Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(641,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("768.641");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.h (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: | \(20.9264843029\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
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 | 641.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.641 |
Dual form | 768.3.h.c.641.1 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 5.65685 | 1.13137 | 0.565685 | − | 0.824621i | \(-0.308612\pi\) | ||||
0.565685 | + | 0.824621i | \(0.308612\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.00000 | −0.857143 | −0.428571 | − | 0.903508i | \(-0.640983\pi\) | ||||
−0.428571 | + | 0.903508i | \(0.640983\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.65685 | −0.514259 | −0.257130 | − | 0.966377i | \(-0.582777\pi\) | ||||
−0.257130 | + | 0.966377i | \(0.582777\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 10.0000i | − | 0.769231i | −0.923077 | − | 0.384615i | \(-0.874334\pi\) | ||
0.923077 | − | 0.384615i | \(-0.125666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −16.0000 | + | 5.65685i | −1.06667 | + | 0.377124i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.6274i | 1.33102i | 0.746387 | + | 0.665512i | \(0.231787\pi\) | ||||
−0.746387 | + | 0.665512i | \(0.768213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.105263i | 0.998614 | + | 0.0526316i | \(0.0167609\pi\) | ||||
−0.998614 | + | 0.0526316i | \(0.983239\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.9706 | − | 6.00000i | 0.808122 | − | 0.285714i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 11.3137i | 0.491900i | 0.969282 | + | 0.245950i | \(0.0791000\pi\) | ||||
−0.969282 | + | 0.245950i | \(0.920900\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000 | 0.280000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.1421 | + | 23.0000i | −0.523783 | + | 0.851852i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −16.9706 | −0.585192 | −0.292596 | − | 0.956236i | \(-0.594519\pi\) | ||||
−0.292596 | + | 0.956236i | \(0.594519\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.0000 | 0.709677 | 0.354839 | − | 0.934928i | \(-0.384536\pi\) | ||||
0.354839 | + | 0.934928i | \(0.384536\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.0000 | − | 5.65685i | 0.484848 | − | 0.171420i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −33.9411 | −0.969746 | ||||||||
\(36\) | 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 | ||||||||
\(45\) | 39.5980 | − | 32.0000i | 0.879955 | − | 0.711111i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 67.8823i | 1.44430i | 0.691735 | + | 0.722152i | \(0.256847\pi\) | ||||
−0.691735 | + | 0.722152i | \(0.743153\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.0000 | −0.265306 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −22.6274 | − | 64.0000i | −0.443675 | − | 1.25490i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −62.2254 | −1.17406 | −0.587032 | − | 0.809564i | \(-0.699704\pi\) | ||||
−0.587032 | + | 0.809564i | \(0.699704\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −32.0000 | −0.581818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | − | 5.65685i | −0.0350877 | − | 0.0992431i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −73.5391 | −1.24643 | −0.623213 | − | 0.782052i | \(-0.714173\pi\) | ||||
−0.623213 | + | 0.782052i | \(0.714173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 86.0000i | 1.40984i | 0.709289 | + | 0.704918i | \(0.249016\pi\) | ||||
−0.709289 | + | 0.704918i | \(0.750984\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −42.0000 | + | 33.9411i | −0.666667 | + | 0.538748i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 56.5685i | − | 0.870285i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000i | 0.0298507i | 0.999889 | + | 0.0149254i | \(0.00475107\pi\) | ||||
−0.999889 | + | 0.0149254i | \(0.995249\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.3137 | − | 32.0000i | −0.163967 | − | 0.463768i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 124.451i | 1.75283i | 0.481558 | + | 0.876414i | \(0.340071\pi\) | ||||
−0.481558 | + | 0.876414i | \(0.659929\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −82.0000 | −1.12329 | −0.561644 | − | 0.827379i | \(-0.689831\pi\) | ||||
−0.561644 | + | 0.827379i | \(0.689831\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −19.7990 | + | 7.00000i | −0.263987 | + | 0.0933333i | ||||
\(76\) | 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 | ||||||||
\(85\) | 128.000i | 1.50588i | ||||||||
\(86\) | 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 | ||||||||
\(91\) | 60.0000i | 0.659341i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −62.2254 | + | 22.0000i | −0.669090 | + | 0.236559i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.3137i | 0.119092i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −94.0000 | −0.969072 | −0.484536 | − | 0.874771i | \(-0.661012\pi\) | ||||
−0.484536 | + | 0.874771i | \(0.661012\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −39.5980 | + | 32.0000i | −0.399980 | + | 0.323232i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 50.9117 | 0.504076 | 0.252038 | − | 0.967717i | \(-0.418899\pi\) | ||||
0.252038 | + | 0.967717i | \(0.418899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −134.000 | −1.30097 | −0.650485 | − | 0.759519i | \(-0.725435\pi\) | ||||
−0.650485 | + | 0.759519i | \(0.725435\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 96.0000 | − | 33.9411i | 0.914286 | − | 0.323249i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −50.9117 | −0.475810 | −0.237905 | − | 0.971288i | \(-0.576461\pi\) | ||||
