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lfunc_lfunctions • Show schema
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{'Lhash': '508034559835507462558081004958', 'a10': [-53.52113640504698, 92.70132753236567], 'a2': [3.253962259455392, 1.1843454058673601], 'a3': [-12.054923850737676, 9.883259126063422], 'a4': [-15.32782583424638, -12.861573004265722], 'a5': [-5.367831279655728, 30.442483947086792], 'a6': [-50.93145979185894, 17.88255851592642], 'a7': [-155.79036911434332, 130.72364126481781], 'a8': [-90.04833082812011, -155.96828413107485], 'a9': [47.6423780941682, -238.2838723236055], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.330363134950478, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [12.054923850737676, -9.883259126063422]]]], 'bad_primes': [3], 'central_character': '27.4', 'coefficient_field': 'CDF', 'conductor': 27, 'conductor_radical': 3, 'conjugate': '4707380911627308089845057528595', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.253962259455392, -1.1843454058673601], [24.513422179807296, 20.56920350996926]], 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'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40076860275539670332861974446', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.68864276463237222434953188872', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.50523649057887931648763813719', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.330363134950478, 'bad_primes': [3], 'central_character': '27.4', 'conductor': 27, 'conductor_radical': 3, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/27/6/e/a/4/9'], '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': '2-3e3-27.4-c5-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-3e3-27.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0809524585993016, 'root_angle': -0.44825952061097657, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40076860275539670332861974446', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '508034559835507462558081004958', 'Lhash_array': ['508034559835507462558081004958'], 'label': '2-3e3-27.4-c5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/27/6/e/a/4/9'}