-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1321687542971192350005153894833', 'a10': [0.0, 0.0], 'a2': [-2.6457513110645907, 0.0], 'a3': [0.0, 0.0], 'a4': [5.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-7.937253933193772, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '1321687542971192350005153894833', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.6457513110645907, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.291502622129181, 0], [11.0, 0]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [0, 0], [19.0, 0]], [[1.0, 0], [5.291502622129181, 0], [23.0, 0]], [[1.0, 0], [-10.583005244258363, 0], [29.0, 0]], [[1.0, 0], [0, 0], [31.0, 0]], [[1.0, 0], [-6.0, 0], [37.0, 0]], [[1.0, 0], [0, 0], [41.0, 0]], [[1.0, 0], [-12.0, 0], [43.0, 0]], [[1.0, 0], [0, 0], [47.0, 0]], [[1.0, 0], [-10.583005244258363, 0], [53.0, 0]], [[1.0, 0], [0, 0], [59.0, 0]], [[1.0, 0], [0, 0], [61.0, 0]], [[1.0, 0], [-4.0, 0], [67.0, 0]], [[1.0, 0], [-5.291502622129181, 0], [71.0, 0]], [[1.0, 0], [0, 0], [73.0, 0]], [[1.0, 0], [-8.0, 0], [79.0, 0]], [[1.0, 0], [0, 0], [83.0, 0]], [[1.0, 0], [0, 0], [89.0, 0]], [[1.0, 0], [0, 0], [97.0, 0]], [[1.0, 0], [0, 0], [101.0, 0]], [[1.0, 0], [0, 0], [103.0, 0]], [[1.0, 0], [-5.291502622129181, 0], [107.0, 0]], [[1.0, 0], [18.0, 0], [109.0, 0]], [[1.0, 0], [21.166010488516726, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-21e2-1.1-c1-0-2', '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/441/2/a/h/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6475855807390626, 0.641687680178108, 0.6229969718375824, 0.588756864133122, 0.5350883161666882, 0.4578746538349797, 0.3537352774904774, 0.2209773077066295, 0.06045860444818428, -0.12368924630774472, -0.3235378791261486, -0.5271145904884974, -0.7185150863760742, -0.8784565563923824, -0.9853291278807691, -1.0167643774507744, -0.951684782779616, -0.7727319213806747, -0.4689001894164793, -0.03813517398996094, 0.5103985754624267, 1.1547063298733047, 1.8593317563445753, 2.5759849283530767, 3.2456213164559644, 3.802032381294194, 4.176842569011781, 4.3056212596217325, 4.134631907151592, 3.62757882966378, 2.7716010093874353, 1.5817260870798164, 0.10305490033275998, -1.5898937950384, -3.396991337631058, -5.199435722045107, -6.869408676274978, -8.281659615100253, -9.325887903133653, -9.91856391631671, -10.012748739732123, -9.604573231095811, -8.735328768516716, -7.488586684549193, -5.982355653217635, -4.356935839597838, -2.7597478972714593, -1.3289105252725106, -0.17762699665164597, 0.6185438093444774, 1.0297401097096723, 1.0739479942671688, 0.8128103283621807, 0.34155544263607196, -0.22560722330615537, -0.7725492321729241, -1.1982247741777852, -1.4310271321195742, -1.4382611781633423, -1.2292201015306794, -0.8513639172460247, -0.3802338777356568, 0.09518814317724081, 0.48914450702775414, 0.7348515374253088, 0.7964956050406491, 0.675257052358385, 0.4081967759737892, 0.060154138839847784, -0.28985471585577927, -0.56513721748022, -0.7074675713536621, -0.689574063256947, -0.5212857775518098, -0.24784240271695687, 0.059570716153170535, 0.31936575376278203, 0.458098773861853, 0.42812579913611754, 0.22042815153613887, -0.13054194275921302, -0.5516188831870062, -0.9449160930715232, -1.2086170268983365, -1.2604235118647835, -1.0585776898681736, -0.6154646135667722, 1.506532684553507e-06, 0.6728638978422105, 1.2644339328262801, 1.6426445082008567, 1.714497302831871, 1.4535781622854924, 0.9159653379659214, 0.2396917870699544, -0.3740129084033708, -0.6957307128832106, -0.5134619680792081, 0.31964170392302976, 1.8451715800027289, 3.976068915434551, 6.496392701603567, 9.086485345228617, 11.37075713254279, 12.980485889302983, 13.620426068498551, 13.126483863961418, 11.502700487135446, 8.929244182017879, 5.7384616551927765, 2.362262417572545, -0.7400560312312849, -3.160230606757515, -4.6107700923576465, -4.972475642177889, -4.310440019441902, -2.855463470484267, -0.9548039969000677, 0.9975787721801848, 2.636977956665226, 