Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(126,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.126");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.d (of order \(5\), degree \(4\), 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: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 376.1 | ||
Root | \(-1.63097i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.376 |
Dual form | 625.2.d.n.251.1 |
$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.15604 | − | 1.56645i | −1.52455 | − | 1.10765i | −0.959173 | − | 0.282818i | \(-0.908731\pi\) |
−0.565377 | − | 0.824832i | \(-0.691269\pi\) | |||||||
\(3\) | 0.234569 | + | 0.721930i | 0.135429 | + | 0.416807i | 0.995656 | − | 0.0931033i | \(-0.0296787\pi\) |
−0.860228 | + | 0.509910i | \(0.829679\pi\) | |||||||
\(4\) | 1.57669 | + | 4.85257i | 0.788347 | + | 2.42628i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.625130 | − | 1.92395i | 0.255208 | − | 0.785451i | ||||
\(7\) | −2.04213 | −0.771852 | −0.385926 | − | 0.922530i | \(-0.626118\pi\) | ||||
−0.385926 | + | 0.922530i | \(0.626118\pi\) | |||||||
\(8\) | 2.55484 | − | 7.86300i | 0.903273 | − | 2.77999i | ||||
\(9\) | 1.96089 | − | 1.42467i | 0.653630 | − | 0.474890i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.09110 | − | 0.792729i | −0.328979 | − | 0.239017i | 0.411019 | − | 0.911627i | \(-0.365173\pi\) |
−0.739997 | + | 0.672610i | \(0.765173\pi\) | |||||||
\(12\) | −3.13337 | + | 2.27653i | −0.904526 | + | 0.657177i | ||||
\(13\) | −1.06761 | + | 0.775663i | −0.296101 | + | 0.215130i | −0.725910 | − | 0.687790i | \(-0.758581\pi\) |
0.429808 | + | 0.902920i | \(0.358581\pi\) | |||||||
\(14\) | 4.40291 | + | 3.19890i | 1.17673 | + | 0.854943i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −9.56969 | + | 6.95279i | −2.39242 | + | 1.73820i | ||||
\(17\) | 1.26301 | − | 3.88713i | 0.306324 | − | 0.942768i | −0.672856 | − | 0.739774i | \(-0.734933\pi\) |
0.979180 | − | 0.202995i | \(-0.0650674\pi\) | |||||||
\(18\) | −6.45944 | −1.52250 | ||||||||
\(19\) | −1.51010 | + | 4.64762i | −0.346442 | + | 1.06624i | 0.614366 | + | 0.789021i | \(0.289412\pi\) |
−0.960807 | + | 0.277216i | \(0.910588\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.479021 | − | 1.47427i | −0.104531 | − | 0.321713i | ||||
\(22\) | 1.11068 | + | 3.41831i | 0.236797 | + | 0.728787i | ||||
\(23\) | 2.21361 | + | 1.60828i | 0.461570 | + | 0.335350i | 0.794147 | − | 0.607726i | \(-0.207918\pi\) |
−0.332577 | + | 0.943076i | \(0.607918\pi\) | |||||||
\(24\) | 6.27582 | 1.28105 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.51685 | 0.689711 | ||||||||
\(27\) | 3.33081 | + | 2.41997i | 0.641015 | + | 0.465724i | ||||
\(28\) | −3.21981 | − | 9.90957i | −0.608488 | − | 1.87273i | ||||
\(29\) | −1.42739 | − | 4.39306i | −0.265060 | − | 0.815771i | −0.991680 | − | 0.128731i | \(-0.958910\pi\) |
0.726619 | − | 0.687040i | \(-0.241090\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.21172 | − | 6.80697i | 0.397236 | − | 1.22257i | −0.529970 | − | 0.848016i | \(-0.677797\pi\) |
0.927206 | − | 0.374551i | \(-0.122203\pi\) | |||||||
\(32\) | 14.9886 | 2.64963 | ||||||||
\(33\) | 0.316357 | − | 0.973647i | 0.0550707 | − | 0.169490i | ||||
\(34\) | −8.81211 | + | 6.40237i | −1.51126 | + | 1.09800i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10.0050 | + | 7.26908i | 1.66751 | + | 1.21151i | ||||
\(37\) | 6.99508 | − | 5.08223i | 1.14998 | − | 0.835513i | 0.161506 | − | 0.986872i | \(-0.448365\pi\) |
0.988479 | + | 0.151359i | \(0.0483649\pi\) | |||||||
\(38\) | 10.5361 | − | 7.65495i | 1.70919 | − | 1.24180i | ||||
\(39\) | −0.810403 | − | 0.588793i | −0.129768 | − | 0.0942823i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.17073 | − | 5.93639i | 1.27605 | − | 0.927108i | 0.276628 | − | 0.960977i | \(-0.410783\pi\) |
0.999426 | + | 0.0338695i | \(0.0107830\pi\) | |||||||
\(42\) | −1.27660 | + | 3.92896i | −0.196983 | + | 0.606252i | ||||
\(43\) | 2.43460 | 0.371272 | 0.185636 | − | 0.982619i | \(-0.440565\pi\) | ||||
0.185636 | + | 0.982619i | \(0.440565\pi\) | |||||||
\(44\) | 2.12644 | − | 6.54452i | 0.320573 | − | 0.986623i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.25333 | − | 6.93505i | −0.332236 | − | 1.02252i | ||||
\(47\) | 2.33985 | + | 7.20133i | 0.341303 | + | 1.05042i | 0.963534 | + | 0.267588i | \(0.0862265\pi\) |
−0.622231 | + | 0.782834i | \(0.713774\pi\) | |||||||
\(48\) | −7.26419 | − | 5.27774i | −1.04849 | − | 0.761776i | ||||
\(49\) | −2.82971 | −0.404244 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.10250 | 0.434437 | ||||||||
\(52\) | −5.44725 | − | 3.95766i | −0.755398 | − | 0.548829i | ||||
\(53\) | −0.191975 | − | 0.590839i | −0.0263698 | − | 0.0811579i | 0.937006 | − | 0.349315i | \(-0.113586\pi\) |
−0.963375 | + | 0.268157i | \(0.913586\pi\) | |||||||
\(54\) | −3.39058 | − | 10.4351i | −0.461399 | − | 1.42004i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.21732 | + | 16.0573i | −0.697193 | + | 2.14574i | ||||
\(57\) | −3.70948 | −0.491333 | ||||||||
\(58\) | −3.80402 | + | 11.7076i | −0.499492 | + | 1.53728i | ||||
\(59\) | 9.17521 | − | 6.66618i | 1.19451 | − | 0.867862i | 0.200777 | − | 0.979637i | \(-0.435653\pi\) |
0.993734 | + | 0.111775i | \(0.0356535\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.523849 | − | 0.380599i | −0.0670720 | − | 0.0487307i | 0.553744 | − | 0.832687i | \(-0.313199\pi\) |
−0.620816 | + | 0.783956i | \(0.713199\pi\) | |||||||
\(62\) | −15.4314 | + | 11.2115i | −1.95978 | + | 1.42387i | ||||
\(63\) | −4.00439 | + | 2.90936i | −0.504506 | + | 0.366545i | ||||
\(64\) | −13.1766 | − | 9.57336i | −1.64708 | − | 1.19667i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.20725 | + | 1.60366i | −0.271694 | + | 0.197397i | ||||
\(67\) | 3.38029 | − | 10.4035i | 0.412969 | − | 1.27099i | −0.501087 | − | 0.865397i | \(-0.667066\pi\) |
0.914055 | − | 0.405590i | \(-0.132934\pi\) | |||||||
\(68\) | 20.8539 | 2.52891 | ||||||||
\(69\) | −0.641823 | + | 1.97533i | −0.0772664 | + | 0.237802i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.912311 | − | 2.80781i | −0.108271 | − | 0.333225i | 0.882213 | − | 0.470851i | \(-0.156053\pi\) |
−0.990484 | + | 0.137625i | \(0.956053\pi\) | |||||||
\(72\) | −6.19241 | − | 19.0583i | −0.729783 | − | 2.24604i | ||||
\(73\) | −10.9533 | − | 7.95802i | −1.28198 | − | 0.931415i | −0.282372 | − | 0.959305i | \(-0.591121\pi\) |
−0.999611 | + | 0.0278896i | \(0.991121\pi\) | |||||||
\(74\) | −23.0428 | −2.67867 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −24.9339 | −2.86011 | ||||||||
\(77\) | 2.22816 | + | 1.61886i | 0.253923 | + | 0.184486i | ||||
\(78\) | 0.824945 | + | 2.53892i | 0.0934067 | + | 0.287476i | ||||
\(79\) | 0.583824 | + | 1.79683i | 0.0656853 | + | 0.202159i | 0.978513 | − | 0.206187i | \(-0.0661057\pi\) |
−0.912827 | + | 0.408346i | \(0.866106\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.28123 | − | 3.94323i | 0.142359 | − | 0.438137i | ||||
\(82\) | −26.9155 | −2.97232 | ||||||||
\(83\) | 0.733857 | − | 2.25858i | 0.0805513 | − | 0.247911i | −0.902668 | − | 0.430337i | \(-0.858395\pi\) |
0.983220 | + | 0.182425i | \(0.0583948\pi\) | |||||||
\(84\) | 6.39875 | − | 4.64896i | 0.698161 | − | 0.507243i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.24909 | − | 3.81368i | −0.566024 | − | 0.411240i | ||||
\(87\) | 2.83666 | − | 2.06096i | 0.304122 | − | 0.220958i | ||||
\(88\) | −9.02081 | + | 6.55400i | −0.961622 | + | 0.698659i | ||||
\(89\) | −5.93723 | − | 4.31365i | −0.629345 | − | 0.457246i | 0.226828 | − | 0.973935i | \(-0.427164\pi\) |
−0.856173 | + | 0.516689i | \(0.827164\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.18020 | − | 1.58400i | 0.228547 | − | 0.166049i | ||||
\(92\) | −4.31411 | + | 13.2775i | −0.449777 | + | 1.38427i | ||||
\(93\) | 5.43296 | 0.563371 | ||||||||
\(94\) | 6.23574 | − | 19.1916i | 0.643167 | − | 1.97946i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.51586 | + | 10.8207i | 0.358836 | + | 1.10438i | ||||
\(97\) | 1.79204 | + | 5.51532i | 0.181954 | + | 0.559996i | 0.999883 | − | 0.0153235i | \(-0.00487782\pi\) |
−0.817929 | + | 0.575319i | \(0.804878\pi\) | |||||||
\(98\) | 6.10097 | + | 4.43261i | 0.616291 | + | 0.447761i | ||||
\(99\) | −3.26890 | −0.328537 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5536 | 1.14962 | 0.574812 | − | 0.818285i | \(-0.305075\pi\) | ||||
0.574812 | + | 0.818285i | \(0.305075\pi\) | |||||||
\(102\) | −6.68912 | − | 4.85993i | −0.662321 | − | 0.481205i | ||||
\(103\) | 3.58680 | + | 11.0390i | 0.353418 | + | 1.08771i | 0.956921 | + | 0.290348i | \(0.0937711\pi\) |
−0.603503 | + | 0.797361i | \(0.706229\pi\) | |||||||
\(104\) | 3.37147 | + | 10.3763i | 0.330599 | + | 1.01748i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.511616 | + | 1.57459i | −0.0496925 | + | 0.152938i | ||||
\(107\) | 10.1703 | 0.983204 | 0.491602 | − | 0.870820i | \(-0.336412\pi\) | ||||
0.491602 | + | 0.870820i | \(0.336412\pi\) | |||||||
\(108\) | −6.49142 | + | 19.9785i | −0.624637 | + | 1.92244i | ||||
\(109\) | −0.966573 | + | 0.702257i | −0.0925809 | + | 0.0672640i | −0.633113 | − | 0.774060i | \(-0.718223\pi\) |
0.540532 | + | 0.841324i | \(0.318223\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.30985 | + | 3.85783i | 0.503988 | + | 0.366169i | ||||
\(112\) | 19.5425 | − | 14.1985i | 1.84660 | − | 1.34163i | ||||
