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lfunc_lfunctions • Show schema
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{'Lhash': '1406251151477003071630155436733', 'a10': [0.0, 0.0], 'a2': [-4.017548262966229, 0.0], 'a3': [3.0, 0.0], 'a4': [8.140694045262965, 0.0], 'a5': [0.0, 0.0], 'a6': [-12.052644788898688, 0.0], 'a7': [1.7584910809647563, 0.0], 'a8': [-0.5652451171559172, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 110.62858126076371, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.017548262966229, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.7584910809647563, 0], [343.0, 0]], [[1.0, 0], [23.37032473195274, 0], [1331.0, 0]], [[1.0, 0], [53.278939717151765, 0], [2197.0, 0]], [[1.0, 0], [20.89450104197813, 0], [4913.0, 0]], [[1.0, 0], [-18.37533586148272, 0], [6859.0, 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'2.95289678907784219660141971165057', '4.42382540569786453077595268294824', '5.11991258855494968772251916250328', '6.56570575846625853088376861931230', '7.16275819960942072123694490003072', '8.103352826718793160629229313001390', '8.299610137938379766091592248044735'], 'prelabel': '2-1875-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.51801222954051, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10933655632223883562419887699', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25030664919541813849766625440', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95289678907784219660141971165', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 110.62858126076371, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 152, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/4/a/g/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': '2-1875-1.1-c3-0-152', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1875-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.51801222954051, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10933655632223883562419887699', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1406251151477003071630155436733', 'Lhash_array': ['1406251151477003071630155436733'], 'label': '2-1875-1.1-c3-0-152', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/4/a/g/1/3'}