Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(97,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.97");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.j (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 289.5 | ||
Character | \(\chi\) | \(=\) | 384.289 |
Dual form | 384.4.j.b.97.5 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.12132 | − | 2.12132i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.29121 | − | 7.29121i | 0.652145 | − | 0.652145i | −0.301364 | − | 0.953509i | \(-0.597442\pi\) |
0.953509 | + | 0.301364i | \(0.0974419\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.1610i | 1.19658i | 0.801278 | + | 0.598292i | \(0.204154\pi\) | ||||
−0.801278 | + | 0.598292i | \(0.795846\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.24116 | + | 8.24116i | −0.225891 | + | 0.225891i | −0.810974 | − | 0.585083i | \(-0.801062\pi\) |
0.585083 | + | 0.810974i | \(0.301062\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −51.9094 | − | 51.9094i | −1.10747 | − | 1.10747i | −0.993482 | − | 0.113986i | \(-0.963638\pi\) |
−0.113986 | − | 0.993482i | \(-0.536362\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −30.9340 | −0.532475 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −58.7304 | −0.837894 | −0.418947 | − | 0.908011i | \(-0.637601\pi\) | ||||
−0.418947 | + | 0.908011i | \(0.637601\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 54.5389 | + | 54.5389i | 0.658531 | + | 0.658531i | 0.955032 | − | 0.296501i | \(-0.0958199\pi\) |
−0.296501 | + | 0.955032i | \(0.595820\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 47.0107 | − | 47.0107i | 0.488503 | − | 0.488503i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 117.989i | − | 1.06967i | −0.844955 | − | 0.534837i | \(-0.820373\pi\) | ||
0.844955 | − | 0.534837i | \(-0.179627\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18.6766i | 0.149413i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19.0919 | − | 19.0919i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −175.283 | − | 175.283i | −1.12239 | − | 1.12239i | −0.991381 | − | 0.131007i | \(-0.958179\pi\) |
−0.131007 | − | 0.991381i | \(-0.541821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.58699 | −0.0381631 | −0.0190816 | − | 0.999818i | \(-0.506074\pi\) | ||||
−0.0190816 | + | 0.999818i | \(0.506074\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 34.9643 | 0.184439 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 161.581 | + | 161.581i | 0.780347 | + | 0.780347i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −265.451 | + | 265.451i | −1.17946 | + | 1.17946i | −0.199574 | + | 0.979883i | \(0.563956\pi\) |
−0.979883 | + | 0.199574i | \(0.936044\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 220.233i | 0.904244i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 98.7545i | 0.376167i | 0.982153 | + | 0.188084i | \(0.0602276\pi\) | ||||
−0.982153 | + | 0.188084i | \(0.939772\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −347.544 | + | 347.544i | −1.23256 | + | 1.23256i | −0.269580 | + | 0.962978i | \(0.586885\pi\) |
−0.962978 | + | 0.269580i | \(0.913115\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 65.6209 | + | 65.6209i | 0.217382 | + | 0.217382i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −141.880 | −0.440327 | −0.220164 | − | 0.975463i | \(-0.570659\pi\) | ||||
−0.220164 | + | 0.975463i | \(0.570659\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −148.112 | −0.431813 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 124.586 | + | 124.586i | 0.342069 | + | 0.342069i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 210.101 | − | 210.101i | 0.544520 | − | 0.544520i | −0.380331 | − | 0.924850i | \(-0.624190\pi\) |
0.924850 | + | 0.380331i | \(0.124190\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 120.176i | 0.294628i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 231.389i | − | 0.537688i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −427.318 | + | 427.318i | −0.942917 | + | 0.942917i | −0.998457 | − | 0.0555392i | \(-0.982312\pi\) |
0.0555392 | + | 0.998457i | \(0.482312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −178.341 | − | 178.341i | −0.374332 | − | 0.374332i | 0.494720 | − | 0.869052i | \(-0.335270\pi\) |
−0.869052 | + | 0.494720i | \(0.835270\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −199.449 | −0.398861 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −756.965 | −1.44446 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −480.715 | − | 480.715i | −0.876547 | − | 0.876547i | 0.116628 | − | 0.993176i | \(-0.462791\pi\) |
−0.993176 | + | 0.116628i | \(0.962791\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −250.293 | + | 250.293i | −0.436693 | + | 0.436693i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 884.186i | 1.47794i | 0.673740 | + | 0.738969i | \(0.264687\pi\) | ||||
−0.673740 | + | 0.738969i | \(0.735313\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 794.543i | − | 1.27389i | −0.770908 | − | 0.636947i | \(-0.780197\pi\) | ||
0.770908 | − | 0.636947i | \(-0.219803\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 39.6190 | − | 39.6190i | 0.0609975 | − | 0.0609975i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −182.633 | − | 182.633i | −0.270298 | − | 0.270298i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −421.166 | −0.599809 | −0.299904 | − | 0.953969i | \(-0.596955\pi\) | ||||
−0.299904 | + | 0.953969i | \(0.596955\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −81.0000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 167.507 | + | 167.507i | 0.221522 | + | 0.221522i | 0.809139 | − | 0.587617i | \(-0.199934\pi\) |
−0.587617 | + | 0.809139i | \(0.699934\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −428.215 | + | 428.215i | −0.546429 | + | 0.546429i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 743.664i | 0.916427i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 664.016i | 0.790849i | 0.918498 | + | 0.395425i | \(0.129403\pi\) | ||||
−0.918498 | + | 0.395425i | \(0.870597\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1150.37 | − | 1150.37i | 1.32518 | − | 1.32518i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.9731 | + | 13.9731i | 0.0155800 | + | 0.0155800i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 795.309 | 0.858916 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1083.81 | −1.13447 | −0.567236 | − | 0.823555i | \(-0.691987\pi\) | ||||
−0.567236 | + | 0.823555i | \(0.691987\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −74.1705 | − | 74.1705i | −0.0752971 | − | 0.0752971i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 600.838 | − | 600.838i | 0.591937 | − | 0.591937i | −0.346217 | − | 0.938154i | \(-0.612534\pi\) |
0.938154 | + | 0.346217i | \(0.112534\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 30.6830i | 0.0293523i | 0.999892 | + | 0.0146762i | \(0.00467173\pi\) | ||||
−0.999892 | + | 0.0146762i | \(0.995328\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 685.529i | − | 0.637150i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −812.356 | + | 812.356i | −0.733957 | + | 0.733957i | −0.971401 | − | 0.237444i | \(-0.923690\pi\) |
0.237444 | + | 0.971401i | \(0.423690\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 148.034 | + | 148.034i | 0.130083 | + | 0.130083i | 0.769151 | − | 0.639067i | \(-0.220679\pi\) |
−0.639067 | + | 0.769151i | \(0.720679\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1126.21 | 0.963022 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1801.39 | 1.49965 | 0.749826 | − | 0.661635i | \(-0.230137\pi\) | ||||
