Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(2177,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.2177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.w (of order \(4\), 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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2177.2 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.2177 |
Dual form | 2880.2.w.j.2753.2 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.707107 | − | 2.12132i | 0.316228 | − | 0.948683i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 2.00000i | 0.755929 | + | 0.755929i | 0.975579 | − | 0.219650i | \(-0.0704915\pi\) |
−0.219650 | + | 0.975579i | \(0.570491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.82843i | − | 0.852803i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||
0.904534 | − | 0.426401i | \(-0.140219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 3.00000i | −0.832050 | + | 0.832050i | −0.987797 | − | 0.155747i | \(-0.950222\pi\) |
0.155747 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41421 | − | 1.41421i | 0.342997 | − | 0.342997i | −0.514496 | − | 0.857493i | \(-0.672021\pi\) |
0.857493 | + | 0.514496i | \(0.172021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.65685 | − | 5.65685i | −1.17954 | − | 1.17954i | −0.979863 | − | 0.199673i | \(-0.936012\pi\) |
−0.199673 | − | 0.979863i | \(-0.563988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | − | 3.00000i | −0.800000 | − | 0.600000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.89949 | −1.83829 | −0.919145 | − | 0.393919i | \(-0.871119\pi\) | ||||
−0.919145 | + | 0.393919i | \(0.871119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.65685 | − | 2.82843i | 0.956183 | − | 0.478091i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | + | 3.00000i | 0.493197 | + | 0.493197i | 0.909312 | − | 0.416115i | \(-0.136609\pi\) |
−0.416115 | + | 0.909312i | \(0.636609\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.41421i | − | 0.220863i | −0.993884 | − | 0.110432i | \(-0.964777\pi\) | ||
0.993884 | − | 0.110432i | \(-0.0352233\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.48528 | − | 8.48528i | 1.23771 | − | 1.23771i | 0.276769 | − | 0.960936i | \(-0.410736\pi\) |
0.960936 | − | 0.276769i | \(-0.0892637\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.07107 | + | 7.07107i | 0.971286 | + | 0.971286i | 0.999599 | − | 0.0283132i | \(-0.00901359\pi\) |
−0.0283132 | + | 0.999599i | \(0.509014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | − | 2.00000i | −0.809040 | − | 0.269680i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.82843 | 0.368230 | 0.184115 | − | 0.982905i | \(-0.441058\pi\) | ||||
0.184115 | + | 0.982905i | \(0.441058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.24264 | + | 8.48528i | 0.526235 | + | 1.05247i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | − | 8.00000i | −0.977356 | − | 0.977356i | 0.0223937 | − | 0.999749i | \(-0.492871\pi\) |
−0.999749 | + | 0.0223937i | \(0.992871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65685i | 0.671345i | 0.941979 | + | 0.335673i | \(0.108964\pi\) | ||||
−0.941979 | + | 0.335673i | \(0.891036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | − | 7.00000i | 0.819288 | − | 0.819288i | −0.166717 | − | 0.986005i | \(-0.553317\pi\) |
0.986005 | + | 0.166717i | \(0.0533166\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.65685 | − | 5.65685i | 0.644658 | − | 0.644658i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.48528 | − | 8.48528i | −0.931381 | − | 0.931381i | 0.0664117 | − | 0.997792i | \(-0.478845\pi\) |
−0.997792 | + | 0.0664117i | \(0.978845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | − | 4.00000i | −0.216930 | − | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.41421 | −0.149906 | −0.0749532 | − | 0.997187i | \(-0.523881\pi\) | ||||
−0.0749532 | + | 0.997187i | \(0.523881\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0000 | −1.25794 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.48528 | − | 2.82843i | −0.870572 | − | 0.290191i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | + | 3.00000i | 0.304604 | + | 0.304604i | 0.842812 | − | 0.538208i | \(-0.180899\pi\) |
−0.538208 | + | 0.842812i | \(0.680899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.41421i | − | 0.140720i | −0.997522 | − | 0.0703598i | \(-0.977585\pi\) | ||
0.997522 | − | 0.0703598i | \(-0.0224147\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | + | 2.00000i | −0.197066 | + | 0.197066i | −0.798741 | − | 0.601675i | \(-0.794500\pi\) |
0.601675 | + | 0.798741i | \(0.294500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.82843 | − | 2.82843i | 0.273434 | − | 0.273434i | −0.557047 | − | 0.830481i | \(-0.688066\pi\) |
0.830481 | + | 0.557047i | \(0.188066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.00000i | − | 0.766261i | −0.923694 | − | 0.383131i | \(-0.874846\pi\) | ||
0.923694 | − | 0.383131i | \(-0.125154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.82843 | − | 2.82843i | −0.266076 | − | 0.266076i | 0.561441 | − | 0.827517i | \(-0.310247\pi\) |
