Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(47,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.be (of order \(18\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 239.3 | ||
Character | \(\chi\) | \(=\) | 432.239 |
Dual form | 432.2.be.c.47.3 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) |
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 | 0 | ||||||||
\(3\) | −0.721706 | + | 1.57453i | −0.416677 | + | 0.909055i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.976679 | + | 0.172215i | 0.436784 | + | 0.0770169i | 0.387717 | − | 0.921779i | \(-0.373264\pi\) |
0.0490676 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.12803 | − | 3.72784i | −1.18229 | − | 1.40899i | −0.891990 | − | 0.452055i | \(-0.850691\pi\) |
−0.290295 | − | 0.956937i | \(-0.593753\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.95828 | − | 2.27269i | −0.652761 | − | 0.757564i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.961816 | − | 5.45473i | −0.289998 | − | 1.64466i | −0.686864 | − | 0.726786i | \(-0.741013\pi\) |
0.396866 | − | 0.917877i | \(-0.370098\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.65607 | − | 0.966729i | 0.736661 | − | 0.268123i | 0.0536791 | − | 0.998558i | \(-0.482905\pi\) |
0.682981 | + | 0.730436i | \(0.260683\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.976032 | + | 1.41352i | −0.252010 | + | 0.364970i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.517267 | − | 0.298644i | −0.125456 | − | 0.0724319i | 0.435959 | − | 0.899967i | \(-0.356409\pi\) |
−0.561415 | + | 0.827535i | \(0.689743\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.141252 | + | 0.0815519i | −0.0324055 | + | 0.0187093i | −0.516115 | − | 0.856519i | \(-0.672622\pi\) |
0.483710 | + | 0.875228i | \(0.339289\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.12712 | − | 2.23477i | 1.77348 | − | 0.487667i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.35924 | + | 4.49693i | 1.11748 | + | 0.937675i | 0.998474 | − | 0.0552184i | \(-0.0175855\pi\) |
0.119004 | + | 0.992894i | \(0.462030\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.77422 | − | 1.37370i | −0.754844 | − | 0.274741i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.99172 | − | 1.44316i | 0.960658 | − | 0.277736i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.610528 | − | 1.67741i | 0.113372 | − | 0.311488i | −0.870010 | − | 0.493034i | \(-0.835888\pi\) |
0.983382 | + | 0.181546i | \(0.0581101\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.26328 | + | 3.88903i | −0.586102 | + | 0.698490i | −0.974852 | − | 0.222854i | \(-0.928463\pi\) |
0.388750 | + | 0.921343i | \(0.372907\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.28277 | + | 2.42230i | 1.61592 | + | 0.421668i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.41309 | − | 4.17960i | −0.407887 | − | 0.706482i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.726277 | − | 1.25795i | 0.119399 | − | 0.206806i | −0.800131 | − | 0.599826i | \(-0.795236\pi\) |
0.919530 | + | 0.393020i | \(0.128570\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.394755 | + | 4.87975i | −0.0632114 | + | 0.781385i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.84382 | − | 10.5608i | −0.600304 | − | 1.64932i | −0.750658 | − | 0.660691i | \(-0.770264\pi\) |
0.150354 | − | 0.988632i | \(-0.451959\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.11082 | + | 1.07750i | −0.931892 | + | 0.164318i | −0.618928 | − | 0.785447i | \(-0.712433\pi\) |
−0.312964 | + | 0.949765i | \(0.601322\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.52122 | − | 2.55694i | −0.226770 | − | 0.381166i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.37666 | − | 5.35065i | 0.930131 | − | 0.780473i | −0.0457098 | − | 0.998955i | \(-0.514555\pi\) |
0.975841 | + | 0.218482i | \(0.0701105\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.89670 | + | 16.4280i | −0.413814 | + | 2.34685i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.843539 | − | 0.598919i | 0.118119 | − | 0.0838654i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.40465i | − | 1.15447i | −0.816579 | − | 0.577234i | \(-0.804132\pi\) | ||
0.816579 | − | 0.577234i | \(-0.195868\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.49316i | − | 0.740697i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0264635 | − | 0.281262i | −0.00350517 | − | 0.0372541i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.35597 | − | 7.69008i | 0.176532 | − | 1.00116i | −0.759828 | − | 0.650124i | \(-0.774717\pi\) |
0.936361 | − | 0.351040i | \(-0.114172\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.16592 | + | 2.65652i | −0.405354 | + | 0.340133i | −0.822559 | − | 0.568680i | \(-0.807454\pi\) |
0.417204 | + | 0.908813i | \(0.363010\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.34667 | + | 14.4092i | −0.295653 | + | 1.81539i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.76061 | − | 0.486770i | 0.342412 | − | 0.0603764i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.02334 | − | 5.55908i | −0.247190 | − | 0.679150i | −0.999786 | − | 0.0206675i | \(-0.993421\pi\) |
0.752596 | − | 0.658483i | \(-0.228801\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.9483 | + | 5.19281i | −1.31803 | + | 0.625141i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.86491 | + | 3.23013i | −0.221325 | + | 0.383345i | −0.955210 | − | 0.295927i | \(-0.904371\pi\) |
0.733886 | + | 0.679273i | \(0.237705\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.05997 | + | 5.30003i | 0.358143 | + | 0.620321i | 0.987651 | − | 0.156673i | \(-0.0500768\pi\) |
−0.629508 | + | 0.776994i | \(0.716743\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.88681 | − | 4.95121i | 0.564280 | − | 0.571716i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −17.3258 | + | 20.6481i | −1.97446 | + | 2.35306i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.05391 | + | 11.1380i | −0.456100 | + | 1.25312i | 0.472266 | + | 0.881456i | \(0.343436\pi\) |
−0.928366 | + | 0.371668i | \(0.878786\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.33026 | + | 8.90115i | −0.147807 | + | 0.989016i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.04948 | + | 3.29374i | 0.993309 | + | 0.361535i | 0.787001 | − | 0.616952i | \(-0.211633\pi\) |
0.206308 | + | 0.978487i | \(0.433855\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.453773 | − | 0.380761i | −0.0492186 | − | 0.0412993i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.20051 | + | 2.17189i | 0.235920 | + | 0.232851i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.45033 | + | 0.837348i | −0.153735 | + | 0.0887587i | −0.574894 | − | 0.818228i | \(-0.694957\pi\) |
0.421159 | + | 0.906987i | \(0.361623\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.9121 | − | 6.87744i | −1.24873 | − | 0.720952i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.76826 | − | 7.94486i | −0.390750 | − | 0.823844i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.152002 | + | 0.0553244i | −0.0155951 | + | 0.00567616i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.34010 | − | 13.2714i | −0.237601 | − | 1.34750i | −0.837066 | − | 0.547102i | \(-0.815731\pi\) |
0.599465 | − | 0.800401i | \(-0.295380\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.5134 | + | 12.8678i | −1.05664 | + | 1.29326i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.98820 | + | 10.7117i | 0.894360 | + | 1.06586i | 0.997463 | + | 0.0711857i | \(0.0226783\pi\) |
−0.103103 | + | 0.994671i | \(0.532877\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.43335 | + | 0.958047i | 0.535364 | + | 0.0943991i | 0.434792 | − | 0.900531i | \(-0.356822\pi\) |
0.100572 | + | 0.994930i | \(0.467933\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.32245 | − | 0.783045i | 0.812188 | − | 0.0764173i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3996 | 1.10204 | 0.551021 | − | 0.834491i | \(-0.314238\pi\) | ||||
0.551021 | + | 0.834491i | \(0.314238\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4472 | 1.00066 | 0.500329 | − | 0.865835i | \(-0.333212\pi\) | ||||
