Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,4,Mod(19,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([16]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.19");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.e (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.55830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 54) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 73.3 | ||
Character | \(\chi\) | \(=\) | 162.73 |
Dual form | 162.4.e.a.91.3 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{5}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.347296 | + | 1.96962i | −0.122788 | + | 0.696364i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.75877 | − | 1.36808i | −0.469846 | − | 0.171010i | ||||
\(5\) | 5.66862 | − | 4.75653i | 0.507016 | − | 0.425437i | −0.353061 | − | 0.935600i | \(-0.614859\pi\) |
0.860078 | + | 0.510163i | \(0.170415\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.1935 | + | 4.07412i | −0.604394 | + | 0.219982i | −0.626049 | − | 0.779784i | \(-0.715329\pi\) |
0.0216544 | + | 0.999766i | \(0.493107\pi\) | |||||||
\(8\) | 4.00000 | − | 6.92820i | 0.176777 | − | 0.306186i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.39985 | + | 12.8169i | 0.234004 | + | 0.405307i | ||||
\(11\) | 46.3308 | + | 38.8761i | 1.26993 | + | 1.06560i | 0.994550 | + | 0.104265i | \(0.0332491\pi\) |
0.275383 | + | 0.961335i | \(0.411195\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.09014 | + | 11.8538i | 0.0445923 | + | 0.252895i | 0.998952 | − | 0.0457631i | \(-0.0145719\pi\) |
−0.954360 | + | 0.298659i | \(0.903461\pi\) | |||||||
\(14\) | −4.13696 | − | 23.4619i | −0.0789750 | − | 0.447890i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.2567 | + | 10.2846i | 0.191511 | + | 0.160697i | ||||
\(17\) | 52.1248 | + | 90.2827i | 0.743654 | + | 1.28805i | 0.950821 | + | 0.309740i | \(0.100242\pi\) |
−0.207167 | + | 0.978305i | \(0.566424\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22.8348 | − | 39.5511i | 0.275720 | − | 0.477560i | −0.694597 | − | 0.719399i | \(-0.744417\pi\) |
0.970316 | + | 0.241839i | \(0.0777506\pi\) | |||||||
\(20\) | −27.8143 | + | 10.1236i | −0.310974 | + | 0.113185i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −92.6616 | + | 77.7523i | −0.897978 | + | 0.753493i | ||||
\(23\) | 13.0410 | + | 4.74653i | 0.118228 | + | 0.0430313i | 0.400457 | − | 0.916316i | \(-0.368852\pi\) |
−0.282229 | + | 0.959347i | \(0.591074\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.1974 | + | 69.1750i | −0.0975794 | + | 0.553400i | ||||
\(26\) | −24.0732 | −0.181583 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 47.6477 | 0.321592 | ||||||||
\(29\) | −29.4992 | + | 167.298i | −0.188892 | + | 1.07126i | 0.731960 | + | 0.681347i | \(0.238606\pi\) |
−0.920852 | + | 0.389912i | \(0.872505\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.5480 | + | 7.11491i | 0.113256 | + | 0.0412218i | 0.398026 | − | 0.917374i | \(-0.369695\pi\) |
−0.284771 | + | 0.958596i | \(0.591917\pi\) | |||||||
\(32\) | −24.5134 | + | 20.5692i | −0.135419 | + | 0.113630i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −195.925 | + | 71.3109i | −0.988261 | + | 0.359698i | ||||
\(35\) | −44.0732 | + | 76.3370i | −0.212849 | + | 0.368666i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 156.422 | + | 270.931i | 0.695017 | + | 1.20381i | 0.970175 | + | 0.242406i | \(0.0779367\pi\) |
−0.275158 | + | 0.961399i | \(0.588730\pi\) | |||||||
\(38\) | 69.9700 | + | 58.7118i | 0.298701 | + | 0.250640i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.2798 | − | 58.2995i | −0.0406343 | − | 0.230449i | ||||
\(41\) | −59.6415 | − | 338.244i | −0.227181 | − | 1.28841i | −0.858471 | − | 0.512863i | \(-0.828585\pi\) |
0.631289 | − | 0.775548i | \(-0.282526\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −308.776 | − | 259.094i | −1.09507 | − | 0.918871i | −0.0979842 | − | 0.995188i | \(-0.531239\pi\) |
−0.997084 | + | 0.0763170i | \(0.975684\pi\) | |||||||
\(44\) | −120.961 | − | 209.511i | −0.414445 | − | 0.717839i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.8779 | + | 24.0373i | −0.0444824 | + | 0.0770458i | ||||
\(47\) | 81.8198 | − | 29.7800i | 0.253929 | − | 0.0924225i | −0.211920 | − | 0.977287i | \(-0.567971\pi\) |
0.465848 | + | 0.884865i | \(0.345749\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −154.056 | + | 129.269i | −0.449144 | + | 0.376876i | ||||
\(50\) | −132.012 | − | 48.0485i | −0.373387 | − | 0.135902i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.36055 | − | 47.4150i | 0.0222961 | − | 0.126448i | ||||
\(53\) | 753.474 | 1.95278 | 0.976392 | − | 0.216006i | \(-0.0693029\pi\) | ||||
0.976392 | + | 0.216006i | \(0.0693029\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 447.547 | 1.09722 | ||||||||
\(56\) | −16.5479 | + | 93.8476i | −0.0394875 | + | 0.223945i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −319.268 | − | 116.204i | −0.722793 | − | 0.263075i | ||||
\(59\) | −263.901 | + | 221.440i | −0.582323 | + | 0.488627i | −0.885709 | − | 0.464241i | \(-0.846327\pi\) |
0.303386 | + | 0.952868i | \(0.401883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 669.676 | − | 243.742i | 1.40563 | − | 0.511606i | 0.475783 | − | 0.879563i | \(-0.342165\pi\) |
0.929843 | + | 0.367957i | \(0.119943\pi\) | |||||||
\(62\) | −20.8026 | + | 36.0311i | −0.0426118 | + | 0.0738058i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32.0000 | − | 55.4256i | −0.0625000 | − | 0.108253i | ||||
\(65\) | 68.2310 | + | 57.2526i | 0.130200 | + | 0.109251i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.10545 | − | 11.9406i | −0.00383912 | − | 0.0217727i | 0.982828 | − | 0.184524i | \(-0.0590743\pi\) |
−0.986667 | + | 0.162751i | \(0.947963\pi\) | |||||||
\(68\) | −72.4110 | − | 410.663i | −0.129134 | − | 0.732356i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −135.048 | − | 113.319i | −0.230591 | − | 0.193488i | ||||
\(71\) | −212.776 | − | 368.538i | −0.355660 | − | 0.616020i | 0.631571 | − | 0.775318i | \(-0.282410\pi\) |
−0.987231 | + | 0.159298i | \(0.949077\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 294.170 | − | 509.518i | 0.471644 | − | 0.816912i | −0.527830 | − | 0.849350i | \(-0.676994\pi\) |
0.999474 | + | 0.0324386i | \(0.0103273\pi\) | |||||||
\(74\) | −587.955 | + | 213.998i | −0.923627 | + | 0.336173i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −139.940 | + | 117.424i | −0.211213 | + | 0.177229i | ||||
\(77\) | −676.991 | − | 246.405i | −1.00195 | − | 0.364681i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 167.873 | − | 952.056i | 0.239079 | − | 1.35588i | −0.594773 | − | 0.803893i | \(-0.702758\pi\) |
0.833852 | − | 0.551988i | \(-0.186131\pi\) | |||||||
\(80\) | 118.398 | 0.165466 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 686.924 | 0.925098 | ||||||||
\(83\) | −55.6100 | + | 315.380i | −0.0735420 | + | 0.417078i | 0.925704 | + | 0.378249i | \(0.123474\pi\) |
−0.999246 | + | 0.0388285i | \(0.987637\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 724.908 | + | 263.845i | 0.925027 | + | 0.336682i | ||||
\(86\) | 617.552 | − | 518.188i | 0.774330 | − | 0.649740i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 454.665 | − | 165.485i | 0.550766 | − | 0.200463i | ||||
\(89\) | 49.8431 | − | 86.3309i | 0.0593636 | − | 0.102821i | −0.834816 | − | 0.550529i | \(-0.814426\pi\) |
0.894180 | + | 0.447708i | \(0.147760\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −71.6896 | − | 124.170i | −0.0825837 | − | 0.143039i | ||||
\(92\) | −42.5245 | − | 35.6823i | −0.0481900 | − | 0.0404362i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 30.2394 | + | 171.496i | 0.0331804 | + | 0.188175i | ||||
\(95\) | −58.6842 | − | 332.815i | −0.0633776 | − | 0.359432i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1273.09 | − | 1068.25i | −1.33260 | − | 1.11818i | −0.983462 | − | 0.181113i | \(-0.942030\pi\) |
−0.349138 | − | 0.937071i | \(-0.613526\pi\) | |||||||
\(98\) | −201.106 | − | 348.326i | −0.207294 | − | 0.359044i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 140.484 | − | 243.326i | 0.140484 | − | 0.243326i | ||||
\(101\) | −231.684 | + | 84.3259i | −0.228251 | + | 0.0830767i | −0.453614 | − | 0.891198i | \(-0.649866\pi\) |
0.225363 | + | 0.974275i | \(0.427643\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −814.444 | + | 683.400i | −0.779122 | + | 0.653761i | −0.943027 | − | 0.332715i | \(-0.892035\pi\) |
0.163906 | + | 0.986476i | \(0.447591\pi\) | |||||||
\(104\) | 90.4858 | + | 32.9341i | 0.0853160 | + | 0.0310525i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −261.679 | + | 1484.05i | −0.239778 | + | 1.35985i | ||||
\(107\) | 1532.32 | 1.38444 | 0.692219 | − | 0.721688i | \(-0.256633\pi\) | ||||
0.692219 | + | 0.721688i | \(0.256633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −767.656 | −0.674570 | −0.337285 | − | 0.941403i | \(-0.609509\pi\) | ||||
