# # NURBS with Extraordinary Points: # High-degree, Non-uniform, Rational Subdivision Schemes # # Thomas J. Cashman Ursula H. Augsdörfer Neil A. Dodgson Malcolm A Sabin # # Auxiliary material: # Precomputed tables containing bounded curvature solutions # # # In the following tables: # Lines beginning '#' are comments # Values are separated by whitespace # The tables are separated by blank lines # # The table for alpha^d_n comes first, followed by beta^d_n, gamma^d_n and finally delta_d # # Degree, d, varies across a line, for odd values from 3 to 27 inclusive (13 columns) # Valency, n, varies down each table, for all values from 3 to 100 inclusive (98 rows) # # The 13 values for delta_d appear in a single row, as this table is only relevant for valency 3 (see the paper for details). # # Alpha 1.33333333 1.33333333 1.33333333 1.33333333 1.33333333 1.33333333 1.33333333 1.33333333 1.33333333 1.33333333 1.33333333 1.33333333 1.33333333 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 2.60788828 8.06413685 13.57430011 19.51044573 25.66015317 32.14617318 38.85068179 45.83255209 53.01208763 60.42313192 68.00985752 75.79526916 83.73755415 4.64121158 15.55975558 29.34728868 45.44638602 63.60683818 83.55664916 105.17824953 128.32352134 152.89362119 178.79812597 205.95157322 234.29669017 263.75752037 7.07872200 24.34496273 47.41703836 75.09122993 107.26307848 143.24812859 183.03693968 226.24323584 272.82451560 322.53518690 375.31687646 431.00281614 489.52758910 9.90851001 34.57099354 68.15325114 108.88811641 156.87410904 210.97805619 271.36314079 337.36510482 409.05257823 485.99251294 568.19947547 655.37119107 747.49201487 13.12501524 46.25770846 91.67569148 147.07282699 212.74485572 287.07754309 370.44232737 461.85821488 561.54169879 668.83836616 783.86818506 906.16493706 1035.79092399 16.72547448 59.39741705 118.01887190 189.74665143 275.04028175 371.77304238 480.54222360 600.01528530 730.58170690 871.33452386 1022.52336090 1183.49127443 1354.40028504 20.70840361 73.97891377 147.18913227 236.95025095 343.84424387 465.19909389 601.84489040 752.06514141 916.43931469 1093.77929947 1284.48266097 1487.67707985 1703.64147958 25.07294960 89.99264993 179.18405996 288.69786603 419.19813287 567.43297822 734.46691546 918.16819723 1119.31792558 1336.41999047 1570.03380814 1819.04872244 2083.87425100 29.81859381 107.43135037 213.99909619 344.99255830 501.12160875 678.51837638 878.48145786 1098.43296474 1339.36409480 1599.44494403 1879.40766786 2177.88148929 2495.41761940 34.94500594 126.28964133 251.62970122 405.83292683 589.62334243 798.47966497 1033.93411874 1292.93188204 1576.68106563 1882.99279760 2212.78092736 2564.39355599 2938.53286243 40.45196732 146.56357180 292.07197011 471.21603421 684.70651990 927.33022099 1200.85331097 1501.71318039 1831.34101887 2187.16416743 2570.28599919 2978.75300423 3413.42639605 46.33932843 168.25022034 335.32271902 541.13864943 786.37165444 1065.07717387 1379.25677864 1724.80907769 2103.39444271 2512.03180026 2952.02130969 3421.08769169 3920.25851918 52.60698412 191.34740545 381.37940629 615.59774364 894.61802132 1211.72411368 1569.15563247 1962.24123491 2392.87683532 2857.64840825 3358.05995645 3891.49448244 4459.15283308 59.25485865 215.85347962 430.24001694 694.59065713 1009.44438555 1367.27263687 1770.55683798 2214.02433415 2699.81335363 3224.05240706 3788.45641354 4390.04683644 5030.20452606 66.28289634 241.76718390 481.90295371 778.11512557 1130.84936523 1531.72323146 1983.46475383 2480.16841501 3024.22199505 3611.27201428 4243.25152312 4916.80069732 5633.48708096 73.69105547 269.08754526 536.36694615 866.16925017 1258.83160637 1705.07578540 2207.88208864 2760.68040331 3366.11576710 4019.32814496 4722.47614064 5471.79892877 6269.05748855 81.47930427 297.81380328 593.63097838 958.75144965 1393.38986054 1887.32987844 2443.81050103 3055.56511719 3725.50417003 4448.23645153 5226.15377478 6055.07460979 6936.96021517 89.64761823 327.94535757 653.69423316 1055.86041011 1534.52301275 2078.48494905 2691.25097888 3364.82593467 4102.39421548 4898.00876382 5754.30249619 6666.65346811 7637.23019173 98.19597815 359.48172943 716.55604870 1157.49503934 1682.23008483 2278.54038853 2950.20408115 3688.46524037 4496.79113174 5368.65411064 6306.93632048 7306.55567573 8369.89505684 107.12436882 392.42253372 782.21588553 1263.65442754 1836.51022716 2487.49559278 3220.67009313 4026.48472759 4908.69885627 5860.17944950 6884.06621520 7974.79717718 9134.97684063 116.43277810 426.76745792 850.67330105 1374.33781457 1997.36270579 2705.34998934 3502.64912677 4378.88560430 5338.12038282 6372.59019199 7485.70083741 8671.39067651 9932.49323209 126.12119615 462.51624642 921.92792981 1489.54456301 2164.78688832 2932.10305007 3796.14118580 4745.66873514 5785.05800849 6905.89058513 8111.84707805 9396.34637489 10762.45853730 136.18961496 499.66868863 995.97946818 1609.27413627 2338.78223020 3167.75429567 4101.14620810 5126.83474009 6249.51351128 7460.08399074 8762.51046657 10149.67252551 11624.88440774 146.63802795 538.22460982 1072.82766246 1733.52608075 2519.34826229 3412.30329566 4417.66409329 5522.38406367 6731.48827881 8035.17309190 9437.69547437 10931.37585394 12519.78039728 157.46642968 578.18386408 1152.47229943 1862.30001146 2706.48457989 3665.74966586 4745.69472059 5932.31702382 7230.98340260 8631.16004670 10137.40574386 11741.46187888 13447.15439086 168.67481558 619.54632883 1234.91319897 1995.59560026 2900.19083324 3928.09306479 5085.23796039 6356.63384680 7747.99974766 9248.04660396 