Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [100,4,Mod(9,100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("100.9");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.i (of order \(10\), degree \(4\), 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: | \(5.90019100057\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 29.2 | ||
Character | \(\chi\) | \(=\) | 100.29 |
Dual form | 100.4.i.a.69.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(77\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{10}\right)\) |
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 | ||||||||
\(3\) | −4.13050 | + | 5.68515i | −0.794916 | + | 1.09411i | 0.198563 | + | 0.980088i | \(0.436373\pi\) |
−0.993478 | + | 0.114020i | \(0.963627\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.7351 | + | 3.12376i | −0.960176 | + | 0.279397i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 21.6979i | − | 1.17157i | −0.810465 | − | 0.585787i | \(-0.800785\pi\) | ||
0.810465 | − | 0.585787i | \(-0.199215\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.91642 | − | 21.2866i | −0.256164 | − | 0.788391i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.15870 | − | 9.72148i | 0.0865804 | − | 0.266467i | −0.898388 | − | 0.439203i | \(-0.855261\pi\) |
0.984968 | + | 0.172736i | \(0.0552608\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 72.0487 | − | 23.4100i | 1.53713 | − | 0.499444i | 0.586548 | − | 0.809914i | \(-0.300486\pi\) |
0.950583 | + | 0.310470i | \(0.100486\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 26.5823 | − | 73.9333i | 0.457568 | − | 1.27263i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −77.2706 | − | 106.354i | −1.10240 | − | 1.51733i | −0.832159 | − | 0.554537i | \(-0.812895\pi\) |
−0.270245 | − | 0.962792i | \(-0.587105\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −93.9419 | + | 68.2527i | −1.13430 | + | 0.824119i | −0.986315 | − | 0.164871i | \(-0.947279\pi\) |
−0.147987 | + | 0.988989i | \(0.547279\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 123.356 | + | 89.6231i | 1.28183 | + | 0.931303i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −85.3897 | − | 27.7448i | −0.774130 | − | 0.251530i | −0.104798 | − | 0.994494i | \(-0.533420\pi\) |
−0.669332 | + | 0.742963i | \(0.733420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 105.484 | − | 67.0676i | 0.843874 | − | 0.536541i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −30.8634 | − | 10.0281i | −0.219988 | − | 0.0714783i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −96.2500 | − | 69.9297i | −0.616316 | − | 0.447780i | 0.235317 | − | 0.971919i | \(-0.424387\pi\) |
−0.851633 | + | 0.524139i | \(0.824387\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −153.445 | + | 111.484i | −0.889016 | + | 0.645908i | −0.935621 | − | 0.353006i | \(-0.885160\pi\) |
0.0466053 | + | 0.998913i | \(0.485160\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 42.2211 | + | 58.1123i | 0.222719 | + | 0.306547i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 67.7789 | + | 232.929i | 0.327335 | + | 1.12492i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 207.811 | − | 67.5217i | 0.923347 | − | 0.300014i | 0.191508 | − | 0.981491i | \(-0.438662\pi\) |
0.731839 | + | 0.681477i | \(0.238662\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −164.508 | + | 506.303i | −0.675444 | + | 2.07880i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17.4430 | − | 53.6840i | −0.0664424 | − | 0.204489i | 0.912323 | − | 0.409470i | \(-0.134286\pi\) |
−0.978766 | + | 0.204982i | \(0.934286\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 305.570i | − | 1.08370i | −0.840476 | − | 0.541849i | \(-0.817724\pi\) | ||
0.840476 | − | 0.541849i | \(-0.182276\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 140.742 | + | 206.908i | 0.466236 | + | 0.685422i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −59.4937 | + | 81.8860i | −0.184639 | + | 0.254134i | −0.891296 | − | 0.453423i | \(-0.850203\pi\) |
0.706656 | + | 0.707557i | \(0.250203\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −127.798 | −0.372588 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 923.804 | 2.53644 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −213.801 | + | 294.272i | −0.554110 | + | 0.762667i | −0.990563 | − | 0.137060i | \(-0.956235\pi\) |
0.436453 | + | 0.899727i | \(0.356235\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.54139 | + | 114.228i | −0.00868221 | + | 0.280045i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 815.992i | − | 1.89615i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 57.9282 | + | 178.285i | 0.127824 | + | 0.393402i | 0.994405 | − | 0.105635i | \(-0.0336874\pi\) |
−0.866581 | + | 0.499036i | \(0.833687\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 48.2368 | − | 148.458i | 0.101247 | − | 0.311607i | −0.887584 | − | 0.460646i | \(-0.847618\pi\) |
0.988831 | + | 0.149039i | \(0.0476178\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −461.873 | + | 150.072i | −0.923659 | + | 0.300115i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −700.322 | + | 476.371i | −1.33637 | + | 0.909025i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 264.782 | + | 364.442i | 0.482811 | + | 0.664532i | 0.979042 | − | 0.203658i | \(-0.0652832\pi\) |
−0.496231 | + | 0.868190i | \(0.665283\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 510.436 | − | 370.853i | 0.890569 | − | 0.647036i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −133.711 | − | 97.1466i | −0.223501 | − | 0.162383i | 0.470400 | − | 0.882453i | \(-0.344110\pi\) |
−0.693901 | + | 0.720070i | \(0.744110\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −921.507 | − | 299.416i | −1.47746 | − | 0.480055i | −0.544104 | − | 0.839018i | \(-0.683130\pi\) |
−0.933352 | + | 0.358963i | \(0.883130\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −54.4138 | + | 876.717i | −0.0837755 | + | 1.34979i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −210.935 | − | 68.5371i | −0.312186 | − | 0.101435i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −450.649 | − | 327.416i | −0.641797 | − | 0.466293i | 0.218670 | − | 0.975799i | \(-0.429828\pi\) |
−0.860467 | + | 0.509506i | \(0.829828\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 673.393 | − | 489.249i | 0.923722 | − | 0.671123i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −732.079 | − | 1007.62i | −0.968146 | − | 1.33254i | −0.942978 | − | 0.332855i | \(-0.891988\pi\) |
−0.0251674 | − | 0.999683i | \(-0.508012\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1161.73 | + | 900.343i | 1.48244 | + | 1.14889i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 795.122 | − | 258.351i | 0.979839 | − | 0.318369i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −150.806 | + | 464.135i | −0.179612 | + | 0.552788i | −0.999814 | − | 0.0192853i | \(-0.993861\pi\) |
0.820202 | + | 0.572074i | \(0.193861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −507.948 | − | 1563.30i | −0.585136 | − | 1.80086i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1332.84i | − | 1.48612i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 795.269 | − | 1026.15i | 0.858873 | − | 1.10822i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 611.867 | − | 842.162i | 0.640471 | − | 0.881532i | −0.358170 | − | 0.933656i | \(-0.616599\pi\) |
0.998641 | + | 0.0521241i | \(0.0165991\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −228.784 | −0.232259 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1166.35 | 1.14907 | 0.574536 | − | 0.818480i | \(-0.305183\pi\) | ||||
0.574536 | + | 0.818480i | \(0.305183\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −626.122 | + | 861.783i | −0.598967 | + | 0.824408i | −0.995613 | − | 0.0935639i | \(-0.970174\pi\) |
0.396646 | + | 0.917972i | \(0.370174\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1604.20 | − | 576.779i | −1.49098 | − | 0.536075i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 533.866i | 0.482344i | 0.970482 | + | 0.241172i | \(0.0775318\pi\) | ||||
−0.970482 | + | 0.241172i | \(0.922468\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.8172 | − | 39.4474i | −0.0112630 | − | 0.0346640i | 0.945267 | − | 0.326298i | \(-0.105801\pi\) |
