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 | 191.6 | ||
Character | \(\chi\) | \(=\) | 432.191 |
Dual form | 432.2.be.b.95.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) |
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 | ||||||||
\(3\) | 1.70424 | + | 0.309120i | 0.983945 | + | 0.178470i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.45395 | − | 1.73275i | −0.650226 | − | 0.774910i | 0.335722 | − | 0.941961i | \(-0.391020\pi\) |
−0.985948 | + | 0.167052i | \(0.946575\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.49276 | − | 4.10134i | −0.564212 | − | 1.55016i | −0.813400 | − | 0.581705i | \(-0.802386\pi\) |
0.249188 | − | 0.968455i | \(-0.419836\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.80889 | + | 1.05363i | 0.936297 | + | 0.351210i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.83629 | + | 1.54083i | 0.553664 | + | 0.464579i | 0.876179 | − | 0.481985i | \(-0.160084\pi\) |
−0.322516 | + | 0.946564i | \(0.604529\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.219577 | − | 1.24528i | −0.0608997 | − | 0.345379i | −0.999999 | − | 0.00173201i | \(-0.999449\pi\) |
0.939099 | − | 0.343647i | \(-0.111662\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.94226 | − | 3.40247i | −0.501489 | − | 0.878515i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.23513 | − | 2.44515i | 1.02717 | − | 0.593036i | 0.110997 | − | 0.993821i | \(-0.464596\pi\) |
0.916172 | + | 0.400784i | \(0.131262\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.93526 | − | 3.42672i | −1.36164 | − | 0.786144i | −0.371799 | − | 0.928313i | \(-0.621259\pi\) |
−0.989842 | + | 0.142170i | \(0.954592\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.27623 | − | 7.45112i | −0.278496 | − | 1.62597i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.43275 | − | 0.885449i | −0.507264 | − | 0.184629i | 0.0756944 | − | 0.997131i | \(-0.475883\pi\) |
−0.582958 | + | 0.812502i | \(0.698105\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0202120 | + | 0.114628i | −0.00404241 | + | 0.0229256i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.46133 | + | 2.66392i | 0.858584 | + | 0.512673i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.76428 | + | 1.72171i | 1.81318 | + | 0.319713i | 0.974411 | − | 0.224773i | \(-0.0721640\pi\) |
0.838770 | + | 0.544486i | \(0.183275\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.15421 | + | 5.91865i | −0.386908 | + | 1.06302i | 0.581477 | + | 0.813563i | \(0.302475\pi\) |
−0.968385 | + | 0.249459i | \(0.919747\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.65319 | + | 3.19359i | 0.461861 | + | 0.555933i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.93619 | + | 8.54973i | −0.834368 | + | 1.44517i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.49781 | + | 4.32633i | 0.410637 | + | 0.711244i | 0.994960 | − | 0.100278i | \(-0.0319731\pi\) |
−0.584323 | + | 0.811521i | \(0.698640\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0107288 | − | 2.19014i | 0.00171798 | − | 0.350703i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.206477 | − | 0.0364075i | 0.0322463 | − | 0.00568590i | −0.157502 | − | 0.987519i | \(-0.550344\pi\) |
0.189748 | + | 0.981833i | \(0.439233\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.863871 | − | 1.02952i | 0.131739 | − | 0.157001i | −0.696142 | − | 0.717904i | \(-0.745102\pi\) |
0.827881 | + | 0.560903i | \(0.189546\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.25831 | − | 6.39903i | −0.336649 | − | 0.953911i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.30035 | − | 1.92917i | 0.773135 | − | 0.281398i | 0.0748282 | − | 0.997196i | \(-0.476159\pi\) |
0.698307 | + | 0.715798i | \(0.253937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.23031 | + | 7.74515i | −1.31862 | + | 1.10645i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.97353 | − | 2.85797i | 1.11652 | − | 0.400196i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0068i | 1.64926i | 0.565670 | + | 0.824632i | \(0.308618\pi\) | ||||
−0.565670 | + | 0.824632i | \(0.691382\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.42214i | − | 0.731121i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.05585 | − | 7.67467i | −1.19948 | − | 1.01654i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.16576 | + | 5.17368i | −0.802713 | + | 0.673556i | −0.948857 | − | 0.315707i | \(-0.897758\pi\) |
0.146144 | + | 0.989263i | \(0.453314\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.59708 | + | 1.30923i | −0.460559 | + | 0.167630i | −0.561871 | − | 0.827225i | \(-0.689918\pi\) |
0.101312 | + | 0.994855i | \(0.467696\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.128280 | − | 13.0930i | 0.0161618 | − | 1.64957i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.83851 | + | 2.19105i | −0.228039 | + | 0.271766i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.97797 | − | 0.525097i | 0.363817 | − | 0.0641508i | 0.0112486 | − | 0.999937i | \(-0.496419\pi\) |
0.352569 | + | 0.935786i | \(0.385308\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.87229 | − | 2.26103i | −0.466169 | − | 0.272196i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.29426 | + | 2.24172i | 0.153600 | + | 0.266043i | 0.932548 | − | 0.361045i | \(-0.117580\pi\) |
−0.778948 | + | 0.627088i | \(0.784247\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.41358 | − | 7.64454i | 0.516570 | − | 0.894726i | −0.483244 | − | 0.875485i | \(-0.660542\pi\) |
0.999815 | − | 0.0192407i | \(-0.00612489\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0698800 | + | 0.189106i | −0.00806905 | + | 0.0218361i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.57833 | − | 9.83137i | 0.407788 | − | 1.12039i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.39249 | − | 0.245534i | −0.156668 | − | 0.0276247i | 0.0947642 | − | 0.995500i | \(-0.469790\pi\) |
−0.251432 | + | 0.967875i | \(0.580901\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.77973 | + | 5.91906i | 0.753303 | + | 0.657674i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.55586 | + | 8.82370i | −0.170777 | + | 0.968527i | 0.772128 | + | 0.635467i | \(0.219192\pi\) |
−0.942906 | + | 0.333060i | \(0.891919\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.3945 | − | 3.78329i | −1.12744 | − | 0.410355i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.1085 | + | 5.95254i | 1.72701 | + | 0.638179i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.4462 | − | 8.91788i | −1.63730 | − | 0.945293i | −0.981759 | − | 0.190130i | \(-0.939109\pi\) |
−0.655537 | − | 0.755163i | \(-0.727558\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.77955 | + | 2.75947i | −0.501033 | + | 0.289271i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.50088 | + | 9.42091i | −0.570414 | + | 0.976903i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.69191 | + | 15.2666i | 0.276185 | + | 1.56632i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.8986 | + | 9.98414i | 1.20812 | + | 1.01374i | 0.999360 | + | 0.0357690i | \(0.0113881\pi\) |
0.208763 | + | 0.977966i | \(0.433056\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.53448 | + | 6.26281i | 0.355229 | + | 0.629436i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.09820 | + | 11.2597i | 0.407786 | + | 1.12038i | 0.958351 | + | 0.285592i | \(0.0921901\pi\) |
−0.550565 | + | 0.834792i | \(0.685588\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.4815 | − | 13.6831i | −1.13130 | − | 1.34823i | −0.929506 | − | 0.368806i | \(-0.879767\pi\) |
−0.201796 | − | 0.979428i | \(-0.564678\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.0554 | + | 13.0449i | −1.07889 | + | 1.27306i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.3881 | 1.58430 | 0.792150 | − | 0.610326i | \(-0.208961\pi\) | ||||
0.792150 | + | 0.610326i | \(0.208961\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.59295 | −0.152577 | −0.0762883 | − | 0.997086i | \(-0.524307\pi\) | ||||
−0.0762883 | + | 0.997086i | \(0.524307\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.91952 | + | 8.14524i | 0.277108 | + | 0.773112i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.82521 | − | 4.55871i | −0.359846 | − | 0.428847i | 0.555500 | − | 0.831517i | \(-0.312527\pi\) |
