Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [187,2,Mod(89,187)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(187, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("187.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.49320251780\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 89.7 | ||
Character | \(\chi\) | \(=\) | 187.89 |
Dual form | 187.2.e.b.166.8 |
$q$-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 \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(122\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0421125i | 0.0297780i | 0.999889 | + | 0.0148890i | \(0.00473950\pi\) | ||||
−0.999889 | + | 0.0148890i | \(0.995261\pi\) | |||||||
\(3\) | −0.440583 | + | 0.440583i | −0.254371 | + | 0.254371i | −0.822760 | − | 0.568389i | \(-0.807567\pi\) |
0.568389 | + | 0.822760i | \(0.307567\pi\) | |||||||
\(4\) | 1.99823 | 0.999113 | ||||||||
\(5\) | 2.27271 | − | 2.27271i | 1.01639 | − | 1.01639i | 0.0165243 | − | 0.999863i | \(-0.494740\pi\) |
0.999863 | − | 0.0165243i | \(-0.00526008\pi\) | |||||||
\(6\) | −0.0185541 | − | 0.0185541i | −0.00757466 | − | 0.00757466i | ||||
\(7\) | −3.03167 | − | 3.03167i | −1.14586 | − | 1.14586i | −0.987358 | − | 0.158505i | \(-0.949333\pi\) |
−0.158505 | − | 0.987358i | \(-0.550667\pi\) | |||||||
\(8\) | 0.168375i | 0.0595297i | ||||||||
\(9\) | 2.61177i | 0.870591i | ||||||||
\(10\) | 0.0957096 | + | 0.0957096i | 0.0302660 | + | 0.0302660i | ||||
\(11\) | −0.707107 | − | 0.707107i | −0.213201 | − | 0.213201i | ||||
\(12\) | −0.880384 | + | 0.880384i | −0.254145 | + | 0.254145i | ||||
\(13\) | 3.32292 | 0.921613 | 0.460806 | − | 0.887501i | \(-0.347560\pi\) | ||||
0.460806 | + | 0.887501i | \(0.347560\pi\) | |||||||
\(14\) | 0.127671 | − | 0.127671i | 0.0341216 | − | 0.0341216i | ||||
\(15\) | 2.00264i | 0.517078i | ||||||||
\(16\) | 3.98936 | 0.997341 | ||||||||
\(17\) | −4.00134 | − | 0.994644i | −0.970466 | − | 0.241237i | ||||
\(18\) | −0.109988 | −0.0259245 | ||||||||
\(19\) | 5.85419i | 1.34304i | 0.740985 | + | 0.671521i | \(0.234359\pi\) | ||||
−0.740985 | + | 0.671521i | \(0.765641\pi\) | |||||||
\(20\) | 4.54139 | − | 4.54139i | 1.01549 | − | 1.01549i | ||||
\(21\) | 2.67140 | 0.582948 | ||||||||
\(22\) | 0.0297780 | − | 0.0297780i | 0.00634870 | − | 0.00634870i | ||||
\(23\) | 3.81234 | + | 3.81234i | 0.794927 | + | 0.794927i | 0.982291 | − | 0.187363i | \(-0.0599942\pi\) |
−0.187363 | + | 0.982291i | \(0.559994\pi\) | |||||||
\(24\) | −0.0741833 | − | 0.0741833i | −0.0151426 | − | 0.0151426i | ||||
\(25\) | − | 5.33044i | − | 1.06609i | ||||||
\(26\) | 0.139937i | 0.0274438i | ||||||||
\(27\) | −2.47245 | − | 2.47245i | −0.475824 | − | 0.475824i | ||||
\(28\) | −6.05796 | − | 6.05796i | −1.14485 | − | 1.14485i | ||||
\(29\) | 0.616737 | − | 0.616737i | 0.114525 | − | 0.114525i | −0.647522 | − | 0.762047i | \(-0.724195\pi\) |
0.762047 | + | 0.647522i | \(0.224195\pi\) | |||||||
\(30\) | −0.0843361 | −0.0153976 | ||||||||
\(31\) | −6.28124 | + | 6.28124i | −1.12814 | + | 1.12814i | −0.137666 | + | 0.990479i | \(0.543960\pi\) |
−0.990479 | + | 0.137666i | \(0.956040\pi\) | |||||||
\(32\) | 0.504753i | 0.0892286i | ||||||||
\(33\) | 0.623078 | 0.108464 | ||||||||
\(34\) | 0.0418870 | − | 0.168506i | 0.00718356 | − | 0.0288986i | ||||
\(35\) | −13.7802 | −2.32928 | ||||||||
\(36\) | 5.21891i | 0.869819i | ||||||||
\(37\) | −0.532669 | + | 0.532669i | −0.0875702 | + | 0.0875702i | −0.749535 | − | 0.661965i | \(-0.769723\pi\) |
0.661965 | + | 0.749535i | \(0.269723\pi\) | |||||||
\(38\) | −0.246535 | −0.0399932 | ||||||||
\(39\) | −1.46402 | + | 1.46402i | −0.234431 | + | 0.234431i | ||||
\(40\) | 0.382669 | + | 0.382669i | 0.0605053 | + | 0.0605053i | ||||
\(41\) | −4.20082 | − | 4.20082i | −0.656057 | − | 0.656057i | 0.298388 | − | 0.954445i | \(-0.403551\pi\) |
−0.954445 | + | 0.298388i | \(0.903551\pi\) | |||||||
\(42\) | 0.112499i | 0.0173590i | ||||||||
\(43\) | 0.849123i | 0.129490i | 0.997902 | + | 0.0647450i | \(0.0206234\pi\) | ||||
−0.997902 | + | 0.0647450i | \(0.979377\pi\) | |||||||
\(44\) | −1.41296 | − | 1.41296i | −0.213012 | − | 0.213012i | ||||
\(45\) | 5.93581 | + | 5.93581i | 0.884858 | + | 0.884858i | ||||
\(46\) | −0.160547 | + | 0.160547i | −0.0236714 | + | 0.0236714i | ||||
\(47\) | −8.83981 | −1.28942 | −0.644709 | − | 0.764428i | \(-0.723022\pi\) | ||||
−0.644709 | + | 0.764428i | \(0.723022\pi\) | |||||||
\(48\) | −1.75764 | + | 1.75764i | −0.253694 | + | 0.253694i | ||||
\(49\) | 11.3820i | 1.62600i | ||||||||
\(50\) | 0.224478 | 0.0317460 | ||||||||
\(51\) | 2.20114 | − | 1.32470i | 0.308222 | − | 0.185495i | ||||
\(52\) | 6.63995 | 0.920796 | ||||||||
\(53\) | − | 3.41117i | − | 0.468560i | −0.972169 | − | 0.234280i | \(-0.924727\pi\) | ||
0.972169 | − | 0.234280i | \(-0.0752733\pi\) | |||||||
\(54\) | 0.104121 | − | 0.104121i | 0.0141691 | − | 0.0141691i | ||||
\(55\) | −3.21410 | −0.433389 | ||||||||
\(56\) | 0.510458 | − | 0.510458i | 0.0682129 | − | 0.0682129i | ||||
\(57\) | −2.57926 | − | 2.57926i | −0.341631 | − | 0.341631i | ||||
\(58\) | 0.0259723 | + | 0.0259723i | 0.00341033 | + | 0.00341033i | ||||
\(59\) | − | 12.4757i | − | 1.62419i | −0.583524 | − | 0.812096i | \(-0.698326\pi\) | ||
0.583524 | − | 0.812096i | \(-0.301674\pi\) | |||||||
\(60\) | 4.00172i | 0.516620i | ||||||||
\(61\) | 8.41215 | + | 8.41215i | 1.07707 | + | 1.07707i | 0.996771 | + | 0.0802943i | \(0.0255860\pi\) |
0.0802943 | + | 0.996771i | \(0.474414\pi\) | |||||||
\(62\) | −0.264519 | − | 0.264519i | −0.0335940 | − | 0.0335940i | ||||
\(63\) | 7.91803 | − | 7.91803i | 0.997578 | − | 0.997578i | ||||
\(64\) | 7.95747 | 0.994684 | ||||||||
\(65\) | 7.55205 | − | 7.55205i | 0.936716 | − | 0.936716i | ||||
\(66\) | 0.0262394i | 0.00322985i | ||||||||
\(67\) | 4.87083 | 0.595066 | 0.297533 | − | 0.954711i | \(-0.403836\pi\) | ||||
0.297533 | + | 0.954711i | \(0.403836\pi\) | |||||||
\(68\) | −7.99557 | − | 1.98752i | −0.969606 | − | 0.241023i | ||||
\(69\) | −3.35930 | −0.404412 | ||||||||
\(70\) | − | 0.580320i | − | 0.0693615i | ||||||
\(71\) | −2.47830 | + | 2.47830i | −0.294120 | + | 0.294120i | −0.838705 | − | 0.544585i | \(-0.816687\pi\) |
0.544585 | + | 0.838705i | \(0.316687\pi\) | |||||||
\(72\) | −0.439758 | −0.0518260 | ||||||||
\(73\) | −3.10492 | + | 3.10492i | −0.363404 | + | 0.363404i | −0.865064 | − | 0.501661i | \(-0.832723\pi\) |
0.501661 | + | 0.865064i | \(0.332723\pi\) | |||||||
\(74\) | −0.0224320 | − | 0.0224320i | −0.00260767 | − | 0.00260767i | ||||
\(75\) | 2.34850 | + | 2.34850i | 0.271182 | + | 0.271182i | ||||
\(76\) | 11.6980i | 1.34185i | ||||||||
\(77\) | 4.28743i | 0.488598i | ||||||||
\(78\) | −0.0616537 | − | 0.0616537i | −0.00698091 | − | 0.00698091i | ||||
\(79\) | −4.40437 | − | 4.40437i | −0.495530 | − | 0.495530i | 0.414513 | − | 0.910043i | \(-0.363952\pi\) |
−0.910043 | + | 0.414513i | \(0.863952\pi\) | |||||||
\(80\) | 9.06667 | − | 9.06667i | 1.01368 | − | 1.01368i | ||||
\(81\) | −5.65668 | −0.628520 | ||||||||
\(82\) | 0.176907 | − | 0.176907i | 0.0195361 | − | 0.0195361i | ||||
\(83\) | − | 6.33683i | − | 0.695557i | −0.937577 | − | 0.347779i | \(-0.886936\pi\) | ||
0.937577 | − | 0.347779i | \(-0.113064\pi\) | |||||||
\(84\) | 5.33807 | 0.582431 | ||||||||
\(85\) | −11.3544 | + | 6.83334i | −1.23156 | + | 0.741180i | ||||
\(86\) | −0.0357587 | −0.00385596 | ||||||||
\(87\) | 0.543447i | 0.0582637i | ||||||||
\(88\) | 0.119059 | − | 0.119059i | 0.0126918 | − | 0.0126918i | ||||
\(89\) | 0.373263 | 0.0395658 | 0.0197829 | − | 0.999804i | \(-0.493702\pi\) | ||||
0.0197829 | + | 0.999804i | \(0.493702\pi\) | |||||||
\(90\) | −0.249972 | + | 0.249972i | −0.0263493 | + | 0.0263493i | ||||
\(91\) | −10.0740 | − | 10.0740i | −1.05604 | − | 1.05604i | ||||
\(92\) | 7.61791 | + | 7.61791i | 0.794222 | + | 0.794222i | ||||
\(93\) | − | 5.53482i | − | 0.573934i | ||||||
\(94\) | − | 0.372267i | − | 0.0383964i | ||||||
\(95\) | 13.3049 | + | 13.3049i | 1.36505 | + | 1.36505i | ||||
\(96\) | −0.222386 | − | 0.222386i | −0.0226971 | − | 0.0226971i | ||||
\(97\) | 8.46506 | − | 8.46506i | 0.859496 | − | 0.859496i | −0.131782 | − | 0.991279i | \(-0.542070\pi\) |
0.991279 | + | 0.131782i | \(0.0420700\pi\) | |||||||
\(98\) | −0.479326 | −0.0484192 | ||||||||
\(99\) | 1.84680 | − | 1.84680i | 0.185611 | − | 0.185611i | ||||
\(100\) | − | 10.6514i | − | 1.06514i | ||||||
\(101\) | 3.81697 | 0.379803 | 0.189902 | − | 0.981803i | \(-0.439183\pi\) | ||||
0.189902 | + | 0.981803i | \(0.439183\pi\) | |||||||
\(102\) | 0.0557863 | + | 0.0926957i | 0.00552367 | + | 0.00917824i | ||||
\(103\) | −9.47135 | −0.933240 | −0.466620 | − | 0.884458i | \(-0.654528\pi\) | ||||
−0.466620 | + | 0.884458i | \(0.654528\pi\) | |||||||
\(104\) | 0.559498i | 0.0548633i | ||||||||
\(105\) | 6.07133 | − | 6.07133i | 0.592501 | − | 0.592501i | ||||
\(106\) | 0.143653 | 0.0139528 | ||||||||
\(107\) | 3.83640 | − | 3.83640i | 0.370879 | − | 0.370879i | −0.496918 | − | 0.867797i | \(-0.665535\pi\) |
0.867797 | + | 0.496918i | \(0.165535\pi\) | |||||||
\(108\) | −4.94052 | − | 4.94052i | −0.475402 | − | 0.475402i | ||||
\(109\) | 12.3314 | + | 12.3314i | 1.18113 | + | 1.18113i | 0.979451 | + | 0.201681i | \(0.0646405\pi\) |
0.201681 | + | 0.979451i | \(0.435359\pi\) | |||||||
