Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,3,Mod(319,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("320.319");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(8.71936845953\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.3 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.319 |
Dual form | 320.3.h.e.319.4 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | 0.942809 | 0.471405 | − | 0.881917i | \(-0.343747\pi\) | ||||
0.471405 | + | 0.881917i | \(0.343747\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | − | 4.89898i | 0.200000 | − | 0.979796i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.48528 | −1.21218 | −0.606092 | − | 0.795395i | \(-0.707263\pi\) | ||||
−0.606092 | + | 0.795395i | \(0.707263\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.111111 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 13.8564i | − | 1.25967i | −0.776728 | − | 0.629837i | \(-0.783122\pi\) | ||
0.776728 | − | 0.629837i | \(-0.216878\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 9.79796i | − | 0.753689i | −0.926277 | − | 0.376845i | \(-0.877009\pi\) | ||
0.926277 | − | 0.376845i | \(-0.122991\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.82843 | − | 13.8564i | 0.188562 | − | 0.923760i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 19.5959i | − | 1.15270i | −0.817203 | − | 0.576351i | \(-0.804476\pi\) | ||
0.817203 | − | 0.576351i | \(-0.195524\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.8564i | 0.729285i | 0.931148 | + | 0.364642i | \(0.118809\pi\) | ||||
−0.931148 | + | 0.364642i | \(0.881191\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −24.0000 | −1.14286 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 25.4558 | 1.10678 | 0.553388 | − | 0.832924i | \(-0.313335\pi\) | ||||
0.553388 | + | 0.832924i | \(0.313335\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.0000 | − | 9.79796i | −0.920000 | − | 0.391918i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −28.2843 | −1.04757 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.0000 | 0.758621 | 0.379310 | − | 0.925270i | \(-0.376161\pi\) | ||||
0.379310 | + | 0.925270i | \(0.376161\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 55.4256i | 1.78792i | 0.448143 | + | 0.893962i | \(0.352085\pi\) | ||||
−0.448143 | + | 0.893962i | \(0.647915\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 39.1918i | − | 1.18763i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.48528 | + | 41.5692i | −0.242437 | + | 1.18769i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 48.9898i | − | 1.32405i | −0.749482 | − | 0.662024i | \(-0.769698\pi\) | ||
0.749482 | − | 0.662024i | \(-0.230302\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 27.7128i | − | 0.710585i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 22.0000 | 0.536585 | 0.268293 | − | 0.963337i | \(-0.413541\pi\) | ||||
0.268293 | + | 0.963337i | \(0.413541\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 59.3970 | 1.38132 | 0.690662 | − | 0.723177i | \(-0.257319\pi\) | ||||
0.690662 | + | 0.723177i | \(0.257319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | + | 4.89898i | −0.0222222 | + | 0.108866i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.48528 | −0.180538 | −0.0902690 | − | 0.995917i | \(-0.528773\pi\) | ||||
−0.0902690 | + | 0.995917i | \(0.528773\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 23.0000 | 0.469388 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 55.4256i | − | 1.08678i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 29.3939i | − | 0.554601i | −0.960783 | − | 0.277301i | \(-0.910560\pi\) | ||
0.960783 | − | 0.277301i | \(-0.0894398\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −67.8823 | − | 13.8564i | −1.23422 | − | 0.251935i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 39.1918i | 0.687576i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 13.8564i | − | 0.234854i | −0.993081 | − | 0.117427i | \(-0.962535\pi\) | ||
0.993081 | − | 0.117427i | \(-0.0374647\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −46.0000 | −0.754098 | −0.377049 | − | 0.926193i | \(-0.623061\pi\) | ||||
−0.377049 | + | 0.926193i | \(0.623061\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.48528 | 0.134687 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −48.0000 | − | 9.79796i | −0.738462 | − | 0.150738i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 59.3970 | 0.886522 | 0.443261 | − | 0.896393i | \(-0.353822\pi\) | ||||
0.443261 | + | 0.896393i | \(0.353822\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 72.0000 | 1.04348 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 27.7128i | − | 0.390321i | −0.980771 | − | 0.195161i | \(-0.937477\pi\) | ||
0.980771 | − | 0.195161i | \(-0.0625228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 78.3837i | 1.07375i | 0.843662 | + | 0.536874i | \(0.180395\pi\) | ||||
−0.843662 | + | 0.536874i | \(0.819605\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −65.0538 | − | 27.7128i | −0.867384 | − | 0.369504i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 117.576i | 1.52695i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −71.0000 | −0.876543 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −76.3675 | −0.920091 | −0.460045 | − | 0.887895i | \(-0.652167\pi\) | ||||
−0.460045 | + | 0.887895i | \(0.652167\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −96.0000 | − | 19.5959i | −1.12941 | − | 0.230540i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 62.2254 | 0.715234 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 146.000 | 1.64045 | 0.820225 | − | 0.572041i | \(-0.193848\pi\) | ||||
0.820225 | + | 0.572041i | \(0.193848\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 83.1384i | 0.913609i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 156.767i | 1.68567i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 67.8823 | + | 13.8564i | 0.714550 | + | 0.145857i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 58.7878i | − | 0.606059i | −0.952981 | − | 0.303030i | \(-0.902002\pi\) | ||
0.952981 | − | 0.303030i | \(-0.0979981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.8564i | 0.139964i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 70.0000 | 0.693069 | 0.346535 | − | 0.938037i | \(-0.387358\pi\) | ||||
0.346535 | + | 0.938037i | \(0.387358\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 25.4558 | 0.247144 | 0.123572 | − | 0.992336i | \(-0.460565\pi\) | ||||
0.123572 | + | 0.992336i | \(0.460565\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −24.0000 | + | 117.576i | −0.228571 | + | 1.11977i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −42.4264 | −0.396508 | −0.198254 | − | 0.980151i | \(-0.563527\pi\) | ||||
−0.198254 | + | 0.980151i | \(0.563527\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 146.000 | 1.33945 | 0.669725 | − | 0.742609i | \(-0.266412\pi\) | ||||