−0.956530 | + | 0.291634i | \(0.905801\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −474.491 | + | 1460.33i | −0.405736 | + | 1.24873i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 947.684 | − | 307.921i | 0.788944 | − | 0.256343i | 0.113290 | − | 0.993562i | \(-0.463861\pi\) |
0.675654 | + | 0.737219i | \(0.263861\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1003.33 | + | 31.1062i | 0.813577 | + | 0.0252232i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −996.638 | − | 1371.75i | −0.787515 | − | 1.08392i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2307.65 | + | 1676.61i | −1.77766 | + | 1.29155i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 992.272 | + | 720.928i | 0.745509 | + | 0.541644i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 377.250 | + | 122.576i | 0.276549 | + | 0.0898561i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −922.880 | + | 1049.48i | −0.660359 | + | 0.750950i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 434.970 | + | 141.330i | 0.303916 | + | 0.0987484i | 0.457005 | − | 0.889464i | \(-0.348922\pi\) |
−0.153089 | + | 0.988212i | \(0.548922\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1737.21 | + | 1262.16i | 1.18568 | + | 0.861449i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1654.05 | + | 1201.74i | −1.10317 | + | 0.801499i | −0.981574 | − | 0.191081i | \(-0.938801\pi\) |
−0.121594 | + | 0.992580i | \(0.538801\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1480.94 | + | 2038.34i | 0.965517 | + | 1.32892i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 362.647 | + | 11.2431i | 0.231198 | + | 0.00716779i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2191.62 | + | 712.102i | −1.36674 | + | 0.444080i | −0.898287 | − | 0.439410i | \(-0.855188\pi\) |
−0.468451 | + | 0.883490i | \(0.655188\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 162.003 | − | 498.595i | 0.0988558 | − | 0.304247i | −0.889384 | − | 0.457162i | \(-0.848866\pi\) |
0.988239 | + | 0.152915i | \(0.0488660\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −219.796 | − | 676.461i | −0.131277 | − | 0.404030i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 774.365i | − | 0.452837i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1251.70 | + | 450.040i | 0.716880 | + | 0.257750i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 527.868 | − | 726.548i | 0.296176 | − | 0.407651i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2120.40 | −1.16584 | −0.582919 | − | 0.812530i | \(-0.698090\pi\) | ||||
−0.582919 | + | 0.812530i | \(0.698090\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2058.88 | 1.10960 | 0.554800 | − | 0.831984i | \(-0.312795\pi\) | ||||
0.554800 | + | 0.831984i | \(0.312795\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1729.47 | + | 2380.41i | −0.913852 | + | 1.25781i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1298.99 | − | 1676.12i | 0.673146 | − | 0.868574i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 489.434i | 0.248797i | 0.992232 | + | 0.124398i | \(0.0397001\pi\) | ||||
−0.992232 | + | 0.124398i | \(0.960300\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −789.874 | − | 2430.98i | −0.393969 | − | 1.21251i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −602.003 | + | 1852.77i | −0.294686 | + | 0.906951i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1758.15 | − | 571.256i | 0.844838 | − | 0.274504i | 0.145556 | − | 0.989350i | \(-0.453503\pi\) |
0.699282 | + | 0.714846i | \(0.253503\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −634.776 | − | 491.952i | −0.299498 | − | 0.232112i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 453.278 | + | 623.884i | 0.210034 | + | 0.289087i | 0.901017 | − | 0.433784i | \(-0.142822\pi\) |
−0.690983 | + | 0.722871i | \(0.742822\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2865.57 | − | 2081.96i | 1.30431 | − | 0.947638i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2102.61 | + | 1527.63i | 0.940295 | + | 0.683164i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3321.57 | + | 1079.24i | 1.45974 | + | 0.474297i | 0.927990 | − | 0.372606i | \(-0.121536\pi\) |
0.531747 | + | 0.846903i | \(0.321536\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1455.22 | − | 2288.78i | −0.628598 | − | 0.988662i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1252.85 | − | 407.075i | −0.532033 | − | 0.172868i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2176.65 | + | 1581.43i | 0.908884 | + | 0.660343i | 0.940732 | − | 0.339150i | \(-0.110139\pi\) |
−0.0318482 | + | 0.999493i | \(0.510139\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3760.76 | + | 2732.35i | −1.54439 | + | 1.12207i | −0.596888 | + | 0.802325i | \(0.703596\pi\) |
−0.947505 | + | 0.319742i | \(0.896404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 644.761 | + | 887.438i | 0.260449 | + | 0.358477i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2019.94 | + | 1374.00i | −0.802752 | + | 0.546046i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1277.99 | + | 415.244i | −0.499764 | + | 0.162383i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −217.589 | + | 669.670i | −0.0837422 | + | 0.257732i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1149.23 | − | 3536.96i | −0.435367 | − | 1.33992i | −0.892710 | − | 0.450632i | \(-0.851199\pi\) |
0.457343 | − | 0.889291i | \(-0.348801\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 5214.19i | − | 1.94469i | −0.233544 | − | 0.972346i | \(-0.575032\pi\) | ||
0.233544 | − | 0.972346i | \(-0.424968\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 184.439 | − | 5949.09i | 0.0677330 | − | 2.18473i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −612.663 | + | 843.258i | −0.221576 | + | 0.304973i | −0.905304 | − | 0.424764i | \(-0.860357\pi\) |
0.683729 | + | 0.729736i | \(0.260357\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2906.35 | −1.03531 | −0.517653 | − | 0.855591i | \(-0.673194\pi\) | ||||
−0.517653 | + | 0.855591i | \(0.673194\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3165.59 | −1.11086 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1517.33 | + | 2088.42i | −0.524608 | + | 0.722061i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 354.948 | + | 521.815i | 0.120930 | + | 0.177781i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2009.55i | 0.674750i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 366.784 | + | 1128.84i | 0.121392 | + | 0.373606i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1395.59 | − | 4295.18i | 0.455338 | − | 1.40138i | −0.415401 | − | 0.909638i | \(-0.636359\pi\) |
0.870738 | − | 0.491746i | \(-0.163641\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1104.59 | − | 358.902i | 0.355329 | − | 0.115453i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 954.527 | + | 3280.32i | 0.302782 | + | 1.04054i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2418.97 | + | 3329.42i | 0.756729 | + | 1.04155i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5508.51 | − | 4002.17i | 1.69968 | − | 1.23489i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8056.99 | − | 5853.75i | −2.45236 | − | 1.78174i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 376.248 | + | 122.250i | 0.112984 | + | 0.0367107i | 0.364963 | − | 0.931022i | \(-0.381082\pi\) |
−0.251979 | + | 0.967733i | \(0.581082\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2157.21 | − | 1781.53i | −0.639174 | − | 0.527861i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4632.87 | + | 1505.31i | 1.35460 | + | 0.440136i | 0.894237 | − | 0.447594i | \(-0.147719\pi\) |
0.460364 | + | 0.887730i | \(0.347719\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −814.725 | − | 591.932i | −0.235103 | − | 0.170812i | 0.463996 | − | 0.885837i | \(-0.346415\pi\) |
−0.699099 | + | 0.715025i | \(0.746415\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1260.91 | − | 916.107i | 0.359143 | − | 0.260933i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2023.06 | − | 2784.51i | −0.568820 | − | 0.782914i | 0.423594 | − | 0.905852i | \(-0.360768\pi\) |
