"""this script builds the T table and A table for the upper
   quantile stundentized range algorithm"""
from statsmodels.compat.python import lmap, lrange

import math

import numpy as np
from numpy.random import random
from scipy.optimize import leastsq
import scipy.stats

# The values for p in [.5, .75, .9, .95, .975, .99, .995, .999]
# were pulled from:
#    http://www.stata.com/stb/stb46/dm64/sturng.pdf
#
# Values for p in [.1, .675, .8, .85] were calculated using R's qtukey function
#
# the table was programmed by Gleason and extends Harter's (1960) table
# using the Copenhaver & Holland (1988) algorithm (C&H). Gleason found
# that the 4th significant digit of the C&H differed from Harter's
# tables on about 20% of the values. Gleason states this was do to
# consevative rounding by Harter. In those event the table reflects
# Harter's orginal approximations.

q0100 = """\
2 0.2010022 0.6351172 0.9504689 1.179321 1.354691 1.495126 1.611354 1.709984 1.795325 1.87032 1.937057 1.997068 2.051505 2.101256 2.147016 2.189342 2.228683 2.265408 2.299823 2.558612 2.729718 2.95625 3.184742938 3.398609188
3 0.193179 0.6294481 0.9564746 1.19723 1.383028 1.532369 1.656225 1.761451 1.852559 1.93265 2.003933 2.068034 2.126178 2.179312 2.228177 2.273367 2.315364 2.354561 2.391287 2.667213 2.849389 3.009265469 3.237758406 3.451624656
4 0.1892648 0.6266441 0.9606115 1.2089 1.401557 1.55691 1.686009 1.795829 1.890994 1.974697 2.049222 2.116253 2.177065 2.232641 2.283754 2.331023 2.37495 2.415949 2.454361 2.742846 2.933173 3.062280938 3.290773875 3.504640125
5 0.1869239 0.6249713 0.963532 1.217021 1.414548 1.574255 1.707205 1.820437 1.91864 2.005066 2.082048 2.151312 2.214162 2.271609 2.324449 2.37332 2.418737 2.461128 2.500844 2.7991 2.9958 3.115296406 3.343789344 3.557655594
6 0.185369 0.6238602 0.9656833 1.22298 1.424151 1.587166 1.723076 1.838955 1.939532 2.028098 2.107021 2.178053 2.242524 2.301465 2.355686 2.40584 2.452454 2.495964 2.536731 2.842892 3.027993254 3.168311875 3.396804813 3.610671063
7 0.1842618 0.6230685 0.9673274 1.227534 1.431536 1.597154 1.735417 1.853415 1.955904 2.046203 2.126704 2.19918 2.264979 2.325144 2.380502 2.431713 2.479315 2.52375 2.565387 2.878126 3.060186557 3.221327344 3.449820281 3.663686531
8 0.1834338 0.6224757 0.9686225 1.231126 1.437392 1.605113 1.745294 1.86503 1.969097 2.060832 2.142645 2.216325 2.283234 2.344427 2.400739 2.45284 2.501275 2.546491 2.588864 2.861237 3.092379859 3.274342813 3.50283575 3.716702
9 0.1827912 0.6220153 0.969668 1.23403 1.442149 1.611608 1.753382 1.874572 1.979964 2.07291 2.155833 2.230535 2.298388 2.360458 2.417585 2.470448 2.519597 2.565484 2.608488 2.871492 3.1631665 3.362394 3.613696 3.7452106
10 0.1822783 0.6216474 0.9705293 1.236426 1.446091 1.617009 1.76013 1.882554 1.989077 2.083059 2.166935 2.242517 2.311185 2.374011 2.431845 2.485368 2.535137 2.581607 2.625162 2.898717 3.1760535 3.45339 3.6807265 3.7737192
11 0.1818593 0.6213467 0.9712507 1.238437 1.449411 1.621571 1.765847 1.889333 1.996831 2.091711 2.176415 2.252763 2.322141 2.38563 2.444082 2.498185 2.548497 2.59548 2.639519 2.923558 3.19971275 3.4758675 3.70202225 3.8022278
12 0.1815106 0.6210962 0.9718637 1.240149 1.452244 1.625478 1.770753 1.895163 2.003512 2.099178 2.184609 2.26163 2.331635 2.395707 2.454706 2.509321 2.560115 2.607554 2.652022 2.94649 3.2224175 3.498345 3.7242725 3.8307364
13 0.181216 0.6208845 0.9723908 1.241623 1.454692 1.62886 1.77501 1.900231 2.009331 2.10569 2.191763 2.269382 2.339943 2.404535 2.46402 2.519093 2.570318 2.618162 2.663015 2.967868 3.242456 3.517044 3.741632 3.859245
14 0.1809637 0.620703 0.972849 1.242906 1.456827 1.631817 1.778739 1.904678 2.014444 2.11142 2.198067 2.276219 2.347278 2.412335 2.472257 2.52774 2.579352 2.627563 2.672763 2.987963 3.245505708 3.503048417 3.748851667 3.878849
15 0.1807453 0.6205458 0.9732508 1.244033 1.458706 1.634424 1.782034 1.908613 2.018974 2.116503 2.203664 2.282296 2.353802 2.41928 2.479596 2.53545 2.587413 2.635954 2.681468 3.006982 3.275778125 3.489052833 3.758247778 3.896564
