Give me an odd prime = Computing the primitive root for q = 4735703723 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 62.000000 min. 46.000000 sec. 537.811000 millisec. COMPUTE ODD LNGammaOdd computation 268.000000 min. 7.000000 sec. 638.970000 millisec. p4735703723-LGodd.qd 1.000000 min. 22.000000 sec. 750.897000 millisec. FFT(LGodd) 1250.000000 min. 10.000000 sec. 305.949000 millisec. p4735703723-fftLGodd.qd 1.000000 min. 41.000000 sec. 986.693000 millisec. AK computation 79.000000 min. 47.000000 sec. 68.156000 millisec. p4735703723-ak.qd 1.000000 min. 50.000000 sec. 152.699000 millisec. FFT(AK) 1349.000000 min. 32.000000 sec. 906.327000 millisec. p4735703723-fftAK.qd 2.000000 min. 18.000000 sec. 279.004000 millisec. Computing the sum and minmax over odd characters *** indexes for minimal and maximal odd characters L'/L (1,chi) chiminodd index = 1053513699 chimaxodd index = 109527127 Kummer_realcorrection = -7.6417361970796018263678225973e+10 Kummer_res = +7.6417361971339304061105974723e+10 Kummer (r) = +1.7216545866766412593076816570e+00 log r = +5.4328579742774874963741350126e-01 H_correction = -5.4393211659362118127955145875e+10 log h1 = +2.2024150311977185933150828848e+10 log Pi_odd = +5.4328579742774874963741350126e-01 *** indexes for minimal and maximal odd characters L (1,chi) chiminoddL index = 2393547739 chimaxoddL index = 4661416525 *** indexes for minimal and maximal odd characters L'(1,chi) chiminoddLprime index = 1053513699 chimaxoddLprime index = 4661416525 *** indexes for minimal and maximal odd characters |b_chi| chiminoddbchi index = 167510273 chimaxoddbchi index = 3406253719 *** First: oddresult = -5718581831.426148580671585484727627566822 , (res = -1.207546368167540150963870905301 ) OddResult computation 151.000000 min. 59.000000 sec. 495.001000 millisec. COMPUTE EVEN loadTable(): initialize table INFO: precomputed table allocated 138 elements INFO: init() time (seconds) = 0.000031 S computation 513.000000 min. 16.000000 sec. 212.380000 millisec. p4735703723-S.qd 1.000000 min. 43.000000 sec. 381.145000 millisec. Sfft 1324.000000 min. 50.000000 sec. 959.112000 millisec. p4735703723-fftS.qd 1.000000 min. 49.000000 sec. 702.507000 millisec. mkLGeven 94.000000 min. 11.000000 sec. 806.308000 millisec. p4735703723-LGeven.qd 1.000000 min. 52.000000 sec. 490.871000 millisec. LGevenfft 1254.000000 min. 42.000000 sec. 85.884000 millisec. p4735703723-fftLGeven.qd 1.000000 min. 48.000000 sec. 992.977000 millisec. Computing the sum and minmax over even characters ... *** indexes for minimal and maximal even characters L'/L (1,chi) chimineven index = 218597746 chimaxeven index = 533164980 *** indexes for minimal and maximal even characters L(1,chi) chiminevenL index = 2046385888 chimaxevenL index = 22876360 *** indexes for minimal and maximal even characters L'(1,chi) chiminevenLprime index = 218597746 chimaxevenLprime index = 22876360 *** indexes for minimal and maximal even characters |b_chi| chiminevenbchi index = 22876360 chimaxevenbchi index = 1524649012 log Pi_even = -3.3390335386229874749740014963e+00 *** Second: evenresult = -5718581802.323617811518709530948008269629 , (res = -11437163604.647235623037419061896016539259 ) EvenResult computation 97.000000 min. 14.000000 sec. 490.632000 millisec. *** RESULTS: -------------- gamma_Kr constants for every intermediate field ---- gammaK_1(4735703723) = 1.056428893764344022673709438089 gammaKplus_1(4735703723) = 14.160541298253937265937194351669 ---- gammaK_331(4735703723) = 19.223284856734784795146394196470 gammaKplus_331(4735703723) = 18.491518772185233967931160702086 ---- gammaK_7153631(4735703723) = -18.651038760350993945818912928063 