−0.915346 | + | 0.402669i | \(0.868083\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00284 | + | 5.50275i | 0.186766 | + | 0.513134i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.695300 | − | 3.72921i | 0.0642805 | − | 0.344766i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.3504 | − | 13.7196i | −1.49884 | − | 1.25768i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.912322 | − | 5.17403i | −0.0829383 | − | 0.470367i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.363142 | + | 0.00177892i | 0.0327434 | + | 0.000160399i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.56650 | + | 5.52322i | −0.855654 | + | 0.494012i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.498482 | + | 0.287799i | 0.0442331 | + | 0.0255380i | 0.521953 | − | 0.852974i | \(-0.325203\pi\) |
−0.477720 | + | 0.878512i | \(0.658537\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.79049 | − | 1.48752i | 0.157644 | − | 0.130968i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.393105 | − | 0.143079i | −0.0343458 | − | 0.0125008i | 0.324790 | − | 0.945786i | \(-0.394706\pi\) |
−0.359136 | + | 0.933285i | \(0.616929\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.19420 | + | 29.4578i | −0.450394 | + | 2.55431i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.87064 | − | 11.6036i | −0.160999 | − | 0.998678i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.23523 | + | 1.27577i | 0.618147 | + | 0.108996i | 0.473948 | − | 0.880553i | \(-0.342828\pi\) |
0.144199 | + | 0.989549i | \(0.453939\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.90843 | + | 10.7383i | −0.331509 | + | 0.910814i | 0.656211 | + | 0.754578i | \(0.272158\pi\) |
−0.987720 | + | 0.156236i | \(0.950064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.62943 | − | 1.64933i | 0.810944 | − | 0.138899i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.51557 | − | 2.62504i | 0.126738 | − | 0.219517i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.2135 | − | 19.4223i | −0.931230 | − | 1.61294i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −18.1249 | + | 10.3464i | −1.49491 | + | 0.853353i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.5485 | − | 2.03631i | 0.946089 | − | 0.166821i | 0.320741 | − | 0.947167i | \(-0.396068\pi\) |
0.625348 | + | 0.780346i | \(0.284957\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.73929 | − | 5.64807i | 0.385678 | − | 0.459634i | −0.537920 | − | 0.842996i | \(-0.680790\pi\) |
0.923598 | + | 0.383363i | \(0.125234\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.4723 | − | 2.40591i | 1.17002 | − | 0.194506i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.3877 | − | 4.87271i | 1.07532 | − | 0.391386i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.59341 | + | 7.21073i | −0.685829 | + | 0.575479i | −0.917703 | − | 0.397267i | \(-0.869959\pi\) |
0.231874 | + | 0.972746i | \(0.425514\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.71154 | + | 20.4625i | −0.294345 | + | 1.62279i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.2993i | 0.890510i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.13355i | − | 0.167113i | −0.996503 | − | 0.0835565i | \(-0.973372\pi\) | ||
0.996503 | − | 0.0835565i | \(-0.0266279\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.67609 | − | 9.24064i | 0.130483 | − | 0.719383i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.742162 | + | 0.622748i | −0.0574302 | + | 0.0481897i | −0.671051 | − | 0.741411i | \(-0.734157\pi\) |
0.613621 | + | 0.789601i | \(0.289712\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.7135 | − | 3.89939i | 0.824115 | − | 0.299953i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.0610 | − | 15.8788i | −0.998798 | − | 1.21429i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.38552 | − | 6.41821i | 0.409453 | − | 0.487967i | −0.521425 | − | 0.853297i | \(-0.674599\pi\) |
0.930878 | + | 0.365330i | \(0.119044\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500301 | − | 0.0882165i | 0.0378192 | − | 0.00666854i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.1072 | + | 6.91126i | −0.910036 | + | 0.519482i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.91202 | + | 8.50787i | 0.367142 | + | 0.635908i | 0.989117 | − | 0.147129i | \(-0.0470031\pi\) |
−0.621976 | + | 0.783036i | \(0.713670\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.82245 | − | 11.8168i | 0.507109 | − | 0.878338i | −0.492857 | − | 0.870110i | \(-0.664048\pi\) |
0.999966 | − | 0.00822799i | \(-0.00261908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.53502 | + | 1.11932i | −0.483082 | + | 0.0827425i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.86476 | − | 10.6183i | 0.284143 | − | 0.780676i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.5445 | + | 2.03561i | 0.844218 | + | 0.148858i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.26593 | − | 22.2741i | 0.310301 | − | 1.62020i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.158946 | − | 0.901427i | 0.0115009 | − | 0.0652250i | −0.978517 | − | 0.206165i | \(-0.933902\pi\) |
0.990018 | + | 0.140940i | \(0.0450126\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.10590 | + | 1.13045i | 0.223567 | + | 0.0813718i | 0.451375 | − | 0.892334i | \(-0.350934\pi\) |
−0.227808 | + | 0.973706i | \(0.573156\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.81057 | + | 3.16576i | −0.272880 | + | 0.226705i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.95985 | + | 1.13152i | 0.139634 | + | 0.0806176i | 0.568189 | − | 0.822898i | \(-0.307644\pi\) |
−0.428556 | + | 0.903515i | \(0.640977\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.82807 | − | 4.51954i | 0.554917 | − | 0.320381i | −0.196186 | − | 0.980567i | \(-0.562856\pi\) |
0.751103 | + | 0.660185i | \(0.229522\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.23751 | + | 0.0256569i | 0.369425 | + | 0.00180970i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.51448 | − | 42.6167i | −0.527413 | − | 2.99111i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.363293 | − | 0.304839i | −0.0253735 | − | 0.0212909i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.90040 | − | 5.05035i | −0.410106 | − | 0.351024i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.61887 | − | 15.4377i | −0.388665 | − | 1.06785i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.7121 | + | 17.5332i | 1.01282 | + | 1.20704i | 0.978206 | + | 0.207634i | \(0.0665764\pi\) |
0.0346162 | + | 0.999401i | \(0.488979\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.51277 | + | 4.22052i | 0.103653 | + | 0.289185i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.03993 | −0.207321 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.4901 | 1.86615 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.88489 | − | 11.6638i | 0.667959 | − | 0.788169i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.97484 | − | 4.73703i | −0.267377 | − | 0.318647i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.89561 | + | 7.95563i | 0.193905 | + | 0.532748i | 0.998100 | − | 0.0616168i | \(-0.0196257\pi\) |
−0.804195 | + | 0.594365i | \(0.797403\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.177549 | + | 0.300682i | −0.0118366 | + | 0.0200455i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.9998 | − | 11.7472i | −0.929200 | − | 0.779691i | 0.0464739 | − | 0.998920i | \(-0.485202\pi\) |
−0.975674 | + | 0.219228i | \(0.929646\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.27137 | − | 12.8816i | −0.150096 | − | 0.851237i | −0.963133 | − | 0.269025i | \(-0.913299\pi\) |
0.813037 | − | 0.582212i | \(-0.197813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.13741 | − | 15.6489i | 0.601197 | − | 1.02962i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.8420 | + | 13.7652i | −1.56194 | + | 0.901789i | −0.564884 | + | 0.825170i | \(0.691079\pi\) |
−0.997060 | + | 0.0766185i | \(0.975588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.0492 | − | 6.37927i | −0.720771 | − | 0.416137i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.29725 | − | 0.848896i | −0.149222 | − | 0.0551417i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.2322 | − | 5.18010i | −0.920604 | − | 0.335073i | −0.162125 | − | 0.986770i | \(-0.551835\pi\) |
