* using log directory 'd:/Rcompile/CRANpkg/local/3.6/DPQ.Rcheck'
* using R version 3.6.3 (2020-02-29)
* using platform: x86_64-w64-mingw32 (64-bit)
* using session charset: ISO8859-1
* checking for file 'DPQ/DESCRIPTION' ... OK
* this is package 'DPQ' version '0.4-3'
* package encoding: UTF-8
* checking package namespace information ... OK
* checking package dependencies ... OK
* checking if this is a source package ... OK
* checking if there is a namespace ... OK
* checking for hidden files and directories ... OK
* checking for portable file names ... OK
* checking whether package 'DPQ' can be installed ... OK
* checking installed package size ... OK
* checking package directory ... OK
* checking 'build' directory ... OK
* checking DESCRIPTION meta-information ... OK
* checking top-level files ... OK
* checking for left-over files ... OK
* checking index information ... OK
* checking package subdirectories ... OK
* checking R files for non-ASCII characters ... OK
* checking R files for syntax errors ... OK
* loading checks for arch 'i386'
** checking whether the package can be loaded ... OK
** checking whether the package can be loaded with stated dependencies ... OK
** checking whether the package can be unloaded cleanly ... OK
** checking whether the namespace can be loaded with stated dependencies ... OK
** checking whether the namespace can be unloaded cleanly ... OK
** checking loading without being on the library search path ... OK
** checking use of S3 registration ... OK
* loading checks for arch 'x64'
** checking whether the package can be loaded ... OK
** checking whether the package can be loaded with stated dependencies ... OK
** checking whether the package can be unloaded cleanly ... OK
** checking whether the namespace can be loaded with stated dependencies ... OK
** checking whether the namespace can be unloaded cleanly ... OK
** checking loading without being on the library search path ... OK
** checking use of S3 registration ... OK
* checking dependencies in R code ... OK
* checking S3 generic/method consistency ... OK
* checking replacement functions ... OK
* checking foreign function calls ... OK
* checking R code for possible problems ... [19s] OK
* checking Rd files ... OK
* checking Rd metadata ... OK
* checking Rd cross-references ... OK
* checking for missing documentation entries ... OK
* checking for code/documentation mismatches ... OK
* checking Rd \usage sections ... OK
* checking Rd contents ... OK
* checking for unstated dependencies in examples ... OK
* checking line endings in C/C++/Fortran sources/headers ... OK
* checking pragmas in C/C++ headers and code ... OK
* checking compiled code ... OK
* checking sizes of PDF files under 'inst/doc' ... OK
* checking installed files from 'inst/doc' ... OK
* checking files in 'vignettes' ... OK
* checking examples ...
** running examples for arch 'i386' ... ERROR
Running examples in 'DPQ-Ex.R' failed
The error most likely occurred in:

> ### Name: p1l1
> ### Title: Numerically Stable p1l1(t) = (t+1)*log(1+t) - t
> ### Aliases: p1l1 p1l1. p1l1p p1l1ser
> 
> ### ** Examples
> 
> t <- seq(-1, 4, by=1/64)
> plot(t, p1l1ser(t, 1), type="l")
> lines(t, p1l1.(t), lwd=5, col=adjustcolor(1, 1/2)) # direct formula
> for(k in 2:6) lines(t, p1l1ser(t, k), col=k)
> 
> ## zoom in
> t <- 2^seq(-59,-1, by=1/4)
> t <- c(-rev(t), 0, t)
> stopifnot(!is.unsorted(t))
> k.s <- 1:12; names(k.s) <- paste0("k=", 1:12)
> 
> ## True function values: use Rmpfr with 256 bits precision: ---
> ### eventually move this to ../tests/ & ../vignettes/
> #### FIXME: eventually replace with  if(requireNamespace("Rmpfr")){ ......}
> #### =====
> if((needRmpfr <- is.na(match("Rmpfr", (srch0 <- search())))))
+     require("Rmpfr")
Loading required package: Rmpfr
Loading required package: gmp

Attaching package: 'gmp'

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

    %*%, apply, crossprod, matrix, tcrossprod

C code of R package 'Rmpfr': GMP using 32 bits per limb


Attaching package: 'Rmpfr'

The following object is masked from 'package:gmp':

    outer

The following object is masked from 'package:DPQ':

    log1mexp

The following objects are masked from 'package:stats':

