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lfunc_lfunctions • Show schema
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{'Lhash': '1815021353589822505980306364528,2221402177963793275390203928775', 'a10': -4, 'a2': -2, 'a3': 1, 'a4': 3, 'a5': 2, 'a6': -2, 'a7': 1, 'a8': -4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2108093666166183, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [5, [1, -2, 1]], [23, [1, 2, 1]]], 'bad_primes': [2, 5, 23], 'central_character': '920.1', 'coefficient_field': '1.1.1.1', 'conductor': 846400, 'conductor_radical': 230, 'degree': 4, 'euler_factors': [[1, 2, 1], [1, -1, 1, -1, 1], [1, -2, 1], [1, -1, 1, -1, 1], [1, 1, 1, 1, 1], [1, -1, 1, -1, 1], [1, -1, 1, -1, 1], [1, 1, 1, 1, 1], [1, 2, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, -1, 1, -1, 1], [1, 0, -2, 0, 1], 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'1.75237733296844512635455440747794', '2.23800770603842573270842725162556', '2.77196485177361156498303926706120', '3.23939339767830745857496642204795', '4.03701478389260513374061105235709', '5.18599575100288424312082578909105', '5.40524009394683732067828430599953', '6.08336028069096918934753856542529', '6.18340504695624293384765577468757', '6.73743174300762861739355692288783', '7.41627007879638152989695592362665', '7.84260532296579166490641690562023', '8.120156723346610306796406912803647', '8.626550527351757292402295285075400', '8.662226952428346057517387772224109', '9.259584203289496598872524031622687', '9.537024907993435210000574219110667', '10.10764631094223678100554350909866', '10.61627378094969053536091561617555'], 'prelabel': '4-920e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6775985622936063, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 1371920111443210912, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43179938798833352707471843045', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.75237733296844512635455440748', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.23800770603842573270842725163', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2108093666166183, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 846400, 'conductor_radical': 230, 'degree': 4, 'dirichlet_coefficients': [1, -2, 1, 3, 2, -2, 1, -4, 0, -4, -1, 3, 1, -2, 2, 5, 1, 0, -1, 6, 1, 2, -2, -4, 3, -2, 0, 3, 0, -4, -1, -6, -1, -2, 2, 0, 0, 2, 1, -8, -1, -2, 0, -3, 0, 4, 0, 5, 0, -6, 1, 3, 0, 0, -2, -4, -1, 0, 0, 6, -1, 2, 0, 7, 2, 2, 0, 3, -2, -4, -1, 0, 0, 0, 3, -3, -1, -2, 0, 10, 0, 2, 0, 3, 2, 0, 0, 4, 0, 0, 1, -6, -1, 0, -2, -6, 1, 0, 0, 9], 'euler11': [1, 1, 1, 1, 1], 'euler13': [1, -1, 1, -1, 1], 'euler17': [1, -1, 1, -1, 1], 'euler19': [1, 1, 1, 1, 1], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 2, 1, 0, 0], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, -1, 1, -1, 1], 'euler31': [1, 1, 1, 1, 1], 'euler37': [1, 0, -2, 0, 1], 'euler41': [1, 1, 1, 1, 1], 'euler43': [1, 0, -2, 0, 1], 'euler47': [1, 0, -2, 0, 1], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 0, -2, 0, 1], 'euler59': [1, 0, -2, 0, 1], 'euler61': [1, 1, 1, 1, 1], 'euler67': [1, 0, -2, 0, 1], 'euler7': [1, -1, 1, -1, 1], 'euler71': [1, 1, 1, 1, 1], 'euler73': [1, 0, -2, 0, 1], 'euler79': [1, 0, -2, 0, 1], 'euler83': [1, 0, -2, 0, 1], 'euler89': [1, 0, -2, 0, 1], 'euler97': [1, -1, 1, -1, 1], 'euler_factors': [[1, 2, 1, 0, 0], [1, -1, 1, -1, 1], [1, -2, 1, 0, 0], [1, -1, 1, -1, 1], [1, 1, 1, 1, 1], [1, -1, 1, -1, 1], [1, -1, 1, -1, 1], [1, 1, 1, 1, 1], [1, 2, 1, 0, 0], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 1, 1, 1, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, -1, 1, -1, 1]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/920/1/p/b'], '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': '4-920e2-1.1-c0e2-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-920e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6775985622936063, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1371920111443210912, 'z1': {'__RealLiteral__': 0, 'data': '1.43179938798833352707471843045', 'prec': 103}}
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{'Lhash': '1815021353589822505980306364528,2221402177963793275390203928775', 'Lhash_array': ['1815021353589822505980306364528', '2221402177963793275390203928775'], 'label': '4-920e2-1.1-c0e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/920/1/p/b'}