Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,3,Mod(449,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.3488158616\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.449 |
Dual form | 600.3.c.a.449.2 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.82843 | − | 1.00000i | −0.942809 | − | 0.333333i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 6.00000i | − | 0.857143i | −0.903508 | − | 0.428571i | \(-0.859017\pi\) | ||
0.903508 | − | 0.428571i | \(-0.140983\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.65685i | 0.514259i | 0.966377 | + | 0.257130i | \(0.0827768\pi\) | ||||
−0.966377 | + | 0.257130i | \(0.917223\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 10.0000i | − | 0.769231i | −0.923077 | − | 0.384615i | \(-0.874334\pi\) | ||
0.923077 | − | 0.384615i | \(-0.125666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.6274 | 1.33102 | 0.665512 | − | 0.746387i | \(-0.268213\pi\) | ||||
0.665512 | + | 0.746387i | \(0.268213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.105263 | −0.0526316 | − | 0.998614i | \(-0.516761\pi\) | ||||
−0.0526316 | + | 0.998614i | \(0.516761\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.00000 | + | 16.9706i | −0.285714 | + | 0.808122i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −11.3137 | −0.491900 | −0.245950 | − | 0.969282i | \(-0.579100\pi\) | ||||
−0.245950 | + | 0.969282i | \(0.579100\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.1421 | − | 23.0000i | −0.523783 | − | 0.851852i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 16.9706i | − | 0.585192i | −0.956236 | − | 0.292596i | \(-0.905481\pi\) | ||
0.956236 | − | 0.292596i | \(-0.0945191\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −22.0000 | −0.709677 | −0.354839 | − | 0.934928i | \(-0.615464\pi\) | ||||
−0.354839 | + | 0.934928i | \(0.615464\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.65685 | − | 16.0000i | 0.171420 | − | 0.484848i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.00000i | − | 0.162162i | −0.996708 | − | 0.0810811i | \(-0.974163\pi\) | ||
0.996708 | − | 0.0810811i | \(-0.0258373\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.0000 | + | 28.2843i | −0.256410 | + | 0.725238i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 33.9411i | 0.827832i | 0.910315 | + | 0.413916i | \(0.135839\pi\) | ||||
−0.910315 | + | 0.413916i | \(0.864161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 82.0000i | − | 1.90698i | −0.301430 | − | 0.953488i | \(-0.597464\pi\) | ||
0.301430 | − | 0.953488i | \(-0.402536\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −67.8823 | −1.44430 | −0.722152 | − | 0.691735i | \(-0.756847\pi\) | ||||
−0.722152 | + | 0.691735i | \(0.756847\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.0000 | 0.265306 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −64.0000 | − | 22.6274i | −1.25490 | − | 0.443675i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −62.2254 | −1.17406 | −0.587032 | − | 0.809564i | \(-0.699704\pi\) | ||||
−0.587032 | + | 0.809564i | \(0.699704\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.65685 | + | 2.00000i | 0.0992431 | + | 0.0350877i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 73.5391i | − | 1.24643i | −0.782052 | − | 0.623213i | \(-0.785827\pi\) | ||
0.782052 | − | 0.623213i | \(-0.214173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −86.0000 | −1.40984 | −0.704918 | − | 0.709289i | \(-0.749016\pi\) | ||||
−0.704918 | + | 0.709289i | \(0.749016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 33.9411 | − | 42.0000i | 0.538748 | − | 0.666667i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000i | 0.0298507i | 0.999889 | + | 0.0149254i | \(0.00475107\pi\) | ||||
−0.999889 | + | 0.0149254i | \(0.995249\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 32.0000 | + | 11.3137i | 0.463768 | + | 0.163967i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 124.451i | − | 1.75283i | −0.481558 | − | 0.876414i | \(-0.659929\pi\) | ||
0.481558 | − | 0.876414i | \(-0.340071\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 82.0000i | − | 1.12329i | −0.827379 | − | 0.561644i | \(-0.810169\pi\) | ||
0.827379 | − | 0.561644i | \(-0.189831\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 33.9411 | 0.440794 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0000 | −0.126582 | −0.0632911 | − | 0.997995i | \(-0.520160\pi\) | ||||
−0.0632911 | + | 0.997995i | \(0.520160\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 17.0000 | + | 79.1960i | 0.209877 | + | 0.977728i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −73.5391 | −0.886013 | −0.443007 | − | 0.896518i | \(-0.646088\pi\) | ||||
−0.443007 | + | 0.896518i | \(0.646088\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.9706 | + | 48.0000i | −0.195064 | + | 0.551724i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 33.9411i | 0.381361i | 0.981652 | + | 0.190680i | \(0.0610694\pi\) | ||||
−0.981652 | + | 0.190680i | \(0.938931\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −60.0000 | −0.659341 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 62.2254 | + | 22.0000i | 0.669090 | + | 0.236559i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 94.0000i | − | 0.969072i | −0.874771 | − | 0.484536i | \(-0.838988\pi\) | ||
0.874771 | − | 0.484536i | \(-0.161012\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −32.0000 | + | 39.5980i | −0.323232 | + | 0.399980i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 50.9117i | 0.504076i | 0.967717 | + | 0.252038i | \(0.0811008\pi\) | ||||
−0.967717 | + | 0.252038i | \(0.918899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 134.000i | 1.30097i | 0.759519 | + | 0.650485i | \(0.225435\pi\) | ||||
−0.759519 | + | 0.650485i | \(0.774565\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −50.9117 | −0.475810 | −0.237905 | − | 0.971288i | \(-0.576461\pi\) | ||||
−0.237905 | + | 0.971288i | \(0.576461\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.0917431 | −0.0458716 | − | 0.998947i | \(-0.514606\pi\) | ||||
