Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 729.1 | ||
Character | \(\chi\) | \(=\) | 847.729 |
Dual form | 847.2.f.y.323.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.18693 | + | 1.58890i | −1.54639 | + | 1.12352i | −0.600233 | + | 0.799825i | \(0.704925\pi\) |
−0.946161 | + | 0.323696i | \(0.895075\pi\) | |||||||
\(3\) | −0.867470 | − | 2.66980i | −0.500834 | − | 1.54141i | −0.807664 | − | 0.589644i | \(-0.799268\pi\) |
0.306830 | − | 0.951764i | \(-0.400732\pi\) | |||||||
\(4\) | 1.64004 | − | 5.04751i | 0.820018 | − | 2.52376i | ||||
\(5\) | 0.360071 | + | 0.261607i | 0.161029 | + | 0.116994i | 0.665381 | − | 0.746503i | \(-0.268269\pi\) |
−0.504353 | + | 0.863498i | \(0.668269\pi\) | |||||||
\(6\) | 6.13913 | + | 4.46034i | 2.50629 | + | 1.82093i | ||||
\(7\) | 0.309017 | − | 0.951057i | 0.116797 | − | 0.359466i | ||||
\(8\) | 2.76267 | + | 8.50263i | 0.976752 | + | 3.00613i | ||||
\(9\) | −3.94826 | + | 2.86858i | −1.31609 | + | 0.956193i | ||||
\(10\) | −1.20312 | −0.380459 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −14.8985 | −4.30083 | ||||||||
\(13\) | −0.364813 | + | 0.265052i | −0.101181 | + | 0.0735122i | −0.637225 | − | 0.770678i | \(-0.719918\pi\) |
0.536044 | + | 0.844190i | \(0.319918\pi\) | |||||||
\(14\) | 0.835334 | + | 2.57089i | 0.223252 | + | 0.687100i | ||||
\(15\) | 0.386087 | − | 1.18825i | 0.0996872 | − | 0.306806i | ||||
\(16\) | −10.9643 | − | 7.96600i | −2.74106 | − | 1.99150i | ||||
\(17\) | −3.90850 | − | 2.83969i | −0.947951 | − | 0.688727i | 0.00237042 | − | 0.999997i | \(-0.499245\pi\) |
−0.950321 | + | 0.311271i | \(0.899245\pi\) | |||||||
\(18\) | 4.07669 | − | 12.5468i | 0.960886 | − | 2.95730i | ||||
\(19\) | −0.335728 | − | 1.03326i | −0.0770212 | − | 0.237047i | 0.905132 | − | 0.425131i | \(-0.139772\pi\) |
−0.982153 | + | 0.188084i | \(0.939772\pi\) | |||||||
\(20\) | 1.91099 | − | 1.38842i | 0.427311 | − | 0.310460i | ||||
\(21\) | −2.80719 | −0.612579 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.57222 | 0.953373 | 0.476687 | − | 0.879073i | \(-0.341838\pi\) | ||||
0.476687 | + | 0.879073i | \(0.341838\pi\) | |||||||
\(24\) | 20.3038 | − | 14.7516i | 4.14449 | − | 3.01115i | ||||
\(25\) | −1.48387 | − | 4.56689i | −0.296774 | − | 0.913378i | ||||
\(26\) | 0.376680 | − | 1.15930i | 0.0738729 | − | 0.227358i | ||||
\(27\) | 4.27033 | + | 3.10257i | 0.821825 | + | 0.597091i | ||||
\(28\) | −4.29367 | − | 3.11953i | −0.811428 | − | 0.589537i | ||||
\(29\) | −0.613187 | + | 1.88719i | −0.113866 | + | 0.350443i | −0.991709 | − | 0.128505i | \(-0.958982\pi\) |
0.877843 | + | 0.478949i | \(0.158982\pi\) | |||||||
\(30\) | 1.04367 | + | 3.21208i | 0.190547 | + | 0.586443i | ||||
\(31\) | −6.68135 | + | 4.85429i | −1.20001 | + | 0.871856i | −0.994285 | − | 0.106755i | \(-0.965954\pi\) |
−0.205721 | + | 0.978611i | \(0.565954\pi\) | |||||||
\(32\) | 18.7549 | 3.31542 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.0596 | 2.23970 | ||||||||
\(35\) | 0.360071 | − | 0.261607i | 0.0608631 | − | 0.0442196i | ||||
\(36\) | 8.00390 | + | 24.6335i | 1.33398 | + | 4.10558i | ||||
\(37\) | 2.26116 | − | 6.95912i | 0.371732 | − | 1.14407i | −0.573926 | − | 0.818907i | \(-0.694580\pi\) |
0.945657 | − | 0.325165i | \(-0.105420\pi\) | |||||||
\(38\) | 2.37596 | + | 1.72624i | 0.385432 | + | 0.280033i | ||||
\(39\) | 1.02410 | + | 0.744051i | 0.163987 | + | 0.119144i | ||||
\(40\) | −1.22959 | + | 3.78429i | −0.194415 | + | 0.598348i | ||||
\(41\) | 0.547186 | + | 1.68407i | 0.0854561 | + | 0.263007i | 0.984649 | − | 0.174545i | \(-0.0558456\pi\) |
−0.899193 | + | 0.437552i | \(0.855846\pi\) | |||||||
\(42\) | 6.13913 | − | 4.46034i | 0.947289 | − | 0.688246i | ||||
\(43\) | −11.4084 | −1.73977 | −0.869884 | − | 0.493257i | \(-0.835806\pi\) | ||||
−0.869884 | + | 0.493257i | \(0.835806\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.17209 | −0.323797 | ||||||||
\(46\) | −9.99913 | + | 7.26479i | −1.47429 | + | 1.07113i | ||||
\(47\) | 0.315996 | + | 0.972536i | 0.0460928 | + | 0.141859i | 0.971454 | − | 0.237227i | \(-0.0762385\pi\) |
−0.925361 | + | 0.379086i | \(0.876238\pi\) | |||||||
\(48\) | −11.7564 | + | 36.1826i | −1.69690 | + | 5.22251i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | 10.5015 | + | 7.62975i | 1.48513 | + | 1.07901i | ||||
\(51\) | −4.19090 | + | 12.8983i | −0.586843 | + | 1.80612i | ||||
\(52\) | 0.739547 | + | 2.27609i | 0.102557 | + | 0.315637i | ||||
\(53\) | 2.88998 | − | 2.09970i | 0.396970 | − | 0.288416i | −0.371336 | − | 0.928499i | \(-0.621100\pi\) |
0.768306 | + | 0.640083i | \(0.221100\pi\) | |||||||
\(54\) | −14.2686 | −1.94171 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.94020 | 1.19468 | ||||||||
\(57\) | −2.46737 | + | 1.79265i | −0.326811 | + | 0.237442i | ||||
\(58\) | −1.65756 | − | 5.10146i | −0.217649 | − | 0.669854i | ||||
\(59\) | −4.44972 | + | 13.6948i | −0.579304 | + | 1.78291i | 0.0417292 | + | 0.999129i | \(0.486713\pi\) |
−0.621033 | + | 0.783784i | \(0.713287\pi\) | |||||||
\(60\) | −5.36452 | − | 3.89755i | −0.692557 | − | 0.503172i | ||||
\(61\) | −3.98817 | − | 2.89758i | −0.510633 | − | 0.370996i | 0.302431 | − | 0.953171i | \(-0.402202\pi\) |
−0.813064 | + | 0.582175i | \(0.802202\pi\) | |||||||
\(62\) | 6.89869 | − | 21.2320i | 0.876135 | − | 2.69647i | ||||
\(63\) | 1.50810 | + | 4.64146i | 0.190003 | + | 0.584769i | ||||
\(64\) | −19.0871 | + | 13.8676i | −2.38588 | + | 1.73345i | ||||
\(65\) | −0.200698 | −0.0248935 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.18858 | −0.756055 | −0.378028 | − | 0.925794i | \(-0.623398\pi\) | ||||
−0.378028 | + | 0.925794i | \(0.623398\pi\) | |||||||
\(68\) | −20.7435 | + | 15.0710i | −2.51552 | + | 1.82763i | ||||
\(69\) | −3.96626 | − | 12.2069i | −0.477482 | − | 1.46954i | ||||
\(70\) | −0.371784 | + | 1.14423i | −0.0444367 | + | 0.136762i | ||||
\(71\) | 4.79072 | + | 3.48066i | 0.568553 | + | 0.413078i | 0.834579 | − | 0.550888i | \(-0.185711\pi\) |
−0.266026 | + | 0.963966i | \(0.585711\pi\) | |||||||
\(72\) | −35.2982 | − | 25.6457i | −4.15994 | − | 3.02237i | ||||
\(73\) | −0.512277 | + | 1.57663i | −0.0599575 | + | 0.184530i | −0.976549 | − | 0.215294i | \(-0.930929\pi\) |
0.916592 | + | 0.399825i | \(0.130929\pi\) | |||||||
\(74\) | 6.11235 | + | 18.8119i | 0.710546 | + | 2.18683i | ||||
\(75\) | −10.9055 | + | 7.92327i | −1.25925 | + | 0.914901i | ||||
\(76\) | −5.76602 | −0.661407 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.42186 | −0.387449 | ||||||||
\(79\) | 2.91920 | − | 2.12092i | 0.328436 | − | 0.238623i | −0.411331 | − | 0.911486i | \(-0.634936\pi\) |
0.739767 | + | 0.672864i | \(0.234936\pi\) | |||||||
\(80\) | −1.86395 | − | 5.73665i | −0.208396 | − | 0.641377i | ||||
\(81\) | 0.0545593 | − | 0.167916i | 0.00606215 | − | 0.0186574i | ||||
\(82\) | −3.87247 | − | 2.81351i | −0.427642 | − | 0.310700i | ||||
\(83\) | 8.74129 | + | 6.35092i | 0.959481 | + | 0.697104i | 0.953030 | − | 0.302875i | \(-0.0979465\pi\) |
0.00645109 | + | 0.999979i | \(0.497947\pi\) | |||||||
\(84\) | −4.60389 | + | 14.1693i | −0.502326 | + | 1.54600i | ||||
\(85\) | −0.664455 | − | 2.04498i | −0.0720703 | − | 0.221809i | ||||
\(86\) | 24.9494 | − | 18.1268i | 2.69037 | − | 1.95467i | ||||
\(87\) | 5.57035 | 0.597204 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.21170 | −0.552439 | −0.276220 | − | 0.961095i | \(-0.589082\pi\) | ||||
−0.276220 | + | 0.961095i | \(0.589082\pi\) | |||||||
\(90\) | 4.75022 | − | 3.45124i | 0.500717 | − | 0.363793i | ||||
\(91\) | 0.139346 | + | 0.428863i | 0.0146074 | + | 0.0449571i | ||||
\(92\) | 7.49860 | − | 23.0783i | 0.781783 | − | 2.40608i | ||||
\(93\) | 18.7558 | + | 13.6269i | 1.94489 | + | 1.41304i | ||||
\(94\) | −2.23632 | − | 1.62478i | −0.230659 | − | 0.167584i | ||||
\(95\) | 0.149423 | − | 0.459877i | 0.0153305 | − | 0.0471824i | ||||
\(96\) | −16.2693 | − | 50.0716i | −1.66047 | − | 5.11042i | ||||
\(97\) | 4.29576 | − | 3.12105i | 0.436168 | − | 0.316895i | −0.347943 | − | 0.937516i | \(-0.613120\pi\) |
0.784110 | + | 0.620621i | \(0.213120\pi\) | |||||||
\(98\) | 2.70320 | 0.273064 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −25.4850 | −2.54850 | ||||||||
\(101\) | −12.5886 | + | 9.14616i | −1.25261 | + | 0.910077i | −0.998371 | − | 0.0570629i | \(-0.981826\pi\) |
−0.254243 | + | 0.967140i | \(0.581826\pi\) | |||||||
\(102\) | −11.3288 | − | 34.8665i | −1.12172 | − | 3.45230i | ||||
\(103\) | −4.37918 | + | 13.4777i | −0.431494 | + | 1.32800i | 0.465143 | + | 0.885235i | \(0.346003\pi\) |
−0.896637 | + | 0.442766i | \(0.853997\pi\) | |||||||
\(104\) | −3.26150 | − | 2.36962i | −0.319816 | − | 0.232360i | ||||
\(105\) | −1.01079 | − | 0.734380i | −0.0986428 | − | 0.0716682i | ||||
\(106\) | −2.98399 | + | 9.18379i | −0.289831 | + | 0.892008i | ||||
\(107\) | −3.63253 | − | 11.1798i | −0.351170 | − | 1.08079i | −0.958197 | − | 0.286109i | \(-0.907638\pi\) |
0.607027 | − | 0.794681i | \(-0.292362\pi\) | |||||||
\(108\) | 22.6638 | − | 16.4662i | 2.18082 | − | 1.58446i | ||||
\(109\) | 15.7800 | 1.51145 | 0.755723 | − | 0.654891i | \(-0.227286\pi\) | ||||
0.755723 | + | 0.654891i | \(0.227286\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.5409 | −1.94966 | ||||||||
\(112\) | −10.9643 | + | 7.96600i | −1.03602 | + | 0.752716i | ||||
\(113\) | −1.83045 | − | 5.63356i | −0.172195 | − | 0.529960i | 0.827300 | − | 0.561761i | \(-0.189876\pi\) |
−0.999494 | + | 0.0318004i | \(0.989876\pi\) | |||||||
\(114\) | 2.54763 | − | 7.84080i | 0.238608 | − | 0.734358i | ||||
\(115\) | 1.64632 | + | 1.19612i | 0.153520 | + | 0.111539i | ||||
\(116\) | 8.51999 | + | 6.19014i | 0.791061 | + | 0.574740i | ||||
