Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), degree \(2\), 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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 76.6 | ||
Character | \(\chi\) | \(=\) | 225.76 |
Dual form | 225.4.e.g.151.6 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.23192 | − | 2.13376i | −0.435551 | − | 0.754397i | 0.561789 | − | 0.827280i | \(-0.310113\pi\) |
−0.997340 | + | 0.0728836i | \(0.976780\pi\) | |||||||
\(3\) | −4.97325 | − | 1.50557i | −0.957103 | − | 0.289747i | ||||
\(4\) | 0.964722 | − | 1.67095i | 0.120590 | − | 0.208869i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.91415 | + | 12.4665i | 0.198283 | + | 0.848235i | ||||
\(7\) | −9.62007 | − | 16.6624i | −0.519435 | − | 0.899688i | −0.999745 | − | 0.0225888i | \(-0.992809\pi\) |
0.480310 | − | 0.877099i | \(-0.340524\pi\) | |||||||
\(8\) | −24.4647 | −1.08120 | ||||||||
\(9\) | 22.4665 | + | 14.9752i | 0.832093 | + | 0.554636i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19.9274 | − | 34.5153i | −0.546213 | − | 0.946069i | −0.998529 | − | 0.0542113i | \(-0.982736\pi\) |
0.452316 | − | 0.891858i | \(-0.350598\pi\) | |||||||
\(12\) | −7.31354 | + | 6.85759i | −0.175936 | + | 0.164968i | ||||
\(13\) | 0.504548 | − | 0.873903i | 0.0107643 | − | 0.0186444i | −0.860593 | − | 0.509293i | \(-0.829907\pi\) |
0.871357 | + | 0.490649i | \(0.163240\pi\) | |||||||
\(14\) | −23.7024 | + | 41.0538i | −0.452481 | + | 0.783720i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 22.4208 | + | 38.8340i | 0.350326 | + | 0.606782i | ||||
\(17\) | −52.6170 | −0.750676 | −0.375338 | − | 0.926888i | \(-0.622473\pi\) | ||||
−0.375338 | + | 0.926888i | \(0.622473\pi\) | |||||||
\(18\) | 4.27635 | − | 66.3864i | 0.0559970 | − | 0.869301i | ||||
\(19\) | −49.5371 | −0.598136 | −0.299068 | − | 0.954232i | \(-0.596676\pi\) | ||||
−0.299068 | + | 0.954232i | \(0.596676\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 22.7565 | + | 97.3503i | 0.236471 | + | 1.01160i | ||||
\(22\) | −49.0982 | + | 85.0405i | −0.475808 | + | 0.824123i | ||||
\(23\) | 13.7009 | − | 23.7307i | 0.124210 | − | 0.215139i | −0.797214 | − | 0.603697i | \(-0.793694\pi\) |
0.921424 | + | 0.388559i | \(0.127027\pi\) | |||||||
\(24\) | 121.669 | + | 36.8333i | 1.03482 | + | 0.313274i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.48626 | −0.0187537 | ||||||||
\(27\) | −89.1854 | − | 108.300i | −0.635694 | − | 0.771941i | ||||
\(28\) | −37.1228 | −0.250555 | ||||||||
\(29\) | 127.477 | + | 220.796i | 0.816269 | + | 1.41382i | 0.908413 | + | 0.418074i | \(0.137295\pi\) |
−0.0921441 | + | 0.995746i | \(0.529372\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 84.3282 | − | 146.061i | 0.488574 | − | 0.846234i | −0.511340 | − | 0.859379i | \(-0.670851\pi\) |
0.999914 | + | 0.0131441i | \(0.00418403\pi\) | |||||||
\(32\) | −42.6170 | + | 73.8149i | −0.235428 | + | 0.407774i | ||||
\(33\) | 47.1388 | + | 201.656i | 0.248661 | + | 1.06375i | ||||
\(34\) | 64.8202 | + | 112.272i | 0.326958 | + | 0.566308i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 46.6967 | − | 23.0935i | 0.216188 | − | 0.106914i | ||||
\(37\) | 419.938 | 1.86588 | 0.932938 | − | 0.360038i | \(-0.117236\pi\) | ||||
0.932938 | + | 0.360038i | \(0.117236\pi\) | |||||||
\(38\) | 61.0260 | + | 105.700i | 0.260519 | + | 0.451232i | ||||
\(39\) | −3.82497 | + | 3.58651i | −0.0157047 | + | 0.0147257i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −199.285 | + | 345.172i | −0.759100 | + | 1.31480i | 0.184210 | + | 0.982887i | \(0.441027\pi\) |
−0.943310 | + | 0.331913i | \(0.892306\pi\) | |||||||
\(42\) | 179.687 | − | 168.485i | 0.660152 | − | 0.618996i | ||||
\(43\) | 179.414 | + | 310.754i | 0.636288 | + | 1.10208i | 0.986241 | + | 0.165316i | \(0.0528642\pi\) |
−0.349953 | + | 0.936767i | \(0.613802\pi\) | |||||||
\(44\) | −76.8977 | −0.263472 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −67.5141 | −0.216400 | ||||||||
\(47\) | 70.6510 | + | 122.371i | 0.219266 | + | 0.379780i | 0.954584 | − | 0.297943i | \(-0.0963004\pi\) |
−0.735318 | + | 0.677723i | \(0.762967\pi\) | |||||||
\(48\) | −53.0371 | − | 226.888i | −0.159484 | − | 0.682259i | ||||
\(49\) | −13.5915 | + | 23.5411i | −0.0396253 | + | 0.0686330i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 261.678 | + | 79.2187i | 0.718475 | + | 0.217507i | ||||
\(52\) | −0.973497 | − | 1.68615i | −0.00259615 | − | 0.00449666i | ||||
\(53\) | −290.878 | −0.753872 | −0.376936 | − | 0.926239i | \(-0.623022\pi\) | ||||
−0.376936 | + | 0.926239i | \(0.623022\pi\) | |||||||
\(54\) | −121.217 | + | 323.718i | −0.305473 | + | 0.815785i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 235.352 | + | 407.641i | 0.561611 | + | 0.972738i | ||||
\(57\) | 246.361 | + | 74.5817i | 0.572478 | + | 0.173308i | ||||
\(58\) | 314.083 | − | 544.008i | 0.711054 | − | 1.23158i | ||||
\(59\) | −14.3659 | + | 24.8825i | −0.0316998 | + | 0.0549056i | −0.881440 | − | 0.472296i | \(-0.843425\pi\) |
0.849740 | + | 0.527202i | \(0.176759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −366.364 | − | 634.561i | −0.768985 | − | 1.33192i | −0.938114 | − | 0.346327i | \(-0.887429\pi\) |
0.169129 | − | 0.985594i | \(-0.445904\pi\) | |||||||
\(62\) | −415.544 | −0.851195 | ||||||||
\(63\) | 33.3939 | − | 518.409i | 0.0667815 | − | 1.03672i | ||||
\(64\) | 568.737 | 1.11082 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 372.212 | − | 349.007i | 0.694184 | − | 0.650907i | ||||
\(67\) | −88.2730 | + | 152.893i | −0.160959 | + | 0.278789i | −0.935213 | − | 0.354086i | \(-0.884792\pi\) |
0.774254 | + | 0.632875i | \(0.218125\pi\) | |||||||
\(68\) | −50.7608 | + | 87.9203i | −0.0905243 | + | 0.156793i | ||||
\(69\) | −103.866 | + | 97.3911i | −0.181218 | + | 0.169920i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −802.814 | −1.34192 | −0.670961 | − | 0.741493i | \(-0.734118\pi\) | ||||
−0.670961 | + | 0.741493i | \(0.734118\pi\) | |||||||
\(72\) | −549.635 | − | 366.363i | −0.899655 | − | 0.599670i | ||||
\(73\) | −512.820 | −0.822205 | −0.411103 | − | 0.911589i | \(-0.634856\pi\) | ||||
−0.411103 | + | 0.911589i | \(0.634856\pi\) | |||||||
\(74\) | −517.332 | − | 896.046i | −0.812684 | − | 1.40761i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −47.7895 | + | 82.7739i | −0.0721294 | + | 0.124932i | ||||
\(77\) | −383.406 | + | 664.079i | −0.567444 | + | 0.982842i | ||||
\(78\) | 12.3648 | + | 3.74324i | 0.0179492 | + | 0.00543383i | ||||
\(79\) | −306.174 | − | 530.309i | −0.436041 | − | 0.755246i | 0.561339 | − | 0.827586i | \(-0.310286\pi\) |
−0.997380 | + | 0.0723406i | \(0.976953\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 280.488 | + | 672.880i | 0.384757 | + | 0.923018i | ||||
\(82\) | 982.017 | 1.32251 | ||||||||
\(83\) | 40.4081 | + | 69.9889i | 0.0534382 | + | 0.0925576i | 0.891507 | − | 0.453007i | \(-0.149649\pi\) |
−0.838069 | + | 0.545564i | \(0.816315\pi\) | |||||||
\(84\) | 184.621 | + | 55.8910i | 0.239807 | + | 0.0725977i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 442.049 | − | 765.651i | 0.554272 | − | 0.960027i | ||||
\(87\) | −301.549 | − | 1290.00i | −0.371603 | − | 1.58968i | ||||
\(88\) | 487.518 | + | 844.405i | 0.590563 | + | 1.02289i | ||||
\(89\) | 24.0097 | 0.0285957 | 0.0142979 | − | 0.999898i | \(-0.495449\pi\) | ||||
0.0142979 | + | 0.999898i | \(0.495449\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.4151 | −0.0223655 | ||||||||
\(92\) | −26.4352 | − | 45.7871i | −0.0299572 | − | 0.0518873i | ||||
\(93\) | −639.290 | + | 599.435i | −0.712810 | + | 0.668371i | ||||
\(94\) | 174.073 | − | 301.504i | 0.191003 | − | 0.330827i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 323.079 | − | 302.937i | 0.343480 | − | 0.322067i | ||||
\(97\) | 683.960 | + | 1184.65i | 0.715934 | + | 1.24003i | 0.962598 | + | 0.270934i | \(0.0873324\pi\) |
−0.246664 | + | 0.969101i | \(0.579334\pi\) | |||||||
\(98\) | 66.9747 | 0.0690353 | ||||||||
\(99\) | 69.1736 | − | 1073.86i | 0.0702243 | − | 1.09017i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −284.206 | − | 492.260i | −0.279996 | − | 0.484967i | 0.691387 | − | 0.722484i | \(-0.257000\pi\) |
−0.971383 | + | 0.237517i | \(0.923666\pi\) | |||||||
\(102\) | −153.334 | − | 655.948i | −0.148846 | − | 0.636750i | ||||
\(103\) | 237.579 | − | 411.499i | 0.227276 | − | 0.393653i | −0.729724 | − | 0.683742i | \(-0.760352\pi\) |
0.957000 | + | 0.290089i | \(0.0936849\pi\) | |||||||
\(104\) | −12.3436 | + | 21.3797i | −0.0116384 | + | 0.0201582i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 358.340 | + | 620.664i | 0.328350 | + | 0.568719i | ||||
\(107\) | −1452.60 | −1.31242 | −0.656208 | − | 0.754580i | \(-0.727841\pi\) | ||||
−0.656208 | + | 0.754580i | \(0.727841\pi\) | |||||||
\(108\) | −267.003 | + | 44.5444i | −0.237893 | + | 0.0396879i | ||||
\(109\) | −1962.92 | −1.72490 | −0.862448 | − | 0.506146i | \(-0.831070\pi\) | ||||
−0.862448 | + | 0.506146i | \(0.831070\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2088.46 | − | 632.247i | −1.78584 | − | 0.540633i | ||||
\(112\) | 431.380 | − | 747.172i | 0.363943 | − | 0.630367i | ||||
\(113\) | −489.143 | + | 847.220i | −0.407210 | + | 0.705308i | −0.994576 | − | 0.104013i | \(-0.966832\pi\) |
0.587366 | + | 0.809321i | \(0.300165\pi\) | |||||||
