Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,3,Mod(401,600)]
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, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.401");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.l (of order \(2\), degree \(1\), 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: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.2 | ||
Root | \(1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.401 |
Dual form | 600.3.l.b.401.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.00000 | 0.857143 | 0.428571 | − | 0.903508i | \(-0.359017\pi\) | ||||
0.428571 | + | 0.903508i | \(0.359017\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −10.0000 | −0.769231 | −0.384615 | − | 0.923077i | \(-0.625666\pi\) | ||||
−0.384615 | + | 0.923077i | \(0.625666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.6274i | 1.33102i | 0.746387 | + | 0.665512i | \(0.231787\pi\) | ||||
−0.746387 | + | 0.665512i | \(0.768213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.105263 | 0.0526316 | − | 0.998614i | \(-0.483239\pi\) | ||||
0.0526316 | + | 0.998614i | \(0.483239\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.00000 | + | 16.9706i | −0.285714 | + | 0.808122i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 11.3137i | 0.491900i | 0.969282 | + | 0.245950i | \(0.0791000\pi\) | ||||
−0.969282 | + | 0.245950i | \(0.920900\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 16.9706i | 0.585192i | 0.956236 | + | 0.292596i | \(0.0945191\pi\) | ||||
−0.956236 | + | 0.292596i | \(0.905481\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −22.0000 | −0.709677 | −0.354839 | − | 0.934928i | \(-0.615464\pi\) | ||||
−0.354839 | + | 0.934928i | \(0.615464\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −16.0000 | − | 5.65685i | −0.484848 | − | 0.171420i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.162162 | 0.0810811 | − | 0.996708i | \(-0.474163\pi\) | ||||
0.0810811 | + | 0.996708i | \(0.474163\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −82.0000 | −1.90698 | −0.953488 | − | 0.301430i | \(-0.902536\pi\) | ||||
−0.953488 | + | 0.301430i | \(0.902536\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 67.8823i | − | 1.44430i | −0.691735 | − | 0.722152i | \(-0.743153\pi\) | ||
0.691735 | − | 0.722152i | \(-0.256847\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.0000 | −0.265306 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −64.0000 | − | 22.6274i | −1.25490 | − | 0.443675i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 62.2254i | 1.17406i | 0.809564 | + | 0.587032i | \(0.199704\pi\) | ||||
−0.809564 | + | 0.587032i | \(0.800296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | + | 5.65685i | −0.0350877 | + | 0.0992431i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 73.5391i | 1.24643i | 0.782052 | + | 0.623213i | \(0.214173\pi\) | ||||
−0.782052 | + | 0.623213i | \(0.785827\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −86.0000 | −1.40984 | −0.704918 | − | 0.709289i | \(-0.749016\pi\) | ||||
−0.704918 | + | 0.709289i | \(0.749016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −42.0000 | − | 33.9411i | −0.666667 | − | 0.538748i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | −0.0298507 | −0.0149254 | − | 0.999889i | \(-0.504751\pi\) | ||||
−0.0149254 | + | 0.999889i | \(0.504751\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −82.0000 | −1.12329 | −0.561644 | − | 0.827379i | \(-0.689831\pi\) | ||||
−0.561644 | + | 0.827379i | \(0.689831\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 33.9411i | 0.440794i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0000 | 0.126582 | 0.0632911 | − | 0.997995i | \(-0.479840\pi\) | ||||
0.0632911 | + | 0.997995i | \(0.479840\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 17.0000 | + | 79.1960i | 0.209877 | + | 0.977728i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 73.5391i | 0.886013i | 0.896518 | + | 0.443007i | \(0.146088\pi\) | ||||
−0.896518 | + | 0.443007i | \(0.853912\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −48.0000 | − | 16.9706i | −0.551724 | − | 0.195064i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 33.9411i | − | 0.381361i | −0.981652 | − | 0.190680i | \(-0.938931\pi\) | ||
0.981652 | − | 0.190680i | \(-0.0610694\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −60.0000 | −0.659341 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.0000 | − | 62.2254i | 0.236559 | − | 0.669090i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 94.0000 | 0.969072 | 0.484536 | − | 0.874771i | \(-0.338988\pi\) | ||||
0.484536 | + | 0.874771i | \(0.338988\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | 134.000 | 1.30097 | 0.650485 | − | 0.759519i | \(-0.274565\pi\) | ||||
0.650485 | + | 0.759519i | \(0.274565\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 50.9117i | − | 0.475810i | −0.971288 | − | 0.237905i | \(-0.923539\pi\) | ||
0.971288 | − | 0.237905i | \(-0.0764607\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.0917431 | 0.0458716 | − | 0.998947i | \(-0.485394\pi\) | ||||
