Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(31,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([2, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.bc (of order \(12\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Character | \(\chi\) | \(=\) | 637.31 |
Dual form | 637.2.bc.a.411.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.16746 | − | 0.312819i | −0.825517 | − | 0.221197i | −0.178760 | − | 0.983893i | \(-0.557208\pi\) |
−0.646757 | + | 0.762696i | \(0.723875\pi\) | |||||||
\(3\) | −1.96915 | − | 1.13689i | −1.13689 | − | 0.656384i | −0.191232 | − | 0.981545i | \(-0.561248\pi\) |
−0.945659 | + | 0.325160i | \(0.894582\pi\) | |||||||
\(4\) | −0.466951 | − | 0.269594i | −0.233476 | − | 0.134797i | ||||
\(5\) | −0.224373 | + | 0.837372i | −0.100343 | + | 0.374484i | −0.997775 | − | 0.0666675i | \(-0.978763\pi\) |
0.897432 | + | 0.441152i | \(0.145430\pi\) | |||||||
\(6\) | 1.94326 | + | 1.94326i | 0.793333 | + | 0.793333i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.17009 | + | 2.17009i | 0.767241 | + | 0.767241i | ||||
\(9\) | 1.08504 | + | 1.87935i | 0.361681 | + | 0.626450i | ||||
\(10\) | 0.523892 | − | 0.907408i | 0.165669 | − | 0.286948i | ||||
\(11\) | 2.53348 | − | 0.678845i | 0.763874 | − | 0.204679i | 0.144210 | − | 0.989547i | \(-0.453936\pi\) |
0.619663 | + | 0.784868i | \(0.287269\pi\) | |||||||
\(12\) | 0.612999 | + | 1.06175i | 0.176958 | + | 0.306500i | ||||
\(13\) | −0.104263 | − | 3.60404i | −0.0289173 | − | 0.999582i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.39383 | − | 1.39383i | 0.359884 | − | 0.359884i | ||||
\(16\) | −1.31545 | − | 2.27842i | −0.328862 | − | 0.569606i | ||||
\(17\) | 1.52363 | − | 2.63901i | 0.369535 | − | 0.640053i | −0.619958 | − | 0.784635i | \(-0.712850\pi\) |
0.989493 | + | 0.144582i | \(0.0461837\pi\) | |||||||
\(18\) | −0.678845 | − | 2.53348i | −0.160005 | − | 0.597147i | ||||
\(19\) | 0.0381629 | − | 0.142426i | 0.00875516 | − | 0.0326747i | −0.961410 | − | 0.275119i | \(-0.911283\pi\) |
0.970165 | + | 0.242445i | \(0.0779493\pi\) | |||||||
\(20\) | 0.330522 | − | 0.330522i | 0.0739070 | − | 0.0739070i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.17009 | −0.675865 | ||||||||
\(23\) | 5.63805 | − | 3.25513i | 1.17561 | − | 0.678741i | 0.220619 | − | 0.975360i | \(-0.429192\pi\) |
0.954996 | + | 0.296619i | \(0.0958590\pi\) | |||||||
\(24\) | −1.80608 | − | 6.74039i | −0.368665 | − | 1.37588i | ||||
\(25\) | 3.67928 | + | 2.12423i | 0.735856 | + | 0.424846i | ||||
\(26\) | −1.00569 | + | 4.24018i | −0.197232 | + | 0.831568i | ||||
\(27\) | 1.88704i | 0.363162i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.78765 | −0.703350 | −0.351675 | − | 0.936122i | \(-0.614388\pi\) | ||||
−0.351675 | + | 0.936122i | \(0.614388\pi\) | |||||||
\(30\) | −2.06325 | + | 1.19122i | −0.376696 | + | 0.217485i | ||||
\(31\) | −9.25250 | + | 2.47920i | −1.66180 | + | 0.445278i | −0.962881 | − | 0.269925i | \(-0.913001\pi\) |
−0.698917 | + | 0.715203i | \(0.746334\pi\) | |||||||
\(32\) | −0.765619 | − | 2.85733i | −0.135344 | − | 0.505109i | ||||
\(33\) | −5.76059 | − | 1.54354i | −1.00279 | − | 0.268697i | ||||
\(34\) | −2.60430 | + | 2.60430i | −0.446635 | + | 0.446635i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 1.17009i | − | 0.195014i | ||||||
\(37\) | −0.741100 | + | 2.76582i | −0.121836 | + | 0.454699i | −0.999707 | − | 0.0241984i | \(-0.992297\pi\) |
0.877871 | + | 0.478897i | \(0.158963\pi\) | |||||||
\(38\) | −0.0891070 | + | 0.154338i | −0.0144551 | + | 0.0250369i | ||||
\(39\) | −3.89210 | + | 7.21545i | −0.623234 | + | 1.15540i | ||||
\(40\) | −2.30408 | + | 1.33026i | −0.364307 | + | 0.210333i | ||||
\(41\) | −2.27378 | − | 2.27378i | −0.355105 | − | 0.355105i | 0.506900 | − | 0.862005i | \(-0.330791\pi\) |
−0.862005 | + | 0.506900i | \(0.830791\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.18342i | − | 0.485467i | −0.970093 | − | 0.242733i | \(-0.921956\pi\) | ||
0.970093 | − | 0.242733i | \(-0.0780440\pi\) | |||||||
\(44\) | −1.36603 | − | 0.366025i | −0.205936 | − | 0.0551804i | ||||
\(45\) | −1.81717 | + | 0.486909i | −0.270888 | + | 0.0725842i | ||||
\(46\) | −7.60045 | + | 2.03653i | −1.12062 | + | 0.300270i | ||||
\(47\) | −7.12626 | − | 1.90947i | −1.03947 | − | 0.278525i | −0.301577 | − | 0.953442i | \(-0.597513\pi\) |
−0.737894 | + | 0.674916i | \(0.764180\pi\) | |||||||
\(48\) | 5.98209i | 0.863440i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.63090 | − | 3.63090i | −0.513486 | − | 0.513486i | ||||
\(51\) | −6.00053 | + | 3.46441i | −0.840242 | + | 0.485114i | ||||
\(52\) | −0.922944 | + | 1.71102i | −0.127989 | + | 0.237276i | ||||
\(53\) | −1.71594 | + | 2.97210i | −0.235703 | + | 0.408249i | −0.959477 | − | 0.281788i | \(-0.909072\pi\) |
0.723774 | + | 0.690037i | \(0.242406\pi\) | |||||||
\(54\) | 0.590303 | − | 2.20304i | 0.0803301 | − | 0.299796i | ||||
\(55\) | 2.27378i | 0.306597i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.237071 | + | 0.237071i | −0.0314008 | + | 0.0314008i | ||||
\(58\) | 4.42192 | + | 1.18485i | 0.580627 | + | 0.155578i | ||||
\(59\) | −3.34963 | − | 12.5010i | −0.436084 | − | 1.62749i | −0.738459 | − | 0.674299i | \(-0.764446\pi\) |
0.302375 | − | 0.953189i | \(-0.402221\pi\) | |||||||
\(60\) | −1.02662 | + | 0.275081i | −0.132536 | + | 0.0355128i | ||||
\(61\) | 7.97398 | − | 4.60378i | 1.02096 | − | 0.589454i | 0.106581 | − | 0.994304i | \(-0.466010\pi\) |
0.914383 | + | 0.404850i | \(0.132676\pi\) | |||||||
\(62\) | 11.5774 | 1.47034 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.83710i | 1.10464i | ||||||||
\(65\) | 3.04132 | + | 0.721344i | 0.377229 | + | 0.0894717i | ||||
\(66\) | 6.24239 | + | 3.60404i | 0.768385 | + | 0.443627i | ||||
\(67\) | −0.384125 | − | 1.43357i | −0.0469283 | − | 0.175139i | 0.938484 | − | 0.345323i | \(-0.112231\pi\) |
−0.985412 | + | 0.170184i | \(0.945564\pi\) | |||||||
\(68\) | −1.42292 | + | 0.821525i | −0.172555 | + | 0.0996245i | ||||
\(69\) | −14.8029 | −1.78206 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.10310 | + | 4.10310i | −0.486949 | + | 0.486949i | −0.907342 | − | 0.420393i | \(-0.861892\pi\) |
0.420393 | + | 0.907342i | \(0.361892\pi\) | |||||||
\(72\) | −1.72371 | + | 6.43299i | −0.203142 | + | 0.758135i | ||||
\(73\) | 2.53495 | + | 9.46056i | 0.296693 | + | 1.10727i | 0.939863 | + | 0.341551i | \(0.110952\pi\) |
−0.643170 | + | 0.765724i | \(0.722381\pi\) | |||||||
\(74\) | 1.73041 | − | 2.99715i | 0.201156 | − | 0.348412i | ||||
\(75\) | −4.83004 | − | 8.36588i | −0.557725 | − | 0.966008i | ||||
\(76\) | −0.0562174 | + | 0.0562174i | −0.00644858 | + | 0.00644858i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.80098 | − | 7.20620i | 0.770060 | − | 0.815942i | ||||
\(79\) | −8.79791 | − | 15.2384i | −0.989842 | − | 1.71446i | −0.618043 | − | 0.786145i | \(-0.712074\pi\) |
−0.371800 | − | 0.928313i | \(-0.621259\pi\) | |||||||
\(80\) | 2.20304 | − | 0.590303i | 0.246307 | − | 0.0659979i | ||||
\(81\) | 5.40049 | − | 9.35393i | 0.600055 | − | 1.03933i | ||||
\(82\) | 1.94326 | + | 3.36583i | 0.214597 | + | 0.371693i | ||||
\(83\) | −10.5474 | − | 10.5474i | −1.15773 | − | 1.15773i | −0.984963 | − | 0.172763i | \(-0.944731\pi\) |
−0.172763 | − | 0.984963i | \(-0.555269\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.86797 | + | 1.86797i | 0.202610 | + | 0.202610i | ||||
\(86\) | −0.995834 | + | 3.71650i | −0.107384 | + | 0.400761i | ||||
\(87\) | 7.45847 | + | 4.30615i | 0.799632 | + | 0.461668i | ||||
\(88\) | 6.97103 | + | 4.02472i | 0.743114 | + | 0.429037i | ||||
\(89\) | −4.63836 | − | 1.24285i | −0.491666 | − | 0.131741i | 0.00446375 | − | 0.999990i | \(-0.498579\pi\) |
−0.496129 | + | 0.868249i | \(0.665246\pi\) | |||||||
\(90\) | 2.27378 | 0.239678 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.51026 | −0.365970 | ||||||||
\(93\) | 21.0382 | + | 5.63716i | 2.18156 | + | 0.584547i | ||||
\(94\) | 7.72228 | + | 4.45846i | 0.796492 | + | 0.459855i | ||||
\(95\) | 0.110701 | + | 0.0639130i | 0.0113576 | + | 0.00655734i | ||||
\(96\) | −1.74085 | + | 6.49694i | −0.177675 | + | 0.663091i | ||||
\(97\) | 4.44330 | + | 4.44330i | 0.451149 | + | 0.451149i | 0.895736 | − | 0.444587i | \(-0.146649\pi\) |
−0.444587 | + | 0.895736i | \(0.646649\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.02472 | + | 4.02472i | 0.404500 | + | 0.404500i | ||||
\(100\) | −1.14536 | − | 1.98383i | −0.114536 | − | 0.198383i | ||||
\(101\) | −0.580109 | + | 1.00478i | −0.0577231 | + | 0.0999793i | −0.893443 | − | 0.449177i | \(-0.851717\pi\) |
0.835720 | + | 0.549156i | \(0.185051\pi\) | |||||||
\(102\) | 8.08909 | − | 2.16746i | 0.800939 | − | 0.214611i | ||||
\(103\) | 2.66052 | + | 4.60816i | 0.262149 | + | 0.454055i | 0.966813 | − | 0.255486i | \(-0.0822355\pi\) |
−0.704664 | + | 0.709541i | \(0.748902\pi\) | |||||||
\(104\) | 7.59483 | − | 8.04735i | 0.744734 | − | 0.789107i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.93302 | − | 2.93302i | 0.284880 | − | 0.284880i | ||||
\(107\) | −5.12423 | − | 8.87543i | −0.495378 | − | 0.858020i | 0.504608 | − | 0.863349i | \(-0.331637\pi\) |
−0.999986 | + | 0.00532858i | \(0.998304\pi\) | |||||||
\(108\) | 0.508736 | − | 0.881157i | 0.0489532 | − | 0.0847894i | ||||
\(109\) | −2.14295 | − | 7.99758i | −0.205257 | − | 0.766030i | −0.989371 | − | 0.145413i | \(-0.953549\pi\) |
0.784114 | − | 0.620617i | \(-0.213118\pi\) | |||||||
\(110\) | 0.711283 | − | 2.65454i | 0.0678181 | − | 0.253101i | ||||
\(111\) | 4.60378 | − | 4.60378i | 0.436972 | − | 0.436972i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.74539 | 0.540481 | 0.270241 | − | 0.962793i | \(-0.412897\pi\) | ||||
0.270241 | + | 0.962793i | \(0.412897\pi\) | |||||||
