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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4563.1024', 'a10': [0.9870502626379128, -0.16041128085776024], 'a2': [-0.7304374183977032, -0.6829796320568416], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.06707764439100236, 0.9977477585156251], 'a5': [-0.6114208080920122, 0.7913056270696619], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.01342520631339747, -0.999909877856721], 'a8': [0.6324453755953773, -0.7746049618276546], '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': '4563.1024', 'coeff_info': ['x^234 - 1', '0.999639527670885 + 0.0268479928100611*I', '\\\\zeta_{234}'], 'conductor': 4563, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_4563.1876', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^145', 0, 'a^56', 'a^83', 0, 'a^175', 'a^201', 0, 'a^228', 'a^193', 0, 0, 'a^86', 0, 'a^112', 'a^162', 0, 'a^195', 'a^139', 0, 'a^104', 'a^104', 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{'__RealLiteral__': 0, 'data': '1.03912079112', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.30227284972', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.190482913344844, 'bad_primes': [3, 13], 'central_character': '4563.1024', 'conductor': 4563, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4563/1024'], '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': '1-4563-4563.1024-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': '1-4563-4563.1024-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.190482913344844, 'root_angle': -0.3794104755643217, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.411942030758', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4563.1024', 'Lhash_array': ['dirichlet_L_4563.1024'], 'factors': ['1-4563-4563.1024-r0-0-0'], 'label': '1-4563-4563.1024-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4563/1024'}
Lfunction data - 1-4563-4563.1024-r0-0-0