10861.64426303 12579.93515865 14407.01293658 180.26318185 662.31190051 1320.15020814 2133.41256636 3100.46671937 4199.33318958 5436.29368149 6795.33469218 8282.53800443 9885.83419084 11610.41349935 13446.79948197 15399.36150474 192.23152526 706.48049114 1408.18319645 2275.75066852 3307.31197521 4479.46977191 5798.86175566 7248.41967085 8834.59872764 10544.52397988 12383.71550339 14342.05801679 16424.20469111 204.57984309 752.05202561 1499.01205204 2422.60969867 3520.72637175 4768.50257409 6172.94206032 7715.88885819 9404.18236593 11224.11694053 13181.55198941 15265.71342700 17481.54637758 217.30813298 799.02643952 1592.63667864 2573.98947672 3740.70970909 5066.43138550 6558.53448002 8197.74230359 9991.28928428 11924.61387921 14003.92439878 16217.76796472 18571.38985986 230.41639295 847.40367733 1689.05699302 2729.88984621 3967.26181228 5373.25601936 6955.63890714 8693.98003750 10595.91978139 12646.01547059 14850.83394988 17198.22354372 19693.73794963 243.90462126 897.18369105 1788.27292295 2890.31067073 4200.38252780 5688.97630981 7364.25524206 9204.60207657 11218.07410304 13388.32228218 15722.28167793 18207.08179812 20848.59305679 257.77281642 948.36643893 1890.28440553 3055.25183100 4440.07172055 6013.59210938 7784.38339301 9729.60842749 11857.75245246 14151.53479385 16618.26846675 19244.34412974 22035.95725589 272.02097713 1000.95188460 1995.09138575 3224.71322232 4686.32927135 6347.10328679 8216.02327581 10268.99908981 12514.95499865 14935.65341335 17538.79507445 20310.01174636 23255.83234034 286.64910227 1054.93999622 2102.69381538 3398.69475259 4939.15507480 6689.50972492 8659.17481337 10822.77405801 13189.68188271 15740.67848879 18483.86215413 21404.08569294 24508.21986677 301.65719083 1110.33074583 2213.09165199 3577.19634046 5198.54903743 7040.81131916 9113.83793522 11390.93332309 13881.93322306 16566.61031868 19453.47027073 22526.56687712 25793.12119116 317.04524194 1167.12410879 2326.28485810 3760.21791395 5464.51107616 7401.00797587 9580.01257702 11973.47687368 14591.70911955 17413.44916012 20447.61991496 23677.45609030 27110.53749927 332.81325485 1225.32006334 2442.27340054 3947.75940916 5737.04111696 7770.09961112 10057.69868005 12570.40469692 15319.00965648 18281.19523535 21466.31151453 24856.75402493 28460.46983139 348.96122886 1284.91859018 2561.05724987 4139.82076922 6016.13909376 8148.08614952 10546.89619072 13181.71677910 16063.83490562 19169.84873737 22509.54544375 26064.46128900 29842.91910328 365.48916338 1345.91967217 2682.63637988 4336.40194337 6301.80494737 8534.96752325 11047.60506013 13807.41310605 16826.18492814 20079.40983426 23577.32203118 27300.57841813 31257.88612353 382.39705786 1408.32329402 2807.01076717 4537.50288626 6594.03862473 8930.74367116 11559.82524362 14447.49366356 17606.05977635 21009.87867300 24669.64156621 28565.10588549 32705.37160830 399.68491184 1472.12944206 2934.18039084 4743.12355720 6892.84007814 9335.41453809 12083.55670039 15101.95843758 18403.45949520 21961.25538250 25786.50430453 29858.04411039 34185.37619368 417.35272489 1537.33810410 3064.14523210 4953.26391964 7198.20926463 9748.98007413 12618.79939320 15770.80741434 19218.38412344 22933.54007626 26927.91047272 31179.39346601 35697.90044616 435.40049661 1603.94926911 3196.90527409 5167.92394069 7510.14614546 10171.44023404 13165.55328792 16454.04058055 20050.83369455 23926.73285445 28093.86027210 32529.15428411 37242.94487155 453.82822667 1671.96292724 3332.46050160 5387.10359063 7828.65068548 10602.79497685 13723.81835332 17151.65792344 20900.80823753 24940.83380568 29284.35388215 33907.32686165 38820.50992274 472.63591476 1741.37906957 3470.81090093 5610.80284266 8153.72285310 11043.04426523 14293.59456083 17863.65943080 21768.30777766 25975.84300875 30499.39146315 35313.91146449 40430.59600605 491.82356060 1812.19768804 3611.95645967 5839.02167246 8485.36261934 11492.18806526 14874.88188420 18590.04509096 22653.33233699 27031.76053376 31738.97315868 36748.90833136 42073.20348697 511.39116393 1884.41877537 3755.89716658 6071.76005794 8823.56995806 11950.22634602 15467.68029937 19330.81489295 23555.88193472 28108.58644328 33003.09909765 38212.31767705 43748.33269492 531.33872452 1958.04232493 3902.63301144 6309.01797912 9168.34484541 12417.15907928 16071.98978416 20085.96882628 24475.95658777 29206.32079328 34291.76939606 39704.13969533 45455.98392747 551.66624217 2033.06833072 4052.16398497 6550.79541763 9519.68725961 12892.98623917 16687.81031832 20855.50688111 25413.55631097 30324.96363399 35604.98415851 41224.37456128 47196.15745397 572.37371669 2109.49678727 4204.49007872 6797.09235692 9877.59718080 13377.70780209 17315.14188301 21639.42904813 26368.68111741 31464.51501057 36942.74347955 42773.02243350 48968.85351871 593.46114790 2187.32768958 4359.61128496 7047.90878164 10242.07459082 13871.32374633 17953.98446100 22437.73531857 27341.33101867 32624.97496367 38305.04744479 44350.08345586 50774.07234362 614.92853566 2266.56103309 4517.52759664 7303.24467808 10613.11947291 14373.83405201 18604.33803634 23250.42568421 28331.50602510 33806.34353003 39691.89613192 45955.55775922 52611.81413080 636.77587980 2347.19681361 4678.23900726 7563.10003325 10990.73181188 14885.23870082 19266.20259434 24077.50013740 29339.20614552 35008.62074289 41103.28961153 47589.44546267 54482.07906443 659.00318021 2429.23502732 4841.74551089 7827.47483561 11374.91159364 15405.53767592 19939.57812137 24918.95867050 30364.43138823 36231.80663257 42539.22794800 49251.74667494 56384.86731285 681.61043675 