−0.337285 | + | 0.941403i | \(0.609509\pi\) | |||||||
\(110\) | −155.431 | + | 881.496i | −0.134726 | + | 0.764066i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −179.097 | − | 65.1858i | −0.151099 | − | 0.0549954i | ||||
\(113\) | −524.906 | + | 440.448i | −0.436982 | + | 0.366672i | −0.834579 | − | 0.550889i | \(-0.814289\pi\) |
0.397596 | + | 0.917560i | \(0.369844\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 96.5014 | − | 35.1236i | 0.0782505 | − | 0.0284808i | ||||
\(116\) | 339.758 | − | 588.479i | 0.271946 | − | 0.471025i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −344.499 | − | 596.690i | −0.268760 | − | 0.465506i | ||||
\(119\) | −951.283 | − | 798.221i | −0.732806 | − | 0.614898i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 404.061 | + | 2291.55i | 0.303577 | + | 1.72167i | ||||
\(122\) | 247.502 | + | 1403.65i | 0.183670 | + | 1.04165i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −63.7428 | − | 53.4866i | −0.0461635 | − | 0.0387358i | ||||
\(125\) | 722.382 | + | 1251.20i | 0.516894 | + | 0.895287i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1337.64 | + | 2316.86i | −0.934617 | + | 1.61880i | −0.159301 | + | 0.987230i | \(0.550924\pi\) |
−0.775316 | + | 0.631574i | \(0.782409\pi\) | |||||||
\(128\) | 120.281 | − | 43.7786i | 0.0830579 | − | 0.0302306i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −136.462 | + | 114.505i | −0.0920654 | + | 0.0772521i | ||||
\(131\) | −890.773 | − | 324.215i | −0.594101 | − | 0.216235i | 0.0274312 | − | 0.999624i | \(-0.491267\pi\) |
−0.621532 | + | 0.783389i | \(0.713490\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −94.4669 | + | 535.749i | −0.0615889 | + | 0.349288i | ||||
\(134\) | 24.2495 | 0.0156331 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 833.996 | 0.525843 | ||||||||
\(137\) | 202.017 | − | 1145.69i | 0.125981 | − | 0.714476i | −0.854739 | − | 0.519058i | \(-0.826283\pi\) |
0.980720 | − | 0.195417i | \(-0.0626062\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −679.027 | − | 247.146i | −0.414348 | − | 0.150810i | 0.126430 | − | 0.991975i | \(-0.459648\pi\) |
−0.540778 | + | 0.841165i | \(0.681870\pi\) | |||||||
\(140\) | 270.096 | − | 226.638i | 0.163052 | − | 0.136817i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 799.775 | − | 291.094i | 0.472645 | − | 0.172029i | ||||
\(143\) | −363.991 | + | 630.450i | −0.212856 | + | 0.368678i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 628.540 | + | 1088.66i | 0.359982 | + | 0.623508i | ||||
\(146\) | 901.390 | + | 756.356i | 0.510956 | + | 0.428743i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −217.299 | − | 1232.37i | −0.120688 | − | 0.684458i | ||||
\(149\) | 209.269 | + | 1186.83i | 0.115061 | + | 0.652541i | 0.986720 | + | 0.162429i | \(0.0519329\pi\) |
−0.871660 | + | 0.490112i | \(0.836956\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −539.880 | − | 453.013i | −0.290959 | − | 0.244144i | 0.485610 | − | 0.874175i | \(-0.338597\pi\) |
−0.776569 | + | 0.630032i | \(0.783042\pi\) | |||||||
\(152\) | −182.679 | − | 316.409i | −0.0974816 | − | 0.168843i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 720.439 | − | 1247.84i | 0.376978 | − | 0.652945i | ||||
\(155\) | 144.653 | − | 52.6492i | 0.0749599 | − | 0.0272832i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2277.87 | − | 1911.36i | 1.15792 | − | 0.971613i | 0.158048 | − | 0.987431i | \(-0.449480\pi\) |
0.999875 | + | 0.0158184i | \(0.00503538\pi\) | |||||||
\(158\) | 1816.88 | + | 661.291i | 0.914832 | + | 0.332971i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −41.1191 | + | 233.198i | −0.0203172 | + | 0.115224i | ||||
\(161\) | −165.313 | −0.0809222 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3208.52 | −1.54179 | −0.770893 | − | 0.636965i | \(-0.780189\pi\) | ||||
−0.770893 | + | 0.636965i | \(0.780189\pi\) | |||||||
\(164\) | −238.566 | + | 1352.98i | −0.113591 | + | 0.644205i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −601.864 | − | 219.061i | −0.281408 | − | 0.102424i | ||||
\(167\) | −782.322 | + | 656.446i | −0.362503 | + | 0.304176i | −0.805787 | − | 0.592205i | \(-0.798258\pi\) |
0.443285 | + | 0.896381i | \(0.353813\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1928.36 | − | 701.866i | 0.877725 | − | 0.319466i | ||||
\(170\) | −771.431 | + | 1336.16i | −0.348036 | + | 0.602816i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 806.157 | + | 1396.31i | 0.357377 | + | 0.618996i | ||||
\(173\) | 1264.45 | + | 1061.00i | 0.555688 | + | 0.466278i | 0.876862 | − | 0.480743i | \(-0.159633\pi\) |
−0.321174 | + | 0.947020i | \(0.604077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −145.295 | − | 824.007i | −0.0627614 | − | 0.355938i | ||||
\(176\) | 168.037 | + | 952.987i | 0.0719676 | + | 0.408148i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 152.728 | + | 128.154i | 0.0643116 | + | 0.0539639i | ||||
\(179\) | −1562.73 | − | 2706.74i | −0.652538 | − | 1.13023i | −0.982505 | − | 0.186236i | \(-0.940371\pi\) |
0.329967 | − | 0.943992i | \(-0.392962\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 383.688 | − | 664.567i | 0.157565 | − | 0.272911i | −0.776425 | − | 0.630210i | \(-0.782969\pi\) |
0.933990 | + | 0.357299i | \(0.116302\pi\) | |||||||
\(182\) | 269.465 | − | 98.0772i | 0.109748 | − | 0.0399448i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 85.0489 | − | 71.3645i | 0.0340755 | − | 0.0285927i | ||||
\(185\) | 2175.39 | + | 791.777i | 0.864529 | + | 0.314663i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1094.86 | + | 6209.28i | −0.428152 | + | 2.42817i | ||||
\(188\) | −348.283 | −0.135113 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 675.898 | 0.258078 | ||||||||
\(191\) | 825.200 | − | 4679.94i | 0.312615 | − | 1.77293i | −0.272680 | − | 0.962105i | \(-0.587910\pi\) |
0.585294 | − | 0.810821i | \(-0.300979\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1130.48 | + | 411.462i | 0.421627 | + | 0.153460i | 0.544115 | − | 0.839010i | \(-0.316865\pi\) |
−0.122489 | + | 0.992470i | \(0.539088\pi\) | |||||||
\(194\) | 2546.17 | − | 2136.49i | 0.942291 | − | 0.790676i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 755.912 | − | 275.130i | 0.275478 | − | 0.100266i | ||||
\(197\) | −2397.51 | + | 4152.62i | −0.867085 | + | 1.50184i | −0.00212390 | + | 0.999998i | \(0.500676\pi\) |
−0.864962 | + | 0.501838i | \(0.832657\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1731.13 | − | 2998.40i | −0.616666 | − | 1.06810i | −0.990090 | − | 0.140436i | \(-0.955150\pi\) |
0.373424 | − | 0.927661i | \(-0.378184\pi\) | |||||||
\(200\) | 430.469 | + | 361.206i | 0.152194 | + | 0.127706i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −85.6268 | − | 485.614i | −0.0298252 | − | 0.169147i | ||||
\(203\) | −351.392 | − | 1992.84i | −0.121492 | − | 0.689016i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1946.95 | − | 1633.69i | −0.663322 | − | 0.556594i | ||||
\(206\) | −1063.18 | − | 1841.48i | −0.359589 | − | 0.622826i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −96.2930 | + | 166.784i | −0.0320996 | + | 0.0555981i | ||||
\(209\) | 2595.55 | − | 944.703i | 0.859033 | − | 0.312663i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 534.632 | − | 448.609i | 0.174434 | − | 0.146368i | −0.551391 | − | 0.834247i | \(-0.685903\pi\) |
0.725825 | + | 0.687879i | \(0.241458\pi\) | |||||||
\(212\) | −2832.13 | − | 1030.81i | −0.917508 | − | 0.333946i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −532.169 | + | 3018.08i | −0.169992 | + | 0.964073i | ||||
\(215\) | −2982.72 | −0.946139 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −247.799 | −0.0775192 | ||||||||
\(218\) | 266.604 | − | 1511.99i | 0.0828290 | − | 0.469746i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1682.23 | − | 612.280i | −0.515526 | − | 0.187636i | ||||
\(221\) | −961.242 | + | 806.578i | −0.292580 | + | 0.245504i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4731.65 | − | 1722.18i | 1.42087 | − | 0.517155i | 0.486571 | − | 0.873641i | \(-0.338247\pi\) |
0.934301 | + | 0.356486i | \(0.116025\pi\) | |||||||
\(224\) | 190.591 | − | 330.113i | 0.0568499 | − | 0.0984669i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −685.216 | − | 1186.83i | −0.201681 | − | 0.349322i | ||||
\(227\) | −2703.98 | − | 2268.91i | −0.790616 | − | 0.663405i | 0.155282 | − | 0.987870i | \(-0.450371\pi\) |
−0.945898 | + | 0.324465i | \(0.894816\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −810.900 | − | 4598.84i | −0.233999 | − | 1.32708i | −0.844711 | − | 0.535222i | \(-0.820228\pi\) |
0.610712 | − | 0.791853i | \(-0.290883\pi\) | |||||||
\(230\) | 35.6655 | + | 202.269i | 0.0102248 | + | 0.0579879i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1041.08 | + | 873.570i | 0.294613 | + | 0.247210i | ||||
\(233\) | 1467.22 | + | 2541.30i | 0.412535 | + | 0.714532i | 0.995166 | − | 0.0982048i | \(-0.0313100\pi\) |