0.669725 | + | 0.742609i | \(0.266412\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 138.564i | − | 1.24832i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 39.1918i | 0.346830i | 0.984849 | + | 0.173415i | \(0.0554803\pi\) | ||||
−0.984849 | + | 0.173415i | \(0.944520\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.4558 | − | 124.708i | 0.221355 | − | 1.08441i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.79796i | 0.0837432i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 166.277i | 1.39728i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −71.0000 | −0.586777 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 62.2254 | 0.505898 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −71.0000 | + | 102.879i | −0.568000 | + | 0.823029i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −110.309 | −0.868572 | −0.434286 | − | 0.900775i | \(-0.642999\pi\) | ||||
−0.434286 | + | 0.900775i | \(0.642999\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 168.000 | 1.30233 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 180.133i | 1.37506i | 0.726154 | + | 0.687532i | \(0.241306\pi\) | ||||
−0.726154 | + | 0.687532i | \(0.758694\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 117.576i | − | 0.884026i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −28.2843 | + | 138.564i | −0.209513 | + | 1.02640i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 215.555i | 1.57339i | 0.617339 | + | 0.786697i | \(0.288211\pi\) | ||||
−0.617339 | + | 0.786697i | \(0.711789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.8564i | − | 0.0996864i | −0.998757 | − | 0.0498432i | \(-0.984128\pi\) | ||
0.998757 | − | 0.0498432i | \(-0.0158722\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.0000 | −0.170213 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −135.765 | −0.949402 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.0000 | − | 107.778i | 0.151724 | − | 0.743293i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 65.0538 | 0.442543 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000 | 0.0134228 | 0.00671141 | − | 0.999977i | \(-0.497864\pi\) | ||||
0.00671141 | + | 0.999977i | \(0.497864\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 27.7128i | − | 0.183529i | −0.995781 | − | 0.0917643i | \(-0.970749\pi\) | ||
0.995781 | − | 0.0917643i | \(-0.0292506\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 19.5959i | 0.128078i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 271.529 | + | 55.4256i | 1.75180 | + | 0.357585i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 68.5857i | − | 0.436852i | −0.975854 | − | 0.218426i | \(-0.929908\pi\) | ||
0.975854 | − | 0.218426i | \(-0.0700922\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 83.1384i | − | 0.522883i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −216.000 | −1.34161 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −110.309 | −0.676740 | −0.338370 | − | 0.941013i | \(-0.609876\pi\) | ||||
−0.338370 | + | 0.941013i | \(0.609876\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −192.000 | − | 39.1918i | −1.16364 | − | 0.237526i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 93.3381 | 0.558911 | 0.279455 | − | 0.960159i | \(-0.409846\pi\) | ||||
0.279455 | + | 0.960159i | \(0.409846\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 73.0000 | 0.431953 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 13.8564i | − | 0.0810316i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 48.9898i | 0.283178i | 0.989926 | + | 0.141589i | \(0.0452211\pi\) | ||||
−0.989926 | + | 0.141589i | \(0.954779\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 195.161 | + | 83.1384i | 1.11521 | + | 0.475077i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 39.1918i | − | 0.221423i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 263.272i | − | 1.47079i | −0.677638 | − | 0.735396i | \(-0.736996\pi\) | ||
0.677638 | − | 0.735396i | \(-0.263004\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.0000 | −0.143646 | −0.0718232 | − | 0.997417i | \(-0.522882\pi\) | ||||
−0.0718232 | + | 0.997417i | \(0.522882\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −130.108 | −0.710971 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −240.000 | − | 48.9898i | −1.29730 | − | 0.264810i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −271.529 | −1.45203 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 240.000 | 1.26984 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 110.851i | − | 0.580373i | −0.956970 | − | 0.290187i | \(-0.906283\pi\) | ||
0.956970 | − | 0.290187i | \(-0.0937174\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 333.131i | − | 1.72607i | −0.505148 | − | 0.863033i | \(-0.668562\pi\) | ||
0.505148 | − | 0.863033i | \(-0.331438\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −135.765 | − | 27.7128i | −0.696228 | − | 0.142117i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 107.778i | − | 0.547094i | −0.961859 | − | 0.273547i | \(-0.911803\pi\) | ||
0.961859 | − | 0.273547i | \(-0.0881969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 249.415i | − | 1.25334i | −0.779283 | − | 0.626672i | \(-0.784417\pi\) | ||
0.779283 | − | 0.626672i | \(-0.215583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 168.000 | 0.835821 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −186.676 | −0.919587 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.0000 | − | 107.778i | 0.107317 | − | 0.525744i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −25.4558 | −0.122975 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 192.000 | 0.918660 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 96.9948i | − | 0.459691i | −0.973227 | − | 0.229846i | \(-0.926178\pi\) | ||
0.973227 | − | 0.229846i | \(-0.0738221\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 78.3837i | − | 0.367998i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 59.3970 | − | 290.985i | 0.276265 | − | 1.35342i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 470.302i | − | 2.16729i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 221.703i | 1.01234i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −192.000 | −0.868778 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 229.103 | 1.02737 | 0.513683 | − | 0.857980i | \(-0.328281\pi\) | ||||
0.513683 | + | 0.857980i | \(0.328281\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 23.0000 | + | 9.79796i | 0.102222 | + | 0.0435465i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 296.985 | 1.30830 | 0.654152 | − | 0.756363i | \(-0.273026\pi\) | ||||
0.654152 | + | 0.756363i | \(0.273026\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 70.0000 | 0.305677 | 0.152838 | − | 0.988251i | \(-0.451159\pi\) | ||||