−0.237905 | + | 0.971288i | \(0.576461\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.0000i | − | 0.0917431i | −0.998947 | − | 0.0458716i | \(-0.985394\pi\) | ||
0.998947 | − | 0.0458716i | \(-0.0146065\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 64.0000i | 0.556522i | ||||||||
\(116\) | 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 | ||||||||
\(125\) | −101.823 | −0.814587 | ||||||||
\(126\) | 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 | ||||||||
\(131\) | −5.65685 | −0.0431821 | −0.0215910 | − | 0.999767i | \(-0.506873\pi\) | ||||
−0.0215910 | + | 0.999767i | \(0.506873\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 12.0000i | − | 0.0902256i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −80.0000 | + | 130.108i | −0.592593 | + | 0.963760i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 101.823i | − | 0.743236i | −0.928386 | − | 0.371618i | \(-0.878803\pi\) | ||
0.928386 | − | 0.371618i | \(-0.121197\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 78.0000i | 0.561151i | 0.959832 | + | 0.280576i | \(0.0905253\pi\) | ||||
−0.959832 | + | 0.280576i | \(0.909475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −67.8823 | − | 192.000i | −0.481434 | − | 1.36170i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 56.5685i | 0.395584i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −96.0000 | −0.662069 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 36.7696 | − | 13.0000i | 0.250133 | − | 0.0884354i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 164.049 | 1.10100 | 0.550499 | − | 0.834836i | \(-0.314437\pi\) | ||||
0.550499 | + | 0.834836i | \(0.314437\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 124.451 | 0.802908 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 86.0000i | 0.547771i | 0.961762 | + | 0.273885i | \(0.0883089\pi\) | ||||
−0.961762 | + | 0.273885i | \(0.911691\pi\) | |||||||
\(158\) | 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 | \(-0.761553\pi\) | ||
0.732301 | − | 0.680982i | \(-0.238447\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 90.5097 | − | 32.0000i | 0.548543 | − | 0.193939i | ||||
\(166\) | 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 | ||||||||
\(171\) | 11.3137 | + | 14.0000i | 0.0661620 | + | 0.0818713i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 186.676 | 1.07905 | 0.539527 | − | 0.841969i | \(-0.318603\pi\) | ||||
0.539527 | + | 0.841969i | \(0.318603\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −42.0000 | −0.240000 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 208.000 | − | 73.5391i | 1.17514 | − | 0.415475i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 152.735 | 0.853269 | 0.426634 | − | 0.904424i | \(-0.359699\pi\) | ||||
0.426634 | + | 0.904424i | \(0.359699\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 90.0000i | 0.497238i | 0.968601 | + | 0.248619i | \(0.0799766\pi\) | ||||
−0.968601 | + | 0.248619i | \(0.920023\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −86.0000 | − | 243.245i | −0.469945 | − | 1.32921i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 33.9411i | − | 0.183466i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 128.000i | − | 0.684492i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 84.8528 | − | 138.000i | 0.448957 | − | 0.730159i | ||||
\(190\) | 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 | \(-0.498351\pi\) | ||||
0.00518135 | + | 0.999987i | \(0.498351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 56.5685 | + | 160.000i | 0.290095 | + | 0.820513i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −84.8528 | −0.430725 | −0.215362 | − | 0.976534i | \(-0.569093\pi\) | ||||
−0.215362 | + | 0.976534i | \(0.569093\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 101.823 | 0.501593 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 192.000i | 0.936585i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 64.0000 | + | 79.1960i | 0.309179 | + | 0.382589i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 11.3137i | − | 0.0541326i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 34.0000i | 0.161137i | 0.996749 | + | 0.0805687i | \(0.0256736\pi\) | ||||
−0.996749 | + | 0.0805687i | \(0.974326\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −124.451 | − | 352.000i | −0.584276 | − | 1.65258i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 463.862i | − | 2.15750i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −132.000 | −0.608295 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 231.931 | − | 82.0000i | 1.05905 | − | 0.374429i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 226.274 | 1.02387 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 278.000 | 1.24664 | 0.623318 | − | 0.781968i | \(-0.285784\pi\) | ||||
0.623318 | + | 0.781968i | \(0.285784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 49.0000 | − | 39.5980i | 0.217778 | − | 0.175991i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 220.617 | 0.971882 | 0.485941 | − | 0.873991i | \(-0.338477\pi\) | ||||
0.485941 | + | 0.873991i | \(0.338477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 58.0000i | 0.253275i | 0.991949 | + | 0.126638i | \(0.0404185\pi\) | ||||
−0.991949 | + | 0.126638i | \(0.959581\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −96.0000 | + | 33.9411i | −0.415584 | + | 0.146931i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 395.980i | 1.69948i | 0.527199 | + | 0.849742i | \(0.323242\pi\) | ||||
−0.527199 | + | 0.849742i | \(0.676758\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 384.000i | 1.63404i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 28.2843 | − | 10.0000i | 0.119343 | − | 0.0421941i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.6274i | − | 0.0946754i | −0.998879 | − | 0.0473377i | \(-0.984926\pi\) | ||
