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lfunc_lfunctions • Show schema
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{'Lhash': '1172777949178062310082477820340', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.692473971915598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [23, [1, 1]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1', 'coefficient_field': '1.1.1.1', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, 1], [1, -4, 7], [1, -6, 11], [1, 1, 13], [1, 0, 17], [1, 2, 19], [1, 1], [1, -9, 29], [1, 5, 31], [1, -2, 37], [1, 9, 41], [1, -4, 43], [1, -3, 47], [1, 6, 53], [1, 0, 59], [1, -2, 61], [1, -10, 67], [1, -3, 71], [1, 7, 73], [1, -10, 79], [1, -12, 83], [1, 0, 89], [1, -8, 97], [1, 6, 101], [1, -4, 103], [1, -18, 107], [1, -20, 109], [1, -12, 113]], 'euler_factors_factorization': [[1], [[[1, 1, 3], 1]], [[[1, 1], 1]], [[[1, -4, 7], 1]], [[[1, -6, 11], 1]], [[[1, 1, 13], 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1.0670993597768197, 1.0424660209118473, 0.9200920496475388, 0.691403765560019, 0.35244848342595, -0.09566375663410459, -0.6465613064710201, -1.2886716318190379, -2.0055454111141087, -2.7764343351385614, -3.577099706376409, -4.380816624621035, -5.159527801629118, -5.885092460020144, -6.530569827298438], 'positive_zeros': ['0.925158674611848011972962077960010', '2.05648279191482247682287196575042', '3.50555919139989069203097099190871', '4.47701693890377834352774704558317', '5.04718544999915992036153081058770', '6.10876762874484982420441460165298', '6.77421173574083519058534893805107', '7.74960017810923075341750161887311', '8.533946654129671485375276039748668', '8.992840943939303376021800431337374'], 'prelabel': '2-1840-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1324837469068570052, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.925158674611848011972962077960', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.05648279191482247682287196575', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50555919139989069203097099191', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.692473971915598, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 4, 0, -2, 0, 6, 0, -1, 0, 1, 0, 0, 0, -2, 0, -4, 0, -1, 0, 1, 0, 5, 0, 9, 0, -5, 0, -6, 0, -4, 0, 2, 0, 1, 0, -9, 0, 4, 0, 2, 0, 3, 0, 9, 0, 0, 0, -6, 0, -6, 0, 2, 0, 0, 0, 2, 0, -8, 0, 1, 0, 10, 0, 1, 0, 3, 0, -7, 0, -1, 0, 24, 0, 10, 0, 1, 0, 12, 0, 0, 0, -9, 0, 0, 0, -4, 0, 5, 0, 2, 0, 8, 0, -12, 0], 'euler11': [1, -6, 11], 'euler13': [1, 1, 13], 'euler17': [1, 0, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -9, 29], 'euler3': [1, 1, 3], 'euler31': [1, 5, 31], 'euler37': [1, -2, 37], 'euler41': [1, 9, 41], 'euler43': [1, -4, 43], 'euler47': [1, -3, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -2, 61], 'euler67': [1, -10, 67], 'euler7': [1, -4, 7], 'euler71': [1, -3, 71], 'euler73': [1, 7, 73], 'euler79': [1, -10, 79], 'euler83': [1, -12, 83], 'euler89': [1, 0, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 1, 0], [1, -4, 7], [1, -6, 11], [1, 1, 13], [1, 0, 17], [1, 2, 19], [1, 1, 0], [1, -9, 29], [1, 5, 31], [1, -2, 37], [1, 9, 41], [1, -4, 43], [1, -3, 47], [1, 6, 53], [1, 0, 59], [1, -2, 61], [1, -10, 67], [1, -3, 71], [1, 7, 73], [1, -10, 79], [1, -12, 83], [1, 0, 89], [1, -8, 97]], 'index': 12, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1840/c', 'ModularForm/GL2/Q/holomorphic/1840/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/1840/2/a/c'], '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': '2-1840-1.1-c1-0-12', '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': '2-1840-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1324837469068570052, 'z1': {'__RealLiteral__': 0, 'data': '0.925158674611848011972962077960', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20677208
{'Lhash': '1172777949178062310082477820340', 'Lhash_array': ['1172777949178062310082477820340'], 'label': '2-1840-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/a/c'}
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id: 24554757
{'Lhash': '1172777949178062310082477820340', 'Lhash_array': ['1172777949178062310082477820340'], 'label': '2-1840-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/a/c/1/1'}
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id: 27846
{'Lhash': '1324837469068570052', 'Lhash_array': ['1324837469068570052'], 'label': '2-1840-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1840/c'}