16 0.1805544 0.6204084 0.973606 1.24503 1.460373 1.636741 1.784965 1.912119 2.023015 2.121043 2.208668 2.287733 2.359646 2.425503 2.486177 2.542369 2.59465 2.643493 2.689292 3.025091 3.281966688 3.49479125 3.763291 3.9179256
17 0.1803861 0.6202871 0.9739223 1.245919 1.461861 1.638813 1.78759 1.915263 2.026643 2.125123 2.21317 2.292628 2.36491 2.431114 2.492114 2.548614 2.601186 2.650304 2.696365 3.032426 3.272395 3.50687125 3.77704 3.9392872
18 0.1802366 0.6201793 0.9742057 1.246717 1.463198 1.640677 1.789955 1.918099 2.029919 2.128809 2.21724 2.297059 2.369678 2.436199 2.497498 2.55428 2.607118 2.656491 2.702792 3.039093 3.282026 3.586406 3.789645 3.9606488
19 0.1801029 0.620083 0.9744612 1.247436 1.464405 1.642363 1.792096 1.920669 2.032891 2.132158 2.22094 2.301089 2.374017 2.44083 2.502404 2.559444 2.612529 2.662134 2.708658 3.045182 3.296680985 3.603883649 3.801248 3.974888443
20 0.1799827 0.6199962 0.9746925 1.248088 1.465502 1.643895 1.794045 1.923011 2.035601 2.135212 2.224318 2.30477 2.377983 2.445065 2.506892 2.564173 2.617485 2.667306 2.714034 3.050762 3.311335993 3.621361325 3.788047375 3.989130221
24 0.1796023 0.6197217 0.9754345 1.250184 1.469033 1.648844 1.800353 1.930604 2.044404 2.145153 2.235327 2.316784 2.390945 2.45892 2.521592 2.579673 2.633745 2.684289 2.731705 3.089271 3.325991 3.638839 3.77484675 4.003372
30 0.1792227 0.6194474 0.9761909 1.252326 1.47266 1.653946 1.806877 1.938484 2.053567 2.155527 2.246844 2.329381 2.404562 2.473504 2.537093 2.596046 2.650947 2.702281 2.750452 3.088623 3.365526818 3.632653344 3.810852875 4.0480485
40 0.1788439 0.6191733 0.976962 1.254517 1.476384 1.659208 1.813634 1.946672 2.063118 2.166372 2.258917 2.342618 2.418905 2.488898 2.553488 2.613394 2.669206 2.731569 2.770415 3.109261 3.405062637 3.629560516 3.846859 4.092725
60 0.1784658 0.6188994 0.9777482 1.256759 1.480212 1.664639 1.820636 1.955191 2.07309 2.177731 2.271599 2.356562 2.434053 2.505196 2.570884 2.631843 2.688663 2.745483 2.802303 3.159123 3.406221516 3.626467688 3.90118925 4.1497775
120 0.1780885 0.6186256 0.9785495 1.259052 1.484147 1.67025 1.827902 1.964066 2.083518 2.189653 2.284954 2.371292 2.450102 2.522511 2.589417 2.651546 2.71243375 2.763748 2.8156585 3.201588 3.459897 3.67055425 3.9555195 4.20683
1e38 0.177712 0.6183521 0.9793662 1.261398 1.488195 1.676051 1.835449 1.973327 2.094446 2.202195 2.299057 2.386902 2.467168 2.540983 2.609248 2.677513 2.745778 2.787396 2.829014 3.236691 3.487830797 3.721309063 4.01874075 4.279424"""

q0300 = """\
2 0.6289521 1.248281 1.638496 1.916298 2.129504 2.301246 2.444313 2.566465 2.672747 2.766604 2.850494 2.926224 2.995161 3.05836 3.116655 3.170712 3.221076 3.268192 3.312433 3.647666 3.871606 4.170521 4.372227 4.52341
3 0.5999117 1.209786 1.598235 1.875707 2.088948 2.260822 2.404037 2.52633 2.632732 2.726691 2.810665 2.886463 2.955453 3.018695 3.077022 3.131103 3.181483 3.228609 3.272854 3.607961 3.831649 4.130021 4.331231 4.48198
4 0.5857155 1.19124 1.579749 1.858059 2.072245 2.245015 2.389043 2.512062 2.619115 2.713659 2.798159 2.874434 2.943859 3.007497 3.066189 3.120607 3.171298 3.218713 3.263228 3.600301 3.825208 4.125075 4.327208 4.478602
5 0.5773226 1.18033 1.569213 1.84843 2.063579 2.237255 2.382108 2.505872 2.613597 2.708749 2.793803 2.870583 2.94047 3.004536 3.063622 3.118406 3.169439 3.217173 3.261987 3.601296 3.827646 4.129353 4.332665 4.48491
6 0.5717854 1.173145 1.562427 1.842442 2.058433 2.232905 2.378487 2.502915 2.611243 2.706943 2.792499 2.869739 2.940051 3.004509 3.06396 3.119085 3.170435 3.218468 3.263562 3.604991 3.832733 4.136241 4.340726 4.493824
7 0.5678608 1.168056 1.5577 1.838389 2.055092 2.230242 2.376451 2.501451 2.610302 2.706482 2.792477 2.870123 2.94081 3.005616 3.065391 3.120818 3.172464 3.220752 3.266098 3.609448 3.838467 4.143645 4.349225 4.503125
8 0.5649349 1.164263 1.55422 1.835477 2.052781 2.228508 2.375251 2.500743 2.610046 2.706641 2.793019 2.871019 2.942034 3.007146 3.067207 3.122901 3.174787 3.223323 3.268893 3.61396 3.844133 4.150832 4.357416 4.512054
