Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(8,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([2, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.r (of order \(36\), degree \(12\), 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: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{36})\) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 368.13 | ||
Character | \(\chi\) | \(=\) | 405.368 |
Dual form | 405.2.r.a.197.13 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.75676 | + | 0.153697i | 1.24222 | + | 0.108680i | 0.689250 | − | 0.724523i | \(-0.257940\pi\) |
0.552967 | + | 0.833203i | \(0.313496\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.09297 | + | 0.192720i | 0.546484 | + | 0.0963599i | ||||
\(5\) | −0.131866 | + | 2.23218i | −0.0589725 | + | 0.998260i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.75943 | + | 1.93217i | 1.04297 | + | 0.730292i | 0.963815 | − | 0.266570i | \(-0.0858904\pi\) |
0.0791502 | + | 0.996863i | \(0.474779\pi\) | |||||||
\(8\) | −1.51630 | − | 0.406292i | −0.536093 | − | 0.143646i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.574736 | + | 3.90113i | −0.181747 | + | 1.23365i | ||||
\(11\) | 1.11880 | − | 3.07388i | 0.337332 | − | 0.926811i | −0.648817 | − | 0.760945i | \(-0.724736\pi\) |
0.986148 | − | 0.165866i | \(-0.0530420\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.506571 | + | 5.79013i | 0.140497 | + | 1.60589i | 0.659893 | + | 0.751359i | \(0.270601\pi\) |
−0.519396 | + | 0.854534i | \(0.673843\pi\) | |||||||
\(14\) | 4.55068 | + | 3.81848i | 1.21622 | + | 1.02053i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.68713 | − | 1.70598i | −1.17178 | − | 0.426494i | ||||
\(17\) | −1.11325 | + | 0.298295i | −0.270003 | + | 0.0723472i | −0.391280 | − | 0.920271i | \(-0.627968\pi\) |
0.121277 | + | 0.992619i | \(0.461301\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.40749 | − | 3.69937i | 1.46998 | − | 0.848693i | 0.470546 | − | 0.882375i | \(-0.344057\pi\) |
0.999433 | + | 0.0336827i | \(0.0107236\pi\) | |||||||
\(20\) | −0.574311 | + | 2.41429i | −0.128420 | + | 0.539851i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.43791 | − | 5.22812i | 0.519765 | − | 1.11464i | ||||
\(23\) | −1.09807 | − | 1.56820i | −0.228963 | − | 0.326993i | 0.688189 | − | 0.725532i | \(-0.258406\pi\) |
−0.917151 | + | 0.398539i | \(0.869517\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96522 | − | 0.588699i | −0.993044 | − | 0.117740i | ||||
\(26\) | 10.2497i | 2.01014i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.64360 | + | 2.64360i | 0.499593 | + | 0.499593i | ||||
\(29\) | −0.381851 | + | 0.320411i | −0.0709079 | + | 0.0594988i | −0.677553 | − | 0.735474i | \(-0.736959\pi\) |
0.606645 | + | 0.794973i | \(0.292515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.573116 | − | 3.25030i | 0.102935 | − | 0.583772i | −0.889090 | − | 0.457732i | \(-0.848662\pi\) |
0.992025 | − | 0.126040i | \(-0.0402269\pi\) | |||||||
\(32\) | −5.12653 | − | 2.39054i | −0.906251 | − | 0.422592i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00157 | + | 0.352930i | −0.343266 | + | 0.0605270i | ||||
\(35\) | −4.67682 | + | 5.90474i | −0.790528 | + | 0.998083i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.17991 | − | 4.40348i | −0.193976 | − | 0.723928i | −0.992530 | − | 0.122004i | \(-0.961068\pi\) |
0.798554 | − | 0.601924i | \(-0.205599\pi\) | |||||||
\(38\) | 11.8250 | − | 5.51409i | 1.91827 | − | 0.894503i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.10686 | − | 3.33107i | 0.175011 | − | 0.526689i | ||||
\(41\) | 1.39279 | − | 1.65986i | 0.217517 | − | 0.259226i | −0.646241 | − | 0.763133i | \(-0.723660\pi\) |
0.863758 | + | 0.503907i | \(0.168105\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.68889 | − | 3.62184i | −0.257554 | − | 0.552325i | 0.734431 | − | 0.678683i | \(-0.237449\pi\) |
−0.991985 | + | 0.126358i | \(0.959671\pi\) | |||||||
\(44\) | 1.81521 | − | 3.14404i | 0.273654 | − | 0.473982i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.68801 | − | 2.92372i | −0.248884 | − | 0.431080i | ||||
\(47\) | 2.84791 | − | 4.06724i | 0.415410 | − | 0.593268i | −0.555851 | − | 0.831282i | \(-0.687608\pi\) |
0.971262 | + | 0.238014i | \(0.0764965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.48701 | + | 4.08553i | 0.212430 | + | 0.583647i | ||||
\(50\) | −8.63222 | − | 1.79734i | −1.22078 | − | 0.254182i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.562207 | + | 6.42605i | −0.0779641 | + | 0.891133i | ||||
\(53\) | −1.25033 | + | 1.25033i | −0.171746 | + | 0.171746i | −0.787746 | − | 0.616000i | \(-0.788752\pi\) |
0.616000 | + | 0.787746i | \(0.288752\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.71392 | + | 2.90271i | 0.905305 | + | 0.391401i | ||||
\(56\) | −3.39910 | − | 4.05089i | −0.454223 | − | 0.541322i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.720066 | + | 0.504196i | −0.0945493 | + | 0.0662041i | ||||
\(59\) | −9.92422 | + | 3.61212i | −1.29202 | + | 0.470258i | −0.894391 | − | 0.447286i | \(-0.852391\pi\) |
−0.397633 | + | 0.917545i | \(0.630168\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.82504 | − | 10.3503i | −0.233672 | − | 1.32522i | −0.845392 | − | 0.534146i | \(-0.820633\pi\) |
0.611720 | − | 0.791074i | \(-0.290478\pi\) | |||||||
\(62\) | 1.50639 | − | 5.62192i | 0.191312 | − | 0.713985i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.000691655 | 0 | 0.000399327i | 8.64569e−5 | 0 | 4.99159e-5i | ||||
\(65\) | −12.9914 | + | 0.367231i | −1.61138 | + | 0.0455494i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.82623 | + | 0.509729i | −0.711787 | + | 0.0622733i | −0.437298 | − | 0.899317i | \(-0.644064\pi\) |
−0.274490 | + | 0.961590i | \(0.588509\pi\) | |||||||
\(68\) | −1.27424 | + | 0.111481i | −0.154524 | + | 0.0135191i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.12360 | + | 9.65440i | −1.09048 | + | 1.15392i | ||||
\(71\) | 6.62671 | + | 3.82593i | 0.786446 | + | 0.454055i | 0.838710 | − | 0.544579i | \(-0.183310\pi\) |
−0.0522640 | + | 0.998633i | \(0.516644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.84806 | + | 6.89704i | −0.216299 | + | 0.807238i | 0.769407 | + | 0.638759i | \(0.220552\pi\) |
−0.985705 | + | 0.168478i | \(0.946115\pi\) | |||||||
\(74\) | −1.39602 | − | 7.91721i | −0.162284 | − | 0.920357i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.71612 | − | 2.80844i | 0.885100 | − | 0.322150i | ||||
\(77\) | 9.02653 | − | 6.32044i | 1.02867 | − | 0.720281i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.08874 | − | 6.06452i | −0.572528 | − | 0.682312i | 0.399620 | − | 0.916681i | \(-0.369142\pi\) |
−0.972148 | + | 0.234369i | \(0.924698\pi\) | |||||||
\(80\) | 4.42611 | − | 10.2375i | 0.494854 | − | 1.14459i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.70191 | − | 2.70191i | 0.298375 | − | 0.298375i | ||||
\(83\) | −0.544416 | + | 6.22270i | −0.0597574 | + | 0.683031i | 0.905948 | + | 0.423389i | \(0.139160\pi\) |
−0.965705 | + | 0.259641i | \(0.916396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.519047 | − | 2.52431i | −0.0562985 | − | 0.273800i | ||||
\(86\) | −2.41031 | − | 6.62228i | −0.259911 | − | 0.714099i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.94533 | + | 4.20637i | −0.313974 | + | 0.448401i | ||||
\(89\) | −0.260380 | − | 0.450992i | −0.0276002 | − | 0.0478050i | 0.851895 | − | 0.523712i | \(-0.175453\pi\) |
−0.879496 | + | 0.475907i | \(0.842120\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.78968 | + | 16.9562i | −1.02624 | + | 1.77750i | ||||
\(92\) | −0.897929 | − | 1.92562i | −0.0936156 | − | 0.200759i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.62822 | − | 6.70745i | 0.580506 | − | 0.691820i | ||||
\(95\) | 7.41270 | + | 14.7905i | 0.760527 | + | 1.51747i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.27963 | − | 1.99563i | 0.434531 | − | 0.202625i | −0.193029 | − | 0.981193i | \(-0.561831\pi\) |
0.627560 | + | 0.778568i | \(0.284054\pi\) | |||||||
\(98\) | 1.98439 | + | 7.40585i | 0.200454 | + | 0.748103i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.31338 | − | 1.60033i | −0.531338 | − | 0.160033i | ||||
\(101\) | 6.92843 | − | 1.22167i | 0.689404 | − | 0.121561i | 0.182038 | − | 0.983291i | \(-0.441730\pi\) |
0.507366 | + | 0.861731i | \(0.330619\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.34471 | + | 2.95859i | 0.625163 | + | 0.291518i | 0.709268 | − | 0.704938i | \(-0.249025\pi\) |
−0.0841052 | + | 0.996457i | \(0.526803\pi\) | |||||||
\(104\) | 1.58437 | − | 8.98539i | 0.155360 | − | 0.881090i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.38870 | + | 2.00436i | −0.232011 | + | 0.194680i | ||||
\(107\) | 3.17818 | + | 3.17818i | 0.307247 | + | 0.307247i | 0.843841 | − | 0.536594i | \(-0.180289\pi\) |
−0.536594 | + | 0.843841i | \(0.680289\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.14715i | 0.301442i | 0.988576 | + | 0.150721i | \(0.0481595\pi\) | ||||
−0.988576 | + | 0.150721i | \(0.951840\pi\) | |||||||
\(110\) | 11.3486 | + | 6.13127i | 1.08205 | + | 0.584593i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.63755 | − | 13.7639i | −0.910663 | − | 1.30056i | ||||