2512.67567071 5008.04710224 8096.36907428 11765.65880528 15934.73096180 20624.46460485 25774.80127714 31407.18176034 37475.90122625 43999.71119994 50942.46149536 58320.17903000 704.59764934 2597.51874067 5177.14377611 8369.78273939 12162.97343485 16472.81854414 21320.86203313 26645.02795055 32467.45726829 38740.90454787 45484.73942100 52661.59001466 60288.01435699 727.96481784 2683.76423405 5349.03552798 8647.71582182 12566.85547146 17019.80040960 22028.77039540 27529.63868483 33545.25791785 40026.81662200 46994.31266024 54409.13231665 62288.37342330 751.71194217 2771.41214819 5523.72235358 8930.16831316 12977.30490486 17575.67654609 22748.18968130 28428.63347430 34640.58371415 41333.63746845 48528.43096270 56185.08847735 64321.25634792 775.83902226 2860.46248056 5701.20424899 9217.14020553 13394.32172573 18140.44694224 23479.11988238 29342.01231360 35753.43466186 42661.36710569 50087.09436965 57989.45856763 66386.66324036 800.34605801 2950.91522883 5881.48121058 9508.63149184 13817.90592527 18714.11158742 24221.56098927 30269.77519775 36883.81076513 44010.00555167 51670.30291912 59822.24265165 68484.59420162 825.23304936 3042.77039083 6064.55323503 9804.64216539 14248.05749567 19296.67047200 24975.51299401 31211.92212205 38031.71202768 45379.55282236 53278.05664603 61683.44078992 70615.04932483 850.49999623 3136.02796458 6250.42031913 10105.17222000 14684.77642926 19888.12358698 25740.97588913 32168.45308203 39197.13845296 46770.00893225 54910.35558268 63573.05303684 72778.02869607 876.14689858 3230.68794820 6439.08246013 10410.22164992 15128.06271914 20488.47092369 26517.94966762 33139.36807358 40380.09004401 48181.37389449 56567.19975881 65491.07944373 74973.53239494 902.17375630 3326.75033999 6630.53965528 10719.79044982 15577.91635894 21097.71247462 27306.43432299 34124.66709278 41580.56680361 49613.64772202 58248.58920199 67437.52005811 77201.56049533 928.58056938 3424.21513834 6824.79190210 11033.87861474 16034.33734244 21715.84823208 28106.42984903 35124.35013592 42798.56873425 51066.83042580 59954.52393767 69412.37492352 79462.11306556 955.36733775 3523.08234176 7021.83919824 11352.48614010 16497.32566426 22342.87818959 28917.93624030 36138.41719957 44034.09583825 52540.92201673 61685.00398947 71415.64407982 81755.19016919 982.53406135 3623.35194887 7221.68154157 11675.61302154 16966.88131914 22978.80234080 29740.95349121 37166.86828045 45287.14811771 54035.92250457 63440.02937931 73447.32756559 84080.79186363 1010.08074021 3725.02395853 7424.31893007 12003.25925507 17443.00430215 23623.62067935 30575.48159684 38209.70337494 46557.72557438 55551.83189825 65219.60012754 75507.42541558 86438.91820841 1038.00737420 3828.09836905 7629.75136186 12335.42483695 17925.69460880 24277.33320018 31421.52055250 39266.92248179 47845.82821040 57088.65020624 67023.71625378 77595.93766238 88829.56925172 1066.31396332 3932.57517980 7837.97883519 12672.10976366 18414.95223482 24939.93989774 32279.07035391 40338.52559659 49151.45602678 58646.37743632 68852.37777385 79712.86433646 91252.74503903 1095.00050753 4038.45438955 8049.00134838 13013.31403193 18910.77717621 25611.44076736 33148.13099680 41424.51271700 50474.60902533 60225.01359578 70705.58470545 81858.20546608 93708.44561815 1124.06700680 4145.73599732 8262.81889996 13359.03763871 19413.16942925 26291.83580443 34028.70247742 42524.88384167 51815.28720724 61824.55869129 72583.33706367 84031.96107774 96196.67102945 1153.51346100 4254.42000222 8479.43148830 13709.28058112 19922.12899042 26981.12500460 34920.78479209 43639.63896716 53173.49057382 63445.01272921 74485.63486300 86234.13119619 98717.42131217 1183.33987036 4364.50640342 8698.83911251 14064.04285644 20437.65585647 27679.30836441 35824.37793737 44768.77809172 54549.21912606 65086.37571527 76412.47811668 88464.71584446 101270.69650252 1213.54623461 4475.99519996 8921.04177086 14423.32446203 20959.75002432 28386.38587868 36739.48191014 45912.30121325 55942.47286524 66748.64765540 78363.86683713 90723.71504438 103856.49663463 1244.13255380 4588.88639092 9146.03946232 14787.12539576 21488.41149104 29102.35754525 37666.09670729 47070.20832989 57353.25179203 68431.82855363 80339.80103609 93011.12881608 106474.82174073 1275.09882787 4703.17997618 9373.83218577 15155.44565517 22023.64025394 29827.22336011 38604.22232595 48242.49943984 58781.55590721 70135.91841574 82340.28072447 95326.95717873 109125.67185003 1306.44505691 4818.87595461 9604.41994017 15528.28523854 22565.43631045 30560.98331908 39553.85876355 49429.17454104 60227.38521191 71860.91724591 84365.30591388 97671.20015001 111809.04699148 1338.17124077 4935.97432567 9837.80272451 15905.64414348 23113.79965815 31303.63742290 40515.00601752 50630.23363175 61690.73970687 73606.82504824 86414.87661124 100043.85774698 114524.94719137 1370.27737949 5054.47508876 10073.98053786 16287.52236807 23668.73029471 32055.18566502 41487.66408530 51845.67671159 63171.61939312 75373.64182672 88488.99282638 102444.92998504 117273.37247449 1402.76347304 5174.37824334 10312.95337960 16673.91991048 24230.22821811 32815.62804414 42471.83296340 53075.50377770 64670.02426930 77161.36758521 90587.65456915 104874.41687935 120054.32286406 1435.62952140 5295.68378887 10554.72124818 17064.83676928 24798.29342624 33584.96455708 43467.51265391 54319.71482950 66185.95433816 78970.00232655 92710.86184720 107332.31844363 122867.79838262 1468.87552458 5418.39172486 10799.28414353 17460.27294348 25372.92591717 34363.19520245 44474.70315048 55578.30986518 67719.40960091 