Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,2,Mod(263,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.263");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.n (of order \(6\), degree \(2\), 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: | \(4.69520363885\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 275.11 | ||
Character | \(\chi\) | \(=\) | 588.275 |
Dual form | 588.2.n.e.263.11 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.29776 | − | 0.561968i | 0.917658 | − | 0.397371i | ||||
\(3\) | 1.27809 | + | 1.16897i | 0.737903 | + | 0.674907i | ||||
\(4\) | 1.36838 | − | 1.45860i | 0.684192 | − | 0.729302i | ||||
\(5\) | 0.432549 | + | 0.249732i | 0.193442 | + | 0.111684i | 0.593593 | − | 0.804766i | \(-0.297709\pi\) |
−0.400151 | + | 0.916449i | \(0.631042\pi\) | |||||||
\(6\) | 2.31558 | + | 0.798808i | 0.945331 | + | 0.326112i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.956154 | − | 2.66191i | 0.338051 | − | 0.941128i | ||||
\(9\) | 0.267006 | + | 2.98809i | 0.0890021 | + | 0.996031i | ||||
\(10\) | 0.701688 | + | 0.0810151i | 0.221893 | + | 0.0256192i | ||||
\(11\) | 0.695249 | + | 1.20421i | 0.209626 | + | 0.363082i | 0.951597 | − | 0.307350i | \(-0.0994422\pi\) |
−0.741971 | + | 0.670432i | \(0.766109\pi\) | |||||||
\(12\) | 3.45398 | − | 0.264615i | 0.997078 | − | 0.0763879i | ||||
\(13\) | −2.75054 | −0.762861 | −0.381431 | − | 0.924397i | \(-0.624568\pi\) | ||||
−0.381431 | + | 0.924397i | \(0.624568\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.260904 | + | 0.824817i | 0.0673652 | + | 0.212967i | ||||
\(16\) | −0.255045 | − | 3.99186i | −0.0637614 | − | 0.997965i | ||||
\(17\) | 5.04311 | − | 2.91164i | 1.22313 | − | 0.706177i | 0.257550 | − | 0.966265i | \(-0.417085\pi\) |
0.965585 | + | 0.260088i | \(0.0837515\pi\) | |||||||
\(18\) | 2.02572 | + | 3.72779i | 0.477468 | + | 0.878649i | ||||
\(19\) | 2.14907 | + | 1.24076i | 0.493030 | + | 0.284651i | 0.725831 | − | 0.687874i | \(-0.241456\pi\) |
−0.232801 | + | 0.972524i | \(0.574789\pi\) | |||||||
\(20\) | 0.956154 | − | 0.289187i | 0.213802 | − | 0.0646643i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.57899 | + | 1.17207i | 0.336643 | + | 0.249886i | ||||
\(23\) | −2.53203 | + | 4.38560i | −0.527964 | + | 0.914460i | 0.471505 | + | 0.881863i | \(0.343711\pi\) |
−0.999469 | + | 0.0325966i | \(0.989622\pi\) | |||||||
\(24\) | 4.33375 | − | 2.28443i | 0.884622 | − | 0.466308i | ||||
\(25\) | −2.37527 | − | 4.11408i | −0.475054 | − | 0.822817i | ||||
\(26\) | −3.56955 | + | 1.54571i | −0.700046 | + | 0.303139i | ||||
\(27\) | −3.15174 | + | 4.13116i | −0.606553 | + | 0.795043i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.32275i | − | 1.17411i | −0.809549 | − | 0.587053i | \(-0.800288\pi\) | ||
0.809549 | − | 0.587053i | \(-0.199712\pi\) | |||||||
\(30\) | 0.802113 | + | 0.923798i | 0.146445 | + | 0.168662i | ||||
\(31\) | −5.98869 | + | 3.45757i | −1.07560 | + | 0.620998i | −0.929706 | − | 0.368302i | \(-0.879939\pi\) |
−0.145894 | + | 0.989300i | \(0.546606\pi\) | |||||||
\(32\) | −2.57429 | − | 5.03717i | −0.455074 | − | 0.890454i | ||||
\(33\) | −0.519097 | + | 2.35181i | −0.0903631 | + | 0.409397i | ||||
\(34\) | 4.90852 | − | 6.61269i | 0.841805 | − | 1.13407i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.72381 | + | 3.69941i | 0.787302 | + | 0.616568i | ||||
\(37\) | −3.67154 | + | 6.35929i | −0.603598 | + | 1.04546i | 0.388674 | + | 0.921375i | \(0.372933\pi\) |
−0.992271 | + | 0.124086i | \(0.960400\pi\) | |||||||
\(38\) | 3.48625 | + | 0.402514i | 0.565545 | + | 0.0652964i | ||||
\(39\) | −3.51542 | − | 3.21530i | −0.562918 | − | 0.514860i | ||||
\(40\) | 1.07835 | − | 0.912624i | 0.170502 | − | 0.144299i | ||||
\(41\) | − | 5.74438i | − | 0.897121i | −0.893753 | − | 0.448560i | \(-0.851937\pi\) | ||
0.893753 | − | 0.448560i | \(-0.148063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.52627i | − | 0.537751i | −0.963175 | − | 0.268875i | \(-0.913348\pi\) | ||
0.963175 | − | 0.268875i | \(-0.0866520\pi\) | |||||||
\(44\) | 2.70783 | + | 0.633726i | 0.408220 | + | 0.0955378i | ||||
\(45\) | −0.630730 | + | 1.35918i | −0.0940237 | + | 0.202614i | ||||
\(46\) | −0.821409 | + | 7.11439i | −0.121110 | + | 1.04896i | ||||
\(47\) | −2.53203 | + | 4.38560i | −0.369334 | + | 0.639705i | −0.989462 | − | 0.144796i | \(-0.953747\pi\) |
0.620128 | + | 0.784501i | \(0.287081\pi\) | |||||||
\(48\) | 4.34041 | − | 5.40008i | 0.626484 | − | 0.779435i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.39452 | − | 4.00429i | −0.762900 | − | 0.566292i | ||||
\(51\) | 9.84916 | + | 2.17393i | 1.37916 | + | 0.304411i | ||||
\(52\) | −3.76379 | + | 4.01194i | −0.521944 | + | 0.556356i | ||||
\(53\) | 4.54223 | − | 2.62246i | 0.623923 | − | 0.360222i | −0.154472 | − | 0.987997i | \(-0.549368\pi\) |
0.778395 | + | 0.627775i | \(0.216034\pi\) | |||||||
\(54\) | −1.76864 | + | 7.13245i | −0.240681 | + | 0.970604i | ||||
\(55\) | 0.694505i | 0.0936470i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.29627 | + | 4.09801i | 0.171696 | + | 0.542794i | ||||
\(58\) | −3.55318 | − | 8.20544i | −0.466556 | − | 1.07743i | ||||
\(59\) | −1.57587 | − | 2.72949i | −0.205161 | − | 0.355349i | 0.745023 | − | 0.667039i | \(-0.232438\pi\) |
−0.950184 | + | 0.311689i | \(0.899105\pi\) | |||||||
\(60\) | 1.56010 | + | 0.748111i | 0.201408 | + | 0.0965807i | ||||
\(61\) | −2.45426 | + | 4.25091i | −0.314236 | + | 0.544273i | −0.979275 | − | 0.202536i | \(-0.935082\pi\) |
0.665039 | + | 0.746809i | \(0.268415\pi\) | |||||||
\(62\) | −5.82886 | + | 7.85256i | −0.740267 | + | 0.997276i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.17154 | − | 5.09039i | −0.771443 | − | 0.636299i | ||||
\(65\) | −1.18974 | − | 0.686897i | −0.147569 | − | 0.0851991i | ||||
\(66\) | 0.647974 | + | 3.34381i | 0.0797601 | + | 0.411594i | ||||
\(67\) | −9.30445 | + | 5.37193i | −1.13672 | + | 0.656286i | −0.945616 | − | 0.325284i | \(-0.894540\pi\) |
−0.191104 | + | 0.981570i | \(0.561207\pi\) | |||||||
\(68\) | 2.65399 | − | 11.3402i | 0.321844 | − | 1.37520i | ||||
\(69\) | −8.36279 | + | 2.64530i | −1.00676 | + | 0.318457i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.54224 | 0.539065 | 0.269532 | − | 0.962991i | \(-0.413131\pi\) | ||||
0.269532 | + | 0.962991i | \(0.413131\pi\) | |||||||
\(72\) | 8.20934 | + | 2.14633i | 0.967480 | + | 0.252947i | ||||
\(73\) | −4.98752 | − | 8.63864i | −0.583745 | − | 1.01108i | −0.995031 | − | 0.0995695i | \(-0.968253\pi\) |
0.411286 | − | 0.911507i | \(-0.365080\pi\) | |||||||
\(74\) | −1.19108 | + | 10.3162i | −0.138460 | + | 1.19923i | ||||
\(75\) | 1.77346 | − | 8.03477i | 0.204781 | − | 0.927776i | ||||
\(76\) | 4.75054 | − | 1.43679i | 0.544924 | − | 0.164811i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.36908 | − | 2.19715i | −0.721156 | − | 0.248778i | ||||
\(79\) | 1.84576 | + | 1.06565i | 0.207664 | + | 0.119895i | 0.600225 | − | 0.799831i | \(-0.295078\pi\) |
−0.392561 | + | 0.919726i | \(0.628411\pi\) | |||||||
\(80\) | 0.886577 | − | 1.79037i | 0.0991223 | − | 0.200169i | ||||
\(81\) | −8.85742 | + | 1.59568i | −0.984157 | + | 0.177298i | ||||
\(82\) | −3.22815 | − | 7.45485i | −0.356490 | − | 0.823250i | ||||
\(83\) | 12.0165 | 1.31899 | 0.659493 | − | 0.751710i | \(-0.270771\pi\) | ||||
0.659493 | + | 0.751710i | \(0.270771\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.90852 | 0.315474 | ||||||||
\(86\) | −1.98165 | − | 4.57626i | −0.213687 | − | 0.493471i | ||||
\(87\) | 7.39112 | − | 8.08102i | 0.792411 | − | 0.866376i | ||||
\(88\) | 3.87026 | − | 0.699285i | 0.412571 | − | 0.0745440i | ||||
\(89\) | −2.12318 | − | 1.22582i | −0.225056 | − | 0.129936i | 0.383233 | − | 0.923652i | \(-0.374811\pi\) |
−0.608289 | + | 0.793715i | \(0.708144\pi\) | |||||||
\(90\) | −0.0547257 | + | 2.11834i | −0.00576860 | + | 0.223293i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.93206 | + | 9.69440i | 0.305688 | + | 1.01071i | ||||
\(93\) | −11.6959 | − | 2.58154i | −1.21280 | − | 0.267693i | ||||
\(94\) | −0.821409 | + | 7.11439i | −0.0847219 | + | 0.733793i | ||||
\(95\) | 0.619718 | + | 1.07338i | 0.0635817 | + | 0.110127i | ||||
\(96\) | 2.59815 | − | 9.44720i | 0.265173 | − | 0.964201i | ||||
\(97\) | −0.526031 | −0.0534104 | −0.0267052 | − | 0.999643i | \(-0.508502\pi\) | ||||
−0.0267052 | + | 0.999643i | \(0.508502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.41265 | + | 2.39900i | −0.342984 | + | 0.241109i | ||||
\(100\) | −9.25110 | − | 2.16508i | −0.925110 | − | 0.216508i | ||||
\(101\) | −13.9396 | + | 8.04803i | −1.38704 | + | 0.800809i | −0.992981 | − | 0.118275i | \(-0.962264\pi\) |
−0.394061 | + | 0.919084i | \(0.628930\pi\) | |||||||
\(102\) | 14.0036 | − | 2.71366i | 1.38656 | − | 0.268692i | ||||
\(103\) | −1.62521 | − | 0.938316i | −0.160137 | − | 0.0924550i | 0.417790 | − | 0.908544i | \(-0.362805\pi\) |
−0.577927 | + | 0.816089i | \(0.696138\pi\) | |||||||
\(104\) | −2.62993 | + | 7.32168i | −0.257886 | + | 0.717950i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.42101 | − | 5.95591i | 0.429406 | − | 0.578490i | ||||
\(107\) | 3.63924 | − | 6.30335i | 0.351819 | − | 0.609368i | −0.634749 | − | 0.772718i | \(-0.718897\pi\) |
0.986568 | + | 0.163350i | \(0.0522300\pi\) | |||||||
\(108\) | 1.71293 | + | 10.2502i | 0.164827 | + | 0.986323i | ||||
\(109\) | 0.921005 | + | 1.59523i | 0.0882163 | + | 0.152795i | 0.906757 | − | 0.421653i | \(-0.138550\pi\) |
−0.818541 | + | 0.574448i | \(0.805217\pi\) | |||||||
\(110\) | 0.390289 | + | 0.901303i | 0.0372126 | + | 0.0859359i | ||||
\(111\) | −12.1264 | + | 3.83579i | −1.15099 | + | 0.364077i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.2728i | 0.966382i | 0.875515 | + | 0.483191i | \(0.160522\pi\) | ||||
−0.875515 | + | 0.483191i | \(0.839478\pi\) | |||||||
\(114\) | 3.98520 | + | 4.58978i | 0.373248 | + | 0.429872i | ||||
