Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,3,Mod(17,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.g (of order \(6\), degree \(2\), 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: | \(2.94278685509\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.2 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.17 |
Dual form | 108.3.g.a.89.2 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.05842 | + | 1.18843i | 0.411684 | + | 0.237686i | 0.691513 | − | 0.722364i | \(-0.256944\pi\) |
−0.279829 | + | 0.960050i | \(0.590278\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.05842 | + | 7.02939i | 0.579775 | + | 1.00420i | 0.995505 | + | 0.0947110i | \(0.0301927\pi\) |
−0.415730 | + | 0.909488i | \(0.636474\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.6168 | − | 10.1711i | 1.60153 | − | 0.924645i | 0.610350 | − | 0.792132i | \(-0.291029\pi\) |
0.991181 | − | 0.132513i | \(-0.0423045\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.05842 | + | 5.29734i | −0.235263 | + | 0.407488i | −0.959349 | − | 0.282222i | \(-0.908929\pi\) |
0.724086 | + | 0.689710i | \(0.242262\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.9653i | 1.05678i | 0.849001 | + | 0.528392i | \(0.177205\pi\) | ||||
−0.849001 | + | 0.528392i | \(0.822795\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.11684 | 0.479834 | 0.239917 | − | 0.970793i | \(-0.422880\pi\) | ||||
0.239917 | + | 0.970793i | \(0.422880\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −29.0584 | − | 16.7769i | −1.26341 | − | 0.729430i | −0.289677 | − | 0.957124i | \(-0.593548\pi\) |
−0.973733 | + | 0.227695i | \(0.926881\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.67527 | − | 16.7581i | −0.387011 | − | 0.670322i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −14.4090 | + | 8.31901i | −0.496860 | + | 0.286863i | −0.727416 | − | 0.686197i | \(-0.759279\pi\) |
0.230556 | + | 0.973059i | \(0.425946\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.1753 | − | 19.3561i | 0.360492 | − | 0.624391i | −0.627549 | − | 0.778577i | \(-0.715942\pi\) |
0.988042 | + | 0.154185i | \(0.0492753\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 19.2926i | 0.551217i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −50.4674 | −1.36398 | −0.681992 | − | 0.731360i | \(-0.738886\pi\) | ||||
−0.681992 | + | 0.731360i | \(0.738886\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −29.9674 | − | 17.3017i | −0.730912 | − | 0.421992i | 0.0878440 | − | 0.996134i | \(-0.472002\pi\) |
−0.818756 | + | 0.574142i | \(0.805336\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.5000 | − | 19.9186i | −0.267442 | − | 0.463223i | 0.700759 | − | 0.713398i | \(-0.252845\pi\) |
−0.968200 | + | 0.250176i | \(0.919512\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 33.1753 | − | 19.1537i | 0.705857 | − | 0.407527i | −0.103668 | − | 0.994612i | \(-0.533058\pi\) |
0.809525 | + | 0.587085i | \(0.199725\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.44158 | + | 14.6212i | −0.172277 | + | 0.298393i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 19.0149i | 0.358771i | 0.983779 | + | 0.179386i | \(0.0574110\pi\) | ||||
−0.983779 | + | 0.179386i | \(0.942589\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 48.3505 | 0.879101 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.96738 | + | 1.71322i | 0.0502945 | + | 0.0290375i | 0.524936 | − | 0.851141i | \(-0.324089\pi\) |
−0.474642 | + | 0.880179i | \(0.657422\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23.1753 | + | 40.1407i | 0.379922 | + | 0.658045i | 0.991051 | − | 0.133487i | \(-0.0426174\pi\) |
−0.611128 | + | 0.791532i | \(0.709284\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.5910 | + | 7.26944i | −0.193708 | + | 0.111838i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.14947 | − | 5.45504i | 0.0470070 | − | 0.0814185i | −0.841565 | − | 0.540157i | \(-0.818365\pi\) |
0.888572 | + | 0.458738i | \(0.151698\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 35.9306i | − | 0.506065i | −0.967458 | − | 0.253033i | \(-0.918572\pi\) | ||
0.967458 | − | 0.253033i | \(-0.0814280\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 47.3505 | 0.648637 | 0.324319 | − | 0.945948i | \(-0.394865\pi\) | ||||
0.324319 | + | 0.945948i | \(0.394865\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 142.993 | + | 82.5571i | 1.85705 | + | 1.07217i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 42.2921 | + | 73.2521i | 0.535343 | + | 0.927242i | 0.999147 | + | 0.0413035i | \(0.0131510\pi\) |
−0.463803 | + | 0.885938i | \(0.653516\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 33.1753 | − | 19.1537i | 0.399702 | − | 0.230768i | −0.286653 | − | 0.958034i | \(-0.592543\pi\) |
0.686355 | + | 0.727266i | \(0.259209\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.3505 | + | 36.9802i | −0.251183 | + | 0.435061i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 143.723i | − | 1.61486i | −0.589963 | − | 0.807430i | \(-0.700858\pi\) | ||
0.589963 | − | 0.807430i | \(-0.299142\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −49.6495 | −0.545599 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.7663 | + | 10.8347i | 0.197540 | + | 0.114050i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −40.3832 | − | 69.9457i | −0.416321 | − | 0.721089i | 0.579245 | − | 0.815154i | \(-0.303347\pi\) |
−0.995566 | + | 0.0940641i | \(0.970014\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −105.942 | + | 61.1654i | −1.04893 | + | 0.605598i | −0.922349 | − | 0.386359i | \(-0.873733\pi\) |
−0.126578 | + | 0.991957i | \(0.540399\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −36.8247 | + | 63.7823i | −0.357522 | + | 0.619246i | −0.987546 | − | 0.157330i | \(-0.949712\pi\) |