80799.54605457 94858.61466775 109818.63469129 125713.79905055 1502.50148253 5542.50205082 11046.64206467 17860.22843189 25954.12568919 35150.31997817 45493.40445269 56851.28888360 69270.39005461 82649.99877185 97030.91303805 112333.36563450 128592.32488768 1536.50739524 5668.01476632 11296.79501091 18264.70323031 26541.89274067 35946.33888117 46523.61655869 58138.65188382 70838.89570258 84521.36048219 99227.75696466 114876.51128526 131503.37591112 1570.89326268 5794.92987087 11549.74298158 18673.69734016 27136.22706941 36751.25190987 47565.33946678 59440.39886334 72424.92654463 86413.63118737 101449.14645397 117448.07165444 134446.95214690 1605.65908489 5923.24736429 11805.48597605 19087.21075945 27737.12867500 37565.05906239 48618.57317529 60756.52982436 74028.48258097 88326.81089025 103695.08151294 120048.04675246 137423.05359312 1640.80486195 6052.96724590 12064.02399377 19505.24348713 28344.59755450 38387.76033701 49683.31768276 62087.04476272 75649.56381343 90260.89959379 105965.56214555 122676.43658919 140431.68028127 1676.33059349 6184.08951552 12325.35703411 19927.79552176 28958.63370733 39219.35573198 50759.57298764 63431.94367850 77288.17023984 92215.89729862 108260.58835807 125333.24117417 143472.83222399 1712.23627983 6316.61417278 12589.48509660 20354.86686239 29579.23713407 40059.84524542 51847.33908858 64791.22657066 78944.30186021 94191.80400824 110580.16015355 128018.46051605 146546.50943179 1748.52192085 6450.54121736 12856.40818073 20786.45750804 30206.40783030 40909.22887649 52946.61598421 66164.89343848 80617.95867766 96188.61972490 112924.27754044 130732.09462302 149652.71191853 1785.18751660 6585.87064897 13126.12628604 21222.56745775 30840.14579537 41767.50662367 54057.40367267 67552.94428096 82309.14069098 98206.34445016 115292.94052040 133474.14350368 152791.43969725 1822.23306678 6722.60246715 13398.63941188 21663.19671060 31480.45103076 42634.67848274 55179.70215186 68955.37909627 84017.84790070 100244.97818494 117686.14909930 136244.60716484 155962.69277819 1859.65857203 6860.73667261 13673.94755843 22108.34526561 32127.32353102 43510.74445836 56313.51142754 70372.19788440 85744.08030655 102304.52093209 120103.90327969 139043.48561434 159166.47117705 1897.46403172 7000.27326298 13952.05072382 22558.01312234 32780.76329922 44395.70454431 57458.83149019 71803.40064893 87487.83791087 104384.97269303 122546.20306738 141870.77885778 162402.77490195 # Beta 1.25597725 1.13695150 1.12042588 1.11720648 1.11492424 1.11427982 1.11359525 1.11354885 1.11328917 1.11339466 1.11329246 1.11343349 1.11339926 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 0.64994561 0.79186586 0.81519051 0.83388649 0.84068864 0.84717432 0.85031743 0.85344610 0.85521393 0.85701373 0.85812813 0.85927985 0.86003724 0.43646183 0.60478995 0.64166882 0.67697884 0.69074274 0.70437099 0.71127309 0.71825683 0.72231350 0.72649775 0.72913405 0.73189440 0.73372911 0.31062878 0.46278772 0.50264497 0.54585002 0.56407723 0.58265202 0.59253968 0.60263226 0.60870278 0.61498092 0.61904409 0.62329927 0.62619077 0.23208770 0.36043104 0.39786318 0.44211897 0.46209026 0.48300114 0.49464097 0.50664286 0.51409968 0.52183664 0.52697489 0.53235490 0.53609193 0.18007084 0.28675421 0.32002095 0.36178838 0.38164393 0.40294112 0.41524312 0.42807092 0.43626581 0.44481020 0.45061441 0.45669963 0.46100958 0.14387888 0.23282529 0.26180196 0.29974224 0.31849564 0.33902226 0.35123529 0.36411198 0.37253016 0.38135851 0.38747138 0.39389661 0.39852369 0.11767599 0.19248801 0.21760382 0.25148637 0.26872921 0.28791609 0.29960141 0.31204684 0.32033772 0.32908490 0.33523870 0.34172804 0.34646713 0.09808410 0.16165846 0.18346614 0.21353378 0.22917538 0.24681270 0.25775324 0.26950899 0.27746090 0.28589859 0.29191326 0.29827806 0.30298090 0.08304261 0.13762188 0.15664540 0.18330447 0.19740849 0.21348231 0.22359874 0.23455167 0.24205284 0.25005392 0.25581960 0.26194197 0.26651006 0.07123725 0.11854436 0.13523544 0.15891819 0.17161305 0.18620585 0.19549711 0.20562151 0.21262555 0.22013113 0.22558852 0.23140232 0.23577573 0.06179756 0.10316153 0.11789553 0.13900465 0.15043807 0.16367316 0.17217896 0.18149799 0.18799840 0.19499274 0.20011646 0.20559100 0.20973748 0.05412819 0.09058312 0.10366764 0.12255802 0.13287543 0.14488754 0.15266628 0.16122805 0.16724117 0.17373423 0.17852044 0.18364804 0.18755418 0.04781059 0.08016949 0.09185577 0.10883219 0.11816749 0.12908814 0.13620449 0.14406789 0.14962202 0.15563804 0.16009587 0.16488308 0.16854773 0.04254341 0.07145241 0.08194598 0.09726709 0.10573953 0.11569043 0.12220870 0.12943533 0.13456412 0.14013440 0.14428025 0.14874188 0.15217151 0.03810508 0.06408316 0.07355290 0.08743722 0.09515113 0.10424174 0.11022259 0.11687241 0.12161094 0.12676945 0.13062335 0.13477857 0.13798406 0.03432974 0.05779791 0.06638336 0.07901539 0.08606129 0.09438852 0.09988747 0.10601663 0.11039921 0.11518003 0.11876332 0.12263323 0.12562777 0.03109115 0.05239423 0.06021138 0.07174716 0.07820323 0.08585218 0.09091922 0.09657912 0.10063813 0.10507397 0.10840798 0.11201400 0.11481176 0.02829182 0.04771473 0.05486060 0.06543254 0.07136624 0.07841128 0.08309099 0.08832802 0.09209340 0.09621486 0.09932010 0.10268310 0.10529835 0.02585552 0.04363559 0.05019187 0.05991270 0.06538230 0.07188832 0.07622021 0.08107596 0.08457496 0.08841024 0.09130597 0.09444575 0.09689236 0.02372189 0.04005835 0.04609420 0.05506033 0.06011622 0.06613989 0.07015887 0.07467040 0.07792769 0.08150247 0.08420652 0.08714155 0.08943270 0.02184266 0.03690391 