0.0458716 | + | 0.998947i | \(0.485394\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | + | 16.9706i | −0.0540541 | + | 0.152888i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 67.8823i | 0.600728i | 0.953825 | + | 0.300364i | \(0.0971081\pi\) | ||||
−0.953825 | + | 0.300364i | \(0.902892\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 70.0000 | + | 56.5685i | 0.598291 | + | 0.483492i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 135.765i | 1.14088i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 89.0000 | 0.735537 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −96.0000 | − | 33.9411i | −0.780488 | − | 0.275944i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −106.000 | −0.834646 | −0.417323 | − | 0.908758i | \(-0.637032\pi\) | ||||
−0.417323 | + | 0.908758i | \(0.637032\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 12.0000 | 0.0902256 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 101.823i | 0.743236i | 0.928386 | + | 0.371618i | \(0.121197\pi\) | ||||
−0.928386 | + | 0.371618i | \(0.878803\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −78.0000 | −0.561151 | −0.280576 | − | 0.959832i | \(-0.590525\pi\) | ||||
−0.280576 | + | 0.959832i | \(0.590525\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 192.000 | + | 67.8823i | 1.36170 | + | 0.481434i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 56.5685i | − | 0.395584i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.0000 | − | 36.7696i | 0.0884354 | − | 0.250133i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 164.049i | 1.10100i | 0.834836 | + | 0.550499i | \(0.185563\pi\) | ||||
−0.834836 | + | 0.550499i | \(0.814437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 218.000 | 1.44371 | 0.721854 | − | 0.692045i | \(-0.243290\pi\) | ||||
0.721854 | + | 0.692045i | \(0.243290\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 128.000 | − | 158.392i | 0.836601 | − | 1.03524i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 86.0000 | 0.547771 | 0.273885 | − | 0.961762i | \(-0.411691\pi\) | ||||
0.273885 | + | 0.961762i | \(0.411691\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −176.000 | − | 62.2254i | −1.10692 | − | 0.391355i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 67.8823i | 0.421629i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 222.000 | 1.36196 | 0.680982 | − | 0.732301i | \(-0.261553\pi\) | ||||
0.680982 | + | 0.732301i | \(0.261553\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 169.706i | 1.01620i | 0.861298 | + | 0.508101i | \(0.169652\pi\) | ||||
−0.861298 | + | 0.508101i | \(0.830348\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −69.0000 | −0.408284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.0000 | − | 11.3137i | −0.0818713 | − | 0.0661620i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 186.676i | 1.07905i | 0.841969 | + | 0.539527i | \(0.181397\pi\) | ||||
−0.841969 | + | 0.539527i | \(0.818603\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −208.000 | − | 73.5391i | −1.17514 | − | 0.415475i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 152.735i | 0.853269i | 0.904424 | + | 0.426634i | \(0.140301\pi\) | ||||
−0.904424 | + | 0.426634i | \(0.859699\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 90.0000 | 0.497238 | 0.248619 | − | 0.968601i | \(-0.420023\pi\) | ||||
0.248619 | + | 0.968601i | \(0.420023\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 86.0000 | − | 243.245i | 0.469945 | − | 1.32921i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −128.000 | −0.684492 | ||||||||
\(188\) | 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 | ||||||||
\(193\) | −2.00000 | −0.0103627 | −0.00518135 | − | 0.999987i | \(-0.501649\pi\) | ||||
−0.00518135 | + | 0.999987i | \(0.501649\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 84.8528i | 0.430725i | 0.976534 | + | 0.215362i | \(0.0690933\pi\) | ||||
−0.976534 | + | 0.215362i | \(0.930907\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 250.000 | 1.25628 | 0.628141 | − | 0.778100i | \(-0.283816\pi\) | ||||
0.628141 | + | 0.778100i | \(0.283816\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | − | 5.65685i | 0.00995025 | − | 0.0281436i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 101.823i | 0.501593i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 64.0000 | − | 79.1960i | 0.309179 | − | 0.382589i | ||||
\(208\) | 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 | ||||||||
\(213\) | 352.000 | + | 124.451i | 1.65258 | + | 0.584276i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −132.000 | −0.608295 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 82.0000 | − | 231.931i | 0.374429 | − | 1.05905i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 226.274i | − | 1.02387i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 278.000 | 1.24664 | 0.623318 | − | 0.781968i | \(-0.285784\pi\) | ||||
0.623318 | + | 0.781968i | \(0.285784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 220.617i | − | 0.971882i | −0.873991 | − | 0.485941i | \(-0.838477\pi\) | ||
0.873991 | − | 0.485941i | \(-0.161523\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 58.0000 | 0.253275 | 0.126638 | − | 0.991949i | \(-0.459581\pi\) | ||||
