Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,3,Mod(639,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.639");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.e (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: | \(34.8774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 639.3 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.639 |
Dual form | 1280.3.e.j.639.8 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 2.82843i | − | 0.942809i | −0.881917 | − | 0.471405i | \(-0.843747\pi\) | ||
0.881917 | − | 0.471405i | \(-0.156253\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.89898 | − | 1.00000i | 0.979796 | − | 0.200000i | ||||
\(6\) | 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 | ||||||||
\(11\) | −13.8564 | −1.25967 | −0.629837 | − | 0.776728i | \(-0.716878\pi\) | ||||
−0.629837 | + | 0.776728i | \(0.716878\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.79796 | −0.753689 | −0.376845 | − | 0.926277i | \(-0.622991\pi\) | ||||
−0.376845 | + | 0.926277i | \(0.622991\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.82843 | − | 13.8564i | −0.188562 | − | 0.923760i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 19.5959i | 1.15270i | 0.817203 | + | 0.576351i | \(0.195524\pi\) | ||||
−0.817203 | + | 0.576351i | \(0.804476\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13.8564 | −0.729285 | −0.364642 | − | 0.931148i | \(-0.618809\pi\) | ||||
−0.364642 | + | 0.931148i | \(0.618809\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 24.0000i | 1.14286i | ||||||||
\(22\) | 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 | ||||||||
\(27\) | − | 28.2843i | − | 1.04757i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.0000i | 0.758621i | 0.925270 | + | 0.379310i | \(0.123839\pi\) | ||||
−0.925270 | + | 0.379310i | \(0.876161\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −41.5692 | + | 8.48528i | −1.18769 | + | 0.242437i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 48.9898 | 1.32405 | 0.662024 | − | 0.749482i | \(-0.269698\pi\) | ||||
0.662024 | + | 0.749482i | \(0.269698\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 27.7128i | 0.710585i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −22.0000 | −0.536585 | −0.268293 | − | 0.963337i | \(-0.586459\pi\) | ||||
−0.268293 | + | 0.963337i | \(0.586459\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 59.3970i | 1.38132i | 0.723177 | + | 0.690662i | \(0.242681\pi\) | ||||
−0.723177 | + | 0.690662i | \(0.757319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.89898 | − | 1.00000i | 0.108866 | − | 0.0222222i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.48528 | 0.180538 | 0.0902690 | − | 0.995917i | \(-0.471227\pi\) | ||||
0.0902690 | + | 0.995917i | \(0.471227\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 23.0000 | 0.469388 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 55.4256 | 1.08678 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 29.3939 | 0.554601 | 0.277301 | − | 0.960783i | \(-0.410560\pi\) | ||||
0.277301 | + | 0.960783i | \(0.410560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −67.8823 | + | 13.8564i | −1.23422 | + | 0.251935i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 39.1918i | 0.687576i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.8564 | −0.234854 | −0.117427 | − | 0.993081i | \(-0.537465\pi\) | ||||
−0.117427 | + | 0.993081i | \(0.537465\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 46.0000i | − | 0.754098i | −0.926193 | − | 0.377049i | \(-0.876939\pi\) | ||
0.926193 | − | 0.377049i | \(-0.123061\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.48528 | −0.134687 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −48.0000 | + | 9.79796i | −0.738462 | + | 0.150738i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 59.3970i | − | 0.886522i | −0.896393 | − | 0.443261i | \(-0.853822\pi\) | ||
0.896393 | − | 0.443261i | \(-0.146178\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 72.0000i | − | 1.04348i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 27.7128i | 0.390321i | 0.980771 | + | 0.195161i | \(0.0625228\pi\) | ||||
−0.980771 | + | 0.195161i | \(0.937477\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 78.3837i | 1.07375i | 0.843662 | + | 0.536874i | \(0.180395\pi\) | ||||
−0.843662 | + | 0.536874i | \(0.819605\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −27.7128 | − | 65.0538i | −0.369504 | − | 0.867384i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 117.576 | 1.52695 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −71.0000 | −0.876543 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 76.3675i | 0.920091i | 0.887895 | + | 0.460045i | \(0.152167\pi\) | ||||
−0.887895 | + | 0.460045i | \(0.847833\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.5959 | + | 96.0000i | 0.230540 | + | 1.12941i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 62.2254 | 0.715234 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −146.000 | −1.64045 | −0.820225 | − | 0.572041i | \(-0.806152\pi\) | ||||
−0.820225 | + | 0.572041i | \(0.806152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 83.1384 | 0.913609 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 156.767 | 1.68567 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −67.8823 | + | 13.8564i | −0.714550 | + | 0.145857i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 58.7878i | 0.606059i | 0.952981 | + | 0.303030i | \(0.0979981\pi\) | ||||
−0.952981 | + | 0.303030i | \(0.902002\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.8564 | −0.139964 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 70.0000i | − | 0.693069i | −0.938037 | − | 0.346535i | \(-0.887358\pi\) | ||
0.938037 | − | 0.346535i | \(-0.112642\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | − | 42.4264i | − | 0.396508i | −0.980151 | − | 0.198254i | \(-0.936473\pi\) | ||
