Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(129,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.2208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 640) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.1 | ||
Root | \(-0.854638 + 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.129 |
Dual form | 1280.2.f.k.129.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.70928 | −0.986851 | −0.493425 | − | 0.869788i | \(-0.664255\pi\) | ||||
−0.493425 | + | 0.869788i | \(0.664255\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.539189 | − | 2.17009i | −0.241133 | − | 0.970492i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.63090i | − | 0.994386i | −0.867640 | − | 0.497193i | \(-0.834364\pi\) | ||
0.867640 | − | 0.497193i | \(-0.165636\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0783777 | −0.0261259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.41855i | 1.63375i | 0.576812 | + | 0.816877i | \(0.304297\pi\) | ||||
−0.576812 | + | 0.816877i | \(0.695703\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.34017 | −1.75845 | −0.879224 | − | 0.476409i | \(-0.841938\pi\) | ||||
−0.879224 | + | 0.476409i | \(0.841938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.921622 | + | 3.70928i | 0.237962 | + | 0.957731i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.41855i | − | 0.829120i | −0.910022 | − | 0.414560i | \(-0.863935\pi\) | ||
0.910022 | − | 0.414560i | \(-0.136065\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.26180i | 0.748307i | 0.927367 | + | 0.374154i | \(0.122067\pi\) | ||||
−0.927367 | + | 0.374154i | \(0.877933\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.49693i | 0.981310i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.36910i | 0.285478i | 0.989760 | + | 0.142739i | \(0.0455909\pi\) | ||||
−0.989760 | + | 0.142739i | \(0.954409\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.41855 | + | 2.34017i | −0.883710 | + | 0.468035i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.26180 | 1.01263 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.00000i | − | 0.371391i | −0.982607 | − | 0.185695i | \(-0.940546\pi\) | ||
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.68035 | 0.840615 | 0.420307 | − | 0.907382i | \(-0.361922\pi\) | ||||
0.420307 | + | 0.907382i | \(0.361922\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 9.26180i | − | 1.61227i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.70928 | + | 1.41855i | −0.965044 | + | 0.239779i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.75872 | 0.946728 | 0.473364 | − | 0.880867i | \(-0.343039\pi\) | ||||
0.473364 | + | 0.880867i | \(0.343039\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.8371 | 1.73533 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.75872 | 1.21171 | 0.605855 | − | 0.795575i | \(-0.292831\pi\) | ||||
0.605855 | + | 0.795575i | \(0.292831\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.44748 | −0.678234 | −0.339117 | − | 0.940744i | \(-0.610128\pi\) | ||||
−0.339117 | + | 0.940744i | \(0.610128\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0422604 | + | 0.170086i | 0.00629981 | + | 0.0253550i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.78765i | 0.698351i | 0.937057 | + | 0.349175i | \(0.113538\pi\) | ||||
−0.937057 | + | 0.349175i | \(0.886462\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0783777 | 0.0111968 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.84324i | 0.818218i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.65983 | 0.227995 | 0.113997 | − | 0.993481i | \(-0.463634\pi\) | ||||
0.113997 | + | 0.993481i | \(0.463634\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.7587 | − | 2.92162i | 1.58555 | − | 0.393951i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.57531i | − | 0.738467i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.26180i | 0.424650i | 0.977199 | + | 0.212325i | \(0.0681035\pi\) | ||||
−0.977199 | + | 0.212325i | \(0.931897\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.49693i | − | 0.319699i | −0.987141 | − | 0.159849i | \(-0.948899\pi\) | ||
0.987141 | − | 0.159849i | \(-0.0511009\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.206204i | 0.0259792i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.41855 | + | 13.7587i | 0.424019 | + | 1.70656i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.86603 | −0.960989 | −0.480494 | − | 0.876998i | \(-0.659543\pi\) | ||||
−0.480494 | + | 0.876998i | \(0.659543\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 2.34017i | − | 0.281724i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.15676 | −0.730672 | −0.365336 | − | 0.930876i | \(-0.619046\pi\) | ||||
−0.365336 | + | 0.930876i | \(0.619046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.5753i | 1.58887i | 0.607350 | + | 0.794435i | \(0.292233\pi\) | ||||
−0.607350 | + | 0.794435i | \(0.707767\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.55252 | − | 4.00000i | 0.872090 | − | 0.461880i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.2557 | 1.62458 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6803 | 1.42665 | 0.713325 | − | 0.700833i | \(-0.247188\pi\) | ||||
0.713325 | + | 0.700833i | \(0.247188\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.75872 | −0.973192 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.9711 | 1.64329 | 0.821644 | − | 0.570001i | \(-0.193057\pi\) | ||||
0.821644 | + | 0.570001i | \(0.193057\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.41855 | + | 1.84324i | −0.804655 | + | 0.199928i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.41855i | 0.366507i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.52359 | −0.903499 | −0.451749 | − | 0.892145i | \(-0.649200\pi\) | ||||
−0.451749 | + | 0.892145i | \(0.649200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.6803i | 1.74858i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.00000 | −0.829561 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.07838 | − | 1.75872i | 0.726226 | − | 0.180441i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.58145i | 0.465176i | 0.972575 | + | 0.232588i | \(0.0747193\pi\) | ||||
−0.972575 | + | 0.232588i | \(0.925281\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.424694i | − | 0.0426833i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 2.31351i | − | 0.230203i | −0.993354 | − | 0.115101i | \(-0.963281\pi\) | ||
0.993354 | − | 0.115101i | \(-0.0367193\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.2062i | 1.59684i | 0.602098 | + | 0.798422i | \(0.294332\pi\) | ||||
−0.602098 | + | 0.798422i | \(0.705668\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.75872 | − | 2.42469i | 0.952354 | − | 0.236626i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.6514 | −1.51308 | −0.756540 | − | 0.653948i | \(-0.773112\pi\) | ||||
−0.756540 | + | 0.653948i | \(0.773112\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.3402i | 1.18197i | 0.806681 | + | 0.590987i | \(0.201262\pi\) | ||||
−0.806681 | + | 0.590987i | \(0.798738\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.84324 | −0.934279 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.36069i | 0.880580i | 0.897856 | + | 0.440290i | \(0.145124\pi\) | ||||
