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lfunc_lfunctions • Show schema
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{'Lhash': '3146349856095177447500378181317', 'a10': -4, 'a2': 1, 'a3': -1, 'a4': 1, 'a5': -4, 'a6': -1, 'a7': 1, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [7, [1, -1]], [11, [1, 1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.1', 'coefficient_field': '1.1.1.1', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, 4, 5], [1, -1], [1, 1], [1, 6, 13], [1, 4, 17], [1, 2, 19], [1, 8, 23], [1, 6, 29], [1, -6, 31], [1, 6, 37], [1, -12, 41], [1, -4, 43], [1, -6, 47], [1, -2, 53], [1, 0, 59], [1, -10, 61], [1, -4, 67], [1, 12, 71], [1, 0, 73], [1, 16, 79], [1, 14, 83], [1, 14, 89], [1, 14, 97], [1, -14, 101], [1, 6, 103], [1, 8, 107], [1, -6, 109], [1, -14, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 1], 1]], [[[1, 4, 5], 1]], [[[1, -1], 1]], [[[1, 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-0.1644846520423079, 0.5856144236241305, 0.9532002493348076, 0.89299842523265, 0.5225100643636775, 0.07323679854214701, -0.20018891904837163, -0.12056125498317809, 0.33790467395184626, 1.0296127492919356], 'positive_zeros': ['2.48203239562124190952326585155110', '4.10732223636165202223499092608872', '4.50182617970418156245344086250213', '5.68884256231510340821014445654805', '7.06196128452260537589494409618512', '7.56853928475057757956492711753781', '8.515253748126092137293786902707577', '10.01228279213210772511711883999981', '10.99555820546878314855420687835501'], 'prelabel': '2-462-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1734542168263096860, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.48203239562124190952326585155', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.10732223636165202223499092609', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50182617970418156245344086250', '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': '1.1', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, -4, -1, 1, 1, 1, -4, -1, -1, -6, 1, 4, 1, -4, 1, -2, -4, -1, -1, -8, -1, 11, -6, -1, 1, -6, 4, 6, 1, 1, -4, -4, 1, -6, -2, 6, -4, 12, -1, 4, -1, -4, -8, 6, -1, 1, 11, 4, -6, 2, -1, 4, 1, 2, -6, 0, 4, 10, 6, 1, 1, 24, 1, 4, -4, 8, -4, -12, 1, 0, -6, -11, -2, -1, 6, -16, -4, 1, 12, -14, -1, 16, 4, 6, -1, -14, -4, -6, -8, -6, 6, 8, -1, -14, 1, -1, 11], 'euler11': [1, 1, 0], 'euler13': [1, 6, 13], 'euler17': [1, 4, 17], 'euler19': [1, 2, 19], 'euler2': [1, -1, 0], 'euler23': [1, 8, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -6, 31], 'euler37': [1, 6, 37], 'euler41': [1, -12, 41], 'euler43': [1, -4, 43], 'euler47': [1, -6, 47], 'euler5': [1, 4, 5], 'euler53': [1, -2, 53], 'euler59': [1, 0, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 12, 71], 'euler73': [1, 0, 73], 'euler79': [1, 16, 79], 'euler83': [1, 14, 83], 'euler89': [1, 14, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 4, 5], [1, -1, 0], [1, 1, 0], [1, 6, 13], [1, 4, 17], [1, 2, 19], [1, 8, 23], [1, 6, 29], [1, -6, 31], [1, 6, 37], [1, -12, 41], [1, -4, 43], [1, -6, 47], [1, -2, 53], [1, 0, 59], [1, -10, 61], [1, -4, 67], [1, 12, 71], [1, 0, 73], [1, 16, 79], [1, 14, 83], [1, 14, 89], [1, 14, 97]], 'index': 8, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/462/e', 'ModularForm/GL2/Q/holomorphic/462/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/462/2/a/e'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-462-1.1-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-462-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1734542168263096860, 'z1': {'__RealLiteral__': 0, 'data': '2.48203239562124190952326585155', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10913815
{'Lhash': '3146349856095177447500378181317', 'Lhash_array': ['3146349856095177447500378181317'], 'label': '2-462-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/a/e'}
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id: 24549430
{'Lhash': '3146349856095177447500378181317', 'Lhash_array': ['3146349856095177447500378181317'], 'label': '2-462-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/a/e/1/1'}
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id: 22333
{'Lhash': '1734542168263096860', 'Lhash_array': ['1734542168263096860'], 'label': '2-462-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/462/e'}