Give me an odd prime = Computing the primitive root for q = 1979990861 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 10.000000 min. 26.000000 sec. 199.481000 millisec. COMPUTE ODD LNGammaOdd computation 110.000000 min. 19.000000 sec. 892.238000 millisec. p1979990861-LGodd.qd 0.000000 min. 26.000000 sec. 255.373000 millisec. FFT(LGodd) 288.000000 min. 46.000000 sec. 981.181000 millisec. p1979990861-fftLGodd.qd 0.000000 min. 36.000000 sec. 588.359000 millisec. AK computation 32.000000 min. 48.000000 sec. 955.185000 millisec. p1979990861-ak.qd 0.000000 min. 33.000000 sec. 716.952000 millisec. FFT(AK) 291.000000 min. 29.000000 sec. 891.403000 millisec. p1979990861-fftAK.qd 0.000000 min. 36.000000 sec. 694.151000 millisec. Computing the sum and minmax over odd characters *** indexes for minimal and maximal odd characters L'/L (1,chi) chiminodd index = 1483278163 chimaxodd index = 1967365879 Kummer_realcorrection = -3.0655017631828801096950337443e+10 Kummer_res = +3.0655017632371585170106883079e+10 Kummer (r) = +1.7207910074413241909252169754e+00 log r = +5.4278407315654563569341031469e-01 H_correction = -2.1878409177241644716828621055e+10 log h1 = +8.7766084551299404532782620237e+09 log Pi_odd = +5.4278407315654563569341031469e-01 *** indexes for minimal and maximal odd characters L (1,chi) chiminoddL index = 1202813783 chimaxoddL index = 12624981 *** indexes for minimal and maximal odd characters L'(1,chi) chiminoddLprime index = 1483278163 chimaxoddLprime index = 12624981 *** indexes for minimal and maximal odd characters |b_chi| chiminoddbchi index = 1967365879 chimaxoddbchi index = 1202813783 *** First: oddresult = -2390930779.623067776307715716426175863967 , (res = -1.207546371408765697483547989177 ) OddResult computation 45.000000 min. 34.000000 sec. 704.525000 millisec. COMPUTE EVEN loadTable(): initialize table INFO: precomputed table allocated 138 elements INFO: init() time (seconds) = 0.000018 S computation 165.000000 min. 55.000000 sec. 933.611000 millisec. p1979990861-S.qd 0.000000 min. 38.000000 sec. 417.653000 millisec. Sfft 290.000000 min. 10.000000 sec. 191.029000 millisec. p1979990861-fftS.qd 0.000000 min. 38.000000 sec. 360.709000 millisec. mkLGeven 38.000000 min. 45.000000 sec. 522.457000 millisec. p1979990861-LGeven.qd 0.000000 min. 32.000000 sec. 750.916000 millisec. LGevenfft 294.000000 min. 16.000000 sec. 819.526000 millisec. p1979990861-fftLGeven.qd 0.000000 min. 34.000000 sec. 676.528000 millisec. Computing the sum and minmax over even characters ... *** indexes for minimal and maximal even characters L'/L (1,chi) chimineven index = 309637700 chimaxeven index = 369160142 *** indexes for minimal and maximal even characters L(1,chi) chiminevenL index = 968493530 chimaxevenL index = 5518394 *** indexes for minimal and maximal even characters L'(1,chi) chiminevenLprime index = 309637700 chimaxevenLprime index = 18429372 *** indexes for minimal and maximal even characters |b_chi| chiminevenbchi index = 1952574386 chimaxevenbchi index = 629004272 log Pi_even = -3.3125223359719193077849543186e+00 *** Second: evenresult = -2390930751.241134834021409163373794695214 , (res = -4781861502.482269668042818326747589390428 ) EvenResult computation 44.000000 min. 7.000000 sec. 333.670000 millisec. *** RESULTS: -------------- gamma_Kr constants for every intermediate field ---- gammaK_1(1979990861) = 1.345895195887944514792446980127 gammaKplus_1(1979990861) = 13.944975535882452811632943231287 ---- gammaK_2(1979990861) = 13.944975535882452811632943231287 gammaKplus_2(1979990861) = 18.514654603917130694449313905541 ---- gammaK_5(1979990861) = 15.424184936926642666362677261889 