−0.897856 | + | 0.440290i | \(0.854876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.97107 | − | 0.738205i | 0.277054 | − | 0.0688379i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.496928 | 0.0459411 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.99386 | −0.824466 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.3607 | −1.66915 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.2618 | −1.19578 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.46081 | + | 8.32684i | 0.667315 | + | 0.744775i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.95055i | 0.173083i | 0.996248 | + | 0.0865417i | \(0.0275816\pi\) | ||||
−0.996248 | + | 0.0865417i | \(0.972418\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.60197 | 0.669316 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5753i | 1.36082i | 0.732831 | + | 0.680410i | \(0.238198\pi\) | ||||
−0.732831 | + | 0.680410i | \(0.761802\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.58145 | 0.744106 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.83710 | − | 11.4186i | −0.244179 | − | 0.982752i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.2039i | − | 1.29896i | −0.760379 | − | 0.649480i | \(-0.774987\pi\) | ||
0.760379 | − | 0.649480i | \(-0.225013\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.58145i | − | 0.218956i | −0.993989 | − | 0.109478i | \(-0.965082\pi\) | ||
0.993989 | − | 0.109478i | \(-0.0349179\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 8.18342i | − | 0.689168i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 34.3545i | − | 2.87287i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.34017 | + | 1.07838i | −0.360432 | + | 0.0895544i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.133969 | −0.0110496 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.81658i | − | 0.148820i | −0.997228 | − | 0.0744101i | \(-0.976293\pi\) | ||
0.997228 | − | 0.0744101i | \(-0.0237074\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.16290 | −0.420151 | −0.210075 | − | 0.977685i | \(-0.567371\pi\) | ||||
−0.210075 | + | 0.977685i | \(0.567371\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.267938i | 0.0216615i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.52359 | − | 10.1568i | −0.202700 | − | 0.815810i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7587 | 1.09807 | 0.549033 | − | 0.835801i | \(-0.314996\pi\) | ||||
0.549033 | + | 0.835801i | \(0.314996\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.83710 | −0.224997 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.60197 | 0.283875 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.29072 | 0.492728 | 0.246364 | − | 0.969177i | \(-0.420764\pi\) | ||||
0.246364 | + | 0.969177i | \(0.420764\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20.0989 | + | 4.99386i | −1.56470 | + | 0.388771i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.89269i | 0.301226i | 0.988593 | + | 0.150613i | \(0.0481247\pi\) | ||||
−0.988593 | + | 0.150613i | \(0.951875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.1978 | 2.09214 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 0.255652i | − | 0.0195502i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.44521 | 0.109877 | 0.0549387 | − | 0.998490i | \(-0.482504\pi\) | ||||
0.0549387 | + | 0.998490i | \(0.482504\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.15676 | + | 11.6248i | 0.465407 | + | 0.878749i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.57531i | − | 0.419066i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 11.9421i | − | 0.892598i | −0.894884 | − | 0.446299i | \(-0.852742\pi\) | ||
0.894884 | − | 0.446299i | \(-0.147258\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.3607i | − | 1.14175i | −0.821037 | − | 0.570876i | \(-0.806604\pi\) | ||
0.821037 | − | 0.570876i | \(-0.193396\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.26794i | 0.315495i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.10504 | − | 12.4969i | −0.228287 | − | 0.918792i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.5236 | 1.35458 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 13.8432i | − | 1.00695i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.3607 | −1.83504 | −0.917518 | − | 0.397695i | \(-0.869810\pi\) | ||||
−0.917518 | + | 0.397695i | \(0.869810\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.58145i | − | 0.329780i | −0.986312 | − | 0.164890i | \(-0.947273\pi\) | ||
0.986312 | − | 0.164890i | \(-0.0527269\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.84324 | − | 23.5174i | −0.418443 | − | 1.68412i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.8638 | −1.20149 | −0.600747 | − | 0.799439i | \(-0.705130\pi\) | ||||
−0.600747 | + | 0.799439i | \(0.705130\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.84324 | 0.697769 | 0.348885 | − | 0.937166i | \(-0.386561\pi\) | ||||
0.348885 | + | 0.937166i | \(0.386561\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.4452 | 0.948352 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.26180 | −0.369306 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.18342 | − | 16.8371i | −0.292183 | − | 1.17595i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.107307i | − | 0.00745836i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.6742 | −1.22255 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5753i | 1.07225i | 0.844139 | + | 0.536124i | \(0.180112\pi\) | ||||
−0.844139 | + | 0.536124i | \(0.819888\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.5236 | 0.721065 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.39803 | + | 9.65142i | 0.163544 | + | 0.658221i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 12.3135i | − | 0.835896i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 23.2039i | − | 1.56798i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.6742i | 1.45796i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.9854i | 1.13743i | 0.822535 | + | 0.568715i | \(0.192559\pi\) | ||||
−0.822535 | + | 0.568715i | \(0.807441\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.346316 | − | 0.183417i | 0.0230877 | − | 0.0122278i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.9649 | 1.32512 | 0.662559 | − | 0.749009i | \(-0.269470\pi\) | ||||
0.662559 | + | 0.749009i | \(0.269470\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.6742i | 1.56444i | 0.623005 | + | 0.782218i | \(0.285912\pi\) | ||||
−0.623005 | + | 0.782218i | \(0.714088\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.3668 | −1.60322 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.5753i | 0.889348i | 0.895693 | + | 0.444674i | \(0.146680\pi\) | ||||
−0.895693 | + | 0.444674i | \(0.853320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.3896 | − | 2.58145i | 0.677744 | − | 0.168395i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.6742 | −1.40789 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.36683 | −0.541206 | −0.270603 | − | 0.962691i | \(-0.587223\pi\) | ||||