0.630024 | + | 0.776575i | \(0.283045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 72.9108i | 0.681410i | 0.940170 | + | 0.340705i | \(0.110666\pi\) | ||||
−0.940170 | + | 0.340705i | \(0.889334\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 31.2989 | 0.287146 | 0.143573 | − | 0.989640i | \(-0.454141\pi\) | ||||
0.143573 | + | 0.989640i | \(0.454141\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.2269 | − | 9.36858i | −0.143601 | − | 0.0829078i | 0.426478 | − | 0.904498i | \(-0.359754\pi\) |
−0.570079 | + | 0.821590i | \(0.693087\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −39.8763 | − | 69.0678i | −0.346751 | − | 0.600590i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −126.285 | + | 72.9108i | −1.06122 | + | 0.612696i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 146.402 | − | 253.576i | 1.20993 | − | 2.09567i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 105.415i | − | 0.843320i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −126.103 | −0.992939 | −0.496469 | − | 0.868054i | \(-0.665370\pi\) | ||||
−0.496469 | + | 0.868054i | \(0.665370\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −140.694 | − | 81.2299i | −1.07400 | − | 0.620075i | −0.144730 | − | 0.989471i | \(-0.546231\pi\) |
−0.929272 | + | 0.369396i | \(0.879565\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 37.0000 | + | 64.0859i | 0.278195 | + | 0.481849i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −90.3832 | + | 52.1827i | −0.659731 | + | 0.380896i | −0.792174 | − | 0.610295i | \(-0.791051\pi\) |
0.132443 | + | 0.991191i | \(0.457718\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −30.6168 | + | 53.0299i | −0.220265 | + | 0.381510i | −0.954888 | − | 0.296965i | \(-0.904026\pi\) |
0.734623 | + | 0.678475i | \(0.237359\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 124.430i | 0.870139i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −39.5463 | −0.272733 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 128.344 | + | 74.0993i | 0.861367 | + | 0.497311i | 0.864470 | − | 0.502685i | \(-0.167654\pi\) |
−0.00310272 | + | 0.999995i | \(0.500988\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −127.526 | − | 220.881i | −0.844542 | − | 1.46279i | −0.886019 | − | 0.463650i | \(-0.846540\pi\) |
0.0414769 | − | 0.999139i | \(-0.486794\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 46.0068 | − | 26.5621i | 0.296818 | − | 0.171368i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −146.227 | + | 253.272i | −0.931381 | + | 1.61320i | −0.150418 | + | 0.988622i | \(0.548062\pi\) |
−0.780963 | + | 0.624577i | \(0.785271\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 272.351i | − | 1.69162i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 93.5326 | 0.573820 | 0.286910 | − | 0.957958i | \(-0.407372\pi\) | ||||
0.286910 | + | 0.957958i | \(0.407372\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 97.2269 | + | 56.1340i | 0.582197 | + | 0.336131i | 0.762006 | − | 0.647570i | \(-0.224215\pi\) |
−0.179809 | + | 0.983702i | \(0.557548\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 65.7921 | + | 113.955i | 0.389302 | + | 0.674292i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 205.227 | − | 118.488i | 1.18628 | − | 0.684900i | 0.228823 | − | 0.973468i | \(-0.426512\pi\) |
0.957460 | + | 0.288568i | \(0.0931790\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 78.5326 | − | 136.022i | 0.448758 | − | 0.777271i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 234.599i | 1.31061i | 0.755366 | + | 0.655304i | \(0.227459\pi\) | ||||
−0.755366 | + | 0.655304i | \(0.772541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 221.636 | 1.22451 | 0.612254 | − | 0.790661i | \(-0.290263\pi\) | ||||
0.612254 | + | 0.790661i | \(0.290263\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −103.883 | − | 59.9770i | −0.561531 | − | 0.324200i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 182.727 | + | 316.492i | 0.977149 | + | 1.69247i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 130.162 | − | 75.1488i | 0.681474 | − | 0.393449i | −0.118936 | − | 0.992902i | \(-0.537948\pi\) |
0.800410 | + | 0.599452i | \(0.204615\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.5000 | − | 42.4352i | 0.126943 | − | 0.219872i | −0.795548 | − | 0.605891i | \(-0.792817\pi\) |
0.922491 | + | 0.386019i | \(0.126150\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 276.827i | 1.40521i | 0.711579 | + | 0.702606i | \(0.247980\pi\) | ||||
−0.711579 | + | 0.702606i | \(0.752020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −198.935 | −0.999672 | −0.499836 | − | 0.866120i | \(-0.666606\pi\) | ||||
−0.499836 | + | 0.866120i | \(0.666606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −116.955 | − | 67.5241i | −0.576134 | − | 0.332631i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −41.1237 | − | 71.2283i | −0.200603 | − | 0.347455i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 160.610 | − | 92.7282i | 0.768469 | − | 0.443676i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −47.0068 | + | 81.4182i | −0.222781 | + | 0.385868i | −0.955651 | − | 0.294500i | \(-0.904847\pi\) |
0.732870 | + | 0.680368i | \(0.238180\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 54.6678i | − | 0.254269i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 181.416 | 0.836017 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −95.1684 | − | 54.9455i | −0.430626 | − | 0.248622i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 77.8763 | + | 134.886i | 0.349221 | + | 0.604869i | 0.986111 | − | 0.166086i | \(-0.0531128\pi\) |
−0.636890 | + | 0.770955i | \(0.719780\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 138.448 | − | 79.9332i | 0.609905 | − | 0.352129i | −0.163023 | − | 0.986622i | \(-0.552125\pi\) |
