Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(47,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.y (of order \(12\), degree \(4\), 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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 335.12 | ||
Character | \(\chi\) | \(=\) | 576.335 |
Dual form | 576.2.y.a.239.12 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 0.412428 | − | 1.68223i | 0.238116 | − | 0.971237i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.289971 | + | 0.0776974i | 0.129679 | + | 0.0347473i | 0.323075 | − | 0.946373i | \(-0.395283\pi\) |
−0.193396 | + | 0.981121i | \(0.561950\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.374023 | − | 0.647827i | 0.141367 | − | 0.244855i | −0.786644 | − | 0.617406i | \(-0.788183\pi\) |
0.928012 | + | 0.372551i | \(0.121517\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.65981 | − | 1.38760i | −0.886602 | − | 0.462533i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.23720 | − | 0.599457i | 0.674542 | − | 0.180743i | 0.0947421 | − | 0.995502i | \(-0.469797\pi\) |
0.579800 | + | 0.814759i | \(0.303131\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.60318 | + | 0.429571i | 0.444642 | + | 0.119142i | 0.474191 | − | 0.880422i | \(-0.342740\pi\) |
−0.0295491 | + | 0.999563i | \(0.509407\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.250297 | − | 0.455753i | 0.0646264 | − | 0.117675i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.74518i | − | 1.63595i | −0.575256 | − | 0.817973i | \(-0.695098\pi\) | ||
0.575256 | − | 0.817973i | \(-0.304902\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.621335 | − | 0.621335i | −0.142544 | − | 0.142544i | 0.632234 | − | 0.774778i | \(-0.282138\pi\) |
−0.774778 | + | 0.632234i | \(0.782138\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.935537 | − | 0.896375i | −0.204151 | − | 0.195605i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.06191 | − | 3.49985i | 1.26400 | − | 0.729769i | 0.290151 | − | 0.956981i | \(-0.406294\pi\) |
0.973845 | + | 0.227212i | \(0.0729611\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.25208 | − | 2.45494i | −0.850416 | − | 0.490988i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.43124 | + | 3.90212i | −0.660343 | + | 0.750964i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.44240 | + | 1.45829i | −1.01063 | + | 0.270797i | −0.725892 | − | 0.687809i | \(-0.758573\pi\) |
−0.284736 | + | 0.958606i | \(0.591906\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.13647 | + | 1.81084i | −0.563326 | + | 0.325236i | −0.754479 | − | 0.656324i | \(-0.772111\pi\) |
0.191153 | + | 0.981560i | \(0.438777\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0857395 | − | 4.01073i | −0.0149253 | − | 0.698178i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.158790 | − | 0.158790i | 0.0268404 | − | 0.0268404i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.74053 | + | 6.74053i | 1.10814 | + | 1.10814i | 0.993396 | + | 0.114740i | \(0.0366036\pi\) |
0.114740 | + | 0.993396i | \(0.463396\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.38383 | − | 2.51975i | 0.221591 | − | 0.403483i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.39492 | − | 2.41607i | −0.217850 | − | 0.377327i | 0.736301 | − | 0.676655i | \(-0.236571\pi\) |
−0.954150 | + | 0.299328i | \(0.903238\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.89907 | − | 7.08744i | −0.289606 | − | 1.08082i | −0.945407 | − | 0.325891i | \(-0.894336\pi\) |
0.655801 | − | 0.754934i | \(-0.272331\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.663453 | − | 0.609023i | −0.0989017 | − | 0.0907878i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.307120 | + | 0.531947i | −0.0447980 | + | 0.0775924i | −0.887555 | − | 0.460702i | \(-0.847598\pi\) |
0.842757 | + | 0.538294i | \(0.180931\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.22021 | + | 5.57757i | 0.460031 | + | 0.796796i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.3470 | − | 2.78190i | −1.58889 | − | 0.389544i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.68523 | − | 2.68523i | 0.368844 | − | 0.368844i | −0.498211 | − | 0.867056i | \(-0.666010\pi\) |
0.867056 | + | 0.498211i | \(0.166010\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.695300 | 0.0937542 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.30149 | + | 0.788974i | −0.172386 | + | 0.104502i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.00225603 | − | 0.00841962i | 0.000293710 | − | 0.00109614i | −0.965779 | − | 0.259367i | \(-0.916486\pi\) |
0.966073 | + | 0.258271i | \(0.0831527\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.72542 | + | 10.1714i | 0.348955 | + | 1.30232i | 0.887924 | + | 0.459991i | \(0.152147\pi\) |
−0.538969 | + | 0.842326i | \(0.681186\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.89375 | + | 1.20410i | −0.238590 | + | 0.151702i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.431499 | + | 0.249126i | 0.0535208 | + | 0.0309003i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.35300 | + | 8.78151i | −0.287464 | + | 1.07283i | 0.659555 | + | 0.751656i | \(0.270745\pi\) |
−0.947020 | + | 0.321176i | \(0.895922\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.38745 | − | 11.6410i | −0.407801 | − | 1.40141i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 15.9645i | − | 1.89463i | −0.320297 | − | 0.947317i | \(-0.603783\pi\) | ||
0.320297 | − | 0.947317i | \(-0.396217\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.17785i | − | 0.957145i | −0.878048 | − | 0.478572i | \(-0.841154\pi\) | ||
0.878048 | − | 0.478572i | \(-0.158846\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.88346 | + | 6.14050i | −0.679363 | + | 0.709044i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.448421 | − | 1.67353i | 0.0511023 | − | 0.190717i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.67035 | + | 4.42848i | 0.862982 | + | 0.498243i | 0.865010 | − | 0.501755i | \(-0.167312\pi\) |
−0.00202794 | + | 0.999998i | \(0.500646\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.14914 | + | 7.38149i | 0.572126 | + | 0.820166i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.353727 | + | 1.32013i | 0.0388266 | + | 0.144903i | 0.982618 | − | 0.185638i | \(-0.0594353\pi\) |
−0.943791 | + | 0.330541i | \(0.892769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.524083 | − | 1.95590i | 0.0568448 | − | 0.212148i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.208577 | + | 9.75681i | 0.0223618 | + | 1.04604i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.7852 | 1.67323 | 0.836613 | − | 0.547794i | \(-0.184532\pi\) | ||||
0.836613 | + | 0.547794i | \(0.184532\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.877914 | − | 0.877914i | 0.0920304 | − | 0.0920304i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.75268 | + | 6.02310i | 0.181745 | + | 0.624567i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.131893 | − | 0.228445i | −0.0135319 | − | 0.0234380i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.62075 | + | 8.00338i | −0.469166 | + | 0.812620i | −0.999379 | − | 0.0352448i | \(-0.988779\pi\) |
0.530212 | + | 0.847865i | \(0.322112\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.78233 | − | 1.50990i | −0.681650 | − | 0.151751i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.08762 | + | 15.2552i | 0.406734 | + | 1.51795i | 0.800835 | + | 0.598885i | \(0.204389\pi\) |
−0.394102 | + | 0.919067i | \(0.628944\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.63994 | + | 9.76866i | 0.555720 | + | 0.962535i | 0.997847 | + | 0.0655828i | \(0.0208906\pi\) |
−0.442127 | + | 0.896952i | \(0.645776\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.201632 | − | 0.332611i | −0.0196773 | − | 0.0324595i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.39963 | + | 9.39963i | 0.908696 | + | 0.908696i | 0.996167 | − | 0.0874707i | \(-0.0278784\pi\) |
−0.0874707 | + | 0.996167i | \(0.527878\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.535130 | − | 0.535130i | 0.0512562 | − | 0.0512562i | −0.681014 | − | 0.732270i | \(-0.738461\pi\) |
0.732270 | + | 0.681014i | \(0.238461\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.1191 | − | 8.55914i | 1.34013 | − | 0.812398i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.53279 | − | 2.03966i | 0.332337 | − | 0.191875i | −0.324541 | − | 0.945872i | \(-0.605210\pi\) |