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 | ||||||||
\(243\) | 31.1127 | + | 241.000i | 0.128036 | + | 0.991770i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −73.5391 | −0.300160 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.0000 | 0.0809717 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 208.000 | − | 73.5391i | 0.835341 | − | 0.295338i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 107.480 | 0.428208 | 0.214104 | − | 0.976811i | \(-0.431317\pi\) | ||||
0.214104 | + | 0.976811i | \(0.431317\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 64.0000i | − | 0.252964i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −128.000 | − | 362.039i | −0.501961 | − | 1.41976i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 181.019i | − | 0.704355i | −0.935933 | − | 0.352178i | \(-0.885441\pi\) | ||
0.935933 | − | 0.352178i | \(-0.114559\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.0000i | 0.138996i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −118.794 | + | 96.0000i | −0.455149 | + | 0.367816i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 214.960i | 0.817340i | 0.912682 | + | 0.408670i | \(0.134007\pi\) | ||||
−0.912682 | + | 0.408670i | \(0.865993\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −352.000 | −1.32830 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.9411 | + | 96.0000i | 0.127120 | + | 0.359551i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −401.637 | −1.49307 | −0.746537 | − | 0.665344i | \(-0.768285\pi\) | ||||
−0.746537 | + | 0.665344i | \(0.768285\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −266.000 | −0.981550 | −0.490775 | − | 0.871286i | \(-0.663286\pi\) | ||||
−0.490775 | + | 0.871286i | \(0.663286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −60.0000 | − | 169.706i | −0.219780 | − | 0.621632i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −39.5980 | −0.143993 | ||||||||
\(276\) | 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 | ||||||||
\(285\) | −11.3137 | − | 32.0000i | −0.0396972 | − | 0.112281i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 203.647i | − | 0.709571i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −223.000 | −0.771626 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 265.872 | − | 94.0000i | 0.913650 | − | 0.323024i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −220.617 | −0.752960 | −0.376480 | − | 0.926425i | \(-0.622866\pi\) | ||||
−0.376480 | + | 0.926425i | \(0.622866\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −416.000 | −1.41017 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 80.0000 | − | 130.108i | 0.269360 | − | 0.438073i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 113.137 | 0.378385 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 492.000i | 1.63455i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −144.000 | + | 50.9117i | −0.475248 | + | 0.168025i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 486.489i | 1.59505i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 30.0000i | − | 0.0977199i | −0.998806 | − | 0.0488599i | \(-0.984441\pi\) | ||
0.998806 | − | 0.0488599i | \(-0.0155588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 379.009 | − | 134.000i | 1.22657 | − | 0.433657i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 576.999i | − | 1.85530i | −0.373447 | − | 0.927651i | \(-0.621824\pi\) | ||
0.373447 | − | 0.927651i | \(-0.378176\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −210.000 | −0.670927 | −0.335463 | − | 0.942053i | \(-0.608893\pi\) | ||||
−0.335463 | + | 0.942053i | \(0.608893\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −237.588 | + | 192.000i | −0.754247 | + | 0.609524i | ||||
\(316\) | 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 | ||||||||
\(325\) | − | 70.0000i | − | 0.215385i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.0000 | + | 28.2843i | 0.0305810 | + | 0.0864962i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 407.294i | − | 1.23797i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 434.000i | − | 1.31118i | −0.755118 | − | 0.655589i | \(-0.772420\pi\) | ||
0.755118 | − | 0.655589i | \(-0.227580\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −33.9411 | − | 42.0000i | −0.101925 | − | 0.126126i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.3137i | 0.0337723i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −510.000 | −1.51335 | −0.756677 | − | 0.653789i | \(-0.773178\pi\) | ||||
−0.756677 | + | 0.653789i | \(0.773178\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −67.8823 | − | 192.000i | −0.200243 | − | 0.566372i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −124.451 | −0.364958 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 372.000 | 1.08455 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −64.0000 | − | 181.019i | −0.185507 | − | 0.524694i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 152.735 | 0.440159 | 0.220079 | − | 0.975482i | \(-0.429368\pi\) | ||||
0.220079 | + | 0.975482i | \(0.429368\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 426.000i | − | 1.22063i | −0.792159 | − | 0.610315i | \(-0.791043\pi\) | ||
0.792159 | − | 0.610315i | \(-0.208957\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 704.000i | 1.98310i | ||||||||
\(356\) | 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 | ||||||||
\(365\) | −463.862 | −1.27085 | ||||||||
\(366\) | 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 | ||||||||
\(371\) | 373.352 | 1.00634 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 218.000i | 0.584450i | 0.956350 | + | 0.292225i | \(0.0943957\pi\) | ||||