0.772928 | + | 0.634493i | \(0.218791\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.1237 | − | 33.1232i | 0.0835095 | − | 0.144643i | −0.821246 | − | 0.570575i | \(-0.806720\pi\) |
0.904755 | + | 0.425932i | \(0.140054\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 157.490i | 0.675921i | 0.941160 | + | 0.337960i | \(0.109737\pi\) | ||||
−0.941160 | + | 0.337960i | \(0.890263\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 91.0516 | 0.387454 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 62.4742 | + | 36.0695i | 0.261398 | + | 0.150918i | 0.624972 | − | 0.780647i | \(-0.285110\pi\) |
−0.363574 | + | 0.931565i | \(0.618444\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −113.370 | − | 196.362i | −0.470413 | − | 0.814779i | 0.529015 | − | 0.848613i | \(-0.322562\pi\) |
−0.999427 | + | 0.0338337i | \(0.989228\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −34.7527 | + | 20.0645i | −0.141848 | + | 0.0818957i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.8832 | + | 48.2950i | −0.112887 | + | 0.195526i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 222.931i | − | 0.888171i | −0.895985 | − | 0.444085i | \(-0.853529\pi\) | ||
0.895985 | − | 0.444085i | \(-0.146471\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −682.557 | −2.69785 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −92.2011 | − | 53.2323i | −0.358759 | − | 0.207130i | 0.309777 | − | 0.950809i | \(-0.399746\pi\) |
−0.668536 | + | 0.743680i | \(0.733079\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −204.818 | − | 354.755i | −0.790803 | − | 1.36971i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −155.344 | + | 89.6877i | −0.590660 | + | 0.341018i | −0.765359 | − | 0.643604i | \(-0.777438\pi\) |
0.174698 | + | 0.984622i | \(0.444105\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.5979 | + | 39.1407i | −0.0852750 | + | 0.147701i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 416.351i | 1.54777i | 0.633324 | + | 0.773887i | \(0.281690\pi\) | ||||
−0.633324 | + | 0.773887i | \(0.718310\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 396.907 | 1.46460 | 0.732302 | − | 0.680980i | \(-0.238446\pi\) | ||||
0.732302 | + | 0.680980i | \(0.238446\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −340.895 | − | 196.816i | −1.23962 | − | 0.715695i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 57.7731 | + | 100.066i | 0.208567 | + | 0.361249i | 0.951263 | − | 0.308379i | \(-0.0997866\pi\) |
−0.742696 | + | 0.669629i | \(0.766453\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −422.564 | + | 243.967i | −1.50379 | + | 0.868211i | −0.503795 | + | 0.863823i | \(0.668063\pi\) |
−0.999990 | + | 0.00438786i | \(0.998603\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 169.825 | − | 294.145i | 0.600087 | − | 1.03938i | −0.392720 | − | 0.919658i | \(-0.628466\pi\) |
0.992807 | − | 0.119724i | \(-0.0382009\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 280.870i | − | 0.978641i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33.7527 | −0.116791 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −122.409 | − | 70.6728i | −0.417778 | − | 0.241204i | 0.276348 | − | 0.961058i | \(-0.410876\pi\) |
−0.694126 | + | 0.719853i | \(0.744209\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.07207 | + | 7.05304i | 0.0138036 | + | 0.0239086i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 177.746 | − | 102.622i | 0.594468 | − | 0.343216i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 93.3437 | − | 161.676i | 0.310112 | − | 0.537130i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 110.169i | 0.361209i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −120.649 | −0.392995 | −0.196498 | − | 0.980504i | \(-0.562957\pi\) | ||||
−0.196498 | + | 0.980504i | \(0.562957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 119.254 | + | 68.8514i | 0.383454 | + | 0.221387i | 0.679320 | − | 0.733842i | \(-0.262275\pi\) |
−0.295866 | + | 0.955229i | \(0.595608\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −129.266 | − | 223.896i | −0.412991 | − | 0.715322i | 0.582224 | − | 0.813029i | \(-0.302183\pi\) |
−0.995215 | + | 0.0977064i | \(0.968849\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.7079 | − | 9.64630i | 0.0527063 | − | 0.0304300i | −0.473415 | − | 0.880839i | \(-0.656979\pi\) |
0.526122 | + | 0.850409i | \(0.323646\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −169.227 | + | 293.110i | −0.530492 | + | 0.918839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 163.787i | 0.507081i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 118.364 | 0.364197 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 269.278 | + | 155.468i | 0.818476 | + | 0.472547i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 98.3953 | + | 170.426i | 0.297267 | + | 0.514881i | 0.975510 | − | 0.219957i | \(-0.0705916\pi\) |
−0.678243 | + | 0.734838i | \(0.737258\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.9659 | − | 7.48585i | 0.0387041 | − | 0.0223458i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −158.720 | + | 274.911i | −0.470979 | + | 0.815760i | −0.999449 | − | 0.0331921i | \(-0.989433\pi\) |
0.528470 | + | 0.848952i | \(0.322766\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 454.659i | − | 1.33331i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 260.687 | 0.760022 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 537.407 | + | 310.272i | 1.54872 | + | 0.894157i | 0.998240 | + | 0.0593116i | \(0.0188906\pi\) |
0.550485 | + | 0.834845i | \(0.314443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 189.512 | + | 328.245i | 0.543015 | + | 0.940529i | 0.998729 | + | 0.0504030i | \(0.0160506\pi\) |
−0.455714 | + | 0.890126i | \(0.650616\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 213.514 | − | 123.272i | 0.604855 | − | 0.349213i | −0.166094 | − | 0.986110i | \(-0.553116\pi\) |