\(110\) | − | 0.135354i | − | 0.0129055i | ||||||
\(111\) | − | 0.469370i | − | 0.0445506i | ||||||
\(112\) | −12.0944 | − | 12.0944i | −1.14282 | − | 1.14282i | ||||
\(113\) | −4.00505 | − | 4.00505i | −0.376763 | − | 0.376763i | 0.493170 | − | 0.869933i | \(-0.335838\pi\) |
−0.869933 | + | 0.493170i | \(0.835838\pi\) | |||||||
\(114\) | 0.108619 | − | 0.108619i | 0.0101731 | − | 0.0101731i | ||||
\(115\) | 17.3287 | 1.61591 | ||||||||
\(116\) | 1.23238 | − | 1.23238i | 0.114424 | − | 0.114424i | ||||
\(117\) | 8.67872i | 0.802348i | ||||||||
\(118\) | 0.525381 | 0.0483653 | ||||||||
\(119\) | 9.11529 | + | 15.1462i | 0.835597 | + | 1.38845i | ||||
\(120\) | −0.337195 | −0.0307815 | ||||||||
\(121\) | 1.00000i | 0.0909091i | ||||||||
\(122\) | −0.354257 | + | 0.354257i | −0.0320729 | + | 0.0320729i | ||||
\(123\) | 3.70161 | 0.333763 | ||||||||
\(124\) | −12.5514 | + | 12.5514i | −1.12714 | + | 1.12714i | ||||
\(125\) | −0.750996 | − | 0.750996i | −0.0671711 | − | 0.0671711i | ||||
\(126\) | 0.333448 | + | 0.333448i | 0.0297059 | + | 0.0297059i | ||||
\(127\) | 11.5162i | 1.02190i | 0.859610 | + | 0.510950i | \(0.170706\pi\) | ||||
−0.859610 | + | 0.510950i | \(0.829294\pi\) | |||||||
\(128\) | 1.34461i | 0.118848i | ||||||||
\(129\) | −0.374109 | − | 0.374109i | −0.0329385 | − | 0.0329385i | ||||
\(130\) | 0.318036 | + | 0.318036i | 0.0278936 | + | 0.0278936i | ||||
\(131\) | 1.71986 | − | 1.71986i | 0.150264 | − | 0.150264i | −0.627972 | − | 0.778236i | \(-0.716115\pi\) |
0.778236 | + | 0.627972i | \(0.216115\pi\) | |||||||
\(132\) | 1.24505 | 0.108368 | ||||||||
\(133\) | 17.7480 | − | 17.7480i | 1.53894 | − | 1.53894i | ||||
\(134\) | 0.205123i | 0.0177199i | ||||||||
\(135\) | −11.2383 | −0.967242 | ||||||||
\(136\) | 0.167474 | − | 0.673726i | 0.0143607 | − | 0.0577716i | ||||
\(137\) | 9.77215 | 0.834891 | 0.417445 | − | 0.908702i | \(-0.362925\pi\) | ||||
0.417445 | + | 0.908702i | \(0.362925\pi\) | |||||||
\(138\) | − | 0.141469i | − | 0.0120426i | ||||||
\(139\) | −2.28918 | + | 2.28918i | −0.194165 | + | 0.194165i | −0.797493 | − | 0.603328i | \(-0.793841\pi\) |
0.603328 | + | 0.797493i | \(0.293841\pi\) | |||||||
\(140\) | −27.5360 | −2.32722 | ||||||||
\(141\) | 3.89467 | − | 3.89467i | 0.327990 | − | 0.327990i | ||||
\(142\) | −0.104368 | − | 0.104368i | −0.00875833 | − | 0.00875833i | ||||
\(143\) | −2.34966 | − | 2.34966i | −0.196489 | − | 0.196489i | ||||
\(144\) | 10.4193i | 0.868276i | ||||||||
\(145\) | − | 2.80333i | − | 0.232804i | ||||||
\(146\) | −0.130756 | − | 0.130756i | −0.0108215 | − | 0.0108215i | ||||
\(147\) | −5.01473 | − | 5.01473i | −0.413608 | − | 0.413608i | ||||
\(148\) | −1.06439 | + | 1.06439i | −0.0874926 | + | 0.0874926i | ||||
\(149\) | −12.9589 | −1.06164 | −0.530818 | − | 0.847486i | \(-0.678115\pi\) | ||||
−0.530818 | + | 0.847486i | \(0.678115\pi\) | |||||||
\(150\) | −0.0989013 | + | 0.0989013i | −0.00807526 | + | 0.00807526i | ||||
\(151\) | − | 12.3703i | − | 1.00668i | −0.864087 | − | 0.503342i | \(-0.832103\pi\) | ||
0.864087 | − | 0.503342i | \(-0.167897\pi\) | |||||||
\(152\) | −0.985701 | −0.0799509 | ||||||||
\(153\) | 2.59779 | − | 10.4506i | 0.210018 | − | 0.844879i | ||||
\(154\) | −0.180554 | −0.0145495 | ||||||||
\(155\) | 28.5509i | 2.29327i | ||||||||
\(156\) | −2.92545 | + | 2.92545i | −0.234223 | + | 0.234223i | ||||
\(157\) | 1.85459 | 0.148012 | 0.0740062 | − | 0.997258i | \(-0.476422\pi\) | ||||
0.0740062 | + | 0.997258i | \(0.476422\pi\) | |||||||
\(158\) | 0.185479 | − | 0.185479i | 0.0147559 | − | 0.0147559i | ||||
\(159\) | 1.50290 | + | 1.50290i | 0.119188 | + | 0.119188i | ||||
\(160\) | 1.14716 | + | 1.14716i | 0.0906908 | + | 0.0906908i | ||||
\(161\) | − | 23.1155i | − | 1.82176i | ||||||
\(162\) | − | 0.238217i | − | 0.0187161i | ||||||
\(163\) | 4.73123 | + | 4.73123i | 0.370578 | + | 0.370578i | 0.867688 | − | 0.497109i | \(-0.165605\pi\) |
−0.497109 | + | 0.867688i | \(0.665605\pi\) | |||||||
\(164\) | −8.39418 | − | 8.39418i | −0.655475 | − | 0.655475i | ||||
\(165\) | 1.41608 | − | 1.41608i | 0.110241 | − | 0.110241i | ||||
\(166\) | 0.266860 | 0.0207123 | ||||||||
\(167\) | 10.3728 | − | 10.3728i | 0.802668 | − | 0.802668i | −0.180844 | − | 0.983512i | \(-0.557883\pi\) |
0.983512 | + | 0.180844i | \(0.0578828\pi\) | |||||||
\(168\) | 0.449798i | 0.0347027i | ||||||||
\(169\) | −1.95819 | −0.150630 | ||||||||
\(170\) | −0.287769 | − | 0.478163i | −0.0220709 | − | 0.0366735i | ||||
\(171\) | −15.2898 | −1.16924 | ||||||||
\(172\) | 1.69674i | 0.129375i | ||||||||
\(173\) | −9.74046 | + | 9.74046i | −0.740554 | + | 0.740554i | −0.972685 | − | 0.232131i | \(-0.925430\pi\) |
0.232131 | + | 0.972685i | \(0.425430\pi\) | |||||||
\(174\) | −0.0228859 | −0.00173498 | ||||||||
\(175\) | −16.1601 | + | 16.1601i | −1.22159 | + | 1.22159i | ||||
\(176\) | −2.82091 | − | 2.82091i | −0.212634 | − | 0.212634i | ||||
\(177\) | 5.49656 | + | 5.49656i | 0.413147 | + | 0.413147i | ||||
\(178\) | 0.0157191i | 0.00117819i | ||||||||
\(179\) | 8.44838i | 0.631462i | 0.948849 | + | 0.315731i | \(0.102250\pi\) | ||||
−0.948849 | + | 0.315731i | \(0.897750\pi\) | |||||||
\(180\) | 11.8611 | + | 11.8611i | 0.884074 | + | 0.884074i | ||||
\(181\) | −16.3200 | − | 16.3200i | −1.21305 | − | 1.21305i | −0.970017 | − | 0.243036i | \(-0.921857\pi\) |
−0.243036 | − | 0.970017i | \(-0.578143\pi\) | |||||||
\(182\) | 0.424242 | − | 0.424242i | 0.0314469 | − | 0.0314469i | ||||
\(183\) | −7.41250 | −0.547948 | ||||||||
\(184\) | −0.641904 | + | 0.641904i | −0.0473218 | + | 0.0473218i | ||||
\(185\) | 2.42121i | 0.178011i | ||||||||
\(186\) | 0.233085 | 0.0170906 | ||||||||
\(187\) | 2.12605 | + | 3.53269i | 0.155472 | + | 0.258336i | ||||
\(188\) | −17.6639 | −1.28828 | ||||||||
\(189\) | 14.9913i | 1.09046i | ||||||||
\(190\) | −0.560302 | + | 0.560302i | −0.0406486 | + | 0.0406486i | ||||
\(191\) | 23.4963 | 1.70013 | 0.850067 | − | 0.526675i | \(-0.176561\pi\) | ||||
0.850067 | + | 0.526675i | \(0.176561\pi\) | |||||||
\(192\) | −3.50592 | + | 3.50592i | −0.253018 | + | 0.253018i | ||||
\(193\) | −1.92992 | − | 1.92992i | −0.138919 | − | 0.138919i | 0.634227 | − | 0.773147i | \(-0.281318\pi\) |
−0.773147 | + | 0.634227i | \(0.781318\pi\) | |||||||
\(194\) | 0.356485 | + | 0.356485i | 0.0255941 | + | 0.0255941i | ||||
\(195\) | 6.65461i | 0.476546i | ||||||||
\(196\) | 22.7439i | 1.62456i | ||||||||
\(197\) | −5.43997 | − | 5.43997i | −0.387582 | − | 0.387582i | 0.486242 | − | 0.873824i | \(-0.338367\pi\) |
−0.873824 | + | 0.486242i | \(0.838367\pi\) | |||||||
\(198\) | 0.0777735 | + | 0.0777735i | 0.00552712 | + | 0.00552712i | ||||
\(199\) | 7.38138 | − | 7.38138i | 0.523252 | − | 0.523252i | −0.395300 | − | 0.918552i | \(-0.629359\pi\) |
0.918552 | + | 0.395300i | \(0.129359\pi\) | |||||||
\(200\) | 0.897515 | 0.0634639 | ||||||||
\(201\) | −2.14600 | + | 2.14600i | −0.151367 | + | 0.151367i | ||||
\(202\) | 0.160742i | 0.0113098i | ||||||||
\(203\) | −3.73948 | −0.262460 | ||||||||
\(204\) | 4.39838 | − | 2.64704i | 0.307948 | − | 0.185330i | ||||
\(205\) | −19.0945 | −1.33362 | ||||||||
\(206\) | − | 0.398862i | − | 0.0277901i | ||||||
\(207\) | −9.95696 | + | 9.95696i | −0.692057 | + | 0.692057i | ||||
\(208\) | 13.2563 | 0.919162 | ||||||||
\(209\) | 4.13954 | − | 4.13954i | 0.286338 | − | 0.286338i | ||||
\(210\) | 0.255679 | + | 0.255679i | 0.0176435 | + | 0.0176435i | ||||
\(211\) | −7.36939 | − | 7.36939i | −0.507330 | − | 0.507330i | 0.406376 | − | 0.913706i | \(-0.366792\pi\) |
−0.913706 | + | 0.406376i | \(0.866792\pi\) | |||||||
\(212\) | − | 6.81629i | − | 0.468145i | ||||||
\(213\) | − | 2.18379i | − | 0.149631i | ||||||
\(214\) | 0.161560 | + | 0.161560i | 0.0110440 | + | 0.0110440i | ||||
\(215\) | 1.92981 | + | 1.92981i | 0.131612 | + | 0.131612i | ||||
\(216\) | 0.416300 | − | 0.416300i | 0.0283256 | − | 0.0283256i | ||||
\(217\) | 38.0853 | 2.58540 | ||||||||
\(218\) | −0.519306 | + | 0.519306i | −0.0351718 | + | 0.0351718i | ||||
\(219\) | − | 2.73595i | − | 0.184878i | ||||||
\(220\) | −6.42250 | −0.433005 | ||||||||
\(221\) | −13.2961 | − | 3.30513i | −0.894394 | − | 0.222327i | ||||
\(222\) | 0.0197663 | 0.00132663 | ||||||||
\(223\) | − | 23.8482i | − | 1.59699i | −0.602000 | − | 0.798496i | \(-0.705629\pi\) | ||
0.602000 | − | 0.798496i | \(-0.294371\pi\) | |||||||
\(224\) | 1.53024 | − | 1.53024i | 0.102244 | − | 0.102244i | ||||
\(225\) | 13.9219 | 0.928127 | ||||||||
\(226\) | 0.168663 | − | 0.168663i | 0.0112193 | − | 0.0112193i | ||||
\(227\) | −14.3074 | − | 14.3074i | −0.949614 | − | 0.949614i | 0.0491757 | − | 0.998790i | \(-0.484341\pi\) |
−0.998790 | + | 0.0491757i | \(0.984341\pi\) | |||||||
\(228\) | −5.15394 | − | 5.15394i | −0.341328 | − | 0.341328i | ||||
\(229\) | − | 27.5015i | − | 1.81735i | −0.417501 | − | 0.908676i | \(-0.637094\pi\) | ||
0.417501 | − | 0.908676i | \(-0.362906\pi\) | |||||||
\(230\) | 0.729755i | 0.0481186i | ||||||||
\(231\) | −1.88897 | − | 1.88897i | −0.124285 | − | 0.124285i | ||||
\(232\) | 0.103843 | + | 0.103843i | 0.00681764 | + | 0.00681764i | ||||
\(233\) | −20.3914 | + | 20.3914i | −1.33589 | + | 1.33589i | −0.435882 | + | 0.900004i | \(0.643563\pi\) |
−0.900004 | + | 0.435882i | \(0.856437\pi\) | |||||||
\(234\) | −0.365483 | −0.0238924 | ||||||||