−0.992414 | + | 0.122938i | \(0.960768\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 382.878 | − | 1064.90i | 0.106282 | − | 0.295601i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3722.81 | − | 1209.62i | 1.02035 | − | 0.331532i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1787.95 | − | 5502.74i | 0.483903 | − | 1.48930i | −0.349661 | − | 0.936876i | \(-0.613703\pi\) |
0.833564 | − | 0.552423i | \(-0.186297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 714.013 | + | 2197.51i | 0.190845 | + | 0.587360i | 1.00000 | 0.000235046i | \(-7.48174e-5\pi\) | |
−0.809155 | + | 0.587595i | \(0.800075\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4972.99i | 1.31283i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1371.92 | − | 399.208i | 0.357750 | − | 0.104100i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5170.59 | + | 7116.70i | −1.33197 | + | 1.83330i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8752.33 | 2.22753 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −494.071 | −0.124245 | −0.0621225 | − | 0.998069i | \(-0.519787\pi\) | ||||
−0.0621225 | + | 0.998069i | \(0.519787\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −539.441 | + | 742.477i | −0.134049 | + | 0.184502i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9917.12 | + | 2885.74i | −2.43543 | + | 0.708674i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 702.353i | 0.170473i | 0.996361 | + | 0.0852365i | \(0.0271646\pi\) | ||||
−0.996361 | + | 0.0852365i | \(0.972835\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1465.08 | − | 4509.05i | −0.351488 | − | 1.08177i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −822.857 | + | 2532.49i | −0.195148 | + | 0.600603i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3521.76 | + | 1144.29i | −0.825708 | + | 0.268289i | −0.691236 | − | 0.722629i | \(-0.742934\pi\) |
−0.134472 | + | 0.990917i | \(0.542934\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1375.94 | − | 3826.90i | 0.318956 | − | 0.887111i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2015.77 | − | 2774.47i | −0.462034 | − | 0.635935i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2421.29 | − | 1759.17i | 0.548806 | − | 0.398731i | −0.278539 | − | 0.960425i | \(-0.589850\pi\) |
0.827345 | + | 0.561694i | \(0.189850\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2415.81 | + | 1755.19i | 0.541514 | + | 0.393433i | 0.824647 | − | 0.565648i | \(-0.191374\pi\) |
−0.283133 | + | 0.959081i | \(0.591374\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10985.7 | + | 3569.47i | 2.43547 | + | 0.791334i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −318.803 | − | 1237.31i | −0.0699075 | − | 0.271319i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2758.32 | − | 896.232i | −0.598308 | − | 0.194402i | −0.00582243 | − | 0.999983i | \(-0.501853\pi\) |
−0.592486 | + | 0.805581i | \(0.701853\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3434.40 | + | 2495.24i | 0.736962 | + | 0.535434i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3024.16 | − | 2197.18i | 0.642016 | − | 0.466452i | −0.218526 | − | 0.975831i | \(-0.570125\pi\) |
0.860542 | + | 0.509379i | \(0.170125\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2475.46 | − | 3407.17i | −0.519967 | − | 0.715673i | 0.465593 | − | 0.884999i | \(-0.345841\pi\) |
−0.985560 | + | 0.169326i | \(0.945841\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2548.96 | + | 8759.75i | 0.529780 | + | 1.82064i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1164.83 | + | 378.476i | −0.239574 | + | 0.0778422i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3822.19 | + | 11763.5i | −0.777975 | + | 2.39436i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2260.50 | + | 6957.11i | 0.455371 | + | 1.40149i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1632.38i | − | 0.325477i | −0.986669 | − | 0.162739i | \(-0.947967\pi\) | ||
0.986669 | − | 0.162739i | \(-0.0520327\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1178.78 | − | 1732.95i | −0.232649 | − | 0.342021i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −194.977 | + | 268.362i | −0.0380932 | + | 0.0524308i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6801.72 | −1.31556 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6630.22 | −1.26963 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4817.61 | + | 6630.88i | −0.913415 | + | 1.25721i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −54.0809 | + | 1744.39i | −0.0101530 | + | 0.327486i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7234.48i | 1.34493i | 0.740129 | + | 0.672465i | \(0.234765\pi\) | ||||
−0.740129 | + | 0.672465i | \(0.765235\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2313.17 | − | 7119.20i | −0.425862 | − | 1.31067i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1288.50 | + | 3965.58i | −0.234932 | + | 0.723047i | 0.762198 | + | 0.647344i | \(0.224120\pi\) |
−0.997130 | + | 0.0757030i | \(0.975880\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1967.15 | + | 639.164i | −0.355238 | + | 0.115424i | −0.481199 | − | 0.876611i | \(-0.659799\pi\) |
0.125961 | + | 0.992035i | \(0.459799\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4489.46 | − | 3053.81i | 0.803023 | − | 0.546231i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 375.457 | + | 516.772i | 0.0665229 | + | 0.0915609i | 0.840982 | − | 0.541063i | \(-0.181978\pi\) |
−0.774459 | + | 0.632624i | \(0.781978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −983.845 | + | 714.805i | −0.172679 | + | 0.125459i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3035.11 | − | 2205.14i | −0.527736 | − | 0.383423i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14517.9 | + | 4717.15i | 2.50092 | + | 0.812597i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6029.95 | − | 7301.52i | 1.02917 | − | 1.24620i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 277.206 | + | 90.0696i | 0.0468793 | + | 0.0152320i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1776.75 | + | 1290.89i | 0.297737 | + | 0.216319i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4988.50 | − | 3624.36i | 0.828377 | − | 0.601851i | −0.0907228 | − | 0.995876i | \(-0.528918\pi\) |
0.919100 | + | 0.394025i | \(0.128918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2874.61 | − | 3956.56i | −0.473056 | − | 0.651106i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3980.89 | − | 3085.20i | −0.649251 | − | 0.503171i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1062.89 | − | 345.353i | 0.171808 | − | 0.0558237i | −0.221850 | − | 0.975081i | \(-0.571210\pi\) |
0.393658 | + | 0.919257i | \(0.371210\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2163.84 | + | 6659.60i | −0.346677 | + | 1.06696i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 599.105 | + | 1843.86i | 0.0951418 | + | 0.292816i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 4669.43i | − | 0.735061i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4321.12 | + | 5575.62i | −0.674323 | + | 0.870091i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7004.14 | − | 9640.38i | 1.08358 | − | 1.49142i | 0.228061 | − | 0.973647i | \(-0.426761\pi\) |
0.855518 | − | 0.517772i | \(-0.173239\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1697.29 | −0.260326 | −0.130163 | − | 0.991493i | \(-0.541550\pi\) | ||||
−0.130163 | + | 0.991493i | \(0.541550\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2458.43 | −0.373849 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5415.44 | − | 7453.72i | 0.816530 | − | 1.12386i | −0.173753 | − | 0.984789i | \(-0.555590\pi\) |
0.990283 | − | 0.139067i | \(-0.0444105\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1738.86 | + | 625.197i | 0.259969 | + | 0.0934705i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 20044.6i | − | 2.97163i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 280.657 | + | 863.774i | 0.0412605 | + | 0.126987i | 0.969565 | − | 0.244834i | \(-0.0787335\pi\) |