−0.270603 | + | 0.962691i | \(0.587223\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.91548 | 0.638712 | 0.319356 | − | 0.947635i | \(-0.396533\pi\) | ||||
0.319356 | + | 0.947635i | \(0.396533\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.814315 | −0.0522383 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.0422604 | − | 0.170086i | −0.00269992 | − | 0.0108664i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 20.6803i | − | 1.31586i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.5897 | −1.62168 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 17.6163i | − | 1.11193i | −0.831204 | − | 0.555967i | \(-0.812348\pi\) | ||
0.831204 | − | 0.555967i | \(-0.187652\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.41855 | −0.466400 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.6803 | − | 3.15061i | 0.794074 | − | 0.197299i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3.68649i | − | 0.229957i | −0.993368 | − | 0.114978i | \(-0.963320\pi\) | ||
0.993368 | − | 0.114978i | \(-0.0366799\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 15.1506i | − | 0.941413i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.156755i | 0.00970292i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 0.107307i | − | 0.00661684i | −0.999995 | − | 0.00330842i | \(-0.998947\pi\) | ||
0.999995 | − | 0.00330842i | \(-0.00105311\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.894960 | − | 3.60197i | −0.0549770 | − | 0.221267i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.5692 | 0.891618 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.85762i | − | 0.235203i | −0.993061 | − | 0.117602i | \(-0.962479\pi\) | ||
0.993061 | − | 0.117602i | \(-0.0375206\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.3074 | −1.29433 | −0.647165 | − | 0.762350i | \(-0.724046\pi\) | ||||
−0.647165 | + | 0.762350i | \(0.724046\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 28.5113i | − | 1.72558i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.6803 | − | 23.9421i | −0.764654 | − | 1.44377i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.44521 | 0.0868344 | 0.0434172 | − | 0.999057i | \(-0.486176\pi\) | ||||
0.0434172 | + | 0.999057i | \(0.486176\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.366835 | −0.0219618 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4391 | −0.742053 | −0.371026 | − | 0.928622i | \(-0.620994\pi\) | ||||
−0.371026 | + | 0.928622i | \(0.620994\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.29072 | −0.373945 | −0.186972 | − | 0.982365i | \(-0.559867\pi\) | ||||
−0.186972 | + | 0.982365i | \(0.559867\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.0989 | + | 3.00614i | −0.716677 | + | 0.178069i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 20.4124i | − | 1.20491i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.31351 | 0.312559 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 7.83096i | − | 0.459059i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.07838 | −0.0629995 | −0.0314998 | − | 0.999504i | \(-0.510028\pi\) | ||||
−0.0314998 | + | 0.999504i | \(0.510028\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.07838 | − | 1.75872i | 0.412119 | − | 0.102397i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.5113i | 1.65439i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 8.68035i | − | 0.501997i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7009i | 0.674427i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.95443i | 0.227176i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.41855 | + | 1.34632i | −0.310265 | + | 0.0770898i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.2267 | −1.43977 | −0.719883 | − | 0.694096i | \(-0.755804\pi\) | ||||
−0.719883 | + | 0.694096i | \(0.755804\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 27.7009i | − | 1.57585i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.8371 | −1.06815 | −0.534077 | − | 0.845436i | \(-0.679341\pi\) | ||||
−0.534077 | + | 0.845436i | \(0.679341\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.2039i | 0.859377i | 0.902977 | + | 0.429689i | \(0.141377\pi\) | ||||
−0.902977 | + | 0.429689i | \(0.858623\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.447480 | − | 0.111183i | 0.0252126 | − | 0.00626444i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.8638 | −0.947163 | −0.473582 | − | 0.880750i | \(-0.657039\pi\) | ||||
−0.473582 | + | 0.880750i | \(0.657039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.8371 | 0.606761 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.7526 | 1.49318 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.1506 | 0.620437 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.0144 | − | 14.8371i | 1.55396 | − | 0.823014i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 21.0928i | − | 1.16643i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.5958 | 0.694430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.5753i | 1.29582i | 0.761719 | + | 0.647908i | \(0.224356\pi\) | ||||
−0.761719 | + | 0.647908i | \(0.775644\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.451356 | −0.0247341 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.24128 | + | 17.0700i | 0.231726 | + | 0.932632i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8371i | 0.808228i | 0.914709 | + | 0.404114i | \(0.132420\pi\) | ||||
−0.914709 | + | 0.404114i | \(0.867580\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 16.0000i | − | 0.869001i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.3607i | 1.37336i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.6225i | − | 1.00552i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.07838 | + | 1.26180i | −0.273411 | + | 0.0679328i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.133969 | −0.00719184 | −0.00359592 | − | 0.999994i | \(-0.501145\pi\) | ||||
−0.00359592 | + | 0.999994i | \(0.501145\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22.3135i | − | 1.19441i | −0.802087 | − | 0.597207i | \(-0.796277\pi\) | ||
0.802087 | − | 0.597207i | \(-0.203723\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −33.3607 | −1.78066 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.8371i | 1.21550i | 0.794130 | + | 0.607748i | \(0.207927\pi\) | ||||
−0.794130 | + | 0.607748i | \(0.792073\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.31965 | + | 13.3607i | 0.176189 | + | 0.709112i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.3730 | 0.813624 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.8843 | −1.68279 | −0.841394 | − | 0.540422i | \(-0.818265\pi\) | ||||
−0.841394 | + | 0.540422i | \(0.818265\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.36069 | 0.440036 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 31.3835 | 1.64721 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.4596 | − | 7.31965i | 1.54199 | − | 0.383128i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.4619i | 1.59010i | 0.606547 | + | 0.795048i | \(0.292554\pi\) | ||||
−0.606547 | + | 0.795048i | \(0.707446\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.608111 | −0.0316570 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.36683i | − | 0.226715i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0722 | 0.521521 | 0.260760 | − | 0.965404i | \(-0.416027\pi\) | ||||