0.152838 | + | 0.988251i | \(0.451159\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 332.554i | 1.43963i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 156.767i | 0.672821i | 0.941715 | + | 0.336411i | \(0.109213\pi\) | ||||
−0.941715 | + | 0.336411i | \(0.890787\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.48528 | + | 41.5692i | −0.0361076 | + | 0.176890i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 332.554i | 1.39144i | 0.718314 | + | 0.695719i | \(0.244914\pi\) | ||||
−0.718314 | + | 0.695719i | \(0.755086\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −122.000 | −0.506224 | −0.253112 | − | 0.967437i | \(-0.581454\pi\) | ||||
−0.253112 | + | 0.967437i | \(0.581454\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 53.7401 | 0.221153 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.0000 | − | 112.677i | 0.0938776 | − | 0.459904i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 135.765 | 0.549654 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −216.000 | −0.867470 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 290.985i | − | 1.15930i | −0.814865 | − | 0.579650i | \(-0.803189\pi\) | ||
0.814865 | − | 0.579650i | \(-0.196811\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 352.727i | − | 1.39418i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −271.529 | − | 55.4256i | −1.06482 | − | 0.217355i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 78.3837i | − | 0.304995i | −0.988304 | − | 0.152497i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152497i | \(-0.0487316\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 415.692i | 1.60499i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.0000 | −0.0842912 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −347.897 | −1.32280 | −0.661400 | − | 0.750033i | \(-0.730038\pi\) | ||||
−0.661400 | + | 0.750033i | \(0.730038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −144.000 | − | 29.3939i | −0.543396 | − | 0.110920i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 412.950 | 1.54663 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −142.000 | −0.527881 | −0.263941 | − | 0.964539i | \(-0.585022\pi\) | ||||
−0.263941 | + | 0.964539i | \(0.585022\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 332.554i | 1.22714i | 0.789642 | + | 0.613568i | \(0.210266\pi\) | ||||
−0.789642 | + | 0.613568i | \(0.789734\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 235.151i | 0.861359i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −135.765 | + | 318.697i | −0.493689 | + | 1.15890i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 88.1816i | − | 0.318345i | −0.987251 | − | 0.159173i | \(-0.949117\pi\) | ||
0.987251 | − | 0.159173i | \(-0.0508826\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 55.4256i | − | 0.198658i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 406.000 | 1.44484 | 0.722420 | − | 0.691455i | \(-0.243030\pi\) | ||||
0.722420 | + | 0.691455i | \(0.243030\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 93.3381 | 0.329817 | 0.164908 | − | 0.986309i | \(-0.447267\pi\) | ||||
0.164908 | + | 0.986309i | \(0.447267\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 192.000 | + | 39.1918i | 0.673684 | + | 0.137515i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −186.676 | −0.650440 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −95.0000 | −0.328720 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 166.277i | − | 0.571398i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 303.737i | 1.03664i | 0.855186 | + | 0.518322i | \(0.173443\pi\) | ||||
−0.855186 | + | 0.518322i | \(0.826557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −67.8823 | − | 13.8564i | −0.230109 | − | 0.0469709i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 391.918i | 1.31959i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 249.415i | − | 0.834165i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −504.000 | −1.67442 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 197.990 | 0.653432 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −46.0000 | + | 225.353i | −0.150820 | + | 0.738862i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −280.014 | −0.912099 | −0.456049 | − | 0.889955i | \(-0.650736\pi\) | ||||
−0.456049 | + | 0.889955i | \(0.650736\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 72.0000 | 0.233010 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 138.564i | − | 0.445544i | −0.974871 | − | 0.222772i | \(-0.928490\pi\) | ||
0.974871 | − | 0.222772i | \(-0.0715105\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 607.473i | − | 1.94081i | −0.241484 | − | 0.970405i | \(-0.577634\pi\) | ||
0.241484 | − | 0.970405i | \(-0.422366\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.48528 | − | 41.5692i | 0.0269374 | − | 0.131966i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 68.5857i | 0.216359i | 0.994131 | + | 0.108179i | \(0.0345021\pi\) | ||||
−0.994131 | + | 0.108179i | \(0.965498\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 304.841i | − | 0.955614i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −120.000 | −0.373832 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 271.529 | 0.840647 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −96.0000 | + | 225.353i | −0.295385 | + | 0.693394i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 412.950 | 1.26285 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 72.0000 | 0.218845 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 180.133i | − | 0.544209i | −0.962268 | − | 0.272105i | \(-0.912280\pi\) | ||
0.962268 | − | 0.272105i | \(-0.0877197\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 48.9898i | 0.147117i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 59.3970 | − | 290.985i | 0.177304 | − | 0.868611i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 470.302i | 1.39555i | 0.716315 | + | 0.697777i | \(0.245828\pi\) | ||||
−0.716315 | + | 0.697777i | \(0.754172\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 110.851i | 0.326995i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 768.000 | 2.25220 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 220.617 | 0.643199 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 72.0000 | − | 352.727i | 0.208696 | − | 1.02240i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −619.426 | −1.78509 | −0.892544 | − | 0.450960i | \(-0.851082\pi\) | ||||
−0.892544 | + | 0.450960i | \(0.851082\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 214.000 | 0.613181 | 0.306590 | − | 0.951842i | \(-0.400812\pi\) | ||||
0.306590 | + | 0.951842i | \(0.400812\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 277.128i | 0.789539i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 352.727i | 0.999225i | 0.866249 | + | 0.499613i | \(0.166524\pi\) | ||||
