Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,2,Mod(35,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.l (of order \(18\), degree \(6\), 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: | \(2.58715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 35.15 | ||
Character | \(\chi\) | \(=\) | 324.35 |
Dual form | 324.2.l.a.287.15 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{13}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36287 | + | 0.377622i | 0.963691 | + | 0.267019i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.71480 | + | 1.02930i | 0.857401 | + | 0.514648i | ||||
\(5\) | −0.420820 | + | 1.15619i | −0.188196 | + | 0.517065i | −0.997527 | − | 0.0702884i | \(-0.977608\pi\) |
0.809330 | + | 0.587354i | \(0.199830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.81474 | + | 0.319988i | 0.685907 | + | 0.120944i | 0.505732 | − | 0.862691i | \(-0.331222\pi\) |
0.180175 | + | 0.983635i | \(0.442334\pi\) | |||||||
\(8\) | 1.94836 | + | 2.05034i | 0.688849 | + | 0.724905i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.01013 | + | 1.41682i | −0.319430 | + | 0.448039i | ||||
\(11\) | −5.09161 | + | 1.85319i | −1.53518 | + | 0.558759i | −0.964883 | − | 0.262681i | \(-0.915393\pi\) |
−0.570295 | + | 0.821440i | \(0.693171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.61776 | − | 2.19656i | 0.726035 | − | 0.609215i | −0.203013 | − | 0.979176i | \(-0.565073\pi\) |
0.929047 | + | 0.369961i | \(0.120629\pi\) | |||||||
\(14\) | 2.35241 | + | 1.12139i | 0.628708 | + | 0.299703i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.88110 | + | 3.53008i | 0.470275 | + | 0.882520i | ||||
\(17\) | 4.18778 | − | 2.41782i | 1.01569 | − | 0.586407i | 0.102835 | − | 0.994698i | \(-0.467209\pi\) |
0.912852 | + | 0.408291i | \(0.133875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.42957 | − | 1.98006i | −0.786798 | − | 0.454258i | 0.0520361 | − | 0.998645i | \(-0.483429\pi\) |
−0.838834 | + | 0.544387i | \(0.816762\pi\) | |||||||
\(20\) | −1.91169 | + | 1.54950i | −0.427467 | + | 0.346478i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.63898 | + | 0.602949i | −1.62864 | + | 0.128549i | ||||
\(23\) | −0.674078 | − | 3.82288i | −0.140555 | − | 0.797126i | −0.970829 | − | 0.239772i | \(-0.922927\pi\) |
0.830274 | − | 0.557355i | \(-0.188184\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.67053 | + | 2.24084i | 0.534106 | + | 0.448168i | ||||
\(26\) | 4.39712 | − | 2.00509i | 0.862345 | − | 0.393230i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.78256 | + | 2.41662i | 0.525854 | + | 0.456698i | ||||
\(29\) | −1.76149 | + | 2.09927i | −0.327101 | + | 0.389824i | −0.904384 | − | 0.426721i | \(-0.859669\pi\) |
0.577282 | + | 0.816545i | \(0.304113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.190727 | − | 0.0336302i | 0.0342555 | − | 0.00604017i | −0.156494 | − | 0.987679i | \(-0.550019\pi\) |
0.190750 | + | 0.981639i | \(0.438908\pi\) | |||||||
\(32\) | 1.23065 | + | 5.52137i | 0.217550 | + | 0.976049i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.62041 | − | 1.71376i | 1.13539 | − | 0.293907i | ||||
\(35\) | −1.13365 | + | 1.96353i | −0.191621 | + | 0.331898i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.47493 | − | 6.01875i | −0.571274 | − | 0.989476i | −0.996435 | − | 0.0843584i | \(-0.973116\pi\) |
0.425161 | − | 0.905118i | \(-0.360217\pi\) | |||||||
\(38\) | −3.92633 | − | 3.99364i | −0.636935 | − | 0.647855i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.19050 | + | 1.38986i | −0.504462 | + | 0.219756i | ||||
\(41\) | −2.51742 | − | 3.00014i | −0.393154 | − | 0.468543i | 0.532766 | − | 0.846263i | \(-0.321153\pi\) |
−0.925920 | + | 0.377720i | \(0.876708\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.57902 | − | 7.08581i | −0.393297 | − | 1.08058i | −0.965486 | − | 0.260454i | \(-0.916128\pi\) |
0.572189 | − | 0.820122i | \(-0.306094\pi\) | |||||||
\(44\) | −10.6386 | − | 2.06291i | −1.60383 | − | 0.310996i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.524929 | − | 5.46462i | 0.0773965 | − | 0.805714i | ||||
\(47\) | −0.343697 | + | 1.94920i | −0.0501334 | + | 0.284321i | −0.999560 | − | 0.0296691i | \(-0.990555\pi\) |
0.949426 | + | 0.313990i | \(0.101666\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.38696 | − | 1.23275i | −0.483852 | − | 0.176108i | ||||
\(50\) | 2.79338 | + | 4.06241i | 0.395044 | + | 0.574512i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.74984 | − | 1.07222i | 0.936035 | − | 0.148690i | ||||
\(53\) | − | 11.2308i | − | 1.54267i | −0.636432 | − | 0.771333i | \(-0.719590\pi\) | ||
0.636432 | − | 0.771333i | \(-0.280410\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.66675i | − | 0.898944i | ||||||
\(56\) | 2.87968 | + | 4.34428i | 0.384814 | + | 0.580529i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.19341 | + | 2.19584i | −0.419315 | + | 0.288328i | ||||
\(59\) | 3.62667 | + | 1.32000i | 0.472152 | + | 0.171849i | 0.567127 | − | 0.823630i | \(-0.308055\pi\) |
−0.0949749 | + | 0.995480i | \(0.530277\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.54693 | + | 14.4444i | −0.326101 | + | 1.84941i | 0.175719 | + | 0.984440i | \(0.443775\pi\) |
−0.501820 | + | 0.864972i | \(0.667336\pi\) | |||||||
\(62\) | 0.272634 | + | 0.0261891i | 0.0346246 | + | 0.00332602i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.407785 | + | 7.98960i | −0.0509731 | + | 0.998700i | ||||
\(65\) | 1.43804 | + | 3.95099i | 0.178367 | + | 0.490060i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.34096 | + | 1.59809i | 0.163824 | + | 0.195238i | 0.841711 | − | 0.539928i | \(-0.181549\pi\) |
−0.677887 | + | 0.735166i | \(0.737104\pi\) | |||||||
\(68\) | 9.66988 | + | 0.164388i | 1.17264 | + | 0.0199350i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.28648 | + | 2.24794i | −0.273287 | + | 0.268680i | ||||
\(71\) | −4.41692 | − | 7.65033i | −0.524192 | − | 0.907927i | −0.999603 | − | 0.0281636i | \(-0.991034\pi\) |
0.475411 | − | 0.879764i | \(-0.342299\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.62025 | − | 4.53841i | 0.306677 | − | 0.531180i | −0.670956 | − | 0.741497i | \(-0.734116\pi\) |
0.977633 | + | 0.210317i | \(0.0674495\pi\) | |||||||
\(74\) | −2.46304 | − | 9.51495i | −0.286323 | − | 1.10609i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.84297 | − | 6.92547i | −0.440819 | − | 0.794406i | ||||
\(77\) | −9.83294 | + | 1.73381i | −1.12057 | + | 0.197586i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.09766 | + | 6.07516i | −0.573532 | + | 0.683508i | −0.972352 | − | 0.233521i | \(-0.924975\pi\) |
0.398820 | + | 0.917029i | \(0.369420\pi\) | |||||||
\(80\) | −4.87306 | + | 0.689385i | −0.544825 | + | 0.0770756i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.29798 | − | 5.03942i | −0.253769 | − | 0.556510i | ||||
\(83\) | −1.39029 | − | 1.16659i | −0.152604 | − | 0.128050i | 0.563289 | − | 0.826260i | \(-0.309536\pi\) |
−0.715893 | + | 0.698210i | \(0.753980\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.03316 | + | 5.85935i | 0.112062 | + | 0.635536i | ||||
\(86\) | −0.839103 | − | 10.6309i | −0.0904828 | − | 1.14636i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −13.7200 | − | 6.82884i | −1.46255 | − | 0.727957i | ||||
\(89\) | 14.2059 | + | 8.20179i | 1.50582 | + | 0.869388i | 0.999977 | + | 0.00676565i | \(0.00215359\pi\) |
0.505848 | + | 0.862623i | \(0.331180\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.45341 | − | 3.14853i | 0.571673 | − | 0.330056i | ||||
\(92\) | 2.77897 | − | 7.24932i | 0.289728 | − | 0.755794i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.20448 | + | 2.52671i | −0.124232 | + | 0.260611i | ||||
\(95\) | 3.73257 | − | 3.13200i | 0.382954 | − | 0.321336i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0876267 | − | 0.0318935i | 0.00889714 | − | 0.00323830i | −0.337568 | − | 0.941301i | \(-0.609604\pi\) |
0.346465 | + | 0.938063i | \(0.387382\pi\) | |||||||
\(98\) | −4.15046 | − | 2.95907i | −0.419259 | − | 0.298911i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.27294 | + | 6.59136i | 0.227294 | + | 0.659136i | ||||
\(101\) | −1.18836 | − | 0.209540i | −0.118246 | − | 0.0208500i | 0.114212 | − | 0.993456i | \(-0.463566\pi\) |
−0.232458 | + | 0.972606i | \(0.574677\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.38263 | + | 14.7887i | −0.530366 | + | 1.45717i | 0.328270 | + | 0.944584i | \(0.393534\pi\) |
−0.858636 | + | 0.512586i | \(0.828688\pi\) | |||||||
\(104\) | 9.60402 | + | 1.08760i | 0.941752 | + | 0.106648i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.24099 | − | 15.3060i | 0.411921 | − | 1.48665i | ||||
\(107\) | 15.2848 | 1.47764 | 0.738820 | − | 0.673903i | \(-0.235384\pi\) | ||||
0.738820 | + | 0.673903i | \(0.235384\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.4401 | −1.19154 | −0.595772 | − | 0.803154i | \(-0.703154\pi\) | ||||
−0.595772 | + | 0.803154i | \(0.703154\pi\) | |||||||
\(110\) | 2.51751 | − | 9.08588i | 0.240035 | − | 0.866304i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.28412 | + | 7.00810i | 0.215829 | + | 0.662204i | ||||
\(113\) | −1.29655 | + | 3.56224i | −0.121969 | + | 0.335107i | −0.985619 | − | 0.168986i | \(-0.945951\pi\) |