0.126638 | + | 0.991949i | \(0.459581\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −96.0000 | − | 33.9411i | −0.415584 | − | 0.146931i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 395.980i | − | 1.69948i | −0.527199 | − | 0.849742i | \(-0.676758\pi\) | ||
0.527199 | − | 0.849742i | \(-0.323242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.0000 | + | 28.2843i | −0.0421941 | + | 0.119343i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.6274i | − | 0.0946754i | −0.998879 | − | 0.0473377i | \(-0.984926\pi\) | ||
0.998879 | − | 0.0473377i | \(-0.0150737\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.0000 | −0.124481 | −0.0622407 | − | 0.998061i | \(-0.519825\pi\) | ||||
−0.0622407 | + | 0.998061i | \(0.519825\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −241.000 | − | 31.1127i | −0.991770 | − | 0.128036i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.0000 | −0.0809717 | ||||||||
\(248\) | 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 | ||||||||
\(253\) | −64.0000 | −0.252964 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 181.019i | − | 0.704355i | −0.935933 | − | 0.352178i | \(-0.885441\pi\) | ||
0.935933 | − | 0.352178i | \(-0.114559\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.0000 | 0.138996 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 96.0000 | − | 118.794i | 0.367816 | − | 0.455149i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 214.960i | 0.817340i | 0.912682 | + | 0.408670i | \(0.134007\pi\) | ||||
−0.912682 | + | 0.408670i | \(0.865993\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 96.0000 | + | 33.9411i | 0.359551 | + | 0.127120i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 401.637i | 1.49307i | 0.665344 | + | 0.746537i | \(0.268285\pi\) | ||||
−0.665344 | + | 0.746537i | \(0.731715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 266.000 | 0.981550 | 0.490775 | − | 0.871286i | \(-0.336714\pi\) | ||||
0.490775 | + | 0.871286i | \(0.336714\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 60.0000 | − | 169.706i | 0.219780 | − | 0.621632i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −346.000 | −1.24910 | −0.624549 | − | 0.780986i | \(-0.714717\pi\) | ||||
−0.624549 | + | 0.780986i | \(0.714717\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 46.0000 | 0.162544 | 0.0812721 | − | 0.996692i | \(-0.474102\pi\) | ||||
0.0812721 | + | 0.996692i | \(0.474102\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 203.647i | 0.709571i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −223.000 | −0.771626 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −94.0000 | + | 265.872i | −0.323024 | + | 0.913650i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 220.617i | 0.752960i | 0.926425 | + | 0.376480i | \(0.122866\pi\) | ||||
−0.926425 | + | 0.376480i | \(0.877134\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 80.0000 | + | 130.108i | 0.269360 | + | 0.438073i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 113.137i | − | 0.378385i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −492.000 | −1.63455 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −144.000 | − | 50.9117i | −0.475248 | − | 0.168025i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.0000 | 0.0977199 | 0.0488599 | − | 0.998806i | \(-0.484441\pi\) | ||||
0.0488599 | + | 0.998806i | \(0.484441\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −210.000 | −0.670927 | −0.335463 | − | 0.942053i | \(-0.608893\pi\) | ||||
−0.335463 | + | 0.942053i | \(0.608893\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 152.735i | − | 0.481814i | −0.970548 | − | 0.240907i | \(-0.922555\pi\) | ||
0.970548 | − | 0.240907i | \(-0.0774449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −96.0000 | −0.300940 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 144.000 | + | 50.9117i | 0.448598 | + | 0.158603i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 45.2548i | 0.140108i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.0000 | + | 28.2843i | −0.0305810 | + | 0.0864962i | ||||
\(328\) | 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 | ||||||||
\(333\) | −42.0000 | − | 33.9411i | −0.126126 | − | 0.101925i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 510.000 | 1.51335 | 0.756677 | − | 0.653789i | \(-0.226822\pi\) | ||||
0.756677 | + | 0.653789i | \(0.226822\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −192.000 | − | 67.8823i | −0.566372 | − | 0.200243i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 124.451i | − | 0.364958i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −372.000 | −1.08455 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 152.735i | 0.440159i | 0.975482 | + | 0.220079i | \(0.0706316\pi\) | ||||
−0.975482 | + | 0.220079i | \(0.929368\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 426.000 | 1.22063 | 0.610315 | − | 0.792159i | \(-0.291043\pi\) | ||||
0.610315 | + | 0.792159i | \(0.291043\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −230.000 | + | 141.421i | −0.655271 | + | 0.402910i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 45.2548i | − | 0.128201i | −0.997943 | − | 0.0641003i | \(-0.979582\pi\) | ||