\(113\) | −0.190621 | + | 0.408788i | −0.0179321 | + | 0.0384556i | −0.915070 | − | 0.403295i | \(-0.867865\pi\) |
0.897138 | + | 0.441751i | \(0.145643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.64530 | − | 2.24429i | 0.339926 | − | 0.209281i | ||||
\(116\) | −0.479100 | + | 0.276609i | −0.0444833 | + | 0.0256825i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.9897 | + | 4.82031i | −1.65608 | + | 0.443746i | ||||
\(119\) | −3.64830 | − | 1.32787i | −0.334439 | − | 0.121726i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.229444 | + | 0.192526i | 0.0208585 | + | 0.0175024i | ||||
\(122\) | −1.61535 | − | 18.4635i | −0.146247 | − | 1.67161i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.25280 | − | 3.44203i | 0.112504 | − | 0.309103i | ||||
\(125\) | 1.96883 | − | 11.0056i | 0.176097 | − | 0.984373i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.534026 | + | 0.143092i | 0.0473871 | + | 0.0126973i | 0.282435 | − | 0.959287i | \(-0.408858\pi\) |
−0.235048 | + | 0.971984i | \(0.575525\pi\) | |||||||
\(128\) | 9.26822 | + | 6.48968i | 0.819203 | + | 0.573612i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −22.8792 | − | 1.35160i | −2.00664 | − | 0.118543i | ||||
\(131\) | −14.1236 | − | 2.49037i | −1.23398 | − | 0.217585i | −0.481648 | − | 0.876365i | \(-0.659962\pi\) |
−0.752336 | + | 0.658780i | \(0.771073\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.8288 | + | 2.17224i | 2.15293 | + | 0.188357i | ||||
\(134\) | −10.3136 | −0.890962 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.80922 | 0.155139 | ||||||||
\(137\) | −3.37255 | − | 0.295060i | −0.288136 | − | 0.0252087i | −0.0578286 | − | 0.998327i | \(-0.518418\pi\) |
−0.230308 | + | 0.973118i | \(0.573973\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.42140 | + | 0.955940i | 0.459837 | + | 0.0810818i | 0.398768 | − | 0.917052i | \(-0.369438\pi\) |
0.0610693 | + | 0.998134i | \(0.480549\pi\) | |||||||
\(140\) | −6.24958 | + | 5.55238i | −0.528186 | + | 0.469262i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.0535 | + | 7.73975i | 0.927590 | + | 0.649505i | ||||
\(143\) | 18.3649 | + | 4.92087i | 1.53575 | + | 0.411504i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.664860 | − | 0.894609i | −0.0552136 | − | 0.0742933i | ||||
\(146\) | −4.30665 | + | 11.8324i | −0.356420 | + | 0.979257i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.440966 | − | 5.04026i | −0.0362472 | − | 0.414307i | ||||
\(149\) | 10.1897 | + | 8.55016i | 0.834771 | + | 0.700456i | 0.956381 | − | 0.292122i | \(-0.0943613\pi\) |
−0.121610 | + | 0.992578i | \(0.538806\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.7660 | + | 5.01040i | 1.12026 | + | 0.407741i | 0.834747 | − | 0.550634i | \(-0.185614\pi\) |
0.285512 | + | 0.958375i | \(0.407836\pi\) | |||||||
\(152\) | −11.2187 | + | 3.00604i | −0.909957 | + | 0.243822i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.8289 | − | 9.71616i | 1.35611 | − | 0.782950i | ||||
\(155\) | 7.17968 | + | 1.70790i | 0.576686 | + | 0.137182i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.34570 | + | 5.03036i | −0.187207 | + | 0.401467i | −0.977402 | − | 0.211389i | \(-0.932201\pi\) |
0.790195 | + | 0.612855i | \(0.209979\pi\) | |||||||
\(158\) | −8.00759 | − | 11.4360i | −0.637050 | − | 0.909802i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.01213 | − | 11.1281i | 0.475300 | − | 0.879753i | ||||
\(161\) | − | 6.44900i | − | 0.508252i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.06235 | + | 5.06235i | 0.396514 | + | 0.396514i | 0.877002 | − | 0.480488i | \(-0.159540\pi\) |
−0.480488 | + | 0.877002i | \(0.659540\pi\) | |||||||
\(164\) | 1.84216 | − | 1.54575i | 0.143848 | − | 0.120703i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.91282 | + | 10.8481i | −0.148463 | + | 0.841978i | ||||
\(167\) | 12.7047 | + | 5.92432i | 0.983123 | + | 0.458438i | 0.846618 | − | 0.532202i | \(-0.178635\pi\) |
0.136505 | + | 0.990639i | \(0.456413\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −20.4665 | + | 3.60879i | −1.57434 | + | 0.277599i | ||||
\(170\) | −0.523863 | − | 4.51439i | −0.0401784 | − | 0.346238i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.14791 | − | 4.28404i | −0.0875269 | − | 0.326655i | ||||
\(173\) | −8.87248 | + | 4.13731i | −0.674563 | + | 0.314554i | −0.729544 | − | 0.683934i | \(-0.760268\pi\) |
0.0549816 | + | 0.998487i | \(0.482490\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.5637 | − | 11.2181i | −0.949727 | − | 0.848011i | ||||
\(176\) | −10.4879 | + | 12.4990i | −0.790558 | + | 0.942151i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.388110 | − | 0.832304i | −0.0290900 | − | 0.0623838i | ||||
\(179\) | −5.82103 | + | 10.0823i | −0.435084 | + | 0.753588i | −0.997303 | − | 0.0734009i | \(-0.976615\pi\) |
0.562218 | + | 0.826989i | \(0.309948\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5182 | − | 18.2180i | −0.781810 | − | 1.35413i | −0.930886 | − | 0.365309i | \(-0.880963\pi\) |
0.149076 | − | 0.988826i | \(-0.452370\pi\) | |||||||
\(182\) | −19.8042 | + | 28.2834i | −1.46799 | + | 2.09650i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.02785 | + | 2.82400i | 0.0757743 | + | 0.208188i | ||||
\(185\) | 9.98494 | − | 2.05309i | 0.734108 | − | 0.150947i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.328585 | + | 3.75574i | −0.0240285 | + | 0.274647i | ||||
\(188\) | 3.89651 | − | 3.89651i | 0.284182 | − | 0.284182i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.7491 | + | 27.1226i | 0.779822 | + | 1.96768i | ||||
\(191\) | −16.1454 | − | 19.2414i | −1.16824 | − | 1.39226i | −0.903854 | − | 0.427841i | \(-0.859274\pi\) |
−0.264388 | − | 0.964416i | \(-0.585170\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.27354 | + | 2.29216i | −0.235635 | + | 0.164993i | −0.685430 | − | 0.728138i | \(-0.740386\pi\) |
0.449795 | + | 0.893132i | \(0.351497\pi\) | |||||||
\(194\) | 7.82501 | − | 2.84807i | 0.561803 | − | 0.204480i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.837894 | + | 4.75193i | 0.0598496 | + | 0.339424i | ||||
\(197\) | −2.68314 | + | 10.0136i | −0.191166 | + | 0.713441i | 0.802060 | + | 0.597243i | \(0.203737\pi\) |
−0.993226 | + | 0.116198i | \(0.962929\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.6933 | − | 6.17378i | −0.758027 | − | 0.437647i | 0.0705597 | − | 0.997508i | \(-0.477521\pi\) |
−0.828587 | + | 0.559860i | \(0.810855\pi\) | |||||||
\(200\) | 7.28959 | + | 2.90997i | 0.515452 | + | 0.205766i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.3593 | − | 1.08130i | 0.869601 | − | 0.0760802i | ||||
\(203\) | −1.67278 | + | 0.146349i | −0.117406 | + | 0.0102717i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.52143 | + | 3.32782i | 0.245948 | + | 0.232425i | ||||
\(206\) | 10.6914 | + | 6.17269i | 0.744906 | + | 0.430072i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.50345 | − | 28.0033i | 0.520271 | − | 1.94168i | ||||
\(209\) | −4.20271 | − | 23.8347i | −0.290707 | − | 1.64868i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.83540 | − | 3.21582i | 0.608254 | − | 0.221386i | −0.0194850 | − | 0.999810i | \(-0.506203\pi\) |
0.627739 | + | 0.778424i | \(0.283980\pi\) | |||||||
\(212\) | −1.60753 | + | 1.12561i | −0.110406 | + | 0.0773070i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.09483 | + | 6.07178i | 0.348275 | + | 0.415058i | ||||
\(215\) | 8.30729 | − | 3.29230i | 0.566553 | − | 0.224533i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.86162 | − | 7.86162i | 0.533682 | − | 0.533682i | ||||
\(218\) | −0.483706 | + | 5.52878i | −0.0327607 | + | 0.374456i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.77869 | + | 4.46647i | 0.457019 | + | 0.301129i | ||||
\(221\) | −2.29111 | − | 6.29477i | −0.154117 | − | 0.423432i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.07893 | − | 11.5379i | 0.541005 | − | 0.772635i | −0.451833 | − | 0.892102i | \(-0.649230\pi\) |
0.992838 | + | 0.119467i | \(0.0381186\pi\) | |||||||
\(224\) | −9.52736 | − | 16.5019i | −0.636573 | − | 1.10258i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.397705 | + | 0.688845i | −0.0264549 | + | 0.0458213i | ||||
\(227\) | 11.1767 | + | 23.9686i | 0.741825 | + | 1.59085i | 0.805301 | + | 0.592866i | \(0.202004\pi\) |
−0.0634761 | + | 0.997983i | \(0.520219\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.42008 | + | 7.65115i | −0.424251 | + | 0.505602i | −0.935254 | − | 0.353976i | \(-0.884829\pi\) |
0.511004 | + | 0.859579i | \(0.329274\pi\) | |||||||
\(230\) | 6.74886 | − | 3.38240i | 0.445007 | − | 0.223029i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.709181 | − | 0.330696i | 0.0465600 | − | 0.0217113i | ||||
\(233\) | −7.01401 | − | 26.1766i | −0.459503 | − | 1.71489i | −0.674500 | − | 0.738274i | \(-0.735641\pi\) |
0.214997 | − | 0.976615i | \(-0.431026\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.70325 | + | 6.89337i | 0.567737 | + | 0.449674i | ||||
\(236\) | −11.5430 | + | 2.03534i | −0.751385 | + | 0.132489i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.20510 | − | 2.89348i | −0.402217 | − | 0.187557i | ||||