−0.0458716 | + | 0.998947i | \(0.514606\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | + | 16.9706i | −0.0540541 | + | 0.152888i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −67.8823 | −0.600728 | −0.300364 | − | 0.953825i | \(-0.597108\pi\) | ||||
−0.300364 | + | 0.953825i | \(0.597108\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 56.5685 | − | 70.0000i | 0.483492 | − | 0.598291i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 135.765i | − | 1.14088i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 89.0000 | 0.735537 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 33.9411 | − | 96.0000i | 0.275944 | − | 0.780488i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 106.000i | 0.834646i | 0.908758 | + | 0.417323i | \(0.137032\pi\) | ||||
−0.908758 | + | 0.417323i | \(0.862968\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −82.0000 | + | 231.931i | −0.635659 | + | 1.79791i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5.65685i | − | 0.0431821i | −0.999767 | − | 0.0215910i | \(-0.993127\pi\) | ||
0.999767 | − | 0.0215910i | \(-0.00687318\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000i | 0.0902256i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 101.823 | 0.743236 | 0.371618 | − | 0.928386i | \(-0.378803\pi\) | ||||
0.371618 | + | 0.928386i | \(0.378803\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 78.0000 | 0.561151 | 0.280576 | − | 0.959832i | \(-0.409475\pi\) | ||||
0.280576 | + | 0.959832i | \(0.409475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 192.000 | + | 67.8823i | 1.36170 | + | 0.481434i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 56.5685 | 0.395584 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −36.7696 | − | 13.0000i | −0.250133 | − | 0.0884354i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 164.049i | − | 1.10100i | −0.834836 | − | 0.550499i | \(-0.814437\pi\) | ||
0.834836 | − | 0.550499i | \(-0.185563\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 218.000 | 1.44371 | 0.721854 | − | 0.692045i | \(-0.243290\pi\) | ||||
0.721854 | + | 0.692045i | \(0.243290\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 158.392 | + | 128.000i | 1.03524 | + | 0.836601i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 86.0000i | − | 0.547771i | −0.961762 | − | 0.273885i | \(-0.911691\pi\) | ||
0.961762 | − | 0.273885i | \(-0.0883089\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 176.000 | + | 62.2254i | 1.10692 | + | 0.391355i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 67.8823i | 0.421629i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 222.000i | 1.36196i | 0.732301 | + | 0.680982i | \(0.238447\pi\) | ||||
−0.732301 | + | 0.680982i | \(0.761553\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 169.706 | 1.01620 | 0.508101 | − | 0.861298i | \(-0.330348\pi\) | ||||
0.508101 | + | 0.861298i | \(0.330348\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 69.0000 | 0.408284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.0000 | − | 11.3137i | −0.0818713 | − | 0.0661620i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −186.676 | −1.07905 | −0.539527 | − | 0.841969i | \(-0.681397\pi\) | ||||
−0.539527 | + | 0.841969i | \(0.681397\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −73.5391 | + | 208.000i | −0.415475 | + | 1.17514i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 152.735i | − | 0.853269i | −0.904424 | − | 0.426634i | \(-0.859699\pi\) | ||
0.904424 | − | 0.426634i | \(-0.140301\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 90.0000 | 0.497238 | 0.248619 | − | 0.968601i | \(-0.420023\pi\) | ||||
0.248619 | + | 0.968601i | \(0.420023\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 243.245 | + | 86.0000i | 1.32921 | + | 0.469945i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 128.000i | 0.684492i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −138.000 | + | 84.8528i | −0.730159 | + | 0.448957i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 271.529i | − | 1.42162i | −0.703385 | − | 0.710809i | \(-0.748329\pi\) | ||
0.703385 | − | 0.710809i | \(-0.251671\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 2.00000i | − | 0.0103627i | −0.999987 | − | 0.00518135i | \(-0.998351\pi\) | ||
0.999987 | − | 0.00518135i | \(-0.00164928\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 84.8528 | 0.430725 | 0.215362 | − | 0.976534i | \(-0.430907\pi\) | ||||
0.215362 | + | 0.976534i | \(0.430907\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −250.000 | −1.25628 | −0.628141 | − | 0.778100i | \(-0.716184\pi\) | ||||
−0.628141 | + | 0.778100i | \(0.716184\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | − | 5.65685i | 0.00995025 | − | 0.0281436i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −101.823 | −0.501593 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −79.1960 | − | 64.0000i | −0.382589 | − | 0.309179i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 11.3137i | − | 0.0541326i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 34.0000 | 0.161137 | 0.0805687 | − | 0.996749i | \(-0.474326\pi\) | ||||
0.0805687 | + | 0.996749i | \(0.474326\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −124.451 | + | 352.000i | −0.584276 | + | 1.65258i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 132.000i | 0.608295i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −82.0000 | + | 231.931i | −0.374429 | + | 1.05905i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 226.274i | − | 1.02387i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 278.000i | 1.24664i | 0.781968 | + | 0.623318i | \(0.214216\pi\) | ||||
−0.781968 | + | 0.623318i | \(0.785784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −220.617 | −0.971882 | −0.485941 | − | 0.873991i | \(-0.661523\pi\) | ||||
−0.485941 | + | 0.873991i | \(0.661523\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −58.0000 | −0.253275 | −0.126638 | − | 0.991949i | \(-0.540419\pi\) | ||||
−0.126638 | + | 0.991949i | \(0.540419\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −96.0000 | − | 33.9411i | −0.415584 | − | 0.146931i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 395.980 | 1.69948 | 0.849742 | − | 0.527199i | \(-0.176758\pi\) | ||||
