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lfunc_lfunctions • Show schema
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{'Lhash': '671143956808168739996491960311,944545040860167303688044240764', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5846.857224180202, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 2, 1]], [19, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '9576.1', 'coefficient_field': '1.1.1.1', 'conductor': 91699776, 'conductor_radical': 798, 'degree': 4, 'euler_factors': [[1], [1], [1, 2, 6, 10, 25], [1, 2, 1], [1, 0, 2, 0, 121], [1, 0, 6, 0, 169], [1, -2, 30, -34, 289], [1, -2, 1], [1, -8, 42, -184, 529], [1, -10, 78, -290, 841], [1, -4, 46, -124, 961], [1, 0, 54, 0, 1369], [1, 4, 86, 164, 1681], [1, -16, 150, -688, 1849], [1, 2, 90, 94, 2209], [1, 2, 102, 106, 2809], [1, 8, 134, 472, 3481], [1, 16, 166, 976, 3721], [1, 12, 150, 804, 4489], [1, -6, 146, -426, 5041], [1, 0, 126, 0, 5329], [1, 24, 302, 1896, 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1.92438091357222, 1.5314451823954967, 1.1404590800855006, 0.773996250433257], 'positive_zeros': ['0.52943922930130364121168689504220', '0.74511465595496916241196092035753', '1.40009131734888899170382690651718', '1.91145173289312730176780547762866', '2.62744838700480254328747733855917', '3.01659255582841408667145002889018', '3.17511968326727805533838633187046', '3.41787713104582311019878868857916', '4.13135328882348988959716002593568', '4.41593323584033033673555554056016', '4.68493701240582109385200006039153', '4.92740482504015199487720013439950', '5.63452705621850259837392143913997', '5.80057983565297474381585157848192', '6.29853771056009229805266866159959', '6.34575278849340594344900133085207', '7.02017564502477463725896315624436', '7.18889788851027380560146848902511', '7.52823803322846159759648154169450', '7.70951484034051205536681935894589'], 'prelabel': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 2029666808149349544, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52943922930130364121168689504', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.74511465595496916241196092036', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.40009131734888899170382690652', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5846.857224180202, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 91699776, 'conductor_radical': 798, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 8, 0, -2, 0, 0, 0, 10, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 16, 0, 0, 0, -2, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, -8, 0, -16, 0, 0, 0, 0, 0, -12, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 2, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 16, 0, 0, 0], 'euler11': [1, 0, 2, 0, 121], 'euler13': [1, 0, 6, 0, 169], 'euler17': [1, -2, 30, -34, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -8, 42, -184, 529], 'euler29': [1, -10, 78, -290, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, 46, -124, 961], 'euler37': [1, 0, 54, 0, 1369], 'euler41': [1, 4, 86, 164, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, 2, 90, 94, 2209], 'euler5': [1, 2, 6, 10, 25], 'euler53': [1, 2, 102, 106, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, 16, 166, 976, 3721], 'euler67': [1, 12, 150, 804, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, -6, 146, -426, 5041], 'euler73': [1, 0, 126, 0, 5329], 'euler79': [1, 24, 302, 1896, 6241], 'euler83': [1, -2, 122, -166, 6889], 'euler89': [1, -4, 102, -356, 7921], 'euler97': [1, -16, 238, -1552, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 2, 6, 10, 25], [1, 2, 1, 0, 0], [1, 0, 2, 0, 121], [1, 0, 6, 0, 169], [1, -2, 30, -34, 289], [1, -2, 1, 0, 0], [1, -8, 42, -184, 529], [1, -10, 78, -290, 841], [1, -4, 46, -124, 961], [1, 0, 54, 0, 1369], [1, 4, 86, 164, 1681], [1, -16, 150, -688, 1849], [1, 2, 90, 94, 2209], [1, 2, 102, 106, 2809], [1, 8, 134, 472, 3481], [1, 16, 166, 976, 3721], [1, 12, 150, 804, 4489], [1, -6, 146, -426, 5041], [1, 0, 126, 0, 5329], [1, 24, 302, 1896, 6241], [1, -2, 122, -166, 6889], [1, -4, 102, -356, 7921], [1, -16, 238, -1552, 9409]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/be'], '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': '4-9576e2-1.1-c1e2-0-5', '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': 0, 'prelabel': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2029666808149349544, 'z1': {'__RealLiteral__': 0, 'data': '0.52943922930130364121168689504', 'prec': 103}}
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{'Lhash': '671143956808168739996491960311,944545040860167303688044240764', 'Lhash_array': ['671143956808168739996491960311', '944545040860167303688044240764'], 'label': '4-9576e2-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/be'}