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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1480.189', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9396926207859084, 0.3420201433256687], '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': [0.766044443118978, -0.6427876096865394], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.189', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.509', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^26', 0, 0, 0, 'a^5', 0, 'a^16', 0, 'a^21', 0, 'a^11', 0, 0, 0, 'a^16', 0, 'a^26', 0, 'a^13', 0, 'a^6', 0, 0, 0, 'a^24', 0, 'a^12', 0, 'a^9', 0, 'a^11', 0, 0, 0, 0, 0, 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'187.00438583035540580196607183273', '187.36842687242676239654128385821', '188.02301064012221606866929358292', '188.69120451146314205646246003886', '189.118992162596626332447560200017', '189.782575820496907202139589718254', '190.21780452941598063786872807652', '190.72612741639531664746565421115', '191.743980938692443020333836005751', '192.22915536746548079215329159295', '192.77042375533045392548210181632', '193.53343404751460173634928385215', '193.81683667929829765460064403788', '194.20185565184443864762625848134', '195.13191869920283245162134498750', '195.762526500828936422860078795951', '196.13100360257280008244535991106', '196.430696870209982537245543028346', '197.60778813002872725054012346750', '198.21347793304965541079653612768', '198.56618877364487375692193177313', '199.15596726979234044554876726550', '199.75969681216186091573574443957'], 'prelabel': '1-1480-1480.189-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.8035848512555048, 'root_number': '-0.815585269995851281961658283131-0.578636904600626356076781068508*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.401792425628', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.613670084605552932994094278091+0.161221164361393693017246170161*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.50500727484', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.51117176032', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.69149821467', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.189', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/189'], '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': '1-1480-1480.189-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': '1-1480-1480.189-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.4017924256277524, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50500727484', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1480.189', 'Lhash_array': ['dirichlet_L_1480.189'], 'label': '1-1480-1480.189-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/189'}
Lfunction data - 1-1480-1480.189-r0-0-0