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lfunc_lfunctions • Show schema
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{'Lhash': '1421791843648129128783297896377', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': -1, 'a8': 3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.32258304601262, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [23, [1, -1]]], 'bad_primes': [3, 5, 23], 'central_character': '5175.1', 'coefficient_field': '1.1.1.1', 'conductor': 5175, 'conductor_radical': 345, 'degree': 2, 'euler_factors': [[1, 1, 2], [1], [1], [1, 1, 7], [1, -1, 11], [1, 1, 13], [1, 0, 17], [1, 5, 19], [1, -1], [1, -5, 29], [1, 2, 31], [1, -4, 37], [1, -5, 41], [1, -9, 43], [1, 6, 47], [1, -2, 53], [1, 8, 59], [1, 8, 61], [1, 8, 67], [1, -10, 71], [1, -3, 73], [1, 3, 79], [1, -3, 83], [1, 10, 89], [1, -2, 97], [1, 10, 101], [1, -17, 103], [1, -12, 107], [1, 4, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [1], [1], [[[1, 1, 7], 1]], [[[1, -1, 11], 1]], [[[1, 1, 13], 1]], [[[1, 0, 17], 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0.1574828097830088, 0.4028286443751145, 0.5090414846898401, 0.47032190708762206, 0.29048468189041604, -0.017298330081017804, -0.4313431537163619], 'positive_zeros': ['1.12159600081611442837319704696204', '2.22295382982141256983342070394231', '3.27564888430751054574439464309070', '4.28837541819658346201034530175270', '4.71237175062719400684561071247708', '5.79964654393675512717580365011050', '6.49811005933712420621745068100990', '7.29742373656822014066497252327538', '8.004819412584731290661091407043547'], 'prelabel': '2-5175-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.4282643883098505, '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': 644513988738908347, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12159600081611442837319704696', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22295382982141256983342070394', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27564888430751054574439464309', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.32258304601262, 'bad_primes': [3, 5, 23], 'central_character': '1.1', 'conductor': 5175, 'conductor_radical': 345, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, -1, 3, 0, 0, 1, 0, -1, 1, 0, -1, 0, 0, -5, 0, 0, -1, 1, 0, 0, 1, 0, 1, 5, 0, -2, -5, 0, 0, 0, 0, 4, 5, 0, 0, 5, 0, 9, -1, 0, -1, -6, 0, -6, 0, 0, 1, 2, 0, 0, -3, 0, -5, -8, 0, -8, 2, 0, 7, 0, 0, -8, 0, 0, 0, 10, 0, 3, -4, 0, 5, -1, 0, -3, 0, 0, -5, 3, 0, 0, -9, 0, 3, -10, 0, 1, -1, 0, 6, 0, 0, 2, 6, 0, 0], 'euler11': [1, -1, 11], 'euler13': [1, 1, 13], 'euler17': [1, 0, 17], 'euler19': [1, 5, 19], 'euler2': [1, 1, 2], 'euler23': [1, -1, 0], 'euler29': [1, -5, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, -4, 37], 'euler41': [1, -5, 41], 'euler43': [1, -9, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, 8, 59], 'euler61': [1, 8, 61], 'euler67': [1, 8, 67], 'euler7': [1, 1, 7], 'euler71': [1, -10, 71], 'euler73': [1, -3, 73], 'euler79': [1, 3, 79], 'euler83': [1, -3, 83], 'euler89': [1, 10, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 2], [1, 0, 0], [1, 0, 0], [1, 1, 7], [1, -1, 11], [1, 1, 13], [1, 0, 17], [1, 5, 19], [1, -1, 0], [1, -5, 29], [1, 2, 31], [1, -4, 37], [1, -5, 41], [1, -9, 43], [1, 6, 47], [1, -2, 53], [1, 8, 59], [1, 8, 61], [1, 8, 67], [1, -10, 71], [1, -3, 73], [1, 3, 79], [1, -3, 83], [1, 10, 89], [1, -2, 97]], 'index': 92, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5175/e', 'ModularForm/GL2/Q/holomorphic/5175/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/5175/2/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': '2-5175-1.1-c1-0-92', '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': '2-5175-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.4282643883098505, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 644513988738908347, 'z1': {'__RealLiteral__': 0, 'data': '1.12159600081611442837319704696', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21446389
{'Lhash': '1421791843648129128783297896377', 'Lhash_array': ['1421791843648129128783297896377'], 'label': '2-5175-1.1-c1-0-92', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5175/2/a/e'}
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id: 24569191
{'Lhash': '1421791843648129128783297896377', 'Lhash_array': ['1421791843648129128783297896377'], 'label': '2-5175-1.1-c1-0-92', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5175/2/a/e/1/1'}
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id: 34080
{'Lhash': '644513988738908347', 'Lhash_array': ['644513988738908347'], 'label': '2-5175-1.1-c1-0-92', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5175/e'}