\(235\) | −20.0903 | + | 20.0903i | −1.31055 | + | 1.31055i | ||||
\(236\) | − | 24.9292i | − | 1.62275i | ||||||
\(237\) | 3.88098 | 0.252097 | ||||||||
\(238\) | −0.637843 | + | 0.383868i | −0.0413452 | + | 0.0248825i | ||||
\(239\) | 15.8428 | 1.02479 | 0.512394 | − | 0.858751i | \(-0.328759\pi\) | ||||
0.512394 | + | 0.858751i | \(0.328759\pi\) | |||||||
\(240\) | 7.98924i | 0.515703i | ||||||||
\(241\) | 10.0506 | − | 10.0506i | 0.647413 | − | 0.647413i | −0.304954 | − | 0.952367i | \(-0.598641\pi\) |
0.952367 | + | 0.304954i | \(0.0986411\pi\) | |||||||
\(242\) | −0.0421125 | −0.00270710 | ||||||||
\(243\) | 9.90959 | − | 9.90959i | 0.635701 | − | 0.635701i | ||||
\(244\) | 16.8094 | + | 16.8094i | 1.07611 | + | 1.07611i | ||||
\(245\) | 25.8681 | + | 25.8681i | 1.65265 | + | 1.65265i | ||||
\(246\) | 0.155884i | 0.00993882i | ||||||||
\(247\) | 19.4530i | 1.23777i | ||||||||
\(248\) | −1.05761 | − | 1.05761i | −0.0671581 | − | 0.0671581i | ||||
\(249\) | 2.79190 | + | 2.79190i | 0.176929 | + | 0.176929i | ||||
\(250\) | 0.0316263 | − | 0.0316263i | 0.00200022 | − | 0.00200022i | ||||
\(251\) | 0.885722 | 0.0559063 | 0.0279532 | − | 0.999609i | \(-0.491101\pi\) | ||||
0.0279532 | + | 0.999609i | \(0.491101\pi\) | |||||||
\(252\) | 15.8220 | − | 15.8220i | 0.996694 | − | 0.996694i | ||||
\(253\) | − | 5.39146i | − | 0.338958i | ||||||
\(254\) | −0.484978 | −0.0304302 | ||||||||
\(255\) | 1.99191 | − | 8.01322i | 0.124738 | − | 0.501807i | ||||
\(256\) | 15.8583 | 0.991144 | ||||||||
\(257\) | 6.69991i | 0.417929i | 0.977923 | + | 0.208964i | \(0.0670093\pi\) | ||||
−0.977923 | + | 0.208964i | \(0.932991\pi\) | |||||||
\(258\) | 0.0157547 | − | 0.0157547i | 0.000980843 | − | 0.000980843i | ||||
\(259\) | 3.22975 | 0.200687 | ||||||||
\(260\) | 15.0907 | − | 15.0907i | 0.935885 | − | 0.935885i | ||||
\(261\) | 1.61078 | + | 1.61078i | 0.0997045 | + | 0.0997045i | ||||
\(262\) | 0.0724274 | + | 0.0724274i | 0.00447458 | + | 0.00447458i | ||||
\(263\) | 4.25215i | 0.262199i | 0.991369 | + | 0.131099i | \(0.0418507\pi\) | ||||
−0.991369 | + | 0.131099i | \(0.958149\pi\) | |||||||
\(264\) | 0.104911i | 0.00645683i | ||||||||
\(265\) | −7.75261 | − | 7.75261i | −0.476239 | − | 0.476239i | ||||
\(266\) | 0.747411 | + | 0.747411i | 0.0458267 | + | 0.0458267i | ||||
\(267\) | −0.164453 | + | 0.164453i | −0.0100644 | + | 0.0100644i | ||||
\(268\) | 9.73302 | 0.594539 | ||||||||
\(269\) | −18.3428 | + | 18.3428i | −1.11838 | + | 1.11838i | −0.126404 | + | 0.991979i | \(0.540344\pi\) |
−0.991979 | + | 0.126404i | \(0.959656\pi\) | |||||||
\(270\) | − | 0.473275i | − | 0.0288026i | ||||||
\(271\) | 14.9592 | 0.908704 | 0.454352 | − | 0.890822i | \(-0.349871\pi\) | ||||
0.454352 | + | 0.890822i | \(0.349871\pi\) | |||||||
\(272\) | −15.9628 | − | 3.96800i | −0.967885 | − | 0.240595i | ||||
\(273\) | 8.87686 | 0.537252 | ||||||||
\(274\) | 0.411530i | 0.0248614i | ||||||||
\(275\) | −3.76919 | + | 3.76919i | −0.227291 | + | 0.227291i | ||||
\(276\) | −6.71264 | −0.404054 | ||||||||
\(277\) | 6.93979 | − | 6.93979i | 0.416972 | − | 0.416972i | −0.467187 | − | 0.884159i | \(-0.654732\pi\) |
0.884159 | + | 0.467187i | \(0.154732\pi\) | |||||||
\(278\) | −0.0964029 | − | 0.0964029i | −0.00578186 | − | 0.00578186i | ||||
\(279\) | −16.4052 | − | 16.4052i | −0.982153 | − | 0.982153i | ||||
\(280\) | − | 2.32025i | − | 0.138661i | ||||||
\(281\) | − | 12.7856i | − | 0.762726i | −0.924425 | − | 0.381363i | \(-0.875455\pi\) | ||
0.924425 | − | 0.381363i | \(-0.124545\pi\) | |||||||
\(282\) | 0.164014 | + | 0.164014i | 0.00976691 | + | 0.00976691i | ||||
\(283\) | 8.74159 | + | 8.74159i | 0.519633 | + | 0.519633i | 0.917460 | − | 0.397827i | \(-0.130236\pi\) |
−0.397827 | + | 0.917460i | \(0.630236\pi\) | |||||||
\(284\) | −4.95221 | + | 4.95221i | −0.293859 | + | 0.293859i | ||||
\(285\) | −11.7238 | −0.694458 | ||||||||
\(286\) | 0.0989502 | − | 0.0989502i | 0.00585105 | − | 0.00585105i | ||||
\(287\) | 25.4710i | 1.50350i | ||||||||
\(288\) | −1.31830 | −0.0776816 | ||||||||
\(289\) | 15.0214 | + | 7.95981i | 0.883610 | + | 0.468224i | ||||
\(290\) | 0.118055 | 0.00693244 | ||||||||
\(291\) | 7.45912i | 0.437261i | ||||||||
\(292\) | −6.20434 | + | 6.20434i | −0.363081 | + | 0.363081i | ||||
\(293\) | 15.5310 | 0.907333 | 0.453667 | − | 0.891171i | \(-0.350116\pi\) | ||||
0.453667 | + | 0.891171i | \(0.350116\pi\) | |||||||
\(294\) | 0.211183 | − | 0.211183i | 0.0123164 | − | 0.0123164i | ||||
\(295\) | −28.3536 | − | 28.3536i | −1.65081 | − | 1.65081i | ||||
\(296\) | −0.0896883 | − | 0.0896883i | −0.00521303 | − | 0.00521303i | ||||
\(297\) | 3.49657i | 0.202892i | ||||||||
\(298\) | − | 0.545733i | − | 0.0316134i | ||||||
\(299\) | 12.6681 | + | 12.6681i | 0.732615 | + | 0.732615i | ||||
\(300\) | 4.69284 | + | 4.69284i | 0.270941 | + | 0.270941i | ||||
\(301\) | 2.57426 | − | 2.57426i | 0.148378 | − | 0.148378i | ||||
\(302\) | 0.520947 | 0.0299771 | ||||||||
\(303\) | −1.68169 | + | 1.68169i | −0.0966108 | + | 0.0966108i | ||||
\(304\) | 23.3545i | 1.33947i | ||||||||
\(305\) | 38.2368 | 2.18943 | ||||||||
\(306\) | 0.440100 | + | 0.109399i | 0.0251589 | + | 0.00625394i | ||||
\(307\) | −29.4466 | −1.68060 | −0.840302 | − | 0.542119i | \(-0.817622\pi\) | ||||
−0.840302 | + | 0.542119i | \(0.817622\pi\) | |||||||
\(308\) | 8.56725i | 0.488164i | ||||||||
\(309\) | 4.17291 | − | 4.17291i | 0.237389 | − | 0.237389i | ||||
\(310\) | −1.20235 | −0.0682890 | ||||||||
\(311\) | 8.53182 | − | 8.53182i | 0.483795 | − | 0.483795i | −0.422546 | − | 0.906341i | \(-0.638864\pi\) |
0.906341 | + | 0.422546i | \(0.138864\pi\) | |||||||
\(312\) | −0.246505 | − | 0.246505i | −0.0139556 | − | 0.0139556i | ||||
\(313\) | −5.96937 | − | 5.96937i | −0.337409 | − | 0.337409i | 0.517982 | − | 0.855391i | \(-0.326683\pi\) |
−0.855391 | + | 0.517982i | \(0.826683\pi\) | |||||||
\(314\) | 0.0781014i | 0.00440752i | ||||||||
\(315\) | − | 35.9908i | − | 2.02785i | ||||||
\(316\) | −8.80092 | − | 8.80092i | −0.495091 | − | 0.495091i | ||||
\(317\) | −14.2038 | − | 14.2038i | −0.797764 | − | 0.797764i | 0.184978 | − | 0.982743i | \(-0.440779\pi\) |
−0.982743 | + | 0.184978i | \(0.940779\pi\) | |||||||
\(318\) | −0.0632911 | + | 0.0632911i | −0.00354919 | + | 0.00354919i | ||||
\(319\) | −0.872197 | −0.0488337 | ||||||||
\(320\) | 18.0850 | − | 18.0850i | 1.01098 | − | 1.01098i | ||||
\(321\) | 3.38050i | 0.188681i | ||||||||
\(322\) | 0.973451 | 0.0542483 | ||||||||
\(323\) | 5.82283 | − | 23.4246i | 0.323991 | − | 1.30338i | ||||
\(324\) | −11.3033 | −0.627963 | ||||||||
\(325\) | − | 17.7126i | − | 0.982521i | ||||||
\(326\) | −0.199244 | + | 0.199244i | −0.0110351 | + | 0.0110351i | ||||
\(327\) | −10.8660 | −0.600891 | ||||||||
\(328\) | 0.707314 | − | 0.707314i | 0.0390549 | − | 0.0390549i | ||||
\(329\) | 26.7994 | + | 26.7994i | 1.47750 | + | 1.47750i | ||||
\(330\) | 0.0596346 | + | 0.0596346i | 0.00328278 | + | 0.00328278i | ||||
\(331\) | 6.00340i | 0.329976i | 0.986296 | + | 0.164988i | \(0.0527586\pi\) | ||||
−0.986296 | + | 0.164988i | \(0.947241\pi\) | |||||||
\(332\) | − | 12.6624i | − | 0.694941i | ||||||
\(333\) | −1.39121 | − | 1.39121i | −0.0762379 | − | 0.0762379i | ||||
\(334\) | 0.436823 | + | 0.436823i | 0.0239019 | + | 0.0239019i | ||||
\(335\) | 11.0700 | − | 11.0700i | 0.604818 | − | 0.604818i | ||||
\(336\) | 10.6572 | 0.581398 | ||||||||
\(337\) | −18.2603 | + | 18.2603i | −0.994703 | + | 0.994703i | −0.999986 | − | 0.00528322i | \(-0.998318\pi\) |
0.00528322 | + | 0.999986i | \(0.498318\pi\) | |||||||
\(338\) | − | 0.0824641i | − | 0.00448546i | ||||||
\(339\) | 3.52911 | 0.191675 | ||||||||
\(340\) | −22.6887 | + | 13.6546i | −1.23047 | + | 0.740523i | ||||
\(341\) | 8.88302 | 0.481043 | ||||||||
\(342\) | − | 0.643893i | − | 0.0348177i | ||||||
\(343\) | 13.2848 | − | 13.2848i | 0.717314 | − | 0.717314i | ||||
\(344\) | −0.142971 | −0.00770850 | ||||||||
\(345\) | −7.63472 | + | 7.63472i | −0.411040 | + | 0.411040i | ||||
\(346\) | −0.410195 | − | 0.410195i | −0.0220522 | − | 0.0220522i | ||||
\(347\) | 7.48979 | + | 7.48979i | 0.402073 | + | 0.402073i | 0.878963 | − | 0.476890i | \(-0.158236\pi\) |
−0.476890 | + | 0.878963i | \(0.658236\pi\) | |||||||
\(348\) | 1.08593i | 0.0582120i | ||||||||
\(349\) | 14.7061i | 0.787198i | 0.919282 | + | 0.393599i | \(0.128770\pi\) | ||||
−0.919282 | + | 0.393599i | \(0.871230\pi\) | |||||||
\(350\) | −0.680544 | − | 0.680544i | −0.0363766 | − | 0.0363766i | ||||
\(351\) | −8.21576 | − | 8.21576i | −0.438525 | − | 0.438525i | ||||
\(352\) | 0.356914 | − | 0.356914i | 0.0190236 | − | 0.0190236i | ||||
\(353\) | −31.0800 | −1.65422 | −0.827110 | − | 0.562040i | \(-0.810017\pi\) | ||||
−0.827110 | + | 0.562040i | \(0.810017\pi\) | |||||||
\(354\) | −0.231474 | + | 0.231474i | −0.0123027 | + | 0.0123027i | ||||
\(355\) | 11.2649i | 0.597880i | ||||||||
\(356\) | 0.745865 | 0.0395308 | ||||||||
\(357\) | −10.6892 | − | 2.65709i | −0.565731 | − | 0.140628i | ||||
\(358\) | −0.355783 | −0.0188037 | ||||||||
\(359\) | 14.3294i | 0.756276i | 0.925749 | + | 0.378138i | \(0.123435\pi\) | ||||
−0.925749 | + | 0.378138i | \(0.876565\pi\) | |||||||
\(360\) | −0.999444 | + | 0.999444i | −0.0526753 | + | 0.0526753i | ||||
\(361\) | −15.2715 | −0.803764 | ||||||||