−0.928304 | + | 0.371821i | \(0.878734\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2047.09 | − | 6300.28i | 0.298453 | − | 0.918542i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8197.17 | + | 2663.42i | −1.18523 | + | 0.385106i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10827.8 | + | 335.692i | 1.55274 | + | 0.0481395i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 475.032 | + | 653.825i | 0.0675653 | + | 0.0929957i | 0.841462 | − | 0.540316i | \(-0.181695\pi\) |
−0.773897 | + | 0.633311i | \(0.781695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1022.10 | + | 742.602i | −0.144197 | + | 0.104765i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6385.07 | + | 4639.02i | 0.893521 | + | 0.649181i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 405.991 | + | 131.914i | 0.0563577 | + | 0.0183117i | 0.337060 | − | 0.941483i | \(-0.390567\pi\) |
−0.280702 | + | 0.959795i | \(0.590567\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2154.51 | − | 9581.61i | −0.296690 | − | 1.31945i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8571.74 | − | 2785.13i | −1.17100 | − | 0.380481i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5806.22 | − | 4218.47i | −0.786928 | − | 0.571737i | 0.120122 | − | 0.992759i | \(-0.461671\pi\) |
−0.907050 | + | 0.421023i | \(0.861671\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2600.13 | + | 1889.11i | −0.349629 | + | 0.254021i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1703.31 | − | 2344.40i | −0.227245 | − | 0.312776i | 0.680135 | − | 0.733087i | \(-0.261921\pi\) |
−0.907380 | + | 0.420311i | \(0.861921\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2478.50 | + | 76.8407i | 0.328094 | + | 0.0101719i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6504.53 | + | 2113.45i | −0.854378 | + | 0.277604i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3376.59 | + | 10392.1i | −0.440103 | + | 1.35450i | 0.447663 | + | 0.894202i | \(0.352256\pi\) |
−0.887766 | + | 0.460295i | \(0.847744\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3647.35 | + | 11225.4i | 0.471750 | + | 1.45190i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 14367.3i | − | 1.84411i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5860.52 | + | 2107.12i | 0.746519 | + | 0.268407i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1951.21 | + | 2685.61i | −0.246671 | + | 0.339513i | −0.914342 | − | 0.404943i | \(-0.867291\pi\) |
0.667671 | + | 0.744456i | \(0.267291\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17705.3 | −2.22149 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1329.14 | −0.165521 | −0.0827606 | − | 0.996569i | \(-0.526374\pi\) | ||||
−0.0827606 | + | 0.996569i | \(0.526374\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8445.65 | + | 11624.4i | −1.04394 | + | 1.43686i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5700.64 | + | 7355.65i | −0.699425 | + | 0.902482i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2233.51i | − | 0.272017i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −382.512 | − | 1177.25i | −0.0462445 | − | 0.142326i | 0.925268 | − | 0.379314i | \(-0.123840\pi\) |
−0.971513 | + | 0.236988i | \(0.923840\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5004.10 | − | 15401.0i | 0.600570 | − | 1.84836i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3868.40 | − | 1256.92i | 0.460899 | − | 0.149755i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11006.5 | + | 8530.05i | 1.30190 | + | 1.00897i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2165.43 | + | 2980.46i | 0.254297 | + | 0.350010i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4397.66 | − | 3195.09i | 0.512744 | − | 0.372531i | −0.301119 | − | 0.953586i | \(-0.597360\pi\) |
0.813864 | + | 0.581056i | \(0.197360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10326.1 | + | 7502.39i | 1.19541 | + | 0.868513i | 0.993825 | − | 0.110959i | \(-0.0353923\pi\) |
0.201580 | + | 0.979472i | \(0.435392\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2154.55 | + | 700.057i | 0.247655 | + | 0.0804680i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15283.7 | − | 6036.30i | −1.74440 | − | 0.688950i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3221.21 | − | 1046.64i | −0.365071 | − | 0.118619i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4402.38 | + | 3198.52i | 0.495452 | + | 0.359967i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8281.88 | − | 6017.14i | 0.925578 | − | 0.672472i | −0.0193281 | − | 0.999813i | \(-0.506153\pi\) |
0.944906 | + | 0.327341i | \(0.106153\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9921.90 | − | 13656.3i | −1.10119 | − | 1.51566i | −0.833794 | − | 0.552075i | \(-0.813836\pi\) |
−0.267398 | − | 0.963586i | \(-0.586164\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7728.68 | + | 5257.19i | −0.851866 | + | 0.579455i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9915.33 | − | 3221.69i | 1.08539 | − | 0.352664i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3575.81 | − | 11005.2i | 0.388756 | − | 1.19647i | −0.544962 | − | 0.838461i | \(-0.683456\pi\) |
0.933718 | − | 0.358008i | \(-0.116544\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 883.902 | + | 2720.37i | 0.0954434 | + | 0.293745i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2361.47i | 0.253266i | 0.991950 | + | 0.126633i | \(0.0404171\pi\) | ||||
−0.991950 | + | 0.126633i | \(0.959583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 169.078 | − | 5453.61i | 0.0180113 | − | 0.580957i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8758.32 | − | 12054.8i | 0.926743 | − | 1.27555i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2824.01 | 0.296823 | 0.148411 | − | 0.988926i | \(-0.452584\pi\) | ||||
0.148411 | + | 0.988926i | \(0.452584\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −576.985 | −0.0602421 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8504.23 | + | 11705.1i | −0.882039 | + | 1.21402i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10336.2 | + | 15195.5i | 1.06499 | + | 1.56566i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1766.11i | 0.180777i | 0.995907 | + | 0.0903884i | \(0.0288108\pi\) | ||||
−0.995907 | + | 0.0903884i | \(0.971189\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1318.30 | + | 4057.32i | 0.134059 | + | 0.412592i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1411.94 | − | 4345.49i | 0.142647 | − | 0.439023i | −0.854054 | − | 0.520185i | \(-0.825863\pi\) |
0.996701 | + | 0.0811616i | \(0.0258630\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13357.1 | + | 4339.98i | −1.34073 | + | 0.435628i | −0.889563 | − | 0.456813i | \(-0.848991\pi\) |
−0.451163 | + | 0.892442i | \(0.648991\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4163.48 | + | 14308.2i | 0.415218 | + | 1.42694i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4902.36 | − | 6747.52i | −0.485769 | − | 0.668603i | 0.493832 | − | 0.869557i | \(-0.335596\pi\) |
−0.979601 | + | 0.200954i | \(0.935596\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7907.61 | − | 5745.21i | 0.778549 | − | 0.565649i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2782.51 | − | 2021.61i | −0.272210 | − | 0.197772i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2970.59 | − | 965.204i | −0.288770 | − | 0.0938269i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5331.84 | + | 13500.0i | −0.515035 | + | 1.30405i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7742.77 | + | 2515.78i | 0.743222 | + | 0.241488i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15477.9 | + | 11245.3i | 1.47641 | + | 1.07268i | 0.978691 | + | 0.205341i | \(0.0658303\pi\) |
0.497723 | + | 0.867336i | \(0.334170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13391.8 | − | 9729.70i | 1.26947 | − | 0.922321i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8046.73 | − | 11075.4i | −0.758052 | − | 1.04337i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3937.73 | + | 10952.0i | −0.368667 | + | 1.02537i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9652.74 | − | 3136.36i | 0.898167 | − | 0.291832i | 0.176687 | − | 0.984267i | \(-0.443462\pi\) |