−0.758479 | + | 0.651698i | \(0.774057\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.45072 | − | 13.8987i | 0.157864 | − | 0.895294i | −0.798256 | − | 0.602319i | \(-0.794244\pi\) |
0.956120 | − | 0.292975i | \(-0.0946453\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.72461 | + | 12.1833i | 0.623834 | + | 0.781557i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 26.8408 | + | 4.73276i | 1.71480 | + | 0.302365i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.96399 | + | 8.14350i | −0.188594 | + | 0.518158i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.37914 | + | 14.5568i | −0.340889 | + | 0.922499i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.336061 | + | 0.582074i | −0.0212120 | + | 0.0367402i | −0.876437 | − | 0.481517i | \(-0.840086\pi\) |
0.855225 | + | 0.518258i | \(0.173419\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.10292 | − | 5.37441i | −0.195079 | − | 0.337886i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.5453 | − | 9.66079i | −1.03610 | − | 0.604982i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.9006 | + | 2.09839i | −0.742337 | + | 0.130894i | −0.532011 | − | 0.846737i | \(-0.678564\pi\) |
−0.210326 | + | 0.977631i | \(0.567453\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.0151 | − | 16.7025i | 0.870856 | − | 1.03785i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25.6127 | + | 15.1240i | 1.58539 | + | 0.936153i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.9065 | − | 8.33729i | 1.41248 | − | 0.514099i | 0.480620 | − | 0.876929i | \(-0.340412\pi\) |
0.931855 | + | 0.362830i | \(0.118189\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.8048 | − | 17.4573i | 1.27803 | − | 1.07239i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.5674 | − | 19.9730i | −1.44230 | − | 1.22233i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 14.6341i | − | 0.892260i | −0.894968 | − | 0.446130i | \(-0.852802\pi\) | ||
0.894968 | − | 0.446130i | \(-0.147198\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5240i | 0.700036i | 0.936743 | + | 0.350018i | \(0.113825\pi\) | ||||
−0.936743 | + | 0.350018i | \(0.886175\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.99852 | + | 3.22536i | −0.544615 | + | 0.195208i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.213738 | + | 0.179348i | −0.0128889 | + | 0.0108151i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.53344 | + | 0.558126i | −0.0921354 | + | 0.0335346i | −0.387677 | − | 0.921795i | \(-0.626722\pi\) |
0.295541 | + | 0.955330i | \(0.404500\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.2870 | + | 14.3551i | −0.735605 | + | 0.859417i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.2140 | + | 18.1313i | −0.907590 | + | 1.08162i | 0.0887421 | + | 0.996055i | \(0.471715\pi\) |
−0.996332 | + | 0.0855691i | \(0.972729\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.5507 | − | 2.03669i | 0.686615 | − | 0.121069i | 0.180552 | − | 0.983565i | \(-0.442211\pi\) |
0.506063 | + | 0.862497i | \(0.331100\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.131530 | + | 26.8501i | −0.00779118 | + | 1.59046i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.457541 | − | 0.792485i | −0.0270078 | − | 0.0467789i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.45753 | − | 5.98862i | 0.203384 | − | 0.352272i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.1919 | + | 20.6935i | 1.00781 | + | 1.21307i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.897942 | − | 2.46708i | 0.0524583 | − | 0.144128i | −0.910696 | − | 0.413077i | \(-0.864454\pi\) |
0.963154 | + | 0.268949i | \(0.0866763\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.9294 | + | 3.16144i | 1.04389 | + | 0.184066i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.08766 | + | 11.7659i | 0.237190 | + | 0.682728i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.568458 | + | 3.22389i | −0.0328748 | + | 0.186442i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.51197 | − | 2.00619i | −0.317705 | − | 0.115635i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.50373 | + | 20.4561i | 0.201284 | + | 1.17517i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.49855 | + | 4.32929i | 0.429366 | + | 0.247895i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.4578 | + | 14.6981i | −1.45296 | + | 0.838865i | −0.998648 | − | 0.0519800i | \(-0.983447\pi\) |
−0.454308 | + | 0.890845i | \(0.650113\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.3375 | − | 26.8684i | −0.872520 | − | 1.52849i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.47343 | + | 19.6988i | 0.196960 | + | 1.11702i | 0.909599 | + | 0.415486i | \(0.136389\pi\) |
−0.712639 | + | 0.701531i | \(0.752500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.4507 | + | 12.9647i | 0.873324 | + | 0.732806i | 0.964795 | − | 0.263002i | \(-0.0847126\pi\) |
−0.0914716 | + | 0.995808i | \(0.529157\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −22.8735 | + | 18.8143i | −1.28877 | + | 1.06007i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.18750 | − | 14.2525i | −0.291359 | − | 0.800503i | −0.995868 | − | 0.0908080i | \(-0.971055\pi\) |
0.704509 | − | 0.709695i | \(-0.251167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.2772 | + | 18.2067i | 0.855361 | + | 1.01938i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.9294 | + | 5.06589i | 1.55887 | + | 0.282751i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.5154 | −1.86485 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.147182 | 0.00816422 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.71477 | − | 0.492411i | −0.150127 | − | 0.0272304i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.8244 | − | 18.8587i | −0.872425 | − | 1.03972i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.76246 | − | 21.3272i | −0.426663 | − | 1.17225i | −0.947825 | − | 0.318790i | \(-0.896723\pi\) |
0.521162 | − | 0.853458i | \(-0.325499\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.45771 | + | 14.7839i | 0.134682 | + | 0.810155i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.23969 | − | 4.39662i | −0.286275 | − | 0.240213i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.768067 | − | 4.35592i | −0.0418393 | − | 0.237282i | 0.956716 | − | 0.291025i | \(-0.0939961\pi\) |
−0.998555 | + | 0.0537423i | \(0.982885\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.10991 | − | 8.95160i | −0.277532 | − | 0.486184i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.0754 | + | 7.54910i | −0.708074 | + | 0.408807i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0855 | + | 11.0190i | 1.03052 | + | 0.594970i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.71231 | + | 9.99714i | 0.0921879 | + | 0.538228i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.10935 | − | 2.22362i | −0.327967 | − | 0.119370i | 0.172788 | − | 0.984959i | \(-0.444722\pi\) |
−0.500756 | + | 0.865589i | \(0.666945\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.48215 | − | 14.0770i | 0.132866 | − | 0.753522i | −0.843456 | − | 0.537199i | \(-0.819482\pi\) |
0.976322 | − | 0.216323i | \(-0.0694065\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.33773 | − | 6.14056i | 0.124779 | − | 0.327759i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.3084 | + | 2.34663i | 0.708335 | + | 0.124898i | 0.516197 | − | 0.856470i | \(-0.327347\pi\) |
0.192137 | + | 0.981368i | \(0.438458\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.00256 | − | 5.50197i | 0.106285 | − | 0.292014i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −23.6241 | − | 28.4359i | −1.25032 | − | 1.50499i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.2376 | − | 21.1961i | 0.645875 | − | 1.11869i | −0.338224 | − | 0.941066i | \(-0.609826\pi\) |
