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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.833', 'a10': [0.9135454576426009, 0.4067366430758002], 'a2': [0.9975640502598242, 0.0697564737441253], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9902680687415704, 0.13917310096006544], 'a5': [0.9396926207859084, 0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.882947592858927, -0.46947156278589075], 'a8': [0.9781476007338057, 0.20791169081775934], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.833', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.209', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 'a^5', 0, 'a^52', 'a^3', 0, 'a^6', 'a^22', 0, 'a^89', 'a^53', 0, 'a^4', 'a^78', 0, 'a^66', 'a^7', 0, 'a^23', 'a^38', 0, 'a^10', 'a^0', 0, 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'194.40325634084387095733504519309', '194.94298936888670001096598207290', '196.05020654564990715576003970607', '196.20345141511198422491040138218', '197.09571146507771945601551138684', '197.32063320973248161768612689352', '198.1892149360901508711652186410', '198.388145884580066319314189671312', '199.60391618631510484444051093806'], 'prelabel': '1-837-837.833-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.10191372278757373, 'root_number': '0.949181486546705938120748060557+0.314729257611975906684847420712*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0509568613938', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.18818027009798295275162516585+0.213004519282158667551298105916*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.3911407059', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.47558246215', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.33066357276', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.833', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/833'], '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': '1-837-837.833-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': '1-837-837.833-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.05095686139378686, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.3911407059', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.833', 'Lhash_array': ['dirichlet_L_837.833'], 'label': '1-837-837.833-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/833'}
Lfunction data - 1-837-837.833-r0-0-0