\(362\) | 0.687275 | − | 0.687275i | 0.0361223 | − | 0.0361223i | ||||
\(363\) | −0.440583 | − | 0.440583i | −0.0231246 | − | 0.0231246i | ||||
\(364\) | −20.1301 | − | 20.1301i | −1.05511 | − | 1.05511i | ||||
\(365\) | 14.1132i | 0.738718i | ||||||||
\(366\) | − | 0.312159i | − | 0.0163168i | ||||||
\(367\) | 15.1132 | + | 15.1132i | 0.788902 | + | 0.788902i | 0.981314 | − | 0.192412i | \(-0.0616310\pi\) |
−0.192412 | + | 0.981314i | \(0.561631\pi\) | |||||||
\(368\) | 15.2088 | + | 15.2088i | 0.792813 | + | 0.792813i | ||||
\(369\) | 10.9716 | − | 10.9716i | 0.571157 | − | 0.571157i | ||||
\(370\) | −0.101963 | −0.00530081 | ||||||||
\(371\) | −10.3415 | + | 10.3415i | −0.536906 | + | 0.536906i | ||||
\(372\) | − | 11.0598i | − | 0.573425i | ||||||
\(373\) | −4.14225 | −0.214477 | −0.107239 | − | 0.994233i | \(-0.534201\pi\) | ||||
−0.107239 | + | 0.994233i | \(0.534201\pi\) | |||||||
\(374\) | −0.148771 | + | 0.0895334i | −0.00769274 | + | 0.00462966i | ||||
\(375\) | 0.661752 | 0.0341727 | ||||||||
\(376\) | − | 1.48841i | − | 0.0767587i | ||||||
\(377\) | 2.04937 | − | 2.04937i | 0.105548 | − | 0.105548i | ||||
\(378\) | −0.631322 | −0.0324717 | ||||||||
\(379\) | 2.74157 | − | 2.74157i | 0.140825 | − | 0.140825i | −0.633180 | − | 0.774005i | \(-0.718251\pi\) |
0.774005 | + | 0.633180i | \(0.218251\pi\) | |||||||
\(380\) | 26.5862 | + | 26.5862i | 1.36384 | + | 1.36384i | ||||
\(381\) | −5.07386 | − | 5.07386i | −0.259942 | − | 0.259942i | ||||
\(382\) | 0.989489i | 0.0506267i | ||||||||
\(383\) | 17.8600i | 0.912604i | 0.889825 | + | 0.456302i | \(0.150826\pi\) | ||||
−0.889825 | + | 0.456302i | \(0.849174\pi\) | |||||||
\(384\) | −0.592414 | − | 0.592414i | −0.0302315 | − | 0.0302315i | ||||
\(385\) | 9.74409 | + | 9.74409i | 0.496605 | + | 0.496605i | ||||
\(386\) | 0.0812740 | − | 0.0812740i | 0.00413674 | − | 0.00413674i | ||||
\(387\) | −2.21772 | −0.112733 | ||||||||
\(388\) | 16.9151 | − | 16.9151i | 0.858734 | − | 0.858734i | ||||
\(389\) | 10.6554i | 0.540249i | 0.962825 | + | 0.270124i | \(0.0870648\pi\) | ||||
−0.962825 | + | 0.270124i | \(0.912935\pi\) | |||||||
\(390\) | −0.280242 | −0.0141906 | ||||||||
\(391\) | −11.4625 | − | 19.0464i | −0.579684 | − | 0.963216i | ||||
\(392\) | −1.91645 | −0.0967955 | ||||||||
\(393\) | 1.51548i | 0.0764457i | ||||||||
\(394\) | 0.229091 | − | 0.229091i | 0.0115414 | − | 0.0115414i | ||||
\(395\) | −20.0197 | −1.00730 | ||||||||
\(396\) | 3.69033 | − | 3.69033i | 0.185446 | − | 0.185446i | ||||
\(397\) | −2.22024 | − | 2.22024i | −0.111431 | − | 0.111431i | 0.649193 | − | 0.760624i | \(-0.275107\pi\) |
−0.760624 | + | 0.649193i | \(0.775107\pi\) | |||||||
\(398\) | 0.310848 | + | 0.310848i | 0.0155814 | + | 0.0155814i | ||||
\(399\) | 15.6389i | 0.782924i | ||||||||
\(400\) | − | 21.2651i | − | 1.06325i | ||||||
\(401\) | 5.43167 | + | 5.43167i | 0.271245 | + | 0.271245i | 0.829601 | − | 0.558357i | \(-0.188568\pi\) |
−0.558357 | + | 0.829601i | \(0.688568\pi\) | |||||||
\(402\) | −0.0903736 | − | 0.0903736i | −0.00450743 | − | 0.00450743i | ||||
\(403\) | −20.8721 | + | 20.8721i | −1.03971 | + | 1.03971i | ||||
\(404\) | 7.62718 | 0.379466 | ||||||||
\(405\) | −12.8560 | + | 12.8560i | −0.638820 | + | 0.638820i | ||||
\(406\) | − | 0.157479i | − | 0.00781555i | ||||||
\(407\) | 0.753308 | 0.0373401 | ||||||||
\(408\) | 0.223046 | + | 0.370618i | 0.0110424 | + | 0.0183483i | ||||
\(409\) | 18.2193 | 0.900889 | 0.450444 | − | 0.892805i | \(-0.351266\pi\) | ||||
0.450444 | + | 0.892805i | \(0.351266\pi\) | |||||||
\(410\) | − | 0.804117i | − | 0.0397125i | ||||||
\(411\) | −4.30544 | + | 4.30544i | −0.212372 | + | 0.212372i | ||||
\(412\) | −18.9259 | −0.932412 | ||||||||
\(413\) | −37.8221 | + | 37.8221i | −1.86110 | + | 1.86110i | ||||
\(414\) | −0.419313 | − | 0.419313i | −0.0206081 | − | 0.0206081i | ||||
\(415\) | −14.4018 | − | 14.4018i | −0.706956 | − | 0.706956i | ||||
\(416\) | 1.67725i | 0.0822342i | ||||||||
\(417\) | − | 2.01714i | − | 0.0987799i | ||||||
\(418\) | 0.174326 | + | 0.174326i | 0.00852658 | + | 0.00852658i | ||||
\(419\) | 3.89911 | + | 3.89911i | 0.190484 | + | 0.190484i | 0.795905 | − | 0.605421i | \(-0.206995\pi\) |
−0.605421 | + | 0.795905i | \(0.706995\pi\) | |||||||
\(420\) | 12.1319 | − | 12.1319i | 0.591976 | − | 0.591976i | ||||
\(421\) | −15.5720 | −0.758933 | −0.379467 | − | 0.925205i | \(-0.623893\pi\) | ||||
−0.379467 | + | 0.925205i | \(0.623893\pi\) | |||||||
\(422\) | 0.310343 | − | 0.310343i | 0.0151073 | − | 0.0151073i | ||||
\(423\) | − | 23.0876i | − | 1.12256i | ||||||
\(424\) | 0.574357 | 0.0278933 | ||||||||
\(425\) | −5.30189 | + | 21.3289i | −0.257179 | + | 1.03460i | ||||
\(426\) | 0.0919651 | 0.00445572 | ||||||||
\(427\) | − | 51.0057i | − | 2.46834i | ||||||
\(428\) | 7.66600 | − | 7.66600i | 0.370550 | − | 0.370550i | ||||
\(429\) | 2.07044 | 0.0999618 | ||||||||
\(430\) | −0.0812692 | + | 0.0812692i | −0.00391915 | + | 0.00391915i | ||||
\(431\) | 17.4564 | + | 17.4564i | 0.840844 | + | 0.840844i | 0.988969 | − | 0.148125i | \(-0.0473238\pi\) |
−0.148125 | + | 0.988969i | \(0.547324\pi\) | |||||||
\(432\) | −9.86350 | − | 9.86350i | −0.474558 | − | 0.474558i | ||||
\(433\) | − | 27.4120i | − | 1.31734i | −0.752433 | − | 0.658669i | \(-0.771120\pi\) | ||
0.752433 | − | 0.658669i | \(-0.228880\pi\) | |||||||
\(434\) | 1.60387i | 0.0769881i | ||||||||
\(435\) | 1.23510 | + | 1.23510i | 0.0592185 | + | 0.0592185i | ||||
\(436\) | 24.6409 | + | 24.6409i | 1.18009 | + | 1.18009i | ||||
\(437\) | −22.3181 | + | 22.3181i | −1.06762 | + | 1.06762i | ||||
\(438\) | 0.115218 | 0.00550532 | ||||||||
\(439\) | −5.64043 | + | 5.64043i | −0.269203 | + | 0.269203i | −0.828779 | − | 0.559576i | \(-0.810964\pi\) |
0.559576 | + | 0.828779i | \(0.310964\pi\) | |||||||
\(440\) | − | 0.541175i | − | 0.0257995i | ||||||
\(441\) | −29.7273 | −1.41558 | ||||||||
\(442\) | 0.139187 | − | 0.559933i | 0.00662046 | − | 0.0266333i | ||||
\(443\) | −19.4155 | −0.922458 | −0.461229 | − | 0.887281i | \(-0.652591\pi\) | ||||
−0.461229 | + | 0.887281i | \(0.652591\pi\) | |||||||
\(444\) | − | 0.937907i | − | 0.0445111i | ||||||
\(445\) | 0.848320 | − | 0.848320i | 0.0402142 | − | 0.0402142i | ||||
\(446\) | 1.00431 | 0.0475553 | ||||||||
\(447\) | 5.70948 | − | 5.70948i | 0.270049 | − | 0.270049i | ||||
\(448\) | −24.1244 | − | 24.1244i | −1.13977 | − | 1.13977i | ||||
\(449\) | −3.24976 | − | 3.24976i | −0.153366 | − | 0.153366i | 0.626254 | − | 0.779619i | \(-0.284587\pi\) |
−0.779619 | + | 0.626254i | \(0.784587\pi\) | |||||||
\(450\) | 0.586286i | 0.0276378i | ||||||||
\(451\) | 5.94085i | 0.279744i | ||||||||
\(452\) | −8.00300 | − | 8.00300i | −0.376429 | − | 0.376429i | ||||
\(453\) | 5.45016 | + | 5.45016i | 0.256071 | + | 0.256071i | ||||
\(454\) | 0.602520 | − | 0.602520i | 0.0282777 | − | 0.0282777i | ||||
\(455\) | −45.7906 | −2.14670 | ||||||||
\(456\) | 0.434283 | − | 0.434283i | 0.0203372 | − | 0.0203372i | ||||
\(457\) | 15.5847i | 0.729023i | 0.931199 | + | 0.364511i | \(0.118764\pi\) | ||||
−0.931199 | + | 0.364511i | \(0.881236\pi\) | |||||||
\(458\) | 1.15816 | 0.0541172 | ||||||||
\(459\) | 7.43390 | + | 12.3523i | 0.346985 | + | 0.576557i | ||||
\(460\) | 34.6266 | 1.61448 | ||||||||
\(461\) | − | 27.3289i | − | 1.27284i | −0.771344 | − | 0.636418i | \(-0.780415\pi\) | ||
0.771344 | − | 0.636418i | \(-0.219585\pi\) | |||||||
\(462\) | 0.0795492 | − | 0.0795492i | 0.00370096 | − | 0.00370096i | ||||
\(463\) | −2.64550 | −0.122947 | −0.0614734 | − | 0.998109i | \(-0.519580\pi\) | ||||
−0.0614734 | + | 0.998109i | \(0.519580\pi\) | |||||||
\(464\) | 2.46039 | − | 2.46039i | 0.114221 | − | 0.114221i | ||||
\(465\) | −12.5790 | − | 12.5790i | −0.583339 | − | 0.583339i | ||||
\(466\) | −0.858734 | − | 0.858734i | −0.0397801 | − | 0.0397801i | ||||
\(467\) | 13.4709i | 0.623358i | 0.950187 | + | 0.311679i | \(0.100891\pi\) | ||||
−0.950187 | + | 0.311679i | \(0.899109\pi\) | |||||||
\(468\) | 17.3421i | 0.801637i | ||||||||
\(469\) | −14.7667 | − | 14.7667i | −0.681865 | − | 0.681865i | ||||
\(470\) | −0.846055 | − | 0.846055i | −0.0390256 | − | 0.0390256i | ||||
\(471\) | −0.817100 | + | 0.817100i | −0.0376500 | + | 0.0376500i | ||||
\(472\) | 2.10059 | 0.0966877 | ||||||||
\(473\) | 0.600420 | − | 0.600420i | 0.0276074 | − | 0.0276074i | ||||
\(474\) | 0.163438i | 0.00750694i | ||||||||
\(475\) | 31.2054 | 1.43180 | ||||||||
\(476\) | 18.2144 | + | 30.2654i | 0.834856 | + | 1.38721i | ||||
\(477\) | 8.90921 | 0.407925 | ||||||||
\(478\) | 0.667182i | 0.0305162i | ||||||||
\(479\) | 26.0378 | − | 26.0378i | 1.18970 | − | 1.18970i | 0.212548 | − | 0.977151i | \(-0.431824\pi\) |
0.977151 | − | 0.212548i | \(-0.0681761\pi\) | |||||||
\(480\) | −1.01084 | −0.0461382 | ||||||||
\(481\) | −1.77002 | + | 1.77002i | −0.0807059 | + | 0.0807059i | ||||
\(482\) | 0.423254 | + | 0.423254i | 0.0192787 | + | 0.0192787i | ||||
\(483\) | 10.1843 | + | 10.1843i | 0.463401 | + | 0.463401i | ||||
\(484\) | 1.99823i | 0.0908285i | ||||||||
\(485\) | − | 38.4773i | − | 1.74716i | ||||||
\(486\) | 0.417318 | + | 0.417318i | 0.0189299 | + | 0.0189299i | ||||
\(487\) | 15.2870 | + | 15.2870i | 0.692721 | + | 0.692721i | 0.962830 | − | 0.270109i | \(-0.0870596\pi\) |
−0.270109 | + | 0.962830i | \(0.587060\pi\) | |||||||
