suppressPackageStartupMessages(library(tidyverse))
theme_set(theme_minimal())
dat <- read_csv("https://projects.fivethirtyeight.com/polls-page/president_approval_polls.csv")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!
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)
Attaching package: 'lubridate'The following objects are masked from 'package:base':
date, intersect, setdiff, uniondat_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 courtesy 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)Loading required package: StanHeaders
rstan version 2.26.3 (Stan version 2.26.1)For execution on a local, multicore CPU with excess RAM we recommend calling
options(mc.cores = parallel::detectCores()).
To avoid recompilation of unchanged Stan programs, we recommend calling
rstan_options(auto_write = TRUE)
For within-chain threading using `reduce_sum()` or `map_rect()` Stan functions,
change `threads_per_chain` option:
rstan_options(threads_per_chain = 1)
Attaching package: 'rstan'The following object is masked from 'package:tidyr':
extractrstan_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….
sstrump <- stan_model("sstrump.stan")recompiling to avoid crashing R sessiontrump_model <- sampling(sstrump,
data = approval_data,
iter = 1000,
refresh = 0,
chains = 2,
control = list(adapt_delta = .95,
max_treedepth = 15))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
https://mc-stan.org/misc/warnings.html#bulk-essWarning: 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
https://mc-stan.org/misc/warnings.html#tail-essDid 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: anon_model.
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] 43.38 0.02 0.45 42.50 43.08 43.38 43.69 44.23 425 1.01
mu[2] 43.31 0.02 0.44 42.48 43.01 43.30 43.61 44.16 460 1.01
mu[3] 43.22 0.02 0.42 42.41 42.95 43.22 43.52 44.03 415 1.01
mu[4] 43.16 0.02 0.41 42.42 42.87 43.15 43.43 44.00 354 1.01
mu[5] 43.12 0.02 0.42 42.35 42.83 43.12 43.39 43.94 321 1.01
mu[6] 43.05 0.03 0.42 42.26 42.76 43.05 43.34 43.89 243 1.01
mu[7] 42.99 0.02 0.41 42.23 42.71 42.98 43.26 43.82 299 1.01
mu[8] 42.91 0.02 0.40 42.10 42.66 42.91 43.16 43.70 282 1.01
mu[9] 42.86 0.02 0.39 42.08 42.60 42.85 43.11 43.65 274 1.01
mu[10] 42.81 0.02 0.39 42.02 42.56 42.83 43.07 43.60 260 1.01
mu[11] 42.79 0.02 0.39 41.97 42.53 42.78 43.05 43.54 265 1.01
mu[12] 42.78 0.02 0.39 41.98 42.52 42.78 43.04 43.54 272 1.00
mu[13] 42.78 0.02 0.39 41.98 42.54 42.79 43.04 43.55 312 1.00
mu[14] 42.81 0.02 0.40 42.05 42.57 42.82 43.07 43.61 304 1.00
mu[15] 42.85 0.02 0.39 42.07 42.58 42.86 43.12 43.58 301 1.01
mu[16] 42.90 0.02 0.39 42.11 42.63 42.91 43.16 43.64 328 1.00
mu[17] 42.93 0.02 0.38 42.14 42.67 42.94 43.19 43.64 332 1.00
mu[18] 42.97 0.02 0.38 42.17 42.72 42.95 43.24 43.69 309 1.00
mu[19] 43.02 0.02 0.38 42.24 42.77 43.02 43.29 43.74 318 1.00
mu[20] 43.04 0.02 0.38 42.28 42.78 43.05 43.30 43.81 316 1.00
mu[21] 43.08 0.02 0.38 42.36 42.82 43.08 43.33 43.86 317 1.00
mu[22] 43.15 0.02 0.39 42.41 42.89 43.13 43.39 43.93 310 1.00
mu[23] 43.22 0.02 0.38 42.50 42.97 43.22 43.47 43.97 297 1.00
mu[24] 43.28 0.02 0.38 42.49 43.04 43.28 43.54 43.99 297 1.00
mu[25] 43.32 0.02 0.36 42.60 43.08 43.32 43.57 43.99 270 1.00
mu[26] 43.35 0.02 0.36 42.60 43.10 43.36 43.60 44.04 282 1.00
mu[27] 43.38 0.02 0.36 42.66 43.14 43.40 43.62 44.06 276 1.00
mu[28] 43.41 0.02 0.36 42.67 43.18 43.42 43.67 44.09 316 1.00
mu[29] 43.45 0.02 0.37 42.70 43.22 43.46 43.71 44.16 304 1.00
mu[30] 43.51 0.02 0.37 42.78 43.26 43.53 43.76 44.20 277 1.00
mu[31] 43.53 0.02 0.37 42.83 43.26 43.52 43.79 44.20 304 1.00
mu[32] 43.55 0.02 0.37 42.83 43.29 43.57 43.82 44.25 297 1.00
mu[33] 43.58 0.02 0.38 42.86 43.31 43.59 43.85 44.30 304 1.00
mu[34] 43.62 0.02 0.39 42.87 43.35 43.63 43.90 44.33 313 1.00
mu[35] 43.65 0.02 0.40 42.87 43.36 43.65 43.92 44.39 315 1.00
mu[36] 43.70 0.02 0.39 42.93 43.43 43.72 43.98 44.43 339 1.00
mu[37] 43.77 0.02 0.40 43.04 43.50 43.79 44.05 44.53 324 1.00
mu[38] 43.81 0.02 0.39 43.06 43.54 43.82 44.08 44.56 351 1.00
mu[39] 43.85 0.02 0.39 43.11 43.57 43.86 44.12 44.59 349 1.00
mu[40] 43.89 0.02 0.38 43.15 43.63 43.90 44.15 44.63 352 1.00
mu[41] 43.91 0.02 0.39 43.14 43.66 43.90 44.19 44.65 330 1.00
mu[42] 43.90 0.02 0.39 43.11 43.64 43.90 44.18 44.66 340 1.00
mu[43] 43.91 0.02 0.39 43.15 43.65 43.91 44.18 44.64 333 1.01
mu[44] 43.94 0.02 0.39 43.21 43.66 43.94 44.21 44.64 322 1.01
mu[45] 43.96 0.02 0.38 43.24 43.70 43.97 44.24 44.67 312 1.01
mu[46] 43.98 0.02 0.38 43.23 43.73 44.00 44.25 44.67 278 1.01
mu[47] 43.96 0.02 0.38 43.20 43.69 43.98 44.24 44.67 256 1.01
mu[48] 43.94 0.02 0.38 43.18 43.68 43.95 44.20 44.67 274 1.01
mu[49] 43.96 0.02 0.38 43.23 43.70 43.94 44.22 44.67 303 1.01
mu[50] 43.94 0.02 0.38 43.18 43.69 43.94 44.21 44.69 310 1.01
mu[51] 43.96 0.02 0.39 43.16 43.69 43.96 44.23 44.67 272 1.01
mu[52] 43.97 0.02 0.38 43.23 43.70 43.98 44.22 44.72 285 1.01
mu[53] 43.96 0.02 0.38 43.22 43.69 43.96 44.22 44.65 273 1.01
mu[54] 43.93 0.02 0.39 43.18 43.67 43.93 44.20 44.70 277 1.01
mu[55] 43.91 0.03 0.39 43.18 43.64 43.90 44.18 44.72 237 1.01
mu[56] 43.89 0.03 0.40 43.12 43.61 43.88 44.16 44.70 254 1.01
mu[57] 43.85 0.03 0.40 43.08 43.57 43.84 44.12 44.61 168 1.02
mu[58] 43.81 0.03 0.40 43.04 43.52 43.82 44.10 44.54 233 1.01
mu[59] 43.80 0.03 0.40 43.03 43.51 43.79 44.08 44.56 229 1.01
mu[60] 43.77 0.02 0.39 43.03 43.49 43.77 44.04 44.55 293 1.01
mu[61] 43.74 0.02 0.39 43.01 43.48 43.73 44.00 44.49 307 1.01
mu[62] 43.72 0.02 0.39 42.97 43.45 43.71 43.97 44.47 313 1.01
mu[63] 43.68 0.02 0.38 42.94 43.42 43.68 43.93 44.44 306 1.01
mu[64] 43.63 0.02 0.38 42.85 43.38 43.63 43.87 44.35 307 1.01
mu[65] 43.66 0.02 0.38 42.94 43.41 43.66 43.91 44.42 303 1.01
mu[66] 43.67 0.02 0.37 42.95 43.40 43.66 43.92 44.38 301 1.01
mu[67] 43.68 0.02 0.37 42.97 43.42 43.68 43.95 44.42 301 1.01
mu[68] 43.68 0.02 0.37 42.96 43.44 43.67 43.94 44.42 319 1.01
mu[69] 43.71 0.02 0.37 42.99 43.44 43.71 43.97 44.43 301 1.00
mu[70] 43.71 0.02 0.38 43.01 43.44 43.69 43.96 44.47 293 1.00
mu[71] 43.72 0.02 0.39 43.02 43.45 43.70 43.98 44.49 300 1.00
mu[72] 43.71 0.02 0.37 43.02 43.45 43.70 43.96 44.47 310 1.00
mu[73] 43.70 0.02 0.37 42.98 43.45 43.70 43.94 44.45 315 1.01
mu[74] 43.67 0.02 0.37 42.94 43.41 43.65 43.92 44.40 326 1.01
mu[75] 43.67 0.02 0.37 42.93 43.42 43.67 43.92 44.41 305 1.01
mu[76] 43.67 0.02 0.38 42.93 43.41 43.67 43.93 44.40 338 1.01
mu[77] 43.69 0.02 0.37 42.99 43.44 43.68 43.94 44.46 369 1.01
mu[78] 43.72 0.02 0.36 43.03 43.48 43.71 43.98 44.40 376 1.01
mu[79] 43.77 0.02 0.37 43.02 43.52 43.77 44.02 44.50 409 1.01
mu[80] 43.81 0.02 0.38 43.07 43.55 43.79 44.07 44.56 393 1.01
mu[81] 43.86 0.02 0.38 43.06 43.62 43.86 44.11 44.61 378 1.00
mu[82] 43.93 0.02 0.39 43.10 43.68 43.93 44.18 44.66 391 1.00
mu[83] 43.97 0.02 0.39 43.16 43.72 43.97 44.25 44.71 414 1.01
mu[84] 44.02 0.02 0.39 43.23 43.77 44.01 44.28 44.76 367 1.01
mu[85] 44.08 0.02 0.39 43.30 43.84 44.10 44.34 44.84 334 1.01
mu[86] 44.16 0.02 0.39 43.37 43.92 44.17 44.42 44.91 284 1.00
mu[87] 44.22 0.02 0.39 43.41 43.98 44.23 44.48 44.95 308 1.00
mu[88] 44.27 0.02 0.39 43.49 44.01 44.26 44.55 44.98 306 1.00
mu[89] 44.34 0.02 0.39 43.57 44.08 44.35 44.61 45.10 302 1.00
mu[90] 44.41 0.02 0.39 43.63 44.16 44.42 44.68 45.19 292 1.01
mu[91] 44.48 0.02 0.39 43.71 44.22 44.48 44.74 45.22 271 1.00
mu[92] 44.52 0.03 0.40 43.78 44.25 44.51 44.80 45.34 248 1.00
mu[93] 44.57 0.02 0.40 43.84 44.28 44.56 44.83 45.38 265 1.00
mu[94] 44.60 0.03 0.39 43.89 44.31 44.59 44.86 45.42 235 1.00
mu[95] 44.66 0.03 0.40 43.89 44.38 44.65 44.94 45.41 211 1.00
mu[96] 44.72 0.03 0.41 43.97 44.43 44.72 45.01 45.55 189 1.00
mu[97] 44.76 0.03 0.41 43.94 44.46 44.75 45.04 45.48 190 1.00
mu[98] 44.82 0.03 0.42 44.01 44.52 44.80 45.12 45.65 184 1.01
mu[99] 44.87 0.03 0.43 44.06 44.58 44.86 45.17 45.72 190 1.01
mu[100] 44.93 0.03 0.42 44.10 44.64 44.93 45.22 45.73 184 1.01
mu[101] 44.99 0.03 0.42 44.18 44.70 44.99 45.28 45.80 182 1.00
mu[102] 45.05 0.03 0.41 44.29 44.77 45.06 45.33 45.87 176 1.01
mu[103] 45.10 0.03 0.42 44.33 44.81 45.10 45.38 45.90 195 1.01
mu[104] 45.15 0.03 0.42 44.37 44.85 45.14 45.43 45.96 202 1.01
mu[105] 45.18 0.03 0.42 44.39 44.90 45.18 45.47 46.02 187 1.01
mu[106] 45.24 0.03 0.42 44.46 44.95 45.23 45.50 46.09 195 1.01
