Give me an odd prime = Computing the primitive root for q = 1326662801 and saving on file Primitive root generation time: 0 min, 0 sec, 0 millisec ****************************************** Now you can call the precomputation programs ****************************************** *** Generating wisdom-outplace-fftwq-estimate *** Saving wisdom-outplace-fftwq-estimate.txt ***** Quadruple precision version: precision forced to 128 bits main steps: COMPUTE, ODDRESULT, EVENRESULT runComputation: steps: COMPUTE, ODDRESULT, EVENRESULT ****** GETTING DIVISORS FROM FILE Plan generation 4.000000 min. 33.000000 sec. 141.050000 millisec. COMPUTE ODD LNGammaOdd computation 108.000000 min. 54.000000 sec. 580.210000 millisec. p1326662801-LGodd.qd 0.000000 min. 33.000000 sec. 591.911000 millisec. FFT(LGodd) 354.000000 min. 55.000000 sec. 303.492000 millisec. p1326662801-fftLGodd.qd 0.000000 min. 23.000000 sec. 853.767000 millisec. AK computation 22.000000 min. 6.000000 sec. 185.985000 millisec. p1326662801-ak.qd 0.000000 min. 21.000000 sec. 146.061000 millisec. FFT(AK) 267.000000 min. 40.000000 sec. 634.086000 millisec. p1326662801-fftAK.qd 0.000000 min. 21.000000 sec. 654.976000 millisec. Computing the sum and minmax over odd characters *** indexes for minimal and maximal odd characters L'/L (1,chi) chiminodd index = 384307399 chimaxodd index = 1254231357 Kummer_realcorrection = -2.0141506596476111949731024673e+10 Kummer_res = +2.0141506597012464117651276488e+10 Kummer (r) = +1.7097585606100537817946120051e+00 log r = +5.3635216792025181479625202766e-01 H_correction = -1.4393680850840091492073266878e+10 log h1 = +5.7478257461723726255780096100e+09 log Pi_odd = +5.3635216792025181479625202766e-01 *** indexes for minimal and maximal odd characters L (1,chi) chiminoddL index = 659354921 chimaxoddL index = 13960939 *** indexes for minimal and maximal odd characters L'(1,chi) chiminoddLprime index = 384307399 chimaxoddLprime index = 13960939 *** indexes for minimal and maximal odd characters |b_chi| chiminoddbchi index = 1312701861 chimaxoddbchi index = 593906131 *** First: oddresult = -1602006854.798864721339392289333087938697 , (res = -1.207546373947711767746619956169 ) OddResult computation 32.000000 min. 11.000000 sec. 623.601000 millisec. COMPUTE EVEN loadTable(): initialize table INFO: precomputed table allocated 138 elements INFO: init() time (seconds) = 0.000016 S computation 111.000000 min. 55.000000 sec. 139.236000 millisec. p1326662801-S.qd 0.000000 min. 19.000000 sec. 996.781000 millisec. Sfft 272.000000 min. 44.000000 sec. 461.034000 millisec. p1326662801-fftS.qd 0.000000 min. 20.000000 sec. 879.766000 millisec. mkLGeven 26.000000 min. 7.000000 sec. 972.854000 millisec. p1326662801-LGeven.qd 0.000000 min. 22.000000 sec. 206.948000 millisec. LGevenfft 271.000000 min. 23.000000 sec. 417.602000 millisec. p1326662801-fftLGeven.qd 0.000000 min. 19.000000 sec. 604.191000 millisec. Computing the sum and minmax over even characters ... *** indexes for minimal and maximal even characters L'/L (1,chi) chimineven index = 642196142 chimaxeven index = 226952352 *** indexes for minimal and maximal even characters L(1,chi) chiminevenL index = 662403442 chimaxevenL index = 38494666 *** indexes for minimal and maximal even characters L'(1,chi) chiminevenLprime index = 642196142 chimaxevenLprime index = 26705190 *** indexes for minimal