9 0.56267 1.161326 1.551554 1.833289 2.051105 2.227323 2.374526 2.500442 2.610136 2.707092 2.793803 2.872112 2.943416 3.008796 3.069108 3.125039 3.177147 3.225893 3.27166 3.618262 3.849473 4.157551 4.365051 4.520364
10 0.5608651 1.158985 1.549445 1.831589 2.049842 2.226484 2.374084 2.500369 2.610403 2.707674 2.794677 2.873258 2.944815 3.010432 3.070966 3.127106 3.179411 3.228343 3.274287 3.62226 3.854408 4.16298725 4.372072 4.51335807
11 0.5593931 1.157076 1.547737 1.830233 2.048863 2.225872 2.373818 2.500424 2.610757 2.708305 2.795566 2.874386 2.946167 3.011994 3.072726 3.129052 3.181532 3.23063 3.276732 3.625936 3.8583805 4.1684235 4.378495 4.527370035
12 0.5581697 1.155489 1.546325 1.829125 2.048085 2.225415 2.373664 2.500554 2.61115 2.708943 2.796432 2.875466 2.947446 3.01346 3.074368 3.13086 3.183497 3.232744 3.278987 3.629302 3.862353 4.17385975 4.384365 4.541382
13 0.557137 1.154148 1.545138 1.828206 2.047454 2.225068 2.373584 2.500725 2.611555 2.709566 2.797258 2.876482 2.948641 3.014823 3.075889 3.13253 3.185309 3.23469 3.28106 3.63238 3.8663255 4.179296 4.3895105 4.547231
14 0.5562535 1.153001 1.544127 1.82743 2.046934 2.224798 2.373553 2.500918 2.611956 2.710162 2.798038 2.877433 2.949752 3.016085 3.077294 3.134069 3.186976 3.236478 3.282963 3.635197 3.870298 4.183625 4.394656 4.552594
15 0.5554892 1.152009 1.543255 1.826767 2.046499 2.224587 2.373555 2.50112 2.612347 2.710728 2.798768 2.878317 2.950781 3.017251 3.078589 3.135487 3.188509 3.238121 3.284712 3.637674 3.8733385 4.187597 4.399177 4.557525
16 0.5548214 1.151142 1.542495 1.826194 2.04613 2.224419 2.373579 2.501325 2.612721 2.711261 2.799449 2.879139 2.951735 3.018329 3.079784 3.136793 3.189921 3.239634 3.28632 3.640151 3.876379 4.191252 4.40334 4.56207
17 0.554233 1.150377 1.541828 1.825694 2.045813 2.224284 2.373618 2.501527 2.613077 2.711761 2.800085 2.879902 2.952618 3.019325 3.080888 3.137998 3.191223 3.241028 3.287802 3.642251 3.878959 4.1944965 4.407184 4.56627
18 0.5537107 1.149699 1.541236 1.825254 2.04554 2.224175 2.373667 2.501725 2.613414 2.71223 2.800678 2.880611 2.953437 3.020248 3.081909 3.139113 3.192426 3.242315 3.28917 3.644351 3.881539 4.197741 4.410743 4.570162
19 0.5532438 1.149092 1.540709 1.824864 2.045301 2.224086 2.373722 2.501915 2.613733 2.71267 2.801231 2.881271 2.954198 3.021104 3.082855 3.140145 3.19354 3.243507 3.290436 3.641213698 3.877674372 4.200632 4.414046 4.573776
20 0.552824 1.148546 1.540235 1.824516 2.045091 2.224013 2.37378 2.502099 2.614034 2.713082 2.801747 2.881885 2.954905 3.0219 3.083734 3.141103 3.194574 3.244613 3.291611 3.647488349 3.885403686 4.203319 4.4207865 4.577142
24 0.5514973 1.146821 1.538745 1.823433 2.044456 2.223827 2.374026 2.502754 2.615077 2.71449 2.8035 2.883965 2.957293 3.02458 3.086693 3.144327 3.198049 3.248329 3.295558 3.653763 3.893133 4.212396 4.427527 4.588561
30 0.5501747 1.1451 1.537267 1.822378 2.04387 2.223711 2.374365 2.503527 2.616262 2.716064 2.805443 2.886257 2.959917 3.027519 3.089932 3.147852 3.201849 3.252391 3.29987 3.646771403 3.901009 4.201241112 4.423813037 4.57425581
40 0.5488561 1.143384 1.535803 1.821351 2.043333 2.223667 2.3748 2.504422 2.617594 2.717812 2.807585 2.888774 2.962791 3.030734 3.093472 3.151703 3.205997 3.256824 3.304577 3.660754702 3.910106 4.223551056 4.431241019 4.602866405
60 0.5475416 1.141671 1.53435 1.820353 2.042846 2.223698 2.375337 2.505445 2.619082 2.719743 2.809939 2.891531 2.965932 3.034243 3.097332 3.1559 3.210518 3.261657 3.30971 3.674738 3.919203 4.245861 4.438669 4.631477
120 0.5462314 1.139963 1.532911 1.819385 2.04241 2.223806 2.375978 2.506602 2.620733 2.721868 2.812516 2.894541 2.969356 3.038064 3.101534 3.160468 3.215439 3.39400025 3.5725615 3.75112275 3.929684 4.256342 4.44915 4.641958
1e38 0.5449254 1.138259 1.531485 1.818447 2.042028 2.223993 2.376728 2.507898 2.622556 2.724195 2.815328 2.897817 2.973079 3.042215 3.106097 3.165428 3.220399 3.39896025 3.5775215 3.75608275 3.934644 4.261302 4.45411 4.646918"""

q0500 = """\
2 1.155 1.908 2.377 2.713 2.973 3.184 3.361 3.513 3.645 3.762 3.867 3.963 4.049 4.129 4.203 4.271 4.335 4.394 4.451 4.878 5.165 5.549 5.810 6.006
