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lfunc_lfunctions • Show schema
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{'Lhash': '1489952502892518279537892600971', 'a10': [11.711923739612013, -6.257676114081851], 'a2': [-2.1057442671810302, -1.8883434754393138], 'a3': [-3.741719653094971, -3.6054866575322184], 'a4': [0.868317837531548, 7.952736895750075], 'a5': [-1.6057093013638133, 4.411650047705335], 'a6': [1.070707503368864, 14.657884753341104], 'a7': [23.13556306265021, 4.079423981827398], 'a8': [13.189043520502068, -18.386112449735055], 'a9': [1.0009319247142998, 26.98144057092], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.37220628061999, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.1057442671810302, 1.8883434754393138]]], [3, [[1.0, 0], [3.741719653094971, 3.6054866575322184]]]], 'bad_primes': [2, 3], 'central_character': '108.11', 'coefficient_field': 'CDF', 'conductor': 108, 'conductor_radical': 6, 'conjugate': '1226089525198865905984248858929', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.1057442671810302, 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'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17536528016810418036730413131', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.38630273589306912199428598202', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.39887197161209375609427289612', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.37220628061999, 'bad_primes': [2, 3], 'central_character': '108.11', 'conductor': 108, 'conductor_radical': 6, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/108/4/l/a/11/12'], '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': '2-108-108.11-c3-0-20', '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': '2-108-108.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5243229350897223, 'root_angle': 0.19143164893035453, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17536528016810418036730413131', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1489952502892518279537892600971', 'Lhash_array': ['1489952502892518279537892600971'], 'label': '2-108-108.11-c3-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/108/4/l/a/11/12'}