Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(136,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.et (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 271.2 | ||
Character | \(\chi\) | \(=\) | 819.271 |
Dual form | 819.2.et.b.136.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.14693 | − | 1.14693i | −0.811001 | − | 0.811001i | 0.173783 | − | 0.984784i | \(-0.444401\pi\) |
−0.984784 | + | 0.173783i | \(0.944401\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.630890i | 0.315445i | ||||||||
\(5\) | −0.395109 | − | 1.47457i | −0.176698 | − | 0.659447i | −0.996256 | − | 0.0864504i | \(-0.972448\pi\) |
0.819558 | − | 0.572996i | \(-0.194219\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0531605 | + | 2.64522i | 0.0200928 | + | 0.999798i | ||||
\(8\) | −1.57027 | + | 1.57027i | −0.555175 | + | 0.555175i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.23806 | + | 2.14439i | −0.391509 | + | 0.678114i | ||||
\(11\) | 0.745574 | + | 2.78252i | 0.224799 | + | 0.838961i | 0.982485 | + | 0.186342i | \(0.0596632\pi\) |
−0.757686 | + | 0.652619i | \(0.773670\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.94467 | − | 2.08061i | −0.816704 | − | 0.577057i | ||||
\(14\) | 2.97290 | − | 3.09485i | 0.794542 | − | 0.827132i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.86376 | 1.21594 | ||||||||
\(17\) | 6.21574 | 1.50754 | 0.753769 | − | 0.657139i | \(-0.228234\pi\) | ||||
0.753769 | + | 0.657139i | \(0.228234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.23387 | + | 0.598564i | 0.512485 | + | 0.137320i | 0.505788 | − | 0.862658i | \(-0.331202\pi\) |
0.00669672 | + | 0.999978i | \(0.497868\pi\) | |||||||
\(20\) | 0.930289 | − | 0.249270i | 0.208019 | − | 0.0557385i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.33623 | − | 4.04647i | 0.498086 | − | 0.862710i | ||||
\(23\) | − | 5.62238i | − | 1.17235i | −0.810185 | − | 0.586174i | \(-0.800633\pi\) | ||
0.810185 | − | 0.586174i | \(-0.199367\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.31189 | − | 1.33477i | 0.462378 | − | 0.266954i | ||||
\(26\) | 0.991014 | + | 5.76363i | 0.194354 | + | 1.13034i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.66884 | + | 0.0335384i | −0.315381 | + | 0.00633816i | ||||
\(29\) | −0.379237 | − | 0.656858i | −0.0704225 | − | 0.121975i | 0.828664 | − | 0.559746i | \(-0.189101\pi\) |
−0.899087 | + | 0.437771i | \(0.855768\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.36292 | + | 2.24084i | 1.50202 | + | 0.402466i | 0.913777 | − | 0.406215i | \(-0.133152\pi\) |
0.588247 | + | 0.808682i | \(0.299818\pi\) | |||||||
\(32\) | −2.43784 | − | 2.43784i | −0.430953 | − | 0.430953i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.12901 | − | 7.12901i | −1.22261 | − | 1.22261i | ||||
\(35\) | 3.87955 | − | 1.12354i | 0.655763 | − | 0.189913i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.26298 | + | 4.26298i | −0.700830 | + | 0.700830i | −0.964589 | − | 0.263759i | \(-0.915038\pi\) |
0.263759 | + | 0.964589i | \(0.415038\pi\) | |||||||
\(38\) | −1.87558 | − | 3.24860i | −0.304259 | − | 0.526992i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.93590 | + | 1.69504i | 0.464207 | + | 0.268010i | ||||
\(41\) | 1.94919 | + | 0.522283i | 0.304412 | + | 0.0815669i | 0.407792 | − | 0.913075i | \(-0.366299\pi\) |
−0.103380 | + | 0.994642i | \(0.532966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.24252 | − | 1.29472i | −0.341981 | − | 0.197443i | 0.319167 | − | 0.947699i | \(-0.396597\pi\) |
−0.661148 | + | 0.750256i | \(0.729930\pi\) | |||||||
\(44\) | −1.75546 | + | 0.470375i | −0.264646 | + | 0.0709116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.44847 | + | 6.44847i | −0.950775 | + | 0.950775i | ||||
\(47\) | 2.13395 | − | 0.571791i | 0.311269 | − | 0.0834043i | −0.0998029 | − | 0.995007i | \(-0.531821\pi\) |
0.411072 | + | 0.911603i | \(0.365155\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99435 | + | 0.281242i | −0.999193 | + | 0.0401774i | ||||
\(50\) | −4.18246 | − | 1.12069i | −0.591488 | − | 0.158489i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.31263 | − | 1.85776i | 0.182030 | − | 0.257625i | ||||
\(53\) | −2.47328 | − | 4.28385i | −0.339732 | − | 0.588433i | 0.644650 | − | 0.764477i | \(-0.277003\pi\) |
−0.984382 | + | 0.176045i | \(0.943670\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.80843 | − | 2.19880i | 0.513529 | − | 0.296486i | ||||
\(56\) | −4.23719 | − | 4.07023i | −0.566218 | − | 0.543908i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.318411 | + | 1.18833i | −0.0418094 | + | 0.156035i | ||||
\(59\) | 0.623268 | + | 0.623268i | 0.0811426 | + | 0.0811426i | 0.746513 | − | 0.665371i | \(-0.231726\pi\) |
−0.665371 | + | 0.746513i | \(0.731726\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.48249 | − | 2.58797i | 0.573924 | − | 0.331355i | −0.184791 | − | 0.982778i | \(-0.559161\pi\) |
0.758715 | + | 0.651423i | \(0.225828\pi\) | |||||||
\(62\) | −7.02159 | − | 12.1617i | −0.891742 | − | 1.54454i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 4.13546i | − | 0.516933i | ||||||
\(65\) | −1.90453 | + | 5.16418i | −0.236228 | + | 0.640538i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.1664 | − | 4.06383i | 1.85287 | − | 0.496476i | 0.853189 | − | 0.521602i | \(-0.174665\pi\) |
0.999684 | + | 0.0251264i | \(0.00799882\pi\) | |||||||
\(68\) | 3.92145i | 0.475545i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.73818 | − | 3.16095i | −0.685844 | − | 0.377805i | ||||
\(71\) | 10.3040 | − | 2.76095i | 1.22286 | − | 0.327665i | 0.411066 | − | 0.911606i | \(-0.365157\pi\) |
0.811796 | + | 0.583941i | \(0.198490\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.80076 | − | 6.72052i | 0.210763 | − | 0.786578i | −0.776852 | − | 0.629683i | \(-0.783185\pi\) |
0.987615 | − | 0.156895i | \(-0.0501484\pi\) | |||||||
\(74\) | 9.77867 | 1.13675 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.377628 | + | 1.40933i | −0.0433169 | + | 0.161661i | ||||
\(77\) | −7.32073 | + | 2.12012i | −0.834275 | + | 0.241611i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.24764 | + | 7.35713i | −0.477897 | + | 0.827742i | −0.999679 | − | 0.0253371i | \(-0.991934\pi\) |
0.521782 | + | 0.853079i | \(0.325267\pi\) | |||||||
\(80\) | −1.92172 | − | 7.17194i | −0.214854 | − | 0.801847i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.63656 | − | 2.83460i | −0.180727 | − | 0.313029i | ||||
\(83\) | 1.51432 | − | 1.51432i | 0.166218 | − | 0.166218i | −0.619096 | − | 0.785315i | \(-0.712501\pi\) |
0.785315 | + | 0.619096i | \(0.212501\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.45590 | − | 9.16553i | −0.266379 | − | 0.994141i | ||||
\(86\) | 1.08706 | + | 4.05696i | 0.117221 | + | 0.437473i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.54006 | − | 3.19856i | −0.590573 | − | 0.340967i | ||||
\(89\) | 5.91573 | + | 5.91573i | 0.627066 | + | 0.627066i | 0.947329 | − | 0.320263i | \(-0.103771\pi\) |
−0.320263 | + | 0.947329i | \(0.603771\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.34712 | − | 7.89989i | 0.560531 | − | 0.828134i | ||||
\(92\) | 3.54710 | 0.369811 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.10329 | − | 1.79169i | −0.320080 | − | 0.184798i | ||||
\(95\) | − | 3.53049i | − | 0.362221i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.933928 | − | 3.48547i | −0.0948260 | − | 0.353896i | 0.902167 | − | 0.431387i | \(-0.141976\pi\) |
−0.996993 | + | 0.0774914i | \(0.975309\pi\) | |||||||
\(98\) | 8.34458 | + | 7.69945i | 0.842930 | + | 0.777762i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.842092 | + | 1.45855i | 0.0842092 | + | 0.145855i | ||||
\(101\) | −9.84474 | + | 17.0516i | −0.979589 | + | 1.69670i | −0.315713 | + | 0.948855i | \(0.602244\pi\) |
−0.663876 | + | 0.747843i | \(0.731090\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.70130 | + | 8.14290i | −0.463233 | + | 0.802344i | −0.999120 | − | 0.0419464i | \(-0.986644\pi\) |
0.535887 | + | 0.844290i | \(0.319977\pi\) | |||||||
\(104\) | 7.89105 | − | 1.35681i | 0.773781 | − | 0.133046i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.07659 | + | 7.74995i | −0.201697 | + | 0.752742i | ||||
\(107\) | −0.0718412 | −0.00694515 | −0.00347258 | − | 0.999994i | \(-0.501105\pi\) | ||||
−0.00347258 | + | 0.999994i | \(0.501105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.89580 | − | 7.07523i | 0.181585 | − | 0.677684i | −0.813751 | − | 0.581214i | \(-0.802578\pi\) |
0.995336 | − | 0.0964705i | \(-0.0307553\pi\) | |||||||
\(110\) | −6.88986 | − | 1.84613i | −0.656922 | − | 0.176022i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.258560 | + | 12.8657i | 0.0244316 | + | 1.21569i | ||||
\(113\) | 8.15754 | − | 14.1293i | 0.767396 | − | 1.32917i | −0.171574 | − | 0.985171i | \(-0.554885\pi\) |
0.938970 | − | 0.343998i | \(-0.111781\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.29059 | + | 2.22146i | −0.773101 | + | 0.207152i | ||||