0.863649 | + | 0.504093i | \(0.168173\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.70366 | + | 0.829382i | 0.438618 | + | 0.0773403i | ||||
\(116\) | −5.18138 | + | 1.78673i | −0.481079 | + | 0.165894i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.44420 | + | 3.16849i | 0.409122 | + | 0.291683i | ||||
\(119\) | 8.37341 | − | 3.04767i | 0.767589 | − | 0.279380i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.0637 | − | 11.8008i | 1.27852 | − | 1.07280i | ||||
\(122\) | −8.92564 | + | 18.7240i | −0.808090 | + | 1.69519i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.361674 | + | 0.138645i | 0.0324793 | + | 0.0124507i | ||||
\(125\) | −9.04242 | + | 5.22065i | −0.808779 | + | 0.466949i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.8485 | + | 6.26340i | 0.962651 | + | 0.555787i | 0.896988 | − | 0.442055i | \(-0.145750\pi\) |
0.0656631 | + | 0.997842i | \(0.479084\pi\) | |||||||
\(128\) | −3.57281 | + | 10.7348i | −0.315794 | + | 0.948828i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.467877 | + | 5.92770i | 0.0410355 | + | 0.519894i | ||||
\(131\) | 0.603670 | + | 3.42359i | 0.0527429 | + | 0.299120i | 0.999756 | − | 0.0220740i | \(-0.00702694\pi\) |
−0.947013 | + | 0.321194i | \(0.895916\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.59018 | − | 4.69072i | −0.484731 | − | 0.406737i | ||||
\(134\) | 1.22407 | + | 2.68436i | 0.105744 | + | 0.231893i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.1167 | + | 3.87560i | 1.12474 | + | 0.332330i | ||||
\(137\) | −3.24936 | + | 3.87244i | −0.277612 | + | 0.330845i | −0.886776 | − | 0.462199i | \(-0.847061\pi\) |
0.609164 | + | 0.793044i | \(0.291505\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.37891 | − | 1.12477i | 0.541052 | − | 0.0954022i | 0.103558 | − | 0.994623i | \(-0.466977\pi\) |
0.437494 | + | 0.899221i | \(0.355866\pi\) | |||||||
\(140\) | −3.96504 | + | 2.20021i | −0.335107 | + | 0.185952i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.13073 | − | 12.0943i | −0.262725 | − | 1.01493i | ||||
\(143\) | −9.25794 | + | 16.0352i | −0.774188 | + | 1.34093i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.68589 | − | 2.92004i | −0.140005 | − | 0.242496i | ||||
\(146\) | 5.28485 | − | 5.19577i | 0.437377 | − | 0.430005i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.236262 | − | 13.8977i | 0.0194206 | − | 1.14238i | ||||
\(149\) | −3.39500 | − | 4.04600i | −0.278129 | − | 0.331461i | 0.608837 | − | 0.793295i | \(-0.291636\pi\) |
−0.886967 | + | 0.461834i | \(0.847192\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.02704 | − | 8.31673i | −0.246337 | − | 0.676806i | −0.999813 | − | 0.0193304i | \(-0.993847\pi\) |
0.753476 | − | 0.657475i | \(-0.228376\pi\) | |||||||
\(152\) | −2.62224 | − | 10.8897i | −0.212692 | − | 0.883269i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −14.0557 | − | 1.35018i | −1.13264 | − | 0.108801i | ||||
\(155\) | −0.0413785 | + | 0.234669i | −0.00332360 | + | 0.0188491i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.32232 | + | 3.39305i | 0.744002 | + | 0.270795i | 0.686079 | − | 0.727527i | \(-0.259330\pi\) |
0.0579223 | + | 0.998321i | \(0.481552\pi\) | |||||||
\(158\) | −9.24154 | + | 6.35463i | −0.735217 | + | 0.505547i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.90165 | − | 0.900636i | −0.545623 | − | 0.0712015i | ||||
\(161\) | − | 7.15323i | − | 0.563754i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.2908i | 1.27600i | 0.770038 | + | 0.637998i | \(0.220237\pi\) | ||||
−0.770038 | + | 0.637998i | \(0.779763\pi\) | |||||||
\(164\) | −1.22884 | − | 7.73581i | −0.0959563 | − | 0.604066i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.45425 | − | 2.11491i | −0.112871 | − | 0.164149i | ||||
\(167\) | −1.16436 | − | 0.423791i | −0.0901007 | − | 0.0327940i | 0.296577 | − | 0.955009i | \(-0.404155\pi\) |
−0.386677 | + | 0.922215i | \(0.626377\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.229648 | + | 1.30240i | −0.0176653 | + | 0.100185i | ||||
\(170\) | −0.804561 | + | 8.37566i | −0.0617070 | + | 0.642383i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.87088 | − | 14.8053i | 0.218902 | − | 1.12890i | ||||
\(173\) | 4.93959 | + | 13.5714i | 0.375550 | + | 1.03181i | 0.973180 | + | 0.230043i | \(0.0738866\pi\) |
−0.597631 | + | 0.801771i | \(0.703891\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.12927 | + | 4.92108i | 0.312144 | + | 0.371998i | ||||
\(176\) | −16.1197 | − | 14.4878i | −1.21507 | − | 1.09206i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.2636 | + | 16.5424i | 1.21901 | + | 1.23991i | ||||
\(179\) | 4.99509 | + | 8.65175i | 0.373351 | + | 0.646662i | 0.990079 | − | 0.140514i | \(-0.0448755\pi\) |
−0.616728 | + | 0.787176i | \(0.711542\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.92900 | + | 10.2693i | −0.440699 | + | 0.763314i | −0.997742 | − | 0.0671706i | \(-0.978603\pi\) |
0.557042 | + | 0.830484i | \(0.311936\pi\) | |||||||
\(182\) | 8.62122 | − | 2.23169i | 0.639048 | − | 0.165424i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.52486 | − | 8.83044i | 0.481019 | − | 0.650989i | ||||
\(185\) | 8.42116 | − | 1.48488i | 0.619136 | − | 0.109170i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.8419 | + | 20.0714i | −1.23160 | + | 1.46776i | ||||
\(188\) | −2.59568 | + | 2.98873i | −0.189310 | + | 0.217976i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.26970 | − | 2.85899i | 0.454852 | − | 0.207413i | ||||
\(191\) | 0.136281 | + | 0.114354i | 0.00986096 | + | 0.00827433i | 0.647705 | − | 0.761891i | \(-0.275729\pi\) |
−0.637844 | + | 0.770166i | \(0.720173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.20989 | − | 6.86163i | −0.0870899 | − | 0.493911i | −0.996886 | − | 0.0788559i | \(-0.974873\pi\) |
0.909796 | − | 0.415055i | \(-0.136238\pi\) | |||||||
\(194\) | 0.131467 | − | 0.0103768i | 0.00943879 | − | 0.000745009i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.53910 | − | 5.60011i | −0.324222 | − | 0.400008i | ||||
\(197\) | −4.71520 | − | 2.72232i | −0.335944 | − | 0.193957i | 0.322533 | − | 0.946558i | \(-0.395466\pi\) |
−0.658477 | + | 0.752601i | \(0.728799\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.18692 | + | 2.99467i | −0.367691 | + | 0.212287i | −0.672449 | − | 0.740143i | \(-0.734758\pi\) |
0.304758 | + | 0.952430i | \(0.401424\pi\) | |||||||
\(200\) | 0.608669 | + | 9.84145i | 0.0430394 | + | 0.695896i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.54045 | − | 0.734326i | −0.108386 | − | 0.0516670i | ||||
\(203\) | −3.86839 | + | 3.24597i | −0.271508 | + | 0.227822i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.52812 | − | 1.64810i | 0.316258 | − | 0.115108i | ||||
\(206\) | −12.9203 | + | 18.1223i | −0.900202 | + | 1.26264i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.6783 | + | 5.10895i | 0.879081 | + | 0.354242i | ||||
\(209\) | 21.1315 | + | 3.72605i | 1.46170 | + | 0.257736i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.87740 | − | 24.3905i | 0.611145 | − | 1.67911i | −0.116531 | − | 0.993187i | \(-0.537177\pi\) |
0.727676 | − | 0.685921i | \(-0.240600\pi\) | |||||||
\(212\) | 11.5598 | − | 19.2586i | 0.793930 | − | 1.32268i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.8311 | + | 5.77189i | 1.42399 | + | 0.394558i | ||||
\(215\) | 9.27787 | 0.632745 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.356880 | 0.0242266 | ||||||||
\(218\) | −16.9541 | − | 4.69765i | −1.14828 | − | 0.318165i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.86206 | − | 11.4322i | 0.462640 | − | 0.770756i | ||||
\(221\) | 5.65172 | − | 15.5280i | 0.380176 | − | 1.04452i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.0110 | + | 3.88113i | 1.47396 | + | 0.259900i | 0.852164 | − | 0.523275i | \(-0.175290\pi\) |
0.621801 | + | 0.783175i | \(0.286401\pi\) | |||||||
\(224\) | 0.466535 | + | 10.4136i | 0.0311717 | + | 0.695790i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.11220 | + | 4.36525i | −0.207021 | + | 0.290372i | ||||
\(227\) | −1.58931 | + | 0.578461i | −0.105486 | + | 0.0383938i | −0.394224 | − | 0.919014i | \(-0.628987\pi\) |
0.288738 | + | 0.957408i | \(0.406764\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.3257 | + | 17.0553i | −1.34316 | + | 1.12704i | −0.362355 | + | 0.932040i | \(0.618027\pi\) |
−0.980803 | + | 0.195003i | \(0.937528\pi\) | |||||||
\(230\) | 6.09726 | + | 2.90654i | 0.402041 | + | 0.191652i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.73623 | + | 0.478467i | −0.507909 | + | 0.0314129i | ||||
\(233\) | −4.08160 | + | 2.35651i | −0.267395 | + | 0.154380i | −0.627703 | − | 0.778453i | \(-0.716005\pi\) |
0.360308 | + | 0.932833i | \(0.382671\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.10902 | − | 1.21764i | −0.137577 | − | 0.0794304i | ||||
\(236\) | 4.86035 | + | 5.99646i | 0.316382 | + | 0.390336i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.5627 | − | 0.991581i | 0.814319 | − | 0.0642746i | ||||
\(239\) | −0.585031 | − | 3.31788i | −0.0378425 | − | 0.214616i | 0.960023 | − | 0.279922i | \(-0.0903086\pi\) |
−0.997865 | + | 0.0653065i | \(0.979197\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.2315 | − | 10.2635i | −0.787901 | − | 0.661127i | 0.157324 | − | 0.987547i | \(-0.449713\pi\) |
