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lfunc_lfunctions • Show schema
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{'Lhash': '1654909481189115866515657670945', 'a10': [0.0, 0.0], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, -3.9689140359382235e-80], 'a9': [-4.582907174496108e-80, 2.645942690417643e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.2039', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '1160617080963327349061963997112', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 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'positive_zeros': ['1.30549339138968095083999445734750', '1.87499124814292530563992315569489', '3.00899310910461612365730960061565', '3.57395742603145474214721015975771', '4.82767970733724140174945465365791', '5.49951932307031143968788975977553', '7.08952523983129606988435928847379', '7.22151741026484969351553466016012', '7.993655932730052409396649925737344', '8.746300465181569890677185170596555'], 'prelabel': '2-3332-476.135-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.2929874272254411, 'root_number': '0.60546434364936736350712946050774 - 0.79587243234656694719841781696280*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.14649371361272054', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30549339138968095083999445735', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.87499124814292530563992315569', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00899310910461612365730960062', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '476.135', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/o/b/2039/1'], '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': '2-3332-476.135-c0-0-8', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-476.135-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.14649371361272054, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30549339138968095083999445735', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1654909481189115866515657670945', 'Lhash_array': ['1654909481189115866515657670945'], 'label': '2-3332-476.135-c0-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/o/b/2039/1'}