0.749826 | + | 0.661635i | \(0.230137\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −860.286 | − | 860.286i | −0.697583 | − | 0.697583i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 467.185 | − | 467.185i | 0.369156 | − | 0.369156i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1301.53i | − | 1.00261i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1195.17i | 0.897946i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 209.490 | − | 209.490i | 0.153570 | − | 0.153570i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1047.58 | + | 1047.58i | 0.749584 | + | 0.749584i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −876.738 | −0.612582 | −0.306291 | − | 0.951938i | \(-0.599088\pi\) | ||||
−0.306291 | + | 0.951938i | \(0.599088\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1474.51 | 1.00638 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1355.99 | + | 1355.99i | 0.904374 | + | 0.904374i | 0.995811 | − | 0.0914368i | \(-0.0291459\pi\) |
−0.0914368 | + | 0.995811i | \(0.529146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1208.64 | + | 1208.64i | −0.787988 | + | 0.787988i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 278.406i | − | 0.177492i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1833.19i | − | 1.14321i | −0.820529 | − | 0.571605i | \(-0.806321\pi\) | ||
0.820529 | − | 0.571605i | \(-0.193679\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 705.601 | − | 705.601i | 0.430563 | − | 0.430563i | −0.458257 | − | 0.888820i | \(-0.651526\pi\) |
0.888820 | + | 0.458257i | \(0.151526\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 300.974 | + | 300.974i | 0.179763 | + | 0.179763i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 855.588 | 0.500335 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2556.05 | −1.46392 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 314.193 | + | 314.193i | 0.176287 | + | 0.176287i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 714.815 | − | 714.815i | 0.393020 | − | 0.393020i | −0.482743 | − | 0.875762i | \(-0.660359\pi\) |
0.875762 | + | 0.482743i | \(0.160359\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3190.79i | − | 1.71962i | −0.510614 | − | 0.859810i | \(-0.670582\pi\) | ||
0.510614 | − | 0.859810i | \(-0.329418\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 528.573i | − | 0.279298i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −48.0271 | + | 48.0271i | −0.0248879 | + | 0.0248879i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −471.880 | − | 471.880i | −0.239874 | − | 0.239874i | 0.576924 | − | 0.816798i | \(-0.304253\pi\) |
−0.816798 | + | 0.576924i | \(0.804253\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −891.381 | −0.444598 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2614.77 | 1.27995 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −275.466 | − | 275.466i | −0.132369 | − | 0.132369i | 0.637818 | − | 0.770187i | \(-0.279837\pi\) |
−0.770187 | + | 0.637818i | \(0.779837\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 254.932 | − | 254.932i | 0.120281 | − | 0.120281i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1754.52i | − | 0.812988i | −0.913653 | − | 0.406494i | \(-0.866751\pi\) | ||
0.913653 | − | 0.406494i | \(-0.133249\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3192.18i | 1.45297i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −490.850 | + | 490.850i | −0.219510 | + | 0.219510i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −972.532 | − | 972.532i | −0.427400 | − | 0.427400i | 0.460342 | − | 0.887742i | \(-0.347727\pi\) |
−0.887742 | + | 0.460342i | \(0.847727\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −413.893 | −0.178785 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1812.96 | 0.769889 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1944.54 | − | 1944.54i | −0.811964 | − | 0.811964i | 0.172964 | − | 0.984928i | \(-0.444665\pi\) |
−0.984928 | + | 0.172964i | \(0.944665\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1388.85 | − | 1388.85i | 0.570345 | − | 0.570345i | −0.361880 | − | 0.932225i | \(-0.617865\pi\) |
0.932225 | + | 0.361880i | \(0.117865\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 756.637i | 0.305641i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3870.92i | 1.53835i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 484.006 | − | 484.006i | 0.189273 | − | 0.189273i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 423.096 | + | 423.096i | 0.162834 | + | 0.162834i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1754.58 | −0.664695 | −0.332347 | − | 0.943157i | \(-0.607841\pi\) | ||||
−0.332347 | + | 0.943157i | \(0.607841\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4111.28 | 1.53335 | 0.766675 | − | 0.642036i | \(-0.221910\pi\) | ||||
0.766675 | + | 0.642036i | \(0.221910\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1605.76 | + | 1605.76i | 0.589698 | + | 0.589698i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 585.319 | − | 585.319i | 0.211686 | − | 0.211686i | −0.593297 | − | 0.804984i | \(-0.702174\pi\) |
0.804984 | + | 0.593297i | \(0.202174\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2620.65i | − | 0.933533i | −0.884381 | − | 0.466766i | \(-0.845419\pi\) | ||
0.884381 | − | 0.466766i | \(-0.154581\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2039.50i | 0.715698i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3884.46 | − | 3884.46i | 1.34303 | − | 1.34303i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 720.039 | + | 720.039i | 0.245316 | + | 0.245316i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1061.91 | 0.356558 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −898.929 | −0.297513 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −969.705 | − | 969.705i | −0.316385 | − | 0.316385i | 0.530992 | − | 0.847377i | \(-0.321819\pi\) |
−0.847377 | + | 0.530992i | \(0.821819\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1875.64 | − | 1875.64i | 0.603365 | − | 0.603365i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5068.04i | 1.60761i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 145.974i | − | 0.0456654i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1685.48 | + | 1685.48i | −0.520065 | + | 0.520065i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3048.66 | + | 3048.66i | 0.927941 | + | 0.927941i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 63.3747 | 0.0190309 | 0.00951544 | − | 0.999955i | \(-0.496971\pi\) | ||||
0.00951544 | + | 0.999955i | \(0.496971\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −168.089 | −0.0498042 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1802.55 | + | 1802.55i | 0.527047 | + | 0.527047i | 0.919691 | − | 0.392644i | \(-0.128439\pi\) |
−0.392644 | + | 0.919691i | \(0.628439\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2895.47 | + | 2895.47i | −0.835538 | + | 0.835538i | −0.988268 | − | 0.152730i | \(-0.951193\pi\) |
0.152730 | + | 0.988268i | \(0.451193\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 774.845i | 0.220697i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4262.01i | − | 1.19834i | −0.800621 | − | 0.599171i | \(-0.795497\pi\) | ||
0.800621 | − | 0.599171i | \(-0.204503\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1034.48 | + | 1034.48i | −0.287157 | + | 0.287157i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 893.428 | + | 893.428i | 0.244871 | + | 0.244871i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3308.14 | 0.895337 | 0.447669 | − | 0.894200i | \(-0.352254\pi\) | ||||