\(114\) | 0.350931 | − | 0.202610i | 0.0328677 | − | 0.0189762i | ||||
\(115\) | 1.46073 | + | 5.45151i | 0.136214 | + | 0.508356i | ||||
\(116\) | 1.76865 | + | 1.02113i | 0.164215 | + | 0.0948096i | ||||
\(117\) | 6.66013 | − | 4.10649i | 0.615729 | − | 0.379645i | ||||
\(118\) | 15.6422i | 1.43998i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.04945 | 0.552237 | ||||||||
\(121\) | −3.56858 | + | 2.06032i | −0.324416 | + | 0.187302i | ||||
\(122\) | −10.7494 | + | 2.88030i | −0.973208 | + | 0.260770i | ||||
\(123\) | 1.89238 | + | 7.06247i | 0.170630 | + | 0.636801i | ||||
\(124\) | 4.98885 | + | 1.33676i | 0.448012 | + | 0.120044i | ||||
\(125\) | −5.66930 | + | 5.66930i | −0.507078 | + | 0.507078i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.37629i | − | 0.654540i | −0.944931 | − | 0.327270i | \(-0.893871\pi\) | ||
0.944931 | − | 0.327270i | \(-0.106129\pi\) | |||||||
\(128\) | 1.23318 | − | 4.60228i | 0.108998 | − | 0.406788i | ||||
\(129\) | −3.61920 | + | 6.26864i | −0.318653 | + | 0.551923i | ||||
\(130\) | −3.32496 | − | 1.79352i | −0.291618 | − | 0.157302i | ||||
\(131\) | 10.3613 | − | 5.98209i | 0.905269 | − | 0.522658i | 0.0263633 | − | 0.999652i | \(-0.491607\pi\) |
0.878906 | + | 0.476995i | \(0.158274\pi\) | |||||||
\(132\) | 2.27378 | + | 2.27378i | 0.197907 | + | 0.197907i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.79380i | 0.154960i | ||||||||
\(135\) | −1.58016 | − | 0.423402i | −0.135998 | − | 0.0364406i | ||||
\(136\) | 9.03328 | − | 2.42046i | 0.774598 | − | 0.207553i | ||||
\(137\) | −2.57300 | + | 0.689433i | −0.219826 | + | 0.0589023i | −0.367051 | − | 0.930201i | \(-0.619633\pi\) |
0.147225 | + | 0.989103i | \(0.452966\pi\) | |||||||
\(138\) | 17.2818 | + | 4.63063i | 1.47112 | + | 0.394186i | ||||
\(139\) | − | 6.36883i | − | 0.540197i | −0.962833 | − | 0.270098i | \(-0.912944\pi\) | ||
0.962833 | − | 0.270098i | \(-0.0870563\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.8618 | + | 11.8618i | 0.998946 | + | 0.998946i | ||||
\(142\) | 6.07372 | − | 3.50667i | 0.509695 | − | 0.294273i | ||||
\(143\) | −2.71073 | − | 9.06000i | −0.226683 | − | 0.757635i | ||||
\(144\) | 2.85464 | − | 4.94438i | 0.237886 | − | 0.412031i | ||||
\(145\) | 0.849848 | − | 3.17168i | 0.0705760 | − | 0.263393i | ||||
\(146\) | − | 11.8378i | − | 0.979701i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.09171 | − | 1.09171i | 0.0897379 | − | 0.0897379i | ||||
\(149\) | −18.2173 | − | 4.88130i | −1.49242 | − | 0.399892i | −0.581865 | − | 0.813286i | \(-0.697677\pi\) |
−0.910552 | + | 0.413394i | \(0.864343\pi\) | |||||||
\(150\) | 3.02186 | + | 11.2777i | 0.246734 | + | 0.920823i | ||||
\(151\) | −10.4396 | + | 2.79727i | −0.849560 | + | 0.227639i | −0.657229 | − | 0.753691i | \(-0.728271\pi\) |
−0.192331 | + | 0.981330i | \(0.561605\pi\) | |||||||
\(152\) | 0.391893 | − | 0.226259i | 0.0317867 | − | 0.0183521i | ||||
\(153\) | 6.61282 | 0.534615 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.30406i | − | 0.666998i | ||||||
\(156\) | 3.76266 | − | 2.31998i | 0.301254 | − | 0.185747i | ||||
\(157\) | 18.2116 | + | 10.5145i | 1.45345 | + | 0.839148i | 0.998675 | − | 0.0514594i | \(-0.0163873\pi\) |
0.454772 | + | 0.890608i | \(0.349721\pi\) | |||||||
\(158\) | 5.50431 | + | 20.5424i | 0.437899 | + | 1.63426i | ||||
\(159\) | 6.75790 | − | 3.90168i | 0.535936 | − | 0.309423i | ||||
\(160\) | 2.56443 | 0.202736 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −9.23093 | + | 9.23093i | −0.725250 | + | 0.725250i | ||||
\(163\) | −2.57540 | + | 9.61152i | −0.201721 | + | 0.752832i | 0.788703 | + | 0.614774i | \(0.210753\pi\) |
−0.990424 | + | 0.138058i | \(0.955914\pi\) | |||||||
\(164\) | 0.448746 | + | 1.67474i | 0.0350412 | + | 0.130776i | ||||
\(165\) | 2.58504 | − | 4.47743i | 0.201245 | − | 0.348567i | ||||
\(166\) | 9.01419 | + | 15.6130i | 0.699637 | + | 1.21181i | ||||
\(167\) | 12.0684 | − | 12.0684i | 0.933884 | − | 0.933884i | −0.0640620 | − | 0.997946i | \(-0.520406\pi\) |
0.997946 | + | 0.0640620i | \(0.0204055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9783 | + | 0.751536i | −0.998328 | + | 0.0578104i | ||||
\(170\) | −1.59644 | − | 2.76511i | −0.122441 | − | 0.212074i | ||||
\(171\) | 0.309076 | − | 0.0828167i | 0.0236356 | − | 0.00633315i | ||||
\(172\) | −0.858232 | + | 1.48650i | −0.0654395 | + | 0.113345i | ||||
\(173\) | 3.74120 | + | 6.47994i | 0.284438 | + | 0.492661i | 0.972473 | − | 0.233017i | \(-0.0748597\pi\) |
−0.688035 | + | 0.725678i | \(0.741526\pi\) | |||||||
\(174\) | −7.36040 | − | 7.36040i | −0.557990 | − | 0.557990i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.87936 | − | 4.87936i | −0.367796 | − | 0.367796i | ||||
\(177\) | −7.61632 | + | 28.4245i | −0.572478 | + | 2.13652i | ||||
\(178\) | 5.02630 | + | 2.90194i | 0.376737 | + | 0.217509i | ||||
\(179\) | −19.6595 | − | 11.3504i | −1.46942 | − | 0.848371i | −0.470010 | − | 0.882661i | \(-0.655750\pi\) |
−0.999412 | + | 0.0342899i | \(0.989083\pi\) | |||||||
\(180\) | 0.979798 | + | 0.262536i | 0.0730298 | + | 0.0195683i | ||||
\(181\) | −1.91735 | −0.142516 | −0.0712579 | − | 0.997458i | \(-0.522701\pi\) | ||||
−0.0712579 | + | 0.997458i | \(0.522701\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.9360 | −1.54763 | ||||||||
\(184\) | 19.2990 | + | 5.17114i | 1.42274 | + | 0.381222i | ||||
\(185\) | −2.14974 | − | 1.24115i | −0.158052 | − | 0.0912515i | ||||
\(186\) | −22.7978 | − | 13.1623i | −1.67161 | − | 0.965106i | ||||
\(187\) | 2.06862 | − | 7.72018i | 0.151272 | − | 0.564556i | ||||
\(188\) | 2.81283 | + | 2.81283i | 0.205147 | + | 0.205147i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.109245 | − | 0.109245i | −0.00792546 | − | 0.00792546i | ||||
\(191\) | 5.00359 | + | 8.66648i | 0.362047 | + | 0.627084i | 0.988298 | − | 0.152538i | \(-0.0487445\pi\) |
−0.626250 | + | 0.779622i | \(0.715411\pi\) | |||||||
\(192\) | 10.0468 | − | 17.4016i | 0.725067 | − | 1.25585i | ||||
\(193\) | 13.9815 | − | 3.74632i | 1.00641 | − | 0.269666i | 0.282280 | − | 0.959332i | \(-0.408909\pi\) |
0.724127 | + | 0.689666i | \(0.242243\pi\) | |||||||
\(194\) | −3.79741 | − | 6.57731i | −0.272638 | − | 0.472224i | ||||
\(195\) | −5.16874 | − | 4.87809i | −0.370141 | − | 0.349327i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.2690 | − | 15.2690i | 1.08787 | − | 1.08787i | 0.0921223 | − | 0.995748i | \(-0.470635\pi\) |
0.995748 | − | 0.0921223i | \(-0.0293651\pi\) | |||||||
\(198\) | −3.43968 | − | 5.95770i | −0.244447 | − | 0.423395i | ||||
\(199\) | −11.2318 | + | 19.4540i | −0.796198 | + | 1.37906i | 0.125877 | + | 0.992046i | \(0.459825\pi\) |
−0.922075 | + | 0.387010i | \(0.873508\pi\) | |||||||
\(200\) | 3.37458 | + | 12.5941i | 0.238619 | + | 0.890539i | ||||
\(201\) | −0.873416 | + | 3.25963i | −0.0616060 | + | 0.229917i | ||||
\(202\) | 0.991567 | − | 0.991567i | 0.0697664 | − | 0.0697664i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.73594 | 0.261568 | ||||||||
\(205\) | 2.41418 | − | 1.39383i | 0.168614 | − | 0.0973491i | ||||
\(206\) | −1.66452 | − | 6.21209i | −0.115973 | − | 0.432817i | ||||
\(207\) | 12.2351 | + | 7.06391i | 0.850395 | + | 0.490976i | ||||
\(208\) | −8.07439 | + | 4.97849i | −0.559858 | + | 0.345196i | ||||
\(209\) | − | 0.386740i | − | 0.0267513i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.8504 | −1.29772 | −0.648859 | − | 0.760909i | \(-0.724753\pi\) | ||||
−0.648859 | + | 0.760909i | \(0.724753\pi\) | |||||||
\(212\) | 1.60252 | − | 0.925216i | 0.110062 | − | 0.0635441i | ||||
\(213\) | 12.7444 | − | 3.41486i | 0.873233 | − | 0.233982i | ||||
\(214\) | 3.20592 | + | 11.9646i | 0.219152 | + | 0.817886i | ||||
\(215\) | 2.66571 | + | 0.714274i | 0.181800 | + | 0.0487131i | ||||
\(216\) | −4.09505 | + | 4.09505i | −0.278633 | + | 0.278633i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.0072i | 0.677772i | ||||||||
\(219\) | 5.76392 | − | 21.5113i | 0.389490 | − | 1.45360i | ||||
\(220\) | 0.612999 | − | 1.06175i | 0.0413284 | − | 0.0715829i | ||||
\(221\) | −9.66995 | − | 5.21608i | −0.650471 | − | 0.350872i | ||||
\(222\) | −6.81487 | + | 3.93457i | −0.457384 | + | 0.264071i | ||||
\(223\) | 4.32131 | + | 4.32131i | 0.289376 | + | 0.289376i | 0.836833 | − | 0.547457i | \(-0.184404\pi\) |
−0.547457 | + | 0.836833i | \(0.684404\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.21953i | 0.614636i | ||||||||
\(226\) | −6.70750 | − | 1.79727i | −0.446176 | − | 0.119553i | ||||
\(227\) | 6.40708 | − | 1.71677i | 0.425253 | − | 0.113946i | −0.0398440 | − | 0.999206i | \(-0.512686\pi\) |
0.465097 | + | 0.885260i | \(0.346019\pi\) | |||||||
\(228\) | 0.174614 | − | 0.0467876i | 0.0115641 | − | 0.00309858i | ||||
\(229\) | 0.361646 | + | 0.0969027i | 0.0238982 | + | 0.00640351i | 0.270748 | − | 0.962650i | \(-0.412729\pi\) |
−0.246850 | + | 0.969054i | \(0.579396\pi\) | |||||||
\(230\) | − | 6.82135i | − | 0.449786i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.21953 | − | 8.21953i | −0.539639 | − | 0.539639i | ||||
\(233\) | 5.33723 | − | 3.08145i | 0.349653 | − | 0.201872i | −0.314879 | − | 0.949132i | \(-0.601964\pi\) |
0.664533 | + | 0.747259i | \(0.268631\pi\) | |||||||
\(234\) | −9.06000 | + | 2.71073i | −0.592271 | + | 0.177206i | ||||
\(235\) | 3.19788 | − | 5.53889i | 0.208607 | − | 0.361318i | ||||
\(236\) | −1.80608 | + | 6.74039i | −0.117566 | + | 0.438762i | ||||
\(237\) | 40.0091i | 2.59887i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.63090 | + | 5.63090i | −0.364232 | + | 0.364232i | −0.865369 | − | 0.501136i | \(-0.832916\pi\) |
0.501136 | + | 0.865369i | \(0.332916\pi\) | |||||||
\(240\) | −5.00924 | − | 1.34222i | −0.323345 | − | 0.0866400i | ||||