−0.866249 | + | 0.499613i | \(0.833476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −135.765 | − | 27.7128i | −0.382435 | − | 0.0780643i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 470.302i | 1.31737i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.7128i | 0.0771945i | 0.999255 | + | 0.0385972i | \(0.0122889\pi\) | ||||
−0.999255 | + | 0.0385972i | \(0.987711\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 169.000 | 0.468144 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −200.818 | −0.553219 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 384.000 | + | 78.3837i | 1.05205 | + | 0.214750i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −246.073 | −0.670499 | −0.335250 | − | 0.942129i | \(-0.608821\pi\) | ||||
−0.335250 | + | 0.942129i | \(0.608821\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.0000 | −0.0596206 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 249.415i | 0.672278i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 382.120i | 1.02445i | 0.858851 | + | 0.512226i | \(0.171179\pi\) | ||||
−0.858851 | + | 0.512226i | \(0.828821\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −200.818 | + | 290.985i | −0.535516 | + | 0.775959i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 215.555i | − | 0.571764i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 290.985i | − | 0.767769i | −0.923381 | − | 0.383885i | \(-0.874586\pi\) | ||
0.923381 | − | 0.383885i | \(-0.125414\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −312.000 | −0.818898 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 568.514 | 1.48437 | 0.742185 | − | 0.670195i | \(-0.233789\pi\) | ||||
0.742185 | + | 0.670195i | \(0.233789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 576.000 | + | 117.576i | 1.49610 | + | 0.305391i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −59.3970 | −0.153481 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −670.000 | −1.72237 | −0.861183 | − | 0.508296i | \(-0.830276\pi\) | ||||
−0.861183 | + | 0.508296i | \(0.830276\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 498.831i | − | 1.27578i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 509.494i | 1.29642i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 362.524i | − | 0.913160i | −0.889682 | − | 0.456580i | \(-0.849074\pi\) | ||
0.889682 | − | 0.456580i | \(-0.150926\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 332.554i | − | 0.833468i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.00498753 | 0.00249377 | − | 0.999997i | \(-0.499206\pi\) | ||||
0.00249377 | + | 0.999997i | \(0.499206\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 543.058 | 1.34754 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −71.0000 | + | 347.828i | −0.175309 | + | 0.858833i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −678.823 | −1.66787 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −650.000 | −1.58924 | −0.794621 | − | 0.607106i | \(-0.792330\pi\) | ||||
−0.794621 | + | 0.607106i | \(0.792330\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 609.682i | 1.48341i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 117.576i | 0.284686i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −76.3675 | + | 374.123i | −0.184018 | + | 0.901501i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 39.1918i | − | 0.0939852i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 540.400i | − | 1.28974i | −0.764293 | − | 0.644869i | \(-0.776912\pi\) | ||
0.764293 | − | 0.644869i | \(-0.223088\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 482.000 | 1.14489 | 0.572447 | − | 0.819942i | \(-0.305994\pi\) | ||||
0.572447 | + | 0.819942i | \(0.305994\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.48528 | 0.0200598 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −192.000 | + | 450.706i | −0.451765 | + | 1.06048i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 390.323 | 0.914105 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −384.000 | −0.895105 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 221.703i | − | 0.514391i | −0.966359 | − | 0.257195i | \(-0.917202\pi\) | ||
0.966359 | − | 0.257195i | \(-0.0827984\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 568.282i | 1.31243i | 0.754575 | + | 0.656214i | \(0.227843\pi\) | ||||
−0.754575 | + | 0.656214i | \(0.772157\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 62.2254 | − | 304.841i | 0.143047 | − | 0.700784i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 352.727i | 0.807155i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 526.543i | 1.19942i | 0.800219 | + | 0.599708i | \(0.204717\pi\) | ||||
−0.800219 | + | 0.599708i | \(0.795283\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −23.0000 | −0.0521542 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 432.749 | 0.976861 | 0.488430 | − | 0.872603i | \(-0.337570\pi\) | ||||
0.488430 | + | 0.872603i | \(0.337570\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 146.000 | − | 715.251i | 0.328090 | − | 1.60731i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.65685 | 0.0126552 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.0000 | −0.0579065 | −0.0289532 | − | 0.999581i | \(-0.509217\pi\) | ||||
−0.0289532 | + | 0.999581i | \(0.509217\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 304.841i | − | 0.675922i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 78.3837i | − | 0.173032i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 407.294 | + | 83.1384i | 0.895151 | + | 0.182722i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 137.171i | − | 0.300156i | −0.988674 | − | 0.150078i | \(-0.952047\pi\) | ||
0.988674 | − | 0.150078i | \(-0.0479525\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 554.256i | 1.20753i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 502.000 | 1.08894 | 0.544469 | − | 0.838781i | \(-0.316731\pi\) | ||||
0.544469 | + | 0.838781i | \(0.316731\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −823.072 | −1.77769 | −0.888847 | − | 0.458204i | \(-0.848493\pi\) | ||||
−0.888847 | + | 0.458204i | \(0.848493\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 768.000 | + | 156.767i | 1.65161 | + | 0.337134i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −178.191 | −0.381565 | −0.190783 | − | 0.981632i | \(-0.561103\pi\) | ||||
−0.190783 | + | 0.981632i | \(0.561103\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −504.000 | −1.07463 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 193.990i | − | 0.411868i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 823.029i | − | 1.74002i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 135.765 | − | 318.697i | 0.285820 | − | 0.670942i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.3939i | 0.0616224i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 775.959i | 1.61996i | 0.586460 | + | 0.809978i | \(0.300521\pi\) | ||||
