Give me an odd prime = Computing the primitive root for q = 9697282541 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 79.000000 min. 1.000000 sec. 825.844000 millisec. COMPUTE ODD LNGammaOdd computation 800.000000 min. 13.000000 sec. 850.376000 millisec. p9697282541-LGodd.qd 4.000000 min. 19.000000 sec. 663.661000 millisec. FFT(LGodd) 2267.000000 min. 18.000000 sec. 75.082000 millisec. p9697282541-fftLGodd.qd 3.000000 min. 47.000000 sec. 563.840000 millisec. AK computation 163.000000 min. 26.000000 sec. 971.597000 millisec. p9697282541-ak.qd 3.000000 min. 47.000000 sec. 817.068000 millisec. FFT(AK) 2176.000000 min. 1.000000 sec. 632.240000 millisec. p9697282541-fftAK.qd 3.000000 min. 51.000000 sec. 754.416000 millisec. Computing the sum and minmax over odd characters *** indexes for minimal and maximal odd characters L'/L (1,chi) chiminodd index = 2873875601 chimaxodd index = 805932141 Kummer_realcorrection = -1.6169218561170454578159257201e+11 Kummer_res = +1.6169218561224962274565292426e+11 Kummer (r) = +1.7247411203480217462905994762e+00 log r = +5.4507696406035224733707316238e-01 H_correction = -1.1485586878831639134395025464e+11 log h1 = +4.6836316823933231401702669620e+10 log Pi_odd = +5.4507696406035224733707316238e-01 *** indexes for minimal and maximal odd characters L (1,chi) chiminoddL index = 4776848155 chimaxoddL index = 9242575699 *** indexes for minimal and maximal odd characters L'(1,chi) chiminoddLprime index = 2873875601 chimaxoddLprime index = 9242575699 *** indexes for minimal and maximal odd characters |b_chi| chiminoddbchi index = 454706841 chimaxoddbchi index = 5269577419 *** First: oddresult = -11709918301.412243377181091708911504995667 , (res = -1.207546366923191351116175723781 ) OddResult computation 249.000000 min. 8.000000 sec. 688.816000 millisec. COMPUTE EVEN loadTable(): initialize table INFO: precomputed table allocated 138 elements INFO: init() time (seconds) = 0.000138 S computation 821.000000 min. 52.000000 sec. 595.144000 millisec. p9697282541-S.qd 3.000000 min. 49.000000 sec. 335.493000 millisec. Sfft 2311.000000 min. 6.000000 sec. 891.009000 millisec. p9697282541-fftS.qd 3.000000 min. 49.000000 sec. 869.952000 millisec. mkLGeven 193.000000 min. 0.000000 sec. 500.320000 millisec. p9697282541-LGeven.qd 3.000000 min. 57.000000 sec. 815.747000 millisec. LGevenfft 2174.000000 min. 50.000000 sec. 224.065000 millisec. p9697282541-fftLGeven.qd 3.000000 min. 52.000000 sec. 567.555000 millisec. Computing the sum and minmax over even characters ... *** indexes for minimal and maximal even characters L'/L (1,chi) chimineven index = 7520366728 chimaxeven index = 9261980258 *** indexes for minimal and maximal even characters L(1,chi) chiminevenL index = 4954072228 chimaxevenL index = 225563536 *** indexes for minimal and maximal even characters L'(1,chi) chiminevenLprime index = 6012758774 chimaxevenLprime index = 225563536 *** indexes for minimal and maximal even characters |b_chi| chiminevenbchi index = 225563536 chimaxevenbchi index = 4863101596 log Pi_even = -3.3695285590772636428126207844e+00 *** Second: evenresult = -11709918271.431143757863218362975183275683 , (res = -23419836542.862287515726436725950366551366 ) EvenResult computation 241.000000 min. 19.000000 sec. 684.994000 millisec. *** RESULTS: -------------- gamma_Kr constants for every intermediate field ---- gammaK_1(9697282541) = 1.140627347418876431835041558495 gammaKplus_1(9697282541) = 14.641924950163702166596210796087 ---- gammaK_2(9697282541) = 14.641924950163702166596210796087 gammaKplus_2(9697282541) = 19.685538977118718733093259241934 ---- gammaK_5(9697282541) = 19.827573357266862522478247234040 gammaKplus_5(9697282541) = 21.530583530837588409757109879449 ---- gammaK_10(9697282541) = 21.530583530837588409757109879449 