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lfunc_lfunctions • Show schema
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{'Lhash': '3045969713287096917052335112583', 'a10': [0.8349769505457066, 0.7006288512444324], 'a2': [0.6862416378687336, 0.7273736415730487], 'a3': [0.9162965771642203, -1.4698301203462711], 'a4': [-0.05814482891047583, 0.9983081582712682], 'a5': [1.082614909045931, -0.12653953473192142], 'a6': [1.6979165510167087, -0.34216865108236405], 'a7': [-0.38748509975006545, -0.19460233127203916], 'a8': [-0.766044443118978, 0.6427876096865394], 'a9': [-1.3208011653542684, -2.6936006165723243], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6862416378687336, -0.7273736415730487]]], [3, [[1.0, 0], [-0.9162965771642203, 1.4698301203462711]]]], 'bad_primes': [2, 3], 'central_character': '162.103', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '2698485340918784286985539746116', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'root_angle': -0.01862752331753452, 'root_number': '0.9982881881156476 - 0.058486694801275114*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00931376165877', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.40284642529944506437164152207', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.68870471290341662728312462710', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.96462170229026245793574890288', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.22', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/a/103/3'], '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': '2-162-81.22-c1-0-7', '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': '2-162-81.22-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': -0.00931376165876726, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.40284642529944506437164152207', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3045969713287096917052335112583', 'Lhash_array': ['3045969713287096917052335112583'], 'label': '2-162-81.22-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/103/3'}