Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(685,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.685");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.g (of order \(2\), degree \(1\), 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: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 685.5 | ||
Root | \(1.12629 + 0.855255i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.685 |
Dual form | 1368.2.g.b.685.6 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.855255 | − | 1.12629i | −0.604757 | − | 0.796410i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.537077 | + | 1.92654i | −0.268538 | + | 0.963269i | ||||
\(5\) | 1.51356i | 0.676885i | 0.940987 | + | 0.338442i | \(0.109900\pi\) | ||||
−0.940987 | + | 0.338442i | \(0.890100\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.580162 | 0.219281 | 0.109640 | − | 0.993971i | \(-0.465030\pi\) | ||||
0.109640 | + | 0.993971i | \(0.465030\pi\) | |||||||
\(8\) | 2.62919 | − | 1.04278i | 0.929558 | − | 0.368677i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.70471 | − | 1.29448i | 0.539078 | − | 0.409351i | ||||
\(11\) | − | 1.31799i | − | 0.397388i | −0.980062 | − | 0.198694i | \(-0.936330\pi\) | ||
0.980062 | − | 0.198694i | \(-0.0636700\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.89230i | − | 1.07953i | −0.841816 | − | 0.539765i | \(-0.818513\pi\) | ||
0.841816 | − | 0.539765i | \(-0.181487\pi\) | |||||||
\(14\) | −0.496186 | − | 0.653433i | −0.132611 | − | 0.174637i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.42310 | − | 2.06940i | −0.855774 | − | 0.517349i | ||||
\(17\) | 1.20142 | 0.291388 | 0.145694 | − | 0.989330i | \(-0.453459\pi\) | ||||
0.145694 | + | 0.989330i | \(0.453459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | −2.91593 | − | 0.812898i | −0.652022 | − | 0.181770i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.48444 | + | 1.12722i | −0.316484 | + | 0.240323i | ||||
\(23\) | −5.85527 | −1.22091 | −0.610454 | − | 0.792052i | \(-0.709013\pi\) | ||||
−0.610454 | + | 0.792052i | \(0.709013\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.70913 | 0.541827 | ||||||||
\(26\) | −4.38387 | + | 3.32891i | −0.859748 | + | 0.652853i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.311591 | + | 1.11770i | −0.0588853 | + | 0.211226i | ||||
\(29\) | 1.29188i | 0.239896i | 0.992780 | + | 0.119948i | \(0.0382727\pi\) | ||||
−0.992780 | + | 0.119948i | \(0.961727\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.96413 | 0.532374 | 0.266187 | − | 0.963921i | \(-0.414236\pi\) | ||||
0.266187 | + | 0.963921i | \(0.414236\pi\) | |||||||
\(32\) | 0.596871 | + | 5.62528i | 0.105513 | + | 0.994418i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.02752 | − | 1.35316i | −0.176219 | − | 0.232064i | ||||
\(35\) | 0.878110i | 0.148428i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.18418i | 0.194677i | 0.995251 | + | 0.0973387i | \(0.0310330\pi\) | ||||
−0.995251 | + | 0.0973387i | \(0.968967\pi\) | |||||||
\(38\) | −1.12629 | + | 0.855255i | −0.182709 | + | 0.138741i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.57830 | + | 3.97943i | 0.249552 | + | 0.629204i | ||||
\(41\) | 9.04577 | 1.41271 | 0.706356 | − | 0.707856i | \(-0.250338\pi\) | ||||
0.706356 | + | 0.707856i | \(0.250338\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.38816i | − | 1.27918i | −0.768715 | − | 0.639592i | \(-0.779104\pi\) | ||
0.768715 | − | 0.639592i | \(-0.220896\pi\) | |||||||
\(44\) | 2.53915 | + | 0.707861i | 0.382792 | + | 0.106714i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.00775 | + | 6.59475i | 0.738352 | + | 0.972343i | ||||
\(47\) | 12.8560 | 1.87524 | 0.937620 | − | 0.347661i | \(-0.113024\pi\) | ||||
0.937620 | + | 0.347661i | \(0.113024\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.66341 | −0.951916 | ||||||||
\(50\) | −2.31700 | − | 3.05128i | −0.327673 | − | 0.431516i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.49866 | + | 2.09046i | 1.03988 | + | 0.289895i | ||||
\(53\) | − | 3.07183i | − | 0.421949i | −0.977492 | − | 0.210974i | \(-0.932336\pi\) | ||
0.977492 | − | 0.210974i | \(-0.0676636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.99485 | 0.268986 | ||||||||
\(56\) | 1.52535 | − | 0.604978i | 0.203834 | − | 0.0808436i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.45503 | − | 1.10488i | 0.191055 | − | 0.145079i | ||||
\(59\) | 0.258163i | 0.0336100i | 0.999859 | + | 0.0168050i | \(0.00534945\pi\) | ||||
−0.999859 | + | 0.0168050i | \(0.994651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 14.7200i | − | 1.88470i | −0.334623 | − | 0.942352i | \(-0.608609\pi\) | ||
0.334623 | − | 0.942352i | \(-0.391391\pi\) | |||||||
\(62\) | −2.53509 | − | 3.33848i | −0.321957 | − | 0.423988i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.82524 | − | 5.48330i | 0.728155 | − | 0.685413i | ||||
\(65\) | 5.89123 | 0.730717 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.54884i | 1.16658i | 0.812265 | + | 0.583288i | \(0.198234\pi\) | ||||
