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lfunc_lfunctions • Show schema
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{'Lhash': '3907741983852841512117967697984', 'a10': [7.3484692283495345, 1.3179845261382144e-60], 'a2': [-1.224744871391589, 0.7071067811865476], 'a3': [2.449489742783178, 1.7320508075688772], 'a4': [1.0, -1.7320508075688772], 'a5': [-4.5, -2.598076211353316], 'a6': [-4.224744871391589, -0.3892695359907653], 'a7': [-3.1742346141747673, -5.497935626894489], 'a8': [0.0, 2.8284271247461903], 'a9': [3.0, 8.48528137423857], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4904644758485345, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.224744871391589, -0.7071067811865476]]], [3, [[1.0, 0], [-2.449489742783178, -1.7320508075688772]]]], 'bad_primes': [2, 3], 'central_character': '18.5', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '5283969117177855887966553783642', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.224744871391589, -0.7071067811865476]], [[1.0, 0], [-2.449489742783178, 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'14.73764241489512448276768414000971', '15.62508536121149116438871026815860', '17.57547673562482447420443834407290', '18.73470949071888080555396036024815'], 'prelabel': '2-18-9.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7003316898788277, 'root_angle': -0.1637290035249483, 'root_number': '0.8706029278710484 - 0.49198632296269984*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0818645017625', 'prec': 54}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.08266487875230505300547482247', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.01625851001993022562047922659', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.333607289168685714296216901136', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4904644758485345, 'bad_primes': [2, 3], 'central_character': '9.5', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/3/d/a/5/1'], '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': '2-18-9.5-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-18-9.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7003316898788277, 'root_angle': -0.08186450176247415, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.08266487875230505300547482247', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3907741983852841512117967697984', 'Lhash_array': ['3907741983852841512117967697984'], 'label': '2-18-9.5-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/3/d/a/5/1'}