Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,3,Mod(17,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("24.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.e (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: | \(0.653952634465\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 24.17 |
Dual form | 24.3.e.a.17.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(13\) | \(17\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | − | 2.82843i | 0.333333 | − | 0.942809i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.65685i | 1.13137i | 0.824621 | + | 0.565685i | \(0.191388\pi\) | ||||
−0.824621 | + | 0.565685i | \(0.808612\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | 5.65685i | 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 | \(-0.374334\pi\) | ||||
0.384615 | + | 0.923077i | \(0.374334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 16.0000 | + | 5.65685i | 1.06667 | + | 0.377124i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 22.6274i | − | 1.33102i | −0.746387 | − | 0.665512i | \(-0.768213\pi\) | ||
0.746387 | − | 0.665512i | \(-0.231787\pi\) | |||||||
\(18\) | 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 | \(-0.920900\pi\) | ||
0.969282 | − | 0.245950i | \(-0.0791000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | −0.280000 | ||||||||
\(26\) | 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 | ||||||||
\(35\) | − | 33.9411i | − | 0.969746i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.162162 | −0.0810811 | − | 0.996708i | \(-0.525837\pi\) | ||||
−0.0810811 | + | 0.996708i | \(0.525837\pi\) | |||||||
\(38\) | 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 | \(-0.0974639\pi\) | ||||
0.953488 | + | 0.301430i | \(0.0974639\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 32.0000 | − | 39.5980i | 0.711111 | − | 0.879955i | ||||
\(46\) | 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 | ||||||||
\(51\) | −64.0000 | − | 22.6274i | −1.25490 | − | 0.443675i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 62.2254i | − | 1.17406i | −0.809564 | − | 0.587032i | \(-0.800296\pi\) | ||
0.809564 | − | 0.587032i | \(-0.199704\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −32.0000 | −0.581818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | − | 5.65685i | 0.0350877 | − | 0.0992431i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 73.5391i | 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 | ||||||||
\(65\) | 56.5685i | 0.870285i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.0298507 | 0.0149254 | − | 0.999889i | \(-0.495249\pi\) | ||||
0.0149254 | + | 0.999889i | \(0.495249\pi\) | |||||||
\(68\) | 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 | \(-0.310169\pi\) | ||||
0.561644 | + | 0.827379i | \(0.310169\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.00000 | + | 19.7990i | −0.0933333 | + | 0.263987i | ||||
\(76\) | 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 | \(-0.853912\pi\) | ||
0.896518 | − | 0.443007i | \(-0.146088\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 128.000 | 1.50588 | ||||||||
\(86\) | 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 | ||||||||
\(95\) | 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 | ||||||||
\(99\) | 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 | \(-0.725435\pi\) | ||||
−0.650485 | + | 0.759519i | \(0.725435\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −96.0000 | − | 33.9411i | −0.914286 | − | 0.323249i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 50.9117i | 0.475810i | 0.971288 | + | 0.237905i | \(0.0764607\pi\) | ||||
−0.971288 | + | 0.237905i | \(0.923539\pi\) | |||||||
\(108\) | 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 | \(-0.902892\pi\) | ||
0.953825 | − | 0.300364i | \(-0.0971081\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 64.0000 | 0.556522 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | 101.823i | 0.814587i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 106.000 | 0.834646 | 0.417323 | − | 0.908758i | \(-0.362968\pi\) | ||||
0.417323 | + | 0.908758i | \(0.362968\pi\) | |||||||
\(128\) | 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 | ||||||||
\(135\) | −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 | ||||||||
\(139\) | −78.0000 | −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 | ||||||||
\(145\) | −96.0000 | −0.662069 | ||||||||
\(146\) | 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 | ||||||||
\(155\) | − | 124.451i | − | 0.802908i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −86.0000 | −0.547771 | −0.273885 | − | 0.961762i | \(-0.588309\pi\) | ||||
−0.273885 | + | 0.961762i | \(0.588309\pi\) | |||||||
\(158\) | 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 | \(-0.738447\pi\) | ||||
−0.680982 | + | 0.732301i | \(0.738447\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −32.0000 | + | 90.5097i | −0.193939 | + | 0.548543i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 169.706i | − | 1.01620i | −0.861298 | − | 0.508101i | \(-0.830348\pi\) | ||