and maximal even characters |b_chi| chiminevenbchi index = 26705190 chimaxevenbchi index = 934454016 log Pi_even = -3.3130101241285237137117110099e+00 *** Second: evenresult = -1602006826.572327054572933807128365368527 , (res = -3204013653.144654109145867614256730737054 ) EvenResult computation 31.000000 min. 5.000000 sec. 18.824000 millisec. *** RESULTS: -------------- gamma_Kr constants for every intermediate field ---- gammaK_1(1326662801) = 1.971468647052498026841663483262 gammaKplus_1(1326662801) = 14.180064623704805532233722390359 ---- gammaK_2(1326662801) = 14.180064623704805532233722390359 gammaKplus_2(1326662801) = 17.541431159429993006276065518694 ---- gammaK_4(1326662801) = 17.541431159429993006276065518694 gammaKplus_4(1326662801) = 20.003234781111117044933205702069 ---- gammaK_5(1326662801) = 17.954371876997156444046331251642 gammaKplus_5(1326662801) = 20.810717691348854026494673535005 ---- gammaK_8(1326662801) = 20.003234781111117044933205702069 gammaKplus_8(1326662801) = 21.831232006465299097010985130134 ---- gammaK_10(1326662801) = 20.810717691348854026494673535005 gammaKplus_10(1326662801) = 21.893810264910677279576079784255 ---- gammaK_20(1326662801) = 21.893810264910677279576079784255 gammaKplus_20(1326662801) = 18.276665207416278191747083720953 ---- gammaK_25(1326662801) = -85.928353513446043870042767788510 gammaKplus_25(1326662801) = -32.027438969393038453066564196094 ---- gammaK_40(1326662801) = 18.276665207416278191747083720953 gammaKplus_40(1326662801) = 17.464693627630495878100309937718 ---- gammaK_50(1326662801) = -32.027438969393038453066564196094 gammaKplus_50(1326662801) = -13.313419400668654118736170242710 ---- gammaK_79(1326662801) = 17.642532368493978410406293034255 gammaKplus_79(1326662801) = 18.745227995465685723132007300402 ---- gammaK_100(1326662801) = -13.313419400668654118736170242710 gammaKplus_100(1326662801) = 2.976299166511314701482419160941 ---- gammaK_158(1326662801) = 18.745227995465685723132007300402 gammaKplus_158(1326662801) = 16.834329697822732259355507626716 ---- gammaK_200(1326662801) = 2.976299166511314701482419160941 gammaKplus_200(1326662801) = 7.474394450569117146768985893087 ---- gammaK_316(1326662801) = 16.834329697822732259355507626716 gammaKplus_316(1326662801) = -6.185022805989279508708221023849 ---- gammaK_395(1326662801) = 14.985406980693963299693379570904 gammaKplus_395(1326662801) = 15.050060758916182149216787521814 ---- gammaK_632(1326662801) = -6.185022805989279508708221023849 gammaKplus_632(1326662801) = 3.780709320149675483497728319989 ---- gammaK_790(1326662801) = 15.050060758916182149216787521814 gammaKplus_790(1326662801) = 15.646598280722033618964974478331 ---- gammaK_1580(1326662801) = 15.646598280722033618964974478331 gammaKplus_1580(1326662801) = 10.936105680396104264604435367844 ---- gammaK_1975(1326662801) = 11.740869134891577920666766505512 gammaKplus_1975(1326662801) = 13.860244868464422923252985845829 ---- gammaK_3160(1326662801) = 10.936105680396104264604435367844 gammaKplus_3160(1326662801) = 13.136170698443965664740961385382 ---- gammaK_3950(1326662801) = 13.860244868464422923252985845829 gammaKplus_3950(1326662801) = -228.131072876169037494762451340832 ---- gammaK_7900(1326662801) = -228.131072876169037494762451340832 gammaKplus_7900(1326662801) = -107.145024783158112682691012519290 ---- gammaK_15800(1326662801) = -107.145024783158112682691012519290 