Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(440,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.440");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 440.6 | ||
Character | \(\chi\) | \(=\) | 441.440 |
Dual form | 441.4.c.b.440.5 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.641037i | 0.226641i | 0.993558 | + | 0.113320i | \(0.0361487\pi\) | ||||
−0.993558 | + | 0.113320i | \(0.963851\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.58907 | 0.948634 | ||||||||
\(5\) | −12.0729 | −1.07984 | −0.539918 | − | 0.841718i | \(-0.681545\pi\) | ||||
−0.539918 | + | 0.841718i | \(0.681545\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 9.99318i | 0.441640i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 7.73920i | − 0.244735i | ||||||||
\(11\) | − 43.9393i | − 1.20438i | −0.798353 | − | 0.602190i | \(-0.794295\pi\) | ||||
0.798353 | − | 0.602190i | \(-0.205705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 66.9783i | 1.42896i | 0.699657 | + | 0.714479i | \(0.253336\pi\) | ||||
−0.699657 | + | 0.714479i | \(0.746664\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 54.3066 | 0.848540 | ||||||||
\(17\) | −39.4310 | −0.562554 | −0.281277 | − | 0.959627i | \(-0.590758\pi\) | ||||
−0.281277 | + | 0.959627i | \(0.590758\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 57.9144i | 0.699288i | 0.936883 | + | 0.349644i | \(0.113698\pi\) | ||||
−0.936883 | + | 0.349644i | \(0.886302\pi\) | |||||||
\(20\) | −91.6223 | −1.02437 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 28.1667 | 0.272962 | ||||||||
\(23\) | − 46.1519i | − 0.418406i | −0.977872 | − | 0.209203i | \(-0.932913\pi\) | ||||
0.977872 | − | 0.209203i | \(-0.0670869\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 20.7555 | 0.166044 | ||||||||
\(26\) | −42.9356 | −0.323860 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 201.623i | 1.29105i | 0.763738 | + | 0.645526i | \(0.223362\pi\) | ||||
−0.763738 | + | 0.645526i | \(0.776638\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 185.521i | 1.07486i | 0.843309 | + | 0.537428i | \(0.180604\pi\) | ||||
−0.843309 | + | 0.537428i | \(0.819396\pi\) | |||||||
\(32\) | 114.758i | 0.633954i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 25.2767i | − 0.127498i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −410.805 | −1.82529 | −0.912647 | − | 0.408748i | \(-0.865966\pi\) | ||||
−0.912647 | + | 0.408748i | \(0.865966\pi\) | |||||||
\(38\) | −37.1253 | −0.158487 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 120.647i | − 0.476899i | ||||||||
\(41\) | −408.886 | −1.55749 | −0.778746 | − | 0.627339i | \(-0.784144\pi\) | ||||
−0.778746 | + | 0.627339i | \(0.784144\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 129.530 | 0.459377 | 0.229688 | − | 0.973264i | \(-0.426229\pi\) | ||||
0.229688 | + | 0.973264i | \(0.426229\pi\) | |||||||
\(44\) | − 333.458i | − 1.14252i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 29.5851 | 0.0948279 | ||||||||
\(47\) | 514.681 | 1.59732 | 0.798658 | − | 0.601785i | \(-0.205544\pi\) | ||||
0.798658 | + | 0.601785i | \(0.205544\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.3051i | 0.0376324i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 508.303i | 1.35556i | ||||||||
\(53\) | 437.584i | 1.13409i | 0.823687 | + | 0.567045i | \(0.191913\pi\) | ||||
−0.823687 | + | 0.567045i | \(0.808087\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 530.475i | 1.30053i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −129.248 | −0.292605 | ||||||||
\(59\) | −607.906 | −1.34140 | −0.670701 | − | 0.741728i | \(-0.734006\pi\) | ||||
−0.670701 | + | 0.741728i | \(0.734006\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 24.5192i | − 0.0514649i | −0.999669 | − | 0.0257324i | \(-0.991808\pi\) | ||||
0.999669 | − | 0.0257324i | \(-0.00819179\pi\) | |||||||
\(62\) | −118.926 | −0.243607 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 360.888 | 0.704860 | ||||||||
\(65\) | − 808.624i | − 1.54304i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 441.499 | 0.805041 | 0.402520 | − | 0.915411i | \(-0.368134\pi\) | ||||
0.402520 | + | 0.915411i | \(0.368134\pi\) | |||||||
\(68\) | −299.245 | −0.533658 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1150.89i | 1.92373i | 0.273518 | + | 0.961867i | \(0.411813\pi\) | ||||
−0.273518 | + | 0.961867i | \(0.588187\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 525.077i | − 0.841858i | −0.907094 | − | 0.420929i | \(-0.861704\pi\) | ||||
0.907094 | − | 0.420929i | \(-0.138296\pi\) | |||||||
\(74\) | − 263.341i | − 0.413686i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 439.517i | 0.663369i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −151.850 | −0.216259 | −0.108130 | − | 0.994137i | \(-0.534486\pi\) | ||||
−0.108130 | + | 0.994137i | \(0.534486\pi\) | |||||||
\(80\) | −655.639 | −0.916284 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 262.111i | − 0.352992i | ||||||||
\(83\) | −1302.05 | −1.72191 | −0.860956 | − | 0.508680i | \(-0.830134\pi\) | ||||
−0.860956 | + | 0.508680i | \(0.830134\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 476.047 | 0.607466 | ||||||||
\(86\) | 83.0338i | 0.104114i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 439.093 | 0.531903 | ||||||||
\(89\) | −583.190 | −0.694584 | −0.347292 | − | 0.937757i | \(-0.612899\pi\) | ||||
−0.347292 | + | 0.937757i | \(0.612899\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 350.250i | − 0.396914i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 329.929i | 0.362017i | ||||||||
\(95\) | − 699.196i | − 0.755116i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1091.84i | 1.14288i | 0.820643 | + | 0.571441i | \(0.193616\pi\) | ||||
−0.820643 | + | 0.571441i | \(0.806384\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 157.515 | 0.157515 | ||||||||
\(101\) | −156.773 | −0.154451 | −0.0772254 | − | 0.997014i | \(-0.524606\pi\) | ||||
−0.0772254 | + | 0.997014i | \(0.524606\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 241.078i | 0.230622i | 0.993329 | + | 0.115311i | \(0.0367865\pi\) | ||||
−0.993329 | + | 0.115311i | \(0.963213\pi\) | |||||||
\(104\) | −669.326 | −0.631085 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −280.507 | −0.257031 | ||||||||
\(107\) | − 12.8374i | − 0.0115985i | −0.999983 | − | 0.00579926i | \(-0.998154\pi\) | ||||
0.999983 | − | 0.00579926i | \(-0.00184597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2066.40 | −1.81583 | −0.907915 | − | 0.419154i | \(-0.862327\pi\) | ||||