0.656878 | + | 0.753997i | \(0.271877\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.02971 | − | 0.543858i | 0.189271 | − | 0.0507150i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.66808 | − | 3.36715i | −0.339114 | − | 0.311293i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.36971 | − | 2.52285i | −0.400570 | − | 0.231269i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.88055 | + | 2.81779i | −0.443686 | + | 0.256162i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.63969 | + | 1.35012i | −0.418347 | + | 0.121736i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.10360 | − | 2.10360i | −0.188152 | − | 0.188152i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.78789i | 0.158650i | 0.996849 | + | 0.0793250i | \(0.0252765\pi\) | ||||
−0.996849 | + | 0.0793250i | \(0.974724\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.7060 | + | 0.271622i | −1.11870 | + | 0.0239150i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.87165 | − | 1.03741i | −0.338268 | − | 0.0906386i | 0.0856865 | − | 0.996322i | \(-0.472692\pi\) |
−0.423954 | + | 0.905684i | \(0.639358\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.634911 | + | 0.170124i | −0.0550538 | + | 0.0147516i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.29814 | + | 0.864903i | −0.111727 | + | 0.0744390i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.396519 | − | 0.686792i | 0.0338769 | − | 0.0586766i | −0.848590 | − | 0.529051i | \(-0.822548\pi\) |
0.882467 | + | 0.470375i | \(0.155881\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.7067 | + | 4.74448i | 1.50186 | + | 0.402422i | 0.913722 | − | 0.406340i | \(-0.133195\pi\) |
0.588137 | + | 0.808762i | \(0.299862\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.768193 | + | 0.736036i | 0.0646935 | + | 0.0619854i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.84415 | 0.321464 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.69144 | −0.140467 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.7109 | − | 3.11680i | 0.883418 | − | 0.257069i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.6146 | − | 3.38007i | −1.03343 | − | 0.276906i | −0.298041 | − | 0.954553i | \(-0.596333\pi\) |
−0.735388 | + | 0.677647i | \(0.763000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.45023 | + | 16.3683i | −0.769049 | + | 1.33203i | 0.169030 | + | 0.985611i | \(0.445937\pi\) |
−0.938079 | + | 0.346421i | \(0.887397\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.35961 | + | 17.9409i | −0.756679 | + | 1.45043i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.05018 | + | 0.281395i | −0.0843526 | + | 0.0226022i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.20155 | − | 2.46555i | −0.734364 | − | 0.196772i | −0.127792 | − | 0.991801i | \(-0.540789\pi\) |
−0.606572 | + | 0.795029i | \(0.707456\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.40971 | − | 5.62463i | −0.270408 | − | 0.446063i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 5.23609i | − | 0.412662i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.24968 | + | 6.24968i | 0.489512 | + | 0.489512i | 0.908152 | − | 0.418640i | \(-0.137493\pi\) |
−0.418640 | + | 0.908152i | \(0.637493\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.286761 | − | 1.16965i | 0.0223243 | − | 0.0910575i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.96426 | + | 4.59817i | −0.616293 | + | 0.355817i | −0.775424 | − | 0.631441i | \(-0.782464\pi\) |
0.159132 | + | 0.987257i | \(0.449131\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.87267 | − | 5.12264i | −0.682513 | − | 0.394049i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.790467 | + | 2.51480i | 0.0604485 | + | 0.192311i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.67137 | − | 2.05554i | 0.583243 | − | 0.156280i | 0.0448800 | − | 0.998992i | \(-0.485709\pi\) |
0.538363 | + | 0.842713i | \(0.319043\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.18075 | + | 1.83641i | −0.240442 | + | 0.138819i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.0132333 | − | 0.00726765i | −0.000994675 | − | 0.000546270i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.99447 | − | 7.99447i | 0.597535 | − | 0.597535i | −0.342121 | − | 0.939656i | \(-0.611145\pi\) |
0.939656 | + | 0.342121i | \(0.111145\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5271 | + | 14.5271i | 1.07979 | + | 1.07979i | 0.996527 | + | 0.0832666i | \(0.0265353\pi\) |
0.0832666 | + | 0.996527i | \(0.473465\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.2347 | − | 0.389813i | 1.34795 | − | 0.0288158i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.43083 | + | 2.47828i | 0.105197 | + | 0.182207i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.04344 | − | 15.0903i | −0.295686 | − | 1.10351i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.24454 | + | 3.68233i | 0.0905268 | + | 0.267850i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.2382 | + | 17.7332i | −0.740813 | + | 1.28313i | 0.211312 | + | 0.977419i | \(0.432226\pi\) |
−0.952125 | + | 0.305708i | \(0.901107\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.37336 | − | 4.11078i | −0.170838 | − | 0.295901i | 0.767875 | − | 0.640600i | \(-0.221314\pi\) |
−0.938713 | + | 0.344699i | \(0.887981\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.597050 | − | 0.623134i | 0.0427556 | − | 0.0446236i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.65282 | + | 6.65282i | −0.473994 | + | 0.473994i | −0.903205 | − | 0.429210i | \(-0.858792\pi\) |
0.429210 | + | 0.903205i | \(0.358792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.8401 | −1.61909 | −0.809544 | − | 0.587059i | \(-0.800286\pi\) | ||||
−0.809544 | + | 0.587059i | \(0.800286\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.8021 | + | 7.58003i | 0.973524 | + | 0.534654i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.09087 | + | 4.07116i | −0.0765637 | + | 0.285740i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.216763 | − | 0.808971i | −0.0151394 | − | 0.0565010i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.9799 | + | 0.897407i | −1.45820 | + | 0.0623741i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.76252 | − | 1.01759i | −0.121916 | − | 0.0703881i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.96884 | − | 14.8119i | 0.273226 | − | 1.01969i | −0.683795 | − | 0.729674i | \(-0.739672\pi\) |
0.957021 | − | 0.290019i | \(-0.0936616\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −26.8559 | − | 6.58420i | −1.84014 | − | 0.451142i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2.20270i | − | 0.150223i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.70918i | 0.183911i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.7570 | − | 3.37277i | −0.929614 | − | 0.227911i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.89753 | − | 10.8137i | 0.194909 | − | 0.727411i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.39965 | + | 3.69484i | 0.428552 | + | 0.247425i | 0.698730 | − | 0.715386i | \(-0.253749\pi\) |
−0.270178 | + | 0.962811i | \(0.587082\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.90324 | + | 12.4298i | 0.526882 | + | 0.828657i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.52301 | + | 20.6122i | 0.366575 | + | 1.36808i | 0.865273 | + | 0.501301i | \(0.167145\pi\) |
−0.498698 | + | 0.866776i | \(0.666188\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.76891 | − | 17.7978i | 0.315138 | − | 1.17611i | −0.608722 | − | 0.793383i | \(-0.708318\pi\) |
0.923861 | − | 0.382729i | \(-0.125016\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.63032 | − | 1.44456i | −0.173063 | − | 0.0950450i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.3249 | 0.938455 | 0.469228 | − | 0.883077i | \(-0.344532\pi\) | ||||
0.469228 | + | 0.883077i | \(0.344532\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.130387 | + | 0.130387i | −0.00850548 | + | 0.00850548i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.6132 | − | 11.0769i | 0.689401 | − | 0.719520i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.4921 | − | 19.9049i | −0.743364 | − | 1.28754i | −0.950955 | − | 0.309328i | \(-0.899896\pi\) |