    dbinom, dgamma, dnbinom, dnorm, dpois, pnorm

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

    cbind, pmax, pmin, rbind

> p1l1.T <- p1l1.(mpfr(t, 256)) # "true" values
> p1l1.n <- asNumeric(p1l1.T)
> p1tab <-
+     cbind(b1 = bd0(t+1, 1),
+           b.10 = bd0(10*t+10,10)/10,
+           dirct = p1l1.(t),
+           p1l1p = p1l1p(t),
+           p1l1  = p1l1 (t),
+           sapply(k.s, function(k) p1l1ser(t,k)))
> matplot(t, p1tab, type="l", ylab = "p1l1*(t)")
> ## (absolute) error:
> ##' legend for matplot()
> mpLeg <- function(leg = colnames(p1tab), xy = "top", col=1:6, lty=1:5, lwd=1,
+                   pch = c(1L:9L, 0L, letters, LETTERS)[seq_along(leg)], ...)
+     legend(xy, legend=leg, col=col, lty=lty, lwd=lwd, pch=pch, ncol=3, ...)
> 
> titAbs <- "Absolute errors of p1l1(t) approximations"
> matplot(t, asNumeric(p1tab - p1l1.T), type="o", main=titAbs); mpLeg()
> i <- abs(t) <= 1/10 ## zoom in a bit
> matplot(t[i], abs(asNumeric((p1tab - p1l1.T)[i,])), type="o", log="y",
+         main=titAbs, ylim = c(1e-18, 0.003)); mpLeg()
Warning in xy.coords(x, y, xlabel, ylabel, log = log) :
  17 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log) :
  1 y value <= 0 omitted from logarithmic plot
> ## Relative Error
> titR <- "|Relative error| of p1l1(t) approximations"
> matplot(t[i], abs(asNumeric((p1tab/p1l1.T - 1)[i,])), type="o", log="y",
+         ylim = c(1e-18, 2^-10), main=titR)
> mpLeg(xy="topright", bg= adjustcolor("gray80", 4/5))
> i <- abs(t) <= 2^-10 # zoom in more
> matplot(t[i], abs(asNumeric((p1tab/p1l1.T - 1)[i,])), type="o", log="y",
+         ylim = c(1e-18, 1e-9))
> mpLeg(xy="topright", bg= adjustcolor("gray80", 4/5))
> 
> 
> ## Correct number of digits
> corDig <- asNumeric(-log10(abs(p1tab/p1l1.T - 1)))
> cbind(t, round(corDig, 1))# correct number of digits
                   t   b1 b.10 dirct p1l1p p1l1  k=1  k=2  k=3  k=4  k=5  k=6
  [1,] -5.000000e-01 15.5 15.5  16.1  16.0 16.0  0.7  1.3  1.8  2.3  2.7  3.1
  [2,] -4.204482e-01 15.4 15.4  15.2  15.8 15.8  0.8  1.5  2.1  2.6  3.1  3.6
  [3,] -3.535534e-01 15.3 16.3  15.6  16.3 16.3  0.9  1.6  2.3  2.9  3.5  4.1
  [4,] -2.973018e-01 15.1 14.8  15.7  15.4 15.4  1.0  1.8  2.5  3.2  3.9  4.5
  [5,] -2.500000e-01 15.6 14.7  15.2  16.4 16.4  1.1  1.9  2.8  3.5  4.3  5.0
  [6,] -2.102241e-01 14.7 14.6  15.6  16.4 16.4  1.1  2.1  3.0  3.8  4.7  5.5
  [7,] -1.767767e-01 16.6 15.6  15.6  15.6 15.6  1.2  2.3  3.2  4.2  5.1  5.9
  [8,] -1.486509e-01 15.8 15.3  14.9  16.8 16.8  1.3  2.4  3.5  4.5  5.4  6.4
  [9,] -1.250000e-01 16.5 16.5  15.4  16.5 16.5  1.4  2.6  3.7  4.8  5.8  6.8
 [10,] -1.051121e-01 15.1 14.8  15.1  15.8 15.8  1.4  2.7  3.9  5.1  6.2  7.3
 [11,] -8.838835e-02 15.1 15.5  15.0  16.1 16.1  1.5  2.9  4.1  5.4  6.6  7.8
 [12,] -7.432544e-02 15.0 14.7  14.7  15.8 15.8  1.6  3.0  4.4  5.7  7.0  8.2
 [13,] -6.250000e-02 15.7 17.6  14.6  15.7 17.6  1.7  3.2  4.6  6.0  7.3  8.7
 [14,] -5.255603e-02 15.1 14.8  14.6  16.0 16.3  1.8  3.3  4.8  6.3  7.7  9.1
 [15,] -4.419417e-02 15.1 15.6  14.4  15.7 16.5  1.8  3.5  5.1  6.6  8.1  9.6
 [16,] -3.716272e-02 14.7 14.7  14.4  16.1 15.7  1.9  3.6  5.3  6.9  8.5 10.0
 [17,] -3.125000e-02 16.5 16.5  14.4  15.7 16.5  2.0  3.8  5.5  7.2  8.8 10.5
 [18,] -2.627801e-02 14.4 14.3  14.2  15.8 17.1  2.1  3.9  5.7  7.5  9.2 10.9
 [19,] -2.209709e-02 14.4 15.8  14.5  15.8 15.8  2.1  4.1  6.0  7.8  9.6 11.4
 [20,] -1.858136e-02 14.4 14.1  13.9  15.9 16.6  2.2  4.2  6.2  8.1 10.0 11.8
 [21,] -1.562500e-02 16.1 16.1  14.3  15.9 15.9  2.3  4.4  6.4  8.4 10.4 12.3
 [22,] -1.313901e-02 14.3 14.3  14.0  16.9 15.8  2.4  4.5  6.6  8.7 10.7 12.7
 [23,] -1.104854e-02 14.4 13.8  13.8  15.7 16.7  2.4  4.7  6.9  9.0 11.1 13.2
 [24,] -9.290681e-03 14.1 13.9  13.9  16.4 15.9  2.5  4.8  7.1  9.3 11.5 13.6
 [25,] -7.812500e-03 15.9 16.0  13.8  15.9 15.9  2.6  5.0  7.3  9.6 11.9 14.1
 [26,] -6.569503e-03 13.9 13.7  14.0  16.3 16.0  2.7  5.1  7.5  9.9 12.2 14.5
 [27,] -5.524272e-03 13.8 13.8  13.9  15.6 15.8  2.7  5.3  7.8 10.2 12.6 15.0
 [28,] -4.645340e-03 14.1 14.0  13.5  16.0 16.2  2.8  5.4  8.0 10.5 13.0 15.4
 [29,] -3.906250e-03 15.8 16.2  13.5  16.2 16.2  2.9  5.6  8.2 10.8 13.4 16.2
 [30,] -3.284752e-03 13.7 13.5  13.9  16.5 15.7  3.0  5.7  8.5 11.1 13.7 15.7
 [31,] -2.762136e-03 13.8 13.3  13.0  15.9 16.1  3.0  5.9  8.7 11.4 14.1 16.1
 [32,] -2.322670e-03 14.1 13.2  13.4  16.4 16.4  3.1  6.0  8.9 11.7 14.5 16.4
 [33,] -1.953125e-03 16.2 15.8  13.7  16.2 16.2  3.2  6.2  9.1 12.0 14.9 16.2
 [34,] -1.642376e-03 13.7 13.5  13.5  16.0 16.0  3.3  6.3  9.4 12.3 15.4 16.0
 [35,] -1.381068e-03 13.8 13.1  13.7  16.2 15.8  3.3  6.5  9.6 12.6 16.2 15.8
 [36,] -1.161335e-03 13.1 13.2  12.7  15.6 15.7  3.4  6.6  9.8 12.9 15.7 16.0
 [37,] -9.765625e-04 16.1 16.1  13.5  15.8 15.8  3.5  6.8 10.0 13.2 15.8 16.1
 [38,] -8.211879e-04 13.7 13.5  12.6  16.4 16.4  3.6  6.9 10.3 13.5 16.4 16.4
 [39,] -6.905340e-04 13.8 12.8  13.3  15.7 16.6  3.6  7.1 10.5 13.8 16.6 16.6
 [40,] -5.806675e-04 13.1 12.6  12.8  15.8 15.8  3.7  7.3 10.7 14.1 15.8 15.8
 [41,] -4.882812e-04 16.3 16.3  12.2  15.8 16.3  3.8  7.4 10.9 14.4 16.3 16.3
 [42,] -4.105940e-04 12.6 12.4  13.7  16.6 16.6  3.9  7.6 11.2 14.7 16.6 16.6
 [43,] -3.452670e-04 12.5 12.5  12.5  15.9 16.0  3.9  7.7 11.4 15.1 16.0 16.0
 [44,] -2.903338e-04 13.1 12.4  14.5  15.5 16.9  4.0  7.9 11.6 15.3 16.9 16.9
 [45,] -2.441406e-04 16.1 15.8  12.3  16.1 16.1  4.1  8.0 11.8 15.8 16.1 16.1
 [46,] -2.052970e-04 12.6 12.3  12.1  16.4 15.9  4.2  8.2 12.1 15.9 15.9 15.9
 [47,] -1.726335e-04 12.5 12.2  12.5  15.8 16.3  4.2  8.3 12.3 16.3 15.8 15.8
 [48,] -1.451669e-04 12.2 12.4  12.2  15.7 16.4  4.3  8.5 12.5 16.4 16.4 16.4
 [49,] -1.220703e-04 15.9 16.1  11.9  15.5 16.1  4.4  8.6 12.7 16.1 16.1 16.1
 [50,] -1.026485e-04 12.1 12.3  12.8  16.4 16.4  4.5  8.8 13.0 16.4 16.4 16.4
 [51,] -8.631675e-05 12.5 12.2  12.2  16.0 16.0  4.5  8.9 13.2 16.0 16.0 16.0
 [52,] -7.258344e-05 12.1 11.7  11.9  15.5 15.9  4.6  9.1 13.4 15.9 15.9 15.9
 [53,] -6.103516e-05 16.0 16.0  11.4  16.0 16.0  4.7  9.2 13.6 16.0 16.0 16.0
 [54,] -5.132424e-05 11.9 12.3  11.3  16.3 16.3  4.8  9.4 13.9 16.3 16.3 16.3
 [55,] -4.315837e-05 12.5 12.2  11.4  16.1 16.1  4.8  9.5 14.1 16.1 16.1 16.1
 [56,] -3.629172e-05 12.1 11.5  12.5  16.1 16.1  4.9  9.7 14.3 16.1 16.1 16.1
 [57,] -3.051758e-05 16.5 16.5  11.6  16.5 16.5  5.0  9.8 14.5 16.5 16.5 16.5
 [58,] -2.566212e-05 11.5 11.2  11.0  15.9 16.5  5.1 10.0 14.8 16.5 16.5 16.5
 [59,] -2.157919e-05 11.3 12.2  10.9  16.3 15.8  5.1 10.1 15.0 15.8 15.8 15.8
 [60,] -1.814586e-05 11.3 11.5  10.7  16.2 16.1  5.2 10.3 15.3 16.1 16.1 16.1
 [61,] -1.525879e-05 16.1 16.1  10.8  15.9 16.1  5.3 10.4 15.4 16.1 16.1 16.1
 [62,] -1.283106e-05 11.5 11.2  12.1  15.7 15.9  5.4 10.6 15.9 16.7 16.7 16.7
 [63,] -1.078959e-05 11.3 10.8  10.8  15.9 16.1  5.4 10.7 16.1 15.9 15.9 15.9
 [64,] -9.072930e-06 11.2 11.5  11.1  15.8 16.9  5.5 10.9 16.9 16.9 16.9 16.9
 [65,] -7.629395e-06 15.9 16.0  10.7  16.0 15.9  5.6 11.0 15.9 16.0 16.0 16.0
 [66,] -6.415531e-06 10.8 10.7  11.0  16.4 16.4  5.7 11.2 16.4 16.4 16.4 16.4
 [67,] -5.394797e-06 10.8 10.8  10.3  17.0 17.0  5.7 11.3 17.0 17.0 17.0 17.0
 [68,] -4.536465e-06 11.2 10.4  10.5  16.8 15.8  5.8 11.5 15.8 15.8 15.8 15.8
 [69,] -3.814697e-06 17.3 17.3  10.4  17.3 17.3  5.9 11.6 17.3 17.3 17.3 17.3
 [70,] -3.207765e-06 10.7 10.7  10.7  15.9 16.8  6.0 11.8 16.8 16.8 16.8 16.8
 [71,] -2.697398e-06 10.8 10.8  10.2  16.8 16.8  6.0 11.9 16.8 16.8 16.8 16.8
 [72,] -2.268233e-06 10.4 10.4  10.2  15.6 15.7  6.1 12.1 15.7 15.7 15.7 15.7
 [73,] -1.907349e-06 16.1 15.8  10.1  16.1 16.1  6.2 12.2 16.1 16.1 16.1 16.1
 [74,] -1.603883e-06 10.3 10.7  10.3  15.6 16.0  6.3 12.4 16.0 16.0 16.0 16.0
 [75,] -1.348699e-06 10.8 10.8  10.5  16.8 16.8  6.3 12.5 16.8 16.8 16.8 16.8
 [76,] -1.134116e-06 10.4 10.4  10.6  15.7 16.0  6.4 12.7 16.0 16.0 16.0 16.0
 [77,] -9.536743e-07 19.1 19.1   9.8  19.1 19.1  6.5 12.8 19.1 19.1 19.1 19.1
 [78,] -8.019413e-07 10.0  9.7  10.2  17.5 15.8  6.6 13.0 15.8 15.8 15.8 15.8
 [79,] -6.743496e-07 10.8 10.8   9.9  16.9 16.9  6.6 13.1 16.9 16.9 16.9 16.9
 [80,] -5.670581e-07 10.4 10.4  11.0  15.7 16.0  6.7 13.3 16.0 16.0 16.0 16.0
 [81,] -4.768372e-07 16.1 15.8   9.5  16.1 16.1  6.8 13.4 16.1 16.1 16.1 16.1
 [82,] -4.009707e-07 10.0  9.7  10.4  16.5 16.5  6.9 13.6 16.5 16.5 16.5 16.5
 [83,] -3.371748e-07 10.8  9.3   9.5  15.7 16.9  6.9 13.7 16.9 16.9 16.9 16.9
 [84,] -2.835291e-07  9.5 10.4   9.5  17.1 17.1  7.0 13.9 17.1 17.1 17.1 17.1
 [85,] -2.384186e-07 20.9 20.9   9.2  20.9 20.9  7.1 14.0 20.9 20.9 20.9 20.9
 [86,] -2.004853e-07  9.3  9.2   9.5  15.7 16.5  7.2 14.2 16.5 16.5 16.5 16.5
 [87,] -1.685874e-07 10.8  9.3   8.8  16.9 16.9  7.3 14.3 16.9 16.9 16.9 16.9
 [88,] -1.417645e-07  9.5  8.9   8.8  16.3 16.3  7.3 14.5 16.3 16.3 16.3 16.3
 [89,] -1.192093e-07 16.1 15.8   8.9  16.1 16.1  7.4 14.6 16.1 16.1 16.1 16.1
 [90,] -1.002427e-07  9.2  9.0   9.3  15.6 16.0  7.5 14.8 16.0 16.0 16.0 16.0
 [91,] -8.429370e-08 10.8  9.3   8.8  16.0 15.9  7.6 14.9 15.9 15.9 15.9 15.9
 [92,] -7.088227e-08  8.9  8.9   8.9  16.0 16.0  7.6 15.1 16.0 16.0 16.0 16.0
 [93,] -5.960464e-08 22.7 22.7   8.6  22.7 22.7  7.7 15.2 22.7 22.7 22.7 22.7
 [94,] -5.012133e-08  8.8  9.0   8.7  15.8 15.8  7.8 15.5 15.8 15.8 15.8 15.8
 [95,] -4.214685e-08  8.6  9.3   8.2  15.8 16.2  7.9 15.8 16.2 16.2 16.2 16.2
 [96,] -3.544113e-08  8.9  8.4   8.1  17.3 15.8  7.9 15.8 17.3 17.3 17.3 17.3
 [97,] -2.980232e-08 16.1 16.1   8.3  16.1 16.1  8.0 16.1 16.1 16.1 16.1 16.1
 [98,] -2.506067e-08  8.5  9.0   8.2  16.3 16.3  8.1 16.3 16.3 16.3 16.3 16.3
 [99,] -2.107342e-08  8.6  9.3   8.2  15.7 16.4  8.2 16.4 16.4 16.4 16.4 16.4
[100,] -1.772057e-08  8.9  8.4   8.7  16.4 16.4  8.2 16.4 16.4 16.4 16.4 16.4
[101,] -1.490116e-08 16.0 16.0   8.0  16.0 16.0  8.3 16.0 16.0 16.0 16.0 16.0
[102,] -1.253033e-08  8.2  9.0   9.7  15.8 15.8  8.4 15.8 15.8 15.8 15.8 15.8
[103,] -1.053671e-08  8.1  9.3   7.6  15.8 16.1  8.5 16.1 16.1 16.1 16.1 16.1
[104,] -8.860283e-09  7.9  7.8   7.7  16.2 16.0  8.5 16.0 16.0 16.0 16.0 16.0
[105,] -7.450581e-09 16.2 15.8   8.6  16.2 16.2  8.6 16.2 16.2 16.2 16.2 16.2
[106,] -6.265167e-09  8.2  9.0   7.7  16.2 16.2  8.7 16.2 16.2 16.2 16.2 16.2
[107,] -5.268356e-09  8.1  9.3   8.8  15.7 16.6  8.8 16.6 16.6 16.6 16.6 16.6
[108,] -4.430142e-09  7.9  7.8   7.7  16.3 16.3  8.8 16.3 16.3 16.3 16.3 16.3
[109,] -3.725290e-09 16.1 15.8   8.9  16.1 16.1  8.9 16.1 16.1 16.1 16.1 16.1
[110,] -3.132583e-09  7.5  9.0   7.2  16.6 15.9  9.0 15.9 15.9 15.9 15.9 15.9
[111,] -2.634178e-09  7.5  9.3   9.1  16.1 15.8  9.1 15.8 15.8 15.8 15.8 15.8
[112,] -2.215071e-09  7.4  7.2   7.0  15.7 15.9  9.1 15.9 15.9 15.9 15.9 15.9
[113,] -1.862645e-09 16.1 15.8   9.2  16.1 16.1  9.2 16.1 16.1 16.1 16.1 16.1
[114,] -1.566292e-09  7.5  9.0   7.0  17.1 17.1  9.3 17.1 17.1 17.1 17.1 17.1
[115,] -1.317089e-09  7.5  9.3   9.4  16.0 15.9  9.4 15.9 15.9 15.9 15.9 15.9
[116,] -1.107535e-09  7.2  7.2   6.6  15.8 17.0  9.4 17.0 17.0 17.0 17.0 17.0
[117,] -9.313226e-10 16.1 15.8   9.5  16.1 16.1  9.5 16.1 16.1 16.1 16.1 16.1
[118,] -7.831458e-10  6.9  9.0   6.6  18.4 15.8  9.6 15.8 15.8 15.8 15.8 15.8
[119,] -6.585445e-10  6.9  9.3   9.7  15.9 16.0  9.7 16.0 16.0 16.0 16.0 16.0
[120,] -5.537677e-10  7.2  7.2   6.4  16.1 16.1  9.7 16.1 16.1 16.1 16.1 16.1
[121,] -4.656613e-10 16.1 15.8   9.8  16.1 16.1  9.8 16.1 16.1 16.1 16.1 16.1
[122,] -3.915729e-10  6.9  6.3   6.4  17.3 17.3  9.9 17.3 17.3 17.3 17.3 17.3
[123,] -3.292723e-10  6.9  9.3  10.0  15.7 16.7 10.0 16.7 16.7 16.7 16.7 16.7
[124,] -2.768839e-10  7.2  6.2   6.6  16.3 16.3 10.0 16.3 16.3 16.3 16.3 16.3
[125,] -2.328306e-10 16.1 15.8  10.1  16.1 16.1 10.1 16.1 16.1 16.1 16.1 16.1
[126,] -1.957865e-10  6.3  6.3   6.0  17.2 15.8 10.2 15.8 15.8 15.8 15.8 15.8
[127,] -1.646361e-10  6.3  9.3  10.3  16.1 15.8 10.3 15.8 15.8 15.8 15.8 15.8
[128,] -1.384419e-10  7.2  6.2   5.8  15.7 16.4 10.3 16.4 16.4 16.4 16.4 16.4
[129,] -1.164153e-10 16.1 15.8  10.4  16.1 16.1 10.4 16.1 16.1 16.1 16.1 16.1
[130,] -9.789323e-11  6.3  6.3   5.8  15.8 17.1 10.5 17.1 17.1 17.1 17.1 17.1
[131,] -8.231806e-11  6.3  5.7  10.6  16.0 15.9 10.6 15.9 15.9 15.9 15.9 15.9
[132,] -6.922096e-11  7.2  5.7   6.0  16.2 16.1 10.6 16.1 16.1 16.1 16.1 16.1
[133,] -5.820766e-11 16.1 15.8  10.7  16.1 16.1 10.7 16.1 16.1 16.1 16.1 16.1
[134,] -4.894661e-11  6.3  6.3   6.0  16.1 16.1 10.8 16.1 16.1 16.1 16.1 16.1
[135,] -4.115903e-11  5.7  5.7  10.9  16.0 16.0 10.9 16.0 16.0 16.0 16.0 16.0
[136,] -3.461048e-11  5.5  5.5   6.0  15.9 15.9 10.9 15.9 15.9 15.9 15.9 15.9
[137,] -2.910383e-11 16.1 15.8  11.0  16.1 16.1 11.0 16.1 16.1 16.1 16.1 16.1
[138,] -2.447331e-11  6.3  5.2   6.0  16.5 16.5 11.1 16.5 16.5 16.5 16.5 16.5
[139,] -2.057952e-11  5.7  5.2  11.2  15.5 16.0 11.2 16.0 16.0 16.0 16.0 16.0
[140,] -1.730524e-11  5.5  5.5   6.0  16.1 16.1 11.2 16.1 16.1 16.1 16.1 16.1
[141,] -1.455192e-11 16.1 15.8  11.3  16.1 16.1 11.3 16.1 16.1 16.1 16.1 16.1
[142,] -1.223665e-11  6.3  5.2   6.0  16.2 16.2 11.4 16.2 16.2 16.2 16.2 16.2
[143,] -1.028976e-11  5.7  5.2  11.5  15.9 16.1 11.5 16.1 16.1 16.1 16.1 16.1
[144,] -8.652621e-12  5.5  5.5   4.6  15.5 15.9 11.5 15.9 15.9 15.9 15.9 15.9
[145,] -7.275958e-12 16.1 15.8  11.6  16.1 16.1 11.6 16.1 16.1 16.1 16.1 16.1
[146,] -6.118327e-12  6.3  5.2   4.6  15.9 15.9 11.7 15.9 15.9 15.9 15.9 15.9
[147,] -5.144879e-12  5.7  5.2  11.8  15.7 16.6 11.8 16.6 16.6 16.6 16.6 16.6
[148,] -4.326310e-12  5.5  5.5   4.2  15.8 17.3 11.8 17.3 17.3 17.3 17.3 17.3
[149,] -3.637979e-12 16.1 15.8  11.9  16.1 16.1 11.9 16.1 16.1 16.1 16.1 16.1
[150,] -3.059163e-12  4.4  4.3   4.7  16.2 16.0 12.0 16.0 16.0 16.0 16.0 16.0
[151,] -2.572439e-12  4.4  4.2  12.1  16.1 15.8 12.1 15.8 15.8 15.8 15.8 15.8
[152,] -2.163155e-12  5.5  4.1   4.0  16.1 16.1 12.1 16.1 16.1 16.1 16.1 16.1
[153,] -1.818989e-12 16.1 15.8  12.2  16.1 16.1 12.2 16.1 16.1 16.1 16.1 16.1
[154,] -1.529582e-12  4.4  4.3   4.0  16.4 16.4 12.3 16.4 16.4 16.4 16.4 16.4
[155,] -1.286220e-12  4.4  4.2  12.4  15.9 15.9 12.4 15.9 15.9 15.9 15.9 15.9
[156,] -1.081578e-12  5.5  4.1   3.6  16.3 16.0 12.4 16.0 16.0 16.0 16.0 16.0
[157,] -9.094947e-13 16.1 15.8  12.5  16.1 16.1 12.5 16.1 16.1 16.1 16.1 16.1
[158,] -7.647908e-13  4.0  3.7   3.6  16.0 16.2 12.6 16.2 16.2 16.2 16.2 16.2
[159,] -6.431099e-13  3.9  3.7  12.7  16.9 16.9 12.7 16.9 16.9 16.9 16.9 16.9
[160,] -5.407888e-13  5.5  3.6   4.0  16.4 16.4 12.7 16.4 16.4 16.4 16.4 16.4
[161,] -4.547474e-13 16.1 15.8  12.8  16.1 16.1 12.8 16.1 16.1 16.1 16.1 16.1
[162,] -3.823954e-13  3.7  3.5   4.0  16.5 16.5 12.9 16.5 16.5 16.5 16.5 16.5
[163,] -3.215549e-13  3.7  3.7  13.0  15.8 15.8 13.0 15.8 15.8 15.8 15.8 15.8
[164,] -2.703944e-13  3.4  3.6   4.0  16.5 16.5 13.0 16.5 16.5 16.5 16.5 16.5
[165,] -2.273737e-13 16.1 15.8  13.1  16.1 16.1 13.1 16.1 16.1 16.1 16.1 16.1
[166,] -1.911977e-13  3.7  3.2   4.0  15.7 16.7 13.2 16.7 16.7 16.7 16.7 16.7
[167,] -1.607775e-13  3.7  3.7  13.3  17.3 17.3 13.3 17.3 17.3 17.3 17.3 17.3
[168,] -1.351972e-13  3.4  3.6   4.0  16.6 16.6 13.3 16.6 16.6 16.6 16.6 16.6
[169,] -1.136868e-13 16.1 15.8  13.4  16.1 16.1 13.4 16.1 16.1 16.1 16.1 16.1
[170,] -9.559885e-14  3.7  3.2   4.0  15.8 15.8 13.5 15.8 15.8 15.8 15.8 15.8
[171,] -8.038873e-14  3.7  2.7  13.6  15.8 15.8 13.6 15.8 15.8 15.8 15.8 15.8
[172,] -6.759860e-14  3.4  2.6   4.0  16.0 16.0 13.6 16.0 16.0 16.0 16.0 16.0
[173,] -5.684342e-14 16.1 15.8  13.7  16.1 16.1 13.7 16.1 16.1 16.1 16.1 16.1
[174,] -4.779943e-14  2.7  3.2   4.0  16.2 16.0 13.8 16.0 16.0 16.0 16.0 16.0
[175,] -4.019437e-14  3.7  2.6  13.9  15.7 17.0 13.9 17.0 17.0 17.0 17.0 17.0
[176,] -3.379930e-14  2.5  2.5   2.2  15.8 16.8 13.9 16.8 16.8 16.8 16.8 16.8
[177,] -2.842171e-14 16.1 15.8  14.0  16.1 16.1 14.0 16.1 16.1 16.1 16.1 16.1
[178,] -2.389971e-14  2.6  2.2   2.2  16.0 16.3 14.1 16.3 16.3 16.3 16.3 16.3
[179,] -2.009718e-14  3.7  2.6  14.2  16.3 16.3 14.2 16.3 16.3 16.3 16.3 16.3
[180,] -1.689965e-14  2.5  2.5   2.2  15.8 15.8 14.2 15.8 15.8 15.8 15.8 15.8
[181,] -1.421085e-14 16.1 15.8  14.3  16.1 16.1 14.3 16.1 16.1 16.1 16.1 16.1
[182,] -1.194986e-14  2.2  2.1   1.8  16.0 16.3 14.4 16.3 16.3 16.3 16.3 16.3
[183,] -1.004859e-14  2.0  1.8  14.5  15.8 16.2 14.5 16.2 16.2 16.2 16.2 16.2
[184,] -8.449825e-15  2.5  1.7   1.6  15.8 16.9 14.5 16.9 16.9 16.9 16.9 16.9
[185,] -7.105427e-15 16.1 15.8  14.6  16.1 16.1 14.6 16.1 16.1 16.1 16.1 16.1
[186,] -5.974928e-15  2.2  1.7   1.6  16.0 16.2 14.7 16.2 16.2 16.2 16.2 16.2
[187,] -5.024296e-15  1.9  1.7  14.7  15.7 15.7 14.8 15.7 15.7 15.7 15.7 15.7
[188,] -4.224912e-15  2.5  1.7   1.2  15.8 15.8 14.8 15.8 15.8 15.8 15.8 15.8
[189,] -3.552714e-15 16.1 15.8  14.9  16.1 16.1 14.9 16.1 16.1 16.1 16.1 16.1
[190,] -2.987464e-15  2.2  1.7   1.2  15.7 16.3 15.0 16.3 16.3 16.3 16.3 16.3
[191,] -2.512148e-15  1.5  1.7  15.0  16.1 15.9 15.1 15.9 15.9 15.9 15.9 15.9
[192,] -2.112456e-15  2.5  1.7   0.9  16.0 16.0 15.1 16.0 16.0 16.0 16.0 16.0
[193,] -1.776357e-15 16.1 15.8  15.2  16.1 16.1 15.2 16.1 16.1 16.1 16.1 16.1
[194,] -1.493732e-15  1.2  1.0   0.9  16.7 16.7 15.3 16.7 16.7 16.7 16.7 16.7
[195,] -1.256074e-15  1.3  1.7  15.3  16.0 16.0 15.5 16.0 16.0 16.0 16.0 16.0
[196,] -1.056228e-15  1.0  1.7   1.2  16.0 16.0 15.4 16.0 16.0 16.0 16.0 16.0
[197,] -8.881784e-16 16.1 16.1  15.5  16.1 16.1 15.5 16.1 16.1 16.1 16.1 16.1
[198,] -7.468660e-16  1.1  1.0   1.2  16.1 16.1 15.6 16.1 16.1 16.1 16.1 16.1
[199,] -6.280370e-16  0.9  0.6  15.5  15.9 15.9 15.9 16.0 16.0 16.0 16.0 16.0
[200,] -5.281140e-16  1.0  1.7   0.4  16.4 15.7 15.7 16.4 16.4 16.4 16.4 16.4
[201,] -4.440892e-16 16.1  0.4  15.8  16.1 15.8 15.8 16.1 16.1 16.1 16.1 16.1
[202,] -3.734330e-16  0.7  1.0   0.4  15.9 15.9 15.9 16.4 16.4 16.4 16.4 16.4
[203,] -3.140185e-16  0.9  0.6  15.6  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[204,] -2.640570e-16  0.5  0.3   0.0  16.3 16.0 16.0 16.0 16.0 16.0 16.0 16.0
[205,] -2.220446e-16 16.1  0.4   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[206,] -1.867165e-16  0.4  1.0   0.4  16.0 16.3 16.3 16.3 16.3 16.3 16.3 16.3
[207,] -1.570092e-16  0.3  0.6   0.0  16.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5
[208,] -1.320285e-16  0.5  0.1  -0.3  15.7 16.2 16.2 16.2 16.2 16.2 16.2 16.2
[209,] -1.110223e-16 16.4 -0.2   0.0  16.4 16.4 16.4 16.4 16.4 16.4 16.4 16.4
[210,] -9.335826e-17  0.4 -0.4  -0.3  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[211,] -7.850462e-17  0.0  0.0  -0.5  16.2 16.2 16.2 16.2 16.2 16.2 16.2 16.2
[212,] -6.601426e-17 -0.3  0.0  -0.7  16.4 16.4 16.4 16.4 16.4 16.4 16.4 16.4
[213,] -5.551115e-17  0.0  0.0   0.0  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[214,] -4.667913e-17  0.0  0.0   0.0  17.2 17.2 17.2 17.2 17.2 17.2 17.2 17.2
[215,] -3.925231e-17  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[216,] -3.300713e-17  0.0  0.0   0.0  16.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5
[217,] -2.775558e-17  0.0  0.0   0.0  17.0 17.0 17.0 17.0 17.0 17.0 17.0 17.0
[218,] -2.333956e-17  0.0  0.0   0.0  18.0 18.0 18.0 18.0 18.0 18.0 18.0 18.0
[219,] -1.962616e-17  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[220,] -1.650356e-17  0.0  0.0   0.0  16.6 16.6 16.6 16.6 16.6 16.6 16.6 16.6
[221,] -1.387779e-17  0.0  0.0   0.0  17.3 17.3 17.3 17.3 17.3 17.3 17.3 17.3
[222,] -1.166978e-17  0.0  0.0   0.0  17.3 17.3 17.3 17.3 17.3 17.3 17.3 17.3
[223,] -9.813078e-18  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[224,] -8.251782e-18  0.0  0.0   0.0  16.6 16.6 16.6 16.6 16.6 16.6 16.6 16.6
[225,] -6.938894e-18  0.0  0.0   0.0  17.6 17.6 17.6 17.6 17.6 17.6 17.6 17.6
[226,] -5.834891e-18  0.0  0.0   0.0  17.2 17.2 17.2 17.2 17.2 17.2 17.2 17.2
[227,] -4.906539e-18  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[228,] -4.125891e-18  0.0  0.0   0.0  16.6 16.6 16.6 16.6 16.6 16.6 16.6 16.6
[229,] -3.469447e-18  0.0  0.0   0.0  17.9 17.9 17.9 17.9 17.9 17.9 17.9 17.9
[230,] -2.917446e-18  0.0  0.0   0.0  17.1 17.1 17.1 17.1 17.1 17.1 17.1 17.1
[231,] -2.453269e-18  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[232,] -2.062946e-18  0.0  0.0   0.0  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[233,] -1.734723e-18  0.0  0.0   0.0  18.2 18.2 18.2 18.2 18.2 18.2 18.2 18.2
[234,]  0.000000e+00  NaN  NaN   NaN   NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN
[235,]  1.734723e-18  0.0  0.0   0.0  18.2 18.2 18.2 18.2 18.2 18.2 18.2 18.2
[236,]  2.062946e-18  0.0  0.0   0.0  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[237,]  2.453269e-18  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[238,]  2.917446e-18  0.0  0.0   0.0  17.0 17.0 17.0 17.0 17.0 17.0 17.0 17.0
[239,]  3.469447e-18  0.0  0.0   0.0  17.9 17.9 17.9 17.9 17.9 17.9 17.9 17.9
[240,]  4.125891e-18  0.0  0.0   0.0  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[241,]  4.906539e-18  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[242,]  5.834891e-18  0.0  0.0   0.0  17.0 17.0 17.0 17.0 17.0 17.0 17.0 17.0
[243,]  6.938894e-18  0.0  0.0   0.0  17.6 17.6 17.6 17.6 17.6 17.6 17.6 17.6
[244,]  8.251782e-18  0.0  0.0   0.0  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[245,]  9.813078e-18  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[246,]  1.166978e-17  0.0  0.0   0.0  16.9 16.9 16.9 16.9 16.9 16.9 16.9 16.9
[247,]  1.387779e-17  0.0  0.0   0.0  17.3 17.3 17.3 17.3 17.3 17.3 17.3 17.3
[248,]  1.650356e-17  0.0  0.0   0.0  16.8 16.8 16.8 16.8 16.8 16.8 16.8 16.8
[249,]  1.962616e-17  0.0  0.0   0.0  16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0
[250,]  2.333956e-17  0.0  0.0   0.0  16.8 16.8 16.8 16.8 16.8 16.8 16.8 16.8
[251,]  2.775558e-17  0.0  0.0   0.0  17.0 17.0 17.0 17.0 17.0 17.0 17.0 17.0
[252,]  3.300713e-17  0.0  0.0   0.0  17.0 17.0 17.0 17.0 17.0 17.0 17.0 17.0
[253,]  3.925231e-17  0.0  0.0   0.0  16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0
[254,]  4.667913e-17  0.0  0.0   0.0  16.6 16.6 16.6 16.6 16.6 16.6 16.6 16.6
[255,]  5.551115e-17  0.0  0.0   0.0  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[256,]  6.601426e-17  0.0  0.0   0.0  18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5
[257,]  7.850462e-17  0.0  0.0   0.0  16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0
[258,]  9.335826e-17  0.0 -0.4   0.0  16.4 16.4 16.4 16.4 16.4 16.4 16.4 16.4
[259,]  1.110223e-16  0.0 -0.2   0.0  16.4 16.4 16.4 16.4 16.4 16.4 16.4 16.4
[260,]  1.320285e-16 -0.3  0.1  -0.3  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[261,]  1.570092e-16  0.0  0.6   0.0  15.5 15.9 15.9 15.9 15.9 15.9 15.9 15.9
[262,]  1.867165e-16  0.4  1.0   0.4  15.6 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[263,]  2.220446e-16 16.1  0.4   0.0  15.8 16.1 16.1 16.4 16.4 16.4 16.4 16.4
[264,]  2.640570e-16  0.5  0.3   0.0  16.0 16.2 16.2 16.0 16.0 16.0 16.0 16.0
[265,]  3.140185e-16  0.3  0.6   0.0  16.5 15.7 15.7 16.5 16.5 16.5 16.5 16.5
[266,]  3.734330e-16  0.4  1.0   0.4  15.9 15.9 15.9 16.6 16.6 16.6 16.6 16.6
[267,]  4.440892e-16 16.4  0.4  15.8  16.4 15.8 15.8 16.4 16.4 16.4 16.4 16.4
[268,]  5.281140e-16  0.5  1.7   0.5  17.6 15.8 15.8 17.6 17.6 17.6 17.6 17.6
[269,]  6.280370e-16  0.9  0.6  16.1  15.8 15.5 15.5 16.1 16.1 16.1 16.1 16.1
[270,]  7.468660e-16  0.7  1.0   0.5  15.7 16.0 15.6 16.0 16.0 16.0 16.0 16.0
[271,]  8.881784e-16 16.4 16.1  15.5  16.4 16.4 15.5 16.4 16.4 16.4 16.4 16.4
[272,]  1.056228e-15  1.0  1.7   1.2  15.9 16.8 15.5 16.8 16.8 16.8 16.8 16.8
[273,]  1.256074e-15  0.9  1.7  15.5  16.2 16.2 15.3 16.2 16.2 16.2 16.2 16.2
[274,]  1.493732e-15  1.1  1.0   1.2  15.9 16.4 15.3 16.4 16.4 16.4 16.4 16.4
[275,]  1.776357e-15 16.4 16.4  15.2  16.4 16.4 15.2 16.4 16.4 16.4 16.4 16.4
[276,]  2.112456e-15  1.0  1.7   1.2  16.0 16.3 15.2 16.3 16.3 16.3 16.3 16.3
[277,]  2.512148e-15  1.3  1.7  15.2  16.5 16.5 15.0 16.5 16.5 16.5 16.5 16.5
[278,]  2.987464e-15  1.2  1.7   1.6  15.4 16.2 15.0 16.2 16.2 16.2 16.2 16.2
[279,]  3.552714e-15 16.4 16.4  14.9  16.4 16.4 14.9 16.4 16.4 16.4 16.4 16.4
[280,]  4.224912e-15  2.5  1.7   1.2  15.5 16.6 14.9 16.6 16.6 16.6 16.6 16.6
[281,]  5.024296e-15  1.5  1.7   1.2  16.8 16.0 14.8 16.0 16.0 16.0 16.0 16.0
[282,]  5.974928e-15  2.2  1.7   1.6  16.4 16.4 14.7 16.4 16.4 16.4 16.4 16.4
[283,]  7.105427e-15 16.4 16.4  14.6  16.4 16.4 14.6 16.4 16.4 16.4 16.4 16.4
[284,]  8.449825e-15  2.5  1.7   1.6  15.9 16.5 14.6 16.5 16.5 16.5 16.5 16.5
[285,]  1.004859e-14  1.9  1.8  14.5  15.7 16.0 14.5 16.0 16.0 16.0 16.0 16.0
[286,]  1.194986e-14  2.2  2.1   1.8  16.2 16.2 14.4 16.2 16.2 16.2 16.2 16.2
[287,]  1.421085e-14 16.4 16.4  14.3  16.4 16.4 14.3 16.4 16.4 16.4 16.4 16.4
[288,]  1.689965e-14  2.5  2.5   2.2  15.9 16.4 14.3 16.4 16.4 16.4 16.4 16.4
[289,]  2.009718e-14  2.0  2.6   1.8  16.9 15.9 14.2 15.9 15.9 15.9 15.9 15.9
[290,]  2.389971e-14  2.2  2.2   2.3  15.7 16.5 14.1 16.5 16.5 16.5 16.5 16.5
[291,]  2.842171e-14 16.4 16.4  14.0  16.4 16.4 14.0 16.4 16.4 16.4 16.4 16.4
[292,]  3.379930e-14  2.5  2.5   2.2  15.7 16.0 13.9 16.0 16.0 16.0 16.0 16.0
[293,]  4.019437e-14  3.7  2.6  13.9  15.8 16.3 13.9 16.3 16.3 16.3 16.3 16.3
[294,]  4.779943e-14  2.6  3.2   4.0  15.6 16.1 13.8 16.1 16.1 16.1 16.1 16.1
[295,]  5.684342e-14 16.4 16.4  13.7  16.4 16.4 13.7 16.4 16.4 16.4 16.4 16.4
[296,]  6.759860e-14  2.5  2.6   4.0  16.0 16.0 13.6 16.0 16.0 16.0 16.0 16.0
[297,]  8.038873e-14  3.7  2.7  13.6  16.0 15.9 13.6 15.9 15.9 15.9 15.9 15.9
[298,]  9.559885e-14  2.7  3.2   2.6  15.8 17.6 13.5 17.6 17.6 17.6 17.6 17.6
[299,]  1.136868e-13 16.4 16.4  13.4  16.4 16.4 13.4 16.4 16.4 16.4 16.4 16.4
[300,]  1.351972e-13  3.4  3.6   4.0  15.9 16.8 13.3 16.8 16.8 16.8 16.8 16.8
[301,]  1.607775e-13  3.7  3.7  13.3  16.3 16.3 13.3 16.3 16.3 16.3 16.3 16.3
[302,]  1.911977e-13  3.7  3.2   4.0  17.4 17.4 13.2 17.4 17.4 17.4 17.4 17.4
[303,]  2.273737e-13 16.4 16.4  13.1  16.4 16.4 13.1 16.4 16.4 16.4 16.4 16.4
[304,]  2.703944e-13  3.4  3.6   4.0  15.8 16.9 13.0 16.9 16.9 16.9 16.9 16.9
[305,]  3.215549e-13  3.7  3.7  13.0  16.1 15.9 13.0 15.9 15.9 15.9 15.9 15.9
[306,]  3.823954e-13  3.7  3.5   4.0  16.8 16.8 12.9 16.8 16.8 16.8 16.8 16.8
[307,]  4.547474e-13 16.4 16.4  12.8  16.4 16.4 12.8 16.4 16.4 16.4 16.4 16.4
[308,]  5.407888e-13  3.4  3.6   4.0  17.3 17.3 12.7 17.3 17.3 17.3 17.3 17.3
[309,]  6.431099e-13  3.7  3.7  12.7  16.1 16.1 12.7 16.1 16.1 16.1 16.1 16.1
[310,]  7.647908e-13  3.7  3.7   4.0  15.9 16.4 12.6 16.4 16.4 16.4 16.4 16.4
[311,]  9.094947e-13 16.4 16.4  12.5  16.4 16.4 12.5 16.4 16.4 16.4 16.4 16.4
[312,]  1.081578e-12  5.5  4.1   3.6  15.8 17.0 12.4 17.0 17.0 17.0 17.0 17.0
[313,]  1.286220e-12  3.9  4.2   3.6  16.2 16.2 12.4 16.2 16.2 16.2 16.2 16.2
[314,]  1.529582e-12  4.0  4.3   4.2  16.0 16.2 12.3 16.2 16.2 16.2 16.2 16.2
[315,]  1.818989e-12 16.4 16.4  12.2  16.4 16.4 12.2 16.4 16.4 16.4 16.4 16.4
[316,]  2.163155e-12  5.5  4.1   4.0  15.9 15.9 12.1 15.9 15.9 15.9 15.9 15.9
[317,]  2.572439e-12  4.4  4.2  12.1  15.6 15.9 12.1 15.9 15.9 15.9 15.9 15.9
[318,]  3.059163e-12  4.4  4.3   4.7  16.0 16.3 12.0 16.3 16.3 16.3 16.3 16.3
[319,]  3.637979e-12 16.4 16.4  11.9  16.4 16.4 11.9 16.4 16.4 16.4 16.4 16.4
[320,]  4.326310e-12  5.5  5.5   4.2  16.0 16.3 11.8 16.3 16.3 16.3 16.3 16.3
[321,]  5.144879e-12  4.4  5.2   4.2  16.6 16.1 11.8 16.1 16.1 16.1 16.1 16.1
[322,]  6.118327e-12  4.4  5.2   4.7  16.0 16.0 11.7 16.0 16.0 16.0 16.0 16.0
[323,]  7.275958e-12 16.4 16.4  11.6  16.4 16.4 11.6 16.4 16.4 16.4 16.4 16.4
[324,]  8.652621e-12  5.5  5.5   4.6  16.1 16.1 11.5 16.1 16.1 16.1 16.1 16.1
[325,]  1.028976e-11  5.7  5.2  11.5  15.9 16.1 11.5 16.1 16.1 16.1 16.1 16.1
[326,]  1.223665e-11  6.3  5.2   6.0  16.3 16.0 11.4 16.0 16.0 16.0 16.0 16.0
[327,]  1.455192e-11 16.4 16.4  11.3  16.4 16.4 11.3 16.4 16.4 16.4 16.4 16.4
[328,]  1.730524e-11  5.5  5.5   6.0  16.5 16.5 11.2 16.5 16.5 16.5 16.5 16.5
[329,]  2.057952e-11  5.7  5.2  11.2  15.8 16.1 11.2 16.1 16.1 16.1 16.1 16.1
[330,]  2.447331e-11  6.3  5.2   6.0  16.3 16.3 11.1 16.3 16.3 16.3 16.3 16.3
[331,]  2.910383e-11 16.4 16.4  11.0  16.4 16.4 11.0 16.4 16.4 16.4 16.4 16.4
[332,]  3.461048e-11  5.5  5.5   6.0  16.1 16.1 10.9 16.1 16.1 16.1 16.1 16.1
[333,]  4.115903e-11  5.7  5.7  10.9  16.4 16.2 10.9 16.2 16.2 16.2 16.2 16.2
[334,]  4.894661e-11  6.3  6.3   6.0  16.2 16.1 10.8 16.1 16.1 16.1 16.1 16.1
[335,]  5.820766e-11 16.4 16.4  10.7  16.4 16.4 10.7 16.4 16.4 16.4 16.4 16.4
[336,]  6.922096e-11  5.5  5.7   6.0  16.6 16.6 10.6 16.6 16.6 16.6 16.6 16.6
[337,]  8.231806e-11  5.7  5.7   5.4  16.3 16.3 10.6 16.3 16.3 16.3 16.3 16.3
[338,]  9.789323e-11  6.3  6.3   5.8  17.0 17.0 10.5 17.0 17.0 17.0 17.0 17.0
[339,]  1.164153e-10 16.4 16.4  10.4  16.4 16.4 10.4 16.4 16.4 16.4 16.4 16.4
[340,]  1.384419e-10  7.2  6.2   5.8  16.1 16.1 10.3 16.1 16.1 16.1 16.1 16.1
[341,]  1.646361e-10  6.3  9.3  10.3  15.6 15.9 10.3 15.9 15.9 15.9 15.9 15.9
[342,]  1.957865e-10  6.3  6.3   6.0  17.0 17.0 10.2 17.0 17.0 17.0 17.0 17.0
[343,]  2.328306e-10 16.4 16.4  10.1  16.4 16.4 10.1 16.4 16.4 16.4 16.4 16.4
[344,]  2.768839e-10  7.2  6.2   6.6  15.8 17.0 10.0 17.0 17.0 17.0 17.0 17.0
[345,]  3.292723e-10  6.3  9.3   6.0  16.5 16.1 10.0 16.1 16.1 16.1 16.1 16.1
[346,]  3.915729e-10  6.3  6.3   6.4  16.9 16.9  9.9 16.9 16.9 16.9 16.9 16.9
[347,]  4.656613e-10 16.4 16.4   9.8  16.4 16.4  9.8 16.4 16.4 16.4 16.4 16.4
[348,]  5.537677e-10  7.2  7.2   6.4  16.4 16.4  9.7 16.4 16.4 16.4 16.4 16.4
[349,]  6.585445e-10  6.9  9.3   9.7  15.8 16.2  9.7 16.2 16.2 16.2 16.2 16.2
[350,]  7.831458e-10  6.9  9.0   6.6  16.8 16.8  9.6 16.8 16.8 16.8 16.8 16.8
[351,]  9.313226e-10 16.4 16.4   9.5  16.4 16.4  9.5 16.4 16.4 16.4 16.4 16.4
[352,]  1.107535e-09  7.2  7.2   6.6  16.0 16.3  9.4 16.3 16.3 16.3 16.3 16.3
[353,]  1.317089e-09  6.9  9.3   6.6  16.3 16.3  9.4 16.3 16.3 16.3 16.3 16.3
[354,]  1.566292e-09  6.9  9.0   7.0  15.5 16.6  9.3 16.6 16.6 16.6 16.6 16.6
[355,]  1.862645e-09 16.4 16.4   9.2  16.4 16.4  9.2 16.4 16.4 16.4 16.4 16.4
[356,]  2.215071e-09  7.2  7.2   7.0  15.4 16.1  9.1 16.1 16.1 16.1 16.1 16.1
[357,]  2.634178e-09  7.5  9.3   9.1  15.6 15.9  9.1 15.9 15.9 15.9 15.9 15.9
[358,]  3.132583e-09  7.5  9.0   7.2  15.7 16.4  9.0 16.4 16.4 16.4 16.4 16.4