0.984099 | − | 0.177623i | \(-0.0568406\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.9848 | + | 24.2225i | 0.736044 | + | 1.27487i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0445772 | − | 9.09983i | 0.00233969 | − | 0.477617i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.6632 | + | 3.46715i | −1.02922 | + | 0.181479i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.9171 | + | 21.3528i | −0.935266 | + | 1.11461i | 0.0579497 | + | 0.998320i | \(0.481544\pi\) |
−0.993216 | + | 0.116287i | \(0.962901\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.618332 | + | 0.115286i | 0.0321891 | + | 0.00600154i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 49.2440 | − | 17.9234i | 2.55662 | − | 0.930535i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.7579 | + | 19.9352i | −1.23014 | + | 1.03221i | −0.231905 | + | 0.972738i | \(0.574496\pi\) |
−0.998230 | + | 0.0594676i | \(0.981060\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.0110 | + | 6.45572i | −0.930083 | + | 0.333372i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.5373i | − | 0.645706i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 21.9119i | − | 1.12554i | −0.826614 | − | 0.562770i | \(-0.809736\pi\) | ||
0.826614 | − | 0.562770i | \(-0.190264\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.760571 | + | 0.644570i | 0.0389652 | + | 0.0330223i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.8681 | − | 13.3149i | 0.810823 | − | 0.680361i | −0.139981 | − | 0.990154i | \(-0.544704\pi\) |
0.950804 | + | 0.309793i | \(0.100260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.2380 | + | 8.09398i | −1.13335 | + | 0.412507i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.51125 | − | 1.98161i | 0.178487 | − | 0.100731i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.6840 | + | 25.8420i | −1.09942 | + | 1.31024i | −0.152673 | + | 0.988277i | \(0.548788\pi\) |
−0.946751 | + | 0.321966i | \(0.895656\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.4681 | + | 2.19846i | −0.630537 | + | 0.111181i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.625719 | − | 0.365357i | −0.0315633 | − | 0.0184298i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.59916 | + | 2.76983i | 0.0804627 | + | 0.139366i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.88109 | + | 15.3825i | −0.445729 | + | 0.772025i | −0.998103 | − | 0.0615713i | \(-0.980389\pi\) |
0.552374 | + | 0.833597i | \(0.313722\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.9582 | + | 48.5976i | −0.899032 | + | 2.43292i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.0232749 | − | 0.0639472i | 0.00116229 | − | 0.00319337i | −0.939110 | − | 0.343616i | \(-0.888348\pi\) |
0.940272 | + | 0.340423i | \(0.110570\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.84341 | + | 1.38300i | 0.390708 | + | 0.0688924i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.398871 | − | 20.3536i | 0.0198201 | − | 1.01138i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.07944 | + | 11.7931i | −0.103074 | + | 0.584563i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.4276 | − | 11.4387i | −1.55399 | − | 0.565607i | −0.584642 | − | 0.811291i | \(-0.698765\pi\) |
−0.969350 | + | 0.245684i | \(0.920987\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.9362 | + | 4.41077i | 0.588771 | + | 0.217567i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.4231 | + | 17.5648i | 1.49702 | + | 0.864305i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.5514 | − | 10.1333i | 0.861565 | − | 0.497425i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.98035 | + | 17.0926i | −0.488740 | + | 0.837026i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.504953 | − | 2.86373i | −0.0246686 | − | 0.139903i | 0.969986 | − | 0.243161i | \(-0.0781843\pi\) |
−0.994655 | + | 0.103258i | \(0.967073\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.9409 | − | 14.2151i | −0.825650 | − | 0.692802i | 0.128638 | − | 0.991692i | \(-0.458939\pi\) |
−0.954288 | + | 0.298889i | \(0.903384\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.9207 | + | 0.165783i | 0.822714 | + | 0.00806062i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.194683 | + | 0.534886i | 0.00944349 | + | 0.0259458i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.7392 | + | 12.7985i | 0.519706 | + | 0.619362i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.39434 | − | 4.00521i | 0.163880 | − | 0.193373i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.6882 | 1.38186 | 0.690930 | − | 0.722922i | \(-0.257201\pi\) | ||||
0.690930 | + | 0.722922i | \(0.257201\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.3114 | −0.879989 | −0.439994 | − | 0.898000i | \(-0.645020\pi\) | ||||
−0.439994 | + | 0.898000i | \(0.645020\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.1067 | − | 36.5667i | −0.628418 | − | 1.75324i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.4048 | + | 13.5917i | 0.545566 | + | 0.650181i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.59114 | + | 26.3514i | 0.457760 | + | 1.25769i | 0.927149 | + | 0.374694i | \(0.122252\pi\) |
−0.469388 | + | 0.882992i | \(0.655526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −34.0875 | + | 12.0299i | −1.62321 | + | 0.572855i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.21984 | − | 4.37997i | −0.248002 | − | 0.208099i | 0.510309 | − | 0.859991i | \(-0.329531\pi\) |
−0.758312 | + | 0.651892i | \(0.773975\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.00558 | + | 39.7306i | 0.332096 | + | 1.88341i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.3109 | + | 0.0994966i | 0.960672 | + | 0.00470603i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.01463 | − | 1.74050i | 0.142269 | − | 0.0821392i | −0.427176 | − | 0.904169i | \(-0.640491\pi\) |
0.569445 | + | 0.822029i | \(0.307158\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.435251 | + | 0.251292i | 0.0204952 | + | 0.0118329i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.82284 | − | 8.16068i | 0.461517 | − | 0.383422i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.7307 | + | 4.26963i | 0.549944 | + | 0.200163i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.671127 | + | 3.80615i | −0.0313940 | + | 0.178044i | −0.996473 | − | 0.0839151i | \(-0.973258\pi\) |
0.965079 | + | 0.261959i | \(0.0843686\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.4080 | + | 0.373421i | 1.18594 | + | 0.0174298i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.36591 | − | 0.769827i | −0.203341 | − | 0.0358544i | 0.0710500 | − | 0.997473i | \(-0.477365\pi\) |
−0.274391 | + | 0.961618i | \(0.588476\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.18880 | − | 17.0036i | 0.287618 | − | 0.790224i | −0.708781 | − | 0.705429i | \(-0.750754\pi\) |
0.996398 | − | 0.0847946i | \(-0.0270234\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.3221 | − | 4.16590i | 1.12791 | − | 0.193189i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.87326 | − | 3.24458i | 0.0866840 | − | 0.150141i | −0.819424 | − | 0.573189i | \(-0.805706\pi\) |
0.906108 | + | 0.423047i | \(0.139040\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.59901 | − | 11.4298i | −0.304714 | − | 0.527780i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.8742 | + | 9.63244i | −0.777524 | + | 0.443839i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.17264 | − | 0.559423i | 0.145878 | − | 0.0257223i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.512762 | − | 0.611086i | 0.0235271 | − | 0.0280386i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.6507 | + | 33.7258i | −0.579238 | + | 1.54420i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.1399 | + | 11.3340i | −1.42282 | + | 0.517864i | −0.934864 | − | 0.355005i | \(-0.884479\pi\) |
−0.487955 | + | 0.872869i | \(0.662257\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.83904 | − | 4.06044i | 0.220641 | − | 0.185140i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.49284 | + | 19.2568i | −0.158930 | + | 0.876213i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 35.1338i | − | 1.59534i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.38462i | 0.0627433i | 0.999508 | + | 0.0313716i | \(0.00998754\pi\) | ||||