−0.586460 | + | 0.809978i | \(0.699479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −480.000 | −0.997921 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −610.940 | −1.26489 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −288.000 | − | 58.7878i | −0.593814 | − | 0.121212i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −347.897 | −0.714367 | −0.357183 | − | 0.934034i | \(-0.616263\pi\) | ||||
−0.357183 | + | 0.934034i | \(0.616263\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −312.000 | −0.638037 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 928.379i | 1.89079i | 0.325923 | + | 0.945396i | \(0.394325\pi\) | ||||
−0.325923 | + | 0.945396i | \(0.605675\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 431.110i | − | 0.874463i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 67.8823 | + | 13.8564i | 0.137136 | + | 0.0279927i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 235.151i | 0.473141i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 512.687i | 1.02743i | 0.857961 | + | 0.513714i | \(0.171731\pi\) | ||||
−0.857961 | + | 0.513714i | \(0.828269\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 264.000 | 0.526946 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 704.278 | 1.40016 | 0.700078 | − | 0.714066i | \(-0.253149\pi\) | ||||
0.700078 | + | 0.714066i | \(0.253149\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 70.0000 | − | 342.929i | 0.138614 | − | 0.679066i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 206.475 | 0.407249 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −170.000 | −0.333988 | −0.166994 | − | 0.985958i | \(-0.553406\pi\) | ||||
−0.166994 | + | 0.985958i | \(0.553406\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 665.108i | − | 1.30158i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 391.918i | − | 0.763973i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.4558 | − | 124.708i | 0.0494288 | − | 0.242151i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 117.576i | 0.227419i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 138.564i | 0.266983i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 722.000 | 1.38580 | 0.692898 | − | 0.721035i | \(-0.256333\pi\) | ||||
0.692898 | + | 0.721035i | \(0.256333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −246.073 | −0.470503 | −0.235252 | − | 0.971935i | \(-0.575591\pi\) | ||||
−0.235252 | + | 0.971935i | \(0.575591\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 552.000 | + | 235.151i | 1.05143 | + | 0.447907i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1086.12 | 2.06094 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 119.000 | 0.224953 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.8564i | 0.0260949i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 215.555i | − | 0.404419i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −42.4264 | + | 207.846i | −0.0793017 | + | 0.388497i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 744.645i | − | 1.38668i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 318.697i | − | 0.591275i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −362.000 | −0.669131 | −0.334566 | − | 0.942372i | \(-0.608590\pi\) | ||||
−0.334566 | + | 0.942372i | \(0.608590\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −73.5391 | −0.135431 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 146.000 | − | 715.251i | 0.267890 | − | 1.31239i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.4264 | −0.0775620 | −0.0387810 | − | 0.999248i | \(-0.512347\pi\) | ||||
−0.0387810 | + | 0.999248i | \(0.512347\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 46.0000 | 0.0837887 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 304.841i | 0.553250i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −678.823 | − | 138.564i | −1.22310 | − | 0.249665i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 656.463i | − | 1.17857i | −0.807925 | − | 0.589285i | \(-0.799410\pi\) | ||
0.807925 | − | 0.589285i | \(-0.200590\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 581.969i | − | 1.04109i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −768.000 | −1.36898 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −517.602 | −0.919364 | −0.459682 | − | 0.888083i | \(-0.652037\pi\) | ||||
−0.459682 | + | 0.888083i | \(0.652037\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 192.000 | + | 39.1918i | 0.339823 | + | 0.0693661i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 602.455 | 1.06253 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −842.000 | −1.47979 | −0.739895 | − | 0.672723i | \(-0.765125\pi\) | ||||
−0.739895 | + | 0.672723i | \(0.765125\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 401.836i | − | 0.703740i | −0.936049 | − | 0.351870i | \(-0.885546\pi\) | ||
0.936049 | − | 0.351870i | \(-0.114454\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 313.535i | − | 0.547181i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −585.484 | − | 249.415i | −1.01823 | − | 0.433766i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.1918i | 0.0679235i | 0.999423 | + | 0.0339617i | \(0.0108124\pi\) | ||||
−0.999423 | + | 0.0339617i | \(0.989188\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 942.236i | − | 1.62735i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 648.000 | 1.11532 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −407.294 | −0.698617 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 48.0000 | + | 9.79796i | 0.0820513 | + | 0.0167486i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 59.3970 | 0.101187 | 0.0505937 | − | 0.998719i | \(-0.483889\pi\) | ||||
0.0505937 | + | 0.998719i | \(0.483889\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −768.000 | −1.30390 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 304.841i | − | 0.515805i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 509.494i | − | 0.859180i | −0.903024 | − | 0.429590i | \(-0.858658\pi\) | ||
0.903024 | − | 0.429590i | \(-0.141342\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 814.587 | + | 166.277i | 1.36905 | + | 0.279457i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 705.453i | − | 1.18166i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 859.097i | − | 1.43422i | −0.696961 | − | 0.717110i | \(-0.745465\pi\) | ||
0.696961 | − | 0.717110i | \(-0.254535\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 598.000 | 0.995008 | 0.497504 | − | 0.867462i | \(-0.334250\pi\) | ||||
0.497504 | + | 0.867462i | \(0.334250\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −59.3970 | −0.0985024 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −71.0000 | + | 347.828i | −0.117355 | + | 0.574922i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 127.279 | 0.209686 | 0.104843 | − | 0.994489i | \(-0.466566\pi\) | ||||
0.104843 | + | 0.994489i | \(0.466566\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −528.000 | −0.866995 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 83.1384i | 0.136069i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 205.757i | 0.335656i | 0.985816 | + | 0.167828i | \(0.0536753\pi\) | ||||