gammaKplus_10(9697282541) = 22.417701218404792465307068798568 ---- gammaK_11(9697282541) = 22.726859682323202943252220454008 gammaKplus_11(9697282541) = 10.243803809094570611051415640047 ---- gammaK_22(9697282541) = 10.243803809094570611051415640047 gammaKplus_22(9697282541) = 12.858449458981030604995503965192 ---- gammaK_23(9697282541) = 19.852448612291195108889479865197 gammaKplus_23(9697282541) = 21.807420347445566966690681090105 ---- gammaK_46(9697282541) = 21.807420347445566966690681090105 gammaKplus_46(9697282541) = 16.294404393177156453513052561666 ---- gammaK_55(9697282541) = 18.921011592196878904446578607815 gammaKplus_55(9697282541) = 15.905215974331286415729470148783 ---- gammaK_110(9697282541) = 15.905215974331286415729470148783 gammaKplus_110(9697282541) = 16.977629539327833065146581697350 ---- gammaK_115(9697282541) = 20.574496528327877116554570004837 gammaKplus_115(9697282541) = 21.829606460608250786264408025044 ---- gammaK_230(9697282541) = 21.829606460608250786264408025044 gammaKplus_230(9697282541) = 20.087877484559362733414637203411 ---- gammaK_253(9697282541) = 21.645209367101842645267701406397 gammaKplus_253(9697282541) = 20.446287442272226695693903339998 ---- gammaK_506(9697282541) = 20.446287442272226695693903339998 gammaKplus_506(9697282541) = 15.295515187311267216357507640996 ---- gammaK_1097(9697282541) = 16.035255832966680848974865461146 gammaKplus_1097(9697282541) = 14.675218144842305433669919353853 ---- gammaK_1265(9697282541) = 15.547001897466889090181298355219 gammaKplus_1265(9697282541) = 16.799937837977075913125745233590 ---- gammaK_1747(9697282541) = 18.294547243304255453602063042827 gammaKplus_1747(9697282541) = 17.250698925403673036703416787554 ---- gammaK_2194(9697282541) = 14.675218144842305433669919353853 gammaKplus_2194(9697282541) = 11.192306604802016251501933244750 ---- gammaK_2530(9697282541) = 16.799937837977075913125745233590 gammaKplus_2530(9697282541) = 13.031684566675124417605723248842 ---- gammaK_3494(9697282541) = 17.250698925403673036703416787554 gammaKplus_3494(9697282541) = 17.140339006394561804655196141415 ---- gammaK_5485(9697282541) = 12.852458176638668970835768878500 gammaKplus_5485(9697282541) = 14.025858602841234017667334581483 ---- gammaK_8735(9697282541) = 17.511716918481365753511099946442 gammaKplus_8735(9697282541) = 17.529845180737509894359693548372 ---- gammaK_10970(9697282541) = 14.025858602841234017667334581483 gammaKplus_10970(9697282541) = 14.150446640869406595730711577516 ---- gammaK_12067(9697282541) = 13.719556663590414495814266943979 gammaKplus_12067(9697282541) = 14.642049273083849350396912064800 ---- gammaK_17470(9697282541) = 17.529845180737509894359693548372 gammaKplus_17470(9697282541) = 15.469144189468479685387118745253 ---- gammaK_19217(9697282541) = 16.675487605047600219585644591714 gammaKplus_19217(9697282541) = -4.809942225678684507054769967149 ---- gammaK_24134(9697282541) = 14.642049273083849350396912064800 gammaKplus_24134(9697282541) = 14.723799311045828564147263531805 ---- gammaK_25231(9697282541) = 13.351239744100441245578614961012 gammaKplus_25231(9697282541) = -22.958221952227624696097883311247 ---- gammaK_38434(9697282541) = -4.809942225678684507054769967149 gammaKplus_38434(9697282541) = 1.907077445468697043710417039767 ---- gammaK_40181(9697282541) = 13.880883868460494188969426379120 gammaKplus_40181(9697282541) = 13.539786242912862516665822249558 ---- gammaK_50462(9697282541) = -22.958221952227624696097883311247 gammaKplus_50462(9697282541) = -4.022363420697768075112576538586 ---- gammaK_60335(9697282541) = 2.262777617309781643848615569291 gammaKplus_60335(9697282541) = 7.115779629067681116988874570144 ---- gammaK_80362(9697282541) = 13.539786242912862516665822249558 gammaKplus_80362(9697282541) = 11.896186663700651232200004576796 ---- gammaK_96085(9697282541) = 