[359,]  3.725290e-09 16.4 16.4   8.9  16.4 16.4  8.9 16.4 16.4 16.4 16.4 16.4
[360,]  4.430142e-09  7.4  7.8   7.2  15.8 17.2  8.8 17.2 17.2 17.2 17.2 17.2
[361,]  5.268356e-09  7.5  9.3   7.2  16.4 16.1  8.8 16.1 16.1 16.1 16.1 16.1
[362,]  6.265167e-09  7.5  9.0   7.6  15.6 16.2  8.7 16.2 16.2 16.2 16.2 16.2
[363,]  7.450581e-09 16.6 16.6   8.6  16.6 16.6  8.6 16.6 16.6 16.6 16.6 16.6
[364,]  8.860283e-09  7.9  7.8   7.8  15.7 16.6  8.5 16.6 16.6 16.6 16.6 16.6
[365,]  1.053671e-08  8.1  9.3   8.5  15.6 16.3  8.5 16.3 16.3 16.3 16.3 16.3
[366,]  1.253033e-08  8.2  9.0   8.1  15.9 16.4  8.4 16.4 16.4 16.4 16.4 16.4
[367,]  1.490116e-08 16.1 16.1   8.3  15.8 16.1  8.3 16.1 16.4 16.4 16.4 16.4
[368,]  1.772057e-08  7.9  8.4   8.0  16.3 16.0  8.2 16.0 16.3 16.3 16.3 16.3
[369,]  2.107342e-08  8.1  9.3   8.2  16.0 16.8  8.2 16.8 16.0 16.0 16.0 16.0
[370,]  2.506067e-08  8.2  9.0   8.1  16.9 15.8  8.1 15.8 16.9 16.9 16.9 16.9
[371,]  2.980232e-08 23.6 16.0   8.0  23.6 16.0  8.0 16.0 23.6 23.6 23.6 23.6
[372,]  3.544113e-08  8.9  8.4   8.3  15.8 15.8  7.9 15.8 15.8 15.8 15.8 15.8
[373,]  4.214685e-08  8.6  9.3   9.1  15.5 16.2  7.9 15.8 16.2 16.2 16.2 16.2
[374,]  5.012133e-08  8.5  9.0   8.3  16.5 15.9  7.8 15.5 15.9 15.9 15.9 15.9
[375,]  5.960464e-08 16.4 16.4   8.3  16.4 16.4  7.7 15.2 16.4 16.4 16.4 16.4
[376,]  7.088227e-08  8.9  8.9   8.9  15.7 16.3  7.6 15.1 16.3 16.3 16.3 16.3
[377,]  8.429370e-08  8.6  9.3   8.8  16.0 15.9  7.6 15.0 15.9 15.9 15.9 15.9
[378,]  1.002427e-07  8.8  9.0   8.7  16.5 16.5  7.5 14.8 16.5 16.5 16.5 16.5
[379,]  1.192093e-07 21.8 21.8   8.6  21.8 21.8  7.4 14.6 21.8 21.8 21.8 21.8
[380,]  1.417645e-07  8.9  8.9   8.8  15.7 16.4  7.3 14.5 16.4 16.4 16.4 16.4
[381,]  1.685874e-07 10.8  9.3   8.8  15.5 15.9  7.3 14.3 15.9 15.9 15.9 15.9
[382,]  2.004853e-07  9.2  9.2   9.5  15.3 17.5  7.2 14.2 17.5 17.5 17.5 17.5
[383,]  2.384186e-07 16.4 16.4   8.9  16.4 16.4  7.1 14.0 16.4 16.4 16.4 16.4
[384,]  2.835291e-07  9.5 10.4   9.0  15.8 18.6  7.0 13.9 18.6 18.6 18.6 18.6
[385,]  3.371748e-07 10.8  9.3   9.5  16.0 15.9  6.9 13.7 15.9 15.9 15.9 15.9
[386,]  4.009707e-07  9.3  9.7   9.2  15.6 16.2  6.9 13.6 16.2 16.2 16.2 16.2
[387,]  4.768372e-07 20.0 20.0   9.2  20.0 20.0  6.8 13.4 20.0 20.0 20.0 20.0
[388,]  5.670581e-07  9.5 10.4  10.6  16.1 16.1  6.7 13.3 16.1 16.1 16.1 16.1
[389,]  6.743496e-07 10.8 10.8   9.9  16.0 15.9  6.6 13.1 15.9 15.9 15.9 15.9
[390,]  8.019413e-07 10.0  9.7   9.6  16.4 15.9  6.6 13.0 15.9 15.9 15.9 15.9
[391,]  9.536743e-07 16.4 16.4   9.5  16.4 16.4  6.5 12.8 16.4 16.4 16.4 16.4
[392,]  1.134116e-06 10.4 10.4  10.4  16.2 16.0  6.4 12.7 16.0 16.0 16.0 16.0
[393,]  1.348699e-06 10.8 10.8  10.5  17.1 15.9  6.3 12.5 15.9 15.9 15.9 15.9
[394,]  1.603883e-06 10.0 10.7  10.2  16.7 16.7  6.3 12.4 16.7 16.7 16.7 16.7
[395,]  1.907349e-06 18.2 18.2   9.8  18.2 18.2  6.2 12.2 18.2 18.2 18.2 18.2
[396,]  2.268233e-06 10.4 10.4  10.0  16.3 16.3  6.1 12.1 16.3 16.3 16.3 16.3
[397,]  2.697398e-06 10.8 10.8  10.3  15.9 15.9  6.0 11.9 15.9 15.9 15.9 15.9
[398,]  3.207765e-06 10.3 10.7  10.3  15.9 16.8  6.0 11.8 16.8 16.8 16.8 16.8
[399,]  3.814697e-06 16.4 16.4  10.1  16.4 16.4  5.9 11.6 16.4 16.4 16.4 16.4
[400,]  4.536465e-06 10.4 10.4  10.0  15.5 16.6  5.8 11.5 16.6 16.6 16.6 16.6
[401,]  5.394797e-06 10.8 10.8  10.3  15.6 15.9  5.7 11.3 15.9 15.9 15.9 15.9
[402,]  6.415531e-06 10.7 10.7  10.9  15.6 16.1  5.7 11.2 16.1 16.1 16.1 16.1
[403,]  7.629395e-06 16.4 16.4  10.5  16.4 16.4  5.6 11.0 16.4 16.4 16.4 16.4
[404,]  9.072930e-06 11.2 11.5  10.7  15.5 16.7  5.5 10.9 16.7 16.7 16.7 16.7
[405,]  1.078959e-05 10.8 10.8  10.5  17.6 15.7  5.4 10.7 15.7 16.0 16.0 16.0
[406,]  1.283106e-05 10.8 11.2  10.7  16.0 16.0  5.4 10.6 16.0 16.0 16.0 16.0
[407,]  1.525879e-05 16.2 15.6  11.0  16.2 16.3  5.3 10.4 15.4 16.3 16.3 16.3
[408,]  1.814586e-05 11.2 11.5  11.2  16.0 16.2  5.2 10.3 15.2 16.2 16.2 16.2
[409,]  2.157919e-05 11.3 12.2  11.7  16.1 16.1  5.1 10.1 15.0 16.1 16.1 16.1
[410,]  2.566212e-05 11.5 11.2  11.9  17.2 17.2  5.1 10.0 14.8 17.2 17.2 17.2
[411,]  3.051758e-05 16.4 16.4  14.5  16.2 16.4  5.0  9.8 14.5 16.4 16.4 16.4
[412,]  3.629172e-05 11.3 11.5  11.8  16.1 16.1  4.9  9.7 14.3 16.1 16.1 16.1
[413,]  4.315837e-05 11.3 12.2  11.2  16.3 16.3  4.8  9.5 14.1 16.3 16.3 16.3
[414,]  5.132424e-05 11.5 12.3  11.2  15.8 16.7  4.8  9.4 13.9 16.7 16.7 16.7
[415,]  6.103516e-05 16.9 16.9  11.6  16.9 16.9  4.7  9.2 13.6 16.9 16.9 16.9
[416,]  7.258344e-05 12.1 11.7  11.6  15.7 16.6  4.6  9.1 13.4 16.6 16.6 16.6
[417,]  8.631675e-05 12.5 12.2  12.3  16.1 16.5  4.5  8.9 13.2 16.5 16.5 16.5
[418,]  1.026485e-04 11.9 12.3  12.5  16.1 16.2  4.5  8.8 13.0 16.2 16.2 16.2
[419,]  1.220703e-04 16.5 16.5  12.7  16.5 16.5  4.4  8.6 12.7 16.5 16.5 16.5
[420,]  1.451669e-04 12.1 12.4  12.2  17.0 17.0  4.3  8.5 12.5 17.0 17.0 17.0
[421,]  1.726335e-04 12.5 12.2  12.0  16.3 16.2  4.2  8.3 12.3 16.2 16.2 16.2
[422,]  2.052970e-04 12.1 12.3  12.7  15.8 15.8  4.2  8.2 12.1 15.8 17.6 17.6
[423,]  2.441406e-04 16.4 15.8  12.6  16.4 16.4  4.1  8.0 11.8 15.5 16.4 16.4
[424,]  2.903338e-04 12.2 12.4  13.0  15.8 16.8  4.0  7.9 11.6 15.3 16.8 16.8
[425,]  3.452670e-04 12.5 12.5  12.2  15.7 15.9  3.9  7.7 11.4 15.1 15.9 15.9
[426,]  4.105940e-04 12.6 12.4  13.0  15.6 16.1  3.9  7.6 11.2 14.7 16.1 16.1
[427,]  4.882812e-04 16.2 16.2  12.7  16.2 16.3  3.8  7.4 10.9 14.4 16.3 16.3
[428,]  5.806675e-04 13.1 12.6  12.6  15.6 16.1  3.7  7.3 10.7 14.1 16.1 16.1
[429,]  6.905340e-04 12.5 12.8  12.2  16.4 16.4  3.6  7.1 10.5 13.8 16.4 16.4
[430,]  8.211879e-04 12.6 13.5  12.3  15.7 16.7  3.6  6.9 10.3 13.5 16.7 16.7
[431,]  9.765625e-04 16.4 16.4  16.4  16.4 16.4  3.5  6.8 10.0 13.2 16.4 16.4
[432,]  1.161335e-03 13.1 13.2  12.8  16.3 16.0  3.4  6.6  9.8 12.9 16.0 16.3
[433,]  1.381068e-03 13.8 13.1  13.6  15.8 16.1  3.3  6.5  9.6 12.6 15.5 16.1
[434,]  1.642376e-03 13.7 13.5  13.1  15.7 16.0  3.3  6.3  9.4 12.3 15.2 16.0
[435,]  1.953125e-03 16.2 16.3  13.0  16.2 16.3  3.2  6.2  9.1 12.0 14.9 16.3
[436,]  2.322670e-03 13.1 13.2  12.8  15.4 16.1  3.1  6.0  8.9 11.7 14.5 16.1
[437,]  2.762136e-03 13.8 13.3  13.3  16.0 15.9  3.0  5.9  8.7 11.4 14.1 15.9
[438,]  3.284752e-03 13.7 13.5  13.5  15.7 16.3  3.0  5.7  8.5 11.1 13.7 16.3
[439,]  3.906250e-03 16.1 16.4  14.6  16.1 16.1  2.9  5.6  8.2 10.8 13.4 16.1
[440,]  4.645340e-03 14.1 13.9  14.2  16.3 16.3  2.8  5.4  8.0 10.5 13.0 15.4
[441,]  5.524272e-03 13.8 13.8  13.5  15.7 16.4  2.7  5.3  7.8 10.2 12.6 15.0
[442,]  6.569503e-03 13.7 13.7  13.8  15.4 16.0  2.7  5.1  7.5  9.9 12.2 14.6
[443,]  7.812500e-03 16.7 16.7  14.8  16.7 16.0  2.6  5.0  7.3  9.6 11.9 14.1
[444,]  9.290681e-03 14.1 14.0  14.0  15.5 15.9  2.5  4.8  7.1  9.3 11.5 13.6
[445,]  1.104854e-02 13.8 13.8  13.7  15.8 16.2  2.4  4.7  6.9  9.0 11.1 13.2
[446,]  1.313901e-02 13.9 14.3  15.6  16.1 16.1  2.4  4.5  6.6  8.7 10.7 12.7
[447,]  1.562500e-02 16.3 15.8  14.0  16.2 16.3  2.3  4.4  6.4  8.4 10.4 12.3
[448,]  1.858136e-02 14.1 14.1  15.1  16.3 15.9  2.2  4.2  6.2  8.1 10.0 11.8
[449,]  2.209709e-02 14.4 15.6  15.0  16.2 16.2  2.1  4.1  6.0  7.8  9.6 11.4
[450,]  2.627801e-02 14.3 14.3  14.0  15.9 15.9  2.1  3.9  5.7  7.5  9.2 10.9
[451,]  3.125000e-02 15.9 16.0  14.7  16.0 16.8  2.0  3.8  5.5  7.2  8.9 10.5
[452,]  3.716272e-02 14.4 14.8  14.8  15.7 15.9  1.9  3.6  5.3  6.9  8.5 10.0
[453,]  4.419417e-02 14.4 17.1  14.4  17.1 16.0  1.8  3.5  5.1  6.6  8.1  9.6
[454,]  5.255603e-02 14.5 14.8  15.6  16.0 16.0  1.8  3.3  4.8  6.3  7.7  9.1
[455,]  6.250000e-02 15.9 16.0  14.5  16.0 17.2  1.7  3.2  4.6  6.0  7.4  8.7
[456,]  7.432544e-02 14.8 14.8  14.8  15.9 15.9  1.6  3.0  4.4  5.7  7.0  8.2
[457,]  8.838835e-02 15.0 16.3  15.2  15.8 15.8  1.5  2.9  4.2  5.4  6.6  7.8
[458,]  1.051121e-01 15.3 14.7  14.5  15.8 15.8  1.5  2.7  3.9  5.1  6.2  7.3
[459,]  1.250000e-01 16.3 15.5  14.9  16.2 16.2  1.4  2.6  3.7  4.8  5.9  6.9
[460,]  1.486509e-01 15.1 15.2  15.4  16.3 16.3  1.3  2.5  3.5  4.5  5.5  6.4
[461,]  1.767767e-01 15.0 16.3  15.4  15.8 15.8  1.2  2.3  3.3  4.2  5.1  6.0
[462,]  2.102241e-01 15.2 16.5  15.2  15.5 15.5  1.2  2.2  3.1  3.9  4.7  5.5
[463,]  2.500000e-01 14.7 14.6  16.1  15.8 15.8  1.1  2.0  2.8  3.6  4.4  5.1
[464,]  2.973018e-01 14.8 14.8  15.0  15.9 15.9  1.0  1.9  2.6  3.3  4.0  4.7
[465,]  3.535534e-01 14.7 15.4  16.3  16.3 16.3  1.0  1.7  2.4  3.0  3.6  4.2
[466,]  4.204482e-01 15.1 15.7  15.3  17.0 17.0  0.9  1.6  2.2  2.7  3.3  3.8
[467,]  5.000000e-01 15.0 15.2  16.4  16.4 16.4  0.8  1.4  2.0  2.4  2.9  3.3
        k=7  k=8  k=9 k=10 k=11 k=12
  [1,]  3.5  3.9  4.3  4.7  5.0  5.4
  [2,]  4.1  4.6  5.0  5.5  5.9  6.3
  [3,]  4.6  5.2  5.7  6.2  6.8  7.3
  [4,]  5.2  5.8  6.4  7.0  7.6  8.2
  [5,]  5.7  6.4  7.1  7.8  8.4  9.1
  [6,]  6.2  7.0  7.8  8.5  9.3 10.0
  [7,]  6.8  7.6  8.5  9.3 10.1 10.9
  [8,]  7.3  8.2  9.2 10.1 11.0 11.9
  [9,]  7.9  8.8  9.8 10.8 11.8 12.8
 [10,]  8.4  9.5 10.5 11.6 12.6 13.7
 [11,]  8.9 10.1 11.2 12.3 13.5 14.6
 [12,]  9.4 10.7 11.9 13.1 14.3 15.3
 [13,] 10.0 11.3 12.6 13.8 15.2 17.6
 [14,] 10.5 11.9 13.2 14.6 16.3 16.0
 [15,] 11.0 12.5 13.9 15.3 16.5 15.7
 [16,] 11.6 13.1 14.6 15.7 16.1 16.1
 [17,] 12.1 13.7 15.2 16.5 16.5 16.5
 [18,] 12.6 14.3 17.1 17.1 17.1 17.1
 [19,] 13.1 14.9 15.8 15.8 15.8 15.8
 [20,] 13.7 15.5 16.6 16.6 16.6 16.6
 [21,] 14.2 15.9 16.1 16.1 16.1 16.1
 [22,] 14.7 15.8 15.8 15.8 15.8 15.8
 [23,] 15.4 16.7 16.7 16.7 16.7 16.7
 [24,] 15.9 15.9 15.9 15.9 15.9 15.9
 [25,] 15.9 16.0 16.0 16.0 16.0 16.0
 [26,] 16.0 16.0 16.0 16.0 16.0 16.0
 [27,] 15.8 15.8 15.8 15.8 15.8 15.8
 [28,] 16.2 16.2 16.2 16.2 16.2 16.2
 [29,] 16.2 16.2 16.2 16.2 16.2 16.2
 [30,] 15.9 15.9 15.9 15.9 15.9 15.9
 [31,] 16.1 16.1 16.1 16.1 16.1 16.1
 [32,] 16.4 16.4 16.4 16.4 16.4 16.4
 [33,] 16.2 16.2 16.2 16.2 16.2 16.2
 [34,] 16.0 16.0 16.0 16.0 16.0 16.0
 [35,] 15.8 15.8 15.8 15.8 15.8 15.8
 [36,] 16.0 16.0 16.0 16.0 16.0 16.0
 [37,] 16.1 16.1 16.1 16.1 16.1 16.1
 [38,] 16.4 16.4 16.4 16.4 16.4 16.4
 [39,] 16.6 16.6 16.6 16.6 16.6 16.6
 [40,] 15.8 15.8 15.8 15.8 15.8 15.8
 [41,] 16.3 16.3 16.3 16.3 16.3 16.3
 [42,] 16.6 16.6 16.6 16.6 16.6 16.6
 [43,] 16.0 16.0 16.0 16.0 16.0 16.0
 [44,] 16.9 16.9 16.9 16.9 16.9 16.9
 [45,] 16.1 16.1 16.1 16.1 16.1 16.1
 [46,] 15.9 15.9 15.9 15.9 15.9 15.9
 [47,] 15.8 15.8 15.8 15.8 15.8 15.8
 [48,] 16.4 16.4 16.4 16.4 16.4 16.4
 [49,] 16.1 16.1 16.1 16.1 16.1 16.1
 [50,] 16.4 16.4 16.4 16.4 16.4 16.4
 [51,] 16.0 16.0 16.0 16.0 16.0 16.0
 [52,] 15.9 15.9 15.9 15.9 15.9 15.9
 [53,] 16.0 16.0 16.0 16.0 16.0 16.0
 [54,] 16.3 16.3 16.3 16.3 16.3 16.3
 [55,] 16.1 16.1 16.1 16.1 16.1 16.1
 [56,] 16.1 16.1 16.1 16.1 16.1 16.1
 [57,] 16.5 16.5 16.5 16.5 16.5 16.5
 [58,] 16.5 16.5 16.5 16.5 16.5 16.5
 [59,] 15.8 15.8 15.8 15.8 15.8 15.8
 [60,] 16.1 16.1 16.1 16.1 16.1 16.1
 [61,] 16.1 16.1 16.1 16.1 16.1 16.1
 [62,] 16.7 16.7 16.7 16.7 16.7 16.7
 [63,] 15.9 15.9 15.9 15.9 15.9 15.9
 [64,] 16.9 16.9 16.9 16.9 16.9 16.9
 [65,] 16.0 16.0 16.0 16.0 16.0 16.0
 [66,] 16.4 16.4 16.4 16.4 16.4 16.4
 [67,] 17.0 17.0 17.0 17.0 17.0 17.0
 [68,] 15.8 15.8 15.8 15.8 15.8 15.8
 [69,] 17.3 17.3 17.3 17.3 17.3 17.3
 [70,] 16.8 16.8 16.8 16.8 16.8 16.8
 [71,] 16.8 16.8 16.8 16.8 16.8 16.8
 [72,] 15.7 15.7 15.7 15.7 15.7 15.7
 [73,] 16.1 16.1 16.1 16.1 16.1 16.1
 [74,] 16.0 16.0 16.0 16.0 16.0 16.0
 [75,] 16.8 16.8 16.8 16.8 16.8 16.8
 [76,] 16.0 16.0 16.0 16.0 16.0 16.0
 [77,] 19.1 19.1 19.1 19.1 19.1 19.1
 [78,] 15.8 15.8 15.8 15.8 15.8 15.8
 [79,] 16.9 16.9 16.9 16.9 16.9 16.9
 [80,] 16.0 16.0 16.0 16.0 16.0 16.0
 [81,] 16.1 16.1 16.1 16.1 16.1 16.1
 [82,] 16.5 16.5 16.5 16.5 16.5 16.5
 [83,] 16.9 16.9 16.9 16.9 16.9 16.9
 [84,] 17.1 17.1 17.1 17.1 17.1 17.1
 [85,] 20.9 20.9 20.9 20.9 20.9 20.9
 [86,] 16.5 16.5 16.5 16.5 16.5 16.5
 [87,] 16.9 16.9 16.9 16.9 16.9 16.9
 [88,] 16.3 16.3 16.3 16.3 16.3 16.3
 [89,] 16.1 16.1 16.1 16.1 16.1 16.1
 [90,] 16.0 16.0 16.0 16.0 16.0 16.0
 [91,] 15.9 15.9 15.9 15.9 15.9 15.9
 [92,] 16.0 16.0 16.0 16.0 16.0 16.0
 [93,] 22.7 22.7 22.7 22.7 22.7 22.7
 [94,] 15.8 15.8 15.8 15.8 15.8 15.8
 [95,] 16.2 16.2 16.2 16.2 16.2 16.2
 [96,] 17.3 17.3 17.3 17.3 17.3 17.3
 [97,] 16.1 16.1 16.1 16.1 16.1 16.1
 [98,] 16.3 16.3 16.3 16.3 16.3 16.3
 [99,] 16.4 16.4 16.4 16.4 16.4 16.4
[100,] 16.4 16.4 16.4 16.4 16.4 16.4
[101,] 16.0 16.0 16.0 16.0 16.0 16.0
[102,] 15.8 15.8 15.8 15.8 15.8 15.8
[103,] 16.1 16.1 16.1 16.1 16.1 16.1
[104,] 16.0 16.0 16.0 16.0 16.0 16.0
[105,] 16.2 16.2 16.2 16.2 16.2 16.2
[106,] 16.2 16.2 16.2 16.2 16.2 16.2
[107,] 16.6 16.6 16.6 16.6 16.6 16.6
[108,] 16.3 16.3 16.3 16.3 16.3 16.3
[109,] 16.1 16.1 16.1 16.1 16.1 16.1
[110,] 15.9 15.9 15.9 15.9 15.9 15.9
[111,] 15.8 15.8 15.8 15.8 15.8 15.8
[112,] 15.9 15.9 15.9 15.9 15.9 15.9
[113,] 16.1 16.1 16.1 16.1 16.1 16.1
[114,] 17.1 17.1 17.1 17.1 17.1 17.1
[115,] 15.9 15.9 15.9 15.9 15.9 15.9
[116,] 17.0 17.0 17.0 17.0 17.0 17.0
[117,] 16.1 16.1 16.1 16.1 16.1 16.1
[118,] 15.8 15.8 15.8 15.8 15.8 15.8
[119,] 16.0 16.0 16.0 16.0 16.0 16.0
[120,] 16.1 16.1 16.1 16.1 16.1 16.1
[121,] 16.1 16.1 16.1 16.1 16.1 16.1
[122,] 17.3 17.3 17.3 17.3 17.3 17.3
[123,] 16.7 16.7 16.7 16.7 16.7 16.7
[124,] 16.3 16.3 16.3 16.3 16.3 16.3
[125,] 16.1 16.1 16.1 16.1 16.1 16.1
[126,] 15.8 15.8 15.8 15.8 15.8 15.8
[127,] 15.8 15.8 15.8 15.8 15.8 15.8
[128,] 16.4 16.4 16.4 16.4 16.4 16.4
[129,] 16.1 16.1 16.1 16.1 16.1 16.1
[130,] 17.1 17.1 17.1 17.1 17.1 17.1
[131,] 15.9 15.9 15.9 15.9 15.9 15.9
[132,] 16.1 16.1 16.1 16.1 16.1 16.1
[133,] 16.1 16.1 16.1 16.1 16.1 16.1
[134,] 16.1 16.1 16.1 16.1 16.1 16.1
[135,] 16.0 16.0 16.0 16.0 16.0 16.0
[136,] 15.9 15.9 15.9 15.9 15.9 15.9
[137,] 16.1 16.1 16.1 16.1 16.1 16.1
[138,] 16.5 16.5 16.5 16.5 16.5 16.5
[139,] 16.0 16.0 16.0 16.0 16.0 16.0
[140,] 16.1 16.1 16.1 16.1 16.1 16.1
[141,] 16.1 16.1 16.1 16.1 16.1 16.1
[142,] 16.2 16.2 16.2 16.2 16.2 16.2
[143,] 16.1 16.1 16.1 16.1 16.1 16.1
[144,] 15.9 15.9 15.9 15.9 15.9 15.9
[145,] 16.1 16.1 16.1 16.1 16.1 16.1
[146,] 15.9 15.9 15.9 15.9 15.9 15.9
[147,] 16.6 16.6 16.6 16.6 16.6 16.6
[148,] 17.3 17.3 17.3 17.3 17.3 17.3
[149,] 16.1 16.1 16.1 16.1 16.1 16.1
[150,] 16.0 16.0 16.0 16.0 16.0 16.0
[151,] 15.8 15.8 15.8 15.8 15.8 15.8
[152,] 16.1 16.1 16.1 16.1 16.1 16.1
[153,] 16.1 16.1 16.1 16.1 16.1 16.1
[154,] 16.4 16.4 16.4 16.4 16.4 16.4
[155,] 15.9 15.9 15.9 15.9 15.9 15.9
[156,] 16.0 16.0 16.0 16.0 16.0 16.0
[157,] 16.1 16.1 16.1 16.1 16.1 16.1
[158,] 16.2 16.2 16.2 16.2 16.2 16.2
[159,] 16.9 16.9 16.9 16.9 16.9 16.9
[160,] 16.4 16.4 16.4 16.4 16.4 16.4
[161,] 16.1 16.1 16.1 16.1 16.1 16.1
[162,] 16.5 16.5 16.5 16.5 16.5 16.5
[163,] 15.8 15.8 15.8 15.8 15.8 15.8
[164,] 16.5 16.5 16.5 16.5 16.5 16.5
[165,] 16.1 16.1 16.1 16.1 16.1 16.1
[166,] 16.7 16.7 16.7 16.7 16.7 16.7
[167,] 17.3 17.3 17.3 17.3 17.3 17.3
[168,] 16.6 16.6 16.6 16.6 16.6 16.6
[169,] 16.1 16.1 16.1 16.1 16.1 16.1
[170,] 15.8 15.8 15.8 15.8 15.8 15.8
[171,] 15.8 15.8 15.8 15.8 15.8 15.8
[172,] 16.0 16.0 16.0 16.0 16.0 16.0
[173,] 16.1 16.1 16.1 16.1 16.1 16.1
[174,] 16.0 16.0 16.0 16.0 16.0 16.0
[175,] 17.0 17.0 17.0 17.0 17.0 17.0
[176,] 16.8 16.8 16.8 16.8 16.8 16.8
[177,] 16.1 16.1 16.1 16.1 16.1 16.1
[178,] 16.3 16.3 16.3 16.3 16.3 16.3
[179,] 16.3 16.3 16.3 16.3 16.3 16.3
[180,] 15.8 15.8 15.8 15.8 15.8 15.8
[181,] 16.1 16.1 16.1 16.1 16.1 16.1
[182,] 16.3 16.3 16.3 16.3 16.3 16.3
[183,] 16.2 16.2 16.2 16.2 16.2 16.2
[184,] 16.9 16.9 16.9 16.9 16.9 16.9
[185,] 16.1 16.1 16.1 16.1 16.1 16.1
[186,] 16.2 16.2 16.2 16.2 16.2 16.2
[187,] 15.7 15.7 15.7 15.7 15.7 15.7
[188,] 15.8 15.8 15.8 15.8 15.8 15.8
[189,] 16.1 16.1 16.1 16.1 16.1 16.1
[190,] 16.3 16.3 16.3 16.3 16.3 16.3
[191,] 15.9 15.9 15.9 15.9 15.9 15.9
[192,] 16.0 16.0 16.0 16.0 16.0 16.0
[193,] 16.1 16.1 16.1 16.1 16.1 16.1
[194,] 16.7 16.7 16.7 16.7 16.7 16.7
[195,] 16.0 16.0 16.0 16.0 16.0 16.0
[196,] 16.0 16.0 16.0 16.0 16.0 16.0
[197,] 16.1 16.1 16.1 16.1 16.1 16.1
[198,] 16.1 16.1 16.1 16.1 16.1 16.1
[199,] 16.0 16.0 16.0 16.0 16.0 16.0
[200,] 16.4 16.4 16.4 16.4 16.4 16.4
[201,] 16.1 16.1 16.1 16.1 16.1 16.1
[202,] 16.4 16.4 16.4 16.4 16.4 16.4
[203,] 16.7 16.7 16.7 16.7 16.7 16.7
[204,] 16.0 16.0 16.0 16.0 16.0 16.0
[205,] 16.1 16.1 16.1 16.1 16.1 16.1
[206,] 16.3 16.3 16.3 16.3 16.3 16.3
[207,] 16.5 16.5 16.5 16.5 16.5 16.5
[208,] 16.2 16.2 16.2 16.2 16.2 16.2
[209,] 16.4 16.4 16.4 16.4 16.4 16.4
[210,] 16.7 16.7 16.7 16.7 16.7 16.7
[211,] 16.2 16.2 16.2 16.2 16.2 16.2
[212,] 16.4 16.4 16.4 16.4 16.4 16.4
[213,] 16.7 16.7 16.7 16.7 16.7 16.7
[214,] 17.2 17.2 17.2 17.2 17.2 17.2
[215,] 16.1 16.1 16.1 16.1 16.1 16.1
[216,] 16.5 16.5 16.5 16.5 16.5 16.5
[217,] 17.0 17.0 17.0 17.0 17.0 17.0
[218,] 18.0 18.0 18.0 18.0 18.0 18.0
[219,] 16.1 16.1 16.1 16.1 16.1 16.1
[220,] 16.6 16.6 16.6 16.6 16.6 16.6
[221,] 17.3 17.3 17.3 17.3 17.3 17.3
[222,] 17.3 17.3 17.3 17.3 17.3 17.3
[223,] 16.1 16.1 16.1 16.1 16.1 16.1
[224,] 16.6 16.6 16.6 16.6 16.6 16.6
[225,] 17.6 17.6 17.6 17.6 17.6 17.6
[226,] 17.2 17.2 17.2 17.2 17.2 17.2
[227,] 16.1 16.1 16.1 16.1 16.1 16.1
[228,] 16.6 16.6 16.6 16.6 16.6 16.6
[229,] 17.9 17.9 17.9 17.9 17.9 17.9
[230,] 17.1 17.1 17.1 17.1 17.1 17.1
[231,] 16.1 16.1 16.1 16.1 16.1 16.1
[232,] 16.7 16.7 16.7 16.7 16.7 16.7
[233,] 18.2 18.2 18.2 18.2 18.2 18.2
[234,]  NaN  NaN  NaN  NaN  NaN  NaN
[235,] 18.2 18.2 18.2 18.2 18.2 18.2
[236,] 16.7 16.7 16.7 16.7 16.7 16.7
[237,] 16.1 16.1 16.1 16.1 16.1 16.1
[238,] 17.0 17.0 17.0 17.0 17.0 17.0
[239,] 17.9 17.9 17.9 17.9 17.9 17.9
[240,] 16.7 16.7 16.7 16.7 16.7 16.7
[241,] 16.1 16.1 16.1 16.1 16.1 16.1
[242,] 17.0 17.0 17.0 17.0 17.0 17.0
[243,] 17.6 17.6 17.6 17.6 17.6 17.6
[244,] 16.7 16.7 16.7 16.7 16.7 16.7
[245,] 16.1 16.1 16.1 16.1 16.1 16.1
[246,] 16.9 16.9 16.9 16.9 16.9 16.9
[247,] 17.3 17.3 17.3 17.3 17.3 17.3
[248,] 16.8 16.8 16.8 16.8 16.8 16.8
[249,] 16.0 16.0 16.0 16.0 16.0 16.0
[250,] 16.8 16.8 16.8 16.8 16.8 16.8
[251,] 17.0 17.0 17.0 17.0 17.0 17.0
[252,] 17.0 17.0 17.0 17.0 17.0 17.0
[253,] 16.0 16.0 16.0 16.0 16.0 16.0
[254,] 16.6 16.6 16.6 16.6 16.6 16.6
[255,] 16.7 16.7 16.7 16.7 16.7 16.7
[256,] 18.5 18.5 18.5 18.5 18.5 18.5
[257,] 16.0 16.0 16.0 16.0 16.0 16.0
[258,] 16.4 16.4 16.4 16.4 16.4 16.4
[259,] 16.4 16.4 16.4 16.4 16.4 16.4
[260,] 16.7 16.7 16.7 16.7 16.7 16.7
[261,] 15.9 15.9 15.9 15.9 15.9 15.9
[262,] 16.1 16.1 16.1 16.1 16.1 16.1
[263,] 16.4 16.4 16.4 16.4 16.4 16.4
[264,] 16.0 16.0 16.0 16.0 16.0 16.0
[265,] 16.5 16.5 16.5 16.5 16.5 16.5
[266,] 16.6 16.6 16.6 16.6 16.6 16.6
[267,] 16.4 16.4 16.4 16.4 16.4 16.4
[268,] 17.6 17.6 17.6 17.6 17.6 17.6
[269,] 16.1 16.1 16.1 16.1 16.1 16.1
[270,] 16.0 16.0 16.0 16.0 16.0 16.0
[271,] 16.4 16.4 16.4 16.4 16.4 16.4
[272,] 16.8 16.8 16.8 16.8 16.8 16.8
[273,] 16.2 16.2 16.2 16.2 16.2 16.2
[274,] 16.4 16.4 16.4 16.4 16.4 16.4
[275,] 16.4 16.4 16.4 16.4 16.4 16.4
[276,] 16.3 16.3 16.3 16.3 16.3 16.3
[277,] 16.5 16.5 16.5 16.5 16.5 16.5
[278,] 16.2 16.2 16.2 16.2 16.2 16.2
[279,] 16.4 16.4 16.4 16.4 16.4 16.4
[280,] 16.6 16.6 16.6 16.6 16.6 16.6
[281,] 16.0 16.0 16.0 16.0 16.0 16.0
[282,] 16.4 16.4 16.4 16.4 16.4 16.4
[283,] 16.4 16.4 16.4 16.4 16.4 16.4
[284,] 16.5 16.5 16.5 16.5 16.5 16.5
[285,] 16.0 16.0 16.0 16.0 16.0 16.0
[286,] 16.2 16.2 16.2 16.2 16.2 16.2
[287,] 16.4 16.4 16.4 16.4 16.4 16.4
[288,] 16.4 16.4 16.4 16.4 16.4 16.4
[289,] 15.9 15.9 15.9 15.9 15.9 15.9
[290,] 16.5 16.5 16.5 16.5 16.5 16.5
[291,] 16.4 16.4 16.4 16.4 16.4 16.4
[292,] 16.0 16.0 16.0 16.0 16.0 16.0
[293,] 16.3 16.3 16.3 16.3 16.3 16.3
[294,] 16.1 16.1 16.1 16.1 16.1 16.1
[295,] 16.4 16.4 16.4 16.4 16.4 16.4
[296,] 16.0 16.0 16.0 16.0 16.0 16.0
[297,] 15.9 15.9 15.9 15.9 15.9 15.9
[298,] 17.6 17.6 17.6 17.6 17.6 17.6
[299,] 16.4 16.4 16.4 16.4 16.4 16.4
[300,] 16.8 16.8 16.8 16.8 16.8 16.8
[301,] 16.3 16.3 16.3 16.3 16.3 16.3
[302,] 17.4 17.4 17.4 17.4 17.4 17.4
[303,] 16.4 16.4 16.4 16.4 16.4 16.4
[304,] 16.9 16.9 16.9 16.9 16.9 16.9
[305,] 15.9 15.9 15.9 15.9 15.9 15.9
[306,] 16.8 16.8 16.8 16.8 16.8 16.8
[307,] 16.4 16.4 16.4 16.4 16.4 16.4
[308,] 17.3 17.3 17.3 17.3 17.3 17.3
[309,] 16.1 16.1 16.1 16.1 16.1 16.1
[310,] 16.4 16.4 16.4 16.4 16.4 16.4
[311,] 16.4 16.4 16.4 16.4 16.4 16.4
[312,] 17.0 17.0 17.0 17.0 17.0 17.0
[313,] 16.2 16.2 16.2 16.2 16.2 16.2
[314,] 16.2 16.2 16.2 16.2 16.2 16.2
[315,] 16.4 16.4 16.4 16.4 16.4 16.4
[316,] 15.9 15.9 15.9 15.9 15.9 15.9
[317,] 15.9 15.9 15.9 15.9 15.9 15.9
[318,] 16.3 16.3 16.3 16.3 16.3 16.3
[319,] 16.4 16.4 16.4 16.4 16.4 16.4
[320,] 16.3 16.3 16.3 16.3 16.3 16.3
[321,] 16.1 16.1 16.1 16.1 16.1 16.1
[322,] 16.0 16.0 16.0 16.0 16.0 16.0
[323,] 16.4 16.4 16.4 16.4 16.4 16.4
[324,] 16.1 16.1 16.1 16.1 16.1 16.1
[325,] 16.1 16.1 16.1 16.1 16.1 16.1
[326,] 16.0 16.0 16.0 16.0 16.0 16.0
[327,] 16.4 16.4 16.4 16.4 16.4 16.4
[328,] 16.5 16.5 16.5 16.5 16.5 16.5
[329,] 16.1 16.1 16.1 16.1 16.1 16.1
[330,] 16.3 16.3 16.3 16.3 16.3 16.3
[331,] 16.4 16.4 16.4 16.4 16.4 16.4
[332,] 16.1 16.1 16.1 16.1 16.1 16.1
[333,] 16.2 16.2 16.2 16.2 16.2 16.2
[334,] 16.1 16.1 16.1 16.1 16.1 16.1
[335,] 16.4 16.4 16.4 16.4 16.4 16.4
[336,] 16.6 16.6 16.6 16.6 16.6 16.6
[337,] 16.3 16.3 16.3 16.3 16.3 16.3
[338,] 17.0 17.0 17.0 17.0 17.0 17.0
[339,] 16.4 16.4 16.4 16.4 16.4 16.4
[340,] 16.1 16.1 16.1 16.1 16.1 16.1
[341,] 15.9 15.9 15.9 15.9 15.9 15.9
[342,] 17.0 17.0 17.0 17.0 17.0 17.0
[343,] 16.4 16.4 16.4 16.4 16.4 16.4
[344,] 17.0 17.0 17.0 17.0 17.0 17.0
[345,] 16.1 16.1 16.1 16.1 16.1 16.1
[346,] 16.9 16.9 16.9 16.9 16.9 16.9
[347,] 16.4 16.4 16.4 16.4 16.4 16.4
[348,] 16.4 16.4 16.4 16.4 16.4 16.4
[349,] 16.2 16.2 16.2 16.2 16.2 16.2
[350,] 16.8 16.8 16.8 16.8 16.8 16.8
[351,] 16.4 16.4 16.4 16.4 16.4 16.4
[352,] 16.3 16.3 16.3 16.3 16.3 16.3
[353,] 16.3 16.3 16.3 16.3 16.3 16.3
[354,] 16.6 16.6 16.6 16.6 16.6 16.6
[355,] 16.4 16.4 16.4 16.4 16.4 16.4
[356,] 16.1 16.1 16.1 16.1 16.1 16.1
[357,] 15.9 15.9 15.9 15.9 15.9 15.9
[358,] 16.4 16.4 16.4 16.4 16.4 16.4
[359,] 16.4 16.4 16.4 16.4 16.4 16.4
[360,] 17.2 17.2 17.2 17.2 17.2 17.2
[361,] 16.1 16.1 16.1 16.1 16.1 16.1
[362,] 16.2 16.2 16.2 16.2 16.2 16.2
[363,] 16.6 16.6 16.6 16.6 16.6 16.6
[364,] 16.6 16.6 16.6 16.6 16.6 16.6
[365,] 16.3 16.3 16.3 16.3 16.3 16.3
[366,] 16.4 16.4 16.4 16.4 16.4 16.4
[367,] 16.4 16.4 16.4 16.4 16.4 16.4
[368,] 16.3 16.3 16.3 16.3 16.3 16.3
[369,] 16.0 16.0 16.0 16.0 16.0 16.0
[370,] 16.9 16.9 16.9 16.9 16.9 16.9
[371,] 23.6 23.6 23.6 23.6 23.6 23.6
[372,] 15.8 15.8 15.8 15.8 15.8 15.8
[373,] 16.2 16.2 16.2 16.2 16.2 16.2
[374,] 15.9 15.9 15.9 15.9 15.9 15.9
[375,] 16.4 16.4 16.4 16.4 16.4 16.4
[376,] 16.3 16.3 16.3 16.3 16.3 16.3
[377,] 15.9 15.9 15.9 15.9 15.9 15.9
[378,] 16.5 16.5 16.5 16.5 16.5 16.5
[379,] 21.8 21.8 21.8 21.8 21.8 21.8
[380,] 16.4 16.4 16.4 16.4 16.4 16.4
[381,] 15.9 15.9 15.9 15.9 15.9 15.9
[382,] 17.5 17.5 17.5 17.5 17.5 17.5
[383,] 16.4 16.4 16.4 16.4 16.4 16.4
[384,] 18.6 18.6 18.6 18.6 18.6 18.6
[385,] 15.9 15.9 15.9 15.9 15.9 15.9
[386,] 16.2 16.2 16.2 16.2 16.2 16.2
[387,] 20.0 20.0 20.0 20.0 20.0 20.0
[388,] 16.1 16.1 16.1 16.1 16.1 16.1
[389,] 15.9 15.9 15.9 15.9 15.9 15.9
[390,] 15.9 15.9 15.9 15.9 15.9 15.9
[391,] 16.4 16.4 16.4 16.4 16.4 16.4
[392,] 16.0 16.0 16.0 16.0 16.0 16.0
[393,] 15.9 15.9 15.9 15.9 15.9 15.9
[394,] 16.7 16.7 16.7 16.7 16.7 16.7
[395,] 18.2 18.2 18.2 18.2 18.2 18.2
[396,] 16.3 16.3 16.3 16.3 16.3 16.3
[397,] 15.9 15.9 15.9 15.9 15.9 15.9
[398,] 16.8 16.8 16.8 16.8 16.8 16.8
[399,] 16.4 16.4 16.4 16.4 16.4 16.4
[400,] 16.6 16.6 16.6 16.6 16.6 16.6
[401,] 15.9 15.9 15.9 15.9 15.9 15.9
[402,] 16.1 16.1 16.1 16.1 16.1 16.1
[403,] 16.4 16.4 16.4 16.4 16.4 16.4
[404,] 16.7 16.7 16.7 16.7 16.7 16.7
[405,] 16.0 16.0 16.0 16.0 16.0 16.0
[406,] 16.0 16.0 16.0 16.0 16.0 16.0
[407,] 16.3 16.3 16.3 16.3 16.3 16.3
[408,] 16.2 16.2 16.2 16.2 16.2 16.2
[409,] 16.1 16.1 16.1 16.1 16.1 16.1
[410,] 17.2 17.2 17.2 17.2 17.2 17.2
[411,] 16.4 16.4 16.4 16.4 16.4 16.4
[412,] 16.1 16.1 16.1 16.1 16.1 16.1
[413,] 16.3 16.3 16.3 16.3 16.3 16.3
[414,] 16.7 16.7 16.7 16.7 16.7 16.7
[415,] 16.9 16.9 16.9 16.9 16.9 16.9
[416,] 16.6 16.6 16.6 16.6 16.6 16.6
[417,] 16.5 16.5 16.5 16.5 16.5 16.5
[418,] 16.2 16.2 16.2 16.2 16.2 16.2
[419,] 16.5 16.5 16.5 16.5 16.5 16.5
[420,] 17.0 17.0 17.0 17.0 17.0 17.0
[421,] 16.2 16.2 16.2 16.2 16.2 16.2
[422,] 17.6 17.6 17.6 17.6 17.6 17.6
[423,] 16.4 16.4 16.4 16.4 16.4 16.4
[424,] 16.8 16.8 16.8 16.8 16.8 16.8
[425,] 15.9 15.9 15.9 15.9 15.9 15.9
[426,] 16.1 16.1 16.1 16.1 16.1 16.1
[427,] 16.3 16.3 16.3 16.3 16.3 16.3
[428,] 16.1 16.1 16.1 16.1 16.1 16.1
[429,] 16.4 16.4 16.4 16.4 16.4 16.4
[430,] 16.7 16.7 16.7 16.7 16.7 16.7
[431,] 16.4 16.4 16.4 16.4 16.4 16.4
[432,] 16.3 16.3 16.3 16.3 16.3 16.3
[433,] 16.1 16.1 16.1 16.1 16.1 16.1
[434,] 16.0 16.0 16.0 16.0 16.0 16.0
[435,] 16.3 16.3 16.3 16.3 16.3 16.3
[436,] 16.1 16.1 16.1 16.1 16.1 16.1
[437,] 15.9 15.9 15.9 15.9 15.9 15.9
[438,] 16.3 16.3 16.3 16.3 16.3 16.3
[439,] 16.4 16.4 16.4 16.4 16.4 16.4
[440,] 16.3 16.3 16.3 16.3 16.3 16.3
[441,] 16.4 16.4 16.4 16.4 16.4 16.4
[442,] 16.0 16.0 16.0 16.0 16.0 16.0
[443,] 16.0 16.7 16.7 16.7 16.7 16.7
[444,] 15.9 16.6 16.6 16.6 16.6 16.6
[445,] 15.2 16.2 16.2 16.2 16.2 16.2
[446,] 14.7 16.1 16.1 16.1 16.1 16.1
[447,] 14.2 16.3 16.3 16.3 16.3 16.3
[448,] 13.7 15.6 15.9 15.9 15.9 15.9
[449,] 13.1 14.9 16.2 16.2 16.2 16.2
[450,] 12.6 14.3 15.9 16.7 16.7 16.7
[451,] 12.1 13.7 15.3 16.8 16.8 16.8
[452,] 11.6 13.1 14.6 15.9 16.6 16.6
[453,] 11.0 12.5 13.9 15.5 16.0 16.0
[454,] 10.5 11.9 13.3 14.6 16.0 16.3
[455,] 10.0 11.3 12.6 13.9 15.2 17.2
[456,]  9.5 10.7 11.9 13.1 14.3 15.5
[457,]  8.9 10.1 11.2 12.4 13.5 14.6
[458,]  8.4  9.5 10.6 11.6 12.7 13.7
[459,]  7.9  8.9  9.9 10.9 11.9 12.8
[460,]  7.4  8.3  9.2 10.1 11.0 11.9
[461,]  6.9  7.7  8.5  9.4 10.2 11.0
[462,]  6.3  7.1  7.9  8.6  9.4 10.1
[463,]  5.8  6.5  7.2  7.9  8.6  9.2
[464,]  5.3  5.9  6.5  7.1  7.7  8.3
[465,]  4.8  5.3  5.9  6.4  6.9  7.4
[466,]  4.3  4.7  5.2  5.7  6.1  6.6
[467,]  3.7  4.1  4.5  4.9  5.3  5.7
> 
> matplot(t, corDig, type="o", ylim = c(1,17))
> (cN <- colnames(corDig))
 [1] "b1"    "b.10"  "dirct" "p1l1p" "p1l1"  "k=1"   "k=2"   "k=3"   "k=4"  
[10] "k=5"   "k=6"   "k=7"   "k=8"   "k=9"   "k=10"  "k=11"  "k=12" 
> legend(-.5, 14, cN, col=1:6, lty=1:5, pch = c(1L:9L, 0L, letters), ncol=2)
> 
> ## plot() function >>>> using global (t, corDig) <<<<<<<<<
> p.relEr <- function(i, ylim = c(11,17), type = "o",
+                     leg.pos = "left", inset=1/128,
+                     main = sprintf(
+                         "Correct #{Digits} in p1l1() approx., notably Taylor(k=1 .. %d)",
+                                    max(k.s)))
+ {
+     if((neg <- all(t[i] < 0)))
+         t  <- -t
+     stopifnot(all(t[i] > 0), length(ylim) == 2) # as we use log="x"
+     matplot(t[i], corDig[i,], type=type, ylim=ylim, log="x", xlab = quote(t), xaxt="n",
+             main=main)
+     legend(leg.pos, cN, col=1:6, lty=1:5, pch = c(1L:9L, 0L, letters), ncol=2,
+            bg=adjustcolor("gray90", 7/8), inset=inset)
+     t.epsC <- -log10(c(1,2,4)* .Machine$double.eps)
+     axis(2, at=t.epsC, labels = expression(epsilon[C], 2*epsilon[C], 4*epsilon[C]),
+          las=2, col=2, line=1)
+     tenRs <- function(t) floor(log10(min(t))) : ceiling(log10(max(t)))
+     tenE <- tenRs(t[i])
+     tE <- 10^tenE
+     abline (h = t.epsC,
+             v = tE, lty=3, col=adjustcolor("gray",.8), lwd=2)
+     AX <- if(requireNamespace("sfsmisc")) sfsmisc::eaxis else axis
+     AX(1, at= tE, labels = as.expression(
+                       lapply(tenE,
+                              if(neg)
+                                  function(e) substitute(-10^{E}, list(E = e+0))
+                              else
+                                  function(e) substitute( 10^{E}, list(E = e+0)))))
+ }
> 
> p.relEr(t > 0, ylim = c(1,17))
> p.relEr(t > 0) # full positive range
> p.relEr(t < 0) # full negative range
> if(FALSE) {## (actually less informative):
+  p.relEr(i = 0 < t & t < .01)  ## positive small t
+  p.relEr(i = -.1 < t & t < 0) ## negative small t
+ }
> 
> ## Find approximate formulas for accuracy of k=k*  approximation
> d.corrD <- cbind(t=t, as.data.frame(corDig))
> names(d.corrD) <- sub("k=", "nC_",  names(d.corrD))
> 
> fmod <- function(k, data, cut.y.at = -log10(2 * .Machine$double.eps),
+                  good.y = -log10(.Machine$double.eps), # ~ 15.654
+                  verbose=FALSE) {
+     varNm <- paste0("nC_",k)
+     stopifnot(is.numeric(y <- get(varNm, data, inherits=FALSE)),
+               is.numeric(t <- data$t))# '$' works for data.frame, list, environment
+     i <- 3 <= y & y <= cut.y.at
+     i.pos <- i & t > 0
+     i.neg <- i & t < 0
+     if(verbose) cat(sprintf("k=%d >> y <= %g ==> #{pos. t} = %d ;  #{neg. t} = %d\n",
+                             k, cut.y.at, sum(i.pos), sum(i.neg)))
+     nCoefLm <- function(x,y) `names<-`(.lm.fit(x=x, y=y)$coeff, c("int", "slp"))
+     nC.t <- function(x,y) { cf <- nCoefLm(x,y); c(cf, t.0 = exp((good.y - cf[[1]])/cf[[2]])) }
+     cbind(pos = nC.t(cbind(1, log( t[i.pos])), y[i.pos]),
+           neg = nC.t(cbind(1, log(-t[i.neg])), y[i.neg]))
+ }
> rr <- sapply(k.s, fmod, data=d.corrD, verbose=TRUE, simplify="array")
k=1 >> y <= 15.3525 ==> #{pos. t} = 165 ;  #{neg. t} = 164
k=2 >> y <= 15.3525 ==> #{pos. t} = 82 ;  #{neg. t} = 82
k=3 >> y <= 15.3525 ==> #{pos. t} = 55 ;  #{neg. t} = 54
k=4 >> y <= 15.3525 ==> #{pos. t} = 42 ;  #{neg. t} = 41
k=5 >> y <= 15.3525 ==> #{pos. t} = 33 ;  #{neg. t} = 32
k=6 >> y <= 15.3525 ==> #{pos. t} = 27 ;  #{neg. t} = 27
k=7 >> y <= 15.3525 ==> #{pos. t} = 23 ;  #{neg. t} = 22
k=8 >> y <= 15.3525 ==> #{pos. t} = 19 ;  #{neg. t} = 19
k=9 >> y <= 15.3525 ==> #{pos. t} = 17 ;  #{neg. t} = 17
k=10 >> y <= 15.3525 ==> #{pos. t} = 14 ;  #{neg. t} = 15
k=11 >> y <= 15.3525 ==> #{pos. t} = 13 ;  #{neg. t} = 13
k=12 >> y <= 15.3525 ==> #{pos. t} = 11 ;  #{neg. t} = 12
> stopifnot(rr["slp",,] < 0) # all slopes are negative (important!)
> matplot(k.s, t(rr["slp",,]), type="o", xlab = quote(k), ylab = quote(slope[k]))
> ## fantastcally close to linear in k
> ## The numbers, nicely arranged
> ftable(aperm(rr, c(3,2,1)))
                    int           slp           t.0
                                                   
