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lfunc_lfunctions • Show schema
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{'Lhash': '1767612445866954394412526103442', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.515792804936482, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [17, [1, 1]]], 'bad_primes': [2, 3, 17], 'central_character': '816.1', 'coefficient_field': '1.1.1.1', 'conductor': 816, 'conductor_radical': 102, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -3, 5], [1, -4, 7], [1, -3, 11], [1, 1, 13], [1, 1], [1, -1, 19], [1, 9, 23], [1, -6, 29], [1, 2, 31], [1, 4, 37], [1, 3, 41], [1, -7, 43], [1, -6, 47], [1, 6, 53], [1, 6, 59], [1, -8, 61], [1, -4, 67], [1, 12, 71], [1, -2, 73], [1, -10, 79], [1, -6, 83], [1, 0, 89], [1, 16, 97], [1, 0, 101], [1, 5, 103], [1, 9, 107], [1, -20, 109], [1, 9, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, -3, 5], 1]], [[[1, -4, 7], 1]], [[[1, -3, 11], 1]], [[[1, 1, 13], 1]], [[[1, 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4.605220476314688, 6.109053695194422, 6.542600860835741, 5.733855824863818, 3.8695361794020777, 1.4387733952143613, -0.9232638142566109], 'positive_zeros': ['1.39440035412653237109928920217197', '2.22032145426687050578358306238169', '4.10168552133706270535583651661881', '5.01602847451418763245834802499832', '5.81241206259765754250513501442080', '6.56329579539546958275321552423496', '7.66773143025981285351749668681989', '8.610578703883184504620815355063776', '9.519241921389692003197336146870383', '10.26871550815822646644778347169468'], 'prelabel': '2-816-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.5526051016435116, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 941019264469485584, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39440035412653237109928920217', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22032145426687050578358306238', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.10168552133706270535583651662', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.515792804936482, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 816, 'conductor_radical': 102, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 3, 0, 4, 0, 1, 0, 3, 0, -1, 0, -3, 0, -1, 0, 1, 0, -4, 0, -9, 0, 4, 0, -1, 0, 6, 0, -2, 0, -3, 0, 12, 0, -4, 0, 1, 0, -3, 0, 7, 0, 3, 0, 6, 0, 9, 0, 1, 0, -6, 0, 9, 0, -1, 0, -6, 0, 8, 0, 4, 0, -3, 0, 4, 0, 9, 0, -12, 0, 2, 0, -4, 0, 12, 0, 10, 0, 1, 0, 6, 0, -3, 0, -6, 0, 0, 0, -4, 0, 2, 0, 3, 0, -16, 0, 3, 0], 'euler11': [1, -3, 11], 'euler13': [1, 1, 13], 'euler17': [1, 1, 0], 'euler19': [1, -1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 9, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 2, 31], 'euler37': [1, 4, 37], 'euler41': [1, 3, 41], 'euler43': [1, -7, 43], 'euler47': [1, -6, 47], 'euler5': [1, -3, 5], 'euler53': [1, 6, 53], 'euler59': [1, 6, 59], 'euler61': [1, -8, 61], 'euler67': [1, -4, 67], 'euler7': [1, -4, 7], 'euler71': [1, 12, 71], 'euler73': [1, -2, 73], 'euler79': [1, -10, 79], 'euler83': [1, -6, 83], 'euler89': [1, 0, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -3, 5], [1, -4, 7], [1, -3, 11], [1, 1, 13], [1, 1, 0], [1, -1, 19], [1, 9, 23], [1, -6, 29], [1, 2, 31], [1, 4, 37], [1, 3, 41], [1, -7, 43], [1, -6, 47], [1, 6, 53], [1, 6, 59], [1, -8, 61], [1, -4, 67], [1, 12, 71], [1, -2, 73], [1, -10, 79], [1, -6, 83], [1, 0, 89], [1, 16, 97]], 'index': 7, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/816/g', 'ModularForm/GL2/Q/holomorphic/816/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/816/2/a/g'], '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': '2-816-1.1-c1-0-7', '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': '2-816-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.5526051016435116, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 941019264469485584, 'z1': {'__RealLiteral__': 0, 'data': '1.39440035412653237109928920217', 'prec': 103}}
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lfunc_instances • Show schema
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id: 15277565
{'Lhash': '1767612445866954394412526103442', 'Lhash_array': ['1767612445866954394412526103442'], 'label': '2-816-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/816/2/a/g'}
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id: 24550657
{'Lhash': '1767612445866954394412526103442', 'Lhash_array': ['1767612445866954394412526103442'], 'label': '2-816-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/816/2/a/g/1/1'}
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id: 96685
{'Lhash': '941019264469485584', 'Lhash_array': ['941019264469485584'], 'label': '2-816-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/816/g'}