29 0.03 0.40 43.57 44.01 44.29 44.53 45.09 192 1.00
mu[488] 44.26 0.03 0.40 43.52 43.98 44.26 44.52 45.06 184 1.00
mu[489] 44.21 0.03 0.41 43.46 43.91 44.21 44.47 45.06 202 1.00
mu[490] 44.15 0.03 0.41 43.38 43.87 44.14 44.40 44.98 217 1.01
mu[491] 44.08 0.03 0.40 43.27 43.81 44.08 44.32 44.90 210 1.01
mu[492] 44.02 0.03 0.41 43.17 43.76 44.02 44.30 44.83 190 1.01
mu[493] 43.98 0.03 0.41 43.17 43.72 43.97 44.25 44.80 206 1.01
mu[494] 43.94 0.03 0.40 43.14 43.68 43.94 44.22 44.70 247 1.00
mu[495] 43.89 0.03 0.40 43.08 43.62 43.89 44.17 44.64 205 1.01
mu[496] 43.83 0.03 0.40 43.05 43.57 43.83 44.11 44.58 228 1.01
mu[497] 43.78 0.03 0.40 43.00 43.52 43.78 44.05 44.55 234 1.00
mu[498] 43.74 0.03 0.39 43.00 43.49 43.75 44.01 44.47 238 1.00
mu[499] 43.71 0.02 0.39 42.95 43.44 43.74 43.99 44.45 260 1.00
mu[500] 43.70 0.02 0.39 42.94 43.44 43.71 43.96 44.42 271 1.00
mu[501] 43.72 0.02 0.39 42.96 43.46 43.73 43.98 44.45 288 1.00
mu[502] 43.71 0.02 0.38 42.94 43.46 43.73 43.96 44.45 301 1.00
mu[503] 43.72 0.02 0.39 42.97 43.47 43.71 43.97 44.48 295 1.00
mu[504] 43.76 0.02 0.39 42.99 43.50 43.75 44.02 44.56 273 1.00
mu[505] 43.82 0.02 0.39 43.05 43.56 43.82 44.08 44.59 271 1.00
mu[506] 43.87 0.02 0.39 43.12 43.61 43.87 44.12 44.67 268 1.00
mu[507] 43.93 0.02 0.40 43.13 43.66 43.93 44.18 44.76 280 1.00
mu[508] 43.96 0.02 0.41 43.21 43.68 43.96 44.23 44.80 285 1.00
mu[509] 43.97 0.02 0.41 43.14 43.70 43.96 44.24 44.81 283 1.00
mu[510] 43.96 0.02 0.41 43.14 43.69 43.97 44.22 44.74 269 1.00
mu[511] 43.96 0.03 0.42 43.15 43.68 43.98 44.24 44.75 237 1.00
mu[512] 43.97 0.03 0.42 43.15 43.69 43.98 44.26 44.77 241 1.00
mu[513] 43.97 0.03 0.41 43.17 43.69 43.98 44.23 44.76 250 1.00
mu[514] 43.99 0.03 0.41 43.19 43.72 44.00 44.27 44.79 232 1.00
mu[515] 43.97 0.03 0.40 43.22 43.70 43.98 44.25 44.75 234 1.00
mu[516] 43.97 0.03 0.40 43.17 43.69 43.98 44.23 44.75 223 1.00
mu[517] 43.99 0.03 0.40 43.19 43.70 44.00 44.27 44.78 203 1.00
mu[518] 44.00 0.03 0.41 43.21 43.71 44.00 44.29 44.77 208 1.00
mu[519] 44.02 0.03 0.41 43.23 43.74 44.04 44.30 44.80 216 1.00
mu[520] 44.04 0.03 0.40 43.26 43.76 44.04 44.33 44.75 231 1.00
mu[521] 44.05 0.03 0.40 43.26 43.78 44.07 44.33 44.78 228 1.00
mu[522] 44.07 0.03 0.39 43.27 43.81 44.09 44.35 44.78 213 1.00
mu[523] 44.07 0.03 0.40 43.26 43.82 44.08 44.35 44.84 195 1.00
mu[524] 44.06 0.03 0.40 43.28 43.78 44.08 44.34 44.87 180 1.00
mu[525] 44.08 0.03 0.40 43.28 43.82 44.08 44.36 44.91 211 1.00
mu[526] 44.10 0.03 0.39 43.30 43.85 44.11 44.36 44.85 223 1.00
mu[527] 44.13 0.03 0.39 43.37 43.85 44.12 44.38 44.95 189 1.00
mu[528] 44.14 0.03 0.40 43.37 43.87 44.13 44.41 44.94 180 1.00
mu[529] 44.14 0.03 0.42 43.33 43.84 44.14 44.41 44.97 182 1.00
mu[530] 44.13 0.03 0.42 43.34 43.86 44.13 44.44 44.97 170 1.00
mu[531] 44.12 0.03 0.42 43.32 43.83 44.12 44.41 44.92 161 1.01
mu[532] 44.09 0.03 0.42 43.28 43.81 44.10 44.38 44.90 160 1.00
mu[533] 44.06 0.03 0.41 43.29 43.77 44.06 44.35 44.85 154 1.01
mu[534] 44.05 0.03 0.41 43.25 43.77 44.03 44.32 44.86 165 1.01
mu[535] 44.05 0.03 0.40 43.21 43.78 44.04 44.32 44.86 182 1.01
mu[536] 44.04 0.03 0.40 43.25 43.78 44.04 44.31 44.81 198 1.01
mu[537] 44.03 0.03 0.41 43.23 43.76 44.04 44.29 44.79 200 1.02
mu[538] 44.01 0.03 0.40 43.17 43.74 44.02 44.29 44.75 201 1.02
mu[539] 44.01 0.03 0.40 43.22 43.73 44.03 44.27 44.76 212 1.01
mu[540] 43.99 0.03 0.39 43.20 43.71 44.00 44.28 44.72 221 1.02
mu[541] 44.00 0.03 0.39 43.20 43.73 44.01 44.26 44.76 206 1.01
mu[542] 44.01 0.02 0.38 43.28 43.75 44.01 44.26 44.75 230 1.01
mu[543] 44.02 0.02 0.37 43.30 43.77 44.03 44.27 44.73 249 1.01
mu[544] 44.02 0.02 0.38 43.30 43.77 44.03 44.29 44.76 276 1.01
mu[545] 44.03 0.02 0.38 43.32 43.77 44.04 44.30 44.77 243 1.01
mu[546] 44.08 0.03 0.38 43.34 43.82 44.08 44.34 44.80 216 1.02
mu[547] 44.10 0.02 0.39 43.34 43.84 44.11 44.38 44.86 247 1.02
mu[548] 44.16 0.03 0.40 43.38 43.90 44.15 44.43 44.93 252 1.02
mu[549] 44.22 0.03 0.40 43.42 43.96 44.23 44.49 44.98 247 1.01
mu[550] 44.28 0.02 0.40 43.48 44.02 44.29 44.54 45.04 258 1.01
mu[551] 44.33 0.03 0.41 43.51 44.07 44.34 44.61 45.11 264 1.01
mu[552] 44.38 0.03 0.42 43.54 44.11 44.38 44.66 45.18 259 1.01
mu[553] 44.42 0.03 0.42 43.58 44.13 44.42 44.72 45.20 264 1.01
mu[554] 44.47 0.03 0.42 43.66 44.19 44.48 44.75 45.25 278 1.01
mu[555] 44.50 0.03 0.43 43.65 44.23 44.52 44.79 45.35 251 1.01