\(116\) | 0.414405 | − | 0.239257i | 0.0384765 | − | 0.0222144i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.42969i | − | 0.131613i | ||||||
\(119\) | 0.330432 | + | 16.4420i | 0.0302906 | + | 1.50723i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.33975 | − | 1.35085i | 0.212704 | − | 0.122805i | ||||
\(122\) | −8.10931 | − | 2.17288i | −0.734182 | − | 0.196724i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.41372 | + | 5.27608i | −0.126956 | + | 0.473806i | ||||
\(125\) | −8.27895 | − | 8.27895i | −0.740492 | − | 0.740492i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9037 | − | 8.60464i | 1.32249 | − | 0.763538i | 0.338362 | − | 0.941016i | \(-0.390127\pi\) |
0.984125 | + | 0.177478i | \(0.0567937\pi\) | |||||||
\(128\) | −9.61876 | + | 9.61876i | −0.850186 | + | 0.850186i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.10731 | − | 3.73858i | 0.711058 | − | 0.327895i | ||||
\(131\) | −4.73734 | − | 2.73511i | −0.413904 | − | 0.238967i | 0.278562 | − | 0.960418i | \(-0.410142\pi\) |
−0.692466 | + | 0.721451i | \(0.743476\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.46458 | + | 5.94089i | −0.126995 | + | 0.515141i | ||||
\(134\) | −22.0557 | − | 12.7339i | −1.90532 | − | 1.10004i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.76040 | + | 9.76040i | −0.836947 | + | 0.836947i | ||||
\(137\) | 1.24060 | − | 1.24060i | 0.105991 | − | 0.105991i | −0.652122 | − | 0.758114i | \(-0.726121\pi\) |
0.758114 | + | 0.652122i | \(0.226121\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.13953 | + | 4.12201i | 0.605567 | + | 0.349624i | 0.771228 | − | 0.636559i | \(-0.219643\pi\) |
−0.165662 | + | 0.986183i | \(0.552976\pi\) | |||||||
\(140\) | 0.708829 | + | 2.44757i | 0.0599070 | + | 0.206857i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.9846 | − | 8.65135i | −1.25748 | − | 0.726005i | ||||
\(143\) | 3.59387 | − | 9.74484i | 0.300534 | − | 0.814904i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.818741 | + | 0.818741i | −0.0679927 | + | 0.0679927i | ||||
\(146\) | −9.77330 | + | 5.64262i | −0.808844 | + | 0.466986i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.68947 | − | 2.68947i | −0.221073 | − | 0.221073i | ||||
\(149\) | −1.15185 | + | 4.29875i | −0.0943628 | + | 0.352167i | −0.996922 | − | 0.0783988i | \(-0.975019\pi\) |
0.902559 | + | 0.430566i | \(0.141686\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.69443 | − | 2.32966i | −0.707542 | − | 0.189585i | −0.112936 | − | 0.993602i | \(-0.536025\pi\) |
−0.594606 | + | 0.804017i | \(0.702692\pi\) | |||||||
\(152\) | −4.44769 | + | 2.56788i | −0.360755 | + | 0.208282i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.8280 | + | 5.96472i | 0.872544 | + | 0.480651i | ||||
\(155\) | − | 13.2171i | − | 1.06162i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.21105 | + | 2.43125i | −0.336078 | + | 0.194035i | −0.658537 | − | 0.752549i | \(-0.728824\pi\) |
0.322458 | + | 0.946584i | \(0.395491\pi\) | |||||||
\(158\) | 13.3098 | − | 3.56636i | 1.05887 | − | 0.283724i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.63155 | + | 4.55797i | −0.208042 | + | 0.360339i | ||||
\(161\) | 14.8724 | − | 0.298889i | 1.17211 | − | 0.0235557i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.17099 | + | 1.65351i | 0.483349 | + | 0.129513i | 0.492262 | − | 0.870447i | \(-0.336170\pi\) |
−0.00891239 | + | 0.999960i | \(0.502837\pi\) | |||||||
\(164\) | −0.329503 | + | 1.22972i | −0.0257299 | + | 0.0960252i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.47364 | −0.269607 | ||||||||
\(167\) | −2.62064 | + | 9.78037i | −0.202791 | + | 0.756828i | 0.787320 | + | 0.616544i | \(0.211468\pi\) |
−0.990111 | + | 0.140283i | \(0.955199\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.34213 | + | 12.2534i | 0.334010 | + | 0.942569i | ||||
\(170\) | −7.69547 | + | 13.3289i | −0.590215 | + | 1.02228i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.816825 | − | 1.41478i | 0.0622823 | − | 0.107876i | ||||
\(173\) | 8.82380 | + | 15.2833i | 0.670861 | + | 1.16197i | 0.977660 | + | 0.210192i | \(0.0674088\pi\) |
−0.306799 | + | 0.951774i | \(0.599258\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.65366 | + | 6.04449i | 0.276190 | + | 0.456920i | ||||
\(176\) | 3.62629 | + | 13.5335i | 0.273342 | + | 1.02013i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 13.5698i | − | 1.01710i | ||||||
\(179\) | 17.5138 | + | 10.1116i | 1.30904 | + | 0.755775i | 0.981936 | − | 0.189213i | \(-0.0605936\pi\) |
0.327105 | + | 0.944988i | \(0.393927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.4649 | −1.29815 | −0.649077 | − | 0.760722i | \(-0.724845\pi\) | ||||
−0.649077 | + | 0.760722i | \(0.724845\pi\) | |||||||
\(182\) | −15.1934 | + | 2.92784i | −1.12621 | + | 0.217026i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.82867 | + | 8.82867i | 0.650858 | + | 0.650858i | ||||
\(185\) | 7.97040 | + | 4.60171i | 0.585995 | + | 0.338324i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.63429 | + | 17.2954i | 0.338893 | + | 1.26477i | ||||
\(188\) | 0.360737 | + | 1.34629i | 0.0263094 | + | 0.0981882i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.04922 | + | 4.04922i | −0.293761 | + | 0.293761i | ||||
\(191\) | 0.0207944 | + | 0.0360170i | 0.00150463 | + | 0.00260610i | 0.866777 | − | 0.498696i | \(-0.166188\pi\) |
−0.865272 | + | 0.501302i | \(0.832854\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.23272 | + | 12.0647i | 0.232696 | + | 0.868434i | 0.979174 | + | 0.203024i | \(0.0650769\pi\) |
−0.746478 | + | 0.665411i | \(0.768256\pi\) | |||||||
\(194\) | −2.92643 | + | 5.06873i | −0.210106 | + | 0.363914i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.177433 | − | 4.41266i | −0.0126738 | − | 0.315190i | ||||
\(197\) | −0.962573 | + | 3.59237i | −0.0685805 | + | 0.255946i | −0.991701 | − | 0.128565i | \(-0.958963\pi\) |
0.923121 | + | 0.384510i | \(0.125630\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.77707 | −0.622190 | −0.311095 | − | 0.950379i | \(-0.600696\pi\) | ||||
−0.311095 | + | 0.950379i | \(0.600696\pi\) | |||||||
\(200\) | −1.53434 | + | 5.72624i | −0.108494 | + | 0.404907i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 30.8482 | − | 8.26575i | 2.17047 | − | 0.581576i | ||||
\(203\) | 1.71737 | − | 1.03808i | 0.120536 | − | 0.0728591i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 3.08057i | − | 0.215156i | ||||||
\(206\) | 14.7314 | − | 3.94726i | 1.02638 | − | 0.275019i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.3221 | − | 10.1196i | −0.993062 | − | 0.701666i | ||||
\(209\) | 6.66206i | 0.460824i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.33665 | − | 5.77924i | −0.229704 | − | 0.397859i | 0.728016 | − | 0.685560i | \(-0.240443\pi\) |
−0.957720 | + | 0.287701i | \(0.907109\pi\) | |||||||
\(212\) | 2.70264 | − | 1.56037i | 0.185618 | − | 0.107167i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.0823968 | + | 0.0823968i | 0.00563253 | + | 0.00563253i | ||||
\(215\) | −1.02311 | + | 3.81830i | −0.0697756 | + | 0.260406i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.48292 | + | 22.2409i | −0.372205 | + | 1.50981i | ||||
\(218\) | −10.2891 | + | 5.94043i | −0.696868 | + | 0.402337i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.38720 | + | 2.40270i | 0.0935249 | + | 0.161990i | ||||
\(221\) | −18.3033 | − | 12.9325i | −1.23121 | − | 0.869936i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.10027 | − | 1.63456i | −0.408505 | − | 0.109458i | 0.0487142 | − | 0.998813i | \(-0.484488\pi\) |
−0.457219 | + | 0.889354i | \(0.651154\pi\) | |||||||
\(224\) | 6.31902 | − | 6.57821i | 0.422207 | − | 0.439525i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −25.5614 | + | 6.84915i | −1.70032 | + | 0.455599i | ||||
\(227\) | −16.6512 | + | 16.6512i | −1.10518 | + | 1.10518i | −0.111402 | + | 0.993775i | \(0.535534\pi\) |
−0.993775 | + | 0.111402i | \(0.964466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.2790 | − | 4.89785i | 1.20791 | − | 0.323659i | 0.401969 | − | 0.915653i | \(-0.368326\pi\) |
0.805942 | + | 0.591995i | \(0.201659\pi\) | |||||||
\(230\) | 12.0566 | + | 6.96086i | 0.794986 | + | 0.458985i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.62695 | + | 0.435940i | 0.106814 | + | 0.0286209i | ||||
\(233\) | −6.36747 | − | 3.67626i | −0.417147 | − | 0.240840i | 0.276709 | − | 0.960954i | \(-0.410756\pi\) |
−0.693856 | + | 0.720114i | \(0.744090\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.68629 | − | 2.92074i | −0.110001 | − | 0.190528i | ||||
\(236\) | −0.393214 | + | 0.393214i | −0.0255960 | + | 0.0255960i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.4788 | − | 19.2368i | 1.19780 | − | 1.24693i | ||||
\(239\) | 4.08646 | + | 4.08646i | 0.264331 | + | 0.264331i | 0.826811 | − | 0.562480i | \(-0.190153\pi\) |
