Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(89,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.r (of order \(6\), degree \(2\), 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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1277.2 | ||
Character | \(\chi\) | \(=\) | 1386.1277 |
Dual form | 1386.2.r.d.89.2 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.651304 | + | 1.12809i | 0.291272 | + | 0.504498i | 0.974111 | − | 0.226071i | \(-0.0725882\pi\) |
−0.682839 | + | 0.730569i | \(0.739255\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.212626 | + | 2.63719i | −0.0803652 | + | 0.996765i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.12809 | − | 0.651304i | −0.356734 | − | 0.205960i | ||||
\(11\) | 0.866025 | + | 0.500000i | 0.261116 | + | 0.150756i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.37037i | − | 0.380073i | −0.981777 | − | 0.190037i | \(-0.939139\pi\) | ||
0.981777 | − | 0.190037i | \(-0.0608607\pi\) | |||||||
\(14\) | −1.13446 | − | 2.39019i | −0.303196 | − | 0.638805i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.86353 | + | 4.95978i | −0.694508 | + | 1.20292i | 0.275838 | + | 0.961204i | \(0.411045\pi\) |
−0.970346 | + | 0.241719i | \(0.922289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.481496 | + | 0.277992i | −0.110463 | + | 0.0637757i | −0.554214 | − | 0.832375i | \(-0.686981\pi\) |
0.443751 | + | 0.896150i | \(0.353648\pi\) | |||||||
\(20\) | 1.30261 | 0.291272 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −5.02204 | + | 2.89948i | −1.04717 | + | 0.604583i | −0.921855 | − | 0.387534i | \(-0.873327\pi\) |
−0.125313 | + | 0.992117i | \(0.539994\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.65161 | − | 2.86067i | 0.330321 | − | 0.572133i | ||||
\(26\) | 0.685187 | + | 1.18678i | 0.134376 | + | 0.232746i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.17756 | + | 1.50274i | 0.411521 | + | 0.283991i | ||||
\(29\) | 6.53981i | 1.21441i | 0.794545 | + | 0.607206i | \(0.207710\pi\) | ||||
−0.794545 | + | 0.607206i | \(0.792290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.660821 | + | 0.381525i | 0.118687 | + | 0.0685239i | 0.558168 | − | 0.829728i | \(-0.311504\pi\) |
−0.439481 | + | 0.898252i | \(0.644838\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5.72706i | − | 0.982183i | ||||||
\(35\) | −3.11348 | + | 1.47775i | −0.526274 | + | 0.249786i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.34141 | − | 5.78749i | −0.549324 | − | 0.951457i | −0.998321 | − | 0.0579236i | \(-0.981552\pi\) |
0.448997 | − | 0.893533i | \(-0.351781\pi\) | |||||||
\(38\) | 0.277992 | − | 0.481496i | 0.0450962 | − | 0.0781090i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.12809 | + | 0.651304i | −0.178367 | + | 0.102980i | ||||
\(41\) | 2.25518 | 0.352200 | 0.176100 | − | 0.984372i | \(-0.443652\pi\) | ||||
0.176100 | + | 0.984372i | \(0.443652\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.91214 | 0.596595 | 0.298298 | − | 0.954473i | \(-0.403581\pi\) | ||||
0.298298 | + | 0.954473i | \(0.403581\pi\) | |||||||
\(44\) | 0.866025 | − | 0.500000i | 0.130558 | − | 0.0753778i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.89948 | − | 5.02204i | 0.427505 | − | 0.740460i | ||||
\(47\) | 0.483428 | + | 0.837321i | 0.0705152 | + | 0.122136i | 0.899127 | − | 0.437687i | \(-0.144202\pi\) |
−0.828612 | + | 0.559823i | \(0.810869\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.90958 | − | 1.12147i | −0.987083 | − | 0.160211i | ||||
\(50\) | 3.30321i | 0.467145i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.18678 | − | 0.685187i | −0.164577 | − | 0.0950183i | ||||
\(53\) | −7.40860 | − | 4.27736i | −1.01765 | − | 0.587540i | −0.104227 | − | 0.994554i | \(-0.533237\pi\) |
−0.913422 | + | 0.407013i | \(0.866570\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.30261i | 0.175644i | ||||||||
\(56\) | −2.63719 | − | 0.212626i | −0.352410 | − | 0.0284134i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.26990 | − | 5.66364i | −0.429359 | − | 0.743672i | ||||
\(59\) | −0.499578 | + | 0.865295i | −0.0650396 | + | 0.112652i | −0.896712 | − | 0.442615i | \(-0.854051\pi\) |
0.831672 | + | 0.555267i | \(0.187384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.127371 | − | 0.0735377i | 0.0163082 | − | 0.00941554i | −0.491824 | − | 0.870695i | \(-0.663670\pi\) |
0.508132 | + | 0.861279i | \(0.330336\pi\) | |||||||
\(62\) | −0.763050 | −0.0969075 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.54591 | − | 0.892530i | 0.191746 | − | 0.110705i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.60430 | + | 6.24283i | −0.440335 | + | 0.762683i | −0.997714 | − | 0.0675752i | \(-0.978474\pi\) |
0.557379 | + | 0.830258i | \(0.311807\pi\) | |||||||
\(68\) | 2.86353 | + | 4.95978i | 0.347254 | + | 0.601462i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.95748 | − | 2.83651i | 0.233963 | − | 0.339028i | ||||
\(71\) | 1.17582i | 0.139544i | 0.997563 | + | 0.0697720i | \(0.0222272\pi\) | ||||
−0.997563 | + | 0.0697720i | \(0.977773\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.44038 | − | 0.831605i | −0.168584 | − | 0.0973320i | 0.413334 | − | 0.910579i | \(-0.364364\pi\) |
−0.581918 | + | 0.813247i | \(0.697698\pi\) | |||||||
\(74\) | 5.78749 | + | 3.34141i | 0.672782 | + | 0.388431i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.555984i | 0.0637757i | ||||||||
\(77\) | −1.50274 | + | 2.17756i | −0.171253 | + | 0.248156i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.361898 | + | 0.626826i | 0.0407167 | + | 0.0705235i | 0.885666 | − | 0.464324i | \(-0.153703\pi\) |
−0.844949 | + | 0.534847i | \(0.820369\pi\) | |||||||
\(80\) | 0.651304 | − | 1.12809i | 0.0728180 | − | 0.126125i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.95305 | + | 1.12759i | −0.215678 | + | 0.124522i | ||||
\(83\) | −5.54322 | −0.608448 | −0.304224 | − | 0.952601i | \(-0.598397\pi\) | ||||
−0.304224 | + | 0.952601i | \(0.598397\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.46011 | −0.809163 | ||||||||
\(86\) | −3.38801 | + | 1.95607i | −0.365338 | + | 0.210928i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | 4.25940 | + | 7.37750i | 0.451496 | + | 0.782014i | 0.998479 | − | 0.0551297i | \(-0.0175572\pi\) |
−0.546983 | + | 0.837144i | \(0.684224\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.61394 | + | 0.291378i | 0.378844 | + | 0.0305447i | ||||
\(92\) | 5.79896i | 0.604583i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.837321 | − | 0.483428i | −0.0863631 | − | 0.0498618i | ||||
\(95\) | −0.627201 | − | 0.362114i | −0.0643494 | − | 0.0371522i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.9667i | 1.31657i | 0.752769 | + | 0.658285i | \(0.228718\pi\) | ||||
−0.752769 | + | 0.658285i | \(0.771282\pi\) | |||||||
\(98\) | 6.54461 | − | 2.48356i | 0.661105 | − | 0.250878i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.65161 | − | 2.86067i | −0.165161 | − | 0.286067i | ||||
\(101\) | 3.67391 | − | 6.36340i | 0.365568 | − | 0.633182i | −0.623299 | − | 0.781983i | \(-0.714208\pi\) |
0.988867 | + | 0.148801i | \(0.0475415\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.4637 | + | 8.92798i | −1.52369 | + | 0.879700i | −0.524079 | + | 0.851670i | \(0.675590\pi\) |
−0.999607 | + | 0.0280307i | \(0.991076\pi\) | |||||||
\(104\) | 1.37037 | 0.134376 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.55471 | 0.830907 | ||||||||
\(107\) | −8.72859 | + | 5.03946i | −0.843825 | + | 0.487183i | −0.858563 | − | 0.512709i | \(-0.828642\pi\) |
0.0147376 | + | 0.999891i | \(0.495309\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.368886 | − | 0.638929i | 0.0353329 | − | 0.0611983i | −0.847818 | − | 0.530287i | \(-0.822084\pi\) |
0.883151 | + | 0.469089i | \(0.155418\pi\) | |||||||
\(110\) | −0.651304 | − | 1.12809i | −0.0620994 | − | 0.107559i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.39019 | − | 1.13446i | 0.225852 | − | 0.107196i | ||||
\(113\) | 4.81235i | 0.452708i | 0.974045 | + | 0.226354i | \(0.0726806\pi\) | ||||
−0.974045 | + | 0.226354i | \(0.927319\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.54176 | − | 3.77689i | −0.610022 | − | 0.352196i | ||||
\(116\) | 5.66364 | + | 3.26990i | 0.525856 | + | 0.303603i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 0.999157i | − | 0.0919798i | ||||||