−0.827517 | + | 0.561441i | \(0.810247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.0000 | + | 8.00000i | −1.49201 | + | 0.746004i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.65685 | 0.518563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.19239 | + | 6.36396i | −0.822192 | + | 0.569210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0000 | − | 10.0000i | −0.887357 | − | 0.887357i | 0.106912 | − | 0.994268i | \(-0.465904\pi\) |
−0.994268 | + | 0.106912i | \(0.965904\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.82843i | − | 0.247121i | −0.992337 | − | 0.123560i | \(-0.960569\pi\) | ||
0.992337 | − | 0.123560i | \(-0.0394313\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000 | − | 8.00000i | 0.693688 | − | 0.693688i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.48528 | + | 8.48528i | −0.724947 | + | 0.724947i | −0.969608 | − | 0.244662i | \(-0.921323\pi\) |
0.244662 | + | 0.969608i | \(0.421323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0000i | 1.35710i | 0.734553 | + | 0.678551i | \(0.237392\pi\) | ||||
−0.734553 | + | 0.678551i | \(0.762608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.48528 | + | 8.48528i | 0.709575 | + | 0.709575i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.00000 | + | 21.0000i | −0.581318 | + | 1.74396i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.7279 | 1.04271 | 0.521356 | − | 0.853339i | \(-0.325426\pi\) | ||||
0.521356 | + | 0.853339i | \(0.325426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.0000 | −1.62758 | −0.813788 | − | 0.581161i | \(-0.802599\pi\) | ||||
−0.813788 | + | 0.581161i | \(0.802599\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.65685 | + | 16.9706i | −0.454369 | + | 1.36311i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | + | 9.00000i | 0.718278 | + | 0.718278i | 0.968252 | − | 0.249974i | \(-0.0804222\pi\) |
−0.249974 | + | 0.968252i | \(0.580422\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 22.6274i | − | 1.78329i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | − | 4.00000i | 0.313304 | − | 0.313304i | −0.532884 | − | 0.846188i | \(-0.678892\pi\) |
0.846188 | + | 0.532884i | \(0.178892\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3137 | − | 11.3137i | 0.875481 | − | 0.875481i | −0.117582 | − | 0.993063i | \(-0.537514\pi\) |
0.993063 | + | 0.117582i | \(0.0375143\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.82843 | − | 2.82843i | −0.215041 | − | 0.215041i | 0.591364 | − | 0.806405i | \(-0.298590\pi\) |
−0.806405 | + | 0.591364i | \(0.798590\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | − | 14.0000i | −0.151186 | − | 1.05830i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.1421 | 1.05703 | 0.528516 | − | 0.848923i | \(-0.322748\pi\) | ||||
0.528516 | + | 0.848923i | \(0.322748\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.00000 | −0.594635 | −0.297318 | − | 0.954779i | \(-0.596092\pi\) | ||||
−0.297318 | + | 0.954779i | \(0.596092\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.48528 | − | 4.24264i | 0.623850 | − | 0.311925i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | − | 4.00000i | −0.292509 | − | 0.292509i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.3137i | − | 0.818631i | −0.912393 | − | 0.409316i | \(-0.865768\pi\) | ||
0.912393 | − | 0.409316i | \(-0.134232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.0000 | + | 15.0000i | −1.07972 | + | 1.07972i | −0.0831899 | + | 0.996534i | \(0.526511\pi\) |
−0.996534 | + | 0.0831899i | \(0.973489\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.48528 | − | 8.48528i | 0.604551 | − | 0.604551i | −0.336966 | − | 0.941517i | \(-0.609401\pi\) |
0.941517 | + | 0.336966i | \(0.109401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12.0000i | − | 0.850657i | −0.905039 | − | 0.425329i | \(-0.860158\pi\) | ||
0.905039 | − | 0.425329i | \(-0.139842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.7990 | − | 19.7990i | −1.38962 | − | 1.38962i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | − | 1.00000i | −0.209529 | − | 0.0698430i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3137 | −0.782586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | − | 16.0000i | −1.08615 | − | 1.08615i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.48528i | 0.570782i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.00000 | + | 6.00000i | −0.401790 | + | 0.401790i | −0.878863 | − | 0.477074i | \(-0.841698\pi\) |
0.477074 | + | 0.878863i | \(0.341698\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.65685 | − | 5.65685i | 0.375459 | − | 0.375459i | −0.494002 | − | 0.869461i | \(-0.664466\pi\) |
0.869461 | + | 0.494002i | \(0.164466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.00000i | − | 0.396491i | −0.980152 | − | 0.198246i | \(-0.936476\pi\) | ||
0.980152 | − | 0.198246i | \(-0.0635244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.24264 | + | 4.24264i | 0.277945 | + | 0.277945i | 0.832288 | − | 0.554343i | \(-0.187031\pi\) |
