Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(13,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.13");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.i (of order \(9\), degree \(6\), 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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Character | \(\chi\) | \(=\) | 108.49 |
Dual form | 108.4.i.a.97.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{7}{9}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −4.14053 | + | 3.13943i | −0.796845 | + | 0.604184i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.27250 | + | 1.55506i | −0.382144 | + | 0.139089i | −0.525947 | − | 0.850517i | \(-0.676289\pi\) |
0.143803 | + | 0.989606i | \(0.454067\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.69568 | − | 26.6305i | −0.253543 | − | 1.43791i | −0.799786 | − | 0.600285i | \(-0.795054\pi\) |
0.546243 | − | 0.837627i | \(-0.316057\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.28791 | − | 25.9978i | 0.269922 | − | 0.962882i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 50.9513 | + | 18.5448i | 1.39658 | + | 0.508315i | 0.927162 | − | 0.374660i | \(-0.122241\pi\) |
0.469420 | + | 0.882975i | \(0.344463\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 42.8395 | + | 35.9466i | 0.913964 | + | 0.766906i | 0.972869 | − | 0.231357i | \(-0.0743166\pi\) |
−0.0589054 | + | 0.998264i | \(0.518761\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.8084 | − | 19.8520i | 0.220474 | − | 0.341718i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 49.3862 | − | 85.5394i | 0.704583 | − | 1.22037i | −0.262259 | − | 0.964998i | \(-0.584467\pi\) |
0.966842 | − | 0.255376i | \(-0.0821993\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −68.0936 | − | 117.942i | −0.822197 | − | 1.42409i | −0.904043 | − | 0.427442i | \(-0.859415\pi\) |
0.0818453 | − | 0.996645i | \(-0.473919\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 103.047 | + | 95.5225i | 1.07080 | + | 0.992606i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 25.4482 | − | 144.324i | 0.230709 | − | 1.30842i | −0.620756 | − | 0.784004i | \(-0.713174\pi\) |
0.851465 | − | 0.524412i | \(-0.175715\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −79.9195 | + | 67.0604i | −0.639356 | + | 0.536483i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 51.4427 | + | 130.525i | 0.366672 | + | 0.930350i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −37.6146 | + | 31.5624i | −0.240857 | + | 0.202103i | −0.755223 | − | 0.655468i | \(-0.772472\pi\) |
0.514366 | + | 0.857570i | \(0.328027\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.6026 | − | 150.871i | 0.154128 | − | 0.874105i | −0.805450 | − | 0.592663i | \(-0.798076\pi\) |
0.959578 | − | 0.281441i | \(-0.0908125\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −269.185 | + | 83.1733i | −1.41997 | + | 0.438746i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 61.4744 | + | 106.477i | 0.296888 | + | 0.514225i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.7745 | − | 20.3941i | 0.0523168 | − | 0.0906154i | −0.838681 | − | 0.544623i | \(-0.816673\pi\) |
0.890998 | + | 0.454008i | \(0.150006\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −290.230 | − | 14.3461i | −1.19164 | − | 0.0589027i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 317.305 | + | 266.251i | 1.20865 | + | 1.01418i | 0.999340 | + | 0.0363307i | \(0.0115670\pi\) |
0.209312 | + | 0.977849i | \(0.432877\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −269.878 | − | 98.2276i | −0.957117 | − | 0.348362i | −0.184214 | − | 0.982886i | \(-0.558974\pi\) |
−0.772903 | + | 0.634524i | \(0.781196\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.29066 | + | 122.409i | 0.0307771 | + | 0.405503i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −48.6186 | − | 275.730i | −0.150888 | − | 0.855730i | −0.962449 | − | 0.271462i | \(-0.912493\pi\) |
0.811561 | − | 0.584268i | \(-0.198618\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −364.820 | + | 132.783i | −1.06361 | + | 0.387124i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 64.0605 | + | 509.223i | 0.175888 | + | 1.39815i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 248.490 | 0.644015 | 0.322007 | − | 0.946737i | \(-0.395642\pi\) | ||||
0.322007 | + | 0.946737i | \(0.395642\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −246.528 | −0.604397 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 652.213 | + | 274.565i | 1.51557 | + | 0.638018i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 243.543 | − | 88.6422i | 0.537399 | − | 0.195597i | −0.0590401 | − | 0.998256i | \(-0.518804\pi\) |
0.596439 | + | 0.802658i | \(0.296582\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −57.5577 | − | 326.426i | −0.120812 | − | 0.685156i | −0.983708 | − | 0.179775i | \(-0.942463\pi\) |
0.862896 | − | 0.505381i | \(-0.168648\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −726.556 | − | 72.0033i | −1.45298 | − | 0.143993i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −238.931 | − | 86.9637i | −0.455934 | − | 0.165946i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 71.5526 | + | 60.0398i | 0.130471 | + | 0.109478i | 0.705688 | − | 0.708523i | \(-0.250638\pi\) |
−0.575217 | + | 0.818001i | \(0.695082\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 347.726 | + | 677.469i | 0.606685 | + | 1.18199i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −333.619 | + | 577.845i | −0.557651 | + | 0.965881i | 0.440040 | + | 0.897978i | \(0.354964\pi\) |
−0.997692 | + | 0.0679028i | \(0.978369\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −106.851 | − | 185.072i | −0.171315 | − | 0.296726i | 0.767565 | − | 0.640971i | \(-0.221468\pi\) |
−0.938880 | + | 0.344245i | \(0.888135\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 120.377 | − | 528.567i | 0.185332 | − | 0.813783i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 254.606 | − | 1443.94i | 0.376818 | − | 2.13704i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −421.142 | + | 353.380i | −0.599775 | + | 0.503271i | −0.891373 | − | 0.453270i | \(-0.850257\pi\) |
0.291598 | + | 0.956541i | \(0.405813\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −622.773 | − | 378.939i | −0.854284 | − | 0.519807i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 310.120 | − | 260.222i | 0.410122 | − | 0.344133i | −0.414268 | − | 0.910155i | \(-0.635962\pi\) |
0.824391 | + | 0.566021i | \(0.191518\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −77.9834 | + | 442.266i | −0.0995116 | + | 0.564358i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 56.6561 | − | 248.773i | 0.0698180 | − | 0.306566i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 504.793 | + | 874.328i | 0.601213 | + | 1.04133i | 0.992638 | + | 0.121122i | \(0.0386492\pi\) |
−0.391424 | + | 0.920210i | \(0.628017\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 756.115 | − | 1309.63i | 0.871015 | − | 1.50864i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 363.501 | + | 708.203i | 0.405304 | + | 0.789647i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 474.337 | + | 398.016i | 0.512273 | + | 0.429848i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −27.6645 | − | 10.0690i | −0.0289578 | − | 0.0105398i | 0.327501 | − | 0.944851i | \(-0.393794\pi\) |
−0.356458 | + | 0.934311i | \(0.616016\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 853.452 | − | 1189.47i | 0.866416 | − | 1.20754i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.0416 | − | 90.9764i | −0.0158039 | − | 0.0896286i | 0.975886 | − | 0.218283i | \(-0.0700455\pi\) |
−0.991690 | + | 0.128654i | \(0.958934\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1917.18 | − | 697.795i | 1.83403 | − | 0.667532i | 0.842330 | − | 0.538963i | \(-0.181184\pi\) |
0.991701 | − | 0.128569i | \(-0.0410385\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −588.813 | − | 247.875i | −0.547260 | − | 0.230382i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −351.086 | −0.317204 | −0.158602 | − | 0.987343i | \(-0.550699\pi\) | ||||
−0.158602 | + | 0.987343i | \(0.550699\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 656.929 | 0.577270 | 0.288635 | − | 0.957439i | \(-0.406799\pi\) | ||||