−0.812265 | + | 0.583288i | \(0.801766\pi\) | |||||||
\(68\) | −0.645257 | + | 2.31459i | −0.0782489 | + | 0.280685i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.989010 | − | 0.751008i | 0.118209 | − | 0.0897627i | ||||
\(71\) | 6.93697 | 0.823267 | 0.411634 | − | 0.911349i | \(-0.364958\pi\) | ||||
0.411634 | + | 0.911349i | \(0.364958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.2934 | 1.78996 | 0.894978 | − | 0.446110i | \(-0.147191\pi\) | ||||
0.894978 | + | 0.446110i | \(0.147191\pi\) | |||||||
\(74\) | 1.33373 | − | 1.01277i | 0.155043 | − | 0.117732i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.92654 | + | 0.537077i | 0.220989 | + | 0.0616069i | ||||
\(77\) | − | 0.764646i | − | 0.0871395i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.1332 | −1.47760 | −0.738798 | − | 0.673927i | \(-0.764606\pi\) | ||||
−0.738798 | + | 0.673927i | \(0.764606\pi\) | |||||||
\(80\) | 3.13216 | − | 5.18106i | 0.350186 | − | 0.579261i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.73645 | − | 10.1882i | −0.854348 | − | 1.12510i | ||||
\(83\) | − | 3.70615i | − | 0.406803i | −0.979095 | − | 0.203402i | \(-0.934800\pi\) | ||
0.979095 | − | 0.203402i | \(-0.0651997\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.81843i | 0.197236i | ||||||||
\(86\) | −9.44754 | + | 7.17402i | −1.01875 | + | 0.773595i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.37436 | − | 3.46523i | −0.146508 | − | 0.369395i | ||||
\(89\) | 8.36653 | 0.886850 | 0.443425 | − | 0.896311i | \(-0.353763\pi\) | ||||
0.443425 | + | 0.896311i | \(0.353763\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2.25816i | − | 0.236720i | ||||||
\(92\) | 3.14473 | − | 11.2804i | 0.327861 | − | 1.17606i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.9952 | − | 14.4796i | −1.13406 | − | 1.49346i | ||||
\(95\) | 1.51356 | 0.155288 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.0442 | 1.73057 | 0.865286 | − | 0.501278i | \(-0.167137\pi\) | ||||
0.865286 | + | 0.501278i | \(0.167137\pi\) | |||||||
\(98\) | 5.69892 | + | 7.50496i | 0.575678 | + | 0.758116i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.45501 | + | 5.21925i | −0.145501 | + | 0.521925i | ||||
\(101\) | − | 1.97721i | − | 0.196739i | −0.995150 | − | 0.0983697i | \(-0.968637\pi\) | ||
0.995150 | − | 0.0983697i | \(-0.0313628\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.30853 | −0.227466 | −0.113733 | − | 0.993511i | \(-0.536281\pi\) | ||||
−0.113733 | + | 0.993511i | \(0.536281\pi\) | |||||||
\(104\) | −4.05879 | − | 10.2336i | −0.397997 | − | 1.00348i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.45979 | + | 2.62720i | −0.336044 | + | 0.255176i | ||||
\(107\) | − | 15.0396i | − | 1.45393i | −0.686675 | − | 0.726965i | \(-0.740930\pi\) | ||
0.686675 | − | 0.726965i | \(-0.259070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.4002i | 1.28351i | 0.766911 | + | 0.641753i | \(0.221793\pi\) | ||||
−0.766911 | + | 0.641753i | \(0.778207\pi\) | |||||||
\(110\) | −1.70611 | − | 2.24679i | −0.162671 | − | 0.214223i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.98595 | − | 1.20059i | −0.187655 | − | 0.113445i | ||||
\(113\) | −4.89717 | −0.460687 | −0.230343 | − | 0.973109i | \(-0.573985\pi\) | ||||
−0.230343 | + | 0.973109i | \(0.573985\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.86230i | − | 0.826414i | ||||||
\(116\) | −2.48885 | − | 0.693837i | −0.231084 | − | 0.0644212i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.290768 | − | 0.220795i | 0.0267673 | − | 0.0203259i | ||||
\(119\) | 0.697020 | 0.0638957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.26291 | 0.842083 | ||||||||
\(122\) | −16.5791 | + | 12.5894i | −1.50100 | + | 1.13979i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.59197 | + | 5.71051i | −0.142963 | + | 0.512819i | ||||
\(125\) | 11.6682i | 1.04364i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.61625 | −0.232155 | −0.116078 | − | 0.993240i | \(-0.537032\pi\) | ||||
−0.116078 | + | 0.993240i | \(0.537032\pi\) | |||||||
\(128\) | −11.1579 | − | 1.87131i | −0.986226 | − | 0.165402i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.03851 | − | 6.63526i | −0.441906 | − | 0.581951i | ||||
\(131\) | 2.64498i | 0.231093i | 0.993302 | + | 0.115547i | \(0.0368620\pi\) | ||||
−0.993302 | + | 0.115547i | \(0.963138\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.580162i | − | 0.0503064i | ||||||
\(134\) | 10.7548 | − | 8.16670i | 0.929073 | − | 0.705495i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.15877 | − | 1.25281i | 0.270862 | − | 0.107428i | ||||
\(137\) | −4.88035 | −0.416957 | −0.208478 | − | 0.978027i | \(-0.566851\pi\) | ||||
−0.208478 | + | 0.978027i | \(0.566851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.3334i | − | 0.876468i | −0.898861 | − | 0.438234i | \(-0.855604\pi\) | ||
0.898861 | − | 0.438234i | \(-0.144396\pi\) | |||||||
\(140\) | −1.69171 | − | 0.471613i | −0.142976 | − | 0.0398585i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.93288 | − | 7.81307i | −0.497877 | − | 0.655659i | ||||