k=1  pos   4.799691e-01 -4.341066e-01  6.604529e-16
     neg   4.756759e-01 -4.343909e-01  6.690917e-16
k=2  pos   7.810080e-01 -8.683662e-01  3.645998e-08
     neg   7.767658e-01 -8.686128e-01  3.645921e-08
k=3  pos   1.014435e+00 -1.301039e+00  1.298301e-05
     neg   9.827922e-01 -1.305341e+00  1.315071e-05
k=4  pos   1.204024e+00 -1.733024e+00  2.393078e-04
     neg   1.141408e+00 -1.743073e+00  2.422326e-04
k=5  pos   1.368501e+00 -2.162254e+00  1.351473e-03
     neg   1.260251e+00 -2.184374e+00  1.375120e-03
k=6  pos   1.506395e+00 -2.592862e+00  4.269765e-03
     neg   1.356588e+00 -2.628147e+00  4.339726e-03
k=7  pos   1.637759e+00 -3.016733e+00  9.599728e-03
     neg   1.449676e+00 -3.069312e+00  9.777136e-03
k=8  pos   1.731648e+00 -3.453572e+00  1.775367e-02
     neg   1.523333e+00 -3.515635e+00  1.796638e-02
k=9  pos   1.824829e+00 -3.885243e+00  2.845884e-02
     neg   1.618873e+00 -3.943160e+00  2.846020e-02
k=10 pos   1.923972e+00 -4.307028e+00  4.126595e-02
     neg   1.675544e+00 -4.390402e+00  4.142931e-02
k=11 pos   1.994784e+00 -4.743501e+00  5.616442e-02
     neg   1.711181e+00 -4.850084e+00  5.643491e-02
k=12 pos   2.070152e+00 -5.172325e+00  7.235500e-02
     neg   1.817454e+00 -5.252709e+00  7.178431e-02
> signif(t(rr["t.0",,]),3) # ==> Should be boundaries for the hybrid p1l1()
          pos      neg
k=1  6.60e-16 6.69e-16
k=2  3.65e-08 3.65e-08
k=3  1.30e-05 1.32e-05
k=4  2.39e-04 2.42e-04
k=5  1.35e-03 1.38e-03
k=6  4.27e-03 4.34e-03
k=7  9.60e-03 9.78e-03
k=8  1.78e-02 1.80e-02
k=9  2.85e-02 2.85e-02
k=10 4.13e-02 4.14e-02
k=11 5.62e-02 5.64e-02
k=12 7.24e-02 7.18e-02
> ##           pos      neg
> ## k=1  6.60e-16 6.69e-16
> ## k=2  3.65e-08 3.65e-08
> ## k=3  1.30e-05 1.32e-05
> ## k=4  2.39e-04 2.42e-04
> ## k=5  1.35e-03 1.38e-03
> ## k=6  4.27e-03 4.34e-03
> ## k=7  9.60e-03 9.78e-03
> ## k=8  1.78e-02 1.80e-02
> ## k=9  2.85e-02 2.85e-02
> ## k=10 4.13e-02 4.14e-02
> ## k=11 5.62e-02 5.64e-02
> ## k=12 7.24e-02 7.18e-02
> 
> ###------------- Well,  p1l1p()  is really basically good enough ... with a small exception:
> rErr1k <- curve(asNumeric(p1l1p(x) / p1l1.(mpfr(x, 4096)) - 1), -.999, .999,
+                 n = 4000, col=2, lwd=2)
> abline(h = c(-8,-4,-2:2,4,8)* 2^-52, lty=2, col=adjustcolor("gray20", 1/4))
> ## well, have a "spike" at around -0.8 -- why?
> 
> plot(abs(y) ~ x, data = rErr1k, ylim = c(4e-17, max(abs(y))),
+      ylab=quote(abs(hat(p)/p - 1)),
+      main = "p1l1p(x) -- Relative Error wrt mpfr(*. 4096) [log]",
+      col=2, lwd=1.5, type = "b", cex=1/2, log="y", yaxt="n")
Error in is.qr(x) : object 'p' not found
Calls: plot ... plot.formula -> do.call -> plot -> plot.default -> hat -> is.qr
Execution halted
** running examples for arch 'x64' ... ERROR
Running examples in 'DPQ-Ex.R' failed
The error most likely occurred in:

> ### Name: p1l1
> ### Title: Numerically Stable p1l1(t) = (t+1)*log(1+t) - t
> ### Aliases: p1l1 p1l1. p1l1p p1l1ser
> 
> ### ** Examples
> 
> t <- seq(-1, 4, by=1/64)
> plot(t, p1l1ser(t, 1), type="l")
> lines(t, p1l1.(t), lwd=5, col=adjustcolor(1, 1/2)) # direct formula
> for(k in 2:6) lines(t, p1l1ser(t, k), col=k)
> 
> ## zoom in
> t <- 2^seq(-59,-1, by=1/4)
> t <- c(-rev(t), 0, t)
> stopifnot(!is.unsorted(t))
> k.s <- 1:12; names(k.s) <- paste0("k=", 1:12)
> 
> ## True function values: use Rmpfr with 256 bits precision: ---
> ### eventually move this to ../tests/ & ../vignettes/
> #### FIXME: eventually replace with  if(requireNamespace("Rmpfr")){ ......}
> #### =====
> if((needRmpfr <- is.na(match("Rmpfr", (srch0 <- search())))))
+     require("Rmpfr")
Loading required package: Rmpfr
Loading required package: gmp

Attaching package: 'gmp'

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

    %*%, apply, crossprod, matrix, tcrossprod

C code of R package 'Rmpfr': GMP using 64 bits per limb


Attaching package: 'Rmpfr'

The following object is masked from 'package:gmp':

    outer

The following object is masked from 'package:DPQ':

    log1mexp

The following objects are masked from 'package:stats':