0.260760 | + | 0.965404i | \(0.416027\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.7526 | − | 14.2329i | −0.658540 | − | 0.734982i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.6803i | 0.653071i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7792i | 0.759159i | 0.925159 | + | 0.379579i | \(0.123931\pi\) | ||||
−0.925159 | + | 0.379579i | \(0.876069\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 3.33403i | − | 0.170808i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.4619i | 0.738966i | 0.929237 | + | 0.369483i | \(0.120465\pi\) | ||||
−0.929237 | + | 0.369483i | \(0.879535\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.68649 | − | 30.9360i | −0.391740 | − | 1.57664i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.348583 | 0.0177195 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.17727i | − | 0.161094i | −0.996751 | − | 0.0805471i | \(-0.974333\pi\) | ||
0.996751 | − | 0.0805471i | \(-0.0256667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.68035 | 0.236695 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 26.6225i | − | 1.34293i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.83710 | − | 27.5174i | −0.344012 | − | 1.38455i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.8227 | 0.543177 | 0.271589 | − | 0.962413i | \(-0.412451\pi\) | ||||
0.271589 | + | 0.962413i | \(0.412451\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.6681 | −0.734321 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.5236 | −0.625398 | −0.312699 | − | 0.949852i | \(-0.601233\pi\) | ||||
−0.312699 | + | 0.949852i | \(0.601233\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.6742 | −1.47818 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.72261 | + | 19.0072i | 0.234668 | + | 0.944475i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.2039i | 1.54672i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.2885 | −0.657072 | −0.328536 | − | 0.944491i | \(-0.606555\pi\) | ||||
−0.328536 | + | 0.944491i | \(0.606555\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.9877i | 1.28188i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.58145 | 0.422266 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.07223 | − | 32.4885i | −0.396250 | − | 1.59480i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.41241i | 0.216077i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 0.255652i | − | 0.0124894i | −0.999981 | − | 0.00624471i | \(-0.998012\pi\) | ||
0.999981 | − | 0.00624471i | \(-0.00198777\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.49693i | 0.121693i | 0.998147 | + | 0.0608464i | \(0.0193800\pi\) | ||||
−0.998147 | + | 0.0608464i | \(0.980620\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 0.375245i | − | 0.0182451i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.00000 | + | 15.1050i | 0.388057 | + | 0.732702i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.56916 | −0.317904 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 58.7214i | 2.83510i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.993857 | 0.0478724 | 0.0239362 | − | 0.999713i | \(-0.492380\pi\) | ||||
0.0239362 | + | 0.999713i | \(0.492380\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 17.6286i | − | 0.847178i | −0.905855 | − | 0.423589i | \(-0.860770\pi\) | ||
0.905855 | − | 0.423589i | \(-0.139230\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.41855 | − | 1.84324i | 0.355692 | − | 0.0883768i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.46573 | −0.213625 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.5113 | 1.93350 | 0.966750 | − | 0.255725i | \(-0.0823142\pi\) | ||||
0.966750 | + | 0.255725i | \(0.0823142\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.00614307 | −0.000292527 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.7093 | 0.841393 | 0.420697 | − | 0.907201i | \(-0.361786\pi\) | ||||
0.420697 | + | 0.907201i | \(0.361786\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.59583 | + | 18.4969i | 0.217863 | + | 0.876839i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.10504i | 0.146863i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.28846 | 0.0608061 | 0.0304030 | − | 0.999538i | \(-0.490321\pi\) | ||||
0.0304030 | + | 0.999538i | \(0.490321\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.0410i | 1.97964i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.82482 | 0.414626 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 36.1978 | − | 8.99386i | 1.69698 | − | 0.421639i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.3545i | 1.23281i | 0.787428 | + | 0.616407i | \(0.211412\pi\) | ||||
−0.787428 | + | 0.616407i | \(0.788588\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 17.9877i | − | 0.839595i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 41.0349i | − | 1.91119i | −0.294690 | − | 0.955593i | \(-0.595217\pi\) | ||
0.294690 | − | 0.955593i | \(-0.404783\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.7708i | − | 1.33709i | −0.743670 | − | 0.668547i | \(-0.766917\pi\) | ||
0.743670 | − | 0.668547i | \(-0.233083\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.31351 | + | 17.3607i | 0.200034 | + | 0.805083i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.12783 | 0.237287 | 0.118644 | − | 0.992937i | \(-0.462145\pi\) | ||||
0.118644 | + | 0.992937i | \(0.462145\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.6947i | 0.955593i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.5174 | −1.08363 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 24.0989i | − | 1.10807i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.63317 | − | 14.4124i | −0.350234 | − | 0.661287i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.130094 | −0.00595657 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.6742 | 0.624790 | 0.312395 | − | 0.949952i | \(-0.398869\pi\) | ||||
0.312395 | + | 0.949952i | \(0.398869\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.5113 | −1.66477 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.15676 | −0.280142 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.94214 | − | 2.47027i | 0.451449 | − | 0.112169i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.51971i | 0.386065i | 0.981192 | + | 0.193033i | \(0.0618323\pi\) | ||||
−0.981192 | + | 0.193033i | \(0.938168\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.7526 | −0.486249 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.73820i | − | 0.213832i | −0.994268 | − | 0.106916i | \(-0.965902\pi\) | ||
0.994268 | − | 0.106916i | \(-0.0340976\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.83710 | −0.307928 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.921622 | + | 0.228990i | −0.0414238 | + | 0.0102923i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.1978i | 0.726570i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0928i | 0.496580i | 0.968686 | + | 0.248290i | \(0.0798686\pi\) | ||||