0.770949 | + | 0.636897i | \(0.219782\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 42.7011 | − | 73.9604i | 0.120285 | − | 0.208339i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 572.791i | − | 1.59552i | −0.602976 | − | 0.797759i | \(-0.706019\pi\) | ||
0.602976 | − | 0.797759i | \(-0.293981\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −277.883 | −0.769759 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 97.4674 | + | 56.2728i | 0.267034 | + | 0.154172i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 93.9279 | + | 162.688i | 0.255934 | + | 0.443291i | 0.965149 | − | 0.261701i | \(-0.0842836\pi\) |
−0.709214 | + | 0.704993i | \(0.750950\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −133.663 | + | 77.1704i | −0.360278 | + | 0.208007i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −75.0584 | + | 130.005i | −0.201229 | + | 0.348539i | −0.948925 | − | 0.315503i | \(-0.897827\pi\) |
0.747696 | + | 0.664042i | \(0.231160\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 101.772i | − | 0.269953i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.6222 | −0.0702432 | −0.0351216 | − | 0.999383i | \(-0.511182\pi\) | ||||
−0.0351216 | + | 0.999383i | \(0.511182\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 444.966 | + | 256.901i | 1.16179 | + | 0.670760i | 0.951733 | − | 0.306929i | \(-0.0993013\pi\) |
0.210058 | + | 0.977689i | \(0.432635\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 196.227 | + | 339.875i | 0.509680 | + | 0.882792i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.1616 | − | 12.7950i | 0.0569707 | − | 0.0328921i | −0.471244 | − | 0.882003i | \(-0.656195\pi\) |
0.528215 | + | 0.849111i | \(0.322862\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 301.402 | − | 522.044i | 0.770849 | − | 1.33515i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 201.045i | 0.508975i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 388.804 | 0.979356 | 0.489678 | − | 0.871903i | \(-0.337114\pi\) | ||||
0.489678 | + | 0.871903i | \(0.337114\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.0842 | + | 19.6785i | 0.0849981 | + | 0.0490736i | 0.541897 | − | 0.840445i | \(-0.317706\pi\) |
−0.456899 | + | 0.889519i | \(0.651040\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 68.3574 | + | 118.398i | 0.169621 | + | 0.293793i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −889.076 | + | 513.308i | −2.18446 | + | 1.26120i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −86.7200 | + | 150.204i | −0.212029 | + | 0.367246i | −0.952350 | − | 0.305009i | \(-0.901341\pi\) |
0.740320 | + | 0.672255i | \(0.234674\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.8118i | 0.0673409i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 91.0516 | 0.219401 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −115.031 | − | 66.4132i | −0.274537 | − | 0.158504i | 0.356411 | − | 0.934329i | \(-0.384000\pi\) |
−0.630948 | + | 0.775825i | \(0.717334\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −317.447 | − | 549.834i | −0.754031 | − | 1.30602i | −0.945855 | − | 0.324590i | \(-0.894774\pi\) |
0.191824 | − | 0.981429i | \(-0.438560\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 301.064 | − | 173.819i | 0.708385 | − | 0.408986i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −188.110 | + | 325.816i | −0.440539 | + | 0.763035i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 602.424i | − | 1.39774i | −0.715251 | − | 0.698868i | \(-0.753687\pi\) | ||
0.715251 | − | 0.698868i | \(-0.246313\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 266.155 | 0.614676 | 0.307338 | − | 0.951600i | \(-0.400562\pi\) | ||||
0.307338 | + | 0.951600i | \(0.400562\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −264.921 | − | 152.952i | −0.606227 | − | 0.350005i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −250.330 | − | 433.584i | −0.570228 | − | 0.987664i | −0.996542 | − | 0.0830886i | \(-0.973522\pi\) |
0.426314 | − | 0.904575i | \(-0.359812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 261.098 | − | 150.745i | 0.589386 | − | 0.340282i | −0.175469 | − | 0.984485i | \(-0.556144\pi\) |
0.764855 | + | 0.644203i | \(0.222811\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 170.804 | − | 295.842i | 0.383830 | − | 0.664813i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 565.321i | 1.25907i | 0.776973 | + | 0.629534i | \(0.216754\pi\) | ||||
−0.776973 | + | 0.629534i | \(0.783246\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −703.907 | −1.56077 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −102.200 | − | 59.0049i | −0.224614 | − | 0.129681i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.1495 | − | 45.2922i | −0.0572198 | − | 0.0991077i | 0.835997 | − | 0.548735i | \(-0.184890\pi\) |
−0.893216 | + | 0.449627i | \(0.851557\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −166.357 | + | 96.0465i | −0.360862 | + | 0.208344i | −0.669459 | − | 0.742849i | \(-0.733474\pi\) |
0.308597 | + | 0.951193i | \(0.400141\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −283.110 | + | 490.361i | −0.611469 | + | 1.05909i | 0.379524 | + | 0.925182i | \(0.376088\pi\) |
−0.990993 | + | 0.133913i | \(0.957246\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 174.405i | 0.373459i | 0.982411 | + | 0.186729i | \(0.0597888\pi\) | ||||
−0.982411 | + | 0.186729i | \(0.940211\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 51.1275 | 0.109014 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −405.187 | − | 233.935i | −0.856633 | − | 0.494577i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −88.2079 | − | 152.781i | −0.185701 | − | 0.321643i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −473.784 | + | 273.539i | −0.989110 | + | 0.571063i | −0.905008 | − | 0.425394i | \(-0.860135\pi\) |