0.288635 | + | 0.957439i | \(0.406799\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.2732 | + | 121.408i | 0.0130600 | + | 0.103815i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −119.983 | + | 43.6704i | −0.0998857 | + | 0.0363554i | −0.391480 | − | 0.920187i | \(-0.628037\pi\) |
0.291594 | + | 0.956542i | \(0.405814\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.705 | + | 656.196i | 0.0938223 | + | 0.532092i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1246.74 | − | 851.757i | 0.985140 | − | 0.673034i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2509.86 | − | 913.514i | −1.93343 | − | 0.703711i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1232.53 | + | 1034.21i | 0.926015 | + | 0.777019i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2149.69 | − | 106.259i | −1.57586 | − | 0.0778947i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 521.342 | − | 902.991i | 0.373042 | − | 0.646127i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −649.026 | − | 1124.15i | −0.453478 | − | 0.785447i | 0.545121 | − | 0.838357i | \(-0.316484\pi\) |
−0.998599 | + | 0.0529102i | \(0.983150\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1425.82 | − | 440.551i | 0.973148 | − | 0.300685i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −196.126 | + | 1112.28i | −0.130806 | + | 0.741837i | 0.846883 | + | 0.531779i | \(0.178476\pi\) |
−0.977689 | + | 0.210058i | \(0.932635\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2821.10 | + | 2367.18i | −1.83925 | + | 1.54331i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −422.763 | − | 477.670i | −0.269523 | − | 0.304528i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1978.63 | + | 1660.27i | −1.23391 | + | 1.03538i | −0.235937 | + | 0.971768i | \(0.575816\pi\) |
−0.997975 | + | 0.0636072i | \(0.979740\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −487.444 | + | 2764.43i | −0.297442 | + | 1.68688i | 0.359666 | + | 0.933081i | \(0.382891\pi\) |
−0.657108 | + | 0.753797i | \(0.728220\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1066.94 | + | 989.031i | 0.637253 | + | 0.590720i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1516.11 | + | 2625.97i | 0.886596 | + | 1.53563i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 111.627 | − | 193.343i | 0.0639317 | − | 0.110733i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1093.68 | − | 1695.12i | 0.613641 | − | 0.951096i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2123.02 | − | 1781.43i | −1.16728 | − | 0.979464i | −0.167300 | − | 0.985906i | \(-0.553505\pi\) |
−0.999979 | + | 0.00644242i | \(0.997949\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −711.587 | − | 258.996i | −0.383497 | − | 0.139582i | 0.143075 | − | 0.989712i | \(-0.454301\pi\) |
−0.526573 | + | 0.850130i | \(0.676523\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1863.92 | − | 1907.34i | −0.984893 | − | 1.00784i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 120.954 | + | 685.966i | 0.0626792 | + | 0.355472i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1105.36 | − | 402.318i | 0.561894 | − | 0.204513i | −0.0454293 | − | 0.998968i | \(-0.514466\pi\) |
0.607323 | + | 0.794455i | \(0.292243\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1028.88 | + | 780.119i | −0.513179 | + | 0.389104i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3962.91 | −1.93988 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2323.45 | 1.11648 | 0.558240 | − | 0.829679i | \(-0.311477\pi\) | ||||
0.558240 | + | 0.829679i | \(0.311477\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1020.76 | − | 773.958i | 0.481610 | − | 0.365167i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3377.16 | − | 1229.19i | 1.56487 | − | 0.569565i | 0.593022 | − | 0.805186i | \(-0.297935\pi\) |
0.971845 | + | 0.235621i | \(0.0757126\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 161.558 | + | 916.240i | 0.0735356 | + | 0.417041i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3562.48 | + | 910.738i | −1.59316 | + | 0.407286i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −315.163 | − | 114.710i | −0.138505 | − | 0.0504118i | 0.271837 | − | 0.962343i | \(-0.412369\pi\) |
−0.410343 | + | 0.911931i | \(0.634591\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2161.13 | + | 1813.40i | 0.933520 | + | 0.783316i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −730.108 | + | 1131.61i | −0.310047 | + | 0.480549i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1838.52 | + | 3184.41i | −0.767695 | + | 1.32969i | 0.171115 | + | 0.985251i | \(0.445263\pi\) |
−0.938810 | + | 0.344436i | \(0.888070\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −208.366 | − | 360.900i | −0.0855675 | − | 0.148207i | 0.820065 | − | 0.572270i | \(-0.193937\pi\) |
−0.905633 | + | 0.424063i | \(0.860604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1263.11 | + | 1170.88i | 0.510229 | + | 0.472971i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.5926 | + | 105.444i | −0.00738896 | + | 0.0419049i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4102.60 | − | 3442.49i | 1.60434 | − | 1.34620i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3234.38 | − | 1982.84i | 1.24479 | − | 0.763126i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1409.52 | + | 1182.73i | −0.533977 | + | 0.448060i | −0.869472 | − | 0.493982i | \(-0.835541\pi\) |
0.335495 | + | 0.942042i | \(0.391096\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 54.6854 | − | 310.136i | 0.0203956 | − | 0.115669i | −0.972910 | − | 0.231183i | \(-0.925740\pi\) |
0.993306 | + | 0.115514i | \(0.0368515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1262.32 | − | 390.032i | 0.463571 | − | 0.143235i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 839.214 | + | 1453.56i | 0.303510 | + | 0.525695i | 0.976929 | − | 0.213566i | \(-0.0685079\pi\) |
−0.673418 | + | 0.739262i | \(0.735175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −255.716 | + | 442.913i | −0.0910917 | + | 0.157775i | −0.907971 | − | 0.419034i | \(-0.862369\pi\) |
0.816879 | + | 0.576809i | \(0.195702\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −484.756 | − | 23.9615i | −0.170110 | − | 0.00840853i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1017.15 | + | 853.488i | 0.351674 | + | 0.295089i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1769.72 | − | 644.127i | −0.602941 | − | 0.219452i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3566.64 | − | 1713.41i | −1.19758 | − | 0.575316i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1282.26 | − | 7272.07i | −0.424382 | − | 2.40679i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2331.59 | + | 848.631i | −0.760728 | + | 0.276882i | −0.693113 | − | 0.720829i | \(-0.743761\pi\) |
−0.0676152 | + | 0.997711i | \(0.521539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −432.748 | − | 3439.95i | −0.139208 | − | 1.10658i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1305.81 | 0.414210 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4142.69 | −1.29596 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1023.44 | + | 430.842i | 0.315789 | + | 0.132939i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5190.53 | − | 1889.20i | 1.57988 | − | 0.575028i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −80.0661 | − | 454.077i | −0.0240432 | − | 0.136355i | 0.970423 | − | 0.241409i | \(-0.0776096\pi\) |
−0.994467 | + | 0.105054i | \(0.966499\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1160.98 | + | 2566.46i | 0.343994 | + | 0.760433i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1280.18 | − | 465.948i | −0.374311 | − | 0.136238i | 0.148012 | − | 0.988986i | \(-0.452712\pi\) |
−0.522324 | + | 0.852747i | \(0.674935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1253.28 | + | 1051.62i | 0.361654 | + | 0.303464i | 0.805450 | − | 0.592664i | \(-0.201924\pi\) |
−0.443796 | + | 0.896128i | \(0.646368\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3478.95 | + | 6777.99i | 0.990902 | + | 1.93056i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2293.06 | − | 3971.70i | 0.644736 | − | 1.11672i | −0.339627 | − | 0.940560i | \(-0.610301\pi\) |
