-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1111156966946315198645924226649,1371729153985493743445040295104,1673020948619203040021047386469,2425104447570882355997051077072,3031655215800642860828217434262,3354083609088630891981017447884', 'a10': 10, 'a2': 2, 'a3': 4, 'a4': 2, 'a5': 5, 'a6': 8, 'a7': 0, 'a8': 0, 'a9': 7, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17318.05984582416, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1]], [13, [1, -6, 15, -20, 15, -6, 1]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': '1.1.1.1', 'conductor': 66809249633371609, 'conductor_radical': 91, 'degree': 12, 'euler_factors': [[1, -2, 2, 0, -4, 4, -4, 8, -16, 0, 32, -64, 64], [1, -4, 9, -8, -12, 62, -137, 186, -108, -216, 729, -972, 729], [1, -5, 7, -4, 19, 1, -146, 5, 475, -500, 4375, -15625, 15625], [1], [1, -4, -17, 40, 382, -418, -3857, -4598, 46222, 53240, -248897, -644204, 1771561], [1, -6, 15, -20, 15, -6, 1], [1, -4, -33, 48, 1080, -470, -20731, -7990, 312120, 235824, -2756193, -5679428, 24137569], [1, -7, -5, 28, 469, 875, -18166, 16625, 169309, 192052, -651605, -17332693, 47045881], [1, 1, -27, -150, 51, 1733, 13694, 39859, 26979, -1825050, -7555707, 6436343, 148035889], [1, 14, 197, 1842, 15410, 101462, 611213, 2942398, 12959810, 44924538, 139334357, 287156086, 594823321], [1, 3, -43, -118, 681, 335, -14122, 10385, 654441, -3515338, -39711403, 85887453, 887503681], [1, -10, -19, 126, 3178, -3932, -126587, -145484, 4350682, 6382278, -35609059, -693439570, 2565726409], [1, 12, 50, 60, 479, 23448, 263036, 961368, 805199, 4135260, 141288050, 1390274412, 4750104241], [1, -18, 329, -3578, 38154, -296162, 2233817, -12734966, 70546746, -284476046, 1124785529, -2646151974, 6321363049], [1, -17, 59, -420, 12425, -71363, 127970, -3354061, 27446825, -43605660, 287901179, -3898865119, 10779215329], [1, 13, -29, -164, 10913, 34735, -380618, 1840955, 30654617, -24415828, -228823949, 5436541409, 22164361129], [1, -22, 163, -1366, 21446, -157474, 757639, -9290966, 74653526, -280547714, 1975129843, -15728334578, 42180533641], [1, 24, 233, 1928, 21078, 166136, 1069181, 10134296, 78431238, 437619368, 3226080953, 20270311224, 51520374361], [1, -14, 31, 146, -1022, 44074, -594409, 2952958, -4587758, 43911398, 624684751, -18901751498, 90458382169], [1, -8, 354, -2100, 55551, -262732, 5072672, -18653972, 280032591, -751613100, 8995735074, -14433834808, 128100283921], [1, -5, 25, -1662, 4155, -26645, 1335370, -1945085, 22141995, -646546254, 709956025, -10365357965, 151334226289], [1, 1, -167, -346, 14695, 22873, -1183810, 1806967, 91711495, -170591494, -6504663527, 3077056399, 243087455521], [1, 46, 1281, 25338, 388758, 4776254, 48068993, 396429082, 2678153862, 14487939006, 60794109201, 181195869578, 326940373369], [1, 11, -91, -1626, 4307, 91583, 367922, 8150887, 34115747, -1146279594, -5709543931, 61424653939, 496981290961], [1, -6, 449, -2470, 94530, -437494, 11714933, -42436918, 889432770, -2254302310, 39749647169, -51524041542, 832972004929], [1, -18, -13, 618, 19376, -84540, -1546027, -8538540, 197654576, 636726018, -1352785213, -189181809018, 1061520150601], [1, 4, -21, 1188, -362, -7292, 2145103, -751076, -3840458, 1298159676, -2363568501, 46370962972, 1194052296529], [1, 20, 3, -132, 34410, 132112, -2704381, 14135984, 393960090, -161705676, 393238803, 280510346140, 1500730351849], [1, -20, 49, 936, 5382, -103538, 233233, -11285642, 63943542, 1212147144, 6916749889, -307724790980, 1677100110841], [1, -22, 621, -8490, 151890, -1649918, 22335917, -186440734, 1939483410, -12250195530, 101252411181, -405335739446, 2081951752609]], 'euler_factors_factorization': [[[[1, -2, 2, 0, -4, 4, -4, 8, -16, 0, 32, -64, 64], 1]], [[[1, -4, 9, -8, -12, 62, -137, 186, -108, -216, 729, -972, 729], 1]], [[[1, -5, 7, -4, 19, 1, -146, 5, 475, -500, 4375, -15625, 15625], 1]], [1], [[[1, -4, -17, 40, 382, -418, -3857, -4598, 46222, 53240, -248897, -644204, 1771561], 1]], [[[1, -1], 6]], [[[1, -4, -33, 48, 1080, -470, -20731, -7990, 312120, 235824, -2756193, -5679428, 24137569], 1]], [[[1, -7, -5, 28, 469, 875, -18166, 16625, 169309, 192052, -651605, -17332693, 47045881], 1]], [[[1, 1, -27, -150, 51, 1733, 13694, 39859, 26979, -1825050, -7555707, 6436343, 148035889], 1]], [[[1, 7, 74, 403, 2146, 5887, 24389], 2]], [[[1, 3, -43, -118, 681, 335, -14122, 10385, 654441, -3515338, -39711403, 85887453, 887503681], 1]], [[[1, -10, -19, 126, 3178, -3932, -126587, -145484, 4350682, 6382278, -35609059, -693439570, 2565726409], 1]], [[[1, 6, 7, -12, 287, 10086, 68921], 2]], [[[1, -9, 124, -673, 5332, -16641, 79507], 2]], [[[1, -17, 59, -420, 12425, -71363, 127970, -3354061, 27446825, -43605660, 287901179, -3898865119, 10779215329], 1]], [[[1, 13, -29, -164, 10913, 34735, -380618, 1840955, 30654617, -24415828, -228823949, 5436541409, 22164361129], 1]], [[[1, -22, 163, -1366, 21446, -157474, 757639, -9290966, 74653526, -280547714, 1975129843, -15728334578, 42180533641], 1]], [[[1, 24, 233, 1928, 21078, 166136, 1069181, 10134296, 78431238, 437619368, 3226080953, 20270311224, 51520374361], 1]], [[[1, -14, 31, 146, -1022, 44074, -594409, 2952958, -4587758, 43911398, 624684751, -18901751498, 90458382169], 1]], [[[1, -4, 169, -374, 11999, -20164, 357911], 2]], [[[1, -5, 25, -1662, 4155, -26645, 1335370, -1945085, 22141995, -646546254, 709956025, -10365357965, 151334226289], 1]], [[[1, 1, -167, -346, 14695, 22873, -1183810, 1806967, 91711495, -170591494, -6504663527, 3077056399, 243087455521], 1]], [[[1, 23, 376, 4021, 31208, 158447, 571787], 2]], [[[1, 11, -91, -1626, 4307, 91583, 367922, 8150887, 34115747, -1146279594, -5709543931, 61424653939, 496981290961], 1]], [[[1, -3, 220, -575, 21340, -28227, 912673], 2]], [[[1, -18, -13, 618, 19376, -84540, -1546027, -8538540, 197654576, 636726018, -1352785213, -189181809018, 1061520150601], 1]], [[[1, 4, -21, 1188, -362, -7292, 2145103, -751076, -3840458, 1298159676, -2363568501, 46370962972, 1194052296529], 