\(241\) | 0.407084 | + | 1.51926i | 0.0262226 | + | 0.0978640i | 0.977797 | − | 0.209555i | \(-0.0672014\pi\) |
−0.951574 | + | 0.307419i | \(0.900535\pi\) | |||||||
\(242\) | 4.81067 | − | 1.28901i | 0.309241 | − | 0.0828610i | ||||
\(243\) | −16.3661 | + | 9.44898i | −1.04989 | + | 0.606152i | ||||
\(244\) | −4.96462 | −0.317827 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 8.83710i | − | 0.563433i | ||||||
\(247\) | −0.517287 | − | 0.122691i | −0.0329142 | − | 0.00780663i | ||||
\(248\) | −25.4588 | − | 14.6987i | −1.61664 | − | 0.933365i | ||||
\(249\) | 8.77819 | + | 32.7607i | 0.556295 | + | 2.07612i | ||||
\(250\) | 8.39213 | − | 4.84520i | 0.530765 | − | 0.306437i | ||||
\(251\) | 12.1069 | 0.764182 | 0.382091 | − | 0.924125i | \(-0.375204\pi\) | ||||
0.382091 | + | 0.924125i | \(0.375204\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0742 | − | 12.0742i | 0.759097 | − | 0.759097i | ||||
\(254\) | −2.30744 | + | 8.61150i | −0.144782 | + | 0.540334i | ||||
\(255\) | −1.55464 | − | 5.80199i | −0.0973553 | − | 0.363335i | ||||
\(256\) | 5.95774 | − | 10.3191i | 0.372359 | − | 0.644944i | ||||
\(257\) | −8.78794 | − | 15.2212i | −0.548176 | − | 0.949469i | −0.998400 | − | 0.0565532i | \(-0.981989\pi\) |
0.450223 | − | 0.892916i | \(-0.351344\pi\) | |||||||
\(258\) | 6.18621 | − | 6.18621i | 0.385137 | − | 0.385137i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.22568 | − | 1.15676i | −0.0760133 | − | 0.0717389i | ||||
\(261\) | −4.10977 | − | 7.11833i | −0.254388 | − | 0.440613i | ||||
\(262\) | −13.9677 | + | 3.74262i | −0.862925 | + | 0.231220i | ||||
\(263\) | 7.26293 | − | 12.5798i | 0.447851 | − | 0.775701i | −0.550395 | − | 0.834905i | \(-0.685523\pi\) |
0.998246 | + | 0.0592033i | \(0.0188560\pi\) | |||||||
\(264\) | −9.15135 | − | 15.8506i | −0.563226 | − | 0.975537i | ||||
\(265\) | −2.10374 | − | 2.10374i | −0.129232 | − | 0.129232i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.72067 | + | 7.72067i | 0.472497 | + | 0.472497i | ||||
\(268\) | −0.207116 | + | 0.772967i | −0.0126516 | + | 0.0472165i | ||||
\(269\) | −20.2782 | − | 11.7076i | −1.23638 | − | 0.713825i | −0.268029 | − | 0.963411i | \(-0.586372\pi\) |
−0.968353 | + | 0.249585i | \(0.919706\pi\) | |||||||
\(270\) | 1.71232 | + | 0.988607i | 0.104208 | + | 0.0601647i | ||||
\(271\) | −3.30104 | − | 0.884511i | −0.200524 | − | 0.0537302i | 0.157159 | − | 0.987573i | \(-0.449766\pi\) |
−0.357683 | + | 0.933843i | \(0.616433\pi\) | |||||||
\(272\) | −8.01703 | −0.486104 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.21953 | 0.194499 | ||||||||
\(275\) | 10.7634 | + | 2.88405i | 0.649058 | + | 0.173915i | ||||
\(276\) | 6.91224 | + | 3.99078i | 0.416068 | + | 0.240217i | ||||
\(277\) | −25.1773 | − | 14.5361i | −1.51276 | − | 0.873391i | −0.999889 | − | 0.0149234i | \(-0.995250\pi\) |
−0.512868 | − | 0.858467i | \(-0.671417\pi\) | |||||||
\(278\) | −1.99229 | + | 7.43533i | −0.119490 | + | 0.445942i | ||||
\(279\) | −14.6987 | − | 14.6987i | −0.879985 | − | 0.879985i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.68455 | + | 9.68455i | 0.577732 | + | 0.577732i | 0.934278 | − | 0.356546i | \(-0.116046\pi\) |
−0.356546 | + | 0.934278i | \(0.616046\pi\) | |||||||
\(282\) | −10.1376 | − | 17.5588i | −0.603683 | − | 1.04561i | ||||
\(283\) | 2.15179 | − | 3.72700i | 0.127910 | − | 0.221547i | −0.794956 | − | 0.606667i | \(-0.792506\pi\) |
0.922867 | + | 0.385119i | \(0.125840\pi\) | |||||||
\(284\) | 3.02212 | − | 0.809775i | 0.179330 | − | 0.0480513i | ||||
\(285\) | −0.145324 | − | 0.251709i | −0.00860827 | − | 0.0149100i | ||||
\(286\) | 0.330522 | + | 11.4251i | 0.0195442 | + | 0.675582i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.53919 | − | 4.53919i | 0.267474 | − | 0.267474i | ||||
\(289\) | 3.85710 | + | 6.68069i | 0.226888 | + | 0.392982i | ||||
\(290\) | −1.98432 | + | 3.43695i | −0.116523 | + | 0.201824i | ||||
\(291\) | −3.69799 | − | 13.8011i | −0.216780 | − | 0.809034i | ||||
\(292\) | 1.36682 | − | 5.10103i | 0.0799869 | − | 0.298515i | ||||
\(293\) | 3.57373 | − | 3.57373i | 0.208780 | − | 0.208780i | −0.594969 | − | 0.803749i | \(-0.702836\pi\) |
0.803749 | + | 0.594969i | \(0.202836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2195 | 0.653227 | ||||||||
\(296\) | −7.61033 | + | 4.39383i | −0.442341 | + | 0.255386i | ||||
\(297\) | 1.28101 | + | 4.78079i | 0.0743317 | + | 0.277410i | ||||
\(298\) | 19.7409 | + | 11.3974i | 1.14356 | + | 0.660235i | ||||
\(299\) | −12.3195 | − | 19.9804i | −0.712453 | − | 1.15550i | ||||
\(300\) | 5.20861i | 0.300719i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.0628 | 0.751678 | ||||||||
\(303\) | 2.28465 | − | 1.31904i | 0.131250 | − | 0.0757770i | ||||
\(304\) | −0.374707 | + | 0.100403i | −0.0214909 | + | 0.00575848i | ||||
\(305\) | 2.06593 | + | 7.71016i | 0.118295 | + | 0.441482i | ||||
\(306\) | −7.72018 | − | 2.06862i | −0.441334 | − | 0.118255i | ||||
\(307\) | −8.59457 | + | 8.59457i | −0.490518 | + | 0.490518i | −0.908469 | − | 0.417952i | \(-0.862748\pi\) |
0.417952 | + | 0.908469i | \(0.362748\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 12.0989i | − | 0.688282i | ||||||
\(310\) | −2.59767 | + | 9.69463i | −0.147538 | + | 0.550618i | ||||
\(311\) | 11.2702 | − | 19.5206i | 0.639077 | − | 1.10691i | −0.346559 | − | 0.938028i | \(-0.612650\pi\) |
0.985636 | − | 0.168885i | \(-0.0540168\pi\) | |||||||
\(312\) | −24.1043 | + | 7.21197i | −1.36464 | + | 0.408297i | ||||
\(313\) | 3.73147 | − | 2.15436i | 0.210915 | − | 0.121772i | −0.390822 | − | 0.920466i | \(-0.627809\pi\) |
0.601737 | + | 0.798695i | \(0.294476\pi\) | |||||||
\(314\) | −17.9722 | − | 17.9722i | −1.01423 | − | 1.01423i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.48747i | 0.533712i | ||||||||
\(317\) | −5.42458 | − | 1.45351i | −0.304675 | − | 0.0816374i | 0.103243 | − | 0.994656i | \(-0.467078\pi\) |
−0.407917 | + | 0.913019i | \(0.633745\pi\) | |||||||
\(318\) | −9.11008 | + | 2.44104i | −0.510868 | + | 0.136887i | ||||
\(319\) | −9.59595 | + | 2.57123i | −0.537270 | + | 0.143961i | ||||
\(320\) | −7.39994 | − | 1.98281i | −0.413669 | − | 0.110842i | ||||
\(321\) | 23.3028i | 1.30063i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.317716 | − | 0.317716i | −0.0176782 | − | 0.0176782i | ||||
\(324\) | −5.04353 | + | 2.91189i | −0.280196 | + | 0.161771i | ||||
\(325\) | 7.27221 | − | 13.4818i | 0.403390 | − | 0.747833i | ||||
\(326\) | 6.01333 | − | 10.4154i | 0.333048 | − | 0.576855i | ||||
\(327\) | −4.87259 | + | 18.1848i | −0.269455 | + | 1.00562i | ||||
\(328\) | − | 9.86861i | − | 0.544903i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.41855 | + | 4.41855i | −0.243233 | + | 0.243233i | ||||
\(331\) | −2.33491 | − | 0.625638i | −0.128338 | − | 0.0343882i | 0.194078 | − | 0.980986i | \(-0.437828\pi\) |
−0.322417 | + | 0.946598i | \(0.604495\pi\) | |||||||
\(332\) | 2.08160 | + | 7.76863i | 0.114243 | + | 0.426359i | ||||
\(333\) | −6.00208 | + | 1.60825i | −0.328912 | + | 0.0881317i | ||||
\(334\) | −17.8646 | + | 10.3141i | −0.977509 | + | 0.564365i | ||||
\(335\) | 1.28662 | 0.0702957 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.1327i | 1.26012i | 0.776546 | + | 0.630061i | \(0.216970\pi\) | ||||
−0.776546 | + | 0.630061i | \(0.783030\pi\) | |||||||
\(338\) | 15.3867 | + | 3.18246i | 0.836923 | + | 0.173103i | ||||
\(339\) | −11.3136 | − | 6.53189i | −0.614468 | − | 0.354763i | ||||
\(340\) | −0.368656 | − | 1.37584i | −0.0199932 | − | 0.0746156i | ||||
\(341\) | −21.7581 | + | 12.5620i | −1.17826 | + | 0.680272i | ||||
\(342\) | −0.386740 | −0.0209125 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.90829 | − | 6.90829i | 0.372470 | − | 0.372470i | ||||
\(345\) | 3.32138 | − | 12.3956i | 0.178817 | − | 0.667354i | ||||
\(346\) | −2.34064 | − | 8.73537i | −0.125833 | − | 0.469616i | ||||
\(347\) | 4.30212 | − | 7.45149i | 0.230950 | − | 0.400017i | −0.727138 | − | 0.686491i | \(-0.759150\pi\) |
0.958088 | + | 0.286474i | \(0.0924834\pi\) | |||||||
\(348\) | −2.32183 | − | 4.02152i | −0.124463 | − | 0.215576i | ||||
\(349\) | −19.0680 | + | 19.0680i | −1.02069 | + | 1.02069i | −0.0209053 | + | 0.999781i | \(0.506655\pi\) |
−0.999781 | + | 0.0209053i | \(0.993345\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.80098 | − | 0.196748i | 0.363010 | − | 0.0105017i | ||||
\(352\) | −3.87936 | − | 6.71925i | −0.206771 | − | 0.358137i | ||||
\(353\) | 6.57373 | − | 1.76143i | 0.349885 | − | 0.0937513i | −0.0795964 | − | 0.996827i | \(-0.525363\pi\) |
0.429481 | + | 0.903076i | \(0.358696\pi\) | |||||||
\(354\) | 17.7834 | − | 30.8018i | 0.945180 | − | 1.63710i | ||||
\(355\) | −2.51520 | − | 4.35645i | −0.133493 | − | 0.231216i | ||||
\(356\) | 1.83083 | + | 1.83083i | 0.0970336 | + | 0.0970336i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.4010 | + | 19.4010i | 1.02538 | + | 1.02538i | ||||
\(359\) | −4.59383 | + | 17.1444i | −0.242453 | + | 0.904848i | 0.732193 | + | 0.681097i | \(0.238497\pi\) |
−0.974646 | + | 0.223751i | \(0.928170\pi\) | |||||||
\(360\) | −5.00005 | − | 2.88678i | −0.263526 | − | 0.152147i | ||||
\(361\) | 16.4357 | + | 9.48913i | 0.865034 | + | 0.499428i | ||||
\(362\) | 2.23843 | + | 0.599785i | 0.117649 | + | 0.0315240i | ||||
\(363\) | 9.36943 | 0.491768 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.49079 | −0.444428 | ||||||||
\(366\) | 24.4419 | + | 6.54918i | 1.27760 | + | 0.342331i | ||||
\(367\) | −19.8152 | − | 11.4403i | −1.03434 | − | 0.597178i | −0.116117 | − | 0.993236i | \(-0.537045\pi\) |
−0.918226 | + | 0.396058i | \(0.870378\pi\) | |||||||
\(368\) | −14.8331 | − | 8.56391i | −0.773230 | − | 0.446425i | ||||
\(369\) | 1.80608 | − | 6.74039i | 0.0940208 | − | 0.350890i | ||||