0.500329 | + | 0.865835i | \(0.333212\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.45652 | + | 2.05141i | 0.138247 | + | 0.194712i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.27678 | − | 0.577786i | −0.308254 | − | 0.0543535i | 0.0173814 | − | 0.999849i | \(-0.494467\pi\) |
−0.325635 | + | 0.945495i | \(0.605578\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.45982 | + | 5.31500i | 0.415880 | + | 0.495627i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.39841 | − | 4.14330i | −0.683983 | − | 0.383048i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.504729 | + | 2.86246i | 0.0462684 | + | 0.262401i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.4923 | + | 6.73066i | −1.68112 | + | 0.611878i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 19.4024 | + | 1.56959i | 1.74946 | + | 0.141525i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.74402 | − | 4.47101i | −0.692646 | − | 0.399899i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.80947 | + | 2.19940i | −0.338036 | + | 0.195165i | −0.659403 | − | 0.751790i | \(-0.729191\pi\) |
0.321367 | + | 0.946955i | \(0.395858\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.71366 | − | 10.3993i | 0.238924 | − | 0.915608i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.04355 | + | 0.875644i | 0.0911755 | + | 0.0765053i | 0.687236 | − | 0.726434i | \(-0.258824\pi\) |
−0.596061 | + | 0.802939i | \(0.703268\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.745854 | + | 0.271469i | 0.0646737 | + | 0.0235393i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.12385 | − | 0.549852i | 0.440990 | − | 0.0473238i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.38622 | + | 3.80861i | −0.118433 | + | 0.325391i | −0.984718 | − | 0.174159i | \(-0.944279\pi\) |
0.866285 | + | 0.499551i | \(0.166501\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0544 | − | 11.9823i | 0.852801 | − | 1.01633i | −0.146830 | − | 0.989162i | \(-0.546907\pi\) |
0.999631 | − | 0.0271664i | \(-0.00864840\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.82269 | + | 13.9018i | 0.321928 | + | 1.17075i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.82789 | − | 13.5583i | −0.654601 | − | 1.13380i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.885166 | − | 1.53315i | 0.0735090 | − | 0.127321i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −23.7758 | − | 16.4171i | −1.96099 | − | 1.35406i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.36175 | + | 6.48884i | 0.193482 | + | 0.531587i | 0.998060 | − | 0.0622599i | \(-0.0198308\pi\) |
−0.804578 | + | 0.593847i | \(0.797609\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.40054 | − | 0.952262i | 0.439490 | − | 0.0774940i | 0.0504750 | − | 0.998725i | \(-0.483926\pi\) |
0.389015 | + | 0.921231i | \(0.372815\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.334228 | + | 1.76042i | 0.0270208 | + | 0.142321i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.85693 | + | 3.23635i | −0.309796 | + | 0.259949i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.626364 | − | 3.55229i | 0.0499893 | − | 0.283503i | −0.949558 | − | 0.313592i | \(-0.898468\pi\) |
0.999547 | + | 0.0300883i | \(0.00957885\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.2334 | + | 6.06568i | 1.04947 | + | 0.481040i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 34.0449i | − | 2.68312i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.07293i | − | 0.397343i | −0.980066 | − | 0.198671i | \(-0.936337\pi\) | ||
0.980066 | − | 0.198671i | \(-0.0636627\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.64914 | + | 3.96444i | 0.673334 | + | 0.308631i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.81056 | + | 10.2682i | −0.140105 | + | 0.794576i | 0.831062 | + | 0.556179i | \(0.187733\pi\) |
−0.971168 | + | 0.238397i | \(0.923378\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.83845 | + | 3.22084i | −0.295265 | + | 0.247757i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.461954 | + | 0.161321i | 0.0353265 | + | 0.0123365i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.5905 | − | 3.45433i | 1.48944 | − | 0.262628i | 0.631094 | − | 0.775707i | \(-0.282606\pi\) |
0.858341 | + | 0.513079i | \(0.171495\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.68493 | + | 18.3667i | 0.505333 | + | 1.38839i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.1296 | + | 7.68499i | 0.836555 | + | 0.577639i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.51483 | + | 13.0161i | −0.561685 | + | 0.972866i | 0.435665 | + | 0.900109i | \(0.356513\pi\) |
−0.997350 | + | 0.0727573i | \(0.976820\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.08688 | + | 3.61458i | 0.155116 | + | 0.268669i | 0.933101 | − | 0.359613i | \(-0.117091\pi\) |
−0.777985 | + | 0.628283i | \(0.783758\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.89791 | − | 6.90206i | −0.140297 | − | 0.510215i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.925978 | − | 1.10354i | 0.0680792 | − | 0.0811337i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.13151 | + | 3.10879i | −0.0827440 | + | 0.227337i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −20.9941 | − | 14.0941i | −1.52710 | − | 1.02520i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.5495 | − | 8.20734i | −1.63162 | − | 0.593862i | −0.646078 | − | 0.763272i | \(-0.723592\pi\) |
−0.985546 | + | 0.169409i | \(0.945814\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.52079 | + | 5.47159i | 0.469377 | + | 0.393854i | 0.846567 | − | 0.532282i | \(-0.178665\pi\) |
−0.377191 | + | 0.926136i | \(0.623110\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.22591 | + | 4.69797i | −0.0877896 | + | 0.336428i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.63484 | − | 2.09858i | 0.258972 | − | 0.149517i | −0.364894 | − | 0.931049i | \(-0.618895\pi\) |
0.623865 | + | 0.781532i | \(0.285561\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.58250 | + | 2.64571i | 0.324845 | + | 0.187549i | 0.653550 | − | 0.756883i | \(-0.273279\pi\) |
−0.328705 | + | 0.944433i | \(0.606612\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.2132 | + | 0.826213i | 0.720383 | + | 0.0582765i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.16288 | + | 2.97105i | −0.572922 | + | 0.208527i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.93545 | − | 10.9765i | −0.135178 | − | 0.766632i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.274751 | − | 20.9862i | −0.0190965 | − | 1.45864i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.580702 | + | 0.692054i | 0.0401680 | + | 0.0478704i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.1463 | + | 1.96540i | 0.767344 | + | 0.135303i | 0.543600 | − | 0.839345i | \(-0.317061\pi\) |
0.223744 | + | 0.974648i | \(0.428172\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.74001 | − | 5.26756i | −0.256261 | − | 0.360927i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.15388 | −0.419691 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.7053 | 1.67711 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.5534 | + | 0.992956i | −0.713136 | + | 0.0670977i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.66260 | − | 0.293162i | −0.111839 | − | 0.0197202i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.2504 | − | 13.4077i | −0.753380 | − | 0.897843i | 0.244030 | − | 0.969768i | \(-0.421530\pi\) |
−0.997410 | + | 0.0719243i | \(0.977086\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.26898 | + | 11.2677i | 0.284599 | + | 0.751182i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.724677 | − | 4.10985i | −0.0480985 | − | 0.272780i | 0.951268 | − | 0.308365i | \(-0.0997817\pi\) |
−0.999367 | + | 0.0355847i | \(0.988671\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.78302 | + | 0.648967i | −0.117825 | + | 0.0428849i | −0.400260 | − | 0.916402i | \(-0.631080\pi\) |
0.282435 | + | 0.959287i | \(0.408858\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −20.0069 | − | 42.1818i | −1.31635 | − | 2.77536i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.7256 | + | 9.07917i | 1.03022 | + | 0.594796i | 0.917047 | − | 0.398779i | \(-0.130566\pi\) |
