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lfunc_lfunctions • Show schema
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{'Lhash': '2451227118685765314030518242800', 'a10': [0, -202.71298654496053], 'a2': [0, -2.132642534515124], 'a3': [9.162361979653552, -12.611547206976592], 'a4': [27.45183581997691, 0], 'a5': [95.05249157522277, 0], 'a6': [-26.895921999643686, -19.540042874433354], 'a7': [0, 0], 'a8': [0, -126.78951382469258], 'a9': [-75.10224590759812, -231.1031212676165], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.57642151250816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-9.162361979653552, 12.611547206976592]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.146', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'conjugate': '1696182439489661539812113600197', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.132642534515124], [-32.0, 0]], [[1.0, 0], [-9.162361979653552, 12.611547206976592]], [[1.0, 0], [-95.05249157522277, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 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'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93367724374874536721865426325', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.77029800908917887853001853818', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75762443890300064790088600126', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.57642151250816, 'bad_primes': [3, 7], 'central_character': '21.20', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 56, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/6/c/c/146/8'], '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': '2-147-21.20-c5-0-56', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-147-21.20-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.23640340936547116, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93367724374874536721865426325', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2451227118685765314030518242800', 'Lhash_array': ['2451227118685765314030518242800'], 'label': '2-147-21.20-c5-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/6/c/c/146/8'}