0.04247825 0.05077248 0.05545837 0.06104916 0.06478609 0.06898635 0.07202411 0.07536165 0.07789038 0.08063771 0.08278570 0.02017882 0.03410817 0.03927145 0.04696519 0.05131910 0.05652034 0.06000243 0.06392072 0.06675884 0.06988013 0.07224844 0.07482366 0.07683991 0.01869860 0.03161872 0.03641439 0.04356950 0.04762459 0.05247428 0.05572561 0.05938795 0.06204424 0.06496816 0.06718959 0.06960692 0.07150192 0.01737587 0.02939238 0.03385803 0.04052833 0.04431363 0.04884519 0.05188706 0.05531659 0.05780701 0.06055053 0.06263732 0.06490970 0.06669305 0.01618902 0.02739333 0.03156164 0.03779412 0.04133512 0.04557803 0.04842934 0.05164665 0.05398548 0.05656387 0.05852708 0.06066623 0.06234672 0.01512000 0.02559164 0.02949115 0.03532702 0.03864618 0.04262648 0.04530402 0.04832750 0.05052754 0.05295451 0.05480415 0.05682070 0.05840631 0.01415369 0.02396214 0.02761789 0.03309340 0.03621058 0.03995138 0.04247010 0.04531614 0.04738888 0.04967679 0.05142190 0.05332549 0.05482349 0.01327732 0.02248356 0.02591758 0.03106477 0.03399756 0.03751940 0.03989265 0.04257595 0.04453171 0.04669166 0.04834044 0.05013978 0.05155681 0.01248004 0.02113782 0.02436958 0.02921684 0.03198089 0.03530209 0.03754180 0.04007553 0.04192360 0.04396562 0.04552546 0.04722848 0.04857056 0.01175260 0.01990946 0.02295623 0.02752880 0.03013807 0.03327499 0.03539188 0.03778787 0.03953662 0.04146977 0.04294739 0.04456128 0.04583390 0.01108706 0.01878521 0.02166236 0.02598276 0.02844972 0.03141704 0.03342073 0.03568964 0.03734663 0.03917911 0.04058058 0.04211187 0.04332004 0.01047658 0.01775361 0.02047487 0.02456324 0.02689909 0.02971000 0.03160915 0.03376060 0.03533267 0.03707190 0.03840276 0.03985739 0.04100566 0.00991524 0.01680477 0.01938242 0.02325682 0.02547163 0.02813800 0.02994043 0.03198313 0.03347648 0.03512919 0.03639447 0.03777785 0.03887041 0.00939791 0.01593005 0.01837513 0.02205182 0.02415466 0.02668721 0.02840001 0.03034182 0.03176208 0.03333441 0.03453869 0.03585576 0.03689640 0.00892008 0.01512193 0.01744436 0.02093801 0.02293708 0.02534552 0.02697510 0.02882319 0.03017546 0.03167299 0.03282046 0.03407572 0.03506793 0.00847784 0.01437381 0.01658257 0.01990643 0.02180916 0.02410228 0.02565447 0.02741534 0.02870431 0.03013212 0.03122659 0.03242418 0.03337115 0.00806772 0.01367990 0.01578311 0.01894918 0.02076231 0.02294811 0.02442823 0.02610781 0.02733772 0.02870047 0.02974544 0.03088912 0.03179379 0.00768670 0.01303506 0.01504010 0.01805931 0.01978897 0.02187474 0.02328761 0.02489131 0.02606606 0.02736801 0.02836669 0.02945993 0.03032499 0.00733208 0.01243480 0.01434835 0.01723063 0.01888241 0.02087479 0.02222485 0.02375763 0.02488078 0.02612583 0.02708115 0.02812714 0.02895506 0.00700146 0.01187508 0.01370325 0.01645767 0.01803668 0.01994175 0.02123303 0.02269943 0.02377426 0.02496598 0.02588065 0.02688232 0.02767538 0.00669274 0.01135233 0.01310070 0.01573555 0.01724645 0.01906977 0.02030600 0.02171018 0.02273969 0.02388138 0.02475789 0.02571794 0.02647824 0.00640402 0.01086337 0.01253704 0.01505990 0.01650698 0.01825367 0.01943825 0.02078404 0.02177099 0.02286569 0.02370633 0.02462724 0.02535672 0.00613360 0.01040535 0.01200899 0.01442683 0.01581403 0.01748877 0.01862484 0.01991576 0.02086270 0.02191320 0.02272009 0.02360417 0.02430463 0.00587997 0.00997571 0.01151362 0.01383283 0.01516376 0.01677088 0.01786133 0.01910064 0.02000992 0.02101881 0.02179391 0.02264327 0.02331638 0.00564177 0.00957215 0.01104828 0.01327475 0.01455276 0.01609624 0.01714374 0.01833443 0.01920823 0.02017790 0.02092302 0.02173964 0.02238693 0.00541776 0.00919260 0.01061060 0.01274976 0.01397792 0.01546144 0.01646846 0.01761332 0.01845364 0.01938630 0.02010311 0.02088882 0.02151172 0.00520685 0.00883519 0.01019841 0.01225530 0.01343645 0.01486342 0.01583224 0.01693383 0.01774254 0.01864024 0.01933032 0.02008680 0.02068664 0.00500803 0.00849824 0.00980979 0.01178904 0.01292582 0.01429939 0.01523212 0.01629283 0.01707167 0.01793631 0.01860109 0.01932993 0.01990795 0.00482039 0.00818020 0.00944297 0.01134888 0.01244373 0.01376682 0.01466543 0.01568747 0.01643804 0.01727140 0.01791223 0.01861489 0.01917224 0.00464311 0.00787970 0.00909635 0.01093290 0.01198810 0.01326343 0.01412974 0.01511517 0.01583897 0.01664270 0.01726083 0.01793868 0.01847642 0.00447544 0.00759546 0.00876847 0.01053938 0.01155702 0.01278712 0.01362283 0.01457356 0.01527198 0.01604761 0.01664422 0.01729853 0.01781767 0.00431669 0.00732634 0.00845800 0.01016672 0.01114877 0.01233598 0.01314268 0.01406050 0.01473484 0.01548380 0.01605998 0.01669194 0.01719342 0.00416625 0.00707127 0.00816374 0.00981347 0.01076176 0.01190828 0.01268743 0.01357401 0.01422549 0.01494912 0.01550589 0.01611661 0.01660129 0.00402355 0.00682930 0.00788457 0.00947831 0.01039454 0.01150242 0.01225541 0.01311230 0.01374204 0.01444160 0.01497991 0.01557043 0.01603914 0.00388805 0.00659954 0.00761948 0.00916003 0.01004579 0.01111694 0.01184505 0.01267372 0.01328278 0.01395944 0.01448018 0.01505147 0.01550498 0.00375930 0.00638119 0.00736754 0.00885751 0.00971429 0.01075049 0.01145494 0.01225674 0.01284613 0.01350097 0.01400498 0.01455797 0.01499699 0.00363683 0.00617350 0.00712790 0.00856973 0.00939893 0.01040186 0.01108376 0.01185997 0.01243061 0.01306467 0.01355275 0.01408828 0.01451348 0.00352026 0.00597579 0.00689976 0.00829574 0.00909866 0.01006990 0.01073032 0.01148214 0.01203490 0.01264915 0.01312202 0.01364090 0.01405292 0.00340921 0.00578743 0.00668240 0.00803469 0.00881256 0.00975356 0.01039350 0.01112205 