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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_896.667', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.4422886902190013, -0.8968727415326883], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9469301294951057, -0.3214394653031616], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.6087614290087207, 0.7933533402912352], 'algebraic': True, 'analytic_conductor': 96.28857261598402, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '896.667', 'coeff_info': ['x^96 - 1', '0.997858923238603 + 0.0654031292301431*I', '\\\\zeta_{96}'], 'conductor': 896, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_896.403', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^65', 0, 'a^91', 0, 0, 0, 'a^130', 0, 'a^71', 0, 'a^21', 0, 'a^60', 0, 'a^116', 0, 'a^157', 0, 0, 0, 'a^106', 0, 'a^86', 0, 'a^3', 0, 'a^57', 0, 'a^104', 0, 'a^136', 0, 0, 0, 'a^67', 0, 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'193.46202704670053255762280668773', '194.08462394723821008381644644799', '194.69213403498641561297884807504', '195.09561201772576636453454151927', '196.0106814952703433931496267822', '196.36536750972371789904267961882', '197.09282970972626388627654437220', '197.39474339097460368369905955212', '198.118029813589592501141170867483', '199.17388720687819704822925701405', '199.60719594105304398824452568618'], 'prelabel': '1-896-896.667-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 96.28857261598402, 'root_angle': -0.9225353802793872, 'root_number': '-0.970533263069128895093026432059-0.240967187136317476562067096182*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.46126769014', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(96)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.894665210935348643024944304803-0.407143682716639250976153124574*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.28105500215', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.44332978508', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.11572144352', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 96.28857261598402, 'bad_primes': [2, 7], 'central_character': '896.667', 'conductor': 896, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/896/667'], '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': '1-896-896.667-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': '1-896-896.667-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 96.28857261598402, 'root_angle': -0.4612676901396936, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.28105500215', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_896.667', 'Lhash_array': ['dirichlet_L_896.667'], 'label': '1-896-896.667-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/896/667'}