\(143\) | −5.13000 | −0.428992 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.95533 | −0.162382 | ||||||||
\(146\) | −13.0798 | − | 17.2249i | −1.08249 | − | 1.42554i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.28136 | − | 0.635994i | −0.187527 | − | 0.0522784i | ||||
\(149\) | − | 8.35324i | − | 0.684324i | −0.939641 | − | 0.342162i | \(-0.888841\pi\) | ||
0.939641 | − | 0.342162i | \(-0.111159\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.84941 | −0.476019 | −0.238009 | − | 0.971263i | \(-0.576495\pi\) | ||||
−0.238009 | + | 0.971263i | \(0.576495\pi\) | |||||||
\(152\) | −1.04278 | − | 2.62919i | −0.0845802 | − | 0.213255i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.861216 | + | 0.653967i | −0.0693988 | + | 0.0526982i | ||||
\(155\) | 4.48639i | 0.360356i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.361645i | 0.0288624i | 0.999896 | + | 0.0144312i | \(0.00459375\pi\) | ||||
−0.999896 | + | 0.0144312i | \(0.995406\pi\) | |||||||
\(158\) | 11.2322 | + | 14.7918i | 0.893587 | + | 1.17677i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.51420 | + | 0.903401i | −0.673107 | + | 0.0714201i | ||||
\(161\) | −3.39700 | −0.267721 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.146029i | − | 0.0114379i | −0.999984 | − | 0.00571894i | \(-0.998180\pi\) | ||
0.999984 | − | 0.00571894i | \(-0.00182041\pi\) | |||||||
\(164\) | −4.85828 | + | 17.4270i | −0.379368 | + | 1.36082i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.17422 | + | 3.16971i | −0.323982 | + | 0.246017i | ||||
\(167\) | −0.406603 | −0.0314639 | −0.0157319 | − | 0.999876i | \(-0.505008\pi\) | ||||
−0.0157319 | + | 0.999876i | \(0.505008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.14999 | −0.165384 | ||||||||
\(170\) | 2.04808 | − | 1.55522i | 0.157081 | − | 0.119280i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 16.1601 | + | 4.50509i | 1.23220 | + | 0.343510i | ||||
\(173\) | 12.6466i | 0.961507i | 0.876856 | + | 0.480753i | \(0.159637\pi\) | ||||
−0.876856 | + | 0.480753i | \(0.840363\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.57174 | 0.118812 | ||||||||
\(176\) | −2.72744 | + | 4.51160i | −0.205589 | + | 0.340075i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.15552 | − | 9.42317i | −0.536329 | − | 0.706297i | ||||
\(179\) | − | 5.55598i | − | 0.415274i | −0.978206 | − | 0.207637i | \(-0.933423\pi\) | ||
0.978206 | − | 0.207637i | \(-0.0665772\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.13401i | 0.678926i | 0.940619 | + | 0.339463i | \(0.110245\pi\) | ||||
−0.940619 | + | 0.339463i | \(0.889755\pi\) | |||||||
\(182\) | −2.54336 | + | 1.93131i | −0.188526 | + | 0.143158i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15.3946 | + | 6.10573i | −1.13490 | + | 0.450120i | ||||
\(185\) | −1.79232 | −0.131774 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.58346i | − | 0.115794i | ||||||
\(188\) | −6.90466 | + | 24.7676i | −0.503574 | + | 1.80636i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.29448 | − | 1.70471i | −0.0939115 | − | 0.123673i | ||||
\(191\) | −5.47532 | −0.396180 | −0.198090 | − | 0.980184i | \(-0.563474\pi\) | ||||
−0.198090 | + | 0.980184i | \(0.563474\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.9697 | 1.22151 | 0.610753 | − | 0.791821i | \(-0.290867\pi\) | ||||
0.610753 | + | 0.791821i | \(0.290867\pi\) | |||||||
\(194\) | −14.5771 | − | 19.1967i | −1.04658 | − | 1.37825i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.57876 | − | 12.8373i | 0.255626 | − | 0.916951i | ||||
\(197\) | − | 23.7727i | − | 1.69374i | −0.531803 | − | 0.846868i | \(-0.678485\pi\) | ||
0.531803 | − | 0.846868i | \(-0.321515\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.5747 | −1.24584 | −0.622918 | − | 0.782287i | \(-0.714053\pi\) | ||||
−0.622918 | + | 0.782287i | \(0.714053\pi\) | |||||||
\(200\) | 7.12282 | − | 2.82502i | 0.503659 | − | 0.199759i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.22692 | + | 1.69102i | −0.156685 | + | 0.118979i | ||||
\(203\) | 0.749498i | 0.0526044i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.6913i | 0.956244i | ||||||||
\(206\) | 1.97438 | + | 2.60008i | 0.137562 | + | 0.181156i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.05472 | + | 13.3237i | −0.558494 | + | 0.923834i | ||||
\(209\) | −1.31799 | −0.0911671 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.2804i | − | 1.18963i | −0.803863 | − | 0.594815i | \(-0.797225\pi\) | ||
0.803863 | − | 0.594815i | \(-0.202775\pi\) | |||||||
\(212\) | 5.91800 | + | 1.64981i | 0.406450 | + | 0.113309i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.9390 | + | 12.8627i | −1.15792 | + | 0.879274i | ||||
\(215\) | 12.6960 | 0.865860 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.71968 | 0.116739 | ||||||||
\(218\) | 15.0926 | − | 11.4606i | 1.02220 | − | 0.776209i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.07139 | + | 3.84316i | −0.0722331 | + | 0.259106i | ||||