−0.562480 | + | 0.826811i | \(0.690153\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.3223 | + | 20.3223i | 1.30907 | + | 1.30907i | 0.922085 | + | 0.386988i | \(0.126485\pi\) |
0.386988 | + | 0.922085i | \(0.373515\pi\) | |||||||
\(242\) | −4.23286 | − | 1.13419i | −0.272098 | − | 0.0729086i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.63272 | + | 2.82796i | 0.104524 | + | 0.181041i | ||||
\(245\) | 3.17824 | + | 10.2025i | 0.203050 | + | 0.651815i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.33263 | − | 6.41038i | −0.339307 | − | 0.407883i | ||||
\(248\) | −16.6508 | + | 9.61333i | −1.05732 | + | 0.610447i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 18.9907i | 1.20108i | ||||||||
\(251\) | 9.72695 | − | 16.8476i | 0.613960 | − | 1.06341i | −0.376606 | − | 0.926373i | \(-0.622909\pi\) |
0.990566 | − | 0.137036i | \(-0.0437576\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.6444 | − | 4.19190i | 0.983554 | − | 0.263543i | ||||
\(254\) | −26.9624 | − | 7.22454i | −1.69177 | − | 0.453308i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.7931 | 0.862070 | ||||||||
\(257\) | 25.2048 | 1.57223 | 0.786116 | − | 0.618080i | \(-0.212089\pi\) | ||||
0.786116 | + | 0.618080i | \(0.212089\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.5031 | − | 11.0499i | −0.714770 | − | 0.686607i | ||||
\(260\) | −3.25803 | − | 1.20155i | −0.202054 | − | 0.0745170i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.29642 | + | 8.57036i | 0.141873 | + | 0.529479i | ||||
\(263\) | 15.6393 | − | 27.0881i | 0.964362 | − | 1.67032i | 0.253041 | − | 0.967455i | \(-0.418569\pi\) |
0.711320 | − | 0.702868i | \(-0.248098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.33961 | + | 5.33961i | −0.328010 | + | 0.328010i | ||||
\(266\) | 8.49354 | − | 5.13401i | 0.520773 | − | 0.314787i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.56383 | + | 9.56834i | 0.156611 | + | 0.584479i | ||||
\(269\) | 9.01798i | 0.549836i | 0.961468 | + | 0.274918i | \(0.0886507\pi\) | ||||
−0.961468 | + | 0.274918i | \(0.911349\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.40845 | + | 2.40845i | 0.146303 | + | 0.146303i | 0.776464 | − | 0.630161i | \(-0.217011\pi\) |
−0.630161 | + | 0.776464i | \(0.717011\pi\) | |||||||
\(272\) | 30.2318 | 1.83308 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.84575 | −0.171918 | ||||||||
\(275\) | 5.43770 | + | 5.43770i | 0.327906 | + | 0.327906i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.02905i | 0.242082i | 0.992648 | + | 0.121041i | \(0.0386232\pi\) | ||||
−0.992648 | + | 0.121041i | \(0.961377\pi\) | |||||||
\(278\) | −3.46088 | − | 12.9162i | −0.207570 | − | 0.774661i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.32768 | + | 7.85620i | −0.258629 | + | 0.469498i | ||||
\(281\) | 3.28511 | − | 3.28511i | 0.195973 | − | 0.195973i | −0.602298 | − | 0.798271i | \(-0.705748\pi\) |
0.798271 | + | 0.602298i | \(0.205748\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.514830 | − | 0.891711i | 0.0306035 | − | 0.0530067i | −0.850318 | − | 0.526269i | \(-0.823590\pi\) |
0.880921 | + | 0.473262i | \(0.156924\pi\) | |||||||
\(284\) | 1.74186 | + | 6.50070i | 0.103360 | + | 0.385745i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.2985 | + | 7.05473i | −0.904622 | + | 0.417155i | ||||
\(287\) | −1.27793 | + | 5.18379i | −0.0754340 | + | 0.305989i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.6354 | 1.27267 | ||||||||
\(290\) | 1.87807 | 0.110284 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.23991 | + | 1.13608i | 0.248122 | + | 0.0664840i | ||||
\(293\) | −24.6989 | + | 6.61806i | −1.44293 | + | 0.386631i | −0.893558 | − | 0.448948i | \(-0.851799\pi\) |
−0.549369 | + | 0.835580i | \(0.685132\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.672792 | − | 1.16531i | 0.0391715 | − | 0.0678470i | ||||
\(296\) | − | 13.3881i | − | 0.778166i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.25144 | − | 3.60927i | 0.362136 | − | 0.209079i | ||||
\(299\) | −11.6980 | + | 16.5561i | −0.676512 | + | 0.957461i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.30560 | − | 6.00078i | 0.190532 | − | 0.345879i | ||||
\(302\) | 7.29993 | + | 12.6438i | 0.420064 | + | 0.727571i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.8650 | + | 2.91127i | 0.623151 | + | 0.166973i | ||||
\(305\) | −5.58721 | − | 5.58721i | −0.319922 | − | 0.319922i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.0195 | − | 14.0195i | −0.800136 | − | 0.800136i | 0.182981 | − | 0.983117i | \(-0.441425\pi\) |
−0.983117 | + | 0.182981i | \(0.941425\pi\) | |||||||
\(308\) | −1.33756 | − | 4.61857i | −0.0762148 | − | 0.263168i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.1590 | + | 15.1590i | −0.860975 | + | 0.860975i | ||||
\(311\) | −3.20853 | − | 5.55733i | −0.181939 | − | 0.315127i | 0.760602 | − | 0.649219i | \(-0.224904\pi\) |
−0.942541 | + | 0.334091i | \(0.891571\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.8008 | − | 12.5867i | −1.23225 | − | 0.711441i | −0.264753 | − | 0.964316i | \(-0.585291\pi\) |
−0.967499 | + | 0.252875i | \(0.918624\pi\) | |||||||
\(314\) | 7.61824 | + | 2.04130i | 0.429922 | + | 0.115197i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.64154 | − | 2.67979i | −0.261107 | − | 0.150750i | ||||
\(317\) | −23.2745 | + | 6.23639i | −1.30723 | + | 0.350271i | −0.844178 | − | 0.536062i | \(-0.819911\pi\) |
−0.463049 | + | 0.886333i | \(0.653245\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.54497 | − | 1.54497i | 0.0865017 | − | 0.0865017i | ||||
\(320\) | −6.09802 | + | 1.63396i | −0.340890 | + | 0.0913411i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −17.4004 | − | 16.7148i | −0.969687 | − | 0.931480i | ||||
\(323\) | 13.8852 | + | 3.72052i | 0.772591 | + | 0.207015i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.58488 | − | 0.879683i | −0.531673 | − | 0.0487960i | ||||
\(326\) | −5.18123 | − | 8.97415i | −0.286962 | − | 0.497032i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.88088 | + | 2.24063i | −0.214286 | + | 0.123718i | ||||
\(329\) | 1.62595 | + | 5.61437i | 0.0896417 | + | 0.309530i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.52989 | + | 5.70964i | −0.0840905 | + | 0.313830i | −0.995140 | − | 0.0984660i | \(-0.968606\pi\) |
0.911050 | + | 0.412296i | \(0.135273\pi\) | |||||||
\(332\) | 0.955370 | + | 0.955370i | 0.0524328 | + | 0.0524328i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.2231 | − | 8.21169i | 0.778252 | − | 0.449324i | ||||
\(335\) | −11.9848 | − | 20.7583i | −0.654799 | − | 1.13414i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 11.5318i | − | 0.628179i | −0.949393 | − | 0.314089i | \(-0.898301\pi\) | ||
0.949393 | − | 0.314089i | \(-0.101699\pi\) | |||||||
\(338\) | 9.07366 | − | 19.0339i | 0.493542 | − | 1.03531i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.78244 | − | 1.54940i | 0.313597 | − | 0.0840280i | ||||
\(341\) | 24.9407i | 1.35061i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.11577 | − | 18.4866i | −0.0602459 | − | 0.998184i | ||||
\(344\) | 5.55442 | − | 1.48830i | 0.299474 | − | 0.0802439i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.40855 | − | 27.6491i | 0.398286 | − | 1.48642i | ||||
\(347\) | −9.07305 | −0.487067 | −0.243533 | − | 0.969893i | \(-0.578307\pi\) | ||||
−0.243533 | + | 0.969893i | \(0.578307\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.77792 | + | 29.0276i | −0.416342 | + | 1.55381i | 0.365789 | + | 0.930698i | \(0.380799\pi\) |
−0.782132 | + | 0.623113i | \(0.785868\pi\) | |||||||
\(350\) | 2.74212 | − | 11.1231i | 0.146572 | − | 0.594554i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.96574 | − | 8.60092i | 0.264675 | − | 0.458431i | ||||
\(353\) | −7.50007 | − | 27.9907i | −0.399189 | − | 1.48979i | −0.814527 | − | 0.580125i | \(-0.803004\pi\) |
0.415338 | − | 0.909667i | \(-0.363663\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.14242 | − | 14.1031i | −0.432155 | − | 0.748514i | ||||
\(356\) | −3.73217 | + | 3.73217i | −0.197805 | + | 0.197805i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.48978 | − | 31.6843i | −0.448699 | − | 1.67457i | ||||
\(359\) | −2.28482 | − | 8.52708i | −0.120588 | − | 0.450042i | 0.879056 | − | 0.476719i | \(-0.158174\pi\) |
−0.999644 | + | 0.0266770i | \(0.991507\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.8226 | − | 6.82577i | −0.622241 | − | 0.359251i | ||||
\(362\) | 20.0310 | + | 20.0310i | 1.05280 | + | 1.05280i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.98396 | + | 3.37344i | 0.261230 | + | 0.176816i | ||||
\(365\) | −10.6214 | −0.555947 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.5082 | − | 6.64427i | −0.600724 | − | 0.346828i | 0.168602 | − | 0.985684i | \(-0.446075\pi\) |
−0.769326 | + | 0.638856i | \(0.779408\pi\) | |||||||
\(368\) | − | 27.3459i | − | 1.42550i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.86364 | − | 14.4193i | −0.200861 | − | 0.749624i | ||||