\(239\) | −4.31982 | + | 24.4989i | −0.279426 | + | 1.58470i | 0.445117 | + | 0.895472i | \(0.353162\pi\) |
−0.724543 | + | 0.689230i | \(0.757949\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.8499 | + | 18.3342i | −1.40747 | + | 1.18101i | −0.449808 | + | 0.893125i | \(0.648508\pi\) |
−0.957665 | + | 0.287885i | \(0.907048\pi\) | |||||||
\(242\) | 0.373487 | + | 0.373487i | 0.0240087 | + | 0.0240087i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 11.6643i | − | 0.746728i | ||||||
\(245\) | −9.31571 | + | 2.78053i | −0.595159 | + | 0.177641i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.6656 | + | 35.2262i | 1.56944 | + | 2.24139i | ||||
\(248\) | −2.18959 | + | 4.69559i | −0.139039 | + | 0.298170i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.15028 | − | 19.0316i | 0.325732 | − | 1.20367i | ||||
\(251\) | −9.61601 | + | 5.55181i | −0.606957 | + | 0.350427i | −0.771774 | − | 0.635897i | \(-0.780630\pi\) |
0.164816 | + | 0.986324i | \(0.447297\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.04899 | + | 1.62082i | −0.380297 | + | 0.101900i | ||||
\(254\) | 0.916163 | + | 0.333456i | 0.0574852 | + | 0.0209229i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.2834 | + | 12.8243i | 0.955211 | + | 0.801518i | ||||
\(257\) | −2.45897 | − | 28.1062i | −0.153386 | − | 1.75321i | −0.549941 | − | 0.835203i | \(-0.685350\pi\) |
0.396555 | − | 0.918011i | \(-0.370206\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.25241 | − | 14.4309i | 0.326369 | − | 0.896691i | ||||
\(260\) | −14.2700 | − | 2.10233i | −0.884985 | − | 0.130381i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.4290 | − | 6.54573i | −1.50923 | − | 0.404397i | ||||
\(263\) | −2.02429 | − | 1.41742i | −0.124823 | − | 0.0874019i | 0.509498 | − | 0.860472i | \(-0.329831\pi\) |
−0.634321 | + | 0.773070i | \(0.718720\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.62608 | − | 2.95583i | −0.161319 | − | 0.181575i | ||||
\(266\) | 43.2844 | + | 7.63221i | 2.65394 | + | 0.467961i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.46612 | − | 0.565712i | −0.394981 | − | 0.0345564i | ||||
\(269\) | −2.07465 | −0.126494 | −0.0632468 | − | 0.997998i | \(-0.520146\pi\) | ||||
−0.0632468 | + | 0.997998i | \(0.520146\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.0921 | −1.09901 | −0.549507 | − | 0.835489i | \(-0.685184\pi\) | ||||
−0.549507 | + | 0.835489i | \(0.685184\pi\) | |||||||
\(272\) | 5.72684 | + | 0.501034i | 0.347241 | + | 0.0303796i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.87941 | − | 1.03670i | −0.355188 | − | 0.0626293i | ||||
\(275\) | −7.36469 | + | 14.6039i | −0.444108 | + | 0.880647i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.0713 | + | 14.7543i | 1.26605 | + | 0.886497i | 0.997058 | − | 0.0766456i | \(-0.0244210\pi\) |
0.268991 | + | 0.963143i | \(0.413310\pi\) | |||||||
\(278\) | 9.37718 | + | 2.51261i | 0.562406 | + | 0.150696i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.49052 | − | 7.05321i | 0.567167 | − | 0.421510i | ||||
\(281\) | −0.952631 | + | 2.61733i | −0.0568292 | + | 0.156137i | −0.964859 | − | 0.262769i | \(-0.915364\pi\) |
0.908029 | + | 0.418906i | \(0.137586\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.78620 | + | 20.4164i | 0.106179 | + | 1.21363i | 0.843140 | + | 0.537694i | \(0.180704\pi\) |
−0.736962 | + | 0.675935i | \(0.763740\pi\) | |||||||
\(284\) | 6.50545 | + | 5.45872i | 0.386028 | + | 0.323916i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 31.5065 | + | 11.4674i | 1.86302 | + | 0.678083i | ||||
\(287\) | 7.05042 | − | 1.88915i | 0.416173 | − | 0.111513i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5721 | + | 7.83584i | −0.798358 | + | 0.460932i | ||||
\(290\) | −1.03050 | − | 1.67380i | −0.0605131 | − | 0.0982890i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.34907 | + | 7.18209i | −0.195989 | + | 0.420300i | ||||
\(293\) | 17.9864 | + | 25.6873i | 1.05078 | + | 1.50067i | 0.854036 | + | 0.520213i | \(0.174148\pi\) |
0.196743 | + | 0.980455i | \(0.436964\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.75422 | − | 22.6289i | −0.393246 | − | 1.31751i | ||||
\(296\) | 7.15639i | 0.415957i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.5867 | + | 16.5867i | 0.960842 | + | 0.960842i | ||||
\(299\) | 8.52385 | − | 7.15236i | 0.492947 | − | 0.413631i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.33764 | − | 13.2574i | 0.134740 | − | 0.764146i | ||||
\(302\) | 23.4134 | + | 10.9179i | 1.34729 | + | 0.628252i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −36.3437 | + | 6.40838i | −2.08446 | + | 0.367546i | ||||
\(305\) | 23.3444 | − | 2.70895i | 1.33669 | − | 0.155114i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.49145 | + | 9.29823i | 0.142195 | + | 0.530678i | 0.999864 | + | 0.0164767i | \(0.00524495\pi\) |
−0.857669 | + | 0.514201i | \(0.828088\pi\) | |||||||
\(308\) | 11.0838 | − | 5.16845i | 0.631557 | − | 0.294500i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.3505 | + | 4.10387i | 0.701460 | + | 0.233084i | ||||
\(311\) | 0.00272616 | − | 0.00324891i | 0.000154586 | − | 0.000184229i | −0.765967 | − | 0.642880i | \(-0.777740\pi\) |
0.766122 | + | 0.642695i | \(0.222184\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0379 | − | 21.5265i | −0.567378 | − | 1.21675i | −0.955460 | − | 0.295122i | \(-0.904640\pi\) |
0.388081 | − | 0.921625i | \(-0.373138\pi\) | |||||||
\(314\) | −4.89398 | + | 8.47662i | −0.276183 | + | 0.478363i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.39308 | − | 7.60903i | −0.247130 | − | 0.428041i | ||||
\(317\) | −0.455273 | + | 0.650197i | −0.0255707 | + | 0.0365187i | −0.831734 | − | 0.555175i | \(-0.812651\pi\) |
0.806163 | + | 0.591693i | \(0.201540\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.557690 | + | 1.53224i | 0.0312246 | + | 0.0857890i | ||||
\(320\) | −0.000982575 | 0.00149124i | −5.49276e−5 | 8.33628e-5i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.991189 | − | 11.3293i | 0.0552368 | − | 0.631359i | ||||
\(323\) | −6.02965 | + | 6.02965i | −0.335499 | + | 0.335499i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.893405 | − | 29.0475i | 0.0495572 | − | 1.61127i | ||||
\(326\) | 8.11527 | + | 9.67140i | 0.449463 | + | 0.535649i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.78627 | + | 1.95097i | −0.153846 | + | 0.107724i | ||||
\(329\) | 15.7172 | − | 5.72060i | 0.866518 | − | 0.315387i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.994980 | − | 5.64281i | −0.0546891 | − | 0.310157i | 0.945176 | − | 0.326560i | \(-0.105890\pi\) |
−0.999865 | + | 0.0164031i | \(0.994778\pi\) | |||||||
\(332\) | −1.79427 | + | 6.69630i | −0.0984733 | + | 0.367507i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 21.4086 | + | 12.3603i | 1.17143 | + | 0.676325i | ||||
\(335\) | −0.369521 | − | 13.0724i | −0.0201891 | − | 0.714221i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.4396 | + | 2.22568i | −1.38578 | + | 0.121240i | −0.755512 | − | 0.655135i | \(-0.772612\pi\) |
−0.630271 | + | 0.776375i | \(0.717056\pi\) | |||||||
\(338\) | −36.5094 | + | 3.19415i | −1.98585 | + | 0.173739i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.0808168 | − | 2.85902i | −0.00438291 | − | 0.155052i | ||||
\(341\) | −9.34986 | − | 5.39814i | −0.506323 | − | 0.292326i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.31243 | − | 8.63010i | 0.124859 | − | 0.465982i | ||||
\(344\) | 1.08934 | + | 6.17798i | 0.0587335 | + | 0.333094i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.2227 | + | 5.90459i | −0.872139 | + | 0.317433i | ||||
\(347\) | −9.96940 | + | 6.98065i | −0.535185 | + | 0.374741i | −0.809702 | − | 0.586842i | \(-0.800371\pi\) |
0.274516 | + | 0.961582i | \(0.411482\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.0762364 | − | 0.0908550i | −0.00408084 | − | 0.00486336i | 0.764000 | − | 0.645216i | \(-0.223233\pi\) |
−0.768081 | + | 0.640353i | \(0.778788\pi\) | |||||||
\(350\) | −20.3472 | − | 21.6386i | −1.08761 | − | 1.15663i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13.0838 | + | 13.0838i | −0.697370 | + | 0.697370i | ||||
\(353\) | 1.88537 | − | 21.5499i | 0.100348 | − | 1.14699i | −0.764387 | − | 0.644758i | \(-0.776958\pi\) |
0.864735 | − | 0.502228i | \(-0.167486\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.41400 | + | 14.2875i | −0.499643 | + | 0.758300i | ||||
\(356\) | −0.197672 | − | 0.543100i | −0.0104766 | − | 0.0287842i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.7758 | + | 16.8175i | −0.622369 | + | 0.888835i | ||||
\(359\) | −15.2804 | − | 26.4664i | −0.806468 | − | 1.39684i | −0.915296 | − | 0.402782i | \(-0.868043\pi\) |
0.108828 | − | 0.994061i | \(-0.465290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.8706 | − | 30.9528i | 0.940558 | − | 1.62910i | ||||
\(362\) | −15.6779 | − | 33.6213i | −0.824011 | − | 1.76710i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.9676 | + | 16.6460i | −0.732102 | + | 0.872485i | ||||
