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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.472', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.984807753012208, -0.17364817766693036], 'a3': [-0.6427876096865394, -0.766044443118978], 'a4': [0.9396926207859084, -0.3420201433256687], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.766044443118978, -0.6427876096865394], 'a7': [0.8660254037844386, 0.5], 'a8': [0.8660254037844386, -0.5], 'a9': [-0.17364817766693036, 0.984807753012208], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.472', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.538', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^35', 'a^23', 'a^34', 0, 'a^22', 'a^3', 'a^33', 'a^10', 0, 0, 'a^21', 'a^13', 'a^2', 0, 'a^32', 'a^35', 'a^9', 0, 0, 'a^26', 0, 'a^7', 'a^20', 0, 'a^12', 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'189.449800406930592257720649650179', '190.22105479982548220373608651306', '190.982241030216285378146436090899', '191.59983424083353126492202992844', '192.16192604586140831164875979026', '192.959841320474967393642045439697', '193.36800367340423073047440524984', '194.06769911454226679764841531324', '194.61178947061278835696428273840', '195.13910709697913323090280055866', '195.87339979759801378898630705644', '196.02576987317990739099800299783', '196.49994451384108824458742913998', '197.55488359468484885356895926083', '197.93371644347442346081919803437', '198.77418520559852861000921279417', '199.48221548249993623994977731309'], 'prelabel': '1-1045-1045.472-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.15230181765741374, 'root_number': '0.887700281463521782148546222922-0.460421774343464566623003712776*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0761509088287', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.74538275980158964494708847269-0.395390831671641591525856416844*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.24014460194', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.98420155354', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.93806247971', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.472', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/472'], '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': '1-1045-1045.472-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': '1-1045-1045.472-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.07615090882870687, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24014460194', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.472', 'Lhash_array': ['dirichlet_L_1045.472'], 'label': '1-1045-1045.472-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/472'}
Lfunction data - 1-1045-1045.472-r0-0-0