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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.994', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9902680687415704, 0.13917310096006544], 'a3': [0.24192189559966773, 0.9702957262759965], 'a4': [0.9612616959383189, -0.27563735581699916], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.374606593415912, -0.9271838545667874], 'a7': [-0.9135454576426009, -0.4067366430758002], 'a8': [-0.9135454576426009, 0.4067366430758002], 'a9': [-0.882947592858927, 0.46947156278589075], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.994', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.1004', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^43', 'a^19', 'a^86', 0, 'a^62', 'a^51', 'a^39', 'a^38', 0, 0, 'a^15', 'a^53', 'a^4', 0, 'a^82', 'a^7', 'a^81', 0, 0, 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'189.27671157603614311637653081324', '189.74768513135818609293800912681', '190.68021872959709161514482074225', '191.05659217980282459774484132867', '191.53951048967020868130274905392', '192.19551500585014828919730215303', '192.73050028665396956511107390320', '193.396582189247839650874307398352', '194.003606228128117711556884624123', '194.2267517125673779570991700225', '195.385397432561834312723088273972', '196.25793784952451500375487155058', '196.70023894729771347374698438659', '197.20953020430623411598497561196', '197.93106912812583944849289126636', '198.25929401446069542535810275053', '198.89672081331592800278159766770', '199.4513453534662855767746230269'], 'prelabel': '1-1045-1045.994-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.33607748303654056, 'root_number': '0.492515506702535140897146668220+0.870303668645344193979943260788*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.168038741518', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.635809934075325621332045726490+0.211535758837909600530347612637*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.75605719779', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.40378665941', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.13759968263', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.994', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/994'], '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': '1-1045-1045.994-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': '1-1045-1045.994-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.16803874151827028, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75605719779', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.994', 'Lhash_array': ['dirichlet_L_1045.994'], 'label': '1-1045-1045.994-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/994'}
Lfunction data - 1-1045-1045.994-r0-0-0