−0.956350 | + | 0.292225i | \(0.905604\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 288.000 | − | 101.823i | 0.768000 | − | 0.271529i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 169.706i | 0.450148i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 142.000i | 0.374670i | 0.982296 | + | 0.187335i | \(0.0599850\pi\) | ||||
−0.982296 | + | 0.187335i | \(0.940015\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 299.813 | − | 106.000i | 0.786911 | − | 0.278215i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 192.000 | 0.498701 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −463.862 | − | 574.000i | −1.19861 | − | 1.48320i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 548.715 | 1.41058 | 0.705289 | − | 0.708920i | \(-0.250817\pi\) | ||||
0.705289 | + | 0.708920i | \(0.250817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −256.000 | −0.654731 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.0000 | − | 5.65685i | 0.0407125 | − | 0.0143940i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −56.5685 | −0.143211 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 310.000i | 0.780856i | 0.920633 | + | 0.390428i | \(0.127673\pi\) | ||||
−0.920633 | + | 0.390428i | \(0.872327\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.0000 | + | 33.9411i | 0.0300752 | + | 0.0850655i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 339.411i | − | 0.846412i | −0.906033 | − | 0.423206i | \(-0.860905\pi\) | ||
0.906033 | − | 0.423206i | \(-0.139095\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 220.000i | − | 0.545906i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 96.1665 | − | 448.000i | 0.237448 | − | 1.10617i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.9411i | 0.0833934i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 270.000 | 0.660147 | 0.330073 | − | 0.943955i | \(-0.392927\pi\) | ||||
0.330073 | + | 0.943955i | \(0.392927\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 101.823 | + | 288.000i | 0.247745 | + | 0.700730i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 441.235 | 1.06836 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −416.000 | −1.00241 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −78.0000 | − | 220.617i | −0.187050 | − | 0.529058i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −50.9117 | −0.121508 | −0.0607538 | − | 0.998153i | \(-0.519350\pi\) | ||||
−0.0607538 | + | 0.998153i | \(0.519350\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 454.000i | − | 1.07838i | −0.842183 | − | 0.539192i | \(-0.818730\pi\) | ||
0.842183 | − | 0.539192i | \(-0.181270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 384.000 | + | 475.176i | 0.907801 | + | 1.12335i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 158.392i | 0.372687i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 516.000i | − | 1.20843i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −56.5685 | − | 160.000i | −0.131861 | − | 0.372960i | ||||
\(430\) | 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 | \(-0.196604\pi\) | ||||
0.815242 | + | 0.579120i | \(0.196604\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 271.529 | − | 96.0000i | 0.624205 | − | 0.220690i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.6274 | −0.0517790 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | −707.107 | −1.59618 | −0.798089 | − | 0.602540i | \(-0.794156\pi\) | ||||
−0.798089 | + | 0.602540i | \(0.794156\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 192.000i | − | 0.431461i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −464.000 | + | 164.049i | −1.03803 | + | 0.366999i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 724.077i | 1.61264i | 0.591477 | + | 0.806322i | \(0.298545\pi\) | ||||
−0.591477 | + | 0.806322i | \(0.701455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 192.000i | − | 0.425721i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −616.597 | + | 218.000i | −1.36114 | + | 0.481236i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 339.411i | 0.745959i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −338.000 | −0.739606 | −0.369803 | − | 0.929110i | \(-0.620575\pi\) | ||||
−0.369803 | + | 0.929110i | \(0.620575\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −520.431 | − | 320.000i | −1.13384 | − | 0.697168i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 774.989 | 1.68110 | 0.840552 | − | 0.541731i | \(-0.182231\pi\) | ||||
0.840552 | + | 0.541731i | \(0.182231\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −74.0000 | −0.159827 | −0.0799136 | − | 0.996802i | \(-0.525464\pi\) | ||||
−0.0799136 | + | 0.996802i | \(0.525464\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −352.000 | + | 124.451i | −0.756989 | + | 0.267636i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −797.616 | −1.70796 | −0.853979 | − | 0.520307i | \(-0.825817\pi\) | ||||
−0.853979 | + | 0.520307i | \(0.825817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 12.0000i | − | 0.0255864i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −86.0000 | − | 243.245i | −0.182590 | − | 0.516443i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 463.862i | 0.980681i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.0000i | 0.0294737i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −435.578 | + | 352.000i | −0.913161 | + | 0.737945i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 316.784i | 0.661344i | 0.943746 | + | 0.330672i | \(0.107275\pi\) | ||||
−0.943746 | + | 0.330672i | \(0.892725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −60.0000 | −0.124740 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 67.8823 | + | 192.000i | 0.140543 | + | 0.397516i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −531.744 | −1.09638 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −134.000 | −0.275154 | −0.137577 | − | 0.990491i | \(-0.543931\pi\) | ||||