\(114\) | −144.359 | − | 617.552i | −0.118600 | − | 0.507360i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 491.918 | 0.393736 | ||||||||
\(117\) | 24.4223 | − | 12.0778i | 0.0192978 | − | 0.00954356i | ||||
\(118\) | 70.7910 | 0.0552275 | ||||||||
\(119\) | 506.179 | + | 876.728i | 0.389928 | + | 0.675374i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −128.704 | + | 222.923i | −0.0966976 | + | 0.167485i | ||||
\(122\) | −902.665 | + | 1563.46i | −0.669864 | + | 1.16024i | ||||
\(123\) | 1510.78 | − | 1416.59i | 1.10750 | − | 1.03845i | ||||
\(124\) | −162.706 | − | 281.816i | −0.117834 | − | 0.204095i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1147.30 | + | 567.387i | −0.811186 | + | 0.401165i | ||||
\(127\) | −865.941 | −0.605038 | −0.302519 | − | 0.953143i | \(-0.597828\pi\) | ||||
−0.302519 | + | 0.953143i | \(0.597828\pi\) | |||||||
\(128\) | −359.705 | − | 623.028i | −0.248389 | − | 0.430222i | ||||
\(129\) | −424.409 | − | 1815.58i | −0.289667 | − | 1.23917i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 734.478 | − | 1272.15i | 0.489860 | − | 0.848462i | −0.510072 | − | 0.860132i | \(-0.670381\pi\) |
0.999932 | + | 0.0116695i | \(0.00371460\pi\) | |||||||
\(132\) | 382.432 | + | 115.775i | 0.252170 | + | 0.0763403i | ||||
\(133\) | 476.550 | + | 825.409i | 0.310693 | + | 0.538136i | ||||
\(134\) | 434.983 | 0.280424 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1287.26 | 0.811628 | ||||||||
\(137\) | −35.7677 | − | 61.9514i | −0.0223054 | − | 0.0386341i | 0.854657 | − | 0.519193i | \(-0.173767\pi\) |
−0.876963 | + | 0.480559i | \(0.840434\pi\) | |||||||
\(138\) | 335.765 | + | 101.647i | 0.207117 | + | 0.0627014i | ||||
\(139\) | −114.532 | + | 198.376i | −0.0698886 | + | 0.121051i | −0.898852 | − | 0.438252i | \(-0.855598\pi\) |
0.828964 | + | 0.559303i | \(0.188931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −167.127 | − | 714.953i | −0.0998199 | − | 0.427020i | ||||
\(142\) | 989.006 | + | 1713.01i | 0.584476 | + | 1.01234i | ||||
\(143\) | −40.2174 | −0.0235185 | ||||||||
\(144\) | −77.8289 | + | 1208.22i | −0.0450399 | + | 0.699202i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 631.755 | + | 1094.23i | 0.358113 | + | 0.620269i | ||||
\(147\) | 103.037 | − | 96.6130i | 0.0578117 | − | 0.0542075i | ||||
\(148\) | 405.124 | − | 701.695i | 0.225006 | − | 0.389723i | ||||
\(149\) | 417.572 | − | 723.256i | 0.229589 | − | 0.397661i | −0.728097 | − | 0.685474i | \(-0.759595\pi\) |
0.957686 | + | 0.287814i | \(0.0929283\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 933.292 | + | 1616.51i | 0.502982 | + | 0.871190i | 0.999994 | + | 0.00344622i | \(0.00109697\pi\) |
−0.497013 | + | 0.867743i | \(0.665570\pi\) | |||||||
\(152\) | 1211.91 | 0.646702 | ||||||||
\(153\) | −1182.12 | − | 787.949i | −0.624632 | − | 0.416352i | ||||
\(154\) | 1889.31 | 0.988604 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.30283 | + | 9.85131i | 0.00118189 | + | 0.00505600i | ||||
\(157\) | 1149.95 | − | 1991.78i | 0.584563 | − | 1.01249i | −0.410367 | − | 0.911921i | \(-0.634599\pi\) |
0.994930 | − | 0.100572i | \(-0.0320673\pi\) | |||||||
\(158\) | −754.367 | + | 1306.60i | −0.379837 | + | 0.657896i | ||||
\(159\) | 1446.61 | + | 437.938i | 0.721533 | + | 0.218432i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −527.215 | −0.258077 | ||||||||
\(162\) | 1090.22 | − | 1427.43i | 0.528741 | − | 0.692281i | ||||
\(163\) | 44.9023 | 0.0215768 | 0.0107884 | − | 0.999942i | \(-0.496566\pi\) | ||||
0.0107884 | + | 0.999942i | \(0.496566\pi\) | |||||||
\(164\) | 384.510 | + | 665.990i | 0.183080 | + | 0.317104i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 99.5595 | − | 172.442i | 0.0465501 | − | 0.0806272i | ||||
\(167\) | 588.281 | − | 1018.93i | 0.272590 | − | 0.472140i | −0.696934 | − | 0.717135i | \(-0.745453\pi\) |
0.969524 | + | 0.244995i | \(0.0787864\pi\) | |||||||
\(168\) | −556.731 | − | 2381.64i | −0.255671 | − | 1.09374i | ||||
\(169\) | 1097.99 | + | 1901.78i | 0.499768 | + | 0.865624i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1112.93 | − | 741.827i | −0.497705 | − | 0.331748i | ||||
\(172\) | 692.339 | 0.306921 | ||||||||
\(173\) | −534.045 | − | 924.994i | −0.234698 | − | 0.406508i | 0.724487 | − | 0.689288i | \(-0.242077\pi\) |
−0.959185 | + | 0.282780i | \(0.908743\pi\) | |||||||
\(174\) | −2381.06 | + | 2232.61i | −1.03740 | + | 0.972724i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 893.579 | − | 1547.72i | 0.382705 | − | 0.662864i | ||||
\(177\) | 108.908 | − | 102.118i | 0.0462487 | − | 0.0433654i | ||||
\(178\) | −29.5781 | − | 51.2308i | −0.0124549 | − | 0.0215725i | ||||
\(179\) | −2779.66 | −1.16068 | −0.580339 | − | 0.814375i | \(-0.697080\pi\) | ||||
−0.580339 | + | 0.814375i | \(0.697080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3568.66 | −1.46550 | −0.732752 | − | 0.680496i | \(-0.761764\pi\) | ||||
−0.732752 | + | 0.680496i | \(0.761764\pi\) | |||||||
\(182\) | 23.9180 | + | 41.4272i | 0.00974132 | + | 0.0168725i | ||||
\(183\) | 866.643 | + | 3707.42i | 0.350077 | + | 1.49760i | ||||
\(184\) | −335.189 | + | 580.564i | −0.134296 | + | 0.232607i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2066.60 | + | 625.631i | 0.814682 | + | 0.246632i | ||||
\(187\) | 1048.52 | + | 1816.09i | 0.410029 | + | 0.710192i | ||||
\(188\) | 272.634 | 0.105765 | ||||||||
\(189\) | −946.579 | + | 2527.90i | −0.364304 | + | 0.972899i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1669.31 | + | 2891.33i | 0.632392 | + | 1.09534i | 0.987061 | + | 0.160344i | \(0.0512603\pi\) |
−0.354669 | + | 0.934992i | \(0.615406\pi\) | |||||||
\(192\) | −2828.48 | − | 856.275i | −1.06316 | − | 0.321856i | ||||
\(193\) | −970.433 | + | 1680.84i | −0.361934 | + | 0.626888i | −0.988279 | − | 0.152658i | \(-0.951217\pi\) |
0.626345 | + | 0.779546i | \(0.284550\pi\) | |||||||
\(194\) | 1685.18 | − | 2918.81i | 0.623652 | − | 1.08020i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 26.2240 | + | 45.4213i | 0.00955684 | + | 0.0165529i | ||||
\(197\) | −1035.75 | −0.374588 | −0.187294 | − | 0.982304i | \(-0.559972\pi\) | ||||
−0.187294 | + | 0.982304i | \(0.559972\pi\) | |||||||
\(198\) | −2376.56 | + | 1175.31i | −0.853005 | + | 0.421847i | ||||
\(199\) | 1565.53 | 0.557675 | 0.278838 | − | 0.960338i | \(-0.410051\pi\) | ||||
0.278838 | + | 0.960338i | \(0.410051\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 669.196 | − | 627.476i | 0.234833 | − | 0.220193i | ||||
\(202\) | −700.242 | + | 1212.85i | −0.243905 | + | 0.422456i | ||||
\(203\) | 2452.67 | − | 4248.14i | 0.847997 | − | 1.46877i | ||||
\(204\) | 384.817 | − | 360.826i | 0.132071 | − | 0.123838i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1170.72 | −0.395961 | ||||||||
\(207\) | 663.184 | − | 327.972i | 0.222678 | − | 0.110124i | ||||
\(208\) | 45.2496 | 0.0150841 | ||||||||
\(209\) | 987.147 | + | 1709.79i | 0.326710 | + | 0.565878i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1692.64 | + | 2931.73i | −0.552255 | + | 0.956534i | 0.445856 | + | 0.895105i | \(0.352899\pi\) |
−0.998111 | + | 0.0614294i | \(0.980434\pi\) | |||||||
\(212\) | −280.617 | + | 486.043i | −0.0909096 | + | 0.157460i | ||||
\(213\) | 3992.60 | + | 1208.69i | 1.28436 | + | 0.388819i | ||||
\(214\) | 1789.50 | + | 3099.50i | 0.571624 | + | 0.990082i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2181.89 | + | 2649.53i | 0.687310 | + | 0.834619i | ||||
\(217\) | −3244.97 | −1.01513 | ||||||||
\(218\) | 2418.17 | + | 4188.39i | 0.751280 | + | 1.30126i | ||||
\(219\) | 2550.38 | + | 772.087i | 0.786935 | + | 0.238232i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.5478 | + | 45.9821i | −0.00808054 | + | 0.0139959i | ||||
\(222\) | 1223.76 | + | 5235.14i | 0.369971 | + | 1.58270i | ||||
\(223\) | −1182.77 | − | 2048.62i | −0.355176 | − | 0.615183i | 0.631972 | − | 0.774991i | \(-0.282246\pi\) |
−0.987148 | + | 0.159808i | \(0.948912\pi\) | |||||||
\(224\) | 1639.92 | 0.489158 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2410.35 | 0.709443 | ||||||||
\(227\) | 488.115 | + | 845.440i | 0.142720 | + | 0.247197i | 0.928520 | − | 0.371283i | \(-0.121082\pi\) |
−0.785800 | + | 0.618480i | \(0.787749\pi\) | |||||||
\(228\) | 362.292 | − | 339.705i | 0.105234 | − | 0.0986733i | ||||
\(229\) | −797.640 | + | 1381.55i | −0.230173 | + | 0.398671i | −0.957859 | − | 0.287240i | \(-0.907262\pi\) |
0.727686 | + | 0.685910i | \(0.240596\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2906.60 | − | 2725.39i | 0.827879 | − | 0.776266i | ||||
\(232\) | −3118.67 | − | 5401.70i | −0.882546 | − | 1.52862i | ||||
\(233\) | −943.571 | −0.265302 | −0.132651 | − | 0.991163i | \(-0.542349\pi\) | ||||
−0.132651 | + | 0.991163i | \(0.542349\pi\) | |||||||
\(234\) | −55.8576 | − | 37.2322i | −0.0156048 | − | 0.0104015i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 27.7183 | + | 48.0095i | 0.00764537 | + | 0.0132422i | ||||
\(237\) | 724.262 | + | 3098.33i | 0.198506 | + | 0.849190i | ||||
\(238\) | 1247.15 | − | 2160.13i | 0.339667 | − | 0.588320i | ||||
\(239\) | −1365.75 | + | 2365.54i | −0.369635 | + | 0.640227i | −0.989508 | − | 0.144475i | \(-0.953851\pi\) |
0.619873 | + | 0.784702i | \(0.287184\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1708.62 | − | 2959.41i | −0.456687 | − | 0.791006i | 0.542096 | − | 0.840317i | \(-0.317631\pi\) |
