-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '571194545052842719014992943916,1338239997174873075680417128711', 'a10': 4, 'a2': 2, 'a3': 0, 'a4': 1, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4476.500062262967, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]], [19, [1, -2, 1]]], 'bad_primes': [3, 7, 19], 'central_character': '8379.1', 'coefficient_field': '1.1.1.1', 'conductor': 70207641, 'conductor_radical': 399, 'degree': 4, 'euler_factors': [[1, -2, 3, -4, 4], [1], [1, -2, 11, -10, 25], [1], [1, 2, 21, 22, 121], [1, 4, 12, 52, 169], [1, 8, 50, 136, 289], [1, -2, 1], [1, -14, 93, -322, 529], [1, -16, 120, -464, 841], [1, -4, 48, -124, 961], [1, -4, 28, -148, 1369], [1, 12, 110, 492, 1681], [1, -2, 37, -86, 1849], [1, 6, 101, 282, 2209], [1, 0, 88, 0, 2809], [1, -8, 126, -472, 3481], [1, 18, 195, 1098, 3721], [1, -8, 142, -536, 4489], [1, -20, 224, -1420, 5041], [1, 2, -53, 146, 5329], [1, 0, 156, 0, 6241], [1, -10, 173, -830, 6889], [1, 20, 276, 1780, 7921], [1, -12, 222, -1164, 9409], [1, -14, 123, -1414, 10201], [1, -12, 242, -1236, 10609], [1, -8, None, -856, 11449], [1, 8, 202, 872, 11881], [1, 8, 224, 904, 12769]], 'euler_factors_factorization': [[[[1, -2, 3, -4, 4], 1]], [1], [[[1, -1, 5], 2]], [1], [[[1, 2, 21, 22, 121], 1]], [[[1, 4, 12, 52, 169], 1]], [[[1, 4, 17], 2]], [[[1, -1], 2]], [[[1, -14, 93, -322, 529], 1]], [[[1, -16, 120, -464, 841], 1]], [[[1, -4, 48, -124, 961], 1]], [[[1, -4, 28, -148, 1369], 1]], [[[1, 12, 110, 492, 1681], 1]], [[[1, -2, 37, -86, 1849], 1]], [[[1, 6, 101, 282, 2209], 1]], [[[1, 0, 88, 0, 2809], 1]], [[[1, -8, 126, -472, 3481], 1]], [[[1, 18, 195, 1098, 3721], 1]], [[[1, -8, 142, -536, 4489], 1]], [[[1, -20, 224, -1420, 5041], 1]], [[[1, 2, -53, 146, 5329], 1]], [[[1, 0, 156, 0, 6241], 1]], [[[1, -10, 173, -830, 6889], 1]], [[[1, 20, 276, 1780, 7921], 1]], [[[1, -12, 222, -1164, 9409], 1]], [[[1, -14, 123, -1414, 10201], 1]], [[[1, -6, 103], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 5, 'label': '4-8379e2-1.1-c1e2-0-5', 'leading_term': '5.65333790627123285130204875025623746832692908360809485395532080000000000000000000000000000', '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}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8379/2/a/bl', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0234375', 'prec': 30}, 'plot_values': [5.653337906271233, 5.627996511443481, 5.5792191450033615, 5.488738200117225, 5.358407775628291, 5.19385630843533, 4.995609780232309, 4.763471604322446, 4.4988920551602645, 4.203788236228716, 3.8799705122973296, 3.529425370001156, 3.1545232995977632, 2.7578954777335194, 2.3424491640285936, 1.911328071976845, 1.4679819749527445, 1.0160815094882982, 0.5595726664164989, 0.10258063529091299, -0.3505398717910008, -0.795317491770246, -1.227127085340254, -1.6413127327477322, -2.0331667623549112, -2.3980577077297602, -2.7314281420002566, -3.0289207650442336, -3.2863954097941885, -3.5000460578906227, -3.666435208557962, -3.7825945577921916, -3.8460726002205012, -3.8550122767648407, -3.8082055476682095, -3.7051424819393954, -3.546064799776599, -3.3319826459774107, -3.0647179694523254, -2.7468875243277036, -2.3819266068477365, -1.974039541957255, -1.528194851040514, -1.0500474306743797, -0.5458977200804795, -0.022592734867538315, 0.5125558061890959, 1.0518817304877937, 1.5874892218023213, 