−0.137577 | + | 0.990491i | \(0.543931\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 222.000 | + | 627.911i | 0.453988 | + | 1.28407i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −50.9117 | −0.103690 | −0.0518449 | − | 0.998655i | \(-0.516510\pi\) | ||||
−0.0518449 | + | 0.998655i | \(0.516510\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 384.000i | − | 0.778905i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −224.000 | + | 181.019i | −0.452525 | + | 0.365696i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 746.705i | − | 1.50242i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 30.0000i | − | 0.0601202i | −0.999548 | − | 0.0300601i | \(-0.990430\pi\) | ||
0.999548 | − | 0.0300601i | \(-0.00956988\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −169.706 | − | 480.000i | −0.338734 | − | 0.958084i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 237.588i | 0.472342i | 0.971712 | + | 0.236171i | \(0.0758925\pi\) | ||||
−0.971712 | + | 0.236171i | \(0.924107\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 288.000 | 0.570297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −195.161 | + | 69.0000i | −0.384934 | + | 0.136095i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 118.794 | 0.233387 | 0.116693 | − | 0.993168i | \(-0.462770\pi\) | ||||
0.116693 | + | 0.993168i | \(0.462770\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 492.000 | 0.962818 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −46.0000 | − | 28.2843i | −0.0896686 | − | 0.0551350i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −758.018 | −1.47188 | ||||||||
\(516\) | 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 | ||||||||
\(525\) | 118.794 | − | 42.0000i | 0.226274 | − | 0.0800000i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 497.803i | 0.944598i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 401.000 | 0.758034 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −514.774 | + | 416.000i | −0.969442 | + | 0.783427i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 339.411 | 0.636794 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −288.000 | −0.538318 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −432.000 | + | 152.735i | −0.804469 | + | 0.284423i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 73.5391 | 0.136436 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 234.000i | − | 0.432532i | −0.976334 | − | 0.216266i | \(-0.930612\pi\) | ||
0.976334 | − | 0.216266i | \(-0.0693879\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −90.0000 | − | 254.558i | −0.165746 | − | 0.468800i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 56.5685i | − | 0.103795i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 290.000i | 0.530165i | 0.964226 | + | 0.265082i | \(0.0853991\pi\) | ||||
−0.964226 | + | 0.265082i | \(0.914601\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 486.489 | + | 602.000i | 0.886137 | + | 1.09654i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 33.9411i | − | 0.0615991i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 60.0000 | 0.108499 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 33.9411 | + | 96.0000i | 0.0611552 | + | 0.172973i | ||||
\(556\) | 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 | ||||||||
\(565\) | 384.000i | 0.679646i | ||||||||
\(566\) | 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 | ||||||||
\(571\) | − | 402.000i | − | 0.704028i | −0.935995 | − | 0.352014i | \(-0.885497\pi\) | ||
0.935995 | − | 0.352014i | \(-0.114503\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 271.529 | + | 768.000i | 0.473873 | + | 1.34031i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 79.1960i | 0.137732i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 98.0000 | 0.169844 | 0.0849220 | − | 0.996388i | \(-0.472936\pi\) | ||||
0.0849220 | + | 0.996388i | \(0.472936\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.65685 | + | 2.00000i | −0.00977004 | + | 0.00345423i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 441.235 | 0.759440 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 352.000 | 0.603774 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −320.000 | − | 395.980i | −0.547009 | − | 0.676889i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −548.715 | −0.934778 | −0.467389 | − | 0.884052i | \(-0.654805\pi\) | ||||
−0.467389 | + | 0.884052i | \(0.654805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.0000i | 0.0747029i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | − | 768.000i | − | 1.29076i | ||||||
\(596\) | 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 | \(-0.392575\pi\) | ||||
0.331115 | + | 0.943590i | \(0.392575\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.3137 | + | 14.0000i | 0.0187624 | + | 0.0232172i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −503.460 | −0.832165 | ||||||||
\(606\) | 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 | ||||||||
\(611\) | 678.823 | 1.11100 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1030.00i | − | 1.68026i | −0.542384 | − | 0.840131i | \(-0.682478\pi\) | ||
0.542384 | − | 0.840131i | \(-0.317522\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −192.000 | − | 543.058i | −0.312195 | − | 0.883021i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1052.17i | − | 1.70531i | −0.522476 | − | 0.852654i | \(-0.674992\pi\) | ||
0.522476 | − | 0.852654i | \(-0.325008\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0000i | 0.0226171i | 0.999936 | + | 0.0113086i | \(0.00359970\pi\) | ||||