−0.999508 | + | 0.0313716i | \(0.990012\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.659524 | − | 3.63610i | 0.0298247 | − | 0.164430i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.4337 | + | 16.3068i | −0.877029 | + | 0.735915i | −0.965566 | − | 0.260158i | \(-0.916225\pi\) |
0.0885369 | + | 0.996073i | \(0.471781\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45.5628 | − | 16.5835i | 2.05204 | − | 0.746883i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.71293 | − | 15.2302i | 0.256777 | − | 0.684546i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.26203 | − | 8.65455i | 0.325746 | − | 0.388210i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.2436 | + | 5.33276i | −1.35389 | + | 0.238727i | −0.803063 | − | 0.595894i | \(-0.796798\pi\) |
−0.550825 | + | 0.834621i | \(0.685687\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.45733 | + | 0.831897i | −0.0651086 | + | 0.0371664i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.84990 | + | 6.66821i | 0.171658 | + | 0.297321i | 0.939000 | − | 0.343918i | \(-0.111754\pi\) |
−0.767341 | + | 0.641239i | \(0.778421\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5517 | − | 23.4722i | 0.603043 | − | 1.04450i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.4638 | − | 3.33376i | 0.864416 | − | 0.148058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.3886 | + | 28.5425i | −0.460468 | + | 1.26513i | 0.464666 | + | 0.885486i | \(0.346174\pi\) |
−0.925134 | + | 0.379640i | \(0.876048\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.9413 | − | 6.69007i | −1.67842 | − | 0.295951i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.3506 | − | 31.0988i | −0.766049 | − | 1.37305i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.01588 | + | 39.7890i | −0.309157 | + | 1.75331i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.7055 | + | 4.62444i | 0.558789 | + | 0.203382i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.1622 | − | 9.27342i | 0.489967 | − | 0.407058i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.8916 | − | 16.1032i | −1.22196 | − | 0.705496i | −0.256621 | − | 0.966512i | \(-0.582609\pi\) |
−0.965334 | + | 0.261016i | \(0.915942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.4157 | − | 17.5605i | 1.32999 | − | 0.767869i | 0.344690 | − | 0.938717i | \(-0.387984\pi\) |
0.985297 | + | 0.170848i | \(0.0546507\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.879903 | + | 0.00431037i | 0.0384021 | + | 0.000188120i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.34864 | + | 30.3336i | 0.232990 | + | 1.32135i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.4848 | − | 10.4760i | −0.542816 | − | 0.455476i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.7701 | + | 8.03588i | −0.988137 | + | 0.348728i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0906752 | − | 0.249128i | −0.00392758 | − | 0.0107909i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.8275 | − | 28.3966i | −1.03015 | − | 1.22769i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.74133 | + | 16.0179i | 0.247757 | + | 0.691222i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.8836 | −1.24410 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.60427 | 0.111966 | 0.0559831 | − | 0.998432i | \(-0.482171\pi\) | ||||
0.0559831 | + | 0.998432i | \(0.482171\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.2799 | − | 18.0298i | 0.655725 | − | 0.773733i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.31606 | + | 2.76018i | 0.0992093 | + | 0.118233i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.87308 | − | 18.8836i | −0.293871 | − | 0.807405i | −0.995491 | − | 0.0948537i | \(-0.969762\pi\) |
0.701620 | − | 0.712552i | \(-0.252461\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.4833 | − | 0.112508i | −0.490094 | − | 0.00480174i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −52.0537 | − | 43.6782i | −2.21756 | − | 1.86076i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.07165 | + | 6.07760i | 0.0455710 | + | 0.258446i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.86883 | − | 16.9016i | 0.418908 | − | 0.717431i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.72320 | − | 5.03634i | 0.369614 | − | 0.213397i | −0.303676 | − | 0.952775i | \(-0.598214\pi\) |
0.673290 | + | 0.739379i | \(0.264881\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.47173 | − | 0.849704i | −0.0622476 | − | 0.0359387i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.0454 | + | 7.03781i | 0.804098 | + | 0.297137i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.5071 | + | 8.91984i | 1.03285 | + | 0.375927i | 0.802165 | − | 0.597102i | \(-0.203681\pi\) |
0.230684 | + | 0.973029i | \(0.425904\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.33744 | + | 13.2563i | −0.0983368 | + | 0.557696i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.1555 | − | 36.6417i | 0.594477 | − | 1.53881i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.55298 | − | 0.626486i | −0.148949 | − | 0.0262636i | 0.0986767 | − | 0.995120i | \(-0.468539\pi\) |
−0.247625 | + | 0.968856i | \(0.579650\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.25538 | − | 14.4390i | 0.219931 | − | 0.604255i | −0.779833 | − | 0.625988i | \(-0.784696\pi\) |
0.999764 | + | 0.0217327i | \(0.00691829\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.549531 | − | 1.48712i | 0.0229570 | − | 0.0621252i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.150668 | − | 0.260965i | 0.00628330 | − | 0.0108830i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.3889 | + | 19.7261i | 0.474124 | + | 0.821208i | 0.999561 | − | 0.0296252i | \(-0.00943137\pi\) |
−0.525437 | + | 0.850833i | \(0.676098\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.94376 | + | 2.88666i | 0.205455 | + | 0.119966i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.5115 | − | 6.79061i | 1.59773 | − | 0.281722i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.5005 | + | 22.0481i | −0.766213 | + | 0.913138i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.47273 | + | 4.21731i | −0.308959 | + | 0.174364i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.66309 | − | 3.15311i | 0.357564 | − | 0.130143i | −0.156991 | − | 0.987600i | \(-0.550179\pi\) |
0.514555 | + | 0.857457i | \(0.327957\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.0674 | − | 27.7468i | 1.36252 | − | 1.14329i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.99029 | + | 2.53422i | 0.123004 | + | 0.104244i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.1512i | 0.991772i | 0.868388 | + | 0.495886i | \(0.165157\pi\) | ||||
−0.868388 | + | 0.495886i | \(0.834843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 48.2789i | 1.97924i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.7380 | − | 5.28258i | 0.603187 | − | 0.216202i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.4644 | + | 11.2980i | −0.550140 | + | 0.461622i | −0.874988 | − | 0.484144i | \(-0.839131\pi\) |
0.324848 | + | 0.945766i | \(0.394687\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.9928 | + | 8.36871i | −0.937898 | + | 0.341367i | −0.765335 | − | 0.643632i | \(-0.777427\pi\) |
−0.172562 | + | 0.984999i | \(0.555205\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.91806 | + | 1.66274i | 0.363171 | + | 0.0677121i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.63884 | + | 9.10361i | −0.310563 | + | 0.370115i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.07547 | + | 0.189635i | −0.0436521 | + | 0.00769705i | −0.195432 | − | 0.980717i | \(-0.562611\pi\) |
0.151779 | + | 0.988414i | \(0.451500\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.367167 | − | 74.9521i | 0.0148783 | − | 3.03721i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.56619 | − | 6.17683i | −0.144273 | − | 0.249888i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.33767 | + | 14.4413i | −0.336755 | + | 0.583277i | −0.983820 | − | 0.179158i | \(-0.942663\pi\) |
0.647065 | + | 0.762435i | \(0.275996\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.524908 | − | 0.631820i | −0.0211663 | − | 0.0254775i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.05382 | − | 11.1378i | 0.163201 | − | 0.448390i | −0.830956 | − | 0.556338i | \(-0.812206\pi\) |
