-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1669974204702379331158277090561', 'a10': [7.647685761101917, 0.0], 'a2': [4.808561978791322, 0.0], 'a3': [0.0, 0.0], 'a4': [15.122268303877508, 0.0], 'a5': [1.5904309427294179, 0.0], 'a6': [0.0, 0.0], 'a7': [34.52716752349533, 0.0], 'a8': [34.24786856877594, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.808561978791322, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.5904309427294179, 0], [125.0, 0]], [[1.0, 0], [-34.52716752349533, 0], [343.0, 0]], [[1.0, 0], [-42.683590640454995, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [45.44942632358657, 0], [4913.0, 0]], [[1.0, 0], [-41.09096092061899, 0], [6859.0, 0]], [[1.0, 0], [-171.73253289189188, 0], [12167.0, 0]], [[1.0, 0], [-178.03962542585344, 0], [24389.0, 0]], [[1.0, 0], [-18.57360667073023, 0], [29791.0, 0]], [[1.0, 0], [331.2687689190874, 0], [50653.0, 0]], [[1.0, 0], [411.934220934686, 0], [68921.0, 0]], [[1.0, 0], [-11.336310650812017, 0], [79507.0, 0]], [[1.0, 0], [494.59245406864716, 0], [103823.0, 0]], [[1.0, 0], [217.80810521099596, 0], [148877.0, 0]], [[1.0, 0], [-775.4136336125301, 0], [205379.0, 0]], [[1.0, 0], [-340.83064675665355, 0], [226981.0, 0]], [[1.0, 0], [-676.1914796035965, 0], [300763.0, 0]], [[1.0, 0], [449.6044003009139, 0], [357911.0, 0]], [[1.0, 0], [-645.0138635883342, 0], [389017.0, 0]], [[1.0, 0], [778.289363994397, 0], [493039.0, 0]], [[1.0, 0], [1056.5016467628825, 0], [571787.0, 0]], [[1.0, 0], [-160.22827167129824, 0], [704969.0, 0]], [[1.0, 0], [-7.234759590268979, 0], [912673.0, 0]], [[1.0, 0], [-1125.6989793010018, 0], [1030301.0, 0]], [[1.0, 0], [-1204.033471382128, 0], [1092727.0, 0]], [[1.0, 0], [1491.7425280895986, 0], [1225043.0, 0]], [[1.0, 0], [-375.42995031795436, 0], [1295029.0, 0]], [[1.0, 0], [810.9989850229026, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 139, 'label': '2-39e2-1.1-c3-0-139', 'leading_term': '8.97485032759044822957733078130', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bn/1/17', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [8.974850327590449, 8.953002234234892, 8.88761927437263, 8.779185556183487, 8.628508354402381, 8.436718530241665, 8.205270685398661, 7.935942638228544, 7.63083372288624, 7.29236134615289, 6.923255194782977, 6.526548470691973, 6.105565543396247, 5.663905449145455, 5.205420733590293, 4.7341912282012135, 4.254492467820724, 3.770758594824221, 3.287539750907549, 2.8094541265215094, 2.341135016014025, 1.8871734088593353, 1.45205682893904, 1.0401053095200303, 0.6554055561106811, 0.30174449756331906, -0.017456447439281618, -0.29920496083801407, -0.5409977750548602, -0.7408754494765234, -0.8974704434908073, -1.010046999217659, -1.0785314324961057, -1.1035315590137944, -1.086344153310393, -1.0289495501936494, -0.9339927480977084, -0.8047506580589778, -0.6450854550175071, -0.4593843236105956, -0.25248624094283967, -0.029596795447010937, 0.2038076054627581, 0.44208444565694605, 0.6795367179129674, 0.9105291547608135, 1.129606538719138, 1.331611371879138, 1.5117980608154118, 1.6659407185888215, 1.7904317071596583, 1.882368145027383, 1.9396237884440786, 1.9609039598944855, 1.9457815420113953, 1.8947124734560177, 1.809029667714163, 1.6909148158996814, 1.5433481178082509, 1.3700365967883972, 1.1753222768469382, 0.9640721167368363, 0.7415521866220786, 0.5132891189399561, 0.28492234717509485, 0.06205104616924766, -0.149920011429373, -0.34593128051889155, -0.5214114865400674, -0.6724084937089726, -0.7957038163567096, -0.8889069405067918, -0.9505261070213311, -0.9800128181047132, -0.977778052347074, -0.9451789920252786, -0.8844759581168872, -0.7987601878314045, -0.6918540478307541, -0.5681862229018331, -0.43264532258431965, -0.290416174823148, -0.14680379463638807, -0.007050597589101005, 0.12384715379786736, 0.24131744979927608, 0.3413789281211747, 0.4207894948678402, 0.4771715029095581, 0.5091084316392789, 0.516208827014343, 0.4991342586375402, 0.4595892049127107, 0.4002720545329267, 0.3247877731074312, 0.23752418294597252, 0.1434951935309554, 0.0481556495054876, -0.042806318847111245, -0.12369250017571089, -0.1890255686138584, -0.2337794164899357, -0.2536001364854827, -0.24500892286623718, -0.20557847026971018, -0.1340750840521975, -0.030559670582587985, 