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lfunc_lfunctions • Show schema
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{'Lhash': '376065987705656655647966397384', 'a10': [-0.5828784078430391, 1.0095750170189974], 'a2': [-1.2273482541295773, 1.3631083310900691], 'a3': [-2.0086043982726007, 0.8942882955478534], 'a4': [-0.1426236588369252, -1.35697346996921], 'a5': [0.6216636060332036, -0.132138678613805], 'a6': [1.24624527539925, -3.835548567378711], 'a7': [1.8009618828590028, 1.9381786028353927], 'a8': [-0.9431170751984607, -0.6852146640197117], 'a9': [1.2273482541295773, -1.3631083310900691], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.763329051202452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-1.8009618828590028, -1.9381786028353927]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 11], 'central_character': '847.753', 'coefficient_field': 'CDF', 'conductor': 847, 'conductor_radical': 77, 'conjugate': '2171001844735378831403946935165', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2273482541295773, -1.3631083310900691], 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{'__RealLiteral__': 0, 'data': '0.313057642887', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.29666375548431820589050022939', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.29659477782854948752086876552', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.50300668331330301094520807504', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.763329051202452, 'bad_primes': [7, 11], 'central_character': '77.60', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/847/2/n/d/753/1'], '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': '2-847-77.60-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': '2-847-77.60-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': 0.313057642887112, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.29666375548431820589050022939', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '376065987705656655647966397384', 'Lhash_array': ['376065987705656655647966397384'], 'label': '2-847-77.60-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/2/n/d/753/1'}