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lfunc_lfunctions • Show schema
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{'Lhash': '327103833930317066063076233551', 'a10': [-11.583123951776999, 0.0], 'a2': [2.3166247903554, 0.0], 'a3': [0.0, 0.0], 'a4': [-2.6332495807107996, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-24.6332495807108, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 130.09921156265813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [5.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '2205.1', 'coefficient_field': 'CDF', 'conductor': 2205, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.3166247903554, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [46.2664991614216, 0], [1331.0, 0]], [[1.0, 0], [61.332495807107996, 0], [2197.0, 0]], [[1.0, 0], [101.332495807108, 0], [4913.0, 0]], [[1.0, 0], [-3.667504192892003, 0], [6859.0, 0]], [[1.0, 0], 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'3.95134973313219901378139161799830', '4.85891926897435628495308125875285', '5.11600439857610325225680719294482', '6.28093293821484073503299374379424', '7.02344270068642938161531517505022', '8.052355647212777719591672763676619', '8.488961836633519815974487581539509'], 'prelabel': '2-2205-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.406104136060573, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25803942653553343656550071592', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18604365952443284349527720437', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94948912226666004718973292477', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 130.09921156265813, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 2205, 'conductor_radical': 105, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2205/4/a/w/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': '2-2205-1.1-c3-0-5', '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': '2-2205-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.406104136060573, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.25803942653553343656550071592', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '327103833930317066063076233551', 'Lhash_array': ['327103833930317066063076233551'], 'label': '2-2205-1.1-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2205/4/a/w/1/2'}