\(488\) | −1.41640 | + | 1.41640i | −0.0641174 | + | 0.0641174i | ||||
\(489\) | −4.16900 | −0.188529 | ||||||||
\(490\) | −1.08937 | + | 1.08937i | −0.0492127 | + | 0.0492127i | ||||
\(491\) | − | 14.5982i | − | 0.658806i | −0.944189 | − | 0.329403i | \(-0.893153\pi\) | ||
0.944189 | − | 0.329403i | \(-0.106847\pi\) | |||||||
\(492\) | 7.39666 | 0.333467 | ||||||||
\(493\) | −3.08120 | + | 1.85434i | −0.138770 | + | 0.0835151i | ||||
\(494\) | −0.819215 | −0.0368582 | ||||||||
\(495\) | − | 8.39450i | − | 0.377305i | ||||||
\(496\) | −25.0582 | + | 25.0582i | −1.12514 | + | 1.12514i | ||||
\(497\) | 15.0268 | 0.674043 | ||||||||
\(498\) | −0.117574 | + | 0.117574i | −0.00526861 | + | 0.00526861i | ||||
\(499\) | 3.59392 | + | 3.59392i | 0.160886 | + | 0.160886i | 0.782959 | − | 0.622073i | \(-0.213709\pi\) |
−0.622073 | + | 0.782959i | \(0.713709\pi\) | |||||||
\(500\) | −1.50066 | − | 1.50066i | −0.0671115 | − | 0.0671115i | ||||
\(501\) | 9.14012i | 0.408351i | ||||||||
\(502\) | 0.0373000i | 0.00166478i | ||||||||
\(503\) | 7.77722 | + | 7.77722i | 0.346769 | + | 0.346769i | 0.858905 | − | 0.512135i | \(-0.171145\pi\) |
−0.512135 | + | 0.858905i | \(0.671145\pi\) | |||||||
\(504\) | 1.33320 | + | 1.33320i | 0.0593855 | + | 0.0593855i | ||||
\(505\) | 8.67488 | − | 8.67488i | 0.386027 | − | 0.386027i | ||||
\(506\) | 0.227048 | 0.0100935 | ||||||||
\(507\) | 0.862743 | − | 0.862743i | 0.0383158 | − | 0.0383158i | ||||
\(508\) | 23.0120i | 1.02099i | ||||||||
\(509\) | −25.8733 | −1.14681 | −0.573406 | − | 0.819271i | \(-0.694378\pi\) | ||||
−0.573406 | + | 0.819271i | \(0.694378\pi\) | |||||||
\(510\) | 0.337457 | + | 0.0838844i | 0.0149428 | + | 0.00371446i | ||||
\(511\) | 18.8262 | 0.832822 | ||||||||
\(512\) | 3.35706i | 0.148363i | ||||||||
\(513\) | 14.4742 | − | 14.4742i | 0.639051 | − | 0.639051i | ||||
\(514\) | −0.282150 | −0.0124451 | ||||||||
\(515\) | −21.5256 | + | 21.5256i | −0.948533 | + | 0.948533i | ||||
\(516\) | −0.747554 | − | 0.747554i | −0.0329093 | − | 0.0329093i | ||||
\(517\) | 6.25069 | + | 6.25069i | 0.274905 | + | 0.274905i | ||||
\(518\) | 0.136013i | 0.00597607i | ||||||||
\(519\) | − | 8.58296i | − | 0.376750i | ||||||
\(520\) | 1.27158 | + | 1.27158i | 0.0557624 | + | 0.0557624i | ||||
\(521\) | 2.23810 | + | 2.23810i | 0.0980528 | + | 0.0980528i | 0.754432 | − | 0.656379i | \(-0.227913\pi\) |
−0.656379 | + | 0.754432i | \(0.727913\pi\) | |||||||
\(522\) | −0.0678338 | + | 0.0678338i | −0.00296901 | + | 0.00296901i | ||||
\(523\) | 35.3598 | 1.54618 | 0.773088 | − | 0.634299i | \(-0.218711\pi\) | ||||
0.773088 | + | 0.634299i | \(0.218711\pi\) | |||||||
\(524\) | 3.43666 | − | 3.43666i | 0.150131 | − | 0.150131i | ||||
\(525\) | − | 14.2398i | − | 0.621474i | ||||||
\(526\) | −0.179069 | −0.00780776 | ||||||||
\(527\) | 31.3810 | − | 18.8858i | 1.36698 | − | 0.822677i | ||||
\(528\) | 2.48569 | 0.108176 | ||||||||
\(529\) | 6.06782i | 0.263818i | ||||||||
\(530\) | 0.326482 | − | 0.326482i | 0.0141815 | − | 0.0141815i | ||||
\(531\) | 32.5836 | 1.41401 | ||||||||
\(532\) | 35.4644 | − | 35.4644i | 1.53758 | − | 1.53758i | ||||
\(533\) | −13.9590 | − | 13.9590i | −0.604631 | − | 0.604631i | ||||
\(534\) | −0.00692555 | − | 0.00692555i | −0.000299698 | − | 0.000299698i | ||||
\(535\) | − | 17.4381i | − | 0.753913i | ||||||
\(536\) | 0.820128i | 0.0354241i | ||||||||
\(537\) | −3.72221 | − | 3.72221i | −0.160625 | − | 0.160625i | ||||
\(538\) | −0.772464 | − | 0.772464i | −0.0333033 | − | 0.0333033i | ||||
\(539\) | 8.04831 | − | 8.04831i | 0.346665 | − | 0.346665i | ||||
\(540\) | −22.4568 | −0.966385 | ||||||||
\(541\) | −1.69022 | + | 1.69022i | −0.0726683 | + | 0.0726683i | −0.742507 | − | 0.669839i | \(-0.766363\pi\) |
0.669839 | + | 0.742507i | \(0.266363\pi\) | |||||||
\(542\) | 0.629968i | 0.0270594i | ||||||||
\(543\) | 14.3806 | 0.617130 | ||||||||
\(544\) | 0.502050 | − | 2.01969i | 0.0215252 | − | 0.0865933i | ||||
\(545\) | 56.0514 | 2.40098 | ||||||||
\(546\) | 0.373827i | 0.0159983i | ||||||||
\(547\) | 13.5713 | − | 13.5713i | 0.580268 | − | 0.580268i | −0.354709 | − | 0.934977i | \(-0.615420\pi\) |
0.934977 | + | 0.354709i | \(0.115420\pi\) | |||||||
\(548\) | 19.5270 | 0.834150 | ||||||||
\(549\) | −21.9706 | + | 21.9706i | −0.937684 | + | 0.937684i | ||||
\(550\) | −0.158730 | − | 0.158730i | −0.00676827 | − | 0.00676827i | ||||
\(551\) | 3.61049 | + | 3.61049i | 0.153812 | + | 0.153812i | ||||
\(552\) | − | 0.565624i | − | 0.0240745i | ||||||
\(553\) | 26.7052i | 1.13562i | ||||||||
\(554\) | 0.292252 | + | 0.292252i | 0.0124166 | + | 0.0124166i | ||||
\(555\) | −1.06674 | − | 1.06674i | −0.0452807 | − | 0.0452807i | ||||
\(556\) | −4.57429 | + | 4.57429i | −0.193993 | + | 0.193993i | ||||
\(557\) | −3.48978 | −0.147867 | −0.0739334 | − | 0.997263i | \(-0.523555\pi\) | ||||
−0.0739334 | + | 0.997263i | \(0.523555\pi\) | |||||||
\(558\) | 0.690864 | − | 0.690864i | 0.0292466 | − | 0.0292466i | ||||
\(559\) | 2.82157i | 0.119340i | ||||||||
\(560\) | −54.9743 | −2.32309 | ||||||||
\(561\) | −2.49315 | − | 0.619741i | −0.105261 | − | 0.0261655i | ||||
\(562\) | 0.538434 | 0.0227125 | ||||||||
\(563\) | 5.42665i | 0.228706i | 0.993440 | + | 0.114353i | \(0.0364795\pi\) | ||||
−0.993440 | + | 0.114353i | \(0.963520\pi\) | |||||||
\(564\) | 7.78243 | − | 7.78243i | 0.327700 | − | 0.327700i | ||||
\(565\) | −18.2046 | −0.765875 | ||||||||
\(566\) | −0.368130 | + | 0.368130i | −0.0154737 | + | 0.0154737i | ||||
\(567\) | 17.1492 | + | 17.1492i | 0.720198 | + | 0.720198i | ||||
\(568\) | −0.417285 | − | 0.417285i | −0.0175089 | − | 0.0175089i | ||||
\(569\) | − | 16.3440i | − | 0.685175i | −0.939486 | − | 0.342588i | \(-0.888697\pi\) | ||
0.939486 | − | 0.342588i | \(-0.111303\pi\) | |||||||
\(570\) | − | 0.493719i | − | 0.0206796i | ||||||
\(571\) | −19.6882 | − | 19.6882i | −0.823924 | − | 0.823924i | 0.162744 | − | 0.986668i | \(-0.447965\pi\) |
−0.986668 | + | 0.162744i | \(0.947965\pi\) | |||||||
\(572\) | −4.69516 | − | 4.69516i | −0.196314 | − | 0.196314i | ||||
\(573\) | −10.3521 | + | 10.3521i | −0.432464 | + | 0.432464i | ||||
\(574\) | −1.07265 | −0.0447714 | ||||||||
\(575\) | 20.3214 | − | 20.3214i | 0.847462 | − | 0.847462i | ||||
\(576\) | 20.7831i | 0.865963i | ||||||||
\(577\) | −30.8328 | −1.28359 | −0.641794 | − | 0.766877i | \(-0.721810\pi\) | ||||
−0.641794 | + | 0.766877i | \(0.721810\pi\) | |||||||
\(578\) | −0.335208 | + | 0.632588i | −0.0139428 | + | 0.0263122i | ||||
\(579\) | 1.70058 | 0.0706739 | ||||||||
\(580\) | − | 5.60169i | − | 0.232597i | ||||||
\(581\) | −19.2112 | + | 19.2112i | −0.797014 | + | 0.797014i | ||||
\(582\) | −0.314122 | −0.0130208 | ||||||||
\(583\) | −2.41206 | + | 2.41206i | −0.0998974 | + | 0.0998974i | ||||
\(584\) | −0.522793 | − | 0.522793i | −0.0216333 | − | 0.0216333i | ||||
\(585\) | 19.7242 | + | 19.7242i | 0.815497 | + | 0.815497i | ||||
\(586\) | 0.654052i | 0.0270186i | ||||||||
\(587\) | 13.1242i | 0.541695i | 0.962622 | + | 0.270848i | \(0.0873040\pi\) | ||||
−0.962622 | + | 0.270848i | \(0.912696\pi\) | |||||||
\(588\) | −10.0206 | − | 10.0206i | −0.413241 | − | 0.413241i | ||||
\(589\) | −36.7716 | − | 36.7716i | −1.51515 | − | 1.51515i | ||||
\(590\) | 1.19404 | − | 1.19404i | 0.0491579 | − | 0.0491579i | ||||
\(591\) | 4.79352 | 0.197179 | ||||||||
\(592\) | −2.12501 | + | 2.12501i | −0.0873373 | + | 0.0873373i | ||||
\(593\) | − | 9.08497i | − | 0.373075i | −0.982448 | − | 0.186538i | \(-0.940273\pi\) | ||
0.982448 | − | 0.186538i | \(-0.0597266\pi\) | |||||||
\(594\) | −0.147250 | −0.00604172 | ||||||||
\(595\) | 55.1393 | + | 13.7064i | 2.26049 | + | 0.561908i | ||||
\(596\) | −25.8948 | −1.06069 | ||||||||
\(597\) | 6.50422i | 0.266200i | ||||||||
\(598\) | −0.533486 | + | 0.533486i | −0.0218159 | + | 0.0218159i | ||||
\(599\) | −29.2400 | −1.19471 | −0.597357 | − | 0.801975i | \(-0.703783\pi\) | ||||
−0.597357 | + | 0.801975i | \(0.703783\pi\) | |||||||
\(600\) | −0.395430 | + | 0.395430i | −0.0161434 | + | 0.0161434i | ||||
\(601\) | 7.83026 | + | 7.83026i | 0.319403 | + | 0.319403i | 0.848538 | − | 0.529135i | \(-0.177483\pi\) |
−0.529135 | + | 0.848538i | \(0.677483\pi\) | |||||||
\(602\) | 0.108409 | + | 0.108409i | 0.00441840 | + | 0.00441840i | ||||
\(603\) | 12.7215i | 0.518060i | ||||||||
\(604\) | − | 24.7188i | − | 1.00579i | ||||||
\(605\) | 2.27271 | + | 2.27271i | 0.0923989 | + | 0.0923989i | ||||
\(606\) | −0.0708204 | − | 0.0708204i | −0.00287688 | − | 0.00287688i | ||||
\(607\) | 3.98442 | − | 3.98442i | 0.161723 | − | 0.161723i | −0.621607 | − | 0.783329i | \(-0.713520\pi\) |
0.783329 | + | 0.621607i | \(0.213520\pi\) | |||||||
\(608\) | −2.95492 | −0.119838 | ||||||||
\(609\) | 1.64755 | − | 1.64755i | 0.0667622 | − | 0.0667622i | ||||
\(610\) | 1.61025i | 0.0651970i | ||||||||
\(611\) | −29.3740 | −1.18835 | ||||||||
\(612\) | 5.19096 | − | 20.8826i | 0.209832 | − | 0.844130i | ||||
\(613\) | 15.3457 | 0.619806 | 0.309903 | − | 0.950768i | \(-0.399703\pi\) | ||||
0.309903 | + | 0.950768i | \(0.399703\pi\) | |||||||
\(614\) | − | 1.24007i | − | 0.0500451i | ||||||
\(615\) | 8.41270 | − | 8.41270i | 0.339233 | − | 0.339233i | ||||
\(616\) | −0.721897 | −0.0290861 | ||||||||