1]], [[[1, 20, 3, -132, 34410, 132112, -2704381, 14135984, 393960090, -161705676, 393238803, 280510346140, 1500730351849], 1]], [[[1, -20, 49, 936, 5382, -103538, 233233, -11285642, 63943542, 1212147144, 6916749889, -307724790980, 1677100110841], 1]], [[[1, -11, 250, -1495, 28250, -140459, 1442897], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 5, 'label': '12-637e6-1.1-c1e6-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/637/2/e/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0208333333333', 'prec': 50}, 'plot_values': [61.350849305895466, 61.454071076246336, 61.38683575991178, 61.17153758618824, 60.830629740913466, 60.38645211605239, 59.86111950013864, 59.27115017342273, 58.61165792901475, 57.87258989413182, 57.044128846510205, 56.1167602111838, 55.08135853708505, 53.93050153504226, 52.662262010105074, 51.27676872040609, 49.77508222193414, 48.15926098899854, 46.43242368675982, 44.59855359138578, 42.661920518120475, 40.62810443596648, 38.50430243964555, 36.2993328322599, 34.023619332804294, 31.689428661155894, 29.31163975935543, 26.90679773853178, 24.49263662715331, 22.08783888212126, 19.711763196288384, 17.384315903150064, 15.126089884920495, 12.957375355177668, 10.897548741263686, 8.964642800972898, 7.174925491872901, 5.542597279212093, 4.079621740267822, 2.7949267210366946, 1.6940040174264404, 0.7787115927574975, 0.047166120489462886, -0.5062670626145094, -0.8909302760165475, -1.11973328433618, -1.2088073294890007, -1.177036748492658, -1.0454919776063427, -0.8368054193071147, -0.574512727508908, -0.2821564418213068, 0.017551047199774378, 0.30351540906796864, 0.5570006855533066, 0.7622986344706165, 0.9073360075679183, 0.9841170367698643, 0.9889511955725693, 0.9225016771214031, 0.7896511917276601, 0.5992025184198418, 0.3634046084552327, 0.09716402232592695, -0.18280953737960381, -0.45891900003180636, -0.7136410413185257, -0.9305235962676554, -1.0952716266750182, -1.1965705806389826, -1.2267134488210056, -1.1820542807940986, -1.0632478773020033, -0.8753362409178059, -0.6277393815445629, -0.3335057552463262, -0.00847940744869906, 0.3296183566251279, 0.6622184364135725, 0.9709540238736437, 1.2387173297494796, 1.4509314185950497, 1.5964817281439985, 1.6683803034170013, 1.6641805987293314, 1.5861440147614174, 1.4411958229259076, 1.240414152576782, 0.9982284426860092, 0.7314257622454257, 0.4580133619408852, 0.19602608408129157, -0.03768474039399637, -0.22872979802434037, -0.36616971348726157, -0.44321566921238137, -0.4576273603864664, -0.4118068568715261, -0.31262590654389083, -0.17077524001161207, 0.00018047467132959008, 0.18493412504606258, 0.3676818553592354, 0.5333757331220216, 0.6689093946752054, 0.7642398011141163, 0.8131678065213285, 0.8137612538068859, 0.7684092461872346, 0.6835117471657554, 0.5688363364661643, 0.43651832899438914, 0.29984885858000404, 0.1719686743078785, 0.06457692460965256, -0.013234156285917238, -0.05592310278461991, -0.062085260486283086, -0.034629098658339956, 0.019465786338813074, 0.08979729094901383, 0.1635527105987982, 0.2268234167894559, 0.2660571362310472, 0.26950216361350193, 0.22853100855133207, 0.13871939378172796, 0.0005682559240136299, -0.1802870530761003, -0.3934142309967005, -0.624336596516761, -0.8556793010366608, -1.0686279104377363, -1.2446714055884696, -1.3676662951784162, -1.4252687849109824, -1.4100755816327355, -1.3204152962159628, -1.1606516360490535, -0.9410724973367484, -0.6773984076540164, -0.3890329111908623, -0.09725139369252343, 0.176644225525713, 0.41316343282376056, 0.5962918133999379, 0.7149339048350384, 0.7639528814453992, 0.7444297157261022, 0.6633037337938013, 0.5324784895287411, 0.3675261098850599, 0.18611620381895286, 0.0060226705899385, -0.1566871211892457, -0.28914129282413525, -0.38273252118300394, -0.4336866072609637, -0.4431313585968312, -0.4165289723825732, -0.3625924251178325, -0.2919027880247232, -0.21540778144163383, -0.14300286096606707, -0.08235202754096206, -0.03801155753706294, -0.01113996567776848, 0.00023621078866313503, 0.00048072914527070426, -0.0047441490386961, -0.009744378594350603, -0.010049253473346405, -0.0034173159245667333, 0.009609662475023099, 0.025731199351839297, 0.03953745081442305, 0.0447386990755908, 0.03583244207284582, 0.009978652933974926, -0.03121638073476074, -0.08033203130800284, -0.1234857520592251, -0.1405985067457513, -0.1067076996491076, 0.005627661729048046, 0.22295698076132228, 0.5668657690214955, 1.0498085908338852, 1.6720955371250394, 2.419002908577915, 3.2589916719951466, 4.143597099782651, 5.009142130376882, 5.781310073832744, 6.384244256433764, 6.745849796711035, 6.804015978464174, 6.513366488610038, 5.851183450518682, 4.8232351983669535, 3.469907266275667, 1.8604563059100079, 0.08706442907306866, -1.741983714744611, -3.510847779643559, -5.105088788754654, -6.420857118170832, -7.377894543532024, -7.927265198835464, -8.055105318948831, -7.782943458462602, -7.164690693320848, -6.280982944620764, -5.229837091006513, -4.115132793841245, -3.034954147387635, -2.071126363746183, -1.2812258865276855, -0.6939199361345925, -0.30793302098865555, -0.09572506804352164, -0.011159866589035018, -0.00011321717379014106, -0.012675584598096451, -0.01534816931194489, -0.0014598411032373186, 0.00182414667299317, -0.06887337562954925, -0.31012497633270614, -0.8431753116755247, -1.8008414621237432, -3.31108571473179, -5.478766889079815, -8.367538854424179, -11.983966068303573, -16.26725285715649, -21.090411389675513, -26.26289711473855, -31.539424498739834, -36.63552510776885, -41.24798226690487, -45.083029201594925, -47.896882060958845, -49.50763916109599, -49.80643558953168, -48.76644728976931, -46.44527975545048, -42.98563643943297, -38.61692448624964, -33.616745103524266, -28.28165001356602, -22.903521775096483, -17.748104417408125, -13.039565524290701, -8.95095639236954, -5.585808999756314, -2.977263939117008, -1.0965873211556558, 0.13373150645347018, 0.8240318892275805, 1.1012404718677307, 