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lfunc_lfunctions • Show schema
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{'Lhash': '1368839792558529384727575858876', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.38732305983134, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '4056.1', 'coefficient_field': '1.1.1.1', 'conductor': 4056, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 4, 5], [1, 0, 7], [1, -2, 11], [1], [1, -2, 17], [1, 8, 19], [1, -4, 23], [1, 6, 29], [1, -4, 31], [1, 6, 37], [1, -12, 41], [1, -4, 43], [1, -6, 47], [1, 2, 53], [1, -14, 59], [1, -10, 61], [1, -4, 67], [1, 2, 71], [1, -2, 73], [1, 8, 79], [1, 14, 83], [1, 0, 89], [1, -10, 97], [1, 6, 101], [1, 8, 103], [1, 0, 107], [1, 10, 109], [1, 18, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, 4, 5], 1]], [[[1, 0, 7], 1]], [[[1, -2, 11], 1]], [1], [[[1, -2, 17], 1]], 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0.08012861655388917, 0.38550242024310405, 0.6502673761919678, 0.8446858240438762, 0.940865511490638, 0.9145783980396995, 0.7469340621085663], 'positive_zeros': ['1.07982419786026350977806526184536', '2.56366631530501777890828445976512', '3.79577968042543841944016859250205', '4.08354909482198954609067612446294', '4.93042833450237846123968605791295', '5.88276127937073140889212399136671', '6.80574519331477775746096519185713', '7.23347904534988993452164843589139', '8.089633598819513356691862674499328'], 'prelabel': '2-4056-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.690986123672358, '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': 1898218339772317454, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07982419786026350977806526185', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56366631530501777890828445977', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79577968042543841944016859250', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.38732305983134, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 4056, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -4, 0, 0, 0, 1, 0, 2, 0, 0, 0, 4, 0, 2, 0, -8, 0, 0, 0, 4, 0, 11, 0, -1, 0, -6, 0, 4, 0, -2, 0, 0, 0, -6, 0, 0, 0, 12, 0, 4, 0, -4, 0, 6, 0, -7, 0, -2, 0, -2, 0, -8, 0, 8, 0, 14, 0, 10, 0, 0, 0, 0, 0, 4, 0, -4, 0, -2, 0, 2, 0, -11, 0, 0, 0, -8, 0, 1, 0, -14, 0, -8, 0, 6, 0, 0, 0, 0, 0, -4, 0, 32, 0, 10, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, 0, 0], 'euler17': [1, -2, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 6, 37], 'euler41': [1, -12, 41], 'euler43': [1, -4, 43], 'euler47': [1, -6, 47], 'euler5': [1, 4, 5], 'euler53': [1, 2, 53], 'euler59': [1, -14, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 2, 71], 'euler73': [1, -2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 14, 83], 'euler89': [1, 0, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 4, 5], [1, 0, 7], [1, -2, 11], [1, 0, 0], [1, -2, 17], [1, 8, 19], [1, -4, 23], [1, 6, 29], [1, -4, 31], [1, 6, 37], [1, -12, 41], [1, -4, 43], [1, -6, 47], [1, 2, 53], [1, -14, 59], [1, -10, 61], [1, -4, 67], [1, 2, 71], [1, -2, 73], [1, 8, 79], [1, 14, 83], [1, 0, 89], [1, -10, 97]], 'index': 36, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4056/a', 'ModularForm/GL2/Q/holomorphic/4056/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/4056/2/a/a'], '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': '2-4056-1.1-c1-0-36', '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': '2-4056-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.690986123672358, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1898218339772317454, 'z1': {'__RealLiteral__': 0, 'data': '1.07982419786026350977806526185', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20000517
{'Lhash': '1368839792558529384727575858876', 'Lhash_array': ['1368839792558529384727575858876'], 'label': '2-4056-1.1-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4056/2/a/a'}
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id: 24564290
{'Lhash': '1368839792558529384727575858876', 'Lhash_array': ['1368839792558529384727575858876'], 'label': '2-4056-1.1-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4056/2/a/a/1/1'}
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id: 88364
{'Lhash': '1898218339772317454', 'Lhash_array': ['1898218339772317454'], 'label': '2-4056-1.1-c1-0-36', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4056/a'}