0.849742 | + | 0.527199i | \(0.176758\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 28.2843 | + | 10.0000i | 0.119343 | + | 0.0421941i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.6274i | 0.0946754i | 0.998879 | + | 0.0473377i | \(0.0150737\pi\) | ||||
−0.998879 | + | 0.0473377i | \(0.984926\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.0000 | −0.124481 | −0.0622407 | − | 0.998061i | \(-0.519825\pi\) | ||||
−0.0622407 | + | 0.998061i | \(0.519825\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 31.1127 | − | 241.000i | 0.128036 | − | 0.991770i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.0000i | 0.0809717i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 208.000 | + | 73.5391i | 0.835341 | + | 0.295338i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 107.480i | − | 0.428208i | −0.976811 | − | 0.214104i | \(-0.931317\pi\) | ||
0.976811 | − | 0.214104i | \(-0.0686832\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 64.0000i | − | 0.252964i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −181.019 | −0.704355 | −0.352178 | − | 0.935933i | \(-0.614559\pi\) | ||||
−0.352178 | + | 0.935933i | \(0.614559\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −36.0000 | −0.138996 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 96.0000 | − | 118.794i | 0.367816 | − | 0.455149i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −214.960 | −0.817340 | −0.408670 | − | 0.912682i | \(-0.634007\pi\) | ||||
−0.408670 | + | 0.912682i | \(0.634007\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.9411 | − | 96.0000i | 0.127120 | − | 0.359551i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 401.637i | − | 1.49307i | −0.665344 | − | 0.746537i | \(-0.731715\pi\) | ||
0.665344 | − | 0.746537i | \(-0.268285\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 266.000 | 0.981550 | 0.490775 | − | 0.871286i | \(-0.336714\pi\) | ||||
0.490775 | + | 0.871286i | \(0.336714\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 169.706 | + | 60.0000i | 0.621632 | + | 0.219780i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 346.000i | 1.24910i | 0.780986 | + | 0.624549i | \(0.214717\pi\) | ||||
−0.780986 | + | 0.624549i | \(0.785283\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −154.000 | − | 124.451i | −0.551971 | − | 0.446060i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 124.451i | − | 0.442885i | −0.975173 | − | 0.221443i | \(-0.928923\pi\) | ||
0.975173 | − | 0.221443i | \(-0.0710766\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 46.0000i | 0.162544i | 0.996692 | + | 0.0812721i | \(0.0258983\pi\) | ||||
−0.996692 | + | 0.0812721i | \(0.974102\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 203.647 | 0.709571 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 223.000 | 0.771626 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −94.0000 | + | 265.872i | −0.323024 | + | 0.913650i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −220.617 | −0.752960 | −0.376480 | − | 0.926425i | \(-0.622866\pi\) | ||||
−0.376480 | + | 0.926425i | \(0.622866\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 130.108 | − | 80.0000i | 0.438073 | − | 0.269360i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 113.137i | 0.378385i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −492.000 | −1.63455 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 50.9117 | − | 144.000i | 0.168025 | − | 0.475248i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 30.0000i | − | 0.0977199i | −0.998806 | − | 0.0488599i | \(-0.984441\pi\) | ||
0.998806 | − | 0.0488599i | \(-0.0155588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 134.000 | − | 379.009i | 0.433657 | − | 1.22657i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 576.999i | 1.85530i | 0.373447 | + | 0.927651i | \(0.378176\pi\) | ||||
−0.373447 | + | 0.927651i | \(0.621824\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 210.000i | − | 0.670927i | −0.942053 | − | 0.335463i | \(-0.891107\pi\) | ||
0.942053 | − | 0.335463i | \(-0.108893\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −152.735 | −0.481814 | −0.240907 | − | 0.970548i | \(-0.577445\pi\) | ||||
−0.240907 | + | 0.970548i | \(0.577445\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 96.0000 | 0.300940 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 144.000 | + | 50.9117i | 0.448598 | + | 0.158603i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −45.2548 | −0.140108 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 28.2843 | + | 10.0000i | 0.0864962 | + | 0.0305810i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 407.294i | 1.23797i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 434.000 | 1.31118 | 0.655589 | − | 0.755118i | \(-0.272420\pi\) | ||||
0.655589 | + | 0.755118i | \(0.272420\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 33.9411 | − | 42.0000i | 0.101925 | − | 0.126126i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 510.000i | − | 1.51335i | −0.653789 | − | 0.756677i | \(-0.726822\pi\) | ||
0.653789 | − | 0.756677i | \(-0.273178\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 192.000 | + | 67.8823i | 0.566372 | + | 0.200243i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 124.451i | − | 0.364958i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 372.000i | − | 1.08455i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 152.735 | 0.440159 | 0.220079 | − | 0.975482i | \(-0.429368\pi\) | ||||
0.220079 | + | 0.975482i | \(0.429368\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −426.000 | −1.22063 | −0.610315 | − | 0.792159i | \(-0.708957\pi\) | ||||
−0.610315 | + | 0.792159i | \(0.708957\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −230.000 | + | 141.421i | −0.655271 | + | 0.402910i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 45.2548 | 0.128201 | 0.0641003 | − | 0.997943i | \(-0.479582\pi\) | ||||