\(617\) | 24.3795 | − | 24.3795i | 0.981482 | − | 0.981482i | −0.0183496 | − | 0.999832i | \(-0.505841\pi\) |
0.999832 | + | 0.0183496i | \(0.00584119\pi\) | |||||||
\(618\) | 0.175732 | + | 0.175732i | 0.00706898 | + | 0.00706898i | ||||
\(619\) | −3.81518 | − | 3.81518i | −0.153345 | − | 0.153345i | 0.626265 | − | 0.779610i | \(-0.284583\pi\) |
−0.779610 | + | 0.626265i | \(0.784583\pi\) | |||||||
\(620\) | 57.0512i | 2.29123i | ||||||||
\(621\) | − | 18.8516i | − | 0.756490i | ||||||
\(622\) | 0.359296 | + | 0.359296i | 0.0144065 | + | 0.0144065i | ||||
\(623\) | −1.13161 | − | 1.13161i | −0.0453370 | − | 0.0453370i | ||||
\(624\) | −5.84052 | + | 5.84052i | −0.233808 | + | 0.233808i | ||||
\(625\) | 23.2386 | 0.929544 | ||||||||
\(626\) | 0.251385 | − | 0.251385i | 0.0100474 | − | 0.0100474i | ||||
\(627\) | 3.64762i | 0.145672i | ||||||||
\(628\) | 3.70589 | 0.147881 | ||||||||
\(629\) | 2.66120 | − | 1.60157i | 0.106109 | − | 0.0638588i | ||||
\(630\) | 1.51566 | 0.0603855 | ||||||||
\(631\) | 10.7782i | 0.429071i | 0.976716 | + | 0.214536i | \(0.0688238\pi\) | ||||
−0.976716 | + | 0.214536i | \(0.931176\pi\) | |||||||
\(632\) | 0.741587 | − | 0.741587i | 0.0294987 | − | 0.0294987i | ||||
\(633\) | 6.49365 | 0.258100 | ||||||||
\(634\) | 0.598157 | − | 0.598157i | 0.0237559 | − | 0.0237559i | ||||
\(635\) | 26.1731 | + | 26.1731i | 1.03865 | + | 1.03865i | ||||
\(636\) | 3.00314 | + | 3.00314i | 0.119082 | + | 0.119082i | ||||
\(637\) | 37.8216i | 1.49855i | ||||||||
\(638\) | − | 0.0367304i | − | 0.00145417i | ||||||
\(639\) | −6.47276 | − | 6.47276i | −0.256058 | − | 0.256058i | ||||
\(640\) | 3.05592 | + | 3.05592i | 0.120796 | + | 0.120796i | ||||
\(641\) | 15.7482 | − | 15.7482i | 0.622015 | − | 0.622015i | −0.324031 | − | 0.946046i | \(-0.605038\pi\) |
0.946046 | + | 0.324031i | \(0.105038\pi\) | |||||||
\(642\) | −0.142362 | −0.00561856 | ||||||||
\(643\) | −14.6821 | + | 14.6821i | −0.579004 | + | 0.579004i | −0.934629 | − | 0.355625i | \(-0.884268\pi\) |
0.355625 | + | 0.934629i | \(0.384268\pi\) | |||||||
\(644\) | − | 46.1900i | − | 1.82014i | ||||||
\(645\) | −1.70048 | −0.0669565 | ||||||||
\(646\) | 0.986468 | + | 0.245214i | 0.0388120 | + | 0.00964782i | ||||
\(647\) | 5.79889 | 0.227978 | 0.113989 | − | 0.993482i | \(-0.463637\pi\) | ||||
0.113989 | + | 0.993482i | \(0.463637\pi\) | |||||||
\(648\) | − | 0.952446i | − | 0.0374156i | ||||||
\(649\) | −8.82162 | + | 8.82162i | −0.346279 | + | 0.346279i | ||||
\(650\) | 0.745924 | 0.0292575 | ||||||||
\(651\) | −16.7797 | + | 16.7797i | −0.657650 | + | 0.657650i | ||||
\(652\) | 9.45407 | + | 9.45407i | 0.370250 | + | 0.370250i | ||||
\(653\) | 0.360205 | + | 0.360205i | 0.0140959 | + | 0.0140959i | 0.714120 | − | 0.700024i | \(-0.246827\pi\) |
−0.700024 | + | 0.714120i | \(0.746827\pi\) | |||||||
\(654\) | − | 0.457594i | − | 0.0178934i | ||||||
\(655\) | − | 7.81747i | − | 0.305454i | ||||||
\(656\) | −16.7586 | − | 16.7586i | −0.654312 | − | 0.654312i | ||||
\(657\) | −8.10935 | − | 8.10935i | −0.316376 | − | 0.316376i | ||||
\(658\) | −1.12859 | + | 1.12859i | −0.0439970 | + | 0.0439970i | ||||
\(659\) | 27.7963 | 1.08279 | 0.541395 | − | 0.840768i | \(-0.317896\pi\) | ||||
0.541395 | + | 0.840768i | \(0.317896\pi\) | |||||||
\(660\) | 2.82964 | − | 2.82964i | 0.110144 | − | 0.110144i | ||||
\(661\) | 3.34455i | 0.130088i | 0.997882 | + | 0.0650439i | \(0.0207187\pi\) | ||||
−0.997882 | + | 0.0650439i | \(0.979281\pi\) | |||||||
\(662\) | −0.252818 | −0.00982606 | ||||||||
\(663\) | 7.31423 | − | 4.40186i | 0.284061 | − | 0.170954i | ||||
\(664\) | 1.06697 | 0.0414063 | ||||||||
\(665\) | − | 80.6720i | − | 3.12833i | ||||||
\(666\) | 0.0585874 | − | 0.0585874i | 0.00227021 | − | 0.00227021i | ||||
\(667\) | 4.70242 | 0.182078 | ||||||||
\(668\) | 20.7271 | − | 20.7271i | 0.801957 | − | 0.801957i | ||||
\(669\) | 10.5071 | + | 10.5071i | 0.406228 | + | 0.406228i | ||||
\(670\) | 0.466185 | + | 0.466185i | 0.0180103 | + | 0.0180103i | ||||
\(671\) | − | 11.8966i | − | 0.459262i | ||||||
\(672\) | 1.34840i | 0.0520156i | ||||||||
\(673\) | −5.72194 | − | 5.72194i | −0.220564 | − | 0.220564i | 0.588172 | − | 0.808736i | \(-0.299848\pi\) |
−0.808736 | + | 0.588172i | \(0.799848\pi\) | |||||||
\(674\) | −0.768988 | − | 0.768988i | −0.0296203 | − | 0.0296203i | ||||
\(675\) | −13.1793 | + | 13.1793i | −0.507270 | + | 0.507270i | ||||
\(676\) | −3.91290 | −0.150496 | ||||||||
\(677\) | −24.2745 | + | 24.2745i | −0.932944 | + | 0.932944i | −0.997889 | − | 0.0649453i | \(-0.979313\pi\) |
0.0649453 | + | 0.997889i | \(0.479313\pi\) | |||||||
\(678\) | 0.148620i | 0.00570771i | ||||||||
\(679\) | −51.3265 | −1.96973 | ||||||||
\(680\) | −1.15057 | − | 1.91181i | −0.0441222 | − | 0.0733144i | ||||
\(681\) | 12.6072 | 0.483108 | ||||||||
\(682\) | 0.374086i | 0.0143245i | ||||||||
\(683\) | 4.42455 | − | 4.42455i | 0.169301 | − | 0.169301i | −0.617371 | − | 0.786672i | \(-0.711802\pi\) |
0.786672 | + | 0.617371i | \(0.211802\pi\) | |||||||
\(684\) | −30.5525 | −1.16820 | ||||||||
\(685\) | 22.2093 | − | 22.2093i | 0.848573 | − | 0.848573i | ||||
\(686\) | 0.559458 | + | 0.559458i | 0.0213602 | + | 0.0213602i | ||||
\(687\) | 12.1167 | + | 12.1167i | 0.462281 | + | 0.462281i | ||||
\(688\) | 3.38746i | 0.129146i | ||||||||
\(689\) | − | 11.3351i | − | 0.431831i | ||||||
\(690\) | −0.321517 | − | 0.321517i | −0.0122400 | − | 0.0122400i | ||||
\(691\) | 31.5883 | + | 31.5883i | 1.20167 | + | 1.20167i | 0.973657 | + | 0.228017i | \(0.0732243\pi\) |
0.228017 | + | 0.973657i | \(0.426776\pi\) | |||||||
\(692\) | −19.4636 | + | 19.4636i | −0.739897 | + | 0.739897i | ||||
\(693\) | −11.1978 | −0.425369 | ||||||||
\(694\) | −0.315414 | + | 0.315414i | −0.0119729 | + | 0.0119729i | ||||
\(695\) | 10.4053i | 0.394695i | ||||||||
\(696\) | −0.0915031 | −0.00346842 | ||||||||
\(697\) | 12.6306 | + | 20.9872i | 0.478416 | + | 0.794946i | ||||
\(698\) | −0.619309 | −0.0234412 | ||||||||
\(699\) | − | 17.9682i | − | 0.679620i | ||||||
\(700\) | −32.2916 | + | 32.2916i | −1.22051 | + | 1.22051i | ||||
\(701\) | 46.1860 | 1.74442 | 0.872210 | − | 0.489132i | \(-0.162686\pi\) | ||||
0.872210 | + | 0.489132i | \(0.162686\pi\) | |||||||
\(702\) | 0.345987 | − | 0.345987i | 0.0130584 | − | 0.0130584i | ||||
\(703\) | −3.11834 | − | 3.11834i | −0.117611 | − | 0.117611i | ||||
\(704\) | −5.62678 | − | 5.62678i | −0.212067 | − | 0.212067i | ||||
\(705\) | − | 17.7029i | − | 0.666731i | ||||||
\(706\) | − | 1.30886i | − | 0.0492594i | ||||||
\(707\) | −11.5718 | − | 11.5718i | −0.435202 | − | 0.435202i | ||||
\(708\) | 10.9834 | + | 10.9834i | 0.412780 | + | 0.412780i | ||||
\(709\) | −34.1833 | + | 34.1833i | −1.28378 | + | 1.28378i | −0.345281 | + | 0.938499i | \(0.612216\pi\) |
−0.938499 | + | 0.345281i | \(0.887784\pi\) | |||||||
\(710\) | −0.474395 | −0.0178037 | ||||||||
\(711\) | 11.5032 | − | 11.5032i | 0.431404 | − | 0.431404i | ||||
\(712\) | 0.0628484i | 0.00235534i | ||||||||
\(713\) | −47.8924 | −1.79359 | ||||||||
\(714\) | 0.111897 | − | 0.450148i | 0.00418764 | − | 0.0168464i | ||||
\(715\) | −10.6802 | −0.399417 | ||||||||
\(716\) | 16.8818i | 0.630902i | ||||||||
\(717\) | −6.98008 | + | 6.98008i | −0.260676 | + | 0.260676i | ||||
\(718\) | −0.603446 | −0.0225204 | ||||||||
\(719\) | −7.44830 | + | 7.44830i | −0.277775 | + | 0.277775i | −0.832220 | − | 0.554445i | \(-0.812930\pi\) |
0.554445 | + | 0.832220i | \(0.312930\pi\) | |||||||
\(720\) | 23.6801 | + | 23.6801i | 0.882505 | + | 0.882505i | ||||
\(721\) | 28.7140 | + | 28.7140i | 1.06936 | + | 1.06936i | ||||
\(722\) | − | 0.643122i | − | 0.0239345i | ||||||
\(723\) | 8.85620i | 0.329366i | ||||||||
\(724\) | −32.6110 | − | 32.6110i | −1.21198 | − | 1.21198i | ||||
\(725\) | −3.28748 | − | 3.28748i | −0.122094 | − | 0.122094i | ||||
\(726\) | 0.0185541 | − | 0.0185541i | 0.000688606 | − | 0.000688606i | ||||
\(727\) | −47.6233 | −1.76625 | −0.883125 | − | 0.469137i | \(-0.844565\pi\) | ||||
−0.883125 | + | 0.469137i | \(0.844565\pi\) | |||||||
\(728\) | 1.69621 | − | 1.69621i | 0.0628659 | − | 0.0628659i | ||||
\(729\) | − | 8.23805i | − | 0.305113i | ||||||
\(730\) | −0.594342 | −0.0219976 | ||||||||
\(731\) | 0.844575 | − | 3.39762i | 0.0312377 | − | 0.125666i | ||||
\(732\) | −14.8119 | −0.547462 | ||||||||
\(733\) | 42.3340i | 1.56364i | 0.623503 | + | 0.781821i | \(0.285709\pi\) | ||||
−0.623503 | + | 0.781821i | \(0.714291\pi\) | |||||||
\(734\) | −0.636455 | + | 0.636455i | −0.0234920 | + | 0.0234920i | ||||
\(735\) | −22.7941 | −0.840771 | ||||||||
\(736\) | −1.92429 | + | 1.92429i | −0.0709302 | + | 0.0709302i | ||||
\(737\) | −3.44420 | − | 3.44420i | −0.126869 | − | 0.126869i | ||||
\(738\) | 0.462041 | + | 0.462041i | 0.0170080 | + | 0.0170080i | ||||
\(739\) | − | 18.3674i | − | 0.675657i | −0.941208 | − | 0.337828i | \(-0.890308\pi\) | ||
0.941208 | − | 0.337828i | \(-0.109692\pi\) | |||||||
\(740\) | 4.83812i | 0.177853i | ||||||||
\(741\) | −8.57066 | − | 8.57066i | −0.314851 | − | 0.314851i | ||||
\(742\) | −0.435508 | − | 0.435508i | −0.0159880 | − | 0.0159880i | ||||
\(743\) | −22.4691 | + | 22.4691i | −0.824310 | + | 0.824310i | −0.986723 | − | 0.162413i | \(-0.948072\pi\) |
0.162413 | + | 0.986723i | \(0.448072\pi\) | |||||||
\(744\) | 0.931927 | 0.0341661 | ||||||||