0.994157 | + | 0.107948i | \(0.0344281\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.4189 | − | 4.65836i | −1.06186 | − | 0.187235i | −0.384680 | − | 0.923050i | \(-0.625688\pi\) |
−0.677183 | + | 0.735815i | \(0.736799\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.49455 | − | 10.4310i | −0.340875 | − | 0.418580i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.5177 | + | 76.6625i | −0.541574 | + | 3.07142i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0265 | + | 8.74492i | 0.961059 | + | 0.349797i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.80382 | − | 28.0465i | −0.191846 | − | 1.12007i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.1571 | + | 12.2150i | 0.843587 | + | 0.487045i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.440800 | − | 0.254496i | 0.0175480 | − | 0.0101313i | −0.491200 | − | 0.871047i | \(-0.663442\pi\) |
0.508748 | + | 0.860915i | \(0.330108\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.6531 | + | 34.4286i | 0.781142 | + | 1.36842i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.226085 | − | 1.28219i | −0.00897190 | − | 0.0508822i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.6717 | + | 9.79369i | 0.462448 | + | 0.388040i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.27348 | + | 7.66041i | 0.0503782 | + | 0.303041i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.51995 | − | 4.17603i | −0.0600345 | − | 0.164943i | 0.906049 | − | 0.423172i | \(-0.139083\pi\) |
−0.966084 | + | 0.258229i | \(0.916861\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.68943 | − | 4.39689i | −0.145497 | − | 0.173397i | 0.688374 | − | 0.725356i | \(-0.258325\pi\) |
−0.833871 | + | 0.551959i | \(0.813880\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.18078 | − | 0.939702i | −0.203993 | − | 0.0370007i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.5457 | 1.20088 | 0.600439 | − | 0.799671i | \(-0.294993\pi\) | ||||
0.600439 | + | 0.799671i | \(0.294993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.2939 | −0.757353 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 46.8499 | + | 8.49774i | 1.83619 | + | 0.333053i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.0659 | + | 21.5301i | 0.706972 | + | 0.842537i | 0.993296 | − | 0.115596i | \(-0.0368778\pi\) |
−0.286324 | + | 0.958133i | \(0.592433\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.323636 | + | 0.889183i | 0.0126455 | + | 0.0347432i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.4518 | − | 16.8224i | 0.797900 | − | 0.656304i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.20561 | + | 3.52893i | 0.163827 | + | 0.137467i | 0.721016 | − | 0.692919i | \(-0.243675\pi\) |
−0.557188 | + | 0.830386i | \(0.688120\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.70979 | − | 9.69669i | −0.0665031 | − | 0.377158i | −0.999835 | − | 0.0181440i | \(-0.994224\pi\) |
0.933332 | − | 0.359014i | \(-0.116887\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.30979 | − | 9.30175i | −0.206215 | − | 0.361250i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 58.5951 | − | 33.8299i | 2.27222 | − | 1.31187i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.2296 | − | 12.8343i | −0.860733 | − | 0.496944i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.47559 | + | 14.4534i | 0.0957117 | + | 0.558801i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.62262 | − | 3.13838i | −0.332872 | − | 0.121156i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.78552 | − | 27.1400i | 0.184468 | − | 1.04617i | −0.742168 | − | 0.670213i | \(-0.766203\pi\) |
0.926637 | − | 0.375958i | \(-0.122686\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.395533 | + | 0.457551i | −0.0152241 | + | 0.0176111i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.6484 | − | 2.23025i | −0.486117 | − | 0.0857155i | −0.0747822 | − | 0.997200i | \(-0.523826\pi\) |
−0.411335 | + | 0.911484i | \(0.634937\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.1865 | − | 63.7043i | 0.889814 | − | 2.44475i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.2278 | − | 24.3478i | −0.775130 | − | 0.933008i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.8372 | + | 18.7705i | −0.414673 | + | 0.718234i | −0.995394 | − | 0.0958684i | \(-0.969437\pi\) |
0.580721 | + | 0.814102i | \(0.302771\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.30908 | − | 14.3918i | −0.317474 | − | 0.549881i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.110982 | − | 22.6554i | 0.00423422 | − | 0.864358i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.9519 | − | 2.63642i | 0.569621 | − | 0.100440i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.6079 | − | 19.7925i | 0.631794 | − | 0.752943i | −0.351256 | − | 0.936279i | \(-0.614245\pi\) |
0.983050 | + | 0.183337i | \(0.0586898\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 20.4097 | − | 23.8450i | 0.775302 | − | 0.905797i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.2895 | − | 8.84067i | 0.921354 | − | 0.335346i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.785435 | − | 0.659058i | 0.0297505 | − | 0.0249636i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −44.8877 | + | 16.0892i | −1.69781 | + | 0.608550i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.91690i | − | 0.261248i | −0.991432 | − | 0.130624i | \(-0.958302\pi\) | ||
0.991432 | − | 0.130624i | \(-0.0416980\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 34.2371i | − | 1.29128i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.8586 | − | 14.2874i | −0.634931 | − | 0.538093i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 40.0623 | − | 33.6162i | 1.50670 | − | 1.26427i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.5668 | + | 7.12175i | −0.734848 | + | 0.267463i | −0.682215 | − | 0.731151i | \(-0.738983\pi\) |
−0.0526325 | + | 0.998614i | \(0.516761\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.65265 | − | 2.15685i | −0.136985 | − | 0.0808881i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.4813 | − | 12.4912i | 0.392529 | − | 0.467798i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.75209 | + | 1.19058i | −0.252514 | + | 0.0445250i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.6539 | − | 13.2276i | −0.846024 | − | 0.493994i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.8797 | − | 29.2366i | −0.629508 | − | 1.09034i | −0.987650 | − | 0.156673i | \(-0.949923\pi\) |
0.358142 | − | 0.933667i | \(-0.383410\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.9798 | + | 67.5150i | −1.45168 | + | 2.51439i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.47298 | − | 22.9292i | 0.315113 | − | 0.852746i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.394712 | + | 1.08446i | −0.0146592 | + | 0.0402759i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.91332 | − | 1.21900i | −0.256401 | − | 0.0452104i | 0.0439701 | − | 0.999033i | \(-0.485999\pi\) |
−0.300371 | + | 0.953822i | \(0.597110\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.8070 | + | 23.7693i | 0.474334 | + | 0.880345i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.14127 | − | 6.47245i | 0.0422113 | − | 0.239392i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.47228 | + | 3.44763i | 0.349867 | + | 0.127341i | 0.510975 | − | 0.859596i | \(-0.329285\pi\) |
−0.161108 | + | 0.986937i | \(0.551507\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 44.2803 | + | 16.3628i | 1.63330 | + | 0.603551i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.27752 | + | 3.62433i | 0.231236 | + | 0.133504i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.2380 | + | 22.6541i | −1.44339 | + | 0.833344i | −0.998074 | − | 0.0620283i | \(-0.980243\pi\) |
−0.445319 | + | 0.895372i | \(0.646910\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.56868 | + | 12.9623i | −0.278042 | + | 0.476181i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.341948 | − | 1.93929i | −0.0125449 | − | 0.0711455i | 0.977893 | − | 0.209108i | \(-0.0670559\pi\) |