\(117\) | 0.680053 | − | 2.09299i | 0.0628709 | − | 0.193497i | ||||
\(118\) | −12.0285 | − | 37.0198i | −1.10731 | − | 3.40795i | ||||
\(119\) | −3.90850 | + | 2.83969i | −0.358292 | + | 0.260314i | ||||
\(120\) | 11.1699 | 1.01967 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 13.3258 | 1.20646 | ||||||||
\(123\) | 4.02144 | − | 2.92175i | 0.362601 | − | 0.263445i | ||||
\(124\) | 13.5444 | + | 41.6854i | 1.21632 | + | 3.74346i | ||||
\(125\) | 1.34810 | − | 4.14904i | 0.120578 | − | 0.371101i | ||||
\(126\) | −10.6729 | − | 7.75433i | −0.950820 | − | 0.690811i | ||||
\(127\) | −8.19835 | − | 5.95645i | −0.727486 | − | 0.528549i | 0.161281 | − | 0.986908i | \(-0.448437\pi\) |
−0.888767 | + | 0.458359i | \(0.848437\pi\) | |||||||
\(128\) | 8.11681 | − | 24.9810i | 0.717432 | − | 2.20803i | ||||
\(129\) | 9.89646 | + | 30.4582i | 0.871334 | + | 2.68169i | ||||
\(130\) | 0.438912 | − | 0.318889i | 0.0384952 | − | 0.0279684i | ||||
\(131\) | −6.83340 | −0.597037 | −0.298519 | − | 0.954404i | \(-0.596492\pi\) | ||||
−0.298519 | + | 0.954404i | \(0.596492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.08644 | −0.0942061 | ||||||||
\(134\) | 13.5340 | − | 9.83302i | 1.16916 | − | 0.849444i | ||||
\(135\) | 0.725966 | + | 2.23429i | 0.0624812 | + | 0.192297i | ||||
\(136\) | 13.3470 | − | 41.0777i | 1.14449 | − | 3.52238i | ||||
\(137\) | −11.7043 | − | 8.50366i | −0.999965 | − | 0.726517i | −0.0378839 | − | 0.999282i | \(-0.512062\pi\) |
−0.962081 | + | 0.272765i | \(0.912062\pi\) | |||||||
\(138\) | 28.0695 | + | 20.3937i | 2.38943 | + | 1.73602i | ||||
\(139\) | −4.54121 | + | 13.9764i | −0.385180 | + | 1.18546i | 0.551169 | + | 0.834394i | \(0.314182\pi\) |
−0.936349 | + | 0.351070i | \(0.885818\pi\) | |||||||
\(140\) | −0.729935 | − | 2.24651i | −0.0616907 | − | 0.189865i | ||||
\(141\) | 2.32236 | − | 1.68729i | 0.195578 | − | 0.142096i | ||||
\(142\) | −16.0074 | −1.34331 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 66.1409 | 5.51174 | ||||||||
\(145\) | −0.714494 | + | 0.519110i | −0.0593355 | + | 0.0431098i | ||||
\(146\) | −1.38479 | − | 4.26193i | −0.114606 | − | 0.352720i | ||||
\(147\) | −0.867470 | + | 2.66980i | −0.0715477 | + | 0.220201i | ||||
\(148\) | −31.4179 | − | 22.8264i | −2.58253 | − | 1.87632i | ||||
\(149\) | −0.810148 | − | 0.588607i | −0.0663699 | − | 0.0482206i | 0.554106 | − | 0.832446i | \(-0.313060\pi\) |
−0.620476 | + | 0.784226i | \(0.713060\pi\) | |||||||
\(150\) | 11.2602 | − | 34.6553i | 0.919391 | − | 2.82959i | ||||
\(151\) | 0.425018 | + | 1.30807i | 0.0345874 | + | 0.106449i | 0.966860 | − | 0.255308i | \(-0.0821769\pi\) |
−0.932272 | + | 0.361757i | \(0.882177\pi\) | |||||||
\(152\) | 7.85795 | − | 5.70914i | 0.637364 | − | 0.463072i | ||||
\(153\) | 23.5777 | 1.90614 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.67568 | −0.295237 | ||||||||
\(156\) | 5.43517 | − | 3.94888i | 0.435162 | − | 0.316163i | ||||
\(157\) | 1.66149 | + | 5.11353i | 0.132601 | + | 0.408104i | 0.995209 | − | 0.0977686i | \(-0.0311705\pi\) |
−0.862608 | + | 0.505873i | \(0.831171\pi\) | |||||||
\(158\) | −3.01416 | + | 9.27663i | −0.239794 | + | 0.738009i | ||||
\(159\) | −8.11274 | − | 5.89425i | −0.643382 | − | 0.467444i | ||||
\(160\) | 6.75308 | + | 4.90640i | 0.533878 | + | 0.387885i | ||||
\(161\) | 1.41289 | − | 4.34844i | 0.111352 | − | 0.342705i | ||||
\(162\) | 0.147485 | + | 0.453911i | 0.0115875 | + | 0.0356626i | ||||
\(163\) | 7.62509 | − | 5.53995i | 0.597243 | − | 0.433922i | −0.247656 | − | 0.968848i | \(-0.579660\pi\) |
0.844899 | + | 0.534926i | \(0.179660\pi\) | |||||||
\(164\) | 9.39775 | 0.733841 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −29.2076 | −2.26695 | ||||||||
\(167\) | −16.1899 | + | 11.7627i | −1.25281 | + | 0.910222i | −0.998382 | − | 0.0568684i | \(-0.981888\pi\) |
−0.254432 | + | 0.967091i | \(0.581888\pi\) | |||||||
\(168\) | −7.75535 | − | 23.8685i | −0.598338 | − | 1.84150i | ||||
\(169\) | −3.95439 | + | 12.1703i | −0.304183 | + | 0.936180i | ||||
\(170\) | 4.70239 | + | 3.41648i | 0.360657 | + | 0.262032i | ||||
\(171\) | 4.28954 | + | 3.11653i | 0.328029 | + | 0.238327i | ||||
\(172\) | −18.7102 | + | 57.5841i | −1.42664 | + | 4.39075i | ||||
\(173\) | 3.35177 | + | 10.3157i | 0.254830 | + | 0.784286i | 0.993863 | + | 0.110617i | \(0.0352827\pi\) |
−0.739033 | + | 0.673669i | \(0.764717\pi\) | |||||||
\(174\) | −12.1820 | + | 8.85072i | −0.923513 | + | 0.670971i | ||||
\(175\) | −4.80191 | −0.362990 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 40.4224 | 3.03833 | ||||||||
\(178\) | 11.3976 | − | 8.28087i | 0.854289 | − | 0.620677i | ||||
\(179\) | 5.20644 | + | 16.0238i | 0.389148 | + | 1.19767i | 0.933426 | + | 0.358769i | \(0.116803\pi\) |
−0.544279 | + | 0.838904i | \(0.683197\pi\) | |||||||
\(180\) | −3.56231 | + | 10.9637i | −0.265519 | + | 0.817184i | ||||
\(181\) | 16.4264 | + | 11.9345i | 1.22096 | + | 0.887082i | 0.996180 | − | 0.0873266i | \(-0.0278324\pi\) |
0.224784 | + | 0.974409i | \(0.427832\pi\) | |||||||
\(182\) | −0.986160 | − | 0.716487i | −0.0730990 | − | 0.0531096i | ||||
\(183\) | −4.27632 | + | 13.1612i | −0.316115 | + | 0.972901i | ||||
\(184\) | 12.6315 | + | 38.8759i | 0.931210 | + | 2.86597i | ||||
\(185\) | 2.63473 | − | 1.91424i | 0.193709 | − | 0.140738i | ||||
\(186\) | −62.6695 | −4.59515 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.42714 | 0.395815 | ||||||||
\(189\) | 4.27033 | − | 3.10257i | 0.310621 | − | 0.225679i | ||||
\(190\) | 0.403920 | + | 1.24314i | 0.0293034 | + | 0.0901867i | ||||
\(191\) | 0.786247 | − | 2.41982i | 0.0568908 | − | 0.175092i | −0.918573 | − | 0.395251i | \(-0.870658\pi\) |
0.975464 | + | 0.220159i | \(0.0706576\pi\) | |||||||
\(192\) | 53.5810 | + | 38.9289i | 3.86688 | + | 2.80945i | ||||
\(193\) | −14.1648 | − | 10.2913i | −1.01960 | − | 0.740784i | −0.0534000 | − | 0.998573i | \(-0.517006\pi\) |
−0.966201 | + | 0.257790i | \(0.917006\pi\) | |||||||
\(194\) | −4.43549 | + | 13.6510i | −0.318450 | + | 0.980088i | ||||
\(195\) | 0.174099 | + | 0.535823i | 0.0124675 | + | 0.0383710i | ||||
\(196\) | −4.29367 | + | 3.11953i | −0.306691 | + | 0.222824i | ||||
\(197\) | −2.16558 | −0.154291 | −0.0771457 | − | 0.997020i | \(-0.524581\pi\) | ||||
−0.0771457 | + | 0.997020i | \(0.524581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.5756 | −1.03324 | −0.516620 | − | 0.856215i | \(-0.672810\pi\) | ||||
−0.516620 | + | 0.856215i | \(0.672810\pi\) | |||||||
\(200\) | 34.7311 | − | 25.2336i | 2.45586 | − | 1.78429i | ||||
\(201\) | 5.36840 | + | 16.5222i | 0.378658 | + | 1.16539i | ||||
\(202\) | 12.9981 | − | 40.0041i | 0.914544 | − | 2.81468i | ||||
\(203\) | 1.60534 | + | 1.16635i | 0.112673 | + | 0.0818617i | ||||
\(204\) | 58.2309 | + | 42.3072i | 4.07698 | + | 2.96210i | ||||
\(205\) | −0.243537 | + | 0.749531i | −0.0170094 | + | 0.0523495i | ||||
\(206\) | −11.8378 | − | 36.4330i | −0.824778 | − | 2.53841i | ||||
\(207\) | −18.0523 | + | 13.1158i | −1.25472 | + | 0.911609i | ||||
\(208\) | 6.11130 | 0.423743 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.37738 | 0.233061 | ||||||||
\(211\) | 2.93701 | − | 2.13386i | 0.202192 | − | 0.146901i | −0.482082 | − | 0.876126i | \(-0.660119\pi\) |
0.684274 | + | 0.729225i | \(0.260119\pi\) | |||||||
\(212\) | −5.85857 | − | 18.0308i | −0.402368 | − | 1.23836i | ||||
\(213\) | 5.13685 | − | 15.8096i | 0.351971 | − | 1.08326i | ||||
\(214\) | 25.7076 | + | 18.6777i | 1.75734 | + | 1.27678i | ||||
\(215\) | −4.10784 | − | 2.98452i | −0.280152 | − | 0.203543i | ||||
\(216\) | −14.5825 | + | 44.8804i | −0.992216 | + | 3.05373i | ||||
\(217\) | 2.55205 | + | 7.85440i | 0.173244 | + | 0.533192i | ||||
\(218\) | −34.5097 | + | 25.0728i | −2.33729 | + | 1.69814i | ||||
\(219\) | 4.65366 | 0.314465 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.17854 | 0.146544 | ||||||||
\(222\) | 44.9216 | − | 32.6374i | 3.01494 | − | 2.19048i | ||||
\(223\) | −1.49583 | − | 4.60370i | −0.100168 | − | 0.308287i | 0.888398 | − | 0.459075i | \(-0.151819\pi\) |
−0.988566 | + | 0.150788i | \(0.951819\pi\) | |||||||
\(224\) | 5.79557 | − | 17.8369i | 0.387233 | − | 1.19178i | ||||
\(225\) | 18.9592 | + | 13.7747i | 1.26395 | + | 0.918311i | ||||
\(226\) | 12.9542 | + | 9.41180i | 0.861702 | + | 0.626063i | ||||
\(227\) | 7.02415 | − | 21.6181i | 0.466209 | − | 1.43484i | −0.391247 | − | 0.920286i | \(-0.627956\pi\) |
0.857456 | − | 0.514558i | \(-0.172044\pi\) | |||||||
\(228\) | 5.00184 | + | 15.3941i | 0.331255 | + | 1.01950i | ||||
\(229\) | 18.3430 | − | 13.3269i | 1.21214 | − | 0.880669i | 0.216714 | − | 0.976235i | \(-0.430466\pi\) |
0.995423 | + | 0.0955657i | \(0.0304660\pi\) | |||||||
\(230\) | −5.50092 | −0.362720 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.7402 | −1.16470 | ||||||||
\(233\) | 0.475121 | − | 0.345196i | 0.0311262 | − | 0.0226145i | −0.572113 | − | 0.820175i | \(-0.693876\pi\) |
0.603240 | + | 0.797560i | \(0.293876\pi\) | |||||||
\(234\) | 1.83832 | + | 5.65776i | 0.120175 | + | 0.369859i | ||||
\(235\) | −0.140641 | + | 0.432849i | −0.00917442 | + | 0.0282360i | ||||
\(236\) | 61.8271 | + | 44.9200i | 4.02460 | + | 2.92404i | ||||
\(237\) | −8.19475 | − | 5.95384i | −0.532306 | − | 0.386743i | ||||
\(238\) | 4.03564 | − | 12.4204i | 0.261592 | − | 0.805097i | ||||
\(239\) | −4.62664 | − | 14.2393i | −0.299272 | − | 0.921065i | −0.981753 | − | 0.190162i | \(-0.939099\pi\) |
0.682481 | − | 0.730904i | \(-0.260901\pi\) | |||||||
\(240\) | −13.6988 | + | 9.95274i | −0.884252 | + | 0.642447i | ||||
\(241\) | −18.2746 | −1.17717 | −0.588586 | − | 0.808435i | \(-0.700315\pi\) | ||||