mu[556] 44.53 0.03 0.43 43.65 44.26 44.55 44.83 45.34 268 1.01
mu[557] 44.57 0.03 0.43 43.71 44.28 44.56 44.87 45.40 271 1.01
mu[558] 44.58 0.03 0.43 43.73 44.28 44.59 44.89 45.38 284 1.01
mu[559] 44.58 0.02 0.43 43.75 44.28 44.58 44.88 45.40 311 1.01
mu[560] 44.58 0.02 0.42 43.79 44.29 44.58 44.87 45.39 304 1.01
mu[561] 44.57 0.02 0.40 43.81 44.30 44.57 44.84 45.35 284 1.01
mu[562] 44.60 0.02 0.40 43.81 44.32 44.61 44.88 45.39 284 1.01
mu[563] 44.63 0.02 0.39 43.87 44.36 44.63 44.90 45.38 300 1.00
mu[564] 44.63 0.02 0.40 43.84 44.36 44.64 44.91 45.41 278 1.00
mu[565] 44.61 0.02 0.40 43.82 44.35 44.62 44.87 45.36 285 1.00
mu[566] 44.59 0.02 0.38 43.80 44.34 44.61 44.84 45.34 274 1.00
mu[567] 44.57 0.02 0.38 43.80 44.32 44.58 44.82 45.33 235 1.00
mu[568] 44.56 0.02 0.38 43.80 44.31 44.57 44.81 45.30 235 1.00
mu[569] 44.61 0.03 0.39 43.86 44.34 44.61 44.87 45.42 203 1.00
mu[570] 44.63 0.03 0.38 43.92 44.38 44.63 44.89 45.40 173 1.00
mu[571] 44.65 0.03 0.38 43.95 44.39 44.63 44.92 45.41 173 1.01
mu[572] 44.65 0.03 0.39 43.92 44.39 44.63 44.91 45.41 187 1.00
mu[573] 44.61 0.03 0.39 43.86 44.34 44.61 44.86 45.34 216 1.00
mu[574] 44.58 0.03 0.39 43.82 44.31 44.59 44.86 45.34 205 1.00
mu[575] 44.54 0.02 0.39 43.82 44.28 44.54 44.81 45.33 249 1.00
mu[576] 44.50 0.02 0.38 43.80 44.24 44.50 44.74 45.26 251 1.00
mu[577] 44.49 0.02 0.37 43.79 44.24 44.48 44.72 45.26 232 1.00
mu[578] 44.45 0.03 0.37 43.72 44.20 44.44 44.68 45.22 222 1.00
mu[579] 44.38 0.02 0.38 43.65 44.14 44.37 44.61 45.18 236 1.00
mu[580] 44.30 0.02 0.38 43.52 44.06 44.30 44.55 45.09 262 1.00
mu[581] 44.21 0.02 0.39 43.43 43.95 44.19 44.47 45.00 289 1.00
mu[582] 44.10 0.03 0.39 43.36 43.84 44.08 44.34 44.92 227 1.00
mu[583] 44.04 0.03 0.40 43.31 43.77 44.03 44.30 44.83 227 1.00
mu[584] 43.95 0.03 0.40 43.16 43.70 43.94 44.18 44.74 210 1.00
mu[585] 43.94 0.03 0.39 43.18 43.68 43.93 44.19 44.71 208 1.00
mu[586] 43.91 0.03 0.39 43.17 43.64 43.88 44.16 44.70 225 1.00
mu[587] 43.89 0.03 0.39 43.15 43.62 43.88 44.14 44.63 219 1.00
mu[588] 43.87 0.03 0.40 43.12 43.60 43.88 44.14 44.67 212 1.00
mu[589] 43.85 0.03 0.39 43.10 43.59 43.85 44.10 44.66 219 1.00
mu[590] 43.86 0.03 0.40 43.08 43.60 43.85 44.14 44.65 222 1.00
mu[591] 43.88 0.03 0.41 43.08 43.60 43.88 44.16 44.69 239 1.00
mu[592] 43.89 0.03 0.40 43.13 43.62 43.86 44.17 44.71 242 1.00
mu[593] 43.90 0.03 0.40 43.11 43.63 43.88 44.17 44.68 241 1.00
mu[594] 43.88 0.03 0.39 43.11 43.62 43.87 44.15 44.65 235 1.00
mu[595] 43.86 0.03 0.39 43.14 43.59 43.85 44.14 44.63 238 1.00
mu[596] 43.87 0.02 0.38 43.18 43.60 43.87 44.13 44.58 242 1.00
mu[597] 43.96 0.03 0.38 43.21 43.69 43.97 44.23 44.65 222 1.00
mu[598] 44.04 0.03 0.38 43.27 43.79 44.04 44.30 44.77 233 1.00
mu[599] 44.13 0.02 0.38 43.42 43.87 44.13 44.40 44.85 246 1.00
mu[600] 44.21 0.02 0.38 43.45 43.96 44.20 44.46 44.94 270 1.00
mu[601] 44.28 0.02 0.39 43.52 44.02 44.26 44.54 45.02 244 1.01
mu[602] 44.34 0.03 0.39 43.59 44.09 44.34 44.60 45.10 244 1.00
mu[603] 44.41 0.02 0.40 43.62 44.14 44.40 44.67 45.20 260 1.00
mu[604] 44.47 0.02 0.39 43.72 44.21 44.47 44.74 45.24 271 1.00
mu[605] 44.52 0.02 0.39 43.77 44.26 44.51 44.78 45.29 277 1.00
mu[606] 44.54 0.02 0.39 43.78 44.28 44.55 44.79 45.29 250 1.01
mu[607] 44.53 0.03 0.39 43.74 44.27 44.52 44.80 45.29 232 1.01
mu[608] 44.52 0.03 0.39 43.75 44.27 44.53 44.78 45.26 232 1.01
mu[609] 44.48 0.03 0.38 43.75 44.22 44.49 44.74 45.25 230 1.01
mu[610] 44.45 0.02 0.38 43.70 44.19 44.44 44.71 45.18 267 1.01
mu[611] 44.44 0.02 0.38 43.66 44.19 44.45 44.70 45.16 254 1.01
mu[612] 44.49 0.02 0.37 43.74 44.24 44.48 44.75 45.22 251 1.01
mu[613] 44.54 0.02 0.38 43.81 44.28 44.55 44.81 45.24 259 1.01
mu[614] 44.57 0.02 0.38 43.79 44.31 44.57 44.83 45.29 234 1.01
mu[615] 44.57 0.03 0.39 43.83 44.29 44.58 44.83 45.29 231 1.01
mu[616] 44.56 0.02 0.38 43.86 44.31 44.56 44.82 45.30 249 1.01
mu[617] 44.59 0.02 0.36 43.92 44.34 44.58 44.83 45.30 262 1.01
mu[618] 44.62 0.02 0.36 43.94 44.37 44.62 44.87 45.32 290 1.00
mu[619] 44.68 0.02 0.36 43.99 44.43 44.67 44.94 45.39 248 1.00
mu[620] 44.74 0.02 0.37 44.06 44.47 44.74 44.99 45.41 273 1.00
mu[621] 44.78 0.02 0.37 44.03 44.54 44.77 45.02 45.47 282 1.00
mu[622] 44.79 0.02 0.38 44.03 44.54 44.79 45.06 45.53 296 1.00
mu[623] 44.80 0.02 0.37 44.06 44.54 44.81 45.06 45.52 287 1.00