\(365\) | −15.1517 | − | 5.03468i | −0.793077 | − | 0.263527i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.9364 | + | 6.49863i | −0.727472 | + | 0.339226i | −0.750825 | − | 0.660502i | \(-0.770344\pi\) |
0.0233530 | + | 0.999727i | \(0.492566\pi\) | |||||||
\(368\) | 2.47147 | + | 9.22364i | 0.128834 | + | 0.480816i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.8567 | − | 2.07214i | 0.928326 | − | 0.107726i | ||||
\(371\) | −5.86604 | + | 1.03434i | −0.304550 | + | 0.0537003i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.2501 | − | 11.7743i | −1.30740 | − | 0.609651i | −0.360976 | − | 0.932575i | \(-0.617556\pi\) |
−0.946425 | + | 0.322924i | \(0.895334\pi\) | |||||||
\(374\) | −1.15449 | + | 6.54744i | −0.0596973 | + | 0.338560i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.97077 | + | 5.01007i | −0.307919 | + | 0.258375i | ||||
\(377\) | −2.04865 | − | 2.04865i | −0.105511 | − | 0.105511i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.6622i | 0.855880i | 0.903807 | + | 0.427940i | \(0.140760\pi\) | ||||
−0.903807 | + | 0.427940i | \(0.859240\pi\) | |||||||
\(380\) | 5.25143 | + | 17.5941i | 0.269393 | + | 0.902558i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −25.4063 | − | 36.2840i | −1.29990 | − | 1.85645i | ||||
\(383\) | 13.4360 | − | 28.8135i | 0.686546 | − | 1.47230i | −0.185381 | − | 0.982667i | \(-0.559352\pi\) |
0.871927 | − | 0.489636i | \(-0.162870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.9180 | + | 20.9823i | 0.658365 | + | 1.06935i | ||||
\(386\) | −6.10313 | + | 3.52364i | −0.310641 | + | 0.179349i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.06210 | − | 1.35639i | 0.256989 | − | 0.0688601i | ||||
\(389\) | 10.3645 | + | 3.77237i | 0.525501 | + | 0.191267i | 0.591128 | − | 0.806577i | \(-0.298683\pi\) |
−0.0656273 | + | 0.997844i | \(0.520905\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.69021 | + | 1.41826i | 0.0854778 | + | 0.0717244i | ||||
\(392\) | −0.594840 | − | 6.79905i | −0.0300440 | − | 0.343404i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.25270 | + | 17.1791i | −0.315006 | + | 0.865473i | ||||
\(395\) | 14.2081 | − | 10.5593i | 0.714888 | − | 0.531294i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.3279 | − | 4.10710i | −0.769286 | − | 0.206129i | −0.147230 | − | 0.989102i | \(-0.547036\pi\) |
−0.622056 | + | 0.782973i | \(0.713702\pi\) | |||||||
\(398\) | −17.8367 | − | 12.4894i | −0.894071 | − | 0.626035i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.2683 | + | 11.2299i | 1.11342 | + | 0.561493i | ||||
\(401\) | 18.2547 | + | 3.21880i | 0.911598 | + | 0.160739i | 0.609729 | − | 0.792610i | \(-0.291278\pi\) |
0.301869 | + | 0.953349i | \(0.402389\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.1100 | + | 1.67191i | 0.951937 | + | 0.0832837i | ||||
\(404\) | 7.80799 | 0.388462 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.96116 | −0.146960 | ||||||||
\(407\) | −14.8559 | − | 1.29972i | −0.736379 | − | 0.0644248i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.3828 | + | 2.71240i | 0.760628 | + | 0.134119i | 0.540491 | − | 0.841350i | \(-0.318238\pi\) |
0.220137 | + | 0.975469i | \(0.429350\pi\) | |||||||
\(410\) | 5.67484 | + | 6.38742i | 0.280260 | + | 0.315452i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.36439 | + | 4.45640i | 0.313551 | + | 0.219551i | ||||
\(413\) | −34.3644 | − | 9.20792i | −1.69096 | − | 0.453092i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.8184 | − | 2.03580i | −0.678318 | − | 0.0999334i | ||||
\(416\) | 11.2446 | − | 30.8943i | 0.551311 | − | 1.51472i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.71983 | − | 42.5179i | −0.181943 | − | 2.07962i | ||||
\(419\) | −8.40402 | − | 7.05181i | −0.410563 | − | 0.344503i | 0.413996 | − | 0.910279i | \(-0.364133\pi\) |
−0.824560 | + | 0.565775i | \(0.808577\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.13716 | − | 1.50580i | −0.201633 | − | 0.0733884i | 0.239230 | − | 0.970963i | \(-0.423105\pi\) |
−0.440863 | + | 0.897575i | \(0.645327\pi\) | |||||||
\(422\) | 16.0159 | − | 4.29146i | 0.779644 | − | 0.208905i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.40387 | − | 1.38788i | 0.116742 | − | 0.0674012i | ||||
\(425\) | 5.70315 | − | 0.825732i | 0.276644 | − | 0.0400539i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.9625 | − | 32.0872i | 0.724086 | − | 1.55281i | ||||
\(428\) | 2.86115 | + | 4.08615i | 0.138299 | + | 0.197512i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.0999 | − | 4.50699i | 0.728184 | − | 0.217346i | ||||
\(431\) | − | 22.9617i | − | 1.10603i | −0.833173 | − | 0.553013i | \(-0.813478\pi\) | ||
0.833173 | − | 0.553013i | \(-0.186522\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.8168 | − | 11.8168i | −0.567878 | − | 0.567878i | 0.363655 | − | 0.931534i | \(-0.381529\pi\) |
−0.931534 | + | 0.363655i | \(0.881529\pi\) | |||||||
\(434\) | 15.0193 | − | 12.6027i | 0.720949 | − | 0.604948i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.606518 | + | 3.43973i | −0.0290469 | + | 0.164733i | ||||
\(437\) | −12.8372 | − | 5.98609i | −0.614087 | − | 0.286353i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.4676 | − | 2.72735i | 0.738226 | − | 0.130169i | 0.208124 | − | 0.978103i | \(-0.433264\pi\) |
0.530103 | + | 0.847933i | \(0.322153\pi\) | |||||||
\(440\) | −9.00098 | − | 7.12918i | −0.429105 | − | 0.339871i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.05744 | − | 11.4105i | −0.145428 | − | 0.542744i | ||||
\(443\) | −21.0959 | + | 9.83716i | −1.00229 | + | 0.467378i | −0.853278 | − | 0.521457i | \(-0.825389\pi\) |
−0.149017 | + | 0.988835i | \(0.547611\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.04103 | − | 0.521744i | 0.0493495 | − | 0.0247330i | ||||
\(446\) | 15.9661 | − | 19.0276i | 0.756016 | − | 0.900984i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.00113700 | + | 0.00243831i | 5.37184e−5 | + | 0.000115199i | ||||
\(449\) | −15.4027 | + | 26.6783i | −0.726900 | + | 1.25903i | 0.231288 | + | 0.972885i | \(0.425706\pi\) |
−0.958187 | + | 0.286142i | \(0.907627\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.54396 | − | 6.13831i | −0.166878 | − | 0.289042i | ||||
\(452\) | −0.287125 | + | 0.410056i | −0.0135052 | + | 0.0192874i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.9509 | + | 43.8248i | 0.748615 | + | 2.05680i | ||||
\(455\) | −36.5584 | − | 24.0883i | −1.71388 | − | 1.12927i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.28713 | − | 26.1420i | 0.106988 | − | 1.22287i | −0.732985 | − | 0.680245i | \(-0.761874\pi\) |
0.839973 | − | 0.542629i | \(-0.182571\pi\) | |||||||
\(458\) | −12.4545 | + | 12.4545i | −0.581961 | + | 0.581961i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.41672 | − | 1.75041i | 0.205931 | − | 0.0816134i | ||||
\(461\) | 12.6198 | + | 15.0397i | 0.587761 | + | 0.700467i | 0.975174 | − | 0.221440i | \(-0.0710756\pi\) |
−0.387413 | + | 0.921906i | \(0.626631\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.86273 | + | 4.80533i | −0.318938 | + | 0.223323i | −0.722072 | − | 0.691818i | \(-0.756810\pi\) |
0.403134 | + | 0.915141i | \(0.367921\pi\) | |||||||
\(464\) | 2.33640 | − | 0.850378i | 0.108464 | − | 0.0394778i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.29867 | − | 47.0641i | −0.384429 | − | 2.18020i | ||||
\(467\) | 0.507459 | − | 1.89386i | 0.0234824 | − | 0.0876375i | −0.953190 | − | 0.302371i | \(-0.902222\pi\) |
0.976673 | + | 0.214734i | \(0.0688884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.0619 | − | 9.85072i | −0.787847 | − | 0.454864i | ||||
\(470\) | 14.2300 | + | 13.4477i | 0.656382 | + | 0.620294i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 16.5157 | − | 1.44494i | 0.760196 | − | 0.0665085i | ||||
\(473\) | −13.0227 | + | 1.13933i | −0.598782 | + | 0.0523867i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.9924 | + | 14.5961i | −1.55968 | + | 0.669715i | ||||
\(476\) | −3.73157 | − | 2.15442i | −0.171036 | − | 0.0987478i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.3543 | + | 42.3747i | −0.519333 | + | 1.93818i | ||||
\(479\) | 3.17060 | + | 17.9814i | 0.144868 | + | 0.821589i | 0.967473 | + | 0.252975i | \(0.0814091\pi\) |
−0.822604 | + | 0.568614i | \(0.807480\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.8990 | − | 9.06251i | 1.13530 | − | 0.413215i | ||||
\(482\) | −41.2029 | + | 28.8506i | −1.87674 | + | 1.31411i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.213671 | + | 0.254643i | 0.00971233 | + | 0.0115747i | ||||
\(485\) | 3.89025 | + | 9.81605i | 0.176647 | + | 0.445724i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.0616 | + | 23.0616i | −1.04502 | + | 1.04502i | −0.0460835 | + | 0.998938i | \(0.514674\pi\) |
−0.998938 | + | 0.0460835i | \(0.985326\pi\) | |||||||
\(488\) | −1.43793 | + | 16.4357i | −0.0650922 | + | 0.744008i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.7928 | + | 3.45293i | −0.758623 | + | 0.155987i | ||||
\(491\) | −1.13497 | − | 3.11830i | −0.0512204 | − | 0.140727i | 0.911444 | − | 0.411423i | \(-0.134968\pi\) |
