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lfunc_lfunctions • Show schema
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{'Lhash': '2032656113151264607848280196711', 'a10': [-0.8978773891157921, 0.5770307602665048], 'a2': [-0.14231483827328514, 0.9898214418809327], 'a3': [-0.41541501300188644, -0.9096319953545183], 'a4': [-0.9594929736144974, -0.28173255684142967], 'a5': [0.698938694557896, 0.8066182526008422], 'a6': [0.9594929736144974, -0.28173255684142967], 'a7': [3.7226992930514395, 2.3924335653762934], 'a8': [0.41541501300188644, -0.9096319953545183], 'a9': [-0.6548607339452851, 0.7557495743542583], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.14231483827328514, -0.9898214418809327]]], [3, [[1.0, 0], [0.41541501300188644, 0.9096319953545183]]], [23, [[1.0, 0], [4.7849189724004875, 0.32334258544439715]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.31', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': 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'root_angle': -0.2629563038326001, 'root_number': '0.6777473818641024 - 0.7352948295591059*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.131478151916', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60348294142352999779041223287', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.95403265836380024578165053345', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.76973497030798439490305308654', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'bad_primes': [2, 3, 23], 'central_character': '23.8', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/2/e/b/31/1'], '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': '2-138-23.8-c1-0-1', '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': '2-138-23.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0497311788708907, 'root_angle': -0.13147815191630005, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60348294142352999779041223287', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2032656113151264607848280196711', 'Lhash_array': ['2032656113151264607848280196711'], 'label': '2-138-23.8-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/2/e/b/31/1'}