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lfunc_lfunctions • Show schema
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{'Lhash': '1651490096052532750610318345770,1962038802695034172582142718041', 'a10': 4, 'a2': -2, 'a3': 0, 'a4': 3, 'a5': -2, 'a6': 0, 'a7': 2, 'a8': -4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 535.4895207048696, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [3, [1]], [7, [1, -2, 1]], [23, [1, 2, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '2898.1', 'coefficient_field': '1.1.1.1', 'conductor': 8398404, 'conductor_radical': 966, 'degree': 4, 'euler_factors': [[1, 2, 1], [1], [1, 2, 8, 10, 25], [1, -2, 1], [1, 0, 10, 0, 121], [1, -4, 18, -52, 169], [1, 2, 32, 34, 289], [1, 4, 42, 76, 361], [1, 2, 1], [1, 16, 122, 464, 841], [1, 10, 60, 310, 961], [1, -8, 78, -296, 1369], [1, -4, 86, -164, 1681], [1, 0, 86, 0, 1849], [1, -6, 76, -282, 2209], [1, 0, 94, 0, 2809], [1, -6, 52, -354, 3481], [1, -6, 104, -366, 3721], [1, 16, 186, 1072, 4489], [1, -4, 38, -284, 5041], [1, 8, 150, 584, 5329], 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'1.54777570597275483446057107967483', '2.30385092076484685652096088854069', '2.47046372628679781854104138468556', '3.49535244114461844856153563601271', '3.73662718221566422543883226725752', '4.17762520132954813782859672028457', '4.39497980279158690824289828255982', '5.34096492615294192951695102539344', '5.69036877399604018393798690692259', '5.92903874395923770611690307388115', '6.30020894599441998167433158156992', '7.07562304732909573071995871291700', '7.21122372819985152531563685800247', '7.61366718325074957265050904203040', '7.76153100644054777353324239759867', '8.418385845216893773065805396349265', '8.419844399867227504734333844764909'], 'prelabel': '4-2898e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.810472586531085, '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': 1083853079875270980, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30279597213553672093675431844', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.54777570597275483446057107967', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.30385092076484685652096088854', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 535.4895207048696, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 8398404, 'conductor_radical': 966, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 3, -2, 0, 2, -4, 0, 4, 0, 0, 4, -4, 0, 5, -2, 0, -4, -6, 0, 0, -2, 0, -4, -8, 0, 6, -16, 0, -10, -6, 0, 4, -4, 0, 8, 8, 0, 8, 4, 0, 0, 0, 0, 4, 6, 0, 3, 8, 0, 12, 0, 0, 0, -8, 0, 32, 6, 0, 6, 20, 0, 7, -8, 0, -16, -6, 0, 8, 4, 0, -8, -16, 0, -12, 0, 0, -12, -10, 0, -8, -8, 0, 4, 0, 0, 0, -18, 0, 8, -6, 0, -12, 8, 0, -14, -6, 0, -12], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, -4, 18, -52, 169], 'euler17': [1, 2, 32, 34, 289], 'euler19': [1, 4, 42, 76, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 2, 1, 0, 0], 'euler29': [1, 16, 122, 464, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 10, 60, 310, 961], 'euler37': [1, -8, 78, -296, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 0, 86, 0, 1849], 'euler47': [1, -6, 76, -282, 2209], 'euler5': [1, 2, 8, 10, 25], 'euler53': [1, 0, 94, 0, 2809], 'euler59': [1, -6, 52, -354, 3481], 'euler61': [1, -6, 104, -366, 3721], 'euler67': [1, 16, 186, 1072, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, -4, 38, -284, 5041], 'euler73': [1, 8, 150, 584, 5329], 'euler79': [1, 12, 146, 948, 6241], 'euler83': [1, 8, 74, 664, 6889], 'euler89': [1, 18, 232, 1602, 7921], 'euler97': [1, 14, 240, 1358, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 2, 8, 10, 25], [1, -2, 1, 0, 0], [1, 0, 10, 0, 121], [1, -4, 18, -52, 169], [1, 2, 32, 34, 289], [1, 4, 42, 76, 361], [1, 2, 1, 0, 0], [1, 16, 122, 464, 841], [1, 10, 60, 310, 961], [1, -8, 78, -296, 1369], [1, -4, 86, -164, 1681], [1, 0, 86, 0, 1849], [1, -6, 76, -282, 2209], [1, 0, 94, 0, 2809], [1, -6, 52, -354, 3481], [1, -6, 104, -366, 3721], [1, 16, 186, 1072, 4489], [1, -4, 38, -284, 5041], [1, 8, 150, 584, 5329], [1, 12, 146, 948, 6241], [1, 8, 74, 664, 6889], [1, 18, 232, 1602, 7921], [1, 14, 240, 1358, 9409]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2898/2/a/w'], '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': '4-2898e2-1.1-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': 2, 'prelabel': '4-2898e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.810472586531085, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1083853079875270980, 'z1': {'__RealLiteral__': 0, 'data': '1.30279597213553672093675431844', 'prec': 103}}
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{'Lhash': '1651490096052532750610318345770,1962038802695034172582142718041', 'Lhash_array': ['1651490096052532750610318345770', '1962038802695034172582142718041'], 'label': '4-2898e2-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2898/2/a/w'}