    dbinom, dgamma, dnbinom, dnorm, dpois, pnorm

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

    cbind, pmax, pmin, rbind

> p1l1.T <- p1l1.(mpfr(t, 256)) # "true" values
> p1l1.n <- asNumeric(p1l1.T)
> p1tab <-
+     cbind(b1 = bd0(t+1, 1),
+           b.10 = bd0(10*t+10,10)/10,
+           dirct = p1l1.(t),
+           p1l1p = p1l1p(t),
+           p1l1  = p1l1 (t),
+           sapply(k.s, function(k) p1l1ser(t,k)))
> matplot(t, p1tab, type="l", ylab = "p1l1*(t)")
> ## (absolute) error:
> ##' legend for matplot()
> mpLeg <- function(leg = colnames(p1tab), xy = "top", col=1:6, lty=1:5, lwd=1,
+                   pch = c(1L:9L, 0L, letters, LETTERS)[seq_along(leg)], ...)
+     legend(xy, legend=leg, col=col, lty=lty, lwd=lwd, pch=pch, ncol=3, ...)
> 
> titAbs <- "Absolute errors of p1l1(t) approximations"
> matplot(t, asNumeric(p1tab - p1l1.T), type="o", main=titAbs); mpLeg()
> i <- abs(t) <= 1/10 ## zoom in a bit
> matplot(t[i], abs(asNumeric((p1tab - p1l1.T)[i,])), type="o", log="y",
+         main=titAbs, ylim = c(1e-18, 0.003)); mpLeg()
Warning in xy.coords(x, y, xlabel, ylabel, log = log) :
  17 y values <= 0 omitted from logarithmic plot
Warning in xy.coords(x, y, xlabel, ylabel, log) :
  1 y value <= 0 omitted from logarithmic plot
> ## Relative Error
> titR <- "|Relative error| of p1l1(t) approximations"
> matplot(t[i], abs(asNumeric((p1tab/p1l1.T - 1)[i,])), type="o", log="y",
+         ylim = c(1e-18, 2^-10), main=titR)
> mpLeg(xy="topright", bg= adjustcolor("gray80", 4/5))
> i <- abs(t) <= 2^-10 # zoom in more
> matplot(t[i], abs(asNumeric((p1tab/p1l1.T - 1)[i,])), type="o", log="y",
+         ylim = c(1e-18, 1e-9))
> mpLeg(xy="topright", bg= adjustcolor("gray80", 4/5))
> 
> 
> ## Correct number of digits
> corDig <- asNumeric(-log10(abs(p1tab/p1l1.T - 1)))
> cbind(t, round(corDig, 1))# correct number of digits
                   t   b1 b.10 dirct p1l1p p1l1  k=1  k=2  k=3  k=4  k=5  k=6
  [1,] -5.000000e-01 15.5 15.5  16.1  16.0 16.0  0.7  1.3  1.8  2.3  2.7  3.1
  [2,] -4.204482e-01 15.4 15.4  15.2  15.8 15.8  0.8  1.5  2.1  2.6  3.1  3.6
  [3,] -3.535534e-01 15.3 16.3  15.6  16.3 16.3  0.9  1.6  2.3  2.9  3.5  4.1
  [4,] -2.973018e-01 15.1 14.8  15.7  16.1 16.1  1.0  1.8  2.5  3.2  3.9  4.5
  [5,] -2.500000e-01 15.6 14.7  15.2  16.4 16.4  1.1  1.9  2.8  3.5  4.3  5.0
  [6,] -2.102241e-01 14.7 14.6  15.6  16.4 16.4  1.1  2.1  3.0  3.8  4.7  5.5
  [7,] -1.767767e-01 16.6 15.6  15.6  15.6 15.6  1.2  2.3  3.2  4.2  5.1  5.9
  [8,] -1.486509e-01 15.8 15.3  14.9  16.8 16.8  1.3  2.4  3.5  4.5  5.4  6.4
  [9,] -1.250000e-01 16.5 16.5  15.4  16.5 16.5  1.4  2.6  3.7  4.8  5.8  6.8
 [10,] -1.051121e-01 15.1 14.8  15.1  15.8 15.8  1.4  2.7  3.9  5.1  6.2  7.3
 [11,] -8.838835e-02 15.1 15.5  15.0  16.1 16.1  1.5  2.9  4.1  5.4  6.6  7.8
 [12,] -7.432544e-02 15.0 14.7  14.7  15.8 15.8  1.6  3.0  4.4  5.7  7.0  8.2
 [13,] -6.250000e-02 15.7 17.6  14.6  15.7 17.6  1.7  3.2  4.6  6.0  7.3  8.7
 [14,] -5.255603e-02 15.1 14.8  14.6  16.0 16.3  1.8  3.3  4.8  6.3  7.7  9.1
 [15,] -4.419417e-02 15.1 15.6  14.4  15.7 16.5  1.8  3.5  5.1  6.6  8.1  9.6
 [16,] -3.716272e-02 14.7 14.7  14.4  16.1 15.7  1.9  3.6  5.3  6.9  8.5 10.0
 [17,] -3.125000e-02 16.5 16.5  14.4  15.7 16.5  2.0  3.8  5.5  7.2  8.8 10.5
 [18,] -2.627801e-02 14.4 14.3  14.2  15.8 17.1  2.1  3.9  5.7  7.5  9.2 10.9
 [19,] -2.209709e-02 14.4 15.8  14.5  15.8 15.8  2.1  4.1  6.0  7.8  9.6 11.4
 [20,] -1.858136e-02 14.4 14.1  13.9  15.9 16.6  2.2  4.2  6.2  8.1 10.0 11.8
 [21,] -1.562500e-02 16.1 16.1  14.3  15.9 15.9  2.3  4.4  6.4  8.4 10.4 12.3
 [22,] -1.313901e-02 14.3 14.3  14.0  16.9 15.8  2.4  4.5  6.6  8.7 10.7 12.7
 [23,] -1.104854e-02 14.4 13.8  13.8  15.7 16.7  2.4  4.7  6.9  9.0 11.1 13.2
 [24,] -9.290681e-03 14.1 13.9  13.9  16.4 15.9  2.5  4.8  7.1  9.3 11.5 13.6
 [25,] -7.812500e-03 15.9 16.0  13.8  15.9 15.9  2.6  5.0  7.3  9.6 11.9 14.1
 [26,] -6.569503e-03 13.9 13.7  14.0  16.3 16.0  2.7  5.1  7.5  9.9 12.2 14.5
 [27,] -5.524272e-03 13.8 13.8  13.9  15.6 15.8  2.7  5.3  7.8 10.2 12.6 15.0
 [28,] -4.645340e-03 14.1 14.0  13.5  16.0 16.2  2.8  5.4  8.0 10.5 13.0 15.4
 [29,] -3.906250e-03 15.8 16.2  13.5  16.2 16.2  2.9  5.6  8.2 10.8 13.4 16.2
 [30,] -3.284752e-03 13.7 13.5  13.9  16.5 15.7  3.0  5.7  8.5 11.1 13.7 15.7
 [31,] -2.762136e-03 13.8 13.3  13.0  15.9 16.1  3.0  5.9  8.7 11.4 14.1 16.1
 [32,] -2.322670e-03 14.1 13.2  13.4  16.4 16.4  3.1  6.0  8.9 11.7 14.5 16.4
 [33,] -1.953125e-03 16.2 15.8  13.7  16.2 16.2  3.2  6.2  9.1 12.0 14.9 16.2
 [34,] -1.642376e-03 13.7 13.5  13.5  16.0 16.0  3.3  6.3  9.4 12.3 15.4 16.0
 [35,] -1.381068e-03 13.8 13.1  13.7  16.2 15.8  3.3  6.5  9.6 12.6 16.2 15.8
 [36,] -1.161335e-03 13.1 13.2  12.7  15.6 15.7  3.4  6.6  9.8 12.9 15.7 16.0
 [37,] -9.765625e-04 16.1 16.1  13.5  15.8 15.8  3.5  6.8 10.0 13.2 15.8 16.1
 [38,] -8.211879e-04 13.7 13.5  12.6  16.4 16.4  3.6  6.9 10.3 13.5 16.4 16.4
 [39,] -6.905340e-04 13.8 12.8  13.3  15.7 16.6  3.6  7.1 10.5 13.8 16.6 16.6
 [40,] -5.806675e-04 13.1 12.6  12.8  15.8 15.8  3.7  7.3 10.7 14.1 15.8 15.8
 [41,] -4.882812e-04 16.3 16.3  12.2  15.8 16.3  3.8  7.4 10.9 14.4 16.3 16.3
 [42,] -4.105940e-04 12.6 12.4  13.7  16.6 16.6  3.9  7.6 11.2 14.7 16.6 16.6
 [43,] -3.452670e-04 12.5 12.5  12.5  15.9 16.0  3.9  7.7 11.4 15.1 16.0 16.0
 [44,] -2.903338e-04 13.1 12.4  14.5  15.5 16.9  4.0  7.9 11.6 15.3 16.9 16.9
 [45,] -2.441406e-04 16.1 15.8  12.3  16.1 16.1  4.1  8.0 11.8 15.8 16.1 16.1
 [46,] -2.052970e-04 12.6 12.3  12.1  16.4 15.9  4.2  8.2 12.1 15.9 15.9 15.9
 [47,] -1.726335e-04 12.5 12.2  12.5  15.8 16.3  4.2  8.3 12.3 16.3 15.8 15.8
 [48,] -1.451669e-04 12.2 12.4  12.2  15.7 16.4  4.3  8.5 12.5 16.4 16.4 16.4
 [49,] -1.220703e-04 15.9 16.1  11.9  15.5 16.1  4.4  8.6 12.7 16.1 16.1 16.1
 [50,] -1.026485e-04 12.1 12.3  12.8  16.4 16.4  4.5  8.8 13.0 16.4 16.4 16.4
 [51,] -8.631675e-05 12.5 12.2  12.2  16.0 16.0  4.5  8.9 13.2 16.0 16.0 16.0
 [52,] -7.258344e-05 12.1 11.7  11.9  15.5 15.9  4.6  9.1 13.4 15.9 15.9 15.9
 [53,] -6.103516e-05 16.0 16.0  11.4  16.0 16.0  4.7  9.2 13.6 16.0 16.0 16.0
 [54,] -5.132424e-05 11.9 12.3  11.3  16.3 16.3  4.8  9.4 13.9 16.3 16.3 16.3
 [55,] -4.315837e-05 12.5 12.2  11.4  16.1 16.1  4.8  9.5 14.1 16.1 16.1 16.1
 [56,] -3.629172e-05 12.1 11.5  12.5  16.1 16.1  4.9  9.7 14.3 16.1 16.1 16.1
 [57,] -3.051758e-05 16.5 16.5  11.6  16.5 16.5  5.0  9.8 14.5 16.5 16.5 16.5
 [58,] -2.566212e-05 11.5 11.2  11.0  15.9 16.5  5.1 10.0 14.8 16.5 16.5 16.5
 [59,] -2.157919e-05 11.3 12.2  10.9  16.3 15.8  5.1 10.1 15.0 15.8 15.8 15.8
 [60,] -1.814586e-05 11.3 11.5  10.7  16.2 16.1  5.2 10.3 15.3 16.1 16.1 16.1
 [61,] -1.525879e-05 16.1 15.9  10.8  15.9 16.1  5.3 10.4 15.4 16.1 16.1 16.1
 [62,] -1.283106e-05 11.5 11.2  12.1  15.7 15.9  5.4 10.6 15.9 16.7 16.7 16.7
 [63,] -1.078959e-05 11.3 10.8  10.8  15.9 16.1  5.4 10.7 16.1 15.9 15.9 15.9
 [64,] -9.072930e-06 11.2 11.5  11.1  15.8 16.9  5.5 10.9 16.9 16.9 16.9 16.9
 [65,] -7.629395e-06 15.9 16.0  10.7  16.0 15.9  5.6 11.0 15.9 16.0 16.0 16.0
 [66,] -6.415531e-06 10.8 10.7  11.0  16.4 16.4  5.7 11.2 16.4 16.4 16.4 16.4
 [67,] -5.394797e-06 10.8 10.8  10.3  17.0 17.0  5.7 11.3 17.0 17.0 17.0 17.0
 [68,] -4.536465e-06 11.2 10.4  10.5  16.8 15.8  5.8 11.5 15.8 15.8 15.8 15.8
 [69,] -3.814697e-06 17.3 17.3  10.4  17.3 17.3  5.9 11.6 17.3 17.3 17.3 17.3
 [70,] -3.207765e-06 10.7 10.7  10.7  15.9 16.8  6.0 11.8 16.8 16.8 16.8 16.8
 [71,] -2.697398e-06 10.8 10.8  10.2  16.8 16.8  6.0 11.9 16.8 16.8 16.8 16.8
 [72,] -2.268233e-06 10.4 10.4  10.2  15.6 15.7  6.1 12.1 15.7 15.7 15.7 15.7
 [73,] -1.907349e-06 16.1 15.8  10.1  16.1 16.1  6.2 12.2 16.1 16.1 16.1 16.1
 [74,] -1.603883e-06 10.3 10.7  10.3  15.6 16.0  6.3 12.4 16.0 16.0 16.0 16.0
 [75,] -1.348699e-06 10.8 10.8  10.5  16.8 16.8  6.3 12.5 16.8 16.8 16.8 16.8
 [76,] -1.134116e-06 10.4 10.4  10.6  15.7 16.0  6.4 12.7 16.0 16.0 16.0 16.0
 [77,] -9.536743e-07 19.1 19.1   9.8  19.1 19.1  6.5 12.8 19.1 19.1 19.1 19.1
 [78,] -8.019413e-07 10.0  9.7  10.2  17.5 15.8  6.6 13.0 15.8 15.8 15.8 15.8
 [79,] -6.743496e-07 10.8 10.8   9.9  16.9 16.9  6.6 13.1 16.9 16.9 16.9 16.9
 [80,] -5.670581e-07 10.4 10.4  11.0  15.7 16.0  6.7 13.3 16.0 16.0 16.0 16.0
 [81,] -4.768372e-07 16.1 15.8   9.5  16.1 16.1  6.8 13.4 16.1 16.1 16.1 16.1
 [82,] -4.009707e-07 10.0  9.7  10.4  16.5 16.5  6.9 13.6 16.5 16.5 16.5 16.5
 [83,] -3.371748e-07 10.8  9.3   9.5  15.7 16.9  6.9 13.7 16.9 16.9 16.9 16.9
 [84,] -2.835291e-07  9.5 10.4   9.5  17.1 17.1  7.0 13.9 17.1 17.1 17.1 17.1
 [85,] -2.384186e-07 20.9 20.9   9.2  20.9 20.9  7.1 14.0 20.9 20.9 20.9 20.9
 [86,] -2.004853e-07  9.3  9.2   9.5  15.7 16.5  7.2 14.2 16.5 16.5 16.5 16.5
 [87,] -1.685874e-07 10.8  9.3   8.8  16.9 16.9  7.3 14.3 16.9 16.9 16.9 16.9
 [88,] -1.417645e-07  9.5  8.9   8.8  16.3 16.3  7.3 14.5 16.3 16.3 16.3 16.3
 [89,] -1.192093e-07 16.1 15.8   8.9  16.1 16.1  7.4 14.6 16.1 16.1 16.1 16.1
 [90,] -1.002427e-07  9.2  9.0   9.3  15.6 16.0  7.5 14.8 16.0 16.0 16.0 16.0
 [91,] -8.429370e-08 10.8  9.3   8.8  16.0 15.9  7.6 14.9 15.9 15.9 15.9 15.9
 [92,] -7.088227e-08  8.9  8.9   8.9  16.0 16.0  7.6 15.1 16.0 16.0 16.0 16.0
 [93,] -5.960464e-08 22.7 22.7   8.6  22.7 22.7  7.7 15.2 22.7 22.7 22.7 22.7
 [94,] -5.012133e-08  8.8  9.0   8.7  15.8 15.8  7.8 15.5 15.8 15.8 15.8 15.8
 [95,] -4.214685e-08  8.6  9.3   8.2  15.8 16.2  7.9 15.8 16.2 16.2 16.2 16.2
 [96,] -3.544113e-08  8.9  8.4   8.1  17.3 15.8  7.9 15.8 17.3 17.3 17.3 17.3
 [97,] -2.980232e-08 16.1 16.1   8.3  16.1 16.1  8.0 16.1 16.1 16.1 16.1 16.1
 [98,] -2.506067e-08  8.5  9.0   8.2  16.3 16.3  8.1 16.3 16.3 16.3 16.3 16.3
 [99,] -2.107342e-08  8.6  9.3   8.2  15.7 16.4  8.2 16.4 16.4 16.4 16.4 16.4
[100,] -1.772057e-08  8.9  8.4   8.7  16.4 16.4  8.2 16.4 16.4 16.4 16.4 16.4
[101,] -1.490116e-08 16.0 16.0   8.0  16.0 16.0  8.3 16.0 16.0 16.0 16.0 16.0
[102,] -1.253033e-08  8.2  9.0   9.7  15.8 15.8  8.4 15.8 15.8 15.8 15.8 15.8
[103,] -1.053671e-08  8.1  9.3   7.6  15.8 16.1  8.5 16.1 16.1 16.1 16.1 16.1
[104,] -8.860283e-09  7.9  7.8   7.7  16.2 16.0  8.5 16.0 16.0 16.0 16.0 16.0
[105,] -7.450581e-09 16.2 15.8   8.6  16.2 16.2  8.6 16.2 16.2 16.2 16.2 16.2
[106,] -6.265167e-09  8.2  9.0   7.7  16.2 16.2  8.7 16.2 16.2 16.2 16.2 16.2
[107,] -5.268356e-09  8.1  9.3   8.8  15.7 16.6  8.8 16.6 16.6 16.6 16.6 16.6
[108,] -4.430142e-09  7.9  7.8   7.7  16.3 16.3  8.8 16.3 16.3 16.3 16.3 16.3
[109,] -3.725290e-09 16.1 15.8   8.9  16.1 16.1  8.9 16.1 16.1 16.1 16.1 16.1
[110,] -3.132583e-09  7.5  9.0   7.2  16.6 15.9  9.0 15.9 15.9 15.9 15.9 15.9
[111,] -2.634178e-09  7.5  9.3   9.1  16.1 15.8  9.1 15.8 15.8 15.8 15.8 15.8
[112,] -2.215071e-09  7.4  7.2   7.0  15.7 15.9  9.1 15.9 15.9 15.9 15.9 15.9
[113,] -1.862645e-09 16.1 15.8   9.2  16.1 16.1  9.2 16.1 16.1 16.1 16.1 16.1
[114,] -1.566292e-09  7.5  9.0   7.0  17.1 17.1  9.3 17.1 17.1 17.1 17.1 17.1
[115,] -1.317089e-09  7.5  9.3   9.4  16.0 15.9  9.4 15.9 15.9 15.9 15.9 15.9
[116,] -1.107535e-09  7.2  7.2   6.6  15.8 17.0  9.4 17.0 17.0 17.0 17.0 17.0
[117,] -9.313226e-10 16.1 15.8   9.5  16.1 16.1  9.5 16.1 16.1 16.1 16.1 16.1
[118,] -7.831458e-10  6.9  9.0   6.6  18.4 15.8  9.6 15.8 15.8 15.8 15.8 15.8
[119,] -6.585445e-10  6.9  9.3   9.7  15.9 16.0  9.7 16.0 16.0 16.0 16.0 16.0
[120,] -5.537677e-10  7.2  7.2   6.4  16.1 16.1  9.7 16.1 16.1 16.1 16.1 16.1
[121,] -4.656613e-10 16.1 15.8   9.8  16.1 16.1  9.8 16.1 16.1 16.1 16.1 16.1
[122,] -3.915729e-10  6.9  6.3   6.4  17.3 17.3  9.9 17.3 17.3 17.3 17.3 17.3
[123,] -3.292723e-10  6.9  9.3  10.0  15.7 16.7 10.0 16.7 16.7 16.7 16.7 16.7
[124,] -2.768839e-10  7.2  6.2   6.6  16.3 16.3 10.0 16.3 16.3 16.3 16.3 16.3
[125,] -2.328306e-10 16.1 15.8  10.1  16.1 16.1 10.1 16.1 16.1 16.1 16.1 16.1
[126,] -1.957865e-10  6.3  6.3   6.0  17.2 15.8 10.2 15.8 15.8 15.8 15.8 15.8
[127,] -1.646361e-10  6.3  9.3  10.3  16.1 15.8 10.3 15.8 15.8 15.8 15.8 15.8
[128,] -1.384419e-10  7.2  6.2   5.8  15.7 16.4 10.3 16.4 16.4 16.4 16.4 16.4
[129,] -1.164153e-10 16.1 15.8  10.4  16.1 16.1 10.4 16.1 16.1 16.1 16.1 16.1
[130,] -9.789323e-11  6.3  6.3   5.8  15.8 17.1 10.5 17.1 17.1 17.1 17.1 17.1
[131,] -8.231806e-11  6.3  5.7  10.6  16.0 15.9 10.6 15.9 15.9 15.9 15.9 15.9
[132,] -6.922096e-11  7.2  5.7   6.0  16.2 16.1 10.6 16.1 16.1 16.1 16.1 16.1
[133,] -5.820766e-11 16.1 15.8  10.7  16.1 16.1 10.7 16.1 16.1 16.1 16.1 16.1
[134,] -4.894661e-11  6.3  6.3   6.0  16.1 16.1 10.8 16.1 16.1 16.1 16.1 16.1
[135,] -4.115903e-11  5.7  5.7  10.9  16.0 16.0 10.9 16.0 16.0 16.0 16.0 16.0
[136,] -3.461048e-11  5.5  5.5   6.0  15.9 15.9 10.9 15.9 15.9 15.9 15.9 15.9
[137,] -2.910383e-11 16.1 15.8  11.0  16.1 16.1 11.0 16.1 16.1 16.1 16.1 16.1
[138,] -2.447331e-11  6.3  5.2   6.0  16.5 16.5 11.1 16.5 16.5 16.5 16.5 16.5
[139,] -2.057952e-11  5.7  5.2  11.2  15.5 16.0 11.2 16.0 16.0 16.0 16.0 16.0
[140,] -1.730524e-11  5.5  5.5   6.0  16.1 16.1 11.2 16.1 16.1 16.1 16.1 16.1
[141,] -1.455192e-11 16.1 15.8  11.3  16.1 16.1 11.3 16.1 16.1 16.1 16.1 16.1
[142,] -1.223665e-11  6.3  5.2   6.0  16.2 16.2 11.4 16.2 16.2 16.2 16.2 16.2
[143,] -1.028976e-11  5.7  5.2  11.5  15.9 16.1 11.5 16.1 16.1 16.1 16.1 16.1
[144,] -8.652621e-12  5.5  5.5   4.6  15.5 15.9 11.5 15.9 15.9 15.9 15.9 15.9
[145,] -7.275958e-12 16.1 15.8  11.6  16.1 16.1 11.6 16.1 16.1 16.1 16.1 16.1
[146,] -6.118327e-12  6.3  5.2   4.6  15.9 15.9 11.7 15.9 15.9 15.9 15.9 15.9
[147,] -5.144879e-12  5.7  5.2  11.8  15.7 16.6 11.8 16.6 16.6 16.6 16.6 16.6
[148,] -4.326310e-12  5.5  5.5   4.2  15.8 17.3 11.8 17.3 17.3 17.3 17.3 17.3
[149,] -3.637979e-12 16.1 15.8  11.9  16.1 16.1 11.9 16.1 16.1 16.1 16.1 16.1
[150,] -3.059163e-12  4.4  4.3   4.7  16.2 16.0 12.0 16.0 16.0 16.0 16.0 16.0
[151,] -2.572439e-12  4.4  4.2  12.1  16.1 15.8 12.1 15.8 15.8 15.8 15.8 15.8
[152,] -2.163155e-12  5.5  4.1   4.0  16.1 16.1 12.1 16.1 16.1 16.1 16.1 16.1
[153,] -1.818989e-12 16.1 15.8  12.2  16.1 16.1 12.2 16.1 16.1 16.1 16.1 16.1
[154,] -1.529582e-12  4.4  4.3   4.0  16.4 16.4 12.3 16.4 16.4 16.4 16.4 16.4
[155,] -1.286220e-12  4.4  4.2  12.4  15.9 15.9 12.4 15.9 15.9 15.9 15.9 15.9
[156,] -1.081578e-12  5.5  4.1   3.6  16.3 16.0 12.4 16.0 16.0 16.0 16.0 16.0
[157,] -9.094947e-13 16.1 15.8  12.5  16.1 16.1 12.5 16.1 16.1 16.1 16.1 16.1
[158,] -7.647908e-13  4.0  3.7   3.6  16.0 16.2 12.6 16.2 16.2 16.2 16.2 16.2
[159,] -6.431099e-13  3.9  3.7  12.7  16.9 16.9 12.7 16.9 16.9 16.9 16.9 16.9
[160,] -5.407888e-13  5.5  3.6   4.0  16.4 16.4 12.7 16.4 16.4 16.4 16.4 16.4
[161,] -4.547474e-13 16.1 15.8  12.8  16.1 16.1 12.8 16.1 16.1 16.1 16.1 16.1
[162,] -3.823954e-13  3.7  3.5   4.0  16.5 16.5 12.9 16.5 16.5 16.5 16.5 16.5
[163,] -3.215549e-13  3.7  3.7  13.0  15.8 15.8 13.0 15.8 15.8 15.8 15.8 15.8
[164,] -2.703944e-13  3.4  3.6   4.0  16.5 16.5 13.0 16.5 16.5 16.5 16.5 16.5
[165,] -2.273737e-13 16.1 15.8  13.1  16.1 16.1 13.1 16.1 16.1 16.1 16.1 16.1
[166,] -1.911977e-13  3.7  3.2   4.0  15.7 16.7 13.2 16.7 16.7 16.7 16.7 16.7
[167,] -1.607775e-13  3.7  3.7  13.3  17.3 17.3 13.3 17.3 17.3 17.3 17.3 17.3
[168,] -1.351972e-13  3.4  3.6   4.0  16.6 16.6 13.3 16.6 16.6 16.6 16.6 16.6
[169,] -1.136868e-13 16.1 15.8  13.4  16.1 16.1 13.4 16.1 16.1 16.1 16.1 16.1
[170,] -9.559885e-14  3.7  3.2   4.0  15.8 15.8 13.5 15.8 15.8 15.8 15.8 15.8
[171,] -8.038873e-14  3.7  2.7  13.6  15.8 15.8 13.6 15.8 15.8 15.8 15.8 15.8
[172,] -6.759860e-14  3.4  2.6   4.0  16.0 16.0 13.6 16.0 16.0 16.0 16.0 16.0
[173,] -5.684342e-14 16.1 15.8  13.7  16.1 16.1 13.7 16.1 16.1 16.1 16.1 16.1
[174,] -4.779943e-14  2.7  3.2   4.0  16.2 16.0 13.8 16.0 16.0 16.0 16.0 16.0
[175,] -4.019437e-14  3.7  2.6  13.9  15.7 17.0 13.9 17.0 17.0 17.0 17.0 17.0
[176,] -3.379930e-14  2.5  2.5   2.2  15.8 16.8 13.9 16.8 16.8 16.8 16.8 16.8
[177,] -2.842171e-14 16.1 15.8  14.0  16.1 16.1 14.0 16.1 16.1 16.1 16.1 16.1
[178,] -2.389971e-14  2.6  2.2   2.2  16.0 16.3 14.1 16.3 16.3 16.3 16.3 16.3
[179,] -2.009718e-14  3.7  2.6  14.2  16.3 16.3 14.2 16.3 16.3 16.3 16.3 16.3
[180,] -1.689965e-14  2.5  2.5   2.2  15.8 15.8 14.2 15.8 15.8 15.8 15.8 15.8
[181,] -1.421085e-14 16.1 15.8  14.3  16.1 16.1 14.3 16.1 16.1 16.1 16.1 16.1
[182,] -1.194986e-14  2.2  2.1   1.8  16.0 16.3 14.4 16.3 16.3 16.3 16.3 16.3
[183,] -1.004859e-14  2.0  1.8  14.5  15.8 16.2 14.5 16.2 16.2 16.2 16.2 16.2
[184,] -8.449825e-15  2.5  1.7   1.6  15.8 16.9 14.5 16.9 16.9 16.9 16.9 16.9
[185,] -7.105427e-15 16.1 15.8  14.6  16.1 16.1 14.6 16.1 16.1 16.1 16.1 16.1
[186,] -5.974928e-15  2.2  1.7   1.6  16.0 16.2 14.7 16.2 16.2 16.2 16.2 16.2
[187,] -5.024296e-15  1.9  1.7  14.7  15.7 15.7 14.8 15.7 15.7 15.7 15.7 15.7
[188,] -4.224912e-15  2.5  1.7   1.2  15.8 15.8 14.8 15.8 15.8 15.8 15.8 15.8
[189,] -3.552714e-15 16.1 15.8  14.9  16.1 16.1 14.9 16.1 16.1 16.1 16.1 16.1
[190,] -2.987464e-15  2.2  1.7   1.2  15.7 16.3 15.0 16.3 16.3 16.3 16.3 16.3
[191,] -2.512148e-15  1.5  1.7  15.0  16.1 15.9 15.1 15.9 15.9 15.9 15.9 15.9
[192,] -2.112456e-15  2.5  1.7   0.9  16.0 16.0 15.1 16.0 16.0 16.0 16.0 16.0
[193,] -1.776357e-15 16.1 15.8  15.2  16.1 16.1 15.2 16.1 16.1 16.1 16.1 16.1
[194,] -1.493732e-15  1.2  1.0   0.9  16.7 16.7 15.3 16.7 16.7 16.7 16.7 16.7
[195,] -1.256074e-15  1.3  1.7  15.3  16.0 16.0 15.5 16.0 16.0 16.0 16.0 16.0
[196,] -1.056228e-15  1.0  1.7   1.2  16.0 16.0 15.4 16.0 16.0 16.0 16.0 16.0
[197,] -8.881784e-16 16.1 16.1  15.5  16.1 16.1 15.5 16.1 16.1 16.1 16.1 16.1
[198,] -7.468660e-16  1.1  1.0   1.2  16.1 16.1 15.6 16.1 16.1 16.1 16.1 16.1
[199,] -6.280370e-16  0.9  0.6  15.5  15.9 15.9 15.9 16.0 16.0 16.0 16.0 16.0
[200,] -5.281140e-16  1.0  1.7   0.4  16.4 15.7 15.7 16.4 16.4 16.4 16.4 16.4
[201,] -4.440892e-16 16.1  0.4  15.8  16.1 15.8 15.8 16.1 16.1 16.1 16.1 16.1
[202,] -3.734330e-16  0.7  1.0   0.4  15.9 15.9 15.9 16.4 16.4 16.4 16.4 16.4
[203,] -3.140185e-16  0.9  0.6  15.6  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[204,] -2.640570e-16  0.5  0.3   0.0  16.3 16.0 16.0 16.0 16.0 16.0 16.0 16.0
[205,] -2.220446e-16 15.8  0.4   0.0  15.5 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[206,] -1.867165e-16  0.4  1.0   0.4  16.0 16.3 16.3 16.3 16.3 16.3 16.3 16.3
[207,] -1.570092e-16  0.3  0.6   0.0  16.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5
[208,] -1.320285e-16  0.5  0.1  -0.3  15.7 16.2 16.2 16.2 16.2 16.2 16.2 16.2
[209,] -1.110223e-16 16.4 -0.2   0.0  16.4 16.4 16.4 16.4 16.4 16.4 16.4 16.4
[210,] -9.335826e-17  0.4 -0.4  -0.3  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[211,] -7.850462e-17  0.0  0.0  -0.5  16.2 16.2 16.2 16.2 16.2 16.2 16.2 16.2
[212,] -6.601426e-17 -0.3  0.0  -0.7  16.4 16.4 16.4 16.4 16.4 16.4 16.4 16.4
[213,] -5.551115e-17  0.0  0.0   0.0  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[214,] -4.667913e-17  0.0  0.0   0.0  17.2 17.2 17.2 17.2 17.2 17.2 17.2 17.2
[215,] -3.925231e-17  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[216,] -3.300713e-17  0.0  0.0   0.0  16.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5
[217,] -2.775558e-17  0.0  0.0   0.0  17.0 17.0 17.0 17.0 17.0 17.0 17.0 17.0
[218,] -2.333956e-17  0.0  0.0   0.0  18.0 18.0 18.0 18.0 18.0 18.0 18.0 18.0
[219,] -1.962616e-17  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[220,] -1.650356e-17  0.0  0.0   0.0  16.6 16.6 16.6 16.6 16.6 16.6 16.6 16.6
[221,] -1.387779e-17  0.0  0.0   0.0  17.3 17.3 17.3 17.3 17.3 17.3 17.3 17.3
[222,] -1.166978e-17  0.0  0.0   0.0  17.3 17.3 17.3 17.3 17.3 17.3 17.3 17.3
[223,] -9.813078e-18  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[224,] -8.251782e-18  0.0  0.0   0.0  16.6 16.6 16.6 16.6 16.6 16.6 16.6 16.6
[225,] -6.938894e-18  0.0  0.0   0.0  17.6 17.6 17.6 17.6 17.6 17.6 17.6 17.6
[226,] -5.834891e-18  0.0  0.0   0.0  17.2 17.2 17.2 17.2 17.2 17.2 17.2 17.2
[227,] -4.906539e-18  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[228,] -4.125891e-18  0.0  0.0   0.0  16.6 16.6 16.6 16.6 16.6 16.6 16.6 16.6
[229,] -3.469447e-18  0.0  0.0   0.0  17.9 17.9 17.9 17.9 17.9 17.9 17.9 17.9
[230,] -2.917446e-18  0.0  0.0   0.0  17.1 17.1 17.1 17.1 17.1 17.1 17.1 17.1
[231,] -2.453269e-18  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[232,] -2.062946e-18  0.0  0.0   0.0  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[233,] -1.734723e-18  0.0  0.0   0.0  18.2 18.2 18.2 18.2 18.2 18.2 18.2 18.2
[234,]  0.000000e+00  NaN  NaN   NaN   NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN
[235,]  1.734723e-18  0.0  0.0   0.0  18.2 18.2 18.2 18.2 18.2 18.2 18.2 18.2
[236,]  2.062946e-18  0.0  0.0   0.0  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[237,]  2.453269e-18  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[238,]  2.917446e-18  0.0  0.0   0.0  17.0 17.0 17.0 17.0 17.0 17.0 17.0 17.0
[239,]  3.469447e-18  0.0  0.0   0.0  17.9 17.9 17.9 17.9 17.9 17.9 17.9 17.9
[240,]  4.125891e-18  0.0  0.0   0.0  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[241,]  4.906539e-18  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[242,]  5.834891e-18  0.0  0.0   0.0  17.0 17.0 17.0 17.0 17.0 17.0 17.0 17.0
[243,]  6.938894e-18  0.0  0.0   0.0  17.6 17.6 17.6 17.6 17.6 17.6 17.6 17.6
[244,]  8.251782e-18  0.0  0.0   0.0  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[245,]  9.813078e-18  0.0  0.0   0.0  16.1 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[246,]  1.166978e-17  0.0  0.0   0.0  16.9 16.9 16.9 16.9 16.9 16.9 16.9 16.9
[247,]  1.387779e-17  0.0  0.0   0.0  17.3 17.3 17.3 17.3 17.3 17.3 17.3 17.3
[248,]  1.650356e-17  0.0  0.0   0.0  16.8 16.8 16.8 16.8 16.8 16.8 16.8 16.8
[249,]  1.962616e-17  0.0  0.0   0.0  16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0
[250,]  2.333956e-17  0.0  0.0   0.0  16.8 16.8 16.8 16.8 16.8 16.8 16.8 16.8
[251,]  2.775558e-17  0.0  0.0   0.0  17.0 17.0 17.0 17.0 17.0 17.0 17.0 17.0
[252,]  3.300713e-17  0.0  0.0   0.0  17.0 17.0 17.0 17.0 17.0 17.0 17.0 17.0
[253,]  3.925231e-17  0.0  0.0   0.0  16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0
[254,]  4.667913e-17  0.0  0.0   0.0  16.6 16.6 16.6 16.6 16.6 16.6 16.6 16.6
[255,]  5.551115e-17  0.0  0.0   0.0  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[256,]  6.601426e-17  0.0  0.0   0.0  18.5 18.5 18.5 18.5 18.5 18.5 18.5 18.5
[257,]  7.850462e-17  0.0  0.0   0.0  16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0
[258,]  9.335826e-17  0.0 -0.4   0.0  16.4 16.4 16.4 16.4 16.4 16.4 16.4 16.4
[259,]  1.110223e-16  0.0 -0.2   0.0  16.4 16.4 16.4 16.4 16.4 16.4 16.4 16.4
[260,]  1.320285e-16 -0.3  0.1  -0.3  16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.7
[261,]  1.570092e-16  0.0  0.6   0.0  15.5 15.9 15.9 15.9 15.9 15.9 15.9 15.9
[262,]  1.867165e-16  0.4  1.0   0.4  15.6 16.1 16.1 16.1 16.1 16.1 16.1 16.1
[263,]  2.220446e-16 16.1  0.4   0.0  15.8 16.1 16.1 16.4 16.4 16.4 16.4 16.4
[264,]  2.640570e-16  0.5  0.3   0.0  16.0 16.2 16.2 16.0 16.0 16.0 16.0 16.0
[265,]  3.140185e-16  0.3  0.6   0.0  16.5 15.7 15.7 16.5 16.5 16.5 16.5 16.5
[266,]  3.734330e-16  0.4  1.0   0.4  15.9 15.9 15.9 16.6 16.6 16.6 16.6 16.6
[267,]  4.440892e-16 16.4  0.4  15.8  16.4 15.8 15.8 16.4 16.4 16.4 16.4 16.4
[268,]  5.281140e-16  0.5  1.7   0.5  17.6 15.8 15.8 17.6 17.6 17.6 17.6 17.6
[269,]  6.280370e-16  0.9  0.6  16.1  15.8 15.5 15.5 16.1 16.1 16.1 16.1 16.1
[270,]  7.468660e-16  0.7  1.0   0.5  15.7 16.0 15.6 16.0 16.0 16.0 16.0 16.0
[271,]  8.881784e-16 16.4 16.1  15.5  16.4 16.4 15.5 16.4 16.4 16.4 16.4 16.4
[272,]  1.056228e-15  1.0  1.7   1.2  15.9 16.8 15.5 16.8 16.8 16.8 16.8 16.8
[273,]  1.256074e-15  0.9  1.7  15.5  16.2 16.2 15.3 16.2 16.2 16.2 16.2 16.2
[274,]  1.493732e-15  1.1  1.0   1.2  15.9 16.4 15.3 16.4 16.4 16.4 16.4 16.4
[275,]  1.776357e-15 16.4 16.4  15.2  16.4 16.4 15.2 16.4 16.4 16.4 16.4 16.4
[276,]  2.112456e-15  1.0  1.7   1.2  16.0 16.3 15.2 16.3 16.3 16.3 16.3 16.3
[277,]  2.512148e-15  1.3  1.7  15.2  16.5 16.5 15.0 16.5 16.5 16.5 16.5 16.5
[278,]  2.987464e-15  1.2  1.7   1.6  15.4 16.2 15.0 16.2 16.2 16.2 16.2 16.2
[279,]  3.552714e-15 16.4 16.4  14.9  16.4 16.4 14.9 16.4 16.4 16.4 16.4 16.4
[280,]  4.224912e-15  2.5  1.7   1.2  15.5 16.6 14.9 16.6 16.6 16.6 16.6 16.6
[281,]  5.024296e-15  1.5  1.7   1.2  16.8 16.0 14.8 16.0 16.0 16.0 16.0 16.0
[282,]  5.974928e-15  2.2  1.7   1.6  16.4 16.4 14.7 16.4 16.4 16.4 16.4 16.4
[283,]  7.105427e-15 16.4 16.4  14.6  16.4 16.4 14.6 16.4 16.4 16.4 16.4 16.4
[284,]  8.449825e-15  2.5  1.7   1.6  15.9 16.5 14.6 16.5 16.5 16.5 16.5 16.5
[285,]  1.004859e-14  1.9  1.8  14.5  15.7 16.0 14.5 16.0 16.0 16.0 16.0 16.0
[286,]  1.194986e-14  2.2  2.1   1.8  16.2 16.2 14.4 16.2 16.2 16.2 16.2 16.2
[287,]  1.421085e-14 16.4 16.4  14.3  16.4 16.4 14.3 16.4 16.4 16.4 16.4 16.4
[288,]  1.689965e-14  2.5  2.5   2.2  15.9 16.4 14.3 16.4 16.4 16.4 16.4 16.4
[289,]  2.009718e-14  2.0  2.6   1.8  16.9 15.9 14.2 15.9 15.9 15.9 15.9 15.9
[290,]  2.389971e-14  2.2  2.2   2.3  15.7 16.5 14.1 16.5 16.5 16.5 16.5 16.5
[291,]  2.842171e-14 16.4 16.4  14.0  16.4 16.4 14.0 16.4 16.4 16.4 16.4 16.4
[292,]  3.379930e-14  2.5  2.5   2.2  15.7 16.0 13.9 16.0 16.0 16.0 16.0 16.0
[293,]  4.019437e-14  3.7  2.6  13.9  15.8 16.3 13.9 16.3 16.3 16.3 16.3 16.3
[294,]  4.779943e-14  2.6  3.2   4.0  15.6 16.1 13.8 16.1 16.1 16.1 16.1 16.1
[295,]  5.684342e-14 16.4 16.4  13.7  16.4 16.4 13.7 16.4 16.4 16.4 16.4 16.4
[296,]  6.759860e-14  2.5  2.6   4.0  16.0 16.0 13.6 16.0 16.0 16.0 16.0 16.0
[297,]  8.038873e-14  3.7  2.7  13.6  16.0 15.9 13.6 15.9 15.9 15.9 15.9 15.9
[298,]  9.559885e-14  2.7  3.2   2.6  15.8 17.6 13.5 17.6 17.6 17.6 17.6 17.6
[299,]  1.136868e-13 16.4 16.4  13.4  16.4 16.4 13.4 16.4 16.4 16.4 16.4 16.4
[300,]  1.351972e-13  3.4  3.6   4.0  15.9 16.8 13.3 16.8 16.8 16.8 16.8 16.8
[301,]  1.607775e-13  3.7  3.7  13.3  16.3 16.3 13.3 16.3 16.3 16.3 16.3 16.3
[302,]  1.911977e-13  3.7  3.2   4.0  17.4 17.4 13.2 17.4 17.4 17.4 17.4 17.4
[303,]  2.273737e-13 16.4 16.4  13.1  16.4 16.4 13.1 16.4 16.4 16.4 16.4 16.4
[304,]  2.703944e-13  3.4  3.6   4.0  15.8 16.9 13.0 16.9 16.9 16.9 16.9 16.9
[305,]  3.215549e-13  3.7  3.7  13.0  16.1 15.9 13.0 15.9 15.9 15.9 15.9 15.9
[306,]  3.823954e-13  3.7  3.5   4.0  16.8 16.8 12.9 16.8 16.8 16.8 16.8 16.8
[307,]  4.547474e-13 16.4 16.4  12.8  16.4 16.4 12.8 16.4 16.4 16.4 16.4 16.4
[308,]  5.407888e-13  3.4  3.6   4.0  17.3 17.3 12.7 17.3 17.3 17.3 17.3 17.3
[309,]  6.431099e-13  3.7  3.7  12.7  16.1 16.1 12.7 16.1 16.1 16.1 16.1 16.1
[310,]  7.647908e-13  3.7  3.7   4.0  15.9 16.4 12.6 16.4 16.4 16.4 16.4 16.4
[311,]  9.094947e-13 16.4 16.4  12.5  16.4 16.4 12.5 16.4 16.4 16.4 16.4 16.4
[312,]  1.081578e-12  5.5  4.1   3.6  15.8 17.0 12.4 17.0 17.0 17.0 17.0 17.0
[313,]  1.286220e-12  3.9  4.2   3.6  16.2 16.2 12.4 16.2 16.2 16.2 16.2 16.2
[314,]  1.529582e-12  4.0  4.3   4.2  16.0 16.2 12.3 16.2 16.2 16.2 16.2 16.2
[315,]  1.818989e-12 16.4 16.4  12.2  16.4 16.4 12.2 16.4 16.4 16.4 16.4 16.4
[316,]  2.163155e-12  5.5  4.1   4.0  15.9 15.9 12.1 15.9 15.9 15.9 15.9 15.9
[317,]  2.572439e-12  4.4  4.2  12.1  15.6 15.9 12.1 15.9 15.9 15.9 15.9 15.9
[318,]  3.059163e-12  4.4  4.3   4.7  16.0 16.3 12.0 16.3 16.3 16.3 16.3 16.3
[319,]  3.637979e-12 16.4 16.4  11.9  16.4 16.4 11.9 16.4 16.4 16.4 16.4 16.4
[320,]  4.326310e-12  5.5  5.5   4.2  16.0 16.3 11.8 16.3 16.3 16.3 16.3 16.3
[321,]  5.144879e-12  4.4  5.2   4.2  16.6 16.1 11.8 16.1 16.1 16.1 16.1 16.1
[322,]  6.118327e-12  4.4  5.2   4.7  16.0 16.0 11.7 16.0 16.0 16.0 16.0 16.0
[323,]  7.275958e-12 16.4 16.4  11.6  16.4 16.4 11.6 16.4 16.4 16.4 16.4 16.4
[324,]  8.652621e-12  5.5  5.5   4.6  16.1 16.1 11.5 16.1 16.1 16.1 16.1 16.1
[325,]  1.028976e-11  5.7  5.2  11.5  15.9 16.1 11.5 16.1 16.1 16.1 16.1 16.1
[326,]  1.223665e-11  6.3  5.2   6.0  16.3 16.0 11.4 16.0 16.0 16.0 16.0 16.0
[327,]  1.455192e-11 16.4 16.4  11.3  16.4 16.4 11.3 16.4 16.4 16.4 16.4 16.4
[328,]  1.730524e-11  5.5  5.5   6.0  16.5 16.5 11.2 16.5 16.5 16.5 16.5 16.5
[329,]  2.057952e-11  5.7  5.2  11.2  15.8 16.1 11.2 16.1 16.1 16.1 16.1 16.1
[330,]  2.447331e-11  6.3  5.2   6.0  16.3 16.3 11.1 16.3 16.3 16.3 16.3 16.3
[331,]  2.910383e-11 16.4 16.4  11.0  16.4 16.4 11.0 16.4 16.4 16.4 16.4 16.4
[332,]  3.461048e-11  5.5  5.5   6.0  16.1 16.1 10.9 16.1 16.1 16.1 16.1 16.1
[333,]  4.115903e-11  5.7  5.7  10.9  16.4 16.2 10.9 16.2 16.2 16.2 16.2 16.2
[334,]  4.894661e-11  6.3  6.3   6.0  16.2 16.1 10.8 16.1 16.1 16.1 16.1 16.1
[335,]  5.820766e-11 16.4 16.4  10.7  16.4 16.4 10.7 16.4 16.4 16.4 16.4 16.4
[336,]  6.922096e-11  5.5  5.7   6.0  16.6 16.6 10.6 16.6 16.6 16.6 16.6 16.6
[337,]  8.231806e-11  5.7  5.7   5.4  16.3 16.3 10.6 16.3 16.3 16.3 16.3 16.3
[338,]  9.789323e-11  6.3  6.3   5.8  17.0 17.0 10.5 17.0 17.0 17.0 17.0 17.0
[339,]  1.164153e-10 16.4 16.4  10.4  16.4 16.4 10.4 16.4 16.4 16.4 16.4 16.4
[340,]  1.384419e-10  7.2  6.2   5.8  16.1 16.1 10.3 16.1 16.1 16.1 16.1 16.1
[341,]  1.646361e-10  6.3  9.3  10.3  15.6 15.9 10.3 15.9 15.9 15.9 15.9 15.9
[342,]  1.957865e-10  6.3  6.3   6.0  17.0 17.0 10.2 17.0 17.0 17.0 17.0 17.0
[343,]  2.328306e-10 16.4 16.4  10.1  16.4 16.4 10.1 16.4 16.4 16.4 16.4 16.4
[344,]  2.768839e-10  7.2  6.2   6.6  15.8 17.0 10.0 17.0 17.0 17.0 17.0 17.0
[345,]  3.292723e-10  6.3  9.3   6.0  16.5 16.1 10.0 16.1 16.1 16.1 16.1 16.1
[346,]  3.915729e-10  6.3  6.3   6.4  16.9 16.9  9.9 16.9 16.9 16.9 16.9 16.9
[347,]  4.656613e-10 16.4 16.4   9.8  16.4 16.4  9.8 16.4 16.4 16.4 16.4 16.4
[348,]  5.537677e-10  7.2  7.2   6.4  16.4 16.4  9.7 16.4 16.4 16.4 16.4 16.4
[349,]  6.585445e-10  6.9  9.3   9.7  15.8 16.2  9.7 16.2 16.2 16.2 16.2 16.2
[350,]  7.831458e-10  6.9  9.0   6.6  16.8 16.8  9.6 16.8 16.8 16.8 16.8 16.8
[351,]  9.313226e-10 16.4 16.4   9.5  16.4 16.4  9.5 16.4 16.4 16.4 16.4 16.4
[352,]  1.107535e-09  7.2  7.2   6.6  16.0 16.3  9.4 16.3 16.3 16.3 16.3 16.3
[353,]  1.317089e-09  6.9  9.3   6.6  16.3 16.3  9.4 16.3 16.3 16.3 16.3 16.3
[354,]  1.566292e-09  6.9  9.0   7.0  15.5 16.6  9.3 16.6 16.6 16.6 16.6 16.6
[355,]  1.862645e-09 16.4 16.4   9.2  16.4 16.4  9.2 16.4 16.4 16.4 16.4 16.4
[356,]  2.215071e-09  7.2  7.2   7.0  15.4 16.1  9.1 16.1 16.1 16.1 16.1 16.1
[357,]  2.634178e-09  7.5  9.3   9.1  15.6 15.9  9.1 15.9 15.9 15.9 15.9 15.9
[358,]  3.132583e-09  7.5  9.0   7.2  15.7 16.4  9.0 16.4 16.4 16.4 16.4 16.4
