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'trace_hash': 1646009676423454580, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26658342085501437107866700878', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.39716261025333494909450183199', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.09546783326443414423385665230', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 152548.95646688485, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 37523281640625, 'conductor_radical': 165, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -3, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 4, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, -22, 0, 0, 3, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 12, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler13': [1, 0, -31, 0, 472, 0, -5239, 0, 28561], 'euler17': [1, 0, -35, 0, 676, 0, -10115, 0, 83521], 'euler19': [1, 12, 130, 792, 4299, 15048, 46930, 82308, 130321], 'euler2': [1, 0, 1, 0, 4, 0, 4, 0, 16], 'euler23': [1, 0, -43, 0, 1176, 0, -22747, 0, 279841], 'euler29': [1, 4, 88, 284, 3678, 8236, 74008, 97556, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 6, 61, 342, 3156, 10602, 58621, 178746, 923521], 'euler37': [1, 0, 65, 0, 3688, 0, 88985, 0, 1874161], 'euler41': [1, 6, 101, 522, 6216, 21402, 169781, 413526, 2825761], 'euler43': [1, 0, -91, 0, 5424, 0, -168259, 0, 3418801], 'euler47': [1, 0, -67, 0, 4584, 0, -148003, 0, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -160, 0, 11406, 0, -449440, 0, 7890481], 'euler59': [1, 34, 661, 8330, 75660, 491470, 2300941, 6982886, 12117361], 'euler61': [1, 22, 417, 4598, 44108, 280478, 1551657, 4993582, 13845841], 'euler67': [1, 0, -191, 0, 18060, 0, -857399, 0, 20151121], 'euler7': [1, 0, -26, 0, 267, 0, -1274, 0, 2401], 'euler71': [1, 6, 85, 654, 12804, 46434, 428485, 2147466, 25411681], 'euler73': [1, 0, -28, 0, -6554, 0, -149212, 0, 28398241], 'euler79': [1, -38, 781, -10982, 113620, -867578, 4874221, -18735482, 38950081], 'euler83': [1, 0, -332, 0, 41334, 0, -2287148, 0, 47458321], 'euler89': [1, -52, 1336, -21788, 245070, -1939132, 10582456, -36658388, 62742241], 'euler97': [1, 0, -346, 0, 48475, 0, -3255514, 0, 88529281], 'euler_factors': [[1, 0, 1, 0, 4, 0, 4, 0, 16], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -26, 0, 267, 0, -1274, 0, 2401], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, 0, -31, 0, 472, 0, -5239, 0, 28561], [1, 0, -35, 0, 676, 0, -10115, 0, 83521], [1, 12, 130, 792, 4299, 15048, 46930, 82308, 130321], [1, 0, -43, 0, 1176, 0, -22747, 0, 279841], [1, 4, 88, 284, 3678, 8236, 74008, 97556, 707281], [1, 6, 61, 342, 3156, 10602, 58621, 178746, 923521], [1, 0, 65, 0, 3688, 0, 88985, 0, 1874161], [1, 6, 101, 522, 6216, 21402, 169781, 413526, 2825761], [1, 0, -91, 0, 5424, 0, -168259, 0, 3418801], [1, 0, -67, 0, 4584, 0, -148003, 0, 4879681], [1, 0, -160, 0, 11406, 0, -449440, 0, 7890481], [1, 34, 661, 8330, 75660, 491470, 2300941, 6982886, 12117361], [1, 22, 417, 4598, 44108, 280478, 1551657, 4993582, 13845841], [1, 0, -191, 0, 18060, 0, -857399, 0, 20151121], [1, 6, 85, 654, 12804, 46434, 428485, 2147466, 25411681], [1, 0, -28, 0, -6554, 0, -149212, 0, 28398241], [1, -38, 781, -10982, 113620, -867578, 4874221, -18735482, 38950081], [1, 0, -332, 0, 41334, 0, -2287148, 0, 47458321], [1, -52, 1336, -21788, 245070, -1939132, 10582456, -36658388, 62742241], [1, 0, -346, 0, 48475, 0, -3255514, 0, 88529281]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2475/2/c/i'], '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': '8-2475e4-1.1-c1e4-0-3', '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': '8-2475e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.4455567143235175, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1646009676423454580, 'z1': {'__RealLiteral__': 0, 'data': '0.26658342085501437107866700878', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '337934633457753655097178558279,503463421275850385055601739278,1388670456368377869543366989115,1768546131963967951808601472140', 'Lhash_array': ['337934633457753655097178558279', '503463421275850385055601739278', '1388670456368377869543366989115', '1768546131963967951808601472140'], 'label': '8-2475e4-1.1-c1e4-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/2/c/i'}