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{'Lhash': '889642144464144341849202108386,1047969393519783877443677069213,1600450256093879036425652759597,1838858856470018129464643118106', 'a10': 0, 'a2': 0, 'a3': 4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 6, 'a8': 0, 'a9': 5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 65047.17062986346, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '2000.1', 'coefficient_field': '1.1.1.1', 'conductor': 16000000000000, 'conductor_radical': 10, 'degree': 8, 'euler_factors': [[1], [1, -4, 11, -26, 53, -78, 99, -108, 81], [1], [1, -6, 31, -98, 305, -686, 1519, -2058, 2401], [1, 0, 12, 0, 198, 0, 1452, 0, 14641], [1, 4, 20, 44, 166, 572, 3380, 8788, 28561], [1, 4, 32, 44, 430, 748, 9248, 19652, 83521], [1, 0, 24, 0, 366, 0, 8664, 0, 130321], [1, -14, 135, -954, 5081, -21942, 71415, -170338, 279841], [1, -10, 63, -60, -67, -1740, 52983, -243890, 707281], [1, -16, 188, -1488, 9654, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 65047.17062986346, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 16000000000000, 'conductor_radical': 10, 'degree': 8, 'dirichlet_coefficients': [1, 0, 4, 0, 0, 0, 6, 0, 5, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 24, 0, 14, 0, 0, 0, 2, 0, 10, 0, 16, 0, 0, 0, 0, 0, 0, 0, -16, 0, 2, 0, 12, 0, 0, 0, 16, 0, 5, 0, -16, 0, -24, 0, 0, 0, 0, 0, -8, 0, 6, 0, 30, 0, 0, 0, -16, 0, 56, 0, 24, 0, -4, 0, 0, 0, 0, 0, 48, 0, 4, 0, 2, 0, 0, 0, 40, 0, 10, 0, -24, 0, 64, 0, 0, 0, -4, 0, 0, 0], 'euler11': [1, 0, 12, 0, 198, 0, 1452, 0, 14641], 'euler13': [1, 4, 20, 44, 166, 572, 3380, 8788, 28561], 'euler17': [1, 4, 32, 44, 430, 748, 9248, 19652, 83521], 'euler19': [1, 0, 24, 0, 366, 0, 8664, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -14, 135, -954, 5081, -21942, 71415, -170338, 279841], 'euler29': [1, -10, 63, -60, -67, -1740, 52983, -243890, 707281], 'euler3': [1, -4, 11, -26, 53, -78, 99, -108, 81], 'euler31': [1, -16, 188, -1488, 9654, -46128, 180668, -476656, 923521], 'euler37': [1, 0, 56, 400, 942, 14800, 76664, 0, 1874161], 'euler41': [1, -2, 51, 368, 69, 15088, 85731, -137842, 2825761], 'euler43': [1, -12, 219, -1614, 15165, -69402, 404931, -954084, 3418801], 'euler47': [1, -16, 239, -2102, 17509, -98794, 527951, -1661168, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 24, 388, 4200, 35766, 222600, 1089892, 3573048, 7890481], 'euler59': [1, 8, 188, 1320, 15206, 77880, 654428, 1643032, 12117361], 'euler61': [1, -6, 143, -688, 12309, -41968, 532103, -1361886, 13845841], 'euler67': [1, 16, 296, 2928, 30030, 196176, 1328744, 4812208, 20151121], 'euler7': [1, -6, 31, -98, 305, -686, 1519, -2058, 2401], 'euler71': [1, -24, 408, -4472, 42974, -317512, 2056728, -8589864, 25411681], 'euler73': [1, 4, 20, 124, 4086, 9052, 106580, 1556068, 28398241], 'euler79': [1, -48, 1152, -17616, 186414, -1391664, 7189632, -23665872, 38950081], 'euler83': [1, -2, 219, -634, 22545, -52622, 1508691, -1143574, 47458321], 'euler89': [1, -10, 219, -2260, 23381, -201140, 1734699, -7049690, 62742241], 'euler97': [1, 4, 244, 668, 31894, 64796, 2295796, 3650692, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 11, -26, 53, -78, 99, -108, 81], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -6, 31, -98, 305, -686, 1519, -2058, 2401], [1, 0, 12, 0, 198, 0, 1452, 0, 14641], [1, 4, 20, 44, 166, 572, 3380, 8788, 28561], [1, 4, 32, 44, 430, 748, 9248, 19652, 83521], [1, 0, 24, 0, 366, 0, 8664, 0, 130321], [1, -14, 135, -954, 5081, -21942, 71415, -170338, 279841], [1, -10, 63, -60, -67, -1740, 52983, -243890, 707281], [1, -16, 188, -1488, 9654, -46128, 180668, -476656, 923521], [1, 0, 56, 400, 942, 14800, 76664, 0, 1874161], [1, -2, 51, 368, 69, 15088, 85731, -137842, 2825761], [1, -12, 219, -1614, 15165, -69402, 404931, -954084, 3418801], [1, -16, 239, -2102, 17509, -98794, 527951, -1661168, 4879681], [1, 24, 388, 4200, 35766, 222600, 1089892, 3573048, 7890481], [1, 8, 188, 1320, 15206, 77880, 654428, 1643032, 12117361], [1, -6, 143, -688, 12309, -41968, 532103, -1361886, 13845841], [1, 16, 296, 2928, 30030, 196176, 1328744, 4812208, 20151121], [1, -24, 408, -4472, 42974, -317512, 2056728, -8589864, 25411681], [1, 4, 20, 124, 4086, 9052, 106580, 1556068, 28398241], [1, -48, 1152, -17616, 186414, -1391664, 7189632, -23665872, 38950081], [1, -2, 219, -634, 22545, -52622, 1508691, -1143574, 47458321], [1, -10, 219, -2260, 23381, -201140, 1734699, -7049690, 62742241], [1, 4, 244, 668, 31894, 64796, 2295796, 3650692, 88529281]], 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2000/2/a/r'], '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': '8-2000e4-1.1-c1e4-0-11', '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': '8-2000e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.99625830049261, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 2300843165531725555, 'z1': {'__RealLiteral__': 0, 'data': '0.70180390740474706208017333128', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '889642144464144341849202108386,1047969393519783877443677069213,1600450256093879036425652759597,1838858856470018129464643118106', 'Lhash_array': ['889642144464144341849202108386', '1047969393519783877443677069213', '1600450256093879036425652759597', '1838858856470018129464643118106'], 'label': '8-2000e4-1.1-c1e4-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2000/2/a/r'}