0.0641003 | + | 0.997943i | \(0.479582\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −135.765 | + | 384.000i | −0.380293 | + | 1.07563i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 441.235i | 1.22907i | 0.788891 | + | 0.614533i | \(0.210655\pi\) | ||||
−0.788891 | + | 0.614533i | \(0.789345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −357.000 | −0.988920 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −251.730 | − | 89.0000i | −0.693471 | − | 0.245179i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 566.000i | − | 1.54223i | −0.636693 | − | 0.771117i | \(-0.719698\pi\) | ||
0.636693 | − | 0.771117i | \(-0.280302\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −192.000 | + | 237.588i | −0.520325 | + | 0.643870i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 373.352i | 1.00634i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 218.000i | − | 0.584450i | −0.956350 | − | 0.292225i | \(-0.905604\pi\) | ||
0.956350 | − | 0.292225i | \(-0.0943957\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −169.706 | −0.450148 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 142.000 | 0.374670 | 0.187335 | − | 0.982296i | \(-0.440015\pi\) | ||||
0.187335 | + | 0.982296i | \(0.440015\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 106.000 | − | 299.813i | 0.278215 | − | 0.786911i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 463.862 | − | 574.000i | 1.19861 | − | 1.48320i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 548.715i | − | 1.41058i | −0.708920 | − | 0.705289i | \(-0.750817\pi\) | ||
0.708920 | − | 0.705289i | \(-0.249183\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −256.000 | −0.654731 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.65685 | + | 16.0000i | −0.0143940 | + | 0.0407125i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 310.000i | − | 0.780856i | −0.920633 | − | 0.390428i | \(-0.872327\pi\) | ||
0.920633 | − | 0.390428i | \(-0.127673\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.0000 | − | 33.9411i | 0.0300752 | − | 0.0850655i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 339.411i | 0.846412i | 0.906033 | + | 0.423206i | \(0.139095\pi\) | ||||
−0.906033 | + | 0.423206i | \(0.860905\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 220.000i | 0.545906i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.9411 | 0.0833934 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 270.000 | 0.660147 | 0.330073 | − | 0.943955i | \(-0.392927\pi\) | ||||
0.330073 | + | 0.943955i | \(0.392927\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −288.000 | − | 101.823i | −0.700730 | − | 0.247745i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −441.235 | −1.06836 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −220.617 | − | 78.0000i | −0.529058 | − | 0.187050i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 50.9117i | 0.121508i | 0.998153 | + | 0.0607538i | \(0.0193505\pi\) | ||||
−0.998153 | + | 0.0607538i | \(0.980650\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −454.000 | −1.07838 | −0.539192 | − | 0.842183i | \(-0.681270\pi\) | ||||
−0.539192 | + | 0.842183i | \(0.681270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −475.176 | − | 384.000i | −1.12335 | − | 0.907801i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 516.000i | 1.20843i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −160.000 | − | 56.5685i | −0.372960 | − | 0.131861i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 248.902i | 0.577498i | 0.957405 | + | 0.288749i | \(0.0932393\pi\) | ||||
−0.957405 | + | 0.288749i | \(0.906761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 706.000i | − | 1.63048i | −0.579120 | − | 0.815242i | \(-0.696604\pi\) | ||
0.579120 | − | 0.815242i | \(-0.303396\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.6274 | 0.0517790 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 486.000 | 1.10706 | 0.553531 | − | 0.832829i | \(-0.313280\pi\) | ||||
0.553531 | + | 0.832829i | \(0.313280\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 91.0000 | + | 73.5391i | 0.206349 | + | 0.166755i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 707.107 | 1.59618 | 0.798089 | − | 0.602540i | \(-0.205844\pi\) | ||||
0.798089 | + | 0.602540i | \(0.205844\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −164.049 | + | 464.000i | −0.366999 | + | 1.03803i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 724.077i | 1.61264i | 0.591477 | + | 0.806322i | \(0.298545\pi\) | ||||
−0.591477 | + | 0.806322i | \(0.701455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −192.000 | −0.425721 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −616.597 | − | 218.000i | −1.36114 | − | 0.481236i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 338.000i | 0.739606i | 0.929110 | + | 0.369803i | \(0.120575\pi\) | ||||
−0.929110 | + | 0.369803i | \(0.879425\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −320.000 | − | 520.431i | −0.697168 | − | 1.13384i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 774.989i | − | 1.68110i | −0.541731 | − | 0.840552i | \(-0.682231\pi\) | ||
0.541731 | − | 0.840552i | \(-0.317769\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 74.0000i | − | 0.159827i | −0.996802 | − | 0.0799136i | \(-0.974536\pi\) | ||
0.996802 | − | 0.0799136i | \(-0.0254644\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 797.616 | 1.70796 | 0.853979 | − | 0.520307i | \(-0.174183\pi\) | ||||
0.853979 | + | 0.520307i | \(0.174183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0000 | 0.0255864 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −86.0000 | + | 243.245i | −0.182590 | + | 0.516443i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 463.862 | 0.980681 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −435.578 | − | 352.000i | −0.913161 | − | 0.737945i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 316.784i | − | 0.661344i | −0.943746 | − | 0.330672i | \(-0.892725\pi\) | ||
0.943746 | − | 0.330672i | \(-0.107275\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −60.0000 | −0.124740 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 67.8823 | − | 192.000i | 0.140543 | − | 0.397516i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 134.000i | − | 0.275154i | −0.990491 | − | 0.137577i | \(-0.956069\pi\) | ||