\(745\) | −29.4519 | + | 29.4519i | −1.07903 | + | 1.07903i | ||||
\(746\) | − | 0.174441i | − | 0.00638672i | ||||||
\(747\) | 16.5504 | 0.605546 | ||||||||
\(748\) | 4.24833 | + | 7.05912i | 0.155334 | + | 0.258107i | ||||
\(749\) | −23.2614 | −0.849953 | ||||||||
\(750\) | 0.0278680i | 0.00101760i | ||||||||
\(751\) | −26.0044 | + | 26.0044i | −0.948915 | + | 0.948915i | −0.998757 | − | 0.0498422i | \(-0.984128\pi\) |
0.0498422 | + | 0.998757i | \(0.484128\pi\) | |||||||
\(752\) | −35.2652 | −1.28599 | ||||||||
\(753\) | −0.390234 | + | 0.390234i | −0.0142209 | + | 0.0142209i | ||||
\(754\) | 0.0863040 | + | 0.0863040i | 0.00314301 | + | 0.00314301i | ||||
\(755\) | −28.1142 | − | 28.1142i | −1.02318 | − | 1.02318i | ||||
\(756\) | 29.9560i | 1.08949i | ||||||||
\(757\) | − | 6.40521i | − | 0.232801i | −0.993202 | − | 0.116401i | \(-0.962864\pi\) | ||
0.993202 | − | 0.116401i | \(-0.0371357\pi\) | |||||||
\(758\) | 0.115454 | + | 0.115454i | 0.00419349 | + | 0.00419349i | ||||
\(759\) | 2.37538 | + | 2.37538i | 0.0862210 | + | 0.0862210i | ||||
\(760\) | −2.24021 | + | 2.24021i | −0.0812611 | + | 0.0812611i | ||||
\(761\) | 25.8600 | 0.937424 | 0.468712 | − | 0.883351i | \(-0.344718\pi\) | ||||
0.468712 | + | 0.883351i | \(0.344718\pi\) | |||||||
\(762\) | 0.213673 | − | 0.213673i | 0.00774055 | − | 0.00774055i | ||||
\(763\) | − | 74.7693i | − | 2.70683i | ||||||
\(764\) | 46.9510 | 1.69863 | ||||||||
\(765\) | −17.8471 | − | 29.6552i | −0.645265 | − | 1.07219i | ||||
\(766\) | −0.752130 | −0.0271756 | ||||||||
\(767\) | − | 41.4556i | − | 1.49688i | ||||||
\(768\) | −6.98690 | + | 6.98690i | −0.252118 | + | 0.252118i | ||||
\(769\) | −7.38242 | −0.266217 | −0.133108 | − | 0.991101i | \(-0.542496\pi\) | ||||
−0.133108 | + | 0.991101i | \(0.542496\pi\) | |||||||
\(770\) | −0.410348 | + | 0.410348i | −0.0147879 | + | 0.0147879i | ||||
\(771\) | −2.95187 | − | 2.95187i | −0.106309 | − | 0.106309i | ||||
\(772\) | −3.85643 | − | 3.85643i | −0.138796 | − | 0.138796i | ||||
\(773\) | 0.0674286i | 0.00242524i | 0.999999 | + | 0.00121262i | \(0.000385989\pi\) | ||||
−0.999999 | + | 0.00121262i | \(0.999614\pi\) | |||||||
\(774\) | − | 0.0933936i | − | 0.00335696i | ||||||
\(775\) | 33.4818 | + | 33.4818i | 1.20270 | + | 1.20270i | ||||
\(776\) | 1.42531 | + | 1.42531i | 0.0511655 | + | 0.0511655i | ||||
\(777\) | −1.42297 | + | 1.42297i | −0.0510489 | + | 0.0510489i | ||||
\(778\) | −0.448724 | −0.0160875 | ||||||||
\(779\) | 24.5924 | − | 24.5924i | 0.881113 | − | 0.881113i | ||||
\(780\) | 13.2974i | 0.476124i | ||||||||
\(781\) | 3.50485 | 0.125413 | ||||||||
\(782\) | 0.802090 | − | 0.482716i | 0.0286827 | − | 0.0172619i | ||||
\(783\) | −3.04970 | −0.108987 | ||||||||
\(784\) | 45.4070i | 1.62168i | ||||||||
\(785\) | 4.21495 | − | 4.21495i | 0.150438 | − | 0.150438i | ||||
\(786\) | −0.0638206 | −0.00227641 | ||||||||
\(787\) | 19.0961 | − | 19.0961i | 0.680701 | − | 0.680701i | −0.279457 | − | 0.960158i | \(-0.590154\pi\) |
0.960158 | + | 0.279457i | \(0.0901545\pi\) | |||||||
\(788\) | −10.8703 | − | 10.8703i | −0.387238 | − | 0.387238i | ||||
\(789\) | −1.87342 | − | 1.87342i | −0.0666956 | − | 0.0666956i | ||||
\(790\) | − | 0.843081i | − | 0.0299955i | ||||||
\(791\) | 24.2840i | 0.863438i | ||||||||
\(792\) | 0.310956 | + | 0.310956i | 0.0110493 | + | 0.0110493i | ||||
\(793\) | 27.9529 | + | 27.9529i | 0.992637 | + | 0.992637i | ||||
\(794\) | 0.0934998 | − | 0.0934998i | 0.00331818 | − | 0.00331818i | ||||
\(795\) | 6.83134 | 0.242282 | ||||||||
\(796\) | 14.7497 | − | 14.7497i | 0.522788 | − | 0.522788i | ||||
\(797\) | 34.1361i | 1.20916i | 0.796543 | + | 0.604581i | \(0.206660\pi\) | ||||
−0.796543 | + | 0.604581i | \(0.793340\pi\) | |||||||
\(798\) | −0.658593 | −0.0233139 | ||||||||
\(799\) | 35.3710 | + | 8.79247i | 1.25134 | + | 0.311055i | ||||
\(800\) | 2.69056 | 0.0951255 | ||||||||
\(801\) | 0.974879i | 0.0344457i | ||||||||
\(802\) | −0.228741 | + | 0.228741i | −0.00807713 | + | 0.00807713i | ||||
\(803\) | 4.39102 | 0.154956 | ||||||||
\(804\) | −4.28820 | + | 4.28820i | −0.151233 | + | 0.151233i | ||||
\(805\) | −52.5348 | − | 52.5348i | −1.85161 | − | 1.85161i | ||||
\(806\) | −0.878976 | − | 0.878976i | −0.0309606 | − | 0.0309606i | ||||
\(807\) | − | 16.1631i | − | 0.568968i | ||||||
\(808\) | 0.642685i | 0.0226096i | ||||||||
\(809\) | −1.17665 | − | 1.17665i | −0.0413689 | − | 0.0413689i | 0.686120 | − | 0.727489i | \(-0.259313\pi\) |
−0.727489 | + | 0.686120i | \(0.759313\pi\) | |||||||
\(810\) | −0.541399 | − | 0.541399i | −0.0190228 | − | 0.0190228i | ||||
\(811\) | 3.97883 | − | 3.97883i | 0.139716 | − | 0.139716i | −0.633790 | − | 0.773505i | \(-0.718502\pi\) |
0.773505 | + | 0.633790i | \(0.218502\pi\) | |||||||
\(812\) | −7.47233 | −0.262227 | ||||||||
\(813\) | −6.59075 | + | 6.59075i | −0.231148 | + | 0.231148i | ||||
\(814\) | 0.0317237i | 0.00111191i | ||||||||
\(815\) | 21.5054 | 0.753303 | ||||||||
\(816\) | 8.78116 | − | 5.28470i | 0.307402 | − | 0.185001i | ||||
\(817\) | −4.97092 | −0.173911 | ||||||||
\(818\) | 0.767262i | 0.0268267i | ||||||||
\(819\) | 26.3110 | − | 26.3110i | 0.919381 | − | 0.919381i | ||||
\(820\) | −38.1551 | −1.33243 | ||||||||
\(821\) | 16.6320 | − | 16.6320i | 0.580459 | − | 0.580459i | −0.354570 | − | 0.935029i | \(-0.615373\pi\) |
0.935029 | + | 0.354570i | \(0.115373\pi\) | |||||||
\(822\) | −0.181313 | − | 0.181313i | −0.00632402 | − | 0.00632402i | ||||
\(823\) | −10.2199 | − | 10.2199i | −0.356242 | − | 0.356242i | 0.506184 | − | 0.862426i | \(-0.331056\pi\) |
−0.862426 | + | 0.506184i | \(0.831056\pi\) | |||||||
\(824\) | − | 1.59474i | − | 0.0555555i | ||||||
\(825\) | − | 3.32128i | − | 0.115632i | ||||||
\(826\) | −1.59278 | − | 1.59278i | −0.0554200 | − | 0.0554200i | ||||
\(827\) | 9.07308 | + | 9.07308i | 0.315502 | + | 0.315502i | 0.847037 | − | 0.531535i | \(-0.178384\pi\) |
−0.531535 | + | 0.847037i | \(0.678384\pi\) | |||||||
\(828\) | −19.8963 | + | 19.8963i | −0.691443 | + | 0.691443i | ||||
\(829\) | 39.8821 | 1.38516 | 0.692580 | − | 0.721341i | \(-0.256474\pi\) | ||||
0.692580 | + | 0.721341i | \(0.256474\pi\) | |||||||
\(830\) | 0.606496 | − | 0.606496i | 0.0210518 | − | 0.0210518i | ||||
\(831\) | 6.11511i | 0.212131i | ||||||||
\(832\) | 26.4421 | 0.916713 | ||||||||
\(833\) | 11.3211 | − | 45.5433i | 0.392252 | − | 1.57798i | ||||
\(834\) | 0.0849470 | 0.00294147 | ||||||||
\(835\) | − | 47.1486i | − | 1.63164i | ||||||
\(836\) | 8.27173 | − | 8.27173i | 0.286084 | − | 0.286084i | ||||
\(837\) | 31.0601 | 1.07360 | ||||||||
\(838\) | −0.164201 | + | 0.164201i | −0.00567224 | + | 0.00567224i | ||||
\(839\) | 8.61493 | + | 8.61493i | 0.297420 | + | 0.297420i | 0.840003 | − | 0.542582i | \(-0.182553\pi\) |
−0.542582 | + | 0.840003i | \(0.682553\pi\) | |||||||
\(840\) | 1.02226 | + | 1.02226i | 0.0352714 | + | 0.0352714i | ||||
\(841\) | 28.2393i | 0.973768i | ||||||||
\(842\) | − | 0.655777i | − | 0.0225996i | ||||||
\(843\) | 5.63312 | + | 5.63312i | 0.194015 | + | 0.194015i | ||||
\(844\) | −14.7257 | − | 14.7257i | −0.506880 | − | 0.506880i | ||||
\(845\) | −4.45039 | + | 4.45039i | −0.153098 | + | 0.153098i | ||||
\(846\) | 0.972276 | 0.0334275 | ||||||||
\(847\) | 3.03167 | − | 3.03167i | 0.104169 | − | 0.104169i | ||||
\(848\) | − | 13.6084i | − | 0.467314i | ||||||
\(849\) | −7.70279 | −0.264359 | ||||||||
\(850\) | −0.898213 | − | 0.223276i | −0.0308084 | − | 0.00765830i | ||||
\(851\) | −4.06143 | −0.139224 | ||||||||
\(852\) | − | 4.36372i | − | 0.149498i | ||||||
\(853\) | −30.4312 | + | 30.4312i | −1.04195 | + | 1.04195i | −0.0428649 | + | 0.999081i | \(0.513649\pi\) |
−0.999081 | + | 0.0428649i | \(0.986351\pi\) | |||||||
\(854\) | 2.14798 | 0.0735023 | ||||||||
\(855\) | −34.7493 | + | 34.7493i | −1.18840 | + | 1.18840i | ||||
\(856\) | 0.645955 | + | 0.645955i | 0.0220783 | + | 0.0220783i | ||||
\(857\) | 10.6678 | + | 10.6678i | 0.364406 | + | 0.364406i | 0.865432 | − | 0.501026i | \(-0.167044\pi\) |
−0.501026 | + | 0.865432i | \(0.667044\pi\) | |||||||
\(858\) | 0.0871915i | 0.00297667i | ||||||||
\(859\) | − | 1.91593i | − | 0.0653706i | −0.999466 | − | 0.0326853i | \(-0.989594\pi\) | ||
0.999466 | − | 0.0326853i | \(-0.0104059\pi\) | |||||||
\(860\) | 3.85620 | + | 3.85620i | 0.131495 | + | 0.131495i | ||||
\(861\) | −11.2221 | − | 11.2221i | −0.382447 | − | 0.382447i | ||||
\(862\) | −0.735132 | + | 0.735132i | −0.0250387 | + | 0.0250387i | ||||
\(863\) | 55.0897 | 1.87527 | 0.937637 | − | 0.347616i | \(-0.113009\pi\) | ||||
0.937637 | + | 0.347616i | \(0.113009\pi\) | |||||||
\(864\) | 1.24798 | − | 1.24798i | 0.0424570 | − | 0.0424570i | ||||
\(865\) | 44.2745i | 1.50538i | ||||||||
\(866\) | 1.15439 | 0.0392278 | ||||||||
\(867\) | −10.1251 | + | 3.11120i | −0.343867 | + | 0.105662i | ||||
\(868\) | 76.1031 | 2.58311 | ||||||||
\(869\) | 6.22872i | 0.211295i | ||||||||
\(870\) | −0.0520131 | + | 0.0520131i | −0.00176341 | + | 0.00176341i | ||||
\(871\) | 16.1854 | 0.548421 | ||||||||
\(872\) | −2.07630 | + | 2.07630i | −0.0703125 | + | 0.0703125i | ||||
\(873\) | 22.1088 | + | 22.1088i | 0.748270 | + | 0.748270i | ||||
\(874\) | −0.939873 | − | 0.939873i | −0.0317917 | − | 0.0317917i | ||||
\(875\) | 4.55354i | 0.153938i | ||||||||
\(876\) | − | 5.46705i | − | 0.184715i | ||||||