\(370\) | 2.12147 | + | 2.12147i | 0.110290 | + | 0.110290i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.30406 | − | 8.30406i | −0.430545 | − | 0.430545i | ||||
\(373\) | −5.25206 | − | 9.09683i | −0.271941 | − | 0.471016i | 0.697418 | − | 0.716665i | \(-0.254332\pi\) |
−0.969359 | + | 0.245649i | \(0.920999\pi\) | |||||||
\(374\) | −4.83004 | + | 8.36588i | −0.249756 | + | 0.432589i | ||||
\(375\) | 17.6091 | − | 4.71834i | 0.909330 | − | 0.243654i | ||||
\(376\) | −11.3209 | − | 19.6083i | −0.583829 | − | 1.01122i | ||||
\(377\) | 0.394912 | + | 13.6509i | 0.0203390 | + | 0.703055i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.64229 | − | 3.64229i | 0.187092 | − | 0.187092i | −0.607346 | − | 0.794438i | \(-0.707766\pi\) |
0.794438 | + | 0.607346i | \(0.207766\pi\) | |||||||
\(380\) | −0.0344612 | − | 0.0596885i | −0.00176782 | − | 0.00306196i | ||||
\(381\) | −8.38604 | + | 14.5250i | −0.429630 | + | 0.744141i | ||||
\(382\) | −3.13044 | − | 11.6830i | −0.160167 | − | 0.597752i | ||||
\(383\) | −8.98925 | + | 33.5483i | −0.459329 | + | 1.71424i | 0.215709 | + | 0.976458i | \(0.430794\pi\) |
−0.675039 | + | 0.737782i | \(0.735873\pi\) | |||||||
\(384\) | −7.66061 | + | 7.66061i | −0.390929 | + | 0.390929i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.4947 | −0.890455 | ||||||||
\(387\) | 5.98276 | − | 3.45415i | 0.304121 | − | 0.175584i | ||||
\(388\) | −0.876916 | − | 3.27269i | −0.0445187 | − | 0.166146i | ||||
\(389\) | 5.62028 | + | 3.24487i | 0.284960 | + | 0.164521i | 0.635667 | − | 0.771964i | \(-0.280725\pi\) |
−0.350707 | + | 0.936485i | \(0.614059\pi\) | |||||||
\(390\) | 4.50832 | + | 7.31184i | 0.228287 | + | 0.370249i | ||||
\(391\) | − | 19.8385i | − | 1.00327i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.2039 | −1.37226 | ||||||||
\(394\) | −22.6023 | + | 13.0494i | −1.13869 | + | 0.657422i | ||||
\(395\) | 14.7343 | − | 3.94803i | 0.741361 | − | 0.198647i | ||||
\(396\) | −0.794307 | − | 2.96439i | −0.0399154 | − | 0.148966i | ||||
\(397\) | 9.41915 | + | 2.52385i | 0.472734 | + | 0.126669i | 0.487317 | − | 0.873225i | \(-0.337976\pi\) |
−0.0145835 | + | 0.999894i | \(0.504642\pi\) | |||||||
\(398\) | 19.1982 | − | 19.1982i | 0.962317 | − | 0.962317i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 11.1773i | − | 0.558864i | ||||||
\(401\) | 3.30257 | − | 12.3254i | 0.164922 | − | 0.615499i | −0.833128 | − | 0.553081i | \(-0.813452\pi\) |
0.998050 | − | 0.0624181i | \(-0.0198812\pi\) | |||||||
\(402\) | 2.03935 | − | 3.53226i | 0.101714 | − | 0.176173i | ||||
\(403\) | 9.89984 | + | 33.0879i | 0.493146 | + | 1.64823i | ||||
\(404\) | 0.541766 | − | 0.312789i | 0.0269539 | − | 0.0155618i | ||||
\(405\) | 6.62099 | + | 6.62099i | 0.329000 | + | 0.329000i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.51026i | 0.372270i | ||||||||
\(408\) | −20.5397 | − | 5.50360i | −1.01687 | − | 0.272469i | ||||
\(409\) | −3.90803 | + | 1.04715i | −0.193240 | + | 0.0517784i | −0.354141 | − | 0.935192i | \(-0.615227\pi\) |
0.160901 | + | 0.986971i | \(0.448560\pi\) | |||||||
\(410\) | −3.25446 | + | 0.872031i | −0.160727 | + | 0.0430665i | ||||
\(411\) | 5.85044 | + | 1.56762i | 0.288581 | + | 0.0773251i | ||||
\(412\) | − | 2.86905i | − | 0.141348i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.0742 | − | 12.0742i | −0.593413 | − | 0.593413i | ||||
\(415\) | 11.1986 | − | 6.46554i | 0.549720 | − | 0.317381i | ||||
\(416\) | −10.2181 | + | 3.05724i | −0.500984 | + | 0.149893i | ||||
\(417\) | −7.24067 | + | 12.5412i | −0.354577 | + | 0.614145i | ||||
\(418\) | −0.120980 | + | 0.451502i | −0.00591730 | + | 0.0220837i | ||||
\(419\) | − | 35.4097i | − | 1.72988i | −0.501878 | − | 0.864939i | \(-0.667357\pi\) | ||
0.501878 | − | 0.864939i | \(-0.332643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9307 | − | 18.9307i | 0.922628 | − | 0.922628i | −0.0745864 | − | 0.997215i | \(-0.523764\pi\) |
0.997215 | + | 0.0745864i | \(0.0237636\pi\) | |||||||
\(422\) | 22.0071 | + | 5.89678i | 1.07129 | + | 0.287051i | ||||
\(423\) | −4.14372 | − | 15.4646i | −0.201475 | − | 0.751914i | ||||
\(424\) | −10.1734 | + | 2.72597i | −0.494066 | + | 0.132385i | ||||
\(425\) | 11.2117 | − | 6.47309i | 0.543848 | − | 0.313991i | ||||
\(426\) | −15.9468 | −0.772624 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.52586i | 0.267102i | ||||||||
\(429\) | −4.96239 | + | 20.9223i | −0.239586 | + | 1.01014i | ||||
\(430\) | −2.88866 | − | 1.66777i | −0.139303 | − | 0.0804269i | ||||
\(431\) | 4.61347 | + | 17.2177i | 0.222223 | + | 0.829348i | 0.983498 | + | 0.180919i | \(0.0579071\pi\) |
−0.761275 | + | 0.648429i | \(0.775426\pi\) | |||||||
\(432\) | 4.29948 | − | 2.48231i | 0.206859 | − | 0.119430i | ||||
\(433\) | 14.3392 | 0.689098 | 0.344549 | − | 0.938768i | \(-0.388032\pi\) | ||||
0.344549 | + | 0.938768i | \(0.388032\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.27933 | + | 5.27933i | −0.253125 | + | 0.253125i | ||||
\(436\) | −1.15545 | + | 4.31221i | −0.0553361 | + | 0.206517i | ||||
\(437\) | −0.248450 | − | 0.927228i | −0.0118850 | − | 0.0443553i | ||||
\(438\) | −13.4583 | + | 23.3104i | −0.643061 | + | 1.11381i | ||||
\(439\) | 9.99061 | + | 17.3042i | 0.476826 | + | 0.825886i | 0.999647 | − | 0.0265559i | \(-0.00845400\pi\) |
−0.522822 | + | 0.852442i | \(0.675121\pi\) | |||||||
\(440\) | −4.93430 | + | 4.93430i | −0.235234 | + | 0.235234i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.65756 | + | 9.11450i | 0.459363 | + | 0.433532i | ||||
\(443\) | 2.81904 | + | 4.88273i | 0.133937 | + | 0.231985i | 0.925191 | − | 0.379502i | \(-0.123905\pi\) |
−0.791254 | + | 0.611488i | \(0.790571\pi\) | |||||||
\(444\) | −3.39090 | + | 0.908588i | −0.160925 | + | 0.0431197i | ||||
\(445\) | 2.08145 | − | 3.60518i | 0.0986702 | − | 0.170902i | ||||
\(446\) | −3.69315 | − | 6.39672i | −0.174876 | − | 0.302894i | ||||
\(447\) | 30.3231 | + | 30.3231i | 1.43423 | + | 1.43423i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.9060 | − | 12.9060i | −0.609073 | − | 0.609073i | 0.333631 | − | 0.942704i | \(-0.391726\pi\) |
−0.942704 | + | 0.333631i | \(0.891726\pi\) | |||||||
\(450\) | 2.88405 | − | 10.7634i | 0.135955 | − | 0.507392i | ||||
\(451\) | −7.30413 | − | 4.21704i | −0.343938 | − | 0.198573i | ||||
\(452\) | −2.68282 | − | 1.54893i | −0.126189 | − | 0.0728553i | ||||
\(453\) | 23.7373 | + | 6.36039i | 1.11528 | + | 0.298837i | ||||
\(454\) | −8.01703 | −0.376258 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.02893 | −0.0481840 | ||||||||
\(457\) | −9.51692 | − | 2.55005i | −0.445183 | − | 0.119286i | 0.0292619 | − | 0.999572i | \(-0.490684\pi\) |
−0.474444 | + | 0.880285i | \(0.657351\pi\) | |||||||
\(458\) | −0.391893 | − | 0.226259i | −0.0183119 | − | 0.0105724i | ||||
\(459\) | 4.97992 | + | 2.87516i | 0.232443 | + | 0.134201i | ||||
\(460\) | 0.787608 | − | 2.93939i | 0.0367224 | − | 0.137050i | ||||
\(461\) | 7.20809 | + | 7.20809i | 0.335714 | + | 0.335714i | 0.854752 | − | 0.519037i | \(-0.173709\pi\) |
−0.519037 | + | 0.854752i | \(0.673709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.06084 | − | 4.06084i | −0.188723 | − | 0.188723i | 0.606421 | − | 0.795144i | \(-0.292605\pi\) |
−0.795144 | + | 0.606421i | \(0.792605\pi\) | |||||||
\(464\) | 4.98246 | + | 8.62988i | 0.231305 | + | 0.400632i | ||||
\(465\) | −9.44081 | + | 16.3520i | −0.437807 | + | 0.758304i | ||||
\(466\) | −7.19492 | + | 1.92787i | −0.333298 | + | 0.0893070i | ||||
\(467\) | 8.68367 | + | 15.0406i | 0.401832 | + | 0.695994i | 0.993947 | − | 0.109860i | \(-0.0350401\pi\) |
−0.592115 | + | 0.805854i | \(0.701707\pi\) | |||||||
\(468\) | −4.21704 | + | 0.121997i | −0.194933 | + | 0.00563929i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.46606 | + | 5.46606i | −0.252131 | + | 0.252131i | ||||
\(471\) | −23.9077 | − | 41.4093i | −1.10161 | − | 1.90804i | ||||
\(472\) | 19.8592 | − | 34.3972i | 0.914094 | − | 1.58326i | ||||
\(473\) | −2.16105 | − | 8.06513i | −0.0993650 | − | 0.370835i | ||||
\(474\) | 12.5156 | − | 46.7089i | 0.574861 | − | 2.14541i | ||||
\(475\) | 0.442957 | − | 0.442957i | 0.0203243 | − | 0.0203243i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.44748 | −0.340997 | ||||||||
\(478\) | 8.33528 | − | 4.81238i | 0.381247 | − | 0.220113i | ||||
\(479\) | 3.61865 | + | 13.5050i | 0.165340 | + | 0.617059i | 0.997997 | + | 0.0632685i | \(0.0201525\pi\) |
−0.832656 | + | 0.553790i | \(0.813181\pi\) | |||||||
\(480\) | −5.04976 | − | 2.91548i | −0.230489 | − | 0.133073i | ||||
\(481\) | 10.0454 | + | 2.38259i | 0.458032 | + | 0.108637i | ||||
\(482\) | − | 1.90101i | − | 0.0865887i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.22180 | 0.100991 | ||||||||
\(485\) | −4.71766 | + | 2.72374i | −0.214218 | + | 0.123679i | ||||
\(486\) | 22.0626 | − | 5.91164i | 1.00078 | − | 0.268158i | ||||
\(487\) | −4.61527 | − | 17.2244i | −0.209138 | − | 0.780513i | −0.988148 | − | 0.153502i | \(-0.950945\pi\) |
0.779010 | − | 0.627011i | \(-0.215722\pi\) | |||||||
\(488\) | 27.2948 | + | 7.31363i | 1.23558 | + | 0.331073i | ||||
\(489\) | 15.9986 | − | 15.9986i | 0.723482 | − | 0.723482i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.72487i | − | 0.0778425i | −0.999242 | − | 0.0389212i | \(-0.987608\pi\) | ||
0.999242 | − | 0.0389212i | \(-0.0123921\pi\) | |||||||
\(492\) | 1.02035 | − | 3.80800i | 0.0460010 | − | 0.171678i | ||||
\(493\) | −5.77099 | + | 9.99564i | −0.259912 | + | 0.450181i | ||||
\(494\) | 0.565531 | + | 0.305054i | 0.0254444 | + | 0.0137250i | ||||
\(495\) | −4.27323 | + | 2.46715i | −0.192068 | + | 0.110890i | ||||
\(496\) | 17.8199 | + | 17.8199i | 0.800135 | + | 0.800135i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 40.9926i | − | 1.83692i | ||||||