−0.990438 | + | 0.137962i | \(0.955945\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.3193 | − | 17.0500i | −0.744443 | − | 0.624662i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.6671 | + | 23.1455i | −0.500055 | + | 0.846850i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.4636 | − | 67.2133i | −0.893882 | − | 2.45592i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.6392 | − | 17.4463i | −0.534191 | − | 0.636624i | 0.429684 | − | 0.902979i | \(-0.358625\pi\) |
−0.963875 | + | 0.266355i | \(0.914180\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.752659 | + | 0.888113i | −0.0274284 | + | 0.0323646i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.6774 | −0.606953 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.2708 | −1.46367 | −0.731834 | − | 0.681483i | \(-0.761335\pi\) | ||||
−0.731834 | + | 0.681483i | \(0.761335\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.62679 | − | 10.1185i | −0.131644 | − | 0.367278i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.9631 | + | 34.5168i | 1.04991 | + | 1.25123i | 0.967027 | + | 0.254675i | \(0.0819684\pi\) |
0.0828832 | + | 0.996559i | \(0.473587\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.37789 | + | 6.53321i | 0.0860855 | + | 0.236518i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −25.2108 | − | 21.5788i | −0.911499 | − | 0.780183i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.79656 | + | 6.54209i | 0.281517 | + | 0.236221i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.24847 | + | 12.7517i | 0.0810817 | + | 0.459837i | 0.998134 | + | 0.0610693i | \(0.0194511\pi\) |
−0.917052 | + | 0.398768i | \(0.869438\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.9301 | − | 0.102530i | −0.753780 | − | 0.00369253i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.17077 | − | 4.14005i | 0.257915 | − | 0.148907i | −0.365468 | − | 0.930824i | \(-0.619091\pi\) |
0.623383 | + | 0.781917i | \(0.285758\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.634903 | − | 0.366561i | −0.0228064 | − | 0.0131673i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29.0482 | − | 24.1328i | 1.04210 | − | 0.865761i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.35025 | − | 0.491452i | −0.0483778 | − | 0.0176081i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.07748 | + | 6.11069i | −0.0385553 | + | 0.218658i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 38.9752 | + | 33.6924i | 1.39286 | + | 1.20407i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.9888 | + | 4.40620i | 0.891888 | + | 0.157264i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.5001 | + | 42.5862i | −0.552519 | + | 1.51803i | 0.277741 | + | 0.960656i | \(0.410414\pi\) |
−0.830260 | + | 0.557377i | \(0.811808\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 41.6155 | − | 7.12791i | 1.48155 | − | 0.253760i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.9867 | + | 22.4936i | −0.461753 | + | 0.799779i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.42020 | + | 4.19191i | 0.0859438 | + | 0.148859i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 40.8529 | − | 23.3203i | 1.44890 | − | 0.827087i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.2457 | + | 3.92252i | −0.787984 | + | 0.138943i | −0.553138 | − | 0.833090i | \(-0.686570\pi\) |
−0.234846 | + | 0.972033i | \(0.575459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.7305 | − | 21.1304i | 0.627261 | − | 0.747541i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.9906 | − | 41.3239i | −1.20100 | − | 1.46011i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.8836 | − | 7.23704i | 0.701677 | − | 0.255390i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.5789 | − | 16.4286i | 0.690065 | − | 0.579033i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.52370 | − | 24.9402i | 0.159242 | − | 0.877935i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.8089i | 1.85666i | 0.371754 | + | 0.928331i | \(0.378756\pi\) | ||||
−0.371754 | + | 0.928331i | \(0.621244\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 0.900633i | − | 0.0316255i | −0.999875 | − | 0.0158127i | \(-0.994966\pi\) | ||
0.999875 | − | 0.0158127i | \(-0.00503356\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.56231 | + | 19.6398i | −0.124936 | + | 0.688797i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.69692 | + | 3.10208i | −0.129497 | + | 0.108661i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.65518 | + | 3.15023i | −0.302806 | + | 0.110213i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.3327 | + | 2.71518i | −0.570710 | + | 0.0948761i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.21658 | + | 2.64162i | −0.0773592 | + | 0.0921931i | −0.803336 | − | 0.595526i | \(-0.796944\pi\) |
0.725977 | + | 0.687719i | \(0.241388\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.9820 | + | 5.28664i | −1.04511 | + | 0.184281i | −0.669740 | − | 0.742595i | \(-0.733595\pi\) |
−0.375367 | + | 0.926876i | \(0.622483\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.419702 | + | 0.239581i | −0.0146121 | + | 0.00834115i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.4911 | + | 21.6352i | 0.434358 | + | 0.752331i | 0.997243 | − | 0.0742047i | \(-0.0236418\pi\) |
−0.562885 | + | 0.826535i | \(0.690308\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.77640 | − | 4.80887i | 0.0964284 | − | 0.167019i | −0.813775 | − | 0.581179i | \(-0.802591\pi\) |
0.910204 | + | 0.414161i | \(0.135925\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.78588 | + | 0.477167i | −0.0966411 | + | 0.0165527i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.1535 | + | 55.3712i | −0.698276 | + | 1.91850i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.15813 | + | 0.380537i | 0.0746853 | + | 0.0131690i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.3775 | + | 20.6664i | −0.877175 | + | 0.714336i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.77532 | + | 10.0683i | −0.0612909 | + | 0.347598i | 0.938705 | + | 0.344722i | \(0.112027\pi\) |
−0.999996 | + | 0.00287636i | \(0.999084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 65.1258 | + | 23.7039i | 2.24572 | + | 0.817374i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −31.5331 | + | 26.1972i | −1.08606 | + | 0.902281i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.3336 | − | 12.8943i | −0.768298 | − | 0.443577i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.8586 | + | 11.4654i | −0.682349 | + | 0.393954i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.3147 | + | 0.0995153i | 0.697199 | + | 0.00341536i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.24580 | − | 12.7366i | −0.0769850 | − | 0.436604i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.8162 | − | 22.5015i | −0.918169 | − | 0.770435i | 0.0554864 | − | 0.998459i | \(-0.482329\pi\) |
−0.973655 | + | 0.228024i | \(0.926773\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.52406 | + | 45.7185i | −0.291517 | + | 1.56354i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.4198 | − | 50.6079i | −0.629207 | − | 1.72873i | −0.683241 | − | 0.730193i | \(-0.739430\pi\) |
0.0540344 | − | 0.998539i | \(-0.482792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.85064 | + | 4.58902i | 0.131382 | + | 0.156575i | 0.827725 | − | 0.561134i | \(-0.189635\pi\) |
−0.696342 | + | 0.717710i | \(0.745191\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.534789 | − | 1.49202i | −0.0182256 | − | 0.0508480i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.82514 | −0.266371 | −0.133185 | − | 0.991091i | \(-0.542521\pi\) | ||||
−0.133185 | + | 0.991091i | \(0.542521\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.9514 | −0.644368 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.74367 | − | 9.13727i | 0.262989 | − | 0.310318i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.17870 | − | 2.59647i | −0.0739073 | − | 0.0880793i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.30779 | − | 3.59312i | −0.0443127 | − | 0.121748i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.9024 | + | 40.5811i | 0.775127 | + | 1.37346i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.9331 | + | 30.9906i | 1.24857 | + | 1.04767i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.226004 | − | 1.28173i | −0.00763162 | − | 0.0432810i | 0.980754 | − | 0.195247i | \(-0.0625508\pi\) |