3.6946531747573514, 4.0420293198232, 3.7041143035573043, 2.8406266046128366, 1.700326372867224, 0.5597202397214375, -0.3396197007625729, -0.8411017492096254, -0.8999325981567935, -0.5819161551117531, -0.03621730277871115, 0.5498067611280658, 1.001612075709967, 1.201292988942528, 1.1135428834753822, 0.788026990418359, 0.33874131379037714, -0.0930618020210732, -0.38163845607105884, -0.4532222492961109, -0.3062000675785934, -0.009674798399280192, 0.3188026572329798, 0.5496835641765407, 0.5813905942713596, 0.37211120411197046, -0.04600160842550333, -0.5746364774188227, -1.0771920579918006, -1.418819487009973, -1.506949013777585, -1.320110481917957, -0.9159223000836099, -0.41500382780893275, 0.035331890604571085, 0.3074453269540257, 0.33602462613367823, 0.14354027095700242, -0.16065452514488668, -0.4093775239041508, -0.4282106270046485, -0.09394183229671171, 0.616402700569759, 1.6019522603742669, 2.64976776185299, 3.482463865144658, 3.83167971926938, 3.5188980110358594, 2.5211494897634807, 1.00120395773389, -0.7101664872764956, -2.180134906417132, -2.975040615011718, -2.7732094639521625, -1.460568692104709, 0.8174866387843762, 3.6649936260474623, 6.5074337294629006, 8.71301645828617, 9.735928295546437, 9.247208521618928, 7.220469660476688, 3.949768807997398, -0.006782445801329998, -3.9456809556927004, -7.171221616030106, -9.146536125143593, -9.60615469529862, -8.603422479184594, -6.482605595280816, -3.7845514859150042, -1.1113023285471844, 1.0152634816567725, 2.265370047776812, 2.5574621782551095, 2.047809554858494, 1.0609215029830155, -0.016553621762107684, -0.8472419305032219, -1.229019781973419, -1.1338095327270699, -0.6921659135251813, -0.13262040157943134, 0.30264856948131613, 0.43861053049349663, 0.22016427305046407, -0.27759413280260736, -0.8821655370452447, -1.386534072443634, -1.6202547934683351, -1.5051783914531673, -1.0781525066643336, -0.47445338931372844, 0.1211606056522419, 0.5383111163130065, 0.6777268623583309, 0.5416232565981607, 0.2277876922510083, -0.11000410853720491, -0.32096575589538195, -0.31461932664462783, -0.09585081862423481, 0.23528489205964534, 0.5196961195776167, 0.599168573087533, 0.3789608471887955, -0.12983256585563607, -0.8048453775199355, -1.4482053715320227, -1.8532023265525344, -1.8798069728141538, -1.512315299311474, -0.8768379913853005, -0.2089425452565872, 0.2213453644451367, 0.20430934903941386, -0.3267444471142035, -1.2553282303350741, -2.302748646975883, -3.1095138357653505, -3.3557422695994163, -2.883804591363115, -1.7819947644074166, -0.39680725626637364, 0.7384668613591381, 1.0453025467721953, 0.07455048389233666, -2.336700934721066, -5.975585534652817, -10.264127118804106, -14.375125127256169, -17.427212629989587, -18.708188835475408, -17.864950903760416, -15.005485433019405, -10.68189310657611, -5.756708500819365], 'positive_zeros': ['1.04262763156758973621639725623873', '2.38459610907231863518447469134109', '4.00801398992300897065524229330236', '6.02340198806629958935966074474717', '6.70112406592555219308003279581979', '7.72390490908741287354403524651053', '8.520751961180749240367235472642433', '9.350293495462748629510472403157892', '9.957838963733577647122838300372887', '10.87499971733367981585631075971059'], 'prelabel': '2-21e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04262763156758973621639725624', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38459610907231863518447469134', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00801398992300897065524229330', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/a/h/1/1'], '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': '2-21e2-1.1-c1-0-2', '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': '2-21e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04262763156758973621639725624', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1321687542971192350005153894833', 'Lhash_array': ['1321687542971192350005153894833'], 'label': '2-21e2-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/a/h/1/1'}