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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_361.305', 'a10': [-0.08257934547233232, -0.9965844930066698], 'a2': [0.9458172417006346, -0.3246994692046835], 'a3': [-0.4016954246529695, -0.9157733266550574], 'a4': [0.7891405093963936, -0.6142127126896678], 'a5': [0.24548548714079915, -0.9694002659393304], 'a6': [-0.6772815716257411, -0.7357239106731316], 'a7': [0.7891405093963936, 0.6142127126896678], 'a8': [0.5469481581224269, -0.8371664782625285], 'a9': [-0.6772815716257411, 0.7357239106731316], 'algebraic': True, 'analytic_conductor': 1.6764769519433462, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]]], 'bad_primes': [19], 'central_character': '361.305', 'coeff_info': ['x^19 - 1', '0.945817241700635 + 0.324699469204683*I', '\\\\zeta_{19}'], 'conductor': 361, 'conductor_radical': 19, 'conjugate': 'dirichlet_L_361.58', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^18', 'a^13', 'a^17', 'a^15', 'a^12', 'a^2', 'a^16', 'a^7', 'a^14', 'a^12', 'a^11', 'a^13', 'a^1', 'a^9', 'a^15', 'a^2', 'a^6', 0, 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'191.57239555830256034263036196756', '192.17817344695453879763193630897', '193.07913344931865748428802065710', '193.67818660837202787932475057328', '194.41862113550892412995048610574', '194.98183133548621587436753432246', '195.67914040206136082074291053914', '196.2705443737428406212871748647', '196.63759714760638538416831920263', '197.06999666898474563465820785049', '198.32452015271026900670535107113', '199.248241367338103639048214615485', '199.83369012165185882979765131391'], 'prelabel': '1-19e2-361.305-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6764769519433462, 'root_angle': -0.703601108033241, 'root_number': '-0.596900025310970337451765104112-0.802315623544601660591291032750*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.351800554017', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(19)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.31409732166427402478709173002-1.08548599580983468914352729023*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.06084284251', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.01646290345', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.21135336059', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.6764769519433462, 'bad_primes': [19], 'central_character': '361.305', 'conductor': 361, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/361/305'], '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': '1-19e2-361.305-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': '1-19e2-361.305-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6764769519433462, 'root_angle': -0.3518005540166205, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06084284251', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_361.305', 'Lhash_array': ['dirichlet_L_361.305'], 'label': '1-19e2-361.305-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/361/305'}
Lfunction data - 1-19e2-361.305-r0-0-0