\(113\) | −3.62647 | + | 2.63479i | −0.341150 | + | 0.247860i | −0.745147 | − | 0.666900i | \(-0.767621\pi\) |
0.403997 | + | 0.914760i | \(0.367621\pi\) | |||||||
\(114\) | 7.99780 | + | 5.81074i | 0.749062 | + | 0.544226i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 19.0671 | − | 13.8530i | 1.77033 | − | 1.28622i | ||||
\(117\) | −0.988400 | + | 3.04198i | −0.0913776 | + | 0.281231i | ||||
\(118\) | −30.2244 | −2.78238 | ||||||||
\(119\) | −2.57922 | + | 7.93803i | −0.236437 | + | 0.727678i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.83711 | − | 8.73173i | −0.257919 | − | 0.793794i | ||||
\(122\) | 0.533249 | + | 1.64117i | 0.0482781 | + | 0.148585i | ||||
\(123\) | 6.20226 | + | 4.50621i | 0.559239 | + | 0.406311i | ||||
\(124\) | 36.5185 | 3.27946 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 13.1910 | 1.17515 | ||||||||
\(127\) | 3.37914 | + | 2.45509i | 0.299850 | + | 0.217854i | 0.727529 | − | 0.686077i | \(-0.240669\pi\) |
−0.427679 | + | 0.903931i | \(0.640669\pi\) | |||||||
\(128\) | 4.14959 | + | 12.7711i | 0.366776 | + | 1.12882i | ||||
\(129\) | 0.571082 | + | 1.75761i | 0.0502809 | + | 0.154749i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.04730 | − | 3.22327i | 0.0915032 | − | 0.281618i | −0.894823 | − | 0.446420i | \(-0.852699\pi\) |
0.986327 | + | 0.164802i | \(0.0526986\pi\) | |||||||
\(132\) | 5.22349 | 0.454646 | ||||||||
\(133\) | 3.08383 | − | 9.49104i | 0.267402 | − | 0.822978i | ||||
\(134\) | −23.5846 | + | 17.1352i | −2.03740 | + | 1.48026i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −27.3377 | − | 19.8620i | −2.34419 | − | 1.70315i | ||||
\(137\) | 6.74394 | − | 4.89976i | 0.576174 | − | 0.418615i | −0.261169 | − | 0.965293i | \(-0.584108\pi\) |
0.837343 | + | 0.546678i | \(0.184108\pi\) | |||||||
\(138\) | 4.47806 | − | 3.25350i | 0.381198 | − | 0.276956i | ||||
\(139\) | 2.77780 | + | 2.01819i | 0.235610 | + | 0.171181i | 0.699325 | − | 0.714804i | \(-0.253484\pi\) |
−0.463715 | + | 0.885984i | \(0.653484\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.65000 | + | 3.37842i | −0.391601 | + | 0.284514i | ||||
\(142\) | −2.43132 | + | 7.48284i | −0.204032 | + | 0.627946i | ||||
\(143\) | 1.77976 | 0.148831 | ||||||||
\(144\) | −8.85968 | + | 27.2673i | −0.738307 | + | 2.27228i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.1498 | + | 34.3156i | 0.922765 | + | 2.83998i | ||||
\(147\) | −0.663763 | − | 2.04285i | −0.0547463 | − | 0.168492i | ||||
\(148\) | 35.6910 | + | 25.9310i | 2.93378 | + | 2.13151i | ||||
\(149\) | 9.96023 | 0.815974 | 0.407987 | − | 0.912988i | \(-0.366231\pi\) | ||||
0.407987 | + | 0.912988i | \(0.366231\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.0404 | −1.71225 | −0.856123 | − | 0.516772i | \(-0.827134\pi\) | ||||
−0.856123 | + | 0.516772i | \(0.827134\pi\) | |||||||
\(152\) | 32.6862 | + | 23.7479i | 2.65120 | + | 1.92621i | ||||
\(153\) | −3.06127 | − | 9.42161i | −0.247489 | − | 0.761692i | ||||
\(154\) | −2.26815 | − | 6.98063i | −0.182772 | − | 0.562516i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.57940 | − | 4.86088i | 0.126453 | − | 0.389182i | ||||
\(157\) | 7.80843 | 0.623181 | 0.311590 | − | 0.950217i | \(-0.399138\pi\) | ||||
0.311590 | + | 0.950217i | \(0.399138\pi\) | |||||||
\(158\) | 1.55590 | − | 4.78856i | 0.123781 | − | 0.380957i | ||||
\(159\) | 0.381513 | − | 0.277185i | 0.0302559 | − | 0.0219822i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.52048 | − | 3.28432i | −0.356264 | − | 0.258841i | ||||
\(162\) | −8.93928 | + | 6.49477i | −0.702336 | + | 0.510277i | ||||
\(163\) | 9.44814 | − | 6.86447i | 0.740035 | − | 0.537667i | −0.152687 | − | 0.988275i | \(-0.548793\pi\) |
0.892722 | + | 0.450608i | \(0.148793\pi\) | |||||||
\(164\) | 41.6895 | + | 30.2892i | 3.25540 | + | 2.36519i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.12019 | + | 3.72004i | −0.397404 | + | 0.288731i | ||||
\(167\) | 2.32133 | − | 7.14431i | 0.179630 | − | 0.552844i | −0.820185 | − | 0.572099i | \(-0.806129\pi\) |
0.999815 | + | 0.0192551i | \(0.00612946\pi\) | |||||||
\(168\) | −12.8160 | −0.988779 | ||||||||
\(169\) | −3.47909 | + | 10.7075i | −0.267622 | + | 0.823656i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.66018 | + | 11.2649i | 0.279901 | + | 0.861447i | ||||
\(172\) | 3.83861 | + | 11.8140i | 0.292692 | + | 0.900812i | ||||
\(173\) | −4.29897 | − | 3.12338i | −0.326844 | − | 0.237466i | 0.412246 | − | 0.911073i | \(-0.364744\pi\) |
−0.739090 | + | 0.673606i | \(0.764744\pi\) | |||||||
\(174\) | −9.34436 | −0.708394 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.9532 | 1.20251 | ||||||||
\(177\) | 6.96474 | + | 5.06018i | 0.523502 | + | 0.380346i | ||||
\(178\) | 6.04377 | + | 18.6008i | 0.453000 | + | 1.39419i | ||||
\(179\) | 0.403805 | + | 1.24279i | 0.0301818 | + | 0.0928901i | 0.965013 | − | 0.262203i | \(-0.0844491\pi\) |
−0.934831 | + | 0.355093i | \(0.884449\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.23062 | + | 19.1759i | −0.463118 | + | 1.42533i | 0.398215 | + | 0.917292i | \(0.369630\pi\) |
−0.861334 | + | 0.508040i | \(0.830370\pi\) | |||||||
\(182\) | −7.18186 | −0.532355 | ||||||||
\(183\) | 0.151887 | − | 0.467459i | 0.0112278 | − | 0.0345556i | ||||
\(184\) | 18.3014 | − | 13.2967i | 1.34919 | − | 0.980247i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −11.7137 | − | 8.51048i | −0.858888 | − | 0.624019i | ||||
\(187\) | −4.45951 | + | 3.24002i | −0.326111 | + | 0.236934i | ||||
\(188\) | −31.2557 | + | 22.7086i | −2.27956 | + | 1.65619i | ||||
\(189\) | −6.80194 | − | 4.94190i | −0.494769 | − | 0.359470i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.2286 | + | 12.5173i | −1.24662 | + | 0.905721i | −0.998021 | − | 0.0628858i | \(-0.979970\pi\) |
−0.248597 | + | 0.968607i | \(0.579970\pi\) | |||||||
\(192\) | 3.82047 | − | 11.7582i | 0.275719 | − | 0.848576i | ||||
\(193\) | −7.99352 | −0.575386 | −0.287693 | − | 0.957723i | \(-0.592888\pi\) | ||||
−0.287693 | + | 0.957723i | \(0.592888\pi\) | |||||||
\(194\) | 4.77580 | − | 14.6984i | 0.342882 | − | 1.05528i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.46159 | − | 13.7314i | −0.318685 | − | 0.980811i | ||||
\(197\) | −6.70611 | − | 20.6393i | −0.477790 | − | 1.47049i | −0.842157 | − | 0.539232i | \(-0.818715\pi\) |
0.364367 | − | 0.931255i | \(-0.381285\pi\) | |||||||
\(198\) | 7.04788 | + | 5.12059i | 0.500871 | + | 0.363904i | ||||
\(199\) | 9.34240 | 0.662265 | 0.331133 | − | 0.943584i | \(-0.392569\pi\) | ||||
0.331133 | + | 0.943584i | \(0.392569\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.30350 | 0.585684 | ||||||||
\(202\) | −24.9100 | − | 18.0982i | −1.75266 | − | 1.27338i | ||||
\(203\) | 2.91492 | + | 8.97120i | 0.204587 | + | 0.629655i | ||||
\(204\) | 4.89170 | + | 15.0551i | 0.342487 | + | 1.05407i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.55887 | − | 29.4192i | 0.665998 | − | 2.04973i | ||||
\(207\) | 6.63192 | 0.460951 | ||||||||
\(208\) | 4.82367 | − | 14.8457i | 0.334461 | − | 1.02937i | ||||
\(209\) | 5.33198 | − | 3.87391i | 0.368821 | − | 0.267964i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.56723 | + | 4.04483i | 0.383264 | + | 0.278457i | 0.762690 | − | 0.646765i | \(-0.223878\pi\) |
−0.379426 | + | 0.925222i | \(0.623878\pi\) | |||||||
\(212\) | 2.56440 | − | 1.86314i | 0.176124 | − | 0.127961i | ||||
\(213\) | 1.81304 | − | 1.31725i | 0.124227 | − | 0.0902565i | ||||
\(214\) | −21.9277 | − | 15.9314i | −1.49894 | − | 1.08905i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 27.5379 | − | 20.0075i | 1.87372 | − | 1.36134i | ||||
\(217\) | −4.51661 | + | 13.9007i | −0.306608 | + | 0.943641i | ||||
\(218\) | 3.18402 | 0.215649 | ||||||||
\(219\) | 3.17583 | − | 9.77421i | 0.214603 | − | 0.660480i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.66671 | + | 5.12961i | 0.112115 | + | 0.345055i | ||||
\(222\) | −5.40513 | − | 16.6353i | −0.362768 | − | 1.11649i | ||||
\(223\) | −6.88875 | − | 5.00497i | −0.461305 | − | 0.335158i | 0.332738 | − | 0.943019i | \(-0.392028\pi\) |
−0.794043 | + | 0.607862i | \(0.792028\pi\) | |||||||
\(224\) | −30.6086 | −2.04512 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.9461 | 0.794643 | ||||||||
\(227\) | −16.9761 | − | 12.3338i | −1.12674 | − | 0.818625i | −0.141524 | − | 0.989935i | \(-0.545200\pi\) |
−0.985217 | + | 0.171310i | \(0.945200\pi\) | |||||||
\(228\) | −5.84872 | − | 18.0005i | −0.387341 | − | 1.19211i | ||||
\(229\) | 9.19724 | + | 28.3062i | 0.607771 | + | 1.87053i | 0.476488 | + | 0.879181i | \(0.341910\pi\) |
0.131283 | + | 0.991345i | \(0.458090\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.646042 | + | 1.98831i | −0.0425064 | + | 0.130821i | ||||
\(232\) | −38.1894 | −2.50726 | ||||||||
\(233\) | −0.701943 | + | 2.16036i | −0.0459858 | + | 0.141530i | −0.971413 | − | 0.237395i | \(-0.923706\pi\) |
0.925427 | + | 0.378925i | \(0.123706\pi\) | |||||||
\(234\) | 6.89616 | − | 5.01035i | 0.450816 | − | 0.327537i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 46.8146 | + | 34.0128i | 3.04737 | + | 2.21404i | ||||
\(237\) | −1.16024 | + | 0.842960i | −0.0753654 | + | 0.0547562i | ||||
\(238\) | 17.9955 | − | 13.0745i | 1.16647 | − | 0.847492i | ||||
\(239\) | −12.4838 | − | 9.06999i | −0.807508 | − | 0.586689i | 0.105599 | − | 0.994409i | \(-0.466324\pi\) |