\(115\) | −2.19045 | + | 1.26466i | −0.204260 | + | 0.117930i | ||||
\(116\) | −9.22238 | − | 8.65196i | −0.856277 | − | 0.803314i | ||||
\(117\) | −0.734410 | − | 8.21886i | −0.0678963 | − | 0.759834i | ||||
\(118\) | −3.57899 | − | 2.65665i | −0.329473 | − | 0.244564i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.44505 | + | 0.0941473i | 0.223202 | + | 0.00859443i | ||||
\(121\) | 4.53326 | − | 7.85183i | 0.412114 | − | 0.713803i | ||||
\(122\) | −0.796182 | + | 6.89589i | −0.0720830 | + | 0.624325i | ||||
\(123\) | 6.71502 | − | 7.34181i | 0.605473 | − | 0.661988i | ||||
\(124\) | −3.15161 | + | 13.4664i | −0.283023 | + | 1.20932i | ||||
\(125\) | − | 4.87005i | − | 0.435590i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.51224i | − | 0.134190i | −0.997747 | − | 0.0670949i | \(-0.978627\pi\) | ||
0.997747 | − | 0.0670949i | \(-0.0213730\pi\) | |||||||
\(128\) | −10.8698 | − | 3.13792i | −0.960767 | − | 0.277356i | ||||
\(129\) | 4.12211 | − | 4.50687i | 0.362931 | − | 0.396808i | ||||
\(130\) | −1.93002 | − | 0.222835i | −0.169274 | − | 0.0195439i | ||||
\(131\) | −3.32518 | + | 5.75939i | −0.290523 | + | 0.503200i | −0.973933 | − | 0.226834i | \(-0.927162\pi\) |
0.683411 | + | 0.730034i | \(0.260496\pi\) | |||||||
\(132\) | 2.72003 | + | 3.97533i | 0.236748 | + | 0.346008i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.05614 | + | 12.2003i | −0.782331 | + | 1.05395i | ||||
\(135\) | −2.39497 | + | 0.999839i | −0.206126 | + | 0.0860524i | ||||
\(136\) | −2.92854 | − | 16.2083i | −0.251121 | − | 1.38985i | ||||
\(137\) | 10.5583 | − | 6.09586i | 0.902060 | − | 0.520805i | 0.0241922 | − | 0.999707i | \(-0.492299\pi\) |
0.877868 | + | 0.478903i | \(0.158965\pi\) | |||||||
\(138\) | −9.36635 | + | 8.13259i | −0.797317 | + | 0.692292i | ||||
\(139\) | 0.0477837i | 0.00405296i | 0.999998 | + | 0.00202648i | \(0.000645050\pi\) | ||||
−0.999998 | + | 0.00202648i | \(0.999355\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.36279 | + | 2.64530i | −0.704274 | + | 0.222774i | ||||
\(142\) | 5.89476 | − | 2.55259i | 0.494677 | − | 0.214209i | ||||
\(143\) | −1.91231 | − | 3.31221i | −0.159915 | − | 0.276981i | ||||
\(144\) | 11.8600 | − | 1.82795i | 0.988330 | − | 0.152329i | ||||
\(145\) | 1.57899 | − | 2.73490i | 0.131128 | − | 0.227121i | ||||
\(146\) | −11.3273 | − | 8.40809i | −0.937451 | − | 0.695859i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.25161 | + | 14.0573i | 0.349480 | + | 1.15550i | ||||
\(149\) | 1.98650 | + | 1.14691i | 0.162740 | + | 0.0939583i | 0.579158 | − | 0.815215i | \(-0.303381\pi\) |
−0.416418 | + | 0.909173i | \(0.636715\pi\) | |||||||
\(150\) | −2.21376 | − | 11.4239i | −0.180752 | − | 0.932755i | ||||
\(151\) | 11.3759 | − | 6.56789i | 0.925759 | − | 0.534487i | 0.0402913 | − | 0.999188i | \(-0.487171\pi\) |
0.885468 | + | 0.464701i | \(0.153838\pi\) | |||||||
\(152\) | 5.35764 | − | 4.53427i | 0.434562 | − | 0.367777i | ||||
\(153\) | 10.0468 | + | 14.2919i | 0.812236 | + | 1.15543i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.45387 | −0.277421 | ||||||||
\(156\) | −9.50029 | + | 0.727834i | −0.760632 | + | 0.0582733i | ||||
\(157\) | 4.20480 | + | 7.28292i | 0.335579 | + | 0.581241i | 0.983596 | − | 0.180386i | \(-0.0577346\pi\) |
−0.648017 | + | 0.761626i | \(0.724401\pi\) | |||||||
\(158\) | 2.99422 | + | 0.345705i | 0.238207 | + | 0.0275028i | ||||
\(159\) | 8.87093 | + | 1.95802i | 0.703511 | + | 0.155281i | ||||
\(160\) | 0.144439 | − | 2.82170i | 0.0114189 | − | 0.223075i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −10.5981 | + | 7.04840i | −0.832667 | + | 0.553774i | ||||
\(163\) | −10.7040 | − | 6.17993i | −0.838399 | − | 0.484050i | 0.0183210 | − | 0.999832i | \(-0.494168\pi\) |
−0.856720 | + | 0.515782i | \(0.827501\pi\) | |||||||
\(164\) | −8.37876 | − | 7.86052i | −0.654272 | − | 0.613803i | ||||
\(165\) | −0.811857 | + | 0.887636i | −0.0632030 | + | 0.0691024i | ||||
\(166\) | 15.5946 | − | 6.75291i | 1.21038 | − | 0.524127i | ||||
\(167\) | −2.36549 | −0.183047 | −0.0915237 | − | 0.995803i | \(-0.529174\pi\) | ||||
−0.0915237 | + | 0.995803i | \(0.529174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.43456 | −0.418043 | ||||||||
\(170\) | 3.77458 | − | 1.63450i | 0.289497 | − | 0.125360i | ||||
\(171\) | −3.13371 | + | 6.75291i | −0.239641 | + | 0.516408i | ||||
\(172\) | −5.14342 | − | 4.82529i | −0.392182 | − | 0.367925i | ||||
\(173\) | 8.28769 | + | 4.78490i | 0.630102 | + | 0.363789i | 0.780791 | − | 0.624792i | \(-0.214816\pi\) |
−0.150690 | + | 0.988581i | \(0.548149\pi\) | |||||||
\(174\) | 5.05067 | − | 14.6408i | 0.382890 | − | 1.10992i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.62971 | − | 3.08247i | 0.348977 | − | 0.232350i | ||||
\(177\) | 1.17660 | − | 5.33067i | 0.0884386 | − | 0.400678i | ||||
\(178\) | −3.44425 | − | 0.397665i | −0.258158 | − | 0.0298062i | ||||
\(179\) | 10.3771 | + | 17.9736i | 0.775619 | + | 1.34341i | 0.934446 | + | 0.356105i | \(0.115895\pi\) |
−0.158827 | + | 0.987306i | \(0.550771\pi\) | |||||||
\(180\) | 1.11942 | + | 2.77986i | 0.0834365 | + | 0.207199i | ||||
\(181\) | 6.43456 | 0.478277 | 0.239138 | − | 0.970985i | \(-0.423135\pi\) | ||||
0.239138 | + | 0.970985i | \(0.423135\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.10595 | + | 2.56406i | −0.599209 | + | 0.189541i | ||||
\(184\) | 9.25306 | + | 10.9333i | 0.682145 | + | 0.806016i | ||||
\(185\) | −3.17624 | + | 1.83380i | −0.233522 | + | 0.134824i | ||||
\(186\) | −16.6292 | + | 3.22246i | −1.21931 | + | 0.236283i | ||||
\(187\) | 7.01244 | + | 4.04864i | 0.512801 | + | 0.296066i | ||||
\(188\) | 2.93206 | + | 9.69440i | 0.213842 | + | 0.707037i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.40745 | + | 1.04474i | 0.102107 | + | 0.0757932i | ||||
\(191\) | −8.76689 | + | 15.1847i | −0.634350 | + | 1.09873i | 0.352303 | + | 0.935886i | \(0.385399\pi\) |
−0.986652 | + | 0.162840i | \(0.947935\pi\) | |||||||
\(192\) | −1.93723 | − | 13.7203i | −0.139807 | − | 0.990179i | ||||
\(193\) | 1.09255 | + | 1.89234i | 0.0786432 | + | 0.136214i | 0.902665 | − | 0.430344i | \(-0.141608\pi\) |
−0.824022 | + | 0.566558i | \(0.808275\pi\) | |||||||
\(194\) | −0.682665 | + | 0.295612i | −0.0490125 | + | 0.0212237i | ||||
\(195\) | −0.717627 | − | 2.26869i | −0.0513903 | − | 0.162464i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.27706i | 0.447222i | 0.974678 | + | 0.223611i | \(0.0717845\pi\) | ||||
−0.974678 | + | 0.223611i | \(0.928215\pi\) | |||||||
\(198\) | −3.08065 | + | 5.03114i | −0.218932 | + | 0.357547i | ||||
\(199\) | 0.749564 | − | 0.432761i | 0.0531352 | − | 0.0306776i | −0.473197 | − | 0.880957i | \(-0.656900\pi\) |
0.526332 | + | 0.850279i | \(0.323567\pi\) | |||||||
\(200\) | −13.2224 | + | 2.38905i | −0.934968 | + | 0.168932i | ||||
\(201\) | −18.1715 | − | 4.01087i | −1.28172 | − | 0.282905i | ||||
\(202\) | −13.5676 | + | 18.2781i | −0.954612 | + | 1.28604i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 16.6484 | − | 11.3912i | 1.16562 | − | 0.797547i | ||||
\(205\) | 1.43456 | − | 2.48472i | 0.100194 | − | 0.173541i | ||||
\(206\) | −2.63644 | − | 0.304397i | −0.183690 | − | 0.0212084i | ||||
\(207\) | −13.7806 | − | 6.39495i | −0.957821 | − | 0.444480i | ||||
\(208\) | 0.701512 | + | 10.9798i | 0.0486411 | + | 0.761309i | ||||
\(209\) | 3.45056i | 0.238680i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.90417i | 0.268774i | 0.990929 | + | 0.134387i | \(0.0429065\pi\) | ||||
−0.990929 | + | 0.134387i | \(0.957094\pi\) | |||||||
\(212\) | 2.39039 | − | 10.2138i | 0.164173 | − | 0.701489i | ||||
\(213\) | 5.80537 | + | 5.30976i | 0.397778 | + | 0.363818i | ||||
\(214\) | 1.18060 | − | 10.2254i | 0.0807041 | − | 0.698994i | ||||
\(215\) | 0.880622 | − | 1.52528i | 0.0600580 | − | 0.104023i | ||||
\(216\) | 7.98324 | + | 12.3397i | 0.543191 | + | 0.839609i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.09171 | + | 1.55265i | 0.141669 | + | 0.105159i | ||||
\(219\) | 3.72385 | − | 16.8712i | 0.251635 | − | 1.14005i | ||||
\(220\) | 1.01301 | + | 0.950350i | 0.0682969 | + | 0.0640726i | ||||
\(221\) | −13.8713 | + | 8.00858i | −0.933082 | + | 0.538715i | ||||
\(222\) | −13.5816 | + | 11.7926i | −0.911537 | + | 0.791467i | ||||
\(223\) | − | 23.5017i | − | 1.57379i | −0.617085 | − | 0.786896i | \(-0.711687\pi\) | ||
0.617085 | − | 0.786896i | \(-0.288313\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.6591 | − | 8.19601i | 0.777271 | − | 0.546401i | ||||
\(226\) | 5.77297 | + | 13.3316i | 0.384012 | + | 0.886808i | ||||
\(227\) | 9.58391 | + | 16.5998i | 0.636107 | + | 1.10177i | 0.986280 | + | 0.165084i | \(0.0527895\pi\) |
−0.350173 | + | 0.936685i | \(0.613877\pi\) | |||||||
\(228\) | 7.75116 | + | 3.71690i | 0.513333 | + | 0.246158i | ||||
\(229\) | 5.73805 | − | 9.93860i | 0.379181 | − | 0.656761i | −0.611762 | − | 0.791042i | \(-0.709539\pi\) |
0.990943 | + | 0.134281i | \(0.0428723\pi\) | |||||||
\(230\) | −2.13199 | + | 2.87219i | −0.140579 | + | 0.189386i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.8306 | − | 6.04552i | −1.10498 | − | 0.396908i | ||||
\(233\) | 17.5088 | + | 10.1087i | 1.14704 | + | 0.662245i | 0.948164 | − | 0.317780i | \(-0.102937\pi\) |
0.198877 | + | 0.980025i | \(0.436271\pi\) | |||||||
\(234\) | −5.57182 | − | 10.2534i | −0.364242 | − | 0.670288i | ||||
\(235\) | −2.19045 | + | 1.26466i | −0.142889 | + | 0.0824971i | ||||
\(236\) | −6.13764 | − | 1.43642i | −0.399526 | − | 0.0935031i | ||||
\(237\) | 1.11332 | + | 3.51963i | 0.0723181 | + | 0.228625i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.90774 | 0.446824 | 0.223412 | − | 0.974724i | \(-0.428280\pi\) | ||||
0.223412 | + | 0.974724i | \(0.428280\pi\) | |||||||
\(240\) | 3.22601 | − | 1.25186i | 0.208238 | − | 0.0808072i | ||||
\(241\) | 4.03326 | + | 6.98581i | 0.259805 | + | 0.449995i | 0.966190 | − | 0.257833i | \(-0.0830084\pi\) |
−0.706385 | + | 0.707828i | \(0.749675\pi\) | |||||||
