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lfunc_lfunctions • Show schema
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{'Lhash': '1989112733738867885195389780705', 'a10': [0.0, 0.0], 'a2': [0.0, 1.0], 'a3': [-1.0, -1.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [1.0, -1.0], 'a7': [2.0, 0.0], 'a8': [0.0, 3.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.595138065691614, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-2.0, 3.0]]]], 'bad_primes': [5, 13], 'central_character': '325.18', 'coefficient_field': 'CDF', 'conductor': 325, 'conductor_radical': 65, 'conjugate': '1758214011041251662170607273413', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0], [-2.0, 0]], [[1.0, 0], [1.0, 1.0], [0, 3.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 0], [7.0, 0]], [[1.0, 0], [1.0, 1.0], [0, 11.0]], [[1.0, 0], [-2.0, 3.0]], [[1.0, 0], [-1.0, -1.0], [0, 17.0]], [[1.0, 0], [-5.0, -5.0], [0, 19.0]], [[1.0, 0], [-3.0, 3.0], [0, -23.0]], [[1.0, 0], [0, 0], [-29.0, 0]], [[1.0, 0], [-5.0, 5.0], [0, 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0.25666793515702424*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0413123351346', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56913327172388475004175740625', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05605240781393840939190521912', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50679979538928923128421638146', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.595138065691614, 'bad_primes': [5, 13], 'central_character': '65.18', 'conductor': 325, 'conductor_radical': 65, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/325/2/f/a/18/1'], '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': '2-325-65.18-c1-0-4', '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': '2-325-65.18-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.610943222367447, 'root_angle': -0.04131233513464198, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56913327172388475004175740625', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1989112733738867885195389780705', 'Lhash_array': ['1989112733738867885195389780705'], 'factors': ['2-325-65.18-c1-0-4'], 'label': '2-325-65.18-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/325/2/f/a/18/1'}