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lfunc_lfunctions • Show schema
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{'Lhash': '1597466182358431410161838667936', 'a10': [-1.1636803696524594, 2.015553524008592], 'a2': [0.8660254037844386, -0.5], 'a3': [0.8660254037844386, 0.5], 'a4': [0.5, -0.8660254037844386], 'a5': [-2.015553524008592, 1.1636803696524594], 'a6': [1.0, 0.0], 'a7': [1.3162857705458995, 2.2950799049833512], 'a8': [0.0, -1.0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [-0.8660254037844386, -0.5]]], [7, [[1.0, 0], [-1.3162857705458995, -2.2950799049833512]]], [11, [[1.0, 0], [-2.4667947038209483, -2.2169627622494974]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.241', 'coefficient_field': 'CDF', 'conductor': 462, 'conductor_radical': 462, 'conjugate': '2462116697340027546875445938930', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], 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'8.151710697231345059762691731134285', '8.796650946620499053980647076503339', '10.12133406456081338848633224552123', '11.48970688004812187178797936308573'], 'prelabel': '2-462-77.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': -0.13972711419286998, 'root_number': '0.9051917388205918 - 0.4250034305402176*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0698635570964', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26017861867522612164791279033', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.35146186828858404039753899816', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03497609907603146582589451583', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'bad_primes': [2, 3, 7, 11], 'central_character': '77.10', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/462/2/p/b/241/5'], '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': '2-462-77.10-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': '2-462-77.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': -0.06986355709643499, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26017861867522612164791279033', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1597466182358431410161838667936', 'Lhash_array': ['1597466182358431410161838667936'], 'label': '2-462-77.10-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/p/b/241/5'}