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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.24', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.4067366430758002, -0.9135454576426009], 'a3': [0.6691306063588582, 0.7431448254773942], 'a4': [-0.6691306063588582, 0.7431448254773942], 'a5': [-0.5877852522924731, -0.8090169943749475], 'a6': [0.4067366430758002, -0.9135454576426009], 'a7': [0.7431448254773942, 0.6691306063588582], 'a8': [0.9510565162951535, 0.30901699437494745], 'a9': [-0.10452846326765347, 0.9945218953682733], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.24', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.6', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^41', 'a^8', 'a^22', 'a^39', 'a^49', 'a^7', 'a^3', 'a^16', 'a^20', 0, 'a^30', 0, 'a^48', 'a^47', 'a^44', 'a^4', 'a^57', 'a^13', 'a^1', 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'193.0330374112134654953229239970', '194.065411714230666037248154011903', '194.89434540580974361678567741186', '195.75576415537391175699632453241', '196.42154062546392378677215706842', '197.43364527618652329169372956424', '198.41110689467986553927469867916', '198.85459300943781543788430499155', '199.39529249604088903990416794930'], 'prelabel': '1-143-143.24-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.028040460025043543, 'root_number': '0.996122434425608664111562302689-0.0879778133053951674895310236546*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0140202300125', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.989934761115656079785850807329-0.117361600213363923769875911749*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.60029256159', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.07565326179', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.27492184331', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.24', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/24'], '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': '1-143-143.24-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': '1-143-143.24-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.014020230012521772, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60029256159', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.24', 'Lhash_array': ['dirichlet_L_143.24'], 'label': '1-143-143.24-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/24'}
Lfunction data - 1-143-143.24-r0-0-0