−0.554343 | + | 0.832288i | \(0.687031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.0000 | − | 24.0000i | −0.782794 | − | 1.56559i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.12132 | + | 0.707107i | 0.135526 | + | 0.0451754i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | + | 12.0000i | 0.763542 | + | 0.763542i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 25.4558i | − | 1.60676i | −0.595468 | − | 0.803379i | \(-0.703033\pi\) | ||
0.595468 | − | 0.803379i | \(-0.296967\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.0000 | + | 16.0000i | −1.00591 | + | 1.00591i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.1421 | + | 14.1421i | −0.882162 | + | 0.882162i | −0.993754 | − | 0.111592i | \(-0.964405\pi\) |
0.111592 | + | 0.993754i | \(0.464405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0000i | 0.745644i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.3137 | − | 11.3137i | −0.697633 | − | 0.697633i | 0.266266 | − | 0.963899i | \(-0.414210\pi\) |
−0.963899 | + | 0.266266i | \(0.914210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.0000 | − | 10.0000i | 1.22859 | − | 0.614295i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.3848 | −1.12094 | −0.560470 | − | 0.828175i | \(-0.689379\pi\) | ||||
−0.560470 | + | 0.828175i | \(0.689379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.48528 | + | 11.3137i | −0.511682 | + | 0.682242i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.0000 | − | 15.0000i | −0.901263 | − | 0.901263i | 0.0942828 | − | 0.995545i | \(-0.469944\pi\) |
−0.995545 | + | 0.0942828i | \(0.969944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7279i | 0.759284i | 0.925133 | + | 0.379642i | \(0.123953\pi\) | ||||
−0.925133 | + | 0.379642i | \(0.876047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | − | 4.00000i | 0.237775 | − | 0.237775i | −0.578153 | − | 0.815928i | \(-0.696226\pi\) |
0.815928 | + | 0.578153i | \(0.196226\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.82843 | − | 2.82843i | 0.166957 | − | 0.166957i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000i | 0.764706i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.48528 | − | 8.48528i | −0.495715 | − | 0.495715i | 0.414386 | − | 0.910101i | \(-0.363996\pi\) |
−0.910101 | + | 0.414386i | \(0.863996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00000 | − | 6.00000i | 0.116445 | − | 0.349334i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 33.9411 | 1.96287 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000 | + | 12.0000i | 0.684876 | + | 0.684876i | 0.961095 | − | 0.276219i | \(-0.0890814\pi\) |
−0.276219 | + | 0.961095i | \(0.589081\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.65685i | 0.320771i | 0.987054 | + | 0.160385i | \(0.0512737\pi\) | ||||
−0.987054 | + | 0.160385i | \(0.948726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.00000 | − | 3.00000i | 0.169570 | − | 0.169570i | −0.617220 | − | 0.786790i | \(-0.711741\pi\) |
0.786790 | + | 0.617220i | \(0.211741\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.24264 | − | 4.24264i | 0.238290 | − | 0.238290i | −0.577851 | − | 0.816142i | \(-0.696109\pi\) |
0.816142 | + | 0.577851i | \(0.196109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.0000i | 1.56770i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.65685 | − | 5.65685i | −0.314756 | − | 0.314756i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.0000 | − | 3.00000i | 1.16487 | − | 0.166410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.9411 | 1.87123 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.6274 | + | 11.3137i | −1.23627 | + | 0.618134i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.00000 | − | 3.00000i | −0.163420 | − | 0.163420i | 0.620660 | − | 0.784080i | \(-0.286865\pi\) |
−0.784080 | + | 0.620660i | \(0.786865\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.6274i | 1.22534i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.65685 | + | 5.65685i | −0.303676 | + | 0.303676i | −0.842450 | − | 0.538774i | \(-0.818888\pi\) |
0.538774 | + | 0.842450i | \(0.318888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.0000i | 1.71292i | 0.516213 | + | 0.856460i | \(0.327341\pi\) | ||||
−0.516213 | + | 0.856460i | \(0.672659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.7279 | − | 12.7279i | −0.677439 | − | 0.677439i | 0.281981 | − | 0.959420i | \(-0.409008\pi\) |
−0.959420 | + | 0.281981i | \(0.909008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0000 | + | 4.00000i | 0.636894 | + | 0.212298i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3137 | 0.597115 | 0.298557 | − | 0.954392i | \(-0.403495\pi\) | ||||
0.298557 | + | 0.954392i | \(0.403495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.89949 | − | 19.7990i | −0.518163 | − | 1.03633i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.0000 | + | 14.0000i | 0.730794 | + | 0.730794i | 0.970777 | − | 0.239983i | \(-0.0771419\pi\) |