mu[107] 45.27 0.03 0.43 44.41 44.99 45.26 45.55 46.13 184 1.01
mu[108] 45.29 0.03 0.42 44.46 45.03 45.29 45.56 46.12 162 1.01
mu[109] 45.31 0.03 0.42 44.46 45.04 45.30 45.58 46.17 174 1.01
mu[110] 45.30 0.03 0.43 44.44 45.02 45.30 45.59 46.15 209 1.01
mu[111] 45.26 0.03 0.43 44.36 44.98 45.28 45.56 46.04 208 1.01
mu[112] 45.27 0.03 0.44 44.35 44.96 45.28 45.57 46.13 197 1.01
mu[113] 45.26 0.03 0.44 44.32 44.97 45.28 45.55 46.06 207 1.01
mu[114] 45.28 0.03 0.43 44.36 44.99 45.31 45.57 46.07 197 1.01
mu[115] 45.28 0.03 0.43 44.37 45.00 45.29 45.57 46.10 221 1.01
mu[116] 45.29 0.03 0.43 44.43 45.01 45.31 45.57 46.10 260 1.01
mu[117] 45.28 0.03 0.43 44.34 45.02 45.29 45.57 46.10 247 1.01
mu[118] 45.28 0.03 0.43 44.42 44.99 45.29 45.56 46.12 219 1.01
mu[119] 45.26 0.03 0.43 44.35 44.98 45.25 45.56 46.10 222 1.01
mu[120] 45.25 0.03 0.43 44.42 44.97 45.24 45.53 46.08 241 1.01
mu[121] 45.24 0.03 0.43 44.42 44.95 45.24 45.51 46.06 249 1.01
mu[122] 45.22 0.03 0.44 44.34 44.94 45.21 45.49 46.11 261 1.01
mu[123] 45.19 0.03 0.44 44.37 44.89 45.18 45.48 46.10 272 1.01
mu[124] 45.17 0.02 0.42 44.34 44.89 45.17 45.47 46.00 291 1.01
mu[125] 45.15 0.02 0.42 44.31 44.86 45.14 45.42 45.99 303 1.01
mu[126] 45.15 0.02 0.43 44.29 44.86 45.14 45.44 45.97 311 1.01
mu[127] 45.14 0.03 0.43 44.32 44.84 45.13 45.43 45.97 283 1.01
mu[128] 45.13 0.02 0.42 44.30 44.86 45.12 45.42 45.94 299 1.01
mu[129] 45.12 0.02 0.41 44.35 44.83 45.11 45.41 45.93 320 1.01
mu[130] 45.10 0.02 0.41 44.32 44.81 45.10 45.40 45.92 319 1.00
mu[131] 45.06 0.02 0.40 44.25 44.77 45.07 45.35 45.80 305 1.01
mu[132] 45.02 0.02 0.41 44.23 44.74 45.04 45.30 45.80 306 1.00
mu[133] 44.98 0.02 0.41 44.19 44.71 44.98 45.26 45.78 308 1.00
mu[134] 44.99 0.02 0.40 44.21 44.72 44.99 45.26 45.74 291 1.00
mu[135] 44.98 0.02 0.40 44.20 44.71 44.99 45.27 45.73 276 1.00
mu[136] 44.98 0.02 0.40 44.17 44.71 44.98 45.26 45.77 280 1.00
mu[137] 44.95 0.02 0.40 44.08 44.69 44.97 45.23 45.69 271 1.01
mu[138] 44.93 0.03 0.40 44.10 44.66 44.96 45.23 45.67 233 1.01
mu[139] 44.96 0.02 0.41 44.14 44.69 44.96 45.25 45.71 291 1.01
mu[140] 45.00 0.03 0.41 44.18 44.73 45.01 45.29 45.77 271 1.00
mu[141] 45.02 0.03 0.41 44.20 44.73 45.05 45.30 45.82 259 1.01
mu[142] 45.05 0.03 0.42 44.19 44.78 45.07 45.34 45.82 266 1.01
mu[143] 45.04 0.03 0.41 44.17 44.77 45.07 45.32 45.79 266 1.00
mu[144] 45.01 0.02 0.40 44.21 44.75 45.02 45.29 45.72 266 1.00
mu[145] 44.99 0.02 0.40 44.16 44.71 45.00 45.26 45.76 308 1.00
mu[146] 44.99 0.02 0.39 44.24 44.72 44.99 45.24 45.72 304 1.00
mu[147] 44.97 0.02 0.40 44.17 44.70 44.95 45.24 45.74 303 1.00
mu[148] 44.96 0.02 0.40 44.24 44.68 44.94 45.24 45.77 298 1.00
mu[149] 44.95 0.02 0.39 44.19 44.70 44.94 45.21 45.71 301 1.00
mu[150] 44.91 0.02 0.40 44.16 44.63 44.89 45.16 45.75 302 1.00
mu[151] 44.88 0.02 0.40 44.13 44.61 44.86 45.13 45.71 287 1.00
mu[152] 44.84 0.02 0.40 44.07 44.59 44.84 45.09 45.66 298 1.00
mu[153] 44.79 0.02 0.41 44.01 44.51 44.79 45.07 45.60 294 1.00
mu[154] 44.74 0.02 0.40 43.99 44.49 44.73 45.01 45.52 280 1.00
mu[155] 44.69 0.02 0.40 43.90 44.43 44.69 44.97 45.46 262 1.00
mu[156] 44.64 0.03 0.40 43.84 44.38 44.63 44.91 45.38 250 1.00
mu[157] 44.60 0.03 0.40 43.76 44.34 44.59 44.86 45.38 250 1.00
mu[158] 44.56 0.03 0.40 43.77 44.29 44.56 44.83 45.36 246 1.00
mu[159] 44.49 0.03 0.41 43.71 44.22 44.49 44.76 45.29 260 1.00
mu[160] 44.45 0.03 0.42 43.64 44.17 44.44 44.73 45.28 261 1.00
mu[161] 44.40 0.03 0.42 43.61 44.11 44.39 44.67 45.27 243 1.00
mu[162] 44.38 0.03 0.42 43.57 44.09 44.36 44.66 45.22 224 1.00
mu[163] 44.36 0.03 0.41 43.56 44.08 44.36 44.65 45.14 219 1.00
mu[164] 44.33 0.03 0.41 43.54 44.06 44.33 44.61 45.10 207 1.00
mu[165] 44.29 0.03 0.40 43.47 44.00 44.29 44.58 45.04 222 1.00
mu[166] 44.22 0.03 0.40 43.45 43.94 44.23 44.50 44.98 207 1.00
mu[167] 44.25 0.03 0.41 43.39 43.99 44.25 44.53 45.02 201 1.00
mu[168] 44.31 0.03 0.41 43.47 44.03 44.31 44.59 45.12 195 1.00
mu[169] 44.37 0.03 0.41 43.61 44.10 44.35 44.64 45.15 209 1.00
mu[170] 44.43 0.03 0.41 43.67 44.17 44.43 44.70 45.24 230 1.00
mu[171] 44.49 0.03 0.40 43.72 44.20 44.49 44.76 45.29 249 1.00
mu[172] 44.53 0.03 0.40 43.79 44.25 44.53 44.79 45.32 255 1.00
mu[173] 44.57 0.02 0.39 43.78 44.32 44.57 44.85 45.34 268 1.00
mu[174] 44.63 0.02 0.40 43.82 44.35 44.64 44.90 45.40 284 1.00
mu[175] 44.70 0.02 0.41 43.94 44.42 44.70 44.97 45.46 305 1.00
mu[176] 44.79 0.02 0.41 43.97 44.50 44.79 45.07 45.57 283 1.00
mu[177] 44.86 0.02 0.41 44.06 44.58 44.84 45.14 45.67 280 1.00
mu[178] 44.89 0.03 0.41 44.11 44.61 44.89 45.19 45.67 268 1.00
mu[179] 44.90 0.03 0.41 44.11 44.62 44.90 45.18 45.72 267 1.00
mu[180] 44.92 0.02 0.42 44.12 44.64 44.93 45.19 45.73 305 1.00
mu[181] 44.92 0.02 0.43 44.11 44.63 44.92 45.22 45.76 303 1.00
mu[182] 44.90 0.02 0.41 44.10 44.61 44.91 45.17 45.70 296 1.00
mu[183] 44.87 0.02 0.41 44.07 44.60 44.86 45.13 45.73 306 1.00
mu[184] 44.83 0.02 0.41 44.05 44.55 44.82 45.08 45.68 311 1.00
mu[185] 44.79 0.02 0.40 44.05 44.52 44.79 45.06 45.58 302 1.00
mu[186] 44.74 0.02 0.41 43.94 44.46 44.73 45.03 45.55 305 1.00
mu[187] 44.68 0.02 0.39 43.95 44.41 44.67 44.95 45.44 279 1.01
mu[188] 44.64 0.02 0.39 43.88 44.37 44.63 44.90 45.43 301 1.01
mu[189] 44.58 0.02 0.40 43.82 44.31 44.57 44.85 45.37 309 1.00
mu[190] 44.56 0.02 0.41 43.77 44.28 44.55 44.83 45.39 315 1.01
mu[191] 44.54 0.02 0.40 43.75 44.26 44.53 44.81 45.30 290 1.01
mu[192] 44.52 0.02 0.40 43.78 44.24 44.51 44.82 45.31 279 1.01
mu[193] 44.50 0.02 0.41 43.75 44.21 44.49 44.78 45.27 287 1.01
mu[194] 44.48 0.03 0.41 43.69 44.21 44.49 44.75 45.29 260 1.01
mu[195] 44.44 0.03 0.41 43.62 44.16 44.45 44.71 45.22 266 1.01
mu[196] 44.40 0.03 0.42 43.55 44.12 44.40 44.69 45.25 260 1.01
mu[197] 44.41 0.03 0.41 43.59 44.12 44.40 44.69 45.21 251 1.01
mu[198] 44.44 0.03 0.42 43.61 44.18 44.43 44.72 45.30 238 1.01
mu[199] 44.46 0.03 0.42 43.61 44.20 44.45 44.76 45.29 267 1.01
mu[200] 44.45 0.03 0.41 43.59 44.17 44.46 44.72 45.26 272 1.00
mu[201] 44.43 0.02 0.41 43.61 44.16 44.43 44.70 45.26 271 1.00
mu[202] 44.46 0.03 0.41 43.66 44.19 44.45 44.73 45.28 261 1.00
mu[203] 44.49 0.03 0.41 43.69 44.21 44.49 44.78 45.29 268 1.00
mu[204] 44.54 0.03 0.41 43.67 44.28 44.56 44.82 45.35 263 1.00
mu[205] 44.60 0.02 0.41 43.80 44.33 44.60 44.88 45.39 275 1.00
mu[206] 44.65 0.02 0.41 43.85 44.37 44.65 44.92 45.49 282 1.00
mu[207] 44.68 0.02 0.41 43.91 44.41 44.69 44.96 45.45 274 1.00
mu[208] 44.72 0.02 0.39 43.96 44.46 44.71 45.00 45.50 295 1.00
mu[209] 44.73 0.02 0.38 43.96 44.49 44.73 44.99 45.47 282 1.00
mu[210] 44.74 0.02 0.38 43.96 44.48 44.74 45.01 45.48 301 1.00
mu[211] 44.74 0.02 0.39 43.95 44.49 44.75 45.00 45.47 307 1.00
mu[212] 44.76 0.02 0.38 43.98 44.54 44.76 45.03 45.47 326 1.00
mu[213] 44.78 0.02 0.38 44.00 44.52 44.78 45.03 45.56 354 1.00
mu[214] 44.77 0.02 0.39 43.99 44.51 44.76 45.04 45.53 350 1.00
mu[215] 44.75 0.02 0.38 44.00 44.49 44.74 44.99 45.55 366 1.00
mu[216] 44.73 0.02 0.38 43.95 44.46 44.73 44.97 45.46 382 1.00
mu[217] 44.68 0.02 0.39 43.92 44.43 44.68 44.96 45.45 397 1.00
mu[218] 44.64 0.02 0.38 43.87 44.39 44.65 44.90 45.36 407 1.00
mu[219] 44.61 0.02 0.38 43.91 44.35 44.60 44.87 45.36 377 1.00
mu[220] 44.56 0.02 0.37 43.86 44.29 44.56 44.79 45.32 406 1.00
mu[221] 44.49 0.02 0.37 43.76 44.24 44.48 44.71 45.26 383 1.00
mu[222] 44.39 0.02 0.36 43.67 44.13 44.39 44.63 45.07 365 1.00
mu[223] 44.33 0.02 0.36 43.60 44.09 44.35 44.56 45.02 390 1.00
mu[224] 44.27 0.02 0.37 43.57 44.01 44.28 44.52 44.92 337 1.00
mu[225] 44.22 0.02 0.37 43.48 43.96 44.22 44.48 44.90 338 1.00
mu[226] 44.18 0.02 0.37 43.42 43.92 44.20 44.43 44.89 314 1.00
mu[227] 44.18 0.02 0.37 43.47 43.92 44.18 44.42 44.88 313 1.00
mu[228] 44.17 0.02 0.36 43.49 43.93 44.19 44.41 44.84 306 1.00
mu[229] 44.16 0.02 0.35 43.45 43.93 44.16 44.40 44.85 348 1.00
mu[230] 44.19 0.02 0.36 43.45 43.95 44.19 44.44 44.91 315 1.00
mu[231] 44.21 0.02 0.37 43.48 43.97 44.22 44.47 44.95 277 1.00
mu[232] 44.24 0.02 0.38 43.53 43.98 44.23 44.50 44.98 319 1.00
mu[233] 44.29 0.02 0.38 43.56 44.03 44.30 44.53 45.05 341 1.00
mu[234] 44.34 0.02 0.37 43.62 44.08 44.35 44.58 45.05 349 1.00
mu[235] 44.35 0.02 0.38 43.62 44.09 44.35 44.60 45.10 341 1.00
mu[236] 44.34 0.02 0.38 43.62 44.07 44.35 44.59 45.10 342 1.00
mu[237] 44.33 0.02 0.37 43.64 44.07 44.32 44.57 45.10 333 1.00
