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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.978', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.3420201433256687, -0.9396926207859084], 'a3': [0.984807753012208, 0.17364817766693036], 'a4': [-0.766044443118978, 0.6427876096865394], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.17364817766693036, -0.984807753012208], 'a7': [0.8660254037844386, -0.5], 'a8': [0.8660254037844386, 0.5], 'a9': [0.9396926207859084, 0.3420201433256687], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.978', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.967', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^25', 'a^1', 'a^14', 0, 'a^26', 'a^33', 'a^3', 'a^2', 0, 0, 'a^15', 'a^35', 'a^22', 0, 'a^28', 'a^25', 'a^27', 0, 0, 'a^34', 0, 'a^5', 'a^4', 0, 'a^24', 'a^3', 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'190.858658332550409793847790321293', '191.59825336435777492204802650499', '192.06372982193582866988805429537', '192.41498852785951447375911789512', '193.00532359786481854877910133047', '193.8201814178168613451477266685', '194.22221401887004394695015898511', '195.06419708020042974684392833261', '195.63038979781339984664763514799', '196.07723667265394244093564571812', '197.17839216021241599801470734370', '197.71889550708932349860433487083', '197.98002047919296263392426760815', '198.7876770815143975778961901388', '199.26928204432004513677715721667', '199.83837745244344664457608009105'], 'prelabel': '1-1045-1045.978-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.3933993269778624, 'root_number': '0.328670846700513800264962460060-0.944444532267071445495135116536*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.196699663489', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.25265204751438350356254465324-0.562024760021555292241563231233*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.02467574006', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.89979959182', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.84980295301', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.978', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/978'], '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': '1-1045-1045.978-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': '1-1045-1045.978-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.1966996634889312, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02467574006', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.978', 'Lhash_array': ['dirichlet_L_1045.978'], 'label': '1-1045-1045.978-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/978'}
Lfunction data - 1-1045-1045.978-r0-0-0