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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_847.221', 'a10': [0.9283679330160726, -0.3716624556603275], 'a2': [-0.32706796331742166, -0.9450008187146685], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.7860530947427875, 0.6181589862206052], 'a5': [0.0475819158237423, 0.998867339183008], 'a6': [-0.6548607339452851, 0.7557495743542583], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.8412535328311812, 0.5406408174555976], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.221', 'coeff_info': ['x^33 - 1', '0.981928697262707 + 0.189251244360410*I', '\\\\zeta_{33}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.23', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 'a^22', 'a^13', 'a^8', 'a^12', 0, 'a^3', 'a^11', 'a^31', 0, 'a^2', 'a^24', 0, 'a^30', 'a^26', 'a^16', 'a^1', 'a^17', 'a^21', 0, 0, 'a^26', 'a^25', 'a^16', 'a^14', 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'192.37819281122057867980735816799', '193.28176363526888826632243610767', '193.54660938923197141224376005029', '194.403064390845826467662857896934', '194.66837887518503488423897408779', '195.17602361329868366335592094859', '195.936716401034239102378038523205', '196.831132789045411426369032322302', '197.21185798488661143647266316417', '198.276358743983098322898510565540', '198.62954789526497529985171567565', '199.38113996542179546312354018505', '199.826776370523083565092886324086'], 'prelabel': '1-847-847.221-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.046343751952017745, 'root_number': '0.989420020224630751635002181203-0.145079369927951073931849152709*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.023171875976', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(33)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.589805757909403720745362384100-0.257059042280824104315369304789*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.931721749886', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.3223055994', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.70073015956', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.221', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/221'], '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': '1-847-847.221-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': '1-847-847.221-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.023171875976008872, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.931721749886', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_847.221', 'Lhash_array': ['dirichlet_L_847.221'], 'label': '1-847-847.221-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/221'}