−0.239983 | + | 0.970777i | \(0.577142\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.2843i | 1.46845i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | − | 5.00000i | 0.258890 | − | 0.258890i | −0.565712 | − | 0.824603i | \(-0.691399\pi\) |
0.824603 | + | 0.565712i | \(0.191399\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.6985 | − | 29.6985i | 1.52955 | − | 1.52955i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.0000i | − | 0.821865i | −0.911666 | − | 0.410932i | \(-0.865203\pi\) | ||
0.911666 | − | 0.410932i | \(-0.134797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.4558 | − | 25.4558i | −1.30073 | − | 1.30073i | −0.927898 | − | 0.372835i | \(-0.878386\pi\) |
−0.372835 | − | 0.927898i | \(-0.621614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | − | 16.0000i | −0.407718 | − | 0.815436i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.2132 | 1.07555 | 0.537776 | − | 0.843088i | \(-0.319265\pi\) | ||||
0.537776 | + | 0.843088i | \(0.319265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.0000 | + | 17.0000i | 0.853206 | + | 0.853206i | 0.990527 | − | 0.137321i | \(-0.0438492\pi\) |
−0.137321 | + | 0.990527i | \(0.543849\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.2132i | 1.05934i | 0.848205 | + | 0.529668i | \(0.177684\pi\) | ||||
−0.848205 | + | 0.529668i | \(0.822316\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.0000 | − | 24.0000i | 1.19553 | − | 1.19553i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.48528 | − | 8.48528i | 0.420600 | − | 0.420600i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 24.0000i | − | 1.18672i | −0.804936 | − | 0.593362i | \(-0.797800\pi\) | ||
0.804936 | − | 0.593362i | \(-0.202200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.65685 | + | 5.65685i | 0.278356 | + | 0.278356i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.0000 | + | 12.0000i | −1.17811 | + | 0.589057i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.4558 | −1.24360 | −0.621800 | − | 0.783176i | \(-0.713598\pi\) | ||||
−0.621800 | + | 0.783176i | \(0.713598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.89949 | + | 1.41421i | −0.480196 | + | 0.0685994i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.2843i | 1.36241i | 0.732095 | + | 0.681203i | \(0.238543\pi\) | ||||
−0.732095 | + | 0.681203i | \(0.761457\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.0000 | − | 23.0000i | 1.10531 | − | 1.10531i | 0.111551 | − | 0.993759i | \(-0.464418\pi\) |
0.993759 | − | 0.111551i | \(-0.0355818\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.6274 | + | 22.6274i | −1.08242 | + | 1.08242i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.0000i | 0.954548i | 0.878755 | + | 0.477274i | \(0.158375\pi\) | ||||
−0.878755 | + | 0.477274i | \(0.841625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.9706 | + | 16.9706i | 0.806296 | + | 0.806296i | 0.984071 | − | 0.177775i | \(-0.0568900\pi\) |
−0.177775 | + | 0.984071i | \(0.556890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00000 | + | 3.00000i | −0.0474045 | + | 0.142214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.41421 | 0.0667409 | 0.0333704 | − | 0.999443i | \(-0.489376\pi\) | ||||
0.0333704 | + | 0.999443i | \(0.489376\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.00000 | −0.188353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.48528 | + | 25.4558i | −0.397796 | + | 1.19339i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.0000 | + | 15.0000i | 0.701670 | + | 0.701670i | 0.964769 | − | 0.263099i | \(-0.0847444\pi\) |
−0.263099 | + | 0.964769i | \(0.584744\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 15.5563i | − | 0.724531i | −0.932075 | − | 0.362266i | \(-0.882003\pi\) | ||
0.932075 | − | 0.362266i | \(-0.117997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0000 | − | 26.0000i | 1.20832 | − | 1.20832i | 0.236752 | − | 0.971570i | \(-0.423917\pi\) |
0.971570 | − | 0.236752i | \(-0.0760830\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.7990 | − | 19.7990i | 0.916188 | − | 0.916188i | −0.0805616 | − | 0.996750i | \(-0.525671\pi\) |
0.996750 | + | 0.0805616i | \(0.0256714\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 32.0000i | − | 1.47762i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.0000 | + | 16.0000i | −0.550598 | + | 0.734130i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.5980 | 1.80928 | 0.904639 | − | 0.426179i | \(-0.140141\pi\) | ||||
0.904639 | + | 0.426179i | \(0.140141\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.0000 | −0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.48528 | − | 4.24264i | 0.385297 | − | 0.192648i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.00000 | + | 6.00000i | 0.271886 | + | 0.271886i | 0.829859 | − | 0.557973i | \(-0.188421\pi\) |
−0.557973 | + | 0.829859i | \(0.688421\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.7696i | 1.65939i | 0.558219 | + | 0.829693i | \(0.311485\pi\) | ||||