1.0946050469403483, 0.921849654988587, 0.679197870238534, 0.43619403534947015, 0.23508671480972218, 0.09394826096360884, 0.012214414708076765, -0.02240551356726066, -0.027052572445792383, -0.018065417780541656, -0.007305328714753274, -0.0007345783662999556, 0.0009466726787313881, 0.00022886551097257027, 0.00011355176299784604, 0.0017031049809586197, 0.002803390068257495, -0.002007425401638823, -0.01982627930260633, -0.05678569966851691, -0.11502949705452348, -0.19019858222228947, -0.27034595483826046, -0.3370077480341088, -0.36858564365519686, -0.34577812211808906, -0.2583605466521911, -0.11215385303309626, 0.06542598416195865, 0.22335366884566699, 0.28874407729511437, 0.17301215578342824, -0.21742294989165137, -0.9666619164530967, -2.1324222425943216, -3.7298967389760858, -5.720880623868995, -8.007835742015862, -10.434754327682318, -12.795904501532723, -14.853960674352237, -16.370800117399845, -17.135615436678986, -16.992055248109452, -15.86219825997213, -13.763161615888487, -10.81524940637215, -7.240806513864698, -3.3395991950923722, 0.543645322764799, 4.057117150766315, 6.8823845151333165, 8.7732039421714, 9.588485894534518, 9.308455008779738, 8.036649787283558, 5.987277710844852, 3.45854560852096, 0.7949131049728732, -1.6590560161974508, -3.604701705634976, -4.8252959644579585, -5.210670922387137, -4.76771351075392, -3.615595596964827, -1.9646981790403517, -0.07913357627066321, 1.763964303072253, 3.3142766380547894, 4.38270854824316, 4.866730063861515, 4.763723298671885, 4.161328769485561, 3.215107071943155, 2.1178090563397824, 1.0642455843249443, 0.21704482899588387, -0.32243313555901254, -0.5309405467427615, -0.4632919479455101, -0.2379876565489649, -0.011322756377169653, 0.055880790038594114, -0.16579604072953297, -0.7430909307573375, -1.660662888671829, -2.8161613877287115, -4.030755180446026, -5.074630787341332, -5.7063150005306, -5.7142035368120725, -4.954749941704175, -3.382038779858358, -1.0635620232336709, 1.8199363715588555, 4.992607367335809, 8.12449114547371, 10.878040134827586, 12.955308984330722, 14.140061148101799, 14.329789538942956, 13.55436643924144, 11.966214933024723, 9.81238863324316, 7.394196349880803, 5.0196763774330995, 2.9564831491403116, 1.3913635793389467, 0.4020921501943158, -0.047709379311506504, -0.09338365410141021, 0.06277403795277409, 0.1951503619109815, 0.10371053238263, -0.34180568793749283, -1.1713736130577268, -2.302518719452, -3.548712319931357, -4.647702048403526, -5.3074485336441155, -5.2598675420878545, -4.31209769293202, -2.387808156818304, 0.44836704949174216, 3.987289181481564, 7.895221688653065, 11.75920963942996, 15.143518082458108, 17.65011469183812, 18.975185864746734, 18.954192046779696, 17.588415862138998, 15.04080647402455, 11.61012654540982, 7.6879211632271165, 3.7040710121410725, 0.06790495261298467, -2.889678173396242, -4.9551383762730765, -6.0494560042604215, -6.225138910337793, -5.644696716340322, -4.545674439113977, -3.197554812628853, -1.8532363764276, -0.7117894026584651, 0.10442414802299545, 0.5569479095751267, 0.6833556003572671, 0.57693959163501, 0.35670669331665417, 0.13694033852801507, 0.002062803130404564, -0.009154084980497919, 0.09225722202112935, 0.25296119289218305, 0.3945589685462561, 0.43579531133814026, 0.3145352258587726, 0.004934535519186053, -0.4740601304019041, -1.0620046877222367, -1.668730005456992, -2.192355852649035, -2.540111360880634, -2.6475893190809807, -2.4933783249584756, -2.1063605402945487, -1.5569918993681031, -0.9419815490550995, -0.364843446572378, 0.08475476652402368, 0.34873587867938877, 0.41206143524808225, 0.3054271153734994, 0.09719441639731084, -0.12236437010764094, -0.2610334317498406, -0.24515048986966415, -0.03687898348515702, 0.3577801817300917, 0.8902100874763691, 1.4789886945439454, 2.0263741225830163, 2.438380107008402, 2.6450830272410064, 2.6144076555517044, 2.3575056822491725, 1.9254457896066155, 1.3979707198551647, 0.8668426337401108, 0.4169246032388547, 0.10860422523655057, -0.032619493706960025, -0.018415348631606925, 0.10812486337161745, 0.28488155717502517, 0.44729816279894385, 0.5441394994014445, 0.5486628600626557, 0.4630663496953748, 0.31539192944402045, 0.1498231124073413, 0.0126168280156875, -0.062445431671242474, -0.06410264220782, -0.006808868031565538, 0.07394356155489444, 0.13343930817481986, 0.1341847827842736, 0.061691264126277526, -0.06550705286030165, -0.1948771338218721, -0.24963643544840905, -0.1486566884833993, 0.1665663316443247, 0.7062857411074271, 1.415436244156255, 2.17095409675848, 2.797616749939004, 3.103700946224439, 2.9345006472935236, 2.2301149486354728, 1.0763157785852886, -0.26280252884872196, -1.3412473235613316, -1.5648446064977195, -0.26891466291898103, 3.1757623292384265, 9.242890948143655, 18.132597374634805, 29.676130476323745, 43.285318921366446, 57.974047578876615, 72.44039930431319, 85.20058660422028, 94.76597025597123, 99.84155169359579, 99.53210791455248, 93.53275822037668, 82.16095026864001, 66.33114624247703, 47.46507026880005, 27.333275704520307, 7.844275465133996, -9.21693128247733, -22.437597622988807, -30.934100349768816, -34.43021928141194, -33.254307972955225, -28.267463427197587, -20.733272479612403, -12.071781131051091, -3.6341954691041383, 3.4778900487396007, 8.536437669398614, 11.241843114733836, 11.712693203736762, 10.406784407751175, 7.983563030106808, 5.15131865862813, 2.529405656464045, 0.5481238318548689, -0.6005752429629561, -0.9563901245100689, -0.7341786038411924, -0.23689083221802612, 0.23923748868130257, 0.4849704777553576, 0.4262430240821097, 0.12839472067326022, -0.24102416520217587, -0.47844756214180234, -0.4219611863618728, -0.019945805969595835, 0.6302445524593615, 1.2859759643211834, 1.6047371091876055, 1.2230103595634572, -0.14738574559109166, -2.6249335017270856, -6.0881484587263355, -10.16482152110741, -14.27373370880195, -17.714756306758304, -19.79537298376825, -19.971292862483153, -17.971409788796556, -13.879910966161402, -8.15434922773438, -1.5752951009132958, 