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lfunc_lfunctions • Show schema
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{'Lhash': '430738372938769751769991647241', 'a10': [-0.7530203962825329, 0.0], 'a2': [-1.0, 0.0], 'a3': [-0.4450418679126288, 0.0], 'a4': [1.0, 0.0], 'a5': [0.7530203962825329, 0.0], 'a6': [0.4450418679126288, 0.0], 'a7': [-1.6038754716096766, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.801937735804838, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 51.279928178066285, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 13, 19], 'central_character': '6422.1', 'coefficient_field': 'CDF', 'conductor': 6422, 'conductor_radical': 494, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0.4450418679126288, 0], [3.0, 0]], [[1.0, 0], [-0.7530203962825329, 0], [5.0, 0]], [[1.0, 0], [1.6038754716096766, 0], [7.0, 0]], [[1.0, 0], [3.6038754716096766, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.4058132074145147, 0], [17.0, 0]], 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'3.38268243412735518275813664819605', '4.45528246335055739215434978238545', '5.42537299189259288773018379558772', '6.12139456677838306510917710530531', '6.37620833273903950312954745428256', '7.62975890065188176774797410667908', '7.912319902498915708627680453969637'], 'prelabel': '2-6422-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.161000501191595, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33979266278990368143120891231', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88472552262529936655715397395', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.58838842449701138410649643717', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 51.279928178066285, 'bad_primes': [2, 13, 19], 'central_character': '1.1', 'conductor': 6422, 'conductor_radical': 494, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6422/2/a/n/1/2'], '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': '2-6422-1.1-c1-0-13', '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': '2-6422-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.161000501191595, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.33979266278990368143120891231', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '430738372938769751769991647241', 'Lhash_array': ['430738372938769751769991647241'], 'label': '2-6422-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6422/2/a/n/1/2'}