0.990491 | − | 0.137577i | \(-0.0439315\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 222.000 | − | 627.911i | 0.453988 | − | 1.28407i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 50.9117i | 0.103690i | 0.998655 | + | 0.0518449i | \(0.0165101\pi\) | ||||
−0.998655 | + | 0.0518449i | \(0.983490\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 384.000i | − | 0.778905i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −746.705 | −1.50242 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.0000 | 0.0601202 | 0.0300601 | − | 0.999548i | \(-0.490430\pi\) | ||||
0.0300601 | + | 0.999548i | \(0.490430\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −480.000 | − | 169.706i | −0.958084 | − | 0.338734i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −237.588 | −0.472342 | −0.236171 | − | 0.971712i | \(-0.575893\pi\) | ||||
−0.236171 | + | 0.971712i | \(0.575893\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −195.161 | − | 69.0000i | −0.384934 | − | 0.136095i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 118.794i | 0.233387i | 0.993168 | + | 0.116693i | \(0.0372295\pi\) | ||||
−0.993168 | + | 0.116693i | \(0.962770\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −492.000 | −0.962818 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 28.2843 | + | 46.0000i | 0.0551350 | + | 0.0896686i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 384.000i | − | 0.742747i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 528.000 | + | 186.676i | 1.01734 | + | 0.359684i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 79.1960i | 0.152008i | 0.997108 | + | 0.0760038i | \(0.0242161\pi\) | ||||
−0.997108 | + | 0.0760038i | \(0.975784\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 494.000i | 0.944551i | 0.881451 | + | 0.472275i | \(0.156567\pi\) | ||||
−0.881451 | + | 0.472275i | \(0.843433\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −497.803 | −0.944598 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −401.000 | −0.758034 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 416.000 | − | 514.774i | 0.783427 | − | 0.969442i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 339.411 | 0.636794 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −152.735 | + | 432.000i | −0.284423 | + | 0.804469i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 73.5391i | 0.136436i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 234.000 | 0.432532 | 0.216266 | − | 0.976334i | \(-0.430612\pi\) | ||||
0.216266 | + | 0.976334i | \(0.430612\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −254.558 | − | 90.0000i | −0.468800 | − | 0.165746i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 290.000i | 0.530165i | 0.964226 | + | 0.265082i | \(0.0853991\pi\) | ||||
−0.964226 | + | 0.265082i | \(0.914601\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −602.000 | − | 486.489i | −1.09654 | − | 0.886137i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.9411i | 0.0615991i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 60.0000i | 0.108499i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −175.362 | −0.314834 | −0.157417 | − | 0.987532i | \(-0.550317\pi\) | ||||
−0.157417 | + | 0.987532i | \(0.550317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −820.000 | −1.46691 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 128.000 | − | 362.039i | 0.228164 | − | 0.645345i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 243.245 | 0.432051 | 0.216026 | − | 0.976388i | \(-0.430691\pi\) | ||||
0.216026 | + | 0.976388i | \(0.430691\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 475.176 | − | 102.000i | 0.838052 | − | 0.179894i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 622.254i | 1.09359i | 0.837266 | + | 0.546796i | \(0.184153\pi\) | ||||
−0.837266 | + | 0.546796i | \(0.815847\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 402.000 | 0.704028 | 0.352014 | − | 0.935995i | \(-0.385497\pi\) | ||||
0.352014 | + | 0.935995i | \(0.385497\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −271.529 | + | 768.000i | −0.473873 | + | 1.34031i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 98.0000i | 0.169844i | 0.996388 | + | 0.0849220i | \(0.0270641\pi\) | ||||
−0.996388 | + | 0.0849220i | \(0.972936\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.00000 | + | 5.65685i | −0.00345423 | + | 0.00977004i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 441.235i | 0.759440i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 352.000i | − | 0.603774i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −548.715 | −0.934778 | −0.467389 | − | 0.884052i | \(-0.654805\pi\) | ||||
−0.467389 | + | 0.884052i | \(0.654805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.0000 | 0.0747029 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −240.000 | − | 84.8528i | −0.406091 | − | 0.143575i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 701.450 | 1.18288 | 0.591442 | − | 0.806348i | \(-0.298559\pi\) | ||||
0.591442 | + | 0.806348i | \(0.298559\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 707.107 | + | 250.000i | 1.18443 | + | 0.418760i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 644.881i | 1.07660i | 0.842754 | + | 0.538298i | \(0.180933\pi\) | ||||
−0.842754 | + | 0.538298i | \(0.819067\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −398.000 | −0.662230 | −0.331115 | − | 0.943590i | \(-0.607425\pi\) | ||||
−0.331115 | + | 0.943590i | \(0.607425\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.3137 | + | 14.0000i | −0.0187624 | + | 0.0232172i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 170.000i | 0.280066i | 0.990147 | + | 0.140033i | \(0.0447208\pi\) | ||||
−0.990147 | + | 0.140033i | \(0.955279\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 288.000 | + | 101.823i | 0.472906 | + | 0.167198i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 678.823i | 1.11100i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1030.00i | 1.68026i | 0.542384 | + | 0.840131i | \(0.317522\pi\) | ||||