\(371\) | 11.2002 | − | 6.77011i | 0.581488 | − | 0.351486i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.12496 | + | 7.14464i | 0.213582 | + | 0.369935i | 0.952833 | − | 0.303495i | \(-0.0981535\pi\) |
−0.739251 | + | 0.673430i | \(0.764820\pi\) | |||||||
\(374\) | 14.5214 | − | 25.1518i | 0.750884 | − | 1.30057i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.45302 | + | 4.24875i | −0.126505 | + | 0.219113i | ||||
\(377\) | −0.249937 | + | 2.72327i | −0.0128724 | + | 0.140256i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.896568 | − | 3.34604i | 0.0460536 | − | 0.171874i | −0.939069 | − | 0.343730i | \(-0.888310\pi\) |
0.985122 | + | 0.171855i | \(0.0549762\pi\) | |||||||
\(380\) | 2.22735 | 0.114261 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.0174592 | − | 0.0651586i | 0.000893291 | − | 0.00333381i | ||||
\(383\) | −33.2559 | − | 8.91088i | −1.69930 | − | 0.455325i | −0.726534 | − | 0.687131i | \(-0.758870\pi\) |
−0.972762 | + | 0.231806i | \(0.925537\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.01876 | + | 9.95723i | 0.306744 | + | 0.507468i | ||||
\(386\) | 10.1296 | − | 17.5450i | 0.515584 | − | 0.893018i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.19894 | − | 0.589205i | 0.111635 | − | 0.0299124i | ||||
\(389\) | 8.07601 | − | 4.66269i | 0.409470 | − | 0.236408i | −0.281092 | − | 0.959681i | \(-0.590697\pi\) |
0.690562 | + | 0.723273i | \(0.257363\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 34.9473i | − | 1.76736i | ||||||
\(392\) | 10.5414 | − | 11.4247i | 0.532421 | − | 0.577032i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.22420 | − | 3.01619i | 0.263191 | − | 0.151954i | ||||
\(395\) | 12.5269 | + | 3.35656i | 0.630295 | + | 0.168887i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.12022 | + | 19.1089i | −0.256977 | + | 0.959049i | 0.710004 | + | 0.704198i | \(0.248693\pi\) |
−0.966980 | + | 0.254852i | \(0.917973\pi\) | |||||||
\(398\) | 10.0667 | + | 10.0667i | 0.504596 | + | 0.504596i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.2445 | − | 6.49199i | 0.562223 | − | 0.324600i | ||||
\(401\) | −8.51496 | + | 8.51496i | −0.425217 | + | 0.425217i | −0.886995 | − | 0.461778i | \(-0.847212\pi\) |
0.461778 | + | 0.886995i | \(0.347212\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.9637 | − | 23.9985i | −0.994463 | − | 1.19545i | ||||
\(404\) | −10.7577 | − | 6.21095i | −0.535214 | − | 0.309006i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.16031 | − | 0.779094i | −0.156843 | − | 0.0386658i | ||||
\(407\) | −15.0402 | − | 8.68346i | −0.745514 | − | 0.430423i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.7865 | + | 13.7865i | −0.681696 | + | 0.681696i | −0.960382 | − | 0.278686i | \(-0.910101\pi\) |
0.278686 | + | 0.960382i | \(0.410101\pi\) | |||||||
\(410\) | −3.53319 | + | 3.53319i | −0.174492 | + | 0.174492i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.13727 | − | 2.96600i | −0.253095 | − | 0.146125i | ||||
\(413\) | −1.61555 | + | 1.68181i | −0.0794959 | + | 0.0827566i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.83129 | − | 1.63465i | −0.138983 | − | 0.0802417i | ||||
\(416\) | 2.10644 | + | 12.2508i | 0.103277 | + | 0.600645i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.64091 | − | 7.64091i | 0.373729 | − | 0.373729i | ||||
\(419\) | 3.34749 | − | 1.93268i | 0.163536 | − | 0.0944174i | −0.415999 | − | 0.909365i | \(-0.636568\pi\) |
0.579534 | + | 0.814948i | \(0.303235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.65782 | + | 3.65782i | 0.178271 | + | 0.178271i | 0.790602 | − | 0.612331i | \(-0.209768\pi\) |
−0.612331 | + | 0.790602i | \(0.709768\pi\) | |||||||
\(422\) | −2.80148 | + | 10.4553i | −0.136374 | + | 0.508955i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.6105 | + | 2.84309i | 0.515293 | + | 0.138072i | ||||
\(425\) | 14.3701 | − | 8.29658i | 0.697052 | − | 0.402443i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.08403 | + | 11.7196i | 0.342820 | + | 0.567150i | ||||
\(428\) | − | 0.0453239i | − | 0.00219081i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.55275 | − | 3.20588i | 0.267778 | − | 0.154601i | ||||
\(431\) | −9.71910 | + | 2.60423i | −0.468153 | + | 0.125441i | −0.485181 | − | 0.874414i | \(-0.661246\pi\) |
0.0170280 | + | 0.999855i | \(0.494580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.80951 | + | 6.59826i | −0.183073 | + | 0.317092i | −0.942926 | − | 0.333004i | \(-0.891938\pi\) |
0.759852 | + | 0.650096i | \(0.225271\pi\) | |||||||
\(434\) | 31.7972 | − | 19.2201i | 1.52631 | − | 0.922596i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.46369 | + | 1.19604i | 0.213772 | + | 0.0572800i | ||||
\(437\) | 3.36536 | − | 12.5597i | 0.160987 | − | 0.600811i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.3628 | 1.06732 | 0.533658 | − | 0.845700i | \(-0.320817\pi\) | ||||
0.533658 | + | 0.845700i | \(0.320817\pi\) | |||||||
\(440\) | −2.52756 | + | 9.43298i | −0.120497 | + | 0.449700i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.15988 | + | 35.8252i | 0.292996 | + | 1.70403i | ||||
\(443\) | 12.8459 | − | 22.2497i | 0.610326 | − | 1.05712i | −0.380859 | − | 0.924633i | \(-0.624372\pi\) |
0.991185 | − | 0.132483i | \(-0.0422951\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.38578 | − | 11.0605i | 0.302715 | − | 0.524318i | ||||
\(446\) | 5.12185 | + | 8.87130i | 0.242527 | + | 0.420068i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.9392 | − | 0.219843i | 0.516828 | − | 0.0103866i | ||||
\(449\) | 0.821652 | + | 3.06645i | 0.0387761 | + | 0.144715i | 0.982600 | − | 0.185735i | \(-0.0594665\pi\) |
−0.943824 | + | 0.330449i | \(0.892800\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.81305i | 0.273726i | ||||||||
\(452\) | 8.91401 | + | 5.14650i | 0.419280 | + | 0.242071i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 38.1954 | 1.79260 | ||||||||
\(455\) | −13.7616 | − | 4.76337i | −0.645155 | − | 0.223310i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.2165 | − | 23.2165i | −1.08602 | − | 1.08602i | −0.995934 | − | 0.0900871i | \(-0.971285\pi\) |
−0.0900871 | − | 0.995934i | \(-0.528715\pi\) | |||||||
\(458\) | −26.5822 | − | 15.3472i | −1.24210 | − | 0.717129i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.40149 | − | 5.23045i | −0.0653450 | − | 0.243871i | ||||
\(461\) | 1.38662 | + | 5.17492i | 0.0645811 | + | 0.241020i | 0.990669 | − | 0.136287i | \(-0.0435169\pi\) |
−0.926088 | + | 0.377307i | \(0.876850\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.0182 | + | 17.0182i | −0.790903 | + | 0.790903i | −0.981641 | − | 0.190738i | \(-0.938912\pi\) |
0.190738 | + | 0.981641i | \(0.438912\pi\) | |||||||
\(464\) | −1.84452 | − | 3.19480i | −0.0856295 | − | 0.148315i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.08663 | + | 11.5194i | 0.142985 | + | 0.533628i | ||||
\(467\) | 3.73447 | − | 6.46829i | 0.172811 | − | 0.299317i | −0.766591 | − | 0.642136i | \(-0.778049\pi\) |
0.939401 | + | 0.342819i | \(0.111382\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.5560 | + | 39.9024i | 0.533605 | + | 1.84252i | ||||
\(470\) | −1.41582 | + | 5.28393i | −0.0653071 | + | 0.243729i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.95740 | −0.0900967 | ||||||||
\(473\) | 1.93062 | − | 7.20516i | 0.0887698 | − | 0.331294i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.96340 | − | 1.59789i | 0.273620 | − | 0.0733162i | ||||
\(476\) | −10.3731 | + | 0.208466i | −0.475449 | + | 0.00955502i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 9.37376i | − | 0.428746i | ||||||
\(479\) | 20.1369 | − | 5.39566i | 0.920078 | − | 0.246534i | 0.232459 | − | 0.972606i | \(-0.425323\pi\) |
0.687619 | + | 0.726072i | \(0.258656\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.4227 | − | 3.68347i | 0.976789 | − | 0.167952i | ||||
\(482\) | − | 46.6164i | − | 2.12332i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.852240 | + | 1.47612i | 0.0387382 | + | 0.0670965i | ||||
\(485\) | −4.77055 | + | 2.75428i | −0.216620 | + | 0.125065i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.2023 | − | 13.2023i | −0.598255 | − | 0.598255i | 0.341593 | − | 0.939848i | \(-0.389034\pi\) |
−0.939848 | + | 0.341593i | \(0.889034\pi\) | |||||||
\(488\) | −2.97492 | + | 11.1025i | −0.134668 | + | 0.502588i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.05634 | − | 15.3468i | 0.363948 | − | 0.693297i | ||||
\(491\) | −26.9636 | + | 15.5675i | −1.21685 | + | 0.702550i | −0.964243 | − | 0.265019i | \(-0.914622\pi\) |
−0.252609 | + | 0.967569i | \(0.581289\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.35724 | − | 4.08286i | −0.106165 | − | 0.183883i | ||||
\(494\) | −1.23611 | + | 13.4684i | −0.0556150 | + | 0.605972i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 40.6752 | + | 10.8989i | 1.82637 | + | 0.489374i | ||||
