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lfunc_lfunctions • Show schema
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{'Lhash': '855416196957010885367762453782,1129309522959727425506317146156', 'a10': 4, 'a2': 2, 'a3': -2, 'a4': 3, 'a5': 2, 'a6': -4, 'a7': -3, 'a8': 4, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2006.6883832423073, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, 2, 1]], [5, [1, -2, 1]], [11, [1, 2, 1]], [17, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 11, 17], 'central_character': '5610.1', 'coefficient_field': '1.1.1.1', 'conductor': 31472100, 'conductor_radical': 5610, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 2, 1], [1, -2, 1], [1, 3, 6, 21, 49], [1, 2, 1], [1, 1, 16, 13, 169], [1, -2, 1], [1, -5, 34, -95, 361], [1, 3, 38, 69, 529], [1, 4, 62, 116, 841], [1, 3, 54, 93, 961], [1, 1, 64, 37, 1369], [1, -20, 182, -820, 1681], [1, -8, 102, -344, 1849], [1, -6, 62, -282, 2209], [1, 4, 110, 212, 2809], [1, -8, 134, -472, 3481], [1, -3, 32, -183, 3721], [1, 11, 154, 737, 4489], [1, -10, 126, -710, 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6.69298704121996, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 874061679667632160, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67480439547222293119396811379', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.890868132556719591976220717401', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.97615875077853964639146140850', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2006.6883832423073, 'bad_primes': [2, 3, 5, 11, 17], 'central_character': '1.1', 'conductor': 31472100, 'conductor_radical': 5610, 'degree': 4, 'dirichlet_coefficients': [1, 2, -2, 3, 2, -4, -3, 4, 3, 4, -2, -6, -1, -6, -4, 5, 2, 6, 5, 6, 6, -4, -3, -8, 3, -2, -4, -9, -4, -8, -3, 6, 4, 4, -6, 9, -1, 10, 2, 8, 20, 12, 8, -6, 6, -6, 6, -10, 3, 6, -4, -3, -4, -8, -4, -12, -10, -8, 8, -12, 3, -6, -9, 7, -2, 8, -11, 6, 6, -12, 10, 12, 10, -2, -6, 15, 6, 4, 6, 10, 5, 40, -11, 18, 4, 16, 8, -8, 20, 12, 3, -9, 6, 12, 10, -12, 11, 6, -6, 9], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 1, 16, 13, 169], 'euler17': [1, -2, 1, 0, 0], 'euler19': [1, -5, 34, -95, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 3, 38, 69, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 3, 54, 93, 961], 'euler37': [1, 1, 64, 37, 1369], 'euler41': [1, -20, 182, -820, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, -6, 62, -282, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, -3, 32, -183, 3721], 'euler67': [1, 11, 154, 737, 4489], 'euler7': [1, 3, 6, 21, 49], 'euler71': [1, -10, 126, -710, 5041], 'euler73': [1, -10, 130, -730, 5329], 'euler79': [1, -6, 126, -474, 6241], 'euler83': [1, 11, 186, 913, 6889], 'euler89': [1, -20, 278, -1780, 7921], 'euler97': [1, -11, 132, -1067, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 3, 6, 21, 49], [1, 2, 1, 0, 0], [1, 1, 16, 13, 169], [1, -2, 1, 0, 0], [1, -5, 34, -95, 361], [1, 3, 38, 69, 529], [1, 4, 62, 116, 841], [1, 3, 54, 93, 961], [1, 1, 64, 37, 1369], [1, -20, 182, -820, 1681], [1, -8, 102, -344, 1849], [1, -6, 62, -282, 2209], [1, 4, 110, 212, 2809], [1, -8, 134, -472, 3481], [1, -3, 32, -183, 3721], [1, 11, 154, 737, 4489], [1, -10, 126, -710, 5041], [1, -10, 130, -730, 5329], [1, -6, 126, -474, 6241], [1, 11, 186, 913, 6889], [1, -20, 278, -1780, 7921], [1, -11, 132, -1067, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5610/2/a/bv'], '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': '4-5610e2-1.1-c1e2-0-2', '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': '4-5610e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.69298704121996, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 874061679667632160, 'z1': {'__RealLiteral__': 0, 'data': '0.67480439547222293119396811379', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '855416196957010885367762453782,1129309522959727425506317146156', 'Lhash_array': ['855416196957010885367762453782', '1129309522959727425506317146156'], 'label': '4-5610e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5610/2/a/bv'}