0.447669 | + | 0.894200i | \(0.352254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3200.02 | −0.855316 | −0.427658 | − | 0.903941i | \(-0.640661\pi\) | ||||
−0.427658 | + | 0.903941i | \(0.640661\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 171.827 | + | 171.827i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1079.91 | + | 1079.91i | −0.281605 | + | 0.281605i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5662.17i | − | 1.45860i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 710.673i | − | 0.180872i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1945.31 | − | 1945.31i | 0.489190 | − | 0.489190i | −0.418860 | − | 0.908051i | \(-0.637570\pi\) |
0.908051 | + | 0.418860i | \(0.137570\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 972.370 | + | 972.370i | 0.241630 | + | 0.241630i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1816.76 | 0.446157 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −82.9830 | −0.0201414 | −0.0100707 | − | 0.999949i | \(-0.503206\pi\) | ||||
−0.0100707 | + | 0.999949i | \(0.503206\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5882.67 | − | 5882.67i | −1.41132 | − | 1.41132i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1577.55 | − | 1577.55i | 0.374130 | − | 0.374130i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2139.57i | 0.501641i | 0.968034 | + | 0.250821i | \(0.0807004\pi\) | ||||
−0.968034 | + | 0.250821i | \(0.919300\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3063.77i | − | 0.710212i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1408.59 | − | 1408.59i | 0.322863 | − | 0.322863i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2564.40 | − | 2564.40i | −0.581243 | − | 0.581243i | 0.354002 | − | 0.935245i | \(-0.384821\pi\) |
−0.935245 | + | 0.354002i | \(0.884821\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1373.88 | 0.307960 | 0.153980 | − | 0.988074i | \(-0.450791\pi\) | ||||
0.153980 | + | 0.988074i | \(0.450791\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4880.59 | −1.08200 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −153.917 | − | 153.917i | −0.0337510 | − | 0.0337510i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1763.08 | + | 1763.08i | −0.382431 | + | 0.382431i | −0.871977 | − | 0.489546i | \(-0.837162\pi\) |
0.489546 | + | 0.871977i | \(0.337162\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 59.2829i | − | 0.0127210i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8170.89i | − | 1.73464i | −0.497748 | − | 0.867321i | \(-0.665840\pi\) | ||
0.497748 | − | 0.867321i | \(-0.334160\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1217.94 | + | 1217.94i | −0.255827 | + | 0.255827i | −0.823354 | − | 0.567528i | \(-0.807900\pi\) |
0.567528 | + | 0.823354i | \(0.307900\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1687.11 | − | 1687.11i | −0.350651 | − | 0.350651i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2188.50 | −0.450116 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1463.75 | −0.297933 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2299.10 | + | 2299.10i | 0.463146 | + | 0.463146i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2994.08 | + | 2994.08i | −0.596984 | + | 0.596984i | −0.939509 | − | 0.342525i | \(-0.888718\pi\) |
0.342525 | + | 0.939509i | \(0.388718\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6231.33i | 1.22984i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 314.679i | 0.0614798i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6124.76 | + | 6124.76i | −1.18463 | + | 1.18463i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7701.94 | − | 7701.94i | −1.47486 | − | 1.47486i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2549.14 | −0.483315 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2600.64 | −0.488238 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5382.02 | + | 5382.02i | 1.00055 | + | 1.00055i | 1.00000 | 0.000548529i | \(0.000174602\pi\) | |
0.000548529 | 1.00000i | \(0.499825\pi\) | ||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 65.0885 | − | 65.0885i | 0.0119830 | − | 0.0119830i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7805.69i | 1.42322i | 0.702577 | + | 0.711608i | \(0.252033\pi\) | ||||
−0.702577 | + | 0.711608i | \(0.747967\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1549.25i | 0.279772i | 0.990168 | + | 0.139886i | \(0.0446736\pi\) | ||||
−0.990168 | + | 0.139886i | \(0.955326\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1454.23 | + | 1454.23i | −0.260116 | + | 0.260116i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6112.35 | + | 6112.35i | 1.08298 | + | 1.08298i | 0.996230 | + | 0.0867460i | \(0.0276468\pi\) |
0.0867460 | + | 0.996230i | \(0.472353\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2889.07 | 0.507076 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3446.53 | 0.599273 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3203.09 | − | 3203.09i | −0.551779 | − | 0.551779i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 969.491 | − | 969.491i | 0.165470 | − | 0.165470i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 628.056i | − | 0.106213i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3144.22i | − | 0.526888i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3539.08 | + | 3539.08i | −0.587690 | + | 0.587690i | −0.937005 | − | 0.349316i | \(-0.886414\pi\) |
0.349316 | + | 0.937005i | \(0.386414\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2389.06 | − | 2389.06i | −0.393152 | − | 0.393152i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7009.98 | −1.14327 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7315.83 | −1.18255 | −0.591274 | − | 0.806471i | \(-0.701375\pi\) | ||||
−0.591274 | + | 0.806471i | \(0.701375\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3821.33 | − | 3821.33i | −0.612231 | − | 0.612231i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 54.2844 | − | 54.2844i | 0.00862072 | − | 0.00862072i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4318.92i | 0.679883i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3649.88i | 0.569574i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1214.48 | − | 1214.48i | 0.187886 | − | 0.187886i | −0.606895 | − | 0.794782i | \(-0.707585\pi\) |
0.794782 | + | 0.606895i | \(0.207585\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3823.99 | + | 3823.99i | 0.586514 | + | 0.586514i | 0.936686 | − | 0.350171i | \(-0.113877\pi\) |
−0.350171 | + | 0.936686i | \(0.613877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1982.10 | −0.301415 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4475.44 | 0.674797 | 0.337399 | − | 0.941362i | \(-0.390453\pi\) | ||||
0.337399 | + | 0.941362i | \(0.390453\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6446.78 | + | 6446.78i | 0.963830 | + | 0.963830i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2760.95 | + | 2760.95i | −0.409314 | + | 0.409314i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1340.95i | − | 0.197138i | −0.995130 | − | 0.0985688i | \(-0.968574\pi\) | ||
0.995130 | − | 0.0985688i | \(-0.0314264\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 910.008i | − | 0.132674i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2535.33 | − | 2535.33i | 0.366585 | − | 0.366585i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5793.18 | − | 5793.18i | −0.830764 | − | 0.830764i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5859.22 | −0.833376 | −0.416688 | − | 0.909050i | \(-0.636809\pi\) | ||||
