CRAN Package Check Results for Package DPQ

Last updated on 2021-05-16 17:46:47 CEST.

Flavor Version Tinstall Tcheck Ttotal Status Flags
r-devel-linux-x86_64-debian-clang 0.4-3 13.54 236.03 249.57 WARN
r-devel-linux-x86_64-debian-gcc 0.4-3 10.94 175.42 186.36 OK
r-devel-linux-x86_64-fedora-clang 0.4-3 314.67 WARN
r-devel-linux-x86_64-fedora-gcc 0.4-3 295.90 OK
r-devel-windows-ix86+x86_64 0.4-3 35.00 453.00 488.00 OK
r-devel-windows-x86_64-gcc10-UCRT 0.4-3 OK
r-patched-linux-x86_64 0.4-3 14.44 230.04 244.48 OK
r-patched-solaris-x86 0.4-3 432.70 OK
r-release-linux-x86_64 0.4-3 14.72 222.40 237.12 OK
r-release-macos-x86_64 0.4-3 WARN
r-release-windows-ix86+x86_64 0.4-3 28.00 431.00 459.00 OK
r-oldrel-macos-x86_64 0.4-3 ERROR
r-oldrel-windows-ix86+x86_64 0.4-3 31.00 423.00 454.00 ERROR

Additional issues

M1mac rchk

Check Details

Version: 0.4-3
Check: whether package can be installed
Result: WARN
    Found the following significant warnings:
     bd0.c:360:13: warning: explicitly assigning value of variable of type 'int' to itself [-Wself-assign]
Flavors: r-devel-linux-x86_64-debian-clang, r-devel-linux-x86_64-fedora-clang, r-release-macos-x86_64, r-oldrel-macos-x86_64

Version: 0.4-3
Check: package dependencies
Result: NOTE
    Package suggested but not available for checking: ‘DPQmpfr’
Flavor: r-oldrel-macos-x86_64

Version: 0.4-3
Check: Rd cross-references
Result: WARN
    Missing link or links in documentation object 'dnbinomR.Rd':
     ‘[Rmpfr]{dnbinom}’
    
    See section 'Cross-references' in the 'Writing R Extensions' manual.
Flavor: r-oldrel-macos-x86_64

Version: 0.4-3
Check: examples
Result: 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 objects are masked from ‘package:stats’:
    
     dbinom, dgamma, 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 7.6 15.4 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
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    [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
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    [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
Flavor: r-oldrel-macos-x86_64

Version: 0.4-3
Check: running examples for arch ‘i386’
Result: 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
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    [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
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    [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
Flavor: r-oldrel-windows-ix86+x86_64

Version: 0.4-3
Check: running examples for arch ‘x64’
Result: 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
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    [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
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    [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
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    [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
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    [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
Flavor: r-oldrel-windows-ix86+x86_64