−0.998783 | + | 0.0493107i | \(0.984298\pi\) | |||||||
\(242\) | 634.217 | 0.168467 | ||||||||
\(243\) | −381.867 | − | 3768.70i | −0.100810 | − | 0.994906i | ||||
\(244\) | −1413.76 | −0.370928 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4883.82 | − | 1478.50i | −1.26578 | − | 0.383193i | ||||
\(247\) | −24.9938 | + | 43.2906i | −0.00643854 | + | 0.0111519i | ||||
\(248\) | −2063.06 | + | 3573.32i | −0.528244 | + | 0.914945i | ||||
\(249\) | −95.5865 | − | 408.910i | −0.0243275 | − | 0.104071i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3164.50 | −0.795782 | −0.397891 | − | 0.917433i | \(-0.630258\pi\) | ||||
−0.397891 | + | 0.917433i | \(0.630258\pi\) | |||||||
\(252\) | −834.019 | − | 555.920i | −0.208485 | − | 0.138967i | ||||
\(253\) | −1092.10 | −0.271382 | ||||||||
\(254\) | 1066.77 | + | 1847.71i | 0.263525 | + | 0.456439i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1388.69 | − | 2405.28i | 0.339036 | − | 0.587227i | ||||
\(257\) | 2774.72 | − | 4805.95i | 0.673471 | − | 1.16649i | −0.303442 | − | 0.952850i | \(-0.598136\pi\) |
0.976913 | − | 0.213636i | \(-0.0685307\pi\) | |||||||
\(258\) | −3351.17 | + | 3142.24i | −0.808661 | + | 0.758246i | ||||
\(259\) | −4039.83 | − | 6997.20i | −0.969201 | − | 1.67871i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −442.506 | + | 6869.50i | −0.104944 | + | 1.62916i | ||||
\(262\) | −3619.29 | −0.853436 | ||||||||
\(263\) | −2068.82 | − | 3583.30i | −0.485053 | − | 0.840136i | 0.514800 | − | 0.857311i | \(-0.327866\pi\) |
−0.999853 | + | 0.0171742i | \(0.994533\pi\) | |||||||
\(264\) | −1153.24 | − | 4933.43i | −0.268851 | − | 1.15012i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1174.15 | − | 2033.68i | 0.270645 | − | 0.468771i | ||||
\(267\) | −119.406 | − | 36.1483i | −0.0273691 | − | 0.00828554i | ||||
\(268\) | 170.318 | + | 294.999i | 0.0388202 | + | 0.0672386i | ||||
\(269\) | −1026.74 | −0.232719 | −0.116359 | − | 0.993207i | \(-0.537122\pi\) | ||||
−0.116359 | + | 0.993207i | \(0.537122\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3400.66 | 0.762270 | 0.381135 | − | 0.924519i | \(-0.375533\pi\) | ||||
0.381135 | + | 0.924519i | \(0.375533\pi\) | |||||||
\(272\) | −1179.72 | − | 2043.33i | −0.262981 | − | 0.455497i | ||||
\(273\) | 96.5564 | + | 29.2309i | 0.0214061 | + | 0.00648035i | ||||
\(274\) | −88.1261 | + | 152.639i | −0.0194303 | + | 0.0336542i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 62.5331 | + | 267.511i | 0.0136379 | + | 0.0583415i | ||||
\(277\) | −1784.41 | − | 3090.68i | −0.387056 | − | 0.670401i | 0.604996 | − | 0.796228i | \(-0.293175\pi\) |
−0.992052 | + | 0.125828i | \(0.959841\pi\) | |||||||
\(278\) | 564.381 | 0.121760 | ||||||||
\(279\) | 4081.84 | − | 2018.64i | 0.875891 | − | 0.433165i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3009.34 | + | 5212.33i | 0.638869 | + | 1.10655i | 0.985681 | + | 0.168618i | \(0.0539306\pi\) |
−0.346813 | + | 0.937934i | \(0.612736\pi\) | |||||||
\(282\) | −1319.65 | + | 1237.38i | −0.278666 | + | 0.261293i | ||||
\(283\) | −2289.08 | + | 3964.81i | −0.480819 | + | 0.832803i | −0.999758 | − | 0.0220082i | \(-0.992994\pi\) |
0.518939 | + | 0.854812i | \(0.326327\pi\) | |||||||
\(284\) | −774.492 | + | 1341.46i | −0.161823 | + | 0.280285i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 49.5448 | + | 85.8141i | 0.0102435 | + | 0.0177423i | ||||
\(287\) | 7668.55 | 1.57721 | ||||||||
\(288\) | −2062.85 | + | 1020.16i | −0.422064 | + | 0.208728i | ||||
\(289\) | −2144.45 | −0.436485 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1617.93 | − | 6921.34i | −0.325926 | − | 1.39428i | ||||
\(292\) | −494.729 | + | 856.895i | −0.0991500 | + | 0.171733i | ||||
\(293\) | 3239.87 | − | 5611.61i | 0.645990 | − | 1.11889i | −0.338082 | − | 0.941117i | \(-0.609778\pi\) |
0.984072 | − | 0.177771i | \(-0.0568886\pi\) | |||||||
\(294\) | −333.082 | − | 100.835i | −0.0660739 | − | 0.0200028i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10273.6 | −2.01738 | ||||||||
\(297\) | −1960.78 | + | 5236.41i | −0.383085 | + | 1.02305i | ||||
\(298\) | −2057.67 | −0.399992 | ||||||||
\(299\) | −13.8255 | − | 23.9466i | −0.00267409 | − | 0.00463166i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3451.95 | − | 5978.95i | 0.661020 | − | 1.14492i | ||||
\(302\) | 2299.49 | − | 3982.83i | 0.438148 | − | 0.758895i | ||||
\(303\) | 672.298 | + | 2876.03i | 0.127467 | + | 0.545292i | ||||
\(304\) | −1110.66 | − | 1923.73i | −0.209543 | − | 0.362938i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −225.009 | + | 3493.05i | −0.0420356 | + | 0.652564i | ||||
\(307\) | −708.452 | −0.131705 | −0.0658526 | − | 0.997829i | \(-0.520977\pi\) | ||||
−0.0658526 | + | 0.997829i | \(0.520977\pi\) | |||||||
\(308\) | 739.761 | + | 1281.30i | 0.136857 | + | 0.237043i | ||||
\(309\) | −1801.08 | + | 1688.80i | −0.331586 | + | 0.310914i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3117.32 | − | 5399.35i | 0.568382 | − | 0.984467i | −0.428344 | − | 0.903616i | \(-0.640903\pi\) |
0.996726 | − | 0.0808511i | \(-0.0257638\pi\) | |||||||
\(312\) | 93.5765 | − | 87.7427i | 0.0169799 | − | 0.0159213i | ||||
\(313\) | −1315.71 | − | 2278.87i | −0.237598 | − | 0.411532i | 0.722427 | − | 0.691448i | \(-0.243027\pi\) |
−0.960024 | + | 0.279916i | \(0.909693\pi\) | |||||||
\(314\) | −5666.63 | −1.01843 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1181.49 | −0.210329 | ||||||||
\(317\) | −251.267 | − | 435.207i | −0.0445191 | − | 0.0771094i | 0.842907 | − | 0.538059i | \(-0.180842\pi\) |
−0.887426 | + | 0.460950i | \(0.847509\pi\) | |||||||
\(318\) | −847.663 | − | 3626.22i | −0.149480 | − | 0.639461i | ||||
\(319\) | 5080.56 | − | 8799.79i | 0.891714 | − | 1.54449i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7224.17 | + | 2187.00i | 1.25612 | + | 0.380269i | ||||
\(322\) | 649.490 | + | 1124.95i | 0.112406 | + | 0.194692i | ||||
\(323\) | 2606.49 | 0.449007 | ||||||||
\(324\) | 1394.94 | + | 180.462i | 0.239187 | + | 0.0309434i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −55.3162 | − | 95.8105i | −0.00939780 | − | 0.0162775i | ||||
\(327\) | 9762.10 | + | 2955.32i | 1.65090 | + | 0.499784i | ||||
\(328\) | 4875.44 | − | 8444.51i | 0.820736 | − | 1.42156i | ||||
\(329\) | 1359.33 | − | 2354.44i | 0.227789 | − | 0.394542i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1543.57 | − | 2673.54i | −0.256321 | − | 0.443961i | 0.708933 | − | 0.705276i | \(-0.249177\pi\) |
−0.965253 | + | 0.261316i | \(0.915844\pi\) | |||||||
\(332\) | 155.930 | 0.0257765 | ||||||||
\(333\) | 9434.54 | + | 6288.65i | 1.55258 | + | 1.03488i | ||||
\(334\) | −2898.87 | −0.474908 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3270.28 | + | 3066.40i | −0.530978 | + | 0.497875i | ||||
\(337\) | −2992.90 | + | 5183.86i | −0.483780 | + | 0.837931i | −0.999826 | − | 0.0186295i | \(-0.994070\pi\) |
0.516047 | + | 0.856560i | \(0.327403\pi\) | |||||||
\(338\) | 2705.28 | − | 4685.69i | 0.435349 | − | 0.754047i | ||||
\(339\) | 3708.18 | − | 3477.00i | 0.594103 | − | 0.557064i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6721.77 | −1.06746 | ||||||||
\(342\) | −211.838 | + | 3288.59i | −0.0334938 | + | 0.519960i | ||||
\(343\) | −6076.36 | −0.956539 | ||||||||
\(344\) | −4389.30 | − | 7602.49i | −0.687951 | − | 1.19157i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1315.81 | + | 2279.05i | −0.204446 | + | 0.354110i | ||||
\(347\) | 503.325 | − | 871.784i | 0.0778671 | − | 0.134870i | −0.824462 | − | 0.565917i | \(-0.808522\pi\) |
0.902329 | + | 0.431047i | \(0.141856\pi\) | |||||||
\(348\) | −2446.43 | − | 740.618i | −0.376846 | − | 0.114084i | ||||
\(349\) | 974.678 | + | 1688.19i | 0.149494 | + | 0.258931i | 0.931040 | − | 0.364916i | \(-0.118902\pi\) |
−0.781547 | + | 0.623847i | \(0.785569\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −139.642 | + | 23.2967i | −0.0212352 | + | 0.00354269i | ||||
\(352\) | 3396.99 | 0.514376 | ||||||||
\(353\) | 1295.87 | + | 2244.50i | 0.195388 | + | 0.338422i | 0.947028 | − | 0.321152i | \(-0.104070\pi\) |
−0.751640 | + | 0.659574i | \(0.770737\pi\) | |||||||
\(354\) | −352.062 | − | 106.581i | −0.0528584 | − | 0.0160020i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 23.1627 | − | 40.1189i | 0.00344837 | − | 0.00597275i | ||||
\(357\) | −1197.38 | − | 5122.28i | −0.177513 | − | 0.759383i | ||||
\(358\) | 3424.33 | + | 5931.11i | 0.505534 | + | 0.875611i | ||||
\(359\) | −605.954 | −0.0890837 | −0.0445418 | − | 0.999008i | \(-0.514183\pi\) | ||||
−0.0445418 | + | 0.999008i | \(0.514183\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4405.08 | −0.642233 | ||||||||
\(362\) | 4396.32 | + | 7614.64i | 0.638302 | + | 1.10557i | ||||
\(363\) | 975.706 | − | 914.877i | 0.141078 | − | 0.132283i | ||||
\(364\) | −18.7302 | + | 32.4417i | −0.00269706 | + | 0.00467145i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6843.09 | − | 6416.46i | 0.977306 | − | 0.916377i | ||||
\(367\) | −4880.13 | − | 8452.63i | −0.694117 | − | 1.20225i | −0.970478 | − | 0.241191i | \(-0.922462\pi\) |
0.276361 | − | 0.961054i | \(-0.410871\pi\) | |||||||
\(368\) | 1228.75 | 0.174056 | ||||||||
\(369\) | −9646.25 | + | 4770.48i | −1.36088 | + | 0.673011i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2798.27 | + | 4846.75i | 0.391587 | + | 0.678249i | ||||