−0.962665 | + | 0.270697i | \(0.912746\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.329519 | − | 0.470602i | 0.0148408 | − | 0.0211949i | ||||
\(494\) | 37.9175 | + | 65.6750i | 1.70599 | + | 2.95486i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.23121 | + | 14.2569i | −0.369592 | + | 0.640153i | ||||
\(497\) | 10.8936 | + | 23.3613i | 0.488643 | + | 1.04790i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.13042 | − | 4.92245i | 0.184903 | − | 0.220359i | −0.665628 | − | 0.746284i | \(-0.731836\pi\) |
0.850531 | + | 0.525925i | \(0.176281\pi\) | |||||||
\(500\) | 4.27287 | − | 11.6494i | 0.191088 | − | 0.520976i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.7463 | + | 8.27524i | −0.792057 | + | 0.369342i | ||||
\(503\) | −1.67013 | − | 6.23303i | −0.0744676 | − | 0.277917i | 0.918644 | − | 0.395085i | \(-0.129285\pi\) |
−0.993112 | + | 0.117168i | \(0.962618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.81335 | + | 15.6266i | 0.0806931 | + | 0.695373i | ||||
\(506\) | −10.8757 | + | 1.91769i | −0.483486 | + | 0.0852516i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.556097 | + | 0.259312i | 0.0246728 | + | 0.0115051i | ||||
\(509\) | 2.35893 | − | 13.3781i | 0.104558 | − | 0.592976i | −0.886838 | − | 0.462080i | \(-0.847103\pi\) |
0.991396 | − | 0.130896i | \(-0.0417854\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.4259 | + | 15.4611i | −0.815112 | + | 0.683960i | ||||
\(512\) | 8.87720 | + | 8.87720i | 0.392320 | + | 0.392320i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 49.7537i | − | 2.19454i | ||||||
\(515\) | −7.44075 | + | 13.7724i | −0.327878 | + | 0.606884i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.31597 | − | 13.3046i | −0.409716 | − | 0.585135i | ||||
\(518\) | 11.4452 | − | 24.5443i | 0.502874 | − | 1.07842i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 19.8481 | + | 4.72146i | 0.870395 | + | 0.207050i | ||||
\(521\) | 26.9126 | − | 15.5380i | 1.17906 | − | 0.680731i | 0.223263 | − | 0.974758i | \(-0.428329\pi\) |
0.955797 | + | 0.294027i | \(0.0949957\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.82198 | − | 1.02410i | 0.167124 | − | 0.0447807i | −0.174287 | − | 0.984695i | \(-0.555762\pi\) |
0.341411 | + | 0.939914i | \(0.389095\pi\) | |||||||
\(524\) | −14.9567 | − | 5.44379i | −0.653386 | − | 0.237813i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.33833 | − | 2.80120i | −0.145558 | − | 0.122138i | ||||
\(527\) | 0.331527 | + | 3.78937i | 0.0144415 | + | 0.165068i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.61296 | − | 18.1689i | 0.287520 | − | 0.789954i | ||||
\(530\) | −4.15909 | − | 5.59630i | −0.180659 | − | 0.243088i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 26.7185 | + | 7.15919i | 1.15839 | + | 0.310390i | ||||
\(533\) | 10.3163 | + | 7.22357i | 0.446850 | + | 0.312888i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.51336 | + | 6.67517i | −0.324831 | + | 0.288593i | ||||
\(536\) | 9.04142 | + | 1.59425i | 0.390530 | + | 0.0688609i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.64466 | − | 0.318866i | −0.157132 | − | 0.0137473i | ||||
\(539\) | 14.2221 | 0.612590 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.8935 | 1.88713 | 0.943565 | − | 0.331186i | \(-0.107449\pi\) | ||||
0.943565 | + | 0.331186i | \(0.107449\pi\) | |||||||
\(542\) | −31.7834 | − | 2.78069i | −1.36521 | − | 0.119441i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.42021 | + | 1.13206i | 0.275264 | + | 0.0485365i | ||||
\(545\) | −7.02499 | − | 0.415003i | −0.300917 | − | 0.0177768i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.7055 | − | 13.7979i | −0.842546 | − | 0.589957i | 0.0706388 | − | 0.997502i | \(-0.477496\pi\) |
−0.913185 | + | 0.407545i | \(0.866385\pi\) | |||||||
\(548\) | −3.62923 | − | 0.972448i | −0.155033 | − | 0.0415409i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.1826 | + | 24.5236i | −0.647387 | + | 1.04569i | ||||
\(551\) | −1.26139 | + | 3.46563i | −0.0537369 | + | 0.147641i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.32430 | − | 26.5669i | −0.0988395 | − | 1.12974i | ||||
\(554\) | 34.7495 | + | 29.1583i | 1.47636 | + | 1.23882i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.74120 | + | 2.08962i | 0.243481 | + | 0.0886198i | ||||
\(557\) | 25.5871 | − | 6.85604i | 1.08416 | − | 0.290500i | 0.327861 | − | 0.944726i | \(-0.393672\pi\) |
0.756299 | + | 0.654226i | \(0.227006\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.1154 | − | 11.6136i | 0.850790 | − | 0.491204i | ||||
\(560\) | 31.9942 | − | 19.6977i | 1.35200 | − | 0.832381i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.07582 | + | 4.45161i | −0.0875632 | + | 0.187780i | ||||
\(563\) | 12.3664 | + | 17.6610i | 0.521181 | + | 0.744323i | 0.990320 | − | 0.138801i | \(-0.0443248\pi\) |
−0.469140 | + | 0.883124i | \(0.655436\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.887351 | − | 0.479406i | −0.0373311 | − | 0.0201687i | ||||
\(566\) | 36.1412i | 1.51913i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.49364 | − | 8.49364i | −0.356385 | − | 0.356385i | ||||
\(569\) | −8.77990 | + | 7.36721i | −0.368073 | + | 0.308850i | −0.807999 | − | 0.589184i | \(-0.799449\pi\) |
0.439926 | + | 0.898034i | \(0.355005\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.87072 | − | 10.6094i | 0.0782872 | − | 0.443989i | −0.920317 | − | 0.391173i | \(-0.872069\pi\) |
0.998604 | − | 0.0528155i | \(-0.0168195\pi\) | |||||||
\(572\) | 19.1239 | + | 8.91764i | 0.799612 | + | 0.372865i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.6763 | − | 2.23517i | 0.529097 | − | 0.0932940i | ||||
\(575\) | 4.52895 | + | 8.43290i | 0.188870 | + | 0.351676i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.65499 | + | 24.8368i | 0.277051 | + | 1.03397i | 0.954454 | + | 0.298357i | \(0.0964385\pi\) |
−0.677403 | + | 0.735612i | \(0.736895\pi\) | |||||||
\(578\) | −25.0472 | + | 11.6797i | −1.04183 | + | 0.485812i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.554262 | − | 1.10591i | −0.0230145 | − | 0.0459205i | ||||
\(581\) | −13.5256 | + | 16.1192i | −0.561137 | + | 0.668737i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.44449 | + | 5.24223i | 0.101241 | + | 0.217111i | ||||
\(584\) | 5.60442 | − | 9.70714i | 0.231913 | − | 0.401684i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.6498 | + | 47.8909i | 1.14220 | + | 1.97835i | ||||
\(587\) | 21.1711 | − | 30.2354i | 0.873824 | − | 1.24795i | −0.0938095 | − | 0.995590i | \(-0.529904\pi\) |
0.967633 | − | 0.252360i | \(-0.0812067\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.35183 | − | 22.9465i | −0.344131 | − | 0.945492i | ||||
\(590\) | −8.38756 | − | 40.7917i | −0.345310 | − | 1.67937i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.98184 | + | 22.6526i | −0.0814533 | + | 0.931016i | ||||
\(593\) | 21.8217 | − | 21.8217i | 0.896109 | − | 0.896109i | −0.0989808 | − | 0.995089i | \(-0.531558\pi\) |
0.995089 | + | 0.0989808i | \(0.0315582\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.44513 | − | 7.96854i | 0.141237 | − | 0.326678i | ||||
\(596\) | 9.48922 | + | 11.3088i | 0.388693 | + | 0.463227i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.0736 | − | 11.2549i | 0.657300 | − | 0.460247i | ||||
\(599\) | −16.2128 | + | 5.90099i | −0.662438 | + | 0.241108i | −0.651289 | − | 0.758830i | \(-0.725771\pi\) |
−0.0111496 | + | 0.999938i | \(0.503549\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.91812 | + | 44.9059i | 0.322987 | + | 1.83175i | 0.523460 | + | 0.852050i | \(0.324641\pi\) |
−0.200473 | + | 0.979699i | \(0.564248\pi\) | |||||||
\(602\) | 6.14430 | − | 22.9308i | 0.250423 | − | 0.934592i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.0802 | + | 8.12919i | 0.572914 | + | 0.330772i | ||||
\(605\) | −0.460008 | + | 0.486771i | −0.0187020 | + | 0.0197901i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.7085 | − | 4.17395i | 1.93643 | − | 0.169416i | 0.947703 | − | 0.319153i | \(-0.103398\pi\) |
0.988726 | + | 0.149737i | \(0.0478428\pi\) | |||||||
\(608\) | −41.6917 | + | 3.64755i | −1.69082 | + | 0.147928i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 41.4268 | − | 1.17102i | 1.67732 | − | 0.0474133i | ||||
\(611\) | 24.9925 | + | 14.4294i | 1.01109 | + | 0.583752i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.15240 | + | 15.4970i | −0.167714 | + | 0.625916i | 0.829965 | + | 0.557816i | \(0.188360\pi\) |
−0.997678 | + | 0.0681004i | \(0.978306\pi\) | |||||||
\(614\) | 2.94778 | + | 16.7177i | 0.118963 | + | 0.674671i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16.2549 | + | 5.91629i | −0.654927 | + | 0.238374i | ||||
\(617\) | −20.9035 | + | 14.6368i | −0.841541 | + | 0.589254i | −0.912894 | − | 0.408198i | \(-0.866157\pi\) |
0.0713522 | + | 0.997451i | \(0.477269\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.5321 | + | 32.8114i | 1.10661 | + | 1.31880i | 0.943193 | + | 0.332245i | \(0.107806\pi\) |
0.163414 | + | 0.986558i | \(0.447749\pi\) | |||||||
\(620\) | 7.51802 | + | 3.25035i | 0.301931 | + | 0.130537i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.00528856 | − | 0.00528856i | 0.000212052 | − | 0.000212052i | ||||
