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lfunc_lfunctions • Show schema
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{'Lhash': '256656453382987217953206655603', 'a10': [-207.33299493803318, -83.7438308774175], 'a2': [2.3511410091698925, 3.23606797749979], 'a3': [-1.612400240293325, -0.5239005962819724], 'a4': [-4.944271909999159, 15.216904260722456], 'a5': [-47.404364773024525, 29.62813190982569], 'a6': [-2.0956023851278895, -6.4496009611733], 'a7': [0.0, -48.28554762538719], 'a8': [-60.867617042889826, 19.777087639996637], 'a9': [-194.26576693299884, -141.14234141240124], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.019190990649033, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.3511410091698925, -3.23606797749979]]], [5, [[1.0, 0], [47.404364773024525, -29.62813190982569]]]], 'bad_primes': [2, 5], 'central_character': '50.39', 'coefficient_field': 'CDF', 'conductor': 50, 'conductor_radical': 10, 'conjugate': '3989443192776862585222585853283', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.3511410091698925, 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'0.452190365115', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20246624214651771449074400464', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66658121630143693687736297885', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47054497802174176583554786572', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.019190990649033, 'bad_primes': [2, 5], 'central_character': '25.14', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/6/e/a/39/10'], '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': '2-50-25.14-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': '2-50-25.14-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8318176125324586, 'root_angle': 0.45219036511532873, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.20246624214651771449074400464', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '256656453382987217953206655603', 'Lhash_array': ['256656453382987217953206655603'], 'label': '2-50-25.14-c5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/6/e/a/39/10'}