/* Copyright (C) 2024 Alessandro Languasco */ /**************** A. LANGUASCO ******************** ************* COMPUTATION OF THE EULER KRONECKER CONSTANTS MOD q(PRIME) *******/ /******* Direct use of the pari/gp lfun functions *****/ {global_eulerkronecker_direct(r1,r2,defaultprecision)=local(minutes, millisec, seconds, rows, n,m,L,Seven,Sodd,q, G, chi, elaptimecomp, EK, EKplus, kappaq, resfile_total); default(realprecision,defaultprecision); resfile_total = fileopen("kappaq-results_TOTAL.csv", "a"); filewrite(resfile_total,"q; EK; EK+; kappaq; accuracy"); print("************ A. LANGUASCO *************"); print("********* COMPUTATION OF THE EULER-KRONECKER **********"); print("******* CONSTANTS IN ONE INTERVAL ********"); print("********* direct use of the lfun command **********"); r1=nextprime(r1); r2=precprime(r2); if (r1>r2, print("error: no odd primes in this interval. END PROGRAM");return); if (r1 < 3, r1=3); print("Interval=[",r1,",",r2,"]"); gettime(); bound=10^(30); forprime(q=r1,r2, Sodd=0; Seven=0; G= znstar(q, 1); for(m=2, q-1, chi=znconreychar(G,m); L=lfuncreate(Mod(m,q)); \\ defines L as the Dirichlet L-function associated with a non-trivial Dirichlet character (Conrey notation) if (zncharisodd(G,chi), Sodd+= lfun(L,1,1)/lfun(L,1), \\ computes the logarithmic derivative of L at 1 Seven+= lfun(L,1,1)/lfun(L,1)); ); EKplus = real(Seven)+Euler; EK = real(Sodd+Seven)+Euler; kappaq = - real(Sodd)/log(q); print("EK(",q")^+ = ", EKplus); print("EK(",q,") = ", EK); \\ final sum print("kappaq(",q,") = ", kappaq); filewrite1(resfile_total,q); filewrite1(resfile_total,";"); prnt = truncate(EK*bound,&e)/bound*1.0; filewrite1(resfile_total,prnt); filewrite1(resfile_total,";"); prnt = truncate(EKplus*bound,&e)/bound*1.0; filewrite1(resfile_total,prnt); filewrite1(resfile_total,";"); prnt = truncate(kappaq*bound,&e)/bound*1.0; filewrite1(resfile_total,prnt); filewrite1(resfile_total,";"); filewrite(resfile_total,defaultprecision); fileflush(resfile_total); ); fileclose(resfile_total); elaptimecomp=gettime(); seconds=floor(elaptimecomp/1000)%60; minutes=floor(elaptimecomp/60000); millisec=elaptimecomp- minutes*60000 - seconds*1000; print("Total computation time: ", minutes, " min, ", seconds, " sec, ", millisec, " millisec"); print("****** END PROGRAM ********"); } /************************************ languasc@languasco1:~/Desktop/EK$ gp2c-run -pmy_ -g -W kappaq-direct-v1.gp GP/PARI CALCULATOR Version 2.15.5 (released) arm64 running darwin (aarch64/GMP-6.3.0 kernel) 64-bit version compiled: Mar 2 2024, Apple clang version 15.0.0 (clang-1500.1.0.2.5) threading engine: pthread (readline v8.1 enabled, extended help enabled) Copyright (C) 2000-2022 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?18 for how to get moral (and possibly technical) support. parisizemax = 2048000000, primelimit = 500000, nbthreads = 8 ? init_kappaq_direct_v1();global_eulerkronecker_direct(3,1000,50) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[3,997] EK(3)^+ = 0.57721566490153286060651209008240243104215933593992 EK(3) = 0.94549728087168070323974999415818907359092364593268 kappaq(3) = -0.33522437330154929965481627201166430344037036607224 EK(5)^+ = 1.4048951416170377485975590797597760777960232886149 EK(5) = 1.7206242125134047616957287886491072983521953749103 kappaq(5) = -0.19617350160396123598034608398644366300819525096422 EK(7)^+ = 1.9571564544497147527138218614254566264775388945427 EK(7) = 2.0875940747173301328154247195731641817078168355413 kappaq(7) = -0.067031676838182540620959092690443836796276976427868 EK(11)^+ = 2.6620740989043317490665407245316840910737527163770 EK(11) = 2.4154259042832678303428796358314601395036269536131 kappaq(11) = 0.10286028644329521655337753522001620349512859490599 EK(13)^+ = 2.8995957241479050955959120301345413396279493393966 EK(13) = 2.6107577374176501969977610885726637441279948139098 kappaq(13) = 0.11260962556239718364461914026008052912674136016327 EK(17)^+ = 3.2317916488510816768920047064208166564597278903039 EK(17) = 3.5819760440975776592717881291931267023758470504221 kappaq(17) = -0.12359972678412871763605045672800700322974804265183 EK(19)^+ = 3.3670281022694336042291173836107641737316573608272 EK(19) = 4.7904094157142833259070393645755453502304748787072 kappaq(19) = -0.48341341882649698812926330994608173041208210936665 EK(23)^+ = 3.5660527418630348550649000563272082025109577524362 EK(23) = 2.6112891761882009255073916496395756545428850492500 kappaq(23) = 0.30450177864286258811719298292967002466181043144169 EK(29)^+ = 3.7745127229181815583754050552748504297092606938361 EK(29) = 3.0937317059942687231627517981871539400148011693822 kappaq(29) = 0.20217440085347281193967314536847771637095197039743 EK(31)^+ = 3.7406341713163176516392786223111779036140819427628 EK(31) = 4.3144429252674750977075744104182724883637534034126 kappaq(31) = -0.16709694002403481084997792975567985102887580053665 EK(37)^+ = 3.8834610323711373913552349338799662758221332187053 EK(37) = 4.3049381899576020179855792641688629478097407376831 