\(119\) | −12.4710 | − | 8.60626i | −1.14322 | − | 0.788935i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | −0.0735377 | + | 0.127371i | −0.00665779 | + | 0.0115316i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.660821 | − | 0.381525i | 0.0593435 | − | 0.0342620i | ||||
\(125\) | 10.8158 | 0.967397 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.5158 | 1.11060 | 0.555299 | − | 0.831651i | \(-0.312604\pi\) | ||||
0.555299 | + | 0.831651i | \(0.312604\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.892530 | + | 1.54591i | −0.0782801 | + | 0.135585i | ||||
\(131\) | 7.42443 | + | 12.8595i | 0.648675 | + | 1.12354i | 0.983440 | + | 0.181237i | \(0.0580100\pi\) |
−0.334764 | + | 0.942302i | \(0.608657\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.630739 | − | 1.32891i | −0.0546920 | − | 0.115231i | ||||
\(134\) | − | 7.20860i | − | 0.622728i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.95978 | − | 2.86353i | −0.425298 | − | 0.245546i | ||||
\(137\) | −18.1030 | − | 10.4518i | −1.54664 | − | 0.892953i | −0.998395 | − | 0.0566359i | \(-0.981963\pi\) |
−0.548246 | − | 0.836317i | \(-0.684704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.21195i | 0.272434i | 0.990679 | + | 0.136217i | \(0.0434944\pi\) | ||||
−0.990679 | + | 0.136217i | \(0.956506\pi\) | |||||||
\(140\) | −0.276969 | + | 3.43523i | −0.0234081 | + | 0.290330i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.587909 | − | 1.01829i | −0.0493363 | − | 0.0854529i | ||||
\(143\) | 0.685187 | − | 1.18678i | 0.0572982 | − | 0.0992434i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.37750 | + | 4.25940i | −0.612668 | + | 0.353724i | ||||
\(146\) | 1.66321 | 0.137648 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.68281 | −0.549324 | ||||||||
\(149\) | −17.7299 | + | 10.2363i | −1.45249 | + | 0.838594i | −0.998622 | − | 0.0524768i | \(-0.983288\pi\) |
−0.453865 | + | 0.891071i | \(0.649955\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.80068 | + | 13.5112i | −0.634810 | + | 1.09952i | 0.351745 | + | 0.936096i | \(0.385588\pi\) |
−0.986555 | + | 0.163428i | \(0.947745\pi\) | |||||||
\(152\) | −0.277992 | − | 0.481496i | −0.0225481 | − | 0.0390545i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.212626 | − | 2.63719i | 0.0171339 | − | 0.212511i | ||||
\(155\) | 0.993956i | 0.0798364i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.72012 | − | 3.87986i | −0.536324 | − | 0.309647i | 0.207264 | − | 0.978285i | \(-0.433544\pi\) |
−0.743588 | + | 0.668638i | \(0.766877\pi\) | |||||||
\(158\) | −0.626826 | − | 0.361898i | −0.0498676 | − | 0.0287911i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.30261i | 0.102980i | ||||||||
\(161\) | −6.57867 | − | 13.8606i | −0.518472 | − | 1.09237i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.36269 | − | 4.09229i | −0.185060 | − | 0.320533i | 0.758537 | − | 0.651630i | \(-0.225915\pi\) |
−0.943597 | + | 0.331097i | \(0.892581\pi\) | |||||||
\(164\) | 1.12759 | − | 1.95305i | 0.0880501 | − | 0.152507i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.80057 | − | 2.77161i | 0.372597 | − | 0.215119i | ||||
\(167\) | 2.49753 | 0.193264 | 0.0966322 | − | 0.995320i | \(-0.469193\pi\) | ||||
0.0966322 | + | 0.995320i | \(0.469193\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1221 | 0.855544 | ||||||||
\(170\) | 6.46065 | − | 3.73006i | 0.495509 | − | 0.286082i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.95607 | − | 3.38801i | 0.149149 | − | 0.258333i | ||||
\(173\) | −7.76337 | − | 13.4466i | −0.590238 | − | 1.02232i | −0.994200 | − | 0.107547i | \(-0.965701\pi\) |
0.403962 | − | 0.914776i | \(-0.367633\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.19295 | + | 4.96386i | 0.543736 | + | 0.375232i | ||||
\(176\) | − | 1.00000i | − | 0.0753778i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.37750 | − | 4.25940i | −0.552967 | − | 0.319256i | ||||
\(179\) | −7.40921 | − | 4.27771i | −0.553790 | − | 0.319731i | 0.196859 | − | 0.980432i | \(-0.436926\pi\) |
−0.750649 | + | 0.660701i | \(0.770259\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.8485i | − | 1.69832i | −0.528140 | − | 0.849158i | \(-0.677110\pi\) | ||
0.528140 | − | 0.849158i | \(-0.322890\pi\) | |||||||
\(182\) | −3.27545 | + | 1.55463i | −0.242793 | + | 0.115237i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.89948 | − | 5.02204i | −0.213752 | − | 0.370230i | ||||
\(185\) | 4.35254 | − | 7.53883i | 0.320005 | − | 0.554266i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.95978 | + | 2.86353i | −0.362695 | + | 0.209402i | ||||
\(188\) | 0.966856 | 0.0705152 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.724229 | 0.0525411 | ||||||||
\(191\) | 14.0830 | − | 8.13084i | 1.01901 | − | 0.588327i | 0.105195 | − | 0.994452i | \(-0.466453\pi\) |
0.913818 | + | 0.406125i | \(0.133120\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.83770 | + | 4.91503i | −0.204262 | + | 0.353792i | −0.949897 | − | 0.312562i | \(-0.898813\pi\) |
0.745635 | + | 0.666354i | \(0.232146\pi\) | |||||||
\(194\) | −6.48336 | − | 11.2295i | −0.465478 | − | 0.806231i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.42602 | + | 5.42313i | −0.316144 | + | 0.387367i | ||||
\(197\) | − | 2.08781i | − | 0.148750i | −0.997230 | − | 0.0743750i | \(-0.976304\pi\) | ||
0.997230 | − | 0.0743750i | \(-0.0236962\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.0881 | + | 8.71113i | 1.06957 | + | 0.617516i | 0.928064 | − | 0.372422i | \(-0.121472\pi\) |
0.141505 | + | 0.989937i | \(0.454806\pi\) | |||||||
\(200\) | 2.86067 | + | 1.65161i | 0.202280 | + | 0.116786i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.34782i | 0.516991i | ||||||||
\(203\) | −17.2467 | − | 1.39054i | −1.21048 | − | 0.0975965i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.46881 | + | 2.54405i | 0.102586 | + | 0.177684i | ||||
\(206\) | 8.92798 | − | 15.4637i | 0.622042 | − | 1.07741i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.18678 | + | 0.685187i | −0.0822883 | + | 0.0475092i | ||||
\(209\) | −0.555984 | −0.0384582 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.5583 | 1.75951 | 0.879753 | − | 0.475431i | \(-0.157708\pi\) | ||||
0.879753 | + | 0.475431i | \(0.157708\pi\) | |||||||
\(212\) | −7.40860 | + | 4.27736i | −0.508825 | + | 0.293770i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.03946 | − | 8.72859i | 0.344490 | − | 0.596674i | ||||
\(215\) | 2.54799 | + | 4.41325i | 0.173772 | + | 0.300981i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.14666 | + | 1.66159i | −0.0778406 | + | 0.112796i | ||||
\(218\) | 0.737772i | 0.0499682i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.12809 | + | 0.651304i | 0.0760559 | + | 0.0439109i | ||||
\(221\) | 6.79675 | + | 3.92411i | 0.457199 | + | 0.263964i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.64025i | 0.645559i | 0.946474 | + | 0.322779i | \(0.104617\pi\) | ||||
−0.946474 | + | 0.322779i | \(0.895383\pi\) | |||||||
\(224\) | −1.50274 | + | 2.17756i | −0.100406 | + | 0.145495i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.40618 | − | 4.16762i | −0.160056 | − | 0.277226i | ||||
\(227\) | −3.53947 | + | 6.13055i | −0.234923 | + | 0.406899i | −0.959250 | − | 0.282558i | \(-0.908817\pi\) |
0.724327 | + | 0.689456i | \(0.242150\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.3612 | + | 9.44614i | −1.08118 | + | 0.624219i | −0.931214 | − | 0.364473i | \(-0.881249\pi\) |
−0.149965 | + | 0.988691i | \(0.547916\pi\) | |||||||
\(230\) | 7.55377 | 0.498081 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.53981 | −0.429359 | ||||||||
\(233\) | 8.01488 | − | 4.62739i | 0.525072 | − | 0.303151i | −0.213935 | − | 0.976848i | \(-0.568628\pi\) |
0.739007 | + | 0.673697i | \(0.235295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.629717 | + | 1.09070i | −0.0410782 | + | 0.0711495i | ||||
\(236\) | 0.499578 | + | 0.865295i | 0.0325198 | + | 0.0563259i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.1034 | + | 1.21772i | 0.979006 | + | 0.0789333i | ||||
\(239\) | − | 4.86932i | − | 0.314970i | −0.987521 | − | 0.157485i | \(-0.949661\pi\) | ||
0.987521 | − | 0.157485i | \(-0.0503386\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.4869 | + | 10.6734i | 1.19085 | + | 0.687535i | 0.958498 | − | 0.285098i | \(-0.0920262\pi\) |
0.232347 | + | 0.972633i | \(0.425360\pi\) | |||||||