mu[238] 44.31 0.02 0.37 43.59 44.07 44.31 44.55 45.06 306 1.00
mu[239] 44.28 0.02 0.36 43.59 44.04 44.28 44.52 44.99 362 1.00
mu[240] 44.27 0.02 0.37 43.57 44.01 44.26 44.51 45.02 304 1.00
mu[241] 44.23 0.02 0.37 43.53 43.96 44.24 44.47 44.97 309 1.00
mu[242] 44.15 0.02 0.36 43.44 43.92 44.15 44.42 44.83 281 1.00
mu[243] 44.08 0.02 0.36 43.41 43.83 44.10 44.33 44.77 317 1.00
mu[244] 44.05 0.02 0.36 43.35 43.78 44.05 44.30 44.78 364 1.00
mu[245] 44.04 0.02 0.36 43.37 43.79 44.04 44.30 44.76 311 1.00
mu[246] 44.06 0.02 0.37 43.34 43.81 44.05 44.32 44.75 353 1.00
mu[247] 44.10 0.02 0.37 43.35 43.84 44.10 44.36 44.82 389 1.00
mu[248] 44.13 0.02 0.37 43.40 43.88 44.13 44.38 44.85 383 1.00
mu[249] 44.14 0.02 0.37 43.43 43.89 44.14 44.38 44.90 379 1.00
mu[250] 44.14 0.02 0.38 43.43 43.89 44.14 44.38 44.90 346 1.00
mu[251] 44.13 0.02 0.37 43.44 43.88 44.12 44.39 44.88 319 1.01
mu[252] 44.14 0.02 0.37 43.44 43.88 44.14 44.38 44.89 346 1.00
mu[253] 44.16 0.02 0.37 43.42 43.91 44.14 44.40 44.89 344 1.01
mu[254] 44.16 0.02 0.36 43.46 43.91 44.15 44.40 44.88 358 1.01
mu[255] 44.17 0.02 0.36 43.50 43.92 44.16 44.41 44.88 331 1.01
mu[256] 44.16 0.02 0.36 43.42 43.90 44.16 44.40 44.86 316 1.01
mu[257] 44.16 0.02 0.36 43.47 43.91 44.16 44.41 44.88 318 1.00
mu[258] 44.14 0.02 0.36 43.39 43.90 44.14 44.40 44.83 340 1.00
mu[259] 44.13 0.02 0.37 43.39 43.88 44.14 44.40 44.87 333 1.00
mu[260] 44.14 0.02 0.37 43.38 43.90 44.15 44.40 44.83 311 1.00
mu[261] 44.15 0.02 0.38 43.40 43.89 44.16 44.41 44.89 281 1.00
mu[262] 44.14 0.02 0.39 43.37 43.88 44.14 44.40 44.90 281 1.00
mu[263] 44.10 0.02 0.39 43.31 43.86 44.10 44.35 44.84 264 1.00
mu[264] 44.04 0.02 0.38 43.27 43.80 44.04 44.28 44.81 268 1.00
mu[265] 43.96 0.02 0.39 43.21 43.71 43.96 44.22 44.75 273 1.00
mu[266] 43.85 0.02 0.40 43.08 43.59 43.85 44.12 44.60 294 1.00
mu[267] 43.77 0.03 0.39 42.99 43.49 43.79 44.02 44.54 239 1.00
mu[268] 43.71 0.02 0.38 42.95 43.47 43.71 43.96 44.47 251 1.00
mu[269] 43.63 0.03 0.39 42.85 43.38 43.64 43.87 44.42 209 1.01
mu[270] 43.53 0.03 0.38 42.76 43.27 43.53 43.78 44.27 229 1.01
mu[271] 43.42 0.02 0.38 42.70 43.16 43.42 43.67 44.17 239 1.01
mu[272] 43.30 0.03 0.38 42.58 43.02 43.30 43.57 44.04 213 1.01
mu[273] 43.18 0.02 0.38 42.41 42.93 43.17 43.44 43.93 259 1.01
mu[274] 43.07 0.03 0.37 42.28 42.82 43.06 43.33 43.78 217 1.01
mu[275] 42.97 0.02 0.38 42.23 42.71 42.98 43.24 43.68 311 1.01
mu[276] 42.90 0.02 0.38 42.12 42.65 42.88 43.15 43.63 347 1.01
mu[277] 42.81 0.02 0.38 42.03 42.56 42.81 43.06 43.54 370 1.01
mu[278] 42.73 0.02 0.37 42.01 42.49 42.72 42.98 43.43 369 1.01
mu[279] 42.67 0.02 0.36 42.00 42.42 42.66 42.92 43.34 376 1.01
mu[280] 42.64 0.02 0.36 41.93 42.38 42.64 42.89 43.34 401 1.01
mu[281] 42.59 0.02 0.36 41.85 42.34 42.59 42.84 43.29 370 1.01
mu[282] 42.57 0.02 0.37 41.85 42.33 42.58 42.82 43.27 372 1.01
mu[283] 42.56 0.02 0.38 41.80 42.31 42.56 42.82 43.28 391 1.01
mu[284] 42.55 0.02 0.38 41.84 42.29 42.55 42.79 43.31 417 1.00
mu[285] 42.52 0.02 0.36 41.79 42.28 42.52 42.77 43.22 397 1.00
mu[286] 42.51 0.02 0.36 41.80 42.27 42.52 42.75 43.21 413 1.00
mu[287] 42.55 0.02 0.37 41.84 42.31 42.55 42.78 43.24 446 1.00
mu[288] 42.59 0.02 0.36 41.92 42.35 42.59 42.83 43.29 381 1.00
mu[289] 42.63 0.02 0.37 41.89 42.38 42.61 42.85 43.36 359 1.00
mu[290] 42.66 0.02 0.36 41.94 42.42 42.66 42.89 43.42 366 1.00
mu[291] 42.70 0.02 0.36 41.96 42.47 42.69 42.94 43.42 372 1.01
mu[292] 42.74 0.02 0.36 42.07 42.50 42.75 42.98 43.43 378 1.01
mu[293] 42.83 0.02 0.37 42.12 42.58 42.84 43.08 43.51 350 1.01
mu[294] 42.92 0.02 0.37 42.19 42.67 42.91 43.17 43.63 334 1.01
mu[295] 43.00 0.02 0.36 42.30 42.75 43.00 43.24 43.70 305 1.01
mu[296] 43.10 0.02 0.37 42.39 42.86 43.10 43.35 43.80 273 1.02
mu[297] 43.21 0.02 0.36 42.50 42.95 43.20 43.47 43.90 214 1.02
mu[298] 43.32 0.02 0.38 42.58 43.07 43.32 43.57 44.10 283 1.02
mu[299] 43.41 0.02 0.38 42.64 43.16 43.40 43.64 44.20 303 1.02
mu[300] 43.49 0.02 0.38 42.73 43.23 43.49 43.73 44.26 312 1.02
mu[301] 43.56 0.02 0.39 42.81 43.29 43.55 43.82 44.33 282 1.02
mu[302] 43.63 0.02 0.40 42.89 43.35 43.63 43.90 44.47 283 1.01
mu[303] 43.71 0.02 0.41 42.94 43.44 43.69 43.96 44.55 268 1.02
mu[304] 43.77 0.02 0.41 43.00 43.48 43.76 44.05 44.62 296 1.02
mu[305] 43.80 0.03 0.43 42.98 43.51 43.81 44.08 44.68 282 1.02
mu[306] 43.85 0.03 0.43 43.04 43.55 43.85 44.15 44.70 287 1.01
mu[307] 43.89 0.03 0.44 43.06 43.58 43.88 44.19 44.77 277 1.01
mu[308] 43.96 0.03 0.44 43.16 43.67 43.95 44.26 44.87 266 1.01
mu[309] 44.05 0.03 0.43 43.23 43.76 44.04 44.33 44.90 289 1.01
mu[310] 44.13 0.03 0.43 43.26 43.84 44.13 44.40 45.01 275 1.01
mu[311] 44.19 0.03 0.43 43.34 43.90 44.19 44.46 45.03 282 1.01
mu[312] 44.25 0.03 0.43 43.41 43.96 44.27 44.52 45.13 273 1.01
mu[313] 44.32 0.02 0.42 43.46 44.05 44.31 44.60 45.16 298 1.00
mu[314] 44.38 0.02 0.42 43.51 44.09 44.38 44.64 45.19 303 1.00
mu[315] 44.43 0.02 0.42 43.60 44.14 44.44 44.70 45.24 304 1.01
mu[316] 44.51 0.02 0.40 43.72 44.23 44.50 44.78 45.29 323 1.00
mu[317] 44.58 0.02 0.40 43.77 44.31 44.58 44.86 45.33 333 1.00
mu[318] 44.62 0.02 0.39 43.82 44.37 44.64 44.89 45.36 335 1.00
mu[319] 44.68 0.02 0.39 43.91 44.40 44.70 44.94 45.44 350 1.00
mu[320] 44.72 0.02 0.38 43.96 44.47 44.72 44.97 45.48 379 1.00
mu[321] 44.75 0.02 0.38 43.99 44.50 44.75 45.00 45.48 369 1.00
mu[322] 44.84 0.02 0.38 44.10 44.58 44.83 45.07 45.60 342 1.00
mu[323] 44.92 0.02 0.38 44.18 44.65 44.92 45.18 45.66 346 1.00
mu[324] 44.99 0.02 0.38 44.22 44.74 44.97 45.24 45.72 373 1.00
mu[325] 45.05 0.02 0.39 44.29 44.78 45.04 45.32 45.79 385 1.00
mu[326] 45.07 0.02 0.39 44.32 44.80 45.06 45.35 45.83 404 1.00
mu[327] 45.07 0.02 0.38 44.31 44.80 45.07 45.32 45.83 360 1.00
mu[328] 45.07 0.02 0.39 44.32 44.79 45.06 45.34 45.82 354 1.00
mu[329] 45.12 0.02 0.41 44.35 44.85 45.12 45.40 45.94 391 1.00
mu[330] 45.19 0.02 0.41 44.40 44.92 45.19 45.46 45.96 407 1.00
mu[331] 45.26 0.02 0.40 44.47 44.99 45.27 45.53 46.01 371 1.00
mu[332] 45.29 0.02 0.42 44.49 45.01 45.30 45.56 46.06 372 1.00
mu[333] 45.31 0.02 0.40 44.51 45.03 45.32 45.58 46.05 353 1.00
mu[334] 45.29 0.02 0.40 44.51 45.01 45.29 45.56 46.07 385 1.00
mu[335] 45.25 0.02 0.39 44.48 45.00 45.25 45.50 46.00 378 1.00
mu[336] 45.29 0.02 0.40 44.50 45.03 45.28 45.56 46.08 344 1.00
mu[337] 45.32 0.02 0.41 44.54 45.05 45.32 45.59 46.14 342 1.00
mu[338] 45.38 0.02 0.41 44.61 45.11 45.38 45.66 46.16 355 1.00
mu[339] 45.42 0.02 0.42 44.61 45.14 45.41 45.70 46.18 386 1.00
mu[340] 45.45 0.02 0.42 44.62 45.16 45.45 45.74 46.26 360 1.00
mu[341] 45.46 0.02 0.42 44.65 45.19 45.47 45.73 46.28 358 1.00
mu[342] 45.44 0.02 0.42 44.63 45.16 45.45 45.70 46.28 329 1.00
mu[343] 45.44 0.02 0.42 44.60 45.16 45.46 45.71 46.31 337 1.00
mu[344] 45.46 0.02 0.42 44.66 45.17 45.46 45.73 46.30 334 1.00
mu[345] 45.46 0.02 0.41 44.71 45.18 45.46 45.75 46.25 327 1.00
mu[346] 45.45 0.02 0.41 44.60 45.18 45.45 45.73 46.27 337 1.00
mu[347] 45.42 0.02 0.41 44.61 45.14 45.43 45.69 46.26 325 1.00
mu[348] 45.39 0.02 0.41 44.56 45.11 45.38 45.66 46.22 321 1.01
mu[349] 45.38 0.02 0.40 44.64 45.12 45.35 45.63 46.21 310 1.01
mu[350] 45.39 0.02 0.40 44.66 45.12 45.37 45.63 46.26 315 1.01
mu[351] 45.41 0.02 0.39 44.71 45.14 45.39 45.66 46.16 355 1.01
mu[352] 45.41 0.02 0.38 44.69 45.15 45.39 45.65 46.21 334 1.01
mu[353] 45.39 0.02 0.39 44.66 45.14 45.37 45.64 46.16 346 1.01
mu[354] 45.36 0.02 0.38 44.67 45.10 45.34 45.60 46.16 316 1.01
mu[355] 45.35 0.02 0.39 44.62 45.08 45.34 45.59 46.15 275 1.02
mu[356] 45.38 0.02 0.39 44.67 45.13 45.37 45.62 46.17 260 1.03
mu[357] 45.42 0.02 0.39 44.67 45.14 45.42 45.69 46.22 261 1.03
mu[358] 45.48 0.02 0.39 44.73 45.23 45.48 45.76 46.22 260 1.03
mu[359] 45.54 0.02 0.39 44.80 45.28 45.56 45.80 46.27 276 1.02
mu[360] 45.56 0.02 0.39 44.76 45.31 45.57 45.83 46.27 265 1.02
mu[361] 45.58 0.02 0.38 44.79 45.32 45.58 45.83 46.33 265 1.03
mu[362] 45.57 0.02 0.38 44.79 45.33 45.56 45.83 46.33 291 1.02
mu[363] 45.54 0.02 0.37 44.83 45.29 45.54 45.80 46.25 335 1.02
mu[364] 45.53 0.02 0.37 44.74 45.29 45.53 45.78 46.24 325 1.01
mu[365] 45.54 0.02 0.37 44.82 45.29 45.54 45.78 46.24 339 1.01
mu[366] 45.55 0.02 0.36 44.82 45.30 45.54 45.78 46.26 315 1.01
mu[367] 45.53 0.02 0.36 44.84 45.29 45.52 45.76 46.28 335 1.00
mu[368] 45.49 0.02 0.37 44.80 45.24 45.48 45.72 46.24 311 1.00
mu[369] 45.45 0.02 0.36 44.78 45.20 45.45 45.69 46.21 292 1.00