0.980151 | − | 0.198254i | \(-0.0635272\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 146.000i | 1.33945i | 0.742609 | + | 0.669725i | \(0.233588\pi\) | ||||
−0.742609 | + | 0.669725i | \(0.766412\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 138.564i | − | 1.24832i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 39.1918i | − | 0.346830i | −0.984849 | − | 0.173415i | \(-0.944520\pi\) | ||
0.984849 | − | 0.173415i | \(-0.0554803\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 124.708 | − | 25.4558i | 1.08441 | − | 0.221355i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.79796 | −0.0837432 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 166.277i | − | 1.39728i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 71.0000 | 0.586777 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 62.2254i | 0.505898i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 102.879 | − | 71.0000i | 0.823029 | − | 0.568000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 110.309 | 0.868572 | 0.434286 | − | 0.900775i | \(-0.357001\pi\) | ||||
0.434286 | + | 0.900775i | \(0.357001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 168.000 | 1.30233 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −180.133 | −1.37506 | −0.687532 | − | 0.726154i | \(-0.741306\pi\) | ||||
−0.687532 | + | 0.726154i | \(0.741306\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 117.576 | 0.884026 | ||||||||
\(134\) | 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 | ||||||||
\(139\) | −13.8564 | −0.0996864 | −0.0498432 | − | 0.998757i | \(-0.515872\pi\) | ||||
−0.0498432 | + | 0.998757i | \(0.515872\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 24.0000i | − | 0.170213i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 135.765 | 0.949402 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.0000 | + | 107.778i | 0.151724 | + | 0.743293i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 65.0538i | − | 0.442543i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2.00000i | − | 0.0134228i | −0.999977 | − | 0.00671141i | \(-0.997864\pi\) | ||
0.999977 | − | 0.00671141i | \(-0.00213632\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 27.7128i | 0.183529i | 0.995781 | + | 0.0917643i | \(0.0292506\pi\) | ||||
−0.995781 | + | 0.0917643i | \(0.970749\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 19.5959i | 0.128078i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 55.4256 | + | 271.529i | 0.357585 | + | 1.75180i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −68.5857 | −0.436852 | −0.218426 | − | 0.975854i | \(-0.570092\pi\) | ||||
−0.218426 | + | 0.975854i | \(0.570092\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 83.1384i | − | 0.522883i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −216.000 | −1.34161 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 110.309i | 0.676740i | 0.941013 | + | 0.338370i | \(0.109876\pi\) | ||||
−0.941013 | + | 0.338370i | \(0.890124\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 39.1918 | + | 192.000i | 0.237526 | + | 1.16364i | ||||
\(166\) | 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 | ||||||||
\(171\) | −13.8564 | −0.0810316 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 48.9898 | 0.283178 | 0.141589 | − | 0.989926i | \(-0.454779\pi\) | ||||
0.141589 | + | 0.989926i | \(0.454779\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −195.161 | + | 83.1384i | −1.11521 | + | 0.475077i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 39.1918i | 0.221423i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 263.272 | 1.47079 | 0.735396 | − | 0.677638i | \(-0.236996\pi\) | ||||
0.735396 | + | 0.677638i | \(0.236996\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.0000i | 0.143646i | 0.997417 | + | 0.0718232i | \(0.0228817\pi\) | ||||
−0.997417 | + | 0.0718232i | \(0.977118\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −130.108 | −0.710971 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 240.000 | − | 48.9898i | 1.29730 | − | 0.264810i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 271.529i | − | 1.45203i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 240.000i | 1.26984i | ||||||||
\(190\) | 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 | \(0.331438\pi\) | ||||
−0.505148 | + | 0.863033i | \(0.668562\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 27.7128 | + | 135.765i | 0.142117 | + | 0.696228i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 107.778 | 0.547094 | 0.273547 | − | 0.961859i | \(-0.411803\pi\) | ||||
0.273547 | + | 0.961859i | \(0.411803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 249.415i | 1.25334i | 0.779283 | + | 0.626672i | \(0.215583\pi\) | ||||
−0.779283 | + | 0.626672i | \(0.784417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −168.000 | −0.835821 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 186.676i | − | 0.919587i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −107.778 | + | 22.0000i | −0.525744 | + | 0.107317i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.4558 | 0.122975 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 192.000 | 0.918660 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 96.9948 | 0.459691 | 0.229846 | − | 0.973227i | \(-0.426178\pi\) | ||||
0.229846 | + | 0.973227i | \(0.426178\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 78.3837 | 0.367998 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 59.3970 | + | 290.985i | 0.276265 | + | 1.35342i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 470.302i | − | 2.16729i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 221.703 | 1.01234 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 192.000i | − | 0.868778i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −229.103 | −1.02737 | −0.513683 | − | 0.857980i | \(-0.671719\pi\) | ||||