\(499\) | 37.6415 | + | 10.0860i | 1.68507 | + | 0.451512i | 0.969109 | − | 0.246633i | \(-0.0793241\pi\) |
0.715957 | + | 0.698145i | \(0.245991\pi\) | |||||||
\(500\) | 4.17570 | − | 1.11888i | 0.186743 | − | 0.0500376i | ||||
\(501\) | −37.4851 | + | 10.0441i | −1.67471 | + | 0.448738i | ||||
\(502\) | −14.1343 | − | 3.78728i | −0.630845 | − | 0.169034i | ||||
\(503\) | − | 20.8862i | − | 0.931272i | −0.884976 | − | 0.465636i | \(-0.845826\pi\) | ||
0.884976 | − | 0.465636i | \(-0.154174\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.711213 | − | 0.711213i | −0.0316486 | − | 0.0316486i | ||||
\(506\) | −17.8731 | + | 10.3190i | −0.794556 | + | 0.458737i | ||||
\(507\) | 26.4106 | + | 13.2750i | 1.17294 | + | 0.589563i | ||||
\(508\) | −1.98861 | + | 3.44437i | −0.0882302 | + | 0.152819i | ||||
\(509\) | 5.58088 | − | 20.8281i | 0.247368 | − | 0.923191i | −0.724810 | − | 0.688949i | \(-0.758072\pi\) |
0.972178 | − | 0.234242i | \(-0.0752609\pi\) | |||||||
\(510\) | 7.25990i | 0.321474i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.9216 | + | 16.9216i | −0.747837 | + | 0.747837i | ||||
\(513\) | 0.268763 | + | 0.0720149i | 0.0118662 | + | 0.00317954i | ||||
\(514\) | 5.49807 | + | 20.5191i | 0.242509 | + | 0.905057i | ||||
\(515\) | −4.45570 | + | 1.19390i | −0.196341 | + | 0.0526095i | ||||
\(516\) | 3.37998 | − | 1.95143i | 0.148795 | − | 0.0859070i | ||||
\(517\) | −19.3505 | −0.851033 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 17.0133i | − | 0.746802i | ||||||
\(520\) | 5.03455 | + | 8.16531i | 0.220780 | + | 0.358072i | ||||
\(521\) | 17.4541 | + | 10.0771i | 0.764678 | + | 0.441487i | 0.830973 | − | 0.556313i | \(-0.187784\pi\) |
−0.0662945 | + | 0.997800i | \(0.521118\pi\) | |||||||
\(522\) | 2.57123 | + | 9.59595i | 0.112540 | + | 0.420003i | ||||
\(523\) | −9.78880 | + | 5.65157i | −0.428034 | + | 0.247126i | −0.698509 | − | 0.715601i | \(-0.746153\pi\) |
0.270475 | + | 0.962727i | \(0.412819\pi\) | |||||||
\(524\) | −6.45095 | −0.281811 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.4143 | + | 12.4143i | −0.541291 | + | 0.541291i | ||||
\(527\) | −7.55477 | + | 28.1948i | −0.329091 | + | 1.22818i | ||||
\(528\) | 4.06091 | + | 15.1555i | 0.176728 | + | 0.659559i | ||||
\(529\) | 9.69174 | − | 16.7866i | 0.421380 | − | 0.729852i | ||||
\(530\) | 1.79794 | + | 3.11412i | 0.0780973 | + | 0.135269i | ||||
\(531\) | 19.8592 | − | 19.8592i | 0.861817 | − | 0.861817i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.95774 | + | 8.43188i | −0.344688 | + | 0.365225i | ||||
\(534\) | −6.59837 | − | 11.4287i | −0.285540 | − | 0.494569i | ||||
\(535\) | 8.58178 | − | 2.29948i | 0.371023 | − | 0.0994152i | ||||
\(536\) | 2.27739 | − | 3.94456i | 0.0983684 | − | 0.170379i | ||||
\(537\) | 25.8084 | + | 44.7015i | 1.11372 | + | 1.92901i | ||||
\(538\) | 20.0115 | + | 20.0115i | 0.862758 | + | 0.862758i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.623710 | + | 0.623710i | 0.0268402 | + | 0.0268402i | ||||
\(541\) | −3.39993 | + | 12.6887i | −0.146174 | + | 0.545531i | 0.853526 | + | 0.521051i | \(0.174460\pi\) |
−0.999700 | + | 0.0244801i | \(0.992207\pi\) | |||||||
\(542\) | 3.57713 | + | 2.06526i | 0.153651 | + | 0.0887104i | ||||
\(543\) | 3.77557 | + | 2.17982i | 0.162025 | + | 0.0935452i | ||||
\(544\) | −8.70702 | − | 2.33304i | −0.373311 | − | 0.100028i | ||||
\(545\) | 7.17778 | 0.307462 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.8999 | 0.551559 | 0.275780 | − | 0.961221i | \(-0.411064\pi\) | ||||
0.275780 | + | 0.961221i | \(0.411064\pi\) | |||||||
\(548\) | 1.38733 | + | 0.371735i | 0.0592639 | + | 0.0158797i | ||||
\(549\) | 17.3042 | + | 9.99061i | 0.738527 | + | 0.426389i | ||||
\(550\) | −11.6636 | − | 6.73400i | −0.497339 | − | 0.287139i | ||||
\(551\) | −0.144548 | + | 0.539459i | −0.00615794 | + | 0.0229817i | ||||
\(552\) | −32.1236 | − | 32.1236i | −1.36727 | − | 1.36727i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 24.8462 | + | 24.8462i | 1.05562 | + | 1.05562i | ||||
\(555\) | 2.82211 | + | 4.88805i | 0.119792 | + | 0.207486i | ||||
\(556\) | −1.71700 | + | 2.97393i | −0.0728170 | + | 0.126123i | ||||
\(557\) | 22.6969 | − | 6.08162i | 0.961699 | − | 0.257687i | 0.256380 | − | 0.966576i | \(-0.417470\pi\) |
0.705320 | + | 0.708890i | \(0.250804\pi\) | |||||||
\(558\) | 12.5620 | + | 21.7581i | 0.531793 | + | 0.921092i | ||||
\(559\) | −11.4732 | + | 0.331912i | −0.485264 | + | 0.0140384i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.8504 | + | 12.8504i | −0.542546 | + | 0.542546i | ||||
\(562\) | −8.27678 | − | 14.3358i | −0.349135 | − | 0.604720i | ||||
\(563\) | 10.8380 | − | 18.7720i | 0.456769 | − | 0.791147i | −0.542019 | − | 0.840366i | \(-0.682340\pi\) |
0.998788 | + | 0.0492194i | \(0.0156733\pi\) | |||||||
\(564\) | −2.34101 | − | 8.73678i | −0.0985744 | − | 0.367885i | ||||
\(565\) | −1.28911 | + | 4.81103i | −0.0542334 | + | 0.202402i | ||||
\(566\) | −3.67799 | + | 3.67799i | −0.154598 | + | 0.154598i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.8082 | −0.747214 | ||||||||
\(569\) | 15.6524 | − | 9.03692i | 0.656183 | − | 0.378847i | −0.134638 | − | 0.990895i | \(-0.542987\pi\) |
0.790821 | + | 0.612047i | \(0.209654\pi\) | |||||||
\(570\) | 0.0909205 | + | 0.339320i | 0.00380824 | + | 0.0142125i | ||||
\(571\) | 7.39319 | + | 4.26846i | 0.309395 | + | 0.178630i | 0.646656 | − | 0.762782i | \(-0.276167\pi\) |
−0.337260 | + | 0.941411i | \(0.609500\pi\) | |||||||
\(572\) | −1.17675 | + | 4.96138i | −0.0492022 | + | 0.207446i | ||||
\(573\) | − | 22.7542i | − | 0.950569i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.6586 | 1.15344 | ||||||||
\(576\) | −16.6080 | + | 9.58864i | −0.692000 | + | 0.399527i | ||||
\(577\) | 11.7009 | − | 3.13524i | 0.487114 | − | 0.130522i | −0.00689906 | − | 0.999976i | \(-0.502196\pi\) |
0.494013 | + | 0.869454i | \(0.335529\pi\) | |||||||
\(578\) | −2.41315 | − | 9.00599i | −0.100374 | − | 0.374600i | ||||
\(579\) | −31.7908 | − | 8.51831i | −1.32118 | − | 0.354009i | ||||
\(580\) | −1.25190 | + | 1.25190i | −0.0519825 | + | 0.0519825i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.2690i | 0.715822i | ||||||||
\(583\) | −2.32971 | + | 8.69461i | −0.0964869 | + | 0.360094i | ||||
\(584\) | −15.0292 | + | 26.0313i | −0.621912 | + | 1.07718i | ||||
\(585\) | 1.94431 | + | 6.49839i | 0.0803872 | + | 0.268676i | ||||
\(586\) | −5.29011 | + | 3.05425i | −0.218532 | + | 0.126170i | ||||
\(587\) | −0.308382 | − | 0.308382i | −0.0127283 | − | 0.0127283i | 0.700714 | − | 0.713442i | \(-0.252865\pi\) |
−0.713442 | + | 0.700714i | \(0.752865\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.41241i | 0.0581972i | ||||||||
\(590\) | −13.0983 | − | 3.50968i | −0.539249 | − | 0.144491i | ||||
\(591\) | −47.4261 | + | 12.7078i | −1.95085 | + | 0.522729i | ||||
\(592\) | 7.27660 | − | 1.94976i | 0.299066 | − | 0.0801346i | ||||
\(593\) | 6.76461 | + | 1.81257i | 0.277789 | + | 0.0744334i | 0.395024 | − | 0.918671i | \(-0.370736\pi\) |
−0.117235 | + | 0.993104i | \(0.537403\pi\) | |||||||
\(594\) | − | 5.98209i | − | 0.245448i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.19061 | + | 7.19061i | 0.294539 | + | 0.294539i | ||||
\(597\) | 44.2341 | − | 25.5386i | 1.81038 | − | 1.04522i | ||||
\(598\) | 8.13220 | + | 27.1800i | 0.332550 | + | 1.11147i | ||||
\(599\) | 8.81545 | − | 15.2688i | 0.360189 | − | 0.623866i | −0.627802 | − | 0.778373i | \(-0.716045\pi\) |
0.987992 | + | 0.154506i | \(0.0493787\pi\) | |||||||
\(600\) | 7.67307 | − | 28.6363i | 0.313252 | − | 1.16907i | ||||
\(601\) | − | 7.14746i | − | 0.291551i | −0.989318 | − | 0.145776i | \(-0.953432\pi\) | ||
0.989318 | − | 0.145776i | \(-0.0465677\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.27739 | − | 2.27739i | 0.0927426 | − | 0.0927426i | ||||
\(604\) | 5.62890 | + | 1.50826i | 0.229037 | + | 0.0613702i | ||||
\(605\) | −0.924561 | − | 3.45051i | −0.0375887 | − | 0.140283i | ||||
\(606\) | −3.07985 | + | 0.825244i | −0.125110 | + | 0.0335232i | ||||
\(607\) | 25.8552 | − | 14.9275i | 1.04943 | − | 0.605888i | 0.126939 | − | 0.991910i | \(-0.459485\pi\) |
0.922489 | + | 0.386022i | \(0.126151\pi\) | |||||||
\(608\) | −0.436175 | −0.0176892 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 9.64754i | − | 0.390618i | ||||||
\(611\) | −6.13883 | + | 25.8824i | −0.248350 | + | 1.04709i | ||||
\(612\) | −3.08787 | − | 1.78278i | −0.124820 | − | 0.0720646i | ||||
\(613\) | −2.35686 | − | 8.79593i | −0.0951928 | − | 0.355264i | 0.901856 | − | 0.432037i | \(-0.142205\pi\) |
−0.997049 | + | 0.0767728i | \(0.975538\pi\) | |||||||
\(614\) | 12.7223 | − | 7.34524i | 0.513431 | − | 0.296430i | ||||
\(615\) | −6.33852 | −0.255594 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4908 | − | 16.4908i | 0.663894 | − | 0.663894i | −0.292402 | − | 0.956296i | \(-0.594454\pi\) |
0.956296 | + | 0.292402i | \(0.0944544\pi\) | |||||||
\(618\) | −3.78477 | + | 14.1249i | −0.152246 | + | 0.568188i | ||||
\(619\) | −8.16997 | − | 30.4907i | −0.328379 | − | 1.22553i | −0.910871 | − | 0.412690i | \(-0.864589\pi\) |
0.582493 | − | 0.812836i | \(-0.302078\pi\) | |||||||
\(620\) | −2.23873 | + | 3.87759i | −0.0899094 | + | 0.155728i | ||||
\(621\) | 6.14257 | + | 10.6392i | 0.246493 | + | 0.426938i | ||||
\(622\) | −19.2639 | + | 19.2639i | −0.772414 | + | 0.772414i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 21.5597 | − | 0.623710i | 0.863079 | − | 0.0249684i | ||||
\(625\) | 7.14588 | + | 12.3770i | 0.285835 | + | 0.495081i | ||||
\(626\) | −5.03025 | + | 1.34785i | −0.201049 | + | 0.0538710i | ||||
\(627\) | −0.439681 | + | 0.761550i | −0.0175592 | + | 0.0304134i | ||||
