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.

Michael DeWitt https://michaeldewittjr.com
09-26-2019

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)
dat_range <- crossing(seq(min(mdy(dat$end_date)),
                 max(mdy("11/1/2019")),
                     "1 day") %>% 
  enframe(name = NULL) %>% 
  set_names("date_range"), pollster = unique(dat$pollster))

formatted_data <- dat %>% 
  mutate(my_end = lubridate::mdy(end_date)) %>% 
  select(my_end, yes, sample_size, pollster) %>% 
  mutate(polling_var = sqrt(.5 * (1-.5)/sample_size)*100) %>% 
  right_join(dat_range, by = c("my_end" = "date_range", "pollster")) 

formatted_data[is.na(formatted_data)] <- -9

sigma <- formatted_data %>% 
  select(my_end, pollster, polling_var) %>%
  pivot_wider(names_from = pollster, 
              values_from = polling_var,
              values_fn = list(polling_var = max)) %>% 
  select(-my_end) %>% 
  as.matrix()

y <- formatted_data %>% 
  select(my_end, pollster, yes) %>%
  pivot_wider(names_from = pollster, 
              values_from = yes,
              values_fn = list(yes = max)) %>% 
  select(-my_end) %>% 
  as.matrix()

Our Model

This is the same model from this blog post courtsey of James Savage and Peter Ellis.


// Base Syntax from James Savage at https://github.com/khakieconomics/stanecon_short_course/blob/80263f84ebe95be3247e591515ea1ead84f26e3f/03-fun_time_series_models.Rmd
//and modification inspired by Peter Ellis at https://github.com/ellisp/ozfedelect/blob/master/model-2pp/model-2pp.R

data {
  int polls; // number of polls
  int T; // number of days
  matrix[T, polls] Y; // polls
  matrix[T, polls] sigma; // polls standard deviations
  real inflator;         // amount by which to multiply the standard error of polls
  real initial_prior;
  real random_walk_sd;
  real mu_sigma;
}
parameters {
  vector[T] mu; // the mean of the polls
  real<lower = 0> tau; // the standard deviation of the random effects
  matrix[T, polls] shrunken_polls;
}
model {
  // prior on initial difference
  mu[1] ~ normal(initial_prior, mu_sigma);
  tau ~ student_t(4, 0, 5);
  // state model
  for(t in 2:T) {
    mu[t] ~ normal(mu[t-1], random_walk_sd);
  }
  
  // measurement model
  for(t in 1:T) {
    for(p in 1:polls) {
      if(Y[t, p] != -9) {
        Y[t,p]~ normal(shrunken_polls[t, p], sigma[t,p] * inflator);
        shrunken_polls[t, p] ~ normal(mu[t], tau);
      } else {
        shrunken_polls[t, p] ~ normal(0, 1);
      }
    }
  }
}

Prep the Data

Now we can put the data in the proper format for Stan. I’m also going to supply the 2016 voteshare as the initial prior. This is probably a favourable place to start.


library(rstan)
rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())
approval_data <- list(
  T = nrow(y),
  polls = ncol(sigma),
  Y = y,
  sigma = sigma,
  initial_prior = 46, # 2016 Election Results
  random_walk_sd = 0.2,
  mu_sigma = 1,
  inflator =sqrt(2)
)

Run the Model

Now we can run the model. Caution, this takes a good while to run…oh how I miss having a cluster….


trump_model <- sampling(sstrump, 
                    data = approval_data, 
                    iter = 1000,
                    refresh = 0,
                    chains = 2,
                    control = list(adapt_delta = .95,
                                     max_treedepth = 15))

Did It Converge?

I’m just going to look quickly at some of the Rhat values. I see that some of my ESS are a little lower than I would like. This isn’t completely surprising given the sparsity of data (57 different polls).


print(trump_model, pars = "mu")

Inference for Stan model: a643d45063962397b14f15d26d605751.
2 chains, each with iter=1000; warmup=500; thin=1; 
post-warmup draws per chain=500, total post-warmup draws=1000.

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

Samples were drawn using NUTS(diag_e) at Fri Sep 27 12:40:40 2019.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at 
convergence, Rhat=1).

Now Let’s see…

Now we can extract the model fit and see how it looks!


mu_trump <- extract(trump_model, pars = "mu", permuted = T)[[1]] %>% 
  as.data.frame

names(mu_trump) <- unique(dat_range$date_range)

mu_ts_trump <- mu_trump %>% reshape2::melt() %>% 
  mutate(date = as.Date(variable)) %>% 
  group_by(date) %>% 
  summarise(median = median(value),
            lower = quantile(value, 0.025),
            upper = quantile(value, 0.975),
            candidate = "Trump")

Partisanship…

Looks like despite a dip in late 2017, Mr. Trump’s approval rating is remarkably stable (as a reminder, it looks like the lowest ever was 25% for President G.W. Bush). It will be curious to see how this changes as more information comes out regarding Mr. Trumps actions with Ukraine.


mu_ts_trump %>% 
  ggplot(aes(date, median))+
  geom_line(color = "#E91D0E")+
  geom_ribbon(aes(ymin = lower, ymax = upper), alpha = .2)+
  labs(
    title = "President Trump's Approval Rating",
    subtitle = "Based on State-Space Modeling\nInitial Prior: 46%",
    caption = "Data: https://github.com/fivethirtyeight/data/tree/master/polls",
    y = "Approval",
    x = NULL
  )+
  geom_vline(xintercept = as.Date(Sys.Date()), color = "orange")

Reuse

Text and figures are licensed under Creative Commons Attribution CC BY 4.0. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ...".

Citation

For attribution, please cite this work as

DeWitt (2019, Sept. 26). Michael DeWitt: Approval Rating Now?. Retrieved from https://michaeldewittjr.com/dewitt_blog/posts/2019-09-26-approval-rating-now/

BibTeX citation

@misc{dewitt2019approval,
  author = {DeWitt, Michael},
  title = {Michael DeWitt: Approval Rating Now?},
  url = {https://michaeldewittjr.com/dewitt_blog/posts/2019-09-26-approval-rating-now/},
  year = {2019}
}