kappaq(37) = -0.11672299614194852383446211331523285226073752805203 EK(41)^+ = 3.9006724333157603953842046028941643558534152980229 EK(41) = 3.9715216279213321602825704001416839913396088095129 kappaq(41) = -0.019078448817730487665286522915234969002032151912850 EK(43)^+ = 4.3746284851137511015088487438856424778033271811333 EK(43) = 4.3786275057469504941377506233629417713984457316710 kappaq(43) = -0.0010632299559158064856030637504448481068631336699467 EK(47)^+ = 4.7833059237403149273608851496384859619066848903595 EK(47) = 4.7993942589074161345275842998765920507611048308415 kappaq(47) = -0.0041786281543999789021427866963319634532999190267539 EK(53)^+ = 4.0673481409391142241545188178142409596662971306324 EK(53) = 4.3377368585970923186969608230695844720453488936767 kappaq(53) = -0.068102981731655092877815133182656743863528073634450 EK(59)^+ = 5.7497749509871786898571451129145755352467266466591 EK(59) = 5.4335163453850039807763443819268861046048867061254 kappaq(59) = 0.077561177537401718955224637346991163330696334932805 EK(61)^+ = 4.7191916044813760122347923279101997897135110081209 EK(61) = 5.0710851905765161959580509811250419048235328007028 kappaq(61) = -0.085600677063319552995034524968639923271692080075411 EK(67)^+ = 5.4947857440923108789445091428462779982143203860543 EK(67) = 5.2921393066289626087342846183066682812359129057679 kappaq(67) = 0.048195303630233224012827541336520280112970883159316 EK(71)^+ = 5.0245922143701382360345345746326215591328192682416 EK(71) = 5.2552581928189461677201312863658226050932548004965 kappaq(71) = -0.054112902001196238161718707411676843964699513124696 EK(73)^+ = 5.5663801890442060777314487652728594473671320449882 EK(73) = 4.0669490904474952920164881562537063948501153283859 kappaq(73) = 0.34948031071361688413935666704538219730616406940649 EK(79)^+ = 4.3139281698384215323481444295216004568791959546551 EK(79) = 4.9982763181706801078943139294476872588687958011347 kappaq(79) = -0.15662119595863141350300197093507991595829559505223 EK(83)^+ = 4.0611989064801548695496047837404518521749353181818 EK(83) = 3.0331361134360741871640381910458526374843058103182 kappaq(83) = 0.23265441872471428918912941623298430416490467432868 EK(89)^+ = 5.4483485155543471926190295324310235565414880845149 EK(89) = 4.1640907988898327688084111037174005245742324072223 kappaq(89) = 0.28611311117214708306357695959919150463987918508399 EK(97)^+ = 4.4456341125634673818638045266444284123648800973279 EK(97) = 4.8912407404038966683075146885659855204899522315333 kappaq(97) = -0.097406509380448235796556853350125854515541112623619 EK(101)^+ = 5.9336455738772699830578989916371624380948830767898 EK(101) = 5.2970128915096697188786003273875617061162709928131 kappaq(101) = 0.13794497457746404614453768490593459517693229972077 EK(103)^+ = 5.5331250863099989881540064493855701030013600441154 EK(103) = 5.1443395512520882211333050322046816301812136836536 kappaq(103) = 0.083885279170642135997577692479563009424227796198184 EK(107)^+ = 5.3574469195959683933260359062011745920690877215121 EK(107) = 5.4582742099702450342168024545281430371307823647266 kappaq(107) = -0.021577355804406921497164663554237492648845371622636 EK(109)^+ = 6.2863931206084202658728231848367306044944021050530 EK(109) = 6.9066381462642365321946983770434987481607235151257 kappaq(109) = -0.13221040972154473105643784360814810822833524091977 EK(113)^+ = 4.7130805255307135534445160973763884847686053443543 EK(113) = 4.0217303825780306757831800661652405740327621937654 kappaq(113) = 0.14624358513937086070302752480595418210155997069449 EK(127)^+ = 5.2842752664164229110871489582523172344053330882054 EK(127) = 5.0885991241533344942321563623983652330373996443941 kappaq(127) = 0.040394010134348489183018827920266470502135326025318 EK(131)^+ = 4.2918242216238936566903623004125872283897349351748 EK(131) = 2.8368263415883790986028579732108972200321685562046 kappaq(131) = 0.29844902340899178332168977446245192290545359397667 EK(137)^+ = 5.1728196640136812695226700468370655424585708036917 EK(137) = 4.9370002261436846869196299971093835111600161827912 kappaq(137) = 0.047930965876723141064902285324590743002905661170764 EK(139)^+ = 5.1567346726778569345620064044498865256403390612904 EK(139) = 5.8891686339986718672638373036939131110967246880617 kappaq(139) = -0.14843202563157933505471190688392359880787671297514 EK(149)^+ = 6.3574427314548761668215197851671875301829081464692 EK(149) = 5.9834247776951598145024278573876732473725317388970 kappaq(149) = 0.074744597741851346493266689740359128703636500773499 EK(151)^+ = 5.6673226941038821844176864438162913776061197090224 EK(151) = 5.0420161135287217991451946102186780399334234208435 kappaq(151) = 0.12463059683992397505077938001381700388641926115098 EK(157)^+ = 5.6776645910097007875207694298997327093792242548478 EK(157) = 7.4080220657222272935084520138958313794593404144469 kappaq(157) = -0.34222178693967349559470290136954292865923861536735 EK(163)^+ = 5.5428961187252254166986016790428105277077908648576 EK(163) = 