−0.907915 | + | 0.419154i | \(0.862327\pi\) | |||||||
\(110\) | −340.055 | −0.294754 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 87.2159i | 0.0726069i | 0.999341 | + | 0.0363035i | \(0.0115583\pi\) | ||||
−0.999341 | + | 0.0363035i | \(0.988442\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 557.188i | 0.451809i | ||||||||
\(116\) | 1530.13i | 1.22474i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 389.691i | − 0.304016i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −599.659 | −0.450533 | ||||||||
\(122\) | 15.7177 | 0.0116640 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1407.93i | 1.01965i | ||||||||
\(125\) | 1258.54 | 0.900535 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1933.38 | 1.35086 | 0.675432 | − | 0.737423i | \(-0.263957\pi\) | ||||
0.675432 | + | 0.737423i | \(0.263957\pi\) | |||||||
\(128\) | 1149.41i | 0.793704i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 518.358 | 0.349716 | ||||||||
\(131\) | 1354.08 | 0.903105 | 0.451553 | − | 0.892244i | \(-0.350870\pi\) | ||||
0.451553 | + | 0.892244i | \(0.350870\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 283.018i | 0.182455i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 394.041i | − 0.248446i | ||||||||
\(137\) | 62.2722i | 0.0388341i | 0.999811 | + | 0.0194171i | \(0.00618103\pi\) | ||||
−0.999811 | + | 0.0194171i | \(0.993819\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2355.95i | − 1.43762i | −0.695208 | − | 0.718808i | \(-0.744688\pi\) | ||||
0.695208 | − | 0.718808i | \(-0.255312\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −737.761 | −0.435997 | ||||||||
\(143\) | 2942.98 | 1.72101 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 2434.18i | − 1.39412i | ||||||||
\(146\) | 336.594 | 0.190799 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3117.63 | −1.73154 | ||||||||
\(149\) | − 358.256i | − 0.196976i | −0.995138 | − | 0.0984881i | \(-0.968599\pi\) | ||||
0.995138 | − | 0.0984881i | \(-0.0314006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 460.319 | 0.248081 | 0.124040 | − | 0.992277i | \(-0.460415\pi\) | ||||
0.124040 | + | 0.992277i | \(0.460415\pi\) | |||||||
\(152\) | −578.749 | −0.308834 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2239.78i | − 1.16067i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 753.605i | − 0.383084i | −0.981484 | − | 0.191542i | \(-0.938651\pi\) | ||||
0.981484 | − | 0.191542i | \(-0.0613489\pi\) | |||||||
\(158\) | − 97.3416i | − 0.0490132i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 1385.46i | − 0.684566i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2413.72 | 1.15986 | 0.579929 | − | 0.814667i | \(-0.303080\pi\) | ||||
0.579929 | + | 0.814667i | \(0.303080\pi\) | |||||||
\(164\) | −3103.06 | −1.47749 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 834.663i | − 0.390256i | ||||||||
\(167\) | 2912.06 | 1.34935 | 0.674676 | − | 0.738114i | \(-0.264283\pi\) | ||||
0.674676 | + | 0.738114i | \(0.264283\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2289.10 | −1.04192 | ||||||||
\(170\) | 305.164i | 0.137677i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 983.016 | 0.435780 | ||||||||
\(173\) | 1739.54 | 0.764478 | 0.382239 | − | 0.924063i | \(-0.375153\pi\) | ||||
0.382239 | + | 0.924063i | \(0.375153\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 2386.19i | − 1.02197i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 373.846i | − 0.157421i | ||||||||
\(179\) | − 2636.53i | − 1.10091i | −0.834864 | − | 0.550456i | \(-0.814454\pi\) | ||||
0.834864 | − | 0.550456i | \(-0.185546\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 208.975i | 0.0858175i | 0.999079 | + | 0.0429087i | \(0.0136625\pi\) | ||||
−0.999079 | + | 0.0429087i | \(0.986338\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 461.204 | 0.184785 | ||||||||
\(185\) | 4959.62 | 1.97102 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1732.57i | 0.677529i | ||||||||
\(188\) | 3905.95 | 1.51527 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 448.211 | 0.171140 | ||||||||
\(191\) | 770.313i | 0.291822i | 0.989298 | + | 0.145911i | \(0.0466112\pi\) | ||||
−0.989298 | + | 0.145911i | \(0.953389\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 860.837 | 0.321059 | 0.160529 | − | 0.987031i | \(-0.448680\pi\) | ||||
0.160529 | + | 0.987031i | \(0.448680\pi\) | |||||||
\(194\) | −699.911 | −0.259024 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1034.13i | 0.374003i | 0.982360 | + | 0.187001i | \(0.0598769\pi\) | ||||
−0.982360 | + | 0.187001i | \(0.940123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 5161.09i | − 1.83849i | −0.393684 | − | 0.919246i | \(-0.628800\pi\) | ||||
0.393684 | − | 0.919246i | \(-0.371200\pi\) | |||||||
\(200\) | 207.414i | 0.0733318i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 100.498i | − 0.0350049i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4936.44 | 1.68184 | ||||||||
\(206\) | −154.540 | −0.0522685 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3637.36i | 1.21253i | ||||||||
\(209\) | 2544.72 | 0.842209 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 136.191 | 0.0444349 | 0.0222174 | − | 0.999753i | \(-0.492927\pi\) | ||||
0.0222174 | + | 0.999753i | \(0.492927\pi\) | |||||||
\(212\) | 3320.85i | 1.07584i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.22927 | 0.00262870 | ||||||||
\(215\) | −1563.81 | −0.496051 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 1324.64i | − 0.411541i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4025.82i | 1.23373i | ||||||||
\(221\) | − 2641.02i | − 0.803866i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2544.16i | − 0.763989i | −0.924165 | − | 0.381994i | \(-0.875237\pi\) | ||||
0.924165 | − | 0.381994i | \(-0.124763\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −55.9086 | −0.0164557 | ||||||||
\(227\) | 4438.19 | 1.29768 | 0.648840 | − | 0.760925i | \(-0.275254\pi\) | ||||
0.648840 | + | 0.760925i | \(0.275254\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 3108.73i | − 0.897077i | −0.893763 | − | 0.448539i | \(-0.851945\pi\) | ||||
0.893763 | − | 0.448539i | \(-0.148055\pi\) | |||||||
\(230\) | −357.179 | −0.102398 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2014.86 | −0.570181 | ||||||||
\(233\) | 4588.02i | 1.29000i | 0.764181 | + | 0.645002i | \(0.223143\pi\) | ||||
