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lfunc_lfunctions • Show schema
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'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 870985526335563723, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69057622283079173193073362078', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82081953332938905818375982573', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00255312100191105218792907301', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 0.278787949318952, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 68574961, 'conductor_radical': 91, 'degree': 8, 'dirichlet_coefficients': [1, 3, 0, 5, 0, 0, -8, 6, 1, 0, 6, 0, -4, -24, 0, 4, 6, 3, -6, 0, 0, 18, 12, 0, 5, -12, 0, -40, 0, 0, -10, 0, 0, 18, 0, 5, 4, -18, 0, 0, 0, 0, -32, 30, 0, 36, 6, 0, 34, 15, 0, -20, 6, 0, 0, -48, 0, 0, -6, 0, -6, -30, -8, -11, 0, 0, 6, 30, 0, 0, 0, 6, -8, 12, 0, -30, -48, 0, -8, 0, 9, 0, 0, 0, 0, -96, 0, 36, 0, 0, 32, 60, 0, 18, 0, 0, -16, 102, 6, 25], 'euler11': [1, -6, 5, -54, 444, -594, 605, -7986, 14641], 'euler13': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler17': [1, -6, 13, 66, -372, 1122, 3757, -29478, 83521], 'euler19': [1, 6, -11, 54, 1164, 1026, -3971, 41154, 130321], 'euler2': [1, -3, 4, -3, 3, -6, 16, -24, 16], 'euler23': [1, -12, 67, -372, 2088, -8556, 35443, -146004, 279841], 'euler29': [1, 0, 76, 0, 3126, 0, 63916, 0, 707281], 'euler3': [1, 0, -1, 0, -8, 0, -9, 0, 81], 'euler31': [1, 10, 13, 250, 3508, 7750, 12493, 297910, 923521], 'euler37': [1, -4, -17, 164, -872, 6068, -23273, -202612, 1874161], 'euler41': [1, 0, 124, 0, 7206, 0, 208444, 0, 2825761], 'euler43': [1, 32, 556, 6176, 48214, 265568, 1028044, 2544224, 3418801], 'euler47': [1, -6, -47, 66, 2988, 3102, -103823, -622938, 4879681], 'euler5': [1, 0, -5, 0, 0, 0, -125, 0, 625], 'euler53': [1, -6, -59, 66, 4308, 3498, -165731, -893262, 7890481], 'euler59': [1, 6, -71, -66, 5844, -3894, -247151, 1232274, 12117361], 'euler61': [1, 6, -95, 54, 11244, 3294, -353495, 1361886, 13845841], 'euler67': [1, -6, -107, -54, 13548, -3618, -480323, -1804578, 20151121], 'euler7': [1, 8, 30, 56, 49, 0, 0, 0, 0], 'euler71': [1, 0, 124, 0, 13926, 0, 625084, 0, 25411681], 'euler73': [1, 8, -53, -232, 3688, -16936, -282437, 3112136, 28398241], 'euler79': [1, 8, -65, -232, 5344, -18328, -405665, 3944312, 38950081], 'euler83': [1, 0, 332, 0, 41334, 0, 2287148, 0, 47458321], 'euler89': [1, 0, -173, 0, 22008, 0, -1370333, 0, 62742241], 'euler97': [1, 16, 124, 2032, 32134, 197104, 1166716, 14602768, 88529281], 'euler_factors': [[1, -3, 4, -3, 3, -6, 16, -24, 16], [1, 0, -1, 0, -8, 0, -9, 0, 81], [1, 0, -5, 0, 0, 0, -125, 0, 625], [1, 8, 30, 56, 49, 0, 0, 0, 0], [1, -6, 5, -54, 444, -594, 605, -7986, 14641], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, -6, 13, 66, -372, 1122, 3757, -29478, 83521], [1, 6, -11, 54, 1164, 1026, -3971, 41154, 130321], [1, -12, 67, -372, 2088, -8556, 35443, -146004, 279841], [1, 0, 76, 0, 3126, 0, 63916, 0, 707281], [1, 10, 13, 250, 3508, 7750, 12493, 297910, 923521], [1, -4, -17, 164, -872, 6068, -23273, -202612, 1874161], [1, 0, 124, 0, 7206, 0, 208444, 0, 2825761], [1, 32, 556, 6176, 48214, 265568, 1028044, 2544224, 3418801], [1, -6, -47, 66, 2988, 3102, -103823, -622938, 4879681], [1, -6, -59, 66, 4308, 3498, -165731, -893262, 7890481], [1, 6, -71, -66, 5844, -3894, -247151, 1232274, 12117361], [1, 6, -95, 54, 11244, 3294, -353495, 1361886, 13845841], [1, -6, -107, -54, 13548, -3618, -480323, -1804578, 20151121], [1, 0, 124, 0, 13926, 0, 625084, 0, 25411681], [1, 8, -53, -232, 3688, -16936, -282437, 3112136, 28398241], [1, 8, -65, -232, 5344, -18328, -405665, 3944312, 38950081], [1, 0, 332, 0, 41334, 0, 2287148, 0, 47458321], [1, 0, -173, 0, 22008, 0, -1370333, 0, 62742241], [1, 16, 124, 2032, 32134, 197104, 1166716, 14602768, 88529281]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/e/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '8-91e4-1.1-c1e4-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-91e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 870985526335563723, 'z1': {'__RealLiteral__': 0, 'data': '1.69057622283079173193073362078', 'prec': 103}}
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{'Lhash': '2143059963603026036978262382969,3575813574560513991062054157778,3806188266055216048220984040972,4250782395969191235641516450959', 'Lhash_array': ['2143059963603026036978262382969', '3575813574560513991062054157778', '3806188266055216048220984040972', '4250782395969191235641516450959'], 'factors': ['2-91-7.4-c1-0-1', '2-91-7.4-c1-0-3', '2-91-7.2-c1-0-5', '2-91-7.2-c1-0-6'], 'label': '8-91e4-1.1-c1e4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/e/b'}