\(242\) | −0.866025 | − | 0.500000i | −0.0556702 | − | 0.0321412i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 0.147075i | − | 0.00941554i | ||||||
\(245\) | −3.23511 | − | 8.52506i | −0.206684 | − | 0.544646i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.380953 | + | 0.659829i | 0.0242394 | + | 0.0419839i | ||||
\(248\) | −0.381525 | + | 0.660821i | −0.0242269 | + | 0.0419622i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.36679 | + | 5.40792i | −0.592408 | + | 0.342027i | ||||
\(251\) | 21.2321 | 1.34016 | 0.670078 | − | 0.742291i | \(-0.266261\pi\) | ||||
0.670078 | + | 0.742291i | \(0.266261\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.79896 | −0.364577 | ||||||||
\(254\) | −10.8390 | + | 6.25791i | −0.680100 | + | 0.392656i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 7.21276 | + | 12.4929i | 0.449920 | + | 0.779284i | 0.998380 | − | 0.0568927i | \(-0.0181193\pi\) |
−0.548461 | + | 0.836176i | \(0.684786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.9732 | − | 7.58136i | 0.992526 | − | 0.471083i | ||||
\(260\) | − | 1.78506i | − | 0.110705i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.8595 | − | 7.42443i | −0.794462 | − | 0.458683i | ||||
\(263\) | 14.7636 | + | 8.52378i | 0.910364 | + | 0.525599i | 0.880548 | − | 0.473956i | \(-0.157175\pi\) |
0.0298158 | + | 0.999555i | \(0.490508\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 11.1434i | − | 0.684536i | ||||||
\(266\) | 1.21069 | + | 0.835497i | 0.0742321 | + | 0.0512276i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.60430 | + | 6.24283i | 0.220168 | + | 0.381342i | ||||
\(269\) | 11.1844 | − | 19.3720i | 0.681927 | − | 1.18113i | −0.292464 | − | 0.956276i | \(-0.594475\pi\) |
0.974392 | − | 0.224857i | \(-0.0721914\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.99443 | + | 1.15148i | −0.121153 | + | 0.0699476i | −0.559352 | − | 0.828930i | \(-0.688950\pi\) |
0.438199 | + | 0.898878i | \(0.355617\pi\) | |||||||
\(272\) | 5.72706 | 0.347254 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.9035 | 1.26283 | ||||||||
\(275\) | 2.86067 | − | 1.65161i | 0.172505 | − | 0.0995956i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.66323 | − | 6.34490i | 0.220102 | − | 0.381228i | −0.734737 | − | 0.678352i | \(-0.762694\pi\) |
0.954839 | + | 0.297124i | \(0.0960276\pi\) | |||||||
\(278\) | −1.60597 | − | 2.78163i | −0.0963199 | − | 0.166831i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.47775 | − | 3.11348i | −0.0883126 | − | 0.186066i | ||||
\(281\) | − | 11.0454i | − | 0.658911i | −0.944171 | − | 0.329456i | \(-0.893135\pi\) | ||
0.944171 | − | 0.329456i | \(-0.106865\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.8803 | + | 14.9420i | 1.53842 | + | 0.888209i | 0.998931 | + | 0.0462173i | \(0.0147167\pi\) |
0.539491 | + | 0.841991i | \(0.318617\pi\) | |||||||
\(284\) | 1.01829 | + | 0.587909i | 0.0604243 | + | 0.0348860i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.37037i | 0.0810319i | ||||||||
\(287\) | −0.479512 | + | 5.94735i | −0.0283047 | + | 0.351061i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.89960 | − | 13.6825i | −0.464683 | − | 0.804854i | ||||
\(290\) | 4.25940 | − | 7.37750i | 0.250121 | − | 0.433222i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.44038 | + | 0.831605i | −0.0842920 | + | 0.0486660i | ||||
\(293\) | 24.4813 | 1.43021 | 0.715106 | − | 0.699016i | \(-0.246379\pi\) | ||||
0.715106 | + | 0.699016i | \(0.246379\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.30151 | −0.0757768 | ||||||||
\(296\) | 5.78749 | − | 3.34141i | 0.336391 | − | 0.194215i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.2363 | − | 17.7299i | 0.592975 | − | 1.02706i | ||||
\(299\) | 3.97337 | + | 6.88208i | 0.229786 | + | 0.398001i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.831824 | + | 10.3171i | −0.0479455 | + | 0.594665i | ||||
\(302\) | − | 15.6014i | − | 0.897757i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.481496 | + | 0.277992i | 0.0276157 | + | 0.0159439i | ||||
\(305\) | 0.165915 | + | 0.0957908i | 0.00950024 | + | 0.00548497i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.72480i | − | 0.497951i | −0.968510 | − | 0.248975i | \(-0.919906\pi\) | ||
0.968510 | − | 0.248975i | \(-0.0800939\pi\) | |||||||
\(308\) | 1.13446 | + | 2.39019i | 0.0646417 | + | 0.136194i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.496978 | − | 0.860791i | −0.0282264 | − | 0.0488896i | ||||
\(311\) | 1.31098 | − | 2.27069i | 0.0743390 | − | 0.128759i | −0.826460 | − | 0.562996i | \(-0.809649\pi\) |
0.900799 | + | 0.434237i | \(0.142982\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.4146 | + | 11.7864i | −1.15390 | + | 0.666205i | −0.949835 | − | 0.312752i | \(-0.898749\pi\) |
−0.204066 | + | 0.978957i | \(0.565416\pi\) | |||||||
\(314\) | 7.75972 | 0.437906 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.723797 | 0.0407167 | ||||||||
\(317\) | 16.3099 | − | 9.41654i | 0.916057 | − | 0.528886i | 0.0336819 | − | 0.999433i | \(-0.489277\pi\) |
0.882375 | + | 0.470547i | \(0.155943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.26990 | + | 5.66364i | −0.183079 | + | 0.317103i | ||||
\(320\) | −0.651304 | − | 1.12809i | −0.0364090 | − | 0.0630623i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.6276 | + | 8.71431i | 0.703709 | + | 0.485629i | ||||
\(323\) | − | 3.18415i | − | 0.177171i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.92018 | − | 2.26332i | −0.217452 | − | 0.125546i | ||||
\(326\) | 4.09229 | + | 2.36269i | 0.226651 | + | 0.130857i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.25518i | 0.124522i | ||||||||
\(329\) | −2.31097 | + | 1.09686i | −0.127408 | + | 0.0604716i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.00063 | − | 1.73314i | −0.0549997 | − | 0.0952622i | 0.837215 | − | 0.546874i | \(-0.184182\pi\) |
−0.892214 | + | 0.451612i | \(0.850849\pi\) | |||||||
\(332\) | −2.77161 | + | 4.80057i | −0.152112 | + | 0.263466i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.16292 | + | 1.24876i | −0.118350 | + | 0.0683293i | ||||
\(335\) | −9.38998 | −0.513029 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.24786 | −0.122449 | −0.0612243 | − | 0.998124i | \(-0.519500\pi\) | ||||
−0.0612243 | + | 0.998124i | \(0.519500\pi\) | |||||||
\(338\) | −9.63200 | + | 5.56104i | −0.523912 | + | 0.302481i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.73006 | + | 6.46065i | −0.202291 | + | 0.350378i | ||||
\(341\) | 0.381525 | + | 0.660821i | 0.0206607 | + | 0.0357855i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.42670 | − | 17.9834i | 0.239020 | − | 0.971015i | ||||
\(344\) | 3.91214i | 0.210928i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.4466 | + | 7.76337i | 0.722891 | + | 0.417361i | ||||
\(347\) | 15.0915 | + | 8.71306i | 0.810152 | + | 0.467741i | 0.847009 | − | 0.531579i | \(-0.178401\pi\) |
−0.0368567 | + | 0.999321i | \(0.511735\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.6300i | 1.31841i | 0.751962 | + | 0.659206i | \(0.229108\pi\) | ||||
−0.751962 | + | 0.659206i | \(0.770892\pi\) | |||||||
\(350\) | −8.71121 | − | 0.702350i | −0.465634 | − | 0.0375422i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | 7.91758 | − | 13.7137i | 0.421410 | − | 0.729904i | −0.574667 | − | 0.818387i | \(-0.694869\pi\) |
0.996078 | + | 0.0884828i | \(0.0282018\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.32643 | + | 0.765815i | −0.0703997 | + | 0.0406453i | ||||
\(356\) | 8.51881 | 0.451496 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.55542 | 0.452168 | ||||||||
\(359\) | −11.6373 | + | 6.71878i | −0.614192 | + | 0.354604i | −0.774604 | − | 0.632446i | \(-0.782051\pi\) |
0.160413 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.34544 | + | 16.1868i | −0.491865 | + | 0.851936i | ||||
\(362\) | 11.4242 | + | 19.7874i | 0.600445 | + | 1.04000i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.05931 | − | 2.98408i | 0.107937 | − | 0.156408i | ||||
\(365\) | − | 2.16651i | − | 0.113400i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.7226 | + | 17.1603i | 1.55151 | + | 0.895763i | 0.998020 | + | 0.0629050i | \(0.0200365\pi\) |
0.553487 | + | 0.832858i | \(0.313297\pi\) | |||||||
\(368\) | 5.02204 | + | 2.89948i | 0.261792 | + | 0.151146i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.70509i | 0.452556i | ||||||||