\(623\) | 0.152893 | − | 1.74758i | 0.00612554 | − | 0.0700152i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.3069 | + | 5.84604i | 0.972275 | + | 0.233842i | ||||
\(626\) | −14.3257 | − | 39.3596i | −0.572571 | − | 1.57313i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.53322 | + | 5.04597i | −0.140991 | + | 0.201356i | ||||
\(629\) | 2.62708 | + | 4.55023i | 0.104748 | + | 0.181430i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.58555 | + | 11.4065i | −0.262167 | + | 0.454086i | −0.966817 | − | 0.255468i | \(-0.917770\pi\) |
0.704651 | + | 0.709554i | \(0.251104\pi\) | |||||||
\(632\) | 5.25209 | + | 11.2631i | 0.208917 | + | 0.448024i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.899738 | + | 1.07227i | −0.0357332 | + | 0.0425851i | ||||
\(635\) | −0.389826 | + | 1.17317i | −0.0154698 | + | 0.0465559i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.9025 | + | 10.6796i | −0.907429 | + | 0.423141i | ||||
\(638\) | 0.744227 | + | 2.77749i | 0.0294642 | + | 0.109962i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.7083 | + | 19.8325i | −0.620924 | + | 0.783950i | ||||
\(641\) | −2.12742 | + | 0.375121i | −0.0840278 | + | 0.0148164i | −0.215504 | − | 0.976503i | \(-0.569139\pi\) |
0.131476 | + | 0.991319i | \(0.458028\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.05710 | + | 1.89186i | 0.159996 | + | 0.0746075i | 0.500967 | − | 0.865466i | \(-0.332978\pi\) |
−0.340970 | + | 0.940074i | \(0.610756\pi\) | |||||||
\(644\) | 1.24285 | − | 7.04855i | 0.0489751 | − | 0.277752i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.5194 | + | 9.66592i | −0.453224 | + | 0.380300i | ||||
\(647\) | 35.0743 | + | 35.0743i | 1.37891 | + | 1.37891i | 0.846461 | + | 0.532451i | \(0.178729\pi\) |
0.532451 | + | 0.846461i | \(0.321271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.5472i | 1.35609i | ||||||||
\(650\) | 6.03400 | − | 50.8922i | 0.236673 | − | 1.99616i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.55737 | + | 6.50860i | 0.178481 | + | 0.254897i | ||||
\(653\) | −1.35569 | + | 2.90729i | −0.0530523 | + | 0.113771i | −0.931047 | − | 0.364899i | \(-0.881103\pi\) |
0.877995 | + | 0.478670i | \(0.158881\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.42137 | − | 31.1979i | 0.289977 | − | 1.21900i | ||||
\(656\) | −9.35984 | + | 5.40391i | −0.365440 | + | 0.210987i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 28.4906 | − | 7.63403i | 1.11068 | − | 0.297606i | ||||
\(659\) | 16.5503 | + | 6.02381i | 0.644708 | + | 0.234654i | 0.643620 | − | 0.765345i | \(-0.277432\pi\) |
0.00108739 | + | 0.999999i | \(0.499654\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.9596 | − | 26.8173i | −1.24309 | − | 1.04307i | −0.997276 | − | 0.0737542i | \(-0.976502\pi\) |
−0.245809 | − | 0.969318i | \(-0.579054\pi\) | |||||||
\(662\) | −0.880660 | − | 10.0660i | −0.0342278 | − | 0.391226i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.35373 | − | 9.21430i | 0.130150 | − | 0.357584i | ||||
\(665\) | −8.12291 | + | 55.1358i | −0.314993 | + | 2.13808i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.921766 | + | 0.246987i | 0.0356909 | + | 0.00956336i | ||||
\(668\) | 12.7441 | + | 8.92355i | 0.493086 | + | 0.345263i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.36002 | − | 23.0218i | 0.0525423 | − | 0.889412i | ||||
\(671\) | −33.8575 | − | 5.96999i | −1.30705 | − | 0.230469i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.51557 | − | 0.657527i | −0.289704 | − | 0.0253458i | −0.0586226 | − | 0.998280i | \(-0.518671\pi\) |
−0.231081 | + | 0.972934i | \(0.574226\pi\) | |||||||
\(674\) | −45.0333 | −1.73462 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23.0647 | −0.887104 | ||||||||
\(677\) | 20.9561 | + | 1.83342i | 0.805407 | + | 0.0704639i | 0.482420 | − | 0.875940i | \(-0.339758\pi\) |
0.322986 | + | 0.946404i | \(0.395313\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.6652 | + | 2.76220i | 0.601177 | + | 0.106004i | ||||
\(680\) | −0.238576 | + | 4.03850i | −0.00914896 | + | 0.154869i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15.5958 | − | 10.9203i | −0.597193 | − | 0.418159i | ||||
\(683\) | −4.72063 | − | 1.26489i | −0.180630 | − | 0.0483997i | 0.167370 | − | 0.985894i | \(-0.446472\pi\) |
−0.348000 | + | 0.937494i | \(0.613139\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.10335 | − | 7.48922i | 0.0421569 | − | 0.286148i | ||||
\(686\) | 5.38880 | − | 14.8056i | 0.205745 | − | 0.565281i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.73728 | + | 19.8572i | 0.0662333 | + | 0.757050i | ||||
\(689\) | −7.87294 | − | 6.60618i | −0.299935 | − | 0.251676i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.6616 | + | 14.4357i | 1.50880 | + | 0.549158i | 0.958322 | − | 0.285692i | \(-0.0922233\pi\) |
0.550478 | + | 0.834850i | \(0.314445\pi\) | |||||||
\(692\) | −10.4947 | + | 2.81204i | −0.398948 | + | 0.106898i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.5867 | + | 10.7311i | −0.705543 | + | 0.407346i | ||||
\(695\) | −2.84873 | + | 11.9755i | −0.108058 | + | 0.454256i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.05540 | + | 2.26330i | −0.0399759 | + | 0.0857287i | ||||
\(698\) | −0.119965 | − | 0.171328i | −0.00454074 | − | 0.00648485i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.5698 | − | 14.6823i | −0.437296 | − | 0.554940i | ||||
\(701\) | − | 3.71261i | − | 0.140223i | −0.997539 | − | 0.0701117i | \(-0.977664\pi\) | ||
0.997539 | − | 0.0701117i | \(-0.0223356\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.8504 | − | 23.8504i | −0.899533 | − | 0.899533i | ||||
\(704\) | 0.00200131 | − | 0.00167930i | 7.54273e−5 | − | 6.32910e-5i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.62429 | − | 37.5682i | 0.249309 | − | 1.41390i | ||||
\(707\) | 21.4790 | + | 10.0158i | 0.807800 | + | 0.376683i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.4462 | + | 3.25257i | −0.692763 | + | 0.122153i | −0.508934 | − | 0.860805i | \(-0.669960\pi\) |
−0.183829 | + | 0.982958i | \(0.558849\pi\) | |||||||
\(710\) | −18.7341 | + | 23.6528i | −0.703077 | + | 0.887673i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.211580 | + | 0.789629i | 0.00792931 | + | 0.0295926i | ||||
\(713\) | −5.72646 | + | 2.67029i | −0.214457 | + | 0.100003i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.4060 | + | 40.3449i | −0.501355 | + | 1.50881i | ||||
\(716\) | −8.30527 | + | 9.89783i | −0.310382 | + | 0.369899i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.7762 | − | 48.8436i | −0.849999 | − | 1.82283i | ||||
\(719\) | 7.23920 | − | 12.5387i | 0.269977 | − | 0.467613i | −0.698879 | − | 0.715240i | \(-0.746317\pi\) |
0.968856 | + | 0.247627i | \(0.0796506\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.7913 | + | 20.4231i | 0.439130 | + | 0.760596i | ||||
\(722\) | 36.1517 | − | 51.6300i | 1.34543 | − | 1.92147i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.98507 | − | 21.9388i | −0.296763 | − | 0.815349i | ||||
\(725\) | 2.08460 | − | 1.36612i | 0.0774200 | − | 0.0507363i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.355020 | − | 4.05790i | 0.0131670 | − | 0.150499i | −0.986765 | − | 0.162156i | \(-0.948155\pi\) |
0.999932 | + | 0.0116572i | \(0.00371069\pi\) | |||||||
\(728\) | 21.7333 | − | 21.7333i | 0.805489 | − | 0.805489i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −25.8441 | − | 11.1735i | −0.956534 | − | 0.413549i | ||||
\(731\) | 2.96054 | + | 3.52824i | 0.109500 | + | 0.130497i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.238710 | + | 0.167146i | −0.00881695 | + | 0.00617370i | −0.577977 | − | 0.816053i | \(-0.696158\pi\) |
0.569160 | + | 0.822227i | \(0.307269\pi\) | |||||||
\(734\) | −25.4816 | + | 9.27456i | −0.940545 | + | 0.342330i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.88042 | + | 10.6644i | 0.0693133 | + | 0.393096i | ||||
\(737\) | −4.95155 | + | 18.4794i | −0.182393 | + | 0.680699i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.493834 | + | 0.285115i | 0.0181660 | + | 0.0104881i | 0.509055 | − | 0.860734i | \(-0.329995\pi\) |
−0.490890 | + | 0.871222i | \(0.663328\pi\) | |||||||
\(740\) | 11.3089 | − | 0.319672i | 0.415723 | − | 0.0117514i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.4642 | + | 0.915499i | −0.384153 | + | 0.0336090i | ||||
\(743\) | 45.2865 | − | 3.96205i | 1.66140 | − | 0.145354i | 0.782594 | − | 0.622533i | \(-0.213896\pi\) |
0.878806 | + | 0.477179i | \(0.158341\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.4291 | + | 21.6177i | −0.748466 | + | 0.792011i | ||||
\(746\) | −42.5487 | − | 24.5655i | −1.55782 | − | 0.899407i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.08294 | + | 4.04158i | −0.0395962 | + | 0.147775i | ||||
\(749\) | 2.62917 | + | 14.9108i | 0.0960678 | + | 0.544827i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.7741 | − | 7.92512i | 0.794547 | − | 0.289192i | 0.0873224 | − | 0.996180i | \(-0.472169\pi\) |
0.707225 | + | 0.706988i | \(0.249947\pi\) | |||||||
\(752\) | −20.2871 | + | 14.2052i | −0.739795 | + | 0.518010i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.28412 | − | 3.91386i | −0.119601 | − | 0.142535i | ||||
