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lfunc_lfunctions • Show schema
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{'Lhash': '1162679616921250014362344531918', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.11613287362019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '8280.1', 'coefficient_field': '1.1.1.1', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1, -2, 7], [1, -2, 11], [1, -2, 13], [1, -8, 17], [1, -4, 19], [1, 1], [1, 2, 29], [1, -8, 31], [1, -8, 37], [1, 2, 41], [1, -8, 43], [1, 8, 47], [1, -6, 53], [1, -8, 59], [1, 8, 61], [1, 16, 67], [1, 8, 71], [1, 10, 73], [1, -10, 79], [1, 6, 83], [1, 4, 89], [1, -10, 97], [1, 6, 101], [1, -10, 103], [1, 6, 107], [1, -20, 109], [1, -16, 113]], 'euler_factors_factorization': [[1], [1], [[[1, 1], 1]], [[[1, -2, 7], 1]], [[[1, -2, 11], 1]], [[[1, -2, 13], 1]], [[[1, -8, 17], 1]], [[[1, -4, 19], 1]], [[[1, 1], 1]], [[[1, 2, 29], 1]], [[[1, -8, 31], 1]], [[[1, -8, 37], 1]], [[[1, 2, 41], 1]], [[[1, -8, 43], 1]], [[[1, 8, 47], 1]], [[[1, -6, 53], 1]], [[[1, -8, 59], 1]], [[[1, 8, 61], 1]], [[[1, 16, 67], 1]], [[[1, 8, 71], 1]], [[[1, 10, 73], 1]], [[[1, -10, 79], 1]], [[[1, 6, 83], 1]], [[[1, 4, 89], 1]], [[[1, -10, 97], 1]], [[[1, 6, 101], 1]], [[[1, -10, 103], 1]], [[[1, 6, 107], 1]], [[[1, -20, 109], 1]], [[[1, -16, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 50, 'label': '2-8280-1.1-c1-0-50', 'leading_term': '2.69067796808690844862580922084000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8280/2/a/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 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-0.6036277923494605, -0.4516338247785645, -0.2543726495658012, -0.03344238699385297, 0.18828973246073907, 0.38816314696845244, 0.5451970695766848, 0.6414721773009859, 0.6633365637155372, 0.6023610974315124, 0.45598334046990285, 0.22779698009066407], 'positive_zeros': ['0.917192495086516521312324524459658', '1.49783985006865674797499573615715', '2.82575453415142609975188364578464', '3.48929419747191510567134442335025', '4.28112548281888838223282221109833', '4.95972647220750506084694373023510', '5.80183476107929501091250268076485', '6.28988115965241922050223454588308', '7.49773612204798321584851241080483', '7.61505212632789996113508767498775'], 'prelabel': '2-8280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1666970092153680541, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.917192495086516521312324524460', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.49783985006865674797499573616', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.82575453415142609975188364578', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 66.11613287362019, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 8, 0, 4, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 8, 0, 0, 0, -2, 0, 8, 0, 0, 0, -2, 0, 8, 0, 0, 0, -8, 0, -3, 0, 0, 0, 6, 0, -2, 0, 0, 0, 8, 0, -8, 0, 0, 0, -2, 0, -16, 0, 0, 0, -8, 0, -10, 0, 0, 0, 4, 0, 10, 0, 0, 0, -6, 0, -8, 0, 0, 0, -4, 0, 4, 0, 0, 0, -4, 0, 10, 0, 0, 0], 'euler11': [1, -2, 11], 'euler13': [1, -2, 13], 'euler17': [1, -8, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, -8, 37], 'euler41': [1, 2, 41], 'euler43': [1, -8, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -8, 59], 'euler61': [1, 8, 61], 'euler67': [1, 16, 67], 'euler7': [1, -2, 7], 'euler71': [1, 8, 71], 'euler73': [1, 10, 73], 'euler79': [1, -10, 79], 'euler83': [1, 6, 83], 'euler89': [1, 4, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -2, 7], [1, -2, 11], [1, -2, 13], [1, -8, 17], [1, -4, 19], [1, 1, 0], [1, 2, 29], [1, -8, 31], [1, -8, 37], [1, 2, 41], [1, -8, 43], [1, 8, 47], [1, -6, 53], [1, -8, 59], [1, 8, 61], [1, 16, 67], [1, 8, 71], [1, 10, 73], [1, -10, 79], [1, 6, 83], [1, 4, 89], [1, -10, 97]], 'index': 50, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/8280/l', 'ModularForm/GL2/Q/holomorphic/8280/2/a/l/1/1', 'ModularForm/GL2/Q/holomorphic/8280/2/a/l'], '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': '2-8280-1.1-c1-0-50', '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': '2-8280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1666970092153680541, 'z1': {'__RealLiteral__': 0, 'data': '0.917192495086516521312324524460', 'prec': 107}}
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lfunc_instances • Show schema
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id: 22309124
{'Lhash': '1162679616921250014362344531918', 'Lhash_array': ['1162679616921250014362344531918'], 'label': '2-8280-1.1-c1-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/a/l'}
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id: 24583371
{'Lhash': '1162679616921250014362344531918', 'Lhash_array': ['1162679616921250014362344531918'], 'label': '2-8280-1.1-c1-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/a/l/1/1'}
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id: 32496
{'Lhash': '1666970092153680541', 'Lhash_array': ['1666970092153680541'], 'label': '2-8280-1.1-c1-0-50', 'type': 'ECQ', 'url': 'EllipticCurve/Q/8280/l'}