0.984362 | − | 0.176155i | \(-0.0563659\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 636.500 | + | 1102.45i | 0.176684 | + | 0.306025i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 634.336 | − | 2785.33i | 0.173859 | − | 0.763403i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 285.319 | − | 1618.12i | 0.0772206 | − | 0.437940i | −0.921545 | − | 0.388271i | \(-0.873072\pi\) |
0.998766 | − | 0.0496686i | \(-0.0158165\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4699.71 | + | 3943.52i | −1.25616 | + | 1.05404i | −0.260080 | + | 0.965587i | \(0.583749\pi\) |
−0.996080 | + | 0.0884567i | \(0.971807\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3768.26 | − | 386.146i | 0.994791 | − | 0.101940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1352.21 | − | 1134.63i | 0.352609 | − | 0.295874i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1322.50 | − | 7500.29i | 0.340684 | − | 1.93211i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −467.112 | + | 2051.06i | −0.118884 | + | 0.522010i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2445.01 | + | 4234.88i | 0.614851 | + | 1.06495i | 0.990411 | + | 0.138154i | \(0.0441170\pi\) |
−0.375560 | + | 0.926798i | \(0.622550\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3973.07 | − | 6881.55i | 0.987291 | − | 1.71004i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1065.57 | − | 2076.04i | −0.261681 | − | 0.509829i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −904.386 | − | 758.870i | −0.219510 | − | 0.184191i | 0.526401 | − | 0.850236i | \(-0.323541\pi\) |
−0.745911 | + | 0.666046i | \(0.767986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −598.395 | − | 217.798i | −0.143562 | − | 0.0522521i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 546.421 | + | 1207.92i | 0.129589 | + | 0.286469i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1187.46 | + | 6734.40i | 0.278410 | + | 1.57894i | 0.727919 | + | 0.685664i | \(0.240488\pi\) |
−0.449509 | + | 0.893276i | \(0.648401\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1061.68 | + | 386.418i | −0.246106 | + | 0.0895754i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4835.01 | − | 2035.41i | −1.10823 | − | 0.466536i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 343.601 | 0.0778801 | 0.0389401 | − | 0.999242i | \(-0.487602\pi\) | ||||
0.0389401 | + | 0.999242i | \(0.487602\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2607.43 | 0.584466 | 0.292233 | − | 0.956347i | \(-0.405602\pi\) | ||||
0.292233 | + | 0.956347i | \(0.405602\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 980.782 | + | 7796.33i | 0.217435 | + | 1.72841i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5315.63 | + | 1934.73i | −1.16562 | + | 0.424249i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.0627023 | + | 0.355603i | 1.36008e−5 | + | 7.71339e-5i | 0.984815 | − | 0.173610i | \(-0.0555431\pi\) |
−0.984801 | + | 0.173687i | \(0.944432\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3728.44 | − | 1791.14i | −0.800057 | − | 0.384348i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4627.50 | + | 1684.27i | 0.982396 | + | 0.357563i | 0.782771 | − | 0.622310i | \(-0.213806\pi\) |
0.199625 | + | 0.979872i | \(0.436028\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4317.90 | − | 3623.15i | −0.906971 | − | 0.761039i | 0.0645695 | − | 0.997913i | \(-0.479433\pi\) |
−0.971540 | + | 0.236874i | \(0.923877\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3213.55 | − | 158.846i | −0.667909 | − | 0.0330148i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5600.43 | − | 9700.22i | 1.15186 | − | 1.99507i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2421.49 | − | 4194.15i | −0.492874 | − | 0.853684i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 146.157 | − | 45.1597i | 0.0294428 | − | 0.00909727i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −397.381 | + | 2253.66i | −0.0792328 | + | 0.449352i | 0.919220 | + | 0.393745i | \(0.128821\pi\) |
−0.998453 | + | 0.0556072i | \(0.982291\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −902.692 | + | 757.448i | −0.178158 | + | 0.149493i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 200.525 | + | 7604.39i | 0.0391773 | + | 1.48570i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6278.12 | − | 5267.97i | 1.21429 | − | 1.01891i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1348.59 | + | 7648.23i | −0.258244 | + | 1.46457i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 352.035 | + | 326.329i | 0.0667455 | + | 0.0618716i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 753.528 | + | 1305.15i | 0.141465 | + | 0.245025i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3242.45 | + | 5616.10i | −0.602790 | + | 1.04406i | 0.389606 | + | 0.920982i | \(0.372611\pi\) |
−0.992397 | + | 0.123082i | \(0.960722\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5747.44 | + | 8908.09i | −1.05812 | + | 1.64001i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2064.12 | + | 1732.01i | 0.376353 | + | 0.315797i | 0.811269 | − | 0.584674i | \(-0.198777\pi\) |
−0.434916 | + | 0.900471i | \(0.643222\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4366.05 | − | 1589.11i | −0.788446 | − | 0.286971i | −0.0837560 | − | 0.996486i | \(-0.526692\pi\) |
−0.704690 | + | 0.709515i | \(0.748914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3216.18 | − | 822.207i | 0.575274 | − | 0.147067i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 860.106 | + | 4877.90i | 0.152392 | + | 0.864260i | 0.961131 | + | 0.276092i | \(0.0890394\pi\) |
−0.808739 | + | 0.588168i | \(0.799849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2501.83 | + | 910.591i | −0.439108 | + | 0.159822i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1453.68 | − | 1102.21i | 0.252762 | − | 0.191650i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13451.5 | −2.31723 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5834.30 | −0.995781 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2720.03 | + | 2062.39i | −0.459994 | + | 0.348777i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7114.53 | + | 2589.48i | −1.19221 | + | 0.433928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −307.323 | − | 1742.92i | −0.0510333 | − | 0.289424i | 0.948601 | − | 0.316475i | \(-0.102499\pi\) |
−0.999634 | + | 0.0270512i | \(0.991388\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −444.391 | − | 454.743i | −0.0731305 | − | 0.0748341i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −399.074 | − | 145.251i | −0.0650859 | − | 0.0236893i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −625.914 | − | 525.204i | −0.101174 | − | 0.0848952i | 0.590797 | − | 0.806820i | \(-0.298813\pi\) |
−0.691972 | + | 0.721925i | \(0.743258\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 359.694 | − | 557.498i | 0.0576280 | − | 0.0893190i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4153.31 | − | 7193.75i | 0.659573 | − | 1.14241i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 611.577 | + | 1059.28i | 0.0962743 | + | 0.166752i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2539.17 | − | 2353.75i | −0.396244 | − | 0.367309i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1301.07 | − | 7378.71i | 0.201282 | − | 1.14153i | −0.701902 | − | 0.712274i | \(-0.747665\pi\) |
0.903184 | − | 0.429254i | \(-0.141223\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9295.98 | − | 7800.25i | 1.42580 | − | 1.19638i | 0.477648 | − | 0.878551i | \(-0.341489\pi\) |
0.948147 | − | 0.317833i | \(-0.102955\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2488.13 | + | 7440.79i | −0.378367 | + | 1.13151i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1902.32 | + | 1596.24i | −0.286828 | + | 0.240678i | −0.774837 | − | 0.632161i | \(-0.782168\pi\) |
0.488008 | + | 0.872839i | \(0.337724\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 526.802 | − | 2987.64i | 0.0787598 | − | 0.446669i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13260.0 | − | 4097.11i | 1.96582 | − | 0.607400i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5053.00 | + | 8752.06i | 0.742862 | + | 1.28667i | 0.951187 | + | 0.308614i | \(0.0998653\pi\) |