\(221\) | − | 4.67630i | − | 0.314562i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6027 | 0.776973 | 0.388487 | − | 0.921454i | \(-0.372998\pi\) | ||||
0.388487 | + | 0.921454i | \(0.372998\pi\) | |||||||
\(224\) | 0.346282 | + | 3.26357i | 0.0231369 | + | 0.218057i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.18833 | + | 5.51565i | 0.278604 | + | 0.366896i | ||||
\(227\) | − | 27.4484i | − | 1.82182i | −0.412609 | − | 0.910908i | \(-0.635382\pi\) | ||
0.412609 | − | 0.910908i | \(-0.364618\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.8680i | 1.44508i | 0.691329 | + | 0.722540i | \(0.257025\pi\) | ||||
−0.691329 | + | 0.722540i | \(0.742975\pi\) | |||||||
\(230\) | −9.98156 | + | 7.57953i | −0.658165 | + | 0.499780i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.34714 | + | 3.39659i | 0.0884439 | + | 0.222997i | ||||
\(233\) | 22.1975 | 1.45421 | 0.727103 | − | 0.686528i | \(-0.240866\pi\) | ||||
0.727103 | + | 0.686528i | \(0.240866\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.4583i | 1.26932i | ||||||||
\(236\) | −0.497361 | − | 0.138654i | −0.0323755 | − | 0.00902557i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.596130 | − | 0.785049i | −0.0386414 | − | 0.0508872i | ||||
\(239\) | −21.1350 | −1.36711 | −0.683555 | − | 0.729899i | \(-0.739567\pi\) | ||||
−0.683555 | + | 0.729899i | \(0.739567\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.2437 | −1.11076 | −0.555382 | − | 0.831595i | \(-0.687428\pi\) | ||||
−0.555382 | + | 0.831595i | \(0.687428\pi\) | |||||||
\(242\) | −7.92215 | − | 10.4328i | −0.509255 | − | 0.670643i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 28.3587 | + | 7.90578i | 1.81548 | + | 0.506116i | ||||
\(245\) | − | 10.0855i | − | 0.644338i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.89230 | −0.247661 | ||||||||
\(248\) | 7.79325 | − | 3.09092i | 0.494872 | − | 0.196274i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.1419 | − | 9.97933i | 0.831165 | − | 0.631148i | ||||
\(251\) | − | 6.08851i | − | 0.384303i | −0.981365 | − | 0.192152i | \(-0.938453\pi\) | ||
0.981365 | − | 0.192152i | \(-0.0615465\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.71717i | 0.485174i | ||||||||
\(254\) | 2.23757 | + | 2.94667i | 0.140397 | + | 0.184891i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.43518 | + | 14.1675i | 0.464699 | + | 0.885469i | ||||
\(257\) | −10.1741 | −0.634643 | −0.317322 | − | 0.948318i | \(-0.602783\pi\) | ||||
−0.317322 | + | 0.948318i | \(0.602783\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.687014i | 0.0426890i | ||||||||
\(260\) | −3.16404 | + | 11.3497i | −0.196226 | + | 0.703877i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.97903 | − | 2.26213i | 0.184045 | − | 0.139755i | ||||
\(263\) | 15.8414 | 0.976822 | 0.488411 | − | 0.872614i | \(-0.337577\pi\) | ||||
0.488411 | + | 0.872614i | \(0.337577\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.64940 | 0.285611 | ||||||||
\(266\) | −0.653433 | + | 0.496186i | −0.0400645 | + | 0.0304231i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −18.3962 | − | 5.12846i | −1.12373 | − | 0.313271i | ||||
\(269\) | 22.8533i | 1.39339i | 0.717367 | + | 0.696695i | \(0.245347\pi\) | ||||
−0.717367 | + | 0.696695i | \(0.754653\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.2830 | 0.746142 | 0.373071 | − | 0.927803i | \(-0.378305\pi\) | ||||
0.373071 | + | 0.927803i | \(0.378305\pi\) | |||||||
\(272\) | −4.11259 | − | 2.48622i | −0.249362 | − | 0.150749i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.17395 | + | 5.49671i | 0.252157 | + | 0.332068i | ||||
\(275\) | − | 3.57060i | − | 0.215316i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 0.643776i | − | 0.0386808i | −0.999813 | − | 0.0193404i | \(-0.993843\pi\) | ||
0.999813 | − | 0.0193404i | \(-0.00615662\pi\) | |||||||
\(278\) | −11.6385 | + | 8.83770i | −0.698028 | + | 0.530050i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.915671 | + | 2.30871i | 0.0547218 | + | 0.137972i | ||||
\(281\) | 8.93027 | 0.532735 | 0.266368 | − | 0.963872i | \(-0.414177\pi\) | ||||
0.266368 | + | 0.963872i | \(0.414177\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 14.7397i | − | 0.876187i | −0.898929 | − | 0.438094i | \(-0.855654\pi\) | ||
0.898929 | − | 0.438094i | \(-0.144346\pi\) | |||||||
\(284\) | −3.72569 | + | 13.3643i | −0.221079 | + | 0.793028i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.38746 | + | 5.77789i | 0.259436 | + | 0.341654i | ||||
\(287\) | 5.24801 | 0.309780 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5566 | −0.915093 | ||||||||
\(290\) | 1.67231 | + | 2.20228i | 0.0982015 | + | 0.129322i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.21373 | + | 29.4633i | −0.480672 | + | 1.72421i | ||||
\(293\) | 23.9816i | 1.40102i | 0.713643 | + | 0.700509i | \(0.247044\pi\) | ||||
−0.713643 | + | 0.700509i | \(0.752956\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.390746 | −0.0227501 | ||||||||
\(296\) | 1.23483 | + | 3.11342i | 0.0717730 | + | 0.180964i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.40820 | + | 7.14415i | −0.545002 | + | 0.413850i | ||||