\(242\) | 1.47063 | − | 12.7374i | 0.0945354 | − | 0.818789i | ||||
\(243\) | −13.1858 | − | 8.31466i | −0.845872 | − | 0.533386i | ||||
\(244\) | 2.84201 | + | 9.39667i | 0.181941 | + | 0.601560i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.58866 | − | 13.3016i | 0.292562 | − | 0.848076i | ||||
\(247\) | −5.91109 | − | 3.41277i | −0.376113 | − | 0.217149i | ||||
\(248\) | 3.47764 | + | 19.2473i | 0.220830 | + | 1.22221i | ||||
\(249\) | 15.3582 | + | 14.0470i | 0.973285 | + | 0.890193i | ||||
\(250\) | −2.73681 | − | 6.32017i | −0.173091 | − | 0.399723i | ||||
\(251\) | 20.4073 | 1.28810 | 0.644048 | − | 0.764985i | \(-0.277254\pi\) | ||||
0.644048 | + | 0.764985i | \(0.277254\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.04155 | −0.442699 | ||||||||
\(254\) | −0.849832 | − | 1.96254i | −0.0533232 | − | 0.123140i | ||||
\(255\) | 3.71734 | + | 3.39999i | 0.232789 | + | 0.212915i | ||||
\(256\) | −15.8699 | + | 2.03621i | −0.991869 | + | 0.127263i | ||||
\(257\) | 23.5645 | + | 13.6050i | 1.46991 | + | 0.848655i | 0.999430 | − | 0.0337537i | \(-0.0107462\pi\) |
0.470484 | + | 0.882409i | \(0.344080\pi\) | |||||||
\(258\) | 2.81681 | − | 8.16535i | 0.175367 | − | 0.508352i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.62993 | + | 0.795420i | −0.163102 | + | 0.0493299i | ||||
\(261\) | 18.8930 | − | 1.68821i | 1.16945 | − | 0.104498i | ||||
\(262\) | −1.07872 | + | 9.34297i | −0.0666433 | + | 0.577211i | ||||
\(263\) | −1.80247 | − | 3.12196i | −0.111145 | − | 0.192508i | 0.805087 | − | 0.593156i | \(-0.202118\pi\) |
−0.916232 | + | 0.400648i | \(0.868785\pi\) | |||||||
\(264\) | 5.76396 | + | 3.63048i | 0.354747 | + | 0.223440i | ||||
\(265\) | 2.61965 | 0.160924 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.28066 | − | 4.04864i | −0.0783749 | − | 0.247772i | ||||
\(268\) | −4.89656 | + | 20.9224i | −0.299105 | + | 1.27804i | ||||
\(269\) | 22.6598 | − | 13.0827i | 1.38160 | − | 0.797664i | 0.389247 | − | 0.921134i | \(-0.372735\pi\) |
0.992348 | + | 0.123469i | \(0.0394020\pi\) | |||||||
\(270\) | −2.54623 | + | 2.64345i | −0.154958 | + | 0.160875i | ||||
\(271\) | −19.9722 | − | 11.5309i | −1.21322 | − | 0.700455i | −0.249764 | − | 0.968307i | \(-0.580353\pi\) |
−0.963460 | + | 0.267851i | \(0.913686\pi\) | |||||||
\(272\) | −12.9091 | − | 19.3888i | −0.782729 | − | 1.17562i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.2766 | − | 13.8444i | 0.620830 | − | 0.836373i | ||||
\(275\) | 3.30281 | − | 5.72063i | 0.199167 | − | 0.344967i | ||||
\(276\) | −7.58507 | + | 15.8178i | −0.456568 | + | 0.952118i | ||||
\(277\) | 10.1455 | + | 17.5725i | 0.609585 | + | 1.05583i | 0.991309 | + | 0.131555i | \(0.0419971\pi\) |
−0.381724 | + | 0.924276i | \(0.624670\pi\) | |||||||
\(278\) | 0.0268529 | + | 0.0620120i | 0.00161053 | + | 0.00371923i | ||||
\(279\) | −11.9306 | − | 16.9716i | −0.714264 | − | 1.01606i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.6637i | − | 1.65028i | −0.564929 | − | 0.825140i | \(-0.691096\pi\) | ||
0.564929 | − | 0.825140i | \(-0.308904\pi\) | |||||||
\(282\) | −9.36635 | + | 8.13259i | −0.557758 | + | 0.484289i | ||||
\(283\) | 15.0435 | − | 8.68535i | 0.894242 | − | 0.516291i | 0.0189142 | − | 0.999821i | \(-0.493979\pi\) |
0.875328 | + | 0.483530i | \(0.160646\pi\) | |||||||
\(284\) | 6.21553 | − | 6.62533i | 0.368824 | − | 0.393141i | ||||
\(285\) | −0.462703 | + | 2.09631i | −0.0274081 | + | 0.124175i | ||||
\(286\) | −4.34308 | − | 3.22382i | −0.256812 | − | 0.190628i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 14.3642 | − | 9.03716i | 0.846417 | − | 0.532520i | ||||
\(289\) | 8.45533 | − | 14.6451i | 0.497373 | − | 0.861474i | ||||
\(290\) | 0.512239 | − | 4.43660i | 0.0300797 | − | 0.260526i | ||||
\(291\) | −0.672313 | − | 0.614916i | −0.0394117 | − | 0.0360470i | ||||
\(292\) | −19.4252 | − | 4.54617i | −1.13677 | − | 0.266044i | ||||
\(293\) | − | 19.9672i | − | 1.16650i | −0.812294 | − | 0.583248i | \(-0.801782\pi\) | ||
0.812294 | − | 0.583248i | \(-0.198218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.57418i | − | 0.0916525i | ||||||
\(296\) | 13.4173 | + | 15.8538i | 0.779866 | + | 0.921482i | ||||
\(297\) | −7.16602 | − | 0.923163i | −0.415815 | − | 0.0535673i | ||||
\(298\) | 3.22253 | + | 0.372066i | 0.186676 | + | 0.0215532i | ||||
\(299\) | 6.96442 | − | 12.0627i | 0.402763 | − | 0.697606i | ||||
\(300\) | −9.29278 | − | 13.5814i | −0.536519 | − | 0.784124i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.0723 | − | 14.9165i | 0.637141 | − | 0.858346i | ||||
\(303\) | −27.2239 | − | 6.00894i | −1.56397 | − | 0.345204i | ||||
\(304\) | 4.40485 | − | 8.89523i | 0.252635 | − | 0.510176i | ||||
\(305\) | −2.12318 | + | 1.22582i | −0.121573 | + | 0.0701901i | ||||
\(306\) | 21.0700 | + | 12.9015i | 1.20449 | + | 0.737530i | ||||
\(307\) | 14.1529i | 0.807746i | 0.914815 | + | 0.403873i | \(0.132336\pi\) | ||||
−0.914815 | + | 0.403873i | \(0.867664\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.980294 | − | 3.09908i | −0.0557670 | − | 0.176300i | ||||
\(310\) | −4.48231 | + | 1.94096i | −0.254578 | + | 0.110239i | ||||
\(311\) | −12.2774 | − | 21.2652i | −0.696190 | − | 1.20584i | −0.969778 | − | 0.243990i | \(-0.921544\pi\) |
0.273588 | − | 0.961847i | \(-0.411790\pi\) | |||||||
\(312\) | −11.9201 | + | 6.28341i | −0.674844 | + | 0.355728i | ||||
\(313\) | 0.0260312 | − | 0.0450873i | 0.00147137 | − | 0.00254848i | −0.865289 | − | 0.501274i | \(-0.832865\pi\) |
0.866760 | + | 0.498725i | \(0.166198\pi\) | |||||||
\(314\) | 9.54960 | + | 7.08856i | 0.538915 | + | 0.400031i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.08007 | − | 1.23401i | 0.229522 | − | 0.0694185i | ||||
\(317\) | −5.86864 | − | 3.38826i | −0.329616 | − | 0.190304i | 0.326055 | − | 0.945351i | \(-0.394281\pi\) |
−0.655671 | + | 0.755047i | \(0.727614\pi\) | |||||||
\(318\) | 12.6127 | − | 2.44414i | 0.707286 | − | 0.137060i | ||||
\(319\) | 7.61390 | − | 4.39589i | 0.426297 | − | 0.246122i | ||||
\(320\) | −1.39826 | − | 3.74308i | −0.0781650 | − | 0.209244i | ||||
\(321\) | 12.0197 | − | 3.80205i | 0.670875 | − | 0.212210i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.4507 | 0.804056 | ||||||||
\(324\) | −9.79289 | + | 15.1030i | −0.544049 | + | 0.839053i | ||||
\(325\) | 6.53326 | + | 11.3159i | 0.362400 | + | 0.627695i | ||||
\(326\) | −17.3641 | − | 2.00482i | −0.961711 | − | 0.111037i | ||||
\(327\) | −0.687654 | + | 3.11547i | −0.0380273 | + | 0.172286i | ||||
\(328\) | −15.2910 | − | 5.49251i | −0.844305 | − | 0.303273i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.554776 | + | 1.60818i | −0.0305394 | + | 0.0885274i | ||||
\(331\) | 15.4949 | + | 8.94598i | 0.851676 | + | 0.491715i | 0.861216 | − | 0.508239i | \(-0.169703\pi\) |
−0.00953987 | + | 0.999954i | \(0.503037\pi\) | |||||||
\(332\) | 16.4433 | − | 17.5274i | 0.902441 | − | 0.961939i | ||||
\(333\) | −19.9825 | − | 9.27294i | −1.09503 | − | 0.508154i | ||||
\(334\) | −3.06985 | + | 1.32933i | −0.167975 | + | 0.0727378i | ||||
\(335\) | −5.36618 | −0.293185 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.09362 | 0.386414 | 0.193207 | − | 0.981158i | \(-0.438111\pi\) | ||||
0.193207 | + | 0.981158i | \(0.438111\pi\) | |||||||
\(338\) | −7.05277 | + | 3.05404i | −0.383620 | + | 0.166118i | ||||
\(339\) | −12.0086 | + | 13.1295i | −0.652217 | + | 0.713096i | ||||
\(340\) | 3.97998 | − | 4.24238i | 0.215845 | − | 0.230076i | ||||
\(341\) | −8.32726 | − | 4.80775i | −0.450946 | − | 0.260354i | ||||
\(342\) | −0.271898 | + | 10.5247i | −0.0147026 | + | 0.569112i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.38661 | − | 3.37165i | −0.506092 | − | 0.181787i | ||||
\(345\) | −4.27793 | − | 0.944236i | −0.230316 | − | 0.0508359i | ||||
\(346\) | 13.4444 | + | 1.55226i | 0.722777 | + | 0.0834501i | ||||
\(347\) | 4.59539 | + | 7.95946i | 0.246694 | + | 0.427286i | 0.962606 | − | 0.270904i | \(-0.0873225\pi\) |
−0.715913 | + | 0.698190i | \(0.753989\pi\) | |||||||
\(348\) | −1.67310 | − | 21.8387i | −0.0896874 | − | 1.17067i | ||||
\(349\) | 22.1330 | 1.18475 | 0.592377 | − | 0.805661i | \(-0.298190\pi\) | ||||
0.592377 | + | 0.805661i | \(0.298190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.66898 | − | 11.3629i | 0.462716 | − | 0.606507i | ||||
\(352\) | 4.27602 | − | 6.60206i | 0.227913 | − | 0.351891i | ||||
\(353\) | −9.28947 | + | 5.36328i | −0.494429 | + | 0.285458i | −0.726410 | − | 0.687262i | \(-0.758813\pi\) |
0.231981 | + | 0.972720i | \(0.425479\pi\) | |||||||
\(354\) | −1.46872 | − | 7.57917i | −0.0780614 | − | 0.402828i | ||||
\(355\) | 1.96474 | + | 1.13434i | 0.104278 | + | 0.0602047i | ||||
\(356\) | −4.69330 | + | 1.41948i | −0.248745 | + | 0.0752325i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.5676 | + | 17.4939i | 1.24559 | + | 0.924584i | ||||
\(359\) | −1.80247 | + | 3.12196i | −0.0951305 | + | 0.164771i | −0.909663 | − | 0.415347i | \(-0.863660\pi\) |
0.814533 | + | 0.580118i | \(0.196993\pi\) | |||||||
\(360\) | 3.01493 | + | 2.97853i | 0.158901 | + | 0.156982i | ||||
\(361\) | −6.42101 | − | 11.1215i | −0.337948 | − | 0.585342i | ||||
\(362\) | 8.35054 | − | 3.61601i | 0.438895 | − | 0.190053i | ||||
\(363\) | 14.9725 | − | 4.73606i | 0.785851 | − | 0.248579i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 4.98218i | − | 0.260779i | ||||||
\(366\) | −9.07870 | + | 7.88283i | −0.474551 | + | 0.412042i | ||||
\(367\) | 13.0134 | − | 7.51328i | 0.679293 | − | 0.392190i | −0.120295 | − | 0.992738i | \(-0.538384\pi\) |
0.799589 | + | 0.600548i | \(0.205051\pi\) | |||||||
\(368\) | 18.1525 | + | 8.98897i | 0.946263 | + | 0.468582i | ||||
\(369\) | 17.1647 | − | 1.53378i | 0.893561 | − | 0.0798456i | ||||
\(370\) | −3.09148 | + | 4.16479i | −0.160718 | + | 0.216517i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −19.7699 | + | 13.5271i | −1.02502 | + | 0.701346i | ||||