−0.582631 | + | 0.812737i | \(0.697977\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 322.156 | − | 557.990i | 0.0894260 | − | 0.154890i | ||||
\(236\) | 1294.89 | − | 471.302i | 0.357162 | − | 0.129996i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1902.57 | − | 1596.44i | 0.518172 | − | 0.434798i | ||||
\(239\) | 2843.49 | + | 1034.94i | 0.769581 | + | 0.280104i | 0.696821 | − | 0.717245i | \(-0.254597\pi\) |
0.0727596 | + | 0.997350i | \(0.476819\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −381.399 | + | 2163.02i | −0.101942 | + | 0.578144i | 0.890455 | + | 0.455071i | \(0.150386\pi\) |
−0.992398 | + | 0.123073i | \(0.960725\pi\) | |||||||
\(242\) | −4653.79 | −1.23619 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2850.62 | −0.747918 | ||||||||
\(245\) | −258.416 | + | 1465.55i | −0.0673860 | + | 0.382165i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 516.557 | + | 188.011i | 0.133068 | + | 0.0484327i | ||||
\(248\) | 127.486 | − | 106.973i | 0.0326425 | − | 0.0273903i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2715.27 | + | 988.276i | −0.686914 | + | 0.250016i | ||||
\(251\) | 1984.26 | − | 3436.84i | 0.498985 | − | 0.864268i | −0.501014 | − | 0.865439i | \(-0.667039\pi\) |
0.999999 | + | 0.00117126i | \(0.000372824\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 419.673 | + | 726.894i | 0.104287 | + | 0.180630i | ||||
\(254\) | −4098.77 | − | 3439.27i | −1.01252 | − | 0.849603i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 44.4539 | + | 252.111i | 0.0108530 | + | 0.0615505i | ||||
\(257\) | −613.781 | − | 3480.92i | −0.148975 | − | 0.844880i | −0.964089 | − | 0.265579i | \(-0.914437\pi\) |
0.815114 | − | 0.579301i | \(-0.196674\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2854.72 | − | 2395.40i | −0.684879 | − | 0.574682i | ||||
\(260\) | −178.138 | − | 308.545i | −0.0424911 | − | 0.0735967i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 947.941 | − | 1641.88i | 0.223527 | − | 0.387160i | ||||
\(263\) | −185.627 | + | 67.5627i | −0.0435219 | + | 0.0158407i | −0.363689 | − | 0.931520i | \(-0.618483\pi\) |
0.320167 | + | 0.947361i | \(0.396261\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4271.15 | − | 3583.92i | 0.990094 | − | 0.830787i | ||||
\(266\) | −1022.41 | − | 372.127i | −0.235669 | − | 0.0857766i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.42178 | + | 47.7623i | −0.00191956 | + | 0.0108864i | ||||
\(269\) | −5218.25 | −1.18276 | −0.591380 | − | 0.806393i | \(-0.701417\pi\) | ||||
−0.591380 | + | 0.806393i | \(0.701417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4679.73 | 1.04898 | 0.524490 | − | 0.851417i | \(-0.324256\pi\) | ||||
0.524490 | + | 0.851417i | \(0.324256\pi\) | |||||||
\(272\) | −289.644 | + | 1642.65i | −0.0645671 | + | 0.366178i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2186.42 | + | 795.790i | 0.482066 | + | 0.175458i | ||||
\(275\) | −3254.38 | + | 2730.75i | −0.713623 | + | 0.598800i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4097.74 | − | 1491.45i | 0.888842 | − | 0.323512i | 0.143069 | − | 0.989713i | \(-0.454303\pi\) |
0.745773 | + | 0.666201i | \(0.232081\pi\) | |||||||
\(278\) | 722.606 | − | 1251.59i | 0.155896 | − | 0.270019i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 352.586 | + | 610.696i | 0.0752537 | + | 0.130343i | ||||
\(281\) | 2704.01 | + | 2268.94i | 0.574049 | + | 0.481685i | 0.882987 | − | 0.469398i | \(-0.155529\pi\) |
−0.308938 | + | 0.951082i | \(0.599973\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −128.070 | − | 726.321i | −0.0269010 | − | 0.152563i | 0.968399 | − | 0.249408i | \(-0.0802360\pi\) |
−0.995299 | + | 0.0968450i | \(0.969125\pi\) | |||||||
\(284\) | 295.585 | + | 1676.35i | 0.0617596 | + | 0.350256i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1115.33 | − | 935.875i | −0.230598 | − | 0.193495i | ||||
\(287\) | 2045.64 | + | 3543.16i | 0.420734 | + | 0.728732i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2977.48 | + | 5157.15i | −0.606042 | + | 1.04969i | ||||
\(290\) | −2362.54 | + | 859.894i | −0.478390 | + | 0.174120i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1802.78 | + | 1512.71i | −0.361300 | + | 0.303167i | ||||
\(293\) | 4406.96 | + | 1604.00i | 0.878694 | + | 0.319818i | 0.741683 | − | 0.670751i | \(-0.234028\pi\) |
0.137011 | + | 0.990569i | \(0.456250\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −442.671 | + | 2510.51i | −0.0873671 | + | 0.495484i | ||||
\(296\) | 2502.75 | 0.491451 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2410.27 | −0.468534 | ||||||||
\(299\) | −29.0068 | + | 164.506i | −0.00561039 | + | 0.0318181i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4511.88 | + | 1642.19i | 0.863987 | + | 0.314466i | ||||
\(302\) | 1079.76 | − | 906.026i | 0.205739 | − | 0.172636i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 686.647 | − | 249.919i | 0.129546 | − | 0.0471508i | ||||
\(305\) | 2636.77 | − | 4567.01i | 0.495019 | − | 0.857398i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1929.12 | − | 3341.33i | −0.358634 | − | 0.621172i | 0.629099 | − | 0.777325i | \(-0.283424\pi\) |
−0.987733 | + | 0.156153i | \(0.950091\pi\) | |||||||
\(308\) | 2207.55 | + | 1852.36i | 0.408399 | + | 0.342688i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 53.4614 | + | 303.195i | 0.00979486 | + | 0.0555494i | ||||
\(311\) | 809.595 | + | 4591.44i | 0.147614 | + | 0.837160i | 0.965231 | + | 0.261398i | \(0.0841834\pi\) |
−0.817617 | + | 0.575762i | \(0.804705\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1018.62 | + | 854.721i | 0.183948 | + | 0.154350i | 0.730112 | − | 0.683328i | \(-0.239468\pi\) |
−0.546164 | + | 0.837678i | \(0.683912\pi\) | |||||||
\(314\) | 2973.55 | + | 5150.34i | 0.534418 | + | 0.925639i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1933.49 | + | 3348.90i | −0.344200 | + | 0.596171i | ||||
\(317\) | 3291.09 | − | 1197.86i | 0.583110 | − | 0.212235i | −0.0335863 | − | 0.999436i | \(-0.510693\pi\) |
0.616696 | + | 0.787201i | \(0.288471\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7870.64 | + | 6604.25i | −1.38141 | + | 1.15914i | ||||
\(320\) | −445.030 | − | 161.978i | −0.0777435 | − | 0.0282963i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 57.4125 | − | 325.603i | 0.00993626 | − | 0.0563513i | ||||
\(323\) | 4761.04 | 0.820159 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −845.478 | −0.144304 | ||||||||
\(326\) | 1114.31 | − | 6319.56i | 0.189312 | − | 1.07364i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2581.99 | − | 939.767i | −0.434654 | − | 0.158201i | ||||
\(329\) | −794.526 | + | 666.687i | −0.133142 | + | 0.111719i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −842.078 | + | 306.491i | −0.139833 | + | 0.0508951i | −0.410989 | − | 0.911640i | \(-0.634816\pi\) |
0.271155 | + | 0.962536i | \(0.412594\pi\) | |||||||
\(332\) | 640.490 | − | 1109.36i | 0.105878 | − | 0.183386i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1021.25 | − | 1768.86i | −0.167306 | − | 0.289783i | ||||
\(335\) | −68.7307 | − | 57.6719i | −0.0112094 | − | 0.00940583i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1035.27 | + | 5871.30i | 0.167343 | + | 0.949051i | 0.946615 | + | 0.322365i | \(0.104478\pi\) |
−0.779272 | + | 0.626686i | \(0.784411\pi\) | |||||||
\(338\) | 712.694 | + | 4041.89i | 0.114691 | + | 0.650443i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2363.80 | − | 1983.47i | −0.377045 | − | 0.316378i | ||||
\(341\) | 629.076 | + | 1089.59i | 0.0999014 | + | 0.173034i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3240.67 | − | 5613.01i | 0.510146 | − | 0.883598i | ||||
\(344\) | −3030.16 | + | 1102.89i | −0.474928 | + | 0.172860i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2528.89 | + | 2121.99i | −0.392931 | + | 0.329708i | ||||
\(347\) | 7751.93 | + | 2821.47i | 1.19927 | + | 0.436497i | 0.862968 | − | 0.505259i | \(-0.168603\pi\) |
0.336298 | + | 0.941756i | \(0.390825\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 333.247 | − | 1889.94i | 0.0511127 | − | 0.289874i | −0.948528 | − | 0.316694i | \(-0.897427\pi\) |
0.999640 | + | 0.0268201i | \(0.00853811\pi\) | |||||||
\(350\) | 1673.44 | 0.255569 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1935.38 | −0.293057 | ||||||||
\(353\) | −549.740 | + | 3117.73i | −0.0828887 | + | 0.470085i | 0.914904 | + | 0.403672i | \(0.132266\pi\) |
−0.997792 | + | 0.0664125i | \(0.978845\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2959.11 | − | 1077.03i | −0.442403 | − | 0.161022i | ||||
\(356\) | −305.457 | + | 256.308i | −0.0454752 | + | 0.0381582i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5873.96 | − | 2137.95i | 0.867174 | − | 0.315626i | ||||
\(359\) | −244.067 | + | 422.736i | −0.0358812 | + | 0.0621480i | −0.883408 | − | 0.468604i | \(-0.844757\pi\) |
0.847527 | + | 0.530752i | \(0.178090\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2386.64 | + | 4133.78i | 0.347957 | + | 0.602680i | ||||