−0.945225 | + | 0.326420i | \(0.894158\pi\) | |||||||
\(242\) | 23.6231 | − | 10.7722i | 1.51855 | − | 0.692462i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −19.2350 | + | 22.1477i | −1.23140 | + | 1.41786i | ||||
\(245\) | 2.85060 | − | 3.39722i | 0.182118 | − | 0.217040i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.3271 | + | 2.34993i | −0.847984 | + | 0.149522i | ||||
\(248\) | 0.440557 | + | 0.325530i | 0.0279754 | + | 0.0206712i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.2950 | + | 3.70042i | −0.904097 | + | 0.234035i | ||||
\(251\) | 8.45736 | − | 14.6486i | 0.533824 | − | 0.924610i | −0.465396 | − | 0.885103i | \(-0.654088\pi\) |
0.999219 | − | 0.0395068i | \(-0.0125787\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.5167 | + | 18.2154i | 0.661178 | + | 1.14519i | ||||
\(254\) | 12.4199 | + | 12.6328i | 0.779293 | + | 0.792653i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.92294 | + | 13.2809i | −0.557684 | + | 0.830054i | ||||
\(257\) | 1.87760 | + | 2.23763i | 0.117121 | + | 0.139580i | 0.821419 | − | 0.570325i | \(-0.193183\pi\) |
−0.704298 | + | 0.709904i | \(0.748738\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.38016 | − | 12.0344i | −0.272170 | − | 0.747781i | ||||
\(260\) | −1.60078 | + | 8.25533i | −0.0992760 | + | 0.511974i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.470100 | + | 4.89384i | −0.0290429 | + | 0.302343i | ||||
\(263\) | −0.00324687 | + | 0.0184139i | −0.000200211 | + | 0.00113545i | −0.984908 | − | 0.173080i | \(-0.944628\pi\) |
0.984707 | + | 0.174216i | \(0.0557391\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.9849 | + | 4.72613i | 0.797659 | + | 0.290324i | ||||
\(266\) | −5.84735 | − | 8.50380i | −0.358524 | − | 0.521401i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.654570 | + | 4.12066i | 0.0399842 | + | 0.251709i | ||||
\(269\) | 16.1328i | 0.983634i | 0.870699 | + | 0.491817i | \(0.163667\pi\) | ||||
−0.870699 | + | 0.491817i | \(0.836333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.8808i | − | 1.38991i | −0.719053 | − | 0.694955i | \(-0.755424\pi\) | ||
0.719053 | − | 0.694955i | \(-0.244576\pi\) | |||||||
\(272\) | 16.4127 | + | 10.2351i | 0.995168 | + | 0.620592i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.89076 | + | 4.05058i | −0.355874 | + | 0.244705i | ||||
\(275\) | −17.7500 | − | 6.46047i | −1.07037 | − | 0.389581i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.19415 | − | 6.77238i | 0.0717497 | − | 0.406913i | −0.927687 | − | 0.373358i | \(-0.878206\pi\) |
0.999437 | − | 0.0335545i | \(-0.0106827\pi\) | |||||||
\(278\) | 9.11834 | + | 0.875903i | 0.546882 | + | 0.0525332i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.23466 | + | 1.50131i | −0.372592 | + | 0.0897204i | ||||
\(281\) | −4.84953 | − | 13.3240i | −0.289298 | − | 0.794841i | −0.996165 | − | 0.0874941i | \(-0.972114\pi\) |
0.706867 | − | 0.707347i | \(-0.250108\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.76714 | − | 9.25651i | −0.461708 | − | 0.550243i | 0.484081 | − | 0.875023i | \(-0.339154\pi\) |
−0.945789 | + | 0.324781i | \(0.894710\pi\) | |||||||
\(284\) | 0.300308 | − | 17.6651i | 0.0178200 | − | 1.04823i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.6726 | + | 18.3578i | −1.10413 | + | 1.08552i | ||||
\(287\) | −3.60845 | − | 6.25001i | −0.213000 | − | 0.368927i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.19169 | − | 5.52817i | 0.187747 | − | 0.325187i | ||||
\(290\) | −1.19496 | − | 4.61625i | −0.0701707 | − | 0.271076i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.16458 | − | 5.08546i | 0.536316 | − | 0.297604i | ||||
\(293\) | −5.78523 | + | 1.02009i | −0.337977 | + | 0.0595944i | −0.340061 | − | 0.940403i | \(-0.610448\pi\) |
0.00208409 | + | 0.999998i | \(0.499337\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.05235 | + | 3.63765i | −0.177715 | + | 0.211792i | ||||
\(296\) | 5.57007 | − | 18.8515i | 0.323754 | − | 1.09572i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.09907 | − | 6.79618i | −0.179524 | − | 0.393692i | ||||
\(299\) | −10.1618 | − | 8.52672i | −0.587669 | − | 0.493113i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.41288 | − | 13.6841i | −0.139076 | − | 0.788741i | ||||
\(302\) | −0.984869 | − | 12.4777i | −0.0566728 | − | 0.718009i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.538424 | − | 15.8314i | 0.0308807 | − | 0.907991i | ||||
\(305\) | −15.6287 | − | 9.02323i | −0.894896 | − | 0.516668i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.55307 | + | 2.05137i | −0.202784 | + | 0.117078i | −0.597954 | − | 0.801531i | \(-0.704019\pi\) |
0.395169 | + | 0.918608i | \(0.370686\pi\) | |||||||
\(308\) | −18.6462 | − | 7.14786i | −1.06246 | − | 0.407287i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.145010 | + | 0.304197i | −0.00823599 | + | 0.0172772i | ||||
\(311\) | 2.76079 | − | 2.31658i | 0.156550 | − | 0.131361i | −0.561148 | − | 0.827715i | \(-0.689640\pi\) |
0.717698 | + | 0.696354i | \(0.245196\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0330 | − | 7.29141i | 1.13233 | − | 0.412135i | 0.293193 | − | 0.956053i | \(-0.405282\pi\) |
0.839138 | + | 0.543919i | \(0.183060\pi\) | |||||||
\(314\) | 11.4238 | + | 8.14458i | 0.644681 | + | 0.459625i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.9946 | + | 5.17069i | −0.843513 | + | 0.290874i | ||||
\(317\) | −34.5729 | − | 6.09614i | −1.94181 | − | 0.342393i | −0.999980 | − | 0.00629824i | \(-0.997995\pi\) |
−0.941828 | − | 0.336095i | \(-0.890894\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.07849 | − | 13.9530i | 0.284341 | − | 0.781220i | ||||
\(320\) | −9.06592 | − | 3.83366i | −0.506800 | − | 0.214308i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.70122 | − | 9.74889i | 0.150533 | − | 0.543285i | ||||
\(323\) | −19.1497 | −1.06552 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.9129 | 0.660810 | ||||||||
\(326\) | −6.15178 | + | 22.2022i | −0.340715 | + | 1.22967i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.24647 | − | 11.0069i | 0.0688249 | − | 0.607755i | ||||
\(329\) | −1.24744 | + | 3.42732i | −0.0687737 | + | 0.188954i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.234592 | + | 0.0413648i | 0.0128943 | + | 0.00227362i | 0.180092 | − | 0.983650i | \(-0.442361\pi\) |
−0.167197 | + | 0.985923i | \(0.553472\pi\) | |||||||
\(332\) | −1.18330 | − | 3.43149i | −0.0649422 | − | 0.188328i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.42683 | − | 1.01726i | −0.0780726 | − | 0.0556619i | ||||
\(335\) | −2.41201 | + | 0.877898i | −0.131782 | + | 0.0479647i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.13534 | + | 4.30906i | −0.279740 | + | 0.234729i | −0.771852 | − | 0.635802i | \(-0.780669\pi\) |
0.492112 | + | 0.870532i | \(0.336225\pi\) | |||||||
\(338\) | −0.804795 | + | 1.68828i | −0.0437751 | + | 0.0918301i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.25934 | + | 11.1111i | −0.230995 | + | 0.602582i | ||||
\(341\) | −0.908782 | + | 0.524685i | −0.0492133 | + | 0.0284133i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9230 | − | 9.77048i | −0.913755 | − | 0.527556i | ||||
\(344\) | 9.50345 | − | 19.0936i | 0.512391 | − | 1.02946i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.60713 | + | 20.3613i | 0.0863997 | + | 1.09463i | ||||
\(347\) | 1.22136 | + | 6.92666i | 0.0655659 | + | 0.371843i | 0.999881 | + | 0.0153957i | \(0.00490079\pi\) |
−0.934316 | + | 0.356447i | \(0.883988\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.45858 | − | 4.58030i | −0.292191 | − | 0.245178i | 0.484894 | − | 0.874573i | \(-0.338858\pi\) |
−0.777085 | + | 0.629395i | \(0.783303\pi\) | |||||||
\(350\) | 3.76933 | + | 8.26607i | 0.201479 | + | 0.441840i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.4981 | − | 25.8320i | −0.879354 | − | 1.37685i | ||||
\(353\) | 10.1110 | − | 12.0498i | 0.538152 | − | 0.641344i | −0.426620 | − | 0.904431i | \(-0.640296\pi\) |
0.964772 | + | 0.263086i | \(0.0847404\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.7040 | − | 1.88740i | 0.568109 | − | 0.100173i | ||||
\(356\) | 15.9183 | + | 28.6866i | 0.843667 | + | 1.52038i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.54054 | + | 13.6774i | 0.187123 | + | 0.722874i | ||||
\(359\) | −6.28667 | + | 10.8888i | −0.331798 | + | 0.574691i | −0.982864 | − | 0.184330i | \(-0.940988\pi\) |
0.651067 | + | 0.759021i | \(0.274322\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.65869 | − | 2.87293i | −0.0872993 | − | 0.151207i | ||||
\(362\) | −11.9584 | + | 11.7568i | −0.628517 | + | 0.617923i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.5923 | + | 0.214070i | 0.660016 | + | 0.0112203i | ||||
\(365\) | 4.14462 | + | 4.93937i | 0.216939 | + | 0.258538i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.46561 | − | 20.5116i | −0.389702 | − | 1.07070i | −0.967136 | − | 0.254260i | \(-0.918168\pi\) |
0.577434 | − | 0.816437i | \(-0.304054\pi\) | |||||||
\(368\) | 12.2271 | − | 9.57077i | 0.637381 | − | 0.498911i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.0376 | + | 1.15633i | 0.625806 | + | 0.0601146i | ||||