0.01165776 0.01225310 0.01271145 0.01321444 0.01361389 0.00330333 0.00560784 0.00647515 0.00778576 0.00853973 0.00945189 0.01007227 0.01077862 0.01129804 0.01187533 0.01231982 0.01280763 0.01319506 0.00320232 0.00543649 0.00627739 0.00754822 0.00827937 0.00916399 0.00976570 0.01045082 0.01095470 0.01151473 0.01194598 0.01241927 0.01279521 0.00310587 0.00527287 0.00608856 0.00732138 0.00803073 0.00888904 0.00947289 0.01013774 0.01062674 0.01117028 0.01158886 0.01204828 0.01241322 0.00301371 0.00511653 0.00590813 0.00710461 0.00779312 0.00862626 0.00919305 0.00983850 0.01031328 0.01084103 0.01124749 0.01169363 0.01204805 0.00292560 0.00496704 0.00573560 0.00689733 0.00756590 0.00837497 0.00892541 0.00955231 0.01001346 0.01052610 0.01092095 0.01135437 0.01169872 0.00284130 0.00482401 0.00557052 0.00669899 0.00734847 0.00813448 0.00866929 0.00927840 0.00972651 0.01022468 0.01060841 0.01102964 0.01136433 0.00276059 0.00468708 0.00541246 0.00650908 0.00714027 0.00790420 0.00842402 0.00901610 0.00945170 0.00993600 0.01030907 0.01071862 0.01104404 0.00268327 0.00455589 0.00526104 0.00632713 0.00694080 0.00768356 0.00818901 0.00876475 0.00918836 0.00965935 0.01002220 0.01042054 0.01073708 0.00260916 0.00443013 0.00511588 0.00615270 0.00674956 0.00747202 0.00796369 0.00852375 0.00893587 0.00939409 0.00974712 0.01013470 0.01044271 0.00253808 0.00430952 0.00497665 0.00598539 0.00656612 0.00726909 0.00774753 0.00829255 0.00869362 0.00913958 0.00948319 0.00986045 0.01016026 0.00246986 0.00419376 0.00484303 0.00582481 0.00639005 0.00707431 0.00754005 0.00807063 0.00846109 0.00889527 0.00922982 0.00959715 0.00988910 0.00240436 0.00408261 0.00471472 0.00567060 0.00622097 0.00688726 0.00734078 0.00785748 0.00823774 0.00866061 0.00898646 0.00934425 0.00962863 0.00234143 0.00397581 0.00459144 0.00552244 0.00605851 0.00670752 0.00714931 0.00765266 0.00802312 0.00843510 0.00875258 0.00910119 0.00937829 0.00228094 0.00387316 0.00447293 0.00538000 0.00590233 0.00653472 0.00696523 0.00745573 0.00781677 0.00821828 0.00852770 0.00886748 0.00913758 0.00222277 0.00377443 0.00435896 0.00524301 0.00575211 0.00636851 0.00678816 0.00726631 0.00761827 0.00800970 0.00831137 0.00864265 0.00890600 0.00216679 0.00367943 0.00424928 0.00511118 0.00560755 0.00620856 0.00661775 0.00708401 0.00742722 0.00780895 0.00810316 0.00842624 0.00868310 0.00211290 0.00358797 0.00414370 0.00498426 0.00546837 0.00605456 0.00645367 0.00690847 0.00724327 0.00761564 0.00790266 0.00821786 0.00846845 0.00206100 0.00349988 0.00404200 0.00486201 0.00533430 0.00590622 0.00629562 0.00673938 0.00706606 0.00742942 0.00770950 0.00801709 0.00826164 0.00201099 0.00341499 0.00394400 0.00474420 0.00520511 0.00576325 0.00614330 0.00657641 0.00689527 0.00724994 0.00752333 0.00782358 0.00806231 0.00196278 0.00333316 0.00384952 0.00463062 0.00508055 0.00562542 0.00599644 0.00641928 0.00673059 0.00707687 0.00734381 0.00763699 0.00787010 0.00191628 0.00325424 0.00375839 0.00452108 0.00496041 0.00549246 0.00585478 0.00626771 0.00657173 0.00690992 0.00717063 0.00745698 0.00768467 0.00187142 0.00317808 0.00367047 0.00441537 0.00484448 0.00536417 0.00571808 0.00612144 0.00641843 0.00674881 0.00700351 0.00728326 0.00750571 0.00182811 0.00310457 0.00358559 0.00431332 0.00473256 0.00524031 0.00558611 0.00598022 0.00627042 0.00659326 0.00684215 0.00711552 0.00733292 0.00178629 0.00303358 0.00350362 0.00421478 0.00462448 0.00512070 0.00545865 0.00584384 0.00612748 0.00644302 0.00668629 0.00695351 0.00716601 0.00174589 0.00296499 0.00342444 0.00411957 0.00452005 0.00500513 0.00533550 0.00571206 0.00598936 0.00629785 0.00653570 0.00679696 0.00700474 0.00170684 0.00289871 0.00334790 0.00402755 0.00441913 0.00489342 0.00521647 0.00558469 0.00585585 0.00615753 0.00639013 0.00664564 0.00684884 0.00166909 0.00283463 0.00327391 0.00393858 0.00432154 0.00478542 0.00510138 0.00546153 0.00572676 0.00602184 0.00624937 0.00649930 0.00669808 0.00163258 0.00277264 0.00320234 0.00385253 0.00422716 0.00468095 0.00499005 0.00534240 0.00560188 0.00589059 0.00611320 0.00635774 0.00655224 0.00159726 0.00271267 0.00313309 0.00376926 0.00413583 0.00457986 0.00488233 0.00522712 0.00548105 0.00576357 0.00598143 0.00622075 0.00641110 0.00156307 0.00265463 0.00306607 0.00368867 0.00404742 0.00448201 0.00477805 0.00511552 0.00536407 0.00564062 0.00585387 0.00608814 0.00627448 0.00152996 0.00259843 0.00300117 0.00361063 0.00396183 0.00438727 0.00467708 0.00500747 0.00525080 0.00552155 0.00573034 0.00595972 0.00614216 0.00149790 0.00254399 0.00293831 0.00353504 0.00387891 0.00429549 0.00457927 0.00490279 0.00514108 0.00540622 0.00561068 0.00583531 0.00601399 0.00146683 0.00249125 0.00287741 0.00346180 0.00379858 0.00420656 0.00448450 0.00480137 0.00503476 0.00529445 0.00549473 0.00571476 0.00588978 0.00143672 0.00244013 0.00281838 0.00339082 0.00372071 0.00412037 0.00439264 0.00470306 0.00493170 0.00518612 0.00538233 0.00559789 0.00576937 0.00140753 0.00239056 0.00276115 0.00332199 0.00364521 0.00403679 0.00430358 0.00460773 0.00483177 0.00508107 0.00527334 0.00548458 0.00565262 0.00137922 0.00234250 0.00270564 0.00325524 0.00357199 0.00395574 0.00421719 0.00451527 0.00473485 0.00497918 0.00516762 0.00537466 0.00553937 0.00135176 0.00229587 0.00265180 0.00319048 0.00350095 0.00387710 0.00413338 0.00442557 0.00464081 0.00488032 0.00506505 0.00526802 0.00542948 # Gamma 1.40124644 1.10031661 1.07577639 1.06081440 1.05260454 1.04727224 1.04364993 1.04090051 1.03891298 1.03724273 1.03599827 1.03487952 