Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(673,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.673");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 722x^{3} + 11881x^{2} + 54936x + 127008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 673.2 | ||
Root | \(-2.93235 + 2.93235i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.673 |
Dual form | 1344.4.c.a.673.5 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 7.86469i | − 0.703440i | −0.936105 | − | 0.351720i | \(-0.885597\pi\) | ||||
0.936105 | − | 0.351720i | \(-0.114403\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 31.0937i | − 0.852283i | −0.904657 | − | 0.426141i | \(-0.859873\pi\) | ||||
0.904657 | − | 0.426141i | \(-0.140127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 48.9584i | 1.04451i | 0.852790 | + | 0.522255i | \(0.174909\pi\) | ||||
−0.852790 | + | 0.522255i | \(0.825091\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −23.5941 | −0.406131 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −43.0937 | −0.614810 | −0.307405 | − | 0.951579i | \(-0.599461\pi\) | ||||
−0.307405 | + | 0.951579i | \(0.599461\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 110.147i | 1.32997i | 0.746858 | + | 0.664983i | \(0.231561\pi\) | ||||
−0.746858 | + | 0.664983i | \(0.768439\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000i | 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 170.469 | 1.54545 | 0.772724 | − | 0.634742i | \(-0.218894\pi\) | ||||
0.772724 | + | 0.634742i | \(0.218894\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 63.1466 | 0.505173 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 78.6878i | 0.503861i | 0.967745 | + | 0.251930i | \(0.0810654\pi\) | ||||
−0.967745 | + | 0.251930i | \(0.918935\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −48.8753 | −0.283170 | −0.141585 | − | 0.989926i | \(-0.545220\pi\) | ||||
−0.141585 | + | 0.989926i | \(0.545220\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −93.2812 | −0.492066 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 55.0529i | 0.265875i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.95843i | − 0.0309178i | −0.999881 | − | 0.0154589i | \(-0.995079\pi\) | ||||
0.999881 | − | 0.0154589i | \(-0.00492091\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 146.875 | 0.603048 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 339.680 | 1.29388 | 0.646940 | − | 0.762541i | \(-0.276048\pi\) | ||||
0.646940 | + | 0.762541i | \(0.276048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 222.293i | 0.788358i | 0.919034 | + | 0.394179i | \(0.128971\pi\) | ||||
−0.919034 | + | 0.394179i | \(0.871029\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 70.7822i | 0.234480i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 314.918 | 0.977350 | 0.488675 | − | 0.872466i | \(-0.337480\pi\) | ||||
0.488675 | + | 0.872466i | \(0.337480\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 129.281i | 0.354961i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 487.731i | − 1.26406i | −0.774945 | − | 0.632028i | \(-0.782223\pi\) | ||||
0.774945 | − | 0.632028i | \(-0.217777\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −244.543 | −0.599530 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 330.440 | 0.767856 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 500.668i | − 1.10477i | −0.833589 | − | 0.552385i | \(-0.813718\pi\) | ||||
0.833589 | − | 0.552385i | \(-0.186282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 29.6040i | 0.0621377i | 0.999517 | + | 0.0310688i | \(0.00989111\pi\) | ||||
−0.999517 | + | 0.0310688i | \(0.990109\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 385.043 | 0.734749 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 380.317i | 0.693480i | 0.937961 | + | 0.346740i | \(0.112711\pi\) | ||||
−0.937961 | + | 0.346740i | \(0.887289\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 511.408i | − 0.892265i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.5976 | −0.0210573 | −0.0105286 | − | 0.999945i | \(-0.503351\pi\) | ||||
−0.0105286 | + | 0.999945i | \(0.503351\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −857.735 | −1.37521 | −0.687605 | − | 0.726085i | \(-0.741338\pi\) | ||||
−0.687605 | + | 0.726085i | \(0.741338\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 189.440i | − 0.291662i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 217.656i | 0.322133i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 799.481 | 1.13859 | 0.569295 | − | 0.822133i | \(-0.307216\pi\) | ||||
0.569295 | + | 0.822133i | \(0.307216\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 178.856i | 0.236530i | 0.992982 | + | 0.118265i | \(0.0377332\pi\) | ||||
−0.992982 | + | 0.118265i | \(0.962267\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 338.919i | 0.432482i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 236.063 | 0.290904 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1029.18 | −1.22576 | −0.612881 | − | 0.790175i | \(-0.709990\pi\) | ||||
−0.612881 | + | 0.790175i | \(0.709990\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 342.709i | − 0.394788i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 146.626i | 0.163488i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 866.269 | 0.935551 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −360.904 | −0.377775 | −0.188888 | − | 0.981999i | \(-0.560488\pi\) | ||||
−0.188888 | + | 0.981999i | \(0.560488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 279.844i | 0.284094i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 768.144i | 0.756764i | 0.925650 | + | 0.378382i | \(0.123519\pi\) | ||||
−0.925650 | + | 0.378382i | \(0.876481\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1769.55 | 1.69280 | 0.846402 | − | 0.532544i | \(-0.178764\pi\) | ||||
0.846402 | + | 0.532544i | \(0.178764\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 165.159 | 0.153503 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1013.38i | − 0.915578i | −0.889061 | − | 0.457789i | \(-0.848641\pi\) | ||||
0.889061 | − | 0.457789i | \(-0.151359\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1221.05i | − 1.07298i | −0.843906 | − | 0.536491i | \(-0.819750\pi\) | ||||
0.843906 | − | 0.536491i | \(-0.180250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.8753 | −0.0178504 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 612.481 | 0.509888 | 0.254944 | − | 0.966956i | \(-0.417943\pi\) | ||||