−0.913107 | + | 0.407720i | \(0.866324\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.91713 | − | 2.84596i | 0.252324 | − | 0.183324i | −0.454432 | − | 0.890781i | \(-0.650158\pi\) |
0.706756 | + | 0.707457i | \(0.250158\pi\) | |||||||
\(242\) | −7.56094 | + | 23.2702i | −0.486035 | + | 1.49586i | ||||
\(243\) | 15.4986 | 0.994235 | ||||||||
\(244\) | 1.02093 | − | 3.14210i | 0.0653584 | − | 0.201152i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.31356 | − | 19.4311i | −0.402538 | − | 1.23888i | ||||
\(247\) | −1.99279 | − | 6.13318i | −0.126798 | − | 0.390245i | ||||
\(248\) | −47.8726 | − | 34.7815i | −3.03991 | − | 2.20862i | ||||
\(249\) | 1.80268 | 0.114240 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.8293 | −1.12537 | −0.562687 | − | 0.826670i | \(-0.690232\pi\) | ||||
−0.562687 | + | 0.826670i | \(0.690232\pi\) | |||||||
\(252\) | −20.4316 | − | 14.8444i | −1.28707 | − | 0.935109i | ||||
\(253\) | −1.14034 | − | 3.50959i | −0.0716923 | − | 0.220646i | ||||
\(254\) | −3.43977 | − | 10.5865i | −0.215831 | − | 0.664258i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.992687 | − | 3.05518i | 0.0620430 | − | 0.190949i | ||||
\(257\) | 5.88929 | 0.367364 | 0.183682 | − | 0.982986i | \(-0.441198\pi\) | ||||
0.183682 | + | 0.982986i | \(0.441198\pi\) | |||||||
\(258\) | 1.52194 | − | 4.68405i | 0.0947518 | − | 0.291616i | ||||
\(259\) | −14.2849 | + | 10.3786i | −0.887618 | + | 0.644892i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.05763 | − | 6.58075i | −0.560653 | − | 0.407338i | ||||
\(262\) | −7.30713 | + | 5.30894i | −0.451436 | + | 0.327987i | ||||
\(263\) | −19.1553 | + | 13.9172i | −1.18117 | + | 0.858168i | −0.992303 | − | 0.123835i | \(-0.960481\pi\) |
−0.188865 | + | 0.982003i | \(0.560481\pi\) | |||||||
\(264\) | −6.84754 | − | 4.97503i | −0.421437 | − | 0.306192i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −21.5161 | + | 15.6324i | −1.31924 | + | 0.958484i | ||||
\(267\) | 1.72146 | − | 5.29812i | 0.105352 | − | 0.324240i | ||||
\(268\) | 55.8132 | 3.40934 | ||||||||
\(269\) | 4.24776 | − | 13.0733i | 0.258991 | − | 0.797091i | −0.734027 | − | 0.679121i | \(-0.762361\pi\) |
0.993017 | − | 0.117970i | \(-0.0376388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.31726 | + | 7.13180i | 0.140764 | + | 0.433226i | 0.996442 | − | 0.0842822i | \(-0.0268597\pi\) |
−0.855678 | + | 0.517508i | \(0.826860\pi\) | |||||||
\(272\) | 14.9398 | + | 45.9801i | 0.905860 | + | 2.78795i | ||||
\(273\) | 1.65495 | + | 1.20239i | 0.100162 | + | 0.0727720i | ||||
\(274\) | −22.2155 | −1.34209 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −10.5974 | −0.637887 | ||||||||
\(277\) | −2.29597 | − | 1.66812i | −0.137952 | − | 0.100228i | 0.516669 | − | 0.856185i | \(-0.327172\pi\) |
−0.654621 | + | 0.755957i | \(0.727172\pi\) | |||||||
\(278\) | −2.82764 | − | 8.70259i | −0.169591 | − | 0.521947i | ||||
\(279\) | −5.36075 | − | 16.4987i | −0.320940 | − | 0.987750i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.09532 | + | 21.8372i | −0.423272 | + | 1.30270i | 0.481368 | + | 0.876519i | \(0.340140\pi\) |
−0.904640 | + | 0.426177i | \(0.859860\pi\) | |||||||
\(282\) | 15.3177 | 0.912158 | ||||||||
\(283\) | −7.76395 | + | 23.8950i | −0.461519 | + | 1.42041i | 0.401789 | + | 0.915732i | \(0.368388\pi\) |
−0.863308 | + | 0.504677i | \(0.831612\pi\) | |||||||
\(284\) | 12.1866 | − | 8.85410i | 0.723143 | − | 0.525394i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.83723 | − | 2.78791i | −0.226900 | − | 0.164853i | ||||
\(287\) | −16.6857 | + | 12.1229i | −0.984925 | + | 0.715590i | ||||
\(288\) | 29.3910 | − | 21.3538i | 1.73188 | − | 1.25828i | ||||
\(289\) | 0.238675 | + | 0.173407i | 0.0140397 | + | 0.0102004i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.56132 | + | 2.58745i | −0.208768 | + | 0.151679i | ||||
\(292\) | 21.3468 | − | 65.6988i | 1.24923 | − | 3.84473i | ||||
\(293\) | −28.8755 | −1.68692 | −0.843461 | − | 0.537190i | \(-0.819486\pi\) | ||||
−0.843461 | + | 0.537190i | \(0.819486\pi\) | |||||||
\(294\) | −1.76894 | + | 5.44423i | −0.103167 | + | 0.317514i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −22.0902 | − | 67.9866i | −1.28397 | − | 3.95164i | ||||
\(297\) | −1.71586 | − | 5.28086i | −0.0995640 | − | 0.306427i | ||||
\(298\) | −21.4747 | − | 15.6022i | −1.24399 | − | 0.903814i | ||||
\(299\) | −3.61076 | −0.208816 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.97176 | −0.286567 | ||||||||
\(302\) | 45.3640 | + | 32.9589i | 2.61041 | + | 1.89657i | ||||
\(303\) | 2.71012 | + | 8.34088i | 0.155692 | + | 0.479171i | ||||
\(304\) | −17.8627 | − | 54.9757i | −1.02450 | − | 3.15308i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.15831 | + | 25.1087i | −0.466380 | + | 1.43537i | ||||
\(307\) | 23.9526 | 1.36704 | 0.683522 | − | 0.729930i | \(-0.260447\pi\) | ||||
0.683522 | + | 0.729930i | \(0.260447\pi\) | |||||||
\(308\) | −4.34247 | + | 13.3648i | −0.247435 | + | 0.761527i | ||||
\(309\) | −7.12806 | + | 5.17884i | −0.405501 | + | 0.294614i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.99984 | + | 5.81222i | 0.453629 | + | 0.329581i | 0.791027 | − | 0.611781i | \(-0.209547\pi\) |
−0.337398 | + | 0.941362i | \(0.609547\pi\) | |||||||
\(312\) | −6.70013 | + | 4.86793i | −0.379320 | + | 0.275592i | ||||
\(313\) | 15.1922 | − | 11.0378i | 0.858712 | − | 0.623891i | −0.0688221 | − | 0.997629i | \(-0.521924\pi\) |
0.927534 | + | 0.373738i | \(0.121924\pi\) | |||||||
\(314\) | −16.8353 | − | 12.2316i | −0.950070 | − | 0.690267i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.79870 | + | 5.66609i | −0.438711 | + | 0.318742i | ||||
\(317\) | −7.99793 | + | 24.6151i | −0.449208 | + | 1.38252i | 0.428594 | + | 0.903497i | \(0.359009\pi\) |
−0.877802 | + | 0.479024i | \(0.840991\pi\) | |||||||
\(318\) | −1.25676 | −0.0704754 | ||||||||
\(319\) | −1.92508 | + | 5.92480i | −0.107784 | + | 0.331725i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.38565 | + | 7.34228i | 0.133154 | + | 0.409806i | ||||
\(322\) | 4.60160 | + | 14.1623i | 0.256437 | + | 0.789232i | ||||
\(323\) | 16.1587 | + | 11.7399i | 0.899092 | + | 0.653228i | ||||
\(324\) | 21.1549 | 1.17527 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −31.1234 | −1.72377 | ||||||||
\(327\) | −0.733709 | − | 0.533071i | −0.0405742 | − | 0.0294789i | ||||
\(328\) | −25.8028 | − | 79.4130i | −1.42472 | − | 4.38485i | ||||
\(329\) | −4.77828 | − | 14.7060i | −0.263435 | − | 0.810770i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.400929 | − | 1.23393i | 0.0220371 | − | 0.0678231i | −0.939433 | − | 0.342732i | \(-0.888648\pi\) |
0.961470 | + | 0.274909i | \(0.0886477\pi\) | |||||||
\(332\) | 12.1170 | 0.665006 | ||||||||
\(333\) | 6.47610 | − | 19.9314i | 0.354888 | − | 1.09223i | ||||
\(334\) | −16.1961 | + | 11.7672i | −0.886212 | + | 0.643871i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 14.8344 | + | 10.7778i | 0.809283 | + | 0.587979i | ||||
\(337\) | 9.12322 | − | 6.62841i | 0.496974 | − | 0.361073i | −0.310886 | − | 0.950447i | \(-0.600626\pi\) |
0.807860 | + | 0.589375i | \(0.200626\pi\) | |||||||
\(338\) | 24.2739 | − | 17.6360i | 1.32033 | − | 0.959273i | ||||
\(339\) | −2.75279 | − | 2.00002i | −0.149511 | − | 0.108626i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.80928 | + | 5.67378i | −0.422896 | + | 0.307252i | ||||
\(342\) | 9.75443 | − | 30.0210i | 0.527459 | − | 1.62335i | ||||
\(343\) | 20.0735 | 1.08387 | ||||||||
\(344\) | 6.22001 | − | 19.1432i | 0.335360 | − | 1.03213i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.37611 | + | 13.4683i | 0.235261 | + | 0.724059i | ||||
\(347\) | 0.665933 | + | 2.04953i | 0.0357492 | + | 0.110025i | 0.967339 | − | 0.253487i | \(-0.0815776\pi\) |
−0.931590 | + | 0.363512i | \(0.881578\pi\) | |||||||
\(348\) | 14.4735 | + | 10.5156i | 0.775860 | + | 0.563695i | ||||
\(349\) | 5.60904 | 0.300245 | 0.150122 | − | 0.988667i | \(-0.452033\pi\) | ||||
0.150122 | + | 0.988667i | \(0.452033\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.43309 | −0.289997 | ||||||||
\(352\) | −16.3540 | − | 11.8819i | −0.871672 | − | 0.633307i | ||||
\(353\) | −5.71587 | − | 17.5916i | −0.304225 | − | 0.936308i | −0.979965 | − | 0.199168i | \(-0.936176\pi\) |
0.675740 | − | 0.737140i | \(-0.263824\pi\) | |||||||
\(354\) | −7.08972 | − | 21.8199i | −0.376814 | − | 1.15971i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.5711 | − | 35.6121i | 0.613266 | − | 1.88744i | ||||
\(357\) | −6.33571 | −0.335321 | ||||||||
\(358\) | 1.07615 | − | 3.31204i | 0.0568761 | − | 0.175047i | ||||
\(359\) | −9.09737 | + | 6.60963i | −0.480141 | + | 0.348843i | −0.801380 | − | 0.598155i | \(-0.795901\pi\) |
0.321239 | + | 0.946998i | \(0.395901\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.94866 | − | 2.86887i | −0.207824 | − | 0.150993i | ||||
\(362\) | 43.4716 | − | 31.5840i | 2.28482 | − | 1.66002i | ||||
\(363\) | 5.63820 | − | 4.09639i | 0.295929 | − | 0.215005i | ||||
\(364\) | 11.1240 | + | 8.08205i | 0.583056 | + | 0.423615i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.05973 | + | 0.769937i | −0.0553929 | + | 0.0402453i | ||||
\(367\) | −8.82789 | + | 27.1695i | −0.460812 | + | 1.41823i | 0.403362 | + | 0.915041i | \(0.367842\pi\) |
−0.864174 | + | 0.503193i | \(0.832158\pi\) | |||||||
\(368\) | −32.3656 | −1.68718 | ||||||||