0.207592 | − | 0.978216i | \(-0.433438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2735 | − | 17.7943i | 0.661777 | − | 1.14623i | −0.318372 | − | 0.947966i | \(-0.603136\pi\) |
0.980148 | − | 0.198265i | \(-0.0635306\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.5410 | − | 5.61770i | 0.932807 | − | 0.360376i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.500405 | + | 1.86754i | 0.0319697 | + | 0.119312i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.729205 | − | 1.26302i | −0.0463982 | − | 0.0803640i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.36665 | − | 0.0505931i | 0.149980 | − | 0.00320621i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.440838 | + | 0.440838i | 0.0278255 | + | 0.0278255i | 0.720883 | − | 0.693057i | \(-0.243737\pi\) |
−0.693057 | + | 0.720883i | \(0.743737\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.4637 | − | 11.4637i | 0.720718 | − | 0.720718i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.07414 | − | 1.68830i | −0.192510 | − | 0.105725i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.78636 | + | 2.76341i | −0.298565 | + | 0.172377i | −0.641798 | − | 0.766874i | \(-0.721811\pi\) |
0.343233 | + | 0.939250i | \(0.388478\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.88781 | − | 1.84558i | 0.427987 | − | 0.114679i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.4992 | + | 3.67311i | 1.02128 | + | 0.227360i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.83474 | − | 2.79134i | −0.298123 | − | 0.172121i | 0.343477 | − | 0.939161i | \(-0.388395\pi\) |
−0.641599 | + | 0.767040i | \(0.721729\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.987272 | − | 0.570002i | 0.0606476 | − | 0.0350149i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.51026 | − | 26.5543i | 0.398421 | − | 1.62510i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.66733 | − | 1.66733i | −0.101659 | − | 0.101659i | 0.654448 | − | 0.756107i | \(-0.272901\pi\) |
−0.756107 | + | 0.654448i | \(0.772901\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 23.2740i | − | 1.41379i | −0.707317 | − | 0.706897i | \(-0.750095\pi\) | ||
0.707317 | − | 0.706897i | \(-0.249905\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.11478 | − | 1.83893i | −0.0674694 | − | 0.111297i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.9844 | − | 2.94326i | −0.662384 | − | 0.177485i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.684687 | + | 0.183461i | −0.0411389 | + | 0.0110231i | −0.279330 | − | 0.960195i | \(-0.590112\pi\) |
0.238191 | + | 0.971218i | \(0.423446\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.8551 | − | 0.464323i | 0.649879 | − | 0.0277983i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.29162 | − | 3.96921i | 0.136707 | − | 0.236783i | −0.789541 | − | 0.613697i | \(-0.789682\pi\) |
0.926248 | + | 0.376914i | \(0.123015\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.0269 | − | 3.75850i | −0.833814 | − | 0.223420i | −0.183437 | − | 0.983031i | \(-0.558722\pi\) |
−0.650377 | + | 0.759612i | \(0.725389\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.438694 | + | 0.127657i | −0.0259860 | + | 0.00756176i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.08693 | −0.123187 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −28.4974 | −1.67632 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.5578 | + | 11.0740i | 0.677531 | + | 0.649169i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.04141 | − | 1.61879i | −0.352943 | − | 0.0945708i | 0.0779914 | − | 0.996954i | \(-0.475149\pi\) |
−0.430934 | + | 0.902383i | \(0.641816\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.00130836 | − | 0.00226615i | 7.61760e−5 | − | 0.000131941i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.33723 | + | 10.7867i | −0.309698 | + | 0.625909i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.2218 | − | 3.00687i | 0.648972 | − | 0.173892i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.30173 | − | 1.42059i | −0.305587 | − | 0.0818817i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.3487 | − | 0.584647i | 1.57114 | − | 0.0335871i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.16117i | 0.181008i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.52060 | + | 4.52060i | 0.258004 | + | 0.258004i | 0.824242 | − | 0.566238i | \(-0.191602\pi\) |
−0.566238 | + | 0.824242i | \(0.691602\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.7592 | − | 5.45881i | 1.06718 | − | 0.310541i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.9637 | + | 6.32992i | −0.621697 | + | 0.358937i | −0.777529 | − | 0.628847i | \(-0.783527\pi\) |
0.155832 | + | 0.987784i | \(0.450194\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.6282 | + | 9.60027i | 0.939879 | + | 0.542640i | 0.889922 | − | 0.456112i | \(-0.150758\pi\) |
0.0499568 | + | 0.998751i | \(0.484092\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.642688 | + | 0.202014i | −0.0362114 | + | 0.0113822i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.0834 | + | 2.96978i | −0.622504 | + | 0.166800i | −0.556266 | − | 0.831004i | \(-0.687766\pi\) |
−0.0662384 | + | 0.997804i | \(0.521100\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.3016 | + | 6.52497i | −0.632767 | + | 0.365328i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.6890 | − | 11.9357i | 1.09893 | − | 0.666185i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.19102 | + | 4.19102i | −0.233194 | + | 0.233194i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.76228 | − | 5.76228i | −0.319634 | − | 0.319634i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.679510 | − | 1.12092i | −0.0375770 | − | 0.0619868i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.229740 | + | 0.397921i | 0.0126660 | + | 0.0219381i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.08741 | − | 18.9865i | −0.279630 | − | 1.04359i | −0.952675 | − | 0.303991i | \(-0.901681\pi\) |
0.673045 | − | 0.739601i | \(-0.264986\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.57534 | − | 27.2816i | −0.469926 | − | 1.49502i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.36460 | + | 2.36356i | −0.0745561 | + | 0.129135i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.99010 | + | 8.64310i | 0.271828 | + | 0.470820i | 0.969330 | − | 0.245763i | \(-0.0790385\pi\) |
−0.697502 | + | 0.716583i | \(0.745705\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.97415 | − | 6.78418i | −0.107221 | − | 0.368466i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.93139 | + | 5.93139i | −0.321203 | + | 0.321203i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0541 | 0.542868 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0777873 | − | 3.63874i | −0.00418793 | − | 0.195903i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.81153 | − | 6.76074i | 0.0972483 | − | 0.362935i | −0.900102 | − | 0.435678i | \(-0.856509\pi\) |
0.997351 | + | 0.0727428i | \(0.0231752\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.23119 | − | 19.5231i | −0.280019 | − | 1.04505i | −0.952403 | − | 0.304843i | \(-0.901396\pi\) |
0.672383 | − | 0.740203i | \(-0.265271\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.17714 | + | 4.78185i | −0.383087 | + | 0.255236i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.37682 | + | 4.83636i | 0.445853 | + | 0.257414i | 0.706077 | − | 0.708135i | \(-0.250463\pi\) |
−0.260224 | + | 0.965548i | \(0.583796\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.24040 | − | 4.62923i | 0.0658335 | − | 0.245694i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.04621 | + | 6.31037i | −0.319999 | + | 0.333980i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 0.846908i | − | 0.0446981i | −0.999750 | − | 0.0223491i | \(-0.992885\pi\) | ||
0.999750 | − | 0.0223491i | \(-0.00711452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.2279i | − | 0.959362i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.72729 | + | 9.37235i | 0.143146 | + | 0.491921i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.635398 | − | 2.37134i | 0.0332582 | − | 0.124121i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.5960 | + | 9.00434i | 0.814103 | + | 0.470023i | 0.848379 | − | 0.529390i | \(-0.177579\pi\) |