1.03403074 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 0.62238235 0.77265408 0.82275301 0.84660838 0.86250145 0.87221026 0.87980189 0.88511514 0.88956058 0.89293013 0.89586137 0.89819995 0.90028675 0.41149061 0.56384829 0.64200085 0.68125752 0.70962433 0.72732022 0.74169607 0.75183098 0.76055385 0.76716902 0.77306581 0.77775624 0.78203568 0.29076841 0.41275368 0.49583833 0.53966910 0.57394355 0.59588615 0.61438166 0.62758306 0.63922427 0.64810207 0.65616603 0.66259332 0.66855103 0.21638887 0.30976567 0.38696971 0.42888393 0.46399962 0.48699707 0.50707514 0.52159031 0.53468505 0.54474185 0.55403222 0.56146528 0.56844924 0.16747479 0.23923226 0.30743172 0.34490312 0.37811997 0.40024034 0.42017434 0.43474323 0.44816792 0.45854749 0.46828750 0.47611238 0.48355616 0.13359042 0.18970668 0.24891422 0.28149868 0.31171484 0.33205831 0.35090011 0.36478525 0.37782699 0.38796675 0.39761986 0.40540345 0.41289325 0.10913071 0.15390967 0.20513595 0.23321771 0.26020855 0.27849817 0.29583429 0.30868372 0.32095777 0.33054085 0.33978351 0.34725804 0.35452627 0.09088087 0.12731060 0.17174674 0.19594645 0.21988273 0.23615610 0.25188265 0.26358226 0.27492259 0.28380255 0.29246684 0.29948861 0.30638170 0.07689182 0.10705031 0.14579415 0.16673394 0.18793157 0.20236044 0.21653187 0.22709708 0.23746753 0.24560311 0.25362248 0.26013079 0.26657436 0.06592580 0.09127926 0.12526491 0.14349106 0.16229467 0.17509244 0.18783336 0.19734166 0.20677610 0.21418495 0.22155352 0.22753851 0.23350896 0.05716563 0.07876804 0.10876630 0.12473436 0.14146845 0.15284713 0.16430529 0.17285825 0.18142393 0.18815329 0.19489851 0.20037909 0.20588311 0.05005382 0.06867758 0.09531758 0.10939959 0.12435148 0.13450415 0.14482707 0.15253041 0.16030712 0.16641645 0.17258211 0.17759174 0.18265273 0.04419919 0.06042101 0.08421536 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0.01900726 0.02187199 0.02377036 0.02582951 0.02734192 0.02895737 0.03021040 0.03154080 0.03260964 0.03374055 0.00823181 0.01095036 0.01568502 0.01803968 0.02076113 0.02256373 0.02452052 0.02595723 0.02749291 0.02868369 0.02994883 0.03096495 0.03204074 0.00782353 0.01040352 0.01490655 0.01714424 0.01973284 0.02144672 0.02330854 0.02467506 0.02613668 0.02726968 0.02847420 0.02944134 0.03046589 0.00744493 0.00989677 0.01418471 0.01631394 0.01877915 0.02041067 0.02218422 0.02348554 0.02487828 0.02595758 0.02710567 0.02802725 0.02900408 0.00709320 0.00942627 0.01351413 0.01554260 0.01789299 0.01944795 0.02113932 0.02237997 0.02370854 0.02473784 0.02583332 0.02671246 0.02764478 0.00676584 0.00898864 0.01289006 0.01482476 0.01706815 0.01855179 0.02016653 0.02135064 0.02261933 0.02360199 0.02464837 0.02548790 0.02637864 0.00646067 0.00858088 0.01230830 0.01415559 0.01629909 0.01771619 0.01925937 0.02039069 0.02160344 0.02254255 0.02354301 0.02434552 0.02519738 0.00617570 0.00820032 0.01176509 0.01353077 0.01558089 0.01693583 0.01841207 0.01949404 0.02065444 0.02155280 0.02251028 0.02327815 0.02409357 0.00590921 0.00784459 0.01125711 0.01294648 0.01490916 0.01620593 0.01761947 0.01865525 0.01976658 0.02062678 0.02154396 0.02227936 0.02306062 0.00565961 0.00751157 0.01078137 0.01239927 0.01427997 0.01552224 0.01687697 0.01786943 0.01893474 0.01975913 0.02063849 0.02134343 0.02209260 0.00542552 0.00719937 0.01033519 0.01188607 0.01368981 0.01488093 0.01618044 0.01713224 0.01815429 0.01894506 0.01978887 0.02046518 0.02118418 0.00520567 0.00690628 0.00991617 0.01140411 0.01313551 0.01427858 0.01552615 0.01643973 0.01742110 0.01818025 0.01899060 0.01963999 0.02033059 0.00499893 0.00663077 0.00952216 0.01095091 0.01261422 0.01371208 0.01491076 0.01578837 0.01673142 0.01746081 0.01823964 0.01886366 0.01952750 0.00480428 0.00637146 0.00915119 0.01052423 0.01212338 0.01317865 0.01433125 0.01517496 0.01608189 0.01678322 0.01753232 0.01813243 0.01877102 0.00462079 0.00612710 0.00880151 0.01012203 0.01166065 0.01267577 0.01378488 0.01459662 0.01546944 0.01614430 0.01686533 0.01744286 0.01805760 0.00444762 0.00589655 0.00847151 0.00974247 0.01122393 0.01220114 0.01326917 0.01405071 0.01489131 0.01554116 0.01623566 0.01679187 0.01738406 0.00428401 0.00567881 0.00815974 0.00938389 0.01081131 0.01175269 0.01278187 0.01353487 0.01434499 0.01497118 0.01564058 0.01617661 0.01674747 0.00412928 0.00547293 0.00786489 0.00904476 0.01042103 0.01132853 0.01232093 0.01304692 0.01382818 0.01443199 0.01507761 0.01559454 0.01614518 0.00398278 0.00527807 0.00758575 0.00872371 0.01005153 0.01092693 0.01188448 0.01258488 0.01333880 0.01392139 0.01454448 0.01504331 0.01557478 0.00384395 0.00509344 0.00732122 0.00841946 0.00970134 0.01054631 0.01147082 0.01214697 0.01287493 0.01343741 0.01403912 0.01452077 0.01503406 0.00371226 0.00491836 0.00707030 0.00813087 0.00936915 0.01018526 0.01107840 0.01173151 0.01243485 0.01297823 0.01355963 0.01402498 0.01452099 0.00358723 0.00475217 0.00683208 0.00785688 0.00905374 0.00984243 0.01070577 0.01133702 0.01201694 0.01254218 0.01310428 0.01355413 0.01403372 0.00346841 0.00459427 0.00660570 0.00759652 0.00875400 0.00951664 0.01035163 0.01096209 0.01161975 0.01212774 0.01267148 0.01310659 0.01357055 0.00335541 0.00444412 0.00639040 0.00734889 0.00846891 0.00920676 0.01001478 0.01060546 0.01124193 0.01173349 0.01225976 0.01268085 0.01312993 0.00324784 0.00430123 0.00618546 0.00711319 0.00819752 0.00891178 0.00969411 0.01026595 0.01088223 0.01135816 0.01186778 0.01227550 0.01271041 0.00314537 0.00416513 0.00599023 0.00688866 0.00793898 0.00863075 0.00938861 0.00994249 