−0.968686 | + | 0.248290i | \(0.920131\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 6.65368i | − | 0.297265i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 8.42082i | − | 0.375466i | −0.982220 | − | 0.187733i | \(-0.939886\pi\) | ||
0.982220 | − | 0.187733i | \(-0.0601139\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.02052 | + | 1.24742i | −0.223410 | + | 0.0555094i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −46.4885 | −2.06463 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 26.0000i | − | 1.15243i | −0.817298 | − | 0.576215i | \(-0.804529\pi\) | ||
0.817298 | − | 0.576215i | \(-0.195471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.7152 | 1.57995 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.1629i | 0.757760i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 35.1689 | − | 8.73820i | 1.54973 | − | 0.385051i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.9421 | −1.14093 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.47027 | −0.108433 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.3135 | 0.451843 | 0.225922 | − | 0.974145i | \(-0.427461\pi\) | ||||
0.225922 | + | 0.974145i | \(0.427461\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.2784 | −0.711806 | −0.355903 | − | 0.934523i | \(-0.615827\pi\) | ||||
−0.355903 | + | 0.934523i | \(0.615827\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.5236 | − | 19.8699i | −0.459287 | − | 0.867194i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 16.0000i | − | 0.696971i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.1256 | 0.918503 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 0.255652i | − | 0.0110944i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −49.1917 | −2.13073 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.43907 | + | 33.9649i | 0.364853 | + | 1.46843i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.4124i | 0.880860i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.424694i | 0.0182929i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 3.36069i | − | 0.144487i | −0.997387 | − | 0.0722437i | \(-0.976984\pi\) | ||
0.997387 | − | 0.0722437i | \(-0.0230159\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 26.2557i | 1.12674i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.7792 | − | 6.65368i | 1.14710 | − | 0.285013i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.51148 | −0.0646263 | −0.0323132 | − | 0.999478i | \(-0.510287\pi\) | ||||
−0.0323132 | + | 0.999478i | \(0.510287\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.195704i | 0.00835243i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.52359 | 0.277914 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 33.3607i | − | 1.41864i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.30737 | + | 21.3607i | 0.225285 | + | 0.906711i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.2290 | −1.53507 | −0.767536 | − | 0.641006i | \(-0.778517\pi\) | ||||
−0.767536 | + | 0.641006i | \(0.778517\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.1978 | 1.19264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.6619 | −1.33677 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.17501 | 0.0916656 | 0.0458328 | − | 0.998949i | \(-0.485406\pi\) | ||||
0.0458328 | + | 0.998949i | \(0.485406\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.3135 | − | 5.04718i | 0.854596 | − | 0.212336i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.0433i | 0.967728i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.1194 | 1.38844 | 0.694219 | − | 0.719764i | \(-0.255750\pi\) | ||||
0.694219 | + | 0.719764i | \(0.255750\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.4657i | 0.772767i | 0.922338 | + | 0.386383i | \(0.126276\pi\) | ||||
−0.922338 | + | 0.386383i | \(0.873724\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 43.3484 | 1.81091 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.20394 | − | 6.04945i | −0.133613 | − | 0.252279i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.2101i | 0.591573i | 0.955254 | + | 0.295787i | \(0.0955818\pi\) | ||||
−0.955254 | + | 0.295787i | \(0.904418\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.83096i | 0.325444i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 39.3874i | − | 1.63406i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.99386i | 0.372487i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.267938 | − | 1.07838i | −0.0110779 | − | 0.0445854i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.7503 | 0.484987 | 0.242494 | − | 0.970153i | \(-0.422035\pi\) | ||||
0.242494 | + | 0.970153i | \(0.422035\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.2663i | 0.629038i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.8248 | 1.18569 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.00000i | 0.328521i | 0.986417 | + | 0.164260i | \(0.0525237\pi\) | ||||
−0.986417 | + | 0.164260i | \(0.947476\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.84939 | + | 19.5174i | 0.198806 | + | 0.800137i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.8248 | −0.688594 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.5646 | 0.840248 | 0.420124 | − | 0.907467i | \(-0.361987\pi\) | ||||
0.420124 | + | 0.907467i | \(0.361987\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.60811 | 0.351132 | 0.175566 | − | 0.984468i | \(-0.443824\pi\) | ||||
0.175566 | + | 0.984468i | \(0.443824\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.616522 | 0.0251067 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.89988 | + | 39.8443i | 0.402487 | + | 1.61990i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 0.259528i | − | 0.0105339i | −0.999986 | − | 0.00526695i | \(-0.998323\pi\) | ||
0.999986 | − | 0.00526695i | \(-0.00167653\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.99386 | 0.364449 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 30.3545i | − | 1.22801i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.1650 | −1.90498 | −0.952488 | − | 0.304576i | \(-0.901485\pi\) | ||||
−0.952488 | + | 0.304576i | \(0.901485\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.15061 | + | 28.7792i | 0.288341 | + | 1.16049i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 40.2967i | − | 1.62228i | −0.584849 | − | 0.811142i | \(-0.698846\pi\) | ||
0.584849 | − | 0.811142i | \(-0.301154\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.6102i | 1.23033i | 0.788399 | + | 0.615164i | \(0.210910\pi\) | ||||
−0.788399 | + | 0.615164i | \(0.789090\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.20394i | 0.289084i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.4247i | 0.898426i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0472 | − | 20.6803i | 0.561887 | − | 0.827214i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 30.2101 | 1.20647 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 19.6865i | − | 0.784952i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.21008 | 0.0879819 | 0.0439909 | − | 0.999032i | \(-0.485993\pi\) | ||||