\(371\) | 3.59371 | − | 20.3809i | 0.186576 | − | 1.05813i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.2207 | − | 5.17591i | −0.736320 | − | 0.267999i | −0.0534826 | − | 0.998569i | \(-0.517032\pi\) |
−0.682838 | + | 0.730570i | \(0.739254\pi\) | |||||||
\(374\) | −30.5326 | + | 20.9947i | −1.57880 | + | 1.08561i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.66618 | + | 3.09306i | −0.240640 | + | 0.159512i | ||||
\(377\) | 9.36459i | 0.482301i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.8363i | 1.32712i | 0.748122 | + | 0.663561i | \(0.230956\pi\) | ||||
−0.748122 | + | 0.663561i | \(0.769044\pi\) | |||||||
\(380\) | 9.62438 | − | 1.52884i | 0.493720 | − | 0.0784278i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.142550 | + | 0.207311i | 0.00729352 | + | 0.0106070i | ||||
\(383\) | −4.37364 | − | 1.59187i | −0.223482 | − | 0.0813410i | 0.227852 | − | 0.973696i | \(-0.426830\pi\) |
−0.451335 | + | 0.892355i | \(0.649052\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.13328 | − | 12.0984i | 0.108722 | − | 0.616592i | ||||
\(386\) | 0.942187 | − | 9.80836i | 0.0479560 | − | 0.499233i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.183090 | + | 0.0355027i | 0.00929501 | + | 0.00180238i | ||||
\(389\) | −9.75902 | − | 26.8127i | −0.494802 | − | 1.35946i | −0.896239 | − | 0.443571i | \(-0.853712\pi\) |
0.401438 | − | 0.915886i | \(-0.368511\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0659 | − | 14.3796i | −0.610200 | − | 0.727208i | ||||
\(392\) | −4.07146 | − | 9.34627i | −0.205640 | − | 0.472058i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.39817 | − | 5.49072i | −0.271956 | − | 0.276619i | ||||
\(395\) | −4.87886 | − | 8.45043i | −0.245482 | − | 0.425187i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.983521 | + | 1.70351i | −0.0493615 | + | 0.0854966i | −0.889650 | − | 0.456642i | \(-0.849052\pi\) |
0.840289 | + | 0.542139i | \(0.182385\pi\) | |||||||
\(398\) | −8.19993 | + | 2.12264i | −0.411025 | + | 0.106398i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.88682 | + | 13.6424i | −0.144341 | + | 0.682121i | ||||
\(401\) | 18.7451 | − | 3.30527i | 0.936087 | − | 0.165057i | 0.315260 | − | 0.949005i | \(-0.397908\pi\) |
0.620827 | + | 0.783948i | \(0.286797\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.425405 | − | 0.506978i | 0.0211909 | − | 0.0252544i | ||||
\(404\) | −1.82213 | − | 1.58250i | −0.0906542 | − | 0.0787321i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.49784 | + | 2.96302i | −0.322483 | + | 0.147052i | ||||
\(407\) | 28.8469 | + | 24.2054i | 1.42989 | + | 1.19982i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.54702 | + | 14.4449i | 0.125942 | + | 0.714252i | 0.980744 | + | 0.195298i | \(0.0625674\pi\) |
−0.854802 | + | 0.518954i | \(0.826322\pi\) | |||||||
\(410\) | 6.79358 | − | 0.536221i | 0.335511 | − | 0.0264821i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −24.4521 | + | 19.8193i | −1.20467 | + | 0.976427i | ||||
\(413\) | 6.15908 | + | 3.55594i | 0.303068 | + | 0.174977i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.93387 | − | 1.11652i | 0.0949297 | − | 0.0548077i | ||||
\(416\) | 15.3495 | + | 11.7504i | 0.752573 | + | 0.576111i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 27.3923 | + | 13.0578i | 1.33980 | + | 0.638679i | ||||
\(419\) | −8.87113 | + | 7.44376i | −0.433383 | + | 0.363651i | −0.833226 | − | 0.552932i | \(-0.813509\pi\) |
0.399843 | + | 0.916583i | \(0.369064\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.16623 | − | 0.424473i | 0.0568386 | − | 0.0206876i | −0.313444 | − | 0.949607i | \(-0.601483\pi\) |
0.370283 | + | 0.928919i | \(0.379261\pi\) | |||||||
\(422\) | 21.3091 | − | 29.8886i | 1.03731 | − | 1.45495i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 23.0269 | − | 21.8816i | 1.11829 | − | 1.06266i | ||||
\(425\) | 16.6015 | + | 2.92730i | 0.805293 | + | 0.141995i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.24404 | + | 25.3978i | −0.447350 | + | 1.22908i | ||||
\(428\) | 26.2105 | + | 15.7326i | 1.26693 | + | 0.760464i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.6445 | + | 3.50353i | 0.609771 | + | 0.168955i | ||||
\(431\) | −33.8486 | −1.63043 | −0.815214 | − | 0.579159i | \(-0.803381\pi\) | ||||
−0.815214 | + | 0.579159i | \(0.803381\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.7047 | 1.04306 | 0.521531 | − | 0.853232i | \(-0.325361\pi\) | ||||
0.521531 | + | 0.853232i | \(0.325361\pi\) | |||||||
\(434\) | 0.486380 | + | 0.134766i | 0.0233470 | + | 0.00646897i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.3323 | − | 12.8045i | −1.02163 | − | 0.613225i | ||||
\(437\) | −5.25776 | + | 14.4456i | −0.251513 | + | 0.691026i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.8270 | + | 6.49360i | 1.75766 | + | 0.309923i | 0.957192 | − | 0.289454i | \(-0.0934737\pi\) |
0.800467 | + | 0.599377i | \(0.204585\pi\) | |||||||
\(440\) | 13.6691 | − | 12.9892i | 0.651649 | − | 0.619237i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.5662 | − | 19.0283i | 0.645280 | − | 0.905084i | ||||
\(443\) | −5.77721 | + | 2.10273i | −0.274484 | + | 0.0999039i | −0.475595 | − | 0.879665i | \(-0.657767\pi\) |
0.201111 | + | 0.979568i | \(0.435545\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.4610 | + | 12.9733i | −0.732922 | + | 0.614994i | ||||
\(446\) | 28.5324 | + | 13.6013i | 1.35105 | + | 0.644040i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.29660 | + | 14.3686i | −0.155750 | + | 0.678850i | ||||
\(449\) | −4.30776 | + | 2.48709i | −0.203296 | + | 0.117373i | −0.598192 | − | 0.801353i | \(-0.704114\pi\) |
0.394896 | + | 0.918726i | \(0.370781\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.3775 | + | 10.6103i | 0.865364 | + | 0.499618i | ||||
\(452\) | −5.88992 | + | 4.77400i | −0.277039 | + | 0.224550i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.38445 | + | 0.188206i | −0.111908 | + | 0.00883296i | ||||
\(455\) | 1.34540 | + | 7.63017i | 0.0630735 | + | 0.357708i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.14455 | + | 6.83409i | 0.380986 | + | 0.319685i | 0.813089 | − | 0.582139i | \(-0.197784\pi\) |
−0.432103 | + | 0.901824i | \(0.642228\pi\) | |||||||
\(458\) | −34.1416 | + | 15.5686i | −1.59533 | + | 0.727473i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.21217 | + | 6.26368i | 0.336269 | + | 0.292046i | ||||
\(461\) | 9.23017 | − | 11.0001i | 0.429892 | − | 0.512325i | −0.506999 | − | 0.861946i | \(-0.669245\pi\) |
0.936891 | + | 0.349621i | \(0.113690\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.9752 | + | 3.16951i | −0.835377 | + | 0.147300i | −0.574944 | − | 0.818192i | \(-0.694976\pi\) |
−0.260433 | + | 0.965492i | \(0.583865\pi\) | |||||||
\(464\) | −10.7241 | − | 2.26929i | −0.497855 | − | 0.105349i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.45255 | + | 1.67031i | −0.298908 | + | 0.0773755i | ||||
\(467\) | 11.4763 | − | 19.8775i | 0.531060 | − | 0.919823i | −0.468283 | − | 0.883579i | \(-0.655127\pi\) |
0.999343 | − | 0.0362446i | \(-0.0115395\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.92212 | + | 3.32921i | 0.0887553 | + | 0.153729i | ||||
\(470\) | −2.41450 | − | 2.45590i | −0.111373 | − | 0.113282i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.35961 | + | 10.0077i | 0.200667 | + | 0.460644i | ||||
\(473\) | 26.2628 | + | 31.2987i | 1.20756 | + | 1.43912i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.72176 | − | 12.9729i | −0.216649 | − | 0.595239i | ||||
\(476\) | 17.4957 | + | 3.39256i | 0.801914 | + | 0.155498i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.455585 | − | 4.74274i | 0.0208380 | − | 0.216928i | ||||
\(479\) | −3.05382 | + | 17.3191i | −0.139533 | + | 0.791329i | 0.832063 | + | 0.554681i | \(0.187160\pi\) |
−0.971596 | + | 0.236648i | \(0.923951\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.3170 | − | 8.12274i | −1.01757 | − | 0.370365i | ||||
\(482\) | −12.7942 | − | 18.6066i | −0.582759 | − | 0.847507i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 36.2630 | − | 5.76040i | 1.64832 | − | 0.261836i | ||||
\(485\) | 0.114735i | 0.00520984i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.6716i | − | 0.710147i | −0.934838 | − | 0.355073i | \(-0.884456\pi\) | ||
0.934838 | − | 0.355073i | \(-0.115544\pi\) | |||||||
\(488\) | −34.5782 | + | 22.9208i | −1.56528 | + | 1.03757i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.16785 | − | 3.55350i | 0.233460 | − | 0.160531i | ||||
\(491\) | 37.6017 | + | 13.6859i | 1.69694 | + | 0.617636i | 0.995471 | − | 0.0950638i | \(-0.0303055\pi\) |
0.701469 | + | 0.712700i | \(0.252528\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.30111 | + | 13.0502i | −0.103637 | + | 0.587754i | ||||
\(494\) | −19.0504 | − | 1.82998i | −0.857120 | − | 0.0823345i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.477493 | + | 0.610018i | 0.0214401 | + | 0.0273906i | ||||
\(497\) | −5.56755 | − | 15.2967i | −0.249739 | − | 0.686152i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.3375 | + | 15.8950i | 0.597067 | + | 0.711556i | 0.976948 | − | 0.213479i | \(-0.0684795\pi\) |
−0.379881 | + | 0.925035i | \(0.624035\pi\) | |||||||
\(500\) | −20.8796 | − | 0.354954i | −0.933763 | − | 0.0158740i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.0579 | − | 16.7703i | 0.761330 | − | 0.748497i | ||||