\(299\) | 22.7905i | 1.31801i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 4.86649i | − | 0.280500i | ||||||
\(302\) | 5.00274 | + | 6.58816i | 0.287875 | + | 0.379106i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.06940 | + | 3.42310i | −0.118688 | + | 0.196328i | ||||
\(305\) | 22.2796 | 1.27573 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.82132i | 0.103948i | 0.998648 | + | 0.0519740i | \(0.0165513\pi\) | ||||
−0.998648 | + | 0.0519740i | \(0.983449\pi\) | |||||||
\(308\) | 1.47312 | + | 0.410674i | 0.0839388 | + | 0.0234003i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.05300 | − | 3.83701i | 0.286991 | − | 0.217928i | ||||
\(311\) | 4.53302 | 0.257044 | 0.128522 | − | 0.991707i | \(-0.458977\pi\) | ||||
0.128522 | + | 0.991707i | \(0.458977\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4149 | 0.701730 | 0.350865 | − | 0.936426i | \(-0.385888\pi\) | ||||
0.350865 | + | 0.936426i | \(0.385888\pi\) | |||||||
\(314\) | 0.407319 | − | 0.309299i | 0.0229863 | − | 0.0174547i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.05352 | − | 25.3015i | 0.396792 | − | 1.42332i | ||||
\(317\) | 23.0948i | 1.29713i | 0.761157 | + | 0.648567i | \(0.224632\pi\) | ||||
−0.761157 | + | 0.648567i | \(0.775368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.70268 | 0.0953317 | ||||||||
\(320\) | 8.29931 | + | 8.81685i | 0.463945 | + | 0.492877i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.90530 | + | 3.82602i | 0.161906 | + | 0.213216i | ||||
\(323\) | − | 1.20142i | − | 0.0668490i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 10.5448i | − | 0.584918i | ||||||
\(326\) | −0.164472 | + | 0.124892i | −0.00910924 | + | 0.00691714i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 23.7830 | − | 9.43271i | 1.31320 | − | 0.520834i | ||||
\(329\) | 7.45856 | 0.411204 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.3743i | 1.44966i | 0.688927 | + | 0.724831i | \(0.258082\pi\) | ||||
−0.688927 | + | 0.724831i | \(0.741918\pi\) | |||||||
\(332\) | 7.14004 | + | 1.99049i | 0.391861 | + | 0.109242i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.347749 | + | 0.457954i | 0.0190280 | + | 0.0250581i | ||||
\(335\) | −14.4527 | −0.789638 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.82102 | 0.208144 | 0.104072 | − | 0.994570i | \(-0.466813\pi\) | ||||
0.104072 | + | 0.994570i | \(0.466813\pi\) | |||||||
\(338\) | 1.83879 | + | 2.42152i | 0.100017 | + | 0.131714i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.50327 | − | 0.976635i | −0.189991 | − | 0.0529655i | ||||
\(341\) | − | 3.90669i | − | 0.211559i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.92699 | −0.428017 | ||||||||
\(344\) | −8.74697 | − | 22.0540i | −0.471605 | − | 1.18907i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.2438 | − | 10.8161i | 0.765754 | − | 0.581478i | ||||
\(347\) | 29.8808i | 1.60408i | 0.597268 | + | 0.802042i | \(0.296253\pi\) | ||||
−0.597268 | + | 0.802042i | \(0.703747\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.7016i | − | 0.679902i | −0.940443 | − | 0.339951i | \(-0.889589\pi\) | ||
0.940443 | − | 0.339951i | \(-0.110411\pi\) | |||||||
\(350\) | −1.34424 | − | 1.77024i | −0.0718524 | − | 0.0946232i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.41404 | − | 0.786668i | 0.395170 | − | 0.0419296i | ||||
\(353\) | −22.8398 | −1.21564 | −0.607820 | − | 0.794074i | \(-0.707956\pi\) | ||||
−0.607820 | + | 0.794074i | \(0.707956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.4995i | 0.557257i | ||||||||
\(356\) | −4.49347 | + | 16.1184i | −0.238153 | + | 0.854275i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.25767 | + | 4.75178i | −0.330728 | + | 0.251140i | ||||
\(359\) | −35.4003 | −1.86835 | −0.934177 | − | 0.356810i | \(-0.883864\pi\) | ||||
−0.934177 | + | 0.356810i | \(0.883864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 10.2876 | − | 7.81191i | 0.540703 | − | 0.410585i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.35044 | + | 1.21281i | 0.228025 | + | 0.0635684i | ||||
\(365\) | 23.1475i | 1.21159i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.2148 | −0.898608 | −0.449304 | − | 0.893379i | \(-0.648328\pi\) | ||||
−0.449304 | + | 0.893379i | \(0.648328\pi\) | |||||||
\(368\) | 20.0432 | + | 12.1169i | 1.04482 | + | 0.631636i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.53289 | + | 2.01868i | 0.0796914 | + | 0.104946i | ||||
\(371\) | − | 1.78216i | − | 0.0925251i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.3506i | 1.05372i | 0.849953 | + | 0.526858i | \(0.176630\pi\) | ||||
−0.849953 | + | 0.526858i | \(0.823370\pi\) | |||||||
\(374\) | −1.78344 | + | 1.35426i | −0.0922196 | + | 0.0700273i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 33.8008 | − | 13.4059i | 1.74314 | − | 0.691358i | ||||
\(377\) | 5.02837 | 0.258974 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.22765i | − | 0.217160i | −0.994088 | − | 0.108580i | \(-0.965370\pi\) | ||