0.0439909 | + | 0.999032i | \(0.485993\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 26.6225i | − | 1.05815i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.23287 | − | 1.05172i | 0.167976 | − | 0.0417361i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.496928 | −0.0196890 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.482553 | 0.0190895 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.92777 | 0.313128 | 0.156564 | − | 0.987668i | \(-0.449958\pi\) | ||||
0.156564 | + | 0.987668i | \(0.449958\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.18115 | 0.204325 | 0.102162 | − | 0.994768i | \(-0.467424\pi\) | ||||
0.102162 | + | 0.994768i | \(0.467424\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.09890 | − | 16.4969i | −0.161394 | − | 0.649566i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.2062i | 0.479875i | 0.970788 | + | 0.239938i | \(0.0771270\pi\) | ||||
−0.970788 | + | 0.239938i | \(0.922873\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.6742 | −0.693773 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.0472i | 0.824904i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.4969 | 1.27170 | 0.635852 | − | 0.771811i | \(-0.280649\pi\) | ||||
0.635852 | + | 0.771811i | \(0.280649\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.7998 | − | 8.39803i | 1.32067 | − | 0.328138i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.06400i | − | 0.0415107i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.4186i | 1.14598i | 0.819561 | + | 0.572992i | \(0.194217\pi\) | ||||
−0.819561 | + | 0.572992i | \(0.805783\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.0677i | 1.01392i | 0.861971 | + | 0.506958i | \(0.169230\pi\) | ||||
−0.861971 | + | 0.506958i | \(0.830770\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 37.0472i | − | 1.43879i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.62702 | − | 18.6225i | −0.179428 | − | 0.722149i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.73820 | 0.106024 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 29.0328i | − | 1.12247i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.5297 | 0.522310 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.62863i | 0.371156i | 0.982629 | + | 0.185578i | \(0.0594158\pi\) | ||||
−0.982629 | + | 0.185578i | \(0.940584\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.2495 | + | 12.3135i | −0.894874 | + | 0.473947i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.0205 | 0.731018 | 0.365509 | − | 0.930808i | \(-0.380895\pi\) | ||||
0.365509 | + | 0.930808i | \(0.380895\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0533 | 0.462564 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.1256 | −1.30769 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.4947 | −0.669415 | −0.334707 | − | 0.942322i | \(-0.608637\pi\) | ||||
−0.334707 | + | 0.942322i | \(0.608637\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.9939 | + | 8.19779i | −1.26063 | + | 0.313222i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 40.4657i | − | 1.54386i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.5236 | −0.400917 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.3090i | 0.620423i | 0.950668 | + | 0.310211i | \(0.100400\pi\) | ||||
−0.950668 | + | 0.310211i | \(0.899600\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.11733 | −0.0424437 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.60197 | + | 1.39189i | −0.212495 | + | 0.0527973i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 26.5236i | − | 1.00465i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 23.2039i | − | 0.877653i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.9672i | 0.489764i | 0.969553 | + | 0.244882i | \(0.0787493\pi\) | ||||
−0.969553 | + | 0.244882i | \(0.921251\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.7838i | 0.708444i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.7587 | + | 4.41241i | −0.668832 | + | 0.166181i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.08661 | −0.228911 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 7.36069i | − | 0.276437i | −0.990402 | − | 0.138218i | \(-0.955862\pi\) | ||
0.990402 | − | 0.138218i | \(-0.0441376\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.993857 | −0.0372725 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.40787i | 0.239977i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −74.5523 | + | 18.5236i | −2.78810 | + | 0.692743i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.3012 | 0.534089 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.3197 | −0.720502 | −0.360251 | − | 0.932856i | \(-0.617309\pi\) | ||||
−0.360251 | + | 0.932856i | \(0.617309\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.6369 | 1.58788 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.9483 | −0.630313 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.68035 | + | 8.83710i | 0.173824 | + | 0.328202i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 21.1545i | − | 0.784577i | −0.919842 | − | 0.392288i | \(-0.871684\pi\) | ||
0.919842 | − | 0.392288i | \(-0.128316\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.6681 | 1.02474 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.2039i | 0.562338i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.7526 | −0.840386 | −0.420193 | − | 0.907435i | \(-0.638038\pi\) | ||||
−0.420193 | + | 0.907435i | \(0.638038\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0722347 | + | 0.290725i | 0.00266442 | + | 0.0107235i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 42.6225i | − | 1.57002i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.4534i | 1.04668i | 0.852125 | + | 0.523338i | \(0.175314\pi\) | ||||
−0.852125 | + | 0.523338i | \(0.824686\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35.3484i | 1.29856i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.79380i | − | 0.139181i | −0.997576 | − | 0.0695904i | \(-0.977831\pi\) | ||
0.997576 | − | 0.0695904i | \(-0.0221692\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.94214 | + | 0.979481i | −0.144429 | + | 0.0358854i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.17340 | −0.0429324 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 41.1773i | 1.50458i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.3607 | −0.633501 | −0.316750 | − | 0.948509i | \(-0.602592\pi\) | ||||
−0.316750 | + | 0.948509i | \(0.602592\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.1112i | 1.09731i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.78378 | + | 11.2039i | 0.101312 | + | 0.407753i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.76487 | −0.173182 | −0.0865910 | − | 0.996244i | \(-0.527597\pi\) | ||||
−0.0865910 | + | 0.996244i | \(0.527597\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.6803 | 0.460267 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.1978 | 0.514670 | 0.257335 | − | 0.966322i | \(-0.417156\pi\) | ||||
0.257335 | + | 0.966322i | \(0.417156\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.4657 | 1.17534 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.581449 | − | 0.144469i | 0.0210223 | − | 0.00522330i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 20.6803i | − | 0.746724i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −54.7091 | −1.97286 | −0.986430 | − | 0.164181i | \(-0.947502\pi\) | ||||