\(503\) | −2.51174 | − | 4.35046i | −0.111993 | − | 0.193977i | 0.804581 | − | 0.593843i | \(-0.202390\pi\) |
−0.916574 | + | 0.399866i | \(0.869057\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.742355 | − | 1.28580i | 0.0330344 | − | 0.0572172i | ||||
\(506\) | 7.45427 | + | 28.7965i | 0.331383 | + | 1.28016i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.1562 | + | 21.9068i | 0.539344 | + | 0.971959i | ||||
\(509\) | 21.4633 | − | 3.78456i | 0.951344 | − | 0.167748i | 0.323623 | − | 0.946186i | \(-0.395099\pi\) |
0.627721 | + | 0.778438i | \(0.283988\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.20730 | − | 7.39758i | 0.274595 | − | 0.327250i | ||||
\(512\) | −17.1759 | + | 14.7305i | −0.759075 | + | 0.651003i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.71393 | + | 3.75862i | 0.0755983 | + | 0.165785i | ||||
\(515\) | −14.8334 | − | 12.4467i | −0.653639 | − | 0.548468i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.86228 | − | 10.5615i | −0.0819030 | − | 0.464495i | ||||
\(518\) | −1.42511 | − | 18.0553i | −0.0626160 | − | 0.793304i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.29904 | + | 10.6464i | −0.232378 | + | 0.466876i | ||||
\(521\) | 8.39768 | + | 4.84840i | 0.367909 | + | 0.212412i | 0.672545 | − | 0.740057i | \(-0.265201\pi\) |
−0.304635 | + | 0.952469i | \(0.598535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.03420 | + | 1.75180i | −0.132676 | + | 0.0766007i | −0.564869 | − | 0.825181i | \(-0.691073\pi\) |
0.432193 | + | 0.901781i | \(0.357740\pi\) | |||||||
\(524\) | −2.48871 | + | 6.49213i | −0.108720 | + | 0.283610i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.0113786 | + | 0.0238696i | −0.000496129 | + | 0.00104076i | ||||
\(527\) | 0.717410 | − | 0.601978i | 0.0312509 | − | 0.0262226i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.45287 | − | 2.71262i | 0.324038 | − | 0.117940i | ||||
\(530\) | 15.9120 | + | 11.3445i | 0.691175 | + | 0.492773i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.75792 | − | 13.7976i | −0.206282 | − | 0.598203i | ||||
\(533\) | −13.1800 | − | 2.32398i | −0.570887 | − | 0.100663i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.43216 | + | 17.6722i | −0.278086 | + | 0.764036i | ||||
\(536\) | −0.663962 | + | 5.86308i | −0.0286788 | + | 0.253247i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.09210 | + | 21.9868i | −0.262649 | + | 0.947919i | ||||
\(539\) | 19.5296 | 0.841200 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.3365 | 1.08930 | 0.544652 | − | 0.838662i | \(-0.316662\pi\) | ||||
0.544652 | + | 0.838662i | \(0.316662\pi\) | |||||||
\(542\) | 8.64030 | − | 31.1835i | 0.371133 | − | 1.33944i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.5033 | + | 20.1468i | 0.793325 | + | 0.863788i | ||||
\(545\) | 5.23503 | − | 14.3831i | 0.224244 | − | 0.616106i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.82129 | − | 1.20278i | −0.291657 | − | 0.0514270i | 0.0259052 | − | 0.999664i | \(-0.491753\pi\) |
−0.317562 | + | 0.948237i | \(0.602864\pi\) | |||||||
\(548\) | −9.55790 | + | 3.29591i | −0.408293 | + | 0.140794i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −21.7512 | − | 15.5075i | −0.927476 | − | 0.661244i | ||||
\(551\) | 10.1979 | − | 3.71172i | 0.434443 | − | 0.158124i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.1949 | + | 9.39364i | −0.476056 | + | 0.399458i | ||||
\(554\) | 4.18487 | − | 8.77890i | 0.177798 | − | 0.372980i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.0963 | + | 4.63703i | 0.512998 | + | 0.196654i | ||||
\(557\) | 1.26444 | − | 0.730025i | 0.0535761 | − | 0.0309322i | −0.472973 | − | 0.881077i | \(-0.656819\pi\) |
0.526549 | + | 0.850145i | \(0.323486\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.3156 | − | 12.8839i | −0.943851 | − | 0.544932i | ||||
\(560\) | −9.06393 | − | 0.308264i | −0.383021 | − | 0.0130265i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.57783 | − | 19.9901i | −0.0665566 | − | 0.843229i | ||||
\(563\) | 5.77946 | + | 32.7770i | 0.243575 | + | 1.38138i | 0.823778 | + | 0.566912i | \(0.191862\pi\) |
−0.580203 | + | 0.814472i | \(0.697027\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.57302 | − | 2.99812i | −0.150318 | − | 0.126132i | ||||
\(566\) | −7.09010 | − | 15.5484i | −0.298019 | − | 0.653549i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.08002 | − | 23.9618i | 0.297071 | − | 1.00541i | ||||
\(569\) | −27.7062 | + | 33.0189i | −1.16150 | + | 1.38423i | −0.252417 | + | 0.967619i | \(0.581225\pi\) |
−0.909087 | + | 0.416607i | \(0.863219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.94615 | − | 1.57745i | 0.374385 | − | 0.0660141i | 0.0167100 | − | 0.999860i | \(-0.494681\pi\) |
0.357675 | + | 0.933846i | \(0.383570\pi\) | |||||||
\(572\) | −32.3805 | + | 17.9681i | −1.35390 | + | 0.751283i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.55768 | − | 9.88055i | −0.106756 | − | 0.412406i | ||||
\(575\) | 6.76632 | − | 11.7196i | 0.282175 | − | 0.488742i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.27460 | − | 2.20767i | −0.0530622 | − | 0.0919064i | 0.838274 | − | 0.545249i | \(-0.183565\pi\) |
−0.891336 | + | 0.453342i | \(0.850231\pi\) | |||||||
\(578\) | 6.43740 | − | 6.32890i | 0.267761 | − | 0.263247i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.114624 | − | 6.74257i | 0.00475950 | − | 0.279970i | ||||
\(581\) | −2.14972 | − | 2.56193i | −0.0891853 | − | 0.106287i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.8128 | + | 57.1827i | 0.861978 | + | 2.36827i | ||||
\(584\) | 14.4105 | − | 3.47005i | 0.596309 | − | 0.143592i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.26970 | − | 0.794383i | −0.341618 | − | 0.0328157i | ||||
\(587\) | −0.223906 | + | 1.26984i | −0.00924160 | + | 0.0524117i | −0.989080 | − | 0.147381i | \(-0.952916\pi\) |
0.979838 | + | 0.199793i | \(0.0640268\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.720701 | − | 0.262314i | −0.0296959 | − | 0.0108084i | ||||
\(590\) | −5.53360 | + | 3.80499i | −0.227815 | + | 0.156649i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.7100 | − | 23.5886i | 0.604577 | − | 0.969487i | ||||
\(593\) | 10.8961i | 0.447448i | 0.974652 | + | 0.223724i | \(0.0718215\pi\) | ||||
−0.974652 | + | 0.223724i | \(0.928179\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.9638i | 0.449472i | ||||||||
\(596\) | −1.65722 | − | 10.4326i | −0.0678823 | − | 0.427334i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.6292 | − | 15.4581i | −0.434661 | − | 0.632128i | ||||
\(599\) | 9.33315 | + | 3.39699i | 0.381342 | + | 0.138797i | 0.525576 | − | 0.850746i | \(-0.323850\pi\) |
−0.144234 | + | 0.989544i | \(0.546072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.10305 | + | 6.25571i | −0.0449943 | + | 0.255176i | −0.999005 | − | 0.0445969i | \(-0.985800\pi\) |
0.954011 | + | 0.299772i | \(0.0969108\pi\) | |||||||
\(602\) | 1.87900 | − | 19.5608i | 0.0765824 | − | 0.797239i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.36960 | − | 17.3773i | 0.137107 | − | 0.707071i | ||||
\(605\) | 7.72576 | + | 21.2263i | 0.314097 | + | 0.862974i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.0100 | + | 23.8470i | 0.812182 | + | 0.967921i | 0.999898 | − | 0.0143022i | \(-0.00455270\pi\) |
−0.187715 | + | 0.982223i | \(0.560108\pi\) | |||||||
\(608\) | 6.71207 | − | 21.3727i | 0.272211 | − | 0.866777i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.8924 | − | 18.1992i | −0.724443 | − | 0.736863i | ||||
\(611\) | 3.38182 | + | 5.85749i | 0.136814 | + | 0.236969i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.32449 | − | 9.22228i | 0.215054 | − | 0.372484i | −0.738235 | − | 0.674543i | \(-0.764341\pi\) |
0.953289 | + | 0.302059i | \(0.0976739\pi\) | |||||||
\(614\) | −5.61700 | + | 1.45402i | −0.226683 | + | 0.0586793i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.7130 | − | 16.7828i | −0.915134 | − | 0.676198i | ||||
\(617\) | −12.1176 | + | 2.13666i | −0.487835 | + | 0.0860185i | −0.412155 | − | 0.911114i | \(-0.635224\pi\) |
−0.0756800 | + | 0.997132i | \(0.524113\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.32369 | + | 2.76926i | −0.0933968 | + | 0.111306i | −0.810719 | − | 0.585436i | \(-0.800923\pi\) |
0.717322 | + | 0.696742i | \(0.245368\pi\) | |||||||
\(620\) | −0.312500 | + | 0.359820i | −0.0125503 | + | 0.0144507i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.63738 | − | 2.11465i | 0.185942 | − | 0.0847897i | ||||
\(623\) | 23.1556 | + | 19.4298i | 0.927709 | + | 0.778440i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.795955 | + | 4.51408i | 0.0318382 | + | 0.180563i | ||||
\(626\) | 30.0556 | − | 2.37231i | 1.20126 | − | 0.0948165i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.4935 | + | 15.4138i | 0.498544 | + | 0.615079i | ||||
\(629\) | −29.1045 | − | 16.8035i | −1.16047 | − | 0.669999i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.363542 | − | 0.209891i | 0.0144724 | − | 0.00835562i | −0.492746 | − | 0.870173i | \(-0.664007\pi\) |
0.507219 | + | 0.861817i | \(0.330674\pi\) | |||||||