3 1.082 1.791 2.230 2.545 2.789 2.986 3.152 3.294 3.418 3.528 3.626 3.715 3.796 3.871 3.940 4.004 4.064 4.120 4.172 4.573 4.842 5.202 5.447 5.630
4 1.048 1.736 2.163 2.468 2.704 2.895 3.055 3.193 3.313 3.419 3.515 3.601 3.680 3.752 3.819 3.881 3.939 3.993 4.044 4.432 4.693 5.043 5.279 5.457
5 1.028 1.705 2.124 2.423 2.655 2.843 3.000 3.135 3.253 3.357 3.451 3.535 3.613 3.684 3.749 3.810 3.867 3.920 3.970 4.351 4.608 4.951 5.184 5.358
6 1.015 1.684 2.098 2.394 2.623 2.808 2.964 3.097 3.213 3.317 3.409 3.493 3.569 3.639 3.704 3.764 3.820 3.873 3.922 4.299 4.552 4.891 5.121 5.294
7 1.006 1.670 2.080 2.374 2.601 2.784 2.938 3.070 3.186 3.288 3.380 3.463 3.538 3.608 3.672 3.732 3.787 3.840 3.889 4.262 4.513 4.849 5.077 5.249
8 .9990 1.659 2.067 2.359 2.584 2.767 2.919 3.051 3.165 3.267 3.358 3.440 3.515 3.584 3.648 3.708 3.763 3.815 3.863 4.234 4.484 4.818 5.045 5.215
9 .9938 1.651 2.057 2.347 2.571 2.753 2.905 3.035 3.149 3.250 3.341 3.423 3.498 3.566 3.630 3.689 3.744 3.796 3.844 4.213 4.461 4.794 5.020 5.189
10 .9897 1.645 2.049 2.338 2.561 2.742 2.893 3.023 3.137 3.237 3.328 3.409 3.484 3.552 3.615 3.674 3.729 3.780 3.829 4.196 4.443 4.775 5.000 5.168
11 .9863 1.639 2.042 2.330 2.553 2.733 2.884 3.013 3.127 3.227 3.317 3.398 3.472 3.540 3.603 3.662 3.717 3.768 3.816 4.182 4.429 4.759 4.983 5.152
12 .9836 1.635 2.037 2.324 2.546 2.726 2.876 3.005 3.118 3.218 3.308 3.389 3.463 3.531 3.594 3.652 3.706 3.757 3.805 4.171 4.417 4.746 4.970 5.138
13 .9812 1.631 2.032 2.319 2.540 2.719 2.869 2.998 3.111 3.210 3.300 3.381 3.455 3.522 3.585 3.643 3.698 3.749 3.796 4.161 4.406 4.735 4.958 5.126
14 .9792 1.628 2.028 2.314 2.535 2.714 2.864 2.992 3.105 3.204 3.293 3.374 3.448 3.515 3.578 3.636 3.690 3.741 3.789 4.153 4.397 4.726 4.948 5.115
15 .9775 1.625 2.025 2.310 2.531 2.709 2.859 2.987 3.099 3.199 3.288 3.368 3.442 3.509 3.572 3.630 3.684 3.735 3.782 4.145 4.390 4.718 4.940 5.107
16 .9760 1.623 2.022 2.307 2.527 2.705 2.855 2.983 3.095 3.194 3.283 3.363 3.436 3.504 3.566 3.624 3.678 3.729 3.776 4.139 4.383 4.710 4.932 5.099
17 .9747 1.621 2.019 2.304 2.524 2.702 2.851 2.979 3.090 3.189 3.278 3.359 3.432 3.499 3.561 3.619 3.673 3.724 3.771 4.133 4.377 4.704 4.926 5.092
18 .9735 1.619 2.017 2.301 2.521 2.699 2.848 2.975 3.087 3.186 3.274 3.354 3.428 3.495 3.557 3.615 3.669 3.719 3.767 4.128 4.372 4.698 4.920 5.086
19 .9724 1.617 2.015 2.299 2.518 2.696 2.845 2.972 3.084 3.182 3.271 3.351 3.424 3.491 3.553 3.611 3.665 3.715 3.763 4.124 4.367 4.693 4.914 5.080
20 .9715 1.616 2.013 2.297 2.516 2.693 2.842 2.969 3.081 3.179 3.268 3.348 3.421 3.488 3.550 3.607 3.661 3.712 3.759 4.120 4.363 4.688 4.909 5.075
24 .9685 1.611 2.007 2.290 2.508 2.685 2.833 2.960 3.071 3.170 3.258 3.337 3.410 3.477 3.539 3.596 3.650 3.700 3.747 4.107 4.349 4.674 4.894 5.060
30 .9656 1.606 2.001 2.283 2.501 2.677 2.825 2.951 3.062 3.160 3.248 3.327 3.400 3.466 3.528 3.585 3.638 3.688 3.735 4.094 4.335 4.659 4.878 5.043
40 .9626 1.602 1.996 2.277 2.494 2.669 2.816 2.942 3.053 3.150 3.238 3.317 3.389 3.455 3.517 3.574 3.627 3.677 3.723 4.080 4.321 4.643 4.862 5.027
60 .9597 1.597 1.990 2.270 2.486 2.661 2.808 2.933 3.043 3.140 3.227 3.306 3.378 3.444 3.505 3.562 3.615 3.665 3.711 4.067 4.306 4.627 4.845 5.009
120 .9568 1.592 1.984 2.263 2.479 2.653 2.799 2.924 3.034 3.130 3.217 3.296 3.367 3.433 3.494 3.550 3.603 3.652 3.699 4.052 4.290 4.610 4.827 4.990
1e38 .9539 1.588 1.978 2.257 2.472 2.645 2.791 2.915 3.024 3.121 3.207 3.285 3.356 3.422 3.482 3.538 3.591 3.640 3.686 4.037 4.274 4.591 4.806 4.968"""

q0675 = """\
2 1.829602 2.751705 3.332700 3.754119 4.082579 4.350351 4.575528 4.769258 4.938876 5.089456 5.22465 5.347168 5.459072 5.56197 5.657136 5.745596 5.828188 5.905606 5.978428 6.534036 6.908522 7.411898 7.753537 8.010516
3 1.660743 2.469725 2.973973 3.338757 3.622958 3.854718 4.049715 4.217574 4.364624 4.495236 4.612559 4.718926 4.816117 4.905518 4.988228 5.065133 5.136955 5.204295 5.267653 5.751485 6.07799 6.517299 6.815682 7.040219
4 1.585479 2.344680 2.814410 3.153343 3.417165 3.632254 3.813232 3.96905 4.105579 4.226877 4.335857 4.434684 4.525004 4.608102 4.684995 4.756504 4.823298 4.885932 4.944872 5.395226 5.699385 6.108899 6.387203 6.596702