\(369\) | 7.56452 | − | 23.2812i | 0.393793 | − | 1.21197i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.392038 | + | 1.20657i | 0.0203536 | + | 0.0626419i | ||||
\(372\) | 8.56612 | + | 26.3638i | 0.444132 | + | 1.36690i | ||||
\(373\) | −11.3948 | − | 8.27884i | −0.590003 | − | 0.428662i | 0.252314 | − | 0.967646i | \(-0.418809\pi\) |
−0.842316 | + | 0.538983i | \(0.818809\pi\) | |||||||
\(374\) | 14.6902 | 0.759613 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 62.6020 | 3.22845 | ||||||||
\(377\) | 4.93144 | + | 3.58290i | 0.253982 | + | 0.184529i | ||||
\(378\) | 6.92400 | + | 21.3099i | 0.356132 | + | 1.09606i | ||||
\(379\) | 6.79538 | + | 20.9140i | 0.349055 | + | 1.07428i | 0.959377 | + | 0.282128i | \(0.0910403\pi\) |
−0.610322 | + | 0.792154i | \(0.708960\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.979760 | + | 3.01539i | −0.0501946 | + | 0.154483i | ||||
\(382\) | 56.7534 | 2.90376 | ||||||||
\(383\) | −4.55603 | + | 14.0220i | −0.232802 | + | 0.716491i | 0.764603 | + | 0.644501i | \(0.222935\pi\) |
−0.997405 | + | 0.0719898i | \(0.977065\pi\) | |||||||
\(384\) | −8.24650 | + | 5.99143i | −0.420828 | + | 0.305749i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.2344 | + | 12.5215i | 0.877205 | + | 0.637327i | ||||
\(387\) | 4.77397 | − | 3.46850i | 0.242675 | − | 0.176314i | ||||
\(388\) | −23.9380 | + | 17.3919i | −1.21527 | + | 0.882942i | ||||
\(389\) | 11.5340 | + | 8.37991i | 0.584795 | + | 0.424879i | 0.840450 | − | 0.541890i | \(-0.182291\pi\) |
−0.255654 | + | 0.966768i | \(0.582291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.04742 | − | 6.57333i | 0.457548 | − | 0.332428i | ||||
\(392\) | −7.22946 | + | 22.2500i | −0.365143 | + | 1.12379i | ||||
\(393\) | 2.57264 | 0.129772 | ||||||||
\(394\) | −17.8719 | + | 55.0039i | −0.900371 | + | 2.77106i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.15406 | − | 15.8626i | −0.259001 | − | 0.797124i | ||||
\(397\) | −1.69670 | − | 5.22192i | −0.0851551 | − | 0.262080i | 0.899408 | − | 0.437110i | \(-0.143998\pi\) |
−0.984563 | + | 0.175029i | \(0.943998\pi\) | |||||||
\(398\) | −20.1426 | − | 14.6344i | −1.00966 | − | 0.733559i | ||||
\(399\) | 7.57525 | 0.379237 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.7528 | 1.33597 | 0.667985 | − | 0.744175i | \(-0.267157\pi\) | ||||
0.667985 | + | 0.744175i | \(0.267157\pi\) | |||||||
\(402\) | −17.9027 | − | 13.0071i | −0.892904 | − | 0.648733i | ||||
\(403\) | 2.91867 | + | 8.98273i | 0.145389 | + | 0.447462i | ||||
\(404\) | 18.2165 | + | 56.0645i | 0.906303 | + | 2.78931i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.76830 | − | 23.9084i | 0.385534 | − | 1.18655i | ||||
\(407\) | −11.6612 | −0.578022 | ||||||||
\(408\) | 7.92640 | − | 24.3950i | 0.392415 | − | 1.20773i | ||||
\(409\) | −4.15340 | + | 3.01762i | −0.205372 | + | 0.149212i | −0.685718 | − | 0.727868i | \(-0.740511\pi\) |
0.480345 | + | 0.877080i | \(0.340511\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.11921 | + | 3.71932i | 0.252512 | + | 0.183461i | ||||
\(412\) | −47.9124 | + | 34.8104i | −2.36047 | + | 1.71498i | ||||
\(413\) | −18.7370 | + | 13.6132i | −0.921985 | + | 0.669861i | ||||
\(414\) | −14.2987 | − | 10.3886i | −0.702743 | − | 0.510572i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.0019 | + | 11.6261i | −0.784560 | + | 0.570016i | ||||
\(417\) | −0.805405 | + | 2.47878i | −0.0394409 | + | 0.121386i | ||||
\(418\) | −17.5643 | −0.859096 | ||||||||
\(419\) | 9.84269 | − | 30.2927i | 0.480847 | − | 1.47989i | −0.357060 | − | 0.934081i | \(-0.616221\pi\) |
0.837907 | − | 0.545813i | \(-0.183779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.951909 | + | 2.92968i | 0.0463932 | + | 0.142784i | 0.971570 | − | 0.236753i | \(-0.0760833\pi\) |
−0.925177 | + | 0.379537i | \(0.876083\pi\) | |||||||
\(422\) | −5.66713 | − | 17.4416i | −0.275871 | − | 0.849045i | ||||
\(423\) | 14.8477 | + | 10.7875i | 0.721920 | + | 0.524506i | ||||
\(424\) | −5.13623 | −0.249437 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.97240 | −0.289364 | ||||||||
\(427\) | 1.06977 | + | 0.777231i | 0.0517697 | + | 0.0376129i | ||||
\(428\) | 16.0355 | + | 49.3523i | 0.775106 | + | 2.38553i | ||||
\(429\) | 0.417477 | + | 1.28486i | 0.0201560 | + | 0.0620337i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.21465 | − | 22.2044i | 0.347517 | − | 1.06955i | −0.612705 | − | 0.790312i | \(-0.709919\pi\) |
0.960222 | − | 0.279237i | \(-0.0900815\pi\) | |||||||
\(432\) | −48.7004 | −2.34310 | ||||||||
\(433\) | 2.53831 | − | 7.81212i | 0.121984 | − | 0.375427i | −0.871356 | − | 0.490651i | \(-0.836759\pi\) |
0.993339 | + | 0.115225i | \(0.0367588\pi\) | |||||||
\(434\) | 31.5128 | − | 22.8954i | 1.51266 | − | 1.09901i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.93174 | − | 3.58312i | −0.236187 | − | 0.171600i | ||||
\(437\) | −10.8175 | + | 7.85936i | −0.517470 | + | 0.375964i | ||||
\(438\) | −22.1581 | + | 16.0988i | −1.05875 | + | 0.769230i | ||||
\(439\) | 19.6686 | + | 14.2901i | 0.938731 | + | 0.682028i | 0.948115 | − | 0.317928i | \(-0.102987\pi\) |
−0.00938352 | + | 0.999956i | \(0.502987\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.54875 | + | 4.03140i | −0.264226 | + | 0.191972i | ||||
\(442\) | 4.44180 | − | 13.6705i | 0.211275 | − | 0.650238i | ||||
\(443\) | 0.0631363 | 0.00299970 | 0.00149985 | − | 0.999999i | \(-0.499523\pi\) | ||||
0.00149985 | + | 0.999999i | \(0.499523\pi\) | |||||||
\(444\) | −10.3484 | + | 31.8490i | −0.491112 | + | 1.51149i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.01236 | + | 21.5818i | 0.332045 | + | 1.02193i | ||||
\(447\) | 2.33636 | + | 7.19059i | 0.110506 | + | 0.340103i | ||||
\(448\) | 26.9083 | + | 19.5500i | 1.27130 | + | 0.923653i | ||||
\(449\) | −11.5711 | −0.546074 | −0.273037 | − | 0.962004i | \(-0.588028\pi\) | ||||
−0.273037 | + | 0.962004i | \(0.588028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.6210 | −0.641389 | ||||||||
\(452\) | −18.5033 | − | 13.4435i | −0.870323 | − | 0.632327i | ||||
\(453\) | −4.93544 | − | 15.1897i | −0.231887 | − | 0.713676i | ||||
\(454\) | 17.2807 | + | 53.1845i | 0.811023 | + | 2.49607i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.47715 | + | 29.1677i | −0.443808 | + | 1.36590i | ||||
\(457\) | −41.3967 | −1.93646 | −0.968228 | − | 0.250071i | \(-0.919546\pi\) | ||||
−0.968228 | + | 0.250071i | \(0.919546\pi\) | |||||||
\(458\) | 24.5108 | − | 75.4364i | 1.14531 | − | 3.52491i | ||||
\(459\) | 13.6136 | − | 9.89086i | 0.635428 | − | 0.461666i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.7614 | − | 17.2637i | −1.10668 | − | 0.804049i | −0.124541 | − | 0.992214i | \(-0.539746\pi\) |
−0.982137 | + | 0.188166i | \(0.939746\pi\) | |||||||
\(462\) | 4.50750 | − | 3.27489i | 0.209708 | − | 0.152362i | ||||
\(463\) | 24.7155 | − | 17.9569i | 1.14863 | − | 0.834527i | 0.160330 | − | 0.987063i | \(-0.448744\pi\) |
0.988298 | + | 0.152536i | \(0.0487441\pi\) | |||||||
\(464\) | 44.2037 | + | 32.1159i | 2.05211 | + | 1.49094i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.89752 | − | 3.55826i | 0.226873 | − | 0.164833i | ||||
\(467\) | 10.1095 | − | 31.1137i | 0.467810 | − | 1.43977i | −0.387605 | − | 0.921826i | \(-0.626697\pi\) |
0.855414 | − | 0.517944i | \(-0.173303\pi\) | |||||||
\(468\) | −16.3198 | −0.754384 | ||||||||
\(469\) | −6.90300 | + | 21.2452i | −0.318751 | + | 0.981014i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.83162 | + | 5.63714i | 0.0843966 | + | 0.259746i | ||||
\(472\) | −28.9749 | − | 89.1756i | −1.33368 | − | 4.10464i | ||||
\(473\) | −2.65638 | − | 1.92998i | −0.122141 | − | 0.0887404i | ||||
\(474\) | 3.82197 | 0.175549 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −42.5864 | −1.95195 | ||||||||
\(477\) | −1.21819 | − | 0.885069i | −0.0557772 | − | 0.0405245i | ||||
\(478\) | 12.7078 | + | 39.1105i | 0.581240 | + | 1.78887i | ||||
\(479\) | −3.81181 | − | 11.7315i | −0.174166 | − | 0.536028i | 0.825428 | − | 0.564507i | \(-0.190934\pi\) |
−0.999594 | + | 0.0284789i | \(0.990934\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.52592 | + | 10.8517i | −0.160768 | + | 0.494793i | ||||
\(482\) | −12.9036 | −0.587741 | ||||||||
\(483\) | 1.31069 | − | 4.03387i | 0.0596383 | − | 0.183548i | ||||
\(484\) | 37.8980 | − | 27.5345i | 1.72264 | − | 1.25157i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −33.4156 | − | 24.2779i | −1.51576 | − | 1.10127i | ||||
\(487\) | −28.5552 | + | 20.7466i | −1.29396 | + | 0.940117i | −0.999877 | − | 0.0156629i | \(-0.995014\pi\) |
−0.294083 | + | 0.955780i | \(0.595014\pi\) | |||||||
\(488\) | −4.33100 | + | 3.14665i | −0.196055 | + | 0.142442i | ||||
\(489\) | 7.17192 | + | 5.21070i | 0.324325 | + | 0.235636i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.3906 | + | 9.00227i | −0.559178 | + | 0.406267i | −0.831158 | − | 0.556036i | \(-0.812322\pi\) |
0.271980 | + | 0.962303i | \(0.412322\pi\) | |||||||
\(492\) | −12.0876 | + | 37.2018i | −0.544951 | + | 1.67719i | ||||
\(493\) | −18.8792 | −0.850278 | ||||||||
\(494\) | −5.31081 | + | 16.3450i | −0.238945 | + | 0.735396i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.1619 | + | 80.5182i | 1.17471 | + | 3.61537i | ||||
\(497\) | 1.86306 | + | 5.73390i | 0.0835696 | + | 0.257201i | ||||
\(498\) | −3.88665 | − | 2.82381i | −0.174165 | − | 0.126538i | ||||
\(499\) | −35.1777 | −1.57477 | −0.787386 | − | 0.616461i | \(-0.788566\pi\) | ||||