5.9296648228872067875549991384354231668855213833285 kappaq(163) = -0.075930049357489864149813121665314356932218545579523 EK(167)^+ = 6.8039479895825990710883911075523446118688628044740 EK(167) = 8.0330017526887247046758335780164740332765660483816 kappaq(167) = -0.24014365944021280833852003089375950358451340566765 EK(173)^+ = 4.7431368086665414331886446726852588581879598406573 EK(173) = 3.3843475365320619034429779889708635609086639186994 kappaq(173) = 0.26367405127729865816849081927478087252962297924753 EK(179)^+ = 5.5907476419669371981030455034358709477064388812779 EK(179) = 3.8623613254990300811212613028176838727761460450748 kappaq(179) = 0.33319023900667356644764667195423954154096269949170 EK(181)^+ = 5.5240111323873546098893525405697146836840673153252 EK(181) = 5.1411184877684813581013666425710859479325999832832 kappaq(181) = 0.073654489425694545929682768408703789316676562685938 EK(191)^+ = 6.2162163368307875468788956080146279782802038591074 EK(191) = 4.6928699020142266400355243481159997940470480750038 kappaq(191) = 0.29003563041521009371851669260944548537678276064813 EK(193)^+ = 6.3351688097030222624874923198880044872816237350967 EK(193) = 5.1634221967391548332007826272036132668030411467434 kappaq(193) = 0.22265164220272986648414991605446887913746981445280 EK(197)^+ = 6.7243128054775893091193161489841156080537837679557 EK(197) = 7.5514871589664064788648512937209635615377374682013 kappaq(197) = -0.15656680982968761706401632930410802459816769193625 EK(199)^+ = 4.9786731402683405911880734747742484942650556025910 EK(199) = 6.4736651360932073869949745977824464085511358297338 kappaq(199) = -0.28243073945825113374187590464789690875837547228430 EK(211)^+ = 5.4392876707770686502759272789102553488346315044956 EK(211) = 7.7361357842458616253281058758472789695245036003098 kappaq(211) = -0.42916834792423304759758741155835957740502736821645 EK(223)^+ = 6.9764071826788041979030114505985827939298444871128 EK(223) = 7.8177797178599136747133673485123386438962617050946 kappaq(223) = -0.15560307139159193261028943218996111711842280630472 EK(227)^+ = 6.1647810583353580008883905231150931049705954668007 EK(227) = 8.0805315695129621869707119375688468328705945069520 kappaq(227) = -0.35313698836012761281070188126727339288530989723542 EK(229)^+ = 5.1936818282522845906258271634895634634720464201514 EK(229) = 7.1629863205809954674577811505815613746059027656064 kappaq(229) = -0.36242275387673008584282014956033543448049319782180 EK(233)^+ = 5.4826869403518065376132639113666459773387876456901 EK(233) = 3.1194835448512754130311529525764078764214734287550 kappaq(233) = 0.43353269576637885322767011654255051505238863029237 EK(239)^+ = 4.8982603822050973109118820035733543316467548710586 EK(239) = 3.9991101720783324951263229791887746797893555983368 kappaq(239) = 0.16418445984355009178289095639754290441926011134051 EK(241)^+ = 6.9109957034902818126224948865512214301738230757328 EK(241) = 6.0375252140103421506570925093474193605955060584693 kappaq(241) = 0.15925302250416084290984470602493088806981564841307 EK(251)^+ = 5.8552247536726242990637753588344031502590784754555 EK(251) = 5.0431370850234735104281111902177063387735820904947 kappaq(251) = 0.14697214465403706305049304438445015657885061582507 EK(257)^+ = 7.4141312649177948294157198665189285117564571820783 EK(257) = 8.1699139123274139167022515522666753450696111536980 kappaq(257) = -0.13619972691794333581162715960433167610959832909683 EK(263)^+ = 6.8876189107818599345263943741976847207653242048882 EK(263) = 7.3034362473681543541434807740588166772634674356102 kappaq(263) = -0.074624164045906778442642890380085572723875069175440 EK(269)^+ = 6.3357246674128234687683983322678003176145861130570 EK(269) = 6.2603483166657710273525275571227687908931132934414 kappaq(269) = 0.013472786285611176254289149447630321814668992828902 EK(271)^+ = 4.9160737537834959531270487331509531689004100152351 EK(271) = 5.9771780485480330422377390597581178908163100973894 kappaq(271) = -0.18941124397606258685110863275619379200620485818444 EK(277)^+ = 6.0730633023953092331441359627937871821832088609821 EK(277) = 4.5928081771407789516477708166064860470489979208356 kappaq(277) = 0.26320243911510013912651854435623076768544631447492 EK(281)^+ = 4.9904374054255822961225280140594018998035561957798 EK(281) = 4.6649643236621145750522085262342843114379638270786 kappaq(281) = 0.057724833014438081725834568053942268032207208655613 EK(283)^+ = 7.0496923027052288834745979203255522601915717776747 EK(283) = 7.1502857974106825140922523118775516498637688318986 kappaq(283) = -0.017818517564561211690503522917113871249223735140391 EK(293)^+ = 5.1267612253191723194158329324083949272420600053894 EK(293) = 3.3843815212195397865846825923761269843934164247718 kappaq(293) = 0.30674766843065088561778101076433770364812978577425 EK(307)^+ = 5.5986205329646683005872681901300798115979733294164 EK(307) = 5.9963861603426890919437659005167827512628773794989 kappaq(307) = -0.069456295139958127570388779996104549522296114883186 EK(311)^+ = 7.4174951063998041873741866238788412139914079748738 