−0.208326 | + | 0.978060i | \(0.566801\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5843.98 | + | 10122.1i | −0.852017 | + | 1.47574i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8350.15 | − | 412.748i | −1.20735 | − | 0.0596794i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 744.320 | + | 624.559i | 0.106738 | + | 0.0895641i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5169.49 | + | 1881.54i | 0.735273 | + | 0.267618i | 0.682395 | − | 0.730983i | \(-0.260938\pi\) |
0.0528780 | + | 0.998601i | \(0.483161\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9234.43 | − | 6308.83i | 1.30278 | − | 0.890040i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1166.83 | − | 6617.42i | −0.163285 | − | 0.926036i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8111.81 | − | 2952.46i | 1.12604 | − | 0.409845i | 0.289188 | − | 0.957272i | \(-0.406615\pi\) |
0.836853 | + | 0.547427i | \(0.184393\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 676.250 | + | 5375.57i | 0.0931237 | + | 0.740249i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2745.95 | −0.375128 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1742.39 | 0.236149 | 0.118075 | − | 0.993005i | \(-0.462328\pi\) | ||||
0.118075 | + | 0.993005i | \(0.462328\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6216.49 | + | 2616.98i | 0.835906 | + | 0.351895i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2574.27 | − | 936.958i | 0.343444 | − | 0.125003i | −0.164539 | − | 0.986371i | \(-0.552614\pi\) |
0.507983 | + | 0.861367i | \(0.330391\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1157.62 | + | 6565.16i | 0.153240 | + | 0.869069i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4520.55 | + | 6300.37i | −0.593779 | + | 0.827560i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6652.69 | + | 2421.38i | 0.867108 | + | 0.315601i | 0.736995 | − | 0.675898i | \(-0.236244\pi\) |
0.130112 | + | 0.991499i | \(0.458466\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11088.6 | − | 9304.41i | −1.43420 | − | 1.20344i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2679.88 | − | 5221.16i | −0.343975 | − | 0.670160i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1249.80 | − | 2164.72i | 0.159201 | − | 0.275744i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2624.35 | + | 4545.52i | 0.331770 | + | 0.574642i | 0.982859 | − | 0.184359i | \(-0.0590210\pi\) |
−0.651089 | + | 0.759001i | \(0.725688\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4249.22 | − | 18658.0i | 0.533150 | − | 2.34103i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −949.429 | + | 5384.48i | −0.118235 | + | 0.670544i | 0.866863 | + | 0.498547i | \(0.166133\pi\) |
−0.985098 | + | 0.171997i | \(0.944978\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6562.94 | − | 5506.96i | 0.811224 | − | 0.680698i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3250.07 | + | 650.568i | 0.398759 | + | 0.0798197i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 978.133 | − | 820.751i | 0.119126 | − | 0.0999585i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 689.848 | − | 3912.32i | 0.0834005 | − | 0.472987i | −0.914290 | − | 0.405061i | \(-0.867250\pi\) |
0.997690 | − | 0.0679269i | \(-0.0216385\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2980.27 | − | 13086.2i | 0.357679 | − | 1.57054i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3504.18 | − | 6069.42i | −0.417505 | − | 0.723140i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −920.329 | + | 1594.06i | −0.108861 | + | 0.188552i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6660.48 | − | 12976.5i | −0.782170 | − | 1.52389i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11193.9 | + | 9392.79i | 1.30515 | + | 1.09515i | 0.989231 | + | 0.146363i | \(0.0467566\pi\) |
0.315917 | + | 0.948787i | \(0.397688\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13068.9 | + | 4756.68i | 1.51292 | + | 0.550657i | 0.959367 | − | 0.282160i | \(-0.0910509\pi\) |
0.553549 | + | 0.832816i | \(0.313273\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7522.70 | − | 745.516i | −0.864696 | − | 0.0856932i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1789.39 | + | 10148.1i | 0.204231 | + | 1.15825i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8422.61 | + | 3065.58i | −0.954563 | + | 0.347433i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14521.6 | − | 6113.20i | −1.63428 | − | 0.687990i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14619.4 | −1.63385 | −0.816927 | − | 0.576741i | \(-0.804324\pi\) | ||||
−0.816927 | + | 0.576741i | \(0.804324\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14257.6 | 1.58239 | 0.791197 | − | 0.611561i | \(-0.209458\pi\) | ||||
0.791197 | + | 0.611561i | \(0.209458\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 144.795 | + | 1150.99i | 0.0159595 | + | 0.126864i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18754.6 | + | 6826.12i | −2.05299 | + | 0.747226i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2645.69 | − | 15004.5i | −0.287635 | − | 1.63126i | −0.695717 | − | 0.718316i | \(-0.744913\pi\) |
0.408081 | − | 0.912946i | \(-0.366198\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 793.309 | + | 10452.2i | 0.0856613 | + | 1.12863i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4770.78 | − | 1736.42i | −0.511663 | − | 0.186230i | 0.0732692 | − | 0.997312i | \(-0.476657\pi\) |
−0.584932 | + | 0.811082i | \(0.698879\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3516.37 | − | 2950.58i | −0.374588 | − | 0.314317i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14383.1 | + | 710.956i | 1.52192 | + | 0.0752283i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7046.08 | − | 12204.2i | 0.740591 | − | 1.28274i | −0.211636 | − | 0.977349i | \(-0.567879\pi\) |
0.952227 | − | 0.305392i | \(-0.0987875\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11229.6 | + | 19450.2i | 1.17246 | + | 2.03076i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3759.45 | − | 1161.60i | 0.389921 | − | 0.120478i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1193.95 | + | 6771.20i | −0.123018 | + | 0.697668i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −949.074 | + | 796.368i | −0.0971462 | + | 0.0815153i | −0.690067 | − | 0.723745i | \(-0.742419\pi\) |
0.592921 | + | 0.805261i | \(0.297975\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13705.5 | + | 2045.73i | 1.39373 | + | 0.208032i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2354.96 | + | 1976.04i | −0.237920 | + | 0.199639i | −0.753950 | − | 0.656932i | \(-0.771854\pi\) |
0.516030 | + | 0.856571i | \(0.327409\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1637.88 | + | 9288.87i | −0.164403 | + | 0.932377i | 0.785274 | + | 0.619148i | \(0.212522\pi\) |
−0.949678 | + | 0.313229i | \(0.898589\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2654.36 | − | 2460.53i | −0.264716 | − | 0.245386i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5454.27 | − | 9447.08i | −0.540457 | − | 0.936100i | −0.998878 | − | 0.0473641i | \(-0.984918\pi\) |
0.458420 | − | 0.888736i | \(-0.348415\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1262.90 | − | 2187.41i | 0.124340 | − | 0.215363i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3313.72 | + | 5136.01i | −0.324179 | + | 0.502452i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11929.0 | − | 10009.7i | −1.15962 | − | 0.973033i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13351.2 | + | 4859.45i | 1.28968 | + | 0.469404i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1810.97 | − | 6460.21i | 0.173834 | − | 0.620110i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2009.10 | − | 11394.2i | −0.191645 | − | 1.08687i | −0.917116 | − | 0.398621i | \(-0.869489\pi\) |
0.725470 | − | 0.688253i | \(-0.241622\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1237.51 | − | 450.418i | 0.117309 | − | 0.0426971i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16408.5 | − | 12441.3i | 1.54578 | − | 1.17205i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 133.855 | 0.0125320 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15337.4 | −1.42711 | −0.713554 | − | 0.700600i | \(-0.752916\pi\) | ||||