mu[370] 45.43 0.02 0.38 44.75 45.16 45.41 45.67 46.17 312 1.00
mu[371] 45.41 0.02 0.38 44.66 45.13 45.40 45.65 46.20 325 1.00
mu[372] 45.42 0.02 0.40 44.65 45.15 45.41 45.68 46.21 332 1.00
mu[373] 45.43 0.02 0.40 44.69 45.15 45.41 45.68 46.25 336 1.00
mu[374] 45.43 0.02 0.39 44.68 45.16 45.43 45.69 46.21 341 1.00
mu[375] 45.40 0.02 0.39 44.63 45.15 45.40 45.66 46.19 345 1.00
mu[376] 45.37 0.02 0.40 44.58 45.09 45.38 45.63 46.13 336 1.00
mu[377] 45.34 0.02 0.39 44.56 45.08 45.35 45.60 46.08 372 1.00
mu[378] 45.29 0.02 0.38 44.53 45.04 45.30 45.56 46.02 403 1.00
mu[379] 45.32 0.02 0.37 44.61 45.05 45.32 45.57 46.04 393 1.00
mu[380] 45.32 0.02 0.37 44.57 45.06 45.33 45.58 46.05 401 1.00
mu[381] 45.33 0.02 0.37 44.62 45.07 45.33 45.59 46.05 420 1.00
mu[382] 45.30 0.02 0.38 44.57 45.03 45.33 45.56 46.03 419 1.00
mu[383] 45.25 0.02 0.38 44.51 44.99 45.24 45.52 45.96 410 1.00
mu[384] 45.17 0.02 0.39 44.43 44.90 45.16 45.45 45.94 435 1.00
mu[385] 45.12 0.02 0.39 44.38 44.86 45.11 45.38 45.89 459 1.00
mu[386] 45.08 0.02 0.39 44.30 44.82 45.08 45.35 45.83 451 1.00
mu[387] 45.03 0.02 0.38 44.30 44.76 45.02 45.31 45.75 428 1.01
mu[388] 44.99 0.02 0.38 44.23 44.71 44.98 45.25 45.76 452 1.01
mu[389] 44.91 0.02 0.38 44.15 44.65 44.89 45.18 45.63 502 1.00
mu[390] 44.83 0.02 0.38 44.09 44.57 44.82 45.09 45.58 555 1.01
mu[391] 44.77 0.02 0.38 44.06 44.52 44.77 45.02 45.54 529 1.01
mu[392] 44.75 0.02 0.37 44.06 44.48 44.75 45.01 45.47 525 1.00
mu[393] 44.76 0.02 0.38 44.06 44.50 44.75 45.01 45.51 543 1.00
mu[394] 44.74 0.02 0.38 44.02 44.48 44.72 44.99 45.52 438 1.00
mu[395] 44.70 0.02 0.38 43.93 44.46 44.70 44.96 45.45 396 1.00
mu[396] 44.63 0.02 0.39 43.84 44.39 44.63 44.89 45.41 425 1.00
mu[397] 44.58 0.02 0.38 43.83 44.33 44.60 44.83 45.31 422 1.01
mu[398] 44.55 0.02 0.38 43.81 44.32 44.55 44.81 45.28 426 1.01
mu[399] 44.55 0.02 0.38 43.84 44.29 44.54 44.80 45.31 401 1.02
mu[400] 44.55 0.02 0.39 43.84 44.29 44.55 44.78 45.37 387 1.01
mu[401] 44.55 0.02 0.38 43.78 44.30 44.54 44.79 45.38 377 1.01
mu[402] 44.54 0.02 0.38 43.78 44.28 44.55 44.78 45.29 314 1.01
mu[403] 44.50 0.02 0.38 43.78 44.25 44.50 44.74 45.25 316 1.01
mu[404] 44.45 0.02 0.38 43.70 44.20 44.44 44.70 45.19 322 1.00
mu[405] 44.46 0.02 0.38 43.73 44.20 44.45 44.71 45.20 335 1.00
mu[406] 44.50 0.02 0.39 43.79 44.22 44.48 44.77 45.29 333 1.00
mu[407] 44.54 0.02 0.39 43.83 44.27 44.52 44.79 45.36 305 1.00
mu[408] 44.54 0.02 0.40 43.77 44.26 44.53 44.82 45.34 283 1.00
mu[409] 44.54 0.02 0.40 43.74 44.26 44.54 44.81 45.30 278 1.00
mu[410] 44.53 0.02 0.41 43.73 44.23 44.53 44.80 45.36 274 1.00
mu[411] 44.49 0.02 0.41 43.75 44.21 44.48 44.77 45.31 281 1.00
mu[412] 44.42 0.02 0.42 43.62 44.13 44.44 44.70 45.23 315 1.00
mu[413] 44.36 0.02 0.43 43.56 44.05 44.36 44.66 45.22 300 1.00
mu[414] 44.30 0.02 0.43 43.44 44.01 44.29 44.57 45.11 339 1.00
mu[415] 44.22 0.02 0.42 43.41 43.93 44.22 44.48 45.02 346 1.00
mu[416] 44.12 0.02 0.43 43.28 43.85 44.13 44.40 44.95 329 1.00
mu[417] 44.03 0.02 0.41 43.16 43.76 44.05 44.29 44.85 333 1.00
mu[418] 43.93 0.02 0.41 43.12 43.67 43.95 44.19 44.73 349 1.00
mu[419] 43.84 0.02 0.40 43.05 43.58 43.85 44.10 44.66 354 1.00
mu[420] 43.83 0.02 0.40 43.07 43.56 43.82 44.09 44.63 352 1.00
mu[421] 43.84 0.02 0.40 43.10 43.56 43.83 44.12 44.61 351 1.00
mu[422] 43.85 0.02 0.39 43.09 43.58 43.84 44.10 44.61 361 1.00
mu[423] 43.85 0.02 0.39 43.08 43.59 43.86 44.11 44.61 341 1.00
mu[424] 43.84 0.02 0.39 43.05 43.59 43.86 44.10 44.56 349 1.00
mu[425] 43.84 0.02 0.39 43.09 43.58 43.85 44.12 44.56 325 1.01
mu[426] 43.84 0.02 0.38 43.08 43.57 43.84 44.11 44.55 302 1.01
mu[427] 43.86 0.02 0.38 43.10 43.60 43.86 44.14 44.56 325 1.01
mu[428] 43.87 0.02 0.37 43.14 43.62 43.88 44.13 44.58 310 1.01
mu[429] 43.89 0.02 0.37 43.15 43.64 43.91 44.14 44.57 287 1.00
mu[430] 43.91 0.02 0.39 43.19 43.64 43.92 44.18 44.64 302 1.00
mu[431] 43.94 0.02 0.38 43.17 43.67 43.95 44.21 44.66 309 1.00
mu[432] 44.02 0.02 0.39 43.25 43.75 44.02 44.30 44.78 322 1.00
mu[433] 44.10 0.02 0.39 43.32 43.83 44.10 44.38 44.86 381 1.00
mu[434] 44.21 0.02 0.40 43.38 43.95 44.21 44.48 44.98 405 1.00
mu[435] 44.30 0.02 0.40 43.53 44.02 44.29 44.57 45.07 344 1.01
mu[436] 44.39 0.02 0.40 43.57 44.11 44.38 44.67 45.13 331 1.01
mu[437] 44.46 0.02 0.40 43.63 44.18 44.46 44.74 45.24 285 1.01
mu[438] 44.49 0.02 0.40 43.64 44.24 44.49 44.76 45.25 318 1.01
mu[439] 44.51 0.02 0.40 43.73 44.24 44.52 44.76 45.27 308 1.00
mu[440] 44.55 0.02 0.39 43.78 44.31 44.56 44.80 45.31 329 1.00
mu[441] 44.59 0.02 0.39 43.78 44.35 44.62 44.86 45.33 325 1.01
mu[442] 44.64 0.02 0.40 43.82 44.37 44.65 44.92 45.40 321 1.00
mu[443] 44.67 0.02 0.39 43.89 44.41 44.69 44.94 45.41 343 1.00
mu[444] 44.67 0.02 0.39 43.90 44.41 44.67 44.93 45.39 333 1.01
mu[445] 44.65 0.02 0.39 43.92 44.38 44.66 44.92 45.39 294 1.01
mu[446] 44.61 0.02 0.39 43.86 44.36 44.62 44.89 45.38 275 1.01
mu[447] 44.57 0.02 0.39 43.83 44.30 44.59 44.81 45.36 270 1.01
mu[448] 44.59 0.03 0.40 43.81 44.32 44.59 44.82 45.37 211 1.01
mu[449] 44.61 0.02 0.39 43.85 44.37 44.60 44.85 45.36 281 1.01
mu[450] 44.63 0.02 0.39 43.87 44.37 44.63 44.89 45.38 281 1.01
mu[451] 44.64 0.02 0.39 43.89 44.37 44.64 44.90 45.39 323 1.01
mu[452] 44.62 0.02 0.39 43.84 44.34 44.62 44.89 45.39 323 1.01
mu[453] 44.61 0.02 0.40 43.82 44.34 44.58 44.87 45.39 297 1.01
mu[454] 44.58 0.02 0.40 43.79 44.31 44.57 44.85 45.39 272 1.01
mu[455] 44.59 0.02 0.40 43.84 44.32 44.58 44.86 45.38 302 1.01
mu[456] 44.59 0.02 0.40 43.80 44.30 44.59 44.87 45.39 295 1.01
mu[457] 44.59 0.02 0.40 43.82 44.32 44.57 44.86 45.41 279 1.01
mu[458] 44.58 0.02 0.40 43.80 44.31 44.57 44.85 45.39 279 1.01
mu[459] 44.55 0.02 0.41 43.77 44.26 44.56 44.83 45.34 290 1.01
mu[460] 44.52 0.02 0.42 43.68 44.22 44.53 44.80 45.33 295 1.00
mu[461] 44.48 0.03 0.43 43.65 44.19 44.50 44.76 45.26 291 1.00
mu[462] 44.45 0.03 0.43 43.60 44.16 44.46 44.75 45.26 278 1.00
mu[463] 44.42 0.03 0.43 43.59 44.13 44.41 44.71 45.25 272 1.00
mu[464] 44.37 0.03 0.43 43.51 44.11 44.37 44.66 45.20 264 1.00
mu[465] 44.33 0.03 0.42 43.53 44.06 44.34 44.61 45.13 252 1.01
mu[466] 44.27 0.03 0.43 43.44 43.98 44.27 44.55 45.08 259 1.00
mu[467] 44.20 0.03 0.43 43.36 43.91 44.22 44.47 45.03 253 1.00
mu[468] 44.15 0.03 0.42 43.33 43.88 44.17 44.43 44.97 248 1.00
mu[469] 44.11 0.03 0.42 43.33 43.82 44.12 44.37 44.93 246 1.00
mu[470] 44.07 0.03 0.42 43.25 43.80 44.06 44.35 44.90 219 1.00
mu[471] 44.08 0.03 0.42 43.24 43.81 44.05 44.35 44.94 238 1.00
mu[472] 44.09 0.03 0.41 43.26 43.81 44.08 44.35 44.97 208 1.00
mu[473] 44.06 0.03 0.42 43.28 43.77 44.07 44.34 44.89 214 1.00
mu[474] 44.05 0.03 0.42 43.20 43.75 44.06 44.32 44.85 216 1.00
mu[475] 44.04 0.03 0.42 43.21 43.75 44.04 44.31 44.85 234 1.00
mu[476] 44.04 0.03 0.42 43.21 43.76 44.04 44.32 44.87 214 1.00
mu[477] 44.05 0.03 0.42 43.23 43.77 44.03 44.35 44.84 219 1.00
mu[478] 44.06 0.03 0.42 43.22 43.76 44.06 44.34 44.86 231 1.00
mu[479] 44.06 0.03 0.42 43.24 43.77 44.06 44.36 44.85 225 1.00
mu[480] 44.06 0.03 0.42 43.23 43.77 44.06 44.37 44.89 246 1.00
mu[481] 44.06 0.03 0.42 43.17 43.78 44.06 44.35 44.85 271 1.00
mu[482] 44.07 0.02 0.41 43.27 43.80 44.07 44.37 44.88 287 1.00
mu[483] 44.09 0.02 0.42 43.21 43.82 44.11 44.38 44.91 309 1.00
mu[484] 44.12 0.02 0.41 43.24 43.84 44.12 44.41 44.92 281 1.00
mu[485] 44.13 0.02 0.42 43.30 43.86 44.14 44.41 44.92 300 1.00
mu[486] 44.12 0.02 0.41 43.25 43.85 44.13 44.40 44.91 290 1.00
mu[487] 44.08 0.02 0.41 43.29 43.80 44.08 44.35 44.87 304 1.00
mu[488] 44.05 0.02 0.40 43.26 43.78 44.04 44.33 44.81 315 1.00
mu[489] 44.02 0.02 0.41 43.20 43.74 44.01 44.31 44.79 335 1.00
mu[490] 43.98 0.02 0.40 43.24 43.69 43.99 44.25 44.75 278 1.00
mu[491] 43.95 0.02 0.39 43.17 43.67 43.96 44.21 44.72 281 1.00
mu[492] 43.95 0.02 0.40 43.16 43.68 43.95 44.21 44.71 293 1.00
mu[493] 43.95 0.02 0.39 43.19 43.67 43.94 44.22 44.74 282 1.00
mu[494] 43.92 0.02 0.40 43.19 43.65 43.93 44.19 44.70 287 1.00
mu[495] 43.89 0.02 0.40 43.13 43.61 43.88 44.16 44.67 261 1.00
mu[496] 43.87 0.03 0.39 43.15 43.60 43.85 44.16 44.64 246 1.00
mu[497] 43.88 0.03 0.39 43.14 43.60 43.86 44.15 44.62 236 1.00
mu[498] 43.87 0.03 0.38 43.16 43.59 43.86 44.13 44.59 225 1.00
mu[499] 43.87 0.02 0.38 43.16 43.60 43.86 44.12 44.59 237 1.00
mu[500] 43.89 0.03 0.38 43.19 43.62 43.89 44.15 44.65 223 1.00