−0.764181 | + | 0.645002i | \(0.776857\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6213.70 | −1.72484 | ||||||||
\(236\) | −4613.45 | −1.27250 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 738.555i | − 0.199888i | −0.994993 | − | 0.0999439i | \(-0.968134\pi\) | ||||
0.994993 | − | 0.0999439i | \(-0.0318663\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 249.739i | − 0.0667515i | −0.999443 | − | 0.0333757i | \(-0.989374\pi\) | ||||
0.999443 | − | 0.0333757i | \(-0.0106258\pi\) | |||||||
\(242\) | − 384.404i | − 0.102109i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 186.078i | − 0.0488213i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3879.01 | −0.999253 | ||||||||
\(248\) | −1853.94 | −0.474700 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 806.768i | 0.204098i | ||||||||
\(251\) | −4098.68 | −1.03070 | −0.515351 | − | 0.856979i | \(-0.672338\pi\) | ||||
−0.515351 | + | 0.856979i | \(0.672338\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2027.88 | −0.503920 | ||||||||
\(254\) | 1239.37i | 0.306161i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2150.30 | 0.524974 | ||||||||
\(257\) | 2675.05 | 0.649280 | 0.324640 | − | 0.945838i | \(-0.394757\pi\) | ||||
0.324640 | + | 0.945838i | \(0.394757\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 6136.71i | − 1.46378i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 868.018i | 0.204681i | ||||||||
\(263\) | − 1884.79i | − 0.441904i | −0.975285 | − | 0.220952i | \(-0.929084\pi\) | ||||
0.975285 | − | 0.220952i | \(-0.0709165\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 5282.91i | − 1.22463i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3350.57 | 0.763689 | ||||||||
\(269\) | 1207.22 | 0.273626 | 0.136813 | − | 0.990597i | \(-0.456314\pi\) | ||||
0.136813 | + | 0.990597i | \(0.456314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4547.57i | 1.01935i | 0.860366 | + | 0.509677i | \(0.170235\pi\) | ||||
−0.860366 | + | 0.509677i | \(0.829765\pi\) | |||||||
\(272\) | −2141.36 | −0.477350 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −39.9188 | −0.00880140 | ||||||||
\(275\) | − 911.983i | − 0.199981i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4272.73 | −0.926799 | −0.463400 | − | 0.886149i | \(-0.653371\pi\) | ||||
−0.463400 | + | 0.886149i | \(0.653371\pi\) | |||||||
\(278\) | 1510.25 | 0.325823 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8218.49i | 1.74475i | 0.488840 | + | 0.872374i | \(0.337420\pi\) | ||||
−0.488840 | + | 0.872374i | \(0.662580\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4817.89i | − 1.01199i | −0.862536 | − | 0.505996i | \(-0.831125\pi\) | ||||
0.862536 | − | 0.505996i | \(-0.168875\pi\) | |||||||
\(284\) | 8734.16i | 1.82492i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1886.56i | 0.390051i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3358.20 | −0.683533 | ||||||||
\(290\) | 1560.40 | 0.315966 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 3984.85i | − 0.798615i | ||||||||
\(293\) | 6857.68 | 1.36734 | 0.683669 | − | 0.729792i | \(-0.260383\pi\) | ||||
0.683669 | + | 0.729792i | \(0.260383\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7339.21 | 1.44849 | ||||||||
\(296\) | − 4105.25i | − 0.806123i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 229.655 | 0.0446428 | ||||||||
\(299\) | 3091.18 | 0.597884 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 295.081i | 0.0562253i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3145.13i | 0.593374i | ||||||||
\(305\) | 296.018i | 0.0555736i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7537.04i | 1.40118i | 0.713565 | + | 0.700589i | \(0.247079\pi\) | ||||
−0.713565 | + | 0.700589i | \(0.752921\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1435.78 | 0.263055 | ||||||||
\(311\) | −5587.52 | −1.01878 | −0.509388 | − | 0.860537i | \(-0.670128\pi\) | ||||
−0.509388 | + | 0.860537i | \(0.670128\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 4221.53i | − 0.762348i | −0.924503 | − | 0.381174i | \(-0.875520\pi\) | ||||
0.924503 | − | 0.381174i | \(-0.124480\pi\) | |||||||
\(314\) | 483.089 | 0.0868226 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1152.40 | −0.205151 | ||||||||
\(317\) | − 8265.70i | − 1.46450i | −0.681034 | − | 0.732252i | \(-0.738469\pi\) | ||||
0.681034 | − | 0.732252i | \(-0.261531\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8859.18 | 1.55492 | ||||||||
\(320\) | −4356.98 | −0.761133 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2283.62i | − 0.393387i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1390.17i | 0.237270i | ||||||||
\(326\) | 1547.28i | 0.262871i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 4086.07i | − 0.687851i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7309.44 | −1.21379 | −0.606893 | − | 0.794783i | \(-0.707584\pi\) | ||||
−0.606893 | + | 0.794783i | \(0.707584\pi\) | |||||||
\(332\) | −9881.36 | −1.63346 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1866.74i | 0.305818i | ||||||||
\(335\) | −5330.19 | −0.869311 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 127.665 | 0.0206361 | 0.0103180 | − | 0.999947i | \(-0.496716\pi\) | ||||
0.0103180 | + | 0.999947i | \(0.496716\pi\) | |||||||
\(338\) | − 1467.40i | − 0.236141i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3612.76 | 0.576263 | ||||||||
\(341\) | 8151.66 | 1.29454 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1294.42i | 0.202879i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1115.11i | 0.173262i | ||||||||
\(347\) | − 5170.57i | − 0.799916i | −0.916533 | − | 0.399958i | \(-0.869025\pi\) | ||||
0.916533 | − | 0.399958i | \(-0.130975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11271.1i | 1.72874i | 0.502855 | + | 0.864370i | \(0.332283\pi\) | ||||
−0.502855 | + | 0.864370i | \(0.667717\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5042.38 | 0.763522 | ||||||||
\(353\) | −1657.92 | −0.249978 | −0.124989 | − | 0.992158i | \(-0.539890\pi\) | ||||
−0.124989 | + | 0.992158i | \(0.539890\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 13894.6i | − 2.07732i | ||||||||
\(356\) | −4425.87 | −0.658906 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1690.11 | 0.249512 | ||||||||
\(359\) | 285.803i | 0.0420170i | 0.999779 | + | 0.0210085i | \(0.00668770\pi\) | ||||
−0.999779 | + | 0.0210085i | \(0.993312\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3504.92 | 0.510996 | ||||||||
