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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2808.2045', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9396926207859084, -0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9396926207859084, 0.3420201433256687], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 301.76150882330705, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '2808.2045', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 2808, 'conductor_radical': 78, 'conjugate': 'dirichlet_L_2808.725', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^17', 0, 'a^1', 0, 0, 0, 'a^13', 0, 0, 0, 0, 0, 'a^3', 0, 'a^0', 0, 0, 0, 'a^17', 0, 'a^16', 0, 0, 0, 'a^10', 0, 'a^5', 0, 0, 0, 'a^0', 0, 'a^0', 0, 0, 0, 'a^14', 0, 'a^25', 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'191.65039532751391685202370478375', '191.90429790623551395316180915777', '192.39755080497690021295975027881', '192.90374817627066977524369237098', '193.66877199078419850532501061465', '193.8384559426189068733679499981', '194.87335631055557136260263841366', '195.08142176361115959836606699758', '195.7825451274635822945113956604', '196.36695685390721281352744661411', '196.90133287748980802576955463002', '197.38911061790225119180135943815', '197.7647680684151365252084894442', '198.648298461564813534277202523725', '199.077582892718157812978020679655', '199.566469522573722383674030600301'], 'prelabel': '1-2808-2808.2045-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 301.76150882330705, 'root_angle': -0.007218307866692565, 'root_number': '0.998971685174085554654467392940-0.0453384188128313009767315569657*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.58708515385200980110355353429-0.0605366094693163317632553921792*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.859915530973', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.44273835391', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.41114606885', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 301.76150882330705, 'bad_primes': [2, 3, 13], 'central_character': '2808.2045', 'conductor': 2808, 'conductor_radical': 78, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2808/2045'], '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': '1-2808-2808.2045-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': '1-2808-2808.2045-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 301.76150882330705, 'root_angle': -0.007218307866692565, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.859915530973', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2808.2045', 'Lhash_array': ['dirichlet_L_2808.2045'], 'factors': ['1-2808-2808.2045-r1-0-0'], 'label': '1-2808-2808.2045-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2808/2045'}
Lfunction data - 1-2808-2808.2045-r1-0-0