\(497\) | 7.85109 | + | 27.1096i | 0.352169 | + | 1.21603i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.9002 | − | 4.79636i | 0.801325 | − | 0.214714i | 0.165159 | − | 0.986267i | \(-0.447186\pi\) |
0.636166 | + | 0.771553i | \(0.280519\pi\) | |||||||
\(500\) | 5.22310 | − | 5.22310i | 0.233584 | − | 0.233584i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.4791 | + | 8.16684i | −1.36035 | + | 0.364504i | ||||
\(503\) | 22.0368 | + | 12.7230i | 0.982573 | + | 0.567289i | 0.903046 | − | 0.429544i | \(-0.141326\pi\) |
0.0795268 | + | 0.996833i | \(0.474659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.0335 | + | 7.77950i | 1.29197 | + | 0.346183i | ||||
\(506\) | −22.7508 | − | 13.1352i | −1.01140 | − | 0.583930i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.42858 | + | 9.40257i | 0.240854 | + | 0.417172i | ||||
\(509\) | 17.5363 | − | 17.5363i | 0.777285 | − | 0.777285i | −0.202084 | − | 0.979368i | \(-0.564771\pi\) |
0.979368 | + | 0.202084i | \(0.0647713\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.8730 | + | 4.40613i | 0.790654 | + | 0.194916i | ||||
\(512\) | 3.41779 | + | 3.41779i | 0.151046 | + | 0.151046i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28.9081 | − | 28.9081i | −1.27508 | − | 1.27508i | ||||
\(515\) | 13.8648 | + | 3.71506i | 0.610955 | + | 0.163705i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.18204 | + | 5.51145i | 0.139946 | + | 0.242393i | ||||
\(518\) | 0.519839 | + | 25.8667i | 0.0228404 | + | 1.13652i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.11853 | − | 11.0998i | −0.224462 | − | 0.486758i | ||||
\(521\) | 3.53287 | − | 2.03970i | 0.154778 | − | 0.0893610i | −0.420611 | − | 0.907241i | \(-0.638184\pi\) |
0.575389 | + | 0.817880i | \(0.304851\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.4455i | 1.28756i | 0.765209 | + | 0.643781i | \(0.222635\pi\) | ||||
−0.765209 | + | 0.643781i | \(0.777365\pi\) | |||||||
\(524\) | 1.72555 | − | 2.98874i | 0.0753810 | − | 0.130564i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −49.0053 | + | 13.1309i | −2.13673 | + | 0.572536i | ||||
\(527\) | 51.9817 | + | 13.9285i | 2.26436 | + | 0.606733i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.61121 | −0.374400 | ||||||||
\(530\) | 12.2483 | 0.532033 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.74805 | − | 0.923987i | −0.162498 | − | 0.0400599i | ||||
\(533\) | −4.65304 | − | 5.59345i | −0.201546 | − | 0.242279i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0283851 | + | 0.105935i | 0.00122720 | + | 0.00457996i | ||||
\(536\) | −17.4341 | + | 30.1967i | −0.753038 | + | 1.30430i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.3430 | − | 10.3430i | 0.445917 | − | 0.445917i | ||||
\(539\) | −5.99736 | − | 19.2522i | −0.258325 | − | 0.829252i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.74099 | − | 36.3539i | −0.418798 | − | 1.56298i | −0.777105 | − | 0.629371i | \(-0.783312\pi\) |
0.358307 | − | 0.933604i | \(-0.383354\pi\) | |||||||
\(542\) | − | 5.52463i | − | 0.237303i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.1530 | − | 15.1530i | −0.649678 | − | 0.649678i | ||||
\(545\) | −11.1820 | −0.478982 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.7251 | −1.57025 | −0.785125 | − | 0.619337i | \(-0.787401\pi\) | ||||
−0.785125 | + | 0.619337i | \(0.787401\pi\) | |||||||
\(548\) | 0.782679 | + | 0.782679i | 0.0334344 | + | 0.0334344i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 12.4733i | − | 0.531864i | ||||||
\(551\) | −0.453995 | − | 1.69433i | −0.0193408 | − | 0.0721810i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.6870 | − | 10.8448i | −0.837177 | − | 0.461169i | ||||
\(554\) | 4.62103 | − | 4.62103i | 0.196329 | − | 0.196329i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.60053 | + | 4.50425i | −0.110287 | + | 0.191023i | ||||
\(557\) | 5.17843 | + | 19.3262i | 0.219417 | + | 0.818876i | 0.984565 | + | 0.175021i | \(0.0559993\pi\) |
−0.765148 | + | 0.643855i | \(0.777334\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.90967 | + | 8.47832i | 0.165361 | + | 0.358595i | ||||
\(560\) | 18.8692 | − | 5.46462i | 0.797368 | − | 0.230922i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.53556 | −0.317869 | ||||||||
\(563\) | −15.6920 | −0.661340 | −0.330670 | − | 0.943746i | \(-0.607275\pi\) | ||||
−0.330670 | + | 0.943746i | \(0.607275\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.0577 | − | 6.44624i | −1.01211 | − | 0.271195i | ||||
\(566\) | −1.61320 | + | 0.432256i | −0.0678079 | + | 0.0181691i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.8447 | + | 20.5155i | −0.496991 | + | 0.860813i | ||||
\(569\) | 5.07533i | 0.212769i | 0.994325 | + | 0.106385i | \(0.0339275\pi\) | ||||
−0.994325 | + | 0.106385i | \(0.966073\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.5642 | + | 10.1407i | −0.735038 | + | 0.424374i | −0.820262 | − | 0.571988i | \(-0.806173\pi\) |
0.0852246 | + | 0.996362i | \(0.472839\pi\) | |||||||
\(572\) | 6.14792 | + | 2.26733i | 0.257057 | + | 0.0948020i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.41113 | − | 4.47974i | 0.309335 | − | 0.186981i | ||||
\(575\) | −7.50459 | − | 12.9983i | −0.312963 | − | 0.542068i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.2962 | − | 6.77811i | −1.05310 | − | 0.282176i | −0.309566 | − | 0.950878i | \(-0.600184\pi\) |
−0.743531 | + | 0.668702i | \(0.766850\pi\) | |||||||
\(578\) | −24.8143 | − | 24.8143i | −1.03214 | − | 1.03214i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.516535 | − | 0.516535i | −0.0214480 | − | 0.0214480i | ||||
\(581\) | 4.08621 | + | 3.92521i | 0.169525 | + | 0.162845i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0759 | − | 10.0759i | 0.417301 | − | 0.417301i | ||||
\(584\) | 7.72537 | + | 13.3807i | 0.319678 | + | 0.553698i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 35.9183 | + | 20.7375i | 1.48377 | + | 0.856657i | ||||
\(587\) | −1.75410 | − | 0.470009i | −0.0723994 | − | 0.0193994i | 0.222438 | − | 0.974947i | \(-0.428599\pi\) |
−0.294837 | + | 0.955548i | \(0.595265\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.3404 | + | 10.0115i | 0.714498 | + | 0.412516i | ||||
\(590\) | −2.10817 | + | 0.564883i | −0.0867921 | + | 0.0232559i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.7341 | + | 20.7341i | −0.852166 | + | 0.852166i | ||||
\(593\) | −30.9506 | + | 8.29320i | −1.27099 | + | 0.340561i | −0.830410 | − | 0.557153i | \(-0.811894\pi\) |
−0.440580 | + | 0.897713i | \(0.645227\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.1143 | − | 6.98362i | 0.988588 | − | 0.286301i | ||||
\(596\) | −2.71203 | − | 0.726687i | −0.111089 | − | 0.0297663i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 32.4054 | − | 5.57186i | 1.32515 | − | 0.227850i | ||||
\(599\) | −1.81349 | − | 3.14105i | −0.0740970 | − | 0.128340i | 0.826596 | − | 0.562795i | \(-0.190274\pi\) |
−0.900693 | + | 0.434456i | \(0.856941\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0032 | − | 12.7035i | 0.897529 | − | 0.518189i | 0.0211313 | − | 0.999777i | \(-0.493273\pi\) |
0.876398 | + | 0.481588i | \(0.159940\pi\) | |||||||
\(602\) | −10.6737 | + | 3.09118i | −0.435030 | + | 0.125987i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.46976 | − | 5.48522i | 0.0598037 | − | 0.223191i | ||||
\(605\) | −2.91638 | − | 2.91638i | −0.118568 | − | 0.118568i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.52942 | − | 2.03771i | 0.143255 | − | 0.0827081i | −0.426660 | − | 0.904412i | \(-0.640310\pi\) |
0.569914 | + | 0.821704i | \(0.306976\pi\) | |||||||
\(608\) | −3.98661 | − | 6.90502i | −0.161679 | − | 0.280035i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.8162i | 0.518915i | ||||||||
\(611\) | −7.47345 | − | 2.75619i | −0.302344 | − | 0.111503i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.4119 | + | 6.00524i | −0.905207 | + | 0.242550i | −0.681251 | − | 0.732050i | \(-0.738564\pi\) |
−0.223956 | + | 0.974599i | \(0.571897\pi\) | |||||||
\(614\) | 32.1588i | 1.29782i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.16637 | − | 14.8247i | 0.329032 | − | 0.597304i | ||||
\(617\) | −0.685439 | + | 0.183663i | −0.0275948 | + | 0.00739399i | −0.272590 | − | 0.962130i | \(-0.587880\pi\) |
0.244995 | + | 0.969524i | \(0.421214\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.54491 | + | 13.2298i | −0.142482 | + | 0.531751i | 0.857372 | + | 0.514697i | \(0.172095\pi\) |
−0.999855 | + | 0.0170541i | \(0.994571\pi\) | |||||||
\(620\) | 8.33851 | 0.334882 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.69391 | + | 10.0538i | −0.108016 | + | 0.403121i | ||||
\(623\) | −15.3339 | + | 15.9629i | −0.614340 | + | 0.639539i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.26294 | + | 3.91952i | −0.0905174 | + | 0.156781i | ||||
\(626\) | 10.5679 | + | 39.4399i | 0.422378 | + | 1.57634i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.53385 | − | 2.65671i | −0.0612073 | − | 0.106014i | ||||