\(362\) | −133.961 | −0.0194498 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6339.22i | 0.909068i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 4406.07i | − 0.626690i | −0.949639 | − | 0.313345i | \(-0.898550\pi\) | ||||
0.949639 | − | 0.313345i | \(-0.101450\pi\) | |||||||
\(368\) | − 2506.35i | − 0.355034i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3179.30i | 0.446713i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12545.1 | −1.74144 | −0.870722 | − | 0.491776i | \(-0.836348\pi\) | ||||
−0.870722 | + | 0.491776i | \(0.836348\pi\) | |||||||
\(374\) | −1110.64 | −0.153556 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5143.29i | 0.705439i | ||||||||
\(377\) | −13504.4 | −1.84486 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4695.85 | 0.636437 | 0.318219 | − | 0.948017i | \(-0.396915\pi\) | ||||
0.318219 | + | 0.948017i | \(0.396915\pi\) | |||||||
\(380\) | − 5306.25i | − 0.716329i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −493.800 | −0.0661387 | ||||||||
\(383\) | −7190.02 | −0.959250 | −0.479625 | − | 0.877474i | \(-0.659227\pi\) | ||||
−0.479625 | + | 0.877474i | \(0.659227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 551.828i | 0.0727651i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8286.06i | 1.08418i | ||||||||
\(389\) | 9187.81i | 1.19753i | 0.800923 | + | 0.598767i | \(0.204342\pi\) | ||||
−0.800923 | + | 0.598767i | \(0.795658\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1819.81i | 0.235376i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −662.914 | −0.0847643 | ||||||||
\(395\) | 1833.28 | 0.233524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11951.8i | 1.51094i | 0.655182 | + | 0.755471i | \(0.272592\pi\) | ||||
−0.655182 | + | 0.755471i | \(0.727408\pi\) | |||||||
\(398\) | 3308.45 | 0.416677 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1127.16 | 0.140895 | ||||||||
\(401\) | − 6844.67i | − 0.852386i | −0.904632 | − | 0.426193i | \(-0.859854\pi\) | ||||
0.904632 | − | 0.426193i | \(-0.140146\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12425.9 | −1.53592 | ||||||||
\(404\) | −1189.76 | −0.146517 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18050.5i | 2.19835i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5166.93i | 0.624666i | 0.949973 | + | 0.312333i | \(0.101110\pi\) | ||||
−0.949973 | + | 0.312333i | \(0.898890\pi\) | |||||||
\(410\) | 3164.45i | 0.381173i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1829.56i | 0.218776i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15719.6 | 1.85938 | ||||||||
\(416\) | −7686.29 | −0.905893 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1631.26i | 0.190879i | ||||||||
\(419\) | −13900.4 | −1.62071 | −0.810356 | − | 0.585938i | \(-0.800726\pi\) | ||||
−0.810356 | + | 0.585938i | \(0.800726\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7800.31 | 0.903003 | 0.451501 | − | 0.892270i | \(-0.350889\pi\) | ||||
0.451501 | + | 0.892270i | \(0.350889\pi\) | |||||||
\(422\) | 87.3033i | 0.0100708i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4372.85 | −0.500859 | ||||||||
\(425\) | −818.411 | −0.0934089 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 97.4241i | − 0.0110027i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 1002.46i | − 0.112426i | ||||||||
\(431\) | − 2085.65i | − 0.233091i | −0.993185 | − | 0.116546i | \(-0.962818\pi\) | ||||
0.993185 | − | 0.116546i | \(-0.0371821\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 1186.95i | − 0.131735i | −0.997828 | − | 0.0658674i | \(-0.979019\pi\) | ||||
0.997828 | − | 0.0658674i | \(-0.0209814\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15682.1 | −1.72256 | ||||||||
\(437\) | 2672.86 | 0.292586 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8692.50i | 0.945035i | 0.881321 | + | 0.472518i | \(0.156655\pi\) | ||||
−0.881321 | + | 0.472518i | \(0.843345\pi\) | |||||||
\(440\) | −5301.13 | −0.574367 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1692.99 | 0.182189 | ||||||||
\(443\) | 6758.69i | 0.724864i | 0.932010 | + | 0.362432i | \(0.118054\pi\) | ||||
−0.932010 | + | 0.362432i | \(0.881946\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7040.81 | 0.750037 | ||||||||
\(446\) | 1630.90 | 0.173151 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 6721.89i | − 0.706516i | −0.935526 | − | 0.353258i | \(-0.885074\pi\) | ||||
0.935526 | − | 0.353258i | \(-0.114926\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17966.1i | 1.87581i | ||||||||
\(452\) | 661.888i | 0.0688774i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2845.05i | 0.294107i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3301.86 | −0.337975 | −0.168988 | − | 0.985618i | \(-0.554050\pi\) | ||||
−0.168988 | + | 0.985618i | \(0.554050\pi\) | |||||||
\(458\) | 1992.81 | 0.203314 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4228.54i | 0.428602i | ||||||||
\(461\) | −7241.19 | −0.731574 | −0.365787 | − | 0.930699i | \(-0.619200\pi\) | ||||
−0.365787 | + | 0.930699i | \(0.619200\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7585.65 | −0.761415 | −0.380707 | − | 0.924696i | \(-0.624319\pi\) | ||||
−0.380707 | + | 0.924696i | \(0.624319\pi\) | |||||||
\(464\) | 10949.5i | 1.09551i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2941.09 | −0.292368 | ||||||||
\(467\) | 2048.56 | 0.202990 | 0.101495 | − | 0.994836i | \(-0.467637\pi\) | ||||
0.101495 | + | 0.994836i | \(0.467637\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 3983.21i | − 0.390919i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 6074.92i | − 0.592417i | ||||||||
\(473\) | − 5691.47i | − 0.553264i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1202.04i | 0.116113i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 473.442 | 0.0453027 | ||||||||
\(479\) | −3297.04 | −0.314500 | −0.157250 | − | 0.987559i | \(-0.550263\pi\) | ||||
−0.157250 | + | 0.987559i | \(0.550263\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 27515.0i | − 2.60827i | ||||||||
\(482\) | 160.092 | 0.0151286 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4550.85 | −0.427390 | ||||||||
\(485\) | − 13181.7i | − 1.23413i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1179.71 | −0.109769 | −0.0548846 | − | 0.998493i | \(-0.517479\pi\) | ||||
−0.0548846 | + | 0.998493i | \(0.517479\pi\) | |||||||
\(488\) | 245.024 | 0.0227290 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7573.80i | 0.696132i | 0.937470 | + | 0.348066i | \(0.113162\pi\) | ||||
