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lfunc_lfunctions • Show schema
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{'Lhash': '535476762261349641270865502932', 'a10': [0.0, 0.0], 'a2': [-1.890803853467415, 0.0], 'a3': [-2.9538817912810384, 0.0], 'a4': [-4.424860787712775, 0.0], 'a5': [0.0, 0.0], 'a6': [5.585211073641418, 0.0], 'a7': [-5.941957992863473, 0.0], 'a8': [23.492974656203494, 0.0], 'a9': [-18.274582363138325, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.025907252726803, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [19.0, 0]]]], 'bad_primes': [5, 19], 'central_character': '475.1', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.890803853467415, 0], [8.0, 0]], [[1.0, 0], [2.9538817912810384, 0], [27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.941957992863473, 0], [343.0, 0]], [[1.0, 0], [-11.517097205150698, 0], [1331.0, 0]], [[1.0, 0], [22.609333622588622, 0], [2197.0, 0]], [[1.0, 0], [120.55951153974291, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.025907252726803, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/4/a/f/1/2'], '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': '2-475-1.1-c3-0-6', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-475-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.293950061412254, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.42241668340230481051776815580', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '535476762261349641270865502932', 'Lhash_array': ['535476762261349641270865502932'], 'factors': ['2-475-1.1-c3-0-6'], 'label': '2-475-1.1-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/4/a/f/1/2'}