−0.558219 | + | 0.829693i | \(0.688515\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.0000 | + | 14.0000i | −0.630528 | + | 0.630528i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.3137 | + | 11.3137i | −0.507489 | + | 0.507489i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000i | 0.179065i | 0.995984 | + | 0.0895323i | \(0.0285372\pi\) | ||||
−0.995984 | + | 0.0895323i | \(0.971463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.48528 | − | 8.48528i | −0.378340 | − | 0.378340i | 0.492163 | − | 0.870503i | \(-0.336206\pi\) |
−0.870503 | + | 0.492163i | \(0.836206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.00000 | − | 1.00000i | −0.133498 | − | 0.0444994i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.41421 | −0.0626839 | −0.0313420 | − | 0.999509i | \(-0.509978\pi\) | ||||
−0.0313420 | + | 0.999509i | \(0.509978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.0000 | 1.23865 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.82843 | + | 5.65685i | 0.124635 | + | 0.249271i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.0000 | − | 24.0000i | −1.05552 | − | 1.05552i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.6985i | 1.30111i | 0.759457 | + | 0.650557i | \(0.225465\pi\) | ||||
−0.759457 | + | 0.650557i | \(0.774535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.3137 | + | 11.3137i | −0.492833 | + | 0.492833i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000i | 1.78261i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.24264 | + | 4.24264i | 0.183769 | + | 0.183769i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00000 | − | 8.00000i | −0.172935 | − | 0.345870i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.82843 | 0.121829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.0000 | −1.71973 | −0.859867 | − | 0.510518i | \(-0.829454\pi\) | ||||
−0.859867 | + | 0.510518i | \(0.829454\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.9706 | − | 5.65685i | −0.726939 | − | 0.242313i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | + | 12.0000i | 0.513083 | + | 0.513083i | 0.915470 | − | 0.402387i | \(-0.131819\pi\) |
−0.402387 | + | 0.915470i | \(0.631819\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 39.5980i | 1.68693i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.7279 | + | 12.7279i | −0.539299 | + | 0.539299i | −0.923323 | − | 0.384024i | \(-0.874538\pi\) |
0.384024 | + | 0.923323i | \(0.374538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.9706 | − | 16.9706i | −0.715224 | − | 0.715224i | 0.252399 | − | 0.967623i | \(-0.418780\pi\) |
−0.967623 | + | 0.252399i | \(0.918780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.00000 | + | 4.00000i | −0.336563 | + | 0.168281i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.5563 | 0.652156 | 0.326078 | − | 0.945343i | \(-0.394273\pi\) | ||||
0.326078 | + | 0.945343i | \(0.394273\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.65685 | + | 39.5980i | 0.235907 | + | 1.65135i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.00000 | + | 7.00000i | 0.291414 | + | 0.291414i | 0.837639 | − | 0.546225i | \(-0.183936\pi\) |
−0.546225 | + | 0.837639i | \(0.683936\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 33.9411i | − | 1.40812i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.0000 | − | 20.0000i | 0.828315 | − | 0.828315i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.48528 | + | 8.48528i | −0.350225 | + | 0.350225i | −0.860193 | − | 0.509968i | \(-0.829657\pi\) |
0.509968 | + | 0.860193i | \(0.329657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.0000i | 1.31854i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.1421 | − | 14.1421i | −0.580748 | − | 0.580748i | 0.354361 | − | 0.935109i | \(-0.384698\pi\) |
−0.935109 | + | 0.354361i | \(0.884698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | − | 12.0000i | 0.163984 | − | 0.491952i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.2843 | −1.15566 | −0.577832 | − | 0.816156i | \(-0.696101\pi\) | ||||
−0.577832 | + | 0.816156i | \(0.696101\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.0000 | −1.63163 | −0.815817 | − | 0.578310i | \(-0.803712\pi\) | ||||
−0.815817 | + | 0.578310i | \(0.803712\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.12132 | − | 6.36396i | 0.0862439 | − | 0.258732i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.0000 | + | 18.0000i | 0.730597 | + | 0.730597i | 0.970738 | − | 0.240141i | \(-0.0771936\pi\) |
−0.240141 | + | 0.970738i | \(0.577194\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.9117i | 2.05967i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.0000 | − | 27.0000i | 1.09052 | − | 1.09052i | 0.0950469 | − | 0.995473i | \(-0.469700\pi\) |
0.995473 | − | 0.0950469i | \(-0.0303001\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.24264 | − | 4.24264i | 0.170802 | − | 0.170802i | −0.616530 | − | 0.787332i | \(-0.711462\pi\) |
0.787332 | + | 0.616530i | \(0.211462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.0000i | 0.964641i | 0.875995 | + | 0.482321i | \(0.160206\pi\) | ||||