−0.937470 | + | 0.348066i | \(0.886838\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 7950.21i | − 0.726287i | ||||||||
\(494\) | − 2486.59i | − 0.226472i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10075.0i | 0.912059i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1819.53 | −0.163233 | −0.0816167 | − | 0.996664i | \(-0.526008\pi\) | ||||
−0.0816167 | + | 0.996664i | \(0.526008\pi\) | |||||||
\(500\) | 9551.12 | 0.854278 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 2627.41i | − 0.233599i | ||||||||
\(503\) | 15635.9 | 1.38602 | 0.693012 | − | 0.720926i | \(-0.256283\pi\) | ||||
0.693012 | + | 0.720926i | \(0.256283\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1892.71 | 0.166781 | ||||||||
\(506\) | − 1299.95i | − 0.114209i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14672.6 | 1.28147 | ||||||||
\(509\) | 3293.79 | 0.286827 | 0.143413 | − | 0.989663i | \(-0.454192\pi\) | ||||
0.143413 | + | 0.989663i | \(0.454192\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 10573.7i | 0.912685i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1714.81i | 0.147153i | ||||||||
\(515\) | − 2910.51i | − 0.249034i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 22614.7i | − 1.92378i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8080.73 | 0.681468 | ||||||||
\(521\) | −3298.04 | −0.277332 | −0.138666 | − | 0.990339i | \(-0.544281\pi\) | ||||
−0.138666 | + | 0.990339i | \(0.544281\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17826.4i | 1.49043i | 0.666824 | + | 0.745215i | \(0.267653\pi\) | ||||
−0.666824 | + | 0.745215i | \(0.732347\pi\) | |||||||
\(524\) | 10276.2 | 0.856716 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1208.22 | 0.100154 | ||||||||
\(527\) | − 7315.28i | − 0.604665i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10037.0 | 0.824937 | ||||||||
\(530\) | 3386.54 | 0.277551 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 27386.5i | − 2.22559i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 154.985i | 0.0125245i | ||||||||
\(536\) | 4411.98i | 0.355538i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 773.871i | 0.0620148i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10418.2 | 0.827939 | 0.413969 | − | 0.910291i | \(-0.364142\pi\) | ||||
0.413969 | + | 0.910291i | \(0.364142\pi\) | |||||||
\(542\) | −2915.16 | −0.231027 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 4525.02i | − 0.356633i | ||||||||
\(545\) | 24947.5 | 1.96080 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −996.607 | −0.0779010 | −0.0389505 | − | 0.999241i | \(-0.512401\pi\) | ||||
−0.0389505 | + | 0.999241i | \(0.512401\pi\) | |||||||
\(548\) | 472.588i | 0.0368394i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 584.615 | 0.0453238 | ||||||||
\(551\) | −11676.9 | −0.902818 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 2738.98i | − 0.210051i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 17879.4i | − 1.36377i | ||||||||
\(557\) | 11137.4i | 0.847229i | 0.905843 | + | 0.423614i | \(0.139239\pi\) | ||||
−0.905843 | + | 0.423614i | \(0.860761\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8675.73i | 0.656430i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5268.36 | −0.395431 | ||||||||
\(563\) | 4191.49 | 0.313766 | 0.156883 | − | 0.987617i | \(-0.449855\pi\) | ||||
0.156883 | + | 0.987617i | \(0.449855\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1052.95i | − 0.0784035i | ||||||||
\(566\) | 3088.45 | 0.229359 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11501.0 | −0.849598 | ||||||||
\(569\) | 2997.85i | 0.220873i | 0.993883 | + | 0.110436i | \(0.0352248\pi\) | ||||
−0.993883 | + | 0.110436i | \(0.964775\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1762.22 | 0.129154 | 0.0645768 | − | 0.997913i | \(-0.479430\pi\) | ||||
0.0645768 | + | 0.997913i | \(0.479430\pi\) | |||||||
\(572\) | 22334.5 | 1.63261 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 957.907i | − 0.0694739i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 15400.1i | − 1.11111i | −0.831478 | − | 0.555557i | \(-0.812505\pi\) | ||||
0.831478 | − | 0.555557i | \(-0.187495\pi\) | |||||||
\(578\) | − 2152.73i | − 0.154917i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 18473.2i | − 1.32251i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19227.1 | 1.36587 | ||||||||
\(584\) | 5247.19 | 0.371798 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4396.03i | 0.309895i | ||||||||
\(587\) | 2642.97 | 0.185838 | 0.0929190 | − | 0.995674i | \(-0.470380\pi\) | ||||
0.0929190 | + | 0.995674i | \(0.470380\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10744.3 | −0.751635 | ||||||||
\(590\) | 4704.71i | 0.328288i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −22309.4 | −1.54884 | ||||||||
\(593\) | 1201.90 | 0.0832312 | 0.0416156 | − | 0.999134i | \(-0.486750\pi\) | ||||
0.0416156 | + | 0.999134i | \(0.486750\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 2718.83i | − 0.186858i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1981.56i | 0.135505i | ||||||||
\(599\) | − 9853.11i | − 0.672099i | −0.941844 | − | 0.336049i | \(-0.890909\pi\) | ||||
0.941844 | − | 0.336049i | \(-0.109091\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 7573.82i | − 0.514047i | −0.966405 | − | 0.257024i | \(-0.917258\pi\) | ||||
0.966405 | − | 0.257024i | \(-0.0827418\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3493.39 | 0.235338 | ||||||||
\(605\) | 7239.64 | 0.486501 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 19797.0i | − 1.32378i | −0.749599 | − | 0.661892i | \(-0.769754\pi\) | ||||
0.749599 | − | 0.661892i | \(-0.230246\pi\) | |||||||
\(608\) | −6646.14 | −0.443317 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −189.759 | −0.0125952 | ||||||||
\(611\) | 34472.4i | 2.28250i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10527.7 | −0.693656 | −0.346828 | − | 0.937929i | \(-0.612741\pi\) | ||||
−0.346828 | + | 0.937929i | \(0.612741\pi\) | |||||||
\(614\) | −4831.52 | −0.317564 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 23133.1i | − 1.50940i | −0.656067 | − | 0.754702i | \(-0.727781\pi\) | ||||
0.656067 | − | 0.754702i | \(-0.272219\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16344.4i | 1.06129i | 0.847595 | + | 0.530643i | \(0.178049\pi\) | ||||
−0.847595 | + | 0.530643i | \(0.821951\pi\) | |||||||
