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lfunc_lfunctions • Show schema
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{'Lhash': '1847563622035549841026914090893', 'a10': [-1.252166517039421, 1.648445496561492], 'a2': [-0.04845130173499534, 0.9245059111038091], 'a3': [-1.02661797675881, 0.8313388457702472], 'a4': [1.1366801397104782, 0.11946989682595208], 'a5': [1.8489593397583939, 1.257517141004529], 'a6': [-0.7188366996862998, -0.9893938372193897], 'a7': [-0.09932383250351391, -2.6438863016962006], 'a8': [-0.4551703834480253, 2.87383269793019], 'a9': [-0.26091487873553254, 1.227507994510106], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3973820353724073, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.8489593397583939, -1.257517141004529]]], [7, [[1.0, 0], [0.09932383250351391, 2.6438863016962006]]]], 'bad_primes': [5, 7], 'central_character': '175.47', 'coefficient_field': 'CDF', 'conductor': 175, 'conductor_radical': 35, 'conjugate': '3044186681953658679033014166037', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'root_angle': -0.2523562392932021, 'root_number': '-0.014804147300902584 - 0.9998904126066482*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.252356239293', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45747071133237516148420694300', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83458875586324885075724724857', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.95760381580388710339361403548', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3973820353724073, 'bad_primes': [5, 7], 'central_character': '175.47', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/2/x/a/47/8'], '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': '2-175-175.47-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-175-175.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.182109146979418, 'root_angle': -0.2523562392932021, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45747071133237516148420694300', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1847563622035549841026914090893', 'Lhash_array': ['1847563622035549841026914090893'], 'factors': ['2-175-175.47-c1-0-6'], 'label': '2-175-175.47-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/2/x/a/47/8'}