0.994088 | − | 0.108580i | \(-0.0346303\pi\) | |||||||
\(380\) | −0.812898 | + | 2.91593i | −0.0417008 | + | 0.149584i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.68280 | + | 6.16682i | 0.239593 | + | 0.315522i | ||||
\(383\) | −9.71281 | −0.496301 | −0.248151 | − | 0.968721i | \(-0.579823\pi\) | ||||
−0.248151 | + | 0.968721i | \(0.579823\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.15734 | 0.0589834 | ||||||||
\(386\) | −14.5134 | − | 19.1129i | −0.738714 | − | 0.972819i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.15403 | + | 32.8362i | −0.464725 | + | 1.66701i | ||||
\(389\) | − | 22.3291i | − | 1.13213i | −0.824361 | − | 0.566064i | \(-0.808466\pi\) | ||
0.824361 | − | 0.566064i | \(-0.191534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.03466 | −0.355758 | ||||||||
\(392\) | −17.5194 | + | 6.94844i | −0.884861 | + | 0.350949i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −26.7751 | + | 20.3317i | −1.34891 | + | 1.02430i | ||||
\(395\) | − | 19.8778i | − | 1.00016i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.9210i | 1.20056i | 0.799789 | + | 0.600281i | \(0.204945\pi\) | ||||
−0.799789 | + | 0.600281i | \(0.795055\pi\) | |||||||
\(398\) | 15.0308 | + | 19.7943i | 0.753428 | + | 0.992197i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.27363 | − | 5.60628i | −0.463681 | − | 0.280314i | ||||
\(401\) | 16.5237 | 0.825154 | 0.412577 | − | 0.910923i | \(-0.364629\pi\) | ||||
0.412577 | + | 0.910923i | \(0.364629\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 11.5373i | − | 0.574713i | ||||||
\(404\) | 3.80916 | + | 1.06191i | 0.189513 | + | 0.0528321i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.844155 | − | 0.641012i | 0.0418947 | − | 0.0318129i | ||||
\(407\) | 1.56073 | 0.0773625 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0228 | 0.792278 | 0.396139 | − | 0.918191i | \(-0.370350\pi\) | ||||
0.396139 | + | 0.918191i | \(0.370350\pi\) | |||||||
\(410\) | 15.4205 | − | 11.7096i | 0.761562 | − | 0.578295i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.23986 | − | 4.44747i | 0.0610834 | − | 0.219111i | ||||
\(413\) | 0.149776i | 0.00737002i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.60949 | 0.275359 | ||||||||
\(416\) | 21.8953 | − | 2.32320i | 1.07350 | − | 0.113904i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.12722 | + | 1.48444i | 0.0551339 | + | 0.0726064i | ||||
\(419\) | 12.7496i | 0.622858i | 0.950269 | + | 0.311429i | \(0.100808\pi\) | ||||
−0.950269 | + | 0.311429i | \(0.899192\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.89293i | − | 0.0922560i | −0.998936 | − | 0.0461280i | \(-0.985312\pi\) | ||
0.998936 | − | 0.0461280i | \(-0.0146882\pi\) | |||||||
\(422\) | −19.4628 | + | 14.7791i | −0.947434 | + | 0.719437i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.20323 | − | 8.07642i | −0.155563 | − | 0.392225i | ||||
\(425\) | 3.25482 | 0.157882 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.53999i | − | 0.413279i | ||||||
\(428\) | 28.9743 | + | 8.07740i | 1.40052 | + | 0.390436i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.8583 | − | 14.2994i | −0.523635 | − | 0.689580i | ||||
\(431\) | −37.2166 | −1.79266 | −0.896331 | − | 0.443386i | \(-0.853777\pi\) | ||||
−0.896331 | + | 0.443386i | \(0.853777\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.0314 | −1.73156 | −0.865780 | − | 0.500425i | \(-0.833177\pi\) | ||||
−0.865780 | + | 0.500425i | \(0.833177\pi\) | |||||||
\(434\) | −1.47076 | − | 1.93686i | −0.0705988 | − | 0.0929723i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −25.8160 | − | 7.19693i | −1.23636 | − | 0.344671i | ||||
\(437\) | 5.85527i | 0.280095i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.6188 | −0.888629 | −0.444315 | − | 0.895871i | \(-0.646553\pi\) | ||||
−0.444315 | + | 0.895871i | \(0.646553\pi\) | |||||||
\(440\) | 5.24484 | − | 2.08018i | 0.250038 | − | 0.0991689i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.26689 | + | 3.99943i | −0.250520 | + | 0.190233i | ||||
\(443\) | 2.26887i | 0.107797i | 0.998546 | + | 0.0538987i | \(0.0171648\pi\) | ||||
−0.998546 | + | 0.0538987i | \(0.982835\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.6633i | 0.600296i | ||||||||
\(446\) | −9.92326 | − | 13.0680i | −0.469880 | − | 0.618789i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.37958 | − | 3.18120i | 0.159670 | − | 0.150298i | ||||
\(449\) | −0.248909 | −0.0117467 | −0.00587337 | − | 0.999983i | \(-0.501870\pi\) | ||||
−0.00587337 | + | 0.999983i | \(0.501870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 11.9222i | − | 0.561395i | ||||||
\(452\) | 2.63016 | − | 9.43458i | 0.123712 | − | 0.443765i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −30.9150 | + | 23.4754i | −1.45091 | + | 1.10176i | ||||
\(455\) | 3.41787 | 0.160232 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.98767 | −0.326869 | −0.163435 | − | 0.986554i | \(-0.552257\pi\) | ||||
−0.163435 | + | 0.986554i | \(0.552257\pi\) | |||||||
