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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_575.234', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9211236531148501, 0.3892701063173915], 'a3': [0.362807705350641, -0.9318640292114523], 'a4': [0.6969375686552934, 0.7171318047589635], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.6969375686552934, -0.7171318047589635], 'a7': [0.9594929736144974, -0.28173255684142967], 'a8': [0.362807705350641, 0.9318640292114523], 'a9': [-0.7367411378764049, -0.6761749002740194], 'algebraic': True, 'analytic_conductor': 2.670288773870981, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [23, [1]]], 'bad_primes': [5, 23], 'central_character': '575.234', 'coeff_info': ['x^110 - 1', '0.998369103926136 + 0.0570888108627680*I', '\\\\zeta_{110}'], 'conductor': 575, 'conductor_radical': 115, 'conjugate': 'dirichlet_L_575.489', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^89', 'a^14', 0, 'a^96', 'a^105', 'a^21', 'a^68', 0, 'a^92', 'a^103', 'a^93', 'a^2', 0, 'a^28', 'a^41', 'a^75', 'a^36', 0, 'a^84', 'a^99', 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'197.82358094709298826875245631719', '198.37457027180337668578009298973', '199.267224374529802742227126270642'], 'prelabel': '1-575-575.234-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.670288773870981, 'root_angle': -0.06944286946652993, 'root_number': '0.906311969171070742445739273272-0.422609293008632402603225066639*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0694428694665', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(110)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.14902536641120384522390309674-0.219210926431910223850160697611*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.28965242796', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.32020775866', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.50897417092', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.670288773870981, 'bad_primes': [5, 23], 'central_character': '575.234', 'conductor': 575, 'conductor_radical': 115, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/575/234'], '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': '1-575-575.234-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': '1-575-575.234-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.670288773870981, 'root_angle': -0.06944286946652993, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28965242796', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_575.234', 'Lhash_array': ['dirichlet_L_575.234'], 'factors': ['1-575-575.234-r0-0-0'], 'label': '1-575-575.234-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/575/234'}
Lfunction data - 1-575-575.234-r0-0-0