gammaKplus_5(1979990861) = 19.077936313151967956071986948612 ---- gammaK_10(1979990861) = 19.077936313151967956071986948612 gammaKplus_10(1979990861) = 18.847030032002795166204333609468 ---- gammaK_41(1979990861) = 20.525817049851359165011756534117 gammaKplus_41(1979990861) = 18.746385941532313806364749362147 ---- gammaK_82(1979990861) = 18.746385941532313806364749362147 gammaKplus_82(1979990861) = 9.377287883547292216721107836884 ---- gammaK_193(1979990861) = 8.928837772848689097573560385552 gammaKplus_193(1979990861) = 13.892265122354043542595549314055 ---- gammaK_205(1979990861) = 17.830253970227038252233636253416 gammaKplus_205(1979990861) = 16.804092247181608224310151649772 ---- gammaK_386(1979990861) = 13.892265122354043542595549314055 gammaKplus_386(1979990861) = -9.582197024332694686976177788328 ---- gammaK_410(1979990861) = 16.804092247181608224310151649772 gammaKplus_410(1979990861) = 16.135006377358056972252522400945 ---- gammaK_965(1979990861) = 14.956675119567596571822265295363 gammaKplus_965(1979990861) = 14.568706027978248650207546411764 ---- gammaK_1930(1979990861) = 14.568706027978248650207546411764 gammaKplus_1930(1979990861) = 9.355863343552820856306202525963 ---- gammaK_7913(1979990861) = 14.692874655593311462770036895057 gammaKplus_7913(1979990861) = 14.500161216727641722018214356145 ---- gammaK_12511(1979990861) = 12.751363670700529995785690033401 gammaKplus_12511(1979990861) = 9.518761464377960228660786453337 ---- gammaK_15826(1979990861) = 14.500161216727641722018214356145 gammaKplus_15826(1979990861) = 12.000489796429666803567977987732 ---- gammaK_25022(1979990861) = 9.518761464377960228660786453337 gammaKplus_25022(1979990861) = 12.799843554241134404993965761743 ---- gammaK_39565(1979990861) = 12.534573898669924396268303253436 gammaKplus_39565(1979990861) = -328.290013391054081032902722364434 ---- gammaK_62555(1979990861) = 9.192509591666903403570092005876 gammaKplus_62555(1979990861) = 9.428591069955069454723285042602 ---- gammaK_79130(1979990861) = -328.290013391054081032902722364434 gammaKplus_79130(1979990861) = -158.216440070705531095161983829248 ---- gammaK_125110(1979990861) = 9.428591069955069454723285042602 gammaKplus_125110(1979990861) = 10.661337785246694264310759137426 ---- gammaK_512951(1979990861) = 8.222505761999501660464258935811 gammaKplus_512951(1979990861) = 9.289997172014857464023806361556 ---- gammaK_1025902(1979990861) = 9.289997172014857464023806361556 gammaKplus_1025902(1979990861) = 6.210602103585714364971707642159 ---- gammaK_2414623(1979990861) = -14.383651862312453188665390346167 gammaKplus_2414623(1979990861) = -3.351654350090699045413806428304 ---- gammaK_2564755(1979990861) = 3.577391821272697804595835039748 gammaKplus_2564755(1979990861) = 5.799106434439023196765735193884 ---- gammaK_4829246(1979990861) = -3.351654350090699045413806428304 gammaKplus_4829246(1979990861) = 0.421911475720892666615717378320 ---- gammaK_5129510(1979990861) = 5.799106434439023196765735193884 gammaKplus_5129510(1979990861) = 4.704146066810824517550105790360 ---- gammaK_12073115(1979990861) = 3.196273721565121096833212674760 gammaKplus_12073115(1979990861) = 4.444836624543179718645133562319 ---- gammaK_24146230(1979990861) = 4.444836624543179718645133562319 gammaKplus_24146230(1979990861) = 4.684953373924087138403229740002 ---- gammaK_98999543(1979990861) = 3.324030713747775537062546443257 gammaKplus_98999543(1979990861) = 1.827500695188140798423199603743 ---- gammaK_197999086(1979990861) = 1.827500695188140798423199603743 gammaKplus_197999086(1979990861) = 0.636326867026012862992282538660 ---- gammaK_494997715(1979990861) = 1.860298427926729205442529634259 