−0.0342756 | + | 0.999412i | \(0.510912\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.357676 | + | 8.36187i | 0.0186199 | + | 0.435301i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.735225 | − | 2.74390i | −0.0381710 | − | 0.142456i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.01296 | − | 18.7086i | 0.259561 | − | 0.968696i | −0.705934 | − | 0.708277i | \(-0.749473\pi\) |
0.965496 | − | 0.260419i | \(-0.0838607\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.40633 | + | 2.67116i | −0.227542 | + | 0.137938i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.35158 | −0.481631 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.14922 | + | 7.14922i | −0.367231 | + | 0.367231i | −0.866466 | − | 0.499235i | \(-0.833614\pi\) |
0.499235 | + | 0.866466i | \(0.333614\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.00765 | + | 0.737378i | 0.154087 | + | 0.0377770i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.80911 | − | 6.59757i | −0.194636 | − | 0.337120i | 0.752145 | − | 0.658998i | \(-0.229019\pi\) |
−0.946781 | + | 0.321878i | \(0.895686\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.260058 | − | 0.450434i | 0.0132538 | − | 0.0229562i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.78336 | + | 21.4864i | −0.243152 | + | 1.09221i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.417448 | − | 1.55794i | −0.0211654 | − | 0.0789905i | 0.954535 | − | 0.298098i | \(-0.0963522\pi\) |
−0.975701 | + | 0.219107i | \(0.929686\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.6071 | − | 40.8887i | −1.19386 | − | 2.06783i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.34194 | + | 6.08516i | −0.168578 | + | 0.306956i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.88010 | + | 1.88010i | 0.0945979 | + | 0.0945979i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.8968 | + | 20.8968i | −1.04878 | + | 1.04878i | −0.0500326 | + | 0.998748i | \(0.515933\pi\) |
−0.998748 | + | 0.0500326i | \(0.984067\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0243326 | + | 1.13823i | 0.00121815 | + | 0.0569829i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.6619 | + | 9.61977i | −0.832057 | + | 0.480388i | −0.854557 | − | 0.519358i | \(-0.826171\pi\) |
0.0224993 | + | 0.999747i | \(0.492838\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.80621 | + | 1.55577i | −0.289228 | + | 0.0774983i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.919576 | + | 2.54049i | 0.0456941 | + | 0.126238i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.1206 | + | 11.0393i | 0.947772 | + | 0.547196i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.69044 | + | 2.70803i | −0.231928 | + | 0.133903i | −0.611461 | − | 0.791275i | \(-0.709418\pi\) |
0.379533 | + | 0.925178i | \(0.376085\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.991807 | − | 0.950290i | −0.0489222 | − | 0.0468743i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.00461065 | − | 0.00461065i | −0.000226875 | − | 0.000226875i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.410282i | 0.0201400i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.2840 | − | 27.8299i | 0.748463 | − | 1.36284i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.50669 | − | 1.74346i | −0.317873 | − | 0.0851738i | 0.0963549 | − | 0.995347i | \(-0.469282\pi\) |
−0.414228 | + | 0.910173i | \(0.635948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0218 | + | 5.09689i | −0.927068 | + | 0.248407i | −0.690604 | − | 0.723233i | \(-0.742655\pi\) |
−0.236464 | + | 0.971640i | \(0.575989\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.55501 | − | 0.988716i | 0.0756071 | − | 0.0480730i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.5590 | + | 28.6810i | −0.803230 | + | 1.39124i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.60869 | + | 2.03874i | 0.368210 | + | 0.0986616i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.58544 | − | 6.46675i | 0.0765456 | − | 0.312218i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.9770 | 1.10676 | 0.553380 | − | 0.832929i | \(-0.313338\pi\) | ||||
0.553380 | + | 0.832929i | \(0.313338\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.38876 | −0.451195 | −0.225598 | − | 0.974221i | \(-0.572433\pi\) | ||||
−0.225598 | + | 0.974221i | \(0.572433\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.697598 | + | 2.84540i | −0.0334473 | + | 0.136426i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.94106 | − | 1.59190i | −0.284199 | − | 0.0761510i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.64587 | − | 4.58278i | 0.126281 | − | 0.218724i | −0.795952 | − | 0.605359i | \(-0.793029\pi\) |
0.922233 | + | 0.386635i | \(0.126363\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.825706 | − | 19.3036i | −0.0393193 | − | 0.919220i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.7945 | + | 5.57188i | −0.987978 | + | 0.264728i | −0.716401 | − | 0.697689i | \(-0.754212\pi\) |
−0.271577 | + | 0.962417i | \(0.587545\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.57724 | + | 1.22647i | 0.216982 | + | 0.0581402i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.8887 | + | 19.8267i | −0.515017 | + | 0.937769i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.9162i | 1.08148i | 0.841189 | + | 0.540742i | \(0.181856\pi\) | ||||
−0.841189 | + | 0.540742i | \(0.818144\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.56905 | − | 4.56905i | −0.215148 | − | 0.215148i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.6377 | + | 22.6482i | 1.11060 | + | 1.06411i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.322781 | − | 0.186358i | 0.0151322 | − | 0.00873658i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.67987 | + | 1.54723i | 0.125359 | + | 0.0723761i | 0.561368 | − | 0.827566i | \(-0.310275\pi\) |
−0.436009 | + | 0.899942i | \(0.643608\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.3205 | + | 23.1443i | 1.22854 | + | 1.08029i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.53371 | − | 0.410957i | 0.0714320 | − | 0.0191402i | −0.222926 | − | 0.974835i | \(-0.571561\pi\) |
0.294358 | + | 0.955695i | \(0.404894\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0991508 | − | 0.0572447i | 0.00460793 | − | 0.00266039i | −0.497694 | − | 0.867353i | \(-0.665820\pi\) |
0.502302 | + | 0.864692i | \(0.332487\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.0402475 | + | 1.88270i | 0.00186644 | + | 0.0873082i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.325359 | + | 0.325359i | −0.0150558 | + | 0.0150558i | −0.714595 | − | 0.699539i | \(-0.753389\pi\) |
0.699539 | + | 0.714595i | \(0.253389\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.80882 | + | 4.80882i | 0.222051 | + | 0.222051i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.94260 | + | 14.4623i | −0.365976 | + | 0.666387i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.49723 | − | 14.7176i | −0.390703 | − | 0.676718i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.11663 | + | 4.16731i | 0.0512344 | + | 0.191209i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.8682 | + | 3.41616i | −0.497621 | + | 0.156415i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.17908 | − | 15.8986i | 0.419403 | − | 0.726427i | −0.576476 | − | 0.817114i | \(-0.695573\pi\) |
0.995879 | + | 0.0906864i | \(0.0289061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.91075 | + | 13.7018i | 0.360699 | + | 0.624749i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.80832 | − | 2.15951i | −0.400793 | − | 0.0982612i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.96173 | + | 1.96173i | −0.0890774 | + | 0.0890774i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.8691 | 1.12693 | 0.563464 | − | 0.826140i | \(-0.309468\pi\) | ||||
0.563464 | + | 0.826140i | \(0.309468\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.0909 | − | 7.93586i | 0.591993 | − | 0.358872i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.0538587 | + | 0.201003i | −0.00243061 | + | 0.00907115i | −0.967130 | − | 0.254281i | \(-0.918161\pi\) |
0.964700 | + | 0.263352i | \(0.0848280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.83640 | + | 36.7100i | 0.443009 | + | 1.65333i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.84936 | − | 0.964797i | −0.0831226 | − | 0.0433644i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.3422 | − | 5.97108i | −0.463912 | − | 0.267840i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.17443 | − | 34.2394i | 0.410704 | − | 1.53277i | −0.382584 | − | 0.923921i | \(-0.624966\pi\) |
