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'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 117457165597743376, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78822635668050129084102553276', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.23666480672488397365551188686', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.29922943881697012518481396061', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 29327719.396729242, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 7213895789838336, 'conductor_radical': 6, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, -24, 0, 0, 0, 0, 0, 16, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 64, 0, 0, 0, 0, 0, -16, 0, 0, 0], 'euler11': [1, 0, 28, 0, 406, 0, 3388, 0, 14641], 'euler13': [1, 8, 40, 136, 514, 1768, 6760, 17576, 28561], 'euler17': [1, 0, 36, 64, 614, 1088, 10404, 0, 83521], 'euler19': [1, 0, 44, -64, 918, -1216, 15884, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -16, 188, -1360, 7846, -31280, 99452, -194672, 279841], 'euler29': [1, 0, 72, 112, 2426, 3248, 60552, 0, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 8, 108, 616, 5022, 19096, 103788, 238328, 923521], 'euler37': [1, 8, 104, 776, 5346, 28712, 142376, 405224, 1874161], 'euler41': [1, 0, 68, -64, 3206, -2624, 114308, 0, 2825761], 'euler43': [1, 0, 76, 64, 3830, 2752, 140524, 0, 3418801], 'euler47': [1, -16, 220, -2000, 16518, -94000, 485980, -1661168, 4879681], 'euler5': [1, 0, 8, 16, 26, 80, 200, 0, 625], 'euler53': [1, 0, 104, 272, 5594, 14416, 292136, 0, 7890481], 'euler59': [1, -16, 204, -1552, 12758, -91568, 710124, -3286064, 12117361], 'euler61': [1, 24, 392, 4568, 40386, 278648, 1458632, 5447544, 13845841], 'euler67': [1, -16, 172, -912, 6134, -61104, 772108, -4812208, 20151121], 'euler7': [1, 8, 44, 168, 510, 1176, 2156, 2744, 2401], 'euler71': [1, -16, 284, -2640, 28070, -187440, 1431644, -5726576, 25411681], 'euler73': [1, 8, 172, 1720, 16006, 125560, 916588, 3112136, 28398241], 'euler79': [1, 24, 396, 4344, 42398, 343176, 2471436, 11832936, 38950081], 'euler83': [1, 0, 252, 128, 28598, 10624, 1736028, 0, 47458321], 'euler89': [1, -8, 188, -2424, 17894, -215736, 1489148, -5639752, 62742241], 'euler97': [1, 16, 356, 4400, 49990, 426800, 3349604, 14602768, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 8, 16, 26, 80, 200, 0, 625], [1, 8, 44, 168, 510, 1176, 2156, 2744, 2401], [1, 0, 28, 0, 406, 0, 3388, 0, 14641], [1, 8, 40, 136, 514, 1768, 6760, 17576, 28561], [1, 0, 36, 64, 614, 1088, 10404, 0, 83521], [1, 0, 44, -64, 918, -1216, 15884, 0, 130321], [1, -16, 188, -1360, 7846, -31280, 99452, -194672, 279841], [1, 0, 72, 112, 2426, 3248, 60552, 0, 707281], [1, 8, 108, 616, 5022, 19096, 103788, 238328, 923521], [1, 8, 104, 776, 5346, 28712, 142376, 405224, 1874161], [1, 0, 68, -64, 3206, -2624, 114308, 0, 2825761], [1, 0, 76, 64, 3830, 2752, 140524, 0, 3418801], [1, -16, 220, -2000, 16518, -94000, 485980, -1661168, 4879681], [1, 0, 104, 272, 5594, 14416, 292136, 0, 7890481], [1, -16, 204, -1552, 12758, -91568, 710124, -3286064, 12117361], [1, 24, 392, 4568, 40386, 278648, 1458632, 5447544, 13845841], [1, -16, 172, -912, 6134, -61104, 772108, -4812208, 20151121], [1, -16, 284, -2640, 28070, -187440, 1431644, -5726576, 25411681], [1, 8, 172, 1720, 16006, 125560, 916588, 3112136, 28398241], [1, 24, 396, 4344, 42398, 343176, 2471436, 11832936, 38950081], [1, 0, 252, 128, 28598, 10624, 1736028, 0, 47458321], [1, -8, 188, -2424, 17894, -215736, 1489148, -5639752, 62742241], [1, 16, 356, 4400, 49990, 426800, 3349604, 14602768, 88529281]], 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9216/2/a/z'], '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': '8-96e8-1.1-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': 4, 'prelabel': '8-96e8-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.578469006927287, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 117457165597743376, 'z1': {'__RealLiteral__': 0, 'data': '0.78822635668050129084102553276', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '999195614161747899264518237138,1567658884525926472825650251265,1646968977950517826600699195139,1742231874951506327528297713471', 'Lhash_array': ['999195614161747899264518237138', '1567658884525926472825650251265', '1646968977950517826600699195139', '1742231874951506327528297713471'], 'label': '8-96e8-1.1-c1e4-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9216/2/a/z'}