\(373\) | −1.32846 | + | 2.30096i | −0.0687850 | + | 0.119139i | −0.898367 | − | 0.439246i | \(-0.855246\pi\) |
0.829582 | + | 0.558385i | \(0.188579\pi\) | |||||||
\(374\) | 11.3757 | + | 1.31341i | 0.588223 | + | 0.0679148i | ||||
\(375\) | 5.69295 | − | 6.22434i | 0.293983 | − | 0.321423i | ||||
\(376\) | 9.25306 | + | 10.9333i | 0.477190 | + | 0.563843i | ||||
\(377\) | 17.3909i | 0.895679i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.7150i | 0.909957i | 0.890502 | + | 0.454979i | \(0.150353\pi\) | ||||
−0.890502 | + | 0.454979i | \(0.849647\pi\) | |||||||
\(380\) | 2.41365 | + | 0.564879i | 0.123818 | + | 0.0289777i | ||||
\(381\) | 1.76777 | − | 1.93278i | 0.0905656 | − | 0.0990191i | ||||
\(382\) | −2.84405 | + | 24.6329i | −0.145514 | + | 1.26033i | ||||
\(383\) | −16.4609 | + | 28.5111i | −0.841111 | + | 1.45685i | 0.0478445 | + | 0.998855i | \(0.484765\pi\) |
−0.888956 | + | 0.457993i | \(0.848569\pi\) | |||||||
\(384\) | −10.2244 | − | 16.7171i | −0.521764 | − | 0.853090i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.48130 | + | 1.84184i | 0.126295 | + | 0.0937473i | ||||
\(387\) | 10.5368 | − | 0.941536i | 0.535617 | − | 0.0478609i | ||||
\(388\) | −0.719813 | + | 0.767271i | −0.0365430 | + | 0.0389523i | ||||
\(389\) | 5.90821 | − | 3.41111i | 0.299558 | − | 0.172950i | −0.342686 | − | 0.939450i | \(-0.611337\pi\) |
0.642244 | + | 0.766500i | \(0.278003\pi\) | |||||||
\(390\) | −2.20624 | − | 2.54094i | −0.111717 | − | 0.128665i | ||||
\(391\) | 29.4894i | 1.49134i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.9824 | + | 3.47394i | −0.553991 | + | 0.175237i | ||||
\(394\) | 3.52751 | + | 8.14615i | 0.177713 | + | 0.410397i | ||||
\(395\) | 0.532254 | + | 0.921890i | 0.0267806 | + | 0.0463853i | ||||
\(396\) | −1.17063 | + | 8.26045i | −0.0588262 | + | 0.415103i | ||||
\(397\) | −10.4221 | + | 18.0516i | −0.523069 | + | 0.905982i | 0.476571 | + | 0.879136i | \(0.341880\pi\) |
−0.999640 | + | 0.0268459i | \(0.991454\pi\) | |||||||
\(398\) | 0.729560 | − | 0.982853i | 0.0365695 | − | 0.0492660i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −15.8170 | + | 10.5310i | −0.790852 | + | 0.526551i | ||||
\(401\) | −3.31292 | − | 1.91271i | −0.165439 | − | 0.0955164i | 0.414994 | − | 0.909824i | \(-0.363784\pi\) |
−0.580434 | + | 0.814308i | \(0.697117\pi\) | |||||||
\(402\) | −25.8363 | + | 5.00665i | −1.28860 | + | 0.249709i | ||||
\(403\) | 16.4721 | − | 9.51017i | 0.820534 | − | 0.473735i | ||||
\(404\) | −7.33586 | + | 31.3452i | −0.364972 | + | 1.55948i | ||||
\(405\) | −4.22976 | − | 1.52177i | −0.210178 | − | 0.0756175i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.2105 | −0.506118 | ||||||||
\(408\) | 15.2041 | − | 24.1390i | 0.752716 | − | 1.19506i | ||||
\(409\) | −1.93456 | − | 3.35075i | −0.0956576 | − | 0.165684i | 0.814225 | − | 0.580549i | \(-0.197162\pi\) |
−0.909883 | + | 0.414865i | \(0.863829\pi\) | |||||||
\(410\) | 0.465381 | − | 4.03076i | 0.0229836 | − | 0.199065i | ||||
\(411\) | 20.6204 | + | 4.55138i | 1.01713 | + | 0.224503i | ||||
\(412\) | −3.59255 | + | 1.08656i | −0.176992 | + | 0.0535310i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −21.4778 | − | 0.554862i | −1.05558 | − | 0.0272700i | ||||
\(415\) | 5.19774 | + | 3.00092i | 0.255147 | + | 0.147309i | ||||
\(416\) | 7.08066 | + | 13.8549i | 0.347158 | + | 0.679293i | ||||
\(417\) | −0.0558579 | + | 0.0610717i | −0.00273537 | + | 0.00299069i | ||||
\(418\) | 1.93910 | + | 4.47802i | 0.0948447 | + | 0.219027i | ||||
\(419\) | 13.5133 | 0.660170 | 0.330085 | − | 0.943951i | \(-0.392923\pi\) | ||||
0.330085 | + | 0.943951i | \(0.392923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3825 | 0.554749 | 0.277374 | − | 0.960762i | \(-0.410536\pi\) | ||||
0.277374 | + | 0.960762i | \(0.410536\pi\) | |||||||
\(422\) | 2.19401 | + | 5.06669i | 0.106803 | + | 0.246642i | ||||
\(423\) | −13.7806 | − | 6.39495i | −0.670038 | − | 0.310933i | ||||
\(424\) | −2.63768 | − | 14.5985i | −0.128097 | − | 0.708965i | ||||
\(425\) | −23.9575 | − | 13.8319i | −1.16211 | − | 0.670944i | ||||
\(426\) | 10.5179 | + | 3.62838i | 0.509595 | + | 0.175796i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.21420 | − | 13.9336i | −0.203701 | − | 0.673507i | ||||
\(429\) | 1.42779 | − | 6.46873i | 0.0689345 | − | 0.312313i | ||||
\(430\) | 0.285681 | − | 2.47434i | 0.0137768 | − | 0.119323i | ||||
\(431\) | −12.9623 | − | 22.4513i | −0.624370 | − | 1.08144i | −0.988662 | − | 0.150155i | \(-0.952023\pi\) |
0.364293 | − | 0.931284i | \(-0.381311\pi\) | |||||||
\(432\) | 17.2949 | + | 11.5277i | 0.832100 | + | 0.554626i | ||||
\(433\) | −23.3825 | −1.12369 | −0.561845 | − | 0.827242i | \(-0.689908\pi\) | ||||
−0.561845 | + | 0.827242i | \(0.689908\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.21511 | − | 1.64963i | 0.250046 | − | 0.0790939i | ||||
\(436\) | 3.58709 | + | 0.839505i | 0.171791 | + | 0.0402050i | ||||
\(437\) | −10.8830 | + | 6.28330i | −0.520604 | + | 0.300571i | ||||
\(438\) | −4.64838 | − | 23.9875i | −0.222108 | − | 1.14617i | ||||
\(439\) | 15.3054 | + | 8.83658i | 0.730487 | + | 0.421747i | 0.818600 | − | 0.574364i | \(-0.194750\pi\) |
−0.0881133 | + | 0.996110i | \(0.528084\pi\) | |||||||
\(440\) | 1.84871 | + | 0.664053i | 0.0881338 | + | 0.0316575i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.5011 | + | 18.1884i | −0.642180 | + | 0.865136i | ||||
\(443\) | 17.5681 | − | 30.4288i | 0.834685 | − | 1.44572i | −0.0596013 | − | 0.998222i | \(-0.518983\pi\) |
0.894286 | − | 0.447495i | \(-0.147684\pi\) | |||||||
\(444\) | −10.9987 | + | 22.9364i | −0.521973 | + | 1.08851i | ||||
\(445\) | −0.612252 | − | 1.06045i | −0.0290235 | − | 0.0502702i | ||||
\(446\) | −13.2072 | − | 30.4997i | −0.625380 | − | 1.44420i | ||||
\(447\) | 1.19822 | + | 3.78801i | 0.0566737 | + | 0.179167i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.52733i | 0.260851i | 0.991458 | + | 0.130425i | \(0.0416343\pi\) | ||||
−0.991458 | + | 0.130425i | \(0.958366\pi\) | |||||||
\(450\) | 10.5248 | − | 17.1885i | 0.496145 | − | 0.810274i | ||||
\(451\) | 6.91742 | − | 3.99377i | 0.325728 | − | 0.188059i | ||||
\(452\) | 14.9839 | + | 14.0571i | 0.704784 | + | 0.661191i | ||||
\(453\) | 22.2171 | + | 4.90381i | 1.04385 | + | 0.230401i | ||||
\(454\) | 21.7662 | + | 16.1568i | 1.02154 | + | 0.758277i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.1480 | + | 0.467760i | 0.568880 | + | 0.0219049i | ||||
\(457\) | −11.9761 | + | 20.7432i | −0.560219 | + | 0.970327i | 0.437258 | + | 0.899336i | \(0.355950\pi\) |
−0.997477 | + | 0.0709914i | \(0.977384\pi\) | |||||||
\(458\) | 1.86147 | − | 16.1226i | 0.0869808 | − | 0.753358i | ||||
\(459\) | −3.86613 | + | 30.0107i | −0.180455 | + | 1.40078i | ||||
\(460\) | −1.15275 | + | 4.92553i | −0.0537471 | + | 0.229654i | ||||
\(461\) | 2.99679i | 0.139574i | 0.997562 | + | 0.0697871i | \(0.0222320\pi\) | ||||
−0.997562 | + | 0.0697871i | \(0.977768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.4152i | 1.04172i | 0.853642 | + | 0.520861i | \(0.174389\pi\) | ||||
−0.853642 | + | 0.520861i | \(0.825611\pi\) | |||||||
\(464\) | −25.2395 | + | 1.61259i | −1.17172 | + | 0.0748626i | ||||
\(465\) | −4.41434 | − | 4.03748i | −0.204710 | − | 0.187234i | ||||
\(466\) | 28.4031 | + | 3.27935i | 1.31575 | + | 0.151913i | ||||
\(467\) | 6.03065 | − | 10.4454i | 0.279065 | − | 0.483355i | −0.692088 | − | 0.721814i | \(-0.743309\pi\) |
0.971153 | + | 0.238459i | \(0.0766421\pi\) | |||||||
\(468\) | −12.9930 | − | 10.1753i | −0.600602 | − | 0.470356i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.13199 | + | 2.87219i | −0.0983414 | + | 0.132484i | ||||
\(471\) | −3.13945 | + | 14.2235i | −0.144658 | + | 0.655384i | ||||
\(472\) | −8.77243 | + | 1.58502i | −0.403784 | + | 0.0729564i | ||||
\(473\) | 4.24635 | − | 2.45163i | 0.195248 | − | 0.112726i | ||||
\(474\) | 3.42275 | + | 3.94200i | 0.157212 | + | 0.181062i | ||||
\(475\) | − | 11.7886i | − | 0.540898i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.04895 | + | 12.8724i | 0.414323 | + | 0.589386i | ||||
\(478\) | 8.96461 | − | 3.88192i | 0.410032 | − | 0.177555i | ||||
\(479\) | 6.70352 | + | 11.6108i | 0.306292 | + | 0.530513i | 0.977548 | − | 0.210713i | \(-0.0675784\pi\) |
−0.671256 | + | 0.741225i | \(0.734245\pi\) | |||||||
\(480\) | 3.48310 | − | 3.43753i | 0.158981 | − | 0.156901i | ||||
\(481\) | 10.0987 | − | 17.4915i | 0.460461 | − | 0.797542i | ||||
\(482\) | 9.16001 | + | 6.79937i | 0.417227 | + | 0.309703i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.24946 | − | 17.3566i | −0.238612 | − | 0.788934i | ||||
\(485\) | −0.227534 | − | 0.131367i | −0.0103318 | − | 0.00596507i | ||||
\(486\) | −21.7847 | − | 3.38045i | −0.988173 | − | 0.153340i | ||||
\(487\) | −10.5727 | + | 6.10416i | −0.479095 | + | 0.276606i | −0.720039 | − | 0.693933i | \(-0.755876\pi\) |
0.240944 | + | 0.970539i | \(0.422543\pi\) | |||||||
\(488\) | 8.96888 | + | 10.5975i | 0.406002 | + | 0.479728i | ||||
\(489\) | −6.45640 | − | 20.4111i | −0.291969 | − | 0.923023i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.8981 | −1.80058 | −0.900288 | − | 0.435294i | \(-0.856644\pi\) | ||||
−0.900288 | + | 0.435294i | \(0.856644\pi\) | |||||||
\(492\) | −1.52005 | − | 19.8410i | −0.0685291 | − | 0.894500i | ||||
\(493\) | −18.4096 | − | 31.8864i | −0.829126 | − | 1.43609i | ||||
\(494\) | −9.58906 | − | 1.10713i | −0.431432 | − | 0.0498121i | ||||
\(495\) | −2.07525 | + | 0.185437i | −0.0932753 | + | 0.00833478i | ||||
\(496\) | 15.3295 | + | 23.0242i | 0.688316 | + | 1.03382i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 27.8253 | + | 9.59891i | 1.24688 | + | 0.430138i | ||||
\(499\) | 7.33971 | + | 4.23758i | 0.328571 | + | 0.189700i | 0.655206 | − | 0.755450i | \(-0.272582\pi\) |
−0.326636 | + | 0.945150i | \(0.605915\pi\) | |||||||
\(500\) | −7.10346 | − | 6.66410i | −0.317677 | − | 0.298028i | ||||