\(362\) | 1175.69 | + | 986.519i | 0.170698 | + | 0.143233i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 99.5901 | + | 564.804i | 0.0143405 | + | 0.0813290i | ||||
\(365\) | −756.001 | − | 4287.49i | −0.108413 | − | 0.614843i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2096.30 | + | 1759.01i | 0.298164 | + | 0.250189i | 0.779580 | − | 0.626303i | \(-0.215433\pi\) |
−0.481416 | + | 0.876492i | \(0.659877\pi\) | |||||||
\(368\) | 111.023 | + | 192.298i | 0.0157269 | + | 0.0272398i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2315.00 | + | 4009.70i | −0.325273 | + | 0.563390i | ||||
\(371\) | −8434.04 | + | 3069.74i | −1.18025 | + | 0.429576i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −104.296 | + | 87.5151i | −0.0144779 | + | 0.0121484i | −0.649998 | − | 0.759936i | \(-0.725230\pi\) |
0.635520 | + | 0.772084i | \(0.280786\pi\) | |||||||
\(374\) | −11849.7 | − | 4312.92i | −1.63832 | − | 0.596299i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 120.958 | − | 685.984i | 0.0165902 | − | 0.0940876i | ||||
\(377\) | −2044.77 | −0.279340 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 839.393 | 0.113764 | 0.0568822 | − | 0.998381i | \(-0.481884\pi\) | ||||
0.0568822 | + | 0.998381i | \(0.481884\pi\) | |||||||
\(380\) | −234.737 | + | 1331.26i | −0.0316888 | + | 0.179716i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8931.10 | + | 3250.65i | 1.19622 | + | 0.435387i | ||||
\(383\) | 384.276 | − | 322.446i | 0.0512678 | − | 0.0430188i | −0.616794 | − | 0.787125i | \(-0.711569\pi\) |
0.668062 | + | 0.744106i | \(0.267124\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5009.64 | + | 1823.36i | −0.663155 | + | 0.241369i | ||||
\(386\) | −1203.03 | + | 2083.72i | −0.158634 | + | 0.274763i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3323.79 | + | 5756.97i | 0.434897 | + | 0.753263i | ||||
\(389\) | 2189.47 | + | 1837.18i | 0.285374 | + | 0.239457i | 0.774226 | − | 0.632910i | \(-0.218140\pi\) |
−0.488852 | + | 0.872367i | \(0.662584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 251.229 | + | 1424.79i | 0.0324941 | + | 0.184283i | ||||
\(392\) | 279.374 | + | 1584.41i | 0.0359962 | + | 0.204145i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7346.41 | − | 6164.37i | −0.939357 | − | 0.788214i | ||||
\(395\) | −3576.88 | − | 6195.33i | −0.455626 | − | 0.789167i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1449.95 | + | 2511.38i | −0.183301 | + | 0.317487i | −0.943003 | − | 0.332785i | \(-0.892012\pi\) |
0.759701 | + | 0.650272i | \(0.225345\pi\) | |||||||
\(398\) | 6506.92 | − | 2368.33i | 0.819504 | − | 0.298275i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −860.938 | + | 722.413i | −0.107617 | + | 0.0903016i | ||||
\(401\) | −8600.41 | − | 3130.29i | −1.07103 | − | 0.389824i | −0.254469 | − | 0.967081i | \(-0.581901\pi\) |
−0.816562 | + | 0.577257i | \(0.804123\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −43.4803 | + | 246.589i | −0.00537446 | + | 0.0304801i | ||||
\(404\) | 986.210 | 0.121450 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4047.17 | 0.494724 | ||||||||
\(407\) | −3285.60 | + | 18633.5i | −0.400150 | + | 2.26936i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14107.1 | − | 5134.57i | −1.70551 | − | 0.620753i | −0.709073 | − | 0.705135i | \(-0.750886\pi\) |
−0.996433 | + | 0.0843820i | \(0.973108\pi\) | |||||||
\(410\) | 3893.91 | − | 3267.38i | 0.469040 | − | 0.393571i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3996.25 | − | 1454.52i | 0.477867 | − | 0.173929i | ||||
\(413\) | 2051.82 | − | 3553.86i | 0.244464 | − | 0.423424i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1184.88 | + | 2052.28i | 0.140153 | + | 0.242753i | ||||
\(416\) | −295.059 | − | 247.584i | −0.0347751 | − | 0.0291798i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 959.277 | + | 5440.33i | 0.112248 | + | 0.636591i | ||||
\(419\) | −1176.74 | − | 6673.65i | −0.137202 | − | 0.778112i | −0.973301 | − | 0.229533i | \(-0.926280\pi\) |
0.836099 | − | 0.548579i | \(-0.184831\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3081.29 | − | 2585.51i | −0.356705 | − | 0.299311i | 0.446771 | − | 0.894648i | \(-0.352574\pi\) |
−0.803476 | + | 0.595338i | \(0.797018\pi\) | |||||||
\(422\) | 697.912 | + | 1208.82i | 0.0805067 | + | 0.139442i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3013.89 | − | 5220.22i | 0.345207 | − | 0.597916i | ||||
\(425\) | −6881.10 | + | 2504.52i | −0.785370 | + | 0.285851i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6503.01 | + | 5456.67i | −0.737008 | + | 0.618424i | ||||
\(428\) | −5759.63 | − | 2096.34i | −0.650473 | − | 0.236753i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1035.89 | − | 5874.82i | 0.116174 | − | 0.658858i | ||||
\(431\) | 9048.23 | 1.01122 | 0.505612 | − | 0.862761i | \(-0.331267\pi\) | ||||
0.505612 | + | 0.862761i | \(0.331267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7204.53 | 0.799602 | 0.399801 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399801 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(434\) | 86.0596 | − | 488.068i | 0.00951842 | − | 0.0539816i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2885.44 | + | 1050.22i | 0.316944 | + | 0.115358i | ||||
\(437\) | 485.520 | − | 407.399i | 0.0531477 | − | 0.0445962i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2182.85 | − | 794.494i | 0.237316 | − | 0.0863761i | −0.220624 | − | 0.975359i | \(-0.570809\pi\) |
0.457941 | + | 0.888983i | \(0.348587\pi\) | |||||||
\(440\) | 1790.19 | − | 3100.70i | 0.193963 | − | 0.335954i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1254.81 | − | 2173.40i | −0.135035 | − | 0.233887i | ||||
\(443\) | −6112.27 | − | 5128.80i | −0.655536 | − | 0.550060i | 0.253209 | − | 0.967412i | \(-0.418514\pi\) |
−0.908745 | + | 0.417351i | \(0.862958\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −128.094 | − | 726.457i | −0.0136455 | − | 0.0773873i | ||||
\(446\) | 1748.75 | + | 9917.63i | 0.185663 | + | 1.05294i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 584.004 | + | 490.037i | 0.0615883 | + | 0.0516788i | ||||
\(449\) | 1253.26 | + | 2170.70i | 0.131726 | + | 0.228155i | 0.924342 | − | 0.381565i | \(-0.124615\pi\) |
−0.792616 | + | 0.609721i | \(0.791282\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10386.4 | − | 17989.7i | 1.08442 | − | 1.87828i | ||||
\(452\) | 2575.57 | − | 937.431i | 0.268019 | − | 0.0975509i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5407.97 | − | 4537.83i | 0.559050 | − | 0.469098i | ||||
\(455\) | −997.000 | − | 362.878i | −0.102725 | − | 0.0373890i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1951.37 | − | 11066.8i | 0.199740 | − | 1.13278i | −0.705764 | − | 0.708447i | \(-0.749396\pi\) |
0.905505 | − | 0.424337i | \(-0.139493\pi\) | |||||||
\(458\) | 9339.58 | 0.952860 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −410.779 | −0.0416362 | ||||||||
\(461\) | 1632.42 | − | 9257.91i | 0.164923 | − | 0.935323i | −0.784222 | − | 0.620481i | \(-0.786937\pi\) |
0.949144 | − | 0.314842i | \(-0.101951\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1847.54 | + | 672.448i | 0.185448 | + | 0.0674974i | 0.433075 | − | 0.901358i | \(-0.357429\pi\) |
−0.247627 | + | 0.968855i | \(0.579651\pi\) | |||||||
\(464\) | −2082.16 | + | 1747.14i | −0.208323 | + | 0.174804i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5514.94 | + | 2007.27i | −0.548229 | + | 0.199539i | ||||
\(467\) | 7125.38 | − | 12341.5i | 0.706046 | − | 1.22291i | −0.260267 | − | 0.965537i | \(-0.583811\pi\) |
0.966313 | − | 0.257370i | \(-0.0828561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 72.2146 | + | 125.079i | 0.00710994 | + | 0.0123148i | ||||
\(470\) | 987.142 | + | 828.310i | 0.0968797 | + | 0.0812917i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 478.573 | + | 2714.12i | 0.0466697 | + | 0.264677i | ||||
\(473\) | −4233.27 | − | 24008.0i | −0.411513 | − | 2.33381i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2457.42 | + | 2062.02i | 0.237377 | + | 0.199183i | ||||
\(476\) | 2483.62 | + | 4301.76i | 0.239153 | + | 0.414225i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3025.97 | + | 5241.14i | −0.289550 | + | 0.501515i | ||||
\(479\) | −2777.79 | + | 1011.03i | −0.264970 | + | 0.0964411i | −0.471089 | − | 0.882086i | \(-0.656139\pi\) |
0.206119 | + | 0.978527i | \(0.433917\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2884.61 | + | 2420.47i | −0.273444 | + | 0.229447i | ||||
\(482\) | −4127.87 | − | 1502.42i | −0.390081 | − | 0.141978i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1616.24 | − | 9166.18i | 0.151789 | − | 0.860836i | ||||
\(485\) | −12297.8 | −1.15137 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4304.17 | 0.400494 | 0.200247 | − | 0.979745i | \(-0.435826\pi\) | ||||
0.200247 | + | 0.979745i | \(0.435826\pi\) | |||||||
