Approval Rating Now?

Given the current controversy regarding President Trump, let’s use a state-space Bayesian model to see what his approval rating currently is. As more surveys go into the field this will change, but let’s just look now.

Political
Bayes
State Space
Author
Affiliation
Published

September 26, 2019

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)

Attaching package: 'lubridate'
The following objects are masked from 'package:base':

    date, intersect, setdiff, union
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 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':

    extract
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….

sstrump <- stan_model("sstrump.stan")
recompiling to avoid crashing R session
trump_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-ess
Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
Running the chains for more iterations may help. See
https://mc-stan.org/misc/warnings.html#tail-ess

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: 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 variables

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")

Reuse

Citation

BibTeX citation:
@online{dewitt2019,
  author = {Michael DeWitt},
  editor = {},
  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.