\(620\) | − 16997.9i | − 1.10105i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 3581.81i | − 0.230896i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17788.6 | −1.13847 | ||||||||
\(626\) | 2706.16 | 0.172779 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 5719.17i | − 0.363407i | ||||||||
\(629\) | 16198.4 | 1.02683 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11124.2 | −0.701819 | −0.350909 | − | 0.936409i | \(-0.614127\pi\) | ||||
−0.350909 | + | 0.936409i | \(0.614127\pi\) | |||||||
\(632\) | − 1517.47i | − 0.0955088i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5298.62 | 0.331917 | ||||||||
\(635\) | −23341.5 | −1.45871 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5679.07i | 0.352408i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 13876.7i | − 0.857070i | ||||||||
\(641\) | 3582.68i | 0.220760i | 0.993889 | + | 0.110380i | \(0.0352068\pi\) | ||||
−0.993889 | + | 0.110380i | \(0.964793\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 14145.6i | − 0.867570i | −0.901016 | − | 0.433785i | \(-0.857178\pi\) | ||||
0.901016 | − | 0.433785i | \(-0.142822\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1463.89 | 0.0891577 | ||||||||
\(647\) | 23914.6 | 1.45314 | 0.726568 | − | 0.687095i | \(-0.241114\pi\) | ||||
0.726568 | + | 0.687095i | \(0.241114\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26711.0i | 1.61556i | ||||||||
\(650\) | −891.152 | −0.0537751 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18317.9 | 1.10028 | ||||||||
\(653\) | 25410.7i | 1.52281i | 0.648276 | + | 0.761406i | \(0.275490\pi\) | ||||
−0.648276 | + | 0.761406i | \(0.724510\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16347.7 | −0.975205 | ||||||||
\(656\) | −22205.2 | −1.32160 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 14977.5i | − 0.885342i | −0.896684 | − | 0.442671i | \(-0.854031\pi\) | ||||
0.896684 | − | 0.442671i | \(-0.145969\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 102.280i | 0.00601852i | 0.999995 | + | 0.00300926i | \(0.000957878\pi\) | ||||
−0.999995 | + | 0.00300926i | \(0.999042\pi\) | |||||||
\(662\) | − 4685.63i | − 0.275094i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 13011.6i | − 0.760465i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9305.30 | 0.540184 | ||||||||
\(668\) | 22099.8 | 1.28004 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 3416.85i | − 0.197022i | ||||||||
\(671\) | −1077.35 | −0.0619833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7778.89 | 0.445549 | 0.222774 | − | 0.974870i | \(-0.428489\pi\) | ||||
0.222774 | + | 0.974870i | \(0.428489\pi\) | |||||||
\(674\) | 81.8380i | 0.00467698i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17372.1 | −0.988400 | ||||||||
\(677\) | 20416.1 | 1.15902 | 0.579510 | − | 0.814965i | \(-0.303244\pi\) | ||||
0.579510 | + | 0.814965i | \(0.303244\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4757.22i | 0.268281i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5225.52i | 0.293395i | ||||||||
\(683\) | 26805.4i | 1.50173i | 0.660458 | + | 0.750863i | \(0.270362\pi\) | ||||
−0.660458 | + | 0.750863i | \(0.729638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 751.808i | − 0.0419345i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7034.35 | 0.389800 | ||||||||
\(689\) | −29308.6 | −1.62056 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32711.2i | 1.80086i | 0.435003 | + | 0.900429i | \(0.356747\pi\) | ||||
−0.435003 | + | 0.900429i | \(0.643253\pi\) | |||||||
\(692\) | 13201.5 | 0.725210 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3314.53 | 0.181294 | ||||||||
\(695\) | 28443.2i | 1.55239i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16122.8 | 0.876174 | ||||||||
\(698\) | −7225.22 | −0.391803 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 503.993i | − 0.0271548i | −0.999908 | − | 0.0135774i | \(-0.995678\pi\) | ||||
0.999908 | − | 0.0135774i | \(-0.00432196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 23791.5i | − 1.27641i | ||||||||
\(704\) | − 15857.2i | − 0.848920i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 1062.79i | − 0.0566553i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13787.5 | 0.730327 | 0.365163 | − | 0.930943i | \(-0.381013\pi\) | ||||
0.365163 | + | 0.930943i | \(0.381013\pi\) | |||||||
\(710\) | 8906.94 | 0.470805 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 5827.92i | − 0.306756i | ||||||||
\(713\) | 8562.15 | 0.449726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35530.4 | −1.85841 | ||||||||
\(716\) | − 20008.8i | − 1.04436i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −183.210 | −0.00952276 | ||||||||
\(719\) | −32223.1 | −1.67138 | −0.835688 | − | 0.549205i | \(-0.814931\pi\) | ||||
−0.835688 | + | 0.549205i | \(0.814931\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2246.78i | 0.115813i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1585.92i | 0.0814094i | ||||||||
\(725\) | 4184.80i | 0.214372i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33807.4i | 1.72469i | 0.506325 | + | 0.862343i | \(0.331004\pi\) | ||||
−0.506325 | + | 0.862343i | \(0.668996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4063.67 | −0.206032 | ||||||||
\(731\) | −5107.51 | −0.258424 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 16442.8i | − 0.828551i | −0.910152 | − | 0.414275i | \(-0.864035\pi\) | ||||
0.910152 | − | 0.414275i | \(-0.135965\pi\) | |||||||
\(734\) | 2824.46 | 0.142034 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5296.30 | 0.265250 | ||||||||
\(737\) | − 19399.2i | − 0.969575i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20205.4 | −1.00578 | −0.502888 | − | 0.864351i | \(-0.667729\pi\) | ||||
−0.502888 | + | 0.864351i | \(0.667729\pi\) | |||||||
\(740\) | 37638.9 | 1.86977 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 14573.9i | − 0.719601i | −0.933029 | − | 0.359800i | \(-0.882845\pi\) | ||||
0.933029 | − | 0.359800i | \(-0.117155\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4325.19i | 0.212702i | ||||||||
\(746\) | − 8041.85i | − 0.394682i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13148.6i | 0.642727i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2689.06 | 0.130659 | 0.0653297 | − | 0.997864i | \(-0.479190\pi\) | ||||
0.0653297 | + | 0.997864i | \(0.479190\pi\) | |||||||
\(752\) | 27950.5 | 1.35539 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 8656.82i | − 0.418120i | ||||||||