−0.999936 | + | 0.0113086i | \(0.996400\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −260.215 | − | 160.000i | −0.419026 | − | 0.257649i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 203.647i | 0.326881i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −751.000 | −1.20160 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.3137 | + | 32.0000i | 0.0180442 | + | 0.0510367i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 135.765 | 0.215842 | ||||||||
\(630\) | 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 | ||||||||
\(635\) | −599.627 | −0.944294 | ||||||||
\(636\) | 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 | \(0.114839\pi\) | ||||
−0.935623 | + | 0.353002i | \(0.885161\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 798.000i | − | 1.24106i | −0.784184 | − | 0.620529i | \(-0.786918\pi\) | ||
0.784184 | − | 0.620529i | \(-0.213082\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 463.862 | + | 1312.00i | 0.719166 | + | 2.03411i | ||||
\(646\) | 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 | ||||||||
\(651\) | 373.352 | − | 132.000i | 0.573506 | − | 0.202765i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 322.441 | 0.493784 | 0.246892 | − | 0.969043i | \(-0.420591\pi\) | ||||
0.246892 | + | 0.969043i | \(0.420591\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.0000 | −0.0488550 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −574.000 | + | 463.862i | −0.873668 | + | 0.706031i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −797.616 | −1.21034 | −0.605172 | − | 0.796095i | \(-0.706896\pi\) | ||||
−0.605172 | + | 0.796095i | \(0.706896\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 986.000i | 1.49168i | 0.666126 | + | 0.745840i | \(0.267951\pi\) | ||||
−0.666126 | + | 0.745840i | \(0.732049\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −640.000 | + | 226.274i | −0.965309 | + | 0.341288i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 67.8823i | − | 0.102079i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 192.000i | − | 0.287856i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −786.303 | + | 278.000i | −1.17534 | + | 0.415546i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 486.489i | − | 0.725022i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 0.0505201 | 0.0252600 | − | 0.999681i | \(-0.491959\pi\) | ||||
0.0252600 | + | 0.999681i | \(0.491959\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −98.9949 | + | 161.000i | −0.146659 | + | 0.238519i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −401.637 | −0.593259 | −0.296630 | − | 0.954993i | \(-0.595863\pi\) | ||||
−0.296630 | + | 0.954993i | \(0.595863\pi\) | |||||||
\(678\) | 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 | \(-0.469636\pi\) | ||||
0.0952472 | + | 0.995454i | \(0.469636\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 576.000i | − | 0.840876i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −58.0000 | − | 164.049i | −0.0844250 | − | 0.238790i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 622.254i | 0.903126i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 578.000i | 0.836469i | 0.908339 | + | 0.418234i | \(0.137351\pi\) | ||||
−0.908339 | + | 0.418234i | \(0.862649\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 237.588 | − | 192.000i | 0.342840 | − | 0.277056i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 441.235i | 0.634870i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −768.000 | −1.10187 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −395.980 | − | 1120.00i | −0.566495 | − | 1.60229i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1238.85 | −1.76726 | −0.883631 | − | 0.468183i | \(-0.844909\pi\) | ||||
−0.883631 | + | 0.468183i | \(0.844909\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | 0.0170697 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −384.000 | − | 1086.12i | −0.544681 | − | 1.54059i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −305.470 | −0.432065 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1222.00i | − | 1.72355i | −0.507287 | − | 0.861777i | \(-0.669352\pi\) | ||
0.507287 | − | 0.861777i | \(-0.330648\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −70.0000 | + | 56.5685i | −0.0984529 | + | 0.0795619i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 248.902i | 0.349091i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 320.000i | 0.447552i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.6274 | + | 64.0000i | 0.0315585 | + | 0.0892608i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 248.902i | − | 0.346177i | −0.984906 | − | 0.173089i | \(-0.944625\pi\) | ||
0.984906 | − | 0.173089i | \(-0.0553747\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 804.000 | 1.11512 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 84.8528 | − | 30.0000i | 0.117362 | − | 0.0414938i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −118.794 | −0.163854 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −870.000 | −1.19670 | −0.598349 | − | 0.801235i | \(-0.704177\pi\) | ||||
−0.598349 | + | 0.801235i | \(0.704177\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −329.000 | − | 650.538i | −0.451303 | − | 0.892371i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1855.45 | 2.53823 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 214.000i | 0.291951i | 0.989288 | + | 0.145975i | \(0.0466321\pi\) | ||||
−0.989288 | + | 0.145975i | \(0.953368\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 208.000 | − | 73.5391i | 0.282993 | − | 0.100053i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 11.3137i | − | 0.0153510i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 958.000i | − | 1.29635i | −0.761493 | − | 0.648173i | \(-0.775533\pi\) | ||