\(632\) | −22.3882 | + | 1.38466i | −0.890555 | + | 0.0550786i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −44.8162 | − | 21.3637i | −1.77988 | − | 0.848461i | ||||
\(635\) | −11.8070 | + | 9.90723i | −0.468546 | + | 0.393156i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.5740 | + | 4.21261i | −0.458581 | + | 0.166910i | ||||
\(638\) | 12.1903 | − | 17.0984i | 0.482618 | − | 0.676930i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.9079 | − | 8.64826i | −0.431175 | − | 0.341852i | ||||
\(641\) | −27.4445 | − | 4.83920i | −1.08399 | − | 0.191137i | −0.397012 | − | 0.917813i | \(-0.629953\pi\) |
−0.686980 | + | 0.726676i | \(0.741064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.89822 | − | 27.1951i | 0.390348 | − | 1.07247i | −0.576495 | − | 0.817100i | \(-0.695580\pi\) |
0.966843 | − | 0.255371i | \(-0.0821977\pi\) | |||||||
\(644\) | 7.36280 | − | 12.2664i | 0.290135 | − | 0.483363i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −26.0985 | − | 7.23137i | −1.02683 | − | 0.284514i | ||||
\(647\) | −20.3805 | −0.801241 | −0.400620 | − | 0.916244i | \(-0.631205\pi\) | ||||
−0.400620 | + | 0.916244i | \(0.631205\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.9118 | −0.820860 | ||||||||
\(650\) | 16.2357 | + | 4.49858i | 0.636817 | + | 0.176449i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.7681 | + | 27.9355i | −0.656689 | + | 1.09404i | ||||
\(653\) | −14.1421 | + | 38.8551i | −0.553424 | + | 1.52052i | 0.275581 | + | 0.961278i | \(0.411130\pi\) |
−0.829005 | + | 0.559241i | \(0.811093\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.21236 | − | 0.742753i | −0.164591 | − | 0.0290218i | ||||
\(656\) | 5.85523 | − | 14.5302i | 0.228608 | − | 0.567310i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.99433 | + | 4.19991i | −0.116731 | + | 0.163730i | ||||
\(659\) | 14.0070 | − | 5.09812i | 0.545634 | − | 0.198595i | −0.0544714 | − | 0.998515i | \(-0.517347\pi\) |
0.600106 | + | 0.799921i | \(0.295125\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.3934 | − | 14.5948i | 0.676525 | − | 0.567672i | −0.238463 | − | 0.971151i | \(-0.576644\pi\) |
0.914989 | + | 0.403479i | \(0.132199\pi\) | |||||||
\(662\) | 0.304096 | + | 0.144962i | 0.0118190 | + | 0.00563409i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.316876 | − | 5.12350i | −0.0122972 | − | 0.198830i | ||||
\(665\) | 7.77584 | − | 4.48939i | 0.301534 | − | 0.174091i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.21264 | + | 5.31892i | 0.356715 | + | 0.205949i | ||||
\(668\) | −1.56044 | − | 1.92519i | −0.0603751 | − | 0.0744877i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.61875 | + | 0.285630i | −0.139805 | + | 0.0110349i | ||||
\(671\) | −13.8002 | − | 78.2651i | −0.532752 | − | 3.02139i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.8262 | − | 21.6708i | −0.995527 | − | 0.835346i | −0.00916851 | − | 0.999958i | \(-0.502918\pi\) |
−0.986358 | + | 0.164612i | \(0.947363\pi\) | |||||||
\(674\) | −8.62597 | + | 3.93345i | −0.332260 | + | 0.151511i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.73436 | + | 1.99698i | −0.0667060 | + | 0.0768071i | ||||
\(677\) | 21.5588 | − | 25.6927i | 0.828571 | − | 0.987452i | −0.171427 | − | 0.985197i | \(-0.554838\pi\) |
0.999997 | − | 0.00225532i | \(-0.000717892\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.169225 | − | 0.0298390i | 0.00649427 | − | 0.00114511i | ||||
\(680\) | −10.0007 | + | 13.5345i | −0.383509 | + | 0.519023i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.43668 | + | 0.371899i | −0.0550133 | + | 0.0142408i | ||||
\(683\) | 13.6418 | − | 23.6283i | 0.521989 | − | 0.904112i | −0.477684 | − | 0.878532i | \(-0.658523\pi\) |
0.999673 | − | 0.0255798i | \(-0.00814320\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.10989 | − | 5.38649i | −0.118823 | − | 0.205807i | ||||
\(686\) | −19.3742 | − | 19.7063i | −0.739710 | − | 0.752392i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.1621 | − | 22.4333i | 0.768672 | − | 0.855260i | ||||
\(689\) | −24.6690 | − | 29.3994i | −0.939816 | − | 1.12003i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.43220 | − | 20.4198i | −0.282734 | − | 0.776806i | −0.997034 | − | 0.0769659i | \(-0.975477\pi\) |
0.714299 | − | 0.699840i | \(-0.246745\pi\) | |||||||
\(692\) | −5.49857 | + | 28.3566i | −0.209024 | + | 1.07796i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.951115 | + | 9.90131i | −0.0361038 | + | 0.375849i | ||||
\(695\) | −1.38392 | + | 7.84859i | −0.0524950 | + | 0.297714i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.7962 | − | 6.47728i | −0.674079 | − | 0.245345i | ||||
\(698\) | −5.70969 | − | 8.30361i | −0.216115 | − | 0.314296i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.01564 | + | 12.6889i | 0.0761842 | + | 0.479596i | ||||
\(701\) | 16.5491i | 0.625051i | 0.949909 | + | 0.312526i | \(0.101175\pi\) | ||||
−0.949909 | + | 0.312526i | \(0.898825\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.5223i | 1.03802i | ||||||||
\(704\) | −12.7300 | − | 41.4356i | −0.479780 | − | 1.56166i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.3301 | − | 12.6041i | 0.689863 | − | 0.474361i | ||||
\(707\) | −2.08952 | − | 0.760521i | −0.0785843 | − | 0.0286023i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.05285 | − | 22.9848i | 0.152208 | − | 0.863214i | −0.809086 | − | 0.587690i | \(-0.800038\pi\) |
0.961294 | − | 0.275524i | \(-0.0888514\pi\) | |||||||
\(710\) | 15.3008 | + | 1.46979i | 0.574230 | + | 0.0551602i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.8618 | + | 45.1070i | 0.407063 | + | 1.69046i | ||||
\(713\) | −0.257129 | − | 0.706456i | −0.00962955 | − | 0.0264570i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.6439 | − | 17.4519i | −0.547651 | − | 0.652665i | ||||
\(716\) | −0.339618 | + | 19.9775i | −0.0126921 | + | 0.746593i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.6797 | + | 12.4660i | −0.473204 | + | 0.465228i | ||||
\(719\) | 25.8381 | + | 44.7529i | 0.963599 | + | 1.66900i | 0.713334 | + | 0.700825i | \(0.247184\pi\) |
0.250265 | + | 0.968177i | \(0.419482\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.5003 | + | 25.1152i | −0.540018 | + | 0.935338i | ||||
\(722\) | −1.17568 | − | 4.54177i | −0.0437545 | − | 0.169027i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.7373 | + | 11.5072i | −0.770694 | + | 0.427661i | ||||
\(725\) | −9.40824 | + | 1.65893i | −0.349413 | + | 0.0616110i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.38738 | − | 8.80393i | 0.273983 | − | 0.326520i | −0.611454 | − | 0.791280i | \(-0.709415\pi\) |
0.885437 | + | 0.464760i | \(0.153859\pi\) | |||||||
\(728\) | 17.0808 | + | 5.04688i | 0.633056 | + | 0.187050i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.78335 | + | 8.29679i | 0.140028 | + | 0.307078i | ||||
\(731\) | −27.9326 | − | 23.4382i | −1.03312 | − | 0.866894i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.49588 | + | 25.4974i | 0.166059 | + | 0.941768i | 0.947966 | + | 0.318373i | \(0.103136\pi\) |
−0.781906 | + | 0.623396i | \(0.785753\pi\) | |||||||
\(734\) | −2.42899 | − | 30.7737i | −0.0896556 | − | 1.13588i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.2780 | − | 8.42645i | 0.747457 | − | 0.310603i | ||||
\(737\) | −9.78921 | − | 5.65181i | −0.360590 | − | 0.208187i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.0700 | + | 15.6289i | −0.995786 | + | 0.574917i | −0.906999 | − | 0.421133i | \(-0.861633\pi\) |
−0.0887874 | + | 0.996051i | \(0.528299\pi\) | |||||||
\(740\) | 15.9690 | + | 6.12159i | 0.587032 | + | 0.225034i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.5940 | − | 26.4194i | 0.462341 | − | 0.969887i | ||||
\(743\) | 36.0136 | − | 30.2190i | 1.32121 | − | 1.10863i | 0.335166 | − | 0.942159i | \(-0.391208\pi\) |
0.986047 | − | 0.166470i | \(-0.0532368\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.10664 | − | 2.22264i | 0.223730 | − | 0.0814311i | ||||
\(746\) | −17.4264 | − | 12.4241i | −0.638025 | − | 0.454880i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −49.5399 | + | 17.0832i | −1.81136 | + | 0.624622i | ||||
\(749\) | 27.7380 | + | 4.89095i | 1.01352 | + | 0.178711i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.24256 | + | 8.90885i | −0.118323 | + | 0.325089i | −0.984689 | − | 0.174320i | \(-0.944227\pi\) |
0.866366 | + | 0.499409i | \(0.166449\pi\) | |||||||
\(752\) | −7.52738 | + | 2.45337i | −0.274495 | + | 0.0894650i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.53628 | + | 12.7627i | −0.128784 | + | 0.464789i | ||||
\(755\) | 10.8896 | 0.396313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.0979 | −1.67546 | −0.837728 | − | 0.546087i | \(-0.816117\pi\) | ||||
−0.837728 | + | 0.546087i | \(0.816117\pi\) | |||||||
\(758\) | −9.75636 | + | 35.2114i | −0.354367 | + | 1.27894i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.6941 | + | 1.55078i | 0.496736 | + | 0.0562526i | ||||
\(761\) | 1.59797 | − | 4.39038i | 0.0579263 | − | 0.159151i | −0.907354 | − | 0.420367i | \(-0.861901\pi\) |
0.965280 | + | 0.261216i | \(0.0841235\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.5755 | − | 3.98067i | −0.817288 | − | 0.144110i | ||||
\(764\) | 0.115992 | + | 0.336367i | 0.00419644 | + | 0.0121693i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.35955 | − | 3.82109i | −0.193649 | − | 0.138062i | ||||