\(755\) | −12.9994 | + | 30.0674i | −0.473096 | + | 1.09426i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.24491 | + | 8.24491i | −0.299666 | + | 0.299666i | −0.840883 | − | 0.541217i | \(-0.817964\pi\) |
0.541217 | + | 0.840883i | \(0.317964\pi\) | |||||||
\(758\) | −2.56092 | + | 29.2715i | −0.0930169 | + | 1.06319i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.23065 | − | 25.4385i | −0.189735 | − | 0.922752i | ||||
\(761\) | −13.7885 | − | 37.8835i | −0.499832 | − | 1.37328i | −0.891437 | − | 0.453144i | \(-0.850302\pi\) |
0.391605 | − | 0.920133i | \(-0.371920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.08083 | + | 8.68433i | −0.220141 | + | 0.314394i | ||||
\(764\) | −13.9383 | − | 24.1418i | −0.504268 | − | 0.873418i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.0323 | − | 48.5534i | 1.01285 | − | 1.75431i | ||||
\(767\) | −25.9420 | − | 55.6327i | −0.936710 | − | 2.00878i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.5646 | + | 16.1656i | −0.489151 | + | 0.582947i | −0.953001 | − | 0.302966i | \(-0.902023\pi\) |
0.463850 | + | 0.885914i | \(0.346468\pi\) | |||||||
\(770\) | 19.4690 | + | 38.8463i | 0.701614 | + | 1.39992i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.01963 | + | 1.87438i | −0.144669 | + | 0.0674605i | ||||
\(773\) | −6.07695 | − | 22.6795i | −0.218573 | − | 0.815724i | −0.984878 | − | 0.173248i | \(-0.944574\pi\) |
0.766306 | − | 0.642476i | \(-0.222093\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.75910 | + | 15.8011i | −0.170952 | + | 0.567592i | ||||
\(776\) | −7.30002 | + | 1.28719i | −0.262055 | + | 0.0462074i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.6281 | + | 8.22014i | 0.632000 | + | 0.294706i | ||||
\(779\) | 2.78384 | − | 15.7879i | 0.0997414 | − | 0.565662i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.1745 | − | 16.0893i | 0.686116 | − | 0.575720i | ||||
\(782\) | 2.75132 | + | 2.75132i | 0.0983870 | + | 0.0983870i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 21.6862i | − | 0.774507i | ||||||
\(785\) | −10.9193 | − | 5.89934i | −0.389728 | − | 0.210557i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.65344 | + | 6.64580i | 0.165877 | + | 0.236897i | 0.893482 | − | 0.449100i | \(-0.148255\pi\) |
−0.727604 | + | 0.685997i | \(0.759366\pi\) | |||||||
\(788\) | −4.86241 | + | 10.4275i | −0.173216 | + | 0.371464i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26.5832 | − | 16.3663i | 0.945787 | − | 0.582288i | ||||
\(791\) | −1.31585 | + | 0.759709i | −0.0467864 | + | 0.0270121i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 59.0051 | − | 15.8104i | 2.09533 | − | 0.561442i | ||||
\(794\) | −26.2962 | − | 9.57104i | −0.933218 | − | 0.339663i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.4976 | − | 8.80855i | −0.372078 | − | 0.312211i | ||||
\(797\) | 1.11177 | + | 12.7075i | 0.0393807 | + | 0.450124i | 0.990129 | + | 0.140160i | \(0.0447616\pi\) |
−0.950748 | + | 0.309964i | \(0.899683\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.95721 | + | 5.37738i | −0.0692410 | + | 0.190238i | ||||
\(800\) | 24.0471 | + | 14.8876i | 0.850192 | + | 0.526354i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 31.5745 | + | 8.46035i | 1.11493 | + | 0.298745i | ||||
\(803\) | 19.1331 | + | 13.3971i | 0.675192 | + | 0.472775i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.3953 | + | 0.850406i | 0.507368 | + | 0.0299729i | ||||
\(806\) | 33.3147 | + | 5.87429i | 1.17346 | + | 0.206913i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.0019 | − | 0.962544i | −0.387047 | − | 0.0338622i | ||||
\(809\) | −37.1510 | −1.30616 | −0.653080 | − | 0.757289i | \(-0.726523\pi\) | ||||
−0.653080 | + | 0.757289i | \(0.726523\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.94368 | −0.173596 | −0.0867981 | − | 0.996226i | \(-0.527664\pi\) | ||||
−0.0867981 | + | 0.996226i | \(0.527664\pi\) | |||||||
\(812\) | −1.85650 | − | 0.162423i | −0.0651503 | − | 0.00569991i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25.8985 | − | 4.56660i | −0.907741 | − | 0.160059i | ||||
\(815\) | −11.9676 | + | 10.6325i | −0.419207 | + | 0.372440i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.2201 | − | 16.9591i | −0.847353 | − | 0.593323i | ||||
\(818\) | 26.6069 | + | 7.12931i | 0.930290 | + | 0.249270i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.20748 | + | 4.31586i | 0.112010 | + | 0.150716i | ||||
\(821\) | −11.5751 | + | 31.8023i | −0.403973 | + | 1.10991i | 0.556333 | + | 0.830959i | \(0.312208\pi\) |
−0.960306 | + | 0.278948i | \(0.910014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.42916 | + | 16.3354i | 0.0498174 | + | 0.569416i | 0.979553 | + | 0.201187i | \(0.0644800\pi\) |
−0.929735 | + | 0.368229i | \(0.879964\pi\) | |||||||
\(824\) | −8.41844 | − | 7.06391i | −0.293270 | − | 0.246083i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −58.9548 | − | 21.4578i | −2.05130 | − | 0.746612i | ||||
\(827\) | −30.9381 | + | 8.28983i | −1.07582 | + | 0.288266i | −0.752883 | − | 0.658154i | \(-0.771338\pi\) |
−0.322939 | + | 0.946420i | \(0.604671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.18006 | + | 1.25866i | −0.0757168 | + | 0.0437151i | −0.537380 | − | 0.843340i | \(-0.680586\pi\) |
0.461664 | + | 0.887055i | \(0.347253\pi\) | |||||||
\(830\) | −23.9627 | − | 5.70025i | −0.831757 | − | 0.197859i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.00196178 | + | 0.00420706i | −6.80126e−5 | + | 0.000145854i | ||||
\(833\) | −2.87411 | − | 4.10466i | −0.0995821 | − | 0.142218i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.8995 | + | 27.5780i | −0.515617 | + | 0.954376i | ||||
\(836\) | − | 26.8606i | − | 0.928992i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.6800 | − | 13.6800i | −0.472568 | − | 0.472568i | ||||
\(839\) | 37.2023 | − | 31.2164i | 1.28437 | − | 1.07771i | 0.291739 | − | 0.956498i | \(-0.405766\pi\) |
0.992627 | − | 0.121213i | \(-0.0386784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.99265 | + | 28.3147i | −0.172160 | + | 0.976370i | ||||
\(842\) | −7.03657 | − | 3.28121i | −0.242496 | − | 0.113078i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.2766 | − | 1.81204i | 0.353734 | − | 0.0623729i | ||||
\(845\) | −5.35662 | − | 46.1607i | −0.184273 | − | 1.58798i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.261140 | + | 0.974587i | 0.00897287 | + | 0.0334872i | ||||
\(848\) | 7.99348 | − | 3.72742i | 0.274497 | − | 0.128000i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.1460 | − | 0.574057i | 0.348004 | − | 0.0196900i | ||||
\(851\) | −5.60993 | + | 6.68566i | −0.192306 | + | 0.229181i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.95780 | + | 8.48753i | 0.135512 | + | 0.290607i | 0.962340 | − | 0.271848i | \(-0.0876347\pi\) |
−0.826828 | + | 0.562455i | \(0.809857\pi\) | |||||||
\(854\) | 31.2172 | − | 54.0698i | 1.06823 | − | 1.85023i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.52781 | − | 6.11035i | −0.120578 | − | 0.208847i | ||||
\(857\) | −31.1992 | + | 44.5570i | −1.06574 | + | 1.52204i | −0.229788 | + | 0.973241i | \(0.573803\pi\) |
−0.835955 | + | 0.548798i | \(0.815086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.1859 | − | 27.9855i | −0.347538 | − | 0.954853i | −0.983143 | − | 0.182839i | \(-0.941471\pi\) |
0.635605 | − | 0.772015i | \(-0.280751\pi\) | |||||||
\(860\) | 9.71410 | − | 1.99741i | 0.331248 | − | 0.0681110i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.52913 | − | 40.3382i | 0.120203 | − | 1.37392i | ||||
\(863\) | −19.0658 | + | 19.0658i | −0.649007 | + | 0.649007i | −0.952753 | − | 0.303746i | \(-0.901763\pi\) |
0.303746 | + | 0.952753i | \(0.401763\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.06522 | − | 20.3505i | −0.274226 | − | 0.691939i | ||||
\(866\) | −18.9430 | − | 22.5754i | −0.643711 | − | 0.767145i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.1076 | − | 7.07741i | 0.343074 | − | 0.240223i | ||||
\(869\) | −24.3349 | + | 8.85719i | −0.825506 | + | 0.300460i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.90279 | − | 33.4764i | −0.200009 | − | 1.13430i | ||||
\(872\) | 1.27866 | − | 4.77202i | 0.0433009 | − | 0.161601i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −21.6319 | − | 12.4892i | −0.731708 | − | 0.422452i | ||||
\(875\) | 26.6976 | − | 26.5651i | 0.902543 | − | 0.898065i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.95512 | + | 0.346028i | −0.133555 | + | 0.0116845i | −0.153737 | − | 0.988112i | \(-0.549131\pi\) |
0.0201823 | + | 0.999796i | \(0.493575\pi\) | |||||||
\(878\) | 27.5920 | − | 2.41399i | 0.931184 | − | 0.0814681i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −26.5171 | − | 25.0591i | −0.893890 | − | 0.844743i | ||||
\(881\) | −11.0930 | − | 6.40454i | −0.373732 | − | 0.215774i | 0.301355 | − | 0.953512i | \(-0.402561\pi\) |
−0.675088 | + | 0.737737i | \(0.735894\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.03874 | + | 30.0010i | −0.270525 | + | 1.00961i | 0.688256 | + | 0.725468i | \(0.258377\pi\) |