0.761493 | − | 0.648173i | \(-0.224467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −56.5685 | + | 20.0000i | −0.0763408 | + | 0.0269906i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1006.92i | − | 1.35521i | −0.735427 | − | 0.677604i | \(-0.763018\pi\) | ||
0.735427 | − | 0.677604i | \(-0.236982\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 928.000 | 1.24564 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −514.774 | + | 416.000i | −0.689121 | + | 0.556894i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 305.470 | 0.407837 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 630.000 | 0.838881 | 0.419441 | − | 0.907783i | \(-0.362226\pi\) | ||||
0.419441 | + | 0.907783i | \(0.362226\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −304.000 | + | 107.480i | −0.403718 | + | 0.142736i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1233.19 | 1.63337 | ||||||||
\(756\) | 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 | ||||||||
\(765\) | 724.077 | + | 896.000i | 0.946506 | + | 1.17124i | ||||
\(766\) | 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 | ||||||||
\(771\) | 181.019 | + | 512.000i | 0.234785 | + | 0.664073i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 186.676 | 0.241496 | 0.120748 | − | 0.992683i | \(-0.461471\pi\) | ||||
0.120748 | + | 0.992683i | \(0.461471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 154.000 | 0.198710 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −36.0000 | − | 101.823i | −0.0463320 | − | 0.131047i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −67.8823 | −0.0871402 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 704.000i | − | 0.901408i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 240.000 | − | 390.323i | 0.306513 | − | 0.498497i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 486.489i | 0.619732i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 514.000i | 0.653113i | 0.945178 | + | 0.326557i | \(0.105888\pi\) | ||||
−0.945178 | + | 0.326557i | \(0.894112\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −214.960 | − | 608.000i | −0.272447 | − | 0.770596i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 407.294i | − | 0.514910i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 860.000 | 1.08449 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 995.606 | − | 352.000i | 1.25234 | − | 0.442767i | ||||
\(796\) | 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 | ||||||||
\(805\) | − | 384.000i | − | 0.477019i | ||||||
\(806\) | 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 | ||||||||
\(811\) | 1454.00i | 1.79285i | 0.443197 | + | 0.896424i | \(0.353844\pi\) | ||||
−0.443197 | + | 0.896424i | \(0.646156\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 752.362 | − | 266.000i | 0.925414 | − | 0.327183i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1255.82i | − | 1.54089i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 164.000 | 0.200734 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 339.411 | + | 420.000i | 0.414422 | + | 0.512821i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −967.322 | −1.17822 | −0.589112 | − | 0.808051i | \(-0.700522\pi\) | ||||
−0.589112 | + | 0.808051i | \(0.700522\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −166.000 | −0.201701 | −0.100851 | − | 0.994902i | \(-0.532156\pi\) | ||||
−0.100851 | + | 0.994902i | \(0.532156\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 112.000 | − | 39.5980i | 0.135758 | − | 0.0479976i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −978.636 | −1.18336 | −0.591678 | − | 0.806174i | \(-0.701534\pi\) | ||||
−0.591678 | + | 0.806174i | \(0.701534\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1258.00i | − | 1.51749i | −0.651387 | − | 0.758745i | \(-0.725813\pi\) | ||
0.651387 | − | 0.758745i | \(-0.274187\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −346.000 | − | 978.636i | −0.416366 | − | 1.17766i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 294.156i | − | 0.353129i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 960.000i | 1.14970i | ||||||||
\(836\) | 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 | ||||||||
\(845\) | 390.323 | 0.461921 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 534.000 | 0.630460 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −46.0000 | − | 130.108i | −0.0541814 | − | 0.153248i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 67.8823 | 0.0797676 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 742.000i | − | 0.869871i | −0.900462 | − | 0.434936i | \(-0.856771\pi\) | ||
0.900462 | − | 0.434936i | \(-0.143229\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 64.0000 | + | 79.1960i | 0.0748538 | + | 0.0926269i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 237.588i | 0.277232i | 0.990346 | + | 0.138616i | \(0.0442654\pi\) | ||||
−0.990346 | + | 0.138616i | \(0.955735\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1230.00i | 1.43190i | 0.698153 | + | 0.715949i | \(0.254006\pi\) | ||||
−0.698153 | + | 0.715949i | \(0.745994\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 203.647 | + | 576.000i | 0.236524 | + | 0.668990i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 45.2548i | − | 0.0524390i | −0.999656 | − | 0.0262195i | \(-0.991653\pi\) | ||
0.999656 | − | 0.0262195i | \(-0.00834688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1056.00 | 1.22081 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 630.739 | − | 223.000i | 0.727496 | − | 0.257209i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 56.5685 | 0.0650961 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | 0.0229621 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −658.000 | + | 531.744i | −0.753723 | + | 0.609100i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 610.940 | 0.698217 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 822.000i | 0.937286i | 0.883388 | + | 0.468643i | \(0.155257\pi\) | ||||