−0.513683 | + | 0.857980i | \(0.671719\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 23.0000 | − | 9.79796i | 0.102222 | − | 0.0435465i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 296.985i | − | 1.30830i | −0.756363 | − | 0.654152i | \(-0.773026\pi\) | ||
0.756363 | − | 0.654152i | \(-0.226974\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 70.0000i | − | 0.305677i | −0.988251 | − | 0.152838i | \(-0.951159\pi\) | ||
0.988251 | − | 0.152838i | \(-0.0488414\pi\) | |||||||
\(230\) | 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 | ||||||||
\(235\) | 41.5692 | − | 8.48528i | 0.176890 | − | 0.0361076i | ||||
\(236\) | 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 | ||||||||
\(243\) | − | 53.7401i | − | 0.221153i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 112.677 | − | 23.0000i | 0.459904 | − | 0.0938776i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 135.765 | 0.549654 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 216.000 | 0.867470 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −290.985 | −1.15930 | −0.579650 | − | 0.814865i | \(-0.696811\pi\) | ||||
−0.579650 | + | 0.814865i | \(0.696811\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −352.727 | −1.39418 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 271.529 | − | 55.4256i | 1.06482 | − | 0.217355i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 78.3837i | 0.304995i | 0.988304 | + | 0.152497i | \(0.0487316\pi\) | ||||
−0.988304 | + | 0.152497i | \(0.951268\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −415.692 | −1.60499 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.0000i | 0.0842912i | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 412.950i | 1.54663i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 142.000i | − | 0.527881i | −0.964539 | − | 0.263941i | \(-0.914978\pi\) | ||
0.964539 | − | 0.263941i | \(-0.0850223\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | −318.697 | + | 135.765i | −1.15890 | + | 0.493689i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 88.1816 | 0.318345 | 0.159173 | − | 0.987251i | \(-0.449117\pi\) | ||||
0.159173 | + | 0.987251i | \(0.449117\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 55.4256i | 0.198658i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −406.000 | −1.44484 | −0.722420 | − | 0.691455i | \(-0.756970\pi\) | ||||
−0.722420 | + | 0.691455i | \(0.756970\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 93.3381i | 0.329817i | 0.986309 | + | 0.164908i | \(0.0527328\pi\) | ||||
−0.986309 | + | 0.164908i | \(0.947267\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 39.1918 | + | 192.000i | 0.137515 | + | 0.673684i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 186.676 | 0.650440 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −95.0000 | −0.328720 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 166.277 | 0.571398 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −303.737 | −1.03664 | −0.518322 | − | 0.855186i | \(-0.673443\pi\) | ||||
−0.518322 | + | 0.855186i | \(0.673443\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −67.8823 | + | 13.8564i | −0.230109 | + | 0.0469709i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 391.918i | 1.31959i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −249.415 | −0.834165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 504.000i | − | 1.67442i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −197.990 | −0.653432 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −46.0000 | − | 225.353i | −0.150820 | − | 0.738862i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 280.014i | 0.912099i | 0.889955 | + | 0.456049i | \(0.150736\pi\) | ||||
−0.889955 | + | 0.456049i | \(0.849264\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 72.0000i | − | 0.233010i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 138.564i | 0.445544i | 0.974871 | + | 0.222772i | \(0.0715105\pi\) | ||||
−0.974871 | + | 0.222772i | \(0.928490\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 607.473i | − | 1.94081i | −0.241484 | − | 0.970405i | \(-0.577634\pi\) | ||
0.241484 | − | 0.970405i | \(-0.422366\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −41.5692 | + | 8.48528i | −0.131966 | + | 0.0269374i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 68.5857 | 0.216359 | 0.108179 | − | 0.994131i | \(-0.465498\pi\) | ||||
0.108179 | + | 0.994131i | \(0.465498\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 304.841i | − | 0.955614i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −120.000 | −0.373832 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 271.529i | − | 0.840647i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −225.353 | + | 96.0000i | −0.693394 | + | 0.295385i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 412.950 | 1.26285 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −72.0000 | −0.218845 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −180.133 | −0.544209 | −0.272105 | − | 0.962268i | \(-0.587720\pi\) | ||||
−0.272105 | + | 0.962268i | \(0.587720\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 48.9898 | 0.147117 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −59.3970 | − | 290.985i | −0.177304 | − | 0.868611i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 470.302i | − | 1.39555i | −0.716315 | − | 0.697777i | \(-0.754172\pi\) | ||
0.716315 | − | 0.697777i | \(-0.245828\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −110.851 | −0.326995 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 768.000i | − | 2.25220i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 220.617 | 0.643199 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −72.0000 | − | 352.727i | −0.208696 | − | 1.02240i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 619.426i | − | 1.78509i | −0.450960 | − | 0.892544i | \(-0.648918\pi\) | ||