\(629\) | −26.4976 | + | 26.4976i | −1.05653 | + | 1.05653i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.371814 | − | 1.38763i | −0.0148017 | − | 0.0552407i | 0.958130 | − | 0.286334i | \(-0.0924365\pi\) |
−0.972932 | + | 0.231093i | \(0.925770\pi\) | |||||||
\(632\) | −4.88274 | − | 18.2226i | −0.194225 | − | 0.724858i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 33.8469 | + | 19.5415i | 1.34423 | + | 0.776093i | ||||
\(635\) | −18.5767 | − | 18.5767i | −0.737194 | − | 0.737194i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.1812 | + | 13.7243i | 0.839229 | + | 0.543778i | ||||
\(638\) | −3.54394 | −0.140306 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 17.9840 | + | 10.3830i | 0.710879 | + | 0.410426i | ||||
\(641\) | − | 11.0407i | − | 0.436083i | −0.975939 | − | 0.218042i | \(-0.930033\pi\) | ||
0.975939 | − | 0.218042i | \(-0.0699669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.5604 | + | 43.1441i | 0.455899 | + | 1.70144i | 0.685431 | + | 0.728138i | \(0.259614\pi\) |
−0.229532 | + | 0.973301i | \(0.573719\pi\) | |||||||
\(644\) | 0.188566 | + | 9.38286i | 0.00743053 | + | 0.369736i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.6581 | − | 20.1924i | −0.458682 | − | 0.794461i | ||||
\(647\) | 5.20304 | − | 9.01192i | 0.204552 | − | 0.354295i | −0.745438 | − | 0.666575i | \(-0.767759\pi\) |
0.949990 | + | 0.312280i | \(0.101093\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.26956 | + | 2.19895i | −0.0498347 | + | 0.0863163i | ||||
\(650\) | 9.98423 | + | 12.0021i | 0.391614 | + | 0.470761i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.04318 | + | 3.89321i | −0.0408542 | + | 0.152470i | ||||
\(653\) | 10.4386 | 0.408493 | 0.204246 | − | 0.978920i | \(-0.434526\pi\) | ||||
0.204246 | + | 0.978920i | \(0.434526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.16133 | + | 8.06620i | −0.0844502 | + | 0.315172i | ||||
\(656\) | 9.48038 | + | 2.54026i | 0.370146 | + | 0.0991804i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.57443 | − | 8.30413i | 0.178330 | − | 0.323729i | ||||
\(659\) | 3.86557 | − | 6.69537i | 0.150581 | − | 0.260815i | −0.780860 | − | 0.624706i | \(-0.785219\pi\) |
0.931441 | + | 0.363892i | \(0.118552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.2687 | − | 11.5938i | 1.68296 | − | 0.450947i | 0.714401 | − | 0.699737i | \(-0.246699\pi\) |
0.968558 | + | 0.248790i | \(0.0800328\pi\) | |||||||
\(662\) | 8.30322 | − | 4.79387i | 0.322714 | − | 0.186319i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.75580i | 0.184561i | ||||||||
\(665\) | 9.33892 | − | 0.187683i | 0.362148 | − | 0.00727802i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.69311 | + | 2.13222i | −0.142998 | + | 0.0825597i | ||||
\(668\) | −6.17033 | − | 1.65334i | −0.238737 | − | 0.0639695i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.0625 | + | 37.5539i | −0.388750 | + | 1.45083i | ||||
\(671\) | 10.5431 | + | 10.5431i | 0.407012 | + | 0.407012i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.6804 | + | 11.3625i | −0.758625 | + | 0.437992i | −0.828802 | − | 0.559542i | \(-0.810977\pi\) |
0.0701768 | + | 0.997535i | \(0.477644\pi\) | |||||||
\(674\) | −13.2262 | + | 13.2262i | −0.509454 | + | 0.509454i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.73054 | + | 2.73941i | −0.297329 | + | 0.105362i | ||||
\(677\) | 7.56955 | + | 4.37028i | 0.290921 | + | 0.167964i | 0.638357 | − | 0.769740i | \(-0.279614\pi\) |
−0.347436 | + | 0.937704i | \(0.612948\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.17017 | − | 2.65573i | 0.351919 | − | 0.101918i | ||||
\(680\) | 18.2488 | + | 10.5359i | 0.699809 | + | 0.404035i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 28.6052 | − | 28.6052i | 1.09535 | − | 1.09535i | ||||
\(683\) | −1.57793 | + | 1.57793i | −0.0603777 | + | 0.0603777i | −0.736651 | − | 0.676273i | \(-0.763594\pi\) |
0.676273 | + | 0.736651i | \(0.263594\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.31951 | − | 1.33917i | −0.0886240 | − | 0.0511671i | ||||
\(686\) | −19.9231 | + | 22.4825i | −0.760668 | + | 0.858387i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.9071 | − | 6.29720i | −0.415828 | − | 0.240078i | ||||
\(689\) | −1.63002 | + | 17.7605i | −0.0620990 | + | 0.676620i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.25857 | + | 3.25857i | −0.123962 | + | 0.123962i | −0.766366 | − | 0.642404i | \(-0.777937\pi\) |
0.642404 | + | 0.766366i | \(0.277937\pi\) | |||||||
\(692\) | −9.64206 | + | 5.56685i | −0.366536 | + | 0.211620i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.4061 | + | 10.4061i | 0.395012 | + | 0.395012i | ||||
\(695\) | 3.25729 | − | 12.1564i | 0.123556 | − | 0.461117i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.1156 | + | 3.24638i | 0.458913 | + | 0.122965i | ||||
\(698\) | 42.2133 | − | 24.3718i | 1.59780 | − | 0.922488i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.81341 | + | 2.30505i | −0.144133 | + | 0.0871228i | ||||
\(701\) | − | 10.7910i | − | 0.407569i | −0.979016 | − | 0.203784i | \(-0.934676\pi\) | ||
0.979016 | − | 0.203784i | \(-0.0653242\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0746 | + | 6.97128i | −0.455403 | + | 0.262927i | ||||
\(704\) | 11.5070 | − | 3.08329i | 0.433686 | − | 0.116206i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.5012 | + | 40.7053i | −0.884481 | + | 1.53197i | ||||
\(707\) | −45.6285 | − | 25.1350i | −1.71604 | − | 0.945300i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.3737 | − | 5.99502i | −0.840262 | − | 0.225148i | −0.187076 | − | 0.982345i | \(-0.559901\pi\) |
−0.653186 | + | 0.757198i | \(0.726568\pi\) | |||||||
\(710\) | −6.83646 | + | 25.5140i | −0.256568 | + | 0.957524i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −18.5786 | −0.696262 | ||||||||
\(713\) | 12.5988 | − | 47.0195i | 0.471830 | − | 1.76090i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.7894 | − | 1.44912i | −0.590490 | − | 0.0541941i | ||||
\(716\) | −6.37929 | + | 11.0493i | −0.238405 | + | 0.412930i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.15942 | + | 12.4005i | −0.267187 | + | 0.462782i | ||||
\(719\) | −17.9493 | − | 31.0890i | −0.669394 | − | 1.15942i | −0.978074 | − | 0.208259i | \(-0.933220\pi\) |
0.308679 | − | 0.951166i | \(-0.400113\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.7897 | − | 12.0031i | −0.811489 | − | 0.447018i | ||||
\(722\) | 5.73099 | + | 21.3883i | 0.213285 | + | 0.795991i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 11.0184i | − | 0.409496i | ||||||
\(725\) | −1.75351 | − | 1.01239i | −0.0651236 | − | 0.0375991i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.7770 | 1.51234 | 0.756168 | − | 0.654377i | \(-0.227069\pi\) | ||||
0.756168 | + | 0.654377i | \(0.227069\pi\) | |||||||
\(728\) | 4.00854 | + | 20.8014i | 0.148566 | + | 0.770952i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.1819 | + | 12.1819i | 0.450874 | + | 0.450874i | ||||
\(731\) | −13.9389 | − | 8.04764i | −0.515549 | − | 0.297653i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.43098 | − | 24.0007i | −0.237533 | − | 0.886487i | −0.976990 | − | 0.213283i | \(-0.931584\pi\) |
0.739457 | − | 0.673204i | \(-0.235082\pi\) | |||||||
\(734\) | 5.57860 | + | 20.8196i | 0.205910 | + | 0.768466i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.7065 | + | 13.7065i | −0.505227 | + | 0.505227i | ||||
\(737\) | 22.6154 | + | 39.1710i | 0.833048 | + | 1.44288i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.9878 | − | 41.0071i | −0.404194 | − | 1.50847i | −0.805538 | − | 0.592544i | \(-0.798124\pi\) |
0.401344 | − | 0.915927i | \(-0.368543\pi\) | |||||||
\(740\) | −2.90317 | + | 5.02844i | −0.106723 | + | 0.184849i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.6107 | − | 5.08105i | −0.756643 | − | 0.186531i | ||||
\(743\) | 6.30753 | − | 23.5400i | 0.231401 | − | 0.863600i | −0.748337 | − | 0.663318i | \(-0.769148\pi\) |
0.979738 | − | 0.200282i | \(-0.0641858\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.79390 | 0.248909 | ||||||||
\(746\) | 3.46336 | − | 12.9254i | 0.126802 | − | 0.473233i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.9115 | + | 2.92373i | −0.398964 | + | 0.106902i | ||||
\(749\) | −0.00381912 | − | 0.190036i | −0.000139547 | − | 0.00694375i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.4458i | 1.03800i | 0.854774 | + | 0.519001i | \(0.173696\pi\) | ||||
−0.854774 | + | 0.519001i | \(0.826304\pi\) | |||||||
\(752\) | 10.3790 | − | 2.78105i | 0.378484 | − | 0.101415i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.41006 | − | 2.83674i | 0.124187 | − | 0.103308i | ||||
\(755\) | 13.7410i | 0.500086i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.0081 | − | 45.0474i | −0.945282 | − | 1.63728i | −0.755187 | − | 0.655510i | \(-0.772454\pi\) |
−0.190095 | − | 0.981766i | \(-0.560880\pi\) | |||||||