mu[624] 44.82 0.02 0.38 44.05 44.56 44.82 45.09 45.54 292 1.00
mu[625] 44.90 0.02 0.38 44.17 44.65 44.91 45.18 45.59 271 1.00
mu[626] 44.97 0.02 0.39 44.22 44.71 44.97 45.25 45.72 293 1.00
mu[627] 45.06 0.02 0.39 44.27 44.78 45.07 45.34 45.79 256 1.00
mu[628] 45.10 0.02 0.39 44.31 44.84 45.11 45.38 45.83 272 1.00
mu[629] 45.17 0.02 0.39 44.39 44.89 45.18 45.45 45.92 283 1.00
mu[630] 45.23 0.02 0.38 44.52 44.97 45.24 45.48 45.96 305 1.00
mu[631] 45.30 0.02 0.37 44.58 45.04 45.30 45.55 46.06 305 1.00
mu[632] 45.37 0.02 0.37 44.59 45.12 45.38 45.63 46.07 309 1.00
mu[633] 45.43 0.02 0.38 44.70 45.18 45.44 45.69 46.14 285 1.01
mu[634] 45.47 0.02 0.38 44.69 45.22 45.46 45.73 46.21 276 1.01
mu[635] 45.51 0.02 0.38 44.78 45.24 45.50 45.77 46.28 265 1.01
mu[636] 45.54 0.02 0.38 44.82 45.27 45.54 45.80 46.29 252 1.01
mu[637] 45.54 0.02 0.38 44.82 45.26 45.54 45.79 46.30 293 1.01
mu[638] 45.56 0.02 0.38 44.82 45.30 45.57 45.83 46.30 283 1.01
mu[639] 45.58 0.02 0.37 44.87 45.32 45.58 45.84 46.31 259 1.01
mu[640] 45.59 0.03 0.39 44.85 45.32 45.58 45.87 46.31 223 1.01
mu[641] 45.59 0.03 0.38 44.85 45.33 45.59 45.84 46.30 205 1.01
mu[642] 45.58 0.03 0.38 44.81 45.33 45.57 45.83 46.29 214 1.01
mu[643] 45.55 0.03 0.38 44.81 45.30 45.54 45.80 46.32 218 1.01
mu[644] 45.55 0.03 0.38 44.76 45.31 45.54 45.79 46.32 218 1.00
mu[645] 45.55 0.03 0.38 44.80 45.30 45.54 45.81 46.35 206 1.01
mu[646] 45.56 0.03 0.37 44.83 45.31 45.56 45.79 46.30 177 1.01
mu[647] 45.58 0.03 0.37 44.88 45.33 45.60 45.82 46.31 201 1.01
mu[648] 45.62 0.03 0.37 44.91 45.36 45.62 45.87 46.30 219 1.00
mu[649] 45.64 0.03 0.38 44.89 45.40 45.64 45.90 46.34 224 1.00
mu[650] 45.63 0.03 0.38 44.88 45.37 45.64 45.89 46.34 196 1.00
mu[651] 45.60 0.02 0.38 44.82 45.34 45.61 45.86 46.36 251 1.00
mu[652] 45.62 0.02 0.39 44.86 45.36 45.64 45.87 46.39 287 1.00
mu[653] 45.65 0.02 0.39 44.91 45.39 45.64 45.90 46.46 300 1.00
mu[654] 45.66 0.02 0.38 44.96 45.41 45.65 45.90 46.44 302 1.00
mu[655] 45.65 0.02 0.37 44.97 45.39 45.63 45.89 46.42 297 1.00
mu[656] 45.63 0.02 0.37 44.93 45.38 45.63 45.87 46.37 280 1.00
mu[657] 45.59 0.02 0.37 44.88 45.33 45.59 45.83 46.30 302 1.00
mu[658] 45.53 0.02 0.37 44.81 45.26 45.52 45.79 46.25 304 1.00
mu[659] 45.48 0.02 0.38 44.74 45.23 45.48 45.73 46.22 323 1.00
mu[660] 45.47 0.02 0.37 44.76 45.20 45.46 45.71 46.20 335 1.00
mu[661] 45.48 0.02 0.38 44.78 45.21 45.49 45.74 46.25 323 1.01
mu[662] 45.52 0.02 0.38 44.82 45.25 45.51 45.77 46.27 295 1.01
mu[663] 45.55 0.02 0.38 44.82 45.28 45.54 45.80 46.27 285 1.00
mu[664] 45.56 0.02 0.38 44.86 45.29 45.56 45.82 46.33 315 1.00
mu[665] 45.56 0.02 0.39 44.80 45.28 45.56 45.83 46.35 311 1.00
mu[666] 45.56 0.02 0.39 44.83 45.28 45.55 45.81 46.36 310 1.00
mu[667] 45.58 0.02 0.38 44.86 45.31 45.56 45.84 46.35 303 1.00
mu[668] 45.61 0.02 0.39 44.83 45.35 45.61 45.87 46.41 275 1.00
mu[669] 45.64 0.02 0.40 44.90 45.36 45.65 45.93 46.41 274 1.00
mu[670] 45.66 0.02 0.40 44.90 45.38 45.65 45.94 46.43 283 1.00
mu[671] 45.66 0.03 0.41 44.87 45.36 45.65 45.95 46.47 254 1.00
mu[672] 45.65 0.03 0.42 44.84 45.38 45.64 45.91 46.47 245 1.01
mu[673] 45.64 0.03 0.41 44.82 45.38 45.64 45.90 46.41 219 1.01
mu[674] 45.65 0.03 0.40 44.84 45.38 45.65 45.93 46.41 218 1.01
mu[675] 45.62 0.03 0.40 44.79 45.36 45.62 45.89 46.41 233 1.00
mu[676] 45.59 0.03 0.40 44.79 45.31 45.61 45.87 46.34 227 1.00
mu[677] 45.56 0.03 0.41 44.73 45.31 45.57 45.84 46.34 249 1.00
mu[678] 45.51 0.02 0.40 44.71 45.25 45.52 45.78 46.25 259 1.01
mu[679] 45.45 0.02 0.39 44.67 45.19 45.46 45.69 46.23 270 1.01
mu[680] 45.40 0.03 0.39 44.66 45.12 45.39 45.66 46.18 226 1.00
mu[681] 45.42 0.03 0.40 44.62 45.15 45.43 45.70 46.20 226 1.00
mu[682] 45.41 0.02 0.39 44.68 45.14 45.40 45.69 46.17 251 1.00
mu[683] 45.39 0.02 0.39 44.63 45.12 45.41 45.66 46.17 251 1.00
mu[684] 45.34 0.02 0.38 44.59 45.08 45.34 45.60 46.06 272 1.00
mu[685] 45.28 0.02 0.38 44.55 45.02 45.29 45.53 46.01 299 1.00
mu[686] 45.22 0.02 0.38 44.45 44.97 45.23 45.47 45.96 251 1.00
mu[687] 45.16 0.02 0.37 44.41 44.93 45.18 45.40 45.89 247 1.00
mu[688] 45.15 0.02 0.37 44.40 44.92 45.16 45.39 45.82 251 1.01
mu[689] 45.14 0.02 0.36 44.42 44.92 45.14 45.37 45.88 298 1.01
mu[690] 45.12 0.02 0.36 44.40 44.89 45.13 45.36 45.86 276 1.01
mu[691] 45.07 0.02 0.36 44.37 44.83 45.07 45.31 45.78 250 1.01