−0.787386 | + | 0.616461i | \(0.788566\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.70221 | 0.254756 | ||||||||
\(502\) | 38.4406 | + | 27.9288i | 1.71569 | + | 1.24652i | ||||
\(503\) | 2.26662 | + | 6.97595i | 0.101064 | + | 0.311042i | 0.988786 | − | 0.149336i | \(-0.0477137\pi\) |
−0.887723 | + | 0.460378i | \(0.847714\pi\) | |||||||
\(504\) | 12.6457 | + | 38.9195i | 0.563284 | + | 1.73361i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.03901 | + | 9.35310i | −0.135100 | + | 0.415796i | ||||
\(507\) | −8.54617 | −0.379549 | ||||||||
\(508\) | −6.58561 | + | 20.2684i | −0.292189 | + | 0.899266i | ||||
\(509\) | −4.61704 | + | 3.35447i | −0.204647 | + | 0.148684i | −0.685388 | − | 0.728178i | \(-0.740367\pi\) |
0.480742 | + | 0.876862i | \(0.340367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.3680 | + | 16.2513i | 0.989502 | + | 0.718915i | ||||
\(512\) | 14.8015 | − | 10.7539i | 0.654139 | − | 0.475260i | ||||
\(513\) | −16.2770 | + | 11.8259i | −0.718647 | + | 0.522128i | ||||
\(514\) | −12.6975 | − | 9.22530i | −0.560065 | − | 0.406911i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.62849 | + | 5.54242i | −0.335826 | + | 0.243992i | ||||
\(517\) | 3.15569 | − | 9.71223i | 0.138787 | − | 0.427143i | ||||
\(518\) | 47.0563 | 2.06753 | ||||||||
\(519\) | 1.24646 | − | 3.83620i | 0.0547135 | − | 0.168391i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.2254 | − | 31.4706i | −0.447983 | − | 1.37875i | −0.879179 | − | 0.476492i | \(-0.841908\pi\) |
0.431196 | − | 0.902258i | \(-0.358092\pi\) | |||||||
\(522\) | 9.22016 | + | 28.3767i | 0.403555 | + | 1.24202i | ||||
\(523\) | 25.4613 | + | 18.4987i | 1.11335 | + | 0.808894i | 0.983187 | − | 0.182600i | \(-0.0584512\pi\) |
0.130159 | + | 0.991493i | \(0.458451\pi\) | |||||||
\(524\) | 17.2924 | 0.755421 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 63.1002 | 2.75130 | ||||||||
\(527\) | −23.6662 | − | 17.1945i | −1.03091 | − | 0.749003i | ||||
\(528\) | 3.74212 | + | 11.5171i | 0.162855 | + | 0.501216i | ||||
\(529\) | −4.79389 | − | 14.7541i | −0.208430 | − | 0.641481i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.49447 | − | 26.1433i | 0.368629 | − | 1.13452i | ||||
\(532\) | 50.9182 | 2.20758 | ||||||||
\(533\) | −4.11851 | + | 12.6755i | −0.178393 | + | 0.549036i | ||||
\(534\) | −12.0108 | + | 8.72636i | −0.519758 | + | 0.377627i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −73.1664 | − | 53.1585i | −3.16031 | − | 2.29610i | ||||
\(537\) | −0.802484 | + | 0.583039i | −0.0346297 | + | 0.0251600i | ||||
\(538\) | −29.6370 | + | 21.5326i | −1.27774 | + | 0.928335i | ||||
\(539\) | 3.08749 | + | 2.24319i | 0.132988 | + | 0.0966212i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5070 | − | 13.4461i | 0.795678 | − | 0.578094i | −0.113965 | − | 0.993485i | \(-0.536355\pi\) |
0.909643 | + | 0.415391i | \(0.136355\pi\) | |||||||
\(542\) | 6.17553 | − | 19.0063i | 0.265262 | − | 0.816392i | ||||
\(543\) | −15.3052 | −0.656808 | ||||||||
\(544\) | 18.9307 | − | 58.2626i | 0.811646 | − | 2.49799i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.68464 | − | 5.18480i | −0.0720961 | − | 0.221889i | ||||
\(547\) | 5.48653 | + | 16.8858i | 0.234587 | + | 0.721984i | 0.997176 | + | 0.0751011i | \(0.0239279\pi\) |
−0.762589 | + | 0.646883i | \(0.776072\pi\) | |||||||
\(548\) | 34.4095 | + | 25.0000i | 1.46990 | + | 1.06795i | ||||
\(549\) | −1.56944 | −0.0669820 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.5728 | 0.961634 | ||||||||
\(552\) | 13.8922 | + | 10.0933i | 0.591293 | + | 0.429600i | ||||
\(553\) | −1.19224 | − | 3.66935i | −0.0506994 | − | 0.156037i | ||||
\(554\) | 2.33717 | + | 7.19307i | 0.0992968 | + | 0.305604i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.41366 | + | 16.6615i | −0.229590 | + | 0.706606i | ||||
\(557\) | −2.27448 | −0.0963727 | −0.0481864 | − | 0.998838i | \(-0.515344\pi\) | ||||
−0.0481864 | + | 0.998838i | \(0.515344\pi\) | |||||||
\(558\) | −14.2865 | + | 43.9692i | −0.604794 | + | 1.86136i | ||||
\(559\) | −2.59920 | + | 1.88843i | −0.109934 | + | 0.0798719i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.38513 | − | 2.45944i | −0.142920 | − | 0.103838i | ||||
\(562\) | 49.5047 | − | 35.9673i | 2.08823 | − | 1.51719i | ||||
\(563\) | 0.321745 | − | 0.233761i | 0.0135599 | − | 0.00985187i | −0.580985 | − | 0.813915i | \(-0.697332\pi\) |
0.594545 | + | 0.804063i | \(0.297332\pi\) | |||||||
\(564\) | −23.7256 | − | 17.2377i | −0.999030 | − | 0.725838i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 54.1698 | − | 39.3567i | 2.27693 | − | 1.65428i | ||||
\(567\) | −2.61644 | + | 8.05258i | −0.109880 | + | 0.338177i | ||||
\(568\) | −24.4086 | −1.02416 | ||||||||
\(569\) | −3.45717 | + | 10.6401i | −0.144932 | + | 0.446055i | −0.997002 | − | 0.0773726i | \(-0.975347\pi\) |
0.852070 | + | 0.523427i | \(0.175347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.84424 | − | 17.9867i | −0.244574 | − | 0.752721i | −0.995706 | − | 0.0925696i | \(-0.970492\pi\) |
0.751132 | − | 0.660152i | \(-0.229508\pi\) | |||||||
\(572\) | 2.80613 | + | 8.63639i | 0.117330 | + | 0.361106i | ||||
\(573\) | −13.0779 | − | 9.50168i | −0.546339 | − | 0.396938i | ||||
\(574\) | 54.9649 | 2.29419 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −39.4768 | −1.64486 | ||||||||
\(577\) | 4.86874 | + | 3.53735i | 0.202688 | + | 0.147262i | 0.684499 | − | 0.729013i | \(-0.260021\pi\) |
−0.481811 | + | 0.876275i | \(0.660021\pi\) | |||||||
\(578\) | −0.242958 | − | 0.747747i | −0.0101057 | − | 0.0311022i | ||||
\(579\) | −1.87504 | − | 5.77077i | −0.0779238 | − | 0.239825i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.49863 | + | 4.61231i | −0.0621737 | + | 0.191351i | ||||
\(582\) | 11.7315 | 0.486285 | ||||||||
\(583\) | −0.258911 | + | 0.796847i | −0.0107230 | + | 0.0330020i | ||||
\(584\) | −90.5577 | + | 65.7940i | −3.74731 | + | 2.72258i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 62.2567 | + | 45.2321i | 2.57180 | + | 1.86852i | ||||
\(587\) | 13.2133 | − | 9.60006i | 0.545373 | − | 0.396237i | −0.280703 | − | 0.959795i | \(-0.590568\pi\) |
0.826077 | + | 0.563558i | \(0.190568\pi\) | |||||||
\(588\) | 8.86653 | − | 6.44191i | 0.365650 | − | 0.265660i | ||||
\(589\) | 28.2963 | + | 20.5585i | 1.16593 | + | 0.847097i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.3271 | − | 9.68268i | 0.548202 | − | 0.398292i | ||||
\(592\) | −31.6052 | + | 97.2707i | −1.29896 | + | 3.99780i | ||||
\(593\) | 8.40604 | 0.345195 | 0.172597 | − | 0.984992i | \(-0.444784\pi\) | ||||
0.172597 | + | 0.984992i | \(0.444784\pi\) | |||||||
\(594\) | −4.57278 | + | 14.0736i | −0.187623 | + | 0.577445i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.7042 | + | 48.3327i | 0.643271 | + | 1.97978i | ||||
\(597\) | 2.19144 | + | 6.74456i | 0.0896897 | + | 0.276037i | ||||
\(598\) | 7.78494 | + | 5.65609i | 0.318350 | + | 0.231295i | ||||
\(599\) | 13.1918 | 0.539001 | 0.269501 | − | 0.963000i | \(-0.413141\pi\) | ||||
0.269501 | + | 0.963000i | \(0.413141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.06690 | −0.247474 | −0.123737 | − | 0.992315i | \(-0.539488\pi\) | ||||
−0.123737 | + | 0.992315i | \(0.539488\pi\) | |||||||
\(602\) | 10.7193 | + | 7.78804i | 0.436886 | + | 0.317417i | ||||
\(603\) | −8.19314 | − | 25.2159i | −0.333650 | − | 1.02687i | ||||
\(604\) | −33.1743 | − | 102.100i | −1.34984 | − | 4.15440i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.22250 | − | 22.2286i | 0.293394 | − | 0.902973i | ||||
\(607\) | −14.9141 | −0.605345 | −0.302672 | − | 0.953095i | \(-0.597879\pi\) | ||||
−0.302672 | + | 0.953095i | \(0.597879\pi\) | |||||||
\(608\) | −22.6343 | + | 69.6613i | −0.917943 | + | 2.82514i | ||||
\(609\) | −5.79283 | + | 4.20874i | −0.234737 | + | 0.170547i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.08385 | − | 5.87326i | −0.327038 | − | 0.237607i | ||||
\(612\) | 40.8923 | − | 29.7100i | 1.65297 | − | 1.20096i | ||||
\(613\) | 29.5107 | − | 21.4408i | 1.19193 | − | 0.865985i | 0.198460 | − | 0.980109i | \(-0.436406\pi\) |
0.993467 | + | 0.114124i | \(0.0364061\pi\) | |||||||
\(614\) | −51.6427 | − | 37.5206i | −2.08413 | − | 1.51421i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.4217 | − | 13.3841i | 0.742230 | − | 0.539261i | ||||
\(617\) | 5.01661 | − | 15.4395i | 0.201961 | − | 0.621572i | −0.797864 | − | 0.602838i | \(-0.794036\pi\) |
0.999825 | − | 0.0187338i | \(-0.00596351\pi\) | |||||||
\(618\) | 23.4808 | 0.944537 | ||||||||
\(619\) | −3.10131 | + | 9.54484i | −0.124652 | + | 0.383639i | −0.993838 | − | 0.110847i | \(-0.964644\pi\) |
0.869186 | + | 0.494486i | \(0.164644\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.48112 | + | 10.7138i | 0.139692 | + | 0.429929i | ||||
\(622\) | −8.14339 | − | 25.0628i | −0.326520 | − | 1.00493i | ||||
\(623\) | 12.1246 | + | 8.80903i | 0.485761 | + | 0.352926i | ||||
\(624\) | 11.8491 | 0.474342 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −50.0451 | −2.00020 | ||||||||
\(627\) | 4.04741 | + | 2.94062i | 0.161638 | + | 0.117437i | ||||
\(628\) | 12.3115 | + | 37.8909i | 0.491283 | + | 1.51201i | ||||
\(629\) | −10.9205 | − | 33.6097i | −0.435427 | − | 1.34011i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.88672 | − | 27.3505i | 0.353775 | − | 1.08881i | −0.602942 | − | 0.797785i | \(-0.706005\pi\) |
0.956716 | − | 0.291022i | \(-0.0939952\pi\) | |||||||