\(372\) | 384.887 | + | 1646.51i | 0.0536436 | + | 0.229482i | ||||
\(373\) | −3911.81 | + | 6775.45i | −0.543018 | + | 0.940535i | 0.455711 | + | 0.890128i | \(0.349385\pi\) |
−0.998729 | + | 0.0504071i | \(0.983948\pi\) | |||||||
\(374\) | 2583.40 | − | 4474.58i | 0.357178 | − | 0.618650i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1728.45 | − | 2993.77i | −0.237069 | − | 0.410616i | ||||
\(377\) | 257.272 | 0.0351464 | ||||||||
\(378\) | 6560.05 | − | 1094.42i | 0.892625 | − | 0.148918i | ||||
\(379\) | 2731.46 | 0.370200 | 0.185100 | − | 0.982720i | \(-0.440739\pi\) | ||||
0.185100 | + | 0.982720i | \(0.440739\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4306.54 | + | 1303.74i | 0.579084 | + | 0.175308i | ||||
\(382\) | 4112.93 | − | 7123.80i | 0.550879 | − | 0.954150i | ||||
\(383\) | −6299.93 | + | 10911.8i | −0.840500 | + | 1.45579i | 0.0489732 | + | 0.998800i | \(0.484405\pi\) |
−0.889473 | + | 0.456988i | \(0.848928\pi\) | |||||||
\(384\) | 850.893 | + | 3640.04i | 0.113078 | + | 0.483737i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4782.00 | 0.630563 | ||||||||
\(387\) | −622.795 | + | 9668.32i | −0.0818048 | + | 1.26994i | ||||
\(388\) | 2639.33 | 0.345339 | ||||||||
\(389\) | 2471.73 | + | 4281.16i | 0.322163 | + | 0.558003i | 0.980934 | − | 0.194340i | \(-0.0622566\pi\) |
−0.658771 | + | 0.752344i | \(0.728923\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −720.902 | + | 1248.64i | −0.0932419 | + | 0.161500i | ||||
\(392\) | 332.511 | − | 575.925i | 0.0428427 | − | 0.0742057i | ||||
\(393\) | −5568.06 | + | 5220.93i | −0.714686 | + | 0.670130i | ||||
\(394\) | 1275.96 | + | 2210.03i | 0.163152 | + | 0.282588i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1727.62 | − | 1151.56i | −0.219233 | − | 0.146131i | ||||
\(397\) | −7067.06 | −0.893415 | −0.446707 | − | 0.894680i | \(-0.647403\pi\) | ||||
−0.446707 | + | 0.894680i | \(0.647403\pi\) | |||||||
\(398\) | −1928.61 | − | 3340.46i | −0.242896 | − | 0.420708i | ||||
\(399\) | −1127.29 | − | 4822.45i | −0.141442 | − | 0.605074i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 458.792 | − | 794.651i | 0.0571346 | − | 0.0989600i | −0.836043 | − | 0.548663i | \(-0.815137\pi\) |
0.893178 | + | 0.449703i | \(0.148470\pi\) | |||||||
\(402\) | −2163.28 | − | 654.898i | −0.268394 | − | 0.0812521i | ||||
\(403\) | −85.0952 | − | 147.389i | −0.0105183 | − | 0.0182183i | ||||
\(404\) | −1096.72 | −0.135059 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12086.0 | −1.47738 | ||||||||
\(407\) | −8368.28 | − | 14494.3i | −1.01917 | − | 1.76525i | ||||
\(408\) | −6401.86 | − | 1938.06i | −0.776812 | − | 0.235167i | ||||
\(409\) | −7367.76 | + | 12761.3i | −0.890739 | + | 1.54281i | −0.0517481 | + | 0.998660i | \(0.516479\pi\) |
−0.838991 | + | 0.544145i | \(0.816854\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 84.6093 | + | 361.951i | 0.0101544 | + | 0.0434397i | ||||
\(412\) | −458.396 | − | 793.965i | −0.0548144 | − | 0.0949414i | ||||
\(413\) | 552.805 | 0.0658638 | ||||||||
\(414\) | −1516.80 | − | 1011.04i | −0.180065 | − | 0.120023i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 43.0047 | + | 74.4863i | 0.00506846 | + | 0.00877883i | ||||
\(417\) | 868.268 | − | 814.137i | 0.101965 | − | 0.0956078i | ||||
\(418\) | 2432.18 | − | 4212.66i | 0.284598 | − | 0.492938i | ||||
\(419\) | 4627.46 | − | 8014.99i | 0.539537 | − | 0.934506i | −0.459392 | − | 0.888234i | \(-0.651932\pi\) |
0.998929 | − | 0.0462722i | \(-0.0147342\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5100.98 | + | 8835.15i | 0.590514 | + | 1.02280i | 0.994163 | + | 0.107886i | \(0.0344082\pi\) |
−0.403649 | + | 0.914914i | \(0.632258\pi\) | |||||||
\(422\) | 8340.80 | 0.962142 | ||||||||
\(423\) | −245.249 | + | 3807.26i | −0.0281901 | + | 0.437625i | ||||
\(424\) | 7116.24 | 0.815083 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2339.52 | − | 10008.2i | −0.266080 | − | 1.13827i | ||||
\(427\) | −7048.89 | + | 12209.0i | −0.798875 | + | 1.38369i | ||||
\(428\) | −1401.36 | + | 2427.23i | −0.158265 | + | 0.274122i | ||||
\(429\) | 200.011 | + | 60.5501i | 0.0225096 | + | 0.00681443i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8057.20 | 0.900468 | 0.450234 | − | 0.892911i | \(-0.351341\pi\) | ||||
0.450234 | + | 0.892911i | \(0.351341\pi\) | |||||||
\(432\) | 2206.13 | − | 5891.61i | 0.245700 | − | 0.656158i | ||||
\(433\) | 4306.26 | 0.477935 | 0.238967 | − | 0.971028i | \(-0.423191\pi\) | ||||
0.238967 | + | 0.971028i | \(0.423191\pi\) | |||||||
\(434\) | 3997.56 | + | 6923.98i | 0.442141 | + | 0.765810i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1893.67 | + | 3279.94i | −0.208006 | + | 0.360276i | ||||
\(437\) | −678.704 | + | 1175.55i | −0.0742948 | + | 0.128682i | ||||
\(438\) | −1494.43 | − | 6393.05i | −0.163029 | − | 0.697424i | ||||
\(439\) | 2360.90 | + | 4089.19i | 0.256673 | + | 0.444571i | 0.965349 | − | 0.260964i | \(-0.0840403\pi\) |
−0.708676 | + | 0.705535i | \(0.750707\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −657.885 | + | 325.352i | −0.0710382 | + | 0.0351314i | ||||
\(442\) | 130.820 | 0.0140779 | ||||||||
\(443\) | −7677.19 | − | 13297.3i | −0.823373 | − | 1.42612i | −0.903157 | − | 0.429311i | \(-0.858756\pi\) |
0.0797840 | − | 0.996812i | \(-0.474577\pi\) | |||||||
\(444\) | −3071.23 | + | 2879.76i | −0.328276 | + | 0.307810i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2914.17 | + | 5047.50i | −0.309395 | + | 0.535888i | ||||
\(447\) | −3165.60 | + | 2968.25i | −0.334962 | + | 0.314079i | ||||
\(448\) | −5471.29 | − | 9476.56i | −0.576996 | − | 0.999387i | ||||
\(449\) | 5448.64 | 0.572688 | 0.286344 | − | 0.958127i | \(-0.407560\pi\) | ||||
0.286344 | + | 0.958127i | \(0.407560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15885.0 | 1.65852 | ||||||||
\(452\) | 943.774 | + | 1634.66i | 0.0982111 | + | 0.170107i | ||||
\(453\) | −2207.73 | − | 9444.45i | −0.228980 | − | 0.979556i | ||||
\(454\) | 1202.64 | − | 2083.04i | 0.124323 | − | 0.215334i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6027.13 | − | 1824.62i | −0.618961 | − | 0.187380i | ||||
\(457\) | 26.3653 | + | 45.6661i | 0.00269873 | + | 0.00467433i | 0.867372 | − | 0.497661i | \(-0.165808\pi\) |
−0.864673 | + | 0.502335i | \(0.832474\pi\) | |||||||
\(458\) | 3930.53 | 0.401008 | ||||||||
\(459\) | 4692.67 | + | 5698.44i | 0.477201 | + | 0.579478i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1583.51 | + | 2742.72i | 0.159982 | + | 0.277096i | 0.934862 | − | 0.355012i | \(-0.115523\pi\) |
−0.774880 | + | 0.632108i | \(0.782190\pi\) | |||||||
\(462\) | −9396.03 | − | 2844.49i | −0.946196 | − | 0.286446i | ||||
\(463\) | −6546.21 | + | 11338.4i | −0.657081 | + | 1.13810i | 0.324287 | + | 0.945959i | \(0.394876\pi\) |
−0.981368 | + | 0.192138i | \(0.938458\pi\) | |||||||
\(464\) | −5716.26 | + | 9900.86i | −0.571920 | + | 0.990594i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1162.41 | + | 2013.35i | 0.115553 | + | 0.200143i | ||||
\(467\) | −13225.4 | −1.31049 | −0.655246 | − | 0.755416i | \(-0.727435\pi\) | ||||
−0.655246 | + | 0.755416i | \(0.727435\pi\) | |||||||
\(468\) | 3.37928 | − | 52.4601i | 0.000333776 | − | 0.00518156i | ||||
\(469\) | 3396.77 | 0.334431 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8717.79 | + | 8174.29i | −0.852854 | + | 0.799684i | ||||
\(472\) | 351.458 | − | 608.743i | 0.0342736 | − | 0.0593637i | ||||
\(473\) | 7150.52 | − | 12385.1i | 0.695098 | − | 1.20394i | ||||
\(474\) | 5718.84 | − | 5362.31i | 0.554167 | − | 0.519618i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1953.29 | 0.188086 | ||||||||
\(477\) | −6535.02 | − | 4355.96i | −0.627291 | − | 0.418125i | ||||
\(478\) | 6729.99 | 0.643981 | ||||||||
\(479\) | 4279.30 | + | 7411.96i | 0.408196 | + | 0.707017i | 0.994688 | − | 0.102939i | \(-0.0328246\pi\) |
−0.586491 | + | 0.809955i | \(0.699491\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 211.879 | − | 366.985i | 0.0200849 | − | 0.0347881i | ||||
\(482\) | −4209.77 | + | 7291.54i | −0.397822 | + | 0.689047i | ||||
\(483\) | 2621.98 | + | 793.761i | 0.247006 | + | 0.0747772i | ||||
\(484\) | 248.328 | + | 430.117i | 0.0233216 | + | 0.0403942i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7571.05 | + | 5457.56i | −0.706646 | + | 0.509383i | ||||
\(487\) | 19531.3 | 1.81735 | 0.908674 | − | 0.417506i | \(-0.137096\pi\) | ||||
0.908674 | + | 0.417506i | \(0.137096\pi\) | |||||||
\(488\) | 8962.96 | + | 15524.3i | 0.831423 | + | 1.44007i | ||||
\(489\) | −223.310 | − | 67.6036i | −0.0206512 | − | 0.00625182i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9744.11 | − | 16877.3i | 0.895612 | − | 1.55125i | 0.0625676 | − | 0.998041i | \(-0.480071\pi\) |
0.833045 | − | 0.553206i | \(-0.186596\pi\) | |||||||
\(492\) | −909.568 | − | 3891.04i | −0.0833465 | − | 0.356548i | ||||
\(493\) | −6707.43 | − | 11617.6i | −0.612754 | − | 1.06132i | ||||
\(494\) | 123.162 | 0.0112173 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7562.83 | 0.684640 | ||||||||
\(497\) | 7723.12 | + | 13376.8i | 0.697041 | + | 1.20731i | ||||
\(498\) | −754.759 | + | 707.705i | −0.0679148 | + | 0.0636807i | ||||
\(499\) | 169.765 | − | 294.042i | 0.0152299 | − | 0.0263790i | −0.858310 | − | 0.513132i | \(-0.828485\pi\) |