−0.875995 | + | 0.482321i | \(0.839794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.82843 | − | 2.82843i | −0.113319 | − | 0.113319i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | + | 24.0000i | 0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.48528 | 0.338330 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28.2843 | + | 14.1421i | −1.12243 | + | 0.561214i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00000 | − | 3.00000i | −0.118864 | − | 0.118864i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 41.0122i | − | 1.61988i | −0.586510 | − | 0.809942i | \(-0.699498\pi\) | ||
0.586510 | − | 0.809942i | \(-0.300502\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.82843 | − | 2.82843i | 0.111197 | − | 0.111197i | −0.649319 | − | 0.760516i | \(-0.724946\pi\) |
0.760516 | + | 0.649319i | \(0.224946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.00000i | − | 0.314027i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.24264 | + | 4.24264i | 0.166027 | + | 0.166027i | 0.785231 | − | 0.619203i | \(-0.212544\pi\) |
−0.619203 | + | 0.785231i | \(0.712544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.00000 | − | 2.00000i | −0.234439 | − | 0.0781465i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.82843 | −0.110180 | −0.0550899 | − | 0.998481i | \(-0.517545\pi\) | ||||
−0.0550899 | + | 0.998481i | \(0.517545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.0000 | 0.622328 | 0.311164 | − | 0.950356i | \(-0.399281\pi\) | ||||
0.311164 | + | 0.950356i | \(0.399281\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.3137 | − | 22.6274i | −0.438727 | − | 0.877454i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 56.0000 | + | 56.0000i | 2.16833 | + | 2.16833i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.0000 | + | 23.0000i | −0.886585 | + | 0.886585i | −0.994193 | − | 0.107609i | \(-0.965681\pi\) |
0.107609 | + | 0.994193i | \(0.465681\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.89949 | + | 9.89949i | −0.380468 | + | 0.380468i | −0.871271 | − | 0.490802i | \(-0.836704\pi\) |
0.490802 | + | 0.871271i | \(0.336704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000i | 0.460518i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.48528 | − | 8.48528i | −0.324680 | − | 0.324680i | 0.525879 | − | 0.850559i | \(-0.323736\pi\) |
−0.850559 | + | 0.525879i | \(0.823736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | + | 24.0000i | 0.458496 | + | 0.916993i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42.4264 | −1.61632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0000 | −0.456502 | −0.228251 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228251 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.9411 | + | 11.3137i | 1.28746 | + | 0.429153i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.00000 | − | 2.00000i | −0.0757554 | − | 0.0757554i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.89949i | 0.373899i | 0.982370 | + | 0.186949i | \(0.0598600\pi\) | ||||
−0.982370 | + | 0.186949i | \(0.940140\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | − | 12.0000i | 0.452589 | − | 0.452589i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.82843 | − | 2.82843i | 0.106374 | − | 0.106374i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 10.0000i | − | 0.375558i | −0.982211 | − | 0.187779i | \(-0.939871\pi\) | ||
0.982211 | − | 0.187779i | \(-0.0601289\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.2548 | + | 45.2548i | 1.69481 | + | 1.69481i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0000 | − | 12.0000i | 0.897549 | − | 0.448775i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.5980 | 1.47676 | 0.738378 | − | 0.674387i | \(-0.235592\pi\) | ||||
0.738378 | + | 0.674387i | \(0.235592\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 39.5980 | + | 29.6985i | 1.47063 | + | 1.10297i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.00000 | − | 6.00000i | −0.222528 | − | 0.222528i | 0.587034 | − | 0.809562i | \(-0.300295\pi\) |
−0.809562 | + | 0.587034i | \(0.800295\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.0000 | − | 29.0000i | 1.07114 | − | 1.07114i | 0.0738717 | − | 0.997268i | \(-0.476464\pi\) |
0.997268 | − | 0.0738717i | \(-0.0235355\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.6274 | + | 22.6274i | −0.833492 | + | 0.833492i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.0000i | 1.03000i | 0.857191 | + | 0.514998i | \(0.172207\pi\) | ||||
−0.857191 | + | 0.514998i | \(0.827793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.7990 | − | 19.7990i | −0.726354 | − | 0.726354i | 0.243537 | − | 0.969892i | \(-0.421692\pi\) |
−0.969892 | + | 0.243537i | \(0.921692\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | − | 27.0000i | 0.329734 | − | 0.989203i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.3137 | 0.413394 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0000 | −0.875772 | −0.437886 | − | 0.899030i | \(-0.644273\pi\) | ||||