\(488\) | 990.008 | − | 5614.62i | 0.0918352 | − | 0.520823i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2796.82 | − | 1017.96i | −0.257852 | − | 0.0938504i | ||||
\(491\) | 2624.29 | − | 2202.04i | 0.241207 | − | 0.202396i | −0.514168 | − | 0.857689i | \(-0.671899\pi\) |
0.755375 | + | 0.655293i | \(0.227455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16641.8 | + | 6057.12i | −1.52030 | + | 0.553345i | ||||
\(494\) | −549.709 | + | 952.123i | −0.0500659 | + | 0.0867167i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 166.421 | + | 288.249i | 0.0150655 | + | 0.0260943i | ||||
\(497\) | 3883.18 | + | 3258.38i | 0.350472 | + | 0.294081i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2427.85 | − | 13769.0i | −0.217806 | − | 1.23524i | −0.875970 | − | 0.482366i | \(-0.839777\pi\) |
0.658163 | − | 0.752875i | \(-0.271334\pi\) | |||||||
\(500\) | −1003.52 | − | 5691.26i | −0.0897577 | − | 0.509041i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6080.12 | + | 5101.83i | 0.540576 | + | 0.453597i | ||||
\(503\) | 80.5977 | + | 139.599i | 0.00714448 | + | 0.0123746i | 0.869576 | − | 0.493800i | \(-0.164392\pi\) |
−0.862431 | + | 0.506175i | \(0.831059\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −912.226 | + | 1580.02i | −0.0803832 | + | 0.139228i | ||||
\(506\) | −1577.45 | + | 574.146i | −0.138590 | + | 0.0504425i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8197.53 | − | 6878.55i | 0.715958 | − | 0.600760i | ||||
\(509\) | 2690.05 | + | 979.096i | 0.234252 | + | 0.0852607i | 0.456479 | − | 0.889734i | \(-0.349110\pi\) |
−0.222227 | + | 0.974995i | \(0.571333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1216.97 | + | 6901.79i | −0.105354 | + | 0.597490i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7069.25 | 0.606636 | ||||||||
\(515\) | −1366.16 | + | 7747.86i | −0.116893 | + | 0.662935i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4948.51 | + | 1801.11i | 0.420958 | + | 0.153216i | ||||
\(518\) | 5709.44 | − | 4790.79i | 0.484283 | − | 0.406362i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 669.581 | − | 243.708i | 0.0564675 | − | 0.0205525i | ||||
\(521\) | −6324.76 | + | 10954.8i | −0.531848 | + | 0.921187i | 0.467461 | + | 0.884014i | \(0.345169\pi\) |
−0.999309 | + | 0.0371736i | \(0.988165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7489.19 | + | 12971.7i | 0.626155 | + | 1.08453i | 0.988316 | + | 0.152417i | \(0.0487058\pi\) |
−0.362161 | + | 0.932116i | \(0.617961\pi\) | |||||||
\(524\) | 2904.66 | + | 2437.30i | 0.242158 | + | 0.203195i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −68.6050 | − | 389.078i | −0.00568692 | − | 0.0322521i | ||||
\(527\) | 376.584 | + | 2135.71i | 0.0311276 | + | 0.176533i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9172.92 | − | 7697.00i | −0.753918 | − | 0.632613i | ||||
\(530\) | 5575.59 | + | 9657.21i | 0.456959 | + | 0.791476i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1088.03 | − | 1884.52i | 0.0886691 | − | 0.153579i | ||||
\(533\) | 3884.80 | − | 1413.95i | 0.315703 | − | 0.114906i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8686.13 | − | 7288.52i | 0.701933 | − | 0.588991i | ||||
\(536\) | −91.1485 | − | 33.1753i | −0.00734518 | − | 0.00267343i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1812.28 | − | 10278.0i | 0.145229 | − | 0.823632i | ||||
\(539\) | −12163.0 | −0.971982 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6564.59 | 0.521689 | 0.260844 | − | 0.965381i | \(-0.415999\pi\) | ||||
0.260844 | + | 0.965381i | \(0.415999\pi\) | |||||||
\(542\) | −1625.25 | + | 9217.28i | −0.128802 | + | 0.730472i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3134.80 | − | 1140.97i | −0.247065 | − | 0.0899244i | ||||
\(545\) | −4351.55 | + | 3651.38i | −0.342018 | + | 0.286987i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5715.92 | + | 2080.43i | −0.446792 | + | 0.162619i | −0.555611 | − | 0.831443i | \(-0.687515\pi\) |
0.108819 | + | 0.994062i | \(0.465293\pi\) | |||||||
\(548\) | −2326.74 | + | 4030.02i | −0.181374 | + | 0.314150i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4248.29 | − | 7358.25i | −0.329359 | − | 0.570467i | ||||
\(551\) | 5943.22 | + | 4986.96i | 0.459510 | + | 0.385574i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1999.69 | + | 11340.8i | 0.153771 | + | 0.872080i | ||||
\(554\) | 1514.46 | + | 8588.95i | 0.116143 | + | 0.658681i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2214.19 | + | 1857.93i | 0.168890 | + | 0.141715i | ||||
\(557\) | −10541.0 | − | 18257.6i | −0.801863 | − | 1.38887i | −0.918389 | − | 0.395680i | \(-0.870509\pi\) |
0.116525 | − | 0.993188i | \(-0.462824\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2425.85 | − | 4201.70i | 0.183547 | − | 0.317912i | ||||
\(560\) | −1325.29 | + | 482.366i | −0.100007 | + | 0.0363994i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5408.02 | + | 4537.87i | −0.405914 | + | 0.340602i | ||||
\(563\) | 11759.2 | + | 4280.00i | 0.880269 | + | 0.320392i | 0.742318 | − | 0.670047i | \(-0.233726\pi\) |
0.137951 | + | 0.990439i | \(0.455948\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −880.482 | + | 4993.46i | −0.0655614 | + | 0.371817i | ||||
\(566\) | 1475.05 | 0.109542 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3404.41 | −0.251489 | ||||||||
\(569\) | 1170.85 | − | 6640.20i | 0.0862644 | − | 0.489230i | −0.910812 | − | 0.412821i | \(-0.864543\pi\) |
0.997077 | − | 0.0764088i | \(-0.0243454\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20826.8 | − | 7580.35i | −1.52640 | − | 0.555565i | −0.563665 | − | 0.826003i | \(-0.690609\pi\) |
−0.962737 | + | 0.270438i | \(0.912832\pi\) | |||||||
\(572\) | 2230.66 | − | 1871.75i | 0.163057 | − | 0.136821i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7689.11 | + | 2798.61i | −0.559124 | + | 0.203504i | ||||
\(575\) | −487.408 | + | 844.216i | −0.0353501 | + | 0.0612282i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4751.88 | − | 8230.49i | −0.342848 | − | 0.593830i | 0.642113 | − | 0.766610i | \(-0.278058\pi\) |
−0.984960 | + | 0.172781i | \(0.944725\pi\) | |||||||
\(578\) | −9123.54 | − | 7655.56i | −0.656555 | − | 0.550915i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −873.159 | − | 4951.93i | −0.0625103 | − | 0.354513i | ||||
\(581\) | −662.422 | − | 3756.78i | −0.0473010 | − | 0.268257i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34909.0 | + | 29292.1i | 2.47990 | + | 2.08089i | ||||
\(584\) | −2353.36 | − | 4076.14i | −0.166751 | − | 0.288822i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4689.79 | + | 8122.95i | −0.330603 | + | 0.572621i | ||||
\(587\) | 7375.59 | − | 2684.50i | 0.518609 | − | 0.188758i | −0.0694363 | − | 0.997586i | \(-0.522120\pi\) |
0.588045 | + | 0.808828i | \(0.299898\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 727.779 | − | 610.679i | 0.0509127 | − | 0.0427209i | ||||
\(590\) | −4791.01 | − | 1743.78i | −0.334309 | − | 0.121679i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −869.197 | + | 4929.46i | −0.0603442 | + | 0.342229i | ||||
\(593\) | 11931.9 | 0.826277 | 0.413139 | − | 0.910668i | \(-0.364432\pi\) | ||||
0.413139 | + | 0.910668i | \(0.364432\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9189.22 | −0.633145 | ||||||||
\(596\) | 837.078 | − | 4747.30i | 0.0575303 | − | 0.326270i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −313.939 | − | 114.264i | −0.0214681 | − | 0.00781375i | ||||
\(599\) | −15419.1 | + | 12938.1i | −1.05176 | + | 0.882533i | −0.993278 | − | 0.115755i | \(-0.963071\pi\) |
−0.0584842 | + | 0.998288i | \(0.518627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1748.24 | − | 636.306i | 0.118656 | − | 0.0431871i | −0.282010 | − | 0.959411i | \(-0.591001\pi\) |
0.400666 | + | 0.916224i | \(0.368779\pi\) | |||||||
\(602\) | −4801.44 | + | 8316.34i | −0.325070 | + | 0.563037i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1409.53 | + | 2441.37i | 0.0949550 | + | 0.164467i | ||||
\(605\) | 13190.3 | + | 11068.0i | 0.886382 | + | 0.743763i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2233.48 | + | 12666.7i | 0.149348 | + | 0.846993i | 0.963773 | + | 0.266724i | \(0.0859413\pi\) |
−0.814425 | + | 0.580269i | \(0.802948\pi\) | |||||||
\(608\) | 253.775 | + | 1439.23i | 0.0169275 | + | 0.0960006i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8079.52 | + | 6779.52i | 0.536279 | + | 0.449992i | ||||
\(611\) | 524.019 | + | 907.628i | 0.0346965 | + | 0.0600961i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13134.7 | + | 22749.9i | −0.865422 | + | 1.49896i | 0.00120540 | + | 0.999999i | \(0.499616\pi\) |
−0.866627 | + | 0.498956i | \(0.833717\pi\) | |||||||
\(614\) | 7251.11 | − | 2639.19i | 0.476598 | − | 0.173467i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4415.11 | + | 3704.71i | −0.288782 | + | 0.242317i | ||||