mu[501] 43.91 0.02 0.38 43.24 43.64 43.89 44.16 44.68 231 1.00
mu[502] 43.89 0.02 0.38 43.20 43.62 43.87 44.15 44.62 227 1.01
mu[503] 43.90 0.03 0.39 43.15 43.65 43.88 44.16 44.66 230 1.01
mu[504] 43.91 0.03 0.38 43.19 43.65 43.89 44.19 44.64 213 1.01
mu[505] 43.90 0.03 0.38 43.17 43.65 43.89 44.16 44.64 218 1.01
mu[506] 43.92 0.03 0.39 43.16 43.66 43.90 44.18 44.73 211 1.01
mu[507] 43.93 0.03 0.40 43.17 43.67 43.92 44.18 44.72 219 1.01
mu[508] 43.89 0.03 0.40 43.14 43.62 43.88 44.13 44.69 225 1.01
mu[509] 43.86 0.03 0.40 43.10 43.59 43.84 44.12 44.67 221 1.01
mu[510] 43.82 0.03 0.40 43.04 43.55 43.81 44.09 44.62 218 1.01
mu[511] 43.78 0.03 0.41 42.97 43.50 43.77 44.04 44.62 190 1.02
mu[512] 43.75 0.03 0.41 42.98 43.48 43.73 44.02 44.57 221 1.01
mu[513] 43.74 0.03 0.42 42.95 43.45 43.75 44.00 44.54 264 1.01
mu[514] 43.74 0.02 0.41 42.95 43.48 43.74 44.01 44.58 279 1.00
mu[515] 43.73 0.03 0.41 42.95 43.45 43.72 43.99 44.50 258 1.00
mu[516] 43.73 0.03 0.41 42.89 43.45 43.73 44.00 44.52 224 1.00
mu[517] 43.75 0.03 0.41 42.93 43.48 43.78 44.03 44.51 214 1.01
mu[518] 43.79 0.03 0.41 42.96 43.50 43.83 44.07 44.52 181 1.01
mu[519] 43.83 0.03 0.40 43.04 43.55 43.83 44.12 44.62 178 1.00
mu[520] 43.89 0.03 0.40 43.13 43.61 43.88 44.16 44.65 186 1.00
mu[521] 43.95 0.03 0.40 43.19 43.67 43.95 44.20 44.73 172 1.00
mu[522] 44.00 0.03 0.41 43.20 43.73 44.00 44.28 44.77 163 1.00
mu[523] 44.04 0.03 0.40 43.29 43.77 44.04 44.33 44.83 161 1.00
mu[524] 44.10 0.03 0.40 43.31 43.83 44.10 44.37 44.88 156 1.00
mu[525] 44.17 0.03 0.41 43.41 43.90 44.17 44.44 44.96 138 1.00
mu[526] 44.23 0.03 0.41 43.44 43.94 44.22 44.50 45.05 145 1.01
mu[527] 44.28 0.03 0.42 43.49 44.00 44.28 44.56 45.09 160 1.00
mu[528] 44.31 0.03 0.40 43.56 44.04 44.30 44.59 45.12 159 1.01
mu[529] 44.32 0.03 0.40 43.57 44.05 44.30 44.60 45.10 153 1.01
mu[530] 44.31 0.03 0.39 43.56 44.06 44.30 44.58 45.07 144 1.01
mu[531] 44.28 0.03 0.39 43.53 44.01 44.28 44.53 45.07 187 1.01
mu[532] 44.30 0.03 0.40 43.52 44.03 44.29 44.57 45.10 232 1.00
mu[533] 44.31 0.03 0.40 43.53 44.04 44.31 44.59 45.10 251 1.00
mu[534] 44.33 0.03 0.41 43.54 44.03 44.33 44.61 45.13 240 1.00
mu[535] 44.34 0.03 0.41 43.52 44.07 44.34 44.63 45.14 230 1.00
mu[536] 44.38 0.03 0.42 43.60 44.11 44.35 44.67 45.23 253 1.00
mu[537] 44.39 0.03 0.42 43.63 44.09 44.39 44.66 45.27 258 1.00
mu[538] 44.40 0.03 0.42 43.59 44.12 44.42 44.68 45.24 259 1.00
mu[539] 44.40 0.03 0.41 43.59 44.11 44.41 44.68 45.21 246 1.00
mu[540] 44.40 0.03 0.42 43.61 44.12 44.40 44.69 45.19 270 1.00
mu[541] 44.40 0.03 0.42 43.57 44.10 44.39 44.70 45.16 268 1.00
mu[542] 44.39 0.03 0.41 43.63 44.10 44.39 44.68 45.19 248 1.00
mu[543] 44.36 0.03 0.42 43.56 44.08 44.35 44.63 45.16 241 1.00
mu[544] 44.30 0.03 0.40 43.52 44.03 44.29 44.54 45.12 247 1.00
mu[545] 44.25 0.03 0.39 43.49 43.99 44.25 44.51 45.07 244 1.00
mu[546] 44.22 0.03 0.40 43.44 43.96 44.23 44.49 45.00 208 1.01
mu[547] 44.21 0.03 0.40 43.46 43.95 44.20 44.47 44.97 192 1.01
mu[548] 44.19 0.03 0.40 43.42 43.94 44.21 44.45 44.98 189 1.01
mu[549] 44.13 0.03 0.39 43.36 43.86 44.15 44.40 44.89 210 1.01
mu[550] 44.05 0.03 0.40 43.27 43.78 44.08 44.33 44.84 204 1.01
mu[551] 43.95 0.03 0.41 43.15 43.67 43.96 44.22 44.72 242 1.01
mu[552] 43.86 0.03 0.41 42.98 43.58 43.87 44.14 44.63 272 1.00
mu[553] 43.77 0.03 0.41 42.96 43.50 43.77 44.07 44.55 253 1.00
mu[554] 43.71 0.03 0.42 42.87 43.42 43.73 43.99 44.51 223 1.00
mu[555] 43.66 0.03 0.41 42.83 43.38 43.69 43.94 44.43 263 1.00
mu[556] 43.62 0.02 0.41 42.76 43.37 43.64 43.91 44.38 272 1.00
mu[557] 43.55 0.02 0.40 42.71 43.30 43.58 43.82 44.33 302 1.00
mu[558] 43.49 0.03 0.40 42.67 43.23 43.49 43.75 44.27 245 1.00
mu[559] 43.41 0.02 0.40 42.58 43.15 43.42 43.70 44.16 283 1.00
mu[560] 43.36 0.02 0.41 42.58 43.10 43.35 43.63 44.16 302 1.00
mu[561] 43.31 0.02 0.41 42.51 43.02 43.32 43.59 44.14 309 1.00
mu[562] 43.29 0.02 0.40 42.50 43.01 43.29 43.55 44.09 326 1.00
mu[563] 43.25 0.02 0.40 42.48 42.99 43.24 43.53 44.04 328 1.00
mu[564] 43.19 0.02 0.40 42.43 42.92 43.18 43.45 44.01 305 1.00
mu[565] 43.14 0.02 0.40 42.37 42.88 43.12 43.40 43.92 320 1.00
mu[566] 43.15 0.02 0.39 42.43 42.87 43.15 43.41 43.93 352 1.00
mu[567] 43.15 0.02 0.40 42.37 42.88 43.14 43.41 43.95 323 1.00
mu[568] 43.15 0.02 0.40 42.36 42.88 43.14 43.42 43.91 352 1.00
mu[569] 43.16 0.02 0.40 42.36 42.88 43.16 43.42 43.95 368 1.00
mu[570] 43.13 0.02 0.41 42.30 42.87 43.13 43.40 43.94 349 1.00
mu[571] 43.10 0.02 0.41 42.26 42.82 43.11 43.35 43.89 339 1.00
mu[572] 43.06 0.02 0.42 42.20 42.79 43.06 43.35 43.86 334 1.00
mu[573] 43.02 0.02 0.42 42.18 42.74 43.02 43.32 43.82 333 1.00
mu[574] 43.00 0.02 0.42 42.17 42.73 43.00 43.29 43.82 348 1.00
mu[575] 42.99 0.02 0.43 42.13 42.69 43.01 43.28 43.81 335 1.00
mu[576] 42.97 0.02 0.43 42.15 42.67 42.97 43.28 43.82 325 1.01
mu[577] 42.98 0.02 0.42 42.19 42.67 42.97 43.26 43.81 346 1.01
mu[578] 42.99 0.02 0.43 42.20 42.69 42.98 43.27 43.76 334 1.01
mu[579] 42.97 0.02 0.42 42.18 42.68 42.96 43.24 43.79 310 1.01
mu[580] 42.94 0.03 0.43 42.11 42.66 42.93 43.23 43.76 279 1.01
mu[581] 42.89 0.02 0.42 42.09 42.62 42.88 43.17 43.72 356 1.01
mu[582] 42.88 0.02 0.42 42.10 42.59 42.89 43.16 43.71 360 1.01
mu[583] 42.88 0.02 0.41 42.08 42.60 42.89 43.16 43.67 353 1.01
mu[584] 42.86 0.02 0.41 42.01 42.60 42.87 43.14 43.65 366 1.01
mu[585] 42.85 0.02 0.40 42.03 42.59 42.84 43.12 43.61 355 1.01
mu[586] 42.83 0.02 0.40 42.03 42.57 42.84 43.10 43.62 334 1.01
mu[587] 42.83 0.02 0.39 42.06 42.57 42.84 43.09 43.53 366 1.01
mu[588] 42.85 0.02 0.39 42.12 42.58 42.86 43.11 43.59 368 1.01
mu[589] 42.88 0.02 0.38 42.14 42.62 42.87 43.14 43.61 391 1.01
mu[590] 42.91 0.02 0.38 42.16 42.64 42.90 43.16 43.66 395 1.01
mu[591] 42.94 0.02 0.37 42.18 42.69 42.95 43.19 43.65 393 1.01
mu[592] 42.93 0.02 0.37 42.22 42.68 42.93 43.17 43.70 393 1.01
mu[593] 42.96 0.02 0.37 42.27 42.70 42.95 43.21 43.69 357 1.01
mu[594] 42.96 0.02 0.37 42.28 42.70 42.94 43.21 43.72 331 1.00
mu[595] 42.96 0.02 0.38 42.29 42.70 42.95 43.22 43.71 341 1.00
mu[596] 42.98 0.02 0.38 42.25 42.71 42.97 43.22 43.77 330 1.00
mu[597] 43.00 0.02 0.39 42.27 42.74 42.97 43.25 43.81 303 1.00
mu[598] 43.01 0.02 0.37 42.35 42.76 42.99 43.23 43.79 276 1.00
mu[599] 43.02 0.02 0.38 42.32 42.76 43.00 43.27 43.78 288 1.00
mu[600] 43.04 0.02 0.38 42.36 42.78 43.01 43.27 43.85 270 1.00
mu[601] 43.03 0.02 0.38 42.34 42.76 43.01 43.27 43.80 275 1.00
mu[602] 43.04 0.02 0.38 42.38 42.78 43.04 43.28 43.81 244 1.00
mu[603] 43.06 0.03 0.38 42.37 42.81 43.05 43.31 43.81 233 1.00
mu[604] 43.12 0.02 0.38 42.41 42.86 43.11 43.35 43.90 267 1.00
mu[605] 43.17 0.02 0.38 42.46 42.92 43.18 43.43 43.97 282 1.00
mu[606] 43.20 0.02 0.38 42.47 42.94 43.18 43.45 44.00 267 1.00
mu[607] 43.20 0.02 0.39 42.48 42.92 43.19 43.45 43.96 269 1.00
mu[608] 43.22 0.03 0.40 42.46 42.94 43.22 43.50 44.02 244 1.00
mu[609] 43.26 0.02 0.40 42.50 42.98 43.24 43.53 44.06 259 1.00
mu[610] 43.28 0.02 0.40 42.52 43.00 43.28 43.54 44.14 272 1.00
mu[611] 43.32 0.03 0.40 42.57 43.04 43.31 43.57 44.14 253 1.00
mu[612] 43.37 0.03 0.40 42.60 43.10 43.35 43.63 44.20 237 1.00
mu[613] 43.38 0.03 0.41 42.57 43.11 43.37 43.66 44.15 252 1.00
mu[614] 43.38 0.03 0.41 42.61 43.10 43.41 43.66 44.16 218 1.01
mu[615] 43.33 0.03 0.40 42.54 43.06 43.34 43.63 44.08 188 1.01
mu[616] 43.29 0.03 0.40 42.47 43.02 43.31 43.57 44.02 181 1.01
mu[617] 43.28 0.03 0.40 42.51 43.02 43.27 43.54 44.04 180 1.01
mu[618] 43.27 0.03 0.39 42.49 42.99 43.27 43.52 44.05 193 1.01
mu[619] 43.25 0.03 0.39 42.49 42.98 43.24 43.51 44.00 158 1.01
mu[620] 43.20 0.03 0.38 42.47 42.93 43.22 43.46 43.96 150 1.00
mu[621] 43.18 0.03 0.40 42.45 42.90 43.18 43.45 43.98 153 1.00
mu[622] 43.19 0.03 0.39 42.44 42.94 43.19 43.44 43.98 205 1.01
mu[623] 43.21 0.03 0.39 42.49 42.94 43.21 43.46 43.98 220 1.00
mu[624] 43.23 0.02 0.38 42.55 42.96 43.22 43.49 43.98 266 1.00
mu[625] 43.27 0.02 0.39 42.56 42.99 43.27 43.52 44.04 289 1.00
mu[626] 43.31 0.02 0.38 42.61 43.06 43.30 43.56 44.10 313 1.00
mu[627] 43.34 0.02 0.38 42.62 43.09 43.33 43.60 44.10 309 1.00
mu[628] 43.37 0.02 0.39 42.63 43.10 43.36 43.65 44.14 293 1.00
mu[629] 43.40 0.02 0.40 42.66 43.14 43.39 43.66 44.19 323 1.00
mu[630] 43.43 0.02 0.40 42.60 43.18 43.41 43.70 44.20 365 1.00
mu[631] 43.46 0.02 0.39 42.68 43.20 43.45 43.74 44.23 380 1.00