0.113171 | + | 0.993576i | \(0.463899\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.14941 | − | 4.12772i | 0.466376 | − | 0.269262i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.6114 | − | 14.4214i | −0.949112 | − | 0.936768i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.3664 | + | 11.2158i | 0.864602 | + | 0.725487i | 0.962954 | − | 0.269665i | \(-0.0869129\pi\) |
−0.0983526 | + | 0.995152i | \(0.531357\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.1799 | − | 9.16473i | −1.62198 | − | 0.590352i | −0.638222 | − | 0.769853i | \(-0.720330\pi\) |
−0.983758 | + | 0.179500i | \(0.942552\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.0551 | − | 8.51854i | −0.837482 | − | 0.546465i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.65828 | + | 15.5460i | −0.361495 | + | 0.993198i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.296336 | + | 0.353160i | −0.0188554 | + | 0.0224710i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.7171 | + | 11.8716i | −0.742544 | + | 0.752329i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.18578 | − | 15.9102i | −0.579801 | − | 1.00425i | −0.995502 | − | 0.0947437i | \(-0.969797\pi\) |
0.415700 | − | 0.909502i | \(-0.363536\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.3749 | − | 33.5584i | 1.21809 | − | 2.10980i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.927009 | − | 0.439682i | 0.0580516 | − | 0.0275339i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.13045 | + | 19.5908i | 0.444786 | + | 1.22204i | 0.936310 | + | 0.351174i | \(0.114218\pi\) |
−0.491525 | + | 0.870864i | \(0.663560\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.96126 | + | 1.22746i | −0.432551 | + | 0.0762705i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.00783 | + | 1.89730i | −0.309977 | + | 0.117440i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.5295 | − | 17.2263i | 1.26590 | − | 1.06222i | 0.270878 | − | 0.962614i | \(-0.412686\pi\) |
0.995027 | − | 0.0996068i | \(-0.0317585\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.44741 | − | 8.20865i | 0.0889135 | − | 0.504253i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.271718 | − | 2.88790i | −0.0166289 | − | 0.176737i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.10651i | 0.372321i | 0.982519 | + | 0.186160i | \(0.0596044\pi\) | ||||
−0.982519 | + | 0.186160i | \(0.940396\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.24989i | − | 0.318908i | −0.987205 | − | 0.159454i | \(-0.949027\pi\) | ||
0.987205 | − | 0.159454i | \(-0.0509734\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.4257 | − | 13.7924i | 1.17570 | − | 0.834756i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.86307 | + | 21.9086i | −0.232952 | + | 1.32114i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.8063 | − | 18.2977i | 1.31022 | − | 1.09940i | 0.321934 | − | 0.946762i | \(-0.395667\pi\) |
0.988282 | − | 0.152640i | \(-0.0487775\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.2290 | − | 0.199378i | 0.911735 | − | 0.0119364i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.99467 | − | 0.528040i | 0.178647 | − | 0.0315002i | −0.0836090 | − | 0.996499i | \(-0.526645\pi\) |
0.262256 | + | 0.964998i | \(0.415534\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.13245 | + | 14.1013i | 0.305092 | + | 0.838235i | 0.993595 | + | 0.113001i | \(0.0360462\pi\) |
−0.688502 | + | 0.725234i | \(0.741732\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0225912 | − | 0.279260i | 0.00133819 | − | 0.0165419i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.3455 | + | 47.3638i | −1.61415 | + | 2.79579i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.32162 | − | 14.4135i | −0.489507 | − | 0.847851i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.5850 | + | 5.89346i | 1.32396 | + | 0.345481i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.3270 | − | 14.6907i | 0.720150 | − | 0.858241i | −0.274495 | − | 0.961588i | \(-0.588511\pi\) |
0.994645 | + | 0.103347i | \(0.0329552\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.64869 | − | 7.27723i | 0.154213 | − | 0.423696i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.6731 | − | 25.8404i | −0.735370 | − | 1.49941i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.5818 | + | 6.76323i | 1.07461 | + | 0.391127i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.1316 | + | 19.4097i | 1.33328 | + | 1.11876i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −23.3528 | + | 6.42147i | −1.34158 | + | 0.368904i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.54958 | + | 2.04935i | −0.203248 | + | 0.117346i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.9719 | + | 8.06666i | 0.797416 | + | 0.460388i | 0.842567 | − | 0.538592i | \(-0.181043\pi\) |
−0.0451507 | + | 0.998980i | \(0.514377\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.42975 | + | 7.86354i | −0.308888 | + | 0.447341i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.9054 | − | 6.51704i | 1.01532 | − | 0.369548i | 0.219849 | − | 0.975534i | \(-0.429444\pi\) |
0.795475 | + | 0.605986i | \(0.207221\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.68661 | + | 9.56523i | 0.0953328 | + | 0.540659i | 0.994645 | + | 0.103352i | \(0.0329567\pi\) |
−0.899312 | + | 0.437307i | \(0.855932\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.77343 | + | 13.6691i | −0.268952 | + | 0.770164i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.4921 | + | 14.8875i | 0.701628 | + | 0.836167i | 0.992710 | − | 0.120531i | \(-0.0384596\pi\) |
−0.291082 | + | 0.956698i | \(0.594015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.73704 | − | 1.71690i | −0.545170 | − | 0.0961281i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.22716 | + | 17.9490i | −0.459195 | + | 1.00182i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0974201 | 0.00542060 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.3526 | −0.629728 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.53979 | + | 16.4494i | −0.416951 | + | 0.909653i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −39.8928 | − | 7.03417i | −2.19936 | − | 0.387807i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.1483 | + | 25.2035i | 1.16241 | + | 1.38531i | 0.908395 | + | 0.418113i | \(0.137308\pi\) |
0.254020 | + | 0.967199i | \(0.418247\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.28119 | + | 0.812814i | −0.234608 | + | 0.0445420i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.01880 | − | 5.77789i | −0.0556629 | − | 0.315680i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.50899 | + | 1.27717i | −0.191147 | + | 0.0695717i | −0.435820 | − | 0.900034i | \(-0.643542\pi\) |
0.244673 | + | 0.969606i | \(0.421319\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.27461 | − | 4.74240i | 0.177853 | − | 0.257572i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.3522 | + | 14.0598i | 1.31875 | + | 0.761380i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 40.8012 | − | 23.5566i | 2.20306 | − | 1.27193i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.5873 | + | 3.18624i | −0.623839 | + | 0.171542i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.2766 | − | 14.4968i | −0.927456 | − | 0.778228i | 0.0479028 | − | 0.998852i | \(-0.484746\pi\) |
−0.975359 | + | 0.220624i | \(0.929191\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.89430 | − | 2.87329i | −0.422572 | − | 0.153804i | 0.121977 | − | 0.992533i | \(-0.461077\pi\) |
−0.544548 | + | 0.838729i | \(0.683299\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.8632 | − | 8.65877i | 0.633211 | − | 0.462171i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.50025 | − | 26.1017i | 0.505648 | − | 1.38926i | −0.380039 | − | 0.924971i | \(-0.624089\pi\) |
0.885686 | − | 0.464285i | \(-0.153688\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.37770 | + | 2.83363i | −0.126195 | + | 0.150394i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.87129 | − | 1.27114i | −0.257816 | − | 0.0672760i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.1197 | − | 19.2599i | −0.586877 | − | 1.01650i | −0.994639 | − | 0.103412i | \(-0.967024\pi\) |