−0.437886 | + | 0.899030i | \(0.644273\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.1421 | + | 42.4264i | −0.514685 | + | 1.54406i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.00000 | − | 9.00000i | −0.327111 | − | 0.327111i | 0.524376 | − | 0.851487i | \(-0.324299\pi\) |
−0.851487 | + | 0.524376i | \(0.824299\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 26.8701i | − | 0.974039i | −0.873391 | − | 0.487019i | \(-0.838084\pi\) | ||
0.873391 | − | 0.487019i | \(-0.161916\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.0000 | − | 16.0000i | 0.579239 | − | 0.579239i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.48528 | + | 8.48528i | −0.306386 | + | 0.306386i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.00000i | 0.288487i | 0.989542 | + | 0.144244i | \(0.0460749\pi\) | ||||
−0.989542 | + | 0.144244i | \(0.953925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.7279 | − | 12.7279i | −0.457792 | − | 0.457792i | 0.440138 | − | 0.897930i | \(-0.354929\pi\) |
−0.897930 | + | 0.440138i | \(0.854929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.0000 | + | 24.0000i | 1.14947 | + | 0.862105i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.65685 | −0.202678 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | 0.572525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.4558 | − | 12.7279i | 0.908558 | − | 0.454279i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | + | 20.0000i | 0.712923 | + | 0.712923i | 0.967146 | − | 0.254223i | \(-0.0818196\pi\) |
−0.254223 | + | 0.967146i | \(0.581820\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 11.3137i | − | 0.402269i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.48528 | − | 8.48528i | 0.300564 | − | 0.300564i | −0.540670 | − | 0.841235i | \(-0.681829\pi\) |
0.841235 | + | 0.540670i | \(0.181829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 24.0000i | − | 0.849059i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.7990 | − | 19.7990i | −0.698691 | − | 0.698691i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −48.0000 | − | 16.0000i | −1.69178 | − | 0.563926i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.8406 | −1.54135 | −0.770677 | − | 0.637226i | \(-0.780082\pi\) | ||||
−0.770677 | + | 0.637226i | \(0.780082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.00000 | −0.280918 | −0.140459 | − | 0.990086i | \(-0.544858\pi\) | ||||
−0.140459 | + | 0.990086i | \(0.544858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.65685 | − | 11.3137i | −0.198151 | − | 0.396302i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 15.5563i | − | 0.542920i | −0.962450 | − | 0.271460i | \(-0.912493\pi\) | ||
0.962450 | − | 0.271460i | \(-0.0875065\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.0000 | − | 26.0000i | 0.906303 | − | 0.906303i | −0.0896686 | − | 0.995972i | \(-0.528581\pi\) |
0.995972 | + | 0.0896686i | \(0.0285808\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.9411 | − | 33.9411i | 1.18025 | − | 1.18025i | 0.200569 | − | 0.979680i | \(-0.435721\pi\) |
0.979680 | − | 0.200569i | \(-0.0642791\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.00000i | − | 0.277851i | −0.990303 | − | 0.138926i | \(-0.955635\pi\) | ||
0.990303 | − | 0.138926i | \(-0.0443649\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.41421 | + | 1.41421i | 0.0489996 | + | 0.0489996i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.0000 | − | 32.0000i | −0.553703 | − | 1.10741i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.3137 | 0.390593 | 0.195296 | − | 0.980744i | \(-0.437433\pi\) | ||||
0.195296 | + | 0.980744i | \(0.437433\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 69.0000 | 2.37931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.6066 | − | 3.53553i | −0.364878 | − | 0.121626i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.00000 | + | 6.00000i | 0.206162 | + | 0.206162i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 33.9411i | − | 1.16349i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.00000 | − | 5.00000i | 0.171197 | − | 0.171197i | −0.616308 | − | 0.787505i | \(-0.711372\pi\) |
0.787505 | + | 0.616308i | \(0.211372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.6985 | − | 29.6985i | 1.01448 | − | 1.01448i | 0.0145873 | − | 0.999894i | \(-0.495357\pi\) |
0.999894 | − | 0.0145873i | \(-0.00464345\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 8.00000i | − | 0.272956i | −0.990643 | − | 0.136478i | \(-0.956422\pi\) | ||
0.990643 | − | 0.136478i | \(-0.0435784\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.65685 | − | 5.65685i | −0.192562 | − | 0.192562i | 0.604240 | − | 0.796802i | \(-0.293477\pi\) |
−0.796802 | + | 0.604240i | \(0.793477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.00000 | + | 4.00000i | −0.272008 | + | 0.136004i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.0000 | 1.62642 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.1127 | − | 5.65685i | −1.05180 | − | 0.191237i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.0000 | + | 15.0000i | 0.506514 | + | 0.506514i | 0.913455 | − | 0.406941i | \(-0.133404\pi\) |