mu[692] 45.00 0.02 0.36 44.26 44.75 45.00 45.25 45.70 252 1.01
mu[693] 44.91 0.02 0.37 44.17 44.64 44.92 45.16 45.63 231 1.01
mu[694] 44.82 0.02 0.37 44.10 44.56 44.82 45.09 45.52 224 1.02
mu[695] 44.77 0.03 0.36 44.08 44.52 44.77 45.02 45.48 193 1.02
mu[696] 44.74 0.03 0.37 44.05 44.48 44.74 45.00 45.46 186 1.02
mu[697] 44.69 0.03 0.38 43.97 44.43 44.69 44.94 45.44 150 1.02
mu[698] 44.64 0.03 0.39 43.88 44.38 44.63 44.92 45.36 190 1.02
mu[699] 44.56 0.03 0.39 43.82 44.31 44.54 44.81 45.37 232 1.01
mu[700] 44.47 0.03 0.40 43.77 44.22 44.46 44.73 45.27 208 1.01
mu[701] 44.42 0.03 0.40 43.66 44.16 44.41 44.68 45.21 230 1.01
mu[702] 44.37 0.03 0.41 43.55 44.11 44.34 44.62 45.19 234 1.01
mu[703] 44.31 0.03 0.41 43.49 44.05 44.30 44.58 45.11 243 1.01
mu[704] 44.25 0.03 0.40 43.44 43.98 44.25 44.52 45.07 243 1.01
mu[705] 44.19 0.03 0.40 43.43 43.91 44.18 44.47 44.95 242 1.01
mu[706] 44.11 0.03 0.40 43.33 43.83 44.09 44.40 44.84 249 1.01
mu[707] 44.04 0.03 0.40 43.26 43.77 44.03 44.32 44.83 249 1.01
mu[708] 43.97 0.02 0.41 43.21 43.68 43.96 44.26 44.72 280 1.01
mu[709] 43.92 0.02 0.41 43.18 43.63 43.92 44.21 44.69 282 1.01
mu[710] 43.87 0.02 0.41 43.05 43.58 43.88 44.14 44.66 276 1.01
mu[711] 43.82 0.03 0.41 43.04 43.54 43.82 44.11 44.62 243 1.02
mu[712] 43.76 0.02 0.40 42.99 43.48 43.76 44.03 44.54 309 1.02
mu[713] 43.67 0.02 0.39 42.91 43.39 43.68 43.94 44.39 367 1.01
mu[714] 43.59 0.02 0.39 42.86 43.32 43.60 43.84 44.30 359 1.01
mu[715] 43.53 0.02 0.38 42.76 43.27 43.53 43.79 44.33 388 1.01
mu[716] 43.43 0.02 0.39 42.65 43.17 43.44 43.71 44.17 411 1.01
mu[717] 43.35 0.02 0.38 42.58 43.09 43.35 43.60 44.07 406 1.01
mu[718] 43.24 0.02 0.38 42.49 42.97 43.24 43.51 43.99 408 1.02
mu[719] 43.14 0.02 0.38 42.38 42.88 43.12 43.39 43.90 436 1.02
mu[720] 43.04 0.02 0.39 42.29 42.78 43.06 43.30 43.80 288 1.02
mu[721] 42.97 0.02 0.39 42.22 42.72 42.97 43.22 43.71 328 1.01
mu[722] 42.87 0.02 0.37 42.13 42.63 42.86 43.12 43.60 349 1.01
mu[723] 42.80 0.02 0.38 42.08 42.54 42.80 43.07 43.53 358 1.02
mu[724] 42.76 0.02 0.38 42.06 42.51 42.74 43.01 43.52 325 1.02
mu[725] 42.73 0.02 0.38 42.01 42.47 42.71 42.99 43.48 260 1.02
mu[726] 42.68 0.02 0.38 41.96 42.40 42.67 42.94 43.43 314 1.02
mu[727] 42.65 0.02 0.39 41.89 42.38 42.66 42.91 43.43 295 1.02
mu[728] 42.62 0.03 0.39 41.85 42.35 42.63 42.88 43.36 235 1.02
mu[729] 42.59 0.02 0.38 41.82 42.35 42.58 42.86 43.34 304 1.02
mu[730] 42.58 0.02 0.39 41.83 42.32 42.58 42.85 43.34 294 1.02
mu[731] 42.61 0.02 0.38 41.90 42.35 42.61 42.86 43.39 319 1.02
mu[732] 42.61 0.02 0.39 41.90 42.36 42.60 42.86 43.42 316 1.01
mu[733] 42.61 0.02 0.39 41.87 42.35 42.61 42.85 43.43 312 1.01
mu[734] 42.62 0.02 0.39 41.92 42.36 42.61 42.86 43.45 306 1.01
mu[735] 42.65 0.02 0.40 41.93 42.38 42.65 42.91 43.45 267 1.01
mu[736] 42.70 0.02 0.39 41.98 42.43 42.68 42.96 43.46 266 1.01
mu[737] 42.78 0.02 0.39 42.06 42.51 42.77 43.04 43.58 240 1.01
mu[738] 42.85 0.02 0.39 42.11 42.59 42.85 43.11 43.61 244 1.00
mu[739] 42.92 0.02 0.38 42.19 42.65 42.91 43.17 43.68 245 1.00
mu[740] 42.99 0.02 0.37 42.30 42.73 42.99 43.24 43.73 237 1.00
mu[741] 43.10 0.02 0.38 42.39 42.84 43.10 43.35 43.81 263 1.00
mu[742] 43.22 0.02 0.38 42.46 42.96 43.21 43.49 43.94 240 1.00
mu[743] 43.33 0.02 0.38 42.61 43.06 43.33 43.59 44.08 249 1.00
mu[744] 43.45 0.02 0.38 42.71 43.18 43.46 43.71 44.19 252 1.00
mu[745] 43.56 0.02 0.39 42.81 43.30 43.55 43.81 44.31 280 1.00
mu[746] 43.65 0.02 0.39 42.88 43.40 43.66 43.91 44.43 262 1.00
mu[747] 43.73 0.02 0.40 42.96 43.48 43.74 43.99 44.49 260 1.00
mu[748] 43.80 0.02 0.40 43.02 43.54 43.80 44.06 44.60 268 1.00
mu[749] 43.89 0.02 0.39 43.12 43.64 43.89 44.16 44.64 271 1.00
mu[750] 43.99 0.02 0.39 43.22 43.72 44.00 44.24 44.79 281 1.00
mu[751] 44.07 0.02 0.39 43.30 43.81 44.07 44.34 44.81 267 1.00
mu[752] 44.14 0.03 0.38 43.36 43.88 44.15 44.40 44.87 223 1.00
mu[753] 44.18 0.03 0.39 43.44 43.93 44.20 44.45 44.90 207 1.00
mu[754] 44.20 0.03 0.39 43.43 43.95 44.22 44.47 44.95 215 1.00
mu[755] 44.19 0.03 0.39 43.38 43.95 44.20 44.45 44.91 236 1.00
mu[756] 44.18 0.02 0.38 43.42 43.94 44.19 44.44 44.90 292 1.00
mu[757] 44.19 0.02 0.37 43.44 43.94 44.21 44.45 44.90 258 1.00
mu[758] 44.22 0.02 0.37 43.44 43.98 44.23 44.46 44.96 280 1.00
mu[759] 44.22 0.02 0.37 43.47 43.99 44.23 44.45 44.92 227 1.00
mu[760] 44.21 0.02 0.36 43.52 43.97 44.21 44.46 44.90 279 1.00