[359,]  3.725290e-09 16.4 16.4   8.9  16.4 16.4  8.9 16.4 16.4 16.4 16.4 16.4
[360,]  4.430142e-09  7.4  7.8   7.2  15.8 17.2  8.8 17.2 17.2 17.2 17.2 17.2
[361,]  5.268356e-09  7.5  9.3   7.2  16.4 16.1  8.8 16.1 16.1 16.1 16.1 16.1
[362,]  6.265167e-09  7.5  9.0   7.6  15.6 16.2  8.7 16.2 16.2 16.2 16.2 16.2
[363,]  7.450581e-09 16.6 16.6   8.6  16.6 16.6  8.6 16.6 16.6 16.6 16.6 16.6
[364,]  8.860283e-09  7.9  7.8   7.8  15.7 16.6  8.5 16.6 16.6 16.6 16.6 16.6
[365,]  1.053671e-08  8.1  9.3   8.5  15.6 16.3  8.5 16.3 16.3 16.3 16.3 16.3
[366,]  1.253033e-08  8.2  9.0   8.1  15.9 16.4  8.4 16.4 16.4 16.4 16.4 16.4
[367,]  1.490116e-08 16.1 16.1   8.3  15.8 16.1  8.3 16.1 16.4 16.4 16.4 16.4
[368,]  1.772057e-08  7.9  8.4   8.0  16.3 16.0  8.2 16.0 16.3 16.3 16.3 16.3
[369,]  2.107342e-08  8.1  9.3   8.2  16.0 16.8  8.2 16.8 16.0 16.0 16.0 16.0
[370,]  2.506067e-08  8.2  9.0   8.1  16.9 15.8  8.1 15.8 16.9 16.9 16.9 16.9
[371,]  2.980232e-08 23.6 16.0   8.0  23.6 16.0  8.0 16.0 23.6 23.6 23.6 23.6
[372,]  3.544113e-08  8.9  8.4   8.3  15.8 15.8  7.9 15.8 15.8 15.8 15.8 15.8
[373,]  4.214685e-08  8.6  9.3   9.1  15.5 16.2  7.9 15.8 16.2 16.2 16.2 16.2
[374,]  5.012133e-08  8.5  9.0   8.3  16.5 15.9  7.8 15.5 15.9 15.9 15.9 15.9
[375,]  5.960464e-08 16.4 16.4   8.3  16.4 16.4  7.7 15.2 16.4 16.4 16.4 16.4
[376,]  7.088227e-08  8.9  8.9   8.9  15.7 16.3  7.6 15.1 16.3 16.3 16.3 16.3
[377,]  8.429370e-08  8.6  9.3   8.8  16.0 15.9  7.6 15.0 15.9 15.9 15.9 15.9
[378,]  1.002427e-07  8.8  9.0   8.7  16.5 16.5  7.5 14.8 16.5 16.5 16.5 16.5
[379,]  1.192093e-07 21.8 21.8   8.6  21.8 21.8  7.4 14.6 21.8 21.8 21.8 21.8
[380,]  1.417645e-07  8.9  8.9   8.8  15.7 16.4  7.3 14.5 16.4 16.4 16.4 16.4
[381,]  1.685874e-07 10.8  9.3   8.8  15.5 15.9  7.3 14.3 15.9 15.9 15.9 15.9
[382,]  2.004853e-07  9.2  9.2   9.5  15.3 17.5  7.2 14.2 17.5 17.5 17.5 17.5
[383,]  2.384186e-07 16.4 16.4   8.9  16.4 16.4  7.1 14.0 16.4 16.4 16.4 16.4
[384,]  2.835291e-07  9.5 10.4   9.0  15.8 18.6  7.0 13.9 18.6 18.6 18.6 18.6
[385,]  3.371748e-07 10.8  9.3   9.5  16.0 15.9  6.9 13.7 15.9 15.9 15.9 15.9
[386,]  4.009707e-07  9.3  9.7   9.2  15.6 16.2  6.9 13.6 16.2 16.2 16.2 16.2
[387,]  4.768372e-07 20.0 20.0   9.2  20.0 20.0  6.8 13.4 20.0 20.0 20.0 20.0
[388,]  5.670581e-07  9.5 10.4  10.6  16.1 16.1  6.7 13.3 16.1 16.1 16.1 16.1
[389,]  6.743496e-07 10.8 10.8   9.9  16.0 15.9  6.6 13.1 15.9 15.9 15.9 15.9
[390,]  8.019413e-07 10.0  9.7   9.6  16.4 15.9  6.6 13.0 15.9 15.9 15.9 15.9
[391,]  9.536743e-07 16.4 16.4   9.5  16.4 16.4  6.5 12.8 16.4 16.4 16.4 16.4
[392,]  1.134116e-06 10.4 10.4  10.4  16.2 16.0  6.4 12.7 16.0 16.0 16.0 16.0
[393,]  1.348699e-06 10.8 10.8  10.5  17.1 15.9  6.3 12.5 15.9 15.9 15.9 15.9
[394,]  1.603883e-06 10.0 10.7  10.2  16.7 16.7  6.3 12.4 16.7 16.7 16.7 16.7
[395,]  1.907349e-06 18.2 18.2   9.8  18.2 18.2  6.2 12.2 18.2 18.2 18.2 18.2
[396,]  2.268233e-06 10.4 10.4  10.0  16.3 16.3  6.1 12.1 16.3 16.3 16.3 16.3
[397,]  2.697398e-06 10.8 10.8  10.3  15.9 15.9  6.0 11.9 15.9 15.9 15.9 15.9
[398,]  3.207765e-06 10.3 10.7  10.3  15.9 16.8  6.0 11.8 16.8 16.8 16.8 16.8
[399,]  3.814697e-06 16.4 16.4  10.1  16.4 16.4  5.9 11.6 16.4 16.4 16.4 16.4
[400,]  4.536465e-06 10.4 10.4  10.0  15.5 16.6  5.8 11.5 16.6 16.6 16.6 16.6
[401,]  5.394797e-06 10.8 10.8  10.3  15.6 15.9  5.7 11.3 15.9 15.9 15.9 15.9
[402,]  6.415531e-06 10.7 10.7  10.9  15.6 16.1  5.7 11.2 16.1 16.1 16.1 16.1
[403,]  7.629395e-06 16.4 16.4  10.5  16.4 16.4  5.6 11.0 16.4 16.4 16.4 16.4
[404,]  9.072930e-06 11.2 11.5  10.7  15.5 16.7  5.5 10.9 16.7 16.7 16.7 16.7
[405,]  1.078959e-05 10.8 10.8  10.5  17.6 15.7  5.4 10.7 15.7 16.0 16.0 16.0
[406,]  1.283106e-05 10.8 11.2  10.7  16.0 16.0  5.4 10.6 16.0 16.0 16.0 16.0
[407,]  1.525879e-05 16.2 16.2  11.0  16.2 16.3  5.3 10.4 15.4 16.3 16.3 16.3
[408,]  1.814586e-05 11.2 11.5  11.2  16.0 16.2  5.2 10.3 15.2 16.2 16.2 16.2
[409,]  2.157919e-05 11.3 12.2  11.7  16.1 16.1  5.1 10.1 15.0 16.1 16.1 16.1
[410,]  2.566212e-05 11.5 11.2  11.9  17.2 17.2  5.1 10.0 14.8 17.2 17.2 17.2
[411,]  3.051758e-05 16.4 16.4  14.5  16.2 16.4  5.0  9.8 14.5 16.4 16.4 16.4
[412,]  3.629172e-05 11.3 11.5  11.8  16.1 16.1  4.9  9.7 14.3 16.1 16.1 16.1
[413,]  4.315837e-05 11.3 12.2  11.2  16.3 16.3  4.8  9.5 14.1 16.3 16.3 16.3
[414,]  5.132424e-05 11.5 12.3  11.2  15.8 16.7  4.8  9.4 13.9 16.7 16.7 16.7
[415,]  6.103516e-05 16.9 16.9  11.6  16.9 16.9  4.7  9.2 13.6 16.9 16.9 16.9
[416,]  7.258344e-05 12.1 11.7  11.6  15.7 16.6  4.6  9.1 13.4 16.6 16.6 16.6
[417,]  8.631675e-05 12.5 12.2  12.3  16.1 16.5  4.5  8.9 13.2 16.5 16.5 16.5
[418,]  1.026485e-04 11.9 12.3  12.5  16.1 16.2  4.5  8.8 13.0 16.2 16.2 16.2
[419,]  1.220703e-04 16.5 16.5  12.7  16.5 16.5  4.4  8.6 12.7 16.5 16.5 16.5
[420,]  1.451669e-04 12.1 12.4  12.2  17.0 17.0  4.3  8.5 12.5 17.0 17.0 17.0
[421,]  1.726335e-04 12.5 12.2  12.0  16.3 16.2  4.2  8.3 12.3 16.2 16.2 16.2
[422,]  2.052970e-04 12.1 12.3  12.7  15.8 15.8  4.2  8.2 12.1 15.8 17.6 17.6
[423,]  2.441406e-04 16.4 15.8  12.6  16.4 16.4  4.1  8.0 11.8 15.5 16.4 16.4
[424,]  2.903338e-04 12.2 12.4  13.0  15.8 16.8  4.0  7.9 11.6 15.3 16.8 16.8
[425,]  3.452670e-04 12.5 12.5  12.2  15.7 15.9  3.9  7.7 11.4 15.1 15.9 15.9
[426,]  4.105940e-04 12.6 12.4  13.0  15.6 16.1  3.9  7.6 11.2 14.7 16.1 16.1
[427,]  4.882812e-04 16.2 16.2  12.7  16.2 16.3  3.8  7.4 10.9 14.4 16.3 16.3
[428,]  5.806675e-04 13.1 12.6  12.6  15.6 16.1  3.7  7.3 10.7 14.1 16.1 16.1
[429,]  6.905340e-04 12.5 12.8  12.2  16.4 16.4  3.6  7.1 10.5 13.8 16.4 16.4
[430,]  8.211879e-04 12.6 13.5  12.3  15.7 16.7  3.6  6.9 10.3 13.5 16.7 16.7
[431,]  9.765625e-04 16.4 16.4  16.4  16.4 16.4  3.5  6.8 10.0 13.2 16.4 16.4
[432,]  1.161335e-03 13.1 13.2  12.8  16.3 16.0  3.4  6.6  9.8 12.9 16.0 16.3
[433,]  1.381068e-03 13.8 13.1  13.6  15.8 16.1  3.3  6.5  9.6 12.6 15.5 16.1
[434,]  1.642376e-03 13.7 13.5  13.1  15.7 16.0  3.3  6.3  9.4 12.3 15.2 16.0
[435,]  1.953125e-03 16.2 16.3  13.0  16.2 16.3  3.2  6.2  9.1 12.0 14.9 16.3
[436,]  2.322670e-03 13.1 13.2  12.8  15.4 16.1  3.1  6.0  8.9 11.7 14.5 16.1
[437,]  2.762136e-03 13.8 13.3  13.3  16.0 15.9  3.0  5.9  8.7 11.4 14.1 15.9
[438,]  3.284752e-03 13.7 13.5  13.5  15.7 16.3  3.0  5.7  8.5 11.1 13.7 16.3
[439,]  3.906250e-03 16.1 16.4  14.6  16.1 16.1  2.9  5.6  8.2 10.8 13.4 16.1
[440,]  4.645340e-03 14.1 13.9  14.2  16.3 16.3  2.8  5.4  8.0 10.5 13.0 15.4
[441,]  5.524272e-03 13.8 13.8  13.5  15.7 16.4  2.7  5.3  7.8 10.2 12.6 15.0
[442,]  6.569503e-03 13.7 13.7  13.8  15.4 16.0  2.7  5.1  7.5  9.9 12.2 14.6
[443,]  7.812500e-03 16.7 16.7  14.8  16.7 16.0  2.6  5.0  7.3  9.6 11.9 14.1
[444,]  9.290681e-03 14.1 14.0  14.0  15.5 15.9  2.5  4.8  7.1  9.3 11.5 13.6
[445,]  1.104854e-02 13.8 13.8  13.7  15.8 16.2  2.4  4.7  6.9  9.0 11.1 13.2
[446,]  1.313901e-02 13.9 14.3  15.6  16.1 16.1  2.4  4.5  6.6  8.7 10.7 12.7
[447,]  1.562500e-02 16.3 15.8  14.0  16.2 16.3  2.3  4.4  6.4  8.4 10.4 12.3
[448,]  1.858136e-02 14.1 14.1  15.1  16.3 15.9  2.2  4.2  6.2  8.1 10.0 11.8
[449,]  2.209709e-02 14.4 15.6  15.0  16.2 16.2  2.1  4.1  6.0  7.8  9.6 11.4
[450,]  2.627801e-02 14.3 14.3  14.0  15.9 15.9  2.1  3.9  5.7  7.5  9.2 10.9
[451,]  3.125000e-02 15.9 16.0  14.7  16.0 16.8  2.0  3.8  5.5  7.2  8.9 10.5
[452,]  3.716272e-02 14.4 14.8  14.8  15.7 15.9  1.9  3.6  5.3  6.9  8.5 10.0
[453,]  4.419417e-02 14.4 17.1  14.4  17.1 16.0  1.8  3.5  5.1  6.6  8.1  9.6
[454,]  5.255603e-02 14.5 14.8  15.6  16.0 16.0  1.8  3.3  4.8  6.3  7.7  9.1
[455,]  6.250000e-02 15.9 16.0  14.5  16.0 17.2  1.7  3.2  4.6  6.0  7.4  8.7
[456,]  7.432544e-02 14.8 14.8  14.8  15.9 15.9  1.6  3.0  4.4  5.7  7.0  8.2
[457,]  8.838835e-02 15.0 16.3  15.2  15.8 15.8  1.5  2.9  4.2  5.4  6.6  7.8
[458,]  1.051121e-01 15.3 14.7  14.5  15.8 15.8  1.5  2.7  3.9  5.1  6.2  7.3
[459,]  1.250000e-01 16.3 15.5  14.9  16.2 16.2  1.4  2.6  3.7  4.8  5.9  6.9
[460,]  1.486509e-01 15.1 15.2  15.4  16.3 16.3  1.3  2.5  3.5  4.5  5.5  6.4
[461,]  1.767767e-01 15.0 16.3  15.4  15.8 15.8  1.2  2.3  3.3  4.2  5.1  6.0
[462,]  2.102241e-01 15.2 16.5  15.2  15.5 15.5  1.2  2.2  3.1  3.9  4.7  5.5
[463,]  2.500000e-01 14.7 14.6  16.1  15.8 15.8  1.1  2.0  2.8  3.6  4.4  5.1
[464,]  2.973018e-01 14.8 14.8  15.0  15.9 15.9  1.0  1.9  2.6  3.3  4.0  4.7
[465,]  3.535534e-01 14.7 15.4  16.3  16.3 16.3  1.0  1.7  2.4  3.0  3.6  4.2
[466,]  4.204482e-01 15.1 15.7  15.3  17.0 17.0  0.9  1.6  2.2  2.7  3.3  3.8
[467,]  5.000000e-01 15.0 15.2  16.4  16.4 16.4  0.8  1.4  2.0  2.4  2.9  3.3
        k=7  k=8  k=9 k=10 k=11 k=12
  [1,]  3.5  3.9  4.3  4.7  5.0  5.4
  [2,]  4.1  4.6  5.0  5.5  5.9  6.3
  [3,]  4.6  5.2  5.7  6.2  6.8  7.3
  [4,]  5.2  5.8  6.4  7.0  7.6  8.2
  [5,]  5.7  6.4  7.1  7.8  8.4  9.1
  [6,]  6.2  7.0  7.8  8.5  9.3 10.0
  [7,]  6.8  7.6  8.5  9.3 10.1 10.9
  [8,]  7.3  8.2  9.2 10.1 11.0 11.9
  [9,]  7.9  8.8  9.8 10.8 11.8 12.8
 [10,]  8.4  9.5 10.5 11.6 12.6 13.7
 [11,]  8.9 10.1 11.2 12.3 13.5 14.6
 [12,]  9.4 10.7 11.9 13.1 14.3 15.3
 [13,] 10.0 11.3 12.6 13.8 15.2 17.6
 [14,] 10.5 11.9 13.2 14.6 16.3 16.0
 [15,] 11.0 12.5 13.9 15.3 16.5 15.7
 [16,] 11.6 13.1 14.6 15.7 16.1 16.1
 [17,] 12.1 13.7 15.2 16.5 16.5 16.5
 [18,] 12.6 14.3 17.1 17.1 17.1 17.1
 [19,] 13.1 14.9 15.8 15.8 15.8 15.8
 [20,] 13.7 15.5 16.6 16.6 16.6 16.6
 [21,] 14.2 15.9 16.1 16.1 16.1 16.1
 [22,] 14.7 15.8 15.8 15.8 15.8 15.8
 [23,] 15.4 16.7 16.7 16.7 16.7 16.7
 [24,] 15.9 15.9 15.9 15.9 15.9 15.9
 [25,] 15.9 16.0 16.0 16.0 16.0 16.0
 [26,] 16.0 16.0 16.0 16.0 16.0 16.0
 [27,] 15.8 15.8 15.8 15.8 15.8 15.8
 [28,] 16.2 16.2 16.2 16.2 16.2 16.2
 [29,] 16.2 16.2 16.2 16.2 16.2 16.2
 [30,] 15.9 15.9 15.9 15.9 15.9 15.9
 [31,] 16.1 16.1 16.1 16.1 16.1 16.1
 [32,] 16.4 16.4 16.4 16.4 16.4 16.4
 [33,] 16.2 16.2 16.2 16.2 16.2 16.2
 [34,] 16.0 16.0 16.0 16.0 16.0 16.0
 [35,] 15.8 15.8 15.8 15.8 15.8 15.8
 [36,] 16.0 16.0 16.0 16.0 16.0 16.0
 [37,] 16.1 16.1 16.1 16.1 16.1 16.1
 [38,] 16.4 16.4 16.4 16.4 16.4 16.4
 [39,] 16.6 16.6 16.6 16.6 16.6 16.6
 [40,] 15.8 15.8 15.8 15.8 15.8 15.8
 [41,] 16.3 16.3 16.3 16.3 16.3 16.3
 [42,] 16.6 16.6 16.6 16.6 16.6 16.6
 [43,] 16.0 16.0 16.0 16.0 16.0 16.0
 [44,] 16.9 16.9 16.9 16.9 16.9 16.9
 [45,] 16.1 16.1 16.1 16.1 16.1 16.1
 [46,] 15.9 15.9 15.9 15.9 15.9 15.9
 [47,] 15.8 15.8 15.8 15.8 15.8 15.8
 [48,] 16.4 16.4 16.4 16.4 16.4 16.4
 [49,] 16.1 16.1 16.1 16.1 16.1 16.1
 [50,] 16.4 16.4 16.4 16.4 16.4 16.4
 [51,] 16.0 16.0 16.0 16.0 16.0 16.0
 [52,] 15.9 15.9 15.9 15.9 15.9 15.9
 [53,] 16.0 16.0 16.0 16.0 16.0 16.0
 [54,] 16.3 16.3 16.3 16.3 16.3 16.3
 [55,] 16.1 16.1 16.1 16.1 16.1 16.1
 [56,] 16.1 16.1 16.1 16.1 16.1 16.1
 [57,] 16.5 16.5 16.5 16.5 16.5 16.5
 [58,] 16.5 16.5 16.5 16.5 16.5 16.5
 [59,] 15.8 15.8 15.8 15.8 15.8 15.8
 [60,] 16.1 16.1 16.1 16.1 16.1 16.1
 [61,] 16.1 16.1 16.1 16.1 16.1 16.1
 [62,] 16.7 16.7 16.7 16.7 16.7 16.7
 [63,] 15.9 15.9 15.9 15.9 15.9 15.9
 [64,] 16.9 16.9 16.9 16.9 16.9 16.9
 [65,] 16.0 16.0 16.0 16.0 16.0 16.0
 [66,] 16.4 16.4 16.4 16.4 16.4 16.4
 [67,] 17.0 17.0 17.0 17.0 17.0 17.0
 [68,] 15.8 15.8 15.8 15.8 15.8 15.8
 [69,] 17.3 17.3 17.3 17.3 17.3 17.3
 [70,] 16.8 16.8 16.8 16.8 16.8 16.8
 [71,] 16.8 16.8 16.8 16.8 16.8 16.8
 [72,] 15.7 15.7 15.7 15.7 15.7 15.7
 [73,] 16.1 16.1 16.1 16.1 16.1 16.1
 [74,] 16.0 16.0 16.0 16.0 16.0 16.0
 [75,] 16.8 16.8 16.8 16.8 16.8 16.8
 [76,] 16.0 16.0 16.0 16.0 16.0 16.0
 [77,] 19.1 19.1 19.1 19.1 19.1 19.1
 [78,] 15.8 15.8 15.8 15.8 15.8 15.8
 [79,] 16.9 16.9 16.9 16.9 16.9 16.9
 [80,] 16.0 16.0 16.0 16.0 16.0 16.0
 [81,] 16.1 16.1 16.1 16.1 16.1 16.1
 [82,] 16.5 16.5 16.5 16.5 16.5 16.5
 [83,] 16.9 16.9 16.9 16.9 16.9 16.9
 [84,] 17.1 17.1 17.1 17.1 17.1 17.1
 [85,] 20.9 20.9 20.9 20.9 20.9 20.9
 [86,] 16.5 16.5 16.5 16.5 16.5 16.5
 [87,] 16.9 16.9 16.9 16.9 16.9 16.9
 [88,] 16.3 16.3 16.3 16.3 16.3 16.3
 [89,] 16.1 16.1 16.1 16.1 16.1 16.1
 [90,] 16.0 16.0 16.0 16.0 16.0 16.0
 [91,] 15.9 15.9 15.9 15.9 15.9 15.9
 [92,] 16.0 16.0 16.0 16.0 16.0 16.0
 [93,] 22.7 22.7 22.7 22.7 22.7 22.7
 [94,] 15.8 15.8 15.8 15.8 15.8 15.8
 [95,] 16.2 16.2 16.2 16.2 16.2 16.2
 [96,] 17.3 17.3 17.3 17.3 17.3 17.3
 [97,] 16.1 16.1 16.1 16.1 16.1 16.1
 [98,] 16.3 16.3 16.3 16.3 16.3 16.3
 [99,] 16.4 16.4 16.4 16.4 16.4 16.4
[100,] 16.4 16.4 16.4 16.4 16.4 16.4
[101,] 16.0 16.0 16.0 16.0 16.0 16.0
[102,] 15.8 15.8 15.8 15.8 15.8 15.8
[103,] 16.1 16.1 16.1 16.1 16.1 16.1
[104,] 16.0 16.0 16.0 16.0 16.0 16.0
[105,] 16.2 16.2 16.2 16.2 16.2 16.2
[106,] 16.2 16.2 16.2 16.2 16.2 16.2
[107,] 16.6 16.6 16.6 16.6 16.6 16.6
[108,] 16.3 16.3 16.3 16.3 16.3 16.3
[109,] 16.1 16.1 16.1 16.1 16.1 16.1
[110,] 15.9 15.9 15.9 15.9 15.9 15.9
[111,] 15.8 15.8 15.8 15.8 15.8 15.8
[112,] 15.9 15.9 15.9 15.9 15.9 15.9
[113,] 16.1 16.1 16.1 16.1 16.1 16.1
[114,] 17.1 17.1 17.1 17.1 17.1 17.1
[115,] 15.9 15.9 15.9 15.9 15.9 15.9
[116,] 17.0 17.0 17.0 17.0 17.0 17.0
[117,] 16.1 16.1 16.1 16.1 16.1 16.1
[118,] 15.8 15.8 15.8 15.8 15.8 15.8
[119,] 16.0 16.0 16.0 16.0 16.0 16.0
[120,] 16.1 16.1 16.1 16.1 16.1 16.1
[121,] 16.1 16.1 16.1 16.1 16.1 16.1
[122,] 17.3 17.3 17.3 17.3 17.3 17.3
[123,] 16.7 16.7 16.7 16.7 16.7 16.7
[124,] 16.3 16.3 16.3 16.3 16.3 16.3
[125,] 16.1 16.1 16.1 16.1 16.1 16.1
[126,] 15.8 15.8 15.8 15.8 15.8 15.8
[127,] 15.8 15.8 15.8 15.8 15.8 15.8
[128,] 16.4 16.4 16.4 16.4 16.4 16.4
[129,] 16.1 16.1 16.1 16.1 16.1 16.1
[130,] 17.1 17.1 17.1 17.1 17.1 17.1
[131,] 15.9 15.9 15.9 15.9 15.9 15.9
[132,] 16.1 16.1 16.1 16.1 16.1 16.1
[133,] 16.1 16.1 16.1 16.1 16.1 16.1
[134,] 16.1 16.1 16.1 16.1 16.1 16.1
[135,] 16.0 16.0 16.0 16.0 16.0 16.0
[136,] 15.9 15.9 15.9 15.9 15.9 15.9
[137,] 16.1 16.1 16.1 16.1 16.1 16.1
[138,] 16.5 16.5 16.5 16.5 16.5 16.5
[139,] 16.0 16.0 16.0 16.0 16.0 16.0
[140,] 16.1 16.1 16.1 16.1 16.1 16.1
[141,] 16.1 16.1 16.1 16.1 16.1 16.1
[142,] 16.2 16.2 16.2 16.2 16.2 16.2
[143,] 16.1 16.1 16.1 16.1 16.1 16.1
[144,] 15.9 15.9 15.9 15.9 15.9 15.9
[145,] 16.1 16.1 16.1 16.1 16.1 16.1
[146,] 15.9 15.9 15.9 15.9 15.9 15.9
[147,] 16.6 16.6 16.6 16.6 16.6 16.6
[148,] 17.3 17.3 17.3 17.3 17.3 17.3
[149,] 16.1 16.1 16.1 16.1 16.1 16.1
[150,] 16.0 16.0 16.0 16.0 16.0 16.0
[151,] 15.8 15.8 15.8 15.8 15.8 15.8
[152,] 16.1 16.1 16.1 16.1 16.1 16.1
[153,] 16.1 16.1 16.1 16.1 16.1 16.1
[154,] 16.4 16.4 16.4 16.4 16.4 16.4
[155,] 15.9 15.9 15.9 15.9 15.9 15.9
[156,] 16.0 16.0 16.0 16.0 16.0 16.0
[157,] 16.1 16.1 16.1 16.1 16.1 16.1
[158,] 16.2 16.2 16.2 16.2 16.2 16.2
[159,] 16.9 16.9 16.9 16.9 16.9 16.9
[160,] 16.4 16.4 16.4 16.4 16.4 16.4
[161,] 16.1 16.1 16.1 16.1 16.1 16.1
[162,] 16.5 16.5 16.5 16.5 16.5 16.5
[163,] 15.8 15.8 15.8 15.8 15.8 15.8
[164,] 16.5 16.5 16.5 16.5 16.5 16.5
[165,] 16.1 16.1 16.1 16.1 16.1 16.1
[166,] 16.7 16.7 16.7 16.7 16.7 16.7
[167,] 17.3 17.3 17.3 17.3 17.3 17.3
[168,] 16.6 16.6 16.6 16.6 16.6 16.6
[169,] 16.1 16.1 16.1 16.1 16.1 16.1
[170,] 15.8 15.8 15.8 15.8 15.8 15.8
[171,] 15.8 15.8 15.8 15.8 15.8 15.8
[172,] 16.0 16.0 16.0 16.0 16.0 16.0
[173,] 16.1 16.1 16.1 16.1 16.1 16.1
[174,] 16.0 16.0 16.0 16.0 16.0 16.0
[175,] 17.0 17.0 17.0 17.0 17.0 17.0
[176,] 16.8 16.8 16.8 16.8 16.8 16.8
[177,] 16.1 16.1 16.1 16.1 16.1 16.1
[178,] 16.3 16.3 16.3 16.3 16.3 16.3
[179,] 16.3 16.3 16.3 16.3 16.3 16.3
[180,] 15.8 15.8 15.8 15.8 15.8 15.8
[181,] 16.1 16.1 16.1 16.1 16.1 16.1
[182,] 16.3 16.3 16.3 16.3 16.3 16.3
[183,] 16.2 16.2 16.2 16.2 16.2 16.2
[184,] 16.9 16.9 16.9 16.9 16.9 16.9
[185,] 16.1 16.1 16.1 16.1 16.1 16.1
[186,] 16.2 16.2 16.2 16.2 16.2 16.2
[187,] 15.7 15.7 15.7 15.7 15.7 15.7
[188,] 15.8 15.8 15.8 15.8 15.8 15.8
[189,] 16.1 16.1 16.1 16.1 16.1 16.1
[190,] 16.3 16.3 16.3 16.3 16.3 16.3
[191,] 15.9 15.9 15.9 15.9 15.9 15.9
[192,] 16.0 16.0 16.0 16.0 16.0 16.0
[193,] 16.1 16.1 16.1 16.1 16.1 16.1
[194,] 16.7 16.7 16.7 16.7 16.7 16.7
[195,] 16.0 16.0 16.0 16.0 16.0 16.0
[196,] 16.0 16.0 16.0 16.0 16.0 16.0
[197,] 16.1 16.1 16.1 16.1 16.1 16.1
[198,] 16.1 16.1 16.1 16.1 16.1 16.1
[199,] 16.0 16.0 16.0 16.0 16.0 16.0
[200,] 16.4 16.4 16.4 16.4 16.4 16.4
[201,] 16.1 16.1 16.1 16.1 16.1 16.1
[202,] 16.4 16.4 16.4 16.4 16.4 16.4
[203,] 16.7 16.7 16.7 16.7 16.7 16.7
[204,] 16.0 16.0 16.0 16.0 16.0 16.0
[205,] 16.1 16.1 16.1 16.1 16.1 16.1
[206,] 16.3 16.3 16.3 16.3 16.3 16.3
[207,] 16.5 16.5 16.5 16.5 16.5 16.5
[208,] 16.2 16.2 16.2 16.2 16.2 16.2
[209,] 16.4 16.4 16.4 16.4 16.4 16.4
[210,] 16.7 16.7 16.7 16.7 16.7 16.7
[211,] 16.2 16.2 16.2 16.2 16.2 16.2
[212,] 16.4 16.4 16.4 16.4 16.4 16.4
[213,] 16.7 16.7 16.7 16.7 16.7 16.7
[214,] 17.2 17.2 17.2 17.2 17.2 17.2
[215,] 16.1 16.1 16.1 16.1 16.1 16.1
[216,] 16.5 16.5 16.5 16.5 16.5 16.5
[217,] 17.0 17.0 17.0 17.0 17.0 17.0
[218,] 18.0 18.0 18.0 18.0 18.0 18.0
[219,] 16.1 16.1 16.1 16.1 16.1 16.1
[220,] 16.6 16.6 16.6 16.6 16.6 16.6
[221,] 17.3 17.3 17.3 17.3 17.3 17.3
[222,] 17.3 17.3 17.3 17.3 17.3 17.3
[223,] 16.1 16.1 16.1 16.1 16.1 16.1
[224,] 16.6 16.6 16.6 16.6 16.6 16.6
[225,] 17.6 17.6 17.6 17.6 17.6 17.6
[226,] 17.2 17.2 17.2 17.2 17.2 17.2
[227,] 16.1 16.1 16.1 16.1 16.1 16.1
[228,] 16.6 16.6 16.6 16.6 16.6 16.6
[229,] 17.9 17.9 17.9 17.9 17.9 17.9
[230,] 17.1 17.1 17.1 17.1 17.1 17.1
[231,] 16.1 16.1 16.1 16.1 16.1 16.1
[232,] 16.7 16.7 16.7 16.7 16.7 16.7
[233,] 18.2 18.2 18.2 18.2 18.2 18.2
[234,]  NaN  NaN  NaN  NaN  NaN  NaN
[235,] 18.2 18.2 18.2 18.2 18.2 18.2
[236,] 16.7 16.7 16.7 16.7 16.7 16.7
[237,] 16.1 16.1 16.1 16.1 16.1 16.1
[238,] 17.0 17.0 17.0 17.0 17.0 17.0
[239,] 17.9 17.9 17.9 17.9 17.9 17.9
[240,] 16.7 16.7 16.7 16.7 16.7 16.7
[241,] 16.1 16.1 16.1 16.1 16.1 16.1
[242,] 17.0 17.0 17.0 17.0 17.0 17.0
[243,] 17.6 17.6 17.6 17.6 17.6 17.6
[244,] 16.7 16.7 16.7 16.7 16.7 16.7
[245,] 16.1 16.1 16.1 16.1 16.1 16.1
[246,] 16.9 16.9 16.9 16.9 16.9 16.9
[247,] 17.3 17.3 17.3 17.3 17.3 17.3
[248,] 16.8 16.8 16.8 16.8 16.8 16.8
[249,] 16.0 16.0 16.0 16.0 16.0 16.0
[250,] 16.8 16.8 16.8 16.8 16.8 16.8
[251,] 17.0 17.0 17.0 17.0 17.0 17.0
[252,] 17.0 17.0 17.0 17.0 17.0 17.0
[253,] 16.0 16.0 16.0 16.0 16.0 16.0
[254,] 16.6 16.6 16.6 16.6 16.6 16.6
[255,] 16.7 16.7 16.7 16.7 16.7 16.7
[256,] 18.5 18.5 18.5 18.5 18.5 18.5
[257,] 16.0 16.0 16.0 16.0 16.0 16.0
[258,] 16.4 16.4 16.4 16.4 16.4 16.4
[259,] 16.4 16.4 16.4 16.4 16.4 16.4
[260,] 16.7 16.7 16.7 16.7 16.7 16.7
[261,] 15.9 15.9 15.9 15.9 15.9 15.9
[262,] 16.1 16.1 16.1 16.1 16.1 16.1
[263,] 16.4 16.4 16.4 16.4 16.4 16.4
[264,] 16.0 16.0 16.0 16.0 16.0 16.0
[265,] 16.5 16.5 16.5 16.5 16.5 16.5
[266,] 16.6 16.6 16.6 16.6 16.6 16.6
[267,] 16.4 16.4 16.4 16.4 16.4 16.4
[268,] 17.6 17.6 17.6 17.6 17.6 17.6
[269,] 16.1 16.1 16.1 16.1 16.1 16.1
[270,] 16.0 16.0 16.0 16.0 16.0 16.0
[271,] 16.4 16.4 16.4 16.4 16.4 16.4
[272,] 16.8 16.8 16.8 16.8 16.8 16.8
[273,] 16.2 16.2 16.2 16.2 16.2 16.2
[274,] 16.4 16.4 16.4 16.4 16.4 16.4
[275,] 16.4 16.4 16.4 16.4 16.4 16.4
[276,] 16.3 16.3 16.3 16.3 16.3 16.3
[277,] 16.5 16.5 16.5 16.5 16.5 16.5
[278,] 16.2 16.2 16.2 16.2 16.2 16.2
[279,] 16.4 16.4 16.4 16.4 16.4 16.4
[280,] 16.6 16.6 16.6 16.6 16.6 16.6
[281,] 16.0 16.0 16.0 16.0 16.0 16.0
[282,] 16.4 16.4 16.4 16.4 16.4 16.4
[283,] 16.4 16.4 16.4 16.4 16.4 16.4
[284,] 16.5 16.5 16.5 16.5 16.5 16.5
[285,] 16.0 16.0 16.0 16.0 16.0 16.0
[286,] 16.2 16.2 16.2 16.2 16.2 16.2
[287,] 16.4 16.4 16.4 16.4 16.4 16.4
[288,] 16.4 16.4 16.4 16.4 16.4 16.4
[289,] 15.9 15.9 15.9 15.9 15.9 15.9
[290,] 16.5 16.5 16.5 16.5 16.5 16.5
[291,] 16.4 16.4 16.4 16.4 16.4 16.4
[292,] 16.0 16.0 16.0 16.0 16.0 16.0
[293,] 16.3 16.3 16.3 16.3 16.3 16.3
[294,] 16.1 16.1 16.1 16.1 16.1 16.1
[295,] 16.4 16.4 16.4 16.4 16.4 16.4
[296,] 16.0 16.0 16.0 16.0 16.0 16.0
[297,] 15.9 15.9 15.9 15.9 15.9 15.9
[298,] 17.6 17.6 17.6 17.6 17.6 17.6
[299,] 16.4 16.4 16.4 16.4 16.4 16.4
[300,] 16.8 16.8 16.8 16.8 16.8 16.8
[301,] 16.3 16.3 16.3 16.3 16.3 16.3
[302,] 17.4 17.4 17.4 17.4 17.4 17.4
[303,] 16.4 16.4 16.4 16.4 16.4 16.4
[304,] 16.9 16.9 16.9 16.9 16.9 16.9
[305,] 15.9 15.9 15.9 15.9 15.9 15.9
[306,] 16.8 16.8 16.8 16.8 16.8 16.8
[307,] 16.4 16.4 16.4 16.4 16.4 16.4
[308,] 17.3 17.3 17.3 17.3 17.3 17.3
[309,] 16.1 16.1 16.1 16.1 16.1 16.1
[310,] 16.4 16.4 16.4 16.4 16.4 16.4
[311,] 16.4 16.4 16.4 16.4 16.4 16.4
[312,] 17.0 17.0 17.0 17.0 17.0 17.0
[313,] 16.2 16.2 16.2 16.2 16.2 16.2
[314,] 16.2 16.2 16.2 16.2 16.2 16.2
[315,] 16.4 16.4 16.4 16.4 16.4 16.4
[316,] 15.9 15.9 15.9 15.9 15.9 15.9
[317,] 15.9 15.9 15.9 15.9 15.9 15.9
[318,] 16.3 16.3 16.3 16.3 16.3 16.3
[319,] 16.4 16.4 16.4 16.4 16.4 16.4
[320,] 16.3 16.3 16.3 16.3 16.3 16.3
[321,] 16.1 16.1 16.1 16.1 16.1 16.1
[322,] 16.0 16.0 16.0 16.0 16.0 16.0
[323,] 16.4 16.4 16.4 16.4 16.4 16.4
[324,] 16.1 16.1 16.1 16.1 16.1 16.1
[325,] 16.1 16.1 16.1 16.1 16.1 16.1
[326,] 16.0 16.0 16.0 16.0 16.0 16.0
[327,] 16.4 16.4 16.4 16.4 16.4 16.4
[328,] 16.5 16.5 16.5 16.5 16.5 16.5
[329,] 16.1 16.1 16.1 16.1 16.1 16.1
[330,] 16.3 16.3 16.3 16.3 16.3 16.3
[331,] 16.4 16.4 16.4 16.4 16.4 16.4
[332,] 16.1 16.1 16.1 16.1 16.1 16.1
[333,] 16.2 16.2 16.2 16.2 16.2 16.2
[334,] 16.1 16.1 16.1 16.1 16.1 16.1
[335,] 16.4 16.4 16.4 16.4 16.4 16.4
[336,] 16.6 16.6 16.6 16.6 16.6 16.6
[337,] 16.3 16.3 16.3 16.3 16.3 16.3
[338,] 17.0 17.0 17.0 17.0 17.0 17.0
[339,] 16.4 16.4 16.4 16.4 16.4 16.4
[340,] 16.1 16.1 16.1 16.1 16.1 16.1
[341,] 15.9 15.9 15.9 15.9 15.9 15.9
[342,] 17.0 17.0 17.0 17.0 17.0 17.0
[343,] 16.4 16.4 16.4 16.4 16.4 16.4
[344,] 17.0 17.0 17.0 17.0 17.0 17.0
[345,] 16.1 16.1 16.1 16.1 16.1 16.1
[346,] 16.9 16.9 16.9 16.9 16.9 16.9
[347,] 16.4 16.4 16.4 16.4 16.4 16.4
[348,] 16.4 16.4 16.4 16.4 16.4 16.4
[349,] 16.2 16.2 16.2 16.2 16.2 16.2
[350,] 16.8 16.8 16.8 16.8 16.8 16.8
[351,] 16.4 16.4 16.4 16.4 16.4 16.4
[352,] 16.3 16.3 16.3 16.3 16.3 16.3
[353,] 16.3 16.3 16.3 16.3 16.3 16.3
[354,] 16.6 16.6 16.6 16.6 16.6 16.6
[355,] 16.4 16.4 16.4 16.4 16.4 16.4
[356,] 16.1 16.1 16.1 16.1 16.1 16.1
[357,] 15.9 15.9 15.9 15.9 15.9 15.9
[358,] 16.4 16.4 16.4 16.4 16.4 16.4
[359,] 16.4 16.4 16.4 16.4 16.4 16.4
[360,] 17.2 17.2 17.2 17.2 17.2 17.2
[361,] 16.1 16.1 16.1 16.1 16.1 16.1
[362,] 16.2 16.2 16.2 16.2 16.2 16.2
[363,] 16.6 16.6 16.6 16.6 16.6 16.6
[364,] 16.6 16.6 16.6 16.6 16.6 16.6
[365,] 16.3 16.3 16.3 16.3 16.3 16.3
[366,] 16.4 16.4 16.4 16.4 16.4 16.4
[367,] 16.4 16.4 16.4 16.4 16.4 16.4
[368,] 16.3 16.3 16.3 16.3 16.3 16.3
[369,] 16.0 16.0 16.0 16.0 16.0 16.0
[370,] 16.9 16.9 16.9 16.9 16.9 16.9
[371,] 23.6 23.6 23.6 23.6 23.6 23.6
[372,] 15.8 15.8 15.8 15.8 15.8 15.8
[373,] 16.2 16.2 16.2 16.2 16.2 16.2
[374,] 15.9 15.9 15.9 15.9 15.9 15.9
[375,] 16.4 16.4 16.4 16.4 16.4 16.4
[376,] 16.3 16.3 16.3 16.3 16.3 16.3
[377,] 15.9 15.9 15.9 15.9 15.9 15.9
[378,] 16.5 16.5 16.5 16.5 16.5 16.5
[379,] 21.8 21.8 21.8 21.8 21.8 21.8
[380,] 16.4 16.4 16.4 16.4 16.4 16.4
[381,] 15.9 15.9 15.9 15.9 15.9 15.9
[382,] 17.5 17.5 17.5 17.5 17.5 17.5
[383,] 16.4 16.4 16.4 16.4 16.4 16.4
[384,] 18.6 18.6 18.6 18.6 18.6 18.6
[385,] 15.9 15.9 15.9 15.9 15.9 15.9
[386,] 16.2 16.2 16.2 16.2 16.2 16.2
[387,] 20.0 20.0 20.0 20.0 20.0 20.0
[388,] 16.1 16.1 16.1 16.1 16.1 16.1
[389,] 15.9 15.9 15.9 15.9 15.9 15.9
[390,] 15.9 15.9 15.9 15.9 15.9 15.9
[391,] 16.4 16.4 16.4 16.4 16.4 16.4
[392,] 16.0 16.0 16.0 16.0 16.0 16.0
[393,] 15.9 15.9 15.9 15.9 15.9 15.9
[394,] 16.7 16.7 16.7 16.7 16.7 16.7
[395,] 18.2 18.2 18.2 18.2 18.2 18.2
[396,] 16.3 16.3 16.3 16.3 16.3 16.3
[397,] 15.9 15.9 15.9 15.9 15.9 15.9
[398,] 16.8 16.8 16.8 16.8 16.8 16.8
[399,] 16.4 16.4 16.4 16.4 16.4 16.4
[400,] 16.6 16.6 16.6 16.6 16.6 16.6
[401,] 15.9 15.9 15.9 15.9 15.9 15.9
[402,] 16.1 16.1 16.1 16.1 16.1 16.1
[403,] 16.4 16.4 16.4 16.4 16.4 16.4
[404,] 16.7 16.7 16.7 16.7 16.7 16.7
[405,] 16.0 16.0 16.0 16.0 16.0 16.0
[406,] 16.0 16.0 16.0 16.0 16.0 16.0
[407,] 16.3 16.3 16.3 16.3 16.3 16.3
[408,] 16.2 16.2 16.2 16.2 16.2 16.2
[409,] 16.1 16.1 16.1 16.1 16.1 16.1
[410,] 17.2 17.2 17.2 17.2 17.2 17.2
[411,] 16.4 16.4 16.4 16.4 16.4 16.4
[412,] 16.1 16.1 16.1 16.1 16.1 16.1
[413,] 16.3 16.3 16.3 16.3 16.3 16.3
[414,] 16.7 16.7 16.7 16.7 16.7 16.7
[415,] 16.9 16.9 16.9 16.9 16.9 16.9
[416,] 16.6 16.6 16.6 16.6 16.6 16.6
[417,] 16.5 16.5 16.5 16.5 16.5 16.5
[418,] 16.2 16.2 16.2 16.2 16.2 16.2
[419,] 16.5 16.5 16.5 16.5 16.5 16.5
[420,] 17.0 17.0 17.0 17.0 17.0 17.0
[421,] 16.2 16.2 16.2 16.2 16.2 16.2
[422,] 17.6 17.6 17.6 17.6 17.6 17.6
[423,] 16.4 16.4 16.4 16.4 16.4 16.4
[424,] 16.8 16.8 16.8 16.8 16.8 16.8
[425,] 15.9 15.9 15.9 15.9 15.9 15.9
[426,] 16.1 16.1 16.1 16.1 16.1 16.1
[427,] 16.3 16.3 16.3 16.3 16.3 16.3
[428,] 16.1 16.1 16.1 16.1 16.1 16.1
[429,] 16.4 16.4 16.4 16.4 16.4 16.4
[430,] 16.7 16.7 16.7 16.7 16.7 16.7
[431,] 16.4 16.4 16.4 16.4 16.4 16.4
[432,] 16.3 16.3 16.3 16.3 16.3 16.3
[433,] 16.1 16.1 16.1 16.1 16.1 16.1
[434,] 16.0 16.0 16.0 16.0 16.0 16.0
[435,] 16.3 16.3 16.3 16.3 16.3 16.3
[436,] 16.1 16.1 16.1 16.1 16.1 16.1
[437,] 15.9 15.9 15.9 15.9 15.9 15.9
[438,] 16.3 16.3 16.3 16.3 16.3 16.3
[439,] 16.4 16.4 16.4 16.4 16.4 16.4
[440,] 16.3 16.3 16.3 16.3 16.3 16.3
[441,] 16.4 16.4 16.4 16.4 16.4 16.4
[442,] 16.0 16.0 16.0 16.0 16.0 16.0
[443,] 16.0 16.7 16.7 16.7 16.7 16.7
[444,] 15.9 16.6 16.6 16.6 16.6 16.6
[445,] 15.2 16.2 16.2 16.2 16.2 16.2
[446,] 14.7 16.1 16.1 16.1 16.1 16.1
[447,] 14.2 16.3 16.3 16.3 16.3 16.3
[448,] 13.7 15.6 15.9 15.9 15.9 15.9
[449,] 13.1 14.9 16.2 16.2 16.2 16.2
[450,] 12.6 14.3 15.9 16.7 16.7 16.7
[451,] 12.1 13.7 15.3 16.8 16.8 16.8
[452,] 11.6 13.1 14.6 15.9 16.6 16.6
[453,] 11.0 12.5 13.9 15.5 16.0 16.0
[454,] 10.5 11.9 13.3 14.6 16.0 16.3
[455,] 10.0 11.3 12.6 13.9 15.2 17.2
[456,]  9.5 10.7 11.9 13.1 14.3 15.5
[457,]  8.9 10.1 11.2 12.4 13.5 14.6
[458,]  8.4  9.5 10.6 11.6 12.7 13.7
[459,]  7.9  8.9  9.9 10.9 11.9 12.8
[460,]  7.4  8.3  9.2 10.1 11.0 11.9
[461,]  6.9  7.7  8.5  9.4 10.2 11.0
[462,]  6.3  7.1  7.9  8.6  9.4 10.1
[463,]  5.8  6.5  7.2  7.9  8.6  9.2
[464,]  5.3  5.9  6.5  7.1  7.7  8.3
[465,]  4.8  5.3  5.9  6.4  6.9  7.4
[466,]  4.3  4.7  5.2  5.7  6.1  6.6
[467,]  3.7  4.1  4.5  4.9  5.3  5.7
> 
> matplot(t, corDig, type="o", ylim = c(1,17))
> (cN <- colnames(corDig))
 [1] "b1"    "b.10"  "dirct" "p1l1p" "p1l1"  "k=1"   "k=2"   "k=3"   "k=4"  
[10] "k=5"   "k=6"   "k=7"   "k=8"   "k=9"   "k=10"  "k=11"  "k=12" 
> legend(-.5, 14, cN, col=1:6, lty=1:5, pch = c(1L:9L, 0L, letters), ncol=2)
> 
> ## plot() function >>>> using global (t, corDig) <<<<<<<<<
> p.relEr <- function(i, ylim = c(11,17), type = "o",
+                     leg.pos = "left", inset=1/128,
+                     main = sprintf(
+                         "Correct #{Digits} in p1l1() approx., notably Taylor(k=1 .. %d)",
+                                    max(k.s)))
+ {
+     if((neg <- all(t[i] < 0)))
+         t  <- -t
+     stopifnot(all(t[i] > 0), length(ylim) == 2) # as we use log="x"
+     matplot(t[i], corDig[i,], type=type, ylim=ylim, log="x", xlab = quote(t), xaxt="n",
+             main=main)
+     legend(leg.pos, cN, col=1:6, lty=1:5, pch = c(1L:9L, 0L, letters), ncol=2,
+            bg=adjustcolor("gray90", 7/8), inset=inset)
+     t.epsC <- -log10(c(1,2,4)* .Machine$double.eps)
+     axis(2, at=t.epsC, labels = expression(epsilon[C], 2*epsilon[C], 4*epsilon[C]),
+          las=2, col=2, line=1)
+     tenRs <- function(t) floor(log10(min(t))) : ceiling(log10(max(t)))
+     tenE <- tenRs(t[i])
+     tE <- 10^tenE
+     abline (h = t.epsC,
+             v = tE, lty=3, col=adjustcolor("gray",.8), lwd=2)
+     AX <- if(requireNamespace("sfsmisc")) sfsmisc::eaxis else axis
+     AX(1, at= tE, labels = as.expression(
+                       lapply(tenE,
+                              if(neg)
+                                  function(e) substitute(-10^{E}, list(E = e+0))
+                              else
+                                  function(e) substitute( 10^{E}, list(E = e+0)))))
+ }
> 
> p.relEr(t > 0, ylim = c(1,17))
> p.relEr(t > 0) # full positive range
> p.relEr(t < 0) # full negative range
> if(FALSE) {## (actually less informative):
+  p.relEr(i = 0 < t & t < .01)  ## positive small t
+  p.relEr(i = -.1 < t & t < 0) ## negative small t
+ }
> 
> ## Find approximate formulas for accuracy of k=k*  approximation
> d.corrD <- cbind(t=t, as.data.frame(corDig))
> names(d.corrD) <- sub("k=", "nC_",  names(d.corrD))
> 
> fmod <- function(k, data, cut.y.at = -log10(2 * .Machine$double.eps),
+                  good.y = -log10(.Machine$double.eps), # ~ 15.654
+                  verbose=FALSE) {
+     varNm <- paste0("nC_",k)
+     stopifnot(is.numeric(y <- get(varNm, data, inherits=FALSE)),
+               is.numeric(t <- data$t))# '$' works for data.frame, list, environment
+     i <- 3 <= y & y <= cut.y.at
+     i.pos <- i & t > 0
+     i.neg <- i & t < 0
+     if(verbose) cat(sprintf("k=%d >> y <= %g ==> #{pos. t} = %d ;  #{neg. t} = %d\n",
+                             k, cut.y.at, sum(i.pos), sum(i.neg)))
+     nCoefLm <- function(x,y) `names<-`(.lm.fit(x=x, y=y)$coeff, c("int", "slp"))
+     nC.t <- function(x,y) { cf <- nCoefLm(x,y); c(cf, t.0 = exp((good.y - cf[[1]])/cf[[2]])) }
+     cbind(pos = nC.t(cbind(1, log( t[i.pos])), y[i.pos]),
+           neg = nC.t(cbind(1, log(-t[i.neg])), y[i.neg]))
+ }
> rr <- sapply(k.s, fmod, data=d.corrD, verbose=TRUE, simplify="array")
k=1 >> y <= 15.3525 ==> #{pos. t} = 165 ;  #{neg. t} = 164
k=2 >> y <= 15.3525 ==> #{pos. t} = 82 ;  #{neg. t} = 82
k=3 >> y <= 15.3525 ==> #{pos. t} = 55 ;  #{neg. t} = 54
k=4 >> y <= 15.3525 ==> #{pos. t} = 42 ;  #{neg. t} = 41
k=5 >> y <= 15.3525 ==> #{pos. t} = 33 ;  #{neg. t} = 32
k=6 >> y <= 15.3525 ==> #{pos. t} = 27 ;  #{neg. t} = 27
k=7 >> y <= 15.3525 ==> #{pos. t} = 23 ;  #{neg. t} = 22
k=8 >> y <= 15.3525 ==> #{pos. t} = 19 ;  #{neg. t} = 19
k=9 >> y <= 15.3525 ==> #{pos. t} = 17 ;  #{neg. t} = 17
k=10 >> y <= 15.3525 ==> #{pos. t} = 14 ;  #{neg. t} = 15
k=11 >> y <= 15.3525 ==> #{pos. t} = 13 ;  #{neg. t} = 13
k=12 >> y <= 15.3525 ==> #{pos. t} = 11 ;  #{neg. t} = 12
> stopifnot(rr["slp",,] < 0) # all slopes are negative (important!)
> matplot(k.s, t(rr["slp",,]), type="o", xlab = quote(k), ylab = quote(slope[k]))
> ## fantastcally close to linear in k
> ## The numbers, nicely arranged
> ftable(aperm(rr, c(3,2,1)))
                    int           slp           t.0
                                                   
