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lfunc_lfunctions • Show schema
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{'Lhash': '3797978164328971521421055433416', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [13.5, -7.794228634059948], 'a4': [-16.0, -27.712812921102035], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [105.5, -75.34421012924616], 'a8': [0.0, 0.0], 'a9': [121.5, -210.4441731196186], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.368060216072594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-13.5, 7.794228634059948]]], [7, [[1.0, 0], [-105.5, 75.34421012924616]]]], 'bad_primes': [3, 7], 'central_character': '21.5', 'coefficient_field': 'CDF', 'conductor': 21, 'conductor_radical': 21, 'conjugate': '1948046618711415125905289020329', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [16.0, 27.712812921102035]], [[1.0, 0], [-13.5, 7.794228634059948]], [[1.0, 0], [0, 0], [-1562.5, -2706.329386826371]], [[1.0, 0], [-105.5, 75.34421012924616]], [[1.0, 0], [0, 0], [80525.5, -139474.25730488764]], [[1.0, 0], [0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.368060216072594, 'bad_primes': [3, 7], 'central_character': '21.5', 'conductor': 21, 'conductor_radical': 21, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/21/6/g/a/5/1'], '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': '2-21-21.5-c5-0-8', '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': '2-21-21.5-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8352275652007284, 'root_angle': 0.17147010095854204, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.99607649272218920312010938558', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3797978164328971521421055433416', 'Lhash_array': ['3797978164328971521421055433416'], 'label': '2-21-21.5-c5-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/21/6/g/a/5/1'}