0.861298 | − | 0.508101i | \(-0.169652\pi\) | |||||||
\(168\) | 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 | \(-0.818603\pi\) | ||
0.841969 | − | 0.539527i | \(-0.181397\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 42.0000 | 0.240000 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 208.000 | + | 73.5391i | 1.17514 | + | 0.415475i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 152.735i | 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 | ||||||||
\(185\) | − | 33.9411i | − | 0.183466i | ||||||
\(186\) | 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 | \(-0.498351\pi\) | ||||
0.00518135 | + | 0.999987i | \(0.498351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 160.000 | + | 56.5685i | 0.820513 | + | 0.290095i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 84.8528i | − | 0.430725i | −0.976534 | − | 0.215362i | \(-0.930907\pi\) | ||
0.976534 | − | 0.215362i | \(-0.0690933\pi\) | |||||||
\(198\) | 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 | ||||||||
\(205\) | −192.000 | −0.936585 | ||||||||
\(206\) | 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 | ||||||||
\(215\) | 463.862i | 2.15750i | ||||||||
\(216\) | 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 | \(-0.714216\pi\) | ||||
−0.623318 | + | 0.781968i | \(0.714216\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 49.0000 | + | 39.5980i | 0.217778 | + | 0.175991i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 220.617i | 0.971882i | 0.873991 | + | 0.485941i | \(0.161523\pi\) | ||||
−0.873991 | + | 0.485941i | \(0.838477\pi\) | |||||||
\(228\) | 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 | \(0.323242\pi\) | ||||
−0.527199 | + | 0.849742i | \(0.676758\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −384.000 | −1.63404 | ||||||||
\(236\) | 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 | ||||||||
\(245\) | − | 73.5391i | − | 0.300160i | ||||||
\(246\) | 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 | ||||||||
\(255\) | 128.000 | − | 362.039i | 0.501961 | − | 1.41976i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 181.019i | 0.704355i | 0.935933 | + | 0.352178i | \(0.114559\pi\) | ||||
−0.935933 | + | 0.352178i | \(0.885441\pi\) | |||||||
\(258\) | 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 | \(-0.865993\pi\) | ||
0.912682 | − | 0.408670i | \(-0.134007\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 352.000 | 1.32830 | ||||||||
\(266\) | 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 | ||||||||
\(275\) | − | 39.5980i | − | 0.143993i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 346.000 | 1.24910 | 0.624549 | − | 0.780986i | \(-0.285283\pi\) | ||||
0.624549 | + | 0.780986i | \(0.285283\pi\) | |||||||
\(278\) | 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 | \(-0.525898\pi\) | ||||
−0.0812721 | + | 0.996692i | \(0.525898\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 32.0000 | + | 11.3137i | 0.112281 | + | 0.0396972i | ||||
\(286\) | 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 | \(-0.877134\pi\) | ||
0.926425 | − | 0.376480i | \(-0.122866\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −416.000 | −1.41017 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −80.0000 | − | 130.108i | −0.269360 | − | 0.438073i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 113.137i | − | 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 | ||||||||
\(305\) | − | 486.489i | − | 1.59505i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.0000 | −0.0977199 | −0.0488599 | − | 0.998806i | \(-0.515559\pi\) | ||||
−0.0488599 | + | 0.998806i | \(0.515559\pi\) | |||||||
\(308\) | 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 | \(-0.391107\pi\) | ||||
0.335463 | + | 0.942053i | \(0.391107\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −192.000 | + | 237.588i | −0.609524 | + | 0.754247i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 152.735i | 0.481814i | 0.970548 | + | 0.240907i | \(0.0774449\pi\) | ||||
−0.970548 | + | 0.240907i | \(0.922555\pi\) | |||||||
\(318\) | 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 | ||||||||
\(325\) | −70.0000 | −0.215385 | ||||||||
\(326\) | 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 | ||||||||
\(335\) | 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 | ||||||||
\(339\) | −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 | ||||||||
\(345\) | 64.0000 | − | 181.019i | 0.185507 | − | 0.524694i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 152.735i | − | 0.440159i | −0.975482 | − | 0.220079i | \(-0.929368\pi\) | ||
0.975482 | − | 0.220079i | \(-0.0706316\pi\) | |||||||
\(348\) | 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 | \(0.0204178\pi\) | ||||
−0.997943 | + | 0.0641003i | \(0.979582\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 704.000 | 1.98310 | ||||||||