\(617\) | 6412.47 | + | 2333.95i | 0.418406 | + | 0.152287i | 0.542639 | − | 0.839966i | \(-0.317425\pi\) |
−0.124234 | + | 0.992253i | \(0.539647\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3289.67 | − | 18656.6i | 0.213607 | − | 1.21143i | −0.669700 | − | 0.742632i | \(-0.733577\pi\) |
0.883307 | − | 0.468795i | \(-0.155312\pi\) | |||||||
\(620\) | −615.744 | −0.0398853 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9324.54 | −0.601093 | ||||||||
\(623\) | −206.199 | + | 1169.41i | −0.0132604 | + | 0.0752032i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1795.53 | + | 653.519i | 0.114914 | + | 0.0418252i | ||||
\(626\) | −2037.23 | + | 1709.44i | −0.130071 | + | 0.109142i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11176.9 | + | 4068.06i | −0.710202 | + | 0.258492i | ||||
\(629\) | −16306.9 | + | 28244.4i | −1.03370 | + | 1.79043i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2944.48 | − | 5099.98i | −0.185765 | − | 0.321755i | 0.758069 | − | 0.652174i | \(-0.226143\pi\) |
−0.943834 | + | 0.330420i | \(0.892810\pi\) | |||||||
\(632\) | −5924.54 | − | 4971.28i | −0.372889 | − | 0.312891i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1216.34 | + | 6898.19i | 0.0761938 | + | 0.432117i | ||||
\(635\) | 3437.66 | + | 19495.9i | 0.214833 | + | 1.21838i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1854.32 | − | 1555.96i | −0.115339 | − | 0.0967806i | ||||
\(638\) | −10274.4 | − | 17795.8i | −0.637566 | − | 1.10430i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 473.591 | − | 820.283i | 0.0292505 | − | 0.0506633i | ||||
\(641\) | 6633.97 | − | 2414.57i | 0.408777 | − | 0.148783i | −0.129443 | − | 0.991587i | \(-0.541319\pi\) |
0.538220 | + | 0.842804i | \(0.319097\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9885.05 | + | 8294.54i | −0.606265 | + | 0.508717i | −0.893452 | − | 0.449158i | \(-0.851724\pi\) |
0.287188 | + | 0.957874i | \(0.407280\pi\) | |||||||
\(644\) | 621.373 | + | 226.161i | 0.0380210 | + | 0.0138385i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1653.49 | + | 9377.42i | −0.100706 | + | 0.571130i | ||||
\(647\) | 23050.1 | 1.40061 | 0.700305 | − | 0.713844i | \(-0.253047\pi\) | ||||
0.700305 | + | 0.713844i | \(0.253047\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20835.5 | −1.26019 | ||||||||
\(650\) | 293.632 | − | 1665.27i | 0.0177187 | − | 0.100488i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12060.1 | + | 4389.52i | 0.724402 | + | 0.263661i | ||||
\(653\) | 4397.76 | − | 3690.16i | 0.263549 | − | 0.221144i | −0.501431 | − | 0.865197i | \(-0.667193\pi\) |
0.764981 | + | 0.644053i | \(0.222749\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6591.59 | + | 2399.14i | −0.393213 | + | 0.143118i | ||||
\(656\) | 2747.69 | − | 4759.15i | 0.163536 | − | 0.283252i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1037.18 | − | 1796.45i | −0.0614491 | − | 0.106433i | ||||
\(659\) | −20829.1 | − | 17477.7i | −1.23124 | − | 1.03313i | −0.998157 | − | 0.0606773i | \(-0.980674\pi\) |
−0.233084 | − | 0.972457i | \(-0.574882\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4738.68 | − | 26874.4i | −0.278840 | − | 1.58138i | −0.726493 | − | 0.687174i | \(-0.758851\pi\) |
0.447653 | − | 0.894207i | \(-0.352260\pi\) | |||||||
\(662\) | −311.220 | − | 1765.01i | −0.0182717 | − | 0.103624i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1962.58 | + | 1646.80i | 0.114703 | + | 0.0962472i | ||||
\(665\) | 2012.81 | + | 3486.29i | 0.117374 | + | 0.203297i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1178.79 | + | 2041.72i | −0.0684300 | + | 0.118524i | ||||
\(668\) | 3838.64 | − | 1397.15i | 0.222338 | − | 0.0809243i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 137.461 | − | 115.344i | 0.00792626 | − | 0.00665092i | ||||
\(671\) | 40502.3 | + | 14741.6i | 2.33022 | + | 0.848130i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 888.691 | − | 5040.02i | 0.0509012 | − | 0.288675i | −0.948722 | − | 0.316111i | \(-0.897623\pi\) |
0.999624 | + | 0.0274354i | \(0.00873406\pi\) | |||||||
\(674\) | −11923.8 | −0.681433 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8208.48 | −0.467028 | ||||||||
\(677\) | 433.103 | − | 2456.25i | 0.0245871 | − | 0.139441i | −0.970043 | − | 0.242933i | \(-0.921891\pi\) |
0.994630 | + | 0.103492i | \(0.0330017\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18602.5 | + | 6770.75i | 1.05140 | + | 0.382677i | ||||
\(680\) | 4727.60 | − | 3966.93i | 0.266611 | − | 0.223713i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2364.55 | + | 860.627i | −0.132762 | + | 0.0483213i | ||||
\(683\) | −1280.87 | + | 2218.53i | −0.0717586 | + | 0.124289i | −0.899672 | − | 0.436566i | \(-0.856194\pi\) |
0.827914 | + | 0.560856i | \(0.189528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4304.37 | − | 7455.39i | −0.240090 | − | 0.415848i | ||||
\(686\) | 9930.00 | + | 8332.26i | 0.552666 | + | 0.463742i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1119.90 | − | 6351.28i | −0.0620579 | − | 0.351948i | ||||
\(689\) | 1574.86 | + | 8931.49i | 0.0870791 | + | 0.493850i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16748.0 | + | 14053.2i | 0.922032 | + | 0.773677i | 0.974370 | − | 0.224952i | \(-0.0722227\pi\) |
−0.0523374 | + | 0.998629i | \(0.516667\pi\) | |||||||
\(692\) | −3301.23 | − | 5717.90i | −0.181350 | − | 0.314107i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8249.43 | + | 14288.4i | −0.451216 | + | 0.781529i | ||||
\(695\) | −5024.70 | + | 1828.84i | −0.274241 | + | 0.0998157i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27428.8 | − | 23015.5i | 1.49059 | − | 1.25075i | ||||
\(698\) | 3606.72 | + | 1312.74i | 0.195582 | + | 0.0711861i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −581.179 | + | 3296.03i | −0.0313807 | + | 0.177969i | ||||
\(701\) | 6799.85 | 0.366372 | 0.183186 | − | 0.983078i | \(-0.441359\pi\) | ||||
0.183186 | + | 0.983078i | \(0.441359\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14287.5 | 0.766519 | ||||||||
\(704\) | 672.149 | − | 3811.95i | 0.0359838 | − | 0.204074i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5949.81 | − | 2165.55i | −0.317173 | − | 0.115441i | ||||
\(707\) | 2249.81 | − | 1887.81i | 0.119678 | − | 0.100422i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11713.5 | + | 4263.38i | −0.620468 | + | 0.225832i | −0.633077 | − | 0.774089i | \(-0.718208\pi\) |
0.0126095 | + | 0.999920i | \(0.495986\pi\) | |||||||
\(710\) | 3149.02 | − | 5454.26i | 0.166451 | − | 0.288302i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −398.745 | − | 690.647i | −0.0209882 | − | 0.0363527i | ||||
\(713\) | 221.155 | + | 185.571i | 0.0116161 | + | 0.00974710i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 935.435 | + | 5305.11i | 0.0489277 | + | 0.277483i | ||||
\(716\) | 2170.93 | + | 12311.9i | 0.113312 | + | 0.642624i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −747.863 | − | 627.532i | −0.0388719 | − | 0.0326174i | ||||
\(719\) | −784.462 | − | 1358.73i | −0.0406892 | − | 0.0704757i | 0.844964 | − | 0.534824i | \(-0.179622\pi\) |
−0.885653 | + | 0.464348i | \(0.846289\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6332.26 | − | 10967.8i | 0.327081 | − | 0.566522i | ||||
\(722\) | −8970.83 | + | 3265.12i | −0.462410 | + | 0.168303i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2351.38 | + | 1973.04i | −0.120702 | + | 0.101281i | ||||
\(725\) | −11213.1 | − | 4081.22i | −0.574403 | − | 0.209066i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2390.05 | − | 13554.7i | 0.121929 | − | 0.691492i | −0.861156 | − | 0.508341i | \(-0.830259\pi\) |
0.983085 | − | 0.183151i | \(-0.0586298\pi\) | |||||||
\(728\) | −1147.03 | −0.0583955 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8707.27 | 0.441466 | ||||||||
\(731\) | 7296.83 | − | 41382.4i | 0.369197 | − | 2.09382i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34358.7 | + | 12505.6i | 1.73133 | + | 0.630154i | 0.998724 | − | 0.0504942i | \(-0.0160797\pi\) |
0.732610 | + | 0.680648i | \(0.238302\pi\) | |||||||
\(734\) | −4192.60 | + | 3518.01i | −0.210834 | + | 0.176910i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −417.312 | + | 151.889i | −0.0208999 | + | 0.00760694i | ||||
\(737\) | 366.656 | − | 635.068i | 0.0183256 | − | 0.0317409i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8065.87 | − | 13970.5i | −0.401499 | − | 0.695417i | 0.592408 | − | 0.805638i | \(-0.298177\pi\) |
−0.993907 | + | 0.110221i | \(0.964844\pi\) | |||||||
\(740\) | −7093.58 | − | 5952.22i | −0.352385 | − | 0.295686i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3117.09 | − | 17677.9i | −0.154221 | − | 0.874632i | ||||
\(743\) | 3481.71 | + | 19745.7i | 0.171913 | + | 0.974967i | 0.941647 | + | 0.336602i | \(0.109278\pi\) |
−0.769734 | + | 0.638365i | \(0.779611\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6831.45 | + | 5732.26i | 0.335953 | + | 0.281898i | ||||
