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lfunc_lfunctions • Show schema
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{'Lhash': '1742700982886623177161711050707', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.058381776159388, 0.0], 'a4': [0.0, 0.0], 'a5': [27.70738845815613, 0.0], 'a6': [0.0, 0.0], 'a7': [103.69000117790135, 0.0], 'a8': [0.0, 0.0], 'a9': [-233.64630091125613, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 110.34406803133069, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [43, [[1.0, 0], [-1849.0, 0]]]], 'bad_primes': [2, 43], 'central_character': '688.1', 'coefficient_field': 'CDF', 'conductor': 688, 'conductor_radical': 86, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.058381776159388, 0], [243.0, 0]], [[1.0, 0], [-27.70738845815613, 0], [3125.0, 0]], [[1.0, 0], [-103.69000117790135, 0], [16807.0, 0]], [[1.0, 0], [-158.32325759803186, 0], [161051.0, 0]], [[1.0, 0], [578.881699989335, 0], [371293.0, 0]], [[1.0, 0], [-253.87148729183173, 0], [1419857.0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 110.34406803133069, 'bad_primes': [2, 43], 'central_character': '1.1', 'conductor': 688, 'conductor_radical': 86, 'degree': 2, 'index': 83, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/688/6/a/e/1/4'], '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': '2-688-1.1-c5-0-83', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-688-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.504478474980598, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37474867488948856245032918495', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1742700982886623177161711050707', 'Lhash_array': ['1742700982886623177161711050707'], 'label': '2-688-1.1-c5-0-83', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/688/6/a/e/1/4'}