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lfunc_lfunctions • Show schema
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{'Lhash': '3038356663743876835460128171380', 'a10': [100.28604244723401, -31.622548910544154], 'a2': [-2.9741924496344456, 2.9741924496344456], 'a3': [-1.2295375648820583, -1.2295375648820583], 'a4': [0.0, -1.6916414549250864], 'a5': [-22.175530600582167, -11.543216301475248], 'a6': [7.313762684028279, 7.651431050965234e-61], 'a7': [13.095800853708795, -13.095800853708795], 'a8': [-42.5558119514243, -42.5558119514243], 'a9': [0.0, -77.9764747530878], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6179487079345525, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [22.175530600582167, 11.543216301475248]]], [7, [[1.0, 0], [-13.095800853708795, 13.095800853708795]]]], 'bad_primes': [5, 7], 'central_character': '35.8', 'coefficient_field': 'CDF', 'conductor': 35, 'conductor_radical': 35, 'conjugate': '309178057960330839395638693092', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.9741924496344456, -2.9741924496344456], 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'root_analytic_conductor': 1.9020906150692591, 'root_angle': 0.5789788057903824, 'root_number': '-0.24558122721788334 + 0.9693760162280467*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.289489402895', 'prec': 47}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.39684078814528806036840330777', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.83747352752917552830315097755', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.14565299041767772032382781919', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.6179487079345525, 'bad_primes': [5, 7], 'central_character': '5.3', 'conductor': 35, 'conductor_radical': 35, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/35/5/g/a/8/4'], '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': '2-35-5.3-c4-0-7', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-35-5.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9020906150692591, 'root_angle': 0.2894894028951912, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '2.39684078814528806036840330777', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3038356663743876835460128171380', 'Lhash_array': ['3038356663743876835460128171380'], 'label': '2-35-5.3-c4-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/35/5/g/a/8/4'}