0.407762 | − | 0.913088i | \(-0.366309\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.48670 | + | 16.4314i | −0.499300 | + | 0.864813i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.74840 | − | 33.9743i | 0.144254 | − | 1.78319i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.07587 | + | 5.70340i | 0.108656 | + | 0.298530i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.99817 | − | 1.23397i | 0.365302 | − | 0.0644125i | 0.0120154 | − | 0.999928i | \(-0.496175\pi\) |
0.353286 | + | 0.935515i | \(0.385064\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.4742 | + | 29.4169i | −0.857613 | + | 1.53138i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.3312 | + | 26.2900i | −1.62664 | + | 1.36491i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.08072 | + | 17.4716i | −0.159514 | + | 0.904646i | 0.795029 | + | 0.606571i | \(0.207456\pi\) |
−0.954543 | + | 0.298075i | \(0.903656\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.6286 | − | 8.96642i | 0.652140 | − | 0.463024i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.04554i | − | 0.259858i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.696553i | 0.0357795i | 0.999840 | + | 0.0178898i | \(0.00569479\pi\) | ||||
−0.999840 | + | 0.0178898i | \(0.994305\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.713701 | − | 7.58544i | −0.0365640 | − | 0.388614i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.97272 | + | 16.8591i | −0.151899 | + | 0.861462i | 0.809667 | + | 0.586889i | \(0.199648\pi\) |
−0.961566 | + | 0.274573i | \(0.911464\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.4776 | + | 17.1828i | −1.04364 | + | 0.875715i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.4156 | + | 11.7780i | 0.732784 | + | 0.598708i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.9672 | + | 2.99177i | −0.860269 | + | 0.151689i | −0.586344 | − | 0.810062i | \(-0.699433\pi\) |
−0.273925 | + | 0.961751i | \(0.588322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.42917 | − | 3.92662i | −0.0722764 | − | 0.198578i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.13186 | + | 1.01114i | −0.107538 | + | 0.0510055i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.87750 | + | 10.1801i | −0.295729 | + | 0.512218i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.24458 | + | 7.35182i | 0.213029 | + | 0.368977i | 0.952661 | − | 0.304034i | \(-0.0983337\pi\) |
−0.739632 | + | 0.673012i | \(0.765000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.965722 | + | 0.978448i | −0.0483466 | + | 0.0489837i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.54824 | − | 7.80389i | 0.327004 | − | 0.389708i | −0.577346 | − | 0.816499i | \(-0.695912\pi\) |
0.904350 | + | 0.426792i | \(0.140356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.90786 | + | 13.4842i | −0.244478 | + | 0.671697i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.83215 | + | 8.46447i | −0.140731 | + | 0.420603i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.56031 | − | 2.75173i | −0.374751 | − | 0.136398i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.6107 | − | 15.6162i | −0.920238 | − | 0.772171i | 0.0538011 | − | 0.998552i | \(-0.482866\pi\) |
−0.974039 | + | 0.226380i | \(0.927311\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.99632 | − | 4.93134i | −0.246450 | − | 0.243245i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −32.9089 | + | 19.0000i | −1.61934 | + | 0.934928i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.27121 | + | 4.77538i | 0.406018 | + | 0.234414i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.6102 | + | 24.4786i | 0.568556 | + | 1.19872i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.0629252 | − | 0.0229029i | 0.00307410 | − | 0.00111888i | −0.340483 | − | 0.940251i | \(-0.610590\pi\) |
0.343557 | + | 0.939132i | \(0.388368\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.84853 | − | 27.4974i | −0.236303 | − | 1.34014i | −0.839853 | − | 0.542814i | \(-0.817359\pi\) |
0.603550 | − | 0.797325i | \(-0.293752\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24.6477 | − | 4.01410i | −1.19841 | − | 0.195172i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.54203 | + | 1.83772i | 0.0747995 | + | 0.0891425i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.8062 | + | 3.49237i | 0.958489 | + | 0.169007i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.9974 | − | 2.54014i | 1.30345 | − | 0.122639i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.9982 | 1.39679 | 0.698397 | − | 0.715710i | \(-0.253897\pi\) | ||||
0.698397 | + | 0.715710i | \(0.253897\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.6912 | −1.23464 | −0.617320 | − | 0.786712i | \(-0.711782\pi\) | ||||
−0.617320 | + | 0.786712i | \(0.711782\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.77516 | + | 2.50020i | 0.0851126 | + | 0.119876i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.12374 | − | 0.198145i | −0.0537556 | − | 0.00947857i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.68012 | − | 10.3446i | −0.414280 | − | 0.493719i | 0.518039 | − | 0.855357i | \(-0.326662\pi\) |
−0.932319 | + | 0.361638i | \(0.882218\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 43.0083 | − | 25.5873i | 2.04801 | − | 1.21844i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.24107 | + | 7.03844i | 0.0589649 | + | 0.334406i | 0.999992 | − | 0.00392386i | \(-0.00124901\pi\) |
−0.941027 | + | 0.338330i | \(0.890138\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.56071 | + | 0.568052i | −0.0739848 | + | 0.0269283i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.9214 | − | 0.964397i | −0.563861 | − | 0.0456144i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.7841 | − | 10.8450i | −0.886477 | − | 0.511807i | −0.0136882 | − | 0.999906i | \(-0.504357\pi\) |
−0.872788 | + | 0.488099i | \(0.837691\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −53.9093 | + | 31.1246i | −2.53849 | + | 1.46560i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.39824 | + | 9.19057i | −0.112679 | + | 0.431810i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.4499 | − | 8.76849i | −0.489898 | − | 0.411073i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.0401 | + | 12.3896i | 1.59233 | + | 0.579561i | 0.977838 | − | 0.209363i | \(-0.0671390\pi\) |
0.614492 | + | 0.788923i | \(0.289361\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.01304 | − | 0.744252i | −0.140637 | − | 0.0347387i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.10359 | + | 11.2745i | −0.191123 | + | 0.525107i | −0.997830 | − | 0.0658453i | \(-0.979026\pi\) |
0.806707 | + | 0.590952i | \(0.201248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.669388 | + | 0.797745i | −0.0311091 | + | 0.0370744i | −0.781375 | − | 0.624062i | \(-0.785481\pi\) |
0.750266 | + | 0.661137i | \(0.229926\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.31215 | − | 8.40853i | −0.107224 | − | 0.389936i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.21810 | + | 3.84186i | 0.102641 | + | 0.177780i | 0.912772 | − | 0.408469i | \(-0.133937\pi\) |
−0.810131 | + | 0.586249i | \(0.800604\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.3943 | + | 24.9317i | −0.664668 | + | 1.15124i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.14113 | + | 3.54993i | 0.236891 | + | 0.163572i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.7550 | + | 32.2965i | 0.540494 | + | 1.48500i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.645144 | − | 0.113756i | 0.0296013 | − | 0.00521950i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.1012 | + | 16.4587i | −0.874583 | + | 0.753591i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.7569 | − | 10.7043i | 0.582876 | − | 0.489091i | −0.303014 | − | 0.952986i | \(-0.597993\pi\) |
0.885890 | + | 0.463895i | \(0.153548\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.712945 | − | 4.04331i | 0.0325075 | − | 0.184359i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 53.6048 | + | 24.5704i | 2.43910 | + | 1.11799i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 13.3649i | − | 0.606867i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.4161i | 0.698570i | 0.937016 | + | 0.349285i | \(0.113576\pi\) | ||||