\(501\) | −3.02330 | − | 2.76520i | −0.135071 | − | 0.123540i | ||||
\(502\) | 26.4838 | − | 11.4682i | 1.18203 | − | 0.511852i | ||||
\(503\) | −42.5519 | −1.89730 | −0.948648 | − | 0.316334i | \(-0.897548\pi\) | ||||
−0.948648 | + | 0.316334i | \(0.897548\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.03941 | −0.357749 | ||||||||
\(506\) | −9.13828 | + | 3.95712i | −0.406246 | + | 0.175916i | ||||
\(507\) | −6.94583 | − | 6.35285i | −0.308475 | − | 0.282140i | ||||
\(508\) | −2.20576 | − | 2.06933i | −0.0978649 | − | 0.0918117i | ||||
\(509\) | −14.9018 | − | 8.60356i | −0.660511 | − | 0.381346i | 0.131961 | − | 0.991255i | \(-0.457873\pi\) |
−0.792472 | + | 0.609909i | \(0.791206\pi\) | |||||||
\(510\) | 6.73492 | + | 2.32335i | 0.298227 | + | 0.102880i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −19.4511 | + | 11.5609i | −0.859626 | + | 0.510924i | ||||
\(513\) | −11.8991 | + | 4.96758i | −0.525359 | + | 0.219324i | ||||
\(514\) | 38.2267 | + | 4.41356i | 1.68611 | + | 0.194674i | ||||
\(515\) | −0.468656 | − | 0.811735i | −0.0206514 | − | 0.0357693i | ||||
\(516\) | −0.933104 | − | 12.1797i | −0.0410776 | − | 0.536179i | ||||
\(517\) | −7.04155 | −0.309687 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.99896 | + | 15.8036i | 0.219430 | + | 0.693701i | ||||
\(520\) | −2.96603 | + | 2.51021i | −0.130069 | + | 0.110080i | ||||
\(521\) | 9.47744 | − | 5.47180i | 0.415214 | − | 0.239724i | −0.277814 | − | 0.960635i | \(-0.589610\pi\) |
0.693028 | + | 0.720911i | \(0.256276\pi\) | |||||||
\(522\) | 23.5699 | − | 12.8081i | 1.03163 | − | 0.560597i | ||||
\(523\) | −4.79287 | − | 2.76716i | −0.209578 | − | 0.121000i | 0.391537 | − | 0.920162i | \(-0.371943\pi\) |
−0.601115 | + | 0.799162i | \(0.705277\pi\) | |||||||
\(524\) | 3.85053 | + | 12.7312i | 0.168211 | + | 0.556164i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.09362 | − | 3.03864i | −0.178490 | − | 0.132491i | ||||
\(527\) | −20.1344 | + | 34.8739i | −0.877069 | + | 1.51913i | ||||
\(528\) | 9.52048 | + | 1.47234i | 0.414326 | + | 0.0640756i | ||||
\(529\) | −1.32230 | − | 2.29030i | −0.0574915 | − | 0.0995782i | ||||
\(530\) | 3.39968 | − | 1.47216i | 0.147673 | − | 0.0639464i | ||||
\(531\) | 7.73521 | − | 5.43764i | 0.335679 | − | 0.235974i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.8001i | 0.684379i | ||||||||
\(534\) | −3.93719 | − | 4.53449i | −0.170379 | − | 0.196226i | ||||
\(535\) | 3.14830 | − | 1.81767i | 0.136113 | − | 0.0785848i | ||||
\(536\) | 5.40311 | + | 29.9040i | 0.233379 | + | 1.29166i | ||||
\(537\) | −7.74788 | + | 35.1023i | −0.334346 | + | 1.51478i | ||||
\(538\) | 22.0551 | − | 29.7123i | 0.950863 | − | 1.28099i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.81887 | + | 4.86147i | −0.0782717 | + | 0.209204i | ||||
\(541\) | −6.26409 | + | 10.8497i | −0.269314 | + | 0.466466i | −0.968685 | − | 0.248293i | \(-0.920130\pi\) |
0.699371 | + | 0.714759i | \(0.253464\pi\) | |||||||
\(542\) | −32.3992 | − | 3.74073i | −1.39167 | − | 0.160678i | ||||
\(543\) | 8.22391 | + | 7.52182i | 0.352922 | + | 0.322792i | ||||
\(544\) | −27.6488 | − | 17.9076i | −1.18543 | − | 0.767782i | ||||
\(545\) | 0.920019i | 0.0394093i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 37.4911i | − | 1.60300i | −0.597992 | − | 0.801502i | \(-0.704034\pi\) | ||
0.597992 | − | 0.801502i | \(-0.295966\pi\) | |||||||
\(548\) | 5.55644 | − | 23.7419i | 0.237359 | − | 1.01420i | ||||
\(549\) | −13.3574 | − | 6.19855i | −0.570081 | − | 0.264548i | ||||
\(550\) | 1.07146 | − | 9.28010i | 0.0456871 | − | 0.395705i | ||||
\(551\) | 7.84505 | − | 13.5880i | 0.334210 | − | 0.578869i | ||||
\(552\) | −0.954556 | + | 24.7903i | −0.0406286 | + | 1.05515i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 23.0417 | + | 17.1036i | 0.978947 | + | 0.726661i | ||||
\(555\) | −6.20318 | − | 1.36918i | −0.263310 | − | 0.0581185i | ||||
\(556\) | 0.0696975 | + | 0.0653865i | 0.00295583 | + | 0.00277301i | ||||
\(557\) | 26.0411 | − | 15.0348i | 1.10340 | − | 0.637046i | 0.166286 | − | 0.986078i | \(-0.446823\pi\) |
0.937111 | + | 0.349031i | \(0.113489\pi\) | |||||||
\(558\) | −25.0205 | − | 15.3205i | −1.05920 | − | 0.648569i | ||||
\(559\) | 9.69912i | 0.410229i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.22976 | + | 13.3719i | 0.178581 | + | 0.564560i | ||||
\(562\) | −15.5461 | − | 35.9010i | −0.655773 | − | 1.51439i | ||||
\(563\) | 3.41956 | + | 5.92285i | 0.144117 | + | 0.249618i | 0.929043 | − | 0.369971i | \(-0.120632\pi\) |
−0.784926 | + | 0.619589i | \(0.787299\pi\) | |||||||
\(564\) | −7.58507 | + | 15.8178i | −0.319389 | + | 0.666049i | ||||
\(565\) | −2.56544 | + | 4.44348i | −0.107929 | + | 0.186939i | ||||
\(566\) | 14.6420 | − | 19.7255i | 0.615449 | − | 0.829124i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.34308 | − | 12.0910i | 0.182232 | − | 0.507329i | ||||
\(569\) | −29.0006 | − | 16.7435i | −1.21577 | − | 0.701924i | −0.251759 | − | 0.967790i | \(-0.581009\pi\) |
−0.964010 | + | 0.265866i | \(0.914342\pi\) | |||||||
\(570\) | 0.577579 | + | 2.98054i | 0.0241921 | + | 0.124841i | ||||
\(571\) | −24.2464 | + | 13.9986i | −1.01468 | + | 0.585825i | −0.912558 | − | 0.408947i | \(-0.865896\pi\) |
−0.102121 | + | 0.994772i | \(0.532563\pi\) | |||||||
\(572\) | −7.44798 | − | 1.74309i | −0.311416 | − | 0.0728821i | ||||
\(573\) | −28.9553 | + | 9.15909i | −1.20963 | + | 0.382627i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0570 | 1.00324 | ||||||||
\(576\) | 13.5627 | − | 19.8003i | 0.565114 | − | 0.825013i | ||||
\(577\) | 18.8181 | + | 32.5939i | 0.783409 | + | 1.35690i | 0.929945 | + | 0.367698i | \(0.119854\pi\) |
−0.146537 | + | 0.989205i | \(0.546813\pi\) | |||||||
\(578\) | 2.74298 | − | 23.7575i | 0.114093 | − | 0.988180i | ||||
\(579\) | −0.815732 | + | 3.69573i | −0.0339007 | + | 0.153589i | ||||
\(580\) | −1.82846 | − | 6.04552i | −0.0759227 | − | 0.251027i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.21807 | − | 0.420198i | −0.0504905 | − | 0.0174178i | ||||
\(583\) | 6.31596 | + | 3.64652i | 0.261580 | + | 0.151023i | ||||
\(584\) | −27.7641 | + | 5.01647i | −1.14889 | + | 0.207583i | ||||
\(585\) | 1.73485 | − | 3.73846i | 0.0717270 | − | 0.154566i | ||||
\(586\) | −11.2209 | − | 25.9127i | −0.463531 | − | 1.07044i | ||||
\(587\) | −19.7791 | −0.816373 | −0.408186 | − | 0.912899i | \(-0.633839\pi\) | ||||
−0.408186 | + | 0.912899i | \(0.633839\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.1601 | −0.707071 | ||||||||
\(590\) | −0.884640 | − | 2.04292i | −0.0364201 | − | 0.0841057i | ||||
\(591\) | −7.33771 | + | 8.02262i | −0.301833 | + | 0.330007i | ||||
\(592\) | 26.3218 | + | 13.0344i | 1.08182 | + | 0.535709i | ||||
\(593\) | −19.5061 | − | 11.2619i | −0.801020 | − | 0.462469i | 0.0428074 | − | 0.999083i | \(-0.486370\pi\) |
−0.843828 | + | 0.536614i | \(0.819703\pi\) | |||||||
\(594\) | −9.81860 | + | 2.82902i | −0.402862 | + | 0.116076i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.39118 | − | 1.32811i | 0.179870 | − | 0.0544013i | ||||
\(597\) | 1.46389 | + | 0.323114i | 0.0599132 | + | 0.0132242i | ||||
\(598\) | 2.25932 | − | 19.5684i | 0.0923903 | − | 0.800210i | ||||
\(599\) | −13.3658 | − | 23.1503i | −0.546113 | − | 0.945895i | −0.998536 | − | 0.0540915i | \(-0.982774\pi\) |
0.452423 | − | 0.891803i | \(-0.350560\pi\) | |||||||
\(600\) | −19.6922 | − | 12.4033i | −0.803929 | − | 0.506361i | ||||
\(601\) | −31.1478 | −1.27055 | −0.635273 | − | 0.772288i | \(-0.719112\pi\) | ||||
−0.635273 | + | 0.772288i | \(0.719112\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.5362 | − | 26.3682i | −0.754851 | − | 1.07380i | ||||
\(604\) | 5.98669 | − | 25.5804i | 0.243595 | − | 1.04085i | ||||
\(605\) | 3.92171 | − | 2.26420i | 0.159440 | − | 0.0920529i | ||||
\(606\) | −38.7071 | + | 7.50079i | −1.57237 | + | 0.304699i | ||||
\(607\) | −10.8934 | − | 6.28933i | −0.442151 | − | 0.255276i | 0.262358 | − | 0.964970i | \(-0.415500\pi\) |
−0.704510 | + | 0.709694i | \(0.748833\pi\) | |||||||
\(608\) | 0.717627 | − | 14.0193i | 0.0291036 | − | 0.568558i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.06651 | + | 2.78398i | −0.0836707 | + | 0.112720i | ||||
\(611\) | 6.96442 | − | 12.0627i | 0.281750 | − | 0.488006i | ||||
\(612\) | 34.5941 | + | 4.90248i | 1.39838 | + | 0.198171i | ||||
\(613\) | −2.27131 | − | 3.93403i | −0.0917374 | − | 0.158894i | 0.816505 | − | 0.577339i | \(-0.195909\pi\) |
−0.908242 | + | 0.418445i | \(0.862575\pi\) | |||||||
\(614\) | 7.95344 | + | 18.3671i | 0.320975 | + | 0.741234i | ||||
\(615\) | 4.73806 | − | 1.49873i | 0.191057 | − | 0.0604348i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.4652i | 1.42777i | 0.700261 | + | 0.713887i | \(0.253067\pi\) | ||||
−0.700261 | + | 0.713887i | \(0.746933\pi\) | |||||||
\(618\) | −3.01377 | − | 3.47098i | −0.121232 | − | 0.139623i | ||||
\(619\) | −35.9030 | + | 20.7286i | −1.44306 | + | 0.833153i | −0.998053 | − | 0.0623719i | \(-0.980134\pi\) |
−0.445011 | + | 0.895525i | \(0.646800\pi\) | |||||||
\(620\) | −4.72622 | + | 5.03782i | −0.189810 | + | 0.202324i | ||||
\(621\) | −10.1373 | − | 24.2825i | −0.406797 | − | 0.974423i | ||||
\(622\) | −27.8836 | − | 20.6976i | −1.11803 | − | 0.829900i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −11.9384 | + | 14.8531i | −0.477920 | + | 0.594600i | ||||
\(625\) | −10.6601 | + | 18.4639i | −0.426405 | + | 0.738556i | ||||
\(626\) | 0.00844472 | − | 0.0731414i | 0.000337519 | − | 0.00292332i | ||||
\(627\) | −4.03361 | + | 4.41012i | −0.161087 | + | 0.176123i | ||||
\(628\) | 16.3767 | + | 3.83271i | 0.653500 | + | 0.152942i | ||||
\(629\) | 42.7609i | 1.70499i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 22.2919i | − | 0.887428i | −0.896168 | − | 0.443714i | \(-0.853661\pi\) | ||
0.896168 | − | 0.443714i | \(-0.146339\pi\) | |||||||
\(632\) | 4.60149 | − | 3.89432i | 0.183037 | − | 0.154908i | ||||
\(633\) | −4.56386 | + | 4.98986i | −0.181397 | + | 0.198329i | ||||