4.867157288111545, 10.14000482719677, 13.369149653901442, 13.988630484793463, 11.84364714004421, 7.230723424304771, 0.8621913343307692, -6.2409106384337845, -12.923631203823524, -18.110617069143267, -20.98716550723953, -21.130804381927554, -18.575444695884368, -13.798690563468572, -7.629421462213525, -1.0829399992590198, 4.8259637467427865, 9.260264789818153, 11.699352491928796, 12.019629547693496, 10.504781422831583, 7.755910045507316, 4.55578508333562, 1.7097177336317995, -0.11120194527255688, -0.4957808228438019, 0.6376338620291797, 3.0431609805286577, 6.212293814174832, 9.484916417828433, 12.185266385489255, 13.761092478294021, 13.90186473740772, 12.581361952841903, 10.048247035404781, 6.77047292991302, 3.3420992181772284, 0.3686789660147462, -1.6541377622412088, -2.430523867265983, -1.903180651033111, -0.24732776787033778, 2.174832864315209, 4.889422255904944, 7.407447464059937, 9.318420992564025, 10.354185154752793, 10.419561906111127, 9.589237856232293, 8.077221307002116, 6.1866574106506595, 4.235771241648696, 2.496652327500592, 1.15426629253132, 0.2883370058949772, -0.12191795824289593, -0.17470617634021549, -0.010017188695113026, 0.2290227649461411, 0.4277773835618011, 0.5190416513045236, 0.48734586989704654, 0.35993057141418733, 0.18822551264561876, 0.027072088949564112, -0.08276898194085397, -0.12485178212218938, -0.10823026327176584, -0.060138229807697244, -0.013198223727118383, 0.007677039159519541, -0.005031197371714472, -0.03785064892274955, -0.059954089321026235, -0.033282705554620054, 0.07465718892425695, 0.27915123096692357, 0.5706954532816213, 0.9135583423645796, 1.2516742998326607, 1.5226199379809724, 1.6723918582762514, 1.6680486938871633, 1.5060402604793532, 1.2142073868232999, 0.8475133331652346, 0.47791107343359496, 0.1763560552431207, -0.0028167868204380213, -0.03269518570519799, 0.08169860205646576, 0.305814172596256, 0.584056791789439, 0.8529446566944384, 1.055330185456564, 1.1521724532350124, 1.129446305911076, 0.9991476071900506, 0.7944462310816461, 0.5593158109654339, 0.3374162867803621, 0.16241940419748158, 0.051623259265592386, 0.004069727985333342, 0.003278487249328864, 0.02370492162071162, 0.038753963596458066, 0.028046394627190288, -0.017679591043288444, -0.09505789241987747, -0.19047978648419223, -0.2848429988816262, -0.35908482159726574, -0.39909300405663045, -0.39883578683684023, -0.36129583676252147, -0.29723665716369707, -0.22112780453988298, -0.14702255544053783, -0.08539385935339532, -0.04147230955564544, -0.015282680121686201, -0.003054552712318049, 0.0006178894692305165, 0.0006346410049529875, 6.610068233683358e-05, -5.001065696111788e-05, 3.9095779260072734e-05, -3.417752482626916e-05, 0.00013846776914955435, 0.0018265682095194864, 0.0062611382940110875, 0.013033762456648286, 0.018514927840858585, 0.015289809673010973, -0.006883646704871941, -0.05842073094106025, -0.1459043925937479, -0.26767996109315284, -0.41055409651724645, -0.5499209020860425, -0.6534348337084964, -0.687492936908144, -0.6256882136755233, -0.45744905069712605, -0.19522678633664303, 0.12181060657027988, 0.43442299768292153, 0.6751630505203133, 0.7833507522142397, 0.7205046212644106, 0.4827667822442982, 0.1079813977382898, -0.32700113533658415, -0.7200007382133599, -0.9648485603972003, -0.9760628923576078, -0.7105077955029881, -0.1780699435993341, 0.5552400606272191, 1.3767507324550217, 2.148230904148003, 2.7340317413849133, 3.032132356429769, 3.0021422376522566, 2.6682808936666187, 2.1110186136538394, 1.4480608104634762, 0.8070038086830267, 0.2958916325520638, -0.022224520166240568, -0.14336652406985126, -0.11823922856093463, -0.03335007272821461, 0.017088061274235473, -0.03863275775128435, -0.22605864220340252, -0.5155944652915868, -0.8300317123930439, -1.0668218625432095, -1.1297846774484301, -0.9629008967680875, -0.5764186346842174, -0.04849746108689231, 0.4917611717530161, 0.896493189089395, 1.039949147028175, 0.8587363246632533, 0.38144292712596134, -0.2717181706110112, -0.9171164114108127, -1.3559000620225818, -1.4314152404921916, -1.0815130377581441, -0.37031866205847885, 0.5181687392484792, 1.3261947360084032, 1.7984889068477063, 1.7722377603315875, 1.2597444013539554, 0.5000487803679234, -0.051602145758064405, 0.2033852478286421, 1.8809454747611754, 5.456005732587773, 11.10393259344125, 18.58244852995899, 27.19130342326797, 35.825106921319914, 43.12033780329467, 47.67917737843229, 48.34296754250975, 44.468162609145736, 36.07052044366728, 23.872789572866125, 9.237907805233712, -6.0171498845760265, -19.910910976977487, -30.675303913216638, -37.06525675579423, -38.54947059541086, -35.378247492581814, -28.515662752369423, -19.456028065248134, -9.942750697949934, -1.5807293194785388, 4.459234077982577, 7.618215517038861, 7.996005110736417, 6.267511768133313, 3.488851628767172, 0.8143692338910695, -0.7828588226832612, -0.7227638788144531, 1.075573392471537, 4.208757768944682, 7.920113339146493, 11.314316751784405, 13.588234878231317, 14.224008922507865, 13.102522169958766, 10.516661148367435, 7.0837194720203085, 3.568114084049663, 0.6859677462560386, -1.0636862302153447, -1.5042373878317026, -0.8003770571051921, 0.6165592943636543, 2.1940980833849144, 3.4180790231533766, 3.947907119837013, 3.6950631643026917, 2.8272048232601485, 1.6947307955340962, 0.6894387954659715, 0.10184468698558888, 0.014697489655720753, 0.26043434048030156, 0.45758246778942047, 0.12547554717555692, -1.1558593622252455, -3.5921781286781727, -7.070195228356599, -11.132545888399218, -15.046310654816782, -17.964211564381408, -19.136277063316687, -18.1074531324937, -14.85588295767101, -9.836082407622504, -3.911269214253326, 1.8264430475175424, 6.309994411152898, 8.741958334690986, 8.778919598901705, 6.613433973736772, 2.9350752025762175, -1.227374053858573, -4.771687004113343, -6.792221735925139, -6.795652217582693, -4.814978590894533, -1.3934178405108155, 2.565477257542602, 6.048606889496352, 