0.10355797095638719, 0.26551561400454315, 0.45124814372966787, 0.6554905758054089, 0.8719329459402683, 1.093423412623127, 1.3122139089452374, 1.5202407927272443, 1.7094312549097794, 1.872024828081665, 2.0008982573712655, 2.0898813124690605, 2.134050877828242, 2.129990889051015, 2.076006401504674, 1.9722812787485389, 1.8209706510529762, 1.626221376949344, 1.3941161839141218, 1.1325398916351417, 0.8509690417303096, 0.5601892682001992, 0.27194773162333136, -0.0014492091903629517, -0.24758031838525627, -0.45438079863604064, -0.6106238448973099, -0.7063944837794403, -0.7335371840932006, -0.6860588484043146, -0.5604696334767117, -0.35604560027332227, -0.07499943490772923, 0.2774516443277914, 0.6931282541996987, 1.1610450805803538, 1.6676803905948012, 2.1973538874378127, 2.73270362141531, 3.2552484840235865, 3.746018959058332, 4.186235449885937, 4.558010796800386, 4.845051675599897, 5.033332535896909, 5.11171567258165, 5.072491968876753, 4.911818809179082, 4.630034599277707, 4.23183317545828, 3.7262860186950864, 3.1267054661448466, 2.450347848885973, 1.71796147651372, 0.9531904120981058, 0.18185080177095642, -0.568898092204015, -1.2714612829386716, -1.8987631487237622, -2.425216689392187, -2.827671805745282, -3.086307142834959, -3.185431072512673, -3.1141597779327204, -2.8669440911412543, -2.4439216194537625, -1.8510766209212663, -1.1001968513245985, -0.20862396270268124, 0.801198286710131, 1.9023660430379778, 3.0643281865146883, 4.253843721658348, 5.436051472902314, 6.575614954106252, 7.637901742970409, 8.59015466402205, 9.40261168021329, 10.0495326635744, 10.510094143027878, 10.769117627527146, 10.817603024055936, 10.653045800113613, 10.279524612454198, 9.707554827250181, 8.953712348665611, 8.040041091878031, 6.99326591825767, 5.843840541969008, 4.6248664930873815, 3.3709243982989303, 2.1168623866587852, 0.8965881802446309, -0.25808870314282295, -1.3185202381451526, -2.260148133023271, -3.0632620272697935, -3.713559651488468, -4.202489132685846, -4.527362640326342, -4.691240035921012, -4.702590708344954, -4.574750939243094, -4.325202550508084, -3.9747058714067447, -3.5463259055492706, -3.0643947180654245, -2.5534553154417505, -2.037232551896695, -1.5376748529374102, -1.0741068750423108, -0.6625277840752843, -0.315082878913933, -0.03972812629062388, 0.15990181987080546, 0.28442095415395297, 0.3384228494723789, 0.3300323718497423, 0.27030345951090645, 0.17249509433935895, 0.05126288296727713, -0.0781928526646053, -0.20098006179867545, -0.30332713922231797, -0.3733149322475676, -0.4014936436013302, -0.38135578025287503, -0.30964375508475966, -0.18647920956712002, -0.015310175083619846, 0.19731861819710483, 0.4421580980685454, 0.7077875623929728, 0.9812584727764511, 1.2488146014387846, 1.4966501321256325, 1.7116656151964589, 1.882182033947994, 1.9985756374423247, 2.0538005142708426, 2.0437719027273595, 1.9675906482949928, 1.827597648230247, 1.6292561298771249, 1.3808687261076902, 1.0931450612409916, 0.7786434832200885, 0.451117252169946, 0.12480056371120082, -0.1863270284635093], 'positive_zeros': ['1.31737736281725822880310159103607', '2.08857326794389811493460054148445', '3.31532481586158121894129071798265', '4.21747840190514633252326273798043', '4.95215756624416929126191919194391', '5.39543339134849956441538637642361', '6.60128150045515041818978576410194', '7.07027472651512352647900471119542', '8.238666685533358079470429583221172', '8.897669603403800540877668535795071'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31737736281725822880310159104', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08857326794389811493460054148', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31532481586158121894129071798', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 139, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/bn/1/17'], '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': '2-39e2-1.1-c3-0-139', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31737736281725822880310159104', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1669974204702379331158277090561', 'Lhash_array': ['1669974204702379331158277090561'], 'factors': ['2-39e2-1.1-c3-0-139'], 'label': '2-39e2-1.1-c3-0-139', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bn/1/17'}