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'3.04633458623868532773860769014049', '4.09408997334598233332207530204193', '4.64352600685496654204004490721535', '5.30302606493196631508172375859684', '5.81285909666774697171903301359625', '6.67412756716473686866330176961326', '7.64906595273599130507597497485893', '8.380038696439269686947720158145440', '8.969613162791716464892144290590342', '9.482729899226382078466074170579003', '9.824922830464044406537568554503265', '10.81561993512749481374342606511790', '11.15401937956331708090151402780360', '12.26406802831175901985188697755997', '12.79982743120159785928907035200874', '13.22438384842196153938317896119857', '13.68193435754841657255604354636896'], 'prelabel': '4-45e2-1.1-c11e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.880088700451848, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c11e2-0', 'trace_hash': 96555005455898816, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.814406944419375495239036276169', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.839303104314245879140973879268', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '2.34645732011858897521570874701', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1195.461267302661, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 2025, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, 13, 0, -3519, 6250, 0, 7784, -67067, 0, 81250, -295568, 0, 657492, 101192, 0, 8258009, -8579948, 0, 17627976, -21993750, 0, -3842384, 29841072, 0, 29296875, 8547396, 0, -27391896, 201881948, 0, -71057008, 206481405, 0, -111539324, 48650000, 0, 705858484, 229163688, 0, -419168750, 327655148, 0, 3192552120, 1040103792, 0, 387933936, -2053064720, 0, 1874275970, 380859375, 0, -2313714348, 2304299452, 0, -1847300000, -522049528, 0, 2624465324, 1478770576, 0, -8264891460, -923741104, 0, -14797114959, 4109325000, 0, 24212177528, 30192837012, 0, 632450000, 20218888256, 0, 25879583268, 9176160292, 0, -62032847544, -2300701312, 0, 22324995440, 51612556250, 0, 4259516924, -48014508984, 0, -53624675000, 41503177560, 0, 19822859056, -79209683076, 0, 5117917728, -105010732368, 0, -26689841360, 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7701585589361325209940623087797432152759121], [1, 37075227452, 14646032091025247894982, 265199622162253164900027713223356, 51165609725977649453468030598885114890323009]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/12/a/c'], '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': '4-45e2-1.1-c11e2-0-2', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11, 11], 'order_of_vanishing': 0, 'prelabel': '4-45e2-1.1-c11e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.880088700451848, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c11e2-0', 'trace_hash': 96555005455898816, 'z1': {'__RealLiteral__': 0, 'data': '0.814406944419375495239036276169', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1032383451923259607664654380753,1063943083957370022412548417596', 'Lhash_array': ['1032383451923259607664654380753', '1063943083957370022412548417596'], 'label': '4-45e2-1.1-c11e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/12/a/c'}