\(458\) | 24.6298 | − | 18.7027i | 1.15088 | − | 0.873922i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17.0736 | + | 4.75974i | 0.796059 | + | 0.221924i | ||||
\(461\) | − | 34.1624i | − | 1.59110i | −0.605888 | − | 0.795550i | \(-0.707182\pi\) | ||
0.605888 | − | 0.795550i | \(-0.292818\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.5311 | 1.60480 | 0.802399 | − | 0.596788i | \(-0.203556\pi\) | ||||
0.802399 | + | 0.596788i | \(0.203556\pi\) | |||||||
\(464\) | 2.67341 | − | 4.42222i | 0.124110 | − | 0.205296i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.9845 | − | 25.0009i | −0.879441 | − | 1.15815i | ||||
\(467\) | 39.6496i | 1.83476i | 0.398008 | + | 0.917382i | \(0.369702\pi\) | ||||
−0.398008 | + | 0.917382i | \(0.630298\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.53987i | 0.255808i | ||||||||
\(470\) | 21.9158 | − | 16.6418i | 1.01090 | − | 0.767631i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.269206 | + | 0.678759i | 0.0123912 | + | 0.0312424i | ||||
\(473\) | −11.0555 | −0.508332 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.70913i | − | 0.124304i | ||||||
\(476\) | −0.374353 | + | 1.34284i | −0.0171585 | + | 0.0615488i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.0758 | + | 23.8042i | 0.826770 | + | 1.08878i | ||||
\(479\) | 24.8669 | 1.13620 | 0.568098 | − | 0.822961i | \(-0.307679\pi\) | ||||
0.568098 | + | 0.822961i | \(0.307679\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.60917 | 0.210160 | ||||||||
\(482\) | 14.7478 | + | 19.4215i | 0.671742 | + | 0.884624i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.97489 | + | 17.8453i | −0.226132 | + | 0.811152i | ||||
\(485\) | 25.7974i | 1.17140i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.7320 | −1.80043 | −0.900214 | − | 0.435448i | \(-0.856590\pi\) | ||||
−0.900214 | + | 0.435448i | \(0.856590\pi\) | |||||||
\(488\) | −15.3497 | − | 38.7016i | −0.694847 | − | 1.75194i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.3592 | + | 8.62566i | −0.513157 | + | 0.389668i | ||||
\(491\) | − | 3.45561i | − | 0.155949i | −0.996955 | − | 0.0779747i | \(-0.975155\pi\) | ||
0.996955 | − | 0.0779747i | \(-0.0248453\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.55209i | 0.0699027i | ||||||||
\(494\) | 3.32891 | + | 4.38387i | 0.149775 | + | 0.197240i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.1465 | − | 6.13397i | −0.455592 | − | 0.275423i | ||||
\(497\) | 4.02457 | 0.180527 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.5837i | − | 0.787156i | −0.919291 | − | 0.393578i | \(-0.871237\pi\) | ||
0.919291 | − | 0.393578i | \(-0.128763\pi\) | |||||||
\(500\) | −22.4793 | − | 6.26674i | −1.00531 | − | 0.280257i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.85745 | + | 5.20723i | −0.306063 | + | 0.232410i | ||||
\(503\) | −2.72712 | −0.121596 | −0.0607981 | − | 0.998150i | \(-0.519365\pi\) | ||||
−0.0607981 | + | 0.998150i | \(0.519365\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.99262 | 0.133170 | ||||||||
\(506\) | 8.69180 | − | 6.60015i | 0.386398 | − | 0.293412i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.40513 | − | 5.04031i | 0.0623425 | − | 0.223628i | ||||
\(509\) | − | 6.73123i | − | 0.298356i | −0.988810 | − | 0.149178i | \(-0.952337\pi\) | ||
0.988810 | − | 0.149178i | \(-0.0476628\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.87264 | 0.392503 | ||||||||
\(512\) | 9.59779 | − | 20.4910i | 0.424166 | − | 0.905584i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.70146 | + | 11.4590i | 0.383805 | + | 0.505436i | ||||
\(515\) | − | 3.49410i | − | 0.153968i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 16.9441i | − | 0.745198i | ||||||
\(518\) | 0.773780 | − | 0.587572i | 0.0339979 | − | 0.0258164i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.4891 | − | 6.14323i | 0.679244 | − | 0.269398i | ||||
\(521\) | −38.2190 | −1.67440 | −0.837202 | − | 0.546894i | \(-0.815810\pi\) | ||||
−0.837202 | + | 0.546894i | \(0.815810\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.37182i | 0.234893i | 0.993079 | + | 0.117447i | \(0.0374709\pi\) | ||||
−0.993079 | + | 0.117447i | \(0.962529\pi\) | |||||||
\(524\) | −5.09566 | − | 1.42056i | −0.222605 | − | 0.0620574i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.5484 | − | 17.8421i | −0.590739 | − | 0.777951i | ||||
\(527\) | 3.56118 | 0.155127 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2842 | 0.490616 | ||||||||
\(530\) | −3.97643 | − | 5.23660i | −0.172725 | − | 0.227463i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.11770 | + | 0.311591i | 0.0484586 | + | 0.0135092i | ||||
\(533\) | − | 35.2089i | − | 1.52506i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.7633 | 0.984143 | ||||||||
\(536\) | 9.95729 | + | 25.1057i | 0.430090 | + | 1.08440i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.7395 | − | 19.5454i | 1.10971 | − | 0.842662i | ||||
\(539\) | 8.78229i | 0.378280i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 34.3497i | − | 1.47681i | −0.674359 | − | 0.738404i | \(-0.735580\pi\) | ||