0.873540 | + | 0.486753i | \(0.161819\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4459.75 | + | 4181.71i | −0.397698 | + | 0.372904i | ||||
\(502\) | 3898.42 | + | 6752.26i | 0.346604 | + | 0.600335i | ||||
\(503\) | −5550.25 | −0.491995 | −0.245998 | − | 0.969270i | \(-0.579116\pi\) | ||||
−0.245998 | + | 0.969270i | \(0.579116\pi\) | |||||||
\(504\) | −816.970 | + | 12682.7i | −0.0722039 | + | 1.12090i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1345.38 | + | 2330.27i | 0.118201 | + | 0.204729i | ||||
\(507\) | −2597.33 | − | 11111.1i | −0.227517 | − | 0.973298i | ||||
\(508\) | −835.393 | + | 1446.94i | −0.0729617 | + | 0.126373i | ||||
\(509\) | −2824.49 | + | 4892.17i | −0.245960 | + | 0.426015i | −0.962401 | − | 0.271633i | \(-0.912436\pi\) |
0.716441 | + | 0.697647i | \(0.245770\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4933.36 | + | 8544.83i | 0.427082 | + | 0.739728i | ||||
\(512\) | −12598.3 | −1.08745 | ||||||||
\(513\) | 4417.99 | + | 5364.88i | 0.380232 | + | 0.461726i | ||||
\(514\) | −13673.0 | −1.17332 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3443.18 | − | 1042.37i | −0.293755 | − | 0.0889294i | ||||
\(517\) | 2815.78 | − | 4877.08i | 0.239532 | − | 0.414882i | ||||
\(518\) | −9953.54 | + | 17240.0i | −0.844273 | + | 1.46232i | ||||
\(519\) | 1263.30 | + | 5404.27i | 0.106845 | + | 0.457074i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11159.0 | −0.938359 | −0.469180 | − | 0.883103i | \(-0.655450\pi\) | ||||
−0.469180 | + | 0.883103i | \(0.655450\pi\) | |||||||
\(522\) | 15203.0 | − | 7518.50i | 1.27474 | − | 0.630414i | ||||
\(523\) | 9476.61 | 0.792320 | 0.396160 | − | 0.918182i | \(-0.370343\pi\) | ||||
0.396160 | + | 0.918182i | \(0.370343\pi\) | |||||||
\(524\) | −1417.13 | − | 2454.55i | −0.118145 | − | 0.204633i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5097.26 | + | 8828.72i | −0.422531 | + | 0.731845i | ||||
\(527\) | −4437.10 | + | 7685.27i | −0.366761 | + | 0.635248i | ||||
\(528\) | −6774.21 | + | 6351.88i | −0.558351 | + | 0.523542i | ||||
\(529\) | 5708.07 | + | 9886.67i | 0.469144 | + | 0.812580i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −695.373 | + | 343.891i | −0.0568298 | + | 0.0281047i | ||||
\(532\) | 1838.95 | 0.149866 | ||||||||
\(533\) | 201.098 | + | 348.312i | 0.0163424 | + | 0.0283059i | ||||
\(534\) | 69.9678 | + | 299.316i | 0.00567004 | + | 0.0242559i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2159.57 | − | 3740.48i | 0.174028 | − | 0.301426i | ||||
\(537\) | 13823.9 | + | 4184.97i | 1.11089 | + | 0.336303i | ||||
\(538\) | 1264.86 | + | 2190.81i | 0.101361 | + | 0.175562i | ||||
\(539\) | 1083.37 | 0.0865754 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8285.40 | 0.658442 | 0.329221 | − | 0.944253i | \(-0.393214\pi\) | ||||
0.329221 | + | 0.944253i | \(0.393214\pi\) | |||||||
\(542\) | −4189.35 | − | 7256.17i | −0.332008 | − | 0.575054i | ||||
\(543\) | 17747.8 | + | 5372.87i | 1.40264 | + | 0.424626i | ||||
\(544\) | 2242.38 | − | 3883.92i | 0.176730 | − | 0.306106i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −56.5787 | − | 242.038i | −0.00443469 | − | 0.0189712i | ||||
\(547\) | 3459.15 | + | 5991.42i | 0.270389 | + | 0.468327i | 0.968961 | − | 0.247212i | \(-0.0795145\pi\) |
−0.698573 | + | 0.715539i | \(0.746181\pi\) | |||||||
\(548\) | −138.023 | −0.0107593 | ||||||||
\(549\) | 1271.75 | − | 19742.7i | 0.0988651 | − | 1.53479i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6314.82 | − | 10937.6i | −0.488240 | − | 0.845657i | ||||
\(552\) | 2541.06 | − | 2382.64i | 0.195932 | − | 0.183717i | ||||
\(553\) | −5890.83 | + | 10203.2i | −0.452990 | + | 0.784602i | ||||
\(554\) | −4396.51 | + | 7614.97i | −0.337165 | + | 0.583988i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 220.984 | + | 382.755i | 0.0168558 | + | 0.0291950i | ||||
\(557\) | 15622.7 | 1.18843 | 0.594216 | − | 0.804305i | \(-0.297462\pi\) | ||||
0.594216 | + | 0.804305i | \(0.297462\pi\) | |||||||
\(558\) | −9335.82 | − | 6222.84i | −0.708274 | − | 0.472104i | ||||
\(559\) | 362.092 | 0.0273969 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2480.31 | − | 10610.5i | −0.186664 | − | 0.798532i | ||||
\(562\) | 7414.56 | − | 12842.4i | 0.556520 | − | 0.963921i | ||||
\(563\) | 4064.65 | − | 7040.18i | 0.304271 | − | 0.527013i | −0.672828 | − | 0.739799i | \(-0.734920\pi\) |
0.977099 | + | 0.212786i | \(0.0682538\pi\) | |||||||
\(564\) | −1355.88 | − | 410.471i | −0.101228 | − | 0.0306453i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11279.9 | 0.837686 | ||||||||
\(567\) | 8513.52 | − | 11146.8i | 0.630572 | − | 0.825609i | ||||
\(568\) | 19640.6 | 1.45088 | ||||||||
\(569\) | −4087.84 | − | 7080.34i | −0.301179 | − | 0.521658i | 0.675224 | − | 0.737613i | \(-0.264047\pi\) |
−0.976403 | + | 0.215955i | \(0.930714\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3939.42 | + | 6823.27i | −0.288721 | + | 0.500079i | −0.973505 | − | 0.228667i | \(-0.926563\pi\) |
0.684784 | + | 0.728746i | \(0.259897\pi\) | |||||||
\(572\) | −38.7986 | + | 67.2011i | −0.00283610 | + | 0.00491227i | ||||
\(573\) | −3948.79 | − | 16892.6i | −0.287894 | − | 1.23158i | ||||
\(574\) | −9447.07 | − | 16362.8i | −0.686957 | − | 1.18984i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12777.5 | + | 8516.95i | 0.924302 | + | 0.616099i | ||||
\(577\) | 16673.4 | 1.20299 | 0.601493 | − | 0.798878i | \(-0.294573\pi\) | ||||
0.601493 | + | 0.798878i | \(0.294573\pi\) | |||||||
\(578\) | 2641.80 | + | 4575.74i | 0.190112 | + | 0.329283i | ||||
\(579\) | 7356.83 | − | 6898.18i | 0.528047 | − | 0.495127i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 777.458 | − | 1346.60i | 0.0555153 | − | 0.0961553i | ||||
\(582\) | −12775.3 | + | 11978.8i | −0.909884 | + | 0.853159i | ||||
\(583\) | 5796.46 | + | 10039.8i | 0.411775 | + | 0.713215i | ||||
\(584\) | 12546.0 | 0.888965 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15965.1 | −1.12545 | ||||||||
\(587\) | 1506.09 | + | 2608.63i | 0.105900 | + | 0.183424i | 0.914105 | − | 0.405477i | \(-0.132894\pi\) |
−0.808206 | + | 0.588900i | \(0.799561\pi\) | |||||||
\(588\) | −62.0335 | − | 265.374i | −0.00435071 | − | 0.0186119i | ||||
\(589\) | −4177.37 | + | 7235.42i | −0.292234 | + | 0.506164i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5151.03 | + | 1559.39i | 0.358519 | + | 0.108536i | ||||
\(592\) | 9415.37 | + | 16307.9i | 0.653664 | + | 1.13218i | ||||
\(593\) | −7922.71 | −0.548645 | −0.274323 | − | 0.961638i | \(-0.588454\pi\) | ||||
−0.274323 | + | 0.961638i | \(0.588454\pi\) | |||||||
\(594\) | 13588.8 | − | 2267.03i | 0.938642 | − | 0.156595i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −805.682 | − | 1395.48i | −0.0553725 | − | 0.0959080i | ||||
\(597\) | −7785.77 | − | 2357.02i | −0.533753 | − | 0.161585i | ||||
\(598\) | −34.0641 | + | 59.0007i | −0.00232940 | + | 0.00403465i | ||||
\(599\) | 11289.3 | − | 19553.6i | 0.770061 | − | 1.33378i | −0.167468 | − | 0.985878i | \(-0.553559\pi\) |
0.937529 | − | 0.347907i | \(-0.113108\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5309.35 | − | 9196.07i | −0.360354 | − | 0.624152i | 0.627665 | − | 0.778484i | \(-0.284011\pi\) |
−0.988019 | + | 0.154332i | \(0.950678\pi\) | |||||||
\(602\) | −17010.2 | −1.15163 | ||||||||
\(603\) | −4272.79 | + | 2113.07i | −0.288560 | + | 0.142705i | ||||
\(604\) | 3601.47 | 0.242619 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5308.52 | − | 4977.57i | 0.355848 | − | 0.333663i | ||||
\(607\) | −6795.28 | + | 11769.8i | −0.454385 | + | 0.787018i | −0.998653 | − | 0.0518935i | \(-0.983474\pi\) |
0.544267 | + | 0.838912i | \(0.316808\pi\) | |||||||
\(608\) | 2111.12 | − | 3656.58i | 0.140818 | − | 0.243904i | ||||
\(609\) | −18593.6 | + | 17434.4i | −1.23719 | + | 1.16006i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 142.587 | 0.00944102 | ||||||||
\(612\) | −2457.04 | + | 1215.11i | −0.162288 | + | 0.0802580i | ||||
\(613\) | 5457.57 | 0.359591 | 0.179796 | − | 0.983704i | \(-0.442456\pi\) | ||||
0.179796 | + | 0.983704i | \(0.442456\pi\) | |||||||
\(614\) | 872.760 | + | 1511.66i | 0.0573643 | + | 0.0993580i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9379.91 | − | 16246.5i | 0.613518 | − | 1.06264i | ||||
\(617\) | −2986.05 | + | 5171.99i | −0.194836 | + | 0.337466i | −0.946847 | − | 0.321685i | \(-0.895751\pi\) |
0.752011 | + | 0.659151i | \(0.229084\pi\) | |||||||
\(618\) | 5822.28 | + | 1762.60i | 0.378975 | + | 0.114729i | ||||
\(619\) | 419.816 | + | 727.143i | 0.0272598 | + | 0.0472154i | 0.879333 | − | 0.476206i | \(-0.157989\pi\) |
−0.852074 | + | 0.523422i | \(0.824655\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3791.97 | + | 632.617i | −0.245034 | + | 0.0408793i | ||||
\(622\) | −15361.2 | −0.990238 | ||||||||
\(623\) | −230.975 | − | 400.060i | −0.0148536 | − | 0.0257272i | ||||
\(624\) | −225.038 | − | 68.1265i | −0.0144370 | − | 0.00437058i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3241.70 | + | 5614.79i | −0.206972 | + | 0.358486i | ||||
\(627\) | −2335.12 | − | 9989.43i | −0.148733 | − | 0.636267i | ||||
\(628\) | −2218.77 | − | 3843.03i | −0.140985 | − | 0.244194i | ||||
\(629\) | −22095.9 | −1.40067 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13699.4 | −0.864284 | −0.432142 | − | 0.901806i | \(-0.642242\pi\) | ||||