−0.958781 | + | 0.284146i | \(0.908290\pi\) | |||||||
\(884\) | −1.29098 | − | 7.32153i | −0.0434205 | − | 0.246250i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38.5723 | + | 14.0392i | −1.29586 | + | 0.471655i | ||||
\(887\) | 28.2142 | − | 19.7558i | 0.947341 | − | 0.663335i | 0.00571031 | − | 0.999984i | \(-0.498182\pi\) |
0.941630 | + | 0.336649i | \(0.109293\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.19713 | + | 1.42668i | 0.0401504 | + | 0.0478493i | ||||
\(890\) | 1.90903 | − | 0.756576i | 0.0639907 | − | 0.0253605i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.0536 | − | 11.0536i | 0.370102 | − | 0.370102i | ||||
\(893\) | 3.20176 | − | 36.5962i | 0.107143 | − | 1.22465i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.7379 | − | 14.3231i | −0.726618 | − | 0.478768i | ||||
\(896\) | 13.0358 | + | 35.8156i | 0.435496 | + | 1.19652i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −31.1593 | + | 44.5000i | −1.03980 | + | 1.48499i | ||||
\(899\) | 0.822588 | + | 1.42476i | 0.0274348 | + | 0.0475185i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.01896 | − | 1.76490i | 0.0339466 | − | 0.0587973i | ||||
\(902\) | −5.28245 | − | 11.3282i | −0.175886 | − | 0.377189i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.455126 | − | 0.542398i | 0.0151373 | − | 0.0180399i | ||||
\(905\) | 42.0528 | − | 21.0761i | 1.39788 | − | 0.700593i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.3482 | − | 13.2190i | 0.941287 | − | 0.438929i | 0.109477 | − | 0.993989i | \(-0.465083\pi\) |
0.831810 | + | 0.555060i | \(0.187305\pi\) | |||||||
\(908\) | 7.59659 | + | 28.3509i | 0.252102 | + | 0.940856i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −60.5220 | − | 47.9362i | −2.00628 | − | 1.58907i | ||||
\(911\) | 14.8888 | − | 2.62530i | 0.493288 | − | 0.0869800i | 0.0785299 | − | 0.996912i | \(-0.474977\pi\) |
0.414758 | + | 0.909932i | \(0.363866\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.5188 | + | 8.63545i | 0.612882 | + | 0.285792i | ||||
\(914\) | 8.03589 | − | 45.5738i | 0.265804 | − | 1.50745i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.49147 | + | 7.12519i | −0.280566 | + | 0.235423i | ||||
\(917\) | −34.1612 | − | 34.1612i | −1.12810 | − | 1.12810i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.84099i | − | 0.0607286i | −0.999539 | − | 0.0303643i | \(-0.990333\pi\) | ||
0.999539 | − | 0.0303643i | \(-0.00966675\pi\) | |||||||
\(920\) | −6.43921 | + | 1.92196i | −0.212294 | + | 0.0633650i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19.8584 | + | 28.3607i | 0.654001 | + | 0.934010i | ||||
\(923\) | −18.7957 | + | 40.3076i | −0.618670 | + | 1.32674i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.26619 | + | 22.5589i | 0.107392 | + | 0.741732i | ||||
\(926\) | −12.7947 | + | 7.38704i | −0.420461 | + | 0.242753i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.72352 | − | 0.729766i | 0.0894041 | − | 0.0239557i | ||||
\(929\) | 43.8338 | + | 15.9542i | 1.43814 | + | 0.523441i | 0.939253 | − | 0.343226i | \(-0.111520\pi\) |
0.498888 | + | 0.866666i | \(0.333742\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.6419 | + | 20.6770i | 0.807605 | + | 0.677661i | ||||
\(932\) | −2.62133 | − | 29.9620i | −0.0858647 | − | 0.981438i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.18256 | − | 3.24907i | 0.0386947 | − | 0.106313i | ||||
\(935\) | −8.34015 | − | 1.22872i | −0.272752 | − | 0.0401833i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.41697 | − | 1.71942i | −0.209633 | − | 0.0561711i | 0.152474 | − | 0.988307i | \(-0.451276\pi\) |
−0.362107 | + | 0.932136i | \(0.617943\pi\) | |||||||
\(938\) | −28.4597 | − | 19.9277i | −0.929243 | − | 0.650663i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.18389 | + | 9.21153i | 0.266929 | + | 0.300447i | ||||
\(941\) | 42.6827 | + | 7.52611i | 1.39142 | + | 0.245344i | 0.818612 | − | 0.574347i | \(-0.194744\pi\) |
0.572805 | + | 0.819692i | \(0.305855\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.13236 | − | 0.361535i | −0.134568 | − | 0.0117732i | ||||
\(944\) | 52.6783 | 1.71453 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.0528 | −0.749511 | ||||||||
\(947\) | −50.2480 | − | 4.39613i | −1.63284 | − | 0.142855i | −0.766478 | − | 0.642270i | \(-0.777993\pi\) |
−0.866363 | + | 0.499415i | \(0.833548\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.8709 | − | 7.20665i | −1.32673 | − | 0.233938i | ||||
\(950\) | −61.9599 | + | 20.4173i | −2.01024 | + | 0.662425i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.99241 | + | 3.49573i | 0.161805 | + | 0.113297i | ||||
\(953\) | −30.3800 | − | 8.14030i | −0.984105 | − | 0.263690i | −0.269333 | − | 0.963047i | \(-0.586803\pi\) |
−0.714773 | + | 0.699357i | \(0.753470\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.0792 | − | 33.5022i | 1.45873 | − | 1.08410i | ||||
\(956\) | −9.44285 | + | 25.9440i | −0.305404 | + | 0.839089i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.80631 | + | 32.0762i | 0.0906677 | + | 1.03634i | ||||
\(959\) | −8.73620 | − | 7.33054i | −0.282107 | − | 0.236716i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.8945 | + | 6.87702i | 0.609498 | + | 0.221839i | ||||
\(962\) | 45.1345 | − | 12.0938i | 1.45519 | − | 0.389918i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −27.4146 | + | 15.8278i | −0.882964 | + | 0.509780i | ||||
\(965\) | −4.68483 | − | 7.60939i | −0.150810 | − | 0.244955i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.62934 | − | 7.78315i | 0.116712 | − | 0.250289i | −0.839270 | − | 0.543715i | \(-0.817017\pi\) |
0.955982 | + | 0.293425i | \(0.0947952\pi\) | |||||||
\(968\) | −0.269684 | − | 0.385149i | −0.00866797 | − | 0.0123791i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.32554 | + | 17.8424i | 0.170993 | + | 0.572884i | ||||
\(971\) | 29.8892i | 0.959189i | 0.877490 | + | 0.479595i | \(0.159216\pi\) | ||||
−0.877490 | + | 0.479595i | \(0.840784\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.1129 | + | 13.1129i | 0.420381 | + | 0.420381i | ||||
\(974\) | −44.0582 | + | 36.9692i | −1.41172 | + | 1.18457i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.10317 | + | 51.6266i | −0.291385 | + | 1.65253i | ||||
\(977\) | 32.5668 | + | 15.1861i | 1.04190 | + | 0.485848i | 0.866776 | − | 0.498698i | \(-0.166188\pi\) |
0.175128 | + | 0.984546i | \(0.443966\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.67761 | + | 0.295808i | −0.0536166 | + | 0.00945406i | ||||
\(980\) | −10.7176 | + | 1.24371i | −0.342362 | + | 0.0397287i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.51459 | − | 5.65254i | −0.0483327 | − | 0.180380i | ||||
\(983\) | 33.2165 | − | 15.4891i | 1.05944 | − | 0.494026i | 0.186806 | − | 0.982397i | \(-0.440186\pi\) |
0.872636 | + | 0.488371i | \(0.162409\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.9984 | − | 7.30971i | −0.700926 | − | 0.232907i | ||||
\(986\) | 0.651216 | − | 0.776090i | 0.0207390 | − | 0.0247157i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.1700 | + | 43.2547i | 0.641693 | + | 1.37611i | ||||
\(989\) | −3.82526 | + | 6.62555i | −0.121636 | + | 0.210680i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.5180 | − | 33.8061i | −0.620009 | − | 1.07389i | −0.989483 | − | 0.144647i | \(-0.953795\pi\) |
0.369474 | − | 0.929241i | \(-0.379538\pi\) | |||||||
\(992\) | −10.7081 | + | 15.2927i | −0.339982 | + | 0.485545i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.5468 | + | 42.7146i | 0.493115 | + | 1.35482i | ||||
\(995\) | 15.1910 | − | 23.0552i | 0.481588 | − | 0.730899i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.41553 | + | 39.0397i | −0.108171 | + | 1.23640i | 0.727088 | + | 0.686544i | \(0.240873\pi\) |
−0.835259 | + | 0.549856i | \(0.814683\pi\) | |||||||
\(998\) | 8.01273 | − | 8.01273i | 0.253638 | − | 0.253638i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 405.2.r.a.368.13 | 192 | ||
3.2 | odd | 2 | 135.2.q.a.113.4 | yes | 192 | ||
5.2 | odd | 4 | inner | 405.2.r.a.287.4 | 192 | ||
15.2 | even | 4 | 135.2.q.a.32.13 | ✓ | 192 | ||
15.8 | even | 4 | 675.2.ba.b.32.4 | 192 | |||
15.14 | odd | 2 | 675.2.ba.b.518.13 | 192 | |||
27.11 | odd | 18 | inner | 405.2.r.a.278.4 | 192 | ||
27.16 | even | 9 | 135.2.q.a.38.13 | yes | 192 | ||
135.43 | odd | 36 | 675.2.ba.b.632.13 | 192 | |||
135.92 | even | 36 | inner | 405.2.r.a.197.13 | 192 | ||
135.97 | odd | 36 | 135.2.q.a.92.4 | yes | 192 | ||
135.124 | even | 18 | 675.2.ba.b.443.4 | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.q.a.32.13 | ✓ | 192 | 15.2 | even | 4 | ||
135.2.q.a.38.13 | yes | 192 | 27.16 | even | 9 | ||
135.2.q.a.92.4 | yes | 192 | 135.97 | odd | 36 | ||
135.2.q.a.113.4 | yes | 192 | 3.2 | odd | 2 | ||
405.2.r.a.197.13 | 192 | 135.92 | even | 36 | inner | ||
405.2.r.a.278.4 | 192 | 27.11 | odd | 18 | inner | ||
405.2.r.a.287.4 | 192 | 5.2 | odd | 4 | inner | ||
405.2.r.a.368.13 | 192 | 1.1 | even | 1 | trivial | ||
675.2.ba.b.32.4 | 192 | 15.8 | even | 4 | |||
675.2.ba.b.443.4 | 192 | 135.124 | even | 18 | |||
675.2.ba.b.518.13 | 192 | 15.14 | odd | 2 | |||
675.2.ba.b.632.13 | 192 | 135.43 | odd | 36 |