0.721480 | + | 0.692435i | \(0.243462\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4014.35 | + | 12354.9i | −0.371238 | + | 1.14255i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4811.02 | − | 14806.8i | −0.442197 | − | 1.36094i | −0.885529 | − | 0.464584i | \(-0.846204\pi\) |
0.443333 | − | 0.896357i | \(-0.353796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15640.1i | 1.42879i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2456.01 | − | 714.665i | 0.223009 | − | 0.0648925i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2107.87 | + | 2901.24i | −0.190244 | + | 0.261848i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10611.0 | −0.951934 | −0.475967 | − | 0.879463i | \(-0.657902\pi\) | ||||
−0.475967 | + | 0.879463i | \(0.657902\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5419.14 | −0.483252 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5705.05 | − | 7852.32i | 0.505717 | − | 0.696059i | −0.477473 | − | 0.878646i | \(-0.658447\pi\) |
0.983190 | + | 0.182587i | \(0.0584472\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12520.9 | + | 3643.39i | −1.10331 | + | 0.321047i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24890.8i | 2.18035i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1294.56 | + | 3984.24i | 0.112731 | + | 0.346951i | 0.991467 | − | 0.130357i | \(-0.0416124\pi\) |
−0.878736 | + | 0.477308i | \(0.841612\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6496.69 | + | 19994.7i | −0.562420 | + | 1.73095i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3583.81 | − | 1164.45i | 0.308439 | − | 0.100218i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4029.48 | − | 11207.2i | 0.344776 | − | 0.958926i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 608.131 | + | 837.020i | 0.0517322 | + | 0.0712033i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19855.4 | + | 14425.8i | −1.67930 | + | 1.22008i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6646.23 | − | 4828.77i | −0.558881 | − | 0.406050i | 0.272169 | − | 0.962250i | \(-0.412259\pi\) |
−0.831049 | + | 0.556199i | \(0.812259\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.7811 | − | 12.6007i | −0.00324241 | − | 0.00105352i | 0.307395 | − | 0.951582i | \(-0.400543\pi\) |
−0.310638 | + | 0.950528i | \(0.600543\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19022.9 | + | 1180.66i | 1.58139 | + | 0.0981493i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23713.5 | + | 7704.99i | 1.96011 | + | 0.636878i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3321.68 | − | 2413.34i | −0.273007 | − | 0.198351i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3394.41 | − | 2466.18i | 0.277410 | − | 0.201550i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2513.49 | − | 3459.52i | −0.204261 | − | 0.281142i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1667.67 | − | 5731.10i | −0.134766 | − | 0.463135i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17981.3 | + | 5842.48i | −1.44497 | + | 0.469500i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −403.674 | + | 1242.38i | −0.0322588 | + | 0.0992823i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4588.47 | + | 14121.9i | 0.364647 | + | 1.12227i | 0.950202 | + | 0.311634i | \(0.100876\pi\) |
−0.585556 | + | 0.810632i | \(0.699124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 32666.5i | − | 2.58168i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 260.818 | + | 383.433i | 0.0204995 | + | 0.0301366i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7212.63 | + | 9927.33i | −0.563784 | + | 0.775982i | −0.991801 | − | 0.127789i | \(-0.959212\pi\) |
0.428018 | + | 0.903770i | \(0.359212\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3493.78 | −0.271604 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13814.8 | 1.06811 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7104.22 | + | 9778.12i | −0.546297 | + | 0.751913i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 531.978 | − | 17159.0i | 0.0406869 | − | 1.31236i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 19030.6i | − | 1.44767i | −0.689975 | − | 0.723833i | \(-0.742378\pi\) | ||
0.689975 | − | 0.723833i | \(-0.257622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7153.41 | − | 22015.9i | −0.541247 | − | 1.66579i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2918.02 | − | 8980.74i | 0.219606 | − | 0.675877i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10540.1 | + | 3424.69i | −0.789011 | + | 0.256365i | −0.675683 | − | 0.737192i | \(-0.736151\pi\) |
−0.113328 | + | 0.993558i | \(0.536151\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9211.61 | + | 6265.90i | −0.685903 | + | 0.466563i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10615.7 | − | 14611.2i | −0.786271 | − | 1.08221i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9054.21 | − | 6578.27i | 0.667087 | − | 0.484667i | −0.201962 | − | 0.979393i | \(-0.564732\pi\) |
0.869049 | + | 0.494726i | \(0.164732\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11658.0 | − | 8470.01i | −0.854415 | − | 0.620768i | 0.0719452 | − | 0.997409i | \(-0.477079\pi\) |
−0.926360 | + | 0.376640i | \(0.877079\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24855.0 | + | 8075.89i | 1.81210 | + | 0.588787i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10868.1 | + | 2800.24i | −0.788224 | + | 0.203093i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5925.78 | − | 1925.40i | −0.427545 | − | 0.138918i | 0.0873370 | − | 0.996179i | \(-0.472164\pi\) |
−0.514882 | + | 0.857261i | \(0.672164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29643.5 | + | 21537.2i | 2.12770 | + | 1.54587i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21863.2 | + | 15884.5i | −1.56117 | + | 1.13425i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2185.42 | + | 3007.98i | 0.155250 | + | 0.213684i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14984.0 | + | 11612.7i | 1.05900 | + | 0.820725i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2304.23 | − | 748.689i | 0.162020 | − | 0.0526435i | −0.226884 | − | 0.973922i | \(-0.572854\pi\) |
0.388904 | + | 0.921278i | \(0.372854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6805.79 | − | 20946.1i | 0.476108 | − | 1.46531i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2263.44 | − | 6966.16i | −0.157539 | − | 0.484855i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5194.92i | 0.359746i | 0.983690 | + | 0.179873i | \(0.0575688\pi\) | ||||
−0.983690 | + | 0.179873i | \(0.942431\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19535.5 | − | 25207.1i | 1.34601 | − | 1.73679i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12004.7 | − | 16523.0i | 0.822981 | − | 1.13274i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3043.04 | −0.207571 | −0.103786 | − | 0.994600i | \(-0.533096\pi\) | ||||
−0.103786 | + | 0.994600i | \(0.533096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24216.3 | 1.64360 | 0.821800 | − | 0.569776i | \(-0.192970\pi\) | ||||
0.821800 | + | 0.569776i | \(0.192970\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5926.36 | − | 8156.94i | 0.400232 | − | 0.550873i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12904.1 | − | 4639.61i | −0.867153 | − | 0.311780i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5077.55i | − | 0.339525i | −0.985485 | − | 0.169762i | \(-0.945700\pi\) | ||
0.985485 | − | 0.169762i | \(-0.0543000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5605.66 | − | 17252.5i | −0.372993 | − | 1.14796i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2369.49 | + | 7292.53i | −0.156889 | + | 0.482855i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13579.1 | + | 4412.13i | −0.894708 | + | 0.290708i | −0.720051 | − | 0.693921i | \(-0.755882\pi\) |
−0.174657 | + | 0.984629i | \(0.555882\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4432.71 | − | 137.427i | −0.290641 | − | 0.00901070i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4002.23 | − | 5508.60i | −0.261141 | − | 0.359429i | 0.658233 | − | 0.752814i | \(-0.271304\pi\) |
−0.919374 | + | 0.393385i | \(0.871304\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2791.82 | − | 2028.38i | 0.181281 | − | 0.131708i | −0.493444 | − | 0.869778i | \(-0.664262\pi\) |