15.328826151230896756732590917837 gammaKplus_96085(9697282541) = 10.265723642449830578715719757895 ---- gammaK_120670(9697282541) = 7.115779629067681116988874570144 gammaKplus_120670(9697282541) = 9.586073862215693522033931629006 ---- gammaK_126155(9697282541) = 11.686222082838159367945004100523 gammaKplus_126155(9697282541) = 5.303926136975306147443788640599 ---- gammaK_192170(9697282541) = 10.265723642449830578715719757895 gammaKplus_192170(9697282541) = 4.697004168674448499867894250994 ---- gammaK_200905(9697282541) = 11.684868156120077097696718992216 gammaKplus_200905(9697282541) = 11.042272403063754238355518707710 ---- gammaK_252310(9697282541) = 5.303926136975306147443788640599 gammaKplus_252310(9697282541) = 0.660554433293997546249949080693 ---- gammaK_277541(9697282541) = 12.318639116474948867602473410804 gammaKplus_277541(9697282541) = 9.395888713055965864884207854380 ---- gammaK_401810(9697282541) = 11.042272403063754238355518707710 gammaKplus_401810(9697282541) = 10.557918899146295823790815061262 ---- gammaK_441991(9697282541) = -2.369869389518161783630548879766 gammaKplus_441991(9697282541) = 3.107874696336454832861755501170 ---- gammaK_555082(9697282541) = 9.395888713055965864884207854380 gammaKplus_555082(9697282541) = 8.085552642444585802036147589679 ---- gammaK_883982(9697282541) = 3.107874696336454832861755501170 gammaKplus_883982(9697282541) = 3.146951365655023267845391226737 ---- gammaK_1387705(9697282541) = 10.231152948880702052936108039300 gammaKplus_1387705(9697282541) = 9.739715660863926787395463746836 ---- gammaK_1916459(9697282541) = -127.101536646114695413707012580569 gammaKplus_1916459(9697282541) = -59.486856480875706995613519056821 ---- gammaK_2209955(9697282541) = 5.876534799100714077999108790625 gammaKplus_2209955(9697282541) = 6.882808807114256881598618171591 ---- gammaK_2775410(9697282541) = 9.739715660863926787395463746836 gammaKplus_2775410(9697282541) = 8.652782132657884798366836649688 ---- gammaK_3832918(9697282541) = -59.486856480875706995613519056821 gammaKplus_3832918(9697282541) = -31.563381651555823093626243125865 ---- gammaK_4419910(9697282541) = 6.882808807114256881598618171591 gammaKplus_4419910(9697282541) = 5.181289312406542464659389216834 ---- gammaK_9582295(9697282541) = -18.903808017969140988715360360834 gammaKplus_9582295(9697282541) = -9.077190247438641920228448588674 ---- gammaK_19164590(9697282541) = -9.077190247438641920228448588674 gammaKplus_19164590(9697282541) = -3.088303105796064573998461211481 ---- gammaK_21081049(9697282541) = -4.395672502640347192883319378422 gammaKplus_21081049(9697282541) = -2.862461499627185194216271870262 ---- gammaK_42162098(9697282541) = -2.862461499627185194216271870262 gammaKplus_42162098(9697282541) = -10.336844796783543002629479242385 ---- gammaK_44078557(9697282541) = -5.749320611493340277637994824748 gammaKplus_44078557(9697282541) = -7.457756453147359271025844782547 ---- gammaK_88157114(9697282541) = -7.457756453147359271025844782547 gammaKplus_88157114(9697282541) = -4.550828166556109216234317149785 ---- gammaK_105405245(9697282541) = -2.368655808822417248807628758432 gammaKplus_105405245(9697282541) = -7.709083178713685604639713988275 ---- gammaK_210810490(9697282541) = -7.709083178713685604639713988275 gammaKplus_210810490(9697282541) = -14.295135750219400284979182239590 ---- gammaK_220392785(9697282541) = -0.233320495550782513041886964451 gammaKplus_220392785(9697282541) = -0.285061051005795878948975700323 ---- gammaK_440785570(9697282541) = -0.285061051005795878948975700323 gammaKplus_440785570(9697282541) = -0.617909599613796672435026502812 ---- gammaK_484864127(9697282541) = 0.360712098648681773843387042204 gammaKplus_484864127(9697282541) = 0.773889917437430492319603415361 ---- gammaK_969728254(9697282541) = 0.773889917437430492319603415361 