\(634\) | −9.52021 | − | 1.09918i | −0.378096 | − | 0.0436540i | ||||
\(635\) | 0.377656 | − | 0.654119i | 0.0149868 | − | 0.0259579i | ||||
\(636\) | 14.9948 | − | 10.2599i | 0.594583 | − | 0.406830i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.41070 | − | 9.98359i | 0.293393 | − | 0.395254i | ||||
\(639\) | 1.21281 | + | 13.5726i | 0.0479779 | + | 0.536926i | ||||
\(640\) | −3.91810 | − | 4.07186i | −0.154876 | − | 0.160954i | ||||
\(641\) | −29.5411 | + | 17.0555i | −1.16680 | + | 0.673653i | −0.952925 | − | 0.303207i | \(-0.901943\pi\) |
−0.213877 | + | 0.976861i | \(0.568609\pi\) | |||||||
\(642\) | 13.4621 | − | 11.6888i | 0.531307 | − | 0.461322i | ||||
\(643\) | 24.2299i | 0.955533i | 0.878487 | + | 0.477766i | \(0.158553\pi\) | ||||
−0.878487 | + | 0.477766i | \(0.841447\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.90852 | − | 0.920019i | 0.114523 | − | 0.0362257i | ||||
\(646\) | 18.7536 | − | 8.12080i | 0.737849 | − | 0.319509i | ||||
\(647\) | −0.714092 | − | 1.23684i | −0.0280738 | − | 0.0486253i | 0.851647 | − | 0.524116i | \(-0.175604\pi\) |
−0.879721 | + | 0.475490i | \(0.842271\pi\) | |||||||
\(648\) | −4.22149 | + | 25.1034i | −0.165836 | + | 0.986153i | ||||
\(649\) | 2.19125 | − | 3.79535i | 0.0860140 | − | 0.148981i | ||||
\(650\) | 14.8378 | + | 11.0139i | 0.581987 | + | 0.432002i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.6612 | + | 7.15630i | −0.926644 | + | 0.280262i | ||||
\(653\) | 4.35426 | + | 2.51393i | 0.170395 | + | 0.0983778i | 0.582772 | − | 0.812636i | \(-0.301968\pi\) |
−0.412377 | + | 0.911013i | \(0.635301\pi\) | |||||||
\(654\) | 0.858379 | + | 4.42958i | 0.0335653 | + | 0.173210i | ||||
\(655\) | −2.87661 | + | 1.66081i | −0.112398 | + | 0.0648933i | ||||
\(656\) | −22.9307 | + | 1.46508i | −0.895295 | + | 0.0572017i | ||||
\(657\) | 24.4814 | − | 17.2097i | 0.955109 | − | 0.671416i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.7930 | 0.771025 | 0.385512 | − | 0.922703i | \(-0.374025\pi\) | ||||
0.385512 | + | 0.922703i | \(0.374025\pi\) | |||||||
\(660\) | 0.183777 | + | 2.39880i | 0.00715349 | + | 0.0933734i | ||||
\(661\) | −11.3306 | − | 19.6252i | −0.440709 | − | 0.763331i | 0.557033 | − | 0.830490i | \(-0.311940\pi\) |
−0.997742 | + | 0.0671595i | \(0.978606\pi\) | |||||||
\(662\) | 25.1361 | + | 2.90215i | 0.976941 | + | 0.112795i | ||||
\(663\) | −27.0905 | − | 5.97948i | −1.05211 | − | 0.232224i | ||||
\(664\) | 11.4897 | − | 31.9870i | 0.445885 | − | 1.24134i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −31.1437 | − | 0.804573i | −1.20679 | − | 0.0311766i | ||||
\(667\) | 27.7290 | + | 16.0094i | 1.07367 | + | 0.619885i | ||||
\(668\) | −3.23691 | + | 3.45032i | −0.125240 | + | 0.133497i | ||||
\(669\) | 27.4729 | − | 30.0372i | 1.06216 | − | 1.16131i | ||||
\(670\) | −6.96403 | + | 3.01562i | −0.269044 | + | 0.116503i | ||||
\(671\) | −6.82530 | −0.263488 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.2766 | −0.434680 | −0.217340 | − | 0.976096i | \(-0.569738\pi\) | ||||
−0.217340 | + | 0.976096i | \(0.569738\pi\) | |||||||
\(674\) | 9.20584 | − | 3.98638i | 0.354596 | − | 0.153550i | ||||
\(675\) | 24.4822 | + | 3.15392i | 0.942320 | + | 0.121394i | ||||
\(676\) | −7.43656 | + | 7.92686i | −0.286022 | + | 0.304879i | ||||
\(677\) | 8.73729 | + | 5.04448i | 0.335801 | + | 0.193875i | 0.658414 | − | 0.752656i | \(-0.271228\pi\) |
−0.322612 | + | 0.946531i | \(0.604561\pi\) | |||||||
\(678\) | −8.20598 | + | 23.7874i | −0.315149 | + | 0.913551i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.78100 | − | 7.74223i | 0.106646 | − | 0.296901i | ||||
\(681\) | −7.15568 | + | 32.4193i | −0.274206 | + | 1.24231i | ||||
\(682\) | −13.5086 | − | 1.55967i | −0.517272 | − | 0.0597229i | ||||
\(683\) | 3.11743 | + | 5.39955i | 0.119285 | + | 0.206608i | 0.919485 | − | 0.393126i | \(-0.128606\pi\) |
−0.800199 | + | 0.599734i | \(0.795273\pi\) | |||||||
\(684\) | 5.56170 | + | 13.8114i | 0.212657 | + | 0.528093i | ||||
\(685\) | 6.08933 | 0.232662 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.9517 | − | 5.99476i | 0.723052 | − | 0.228714i | ||||
\(688\) | −14.0764 | + | 0.899358i | −0.536656 | + | 0.0342877i | ||||
\(689\) | −12.4936 | + | 7.21316i | −0.475967 | + | 0.274799i | ||||
\(690\) | −6.08238 | + | 1.17866i | −0.231552 | + | 0.0448709i | ||||
\(691\) | 14.7810 | + | 8.53381i | 0.562295 | + | 0.324641i | 0.754066 | − | 0.656798i | \(-0.228090\pi\) |
−0.191771 | + | 0.981440i | \(0.561423\pi\) | |||||||
\(692\) | 18.3200 | − | 5.54087i | 0.696423 | − | 0.210632i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.4367 | + | 7.74704i | 0.396172 | + | 0.294074i | ||||
\(695\) | −0.0119331 | + | 0.0206688i | −0.000452650 | + | 0.000784012i | ||||
\(696\) | −14.4439 | − | 27.4012i | −0.547495 | − | 1.03864i | ||||
\(697\) | −16.7256 | − | 28.9695i | −0.633526 | − | 1.09730i | ||||
\(698\) | 28.7235 | − | 12.4380i | 1.08720 | − | 0.470787i | ||||
\(699\) | 10.5610 | + | 33.3872i | 0.399452 | + | 1.26282i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.4324i | − | 0.809489i | −0.914430 | − | 0.404744i | \(-0.867360\pi\) | ||
0.914430 | − | 0.404744i | \(-0.132640\pi\) | |||||||
\(702\) | 4.86471 | − | 19.6181i | 0.183607 | − | 0.740436i | ||||
\(703\) | −15.7808 | + | 9.11104i | −0.595183 | + | 0.343629i | ||||
\(704\) | 1.83913 | − | 10.9709i | 0.0693147 | − | 0.413481i | ||||
\(705\) | −4.27793 | − | 0.944236i | −0.161116 | − | 0.0355620i | ||||
\(706\) | −9.04155 | + | 12.1807i | −0.340283 | + | 0.458425i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.16529 | − | 9.01060i | −0.231706 | − | 0.338639i | ||||
\(709\) | 4.27131 | − | 7.39813i | 0.160412 | − | 0.277843i | −0.774604 | − | 0.632446i | \(-0.782051\pi\) |
0.935017 | + | 0.354604i | \(0.115384\pi\) | |||||||
\(710\) | 3.18724 | + | 0.367990i | 0.119615 | + | 0.0138104i | ||||
\(711\) | −2.69143 | + | 5.79983i | −0.100937 | + | 0.217511i | ||||
\(712\) | −5.29310 | + | 4.47964i | −0.198367 | + | 0.167882i | ||||
\(713\) | − | 35.0186i | − | 1.31146i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1.91026i | − | 0.0714396i | ||||||
\(716\) | 40.4162 | + | 9.45880i | 1.51042 | + | 0.353492i | ||||
\(717\) | 8.82868 | + | 8.07495i | 0.329713 | + | 0.301565i | ||||
\(718\) | −0.584734 | + | 5.06450i | −0.0218221 | + | 0.189005i | ||||
\(719\) | 13.7366 | − | 23.7924i | 0.512287 | − | 0.887308i | −0.487611 | − | 0.873061i | \(-0.662132\pi\) |
0.999899 | − | 0.0142470i | \(-0.00453511\pi\) | |||||||
\(720\) | 5.58651 | + | 2.17114i | 0.208197 | + | 0.0809134i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −14.5829 | − | 10.8247i | −0.542719 | − | 0.402854i | ||||
\(723\) | −3.01137 | + | 13.6432i | −0.111994 | + | 0.507397i | ||||
\(724\) | 8.80495 | − | 9.38546i | 0.327233 | − | 0.348808i | ||||
\(725\) | −26.0123 | + | 15.0182i | −0.966074 | + | 0.557763i | ||||
\(726\) | 16.7692 | − | 14.5603i | 0.622364 | − | 0.540385i | ||||
\(727\) | − | 45.7930i | − | 1.69837i | −0.528096 | − | 0.849185i | \(-0.677094\pi\) | ||
0.528096 | − | 0.849185i | \(-0.322906\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.13303 | − | 26.0407i | −0.264186 | − | 0.964472i | ||||
\(730\) | −2.79982 | − | 6.46569i | −0.103626 | − | 0.239306i | ||||
\(731\) | −10.2672 | − | 17.7834i | −0.379747 | − | 0.657741i | ||||
\(732\) | −7.35212 | + | 15.3320i | −0.271742 | + | 0.566686i | ||||
\(733\) | −21.6466 | + | 37.4930i | −0.799535 | + | 1.38483i | 0.120385 | + | 0.992727i | \(0.461587\pi\) |
−0.919919 | + | 0.392107i | \(0.871746\pi\) | |||||||
\(734\) | 12.6661 | − | 17.0636i | 0.467514 | − | 0.629828i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.6091 | + | 1.46446i | 1.05455 | + | 0.0539807i | ||||
\(737\) | −12.9378 | − | 7.46966i | −0.476571 | − | 0.275148i | ||||
\(738\) | 21.4138 | − | 11.6365i | 0.788255 | − | 0.428346i | ||||
\(739\) | −4.48246 | + | 2.58795i | −0.164890 | + | 0.0951993i | −0.580174 | − | 0.814492i | \(-0.697016\pi\) |
0.415284 | + | 0.909692i | \(0.363682\pi\) | |||||||
\(740\) | −1.67153 | + | 7.14223i | −0.0614466 | + | 0.262553i | ||||
\(741\) | −3.56544 | − | 11.2717i | −0.130980 | − | 0.414077i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.5492 | −1.81778 | −0.908891 | − | 0.417034i | \(-0.863070\pi\) | ||||
−0.908891 | + | 0.417034i | \(0.863070\pi\) | |||||||
\(744\) | −18.0549 | + | 28.6650i | −0.661924 | + | 1.05091i | ||||
\(745\) | 0.572839 | + | 0.992187i | 0.0209872 | + | 0.0363509i | ||||
\(746\) | −0.430963 | + | 3.73265i | −0.0157787 | + | 0.136662i | ||||
\(747\) | 3.20849 | + | 35.9066i | 0.117393 | + | 1.31375i | ||||
\(748\) | 15.5011 | − | 4.68828i | 0.566775 | − | 0.171420i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.89023 | − | 11.2770i | 0.142051 | − | 0.411777i | ||||
\(751\) | −26.4899 | − | 15.2939i | −0.966630 | − | 0.558084i | −0.0684228 | − | 0.997656i | \(-0.521797\pi\) |
−0.898207 | + | 0.439572i | \(0.855130\pi\) | |||||||
\(752\) | 18.1525 | + | 8.98897i | 0.661953 | + | 0.327794i | ||||
\(753\) | 26.0822 | + | 23.8555i | 0.950489 | + | 0.869344i | ||||
\(754\) | 9.77315 | + | 22.5694i | 0.355917 | + | 0.821927i | ||||
\(755\) | 6.56086 | 0.238774 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.4533 | 1.68837 | 0.844187 | − | 0.536049i | \(-0.180084\pi\) | ||||
0.844187 | + | 0.536049i | \(0.180084\pi\) | |||||||
\(758\) | 9.95524 | + | 22.9899i | 0.361591 | + | 0.835030i | ||||
\(759\) | −8.99971 | − | 8.23138i | −0.326669 | − | 0.298780i | ||||
\(760\) | 3.44980 | − | 0.623315i | 0.125137 | − | 0.0226100i | ||||
\(761\) | 34.1633 | + | 19.7242i | 1.23842 | + | 0.715002i | 0.968771 | − | 0.247956i | \(-0.0797589\pi\) |
0.269649 | + | 0.962959i | \(0.413092\pi\) | |||||||
\(762\) | 1.20799 | − | 3.50172i | 0.0437609 | − | 0.126854i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.1520 | + | 33.5659i | 0.367285 | + | 1.21437i | ||||