−0.713554 | + | 0.700600i | \(0.752916\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9620.29 | + | 7294.31i | −0.889661 | + | 0.674560i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6647.78 | + | 2419.59i | −0.611018 | + | 0.222392i | −0.628949 | − | 0.777447i | \(-0.716514\pi\) |
0.0179304 | + | 0.999839i | \(0.494292\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 842.185 | + | 4776.27i | 0.0769374 | + | 0.436334i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1796.67 | + | 6409.19i | −0.163140 | + | 0.581963i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16954.9 | + | 6171.06i | 1.53024 | + | 0.556962i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10522.3 | + | 8829.24i | 0.943972 | + | 0.792087i | 0.978272 | − | 0.207325i | \(-0.0664758\pi\) |
−0.0343001 | + | 0.999412i | \(0.510920\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10124.3 | + | 15691.9i | −0.902833 | + | 1.39932i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1396.87 | − | 2419.45i | 0.123824 | − | 0.214469i | −0.797449 | − | 0.603387i | \(-0.793818\pi\) |
0.921273 | + | 0.388918i | \(0.127151\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 210.012 | + | 363.751i | 0.0185057 | + | 0.0320529i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3545.41 | − | 3286.51i | −0.310566 | − | 0.287888i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1433.78 | + | 8131.38i | −0.124855 | + | 0.708089i | 0.856539 | + | 0.516083i | \(0.172610\pi\) |
−0.981394 | + | 0.192006i | \(0.938501\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4426.81 | + | 3714.54i | −0.383230 | + | 0.321568i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11891.4 | − | 14955.1i | 1.02342 | − | 1.28710i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7106.03 | + | 5962.66i | −0.608017 | + | 0.510187i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2636.16 | − | 14950.4i | 0.224252 | − | 1.27180i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1665.07 | − | 514.474i | 0.140825 | − | 0.0435123i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10192.6 | + | 17654.1i | 0.857094 | + | 1.48453i | 0.874689 | + | 0.484685i | \(0.161066\pi\) |
−0.0175944 | + | 0.999845i | \(0.505601\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7162.07 | + | 12405.1i | −0.598806 | + | 1.03716i | 0.394192 | + | 0.919028i | \(0.371025\pi\) |
−0.992998 | + | 0.118134i | \(0.962309\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14641.3 | − | 723.718i | −1.21714 | − | 0.0601631i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11591.6 | − | 9726.52i | −0.958138 | − | 0.803973i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8748.46 | − | 3184.18i | −0.719032 | − | 0.261706i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −529.589 | − | 6977.59i | −0.0432810 | − | 0.570248i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4022.38 | + | 22812.1i | 0.326883 | + | 1.85385i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1500.02 | − | 545.962i | 0.121218 | − | 0.0441196i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2384.81 | − | 18957.0i | −0.191642 | − | 1.52338i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21050.5 | −1.68221 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9772.64 | −0.776633 | −0.388317 | − | 0.921526i | \(-0.626943\pi\) | ||||
−0.388317 | + | 0.921526i | \(0.626943\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1995.77 | + | 840.166i | 0.157729 | + | 0.0663996i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2806.73 | + | 1021.57i | −0.220600 | + | 0.0802919i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2487.70 | + | 14108.5i | 0.194454 | + | 1.10280i | 0.913194 | + | 0.407525i | \(0.133608\pi\) |
−0.718740 | + | 0.695279i | \(0.755281\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8905.83 | − | 882.587i | −0.692334 | − | 0.0686118i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6283.83 | + | 2287.13i | 0.485844 | + | 0.176833i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11388.2 | + | 9555.87i | 0.875728 | + | 0.734823i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −254.051 | − | 494.964i | −0.0194304 | − | 0.0378560i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7088.20 | − | 12277.1i | 0.539204 | − | 0.933929i | −0.459743 | − | 0.888052i | \(-0.652058\pi\) |
0.998947 | − | 0.0458770i | \(-0.0146082\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8030.49 | − | 13909.2i | −0.607609 | − | 1.05241i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6179.45 | + | 27133.6i | −0.465056 | + | 2.04203i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2412.55 | + | 13682.2i | −0.180598 | + | 1.02422i | 0.750884 | + | 0.660435i | \(0.229628\pi\) |
−0.931482 | + | 0.363788i | \(0.881483\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 444.719 | − | 373.164i | 0.0331141 | − | 0.0277860i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7167.00 | + | 18364.1i | −0.530839 | + | 1.36018i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1899.81 | − | 1594.13i | 0.139972 | − | 0.117451i | −0.570113 | − | 0.821566i | \(-0.693101\pi\) |
0.710086 | + | 0.704115i | \(0.248656\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 680.576 | − | 3859.74i | 0.0498795 | − | 0.282881i | −0.949658 | − | 0.313288i | \(-0.898569\pi\) |
0.999538 | + | 0.0304075i | \(0.00968049\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2123.06 | − | 9322.24i | 0.154786 | − | 0.679654i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7644.60 | + | 13240.8i | 0.554438 | + | 0.960315i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9634.98 | − | 16688.3i | 0.695164 | − | 1.20406i | −0.274962 | − | 0.961455i | \(-0.588665\pi\) |
0.970125 | − | 0.242604i | \(-0.0780016\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 747.227 | + | 1455.81i | 0.0536333 | + | 0.104493i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8386.07 | − | 7036.74i | −0.598817 | − | 0.502467i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12660.9 | + | 4608.20i | 0.899420 | + | 0.327362i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4002.17 | + | 5577.90i | −0.282854 | + | 0.394218i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2051.32 | − | 11633.6i | −0.144237 | − | 0.818007i | −0.967977 | − | 0.251040i | \(-0.919228\pi\) |
0.823740 | − | 0.566968i | \(-0.191884\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19605.5 | + | 7135.80i | −1.37153 | + | 0.499194i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8038.15 | − | 3383.85i | −0.559468 | − | 0.235521i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13127.9 | −0.909101 | −0.454551 | − | 0.890721i | \(-0.650200\pi\) | ||||
−0.454551 | + | 0.890721i | \(0.650200\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12143.9 | 0.836728 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −331.698 | − | 2636.70i | −0.0227395 | − | 0.180759i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26377.9 | − | 9600.77i | 1.79928 | − | 0.654886i | 0.800855 | − | 0.598858i | \(-0.204378\pi\) |
0.998429 | − | 0.0560284i | \(-0.0178437\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2662.66 | − | 15100.7i | −0.180719 | − | 1.02491i | −0.931333 | − | 0.364167i | \(-0.881354\pi\) |
0.750615 | − | 0.660740i | \(-0.229758\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2082.37 | − | 1422.65i | 0.140631 | − | 0.0960774i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6874.24 | − | 2502.02i | −0.461946 | − | 0.168135i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20854.2 | − | 17498.7i | −1.39447 | − | 1.17010i | −0.963491 | − | 0.267740i | \(-0.913723\pi\) |
−0.430981 | − | 0.902361i | \(-0.641832\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6890.99 | − | 340.622i | −0.458517 | − | 0.0226645i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7828.75 | − | 13559.8i | 0.518359 | − | 0.897824i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2651.31 | + | 4592.20i | 0.174690 | + | 0.302573i | 0.940054 | − | 0.341025i | \(-0.110774\pi\) |
−0.765364 | + | 0.643598i | \(0.777441\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9349.78 | − | 2888.91i | 0.613040 | − | 0.189418i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1200.77 | + | 6809.92i | −0.0783489 | + | 0.444339i | 0.920246 | + | 0.391341i | \(0.127989\pi\) |