−0.937016 | + | 0.349285i | \(0.886424\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.98748 | + | 3.66117i | 0.361206 | + | 0.165564i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.16739 | − | 6.62060i | 0.0526836 | − | 0.298784i | −0.947069 | − | 0.321030i | \(-0.895971\pi\) |
0.999753 | + | 0.0222468i | \(0.00708195\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.816756 | + | 0.685340i | −0.0367848 | + | 0.0308661i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.4843 | + | 10.7572i | −0.561126 | + | 0.483498i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.8749 | − | 3.15183i | 0.801799 | − | 0.141379i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.8160 | − | 32.4641i | −0.528956 | − | 1.45329i | −0.860302 | − | 0.509785i | \(-0.829725\pi\) |
0.331346 | − | 0.943509i | \(-0.392497\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.8609 | − | 10.2614i | −0.663935 | − | 0.458445i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.55590 | − | 13.0872i | 0.336901 | − | 0.583530i | −0.646947 | − | 0.762535i | \(-0.723955\pi\) |
0.983848 | + | 0.179005i | \(0.0572879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.93387 | + | 12.0098i | 0.308553 | + | 0.534430i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.30108 | − | 8.36825i | −0.102194 | − | 0.371647i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.27599 | + | 6.28768i | −0.233854 | + | 0.278696i | −0.870191 | − | 0.492715i | \(-0.836004\pi\) |
0.636337 | + | 0.771411i | \(0.280449\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.1860 | − | 27.9858i | 0.450601 | − | 1.23802i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.587399 | + | 0.610934i | −0.0259343 | + | 0.0269734i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.14165 | + | 1.87141i | 0.226568 | + | 0.0824641i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −35.3195 | − | 29.6366i | −1.55335 | − | 1.30342i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.69961 | + | 33.3388i | −0.381870 | + | 1.46341i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.45686 | + | 1.41847i | −0.107637 | + | 0.0621444i | −0.552852 | − | 0.833279i | \(-0.686461\pi\) |
0.445215 | + | 0.895424i | \(0.353127\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.4086 | − | 15.2470i | −1.15477 | − | 0.666705i | −0.204722 | − | 0.978820i | \(-0.565629\pi\) |
−0.950044 | + | 0.312116i | \(0.898962\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −33.7434 | − | 2.72973i | −1.47268 | − | 0.119135i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.84942 | − | 1.03710i | 0.124123 | − | 0.0451770i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.50510 | + | 25.5497i | 0.195874 | + | 1.11086i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.1326 | + | 11.9776i | −0.873679 | + | 0.519786i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.4189 | − | 24.3343i | −0.884441 | − | 1.05404i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.1338 | + | 1.96318i | 0.481355 | + | 0.0848758i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.0707 | − | 21.2261i | −0.650348 | − | 0.915973i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 92.3962 | 3.97979 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.3176 | 1.51842 | 0.759212 | − | 0.650844i | \(-0.225585\pi\) | ||||
0.759212 | + | 0.650844i | \(0.225585\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.19737 | + | 0.677188i | −0.308869 | + | 0.0290609i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.2035 | + | 1.79916i | 0.437072 | + | 0.0770676i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.0568 | + | 15.5605i | 0.558270 | + | 0.665320i | 0.969179 | − | 0.246356i | \(-0.0792332\pi\) |
−0.410909 | + | 0.911676i | \(0.634789\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.2372 | + | 1.99294i | 0.522272 | + | 0.0850567i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0505578 | + | 0.286728i | 0.00215384 | + | 0.0122150i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 54.2015 | − | 19.7277i | 2.30488 | − | 0.838909i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.06927 | + | 2.25441i | 0.0453879 | + | 0.0956943i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.5321 | + | 15.3183i | 1.12420 | + | 0.649059i | 0.942471 | − | 0.334289i | \(-0.108496\pi\) |
0.181733 | + | 0.983348i | \(0.441830\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.1891 | + | 8.76943i | −0.642431 | + | 0.370908i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.07827 | − | 4.02522i | −0.172185 | − | 0.169945i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.2500 | − | 12.7963i | −0.642712 | − | 0.539299i | 0.262138 | − | 0.965030i | \(-0.415572\pi\) |
−0.904850 | + | 0.425731i | \(0.860017\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.10086 | − | 1.12862i | −0.130454 | − | 0.0474815i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 37.3432 | − | 22.8841i | 1.56827 | − | 0.961040i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.77000 | + | 7.61051i | −0.116124 | + | 0.319049i | −0.984115 | − | 0.177531i | \(-0.943189\pi\) |
0.867991 | + | 0.496580i | \(0.165411\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7051 | − | 16.3331i | 0.573540 | − | 0.683518i | −0.398814 | − | 0.917032i | \(-0.630578\pi\) |
0.972353 | + | 0.233514i | \(0.0750224\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29.1968 | − | 29.5815i | 1.21971 | − | 1.23579i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.0495 | − | 24.3344i | −0.585904 | − | 1.01482i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.0682767 | − | 0.118259i | 0.00284239 | − | 0.00492317i | −0.864601 | − | 0.502460i | \(-0.832429\pi\) |
0.867443 | + | 0.497536i | \(0.165762\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.3213 | + | 6.31829i | −0.553613 | + | 0.262579i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.0285 | − | 44.0380i | −0.664975 | − | 1.82700i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −45.8451 | + | 8.08372i | −1.89871 | + | 0.334794i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.51233 | − | 5.32079i | −0.269252 | − | 0.219987i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.3306 | + | 17.8985i | −0.880407 | + | 0.738749i | −0.966263 | − | 0.257558i | \(-0.917082\pi\) |
0.0858556 | + | 0.996308i | \(0.472638\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.143788 | − | 0.815460i | 0.00592466 | − | 0.0336004i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.680984 | + | 7.23771i | 0.0280119 | + | 0.297720i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 16.6379i | − | 0.683238i | −0.939839 | − | 0.341619i | \(-0.889025\pi\) | ||
0.939839 | − | 0.341619i | \(-0.110975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.88263i | 0.118176i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.47297 | + | 5.30586i | −0.305848 | + | 0.217154i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.24539 | − | 24.0768i | 0.173462 | − | 0.983752i | −0.766442 | − | 0.642314i | \(-0.777975\pi\) |
0.939904 | − | 0.341439i | \(-0.110914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.7637 | − | 25.8138i | 1.25488 | − | 1.05297i | 0.258671 | − | 0.965965i | \(-0.416715\pi\) |
0.996208 | − | 0.0870032i | \(-0.0277290\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.67181 | + | 15.4847i | −0.353144 | + | 0.630585i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.2202 | + | 3.38904i | −0.781413 | + | 0.137784i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.65409 | − | 15.5345i | −0.229493 | − | 0.630526i | 0.770483 | − | 0.637460i | \(-0.220015\pi\) |
−0.999976 | + | 0.00693444i | \(0.997793\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.21320 | − | 14.9969i | 0.0491613 | − | 0.607706i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.7642 | − | 20.3762i | 0.475929 | − | 0.824333i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00864 | − | 1.74701i | −0.0407385 | − | 0.0705611i | 0.844937 | − | 0.534865i | \(-0.179638\pi\) |
−0.885676 | + | 0.464304i | \(0.846304\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.6796 | + | 4.87437i | 0.753236 | + | 0.196554i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.7709 | − | 24.7538i | 0.836204 | − | 0.996549i | −0.163746 | − | 0.986503i | \(-0.552358\pi\) |