2.1113623291247428, 2.615530947099217, 3.092166207175051, 3.533781993475468, 3.933302524585863, 4.284290067520032, 4.580971904385594, 4.818481764579502, 4.992835520780628, 5.101171655910047, 5.1416683928263325, 5.113767568152459, 5.018030285559416, 4.856329102698349, 4.63164439713433, 4.348211867889745, 4.0112671926380274, 3.6271394226585483, 3.2029566864538257, 2.74668086633404, 2.2667915284254017, 1.7722628996492606, 1.2722463576797065, 0.7759966364787931, 0.29257465154161044, -0.169264574347872, -0.6013275489674037, -0.9961155983958492, -1.3470204730062134, -1.648458784331333, -1.8959938214487138, -2.086450108404145, -2.2179541069460864, -2.2900091955019763, -2.303455512923306, -2.2604892956602214, -2.1645501133933926, -2.020274182812887, -1.8333248232851374, -1.6102765677496829, -1.358410966659752, -1.0855362877868981, -0.7997750383986095, -0.5093318822874663, -0.22230082883779334, 0.05359926025492208, 0.31117129122270487, 0.5440127136180387, 0.7465938672125498, 0.9145128602319, 1.044490673942644, 1.1345830485410997, 1.1840864753093925, 1.193686280434952, 1.1652777452411716, 1.1020367289644577, 1.0081701192668486, 0.8889046239663521, 0.7501893500685319, 0.5986087674878986, 0.441066321937539, 0.28463776228699034, 0.13626743092811344, 0.002586818487985581, -0.11034596144055817, -0.19723159489353875, -0.2537214540540502, -0.2765739551936195, -0.2637608582772351, -0.21456347472938814, -0.12958745370655275, -0.010773904595987559, 0.1386710410581951, 0.314365355571181, 0.5108886337903965, 0.7219743353776951, 0.9406863390576095, 1.1597038589478792, 1.3715024596709111, 1.5687086213700863, 1.7442485217408736, 1.8917391167276505, 2.005570779971344, 2.081295648246432, 2.1156177425124816, 2.106738252793384, 2.054238227700226, 1.9593448598277514, 1.8247058106532315, 1.6545500871395475, 1.4543677266566504, 1.230952476531926, 0.9920138666564707, 0.746104935586973, 0.5022037198814676, 0.26954560620411866, 0.05721638877857722, -0.1260767895377771, -0.27235937633140017, -0.37463557613913656, -0.4271545721973633, -0.4256248152376919, -0.3673698467506663, -0.2514635845172626, -0.07876890798995109, 0.14804479744870375, 0.42456961557062683, 0.7447840696731318, 1.1012002743241374, 1.4851384425161482, 1.8869124220139988, 2.2962416264470913, 2.7024261742917437, 3.094866296186098, 3.4631771403546097, 3.7977717493057694, 4.089871743692839, 4.332101954393108, 4.5183660466218045, 4.644400082816583, 4.707500071744241, 4.706988318273225, 4.643800421282396, 4.520831318525113, 4.342409464097272, 4.114507073439099, 3.8441460763009885, 3.539476545587428, 3.2091699345476585, 2.862388033347605, 2.508222167837814, 2.1555894003945038, 1.8127711296683553, 1.4872813652492378, 1.1855451361381355, 0.912784233369678, 0.6728568471668274, 0.4681991219336475, 0.29982531169228605, 0.16735003090194828, 0.06912631784658738, 0.002355899983629366, -0.036675706491915476, -0.05241221237691981, -0.04974702270036839, -0.03378719130029431, -0.009585371782431348, 0.018106507694369688, 0.04504353739328072, 0.06770190317841102, 0.08338681993074822, 0.090376345583933, 0.08791374872217675, 0.0762552347895612, 0.05655135893599274, 0.03079070435671878, 0.0015954045512643455, -0.027926776605350614, -0.054432280525869306, -0.07454961012192496, -0.08512632560871292, -0.08345086516641287, -0.06745013465713387, -0.0358729027812327, 