0.997943 | − | 0.0641003i | \(-0.0204178\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −384.000 | − | 135.765i | −1.07563 | − | 0.380293i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 441.235i | − | 1.22907i | −0.788891 | − | 0.614533i | \(-0.789345\pi\) | ||
0.788891 | − | 0.614533i | \(-0.210655\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −357.000 | −0.988920 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −89.0000 | + | 251.730i | −0.245179 | + | 0.693471i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 566.000 | 1.54223 | 0.771117 | − | 0.636693i | \(-0.219698\pi\) | ||||
0.771117 | + | 0.636693i | \(0.219698\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 192.000 | − | 237.588i | 0.520325 | − | 0.643870i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 373.352i | 1.00634i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −218.000 | −0.584450 | −0.292225 | − | 0.956350i | \(-0.594396\pi\) | ||||
−0.292225 | + | 0.956350i | \(0.594396\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 169.706i | − | 0.450148i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −142.000 | −0.374670 | −0.187335 | − | 0.982296i | \(-0.559985\pi\) | ||||
−0.187335 | + | 0.982296i | \(0.559985\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 106.000 | − | 299.813i | 0.278215 | − | 0.786911i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 574.000 | + | 463.862i | 1.48320 | + | 1.19861i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 548.715i | 1.41058i | 0.708920 | + | 0.705289i | \(0.249183\pi\) | ||||
−0.708920 | + | 0.705289i | \(0.750817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −256.000 | −0.654731 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.0000 | + | 5.65685i | 0.0407125 | + | 0.0143940i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 310.000 | 0.780856 | 0.390428 | − | 0.920633i | \(-0.372327\pi\) | ||||
0.390428 | + | 0.920633i | \(0.372327\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 220.000 | 0.545906 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.9411i | 0.0833934i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −270.000 | −0.660147 | −0.330073 | − | 0.943955i | \(-0.607073\pi\) | ||||
−0.330073 | + | 0.943955i | \(0.607073\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −288.000 | − | 101.823i | −0.700730 | − | 0.247745i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 441.235i | 1.06836i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 78.0000 | − | 220.617i | 0.187050 | − | 0.529058i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 50.9117i | − | 0.121508i | −0.998153 | − | 0.0607538i | \(-0.980650\pi\) | ||
0.998153 | − | 0.0607538i | \(-0.0193505\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −454.000 | −1.07838 | −0.539192 | − | 0.842183i | \(-0.681270\pi\) | ||||
−0.539192 | + | 0.842183i | \(0.681270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −384.000 | + | 475.176i | −0.907801 | + | 1.12335i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −516.000 | −1.20843 | ||||||||
\(428\) | 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 | ||||||||
\(433\) | −706.000 | −1.63048 | −0.815242 | − | 0.579120i | \(-0.803396\pi\) | ||||
−0.815242 | + | 0.579120i | \(0.803396\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.6274i | 0.0517790i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −486.000 | −1.10706 | −0.553531 | − | 0.832829i | \(-0.686720\pi\) | ||||
−0.553531 | + | 0.832829i | \(0.686720\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 91.0000 | + | 73.5391i | 0.206349 | + | 0.166755i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 707.107i | − | 1.59618i | −0.602540 | − | 0.798089i | \(-0.705844\pi\) | ||
0.602540 | − | 0.798089i | \(-0.294156\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −464.000 | − | 164.049i | −1.03803 | − | 0.366999i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 724.077i | − | 1.61264i | −0.591477 | − | 0.806322i | \(-0.701455\pi\) | ||
0.591477 | − | 0.806322i | \(-0.298545\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −192.000 | −0.425721 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −218.000 | + | 616.597i | −0.481236 | + | 1.36114i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −338.000 | −0.739606 | −0.369803 | − | 0.929110i | \(-0.620575\pi\) | ||||
−0.369803 | + | 0.929110i | \(0.620575\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | −74.0000 | −0.159827 | −0.0799136 | − | 0.996802i | \(-0.525464\pi\) | ||||
−0.0799136 | + | 0.996802i | \(0.525464\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 797.616i | 1.70796i | 0.520307 | + | 0.853979i | \(0.325817\pi\) | ||||
−0.520307 | + | 0.853979i | \(0.674183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0000 | −0.0255864 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −86.0000 | + | 243.245i | −0.182590 | + | 0.516443i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 463.862i | − | 0.980681i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 352.000 | − | 435.578i | 0.737945 | − | 0.913161i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 316.784i | 0.661344i | 0.943746 | + | 0.330672i | \(0.107275\pi\) | ||||