0.254944 | + | 0.966956i | \(0.417943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1340.69i | − 1.08713i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 440.626i | − 0.348170i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 301.656 | 0.232376 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 364.180 | 0.273614 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1019.04i | − 0.747022i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1479.72i | − 1.05880i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1373.22 | 0.959479 | 0.479740 | − | 0.877411i | \(-0.340731\pi\) | ||||
0.479740 | + | 0.877411i | \(0.340731\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 666.880 | 0.455159 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 272.851i | 0.181978i | 0.995852 | + | 0.0909890i | \(0.0290028\pi\) | ||||
−0.995852 | + | 0.0909890i | \(0.970997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 771.026i | − 0.502680i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 212.347 | 0.135377 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1240.86 | −0.773821 | −0.386910 | − | 0.922117i | \(-0.626458\pi\) | ||||
−0.386910 | + | 0.922117i | \(0.626458\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1471.37i | 0.897844i | 0.893571 | + | 0.448922i | \(0.148192\pi\) | ||||
−0.893571 | + | 0.448922i | \(0.851808\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 944.753i | − 0.564273i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1522.30 | 0.890218 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 618.856 | 0.354436 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 147.000i | − 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 581.360i | 0.319644i | 0.987146 | + | 0.159822i | \(0.0510920\pi\) | ||||
−0.987146 | + | 0.159822i | \(0.948908\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2709.31 | −1.46013 | −0.730067 | − | 0.683375i | \(-0.760511\pi\) | ||||
−0.730067 | + | 0.683375i | \(0.760511\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 387.844 | 0.204937 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 384.389i | 0.199193i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2885.43i | − 1.46677i | −0.679815 | − | 0.733383i | \(-0.737940\pi\) | ||||
0.679815 | − | 0.733383i | \(-0.262060\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1463.19 | −0.729803 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1193.29 | −0.584125 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3230.08i | 1.55215i | 0.630643 | + | 0.776073i | \(0.282791\pi\) | ||||
−0.630643 | + | 0.776073i | \(0.717209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 733.628i | 0.346139i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −234.777 | −0.108788 | −0.0543939 | − | 0.998520i | \(-0.517323\pi\) | ||||
−0.0543939 | + | 0.998520i | \(0.517323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −199.927 | −0.0910002 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 991.319i | − 0.443322i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1892.43i | − 0.831667i | −0.909441 | − | 0.415834i | \(-0.863490\pi\) | ||||
0.909441 | − | 0.415834i | \(-0.136510\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −442.026 | −0.190937 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1502.00 | −0.637839 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 340.579i | 0.142213i | 0.997469 | + | 0.0711064i | \(0.0226530\pi\) | ||||
−0.997469 | + | 0.0711064i | \(0.977347\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3788.51i | − 1.55579i | −0.628396 | − | 0.777894i | \(-0.716288\pi\) | ||||
0.628396 | − | 0.777894i | \(-0.283712\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 88.8119 | 0.0358752 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −54.7259 | −0.0217488 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1339.94i | 0.523992i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 189.000i | − 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5076.47 | 1.92314 | 0.961572 | − | 0.274554i | \(-0.0885303\pi\) | ||||
0.961572 | + | 0.274554i | \(0.0885303\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2335.52 | −0.871059 | −0.435530 | − | 0.900174i | \(-0.643439\pi\) | ||||
−0.435530 | + | 0.900174i | \(0.643439\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1155.13i | − 0.424208i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3157.61i | − 1.14198i | −0.820957 | − | 0.570990i | \(-0.806559\pi\) | ||||
0.820957 | − | 0.570990i | \(-0.193441\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4559.29 | 1.62412 | 0.812059 | − | 0.583575i | \(-0.198347\pi\) | ||||
0.812059 | + | 0.583575i | \(0.198347\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1140.95 | 0.400381 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 550.815i | − 0.190441i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 2671.48i | − 0.910167i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1534.22 | −0.515150 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3424.87 | 1.13351 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 4066.41i | − 1.32675i | −0.748289 | − | 0.663373i | \(-0.769124\pi\) | ||||
0.748289 | − | 0.663373i | \(-0.230876\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 37.7929i | 0.0121574i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1748.27 | 0.554562 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 342.127 | 0.107028 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2573.21i | 0.793978i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2109.80i | − 0.642175i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3158.95 | 0.948604 | 0.474302 | − | 0.880362i | \(-0.342700\pi\) | ||||
0.474302 | + | 0.880362i | \(0.342700\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −568.319 | −0.168391 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4076.18i | 1.19183i | 0.803047 | + | 0.595915i | \(0.203211\pi\) | ||||
−0.803047 | + | 0.595915i | \(0.796789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2728.36i | 0.787314i | 0.919257 | + | 0.393657i | \(0.128790\pi\) | ||||
−0.919257 | + | 0.393657i | \(0.871210\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 652.968 | 0.185983 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1799.32 | 0.505910 | 0.252955 | − | 0.967478i | \(-0.418597\pi\) | ||||
0.252955 | + | 0.967478i | \(0.418597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 2476.73i | − 0.687507i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2398.44i | − 0.657366i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 515.306 | 0.139466 | 0.0697330 | − | 0.997566i | \(-0.477785\pi\) | ||||