0.011597798012409174, 0.07424893305744164, 0.15032791844553367, 0.23707103880717598, 0.33079219562877527, 0.42705146996609655, 0.5208153869861927, 0.6067566845895307, 0.6794413722592028, 0.7337258312463179, 0.7649159392865222, 0.7692073932729687, 0.743762433154215, 0.6871278993746106, 0.5991861199059846, 0.4814854883506582, 0.3370423520634908, 0.17053164896924683, -0.012057229460918577, -0.20339840665886694, -0.39528942318369037, -0.5787952149385779, -0.7447703179347485, -0.8841327641858917, -0.9883808062660537, -1.0499309205129974, -1.0625592571592155, -1.0217177534995177, -0.9248421215232322, -0.7715538310922981, -0.5638004659195087, -0.30586120755464136, -0.004318151640001742, 0.33219171911169487, 0.693139784254234, 1.066626986668104, 1.4396148226036745, 1.798695950974232, 2.1303037847250783, 2.4216666316099382, 2.6608995891706106, 2.838043165257005, 2.9449518442731075, 2.9763003442097675, 2.929211240732777, 2.804113622421457, 2.604093776649782, 2.3355126911806217, 2.0071124389029453, 1.6303377688528933, 1.2182780850494497, 0.7856879740443294, 0.34788178899894284, -0.07950027552461462, -0.48150854949251365, -0.8442812514072509, -1.1558384325101592, -1.4065233748515114, -1.5894673449117869, -1.7009493410515588, -1.7404717918199395, -1.7109310323017288, -1.618304120024586, -1.4715625331021178, -1.2820334111412128, -1.0630444615835357, -0.8290779371724964, -0.5951955646835483, -0.37614003913802996, -0.18564323616795522, -0.0356403433981579, 0.064398559528324, 0.10799558881182714, 0.09215940351659946, 0.01755358072404446, -0.11131415818700803, -0.2863160540457303, -0.49590283605090113, -0.7256793946886807, -0.9590037360522271, -1.1778037737434426, -1.3635098250994997, -1.4979511634352831, -1.5644806970476566, -1.5487683358647433, -1.4399219483368966, -1.2310080730763813, -0.919950783413136, -0.509658200260843, -0.008497466227165731, 0.570019348379355, 1.2073302846164051, 1.8805351475156533, 2.5631192277974435, 3.2259321164856183, 3.8384933942688426, 4.370040022336345, 4.791262171775499, 5.075186032621498, 5.199102541569312, 5.145060440211556, 4.90170202594816, 4.464193223077393, 3.8356800134639166, 3.0265712496845563, 2.055380315876843, 0.9473880111122148, -0.2652698436064458, -1.5454174989168095, -2.8515183680792866, -4.1397299022834355, -5.365226162462312, -6.4841956774358405, -7.455563313484015, -8.242626683922154, -8.814849714677296, -9.148881058524458, -9.230062783809625, -9.052672052928212, -8.62082155522441, -7.9478981958032175, -7.056623905296536, -5.977809715921279, -4.749482101815832, -3.415201623269409, -2.022317879599379, -0.6201941820292828, 0.7421944386962304, 2.0177540360771733, 3.1639992876257703, 4.143918435957896, 4.928634923030822, 5.497393515506682, 5.839774170936007, 5.954691182433264, 5.851856896530559, 5.549852488570633, 5.076675783794788, 4.4671032446116286, 3.7623261477911734, 3.006948751625485, 2.2478897497107515, 1.5314272451290487, 0.9016856822676976, 0.39813043091181616, 0.054046906027320624, -0.10519415455483908, -0.06324633438146232, 0.18642734824238025, 0.6402094150665901, 1.2844939061269836, 2.0963265078582456, 3.044342894724181, 4.090438288737447, 5.191150253463773, 6.300214800485965, 7.369976276919348, 8.35452426307353, 9.21070146157243, 9.901408243049937, 10.395848962321464, 10.672560202963778, 10.718674781186527, 10.532282245974018, 10.120672533083694, 