−0.416688 | + | 0.909050i | \(0.636809\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −888.790 | −0.125389 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4656.05 | + | 4656.05i | 0.651563 | + | 0.651563i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4717.98 | − | 4717.98i | 0.654927 | − | 0.654927i | −0.299248 | − | 0.954175i | \(-0.596736\pi\) |
0.954175 | + | 0.299248i | \(0.0967359\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 4444.49i | − | 0.612033i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18197.7i | 2.48602i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −252.484 | + | 252.484i | −0.0342197 | + | 0.0342197i | −0.724010 | − | 0.689790i | \(-0.757703\pi\) |
0.689790 | + | 0.724010i | \(0.257703\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1859.84 | + | 1859.84i | 0.250086 | + | 0.250086i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2526.32 | 0.337047 | 0.168524 | − | 0.985698i | \(-0.446100\pi\) | ||||
0.168524 | + | 0.985698i | \(0.446100\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2663.23 | −0.352547 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3127.90 | − | 3127.90i | −0.410853 | − | 0.410853i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1772.59 | + | 1772.59i | −0.231038 | + | 0.231038i | −0.813126 | − | 0.582088i | \(-0.802236\pi\) |
0.582088 | + | 0.813126i | \(0.302236\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6929.56i | 0.896274i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5752.96i | − | 0.738418i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3070.81 | + | 3070.81i | −0.391163 | + | 0.391163i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4182.28 | − | 4182.28i | −0.528722 | − | 0.528722i | 0.391469 | − | 0.920191i | \(-0.371967\pi\) |
−0.920191 | + | 0.391469i | \(0.871967\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5127.82 | 0.643389 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5929.46 | −0.738411 | −0.369206 | − | 0.929348i | \(-0.620370\pi\) | ||||
−0.369206 | + | 0.929348i | \(0.620370\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 341.927 | + | 341.927i | 0.0422645 | + | 0.0422645i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −590.588 | + | 590.588i | −0.0724606 | + | 0.0724606i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4375.25i | − | 0.532858i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9651.64i | 1.16685i | 0.812166 | + | 0.583427i | \(0.198288\pi\) | ||||
−0.812166 | + | 0.583427i | \(0.801712\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3888.78 | + | 3888.78i | −0.466713 | + | 0.466713i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9469.82 | − | 9469.82i | −1.12828 | − | 1.12828i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2442.66 | 0.288929 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2993.61 | −0.351553 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.7232 | − | 39.7232i | −0.00463152 | − | 0.00463152i | 0.704787 | − | 0.709419i | \(-0.251042\pi\) |
−0.709419 | + | 0.704787i | \(0.751042\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1741.60 | + | 1741.60i | −0.201616 | + | 0.201616i | −0.800692 | − | 0.599076i | \(-0.795535\pi\) |
0.599076 | + | 0.800692i | \(0.295535\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1276.92i | − | 0.146776i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1096.88i | − | 0.125192i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3952.23 | − | 3952.23i | 0.447919 | − | 0.447919i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1814.98 | − | 1814.98i | −0.204261 | − | 0.204261i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 115.905 | 0.0129535 | 0.00647673 | − | 0.999979i | \(-0.497938\pi\) | ||||
0.00647673 | + | 0.999979i | \(0.497938\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10706.1 | 1.18823 | 0.594115 | − | 0.804380i | \(-0.297502\pi\) | ||||
0.594115 | + | 0.804380i | \(0.297502\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5422.21 | + | 5422.21i | 0.597643 | + | 0.597643i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6435.02 | − | 6435.02i | 0.704414 | − | 0.704414i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1275.83i | − | 0.138706i | −0.997592 | − | 0.0693531i | \(-0.977906\pi\) | ||
0.997592 | − | 0.0693531i | \(-0.0220935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 1333.01i | − | 0.143938i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1291.45 | + | 1291.45i | −0.138507 | + | 0.138507i | −0.772961 | − | 0.634454i | \(-0.781225\pi\) |
0.634454 | + | 0.772961i | \(0.281225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4841.48 | + | 4841.48i | 0.515749 | + | 0.515749i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3032.70 | −0.320899 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2137.82 | 0.224699 | 0.112350 | − | 0.993669i | \(-0.464162\pi\) | ||||
0.112350 | + | 0.993669i | \(0.464162\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −813.852 | − | 813.852i | −0.0849729 | − | 0.0849729i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6768.69 | + | 6768.69i | −0.702032 | + | 0.702032i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 16775.1i | − | 1.72842i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 15629.9i | − | 1.59986i | −0.600092 | − | 0.799931i | \(-0.704869\pi\) | ||
0.600092 | − | 0.799931i | \(-0.295131\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1121.27 | + | 1121.27i | −0.114023 | + | 0.114023i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2333.25 | + | 2333.25i | 0.235727 | + | 0.235727i | 0.815078 | − | 0.579351i | \(-0.196694\pi\) |
−0.579351 | + | 0.815078i | \(0.696694\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16917.7 | −1.69812 | −0.849061 | − | 0.528294i | \(-0.822832\pi\) | ||||
−0.849061 | + | 0.528294i | \(0.822832\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 203.762 | 0.0203209 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3249.62 | − | 3249.62i | −0.322001 | − | 0.322001i | 0.527533 | − | 0.849534i | \(-0.323117\pi\) |
−0.849534 | + | 0.527533i | \(0.823117\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10653.1 | − | 10653.1i | 1.04886 | − | 1.04886i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2002.02i | 0.195856i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5728.34i | − | 0.556848i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1018.60 | + | 1018.60i | −0.0983929 | + | 0.0983929i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1890.91 | + | 1890.91i | 0.181507 | + | 0.181507i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9780.09 | 0.932910 | 0.466455 | − | 0.884545i | \(-0.345531\pi\) | ||||
0.466455 | + | 0.884545i | \(0.345531\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27558.8 | 2.61242 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5546.76 | − | 5546.76i | −0.522539 | − | 0.522539i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7902.25 | + | 7902.25i | −0.739840 | + | 0.739840i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2710.17i | 0.252176i | 0.992019 | + | 0.126088i | \(0.0402421\pi\) | ||||
−0.992019 | + | 0.126088i | \(0.959758\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1168.70i | 0.108079i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1884.20 | − | 1884.20i | 0.173183 | − | 0.173183i | −0.615193 | − | 0.788376i | \(-0.710922\pi\) |