\(371\) | 12.8555 | − | 18.6284i | 0.667423 | − | 0.967140i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.02865 | − | 8.70988i | −0.260374 | − | 0.450980i | 0.705968 | − | 0.708244i | \(-0.250512\pi\) |
−0.966341 | + | 0.257264i | \(0.917179\pi\) | |||||||
\(374\) | 2.86353 | − | 4.95978i | 0.148070 | − | 0.256464i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.837321 | + | 0.483428i | −0.0431816 | + | 0.0249309i | ||||
\(377\) | 8.96198 | 0.461566 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.33975 | 0.222918 | 0.111459 | − | 0.993769i | \(-0.464448\pi\) | ||||
0.111459 | + | 0.993769i | \(0.464448\pi\) | |||||||
\(380\) | −0.627201 | + | 0.362114i | −0.0321747 | + | 0.0185761i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.13084 | + | 14.0830i | −0.416010 | + | 0.720551i | ||||
\(383\) | −8.82958 | − | 15.2933i | −0.451170 | − | 0.781450i | 0.547289 | − | 0.836944i | \(-0.315660\pi\) |
−0.998459 | + | 0.0554940i | \(0.982327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.43523 | − | 0.276969i | −0.175076 | − | 0.0141156i | ||||
\(386\) | − | 5.67539i | − | 0.288870i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.2295 | + | 6.48336i | 0.570092 | + | 0.329143i | ||||
\(389\) | 1.71694 | + | 0.991276i | 0.0870523 | + | 0.0502597i | 0.542894 | − | 0.839801i | \(-0.317328\pi\) |
−0.455842 | + | 0.890061i | \(0.650662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 33.2110i | − | 1.67955i | ||||||
\(392\) | 1.12147 | − | 6.90958i | 0.0566430 | − | 0.348986i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.04390 | + | 1.80809i | 0.0525911 | + | 0.0910905i | ||||
\(395\) | −0.471412 | + | 0.816509i | −0.0237193 | + | 0.0410830i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.6030 | − | 18.8234i | 1.63630 | − | 0.944717i | 0.654206 | − | 0.756316i | \(-0.273003\pi\) |
0.982092 | − | 0.188401i | \(-0.0603305\pi\) | |||||||
\(398\) | −17.4223 | −0.873299 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.30321 | −0.165161 | ||||||||
\(401\) | −28.2285 | + | 16.2978i | −1.40967 | + | 0.813871i | −0.995356 | − | 0.0962648i | \(-0.969310\pi\) |
−0.414310 | + | 0.910136i | \(0.635977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.522832 | − | 0.905572i | 0.0260441 | − | 0.0451097i | ||||
\(404\) | −3.67391 | − | 6.36340i | −0.182784 | − | 0.316591i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.6314 | − | 7.41913i | 0.775772 | − | 0.368205i | ||||
\(407\) | − | 6.68281i | − | 0.331255i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.7939 | + | 17.7789i | 1.52266 | + | 0.879110i | 0.999641 | + | 0.0267904i | \(0.00852867\pi\) |
0.523022 | + | 0.852319i | \(0.324805\pi\) | |||||||
\(410\) | −2.54405 | − | 1.46881i | −0.125642 | − | 0.0725394i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.8560i | 0.879700i | ||||||||
\(413\) | −2.17573 | − | 1.50147i | −0.107061 | − | 0.0738825i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.61032 | − | 6.25326i | −0.177224 | − | 0.306961i | ||||
\(416\) | 0.685187 | − | 1.18678i | 0.0335940 | − | 0.0581866i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.481496 | − | 0.277992i | 0.0235507 | − | 0.0135970i | ||||
\(419\) | −4.47363 | −0.218551 | −0.109275 | − | 0.994012i | \(-0.534853\pi\) | ||||
−0.109275 | + | 0.994012i | \(0.534853\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.772473 | 0.0376480 | 0.0188240 | − | 0.999823i | \(-0.494008\pi\) | ||||
0.0188240 | + | 0.999823i | \(0.494008\pi\) | |||||||
\(422\) | −22.1341 | + | 12.7791i | −1.07747 | + | 0.622079i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.27736 | − | 7.40860i | 0.207727 | − | 0.359793i | ||||
\(425\) | 9.45884 | + | 16.3832i | 0.458821 | + | 0.794702i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.166851 | + | 0.351538i | 0.00807447 | + | 0.0170121i | ||||
\(428\) | 10.0789i | 0.487183i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.41325 | − | 2.54799i | −0.212826 | − | 0.122875i | ||||
\(431\) | −7.03670 | − | 4.06264i | −0.338946 | − | 0.195690i | 0.320860 | − | 0.947127i | \(-0.396028\pi\) |
−0.659806 | + | 0.751436i | \(0.729361\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 34.5052i | − | 1.65822i | −0.559088 | − | 0.829108i | \(-0.688849\pi\) | ||
0.559088 | − | 0.829108i | \(-0.311151\pi\) | |||||||
\(434\) | 0.162245 | − | 2.01231i | 0.00778799 | − | 0.0965940i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.368886 | − | 0.638929i | −0.0176664 | − | 0.0305992i | ||||
\(437\) | 1.61206 | − | 2.79217i | 0.0771154 | − | 0.133568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.2137 | − | 7.05159i | 0.582929 | − | 0.336554i | −0.179368 | − | 0.983782i | \(-0.557405\pi\) |
0.762296 | + | 0.647228i | \(0.224072\pi\) | |||||||
\(440\) | −1.30261 | −0.0620994 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.84821 | −0.373301 | ||||||||
\(443\) | −13.6938 | + | 7.90614i | −0.650614 | + | 0.375632i | −0.788691 | − | 0.614789i | \(-0.789241\pi\) |
0.138077 | + | 0.990421i | \(0.455908\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.54833 | + | 9.61000i | −0.263016 | + | 0.455558i | ||||
\(446\) | −4.82012 | − | 8.34870i | −0.228240 | − | 0.395322i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.212626 | − | 2.63719i | 0.0100457 | − | 0.124596i | ||||
\(449\) | − | 33.1895i | − | 1.56631i | −0.621828 | − | 0.783154i | \(-0.713610\pi\) | ||
0.621828 | − | 0.783154i | \(-0.286390\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.95305 | + | 1.12759i | 0.0919653 | + | 0.0530962i | ||||
\(452\) | 4.16762 | + | 2.40618i | 0.196028 | + | 0.113177i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 7.07894i | − | 0.332231i | ||||||
\(455\) | 2.02507 | + | 4.26663i | 0.0949369 | + | 0.200023i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.53304 | − | 14.7797i | −0.399159 | − | 0.691363i | 0.594463 | − | 0.804123i | \(-0.297364\pi\) |
−0.993622 | + | 0.112759i | \(0.964031\pi\) | |||||||
\(458\) | 9.44614 | − | 16.3612i | 0.441389 | − | 0.764509i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.54176 | + | 3.77689i | −0.305011 | + | 0.176098i | ||||
\(461\) | 32.1100 | 1.49551 | 0.747755 | − | 0.663974i | \(-0.231132\pi\) | ||||
0.747755 | + | 0.663974i | \(0.231132\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.5146 | 0.999867 | 0.499933 | − | 0.866064i | \(-0.333358\pi\) | ||||
0.499933 | + | 0.866064i | \(0.333358\pi\) | |||||||
\(464\) | 5.66364 | − | 3.26990i | 0.262928 | − | 0.151801i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.62739 | + | 8.01488i | −0.214360 | + | 0.371282i | ||||
\(467\) | 19.8774 | + | 34.4287i | 0.919817 | + | 1.59317i | 0.799691 | + | 0.600411i | \(0.204996\pi\) |
0.120126 | + | 0.992759i | \(0.461670\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.6972 | − | 10.8326i | −0.724828 | − | 0.500204i | ||||
\(470\) | − | 1.25943i | − | 0.0580934i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.865295 | − | 0.499578i | −0.0398284 | − | 0.0229950i | ||||
\(473\) | 3.38801 | + | 1.95607i | 0.155781 | + | 0.0899401i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.83653i | 0.0842659i | ||||||||
\(476\) | −13.6888 | + | 6.49710i | −0.627423 | + | 0.297794i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.43466 | + | 4.21695i | 0.111359 | + | 0.192879i | ||||
\(479\) | 5.58073 | − | 9.66610i | 0.254990 | − | 0.441655i | −0.709903 | − | 0.704300i | \(-0.751261\pi\) |
0.964893 | + | 0.262644i | \(0.0845945\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.93102 | + | 4.57898i | −0.361623 | + | 0.208783i | ||||
\(482\) | −21.3468 | −0.972321 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −14.6276 | + | 8.44528i | −0.664207 | + | 0.383480i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.5154 | + | 23.4094i | −0.612442 | + | 1.06078i | 0.378385 | + | 0.925648i | \(0.376479\pi\) |
−0.990828 | + | 0.135133i | \(0.956854\pi\) | |||||||
\(488\) | 0.0735377 | + | 0.127371i | 0.00332890 | + | 0.00576582i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.06422 | + | 5.76536i | 0.319129 | + | 0.260453i | ||||
\(491\) | 21.7459i | 0.981380i | 0.871334 | + | 0.490690i | \(0.163255\pi\) | ||||
−0.871334 | + | 0.490690i | \(0.836745\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.4360 | − | 18.7269i | −1.46084 | − | 0.843419i | ||||