−0.986430 | + | 0.164181i | \(0.947502\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.30122i | 0.226933i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.0205 | 0.396381 | 0.198190 | − | 0.980164i | \(-0.436494\pi\) | ||||
0.198190 | + | 0.980164i | \(0.436494\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.6803 | + | 10.9528i | −0.742860 | + | 0.393437i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25.8966i | 0.929034i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.3074i | 0.906731i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 33.3607i | − | 1.19374i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 10.5236i | − | 0.376082i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.41855 | − | 29.8576i | −0.264779 | − | 1.06566i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.6925 | 1.20101 | 0.600503 | − | 0.799622i | \(-0.294967\pi\) | ||||
0.600503 | + | 0.799622i | \(0.294967\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.183417i | 0.00652984i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.6270 | 0.875636 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.8310i | 0.562174i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.52973 | + | 6.15676i | 0.0542541 | + | 0.218358i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.7009 | −0.839528 | −0.419764 | − | 0.907633i | \(-0.637887\pi\) | ||||
−0.419764 | + | 0.907633i | \(0.637887\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.3668 | 0.579017 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.668060 | 0.0236047 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −73.5585 | −2.59582 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.94214 | − | 7.81658i | −0.0684515 | − | 0.275498i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.59374i | 0.232110i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.0349 | −1.16145 | −0.580723 | − | 0.814102i | \(-0.697230\pi\) | ||||
−0.580723 | + | 0.814102i | \(0.697230\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6.26794i | − | 0.220097i | −0.993926 | − | 0.110049i | \(-0.964899\pi\) | ||
0.993926 | − | 0.110049i | \(-0.0351006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 36.4202 | 1.27731 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.39189 | − | 13.6514i | −0.118813 | − | 0.478188i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.5068i | − | 0.507528i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 1.30737i | − | 0.0456831i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 15.0616i | − | 0.525652i | −0.964843 | − | 0.262826i | \(-0.915345\pi\) | ||
0.964843 | − | 0.262826i | \(-0.0846545\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.5669i | 1.17007i | 0.811009 | + | 0.585034i | \(0.198919\pi\) | ||||
−0.811009 | + | 0.585034i | \(0.801081\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.6742 | + | 40.9237i | 0.754599 | + | 1.42478i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.6576 | −0.370600 | −0.185300 | − | 0.982682i | \(-0.559326\pi\) | ||||
−0.185300 | + | 0.982682i | \(0.559326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 52.4846i | − | 1.82287i | −0.411447 | − | 0.911433i | \(-0.634977\pi\) | ||
0.411447 | − | 0.911433i | \(-0.365023\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.47027 | −0.0856926 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 0.267938i | − | 0.00928351i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.44748 | − | 2.09890i | 0.292337 | − | 0.0726353i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.6270 | 0.851234 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.2101 | −0.628682 | −0.314341 | − | 0.949310i | \(-0.601783\pi\) | ||||
−0.314341 | + | 0.949310i | \(0.601783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.2618 | 0.732295 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.6647 | − | 59.0216i | −0.504483 | − | 2.03040i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.3051i | 1.65978i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.7526 | 0.369028 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.88428i | 0.270270i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.7542 | 0.676371 | 0.338185 | − | 0.941080i | \(-0.390187\pi\) | ||||
0.338185 | + | 0.941080i | \(0.390187\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.554787 | + | 0.137845i | −0.0189733 | + | 0.00471419i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.9939i | 1.67360i | 0.547510 | + | 0.836799i | \(0.315576\pi\) | ||||
−0.547510 | + | 0.836799i | \(0.684424\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.3090i | 0.829412i | 0.909956 | + | 0.414706i | \(0.136115\pi\) | ||||
−0.909956 | + | 0.414706i | \(0.863885\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 34.8904i | 1.18906i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.3584i | 1.50998i | 0.655737 | + | 0.754989i | \(0.272358\pi\) | ||||
−0.655737 | + | 0.754989i | \(0.727642\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.779243 | − | 3.13624i | −0.0264950 | − | 0.106635i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.08225 | −0.308449 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 68.7091i | 2.33080i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.8720 | 1.68985 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.359084i | − | 0.0121531i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.9071 | − | 19.6286i | 0.740594 | − | 0.663569i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.9565 | 1.28170 | 0.640850 | − | 0.767666i | \(-0.278582\pi\) | ||||
0.640850 | + | 0.767666i | \(0.278582\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.84324 | 0.0621711 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.0661 | 0.844498 | 0.422249 | − | 0.906480i | \(-0.361241\pi\) | ||||
0.422249 | + | 0.906480i | \(0.361241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.1278 | 0.711008 | 0.355504 | − | 0.934675i | \(-0.384309\pi\) | ||||
0.355504 | + | 0.934675i | \(0.384309\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.0989 | + | 3.00614i | −0.406700 | + | 0.101050i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 36.1894i | − | 1.21512i | −0.794274 | − | 0.607560i | \(-0.792148\pi\) | ||
0.794274 | − | 0.607560i | \(-0.207852\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.13170 | 0.172112 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 47.4596i | − | 1.58996i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.6163 | −0.522581 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.9155 | + | 6.43907i | −0.866259 | + | 0.215234i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.8371i | 0.495396i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 9.36069i | − | 0.312197i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.67420i | − | 0.189035i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 20.0000i | − | 0.665558i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.3340 | + | 8.28231i | −1.10806 | + | 0.275313i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.2678 | 1.17105 | 0.585523 | − | 0.810656i | \(-0.300889\pi\) | ||||