0.450960 | − | 0.892544i | \(-0.351082\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 214.000i | 0.613181i | 0.951842 | + | 0.306590i | \(0.0991881\pi\) | ||||
−0.951842 | + | 0.306590i | \(0.900812\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 277.128i | 0.789539i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 352.727i | − | 0.999225i | −0.866249 | − | 0.499613i | \(-0.833476\pi\) | ||
0.866249 | − | 0.499613i | \(-0.166524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.7128 | + | 135.765i | 0.0780643 | + | 0.382435i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −470.302 | −1.31737 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 27.7128i | − | 0.0771945i | −0.999255 | − | 0.0385972i | \(-0.987711\pi\) | ||
0.999255 | − | 0.0385972i | \(-0.0122889\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −169.000 | −0.468144 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 200.818i | − | 0.553219i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 78.3837 | + | 384.000i | 0.214750 | + | 1.05205i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 246.073 | 0.670499 | 0.335250 | − | 0.942129i | \(-0.391179\pi\) | ||||
0.335250 | + | 0.942129i | \(0.391179\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.0000 | −0.0596206 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −249.415 | −0.672278 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −382.120 | −1.02445 | −0.512226 | − | 0.858851i | \(-0.671179\pi\) | ||||
−0.512226 | + | 0.858851i | \(0.671179\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −200.818 | − | 290.985i | −0.535516 | − | 0.775959i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 215.555i | − | 0.571764i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −290.985 | −0.767769 | −0.383885 | − | 0.923381i | \(-0.625414\pi\) | ||||
−0.383885 | + | 0.923381i | \(0.625414\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 312.000i | − | 0.818898i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −568.514 | −1.48437 | −0.742185 | − | 0.670195i | \(-0.766211\pi\) | ||||
−0.742185 | + | 0.670195i | \(0.766211\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 576.000 | − | 117.576i | 1.49610 | − | 0.305391i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 59.3970i | 0.153481i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 670.000i | 1.72237i | 0.508296 | + | 0.861183i | \(0.330276\pi\) | ||||
−0.508296 | + | 0.861183i | \(0.669724\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 498.831i | 1.27578i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 509.494i | 1.29642i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −362.524 | −0.913160 | −0.456580 | − | 0.889682i | \(-0.650926\pi\) | ||||
−0.456580 | + | 0.889682i | \(0.650926\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − | 543.058i | − | 1.34754i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −347.828 | + | 71.0000i | −0.858833 | + | 0.175309i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −678.823 | −1.66787 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 650.000 | 1.58924 | 0.794621 | − | 0.607106i | \(-0.207670\pi\) | ||||
0.794621 | + | 0.607106i | \(0.207670\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 609.682 | 1.48341 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 117.576 | 0.284686 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 76.3675 | + | 374.123i | 0.184018 | + | 0.901501i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 39.1918i | 0.0939852i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 540.400 | 1.28974 | 0.644869 | − | 0.764293i | \(-0.276912\pi\) | ||||
0.644869 | + | 0.764293i | \(0.276912\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 482.000i | − | 1.14489i | −0.819942 | − | 0.572447i | \(-0.805994\pi\) | ||
0.819942 | − | 0.572447i | \(-0.194006\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.48528 | 0.0200598 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 192.000 | + | 450.706i | 0.451765 | + | 1.06048i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 390.323i | 0.914105i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 384.000i | − | 0.895105i | ||||||
\(430\) | 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 | \(-0.772157\pi\) | ||
0.754575 | − | 0.656214i | \(-0.227843\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 304.841 | − | 62.2254i | 0.700784 | − | 0.143047i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −352.727 | −0.807155 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 526.543i | − | 1.19942i | −0.800219 | − | 0.599708i | \(-0.795283\pi\) | ||
0.800219 | − | 0.599708i | \(-0.204717\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 23.0000 | 0.0521542 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 432.749i | 0.976861i | 0.872603 | + | 0.488430i | \(0.162430\pi\) | ||||
−0.872603 | + | 0.488430i | \(0.837570\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −715.251 | + | 146.000i | −1.60731 | + | 0.328090i | ||||
\(446\) | 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 | ||||||||
\(451\) | 304.841 | 0.675922 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 78.3837 | 0.173032 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 554.256 | 1.20753 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 502.000i | 1.08894i | 0.838781 | + | 0.544469i | \(0.183269\pi\) | ||||
−0.838781 | + | 0.544469i | \(0.816731\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 823.072 | 1.77769 | 0.888847 | − | 0.458204i | \(-0.151507\pi\) | ||||
0.888847 | + | 0.458204i | \(0.151507\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 768.000 | − | 156.767i | 1.65161 | − | 0.337134i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 178.191i | 0.381565i | 0.981632 | + | 0.190783i | \(0.0611025\pi\) | ||||