\(746\) | −136.149 | − | 235.818i | −0.00668201 | − | 0.0115736i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12610.1 | − | 21841.4i | 0.616407 | − | 1.06765i | ||||
\(749\) | −17152.1 | + | 6242.84i | −0.836746 | + | 0.304551i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13793.4 | − | 11574.0i | 0.670210 | − | 0.562373i | −0.242918 | − | 0.970047i | \(-0.578105\pi\) |
0.913127 | + | 0.407674i | \(0.133660\pi\) | |||||||
\(752\) | 1309.12 | + | 476.480i | 0.0634822 | + | 0.0231056i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 710.142 | − | 4027.41i | 0.0342995 | − | 0.194522i | ||||
\(755\) | −5215.14 | −0.251389 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33197.8 | −1.59392 | −0.796959 | − | 0.604034i | \(-0.793559\pi\) | ||||
−0.796959 | + | 0.604034i | \(0.793559\pi\) | |||||||
\(758\) | −291.518 | + | 1653.28i | −0.0139689 | + | 0.0792215i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2540.54 | − | 924.683i | −0.121257 | − | 0.0441339i | ||||
\(761\) | −12058.7 | + | 10118.4i | −0.574412 | + | 0.481989i | −0.883107 | − | 0.469172i | \(-0.844552\pi\) |
0.308695 | + | 0.951161i | \(0.400108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8592.79 | − | 3127.52i | 0.407706 | − | 0.148393i | ||||
\(764\) | −9504.28 | + | 16461.9i | −0.450069 | + | 0.779542i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 501.636 | + | 868.860i | 0.0236617 | + | 0.0409833i | ||||
\(767\) | −3176.48 | − | 2665.38i | −0.149539 | − | 0.125478i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1156.79 | + | 6560.48i | 0.0542456 | + | 0.307642i | 0.999843 | − | 0.0176957i | \(-0.00563302\pi\) |
−0.945598 | + | 0.325338i | \(0.894522\pi\) | |||||||
\(770\) | −1851.49 | − | 10500.3i | −0.0866532 | − | 0.491435i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3686.31 | − | 3093.18i | −0.171857 | − | 0.144205i | ||||
\(773\) | 5109.26 | + | 8849.49i | 0.237732 | + | 0.411765i | 0.960063 | − | 0.279783i | \(-0.0902625\pi\) |
−0.722331 | + | 0.691548i | \(0.756929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −730.610 | + | 1265.45i | −0.0338636 | + | 0.0586534i | ||||
\(776\) | −12493.4 | + | 4547.21i | −0.577945 | + | 0.210355i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4378.94 | + | 3674.37i | −0.201790 | + | 0.169322i | ||||
\(779\) | −14739.8 | − | 5364.86i | −0.677932 | − | 0.246747i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4469.28 | − | 25346.6i | 0.204768 | − | 1.16130i | ||||
\(782\) | −2893.54 | −0.132318 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3217.70 | −0.146579 | ||||||||
\(785\) | 3820.93 | − | 21669.5i | 0.173726 | − | 0.985247i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8402.50 | + | 3058.26i | 0.380580 | + | 0.138520i | 0.525224 | − | 0.850964i | \(-0.323981\pi\) |
−0.144644 | + | 0.989484i | \(0.546204\pi\) | |||||||
\(788\) | 14692.8 | − | 12328.7i | 0.664226 | − | 0.557352i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13444.7 | − | 4893.46i | 0.605493 | − | 0.220381i | ||||
\(791\) | 4081.12 | − | 7068.70i | 0.183449 | − | 0.317742i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4288.97 | + | 7428.72i | 0.192063 | + | 0.332663i | ||||
\(794\) | −4442.89 | − | 3728.03i | −0.198580 | − | 0.166628i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2404.86 | + | 13638.6i | 0.107083 | + | 0.607298i | ||||
\(797\) | −5814.54 | − | 32975.9i | −0.258421 | − | 1.46558i | −0.787137 | − | 0.616779i | \(-0.788437\pi\) |
0.528716 | − | 0.848799i | \(-0.322674\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6953.46 | + | 5834.64i | 0.307879 | + | 0.258341i | ||||
\(800\) | −1123.87 | − | 1946.61i | −0.0496687 | − | 0.0860288i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9152.36 | − | 15852.4i | 0.402969 | − | 0.697963i | ||||
\(803\) | 33437.2 | − | 12170.2i | 1.46946 | − | 0.534839i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −937.095 | + | 786.316i | −0.0410289 | + | 0.0344273i | ||||
\(806\) | −470.585 | − | 171.279i | −0.0205653 | − | 0.00748516i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −342.507 | + | 1942.46i | −0.0149126 | + | 0.0845734i | ||||
\(809\) | −18877.7 | −0.820399 | −0.410200 | − | 0.911996i | \(-0.634541\pi\) | ||||
−0.410200 | + | 0.911996i | \(0.634541\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11057.8 | −0.478784 | −0.239392 | − | 0.970923i | \(-0.576948\pi\) | ||||
−0.239392 | + | 0.970923i | \(0.576948\pi\) | |||||||
\(812\) | −1405.57 | + | 7971.38i | −0.0607460 | + | 0.344508i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −35559.8 | − | 12942.7i | −1.53117 | − | 0.557300i | ||||
\(815\) | −18187.9 | + | 15261.5i | −0.781710 | + | 0.655933i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17298.3 | + | 6296.07i | −0.740748 | + | 0.269610i | ||||
\(818\) | 15012.5 | − | 26002.4i | 0.641686 | − | 1.11143i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5083.13 | + | 8804.25i | 0.216477 | + | 0.374948i | ||||
\(821\) | −11528.4 | − | 9673.49i | −0.490067 | − | 0.411215i | 0.363984 | − | 0.931405i | \(-0.381416\pi\) |
−0.854050 | + | 0.520191i | \(0.825861\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2003.08 | − | 11360.0i | −0.0848395 | − | 0.481148i | −0.997391 | − | 0.0721870i | \(-0.977002\pi\) |
0.912552 | − | 0.408961i | \(-0.134109\pi\) | |||||||
\(824\) | 1476.96 | + | 8376.23i | 0.0624420 | + | 0.354126i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6287.14 | + | 5275.54i | 0.264840 | + | 0.222227i | ||||
\(827\) | −3374.22 | − | 5844.32i | −0.141878 | − | 0.245740i | 0.786326 | − | 0.617812i | \(-0.211981\pi\) |
−0.928204 | + | 0.372072i | \(0.878647\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7810.47 | + | 13528.1i | −0.327224 | + | 0.566769i | −0.981960 | − | 0.189089i | \(-0.939447\pi\) |
0.654736 | + | 0.755858i | \(0.272780\pi\) | |||||||
\(830\) | −4453.71 | + | 1621.02i | −0.186253 | + | 0.0677907i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 590.117 | − | 495.167i | 0.0245897 | − | 0.0206332i | ||||
\(833\) | −19700.9 | − | 7170.53i | −0.819442 | − | 0.298252i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1312.28 | + | 7442.29i | −0.0543870 | + | 0.308444i | ||||
\(836\) | −11048.5 | −0.457082 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13553.2 | 0.558696 | ||||||||
\(839\) | −6175.43 | + | 35022.6i | −0.254111 | + | 1.44114i | 0.544232 | + | 0.838935i | \(0.316821\pi\) |
−0.798344 | + | 0.602202i | \(0.794290\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4200.37 | − | 1528.81i | −0.172224 | − | 0.0626844i | ||||
\(842\) | 6162.57 | − | 5171.01i | 0.252228 | − | 0.211645i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2623.29 | + | 954.800i | −0.106988 | + | 0.0389403i | ||||
\(845\) | 7592.69 | − | 13150.9i | 0.309108 | − | 0.535391i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13858.9 | − | 24004.3i | −0.562216 | − | 0.973787i | ||||
\(848\) | 9235.11 | + | 7749.18i | 0.373980 | + | 0.313806i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2543.15 | − | 14422.9i | −0.102623 | − | 0.582003i | ||||
\(851\) | 753.917 | + | 4275.67i | 0.0303689 | + | 0.172231i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13397.6 | + | 11241.9i | 0.537779 | + | 0.451250i | 0.870778 | − | 0.491677i | \(-0.163616\pi\) |
−0.332998 | + | 0.942927i | \(0.608060\pi\) | |||||||
\(854\) | −8489.07 | − | 14703.5i | −0.340152 | − | 0.589161i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6129.27 | − | 10616.2i | 0.244736 | − | 0.423896i | ||||
\(857\) | 12430.2 | − | 4524.21i | 0.495456 | − | 0.180331i | −0.0821930 | − | 0.996616i | \(-0.526192\pi\) |
0.577649 | + | 0.816285i | \(0.303970\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26244.1 | + | 22021.4i | −1.04242 | + | 0.874693i | −0.992276 | − | 0.124050i | \(-0.960412\pi\) |
−0.0501419 | + | 0.998742i | \(0.515967\pi\) | |||||||
\(860\) | 11211.4 | + | 4080.60i | 0.444540 | + | 0.161799i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3142.42 | + | 17821.5i | −0.124166 | + | 0.704181i | ||||
\(863\) | −26527.5 | −1.04636 | −0.523179 | − | 0.852223i | \(-0.675254\pi\) | ||||
−0.523179 | + | 0.852223i | \(0.675254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12214.3 | 0.480115 | ||||||||
\(866\) | −2502.11 | + | 14190.2i | −0.0981814 | + | 0.556814i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 931.419 | + | 339.009i | 0.0364221 | + | 0.0132566i | ||||
\(869\) | 44790.0 | − | 37583.2i | 1.74844 | − | 1.46712i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 137.140 | − | 49.9149i | 0.00533503 | − | 0.00194179i | ||||
\(872\) | −3070.63 | + | 5318.48i | −0.119248 | + | 0.206544i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 633.801 | + | 1097.78i | 0.0245293 | + | 0.0424860i | ||||
\(875\) | −13183.5 | − | 11062.3i | −0.509355 | − | 0.427399i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1772.16 | − | 10050.4i | −0.0682345 | − | 0.386977i | −0.999730 | − | 0.0232250i | \(-0.992607\pi\) |