gammaKplus_494997715(1979990861) = 0.143447351948088633527920842260 ---- gammaK_989995430(1979990861) = 0.143447351948088633527920842260 gammaKplus_989995430(1979990861) = 0.577215664901532865549427242513 -------------- Other quantities -------------- [1] EK(1979990861) = 1.345895195887944514792446980127 [2] EKplus(1979990861) = 13.944975535882452811632943231287 [3] EK(1979990861)diff = -12.599080339994508296840496664751 -------------- [4] min_even(1979990861) = 0.000008535526609738935736431518 [5] min_odd(1979990861) = 0.000024599834254991829390504872 [6] min_{chi neq chi_0}|L'/L(1,chi)|(1979990861) = 0.000008535526609738935736431518 -------------- [7] max_even(1979990861) = 3.155824673967458526110780762219 [8] max_odd(1979990861) = 3.308142528903790595221038964921 [9] max_{chi neq chi_0}|L'/L(1,chi)|(1979990861) = 3.308142528903790595221038964921 -------------- [10] Kummer_ratio(1979990861) = 1.720791007441324190925216975368 [11] log(Kummer) = log r(1979990861) = 0.542784073156545635693410314694 [12] logh_1(1979990861) = 8776608455.129940453278262023726780369695 -------------- [13] Pi(1979990861,1.0Q) = 15.954457588444048917651964975822 [14] Laurent series of zeta_{Q(zeta_q)} at 1: c_{-1} = Pi(q,1)^(-1) = 0.062678407865417412573914260828 [15] c_{0} = c_{-1} * EK = 0.084358568031970450712584942837 -------------- [16] minL_even(1979990861) = 0.226245620302622684571155266242 [17] minL_odd(1979990861) = 0.226610513012550476033876341801 [18] minL_{chi neq chi_0}|L(1,chi)|(1979990861) = 0.226245620302622684571155266242 -------------- [19] maxL_even(1979990861) = 6.265594223544786022846682901503 [20] maxL_odd(1979990861) = 6.735416731968883937670857116197 [21] maxL_{chi neq chi_0}|L(1,chi)|(1979990861) = 6.735416731968883937670857116197 -------------- [22] minLprime_even(1979990861) = 0.000010281689881076025433877930 [23] minLprime_odd(1979990861) = 0.000017197795209833562681693413 [24] minLprime_{chi neq chi_0}|Lprime(1,chi)|(1979990861) = 0.000010281689881076025433877930 -------------- [25] maxLprime_even(1979990861) = 19.432204626947757703370473754923 [26] maxLprime_odd(1979990861) = 22.281718540916448371026454711473 [27] maxLprime_{chi neq chi_0}|Lprime(1,chi)|(1979990861) = 22.281718540916448371026454711473 -------------- [28] minbchi_even(1979990861) = 15.936416794582093063196411839072 [29] minbchi_odd(1979990861) = 15.690600889195323012765896402146 [30] minbchi_{chi neq chi_0}(1979990861) = 15.690600889195323012765896402146 -------------- [31] maxbchi_even(1979990861) = 21.922912651722804162068549482261 [32] maxbchi_odd(1979990861) = 21.836382285661974537370816195746 [33] maxbchi_{chi neq chi_0}(1979990861) = 21.922912651722804162068549482261 -------------- ******** the quadratic character is even [34] L(1,chi_quad)(1979990861) = 0.761022468060977820221673884097 [35] L(1,chi_quad)/log(1979990861) = 0.035551235091700648925101927588 [36] L(1,chi_quad)/loglog(1979990861) = 0.248400774520156111459812660853 [37] Lprime(1,chi_quad)(1979990861) = -0.330107432090476744758505327289 [38] Lderlog(1,chi_quad)(1979990861) = -0.433768312953444232021506400253 -------------- *** A priori (closed formulas) norms *** N1LGeven = +6.8621253036855166438017716735e+08 N00LGeven = +2.0261628180136237057543914980e+01 N00LGodd = +2.1406358065402588382946080938e+01 N1Seven = +3.9725671761426537330785438822e+09 N00Seven = +4.5823216564918834954684468205e+02 N1AKodd = +4.9499771475000000012626320905e+08 N00AKodd = +9.9999999898989432759811107027e-01 N2AKodd = +1.8165860186991788402414070922e+04 TOTAL TIME 1619.000000 min. 47.000000 sec. 911.653000 millisec. removing unneeded files for 1979990861 ... DONE