−0.0841020 | + | 0.996457i | \(0.526802\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 154.351 | − | 267.343i | 0.320895 | − | 0.555807i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 191.970i | − | 0.395815i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −769.945 | −1.58100 | −0.790498 | − | 0.612464i | \(-0.790178\pi\) | ||||
−0.790498 | + | 0.612464i | \(0.790178\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 154.916 | + | 89.4407i | 0.315511 | + | 0.182160i | 0.649390 | − | 0.760456i | \(-0.275024\pi\) |
−0.333879 | + | 0.942616i | \(0.608358\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −149.454 | − | 258.861i | −0.303152 | − | 0.525074i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 252.571 | − | 145.822i | 0.508190 | − | 0.293404i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 192.655 | − | 333.688i | 0.386082 | − | 0.668713i | −0.605837 | − | 0.795589i | \(-0.707162\pi\) |
0.991919 | + | 0.126876i | \(0.0404949\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 67.6630i | 0.134519i | 0.997736 | + | 0.0672594i | \(0.0214255\pi\) | ||||
−0.997736 | + | 0.0672594i | \(0.978574\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −290.763 | −0.575769 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −523.292 | − | 302.123i | −1.02808 | − | 0.593562i | −0.111645 | − | 0.993748i | \(-0.535612\pi\) |
−0.916434 | + | 0.400187i | \(0.868945\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 192.168 | + | 332.846i | 0.376063 | + | 0.651361i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −151.602 | + | 87.5273i | −0.294372 | + | 0.169956i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 389.629 | − | 674.857i | 0.753634 | − | 1.30533i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 273.678i | 0.525294i | 0.964892 | + | 0.262647i | \(0.0845954\pi\) | ||||
−0.964892 | + | 0.262647i | \(0.915405\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 687.402 | 1.31434 | 0.657172 | − | 0.753740i | \(-0.271752\pi\) | ||||
0.657172 | + | 0.753740i | \(0.271752\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 347.739 | + | 200.767i | 0.659846 | + | 0.380962i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 298.428 | + | 516.892i | 0.564136 | + | 0.977112i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 183.306 | − | 105.832i | 0.343913 | − | 0.198558i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −86.6495 | + | 150.081i | −0.161962 | + | 0.280526i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 343.440i | 0.637180i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 664.543 | 1.22836 | 0.614180 | − | 0.789166i | \(-0.289487\pi\) | ||||
0.614180 | + | 0.789166i | \(0.289487\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 64.4264 | + | 37.1966i | 0.118214 | + | 0.0682507i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −259.603 | − | 449.646i | −0.474594 | − | 0.822022i | 0.524982 | − | 0.851113i | \(-0.324072\pi\) |
−0.999577 | + | 0.0290914i | \(0.990739\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −131.364 | + | 75.8431i | −0.238410 | + | 0.137646i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −343.278 | + | 594.576i | −0.620757 | + | 1.07518i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 422.648i | − | 0.758794i | −0.925234 | − | 0.379397i | \(-0.876131\pi\) | ||
0.925234 | − | 0.379397i | \(-0.123869\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 140.687 | 0.251677 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −798.799 | − | 461.187i | −1.41883 | − | 0.819159i | −0.422630 | − | 0.906302i | \(-0.638893\pi\) |
−0.996196 | + | 0.0871428i | \(0.972226\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.2678 | − | 38.5690i | −0.0394121 | − | 0.0682637i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 914.445 | − | 527.955i | 1.60711 | − | 0.927865i | 0.617097 | − | 0.786887i | \(-0.288309\pi\) |
0.990013 | − | 0.140978i | \(-0.0450247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −401.524 | + | 695.460i | −0.703195 | + | 1.21797i | 0.264144 | + | 0.964483i | \(0.414911\pi\) |
−0.967339 | + | 0.253486i | \(0.918423\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 649.283i | 1.12919i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −96.6495 | −0.167503 | −0.0837517 | − | 0.996487i | \(-0.526690\pi\) | ||||
−0.0837517 | + | 0.996487i | \(0.526690\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 269.278 | + | 155.468i | 0.463474 | + | 0.267587i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 193.402 | + | 334.982i | 0.331736 | + | 0.574584i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 870.497 | − | 502.582i | 1.48296 | − | 0.856187i | 0.483146 | − | 0.875540i | \(-0.339494\pi\) |
0.999813 | + | 0.0193528i | \(0.00616056\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 101.883 | − | 176.467i | 0.172976 | − | 0.299604i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 752.444i | 1.26888i | 0.772973 | + | 0.634439i | \(0.218769\pi\) | ||||
−0.772973 | + | 0.634439i | \(0.781231\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −346.598 | −0.582517 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0857 | + | 13.9059i | 0.0402099 | + | 0.0232152i | 0.519970 | − | 0.854184i | \(-0.325943\pi\) |
−0.479760 | + | 0.877400i | \(0.659276\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 475.356 | + | 823.340i | 0.790942 | + | 1.36995i | 0.925385 | + | 0.379030i | \(0.123742\pi\) |
−0.134443 | + | 0.990921i | \(0.542925\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 602.715 | − | 347.978i | 0.996223 | − | 0.575169i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 161.306 | − | 279.390i | 0.265743 | − | 0.460280i | −0.702015 | − | 0.712162i | \(-0.747716\pi\) |
