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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_115.48', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9096319953545183, -0.41541501300188644], 'a3': [-0.28173255684142967, -0.9594929736144974], 'a4': [0.6548607339452851, -0.7557495743542583], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.6548607339452851, -0.7557495743542583], 'a7': [-0.9898214418809327, 0.14231483827328514], 'a8': [0.28173255684142967, -0.9594929736144974], 'a9': [-0.8412535328311812, 0.5406408174555976], 'algebraic': True, 'analytic_conductor': 12.358466351381878, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [23, [1]]], 'bad_primes': [5, 23], 'central_character': '115.48', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 115, 'conductor_radical': 115, 'conjugate': 'dirichlet_L_115.12', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^41', 'a^31', 'a^38', 0, 'a^28', 'a^21', 'a^35', 'a^18', 0, 'a^36', 'a^25', 'a^23', 'a^18', 0, 'a^32', 'a^17', 'a^15', 'a^38', 0, 'a^8', 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'199.16215621955885300947250714609', '199.91073216037246589813074690585'], 'prelabel': '1-115-115.48-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.358466351381878, 'root_angle': 0.9730419727007579, 'root_number': '-0.996415848431271110714632291998+0.0845899343597697610411098418946*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.48652098635', 'prec': 44}, 'spectral_label': 'r1-0', 'st_group': 'mu(44)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.931187920271082317123819973308-0.922949446520333600200915924658*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.505717620232', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.24092777138', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.44116626245', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12.358466351381878, 'bad_primes': [5, 23], 'central_character': '115.48', 'conductor': 115, 'conductor_radical': 115, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/115/48'], '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': '1-115-115.48-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': '1-115-115.48-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.358466351381878, 'root_angle': 0.48652098635037894, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.505717620232', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_115.48', 'Lhash_array': ['dirichlet_L_115.48'], 'label': '1-115-115.48-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/115/48'}
Lfunction data - 1-115-115.48-r1-0-0