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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4563.1022', 'a10': [0.6324453755953773, -0.7746049618276546], 'a2': [-0.6829796320568416, -0.7304374183977032], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.06707764439100236, 0.9977477585156251], 'a5': [0.1338531386752616, 0.9910011792459085], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.51158150864681, -0.8592347525622168], 'a8': [0.7746049618276546, -0.6324453755953773], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 21.190482913344844, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '4563.1022', 'coeff_info': ['x^468 - 1', '0.999909877856721 + 0.0134252063133975*I', '\\\\zeta_{468}'], 'conductor': 4563, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_4563.317', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^295', 0, 'a^122', 'a^107', 0, 'a^391', 'a^417', 0, 'a^402', 'a^433', 0, 0, 'a^218', 0, 'a^244', 'a^456', 0, 'a^273', 'a^229', 0, 'a^260', 'a^104', 0, 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'types': ['DIR'], 'values': [[1, '0.709828498971807869207133226592-0.237447577384220069512908534208*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.202860914375', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.39905968495', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.91276407329', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.190482913344844, 'bad_primes': [3, 13], 'central_character': '4563.1022', 'conductor': 4563, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4563/1022'], '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': '1-4563-4563.1022-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': '1-4563-4563.1022-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.190482913344844, 'root_angle': -0.4539228577690116, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.202860914375', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4563.1022', 'Lhash_array': ['dirichlet_L_4563.1022'], 'factors': ['1-4563-4563.1022-r0-0-0'], 'label': '1-4563-4563.1022-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4563/1022'}
Lfunction data - 1-4563-4563.1022-r0-0-0