−0.985816 | + | 0.167828i | \(0.946325\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 62.2254 | − | 304.841i | 0.101180 | − | 0.495676i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 431.110i | 0.698720i | 0.936989 | + | 0.349360i | \(0.113601\pi\) | ||||
−0.936989 | + | 0.349360i | \(0.886399\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.5692i | 0.0671554i | 0.999436 | + | 0.0335777i | \(0.0106901\pi\) | ||||
−0.999436 | + | 0.0335777i | \(0.989310\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −720.000 | −1.15942 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1238.85 | −1.98853 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 433.000 | + | 450.706i | 0.692800 | + | 0.721130i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 543.058 | 0.866121 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −960.000 | −1.52623 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 969.948i | 1.53716i | 0.639753 | + | 0.768580i | \(0.279037\pi\) | ||||
−0.639753 | + | 0.768580i | \(0.720963\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 274.343i | − | 0.433401i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −110.309 | + | 540.400i | −0.173714 | + | 0.851023i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 225.353i | − | 0.353772i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.7128i | 0.0433690i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 166.000 | 0.258970 | 0.129485 | − | 0.991581i | \(-0.458668\pi\) | ||||
0.129485 | + | 0.991581i | \(0.458668\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −144.250 | −0.224339 | −0.112169 | − | 0.993689i | \(-0.535780\pi\) | ||||
−0.112169 | + | 0.993689i | \(0.535780\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 168.000 | − | 823.029i | 0.260465 | − | 1.27601i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −687.308 | −1.06230 | −0.531150 | − | 0.847278i | \(-0.678240\pi\) | ||||
−0.531150 | + | 0.847278i | \(0.678240\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −192.000 | −0.295840 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1330.22i | − | 2.04334i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.3939i | 0.0450136i | 0.999747 | + | 0.0225068i | \(0.00716474\pi\) | ||||
−0.999747 | + | 0.0225068i | \(0.992835\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 882.469 | + | 180.133i | 1.34728 | + | 0.275013i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 78.3837i | − | 0.119305i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 623.538i | 0.946189i | 0.881012 | + | 0.473094i | \(0.156863\pi\) | ||||
−0.881012 | + | 0.473094i | \(0.843137\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 98.0000 | 0.148260 | 0.0741301 | − | 0.997249i | \(-0.476382\pi\) | ||||
0.0741301 | + | 0.997249i | \(0.476382\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −543.058 | −0.819092 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −576.000 | − | 117.576i | −0.866165 | − | 0.176805i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 560.029 | 0.839623 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 648.000 | 0.968610 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 637.395i | 0.949918i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 489.898i | 0.727932i | 0.931412 | + | 0.363966i | \(0.118577\pi\) | ||||
−0.931412 | + | 0.363966i | \(0.881423\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 650.538 | + | 277.128i | 0.963760 | + | 0.410560i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 146.969i | − | 0.217089i | −0.994092 | − | 0.108545i | \(-0.965381\pi\) | ||
0.994092 | − | 0.108545i | \(-0.0346190\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 498.831i | 0.734655i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 840.000 | 1.23348 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 398.808 | 0.583907 | 0.291953 | − | 0.956433i | \(-0.405695\pi\) | ||||
0.291953 | + | 0.956433i | \(0.405695\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1056.00 | + | 215.555i | 1.54161 | + | 0.314679i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 197.990 | 0.288195 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −288.000 | −0.417997 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 789.815i | 1.14300i | 0.820601 | + | 0.571502i | \(0.193639\pi\) | ||||
−0.820601 | + | 0.571502i | \(0.806361\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 117.576i | − | 0.169662i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −67.8823 | − | 13.8564i | −0.0976723 | − | 0.0199373i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 431.110i | − | 0.618523i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 443.405i | 0.634342i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −718.000 | −1.02425 | −0.512126 | − | 0.858911i | \(-0.671142\pi\) | ||||
−0.512126 | + | 0.858911i | \(0.671142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 678.823 | 0.965608 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.0000 | + | 117.576i | −0.0340426 | + | 0.166774i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −593.970 | −0.840127 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 838.000 | 1.18195 | 0.590973 | − | 0.806691i | \(-0.298744\pi\) | ||||
0.590973 | + | 0.806691i | \(0.298744\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1410.91i | 1.97883i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −135.765 | + | 665.108i | −0.189880 | + | 0.930220i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 940.604i | 1.31186i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 221.703i | 0.308348i | 0.988044 | + | 0.154174i | \(0.0492717\pi\) | ||||
−0.988044 | + | 0.154174i | \(0.950728\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −216.000 | −0.299584 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −345.068 | −0.477273 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −506.000 | − | 215.555i | −0.697931 | − | 0.297317i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −347.897 | −0.478537 | −0.239269 | − | 0.970953i | \(-0.576908\pi\) | ||||
−0.239269 | + | 0.970953i | \(0.576908\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 791.000 | 1.08505 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1163.94i | − | 1.59225i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 676.059i | 0.922318i | 0.887317 | + | 0.461159i | \(0.152566\pi\) | ||||
−0.887317 | + | 0.461159i | \(0.847434\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 65.0538 | − | 318.697i | 0.0885086 | − | 0.433602i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 823.029i | − | 1.11673i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 235.559i | 0.318754i | 0.987218 | + | 0.159377i | \(0.0509485\pi\) | ||||