mu[632] 43.47 0.02 0.39 42.75 43.20 43.48 43.74 44.22 358 1.00
mu[633] 43.45 0.02 0.39 42.70 43.19 43.46 43.72 44.19 335 1.00
mu[634] 43.41 0.02 0.39 42.67 43.15 43.42 43.67 44.18 346 1.00
mu[635] 43.35 0.02 0.39 42.56 43.08 43.37 43.64 44.11 348 1.00
mu[636] 43.29 0.02 0.40 42.49 43.02 43.29 43.57 44.05 324 1.00
mu[637] 43.19 0.02 0.39 42.42 42.93 43.20 43.48 43.95 298 1.00
mu[638] 43.13 0.02 0.39 42.34 42.87 43.14 43.40 43.88 294 1.00
mu[639] 43.09 0.02 0.38 42.36 42.84 43.10 43.34 43.82 260 1.00
mu[640] 42.98 0.03 0.39 42.22 42.72 42.99 43.23 43.77 235 1.01
mu[641] 42.84 0.03 0.39 42.07 42.59 42.84 43.09 43.61 223 1.01
mu[642] 42.70 0.03 0.40 41.89 42.45 42.70 42.98 43.50 226 1.01
mu[643] 42.55 0.03 0.41 41.72 42.29 42.56 42.82 43.36 214 1.01
mu[644] 42.43 0.03 0.40 41.66 42.15 42.42 42.72 43.25 228 1.01
mu[645] 42.32 0.03 0.41 41.51 42.05 42.31 42.60 43.11 242 1.01
mu[646] 42.20 0.03 0.40 41.38 41.93 42.21 42.47 42.97 221 1.02
mu[647] 42.10 0.03 0.41 41.28 41.85 42.11 42.38 42.91 217 1.02
mu[648] 42.01 0.03 0.41 41.18 41.73 42.03 42.28 42.83 216 1.02
mu[649] 41.92 0.03 0.40 41.12 41.65 41.92 42.21 42.74 220 1.02
mu[650] 41.85 0.03 0.39 41.07 41.59 41.84 42.10 42.61 223 1.02
mu[651] 41.82 0.03 0.39 41.05 41.56 41.81 42.07 42.63 216 1.02
mu[652] 41.82 0.03 0.39 41.09 41.55 41.83 42.09 42.63 225 1.02
mu[653] 41.80 0.03 0.39 41.04 41.53 41.79 42.07 42.55 212 1.03
mu[654] 41.79 0.02 0.38 41.07 41.55 41.79 42.03 42.53 249 1.02
mu[655] 41.78 0.02 0.37 41.04 41.53 41.77 42.02 42.54 230 1.03
mu[656] 41.75 0.02 0.38 41.03 41.50 41.74 42.00 42.53 248 1.03
mu[657] 41.76 0.03 0.39 41.04 41.49 41.75 42.04 42.58 241 1.03
mu[658] 41.76 0.03 0.40 41.03 41.48 41.75 42.04 42.56 235 1.03
mu[659] 41.76 0.02 0.40 41.00 41.48 41.74 42.04 42.54 256 1.03
mu[660] 41.74 0.02 0.38 40.99 41.50 41.73 42.00 42.50 301 1.02
mu[661] 41.70 0.02 0.39 40.97 41.45 41.68 41.96 42.52 307 1.02
mu[662] 41.65 0.02 0.39 40.90 41.41 41.66 41.90 42.49 286 1.02
mu[663] 41.61 0.02 0.39 40.81 41.34 41.60 41.86 42.39 288 1.01
mu[664] 41.59 0.02 0.39 40.84 41.31 41.60 41.86 42.39 316 1.01
mu[665] 41.58 0.02 0.40 40.79 41.32 41.58 41.84 42.39 282 1.02
mu[666] 41.58 0.02 0.40 40.80 41.32 41.57 41.84 42.38 327 1.02
mu[667] 41.52 0.02 0.40 40.75 41.23 41.53 41.81 42.31 340 1.02
mu[668] 41.47 0.02 0.40 40.68 41.21 41.46 41.72 42.26 364 1.02
mu[669] 41.38 0.02 0.41 40.57 41.11 41.36 41.65 42.17 395 1.01
mu[670] 41.27 0.02 0.41 40.44 41.00 41.27 41.55 42.03 375 1.02
mu[671] 41.14 0.02 0.41 40.34 40.88 41.15 41.41 41.91 339 1.02
mu[672] 41.00 0.02 0.41 40.21 40.72 41.00 41.28 41.83 328 1.02
mu[673] 40.85 0.02 0.40 40.05 40.57 40.85 41.11 41.61 313 1.02
mu[674] 40.72 0.02 0.40 39.90 40.45 40.72 40.99 41.53 343 1.02
mu[675] 40.58 0.02 0.38 39.84 40.33 40.58 40.85 41.34 338 1.02
mu[676] 40.48 0.02 0.38 39.72 40.25 40.49 40.73 41.23 343 1.02
mu[677] 40.38 0.02 0.39 39.66 40.13 40.39 40.64 41.10 324 1.02
mu[678] 40.28 0.02 0.39 39.48 40.02 40.28 40.54 40.96 333 1.02
mu[679] 40.15 0.02 0.39 39.37 39.89 40.16 40.41 40.87 321 1.01
mu[680] 40.02 0.02 0.38 39.28 39.76 40.04 40.29 40.73 346 1.01
mu[681] 39.90 0.02 0.37 39.13 39.66 39.91 40.16 40.57 329 1.01
mu[682] 39.76 0.02 0.38 38.99 39.51 39.77 40.01 40.46 287 1.01
mu[683] 39.66 0.02 0.38 38.89 39.41 39.68 39.92 40.34 276 1.01
mu[684] 39.58 0.02 0.38 38.84 39.31 39.59 39.84 40.26 285 1.00
mu[685] 39.46 0.02 0.38 38.70 39.20 39.46 39.72 40.17 296 1.00
mu[686] 39.36 0.02 0.38 38.58 39.09 39.35 39.62 40.11 280 1.00
mu[687] 39.29 0.02 0.38 38.52 39.03 39.30 39.55 40.03 282 1.00
mu[688] 39.22 0.02 0.38 38.43 38.98 39.23 39.47 39.96 256 1.00
mu[689] 39.17 0.02 0.37 38.44 38.94 39.17 39.42 39.91 266 1.00
mu[690] 39.15 0.02 0.37 38.43 38.91 39.14 39.39 39.92 277 1.00
mu[691] 39.14 0.02 0.37 38.42 38.89 39.13 39.39 39.88 255 1.00
mu[692] 39.14 0.02 0.39 38.39 38.87 39.13 39.41 39.89 256 1.00
mu[693] 39.13 0.02 0.39 38.35 38.86 39.13 39.39 39.86 293 1.00
mu[694] 39.14 0.02 0.39 38.40 38.88 39.15 39.41 39.88 320 1.00
mu[695] 39.19 0.02 0.38 38.44 38.93 39.20 39.45 39.89 292 1.00
mu[696] 39.25 0.02 0.37 38.54 38.99 39.27 39.50 40.03 300 1.00
mu[697] 39.28 0.02 0.38 38.53 39.02 39.28 39.53 40.03 296 1.00
mu[698] 39.31 0.02 0.37 38.57 39.05 39.31 39.54 40.05 301 1.00
mu[699] 39.38 0.02 0.37 38.63 39.13 39.38 39.64 40.09 251 1.00
mu[700] 39.40 0.02 0.37 38.69 39.15 39.42 39.65 40.11 254 1.00
mu[701] 39.45 0.02 0.38 38.68 39.18 39.44 39.71 40.19 265 1.01
mu[702] 39.49 0.02 0.39 38.74 39.23 39.49 39.74 40.28 261 1.01
mu[703] 39.56 0.02 0.38 38.81 39.31 39.55 39.80 40.32 283 1.01
mu[704] 39.62 0.02 0.38 38.87 39.36 39.62 39.86 40.37 295 1.01
mu[705] 39.66 0.02 0.38 38.93 39.40 39.65 39.92 40.44 278 1.01
mu[706] 39.71 0.02 0.39 39.00 39.45 39.70 39.97 40.48 305 1.01
mu[707] 39.74 0.02 0.39 39.07 39.47 39.73 40.00 40.53 311 1.01
mu[708] 39.75 0.02 0.39 39.02 39.49 39.73 40.00 40.54 318 1.01
mu[709] 39.75 0.02 0.38 38.96 39.49 39.75 40.01 40.52 325 1.01
mu[710] 39.75 0.02 0.38 39.01 39.50 39.75 40.00 40.50 344 1.01
mu[711] 39.76 0.02 0.38 38.99 39.50 39.75 40.01 40.49 328 1.01
mu[712] 39.77 0.02 0.37 39.05 39.51 39.76 40.01 40.48 311 1.01
mu[713] 39.82 0.02 0.39 39.07 39.56 39.82 40.08 40.55 304 1.01
mu[714] 39.84 0.02 0.39 39.11 39.56 39.86 40.11 40.62 316 1.01
mu[715] 39.85 0.02 0.39 39.12 39.58 39.85 40.14 40.58 361 1.00
mu[716] 39.87 0.02 0.38 39.14 39.61 39.88 40.13 40.61 358 1.00
mu[717] 39.88 0.02 0.37 39.17 39.63 39.87 40.13 40.61 421 1.00
mu[718] 39.87 0.02 0.37 39.15 39.62 39.88 40.13 40.58 385 1.00
mu[719] 39.85 0.02 0.39 39.09 39.58 39.86 40.12 40.59 387 1.00
mu[720] 39.85 0.02 0.40 39.13 39.57 39.85 40.12 40.61 376 1.00
mu[721] 39.81 0.02 0.40 39.07 39.54 39.80 40.08 40.59 365 1.00
mu[722] 39.76 0.02 0.39 39.03 39.51 39.75 40.03 40.54 360 1.00
mu[723] 39.71 0.02 0.39 38.96 39.43 39.71 39.97 40.49 351 1.00
mu[724] 39.66 0.02 0.38 38.92 39.40 39.68 39.92 40.43 320 1.00
mu[725] 39.62 0.02 0.39 38.88 39.34 39.62 39.88 40.38 308 1.00
mu[726] 39.58 0.02 0.38 38.85 39.31 39.57 39.86 40.30 332 1.00
mu[727] 39.52 0.02 0.38 38.75 39.27 39.53 39.78 40.24 281 1.01
mu[728] 39.47 0.02 0.38 38.75 39.20 39.48 39.72 40.25 292 1.01
mu[729] 39.43 0.02 0.38 38.69 39.18 39.44 39.68 40.18 287 1.01
mu[730] 39.41 0.02 0.38 38.66 39.16 39.41 39.67 40.14 259 1.01
mu[731] 39.38 0.02 0.37 38.65 39.12 39.38 39.62 40.09 255 1.01
mu[732] 39.34 0.02 0.37 38.57 39.09 39.34 39.59 40.08 283 1.01
mu[733] 39.30 0.02 0.38 38.55 39.06 39.30 39.56 40.00 325 1.01
mu[734] 39.25 0.02 0.38 38.47 39.02 39.27 39.51 39.96 281 1.01
mu[735] 39.23 0.02 0.38 38.45 38.99 39.22 39.49 39.96 264 1.01
mu[736] 39.20 0.02 0.39 38.41 38.97 39.22 39.46 39.94 260 1.02
mu[737] 39.20 0.02 0.38 38.47 38.95 39.22 39.47 39.92 256 1.02
mu[738] 39.22 0.02 0.37 38.47 38.97 39.22 39.48 39.89 309 1.02
mu[739] 39.20 0.02 0.37 38.42 38.96 39.21 39.44 39.93 265 1.02
mu[740] 39.21 0.02 0.38 38.44 38.96 39.22 39.46 39.92 235 1.02
mu[741] 39.21 0.03 0.38 38.47 38.95 39.20 39.45 39.93 230 1.02
mu[742] 39.22 0.03 0.39 38.46 38.96 39.21 39.50 39.96 187 1.02
mu[743] 39.23 0.02 0.38 38.49 38.96 39.23 39.51 39.94 280 1.02
mu[744] 39.27 0.02 0.38 38.55 39.00 39.29 39.55 39.98 278 1.02
mu[745] 39.30 0.02 0.38 38.56 39.05 39.31 39.56 40.02 276 1.01
mu[746] 39.38 0.02 0.38 38.65 39.12 39.38 39.64 40.10 275 1.01
mu[747] 39.45 0.02 0.39 38.70 39.19 39.45 39.71 40.16 258 1.01
mu[748] 39.49 0.02 0.39 38.73 39.22 39.49 39.74 40.25 270 1.01
mu[749] 39.54 0.02 0.38 38.80 39.28 39.55 39.81 40.29 262 1.01
mu[750] 39.57 0.02 0.38 38.81 39.33 39.57 39.82 40.28 243 1.01
mu[751] 39.61 0.02 0.37 38.88 39.36 39.61 39.85 40.31 278 1.01
mu[752] 39.64 0.02 0.37 38.91 39.41 39.64 39.87 40.35 282 1.00
mu[753] 39.65 0.02 0.37 38.89 39.42 39.66 39.89 40.40 262 1.00
mu[754] 39.68 0.02 0.38 38.92 39.44 39.68 39.92 40.43 290 1.01
mu[755] 39.71 0.02 0.39 38.97 39.44 39.71 39.96 40.50 276 1.01
mu[756] 39.75 0.02 0.38 39.03 39.50 39.74 40.00 40.57 315 1.01
mu[757] 39.82 0.02 0.38 39.05 39.57 39.81 40.07 40.56 315 1.01
mu[758] 39.87 0.02 0.38 39.14 39.61 39.87 40.13 40.58 305 1.00
mu[759] 39.92 0.02 0.38 39.19 39.67 39.91 40.16 40.70 299 1.00
mu[760] 39.95 0.02 0.38 39.22 39.69 39.95 40.20 40.73 293 1.01
mu[761] 39.96 0.02 0.39 39.21 39.71 39.96 40.22 40.70 337 1.01
mu[762] 39.98 0.02 0.39 39.20 39.73 39.99 40.25 40.75 335 1.01