0.788376 | + | 0.615193i | \(0.210922\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10294.4 | + | 10294.4i | 0.940443 | + | 0.940443i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1081.58 | −0.0982093 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19594.5 | −1.76848 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11085.6 | + | 11085.6i | 0.994509 | + | 0.994509i | 0.999985 | − | 0.00547579i | \(-0.00174301\pi\) |
−0.00547579 | + | 0.999985i | \(0.501743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3721.90 | + | 3721.90i | −0.331901 | + | 0.331901i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 9544.26i | − | 0.846039i | −0.906121 | − | 0.423020i | \(-0.860970\pi\) | ||
0.906121 | − | 0.423020i | \(-0.139030\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 8761.67i | − | 0.772058i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6771.63 | − | 6771.63i | 0.593173 | − | 0.593173i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1874.95 | − | 1874.95i | −0.163272 | − | 0.163272i | 0.620742 | − | 0.784015i | \(-0.286831\pi\) |
−0.784015 | + | 0.620742i | \(0.786831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17607.9 | 1.52432 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2082.50 | 0.179229 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 223.716 | + | 223.716i | 0.0191420 | + | 0.0191420i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1169.26 | − | 1169.26i | 0.0994660 | − | 0.0994660i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4126.10i | 0.348971i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12549.3i | 1.05527i | 0.849471 | + | 0.527635i | \(0.176921\pi\) | ||||
−0.849471 | + | 0.527635i | \(0.823079\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5583.16 | − | 5583.16i | 0.466797 | − | 0.466797i | −0.434078 | − | 0.900875i | \(-0.642926\pi\) |
0.900875 | + | 0.434078i | \(0.142926\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 877.999 | + | 877.999i | 0.0729886 | + | 0.0729886i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 386.856 | 0.0319767 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1754.51 | −0.144202 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3845.87 | − | 3845.87i | −0.314306 | − | 0.314306i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5126.29 | − | 5126.29i | 0.416593 | − | 0.416593i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11846.1i | 0.957293i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8249.97i | 0.662966i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1220.61 | − | 1220.61i | 0.0975428 | − | 0.0975428i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7722.24 | + | 7722.24i | 0.613688 | + | 0.613688i | 0.943905 | − | 0.330217i | \(-0.107122\pi\) |
−0.330217 | + | 0.943905i | \(0.607122\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5892.40 | −0.465685 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2158.70 | 0.169667 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7464.17 | − | 7464.17i | −0.583446 | − | 0.583446i | 0.352403 | − | 0.935848i | \(-0.385365\pi\) |
−0.935848 | + | 0.352403i | \(0.885365\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1605.07 | − | 1605.07i | 0.124777 | − | 0.124777i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 19119.5i | − | 1.47826i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 9333.48i | − | 0.717722i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8211.46 | − | 8211.46i | 0.628031 | − | 0.628031i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10501.3 | + | 10501.3i | 0.798841 | + | 0.798841i | 0.982913 | − | 0.184072i | \(-0.0589280\pi\) |
−0.184072 | + | 0.982913i | \(0.558928\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36081.6 | 2.73004 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2053.47 | −0.154541 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16986.4 | − | 16986.4i | −1.27157 | − | 1.27157i | −0.945266 | − | 0.326300i | \(-0.894198\pi\) |
−0.326300 | − | 0.945266i | \(-0.605802\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13134.3 | − | 13134.3i | 0.977991 | − | 0.977991i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1795.04i | − | 0.132954i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10274.2i | 0.756971i | 0.925607 | + | 0.378486i | \(0.123555\pi\) | ||||
−0.925607 | + | 0.378486i | \(0.876445\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5116.90 | − | 5116.90i | 0.375019 | − | 0.375019i | −0.494283 | − | 0.869301i | \(-0.664569\pi\) |
0.869301 | + | 0.494283i | \(0.164569\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3722.02 | + | 3722.02i | 0.271361 | + | 0.271361i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2203.64 | 0.159823 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4648.41 | 0.335383 | 0.167691 | − | 0.985840i | \(-0.446369\pi\) | ||||
0.167691 | + | 0.985840i | \(0.446369\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8721.34 | − | 8721.34i | −0.625987 | − | 0.625987i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3712.13 | + | 3712.13i | −0.265069 | + | 0.265069i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3462.95i | 0.246004i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 6812.68i | − | 0.481487i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16839.3 | − | 16839.3i | 1.18404 | − | 1.18404i | 0.205351 | − | 0.978688i | \(-0.434166\pi\) |
0.978688 | − | 0.205351i | \(-0.0658337\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −359.247 | − | 359.247i | −0.0251316 | − | 0.0251316i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2483.30 | −0.172841 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15004.6 | 1.03906 | 0.519530 | − | 0.854452i | \(-0.326107\pi\) | ||||
0.519530 | + | 0.854452i | \(0.326107\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9489.70 | − | 9489.70i | −0.653848 | − | 0.653848i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5559.24 | + | 5559.24i | −0.381113 | + | 0.381113i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7740.90i | 0.528021i | 0.964520 | + | 0.264011i | \(0.0850454\pi\) | ||||
−0.964520 | + | 0.264011i | \(0.914955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19210.1i | 1.30382i | 0.758295 | + | 0.651912i | \(0.226033\pi\) | ||||
−0.758295 | + | 0.651912i | \(0.773967\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4326.43 | − | 4326.43i | 0.292182 | − | 0.292182i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8714.21 | + | 8714.21i | 0.585592 | + | 0.585592i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25349.2 | −1.69505 | −0.847524 | − | 0.530758i | \(-0.821907\pi\) | ||||
−0.847524 | + | 0.530758i | \(0.821907\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16480.4 | −1.09658 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7364.93 | + | 7364.93i | 0.487648 | + | 0.487648i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12517.8 | + | 12517.8i | −0.824780 | + | 0.824780i | −0.986789 | − | 0.162010i | \(-0.948202\pi\) |
0.162010 | + | 0.986789i | \(0.448202\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 3054.87i | − | 0.200300i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12650.0i | − | 0.825399i | −0.910867 | − | 0.412700i | \(-0.864586\pi\) | ||
0.910867 | − | 0.412700i | \(-0.135414\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5166.55 | + | 5166.55i | −0.335479 | + | 0.335479i | −0.854663 | − | 0.519184i | \(-0.826236\pi\) |