0.0697330 | + | 0.997566i | \(0.477785\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2837.68 | 0.758469 | 0.379235 | − | 0.925301i | \(-0.376187\pi\) | ||||
0.379235 | + | 0.925301i | \(0.376187\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 385.370i | − 0.100491i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5392.60 | −1.38916 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 536.567 | 0.136560 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 3739.61i | − 0.940406i | −0.882558 | − | 0.470203i | \(-0.844181\pi\) | ||||
0.882558 | − | 0.470203i | \(-0.155819\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5300.53i | − 1.31716i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1016.76 | 0.249693 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1082.08 | 0.262640 | 0.131320 | − | 0.991340i | \(-0.458078\pi\) | ||||
0.131320 | + | 0.991340i | \(0.458078\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 48.7090i | 0.0116858i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 708.190i | − 0.167954i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6367.81 | 1.49299 | 0.746494 | − | 0.665392i | \(-0.231736\pi\) | ||||
0.746494 | + | 0.665392i | \(0.231736\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3835.85 | −0.889187 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3087.54i | 0.707694i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4265.99i | 0.966923i | 0.875366 | + | 0.483461i | \(0.160621\pi\) | ||||
−0.875366 | + | 0.483461i | \(0.839379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2158.77 | 0.483896 | 0.241948 | − | 0.970289i | \(-0.422214\pi\) | ||||
0.241948 | + | 0.970289i | \(0.422214\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1028.13 | −0.227931 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1963.46i | − 0.430550i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4738.38i | − 1.02780i | −0.857849 | − | 0.513901i | \(-0.828200\pi\) | ||||
0.857849 | − | 0.513901i | \(-0.171800\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 439.877 | 0.0943899 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4054.46 | 0.860742 | 0.430371 | − | 0.902652i | \(-0.358383\pi\) | ||||
0.430371 | + | 0.902652i | \(0.358383\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 583.193i | 0.122499i | 0.998122 | + | 0.0612495i | \(0.0195085\pi\) | ||||
−0.998122 | + | 0.0612495i | \(0.980491\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 2598.81i | − 0.540141i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2377.76 | −0.489041 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3055.93 | −0.622009 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1082.71i | 0.218109i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6986.16i | 1.39295i | 0.717579 | + | 0.696477i | \(0.245250\pi\) | ||||
−0.717579 | + | 0.696477i | \(0.754750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3937.60 | −0.777139 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 839.531 | 0.164022 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8345.91i | 1.61424i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1556.05i | − 0.297971i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2304.43 | 0.436918 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 232.826 | 0.0437101 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7409.11i | 1.37739i | 0.725049 | + | 0.688697i | \(0.241817\pi\) | ||||
−0.725049 | + | 0.688697i | \(0.758183\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 5308.65i | − 0.977341i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3756.12 | 0.684856 | 0.342428 | − | 0.939544i | \(-0.388751\pi\) | ||||
0.342428 | + | 0.939544i | \(0.388751\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7988.13 | 1.44254 | 0.721271 | − | 0.692653i | \(-0.243558\pi\) | ||||
0.721271 | + | 0.692653i | \(0.243558\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 495.476i | − 0.0886251i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 968.306i | − 0.171563i | −0.996314 | − | 0.0857815i | \(-0.972661\pi\) | ||||
0.996314 | − | 0.0857815i | \(-0.0273387\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2446.70 | 0.429432 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3040.13 | −0.528609 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 4746.63i | − 0.817676i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3091.56i | 0.527658i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3663.14 | −0.619486 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2204.42 | −0.369404 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 11428.0i | − 1.89770i | −0.315721 | − | 0.948852i | \(-0.602246\pi\) | ||||
0.315721 | − | 0.948852i | \(-0.397754\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 62.6258i | 0.0103059i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2991.08 | 0.487821 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8189.96 | 1.32384 | 0.661922 | − | 0.749572i | \(-0.269741\pi\) | ||||
0.661922 | + | 0.749572i | \(0.269741\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1837.44i | − 0.294384i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1519.71i | 0.241341i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4022.07 | −0.627655 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1519.83i | − 0.235126i | −0.993065 | − | 0.117563i | \(-0.962492\pi\) | ||||
0.993065 | − | 0.117563i | \(-0.0375081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5156.67i | 0.790918i | 0.918484 | + | 0.395459i | \(0.129414\pi\) | ||||
−0.918484 | + | 0.395459i | \(0.870586\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1321.88 | −0.201016 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3904.42 | −0.588700 | −0.294350 | − | 0.955698i | \(-0.595103\pi\) | ||||
−0.294350 | + | 0.955698i | \(0.595103\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 99.0766i | 0.0148125i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 904.968i | − 0.134162i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4589.29 | 0.674689 | 0.337345 | − | 0.941381i | \(-0.390471\pi\) | ||||
0.337345 | + | 0.941381i | \(0.390471\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5273.27 | −0.768810 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1092.54i | − 0.157971i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6745.82i | 0.967377i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1951.21 | 0.277527 | 0.138763 | − | 0.990326i | \(-0.455687\pi\) | ||||