0.793288 | − | 0.608847i | \(-0.208368\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.45050 | + | 15.2941i | 0.198833 | + | 0.683292i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.4177i | 1.75755i | 0.477239 | + | 0.878773i | \(0.341638\pi\) | ||||
−0.477239 | + | 0.878773i | \(0.658362\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.74117i | 0.210979i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.2768 | + | 12.8132i | −0.545232 | + | 0.569053i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.2393 | + | 38.2137i | −0.453850 | + | 1.69379i | 0.237598 | + | 0.971364i | \(0.423640\pi\) |
−0.691447 | + | 0.722427i | \(0.743027\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.29783 | − | 3.05870i | −0.234362 | − | 0.135309i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.55648 | − | 0.292576i | 0.201173 | − | 0.0129175i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.876418 | + | 3.27084i | 0.0386196 | + | 0.144130i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.368210 | + | 1.37418i | −0.0161939 | + | 0.0604363i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.294001 | − | 13.7528i | −0.0129052 | − | 0.603680i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.5152 | −0.942596 | −0.471298 | − | 0.881974i | \(-0.656214\pi\) | ||||
−0.471298 | + | 0.881974i | \(0.656214\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.8248 | + | 18.8248i | −0.823149 | + | 0.823149i | −0.986558 | − | 0.163409i | \(-0.947751\pi\) |
0.163409 | + | 0.986558i | \(0.447751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.77743 | + | 6.10815i | 0.0775735 | + | 0.266581i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.2144 | + | 21.1560i | 0.532069 | + | 0.921571i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.9979 | − | 22.5130i | 0.565125 | − | 0.978825i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0176837 | + | 0.0192641i | −0.000767405 | + | 0.000835990i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.19843 | − | 4.47261i | −0.0519099 | − | 0.193730i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.99529 | + | 3.45594i | 0.0862639 | + | 0.149413i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.1514 | − | 16.7457i | −0.438065 | − | 0.722630i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.5478 | + | 10.5478i | 0.454325 | + | 0.454325i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.5988 | − | 17.5988i | 0.756630 | − | 0.756630i | −0.219078 | − | 0.975707i | \(-0.570305\pi\) |
0.975707 | + | 0.219078i | \(0.0703048\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.4294 | − | 18.4466i | 1.30585 | − | 0.791620i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.196750 | − | 0.113594i | 0.00842786 | − | 0.00486583i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.1328 | + | 7.80612i | −1.24563 | + | 0.333765i | −0.820647 | − | 0.571436i | \(-0.806387\pi\) |
−0.424983 | + | 0.905201i | \(0.639720\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.86476 | − | 30.8358i | 0.292981 | − | 1.31604i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.28764 | + | 2.47547i | 0.182660 | + | 0.105459i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.73777 | − | 3.31270i | 0.243995 | − | 0.140871i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.75915 | − | 1.38488i | 0.202015 | − | 0.0587850i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.0618 | + | 25.0618i | 1.06190 | + | 1.06190i | 0.997953 | + | 0.0639497i | \(0.0203697\pi\) |
0.0639497 | + | 0.997953i | \(0.479630\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12.1782i | − | 0.515084i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.0531 | + | 0.578328i | −1.14218 | + | 0.0244170i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.8780 | − | 3.71859i | −0.584886 | − | 0.156720i | −0.0457710 | − | 0.998952i | \(-0.514574\pi\) |
−0.539115 | + | 0.842232i | \(0.681241\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.18288 | − | 0.316952i | 0.0497642 | − | 0.0133343i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.70782 | − | 0.574901i | 0.281702 | − | 0.0241436i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.1987 | − | 24.5928i | 0.595239 | − | 1.03098i | −0.398274 | − | 0.917267i | \(-0.630391\pi\) |
0.993513 | − | 0.113718i | \(-0.0362761\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.3238 | + | 4.64190i | 0.724978 | + | 0.194257i | 0.602392 | − | 0.798201i | \(-0.294214\pi\) |
0.122586 | + | 0.992458i | \(0.460881\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.6087 | + | 24.5368i | 1.06982 | + | 1.02504i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.3677 | −1.43323 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.1199 | −0.421295 | −0.210648 | − | 0.977562i | \(-0.567557\pi\) | ||||
−0.210648 | + | 0.977562i | \(0.567557\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.89413 | + | 2.29714i | −0.328069 | + | 0.0954660i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.987517 | + | 0.264604i | 0.0409691 | + | 0.0109776i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.39772 | − | 7.61707i | 0.182135 | − | 0.315467i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.802016 | − | 1.26137i | −0.0331593 | − | 0.0521514i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.9306 | − | 5.60833i | 0.863897 | − | 0.231480i | 0.200450 | − | 0.979704i | \(-0.435760\pi\) |
0.663447 | + | 0.748224i | \(0.269093\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.07394 | + | 0.823658i | 0.126659 | + | 0.0339383i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.44778 | + | 13.9354i | 0.347495 | + | 0.573226i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 20.8755i | − | 0.857256i | −0.903481 | − | 0.428628i | \(-0.858997\pi\) | ||
0.903481 | − | 0.428628i | \(-0.141003\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.07107 | − | 1.07107i | −0.0439095 | − | 0.0439095i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.41988 | + | 38.4223i | −0.385530 | + | 1.57252i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.64766 | − | 5.57008i | 0.394193 | − | 0.227587i | −0.289782 | − | 0.957093i | \(-0.593583\pi\) |
0.683975 | + | 0.729505i | \(0.260250\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.0323 | + | 12.1430i | 0.857927 | + | 0.495324i | 0.863317 | − | 0.504661i | \(-0.168383\pi\) |
−0.00539080 | + | 0.999985i | \(0.501716\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.4437 | − | 20.0921i | 0.751087 | − | 0.818213i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.63415 | + | 0.437870i | −0.0664377 | + | 0.0178019i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.4924 | + | 13.5633i | −0.953525 | + | 0.550518i | −0.894174 | − | 0.447719i | \(-0.852236\pi\) |
−0.0593510 | + | 0.998237i | \(0.518903\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.39874 | + | 3.51415i | 0.259290 | + | 0.142401i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.720877 | + | 0.720877i | −0.0291636 | + | 0.0291636i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.5272 | − | 25.5272i | −1.03103 | − | 1.03103i | −0.999503 | − | 0.0315305i | \(-0.989962\pi\) |
−0.0315305 | − | 0.999503i | \(-0.510038\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.45028 | + | 0.0310033i | −0.0584808 | + | 0.00125017i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.82807 | − | 6.63041i | −0.154112 | − | 0.266930i | 0.778623 | − | 0.627492i | \(-0.215918\pi\) |
−0.932735 | + | 0.360562i | \(0.882585\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.43446 | + | 31.4778i | 0.339009 | + | 1.26520i | 0.899457 | + | 0.437010i | \(0.143963\pi\) |
−0.560447 | + | 0.828190i | \(0.689371\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.14306 | + | 35.6632i | −0.286641 | + | 1.43111i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.90402 | − | 10.2261i | 0.236540 | − | 0.409699i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.8282 | + | 20.4870i | 0.473126 | + | 0.819479i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.43873 | + | 2.54528i | −0.0973936 | + | 0.101649i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 45.4661 | − | 45.4661i | 1.81285 | − | 1.81285i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.5675 | 0.818781 | 0.409390 | − | 0.912359i | \(-0.365741\pi\) | ||||