−0.943746 | + | 0.330672i | \(0.892725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −60.0000 | −0.124740 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −192.000 | − | 67.8823i | −0.397516 | − | 0.140543i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 134.000 | 0.275154 | 0.137577 | − | 0.990491i | \(-0.456069\pi\) | ||||
0.137577 | + | 0.990491i | \(0.456069\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | −384.000 | −0.778905 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 746.705i | − | 1.50242i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.0000 | −0.0601202 | −0.0300601 | − | 0.999548i | \(-0.509570\pi\) | ||||
−0.0300601 | + | 0.999548i | \(0.509570\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −480.000 | − | 169.706i | −0.958084 | − | 0.338734i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 237.588i | 0.472342i | 0.971712 | + | 0.236171i | \(0.0758925\pi\) | ||||
−0.971712 | + | 0.236171i | \(0.924107\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 69.0000 | − | 195.161i | 0.136095 | − | 0.384934i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 118.794i | − | 0.233387i | −0.993168 | − | 0.116693i | \(-0.962770\pi\) | ||
0.993168 | − | 0.116693i | \(-0.0372295\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −492.000 | −0.962818 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 46.0000 | − | 28.2843i | 0.0896686 | − | 0.0551350i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 384.000 | 0.742747 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 494.000 | 0.944551 | 0.472275 | − | 0.881451i | \(-0.343433\pi\) | ||||
0.472275 | + | 0.881451i | \(0.343433\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 497.803i | − | 0.944598i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 401.000 | 0.758034 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 416.000 | − | 514.774i | 0.783427 | − | 0.969442i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 339.411i | − | 0.636794i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −432.000 | − | 152.735i | −0.804469 | − | 0.284423i | ||||
\(538\) | 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 | ||||||||
\(543\) | −90.0000 | + | 254.558i | −0.165746 | + | 0.468800i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −290.000 | −0.530165 | −0.265082 | − | 0.964226i | \(-0.585399\pi\) | ||||
−0.265082 | + | 0.964226i | \(0.585399\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 602.000 | + | 486.489i | 1.09654 | + | 0.886137i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.9411i | 0.0615991i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 60.0000 | 0.108499 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 175.362i | − | 0.314834i | −0.987532 | − | 0.157417i | \(-0.949683\pi\) | ||
0.987532 | − | 0.157417i | \(-0.0503167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 820.000 | 1.46691 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 128.000 | − | 362.039i | 0.228164 | − | 0.645345i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 243.245i | − | 0.432051i | −0.976388 | − | 0.216026i | \(-0.930691\pi\) | ||
0.976388 | − | 0.216026i | \(-0.0693094\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 102.000 | + | 475.176i | 0.179894 | + | 0.838052i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 622.254i | − | 1.09359i | −0.837266 | − | 0.546796i | \(-0.815847\pi\) | ||
0.837266 | − | 0.546796i | \(-0.184153\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 402.000 | 0.704028 | 0.352014 | − | 0.935995i | \(-0.385497\pi\) | ||||
0.352014 | + | 0.935995i | \(0.385497\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 768.000 | + | 271.529i | 1.34031 | + | 0.473873i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −98.0000 | −0.169844 | −0.0849220 | − | 0.996388i | \(-0.527064\pi\) | ||||
−0.0849220 | + | 0.996388i | \(0.527064\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.00000 | − | 5.65685i | 0.00345423 | − | 0.00977004i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 441.235i | 0.759440i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −352.000 | −0.603774 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 548.715i | − | 0.934778i | −0.884052 | − | 0.467389i | \(-0.845195\pi\) | ||
0.884052 | − | 0.467389i | \(-0.154805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44.0000 | −0.0747029 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −240.000 | − | 84.8528i | −0.406091 | − | 0.143575i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 701.450i | − | 1.18288i | −0.806348 | − | 0.591442i | \(-0.798559\pi\) | ||
0.806348 | − | 0.591442i | \(-0.201441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −250.000 | + | 707.107i | −0.418760 | + | 1.18443i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 644.881i | − | 1.07660i | −0.842754 | − | 0.538298i | \(-0.819067\pi\) | ||
0.842754 | − | 0.538298i | \(-0.180933\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −398.000 | −0.662230 | −0.331115 | − | 0.943590i | \(-0.607425\pi\) | ||||
−0.331115 | + | 0.943590i | \(0.607425\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.0000 | + | 11.3137i | 0.0232172 | + | 0.0187624i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −170.000 | −0.280066 | −0.140033 | − | 0.990147i | \(-0.544721\pi\) | ||||