−0.588586 | + | 0.808435i | \(0.700315\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3396 | 0.984037 | ||||||||
\(244\) | −21.1663 | + | 15.3782i | −1.35503 | + | 0.984489i | ||||
\(245\) | −0.137535 | − | 0.423289i | −0.00878678 | − | 0.0270429i | ||||
\(246\) | −4.15226 | + | 12.7793i | −0.264738 | + | 0.814781i | ||||
\(247\) | 0.396346 | + | 0.287962i | 0.0252189 | + | 0.0183226i | ||||
\(248\) | −59.7326 | − | 43.3983i | −3.79302 | − | 2.75579i | ||||
\(249\) | 9.37286 | − | 28.8467i | 0.593981 | − | 1.82809i | ||||
\(250\) | 3.64419 | + | 11.2157i | 0.230479 | + | 0.709341i | ||||
\(251\) | −8.54717 | + | 6.20988i | −0.539493 | + | 0.391964i | −0.823897 | − | 0.566740i | \(-0.808204\pi\) |
0.284404 | + | 0.958705i | \(0.408204\pi\) | |||||||
\(252\) | 25.9012 | 1.63162 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 27.3934 | 1.71882 | ||||||||
\(255\) | −4.88329 | + | 3.54792i | −0.305804 | + | 0.222179i | ||||
\(256\) | 7.36011 | + | 22.6521i | 0.460007 | + | 1.41576i | ||||
\(257\) | −6.01593 | + | 18.5151i | −0.375264 | + | 1.15494i | 0.568037 | + | 0.823003i | \(0.307703\pi\) |
−0.943301 | + | 0.331940i | \(0.892297\pi\) | |||||||
\(258\) | −70.0378 | − | 50.8855i | −4.36036 | − | 3.16799i | ||||
\(259\) | −5.91978 | − | 4.30097i | −0.367837 | − | 0.267249i | ||||
\(260\) | −0.329152 | + | 1.01303i | −0.0204131 | + | 0.0628251i | ||||
\(261\) | −2.99255 | − | 9.21011i | −0.185234 | − | 0.570092i | ||||
\(262\) | 14.9442 | − | 10.8576i | 0.923255 | − | 0.670784i | ||||
\(263\) | 21.1885 | 1.30654 | 0.653269 | − | 0.757126i | \(-0.273397\pi\) | ||||
0.653269 | + | 0.757126i | \(0.273397\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.58989 | 0.0976665 | ||||||||
\(266\) | 2.37596 | − | 1.72624i | 0.145680 | − | 0.105843i | ||||
\(267\) | 4.52099 | + | 13.9142i | 0.276680 | + | 0.851534i | ||||
\(268\) | −10.1495 | + | 31.2369i | −0.619979 | + | 1.90810i | ||||
\(269\) | −18.7339 | − | 13.6110i | −1.14223 | − | 0.829877i | −0.154799 | − | 0.987946i | \(-0.549473\pi\) |
−0.987428 | + | 0.158069i | \(0.949473\pi\) | |||||||
\(270\) | −5.13771 | − | 3.73276i | −0.312671 | − | 0.227169i | ||||
\(271\) | 8.28882 | − | 25.5104i | 0.503510 | − | 1.54964i | −0.299751 | − | 0.954017i | \(-0.596904\pi\) |
0.803261 | − | 0.595627i | \(-0.203096\pi\) | |||||||
\(272\) | 20.2328 | + | 62.2702i | 1.22680 | + | 3.77569i | ||||
\(273\) | 1.02410 | − | 0.744051i | 0.0619813 | − | 0.0450320i | ||||
\(274\) | 39.1079 | 2.36260 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −68.1193 | −4.10030 | ||||||||
\(277\) | 11.3673 | − | 8.25884i | 0.682996 | − | 0.496226i | −0.191354 | − | 0.981521i | \(-0.561288\pi\) |
0.874350 | + | 0.485295i | \(0.161288\pi\) | |||||||
\(278\) | −12.2758 | − | 37.7810i | −0.736252 | − | 2.26595i | ||||
\(279\) | 12.4548 | − | 38.3320i | 0.745650 | − | 2.29488i | ||||
\(280\) | 3.21911 | + | 2.33882i | 0.192378 | + | 0.139771i | ||||
\(281\) | 1.41204 | + | 1.02591i | 0.0842352 | + | 0.0612004i | 0.629106 | − | 0.777320i | \(-0.283421\pi\) |
−0.544871 | + | 0.838520i | \(0.683421\pi\) | |||||||
\(282\) | −2.39790 | + | 7.37998i | −0.142793 | + | 0.439472i | ||||
\(283\) | −1.44166 | − | 4.43697i | −0.0856977 | − | 0.263750i | 0.899020 | − | 0.437907i | \(-0.144280\pi\) |
−0.984718 | + | 0.174157i | \(0.944280\pi\) | |||||||
\(284\) | 25.4256 | − | 18.4728i | 1.50873 | − | 1.09616i | ||||
\(285\) | −1.35740 | −0.0804053 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.77073 | 0.104523 | ||||||||
\(288\) | −74.0491 | + | 53.7998i | −4.36338 | + | 3.17018i | ||||
\(289\) | 1.95924 | + | 6.02993i | 0.115250 | + | 0.354702i | ||||
\(290\) | 0.737736 | − | 2.27052i | 0.0433213 | − | 0.133329i | ||||
\(291\) | −12.0590 | − | 8.76138i | −0.706911 | − | 0.513601i | ||||
\(292\) | 7.11789 | + | 5.17145i | 0.416543 | + | 0.302636i | ||||
\(293\) | 4.48359 | − | 13.7991i | 0.261934 | − | 0.806151i | −0.730450 | − | 0.682967i | \(-0.760689\pi\) |
0.992384 | − | 0.123184i | \(-0.0393106\pi\) | |||||||
\(294\) | −2.34494 | − | 7.21698i | −0.136760 | − | 0.420903i | ||||
\(295\) | −5.18487 | + | 3.76703i | −0.301875 | + | 0.219325i | ||||
\(296\) | 65.4177 | 3.80232 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.70698 | 0.156811 | ||||||||
\(299\) | −1.66800 | + | 1.21187i | −0.0964631 | + | 0.0700845i | ||||
\(300\) | 22.1075 | + | 68.0399i | 1.27638 | + | 3.92828i | ||||
\(301\) | −3.52540 | + | 10.8501i | −0.203200 | + | 0.625387i | ||||
\(302\) | −3.00787 | − | 2.18535i | −0.173084 | − | 0.125753i | ||||
\(303\) | 35.3386 | + | 25.6750i | 2.03015 | + | 1.47499i | ||||
\(304\) | −4.54997 | + | 14.0034i | −0.260959 | + | 0.803149i | ||||
\(305\) | −0.677999 | − | 2.08667i | −0.0388221 | − | 0.119482i | ||||
\(306\) | −51.5628 | + | 37.4625i | −2.94765 | + | 2.14159i | ||||
\(307\) | 2.35679 | 0.134509 | 0.0672547 | − | 0.997736i | \(-0.478576\pi\) | ||||
0.0672547 | + | 0.997736i | \(0.478576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 39.7816 | 2.26310 | ||||||||
\(310\) | 8.03845 | − | 5.84028i | 0.456553 | − | 0.331706i | ||||
\(311\) | −6.18189 | − | 19.0259i | −0.350543 | − | 1.07886i | −0.958549 | − | 0.284927i | \(-0.908031\pi\) |
0.608007 | − | 0.793932i | \(-0.291969\pi\) | |||||||
\(312\) | −3.49714 | + | 10.7631i | −0.197987 | + | 0.609341i | ||||
\(313\) | −15.1715 | − | 11.0228i | −0.857545 | − | 0.623043i | 0.0696707 | − | 0.997570i | \(-0.477805\pi\) |
−0.927216 | + | 0.374527i | \(0.877805\pi\) | |||||||
\(314\) | −11.7584 | − | 8.54301i | −0.663567 | − | 0.482110i | ||||
\(315\) | −0.671214 | + | 2.06578i | −0.0378186 | + | 0.116394i | ||||
\(316\) | −5.91779 | − | 18.2131i | −0.332902 | − | 1.02457i | ||||
\(317\) | −3.39951 | + | 2.46989i | −0.190936 | + | 0.138723i | −0.679146 | − | 0.734003i | \(-0.737650\pi\) |
0.488211 | + | 0.872726i | \(0.337650\pi\) | |||||||
\(318\) | 27.1074 | 1.52011 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −10.5005 | −0.586999 | ||||||||
\(321\) | −26.6966 | + | 19.3962i | −1.49006 | + | 1.08259i | ||||
\(322\) | 3.81933 | + | 11.7547i | 0.212843 | + | 0.655063i | ||||
\(323\) | −1.62196 | + | 4.99188i | −0.0902482 | + | 0.277755i | ||||
\(324\) | −0.758081 | − | 0.550778i | −0.0421156 | − | 0.0305988i | ||||
\(325\) | 1.75180 | + | 1.27276i | 0.0971722 | + | 0.0705998i | ||||
\(326\) | −7.87313 | + | 24.2310i | −0.436052 | + | 1.34203i | ||||
\(327\) | −13.6886 | − | 42.1293i | −0.756984 | − | 2.32976i | ||||
\(328\) | −12.8073 | + | 9.30504i | −0.707164 | + | 0.513785i | ||||
\(329\) | 1.02259 | 0.0563770 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.0682694 | −0.00375242 | −0.00187621 | − | 0.999998i | \(-0.500597\pi\) | ||||
−0.00187621 | + | 0.999998i | \(0.500597\pi\) | |||||||
\(332\) | 46.3924 | − | 33.7060i | 2.54611 | − | 1.84986i | ||||
\(333\) | 11.0352 | + | 33.9627i | 0.604723 | + | 1.86115i | ||||
\(334\) | 16.7166 | − | 51.4483i | 0.914689 | − | 2.81512i | ||||
\(335\) | −2.22833 | − | 1.61897i | −0.121747 | − | 0.0884540i | ||||
\(336\) | 30.7788 | + | 22.3621i | 1.67912 | + | 1.21995i | ||||
\(337\) | 6.71992 | − | 20.6818i | 0.366058 | − | 1.12661i | −0.583259 | − | 0.812287i | \(-0.698223\pi\) |
0.949316 | − | 0.314323i | \(-0.101777\pi\) | |||||||
\(338\) | −10.6895 | − | 32.8988i | −0.581431 | − | 1.78946i | ||||
\(339\) | −13.4526 | + | 9.77388i | −0.730644 | + | 0.530844i | ||||
\(340\) | −11.4118 | −0.618892 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −14.3328 | −0.775028 | ||||||||
\(343\) | −0.809017 | + | 0.587785i | −0.0436828 | + | 0.0317374i | ||||
\(344\) | −31.5177 | − | 97.0016i | −1.69932 | − | 5.22998i | ||||
\(345\) | 1.76527 | − | 5.43295i | 0.0950391 | − | 0.292500i | ||||
\(346\) | −23.7206 | − | 17.2341i | −1.27523 | − | 0.926509i | ||||
\(347\) | −19.3639 | − | 14.0687i | −1.03951 | − | 0.755248i | −0.0693194 | − | 0.997595i | \(-0.522083\pi\) |
−0.970190 | + | 0.242347i | \(0.922083\pi\) | |||||||
\(348\) | 9.13557 | − | 28.1164i | 0.489718 | − | 1.50720i | ||||
\(349\) | −8.16270 | − | 25.1222i | −0.436939 | − | 1.34476i | −0.891086 | − | 0.453834i | \(-0.850056\pi\) |
0.454147 | − | 0.890927i | \(-0.349944\pi\) | |||||||
\(350\) | 10.5015 | − | 7.62975i | 0.561326 | − | 0.407827i | ||||
\(351\) | −2.38021 | −0.127046 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.44182 | −0.236414 | −0.118207 | − | 0.992989i | \(-0.537715\pi\) | ||||
−0.118207 | + | 0.992989i | \(0.537715\pi\) | |||||||
\(354\) | −88.4010 | + | 64.2271i | −4.69846 | + | 3.41363i | ||||
\(355\) | 0.814434 | + | 2.50657i | 0.0432256 | + | 0.133035i | ||||
\(356\) | −8.54738 | + | 26.3061i | −0.453010 | + | 1.39422i | ||||
\(357\) | 10.9719 | + | 7.97156i | 0.580695 | + | 0.421900i | ||||
\(358\) | −36.8463 | − | 26.7704i | −1.94739 | − | 1.41486i | ||||
\(359\) | −4.49080 | + | 13.8212i | −0.237015 | + | 0.729458i | 0.759833 | + | 0.650119i | \(0.225281\pi\) |
−0.996848 | + | 0.0793387i | \(0.974719\pi\) | |||||||
\(360\) | −6.00079 | − | 18.4685i | −0.316269 | − | 0.973377i | ||||
\(361\) | 14.4164 | − | 10.4741i | 0.758758 | − | 0.551270i | ||||
\(362\) | −54.8860 | −2.88475 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.39322 | 0.125439 | ||||||||
\(365\) | −0.596913 | + | 0.433682i | −0.0312438 | + | 0.0227000i | ||||
\(366\) | −11.5597 | − | 35.5772i | −0.604237 | − | 1.85965i | ||||
\(367\) | 1.53939 | − | 4.73777i | 0.0803557 | − | 0.247309i | −0.902806 | − | 0.430049i | \(-0.858496\pi\) |
0.983161 | + | 0.182739i | \(0.0584964\pi\) | |||||||
\(368\) | −50.1310 | − | 36.4223i | −2.61326 | − | 1.89864i | ||||
\(369\) | −6.99131 | − | 5.07948i | −0.363953 | − | 0.264427i | ||||
