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lfunc_lfunctions • Show schema
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{'Lhash': '907970991961867959037697649541', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-9.0, 0.0], 'a4': [0.0, 0.0], 'a5': [59.11228777523818, 0.0], 'a6': [0.0, 0.0], 'a7': [213.33142572287804, 0.0], 'a8': [0.0, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 177.06373707353066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [9.0, 0]]], [23, [[1.0, 0], [529.0, 0]]]], 'bad_primes': [2, 3, 23], 'central_character': '1104.1', 'coefficient_field': 'CDF', 'conductor': 1104, 'conductor_radical': 138, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [-59.11228777523818, 0], [3125.0, 0]], [[1.0, 0], [-213.33142572287804, 0], [16807.0, 0]], [[1.0, 0], [126.52827629474035, 0], [161051.0, 0]], [[1.0, 0], [884.8249725872421, 0], [371293.0, 0]], [[1.0, 0], [1179.9768176835032, 0], [1419857.0, 0]], [[1.0, 0], [-1866.1859418735621, 0], 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'positive_zeros': ['0.71626281863345919185195161957072', '1.86775682483801940134749855614326', '2.43246183019761534113611735159133', '4.17947168033845633895659373355951', '5.20093306216359464471033720483569', '5.34728356545657878823304812280969', '6.58303243157568296666509564246040', '7.50279976997768361363030323144990', '8.155780508294512096787089533567090', '9.376837489818463934051585563115441'], 'prelabel': '2-1104-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.306529865954184, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71626281863345919185195161957', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86775682483801940134749855614', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.43246183019761534113611735159', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 177.06373707353066, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 1104, 'conductor_radical': 138, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1104/6/a/i/1/3'], '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': '2-1104-1.1-c5-0-38', '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': '2-1104-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.306529865954184, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71626281863345919185195161957', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '907970991961867959037697649541', 'Lhash_array': ['907970991961867959037697649541'], 'label': '2-1104-1.1-c5-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1104/6/a/i/1/3'}