−0.432142 | + | 0.901806i | \(0.642242\pi\) | |||||||
\(632\) | 7490.44 | + | 12973.8i | 0.471446 | + | 0.816568i | ||||
\(633\) | 12831.8 | − | 12031.9i | 0.805718 | − | 0.755487i | ||||
\(634\) | −619.084 | + | 1072.29i | −0.0387807 | + | 0.0671702i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2127.35 | − | 1994.72i | 0.132634 | − | 0.124365i | ||||
\(637\) | 13.7151 | + | 23.7552i | 0.000853080 | + | 0.00147758i | ||||
\(638\) | −25035.5 | −1.55355 | ||||||||
\(639\) | −18036.4 | − | 12022.3i | −1.11660 | − | 0.744279i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3969.68 | + | 6875.69i | 0.244607 | + | 0.423671i | 0.962021 | − | 0.272975i | \(-0.0880078\pi\) |
−0.717414 | + | 0.696647i | \(0.754674\pi\) | |||||||
\(642\) | −4233.11 | − | 18108.8i | −0.260230 | − | 1.11324i | ||||
\(643\) | 3817.98 | − | 6612.93i | 0.234162 | − | 0.405581i | −0.724867 | − | 0.688889i | \(-0.758099\pi\) |
0.959029 | + | 0.283308i | \(0.0914320\pi\) | |||||||
\(644\) | −508.617 | + | 880.950i | −0.0311216 | + | 0.0539042i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3211.00 | − | 5561.62i | −0.195565 | − | 0.338729i | ||||
\(647\) | −22084.3 | −1.34192 | −0.670962 | − | 0.741491i | \(-0.734119\pi\) | ||||
−0.670962 | + | 0.741491i | \(0.734119\pi\) | |||||||
\(648\) | −6862.04 | − | 16461.8i | −0.415997 | − | 0.997963i | ||||
\(649\) | 1145.10 | 0.0692593 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16138.1 | + | 4885.54i | 0.971583 | + | 0.294131i | ||||
\(652\) | 43.3182 | − | 75.0294i | 0.00260195 | − | 0.00450671i | ||||
\(653\) | −3318.99 | + | 5748.65i | −0.198900 | + | 0.344506i | −0.948172 | − | 0.317757i | \(-0.897070\pi\) |
0.749272 | + | 0.662263i | \(0.230404\pi\) | |||||||
\(654\) | −5720.24 | − | 24470.7i | −0.342017 | − | 1.46312i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17872.6 | −1.06373 | ||||||||
\(657\) | −11521.3 | − | 7679.57i | −0.684151 | − | 0.456025i | ||||
\(658\) | −6698.39 | −0.396855 | ||||||||
\(659\) | −11906.1 | − | 20622.0i | −0.703789 | − | 1.21900i | −0.967127 | − | 0.254295i | \(-0.918157\pi\) |
0.263338 | − | 0.964704i | \(-0.415177\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 499.912 | − | 865.873i | 0.0294165 | − | 0.0509509i | −0.850942 | − | 0.525259i | \(-0.823968\pi\) |
0.880359 | + | 0.474308i | \(0.157302\pi\) | |||||||
\(662\) | −3803.12 | + | 6587.20i | −0.223282 | + | 0.386735i | ||||
\(663\) | 201.258 | − | 188.711i | 0.0117892 | − | 0.0110542i | ||||
\(664\) | −988.571 | − | 1712.26i | −0.0577771 | − | 0.100073i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1795.80 | − | 27878.2i | 0.104483 | − | 1.62201i | ||||
\(667\) | 6986.19 | 0.405557 | ||||||||
\(668\) | −1135.06 | − | 1965.97i | −0.0657435 | − | 0.113871i | ||||
\(669\) | 2797.88 | + | 11969.1i | 0.161692 | + | 0.691705i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14601.4 | + | 25290.3i | −0.840059 | + | 1.45502i | ||||
\(672\) | −8155.72 | − | 2469.01i | −0.468175 | − | 0.141732i | ||||
\(673\) | −5311.03 | − | 9198.98i | −0.304198 | − | 0.526886i | 0.672884 | − | 0.739748i | \(-0.265055\pi\) |
−0.977082 | + | 0.212861i | \(0.931722\pi\) | |||||||
\(674\) | 14748.1 | 0.842843 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4237.02 | 0.241069 | ||||||||
\(677\) | −12453.9 | − | 21570.8i | −0.707005 | − | 1.22457i | −0.965963 | − | 0.258680i | \(-0.916713\pi\) |
0.258959 | − | 0.965888i | \(-0.416621\pi\) | |||||||
\(678\) | −11987.3 | − | 3628.95i | −0.679010 | − | 0.205559i | ||||
\(679\) | 13159.5 | − | 22792.9i | 0.743763 | − | 1.28823i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1154.65 | − | 4939.48i | −0.0649725 | − | 0.277946i | ||||
\(682\) | 8280.72 | + | 14342.6i | 0.464934 | + | 0.805289i | ||||
\(683\) | 17115.6 | 0.958874 | 0.479437 | − | 0.877576i | \(-0.340841\pi\) | ||||
0.479437 | + | 0.877576i | \(0.340841\pi\) | |||||||
\(684\) | −2313.22 | + | 1143.98i | −0.129310 | + | 0.0639493i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7485.62 | + | 12965.5i | 0.416622 | + | 0.721610i | ||||
\(687\) | 6046.89 | − | 5669.91i | 0.335813 | − | 0.314877i | ||||
\(688\) | −8045.23 | + | 13934.7i | −0.445816 | + | 0.772176i | ||||
\(689\) | −146.762 | + | 254.199i | −0.00811493 | + | 0.0140555i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14449.9 | − | 25028.0i | −0.795514 | − | 1.37787i | −0.922512 | − | 0.385967i | \(-0.873868\pi\) |
0.126999 | − | 0.991903i | \(-0.459466\pi\) | |||||||
\(692\) | −2060.82 | −0.113209 | ||||||||
\(693\) | −18558.5 | + | 9177.96i | −1.01729 | + | 0.503091i | ||||
\(694\) | −2480.23 | −0.135660 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7377.30 | + | 31559.4i | 0.401775 | + | 1.71876i | ||||
\(697\) | 10485.8 | − | 18161.9i | 0.569839 | − | 0.986989i | ||||
\(698\) | 2401.46 | − | 4159.45i | 0.130224 | − | 0.225555i | ||||
\(699\) | 4692.62 | + | 1420.61i | 0.253921 | + | 0.0768706i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 576.680 | 0.0310712 | 0.0155356 | − | 0.999879i | \(-0.495055\pi\) | ||||
0.0155356 | + | 0.999879i | \(0.495055\pi\) | |||||||
\(702\) | 221.738 | + | 269.263i | 0.0119216 | + | 0.0144767i | ||||
\(703\) | −20802.5 | −1.11605 | ||||||||
\(704\) | −11333.5 | − | 19630.2i | −0.606742 | − | 1.05091i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3192.82 | − | 5530.12i | 0.170203 | − | 0.294800i | ||||
\(707\) | −5468.17 | + | 9471.15i | −0.290879 | + | 0.503818i | ||||
\(708\) | −65.5683 | − | 280.495i | −0.00348052 | − | 0.0148893i | ||||
\(709\) | −2858.78 | − | 4951.55i | −0.151430 | − | 0.262284i | 0.780324 | − | 0.625376i | \(-0.215054\pi\) |
−0.931753 | + | 0.363092i | \(0.881721\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1062.81 | − | 16499.2i | 0.0560600 | − | 0.870279i | ||||
\(712\) | −587.389 | −0.0309176 | ||||||||
\(713\) | −2310.75 | − | 4002.33i | −0.121372 | − | 0.210222i | ||||
\(714\) | −9454.62 | + | 8865.18i | −0.495560 | + | 0.464665i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2681.60 | + | 4644.66i | −0.139966 | + | 0.242429i | ||||
\(717\) | 10353.7 | − | 9708.22i | 0.539284 | − | 0.505663i | ||||
\(718\) | 746.490 | + | 1292.96i | 0.0388005 | + | 0.0672044i | ||||
\(719\) | −14799.9 | −0.767655 | −0.383827 | − | 0.923405i | \(-0.625394\pi\) | ||||
−0.383827 | + | 0.923405i | \(0.625394\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9142.12 | −0.472219 | ||||||||
\(722\) | 5426.72 | + | 9399.36i | 0.279725 | + | 0.484498i | ||||
\(723\) | 4041.78 | + | 17290.3i | 0.207905 | + | 0.889398i | ||||
\(724\) | −3442.76 | + | 5963.04i | −0.176725 | + | 0.306098i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3154.12 | − | 954.860i | −0.161240 | − | 0.0488129i | ||||
\(727\) | −3205.20 | − | 5551.57i | −0.163513 | − | 0.283214i | 0.772613 | − | 0.634877i | \(-0.218949\pi\) |
−0.936126 | + | 0.351664i | \(0.885616\pi\) | |||||||
\(728\) | 474.985 | 0.0241815 | ||||||||
\(729\) | −3774.92 | + | 19317.6i | −0.191786 | + | 0.981437i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9440.23 | − | 16351.0i | −0.477646 | − | 0.827308i | ||||
\(732\) | 7030.97 | + | 2128.51i | 0.355017 | + | 0.107476i | ||||
\(733\) | 8934.62 | − | 15475.2i | 0.450215 | − | 0.779796i | −0.548184 | − | 0.836358i | \(-0.684681\pi\) |
0.998399 | + | 0.0565621i | \(0.0180139\pi\) | |||||||
\(734\) | −12023.9 | + | 20826.0i | −0.604647 | + | 1.04728i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1167.79 | + | 2022.66i | 0.0584853 | + | 0.101299i | ||||
\(737\) | 7036.21 | 0.351672 | ||||||||
\(738\) | 22062.5 | + | 14705.9i | 1.10045 | + | 0.733511i | ||||
\(739\) | 11099.7 | 0.552516 | 0.276258 | − | 0.961084i | \(-0.410906\pi\) | ||||
0.276258 | + | 0.961084i | \(0.410906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 189.478 | − | 177.665i | 0.00939358 | − | 0.00880795i | ||||
\(742\) | 6894.52 | − | 11941.7i | 0.341113 | − | 0.590825i | ||||
\(743\) | −5428.81 | + | 9402.97i | −0.268053 | + | 0.464282i | −0.968359 | − | 0.249561i | \(-0.919714\pi\) |
0.700306 | + | 0.713843i | \(0.253047\pi\) | |||||||
\(744\) | 15640.0 | − | 14665.0i | 0.770687 | − | 0.722639i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 19276.2 | 0.946049 | ||||||||
\(747\) | −140.268 | + | 2177.53i | −0.00687032 | + | 0.106655i | ||||
\(748\) | 4046.13 | 0.197782 | ||||||||
\(749\) | 13974.1 | + | 24203.9i | 0.681715 | + | 1.18076i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16117.0 | − | 27915.4i | 0.783111 | − | 1.35639i | −0.147010 | − | 0.989135i | \(-0.546965\pi\) |
0.930121 | − | 0.367253i | \(-0.119702\pi\) | |||||||
\(752\) | −3168.11 | + | 5487.33i | −0.153629 | + | 0.266093i | ||||
\(753\) | 15737.8 | + | 4764.38i | 0.761645 | + | 0.230576i | ||||
\(754\) | −316.940 | − | 548.956i | −0.0153081 | − | 0.0265143i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3310.81 | + | 4020.41i | 0.159276 | + | 0.193414i | ||||
\(757\) | −9410.28 | −0.451813 | −0.225906 | − | 0.974149i | \(-0.572534\pi\) | ||||
−0.225906 | + | 0.974149i | \(0.572534\pi\) | |||||||
\(758\) | −3364.96 | − | 5828.27i | −0.161241 | − | 0.279278i | ||||
\(759\) | 5431.27 | + | 1644.23i | 0.259740 | + | 0.0786321i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17383.6 | + | 30109.2i | −0.828060 | + | 1.43424i | 0.0714983 | + | 0.997441i | \(0.477222\pi\) |