\(370\) | −2.72044 | + | 8.37264i | −0.141429 | + | 0.435273i | ||||
\(371\) | −1.10388 | − | 3.39738i | −0.0573104 | − | 0.176383i | ||||
\(372\) | 99.5422 | − | 72.3217i | 5.16103 | − | 3.74970i | ||||
\(373\) | −13.6638 | −0.707485 | −0.353743 | − | 0.935343i | \(-0.615091\pi\) | ||||
−0.353743 | + | 0.935343i | \(0.615091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.2465 | −0.632408 | ||||||||
\(376\) | −7.39613 | + | 5.37360i | −0.381426 | + | 0.277122i | ||||
\(377\) | −0.276506 | − | 0.850999i | −0.0142408 | − | 0.0438287i | ||||
\(378\) | −4.40924 | + | 13.5702i | −0.226787 | + | 0.697978i | ||||
\(379\) | 6.76526 | + | 4.91525i | 0.347508 | + | 0.252479i | 0.747823 | − | 0.663898i | \(-0.231099\pi\) |
−0.400315 | + | 0.916378i | \(0.631099\pi\) | |||||||
\(380\) | −2.07618 | − | 1.50843i | −0.106506 | − | 0.0773808i | ||||
\(381\) | −8.79069 | + | 27.0550i | −0.450361 | + | 1.38607i | ||||
\(382\) | 2.12538 | + | 6.54124i | 0.108744 | + | 0.334679i | ||||
\(383\) | 1.60735 | − | 1.16781i | 0.0821316 | − | 0.0596721i | −0.545962 | − | 0.837810i | \(-0.683836\pi\) |
0.628093 | + | 0.778138i | \(0.283836\pi\) | |||||||
\(384\) | −73.7352 | −3.76278 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 47.3292 | 2.40899 | ||||||||
\(387\) | 45.0434 | − | 32.7260i | 2.28969 | − | 1.66355i | ||||
\(388\) | −8.70834 | − | 26.8015i | −0.442099 | − | 1.36064i | ||||
\(389\) | 4.58350 | − | 14.1066i | 0.232393 | − | 0.715231i | −0.765064 | − | 0.643955i | \(-0.777293\pi\) |
0.997457 | − | 0.0712769i | \(-0.0227074\pi\) | |||||||
\(390\) | −1.23211 | − | 0.895181i | −0.0623904 | − | 0.0453293i | ||||
\(391\) | −17.8705 | − | 12.9837i | −0.903751 | − | 0.656614i | ||||
\(392\) | 2.76267 | − | 8.50263i | 0.139536 | − | 0.429448i | ||||
\(393\) | 5.92777 | + | 18.2438i | 0.299016 | + | 0.920278i | ||||
\(394\) | 4.73598 | − | 3.44089i | 0.238595 | − | 0.173350i | ||||
\(395\) | 1.60597 | 0.0808050 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.4630 | 0.575314 | 0.287657 | − | 0.957734i | \(-0.407124\pi\) | ||||
0.287657 | + | 0.957734i | \(0.407124\pi\) | |||||||
\(398\) | 31.8759 | − | 23.1592i | 1.59780 | − | 1.16087i | ||||
\(399\) | 0.942452 | + | 2.90057i | 0.0471816 | + | 0.145210i | ||||
\(400\) | −20.1103 | + | 61.8931i | −1.00551 | + | 3.09465i | ||||
\(401\) | −3.48710 | − | 2.53353i | −0.174138 | − | 0.126518i | 0.497302 | − | 0.867577i | \(-0.334324\pi\) |
−0.671440 | + | 0.741059i | \(0.734324\pi\) | |||||||
\(402\) | −37.9925 | − | 27.6032i | −1.89489 | − | 1.37672i | ||||
\(403\) | 1.15080 | − | 3.54181i | 0.0573256 | − | 0.176430i | ||||
\(404\) | 25.5196 | + | 78.5412i | 1.26965 | + | 3.90757i | ||||
\(405\) | 0.0635733 | − | 0.0461887i | 0.00315898 | − | 0.00229514i | ||||
\(406\) | −5.36399 | −0.266210 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −121.247 | −6.00263 | ||||||||
\(409\) | 7.53358 | − | 5.47347i | 0.372512 | − | 0.270646i | −0.385740 | − | 0.922608i | \(-0.626054\pi\) |
0.758252 | + | 0.651962i | \(0.226054\pi\) | |||||||
\(410\) | −0.658329 | − | 2.02613i | −0.0325126 | − | 0.100063i | ||||
\(411\) | −12.5499 | + | 38.6247i | −0.619043 | + | 1.90522i | ||||
\(412\) | 60.8471 | + | 44.2080i | 2.99772 | + | 2.17797i | ||||
\(413\) | 11.6495 | + | 8.46386i | 0.573235 | + | 0.416479i | ||||
\(414\) | 18.6395 | − | 57.3666i | 0.916083 | − | 2.81941i | ||||
\(415\) | 1.48604 | + | 4.57356i | 0.0729469 | + | 0.224507i | ||||
\(416\) | −6.84201 | + | 4.97101i | −0.335457 | + | 0.243724i | ||||
\(417\) | 41.2535 | 2.02019 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.3424 | −1.28691 | −0.643454 | − | 0.765485i | \(-0.722499\pi\) | ||||
−0.643454 | + | 0.765485i | \(0.722499\pi\) | |||||||
\(420\) | −5.36452 | + | 3.89755i | −0.261762 | + | 0.190181i | ||||
\(421\) | 4.38162 | + | 13.4852i | 0.213547 | + | 0.657230i | 0.999254 | + | 0.0386309i | \(0.0122997\pi\) |
−0.785706 | + | 0.618600i | \(0.787700\pi\) | |||||||
\(422\) | −3.03254 | + | 9.33321i | −0.147622 | + | 0.454334i | ||||
\(423\) | −4.03743 | − | 2.93337i | −0.196307 | − | 0.142625i | ||||
\(424\) | 25.8370 | + | 18.7717i | 1.25476 | + | 0.911634i | ||||
\(425\) | −7.16884 | + | 22.0634i | −0.347740 | + | 1.07023i | ||||
\(426\) | 13.8859 | + | 42.7365i | 0.672775 | + | 2.07059i | ||||
\(427\) | −3.98817 | + | 2.89758i | −0.193001 | + | 0.140223i | ||||
\(428\) | −62.3876 | −3.01562 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.7257 | 0.661911 | ||||||||
\(431\) | −6.14474 | + | 4.46441i | −0.295981 | + | 0.215043i | −0.725858 | − | 0.687845i | \(-0.758557\pi\) |
0.429877 | + | 0.902888i | \(0.358557\pi\) | |||||||
\(432\) | −22.1059 | − | 68.0348i | −1.06357 | − | 3.27333i | ||||
\(433\) | 6.92224 | − | 21.3045i | 0.332662 | − | 1.02383i | −0.635201 | − | 0.772347i | \(-0.719083\pi\) |
0.967862 | − | 0.251480i | \(-0.0809174\pi\) | |||||||
\(434\) | −18.0610 | − | 13.1221i | −0.866956 | − | 0.629880i | ||||
\(435\) | 2.00572 | + | 1.45724i | 0.0961669 | + | 0.0698694i | ||||
\(436\) | 25.8797 | − | 79.6496i | 1.23941 | − | 3.81452i | ||||
\(437\) | −1.53502 | − | 4.72431i | −0.0734300 | − | 0.225994i | ||||
\(438\) | −10.1772 | + | 7.39419i | −0.486287 | + | 0.353308i | ||||
\(439\) | 15.4051 | 0.735244 | 0.367622 | − | 0.929975i | \(-0.380172\pi\) | ||||
0.367622 | + | 0.929975i | \(0.380172\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.88032 | 0.232396 | ||||||||
\(442\) | −4.76431 | + | 3.46147i | −0.226615 | + | 0.164646i | ||||
\(443\) | 6.55423 | + | 20.1718i | 0.311401 | + | 0.958393i | 0.977211 | + | 0.212272i | \(0.0680861\pi\) |
−0.665810 | + | 0.746121i | \(0.731914\pi\) | |||||||
\(444\) | −33.6879 | + | 103.681i | −1.59875 | + | 4.92046i | ||||
\(445\) | −1.87658 | − | 1.36342i | −0.0889586 | − | 0.0646322i | ||||
\(446\) | 10.5861 | + | 7.69125i | 0.501267 | + | 0.364191i | ||||
\(447\) | −0.868682 | + | 2.67353i | −0.0410873 | + | 0.126454i | ||||
\(448\) | 7.29061 | + | 22.4382i | 0.344449 | + | 1.06010i | ||||
\(449\) | 9.41020 | − | 6.83691i | 0.444095 | − | 0.322654i | −0.343165 | − | 0.939275i | \(-0.611499\pi\) |
0.787260 | + | 0.616621i | \(0.211499\pi\) | |||||||
\(450\) | −63.3490 | −2.98630 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −31.4375 | −1.47869 | ||||||||
\(453\) | 3.12359 | − | 2.26942i | 0.146759 | − | 0.106627i | ||||
\(454\) | 18.9876 | + | 58.4380i | 0.891134 | + | 2.74263i | ||||
\(455\) | −0.0620190 | + | 0.190875i | −0.00290750 | + | 0.00894836i | ||||
\(456\) | −22.0588 | − | 16.0266i | −1.03300 | − | 0.750516i | ||||
\(457\) | −25.5630 | − | 18.5726i | −1.19579 | − | 0.868790i | −0.201923 | − | 0.979401i | \(-0.564719\pi\) |
−0.993864 | + | 0.110612i | \(0.964719\pi\) | |||||||
\(458\) | −18.9396 | + | 58.2902i | −0.884992 | + | 2.72372i | ||||
\(459\) | −7.88022 | − | 24.2528i | −0.367817 | − | 1.13203i | ||||
\(460\) | 8.73748 | − | 6.34815i | 0.407387 | − | 0.295984i | ||||
\(461\) | −8.86324 | −0.412802 | −0.206401 | − | 0.978467i | \(-0.566175\pi\) | ||||
−0.206401 | + | 0.978467i | \(0.566175\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.6132 | −1.19035 | −0.595173 | − | 0.803597i | \(-0.702917\pi\) | ||||
−0.595173 | + | 0.803597i | \(0.702917\pi\) | |||||||
\(464\) | 21.7565 | − | 15.8070i | 1.01002 | − | 0.733823i | ||||
\(465\) | 3.18854 | + | 9.81331i | 0.147865 | + | 0.455081i | ||||
\(466\) | −0.490577 | + | 1.50984i | −0.0227255 | + | 0.0699420i | ||||
\(467\) | −16.6174 | − | 12.0732i | −0.768959 | − | 0.558682i | 0.132686 | − | 0.991158i | \(-0.457640\pi\) |
−0.901645 | + | 0.432476i | \(0.857640\pi\) | |||||||
\(468\) | −9.44907 | − | 6.86515i | −0.436784 | − | 0.317342i | ||||
\(469\) | −1.91238 | + | 5.88569i | −0.0883053 | + | 0.271776i | ||||
\(470\) | −0.380181 | − | 1.17008i | −0.0175364 | − | 0.0539716i | ||||
\(471\) | 12.2108 | − | 8.87167i | 0.562644 | − | 0.408785i | ||||
\(472\) | −128.735 | −5.92551 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 27.3814 | 1.25767 | ||||||||
\(475\) | −4.22062 | + | 3.06646i | −0.193655 | + | 0.140699i | ||||
\(476\) | 7.92330 | + | 24.3854i | 0.363164 | + | 1.11770i | ||||
\(477\) | −5.38727 | + | 16.5803i | −0.246666 | + | 0.759160i | ||||
\(478\) | 32.7430 | + | 23.7892i | 1.49763 | + | 1.08809i | ||||
\(479\) | 22.2874 | + | 16.1927i | 1.01834 | + | 0.739866i | 0.965941 | − | 0.258761i | \(-0.0833141\pi\) |
0.0523962 | + | 0.998626i | \(0.483314\pi\) | |||||||
\(480\) | 7.24100 | − | 22.2855i | 0.330505 | − | 1.01719i | ||||
\(481\) | 1.01963 | + | 3.13810i | 0.0464911 | + | 0.143085i | ||||
\(482\) | 39.9654 | − | 29.0365i | 1.82037 | − | 1.32258i | ||||
\(483\) | −12.8351 | −0.584017 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.36327 | 0.107310 | ||||||||
\(486\) | −33.5467 | + | 24.3731i | −1.52171 | + | 1.10559i | ||||
\(487\) | −3.73952 | − | 11.5091i | −0.169454 | − | 0.521525i | 0.829883 | − | 0.557937i | \(-0.188407\pi\) |
−0.999337 | + | 0.0364123i | \(0.988407\pi\) | |||||||
\(488\) | 13.6190 | − | 41.9150i | 0.616503 | − | 1.89740i | ||||
\(489\) | −21.4051 | − | 15.5517i | −0.967971 | − | 0.703272i | ||||
\(490\) | 0.973343 | + | 0.707175i | 0.0439711 | + | 0.0319469i | ||||
\(491\) | −12.1712 | + | 37.4590i | −0.549277 | + | 1.69050i | 0.161320 | + | 0.986902i | \(0.448425\pi\) |
−0.710597 | + | 0.703599i | \(0.751575\pi\) | |||||||
\(492\) | −8.15226 | − | 25.0901i | −0.367532 | − | 1.13115i | ||||
\(493\) | 7.75569 | − | 5.63484i | 0.349299 | − | 0.253780i | ||||
\(494\) | −1.32432 | −0.0595842 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 111.925 | 5.02560 | ||||||||
\(497\) | 4.79072 | − | 3.48066i | 0.214893 | − | 0.156129i | ||||