\(877\) | 30.1385 | + | 30.1385i | 1.01770 | + | 1.01770i | 0.999840 | + | 0.0178634i | \(0.00568641\pi\) |
0.0178634 | + | 0.999840i | \(0.494314\pi\) | |||||||
\(878\) | −0.237533 | − | 0.237533i | −0.00801634 | − | 0.00801634i | ||||
\(879\) | −6.84271 | + | 6.84271i | −0.230799 | + | 0.230799i | ||||
\(880\) | −12.8222 | −0.432237 | ||||||||
\(881\) | −15.1513 | + | 15.1513i | −0.510461 | + | 0.510461i | −0.914668 | − | 0.404207i | \(-0.867548\pi\) |
0.404207 | + | 0.914668i | \(0.367548\pi\) | |||||||
\(882\) | − | 1.25189i | − | 0.0421533i | ||||||
\(883\) | 11.2898 | 0.379931 | 0.189965 | − | 0.981791i | \(-0.439162\pi\) | ||||
0.189965 | + | 0.981791i | \(0.439162\pi\) | |||||||
\(884\) | −26.5687 | − | 6.60439i | −0.893601 | − | 0.222130i | ||||
\(885\) | 24.9842 | 0.839835 | ||||||||
\(886\) | − | 0.817636i | − | 0.0274690i | ||||||
\(887\) | −36.1491 | + | 36.1491i | −1.21377 | + | 1.21377i | −0.243989 | + | 0.969778i | \(0.578456\pi\) |
−0.969778 | + | 0.243989i | \(0.921544\pi\) | |||||||
\(888\) | 0.0790303 | 0.00265208 | ||||||||
\(889\) | 34.9134 | − | 34.9134i | 1.17096 | − | 1.17096i | ||||
\(890\) | 0.0357249 | + | 0.0357249i | 0.00119750 | + | 0.00119750i | ||||
\(891\) | 3.99988 | + | 3.99988i | 0.134001 | + | 0.134001i | ||||
\(892\) | − | 47.6541i | − | 1.59558i | ||||||
\(893\) | − | 51.7499i | − | 1.73174i | ||||||
\(894\) | 0.240440 | + | 0.240440i | 0.00804153 | + | 0.00804153i | ||||
\(895\) | 19.2007 | + | 19.2007i | 0.641810 | + | 0.641810i | ||||
\(896\) | 4.07643 | − | 4.07643i | 0.136184 | − | 0.136184i | ||||
\(897\) | −11.1627 | −0.372712 | ||||||||
\(898\) | 0.136855 | − | 0.136855i | 0.00456693 | − | 0.00456693i | ||||
\(899\) | 7.74775i | 0.258402i | ||||||||
\(900\) | 27.8191 | 0.927304 | ||||||||
\(901\) | −3.39290 | + | 13.6492i | −0.113034 | + | 0.454722i | ||||
\(902\) | −0.250184 | −0.00833022 | ||||||||
\(903\) | 2.26835i | 0.0754859i | ||||||||
\(904\) | 0.674352 | − | 0.674352i | 0.0224286 | − | 0.0224286i | ||||
\(905\) | −74.1811 | −2.46586 | ||||||||
\(906\) | −0.229520 | + | 0.229520i | −0.00762530 | + | 0.00762530i | ||||
\(907\) | −2.74071 | − | 2.74071i | −0.0910037 | − | 0.0910037i | 0.660139 | − | 0.751143i | \(-0.270497\pi\) |
−0.751143 | + | 0.660139i | \(0.770497\pi\) | |||||||
\(908\) | −28.5894 | − | 28.5894i | −0.948772 | − | 0.948772i | ||||
\(909\) | 9.96907i | 0.330653i | ||||||||
\(910\) | − | 1.92836i | − | 0.0639244i | ||||||
\(911\) | 5.34710 | + | 5.34710i | 0.177157 | + | 0.177157i | 0.790115 | − | 0.612958i | \(-0.210021\pi\) |
−0.612958 | + | 0.790115i | \(0.710021\pi\) | |||||||
\(912\) | −10.2896 | − | 10.2896i | −0.340722 | − | 0.340722i | ||||
\(913\) | −4.48082 | + | 4.48082i | −0.148293 | + | 0.148293i | ||||
\(914\) | −0.656312 | −0.0217089 | ||||||||
\(915\) | −16.8465 | + | 16.8465i | −0.556927 | + | 0.556927i | ||||
\(916\) | − | 54.9543i | − | 1.81574i | ||||||
\(917\) | −10.4281 | −0.344365 | ||||||||
\(918\) | −0.520187 | + | 0.313060i | −0.0171687 | + | 0.0103325i | ||||
\(919\) | 33.0326 | 1.08965 | 0.544823 | − | 0.838551i | \(-0.316597\pi\) | ||||
0.544823 | + | 0.838551i | \(0.316597\pi\) | |||||||
\(920\) | 2.91772i | 0.0961945i | ||||||||
\(921\) | 12.9737 | − | 12.9737i | 0.427496 | − | 0.427496i | ||||
\(922\) | 1.15089 | 0.0379026 | ||||||||
\(923\) | −8.23520 | + | 8.23520i | −0.271065 | + | 0.271065i | ||||
\(924\) | −3.77458 | − | 3.77458i | −0.124175 | − | 0.124175i | ||||
\(925\) | 2.83936 | + | 2.83936i | 0.0933576 | + | 0.0933576i | ||||
\(926\) | − | 0.111409i | − | 0.00366112i | ||||||
\(927\) | − | 24.7370i | − | 0.812470i | ||||||
\(928\) | 0.311300 | + | 0.311300i | 0.0102189 | + | 0.0102189i | ||||
\(929\) | −9.16467 | − | 9.16467i | −0.300683 | − | 0.300683i | 0.540598 | − | 0.841281i | \(-0.318198\pi\) |
−0.841281 | + | 0.540598i | \(0.818198\pi\) | |||||||
\(930\) | 0.529735 | − | 0.529735i | 0.0173707 | − | 0.0173707i | ||||
\(931\) | −66.6325 | −2.18379 | ||||||||
\(932\) | −40.7467 | + | 40.7467i | −1.33470 | + | 1.33470i | ||||
\(933\) | 7.51795i | 0.246126i | ||||||||
\(934\) | −0.567293 | −0.0185624 | ||||||||
\(935\) | 12.8607 | + | 3.19689i | 0.420590 | + | 0.104549i | ||||
\(936\) | −1.46128 | −0.0477635 | ||||||||
\(937\) | − | 45.8455i | − | 1.49771i | −0.662735 | − | 0.748854i | \(-0.730604\pi\) | ||
0.662735 | − | 0.748854i | \(-0.269396\pi\) | |||||||
\(938\) | 0.621865 | − | 0.621865i | 0.0203046 | − | 0.0203046i | ||||
\(939\) | 5.26001 | 0.171654 | ||||||||
\(940\) | −40.1451 | + | 40.1451i | −1.30939 | + | 1.30939i | ||||
\(941\) | −9.19706 | − | 9.19706i | −0.299816 | − | 0.299816i | 0.541126 | − | 0.840942i | \(-0.317998\pi\) |
−0.840942 | + | 0.541126i | \(0.817998\pi\) | |||||||
\(942\) | −0.0344102 | − | 0.0344102i | −0.00112114 | − | 0.00112114i | ||||
\(943\) | − | 32.0298i | − | 1.04304i | ||||||
\(944\) | − | 49.7699i | − | 1.61987i | ||||||
\(945\) | 34.0709 | + | 34.0709i | 1.10833 | + | 1.10833i | ||||
\(946\) | 0.0252852 | + | 0.0252852i | 0.000822093 | + | 0.000822093i | ||||
\(947\) | 15.3572 | − | 15.3572i | 0.499042 | − | 0.499042i | −0.412098 | − | 0.911140i | \(-0.635204\pi\) |
0.911140 | + | 0.412098i | \(0.135204\pi\) | |||||||
\(948\) | 7.75507 | 0.251873 | ||||||||
\(949\) | −10.3174 | + | 10.3174i | −0.334918 | + | 0.334918i | ||||
\(950\) | 1.31414i | 0.0426363i | ||||||||
\(951\) | 12.5159 | 0.405856 | ||||||||
\(952\) | −2.55024 | + | 1.53479i | −0.0826537 | + | 0.0497428i | ||||
\(953\) | 15.5511 | 0.503748 | 0.251874 | − | 0.967760i | \(-0.418953\pi\) | ||||
0.251874 | + | 0.967760i | \(0.418953\pi\) | |||||||
\(954\) | 0.375189i | 0.0121472i | ||||||||
\(955\) | 53.4004 | − | 53.4004i | 1.72800 | − | 1.72800i | ||||
\(956\) | 31.6576 | 1.02388 | ||||||||
\(957\) | 0.384275 | − | 0.384275i | 0.0124219 | − | 0.0124219i | ||||
\(958\) | 1.09652 | + | 1.09652i | 0.0354269 | + | 0.0354269i | ||||
\(959\) | −29.6259 | − | 29.6259i | −0.956670 | − | 0.956670i | ||||
\(960\) | 15.9359i | 0.514329i | ||||||||
\(961\) | − | 47.9081i | − | 1.54542i | ||||||
\(962\) | −0.0745399 | − | 0.0745399i | −0.00240326 | − | 0.00240326i | ||||
\(963\) | 10.0198 | + | 10.0198i | 0.322884 | + | 0.322884i | ||||
\(964\) | 20.0833 | − | 20.0833i | 0.646839 | − | 0.646839i | ||||
\(965\) | −8.77233 | −0.282391 | ||||||||
\(966\) | −0.428886 | + | 0.428886i | −0.0137992 | + | 0.0137992i | ||||
\(967\) | − | 14.2821i | − | 0.459282i | −0.973275 | − | 0.229641i | \(-0.926245\pi\) | ||
0.973275 | − | 0.229641i | \(-0.0737553\pi\) | |||||||
\(968\) | −0.168375 | −0.00541179 | ||||||||
\(969\) | 7.75502 | + | 12.8859i | 0.249127 | + | 0.413955i | ||||
\(970\) | 1.62037 | 0.0520271 | ||||||||
\(971\) | − | 34.3172i | − | 1.10129i | −0.834739 | − | 0.550646i | \(-0.814381\pi\) | ||
0.834739 | − | 0.550646i | \(-0.185619\pi\) | |||||||
\(972\) | 19.8016 | − | 19.8016i | 0.635137 | − | 0.635137i | ||||
\(973\) | 13.8800 | 0.444974 | ||||||||
\(974\) | −0.643775 | + | 0.643775i | −0.0206279 | + | 0.0206279i | ||||
\(975\) | 7.80389 | + | 7.80389i | 0.249924 | + | 0.249924i | ||||
\(976\) | 33.5591 | + | 33.5591i | 1.07420 | + | 1.07420i | ||||
\(977\) | 40.5801i | 1.29827i | 0.760673 | + | 0.649136i | \(0.224869\pi\) | ||||
−0.760673 | + | 0.649136i | \(0.775131\pi\) | |||||||
\(978\) | − | 0.175567i | − | 0.00561401i | ||||||
\(979\) | −0.263937 | − | 0.263937i | −0.00843547 | − | 0.00843547i | ||||
\(980\) | 51.6903 | + | 51.6903i | 1.65118 | + | 1.65118i | ||||
\(981\) | −32.2068 | + | 32.2068i | −1.02828 | + | 1.02828i | ||||
\(982\) | 0.614765 | 0.0196180 | ||||||||
\(983\) | 6.75509 | − | 6.75509i | 0.215454 | − | 0.215454i | −0.591126 | − | 0.806579i | \(-0.701316\pi\) |
0.806579 | + | 0.591126i | \(0.201316\pi\) | |||||||
\(984\) | 0.623261i | 0.0198688i | ||||||||
\(985\) | −24.7270 | −0.787867 | ||||||||
\(986\) | −0.0780908 | − | 0.129757i | −0.00248692 | − | 0.00413231i | ||||
\(987\) | −23.6147 | −0.751664 | ||||||||
\(988\) | 38.8715i | 1.23667i | ||||||||
\(989\) | −3.23714 | + | 3.23714i | −0.102935 | + | 0.102935i | ||||
\(990\) | 0.353514 | 0.0112354 | ||||||||
\(991\) | 35.4347 | − | 35.4347i | 1.12562 | − | 1.12562i | 0.134740 | − | 0.990881i | \(-0.456980\pi\) |
0.990881 | − | 0.134740i | \(-0.0430198\pi\) | |||||||
\(992\) | −3.17048 | − | 3.17048i | −0.100663 | − | 0.100663i | ||||
\(993\) | −2.64499 | − | 2.64499i | −0.0839363 | − | 0.0839363i | ||||
\(994\) | 0.632815i | 0.0200717i | ||||||||
\(995\) | − | 33.5515i | − | 1.06365i | ||||||
\(996\) | 5.57885 | + | 5.57885i | 0.176773 | + | 0.176773i | ||||
\(997\) | 38.7189 | + | 38.7189i | 1.22624 | + | 1.22624i | 0.965375 | + | 0.260865i | \(0.0840078\pi\) |
0.260865 | + | 0.965375i | \(0.415992\pi\) | |||||||
\(998\) | −0.151349 | + | 0.151349i | −0.00479087 | + | 0.00479087i | ||||
\(999\) | 2.63400 | 0.0833359 |
(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 | 187.2.e.b.89.7 | ✓ | 28 | |
17.8 | even | 8 | 3179.2.a.be.1.7 | 14 | |||
17.9 | even | 8 | 3179.2.a.bd.1.7 | 14 | |||
17.13 | even | 4 | inner | 187.2.e.b.166.8 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.2.e.b.89.7 | ✓ | 28 | 1.1 | even | 1 | trivial | |
187.2.e.b.166.8 | yes | 28 | 17.13 | even | 4 | inner | |
3179.2.a.bd.1.7 | 14 | 17.9 | even | 8 | |||
3179.2.a.be.1.7 | 14 | 17.8 | even | 8 |