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lfunc_lfunctions • Show schema
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{'Lhash': '2486441873916814866500734407003', 'a10': -2, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': 2, 'a6': 1, 'a7': 4, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [13, [1, -1]]], 'bad_primes': [2, 3, 13], 'central_character': '78.1', 'coefficient_field': '1.1.1.1', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, -2, 5], [1, -4, 7], [1, 4, 11], [1, -1], [1, -2, 17], [1, 8, 19], [1, 0, 23], [1, -6, 29], [1, 4, 31], [1, 2, 37], [1, 10, 41], [1, -4, 43], [1, -8, 47], [1, 10, 53], [1, -4, 59], [1, 2, 61], [1, 16, 67], [1, 8, 71], [1, -2, 73], [1, -8, 79], [1, -12, 83], [1, -14, 89], [1, -10, 97], [1, 2, 101], [1, -16, 103], [1, -12, 107], [1, 2, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [[[1, -2, 5], 1]], [[[1, -4, 7], 1]], [[[1, 4, 11], 1]], 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3.107767898227066, 4.407505039243145, 5.225025743221931, 5.360662809338264, 4.725338756933028, 3.3626322174917136, 1.4455680225756713, -0.7518625905514551, -2.9032440498031256, -4.6889213218658945], 'positive_zeros': ['1.96145678743744747791090034637600', '4.91686329817785172521042266230368', '6.10664918750757402239876678097578', '7.70223650354535578507572334847258', '8.724491555695013698121297530874378', '10.33346044923143313228856689356504', '10.80469174604554316475352751747463', '12.08425672990514369865643110698984', '13.34702172357780953528143324387763', '14.56548660784257462371286700961969'], 'prelabel': '2-78-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.7891977798790284, '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': 124393021660496081, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96145678743744747791090034638', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.91686329817785172521042266230', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.10664918750757402239876678098', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 2, 1, 4, -1, 1, -2, -4, -1, 1, -4, -2, 1, 2, -1, -8, 2, -4, 4, 0, 1, -1, -1, -1, 4, 6, 2, -4, -1, 4, -2, 8, 1, -2, 8, -1, -2, -10, 4, 4, -4, 2, 0, 8, -1, 9, 1, -2, 1, -10, 1, -8, -4, 8, -6, 4, -2, -2, 4, 4, 1, 2, -4, -16, 2, 0, -8, -8, -1, 2, 2, 1, -8, -16, 1, 8, 2, 1, 10, 12, -4, 4, -4, -6, 4, 14, -2, 4, 0, 4, -8, -16, 1, 10, -9, -4, -1], 'euler11': [1, 4, 11], 'euler13': [1, -1, 0], 'euler17': [1, -2, 17], 'euler19': [1, 8, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 10, 41], 'euler43': [1, -4, 43], 'euler47': [1, -8, 47], 'euler5': [1, -2, 5], 'euler53': [1, 10, 53], 'euler59': [1, -4, 59], 'euler61': [1, 2, 61], 'euler67': [1, 16, 67], 'euler7': [1, -4, 7], 'euler71': [1, 8, 71], 'euler73': [1, -2, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -14, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, -2, 5], [1, -4, 7], [1, 4, 11], [1, -1, 0], [1, -2, 17], [1, 8, 19], [1, 0, 23], [1, -6, 29], [1, 4, 31], [1, 2, 37], [1, 10, 41], [1, -4, 43], [1, -8, 47], [1, 10, 53], [1, -4, 59], [1, 2, 61], [1, 16, 67], [1, 8, 71], [1, -2, 73], [1, -8, 79], [1, -12, 83], [1, -14, 89], [1, -10, 97]], 'index': 0, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/78/a', 'ModularForm/GL2/Q/holomorphic/78/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/78/2/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': '2-78-1.1-c1-0-0', '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': '2-78-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 124393021660496081, 'z1': {'__RealLiteral__': 0, 'data': '1.96145678743744747791090034638', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9959688
{'Lhash': '2486441873916814866500734407003', 'Lhash_array': ['2486441873916814866500734407003'], 'label': '2-78-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/a/a'}
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id: 24546438
{'Lhash': '2486441873916814866500734407003', 'Lhash_array': ['2486441873916814866500734407003'], 'label': '2-78-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/a/a/1/1'}
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id: 21856
{'Lhash': '124393021660496081', 'Lhash_array': ['124393021660496081'], 'label': '2-78-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/78/a'}