\(628\) | −5.66930 | − | 9.81952i | −0.226230 | − | 0.391841i | ||||
\(629\) | 6.16986 | + | 6.16986i | 0.246009 | + | 0.246009i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.75154 | + | 3.75154i | 0.149346 | + | 0.149346i | 0.777826 | − | 0.628480i | \(-0.216322\pi\) |
−0.628480 | + | 0.777826i | \(0.716322\pi\) | |||||||
\(632\) | 13.9765 | − | 52.1609i | 0.555955 | − | 2.07485i | ||||
\(633\) | 37.1194 | + | 21.4309i | 1.47536 | + | 0.851801i | ||||
\(634\) | 5.87828 | + | 3.39383i | 0.233456 | + | 0.134786i | ||||
\(635\) | 6.17670 | + | 1.65504i | 0.245115 | + | 0.0656783i | ||||
\(636\) | −4.20748 | −0.166837 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.0072 | 0.475369 | ||||||||
\(639\) | −12.1632 | − | 3.25912i | −0.481169 | − | 0.128929i | ||||
\(640\) | 3.57713 | + | 2.06526i | 0.141398 | + | 0.0816364i | ||||
\(641\) | 22.2523 | + | 12.8474i | 0.878912 | + | 0.507440i | 0.870300 | − | 0.492523i | \(-0.163925\pi\) |
0.00861267 | + | 0.999963i | \(0.497258\pi\) | |||||||
\(642\) | 7.28955 | − | 27.2050i | 0.287696 | − | 1.07370i | ||||
\(643\) | 22.1537 | + | 22.1537i | 0.873658 | + | 0.873658i | 0.992869 | − | 0.119211i | \(-0.0380363\pi\) |
−0.119211 | + | 0.992869i | \(0.538036\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.43713 | − | 4.43713i | −0.174712 | − | 0.174712i | ||||
\(646\) | 0.271532 | + | 0.470308i | 0.0106833 | + | 0.0185040i | ||||
\(647\) | −16.2223 | + | 28.0978i | −0.637764 | + | 1.10464i | 0.348159 | + | 0.937436i | \(0.386807\pi\) |
−0.985922 | + | 0.167204i | \(0.946526\pi\) | |||||||
\(648\) | 32.0184 | − | 8.57929i | 1.25780 | − | 0.337027i | ||||
\(649\) | −16.9724 | − | 29.3971i | −0.666226 | − | 1.15394i | ||||
\(650\) | −12.7073 | + | 13.4645i | −0.498423 | + | 0.528120i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.79380 | − | 3.79380i | 0.148577 | − | 0.148577i | ||||
\(653\) | −15.8257 | − | 27.4109i | −0.619308 | − | 1.07267i | −0.989612 | − | 0.143762i | \(-0.954080\pi\) |
0.370304 | − | 0.928910i | \(-0.379253\pi\) | |||||||
\(654\) | 11.3771 | − | 19.7057i | 0.444879 | − | 0.770553i | ||||
\(655\) | 2.68444 | + | 10.0185i | 0.104890 | + | 0.391454i | ||||
\(656\) | −2.18960 | + | 8.17169i | −0.0854894 | + | 0.319051i | ||||
\(657\) | −15.0292 | + | 15.0292i | −0.586344 | + | 0.586344i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.5330 | 1.18940 | 0.594699 | − | 0.803948i | \(-0.297271\pi\) | ||||
0.594699 | + | 0.803948i | \(0.297271\pi\) | |||||||
\(660\) | −2.41418 | + | 1.39383i | −0.0939718 | + | 0.0542546i | ||||
\(661\) | 3.37071 | + | 12.5797i | 0.131105 | + | 0.489292i | 0.999984 | − | 0.00573384i | \(-0.00182515\pi\) |
−0.868878 | + | 0.495026i | \(0.835158\pi\) | |||||||
\(662\) | 2.53020 | + | 1.46081i | 0.0983390 | + | 0.0567760i | ||||
\(663\) | 13.1115 | + | 21.2649i | 0.509208 | + | 0.825862i | ||||
\(664\) | − | 45.7775i | − | 1.77651i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.51026 | 0.291017 | ||||||||
\(667\) | −21.3550 | + | 12.3293i | −0.826868 | + | 0.477392i | ||||
\(668\) | −8.88896 | + | 2.38179i | −0.343924 | + | 0.0921542i | ||||
\(669\) | −3.59646 | − | 13.4222i | −0.139047 | − | 0.518931i | ||||
\(670\) | −1.50208 | − | 0.402480i | −0.0580302 | − | 0.0155492i | ||||
\(671\) | 17.0767 | − | 17.0767i | 0.659239 | − | 0.659239i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.6319i | 0.872397i | 0.899850 | + | 0.436199i | \(0.143675\pi\) | ||||
−0.899850 | + | 0.436199i | \(0.856325\pi\) | |||||||
\(674\) | 7.23637 | − | 27.0065i | 0.278734 | − | 1.04025i | ||||
\(675\) | −4.00852 | + | 6.94295i | −0.154288 | + | 0.267234i | ||||
\(676\) | 6.26282 | + | 3.14794i | 0.240878 | + | 0.121074i | ||||
\(677\) | −9.28744 | + | 5.36211i | −0.356945 | + | 0.206082i | −0.667740 | − | 0.744395i | \(-0.732738\pi\) |
0.310795 | + | 0.950477i | \(0.399405\pi\) | |||||||
\(678\) | 11.1648 | + | 11.1648i | 0.428781 | + | 0.428781i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.10731i | 0.310901i | ||||||||
\(681\) | −14.5683 | − | 3.90357i | −0.558259 | − | 0.149585i | ||||
\(682\) | 29.3312 | − | 7.85928i | 1.12315 | − | 0.300947i | ||||
\(683\) | 5.06387 | − | 1.35686i | 0.193763 | − | 0.0519188i | −0.160632 | − | 0.987014i | \(-0.551353\pi\) |
0.354396 | + | 0.935096i | \(0.384687\pi\) | |||||||
\(684\) | −0.166650 | − | 0.0446538i | −0.00637204 | − | 0.00170738i | ||||
\(685\) | − | 2.30925i | − | 0.0882319i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.601968 | − | 0.601968i | −0.0229665 | − | 0.0229665i | ||||
\(688\) | −7.25318 | + | 4.18762i | −0.276525 | + | 0.159652i | ||||
\(689\) | 10.8905 | + | 5.87445i | 0.414894 | + | 0.223799i | ||||
\(690\) | −7.75513 | + | 13.4323i | −0.295233 | + | 0.511358i | ||||
\(691\) | −0.0974114 | + | 0.363544i | −0.00370571 | + | 0.0138299i | −0.967754 | − | 0.251897i | \(-0.918945\pi\) |
0.964048 | + | 0.265727i | \(0.0856121\pi\) | |||||||
\(692\) | − | 4.03442i | − | 0.153366i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.35350 | + | 7.35350i | −0.279135 | + | 0.279135i | ||||
\(695\) | 5.33308 | + | 1.42899i | 0.202295 | + | 0.0542049i | ||||
\(696\) | 6.84081 | + | 25.5302i | 0.259300 | + | 0.967721i | ||||
\(697\) | −9.46493 | + | 2.53612i | −0.358510 | + | 0.0960624i | ||||
\(698\) | 28.2259 | − | 16.2962i | 1.06837 | − | 0.616822i | ||||
\(699\) | −14.0131 | −0.530024 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 34.0349i | − | 1.28548i | −0.766084 | − | 0.642740i | \(-0.777798\pi\) | ||
0.766084 | − | 0.642740i | \(-0.222202\pi\) | |||||||
\(702\) | −8.00140 | − | 1.89778i | −0.301993 | − | 0.0716272i | ||||
\(703\) | 0.365642 | + | 0.211104i | 0.0137905 | + | 0.00796192i | ||||
\(704\) | 5.99902 | + | 22.3886i | 0.226096 | + | 0.843804i | ||||
\(705\) | −12.5942 | + | 7.27129i | −0.474327 | + | 0.273853i | ||||
\(706\) | −8.22556 | −0.309573 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 11.2195 | − | 11.2195i | 0.421656 | − | 0.421656i | ||||
\(709\) | 4.20888 | − | 15.7077i | 0.158068 | − | 0.589917i | −0.840755 | − | 0.541415i | \(-0.817889\pi\) |
0.998823 | − | 0.0485016i | \(-0.0154446\pi\) | |||||||
\(710\) | 1.57360 | + | 5.87277i | 0.0590563 | + | 0.220401i | ||||
\(711\) | 19.0922 | − | 33.0687i | 0.716015 | − | 1.24017i | ||||
\(712\) | −7.36857 | − | 12.7627i | −0.276149 | − | 0.478304i | ||||
\(713\) | −44.0960 | + | 44.0960i | −1.65141 | + | 1.65141i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.19481 | − | 0.237071i | 0.306469 | − | 0.00886596i | ||||
\(716\) | 6.12003 | + | 10.6002i | 0.228716 | + | 0.396148i | ||||
\(717\) | 17.4898 | − | 4.68638i | 0.653169 | − | 0.175016i | ||||
\(718\) | 10.7262 | − | 18.5783i | 0.400298 | − | 0.693337i | ||||
\(719\) | −17.5222 | − | 30.3494i | −0.653469 | − | 1.13184i | −0.982275 | − | 0.187444i | \(-0.939980\pi\) |
0.328806 | − | 0.944397i | \(-0.393354\pi\) | |||||||
\(720\) | 3.49978 | + | 3.49978i | 0.130429 | + | 0.130429i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −16.2195 | − | 16.2195i | −0.603629 | − | 0.603629i | ||||
\(723\) | 0.925620 | − | 3.45446i | 0.0344242 | − | 0.128473i | ||||
\(724\) | 0.895311 | + | 0.516908i | 0.0332740 | + | 0.0192107i | ||||
\(725\) | −13.9358 | − | 8.04585i | −0.517564 | − | 0.298816i | ||||
\(726\) | −10.9384 | − | 2.93094i | −0.405962 | − | 0.108777i | ||||
\(727\) | 15.0936 | 0.559789 | 0.279895 | − | 0.960031i | \(-0.409700\pi\) | ||||
0.279895 | + | 0.960031i | \(0.409700\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.5669 | 0.391367 | ||||||||
\(730\) | 9.91262 | + | 2.65608i | 0.366883 | + | 0.0983059i | ||||
\(731\) | −8.40106 | − | 4.85035i | −0.310724 | − | 0.179397i | ||||
\(732\) | 9.77609 | + | 5.64423i | 0.361335 | + | 0.208617i | ||||
\(733\) | −5.42285 | + | 20.2383i | −0.200297 | + | 0.747520i | 0.790534 | + | 0.612418i | \(0.209803\pi\) |
−0.990832 | + | 0.135102i | \(0.956864\pi\) | |||||||
\(734\) | 19.5546 | + | 19.5546i | 0.721773 | + | 0.721773i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.6176 | − | 13.6176i | −0.501950 | − | 0.501950i | ||||
\(737\) | −1.94635 | − | 3.37117i | −0.0716946 | − | 0.124179i | ||||
\(738\) | −4.21704 | + | 7.30413i | −0.155231 | + | 0.268869i | ||||
\(739\) | −22.0435 | + | 5.90653i | −0.810883 | + | 0.217275i | −0.640357 | − | 0.768078i | \(-0.721213\pi\) |
−0.170526 | + | 0.985353i | \(0.554547\pi\) | |||||||
\(740\) | 0.669216 | + | 1.15912i | 0.0246009 | + | 0.0426100i | ||||
\(741\) | 0.879132 | + | 0.829697i | 0.0322957 | + | 0.0304797i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.1350 | + | 24.1350i | −0.885428 | + | 0.885428i | −0.994080 | − | 0.108652i | \(-0.965347\pi\) |
0.108652 | + | 0.994080i | \(0.465347\pi\) | |||||||
\(744\) | 33.4215 | + | 57.8878i | 1.22529 | + | 2.12227i | ||||
\(745\) | 8.17494 | − | 14.1594i | 0.299506 | − | 0.518760i | ||||
\(746\) | 3.28589 | + | 12.2631i | 0.120305 | + | 0.448984i | ||||
\(747\) | 8.37786 | − | 31.2666i | 0.306530 | − | 1.14399i | ||||
\(748\) | −3.04726 | + | 3.04726i | −0.111419 | + | 0.111419i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −22.0338 | −0.804562 | ||||||||
\(751\) | −14.5293 | + | 8.38849i | −0.530181 | + | 0.306100i | −0.741090 | − | 0.671405i | \(-0.765691\pi\) |
0.210909 | + | 0.977506i | \(0.432358\pi\) | |||||||
\(752\) | 5.02363 | + | 18.7484i | 0.183193 | + | 0.683686i | ||||
\(753\) | −23.8404 | − | 13.7643i | −0.868792 | − | 0.501597i | ||||
\(754\) | 3.80921 | − | 16.0603i | 0.138723 | − | 0.584883i | ||||
\(755\) | − | 9.36943i | − | 0.340989i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.7321 | −0.753520 | −0.376760 | − | 0.926311i | \(-0.622962\pi\) | ||||
−0.376760 | + | 0.926311i | \(0.622962\pi\) | |||||||