−0.883388 | + | 0.468643i | \(0.844743\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 624.000 | − | 220.617i | 0.709898 | − | 0.250987i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 656.195i | − | 0.744830i | −0.928066 | − | 0.372415i | \(-0.878530\pi\) | ||
0.928066 | − | 0.372415i | \(-0.121470\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 962.000i | 1.08947i | 0.838609 | + | 0.544734i | \(0.183369\pi\) | ||||
−0.838609 | + | 0.544734i | \(0.816631\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1176.63 | − | 416.000i | 1.32952 | − | 0.470056i | ||||
\(886\) | 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 | ||||||||
\(891\) | −96.1665 | + | 448.000i | −0.107931 | + | 0.502806i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −135.765 | −0.152032 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 864.000 | 0.965363 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −320.000 | + | 113.137i | −0.356745 | + | 0.126128i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −373.352 | −0.415297 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1408.00i | − | 1.56271i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −492.000 | − | 1391.59i | −0.544850 | − | 1.54107i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 509.117i | 0.562560i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1042.00i | − | 1.14884i | −0.818560 | − | 0.574421i | \(-0.805227\pi\) | ||
0.818560 | − | 0.574421i | \(-0.194773\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 356.382 | − | 288.000i | 0.392059 | − | 0.316832i | ||||
\(910\) | 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 | ||||||||
\(915\) | −486.489 | − | 1376.00i | −0.531682 | − | 1.50383i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.9411 | 0.0370132 | ||||||||
\(918\) | 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 | ||||||||
\(923\) | 1244.51 | 1.34833 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 42.0000i | − | 0.0454054i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −938.000 | + | 758.018i | −1.01187 | + | 0.817711i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 45.2548i | − | 0.0487135i | −0.999703 | − | 0.0243567i | \(-0.992246\pi\) | ||
0.999703 | − | 0.0243567i | \(-0.00775376\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 26.0000i | − | 0.0279270i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 576.999 | + | 1632.00i | 0.618434 | + | 1.74920i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 724.077i | − | 0.774414i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 462.000 | 0.493063 | 0.246531 | − | 0.969135i | \(-0.420709\pi\) | ||||
0.246531 | + | 0.969135i | \(0.420709\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 593.970 | − | 210.000i | 0.632556 | − | 0.223642i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −356.382 | −0.378727 | −0.189363 | − | 0.981907i | \(-0.560642\pi\) | ||||
−0.189363 | + | 0.981907i | \(0.560642\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −384.000 | −0.407211 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 480.000 | − | 780.646i | 0.507937 | − | 0.826080i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 695.793 | 0.734734 | 0.367367 | − | 0.930076i | \(-0.380259\pi\) | ||||
0.367367 | + | 0.930076i | \(0.380259\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 820.000i | 0.864067i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 432.000 | − | 152.735i | 0.454259 | − | 0.160605i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1527.35i | − | 1.60268i | −0.598212 | − | 0.801338i | \(-0.704122\pi\) | ||
0.598212 | − | 0.801338i | \(-0.295878\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1536.00i | − | 1.60838i | ||||||
\(956\) | 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 | ||||||||
\(965\) | 11.3137 | 0.0117241 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −70.0000 | −0.0723888 | −0.0361944 | − | 0.999345i | \(-0.511524\pi\) | ||||
−0.0361944 | + | 0.999345i | \(0.511524\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 128.000 | − | 45.2548i | 0.132095 | − | 0.0467026i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 627.911 | 0.646664 | 0.323332 | − | 0.946286i | \(-0.395197\pi\) | ||||
0.323332 | + | 0.946286i | \(0.395197\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 468.000i | − | 0.480987i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 70.0000 | + | 197.990i | 0.0717949 | + | 0.203067i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1018.23i | 1.04220i | 0.853494 | + | 0.521102i | \(0.174479\pi\) | ||||
−0.853494 | + | 0.521102i | \(0.825521\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 192.000i | 0.196118i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −56.5685 | − | 70.0000i | −0.0576642 | − | 0.0713558i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 644.881i | 0.656034i | 0.944672 | + | 0.328017i | \(0.106380\pi\) | ||||
−0.944672 | + | 0.328017i | \(0.893620\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −480.000 | −0.487310 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 407.294 | + | 1152.00i | 0.412658 | + | 1.16717i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 927.724 | 0.938043 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 854.000 | 0.861756 | 0.430878 | − | 0.902410i | \(-0.358204\pi\) | ||||
0.430878 | + | 0.902410i | \(0.358204\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 434.000 | + | 1227.54i | 0.437059 | + | 1.23619i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1414.21 | 1.42132 | ||||||||
\(996\) | 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 \(a_p\))