\(767\) | 12.3932 | − | 4.51075i | 0.447492 | − | 0.162874i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.4826 | − | 15.5088i | 0.666501 | − | 0.559261i | −0.245526 | − | 0.969390i | \(-0.578961\pi\) |
0.912028 | + | 0.410129i | \(0.134516\pi\) | |||||||
\(770\) | 7.47599 | − | 15.6829i | 0.269416 | − | 0.565173i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.98793 | − | 13.0117i | 0.179519 | − | 0.468301i | ||||
\(773\) | 37.2078 | − | 21.4820i | 1.33827 | − | 0.772652i | 0.351722 | − | 0.936105i | \(-0.385596\pi\) |
0.986551 | + | 0.163452i | \(0.0522630\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.584701 | + | 0.337577i | 0.0210031 | + | 0.0121261i | ||||
\(776\) | 0.236121 | + | 0.117524i | 0.00847625 | + | 0.00421888i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.17516 | − | 40.2273i | −0.113835 | − | 1.44222i | ||||
\(779\) | 2.69319 | + | 15.2738i | 0.0964935 | + | 0.547242i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.6668 | + | 30.7671i | 1.31204 | + | 1.10093i | ||||
\(782\) | −11.0142 | − | 24.1538i | −0.393866 | − | 0.863739i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.01949 | − | 14.2752i | −0.0721247 | − | 0.509828i | ||||
\(785\) | −7.84603 | + | 9.35054i | −0.280037 | + | 0.333735i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.5797 | − | 3.45243i | 0.697940 | − | 0.123066i | 0.186590 | − | 0.982438i | \(-0.440257\pi\) |
0.511350 | + | 0.859372i | \(0.329145\pi\) | |||||||
\(788\) | −5.28356 | − | 9.52158i | −0.188219 | − | 0.339192i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.45816 | − | 13.3592i | −0.123036 | − | 0.475298i | ||||
\(791\) | −3.49277 | + | 6.04966i | −0.124189 | + | 0.215101i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.0606 | + | 43.4063i | 0.889930 | + | 1.54140i | ||||
\(794\) | −1.98369 | + | 1.95025i | −0.0703985 | + | 0.0692119i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.9770 | − | 0.203609i | −0.424512 | − | 0.00721673i | ||||
\(797\) | −0.657198 | − | 0.783218i | −0.0232792 | − | 0.0277430i | 0.754279 | − | 0.656554i | \(-0.227986\pi\) |
−0.777558 | + | 0.628811i | \(0.783542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.27349 | + | 8.99384i | 0.115808 | + | 0.318179i | ||||
\(800\) | −9.08602 | + | 17.5027i | −0.321239 | + | 0.618812i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26.7952 | + | 2.57394i | 0.946172 | + | 0.0908888i | ||||
\(803\) | −4.93074 | + | 27.9636i | −0.174002 | + | 0.986815i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.27052 | + | 3.01022i | 0.291498 | + | 0.106096i | ||||
\(806\) | 0.771215 | − | 0.530300i | 0.0271649 | − | 0.0186790i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.88573 | − | 2.84480i | −0.0663396 | − | 0.100080i | ||||
\(809\) | 7.34131i | 0.258107i | 0.991638 | + | 0.129053i | \(0.0411938\pi\) | ||||
−0.991638 | + | 0.129053i | \(0.958806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 51.3514i | − | 1.80319i | −0.432581 | − | 0.901595i | \(-0.642397\pi\) | ||
0.432581 | − | 0.901595i | \(-0.357603\pi\) | |||||||
\(812\) | −9.97459 | + | 1.58447i | −0.350039 | + | 0.0556040i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 30.1739 | + | 43.8819i | 1.05759 | + | 1.53806i | ||||
\(815\) | −18.8353 | − | 6.85550i | −0.659773 | − | 0.240138i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.18541 | + | 29.4079i | −0.181415 | + | 1.02885i | ||||
\(818\) | −1.98346 | + | 20.6482i | −0.0693499 | + | 0.721947i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.46122 | + | 1.83461i | 0.330400 | + | 0.0640673i | ||||
\(821\) | 11.7882 | + | 32.3878i | 0.411411 | + | 1.13034i | 0.956441 | + | 0.291926i | \(0.0942960\pi\) |
−0.545030 | + | 0.838416i | \(0.683482\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.1050 | − | 35.8777i | −1.04939 | − | 1.25062i | −0.967204 | − | 0.254001i | \(-0.918253\pi\) |
−0.0821894 | − | 0.996617i | \(-0.526191\pi\) | |||||||
\(824\) | −40.8091 | + | 17.7774i | −1.42165 | + | 0.619305i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.05119 | + | 7.17208i | 0.245342 | + | 0.249548i | ||||
\(827\) | 19.3141 | + | 33.4530i | 0.671616 | + | 1.16327i | 0.977446 | + | 0.211187i | \(0.0677329\pi\) |
−0.305830 | + | 0.952086i | \(0.598934\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.2958 | − | 23.0290i | 0.461782 | − | 0.799830i | −0.537268 | − | 0.843412i | \(-0.680543\pi\) |
0.999050 | + | 0.0435815i | \(0.0138768\pi\) | |||||||
\(830\) | 3.05722 | − | 0.791393i | 0.106118 | − | 0.0274696i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16.4821 | + | 21.8105i | 0.571415 | + | 0.756145i | ||||
\(833\) | −17.1644 | + | 3.02655i | −0.594712 | + | 0.104864i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.979970 | − | 1.16788i | 0.0339132 | − | 0.0404162i | ||||
\(836\) | 32.4011 | + | 28.1400i | 1.12062 | + | 0.973243i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.9011 | + | 6.79491i | −0.514749 | + | 0.234726i | ||||
\(839\) | −38.1735 | − | 32.0314i | −1.31790 | − | 1.10585i | −0.986747 | − | 0.162268i | \(-0.948119\pi\) |
−0.331150 | − | 0.943578i | \(-0.607437\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.73174 | + | 21.1637i | 0.128681 | + | 0.729784i | ||||
\(842\) | 1.74971 | − | 0.138105i | 0.0602988 | − | 0.00475942i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 40.3280 | − | 32.6873i | 1.38815 | − | 1.12514i | ||||
\(845\) | −1.40919 | − | 0.813594i | −0.0484775 | − | 0.0279885i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.2980 | − | 16.9152i | 1.00669 | − | 0.581214i | ||||
\(848\) | 39.6455 | − | 21.1262i | 1.36143 | − | 0.725476i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 21.5202 | + | 10.2586i | 0.738138 | + | 0.351868i | ||||
\(851\) | −20.6666 | + | 17.3413i | −0.708442 | + | 0.594453i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.7953 | + | 12.6644i | −1.19137 | + | 0.433622i | −0.860203 | − | 0.509951i | \(-0.829664\pi\) |
−0.331164 | + | 0.943573i | \(0.607441\pi\) | |||||||
\(854\) | −22.1891 | + | 31.1230i | −0.759297 | + | 1.06501i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.7803 | + | 31.3391i | 1.01787 | + | 1.07115i | ||||
\(857\) | 30.2150 | + | 5.32771i | 1.03212 | + | 0.181991i | 0.663959 | − | 0.747769i | \(-0.268875\pi\) |
0.368165 | + | 0.929761i | \(0.379986\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.72321 | − | 18.4719i | 0.229393 | − | 0.630252i | −0.770582 | − | 0.637341i | \(-0.780034\pi\) |
0.999975 | + | 0.00708895i | \(0.00225650\pi\) | |||||||
\(860\) | 15.9097 | + | 9.54967i | 0.542517 | + | 0.325641i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −46.1311 | − | 12.7820i | −1.57123 | − | 0.435356i | ||||
\(863\) | −5.14051 | −0.174985 | −0.0874925 | − | 0.996165i | \(-0.527885\pi\) | ||||
−0.0874925 | + | 0.996165i | \(0.527885\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.7698 | −0.604193 | ||||||||
\(866\) | 29.5806 | + | 8.19618i | 1.00519 | + | 0.278518i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.611979 | + | 0.367335i | 0.0207719 | + | 0.0124682i | ||||
\(869\) | 14.6969 | − | 40.3793i | 0.498557 | − | 1.36977i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.02060 | + | 1.23792i | 0.237884 | + | 0.0419454i | ||||
\(872\) | −24.2377 | − | 25.5064i | −0.820794 | − | 0.863755i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.6206 | + | 17.7019i | −0.426898 | + | 0.598776i | ||||
\(875\) | −18.0802 | + | 6.58065i | −0.611222 | + | 0.222467i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.7096 | − | 33.3203i | 1.34090 | − | 1.12515i | 0.359504 | − | 0.933143i | \(-0.382946\pi\) |
0.981394 | − | 0.192004i | \(-0.0614986\pi\) | |||||||
\(878\) | 47.7382 | + | 22.7566i | 1.61109 | + | 0.767999i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 23.5342 | − | 12.5408i | 0.793336 | − | 0.422751i | ||||
\(881\) | 28.7442 | − | 16.5955i | 0.968418 | − | 0.559116i | 0.0696643 | − | 0.997570i | \(-0.477807\pi\) |
0.898754 | + | 0.438454i | \(0.144474\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.2856 | + | 18.0627i | 1.05284 | + | 0.607859i | 0.923444 | − | 0.383733i | \(-0.125362\pi\) |
0.129399 | + | 0.991593i | \(0.458695\pi\) | |||||||
\(884\) | 25.6745 | − | 20.8101i | 0.863525 | − | 0.699920i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.66760 | + | 0.684138i | −0.291194 | + | 0.0229841i | ||||
\(887\) | 4.04900 | + | 22.9630i | 0.135952 | + | 0.771023i | 0.974192 | + | 0.225721i | \(0.0724739\pi\) |
−0.838240 | + | 0.545302i | \(0.816415\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.6830 | + | 14.8378i | 0.593070 | + | 0.497645i | ||||
\(890\) | −25.9703 | + | 11.8425i | −0.870525 | + | 0.396960i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 33.7497 | + | 29.3112i | 1.13002 | + | 0.981412i | ||||
\(893\) | 5.03828 | − | 6.00439i | 0.168600 | − | 0.200929i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.1051 | + | 2.13446i | −0.404630 | + | 0.0713472i | ||||
\(896\) | −9.91870 | + | 18.3375i | −0.331361 | + | 0.612614i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.81008 | + | 1.76286i | −0.227255 | + | 0.0588273i | ||||