\(758\) | −4.86597 | + | 2.80937i | −0.176740 | + | 0.102041i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.54383 | + | 5.54383i | 0.201096 | + | 0.201096i | ||||
\(761\) | −1.53417 | + | 5.72561i | −0.0556137 | + | 0.207553i | −0.988142 | − | 0.153544i | \(-0.950931\pi\) |
0.932528 | + | 0.361098i | \(0.117598\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.8163 | + | 4.63869i | 0.681196 | + | 0.167932i | ||||
\(764\) | −0.0227228 | + | 0.0131190i | −0.000822080 | + | 0.000474628i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.9220 | + | 48.3623i | 1.00886 | + | 1.74740i | ||||
\(767\) | −0.538541 | − | 3.13210i | −0.0194456 | − | 0.113093i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.310861 | + | 0.0832949i | 0.0112099 | + | 0.00300369i | 0.264420 | − | 0.964408i | \(-0.414820\pi\) |
−0.253210 | + | 0.967411i | \(0.581486\pi\) | |||||||
\(770\) | 4.51715 | − | 18.3233i | 0.162787 | − | 0.660326i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.61148 | + | 2.03949i | −0.273943 | + | 0.0734028i | ||||
\(773\) | −22.4820 | + | 22.4820i | −0.808623 | + | 0.808623i | −0.984425 | − | 0.175802i | \(-0.943748\pi\) |
0.175802 | + | 0.984425i | \(0.443748\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.3251 | − | 5.98200i | 0.801942 | − | 0.214880i | ||||
\(776\) | 6.93965 | + | 4.00661i | 0.249119 | + | 0.143829i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.6104 | − | 3.91484i | −0.523807 | − | 0.140354i | ||||
\(779\) | 4.04161 | + | 2.33343i | 0.144806 | + | 0.0836037i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.3648 | + | 26.6126i | 0.549796 | + | 0.952274i | ||||
\(782\) | −40.0820 | + | 40.0820i | −1.43333 | + | 1.43333i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −34.0188 | + | 1.36789i | −1.21496 | + | 0.0488533i | ||||
\(785\) | 5.24887 | + | 5.24887i | 0.187340 | + | 0.187340i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.7400 | + | 23.7400i | 0.846239 | + | 0.846239i | 0.989662 | − | 0.143423i | \(-0.0458108\pi\) |
−0.143423 | + | 0.989662i | \(0.545811\pi\) | |||||||
\(788\) | −2.26639 | − | 0.607277i | −0.0807368 | − | 0.0216334i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.5177 | − | 18.2172i | −0.374202 | − | 0.648137i | ||||
\(791\) | 37.8086 | + | 20.8273i | 1.34432 | + | 0.740535i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.5840 | − | 1.70561i | −0.659937 | − | 0.0605678i | ||||
\(794\) | 27.7891 | − | 16.0440i | 0.986198 | − | 0.569382i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 5.53736i | − | 0.196267i | ||||||
\(797\) | −6.34434 | + | 10.9887i | −0.224728 | + | 0.389240i | −0.956238 | − | 0.292591i | \(-0.905483\pi\) |
0.731510 | + | 0.681831i | \(0.238816\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.2641 | − | 3.55410i | 0.469250 | − | 0.125735i | ||||
\(800\) | −8.88996 | − | 2.38206i | −0.314308 | − | 0.0842185i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.5321 | 0.689703 | ||||||||
\(803\) | 20.0426 | 0.707287 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.31697 | − | 21.8123i | −0.222644 | − | 0.768783i | ||||
\(806\) | −4.62759 | + | 50.4215i | −0.163000 | + | 1.77602i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.3167 | − | 42.2346i | −0.398121 | − | 1.48581i | ||||
\(809\) | −21.4022 | + | 37.0698i | −0.752463 | + | 1.30330i | 0.194163 | + | 0.980969i | \(0.437801\pi\) |
−0.946626 | + | 0.322334i | \(0.895533\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.51360 | − | 1.51360i | 0.0531496 | − | 0.0531496i | −0.680032 | − | 0.733182i | \(-0.738034\pi\) |
0.733182 | + | 0.680032i | \(0.238034\pi\) | |||||||
\(812\) | 0.654916 | + | 1.08347i | 0.0229830 | + | 0.0380224i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.29072 | + | 27.2093i | 0.255539 | + | 0.953686i | ||||
\(815\) | − | 9.75286i | − | 0.341628i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.23453 | − | 4.23453i | −0.148147 | − | 0.148147i | ||||
\(818\) | 31.6242 | 1.10571 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.94350 | 0.0678699 | ||||||||
\(821\) | −26.6039 | − | 26.6039i | −0.928481 | − | 0.928481i | 0.0691268 | − | 0.997608i | \(-0.477979\pi\) |
−0.997608 | + | 0.0691268i | \(0.977979\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 44.4969i | − | 1.55107i | −0.631308 | − | 0.775533i | \(-0.717481\pi\) | ||
0.631308 | − | 0.775533i | \(-0.282519\pi\) | |||||||
\(824\) | −5.40424 | − | 20.1689i | −0.188266 | − | 0.702616i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.78184 | − | 0.0760030i | 0.131587 | − | 0.00264448i | ||||
\(827\) | −12.3898 | + | 12.3898i | −0.430835 | + | 0.430835i | −0.888912 | − | 0.458077i | \(-0.848538\pi\) |
0.458077 | + | 0.888912i | \(0.348538\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.1381 | + | 36.6122i | −0.734155 | + | 1.27159i | 0.220938 | + | 0.975288i | \(0.429088\pi\) |
−0.955093 | + | 0.296306i | \(0.904245\pi\) | |||||||
\(830\) | 1.37247 | + | 5.12212i | 0.0476390 | + | 0.177791i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.60428 | + | 12.1776i | −0.298300 | + | 0.422181i | ||||
\(833\) | −43.4750 | + | 1.74813i | −1.50632 | + | 0.0605690i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.4573 | 0.534920 | ||||||||
\(836\) | −4.20302 | −0.145365 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.05597 | − | 1.62269i | −0.209200 | − | 0.0560550i | ||||
\(839\) | −25.6907 | + | 6.88379i | −0.886940 | + | 0.237655i | −0.673399 | − | 0.739279i | \(-0.735166\pi\) |
−0.213541 | + | 0.976934i | \(0.568500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.2124 | − | 24.6165i | 0.490081 | − | 0.848846i | ||||
\(842\) | − | 8.39052i | − | 0.289156i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.64606 | − | 2.10506i | 0.125503 | − | 0.0724590i | ||||
\(845\) | 16.3529 | − | 11.2442i | 0.562555 | − | 0.386812i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.69769 | + | 6.11733i | 0.127054 | + | 0.210194i | ||||
\(848\) | −12.0295 | − | 20.8356i | −0.413093 | − | 0.715498i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −25.9971 | − | 6.96589i | −0.891691 | − | 0.238928i | ||||
\(851\) | 23.9681 | + | 23.9681i | 0.821616 | + | 0.821616i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.950856 | − | 0.950856i | −0.0325567 | − | 0.0325567i | 0.690641 | − | 0.723198i | \(-0.257328\pi\) |
−0.723198 | + | 0.690641i | \(0.757328\pi\) | |||||||
\(854\) | 5.31665 | − | 21.5664i | 0.181932 | − | 0.737987i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.112810 | − | 0.112810i | 0.00385578 | − | 0.00385578i | ||||
\(857\) | 21.1903 | + | 36.7026i | 0.723845 | + | 1.25374i | 0.959447 | + | 0.281887i | \(0.0909605\pi\) |
−0.235602 | + | 0.971850i | \(0.575706\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.83030 | − | 3.36613i | −0.198927 | − | 0.114851i | 0.397228 | − | 0.917720i | \(-0.369972\pi\) |
−0.596155 | + | 0.802869i | \(0.703306\pi\) | |||||||
\(860\) | −2.40893 | − | 0.645470i | −0.0821437 | − | 0.0220103i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.1340 | + | 8.16026i | 0.481405 | + | 0.277939i | ||||
\(863\) | −17.8200 | + | 4.77484i | −0.606598 | + | 0.162537i | −0.549028 | − | 0.835804i | \(-0.685002\pi\) |
−0.0575702 | + | 0.998341i | \(0.518335\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.0499 | − | 19.0499i | 0.647715 | − | 0.647715i | ||||
\(866\) | 11.9370 | − | 3.19850i | 0.405634 | − | 0.108689i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.0315 | − | 3.45912i | −0.476261 | − | 0.117410i | ||||
\(869\) | −23.6383 | − | 6.33386i | −0.801874 | − | 0.214861i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.1153 | − | 19.5888i | −1.79974 | − | 0.663740i | ||||
\(872\) | 8.13311 | + | 14.0870i | 0.275422 | + | 0.477045i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18.2649 | + | 10.5452i | −0.617819 | + | 0.356698i | ||||
\(875\) | 21.4595 | − | 22.3397i | 0.725464 | − | 0.755221i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.89991 | − | 14.5547i | 0.131691 | − | 0.491476i | −0.868299 | − | 0.496041i | \(-0.834787\pi\) |
0.999990 | + | 0.00456529i | \(0.00145318\pi\) | |||||||
\(878\) | −25.6485 | − | 25.6485i | −0.865595 | − | 0.865595i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 18.5233 | − | 10.6944i | 0.624420 | − | 0.360509i | ||||
\(881\) | 22.3633 | + | 38.7344i | 0.753439 | + | 1.30500i | 0.946146 | + | 0.323739i | \(0.104940\pi\) |
−0.192707 | + | 0.981256i | \(0.561727\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 46.5076i | − | 1.56510i | −0.622585 | − | 0.782552i | \(-0.713917\pi\) | ||
0.622585 | − | 0.782552i | \(-0.286083\pi\) | |||||||
\(884\) | 8.15899 | − | 11.5474i | 0.274417 | − | 0.388380i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40.2522 | + | 10.7855i | −1.35230 | + | 0.362347i | ||||
\(887\) | − | 46.0518i | − | 1.54627i | −0.634244 | − | 0.773133i | \(-0.718688\pi\) | ||