EK(311) = 6.2765070374779370397351769075332039139189204771738 kappaq(311) = 0.19878558100951883020411672139914383118820394360351 EK(313)^+ = 6.9252515702972654450925529238234875596973240740694 EK(313) = 7.2604587972867604195545687647308107451526892588479 kappaq(313) = -0.058335428782145955572971075926262967153852414837061 EK(317)^+ = 7.4565747895350685259492119903366156279220633882479 EK(317) = 9.2197331159730636838126573441797039426208010369487 kappaq(317) = -0.30616225031581294013184198280553820807534052545745 EK(331)^+ = 5.3510069293585968967323796163497011668461795816997 EK(331) = 6.6383608524182736863875187041105443368520767488008 kappaq(331) = -0.22187653539144060975908679048490934445980356752847 EK(337)^+ = 6.2884917043731187509750143177664429882295531747776 EK(337) = 7.0892479266623628087854184653068416563321599558087 kappaq(337) = -0.13758501929812954798300096994897685060339260710235 EK(347)^+ = 6.6128364094557805819912414629482997030974726528781 EK(347) = 5.8759795351089441426102858559815303143059531326520 kappaq(347) = 0.12597298014174052159355424378815788935927650654388 EK(349)^+ = 8.2481356207985417087218182735000491087966959233873 EK(349) = 8.3750955295333455070588297047982186362219753662013 kappaq(349) = -0.021683748794506169104750643621093075066599060579661 EK(353)^+ = 8.1600009432486158019984274874475157814223510448969 EK(353) = 9.2420848631078101521696380717906551551117569545529 kappaq(353) = -0.18445236714113381207847863076734049428126113990486 EK(359)^+ = 6.2230288684842627786910280266327217715877615568491 EK(359) = 5.3579520546115193742778465981730082544083949491654 kappaq(359) = 0.14703882547137198499850501485862640516978115305435 EK(367)^+ = 6.0989726198261623204168153931660480433050415280528 EK(367) = 6.5082915402110063806969664492809341554825681554276 kappaq(367) = -0.069313097303205530130205666424283884977088403348675 EK(373)^+ = 6.2690471255010987917106116627132932228547931301336 EK(373) = 5.8154771375013962552824363344547497284771555836504 kappaq(373) = 0.076596129588533742221629674966844034516317652478914 EK(379)^+ = 5.9020476417665899760823849677248396653101687136226 EK(379) = 8.2105450187040456865791519348171005211318333923226 kappaq(379) = -0.38879718745317673027871466940581102493055237583885 EK(383)^+ = 7.1531113754267134193011574702584035034688338583117 EK(383) = 8.5252173094323842868622508053020851913162790457071 kappaq(383) = -0.23068222303693631634869109584177125151293972664553 EK(389)^+ = 7.8858515554527376234366212911231780706235784329331 EK(389) = 9.2159251688420073194539746757001963564807602258765 kappaq(389) = -0.22303276887102462869425514681098460308943279189789 EK(397)^+ = 6.5700521963699188758343249655678311085082858376205 EK(397) = 6.5655755008089978665914380005691680969205892988563 kappaq(397) = 0.00074811885537105170137758011634973570059475584302765 EK(401)^+ = 7.8699346245386301558627282891735887990191539329616 EK(401) = 6.7576182566183800888843377550239602746277879313366 kappaq(401) = 0.18557282715449132242832989073597885626497944705702 EK(409)^+ = 6.5514973350298503501014108667821027481319750120711 EK(409) = 5.0597818376066370460763453229919246637529496755736 kappaq(409) = 0.24805223704755666935204699113256632684184886697163 EK(419)^+ = 6.4008760179497774521417551470861559446305353874001 EK(419) = 5.4509220068182143198593659966531625017670406387691 kappaq(419) = 0.15733261338813341285263968771040163424547788765079 EK(421)^+ = 6.7686446727123178795601605779142357714899231229706 EK(421) = 7.8211429920678601381547856923278639855711309748558 kappaq(421) = -0.17417876417855254893005903076879994447103452995391 EK(431)^+ = 5.4151512187719910402484717518901864146898103689660 EK(431) = 4.6348414028558560867891216514991081065289635786145 kappaq(431) = 0.12863434088639680424224145117612195615421363557555 EK(433)^+ = 6.6885665766654482314398410141158472191896603151269 EK(433) = 6.1769871249863692812996189867451049163439090899288 kappaq(433) = 0.084269733696337528785456854927698128080325573428674 EK(439)^+ = 5.9058278397737344227141852122863435241131866911785 EK(439) = 8.6309367895251997821464863586686632413145777377160 kappaq(439) = -0.44787726396938972321476266283783670375341868735299 EK(443)^+ = 5.7461329117190914484512395899403066641692633495672 EK(443) = 3.1413473122066410000677265539564195770109154739936 kappaq(443) = 0.42746463859609776145408337185885918790887771055364 EK(449)^+ = 7.1396685761362460472949056229485724501200517042106 EK(449) = 7.9939852269509511270056026468397152520987367550222 kappaq(449) = -0.13989085459781911118594463852679794411216138926883 EK(457)^+ = 8.0152842265604803757169535132576465425784619653553 EK(457) = 9.5181053619582801586556114922936313165067164846239 kappaq(457) = -0.24537123627191897513211371142713894629462632015334 EK(461)^+ = 7.2136965484285743184512725795400627402461951429016 EK(461) = 6.9768219529342472397006935812999263054567262294432 kappaq(461) = 0.038620450496409517715179339278985715347893520482964 