0.138763 | + | 0.990326i | \(0.455687\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3057.12 | −0.431294 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3414.12i | 0.477768i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6271.39i | 0.870564i | 0.900294 | + | 0.435282i | \(0.143351\pi\) | ||||
−0.900294 | + | 0.435282i | \(0.856649\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4439.15 | −0.611297 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3852.43 | −0.526287 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 461.952i | 0.0626092i | 0.999510 | + | 0.0313046i | \(0.00996619\pi\) | ||||
−0.999510 | + | 0.0313046i | \(0.990034\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 4119.67i | − 0.553956i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10155.8 | 1.35493 | 0.677465 | − | 0.735555i | \(-0.263078\pi\) | ||||
0.677465 | + | 0.735555i | \(0.263078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1711.80 | 0.226601 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 2000.64i | − 0.262786i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 4781.94i | − 0.623276i | −0.950201 | − | 0.311638i | \(-0.899122\pi\) | ||||
0.950201 | − | 0.311638i | \(-0.100878\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7346.16 | −0.950157 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 818.554 | 0.105065 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 6287.68i | − 0.800930i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 10238.8i | − 1.29438i | −0.762329 | − | 0.647190i | \(-0.775944\pi\) | ||||
0.762329 | − | 0.647190i | \(-0.224056\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2313.08 | −0.290222 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12493.0 | −1.55578 | −0.777891 | − | 0.628399i | \(-0.783710\pi\) | ||||
−0.777891 | + | 0.628399i | \(0.783710\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2392.86i | − 0.295773i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 637.040i | − 0.0781600i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −216.363 | −0.0263507 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4755.09 | −0.574876 | −0.287438 | − | 0.957799i | \(-0.592803\pi\) | ||||
−0.287438 | + | 0.957799i | \(0.592803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3722.57i | 0.446766i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3504.68i | 0.417564i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1406.64 | 0.166384 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4414.12 | 0.518371 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1948.68i | 0.227205i | 0.993526 | + | 0.113603i | \(0.0362391\pi\) | ||||
−0.993526 | + | 0.113603i | \(0.963761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1727.58i | − 0.199993i | −0.994988 | − | 0.0999963i | \(-0.968117\pi\) | ||||
0.994988 | − | 0.0999963i | \(-0.0318831\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2834.26 | −0.325783 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2721.22 | −0.310585 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 207.228i | − 0.0234858i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 4566.90i | − 0.513967i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9457.57 | 1.05697 | 0.528486 | − | 0.848942i | \(-0.322760\pi\) | ||||
0.528486 | + | 0.848942i | \(0.322760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 557.783 | 0.0619061 | 0.0309530 | − | 0.999521i | \(-0.490146\pi\) | ||||
0.0309530 | + | 0.999521i | \(0.490146\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 1856.57i | − 0.204633i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18776.6i | 2.05539i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7961.06 | −0.865514 | −0.432757 | − | 0.901511i | \(-0.642459\pi\) | ||||
−0.432757 | + | 0.901511i | \(0.642459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −441.000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 778.834i | − 0.0835294i | −0.999127 | − | 0.0417647i | \(-0.986702\pi\) | ||||
0.999127 | − | 0.0417647i | \(-0.0132980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8094.18i | 0.862250i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1744.08 | 0.184546 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1899.25 | −0.199624 | −0.0998118 | − | 0.995006i | \(-0.531824\pi\) | ||||
−0.0998118 | + | 0.995006i | \(0.531824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 10561.9i | − 1.10275i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8127.92i | 0.843009i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2695.30 | −0.277709 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 535.528 | 0.0548161 | 0.0274080 | − | 0.999624i | \(-0.491275\pi\) | ||||
0.0274080 | + | 0.999624i | \(0.491275\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1163.53i | − 0.118320i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6361.75i | 0.642725i | 0.946956 | + | 0.321363i | \(0.104141\pi\) | ||||
−0.946956 | + | 0.321363i | \(0.895859\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4102.49 | −0.411791 | −0.205895 | − | 0.978574i | \(-0.566011\pi\) | ||||
−0.205895 | + | 0.978574i | \(0.566011\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1153.17 | 0.115004 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11503.7i | 1.13989i | 0.821683 | + | 0.569945i | \(0.193035\pi\) | ||||
−0.821683 | + | 0.569945i | \(0.806965\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 2662.22i | − 0.262111i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8656.29 | −0.846838 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6911.92 | 0.671904 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6955.38i | 0.671863i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4389.58i | 0.421352i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5430.09 | 0.517969 | 0.258985 | − | 0.965881i | \(-0.416612\pi\) | ||||
0.258985 | + | 0.965881i | \(0.416612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 340.674 | 0.0322939 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3579.86i | 0.337245i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2838.40i | 0.265742i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9563.99 | −0.889909 | −0.444955 | − | 0.895553i | \(-0.646780\pi\) | ||||
−0.444955 | + | 0.895553i | \(0.646780\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9690.25 | 0.896132 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12301.3i | 1.13065i | 0.824868 | + | 0.565325i | \(0.191249\pi\) | ||||