\(758\) | −5.39160 | + | 3.11284i | −0.195832 | + | 0.113063i | ||||
\(759\) | −37.5029 | + | 10.0489i | −1.36127 | + | 0.364751i | ||||
\(760\) | 0.101533 | + | 0.378927i | 0.00368299 | + | 0.0137451i | ||||
\(761\) | 2.88682 | + | 0.773522i | 0.104647 | + | 0.0280402i | 0.310763 | − | 0.950488i | \(-0.399416\pi\) |
−0.206115 | + | 0.978528i | \(0.566082\pi\) | |||||||
\(762\) | 14.3341 | − | 14.3341i | 0.519268 | − | 0.519268i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 5.39576i | − | 0.195212i | ||||||
\(765\) | −1.48374 | + | 5.53739i | −0.0536447 | + | 0.200205i | ||||
\(766\) | 20.9891 | − | 36.3542i | 0.758368 | − | 1.31353i | ||||
\(767\) | −44.7048 | + | 13.3756i | −1.61420 | + | 0.482964i | ||||
\(768\) | −23.4634 | + | 13.5466i | −0.846663 | + | 0.488821i | ||||
\(769\) | −25.9456 | − | 25.9456i | −0.935621 | − | 0.935621i | 0.0624284 | − | 0.998049i | \(-0.480115\pi\) |
−0.998049 | + | 0.0624284i | \(0.980115\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39.9637i | 1.43926i | ||||||||
\(772\) | −7.53864 | − | 2.01997i | −0.271322 | − | 0.0727004i | ||||
\(773\) | 1.30004 | − | 0.348344i | 0.0467591 | − | 0.0125291i | −0.235364 | − | 0.971907i | \(-0.575628\pi\) |
0.282123 | + | 0.959378i | \(0.408961\pi\) | |||||||
\(774\) | −8.06513 | + | 2.16105i | −0.289895 | + | 0.0776772i | ||||
\(775\) | −39.3089 | − | 10.5328i | −1.41202 | − | 0.378349i | ||||
\(776\) | 19.2847i | 0.692280i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.54638 | − | 5.54638i | −0.198847 | − | 0.198847i | ||||
\(779\) | −0.410619 | + | 0.237071i | −0.0147120 | + | 0.00849395i | ||||
\(780\) | 1.09844 | + | 3.67129i | 0.0393306 | + | 0.131453i | ||||
\(781\) | −7.60977 | + | 13.1805i | −0.272299 | + | 0.471636i | ||||
\(782\) | −6.20585 | + | 23.1606i | −0.221921 | + | 0.828220i | ||||
\(783\) | − | 7.14746i | − | 0.255430i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.8908 | + | 12.8908i | −0.460091 | + | 0.460091i | ||||
\(786\) | 31.7594 | + | 8.50991i | 1.13282 | + | 0.303538i | ||||
\(787\) | −9.07805 | − | 33.8797i | −0.323597 | − | 1.20768i | −0.915714 | − | 0.401830i | \(-0.868374\pi\) |
0.592117 | − | 0.805852i | \(-0.298292\pi\) | |||||||
\(788\) | −11.2463 | + | 3.01344i | −0.400633 | + | 0.107349i | ||||
\(789\) | −28.6036 | + | 16.5143i | −1.01832 | + | 0.587925i | ||||
\(790\) | −18.4366 | −0.655946 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 17.4680i | 0.620698i | ||||||||
\(793\) | −17.4236 | − | 28.2586i | −0.618731 | − | 1.00349i | ||||
\(794\) | −10.2069 | − | 5.89298i | −0.362231 | − | 0.209134i | ||||
\(795\) | 1.75086 | + | 6.53431i | 0.0620967 | + | 0.231748i | ||||
\(796\) | 10.4894 | − | 6.05604i | 0.371786 | − | 0.214651i | ||||
\(797\) | 34.9017 | 1.23628 | 0.618141 | − | 0.786067i | \(-0.287886\pi\) | ||||
0.618141 | + | 0.786067i | \(0.287886\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.8969 | + | 15.8969i | −0.562392 | + | 0.562392i | ||||
\(800\) | 3.25270 | − | 12.1393i | 0.115000 | − | 0.429187i | ||||
\(801\) | −2.69708 | − | 10.0656i | −0.0952967 | − | 0.355652i | ||||
\(802\) | −7.71121 | + | 13.3562i | −0.272292 | + | 0.471624i | ||||
\(803\) | 12.8445 | + | 22.2473i | 0.453272 | + | 0.785091i | ||||
\(804\) | 1.28662 | − | 1.28662i | 0.0453757 | − | 0.0453757i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.20710 | − | 41.7256i | −0.0425182 | − | 1.46972i | ||||
\(807\) | 26.6205 | + | 46.1081i | 0.937088 | + | 1.62308i | ||||
\(808\) | −3.43935 | + | 0.921570i | −0.120996 | + | 0.0324207i | ||||
\(809\) | −5.13090 | + | 8.88698i | −0.180393 | + | 0.312449i | −0.942014 | − | 0.335573i | \(-0.891070\pi\) |
0.761622 | + | 0.648022i | \(0.224404\pi\) | |||||||
\(810\) | −5.65855 | − | 9.80090i | −0.198821 | − | 0.344368i | ||||
\(811\) | −13.3684 | − | 13.3684i | −0.469428 | − | 0.469428i | 0.432301 | − | 0.901729i | \(-0.357702\pi\) |
−0.901729 | + | 0.432301i | \(0.857702\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.49466 | + | 5.49466i | 0.192706 | + | 0.192706i | ||||
\(814\) | 2.34935 | − | 8.76790i | 0.0823448 | − | 0.307315i | ||||
\(815\) | −7.47057 | − | 4.31313i | −0.261683 | − | 0.151082i | ||||
\(816\) | 15.7868 | + | 9.11450i | 0.552647 | + | 0.319071i | ||||
\(817\) | −0.453401 | − | 0.121488i | −0.0158625 | − | 0.00425034i | ||||
\(818\) | 4.89002 | 0.170976 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.50307 | −0.0524895 | ||||||||
\(821\) | −23.6423 | − | 6.33494i | −0.825122 | − | 0.221091i | −0.178538 | − | 0.983933i | \(-0.557137\pi\) |
−0.646585 | + | 0.762842i | \(0.723803\pi\) | |||||||
\(822\) | −6.33976 | − | 3.66026i | −0.221124 | − | 0.127666i | ||||
\(823\) | −30.3777 | − | 17.5386i | −1.05890 | − | 0.611356i | −0.133772 | − | 0.991012i | \(-0.542709\pi\) |
−0.925128 | + | 0.379656i | \(0.876042\pi\) | |||||||
\(824\) | −4.22654 | + | 15.7737i | −0.147239 | + | 0.549502i | ||||
\(825\) | −17.9160 | − | 17.9160i | −0.623753 | − | 0.623753i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.4173 | − | 19.4173i | −0.675207 | − | 0.675207i | 0.283705 | − | 0.958912i | \(-0.408436\pi\) |
−0.958912 | + | 0.283705i | \(0.908436\pi\) | |||||||
\(828\) | −3.80878 | − | 6.59701i | −0.132364 | − | 0.229262i | ||||
\(829\) | −4.58045 | + | 7.93358i | −0.159086 | + | 0.275545i | −0.934539 | − | 0.355860i | \(-0.884188\pi\) |
0.775453 | + | 0.631405i | \(0.217521\pi\) | |||||||
\(830\) | −15.0965 | + | 4.04509i | −0.524006 | + | 0.140407i | ||||
\(831\) | 33.0520 | + | 57.2477i | 1.14656 | + | 1.98590i | ||||
\(832\) | 31.8493 | − | 0.921381i | 1.10418 | − | 0.0319432i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 12.3763 | − | 12.3763i | 0.428556 | − | 0.428556i | ||||
\(835\) | 7.39794 | + | 12.8136i | 0.256016 | + | 0.443433i | ||||
\(836\) | −0.104263 | + | 0.180589i | −0.00360601 | + | 0.00624579i | ||||
\(837\) | −4.67836 | − | 17.4599i | −0.161708 | − | 0.603501i | ||||
\(838\) | −11.0768 | + | 41.3393i | −0.382643 | + | 1.42804i | ||||
\(839\) | −26.1882 | + | 26.1882i | −0.904116 | + | 0.904116i | −0.995789 | − | 0.0916731i | \(-0.970779\pi\) |
0.0916731 | + | 0.995789i | \(0.470779\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.6537 | −0.505299 | ||||||||
\(842\) | −28.0227 | + | 16.1789i | −0.965727 | + | 0.557563i | ||||
\(843\) | −8.06009 | − | 30.0806i | −0.277604 | − | 1.03603i | ||||
\(844\) | 8.80223 | + | 5.08197i | 0.302985 | + | 0.174929i | ||||
\(845\) | 2.28266 | − | 11.0363i | 0.0785258 | − | 0.379659i | ||||
\(846\) | 19.3505i | 0.665283i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.02893 | 0.310055 | ||||||||
\(849\) | −8.47439 | + | 4.89269i | −0.290840 | + | 0.167917i | ||||
\(850\) | −15.1141 | + | 4.04981i | −0.518410 | + | 0.138907i | ||||
\(851\) | 4.82476 | + | 18.0062i | 0.165391 | + | 0.617246i | ||||
\(852\) | −6.87165 | − | 1.84125i | −0.235419 | − | 0.0630803i | ||||
\(853\) | 7.70865 | − | 7.70865i | 0.263939 | − | 0.263939i | −0.562713 | − | 0.826652i | \(-0.690242\pi\) |
0.826652 | + | 0.562713i | \(0.190242\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.277394i | 0.00948666i | ||||||||
\(856\) | 8.14042 | − | 30.3805i | 0.278234 | − | 1.03838i | ||||
\(857\) | −11.2070 | + | 19.4112i | −0.382825 | + | 0.663073i | −0.991465 | − | 0.130374i | \(-0.958382\pi\) |
0.608640 | + | 0.793447i | \(0.291716\pi\) | |||||||
\(858\) | 12.3383 | − | 22.8736i | 0.421222 | − | 0.780892i | ||||
\(859\) | 37.7323 | − | 21.7847i | 1.28741 | − | 0.743286i | 0.309217 | − | 0.950991i | \(-0.399933\pi\) |
0.978191 | + | 0.207706i | \(0.0665996\pi\) | |||||||
\(860\) | −1.05219 | − | 1.05219i | −0.0358794 | − | 0.0358794i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 21.5441i | − | 0.733795i | ||||||
\(863\) | 12.3337 | + | 3.30482i | 0.419846 | + | 0.112497i | 0.462556 | − | 0.886590i | \(-0.346933\pi\) |
−0.0427101 | + | 0.999088i | \(0.513599\pi\) | |||||||
\(864\) | 5.39190 | − | 1.44475i | 0.183436 | − | 0.0491516i | ||||
\(865\) | −6.26555 | + | 1.67885i | −0.213035 | + | 0.0570826i | ||||
\(866\) | −16.7404 | − | 4.48558i | −0.568862 | − | 0.152426i | ||||
\(867\) | − | 17.5404i | − | 0.595703i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.6339 | − | 32.6339i | −1.10703 | − | 1.10703i | ||||
\(870\) | 7.81487 | − | 4.51192i | 0.264949 | − | 0.152968i | ||||
\(871\) | −5.12661 | + | 1.53387i | −0.173709 | + | 0.0519732i | ||||
\(872\) | 12.7051 | − | 22.0058i | 0.430248 | − | 0.745211i | ||||
\(873\) | −3.52934 | + | 13.1717i | −0.119450 | + | 0.445794i | ||||
\(874\) | 1.16022i | 0.0392450i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.49079 | + | 8.49079i | −0.286877 | + | 0.286877i | ||||
\(877\) | 6.58365 | + | 1.76408i | 0.222314 | + | 0.0595689i | 0.368257 | − | 0.929724i | \(-0.379955\pi\) |
−0.145943 | + | 0.989293i | \(0.546621\pi\) | |||||||
\(878\) | −6.25050 | − | 23.3272i | −0.210944 | − | 0.787255i | ||||
\(879\) | −11.1002 | + | 2.97428i | −0.374399 | + | 0.100320i | ||||
\(880\) | 5.18064 | − | 2.99104i | 0.174639 | − | 0.100828i | ||||
\(881\) | 3.46947 | 0.116889 | 0.0584447 | − | 0.998291i | \(-0.481386\pi\) | ||||
0.0584447 | + | 0.998291i | \(0.481386\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 47.0772i | − | 1.58427i | −0.610344 | − | 0.792136i | \(-0.708969\pi\) | ||
0.610344 | − | 0.792136i | \(-0.291031\pi\) | |||||||
\(884\) | 3.10917 | + | 5.04262i | 0.104573 | + | 0.169602i | ||||
\(885\) | −22.0930 | − | 12.7554i | −0.742648 | − | 0.428768i | ||||
\(886\) | −1.76370 | − | 6.58222i | −0.0592527 | − | 0.221134i | ||||
\(887\) | 4.98590 | − | 2.87861i | 0.167410 | − | 0.0966543i | −0.413954 | − | 0.910298i | \(-0.635853\pi\) |
0.581364 | + | 0.813644i | \(0.302519\pi\) | |||||||