0.634244 | − | 0.773133i | \(-0.281312\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.5534 | + | 38.9660i | 0.789957 | + | 1.30688i | ||||
\(890\) | −20.0096 | + | 5.36156i | −0.670724 | + | 0.179720i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.03123 | − | 3.84860i | 0.0345281 | − | 0.128861i | ||||
\(893\) | 5.10923 | 0.170974 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.99036 | − | 29.8204i | 0.267088 | − | 0.996787i | ||||
\(896\) | −25.9550 | − | 24.9324i | −0.867097 | − | 0.832932i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.57462 | − | 4.45937i | 0.0859161 | − | 0.148811i | ||||
\(899\) | −1.69962 | − | 6.34305i | −0.0566854 | − | 0.211553i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.3733 | − | 26.6273i | −0.512158 | − | 0.887085i | ||||
\(902\) | 6.66715 | − | 6.66715i | 0.221992 | − | 0.221992i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.37724 | + | 34.9963i | 0.311882 | + | 1.16396i | ||||
\(905\) | 6.90054 | + | 25.7532i | 0.229382 | + | 0.856064i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.6067 | + | 15.9387i | 0.916666 | + | 0.529237i | 0.882570 | − | 0.470181i | \(-0.155811\pi\) |
0.0340961 | + | 0.999419i | \(0.489145\pi\) | |||||||
\(908\) | −10.5051 | − | 10.5051i | −0.348623 | − | 0.348623i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.3203 | + | 21.2468i | 0.342116 | + | 0.704326i | ||||
\(911\) | −34.8516 | −1.15469 | −0.577343 | − | 0.816502i | \(-0.695910\pi\) | ||||
−0.577343 | + | 0.816502i | \(0.695910\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.34267 | + | 3.08459i | 0.176817 | + | 0.102085i | ||||
\(914\) | 53.2553i | 1.76153i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.09000 | + | 11.5320i | 0.102096 | + | 0.381029i | ||||
\(917\) | 6.98311 | − | 12.6767i | 0.230603 | − | 0.418621i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.90511 | + | 3.29975i | 0.0628439 | + | 0.108849i | 0.895736 | − | 0.444587i | \(-0.146650\pi\) |
−0.832892 | + | 0.553436i | \(0.813316\pi\) | |||||||
\(920\) | 9.53018 | − | 16.5068i | 0.314201 | − | 0.544212i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.34491 | − | 7.52561i | 0.143092 | − | 0.247843i | ||||
\(923\) | −36.0864 | − | 13.3085i | −1.18780 | − | 0.438056i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.16544 | + | 15.5456i | −0.136959 | + | 0.511137i | ||||
\(926\) | 39.0373 | 1.28285 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.676794 | + | 2.52583i | −0.0222169 | + | 0.0829145i | ||||
\(929\) | −36.3444 | − | 9.73846i | −1.19242 | − | 0.319509i | −0.392579 | − | 0.919718i | \(-0.628417\pi\) |
−0.799843 | + | 0.600210i | \(0.795084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.7928 | − | 3.55830i | −0.517588 | − | 0.116619i | ||||
\(932\) | 2.31931 | − | 4.01717i | 0.0759717 | − | 0.131587i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.7018 | + | 3.13550i | −0.382895 | + | 0.102597i | ||||
\(935\) | 23.6722 | − | 13.6672i | 0.774164 | − | 0.446964i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 38.0350i | − | 1.24255i | −0.783593 | − | 0.621275i | \(-0.786615\pi\) | ||
0.783593 | − | 0.621275i | \(-0.213385\pi\) | |||||||
\(938\) | 32.5114 | − | 59.0191i | 1.06153 | − | 1.92704i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.84266 | − | 1.06386i | 0.0601010 | − | 0.0346993i | ||||
\(941\) | 25.3679 | + | 6.79732i | 0.826971 | + | 0.221586i | 0.647392 | − | 0.762157i | \(-0.275860\pi\) |
0.179579 | + | 0.983744i | \(0.442526\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.93648 | − | 10.9591i | 0.0956248 | − | 0.356877i | ||||
\(944\) | 3.03143 | + | 3.03143i | 0.0986645 | + | 0.0986645i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.4781 | + | 6.04952i | −0.340672 | + | 0.196687i | ||||
\(947\) | 5.51091 | − | 5.51091i | 0.179081 | − | 0.179081i | −0.611874 | − | 0.790955i | \(-0.709584\pi\) |
0.790955 | + | 0.611874i | \(0.209584\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.2854 | + | 16.0430i | −0.626031 | + | 0.520779i | ||||
\(950\) | −8.67226 | − | 5.00693i | −0.281365 | − | 0.162446i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −26.3372 | − | 25.2995i | −0.853595 | − | 0.819962i | ||||
\(953\) | 7.95143 | + | 4.59076i | 0.257572 | + | 0.148709i | 0.623227 | − | 0.782041i | \(-0.285821\pi\) |
−0.365654 | + | 0.930751i | \(0.619155\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0448934 | − | 0.0448934i | 0.00145272 | − | 0.00145272i | ||||
\(956\) | −2.57811 | + | 2.57811i | −0.0833820 | + | 0.0833820i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −29.2840 | − | 16.9071i | −0.946124 | − | 0.546245i | ||||
\(959\) | 3.34759 | + | 3.21569i | 0.108099 | + | 0.103840i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.0702 | + | 21.9798i | 1.22807 | + | 0.709027i | ||||
\(962\) | −28.7949 | − | 20.3456i | −0.928386 | − | 0.655968i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.8211 | + | 12.8211i | −0.412940 | + | 0.412940i | ||||
\(965\) | 16.5129 | − | 9.53373i | 0.531569 | − | 0.306902i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.3315 | + | 29.3315i | 0.943237 | + | 0.943237i | 0.998473 | − | 0.0552359i | \(-0.0175911\pi\) |
−0.0552359 | + | 0.998473i | \(0.517591\pi\) | |||||||
\(968\) | −1.55283 | + | 5.79525i | −0.0499099 | + | 0.186266i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.63045 | + | 2.31252i | 0.277107 | + | 0.0742506i | ||||
\(971\) | −32.5158 | + | 18.7730i | −1.04348 | + | 0.602455i | −0.920818 | − | 0.389993i | \(-0.872478\pi\) |
−0.122665 | + | 0.992448i | \(0.539144\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.5241 | + | 19.1047i | −0.337386 | + | 0.612469i | ||||
\(974\) | 30.2843i | 0.970371i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.8017 | − | 12.5872i | 0.697857 | − | 0.402908i | ||||
\(977\) | −27.8219 | + | 7.45485i | −0.890101 | + | 0.238502i | −0.674760 | − | 0.738037i | \(-0.735753\pi\) |
−0.215341 | + | 0.976539i | \(0.569086\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0500 | + | 20.8712i | −0.385120 | + | 0.667047i | ||||
\(980\) | −6.43666 | + | 2.00512i | −0.205612 | + | 0.0640512i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 48.7801 | + | 13.0706i | 1.55664 | + | 0.417099i | ||||
\(983\) | −5.09738 | + | 19.0237i | −0.162581 | + | 0.606762i | 0.835755 | + | 0.549102i | \(0.185030\pi\) |
−0.998336 | + | 0.0576591i | \(0.981636\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.67752 | 0.180901 | ||||||||
\(986\) | −1.97916 | + | 7.38633i | −0.0630293 | + | 0.235229i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.04424 | − | 3.36430i | 0.128665 | − | 0.107033i | ||||
\(989\) | −7.27941 | + | 12.6083i | −0.231472 | + | 0.400921i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.6102 | + | 30.5018i | −0.559407 | + | 0.968921i | 0.438139 | + | 0.898907i | \(0.355638\pi\) |
−0.997546 | + | 0.0700140i | \(0.977696\pi\) | |||||||
\(992\) | −14.9246 | − | 25.8502i | −0.473858 | − | 0.820746i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22.0881 | − | 40.0974i | 0.700593 | − | 1.27181i | ||||
\(995\) | 3.46790 | + | 12.9424i | 0.109940 | + | 0.410301i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.6156i | 1.15963i | 0.814749 | + | 0.579814i | \(0.196875\pi\) | ||||
−0.814749 | + | 0.579814i | \(0.803125\pi\) | |||||||
\(998\) | −26.0314 | − | 15.0292i | −0.824009 | − | 0.475742i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 819.2.et.b.271.2 | 28 | ||
3.2 | odd | 2 | 91.2.ba.a.89.6 | yes | 28 | ||
7.3 | odd | 6 | 819.2.gh.b.388.6 | 28 | |||
13.6 | odd | 12 | 819.2.gh.b.19.6 | 28 | |||
21.2 | odd | 6 | 637.2.bd.b.440.6 | 28 | |||
21.5 | even | 6 | 637.2.bd.a.440.6 | 28 | |||
21.11 | odd | 6 | 637.2.x.a.570.2 | 28 | |||
21.17 | even | 6 | 91.2.w.a.24.2 | yes | 28 | ||
21.20 | even | 2 | 637.2.bb.a.362.6 | 28 | |||
39.32 | even | 12 | 91.2.w.a.19.2 | ✓ | 28 | ||
91.45 | even | 12 | inner | 819.2.et.b.136.2 | 28 | ||
273.32 | even | 12 | 637.2.bb.a.227.6 | 28 | |||
273.110 | odd | 12 | 637.2.bd.b.97.6 | 28 | |||
273.149 | even | 12 | 637.2.bd.a.97.6 | 28 | |||
273.188 | odd | 12 | 637.2.x.a.19.2 | 28 | |||
273.227 | odd | 12 | 91.2.ba.a.45.6 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.w.a.19.2 | ✓ | 28 | 39.32 | even | 12 | ||
91.2.w.a.24.2 | yes | 28 | 21.17 | even | 6 | ||
91.2.ba.a.45.6 | yes | 28 | 273.227 | odd | 12 | ||
91.2.ba.a.89.6 | yes | 28 | 3.2 | odd | 2 | ||
637.2.x.a.19.2 | 28 | 273.188 | odd | 12 | |||
637.2.x.a.570.2 | 28 | 21.11 | odd | 6 | |||
637.2.bb.a.227.6 | 28 | 273.32 | even | 12 | |||
637.2.bb.a.362.6 | 28 | 21.20 | even | 2 | |||
637.2.bd.a.97.6 | 28 | 273.149 | even | 12 | |||
637.2.bd.a.440.6 | 28 | 21.5 | even | 6 | |||
637.2.bd.b.97.6 | 28 | 273.110 | odd | 12 | |||
637.2.bd.b.440.6 | 28 | 21.2 | odd | 6 | |||
819.2.et.b.136.2 | 28 | 91.45 | even | 12 | inner | ||
819.2.et.b.271.2 | 28 | 1.1 | even | 1 | trivial | ||
819.2.gh.b.19.6 | 28 | 13.6 | odd | 12 | |||
819.2.gh.b.388.6 | 28 | 7.3 | odd | 6 |