\(356\) | 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 | ||||||||
\(365\) | 463.862i | 1.27085i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −566.000 | −1.54223 | −0.771117 | − | 0.636693i | \(-0.780302\pi\) | ||||
−0.771117 | + | 0.636693i | \(0.780302\pi\) | |||||||
\(368\) | 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 | \(-0.405604\pi\) | ||||
0.292225 | + | 0.956350i | \(0.405604\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 288.000 | + | 101.823i | 0.768000 | + | 0.271529i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 169.706i | 0.450148i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −142.000 | −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 | ||||||||
\(385\) | 192.000 | 0.498701 | ||||||||
\(386\) | 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 | ||||||||
\(395\) | 56.5685i | 0.143211i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −310.000 | −0.780856 | −0.390428 | − | 0.920633i | \(-0.627673\pi\) | ||||
−0.390428 | + | 0.920633i | \(0.627673\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | −448.000 | + | 96.1665i | −1.10617 | + | 0.237448i | ||||
\(406\) | 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 | ||||||||
\(415\) | 416.000 | 1.00241 | ||||||||
\(416\) | 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 | ||||||||
\(425\) | 158.392i | 0.372687i | ||||||||
\(426\) | 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 | \(-0.196604\pi\) | ||||
0.815242 | + | 0.579120i | \(0.196604\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −96.0000 | + | 271.529i | −0.220690 | + | 0.624205i | ||||
\(436\) | 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 | \(0.294156\pi\) | ||||
−0.602540 | + | 0.798089i | \(0.705844\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 192.000 | 0.431461 | ||||||||
\(446\) | 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 | ||||||||
\(455\) | − | 339.411i | − | 0.745959i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 338.000 | 0.739606 | 0.369803 | − | 0.929110i | \(-0.379425\pi\) | ||||
0.369803 | + | 0.929110i | \(0.379425\pi\) | |||||||
\(458\) | 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 | \(-0.474536\pi\) | ||||
0.0799136 | + | 0.996802i | \(0.474536\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −352.000 | − | 124.451i | −0.756989 | − | 0.267636i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 797.616i | − | 1.70796i | −0.520307 | − | 0.853979i | \(-0.674183\pi\) | ||
0.520307 | − | 0.853979i | \(-0.325817\pi\) | |||||||
\(468\) | 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 | ||||||||
\(475\) | −14.0000 | −0.0294737 | ||||||||
\(476\) | 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 | ||||||||
\(485\) | − | 531.744i | − | 1.09638i | ||||||
\(486\) | 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 | ||||||||
\(491\) | 50.9117i | 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 | ||||||||
\(495\) | 224.000 | + | 181.019i | 0.452525 | + | 0.365696i | ||||
\(496\) | 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 | \(-0.924107\pi\) | ||
0.971712 | − | 0.236171i | \(-0.0758925\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −288.000 | −0.570297 | ||||||||
\(506\) | 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 | ||||||||
\(515\) | − | 758.018i | − | 1.47188i | ||||||
\(516\) | 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 | \(-0.656567\pi\) | ||||
−0.472275 | + | 0.881451i | \(0.656567\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 42.0000 | − | 118.794i | 0.0800000 | − | 0.226274i | ||||
\(526\) | 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 | ||||||||
\(535\) | −288.000 | −0.538318 | ||||||||
\(536\) | 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 | ||||||||
\(545\) | 56.5685i | 0.103795i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 290.000 | 0.530165 | 0.265082 | − | 0.964226i | \(-0.414601\pi\) | ||||
0.265082 | + | 0.964226i | \(0.414601\pi\) | |||||||
\(548\) | 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 | ||||||||
\(555\) | −96.0000 | − | 33.9411i | −0.172973 | − | 0.0611552i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 175.362i | 0.314834i | 0.987532 | + | 0.157417i | \(0.0503167\pi\) | ||||
−0.987532 | + | 0.157417i | \(0.949683\pi\) | |||||||
\(558\) | 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 | \(0.0693094\pi\) | ||||
−0.976388 | + | 0.216026i | \(0.930691\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 384.000 | 0.679646 | ||||||||
\(566\) | 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 | ||||||||
\(575\) | 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 | ||||||||
\(579\) | 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 | ||||||||
\(585\) | 320.000 | − | 395.980i | 0.547009 | − | 0.676889i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 548.715i | 0.934778i | 0.884052 | + | 0.467389i | \(0.154805\pi\) | ||||