−0.981632 | + | 0.190783i | \(0.938897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 504.000i | 1.07463i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 193.990i | 0.411868i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 823.029i | − | 1.74002i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −318.697 | + | 135.765i | −0.670942 | + | 0.285820i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.3939 | 0.0616224 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 610.940i | 1.26489i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 58.7878 | + | 288.000i | 0.121212 | + | 0.593814i | ||||
\(486\) | 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 | ||||||||
\(491\) | 928.379 | 1.89079 | 0.945396 | − | 0.325923i | \(-0.105675\pi\) | ||||
0.945396 | + | 0.325923i | \(0.105675\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −431.110 | −0.874463 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −67.8823 | + | 13.8564i | −0.137136 | + | 0.0279927i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 235.151i | − | 0.473141i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −512.687 | −1.02743 | −0.513714 | − | 0.857961i | \(-0.671731\pi\) | ||||
−0.513714 | + | 0.857961i | \(0.671731\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 264.000i | − | 0.526946i | ||||||
\(502\) | 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 | ||||||||
\(507\) | 206.475i | 0.407249i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 170.000i | − | 0.333988i | −0.985958 | − | 0.166994i | \(-0.946594\pi\) | ||
0.985958 | − | 0.166994i | \(-0.0534061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 665.108i | − | 1.30158i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 391.918i | 0.763973i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 124.708 | − | 25.4558i | 0.242151 | − | 0.0494288i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −117.576 | −0.227419 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 138.564i | − | 0.266983i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −722.000 | −1.38580 | −0.692898 | − | 0.721035i | \(-0.743667\pi\) | ||||
−0.692898 | + | 0.721035i | \(0.743667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 246.073i | − | 0.470503i | −0.971935 | − | 0.235252i | \(-0.924409\pi\) | ||
0.971935 | − | 0.235252i | \(-0.0755914\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 235.151 | + | 552.000i | 0.447907 | + | 1.05143i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1086.12 | −2.06094 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 119.000 | 0.224953 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.8564 | −0.0260949 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 215.555 | 0.404419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −42.4264 | − | 207.846i | −0.0793017 | − | 0.388497i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 744.645i | − | 1.38668i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −318.697 | −0.591275 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 362.000i | − | 0.669131i | −0.942372 | − | 0.334566i | \(-0.891410\pi\) | ||
0.942372 | − | 0.334566i | \(-0.108590\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 73.5391 | 0.135431 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 146.000 | + | 715.251i | 0.267890 | + | 1.31239i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.4264i | 0.0775620i | 0.999248 | + | 0.0387810i | \(0.0123475\pi\) | ||||
−0.999248 | + | 0.0387810i | \(0.987653\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 46.0000i | − | 0.0837887i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 304.841i | − | 0.553250i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −138.564 | − | 678.823i | −0.249665 | − | 1.22310i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −656.463 | −1.17857 | −0.589285 | − | 0.807925i | \(-0.700590\pi\) | ||||
−0.589285 | + | 0.807925i | \(0.700590\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 581.969i | − | 1.04109i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −768.000 | −1.36898 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 517.602i | 0.919364i | 0.888083 | + | 0.459682i | \(0.152037\pi\) | ||||
−0.888083 | + | 0.459682i | \(0.847963\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −39.1918 | − | 192.000i | −0.0693661 | − | 0.339823i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 602.455 | 1.06253 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 842.000 | 1.47979 | 0.739895 | − | 0.672723i | \(-0.234875\pi\) | ||||
0.739895 | + | 0.672723i | \(0.234875\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −401.836 | −0.703740 | −0.351870 | − | 0.936049i | \(-0.614454\pi\) | ||||
−0.351870 | + | 0.936049i | \(0.614454\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −313.535 | −0.547181 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 585.484 | − | 249.415i | 1.01823 | − | 0.433766i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 39.1918i | − | 0.0679235i | −0.999423 | − | 0.0339617i | \(-0.989188\pi\) | ||
0.999423 | − | 0.0339617i | \(-0.0108124\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 942.236 | 1.62735 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 648.000i | − | 1.11532i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −407.294 | −0.698617 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −48.0000 | + | 9.79796i | −0.0820513 | + | 0.0167486i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 59.3970i | 0.101187i | 0.998719 | + | 0.0505937i | \(0.0161113\pi\) | ||||
−0.998719 | + | 0.0505937i | \(0.983889\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 768.000i | − | 1.30390i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 304.841i | − | 0.515805i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 509.494i | 0.859180i | 0.903024 | + | 0.429590i | \(0.141342\pi\) | ||||