0.409390 | + | 0.912359i | \(0.365741\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.2802 | − | 12.7853i | −0.925304 | − | 0.508172i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.138915 | + | 0.518437i | −0.00551266 | + | 0.0205735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.76662 | + | 10.3252i | 0.109617 | + | 0.409098i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.1523 | + | 42.4624i | −0.876331 | + | 1.67979i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.3382 | + | 7.12347i | 0.487330 | + | 0.281360i | 0.723466 | − | 0.690360i | \(-0.242548\pi\) |
−0.236136 | + | 0.971720i | \(0.575881\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.10018 | + | 11.5700i | −0.122259 | + | 0.456277i | −0.999727 | − | 0.0233581i | \(-0.992564\pi\) |
0.877468 | + | 0.479635i | \(0.159231\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.70546 | − | 0.908457i | −0.145902 | − | 0.0357705i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 3.24662i | − | 0.127638i | −0.997961 | − | 0.0638189i | \(-0.979672\pi\) | ||
0.997961 | − | 0.0638189i | \(-0.0203280\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.0201888i | − | 0.000792479i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.55747 | + | 1.11734i | 0.178621 | + | 0.0437921i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.0259859 | + | 0.0969809i | −0.00101691 | + | 0.00379516i | −0.966432 | − | 0.256921i | \(-0.917292\pi\) |
0.965416 | + | 0.260716i | \(0.0839587\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.04206 | − | 0.601635i | −0.0407167 | − | 0.0235078i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.3476 | + | 21.7515i | −0.442711 | + | 0.848606i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.94194 | − | 18.4436i | −0.192511 | − | 0.718459i | −0.992897 | − | 0.118975i | \(-0.962039\pi\) |
0.800387 | − | 0.599484i | \(-0.204628\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.13036 | + | 26.6109i | −0.277339 | + | 1.03504i | 0.676919 | + | 0.736058i | \(0.263315\pi\) |
−0.954258 | + | 0.298985i | \(0.903352\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.9962 | − | 9.33421i | −0.660077 | − | 0.362511i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.197324 | −0.00765189 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.8876 | + | 27.8876i | −1.07981 | + | 1.07981i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.85497 | − | 9.24183i | 0.342353 | − | 0.357310i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.1947 | + | 21.1218i | 0.470769 | + | 0.815396i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.3890 | − | 37.0468i | 0.824484 | − | 1.42805i | −0.0778289 | − | 0.996967i | \(-0.524799\pi\) |
0.902313 | − | 0.431082i | \(-0.141868\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.1694 | − | 8.16865i | 0.930281 | − | 0.314412i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.00745 | + | 7.49190i | 0.0771525 | + | 0.287937i | 0.993713 | − | 0.111960i | \(-0.0357127\pi\) |
−0.916560 | + | 0.399897i | \(0.869046\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.45654 | + | 5.98690i | 0.132650 | + | 0.229756i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.9523 | − | 0.789949i | 1.41601 | − | 0.0302709i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.9083 | − | 31.9083i | −1.22094 | − | 1.22094i | −0.967299 | − | 0.253637i | \(-0.918373\pi\) |
−0.253637 | − | 0.967299i | \(-0.581627\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.168341 | − | 0.168341i | 0.00643198 | − | 0.00643198i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.9732 | − | 15.3627i | −1.06724 | − | 0.586125i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.45840 | − | 3.15141i | 0.207948 | − | 0.120059i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.1485 | + | 7.81032i | −1.10886 | + | 0.297118i | −0.766368 | − | 0.642402i | \(-0.777938\pi\) |
−0.342493 | + | 0.939520i | \(0.611271\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.51490 | + | 3.82904i | −0.133520 | + | 0.145453i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.76578 | + | 2.75152i | 0.180776 | + | 0.104371i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.2968 | + | 9.40898i | −0.617286 | + | 0.356390i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.90799 | − | 24.0978i | 0.223461 | − | 0.911462i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.92803 | − | 6.92803i | −0.261668 | − | 0.261668i | 0.564063 | − | 0.825732i | \(-0.309237\pi\) |
−0.825732 | + | 0.564063i | \(0.809237\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 8.37625i | − | 0.315916i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.165565 | + | 0.273116i | 0.00623555 | + | 0.0102861i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.4116 | + | 3.05773i | 0.429178 | + | 0.114998i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.8255 | + | 3.97247i | −0.556782 | + | 0.149189i | −0.526228 | − | 0.850344i | \(-0.676394\pi\) |
−0.0305546 | + | 0.999533i | \(0.509727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.2567 | − | 22.4223i | −0.534668 | − | 0.840901i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.6753 | + | 21.9543i | −0.474695 | + | 0.822195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.11469 | + | 0.298680i | 0.0416871 | + | 0.0111700i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −38.2244 | + | 11.1231i | −1.42752 | + | 0.415398i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.93438 | 0.258609 | 0.129304 | − | 0.991605i | \(-0.458726\pi\) | ||||
0.129304 | + | 0.991605i | \(0.458726\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.43787 | 0.314243 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.6970 | − | 24.6213i | −0.955682 | − | 0.915677i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.7215 | + | 7.16001i | 0.992412 | + | 0.265916i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.03023 | − | 12.1767i | 0.260737 | − | 0.451610i | −0.705701 | − | 0.708510i | \(-0.749368\pi\) |
0.966438 | + | 0.256900i | \(0.0827011\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.45315 | − | 26.7783i | −0.127894 | − | 0.991788i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −47.8061 | + | 12.8096i | −1.76817 | + | 0.473780i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.233976 | + | 0.0626936i | 0.00864209 | + | 0.00231564i | 0.263138 | − | 0.964758i | \(-0.415243\pi\) |
−0.254495 | + | 0.967074i | \(0.581909\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.34801 | − | 0.0715722i | 0.123493 | − | 0.00263998i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.0565i | 0.775627i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.77417 | + | 6.77417i | 0.249192 | + | 0.249192i | 0.820639 | − | 0.571447i | \(-0.193618\pi\) |
−0.571447 | + | 0.820639i | \(0.693618\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.42544 | + | 0.705786i | −0.0891006 | + | 0.0259277i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.26562 | − | 3.04011i | 0.193177 | − | 0.111531i | −0.400292 | − | 0.916388i | \(-0.631091\pi\) |
0.593469 | + | 0.804857i | \(0.297758\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.39524 | − | 1.96024i | −0.124392 | − | 0.0718178i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.890964 | − | 4.00212i | 0.0325987 | − | 0.146430i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.60501 | − | 2.57365i | 0.350959 | − | 0.0940393i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.6001 | − | 12.4708i | 0.788199 | − | 0.455067i | −0.0511293 | − | 0.998692i | \(-0.516282\pi\) |
0.839328 | + | 0.543625i | \(0.182949\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.923406 | − | 0.559778i | 0.0336508 | − | 0.0203994i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.01206 | + | 4.01206i | −0.146014 | + | 0.146014i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.5078 | + | 27.5078i | 0.999789 | + | 0.999789i | 1.00000 | 0.000211103i | \(-6.71963e-5\pi\) | |