−0.824868 | + | 0.565325i | \(0.808751\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 3390.95i | − 0.309778i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2200.88 | 0.199843 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 88.1835 | 0.00795889 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 4750.89i | − 0.426211i | −0.977029 | − | 0.213105i | \(-0.931642\pi\) | ||||
0.977029 | − | 0.213105i | \(-0.0683578\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 704.330i | 0.0628087i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2463.79 | 0.218400 | 0.109200 | − | 0.994020i | \(-0.465171\pi\) | ||||
0.109200 | + | 0.994020i | \(0.465171\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6041.22 | 0.532338 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 599.782i | 0.0525390i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14836.9i | 1.29201i | 0.763334 | + | 0.646004i | \(0.223561\pi\) | ||||
−0.763334 | + | 0.646004i | \(0.776439\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6004.15 | 0.519780 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2973.96 | −0.255952 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 13917.0i | − 1.19079i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 9791.96i | − 0.832979i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5677.28 | −0.480163 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13196.5 | 1.10969 | 0.554844 | − | 0.831955i | \(-0.312778\pi\) | ||||
0.554844 | + | 0.831955i | \(0.312778\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15562.4i | 1.30114i | 0.759447 | + | 0.650569i | \(0.225470\pi\) | ||||
−0.759447 | + | 0.650569i | \(0.774530\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1326.08i | 0.110238i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2106.22 | 0.174095 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16892.8 | 1.38841 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4506.01i | 0.368257i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16630.2i | 1.35147i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7969.90 | −0.644054 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1021.74 | 0.0821066 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1523.59i | − 0.121755i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13421.8i | 1.06663i | 0.845917 | + | 0.533315i | \(0.179054\pi\) | ||||
−0.845917 | + | 0.533315i | \(0.820946\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11365.5 | −0.898234 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9603.15 | −0.754778 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 12508.9i | − 0.977770i | −0.872348 | − | 0.488885i | \(-0.837404\pi\) | ||||
0.872348 | − | 0.488885i | \(-0.162596\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 266.436i | − 0.0207126i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8667.19 | −0.670118 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5596.37 | −0.430347 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 164.178i | 0.0125567i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24112.0i | 1.83421i | 0.398643 | + | 0.917106i | \(0.369481\pi\) | ||||
−0.398643 | + | 0.917106i | \(0.630519\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10883.1 | −0.823447 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4019.83 | 0.302527 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 10716.1i | − 0.802186i | −0.916037 | − | 0.401093i | \(-0.868630\pi\) | ||||
0.916037 | − | 0.401093i | \(-0.131370\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 4816.97i | − 0.358675i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8706.37 | −0.641459 | −0.320729 | − | 0.947171i | \(-0.603928\pi\) | ||||
−0.320729 | + | 0.947171i | \(0.603928\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2840.30i | 0.208166i | 0.994569 | + | 0.104083i | \(0.0331908\pi\) | ||||
−0.994569 | + | 0.104083i | \(0.966809\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 15229.4i | − 1.11033i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10764.6 | 0.780718 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2485.56 | −0.179333 | −0.0896665 | − | 0.995972i | \(-0.528580\pi\) | ||||
−0.0896665 | + | 0.995972i | \(0.528580\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7006.56i | 0.502906i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1251.99i | − 0.0893998i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15165.4 | −1.07733 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3465.39 | −0.244916 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9350.79i | 0.657493i | 0.944418 | + | 0.328746i | \(0.106626\pi\) | ||||
−0.944418 | + | 0.328746i | \(0.893374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 5383.45i | − 0.376606i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9472.82 | −0.659323 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14248.9 | 0.986732 | 0.493366 | − | 0.869822i | \(-0.335766\pi\) | ||||
0.493366 | + | 0.869822i | \(0.335766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 2372.43i | − 0.163463i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 13677.9i | − 0.937685i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27065.7 | −1.84620 | −0.923102 | − | 0.384555i | \(-0.874355\pi\) | ||||
−0.923102 | + | 0.384555i | \(0.874355\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16949.1 | −1.15036 | −0.575181 | − | 0.818026i | \(-0.695068\pi\) | ||||
−0.575181 | + | 0.818026i | \(0.695068\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 3422.85i | − 0.231160i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 2864.16i | − 0.192471i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16657.8 | −1.11387 | −0.556937 | − | 0.830555i | \(-0.688023\pi\) | ||||
−0.556937 | + | 0.830555i | \(0.688023\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1652.44 | −0.109951 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15417.9i | 1.02085i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 3871.55i | − 0.255091i | −0.991833 | − | 0.127545i | \(-0.959290\pi\) | ||||
0.991833 | − | 0.127545i | \(-0.0407098\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8014.44 | −0.525485 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27607.7 | 1.80137 | 0.900683 | − | 0.434476i | \(-0.143067\pi\) | ||||