k=1  pos   4.799691e-01 -4.341066e-01  6.604529e-16
     neg   4.756759e-01 -4.343909e-01  6.690917e-16
k=2  pos   7.810080e-01 -8.683662e-01  3.645998e-08
     neg   7.767658e-01 -8.686128e-01  3.645921e-08
k=3  pos   1.014435e+00 -1.301039e+00  1.298301e-05
     neg   9.827922e-01 -1.305341e+00  1.315071e-05
k=4  pos   1.204024e+00 -1.733024e+00  2.393078e-04
     neg   1.141408e+00 -1.743073e+00  2.422326e-04
k=5  pos   1.368501e+00 -2.162254e+00  1.351473e-03
     neg   1.260251e+00 -2.184374e+00  1.375120e-03
k=6  pos   1.506395e+00 -2.592862e+00  4.269765e-03
     neg   1.356588e+00 -2.628147e+00  4.339726e-03
k=7  pos   1.637759e+00 -3.016733e+00  9.599728e-03
     neg   1.449676e+00 -3.069312e+00  9.777136e-03
k=8  pos   1.731648e+00 -3.453572e+00  1.775367e-02
     neg   1.523333e+00 -3.515635e+00  1.796638e-02
k=9  pos   1.824829e+00 -3.885243e+00  2.845884e-02
     neg   1.618873e+00 -3.943160e+00  2.846020e-02
k=10 pos   1.923972e+00 -4.307028e+00  4.126595e-02
     neg   1.675544e+00 -4.390402e+00  4.142931e-02
k=11 pos   1.994784e+00 -4.743501e+00  5.616442e-02
     neg   1.711181e+00 -4.850084e+00  5.643491e-02
k=12 pos   2.070152e+00 -5.172325e+00  7.235500e-02
     neg   1.817454e+00 -5.252709e+00  7.178431e-02
> signif(t(rr["t.0",,]),3) # ==> Should be boundaries for the hybrid p1l1()
          pos      neg
k=1  6.60e-16 6.69e-16
k=2  3.65e-08 3.65e-08
k=3  1.30e-05 1.32e-05
k=4  2.39e-04 2.42e-04
k=5  1.35e-03 1.38e-03
k=6  4.27e-03 4.34e-03
k=7  9.60e-03 9.78e-03
k=8  1.78e-02 1.80e-02
k=9  2.85e-02 2.85e-02
k=10 4.13e-02 4.14e-02
k=11 5.62e-02 5.64e-02
k=12 7.24e-02 7.18e-02
> ##           pos      neg
> ## k=1  6.60e-16 6.69e-16
> ## k=2  3.65e-08 3.65e-08
> ## k=3  1.30e-05 1.32e-05
> ## k=4  2.39e-04 2.42e-04
> ## k=5  1.35e-03 1.38e-03
> ## k=6  4.27e-03 4.34e-03
> ## k=7  9.60e-03 9.78e-03
> ## k=8  1.78e-02 1.80e-02
> ## k=9  2.85e-02 2.85e-02
> ## k=10 4.13e-02 4.14e-02
> ## k=11 5.62e-02 5.64e-02
> ## k=12 7.24e-02 7.18e-02
> 
> ###------------- Well,  p1l1p()  is really basically good enough ... with a small exception:
> rErr1k <- curve(asNumeric(p1l1p(x) / p1l1.(mpfr(x, 4096)) - 1), -.999, .999,
+                 n = 4000, col=2, lwd=2)
> abline(h = c(-8,-4,-2:2,4,8)* 2^-52, lty=2, col=adjustcolor("gray20", 1/4))
> ## well, have a "spike" at around -0.8 -- why?
> 
> plot(abs(y) ~ x, data = rErr1k, ylim = c(4e-17, max(abs(y))),
+      ylab=quote(abs(hat(p)/p - 1)),
+      main = "p1l1p(x) -- Relative Error wrt mpfr(*. 4096) [log]",
+      col=2, lwd=1.5, type = "b", cex=1/2, log="y", yaxt="n")
Error in is.qr(x) : object 'p' not found
Calls: plot ... plot.formula -> do.call -> plot -> plot.default -> hat -> is.qr
Execution halted
* checking for unstated dependencies in 'tests' ... OK
* checking tests ...
** running tests for arch 'i386' ... [152s] OK
  Running 'chisq-nonc-ex.R' [34s]
  Running 'dnbinom-tst.R' [0s]
  Running 'dnchisq-tst.R' [0s]
  Running 'hyper-dist-ex.R' [46s]
  Running 'pnbeta-tst.R' [0s]
  Running 'pnt-prec.R' [17s]
  Running 'ppois-ex.R' [2s]
  Running 'qPoisBinom-ex.R' [1s]
  Running 'qbeta-dist.R' [16s]
  Running 'qbeta-tst.R' [1s]
  Running 'qgamma-ex.R' [19s]
  Running 't-nonc-tst.R' [7s]
  Running 'wienergerm-pchisq-tst.R' [0s]
  Running 'wienergerm_nchisq.R' [8s]
** running tests for arch 'x64' ... [146s] OK
  Running 'chisq-nonc-ex.R' [35s]
  Running 'dnbinom-tst.R' [0s]
  Running 'dnchisq-tst.R' [0s]
  Running 'hyper-dist-ex.R' [41s]
  Running 'pnbeta-tst.R' [0s]
  Running 'pnt-prec.R' [17s]
  Running 'ppois-ex.R' [2s]
  Running 'qPoisBinom-ex.R' [1s]
  Running 'qbeta-dist.R' [13s]
  Running 'qbeta-tst.R' [1s]
  Running 'qgamma-ex.R' [19s]
  Running 't-nonc-tst.R' [7s]
  Running 'wienergerm-pchisq-tst.R' [0s]
  Running 'wienergerm_nchisq.R' [8s]
* checking for unstated dependencies in vignettes ... OK
* checking package vignettes in 'inst/doc' ... OK
* checking re-building of vignette outputs ... [33s] OK
* checking PDF version of manual ... OK
* DONE
Status: 2 ERRORs