0.999950 | − | 0.0100465i | \(-0.00319796\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.84499 | − | 13.3115i | 0.194737 | − | 0.535035i | −0.803441 | − | 0.595385i | \(-0.797000\pi\) |
0.998177 | + | 0.0603502i | \(0.0192217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 33.2416 | + | 14.7132i | 1.33394 | + | 0.590421i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.65818 | + | 2.78735i | 0.306818 | + | 0.111673i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.59041 | + | 7.20821i | 0.343616 | + | 0.288328i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.50875 | + | 0.414873i | −0.0602538 | + | 0.0165684i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.751359 | + | 0.433797i | −0.0299586 | + | 0.0172966i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.0965 | − | 7.56128i | −0.521365 | − | 0.301010i | 0.216128 | − | 0.976365i | \(-0.430657\pi\) |
−0.737493 | + | 0.675355i | \(0.763990\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.1389 | + | 16.1318i | −0.442733 | + | 0.641180i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.09940 | + | 1.49206i | −0.162680 | + | 0.0592106i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.18759 | + | 46.4341i | 0.324404 | + | 1.83979i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.9931 | − | 2.08712i | 0.434881 | − | 0.0825653i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.66991 | + | 3.18187i | 0.105455 | + | 0.125676i | 0.816190 | − | 0.577783i | \(-0.196082\pi\) |
−0.710735 | + | 0.703460i | \(0.751638\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.0780 | − | 7.59582i | −1.69883 | − | 0.299550i | −0.761546 | − | 0.648111i | \(-0.775559\pi\) |
−0.937286 | + | 0.348561i | \(0.886671\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.44129 | − | 9.68946i | 0.174876 | − | 0.381522i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.1823 | −0.478936 | −0.239468 | − | 0.970904i | \(-0.576973\pi\) | ||||
−0.239468 | + | 0.970904i | \(0.576973\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −43.2515 | −1.69777 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.8300 | + | 38.8992i | −0.698812 | + | 1.52458i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.7762 | + | 6.48464i | 1.43916 | + | 0.253763i | 0.838135 | − | 0.545463i | \(-0.183646\pi\) |
0.601030 | + | 0.799227i | \(0.294757\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.868416 | + | 1.03494i | 0.0339318 | + | 0.0404384i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.05305 | − | 17.3333i | 0.236152 | − | 0.676238i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.48344 | + | 8.41298i | 0.0577865 | + | 0.327723i | 0.999973 | − | 0.00736587i | \(-0.00234465\pi\) |
−0.942186 | + | 0.335089i | \(0.891234\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.439161 | − | 0.159841i | 0.0170814 | − | 0.00621711i | −0.333465 | − | 0.942762i | \(-0.608218\pi\) |
0.350547 | + | 0.936545i | \(0.385996\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.66150 | − | 2.40624i | 0.0645274 | − | 0.0934507i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.681709 | + | 0.393585i | 0.0264355 | + | 0.0152626i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.8152 | − | 6.24415i | 0.418765 | − | 0.241774i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.2302 | − | 8.03764i | 1.13010 | − | 0.310753i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.5356 | + | 14.7141i | 0.676956 | + | 0.568033i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.43038 | + | 1.61253i | 0.170779 | + | 0.0621584i | 0.425994 | − | 0.904726i | \(-0.359924\pi\) |
−0.255216 | + | 0.966884i | \(0.582147\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.8223 | − | 1.41036i | −0.801452 | − | 0.0542846i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.86735 | − | 27.1103i | 0.379233 | − | 1.04193i | −0.592442 | − | 0.805613i | \(-0.701836\pi\) |
0.971675 | − | 0.236321i | \(-0.0759417\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −42.1537 | + | 50.2368i | −1.61771 | + | 1.92791i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.99407 | + | 1.82507i | 0.268014 | + | 0.0699370i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.0332 | − | 38.1626i | −0.843076 | − | 1.46025i | −0.887282 | − | 0.461228i | \(-0.847409\pi\) |
0.0442060 | − | 0.999022i | \(-0.485924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.00979 | + | 3.48106i | −0.0767902 | + | 0.133004i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.265000 | − | 3.27578i | 0.0101104 | − | 0.124979i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.12502 | − | 22.3233i | −0.309539 | − | 0.850451i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.2765 | − | 7.27817i | 1.57023 | − | 0.276875i | 0.680289 | − | 0.732944i | \(-0.261854\pi\) |
0.889944 | + | 0.456069i | \(0.150743\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 80.8555 | − | 1.05856i | 3.07144 | − | 0.0402114i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.8834 | − | 9.97138i | 0.450764 | − | 0.378236i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.16564 | + | 6.61070i | −0.0441519 | + | 0.250398i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.6447 | + | 18.2079i | −0.969970 | + | 0.688686i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.277648i | 0.0104866i | 0.999986 | + | 0.00524332i | \(0.00166901\pi\) | ||||
−0.999986 | + | 0.00524332i | \(0.998331\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.236917i | 0.00893550i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.33944 | + | 14.2360i | 0.0504461 | + | 0.536157i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.8162 | − | 67.0132i | 0.444395 | − | 2.52029i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.9969 | + | 22.6531i | −1.01389 | + | 0.850754i | −0.988847 | − | 0.148933i | \(-0.952416\pi\) |
−0.0250415 | + | 0.999686i | \(0.507972\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 33.2520 | − | 12.5981i | 1.24705 | − | 0.472465i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −34.9774 | + | 6.16746i | −1.30991 | + | 0.230973i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.31040 | − | 14.5902i | −0.198598 | − | 0.545642i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.3061 | + | 12.9513i | −1.01977 | + | 0.483677i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.5033 | + | 44.1730i | −0.951113 | + | 1.64738i | −0.208091 | + | 0.978109i | \(0.566725\pi\) |
−0.743022 | + | 0.669267i | \(0.766608\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4243 | − | 23.2515i | −0.499945 | − | 0.865931i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.6026 | − | 33.0322i | 1.21250 | − | 1.22848i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.60853 | + | 5.49224i | −0.171157 | + | 0.203977i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.74866 | + | 10.2994i | −0.139030 | + | 0.381982i | −0.989594 | − | 0.143890i | \(-0.954039\pi\) |
0.850564 | + | 0.525872i | \(0.176261\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.8346 | − | 14.4077i | 0.845726 | − | 0.533618i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.48272 | + | 1.26761i | 0.128813 | + | 0.0468841i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.12425 | − | 4.29976i | −0.189269 | − | 0.158815i | 0.543230 | − | 0.839584i | \(-0.317201\pi\) |
−0.732498 | + | 0.680769i | \(0.761646\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20.3940 | − | 20.1288i | −0.752245 | − | 0.742461i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28.3772 | + | 16.3836i | −1.04529 | + | 0.603497i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.5944 | − | 8.42609i | −0.536864 | − | 0.309959i | 0.206943 | − | 0.978353i | \(-0.433649\pi\) |
−0.743807 | + | 0.668394i | \(0.766982\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.342193 | − | 0.721468i | −0.0125708 | − | 0.0265038i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5585 | + | 3.84299i | −0.387355 | + | 0.140986i | −0.528354 | − | 0.849024i | \(-0.677191\pi\) |