EK(463)^+ = 7.8367533472391823426046850885120742019495167928959 EK(463) = 8.0597558401770640106045006220714767099239711037682 kappaq(463) = -0.036333074275340449015217357910305300294076856369393 EK(467)^+ = 6.1034120581421523159106585801501815507359088519823 EK(467) = 6.8505969862715558880453887864555328035319144997847 kappaq(467) = -0.12156604321142185316176713581986652787654385035139 EK(479)^+ = 7.4197649116542364258010816181016107595599193667777 EK(479) = 6.5237394130152083030415961903806211412514622698229 kappaq(479) = 0.14518291749520691307799960013036073692301568406748 EK(487)^+ = 7.4782635080093695215088281004533410145190091225411 EK(487) = 6.6093476219931405131370775153343325758931486781181 kappaq(487) = 0.14041350994944148507369292848838547045499123584964 EK(491)^+ = 6.4371861098554383488322087571534738853218049467736 EK(491) = 4.8081124780825493779089329136546476399527964028068 kappaq(491) = 0.26290459466350738229118356945197845987712553252449 EK(499)^+ = 6.1028033734225852557832539051084523307695488768444 EK(499) = 7.4649836990025736312127388516386131784098701708879 kappaq(499) = -0.21926069423772309374886720765786162332948946705310 EK(503)^+ = 6.6118440616828840472438231429581801409589899970412 EK(503) = 5.6460052360413472426171648742951643841212182336455 kappaq(503) = 0.15526482202347865242716774643626196609614528430074 EK(509)^+ = 6.1156107783561942271794241057446436575822333756736 EK(509) = 3.6427601368440491570519226048435275916963725104317 kappaq(509) = 0.39677035972789315013430288634011376342774682201693 EK(521)^+ = 7.3320369322938332936503739999255065165313594864211 EK(521) = 9.8827751793320977438862631663672486232745194646563 kappaq(521) = -0.40774299324839094350892839188630162896378274939158 EK(523)^+ = 6.9632430917783513236408279567917429808216909464760 EK(523) = 6.8943163581207119202188363076431418311052471703259 kappaq(523) = 0.011011396537186197983927501061215446794345228815504 EK(541)^+ = 7.3645299960380477344506933449326361722823686296955 EK(541) = 7.7204230140363792990828045372126222930746111544251 kappaq(541) = -0.056550025070562764651312824901770616319890164365813 EK(547)^+ = 6.2080185497069825031874594389278173595199466352989 EK(547) = 8.4949592882452733770571794242968748185709403858260 kappaq(547) = -0.36275030699903795681242524297364493746908476993433 EK(557)^+ = 7.5755367300839750773648489481052669660649630373899 EK(557) = 7.5913336758237463808699738239750697049819432541276 kappaq(557) = -0.0024985026077726933136408281166379740979238387283302 EK(563)^+ = 7.0195185213379697667204411123243372410505134776107 EK(563) = 7.5392337936043216174695553453484632248266939970925 kappaq(563) = -0.082061002005529751422431640627840981251862833215513 EK(569)^+ = 7.3192668210189551156950355576689517159930002569772 EK(569) = 8.5220198686793768371757489742673519381212281540166 kappaq(569) = -0.18959264130993398046325543963453304440853664307459 EK(571)^+ = 8.0792104363180646849515944931538536858523588441223 EK(571) = 8.0362858074020746655742841427898113021475337782161 kappaq(571) = 0.0067625644967052953844123307123506644048465202757796 EK(577)^+ = 5.5622030473611919236186782994038996935580029481242 EK(577) = 6.0159402046987363840252907707737622366227189469191 kappaq(577) = -0.071366532593572706997338782409375924500034270132515 EK(587)^+ = 7.4723299901579154285647027316182790916569754135954 EK(587) = 9.2275738332464639380986194302793000201485401759787 kappaq(587) = -0.27533129559421526097535132853205822290181444325538 EK(593)^+ = 5.0897018978623705326288687883376118100773534396850 EK(593) = 4.7865371644086118598644379469123073760000039234619 kappaq(593) = 0.047479327097910440102634939653006113849139106579933 EK(599)^+ = 7.2070694203766996810298246128377909200316923729271 EK(599) = 7.4794727006639790743274311081308527111029609588331 kappaq(599) = -0.042594548496272768170014013524758276604739348590273 EK(601)^+ = 5.7448608032100227436661858007525013487228604437689 EK(601) = 5.9205701951757229806895459595362387299287287202364 kappaq(601) = -0.027460621240038493801636892036171049495381114169268 EK(607)^+ = 6.4484541345395120331798096129290552767033044390071 EK(607) = 7.6247561388453742946308262576565103809720210454156 kappaq(607) = -0.18355258167005732062232805623438314355895993625852 EK(613)^+ = 7.2069055842431362386757270610570387049873965755243 EK(613) = 8.3270703118909633323691177530975689127840426988653 kappaq(613) = -0.17452493568510916393047154081726525745120481748357 EK(617)^+ = 7.2670148852726182758436958618895856926344817212644 EK(617) = 8.6095964695965016690404297691461443209060954161584 kappaq(617) = -0.20896637415151362292676831132340650245825232879009 EK(619)^+ = 5.8693743056259033306329568935131629166362123553287 EK(619) = 7.5382986662050311370865708779344345147570995448715 kappaq(619) = -0.25962928262407377256545217382137716635699908184484 EK(631)^+ = 8.4081902843952756785883479426374907540961009786987 EK(631) = 7.1824539183025476265510927836708637582928352710417 