0.931496 | − | 0.363752i | \(-0.118505\pi\) | |||||||
\(878\) | 806.750 | + | 4575.31i | 0.0310097 | + | 0.175865i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5485.46 | + | 4602.84i | 0.210130 | + | 0.176320i | ||||
\(881\) | 3285.54 | + | 5690.72i | 0.125644 | + | 0.217622i | 0.921985 | − | 0.387227i | \(-0.126567\pi\) |
−0.796340 | + | 0.604849i | \(0.793234\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8202.95 | + | 14207.9i | −0.312629 | + | 0.541489i | −0.978931 | − | 0.204193i | \(-0.934543\pi\) |
0.666302 | + | 0.745682i | \(0.267876\pi\) | |||||||
\(884\) | 4716.55 | − | 1716.68i | 0.179451 | − | 0.0653149i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12224.5 | − | 10257.6i | 0.463534 | − | 0.388951i | ||||
\(887\) | −27634.7 | − | 10058.2i | −1.04609 | − | 0.380747i | −0.238906 | − | 0.971043i | \(-0.576789\pi\) |
−0.807187 | + | 0.590296i | \(0.799011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5533.77 | − | 31383.6i | 0.208770 | − | 1.18399i | ||||
\(890\) | 1475.33 | 0.0555653 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20141.2 | −0.756030 | ||||||||
\(893\) | 690.511 | − | 3916.08i | 0.0258758 | − | 0.146749i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21733.2 | − | 7910.24i | −0.811689 | − | 0.295431i | ||||
\(896\) | −1168.01 | + | 980.074i | −0.0435495 | + | 0.0365424i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4710.70 | + | 1714.55i | −0.175054 | + | 0.0637143i | ||||
\(899\) | −1766.96 | + | 3060.47i | −0.0655523 | + | 0.113540i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39274.6 | + | 68025.7i | 1.45220 | + | 2.51528i | ||||
\(902\) | 31825.7 | + | 26704.9i | 1.17481 | + | 0.985784i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 951.892 | + | 5398.45i | 0.0350215 | + | 0.198617i | ||||
\(905\) | −986.055 | − | 5592.20i | −0.0362183 | − | 0.205404i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37157.2 | − | 31178.6i | −1.36029 | − | 1.14142i | −0.975892 | − | 0.218256i | \(-0.929963\pi\) |
−0.384402 | − | 0.923166i | \(-0.625592\pi\) | |||||||
\(908\) | 7059.60 | + | 12227.6i | 0.258019 | + | 0.446902i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1060.98 | − | 1837.68i | 0.0386498 | − | 0.0669434i | ||||
\(911\) | 76.7148 | − | 27.9219i | 0.00278998 | − | 0.00101547i | −0.340625 | − | 0.940199i | \(-0.610639\pi\) |
0.343415 | + | 0.939184i | \(0.388416\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14837.2 | + | 12449.9i | −0.537831 | + | 0.451294i | ||||
\(914\) | 21119.6 | + | 7686.90i | 0.764304 | + | 0.278184i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3243.60 | + | 18395.4i | −0.117000 | + | 0.663538i | ||||
\(917\) | 11291.8 | 0.406639 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28051.4 | 1.00689 | 0.503444 | − | 0.864028i | \(-0.332066\pi\) | ||||
0.503444 | + | 0.864028i | \(0.332066\pi\) | |||||||
\(920\) | 142.662 | − | 809.076i | 0.00511242 | − | 0.0289940i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17667.6 | + | 6430.47i | 0.631075 | + | 0.229692i | ||||
\(923\) | 3923.83 | − | 3292.49i | 0.139929 | − | 0.117414i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20649.6 | + | 7515.85i | −0.734006 | + | 0.267156i | ||||
\(926\) | −1966.11 | + | 3405.40i | −0.0697735 | + | 0.120851i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2718.07 | − | 4707.83i | −0.0961475 | − | 0.166532i | ||||
\(929\) | 24607.0 | + | 20647.7i | 0.869030 | + | 0.729203i | 0.963894 | − | 0.266287i | \(-0.0857970\pi\) |
−0.0948634 | + | 0.995490i | \(0.530241\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1594.86 | + | 9044.93i | 0.0561435 | + | 0.318405i | ||||
\(932\) | −2038.24 | − | 11559.4i | −0.0716360 | − | 0.406268i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21833.4 | + | 18320.4i | 0.764895 | + | 0.641823i | ||||
\(935\) | 23328.3 | + | 40405.8i | 0.815954 | + | 1.41327i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4147.52 | + | 7183.72i | −0.144604 | + | 0.250461i | −0.929225 | − | 0.369514i | \(-0.879524\pi\) |
0.784621 | + | 0.619975i | \(0.212857\pi\) | |||||||
\(938\) | −271.438 | + | 98.7955i | −0.00944859 | + | 0.00343900i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1974.28 | + | 1656.62i | −0.0685043 | + | 0.0574819i | ||||
\(941\) | −26036.6 | − | 9476.55i | −0.901986 | − | 0.328296i | −0.150938 | − | 0.988543i | \(-0.548229\pi\) |
−0.751048 | + | 0.660247i | \(0.770452\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 827.701 | − | 4694.13i | 0.0285829 | − | 0.162102i | ||||
\(944\) | −5511.98 | −0.190042 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 48756.8 | 1.67571 | ||||||||
\(947\) | −6408.08 | + | 36342.0i | −0.219889 | + | 1.24705i | 0.652330 | + | 0.757935i | \(0.273792\pi\) |
−0.872219 | + | 0.489116i | \(0.837319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6654.56 | + | 2422.06i | 0.227625 | + | 0.0828487i | ||||
\(950\) | −4914.85 | + | 4124.05i | −0.167851 | + | 0.140844i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9335.37 | + | 3397.80i | −0.317816 | + | 0.115676i | ||||
\(953\) | −18315.5 | + | 31723.4i | −0.622559 | + | 1.07830i | 0.366449 | + | 0.930438i | \(0.380574\pi\) |
−0.989008 | + | 0.147865i | \(0.952760\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17582.6 | − | 30453.9i | −0.595768 | − | 1.03190i | ||||
\(956\) | −9272.12 | − | 7780.23i | −0.313684 | − | 0.263212i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1026.63 | − | 5822.31i | −0.0346231 | − | 0.196357i | ||||
\(959\) | 2406.41 | + | 13647.4i | 0.0810291 | + | 0.459539i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22489.7 | − | 18871.1i | −0.754917 | − | 0.633450i | ||||
\(962\) | −3765.59 | − | 6522.19i | −0.126203 | − | 0.218590i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4392.78 | − | 7608.52i | 0.146766 | − | 0.254205i | ||||
\(965\) | 8365.40 | − | 3044.76i | 0.279059 | − | 0.101569i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7350.22 | − | 6167.57i | 0.244434 | − | 0.205104i | −0.512337 | − | 0.858784i | \(-0.671220\pi\) |
0.756771 | + | 0.653680i | \(0.226776\pi\) | |||||||
\(968\) | 17492.5 | + | 6366.76i | 0.580818 | + | 0.211400i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4270.97 | − | 24221.9i | 0.141374 | − | 0.801771i | ||||
\(971\) | 43330.1 | 1.43206 | 0.716030 | − | 0.698070i | \(-0.245958\pi\) | ||||
0.716030 | + | 0.698070i | \(0.245958\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8607.62 | 0.283605 | ||||||||
\(974\) | −1494.82 | + | 8477.56i | −0.0491758 | + | 0.278890i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10714.8 | + | 3899.87i | 0.351406 | + | 0.127901i | ||||
\(977\) | −40390.4 | + | 33891.6i | −1.32262 | + | 1.10981i | −0.336884 | + | 0.941546i | \(0.609373\pi\) |
−0.985741 | + | 0.168268i | \(0.946183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5665.48 | − | 2062.07i | 0.184954 | − | 0.0673176i | ||||
\(980\) | 2976.31 | − | 5155.13i | 0.0970151 | − | 0.168035i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3425.76 | + | 5933.60i | 0.111324 | + | 0.192819i | ||||
\(983\) | −15775.7 | − | 13237.4i | −0.511868 | − | 0.429509i | 0.349918 | − | 0.936780i | \(-0.386210\pi\) |
−0.861786 | + | 0.507272i | \(0.830654\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6161.47 | + | 34943.4i | 0.199310 | + | 1.13035i | ||||
\(986\) | −6150.56 | − | 34881.5i | −0.198655 | − | 1.12663i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1684.40 | − | 1413.38i | −0.0542389 | − | 0.0455119i | ||||
\(989\) | −2796.95 | − | 4844.46i | −0.0899270 | − | 0.155758i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1290.22 | + | 2234.73i | −0.0413574 | + | 0.0716332i | −0.885963 | − | 0.463756i | \(-0.846502\pi\) |
0.844606 | + | 0.535389i | \(0.179835\pi\) | |||||||
\(992\) | −625.537 | + | 227.677i | −0.0200210 | + | 0.00728705i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7766.36 | + | 6516.75i | −0.247821 | + | 0.207946i | ||||
\(995\) | −24075.1 | − | 8762.63i | −0.767068 | − | 0.279190i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4604.11 | + | 26111.2i | −0.146252 | + | 0.829438i | 0.820101 | + | 0.572219i | \(0.193917\pi\) |
−0.966353 | + | 0.257219i | \(0.917194\pi\) | |||||||
\(998\) | 27962.8 | 0.886922 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 162.4.e.a.73.3 | 24 | ||
3.2 | odd | 2 | 54.4.e.a.25.1 | yes | 24 | ||
27.11 | odd | 18 | 1458.4.a.h.1.4 | 12 | |||
27.13 | even | 9 | inner | 162.4.e.a.91.3 | 24 | ||
27.14 | odd | 18 | 54.4.e.a.13.1 | ✓ | 24 | ||
27.16 | even | 9 | 1458.4.a.e.1.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.4.e.a.13.1 | ✓ | 24 | 27.14 | odd | 18 | ||
54.4.e.a.25.1 | yes | 24 | 3.2 | odd | 2 | ||
162.4.e.a.73.3 | 24 | 1.1 | even | 1 | trivial | ||
162.4.e.a.91.3 | 24 | 27.13 | even | 9 | inner | ||
1458.4.a.e.1.9 | 12 | 27.16 | even | 9 | |||
1458.4.a.h.1.4 | 12 | 27.11 | odd | 18 |