−0.140033 | + | 0.990147i | \(0.544721\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −288.000 | − | 101.823i | −0.472906 | − | 0.167198i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 678.823i | 1.11100i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1030.00 | 1.68026 | 0.840131 | − | 0.542384i | \(-0.182478\pi\) | ||||
0.840131 | + | 0.542384i | \(0.182478\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1052.17i | 1.70531i | 0.522476 | + | 0.852654i | \(0.325008\pi\) | ||||
−0.522476 | + | 0.852654i | \(0.674992\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0000 | −0.0226171 | −0.0113086 | − | 0.999936i | \(-0.503600\pi\) | ||||
−0.0113086 | + | 0.999936i | \(0.503600\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 160.000 | + | 260.215i | 0.257649 | + | 0.419026i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 203.647i | − | 0.326881i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −32.0000 | − | 11.3137i | −0.0510367 | − | 0.0180442i | ||||
\(628\) | 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 | ||||||||
\(633\) | −34.0000 | + | 96.1665i | −0.0537125 | + | 0.151922i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 130.000 | 0.204082 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 798.000 | 1.24106 | 0.620529 | − | 0.784184i | \(-0.286918\pi\) | ||||
0.620529 | + | 0.784184i | \(0.286918\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 147.078i | − | 0.227323i | −0.993520 | − | 0.113662i | \(-0.963742\pi\) | ||
0.993520 | − | 0.113662i | \(-0.0362580\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −416.000 | −0.640986 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 132.000 | − | 373.352i | 0.202765 | − | 0.573506i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 322.441i | 0.493784i | 0.969043 | + | 0.246892i | \(0.0794092\pi\) | ||||
−0.969043 | + | 0.246892i | \(0.920591\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 574.000 | + | 463.862i | 0.873668 | + | 0.706031i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 797.616i | − | 1.21034i | −0.796095 | − | 0.605172i | \(-0.793104\pi\) | ||
0.796095 | − | 0.605172i | \(-0.206896\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 986.000 | 1.49168 | 0.745840 | − | 0.666126i | \(-0.232049\pi\) | ||||
0.745840 | + | 0.666126i | \(0.232049\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 640.000 | + | 226.274i | 0.965309 | + | 0.341288i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −192.000 | −0.287856 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −278.000 | + | 786.303i | −0.415546 | + | 1.17534i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 486.489i | − | 0.725022i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.0000 | −0.0505201 | −0.0252600 | − | 0.999681i | \(-0.508041\pi\) | ||||
−0.0252600 | + | 0.999681i | \(0.508041\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 401.637i | 0.593259i | 0.954993 | + | 0.296630i | \(0.0958627\pi\) | ||||
−0.954993 | + | 0.296630i | \(0.904137\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 564.000 | 0.830633 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 624.000 | + | 220.617i | 0.916300 | + | 0.323961i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 130.108i | 0.190494i | 0.995454 | + | 0.0952472i | \(0.0303641\pi\) | ||||
−0.995454 | + | 0.0952472i | \(0.969636\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −58.0000 | + | 164.049i | −0.0844250 | + | 0.238790i | ||||
\(688\) | 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 | ||||||||
\(693\) | 192.000 | − | 237.588i | 0.277056 | − | 0.342840i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −768.000 | −1.10187 | ||||||||
\(698\) | 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 | ||||||||
\(703\) | 12.0000 | 0.0170697 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 305.470i | 0.432065i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1222.00 | −1.72355 | −0.861777 | − | 0.507287i | \(-0.830648\pi\) | ||||
−0.861777 | + | 0.507287i | \(0.830648\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −70.0000 | − | 56.5685i | −0.0984529 | − | 0.0795619i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 248.902i | − | 0.349091i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 64.0000 | + | 22.6274i | 0.0892608 | + | 0.0315585i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 248.902i | − | 0.346177i | −0.984906 | − | 0.173089i | \(-0.944625\pi\) | ||
0.984906 | − | 0.173089i | \(-0.0553747\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 804.000 | 1.11512 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.0000 | − | 84.8528i | 0.0414938 | − | 0.117362i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 870.000 | 1.19670 | 0.598349 | − | 0.801235i | \(-0.295823\pi\) | ||||
0.598349 | + | 0.801235i | \(0.295823\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 329.000 | − | 650.538i | 0.451303 | − | 0.892371i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1855.45i | − | 2.53823i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 214.000 | 0.291951 | 0.145975 | − | 0.989288i | \(-0.453368\pi\) | ||||