5 1.543029 2.27426 2.72431 3.048331 3.300303 3.505645 3.678397 3.827131 3.957462 4.073264 4.177319 4.27169 4.35795 4.437321 4.510774 4.579091 4.642911 4.702763 4.759089 5.189651 5.480611 5.872552 6.139026 6.339673
6 1.515809 2.229127 2.666435 2.980707 3.224876 3.423769 3.591058 3.735076 3.861273 3.973403 4.074164 4.165554 4.249094 4.325968 4.397115 4.463293 4.525119 4.583105 4.637678 5.054965 5.337079 5.717251 5.975813 6.170546
7 1.496881 2.197746 2.626119 2.933501 3.17212 3.366405 3.529778 3.670406 3.793624 3.903106 4.001488 4.090723 4.172295 4.247362 4.31684 4.381468 4.441849 4.498482 4.551786 4.959448 5.235148 5.606794 5.859629 6.050083
8 1.482962 2.174667 2.596423 2.898666 3.133126 3.323942 3.484357 3.622418 3.743376 3.850846 3.947419 4.035012 4.115085 4.188774 4.256978 4.320423 4.379701 4.435301 4.487633 4.887938 5.158734 5.523864 5.772325 5.959514
9 1.472298 2.156982 2.573637 2.871897 3.103116 3.29122 3.449316 3.585359 3.704538 3.810421 3.905564 3.991859 4.070746 4.143343 4.210539 4.273046 4.331448 4.386229 4.437792 4.832253 5.099153 5.459107 5.704096 5.888693
10 1.463868 2.142999 2.555601 2.85068 3.079300 3.265222 3.421445 3.555857 3.673594 3.778189 3.872171 3.957411 4.035332 4.107041 4.173413 4.235156 4.292845 4.346957 4.39789 4.787576 5.05129 5.407011 5.649161 5.831642
11 1.457037 2.131666 2.540969 2.833447 3.059936 3.244061 3.398740 3.531802 3.648345 3.751871 3.844888 3.929251 4.006369 4.077337 4.143024 4.204129 4.261223 4.314777 4.365186 4.750882 5.01193 5.36411 5.603886 5.784574
12 1.451389 2.122295 2.528860 2.819172 3.043878 3.226497 3.379879 3.511805 3.627341 3.729965 3.822167 3.905787 3.982224 4.052565 4.117671 4.178235 4.234823 4.287903 4.337867 4.720168 4.978946 5.32811 5.565864 5.745066
13 1.446642 2.114418 2.518673 2.807152 3.030346 3.211683 3.363958 3.494914 3.609588 3.71144 3.802942 3.885925 3.961777 4.031579 4.096185 4.156283 4.212436 4.265108 4.314686 4.694058 4.950875 5.297431 5.533435 5.711335
14 1.442597 2.107703 2.509984 2.796892 3.018785 3.199019 3.350338 3.480454 3.594382 3.695564 3.786459 3.868888 3.944232 4.013564 4.077734 4.137427 4.1932 4.245515 4.294759 4.671571 4.926672 5.270944 5.505418 5.682176
15 1.439108 2.101911 2.502485 2.788030 3.008793 3.188066 3.338551 3.467934 3.581209 3.681803 3.772166 3.854108 3.929005 3.997925 4.061712 4.121047 4.176486 4.228488 4.277436 4.651989 4.905573 5.247825 5.480945 5.656694
16 1.436068 2.096865 2.495948 2.7803 3.000071 3.178498 3.328250 3.456985 3.569684 3.669759 3.75965 3.841162 3.915663 3.984216 4.047663 4.106681 4.161824 4.213546 4.262231 4.634774 4.887015 5.227455 5.459365 5.634213
17 1.433397 2.092428 2.490198 2.773497 2.992391 3.170069 3.319169 3.447329 3.559514 3.659127 3.748598 3.829725 3.903873 3.972099 4.035242 4.093976 4.148852 4.200325 4.248775 4.619514 4.870529 5.209359 5.440181 5.614218
18 1.431030 2.088497 2.485101 2.767464 2.985576 3.162585 3.311102 3.438749 3.550474 3.649671 3.738765 3.819547 3.893377 3.961308 4.024178 4.082656 4.137293 4.188541 4.236778 4.605888 4.855804 5.193166 5.423003 5.596306
19 1.428918 2.08499 2.480552 2.762076 2.979488 3.155896 3.30389 3.431072 3.542383 3.641206 3.729960 3.810429 3.883971 3.951636 4.014258 4.072505 4.126925 4.177969 4.226014 4.593643 4.84256 5.178585 5.407524 5.580158
20 1.427023 2.081842 2.476467 2.757236 2.974016 3.149882 3.297401 3.424164 3.535099 3.633583 3.722027 3.802213 3.875493 3.942916 4.005312 4.063349 4.117571 4.168429 4.216298 4.582577 4.830579 5.16538 5.393498 5.565519
24 1.421053 2.071924 2.463589 2.741964 2.956732 3.130867 3.276871 3.402288 3.512015 3.609405 3.696852 3.776122 3.848556 3.915194 3.976858 4.03421 4.087789 4.138042 4.185340 4.547205 4.792208 5.122986 5.348394 5.518394
30 1.415131 2.062082 2.450796 2.726770 2.939512 3.111895 3.256356 3.380399 3.488888 3.585153 3.67157 3.749892 3.821449 3.887270 3.948172 4.00481 4.057717 4.107336 4.154034 4.511241 4.753052 5.079524 5.302021 5.469846
40 1.409257 2.052316 2.438086 2.711654 2.922351 3.092956 3.235846 3.358481 3.465697 3.5608 3.646150 3.723487 3.794128 3.859096 3.919198 3.975085 4.027284 4.076232 4.122296 4.474532 4.712898 5.034679 5.253982 5.419412