−0.903024 | + | 0.429590i | \(0.858658\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −166.277 | − | 814.587i | −0.279457 | − | 1.36905i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 705.453 | 1.18166 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 859.097i | 1.43422i | 0.696961 | + | 0.717110i | \(0.254535\pi\) | ||||
−0.696961 | + | 0.717110i | \(0.745465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −598.000 | −0.995008 | −0.497504 | − | 0.867462i | \(-0.665750\pi\) | ||||
−0.497504 | + | 0.867462i | \(0.665750\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 59.3970i | − | 0.0985024i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 347.828 | − | 71.0000i | 0.574922 | − | 0.117355i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −127.279 | −0.209686 | −0.104843 | − | 0.994489i | \(-0.533434\pi\) | ||||
−0.104843 | + | 0.994489i | \(0.533434\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −528.000 | −0.866995 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −83.1384 | −0.136069 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −205.757 | −0.335656 | −0.167828 | − | 0.985816i | \(-0.553675\pi\) | ||||
−0.167828 | + | 0.985816i | \(0.553675\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | 41.5692 | 0.0671554 | 0.0335777 | − | 0.999436i | \(-0.489310\pi\) | ||||
0.0335777 | + | 0.999436i | \(0.489310\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 720.000i | − | 1.15942i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1238.85 | 1.98853 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 433.000 | − | 450.706i | 0.692800 | − | 0.721130i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 543.058i | − | 0.866121i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 960.000i | 1.52623i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 969.948i | − | 1.53716i | −0.639753 | − | 0.768580i | \(-0.720963\pi\) | ||
0.639753 | − | 0.768580i | \(-0.279037\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 274.343i | − | 0.433401i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 540.400 | − | 110.309i | 0.851023 | − | 0.173714i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −225.353 | −0.353772 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 144.250i | 0.224339i | 0.993689 | + | 0.112169i | \(0.0357799\pi\) | ||||
−0.993689 | + | 0.112169i | \(0.964220\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 823.029 | − | 168.000i | 1.27601 | − | 0.260465i | ||||
\(646\) | 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 | ||||||||
\(651\) | −1330.22 | −2.04334 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.3939 | 0.0450136 | 0.0225068 | − | 0.999747i | \(-0.492835\pi\) | ||||
0.0225068 | + | 0.999747i | \(0.492835\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −882.469 | + | 180.133i | −1.34728 | + | 0.275013i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 78.3837i | 0.119305i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −623.538 | −0.946189 | −0.473094 | − | 0.881012i | \(-0.656863\pi\) | ||||
−0.473094 | + | 0.881012i | \(0.656863\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 98.0000i | − | 0.148260i | −0.997249 | − | 0.0741301i | \(-0.976382\pi\) | ||
0.997249 | − | 0.0741301i | \(-0.0236180\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −543.058 | −0.819092 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 576.000 | − | 117.576i | 0.866165 | − | 0.176805i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 560.029i | 0.839623i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 648.000i | 0.968610i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 637.395i | 0.949918i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 489.898i | − | 0.727932i | −0.931412 | − | 0.363966i | \(-0.881423\pi\) | ||
0.931412 | − | 0.363966i | \(-0.118577\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −277.128 | − | 650.538i | −0.410560 | − | 0.963760i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 146.969 | 0.217089 | 0.108545 | − | 0.994092i | \(-0.465381\pi\) | ||||
0.108545 | + | 0.994092i | \(0.465381\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 498.831i | − | 0.734655i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −840.000 | −1.23348 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 398.808i | 0.583907i | 0.956433 | + | 0.291953i | \(0.0943052\pi\) | ||||
−0.956433 | + | 0.291953i | \(0.905695\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 215.555 | + | 1056.00i | 0.314679 | + | 1.54161i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −197.990 | −0.288195 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −288.000 | −0.417997 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −789.815 | −1.14300 | −0.571502 | − | 0.820601i | \(-0.693639\pi\) | ||||
−0.571502 | + | 0.820601i | \(0.693639\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 117.576 | 0.169662 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −67.8823 | + | 13.8564i | −0.0976723 | + | 0.0199373i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 431.110i | − | 0.618523i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 443.405 | 0.634342 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 718.000i | − | 1.02425i | −0.858911 | − | 0.512126i | \(-0.828858\pi\) | ||
0.858911 | − | 0.512126i | \(-0.171142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −678.823 | −0.965608 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.0000 | − | 117.576i | −0.0340426 | − | 0.166774i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 593.970i | 0.840127i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 838.000i | − | 1.18195i | −0.806691 | − | 0.590973i | \(-0.798744\pi\) | ||