8.20539480859846, 8.576396245348677, 7.22261438918743, 4.7214546657727245, 2.0213944685223066, 0.18051411580761167, 0.07838357441934951, 2.1668935977198807, 6.319037017396617, 11.821278846451731, 17.53939861988076, 22.191021427284976, 24.656389076809877, 24.260968228898076, 20.962656082523218, 15.403035369586464, 8.798506216009631, 2.6394366395511786, -1.6587618913796527, -3.0841021857532835, -1.2711658649646163, 3.3988084263512546, 9.881339709184418, 16.704908626167047, 22.298606877737534, 25.337990453489404, 25.03316338432452, 21.305463455023336, 14.811275456632027, 6.741760958503718, -1.4625087916628983, -8.426184234286923, -13.123384907661475, -15.074133255452976, -14.414567870586547, -11.796582578101175, -8.177875647774286, -4.56481259864038, -1.7666020624761483, -0.21582903868812545, 0.10255905211065766, -0.4053303863039937, -1.0938482992466012, -1.2767916951398948, -0.42425229569154443, 1.6882239115230864, 4.919430282383629, 8.814929318008756, 12.72927651986175, 15.983859698611806, 18.022788522481743, 18.53817956246813, 17.54488695146999, 15.332076103357958, 12.363555476195629, 9.158291980334697, 6.176445276380641, 3.7380563762659773, 1.986547389020247, 0.8947982874324072, 0.32115990467295835, 0.08141686391541283, 0.01084749410585856, 0.0001734178298359526, 1.7628419040896303e-05, 0.0001294381403611901, -0.0011365863332912657, -0.01891726062858632, -0.08192361519663308, -0.2066030259347328, -0.3551424718697988, -0.39641888067451597, -0.09042797620172578, 0.886984063933339, 2.872237084504301, 6.1007614107296515, 10.57939811210724, 15.99915275168152, 21.706672200428272, 26.754459951941396, 30.03506547529468, 30.49395776431701, 27.413417131806263, 20.620611491825652, 10.601566173460764, -1.5048757832129729, -14.051811973328011, -25.145535666430042, -32.972136138090384, -36.17062666857641, -34.12356524343766, -27.11107016579012, -16.297076039307694, -3.5297385827406313, 9.044290636124009, 19.37162798766135, 25.851796698921124, 27.615989844258657, 24.667414553984223, 17.862986599813762, 8.720846875727709, -0.9535624651792036, -9.430427337142193, -15.364479166946039, -18.008867157176805, -17.30588105585612, -13.840477929578762, -8.629245336313547, -2.8603803665673255, 2.358931609656186, 6.205012062310292, 8.260375954216247, 8.54372311677286, 7.418781859925112, 5.447713834033391, 3.2326116994916676, 1.2780282505761484, -0.10026396692728172, -0.8085801464298401, -0.9417931678007695, -0.7101926076294365, -0.3553086031005044, -0.07671013367525108, 0.01417066676445637, -0.09458715076621736, -0.3373531713457333, -0.6110624623303882, -0.8171973396613645, -0.8934955285326827, -0.8287729917904314, -0.659227610185294, -0.4454395866825341, -0.24698253632727293, -0.10330253237699567, -0.025431811989466934, 0.00050698564008128, 0.0010590656643866855, -5.990933424928877e-05, 0.006398106551364456, 0.012574884692066541, 0.0004768975013138334, -0.04464371929694458, -0.12033454505090053, -0.19855513800440114, -0.22719308156844023, -0.14243727958421146, 0.11082179307073793, 0.5570132288878582, 1.1765211163952818, 1.9031998275218613, 2.6337307511729424, 3.2480039277872264, 3.6358141210928525, 3.7256593912182367, 3.5098613369822806, 3.0387437119837686, 2.4043420182677253, 1.717727076768049, 1.0836715519624303, 0.5793078822353013, 0.24064676401546517, 0.05898762077037412, -0.006388474635040389, -0.00871036237751185, 0.005065988005041423, 0.006847405163165694, -0.009172146839339423, -0.03229684919428043, -0.046872958314622404, -0.04376078683619666, -0.02629010799701492, -0.007609749208326796, 0.00012454147568684117, 0.0006394305661293113, 0.026045786576043947, 0.14047846179793866, 0.4303510104958044, 0.9812198069455524, 1.8498111858427633, 3.0370539343817287, 4.469230625686965, 5.994684475858222, 7.399813526372511, 8.450197943562616, 8.962192144192274, 8.836261755529105, 8.075428759378218, 6.787371834769216, 5.165095201244009, 3.453920624764759, 1.9084254698809835, 0.7196399303700701, -0.02191766482753546, -0.3312907371764219, -0.30925586470030675, -0.10493247242230468, 0.1282315863212717, 0.27358757336959766, 0.27717354663267474, 0.1509710986520096, -0.04459058002458092, -0.23098906453634913, -0.34396245818204546, -0.3560762689506091, -0.28196265179637353, -0.16645681979579746, -0.061553993158567494, -0.0022175654337453165, 0.008311474656426565, -0.004117631801032437, -0.006605641822715267, 0.006732037198376327, -0.018827720211851477, -0.216959985931037, -0.7918865975763257, -1.9803836787445699, -3.9892517391420723, -6.921347963972384, -10.708518203307236, -15.076484093508489, -19.577598881089543, -23.65471768501642, -26.73418982477192, -28.33429338964675, -28.16372258372951, -26.197167801604447, -22.71689903832001, -18.23338770355755, -13.373159521110487, -8.756057736205669, -4.881244683417272, -2.0466007281627747, -0.3160552619148411, 0.45741527668692605, 0.5597801012446157, 0.3216128970598454, 0.0280465953998086, -0.14398486127113075, -0.14684375294219523, -0.039257714061746336, 0.06594311012237178, 0.06252273687864357, -0.09957980919000324, -0.3916701521184947, -0.7205942235596008, -0.9683281104619094, -1.038020833475072, -0.8913294722974515, -0.564371286384037, -0.15727137372295594, 0.20210991334205636, 0.412165706454955, 0.4353191192519428, 0.3090475143657116, 0.12766753724877009, 0.0010120885639320052, 0.0037012366035154435, 0.1363978839153602, 0.322133183684433, 0.442601944187312, 0.4039207626613022, 0.20836708319288952, 0.0005078735573834531, 0.05274504262180316, 0.6734913858720667, 2.0468129568082296, 4.0383504750295085, 6.023571400203986, 6.7996196667077395, 4.63491394699212, -2.513524484936389, -16.621783715778893, -39.1083899852182, -70.34802265671938, -109.41919207218652, -153.98393258740148, -200.38378937375307, -244.00052289949338, -279.8415247968555, -303.3885670573628, -311.73486824129634, -303.83922825979334, -280.5894078594223, -244.66906724385348, -200.15711167432573, -151.98372035698716, -105.28322678499651, -64.31849483209908, -31.902303348760807, -9.204248317899076, 