\(632\) | 15.6200 | 0.621330 | ||||||||
\(633\) | −1.61418 | + | 4.96794i | −0.0641580 | + | 0.197458i | ||||
\(634\) | 55.8023 | − | 40.5427i | 2.21619 | − | 1.61016i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.94659 | + | 1.41428i | 0.0771873 | + | 0.0560799i | ||||
\(637\) | 3.02102 | − | 2.19490i | 0.119697 | − | 0.0869652i | ||||
\(638\) | 13.4315 | − | 9.75855i | 0.531758 | − | 0.386345i | ||||
\(639\) | −5.78914 | − | 4.20606i | −0.229015 | − | 0.166389i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.7595 | − | 10.7234i | 0.582963 | − | 0.423548i | −0.256828 | − | 0.966457i | \(-0.582677\pi\) |
0.839791 | + | 0.542909i | \(0.182677\pi\) | |||||||
\(642\) | 6.35779 | − | 19.5673i | 0.250922 | − | 0.772258i | ||||
\(643\) | −33.9734 | −1.33978 | −0.669890 | − | 0.742461i | \(-0.733659\pi\) | ||||
−0.669890 | + | 0.742461i | \(0.733659\pi\) | |||||||
\(644\) | 8.80997 | − | 27.1143i | 0.347162 | − | 1.06845i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.4486 | − | 50.6236i | −0.647162 | − | 1.99176i | ||||
\(647\) | 14.6390 | + | 45.0542i | 0.575518 | + | 1.77126i | 0.634408 | + | 0.772999i | \(0.281244\pi\) |
−0.0588895 | + | 0.998265i | \(0.518756\pi\) | |||||||
\(648\) | −27.7322 | − | 20.1487i | −1.08943 | − | 0.791514i | ||||
\(649\) | −15.2955 | −0.600402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.0948 | −0.434840 | ||||||||
\(652\) | 48.2071 | + | 35.0245i | 1.88794 | + | 1.37167i | ||||
\(653\) | −11.5560 | − | 35.5657i | −0.452220 | − | 1.39179i | −0.874368 | − | 0.485264i | \(-0.838723\pi\) |
0.422147 | − | 0.906527i | \(-0.361277\pi\) | |||||||
\(654\) | 0.746875 | + | 2.29864i | 0.0292051 | + | 0.0898841i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −36.9170 | + | 113.619i | −1.44137 | + | 4.43607i | ||||
\(657\) | −32.8157 | −1.28026 | ||||||||
\(658\) | −12.7342 | + | 39.1918i | −0.496430 | + | 1.52785i | ||||
\(659\) | 7.67072 | − | 5.57311i | 0.298809 | − | 0.217097i | −0.428271 | − | 0.903650i | \(-0.640877\pi\) |
0.727080 | + | 0.686553i | \(0.240877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.10389 | + | 5.16128i | 0.276309 | + | 0.200750i | 0.717306 | − | 0.696758i | \(-0.245375\pi\) |
−0.440997 | + | 0.897509i | \(0.645375\pi\) | |||||||
\(662\) | −2.79732 | + | 2.03237i | −0.108721 | + | 0.0789904i | ||||
\(663\) | −3.31226 | + | 2.40650i | −0.128637 | + | 0.0934606i | ||||
\(664\) | −15.8843 | − | 11.5406i | −0.616431 | − | 0.447863i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −45.1843 | + | 32.8283i | −1.75086 | + | 1.27207i | ||||
\(667\) | 3.90560 | − | 12.0202i | 0.151225 | − | 0.465424i | ||||
\(668\) | 38.3283 | 1.48297 | ||||||||
\(669\) | 1.99735 | − | 6.14721i | 0.0772220 | − | 0.237665i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.269859 | + | 0.830541i | 0.0104178 | + | 0.0320627i | ||||
\(672\) | −7.17984 | − | 22.0973i | −0.276969 | − | 0.852421i | ||||
\(673\) | −38.8538 | − | 28.2289i | −1.49770 | − | 1.08814i | −0.971285 | − | 0.237919i | \(-0.923535\pi\) |
−0.526418 | − | 0.850226i | \(-0.676465\pi\) | |||||||
\(674\) | −30.0531 | −1.15760 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −57.4444 | −2.20940 | ||||||||
\(677\) | 12.4711 | + | 9.06078i | 0.479303 | + | 0.348234i | 0.801056 | − | 0.598590i | \(-0.204272\pi\) |
−0.321753 | + | 0.946824i | \(0.604272\pi\) | |||||||
\(678\) | 2.80219 | + | 8.62425i | 0.107617 | + | 0.331213i | ||||
\(679\) | −3.65957 | − | 11.2630i | −0.140441 | − | 0.432234i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.92210 | − | 15.1487i | 0.188615 | − | 0.580499i | ||||
\(682\) | 25.7248 | 0.985055 | ||||||||
\(683\) | −8.59751 | + | 26.4604i | −0.328975 | + | 1.01248i | 0.640640 | + | 0.767842i | \(0.278669\pi\) |
−0.969614 | + | 0.244638i | \(0.921331\pi\) | |||||||
\(684\) | −48.8926 | + | 35.5225i | −1.86945 | + | 1.35824i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −43.2793 | − | 31.4443i | −1.65241 | − | 1.20055i | ||||
\(687\) | −18.2777 | + | 13.2795i | −0.697338 | + | 0.506646i | ||||
\(688\) | −23.2983 | + | 16.9272i | −0.888240 | + | 0.645344i | ||||
\(689\) | 0.663246 | + | 0.481877i | 0.0252677 | + | 0.0183580i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2824 | − | 11.8298i | 0.619411 | − | 0.450028i | −0.233305 | − | 0.972404i | \(-0.574954\pi\) |
0.852716 | + | 0.522375i | \(0.174954\pi\) | |||||||
\(692\) | 8.37826 | − | 25.7856i | 0.318494 | − | 0.980223i | ||||
\(693\) | 6.67552 | 0.253582 | ||||||||
\(694\) | 1.77472 | − | 5.46203i | 0.0673675 | − | 0.207336i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.95807 | − | 27.5701i | −0.339555 | − | 1.04504i | ||||
\(697\) | −12.7558 | − | 39.2584i | −0.483162 | − | 1.48702i | ||||
\(698\) | −12.0933 | − | 8.78630i | −0.457738 | − | 0.332566i | ||||
\(699\) | −1.72428 | −0.0652184 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.6216 | 1.19433 | 0.597166 | − | 0.802118i | \(-0.296293\pi\) | ||||
0.597166 | + | 0.802118i | \(0.296293\pi\) | |||||||
\(702\) | 11.7140 | + | 8.51069i | 0.442115 | + | 0.321215i | ||||
\(703\) | 13.0570 | + | 40.1852i | 0.492453 | + | 1.51561i | ||||
\(704\) | 6.78788 | + | 20.8910i | 0.255828 | + | 0.787358i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.2329 | + | 46.8819i | −0.573296 | + | 1.76442i | ||||
\(707\) | −23.5939 | −0.887340 | ||||||||
\(708\) | −13.5736 | + | 41.7752i | −0.510127 | + | 1.57001i | ||||
\(709\) | 3.85098 | − | 2.79790i | 0.144627 | − | 0.105077i | −0.513119 | − | 0.858317i | \(-0.671510\pi\) |
0.657746 | + | 0.753240i | \(0.271510\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.70470 | + | 2.69162i | 0.138937 | + | 0.100944i | ||||
\(712\) | −49.0869 | + | 35.6637i | −1.83961 | + | 1.33655i | ||||
\(713\) | 15.8434 | − | 11.5109i | 0.593341 | − | 0.431087i | ||||
\(714\) | 13.6600 | + | 9.92460i | 0.511214 | + | 0.371419i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.39402 | + | 3.91899i | −0.201584 | + | 0.146459i | ||||
\(717\) | 3.61959 | − | 11.1400i | 0.135176 | − | 0.416029i | ||||
\(718\) | 29.9680 | 1.11840 | ||||||||
\(719\) | −7.12986 | + | 21.9435i | −0.265899 | + | 0.818353i | 0.725586 | + | 0.688132i | \(0.241569\pi\) |
−0.991485 | + | 0.130221i | \(0.958431\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.32471 | − | 22.5431i | −0.272786 | − | 0.839550i | ||||
\(722\) | 4.01951 | + | 12.3708i | 0.149591 | + | 0.460393i | ||||
\(723\) | 2.97342 | + | 2.16032i | 0.110583 | + | 0.0803431i | ||||
\(724\) | −102.876 | −3.82336 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −18.5730 | −0.689309 | ||||||||
\(727\) | −12.6050 | − | 9.15810i | −0.467495 | − | 0.339655i | 0.328969 | − | 0.944341i | \(-0.393299\pi\) |
−0.796464 | + | 0.604686i | \(0.793299\pi\) | |||||||
\(728\) | −6.88497 | − | 21.1897i | −0.255174 | − | 0.785344i | ||||
\(729\) | −0.208202 | − | 0.640779i | −0.00771118 | − | 0.0237326i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.07491 | − | 9.46360i | 0.113730 | − | 0.350024i | ||||
\(732\) | 2.50786 | 0.0926931 | ||||||||
\(733\) | 5.32175 | − | 16.3787i | 0.196563 | − | 0.604960i | −0.803391 | − | 0.595451i | \(-0.796973\pi\) |
0.999955 | − | 0.00950846i | \(-0.00302668\pi\) | |||||||
\(734\) | 61.5930 | − | 44.7499i | 2.27344 | − | 1.65175i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 33.1789 | + | 24.1059i | 1.22299 | + | 0.888555i | ||||
\(737\) | −11.9354 | + | 8.67156i | −0.439645 | + | 0.319421i | ||||
\(738\) | −52.7784 | + | 38.3457i | −1.94280 | + | 1.41153i | ||||
\(739\) | 22.2381 | + | 16.1569i | 0.818043 | + | 0.594343i | 0.916151 | − | 0.400833i | \(-0.131279\pi\) |
−0.0981086 | + | 0.995176i | \(0.531279\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.96028 | − | 2.87731i | 0.145485 | − | 0.105701i | ||||
\(742\) | 1.04479 | − | 3.21552i | 0.0383553 | − | 0.118045i | ||||
\(743\) | 48.4801 | 1.77856 | 0.889280 | − | 0.457362i | \(-0.151206\pi\) | ||||
0.889280 | + | 0.457362i | \(0.151206\pi\) | |||||||
\(744\) | 13.8803 | − | 42.7193i | 0.508878 | − | 1.56617i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.5993 | + | 35.6990i | 0.424681 | + | 1.30703i | ||||
\(747\) | −1.77872 | − | 5.47433i | −0.0650799 | − | 0.200295i | ||||
\(748\) | −22.7537 | − | 16.5315i | −0.831958 | − | 0.604453i | ||||
\(749\) | −20.7691 | −0.758888 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.29720 | 0.120316 | 0.0601582 | − | 0.998189i | \(-0.480839\pi\) | ||||
0.0601582 | + | 0.998189i | \(0.480839\pi\) | |||||||
\(752\) | −72.4610 | − | 52.6460i | −2.64238 | − | 1.91980i | ||||
\(753\) | −4.18220 | − | 12.8715i | −0.152408 | − | 0.469063i | ||||
\(754\) | −5.01993 | − | 15.4497i | −0.182815 | − | 0.562647i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 13.2563 | − | 40.7987i | 0.482128 | − | 1.48384i | ||||
\(757\) | −35.7934 | −1.30093 | −0.650466 | − | 0.759535i | \(-0.725426\pi\) | ||||
−0.650466 | + | 0.759535i | \(0.725426\pi\) | |||||||
\(758\) | 18.1098 | − | 55.7362i | 0.657777 | − | 2.02443i | ||||
\(759\) | 2.26619 | − | 1.64649i | 0.0822576 | − | 0.0597636i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.537277 | + | 0.390354i | 0.0194763 | + | 0.0141503i | 0.597481 | − | 0.801883i | \(-0.296168\pi\) |
−0.578005 | + | 0.816034i | \(0.696168\pi\) | |||||||
\(762\) | 6.83588 | − | 4.96656i | 0.247638 | − | 0.179919i | ||||
\(763\) | 1.97387 | − | 1.43410i | 0.0714588 | − | 0.0519179i | ||||