0.674725 | + | 0.738069i | \(0.264262\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2357.19 | + | 1712.60i | 0.152320 | + | 0.110667i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10070.7 | + | 3272.18i | 0.647633 | + | 0.210429i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6628.87 | − | 14149.2i | 0.424248 | − | 0.905546i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7932.65 | − | 2577.47i | −0.505262 | − | 0.164170i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23238.8 | − | 16884.0i | −1.47312 | − | 1.07028i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2201.81 | − | 1599.71i | 0.138911 | − | 0.100925i | −0.516160 | − | 0.856492i | \(-0.672639\pi\) |
0.655070 | + | 0.755568i | \(0.272639\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18654.3 | + | 25675.4i | 1.17131 | + | 1.61217i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5110.93 | − | 158.453i | −0.319403 | − | 0.00990241i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9207.65 | + | 2991.75i | −0.572716 | + | 0.186087i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1143.12 | + | 3518.15i | −0.0707683 | + | 0.217803i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −103.030 | − | 317.094i | −0.00634858 | − | 0.0195389i | 0.947832 | − | 0.318770i | \(-0.103270\pi\) |
−0.954181 | + | 0.299231i | \(0.903270\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5012.26i | − | 0.307409i | −0.988117 | − | 0.153705i | \(-0.950880\pi\) | ||
0.988117 | − | 0.153705i | \(-0.0491204\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −22591.8 | − | 8122.76i | −1.37915 | − | 0.495866i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12063.0 | + | 16603.2i | −0.732989 | + | 1.00887i | 0.266003 | + | 0.963972i | \(0.414297\pi\) |
−0.998991 | + | 0.0449001i | \(0.985703\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1916.17 | 0.115896 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28919.8 | −1.74110 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6119.25 | + | 8422.43i | −0.366715 | + | 0.504740i | −0.952004 | − | 0.306085i | \(-0.900981\pi\) |
0.585289 | + | 0.810824i | \(0.300981\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14002.4 | − | 18067.6i | 0.835299 | − | 1.07780i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21686.6i | 1.28779i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5544.33 | + | 17063.7i | 0.327734 | + | 1.00866i | 0.970192 | + | 0.242339i | \(0.0779148\pi\) |
−0.642458 | + | 0.766321i | \(0.722085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2527.45 | + | 7778.69i | −0.148724 | + | 0.457725i | −0.997471 | − | 0.0710739i | \(-0.977357\pi\) |
0.848747 | + | 0.528799i | \(0.177357\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 66558.9 | − | 21626.3i | 3.89884 | − | 1.26681i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22265.3 | − | 17255.6i | −1.29836 | − | 1.00623i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6278.57 | + | 8641.71i | 0.364479 | + | 0.501662i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2249.10 | + | 1634.07i | −0.129978 | + | 0.0944347i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1290.86 | − | 937.866i | −0.0742670 | − | 0.0539581i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12208.1 | − | 3966.64i | −0.699237 | − | 0.227196i | −0.0622392 | − | 0.998061i | \(-0.519824\pi\) |
−0.636998 | + | 0.770865i | \(0.719824\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3928.17 | + | 1012.12i | −0.223993 | + | 0.0577136i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30665.9 | − | 9963.94i | −1.74089 | − | 0.565650i | −0.745942 | − | 0.666011i | \(-0.768000\pi\) |
−0.994951 | + | 0.100361i | \(0.968000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18273.1 | − | 13276.2i | −1.03278 | − | 0.750359i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27694.0 | + | 20120.9i | −1.55835 | + | 1.13221i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15493.3 | + | 21324.6i | 0.867984 | + | 1.19468i | 0.979606 | + | 0.200927i | \(0.0643954\pi\) |
−0.111622 | + | 0.993751i | \(0.535605\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21302.8 | − | 14490.6i | 1.18823 | − | 0.808257i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6730.45 | − | 2186.86i | 0.373774 | − | 0.121447i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8515.16 | + | 26207.0i | −0.470830 | + | 1.44907i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −729.463 | − | 2245.06i | −0.0401593 | − | 0.123598i | 0.928967 | − | 0.370163i | \(-0.120698\pi\) |
−0.969126 | + | 0.246565i | \(0.920698\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4964.12i | 0.272109i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −181.631 | + | 5858.53i | −0.00991318 | + | 0.319750i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4361.67 | + | 6003.32i | −0.237030 | + | 0.326244i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24186.6 | 1.30876 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25470.3 | 1.37232 | 0.686162 | − | 0.727449i | \(-0.259294\pi\) | ||||
0.686162 | + | 0.727449i | \(0.259294\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14913.6 | + | 20526.8i | −0.800108 | + | 1.10125i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4472.62 | + | 6575.28i | 0.238934 | + | 0.351262i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 25307.3i | − | 1.34622i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8522.02 | + | 26228.1i | 0.451412 | + | 1.38930i | 0.875296 | + | 0.483587i | \(0.160666\pi\) |
−0.423884 | + | 0.905716i | \(0.639334\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3852.67 | + | 11857.3i | −0.203216 | + | 0.625434i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16195.7 | − | 5262.31i | 0.850679 | − | 0.276402i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2418.93 | + | 8312.88i | 0.126521 | + | 0.434803i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23898.8 | + | 32893.8i | 1.24479 | + | 1.71331i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25532.5 | − | 18550.5i | 1.32434 | − | 0.962192i | 0.324476 | − | 0.945894i | \(-0.394812\pi\) |
0.999867 | − | 0.0162976i | \(-0.00518792\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18698.9 | + | 13585.5i | 0.965855 | + | 0.701735i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15442.4 | − | 5017.53i | −0.794341 | − | 0.258097i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14842.9 | − | 921.229i | −0.760346 | − | 0.0471912i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13683.1 | + | 4445.90i | 0.698042 | + | 0.226808i | 0.636477 | − | 0.771295i | \(-0.280391\pi\) |
0.0615649 | + | 0.998103i | \(0.480391\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10090.6 | − | 7331.24i | −0.512655 | − | 0.372466i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32498.5 | + | 23611.6i | −1.64433 | + | 1.19467i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −999.203 | − | 1375.29i | −0.0503498 | − | 0.0693006i | 0.783100 | − | 0.621896i | \(-0.213637\pi\) |
−0.833450 | + | 0.552596i | \(0.813637\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3397.15 | + | 9448.50i | −0.170484 | + | 0.474167i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4379.28 | − | 1422.91i | 0.218878 | − | 0.0711177i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3897.45 | − | 11995.1i | 0.194005 | − | 0.597087i | −0.805982 | − | 0.591941i | \(-0.798362\pi\) |
0.999987 | − | 0.00514600i | \(-0.00163803\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19102.4 | − | 58791.1i | −0.947023 | − | 2.91464i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1238.58i | 0.0611561i | 0.999532 | + | 0.0305780i | \(0.00973481\pi\) | ||||
−0.999532 | + | 0.0305780i | \(0.990265\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22762.7 | − | 6623.61i | 1.11941 | − | 0.325732i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16385.4 | + | 22552.6i | −0.802557 | + | 1.10463i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11583.8 | 0.565102 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12120.2 | −0.588912 | −0.294456 | − | 0.955665i | \(-0.595139\pi\) | ||||