kappaq(631) = 0.19011605657089186515952818038357138432158730744469 EK(641)^+ = 6.1950935439500988553768609016368528439418145343755 EK(641) = 4.0885391817144730330350809763625199782081170557782 kappaq(641) = 0.32593915535692143179922034826551952813541230352701 EK(643)^+ = 8.7036227939782962068436148400809749337123735478600 EK(643) = 8.5750322990810121179558558573127947129612866327808 kappaq(643) = 0.019886733189759427898093298165574887653132739085112 EK(647)^+ = 7.7557562070152780798220142543116916446803157849885 EK(647) = 8.6469037688449414864836189684281015979439170939086 kappaq(647) = -0.13768539587982322413737099720134484225825834177465 EK(653)^+ = 5.8745009107971231059994513148295779485639457207558 EK(653) = 4.1015059442361711878661857427782858878962325064573 kappaq(653) = 0.27354375813142251149320680741682200691648573596332 EK(659)^+ = 6.7239189763241796553013936121909035138219721093421 EK(659) = 4.2338570203212578958594300667088987679765974742368 kappaq(659) = 0.38363395741115584022825925101721227093697302817114 EK(661)^+ = 6.1495091655313699610755841104619944744402921617773 EK(661) = 7.4489425711907795191925426501302963830782362947743 kappaq(661) = -0.20010512219987197605456572590479558290602715565394 EK(673)^+ = 8.1841406248429935512030130832858510314353517271815 EK(673) = 8.0579093579090843847525381118401040283167296970021 kappaq(673) = 0.019385166425234903510111836048286982214634447942379 EK(677)^+ = 7.1143237619842113259729762191736017964410894496295 EK(677) = 7.7325238032993057747803095841133688183646348289911 kappaq(677) = -0.094849834462250448508720537392680867869615379670182 EK(683)^+ = 6.2979983150799233985690795898677124431285792096015 EK(683) = 5.5178848931140049046148475763830451170328506891598 kappaq(683) = 0.11953022851491559372176583172904091785313114367128 EK(691)^+ = 5.6866397425761392937907569177288223342820215768742 EK(691) = 7.5884625585738225649665107748911095371899017788216 kappaq(691) = -0.29088133127470168355115898106061348090466153950710 EK(701)^+ = 7.8909437789892991964091872075447773654835881840936 EK(701) = 8.4622491590949549382721303493630806219996363638487 kappaq(701) = -0.087188812276913764965555516461491113610870888449175 EK(709)^+ = 7.7500088467543019946569494588203825942740443144381 EK(709) = 7.3238871984091824471845414441903321090271253968861 kappaq(709) = 0.064919413083159646396701312314164195469039897987117 EK(719)^+ = 5.6577119644953085107926755814992932063172344888503 EK(719) = 4.4606015361677298669424238587965829688800437452768 kappaq(719) = 0.18199082699157515257823939283595622559516855875202 EK(727)^+ = 6.2246634887536667248100480699683390468052347681478 EK(727) = 5.9172517732092652776241827980273697543893774217976 kappaq(727) = 0.046655812079948584302413751120257621407542625176255 EK(733)^+ = 8.4140299051018485710704349663784795075113926082799 EK(733) = 8.5238229308147905595836073455022631976596682296446 kappaq(733) = -0.016642504300237507705799731068443857810356610967492 EK(739)^+ = 7.6415188342107404652055337371208726184786267382199 EK(739) = 6.8771999420883237882758910841403029533492436849371 kappaq(739) = 0.11571300814433172414836101100763171442472931897460 EK(743)^+ = 5.9712568831525602747644342931255303923202954742479 EK(743) = 5.9227097891951521164945348566602465246246007699627 kappaq(743) = 0.0073437189713478734969452471424441763130696362961355 EK(751)^+ = 7.7832611461001765720496372378158849847786808607854 EK(751) = 7.5784902687069601315997421108020522815328141963636 kappaq(751) = 0.030925590148469386161588553586249166946746735629609 EK(757)^+ = 8.3276877028643679402058479514171115827192514131995 EK(757) = 8.6725625113184217584535707969928147206475279318307 kappaq(757) = -0.052022312742514114454595810552445222375819890954224 EK(761)^+ = 5.8206201402404629587623956954035429426538290742191 EK(761) = 2.8731902148342953537841000688407124900265960596700 kappaq(761) = 0.44424910412172523675192426760812794671796281379524 EK(769)^+ = 7.7073854121729046452423976634654639746757371590877 EK(769) = 8.7658335434482931211740659279904289085473025210381 kappaq(769) = -0.15928271503469437768463160488773064649511762665628 EK(773)^+ = 7.9400242185828840534914291467183570349586644286017 EK(773) = 7.2973907565680787043305232191886369389943180165139 kappaq(773) = 0.096632555915274919995984608182250471868245935628481 EK(787)^+ = 7.8105699474682749691472984870106960565337325080889 EK(787) = 8.0944743342927799595077971991215369667780128460245 kappaq(787) = -0.042575685211717990064154229651440821630416932558983 EK(797)^+ = 7.4988496648248864045181136481288393734679935565148 EK(797) = 7.1058840608562820530133448444954759019879484781660 kappaq(797) = 0.058819660486877031151706605185711995136692209736993 EK(809)^+ = 6.2323848901092646212572588930415752082737432825145 EK(809) = 4.1222371860443252377699364905230995095811632967305 kappaq(809) = 0.31514502305154962566088746291716708379664329100198 EK(811)^+ = 6.2040244603011074684379601868542118629216963302766 EK(811) = 