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lfunc_lfunctions • Show schema
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{'Lhash': '2121265353781314762449156711700,2161965867885226845678092613416', 'a10': 4, 'a2': 2, 'a3': -2, 'a4': 3, 'a5': 2, 'a6': -4, 'a7': -4, 'a8': 4, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 539.9333980933646, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, 2, 1]], [5, [1, -2, 1]], [97, [1, 2, 1]]], 'bad_primes': [2, 3, 5, 97], 'central_character': '2910.1', 'coefficient_field': '1.1.1.1', 'conductor': 8468100, 'conductor_radical': 2910, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 2, 1], [1, -2, 1], [1, 4, 18, 28, 49], [1, 4, 26, 44, 121], [1, -4, 24, -52, 169], [1, 4, 32, 68, 289], [1, 12, 68, 228, 361], [1, 4, -4, 92, 529], [1, 4, 38, 116, 841], [1, -4, 66, -124, 961], [1, 4, 24, 148, 1369], [1, 4, 80, 164, 1681], [1, 8, 78, 344, 1849], [1, 0, 70, 0, 2209], [1, 0, 10, 0, 2809], [1, 12, 130, 708, 3481], [1, 4, 126, 244, 3721], [1, 4, 132, 268, 4489], [1, 20, 236, 1420, 5041], [1, 0, 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'1.70549035159687046531176410066567', '2.63222500326033397852903827884995', '2.73509757291269821587542591904435', '3.57407673523949968491905169842699', '3.80352769606223704818252881294087', '4.36546076028463168090325177823708', '4.72483653494599460499204992641515', '5.14522999382221263336366431870387', '5.46904086196127799753712223055086', '6.17981405824955903208918252664411', '6.33111904530028142937286194548807', '6.39726087040750620133838787097398', '6.42412884059089968485757139597217', '7.36658840448366674776896360928268', '7.45726448283998034758345206389287', '8.343261729843645483978683095874321', '8.387514582807915672683091317911569'], 'prelabel': '4-2910e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.820421868280058, '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': 1053667913495903950, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67338330719789782119205927170', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.70549035159687046531176410067', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63222500326033397852903827885', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 539.9333980933646, 'bad_primes': [2, 3, 5, 97], 'central_character': '1.1', 'conductor': 8468100, 'conductor_radical': 2910, 'degree': 4, 'dirichlet_coefficients': [1, 2, -2, 3, 2, -4, -4, 4, 3, 4, -4, -6, 4, -8, -4, 5, -4, 6, -12, 6, 8, -8, -4, -8, 3, 8, -4, -12, -4, -8, 4, 6, 8, -8, -8, 9, -4, -24, -8, 8, -4, 16, -8, -12, 6, -8, 0, -10, -2, 6, 8, 12, 0, -8, -8, -16, 24, -8, -12, -12, -4, 8, -12, 7, 8, 16, -4, -12, 8, -16, -20, 12, 0, -8, -6, -36, 16, -16, 4, 10, 5, -8, -4, 24, -8, -16, 8, -16, 12, 12, -16, -12, -8, 0, -24, -12, -2, -4, -12, 9], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, -4, 24, -52, 169], 'euler17': [1, 4, 32, 68, 289], 'euler19': [1, 12, 68, 228, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 4, -4, 92, 529], 'euler29': [1, 4, 38, 116, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -4, 66, -124, 961], 'euler37': [1, 4, 24, 148, 1369], 'euler41': [1, 4, 80, 164, 1681], 'euler43': [1, 8, 78, 344, 1849], 'euler47': [1, 0, 70, 0, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 0, 10, 0, 2809], 'euler59': [1, 12, 130, 708, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 4, 132, 268, 4489], 'euler7': [1, 4, 18, 28, 49], 'euler71': [1, 20, 236, 1420, 5041], 'euler73': [1, 0, 50, 0, 5329], 'euler79': [1, -4, 66, -316, 6241], 'euler83': [1, 4, 74, 332, 6889], 'euler89': [1, -12, 190, -1068, 7921], 'euler97': [1, 2, 1, 0, 0], 'euler_factors': [[1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 4, 18, 28, 49], [1, 4, 26, 44, 121], [1, -4, 24, -52, 169], [1, 4, 32, 68, 289], [1, 12, 68, 228, 361], [1, 4, -4, 92, 529], [1, 4, 38, 116, 841], [1, -4, 66, -124, 961], [1, 4, 24, 148, 1369], [1, 4, 80, 164, 1681], [1, 8, 78, 344, 1849], [1, 0, 70, 0, 2209], [1, 0, 10, 0, 2809], [1, 12, 130, 708, 3481], [1, 4, 126, 244, 3721], [1, 4, 132, 268, 4489], [1, 20, 236, 1420, 5041], [1, 0, 50, 0, 5329], [1, -4, 66, -316, 6241], [1, 4, 74, 332, 6889], [1, -12, 190, -1068, 7921], [1, 2, 1, 0, 0]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2910/2/a/n'], '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': '4-2910e2-1.1-c1e2-0-8', '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': '4-2910e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.820421868280058, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1053667913495903950, 'z1': {'__RealLiteral__': 0, 'data': '1.67338330719789782119205927170', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2121265353781314762449156711700,2161965867885226845678092613416', 'Lhash_array': ['2121265353781314762449156711700', '2161965867885226845678092613416'], 'factors': ['2-2910-1.1-c1-0-56', '2-2910-1.1-c1-0-57'], 'label': '4-2910e2-1.1-c1e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2910/2/a/n'}