\(764\) | −87.9054 | − | 63.8670i | −3.18030 | − | 2.31063i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.7878 | − | 23.0952i | 1.14854 | − | 0.834463i | ||||
\(767\) | −4.62482 | + | 14.2337i | −0.166993 | + | 0.513951i | ||||
\(768\) | 2.43848 | 0.0879911 | ||||||||
\(769\) | 7.94452 | − | 24.4507i | 0.286487 | − | 0.881716i | −0.699462 | − | 0.714669i | \(-0.746577\pi\) |
0.985949 | − | 0.167046i | \(-0.0534229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.38145 | + | 4.25166i | 0.0497516 | + | 0.153120i | ||||
\(772\) | −12.6033 | − | 38.7891i | −0.453604 | − | 1.39605i | ||||
\(773\) | 31.1842 | + | 22.6567i | 1.12162 | + | 0.814904i | 0.984454 | − | 0.175644i | \(-0.0562008\pi\) |
0.137165 | + | 0.990548i | \(0.456201\pi\) | |||||||
\(774\) | −15.7261 | −0.565264 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 47.9453 | 1.72114 | ||||||||
\(777\) | −10.8434 | − | 7.87818i | −0.389004 | − | 0.282628i | ||||
\(778\) | −11.7409 | − | 36.1349i | −0.420933 | − | 1.29550i | ||||
\(779\) | 15.2514 | + | 46.9390i | 0.546439 | + | 1.68177i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.23041 | + | 3.78681i | −0.0440275 | + | 0.135503i | ||||
\(782\) | −29.8034 | −1.06577 | ||||||||
\(783\) | 5.87673 | − | 18.0867i | 0.210017 | − | 0.646366i | ||||
\(784\) | 27.0794 | − | 19.6744i | 0.967123 | − | 0.702656i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.54671 | − | 4.02992i | −0.197845 | − | 0.143743i | ||||
\(787\) | 29.3116 | − | 21.2962i | 1.04485 | − | 0.759126i | 0.0736214 | − | 0.997286i | \(-0.476544\pi\) |
0.971226 | + | 0.238160i | \(0.0765444\pi\) | |||||||
\(788\) | 89.5800 | − | 65.0837i | 3.19115 | − | 2.31851i | ||||
\(789\) | −14.5405 | − | 10.5643i | −0.517654 | − | 0.376098i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.40573 | − | 5.38058i | 0.263317 | − | 0.191311i | ||||
\(792\) | −8.35153 | + | 25.7034i | −0.296759 | + | 0.913329i | ||||
\(793\) | 0.854482 | 0.0303436 | ||||||||
\(794\) | −4.52174 | + | 13.9165i | −0.160470 | + | 0.493877i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.7301 | + | 45.3346i | 0.522095 | + | 1.60684i | ||||
\(797\) | 10.4533 | + | 32.1719i | 0.370275 | + | 1.13959i | 0.946612 | + | 0.322376i | \(0.104482\pi\) |
−0.576337 | + | 0.817212i | \(0.695518\pi\) | |||||||
\(798\) | −16.3325 | − | 11.8663i | −0.578165 | − | 0.420062i | ||||
\(799\) | 30.9478 | 1.09485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.7878 | −0.628501 | ||||||||
\(802\) | −57.6801 | − | 41.9070i | −2.03675 | − | 1.47979i | ||||
\(803\) | 5.64254 | + | 17.3660i | 0.199121 | + | 0.612831i | ||||
\(804\) | 13.0921 | + | 40.2933i | 0.461722 | + | 1.42103i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.77828 | − | 23.9391i | 0.273978 | − | 0.843218i | ||||
\(807\) | 10.4344 | 0.367308 | ||||||||
\(808\) | 29.5176 | − | 90.8458i | 1.03842 | − | 3.19594i | ||||
\(809\) | 1.18448 | − | 0.860572i | 0.0416439 | − | 0.0302561i | −0.566769 | − | 0.823877i | \(-0.691807\pi\) |
0.608413 | + | 0.793621i | \(0.291807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.9177 | + | 23.9161i | 1.15590 | + | 0.839808i | 0.989254 | − | 0.146210i | \(-0.0467075\pi\) |
0.166642 | + | 0.986017i | \(0.446707\pi\) | |||||||
\(812\) | −38.9374 | + | 28.2897i | −1.36644 | + | 0.992774i | ||||
\(813\) | −4.60510 | + | 3.34580i | −0.161508 | + | 0.117342i | ||||
\(814\) | 25.1419 | + | 18.2667i | 0.881224 | + | 0.640247i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −29.6900 | + | 21.5710i | −1.03936 | + | 0.755137i | ||||
\(817\) | −3.67649 | + | 11.3151i | −0.128624 | + | 0.395865i | ||||
\(818\) | 13.6819 | 0.478375 | ||||||||
\(819\) | 2.01844 | − | 6.21212i | 0.0705300 | − | 0.217069i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.25608 | − | 28.4873i | −0.323040 | − | 0.994214i | −0.972318 | − | 0.233663i | \(-0.924929\pi\) |
0.649278 | − | 0.760551i | \(-0.275071\pi\) | |||||||
\(822\) | −5.21107 | − | 16.0380i | −0.181757 | − | 0.559390i | ||||
\(823\) | −15.3203 | − | 11.1308i | −0.534030 | − | 0.387996i | 0.287833 | − | 0.957681i | \(-0.407065\pi\) |
−0.821863 | + | 0.569685i | \(0.807065\pi\) | |||||||
\(824\) | 95.9636 | 3.34305 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 61.7221 | 2.14759 | ||||||||
\(827\) | −16.3938 | − | 11.9108i | −0.570069 | − | 0.414179i | 0.265061 | − | 0.964232i | \(-0.414608\pi\) |
−0.835130 | + | 0.550052i | \(0.814608\pi\) | |||||||
\(828\) | 10.4565 | + | 32.1819i | 0.363389 | + | 1.11840i | ||||
\(829\) | 5.14205 | + | 15.8256i | 0.178591 | + | 0.549646i | 0.999779 | − | 0.0210110i | \(-0.00668850\pi\) |
−0.821188 | + | 0.570657i | \(0.806689\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.665702 | − | 2.04882i | 0.0230930 | − | 0.0710728i | ||||
\(832\) | 21.4932 | 0.745142 | ||||||||
\(833\) | −3.57394 | + | 10.9995i | −0.123830 | + | 0.381109i | ||||
\(834\) | 5.61939 | − | 4.08272i | 0.194583 | − | 0.141373i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 27.2053 | + | 19.7658i | 0.940915 | + | 0.683615i | ||||
\(837\) | 23.8395 | − | 17.3204i | 0.824014 | − | 0.598681i | ||||
\(838\) | −68.6734 | + | 49.8941i | −2.37228 | + | 1.72356i | ||||
\(839\) | 5.77368 | + | 4.19482i | 0.199330 | + | 0.144821i | 0.682973 | − | 0.730444i | \(-0.260687\pi\) |
−0.483643 | + | 0.875265i | \(0.660687\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.19993 | − | 4.50452i | 0.213791 | − | 0.155328i | ||||
\(842\) | 2.53685 | − | 7.80762i | 0.0874256 | − | 0.269068i | ||||
\(843\) | −17.4293 | −0.600295 | ||||||||
\(844\) | −10.8500 | + | 33.3928i | −0.373472 | + | 1.14943i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −15.1141 | − | 46.5165i | −0.519635 | − | 1.59927i | ||||
\(847\) | 5.79375 | + | 17.8313i | 0.199075 | + | 0.612691i | ||||
\(848\) | 5.94512 | + | 4.31938i | 0.204156 | + | 0.148328i | ||||
\(849\) | −19.0717 | −0.654539 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.6581 | 0.810988 | ||||||||
\(852\) | 9.25066 | + | 6.72100i | 0.316922 | + | 0.230258i | ||||
\(853\) | 9.83454 | + | 30.2676i | 0.336728 | + | 1.03634i | 0.965864 | + | 0.259048i | \(0.0834088\pi\) |
−0.629136 | + | 0.777295i | \(0.716591\pi\) | |||||||
\(854\) | −1.08896 | − | 3.35148i | −0.0372636 | − | 0.114685i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.9836 | − | 79.9693i | 0.888102 | − | 2.73330i | ||||
\(857\) | 43.1535 | 1.47409 | 0.737047 | − | 0.675842i | \(-0.236220\pi\) | ||||
0.737047 | + | 0.675842i | \(0.236220\pi\) | |||||||
\(858\) | 1.11258 | − | 3.42417i | 0.0379829 | − | 0.116899i | ||||
\(859\) | −24.9917 | + | 18.1576i | −0.852707 | + | 0.619528i | −0.925891 | − | 0.377791i | \(-0.876684\pi\) |
0.0731840 | + | 0.997318i | \(0.476684\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.6658 | − | 9.20225i | −0.431650 | − | 0.313612i | ||||
\(862\) | −50.3373 | + | 36.5722i | −1.71449 | + | 1.24565i | ||||
\(863\) | −30.8972 | + | 22.4481i | −1.05175 | + | 0.764143i | −0.972545 | − | 0.232715i | \(-0.925239\pi\) |
−0.0792075 | + | 0.996858i | \(0.525239\pi\) | |||||||
\(864\) | 49.9241 | + | 36.2720i | 1.69845 | + | 1.23400i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.7100 | + | 12.8671i | −0.601812 | + | 0.437242i | ||||
\(867\) | −0.0692023 | + | 0.212983i | −0.00235023 | + | 0.00723327i | ||||
\(868\) | −74.5754 | −2.53125 | ||||||||
\(869\) | 0.787387 | − | 2.42333i | 0.0267103 | − | 0.0822057i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.46076 | + | 13.7288i | 0.151147 | + | 0.465183i | ||||
\(872\) | 3.05240 | + | 9.39432i | 0.103367 | + | 0.318132i | ||||
\(873\) | 11.3715 | + | 8.26187i | 0.384867 | + | 0.279622i | ||||
\(874\) | 35.6343 | 1.20535 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 52.4373 | 1.77169 | ||||||||
\(877\) | 25.6658 | + | 18.6473i | 0.866674 | + | 0.629675i | 0.929692 | − | 0.368337i | \(-0.120073\pi\) |
−0.0630186 | + | 0.998012i | \(0.520073\pi\) | |||||||
\(878\) | −20.0215 | − | 61.6200i | −0.675694 | − | 2.07957i | ||||
\(879\) | −6.77330 | − | 20.8461i | −0.228458 | − | 0.703121i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.8789 | + | 36.5595i | −0.400210 | + | 1.23172i | 0.524619 | + | 0.851337i | \(0.324208\pi\) |
−0.924829 | + | 0.380383i | \(0.875792\pi\) | |||||||
\(882\) | 18.2783 | 0.615464 | ||||||||
\(883\) | −3.75447 | + | 11.5551i | −0.126348 | + | 0.388859i | −0.994144 | − | 0.108061i | \(-0.965536\pi\) |
0.867796 | + | 0.496920i | \(0.165536\pi\) | |||||||
\(884\) | −22.2639 | + | 16.1756i | −0.748815 | + | 0.544046i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.136124 | − | 0.0989002i | −0.00457319 | − | 0.00332262i | ||||
\(887\) | −19.6131 | + | 14.2498i | −0.658544 | + | 0.478460i | −0.866171 | − | 0.499748i | \(-0.833426\pi\) |
0.207627 | + | 0.978208i | \(0.433426\pi\) | |||||||
\(888\) | 43.8999 | − | 31.8952i | 1.47318 | − | 1.07033i | ||||
\(889\) | −6.90064 | − | 5.01361i | −0.231440 | − | 0.168151i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.52386 | + | 3.28678i | −0.151555 | + | 0.110111i | ||||
\(892\) | 13.4255 | − | 41.3194i | 0.449519 | − | 1.38348i | ||||
\(893\) | −37.0025 | −1.23824 | ||||||||
\(894\) | 6.22644 | − | 19.1630i | 0.208243 | − | 0.640907i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.47400 | − | 26.0803i | −0.283097 | − | 0.871282i | ||||
\(897\) | −0.846974 | − | 2.60672i | −0.0282796 | − | 0.0870358i | ||||
