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lfunc_lfunctions • Show schema
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{'Lhash': '973137842534824668717734550908', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-4.0, 0], 'a6': [0, 0], 'a7': [0, 11.313708498984761], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.77945290861241, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '2304.1279', 'coefficient_field': 'CDF', 'conductor': 2304, 'conductor_radical': 6, 'conjugate': '804306971231310842714097761255', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.0, 0], [25.0, 0]], [[1.0, 0], [0, -11.313708498984761], [-49.0, 0]], [[1.0, 0], [0, 14.142135623730951], [-121.0, 0]], [[1.0, 0], [-20.0, 0], [169.0, 0]], [[1.0, 0], [-10.0, 0], [289.0, 0]], [[1.0, 0], [0, 14.142135623730951], [-361.0, 0]], [[1.0, 0], [0, -11.313708498984761], [-529.0, 0]], [[1.0, 0], [20.0, 0], [841.0, 0]], 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'7.41852044335674216715256851284782', '7.86381253846379394250593175967455', '8.667599103170719997838009395824583'], 'prelabel': '2-48e2-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.923348591890452, 'root_angle': 0.0, 'root_number': '1', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76767039936684423367409329050', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.71901595482786563279102616159', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34904623498636734048225918846', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.77945290861241, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 2304, 'conductor_radical': 6, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2304/3/g/h/1279/2'], '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': '2-48e2-4.3-c2-0-41', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-48e2-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.923348591890452, 'root_angle': 0.0, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76767039936684423367409329050', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '973137842534824668717734550908', 'Lhash_array': ['973137842534824668717734550908'], 'label': '2-48e2-4.3-c2-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2304/3/g/h/1279/2'}