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lfunc_lfunctions • Show schema
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{'Lhash': '2405994484799705582207914915179', 'a10': 2, 'a2': 2, 'a3': 0, 'a4': 2, 'a5': 1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.233941281861857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -1]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': '1.1.1.1', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, -2, 2], [1], [1, -1], [1, 0, 7], [1, -5, 11], [1, -4, 13], [1, 4, 17], [1, 5, 19], [1, -6, 23], [1, 5, 29], [1, 9, 31], [1, 10, 37], [1, -7, 41], [1, 2, 43], [1, -2, 47], [1, -8, 53], [1, 1, 59], [1, 2, 61], [1, -6, 67], [1, -1, 71], [1, 8, 73], [1, -12, 79], [1, -6, 83], [1, 9, 89], [1, -14, 97], [1, 3, 101], [1, -2, 103], [1, 6, 107], [1, 1, 109], [1, 16, 113]], 'euler_factors_factorization': [[[[1, -2, 2], 1]], [1], [[[1, -1], 1]], [[[1, 0, 7], 1]], [[[1, -5, 11], 1]], [[[1, -4, 13], 1]], [[[1, 4, 17], 1]], 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0.8560912905237921, 0.40845707954449617, -0.2796227409540066, -1.002194521119616, -1.5357189755330178, -1.7170298011721445, -1.4996777705192539], 'positive_zeros': ['1.89799498723585767421033230964833', '3.49410387761142976656546809270858', '4.23466268327432431147155666300211', '5.41659698665533312416876873682844', '6.35526976205125359438346080603341', '6.94257636940465251066789252595483', '8.824991276786141939896068673100164', '9.161742231918082706521428553591798', '10.84103814713817700544872039181336', '11.31548780266267451963425405875273'], 'prelabel': '2-405-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 336291471247593082, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89799498723585767421033230965', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.49410387761142976656546809271', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.23466268327432431147155666300', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.233941281861857, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 5, 0, 4, 0, 0, -4, -4, 0, -5, 2, 0, 10, 6, 0, 1, 8, 0, 0, -5, 0, -9, -8, 0, -8, 0, 0, -10, -10, 0, 0, 7, 0, -2, 10, 0, 12, 2, 0, -7, 2, 0, 8, 8, 0, 5, 0, 0, -10, -1, 0, -2, -18, 0, -8, 4, 0, 6, -8, 0, 0, 1, 0, -8, -20, 0, -10, 0, 0, 12, -4, 0, 14, 6, 0, -4, -4, 0, 0, -9, 0, 0, 12, 0, 4, -5, 0, 14, -14, 0, 2], 'euler11': [1, -5, 11], 'euler13': [1, -4, 13], 'euler17': [1, 4, 17], 'euler19': [1, 5, 19], 'euler2': [1, -2, 2], 'euler23': [1, -6, 23], 'euler29': [1, 5, 29], 'euler3': [1, 0, 0], 'euler31': [1, 9, 31], 'euler37': [1, 10, 37], 'euler41': [1, -7, 41], 'euler43': [1, 2, 43], 'euler47': [1, -2, 47], 'euler5': [1, -1, 0], 'euler53': [1, -8, 53], 'euler59': [1, 1, 59], 'euler61': [1, 2, 61], 'euler67': [1, -6, 67], 'euler7': [1, 0, 7], 'euler71': [1, -1, 71], 'euler73': [1, 8, 73], 'euler79': [1, -12, 79], 'euler83': [1, -6, 83], 'euler89': [1, 9, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, -2, 2], [1, 0, 0], [1, -1, 0], [1, 0, 7], [1, -5, 11], [1, -4, 13], [1, 4, 17], [1, 5, 19], [1, -6, 23], [1, 5, 29], [1, 9, 31], [1, 10, 37], [1, -7, 41], [1, 2, 43], [1, -2, 47], [1, -8, 53], [1, 1, 59], [1, 2, 61], [1, -6, 67], [1, -1, 71], [1, 8, 73], [1, -12, 79], [1, -6, 83], [1, 9, 89], [1, -14, 97]], 'index': 8, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/405/f', 'ModularForm/GL2/Q/holomorphic/405/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/405/2/a/f'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-405-1.1-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-405-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 336291471247593082, 'z1': {'__RealLiteral__': 0, 'data': '1.89799498723585767421033230965', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10597290
{'Lhash': '2405994484799705582207914915179', 'Lhash_array': ['2405994484799705582207914915179'], 'label': '2-405-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/2/a/f'}
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id: 24549247
{'Lhash': '2405994484799705582207914915179', 'Lhash_array': ['2405994484799705582207914915179'], 'label': '2-405-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/2/a/f/1/1'}
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id: 92978
{'Lhash': '336291471247593082', 'Lhash_array': ['336291471247593082'], 'label': '2-405-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/405/f'}