mu[761] 44.19 0.02 0.37 43.48 43.94 44.19 44.46 44.87 280 1.00
mu[762] 44.18 0.02 0.37 43.50 43.93 44.18 44.46 44.91 266 1.00
mu[763] 44.17 0.02 0.37 43.43 43.93 44.18 44.43 44.92 328 1.01
mu[764] 44.14 0.02 0.36 43.44 43.88 44.13 44.38 44.87 320 1.00
mu[765] 44.14 0.02 0.37 43.40 43.90 44.13 44.37 44.88 294 1.00
mu[766] 44.14 0.02 0.36 43.43 43.90 44.14 44.37 44.90 270 1.01
mu[767] 44.12 0.02 0.37 43.39 43.88 44.13 44.36 44.86 229 1.01
mu[768] 44.09 0.02 0.36 43.37 43.86 44.10 44.34 44.79 253 1.01
mu[769] 44.07 0.02 0.37 43.31 43.84 44.07 44.31 44.79 254 1.01
mu[770] 44.04 0.02 0.37 43.31 43.79 44.05 44.27 44.79 264 1.01
mu[771] 44.04 0.02 0.37 43.34 43.79 44.06 44.28 44.77 291 1.01
mu[772] 44.05 0.02 0.37 43.30 43.81 44.05 44.30 44.81 269 1.00
mu[773] 44.13 0.02 0.38 43.40 43.87 44.13 44.37 44.90 240 1.01
mu[774] 44.19 0.03 0.38 43.46 43.93 44.19 44.44 44.92 203 1.02
mu[775] 44.24 0.03 0.39 43.49 43.97 44.24 44.50 44.96 228 1.01
mu[776] 44.25 0.03 0.39 43.45 43.99 44.26 44.52 45.01 210 1.01
mu[777] 44.28 0.03 0.39 43.56 44.01 44.27 44.55 44.99 219 1.01
mu[778] 44.29 0.03 0.39 43.53 44.02 44.29 44.55 45.05 228 1.01
mu[779] 44.31 0.02 0.39 43.54 44.04 44.30 44.60 45.08 264 1.01
mu[780] 44.32 0.02 0.39 43.58 44.04 44.31 44.60 45.11 266 1.01
mu[781] 44.30 0.02 0.39 43.49 44.05 44.30 44.56 45.06 256 1.01
mu[782] 44.27 0.02 0.39 43.49 44.01 44.26 44.55 44.99 256 1.00
mu[783] 44.23 0.02 0.38 43.49 43.98 44.23 44.50 44.94 294 1.00
mu[784] 44.20 0.02 0.37 43.49 43.96 44.20 44.45 44.91 292 1.00
mu[785] 44.17 0.02 0.36 43.49 43.94 44.17 44.41 44.86 274 1.00
mu[786] 44.15 0.02 0.36 43.45 43.92 44.15 44.39 44.83 268 1.00
mu[787] 44.17 0.02 0.36 43.49 43.93 44.17 44.41 44.84 245 1.00
mu[788] 44.17 0.02 0.36 43.50 43.92 44.17 44.42 44.89 264 1.00
mu[789] 44.18 0.02 0.35 43.49 43.94 44.18 44.42 44.88 246 1.00
mu[790] 44.23 0.02 0.37 43.52 43.98 44.23 44.47 44.93 260 1.00
mu[791] 44.28 0.02 0.37 43.56 44.04 44.28 44.54 44.95 234 1.00
mu[792] 44.34 0.02 0.37 43.60 44.08 44.34 44.58 45.04 246 1.00
mu[793] 44.40 0.02 0.37 43.65 44.15 44.40 44.65 45.16 264 1.00
mu[794] 44.50 0.02 0.37 43.81 44.25 44.49 44.75 45.25 286 1.00
mu[795] 44.57 0.02 0.37 43.87 44.31 44.56 44.84 45.32 337 1.00
mu[796] 44.63 0.02 0.37 43.92 44.38 44.63 44.89 45.37 322 1.00
mu[797] 44.67 0.02 0.38 43.94 44.41 44.67 44.92 45.44 378 1.00
mu[798] 44.72 0.02 0.38 44.00 44.46 44.71 44.96 45.51 365 1.00
mu[799] 44.76 0.02 0.39 44.01 44.49 44.76 45.01 45.54 396 1.00
mu[800] 44.78 0.02 0.38 44.05 44.52 44.79 45.05 45.54 369 1.00
mu[801] 44.80 0.02 0.37 44.04 44.55 44.79 45.06 45.51 316 1.00
mu[802] 44.81 0.02 0.38 44.07 44.56 44.82 45.06 45.52 326 1.00
mu[803] 44.80 0.02 0.37 44.06 44.57 44.80 45.06 45.51 341 1.00
mu[804] 44.79 0.02 0.38 44.05 44.53 44.80 45.04 45.51 301 1.00
mu[805] 44.78 0.02 0.38 44.02 44.53 44.79 45.03 45.52 259 1.00
mu[806] 44.78 0.02 0.37 44.07 44.53 44.79 45.02 45.51 235 1.00
mu[807] 44.78 0.02 0.38 44.03 44.51 44.78 45.03 45.55 254 1.00
mu[808] 44.76 0.02 0.37 44.06 44.50 44.76 44.99 45.54 266 1.00
mu[809] 44.74 0.02 0.39 43.99 44.47 44.74 45.00 45.49 275 1.00
mu[810] 44.70 0.02 0.38 43.93 44.46 44.70 44.96 45.45 268 1.00
mu[811] 44.67 0.02 0.39 43.89 44.41 44.66 44.93 45.43 247 1.00
mu[812] 44.64 0.02 0.38 43.88 44.38 44.64 44.89 45.40 243 1.00
mu[813] 44.61 0.02 0.37 43.91 44.35 44.61 44.86 45.35 241 1.00
mu[814] 44.60 0.02 0.37 43.86 44.34 44.60 44.86 45.36 249 1.00
mu[815] 44.64 0.02 0.38 43.91 44.38 44.63 44.89 45.33 236 1.00
mu[816] 44.67 0.02 0.38 43.97 44.41 44.66 44.91 45.39 229 1.00
mu[817] 44.66 0.03 0.38 43.90 44.40 44.67 44.92 45.44 219 1.00
mu[818] 44.64 0.03 0.38 43.93 44.37 44.63 44.89 45.42 216 1.00
mu[819] 44.64 0.03 0.38 43.93 44.37 44.63 44.88 45.43 221 1.00
mu[820] 44.66 0.03 0.38 43.93 44.40 44.65 44.91 45.40 206 1.00
mu[821] 44.69 0.02 0.38 43.95 44.44 44.68 44.94 45.46 233 1.00
mu[822] 44.70 0.03 0.39 43.97 44.42 44.69 44.95 45.42 232 1.00
mu[823] 44.73 0.03 0.39 43.98 44.47 44.73 44.99 45.49 200 1.00
mu[824] 44.75 0.03 0.40 44.00 44.47 44.74 45.02 45.52 192 1.00
mu[825] 44.76 0.03 0.40 43.93 44.49 44.76 45.01 45.57 225 1.00
mu[826] 44.76 0.03 0.40 43.95 44.51 44.77 45.04 45.51 212 1.01
mu[827] 44.81 0.03 0.40 44.02 44.56 44.81 45.08 45.50 206 1.01
mu[828] 44.85 0.03 0.39 44.07 44.60 44.85 45.11 45.57 204 1.01