−0.998595 | + | 0.0529978i | \(0.983122\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1564.51 | − | 1312.78i | 0.101588 | − | 0.0852424i | −0.590579 | − | 0.806980i | \(-0.701101\pi\) |
0.692167 | + | 0.721737i | \(0.256656\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20146.9 | − | 4102.78i | 1.30188 | − | 0.265119i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20913.4 | − | 17548.5i | 1.34491 | − | 1.12851i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1441.31 | − | 8174.07i | 0.0922438 | − | 0.523140i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 28139.4 | + | 26084.6i | 1.79231 | + | 1.66143i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1163.00 | − | 2014.38i | −0.0737231 | − | 0.127692i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7978.31 | + | 13818.8i | −0.503346 | + | 0.871821i | 0.496646 | + | 0.867953i | \(0.334565\pi\) |
−0.999993 | + | 0.00386809i | \(0.998769\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6989.81 | − | 10833.7i | 0.438894 | − | 0.680252i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4521.08 | + | 3793.64i | 0.282541 | + | 0.237080i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20401.8 | − | 7425.64i | −1.26899 | − | 0.461875i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12591.3 | + | 12884.6i | 0.779507 | + | 0.797666i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 95.6010 | + | 542.180i | 0.00589081 | + | 0.0334085i | 0.987611 | − | 0.156919i | \(-0.0501561\pi\) |
−0.981721 | + | 0.190327i | \(0.939045\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10646.4 | + | 3874.97i | −0.652959 | + | 0.237658i | −0.647194 | − | 0.762326i | \(-0.724058\pi\) |
−0.00576568 | + | 0.999983i | \(0.501835\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5406.72 | + | 4099.49i | −0.330061 | + | 0.250259i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21233.5 | 1.29022 | 0.645112 | − | 0.764088i | \(-0.276811\pi\) | ||||
0.645112 | + | 0.764088i | \(0.276811\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14052.7 | 0.849947 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17152.9 | − | 13005.7i | 1.03268 | − | 0.783001i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21181.2 | − | 7709.31i | 1.26935 | − | 0.462004i | 0.382451 | − | 0.923976i | \(-0.375080\pi\) |
0.886895 | + | 0.461971i | \(0.152858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −891.725 | − | 5057.22i | −0.0531948 | − | 0.301682i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5590.18 | + | 1429.11i | −0.331954 | + | 0.0848630i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12762.0 | − | 4644.99i | −0.754381 | − | 0.274572i | −0.0639327 | − | 0.997954i | \(-0.520364\pi\) |
−0.690448 | + | 0.723382i | \(0.742587\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1688.35 | + | 1416.69i | 0.0993481 | + | 0.0833630i | 0.691109 | − | 0.722751i | \(-0.257123\pi\) |
−0.591761 | + | 0.806114i | \(0.701567\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15560.5 | + | 24117.6i | −0.911492 | + | 1.41274i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8372.03 | − | 14500.8i | 0.488201 | − | 0.845588i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3597.97 | + | 6231.87i | 0.208867 | + | 0.361768i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1757.06 | + | 1628.76i | 0.101543 | + | 0.0941276i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3120.85 | − | 17699.2i | 0.179552 | − | 1.01829i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −468.396 | + | 393.031i | −0.0268281 | + | 0.0225115i | −0.656103 | − | 0.754671i | \(-0.727796\pi\) |
0.629275 | + | 0.777183i | \(0.283352\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12864.3 | − | 6981.69i | −0.733551 | − | 0.398112i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10915.1 | − | 9158.89i | 0.619650 | − | 0.519948i | −0.278044 | − | 0.960568i | \(-0.589686\pi\) |
0.897693 | + | 0.440621i | \(0.145242\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −138.240 | + | 784.000i | −0.00781322 | + | 0.0443110i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6763.44 | − | 2089.78i | 0.380581 | − | 0.117592i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7351.56 | + | 12733.3i | 0.411859 | + | 0.713360i | 0.995093 | − | 0.0989436i | \(-0.0315464\pi\) |
−0.583234 | + | 0.812304i | \(0.698213\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5871.89 | − | 10170.4i | 0.327523 | − | 0.567286i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8490.72 | − | 419.696i | −0.471530 | − | 0.0233077i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10645.2 | + | 8932.37i | 0.588606 | + | 0.493899i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17454.4 | − | 6352.88i | −0.960921 | − | 0.349747i | −0.186527 | − | 0.982450i | \(-0.559723\pi\) |
−0.774394 | + | 0.632703i | \(0.781945\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −35683.7 | − | 17142.5i | −1.95601 | − | 0.939667i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2216.26 | − | 12569.0i | −0.120961 | − | 0.686002i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38445.4 | − | 13993.0i | 2.08927 | − | 0.760433i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2974.41 | + | 23643.8i | 0.160948 | + | 1.27939i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3749.76 | 0.202035 | 0.101017 | − | 0.994885i | \(-0.467790\pi\) | ||||
0.101017 | + | 0.994885i | \(0.467790\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3207.09 | −0.172059 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6096.52 | − | 2566.48i | −0.325685 | − | 0.137105i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2347.42 | + | 854.391i | −0.124871 | + | 0.0454494i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 101.160 | + | 573.705i | 0.00535843 | + | 0.0303892i | 0.987370 | − | 0.158433i | \(-0.0506442\pi\) |
−0.982011 | + | 0.188822i | \(0.939533\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6117.87 | + | 13524.2i | 0.322698 | + | 0.713357i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21097.3 | − | 7678.78i | −1.10813 | − | 0.403328i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10561.1 | − | 8861.84i | −0.552397 | − | 0.463516i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3898.62 | + | 7595.61i | 0.203064 | + | 0.395625i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13076.5 | + | 22649.2i | −0.678264 | + | 1.17479i | 0.297239 | + | 0.954803i | \(0.403934\pi\) |
−0.975503 | + | 0.219985i | \(0.929399\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27585.1 | − | 47778.8i | −1.42486 | − | 2.46793i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7078.83 | − | 31082.7i | 0.364128 | − | 1.59886i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 889.551 | − | 5044.90i | 0.0455684 | − | 0.258431i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8156.67 | − | 6844.26i | 0.416113 | − | 0.349160i | −0.410569 | − | 0.911829i | \(-0.634670\pi\) |
0.826682 | + | 0.562669i | \(0.190226\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14390.3 | + | 13429.1i | −0.731103 | + | 0.682267i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21730.6 | + | 18234.1i | −1.09950 | + | 0.922590i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3183.40 | + | 18053.9i | −0.160411 | + | 0.909738i | 0.793259 | + | 0.608884i | \(0.208383\pi\) |
−0.953670 | + | 0.300853i | \(0.902729\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2036.73 | + | 8943.14i | −0.102212 | + | 0.448807i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2532.28 | + | 4386.04i | 0.126564 | + | 0.219215i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4580.62 | + | 7933.86i | −0.228012 | + | 0.394928i | −0.957219 | − | 0.289365i | \(-0.906556\pi\) |
0.729207 | + | 0.684293i | \(0.239889\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18070.8 | + | 35207.0i | 0.895880 | + | 1.74543i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19612.0 | + | 16456.4i | 0.968362 | + | 0.812552i | 0.982293 | − | 0.187351i | \(-0.0599902\pi\) |
