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lfunc_lfunctions • Show schema
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{'Lhash': '1564421399687764271116756254394', 'a10': [-14.441901530770915, 0.0], 'a2': [1.4661016243026255, 0.0], 'a3': [0.0, 0.0], 'a4': [-5.850546027217203, 0.0], 'a5': [-9.850546027217204, 0.0], 'a6': [0.0, 0.0], 'a7': [29.939603331021075, 0.0], 'a8': [-20.306308027981416, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4661016243026255, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [9.850546027217204, 0], [125.0, 0]], [[1.0, 0], [-29.939603331021075, 0], [343.0, 0]], [[1.0, 0], [46.92574286102778, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-48.26163581707358, 0], [4913.0, 0]], [[1.0, 0], [-120.30020602990999, 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'3.72903590617930109952302730859731', '4.60797453178107970733814881624505', '5.15345175896201926381732051056458', '5.86996071652431033583379712785031', '7.44347447243537547688743538088162', '8.021136345663474963516144953087412', '8.309029116802398372080305134742548'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23411088150481203830956589587', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71773770013627145978133151951', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72903590617930109952302730860', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 127, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/v/1/3'], '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': '2-39e2-1.1-c3-0-127', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23411088150481203830956589587', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1564421399687764271116756254394', 'Lhash_array': ['1564421399687764271116756254394'], 'label': '2-39e2-1.1-c3-0-127', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/v/1/3'}