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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_115.42', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.7557495743542583, -0.6548607339452851], 'a3': [-0.5406408174555976, -0.8412535328311812], 'a4': [0.14231483827328514, 0.9898214418809327], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.14231483827328514, 0.9898214418809327], 'a7': [0.28173255684142967, 0.9594929736144974], 'a8': [0.5406408174555976, -0.8412535328311812], 'a9': [-0.41541501300188644, 0.9096319953545183], 'algebraic': True, 'analytic_conductor': 0.5340577547741961, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [23, [1]]], 'bad_primes': [5, 23], 'central_character': '115.42', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 115, 'conductor_radical': 115, 'conjugate': 'dirichlet_L_115.63', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^27', 'a^29', 'a^10', 0, 'a^12', 'a^9', 'a^37', 'a^14', 0, 'a^6', 'a^39', 'a^13', 'a^36', 0, 'a^20', 'a^1', 'a^41', 'a^32', 0, 'a^38', 'a^33', 0, 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'198.67483523403381246054514647153', '199.624080772438193124555135533639'], 'prelabel': '1-115-115.42-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5340577547741961, 'root_angle': -0.0922909898108416, 'root_number': '0.958260832057817007830461385862-0.285895396506939628515270881672*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0461454949054', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(44)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.645910251991600307110171640515-0.159312815843135425185961284842*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.47960644088', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.58996344912', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.64496241348', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5340577547741961, 'bad_primes': [5, 23], 'central_character': '115.42', 'conductor': 115, 'conductor_radical': 115, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/115/42'], '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': '1-115-115.42-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': '1-115-115.42-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5340577547741961, 'root_angle': -0.0461454949054208, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47960644088', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_115.42', 'Lhash_array': ['dirichlet_L_115.42'], 'label': '1-115-115.42-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/115/42'}
Lfunction data - 1-115-115.42-r0-0-0