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{'algebraic': True, 'analytic_conductor': 51874.70556843709, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 12759898410000, 'conductor_radical': 210, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 8, -8, 0, 0, 0, 0, 8, 0, 0, 0, -20, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 24, 0, 0, -4, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, -16, 0, 0, 16, 12, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, -16], 'euler11': [1, 0, 32, 0, 498, 0, 3872, 0, 14641], 'euler13': [1, 0, -38, 0, 675, 0, -6422, 0, 28561], 'euler17': [1, 0, -66, 0, 1667, 0, -19074, 0, 83521], 'euler19': [1, -8, 88, -440, 2626, -8360, 31768, -54872, 130321], 'euler2': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, -78, 0, 2555, 0, -41262, 0, 279841], 'euler29': [1, 20, 254, 2120, 13411, 61480, 213614, 487780, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -4, 118, -352, 5419, -10912, 113398, -119164, 923521], 'euler37': [1, 0, -8, 0, -702, 0, -10952, 0, 1874161], 'euler41': [1, 0, 116, 0, 6726, 0, 194996, 0, 2825761], 'euler43': [1, 0, -122, 0, 7323, 0, -225578, 0, 3418801], 'euler47': [1, 0, 12, 0, 2918, 0, 26508, 0, 4879681], 'euler5': [1, -4, 8, -20, 25, 0, 0, 0, 0], 'euler53': [1, 0, -182, 0, 13683, 0, -511238, 0, 7890481], 'euler59': [1, 20, 338, 3560, 32923, 210040, 1176578, 4107580, 12117361], 'euler61': [1, -24, 412, -4680, 42966, -285480, 1533052, -5447544, 13845841], 'euler67': [1, 0, -218, 0, 20859, 0, -978602, 0, 20151121], 'euler7': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler71': [1, 12, 326, 2592, 36219, 184032, 1643366, 4294932, 25411681], 'euler73': [1, 0, -92, 0, 11238, 0, -490268, 0, 28398241], 'euler79': [1, -16, 400, -3952, 50818, -312208, 2496400, -7888624, 38950081], 'euler83': [1, 0, -212, 0, 21558, 0, -1460468, 0, 47458321], 'euler89': [1, 44, 1082, 17072, 191395, 1519408, 8570522, 31018636, 62742241], 'euler97': [1, 0, -88, 0, 17298, 0, -827992, 0, 88529281], 'euler_factors': [[1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 8, -20, 25, 0, 0, 0, 0], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, 32, 0, 498, 0, 3872, 0, 14641], [1, 0, -38, 0, 675, 0, -6422, 0, 28561], [1, 0, -66, 0, 1667, 0, -19074, 0, 83521], [1, -8, 88, -440, 2626, -8360, 31768, -54872, 130321], [1, 0, -78, 0, 2555, 0, -41262, 0, 279841], [1, 20, 254, 2120, 13411, 61480, 213614, 487780, 707281], [1, -4, 118, -352, 5419, -10912, 113398, -119164, 923521], [1, 0, -8, 0, -702, 0, -10952, 0, 1874161], [1, 0, 116, 0, 6726, 0, 194996, 0, 2825761], [1, 0, -122, 0, 7323, 0, -225578, 0, 3418801], [1, 0, 12, 0, 2918, 0, 26508, 0, 4879681], [1, 0, -182, 0, 13683, 0, -511238, 0, 7890481], [1, 20, 338, 3560, 32923, 210040, 1176578, 4107580, 12117361], [1, -24, 412, -4680, 42966, -285480, 1533052, -5447544, 13845841], [1, 0, -218, 0, 20859, 0, -978602, 0, 20151121], [1, 12, 326, 2592, 36219, 184032, 1643366, 4294932, 25411681], [1, 0, -92, 0, 11238, 0, -490268, 0, 28398241], [1, -16, 400, -3952, 50818, -312208, 2496400, -7888624, 38950081], [1, 0, -212, 0, 21558, 0, -1460468, 0, 47458321], [1, 44, 1082, 17072, 191395, 1519408, 8570522, 31018636, 62742241], [1, 0, -88, 0, 17298, 0, -827992, 0, 88529281]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1890/2/g/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': '8-1890e4-1.1-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': '8-1890e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.884807071402903, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1243154347747105768, 'z1': {'__RealLiteral__': 0, 'data': '0.07501489018377843716941115833', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '95092670567521449634851025542,1161260347787002405543838846605,1593387769417097254352567251850,1817568469940540395888360474677', 'Lhash_array': ['95092670567521449634851025542', '1161260347787002405543838846605', '1593387769417097254352567251850', '1817568469940540395888360474677'], 'label': '8-1890e4-1.1-c1e4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1890/2/g/r'}