−0.987218 | + | 0.159377i | \(0.949052\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 384.000 | 0.518219 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1349.16 | 1.81583 | 0.907914 | − | 0.419157i | \(-0.137674\pi\) | ||||
0.907914 | + | 0.419157i | \(0.137674\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00000 | − | 9.79796i | 0.00268456 | − | 0.0131516i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 76.3675 | 0.102232 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 360.000 | 0.480641 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1163.94i | 1.54985i | 0.632053 | + | 0.774926i | \(0.282213\pi\) | ||||
−0.632053 | + | 0.774926i | \(0.717787\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 823.029i | − | 1.09300i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −135.765 | − | 27.7128i | −0.179821 | − | 0.0367057i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1205.15i | 1.59201i | 0.605292 | + | 0.796003i | \(0.293056\pi\) | ||||
−0.605292 | + | 0.796003i | \(0.706944\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 997.661i | − | 1.31444i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 530.000 | 0.696452 | 0.348226 | − | 0.937411i | \(-0.386784\pi\) | ||||
0.348226 | + | 0.937411i | \(0.386784\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1238.85 | −1.62366 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 96.0000 | + | 19.5959i | 0.125490 | + | 0.0256156i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −135.765 | −0.177007 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 386.000 | 0.501951 | 0.250975 | − | 0.967993i | \(-0.419249\pi\) | ||||
0.250975 | + | 0.967993i | \(0.419249\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 221.703i | − | 0.287552i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 695.655i | − | 0.899942i | −0.893043 | − | 0.449971i | \(-0.851434\pi\) | ||
0.893043 | − | 0.449971i | \(-0.148566\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 543.058 | − | 1274.79i | 0.700720 | − | 1.64489i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1175.76i | 1.51320i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 304.841i | 0.391323i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −384.000 | −0.491677 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −622.254 | −0.794705 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −336.000 | − | 68.5857i | −0.428025 | − | 0.0873703i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1298.25 | −1.64962 | −0.824808 | − | 0.565413i | \(-0.808717\pi\) | ||||
−0.824808 | + | 0.565413i | \(0.808717\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −984.000 | −1.24715 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 332.554i | − | 0.420422i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 450.706i | 0.568356i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −407.294 | − | 83.1384i | −0.512319 | − | 0.104577i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1361.92i | 1.70880i | 0.519613 | + | 0.854402i | \(0.326076\pi\) | ||||
−0.519613 | + | 0.854402i | \(0.673924\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 166.277i | 0.208106i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −146.000 | −0.182272 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1086.12 | 1.35257 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −216.000 | + | 1058.18i | −0.268323 | + | 1.31451i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −401.637 | −0.497691 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1006.00 | −1.24351 | −0.621755 | − | 0.783212i | \(-0.713580\pi\) | ||||
−0.621755 | + | 0.783212i | \(0.713580\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 651.251i | 0.803022i | 0.915854 | + | 0.401511i | \(0.131515\pi\) | ||||
−0.915854 | + | 0.401511i | \(0.868485\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 940.604i | 1.15695i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −110.309 | + | 540.400i | −0.135348 | + | 0.663067i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 823.029i | 1.00738i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 83.1384i | − | 0.101512i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 482.000 | 0.587089 | 0.293544 | − | 0.955945i | \(-0.405165\pi\) | ||||
0.293544 | + | 0.955945i | \(0.405165\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 636.396 | 0.773264 | 0.386632 | − | 0.922234i | \(-0.373638\pi\) | ||||
0.386632 | + | 0.922234i | \(0.373638\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −384.000 | + | 901.412i | −0.465455 | + | 1.09262i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 398.808 | 0.482235 | 0.241117 | − | 0.970496i | \(-0.422486\pi\) | ||||
0.241117 | + | 0.970496i | \(0.422486\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1106.00 | 1.33414 | 0.667069 | − | 0.744996i | \(-0.267549\pi\) | ||||
0.667069 | + | 0.744996i | \(0.267549\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 249.415i | − | 0.300139i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 450.706i | − | 0.541064i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 93.3381 | − | 457.261i | 0.111782 | − | 0.547618i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 1567.67i | − | 1.87297i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 360.267i | 0.429400i | 0.976680 | + | 0.214700i | \(0.0688774\pi\) | ||||
−0.976680 | + | 0.214700i | \(0.931123\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −357.000 | −0.424495 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1148.34 | 1.36221 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 73.0000 | − | 357.626i | 0.0863905 | − | 0.423225i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 602.455 | 0.711281 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 264.000 | 0.310954 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1247.08i | − | 1.46542i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 676.059i | 0.792566i | 0.918128 | + | 0.396283i | \(0.129700\pi\) | ||||
−0.918128 | + | 0.396283i | \(0.870300\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −67.8823 | − | 13.8564i | −0.0793944 | − | 0.0162063i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1077.78i | 1.25761i | 0.777561 | + | 0.628807i | \(0.216457\pi\) | ||||
−0.777561 | + | 0.628807i | \(0.783543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 568.113i | − | 0.661365i | −0.943742 | − | 0.330683i | \(-0.892721\pi\) | ||
0.943742 | − | 0.330683i | \(-0.107279\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −528.000 | −0.613240 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 195.161 | 0.226143 | 0.113072 | − | 0.993587i | \(-0.463931\pi\) | ||||