−0.0139313 | + | 0.999903i | \(0.504435\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11840.8 | + | 4309.71i | 0.582302 | + | 0.211940i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4505.07 | − | 9958.93i | −0.220659 | − | 0.487789i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1648.59 | + | 9349.61i | 0.0804247 | + | 0.456111i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11820.2 | + | 4302.20i | −0.574334 | + | 0.209040i | −0.612825 | − | 0.790218i | \(-0.709967\pi\) |
0.0384913 | + | 0.999259i | \(0.487745\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −23418.7 | − | 9858.68i | −1.13337 | − | 0.477118i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3443.01 | 0.165966 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31497.3 | −1.51227 | −0.756134 | − | 0.654416i | \(-0.772914\pi\) | ||||
−0.756134 | + | 0.654416i | \(0.772914\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5153.60 | + | 40966.4i | 0.246461 | + | 1.95914i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22625.0 | − | 8234.84i | 1.07774 | − | 0.392264i | 0.258672 | − | 0.965965i | \(-0.416715\pi\) |
0.819064 | + | 0.573702i | \(0.194493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3084.73 | − | 17494.4i | −0.146362 | − | 0.830063i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10929.6 | + | 5250.59i | 0.516550 | + | 0.248151i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13619.6 | + | 4957.13i | 0.641168 | + | 0.233366i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17213.9 | + | 14444.1i | 0.807214 | + | 0.677333i | 0.949941 | − | 0.312429i | \(-0.101143\pi\) |
−0.142727 | + | 0.989762i | \(0.545587\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6127.05 | + | 302.860i | 0.286200 | + | 0.0141469i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16376.9 | + | 28365.5i | −0.762011 | + | 1.31984i | 0.179801 | + | 0.983703i | \(0.442455\pi\) |
−0.941812 | + | 0.336139i | \(0.890879\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7991.41 | + | 13841.5i | 0.370400 | + | 0.641551i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3161.43 | − | 976.823i | 0.145966 | − | 0.0451008i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9795.57 | − | 55553.5i | 0.450530 | − | 2.55508i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27714.3 | + | 23255.1i | −1.26978 | + | 1.06547i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6054.65 | − | 3285.97i | −0.276342 | − | 0.149976i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4097.02 | + | 3437.81i | −0.186279 | + | 0.156307i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5068.73 | + | 28746.2i | −0.229582 | + | 1.30202i | 0.624148 | + | 0.781306i | \(0.285446\pi\) |
−0.853730 | + | 0.520716i | \(0.825665\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26058.9 | − | 24156.0i | −1.17582 | − | 1.08996i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1726.37 | + | 2990.16i | 0.0776012 | + | 0.134409i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9268.14 | − | 16052.9i | 0.415033 | − | 0.718859i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3182.76 | − | 4933.03i | 0.141988 | − | 0.220071i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12766.2 | − | 10712.1i | −0.567381 | − | 0.476089i | 0.313395 | − | 0.949623i | \(-0.398534\pi\) |
−0.880776 | + | 0.473534i | \(0.842978\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25986.9 | − | 9458.44i | −1.15062 | − | 0.418793i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26409.5 | − | 6751.51i | 1.16496 | − | 0.297819i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2012.10 | − | 11411.2i | −0.0884252 | − | 0.501485i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16931.5 | − | 6162.57i | 0.741314 | − | 0.269816i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1422.69 | + | 1078.71i | −0.0620583 | + | 0.0470539i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5273.69 | −0.229188 | −0.114594 | − | 0.993412i | \(-0.536557\pi\) | ||||
−0.114594 | + | 0.993412i | \(0.536557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2370.93 | 0.102657 | 0.0513283 | − | 0.998682i | \(-0.483654\pi\) | ||||
0.0513283 | + | 0.998682i | \(0.483654\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10796.1 | + | 8185.86i | −0.465728 | + | 0.353125i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9926.93 | + | 3613.11i | −0.426657 | + | 0.155290i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6791.86 | + | 38518.5i | 0.290841 | + | 1.64944i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −28537.0 | − | 29201.8i | −1.21754 | − | 1.24590i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9376.22 | + | 3412.67i | 0.398578 | + | 0.145070i | 0.533529 | − | 0.845782i | \(-0.320866\pi\) |
−0.134951 | + | 0.990852i | \(0.543088\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10088.6 | + | 8465.38i | 0.427300 | + | 0.358548i | 0.830932 | − | 0.556374i | \(-0.187808\pi\) |
−0.403632 | + | 0.914922i | \(0.632252\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15935.5 | − | 24698.9i | 0.672490 | − | 1.04231i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8360.67 | + | 14481.1i | −0.351547 | + | 0.608897i | −0.986521 | − | 0.163637i | \(-0.947677\pi\) |
0.634974 | + | 0.772533i | \(0.281011\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1210.13 | − | 2096.00i | −0.0506990 | − | 0.0878132i | 0.839562 | − | 0.543264i | \(-0.182812\pi\) |
−0.890261 | + | 0.455450i | \(0.849478\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.37601 | − | 1.27553i | −5.74408e−5 | − | 5.32463e-5i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6658.83 | + | 37764.1i | −0.276969 | + | 1.57077i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12517.5 | + | 10503.4i | −0.518784 | + | 0.435312i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21060.9 | − | 4288.91i | 0.869738 | − | 0.177117i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10927.3 | + | 9169.08i | −0.449645 | + | 0.377297i | −0.839304 | − | 0.543662i | \(-0.817037\pi\) |
0.389659 | + | 0.920959i | \(0.372593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3816.43 | + | 21644.1i | −0.156482 | + | 0.887452i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24447.9 | + | 7553.95i | −0.998851 | + | 0.308626i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2115.07 | − | 3663.40i | −0.0861071 | − | 0.149142i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21754.0 | − | 37679.1i | 0.882500 | − | 1.52854i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29253.0 | + | 1445.98i | 1.18252 | + | 0.0584521i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2643.71 | − | 2218.34i | −0.106493 | − | 0.0893580i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13748.6 | − | 5004.09i | −0.551869 | − | 0.200864i | 0.0510079 | − | 0.998698i | \(-0.483757\pi\) |
−0.602877 | + | 0.797834i | \(0.705979\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13804.5 | − | 9431.02i | 0.552167 | − | 0.377233i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.9693 | − | 192.649i | −0.00135399 | − | 0.00767885i | 0.984123 | − | 0.177486i | \(-0.0567965\pi\) |
−0.985477 | + | 0.169807i | \(0.945685\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24809.7 | − | 9030.01i | 0.985445 | − | 0.358673i | 0.201490 | − | 0.979490i | \(-0.435422\pi\) |
0.783955 | + | 0.620818i | \(0.213199\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7264.50 | + | 57746.2i | 0.287542 | + | 2.28570i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2803.15 | −0.110568 | −0.0552840 | − | 0.998471i | \(-0.517606\pi\) | ||||
−0.0552840 | + | 0.998471i | \(0.517606\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1524.92 | 0.0599407 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23193.5 | + | 9763.86i | 0.908527 | + | 0.382466i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28011.1 | + | 10195.2i | −1.09346 | + | 0.397985i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 907.051 | + | 5144.14i | 0.0352862 | + | 0.200118i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −463.389 | + | 645.834i | −0.0179649 | + | 0.0250380i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26495.1 | − | 9643.44i | −1.02366 | − | 0.372580i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15359.2 | + | 12887.9i | 0.591385 | + | 0.496231i | 0.888663 | − | 0.458560i | \(-0.151635\pi\) |