−0.899558 | + | 0.436801i | \(0.856111\pi\) | |||||||
\(762\) | −2523.48 | − | 10795.2i | −0.119969 | − | 0.513215i | ||||
\(763\) | 18883.4 | + | 32707.0i | 0.895971 | + | 1.55187i | ||||
\(764\) | 6441.68 | 0.305042 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31044.2 | 1.46432 | ||||||||
\(767\) | 14.4966 | + | 25.1089i | 0.000682454 | + | 0.00118204i | ||||
\(768\) | −10527.6 | + | 9871.30i | −0.494640 | + | 0.463802i | ||||
\(769\) | 14543.2 | − | 25189.6i | 0.681980 | − | 1.18122i | −0.292396 | − | 0.956297i | \(-0.594452\pi\) |
0.974376 | − | 0.224927i | \(-0.0722143\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21035.1 | + | 19723.7i | −0.982568 | + | 0.921311i | ||||
\(772\) | 1872.40 | + | 3243.08i | 0.0872915 | + | 0.151193i | ||||
\(773\) | −2942.77 | −0.136927 | −0.0684633 | − | 0.997654i | \(-0.521810\pi\) | ||||
−0.0684633 | + | 0.997654i | \(0.521810\pi\) | |||||||
\(774\) | 21397.1 | − | 10581.7i | 0.993672 | − | 0.491412i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16732.9 | − | 28982.2i | −0.774065 | − | 1.34072i | ||||
\(777\) | 9556.33 | + | 40881.1i | 0.441225 | + | 1.88752i | ||||
\(778\) | 6089.97 | − | 10548.1i | 0.280637 | − | 0.486078i | ||||
\(779\) | 9872.01 | − | 17098.8i | 0.454045 | − | 0.786430i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15998.0 | + | 27709.4i | 0.732975 | + | 1.26955i | ||||
\(782\) | 3552.39 | 0.162446 | ||||||||
\(783\) | 12543.2 | − | 33497.5i | 0.572488 | − | 1.52887i | ||||
\(784\) | −1218.93 | −0.0555270 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17999.6 | + | 5449.10i | 0.816827 | + | 0.247281i | ||||
\(787\) | −16914.6 | + | 29296.9i | −0.766124 | + | 1.32697i | 0.173527 | + | 0.984829i | \(0.444484\pi\) |
−0.939650 | + | 0.342136i | \(0.888850\pi\) | |||||||
\(788\) | −999.207 | + | 1730.68i | −0.0451717 | + | 0.0782397i | ||||
\(789\) | 4893.85 | + | 20935.4i | 0.220818 | + | 0.944640i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18822.4 | 0.846076 | ||||||||
\(792\) | −1692.31 | + | 26271.5i | −0.0759262 | + | 1.17868i | ||||
\(793\) | −739.392 | −0.0331105 | ||||||||
\(794\) | 8706.09 | + | 15079.4i | 0.389128 | + | 0.673989i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1510.30 | − | 2615.92i | 0.0672502 | − | 0.116481i | ||||
\(797\) | 11452.3 | − | 19836.0i | 0.508987 | − | 0.881591i | −0.490959 | − | 0.871183i | \(-0.663353\pi\) |
0.999946 | − | 0.0104085i | \(-0.00331319\pi\) | |||||||
\(798\) | −8901.20 | + | 8346.27i | −0.394861 | + | 0.370244i | ||||
\(799\) | −3717.44 | − | 6438.80i | −0.164598 | − | 0.285092i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 539.413 | + | 359.549i | 0.0237943 | + | 0.0158602i | ||||
\(802\) | −2260.79 | −0.0995402 | ||||||||
\(803\) | 10219.2 | + | 17700.1i | 0.449099 | + | 0.777863i | ||||
\(804\) | −402.891 | − | 1723.53i | −0.0176727 | − | 0.0756023i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −209.662 | + | 363.145i | −0.00916256 | + | 0.0158700i | ||||
\(807\) | 5106.23 | + | 1545.83i | 0.222736 | + | 0.0674297i | ||||
\(808\) | 6953.01 | + | 12043.0i | 0.302730 | + | 0.524344i | ||||
\(809\) | −30665.7 | −1.33269 | −0.666347 | − | 0.745642i | \(-0.732143\pi\) | ||||
−0.666347 | + | 0.745642i | \(0.732143\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35135.2 | −1.52129 | −0.760644 | − | 0.649169i | \(-0.775117\pi\) | ||||
−0.760644 | + | 0.649169i | \(0.775117\pi\) | |||||||
\(812\) | −4732.28 | − | 8196.56i | −0.204520 | − | 0.354240i | ||||
\(813\) | −16912.3 | − | 5119.93i | −0.729571 | − | 0.220866i | ||||
\(814\) | −20618.2 | + | 35711.8i | −0.887798 | + | 1.53771i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2790.65 | + | 11938.2i | 0.119721 | + | 0.512156i | ||||
\(817\) | −8887.65 | − | 15393.9i | −0.380587 | − | 0.659196i | ||||
\(818\) | 36306.1 | 1.55185 | ||||||||
\(819\) | −436.190 | − | 290.745i | −0.0186102 | − | 0.0124047i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17218.5 | − | 29823.3i | −0.731948 | − | 1.26777i | −0.956050 | − | 0.293205i | \(-0.905278\pi\) |
0.224102 | − | 0.974566i | \(-0.428055\pi\) | |||||||
\(822\) | 668.083 | − | 626.432i | 0.0283480 | − | 0.0265807i | ||||
\(823\) | 21400.9 | − | 37067.4i | 0.906426 | − | 1.56998i | 0.0874340 | − | 0.996170i | \(-0.472133\pi\) |
0.818992 | − | 0.573805i | \(-0.194533\pi\) | |||||||
\(824\) | −5812.30 | + | 10067.2i | −0.245729 | + | 0.425616i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −681.014 | − | 1179.55i | −0.0286871 | − | 0.0496875i | ||||
\(827\) | 23589.1 | 0.991868 | 0.495934 | − | 0.868360i | \(-0.334826\pi\) | ||||
0.495934 | + | 0.868360i | \(0.334826\pi\) | |||||||
\(828\) | 91.7638 | − | 1424.55i | 0.00385146 | − | 0.0597904i | ||||
\(829\) | −26766.2 | −1.12139 | −0.560693 | − | 0.828024i | \(-0.689465\pi\) | ||||
−0.560693 | + | 0.828024i | \(0.689465\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4221.06 | + | 18057.3i | 0.176206 | + | 0.753791i | ||||
\(832\) | 286.955 | − | 497.021i | 0.0119572 | − | 0.0207105i | ||||
\(833\) | 715.142 | − | 1238.66i | 0.0297458 | − | 0.0515212i | ||||
\(834\) | −2806.81 | − | 849.717i | −0.116537 | − | 0.0352797i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3809.29 | 0.157592 | ||||||||
\(837\) | −23339.3 | + | 3893.71i | −0.963826 | + | 0.160796i | ||||
\(838\) | −22802.7 | −0.939985 | ||||||||
\(839\) | 15167.2 | + | 26270.3i | 0.624110 | + | 1.08099i | 0.988712 | + | 0.149827i | \(0.0478716\pi\) |
−0.364602 | + | 0.931163i | \(0.618795\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20306.0 | + | 35171.1i | −0.832590 | + | 1.44209i | ||||
\(842\) | 12568.0 | − | 21768.5i | 0.514398 | − | 0.890964i | ||||
\(843\) | −7118.67 | − | 30453.0i | −0.290842 | − | 1.24420i | ||||
\(844\) | 3265.85 | + | 5656.61i | 0.133193 | + | 0.230697i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8425.90 | − | 4166.96i | 0.342421 | − | 0.169342i | ||||
\(847\) | 4952.58 | 0.200912 | ||||||||
\(848\) | −6521.74 | − | 11296.0i | −0.264101 | − | 0.457436i | ||||
\(849\) | 17353.5 | − | 16271.6i | 0.701496 | − | 0.657762i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5753.54 | − | 9965.43i | 0.231761 | − | 0.401422i | ||||
\(852\) | 5871.41 | − | 5505.37i | 0.236093 | − | 0.221374i | ||||
\(853\) | 3266.89 | + | 5658.41i | 0.131133 | + | 0.227128i | 0.924113 | − | 0.382118i | \(-0.124805\pi\) |
−0.792981 | + | 0.609247i | \(0.791472\pi\) | |||||||
\(854\) | 34734.8 | 1.39180 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35537.5 | 1.41898 | ||||||||
\(857\) | 18776.5 | + | 32521.9i | 0.748417 | + | 1.29630i | 0.948581 | + | 0.316534i | \(0.102519\pi\) |
−0.200164 | + | 0.979762i | \(0.564147\pi\) | |||||||
\(858\) | −117.199 | − | 501.368i | −0.00466331 | − | 0.0199492i | ||||
\(859\) | −18319.0 | + | 31729.4i | −0.727631 | + | 1.26029i | 0.230251 | + | 0.973131i | \(0.426045\pi\) |
−0.957882 | + | 0.287163i | \(0.907288\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −38137.6 | − | 11545.6i | −1.50956 | − | 0.456993i | ||||
\(862\) | −9925.86 | − | 17192.1i | −0.392200 | − | 0.679310i | ||||
\(863\) | −14614.7 | −0.576467 | −0.288233 | − | 0.957560i | \(-0.593068\pi\) | ||||
−0.288233 | + | 0.957560i | \(0.593068\pi\) | |||||||
\(864\) | 11795.0 | − | 1967.77i | 0.464437 | − | 0.0774826i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5304.99 | − | 9188.52i | −0.208165 | − | 0.360553i | ||||
\(867\) | 10664.9 | + | 3228.62i | 0.417761 | + | 0.126470i | ||||
\(868\) | −3130.50 | + | 5422.18i | −0.122415 | + | 0.212028i | ||||
\(869\) | −12202.5 | + | 21135.4i | −0.476343 | + | 0.825050i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 89.0759 | + | 154.284i | 0.00346524 | + | 0.00600197i | ||||
\(872\) | 48022.2 | 1.86495 | ||||||||
\(873\) | −2374.21 | + | 36857.5i | −0.0920446 | + | 1.42891i | ||||
\(874\) | 3344.45 | 0.129437 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3750.53 | − | 3516.71i | 0.144656 | − | 0.135638i | ||||
\(877\) | 694.282 | − | 1202.53i | 0.0267323 | − | 0.0463017i | −0.852350 | − | 0.522972i | \(-0.824823\pi\) |
0.879082 | + | 0.476670i | \(0.158156\pi\) | |||||||
\(878\) | 5816.90 | − | 10075.2i | 0.223589 | − | 0.387267i | ||||
\(879\) | −24561.4 | + | 23030.1i | −0.942474 | + | 0.883717i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23664.2 | 0.904957 | 0.452478 | − | 0.891775i | \(-0.350540\pi\) | ||||
0.452478 | + | 0.891775i | \(0.350540\pi\) | |||||||
\(882\) | 1504.69 | + | 1002.96i | 0.0574438 | + | 0.0382895i | ||||
\(883\) | −49607.6 | −1.89063 | −0.945317 | − | 0.326152i | \(-0.894248\pi\) | ||||
−0.945317 | + | 0.326152i | \(0.894248\pi\) | |||||||
\(884\) | 51.2225 | + | 88.7200i | 0.00194887 | + | 0.00337554i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18915.4 | + | 32762.5i | −0.717242 | + | 1.24230i | ||||
\(887\) | 5738.51 | − | 9939.40i | 0.217227 | − | 0.376248i | −0.736732 | − | 0.676185i | \(-0.763632\pi\) |
0.953959 | + | 0.299936i | \(0.0969655\pi\) | |||||||
\(888\) | 51093.4 | + | 15467.7i | 1.93084 | + | 0.584530i | ||||
\(889\) | 8330.41 | + | 14428.7i | 0.314278 | + | 0.544345i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17635.3 | − | 23089.9i | 0.663079 | − | 0.868171i | ||||
\(892\) | −4564.19 | −0.171323 | ||||||||
\(893\) | −3499.84 | − | 6061.91i | −0.131151 | − | 0.227160i | ||||