\(765\) | 0.776595 | + | 8.69095i | 0.0280778 | + | 0.314222i | ||||
\(766\) | −5.34004 | + | 46.2511i | −0.192943 | + | 1.67112i | ||||
\(767\) | 4.33449 | + | 7.50756i | 0.156509 | + | 0.271082i | ||||
\(768\) | −22.6634 | − | 15.9490i | −0.817794 | − | 0.575511i | ||||
\(769\) | −39.7256 | −1.43254 | −0.716270 | − | 0.697823i | \(-0.754152\pi\) | ||||
−0.716270 | + | 0.697823i | \(0.754152\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.2136 | + | 44.9346i | 0.511891 | + | 1.61828i | ||||
\(772\) | 4.25520 | + | 0.995865i | 0.153148 | + | 0.0358420i | ||||
\(773\) | 18.9935 | − | 10.9659i | 0.683149 | − | 0.394416i | −0.117891 | − | 0.993026i | \(-0.537613\pi\) |
0.801040 | + | 0.598610i | \(0.204280\pi\) | |||||||
\(774\) | 13.1452 | − | 7.14324i | 0.472494 | − | 0.256758i | ||||
\(775\) | 28.4495 | + | 16.4253i | 1.02194 | + | 0.590015i | ||||
\(776\) | −0.502967 | + | 1.40025i | −0.0180554 | + | 0.0502660i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.75054 | − | 7.74704i | 0.206167 | − | 0.277745i | ||||
\(779\) | 7.12742 | − | 12.3451i | 0.255366 | − | 0.442307i | ||||
\(780\) | −4.29111 | − | 2.05771i | −0.153646 | − | 0.0736777i | ||||
\(781\) | 3.15799 | + | 5.46980i | 0.113002 | + | 0.195725i | ||||
\(782\) | 16.5721 | + | 38.2703i | 0.592617 | + | 1.36854i | ||||
\(783\) | 26.1203 | + | 19.9277i | 0.933464 | + | 0.712157i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.20029i | 0.149915i | ||||||||
\(786\) | −12.3004 | + | 10.6801i | −0.438740 | + | 0.380948i | ||||
\(787\) | −4.36864 | + | 2.52223i | −0.155725 | + | 0.0899080i | −0.575838 | − | 0.817564i | \(-0.695324\pi\) |
0.420112 | + | 0.907472i | \(0.361991\pi\) | |||||||
\(788\) | 9.15574 | + | 8.58944i | 0.326160 | + | 0.305986i | ||||
\(789\) | 1.34578 | − | 6.09717i | 0.0479111 | − | 0.217065i | ||||
\(790\) | 1.20881 | + | 0.897287i | 0.0430076 | + | 0.0319240i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.12291 | + | 11.3780i | 0.110968 | + | 0.404299i | ||||
\(793\) | 6.75054 | − | 11.6923i | 0.239719 | − | 0.415205i | ||||
\(794\) | −3.38101 | + | 29.2835i | −0.119987 | + | 1.03923i | ||||
\(795\) | 3.34813 | + | 3.06230i | 0.118746 | + | 0.108608i | ||||
\(796\) | 0.394466 | − | 1.68550i | 0.0139815 | − | 0.0597410i | ||||
\(797\) | 28.3335i | 1.00362i | 0.864977 | + | 0.501812i | \(0.167333\pi\) | ||||
−0.864977 | + | 0.501812i | \(0.832667\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.4894i | 1.04326i | ||||||||
\(800\) | −14.6087 | + | 22.5554i | −0.516496 | + | 0.797455i | ||||
\(801\) | 3.09595 | − | 6.67155i | 0.109390 | − | 0.235728i | ||||
\(802\) | −5.37427 | − | 0.620500i | −0.189772 | − | 0.0219106i | ||||
\(803\) | 6.93514 | − | 12.0120i | 0.244736 | − | 0.423895i | ||||
\(804\) | −30.7159 | + | 21.0166i | −1.08327 | + | 0.741200i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.0325 | − | 21.5987i | 0.564721 | − | 0.760783i | ||||
\(807\) | 44.2545 | + | 9.76797i | 1.55783 | + | 0.343849i | ||||
\(808\) | 8.09475 | + | 44.8011i | 0.284772 | + | 1.57610i | ||||
\(809\) | −17.5088 | + | 10.1087i | −0.615577 | + | 0.355404i | −0.775145 | − | 0.631783i | \(-0.782323\pi\) |
0.159568 | + | 0.987187i | \(0.448990\pi\) | |||||||
\(810\) | −6.34442 | + | 0.402085i | −0.222920 | + | 0.0141278i | ||||
\(811\) | − | 1.33368i | − | 0.0468317i | −0.999726 | − | 0.0234158i | \(-0.992546\pi\) | ||
0.999726 | − | 0.0234158i | \(-0.00745418\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0468 | − | 38.0845i | −0.422500 | − | 1.33568i | ||||
\(814\) | −13.2509 | + | 5.73799i | −0.464443 | + | 0.201117i | ||||
\(815\) | −3.08666 | − | 5.34625i | −0.108121 | − | 0.187271i | ||||
\(816\) | 6.16605 | − | 39.8709i | 0.215855 | − | 1.39576i | ||||
\(817\) | 4.37527 | − | 7.57819i | 0.153071 | − | 0.265127i | ||||
\(818\) | −4.39361 | − | 3.26133i | −0.153619 | − | 0.114030i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.66120 | − | 5.49251i | −0.0580117 | − | 0.191807i | ||||
\(821\) | 4.59977 | + | 2.65568i | 0.160533 | + | 0.0926838i | 0.578114 | − | 0.815956i | \(-0.303789\pi\) |
−0.417581 | + | 0.908640i | \(0.637122\pi\) | |||||||
\(822\) | 29.3181 | − | 5.68136i | 1.02259 | − | 0.198160i | ||||
\(823\) | −13.2508 | + | 7.65035i | −0.461894 | + | 0.266675i | −0.712840 | − | 0.701326i | \(-0.752592\pi\) |
0.250946 | + | 0.968001i | \(0.419258\pi\) | |||||||
\(824\) | −4.05167 | + | 3.42899i | −0.141146 | + | 0.119455i | ||||
\(825\) | 10.9085 | − | 3.45056i | 0.379786 | − | 0.120133i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.288306 | 0.0100254 | 0.00501270 | − | 0.999987i | \(-0.498404\pi\) | ||||
0.00501270 | + | 0.999987i | \(0.498404\pi\) | |||||||
\(828\) | −28.1849 | + | 11.3497i | −0.979493 | + | 0.394431i | ||||
\(829\) | −20.5551 | − | 35.6025i | −0.713908 | − | 1.23653i | −0.963379 | − | 0.268143i | \(-0.913590\pi\) |
0.249471 | − | 0.968382i | \(-0.419743\pi\) | |||||||
\(830\) | 8.43186 | + | 0.973522i | 0.292674 | + | 0.0337914i | ||||
\(831\) | −7.57498 | + | 34.3190i | −0.262773 | + | 1.19051i | ||||
\(832\) | 16.9750 | + | 14.0013i | 0.588504 | + | 0.485408i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.0381700 | + | 0.110647i | −0.00132172 | + | 0.00383139i | ||||
\(835\) | −1.02319 | − | 0.590740i | −0.0354090 | − | 0.0204434i | ||||
\(836\) | 5.03300 | + | 4.72170i | 0.174070 | + | 0.163303i | ||||
\(837\) | 4.59102 | − | 35.6376i | 0.158689 | − | 1.23182i | ||||
\(838\) | 17.5371 | − | 7.59406i | 0.605810 | − | 0.262333i | ||||
\(839\) | −25.7705 | −0.889695 | −0.444848 | − | 0.895606i | \(-0.646742\pi\) | ||||
−0.444848 | + | 0.895606i | \(0.646742\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.9772 | −0.378523 | ||||||||
\(842\) | 14.7718 | − | 6.39659i | 0.509070 | − | 0.220441i | ||||
\(843\) | 32.3381 | − | 35.3566i | 1.11378 | − | 1.21775i | ||||
\(844\) | 5.69463 | + | 5.34240i | 0.196017 | + | 0.183893i | ||||
\(845\) | −2.35071 | − | 1.35718i | −0.0808669 | − | 0.0466885i | ||||
\(846\) | −21.4778 | − | 0.554862i | −0.738421 | − | 0.0190766i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.6270 | − | 17.4631i | −0.399271 | − | 0.599685i | ||||
\(849\) | 29.3798 | + | 6.48478i | 1.00831 | + | 0.222557i | ||||
\(850\) | −38.8642 | − | 4.48717i | −1.33303 | − | 0.153909i | ||||
\(851\) | −18.5929 | − | 32.2038i | −0.637355 | − | 1.10393i | ||||
\(852\) | 15.6888 | − | 1.20195i | 0.537490 | − | 0.0411780i | ||||
\(853\) | 51.4656 | 1.76215 | 0.881074 | − | 0.472978i | \(-0.156821\pi\) | ||||
0.881074 | + | 0.472978i | \(0.156821\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.04190 | + | 2.13838i | −0.104031 | + | 0.0731309i | ||||
\(856\) | −13.2993 | − | 15.7143i | −0.454560 | − | 0.537104i | ||||
\(857\) | 30.8099 | − | 17.7881i | 1.05245 | − | 0.607631i | 0.129114 | − | 0.991630i | \(-0.458787\pi\) |
0.923334 | + | 0.383999i | \(0.125453\pi\) | |||||||
\(858\) | −1.78227 | − | 9.19726i | −0.0608459 | − | 0.313989i | ||||
\(859\) | −44.4334 | − | 25.6536i | −1.51605 | − | 0.875290i | −0.999823 | − | 0.0188372i | \(-0.994004\pi\) |
−0.516225 | − | 0.856453i | \(-0.672663\pi\) | |||||||
\(860\) | −1.01975 | − | 3.37165i | −0.0347732 | − | 0.114972i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.4388 | − | 21.8521i | −1.00269 | − | 0.744286i | ||||
\(863\) | 5.89152 | − | 10.2044i | 0.200550 | − | 0.347362i | −0.748156 | − | 0.663523i | \(-0.769061\pi\) |
0.948706 | + | 0.316161i | \(0.102394\pi\) | |||||||
\(864\) | 28.9228 | + | 5.24106i | 0.983975 | + | 0.178305i | ||||
\(865\) | 2.38989 | + | 4.13941i | 0.0812587 | + | 0.140744i | ||||
\(866\) | −30.3450 | + | 13.1402i | −1.03116 | + | 0.446522i | ||||
\(867\) | 27.9263 | − | 8.83360i | 0.948428 | − | 0.300005i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.96357i | 0.100532i | ||||||||
\(870\) | 5.84095 | − | 5.07156i | 0.198027 | − | 0.171942i | ||||
\(871\) | 25.5922 | − | 14.7757i | 0.867160 | − | 0.500655i | ||||
\(872\) | 5.12698 | − | 0.926351i | 0.173621 | − | 0.0313702i | ||||
\(873\) | −0.140454 | − | 1.57183i | −0.00475364 | − | 0.0531984i | ||||
\(874\) | −10.5925 | + | 14.2701i | −0.358298 | + | 0.482694i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −19.5127 | − | 28.5179i | −0.659273 | − | 0.963531i | ||||
\(877\) | −0.664314 | + | 1.15063i | −0.0224323 | + | 0.0388539i | −0.877024 | − | 0.480447i | \(-0.840474\pi\) |
0.854591 | + | 0.519301i | \(0.173808\pi\) | |||||||
\(878\) | 24.8287 | + | 2.86666i | 0.837927 | + | 0.0967450i | ||||
\(879\) | 23.3411 | − | 25.5198i | 0.787275 | − | 0.860760i | ||||
\(880\) | 2.77237 | − | 0.177130i | 0.0934564 | − | 0.00597106i | ||||
\(881\) | − | 23.8258i | − | 0.802713i | −0.915922 | − | 0.401356i | \(-0.868539\pi\) | ||
0.915922 | − | 0.401356i | \(-0.131461\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.2235i | 1.01710i | 0.861032 | + | 0.508551i | \(0.169819\pi\) | ||||
−0.861032 | + | 0.508551i | \(0.830181\pi\) | |||||||
\(884\) | −7.29989 | + | 31.1915i | −0.245522 | + | 1.04908i | ||||
\(885\) | 1.84018 | − | 2.01194i | 0.0618569 | − | 0.0676307i | ||||
\(886\) | 5.69923 | − | 49.3621i | 0.191469 | − | 1.65835i | ||||
\(887\) | −10.9556 | + | 18.9756i | −0.367852 | + | 0.637138i | −0.989229 | − | 0.146373i | \(-0.953240\pi\) |
0.621377 | + | 0.783511i | \(0.286573\pi\) | |||||||
\(888\) | −1.38415 | + | 35.9470i | −0.0464489 | + | 1.20630i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.39050 | − | 1.03215i | −0.0466096 | − | 0.0345978i | ||||
\(891\) | −8.07964 | − | 9.55676i | −0.270678 | − | 0.320164i | ||||
\(892\) | −34.2797 | − | 32.1594i | −1.14777 | − | 1.07678i | ||||
\(893\) | −10.8830 | + | 6.28330i | −0.364185 | + | 0.210262i | ||||
\(894\) | 3.68374 | + | 4.24259i | 0.123203 | + | 0.141893i | ||||
\(895\) | 10.3660i | 0.346496i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.0021 | − | 7.27599i | 0.768019 | − | 0.242938i | ||||