−0.297279 | + | 0.954791i | \(0.596079\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5429.84 | − | 10578.9i | −0.208355 | − | 0.405935i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18708.5 | − | 32404.1i | 0.715443 | − | 1.23918i | −0.247345 | − | 0.968927i | \(-0.579558\pi\) |
0.962788 | − | 0.270256i | \(-0.0871085\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3348.08 | + | 5799.04i | 0.127601 | + | 0.221012i | 0.922747 | − | 0.385407i | \(-0.125939\pi\) |
−0.795146 | + | 0.606419i | \(0.792606\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1359.66 | − | 5970.17i | 0.0516434 | − | 0.226763i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5380.75 | − | 30515.7i | 0.203684 | − | 1.15515i | −0.695813 | − | 0.718223i | \(-0.744956\pi\) |
0.899497 | − | 0.436927i | \(-0.143933\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26888.9 | + | 22562.5i | −1.01443 | + | 0.851206i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −24703.8 | − | 30856.6i | −0.928852 | − | 1.16020i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29209.4 | + | 24509.6i | −1.09457 | + | 0.918457i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2903.12 | − | 16464.4i | 0.108425 | − | 0.614910i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9456.28 | + | 41521.9i | −0.351991 | + | 1.54557i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3761.20 | + | 6514.59i | 0.139536 | + | 0.241684i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12272.0 | − | 21255.7i | 0.453762 | − | 0.785938i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18427.3 | − | 35901.5i | −0.679093 | − | 1.32307i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1451.47 | + | 1217.93i | 0.0533131 | + | 0.0447350i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1562.19 | − | 568.589i | −0.0571902 | − | 0.0208155i | 0.313267 | − | 0.949665i | \(-0.398577\pi\) |
−0.370457 | + | 0.928850i | \(0.620799\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2482.10 | − | 245.981i | −0.0905676 | − | 0.00897544i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5763.36 | − | 32685.6i | −0.209603 | − | 1.18872i | −0.890030 | − | 0.455903i | \(-0.849317\pi\) |
0.680426 | − | 0.732816i | \(-0.261795\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20626.8 | − | 7507.55i | 0.747698 | − | 0.272140i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7217.43 | − | 3038.35i | −0.260766 | − | 0.109776i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30541.6 | 1.09986 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20905.7 | 0.750397 | 0.375199 | − | 0.926944i | \(-0.377575\pi\) | ||||
0.375199 | + | 0.926944i | \(0.377575\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4205.90 | − | 33433.1i | −0.150477 | − | 1.19615i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35063.6 | + | 12762.1i | −1.25041 | + | 0.455113i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 426.622 | + | 2419.49i | 0.0151646 | + | 0.0860027i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4168.95 | − | 54927.9i | −0.147709 | − | 1.94614i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20083.7 | − | 7309.88i | −0.709285 | − | 0.258159i | −0.0379151 | − | 0.999281i | \(-0.512072\pi\) |
−0.671370 | + | 0.741122i | \(0.734294\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40502.6 | + | 33985.7i | 1.42580 | + | 1.19639i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13984.1 | − | 691.233i | −0.490694 | − | 0.0242550i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12175.1 | + | 21087.9i | −0.425848 | + | 0.737590i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 704.534 | + | 1220.29i | 0.0245636 | + | 0.0425454i | 0.878046 | − | 0.478576i | \(-0.158847\pi\) |
−0.853482 | + | 0.521122i | \(0.825514\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23066.6 | − | 7127.16i | 0.801652 | − | 0.247696i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3094.69 | − | 17550.9i | 0.107209 | − | 0.608015i | −0.883105 | − | 0.469175i | \(-0.844551\pi\) |
0.990315 | − | 0.138840i | \(-0.0443374\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46501.1 | − | 39019.0i | 1.60582 | − | 1.34744i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10735.4 | + | 13501.4i | −0.369549 | + | 0.464761i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27667.7 | + | 23216.0i | −0.949399 | + | 0.796640i | −0.979196 | − | 0.202916i | \(-0.934958\pi\) |
0.0297975 | + | 0.999556i | \(0.490514\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2075.25 | − | 11769.3i | 0.0709856 | − | 0.402579i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18875.1 | − | 17496.8i | −0.643605 | − | 0.596608i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22472.0 | + | 38922.7i | 0.763841 | + | 1.32301i | 0.940857 | + | 0.338804i | \(0.110022\pi\) |
−0.177016 | + | 0.984208i | \(0.556644\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4182.97 | − | 7245.12i | 0.141736 | − | 0.245494i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7500.15 | − | 11624.7i | 0.253339 | − | 0.392656i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53504.8 | + | 44895.9i | 1.80163 | + | 1.51175i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5940.00 | + | 2161.98i | 0.199389 | + | 0.0725717i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2558.69 | + | 9127.48i | −0.0856204 | + | 0.305430i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 248.638 | + | 1410.10i | 0.00829425 | + | 0.0470390i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35745.8 | + | 13010.4i | −1.18873 | + | 0.432664i | −0.859279 | − | 0.511507i | \(-0.829087\pi\) |
−0.329455 | + | 0.944171i | \(0.606865\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 55696.4 | − | 42230.2i | 1.84647 | − | 1.40003i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −885.777 | −0.0292749 | −0.0146374 | − | 0.999893i | \(-0.504659\pi\) | ||||
−0.0146374 | + | 0.999893i | \(0.504659\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 75907.1 | 2.50100 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 24157.1 | − | 18316.4i | 0.793482 | − | 0.601635i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48395.1 | − | 17614.4i | 1.58475 | − | 0.576801i | 0.608518 | − | 0.793540i | \(-0.291764\pi\) |
0.976229 | + | 0.216740i | \(0.0695422\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9505.69 | + | 53909.5i | 0.310320 | + | 1.75991i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4787.64 | − | 17078.7i | 0.155818 | − | 0.555843i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17316.6 | − | 6302.71i | −0.561864 | − | 0.204502i | 0.0454457 | − | 0.998967i | \(-0.485529\pi\) |
−0.607310 | + | 0.794465i | \(0.707751\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5845.93 | − | 4905.31i | −0.189103 | − | 0.158676i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21328.4 | − | 33057.4i | 0.687832 | − | 1.06609i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21044.5 | + | 36450.1i | −0.676618 | + | 1.17194i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10476.8 | − | 18146.4i | −0.335829 | − | 0.581673i | 0.647815 | − | 0.761798i | \(-0.275683\pi\) |
−0.983644 | + | 0.180125i | \(0.942350\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6744.25 | + | 6251.77i | 0.215531 | + | 0.199792i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 403.789 | − | 2290.00i | 0.0128653 | − | 0.0729628i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.20726 | − | 1.01301i | 3.83495e−5 | − | 3.21790e-5i | −0.642768 | − | 0.766061i | \(-0.722214\pi\) |
0.642807 | + | 0.766028i | \(0.277770\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3267.65 | + | 487.740i | 0.103487 | + | 0.0154468i |
(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 | 108.4.i.a.49.2 | ✓ | 54 | |
3.2 | odd | 2 | 324.4.i.a.37.5 | 54 | |||
27.11 | odd | 18 | 324.4.i.a.289.5 | 54 | |||
27.16 | even | 9 | inner | 108.4.i.a.97.2 | yes | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.i.a.49.2 | ✓ | 54 | 1.1 | even | 1 | trivial | |
108.4.i.a.97.2 | yes | 54 | 27.16 | even | 9 | inner | |
324.4.i.a.37.5 | 54 | 3.2 | odd | 2 | |||
324.4.i.a.289.5 | 54 | 27.11 | odd | 18 |