0.900683 | + | 0.434476i | \(0.143067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11637.0i | 0.755625i | 0.925882 | + | 0.377813i | \(0.123324\pi\) | ||||
−0.925882 | + | 0.377813i | \(0.876676\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4602.67i | 0.297422i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7204.26 | 0.463295 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3744.18 | −0.239628 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 10274.6i | − 0.654431i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 299.865i | 0.0190086i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14402.0 | −0.908613 | −0.454306 | − | 0.890846i | \(-0.650113\pi\) | ||||
−0.454306 | + | 0.890846i | \(0.650113\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12199.2 | −0.765997 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 10800.0i | − 0.674936i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2398.96i | 0.149216i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 113.379 | 0.00701908 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20510.6 | −1.26384 | −0.631918 | − | 0.775035i | \(-0.717732\pi\) | ||||
−0.631918 | + | 0.775035i | \(0.717732\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11283.3i | 0.692020i | 0.938231 | + | 0.346010i | \(0.112464\pi\) | ||||
−0.938231 | + | 0.346010i | \(0.887536\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 5244.80i | − 0.320177i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26999.9 | −1.64061 | −0.820306 | − | 0.571925i | \(-0.806197\pi\) | ||||
−0.820306 | + | 0.571925i | \(0.806197\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15567.6 | −0.941577 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 1026.38i | − 0.0617927i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18706.7i | 1.12105i | 0.828136 | + | 0.560527i | \(0.189401\pi\) | ||||
−0.828136 | + | 0.560527i | \(0.810599\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2145.89 | 0.128011 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7719.62 | 0.458403 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 26475.4i | − 1.56500i | −0.622651 | − | 0.782500i | \(-0.713944\pi\) | ||||
0.622651 | − | 0.782500i | \(-0.286056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 14782.9i | − 0.869876i | −0.900460 | − | 0.434938i | \(-0.856770\pi\) | ||||
0.900460 | − | 0.434938i | \(-0.143230\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6329.40 | −0.370760 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6063.88 | −0.353605 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13413.9i | 0.778691i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 9476.84i | − 0.547677i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 920.498 | 0.0529589 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30451.4 | 1.74416 | 0.872078 | − | 0.489367i | \(-0.162772\pi\) | ||||
0.872078 | + | 0.489367i | \(0.162772\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1704.96i | 0.0972205i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29136.3i | 1.65406i | 0.562158 | + | 0.827030i | \(0.309971\pi\) | ||||
−0.562158 | + | 0.827030i | \(0.690029\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2526.32 | 0.142786 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12228.5 | 0.688104 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 22580.3i | − 1.26502i | −0.774552 | − | 0.632510i | \(-0.782025\pi\) | ||||
0.774552 | − | 0.632510i | \(-0.217975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9758.95i | 0.544336i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8185.08 | 0.454556 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23878.5 | 1.32032 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17484.1i | 0.962558i | 0.876567 | + | 0.481279i | \(0.159828\pi\) | ||||
−0.876567 | + | 0.481279i | \(0.840172\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1958.91i | − 0.107378i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11571.9 | 0.631579 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14638.1 | −0.795491 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 5397.95i | − 0.292088i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16469.3i | 0.887355i | 0.896186 | + | 0.443678i | \(0.146326\pi\) | ||||
−0.896186 | + | 0.443678i | \(0.853674\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 766.447 | 0.0411196 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7430.19 | −0.396932 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 5377.01i | − 0.286030i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21999.8i | 1.16533i | 0.812712 | + | 0.582666i | \(0.197990\pi\) | ||||
−0.812712 | + | 0.582666i | \(0.802010\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7195.33 | −0.379530 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8331.74 | −0.437624 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 11972.4i | − 0.626214i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1545.92i | − 0.0805208i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24993.7 | 1.29639 | 0.648197 | − | 0.761472i | \(-0.275523\pi\) | ||||
0.648197 | + | 0.761472i | \(0.275523\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12386.8 | −0.639820 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 8513.04i | − 0.437903i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4968.87i | 0.254537i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22235.5 | −1.13435 | −0.567173 | − | 0.823598i | \(-0.691963\pi\) | ||||
−0.567173 | + | 0.823598i | \(0.691963\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 9579.44i | − 0.484690i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 23498.3i | − 1.18408i | −0.805910 | − | 0.592038i | \(-0.798324\pi\) | ||||
0.805910 | − | 0.592038i | \(-0.201676\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1156.11 | −0.0580187 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11825.5 | 0.591041 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8773.06i | 0.436701i | 0.975870 | + | 0.218351i | \(0.0700677\pi\) | ||||
−0.975870 | + | 0.218351i | \(0.929932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16177.8i | 0.802033i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5806.02 | 0.286679 | 0.143339 | − | 0.989674i | \(-0.454216\pi\) | ||||
0.143339 | + | 0.989674i | \(0.454216\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4572.22 | 0.224850 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1609.70i | − 0.0788432i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7093.64i | 0.346056i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18504.6 | −0.899125 | −0.449562 | − | 0.893249i | \(-0.648420\pi\) | ||||