−0.000211103 | 1.00000i | \(0.500067\pi\) | ||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.5567 | − | 24.0126i | −0.528374 | − | 0.871602i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.41665 | − | 5.91781i | −0.123854 | − | 0.214521i | 0.797431 | − | 0.603411i | \(-0.206192\pi\) |
−0.921284 | + | 0.388890i | \(0.872859\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.146521 | − | 0.546823i | −0.00530440 | − | 0.0197963i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.10797 | + | 4.47511i | −0.148524 | + | 0.161798i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.00723364 | − | 0.0125290i | 0.000261192 | − | 0.000452397i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.16390 | − | 2.01594i | −0.0419714 | − | 0.0726966i | 0.844277 | − | 0.535908i | \(-0.180031\pi\) |
−0.886248 | + | 0.463211i | \(0.846697\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.67466 | + | 9.19148i | 0.0963256 | + | 0.331023i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.66783 | − | 4.66783i | 0.167890 | − | 0.167890i | −0.618161 | − | 0.786051i | \(-0.712122\pi\) |
0.786051 | + | 0.618161i | \(0.212122\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.7820 | 0.638749 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.263971 | − | 12.3481i | −0.00946991 | − | 0.442984i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.634477 | + | 2.36790i | −0.0227325 | + | 0.0848389i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.57001 | − | 35.7158i | −0.342442 | − | 1.27801i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.9838 | − | 26.2406i | 0.464002 | − | 0.937764i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.47661 | − | 1.42987i | −0.0883942 | − | 0.0510344i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.60400 | + | 28.3785i | −0.271053 | + | 1.01158i | 0.687387 | + | 0.726291i | \(0.258758\pi\) |
−0.958440 | + | 0.285293i | \(0.907909\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.68965 | + | 6.98192i | −0.238158 | + | 0.248563i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.05151i | − | 0.108499i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.4774i | 0.620640i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.551696 | − | 1.89590i | −0.0195666 | − | 0.0672408i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.9954 | − | 48.4997i | 0.460322 | − | 1.71795i | −0.211629 | − | 0.977350i | \(-0.567877\pi\) |
0.671951 | − | 0.740596i | \(-0.265457\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.58808 | + | 2.07158i | 0.126937 | + | 0.0732871i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −41.9855 | − | 21.9035i | −1.48349 | − | 0.773923i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.90227 | − | 18.2955i | −0.172997 | − | 0.645634i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.406831 | − | 1.51831i | 0.0143389 | − | 0.0535135i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.49249 | + | 2.11718i | −0.122942 | + | 0.0745284i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −54.3452 | −1.91068 | −0.955338 | − | 0.295515i | \(-0.904509\pi\) | ||||
−0.955338 | + | 0.295515i | \(0.904509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.9318 | − | 22.9318i | 0.805245 | − | 0.805245i | −0.178665 | − | 0.983910i | \(-0.557178\pi\) |
0.983910 | + | 0.178665i | \(0.0571779\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −39.1522 | − | 9.59884i | −1.37313 | − | 0.336646i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.32664 | + | 2.29781i | 0.0464701 | + | 0.0804886i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.22372 | + | 5.58364i | −0.112784 | + | 0.195347i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.55327 | + | 1.11689i | −0.124161 | + | 0.0390272i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.2724 | − | 42.0690i | −0.393408 | − | 1.46822i | −0.824475 | − | 0.565899i | \(-0.808529\pi\) |
0.431067 | − | 0.902320i | \(-0.358137\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.52571 | + | 4.37465i | 0.0880406 | + | 0.152491i | 0.906683 | − | 0.421813i | \(-0.138606\pi\) |
−0.818642 | + | 0.574304i | \(0.805273\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.48152 | + | 17.2644i | −0.330104 | + | 0.601070i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.8757 | − | 27.8757i | −0.969334 | − | 0.969334i | 0.0302095 | − | 0.999544i | \(-0.490383\pi\) |
−0.999544 | + | 0.0302095i | \(0.990383\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.00281 | − | 3.00281i | 0.104292 | − | 0.104292i | −0.653035 | − | 0.757327i | \(-0.726505\pi\) |
0.757327 | + | 0.653035i | \(0.226505\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.0262402 | + | 1.22747i | 0.000910263 | + | 0.0425804i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37.6217 | − | 21.7209i | 1.30352 | − | 0.752585i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.66667 | + | 0.714531i | −0.0922838 | + | 0.0247274i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.69585 | − | 18.4523i | 0.127747 | − | 0.637805i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.29143 | − | 3.63236i | −0.217204 | − | 0.125403i | 0.387451 | − | 0.921890i | \(-0.373356\pi\) |
−0.604655 | + | 0.796487i | \(0.706689\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.37837 | − | 1.37315i | 0.0820126 | − | 0.0473500i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.73200 | − | 5.49206i | −0.197420 | − | 0.189156i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.17480 | − | 2.17480i | −0.0748154 | − | 0.0748154i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.21567i | 0.144852i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.1078 | + | 22.0464i | −0.415538 | + | 0.756632i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 64.4513 | + | 17.2697i | 2.20936 | + | 0.591997i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.4188 | + | 7.07889i | −0.904562 | + | 0.242377i | −0.680974 | − | 0.732307i | \(-0.738443\pi\) |
−0.223587 | + | 0.974684i | \(0.571777\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0338191 | + | 0.790634i | 0.00115659 | + | 0.0270391i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.27792 | − | 5.67752i | 0.111971 | − | 0.193940i | −0.804594 | − | 0.593826i | \(-0.797617\pi\) |
0.916565 | + | 0.399886i | \(0.130950\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.2003 | + | 8.89601i | 1.13278 | + | 0.303528i | 0.776045 | − | 0.630677i | \(-0.217223\pi\) |
0.356736 | + | 0.934205i | \(0.383890\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.860707 | + | 3.51069i | −0.0293328 | + | 0.119644i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.5164 | 1.34515 | 0.672576 | − | 0.740028i | \(-0.265188\pi\) | ||||
0.672576 | + | 0.740028i | \(0.265188\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.38418 | 0.0810646 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.7532 | + | 47.9393i | −0.399158 | + | 1.62810i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.8148 | + | 5.30936i | 0.672171 | + | 0.180108i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.54456 | + | 13.0676i | −0.255638 | + | 0.442777i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.3958 | − | 14.8757i | 0.791828 | − | 0.503466i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.14957 | + | 0.575974i | −0.0726686 | + | 0.0194715i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.2823 | − | 12.4013i | −1.56284 | − | 0.418763i | −0.629281 | − | 0.777178i | \(-0.716651\pi\) |
−0.933562 | + | 0.358415i | \(0.883317\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.21483 | + | 9.49542i | −0.175892 | + | 0.320273i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.6718i | − | 0.797522i | −0.917055 | − | 0.398761i | \(-0.869440\pi\) | ||
0.917055 | − | 0.398761i | \(-0.130560\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.40173 | + | 7.40173i | 0.249088 | + | 0.249088i | 0.820596 | − | 0.571508i | \(-0.193641\pi\) |
−0.571508 | + | 0.820596i | \(0.693641\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.00327259 | − | 0.00313560i | −0.000110007 | − | 0.000105402i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.6764 | − | 11.3602i | 0.660669 | − | 0.381438i | −0.131863 | − | 0.991268i | \(-0.542096\pi\) |
