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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_31.16', 'a10': [0.30901699437494745, -0.9510565162951535], 'a2': [0.30901699437494745, -0.9510565162951535], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [1.0, 0.0], 'a6': [1.0, 0.0], 'a7': [-0.8090169943749475, -0.5877852522924731], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'analytic_normalization': 0, 'bad_lfactors': [[31, [1]]], 'bad_primes': [31], 'central_character': '31.16', 'coeff_info': ['x^5 - 1', '0.309016994374947 + 0.951056516295154*I', '\\\\zeta_{5}'], 'conductor': 31, 'conductor_radical': 31, 'conjugate': 'dirichlet_L_31.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^1', 'a^3', 'a^0', 'a^0', 'a^3', 'a^2', 'a^2', 'a^4', 'a^3', 'a^4', 'a^1', 'a^2', 'a^1', 'a^1', 'a^2', 'a^1', 'a^4', 'a^3', 'a^4', 'a^2', 'a^2', 'a^3', 'a^0', 'a^0', 'a^3', 'a^1', 'a^4', 'a^0', 0, 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'190.28627910444412897936815718505', '190.84017626232400777006620482444', '192.028584479963781318120650410641', '192.68518518644861925058777536428', '193.424621113702252422254871307197', '194.18150058477167266795596970840', '194.82633818469485741516250506644', '196.508282604913369285027166477716', '197.11581018446398947265643174684', '198.02212068994748568740072156556', '199.304479750432382046134363078960'], 'prelabel': '1-31-31.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': -0.09764150081108221, 'root_number': '0.817638170872472981395849545757-0.575732421817910716377669497609*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0976415008111', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(5)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.07040884824480725844346222457-0.274475454368188926877873310079*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.58899933972', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.19315521766', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.88345510751', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.16', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/16'], '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': '1-31-31.16-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': '1-31-31.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': -0.09764150081108221, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.58899933972', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_31.16', 'Lhash_array': ['dirichlet_L_31.16'], 'factors': ['1-31-31.16-r0-0-0'], 'label': '1-31-31.16-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/31/16'}
Lfunction data - 1-31-31.16-r0-0-0