−0.542384 | + | 0.840131i | \(0.682478\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1052.17 | 1.70531 | 0.852654 | − | 0.522476i | \(-0.174992\pi\) | ||||
0.852654 | + | 0.522476i | \(0.174992\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0000 | 0.0226171 | 0.0113086 | − | 0.999936i | \(-0.496400\pi\) | ||||
0.0113086 | + | 0.999936i | \(0.496400\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 160.000 | + | 260.215i | 0.257649 | + | 0.419026i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 203.647 | 0.326881 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.3137 | + | 32.0000i | −0.0180442 | + | 0.0510367i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 135.765i | − | 0.215842i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1114.00 | 1.76545 | 0.882726 | − | 0.469888i | \(-0.155706\pi\) | ||||
0.882726 | + | 0.469888i | \(0.155706\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −96.1665 | − | 34.0000i | −0.151922 | − | 0.0537125i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 130.000i | − | 0.204082i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 704.000 | − | 871.156i | 1.10172 | − | 1.36331i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 452.548i | − | 0.706004i | −0.935623 | − | 0.353002i | \(-0.885161\pi\) | ||
0.935623 | − | 0.353002i | \(-0.114839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 798.000i | 1.24106i | 0.784184 | + | 0.620529i | \(0.213082\pi\) | ||||
−0.784184 | + | 0.620529i | \(0.786918\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −147.078 | −0.227323 | −0.113662 | − | 0.993520i | \(-0.536258\pi\) | ||||
−0.113662 | + | 0.993520i | \(0.536258\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 416.000 | 0.640986 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 132.000 | − | 373.352i | 0.202765 | − | 0.573506i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −322.441 | −0.493784 | −0.246892 | − | 0.969043i | \(-0.579409\pi\) | ||||
−0.246892 | + | 0.969043i | \(0.579409\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 463.862 | − | 574.000i | 0.706031 | − | 0.873668i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 797.616i | 1.21034i | 0.796095 | + | 0.605172i | \(0.206896\pi\) | ||||
−0.796095 | + | 0.605172i | \(0.793104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 986.000 | 1.49168 | 0.745840 | − | 0.666126i | \(-0.232049\pi\) | ||||
0.745840 | + | 0.666126i | \(0.232049\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −226.274 | + | 640.000i | −0.341288 | + | 0.965309i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 192.000i | 0.287856i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 278.000 | − | 786.303i | 0.415546 | − | 1.17534i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 486.489i | − | 0.725022i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 34.0000i | − | 0.0505201i | −0.999681 | − | 0.0252600i | \(-0.991959\pi\) | ||
0.999681 | − | 0.0252600i | \(-0.00804137\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 401.637 | 0.593259 | 0.296630 | − | 0.954993i | \(-0.404137\pi\) | ||||
0.296630 | + | 0.954993i | \(0.404137\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −564.000 | −0.830633 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 624.000 | + | 220.617i | 0.916300 | + | 0.323961i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −130.108 | −0.190494 | −0.0952472 | − | 0.995454i | \(-0.530364\pi\) | ||||
−0.0952472 | + | 0.995454i | \(0.530364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 164.049 | + | 58.0000i | 0.238790 | + | 0.0844250i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 622.254i | 0.903126i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 578.000 | 0.836469 | 0.418234 | − | 0.908339i | \(-0.362649\pi\) | ||||
0.418234 | + | 0.908339i | \(0.362649\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 237.588 | + | 192.000i | 0.342840 | + | 0.277056i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 768.000i | 1.10187i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1120.00 | − | 395.980i | −1.60229 | − | 0.566495i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1238.85i | 1.76726i | 0.468183 | + | 0.883631i | \(0.344909\pi\) | ||||
−0.468183 | + | 0.883631i | \(0.655091\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000i | 0.0170697i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 305.470 | 0.432065 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1222.00 | 1.72355 | 0.861777 | − | 0.507287i | \(-0.169352\pi\) | ||||
0.861777 | + | 0.507287i | \(0.169352\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −70.0000 | − | 56.5685i | −0.0984529 | − | 0.0795619i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 248.902 | 0.349091 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.6274 | − | 64.0000i | 0.0315585 | − | 0.0892608i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 248.902i | 0.346177i | 0.984906 | + | 0.173089i | \(0.0553747\pi\) | ||||
−0.984906 | + | 0.173089i | \(0.944625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 804.000 | 1.11512 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 84.8528 | + | 30.0000i | 0.117362 | + | 0.0414938i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 870.000i | − | 1.19670i | −0.801235 | − | 0.598349i | \(-0.795823\pi\) | ||
0.801235 | − | 0.598349i | \(-0.204177\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −329.000 | + | 650.538i | −0.451303 | + | 0.892371i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1855.45i | − | 2.53823i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 214.000i | 0.291951i | 0.989288 | + | 0.145975i | \(0.0466321\pi\) | ||||
−0.989288 | + | 0.145975i | \(0.953368\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.3137 | −0.0153510 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 958.000 | 1.29635 | 0.648173 | − | 0.761493i | \(-0.275533\pi\) | ||||