gammaKplus_15800(1326662801) = -47.393323285447424313497829212834 ---- gammaK_41983(1326662801) = 7.464275223241908016351262603296 gammaKplus_41983(1326662801) = 10.195416641876071356135180143652 ---- gammaK_83966(1326662801) = 10.195416641876071356135180143652 gammaKplus_83966(1326662801) = 9.794216102548966244735084794180 ---- gammaK_167932(1326662801) = 9.794216102548966244735084794180 gammaKplus_167932(1326662801) = 6.051451785455782705879428510306 ---- gammaK_209915(1326662801) = 10.455080030323518597472664373570 gammaKplus_209915(1326662801) = 8.259513431511472980550605642055 ---- gammaK_335864(1326662801) = 6.051451785455782705879428510306 gammaKplus_335864(1326662801) = 8.352675144684238782627671623029 ---- gammaK_419830(1326662801) = 8.259513431511472980550605642055 gammaKplus_419830(1326662801) = 5.986391966872455906526779976509 ---- gammaK_839660(1326662801) = 5.986391966872455906526779976509 gammaKplus_839660(1326662801) = 7.235301451479272138502978977303 ---- gammaK_1049575(1326662801) = -0.943633741832216894803219976831 gammaKplus_1049575(1326662801) = 3.140045670956909936886221100551 ---- gammaK_1679320(1326662801) = 7.235301451479272138502978977303 gammaKplus_1679320(1326662801) = 7.777412564293430038461558010928 ---- gammaK_2099150(1326662801) = 3.140045670956909936886221100551 gammaKplus_2099150(1326662801) = 5.394336121249122127586641066474 ---- gammaK_3316657(1326662801) = 6.903493903890211450745110127464 gammaKplus_3316657(1326662801) = 7.288658476167961659539423337586 ---- gammaK_4198300(1326662801) = 5.394336121249122127586641066474 gammaKplus_4198300(1326662801) = -0.429415499175932409737354706444 ---- gammaK_6633314(1326662801) = 7.288658476167961659539423337586 gammaKplus_6633314(1326662801) = 5.913158568295220495281421556098 ---- gammaK_8396600(1326662801) = -0.429415499175932409737354706444 gammaKplus_8396600(1326662801) = 2.467704366913843959864022335086 ---- gammaK_13266628(1326662801) = 5.913158568295220495281421556098 gammaKplus_13266628(1326662801) = 7.004126323217652372343703281546 ---- gammaK_16583285(1326662801) = 2.271855617513320899141776398462 gammaKplus_16583285(1326662801) = 4.979617865211413547432266880585 ---- gammaK_26533256(1326662801) = 7.004126323217652372343703281546 gammaKplus_26533256(1326662801) = 4.238093518239747561967287660072 ---- gammaK_33166570(1326662801) = 4.979617865211413547432266880585 gammaKplus_33166570(1326662801) = 3.764347977042203010938902799478 ---- gammaK_66333140(1326662801) = 3.764347977042203010938902799478 gammaKplus_66333140(1326662801) = 0.288401355778515607113847918568 ---- gammaK_82916425(1326662801) = 1.863223973405452109957432189747 gammaKplus_82916425(1326662801) = 2.166301685059145382349937009783 ---- gammaK_132666280(1326662801) = 0.288401355778515607113847918568 gammaKplus_132666280(1326662801) = 2.161586823246511520136905937041 ---- gammaK_165832850(1326662801) = 2.166301685059145382349937009783 gammaKplus_165832850(1326662801) = 0.475557998586546374140028949280 ---- gammaK_331665700(1326662801) = 0.475557998586546374140028949280 gammaKplus_331665700(1326662801) = -0.264379719909892864652810175956 ---- gammaK_663331400(1326662801) = -0.264379719909892864652810175956 gammaKplus_663331400(1326662801) = 0.577215664901532865549427242513 -------------- Other quantities -------------- [1] EK(1326662801) = 