\(498\) | 25.3367 | + | 77.9783i | 1.13536 | + | 3.49429i | ||||
\(499\) | −10.7486 | + | 33.0808i | −0.481173 | + | 1.48090i | 0.356274 | + | 0.934382i | \(0.384047\pi\) |
−0.837447 | + | 0.546518i | \(0.815953\pi\) | |||||||
\(500\) | −18.7314 | − | 13.6092i | −0.837693 | − | 0.608620i | ||||
\(501\) | 45.4482 | + | 33.0200i | 2.03048 | + | 1.47523i | ||||
\(502\) | 8.82520 | − | 27.1612i | 0.393888 | − | 1.21226i | ||||
\(503\) | 0.998818 | + | 3.07404i | 0.0445351 | + | 0.137065i | 0.970852 | − | 0.239681i | \(-0.0770429\pi\) |
−0.926317 | + | 0.376746i | \(0.877043\pi\) | |||||||
\(504\) | −35.2982 | + | 25.6457i | −1.57231 | + | 1.14235i | ||||
\(505\) | −6.92550 | −0.308181 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.9227 | 1.59538 | ||||||||
\(508\) | −43.5109 | + | 31.6125i | −1.93048 | + | 1.40258i | ||||
\(509\) | −4.08573 | − | 12.5746i | −0.181097 | − | 0.557359i | 0.818763 | − | 0.574132i | \(-0.194661\pi\) |
−0.999859 | + | 0.0167737i | \(0.994661\pi\) | |||||||
\(510\) | 5.04214 | − | 15.5181i | 0.223270 | − | 0.687154i | ||||
\(511\) | 1.34116 | + | 0.974409i | 0.0593294 | + | 0.0431053i | ||||
\(512\) | −9.58778 | − | 6.96593i | −0.423724 | − | 0.307854i | ||||
\(513\) | 1.77211 | − | 5.45399i | 0.0782406 | − | 0.240800i | ||||
\(514\) | −16.2622 | − | 50.0501i | −0.717297 | − | 2.20761i | ||||
\(515\) | −5.10269 | + | 3.70732i | −0.224851 | + | 0.163364i | ||||
\(516\) | 169.969 | 7.48245 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 19.7800 | 0.869082 | ||||||||
\(519\) | 24.6332 | − | 17.8971i | 1.08128 | − | 0.785594i | ||||
\(520\) | −0.554463 | − | 1.70646i | −0.0243148 | − | 0.0748332i | ||||
\(521\) | 2.25656 | − | 6.94499i | 0.0988619 | − | 0.304266i | −0.889379 | − | 0.457171i | \(-0.848863\pi\) |
0.988241 | + | 0.152905i | \(0.0488629\pi\) | |||||||
\(522\) | 21.1784 | + | 15.3870i | 0.926955 | + | 0.673472i | ||||
\(523\) | −6.77962 | − | 4.92568i | −0.296452 | − | 0.215385i | 0.429609 | − | 0.903015i | \(-0.358651\pi\) |
−0.726061 | + | 0.687630i | \(0.758651\pi\) | |||||||
\(524\) | −11.2070 | + | 34.4917i | −0.489581 | + | 1.50678i | ||||
\(525\) | 4.16551 | + | 12.8201i | 0.181798 | + | 0.559516i | ||||
\(526\) | −46.3378 | + | 33.6664i | −2.02042 | + | 1.46792i | ||||
\(527\) | 39.8988 | 1.73802 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.09483 | −0.0910794 | ||||||||
\(530\) | −3.47699 | + | 2.52618i | −0.151031 | + | 0.109730i | ||||
\(531\) | −21.7160 | − | 66.8351i | −0.942396 | − | 2.90040i | ||||
\(532\) | −1.78180 | + | 5.48381i | −0.0772507 | + | 0.237753i | ||||
\(533\) | −0.645985 | − | 0.469336i | −0.0279807 | − | 0.0203292i | ||||
\(534\) | −31.9953 | − | 23.2460i | −1.38457 | − | 1.00595i | ||||
\(535\) | 1.61674 | − | 4.97581i | 0.0698977 | − | 0.215123i | ||||
\(536\) | −17.0970 | − | 52.6192i | −0.738479 | − | 2.27280i | ||||
\(537\) | 38.2638 | − | 27.8003i | 1.65120 | − | 1.19967i | ||||
\(538\) | 62.5963 | 2.69872 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 12.4682 | 0.536548 | ||||||||
\(541\) | 3.07239 | − | 2.23222i | 0.132092 | − | 0.0959706i | −0.519777 | − | 0.854302i | \(-0.673985\pi\) |
0.651869 | + | 0.758331i | \(0.273985\pi\) | |||||||
\(542\) | 22.4063 | + | 68.9595i | 0.962433 | + | 2.96206i | ||||
\(543\) | 17.6132 | − | 54.2079i | 0.755855 | − | 2.32628i | ||||
\(544\) | −73.3034 | − | 53.2580i | −3.14286 | − | 2.28342i | ||||
\(545\) | 5.68191 | + | 4.12815i | 0.243386 | + | 0.176830i | ||||
\(546\) | −1.05741 | + | 3.25438i | −0.0452530 | + | 0.139275i | ||||
\(547\) | 2.80892 | + | 8.64496i | 0.120101 | + | 0.369632i | 0.992977 | − | 0.118310i | \(-0.0377477\pi\) |
−0.872876 | + | 0.487942i | \(0.837748\pi\) | |||||||
\(548\) | −62.1178 | + | 45.1312i | −2.65354 | + | 1.92791i | ||||
\(549\) | 24.0583 | 1.02678 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.15583 | 0.0918416 | ||||||||
\(552\) | 92.8332 | − | 67.4473i | 3.95125 | − | 2.87075i | ||||
\(553\) | −1.11504 | − | 3.43173i | −0.0474161 | − | 0.145932i | ||||
\(554\) | −11.7371 | + | 36.1230i | −0.498661 | + | 1.53472i | ||||
\(555\) | −7.39619 | − | 5.37365i | −0.313951 | − | 0.228099i | ||||
\(556\) | 63.0984 | + | 45.8436i | 2.67597 | + | 1.94420i | ||||
\(557\) | 5.63561 | − | 17.3446i | 0.238788 | − | 0.734915i | −0.757808 | − | 0.652478i | \(-0.773730\pi\) |
0.996596 | − | 0.0824374i | \(-0.0262704\pi\) | |||||||
\(558\) | 33.6678 | + | 103.619i | 1.42527 | + | 4.38654i | ||||
\(559\) | 4.16194 | − | 3.02382i | 0.176031 | − | 0.127894i | ||||
\(560\) | −6.03187 | −0.254893 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.71809 | −0.199021 | ||||||||
\(563\) | 12.6000 | − | 9.15442i | 0.531026 | − | 0.385813i | −0.289716 | − | 0.957113i | \(-0.593561\pi\) |
0.820741 | + | 0.571300i | \(0.193561\pi\) | |||||||
\(564\) | −4.70787 | − | 14.4893i | −0.198237 | − | 0.610112i | ||||
\(565\) | 0.814684 | − | 2.50734i | 0.0342740 | − | 0.105485i | ||||
\(566\) | 10.2027 | + | 7.41270i | 0.428852 | + | 0.311579i | ||||
\(567\) | −0.142838 | − | 0.103778i | −0.00599864 | − | 0.00435827i | ||||
\(568\) | −16.3596 | + | 50.3496i | −0.686433 | + | 2.11262i | ||||
\(569\) | 7.54788 | + | 23.2300i | 0.316423 | + | 0.973851i | 0.975165 | + | 0.221482i | \(0.0710892\pi\) |
−0.658741 | + | 0.752370i | \(0.728911\pi\) | |||||||
\(570\) | 2.96854 | − | 2.15677i | 0.124338 | − | 0.0903371i | ||||
\(571\) | −14.9541 | −0.625808 | −0.312904 | − | 0.949785i | \(-0.601302\pi\) | ||||
−0.312904 | + | 0.949785i | \(0.601302\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.14247 | −0.298381 | ||||||||
\(574\) | −3.87247 | + | 2.81351i | −0.161634 | + | 0.117434i | ||||
\(575\) | −6.78459 | − | 20.8808i | −0.282937 | − | 0.870790i | ||||
\(576\) | 35.5805 | − | 109.506i | 1.48252 | − | 4.56273i | ||||
\(577\) | 17.3682 | + | 12.6187i | 0.723046 | + | 0.525324i | 0.887356 | − | 0.461085i | \(-0.152540\pi\) |
−0.164310 | + | 0.986409i | \(0.552540\pi\) | |||||||
\(578\) | −13.8657 | − | 10.0740i | −0.576736 | − | 0.419023i | ||||
\(579\) | −15.1882 | + | 46.7444i | −0.631199 | + | 1.94263i | ||||
\(580\) | 1.44842 | + | 4.45778i | 0.0601423 | + | 0.185099i | ||||
\(581\) | 8.74129 | − | 6.35092i | 0.362650 | − | 0.263481i | ||||
\(582\) | 40.2932 | 1.67021 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −14.8207 | −0.613286 | ||||||||
\(585\) | 0.792408 | − | 0.575718i | 0.0327620 | − | 0.0238030i | ||||
\(586\) | 12.1200 | + | 37.3016i | 0.500674 | + | 1.54092i | ||||
\(587\) | −6.38924 | + | 19.6641i | −0.263712 | + | 0.811623i | 0.728275 | + | 0.685285i | \(0.240322\pi\) |
−0.991987 | + | 0.126338i | \(0.959678\pi\) | |||||||
\(588\) | 12.0532 | + | 8.75713i | 0.497064 | + | 0.361138i | ||||
\(589\) | 7.25887 | + | 5.27388i | 0.299097 | + | 0.217306i | ||||
\(590\) | 5.35353 | − | 16.4765i | 0.220401 | − | 0.678326i | ||||
\(591\) | 1.87858 | + | 5.78167i | 0.0772744 | + | 0.237826i | ||||
\(592\) | −80.2282 | + | 58.2892i | −3.29736 | + | 2.39567i | ||||
\(593\) | 3.30237 | 0.135612 | 0.0678060 | − | 0.997699i | \(-0.478400\pi\) | ||||
0.0678060 | + | 0.997699i | \(0.478400\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.15022 | −0.0881505 | ||||||||
\(596\) | −4.29967 | + | 3.12390i | −0.176121 | + | 0.127960i | ||||
\(597\) | 12.6439 | + | 38.9140i | 0.517481 | + | 1.59264i | ||||
\(598\) | 1.72226 | − | 5.30057i | 0.0704285 | − | 0.216757i | ||||
\(599\) | −31.4880 | − | 22.8773i | −1.28656 | − | 0.934743i | −0.286833 | − | 0.957981i | \(-0.592602\pi\) |
−0.999730 | + | 0.0232380i | \(0.992602\pi\) | |||||||
\(600\) | −97.4969 | − | 70.8356i | −3.98029 | − | 2.89185i | ||||
\(601\) | 13.7137 | − | 42.2063i | 0.559392 | − | 1.72163i | −0.124663 | − | 0.992199i | \(-0.539785\pi\) |
0.684054 | − | 0.729431i | \(-0.260215\pi\) | |||||||
\(602\) | −9.52984 | − | 29.3298i | −0.388407 | − | 1.19539i | ||||
\(603\) | 24.4341 | − | 17.7524i | 0.995034 | − | 0.722935i | ||||
\(604\) | 7.29954 | 0.297014 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −118.078 | −4.79660 | ||||||||
\(607\) | 15.2952 | − | 11.1126i | 0.620812 | − | 0.451046i | −0.232393 | − | 0.972622i | \(-0.574656\pi\) |
0.853205 | + | 0.521576i | \(0.174656\pi\) | |||||||
\(608\) | −6.29652 | − | 19.3787i | −0.255358 | − | 0.785910i | ||||
\(609\) | 1.72133 | − | 5.29771i | 0.0697519 | − | 0.214674i | ||||
\(610\) | 4.79824 | + | 3.48612i | 0.194275 | + | 0.141149i | ||||
\(611\) | −0.373052 | − | 0.271038i | −0.0150921 | − | 0.0109650i | ||||
\(612\) | 38.6682 | − | 119.009i | 1.56307 | − | 4.81064i | ||||
\(613\) | −2.99164 | − | 9.20733i | −0.120831 | − | 0.371881i | 0.872287 | − | 0.488994i | \(-0.162636\pi\) |
−0.993119 | + | 0.117113i | \(0.962636\pi\) | |||||||
\(614\) | −5.15415 | + | 3.74471i | −0.208004 | + | 0.151124i | ||||
\(615\) | 2.21236 | 0.0892108 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.2775 | −1.05789 | −0.528947 | − | 0.848655i | \(-0.677413\pi\) | ||||
−0.528947 | + | 0.848655i | \(0.677413\pi\) | |||||||
\(618\) | −86.9997 | + | 63.2090i | −3.49964 | + | 2.54264i | ||||
\(619\) | −7.66219 | − | 23.5818i | −0.307970 | − | 0.947833i | −0.978552 | − | 0.205998i | \(-0.933956\pi\) |
0.670583 | − | 0.741835i | \(-0.266044\pi\) | |||||||
\(620\) | −6.02824 | + | 18.5530i | −0.242100 | + | 0.745107i | ||||
\(621\) | 19.5249 | + | 14.1856i | 0.783506 | + | 0.569250i | ||||
\(622\) | 43.7496 | + | 31.7859i | 1.75420 | + | 1.27450i | ||||
\(623\) | −1.61050 | + | 4.95662i | −0.0645235 | + | 0.198583i | ||||
\(624\) | −5.30137 | − | 16.3159i | −0.212225 | − | 0.653160i | ||||
\(625\) | −17.8533 | + | 12.9712i | −0.714132 | + | 0.518847i | ||||