\(494\) | −0.659829 | − | 0.380953i | −0.0296871 | − | 0.0171399i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.763050i | − | 0.0342620i | ||||||
\(497\) | −3.10086 | − | 0.250010i | −0.139093 | − | 0.0112145i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.55069 | + | 14.8102i | 0.382782 | + | 0.662997i | 0.991459 | − | 0.130421i | \(-0.0416328\pi\) |
−0.608677 | + | 0.793418i | \(0.708300\pi\) | |||||||
\(500\) | 5.40792 | − | 9.36679i | 0.241849 | − | 0.418895i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.3875 | + | 10.6160i | −0.820675 | + | 0.473817i | ||||
\(503\) | −20.0922 | −0.895867 | −0.447933 | − | 0.894067i | \(-0.647840\pi\) | ||||
−0.447933 | + | 0.894067i | \(0.647840\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.57133 | 0.425919 | ||||||||
\(506\) | 5.02204 | − | 2.89948i | 0.223257 | − | 0.128898i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.25791 | − | 10.8390i | 0.277650 | − | 0.480903i | ||||
\(509\) | −5.05011 | − | 8.74704i | −0.223842 | − | 0.387706i | 0.732129 | − | 0.681166i | \(-0.238527\pi\) |
−0.955971 | + | 0.293460i | \(0.905193\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.49937 | − | 3.62175i | 0.110565 | − | 0.160217i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.4929 | − | 7.21276i | −0.551037 | − | 0.318141i | ||||
\(515\) | −20.1432 | − | 11.6297i | −0.887614 | − | 0.512464i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.966856i | 0.0425223i | ||||||||
\(518\) | −10.0425 | + | 14.5522i | −0.441242 | + | 0.639389i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.892530 | + | 1.54591i | 0.0391400 | + | 0.0677925i | ||||
\(521\) | 16.2935 | − | 28.2211i | 0.713829 | − | 1.23639i | −0.249580 | − | 0.968354i | \(-0.580293\pi\) |
0.963409 | − | 0.268035i | \(-0.0863741\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.5548 | − | 14.7541i | 1.11743 | − | 0.645150i | 0.176689 | − | 0.984267i | \(-0.443461\pi\) |
0.940744 | + | 0.339116i | \(0.110128\pi\) | |||||||
\(524\) | 14.8489 | 0.648675 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.0476 | −0.743309 | ||||||||
\(527\) | −3.78456 | + | 2.18502i | −0.164858 | + | 0.0951808i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.31396 | − | 9.20404i | 0.231042 | − | 0.400176i | ||||
\(530\) | 5.57172 | + | 9.65050i | 0.242020 | + | 0.419191i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.46624 | − | 0.118217i | −0.0635694 | − | 0.00512535i | ||||
\(533\) | − | 3.09044i | − | 0.133862i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.3699 | − | 6.56444i | −0.491565 | − | 0.283805i | ||||
\(536\) | −6.24283 | − | 3.60430i | −0.269649 | − | 0.155682i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.3689i | 0.964391i | ||||||||
\(539\) | −5.42313 | − | 4.42602i | −0.233591 | − | 0.190642i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9017 | − | 20.6144i | −0.511694 | − | 0.886281i | −0.999908 | − | 0.0135565i | \(-0.995685\pi\) |
0.488214 | − | 0.872724i | \(-0.337649\pi\) | |||||||
\(542\) | 1.15148 | − | 1.99443i | 0.0494604 | − | 0.0856679i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.95978 | + | 2.86353i | −0.212649 | + | 0.122773i | ||||
\(545\) | 0.961028 | 0.0411659 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.4345 | −1.85713 | −0.928563 | − | 0.371174i | \(-0.878955\pi\) | ||||
−0.928563 | + | 0.371174i | \(0.878955\pi\) | |||||||
\(548\) | −18.1030 | + | 10.4518i | −0.773320 | + | 0.446477i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.65161 | + | 2.86067i | −0.0704247 | + | 0.121979i | ||||
\(551\) | −1.81801 | − | 3.14889i | −0.0774500 | − | 0.134147i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.73001 | + | 0.821116i | −0.0735676 | + | 0.0349174i | ||||
\(554\) | 7.32646i | 0.311271i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.78163 | + | 1.60597i | 0.117967 | + | 0.0681085i | ||||
\(557\) | 13.5945 | + | 7.84877i | 0.576016 | + | 0.332563i | 0.759549 | − | 0.650451i | \(-0.225420\pi\) |
−0.183532 | + | 0.983014i | \(0.558753\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.36109i | − | 0.226750i | ||||||
\(560\) | 2.83651 | + | 1.95748i | 0.119865 | + | 0.0827185i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.52268 | + | 9.56557i | 0.232960 | + | 0.403499i | ||||
\(563\) | −16.4468 | + | 28.4867i | −0.693151 | + | 1.20057i | 0.277649 | + | 0.960683i | \(0.410445\pi\) |
−0.970800 | + | 0.239890i | \(0.922889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.42878 | + | 3.13431i | −0.228390 | + | 0.131861i | ||||
\(566\) | −29.8840 | −1.25612 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.17582 | −0.0493363 | ||||||||
\(569\) | −9.79385 | + | 5.65448i | −0.410580 | + | 0.237048i | −0.691039 | − | 0.722818i | \(-0.742847\pi\) |
0.280459 | + | 0.959866i | \(0.409513\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.1162 | − | 17.5218i | 0.423350 | − | 0.733264i | −0.572915 | − | 0.819615i | \(-0.694187\pi\) |
0.996265 | + | 0.0863510i | \(0.0275207\pi\) | |||||||
\(572\) | −0.685187 | − | 1.18678i | −0.0286491 | − | 0.0496217i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.55841 | − | 5.39032i | −0.106786 | − | 0.224987i | ||||
\(575\) | 19.1552i | 0.798826i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.8277 | − | 10.2928i | −0.742178 | − | 0.428497i | 0.0806827 | − | 0.996740i | \(-0.474290\pi\) |
−0.822861 | + | 0.568243i | \(0.807623\pi\) | |||||||
\(578\) | 13.6825 | + | 7.89960i | 0.569118 | + | 0.328580i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.51881i | 0.353724i | ||||||||
\(581\) | 1.17864 | − | 14.6185i | 0.0488980 | − | 0.606480i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.27736 | − | 7.40860i | −0.177150 | − | 0.306833i | ||||
\(584\) | 0.831605 | − | 1.44038i | 0.0344121 | − | 0.0596034i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.2014 | + | 12.2406i | −0.875822 | + | 0.505656i | ||||
\(587\) | 26.7987 | 1.10610 | 0.553050 | − | 0.833148i | \(-0.313464\pi\) | ||||
0.553050 | + | 0.833148i | \(0.313464\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.424243 | −0.0174806 | ||||||||
\(590\) | 1.12714 | − | 0.650755i | 0.0464036 | − | 0.0267912i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.34141 | + | 5.78749i | −0.137331 | + | 0.237864i | ||||
\(593\) | 19.4485 | + | 33.6858i | 0.798653 | + | 1.38331i | 0.920493 | + | 0.390759i | \(0.127787\pi\) |
−0.121840 | + | 0.992550i | \(0.538879\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.58622 | − | 19.6738i | 0.0650286 | − | 0.806546i | ||||
\(596\) | 20.4727i | 0.838594i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.88208 | − | 3.97337i | −0.281429 | − | 0.162483i | ||||
\(599\) | −24.0811 | − | 13.9032i | −0.983926 | − | 0.568070i | −0.0804730 | − | 0.996757i | \(-0.525643\pi\) |
−0.903453 | + | 0.428687i | \(0.858976\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.32197i | − | 0.298669i | −0.988787 | − | 0.149335i | \(-0.952287\pi\) | ||
0.988787 | − | 0.149335i | \(-0.0477132\pi\) | |||||||
\(602\) | −4.43815 | − | 9.35075i | −0.180885 | − | 0.381108i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.80068 | + | 13.5112i | 0.317405 | + | 0.549762i | ||||
\(605\) | −0.651304 | + | 1.12809i | −0.0264793 | + | 0.0458635i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.43361 | + | 3.13710i | −0.220543 | + | 0.127331i | −0.606202 | − | 0.795311i | \(-0.707308\pi\) |
0.385658 | + | 0.922642i | \(0.373974\pi\) | |||||||
\(608\) | −0.555984 | −0.0225481 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.191582 | −0.00775691 | ||||||||
\(611\) | 1.14744 | − | 0.662477i | 0.0464206 | − | 0.0268009i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.08473 | + | 5.34292i | −0.124591 | + | 0.215798i | −0.921573 | − | 0.388205i | \(-0.873095\pi\) |
0.796982 | + | 0.604003i | \(0.206429\pi\) | |||||||
\(614\) | 4.36240 | + | 7.55590i | 0.176052 | + | 0.304931i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.17756 | − | 1.50274i | −0.0877365 | − | 0.0605470i | ||||
\(617\) | 3.03336i | 0.122119i | 0.998134 | + | 0.0610593i | \(0.0194479\pi\) | ||||
−0.998134 | + | 0.0610593i | \(0.980552\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.9228 | + | 17.8533i | 1.24289 | + | 0.717583i | 0.969682 | − | 0.244371i | \(-0.0785816\pi\) |
0.273209 | + | 0.961955i | \(0.411915\pi\) | |||||||
\(620\) | 0.860791 | + | 0.496978i | 0.0345702 | + | 0.0199591i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.62196i | 0.105131i | ||||||||