7.7804919733952869404943889592427134366876655795664 kappaq(811) = -0.23535449766385484249290019770376165842524696575865 EK(821)^+ = 7.7746849052166363728809967305531838953725287181863 EK(821) = 7.1246915343315231950342140649990894051940918203923 kappaq(821) = 0.096861803511194817694770007831224148806210498013761 EK(823)^+ = 7.8940011439340332209401981004331460547554628901805 EK(823) = 8.1248529586026045128406048661394298890109989045768 kappaq(823) = -0.034388994619879620513739570904517362293803467392203 EK(827)^+ = 7.4062423601754571412795568065341358816801470266045 EK(827) = 8.5728049269940090520010072808550123632338883294071 kappaq(827) = -0.17365234920906521803926817697871121590931130010739 EK(829)^+ = 6.4066856660194370822181546290419939615547701404898 EK(829) = 7.7187122586458058422170152972954711262951783374372 kappaq(829) = -0.19523565632351732929761703563741851137248891414373 EK(839)^+ = 8.0964927880809689063392424608424217573064192038999 EK(839) = 8.8749946521220046509199543565532859138950659947198 kappaq(839) = -0.11563836872978122506021170809492169799453014721165 EK(853)^+ = 7.3320420288409205564680581410634858367338327476329 EK(853) = 6.8899197009443675558630604916728859357837663911550 kappaq(853) = 0.065511643256111743290917202609224922492942643647305 EK(857)^+ = 8.8645284647147164545905062631018980478212806826071 EK(857) = 8.4511152876118366965161247606177757322683406093921 kappaq(857) = 0.061215218394828596351971508897738321146696571592792 EK(859)^+ = 8.1670323350222063375758817931717688302403485570708 EK(859) = 9.2458066986835549492359665695850060688918463741493 kappaq(859) = -0.15968195125070957018294354689511290972534615888501 EK(863)^+ = 8.2005063950701734575821694757171512406888389736740 EK(863) = 7.7262054853553359061477954897944722201240347732132 kappaq(863) = 0.070158552601870909036548126563924120242539744496236 EK(877)^+ = 6.3714058873427885521907960069681420516879930492456 EK(877) = 8.8331256340279359515778837924853439685844854278104 kappaq(877) = -0.36327266384527084317933489298261011367613735030405 EK(881)^+ = 9.2543114664736735299629301154386416591573262293481 EK(881) = 8.2237047935000600465494046213929621411218437021115 kappaq(881) = 0.15198317575591019235066884719080416720242528701076 EK(883)^+ = 7.1813761547246011739914053475067136287722360607302 EK(883) = 6.1067330767224103106367313686385243081014897704390 kappaq(883) = 0.15842423092239613732571154754138681677075034415565 EK(887)^+ = 8.1038863039077211656381307141603037908735454070934 EK(887) = 8.3360219162062370546761959777676487335382564619992 kappaq(887) = -0.034198720345486031699283336100881740978606384079859 EK(907)^+ = 7.5617969741129122797588679288975572563224697406842 EK(907) = 8.5510794596436987607464945191969834952529057460756 kappaq(907) = -0.14526604880549320104254668451946418122322675321929 EK(911)^+ = 6.2965552249211657591924583332098941006966151239216 EK(911) = 5.8993311885477576907294294607622273953713072433110 kappaq(911) = 0.058290635536702959098297788733250060773397429151501 EK(919)^+ = 7.6179309827115905513410143323895559611221741503110 EK(919) = 7.3031233521821295926256357610101931057925973997138 kappaq(919) = 0.046137246025493658435384125040273620492085041330376 EK(929)^+ = 8.4403734804637748022765533033397936398208409164937 EK(929) = 8.0095654978023564543313888988521554718499128351044 kappaq(929) = 0.063037917470448604187531863614795886935279110675964 EK(937)^+ = 6.2686833507126920751666403928842276971645097127215 EK(937) = 6.7676029748518682633952552112160142997985071587830 kappaq(937) = -0.072912862331977817247297121763485280080897823882181 EK(941)^+ = 8.3521971037571735406921873794724039934212718605197 EK(941) = 7.5750368246740103371619608575322928951703523054207 kappaq(941) = 0.11350470761032558638280582884199965320530786640265 EK(947)^+ = 7.9534350625815999932200950030846454725610481048223 EK(947) = 6.1141948363910672807317105645961096651046986953934 kappaq(947) = 0.26837296916155390413193825022814500167043951364715 EK(953)^+ = 7.0887354776666205402868892837835450018528478417626 EK(953) = 6.1557160878563993226066967132330963386916218143653 kappaq(953) = 0.13601629288448688175139207259968390859801855440785 EK(967)^+ = 7.0690390380345782912524978625438476996906729766496 EK(967) = 9.5418970696894446258023225288403410948747165576575 kappaq(967) = -0.35973037922754987232081991587417452200820537640843 EK(971)^+ = 8.5742023305368852546498088409694658280994453664377 EK(971) = 7.9238984921447508820979593901654706403894237953316 kappaq(971) = 0.094543904158954407172899643305151797302848942563042 EK(977)^+ = 6.6099865372512826200050451495130759417092060703982 EK(977) = 8.0666986560419767819952664799803214506822755136771 kappaq(977) = -0.21159342626635128457125657097254076963845899526217 EK(983)^+ = 7.1675264338493074696092816322327814176317747311569 EK(983) = 9.2399886216167666697734398490171814986338872886986 kappaq(983) = -0.30076618070061075796074088488331102057587890779100 EK(991)^+ = 