0.806691 | − | 0.590973i | \(-0.201256\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1410.91i | 1.97883i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 665.108 | − | 135.765i | 0.930220 | − | 0.189880i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 940.604 | 1.31186 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 345.068i | 0.477273i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 215.555 | + | 506.000i | 0.297317 | + | 0.697931i | ||||
\(726\) | 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 | ||||||||
\(731\) | −1163.94 | −1.59225 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 676.059 | 0.922318 | 0.461159 | − | 0.887317i | \(-0.347434\pi\) | ||||
0.461159 | + | 0.887317i | \(0.347434\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −65.0538 | − | 318.697i | −0.0885086 | − | 0.433602i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 823.029i | 1.11673i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −235.559 | −0.318754 | −0.159377 | − | 0.987218i | \(-0.550948\pi\) | ||||
−0.159377 | + | 0.987218i | \(0.550948\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 384.000i | − | 0.518219i | ||||||
\(742\) | 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 | ||||||||
\(747\) | 76.3675i | 0.102232i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 360.000i | 0.480641i | ||||||||
\(750\) | 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 | ||||||||
\(755\) | 27.7128 | + | 135.765i | 0.0367057 | + | 0.179821i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1205.15 | −1.59201 | −0.796003 | − | 0.605292i | \(-0.793056\pi\) | ||||
−0.796003 | + | 0.605292i | \(0.793056\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 997.661i | 1.31444i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −530.000 | −0.696452 | −0.348226 | − | 0.937411i | \(-0.613216\pi\) | ||||
−0.348226 | + | 0.937411i | \(0.613216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1238.85i | − | 1.62366i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19.5959 | + | 96.0000i | 0.0256156 | + | 0.125490i | ||||
\(766\) | 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 | ||||||||
\(771\) | 221.703 | 0.287552 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 695.655 | 0.899942 | 0.449971 | − | 0.893043i | \(-0.351434\pi\) | ||||
0.449971 | + | 0.893043i | \(0.351434\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 543.058 | + | 1274.79i | 0.700720 | + | 1.64489i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1175.76i | 1.51320i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 304.841 | 0.391323 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 384.000i | − | 0.491677i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 622.254 | 0.794705 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −336.000 | + | 68.5857i | −0.428025 | + | 0.0873703i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1298.25i | 1.64962i | 0.565413 | + | 0.824808i | \(0.308717\pi\) | ||||
−0.565413 | + | 0.824808i | \(0.691283\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 984.000i | 1.24715i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 332.554i | 0.420422i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 450.706i | 0.568356i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −83.1384 | − | 407.294i | −0.104577 | − | 0.512319i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1361.92 | 1.70880 | 0.854402 | − | 0.519613i | \(-0.173924\pi\) | ||||
0.854402 | + | 0.519613i | \(0.173924\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 166.277i | 0.208106i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −146.000 | −0.182272 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1086.12i | − | 1.35257i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1058.18 | + | 216.000i | −1.31451 | + | 0.268323i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −401.637 | −0.497691 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1006.00 | 1.24351 | 0.621755 | − | 0.783212i | \(-0.286420\pi\) | ||||
0.621755 | + | 0.783212i | \(0.286420\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 651.251 | 0.803022 | 0.401511 | − | 0.915854i | \(-0.368485\pi\) | ||||
0.401511 | + | 0.915854i | \(0.368485\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 940.604 | 1.15695 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 110.309 | + | 540.400i | 0.135348 | + | 0.663067i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 823.029i | − | 1.00738i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 83.1384 | 0.101512 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 482.000i | − | 0.587089i | −0.955945 | − | 0.293544i | \(-0.905165\pi\) | ||
0.955945 | − | 0.293544i | \(-0.0948349\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | 398.808i | 0.482235i | 0.970496 | + | 0.241117i | \(0.0775139\pi\) | ||||
−0.970496 | + | 0.241117i | \(0.922486\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1106.00i | 1.33414i | 0.744996 | + | 0.667069i | \(0.232451\pi\) | ||||
−0.744996 | + | 0.667069i | \(0.767549\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 249.415i | − | 0.300139i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 450.706i | 0.541064i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 457.261 | − | 93.3381i | 0.547618 | − | 0.111782i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1567.67 | 1.87297 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 360.267i | − | 0.429400i | −0.976680 | − | 0.214700i | \(-0.931123\pi\) | ||