0.967758 | + | 0.251882i | \(0.0810495\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 234.321i | 0.383504i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 138.206 | 0.225459 | 0.112730 | − | 0.993626i | \(-0.464041\pi\) | ||||
0.112730 | + | 0.993626i | \(0.464041\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 682.084 | + | 393.802i | 1.10548 | + | 0.638252i | 0.937656 | − | 0.347564i | \(-0.112991\pi\) |
0.167829 | + | 0.985816i | \(0.446324\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 121.747 | + | 210.873i | 0.196684 | + | 0.340667i | 0.947451 | − | 0.319900i | \(-0.103649\pi\) |
−0.750767 | + | 0.660567i | \(0.770316\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1010.28 | − | 583.287i | 1.62164 | − | 0.936255i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −116.603 | + | 201.963i | −0.186565 | + | 0.323140i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 906.662i | − | 1.44143i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 111.924 | 0.177376 | 0.0886879 | − | 0.996059i | \(-0.471733\pi\) | ||||
0.0886879 | + | 0.996059i | \(0.471733\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −259.574 | − | 149.865i | −0.408777 | − | 0.236008i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −51.6358 | − | 89.4359i | −0.0810609 | − | 0.140402i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −632.095 | + | 364.940i | −0.986107 | + | 0.569329i | −0.904108 | − | 0.427303i | \(-0.859464\pi\) |
−0.0819990 | + | 0.996632i | \(0.526130\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 288.500 | − | 499.697i | 0.448678 | − | 0.777133i | −0.549622 | − | 0.835413i | \(-0.685228\pi\) |
0.998300 | + | 0.0582801i | \(0.0185617\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 129.029i | 0.199426i | 0.995016 | + | 0.0997130i | \(0.0317925\pi\) | ||||
−0.995016 | + | 0.0997130i | \(0.968208\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 69.7011 | 0.107398 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1026.62 | − | 592.717i | −1.57215 | − | 0.907682i | −0.995905 | − | 0.0904070i | \(-0.971183\pi\) |
−0.576247 | − | 0.817275i | \(-0.695483\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −193.072 | − | 334.411i | −0.294767 | − | 0.510551i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −947.808 | + | 547.217i | −1.43825 | + | 0.830375i | −0.997728 | − | 0.0673658i | \(-0.978541\pi\) |
−0.440524 | + | 0.897741i | \(0.645207\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −604.876 | + | 1047.68i | −0.915093 | + | 1.58499i | −0.108327 | + | 0.994115i | \(0.534549\pi\) |
−0.806765 | + | 0.590872i | \(0.798784\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 175.888i | 0.264493i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 558.269 | 0.836984 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 816.550 | + | 471.435i | 1.21692 | + | 0.702586i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −508.615 | − | 880.948i | −0.755743 | − | 1.30899i | −0.945004 | − | 0.327059i | \(-0.893942\pi\) |
0.189260 | − | 0.981927i | \(-0.439391\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −689.890 | + | 398.308i | −1.01904 | + | 0.588343i | −0.913826 | − | 0.406107i | \(-0.866886\pi\) |
−0.105214 | + | 0.994450i | \(0.533553\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 327.784 | − | 567.738i | 0.482745 | − | 0.836139i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 400.485i | 0.586361i | 0.956057 | + | 0.293181i | \(0.0947138\pi\) | ||||
−0.956057 | + | 0.293181i | \(0.905286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −248.062 | −0.362135 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −100.728 | − | 58.1556i | −0.146195 | − | 0.0844057i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 216.423 | + | 374.855i | 0.313202 | + | 0.542482i | 0.979054 | − | 0.203602i | \(-0.0652650\pi\) |
−0.665852 | + | 0.746084i | \(0.731932\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −126.045 | + | 72.7720i | −0.181359 | + | 0.104708i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 310.830 | − | 538.373i | 0.445954 | − | 0.772415i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 65.4412i | 0.0933541i | 0.998910 | + | 0.0466770i | \(0.0148632\pi\) | ||||
−0.998910 | + | 0.0466770i | \(0.985137\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −460.103 | −0.654485 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −859.911 | − | 496.470i | −1.21628 | − | 0.702221i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −100.461 | − | 174.003i | −0.141693 | − | 0.245420i | 0.786441 | − | 0.617665i | \(-0.211921\pi\) |
−0.928134 | + | 0.372245i | \(0.878588\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −649.471 | + | 374.972i | −0.910899 | + | 0.525908i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −147.876 | + | 256.129i | −0.206820 | + | 0.358223i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1062.98i | − | 1.47841i | −0.673478 | − | 0.739207i | \(-0.735200\pi\) | ||
0.673478 | − | 0.739207i | \(-0.264800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −597.801 | −0.829128 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 278.821 | + | 160.977i | 0.384581 | + | 0.222038i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −495.629 | − | 858.455i | −0.681746 | − | 1.18082i | −0.974448 | − | 0.224614i | \(-0.927888\pi\) |
0.292702 | − | 0.956204i | \(-0.405446\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 357.844 | − | 206.601i | 0.489526 | − | 0.282628i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 590.134 | − | 1022.14i | 0.805095 | − | 1.39446i | −0.111133 | − | 0.993806i | \(-0.535448\pi\) |
0.916227 | − | 0.400659i | \(-0.131219\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 128.134i | − | 0.173859i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 599.351 | 0.811029 | 0.405515 | − | 0.914089i | \(-0.367092\pi\) | ||||