0.01053953 0.01100055 0.01149429 0.01188927 0.01231066 0.00304767 0.00403540 0.00580411 0.00667460 0.00769249 0.00836282 0.00909732 0.00963408 0.01021276 0.01065957 0.01113815 0.01152099 0.01192947 0.00295446 0.00391165 0.00562653 0.00647037 0.00745730 0.00810717 0.00881938 0.00933980 0.00990095 0.01033419 0.01079831 0.01116954 0.01156570 0.00286546 0.00379350 0.00545699 0.00627538 0.00723274 0.00786308 0.00855398 0.00905880 0.00960320 0.01002348 0.01047378 0.01083393 0.01121831 0.00278042 0.00368064 0.00529499 0.00608907 0.00701818 0.00762985 0.00830039 0.00879029 0.00931869 0.00972657 0.01016365 0.01051321 0.01088633 0.00269912 0.00357275 0.00514011 0.00591095 0.00681303 0.00740684 0.00805792 0.00853355 0.00904663 0.00944266 0.00986710 0.01020652 0.01056887 0.00262134 0.00346954 0.00499194 0.00574054 0.00661675 0.00719348 0.00782592 0.00828789 0.00878632 0.00917101 0.00958334 0.00991305 0.01026509 0.00254687 0.00337074 0.00485008 0.00557739 0.00642883 0.00698921 0.00760379 0.00805270 0.00853707 0.00891090 0.00931163 0.00963205 0.00997421 0.00247553 0.00327611 0.00471418 0.00542110 0.00624881 0.00679351 0.00739099 0.00782737 0.00829829 0.00866170 0.00905132 0.00936284 0.00969551 0.00240714 0.00318541 0.00458393 0.00527130 0.00607624 0.00660593 0.00718700 0.00761137 0.00806938 0.00842282 0.00880177 0.00910474 0.00942833 0.00234156 0.00309844 0.00445900 0.00512762 0.00591073 0.00642601 0.00699134 0.00740419 0.00784982 0.00819367 0.00856240 0.00885718 0.00917204 0.00227862 0.00301498 0.00433911 0.00498975 0.00575190 0.00625334 0.00680357 0.00720536 0.00763910 0.00797375 0.00833266 0.00861957 0.00892606 0.00221818 0.00293485 0.00422399 0.00485736 0.00559938 0.00608755 0.00662326 0.00701443 0.00743674 0.00776257 0.00811204 0.00839139 0.00868983 0.00216012 0.00285787 0.00411340 0.00473017 0.00545285 0.00592826 0.00645003 0.00683099 0.00724233 0.00755967 0.00790007 0.00817215 0.00846286 0.00210431 0.00278389 0.00400710 0.00460792 0.00531200 0.00577514 0.00628350 0.00665465 0.00705544 0.00736462 0.00769629 0.00796139 0.00824466 0.00205063 0.00271275 0.00390486 0.00449035 0.00517654 0.00562789 0.00612334 0.00648506 0.00687568 0.00717702 0.00750030 0.00775868 0.00803479 0.00199899 0.00264430 0.00380649 0.00437722 0.00504620 0.00548619 0.00596923 0.00632187 0.00670272 0.00699649 0.00731170 0.00756361 0.00783283 0.00194927 0.00257841 0.00371180 0.00426832 0.00492072 0.00534978 0.00582087 0.00616476 0.00653619 0.00682270 0.00713012 0.00737580 0.00763839 0.00190138 0.00251496 0.00362059 0.00416343 0.00479986 0.00521840 0.00567797 0.00601343 0.00637580 0.00665529 0.00695522 0.00719490 0.00745109 0.00185524 0.00245383 0.00353271 0.00406237 0.00468340 0.00509180 0.00554027 0.00586761 0.00622124 0.00649398 0.00678668 0.00702057 0.00727060 0.00181076 0.00239489 0.00344799 0.00396494 0.00457114 0.00496975 0.00540752 0.00572703 0.00607223 0.00633846 0.00662419 0.00685251 0.00709659 0.00176786 0.00233806 0.00336628 0.00387098 0.00446286 0.00485204 0.00527948 0.00559144 0.00592851 0.00618845 0.00646746 0.00669040 0.00692875 0.00172647 0.00228323 0.00328745 0.00378031 0.00435838 0.00473846 0.00515594 0.00546062 0.00578983 0.00604371 0.00631624 0.00653398 0.00676679 0.00168651 0.00223031 0.00321135 0.00369280 0.00425754 0.00462883 0.00503668 0.00533433 0.00565597 0.00590399 0.00617025 0.00638298 0.00661044 0.00164792 0.00217920 0.00313787 0.00360830 0.00416015 0.00452295 0.00492152 0.00521237 0.00552669 0.00576906 0.00602927 0.00623715 0.00645945 0.00161065 0.00212984 0.00306688 0.00352666 0.00406607 0.00442067 0.00481026 0.00509455 0.00540179 0.00563870 0.00589306 0.00609626 0.00631357 0.00157463 0.00208213 0.00299827 0.00344776 0.00397514 0.00432182 0.00470273 0.00498067 0.00528108 0.00551271 0.00576141 0.00596010 0.00617258 0.00153980 0.00203601 0.00293194 0.00337148 0.00388723 0.00422626 0.00459877 0.00487058 0.00516437 0.00539090 0.00563413 0.00582844 0.00603625 0.00150611 0.00199141 0.00286779 0.00329771 0.00380221 0.00413382 0.00449821 0.00476409 0.00505149 0.00527308 0.00551102 0.00570110 0.00590440 0.00147352 0.00194826 0.00280572 0.00322633 0.00371994 0.00404439 0.00440092 0.00466106 0.00494227 0.00515908 0.00539190 0.00557788 0.00577681 0.00144198 0.00190650 0.00274565 0.00315725 0.00364032 0.00395783 0.00430676 0.00456134 0.00483655 0.00504874 0.00527660 0.00545862 0.00565332 0.00141143 0.00186606 0.00268748 0.00309036 0.00356323 0.00387401 0.00421558 0.00446478 0.00473419 0.00494189 0.00516496 0.00534314 0.00553374 0.00138185 0.00182690 0.00263115 0.00302558 0.00348856 0.00379284 0.00412727 0.00437126 0.00463505 0.00483841 0.00505683 0.00523128 0.00541791 0.00135319 0.00178896 0.00257656 0.00296281 0.00341621 0.00371419 0.00404171 0.00428064 0.00453899 0.00473814 0.00495205 0.00512290 0.00530569 0.00132541 0.00175219 0.00252366 0.00290197 0.00334609 0.00363796 0.00395877 0.00419282 0.00444588 0.00464096 0.00485050 0.00501786 0.00519691 0.00129848 0.00171655 0.00247238 0.00284300 0.00327811 0.00356405 0.00387837 0.00410766 0.00435561 0.00454673 0.00475204 0.00491601 0.00509145 0.00127236 0.00168198 0.00242264 0.00278580 0.00321218 0.00349237 0.00380039 0.00402508 0.00426806 0.00445535 0.00465654 0.00481723 0.00498916 0.00124702 0.00164844 0.00237438 0.00273031 0.00314822 0.00342284 0.00372474 0.00394496 0.00418312 0.00436669 0.00456390 0.00472140 0.00488992 # Delta 0.00128865 0.08134837 0.19154976 0.35369444 0.57322966 0.85496104 1.20306104 1.62123001 2.11284814 2.68105261 3.32827679 4.05722989 4.86955699