60 1.40343 2.042626 2.425459 2.696611 2.905244 3.074043 3.215327 3.336516 3.442417 3.536316 3.620555 3.696861 3.766541 3.830609 3.889866 3.944956 3.996401 4.044636 4.09002 4.436878 4.671454 4.987998 5.203693 5.366394
120 1.397651 2.033010 2.412913 2.681639 2.888185 3.055146 3.194785 3.314484 3.419022 3.511665 3.59474 3.66996 3.738623 3.801735 3.86009 3.914325 3.96496 4.012423 4.057072 4.398008 4.628308 4.938805 5.150236 5.309666
1e38 1.391918 2.023469 2.400447 2.666735 2.871167 3.036254 3.174203 3.292360 3.395479 3.486805 3.568651 3.642718 3.710296 3.772381 3.829761 3.883069 3.93282 3.979437 4.023276 4.357546 4.582861 4.886029 5.092081 5.247256"""

q0750 = """\
2 2.267583 3.308014 3.969236 4.451126 4.82785 5.13561 5.394819 5.618097 5.813776 5.987632 6.143829 6.285461 6.41489 6.533954 6.644113 6.746546 6.842214 6.931913 7.01631 7.660853 8.09584 8.68119 9.0788 9.377929
3 2.011896 2.883775 3.431223 3.829258 4.140443 4.394852 4.609323 4.794233 4.956425 5.10064 5.230299 5.347941 5.455509 5.554514 5.646158 5.73141 5.811064 5.885775 5.956093 6.493827 6.857365 7.3472 7.680302 7.931152
4 1.901267 2.701018 3.198596 3.559322 3.841087 4.071417 4.265624 4.433118 4.580085 4.710812 4.828384 4.935098 5.032703 5.122566 5.205771 5.283192 5.355547 5.423427 5.48733 5.976418 6.307462 6.753955 7.057827 7.286775
5 1.839820 2.599651 3.069171 3.40865 3.673526 3.889955 4.072422 4.229795 4.367901 4.490764 4.601285 4.701617 4.793402 4.877922 4.956192 5.029034 5.09712 5.161005 5.221154 5.681792 5.993844 6.415033 6.70187 6.918073
6 1.800788 2.535293 2.986795 3.312495 3.566338 3.773641 3.948369 4.099056 4.231292 4.348941 4.45478 4.550869 4.638783 4.719746 4.794731 4.864523 4.929764 4.990987 5.048635 5.490302 5.789693 6.194025 6.469523 6.677248
7 1.773818 2.490830 2.929770 3.245783 3.491823 3.692639 3.86185 4.007755 4.135786 4.249692 4.352165 4.445203 4.530329 4.608729 4.681345 4.748937 4.812126 4.871427 4.927269 5.35523 5.64547 6.037624 6.304935 6.506543
8 1.754075 2.458283 2.887956 3.196776 3.436989 3.632943 3.798002 3.940301 4.065154 4.176226 4.276148 4.366871 4.44988 4.526332 4.597147 4.663065 4.724692 4.782528 4.836995 5.254505 5.537762 5.920623 6.18169 6.378634
9 1.739001 2.433431 2.855984 3.159245 3.394934 3.587097 3.748912 3.888384 4.010742 4.119586 4.2175 4.306396 4.387735 4.462649 4.532041 4.596635 4.657026 4.713704 4.767081 5.176307 5.454025 5.829512 6.085625 6.27887
10 1.727116 2.413835 2.830746 3.129578 3.361648 3.550769 3.709972 3.847165 3.967506 4.074547 4.170832 4.258248 4.33823 4.411895 4.480128 4.543645 4.60303 4.658765 4.711254 5.113722 5.386914 5.756374 6.008439 6.198662
11 1.717506 2.397989 2.810315 3.105535 3.334641 3.521265 3.678317 3.813629 3.932304 4.037852 4.132788 4.218976 4.297831 4.370457 4.437728 4.500349 4.558895 4.613844 4.665594 5.062423 5.331834 5.696254 5.944934 6.13263
12 1.709576 2.384911 2.793439 3.085654 3.312288 3.496821 3.65207 3.785802 3.903075 4.007365 4.101163 4.186312 4.264215 4.335963 4.402419 4.46428 4.522117 4.5764 4.627523 5.019561 5.285754 5.645883 5.891679 6.077222
13 1.70292 2.373934 2.779263 3.068939 3.293478 3.476235 3.62995 3.762334 3.878409 3.981623 4.074447 4.158707 4.235793 4.306786 4.372542 4.433751 4.490977 4.544687 4.595269 4.983178 5.246593 5.603014 5.846316 6.029999
14 1.697255 2.364590 2.767188 3.05469 3.27743 3.458659 3.611050 3.742271 3.85731 3.959593 4.051572 4.13506 4.211437 4.281774 4.346922 4.407563 4.464258 4.517468 4.567581 4.951886 5.212872 5.566049 5.807169 5.989222
15 1.692374 2.356539 2.756778 3.042397 3.263576 3.443476 3.594714 3.724919 3.839053 3.940521 4.031759 4.114571 4.190326 4.260088 4.324701 4.384844 4.441071 4.493842 4.54354 4.92467 5.183511 5.533819 5.773008 5.95362
16 1.688126 2.349531 2.747712 3.031684 3.251494 3.430227 3.580451 3.709761 3.823097 3.923845 4.01443 4.096644 4.171848 4.2411 4.305239 4.364939 4.420752 4.473133 4.522464 4.900769 5.1577 5.505449 5.742915 5.92224