0.405515 | + | 0.914089i | \(0.367092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −287.083 | − | 165.747i | −0.386383 | − | 0.223078i | 0.294209 | − | 0.955741i | \(-0.404944\pi\) |
−0.680592 | + | 0.732663i | \(0.738277\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 176.124 | + | 305.055i | 0.236408 | + | 0.409470i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −512.519 | + | 295.903i | −0.684271 | + | 0.395064i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −76.0448 | + | 131.713i | −0.101258 | + | 0.175384i | −0.912203 | − | 0.409738i | \(-0.865620\pi\) |
0.810945 | + | 0.585122i | \(0.198953\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 606.222i | − | 0.802943i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1179.61 | −1.55827 | −0.779134 | − | 0.626858i | \(-0.784341\pi\) | ||||
−0.779134 | + | 0.626858i | \(0.784341\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1162.58 | + | 671.214i | 1.52770 | + | 0.882016i | 0.999458 | + | 0.0329205i | \(0.0104808\pi\) |
0.528239 | + | 0.849096i | \(0.322853\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 127.024 | + | 220.013i | 0.166480 | + | 0.288352i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.1510 | + | 10.4795i | −0.0236649 | + | 0.0136629i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −548.512 | + | 950.051i | −0.713280 | + | 1.23544i | 0.250339 | + | 0.968158i | \(0.419458\pi\) |
−0.963619 | + | 0.267279i | \(0.913876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1181.39i | 1.52832i | 0.645028 | + | 0.764159i | \(0.276846\pi\) | ||||
−0.645028 | + | 0.764159i | \(0.723154\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −432.495 | −0.558058 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −273.208 | − | 157.737i | −0.350716 | − | 0.202486i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −365.454 | − | 632.984i | −0.467931 | − | 0.810479i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −601.993 | + | 347.561i | −0.766870 | + | 0.442753i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.0311 | − | 31.2308i | 0.0229112 | − | 0.0396834i | −0.854342 | − | 0.519710i | \(-0.826040\pi\) |
0.877254 | + | 0.480027i | \(0.159373\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 152.087i | − | 0.192271i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −283.519 | −0.357527 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 115.618 | + | 66.7523i | 0.145067 | + | 0.0837544i | 0.570777 | − | 0.821105i | \(-0.306642\pi\) |
−0.425710 | + | 0.904860i | \(0.639976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 344.103 | + | 596.004i | 0.430667 | + | 0.745938i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 834.167 | − | 481.607i | 1.03881 | − | 0.599759i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 323.670 | − | 560.613i | 0.402074 | − | 0.696413i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1053.66i | − | 1.30242i | −0.758898 | − | 0.651209i | \(-0.774262\pi\) | ||
0.758898 | − | 0.651209i | \(-0.225738\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 434.464 | 0.535714 | 0.267857 | − | 0.963459i | \(-0.413684\pi\) | ||||
0.267857 | + | 0.963459i | \(0.413684\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 192.530 | + | 111.157i | 0.236233 | + | 0.136389i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −104.844 | − | 181.595i | −0.128328 | − | 0.222270i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −252.436 | + | 145.744i | −0.307474 | + | 0.177520i | −0.645796 | − | 0.763510i | \(-0.723474\pi\) |
0.338322 | + | 0.941031i | \(0.390141\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −168.409 | + | 291.693i | −0.204628 | + | 0.354426i | −0.950014 | − | 0.312207i | \(-0.898932\pi\) |
0.745386 | + | 0.666633i | \(0.232265\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1029.27i | − | 1.24458i | −0.782785 | − | 0.622292i | \(-0.786202\pi\) | ||
0.782785 | − | 0.622292i | \(-0.213798\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 790.674 | 0.953768 | 0.476884 | − | 0.878966i | \(-0.341766\pi\) | ||||
0.476884 | + | 0.878966i | \(0.341766\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −262.675 | − | 151.656i | −0.315336 | − | 0.182060i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 133.423 | + | 231.095i | 0.159788 | + | 0.276760i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −655.031 | + | 378.182i | −0.780728 | + | 0.450754i | −0.836688 | − | 0.547679i | \(-0.815511\pi\) |
0.0559600 | + | 0.998433i | \(0.482178\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −282.088 | + | 488.591i | −0.335420 | + | 0.580964i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 312.757i | 0.370127i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2376.65 | 2.80596 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1466.50 | + | 846.686i | 1.72327 | + | 0.994930i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 599.175 | + | 1037.80i | 0.702433 | + | 1.21665i | 0.967610 | + | 0.252450i | \(0.0812362\pi\) |
−0.265177 | + | 0.964200i | \(0.585430\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −605.629 | + | 349.660i | −0.706685 | + | 0.408005i | −0.809832 | − | 0.586661i | \(-0.800442\pi\) |
0.103147 | + | 0.994666i | \(0.467109\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 278.734 | − | 482.781i | 0.324486 | − | 0.562027i | −0.656922 | − | 0.753959i | \(-0.728142\pi\) |
0.981408 | + | 0.191932i | \(0.0614753\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 99.3954i | 0.115174i | 0.998340 | + | 0.0575871i | \(0.0183407\pi\) | ||||