0.519184 | + | 0.854663i | \(0.326236\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2252.64 | − | 2252.64i | −0.145564 | − | 0.145564i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14715.3 | −0.946318 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12941.6 | 0.828263 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1906.92 | + | 1906.92i | 0.121459 | + | 0.121459i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15590.0 | − | 15590.0i | 0.988260 | − | 0.988260i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12728.9i | 0.803056i | 0.915847 | + | 0.401528i | \(0.131521\pi\) | ||||
−0.915847 | + | 0.401528i | \(0.868479\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4114.11i | 0.258327i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6392.48 | + | 6392.48i | −0.399493 | + | 0.399493i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7688.40 | + | 7688.40i | 0.478219 | + | 0.478219i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7957.67 | −0.492646 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8725.04 | 0.537626 | 0.268813 | − | 0.963192i | \(-0.413369\pi\) | ||||
0.268813 | + | 0.963192i | \(0.413369\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11974.6 | + | 11974.6i | 0.734418 | + | 0.734418i | 0.971492 | − | 0.237073i | \(-0.0761882\pi\) |
−0.237073 | + | 0.971492i | \(0.576188\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10750.9 | − | 10750.9i | 0.656306 | − | 0.656306i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16791.7i | 1.02033i | 0.860078 | + | 0.510163i | \(0.170415\pi\) | ||||
−0.860078 | + | 0.510163i | \(0.829585\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7043.20i | − | 0.425994i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −309.659 | + | 309.659i | −0.0186428 | + | 0.0186428i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12379.7 | − | 12379.7i | −0.741894 | − | 0.741894i | 0.231049 | − | 0.972942i | \(-0.425784\pi\) |
−0.972942 | + | 0.231049i | \(0.925784\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19773.5 | 1.17957 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7150.89 | 0.424631 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2164.94 | + | 2164.94i | 0.127973 | + | 0.127973i | 0.768192 | − | 0.640219i | \(-0.221157\pi\) |
−0.640219 | + | 0.768192i | \(0.721157\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16951.5 | + | 16951.5i | −0.997481 | + | 0.997481i | −0.999997 | − | 0.00251552i | \(-0.999199\pi\) |
0.00251552 | + | 0.999997i | \(0.499199\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 12934.4i | − | 0.757661i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17624.9i | 1.02777i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20681.6 | + | 20681.6i | −1.20059 | + | 1.20059i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −134.438 | − | 134.438i | −0.00776932 | − | 0.00776932i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2939.48 | 0.169117 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3167.92 | −0.181448 | −0.0907238 | − | 0.995876i | \(-0.528918\pi\) | ||||
−0.0907238 | + | 0.995876i | \(0.528918\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 356.571 | + | 356.571i | 0.0203325 | + | 0.0203325i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8613.73 | + | 8613.73i | −0.488999 | + | 0.488999i | −0.907990 | − | 0.418991i | \(-0.862384\pi\) |
0.418991 | + | 0.907990i | \(0.362384\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 24018.3i | − | 1.35749i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 7647.58i | − | 0.430332i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23079.8 | + | 23079.8i | −1.29301 | + | 1.29301i | −0.360093 | + | 0.932916i | \(0.617255\pi\) |
−0.932916 | + | 0.360093i | \(0.882745\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13366.1 | − | 13366.1i | −0.745539 | − | 0.745539i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12284.4 | 0.682214 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21812.4 | −1.20608 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10996.2 | + | 10996.2i | 0.605375 | + | 0.605375i | 0.941734 | − | 0.336359i | \(-0.109196\pi\) |
−0.336359 | + | 0.941734i | \(0.609196\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1643.69 | − | 1643.69i | 0.0900993 | − | 0.0900993i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 10289.4i | − | 0.561580i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 5799.89i | − | 0.315188i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9041.10 | + | 9041.10i | −0.489221 | + | 0.489221i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15045.8 | + | 15045.8i | 0.810659 | + | 0.810659i | 0.984733 | − | 0.174074i | \(-0.0556931\pi\) |
−0.174074 | + | 0.984733i | \(0.555693\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28954.8 | −1.55342 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4388.92 | 0.234463 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13315.2 | + | 13315.2i | 0.708302 | + | 0.708302i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13939.7 | − | 13939.7i | 0.738388 | − | 0.738388i | −0.233878 | − | 0.972266i | \(-0.575141\pi\) |
0.972266 | + | 0.233878i | \(0.0751415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 3790.50i | − | 0.199936i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 777.195i | 0.0408221i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6238.27 | − | 6238.27i | 0.326291 | − | 0.326291i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7017.62 | − | 7017.62i | −0.365520 | − | 0.365520i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32099.6 | −1.66497 | −0.832484 | − | 0.554050i | \(-0.813082\pi\) | ||||
−0.832484 | + | 0.554050i | \(0.813082\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −679.968 | −0.0351225 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6788.26 | + | 6788.26i | 0.349181 | + | 0.349181i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3273.69 | − | 3273.69i | 0.167699 | − | 0.167699i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1706.65i | − | 0.0870646i | −0.999052 | − | 0.0435323i | \(-0.986139\pi\) | ||
0.999052 | − | 0.0435323i | \(-0.0138611\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 729.000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20411.4 | − | 20411.4i | 1.03275 | − | 1.03275i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19995.6 | − | 19995.6i | −1.00758 | − | 1.00758i | −0.999971 | − | 0.00760565i | \(-0.997579\pi\) |
−0.00760565 | − | 0.999971i | \(-0.502421\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4581.69 | 0.229930 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7923.30 | 0.396009 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3123.50 | + | 3123.50i | 0.155480 | + | 0.155480i | 0.780560 | − | 0.625080i | \(-0.214934\pi\) |
−0.625080 | + | 0.780560i | \(0.714934\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12011.3 | + | 12011.3i | −0.595473 | + | 0.595473i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7764.79i | 0.383395i | 0.981454 | + | 0.191698i | \(0.0613993\pi\) | ||||
−0.981454 | + | 0.191698i | \(0.938601\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 10423.7i | − | 0.512612i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1507.56 | + | 1507.56i | −0.0738406 | + | 0.0738406i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18002.7 | − | 18002.7i | −0.878241 | − | 0.878241i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7697.83 | 0.374032 | 0.187016 | − | 0.982357i | \(-0.440118\pi\) | ||||
0.187016 | + | 0.982357i | \(0.440118\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8253.25 | −0.399422 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23264.7 | − | 23264.7i | −1.12144 | − | 1.12144i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3022.39 | + | 3022.39i | −0.145113 | + | 0.145113i | −0.775931 | − | 0.630818i | \(-0.782720\pi\) |