\(898\) | 24.9477 | + | 18.1256i | 0.832517 | + | 0.604859i | ||||
\(899\) | −33.0604 | −1.10263 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.53913 | −0.0845908 | ||||||||
\(902\) | 29.3675 | + | 21.3367i | 0.977830 | + | 0.710435i | ||||
\(903\) | −1.16622 | − | 3.58926i | −0.0388095 | − | 0.119443i | ||||
\(904\) | 11.4523 | + | 35.2464i | 0.380896 | + | 1.17228i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.1530 | + | 40.4808i | −0.436980 | + | 1.34489i | ||||
\(907\) | 32.5046 | 1.07930 | 0.539649 | − | 0.841890i | \(-0.318557\pi\) | ||||
0.539649 | + | 0.841890i | \(0.318557\pi\) | |||||||
\(908\) | 33.0847 | − | 101.824i | 1.09795 | − | 3.37915i | ||||
\(909\) | 22.6553 | − | 16.4600i | 0.751429 | − | 0.545945i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.7794 | − | 25.9953i | −1.18542 | − | 0.861261i | −0.192651 | − | 0.981267i | \(-0.561709\pi\) |
−0.992773 | + | 0.120006i | \(0.961709\pi\) | |||||||
\(912\) | 35.4986 | − | 25.7913i | 1.17548 | − | 0.854034i | ||||
\(913\) | −2.59115 | + | 1.88258i | −0.0857547 | + | 0.0623044i | ||||
\(914\) | 89.2529 | + | 64.8460i | 2.95222 | + | 2.14492i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −122.856 | + | 89.2604i | −4.05929 | + | 2.94925i | ||||
\(917\) | −2.13873 | + | 6.58232i | −0.0706270 | + | 0.217367i | ||||
\(918\) | −44.8450 | −1.48011 | ||||||||
\(919\) | −12.2969 | + | 37.8460i | −0.405637 | + | 1.24842i | 0.514724 | + | 0.857356i | \(0.327894\pi\) |
−0.920362 | + | 0.391068i | \(0.872106\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.61854 | + | 17.2921i | 0.185137 | + | 0.569793i | ||||
\(922\) | 24.1878 | + | 74.4423i | 0.796582 | + | 2.45163i | ||||
\(923\) | 3.15190 | + | 2.28999i | 0.103746 | + | 0.0753760i | ||||
\(924\) | −10.6670 | −0.350920 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −81.4163 | −2.67551 | ||||||||
\(927\) | 22.7603 | + | 16.5363i | 0.747547 | + | 0.543124i | ||||
\(928\) | −21.3946 | − | 65.8458i | −0.702312 | − | 2.16149i | ||||
\(929\) | −2.05379 | − | 6.32093i | −0.0673828 | − | 0.207383i | 0.911696 | − | 0.410866i | \(-0.134774\pi\) |
−0.979078 | + | 0.203483i | \(0.934774\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.27316 | − | 13.1514i | 0.140047 | − | 0.431020i | ||||
\(932\) | −11.5900 | −0.379644 | ||||||||
\(933\) | −2.31950 | + | 7.13870i | −0.0759371 | + | 0.233710i | ||||
\(934\) | −70.5346 | + | 51.2464i | −2.30796 | + | 1.67683i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 21.3939 | + | 15.5436i | 0.699281 | + | 0.508057i | ||||
\(937\) | 0.185738 | − | 0.134947i | 0.00606781 | − | 0.00440852i | −0.584747 | − | 0.811216i | \(-0.698806\pi\) |
0.590815 | + | 0.806807i | \(0.298806\pi\) | |||||||
\(938\) | 48.1628 | − | 34.9924i | 1.57257 | − | 1.14254i | ||||
\(939\) | 11.5321 | + | 8.37857i | 0.376336 | + | 0.273424i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.9337 | + | 16.6623i | −0.747618 | + | 0.543176i | −0.895088 | − | 0.445890i | \(-0.852887\pi\) |
0.147470 | + | 0.989067i | \(0.452887\pi\) | |||||||
\(942\) | 4.88129 | − | 15.0231i | 0.159041 | − | 0.489478i | ||||
\(943\) | 27.6342 | 0.899894 | ||||||||
\(944\) | −41.4554 | + | 127.587i | −1.34926 | + | 4.15259i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.70405 | + | 8.32221i | 0.0879162 | + | 0.270578i | ||||
\(947\) | −14.8339 | − | 45.6542i | −0.482038 | − | 1.48356i | −0.836225 | − | 0.548386i | \(-0.815242\pi\) |
0.354187 | − | 0.935175i | \(-0.384758\pi\) | |||||||
\(948\) | −5.91986 | − | 4.30103i | −0.192268 | − | 0.139691i | ||||
\(949\) | 17.8666 | 0.579973 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.6464 | −0.637080 | ||||||||
\(952\) | 55.8272 | + | 40.5608i | 1.80937 | + | 1.31458i | ||||
\(953\) | 8.30900 | + | 25.5725i | 0.269155 | + | 0.828374i | 0.990707 | + | 0.136014i | \(0.0434291\pi\) |
−0.721552 | + | 0.692360i | \(0.756571\pi\) | |||||||
\(954\) | 1.24005 | + | 3.81649i | 0.0401482 | + | 0.123563i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 24.3296 | − | 74.8789i | 0.786877 | − | 2.42176i | ||||
\(957\) | −4.72886 | −0.152862 | ||||||||
\(958\) | −10.1585 | + | 31.2647i | −0.328207 | + | 1.01012i | ||||
\(959\) | −13.7720 | + | 10.0059i | −0.444721 | + | 0.323109i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.3636 | − | 11.8888i | −0.527857 | − | 0.383511i | ||||
\(962\) | 24.6007 | − | 17.8734i | 0.793157 | − | 0.576262i | ||||
\(963\) | 19.9429 | − | 14.4894i | 0.642652 | − | 0.466914i | ||||
\(964\) | 19.9863 | + | 14.5209i | 0.643716 | + | 0.467687i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9.14477 | + | 6.64407i | −0.294228 | + | 0.213769i | ||||
\(967\) | 1.16813 | − | 3.59515i | 0.0375647 | − | 0.115612i | −0.930516 | − | 0.366252i | \(-0.880641\pi\) |
0.968080 | + | 0.250640i | \(0.0806409\pi\) | |||||||
\(968\) | −75.9059 | −2.43971 | ||||||||
\(969\) | −4.68510 | + | 14.4193i | −0.150507 | + | 0.463213i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.48802 | + | 10.7350i | 0.111936 | + | 0.344503i | 0.991296 | − | 0.131655i | \(-0.0420290\pi\) |
−0.879360 | + | 0.476158i | \(0.842029\pi\) | |||||||
\(972\) | 24.4366 | + | 75.2080i | 0.783803 | + | 2.41230i | ||||
\(973\) | −5.67262 | − | 4.12140i | −0.181856 | − | 0.132126i | ||||
\(974\) | 94.0648 | 3.01403 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.65930 | 0.245168 | ||||||||
\(977\) | 16.4067 | + | 11.9201i | 0.524896 | + | 0.381359i | 0.818445 | − | 0.574585i | \(-0.194836\pi\) |
−0.293549 | + | 0.955944i | \(0.594836\pi\) | |||||||
\(978\) | −7.30061 | − | 22.4690i | −0.233448 | − | 0.718478i | ||||
\(979\) | 3.05855 | + | 9.41323i | 0.0977515 | + | 0.300848i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.894860 | + | 2.75410i | −0.0285707 | + | 0.0879315i | ||||
\(982\) | 40.8162 | 1.30250 | ||||||||
\(983\) | 8.74910 | − | 26.9270i | 0.279053 | − | 0.858837i | −0.709065 | − | 0.705143i | \(-0.750883\pi\) |
0.988118 | − | 0.153694i | \(-0.0491171\pi\) | |||||||
\(984\) | 51.2781 | − | 37.2557i | 1.63469 | − | 1.18767i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 40.7044 | + | 29.5735i | 1.29629 | + | 0.941811i | ||||
\(987\) | 9.49590 | − | 6.89917i | 0.302258 | − | 0.219603i | ||||
\(988\) | 26.6196 | − | 19.3403i | 0.846883 | − | 0.615297i | ||||
\(989\) | 5.38925 | + | 3.91552i | 0.171368 | + | 0.124506i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.3040 | + | 14.0252i | −0.613211 | + | 0.445524i | −0.850544 | − | 0.525905i | \(-0.823727\pi\) |
0.237333 | + | 0.971428i | \(0.423727\pi\) | |||||||
\(992\) | 33.1505 | − | 102.027i | 1.05253 | − | 3.23935i | ||||
\(993\) | 0.984859 | 0.0312536 | ||||||||
\(994\) | 4.96507 | − | 15.2809i | 0.157482 | − | 0.484681i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.84227 | + | 8.74762i | 0.0900609 | + | 0.277179i | ||||
\(997\) | −4.22488 | − | 13.0028i | −0.133803 | − | 0.411804i | 0.861599 | − | 0.507590i | \(-0.169464\pi\) |
−0.995402 | + | 0.0957860i | \(0.969464\pi\) | |||||||
\(998\) | 75.8446 | + | 55.1043i | 2.40082 | + | 1.74430i | ||||
\(999\) | 35.5982 | 1.12628 |
(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 | 625.2.d.n.376.1 | 16 | ||
5.2 | odd | 4 | 625.2.e.k.249.8 | 32 | |||
5.3 | odd | 4 | 625.2.e.k.249.1 | 32 | |||
5.4 | even | 2 | 625.2.d.p.376.4 | 16 | |||
25.2 | odd | 20 | 625.2.e.k.374.1 | 32 | |||
25.3 | odd | 20 | 625.2.e.j.499.8 | 32 | |||
25.4 | even | 10 | 625.2.d.q.126.1 | 16 | |||
25.6 | even | 5 | 625.2.a.g.1.8 | yes | 8 | ||
25.8 | odd | 20 | 625.2.b.d.624.1 | 16 | |||
25.9 | even | 10 | 625.2.d.q.501.1 | 16 | |||
25.11 | even | 5 | inner | 625.2.d.n.251.1 | 16 | ||
25.12 | odd | 20 | 625.2.e.j.124.8 | 32 | |||
25.13 | odd | 20 | 625.2.e.j.124.1 | 32 | |||
25.14 | even | 10 | 625.2.d.p.251.4 | 16 | |||
25.16 | even | 5 | 625.2.d.m.501.4 | 16 | |||
25.17 | odd | 20 | 625.2.b.d.624.16 | 16 | |||
25.19 | even | 10 | 625.2.a.e.1.1 | ✓ | 8 | ||
25.21 | even | 5 | 625.2.d.m.126.4 | 16 | |||
25.22 | odd | 20 | 625.2.e.j.499.1 | 32 | |||
25.23 | odd | 20 | 625.2.e.k.374.8 | 32 | |||
75.44 | odd | 10 | 5625.2.a.be.1.8 | 8 | |||
75.56 | odd | 10 | 5625.2.a.s.1.1 | 8 | |||
100.19 | odd | 10 | 10000.2.a.bn.1.5 | 8 | |||
100.31 | odd | 10 | 10000.2.a.be.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.1 | ✓ | 8 | 25.19 | even | 10 | ||
625.2.a.g.1.8 | yes | 8 | 25.6 | even | 5 | ||
625.2.b.d.624.1 | 16 | 25.8 | odd | 20 | |||
625.2.b.d.624.16 | 16 | 25.17 | odd | 20 | |||
625.2.d.m.126.4 | 16 | 25.21 | even | 5 | |||
625.2.d.m.501.4 | 16 | 25.16 | even | 5 | |||
625.2.d.n.251.1 | 16 | 25.11 | even | 5 | inner | ||
625.2.d.n.376.1 | 16 | 1.1 | even | 1 | trivial | ||
625.2.d.p.251.4 | 16 | 25.14 | even | 10 | |||
625.2.d.p.376.4 | 16 | 5.4 | even | 2 | |||
625.2.d.q.126.1 | 16 | 25.4 | even | 10 | |||
625.2.d.q.501.1 | 16 | 25.9 | even | 10 | |||
625.2.e.j.124.1 | 32 | 25.13 | odd | 20 | |||
625.2.e.j.124.8 | 32 | 25.12 | odd | 20 | |||
625.2.e.j.499.1 | 32 | 25.22 | odd | 20 | |||
625.2.e.j.499.8 | 32 | 25.3 | odd | 20 | |||
625.2.e.k.249.1 | 32 | 5.3 | odd | 4 | |||
625.2.e.k.249.8 | 32 | 5.2 | odd | 4 | |||
625.2.e.k.374.1 | 32 | 25.2 | odd | 20 | |||
625.2.e.k.374.8 | 32 | 25.23 | odd | 20 | |||
5625.2.a.s.1.1 | 8 | 75.56 | odd | 10 | |||
5625.2.a.be.1.8 | 8 | 75.44 | odd | 10 | |||
10000.2.a.be.1.4 | 8 | 100.31 | odd | 10 | |||
10000.2.a.bn.1.5 | 8 | 100.19 | odd | 10 |