9.501763887340527, 8.701480355101582, 7.7541593699580815, 6.699382262176952, 5.581467579951872, 4.446179469895332, 3.3395860404979767, 2.305095772971766, 1.3820791394836243, 0.6036224212361453, -0.004648058391878388, -0.42584119534743387, -0.6523798751236479, -0.6862369046214346, -0.5386449647180722, -0.22942333461105965, 0.21427661773347187, 0.759250688670628, 1.3683614601009366, 2.002006839703292, 2.620830427958075, 3.1869315659413955, 3.666772111085622, 4.031738027937931, 4.2608075502939355, 4.340209898090164, 4.26546682348874, 4.040080466758534, 3.6766857480123907, 3.19489937888926, 2.621499240702632, 1.9877398011081076, 1.328670305250659, 0.6803330680904506, 0.078505105689254, -0.4437779255134026, -0.8576575532818859, -1.140224524511611, -1.2757004964060448, -1.2562700181908246, -1.0826329292761097, -0.7638517393123863, -0.3170335290093638, 0.2336503912505307, 0.8582102928843406, 1.5223193987818628, 2.1893486110906326, 2.821919416895948, 3.384421404157081, 3.844193269546199, 4.174113251348279, 4.353043343029215, 4.368064385136227, 4.213974065269427, 3.8948093346536474, 3.4223895311220085, 2.8169141936361055, 2.1047473335649203, 1.318067990971709, 0.492257801147351, -0.33522528738366536, -1.127401237900911, -1.8493448125078096, -2.4702270018975443, -2.964931084996248, -3.315220529246029, -3.510986662887805, -3.5503505896428313, -3.440227345907072, -3.1953773252141913, -2.8381332397471666, -2.3966209919867816, -1.903691654481048, -1.3946901055619823, -0.9058222694962739, -0.47192922091322986, -0.12465904921286229, 0.10931176067811989, 0.20987318076722244, 0.16447849710131981, -0.0308882139015383, -0.3716559830251202, -0.8445985710455823, -1.428672186872508, -2.0959328167722653, -2.813028655670659, -3.54298075308749, -4.246953806671915, -4.8865893025395835, -5.42562531838912, -5.832343988660023, -6.080653318038986, -6.152172391269471, -6.036516392238741, -5.7326026031801405, -5.248065743305802, -4.599513727147486, -3.8112034257549787, -2.914177210826039, -1.9445049153071494, -0.941448171638224, 0.05431576685969312, 1.0031702031342882, 1.8679177406542748, 2.616450443206923, 3.2223302416004382, 3.667185120711878, 3.9403035650074765, 4.040364404111511, 3.97403646876079, 3.756805181090462, 3.410770001810958, 2.964532232426857, 2.4505432378519085, 1.9042215094900425, 1.36129027344802, 0.8564549140687455, 0.4211594212448009, 0.08224217068380504, -0.13955459707765655, -0.2305372048637375, -0.1846390527822362, -0.0036522880383370016, 0.3030760382550348, 0.7192306402172591, 1.222533773756609, 1.786437337325766, 2.381106413962849, 2.9745379899758704, 3.5352080774504864, 4.038498238966296, 4.4605002088305765, 4.7645301810681495, 4.930351445310398], 'positive_zeros': ['0.45059304586768951778828774254876', '1.05568521557433465559119258007534', '1.72563003880105871263718893999213', '2.19846638818811275826015644717984', '2.62548876893381550671462056413486', '2.81435699176931005484273141129093', '3.40532119917113448227826210074924', '3.59471129435026268497584483392524', '4.45419551497814991871024807532968', '4.57856578128829407279366795195197', '4.80593901626654231046243005464742', '4.98711705259485142364187464826431', '5.41256067580243381231398531207201', '5.74250233009827087768408143641904', '6.22993282204430689929273626205336', '6.63984849171206317592199153185727', '6.73040059535711733973809028427348', '7.07849168213727086924731594791814', '7.49500824789736660604985527016802', '7.955847194745948757466401449730532'], 