mu[829] 44.91 0.03 0.40 44.11 44.64 44.92 45.18 45.68 230 1.01
mu[830] 44.96 0.03 0.40 44.19 44.70 44.97 45.22 45.75 221 1.01
mu[831] 45.00 0.03 0.41 44.16 44.73 45.00 45.28 45.79 221 1.01
mu[832] 45.02 0.03 0.42 44.18 44.74 45.03 45.30 45.85 213 1.01
mu[833] 45.03 0.03 0.42 44.19 44.76 45.02 45.32 45.85 200 1.01
mu[834] 45.03 0.03 0.41 44.21 44.77 45.04 45.29 45.85 193 1.01
mu[835] 45.03 0.03 0.42 44.19 44.77 45.04 45.30 45.85 179 1.01
mu[836] 45.01 0.03 0.42 44.17 44.74 45.03 45.30 45.80 154 1.02
mu[837] 45.01 0.03 0.42 44.17 44.75 45.03 45.30 45.82 157 1.02
mu[838] 44.97 0.03 0.42 44.14 44.69 44.96 45.25 45.80 157 1.02
mu[839] 44.89 0.04 0.43 44.07 44.60 44.89 45.17 45.74 146 1.02
mu[840] 44.81 0.03 0.43 43.96 44.54 44.82 45.10 45.62 161 1.02
mu[841] 44.75 0.03 0.43 43.91 44.46 44.76 45.04 45.61 178 1.02
mu[842] 44.70 0.03 0.42 43.89 44.42 44.71 45.00 45.53 176 1.02
mu[843] 44.67 0.03 0.42 43.83 44.40 44.67 44.97 45.46 177 1.02
mu[844] 44.62 0.03 0.42 43.82 44.33 44.62 44.91 45.43 183 1.02
mu[845] 44.59 0.03 0.43 43.74 44.29 44.59 44.89 45.40 194 1.01
mu[846] 44.54 0.03 0.42 43.73 44.25 44.55 44.82 45.33 198 1.01
mu[847] 44.50 0.03 0.42 43.72 44.20 44.50 44.78 45.32 213 1.01
mu[848] 44.45 0.03 0.41 43.67 44.15 44.45 44.74 45.25 221 1.02
mu[849] 44.42 0.03 0.41 43.61 44.14 44.42 44.70 45.24 226 1.01
mu[850] 44.47 0.03 0.41 43.70 44.18 44.48 44.76 45.24 235 1.01
mu[851] 44.50 0.03 0.42 43.70 44.20 44.51 44.78 45.32 264 1.01
mu[852] 44.51 0.03 0.42 43.71 44.22 44.51 44.80 45.37 257 1.01
mu[853] 44.53 0.03 0.41 43.75 44.24 44.52 44.82 45.33 252 1.00
mu[854] 44.56 0.03 0.41 43.81 44.27 44.55 44.85 45.40 261 1.00
mu[855] 44.60 0.03 0.42 43.84 44.31 44.60 44.91 45.38 243 1.00
mu[856] 44.64 0.03 0.42 43.85 44.34 44.64 44.94 45.49 250 1.01
mu[857] 44.70 0.03 0.42 43.89 44.41 44.70 45.00 45.50 246 1.00
mu[858] 44.76 0.03 0.42 43.92 44.48 44.75 45.05 45.62 265 1.01
mu[859] 44.80 0.02 0.41 44.00 44.52 44.78 45.08 45.63 278 1.00
mu[860] 44.85 0.02 0.42 44.05 44.56 44.84 45.14 45.69 291 1.01
mu[861] 44.89 0.02 0.40 44.09 44.61 44.91 45.16 45.69 272 1.01
mu[862] 44.95 0.02 0.41 44.16 44.68 44.94 45.22 45.70 281 1.01
mu[863] 44.99 0.02 0.41 44.23 44.71 44.98 45.25 45.78 287 1.01
mu[864] 45.02 0.02 0.41 44.25 44.73 45.01 45.29 45.83 307 1.01
mu[865] 45.04 0.02 0.40 44.25 44.77 45.05 45.31 45.79 326 1.00
mu[866] 45.07 0.02 0.40 44.32 44.81 45.06 45.33 45.83 333 1.00
mu[867] 45.09 0.02 0.39 44.34 44.83 45.09 45.38 45.83 329 1.01
mu[868] 45.10 0.02 0.40 44.32 44.83 45.10 45.39 45.87 324 1.00
mu[869] 45.12 0.02 0.39 44.36 44.85 45.10 45.40 45.86 317 1.00
mu[870] 45.14 0.02 0.38 44.38 44.86 45.15 45.40 45.87 290 1.00
mu[871] 45.16 0.02 0.37 44.44 44.89 45.16 45.42 45.90 273 1.00
mu[872] 45.19 0.02 0.39 44.41 44.93 45.18 45.44 45.95 261 1.00
mu[873] 45.20 0.03 0.38 44.45 44.95 45.20 45.45 45.95 203 1.00
mu[874] 45.18 0.03 0.40 44.38 44.92 45.18 45.45 45.91 243 1.00
mu[875] 45.15 0.03 0.39 44.42 44.88 45.16 45.43 45.85 180 1.00
mu[876] 45.13 0.03 0.39 44.42 44.85 45.13 45.41 45.83 189 1.00
mu[877] 45.11 0.03 0.39 44.37 44.84 45.13 45.38 45.86 156 1.00
mu[878] 45.15 0.04 0.40 44.33 44.87 45.16 45.42 45.93 130 1.00
mu[879] 45.19 0.03 0.41 44.35 44.91 45.19 45.48 45.98 136 1.00
mu[880] 45.19 0.04 0.42 44.31 44.90 45.20 45.49 45.99 116 1.01
mu[881] 45.20 0.04 0.42 44.38 44.92 45.21 45.49 46.02 117 1.01
mu[882] 45.21 0.04 0.41 44.42 44.92 45.22 45.49 45.96 114 1.00
mu[883] 45.23 0.04 0.41 44.40 44.96 45.23 45.50 46.00 129 1.01
mu[884] 45.25 0.03 0.42 44.42 44.97 45.27 45.53 46.04 187 1.00
mu[885] 45.27 0.03 0.41 44.47 45.00 45.28 45.58 46.03 205 1.00
mu[886] 45.28 0.03 0.41 44.47 45.02 45.29 45.57 46.05 206 1.00
mu[887] 45.29 0.03 0.41 44.42 45.02 45.30 45.56 46.06 225 1.00
mu[888] 45.29 0.03 0.41 44.45 45.02 45.29 45.57 46.02 220 1.00
mu[889] 45.28 0.03 0.41 44.44 45.01 45.28 45.57 46.05 236 1.00
mu[890] 45.29 0.03 0.40 44.47 45.04 45.29 45.56 46.05 237 1.00
mu[891] 45.30 0.03 0.40 44.54 45.02 45.30 45.58 46.08 242 1.00
mu[892] 45.32 0.03 0.40 44.49 45.04 45.33 45.59 46.07 224 1.00
mu[893] 45.34 0.03 0.41 44.53 45.06 45.34 45.61 46.12 221 1.00
mu[894] 45.35 0.03 0.41 44.54 45.06 45.36 45.63 46.16 226 1.00
mu[895] 45.36 0.03 0.42 44.53 45.08 45.38 45.64 46.17 229 1.00
mu[896] 45.37 0.03 0.41 44.53 45.10 45.40 45.65 46.18 243 1.00
mu[897] 45.39 0.03 0.41 44.59 45.11 45.39 45.67 46.16 254 1.00
