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lfunc_lfunctions • Show schema
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{'Lhash': '397551126525290885103422832415', 'a10': [-8.121320343559642, 4.688846486529344], 'a2': [0.7071067811865476, -1.224744871391589], 'a3': [0, 0], 'a4': [-1.0, -1.7320508075688772], 'a5': [-5.742640687119285, -3.3155151465676167], 'a6': [0, 0], 'a7': [0, 0], 'a8': [-2.8284271247461903, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.03275931657819, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 1.224744871391589]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.19', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '1383662790792582528460865374457', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, 1.224744871391589]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.742640687119285, 3.3155151465676167], [12.5, 21.650635094610966]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'7.26401682784675859745365888040037', '8.075738702052207823594699162513802', '8.603731422066333938645164384283402', '10.04632834159786011010691470829903'], 'prelabel': '2-882-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.902321829151794, 'root_angle': -0.1868396197206128, 'root_number': '0.83262043355876010118361245995557619348165105650587702358 - 0.5538440336596778361168746798041453088456432212030186487*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0934198098603064', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31361254154237396522775822579', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59883205973950040642520141965', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57952353694507419417180154458', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.03275931657819, 'bad_primes': [2, 3, 7], 'central_character': '7.5', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/3/n/b/19/2'], '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': '2-882-7.5-c2-0-4', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-882-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.902321829151794, 'root_angle': -0.0934198098603064, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31361254154237396522775822579', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '397551126525290885103422832415', 'Lhash_array': ['397551126525290885103422832415'], 'label': '2-882-7.5-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/3/n/b/19/2'}