mu[763] 39.98 0.02 0.39 39.18 39.71 39.98 40.23 40.73 293 1.01
mu[764] 40.00 0.02 0.39 39.18 39.73 40.02 40.27 40.75 243 1.01
mu[765] 40.01 0.02 0.38 39.27 39.74 40.03 40.27 40.69 242 1.01
mu[766] 40.03 0.02 0.37 39.25 39.78 40.04 40.28 40.75 234 1.01
mu[767] 40.06 0.02 0.37 39.30 39.81 40.06 40.33 40.76 245 1.01
mu[768] 40.13 0.03 0.38 39.39 39.88 40.14 40.39 40.84 224 1.01
mu[769] 40.19 0.03 0.38 39.43 39.95 40.20 40.45 40.93 199 1.01
mu[770] 40.25 0.03 0.39 39.48 39.99 40.25 40.52 41.03 214 1.01
mu[771] 40.31 0.03 0.39 39.58 40.04 40.32 40.57 41.11 194 1.01
mu[772] 40.38 0.03 0.38 39.60 40.14 40.39 40.65 41.13 219 1.00
mu[773] 40.40 0.02 0.38 39.65 40.14 40.41 40.67 41.13 234 1.00
mu[774] 40.42 0.02 0.38 39.67 40.16 40.41 40.67 41.17 242 1.00
mu[775] 40.43 0.02 0.39 39.63 40.17 40.43 40.68 41.14 270 1.01
mu[776] 40.42 0.02 0.38 39.68 40.17 40.42 40.69 41.12 254 1.01
mu[777] 40.40 0.02 0.37 39.67 40.17 40.41 40.65 41.10 264 1.01
mu[778] 40.37 0.02 0.38 39.65 40.11 40.37 40.63 41.09 304 1.01
mu[779] 40.34 0.02 0.38 39.61 40.09 40.33 40.60 41.03 257 1.01
mu[780] 40.29 0.02 0.38 39.55 40.03 40.30 40.55 41.01 257 1.01
mu[781] 40.27 0.02 0.38 39.51 40.02 40.26 40.53 40.97 277 1.01
mu[782] 40.28 0.02 0.39 39.50 40.03 40.29 40.54 40.99 273 1.01
mu[783] 40.29 0.02 0.39 39.51 40.03 40.31 40.53 41.06 270 1.01
mu[784] 40.28 0.02 0.39 39.47 40.04 40.29 40.53 41.07 277 1.01
mu[785] 40.26 0.03 0.37 39.55 39.98 40.26 40.54 41.00 204 1.01
mu[786] 40.21 0.02 0.38 39.45 39.96 40.22 40.45 40.94 242 1.01
mu[787] 40.12 0.03 0.38 39.41 39.86 40.13 40.37 40.85 228 1.01
mu[788] 40.01 0.02 0.39 39.24 39.75 40.00 40.27 40.77 266 1.01
mu[789] 39.88 0.03 0.39 39.10 39.62 39.87 40.15 40.62 223 1.01
mu[790] 39.74 0.03 0.39 38.97 39.46 39.74 40.00 40.48 219 1.01
mu[791] 39.57 0.02 0.39 38.83 39.30 39.56 39.84 40.34 250 1.01
mu[792] 39.40 0.02 0.39 38.69 39.13 39.39 39.66 40.18 279 1.01
mu[793] 39.29 0.02 0.37 38.59 39.03 39.29 39.53 40.00 281 1.01
mu[794] 39.17 0.02 0.38 38.42 38.93 39.18 39.42 39.93 314 1.01
mu[795] 39.10 0.02 0.37 38.35 38.85 39.11 39.35 39.83 308 1.01
mu[796] 39.02 0.02 0.37 38.32 38.79 39.04 39.26 39.74 446 1.00
mu[797] 38.92 0.02 0.38 38.19 38.67 38.92 39.16 39.65 399 1.00
mu[798] 38.83 0.02 0.38 38.09 38.57 38.82 39.08 39.58 422 1.00
mu[799] 38.75 0.02 0.38 38.02 38.50 38.76 39.00 39.54 423 1.00
mu[800] 38.72 0.02 0.37 38.01 38.48 38.72 38.97 39.45 443 1.00
mu[801] 38.68 0.02 0.37 37.93 38.44 38.67 38.94 39.40 376 1.00
mu[802] 38.66 0.02 0.37 37.96 38.42 38.68 38.91 39.35 378 1.00
mu[803] 38.65 0.02 0.35 37.97 38.42 38.64 38.88 39.36 361 1.00
mu[804] 38.67 0.02 0.36 37.99 38.42 38.66 38.90 39.38 415 1.00
mu[805] 38.72 0.02 0.36 38.08 38.48 38.71 38.95 39.47 398 1.00
mu[806] 38.76 0.02 0.36 38.05 38.54 38.75 38.98 39.51 343 1.00
mu[807] 38.83 0.02 0.36 38.13 38.59 38.82 39.07 39.60 363 1.00
mu[808] 38.84 0.02 0.37 38.13 38.61 38.82 39.08 39.59 366 1.00
mu[809] 38.89 0.02 0.38 38.16 38.64 38.89 39.13 39.60 379 1.00
mu[810] 38.94 0.02 0.38 38.22 38.68 38.94 39.18 39.68 375 1.00
mu[811] 38.95 0.02 0.38 38.23 38.70 38.96 39.20 39.70 361 1.00
mu[812] 38.96 0.02 0.37 38.20 38.71 38.97 39.21 39.64 408 1.00
mu[813] 38.98 0.02 0.37 38.24 38.72 38.99 39.25 39.68 369 1.00
mu[814] 39.00 0.02 0.39 38.24 38.75 39.01 39.27 39.75 354 1.00
mu[815] 38.97 0.02 0.39 38.19 38.71 38.97 39.25 39.71 352 1.00
mu[816] 38.97 0.02 0.38 38.24 38.70 38.96 39.24 39.65 368 1.00
mu[817] 38.96 0.02 0.37 38.27 38.71 38.97 39.21 39.68 393 1.00
mu[818] 38.95 0.02 0.36 38.23 38.71 38.95 39.20 39.60 363 1.00
mu[819] 38.94 0.02 0.37 38.19 38.69 38.97 39.19 39.69 340 1.00
mu[820] 38.98 0.02 0.38 38.23 38.74 38.98 39.25 39.74 290 1.00
mu[821] 39.03 0.02 0.38 38.28 38.75 39.04 39.30 39.77 334 1.00
mu[822] 39.07 0.02 0.37 38.35 38.81 39.07 39.34 39.76 334 1.00
mu[823] 39.14 0.02 0.38 38.40 38.87 39.13 39.40 39.89 302 1.00
mu[824] 39.22 0.02 0.39 38.51 38.94 39.20 39.48 39.98 287 1.00
mu[825] 39.29 0.02 0.39 38.57 39.02 39.29 39.55 40.09 297 1.00
mu[826] 39.39 0.02 0.39 38.67 39.13 39.38 39.67 40.19 249 1.01
mu[827] 39.48 0.02 0.39 38.75 39.20 39.47 39.75 40.24 270 1.00
mu[828] 39.59 0.02 0.39 38.85 39.33 39.57 39.85 40.33 262 1.00
mu[829] 39.66 0.03 0.39 38.92 39.40 39.65 39.93 40.45 228 1.01
mu[830] 39.78 0.03 0.40 39.05 39.50 39.76 40.06 40.60 202 1.01
mu[831] 39.92 0.03 0.40 39.16 39.66 39.91 40.18 40.76 224 1.01
mu[832] 40.01 0.03 0.40 39.22 39.73 40.01 40.29 40.78 248 1.01
mu[833] 40.10 0.02 0.40 39.32 39.85 40.09 40.37 40.89 265 1.01
mu[834] 40.20 0.02 0.40 39.42 39.93 40.20 40.46 40.99 281 1.00
mu[835] 40.29 0.02 0.39 39.54 40.04 40.29 40.55 41.05 256 1.00
mu[836] 40.39 0.02 0.39 39.63 40.13 40.38 40.65 41.15 252 1.00
mu[837] 40.50 0.03 0.39 39.71 40.25 40.48 40.78 41.27 241 1.00
mu[838] 40.62 0.03 0.40 39.83 40.35 40.62 40.89 41.39 241 1.00
mu[839] 40.72 0.03 0.40 39.93 40.46 40.72 41.00 41.48 231 1.00
mu[840] 40.80 0.03 0.39 40.03 40.53 40.80 41.07 41.55 216 1.00
mu[841] 40.86 0.03 0.40 40.05 40.58 40.86 41.12 41.60 208 1.00
mu[842] 40.91 0.03 0.40 40.13 40.64 40.91 41.18 41.73 186 1.01
mu[843] 40.95 0.03 0.41 40.13 40.66 40.95 41.24 41.76 176 1.01
mu[844] 40.98 0.03 0.41 40.19 40.70 40.97 41.26 41.77 166 1.01
mu[845] 41.01 0.03 0.42 40.22 40.72 41.00 41.31 41.79 180 1.01
mu[846] 41.04 0.03 0.43 40.24 40.73 41.04 41.34 41.87 185 1.01
mu[847] 41.02 0.03 0.43 40.20 40.71 41.03 41.33 41.81 187 1.01
mu[848] 41.00 0.03 0.43 40.20 40.71 40.99 41.29 41.80 199 1.01
mu[849] 41.00 0.03 0.42 40.18 40.71 40.99 41.30 41.83 191 1.01
mu[850] 40.97 0.03 0.43 40.09 40.69 40.98 41.26 41.80 191 1.01
mu[851] 40.92 0.03 0.42 40.08 40.64 40.93 41.22 41.71 189 1.01
mu[852] 40.89 0.03 0.42 40.04 40.61 40.91 41.18 41.70 203 1.01
mu[853] 40.87 0.03 0.42 40.03 40.58 40.87 41.17 41.68 208 1.01
mu[854] 40.89 0.03 0.41 40.07 40.60 40.90 41.17 41.72 199 1.01
mu[855] 40.92 0.03 0.41 40.16 40.63 40.92 41.20 41.74 204 1.01
mu[856] 40.96 0.03 0.41 40.24 40.67 40.96 41.22 41.76 210 1.01
mu[857] 41.00 0.03 0.40 40.26 40.72 40.99 41.28 41.84 213 1.01
mu[858] 41.04 0.02 0.39 40.34 40.77 41.03 41.31 41.80 262 1.01
mu[859] 41.03 0.03 0.40 40.30 40.74 41.03 41.29 41.82 227 1.01
mu[860] 41.07 0.02 0.39 40.33 40.80 41.07 41.33 41.84 246 1.01
mu[861] 41.10 0.02 0.39 40.32 40.85 41.09 41.36 41.88 262 1.01
mu[862] 41.13 0.02 0.39 40.39 40.86 41.14 41.39 41.89 299 1.01
mu[863] 41.19 0.02 0.38 40.45 40.92 41.19 41.47 41.90 262 1.01
mu[864] 41.17 0.02 0.38 40.49 40.90 41.17 41.45 41.92 266 1.01
mu[865] 41.11 0.02 0.38 40.38 40.83 41.12 41.38 41.84 280 1.01
mu[866] 41.06 0.02 0.38 40.34 40.80 41.07 41.32 41.78 283 1.01
mu[867] 41.00 0.02 0.38 40.27 40.75 41.00 41.25 41.74 290 1.01
mu[868] 41.01 0.02 0.39 40.28 40.73 41.02 41.27 41.77 273 1.01
mu[869] 41.03 0.02 0.39 40.27 40.76 41.02 41.29 41.78 267 1.01
mu[870] 41.04 0.02 0.39 40.28 40.77 41.04 41.30 41.80 298 1.01
mu[871] 41.01 0.03 0.39 40.27 40.75 41.00 41.27 41.80 221 1.02
mu[872] 40.97 0.03 0.40 40.20 40.71 40.97 41.22 41.76 231 1.02
mu[873] 40.93 0.03 0.40 40.13 40.68 40.94 41.20 41.67 238 1.02
mu[874] 40.89 0.03 0.39 40.12 40.63 40.88 41.16 41.68 220 1.02
mu[875] 40.87 0.03 0.39 40.09 40.62 40.88 41.13 41.60 130 1.03
mu[876] 40.91 0.03 0.40 40.12 40.65 40.91 41.18 41.67 134 1.03
mu[877] 40.96 0.03 0.42 40.15 40.69 40.96 41.24 41.77 144 1.02
mu[878] 40.99 0.04 0.41 40.17 40.71 40.99 41.27 41.77 117 1.03
mu[879] 41.03 0.04 0.41 40.25 40.75 41.01 41.30 41.87 117 1.03
mu[880] 41.10 0.03 0.40 40.30 40.83 41.09 41.39 41.88 161 1.02
mu[881] 41.16 0.03 0.40 40.41 40.88 41.15 41.44 41.91 173 1.02
mu[882] 41.21 0.03 0.40 40.44 40.93 41.19 41.47 42.06 176 1.02
mu[883] 41.28 0.03 0.39 40.54 41.02 41.28 41.52 42.12 191 1.02
mu[884] 41.36 0.03 0.38 40.66 41.10 41.36 41.61 42.15 208 1.02
mu[885] 41.44 0.03 0.38 40.71 41.18 41.43 41.68 42.20 232 1.01
mu[886] 41.48 0.02 0.38 40.77 41.23 41.46 41.73 42.25 250 1.01
mu[887] 41.50 0.02 0.40 40.78 41.21 41.50 41.77 42.32 253 1.00
mu[888] 41.51 0.03 0.40 40.75 41.24 41.51 41.77 42.33 244 1.00
mu[889] 41.48 0.03 0.39 40.73 41.21 41.48 41.74 42.27 214 1.01
mu[890] 41.44 0.03 0.40 40.64 41.16 41.43 41.74 42.25 218 1.01
mu[891] 41.42 0.03 0.39 40.65 41.15 41.42 41.68 42.22 210 1.00
mu[892] 41.42 0.03 0.39 40.70 41.16 41.42 41.69 42.17 211 1.00
mu[893] 41.40 0.03 0.39 40.65 41.13 41.40 41.67 42.20 199 1.00