0.140999 | + | 0.990010i | \(0.454969\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.18919 | + | 6.74425i | 0.0435687 | + | 0.247090i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.2358 | − | 27.0168i | −0.374507 | − | 0.988491i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35.6584 | − | 42.4960i | −1.30293 | − | 1.55277i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.3569 | − | 8.17398i | −1.69159 | − | 0.298273i | −0.756844 | − | 0.653595i | \(-0.773260\pi\) |
−0.934744 | + | 0.355322i | \(0.884371\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.6806 | − | 2.98077i | 1.15450 | − | 0.108625i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.43859 | 0.197931 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.8478 | −1.26656 | −0.633282 | − | 0.773921i | \(-0.718292\pi\) | ||||
−0.633282 | + | 0.773921i | \(0.718292\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 38.8557 | + | 54.7257i | 1.41037 | + | 1.98642i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.01971 | + | 1.41409i | 0.290714 | + | 0.0512608i | 0.317103 | − | 0.948391i | \(-0.397290\pi\) |
−0.0263892 | + | 0.999652i | \(0.508401\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.6791 | − | 38.9455i | −1.18306 | − | 1.40992i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0232635 | + | 1.77692i | 0.000841093 | + | 0.0642448i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.83268 | − | 21.7362i | −0.138390 | − | 0.784850i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.8466 | + | 12.3191i | −1.22054 | + | 0.444240i | −0.870347 | − | 0.492438i | \(-0.836106\pi\) |
−0.350191 | + | 0.936678i | \(0.613883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.9923 | − | 2.91166i | −1.29623 | − | 0.104861i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.6182 | + | 13.0586i | 0.813521 | + | 0.469687i | 0.848177 | − | 0.529713i | \(-0.177700\pi\) |
−0.0346560 | + | 0.999399i | \(0.511034\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.6587 | − | 10.1953i | 0.634319 | − | 0.366224i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.09131 | − | 11.8466i | 0.110900 | − | 0.424993i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.40420 | + | 1.17827i | 0.0503108 | + | 0.0422158i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.4132 | + | 7.06581i | 0.694657 | + | 0.252835i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.626818 | − | 9.25427i | 0.0224006 | − | 0.330721i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.22351 | − | 3.36157i | 0.0436690 | − | 0.119980i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.45027 | − | 7.68713i | 0.229927 | − | 0.274017i | −0.638729 | − | 0.769432i | \(-0.720540\pi\) |
0.868656 | + | 0.495415i | \(0.164984\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.3071 | + | 44.7567i | 0.438143 | + | 1.59338i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.09599 | + | 14.0227i | 0.287860 | + | 0.498589i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.84076 | + | 10.1165i | −0.207411 | + | 0.359247i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.8802 | + | 8.20321i | 0.421346 | + | 0.290938i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.1056 | − | 27.7648i | −0.357957 | − | 0.983479i | −0.979737 | − | 0.200287i | \(-0.935812\pi\) |
0.621780 | − | 0.783192i | \(-0.286410\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.89638 | + | 0.863363i | −0.173221 | + | 0.0305436i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.74319 | + | 1.65639i | 0.167592 | + | 0.0585256i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.9671 | − | 21.7890i | 0.916359 | − | 0.768916i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.86305 | − | 33.2510i | 0.206645 | − | 1.17194i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.61488 | − | 4.40710i | −0.338460 | − | 0.155137i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.4236i | 1.87827i | 0.343544 | + | 0.939137i | \(0.388373\pi\) | ||||
−0.343544 | + | 0.939137i | \(0.611627\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.40265i | − | 0.189713i | −0.995491 | − | 0.0948564i | \(-0.969761\pi\) | ||
0.995491 | − | 0.0948564i | \(-0.0302392\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.26610 | + | 3.78888i | 0.289905 | + | 0.132882i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.873635 | − | 4.95463i | 0.0306021 | − | 0.173553i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.775294 | − | 0.650549i | 0.0271241 | − | 0.0227598i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.69690 | + | 40.5405i | 0.268952 | + | 1.41660i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.1911 | + | 4.08921i | −0.809374 | + | 0.142714i | −0.562996 | − | 0.826459i | \(-0.690351\pi\) |
−0.246378 | + | 0.969174i | \(0.579240\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.0930 | + | 30.4778i | 0.386679 | + | 1.06239i | 0.968487 | + | 0.249065i | \(0.0801232\pi\) |
−0.581808 | + | 0.813326i | \(0.697655\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −31.7077 | − | 21.8941i | −1.10392 | − | 0.762254i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.42861 | + | 14.5988i | −0.293091 | + | 0.507649i | −0.974539 | − | 0.224218i | \(-0.928017\pi\) |
0.681448 | + | 0.731867i | \(0.261351\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.71256 | + | 6.43035i | 0.128943 | + | 0.223335i | 0.923267 | − | 0.384158i | \(-0.125508\pi\) |
−0.794325 | + | 0.607494i | \(0.792175\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.0725 | + | 47.5403i | 0.453480 | + | 1.64915i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.40449 | − | 7.63257i | 0.221902 | − | 0.264453i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.53667 | + | 9.71692i | −0.122392 | + | 0.336268i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.6769 | + | 24.1224i | −0.369048 | + | 0.833791i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.78863 | − | 1.01498i | −0.0962742 | − | 0.0350410i | 0.293434 | − | 0.955979i | \(-0.405202\pi\) |
−0.389708 | + | 0.920938i | \(0.627424\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.7743 | + | 16.5926i | 0.681873 | + | 0.572159i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.32985 | + | 5.09628i | −0.0458025 | + | 0.175525i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.30361 | + | 2.48469i | −0.148049 | + | 0.0854760i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 82.9355 | + | 47.8828i | 2.84970 | + | 1.64527i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.9070 | − | 2.09579i | −0.889126 | − | 0.0719273i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.54920 | − | 3.47563i | 0.327343 | − | 0.119143i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.36004 | + | 41.7409i | 0.252003 | + | 1.42918i | 0.803650 | + | 0.595102i | \(0.202888\pi\) |
−0.551647 | + | 0.834078i | \(0.686000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.423399 | + | 0.237114i | 0.0144799 | + | 0.00810913i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.3690 | − | 26.6583i | −0.764109 | − | 0.910630i | 0.233991 | − | 0.972239i | \(-0.424821\pi\) |
−0.998100 | + | 0.0616091i | \(0.980377\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.70740 | − | 0.301061i | −0.0582557 | − | 0.0102721i | 0.144444 | − | 0.989513i | \(-0.453861\pi\) |
−0.202700 | + | 0.979241i | \(0.564972\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −54.8402 | − | 77.2389i | −1.86895 | − | 2.63230i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.889378 | 0.0302748 | 0.0151374 | − | 0.999885i | \(-0.495181\pi\) | ||||
0.0151374 | + | 0.999885i | \(0.495181\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.7285 | 0.670789 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.7002 | − | 2.70035i | 0.974710 | − | 0.0917087i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 64.6539 | + | 11.4002i | 2.19323 | + | 0.386726i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.7483 | − | 12.8093i | −0.364191 | − | 0.434026i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25.5792 | + | 31.3074i | −0.865723 | + | 1.05959i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.55631 | + | 42.8539i | 0.255450 | + | 1.44873i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.0682 | − | 9.85200i | 0.914026 | − | 0.332678i | 0.158167 | − | 0.987412i | \(-0.449442\pi\) |
