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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1080.139', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.17364817766693036, -0.984807753012208], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 116.06211877819503, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1080.139', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 1080, 'conductor_radical': 30, 'conjugate': 'dirichlet_L_1080.979', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^14', 0, 0, 0, 'a^8', 0, 'a^16', 0, 0, 0, 'a^3', 0, 'a^6', 0, 0, 0, 'a^22', 0, 0, 0, 0, 0, 'a^11', 0, 'a^13', 0, 0, 0, 0, 0, 'a^12', 0, 0, 0, 'a^16', 0, 'a^17', 0, 0, 0, 'a^14', 0, 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'192.15911045623443676701203483591', '192.81688677325209428883250904570', '193.82914795237522988563734635111', '194.11444534601468387548786626214', '194.497126125868909567063066320132', '195.355930798117082403410652724074', '195.93588735532545095680733050814', '196.601764491906315264603770033620', '197.049056403816666519620308580350', '197.78728557771404051056602179842', '198.44415209422507705431623491687', '198.71323149695246234945118744420', '199.766964563715005124309771284083', '199.9237006675827251886990137874'], 'prelabel': '1-1080-1080.139-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 116.06211877819503, 'root_angle': -0.49074074074074076, 'root_number': '-0.998308158271268208047820708783-0.0581448289104758285387480168469*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.490740740741', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.910545942697434179343223038004-0.123468150702261025833589905637*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0881859228282', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.23845222069', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.26870365008', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 116.06211877819503, 'bad_primes': [2, 3, 5], 'central_character': '1080.139', 'conductor': 1080, 'conductor_radical': 30, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1080/139'], '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': '1-1080-1080.139-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1080-1080.139-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 116.06211877819503, 'root_angle': -0.49074074074074076, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0881859228282', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1080.139', 'Lhash_array': ['dirichlet_L_1080.139'], 'factors': ['1-1080-1080.139-r1-0-0'], 'label': '1-1080-1080.139-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1080/139'}
Lfunction data - 1-1080-1080.139-r1-0-0