\(626\) | 50.6931 | 2.02611 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 28.5355 | 1.13869 | ||||||||
\(629\) | −28.5995 | + | 20.7787i | −1.14034 | + | 0.828503i | ||||
\(630\) | −1.81442 | − | 5.58422i | −0.0722884 | − | 0.222481i | ||||
\(631\) | −3.64972 | + | 11.2327i | −0.145293 | + | 0.447166i | −0.997049 | − | 0.0767733i | \(-0.975538\pi\) |
0.851755 | + | 0.523940i | \(0.175538\pi\) | |||||||
\(632\) | 26.0982 | + | 18.9615i | 1.03813 | + | 0.754247i | ||||
\(633\) | −8.24474 | − | 5.99015i | −0.327699 | − | 0.238087i | ||||
\(634\) | 3.51010 | − | 10.8030i | 0.139404 | − | 0.429041i | ||||
\(635\) | −1.39374 | − | 4.28949i | −0.0553089 | − | 0.170223i | ||||
\(636\) | −43.0565 | + | 31.2824i | −1.70730 | + | 1.24043i | ||||
\(637\) | 0.450933 | 0.0178666 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.8995 | −1.14325 | ||||||||
\(640\) | 9.45783 | − | 6.87151i | 0.373853 | − | 0.271620i | ||||
\(641\) | −6.95851 | − | 21.4161i | −0.274845 | − | 0.845885i | −0.989260 | − | 0.146164i | \(-0.953307\pi\) |
0.714416 | − | 0.699722i | \(-0.246693\pi\) | |||||||
\(642\) | 27.5651 | − | 84.8365i | 1.08791 | − | 3.34823i | ||||
\(643\) | −11.2374 | − | 8.16442i | −0.443158 | − | 0.321973i | 0.343730 | − | 0.939068i | \(-0.388309\pi\) |
−0.786889 | + | 0.617095i | \(0.788309\pi\) | |||||||
\(644\) | −19.6316 | − | 14.2632i | −0.773593 | − | 0.562048i | ||||
\(645\) | −4.40464 | + | 13.5561i | −0.173432 | + | 0.533770i | ||||
\(646\) | −4.38447 | − | 13.4940i | −0.172505 | − | 0.530915i | ||||
\(647\) | −41.1074 | + | 29.8663i | −1.61610 | + | 1.17417i | −0.779320 | + | 0.626627i | \(0.784435\pi\) |
−0.836780 | + | 0.547539i | \(0.815565\pi\) | |||||||
\(648\) | 1.57846 | 0.0620078 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.85334 | −0.229587 | ||||||||
\(651\) | 18.7558 | − | 13.6269i | 0.735099 | − | 0.534081i | ||||
\(652\) | −15.4576 | − | 47.5735i | −0.605364 | − | 1.86312i | ||||
\(653\) | −1.48764 | + | 4.57849i | −0.0582159 | + | 0.179170i | −0.975936 | − | 0.218058i | \(-0.930028\pi\) |
0.917720 | + | 0.397228i | \(0.130028\pi\) | |||||||
\(654\) | 96.8753 | + | 70.3840i | 3.78812 | + | 2.75223i | ||||
\(655\) | −2.46051 | − | 1.78766i | −0.0961401 | − | 0.0698499i | ||||
\(656\) | 7.41577 | − | 22.8234i | 0.289537 | − | 0.891104i | ||||
\(657\) | −2.50008 | − | 7.69444i | −0.0975373 | − | 0.300189i | ||||
\(658\) | −2.23632 | + | 1.62478i | −0.0871810 | + | 0.0633407i | ||||
\(659\) | −28.0409 | −1.09232 | −0.546159 | − | 0.837681i | \(-0.683911\pi\) | ||||
−0.546159 | + | 0.837681i | \(0.683911\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.7390 | −1.62346 | −0.811730 | − | 0.584033i | \(-0.801474\pi\) | ||||
−0.811730 | + | 0.584033i | \(0.801474\pi\) | |||||||
\(662\) | 0.149300 | − | 0.108473i | 0.00580273 | − | 0.00421593i | ||||
\(663\) | −1.88981 | − | 5.81625i | −0.0733943 | − | 0.225884i | ||||
\(664\) | −29.8502 | + | 91.8695i | −1.15841 | + | 3.56523i | ||||
\(665\) | −0.391195 | − | 0.284220i | −0.0151699 | − | 0.0110216i | ||||
\(666\) | −78.0965 | − | 56.7404i | −3.02618 | − | 2.19865i | ||||
\(667\) | −2.80362 | + | 8.62866i | −0.108557 | + | 0.334103i | ||||
\(668\) | 32.8201 | + | 101.010i | 1.26985 | + | 3.90819i | ||||
\(669\) | −10.9934 | + | 7.98714i | −0.425028 | + | 0.308801i | ||||
\(670\) | 7.44559 | 0.287648 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −52.6484 | −2.03096 | ||||||||
\(673\) | 23.2792 | − | 16.9133i | 0.897348 | − | 0.651962i | −0.0404352 | − | 0.999182i | \(-0.512874\pi\) |
0.937784 | + | 0.347220i | \(0.112874\pi\) | |||||||
\(674\) | 18.1653 | + | 55.9070i | 0.699700 | + | 2.15346i | ||||
\(675\) | 7.83249 | − | 24.1059i | 0.301473 | − | 0.927838i | ||||
\(676\) | 54.9446 | + | 39.9196i | 2.11326 | + | 1.53537i | ||||
\(677\) | 9.93971 | + | 7.22162i | 0.382014 | + | 0.277549i | 0.762175 | − | 0.647371i | \(-0.224131\pi\) |
−0.380161 | + | 0.924920i | \(0.624131\pi\) | |||||||
\(678\) | 13.8902 | − | 42.7496i | 0.533450 | − | 1.64179i | ||||
\(679\) | −1.64083 | − | 5.04996i | −0.0629694 | − | 0.193800i | ||||
\(680\) | 15.5521 | − | 11.2992i | 0.596394 | − | 0.433306i | ||||
\(681\) | −63.8092 | −2.44517 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.5940 | 1.17065 | 0.585323 | − | 0.810800i | \(-0.300968\pi\) | ||||
0.585323 | + | 0.810800i | \(0.300968\pi\) | |||||||
\(684\) | 22.7657 | − | 16.5403i | 0.870470 | − | 0.632433i | ||||
\(685\) | −1.98976 | − | 6.12384i | −0.0760247 | − | 0.233980i | ||||
\(686\) | 0.835334 | − | 2.57089i | 0.0318932 | − | 0.0981571i | ||||
\(687\) | −51.4922 | − | 37.4113i | −1.96455 | − | 1.42733i | ||||
\(688\) | 125.085 | + | 90.8795i | 4.76881 | + | 3.46475i | ||||
\(689\) | −0.497774 | + | 1.53199i | −0.0189637 | + | 0.0583642i | ||||
\(690\) | 4.77188 | + | 14.6863i | 0.181662 | + | 0.559099i | ||||
\(691\) | 13.8440 | − | 10.0583i | 0.526651 | − | 0.382634i | −0.292453 | − | 0.956280i | \(-0.594471\pi\) |
0.819103 | + | 0.573646i | \(0.194471\pi\) | |||||||
\(692\) | 57.5655 | 2.18831 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 64.7013 | 2.45603 | ||||||||
\(695\) | −5.29148 | + | 3.84449i | −0.200717 | + | 0.145830i | ||||
\(696\) | 15.3890 | + | 47.3626i | 0.583320 | + | 1.79528i | ||||
\(697\) | 2.64355 | − | 8.13601i | 0.100132 | − | 0.308173i | ||||
\(698\) | 57.7679 | + | 41.9709i | 2.18655 | + | 1.58862i | ||||
\(699\) | −1.33376 | − | 0.969031i | −0.0504473 | − | 0.0366521i | ||||
\(700\) | −7.87531 | + | 24.2377i | −0.297659 | + | 0.916099i | ||||
\(701\) | 4.20065 | + | 12.9283i | 0.158657 | + | 0.488295i | 0.998513 | − | 0.0545140i | \(-0.0173609\pi\) |
−0.839856 | + | 0.542809i | \(0.817361\pi\) | |||||||
\(702\) | 5.20536 | − | 3.78192i | 0.196464 | − | 0.142739i | ||||
\(703\) | −7.94974 | −0.299830 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.27762 | 0.0481180 | ||||||||
\(706\) | 9.71395 | − | 7.05760i | 0.365589 | − | 0.265616i | ||||
\(707\) | 4.80842 | + | 14.7988i | 0.180839 | + | 0.556566i | ||||
\(708\) | 66.2942 | − | 204.032i | 2.49149 | − | 7.66801i | ||||
\(709\) | −23.9465 | − | 17.3982i | −0.899330 | − | 0.653401i | 0.0389641 | − | 0.999241i | \(-0.487594\pi\) |
−0.938294 | + | 0.345839i | \(0.887594\pi\) | |||||||
\(710\) | −5.76379 | − | 4.18764i | −0.216311 | − | 0.157159i | ||||
\(711\) | −5.44173 | + | 16.7479i | −0.204081 | + | 0.628096i | ||||
\(712\) | −14.3982 | − | 44.3132i | −0.539596 | − | 1.66071i | ||||
\(713\) | −30.5486 | + | 22.1949i | −1.14405 | + | 0.831204i | ||||
\(714\) | −36.6608 | −1.37200 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 89.4190 | 3.34174 | ||||||||
\(717\) | −34.0026 | + | 24.7044i | −1.26985 | + | 0.922601i | ||||
\(718\) | −12.1395 | − | 37.3615i | −0.453042 | − | 1.39432i | ||||
\(719\) | 14.0728 | − | 43.3118i | 0.524828 | − | 1.61526i | −0.239826 | − | 0.970816i | \(-0.577091\pi\) |
0.764655 | − | 0.644440i | \(-0.222909\pi\) | |||||||
\(720\) | 23.8154 | + | 17.3029i | 0.887548 | + | 0.644841i | ||||
\(721\) | 11.4649 | + | 8.32970i | 0.426973 | + | 0.310214i | ||||
\(722\) | −14.8854 | + | 45.8124i | −0.553976 | + | 1.70496i | ||||
\(723\) | 15.8527 | + | 48.7895i | 0.589568 | + | 1.81450i | ||||
\(724\) | 87.1793 | − | 63.3394i | 3.23999 | − | 2.35399i | ||||
\(725\) | 9.52850 | 0.353880 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.8796 | −1.62740 | −0.813702 | − | 0.581283i | \(-0.802551\pi\) | ||||
−0.813702 | + | 0.581283i | \(0.802551\pi\) | |||||||
\(728\) | −3.26150 | + | 2.36962i | −0.120879 | + | 0.0878238i | ||||
\(729\) | −13.4703 | − | 41.4574i | −0.498901 | − | 1.53546i | ||||
\(730\) | 0.616330 | − | 1.89687i | 0.0228114 | − | 0.0702062i | ||||
\(731\) | 44.5898 | + | 32.3964i | 1.64921 | + | 1.19822i | ||||
\(732\) | 59.4178 | + | 43.1696i | 2.19615 | + | 1.59559i | ||||
\(733\) | 4.35337 | − | 13.3983i | 0.160795 | − | 0.494877i | −0.837907 | − | 0.545814i | \(-0.816221\pi\) |
0.998702 | + | 0.0509365i | \(0.0162206\pi\) | |||||||
\(734\) | 4.16128 | + | 12.8071i | 0.153596 | + | 0.472719i | ||||
\(735\) | −1.01079 | + | 0.734380i | −0.0372835 | + | 0.0270880i | ||||
\(736\) | 85.7513 | 3.16083 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 23.3603 | 0.859904 | ||||||||
\(739\) | 31.9542 | − | 23.2161i | 1.17545 | − | 0.854016i | 0.183801 | − | 0.982963i | \(-0.441160\pi\) |
0.991651 | + | 0.128947i | \(0.0411598\pi\) | |||||||
\(740\) | −5.34112 | − | 16.4383i | −0.196343 | − | 0.604283i | ||||
\(741\) | 0.424983 | − | 1.30796i | 0.0156121 | − | 0.0480492i | ||||
\(742\) | 7.81220 | + | 5.67589i | 0.286795 | + | 0.208369i | ||||
\(743\) | −15.0608 | − | 10.9423i | −0.552528 | − | 0.401435i | 0.276189 | − | 0.961103i | \(-0.410928\pi\) |
−0.828717 | + | 0.559668i | \(0.810928\pi\) | |||||||
\(744\) | −64.0484 | + | 197.121i | −2.34813 | + | 7.22679i | ||||
\(745\) | −0.137727 | − | 0.423881i | −0.00504593 | − | 0.0155298i | ||||
\(746\) | 29.8818 | − | 21.7104i | 1.09405 | − | 0.794875i | ||||
\(747\) | −52.7310 | −1.92933 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.7551 | −0.429523 | ||||||||
\(750\) | 26.7823 | − | 19.4585i | 0.977952 | − | 0.710524i | ||||
\(751\) | −4.88432 | − | 15.0324i | −0.178231 | − | 0.548539i | 0.821535 | − | 0.570158i | \(-0.193118\pi\) |
−0.999766 | + | 0.0216187i | \(0.993118\pi\) | |||||||
\(752\) | 4.28256 | − | 13.1804i | 0.156169 | − | 0.480638i | ||||
\(753\) | 23.9935 | + | 17.4323i | 0.874373 | + | 0.635269i | ||||
\(754\) | 1.95685 | + | 1.42174i | 0.0712643 | + | 0.0517765i | ||||
\(755\) | −0.189164 | + | 0.582185i | −0.00688437 | + | 0.0211879i | ||||
\(756\) | −8.65679 | − | 26.6429i | −0.314844 | − | 0.968992i | ||||