mu[898] 45.39 0.02 0.40 44.60 45.11 45.39 45.66 46.17 261 1.00
mu[899] 45.39 0.03 0.39 44.60 45.12 45.40 45.65 46.17 240 1.00
mu[900] 45.37 0.03 0.40 44.62 45.11 45.37 45.64 46.19 240 1.00
mu[901] 45.37 0.02 0.39 44.58 45.10 45.39 45.62 46.16 270 1.00
mu[902] 45.34 0.02 0.39 44.57 45.08 45.35 45.59 46.13 261 1.00
mu[903] 45.34 0.02 0.39 44.58 45.08 45.34 45.62 46.12 274 1.00
mu[904] 45.35 0.02 0.39 44.60 45.08 45.33 45.61 46.14 251 1.00
mu[905] 45.39 0.02 0.38 44.68 45.13 45.36 45.65 46.15 244 1.00
mu[906] 45.41 0.02 0.38 44.66 45.14 45.40 45.67 46.19 248 1.00
mu[907] 45.39 0.03 0.39 44.66 45.12 45.39 45.66 46.18 245 1.00
mu[908] 45.36 0.03 0.39 44.63 45.08 45.36 45.62 46.18 241 1.00
mu[909] 45.33 0.02 0.41 44.60 45.05 45.31 45.60 46.21 270 1.00
mu[910] 45.29 0.02 0.40 44.53 45.03 45.27 45.54 46.16 271 1.00
mu[911] 45.27 0.02 0.40 44.54 45.01 45.27 45.52 46.10 294 1.00
mu[912] 45.23 0.02 0.40 44.46 44.97 45.20 45.50 46.10 280 1.00
mu[913] 45.19 0.02 0.39 44.42 44.92 45.17 45.43 46.05 273 1.00
mu[914] 45.15 0.02 0.40 44.35 44.88 45.13 45.40 45.98 280 1.00
mu[915] 45.09 0.02 0.39 44.35 44.83 45.08 45.34 45.89 303 1.00
mu[916] 45.04 0.02 0.40 44.27 44.78 45.02 45.31 45.82 333 1.00
mu[917] 45.01 0.02 0.40 44.23 44.76 45.00 45.27 45.82 318 1.00
mu[918] 44.97 0.02 0.38 44.23 44.72 44.97 45.22 45.72 312 1.00
mu[919] 44.96 0.02 0.38 44.21 44.70 44.97 45.22 45.72 301 1.00
mu[920] 44.93 0.02 0.36 44.22 44.66 44.93 45.17 45.66 300 1.00
mu[921] 44.89 0.02 0.38 44.18 44.62 44.89 45.15 45.66 297 1.00
mu[922] 44.88 0.02 0.38 44.18 44.63 44.87 45.15 45.63 299 1.00
mu[923] 44.86 0.02 0.39 44.09 44.58 44.86 45.10 45.66 283 1.00
mu[924] 44.85 0.02 0.39 44.10 44.57 44.84 45.12 45.63 254 1.01
mu[925] 44.84 0.03 0.39 44.10 44.56 44.84 45.10 45.61 245 1.01
mu[926] 44.81 0.03 0.41 44.03 44.53 44.82 45.09 45.60 227 1.01
mu[927] 44.81 0.03 0.40 44.06 44.53 44.82 45.08 45.62 219 1.01
mu[928] 44.79 0.03 0.41 44.00 44.51 44.77 45.06 45.58 230 1.01
mu[929] 44.76 0.03 0.41 44.04 44.48 44.74 45.05 45.54 235 1.01
mu[930] 44.72 0.03 0.40 43.97 44.45 44.71 44.99 45.51 235 1.01
mu[931] 44.69 0.03 0.40 43.92 44.43 44.69 44.97 45.44 255 1.00
mu[932] 44.66 0.03 0.40 43.93 44.39 44.66 44.91 45.46 255 1.01
mu[933] 44.63 0.03 0.40 43.87 44.37 44.63 44.90 45.42 253 1.01
mu[934] 44.59 0.03 0.40 43.86 44.32 44.59 44.86 45.34 251 1.00
mu[935] 44.57 0.03 0.40 43.77 44.31 44.57 44.83 45.35 247 1.00
mu[936] 44.55 0.02 0.40 43.77 44.29 44.56 44.83 45.35 262 1.00
mu[937] 44.56 0.02 0.40 43.78 44.28 44.58 44.80 45.36 284 1.00
mu[938] 44.55 0.02 0.40 43.76 44.28 44.55 44.80 45.39 275 1.00
mu[939] 44.53 0.02 0.40 43.72 44.26 44.53 44.79 45.31 255 1.00
mu[940] 44.55 0.02 0.39 43.76 44.28 44.56 44.80 45.31 247 1.00
mu[941] 44.57 0.03 0.41 43.78 44.29 44.58 44.85 45.36 236 1.00
mu[942] 44.60 0.03 0.41 43.76 44.33 44.62 44.88 45.36 223 1.00
mu[943] 44.63 0.03 0.41 43.79 44.35 44.64 44.92 45.42 243 1.00
mu[944] 44.63 0.03 0.42 43.79 44.35 44.63 44.92 45.47 208 1.00
mu[945] 44.65 0.03 0.42 43.86 44.38 44.64 44.93 45.44 180 1.00
mu[946] 44.68 0.03 0.40 43.88 44.39 44.69 44.96 45.45 163 1.00
mu[947] 44.70 0.03 0.40 43.91 44.42 44.72 44.98 45.48 174 1.00
mu[948] 44.77 0.03 0.41 44.00 44.50 44.77 45.05 45.55 177 1.00
mu[949] 44.82 0.03 0.41 44.03 44.55 44.82 45.09 45.66 164 1.01
mu[950] 44.86 0.03 0.40 44.06 44.58 44.87 45.13 45.64 196 1.01
mu[951] 44.89 0.03 0.40 44.03 44.62 44.89 45.16 45.68 181 1.01
mu[952] 44.98 0.03 0.41 44.13 44.72 44.98 45.25 45.77 186 1.01
mu[953] 45.04 0.03 0.41 44.20 44.76 45.05 45.31 45.86 239 1.01
mu[954] 45.10 0.03 0.41 44.27 44.82 45.12 45.36 45.90 199 1.02
mu[955] 45.15 0.03 0.41 44.34 44.87 45.15 45.43 45.93 265 1.01
mu[956] 45.18 0.03 0.41 44.36 44.90 45.18 45.48 45.97 263 1.01
mu[957] 45.21 0.03 0.41 44.41 44.91 45.19 45.50 46.01 211 1.02
mu[958] 45.24 0.03 0.42 44.45 44.95 45.22 45.53 46.02 254 1.01
mu[959] 45.27 0.02 0.42 44.45 44.96 45.26 45.56 46.09 296 1.01
mu[960] 45.31 0.02 0.41 44.55 45.04 45.30 45.60 46.08 268 1.01
mu[961] 45.36 0.03 0.40 44.62 45.10 45.35 45.63 46.14 181 1.01
mu[962] 45.42 0.03 0.40 44.64 45.15 45.40 45.70 46.21 189 1.01
mu[963] 45.47 0.03 0.41 44.70 45.18 45.47 45.75 46.30 177 1.01
mu[964] 45.50 0.03 0.41 44.73 45.21 45.48 45.77 46.34 188 1.01
mu[965] 45.51 0.03 0.42 44.69 45.24 45.52 45.80 46.36 188 1.01