−0.449562 | + | 0.893249i | \(0.648420\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11218.8 | −0.542944 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21307.9i | 1.02712i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35271.9i | 1.69350i | 0.531991 | + | 0.846750i | \(0.321444\pi\) | ||||
−0.531991 | + | 0.846750i | \(0.678556\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15901.6 | −0.760462 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6989.26 | −0.332931 | −0.166465 | − | 0.986047i | \(-0.553235\pi\) | ||||
−0.166465 | + | 0.986047i | \(0.553235\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8547.32i | 0.405549i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 3050.27i | − 0.144161i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24511.9 | 1.15394 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14248.4 | −0.668152 | −0.334076 | − | 0.942546i | \(-0.608424\pi\) | ||||
−0.334076 | + | 0.942546i | \(0.608424\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 3246.25i | − 0.151635i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 11637.6i | − 0.541496i | −0.962650 | − | 0.270748i | \(-0.912729\pi\) | ||||
0.962650 | − | 0.270748i | \(-0.0872711\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3086.31 | −0.143050 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 146.127 | 0.00674681 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37414.6i | 1.72082i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 391.708i | 0.0179467i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2124.57 | −0.0969680 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22693.0 | −1.03178 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 14596.1i | − 0.661112i | −0.943786 | − | 0.330556i | \(-0.892764\pi\) | ||||
0.943786 | − | 0.330556i | \(-0.107236\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 19103.4i | − 0.861977i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4287.36 | −0.192720 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1449.36 | −0.0649034 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11507.6i | 0.513373i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8911.71i | 0.396072i | 0.980195 | + | 0.198036i | \(0.0634562\pi\) | ||||
−0.980195 | + | 0.198036i | \(0.936544\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13571.0 | −0.600884 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9262.62 | 0.408587 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26670.2i | 1.17207i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9384.83i | 0.410896i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12798.0 | 0.558253 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14318.4 | 0.622260 | 0.311130 | − | 0.950367i | \(-0.399292\pi\) | ||||
0.311130 | + | 0.950367i | \(0.399292\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 17454.9i | − 0.755762i | −0.925854 | − | 0.377881i | \(-0.876653\pi\) | ||||
0.925854 | − | 0.377881i | \(-0.123347\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 6476.31i | − 0.279378i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25403.6 | 1.09184 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24484.8 | −1.04849 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3084.38i | 0.131596i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 29192.7i | − 1.24096i | −0.784220 | − | 0.620482i | \(-0.786937\pi\) | ||||
0.784220 | − | 0.620482i | \(-0.213063\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13828.3 | 0.585693 | 0.292846 | − | 0.956159i | \(-0.405398\pi\) | ||||
0.292846 | + | 0.956159i | \(0.405398\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5890.39 | −0.248578 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 37841.9i | − 1.59116i | −0.605846 | − | 0.795582i | \(-0.707165\pi\) | ||||
0.605846 | − | 0.795582i | \(-0.292835\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 4910.72i | − 0.205738i | −0.994695 | − | 0.102869i | \(-0.967198\pi\) | ||||
0.994695 | − | 0.102869i | \(-0.0328022\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14215.1 | −0.593402 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2111.59 | −0.0878300 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1846.45i | 0.0765257i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1319.63i | − 0.0544960i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19949.5 | 0.820899 | 0.410450 | − | 0.911883i | \(-0.365372\pi\) | ||||
0.410450 | + | 0.911883i | \(0.365372\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18197.2 | 0.746124 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 12163.4i | − 0.496950i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1572.37i | 0.0640132i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2549.26 | −0.103416 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1749.58 | 0.0707248 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1186.20i | − 0.0477819i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3800.95i | 0.152570i | 0.997086 | + | 0.0762849i | \(0.0243059\pi\) | ||||
−0.997086 | + | 0.0762849i | \(0.975694\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7796.42 | −0.311850 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3277.49 | −0.130638 | −0.0653192 | − | 0.997864i | \(-0.520807\pi\) | ||||
−0.0653192 | + | 0.997864i | \(0.520807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 16774.9i | − 0.666300i | −0.942874 | − | 0.333150i | \(-0.891888\pi\) | ||||
0.942874 | − | 0.333150i | \(-0.108112\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7133.28i | 0.282348i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5411.95 | −0.213470 | −0.106735 | − | 0.994287i | \(-0.534040\pi\) | ||||
−0.106735 | + | 0.994287i | \(0.534040\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14883.3 | −0.585028 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9167.79i | 0.359117i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 24858.9i | − 0.970402i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18619.7 | −0.724346 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3248.13 | 0.125925 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10358.0i | 0.400188i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 29953.6i | − 1.15332i | −0.816984 | − | 0.576661i | \(-0.804355\pi\) | ||||