\(757\) | 2.92145 | − | 2.12256i | 0.106182 | − | 0.0771458i | −0.533427 | − | 0.845846i | \(-0.679096\pi\) |
0.639609 | + | 0.768700i | \(0.279096\pi\) | |||||||
\(758\) | −22.6050 | −0.821051 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.32297 | 0.156811 | ||||||||
\(761\) | −32.0224 | + | 23.2657i | −1.16081 | + | 0.843380i | −0.989881 | − | 0.141903i | \(-0.954678\pi\) |
−0.170932 | + | 0.985283i | \(0.554678\pi\) | |||||||
\(762\) | −23.7630 | − | 73.1349i | −0.860841 | − | 2.64940i | ||||
\(763\) | 4.87628 | − | 15.0076i | 0.176533 | − | 0.543313i | ||||
\(764\) | −10.9246 | − | 7.93718i | −0.395238 | − | 0.287157i | ||||
\(765\) | 8.48964 | + | 6.16808i | 0.306943 | + | 0.223007i | ||||
\(766\) | −1.65963 | + | 5.10782i | −0.0599649 | + | 0.184553i | ||||
\(767\) | −2.00652 | − | 6.17545i | −0.0724514 | − | 0.222982i | ||||
\(768\) | 54.0918 | − | 39.3000i | 1.95187 | − | 1.41812i | ||||
\(769\) | −10.5472 | −0.380341 | −0.190171 | − | 0.981751i | \(-0.560904\pi\) | ||||
−0.190171 | + | 0.981751i | \(0.560904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54.6503 | 1.96818 | ||||||||
\(772\) | −75.1761 | + | 54.6187i | −2.70565 | + | 1.96577i | ||||
\(773\) | 12.8437 | + | 39.5289i | 0.461957 | + | 1.42176i | 0.862770 | + | 0.505597i | \(0.168728\pi\) |
−0.400813 | + | 0.916160i | \(0.631272\pi\) | |||||||
\(774\) | −46.5086 | + | 143.139i | −1.67172 | + | 5.14502i | ||||
\(775\) | 32.0833 | + | 23.3099i | 1.15246 | + | 0.837315i | ||||
\(776\) | 38.4049 | + | 27.9028i | 1.37866 | + | 1.00165i | ||||
\(777\) | −6.34749 | + | 19.5356i | −0.227715 | + | 0.700835i | ||||
\(778\) | 12.3901 | + | 38.1328i | 0.444207 | + | 1.36713i | ||||
\(779\) | 1.55638 | − | 1.13077i | 0.0557630 | − | 0.0405142i | ||||
\(780\) | 2.99010 | 0.107063 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 59.7114 | 2.13527 | ||||||||
\(783\) | −8.47367 | + | 6.15648i | −0.302824 | + | 0.220015i | ||||
\(784\) | 4.18797 | + | 12.8893i | 0.149570 | + | 0.460331i | ||||
\(785\) | −0.739482 | + | 2.27589i | −0.0263932 | + | 0.0812300i | ||||
\(786\) | −41.9512 | − | 30.4793i | −1.49635 | − | 1.08716i | ||||
\(787\) | −9.34204 | − | 6.78739i | −0.333008 | − | 0.241944i | 0.408698 | − | 0.912670i | \(-0.365983\pi\) |
−0.741706 | + | 0.670725i | \(0.765983\pi\) | |||||||
\(788\) | −3.55164 | + | 10.9308i | −0.126522 | + | 0.389394i | ||||
\(789\) | −18.3804 | − | 56.5690i | −0.654359 | − | 2.01391i | ||||
\(790\) | −3.51214 | + | 2.55172i | −0.124956 | + | 0.0907862i | ||||
\(791\) | −5.92347 | −0.210614 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.22294 | 0.0789390 | ||||||||
\(794\) | −25.0689 | + | 18.2136i | −0.889662 | + | 0.646377i | ||||
\(795\) | −1.37919 | − | 4.24470i | −0.0489147 | − | 0.150544i | ||||
\(796\) | −23.9046 | + | 73.5707i | −0.847275 | + | 2.60765i | ||||
\(797\) | −34.2340 | − | 24.8724i | −1.21263 | − | 0.881027i | −0.217163 | − | 0.976135i | \(-0.569680\pi\) |
−0.995467 | + | 0.0951081i | \(0.969680\pi\) | |||||||
\(798\) | −6.66979 | − | 4.84588i | −0.236108 | − | 0.171542i | ||||
\(799\) | 1.52663 | − | 4.69849i | 0.0540084 | − | 0.166221i | ||||
\(800\) | −27.8298 | − | 85.6513i | −0.983932 | − | 3.02823i | ||||
\(801\) | 20.5772 | − | 14.9502i | 0.727058 | − | 0.528239i | ||||
\(802\) | 11.6516 | 0.411431 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 92.2006 | 3.25167 | ||||||||
\(805\) | 1.64632 | − | 1.19612i | 0.0580253 | − | 0.0421578i | ||||
\(806\) | 3.11085 | + | 9.57421i | 0.109575 | + | 0.337237i | ||||
\(807\) | −20.0875 | + | 61.8229i | −0.707113 | + | 2.17627i | ||||
\(808\) | −112.545 | − | 81.7685i | −3.95931 | − | 2.87661i | ||||
\(809\) | 14.5473 | + | 10.5692i | 0.511456 | + | 0.371594i | 0.813375 | − | 0.581739i | \(-0.197628\pi\) |
−0.301920 | + | 0.953333i | \(0.597628\pi\) | |||||||
\(810\) | −0.0656413 | + | 0.202023i | −0.00230640 | + | 0.00709837i | ||||
\(811\) | 9.61662 | + | 29.5969i | 0.337685 | + | 1.03929i | 0.965384 | + | 0.260832i | \(0.0839968\pi\) |
−0.627699 | + | 0.778456i | \(0.716003\pi\) | |||||||
\(812\) | 8.51999 | − | 6.19014i | 0.298993 | − | 0.217231i | ||||
\(813\) | −75.2978 | −2.64081 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.19486 | 0.146940 | ||||||||
\(816\) | 148.698 | − | 108.035i | 5.20545 | − | 3.78198i | ||||
\(817\) | 3.83012 | + | 11.7879i | 0.133999 | + | 0.412407i | ||||
\(818\) | −7.77864 | + | 23.9402i | −0.271974 | + | 0.837050i | ||||
\(819\) | −1.78040 | − | 1.29354i | −0.0622123 | − | 0.0451999i | ||||
\(820\) | 3.38386 | + | 2.45852i | 0.118169 | + | 0.0858551i | ||||
\(821\) | 15.1009 | − | 46.4758i | 0.527025 | − | 1.62202i | −0.233253 | − | 0.972416i | \(-0.574937\pi\) |
0.760277 | − | 0.649599i | \(-0.225063\pi\) | |||||||
\(822\) | −33.9249 | − | 104.410i | −1.18327 | − | 3.64172i | ||||
\(823\) | −23.9325 | + | 17.3879i | −0.834233 | + | 0.606106i | −0.920754 | − | 0.390144i | \(-0.872425\pi\) |
0.0865208 | + | 0.996250i | \(0.472425\pi\) | |||||||
\(824\) | −126.695 | −4.41361 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −38.9249 | −1.35437 | ||||||||
\(827\) | −20.5429 | + | 14.9253i | −0.714346 | + | 0.519003i | −0.884573 | − | 0.466402i | \(-0.845550\pi\) |
0.170227 | + | 0.985405i | \(0.445550\pi\) | |||||||
\(828\) | 36.5956 | + | 112.630i | 1.27178 | + | 3.91415i | ||||
\(829\) | 2.19272 | − | 6.74851i | 0.0761565 | − | 0.234385i | −0.905730 | − | 0.423855i | \(-0.860677\pi\) |
0.981887 | + | 0.189469i | \(0.0606767\pi\) | |||||||
\(830\) | −10.5168 | − | 7.64090i | −0.365043 | − | 0.265220i | ||||
\(831\) | −31.9102 | − | 23.1841i | −1.10695 | − | 0.804249i | ||||
\(832\) | 3.28758 | − | 10.1181i | 0.113976 | − | 0.350783i | ||||
\(833\) | 1.49291 | + | 4.59472i | 0.0517264 | + | 0.159198i | ||||
\(834\) | −90.2187 | + | 65.5477i | −3.12402 | + | 2.26973i | ||||
\(835\) | −8.90671 | −0.308230 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −43.5923 | −1.50677 | ||||||||
\(838\) | 57.6089 | − | 41.8553i | 1.99007 | − | 1.44587i | ||||
\(839\) | −7.33250 | − | 22.5671i | −0.253146 | − | 0.779103i | −0.994189 | − | 0.107646i | \(-0.965669\pi\) |
0.741043 | − | 0.671457i | \(-0.234331\pi\) | |||||||
\(840\) | 3.45169 | − | 10.6232i | 0.119095 | − | 0.366536i | ||||
\(841\) | 20.2760 | + | 14.7314i | 0.699172 | + | 0.507978i | ||||
\(842\) | −31.0090 | − | 22.5293i | −1.06864 | − | 0.776413i | ||||
\(843\) | 1.51406 | − | 4.65980i | 0.0521470 | − | 0.160492i | ||||
\(844\) | −5.95389 | − | 18.3242i | −0.204941 | − | 0.630744i | ||||
\(845\) | −4.60771 | + | 3.34769i | −0.158510 | + | 0.115164i | ||||
\(846\) | 13.4904 | 0.463810 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −48.4127 | −1.66250 | ||||||||
\(849\) | −10.5952 | + | 7.69787i | −0.363627 | + | 0.264190i | ||||
\(850\) | −19.3788 | − | 59.6418i | −0.664687 | − | 2.04570i | ||||
\(851\) | 10.3385 | − | 31.8186i | 0.354399 | − | 1.09073i | ||||
\(852\) | −71.3746 | − | 51.8566i | −2.44525 | − | 1.77658i | ||||
\(853\) | 31.2719 | + | 22.7204i | 1.07073 | + | 0.777931i | 0.976043 | − | 0.217576i | \(-0.0698149\pi\) |
0.0946872 | + | 0.995507i | \(0.469815\pi\) | |||||||
\(854\) | 4.11790 | − | 12.6736i | 0.140912 | − | 0.433682i | ||||
\(855\) | 0.729232 | + | 2.24435i | 0.0249392 | + | 0.0767550i | ||||
\(856\) | 85.0221 | − | 61.7722i | 2.90600 | − | 2.11133i | ||||
\(857\) | 34.0838 | 1.16428 | 0.582139 | − | 0.813089i | \(-0.302216\pi\) | ||||
0.582139 | + | 0.813089i | \(0.302216\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.7283 | 1.93555 | 0.967773 | − | 0.251825i | \(-0.0810308\pi\) | ||||
0.967773 | + | 0.251825i | \(0.0810308\pi\) | |||||||
\(860\) | −21.8014 | + | 15.8397i | −0.743422 | + | 0.540128i | ||||
\(861\) | −1.53606 | − | 4.72749i | −0.0523486 | − | 0.161112i | ||||
\(862\) | 6.34462 | − | 19.5267i | 0.216099 | − | 0.665083i | ||||
\(863\) | −19.7343 | − | 14.3378i | −0.671764 | − | 0.488065i | 0.198851 | − | 0.980030i | \(-0.436279\pi\) |
−0.870615 | + | 0.491964i | \(0.836279\pi\) | |||||||
\(864\) | 80.0893 | + | 58.1883i | 2.72469 | + | 1.97961i | ||||
\(865\) | −1.49178 | + | 4.59122i | −0.0507220 | + | 0.156106i | ||||
\(866\) | 18.7122 | + | 57.5902i | 0.635866 | + | 1.95699i | ||||
\(867\) | 14.3991 | − | 10.4616i | 0.489019 | − | 0.355293i | ||||
\(868\) | 43.8306 | 1.48771 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −6.70178 | −0.227212 | ||||||||
\(871\) | 2.25767 | − | 1.64029i | 0.0764983 | − | 0.0555792i | ||||
\(872\) | 43.5949 | + | 134.171i | 1.47631 | + | 4.54361i | ||||
\(873\) | −8.00779 | + | 24.6454i | −0.271023 | + | 0.834122i | ||||
\(874\) | 10.8634 | + | 7.89274i | 0.367461 | + | 0.266976i | ||||
\(875\) | −3.52938 | − | 2.56425i | −0.119315 | − | 0.0866874i | ||||
\(876\) | 7.63217 | − | 23.4894i | 0.257867 | − | 0.793633i | ||||
\(877\) | 9.42347 | + | 29.0025i | 0.318208 | + | 0.979344i | 0.974414 | + | 0.224762i | \(0.0721604\pi\) |
−0.656206 | + | 0.754582i | \(0.727840\pi\) | |||||||
\(878\) | −33.6898 | + | 24.4771i | −1.13698 | + | 0.826062i | ||||
\(879\) | −40.7301 | −1.37379 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.10056 | 0.0707697 | 0.0353848 | − | 0.999374i | \(-0.488734\pi\) | ||||
0.0353848 | + | 0.999374i | \(0.488734\pi\) | |||||||
\(882\) | −10.6729 | + | 7.75433i | −0.359376 | + | 0.261102i | ||||
\(883\) | 13.9662 | + | 42.9835i | 0.469999 | + | 1.44651i | 0.852585 | + | 0.522589i | \(0.175034\pi\) |
−0.382585 | + | 0.923920i | \(0.624966\pi\) | |||||||
\(884\) | 3.57288 | − | 10.9962i | 0.120169 | − | 0.369842i | ||||
\(885\) | 14.5549 | + | 10.5748i | 0.489259 | + | 0.355467i | ||||
\(886\) | −46.3847 | − | 33.7004i | −1.55832 | − | 1.13219i | ||||