\(888\) | 19.9812 | 0.670526 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.55777 | + | 3.55777i | −0.119257 | + | 0.119257i | ||||
\(891\) | 7.33219 | − | 27.3641i | 0.245638 | − | 0.916732i | ||||
\(892\) | −0.852839 | − | 3.18284i | −0.0285552 | − | 0.106569i | ||||
\(893\) | −0.543917 | + | 0.942091i | −0.0182015 | + | 0.0315259i | ||||
\(894\) | −25.9153 | − | 44.8865i | −0.866736 | − | 1.50123i | ||||
\(895\) | 13.9156 | − | 13.9156i | 0.465148 | − | 0.465148i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.54339 | + | 53.3503i | 0.0515324 | + | 1.78132i | ||||
\(898\) | 11.0300 | + | 19.1045i | 0.368075 | + | 0.637525i | ||||
\(899\) | 35.0453 | − | 9.39035i | 1.16883 | − | 0.313186i | ||||
\(900\) | 2.48554 | − | 4.30507i | 0.0828512 | − | 0.143502i | ||||
\(901\) | 5.22892 | + | 9.05676i | 0.174201 | + | 0.301724i | ||||
\(902\) | 7.20809 | + | 7.20809i | 0.240003 | + | 0.240003i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.4680 | + | 12.4680i | 0.414679 | + | 0.414679i | ||||
\(905\) | 0.430203 | − | 1.60554i | 0.0143004 | − | 0.0533699i | ||||
\(906\) | −25.7226 | − | 14.8510i | −0.854577 | − | 0.493390i | ||||
\(907\) | 11.3806 | + | 6.57058i | 0.377886 | + | 0.218172i | 0.676898 | − | 0.736077i | \(-0.263324\pi\) |
−0.299012 | + | 0.954249i | \(0.596657\pi\) | |||||||
\(908\) | −3.45463 | − | 0.925665i | −0.114646 | − | 0.0307193i | ||||
\(909\) | −2.51778 | −0.0835093 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.8394 | 0.756702 | 0.378351 | − | 0.925662i | \(-0.376491\pi\) | ||||
0.378351 | + | 0.925662i | \(0.376491\pi\) | |||||||
\(912\) | 0.852003 | + | 0.228294i | 0.0282126 | + | 0.00755956i | ||||
\(913\) | −33.8817 | − | 19.5616i | −1.12132 | − | 0.647394i | ||||
\(914\) | 10.3129 | + | 5.95415i | 0.341120 | + | 0.196946i | ||||
\(915\) | 4.69748 | − | 17.5312i | 0.155294 | − | 0.579564i | ||||
\(916\) | −0.142747 | − | 0.142747i | −0.00471648 | − | 0.00471648i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.91443 | − | 4.91443i | −0.162201 | − | 0.162201i | ||||
\(919\) | −17.5132 | − | 30.3338i | −0.577709 | − | 1.00062i | −0.995742 | − | 0.0921887i | \(-0.970614\pi\) |
0.418033 | − | 0.908432i | \(-0.362720\pi\) | |||||||
\(920\) | −8.66034 | + | 15.0002i | −0.285523 | + | 0.494541i | ||||
\(921\) | 26.6951 | − | 7.15293i | 0.879634 | − | 0.235697i | ||||
\(922\) | −6.16030 | − | 10.6700i | −0.202879 | − | 0.351396i | ||||
\(923\) | 15.2156 | + | 14.3600i | 0.500826 | + | 0.472664i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.60197 | + | 8.60197i | −0.282831 | + | 0.282831i | ||||
\(926\) | 3.47055 | + | 6.01117i | 0.114049 | + | 0.197539i | ||||
\(927\) | −5.77356 | + | 10.0001i | −0.189629 | + | 0.328447i | ||||
\(928\) | 2.89990 | + | 10.8226i | 0.0951938 | + | 0.355268i | ||||
\(929\) | −5.86238 | + | 21.8787i | −0.192339 | + | 0.717817i | 0.800601 | + | 0.599198i | \(0.204514\pi\) |
−0.992940 | + | 0.118620i | \(0.962153\pi\) | |||||||
\(930\) | 16.1369 | − | 16.1369i | 0.529151 | − | 0.529151i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.32297 | −0.108847 | ||||||||
\(933\) | −44.3857 | + | 25.6261i | −1.45312 | + | 0.838960i | ||||
\(934\) | −5.43284 | − | 20.2756i | −0.177768 | − | 0.663439i | ||||
\(935\) | 6.00053 | + | 3.46441i | 0.196238 | + | 0.113298i | ||||
\(936\) | 23.3645 | + | 5.54162i | 0.763692 | + | 0.181134i | ||||
\(937\) | 39.2356i | 1.28177i | 0.767636 | + | 0.640886i | \(0.221433\pi\) | ||||
−0.767636 | + | 0.640886i | \(0.778567\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.79711 | −0.319717 | ||||||||
\(940\) | −2.98651 | + | 1.72426i | −0.0974092 | + | 0.0562392i | ||||
\(941\) | 43.2616 | − | 11.5919i | 1.41029 | − | 0.377886i | 0.528260 | − | 0.849083i | \(-0.322845\pi\) |
0.882028 | + | 0.471197i | \(0.156178\pi\) | |||||||
\(942\) | 14.9576 | + | 55.8224i | 0.487344 | + | 1.81879i | ||||
\(943\) | −20.2212 | − | 5.41824i | −0.658491 | − | 0.176442i | ||||
\(944\) | −24.0763 | + | 24.0763i | −0.783615 | + | 0.783615i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.0917i | 0.328110i | ||||||||
\(947\) | −4.24398 | + | 15.8388i | −0.137911 | + | 0.514691i | 0.862058 | + | 0.506810i | \(0.169175\pi\) |
−0.999969 | + | 0.00788104i | \(0.997491\pi\) | |||||||
\(948\) | 10.7862 | − | 18.6823i | 0.350320 | − | 0.606773i | ||||
\(949\) | 33.8320 | − | 10.1225i | 1.09823 | − | 0.328589i | ||||
\(950\) | −0.655699 | + | 0.378568i | −0.0212737 | + | 0.0122824i | ||||
\(951\) | 9.02935 | + | 9.02935i | 0.292797 | + | 0.292797i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.1939i | 1.20483i | 0.798183 | + | 0.602415i | \(0.205795\pi\) | ||||
−0.798183 | + | 0.602415i | \(0.794205\pi\) | |||||||
\(954\) | 8.69461 | + | 2.32971i | 0.281498 | + | 0.0754273i | ||||
\(955\) | −8.37974 | + | 2.24535i | −0.271162 | + | 0.0726577i | ||||
\(956\) | 4.14741 | − | 1.11130i | 0.134137 | − | 0.0359419i | ||||
\(957\) | 21.8191 | + | 5.84641i | 0.705312 | + | 0.188988i | ||||
\(958\) | − | 16.8985i | − | 0.545965i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 12.3174 | + | 12.3174i | 0.397542 | + | 0.397542i | ||||
\(961\) | 52.6156 | − | 30.3776i | 1.69728 | − | 0.979923i | ||||
\(962\) | −10.9823 | − | 5.92397i | −0.354083 | − | 0.190996i | ||||
\(963\) | 11.1200 | − | 19.2605i | 0.358338 | − | 0.620659i | ||||
\(964\) | 0.219495 | − | 0.819167i | 0.00706946 | − | 0.0263836i | ||||
\(965\) | 12.5483i | 0.403943i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.8785 | − | 34.8785i | 1.12162 | − | 1.12162i | 0.130117 | − | 0.991499i | \(-0.458465\pi\) |
0.991499 | − | 0.130117i | \(-0.0415354\pi\) | |||||||
\(968\) | −12.2152 | − | 3.27305i | −0.392611 | − | 0.105200i | ||||
\(969\) | 0.264423 | + | 0.986841i | 0.00849450 | + | 0.0317019i | ||||
\(970\) | 6.35970 | − | 1.70408i | 0.204198 | − | 0.0547146i | ||||
\(971\) | 11.8674 | − | 6.85166i | 0.380844 | − | 0.219880i | −0.297342 | − | 0.954771i | \(-0.596100\pi\) |
0.678185 | + | 0.734891i | \(0.262767\pi\) | |||||||
\(972\) | 10.1896 | 0.326831 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 21.5525i | 0.690587i | ||||||||
\(975\) | −29.6474 | + | 18.2799i | −0.949476 | + | 0.585426i | ||||
\(976\) | −20.9787 | − | 12.1121i | −0.671513 | − | 0.387698i | ||||
\(977\) | 2.12665 | + | 7.93676i | 0.0680375 | + | 0.253919i | 0.991565 | − | 0.129614i | \(-0.0413738\pi\) |
−0.923527 | + | 0.383533i | \(0.874707\pi\) | |||||||
\(978\) | −23.6823 | + | 13.6730i | −0.757278 | + | 0.437215i | ||||
\(979\) | −12.5949 | −0.402535 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.7051 | − | 12.7051i | 0.405642 | − | 0.405642i | ||||
\(982\) | −0.539573 | + | 2.01372i | −0.0172185 | + | 0.0642602i | ||||
\(983\) | 4.48959 | + | 16.7554i | 0.143196 | + | 0.534413i | 0.999829 | + | 0.0184877i | \(0.00588516\pi\) |
−0.856634 | + | 0.515925i | \(0.827448\pi\) | |||||||
\(984\) | −11.2195 | + | 19.4328i | −0.357666 | + | 0.619495i | ||||
\(985\) | 9.35987 | + | 16.2118i | 0.298230 | + | 0.516550i | ||||
\(986\) | 9.86420 | − | 9.86420i | 0.314140 | − | 0.314140i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.208471 | + | 0.196748i | 0.00663235 | + | 0.00625940i | ||||
\(989\) | −10.3624 | − | 17.9483i | −0.329506 | − | 0.570722i | ||||
\(990\) | 5.76059 | − | 1.54354i | 0.183083 | − | 0.0490571i | ||||
\(991\) | −20.2787 | + | 35.1238i | −0.644175 | + | 1.11574i | 0.340317 | + | 0.940311i | \(0.389466\pi\) |
−0.984491 | + | 0.175433i | \(0.943868\pi\) | |||||||
\(992\) | 14.1678 | + | 24.5393i | 0.449827 | + | 0.779124i | ||||
\(993\) | 3.88652 | + | 3.88652i | 0.123335 | + | 0.123335i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.7701 | − | 13.7701i | −0.436542 | − | 0.436542i | ||||
\(996\) | 4.73310 | − | 17.6642i | 0.149974 | − | 0.559711i | ||||
\(997\) | −15.1282 | − | 8.73430i | −0.479116 | − | 0.276618i | 0.240932 | − | 0.970542i | \(-0.422547\pi\) |
−0.720048 | + | 0.693924i | \(0.755880\pi\) | |||||||
\(998\) | −40.7897 | − | 23.5500i | −1.29118 | − | 0.745461i | ||||
\(999\) | −5.21923 | − | 1.39849i | −0.165129 | − | 0.0442462i |
(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 | 637.2.bc.a.31.1 | 24 | ||
7.2 | even | 3 | inner | 637.2.bc.a.460.6 | 24 | ||
7.3 | odd | 6 | 91.2.i.a.83.5 | yes | 12 | ||
7.4 | even | 3 | 91.2.i.a.83.6 | yes | 12 | ||
7.5 | odd | 6 | inner | 637.2.bc.a.460.5 | 24 | ||
7.6 | odd | 2 | inner | 637.2.bc.a.31.2 | 24 | ||
13.8 | odd | 4 | inner | 637.2.bc.a.619.5 | 24 | ||
21.11 | odd | 6 | 819.2.y.h.811.2 | 12 | |||
21.17 | even | 6 | 819.2.y.h.811.1 | 12 | |||
91.34 | even | 4 | inner | 637.2.bc.a.619.6 | 24 | ||
91.47 | even | 12 | inner | 637.2.bc.a.411.1 | 24 | ||
91.60 | odd | 12 | 91.2.i.a.34.6 | yes | 12 | ||
91.73 | even | 12 | 91.2.i.a.34.5 | ✓ | 12 | ||
91.86 | odd | 12 | inner | 637.2.bc.a.411.2 | 24 | ||
273.164 | odd | 12 | 819.2.y.h.307.2 | 12 | |||
273.242 | even | 12 | 819.2.y.h.307.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.i.a.34.5 | ✓ | 12 | 91.73 | even | 12 | ||
91.2.i.a.34.6 | yes | 12 | 91.60 | odd | 12 | ||
91.2.i.a.83.5 | yes | 12 | 7.3 | odd | 6 | ||
91.2.i.a.83.6 | yes | 12 | 7.4 | even | 3 | ||
637.2.bc.a.31.1 | 24 | 1.1 | even | 1 | trivial | ||
637.2.bc.a.31.2 | 24 | 7.6 | odd | 2 | inner | ||
637.2.bc.a.411.1 | 24 | 91.47 | even | 12 | inner | ||
637.2.bc.a.411.2 | 24 | 91.86 | odd | 12 | inner | ||
637.2.bc.a.460.5 | 24 | 7.5 | odd | 6 | inner | ||
637.2.bc.a.460.6 | 24 | 7.2 | even | 3 | inner | ||
637.2.bc.a.619.5 | 24 | 13.8 | odd | 4 | inner | ||
637.2.bc.a.619.6 | 24 | 91.34 | even | 4 | inner | ||
819.2.y.h.307.1 | 12 | 273.242 | even | 12 | |||
819.2.y.h.307.2 | 12 | 273.164 | odd | 12 | |||
819.2.y.h.811.1 | 12 | 21.17 | even | 6 | |||
819.2.y.h.811.2 | 12 | 21.11 | odd | 6 |