−0.294456 | + | 0.955665i | \(0.595139\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2040.76 | − | 2808.87i | 0.0987643 | − | 0.135937i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22102.3 | + | 6431.45i | −1.06541 | + | 0.310019i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25512.4i | 1.22492i | 0.790501 | + | 0.612460i | \(0.209820\pi\) | ||||
−0.790501 | + | 0.612460i | \(0.790180\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1992.93 | − | 6133.61i | −0.0953080 | − | 0.293328i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2982.29 | + | 9178.54i | −0.142060 | + | 0.437217i | −0.996621 | − | 0.0821345i | \(-0.973826\pi\) |
0.854561 | + | 0.519351i | \(0.173826\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −855.924 | + | 278.106i | −0.0406114 | + | 0.0131955i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11130.2 | − | 30956.4i | 0.526030 | − | 1.46305i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8347.30 | + | 11489.1i | 0.392964 | + | 0.540869i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28254.5 | − | 20528.1i | 1.32495 | − | 0.962630i | 0.325090 | − | 0.945683i | \(-0.394605\pi\) |
0.999856 | − | 0.0169466i | \(-0.00539452\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3992.98 | − | 2901.07i | −0.186516 | − | 0.135512i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7250.45 | − | 2355.81i | −0.337361 | − | 0.109615i | 0.135437 | − | 0.990786i | \(-0.456756\pi\) |
−0.472799 | + | 0.881171i | \(0.656756\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8709.04 | + | 22051.0i | −0.403662 | + | 1.02206i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 31686.1 | + | 10295.4i | 1.46298 | + | 0.475350i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5302.71 | + | 3852.64i | 0.243889 | + | 0.177195i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1366.76 | + | 993.010i | −0.0626204 | + | 0.0454964i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2269.34 | + | 3123.48i | 0.103575 | + | 0.142559i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1528.87 | − | 5254.12i | −0.0695131 | − | 0.238888i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2953.21 | + | 959.556i | −0.133762 | + | 0.0434619i | −0.375133 | − | 0.926971i | \(-0.622403\pi\) |
0.241371 | + | 0.970433i | \(0.422403\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8041.19 | − | 24748.3i | 0.362832 | − | 1.11668i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6681.24 | − | 20562.7i | −0.300325 | − | 0.924307i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 11825.4i | − | 0.529549i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16073.2 | + | 23629.4i | 0.717052 | + | 1.05415i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12112.5 | + | 16671.5i | −0.538328 | + | 0.740945i | −0.988371 | − | 0.152062i | \(-0.951409\pi\) |
0.450043 | + | 0.893007i | \(0.351409\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13306.0 | 0.589152 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10922.9 | 0.481823 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5821.53 | + | 8012.65i | −0.255837 | + | 0.352130i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 674.939 | − | 21770.2i | 0.0295509 | − | 0.953167i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21031.7i | 0.917410i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3089.44 | − | 9508.32i | −0.134263 | − | 0.413220i | 0.861211 | − | 0.508247i | \(-0.169706\pi\) |
−0.995475 | + | 0.0950270i | \(0.969706\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −311.514 | + | 958.741i | −0.0134879 | + | 0.0415116i | −0.957574 | − | 0.288188i | \(-0.906947\pi\) |
0.944086 | + | 0.329699i | \(0.106947\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19957.1 | + | 6484.44i | −0.860916 | + | 0.279728i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17089.4 | + | 11624.5i | −0.734497 | + | 0.499618i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20856.0 | + | 28705.8i | 0.893096 | + | 1.22924i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29764.2 | + | 21624.9i | −1.26989 | + | 0.922632i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13538.2 | − | 9836.04i | −0.575499 | − | 0.418125i | 0.261600 | − | 0.965176i | \(-0.415750\pi\) |
−0.837099 | + | 0.547052i | \(0.815750\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26157.4 | − | 8499.06i | −1.10789 | − | 0.359974i | −0.302753 | − | 0.953069i | \(-0.597906\pi\) |
−0.805133 | + | 0.593095i | \(0.797906\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8351.11 | + | 3298.27i | 0.352422 | + | 0.139189i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39479.3 | − | 12827.6i | −1.66001 | − | 0.539370i | −0.679136 | − | 0.734012i | \(-0.737645\pi\) |
−0.980874 | + | 0.194642i | \(0.937645\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 600.231 | + | 436.094i | 0.0251470 | + | 0.0182704i | 0.600288 | − | 0.799784i | \(-0.295053\pi\) |
−0.575141 | + | 0.818054i | \(0.695053\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16488.5 | − | 11979.6i | 0.688302 | − | 0.500080i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9874.99 | + | 13591.8i | 0.410742 | + | 0.565338i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6814.84 | − | 5281.52i | −0.282440 | − | 0.218891i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5853.81 | − | 1902.02i | 0.241741 | − | 0.0785464i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −874.305 | + | 2690.83i | −0.0359766 | + | 0.110725i | −0.967432 | − | 0.253131i | \(-0.918540\pi\) |
0.931456 | + | 0.363855i | \(0.118540\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3162.72 | − | 9733.85i | −0.129678 | − | 0.399108i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26268.3i | 1.07322i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24258.6 | + | 31301.4i | −0.987601 | + | 1.27432i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15642.6 | − | 21530.2i | 0.634576 | − | 0.873419i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29595.2 | 1.19635 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19618.3 | −0.790253 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22637.0 | − | 31157.2i | 0.908648 | − | 1.25065i | −0.0589779 | − | 0.998259i | \(-0.518784\pi\) |
0.967626 | − | 0.252388i | \(-0.0812159\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27343.6 | − | 9831.25i | −1.09372 | − | 0.393242i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 27324.6i | − | 1.08914i | −0.838716 | − | 0.544569i | \(-0.816693\pi\) | ||
0.838716 | − | 0.544569i | \(-0.183307\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2696.47 | − | 8298.89i | −0.107104 | − | 0.329633i | 0.883114 | − | 0.469158i | \(-0.155442\pi\) |
−0.990219 | + | 0.139525i | \(0.955442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2659.64 | − | 8185.52i | 0.105273 | − | 0.323998i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1064.27 | + | 345.802i | −0.0419793 | + | 0.0136399i | −0.329931 | − | 0.944005i | \(-0.607026\pi\) |
0.287952 | + | 0.957645i | \(0.407026\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39028.7 | − | 1210.00i | −1.53412 | − | 0.0475622i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −51089.7 | − | 70318.9i | −2.00127 | − | 2.75451i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4606.43 | + | 3346.77i | −0.179819 | + | 0.130646i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27608.8 | + | 20059.0i | 1.07404 | + | 0.780336i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22158.7 | − | 7199.79i | −0.859057 | − | 0.279125i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22771.6 | + | 20024.5i | 0.879794 | + | 0.773661i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9244.36 | − | 3003.67i | −0.355940 | − | 0.115652i | 0.125588 | − | 0.992082i | \(-0.459918\pi\) |
−0.481529 | + | 0.876430i | \(0.659918\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9280.34 | + | 6742.57i | 0.356107 | + | 0.258727i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20534.5 | − | 14919.2i | 0.785272 | − | 0.570533i | −0.121285 | − | 0.992618i | \(-0.538701\pi\) |