0.648173 | + | 0.761493i | \(0.275533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.0000 | − | 56.5685i | 0.0269906 | − | 0.0763408i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1006.92 | 1.35521 | 0.677604 | − | 0.735427i | \(-0.263018\pi\) | ||||
0.677604 | + | 0.735427i | \(0.263018\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −514.774 | − | 416.000i | −0.689121 | − | 0.556894i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 305.470i | 0.407837i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −630.000 | −0.838881 | −0.419441 | − | 0.907783i | \(-0.637774\pi\) | ||||
−0.419441 | + | 0.907783i | \(0.637774\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −107.480 | + | 304.000i | −0.142736 | + | 0.403718i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 602.000i | 0.795244i | 0.917549 | + | 0.397622i | \(0.130165\pi\) | ||||
−0.917549 | + | 0.397622i | \(0.869835\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −64.0000 | + | 181.019i | −0.0843215 | + | 0.238497i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1097.43i | 1.44209i | 0.692889 | + | 0.721044i | \(0.256338\pi\) | ||||
−0.692889 | + | 0.721044i | \(0.743662\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 60.0000i | 0.0786370i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −735.391 | −0.958789 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −770.000 | −1.00130 | −0.500650 | − | 0.865650i | \(-0.666906\pi\) | ||||
−0.500650 | + | 0.865650i | \(0.666906\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 512.000 | + | 181.019i | 0.664073 | + | 0.234785i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 186.676 | 0.241496 | 0.120748 | − | 0.992683i | \(-0.461471\pi\) | ||||
0.120748 | + | 0.992683i | \(0.461471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 101.823 | + | 36.0000i | 0.131047 | + | 0.0463320i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 67.8823i | − | 0.0871402i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 704.000 | 0.901408 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −390.323 | + | 240.000i | −0.498497 | + | 0.306513i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 514.000i | 0.653113i | 0.945178 | + | 0.326557i | \(0.105888\pi\) | ||||
−0.945178 | + | 0.326557i | \(0.894112\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 608.000 | + | 214.960i | 0.770596 | + | 0.272447i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 407.294i | 0.514910i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 860.000i | 1.08449i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 707.107 | 0.887211 | 0.443605 | − | 0.896222i | \(-0.353699\pi\) | ||||
0.443605 | + | 0.896222i | \(0.353699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1536.00 | −1.92240 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −192.000 | + | 237.588i | −0.239700 | + | 0.296614i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 463.862 | 0.577661 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −401.637 | + | 1136.00i | −0.497691 | + | 1.40768i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 758.018i | − | 0.936982i | −0.883468 | − | 0.468491i | \(-0.844798\pi\) | ||
0.883468 | − | 0.468491i | \(-0.155202\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1454.00 | −1.79285 | −0.896424 | − | 0.443197i | \(-0.853844\pi\) | ||||
−0.896424 | + | 0.443197i | \(0.853844\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −752.362 | − | 266.000i | −0.925414 | − | 0.327183i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 164.000i | 0.200734i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −420.000 | − | 339.411i | −0.512821 | − | 0.414422i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 967.322i | − | 1.17822i | −0.808051 | − | 0.589112i | \(-0.799478\pi\) | ||
0.808051 | − | 0.589112i | \(-0.200522\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 166.000i | 0.201701i | 0.994902 | + | 0.100851i | \(0.0321564\pi\) | ||||
−0.994902 | + | 0.100851i | \(0.967844\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −978.636 | −1.18336 | −0.591678 | − | 0.806174i | \(-0.701534\pi\) | ||||
−0.591678 | + | 0.806174i | \(0.701534\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1258.00 | −1.51749 | −0.758745 | − | 0.651387i | \(-0.774187\pi\) | ||||
−0.758745 | + | 0.651387i | \(0.774187\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 346.000 | − | 978.636i | 0.416366 | − | 1.17766i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 294.156 | 0.353129 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 311.127 | + | 506.000i | 0.371717 | + | 0.604540i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1323.70i | − | 1.57772i | −0.614575 | − | 0.788858i | \(-0.710673\pi\) | ||
0.614575 | − | 0.788858i | \(-0.289327\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 553.000 | 0.657551 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −124.451 | + | 352.000i | −0.147628 | + | 0.417556i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 534.000i | − | 0.630460i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 46.0000 | − | 130.108i | 0.0541814 | − | 0.153248i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 67.8823i | 0.0797676i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 742.000i | 0.869871i | 0.900462 | + | 0.434936i | \(0.143229\pi\) | ||||
−0.900462 | + | 0.434936i | \(0.856771\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −237.588 | −0.277232 | −0.138616 | − | 0.990346i | \(-0.544265\pi\) | ||||
−0.138616 | + | 0.990346i | \(0.544265\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1230.00 | 1.43190 | 0.715949 | − | 0.698153i | \(-0.245994\pi\) | ||||
0.715949 | + | 0.698153i | \(0.245994\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −576.000 | − | 203.647i | −0.668990 | − | 0.236524i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45.2548 | −0.0524390 | −0.0262195 | − | 0.999656i | \(-0.508347\pi\) | ||||