'prelabel': '4-8379e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.179648638763823, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 53907645323329012, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45059304586768951778828774255', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.05568521557433465559119258008', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.72563003880105871263718893999', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4476.500062262967, 'bad_primes': [3, 7, 19], 'central_character': '1.1', 'conductor': 70207641, 'conductor_radical': 399, 'degree': 4, 'dirichlet_coefficients': [1, 2, 0, 1, 2, 0, 0, 0, 0, 4, -2, 0, -4, 0, 0, 1, -8, 0, 2, 2, 0, -4, 14, 0, -7, -8, 0, 0, 16, 0, 4, -2, 0, -16, 0, 0, 4, 4, 0, 0, -12, 0, 2, -2, 0, 28, -6, 0, 0, -14, 0, -4, 0, 0, -4, 0, 0, 32, 8, 0, -18, 8, 0, -11, -8, 0, 8, -8, 0, 0, 20, 0, -2, 8, 0, 2, 0, 0, 0, 2, 0, -24, 10, 0, -16, 4, 0, 0, -20, 0, 0, 14, 0, -12, 4, 0, 12, 0, 0, -7], 'euler11': [1, 2, 21, 22, 121], 'euler13': [1, 4, 12, 52, 169], 'euler17': [1, 8, 50, 136, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, -2, 3, -4, 4], 'euler23': [1, -14, 93, -322, 529], 'euler29': [1, -16, 120, -464, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, 48, -124, 961], 'euler37': [1, -4, 28, -148, 1369], 'euler41': [1, 12, 110, 492, 1681], 'euler43': [1, -2, 37, -86, 1849], 'euler47': [1, 6, 101, 282, 2209], 'euler5': [1, -2, 11, -10, 25], 'euler53': [1, 0, 88, 0, 2809], 'euler59': [1, -8, 126, -472, 3481], 'euler61': [1, 18, 195, 1098, 3721], 'euler67': [1, -8, 142, -536, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -20, 224, -1420, 5041], 'euler73': [1, 2, -53, 146, 5329], 'euler79': [1, 0, 156, 0, 6241], 'euler83': [1, -10, 173, -830, 6889], 'euler89': [1, 20, 276, 1780, 7921], 'euler97': [1, -12, 222, -1164, 9409], 'euler_factors': [[1, -2, 3, -4, 4], [1, 0, 0, 0, 0], [1, -2, 11, -10, 25], [1, 0, 0, 0, 0], [1, 2, 21, 22, 121], [1, 4, 12, 52, 169], [1, 8, 50, 136, 289], [1, -2, 1, 0, 0], [1, -14, 93, -322, 529], [1, -16, 120, -464, 841], [1, -4, 48, -124, 961], [1, -4, 28, -148, 1369], [1, 12, 110, 492, 1681], [1, -2, 37, -86, 1849], [1, 6, 101, 282, 2209], [1, 0, 88, 0, 2809], [1, -8, 126, -472, 3481], [1, 18, 195, 1098, 3721], [1, -8, 142, -536, 4489], [1, -20, 224, -1420, 5041], [1, 2, -53, 146, 5329], [1, 0, 156, 0, 6241], [1, -10, 173, -830, 6889], [1, 20, 276, 1780, 7921], [1, -12, 222, -1164, 9409]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8379/2/a/bl'], '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': '4-8379e2-1.1-c1e2-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-8379e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.179648638763823, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 53907645323329012, 'z1': {'__RealLiteral__': 0, 'data': '0.45059304586768951778828774255', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '571194545052842719014992943916,1338239997174873075680417128711', 'Lhash_array': ['571194545052842719014992943916', '1338239997174873075680417128711'], 'factors': ['2-8379-1.1-c1-0-35', '2-8379-1.1-c1-0-186'], 'label': '4-8379e2-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8379/2/a/bl'}