\(755\) | −5557.39 | −0.267886 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11192.8 | 0.537395 | 0.268697 | − | 0.963225i | \(-0.413407\pi\) | ||||
0.268697 | + | 0.963225i | \(0.413407\pi\) | |||||||
\(758\) | 3010.22i | 0.144243i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6987.19 | 0.333490 | ||||||||
\(761\) | 29063.4 | 1.38442 | 0.692212 | − | 0.721694i | \(-0.256636\pi\) | ||||
0.692212 | + | 0.721694i | \(0.256636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5845.96i | 0.276832i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 4609.07i | − 0.217405i | ||||||||
\(767\) | − 40716.6i | − 1.91681i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 40870.3i | − 1.91654i | −0.285861 | − | 0.958271i | \(-0.592280\pi\) | ||||
0.285861 | − | 0.958271i | \(-0.407720\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6532.95 | 0.304567 | ||||||||
\(773\) | −40291.6 | −1.87476 | −0.937378 | − | 0.348313i | \(-0.886755\pi\) | ||||
−0.937378 | + | 0.348313i | \(0.886755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3850.59i | 0.178474i | ||||||||
\(776\) | −10911.0 | −0.504743 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5889.73 | −0.271410 | ||||||||
\(779\) | − 23680.4i | − 1.08914i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50569.1 | 2.31691 | ||||||||
\(782\) | −1166.57 | −0.0533458 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9098.22i | 0.413668i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 5001.02i | − 0.226515i | −0.993566 | − | 0.113257i | \(-0.963872\pi\) | ||||
0.993566 | − | 0.113257i | \(-0.0361284\pi\) | |||||||
\(788\) | 7848.07i | 0.354792i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1175.20i | 0.0529262i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1642.25 | 0.0735411 | ||||||||
\(794\) | −7661.56 | −0.342441 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 39167.9i | − 1.74406i | ||||||||
\(797\) | 8762.59 | 0.389444 | 0.194722 | − | 0.980858i | \(-0.437620\pi\) | ||||
0.194722 | + | 0.980858i | \(0.437620\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20294.4 | −0.898577 | ||||||||
\(800\) | 2381.86i | 0.105264i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4387.69 | 0.193185 | ||||||||
\(803\) | −23071.5 | −1.01392 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 7965.46i | − 0.348103i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 1566.66i | − 0.0682116i | ||||||||
\(809\) | 38643.8i | 1.67941i | 0.543043 | + | 0.839705i | \(0.317272\pi\) | ||||
−0.543043 | + | 0.839705i | \(0.682728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3577.67i | 0.154906i | 0.996996 | + | 0.0774530i | \(0.0246788\pi\) | ||||
−0.996996 | + | 0.0774530i | \(0.975321\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11571.0 | −0.498236 | ||||||||
\(815\) | −29140.6 | −1.25246 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7501.68i | 0.321237i | ||||||||
\(818\) | −3312.20 | −0.141575 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 37463.0 | 1.59545 | ||||||||
\(821\) | − 21009.0i | − 0.893081i | −0.894763 | − | 0.446541i | \(-0.852656\pi\) | ||||
0.894763 | − | 0.446541i | \(-0.147344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31309.2 | 1.32609 | 0.663044 | − | 0.748580i | \(-0.269264\pi\) | ||||
0.663044 | + | 0.748580i | \(0.269264\pi\) | |||||||
\(824\) | −2409.13 | −0.101852 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27813.3i | 1.16949i | 0.811219 | + | 0.584743i | \(0.198805\pi\) | ||||
−0.811219 | + | 0.584743i | \(0.801195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35061.5i | 1.46892i | 0.678652 | + | 0.734460i | \(0.262565\pi\) | ||||
−0.678652 | + | 0.734460i | \(0.737435\pi\) | |||||||
\(830\) | 10076.8i | 0.421412i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24171.7i | 1.00722i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35157.1 | −1.45708 | ||||||||
\(836\) | 19312.0 | 0.798948 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 8910.66i | − 0.367320i | ||||||||
\(839\) | −4808.56 | −0.197866 | −0.0989332 | − | 0.995094i | \(-0.531543\pi\) | ||||
−0.0989332 | + | 0.995094i | \(0.531543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16263.0 | −0.666816 | ||||||||
\(842\) | 5000.29i | 0.204657i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1033.56 | 0.0421524 | ||||||||
\(845\) | 27636.1 | 1.12510 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 23763.7i | 0.962320i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 524.632i | − 0.0211703i | ||||||||
\(851\) | 18959.4i | 0.763714i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9486.81i | 0.380800i | 0.981707 | + | 0.190400i | \(0.0609784\pi\) | ||||
−0.981707 | + | 0.190400i | \(0.939022\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 128.287 | 0.00512237 | ||||||||
\(857\) | 22524.7 | 0.897818 | 0.448909 | − | 0.893577i | \(-0.351813\pi\) | ||||
0.448909 | + | 0.893577i | \(0.351813\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27644.3i | 1.09804i | 0.835811 | + | 0.549018i | \(0.184998\pi\) | ||||
−0.835811 | + | 0.549018i | \(0.815002\pi\) | |||||||
\(860\) | −11867.9 | −0.470571 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1336.98 | 0.0528280 | ||||||||
\(863\) | − 20158.0i | − 0.795116i | −0.917577 | − | 0.397558i | \(-0.869858\pi\) | ||||
0.917577 | − | 0.397558i | \(-0.130142\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21001.3 | −0.825510 | ||||||||
\(866\) | 760.879 | 0.0298565 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6672.18i | 0.260458i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29570.9i | 1.15037i | ||||||||
\(872\) | − 20649.9i | − 0.801944i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1713.40i | 0.0663120i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30973.1 | −1.19258 | −0.596288 | − | 0.802771i | \(-0.703358\pi\) | ||||
−0.596288 | + | 0.802771i | \(0.703358\pi\) | |||||||
\(878\) | −5572.22 | −0.214184 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 28808.3i | 1.10355i | ||||||||
\(881\) | −10973.0 | −0.419626 | −0.209813 | − | 0.977741i | \(-0.567286\pi\) | ||||
−0.209813 | + | 0.977741i | \(0.567286\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42025.5 | 1.60167 | 0.800833 | − | 0.598888i | \(-0.204390\pi\) | ||||
0.800833 | + | 0.598888i | \(0.204390\pi\) | |||||||
\(884\) | − 20042.9i | − 0.762574i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4332.57 | −0.164284 | ||||||||
\(887\) | −4681.12 | −0.177200 | −0.0886002 | − | 0.996067i | \(-0.528239\pi\) | ||||