0.113072 | + | 0.993587i | \(0.463931\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 240.000 | + | 48.9898i | 0.277457 | + | 0.0566356i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −268.701 | −0.309920 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 581.969i | − | 0.668162i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 58.7878i | 0.0673399i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 602.455 | − | 872.954i | 0.688520 | − | 0.997661i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 244.949i | 0.279303i | 0.990201 | + | 0.139652i | \(0.0445983\pi\) | ||||
−0.990201 | + | 0.139652i | \(0.955402\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 859.097i | 0.977357i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 550.000 | 0.624291 | 0.312145 | − | 0.950034i | \(-0.398952\pi\) | ||||
0.312145 | + | 0.950034i | \(0.398952\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 636.396 | 0.720720 | 0.360360 | − | 0.932813i | \(-0.382654\pi\) | ||||
0.360360 | + | 0.932813i | \(0.382654\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −192.000 | − | 39.1918i | −0.216949 | − | 0.0442846i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1230.37 | −1.38711 | −0.693555 | − | 0.720404i | \(-0.743956\pi\) | ||||
−0.693555 | + | 0.720404i | \(0.743956\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 936.000 | 1.05287 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 983.805i | 1.10416i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 117.576i | − | 0.131664i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1289.76 | − | 263.272i | −1.44108 | − | 0.294158i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 705.453i | − | 0.786458i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1219.36i | 1.35636i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −576.000 | −0.639290 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1425.53 | −1.57866 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.0000 | + | 127.373i | −0.0287293 | + | 0.140744i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −585.484 | −0.645518 | −0.322759 | − | 0.946481i | \(-0.604610\pi\) | ||||
−0.322759 | + | 0.946481i | \(0.604610\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −70.0000 | −0.0770077 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 886.810i | − | 0.973447i | −0.873556 | − | 0.486723i | \(-0.838192\pi\) | ||
0.873556 | − | 0.486723i | \(-0.161808\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1058.18i | 1.15901i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −130.108 | + | 637.395i | −0.142194 | + | 0.696606i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1528.48i | − | 1.66683i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 193.990i | − | 0.211088i | −0.994415 | − | 0.105544i | \(-0.966342\pi\) | ||
0.994415 | − | 0.105544i | \(-0.0336584\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −792.000 | −0.859935 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −271.529 | −0.294181 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −480.000 | + | 1126.77i | −0.518919 | + | 1.21812i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.4558 | −0.0274605 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1318.00 | 1.41873 | 0.709365 | − | 0.704841i | \(-0.248982\pi\) | ||||
0.709365 | + | 0.704841i | \(0.248982\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 318.697i | 0.342317i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 391.918i | − | 0.420063i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −271.529 | + | 1330.22i | −0.290405 | + | 1.42269i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 548.686i | 0.585577i | 0.956177 | + | 0.292789i | \(0.0945832\pi\) | ||||
−0.956177 | + | 0.292789i | \(0.905417\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1718.19i | − | 1.82981i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1654.00 | 1.75770 | 0.878852 | − | 0.477094i | \(-0.158310\pi\) | ||||
0.878852 | + | 0.477094i | \(0.158310\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 560.029 | 0.593880 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 240.000 | − | 1175.76i | 0.253968 | − | 1.24419i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1417.04 | 1.49635 | 0.748174 | − | 0.663502i | \(-0.230931\pi\) | ||||
0.748174 | + | 0.663502i | \(0.230931\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 768.000 | 0.809273 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 193.990i | 0.203985i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 137.171i | 0.143936i | 0.997407 | + | 0.0719682i | \(0.0229280\pi\) | ||||
−0.997407 | + | 0.0719682i | \(0.977072\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −543.058 | − | 110.851i | −0.568647 | − | 0.116075i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 862.220i | − | 0.900962i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1829.05i | − | 1.90724i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2111.00 | −2.19667 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.4264 | 0.0440565 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1632.00 | − | 333.131i | −1.69119 | − | 0.345213i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1450.98 | 1.50050 | 0.750250 | − | 0.661154i | \(-0.229933\pi\) | ||||
0.750250 | + | 0.661154i | \(0.229933\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 768.000 | 0.792570 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 817.528i | 0.841944i | 0.907074 | + | 0.420972i | \(0.138311\pi\) | ||||
−0.907074 | + | 0.420972i | \(0.861689\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 117.576i | 0.120838i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −271.529 | + | 637.395i | −0.278491 | + | 0.653738i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1704.84i | − | 1.74498i | −0.488633 | − | 0.872490i | \(-0.662504\pi\) | ||
0.488633 | − | 0.872490i | \(-0.337496\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2023.04i | − | 2.06643i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −146.000 | −0.148828 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 738.219 | 0.750986 | 0.375493 | − | 0.926825i | \(-0.377473\pi\) | ||||
0.375493 | + | 0.926825i | \(0.377473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −528.000 | − | 107.778i | −0.536041 | − | 0.109419i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 203.647 | 0.206329 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1512.00 | 1.52882 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 775.959i | − | 0.783006i | −0.920177 | − | 0.391503i | \(-0.871955\pi\) | ||
0.920177 | − | 0.391503i | \(-0.128045\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 509.494i | − | 0.513085i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1221.88 | − | 249.415i | −1.22802 | − | 0.250669i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1420.70i | 1.42498i | 0.701683 | + | 0.712489i | \(0.252432\pi\) | ||||
−0.701683 | + | 0.712489i | \(0.747568\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1385.64i | 1.38703i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))