8.3111699483937153765502529009034594944808041526502 EK(991) = 9.1804494553434858408790515924813535097505692718248 kappaq(991) = -0.12600601208007456794612098173757623441561514095189 EK(997)^+ = 6.5137053636937670884410424573559565608448834020513 EK(997) = 7.5660697961049464348173831168058789211820813864311 kappaq(997) = -0.15241164633911842545641973168585206970077964353698 Total computation time: 27 min, 30 sec, 396 millisec ****** END PROGRAM ******** ? for(n=1,10,m=nextprime(n*10^3); init_kappaq_direct_v1();global_eulerkronecker_direct(m,m,50)) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[1009,1009] EK(1009)^+ = 6.2733540844322103172186250111822928458236229724449 EK(1009) = 8.4421351518492992758606946727420994594828542591508 kappaq(1009) = -0.31355651650170380534761860586860950033215944523343 Total computation time: 0 min, 27 sec, 923 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[2003,2003] EK(2003)^+ = 6.9935258611413978746616842141969266535896705017389 EK(2003) = 5.7934213690793633280384982162528099826812400204472 kappaq(2003) = 0.15785860796796903172089694876398527262243476993557 Total computation time: 1 min, 17 sec, 23 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[3001,3001] EK(3001)^+ = 8.6459700672984138998934976577488976511331869658562 EK(3001) = 8.6474651369683869388023453509157858668771668480820 kappaq(3001) = -0.00018672730489542979101599490444571525646193726973192 Total computation time: 2 min, 19 sec, 333 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[4001,4001] EK(4001)^+ = 8.7805380094230735872867993849519473314695459179410 EK(4001) = 7.0034355462031439943568517684321787497539950051076 kappaq(4001) = 0.21425588018573803459245942905866574339559053391735 Total computation time: 3 min, 33 sec, 556 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[5003,5003] EK(5003)^+ = 7.2440224742791062634412330617882944569576104435395 EK(5003) = 5.5492930045816142277368795404060581094964038266354 kappaq(5003) = 0.19896344832655115537862636141948989376788500090496 Total computation time: 5 min, 1 sec, 707 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[6007,6007] EK(6007)^+ = 9.8742666472425769486896123420917921769327511652767 EK(6007) = 8.3116101219984838165629034403801093820521447943891 kappaq(6007) = 0.17960163955734486393539596291142712383573497291976 Total computation time: 6 min, 34 sec, 253 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[7001,7001] EK(7001)^+ = 9.6833327734910786447084880544453285513626638579475 EK(7001) = 8.5052778761008771393168780384663575965235771440965 kappaq(7001) = 0.13305629180153390104527427758838956351286762792629 Total computation time: 8 min, 19 sec, 82 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[8009,8009] EK(8009)^+ = 11.443142155624708487608710920626026219892242320113 EK(8009) = 11.686846391549357535345086996047484954469293677630 kappaq(8009) = -0.027113432065738159808655683917314367260531009869271 Total computation time: 9 min, 59 sec, 344 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[9001,9001] EK(9001)^+ = 9.4868388831454962767492760006912903546499633927624 EK(9001) = 10.109478431838340935822503580226100151887118423201 kappaq(9001) = -0.068383671436367567538774232643977764891783686891994 Total computation time: 12 min, 10 sec, 530 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[10007,10007] EK(10007)^+ = 11.060162475902474193330828306321911331664543533969 EK(10007) = 12.664612004560692327538935678332147971765373810781 kappaq(10007) = -0.17418766029901389459244009721828067771255460085749 Total computation time: 14 min, 46 sec, 218 millisec ****** END PROGRAM ******** ? init_kappaq_direct_v1();global_eulerkronecker_direct(2053,2053,50) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[2053,2053] EK(2053)^+ = 10.878196891200347717581652854918501335414219282305 EK(2053) = 11.244431809366706334916103219284213775591448944439 kappaq(2053) = -0.048017852514017525967531410494807761972886758895393 Total computation time: 1 min, 20 sec, 202 millisec ****** END PROGRAM ******** ****************** larger q's ********************** ? init_kappaq_direct_v1();global_eulerkronecker_direct(20011,20011,50) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[20011,20011] EK(20011)^+ = 10.548980769217096945967222622080157907431305136535 EK(20011) = 10.799680311299920518643040289917348475045407594062 kappaq(20011) = -0.025312863019768560168817000073462601916741496687606 Total computation time: 42 min, 53 sec, 129 millisec ****** END PROGRAM ******** ? init_kappaq_direct_v1();global_eulerkronecker_direct(30011,30011,50) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* direct use of the lfun command ********** Interval=[30011,30011] EK(30011)^+ = 11.012703950054089327849887767413761503023455248047 EK(30011) = 10.333079972124024225513606225526510151166579999262 kappaq(30011) = 0.065923264260528130962044638814851917521545306585295 Total computation time: 81 min, 12 sec, 561 millisec ****** END PROGRAM ******** *******/