−0.0886002 | + | 0.996067i | \(0.528239\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4513.42i | 0.169989i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 19307.8i | − 0.724746i | ||||||||
\(893\) | 29807.4i | 1.11698i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31830.6i | 1.18880i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4308.98 | 0.160125 | ||||||||
\(899\) | −37405.4 | −1.38770 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 17254.3i | − 0.637986i | ||||||||
\(902\) | −11517.0 | −0.425136 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −871.564 | −0.0320661 | ||||||||
\(905\) | − 2522.94i | − 0.0926687i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48406.5 | −1.77212 | −0.886060 | − | 0.463571i | \(-0.846568\pi\) | ||||
−0.886060 | + | 0.463571i | \(0.846568\pi\) | |||||||
\(908\) | 33681.8 | 1.23102 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 20920.5i | − 0.760842i | −0.924813 | − | 0.380421i | \(-0.875779\pi\) | ||||
0.924813 | − | 0.380421i | \(-0.124221\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57211.1i | 2.07384i | ||||||||
\(914\) | − 2116.62i | − 0.0765990i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 23592.4i | − 0.850998i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33471.4 | 1.20143 | 0.600717 | − | 0.799462i | \(-0.294882\pi\) | ||||
0.600717 | + | 0.799462i | \(0.294882\pi\) | |||||||
\(920\) | −5568.08 | −0.199537 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 4641.87i | − 0.165805i | ||||||||
\(923\) | −77084.5 | −2.74893 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8526.48 | −0.303080 | ||||||||
\(926\) | − 4862.68i | − 0.172568i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23137.9 | −0.818468 | ||||||||
\(929\) | −9370.97 | −0.330949 | −0.165475 | − | 0.986214i | \(-0.552916\pi\) | ||||
−0.165475 | + | 0.986214i | \(0.552916\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 34818.8i | 1.22374i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1313.20i | 0.0460057i | ||||||||
\(935\) | − 20917.2i | − 0.731620i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29702.0i | 1.03556i | 0.855513 | + | 0.517781i | \(0.173242\pi\) | ||||
−0.855513 | + | 0.517781i | \(0.826758\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −47156.2 | −1.63624 | ||||||||
\(941\) | 4903.33 | 0.169866 | 0.0849331 | − | 0.996387i | \(-0.472932\pi\) | ||||
0.0849331 | + | 0.996387i | \(0.472932\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18870.8i | 0.651664i | ||||||||
\(944\) | −33013.3 | −1.13823 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3648.44 | 0.125392 | ||||||||
\(947\) | 21004.5i | 0.720755i | 0.932807 | + | 0.360378i | \(0.117352\pi\) | ||||
−0.932807 | + | 0.360378i | \(0.882648\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35168.8 | 1.20298 | ||||||||
\(950\) | −770.555 | −0.0263159 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 4598.25i | − 0.156298i | −0.996942 | − | 0.0781489i | \(-0.975099\pi\) | ||||
0.996942 | − | 0.0781489i | \(-0.0249010\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 9299.94i | − 0.315119i | ||||||||
\(956\) | − 5604.95i | − 0.189620i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 2113.52i | − 0.0712785i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4627.06 | −0.155317 | ||||||||
\(962\) | 17638.2 | 0.591140 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 1895.29i | − 0.0633227i | ||||||||
\(965\) | −10392.8 | −0.346691 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52408.6 | 1.74286 | 0.871431 | − | 0.490518i | \(-0.163192\pi\) | ||||
0.871431 | + | 0.490518i | \(0.163192\pi\) | |||||||
\(968\) | − 5992.50i | − 0.198973i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8449.97 | 0.279703 | ||||||||
\(971\) | −48712.4 | −1.60994 | −0.804971 | − | 0.593314i | \(-0.797819\pi\) | ||||
−0.804971 | + | 0.593314i | \(0.797819\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 756.236i | − 0.0248782i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 1331.55i | − 0.0436700i | ||||||||
\(977\) | 11655.7i | 0.381676i | 0.981622 | + | 0.190838i | \(0.0611206\pi\) | ||||
−0.981622 | + | 0.190838i | \(0.938879\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25624.9i | 0.836544i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4855.09 | −0.157772 | ||||||||
\(983\) | −40457.2 | −1.31270 | −0.656350 | − | 0.754457i | \(-0.727900\pi\) | ||||
−0.656350 | + | 0.754457i | \(0.727900\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 12484.9i | − 0.403861i | ||||||||
\(986\) | 5096.38 | 0.164606 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −29438.1 | −0.947925 | ||||||||
\(989\) | − 5978.07i | − 0.192206i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9660.88 | 0.309675 | 0.154838 | − | 0.987940i | \(-0.450515\pi\) | ||||
0.154838 | + | 0.987940i | \(0.450515\pi\) | |||||||
\(992\) | −21290.0 | −0.681410 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 62309.4i | 1.98527i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4997.01i | 0.158733i | 0.996846 | + | 0.0793665i | \(0.0252897\pi\) | ||||
−0.996846 | + | 0.0793665i | \(0.974710\pi\) | |||||||
\(998\) | − 1166.39i | − 0.0369954i | ||||||||
\(999\) | 0 | 0 |
(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 | 441.4.c.b.440.6 | yes | 24 | |
3.2 | odd | 2 | inner | 441.4.c.b.440.19 | yes | 24 | |
7.2 | even | 3 | 441.4.p.d.80.14 | 48 | |||
7.3 | odd | 6 | 441.4.p.d.215.11 | 48 | |||
7.4 | even | 3 | 441.4.p.d.215.12 | 48 | |||
7.5 | odd | 6 | 441.4.p.d.80.13 | 48 | |||
7.6 | odd | 2 | inner | 441.4.c.b.440.20 | yes | 24 | |
21.2 | odd | 6 | 441.4.p.d.80.11 | 48 | |||
21.5 | even | 6 | 441.4.p.d.80.12 | 48 | |||
21.11 | odd | 6 | 441.4.p.d.215.13 | 48 | |||
21.17 | even | 6 | 441.4.p.d.215.14 | 48 | |||
21.20 | even | 2 | inner | 441.4.c.b.440.5 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.4.c.b.440.5 | ✓ | 24 | 21.20 | even | 2 | inner | |
441.4.c.b.440.6 | yes | 24 | 1.1 | even | 1 | trivial | |
441.4.c.b.440.19 | yes | 24 | 3.2 | odd | 2 | inner | |
441.4.c.b.440.20 | yes | 24 | 7.6 | odd | 2 | inner | |
441.4.p.d.80.11 | 48 | 21.2 | odd | 6 | |||
441.4.p.d.80.12 | 48 | 21.5 | even | 6 | |||
441.4.p.d.80.13 | 48 | 7.5 | odd | 6 | |||
441.4.p.d.80.14 | 48 | 7.2 | even | 3 | |||
441.4.p.d.215.11 | 48 | 7.3 | odd | 6 | |||
441.4.p.d.215.12 | 48 | 7.4 | even | 3 | |||
441.4.p.d.215.13 | 48 | 21.11 | odd | 6 | |||
441.4.p.d.215.14 | 48 | 21.17 | even | 6 |