0.976680 | − | 0.214700i | \(-0.0688774\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 357.000 | 0.424495 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1148.34i | 1.36221i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −357.626 | + | 73.0000i | −0.423225 | + | 0.0863905i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −602.455 | −0.711281 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 264.000 | 0.310954 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1247.08 | 1.46542 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −676.059 | −0.792566 | −0.396283 | − | 0.918128i | \(-0.629700\pi\) | ||||
−0.396283 | + | 0.918128i | \(0.629700\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | −568.113 | −0.661365 | −0.330683 | − | 0.943742i | \(-0.607279\pi\) | ||||
−0.330683 | + | 0.943742i | \(0.607279\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 528.000i | − | 0.613240i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −195.161 | −0.226143 | −0.113072 | − | 0.993587i | \(-0.536069\pi\) | ||||
−0.113072 | + | 0.993587i | \(0.536069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 240.000 | − | 48.9898i | 0.277457 | − | 0.0566356i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 268.701i | 0.309920i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 581.969i | 0.668162i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 58.7878i | 0.0673399i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −872.954 | + | 602.455i | −0.997661 | + | 0.688520i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 244.949 | 0.279303 | 0.139652 | − | 0.990201i | \(-0.455402\pi\) | ||||
0.139652 | + | 0.990201i | \(0.455402\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − | 636.396i | − | 0.720720i | −0.932813 | − | 0.360360i | \(-0.882654\pi\) | ||
0.932813 | − | 0.360360i | \(-0.117346\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 39.1918 | + | 192.000i | 0.0442846 | + | 0.216949i | ||||
\(886\) | 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 | ||||||||
\(891\) | 983.805 | 1.10416 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −117.576 | −0.131664 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1289.76 | − | 263.272i | 1.44108 | − | 0.294158i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 705.453i | 0.786458i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1219.36 | −1.35636 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 576.000i | 0.639290i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1425.53 | −1.57866 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.0000 | + | 127.373i | 0.0287293 | + | 0.140744i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 585.484i | − | 0.645518i | −0.946481 | − | 0.322759i | \(-0.895390\pi\) | ||
0.946481 | − | 0.322759i | \(-0.104610\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 70.0000i | − | 0.0770077i | ||||||
\(910\) | 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 | ||||||||
\(915\) | −637.395 | + | 130.108i | −0.696606 | + | 0.142194i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1528.48 | 1.66683 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 193.990i | 0.211088i | 0.994415 | + | 0.105544i | \(0.0336584\pi\) | ||||
−0.994415 | + | 0.105544i | \(0.966342\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 792.000 | 0.859935 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 271.529i | − | 0.294181i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1126.77 | − | 480.000i | 1.21812 | − | 0.518919i | ||||
\(926\) | 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 | ||||||||
\(931\) | −318.697 | −0.342317 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 391.918 | 0.420063 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | −1718.19 | −1.82981 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1654.00i | 1.75770i | 0.477094 | + | 0.878852i | \(0.341690\pi\) | ||||
−0.477094 | + | 0.878852i | \(0.658310\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −560.029 | −0.593880 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 240.000 | + | 1175.76i | 0.253968 | + | 1.24419i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1417.04i | − | 1.49635i | −0.663502 | − | 0.748174i | \(-0.730931\pi\) | ||
0.663502 | − | 0.748174i | \(-0.269069\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 768.000i | − | 0.809273i | ||||||
\(950\) | 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 | ||||||||
\(955\) | −110.851 | − | 543.058i | −0.116075 | − | 0.568647i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −862.220 | −0.900962 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1829.05i | − | 1.90724i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2111.00 | −2.19667 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 42.4264i | − | 0.0440565i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 333.131 | + | 1632.00i | 0.345213 | + | 1.69119i | ||||
\(966\) | 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 | ||||||||
\(971\) | 817.528 | 0.841944 | 0.420972 | − | 0.907074i | \(-0.361689\pi\) | ||||
0.420972 | + | 0.907074i | \(0.361689\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 117.576 | 0.120838 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 271.529 | + | 637.395i | 0.278491 | + | 0.653738i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1704.84i | 1.74498i | 0.488633 | + | 0.872490i | \(0.337496\pi\) | ||||
−0.488633 | + | 0.872490i | \(0.662504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2023.04 | 2.06643 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 146.000i | 0.148828i | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 203.647i | 0.206329i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1512.00i | 1.52882i | ||||||||
\(990\) | 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 | ||||||||
\(995\) | 249.415 | + | 1221.88i | 0.250669 | + | 1.22802i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1420.70 | −1.42498 | −0.712489 | − | 0.701683i | \(-0.752432\pi\) | ||||
−0.712489 | + | 0.701683i | \(0.752432\pi\) | |||||||
\(998\) | 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 \(a_p\))