\(887\) | 1.60305 | − | 4.93369i | 0.0538252 | − | 0.165657i | −0.920530 | − | 0.390671i | \(-0.872243\pi\) |
0.974355 | + | 0.225014i | \(0.0722429\pi\) | |||||||
\(888\) | −56.7478 | − | 174.652i | −1.90433 | − | 5.86093i | ||||
\(889\) | −8.19835 | + | 5.95645i | −0.274964 | + | 0.199773i | ||||
\(890\) | 6.27029 | 0.210181 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.6905 | −0.860181 | ||||||||
\(893\) | 0.898798 | − | 0.653015i | 0.0300771 | − | 0.0218523i | ||||
\(894\) | −2.34822 | − | 7.22707i | −0.0785362 | − | 0.241710i | ||||
\(895\) | −2.31724 | + | 7.13174i | −0.0774569 | + | 0.238388i | ||||
\(896\) | −21.2501 | − | 15.4391i | −0.709916 | − | 0.515784i | ||||
\(897\) | 4.68240 | + | 3.40196i | 0.156341 | + | 0.113588i | ||||
\(898\) | −9.71630 | + | 29.9037i | −0.324237 | + | 0.997899i | ||||
\(899\) | −5.06407 | − | 15.5856i | −0.168896 | − | 0.519809i | ||||
\(900\) | 100.622 | − | 73.1058i | 3.35405 | − | 2.43686i | ||||
\(901\) | −17.2580 | −0.574947 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 32.0256 | 1.06575 | ||||||||
\(904\) | 42.8431 | − | 31.1273i | 1.42494 | − | 1.03528i | ||||
\(905\) | 2.79253 | + | 8.59451i | 0.0928267 | + | 0.285691i | ||||
\(906\) | −3.22520 | + | 9.92614i | −0.107150 | + | 0.329774i | ||||
\(907\) | 31.2663 | + | 22.7163i | 1.03818 | + | 0.754283i | 0.969930 | − | 0.243386i | \(-0.0782580\pi\) |
0.0682513 | + | 0.997668i | \(0.478258\pi\) | |||||||
\(908\) | −97.5978 | − | 70.9089i | −3.23890 | − | 2.35320i | ||||
\(909\) | 23.4666 | − | 72.2229i | 0.778339 | − | 2.39548i | ||||
\(910\) | −0.167650 | − | 0.515973i | −0.00555753 | − | 0.0171043i | ||||
\(911\) | 14.8851 | − | 10.8146i | 0.493165 | − | 0.358305i | −0.313235 | − | 0.949676i | \(-0.601413\pi\) |
0.806400 | + | 0.591370i | \(0.201413\pi\) | |||||||
\(912\) | 41.3331 | 1.36868 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 85.4145 | 2.82526 | ||||||||
\(915\) | −4.98283 | + | 3.62024i | −0.164727 | + | 0.119681i | ||||
\(916\) | −37.1848 | − | 114.443i | −1.22862 | − | 3.78130i | ||||
\(917\) | −2.11164 | + | 6.49895i | −0.0697324 | + | 0.214614i | ||||
\(918\) | 55.7688 | + | 40.5184i | 1.84064 | + | 1.33731i | ||||
\(919\) | −14.2819 | − | 10.3764i | −0.471115 | − | 0.342285i | 0.326761 | − | 0.945107i | \(-0.394043\pi\) |
−0.797876 | + | 0.602822i | \(0.794043\pi\) | |||||||
\(920\) | −5.62195 | + | 17.3026i | −0.185350 | + | 0.570449i | ||||
\(921\) | −2.04445 | − | 6.29216i | −0.0673668 | − | 0.207334i | ||||
\(922\) | 19.3833 | − | 14.0828i | 0.638355 | − | 0.463792i | ||||
\(923\) | −2.67027 | −0.0878930 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.1368 | −1.15529 | ||||||||
\(926\) | 56.0143 | − | 40.6968i | 1.84075 | − | 1.33738i | ||||
\(927\) | −21.3718 | − | 65.7757i | −0.701942 | − | 2.16036i | ||||
\(928\) | −11.5002 | + | 35.3941i | −0.377513 | + | 1.16187i | ||||
\(929\) | 10.8800 | + | 7.90475i | 0.356960 | + | 0.259346i | 0.751783 | − | 0.659411i | \(-0.229194\pi\) |
−0.394823 | + | 0.918757i | \(0.629194\pi\) | |||||||
\(930\) | −22.5655 | − | 16.3948i | −0.739951 | − | 0.537606i | ||||
\(931\) | −0.335728 | + | 1.03326i | −0.0110030 | + | 0.0338638i | ||||
\(932\) | −0.963164 | − | 2.96432i | −0.0315495 | − | 0.0970994i | ||||
\(933\) | −45.4327 | + | 33.0088i | −1.48740 | + | 1.08066i | ||||
\(934\) | 55.5241 | 1.81680 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 19.6747 | 0.643087 | ||||||||
\(937\) | 6.95415 | − | 5.05249i | 0.227182 | − | 0.165058i | −0.468372 | − | 0.883532i | \(-0.655159\pi\) |
0.695554 | + | 0.718474i | \(0.255159\pi\) | |||||||
\(938\) | −5.16953 | − | 15.9102i | −0.168791 | − | 0.519485i | ||||
\(939\) | −16.2677 | + | 50.0668i | −0.530876 | + | 1.63387i | ||||
\(940\) | 1.95415 | + | 1.41978i | 0.0637375 | + | 0.0463080i | ||||
\(941\) | 27.2619 | + | 19.8069i | 0.888712 | + | 0.645687i | 0.935542 | − | 0.353216i | \(-0.114912\pi\) |
−0.0468300 | + | 0.998903i | \(0.514912\pi\) | |||||||
\(942\) | −12.6080 | + | 38.8035i | −0.410791 | + | 1.26428i | ||||
\(943\) | 2.50185 | + | 7.69991i | 0.0814715 | + | 0.250744i | ||||
\(944\) | 157.881 | − | 114.707i | 5.13858 | − | 3.73340i | ||||
\(945\) | 2.34928 | 0.0764220 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.3289 | −0.498121 | −0.249061 | − | 0.968488i | \(-0.580122\pi\) | ||||
−0.249061 | + | 0.968488i | \(0.580122\pi\) | |||||||
\(948\) | −43.4918 | + | 31.5986i | −1.41255 | + | 1.02628i | ||||
\(949\) | −0.231003 | − | 0.710953i | −0.00749867 | − | 0.0230785i | ||||
\(950\) | 4.35792 | − | 13.4123i | 0.141389 | − | 0.435152i | ||||
\(951\) | 9.54308 | + | 6.93345i | 0.309456 | + | 0.224833i | ||||
\(952\) | −34.9428 | − | 25.3874i | −1.13250 | − | 0.822811i | ||||
\(953\) | 13.8865 | − | 42.7382i | 0.449827 | − | 1.38443i | −0.427275 | − | 0.904122i | \(-0.640527\pi\) |
0.877102 | − | 0.480304i | \(-0.159473\pi\) | |||||||
\(954\) | −14.5628 | − | 44.8198i | −0.471489 | − | 1.45109i | ||||
\(955\) | 0.916146 | − | 0.665619i | 0.0296458 | − | 0.0215389i | ||||
\(956\) | −79.4610 | −2.56995 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −74.4697 | −2.40601 | ||||||||
\(959\) | −11.7043 | + | 8.50366i | −0.377951 | + | 0.274598i | ||||
\(960\) | 9.10891 | + | 28.0343i | 0.293989 | + | 0.904804i | ||||
\(961\) | 11.4968 | − | 35.3837i | 0.370866 | − | 1.14141i | ||||
\(962\) | −7.21598 | − | 5.24272i | −0.232653 | − | 0.169032i | ||||
\(963\) | 46.4123 | + | 33.7205i | 1.49561 | + | 1.08663i | ||||
\(964\) | −29.9710 | + | 92.2414i | −0.965302 | + | 2.97090i | ||||
\(965\) | −2.40804 | − | 7.41119i | −0.0775176 | − | 0.238575i | ||||
\(966\) | 28.0695 | − | 20.3937i | 0.903120 | − | 0.656155i | ||||
\(967\) | 33.9453 | 1.09161 | 0.545804 | − | 0.837913i | \(-0.316224\pi\) | ||||
0.545804 | + | 0.837913i | \(0.316224\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.7343 | 0.473334 | ||||||||
\(970\) | −5.16830 | + | 3.75499i | −0.165944 | + | 0.120565i | ||||
\(971\) | −17.1381 | − | 52.7456i | −0.549988 | − | 1.69269i | −0.708826 | − | 0.705383i | \(-0.750775\pi\) |
0.158839 | − | 0.987305i | \(-0.449225\pi\) | |||||||
\(972\) | 25.1575 | − | 77.4269i | 0.806928 | − | 2.48347i | ||||
\(973\) | 11.8890 | + | 8.63790i | 0.381145 | + | 0.276918i | ||||
\(974\) | 26.4648 | + | 19.2278i | 0.847986 | + | 0.616098i | ||||
\(975\) | 1.87837 | − | 5.78102i | 0.0601559 | − | 0.185141i | ||||
\(976\) | 20.6452 | + | 63.5395i | 0.660838 | + | 2.03385i | ||||
\(977\) | 30.6835 | − | 22.2928i | 0.981651 | − | 0.713211i | 0.0235741 | − | 0.999722i | \(-0.492495\pi\) |
0.958077 | + | 0.286511i | \(0.0924954\pi\) | |||||||
\(978\) | 71.5215 | 2.28701 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.36212 | −0.0754551 | ||||||||
\(981\) | −62.3034 | + | 45.2661i | −1.98920 | + | 1.44523i | ||||
\(982\) | −32.9011 | − | 101.259i | −1.04992 | − | 3.23131i | ||||
\(983\) | 9.74444 | − | 29.9903i | 0.310799 | − | 0.956542i | −0.666650 | − | 0.745371i | \(-0.732272\pi\) |
0.977449 | − | 0.211171i | \(-0.0677277\pi\) | |||||||
\(984\) | 35.9525 | + | 26.1210i | 1.14612 | + | 0.832708i | ||||
\(985\) | −0.779764 | − | 0.566532i | −0.0248453 | − | 0.0180512i | ||||
\(986\) | −8.00798 | + | 24.6460i | −0.255026 | + | 0.784889i | ||||
\(987\) | −0.887062 | − | 2.73010i | −0.0282355 | − | 0.0868999i | ||||
\(988\) | 2.10352 | − | 1.52829i | 0.0669217 | − | 0.0486215i | ||||
\(989\) | −52.1618 | −1.65865 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.8173 | 1.26484 | 0.632419 | − | 0.774627i | \(-0.282062\pi\) | ||||
0.632419 | + | 0.774627i | \(0.282062\pi\) | |||||||
\(992\) | −125.308 | + | 91.0414i | −3.97853 | + | 2.89057i | ||||
\(993\) | 0.0592216 | + | 0.182265i | 0.00187934 | + | 0.00578402i | ||||
\(994\) | −4.94655 | + | 15.2239i | −0.156895 | + | 0.482874i | ||||
\(995\) | −5.24827 | − | 3.81309i | −0.166381 | − | 0.120883i | ||||
\(996\) | −130.232 | − | 94.6193i | −4.12657 | − | 2.99813i | ||||
\(997\) | −5.78448 | + | 17.8028i | −0.183196 | + | 0.563821i | −0.999913 | − | 0.0132190i | \(-0.995792\pi\) |
0.816716 | + | 0.577040i | \(0.195792\pi\) | |||||||
\(998\) | −29.0556 | − | 89.4239i | −0.919738 | − | 2.83066i | ||||
\(999\) | 31.2471 | − | 22.7023i | 0.988613 | − | 0.718269i |
(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 | 847.2.f.y.729.1 | 24 | ||
11.2 | odd | 10 | 847.2.a.m.1.1 | ✓ | 6 | ||
11.3 | even | 5 | inner | 847.2.f.y.148.6 | 24 | ||
11.4 | even | 5 | inner | 847.2.f.y.323.1 | 24 | ||
11.5 | even | 5 | inner | 847.2.f.y.372.6 | 24 | ||
11.6 | odd | 10 | 847.2.f.z.372.1 | 24 | |||
11.7 | odd | 10 | 847.2.f.z.323.6 | 24 | |||
11.8 | odd | 10 | 847.2.f.z.148.1 | 24 | |||
11.9 | even | 5 | 847.2.a.n.1.6 | yes | 6 | ||
11.10 | odd | 2 | 847.2.f.z.729.6 | 24 | |||
33.2 | even | 10 | 7623.2.a.cs.1.6 | 6 | |||
33.20 | odd | 10 | 7623.2.a.cp.1.1 | 6 | |||
77.13 | even | 10 | 5929.2.a.bj.1.1 | 6 | |||
77.20 | odd | 10 | 5929.2.a.bm.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.m.1.1 | ✓ | 6 | 11.2 | odd | 10 | ||
847.2.a.n.1.6 | yes | 6 | 11.9 | even | 5 | ||
847.2.f.y.148.6 | 24 | 11.3 | even | 5 | inner | ||
847.2.f.y.323.1 | 24 | 11.4 | even | 5 | inner | ||
847.2.f.y.372.6 | 24 | 11.5 | even | 5 | inner | ||
847.2.f.y.729.1 | 24 | 1.1 | even | 1 | trivial | ||
847.2.f.z.148.1 | 24 | 11.8 | odd | 10 | |||
847.2.f.z.323.6 | 24 | 11.7 | odd | 10 | |||
847.2.f.z.372.1 | 24 | 11.6 | odd | 10 | |||
847.2.f.z.729.6 | 24 | 11.10 | odd | 2 | |||
5929.2.a.bj.1.1 | 6 | 77.13 | even | 10 | |||
5929.2.a.bm.1.6 | 6 | 77.20 | odd | 10 | |||
7623.2.a.cp.1.1 | 6 | 33.20 | odd | 10 | |||
7623.2.a.cs.1.6 | 6 | 33.2 | even | 10 |