0.145975 | + | 0.989288i | \(0.453368\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 11.3137i | − | 0.0153510i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −958.000 | −1.29635 | −0.648173 | − | 0.761493i | \(-0.724467\pi\) | ||||
−0.648173 | + | 0.761493i | \(0.724467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.0000 | − | 56.5685i | 0.0269906 | − | 0.0763408i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1006.92i | − | 1.35521i | −0.735427 | − | 0.677604i | \(-0.763018\pi\) | ||
0.735427 | − | 0.677604i | \(-0.236982\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 416.000 | − | 514.774i | 0.556894 | − | 0.689121i | ||||
\(748\) | 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 | ||||||||
\(753\) | 304.000 | + | 107.480i | 0.403718 | + | 0.142736i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −602.000 | −0.795244 | −0.397622 | − | 0.917549i | \(-0.630165\pi\) | ||||
−0.397622 | + | 0.917549i | \(0.630165\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 60.0000 | 0.0786370 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 735.391i | − | 0.958789i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 770.000 | 1.00130 | 0.500650 | − | 0.865650i | \(-0.333094\pi\) | ||||
0.500650 | + | 0.865650i | \(0.333094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 512.000 | + | 181.019i | 0.664073 | + | 0.234785i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 186.676i | − | 0.241496i | −0.992683 | − | 0.120748i | \(-0.961471\pi\) | ||
0.992683 | − | 0.120748i | \(-0.0385293\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −36.0000 | + | 101.823i | −0.0463320 | + | 0.131047i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 67.8823i | 0.0871402i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 704.000 | 0.901408 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 240.000 | + | 390.323i | 0.306513 | + | 0.498497i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −514.000 | −0.653113 | −0.326557 | − | 0.945178i | \(-0.605888\pi\) | ||||
−0.326557 | + | 0.945178i | \(0.605888\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −608.000 | − | 214.960i | −0.770596 | − | 0.272447i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 407.294i | 0.514910i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 860.000 | 1.08449 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 707.107i | 0.887211i | 0.896222 | + | 0.443605i | \(0.146301\pi\) | ||||
−0.896222 | + | 0.443605i | \(0.853699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1536.00 | 1.92240 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −192.000 | + | 237.588i | −0.239700 | + | 0.296614i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 463.862i | − | 0.577661i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1136.00 | − | 401.637i | −1.40768 | − | 0.497691i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 758.018i | 0.936982i | 0.883468 | + | 0.468491i | \(0.155202\pi\) | ||||
−0.883468 | + | 0.468491i | \(0.844798\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1454.00 | −1.79285 | −0.896424 | − | 0.443197i | \(-0.853844\pi\) | ||||
−0.896424 | + | 0.443197i | \(0.853844\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −266.000 | + | 752.362i | −0.327183 | + | 0.925414i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −164.000 | −0.200734 | ||||||||
\(818\) | 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 | ||||||||
\(823\) | 166.000 | 0.201701 | 0.100851 | − | 0.994902i | \(-0.467844\pi\) | ||||
0.100851 | + | 0.994902i | \(0.467844\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 978.636i | − | 1.18336i | −0.806174 | − | 0.591678i | \(-0.798466\pi\) | ||
0.806174 | − | 0.591678i | \(-0.201534\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1258.00 | 1.51749 | 0.758745 | − | 0.651387i | \(-0.225813\pi\) | ||||
0.758745 | + | 0.651387i | \(0.225813\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 346.000 | − | 978.636i | 0.416366 | − | 1.17766i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 294.156i | − | 0.353129i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −506.000 | + | 311.127i | −0.604540 | + | 0.371717i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1323.70i | 1.57772i | 0.614575 | + | 0.788858i | \(0.289327\pi\) | ||||
−0.614575 | + | 0.788858i | \(0.710673\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 553.000 | 0.657551 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 352.000 | + | 124.451i | 0.417556 | + | 0.147628i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 534.000 | 0.630460 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −46.0000 | + | 130.108i | −0.0541814 | + | 0.153248i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 67.8823i | 0.0797676i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 742.000 | 0.869871 | 0.434936 | − | 0.900462i | \(-0.356771\pi\) | ||||
0.434936 | + | 0.900462i | \(0.356771\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 237.588i | − | 0.277232i | −0.990346 | − | 0.138616i | \(-0.955735\pi\) | ||
0.990346 | − | 0.138616i | \(-0.0442654\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1230.00 | −1.43190 | −0.715949 | − | 0.698153i | \(-0.754006\pi\) | ||||