gammaKplus_7153631(4735703723) = -4.984748623671112956600100779609 ---- gammaK_2367851861(4735703723) = 0.464104660707815945702908514986 gammaKplus_2367851861(4735703723) = 0.577215664901532865549427242513 -------------- Other quantities -------------- [1] EK(4735703723) = 1.056428893764344022673709438089 [2] EKplus(4735703723) = 14.160541298253937265937194351669 [3] EK(4735703723)diff = -13.104112404489593243263484086400 -------------- [4] min_even(4735703723) = 0.000012608171961461755936741663 [5] min_odd(4735703723) = 0.000036894628865902820197275954 [6] min_{chi neq chi_0}|L'/L(1,chi)|(4735703723) = 0.000012608171961461755936741663 -------------- [7] max_even(4735703723) = 3.354587420890358498148316982319 [8] max_odd(4735703723) = 3.346369634315847686770484229825 [9] max_{chi neq chi_0}|L'/L(1,chi)|(4735703723) = 3.354587420890358498148316982319 -------------- [10] Kummer_ratio(4735703723) = 1.721654586676641259307681656987 [11] log(Kummer) = log r(4735703723) = 0.543285797427748749637413501255 [12] logh_1(4735703723) = 22024150311.977185933150828848042182143339 -------------- [13] Pi(4735703723,1.0Q) = 16.374868340189785529016869523684 [14] Laurent series of zeta_{Q(zeta_q)} at 1: c_{-1} = Pi(q,1)^(-1) = 0.061069193304329795352852547185 [15] c_{0} = c_{-1} * EK = 0.064515260325574010683200358515 -------------- [16] minL_even(4735703723) = 0.228619959448219761661550623832 [17] minL_odd(4735703723) = 0.222456671429765976154836294524 [18] minL_{chi neq chi_0}|L(1,chi)|(4735703723) = 0.222456671429765976154836294524 -------------- [19] maxL_even(4735703723) = 6.833998279331400599241566426285 [20] maxL_odd(4735703723) = 6.681995275257390140738066994084 [21] maxL_{chi neq chi_0}|L(1,chi)|(4735703723) = 6.833998279331400599241566426285 -------------- [22] minLprime_even(4735703723) = 0.000016910172985514481822170484 [23] minLprime_odd(4735703723) = 0.000032613732836533921179704578 [24] minLprime_{chi neq chi_0}|Lprime(1,chi)|(4735703723) = 0.000016910172985514481822170484 -------------- [25] maxLprime_even(4735703723) = 22.446410831132053200818903562379 [26] maxLprime_odd(4735703723) = 21.968341232264072769956063032329 [27] maxLprime_{chi neq chi_0}|Lprime(1,chi)|(4735703723) = 22.446410831132053200818903562379 -------------- [28] minbchi_even(4735703723) = 16.579604675305928028091200073418 [29] minbchi_odd(4735703723) = 16.576797341308234180876086284291 [30] minbchi_{chi neq chi_0}(4735703723) = 16.576797341308234180876086284291 -------------- [31] maxbchi_even(4735703723) = 22.690679634520952395836210269263 [32] maxbchi_odd(4735703723) = 22.719898620995451864735721344389 [33] maxbchi_{chi neq chi_0}(4735703723) = 22.719898620995451864735721344389 -------------- ******** the quadratic character is odd [34] L(1,chi_quad)(4735703723) = 0.744260789346737045232640542213 [35] L(1,chi_quad)/log(4735703723) = 0.033407287649034232250708410901 [36] L(1,chi_quad)/loglog(4735703723) = 0.239804295065829288797131523537 [37] Lprime(1,chi_quad)(4735703723) = -0.084184085265017838985046004753 [38] Lderlog(1,chi_quad)(4735703723) = -0.113111004193716919846518727527 -------------- *** A priori (closed formulas) norms *** N1LGeven = +1.6412698302965714359202758020e+09 N00LGeven = +2.1133666288233676069498725663e+01 N00LGodd = +2.2278396173839304397228845766e+01 N1Seven = +9.5015094467965930129541260553e+09 N00Seven = +4.9632693608939944747291684028e+02 N1AKodd = +1.1839259302500000000527904647e+09 N00AKodd = +9.9999999957767628276943202682e-01 N2AKodd = +2.8094197858869958015637817264e+04 TOTAL TIME 6467.000000 min. 58.000000 sec. 647.431000 millisec. removing unneeded files for 4735703723 ... DONE