gammaKplus_969728254(9697282541) = 1.615978611880220701051314549647 ---- gammaK_2424320635(9697282541) = 1.854067554105972998080461070677 gammaKplus_2424320635(9697282541) = -0.193007471873149606412417247532 ---- gammaK_4848641270(9697282541) = -0.193007471873149606412417247532 gammaKplus_4848641270(9697282541) = 0.577215664901532865549427242513 -------------- Other quantities -------------- [1] EK(9697282541) = 1.140627347418876431835041558495 [2] EKplus(9697282541) = 14.641924950163702166596210796087 [3] EK(9697282541)diff = -13.501297602744825734761169237592 -------------- [4] min_even(9697282541) = 0.000033602047242855219582039234 [5] min_odd(9697282541) = 0.000015944645983049351359080235 [6] min_{chi neq chi_0}|L'/L(1,chi)|(9697282541) = 0.000015944645983049351359080235 -------------- [7] max_even(9697282541) = 3.283657654431465632417319794659 [8] max_odd(9697282541) = 3.494035962476399309272417184681 [9] max_{chi neq chi_0}|L'/L(1,chi)|(9697282541) = 3.494035962476399309272417184681 -------------- [10] Kummer_ratio(9697282541) = 1.724741120348021746290599476211 [11] log(Kummer) = log r(9697282541) = 0.545076964060352247337073162384 [12] logh_1(9697282541) = 46836316823.933231401702669620455023435359 -------------- [13] Pi(9697282541,1.0Q) = 16.851700894823612771522831437422 [14] Laurent series of zeta_{Q(zeta_q)} at 1: c_{-1} = Pi(q,1)^(-1) = 0.059341190912495544159703626781 [15] c_{0} = c_{-1} * EK = 0.067686185183196927994472219505 -------------- [16] minL_even(9697282541) = 0.225453319397634441618450215170 [17] minL_odd(9697282541) = 0.224659636397176314214982007854 [18] minL_{chi neq chi_0}|L(1,chi)|(9697282541) = 0.224659636397176314214982007854 -------------- [19] maxL_even(9697282541) = 6.650602137112498448249998103798 [20] maxL_odd(9697282541) = 6.761561320170006711894818315965 [21] maxL_{chi neq chi_0}|L(1,chi)|(9697282541) = 6.761561320170006711894818315965 -------------- [22] minLprime_even(9697282541) = 0.000031103011789415608459970744 [23] minLprime_odd(9697282541) = 0.000011885330678361889083957006 [24] minLprime_{chi neq chi_0}|Lprime(1,chi)|(9697282541) = 0.000011885330678361889083957006 -------------- [25] maxLprime_even(9697282541) = 21.519454628559848653398294166442 [26] maxLprime_odd(9697282541) = 22.799882242407409937307396248669 [27] maxLprime_{chi neq chi_0}|Lprime(1,chi)|(9697282541) = 22.799882242407409937307396248669 -------------- [28] minbchi_even(9697282541) = 17.344578064795068977909253970371 [29] minbchi_odd(9697282541) = 17.210647336720315934999009183615 [30] minbchi_{chi neq chi_0}(9697282541) = 17.210647336720315934999009183615 -------------- [31] maxbchi_even(9697282541) = 23.466418220763671681559588358165 [32] maxbchi_odd(9697282541) = 23.450173284096353446143210250554 [33] maxbchi_{chi neq chi_0}(9697282541) = 23.466418220763671681559588358165 -------------- ******** the quadratic character is even [34] L(1,chi_quad)(9697282541) = 0.833244962451791015593380541720 [35] L(1,chi_quad)/log(9697282541) = 0.036235743465017725775914996709 [36] L(1,chi_quad)/loglog(9697282541) = 0.265763990329193982318437139599 [37] Lprime(1,chi_quad)(9697282541) = -0.641784548681320992108866220013 [38] Lderlog(1,chi_quad)(9697282541) = -0.770223136774682471961844490045 -------------- *** A priori (closed formulas) norms *** N1LGeven = +3.3608220143495367697863514572e+09 N00LGeven = +2.1850381646944519576948818491e+01 N00LGodd = +2.2995111532674872831575738204e+01 N1Seven = +1.9456205122248834980661822566e+10 N00Seven = +5.2877515440563193167871070692e+02 N1AKodd = +2.4243206347500000000257804183e+09 N00AKodd = +9.9999999979375665383121273335e-01 N2AKodd = +4.0202161090336093191695559490e+04 TOTAL TIME 11522.000000 min. 21.000000 sec. 285.712000 millisec. removing unneeded files for 9697282541 ... DONE