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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_6017.1009', 'a10': [-0.25603909005754716, 0.9666664286932195], 'a2': [-0.8249400873976409, 0.5652201802876227], 'a3': [0.3930250316539236, 0.9195277725514507], 'a4': [0.36105229559125473, -0.9325455698507635], 'a5': [0.7575962824332592, -0.6527234275275443], 'a6': [-0.8439577573430553, -0.5364096418041724], 'a7': [0.6016618382470009, -0.7987509201229377], 'a8': [0.22924706283730373, 0.9733682675023206], 'a9': [-0.6910626489868646, 0.7227948638273916], 'algebraic': True, 'analytic_conductor': 27.942830525881202, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [547, [1]]], 'bad_primes': [11, 547], 'central_character': '6017.1009', 'coeff_info': ['x^910 - 1', '0.999976163349375 + 0.00690454437773179*I', '\\\\zeta_{910}'], 'conductor': 6017, 'conductor_radical': 6017, 'conjugate': 'dirichlet_L_6017.1789', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^368', 'a^169', 'a^736', 'a^807', 'a^537', 'a^776', 'a^194', 'a^338', 'a^265', 0, 'a^905', 'a^143', 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[1, 'a^387'], [1, 'a^571'], [1, 'a^398'], [1, 'a^742'], [1, 'a^425'], [1, 'a^318'], [1, 'a^688']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-6017-6017.1009-r0-0-0', 'leading_term': '-0.0670892418324589956486218152507+0.190839193902277015118029266681*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/6017/1009', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.2022883197293533, -1.4643542036840675, -2.558883982260425, -2.316077785080223, -0.6858277360418186, 0.44794130479567, -0.6576913941264891, -2.941973996916854, -3.059043908682695, 0.6305423360669113, 5.298856763078803, 6.325483592758154, 2.8167184907972063, -1.130681769391947, -1.5561561765093817, 0.4747944658558503, 0.9596854522902196, -0.9688292961569978, -1.9049620547958028, 0.3176589180931439, 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'199.06293014301018473652736765264', '199.248249570892574826150988799469', '199.91501676648761026043109142963'], 'prelabel': '1-6017-6017.1009-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.942830525881202, 'root_angle': -0.7847883260159735, 'root_number': '-0.780014452548866599639316391446-0.625761499147152657277466990502*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(910)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.747704050625716791436842656373+0.298394464008404844076981898553*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.38340728925', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.76380872464', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.77223952714', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 27.942830525881202, 'bad_primes': [11, 547], 'central_character': '6017.1009', 'conductor': 6017, 'conductor_radical': 6017, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6017/1009'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-6017-6017.1009-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-6017-6017.1009-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.942830525881202, 'root_angle': -0.39239416300798674, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38340728925', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_6017.1009', 'Lhash_array': ['dirichlet_L_6017.1009'], 'label': '1-6017-6017.1009-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6017/1009'}
Lfunction data - 1-6017-6017.1009-r0-0-0