0.792532 | + | 0.609830i | \(0.208762\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.15825 | + | 0.668713i | 0.0388463 | + | 0.0224279i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.9445 | + | 13.4272i | 0.534162 | + | 0.449828i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.521341 | − | 0.139693i | 0.0174460 | − | 0.00467465i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.93931 | − | 1.69701i | 0.0982504 | − | 0.0567249i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.430068 | − | 20.1177i | −0.0143595 | − | 0.671712i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.4292 | − | 14.4292i | 0.481240 | − | 0.481240i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.1123 | − | 18.1123i | −0.603409 | − | 0.603409i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.57635 | + | 8.33285i | −0.152291 | + | 0.277300i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.08372 | + | 5.34117i | 0.102506 | + | 0.177546i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.73443 | + | 28.8653i | 0.256818 | + | 0.958456i | 0.967070 | + | 0.254509i | \(0.0819140\pi\) |
−0.710253 | + | 0.703947i | \(0.751419\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.2959 | − | 46.2479i | 0.341492 | − | 1.53395i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.23081 | − | 3.86388i | 0.0739100 | − | 0.128016i | −0.826702 | − | 0.562640i | \(-0.809786\pi\) |
0.900612 | + | 0.434625i | \(0.143119\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.58272 | + | 2.74135i | 0.0523804 | + | 0.0907255i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.31782 | + | 1.30376i | 0.175802 | + | 0.0431009i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.12015 | + | 2.12015i | −0.0700134 | + | 0.0700134i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.4889 | 1.43457 | 0.717283 | − | 0.696782i | \(-0.245385\pi\) | ||||
0.717283 | + | 0.696782i | \(0.245385\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.46912 | − | 5.74028i | 0.312018 | − | 0.189149i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.85787 | − | 25.5939i | 0.225730 | − | 0.842435i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.1137 | − | 45.2089i | −0.398295 | − | 1.48646i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.44616 | − | 33.8087i | −0.0474980 | − | 1.11042i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.8981 | + | 19.5711i | 1.11216 | + | 0.642107i | 0.939389 | − | 0.342854i | \(-0.111394\pi\) |
0.172774 | + | 0.984962i | \(0.444727\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.46471 | − | 5.46638i | 0.0480040 | − | 0.179153i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.12664 | + | 21.0542i | 0.200577 | + | 0.689284i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 4.68992i | − | 0.153377i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.6928i | 1.13336i | 0.823936 | + | 0.566682i | \(0.191773\pi\) | ||||
−0.823936 | + | 0.566682i | \(0.808227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.0078 | − | 24.0130i | 0.750831 | − | 0.783634i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.32091 | + | 23.5900i | −0.206056 | + | 0.769011i | 0.783069 | + | 0.621934i | \(0.213653\pi\) |
−0.989125 | + | 0.147076i | \(0.953014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.9118 | − | 9.76401i | −0.550723 | − | 0.317960i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0747714 | + | 1.16447i | 0.00243231 | + | 0.0378801i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.8890 | − | 51.8344i | −0.451331 | − | 1.68439i | −0.698656 | − | 0.715458i | \(-0.746218\pi\) |
0.247325 | − | 0.968933i | \(-0.420449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.51297 | − | 13.1106i | 0.114036 | − | 0.425587i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.424764 | + | 19.8696i | 0.0137739 | + | 0.644317i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.6369 | 1.31636 | 0.658180 | − | 0.752861i | \(-0.271327\pi\) | ||||
0.658180 | + | 0.752861i | \(0.271327\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.34661 | + | 4.34661i | −0.140653 | + | 0.140653i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.31542 | + | 21.7029i | 0.204148 | + | 0.701556i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.296615 | − | 0.513752i | −0.00957819 | − | 0.0165899i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.94172 | + | 15.4875i | −0.288443 | + | 0.499597i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.9583 | − | 38.0441i | −0.385350 | − | 1.22595i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.368808 | − | 1.37641i | −0.0118724 | − | 0.0443082i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.97787 | + | 5.15783i | 0.0957620 | + | 0.165865i | 0.909926 | − | 0.414770i | \(-0.136138\pi\) |
−0.814164 | + | 0.580634i | \(0.802805\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.32177 | + | 8.77876i | 0.170960 | + | 0.282014i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.0165 | − | 17.0165i | −0.546085 | − | 0.546085i | 0.379221 | − | 0.925306i | \(-0.376192\pi\) |
−0.925306 | + | 0.379221i | \(0.876192\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.69630 | − | 9.69630i | 0.310849 | − | 0.310849i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.0700 | + | 7.31697i | −0.386550 | + | 0.234330i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.2439 | + | 5.91431i | −0.327731 | + | 0.189215i | −0.654833 | − | 0.755773i | \(-0.727261\pi\) |
0.327102 | + | 0.944989i | \(0.393928\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.3147 | − | 9.46254i | 1.12866 | − | 0.302424i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.16589 | + | 0.680796i | −0.0691515 | + | 0.0217361i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.2947 | − | 22.1094i | −1.22141 | − | 0.705181i | −0.256192 | − | 0.966626i | \(-0.582468\pi\) |
−0.965218 | + | 0.261445i | \(0.915801\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.44603 | + | 1.41222i | −0.0779370 | + | 0.0449970i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.764146 | − | 0.222361i | 0.0243230 | − | 0.00707784i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.3170 | − | 36.3170i | −1.15481 | − | 1.15481i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 21.3026i | − | 0.676701i | −0.941020 | − | 0.338350i | \(-0.890131\pi\) | ||
0.941020 | − | 0.338350i | \(-0.109869\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.0379 | + | 0.727646i | −1.08016 | + | 0.0230911i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.62295 | − | 1.77461i | −0.209962 | − | 0.0562590i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.1547 | + | 7.81197i | −0.923338 | + | 0.247408i | −0.689012 | − | 0.724750i | \(-0.741955\pi\) |
−0.234326 | + | 0.972158i | \(0.575288\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49.4308 | + | 3.17399i | −1.56392 | + | 0.100421i |
(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 | 576.2.y.a.335.12 | 88 | ||
3.2 | odd | 2 | 1728.2.z.a.143.11 | 88 | |||
4.3 | odd | 2 | 144.2.u.a.11.21 | ✓ | 88 | ||
9.4 | even | 3 | 1728.2.z.a.719.11 | 88 | |||
9.5 | odd | 6 | inner | 576.2.y.a.527.2 | 88 | ||
12.11 | even | 2 | 432.2.v.a.251.2 | 88 | |||
16.3 | odd | 4 | inner | 576.2.y.a.47.2 | 88 | ||
16.13 | even | 4 | 144.2.u.a.83.15 | yes | 88 | ||
36.23 | even | 6 | 144.2.u.a.59.15 | yes | 88 | ||
36.31 | odd | 6 | 432.2.v.a.395.8 | 88 | |||
48.29 | odd | 4 | 432.2.v.a.35.8 | 88 | |||
48.35 | even | 4 | 1728.2.z.a.1007.11 | 88 | |||
144.13 | even | 12 | 432.2.v.a.179.2 | 88 | |||
144.67 | odd | 12 | 1728.2.z.a.1583.11 | 88 | |||
144.77 | odd | 12 | 144.2.u.a.131.21 | yes | 88 | ||
144.131 | even | 12 | inner | 576.2.y.a.239.12 | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.u.a.11.21 | ✓ | 88 | 4.3 | odd | 2 | ||
144.2.u.a.59.15 | yes | 88 | 36.23 | even | 6 | ||
144.2.u.a.83.15 | yes | 88 | 16.13 | even | 4 | ||
144.2.u.a.131.21 | yes | 88 | 144.77 | odd | 12 | ||
432.2.v.a.35.8 | 88 | 48.29 | odd | 4 | |||
432.2.v.a.179.2 | 88 | 144.13 | even | 12 | |||
432.2.v.a.251.2 | 88 | 12.11 | even | 2 | |||
432.2.v.a.395.8 | 88 | 36.31 | odd | 6 | |||
576.2.y.a.47.2 | 88 | 16.3 | odd | 4 | inner | ||
576.2.y.a.239.12 | 88 | 144.131 | even | 12 | inner | ||
576.2.y.a.335.12 | 88 | 1.1 | even | 1 | trivial | ||
576.2.y.a.527.2 | 88 | 9.5 | odd | 6 | inner | ||
1728.2.z.a.143.11 | 88 | 3.2 | odd | 2 | |||
1728.2.z.a.719.11 | 88 | 9.4 | even | 3 | |||
1728.2.z.a.1007.11 | 88 | 48.35 | even | 4 | |||
1728.2.z.a.1583.11 | 88 | 144.67 | odd | 12 |