−0.998340 | + | 0.0575871i | \(0.981659\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 563.258 | 0.651165 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1490.11 | + | 860.314i | 1.71474 | + | 0.990004i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.2648 | + | 33.3676i | 0.0221180 | + | 0.0383096i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 741.004 | − | 427.819i | 0.846861 | − | 0.488936i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −401.292 | + | 695.058i | −0.457574 | + | 0.792541i | −0.998832 | − | 0.0483154i | \(-0.984615\pi\) |
0.541258 | + | 0.840856i | \(0.317948\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 524.266i | − | 0.595080i | −0.954709 | − | 0.297540i | \(-0.903834\pi\) | ||
0.954709 | − | 0.297540i | \(-0.0961662\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −993.894 | −1.12559 | −0.562794 | − | 0.826597i | \(-0.690273\pi\) | ||||
−0.562794 | + | 0.826597i | \(0.690273\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −616.643 | − | 356.019i | −0.695200 | − | 0.401374i | 0.110357 | − | 0.993892i | \(-0.464801\pi\) |
−0.805557 | + | 0.592518i | \(0.798134\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −511.780 | − | 886.429i | −0.575681 | − | 0.997108i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 302.454 | − | 174.622i | 0.338694 | − | 0.195545i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −278.804 | + | 482.903i | −0.311513 | + | 0.539557i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 371.869i | 0.413647i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −341.609 | −0.379144 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 456.220 | + | 263.399i | 0.504111 | + | 0.291048i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 374.473 | + | 648.606i | 0.412870 | + | 0.715111i | 0.995202 | − | 0.0978396i | \(-0.0311932\pi\) |
−0.582333 | + | 0.812951i | \(0.697860\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.87633 | − | 2.23800i | 0.00425503 | − | 0.00245664i | −0.497871 | − | 0.867251i | \(-0.665885\pi\) |
0.502126 | + | 0.864794i | \(0.332551\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 389.629 | − | 674.857i | 0.426757 | − | 0.739165i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1318.66i | − | 1.43802i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1592.91 | −1.73331 | −0.866653 | − | 0.498912i | \(-0.833733\pi\) | ||||
−0.866653 | + | 0.498912i | \(0.833733\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 190.337 | + | 109.891i | 0.206215 | + | 0.119059i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 488.285 | + | 845.735i | 0.527876 | + | 0.914308i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 770.784 | − | 445.012i | 0.829692 | − | 0.479023i | −0.0240553 | − | 0.999711i | \(-0.507658\pi\) |
0.853747 | + | 0.520688i | \(0.174324\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −76.9605 | + | 133.300i | −0.0826644 | + | 0.143179i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 868.633i | 0.929019i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 443.554 | 0.473377 | 0.236688 | − | 0.971586i | \(-0.423938\pi\) | ||||
0.236688 | + | 0.971586i | \(0.423938\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 69.7458 | + | 40.2678i | 0.0741188 | + | 0.0427925i | 0.536601 | − | 0.843836i | \(-0.319708\pi\) |
−0.462483 | + | 0.886628i | \(0.653041\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 580.536 | + | 1005.52i | 0.615627 | + | 1.06630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −245.861 | + | 141.948i | −0.259621 | + | 0.149892i | −0.624162 | − | 0.781295i | \(-0.714559\pi\) |
0.364541 | + | 0.931187i | \(0.381226\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −144.818 | + | 250.832i | −0.152601 | + | 0.264312i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1123.17i | − | 1.17857i | −0.807927 | − | 0.589283i | \(-0.799410\pi\) | ||
0.807927 | − | 0.589283i | \(-0.200590\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 357.237 | 0.374070 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −733.626 | − | 423.559i | −0.764991 | − | 0.441668i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 230.727 | + | 399.631i | 0.240090 | + | 0.415849i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 100.863 | − | 58.2331i | 0.104521 | − | 0.0603452i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 699.536 | − | 1211.63i | 0.723409 | − | 1.25298i | −0.236217 | − | 0.971700i | \(-0.575907\pi\) |
0.959626 | − | 0.281281i | \(-0.0907592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1705.41i | 1.75634i | 0.478345 | + | 0.878172i | \(0.341237\pi\) | ||||
−0.478345 | + | 0.878172i | \(0.658763\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −497.024 | −0.510816 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1005.50 | − | 580.524i | −1.02917 | − | 0.594190i | −0.112422 | − | 0.993661i | \(-0.535861\pi\) |
−0.916746 | + | 0.399470i | \(0.869194\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1461.81 | − | 2531.94i | −1.49317 | − | 2.58625i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1023.46 | − | 590.895i | 1.04116 | − | 0.601114i | 0.120999 | − | 0.992653i | \(-0.461390\pi\) |
0.920162 | + | 0.391539i | \(0.128057\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −328.989 | + | 569.826i | −0.333999 | + | 0.578504i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 771.737i | 0.780320i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −969.527 | −0.978332 | −0.489166 | − | 0.872191i | \(-0.662699\pi\) | ||||
−0.489166 | + | 0.872191i | \(0.662699\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −409.492 | − | 236.420i | −0.411549 | − | 0.237608i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −390.124 | − | 675.714i | −0.391298 | − | 0.677747i | 0.601323 | − | 0.799006i | \(-0.294640\pi\) |
−0.992621 | + | 0.121258i | \(0.961307\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))