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lfunc_lfunctions • Show schema
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{'Lhash': '746749142273225911195488217520,2649895214228754966035637259899', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 107.0937724367904, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '1296.1', 'coefficient_field': '1.1.1.1', 'conductor': 1679616, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, -4, 11, -20, 25], [1, 3, 2, 21, 49], [1, 4, 5, 44, 121], [1, 1, -12, 13, 169], [1, -8, 50, -136, 289], [1, -2, 39, -38, 361], [1, 4, -7, 92, 529], [1, 0, -29, 0, 841], [1, 4, -15, 124, 961], [1, 18, 155, 666, 1369], [1, 0, -41, 0, 1681], [1, 8, 21, 344, 1849], [1, -12, 97, -564, 2209], [1, -16, 170, -848, 2809], [1, 4, -43, 236, 3481], [1, -5, -36, -305, 3721], [1, -11, 54, -737, 4489], [1, -16, 206, -1136, 5041], [1, -2, 147, -146, 5329], [1, 5, -54, 395, 6241], [1, 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'5.80859836593850024484642033298363', '6.71989860919864914066355616211162', '6.86744122284269292709356725206161', '7.29505925695317916880085097213570', '7.83627492024691991556789911609695', '8.332802935702372913146679334186405', '8.638132438245300380460439515168138', '9.333154307785100565864704958112476', '9.480909892471938857558869721816781', '10.02170884125391701651409685081714'], 'prelabel': '4-6e8-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.216925877597733, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1391299599220376118, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58908120434667112569858788197', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.64762828548782518679932198388', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.09039873743732264497871344375', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 107.0937724367904, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 1679616, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, -3, 0, 0, 0, -4, 0, -1, 0, 0, 0, 8, 0, 2, 0, 0, 0, -4, 0, 5, 0, 0, 0, 0, 0, -4, 0, 0, 0, -12, 0, -18, 0, 0, 0, 0, 0, -8, 0, 0, 0, 12, 0, 7, 0, 0, 0, 16, 0, -16, 0, 0, 0, -4, 0, 5, 0, 0, 0, -4, 0, 11, 0, 0, 0, 16, 0, 2, 0, 0, 0, 12, 0, -5, 0, 0, 0, -8, 0, 32, 0, 0, 0, -24, 0, 3, 0, 0, 0, 8, 0, -5, 0, 0, 0], 'euler11': [1, 4, 5, 44, 121], 'euler13': [1, 1, -12, 13, 169], 'euler17': [1, -8, 50, -136, 289], 'euler19': [1, -2, 39, -38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 4, -7, 92, 529], 'euler29': [1, 0, -29, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 4, -15, 124, 961], 'euler37': [1, 18, 155, 666, 1369], 'euler41': [1, 0, -41, 0, 1681], 'euler43': [1, 8, 21, 344, 1849], 'euler47': [1, -12, 97, -564, 2209], 'euler5': [1, -4, 11, -20, 25], 'euler53': [1, -16, 170, -848, 2809], 'euler59': [1, 4, -43, 236, 3481], 'euler61': [1, -5, -36, -305, 3721], 'euler67': [1, -11, 54, -737, 4489], 'euler7': [1, 3, 2, 21, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, -2, 147, -146, 5329], 'euler79': [1, 5, -54, 395, 6241], 'euler83': [1, 8, -19, 664, 6889], 'euler89': [1, 24, 322, 2136, 7921], 'euler97': [1, 5, -72, 485, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -4, 11, -20, 25], [1, 3, 2, 21, 49], [1, 4, 5, 44, 121], [1, 1, -12, 13, 169], [1, -8, 50, -136, 289], [1, -2, 39, -38, 361], [1, 4, -7, 92, 529], [1, 0, -29, 0, 841], [1, 4, -15, 124, 961], [1, 18, 155, 666, 1369], [1, 0, -41, 0, 1681], [1, 8, 21, 344, 1849], [1, -12, 97, -564, 2209], [1, -16, 170, -848, 2809], [1, 4, -43, 236, 3481], [1, -5, -36, -305, 3721], [1, -11, 54, -737, 4489], [1, -16, 206, -1136, 5041], [1, -2, 147, -146, 5329], [1, 5, -54, 395, 6241], [1, 8, -19, 664, 6889], [1, 24, 322, 2136, 7921], [1, 5, -72, 485, 9409]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1296/2/i/q'], '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': '4-6e8-1.1-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': 0, 'prelabel': '4-6e8-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.216925877597733, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1391299599220376118, 'z1': {'__RealLiteral__': 0, 'data': '0.58908120434667112569858788197', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '746749142273225911195488217520,2649895214228754966035637259899', 'Lhash_array': ['746749142273225911195488217520', '2649895214228754966035637259899'], 'factors': ['2-6e4-9.7-c1-0-3', '2-6e4-9.4-c1-0-21'], 'label': '4-6e8-1.1-c1e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1296/2/i/q'}