−0.406941 | + | 0.913455i | \(0.633404\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.0122i | 1.38174i | 0.722981 | + | 0.690868i | \(0.242771\pi\) | ||||
−0.722981 | + | 0.690868i | \(0.757229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | − | 20.0000i | 0.673054 | − | 0.673054i | −0.285365 | − | 0.958419i | \(-0.592115\pi\) |
0.958419 | + | 0.285365i | \(0.0921149\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.9411 | + | 33.9411i | −1.13963 | + | 1.13963i | −0.151115 | + | 0.988516i | \(0.548286\pi\) |
−0.988516 | + | 0.151115i | \(0.951714\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 40.0000i | − | 1.34156i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.9411 | − | 33.9411i | −1.13580 | − | 1.13580i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.0000 | − | 30.0000i | 0.334263 | − | 1.00279i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 79.1960 | 2.64133 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.0000 | 0.666297 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.65685 | + | 16.9706i | −0.188040 | + | 0.564121i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0000 | − | 16.0000i | −0.531271 | − | 0.531271i | 0.389679 | − | 0.920951i | \(-0.372586\pi\) |
−0.920951 | + | 0.389679i | \(0.872586\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 28.2843i | − | 0.937100i | −0.883437 | − | 0.468550i | \(-0.844777\pi\) | ||
0.883437 | − | 0.468550i | \(-0.155223\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0000 | + | 24.0000i | −0.794284 | + | 0.794284i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.65685 | − | 5.65685i | 0.186806 | − | 0.186806i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.0000i | 1.05558i | 0.849374 | + | 0.527791i | \(0.176980\pi\) | ||||
−0.849374 | + | 0.527791i | \(0.823020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.9706 | − | 16.9706i | −0.558593 | − | 0.558593i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.00000 | − | 21.0000i | −0.0986394 | − | 0.690476i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.3553 | 1.15997 | 0.579986 | − | 0.814627i | \(-0.303058\pi\) | ||||
0.579986 | + | 0.814627i | \(0.303058\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | 0.131095 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.3137 | + | 5.65685i | −0.369998 | + | 0.184999i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.0000 | + | 37.0000i | 1.20874 | + | 1.20874i | 0.971436 | + | 0.237301i | \(0.0762628\pi\) |
0.237301 | + | 0.971436i | \(0.423737\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.1838i | 1.24476i | 0.782717 | + | 0.622378i | \(0.213833\pi\) | ||||
−0.782717 | + | 0.622378i | \(0.786167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.00000 | + | 8.00000i | −0.260516 | + | 0.260516i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.6274 | − | 22.6274i | 0.735292 | − | 0.735292i | −0.236371 | − | 0.971663i | \(-0.575958\pi\) |
0.971663 | + | 0.236371i | \(0.0759580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.0000i | 1.36338i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.4558 | + | 25.4558i | 0.824596 | + | 0.824596i | 0.986763 | − | 0.162168i | \(-0.0518485\pi\) |
−0.162168 | + | 0.986763i | \(0.551849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.0000 | − | 8.00000i | −0.776622 | − | 0.258874i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.9411 | −1.09602 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.2132 | + | 42.4264i | 0.682877 | + | 1.36575i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.00000 | − | 2.00000i | −0.0643157 | − | 0.0643157i | 0.674217 | − | 0.738533i | \(-0.264481\pi\) |
−0.738533 | + | 0.674217i | \(0.764481\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.7401i | 1.72460i | 0.506396 | + | 0.862301i | \(0.330978\pi\) | ||||
−0.506396 | + | 0.862301i | \(0.669022\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.0000 | + | 32.0000i | −1.02587 | + | 1.02587i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.7279 | − | 12.7279i | 0.407202 | − | 0.407202i | −0.473560 | − | 0.880762i | \(-0.657031\pi\) |
0.880762 | + | 0.473560i | \(0.157031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.00000i | 0.127841i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.1421 | + | 14.1421i | 0.451064 | + | 0.451064i | 0.895708 | − | 0.444644i | \(-0.146670\pi\) |
−0.444644 | + | 0.895708i | \(0.646670\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0000 | − | 24.0000i | −0.382352 | − | 0.764704i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.4558 | − | 8.48528i | −0.807005 | − | 0.269002i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0000 | + | 11.0000i | 0.348373 | + | 0.348373i | 0.859503 | − | 0.511130i | \(-0.170773\pi\) |
−0.511130 | + | 0.859503i | \(0.670773\pi\) | |||||||
\(998\) | 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 \(a_p\))