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lfunc_lfunctions • Show schema
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{'Lhash': '1271266188177892754820904101817', 'a10': [-8.8379274837743, 0], 'a2': [0, -2.8284271247461903], 'a3': [0, 0], 'a4': [-8.0, 0], 'a5': [0, -3.124679227705884], 'a6': [0, 0], 'a7': [18.520259177452136, 0], 'a8': [0, 22.627416997969522], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.073846045693166, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 2.8284271247461903]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-18.520259177452136, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.323', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '791739411793178470476071077911', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.8284271247461903]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.124679227705884], [-625.0, 0]], [[1.0, 0], [-18.520259177452136, 0]], [[1.0, 0], [0, -141.2660566189793], [-14641.0, 0]], [[1.0, 0], [237.62349990433026, 0], [28561.0, 0]], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.073846045693166, 'bad_primes': [2, 3, 7], 'central_character': '3.2', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/5/b/a/323/3'], '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': '2-378-3.2-c4-0-21', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-378-3.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.250907617753854, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00285219598287761496904386527', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1271266188177892754820904101817', 'Lhash_array': ['1271266188177892754820904101817'], 'label': '2-378-3.2-c4-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/5/b/a/323/3'}