\(894\) | 10233.3 | + | 3097.97i | 0.382833 | + | 0.115897i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6920.78 | + | 11987.1i | −0.258044 | + | 0.446945i | ||||
\(897\) | 32.7047 | + | 139.908i | 0.00121737 | + | 0.00520778i | ||||
\(898\) | −6712.31 | − | 11626.1i | −0.249435 | − | 0.432034i | ||||
\(899\) | 42999.4 | 1.59523 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15305.1 | 0.565914 | ||||||||
\(902\) | −19569.1 | − | 33894.6i | −0.722371 | − | 1.25118i | ||||
\(903\) | −26169.2 | + | 24537.7i | −0.964402 | + | 0.904278i | ||||
\(904\) | 11966.7 | − | 20727.0i | 0.440273 | − | 0.762576i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −17432.4 | + | 16345.6i | −0.639241 | + | 0.599389i | ||||
\(907\) | −5866.89 | − | 10161.8i | −0.214782 | − | 0.372013i | 0.738423 | − | 0.674337i | \(-0.235571\pi\) |
−0.953205 | + | 0.302325i | \(0.902237\pi\) | |||||||
\(908\) | 1883.58 | 0.0688424 | ||||||||
\(909\) | 986.558 | − | 15315.4i | 0.0359979 | − | 0.558834i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17506.7 | + | 30322.5i | 0.636688 | + | 1.10278i | 0.986155 | + | 0.165827i | \(0.0530293\pi\) |
−0.349467 | + | 0.936949i | \(0.613637\pi\) | |||||||
\(912\) | 2627.30 | + | 11239.4i | 0.0953933 | + | 0.408084i | ||||
\(913\) | 1610.46 | − | 2789.40i | 0.0583773 | − | 0.101112i | ||||
\(914\) | 64.9602 | − | 112.514i | 0.00235087 | − | 0.00407182i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1539.00 | + | 2665.63i | 0.0555132 | + | 0.0961516i | ||||
\(917\) | −28262.9 | −1.01780 | ||||||||
\(918\) | 6378.07 | − | 17033.1i | 0.229311 | − | 0.612391i | ||||
\(919\) | 16026.6 | 0.575264 | 0.287632 | − | 0.957741i | \(-0.407132\pi\) | ||||
0.287632 | + | 0.957741i | \(0.407132\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3523.31 | + | 1066.63i | 0.126055 | + | 0.0381612i | ||||
\(922\) | 3901.54 | − | 6757.66i | 0.139360 | − | 0.241379i | ||||
\(923\) | −405.058 | + | 701.581i | −0.0144449 | + | 0.0250193i | ||||
\(924\) | −1749.93 | − | 7486.02i | −0.0623034 | − | 0.266528i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 32257.8 | 1.14477 | ||||||||
\(927\) | 11499.9 | − | 5687.16i | 0.407449 | − | 0.201500i | ||||
\(928\) | −21730.7 | −0.768691 | ||||||||
\(929\) | −12943.4 | − | 22418.6i | −0.457114 | − | 0.791745i | 0.541693 | − | 0.840577i | \(-0.317784\pi\) |
−0.998807 | + | 0.0488314i | \(0.984450\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 673.282 | − | 1166.16i | 0.0237013 | − | 0.0410519i | ||||
\(932\) | −910.284 | + | 1576.66i | −0.0319929 | + | 0.0554132i | ||||
\(933\) | −23632.3 | + | 22159.0i | −0.829247 | + | 0.777549i | ||||
\(934\) | 16292.7 | + | 28219.8i | 0.570786 | + | 0.988631i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −597.483 | + | 295.480i | −0.0208647 | + | 0.0103185i | ||||
\(937\) | −6331.15 | −0.220736 | −0.110368 | − | 0.993891i | \(-0.535203\pi\) | ||||
−0.110368 | + | 0.993891i | \(0.535203\pi\) | |||||||
\(938\) | −4184.56 | − | 7247.88i | −0.145662 | − | 0.252294i | ||||
\(939\) | 3112.34 | + | 13314.3i | 0.108165 | + | 0.462721i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14377.4 | − | 24902.3i | 0.498075 | − | 0.862691i | −0.501923 | − | 0.864912i | \(-0.667374\pi\) |
0.999998 | + | 0.00222173i | \(0.000707200\pi\) | |||||||
\(942\) | 28181.6 | + | 8531.52i | 0.974741 | + | 0.295087i | ||||
\(943\) | 5460.78 | + | 9458.35i | 0.188576 | + | 0.326624i | ||||
\(944\) | −1288.39 | −0.0444210 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35235.6 | −1.21100 | ||||||||
\(947\) | −14620.3 | − | 25323.2i | −0.501687 | − | 0.868947i | −0.999998 | − | 0.00194886i | \(-0.999380\pi\) |
0.498311 | − | 0.866998i | \(-0.333954\pi\) | |||||||
\(948\) | 5875.86 | + | 1778.82i | 0.201307 | + | 0.0609424i | ||||
\(949\) | −258.742 | + | 448.154i | −0.00885050 | + | 0.0153295i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 594.379 | + | 2542.70i | 0.0202672 | + | 0.0867010i | ||||
\(952\) | −12383.5 | − | 21448.9i | −0.421588 | − | 0.730212i | ||||
\(953\) | 28758.3 | 0.977517 | 0.488758 | − | 0.872419i | \(-0.337450\pi\) | ||||
0.488758 | + | 0.872419i | \(0.337450\pi\) | |||||||
\(954\) | −1243.90 | + | 19310.4i | −0.0422145 | + | 0.655341i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2635.13 | + | 4564.19i | 0.0891489 | + | 0.154410i | ||||
\(957\) | −38515.6 | + | 36114.4i | −1.30098 | + | 1.21987i | ||||
\(958\) | 10543.5 | − | 18261.9i | 0.355581 | − | 0.615884i | ||||
\(959\) | −688.175 | + | 1191.95i | −0.0231724 | + | 0.0401358i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 673.025 | + | 1165.71i | 0.0225916 | + | 0.0391297i | ||||
\(962\) | −1044.08 | −0.0349920 | ||||||||
\(963\) | −32634.9 | − | 21753.0i | −1.09205 | − | 0.727914i | ||||
\(964\) | −6593.36 | −0.220288 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1536.39 | − | 6572.51i | −0.0511722 | − | 0.218910i | ||||
\(967\) | −22347.6 | + | 38707.1i | −0.743174 | + | 1.28721i | 0.207869 | + | 0.978157i | \(0.433347\pi\) |
−0.951043 | + | 0.309058i | \(0.899986\pi\) | |||||||
\(968\) | 3148.71 | − | 5453.73i | 0.104549 | − | 0.181084i | ||||
\(969\) | −12962.8 | − | 3924.26i | −0.429746 | − | 0.130099i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30462.4 | −1.00678 | −0.503391 | − | 0.864059i | \(-0.667914\pi\) | ||||
−0.503391 | + | 0.864059i | \(0.667914\pi\) | |||||||
\(972\) | −6665.69 | − | 2997.67i | −0.219961 | − | 0.0989200i | ||||
\(973\) | 4407.24 | 0.145210 | ||||||||
\(974\) | −24061.1 | − | 41675.1i | −0.791548 | − | 1.37100i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16428.4 | − | 28454.8i | 0.538790 | − | 0.933212i | ||||
\(977\) | −5904.00 | + | 10226.0i | −0.193332 | + | 0.334861i | −0.946353 | − | 0.323136i | \(-0.895263\pi\) |
0.753020 | + | 0.657997i | \(0.228596\pi\) | |||||||
\(978\) | 130.852 | + | 559.773i | 0.00427831 | + | 0.0183022i | ||||
\(979\) | −478.451 | − | 828.701i | −0.0156194 | − | 0.0270535i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44099.9 | − | 29395.1i | −1.43527 | − | 0.956690i | ||||
\(982\) | −48016.1 | −1.56034 | ||||||||
\(983\) | −12351.5 | − | 21393.3i | −0.400763 | − | 0.694142i | 0.593055 | − | 0.805162i | \(-0.297922\pi\) |
−0.993818 | + | 0.111020i | \(0.964588\pi\) | |||||||
\(984\) | −36960.6 | + | 34656.4i | −1.19742 | + | 1.12277i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16526.1 | + | 28624.1i | −0.533771 | + | 0.924519i | ||||
\(987\) | −10305.1 | + | 9662.63i | −0.332335 | + | 0.311616i | ||||
\(988\) | 48.2242 | + | 83.5268i | 0.00155285 | + | 0.00268962i | ||||
\(989\) | 9832.55 | 0.316134 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14443.0 | 0.462965 | 0.231482 | − | 0.972839i | \(-0.425642\pi\) | ||||
0.231482 | + | 0.972839i | \(0.425642\pi\) | |||||||
\(992\) | 7187.63 | + | 12449.3i | 0.230048 | + | 0.398455i | ||||
\(993\) | 3651.35 | + | 15620.1i | 0.116689 | + | 0.499184i | ||||
\(994\) | 19028.6 | − | 32958.5i | 0.607194 | − | 1.05169i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −775.482 | − | 234.765i | −0.0246708 | − | 0.00746867i | ||||
\(997\) | −23834.7 | − | 41282.9i | −0.757123 | − | 1.31138i | −0.944312 | − | 0.329051i | \(-0.893271\pi\) |
0.187189 | − | 0.982324i | \(-0.440062\pi\) | |||||||
\(998\) | −836.551 | −0.0265336 | ||||||||
\(999\) | −37452.4 | − | 45479.4i | −1.18613 | − | 1.44035i |
(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 | 225.4.e.g.76.6 | 32 | ||
5.2 | odd | 4 | 45.4.j.a.4.11 | yes | 32 | ||
5.3 | odd | 4 | 45.4.j.a.4.6 | ✓ | 32 | ||
5.4 | even | 2 | inner | 225.4.e.g.76.11 | 32 | ||
9.4 | even | 3 | 2025.4.a.bk.1.11 | 16 | |||
9.5 | odd | 6 | 2025.4.a.bl.1.6 | 16 | |||
9.7 | even | 3 | inner | 225.4.e.g.151.6 | 32 | ||
15.2 | even | 4 | 135.4.j.a.64.6 | 32 | |||
15.8 | even | 4 | 135.4.j.a.64.11 | 32 | |||
45.2 | even | 12 | 135.4.j.a.19.11 | 32 | |||
45.4 | even | 6 | 2025.4.a.bk.1.6 | 16 | |||
45.7 | odd | 12 | 45.4.j.a.34.6 | yes | 32 | ||
45.13 | odd | 12 | 405.4.b.e.244.6 | 16 | |||
45.14 | odd | 6 | 2025.4.a.bl.1.11 | 16 | |||
45.22 | odd | 12 | 405.4.b.e.244.11 | 16 | |||
45.23 | even | 12 | 405.4.b.f.244.11 | 16 | |||
45.32 | even | 12 | 405.4.b.f.244.6 | 16 | |||
45.34 | even | 6 | inner | 225.4.e.g.151.11 | 32 | ||
45.38 | even | 12 | 135.4.j.a.19.6 | 32 | |||
45.43 | odd | 12 | 45.4.j.a.34.11 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.j.a.4.6 | ✓ | 32 | 5.3 | odd | 4 | ||
45.4.j.a.4.11 | yes | 32 | 5.2 | odd | 4 | ||
45.4.j.a.34.6 | yes | 32 | 45.7 | odd | 12 | ||
45.4.j.a.34.11 | yes | 32 | 45.43 | odd | 12 | ||
135.4.j.a.19.6 | 32 | 45.38 | even | 12 | |||
135.4.j.a.19.11 | 32 | 45.2 | even | 12 | |||
135.4.j.a.64.6 | 32 | 15.2 | even | 4 | |||
135.4.j.a.64.11 | 32 | 15.8 | even | 4 | |||
225.4.e.g.76.6 | 32 | 1.1 | even | 1 | trivial | ||
225.4.e.g.76.11 | 32 | 5.4 | even | 2 | inner | ||
225.4.e.g.151.6 | 32 | 9.7 | even | 3 | inner | ||
225.4.e.g.151.11 | 32 | 45.34 | even | 6 | inner | ||
405.4.b.e.244.6 | 16 | 45.13 | odd | 12 | |||
405.4.b.e.244.11 | 16 | 45.22 | odd | 12 | |||
405.4.b.f.244.6 | 16 | 45.32 | even | 12 | |||
405.4.b.f.244.11 | 16 | 45.23 | even | 12 | |||
2025.4.a.bk.1.6 | 16 | 45.4 | even | 6 | |||
2025.4.a.bk.1.11 | 16 | 9.4 | even | 3 | |||
2025.4.a.bl.1.6 | 16 | 9.5 | odd | 6 | |||
2025.4.a.bl.1.11 | 16 | 45.14 | odd | 6 |