0.906556 | + | 0.422085i | \(0.138701\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19505.2 | + | 26846.6i | 0.743378 | + | 1.02317i | 0.998417 | + | 0.0562412i | \(0.0179116\pi\) |
−0.255039 | + | 0.966931i | \(0.582088\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14721.0 | + | 456.394i | 0.559144 | + | 0.0173351i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21136.1 | − | 6867.54i | 0.800091 | − | 0.259965i | 0.119696 | − | 0.992811i | \(-0.461808\pi\) |
0.680395 | + | 0.732845i | \(0.261808\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3066.57 | − | 9437.93i | 0.115691 | − | 0.356061i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2629.18 | − | 8091.77i | −0.0988560 | − | 0.304247i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 11753.1i | − | 0.440429i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28306.5 | − | 10177.4i | −1.05719 | − | 0.380105i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28094.5 | − | 38668.8i | 1.04576 | − | 1.43937i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22565.1 | 0.837140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47817.4 | 1.76807 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27386.2 | − | 37693.8i | 1.00925 | − | 1.38912i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31836.9 | − | 41079.7i | 1.16939 | − | 1.50888i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25904.8i | 0.948351i | 0.880430 | + | 0.474176i | \(0.157254\pi\) | ||||
−0.880430 | + | 0.474176i | \(0.842746\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8066.97 | − | 24827.6i | −0.294350 | − | 0.905917i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4719.03 | + | 14523.7i | −0.171623 | + | 0.528201i | −0.999463 | − | 0.0327629i | \(-0.989569\pi\) |
0.827840 | + | 0.560964i | \(0.189569\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12108.0 | + | 3934.12i | −0.438900 | + | 0.142607i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9693.71 | − | 7512.65i | −0.350234 | − | 0.271432i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26075.2 | + | 35889.4i | 0.939016 | + | 1.29244i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10425.0 | − | 7574.22i | 0.374200 | − | 0.271872i | −0.384751 | − | 0.923021i | \(-0.625713\pi\) |
0.758950 | + | 0.651149i | \(0.225713\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −41129.1 | − | 29882.1i | −1.47150 | − | 1.06911i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11907.9 | − | 3869.11i | −0.424651 | − | 0.137978i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17392.2 | − | 21059.8i | 0.618219 | − | 0.748587i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22674.9 | + | 7367.53i | 0.803389 | + | 0.261037i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22883.7 | − | 16626.0i | −0.808169 | − | 0.587169i | 0.105130 | − | 0.994458i | \(-0.466474\pi\) |
−0.913299 | + | 0.407289i | \(0.866474\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12005.5 | − | 8722.54i | 0.422627 | − | 0.307056i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17222.8 | − | 23705.1i | −0.604340 | − | 0.831802i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12422.2 | − | 8449.82i | 0.434492 | − | 0.295549i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41152.7 | + | 13371.3i | −1.43479 | + | 0.466192i | −0.920269 | − | 0.391286i | \(-0.872030\pi\) |
−0.514522 | + | 0.857477i | \(0.672030\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4491.56 | − | 13823.6i | 0.156098 | − | 0.480421i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12782.0 | + | 39339.0i | 0.442808 | + | 1.36282i | 0.884870 | + | 0.465837i | \(0.154247\pi\) |
−0.442063 | + | 0.896984i | \(0.645753\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5068.02i | 0.175013i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 243.951 | − | 7868.67i | 0.00839760 | − | 0.270865i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13747.3 | − | 18921.5i | 0.471728 | − | 0.649277i | −0.505161 | − | 0.863025i | \(-0.668567\pi\) |
0.976889 | + | 0.213748i | \(0.0685670\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −73402.7 | −2.51080 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4488.75 | −0.153058 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12271.5 | + | 16890.2i | −0.417116 | + | 0.574111i | −0.964936 | − | 0.262485i | \(-0.915458\pi\) |
0.547820 | + | 0.836596i | \(0.315458\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23385.6 | + | 34379.6i | 0.792400 | + | 1.16492i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 8545.81i | − | 0.288659i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15451.1 | + | 47553.6i | 0.520273 | + | 1.60124i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1910.65 | − | 5880.39i | 0.0641353 | − | 0.197388i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11364.2 | − | 3692.44i | 0.380276 | − | 0.123559i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16287.9 | + | 55974.8i | 0.543342 | + | 1.86725i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21294.1 | − | 29308.8i | −0.708140 | − | 0.974671i | −0.999835 | − | 0.0181600i | \(-0.994219\pi\) |
0.291695 | − | 0.956511i | \(-0.405781\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −86783.8 | + | 63052.2i | −2.87709 | + | 2.09033i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19540.3 | − | 14196.9i | −0.645807 | − | 0.469206i | 0.216033 | − | 0.976386i | \(-0.430688\pi\) |
−0.861840 | + | 0.507180i | \(0.830688\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10818.5 | − | 3515.13i | −0.356448 | − | 0.115817i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16603.5 | + | 64440.1i | 0.545373 | + | 2.11665i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42244.7 | + | 13726.1i | 1.38334 | + | 0.449476i | 0.903767 | − | 0.428024i | \(-0.140790\pi\) |
0.479577 | + | 0.877500i | \(0.340790\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4035.72 | + | 2932.12i | 0.131749 | + | 0.0957213i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −751.049 | + | 545.669i | −0.0244436 | + | 0.0177593i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22962.8 | − | 31605.6i | −0.745066 | − | 1.02550i | −0.998311 | − | 0.0580937i | \(-0.981498\pi\) |
0.253245 | − | 0.967402i | \(-0.418502\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3942.86 | − | 10966.3i | 0.127543 | − | 0.354735i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14677.8 | + | 4769.09i | −0.473352 | + | 0.153801i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8477.98 | + | 26092.5i | −0.272583 | + | 0.838923i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17152.9 | + | 52791.3i | 0.549829 | + | 1.69220i | 0.709222 | + | 0.704985i | \(0.249046\pi\) |
−0.159393 | + | 0.987215i | \(0.550954\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43330.8i | 1.38475i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31199.9 | − | 9078.73i | 0.994075 | − | 0.289261i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18514.2 | + | 25482.5i | −0.588114 | + | 0.809469i | −0.994556 | − | 0.104208i | \(-0.966769\pi\) |
0.406442 | + | 0.913677i | \(0.366769\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7090.86 | −0.224569 |
(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 | 100.4.i.a.29.2 | ✓ | 32 | |
5.2 | odd | 4 | 500.4.g.b.101.14 | 64 | |||
5.3 | odd | 4 | 500.4.g.b.101.3 | 64 | |||
5.4 | even | 2 | 500.4.i.a.149.7 | 32 | |||
25.6 | even | 5 | 500.4.i.a.349.7 | 32 | |||
25.8 | odd | 20 | 500.4.g.b.401.3 | 64 | |||
25.12 | odd | 20 | 2500.4.a.g.1.6 | 32 | |||
25.13 | odd | 20 | 2500.4.a.g.1.27 | 32 | |||
25.17 | odd | 20 | 500.4.g.b.401.14 | 64 | |||
25.19 | even | 10 | inner | 100.4.i.a.69.2 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.4.i.a.29.2 | ✓ | 32 | 1.1 | even | 1 | trivial | |
100.4.i.a.69.2 | yes | 32 | 25.19 | even | 10 | inner | |
500.4.g.b.101.3 | 64 | 5.3 | odd | 4 | |||
500.4.g.b.101.14 | 64 | 5.2 | odd | 4 | |||
500.4.g.b.401.3 | 64 | 25.8 | odd | 20 | |||
500.4.g.b.401.14 | 64 | 25.17 | odd | 20 | |||
500.4.i.a.149.7 | 32 | 5.4 | even | 2 | |||
500.4.i.a.349.7 | 32 | 25.6 | even | 5 | |||
2500.4.a.g.1.6 | 32 | 25.12 | odd | 20 | |||
2500.4.a.g.1.27 | 32 | 25.13 | odd | 20 |