0.585523 | + | 0.810656i | \(0.300889\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.181328i | 0.00601426i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0061 | 0.497176 | 0.248588 | − | 0.968609i | \(-0.420034\pi\) | ||||
0.248588 | + | 0.968609i | \(0.420034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 81.1215i | 2.68473i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.26180 | − | 2.30122i | 0.306186 | − | 0.0760761i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 40.9770 | 1.35318 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.8781 | −1.08455 | −0.542275 | − | 0.840201i | \(-0.682437\pi\) | ||||
−0.542275 | + | 0.840201i | \(0.682437\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 43.1194 | 1.42083 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.0349 | 1.28485 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.4452 | + | 13.4764i | −0.836633 | + | 0.443102i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1.27021i | − | 0.0417190i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.2290 | 0.991781 | 0.495890 | − | 0.868385i | \(-0.334842\pi\) | ||||
0.495890 | + | 0.868385i | \(0.334842\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.255652i | 0.00837866i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.1978 | 1.05411 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.98771 | − | 40.1978i | −0.326633 | − | 1.31461i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28.4124i | − | 0.928193i | −0.885785 | − | 0.464096i | \(-0.846379\pi\) | ||
0.885785 | − | 0.464096i | \(-0.153621\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 25.9877i | − | 0.848077i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.0821i | 1.37184i | 0.727679 | + | 0.685918i | \(0.240599\pi\) | ||||
−0.727679 | + | 0.685918i | \(0.759401\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.6225i | 0.345916i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −30.0410 | + | 7.46412i | −0.977235 | + | 0.242808i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.2739 | −0.723805 | −0.361902 | − | 0.932216i | \(-0.617873\pi\) | ||||
−0.361902 | + | 0.932216i | \(0.617873\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 86.0698i | − | 2.79394i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.8248 | 0.934709 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.6681i | 0.475145i | 0.971370 | + | 0.237573i | \(0.0763517\pi\) | ||||
−0.971370 | + | 0.237573i | \(0.923648\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.6742 | + | 55.0349i | 0.442487 | + | 1.78089i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18.5236 | −0.598783 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.0000 | −1.29167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.09436 | −0.293367 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.22672 | 0.0395306 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.94214 | + | 2.47027i | −0.320049 | + | 0.0795207i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.403997i | 0.0129917i | 0.999979 | + | 0.00649584i | \(0.00206770\pi\) | ||||
−0.999979 | + | 0.00649584i | \(0.997932\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19.0595 | −0.612278 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 46.8326i | − | 1.50293i | −0.659774 | − | 0.751464i | \(-0.729348\pi\) | ||
0.659774 | − | 0.751464i | \(-0.270652\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.79153 | −0.217726 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −47.8843 | + | 25.3607i | −1.53352 | + | 0.812192i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 53.6041i | − | 1.71495i | −0.514529 | − | 0.857473i | \(-0.672033\pi\) | ||
0.514529 | − | 0.857473i | \(-0.327967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 46.1855i | − | 1.47610i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 0.967195i | − | 0.0308802i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 19.9916i | − | 0.637633i | −0.947817 | − | 0.318816i | \(-0.896715\pi\) | ||
0.947817 | − | 0.318816i | \(-0.103285\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.09275 | + | 36.5958i | 0.289719 | + | 1.16604i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.5297 | −0.685299 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 6.08906i | − | 0.193621i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.6270 | 0.782303 | 0.391152 | − | 0.920326i | \(-0.372077\pi\) | ||||
0.391152 | + | 0.920326i | \(0.372077\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 40.2967i | − | 1.27878i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.30737 | − | 21.3607i | −0.168255 | − | 0.677179i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.9795 | −0.664427 | −0.332213 | − | 0.943204i | \(-0.607795\pi\) | ||||
−0.332213 | + | 0.943204i | \(0.607795\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 30.3012 | 0.958688 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1280.2.f.k.129.1 | 6 | ||
4.3 | odd | 2 | 1280.2.f.i.129.5 | 6 | |||
5.4 | even | 2 | 1280.2.f.j.129.5 | 6 | |||
8.3 | odd | 2 | 1280.2.f.l.129.2 | 6 | |||
8.5 | even | 2 | 1280.2.f.j.129.6 | 6 | |||
16.3 | odd | 4 | 640.2.c.a.129.5 | yes | 6 | ||
16.5 | even | 4 | 640.2.c.c.129.5 | yes | 6 | ||
16.11 | odd | 4 | 640.2.c.d.129.2 | yes | 6 | ||
16.13 | even | 4 | 640.2.c.b.129.2 | yes | 6 | ||
20.19 | odd | 2 | 1280.2.f.l.129.1 | 6 | |||
40.19 | odd | 2 | 1280.2.f.i.129.6 | 6 | |||
40.29 | even | 2 | inner | 1280.2.f.k.129.2 | 6 | ||
80.3 | even | 4 | 3200.2.a.bs.1.1 | 3 | |||
80.13 | odd | 4 | 3200.2.a.br.1.3 | 3 | |||
80.19 | odd | 4 | 640.2.c.a.129.2 | ✓ | 6 | ||
80.27 | even | 4 | 3200.2.a.bv.1.1 | 3 | |||
80.29 | even | 4 | 640.2.c.b.129.5 | yes | 6 | ||
80.37 | odd | 4 | 3200.2.a.bo.1.3 | 3 | |||
80.43 | even | 4 | 3200.2.a.bp.1.3 | 3 | |||
80.53 | odd | 4 | 3200.2.a.bu.1.1 | 3 | |||
80.59 | odd | 4 | 640.2.c.d.129.5 | yes | 6 | ||
80.67 | even | 4 | 3200.2.a.bq.1.3 | 3 | |||
80.69 | even | 4 | 640.2.c.c.129.2 | yes | 6 | ||
80.77 | odd | 4 | 3200.2.a.bt.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.2.c.a.129.2 | ✓ | 6 | 80.19 | odd | 4 | ||
640.2.c.a.129.5 | yes | 6 | 16.3 | odd | 4 | ||
640.2.c.b.129.2 | yes | 6 | 16.13 | even | 4 | ||
640.2.c.b.129.5 | yes | 6 | 80.29 | even | 4 | ||
640.2.c.c.129.2 | yes | 6 | 80.69 | even | 4 | ||
640.2.c.c.129.5 | yes | 6 | 16.5 | even | 4 | ||
640.2.c.d.129.2 | yes | 6 | 16.11 | odd | 4 | ||
640.2.c.d.129.5 | yes | 6 | 80.59 | odd | 4 | ||
1280.2.f.i.129.5 | 6 | 4.3 | odd | 2 | |||
1280.2.f.i.129.6 | 6 | 40.19 | odd | 2 | |||
1280.2.f.j.129.5 | 6 | 5.4 | even | 2 | |||
1280.2.f.j.129.6 | 6 | 8.5 | even | 2 | |||
1280.2.f.k.129.1 | 6 | 1.1 | even | 1 | trivial | ||
1280.2.f.k.129.2 | 6 | 40.29 | even | 2 | inner | ||
1280.2.f.l.129.1 | 6 | 20.19 | odd | 2 | |||
1280.2.f.l.129.2 | 6 | 8.3 | odd | 2 | |||
3200.2.a.bo.1.3 | 3 | 80.37 | odd | 4 | |||
3200.2.a.bp.1.3 | 3 | 80.43 | even | 4 | |||
3200.2.a.bq.1.3 | 3 | 80.67 | even | 4 | |||
3200.2.a.br.1.3 | 3 | 80.13 | odd | 4 | |||
3200.2.a.bs.1.1 | 3 | 80.3 | even | 4 | |||
3200.2.a.bt.1.1 | 3 | 80.77 | odd | 4 | |||
3200.2.a.bu.1.1 | 3 | 80.53 | odd | 4 | |||
3200.2.a.bv.1.1 | 3 | 80.27 | even | 4 |