-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1475860657061533815597011087188', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.369562825556503, 0.0], 'a4': [0.0, 0.0], 'a5': [3.21030803077811, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [2.614827984259317, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.21230790698127, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7, 17], 'central_character': '6664.1', 'coefficient_field': 'CDF', 'conductor': 6664, 'conductor_radical': 238, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.369562825556503, 0], [3.0, 0]], [[1.0, 0], [-3.21030803077811, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0359720423610896, 0], [11.0, 0]], [[1.0, 0], [-5.149138118268208, 0], [13.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.8081033378650795, 0], [19.0, 0]], [[1.0, 0], [-3.121982406285511, 0], [23.0, 0]], [[1.0, 0], [4.894113701789501, 0], [29.0, 0]], [[1.0, 0], [-8.763966102527526, 0], [31.0, 0]], [[1.0, 0], [-4.484101234634298, 0], [37.0, 0]], [[1.0, 0], [3.746569648320721, 0], [41.0, 0]], [[1.0, 0], [-4.186482493799974, 0], [43.0, 0]], [[1.0, 0], [2.5176860293883263, 0], [47.0, 0]], [[1.0, 0], [1.0523535821315093, 0], [53.0, 0]], [[1.0, 0], [-6.739125651113006, 0], [59.0, 0]], [[1.0, 0], [7.560522918594088, 0], [61.0, 0]], [[1.0, 0], [4.3015280662019295, 0], [67.0, 0]], [[1.0, 0], [-14.79177295191215, 0], [71.0, 0]], [[1.0, 0], [12.712027451247964, 0], [73.0, 0]], [[1.0, 0], [-8.447771773538916, 0], [79.0, 0]], [[1.0, 0], [-12.534382121047775, 0], [83.0, 0]], [[1.0, 0], [-0.3410347804031288, 0], [89.0, 0]], [[1.0, 0], [15.047354344648511, 0], [97.0, 0]], [[1.0, 0], [1.9330521421206954, 0], [101.0, 0]], [[1.0, 0], [8.025491588816447, 0], [103.0, 0]], [[1.0, 0], [-6.316973036875013, 0], [107.0, 0]], [[1.0, 0], [-6.801674255093748, 0], [109.0, 0]], [[1.0, 0], [4.19917643983154, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 105, 'label': '2-6664-1.1-c1-0-105', 'leading_term': '4.92331337104220390059180281853', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/6664/2/a/u/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [4.9233133710422035, 4.913278211277682, 4.8830648521184505, 4.832362012873826, 4.76069117400545, 4.667463904088557, 4.552056286518002, 4.413895380201178, 4.252552126144621, 4.06783504290987, 3.859879357434507, 3.6292267851228095, 3.376891895530209, 3.1044117875853905, 2.813876589501284, 2.5079390600571205, 2.189802289183582, 1.8631851806601287, 1.5322660586479624, 1.2016053832542282, 0.8760491947287529, 0.5606155312312529, 0.2603666743651319, -0.019729343668818726, -0.27494400623283277, -0.5009359264833074, -0.6938960198847799, -0.8506852011390814, -0.9689594713905326, -1.047277325340499, -1.0851846513712091, -1.08327273070459, -1.0432055668015188, -0.9677135886307272, -0.8605517577476905, -0.7264212474007758, -0.570855121778304, -0.4000697867723857, -0.22078536500857035, -0.04001951640835387, 0.13513947381011307, 0.29777334213428985, 0.441380237474387, 0.56011810683477, 0.6490358551424376, 0.704282913311721, 0.7232880617499738, 0.7048989468703809, 0.6494747005507941, 0.5589254160285467, 0.4366939211773128, 0.2876772775830019, 0.11808766135627805, -0.06474532555076055, -0.2526263940694073, -0.4367933861490025, -0.6082538738136862, -0.7581481423393773, -0.878125396138317, -0.9607186924027038, -0.9997032908819699, -0.9904228778956974, -0.9300685278459463, -0.8178963309255132, -0.6553713392050667, -0.4462278337031971, -0.19643883170769152, 0.08590885311267585, 0.39083393197495825, 0.7067703046470282, 1.0209589925659148, 1.319910345711746, 1.589920894097981, 1.8176260471105006, 1.9905673088914182, 2.097750924341302, 2.130174021020557, 2.0812944569929397, 1.94742177379354, 1.728008893356424, 1.4258274468316432, 1.0470137924759928, 0.6009777329285662, 0.10017149938070359, -0.4402774861227124, -1.0030604761308477, -1.5692923422164358, -2.119206499258553, -2.632913836629624, -3.0911957415099836, -3.4762985153948516, -3.7726950419752496, -3.96777959352122, -4.052463232128364, -4.02164037150385, -3.8745016419020684, -3.6146741003541596, -3.250176836112275, -2.793187860321334, -2.2596265100260142, -1.6685640713087102, -1.0414835430242873, -0.40141702429647097, 0.22800426759554707, 0.8235472073434159, 1.3633776102930673, 1.8280195994505986, 2.2012289037954385, 2.4707381510104476, 2.6288369368838196, 2.6727560910802093, 2.6048338641833553, 2.432451391725757, 2.1677353267625428, 1.8270364921652564, 