\(623\) | −20.3616 | + | 9.66422i | −0.815769 | + | 0.387189i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.21363 | − | 2.10207i | −0.0485453 | − | 0.0840830i | ||||
\(626\) | 11.7864 | − | 20.4146i | 0.471078 | − | 0.815931i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.72012 | + | 3.87986i | −0.268162 | + | 0.154823i | ||||
\(629\) | 38.2729 | 1.52604 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.45597 | 0.217199 | 0.108599 | − | 0.994086i | \(-0.465363\pi\) | ||||
0.108599 | + | 0.994086i | \(0.465363\pi\) | |||||||
\(632\) | −0.626826 | + | 0.361898i | −0.0249338 | + | 0.0143955i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.41654 | + | 16.3099i | −0.373979 | + | 0.647750i | ||||
\(635\) | 8.15160 | + | 14.1190i | 0.323486 | + | 0.560295i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.53684 | + | 9.46871i | −0.0608918 | + | 0.375164i | ||||
\(638\) | − | 6.53981i | − | 0.258913i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.12809 | + | 0.651304i | 0.0445917 | + | 0.0257451i | ||||
\(641\) | −32.8636 | − | 18.9738i | −1.29804 | − | 0.749421i | −0.317971 | − | 0.948101i | \(-0.603001\pi\) |
−0.980064 | + | 0.198680i | \(0.936335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.15376i | − | 0.0849360i | −0.999098 | − | 0.0424680i | \(-0.986478\pi\) | ||
0.999098 | − | 0.0424680i | \(-0.0135221\pi\) | |||||||
\(644\) | −15.2930 | − | 1.23301i | −0.602628 | − | 0.0485875i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.59208 | + | 2.75756i | 0.0626394 | + | 0.108495i | ||||
\(647\) | 2.88258 | − | 4.99277i | 0.113326 | − | 0.196286i | −0.803783 | − | 0.594922i | \(-0.797183\pi\) |
0.917109 | + | 0.398636i | \(0.130516\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.865295 | + | 0.499578i | −0.0339658 | + | 0.0196102i | ||||
\(650\) | 4.52663 | 0.177549 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.72537 | −0.185060 | ||||||||
\(653\) | −18.1451 | + | 10.4761i | −0.710071 | + | 0.409960i | −0.811087 | − | 0.584925i | \(-0.801124\pi\) |
0.101016 | + | 0.994885i | \(0.467791\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.67112 | + | 16.7509i | −0.377882 | + | 0.654511i | ||||
\(656\) | −1.12759 | − | 1.95305i | −0.0440251 | − | 0.0762536i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.45293 | − | 2.10539i | 0.0566411 | − | 0.0820766i | ||||
\(659\) | 29.5567i | 1.15137i | 0.817673 | + | 0.575683i | \(0.195264\pi\) | ||||
−0.817673 | + | 0.575683i | \(0.804736\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.57741 | − | 2.06542i | −0.139145 | − | 0.0803356i | 0.428811 | − | 0.903394i | \(-0.358933\pi\) |
−0.567957 | + | 0.823059i | \(0.692266\pi\) | |||||||
\(662\) | 1.73314 | + | 1.00063i | 0.0673605 | + | 0.0388906i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 5.54322i | − | 0.215119i | ||||||
\(665\) | 1.08833 | − | 1.57705i | 0.0422034 | − | 0.0611555i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.9620 | − | 32.8432i | −0.734213 | − | 1.27169i | ||||
\(668\) | 1.24876 | − | 2.16292i | 0.0483161 | − | 0.0836860i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.13196 | − | 4.69499i | 0.314165 | − | 0.181383i | ||||
\(671\) | 0.147075 | 0.00567778 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0120 | 0.540123 | 0.270061 | − | 0.962843i | \(-0.412956\pi\) | ||||
0.270061 | + | 0.962843i | \(0.412956\pi\) | |||||||
\(674\) | 1.94670 | − | 1.12393i | 0.0749841 | − | 0.0432921i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.56104 | − | 9.63200i | 0.213886 | − | 0.370462i | ||||
\(677\) | 3.80304 | + | 6.58706i | 0.146163 | + | 0.253161i | 0.929806 | − | 0.368050i | \(-0.119974\pi\) |
−0.783643 | + | 0.621211i | \(0.786641\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.1957 | − | 2.75707i | −1.31231 | − | 0.105807i | ||||
\(680\) | − | 7.46011i | − | 0.286082i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.660821 | − | 0.381525i | −0.0253041 | − | 0.0146094i | ||||
\(683\) | 15.2464 | + | 8.80252i | 0.583388 | + | 0.336819i | 0.762479 | − | 0.647013i | \(-0.223982\pi\) |
−0.179091 | + | 0.983833i | \(0.557316\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 27.2291i | − | 1.04037i | ||||||
\(686\) | 5.15808 | + | 17.7875i | 0.196937 | + | 0.679129i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.95607 | − | 3.38801i | −0.0745744 | − | 0.129167i | ||||
\(689\) | −5.86158 | + | 10.1526i | −0.223308 | + | 0.386781i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.2387 | + | 23.8092i | −1.56879 | + | 0.905744i | −0.572485 | + | 0.819915i | \(0.694020\pi\) |
−0.996310 | + | 0.0858285i | \(0.972646\pi\) | |||||||
\(692\) | −15.5267 | −0.590238 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.4261 | −0.661486 | ||||||||
\(695\) | −3.62337 | + | 2.09196i | −0.137442 | + | 0.0793524i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.45778 | + | 11.1852i | −0.244606 | + | 0.423670i | ||||
\(698\) | −12.3150 | − | 21.3302i | −0.466129 | − | 0.807360i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.89530 | − | 3.74735i | 0.298414 | − | 0.141637i | ||||
\(701\) | − | 40.9069i | − | 1.54503i | −0.634994 | − | 0.772517i | \(-0.718998\pi\) | ||
0.634994 | − | 0.772517i | \(-0.281002\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.21775 | + | 1.85777i | 0.121360 | + | 0.0700670i | ||||
\(704\) | −0.866025 | − | 0.500000i | −0.0326396 | − | 0.0188445i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.8352i | 0.595964i | ||||||||
\(707\) | 16.0003 | + | 11.0418i | 0.601755 | + | 0.415271i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.08240 | − | 5.33888i | −0.115762 | − | 0.200506i | 0.802322 | − | 0.596891i | \(-0.203598\pi\) |
−0.918084 | + | 0.396386i | \(0.870264\pi\) | |||||||
\(710\) | 0.765815 | − | 1.32643i | 0.0287405 | − | 0.0497801i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.37750 | + | 4.25940i | −0.276484 | + | 0.159628i | ||||
\(713\) | −4.42490 | −0.165714 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.78506 | 0.0667575 | ||||||||
\(716\) | −7.40921 | + | 4.27771i | −0.276895 | + | 0.159866i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.71878 | − | 11.6373i | 0.250743 | − | 0.434299i | ||||
\(719\) | −9.93587 | − | 17.2094i | −0.370545 | − | 0.641804i | 0.619104 | − | 0.785309i | \(-0.287496\pi\) |
−0.989650 | + | 0.143505i | \(0.954163\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.2568 | − | 42.6792i | −0.754404 | − | 1.58945i | ||||
\(722\) | − | 18.6909i | − | 0.695603i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.7874 | − | 11.4242i | −0.735392 | − | 0.424579i | ||||
\(725\) | 18.7082 | + | 10.8012i | 0.694805 | + | 0.401146i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.4001i | 1.57253i | 0.617888 | + | 0.786266i | \(0.287989\pi\) | ||||
−0.617888 | + | 0.786266i | \(0.712011\pi\) | |||||||
\(728\) | −0.291378 | + | 3.61394i | −0.0107992 | + | 0.133942i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.08326 | + | 1.87625i | 0.0400931 | + | 0.0694433i | ||||
\(731\) | −11.2025 | + | 19.4033i | −0.414340 | + | 0.717658i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.9313 | + | 8.62060i | −0.551501 | + | 0.318409i | −0.749727 | − | 0.661747i | \(-0.769815\pi\) |
0.198226 | + | 0.980156i | \(0.436482\pi\) | |||||||
\(734\) | −34.3207 | −1.26680 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.79896 | −0.213752 | ||||||||
\(737\) | −6.24283 | + | 3.60430i | −0.229958 | + | 0.132766i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.99251 | − | 17.3075i | 0.367581 | − | 0.636668i | −0.621606 | − | 0.783330i | \(-0.713520\pi\) |
0.989187 | + | 0.146662i | \(0.0468529\pi\) | |||||||
\(740\) | −4.35254 | − | 7.53883i | −0.160003 | − | 0.277133i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.81896 | + | 22.5604i | −0.0667761 | + | 0.828220i | ||||
\(743\) | − | 5.37602i | − | 0.197227i | −0.995126 | − | 0.0986136i | \(-0.968559\pi\) | ||
0.995126 | − | 0.0986136i | \(-0.0314408\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.0951 | − | 13.3339i | −0.846138 | − | 0.488518i | ||||
\(746\) | 8.70988 | + | 5.02865i | 0.318891 | + | 0.184112i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.72706i | 0.209402i | ||||||||
\(749\) | −11.4341 | − | 24.0905i | −0.417793 | − | 0.880248i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.6527 | − | 39.2356i | −0.826607 | − | 1.43173i | −0.900685 | − | 0.434473i | \(-0.856935\pi\) |
