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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.109', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.766044443118978, 0.6427876096865394], 'a3': [-0.9396926207859084, -0.3420201433256687], 'a4': [0.17364817766693036, -0.984807753012208], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9396926207859084, -0.3420201433256687], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.5, 0.8660254037844386], 'a9': [0.766044443118978, 0.6427876096865394], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.109', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.604', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^10', 'a^14', 0, 'a^17', 'a^6', 'a^3', 'a^2', 0, 0, 'a^6', 'a^17', 'a^13', 0, 'a^10', 'a^16', 'a^9', 0, 0, 'a^16', 0, 'a^5', 'a^13', 0, 'a^6', 'a^12', 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'192.20648267658702937116812261085', '192.76737098510387841670630814868', '193.51837398870572844108731044138', '194.04352102606795384333284015329', '194.78978166541606846402123400717', '195.423001305239120323984733792134', '195.94482382729780643966682948342', '196.6002388359600684222536719440', '196.80455761417599850960071021682', '197.79883619239738637465557833492', '198.34131752534472726380352285680', '199.07106508425329266524144821604', '199.59858852646794245197881388650', '199.92889098278058627474744298326'], 'prelabel': '1-1045-1045.109-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.13027447942595666, 'root_number': '0.683288905530775469598864125031+0.730148116191882669896063340246*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.130274479426', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.574122194235014396219670699841+0.140943564709361001005895272405*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.796098913431', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.80291838676', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.10239049398', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.109', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/109'], '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': '1-1045-1045.109-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': '1-1045-1045.109-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.13027447942595666, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.796098913431', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.109', 'Lhash_array': ['dirichlet_L_1045.109'], 'factors': ['1-1045-1045.109-r0-0-0'], 'label': '1-1045-1045.109-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/109'}
Lfunction data - 1-1045-1045.109-r0-0-0