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lfunc_lfunctions • Show schema
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{'Lhash': '3267273504816153220826459279697', 'a10': 6, 'a2': 2, 'a3': 0, 'a4': 2, 'a5': 3, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4293221961809195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[179, [1, -1]]], 'bad_primes': [179], 'central_character': '179.1', 'coefficient_field': '1.1.1.1', 'conductor': 179, 'conductor_radical': 179, 'degree': 2, 'euler_factors': [[1, -2, 2], [1, 0, 3], [1, -3, 5], [1, 4, 7], [1, -4, 11], [1, 1, 13], [1, -1, 17], [1, 3, 19], [1, -6, 23], [1, -3, 29], [1, 8, 31], [1, -2, 37], [1, -12, 41], [1, 11, 43], [1, -1, 47], [1, 0, 53], [1, 5, 59], [1, -14, 61], [1, 9, 67], [1, 0, 71], [1, -10, 73], [1, -10, 79], [1, -17, 83], [1, 1, 89], [1, 14, 97], [1, -9, 101], [1, 6, 103], [1, 4, 107], [1, 14, 109], [1, 4, 113]], 'euler_factors_factorization': [[[[1, -2, 2], 1]], [[[1, 0, 3], 1]], [[[1, -3, 5], 1]], [[[1, 4, 7], 1]], [[[1, -4, 11], 1]], [[[1, 1, 13], 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{'__RealLiteral__': 0, 'data': '3.65455224933898053965548391576', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.26927125289354544444142895540', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4293221961809195, 'bad_primes': [179], 'central_character': '1.1', 'conductor': 179, 'conductor_radical': 179, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 2, 3, 0, -4, 0, -3, 6, 4, 0, -1, -8, 0, -4, 1, -6, -3, 6, 0, 8, 6, 0, 4, -2, 0, -8, 3, 0, -8, -8, 0, 2, -12, -6, 2, -6, 0, 0, 12, 0, -11, 8, -9, 12, 1, 0, 9, 8, 0, -2, 0, 0, 12, 0, 0, 6, -5, 0, 14, -16, 12, -8, -3, 0, -9, 2, 0, -24, 0, 0, 10, 4, 0, -6, -16, 0, 10, -12, 9, 24, 17, 0, 3, -22, 0, 0, -1, -18, 4, 12, 0, 2, -9, 0, -14, 18, -12, 8], 'euler11': [1, -4, 11], 'euler13': [1, 1, 13], 'euler17': [1, -1, 17], 'euler19': [1, 3, 19], 'euler2': [1, -2, 2], 'euler23': [1, -6, 23], 'euler29': [1, -3, 29], 'euler3': [1, 0, 3], 'euler31': [1, 8, 31], 'euler37': [1, -2, 37], 'euler41': [1, -12, 41], 'euler43': [1, 11, 43], 'euler47': [1, -1, 47], 'euler5': [1, -3, 5], 'euler53': [1, 0, 53], 'euler59': [1, 5, 59], 'euler61': [1, -14, 61], 'euler67': [1, 9, 67], 'euler7': [1, 4, 7], 'euler71': [1, 0, 71], 'euler73': [1, -10, 73], 'euler79': [1, -10, 79], 'euler83': [1, -17, 83], 'euler89': [1, 1, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, -2, 2], [1, 0, 3], [1, -3, 5], [1, 4, 7], [1, -4, 11], [1, 1, 13], [1, -1, 17], [1, 3, 19], [1, -6, 23], [1, -3, 29], [1, 8, 31], [1, -2, 37], [1, -12, 41], [1, 11, 43], [1, -1, 47], [1, 0, 53], [1, 5, 59], [1, -14, 61], [1, 9, 67], [1, 0, 71], [1, -10, 73], [1, -10, 79], [1, -17, 83], [1, 1, 89], [1, 14, 97]], 'index': 10, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/179/a', 'ModularForm/GL2/Q/holomorphic/179/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/179/2/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': '2-179-1.1-c1-0-10', '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': '2-179-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.1955426367055755, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1179237647618595272, 'z1': {'__RealLiteral__': 0, 'data': '2.57742433461389850447314956434', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10008878
{'Lhash': '3267273504816153220826459279697', 'Lhash_array': ['3267273504816153220826459279697'], 'label': '2-179-1.1-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/179/2/a/a'}
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id: 24547762
{'Lhash': '3267273504816153220826459279697', 'Lhash_array': ['3267273504816153220826459279697'], 'label': '2-179-1.1-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/179/2/a/a/1/1'}
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id: 21943
{'Lhash': '1179237647618595272', 'Lhash_array': ['1179237647618595272'], 'label': '2-179-1.1-c1-0-10', 'type': 'ECQ', 'url': 'EllipticCurve/Q/179/a'}