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lfunc_lfunctions • Show schema
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{'Lhash': '1206067890054741507860797125668', 'a10': [0.0, 0.0], 'a2': [1.8945143887779061, 0.0], 'a3': [-3.4393573865992733, 0.0], 'a4': [1.5891847692865229, 0.0], 'a5': [0.0, 0.0], 'a6': [-6.5159120570618985, 0.0], 'a7': [4.541800845382854, 0.0], 'a8': [-0.7782953657157977, 0.0], 'a9': [8.829179232754983, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.72183505611902, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 11, 19], 'central_character': '5225.1', 'coefficient_field': 'CDF', 'conductor': 5225, 'conductor_radical': 1045, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8945143887779061, 0], [2.0, 0]], [[1.0, 0], [3.4393573865992733, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.541800845382854, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.1206028212544656, 0], [13.0, 0]], [[1.0, 0], [-4.2479926653478595, 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'4.24716014731002472222784101112219', '4.72866273912854546379782721823817', '5.16861181172217923034127119774243', '5.84408757807284018855881238498104', '6.34138313029646554758718172952901', '7.17614663544911074467494623435543', '7.86196330961411207484807499658401'], 'prelabel': '2-5225-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.459244155171642, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.951419807506579127262245606042', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.61109632673347589547063695012', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19598651054950569522782563713', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.72183505611902, 'bad_primes': [5, 11, 19], 'central_character': '1.1', 'conductor': 5225, 'conductor_radical': 1045, 'degree': 2, 'index': 130, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5225/2/a/y/1/12'], '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': '2-5225-1.1-c1-0-130', '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': '2-5225-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.459244155171642, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.951419807506579127262245606042', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1206067890054741507860797125668', 'Lhash_array': ['1206067890054741507860797125668'], 'factors': ['2-5225-1.1-c1-0-130'], 'label': '2-5225-1.1-c1-0-130', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5225/2/a/y/1/12'}