0.816984 | − | 0.576661i | \(-0.195645\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20958.5 | 0.804223 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8509.06 | 0.325400 | 0.162700 | − | 0.986676i | \(-0.447980\pi\) | ||||
0.162700 | + | 0.986676i | \(0.447980\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3532.20i | − 0.134618i | −0.997732 | − | 0.0673091i | \(-0.978559\pi\) | ||||
0.997732 | − | 0.0673091i | \(-0.0214414\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11812.8i | 0.448681i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30349.5 | −1.14886 | −0.574429 | − | 0.818555i | \(-0.694776\pi\) | ||||
−0.574429 | + | 0.818555i | \(0.694776\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9612.56 | −0.362649 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 2518.59i | − 0.0946981i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34687.1i | 1.29984i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2678.55 | 0.100038 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25037.7 | 0.931980 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 3845.89i | − 0.142678i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21018.1i | 0.777154i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4668.16 | −0.172034 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29795.5 | −1.09440 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 36207.2i | − 1.32551i | −0.748835 | − | 0.662756i | \(-0.769387\pi\) | ||||
0.748835 | − | 0.662756i | \(-0.230613\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 6913.29i | − 0.252255i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40684.8 | 1.47964 | 0.739818 | − | 0.672808i | \(-0.234912\pi\) | ||||
0.739818 | + | 0.672808i | \(0.234912\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5561.29 | 0.201590 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 698.478i | − 0.0252360i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1909.96i | − 0.0687812i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46932.9 | −1.68463 | −0.842314 | − | 0.538986i | \(-0.818807\pi\) | ||||
−0.842314 | + | 0.538986i | \(0.818807\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22227.3 | 0.795239 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 616.761i | − 0.0219945i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 439.401i | − 0.0156188i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15925.9 | −0.564268 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9916.16 | −0.350203 | −0.175101 | − | 0.984550i | \(-0.556025\pi\) | ||||
−0.175101 | + | 0.984550i | \(0.556025\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5397.18i | 0.189995i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 11268.4i | − 0.395402i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10538.3 | 0.368597 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38298.5 | 1.33528 | 0.667640 | − | 0.744484i | \(-0.267305\pi\) | ||||
0.667640 | + | 0.744484i | \(0.267305\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 23964.4i | − 0.832852i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37798.8i | 1.30947i | 0.755861 | + | 0.654733i | \(0.227219\pi\) | ||||
−0.755861 | + | 0.654733i | \(0.772781\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57905.0 | 1.99963 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1486.43 | −0.0511677 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7106.74i | 0.243863i | 0.992539 | + | 0.121931i | \(0.0389088\pi\) | ||||
−0.992539 | + | 0.121931i | \(0.961091\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 41993.4i | − 1.43642i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2904.92 | −0.0990520 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50709.2 | 1.72364 | 0.861821 | − | 0.507212i | \(-0.169324\pi\) | ||||
0.861821 | + | 0.507212i | \(0.169324\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 39924.9i | − 1.35282i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 7340.09i | − 0.247933i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8685.99 | 0.292477 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27402.2 | −0.919815 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9120.39i | 0.305193i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18368.2i | 0.612738i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26572.3 | 0.883667 | 0.441833 | − | 0.897097i | \(-0.354328\pi\) | ||||
0.441833 | + | 0.897097i | \(0.354328\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14239.9 | −0.472086 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24027.0i | 0.794091i | 0.917799 | + | 0.397045i | \(0.129964\pi\) | ||||
−0.917799 | + | 0.397045i | \(0.870036\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 10299.6i | − 0.339353i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9274.67 | 0.304643 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9671.08 | 0.316689 | 0.158345 | − | 0.987384i | \(-0.449384\pi\) | ||||
0.158345 | + | 0.987384i | \(0.449384\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32001.0i | 1.04470i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10989.4i | 0.357660i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24568.3 | −0.797159 | −0.398579 | − | 0.917134i | \(-0.630497\pi\) | ||||
−0.398579 | + | 0.917134i | \(0.630497\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24833.6 | −0.803314 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6613.27i | 0.213275i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37894.2i | 1.21837i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33699.2 | 1.08021 | 0.540106 | − | 0.841597i | \(-0.318384\pi\) | ||||
0.540106 | + | 0.841597i | \(0.318384\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34284.0 | −1.09564 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 35857.4i | − 1.14247i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 43096.4i | − 1.36898i | −0.729020 | − | 0.684492i | \(-0.760024\pi\) | ||||
0.729020 | − | 0.684492i | \(-0.239976\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 187.877 | 0.00595013 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1344.4.c.a.673.2 | ✓ | 6 | |
4.3 | odd | 2 | 1344.4.c.d.673.5 | yes | 6 | ||
8.3 | odd | 2 | 1344.4.c.d.673.2 | yes | 6 | ||
8.5 | even | 2 | inner | 1344.4.c.a.673.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.c.a.673.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1344.4.c.a.673.5 | yes | 6 | 8.5 | even | 2 | inner | |
1344.4.c.d.673.2 | yes | 6 | 8.3 | odd | 2 | ||
1344.4.c.d.673.5 | yes | 6 | 4.3 | odd | 2 |