***** Quadruple precision version: precision forced to 128 bits main steps: ALL runComputation: steps: ALL ****** GETTING DIVISORS FROM FILE Plan generation 0.000000 min. 54.000000 sec. 846.556000 millisec. COMPUTE ODD LNGammaOdd computation 3.000000 min. 51.000000 sec. 23.846000 millisec. -temp-LGodd.qd 0.000000 min. 1.000000 sec. 470.959000 millisec. FFT(LGodd) 14.000000 min. 25.000000 sec. 650.602000 millisec. -temp-fftLGodd.qd 0.000000 min. 1.000000 sec. 512.479000 millisec. AK computation 1.000000 min. 6.000000 sec. 980.088000 millisec. -temp-ak.qd 0.000000 min. 1.000000 sec. 475.042000 millisec. FFT(AK) 14.000000 min. 24.000000 sec. 950.404000 millisec. -temp-fftAK.qd 0.000000 min. 1.000000 sec. 564.004000 millisec. Computing the sum and minmax over odd characters *** indexes for minimal and maximal odd characters L'/L (1,chi) chiminodd index = 39494895 chimaxodd index = 17282055 Kummer_realcorrection = -1.3606952224005851299845169499e+09 Kummer_res = +1.3606952218663838164090741501e+09 Kummer (r) = +5.8613724310507525700456221467e-01 log r = -5.3420131357544279978582971142e-01 H_correction = -9.8183695664463794846683987172e+08 log h1 = +3.7885826522174586794223427842e+08 log Pi_odd = -5.3420131357544279978582971142e-01 *** indexes for minimal and maximal odd characters L (1,chi) chiminoddL index = 50356029 chimaxoddL index = 102321923 *** indexes for minimal and maximal odd characters L'(1,chi) chiminoddLprime index = 39494895 chimaxoddLprime index = 102321923 *** indexes for minimal and maximal odd characters |b_chi| chiminoddbchi index = 276175 chimaxoddbchi index = 49914779 *** First: oddresult = -123891949.595005510972257619629303701504 , (res = -1.207546248932014919421242099518 ) OddResult computation 1.000000 min. 34.000000 sec. 144.575000 millisec. COMPUTE EVEN loadTable(): initialize table INFO: precomputed table allocated 138 elements INFO: init() time (seconds) = 0.000010 S computation 5.000000 min. 49.000000 sec. 455.759000 millisec. -temp-S.qd 0.000000 min. 1.000000 sec. 470.989000 millisec. Sfft 14.000000 min. 22.000000 sec. 4.745000 millisec. -temp-fftS.qd 0.000000 min. 1.000000 sec. 529.677000 millisec. mkLGeven 1.000000 min. 19.000000 sec. 594.789000 millisec. -temp-LGeven.qd 0.000000 min. 1.000000 sec. 461.382000 millisec. LGevenfft 14.000000 min. 21.000000 sec. 380.456000 millisec. -temp-fftLGeven.qd 0.000000 min. 1.000000 sec. 465.821000 millisec. Computing the sum and minmax over even characters ... *** indexes for minimal and maximal even characters L'/L (1,chi) chimineven index = 48427318 chimaxeven index = 3750800 *** indexes for minimal and maximal even characters L(1,chi) chiminevenL index = 54427472 chimaxevenL index = 1596468 *** indexes for minimal and maximal even characters L'(1,chi) chiminevenLprime index = 48427318 chimaxevenLprime index = 102213060 *** indexes for minimal and maximal even characters |b_chi| chiminevenbchi index = 102213060 chimaxevenbchi index = 77674460 log Pi_even = -3.1703277009546545571511034736e+00 *** Second: evenresult = -123891946.453708271032900758196367452250 , (res = -247783892.907416542065801516392734904499 ) EvenResult computation 1.000000 min. 28.000000 sec. 199.901000 millisec. Inverse plan generation time 0.000000 min. 54.000000 sec. 917.512000 millisec. INVERSE LGodd FFT_INV(): Initial copy and normalization time 0.000000 min. 3.000000 sec. 711.502000 millisec. FFT_INV(): fftwq inverse plan execute time 14.000000 min. 25.000000 sec. 826.288000 millisec. -temp-fftLGodd_INV.qd 0.000000 min. 1.000000 sec. 514.662000 millisec. FFT_INV(): Result copy 0.000000 min. 1.000000 sec. 514.746000 millisec. INVERSE AK FFT_INV(): Initial copy and normalization time 0.000000 min. 3.000000 sec. 250.305000 millisec. FFT_INV(): fftwq inverse plan execute time 14.000000 min. 24.000000 sec. 932.730000 millisec. -temp-fftAK_INV.qd 0.000000 min. 1.000000 sec. 577.833000 millisec. FFT_INV(): Result copy 0.000000 min. 1.000000 sec. 577.940000 millisec. INVERSE S