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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_81.32', 'a10': [0.17364817766693036, 0.984807753012208], 'a2': [0.8354878114129364, 0.549508978070806], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.39607976603915684, 0.918216106880274], 'a5': [0.6862416378687336, 0.7273736415730487], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.993238357741943, 0.11609291412523023], 'a8': [-0.17364817766693036, 0.984807753012208], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 8.704658908364626, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '81.32', 'coeff_info': ['x^54 - 1', '0.993238357741943 + 0.116092914125230*I', '\\\\zeta_{54}'], 'conductor': 81, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_81.38', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 0, 'a^10', 'a^7', 0, 'a^26', 'a^15', 0, 'a^12', 'a^11', 0, 'a^40', 'a^31', 0, 'a^20', 'a^3', 0, 'a^24', 'a^17', 0, 'a^16', 'a^1', 0, 'a^14', 'a^45', 0, 'a^36', 'a^23', 0, 'a^46', 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'unitary', 'types': ['DIR'], 'values': [[1, '1.42472837656811533931782953453+0.986464786095768755540832984664*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.46008071686', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.70234271781', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.51512129603', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 8.704658908364626, 'bad_primes': [3], 'central_character': '81.32', 'conductor': 81, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/81/32'], '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': '1-3e4-81.32-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': '1-3e4-81.32-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.704658908364626, 'root_angle': 0.31790123456790126, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.46008071686', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_81.32', 'Lhash_array': ['dirichlet_L_81.32'], 'factors': ['1-3e4-81.32-r1-0-0'], 'label': '1-3e4-81.32-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/81/32'}
Lfunction data - 1-3e4-81.32-r1-0-0