4.148965662439021, 9.735817261763382, 9.861994571140746, 7.006806700177437, 3.3176338198912654, 0.2819159228556905, -1.3870734308236266, -1.6687131036459375, -1.0140679518127098, -0.06310433088636606, 0.6141787672704322, 0.6909846393230609, 0.14324500897562203, -0.7998244379936224, -1.7832248656707916, -2.470360233292724, -2.6551461535942456, -2.316340421346603, -1.6053621188349896, -0.7785305003141905, -0.09846785268792412, 0.2537333691053111, 0.22457590433178046, -0.1114329223546798, -0.5910892529198691, -1.0265867891388545, -1.2752809862713672, -1.2802928047854802, -1.07329056814964, -0.7476636887270961, -0.4152280622155778, -0.16356652705381006, -0.028186982080486166, 0.010860836893890773, 0.004675152532952471, -0.00013407650927956002, 0.009530109780564665, 0.005339951423455193, -0.06245372657477277, -0.22112247003035732, -0.42330651905834144, -0.5083260255407382, -0.19742456160213512, 0.8656026539885844, 3.0360580857184023, 6.568151734018861, 11.514626113133126, 17.654412847409088, 24.472475439051905, 31.220743412528535, 37.08929153372003, 41.33305564389875, 43.39317586810344, 42.99772550258517, 40.21189225141452, 35.44277640694463, 29.39571713806215, 22.867968085380763, 16.591656618378856, 11.127413193128982, 6.805047727121299, 3.7173876458688575, 1.757013773765554, 0.6791271521850029, 0.19109529945352263, 0.02840871421223557, -7.353377849673928e-05, -0.00030797838353836696, -0.008265807727497654, -0.019899901400906604, -0.021570104980093634, -0.009743443473403349, 0.004614110423626745, 0.0047386808216743894, -0.017484143560313678, -0.05054859666594594, -0.062023670611890507, -0.008530602934975626, 0.14610081358692356, 0.4115284171131638, 0.7603797494774693, 1.130850945264575, 1.4411394216271218, 1.6120891494968312, 1.5912722552491303, 1.3716779876713254, 0.9979575286967592, 0.5504846854461581, 0.12146573006685621, -0.2101506359818731, -0.39849819762636113, -0.4402064174961424, -0.3710814381595055, -0.2476836714972714, -0.12532721731268848, -0.04066577125011875, -0.003857560326266389, -0.001987586799627903, -0.011389694468687527, -0.013178472489685258, -0.004569586897147353, -0.0008076184051975337, -0.02680752847996763, -0.10199469059068432, -0.22567377035519617, -0.3706412152228549, -0.4888094243312651, -0.5282654570041685, -0.4566580993566491, -0.2828241784311549, -0.06599902520819889, 0.09821081167398651, 0.10765420876957804, -0.10869391991253759, -0.5566022731545445, -1.1577661818997331, -1.7554358472506038, -2.153265322682166, -2.1725224884158263, -1.7109749284903186, -0.7858955791012118, 0.4562245556885028, 1.7766183516486027, 2.903067685552717, 3.600484413065975, 3.7350835736432355, 3.312093732709309, 2.4771391240574223, 1.4749682157347237, 0.5588278076770455, -0.08539618369301431, -0.38515461055109856, -0.3879658410406662, -0.22777388620651626, -0.061204500639474683, 0.005712998119407106, -0.03749726009060948, -0.10942828940029858, -0.09068084772228649, 0.08799574884474956, 0.3554836978247243, 0.4507398271435068, -0.05556055398183852, -1.6602450858340894, -4.765371196497021, -9.494827215936132, -15.550461638469539, -22.18178938207809, -28.282562005621344, -32.607804956326355, -34.071685466188455, -32.06428593451698, -26.70101211750975, -18.842583962200248, -9.937281492662542, -1.7108806942004426, 4.2381042245496925, 6.848477260344006, 5.9115202001805205, 2.1245708414508555, -3.1070005660434923, -8.050568070075716, -11.118383199144226, -11.319291840882952, -8.58237323154472, -3.779181935109704, 1.5320973239876075, 5.551380541826434, 6.753297569507077, 4.3409790768280905, -1.4802602116094075, -9.542258009441396, -18.034927242637917, -25.001795697916204, -28.873166912143624, -28.886152038948886, -25.265458290068846, -19.116077975183693, -12.06566989595033, -5.77583330153816, -1.4671012267218728, 0.4072730062200274, 0.2226852093648717, -1.069733392672058, -2.3397691273601495, -2.6967423233300862, -1.801735166112199, 0.023050168492556703, 1.9372723914626881, 2.9944566212861146, 2.591163766659752, 0.7803752026671464, -1.6783287655027452, -3.585837950927083, -3.836889228153363, -2.1070249943220802, 0.5531361039780911, 1.459172294891933, -3.4601016338014743, -18.867300658246236, -48.88878133758256, -95.90391845232091, -159.46829762018766, -235.67291851560313, -317.1605560522942, -394.0907778012067, -456.4086575981893, -495.42770237818803, -505.2443048528962, -483.8315943351825, -433.47567985060226, -360.6188703137364, -275.09028213423085, -187.62325400047996, -107.88095435338687, -43.05215904741059, 2.965291622652385, 29.736481891951083, 39.89212301655083, 37.99524082181772, 29.222334483938845, 18.234056399502016, 8.416474479142689, 1.5834178780778725, -1.908582533063078, -2.7554244722984365, -2.106555690339523, -1.0385969313988321, -0.23543968110361937, 0.09060375821214585, 0.07878327574741145, -0.0020513875426980146, 0.03713403779326731, 0.1934410718715934, 0.2882313285120392, 0.08821174673605095, -0.5337443850085263, -1.4873476088978974, -2.45452672569447, -2.987658479595475, -2.682481195486802, -1.3626841877872928, 0.7976079647126137, 3.2918747164130826, 5.426438888946367, 6.546293757379591, 6.267675257080935, 4.631244298443053, 2.1078875990193318, -0.5383128452668507, -2.5045885651801547, -3.2375932661798523, -2.6539157937437414, -1.2015506872849107, 0.2933459595718354, 0.9146580093015119, -0.004344211847004285, -2.5765518056176595, -6.190504183894332, -9.56506447397305, -11.1285714059516, -9.486826036703807, -3.844449526559097, 5.69647577414763, 18.04902646462543, 31.27353928483382, 42.91600789334407, 50.69691992545451, 53.10107846128472, 49.74887617152905, 41.48579914456703, 30.153372991932468, 18.091173418055394, 7.6173872495074155, 0.5023508270119765, -2.418577251064749, -1.3863167179602844, 2.421069505671751, 7.318591998442258, 11.637089956757718, 14.120142319756871, 14.172649818772774, 11.923579018794529, 8.117541820774067, 