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lfunc_lfunctions • Show schema
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{'Lhash': '3501366303336240058559416370564', 'a10': 2, 'a2': 2, 'a3': 0, 'a4': 2, 'a5': 1, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0779804272872857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -1]]], 'bad_primes': [3, 5], 'central_character': '135.1', 'coefficient_field': '1.1.1.1', 'conductor': 135, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, -2, 2], [1], [1, -1], [1, 3, 7], [1, -2, 11], [1, 5, 13], [1, -8, 17], [1, -1, 19], [1, 6, 23], [1, 2, 29], [1, 0, 31], [1, -5, 37], [1, -10, 41], [1, -4, 43], [1, 4, 47], [1, -2, 53], [1, -8, 59], [1, -7, 61], [1, 9, 67], [1, 2, 71], [1, 5, 73], [1, 3, 79], [1, 6, 83], [1, -12, 89], [1, 13, 97], [1, 0, 101], [1, -17, 103], [1, 6, 107], [1, 10, 109], [1, 10, 113]], 'euler_factors_factorization': [[[[1, -2, 2], 1]], [1], [[[1, -1], 1]], [[[1, 3, 7], 1]], [[[1, -2, 11], 1]], [[[1, 5, 13], 1]], [[[1, -8, 17], 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1.6854954751637345, 0.9338679767156466, 0.21880055373969076, -0.3149940850186111, -0.5832541019891105, -0.5813049822130347, -0.3802619305194396, -0.10164964352285466], 'positive_zeros': ['2.76209099156017414000056665621258', '3.97301637909484367451284003600009', '5.43765056456230093289829322534078', '6.25177698744351379012073167483721', '7.49513099271809325678009295870949', '9.412404196511086823579961082776107', '10.03955482032079710811421473574670', '11.78160851319161857295959451588120', '12.42586889673726624358472238396274', '13.16883187435091588893861858662507'], 'prelabel': '2-135-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.0382583624933082, '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': 1505421112285133339, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.76209099156017414000056665621', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.97301637909484367451284003600', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.43765056456230093289829322534', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0779804272872857, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 135, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 2, 1, 0, -3, 0, 0, 2, 2, 0, -5, -6, 0, -4, 8, 0, 1, 2, 0, 4, -6, 0, 1, -10, 0, -6, -2, 0, 0, -8, 0, 16, -3, 0, 5, 2, 0, 0, 10, 0, 4, 4, 0, -12, -4, 0, 2, 2, 0, -10, 2, 0, 2, 0, 0, -4, 8, 0, 7, 0, 0, -8, -5, 0, -9, 16, 0, -6, -2, 0, -5, 10, 0, 2, -6, 0, -3, -4, 0, 20, -6, 0, 8, 8, 0, 0, 12, 0, 15, -12, 0, -8, 1, 0, -13, 4, 0, 2], 'euler11': [1, -2, 11], 'euler13': [1, 5, 13], 'euler17': [1, -8, 17], 'euler19': [1, -1, 19], 'euler2': [1, -2, 2], 'euler23': [1, 6, 23], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -5, 37], 'euler41': [1, -10, 41], 'euler43': [1, -4, 43], 'euler47': [1, 4, 47], 'euler5': [1, -1, 0], 'euler53': [1, -2, 53], 'euler59': [1, -8, 59], 'euler61': [1, -7, 61], 'euler67': [1, 9, 67], 'euler7': [1, 3, 7], 'euler71': [1, 2, 71], 'euler73': [1, 5, 73], 'euler79': [1, 3, 79], 'euler83': [1, 6, 83], 'euler89': [1, -12, 89], 'euler97': [1, 13, 97], 'euler_factors': [[1, -2, 2], [1, 0, 0], [1, -1, 0], [1, 3, 7], [1, -2, 11], [1, 5, 13], [1, -8, 17], [1, -1, 19], [1, 6, 23], [1, 2, 29], [1, 0, 31], [1, -5, 37], [1, -10, 41], [1, -4, 43], [1, 4, 47], [1, -2, 53], [1, -8, 59], [1, -7, 61], [1, 9, 67], [1, 2, 71], [1, 5, 73], [1, 3, 79], [1, 6, 83], [1, -12, 89], [1, 13, 97]], 'index': 4, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/135/b', 'ModularForm/GL2/Q/holomorphic/135/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/135/2/a/b'], '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': '2-135-1.1-c1-0-4', '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': '2-135-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.0382583624933082, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1505421112285133339, 'z1': {'__RealLiteral__': 0, 'data': '2.76209099156017414000056665621', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9978470
{'Lhash': '3501366303336240058559416370564', 'Lhash_array': ['3501366303336240058559416370564'], 'label': '2-135-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/135/2/a/b'}
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id: 24547125
{'Lhash': '3501366303336240058559416370564', 'Lhash_array': ['3501366303336240058559416370564'], 'label': '2-135-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/135/2/a/b/1/1'}
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id: 22061
{'Lhash': '1505421112285133339', 'Lhash_array': ['1505421112285133339'], 'label': '2-135-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/135/b'}