0.755859 | + | 0.654734i | \(0.227219\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.2345 | + | 30.0116i | 0.480118 | + | 1.01227i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.8607 | + | 23.0136i | 1.34294 | + | 0.775346i | 0.987238 | − | 0.159253i | \(-0.0509086\pi\) |
0.355702 | + | 0.934600i | \(0.384242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.676778 | + | 0.390738i | −0.0227754 | + | 0.0131494i | −0.511344 | − | 0.859376i | \(-0.670852\pi\) |
0.488569 | + | 0.872525i | \(0.337519\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.54662 | + | 9.42246i | 0.320906 | + | 0.316732i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.7042 | + | 13.1774i | 0.527297 | + | 0.442455i | 0.867167 | − | 0.498018i | \(-0.165939\pi\) |
−0.339870 | + | 0.940473i | \(0.610383\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.1152 | + | 7.32132i | 0.674641 | + | 0.245549i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 49.8328 | − | 1.30505i | 1.66946 | − | 0.0437207i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.464360 | + | 1.27582i | −0.0155392 | + | 0.0426937i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.58114 | + | 11.4184i | −0.320262 | + | 0.381673i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.0595 | + | 24.3765i | −0.803323 | + | 0.813909i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.53118 | + | 7.84823i | 0.151123 | + | 0.261753i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.51000 | + | 4.34745i | −0.0836203 | + | 0.144835i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −47.2554 | + | 22.4133i | −1.57256 | + | 0.745867i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.41573 | + | 3.88967i | 0.0470603 | + | 0.129297i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.2340 | − | 5.86006i | 1.10352 | − | 0.194580i | 0.407925 | − | 0.913016i | \(-0.366253\pi\) |
0.695594 | + | 0.718436i | \(0.255141\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.74301 | − | 41.4040i | 0.223652 | − | 1.37328i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.14960 | − | 5.16013i | 0.203745 | − | 0.170963i | −0.535206 | − | 0.844722i | \(-0.679766\pi\) |
0.738951 | + | 0.673759i | \(0.235321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.26253 | − | 52.5304i | 0.306545 | − | 1.73850i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.665011 | − | 7.06795i | −0.0219846 | − | 0.233659i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 6.62924i | − | 0.218917i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.8941i | 0.722219i | 0.932523 | + | 0.361110i | \(0.117602\pi\) | ||||
−0.932523 | + | 0.361110i | \(0.882398\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.7848 | + | 16.1773i | −0.750783 | + | 0.533062i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.83068 | + | 10.3823i | −0.0602575 | + | 0.341737i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.46918 | + | 3.75009i | −0.146946 | + | 0.123302i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.46269 | − | 14.2245i | −0.277951 | − | 0.467193i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.73598 | + | 1.36406i | −0.253809 | + | 0.0447534i | −0.299105 | − | 0.954220i | \(-0.596688\pi\) |
0.0452958 | + | 0.998974i | \(0.485577\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.930569 | − | 2.55672i | −0.0304982 | − | 0.0837930i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.66118 | + | 32.8960i | −0.0871230 | + | 1.07697i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.64050 | + | 2.84143i | −0.0536501 | + | 0.0929247i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.3774 | − | 21.4384i | −0.404353 | − | 0.700361i | 0.589893 | − | 0.807482i | \(-0.299170\pi\) |
−0.994246 | + | 0.107121i | \(0.965837\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.2780 | − | 4.24767i | −0.531211 | − | 0.138617i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.9112 | + | 28.4963i | −0.779483 | + | 0.928952i | −0.998910 | − | 0.0466768i | \(-0.985137\pi\) |
0.219427 | + | 0.975629i | \(0.429581\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.8913 | − | 73.8834i | 0.875703 | − | 2.40597i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.0773 | − | 17.3809i | −0.588055 | − | 0.565402i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.6638 | − | 15.8923i | −1.41888 | − | 0.516432i | −0.485160 | − | 0.874425i | \(-0.661239\pi\) |
−0.933724 | + | 0.357994i | \(0.883461\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.2512 | + | 11.1191i | 0.430152 | + | 0.360940i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.4565 | + | 8.92480i | −1.05247 | + | 0.289406i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.6424 | + | 23.4649i | −1.31654 | + | 0.760102i | −0.983170 | − | 0.182695i | \(-0.941518\pi\) |
−0.333366 | + | 0.942798i | \(0.608184\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.6102 | − | 11.8993i | −0.666930 | − | 0.385052i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.73059 | − | 14.0922i | 0.314545 | − | 0.455535i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.5340 | − | 6.74584i | 0.598495 | − | 0.217834i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.907570 | + | 5.14708i | 0.0292764 | + | 0.166035i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.3237 | − | 25.9078i | −0.719370 | − | 0.834868i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.42643 | + | 6.46697i | 0.174683 | + | 0.208179i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.80328 | − | 1.72858i | −0.315252 | − | 0.0555875i | 0.0137833 | − | 0.999905i | \(-0.495612\pi\) |
−0.329036 | + | 0.944318i | \(0.606724\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.0703086 | + | 0.153391i | −0.00225864 | + | 0.00492762i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.9553 | 1.41059 | 0.705297 | − | 0.708912i | \(-0.250814\pi\) | ||||
0.705297 | + | 0.708912i | \(0.250814\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −76.1186 | −2.44025 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.19322 | − | 17.8750i | 0.262393 | − | 0.572457i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.3818 | + | 4.29916i | 0.780042 | + | 0.137542i | 0.549471 | − | 0.835513i | \(-0.314829\pi\) |
0.230571 | + | 0.973055i | \(0.425940\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.96246 | + | 7.10578i | 0.190561 | + | 0.227102i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.4585 | − | 23.7432i | −0.653191 | − | 0.758063i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.54624 | + | 8.76918i | 0.0493175 | + | 0.279693i | 0.999487 | − | 0.0320417i | \(-0.0102009\pi\) |
−0.950169 | + | 0.311735i | \(0.899090\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.91148 | − | 1.42366i | 0.124630 | − | 0.0453616i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 39.8664 | − | 57.7357i | 1.26896 | − | 1.83775i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37.5948 | − | 21.7054i | −1.19545 | − | 0.690191i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.0679 | + | 8.12210i | −0.446881 | + | 0.258007i | −0.706512 | − | 0.707701i | \(-0.749732\pi\) |
0.259631 | + | 0.965708i | \(0.416399\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −54.9465 | + | 15.1090i | −1.74368 | + | 0.479471i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.02001 | + | 3.37319i | 0.127443 | + | 0.106937i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.49390 | + | 2.36359i | 0.205664 | + | 0.0748555i | 0.442798 | − | 0.896621i | \(-0.353986\pi\) |
−0.237134 | + | 0.971477i | \(0.576208\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.80996 | − | 7.32747i | 0.0572645 | − | 0.231831i |
(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 | 432.2.be.c.239.3 | yes | 36 | |
4.3 | odd | 2 | 432.2.be.b.239.4 | yes | 36 | ||
27.20 | odd | 18 | 432.2.be.b.47.4 | ✓ | 36 | ||
108.47 | even | 18 | inner | 432.2.be.c.47.3 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.be.b.47.4 | ✓ | 36 | 27.20 | odd | 18 | ||
432.2.be.b.239.4 | yes | 36 | 4.3 | odd | 2 | ||
432.2.be.c.47.3 | yes | 36 | 108.47 | even | 18 | inner | |
432.2.be.c.239.3 | yes | 36 | 1.1 | even | 1 | trivial |