−0.988386 | + | 0.151966i | \(0.951440\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.29293 | − | 3.92692i | 0.0773387 | − | 0.132452i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.9169 | − | 21.3140i | 1.24376 | − | 0.718086i | 0.273904 | − | 0.961757i | \(-0.411685\pi\) |
0.969858 | + | 0.243671i | \(0.0783517\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.6250 | + | 10.1758i | 0.593129 | + | 0.342443i | 0.766334 | − | 0.642443i | \(-0.222079\pi\) |
−0.173205 | + | 0.984886i | \(0.555412\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29.5788 | + | 10.9302i | 0.994281 | + | 0.367414i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.8177 | + | 14.1285i | 1.30337 | + | 0.474388i | 0.898093 | − | 0.439805i | \(-0.144952\pi\) |
0.405278 | + | 0.914193i | \(0.367175\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.436243 | − | 2.47406i | 0.0146311 | − | 0.0829773i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.32928 | + | 21.3156i | 0.111535 | + | 0.714099i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −38.0697 | − | 6.71271i | −1.27395 | − | 0.224632i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.60018 | − | 20.8813i | 0.254046 | − | 0.697985i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.96536 | + | 5.31857i | −0.0656214 | + | 0.177582i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.2245 | + | 54.0825i | −1.04140 | + | 1.80375i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.3585 | + | 50.8504i | 0.978073 | + | 1.69407i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.77359 | − | 5.12290i | −0.291967 | − | 0.170479i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.3951 | + | 5.35948i | −1.01037 | + | 0.178155i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.24815 | + | 11.0215i | −0.307080 | + | 0.365963i | −0.897409 | − | 0.441199i | \(-0.854553\pi\) |
0.590330 | + | 0.807162i | \(0.298998\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.352178 | + | 35.9453i | −0.0116810 | + | 1.19223i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.9959 | + | 14.1934i | −1.29199 | + | 0.470247i | −0.894381 | − | 0.447306i | \(-0.852383\pi\) |
−0.397613 | + | 0.917553i | \(0.630161\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.4529 | + | 13.8056i | −0.544510 | + | 0.456898i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.4411 | + | 9.69612i | 0.378231 | + | 0.320544i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.82584i | 0.0602946i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.14658i | 0.202757i | 0.994848 | + | 0.101379i | \(0.0323253\pi\) | ||||
−0.994848 | + | 0.101379i | \(0.967675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −47.9298 | + | 17.1796i | −1.57934 | + | 0.566087i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.50739 | − | 2.10395i | 0.0825316 | − | 0.0692522i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.546405 | + | 0.198875i | −0.0179657 | + | 0.00653897i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.8333 | − | 50.5315i | −0.585722 | − | 1.65967i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.3476 | + | 39.7422i | −1.09410 | + | 1.30390i | −0.144824 | + | 0.989457i | \(0.546262\pi\) |
−0.949277 | + | 0.314441i | \(0.898183\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 81.3248 | − | 14.3397i | 2.66531 | − | 0.469966i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.169716 | + | 34.6453i | −0.00555626 | + | 1.13424i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.2579 | − | 22.9634i | −0.433581 | − | 0.750985i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.59393 | + | 4.49282i | −0.0847400 | + | 0.146774i | −0.905280 | − | 0.424815i | \(-0.860339\pi\) |
0.820540 | + | 0.571589i | \(0.193673\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.3241 | + | 26.8710i | 0.728519 | + | 0.876903i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.88354 | − | 7.92247i | 0.0940008 | − | 0.258265i | −0.883777 | − | 0.467908i | \(-0.845008\pi\) |
0.977778 | + | 0.209643i | \(0.0672301\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.534545 | − | 0.0942547i | −0.0174072 | − | 0.00306935i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −44.7978 | + | 24.9936i | −1.45727 | + | 0.813041i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.81475 | + | 55.6622i | −0.318936 | + | 1.80878i | 0.230310 | + | 0.973117i | \(0.426026\pi\) |
−0.549246 | + | 0.835661i | \(0.685085\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.4887 | − | 3.81759i | −0.340479 | − | 0.123924i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.43503 | − | 25.8934i | −0.143816 | − | 0.839650i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.7588 | − | 11.4077i | −0.640049 | − | 0.369532i | 0.144584 | − | 0.989492i | \(-0.453815\pi\) |
−0.784633 | + | 0.619960i | \(0.787149\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.79305 | + | 1.03522i | −0.0580217 | + | 0.0334988i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.4081 | + | 35.7511i | 0.659699 | + | 1.15567i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.56815 | − | 31.5785i | −0.179805 | − | 1.01972i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.64243 | − | 5.57366i | −0.214272 | − | 0.179796i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 46.0325 | + | 17.2670i | 1.48338 | + | 0.556422i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.55702 | − | 7.02537i | −0.0823135 | − | 0.226155i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.38006 | + | 6.41170i | 0.173011 | + | 0.206186i | 0.845581 | − | 0.533847i | \(-0.179254\pi\) |
−0.672570 | + | 0.740033i | \(0.734810\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −57.1184 | − | 10.3603i | −1.83491 | − | 0.332820i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.7798 | 0.410123 | 0.205061 | − | 0.978749i | \(-0.434261\pi\) | ||||
0.205061 | + | 0.978749i | \(0.434261\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49.8759 | 1.59895 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.250835 | + | 0.0454970i | 0.00803314 | + | 0.00145707i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.6162 | + | 29.3365i | 0.787543 | + | 0.938557i | 0.999248 | − | 0.0387762i | \(-0.0123459\pi\) |
−0.211705 | + | 0.977334i | \(0.567902\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.6228 | − | 40.1759i | −0.467348 | − | 1.28403i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.47441 | − | 1.67838i | −0.142857 | − | 0.0535864i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.2171 | − | 20.3206i | −0.772407 | − | 0.648126i | 0.168917 | − | 0.985630i | \(-0.445973\pi\) |
−0.941324 | + | 0.337504i | \(0.890417\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.888884 | − | 5.04111i | −0.0283222 | − | 0.160623i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.1389 | − | 37.0315i | −0.672860 | − | 1.17872i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.01317 | + | 1.73966i | −0.0958133 | + | 0.0553178i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.3761 | + | 19.2697i | 1.06023 | + | 0.612122i | 0.925495 | − | 0.378760i | \(-0.123650\pi\) |
0.134731 | + | 0.990882i | \(0.456983\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.63647 | − | 38.7462i | −0.210602 | − | 1.22957i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.2129 | − | 6.99291i | −0.609088 | − | 0.221690i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.0294 | − | 56.8793i | 0.317633 | − | 1.80139i | −0.239428 | − | 0.970914i | \(-0.576960\pi\) |
0.557061 | − | 0.830471i | \(-0.311929\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.381463 | + | 25.9552i | −0.0120689 | + | 0.821185i |
(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.b.191.6 | yes | 36 | |
4.3 | odd | 2 | 432.2.be.c.191.1 | yes | 36 | ||
27.14 | odd | 18 | 432.2.be.c.95.1 | yes | 36 | ||
108.95 | even | 18 | inner | 432.2.be.b.95.6 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.be.b.95.6 | ✓ | 36 | 108.95 | even | 18 | inner | |
432.2.be.b.191.6 | yes | 36 | 1.1 | even | 1 | trivial | |
432.2.be.c.95.1 | yes | 36 | 27.14 | odd | 18 | ||
432.2.be.c.191.1 | yes | 36 | 4.3 | odd | 2 |