17 1.684395 2.343375 2.739744 3.022264 3.240865 3.418565 3.567889 3.696405 3.809031 3.909139 3.999142 4.080823 4.155535 4.224333 4.288048 4.347353 4.402795 4.454828 4.50383 4.879604 5.134819 5.48027 5.716186 5.894353
18 1.681092 2.337926 2.732687 3.013916 3.23144 3.408218 3.55674 3.684546 3.796536 3.896071 3.985552 4.066754 4.141026 4.209415 4.27275 4.331699 4.386808 4.438527 4.487232 4.860723 5.114389 5.457759 5.692272 5.86939
19 1.678147 2.333067 2.726393 3.006467 3.223026 3.398978 3.546777 3.673945 3.785363 3.884381 3.973391 4.054162 4.128035 4.196054 4.259045 4.317673 4.37248 4.423914 4.472351 4.843772 5.096029 5.437505 5.67074 5.846902
20 1.675506 2.328708 2.720745 2.999780 3.215469 3.390674 3.537821 3.664411 3.775312 3.873861 3.962444 4.042823 4.116334 4.184018 4.246696 4.305031 4.359563 4.410739 4.458932 4.828464 5.079434 5.419178 5.651242 5.82653
24 1.667194 2.314991 2.702957 2.978701 3.191627 3.364455 3.50952 3.63426 3.7435 3.840544 3.927753 4.006868 4.079211 4.14581 4.207477 4.264864 4.318505 4.368841 4.416241 4.779619 5.026378 5.360437 5.58865 5.761054
30 1.658964 2.301406 2.68532 2.957771 3.167919 3.338345 3.481298 3.604155 3.711699 3.8072 3.892996 3.970809 4.041947 4.107423 4.168039 4.224442 4.277156 4.326617 4.373187 4.730101 4.9724 5.300398 5.524486 5.693793
40 1.650814 2.28795 2.667830 2.936984 3.144337 3.312335 3.453142 3.574077 3.679882 3.773798 3.858136 3.934602 4.004488 4.068796 4.128318 4.183691 4.235434 4.283976 4.329675 4.679735 4.917252 5.238689 5.458277 5.62419
60 1.642744 2.274622 2.650486 2.916339 3.120874 3.286413 3.425034 3.544004 3.648023 3.740302 3.823131 3.898196 3.966776 4.029861 4.088234 4.142523 4.19324 4.24081 4.285584 4.628295 4.860604 5.174794 5.389348 5.551435
120 1.634753 2.261421 2.633285 2.895829 3.097525 3.260567 3.396959 3.513912 3.616089 3.706672 3.787929 3.861531 3.92874 3.990536 4.047692 4.10083 4.150455 4.196985 4.240768 4.575490 4.802013 5.107977 5.316696 5.474283
1e38 1.626840 2.248346 2.616224 2.875451 3.074279 3.234786 3.368898 3.483775 3.584045 3.672862 3.752475 3.824535 3.890294 3.950721 4.006580 4.058483 4.106932 4.152338 4.195044 4.520933 4.740866 5.037152 5.238766 5.390726"""

q0800 = """\
2 2.666345 3.820436 4.558532 5.098158 5.520848 5.866626 6.158145 6.409446 6.62982 6.825717 7.001791 7.161505 7.307502 7.441845 7.566171 7.681802 7.789818 7.891113 7.986436 8.714887 9.206808 9.868718 10.31830 10.65683
3 2.316120 3.245426 3.832597 4.261107 4.596942 4.871989 5.104169 5.304561 5.480484 5.637021 5.777843 5.905682 6.022626 6.130305 6.230013 6.322797 6.409513 6.49087 6.567462 7.153711 7.55053 8.085698 8.449862 8.724212
4 2.168283 3.003795 3.52645 3.90676 4.204595 4.44853 4.654519 4.832388 4.988615 5.127694 5.25287 5.366554 5.470593 5.566425 5.655195 5.737827 5.815079 5.887577 5.955847 6.47896 6.833568 7.31242 7.638648 7.884592
5 2.087215 2.871505 3.358337 3.711564 3.987876 4.214094 4.405111 4.57007 4.714986 4.844026 4.960193 5.065723 5.162321 5.25132 5.333779 5.410553 5.482342 5.549725 5.613191 6.099852 6.430105 6.876484 7.180827 7.410389
6 2.036122 2.788188 3.252203 3.588013 3.850385 4.06507 4.246305 4.402806 4.540296 4.662734 4.772969 4.873124 4.964814 5.049304 5.127595 5.200498 5.268677 5.33268 5.392969 5.855517 6.169658 6.594568 6.884463 7.103222
7 2.001005 2.730943 3.179141 3.502777 3.755348 3.961886 4.136188 4.286677 4.418877 4.536604 4.642603 4.738913 4.82709 4.908349 4.983652 5.05378 5.119368 5.180945 5.238953 5.684175 5.986732 6.39621 6.675724 6.886723
8 1.975395 2.689205 3.125785 3.440421 3.685706 3.886163 4.055272 4.201248 4.329470 4.443647 4.546448 4.639854 4.725375 4.804189 4.87723 4.945254 5.008879 5.068616 5.124894 5.556957 5.850708 6.248453 6.520077 6.725179
9 1.955898 2.657432 3.085114 3.392817 3.632464 3.828199 3.993263 4.135716 4.260824 4.37222 4.472512 4.563637 4.64707 4.723960 4.79522 4.861587 4.923664 4.981949 5.036862 5.458529 5.745314 6.133773 6.399153 6.59959
10 1.940561 2.632439 3.053086 3.355281 3.590431 3.782386 3.944205 4.083824 4.206424 4.315576 4.413841 4.503121 4.584862 4.660193 4.730009 4.795032 4.855852 4.912959 4.966762 5.37997 5.661078 6.041965 6.302252 6.498885