0.630818 | + | 0.775931i | \(0.282720\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 4125.42i | − | 0.197290i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 26737.7i | − | 1.27364i | −0.771012 | − | 0.636820i | \(-0.780249\pi\) | ||
0.771012 | − | 0.636820i | \(-0.219751\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3280.59 | + | 3280.59i | −0.155656 | + | 0.155656i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3853.94 | − | 3853.94i | −0.182143 | − | 0.182143i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 44363.7 | 2.08850 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14158.4 | −0.663934 | −0.331967 | − | 0.943291i | \(-0.607712\pi\) | ||||
−0.331967 | + | 0.943291i | \(0.607712\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 176.033 | + | 176.033i | 0.00822269 | + | 0.00822269i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15285.5 | + | 15285.5i | −0.711231 | + | 0.711231i | −0.966793 | − | 0.255562i | \(-0.917740\pi\) |
0.255562 | + | 0.966793i | \(0.417740\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 123.022i | − | 0.00570206i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24958.1i | 1.15234i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5385.96 | + | 5385.96i | −0.247718 | + | 0.247718i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7286.72 | − | 7286.72i | −0.333853 | − | 0.333853i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6692.97 | −0.305476 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6881.16 | −0.312865 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11317.7 | + | 11317.7i | 0.512622 | + | 0.512622i | 0.915329 | − | 0.402707i | \(-0.131931\pi\) |
−0.402707 | + | 0.915329i | \(0.631931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4538.72 | − | 4538.72i | 0.204794 | − | 0.204794i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39920.7i | 1.79446i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18515.2i | 0.829121i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6499.25 | + | 6499.25i | −0.289943 | + | 0.289943i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24453.7 | − | 24453.7i | −1.08682 | − | 1.08682i | −0.995854 | − | 0.0909639i | \(-0.971005\pi\) |
−0.0909639 | − | 0.995854i | \(-0.528995\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8332.68 | 0.368948 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5976.15 | −0.263616 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6547.96 | + | 6547.96i | 0.287761 | + | 0.287761i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19064.8 | − | 19064.8i | 0.834717 | − | 0.834717i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10879.8i | 0.474583i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 4516.01i | − | 0.196260i | −0.995174 | − | 0.0981301i | \(-0.968714\pi\) | ||
0.995174 | − | 0.0981301i | \(-0.0312861\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14460.0 | − | 14460.0i | 0.626092 | − | 0.626092i | −0.320990 | − | 0.947082i | \(-0.604016\pi\) |
0.947082 | + | 0.320990i | \(0.104016\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2914.44 | − | 2914.44i | −0.125724 | − | 0.125724i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4016.96 | −0.172648 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37909.4 | −1.62336 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10353.3 | + | 10353.3i | 0.441726 | + | 0.441726i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20286.7 | + | 20286.7i | −0.862377 | + | 0.862377i | −0.991614 | − | 0.129237i | \(-0.958747\pi\) |
0.129237 | + | 0.991614i | \(0.458747\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 27490.2i | − | 1.16434i | −0.813068 | − | 0.582168i | \(-0.802204\pi\) | ||
0.813068 | − | 0.582168i | \(-0.197796\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 653.013i | 0.0275576i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4576.46 | − | 4576.46i | 0.192429 | − | 0.192429i | −0.604316 | − | 0.796745i | \(-0.706553\pi\) |
0.796745 | + | 0.604316i | \(0.206553\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14697.8 | + | 14697.8i | 0.615772 | + | 0.615772i | 0.944444 | − | 0.328672i | \(-0.106601\pi\) |
−0.328672 | + | 0.944444i | \(0.606601\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7480.13 | 0.312254 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8698.66 | 0.361814 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12792.6 | − | 12792.6i | −0.530186 | − | 0.530186i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −125.758 | + | 125.758i | −0.00519335 | + | 0.00519335i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9206.59i | 0.378840i | 0.981896 | + | 0.189420i | \(0.0606608\pi\) | ||||
−0.981896 | + | 0.189420i | \(0.939339\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37059.4i | 1.51951i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17333.1 | + | 17333.1i | −0.708165 | + | 0.708165i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23274.8 | + | 23274.8i | 0.947548 | + | 0.947548i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26486.1 | −1.07447 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5167.27 | 0.208881 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31320.4 | + | 31320.4i | 1.26163 | + | 1.26163i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17252.0 | − | 17252.0i | 0.692494 | − | 0.692494i | −0.270286 | − | 0.962780i | \(-0.587118\pi\) |
0.962780 | + | 0.270286i | \(0.0871184\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7157.79i | 0.286305i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 22957.2i | − | 0.915057i | −0.889195 | − | 0.457529i | \(-0.848735\pi\) | ||
0.889195 | − | 0.457529i | \(-0.151265\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6376.26 | + | 6376.26i | −0.253266 | + | 0.253266i | −0.822308 | − | 0.569043i | \(-0.807314\pi\) |
0.569043 | + | 0.822308i | \(0.307314\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4642.51 | + | 4642.51i | 0.183759 | + | 0.183759i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35795.9 | −1.41194 | −0.705971 | − | 0.708241i | \(-0.749489\pi\) | ||||
−0.705971 | + | 0.708241i | \(0.749489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14181.9 | −0.557454 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3105.07 | + | 3105.07i | 0.121631 | + | 0.121631i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3470.90 | − | 3470.90i | 0.135492 | − | 0.135492i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49907.3i | 1.94150i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 9754.25i | − | 0.378157i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23215.4 | + | 23215.4i | −0.896940 | + | 0.896940i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9797.22 | − | 9797.22i | −0.377228 | − | 0.377228i | 0.492873 | − | 0.870101i | \(-0.335947\pi\) |
−0.870101 | + | 0.492873i | \(0.835947\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12702.8 | 0.487435 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3227.81 | −0.123437 | −0.0617183 | − | 0.998094i | \(-0.519658\pi\) | ||||
−0.0617183 | + | 0.998094i | \(0.519658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33226.7 | − | 33226.7i | −1.26633 | − | 1.26633i | −0.947972 | − | 0.318354i | \(-0.896870\pi\) |
−0.318354 | − | 0.947972i | \(-0.603130\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13218.7 | − | 13218.7i | 0.502079 | − | 0.502079i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3411.07i | 0.129123i | 0.997914 | + | 0.0645617i | \(0.0205649\pi\) | ||||
