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{'Lhash': '1253285626081049616888104263394,1716689499266967046597621345448,1995181696827380335276780739112,2500406615251068124495576912607', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -8, 'a5': -4, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43153.62199339725, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 4, 6, 4, 1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '1805.1', 'coefficient_field': '1.1.1.1', 'conductor': 10614726900625, 'conductor_radical': 95, 'degree': 8, 'euler_factors': [[1, 0, 8, 0, 24, 0, 32, 0, 16], [1, 0, 2, 0, -1, 0, 18, 0, 81], [1, 4, 6, 4, 1], [1, -2, 27, -40, 281, -280, 1323, -686, 2401], [1, 10, 59, 280, 1081, 3080, 7139, 13310, 14641], [1, 0, 42, 0, 759, 0, 7098, 0, 28561], [1, -2, 47, -80, 1141, -1360, 13583, -9826, 83521], [1], [1, -4, 58, -200, 1971, -4600, 30682, -48668, 279841], [1, 0, 96, 0, 3966, 0, 80736, 0, 707281], [1, 0, 74, 0, 2791, 0, 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-
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{'algebraic': True, 'analytic_conductor': 43153.62199339725, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 10614726900625, 'conductor_radical': 95, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, -8, -4, 0, 2, 0, -2, 0, -10, 0, 0, 0, 0, 40, 2, 0, 0, 32, 0, 0, 4, 0, 10, 0, 0, -16, 0, 0, 0, 0, 0, 0, -8, 16, 0, 0, 0, 0, 0, 0, -34, 80, 8, 0, -8, 0, -23, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, -20, 0, -4, -160, 0, 0, 0, -16, 0, 0, 0, 0, -44, 0, 0, 0, -20, 0, 0, -160, 5, 0, 16, 0, -8, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 20, -80], 'euler11': [1, 10, 59, 280, 1081, 3080, 7139, 13310, 14641], 'euler13': [1, 0, 42, 0, 759, 0, 7098, 0, 28561], 'euler17': [1, -2, 47, -80, 1141, -1360, 13583, -9826, 83521], 'euler19': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler2': [1, 0, 8, 0, 24, 0, 32, 0, 16], 'euler23': [1, -4, 58, -200, 1971, -4600, 30682, -48668, 279841], 'euler29': [1, 0, 96, 0, 3966, 0, 80736, 0, 707281], 'euler3': [1, 0, 2, 0, -1, 0, 18, 0, 81], 'euler31': [1, 0, 74, 0, 2791, 0, 71114, 0, 923521], 'euler37': [1, 0, 18, 0, 2799, 0, 24642, 0, 1874161], 'euler41': [1, 0, -6, 0, 951, 0, -10086, 0, 2825761], 'euler43': [1, 34, 603, 6800, 53201, 292400, 1114947, 2703238, 3418801], 'euler47': [1, 8, 122, 800, 8731, 37600, 269498, 830584, 4879681], 'euler5': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler53': [1, 0, 27, 0, 1449, 0, 75843, 0, 7890481], 'euler59': [1, 0, 211, 0, 18061, 0, 734491, 0, 12117361], 'euler61': [1, 20, 384, 4060, 39806, 247660, 1428864, 4539620, 13845841], 'euler67': [1, 0, 203, 0, 18829, 0, 911267, 0, 20151121], 'euler7': [1, -2, 27, -40, 281, -280, 1323, -686, 2401], 'euler71': [1, 0, 114, 0, 6111, 0, 574674, 0, 25411681], 'euler73': [1, 44, 1018, 14960, 152611, 1092080, 5424922, 17116748, 28398241], 'euler79': [1, 0, -134, 0, 15351, 0, -836294, 0, 38950081], 'euler83': [1, -16, 338, -3520, 43171, -292160, 2328482, -9148592, 47458321], 'euler89': [1, 0, 111, 0, 15921, 0, 879231, 0, 62742241], 'euler97': [1, 0, 258, 0, 35439, 0, 2427522, 0, 88529281], 'euler_factors': [[1, 0, 8, 0, 24, 0, 32, 0, 16], [1, 0, 2, 0, -1, 0, 18, 0, 81], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, -2, 27, -40, 281, -280, 1323, -686, 2401], [1, 10, 59, 280, 1081, 3080, 7139, 13310, 14641], [1, 0, 42, 0, 759, 0, 7098, 0, 28561], [1, -2, 47, -80, 1141, -1360, 13583, -9826, 83521], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 58, -200, 1971, -4600, 30682, -48668, 279841], [1, 0, 96, 0, 3966, 0, 80736, 0, 707281], [1, 0, 74, 0, 2791, 0, 71114, 0, 923521], [1, 0, 18, 0, 2799, 0, 24642, 0, 1874161], [1, 0, -6, 0, 951, 0, -10086, 0, 2825761], [1, 34, 603, 6800, 53201, 292400, 1114947, 2703238, 3418801], [1, 8, 122, 800, 8731, 37600, 269498, 830584, 4879681], [1, 0, 27, 0, 1449, 0, 75843, 0, 7890481], [1, 0, 211, 0, 18061, 0, 734491, 0, 12117361], [1, 20, 384, 4060, 39806, 247660, 1428864, 4539620, 13845841], [1, 0, 203, 0, 18829, 0, 911267, 0, 20151121], [1, 0, 114, 0, 6111, 0, 574674, 0, 25411681], [1, 44, 1018, 14960, 152611, 1092080, 5424922, 17116748, 28398241], [1, 0, -134, 0, 15351, 0, -836294, 0, 38950081], [1, -16, 338, -3520, 43171, -292160, 2328482, -9148592, 47458321], [1, 0, 111, 0, 15921, 0, 879231, 0, 62742241], [1, 0, 258, 0, 35439, 0, 2427522, 0, 88529281]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1805/2/a/k'], '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': '8-1805e4-1.1-c1e4-0-4', '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': 4, 'prelabel': '8-1805e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 2031799942448148973, 'z1': {'__RealLiteral__': 0, 'data': '0.988668033490779323044994557794', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1253285626081049616888104263394,1716689499266967046597621345448,1995181696827380335276780739112,2500406615251068124495576912607', 'Lhash_array': ['1253285626081049616888104263394', '1716689499266967046597621345448', '1995181696827380335276780739112', '2500406615251068124495576912607'], 'label': '8-1805e4-1.1-c1e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/a/k'}