11 1.928182 2.612267 3.027211 3.324922 3.556399 3.745257 3.904411 4.041698 4.16223 4.269529 4.366119 4.453871 4.534212 4.608251 4.676869 4.740775 4.800552 4.85668 4.909561 5.315725 5.5921 5.966667 6.222702 6.41616
12 1.917981 2.595645 3.005872 3.299861 3.528278 3.714552 3.871475 4.006806 4.125603 4.231343 4.326522 4.412988 4.492148 4.565096 4.632701 4.695665 4.754559 4.809858 4.861959 5.262152 5.534506 5.9037 6.156119 6.346875
13 1.909431 2.581711 2.987972 3.278821 3.504650 3.688731 3.843759 3.977426 4.094742 4.199153 4.293127 4.378492 4.45664 4.528654 4.595391 4.657546 4.715682 4.770269 4.8217 5.216755 5.485643 5.850201 6.099497 6.287919
14 1.90216 2.569864 2.972742 3.260906 3.484516 3.666713 3.82011 3.952342 4.068380 4.171642 4.264573 4.348985 4.426256 4.497459 4.563444 4.624895 4.682373 4.736342 4.787189 5.177769 5.443632 5.804138 6.050703 6.237084
15 1.895903 2.559666 2.959626 3.245467 3.467154 3.647714 3.799691 3.930673 4.045596 4.147854 4.239872 4.32345 4.399954 4.470446 4.53577 4.596605 4.653505 4.706931 4.757265 5.143906 5.4071 5.764029 6.00818 6.192757
16 1.89046 2.550797 2.948212 3.232024 3.452027 3.631152 3.781882 3.911763 4.025705 4.127077 4.218291 4.301132 4.376957 4.446821 4.511561 4.571849 4.628237 4.681181 4.731062 5.114203 5.375025 5.728765 5.970765 6.153733
17 1.885683 2.543012 2.93819 3.220213 3.438729 3.616585 3.766210 3.895117 4.008187 4.108772 4.19927 4.281455 4.356676 4.42598 4.490198 4.549999 4.605930 4.658444 4.707919 5.08793 5.346623 5.697501 5.937567 6.119088
18 1.881457 2.536125 2.929319 3.209754 3.426947 3.603672 3.752313 3.880348 3.992639 4.09252 4.182377 4.263975 4.338653 4.407454 4.471204 4.530568 4.586089 4.638215 4.687324 5.064516 5.321288 5.66958 5.907896 6.088107
19 1.877691 2.529988 2.921412 3.200427 3.416435 3.592147 3.739903 3.867156 3.978745 4.077993 4.167272 4.24834 4.322529 4.390877 4.454204 4.513172 4.568321 4.620098 4.668877 5.043513 5.298541 5.644481 5.881205 6.060224
20 1.874315 2.524485 2.914320 3.192058 3.407000 3.581797 3.728755 3.855300 3.966255 4.064929 4.153685 4.234272 4.308018 4.375954 4.438897 4.497506 4.552317 4.603776 4.652254 5.024562 5.277998 5.621789 5.857057 6.034984
24 1.863701 2.507187 2.89201 3.165709 3.377268 3.549158 3.69357 3.817854 3.92678 4.023614 4.110690 4.189731 4.262048 4.328656 4.390359 4.447807 4.501527 4.551956 4.599461 4.964202 5.212441 5.549191 5.779675 5.954012
30 1.853207 2.490080 2.869925 3.139592 3.347756 3.516716 3.658554 3.780544 3.887403 3.982357 4.067712 4.145167 4.216014 4.281252 4.341675 4.397921 4.450509 4.49987 4.546362 4.903188 5.145946 5.47522 5.700597 5.871091
40 1.842829 2.473164 2.848060 3.113699 3.318456 3.484461 3.62369 3.743347 3.848096 3.941126 4.024712 4.100533 4.16986 4.233681 4.292775 4.34777 4.399178 4.447421 4.492854 4.841333 5.078248 5.399473 5.619306 5.785608
60 1.832568 2.456435 2.826413 3.088026 3.289358 3.452379 3.588962 3.70624 3.808829 3.899882 3.981645 4.055774 4.123524 4.185868 4.243575 4.297261 4.34743 4.394499 4.438814 4.778404 5.009002 5.321406 5.535087 5.696698
120 1.822478 2.439890 2.804980 3.062567 3.260456 3.420458 3.55435 3.669198 3.769570 3.858583 3.938458 4.010829 4.076934 4.137731 4.193979 4.246285 4.295145 4.340968 4.384094 4.714106 4.937761 5.24027 5.446912 5.603078
1e38 1.812388 2.423529 2.783758 3.037317 3.231739 3.388684 3.519834 3.632192 3.73028 3.817183 3.895093 3.965627 4.030005 4.089173 4.143877 4.194716 4.242179 4.286668 4.328517 4.648069 4.863937 5.155024 5.353283 5.50281"""

q0850 = """\
2 3.226562 4.548022 5.398759 6.022701 6.512387 6.913502 7.251997 7.54401 7.800236 8.028116 8.233021 8.418953 8.588968 8.74545 8.890294 9.02503 9.150913 9.268977 9.380094 10.22972 10.80450 11.58094 12.11086 12.51097
3 2.721399 3.731515 4.374509 4.845675 5.215912 5.5197 5.776502 5.998388 6.193356 6.366968 6.523249 6.665198 6.795111 6.914781 7.025634 7.128823 7.225292 7.315823 7.401073 8.054202 8.496827 9.094477 9.501702 9.808753
4 2.514747 3.399285 3.956491 4.363675 4.68348 4.945965 5.16798 5.359938 5.52872 5.679113 5.814574 5.937683 6.050411 6.154302 6.25058 6.34024 6.424092 6.502812 6.576963 7.145835 7.532079 8.054293 8.410406 8.679063