0.0740775 | − | 0.997252i | \(-0.476399\pi\) | |||||||
\(752\) | 0.483428 | − | 0.837321i | 0.0176288 | − | 0.0305340i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.76130 | + | 4.48099i | −0.282650 | + | 0.163188i | ||||
\(755\) | −20.3225 | −0.739610 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.5594 | −0.492823 | −0.246412 | − | 0.969165i | \(-0.579251\pi\) | ||||
−0.246412 | + | 0.969165i | \(0.579251\pi\) | |||||||
\(758\) | −3.75833 | + | 2.16987i | −0.136509 | + | 0.0788133i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.362114 | − | 0.627201i | 0.0131353 | − | 0.0227510i | ||||
\(761\) | 15.4116 | + | 26.6938i | 0.558672 | + | 0.967648i | 0.997608 | + | 0.0691296i | \(0.0220222\pi\) |
−0.438936 | + | 0.898518i | \(0.644644\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.60655 | + | 1.10868i | 0.0581608 | + | 0.0401368i | ||||
\(764\) | − | 16.2617i | − | 0.588327i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.2933 | + | 8.82958i | 0.552569 | + | 0.319026i | ||||
\(767\) | 1.18578 | + | 0.684609i | 0.0428160 | + | 0.0247198i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17.6776i | − | 0.637470i | −0.947844 | − | 0.318735i | \(-0.896742\pi\) | ||
0.947844 | − | 0.318735i | \(-0.103258\pi\) | |||||||
\(770\) | 3.11348 | − | 1.47775i | 0.112202 | − | 0.0532545i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.83770 | + | 4.91503i | 0.102131 | + | 0.176896i | ||||
\(773\) | 6.74571 | − | 11.6839i | 0.242626 | − | 0.420241i | −0.718835 | − | 0.695180i | \(-0.755324\pi\) |
0.961462 | + | 0.274939i | \(0.0886578\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.18283 | − | 1.26026i | 0.0784096 | − | 0.0452698i | ||||
\(776\) | −12.9667 | −0.465478 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.98255 | −0.0710779 | ||||||||
\(779\) | −1.08586 | + | 0.626922i | −0.0389050 | + | 0.0224618i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.587909 | + | 1.01829i | −0.0210370 | + | 0.0364372i | ||||
\(782\) | 16.6055 | + | 28.7615i | 0.593811 | + | 1.02851i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.48356 | + | 6.54461i | 0.0886987 | + | 0.233736i | ||||
\(785\) | − | 10.1079i | − | 0.360766i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.1209 | + | 17.3903i | 1.07370 | + | 0.619898i | 0.929189 | − | 0.369606i | \(-0.120507\pi\) |
0.144507 | + | 0.989504i | \(0.453841\pi\) | |||||||
\(788\) | −1.80809 | − | 1.04390i | −0.0644107 | − | 0.0371875i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 0.942824i | − | 0.0335442i | ||||||
\(791\) | −12.6911 | − | 1.02323i | −0.451244 | − | 0.0363820i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.100774 | − | 0.174546i | −0.00357859 | − | 0.00619831i | ||||
\(794\) | −18.8234 | + | 32.6030i | −0.668016 | + | 1.15704i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.0881 | − | 8.71113i | 0.534785 | − | 0.308758i | ||||
\(797\) | −11.4732 | −0.406401 | −0.203201 | − | 0.979137i | \(-0.565134\pi\) | ||||
−0.203201 | + | 0.979137i | \(0.565134\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.53724 | −0.195893 | ||||||||
\(800\) | 2.86067 | − | 1.65161i | 0.101140 | − | 0.0583931i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.2978 | − | 28.2285i | 0.575494 | − | 0.996784i | ||||
\(803\) | −0.831605 | − | 1.44038i | −0.0293467 | − | 0.0508300i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.3513 | − | 16.4488i | 0.400082 | − | 0.579745i | ||||
\(806\) | 1.04566i | 0.0368319i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.36340 | + | 3.67391i | 0.223864 | + | 0.129248i | ||||
\(809\) | 22.0848 | + | 12.7507i | 0.776460 | + | 0.448289i | 0.835174 | − | 0.549985i | \(-0.185367\pi\) |
−0.0587142 | + | 0.998275i | \(0.518700\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.6249i | 0.654008i | 0.945023 | + | 0.327004i | \(0.106039\pi\) | ||||
−0.945023 | + | 0.327004i | \(0.893961\pi\) | |||||||
\(812\) | −9.82761 | + | 14.2408i | −0.344881 | + | 0.499756i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.34141 | + | 5.78749i | 0.117116 | + | 0.202851i | ||||
\(815\) | 3.07766 | − | 5.33066i | 0.107806 | − | 0.186725i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.88368 | + | 1.08754i | −0.0659015 | + | 0.0380483i | ||||
\(818\) | −35.5578 | −1.24325 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.93762 | 0.102586 | ||||||||
\(821\) | −19.2122 | + | 11.0922i | −0.670512 | + | 0.387120i | −0.796270 | − | 0.604941i | \(-0.793197\pi\) |
0.125759 | + | 0.992061i | \(0.459863\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.8996 | + | 37.9312i | −0.763371 | + | 1.32220i | 0.177732 | + | 0.984079i | \(0.443124\pi\) |
−0.941103 | + | 0.338119i | \(0.890209\pi\) | |||||||
\(824\) | −8.92798 | − | 15.4637i | −0.311021 | − | 0.538704i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.63497 | + | 0.212447i | 0.0916823 | + | 0.00739198i | ||||
\(827\) | 36.7143i | 1.27668i | 0.769754 | + | 0.638341i | \(0.220379\pi\) | ||||
−0.769754 | + | 0.638341i | \(0.779621\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.1439 | + | 18.5583i | 1.11640 | + | 0.644555i | 0.940480 | − | 0.339849i | \(-0.110376\pi\) |
0.175922 | + | 0.984404i | \(0.443709\pi\) | |||||||
\(830\) | 6.25326 | + | 3.61032i | 0.217054 | + | 0.125316i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.37037i | 0.0475092i | ||||||||
\(833\) | 25.3480 | − | 31.0586i | 0.878258 | − | 1.07612i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.62665 | + | 2.81744i | 0.0562925 | + | 0.0975015i | ||||
\(836\) | −0.277992 | + | 0.481496i | −0.00961455 | + | 0.0166529i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.87427 | − | 2.23681i | 0.133835 | − | 0.0772694i | ||||
\(839\) | −11.7171 | −0.404517 | −0.202259 | − | 0.979332i | \(-0.564828\pi\) | ||||
−0.202259 | + | 0.979332i | \(0.564828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.7691 | −0.474796 | ||||||||
\(842\) | −0.668981 | + | 0.386236i | −0.0230546 | + | 0.0133106i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.7791 | − | 22.1341i | 0.439876 | − | 0.761888i | ||||
\(845\) | 7.24385 | + | 12.5467i | 0.249196 | + | 0.431620i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.39019 | + | 1.13446i | −0.0821279 | + | 0.0389804i | ||||
\(848\) | 8.55471i | 0.293770i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −16.3832 | − | 9.45884i | −0.561939 | − | 0.324436i | ||||
\(851\) | 33.5614 | + | 19.3767i | 1.15047 | + | 0.664224i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.99115i | − | 0.205133i | −0.994726 | − | 0.102567i | \(-0.967295\pi\) | ||
0.994726 | − | 0.102567i | \(-0.0327055\pi\) | |||||||
\(854\) | −0.320266 | − | 0.221016i | −0.0109593 | − | 0.00756300i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.03946 | − | 8.72859i | −0.172245 | − | 0.298337i | ||||
\(857\) | −24.0477 | + | 41.6518i | −0.821453 | + | 1.42280i | 0.0831470 | + | 0.996537i | \(0.473503\pi\) |
−0.904600 | + | 0.426261i | \(0.859830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.0197 | − | 23.6827i | 1.39957 | − | 0.808045i | 0.405226 | − | 0.914216i | \(-0.367193\pi\) |
0.994348 | + | 0.106172i | \(0.0338594\pi\) | |||||||
\(860\) | 5.09598 | 0.173772 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.12528 | 0.276748 | ||||||||
\(863\) | −25.1635 | + | 14.5281i | −0.856574 | + | 0.494543i | −0.862864 | − | 0.505437i | \(-0.831331\pi\) |
0.00628929 | + | 0.999980i | \(0.497998\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.1126 | − | 17.5156i | 0.343840 | − | 0.595548i | ||||
\(866\) | 17.2526 | + | 29.8824i | 0.586268 | + | 1.01545i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.865648 | + | 1.82383i | 0.0293820 | + | 0.0619050i | ||||
\(869\) | 0.723797i | 0.0245531i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.55501 | + | 4.93924i | 0.289875 | + | 0.167360i | ||||
\(872\) | 0.638929 | + | 0.368886i | 0.0216369 | + | 0.0124921i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.22413i | 0.109058i | ||||||||
\(875\) | −2.29973 | + | 28.5234i | −0.0777451 | + | 0.964268i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.48397 | − | 2.57031i | −0.0501100 | − | 0.0867931i | 0.839882 | − | 0.542768i | \(-0.182624\pi\) |
−0.889992 | + | 0.455975i | \(0.849291\pi\) | |||||||
