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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.369', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9135454576426009, -0.4067366430758002], 'a3': [0.6691306063588582, -0.7431448254773942], 'a4': [0.6691306063588582, 0.7431448254773942], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.9135454576426009, 0.4067366430758002], 'a7': [0.30901699437494745, -0.9510565162951535], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [-0.10452846326765347, -0.9945218953682733], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.369', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.354', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 'a^26', 'a^4', 0, 'a^13', 'a^24', 'a^21', 'a^22', 0, 0, 'a^0', 'a^7', 'a^11', 0, 'a^8', 'a^8', 'a^9', 0, 0, 'a^20', 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'188.92523384276774314652265961455', '189.77901562786053293215669179008', '190.316982939740106843749116795709', '190.73489480404010344096740800036', '191.27577409896589368341893166788', '191.93524923025782714529407374356', '192.24434675930160809508977437528', '193.012176616149905457082053067472', '193.56068229541907488687347310180', '194.50377715026928692589322254382', '195.06058058422001112033333556023', '195.39743157606631202739475540320', '196.54781542978882197312662749585', '196.92946676870967908499858430334', '197.48013900777012614995740559995', '197.98938143317117409080106587975', '198.602438064032430693429244378836', '199.082347047554995740521281255509'], 'prelabel': '1-1045-1045.369-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.6285083104681106, 'root_number': '-0.392842689506861736093466275578-0.919605687945118912761524781201*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.314254155234', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.811553315974381828025302273702-0.490526431993513373421119050331*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.739386849377', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.66176142513', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.47532787086', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.369', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/369'], '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': '1-1045-1045.369-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': '1-1045-1045.369-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.3142541552340553, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.739386849377', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.369', 'Lhash_array': ['dirichlet_L_1045.369'], 'label': '1-1045-1045.369-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/369'}
Lfunction data - 1-1045-1045.369-r0-0-0