−0.884052 | + | 0.467389i | \(0.845195\pi\) | |||||||
\(588\) | 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 | \(0.201441\pi\) | ||||
−0.806348 | + | 0.591442i | \(0.798559\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −768.000 | −1.29076 | ||||||||
\(596\) | 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 | ||||||||
\(605\) | 503.460i | 0.832165i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 170.000 | 0.280066 | 0.140033 | − | 0.990147i | \(-0.455279\pi\) | ||||
0.140033 | + | 0.990147i | \(0.455279\pi\) | |||||||
\(608\) | 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 | \(-0.817522\pi\) | ||||
−0.840131 | + | 0.542384i | \(0.817522\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | −14.0000 | −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 | ||||||||
\(625\) | −751.000 | −1.20160 | ||||||||
\(626\) | 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 | ||||||||
\(635\) | 599.627i | 0.944294i | ||||||||
\(636\) | 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 | \(-0.713082\pi\) | ||||
−0.620529 | + | 0.784184i | \(0.713082\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1312.00 | + | 463.862i | 2.03411 | + | 0.719166i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 147.078i | 0.227323i | 0.993520 | + | 0.113662i | \(0.0362580\pi\) | ||||
−0.993520 | + | 0.113662i | \(0.963742\pi\) | |||||||
\(648\) | 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 | \(-0.920591\pi\) | ||
0.969043 | − | 0.246892i | \(-0.0794092\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.0000 | 0.0488550 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −574.000 | − | 463.862i | −0.873668 | − | 0.706031i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 797.616i | − | 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 | ||||||||
\(665\) | − | 67.8823i | − | 0.102079i | ||||||
\(666\) | 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 | \(-0.491959\pi\) | ||||
0.0252600 | + | 0.999681i | \(0.491959\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 161.000 | − | 98.9949i | 0.238519 | − | 0.146659i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 401.637i | − | 0.593259i | −0.954993 | − | 0.296630i | \(-0.904137\pi\) | ||
0.954993 | − | 0.296630i | \(-0.0958627\pi\) | |||||||
\(678\) | 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 | \(-0.969636\pi\) | ||
0.995454 | − | 0.0952472i | \(-0.0303641\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 576.000 | 0.840876 | ||||||||
\(686\) | 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 | ||||||||
\(695\) | − | 441.235i | − | 0.634870i | ||||||
\(696\) | 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 | ||||||||
\(705\) | −384.000 | + | 1086.12i | −0.544681 | + | 1.54059i | ||||
\(706\) | 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 | ||||||||
\(715\) | −320.000 | −0.447552 | ||||||||
\(716\) | 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 | ||||||||
\(725\) | − | 118.794i | − | 0.163854i | ||||||
\(726\) | 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 | ||||||||
\(731\) | − | 1855.45i | − | 2.53823i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −214.000 | −0.291951 | −0.145975 | − | 0.989288i | \(-0.546632\pi\) | ||||
−0.145975 | + | 0.989288i | \(0.546632\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −208.000 | − | 73.5391i | −0.282993 | − | 0.100053i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.3137i | 0.0153510i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −958.000 | −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 | \(0.236982\pi\) | ||||
−0.735427 | + | 0.677604i | \(0.763018\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −928.000 | −1.24564 | ||||||||
\(746\) | 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 | ||||||||
\(755\) | 1233.19i | 1.63337i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 602.000 | 0.795244 | 0.397622 | − | 0.917549i | \(-0.369835\pi\) | ||||
0.397622 | + | 0.917549i | \(0.369835\pi\) | |||||||
\(758\) | 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 | ||||||||
\(765\) | −896.000 | − | 724.077i | −1.17124 | − | 0.946506i | ||||
\(766\) | 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 | \(0.0385293\pi\) | ||||
−0.992683 | + | 0.120748i | \(0.961471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 154.000 | 0.198710 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 36.0000 | − | 101.823i | 0.0463320 | − | 0.131047i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 67.8823i | 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 | ||||||||
\(785\) | − | 486.489i | − | 0.619732i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 514.000 | 0.653113 | 0.326557 | − | 0.945178i | \(-0.394112\pi\) | ||||
0.326557 | + | 0.945178i | \(0.394112\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −608.000 | − | 214.960i | −0.770596 | − | 0.272447i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 407.294i | 0.514910i |