−0.997914 | + | 0.0645617i | \(0.979435\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 19429.4i | − | 0.733006i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 667.534 | − | 667.534i | 0.0250990 | − | 0.0250990i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7738.00 | − | 7738.00i | −0.289969 | − | 0.289969i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28356.0 | −1.05904 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25985.2 | 0.967246 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1154.59 | + | 1154.59i | 0.0428339 | + | 0.0428339i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12339.3 | + | 12339.3i | −0.456250 | + | 0.456250i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 32676.6i | 1.20422i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 20252.8i | − | 0.743896i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11317.0 | + | 11317.0i | −0.414305 | + | 0.414305i | −0.883235 | − | 0.468930i | \(-0.844640\pi\) |
0.468930 | + | 0.883235i | \(0.344640\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5407.54 | + | 5407.54i | 0.197312 | + | 0.197312i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5574.60 | 0.202738 | 0.101369 | − | 0.994849i | \(-0.467678\pi\) | ||||
0.101369 | + | 0.994849i | \(0.467678\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2760.91 | −0.100080 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5516.80 | + | 5516.80i | 0.199322 | + | 0.199322i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30050.1 | + | 30050.1i | −1.08216 | + | 1.08216i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 10717.9i | − | 0.384713i | −0.981325 | − | 0.192356i | \(-0.938387\pi\) | ||
0.981325 | − | 0.192356i | \(-0.0616130\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 22834.0i | − | 0.816944i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45897.6 | − | 45897.6i | 1.63677 | − | 1.63677i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4957.72 | − | 4957.72i | −0.176226 | − | 0.176226i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −276.147 | −0.00978410 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5276.25 | −0.186338 | −0.0931692 | − | 0.995650i | \(-0.529700\pi\) | ||||
−0.0931692 | + | 0.995650i | \(0.529700\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8077.87 | − | 8077.87i | −0.284362 | − | 0.284362i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16558.4 | − | 16558.4i | 0.581025 | − | 0.581025i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 7057.98i | − | 0.246867i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34230.9i | 1.19346i | 0.802441 | + | 0.596731i | \(0.203534\pi\) | ||||
−0.802441 | + | 0.596731i | \(0.796466\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3286.45 | − | 3286.45i | 0.114216 | − | 0.114216i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2969.85 | − | 2969.85i | −0.102884 | − | 0.102884i | 0.653791 | − | 0.756675i | \(-0.273178\pi\) |
−0.756675 | + | 0.653791i | \(0.773178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11652.0 | 0.402376 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6169.76 | 0.212383 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37250.4 | − | 37250.4i | −1.27822 | − | 1.27822i | −0.941663 | − | 0.336557i | \(-0.890737\pi\) |
−0.336557 | − | 0.941663i | \(-0.609263\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41244.3 | + | 41244.3i | −1.41080 | + | 1.41080i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 25932.5i | − | 0.884247i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 39434.0i | − | 1.34039i | −0.742185 | − | 0.670195i | \(-0.766210\pi\) | ||
0.742185 | − | 0.670195i | \(-0.233790\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12793.0 | + | 12793.0i | −0.433478 | + | 0.433478i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6128.65 | − | 6128.65i | −0.207013 | − | 0.207013i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40625.3 | 1.36795 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29747.6 | −0.998544 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7311.20 | − | 7311.20i | −0.244652 | − | 0.244652i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29976.2 | − | 29976.2i | 0.999967 | − | 0.999967i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2688.08i | 0.0893927i | 0.999001 | + | 0.0446964i | \(0.0142320\pi\) | ||||
−0.999001 | + | 0.0446964i | \(0.985768\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13589.6i | 0.450526i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33370.7 | + | 33370.7i | −1.10290 | + | 1.10290i | −0.108840 | + | 0.994059i | \(0.534714\pi\) |
−0.994059 | + | 0.108840i | \(0.965286\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15636.9 | + | 15636.9i | 0.515205 | + | 0.515205i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4113.20 | −0.135105 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8643.45 | 0.283039 | 0.141519 | − | 0.989936i | \(-0.454801\pi\) | ||||
0.141519 | + | 0.989936i | \(0.454801\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5472.27 | − | 5472.27i | −0.178646 | − | 0.178646i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1332.31 | + | 1332.31i | −0.0433612 | + | 0.0433612i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50643.1i | 1.64320i | 0.570067 | + | 0.821598i | \(0.306917\pi\) | ||||
−0.570067 | + | 0.821598i | \(0.693083\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 8535.36i | − | 0.276101i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6669.89 | + | 6669.89i | −0.215101 | + | 0.215101i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41006.6 | + | 41006.6i | 1.31844 | + | 1.31844i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11424.2 | −0.366198 | −0.183099 | − | 0.983094i | \(-0.558613\pi\) | ||||
−0.183099 | + | 0.983094i | \(0.558613\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15015.0 | 0.479846 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19107.7 | − | 19107.7i | −0.608799 | − | 0.608799i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35877.3 | + | 35877.3i | −1.13967 | + | 1.13967i | −0.151155 | + | 0.988510i | \(0.548299\pi\) |
−0.988510 | + | 0.151155i | \(0.951701\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10135.9i | 0.321007i |
(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 | 384.4.j.b.289.5 | 24 | ||
4.3 | odd | 2 | 384.4.j.a.289.8 | 24 | |||
8.3 | odd | 2 | 192.4.j.a.145.2 | 24 | |||
8.5 | even | 2 | 48.4.j.a.13.3 | ✓ | 24 | ||
16.3 | odd | 4 | 192.4.j.a.49.2 | 24 | |||
16.5 | even | 4 | inner | 384.4.j.b.97.5 | 24 | ||
16.11 | odd | 4 | 384.4.j.a.97.8 | 24 | |||
16.13 | even | 4 | 48.4.j.a.37.3 | yes | 24 | ||
24.5 | odd | 2 | 144.4.k.b.109.10 | 24 | |||
24.11 | even | 2 | 576.4.k.b.145.9 | 24 | |||
48.29 | odd | 4 | 144.4.k.b.37.10 | 24 | |||
48.35 | even | 4 | 576.4.k.b.433.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.4.j.a.13.3 | ✓ | 24 | 8.5 | even | 2 | ||
48.4.j.a.37.3 | yes | 24 | 16.13 | even | 4 | ||
144.4.k.b.37.10 | 24 | 48.29 | odd | 4 | |||
144.4.k.b.109.10 | 24 | 24.5 | odd | 2 | |||
192.4.j.a.49.2 | 24 | 16.3 | odd | 4 | |||
192.4.j.a.145.2 | 24 | 8.3 | odd | 2 | |||
384.4.j.a.97.8 | 24 | 16.11 | odd | 4 | |||
384.4.j.a.289.8 | 24 | 4.3 | odd | 2 | |||
384.4.j.b.97.5 | 24 | 16.5 | even | 4 | inner | ||
384.4.j.b.289.5 | 24 | 1.1 | even | 1 | trivial | ||
576.4.k.b.145.9 | 24 | 24.11 | even | 2 | |||
576.4.k.b.433.9 | 24 | 48.35 | even | 4 |