\(899\) | −0.265365 | + | 0.459625i | −0.00885041 | + | 0.0153294i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.1540 | − | 47.0321i | −0.904630 | − | 1.56687i | ||||
\(902\) | 21.0394 | + | 21.4001i | 0.700536 | + | 0.712547i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.82994 | + | 4.28216i | −0.326939 | + | 0.142422i | ||||
\(905\) | −9.37829 | − | 11.1766i | −0.311745 | − | 0.371523i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.67374 | + | 12.8410i | 0.155189 | + | 0.426379i | 0.992784 | − | 0.119913i | \(-0.0382614\pi\) |
−0.837595 | + | 0.546291i | \(0.816039\pi\) | |||||||
\(908\) | −3.32076 | − | 0.643923i | −0.110203 | − | 0.0213693i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.04772 | + | 10.9069i | −0.0347314 | + | 0.361562i | ||||
\(911\) | 4.68110 | − | 26.5479i | 0.155092 | − | 0.879570i | −0.803610 | − | 0.595156i | \(-0.797090\pi\) |
0.958702 | − | 0.284413i | \(-0.0917988\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.24072 | + | 3.36335i | 0.305823 | + | 0.111311i | ||||
\(914\) | 8.51922 | + | 12.3895i | 0.281791 | + | 0.409808i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −52.4094 | + | 8.32528i | −1.73166 | + | 0.275075i | ||||
\(917\) | 6.40608i | 0.211547i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 10.8263i | − | 0.357127i | −0.983928 | − | 0.178563i | \(-0.942855\pi\) | ||
0.983928 | − | 0.178563i | \(-0.0571449\pi\) | |||||||
\(920\) | 7.46391 | + | 11.2600i | 0.246078 | + | 0.371232i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.7334 | − | 11.5061i | 0.551084 | − | 0.378934i | ||||
\(923\) | −28.3668 | − | 10.3247i | −0.933705 | − | 0.339841i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.20716 | − | 23.8600i | 0.138331 | − | 0.784512i | ||||
\(926\) | −25.6946 | − | 2.46821i | −0.844377 | − | 0.0811105i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.7586 | − | 7.14240i | −0.451648 | − | 0.234461i | ||||
\(929\) | −5.88119 | − | 16.1584i | −0.192956 | − | 0.530141i | 0.805054 | − | 0.593201i | \(-0.202136\pi\) |
−0.998010 | + | 0.0630604i | \(0.979914\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.17490 | + | 10.9342i | 0.300695 | + | 0.358355i | ||||
\(932\) | −9.42470 | − | 0.160220i | −0.308716 | − | 0.00524819i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.1469 | − | 22.7567i | 0.757389 | − | 0.744622i | ||||
\(935\) | −16.1190 | − | 27.9189i | −0.527147 | − | 0.913046i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.74943 | − | 16.8865i | 0.318500 | − | 0.551658i | −0.661675 | − | 0.749791i | \(-0.730154\pi\) |
0.980175 | + | 0.198132i | \(0.0634876\pi\) | |||||||
\(938\) | 1.36241 | + | 5.26310i | 0.0444842 | + | 0.171846i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.36324 | − | 4.25883i | −0.0770804 | − | 0.138908i | ||||
\(941\) | 2.10956 | − | 0.371973i | 0.0687698 | − | 0.0121260i | −0.139157 | − | 0.990270i | \(-0.544439\pi\) |
0.207927 | + | 0.978144i | \(0.433328\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.77225 | + | 11.6461i | −0.318228 | + | 0.379250i | ||||
\(944\) | 2.16242 | + | 15.2855i | 0.0703807 | + | 0.497500i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.9735 | + | 52.5733i | 0.779446 | + | 1.70931i | ||||
\(947\) | 32.2731 | + | 27.0803i | 1.04873 | + | 0.879992i | 0.992960 | − | 0.118452i | \(-0.0377930\pi\) |
0.0557737 | + | 0.998443i | \(0.482237\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.10970 | − | 17.6360i | −0.100945 | − | 0.572488i | ||||
\(950\) | −1.53626 | − | 19.4634i | −0.0498428 | − | 0.631476i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 22.5632 | + | 11.2304i | 0.731277 | + | 0.363978i | ||||
\(953\) | −19.8498 | − | 11.4603i | −0.642999 | − | 0.371236i | 0.142770 | − | 0.989756i | \(-0.454399\pi\) |
−0.785769 | + | 0.618520i | \(0.787732\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.189565 | + | 0.109445i | −0.00613417 | + | 0.00354156i | ||||
\(956\) | 2.41186 | − | 6.29167i | 0.0780053 | − | 0.203487i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.7020 | + | 22.4504i | −0.345766 | + | 0.725339i | ||||
\(959\) | −7.13588 | + | 5.98771i | −0.230430 | + | 0.193353i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0952 | + | 10.5898i | −0.938556 | + | 0.341606i | ||||
\(962\) | −27.3478 | − | 19.4976i | −0.881728 | − | 0.628628i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.4105 | − | 30.1897i | −0.335299 | − | 0.972343i | ||||
\(965\) | 8.44252 | + | 1.48864i | 0.271774 | + | 0.0479212i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.1549 | + | 38.8902i | −0.455190 | + | 1.25062i | 0.473837 | + | 0.880613i | \(0.342869\pi\) |
−0.929027 | + | 0.370012i | \(0.879354\pi\) | |||||||
\(968\) | 51.5968 | + | 5.84305i | 1.65838 | + | 0.187803i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.0433264 | + | 0.156368i | −0.00139113 | + | 0.00502068i | ||||
\(971\) | −14.7098 | −0.472061 | −0.236030 | − | 0.971746i | \(-0.575847\pi\) | ||||
−0.236030 | + | 0.971746i | \(0.575847\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.9360 | 0.382650 | ||||||||
\(974\) | 5.91793 | − | 21.3582i | 0.189623 | − | 0.684362i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −55.7808 | + | 18.1804i | −1.78550 | + | 0.581941i | ||||
\(977\) | 11.1196 | − | 30.5509i | 0.355748 | − | 0.977409i | −0.624741 | − | 0.780832i | \(-0.714795\pi\) |
0.980488 | − | 0.196577i | \(-0.0629825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −87.5305 | − | 15.4340i | −2.79749 | − | 0.493273i | ||||
\(980\) | 8.38496 | − | 2.89144i | 0.267848 | − | 0.0923637i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 46.0779 | + | 32.8513i | 1.47041 | + | 1.04833i | ||||
\(983\) | −49.0400 | + | 17.8491i | −1.56413 | + | 0.569298i | −0.971679 | − | 0.236306i | \(-0.924063\pi\) |
−0.592455 | + | 0.805604i | \(0.701841\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.13178 | − | 4.30607i | 0.163512 | − | 0.137203i | ||||
\(986\) | −8.06417 | + | 16.9168i | −0.256815 | + | 0.538740i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25.2721 | − | 9.68788i | −0.804014 | − | 0.308212i | ||||
\(989\) | −25.3498 | + | 14.6357i | −0.806075 | + | 0.465388i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.1645 | − | 9.90990i | −0.545247 | − | 0.314798i | 0.201956 | − | 0.979395i | \(-0.435270\pi\) |
−0.747203 | + | 0.664596i | \(0.768604\pi\) | |||||||
\(992\) | 0.420402 | + | 1.01168i | 0.0133478 | + | 0.0321210i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.81144 | − | 22.9498i | −0.0574554 | − | 0.727923i | ||||
\(995\) | −1.27966 | − | 7.25731i | −0.0405679 | − | 0.230072i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.62058 | + | 1.35983i | 0.0513244 | + | 0.0430663i | 0.668089 | − | 0.744081i | \(-0.267113\pi\) |
−0.616765 | + | 0.787148i | \(0.711557\pi\) | |||||||
\(998\) | 12.1749 | + | 26.6992i | 0.385389 | + | 0.845149i | ||||
\(999\) | 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 | 324.2.l.a.35.15 | 96 | ||
3.2 | odd | 2 | 108.2.l.a.11.2 | ✓ | 96 | ||
4.3 | odd | 2 | inner | 324.2.l.a.35.5 | 96 | ||
9.2 | odd | 6 | 972.2.l.d.755.9 | 96 | |||
9.4 | even | 3 | 972.2.l.b.431.4 | 96 | |||
9.5 | odd | 6 | 972.2.l.c.431.13 | 96 | |||
9.7 | even | 3 | 972.2.l.a.755.8 | 96 | |||
12.11 | even | 2 | 108.2.l.a.11.12 | yes | 96 | ||
27.4 | even | 9 | 972.2.l.d.215.11 | 96 | |||
27.5 | odd | 18 | inner | 324.2.l.a.287.5 | 96 | ||
27.13 | even | 9 | 972.2.l.c.539.1 | 96 | |||
27.14 | odd | 18 | 972.2.l.b.539.16 | 96 | |||
27.22 | even | 9 | 108.2.l.a.59.12 | yes | 96 | ||
27.23 | odd | 18 | 972.2.l.a.215.6 | 96 | |||
36.7 | odd | 6 | 972.2.l.a.755.6 | 96 | |||
36.11 | even | 6 | 972.2.l.d.755.11 | 96 | |||
36.23 | even | 6 | 972.2.l.c.431.1 | 96 | |||
36.31 | odd | 6 | 972.2.l.b.431.16 | 96 | |||
108.23 | even | 18 | 972.2.l.a.215.8 | 96 | |||
108.31 | odd | 18 | 972.2.l.d.215.9 | 96 | |||
108.59 | even | 18 | inner | 324.2.l.a.287.15 | 96 | ||
108.67 | odd | 18 | 972.2.l.c.539.13 | 96 | |||
108.95 | even | 18 | 972.2.l.b.539.4 | 96 | |||
108.103 | odd | 18 | 108.2.l.a.59.2 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.l.a.11.2 | ✓ | 96 | 3.2 | odd | 2 | ||
108.2.l.a.11.12 | yes | 96 | 12.11 | even | 2 | ||
108.2.l.a.59.2 | yes | 96 | 108.103 | odd | 18 | ||
108.2.l.a.59.12 | yes | 96 | 27.22 | even | 9 | ||
324.2.l.a.35.5 | 96 | 4.3 | odd | 2 | inner | ||
324.2.l.a.35.15 | 96 | 1.1 | even | 1 | trivial | ||
324.2.l.a.287.5 | 96 | 27.5 | odd | 18 | inner | ||
324.2.l.a.287.15 | 96 | 108.59 | even | 18 | inner | ||
972.2.l.a.215.6 | 96 | 27.23 | odd | 18 | |||
972.2.l.a.215.8 | 96 | 108.23 | even | 18 | |||
972.2.l.a.755.6 | 96 | 36.7 | odd | 6 | |||
972.2.l.a.755.8 | 96 | 9.7 | even | 3 | |||
972.2.l.b.431.4 | 96 | 9.4 | even | 3 | |||
972.2.l.b.431.16 | 96 | 36.31 | odd | 6 | |||
972.2.l.b.539.4 | 96 | 108.95 | even | 18 | |||
972.2.l.b.539.16 | 96 | 27.14 | odd | 18 | |||
972.2.l.c.431.1 | 96 | 36.23 | even | 6 | |||
972.2.l.c.431.13 | 96 | 9.5 | odd | 6 | |||
972.2.l.c.539.1 | 96 | 27.13 | even | 9 | |||
972.2.l.c.539.13 | 96 | 108.67 | odd | 18 | |||
972.2.l.d.215.9 | 96 | 108.31 | odd | 18 | |||
972.2.l.d.215.11 | 96 | 27.4 | even | 9 | |||
972.2.l.d.755.9 | 96 | 9.2 | odd | 6 | |||
972.2.l.d.755.11 | 96 | 36.11 | even | 6 |