mu[966] 45.52 0.03 0.43 44.70 45.23 45.53 45.83 46.37 175 1.01
mu[967] 45.54 0.03 0.42 44.73 45.26 45.54 45.83 46.36 164 1.01
mu[968] 45.56 0.04 0.41 44.72 45.28 45.57 45.83 46.33 139 1.01
mu[969] 45.59 0.04 0.42 44.78 45.31 45.59 45.88 46.42 124 1.02
mu[970] 45.60 0.04 0.42 44.76 45.31 45.63 45.88 46.42 120 1.02
mu[971] 45.61 0.04 0.43 44.73 45.32 45.63 45.91 46.42 122 1.02
mu[972] 45.58 0.04 0.45 44.64 45.27 45.58 45.88 46.43 101 1.02
mu[973] 45.57 0.05 0.46 44.64 45.26 45.59 45.88 46.43 102 1.02
mu[974] 45.57 0.05 0.46 44.62 45.25 45.60 45.90 46.44 97 1.02
mu[975] 45.57 0.05 0.48 44.59 45.25 45.58 45.91 46.45 102 1.02
mu[976] 45.56 0.05 0.50 44.53 45.23 45.57 45.91 46.52 85 1.02
mu[977] 45.54 0.06 0.53 44.46 45.18 45.56 45.91 46.53 83 1.01
mu[978] 45.54 0.06 0.56 44.42 45.17 45.56 45.92 46.58 86 1.01
mu[979] 45.55 0.06 0.59 44.35 45.17 45.57 45.95 46.59 87 1.01
mu[980] 45.54 0.07 0.62 44.29 45.15 45.55 45.98 46.69 82 1.01
mu[981] 45.53 0.07 0.65 44.18 45.13 45.55 45.98 46.79 79 1.01
mu[982] 45.53 0.08 0.67 44.10 45.09 45.55 46.00 46.84 77 1.01
mu[983] 45.54 0.08 0.70 44.06 45.06 45.56 46.03 46.85 75 1.01
mu[984] 45.54 0.08 0.72 44.04 45.06 45.53 46.04 46.87 73 1.01
mu[985] 45.54 0.09 0.75 43.98 45.07 45.56 46.04 46.93 74 1.01
mu[986] 45.54 0.09 0.78 43.97 45.05 45.55 46.05 47.04 72 1.01
mu[987] 45.55 0.09 0.80 43.95 45.06 45.54 46.07 47.18 72 1.01
mu[988] 45.56 0.10 0.82 43.93 45.02 45.57 46.11 47.23 73 1.01
mu[989] 45.56 0.10 0.84 43.87 45.02 45.58 46.12 47.25 74 1.01
mu[990] 45.56 0.10 0.86 43.81 45.01 45.56 46.11 47.38 76 1.01
mu[991] 45.55 0.10 0.87 43.85 44.97 45.54 46.14 47.36 72 1.01
mu[992] 45.54 0.10 0.88 43.89 44.94 45.54 46.11 47.38 71 1.01
mu[993] 45.54 0.11 0.91 43.79 44.96 45.55 46.13 47.43 67 1.01
mu[994] 45.54 0.12 0.94 43.73 44.91 45.53 46.18 47.49 66 1.02
mu[995] 45.55 0.12 0.96 43.67 44.91 45.54 46.17 47.53 67 1.02
mu[996] 45.55 0.12 0.97 43.64 44.89 45.54 46.16 47.64 68 1.02
mu[997] 45.56 0.12 0.99 43.59 44.93 45.55 46.18 47.59 68 1.02
mu[998] 45.57 0.12 0.99 43.67 44.90 45.54 46.20 47.60 71 1.02
mu[999] 45.57 0.12 1.01 43.59 44.89 45.52 46.23 47.68 68 1.02
mu[1000] 45.57 0.12 1.03 43.57 44.87 45.51 46.22 47.63 68 1.02
mu[1001] 45.56 0.12 1.04 43.60 44.87 45.53 46.21 47.68 70 1.02
mu[1002] 45.57 0.12 1.06 43.60 44.85 45.53 46.25 47.74 74 1.02
mu[1003] 45.57 0.13 1.08 43.51 44.86 45.51 46.26 47.80 73 1.02
mu[1004] 45.57 0.13 1.10 43.54 44.82 45.54 46.26 47.75 74 1.02
mu[1005] 45.57 0.12 1.11 43.43 44.82 45.55 46.27 47.85 78 1.02
mu[1006] 45.57 0.13 1.12 43.48 44.79 45.54 46.28 47.87 79 1.02
mu[1007] 45.56 0.13 1.14 43.47 44.77 45.52 46.32 47.94 82 1.02
mu[1008] 45.56 0.13 1.14 43.42 44.79 45.52 46.33 48.02 81 1.02
mu[1009] 45.57 0.13 1.17 43.33 44.81 45.56 46.31 48.04 84 1.02
mu[1010] 45.58 0.13 1.19 43.30 44.78 45.53 46.29 48.08 84 1.02
mu[1011] 45.57 0.13 1.22 43.31 44.71 45.55 46.35 48.08 86 1.02
mu[1012] 45.57 0.13 1.23 43.30 44.72 45.54 46.35 48.12 91 1.02
mu[1013] 45.55 0.13 1.24 43.25 44.67 45.53 46.34 48.13 92 1.02
mu[1014] 45.56 0.13 1.26 43.25 44.69 45.53 46.35 48.16 93 1.02
Samples were drawn using NUTS(diag_e) at Fri Sep 27 12:40:40 2019.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).Now Let’s see…
Now we can extract the model fit and see how it looks!
mu_trump <- extract(trump_model, pars = "mu", permuted = T)[[1]] %>%
as.data.frame
names(mu_trump) <- unique(dat_range$date_range)
mu_ts_trump <- mu_trump %>% reshape2::melt() %>%
mutate(date = as.Date(variable)) %>%
group_by(date) %>%
summarise(median = median(value),
lower = quantile(value, 0.025),
upper = quantile(value, 0.975),
candidate = "Trump")Partisanship…
Looks like despite a dip in late 2017, Mr. Trump’s approval rating is remarkably stable (as a reminder, it looks like the lowest ever was 25% for President G.W. Bush). It will be curious to see how this changes as more information comes out regarding Mr. Trumps actions with Ukraine.
mu_ts_trump %>%
ggplot(aes(date, median))+
geom_line(color = "#E91D0E")+
geom_ribbon(aes(ymin = lower, ymax = upper), alpha = .2)+
labs(
title = "President Trump's Approval Rating",
subtitle = "Based on State-Space Modeling\nInitial Prior: 46%",
caption = "Data: https://github.com/fivethirtyeight/data/tree/master/polls",
y = "Approval",
x = NULL
)+
geom_vline(xintercept = as.Date(Sys.Date()), color = "orange")