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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_6369.3071', 'a10': [-0.5824776968678022, -0.8128466845916152], 'a2': [0.8457278217039732, 0.5336145159156115], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.43051109680829514, 0.9025852843498606], 'a5': [-0.9263643838751181, -0.37662850169321077], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9986295347545738, 0.052335956242943835], 'a8': [-0.11753739745783764, 0.9930684569549263], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 684.4441060169668, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [11, [1]], [193, [1]]], 'bad_primes': [3, 11, 193], 'central_character': '6369.3071', 'coeff_info': ['x^960 - 1', '0.999978581664129 + 0.00654493796735186*I', '\\\\zeta_{960}'], 'conductor': 6369, 'conductor_radical': 6369, 'conjugate': 'dirichlet_L_6369.1964', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^86', 0, 'a^172', 'a^539', 0, 'a^472', 'a^258', 0, 'a^625', 0, 0, 'a^351', 'a^558', 0, 'a^344', 'a^869', 0, 'a^203', 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'199.8607577245918086203862595568'], 'prelabel': '1-6369-6369.3071-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 684.4441060169668, 'root_angle': 0.5855025398123145, 'root_number': '-0.265395539984128997386335037176+0.964139620260744489760596328730*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(960)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.04010172242729877710631049868+0.398506121941290190373575246174*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.463528147568', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.84715152622', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.69848523035', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 684.4441060169668, 'bad_primes': [3, 11, 193], 'central_character': '6369.3071', 'conductor': 6369, 'conductor_radical': 6369, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6369/3071'], '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': '1-6369-6369.3071-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-6369-6369.3071-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 684.4441060169668, 'root_angle': 0.29275126990615724, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.463528147568', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_6369.3071', 'Lhash_array': ['dirichlet_L_6369.3071'], 'label': '1-6369-6369.3071-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6369/3071'}
Lfunction data - 1-6369-6369.3071-r1-0-0