mu[894] 41.42 0.03 0.39 40.69 41.13 41.41 41.69 42.18 219 1.00
mu[895] 41.44 0.03 0.39 40.70 41.16 41.43 41.68 42.23 218 1.00
mu[896] 41.47 0.02 0.39 40.76 41.20 41.45 41.72 42.20 245 1.00
mu[897] 41.49 0.02 0.39 40.75 41.22 41.49 41.75 42.33 259 1.00
mu[898] 41.55 0.02 0.40 40.78 41.26 41.54 41.83 42.35 264 1.00
mu[899] 41.67 0.03 0.40 40.91 41.39 41.67 41.94 42.49 248 1.00
mu[900] 41.80 0.03 0.40 41.02 41.54 41.81 42.06 42.58 250 1.00
mu[901] 41.95 0.02 0.39 41.16 41.70 41.96 42.19 42.72 255 1.00
mu[902] 42.11 0.03 0.39 41.33 41.85 42.11 42.38 42.92 242 1.00
mu[903] 42.27 0.03 0.40 41.48 42.01 42.27 42.52 43.05 219 1.01
mu[904] 42.46 0.03 0.40 41.65 42.18 42.44 42.73 43.27 237 1.01
mu[905] 42.64 0.03 0.41 41.86 42.37 42.64 42.90 43.49 232 1.00
mu[906] 42.77 0.03 0.41 41.97 42.50 42.77 43.03 43.64 225 1.01
mu[907] 42.91 0.03 0.40 42.14 42.65 42.91 43.16 43.75 222 1.01
mu[908] 43.05 0.03 0.40 42.30 42.77 43.03 43.30 43.86 210 1.00
mu[909] 43.16 0.03 0.40 42.43 42.90 43.15 43.43 43.99 241 1.00
mu[910] 43.27 0.02 0.40 42.50 43.02 43.25 43.53 44.09 283 1.00
mu[911] 43.38 0.02 0.40 42.63 43.10 43.38 43.65 44.22 277 1.00
mu[912] 43.49 0.02 0.40 42.70 43.23 43.49 43.74 44.29 264 1.00
mu[913] 43.58 0.03 0.40 42.82 43.30 43.58 43.83 44.38 252 1.00
mu[914] 43.65 0.03 0.40 42.89 43.39 43.65 43.90 44.46 249 1.00
mu[915] 43.68 0.03 0.40 42.90 43.43 43.68 43.94 44.44 242 1.00
mu[916] 43.70 0.03 0.40 42.85 43.42 43.70 43.96 44.49 254 1.00
mu[917] 43.69 0.03 0.40 42.91 43.42 43.70 43.96 44.45 252 1.00
mu[918] 43.68 0.03 0.39 42.91 43.41 43.67 43.94 44.46 238 1.00
mu[919] 43.69 0.02 0.38 42.98 43.43 43.68 43.94 44.44 232 1.00
mu[920] 43.70 0.02 0.39 42.99 43.43 43.70 43.97 44.47 256 1.00
mu[921] 43.74 0.02 0.38 43.02 43.47 43.73 43.99 44.45 237 1.00
mu[922] 43.79 0.03 0.37 43.06 43.52 43.79 44.04 44.55 222 1.00
mu[923] 43.79 0.03 0.39 43.08 43.52 43.79 44.04 44.58 227 1.00
mu[924] 43.77 0.03 0.39 43.01 43.51 43.78 44.04 44.55 228 1.00
mu[925] 43.78 0.02 0.39 43.04 43.52 43.77 44.06 44.58 242 1.00
mu[926] 43.77 0.02 0.37 43.06 43.52 43.76 44.00 44.53 273 1.00
mu[927] 43.78 0.02 0.39 43.03 43.51 43.77 44.05 44.53 277 1.00
mu[928] 43.78 0.02 0.39 43.05 43.52 43.77 44.06 44.51 279 1.00
mu[929] 43.82 0.02 0.39 43.10 43.57 43.80 44.10 44.58 303 1.00
mu[930] 43.82 0.02 0.39 43.08 43.57 43.80 44.09 44.59 315 1.00
mu[931] 43.78 0.02 0.39 43.04 43.53 43.77 44.04 44.56 296 1.00
mu[932] 43.73 0.02 0.39 42.96 43.49 43.73 44.00 44.52 303 1.00
mu[933] 43.68 0.02 0.39 42.91 43.41 43.69 43.96 44.43 309 1.01
mu[934] 43.61 0.02 0.39 42.82 43.34 43.62 43.88 44.33 303 1.01
mu[935] 43.55 0.02 0.38 42.77 43.29 43.56 43.81 44.27 329 1.01
mu[936] 43.49 0.02 0.40 42.70 43.23 43.48 43.76 44.23 316 1.01
mu[937] 43.39 0.02 0.38 42.63 43.13 43.40 43.66 44.15 324 1.01
mu[938] 43.28 0.02 0.39 42.49 43.01 43.29 43.55 44.00 264 1.02
mu[939] 43.17 0.02 0.39 42.40 42.91 43.17 43.43 43.97 273 1.01
mu[940] 43.07 0.02 0.39 42.30 42.82 43.06 43.31 43.89 246 1.02
mu[941] 42.98 0.02 0.38 42.21 42.72 42.99 43.24 43.74 265 1.02
mu[942] 42.91 0.02 0.38 42.16 42.66 42.93 43.16 43.67 259 1.02
mu[943] 42.83 0.02 0.39 42.12 42.55 42.82 43.10 43.61 282 1.02
mu[944] 42.78 0.02 0.38 42.06 42.50 42.79 43.03 43.54 266 1.02
mu[945] 42.75 0.02 0.38 41.99 42.47 42.74 43.00 43.49 249 1.01
mu[946] 42.69 0.02 0.38 41.96 42.43 42.70 42.96 43.43 245 1.01
mu[947] 42.66 0.03 0.38 41.92 42.41 42.65 42.93 43.41 231 1.01
mu[948] 42.64 0.02 0.37 41.93 42.39 42.63 42.89 43.39 280 1.01
mu[949] 42.71 0.02 0.37 41.96 42.45 42.71 42.94 43.47 298 1.01
mu[950] 42.79 0.02 0.38 42.01 42.54 42.80 43.05 43.54 306 1.01
mu[951] 42.92 0.02 0.38 42.16 42.66 42.93 43.18 43.68 282 1.01
mu[952] 43.08 0.02 0.39 42.29 42.84 43.07 43.33 43.89 289 1.01
mu[953] 43.23 0.02 0.38 42.47 42.98 43.21 43.48 43.98 300 1.01
mu[954] 43.38 0.02 0.39 42.60 43.12 43.38 43.63 44.14 319 1.00
mu[955] 43.54 0.02 0.40 42.77 43.29 43.54 43.80 44.32 305 1.00
mu[956] 43.68 0.02 0.38 42.94 43.44 43.68 43.94 44.42 299 1.00
mu[957] 43.85 0.02 0.39 43.09 43.60 43.84 44.11 44.64 270 1.00
mu[958] 43.98 0.02 0.39 43.23 43.71 43.98 44.24 44.75 247 1.01
mu[959] 44.08 0.03 0.39 43.34 43.81 44.07 44.32 44.89 237 1.01
mu[960] 44.20 0.03 0.40 43.43 43.93 44.20 44.47 45.02 218 1.01
mu[961] 44.35 0.02 0.41 43.58 44.07 44.34 44.63 45.15 275 1.00
mu[962] 44.47 0.02 0.40 43.73 44.16 44.45 44.73 45.24 274 1.00
mu[963] 44.58 0.02 0.39 43.88 44.30 44.59 44.86 45.37 254 1.01
mu[964] 44.71 0.02 0.39 43.99 44.45 44.70 44.98 45.45 244 1.00
mu[965] 44.80 0.02 0.39 44.01 44.54 44.79 45.06 45.57 250 1.00
mu[966] 44.95 0.02 0.38 44.18 44.70 44.95 45.21 45.66 236 1.00
mu[967] 45.09 0.02 0.37 44.31 44.85 45.10 45.35 45.77 256 1.01
mu[968] 45.22 0.02 0.37 44.50 44.96 45.23 45.46 45.91 238 1.01
mu[969] 45.33 0.02 0.38 44.59 45.05 45.34 45.58 46.06 248 1.01
mu[970] 45.42 0.02 0.37 44.65 45.17 45.42 45.67 46.16 271 1.01
mu[971] 45.51 0.02 0.36 44.78 45.26 45.51 45.76 46.21 294 1.01
mu[972] 45.57 0.02 0.36 44.85 45.33 45.58 45.80 46.29 277 1.01
mu[973] 45.61 0.02 0.36 44.84 45.38 45.60 45.85 46.31 299 1.01
mu[974] 45.66 0.02 0.37 44.93 45.41 45.66 45.90 46.42 260 1.01
mu[975] 45.71 0.02 0.38 44.99 45.46 45.72 45.95 46.49 237 1.02
mu[976] 45.71 0.02 0.38 45.01 45.46 45.72 45.95 46.49 288 1.02
mu[977] 45.70 0.03 0.40 44.96 45.43 45.68 45.95 46.47 250 1.02
mu[978] 45.67 0.02 0.40 44.92 45.39 45.67 45.92 46.48 290 1.02
mu[979] 45.64 0.02 0.40 44.89 45.35 45.65 45.90 46.47 299 1.02
mu[980] 45.60 0.03 0.41 44.81 45.31 45.60 45.89 46.43 267 1.02
mu[981] 45.57 0.02 0.42 44.79 45.27 45.57 45.85 46.43 325 1.02
mu[982] 45.57 0.02 0.41 44.82 45.29 45.56 45.85 46.42 326 1.02
mu[983] 45.56 0.02 0.41 44.79 45.27 45.56 45.83 46.34 315 1.02
mu[984] 45.52 0.02 0.39 44.76 45.25 45.52 45.81 46.22 317 1.02
mu[985] 45.53 0.02 0.39 44.81 45.26 45.53 45.80 46.28 262 1.02
mu[986] 45.52 0.02 0.38 44.76 45.25 45.51 45.77 46.27 280 1.02
mu[987] 45.55 0.02 0.38 44.78 45.30 45.55 45.82 46.30 291 1.02
mu[988] 45.61 0.02 0.38 44.87 45.35 45.61 45.85 46.36 311 1.01
mu[989] 45.67 0.02 0.38 44.93 45.41 45.66 45.93 46.45 322 1.01
mu[990] 45.76 0.02 0.38 45.03 45.50 45.77 46.01 46.50 323 1.01
mu[991] 45.82 0.02 0.38 45.07 45.58 45.83 46.06 46.56 326 1.01
mu[992] 45.86 0.02 0.38 45.09 45.62 45.87 46.12 46.63 321 1.01
mu[993] 45.91 0.02 0.39 45.08 45.65 45.91 46.15 46.69 337 1.01
mu[994] 45.98 0.02 0.38 45.23 45.73 45.99 46.24 46.75 381 1.01
mu[995] 46.07 0.02 0.38 45.31 45.83 46.06 46.31 46.85 385 1.01
mu[996] 46.15 0.02 0.38 45.41 45.89 46.14 46.41 46.94 385 1.00
mu[997] 46.23 0.02 0.38 45.49 45.97 46.23 46.50 46.99 389 1.00
mu[998] 46.31 0.02 0.37 45.61 46.07 46.31 46.57 47.00 371 1.00
mu[999] 46.38 0.02 0.38 45.65 46.13 46.37 46.64 47.16 356 1.00
mu[1000] 46.43 0.02 0.39 45.68 46.18 46.40 46.68 47.21 336 1.00
mu[1001] 46.45 0.02 0.39 45.68 46.19 46.44 46.70 47.20 329 1.00
mu[1002] 46.50 0.02 0.40 45.70 46.23 46.49 46.76 47.32 313 1.01
mu[1003] 46.55 0.02 0.42 45.78 46.26 46.55 46.83 47.42 332 1.00
mu[1004] 46.63 0.02 0.42 45.84 46.35 46.61 46.90 47.48 319 1.00
mu[1005] 46.69 0.03 0.45 45.79 46.38 46.70 46.97 47.59 315 1.00
mu[1006] 46.72 0.03 0.46 45.84 46.40 46.72 47.03 47.62 295 1.00
mu[1007] 46.72 0.03 0.47 45.85 46.42 46.71 47.02 47.64 292 1.00
mu[1008] 46.71 0.03 0.49 45.74 46.39 46.70 47.02 47.66 289 1.00
mu[1009] 46.70 0.03 0.51 45.70 46.37 46.70 47.03 47.75 299 1.00
mu[1010] 46.71 0.03 0.53 45.67 46.36 46.69 47.06 47.79 314 1.00
mu[1011] 46.71 0.03 0.55 45.66 46.34 46.68 47.06 47.89 334 1.00
mu[1012] 46.72 0.03 0.57 45.62 46.36 46.71 47.09 47.92 352 1.00
mu[1013] 46.70 0.03 0.60 45.52 46.31 46.71 47.08 47.90 386 1.00
mu[1014] 46.69 0.03 0.63 45.46 46.26 46.69 47.11 48.00 427 1.00
Samples were drawn using NUTS(diag_e) at Wed Jun 1 19:32:10 2022.
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")No id variables; using all as measure variablesPartisanship…
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")
Reuse
Citation
BibTeX citation:
@online{dewitt2019,
author = {Michael DeWitt},
title = {Approval {Rating} {Now?}},
date = {2019-09-26},
url = {https://michaeldewittjr.com/programming/2019-09-26-approval-rating-now},
langid = {en}
}
For attribution, please cite this work as:
Michael DeWitt. 2019. “Approval Rating Now?” September 26,
2019. https://michaeldewittjr.com/programming/2019-09-26-approval-rating-now.