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lfunc_lfunctions • Show schema
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{'Lhash': '1449693465911390628356015565933,1726082215327436130644752740778', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2482.695136051794, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [5, [1, -2, 1]], [13, [1, 2, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '6240.1', 'coefficient_field': '1.1.1.1', 'conductor': 38937600, 'conductor_radical': 390, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, -2, 1], [1, 0, 6, 0, 49], [1, 8, 38, 88, 121], [1, 2, 1], [1, -4, 30, -68, 289], [1, 0, 30, 0, 361], [1, 0, 38, 0, 529], [1, 4, 54, 116, 841], [1, -8, 46, -248, 961], [1, -4, 46, -148, 1369], [1, -12, 86, -492, 1681], [1, 8, 70, 344, 1849], [1, 8, 78, 376, 2209], [1, -4, -18, -212, 2809], [1, 8, 134, 472, 3481], [1, 4, 126, 244, 3721], [1, 0, 134, 0, 4489], [1, 16, 206, 1136, 5041], [1, -12, 174, -876, 5329], [1, 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'1.36163877886909068404871055992427', '2.20756887601342391484529583850047', '2.46412081208854751346991094724416', '3.06763354007824267055826391951304', '3.09048257757754632206312473516545', '4.02942235834725422079721166915626', '4.37713589862849578523092936946552', '4.85050535994677646438217569338990', '5.06839996635424300269417879592760', '5.49451779205494916079187629934058', '5.56534966430287245836261513492047', '6.16020434400621363874343855174881', '6.19859125501433445460824016675560', '6.88815625544501699846327504971687', '7.01733963206345011554946556650926', '7.69857981961503792669088667115787', '7.71981093309745841320485582719296'], 'prelabel': '4-6240e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 554386994578008503, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14360649981184563108810772519', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.36163877886909068404871055992', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.20756887601342391484529583850', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2482.695136051794, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 38937600, 'conductor_radical': 390, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 2, 0, 0, 0, 3, 0, -8, 0, -2, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 3, 0, -4, 0, -4, 0, 8, 0, 16, 0, 0, 0, 4, 0, 4, 0, 12, 0, -8, 0, 6, 0, -8, 0, -6, 0, -8, 0, 4, 0, -16, 0, 0, 0, -8, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, -16, 0, 12, 0, -6, 0, 0, 0, 0, 0, 5, 0, -8, 0, 8, 0, 8, 0, -4, 0, 0, 0, -16, 0, 0, 0, -20, 0, -24, 0], 'euler11': [1, 8, 38, 88, 121], 'euler13': [1, 2, 1, 0, 0], 'euler17': [1, -4, 30, -68, 289], 'euler19': [1, 0, 30, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 38, 0, 529], 'euler29': [1, 4, 54, 116, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -8, 46, -248, 961], 'euler37': [1, -4, 46, -148, 1369], 'euler41': [1, -12, 86, -492, 1681], 'euler43': [1, 8, 70, 344, 1849], 'euler47': [1, 8, 78, 376, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -4, -18, -212, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, 134, 0, 4489], 'euler7': [1, 0, 6, 0, 49], 'euler71': [1, 16, 206, 1136, 5041], 'euler73': [1, -12, 174, -876, 5329], 'euler79': [1, 0, 126, 0, 6241], 'euler83': [1, 8, 54, 664, 6889], 'euler89': [1, 4, 150, 356, 7921], 'euler97': [1, 20, 222, 1940, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 0, 6, 0, 49], [1, 8, 38, 88, 121], [1, 2, 1, 0, 0], [1, -4, 30, -68, 289], [1, 0, 30, 0, 361], [1, 0, 38, 0, 529], [1, 4, 54, 116, 841], [1, -8, 46, -248, 961], [1, -4, 46, -148, 1369], [1, -12, 86, -492, 1681], [1, 8, 70, 344, 1849], [1, 8, 78, 376, 2209], [1, -4, -18, -212, 2809], [1, 8, 134, 472, 3481], [1, 4, 126, 244, 3721], [1, 0, 134, 0, 4489], [1, 16, 206, 1136, 5041], [1, -12, 174, -876, 5329], [1, 0, 126, 0, 6241], [1, 8, 54, 664, 6889], [1, 4, 150, 356, 7921], [1, 20, 222, 1940, 9409]], 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6240/2/a/bn'], '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': '4-6240e2-1.1-c1e2-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-6240e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 554386994578008503, 'z1': {'__RealLiteral__': 0, 'data': '1.14360649981184563108810772519', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1449693465911390628356015565933,1726082215327436130644752740778', 'Lhash_array': ['1449693465911390628356015565933', '1726082215327436130644752740778'], 'label': '4-6240e2-1.1-c1e2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6240/2/a/bn'}