−0.0262195 | + | 0.999656i | \(0.508347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −630.739 | − | 223.000i | −0.727496 | − | 0.257209i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 56.5685i | − | 0.0650961i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | 0.0229621 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 531.744 | − | 658.000i | 0.609100 | − | 0.753723i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 822.000i | − | 0.937286i | −0.883388 | − | 0.468643i | \(-0.844743\pi\) | ||
0.883388 | − | 0.468643i | \(-0.155257\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 624.000 | + | 220.617i | 0.709898 | + | 0.250987i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 656.195i | 0.744830i | 0.928066 | + | 0.372415i | \(0.121470\pi\) | ||||
−0.928066 | + | 0.372415i | \(0.878530\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 962.000i | − | 1.08947i | −0.838609 | − | 0.544734i | \(-0.816631\pi\) | ||
0.838609 | − | 0.544734i | \(-0.183369\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1142.68 | 1.28826 | 0.644129 | − | 0.764917i | \(-0.277220\pi\) | ||||
0.644129 | + | 0.764917i | \(0.277220\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 636.000 | 0.715411 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −448.000 | + | 96.1665i | −0.502806 | + | 0.107931i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 135.765 | 0.152032 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 113.137 | − | 320.000i | 0.126128 | − | 0.356745i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 373.352i | 0.415297i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1408.00 | −1.56271 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1391.59 | + | 492.000i | 1.54107 | + | 0.544850i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1042.00i | 1.14884i | 0.818560 | + | 0.574421i | \(0.194773\pi\) | ||||
−0.818560 | + | 0.574421i | \(0.805227\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −288.000 | + | 356.382i | −0.316832 | + | 0.392059i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1606.55i | − | 1.76350i | −0.471719 | − | 0.881749i | \(-0.656366\pi\) | ||
0.471719 | − | 0.881749i | \(-0.343634\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 416.000i | − | 0.455641i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.9411 | −0.0370132 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 614.000 | 0.668118 | 0.334059 | − | 0.942552i | \(-0.391582\pi\) | ||||
0.334059 | + | 0.942552i | \(0.391582\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.0000 | + | 84.8528i | −0.0325733 | + | 0.0921312i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1244.51 | −1.34833 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −758.018 | + | 938.000i | −0.817711 | + | 1.01187i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 45.2548i | − | 0.0487135i | −0.999703 | − | 0.0243567i | \(-0.992246\pi\) | ||
0.999703 | − | 0.0243567i | \(-0.00775376\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.0000 | −0.0279270 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 576.999 | − | 1632.00i | 0.618434 | − | 1.74920i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 462.000i | − | 0.493063i | −0.969135 | − | 0.246531i | \(-0.920709\pi\) | ||
0.969135 | − | 0.246531i | \(-0.0792909\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −210.000 | + | 593.970i | −0.223642 | + | 0.632556i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 356.382i | 0.378727i | 0.981907 | + | 0.189363i | \(0.0606424\pi\) | ||||
−0.981907 | + | 0.189363i | \(0.939358\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 384.000i | − | 0.407211i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −695.793 | −0.734734 | −0.367367 | − | 0.930076i | \(-0.619741\pi\) | ||||
−0.367367 | + | 0.930076i | \(0.619741\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −820.000 | −0.864067 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 432.000 | + | 152.735i | 0.454259 | + | 0.160605i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1527.35 | −1.60268 | −0.801338 | − | 0.598212i | \(-0.795878\pi\) | ||||
−0.801338 | + | 0.598212i | \(0.795878\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −271.529 | − | 96.0000i | −0.283729 | − | 0.100313i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 610.940i | − | 0.637060i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −477.000 | −0.496358 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −356.382 | − | 288.000i | −0.370075 | − | 0.299065i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 70.0000i | − | 0.0723888i | −0.999345 | − | 0.0361944i | \(-0.988476\pi\) | ||
0.999345 | − | 0.0361944i | \(-0.0115236\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 128.000 | + | 45.2548i | 0.132095 | + | 0.0467026i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 627.911i | − | 0.646664i | −0.946286 | − | 0.323332i | \(-0.895197\pi\) | ||
0.946286 | − | 0.323332i | \(-0.104803\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 468.000i | − | 0.480987i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1018.23 | 1.04220 | 0.521102 | − | 0.853494i | \(-0.325521\pi\) | ||||
0.521102 | + | 0.853494i | \(0.325521\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −192.000 | −0.196118 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −70.0000 | − | 56.5685i | −0.0713558 | − | 0.0576642i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −644.881 | −0.656034 | −0.328017 | − | 0.944672i | \(-0.606380\pi\) | ||||
−0.328017 | + | 0.944672i | \(0.606380\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 407.294 | − | 1152.00i | 0.412658 | − | 1.16717i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 927.724i | 0.938043i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −854.000 | −0.861756 | −0.430878 | − | 0.902410i | \(-0.641796\pi\) | ||||
−0.430878 | + | 0.902410i | \(0.641796\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1227.54 | − | 434.000i | −1.23619 | − | 0.437059i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 518.000i | − | 0.519559i | −0.965668 | − | 0.259779i | \(-0.916350\pi\) | ||
0.965668 | − | 0.259779i | \(-0.0836498\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −138.000 | + | 84.8528i | −0.138138 | + | 0.0849378i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))