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lfunc_lfunctions • Show schema
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{'Lhash': '3189277974859191817227541294178', 'a10': [-0.18258535996841205, 0.501649153636206], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [1.08684112613441, -1.3486201713391683], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [0.3431482308517112, -0.40894813690987414], 'a6': [-0.5600413219018414, 1.639009980983166], 'a7': [-0.7165074073694839, -1.2410272335633972], 'a8': [-0.5, 0.8660254037844386], 'a9': [-0.6375527330857754, -2.931471731491685], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9396926207859084, -0.3420201433256687]]], [3, [[1.0, 0], [-1.08684112613441, 1.3486201713391683]]], [19, [[1.0, 0], [4.356527904876909, -0.14375191834827536]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.71', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '2016445087061890568575656107539', 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'0.111323125378', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.51589671024885738769020426549', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.95619283489636826910107381957', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.80112781434154559381475433484', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '57.14', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/l/b/71/3'], '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': '2-114-57.14-c1-0-4', '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': '2-114-57.14-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.11132312537822751, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.51589671024885738769020426549', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3189277974859191817227541294178', 'Lhash_array': ['3189277974859191817227541294178'], 'label': '2-114-57.14-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/l/b/71/3'}