FFT_INV(): Initial copy and normalization time 0.000000 min. 3.000000 sec. 239.606000 millisec. FFT_INV(): fftwq inverse plan execute time 14.000000 min. 22.000000 sec. 301.720000 millisec. -temp-fftS_INV.qd 0.000000 min. 1.000000 sec. 623.251000 millisec. FFT_INV(): Result copy 0.000000 min. 1.000000 sec. 623.489000 millisec. INVERSE LGeven FFT_INV(): Initial copy and normalization time 0.000000 min. 3.000000 sec. 185.407000 millisec. FFT_INV(): fftwq inverse plan execute time 14.000000 min. 24.000000 sec. 20.586000 millisec. -temp-fftLGeven_INV.qd 0.000000 min. 1.000000 sec. 598.878000 millisec. FFT_INV(): Result copy 0.000000 min. 1.000000 sec. 598.964000 millisec. NORM OF S ... Measures for S NDIFF_2 = Norm2(S - fft(fft(S)) = +4.5038854507523433104960606713e-29 NBASE_2 = Norm2(S) = +4.9789590457792986693709792194e+04 Inverse precision for S in Norm2: NDIFF_2 / NBASE_2 = +9.0458375121006893055161594333e-34 NDIFF_1 = Norm1(S - fft(fft(S)) = +2.8342581787225570368921266388e-25 NBASE_1 = Norm1(S) = +2.0584815225061033187032116686e+08 Inverse precision for S in Norm1: NDIFF_1 / NBASE_1 = +1.3768684089386347990305995943e-33 NDIFF_0 = Norm00(S - fft(fft(S)) = +1.2523830349666451256527492116e-31 NBASE_0 = Norm00(S) = +3.4026708907672543207311792907e+02 Inverse precision for S in Norm0: NDIFF_0 / NBASE_0 = +3.6805882060614166692432162070e-34 NORM OF AK ... Measures for AK NDIFF_2 = Norm2(AK - fft(fft(AK)) = +3.8930766336514756486957559066e-30 NBASE_2 = Norm2(AK) = +4.1351762558162705134709504673e+03 Inverse precision for AK in Norm2: NDIFF_2 / NBASE_2 = +9.4145361474634285526426158088e-34 NDIFF_1 = Norm1(AK - fft(fft(AK)) = +2.4695005124568827595366079920e-26 NBASE_1 = Norm1(AK) = +2.5649524250000002436692321171e+07 Inverse precision for AK in Norm1: NDIFF_1 / NBASE_1 = +9.6278608850099140725203162941e-34 NDIFF_0 = Norm00(AK - fft(fft(AK)) = +2.3222484804651899586737223362e-33 NBASE_0 = Norm00(AK) = +9.9999998050646143063527911955e-01 Inverse precision for AK in Norm0: NDIFF_0 / NBASE_0 = +2.3222485257340311627204203695e-33 NORM OF LGODD ... Measures for LGodd NDIFF_2 = Norm2(LGodd - fft(fft(LGodd)) = +1.2177989096033987908870811577e-29 NBASE_2 = Norm2(LGodd) = +1.2941856978049309584308086531e+04 Inverse precision for LGodd in Norm2: NDIFF_2 / NBASE_2 = +9.4097694918813286291154169513e-34 NDIFF_1 = Norm1(LGodd - fft(fft(LGodd)) = +7.7122564885528000283733228333e-26 NBASE_1 = Norm1(LGodd) = +7.0638900654391054167927798281e+07 Inverse precision for LGodd in Norm1: NDIFF_1 / NBASE_1 = +1.0917860296674069019175317309e-33 NDIFF_0 = Norm00(LGodd - fft(fft(LGodd)) = +9.7445203810961361996520811898e-33 NBASE_0 = Norm00(LGodd) = +1.8446329951012209800425560925e+01 Inverse precision for LGodd in Norm0: NDIFF_0 / NBASE_0 = +5.2826336767121650893431321357e-34 NORM OF LGEVEN ... Measures for LGeven NDIFF_2 = Norm2(LGeven - fft(fft(LGeven)) = +7.4175333073646078602986946766e-30 NBASE_2 = Norm2(LGeven) = +8.1754740856969453845419696397e+03 Inverse precision for LGeven in Norm2: NDIFF_2 / NBASE_2 = +9.0729090810056376681195417489e-34 NDIFF_1 = Norm1(LGeven - fft(fft(LGeven)) = +4.6848541599410398728018751110e-26 NBASE_1 = Norm1(LGeven) = +3.5557781956591474441814272686e+07 Inverse precision for LGeven in Norm1: NDIFF_1 / NBASE_1 = +1.3175327318391949191827180312e-33 NDIFF_0 = Norm00(LGeven - fft(fft(LGeven)) = +7.8389013175860814022220573255e-33 NBASE_0 = Norm00(LGeven) = +1.7301600076414785648131318434e+01 Inverse precision for LGeven in Norm0: NDIFF_0 / NBASE_0 = +4.5307377831903094217785298359e-34 *** RESULTS: -------------- gamma_Kr constants for every intermediate field ---- gammaK_1(102598099) = 22.839530312914120910266101787371 gammaKplus_1(102598099) = 12.071475243222066163560048446579 ---- gammaK_3(102598099) = 21.778468667916579307805248385739 gammaKplus_3(102598099) = 16.993570760057499354031345661941 ---- gammaK_227(102598099) = 15.530776903718506689956134562347 gammaKplus_227(102598099) = 9.110965604489226097296268660718 ---- gammaK_681(102598099) = 14.543987839912352870966520283280 gammaKplus_681(102598099) = 12.417600149000888645293108431755 ---- gammaK_75329(102598099) = 3.237814523139207336139843355838 gammaKplus_75329(102598099) = 6.453850797318609309557327420113 ---- gammaK_225987(102598099) = -59.159356906043363038194160625690 gammaKplus_225987(102598099) = -25.481770822846750398477458844041 ---- gammaK_17099683(102598099) = 0.310478242872609880383329142812 gammaKplus_17099683(102598099) = -0.524250763127726965160639218495 ---- gammaK_51299049(102598099) = 0.213310339503028739484433666679 gammaKplus_51299049(102598099) = 0.577215664901532865549427242513 -------------- Other quantities -------------- [1] EK(102598099) = 22.839530312914120910266101787371 [2] EKplus(102598099) = 12.071475243222066163560048446579 [3] EK(102598099)diff = 10.768055069692054746706053340792 -------------- [4] min_even(102598099) = 0.000050426748971717291837067117 [5] min_odd(102598099) = 0.000107946750897344946440420128 [6] min_{chi neq chi_0}|L'/L(1,chi)|(102598099) = 0.000050426748971717291837067117 -------------- [7] max_even(102598099) = 2.959675102017147797294860658082 [8] max_odd(102598099) = 3.036889753774452121461570363620 [9] max_{chi neq chi_0}|L'/L(1,chi)|(102598099) = 3.036889753774452121461570363620 -------------- [10] Kummer_ratio(102598099) = 0.586137243105075257004562214671 [11] log(Kummer) = log r(102598099) = -0.534201313575442799785829711416 [12] logh_1(102598099) = 378858265.221745867942234278418306517036 -------------- [13] Pi(102598099,1.0Q) = 40.630906243179296884957502582913 [14] Laurent series of zeta_{Q(zeta_q)} at 1: c_{-1} = Pi(q,1)^(-1) = 0.024611806441503377121015731413 [15] c_{0} = c_{-1} * EK = 0.562122099276291403513406264382 -------------- [16] minL_even(102598099) = 0.241345780117900403973888831998 [17] minL_odd(102598099) = 0.235025107487927007441073715090 [18] minL_{chi neq chi_0}|L(1,chi)|(102598099) = 0.235025107487927007441073715090 -------------- [19] maxL_even(102598099) = 5.990648500204430660422853576456 [20] maxL_odd(102598099) = 6.208031027559432793689954986265 [21] maxL_{chi neq chi_0}|L(1,chi)|(102598099) = 6.208031027559432793689954986265 -------------- [22] minLprime_even(102598099) = 0.000041617337445154337622474489 [23] minLprime_odd(102598099) = 0.000084134653833719248153165193 [24] minLprime_{chi neq chi_0}|Lprime(1,chi)|(102598099) = 0.000041617337445154337622474489 -------------- [25] maxLprime_even(102598099) = 16.858576470551891332760313144330 [26] maxLprime_odd(102598099) = 18.571980293561072713500240545000 [27] maxLprime_{chi neq chi_0}|Lprime(1,chi)|(102598099) = 18.571980293561072713500240545000 -------------- [28] minbchi_even(102598099) = 13.232725197997383910767145573517 [29] minbchi_odd(102598099) = 13.047130862596622536703439699839 [30] minbchi_{chi neq chi_0}(102598099) = 13.047130862596622536703439699839 -------------- [31] maxbchi_even(102598099) = 18.599592410457034683729201628600 [32] maxbchi_odd(102598099) = 18.644473496935030936383263508420 [33] maxbchi_{chi neq chi_0}(102598099) = 18.644473496935030936383263508420 -------------- ******** the quadratic character is odd [34] L(1,chi_quad)(102598099) = 0.633028437761885932593356716018 [35] L(1,chi_quad)/log(102598099) = 0.034317310763543620944986482938 [36] L(1,chi_quad)/loglog(102598099) = 0.217172439821026401853026924828 [37] Lprime(1,chi_quad)(102598099) = -0.230362419630245817277902100038 [38] Lderlog(1,chi_quad)(102598099) = -0.363905325398504126064993575834 -------------- *** A priori (closed formulas) norms *** N1LGeven = +3.5557781956591500733021938531e+07 N00LGeven = +1.7301600076414785648131318434e+01 N00LGodd = +1.8446329951012209747488525105e+01 N1Seven = +2.0584815225061033847727631899e+08 N00Seven = +3.4026708907672543207311792898e+02 N1AKodd = +2.5649524250000002436692321171e+07 N00AKodd = +9.9999998050646143063527911955e-01 N2AKodd = +4.1351762558162705134709504673e+03 TOTAL TIME 137.000000 min. 55.000000 sec. 319.193000 millisec.