1.971468647052498026841663483262 [2] EKplus(1326662801) = 14.180064623704805532233722390359 [3] EK(1326662801)diff = -12.208595976652307505392058907097 -------------- [4] min_even(1326662801) = 0.000077406922277222745503011315 [5] min_odd(1326662801) = 0.000035892497676439630879999508 [6] min_{chi neq chi_0}|L'/L(1,chi)|(1326662801) = 0.000035892497676439630879999508 -------------- [7] max_even(1326662801) = 3.137317616203131303176212751562 [8] max_odd(1326662801) = 3.235120564762330786760489690522 [9] max_{chi neq chi_0}|L'/L(1,chi)|(1326662801) = 3.235120564762330786760489690522 -------------- [10] Kummer_ratio(1326662801) = 1.709758560610053781794612005067 [11] log(Kummer) = log r(1326662801) = 0.536352167920251814796252027658 [12] logh_1(1326662801) = 5747825746.172372625578009610015432443661 -------------- [13] Pi(1326662801,1.0Q) = 16.065240392682401474452179507003 [14] Laurent series of zeta_{Q(zeta_q)} at 1: c_{-1} = Pi(q,1)^(-1) = 0.062246189634080584657003832592 [15] c_{0} = c_{-1} * EK = 0.122716411262074077456913542720 -------------- [16] minL_even(1326662801) = 0.231896319482485214792566555989 [17] minL_odd(1326662801) = 0.223114537979856418702983817607 [18] minL_{chi neq chi_0}|L(1,chi)|(1326662801) = 0.223114537979856418702983817607 -------------- [19] maxL_even(1326662801) = 6.255635604317950601484240882800 [20] maxL_odd(1326662801) = 6.577960582958033100424232640390 [21] maxL_{chi neq chi_0}|L(1,chi)|(1326662801) = 6.577960582958033100424232640390 -------------- [22] minLprime_even(1326662801) = 0.000059577696925070535504029511 [23] minLprime_odd(1326662801) = 0.000024355612390980781729937943 [24] minLprime_{chi neq chi_0}|Lprime(1,chi)|(1326662801) = 0.000024355612390980781729937943 -------------- [25] maxLprime_even(1326662801) = 18.816822631215113342881519838977 [26] maxLprime_odd(1326662801) = 21.233712903393687473657174058463 [27] maxLprime_{chi neq chi_0}|Lprime(1,chi)|(1326662801) = 21.233712903393687473657174058463 -------------- [28] minbchi_even(1326662801) = 15.570093278170383095332206041246 [29] minbchi_odd(1326662801) = 15.364501571602267983376972014437 [30] minbchi_{chi neq chi_0}(1326662801) = 15.364501571602267983376972014437 -------------- [31] maxbchi_even(1326662801) = 21.439682464192196773734440789360 [32] maxbchi_odd(1326662801) = 21.407253183874428372079582692116 [33] maxbchi_{chi neq chi_0}(1326662801) = 21.439682464192196773734440789360 -------------- ******** the quadratic character is even [34] L(1,chi_quad)(1326662801) = 1.967798498547232458758462716207 [35] L(1,chi_quad)/log(1326662801) = 0.093678226514330081943033466275 [36] L(1,chi_quad)/loglog(1326662801) = 0.646280653769964003098205644826 [37] Lprime(1,chi_quad)(1326662801) = -1.656090134616203876840647118637 [38] Lderlog(1,chi_quad)(1326662801) = -0.841595384811425730202237418469 -------------- *** A priori (closed formulas) norms *** N1LGeven = +4.5978627918391507914351219472e+08 N00LGeven = +1.9861202567901907010836965839e+01 N00LGodd = +2.1005932452881130321609358239e+01 N1Seven = +2.6617582143628391631215467564e+09 N00Seven = +4.4124919825156241149171260586e+02 N1AKodd = +3.3166569975000000018844276014e+08 N00AKodd = +9.9999999849245791885288566254e-01 N2AKodd = +1.4869783668007189054170653291e+04 TOTAL TIME 1506.000000 min. 49.000000 sec. 871.563000 millisec. removing unneeded files for 1326662801 ... DONE