\(878\) | −7.05159 | + | 12.2137i | −0.237980 | + | 0.412193i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.12809 | − | 0.651304i | 0.0380280 | − | 0.0219555i | ||||
\(881\) | 7.81186 | 0.263188 | 0.131594 | − | 0.991304i | \(-0.457990\pi\) | ||||
0.131594 | + | 0.991304i | \(0.457990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.07807 | 0.103585 | 0.0517927 | − | 0.998658i | \(-0.483507\pi\) | ||||
0.0517927 | + | 0.998658i | \(0.483507\pi\) | |||||||
\(884\) | 6.79675 | − | 3.92411i | 0.228599 | − | 0.131982i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.90614 | − | 13.6938i | 0.265612 | − | 0.460054i | ||||
\(887\) | −10.5062 | − | 18.1974i | −0.352765 | − | 0.611007i | 0.633968 | − | 0.773360i | \(-0.281425\pi\) |
−0.986733 | + | 0.162352i | \(0.948092\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.66119 | + | 33.0066i | −0.0892535 | + | 1.10701i | ||||
\(890\) | − | 11.0967i | − | 0.371961i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.34870 | + | 4.82012i | 0.279535 | + | 0.161390i | ||||
\(893\) | −0.465537 | − | 0.268778i | −0.0155786 | − | 0.00899431i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 11.1444i | − | 0.372515i | ||||||
\(896\) | 1.13446 | + | 2.39019i | 0.0378995 | + | 0.0798506i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.5947 | + | 28.7429i | 0.553773 | + | 0.959163i | ||||
\(899\) | −2.49510 | + | 4.32164i | −0.0832163 | + | 0.144135i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.4295 | − | 24.4967i | 1.41353 | − | 0.816103i | ||||
\(902\) | −2.25518 | −0.0750894 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.81235 | −0.160056 | ||||||||
\(905\) | 25.7752 | − | 14.8813i | 0.856797 | − | 0.494672i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.8569 | + | 29.1970i | −0.559724 | + | 0.969470i | 0.437796 | + | 0.899075i | \(0.355759\pi\) |
−0.997519 | + | 0.0703952i | \(0.977574\pi\) | |||||||
\(908\) | 3.53947 | + | 6.13055i | 0.117462 | + | 0.203449i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.88708 | − | 2.68248i | −0.128856 | − | 0.0889232i | ||||
\(911\) | − | 22.8272i | − | 0.756298i | −0.925745 | − | 0.378149i | \(-0.876561\pi\) | ||
0.925745 | − | 0.378149i | \(-0.123439\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.80057 | − | 2.77161i | −0.158876 | − | 0.0917269i | ||||
\(914\) | 14.7797 | + | 8.53304i | 0.488868 | + | 0.282248i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.8923i | 0.624219i | ||||||||
\(917\) | −35.4916 | + | 16.8454i | −1.17204 | + | 0.556284i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.07735 | + | 13.9904i | 0.266447 | + | 0.461500i | 0.967942 | − | 0.251175i | \(-0.0808169\pi\) |
−0.701495 | + | 0.712675i | \(0.747484\pi\) | |||||||
\(920\) | 3.77689 | − | 6.54176i | 0.124520 | − | 0.215675i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27.8081 | + | 16.0550i | −0.915810 | + | 0.528743i | ||||
\(923\) | 1.61131 | 0.0530369 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.0747 | −0.725813 | ||||||||
\(926\) | −18.6322 | + | 10.7573i | −0.612291 | + | 0.353506i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.26990 | + | 5.66364i | −0.107340 | + | 0.185918i | ||||
\(929\) | −12.8229 | − | 22.2099i | −0.420706 | − | 0.728685i | 0.575302 | − | 0.817941i | \(-0.304884\pi\) |
−0.996009 | + | 0.0892562i | \(0.971551\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.63870 | − | 1.38082i | 0.119253 | − | 0.0452546i | ||||
\(932\) | − | 9.25479i | − | 0.303151i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34.4287 | − | 19.8774i | −1.12654 | − | 0.650409i | ||||
\(935\) | −6.46065 | − | 3.73006i | −0.211286 | − | 0.121986i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.9317i | 1.43518i | 0.696463 | + | 0.717592i | \(0.254756\pi\) | ||||
−0.696463 | + | 0.717592i | \(0.745244\pi\) | |||||||
\(938\) | 19.0105 | + | 1.53274i | 0.620714 | + | 0.0500457i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.629717 | + | 1.09070i | 0.0205391 | + | 0.0355748i | ||||
\(941\) | −21.9166 | + | 37.9607i | −0.714460 | + | 1.23748i | 0.248707 | + | 0.968579i | \(0.419994\pi\) |
−0.963167 | + | 0.268903i | \(0.913339\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.3256 | + | 6.53886i | −0.368813 | + | 0.212934i | ||||
\(944\) | 0.999157 | 0.0325198 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.91214 | −0.127195 | ||||||||
\(947\) | 15.4512 | − | 8.92077i | 0.502097 | − | 0.289886i | −0.227482 | − | 0.973782i | \(-0.573049\pi\) |
0.729579 | + | 0.683896i | \(0.239716\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.13961 | + | 1.97386i | −0.0369933 | + | 0.0640743i | ||||
\(950\) | −0.918266 | − | 1.59048i | −0.0297925 | − | 0.0516021i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.60626 | − | 12.4710i | 0.278931 | − | 0.404189i | ||||
\(953\) | − | 5.09951i | − | 0.165189i | −0.996583 | − | 0.0825946i | \(-0.973679\pi\) | ||
0.996583 | − | 0.0825946i | \(-0.0263207\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.3447 | + | 10.5913i | 0.593620 | + | 0.342726i | ||||
\(956\) | −4.21695 | − | 2.43466i | −0.136386 | − | 0.0787425i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.1615i | 0.360610i | ||||||||
\(959\) | 31.4125 | − | 45.5187i | 1.01436 | − | 1.46988i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.2089 | − | 26.3425i | −0.490609 | − | 0.849760i | ||||
\(962\) | 4.57898 | − | 7.93102i | 0.147632 | − | 0.255706i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18.4869 | − | 10.6734i | 0.595423 | − | 0.343767i | ||||
\(965\) | −7.39281 | −0.237983 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.1081 | −1.16116 | −0.580578 | − | 0.814204i | \(-0.697174\pi\) | ||||
−0.580578 | + | 0.814204i | \(0.697174\pi\) | |||||||
\(968\) | −0.866025 | + | 0.500000i | −0.0278351 | + | 0.0160706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.44528 | − | 14.6276i | 0.271161 | − | 0.469665i | ||||
\(971\) | 15.1490 | + | 26.2388i | 0.486153 | + | 0.842042i | 0.999873 | − | 0.0159157i | \(-0.00506633\pi\) |
−0.513720 | + | 0.857958i | \(0.671733\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.47053 | − | 0.682945i | −0.271553 | − | 0.0218942i | ||||
\(974\) | − | 27.0308i | − | 0.866124i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.127371 | − | 0.0735377i | −0.00407705 | − | 0.00235388i | ||||
\(977\) | 21.0168 | + | 12.1341i | 0.672388 | + | 0.388203i | 0.796981 | − | 0.604005i | \(-0.206429\pi\) |
−0.124593 | + | 0.992208i | \(0.539763\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.51881i | 0.272262i | ||||||||
\(980\) | −9.00048 | − | 1.46084i | −0.287510 | − | 0.0466649i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.8730 | − | 18.8325i | −0.346970 | − | 0.600970i | ||||
\(983\) | 29.2363 | − | 50.6388i | 0.932493 | − | 1.61513i | 0.153449 | − | 0.988157i | \(-0.450962\pi\) |
0.779044 | − | 0.626969i | \(-0.215705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.35524 | − | 1.35980i | 0.0750441 | − | 0.0433267i | ||||
\(986\) | 37.4539 | 1.19277 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.761905 | 0.0242394 | ||||||||
\(989\) | −19.6469 | + | 11.3432i | −0.624736 | + | 0.360691i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.1078 | − | 38.2918i | 0.702277 | − | 1.21638i | −0.265388 | − | 0.964142i | \(-0.585500\pi\) |
0.967665 | − | 0.252238i | \(-0.0811665\pi\) | |||||||
\(992\) | 0.381525 | + | 0.660821i | 0.0121134 | + | 0.0209811i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.81043 | − | 1.33392i | 0.0891414 | − | 0.0423092i | ||||
\(995\) | 22.6944i | 0.719461i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.7758 | − | 19.5005i | −1.06969 | − | 0.617586i | −0.141593 | − | 0.989925i | \(-0.545223\pi\) |
−0.928097 | + | 0.372339i | \(0.878556\pi\) | |||||||
\(998\) | −14.8102 | − | 8.55069i | −0.468810 | − | 0.270667i | ||||
\(999\) | 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 | 1386.2.r.d.1277.2 | yes | 24 | |
3.2 | odd | 2 | inner | 1386.2.r.d.1277.11 | yes | 24 | |
7.5 | odd | 6 | inner | 1386.2.r.d.89.11 | yes | 24 | |
21.5 | even | 6 | inner | 1386.2.r.d.89.2 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.r.d.89.2 | ✓ | 24 | 21.5 | even | 6 | inner | |
1386.2.r.d.89.11 | yes | 24 | 7.5 | odd | 6 | inner | |
1386.2.r.d.1277.2 | yes | 24 | 1.1 | even | 1 | trivial | |
1386.2.r.d.1277.11 | yes | 24 | 3.2 | odd | 2 | inner |