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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_69.50', 'a10': [-0.9594929736144974, -0.28173255684142967], 'a2': [0.6548607339452851, -0.7557495743542583], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.14231483827328514, -0.9898214418809327], 'a5': [-0.41541501300188644, -0.9096319953545183], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9594929736144974, 0.28173255684142967], 'a8': [-0.8412535328311812, -0.5406408174555976], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 7.415079810829127, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]]], 'bad_primes': [3, 23], 'central_character': '69.50', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 69, 'conductor_radical': 69, 'conjugate': 'dirichlet_L_69.29', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 0, 'a^16', 'a^15', 0, 'a^10', 'a^13', 0, 'a^12', 'a^3', 0, 'a^12', 'a^7', 0, 'a^10', 'a^17', 0, 'a^16', 'a^9', 0, 'a^0', 0, 0, 'a^8', 'a^9', 0, 'a^4', 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'189.07584703433493522365906671342', '190.36286241576280107146095817214', '190.96120260938128313756449463293', '191.68083900818963376900057180668', '192.70259352294012095102799536326', '193.17491226424979865341421617399', '193.93507378211278366894165176754', '194.96091972156999084408157793678', '195.69488184232113134161092709097', '196.3439914422040609798796595850', '196.94044069035480415142736476403', '198.29108114822163128962865091318', '199.24416500828055705098353471991'], 'prelabel': '1-69-69.50-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.415079810829127, 'root_angle': 0.9920233519760311, 'root_number': '-0.999686030197149711251475302350+0.0250567561480626547575050880871*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.496011675988', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.783762715261005148231104449478-0.768587358979681404843119777470*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.513078097055', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.54014861417', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.15427515008', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 7.415079810829127, 'bad_primes': [3, 23], 'central_character': '69.50', 'conductor': 69, 'conductor_radical': 69, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/69/50'], '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': '1-69-69.50-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': '1-69-69.50-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.415079810829127, 'root_angle': 0.49601167598801554, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.513078097055', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_69.50', 'Lhash_array': ['dirichlet_L_69.50'], 'label': '1-69-69.50-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/69/50'}
Lfunction data - 1-69-69.50-r1-0-0