−0.715949 | + | 0.698153i | \(0.754006\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −576.000 | − | 203.647i | −0.668990 | − | 0.236524i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.2548i | 0.0524390i | 0.999656 | + | 0.0262195i | \(0.00834688\pi\) | ||||
−0.999656 | + | 0.0262195i | \(0.991653\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 223.000 | − | 630.739i | 0.257209 | − | 0.727496i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 56.5685i | 0.0650961i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | 0.0229621 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −658.000 | − | 531.744i | −0.753723 | − | 0.609100i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 822.000 | 0.937286 | 0.468643 | − | 0.883388i | \(-0.344743\pi\) | ||||
0.468643 | + | 0.883388i | \(0.344743\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −962.000 | −1.08947 | −0.544734 | − | 0.838609i | \(-0.683369\pi\) | ||||
−0.544734 | + | 0.838609i | \(0.683369\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1142.68i | 1.28826i | 0.764917 | + | 0.644129i | \(0.222780\pi\) | ||||
−0.764917 | + | 0.644129i | \(0.777220\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −636.000 | −0.715411 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −448.000 | + | 96.1665i | −0.502806 | + | 0.107931i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 135.765i | − | 0.152032i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 320.000 | + | 113.137i | 0.356745 | + | 0.126128i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 373.352i | − | 0.415297i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1408.00 | −1.56271 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 492.000 | − | 1391.59i | 0.544850 | − | 1.54107i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1042.00 | −1.14884 | −0.574421 | − | 0.818560i | \(-0.694773\pi\) | ||||
−0.574421 | + | 0.818560i | \(0.694773\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −416.000 | −0.455641 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 33.9411i | − | 0.0370132i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −614.000 | −0.668118 | −0.334059 | − | 0.942552i | \(-0.608418\pi\) | ||||
−0.334059 | + | 0.942552i | \(0.608418\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.0000 | + | 84.8528i | −0.0325733 | + | 0.0921312i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1244.51i | 1.34833i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −938.000 | − | 758.018i | −1.01187 | − | 0.817711i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45.2548i | 0.0487135i | 0.999703 | + | 0.0243567i | \(0.00775376\pi\) | ||||
−0.999703 | + | 0.0243567i | \(0.992246\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.0000 | −0.0279270 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1632.00 | − | 576.999i | −1.74920 | − | 0.618434i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 462.000 | 0.493063 | 0.246531 | − | 0.969135i | \(-0.420709\pi\) | ||||
0.246531 | + | 0.969135i | \(0.420709\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | −384.000 | −0.407211 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 695.793i | − | 0.734734i | −0.930076 | − | 0.367367i | \(-0.880259\pi\) | ||
0.930076 | − | 0.367367i | \(-0.119741\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 820.000 | 0.864067 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 432.000 | + | 152.735i | 0.454259 | + | 0.160605i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1527.35i | 1.60268i | 0.598212 | + | 0.801338i | \(0.295878\pi\) | ||||
−0.598212 | + | 0.801338i | \(0.704122\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 96.0000 | − | 271.529i | 0.100313 | − | 0.283729i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 610.940i | 0.637060i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −477.000 | −0.496358 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −288.000 | + | 356.382i | −0.299065 | + | 0.370075i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 70.0000 | 0.0723888 | 0.0361944 | − | 0.999345i | \(-0.488476\pi\) | ||||
0.0361944 | + | 0.999345i | \(0.488476\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | −468.000 | −0.480987 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1018.23i | 1.04220i | 0.853494 | + | 0.521102i | \(0.174479\pi\) | ||||
−0.853494 | + | 0.521102i | \(0.825521\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 192.000 | 0.196118 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −70.0000 | − | 56.5685i | −0.0713558 | − | 0.0576642i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 644.881i | 0.656034i | 0.944672 | + | 0.328017i | \(0.106380\pi\) | ||||
−0.944672 | + | 0.328017i | \(0.893620\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1152.00 | + | 407.294i | 1.16717 | + | 0.412658i | ||||
\(988\) | 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 | ||||||||
\(993\) | −434.000 | + | 1227.54i | −0.437059 | + | 1.23619i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 518.000 | 0.519559 | 0.259779 | − | 0.965668i | \(-0.416350\pi\) | ||||
0.259779 | + | 0.965668i | \(0.416350\pi\) | |||||||
\(998\) | 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 \(a_p\))