3.8664673619242307, 0.2236648448599195, -2.110387125390831, -2.9191843334650915, -2.4477012730503764, -1.2518534312414673, 0.02669425367995217, 0.8782804551125457, 1.0712908959297178, 0.6859470231017634, 0.04092363241878431, -0.4515283970331375, -0.45280685230230105, 0.1764738912025731, 1.3357143696179692, 2.7284357379972812, 3.9684295372493588, 4.710091849454195, 4.762347408297457, 4.140643139829833, 3.0484192493353834, 1.8024097893051203, 0.7290483896091781, 0.06581117605198827, -0.10013346832482453, 0.16483231831398684, 0.6823423833861416, 1.2303497994434023, 1.6154721717572191, 1.7289763040909298, 1.5712081612389304, 1.225113728205968, 0.8108379787431741, 0.43961089301707357, 0.17997765660595627, 0.04524353520438488, 0.0029431627985620776, 0.00047211910297287915, -0.0058447089126063174, -0.03214522078466915, -0.06459426759709408, -0.07191935958891636, -0.02636752093014811, 0.07833154184192169, 0.22016885712520473, 0.355578505641333, 0.4365219740747361, 0.43080952418248336, 0.3371742564349196, 0.18637997235962475, 0.02924920478329532, -0.08318711007629923, -0.11959296841508756, -0.08016094564555366, 0.005205560088107129, 0.09157532301949288, 0.13925634036992757, 0.13122530070792426, 0.0803626956068874, 0.022893192958237624, -0.0003662700314766558, 0.033586723052156674, 0.11572415617029647, 0.20514159826171338, 0.2451945461529561, 0.19172936849204272, 0.04333336546616265, -0.14473488783184887, -0.268677893268243, -0.20581961743908134, 0.1414525028667103, 0.8003371275466381, 1.697215126179946, 2.663511278352662, 3.475606239234278, 3.9179868403814, 3.85217030498543, 3.2713939387962085, 2.3215254510932395, 1.2642389543364685, 0.4036202282496475, -0.003972818876403133, 0.16780975633895415, 0.8664377491379855, 1.8657660558072304, 2.8290325053865493, 3.407024596117988, 3.3425406222189453, 2.5510907991294314, 1.1550496000923773, -0.5414374156537007, -2.144651328031989, -3.284514366610275, -3.718565449348, -3.399600610265215, -2.486348354814218, -1.2881095615158704, -0.16937964112634, 0.5536818622307876, 0.6981269516095878, 0.2583610096027185, -0.6008984150237535, -1.6065820584896418, -2.473520017374585, -2.9864241125740563, -3.0504406078977135, -2.701318934309083, -2.0779331122495583, -1.368389699708397, -0.7427954918833829, -0.30547812607976826, -0.07672277023626843, -0.004749145454624, -0.00062283296362794, 0.017303746358865807, 0.08507525375253346, 0.17892058924314552, 0.2324916829708909, 0.17682365613887513, -0.01613093302227495, -0.3186376733104629, -0.6740018785320628, -1.0235423129218633, -1.3239235383671735], 'positive_zeros': ['0.876548290787904101379704083952203', '1.08210350213104928818412929753922', '1.31978081998146039087572749673739', '1.58387225089837139744746406109989', '1.91307008976626801927001923979107', '2.08332049483295383558027868615439', '2.39155427785449701940472030599438', '2.47256243152806849617862955025613', '2.64590543205261566460566741738262', '2.96550861823738999045185561556009', '3.18823143946371564697327092320534', '3.47822152447108134984713502528815', '3.50262948687422162439013602051722', '3.58972026829573545022849499640374', '3.71405324026360066855495574597484', '3.83257658587863719919889198070477', '4.20936416378128946540106961963010', '4.61416621282429080495741762373504', '4.62470290957021935952555385930527', '4.68944052630972722170433019944760', '4.70998185669572303304709404730230', '5.37215047726054079495927231925490', '5.56761446432212740741097057824793', '5.67122503739849240914972191274729', '5.71582689338271742010158067868339', '5.72534939361844554467738463342923', '5.78685725060117792074664621809875', '6.01325808410659485710130239388772', '6.09471675877314802475407713192231', '6.45534730108446738766102693741960', '6.65225756346038314885482189277145', '6.81335297347388348175700438509494', '7.02777416599044518470485394883604', '7.12641492194455636591173565909329', '7.15496490527734209652541508051026', '7.38307217759669385539852075184785', '7.70445469248917101752760524612033', '7.74278982051750506516985948995497', '7.79855568095427180711751615574763', '7.997065527556914409427668269666439', '8.271251076790563004188167919302693', '8.475884229959288557371536029933068', '8.604753431381280732732916535242683', '8.628196276401745219391195245179326', '8.750255457015012957342084122697836', '8.995400477218640636127098765262411', '9.092132218921289644163155241816264', '9.169121379783445561005655331658046', '9.450651876850462695559479060784004', '9.483387305758148563871513835442079', '9.669110103213298479157885117712304', '9.731008586006313002753001951980662', '9.823320444566864810393589312745908', '9.907553015569126528213349535960317', '10.10001724661199182003023669767958', '10.16903479765052870592559821951427', '10.52992147417757560736646658668561', '10.71835356600618835922273271249023', '10.90391527646709271476664276980566', '10.98874369331260872979812931200058'], 'prelabel': '12-637e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e6-0', 'trace_hash': 1511294524112240661, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.876548290787904101379704083952', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.08210350213104928818412929754', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.31978081998146039087572749674', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 17318.05984582416, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 66809249633371609, 'conductor_radical': 91, 'degree': 12, 'dirichlet_coefficients': [1, 2, 4, 2, 5, 8, 0, 0, 7, 10, 4, 8, 6, 0, 20, 0, 4, 14, 7, 10, 0, 8, -1, 0, 18, 12, 0, 0, -14, 40, -3, 4, 16, 8, 0, 14, 10, 14, 24, 0, -12, 0, 18, 8, 35, -2, 17, 0, 0, 36, 16, 12, -13, 0, 20, 0, 28, -28, 22, 40, -24, -6, 0, 12, 30, 32, 14, 8, -4, 0, 8, 0, 5, 20, 72, 14, 0, 48, -1, 0, -19, -24, -46, 0, 20, 36, -56, 0, -11, 70, 0, -2, -12, 34, 35, 16, 6, 0, 28, 36], 'euler11': [1, -4, -17, 40, 382, -418, -3857, -4598, 46222, 53240, -248897, -644204, 1771561], 