\(898\) | 3.10618 | + | 7.17317i | 0.103655 | + | 0.239372i | ||||
\(899\) | 21.8614 | + | 37.8650i | 0.729117 | + | 1.26287i | ||||
\(900\) | 3.99936 | − | 28.2212i | 0.133312 | − | 0.940708i | ||||
\(901\) | 15.2713 | − | 26.4507i | 0.508761 | − | 0.881200i | ||||
\(902\) | 6.73281 | − | 9.07034i | 0.224178 | − | 0.302009i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.3452 | + | 9.82235i | 0.909489 | + | 0.326687i | ||||
\(905\) | 2.78326 | + | 1.60692i | 0.0925187 | + | 0.0534157i | ||||
\(906\) | 31.5883 | − | 6.12129i | 1.04945 | − | 0.203366i | ||||
\(907\) | 42.4039 | − | 24.4819i | 1.40800 | − | 0.812907i | 0.412802 | − | 0.910821i | \(-0.364550\pi\) |
0.995195 | + | 0.0979134i | \(0.0312168\pi\) | |||||||
\(908\) | 37.3270 | + | 8.73583i | 1.23874 | + | 0.289909i | ||||
\(909\) | −27.7702 | − | 39.5040i | −0.921081 | − | 1.31026i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.8251 | 1.71704 | 0.858522 | − | 0.512777i | \(-0.171383\pi\) | ||||
0.858522 | + | 0.512777i | \(0.171383\pi\) | |||||||
\(912\) | 16.0281 | − | 6.21972i | 0.530742 | − | 0.205955i | ||||
\(913\) | 8.35449 | + | 14.4704i | 0.276493 | + | 0.478900i | ||||
\(914\) | −3.88515 | + | 33.6500i | −0.128509 | + | 1.11304i | ||||
\(915\) | −4.14655 | − | 0.915237i | −0.137081 | − | 0.0302568i | ||||
\(916\) | −6.64461 | − | 21.9694i | −0.219544 | − | 0.725889i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 11.8477 | + | 41.1194i | 0.391033 | + | 1.35714i | ||||
\(919\) | −43.7375 | − | 25.2518i | −1.44277 | − | 0.832981i | −0.444732 | − | 0.895664i | \(-0.646701\pi\) |
−0.998034 | + | 0.0626826i | \(0.980034\pi\) | |||||||
\(920\) | 1.27200 | + | 7.03999i | 0.0419365 | + | 0.232102i | ||||
\(921\) | −16.5443 | + | 18.0886i | −0.545153 | + | 0.596038i | ||||
\(922\) | 1.68410 | + | 3.88912i | 0.0554628 | + | 0.128081i | ||||
\(923\) | −12.4936 | −0.411232 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.8836 | 1.14696 | ||||||||
\(926\) | 12.5966 | + | 29.0896i | 0.413950 | + | 0.955944i | ||||
\(927\) | 2.36984 | − | 5.10682i | 0.0778356 | − | 0.167730i | ||||
\(928\) | −31.8488 | + | 16.2766i | −1.04549 | + | 0.534304i | ||||
\(929\) | 1.07011 | + | 0.617830i | 0.0351093 | + | 0.0202703i | 0.517452 | − | 0.855712i | \(-0.326881\pi\) |
−0.482343 | + | 0.875983i | \(0.660214\pi\) | |||||||
\(930\) | −7.99770 | − | 2.75898i | −0.262255 | − | 0.0904705i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 38.7034 | − | 11.7058i | 1.26777 | − | 0.383436i | ||||
\(933\) | 9.16676 | − | 41.5307i | 0.300106 | − | 1.35965i | ||||
\(934\) | 1.95639 | − | 16.9447i | 0.0640151 | − | 0.554447i | ||||
\(935\) | 2.02215 | + | 3.50247i | 0.0661314 | + | 0.114543i | ||||
\(936\) | −22.5801 | − | 5.90356i | −0.738053 | − | 0.192964i | ||||
\(937\) | 29.4139 | 0.960909 | 0.480455 | − | 0.877020i | \(-0.340472\pi\) | ||||
0.480455 | + | 0.877020i | \(0.340472\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.0859759 | − | 0.0271957i | 0.00280572 | − | 0.000887499i | ||||
\(940\) | −1.15275 | + | 4.92553i | −0.0375984 | + | 0.160653i | ||||
\(941\) | −38.8530 | + | 22.4318i | −1.26657 | + | 0.731256i | −0.974338 | − | 0.225090i | \(-0.927732\pi\) |
−0.292235 | + | 0.956346i | \(0.594399\pi\) | |||||||
\(942\) | 3.91888 | + | 20.2230i | 0.127684 | + | 0.658901i | ||||
\(943\) | 25.1925 | + | 14.5449i | 0.820381 | + | 0.473647i | ||||
\(944\) | −10.4938 | + | 6.98680i | −0.341545 | + | 0.227401i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.13303 | − | 5.56796i | 0.134376 | − | 0.181030i | ||||
\(947\) | −8.77882 | + | 15.2054i | −0.285273 | + | 0.494108i | −0.972675 | − | 0.232169i | \(-0.925418\pi\) |
0.687402 | + | 0.726277i | \(0.258751\pi\) | |||||||
\(948\) | 6.65720 | + | 3.19231i | 0.216216 | + | 0.103682i | ||||
\(949\) | 13.7183 | + | 23.7609i | 0.445316 | + | 0.771311i | ||||
\(950\) | −6.62481 | − | 15.2988i | −0.214937 | − | 0.496359i | ||||
\(951\) | −3.53984 | − | 11.1908i | −0.114787 | − | 0.362886i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 37.1546i | − | 1.20356i | −0.798663 | − | 0.601778i | \(-0.794459\pi\) | ||
0.798663 | − | 0.601778i | \(-0.205541\pi\) | |||||||
\(954\) | 18.9773 | + | 11.6201i | 0.614412 | + | 0.376215i | ||||
\(955\) | −7.58422 | + | 4.37875i | −0.245420 | + | 0.141693i | ||||
\(956\) | 9.45244 | − | 10.0756i | 0.305714 | − | 0.325870i | ||||
\(957\) | 14.8699 | + | 3.28212i | 0.480675 | + | 0.106096i | ||||
\(958\) | 15.2245 | + | 11.3010i | 0.491881 | + | 0.365118i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.58846 | − | 6.41850i | 0.0835422 | − | 0.207156i | ||||
\(961\) | 8.40960 | − | 14.5658i | 0.271277 | − | 0.469866i | ||||
\(962\) | 3.27610 | − | 28.3749i | 0.105626 | − | 0.914845i | ||||
\(963\) | 19.8067 | + | 9.19136i | 0.638262 | + | 0.296187i | ||||
\(964\) | 15.7086 | + | 3.67635i | 0.505939 | + | 0.118407i | ||||
\(965\) | 1.09138i | 0.0351326i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 53.9045i | − | 1.73345i | −0.498786 | − | 0.866725i | \(-0.666221\pi\) | ||
0.498786 | − | 0.866725i | \(-0.333779\pi\) | |||||||
\(968\) | −16.5664 | − | 19.5747i | −0.532464 | − | 0.629154i | ||||
\(969\) | 18.4692 | + | 16.8924i | 0.593316 | + | 0.542663i | ||||
\(970\) | −0.369110 | − | 0.0426165i | −0.0118514 | − | 0.00136833i | ||||
\(971\) | 19.1783 | − | 33.2177i | 0.615460 | − | 1.06601i | −0.374844 | − | 0.927088i | \(-0.622304\pi\) |
0.990304 | − | 0.138920i | \(-0.0443631\pi\) | |||||||
\(972\) | −30.1711 | + | 7.85526i | −0.967738 | + | 0.251957i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.2906 | + | 13.8633i | −0.329731 | + | 0.444208i | ||||
\(975\) | −4.87795 | + | 22.0999i | −0.156220 | + | 0.707764i | ||||
\(976\) | 17.5950 | + | 8.71290i | 0.563202 | + | 0.278893i | ||||
\(977\) | 15.5907 | − | 9.00127i | 0.498789 | − | 0.287976i | −0.229424 | − | 0.973327i | \(-0.573684\pi\) |
0.728214 | + | 0.685350i | \(0.240351\pi\) | |||||||
\(978\) | −19.8493 | − | 22.8605i | −0.634710 | − | 0.730999i | ||||
\(979\) | − | 3.40899i | − | 0.108952i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.52078 | + | 3.17799i | −0.144337 | + | 0.101465i | ||||
\(982\) | −51.7783 | + | 22.4214i | −1.65231 | + | 0.715497i | ||||
\(983\) | −6.87845 | − | 11.9138i | −0.219388 | − | 0.379992i | 0.735233 | − | 0.677815i | \(-0.237073\pi\) |
−0.954621 | + | 0.297823i | \(0.903740\pi\) | |||||||
\(984\) | −13.1226 | − | 24.8947i | −0.418335 | − | 0.793613i | ||||
\(985\) | −1.56758 | + | 2.71514i | −0.0499474 | + | 0.0865114i | ||||
\(986\) | −41.8104 | − | 31.0354i | −1.33151 | − | 0.988368i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.0665 | + | 3.95195i | −0.415701 | + | 0.125728i | ||||
\(989\) | 15.4648 | + | 8.92860i | 0.491751 | + | 0.283913i | ||||
\(990\) | −2.58897 | + | 1.40687i | −0.0822829 | + | 0.0447134i | ||||
\(991\) | 1.60779 | − | 0.928258i | 0.0510731 | − | 0.0294871i | −0.474246 | − | 0.880392i | \(-0.657279\pi\) |
0.525319 | + | 0.850905i | \(0.323946\pi\) | |||||||
\(992\) | 32.8330 | + | 21.2653i | 1.04245 | + | 0.675172i | ||||
\(993\) | 9.34619 | + | 29.5468i | 0.296593 | + | 0.937640i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.432298 | 0.0137048 | ||||||||
\(996\) | 41.5049 | − | 3.17976i | 1.31513 | − | 0.100755i | ||||
\(997\) | 30.1748 | + | 52.2642i | 0.955644 | + | 1.65522i | 0.732888 | + | 0.680350i | \(0.238172\pi\) |
0.222756 | + | 0.974874i | \(0.428495\pi\) | |||||||
\(998\) | 11.9066 | + | 1.37471i | 0.376897 | + | 0.0435156i | ||||
\(999\) | −14.6995 | − | 35.2106i | −0.465073 | − | 1.11401i |
(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 | 588.2.n.e.275.11 | 24 | ||
3.2 | odd | 2 | inner | 588.2.n.e.275.2 | 24 | ||
4.3 | odd | 2 | inner | 588.2.n.e.275.7 | 24 | ||
7.2 | even | 3 | 588.2.e.d.491.3 | 12 | |||
7.3 | odd | 6 | 84.2.n.a.11.6 | yes | 24 | ||
7.4 | even | 3 | inner | 588.2.n.e.263.6 | 24 | ||
7.5 | odd | 6 | 588.2.e.e.491.3 | 12 | |||
7.6 | odd | 2 | 84.2.n.a.23.11 | yes | 24 | ||
12.11 | even | 2 | inner | 588.2.n.e.275.6 | 24 | ||
21.2 | odd | 6 | 588.2.e.d.491.10 | 12 | |||
21.5 | even | 6 | 588.2.e.e.491.10 | 12 | |||
21.11 | odd | 6 | inner | 588.2.n.e.263.7 | 24 | ||
21.17 | even | 6 | 84.2.n.a.11.7 | yes | 24 | ||
21.20 | even | 2 | 84.2.n.a.23.2 | yes | 24 | ||
28.3 | even | 6 | 84.2.n.a.11.2 | ✓ | 24 | ||
28.11 | odd | 6 | inner | 588.2.n.e.263.2 | 24 | ||
28.19 | even | 6 | 588.2.e.e.491.9 | 12 | |||
28.23 | odd | 6 | 588.2.e.d.491.9 | 12 | |||
28.27 | even | 2 | 84.2.n.a.23.7 | yes | 24 | ||
84.11 | even | 6 | inner | 588.2.n.e.263.11 | 24 | ||
84.23 | even | 6 | 588.2.e.d.491.4 | 12 | |||
84.47 | odd | 6 | 588.2.e.e.491.4 | 12 | |||
84.59 | odd | 6 | 84.2.n.a.11.11 | yes | 24 | ||
84.83 | odd | 2 | 84.2.n.a.23.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.n.a.11.2 | ✓ | 24 | 28.3 | even | 6 | ||
84.2.n.a.11.6 | yes | 24 | 7.3 | odd | 6 | ||
84.2.n.a.11.7 | yes | 24 | 21.17 | even | 6 | ||
84.2.n.a.11.11 | yes | 24 | 84.59 | odd | 6 | ||
84.2.n.a.23.2 | yes | 24 | 21.20 | even | 2 | ||
84.2.n.a.23.6 | yes | 24 | 84.83 | odd | 2 | ||
84.2.n.a.23.7 | yes | 24 | 28.27 | even | 2 | ||
84.2.n.a.23.11 | yes | 24 | 7.6 | odd | 2 | ||
588.2.e.d.491.3 | 12 | 7.2 | even | 3 | |||
588.2.e.d.491.4 | 12 | 84.23 | even | 6 | |||
588.2.e.d.491.9 | 12 | 28.23 | odd | 6 | |||
588.2.e.d.491.10 | 12 | 21.2 | odd | 6 | |||
588.2.e.e.491.3 | 12 | 7.5 | odd | 6 | |||
588.2.e.e.491.4 | 12 | 84.47 | odd | 6 | |||
588.2.e.e.491.9 | 12 | 28.19 | even | 6 | |||
588.2.e.e.491.10 | 12 | 21.5 | even | 6 | |||
588.2.n.e.263.2 | 24 | 28.11 | odd | 6 | inner | ||
588.2.n.e.263.6 | 24 | 7.4 | even | 3 | inner | ||
588.2.n.e.263.7 | 24 | 21.11 | odd | 6 | inner | ||
588.2.n.e.263.11 | 24 | 84.11 | even | 6 | inner | ||
588.2.n.e.275.2 | 24 | 3.2 | odd | 2 | inner | ||
588.2.n.e.275.6 | 24 | 12.11 | even | 2 | inner | ||
588.2.n.e.275.7 | 24 | 4.3 | odd | 2 | inner | ||
588.2.n.e.275.11 | 24 | 1.1 | even | 1 | trivial |