1.4302042669068316, 0.9996866523901219, 0.5594950424171339, 0.1340801595345502, -0.2528289981618106, -0.5793683629347034, -0.8266089370764236, -0.9795009737304359, -1.0276443050806112, -0.9658444226620192, -0.794423607161777, -0.5192678643685136, -0.15160311859554224, 0.2924925662396837, 0.7928206866024335, 1.3260053056267482, 1.866603567748516, 2.3883307310197206, 2.865340047969471, 3.273494068590452, 3.5915633677705223, 3.8022914185197276, 3.8932702748608894, 3.857580654798332, 3.694161519944532, 3.4078877817299262, 3.0093496497189136, 2.514342611047197, 1.9430922766110987, 1.3192525272178977, 0.6687277566758779, 0.018379835479547493, -0.6053128725335775, -1.1775739404879335, -1.6765548666687553, -2.08440315540237, -2.3881150856086957, -2.5801270758503945, -2.658613549487804, -2.6274751441214548, -2.496018135720374, -2.2783431202646045, -1.9924773471829604, -1.6592996889557652, -1.3013192009494738, -0.9413768485645413, -0.6013447066764732, -0.30089743459944956, -0.056427002349184865, 0.11983635541873199, 0.22044575219863072, 0.2430655359076787, 0.19048638183056466, 0.07032708486724641, -0.10555864409286835, -0.3219341255795887, -0.5612381577050816, -0.8047846727950378, -1.034029061968807, -1.2318217890087964, -1.383569872493663, -1.4782316598810836, -1.5090798472216074, -1.474181421405474, -1.3765603585634527, -1.2240285146003345, -1.0286910303993322, -0.8061534766867189, -0.5744775818291504, -0.3529494673363371, -0.1607377339050805, -0.0155275677594063, 0.06777939315949695, 0.07821173676150628, 0.009641472982778499, -0.1386033132087075, -0.36147583409689904, -0.6483262661129662, -0.9834003724697883, -1.3467011613255384, -1.7151696279073518, -2.0641186792530446, -2.3688359165237367, -2.6062573166083314, -2.7566060119205273, -2.8048889800716177, -2.7421498025944984, -2.566387598514237, -2.283070230640776, -1.9051929710174837, -1.4528607009736165, -0.9524008391250254, -0.43504378118481063, 0.06476413728989772, 0.5113250825125426, 0.8698212547344949, 1.1084891763620768, 1.2007056488862142, 1.126855431430256, 0.8758598726132314, 0.44626259430213255, -0.15320795932557008, -0.9036500199048295, -1.7765917871904633, -2.73516915715575, -3.735825601670838, -4.730449327489235, -5.668834654025205, -6.501332594938133, -7.181541393127893, -7.668882277745577, -7.930909495753497, -7.945216661911539, -7.700823036321329, -7.198952296933755, -6.453151061569134, -5.488732778919101, -4.3415723356458455, -3.05631538034637, -1.6841015391992085, -0.27993017167039064, 1.1001808039601384, 2.402079632964506, 3.5762426715876363, 4.580254473262901, 5.380863962867012, 5.955500477113535, 6.293166495485867, 6.394662098698369, 6.272137171632701, 5.948008520412628, 5.453317775423544, 4.825639722680675, 4.106677370281608, 3.339697891965814, 2.566971442711796, 1.827372208977591, 1.154288124865575, 0.5739633234544791, 0.10436709727814567, -0.24535305561940718, -0.4748163918392051], 'positive_zeros': ['1.16424877390963883481327085707705', '1.99185714700509099805800239616359', '2.67370302030315156983099180161489', '3.38740078428892360077121012725016', '4.22449555023333556858740438681507', '5.21185371365240256325216797887220', '6.00907651561990557702040494976299', '6.46744846474349687225230628145666', '7.41551870701870184661799257061520', '8.291505860442184728473503501885790'], 'prelabel': '2-6664-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.294676682827093, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16424877390963883481327085708', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.99185714700509099805800239616', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.67370302030315156983099180161', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 53.21230790698127, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 6664, 'conductor_radical': 238, 'degree': 2, 'index': 105, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6664/2/a/u/1/5'], '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': '2-6664-1.1-c1-0-105', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6664-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.294676682827093, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16424877390963883481327085708', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1475860657061533815597011087188', 'Lhash_array': ['1475860657061533815597011087188'], 'factors': ['2-6664-1.1-c1-0-105'], 'label': '2-6664-1.1-c1-0-105', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6664/2/a/u/1/5'}