'euler13': [1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0], 'euler17': [1, -4, -33, 48, 1080, -470, -20731, -7990, 312120, 235824, -2756193, -5679428, 24137569], 'euler19': [1, -7, -5, 28, 469, 875, -18166, 16625, 169309, 192052, -651605, -17332693, 47045881], 'euler2': [1, -2, 2, 0, -4, 4, -4, 8, -16, 0, 32, -64, 64], 'euler23': [1, 1, -27, -150, 51, 1733, 13694, 39859, 26979, -1825050, -7555707, 6436343, 148035889], 'euler29': [1, 14, 197, 1842, 15410, 101462, 611213, 2942398, 12959810, 44924538, 139334357, 287156086, 594823321], 'euler3': [1, -4, 9, -8, -12, 62, -137, 186, -108, -216, 729, -972, 729], 'euler31': [1, 3, -43, -118, 681, 335, -14122, 10385, 654441, -3515338, -39711403, 85887453, 887503681], 'euler37': [1, -10, -19, 126, 3178, -3932, -126587, -145484, 4350682, 6382278, -35609059, -693439570, 2565726409], 'euler41': [1, 12, 50, 60, 479, 23448, 263036, 961368, 805199, 4135260, 141288050, 1390274412, 4750104241], 'euler43': [1, -18, 329, -3578, 38154, -296162, 2233817, -12734966, 70546746, -284476046, 1124785529, -2646151974, 6321363049], 'euler47': [1, -17, 59, -420, 12425, -71363, 127970, -3354061, 27446825, -43605660, 287901179, -3898865119, 10779215329], 'euler5': [1, -5, 7, -4, 19, 1, -146, 5, 475, -500, 4375, -15625, 15625], 'euler53': [1, 13, -29, -164, 10913, 34735, -380618, 1840955, 30654617, -24415828, -228823949, 5436541409, 22164361129], 'euler59': [1, -22, 163, -1366, 21446, -157474, 757639, -9290966, 74653526, -280547714, 1975129843, -15728334578, 42180533641], 'euler61': [1, 24, 233, 1928, 21078, 166136, 1069181, 10134296, 78431238, 437619368, 3226080953, 20270311224, 51520374361], 'euler67': [1, -14, 31, 146, -1022, 44074, -594409, 2952958, -4587758, 43911398, 624684751, -18901751498, 90458382169], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, -8, 354, -2100, 55551, -262732, 5072672, -18653972, 280032591, -751613100, 8995735074, -14433834808, 128100283921], 'euler73': [1, -5, 25, -1662, 4155, -26645, 1335370, -1945085, 22141995, -646546254, 709956025, -10365357965, 151334226289], 'euler79': [1, 1, -167, -346, 14695, 22873, -1183810, 1806967, 91711495, -170591494, -6504663527, 3077056399, 243087455521], 'euler83': [1, 46, 1281, 25338, 388758, 4776254, 48068993, 396429082, 2678153862, 14487939006, 60794109201, 181195869578, 326940373369], 'euler89': [1, 11, -91, -1626, 4307, 91583, 367922, 8150887, 34115747, -1146279594, -5709543931, 61424653939, 496981290961], 'euler97': [1, -6, 449, -2470, 94530, -437494, 11714933, -42436918, 889432770, -2254302310, 39749647169, -51524041542, 832972004929], 'euler_factors': [[1, -2, 2, 0, -4, 4, -4, 8, -16, 0, 32, -64, 64], [1, -4, 9, -8, -12, 62, -137, 186, -108, -216, 729, -972, 729], [1, -5, 7, -4, 19, 1, -146, 5, 475, -500, 4375, -15625, 15625], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, -17, 40, 382, -418, -3857, -4598, 46222, 53240, -248897, -644204, 1771561], [1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0], [1, -4, -33, 48, 1080, -470, -20731, -7990, 312120, 235824, -2756193, -5679428, 24137569], [1, -7, -5, 28, 469, 875, -18166, 16625, 169309, 192052, -651605, -17332693, 47045881], [1, 1, -27, -150, 51, 1733, 13694, 39859, 26979, -1825050, -7555707, 6436343, 148035889], [1, 14, 197, 1842, 15410, 101462, 611213, 2942398, 12959810, 44924538, 139334357, 287156086, 594823321], [1, 3, -43, -118, 681, 335, -14122, 10385, 654441, -3515338, -39711403, 85887453, 887503681], [1, -10, -19, 126, 3178, -3932, -126587, -145484, 4350682, 6382278, -35609059, -693439570, 2565726409], [1, 12, 50, 60, 479, 23448, 263036, 961368, 805199, 4135260, 141288050, 1390274412, 4750104241], [1, -18, 329, -3578, 38154, -296162, 2233817, -12734966, 70546746, -284476046, 1124785529, -2646151974, 6321363049], [1, -17, 59, -420, 12425, -71363, 127970, -3354061, 27446825, -43605660, 287901179, -3898865119, 10779215329], [1, 13, -29, -164, 10913, 34735, -380618, 1840955, 30654617, -24415828, -228823949, 5436541409, 22164361129], [1, -22, 163, -1366, 21446, -157474, 757639, -9290966, 74653526, -280547714, 1975129843, -15728334578, 42180533641], [1, 24, 233, 1928, 21078, 166136, 1069181, 10134296, 78431238, 437619368, 3226080953, 20270311224, 51520374361], [1, -14, 31, 146, -1022, 44074, -594409, 2952958, -4587758, 43911398, 624684751, -18901751498, 90458382169], [1, -8, 354, -2100, 55551, -262732, 5072672, -18653972, 280032591, -751613100, 8995735074, -14433834808, 128100283921], [1, -5, 25, -1662, 4155, -26645, 1335370, -1945085, 22141995, -646546254, 709956025, -10365357965, 151334226289], [1, 1, -167, -346, 14695, 22873, -1183810, 1806967, 91711495, -170591494, -6504663527, 3077056399, 243087455521], [1, 46, 1281, 25338, 388758, 4776254, 48068993, 396429082, 2678153862, 14487939006, 60794109201, 181195869578, 326940373369], [1, 11, -91, -1626, 4307, 91583, 367922, 8150887, 34115747, -1146279594, -5709543931, 61424653939, 496981290961], [1, -6, 449, -2470, 94530, -437494, 11714933, -42436918, 889432770, -2254302310, 39749647169, -51524041542, 832972004929]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/e/l'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '12-637e6-1.1-c1e6-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-637e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 1511294524112240661, 'z1': {'__RealLiteral__': 0, 'data': '0.876548290787904101379704083952', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1111156966946315198645924226649,1371729153985493743445040295104,1673020948619203040021047386469,2425104447570882355997051077072,3031655215800642860828217434262,3354083609088630891981017447884', 'Lhash_array': ['1111156966946315198645924226649', '1371729153985493743445040295104', '1673020948619203040021047386469', '2425104447570882355997051077072', '3031655215800642860828217434262', '3354083609088630891981017447884'], 'label': '12-637e6-1.1-c1e6-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/e/l'}