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lfunc_lfunctions • Show schema
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{'Lhash': '2062744852386390881739575489892', 'a10': [0.7557752980594805, 1.108518766531201], 'a2': [-1.0232739125839008, -0.401605416390038], 'a3': [0.0, 0.0], 'a4': [-0.580301153958704, -0.5384407840531972], 'a5': [-1.008421114770422, -0.6875298746362158], 'a6': [0.0, 0.0], 'a7': [2.620562035803691, -0.3642178146444986], 'a8': [1.3314698998964454, 2.764825736026996], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.620562035803691, 0.3642178146444986]]]], 'bad_primes': [3, 7], 'central_character': '441.395', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '821262418880579321923895815091', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0232739125839008, 0.401605416390038], [1.4661037436596527, 1.3603454755418387]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.008421114770422, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62721877149351068458249528010', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.61007919565813385666159313605', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.46999510885093337903064151464', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '147.101', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/bg/a/395/6'], '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': '2-21e2-147.101-c1-0-9', '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': '2-21e2-147.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.31386709863988094, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62721877149351068458249528010', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2062744852386390881739575489892', 'Lhash_array': ['2062744852386390881739575489892'], 'label': '2-21e2-147.101-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/bg/a/395/6'}