0.674359 | − | 0.738404i | \(-0.264420\pi\) | |||||||
\(542\) | −10.5051 | − | 13.8343i | −0.451234 | − | 0.594235i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.717095 | + | 6.75834i | 0.0307452 | + | 0.289761i | ||||
\(545\) | −20.2820 | −0.868786 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.58358i | 0.110466i | 0.998473 | + | 0.0552330i | \(0.0175902\pi\) | ||||
−0.998473 | + | 0.0552330i | \(0.982410\pi\) | |||||||
\(548\) | 2.62112 | − | 9.40218i | 0.111969 | − | 0.401641i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.02155 | + | 3.05378i | −0.171480 | + | 0.130214i | ||||
\(551\) | 1.29188 | 0.0550358 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.61936 | −0.324008 | ||||||||
\(554\) | −0.725081 | + | 0.550593i | −0.0308057 | + | 0.0233924i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.9077 | + | 5.54983i | 0.844275 | + | 0.235365i | ||||
\(557\) | − | 0.498941i | − | 0.0211408i | −0.999944 | − | 0.0105704i | \(-0.996635\pi\) | ||
0.999944 | − | 0.0105704i | \(-0.00336472\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.6492 | −1.38092 | ||||||||
\(560\) | 1.81716 | − | 3.00586i | 0.0767890 | − | 0.127021i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.63766 | − | 10.0581i | −0.322175 | − | 0.424276i | ||||
\(563\) | 32.5553i | 1.37204i | 0.727581 | + | 0.686021i | \(0.240644\pi\) | ||||
−0.727581 | + | 0.686021i | \(0.759356\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 7.41216i | − | 0.311832i | ||||||
\(566\) | −16.6013 | + | 12.6062i | −0.697804 | + | 0.529880i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.2386 | − | 7.23371i | 0.765275 | − | 0.303520i | ||||
\(569\) | −13.6834 | −0.573636 | −0.286818 | − | 0.957985i | \(-0.592598\pi\) | ||||
−0.286818 | + | 0.957985i | \(0.592598\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 12.2520i | − | 0.512732i | −0.966580 | − | 0.256366i | \(-0.917475\pi\) | ||
0.966580 | − | 0.256366i | \(-0.0825253\pi\) | |||||||
\(572\) | 2.75520 | − | 9.88314i | 0.115201 | − | 0.413235i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.48839 | − | 5.91081i | −0.187342 | − | 0.246712i | ||||
\(575\) | −15.8627 | −0.661521 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.6672 | 0.610605 | 0.305302 | − | 0.952255i | \(-0.401242\pi\) | ||||
0.305302 | + | 0.952255i | \(0.401242\pi\) | |||||||
\(578\) | 13.3048 | + | 17.5213i | 0.553409 | + | 0.728789i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.05017 | − | 3.76703i | 0.0436057 | − | 0.156417i | ||||
\(581\) | − | 2.15017i | − | 0.0892040i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.04864 | −0.167677 | ||||||||
\(584\) | 40.2092 | − | 15.9476i | 1.66387 | − | 0.659915i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.0103 | − | 20.5104i | 1.11579 | − | 0.847275i | ||||
\(587\) | − | 5.53206i | − | 0.228333i | −0.993462 | − | 0.114166i | \(-0.963580\pi\) | ||
0.993462 | − | 0.114166i | \(-0.0364197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.96413i | − | 0.122135i | ||||||
\(590\) | 0.334187 | + | 0.440095i | 0.0137583 | + | 0.0181184i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.45053 | − | 4.05355i | 0.100716 | − | 0.166600i | ||||
\(593\) | −21.5870 | −0.886470 | −0.443235 | − | 0.896405i | \(-0.646169\pi\) | ||||
−0.443235 | + | 0.896405i | \(0.646169\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.05498i | 0.0432500i | ||||||||
\(596\) | 16.0928 | + | 4.48633i | 0.659188 | + | 0.183767i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 25.6688 | − | 19.4917i | 1.04967 | − | 0.797073i | ||||
\(599\) | 28.3513 | 1.15840 | 0.579202 | − | 0.815184i | \(-0.303364\pi\) | ||||
0.579202 | + | 0.815184i | \(0.303364\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.9758 | −0.896410 | −0.448205 | − | 0.893931i | \(-0.647936\pi\) | ||||
−0.448205 | + | 0.893931i | \(0.647936\pi\) | |||||||
\(602\) | −5.48110 | + | 4.16209i | −0.223393 | + | 0.169634i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.14158 | − | 11.2691i | 0.127829 | − | 0.458534i | ||||
\(605\) | 14.0200i | 0.569993i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.89484 | −0.320441 | −0.160221 | − | 0.987081i | \(-0.551221\pi\) | ||||
−0.160221 | + | 0.987081i | \(0.551221\pi\) | |||||||
\(608\) | 5.62528 | − | 0.596871i | 0.228135 | − | 0.0242063i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.0548 | − | 25.0934i | −0.771505 | − | 1.01600i | ||||
\(611\) | − | 50.0394i | − | 2.02438i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.5174i | 1.19220i | 0.802912 | + | 0.596098i | \(0.203283\pi\) | ||||
−0.802912 | + | 0.596098i | \(0.796717\pi\) | |||||||
\(614\) | 2.05134 | − | 1.55769i | 0.0827853 | − | 0.0628633i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.797354 | − | 2.01040i | −0.0321263 | − | 0.0810012i | ||||
\(617\) | −3.08379 | −0.124149 | −0.0620744 | − | 0.998072i | \(-0.519772\pi\) | ||||
−0.0620744 | + | 0.998072i | \(0.519772\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.9487i | − | 0.440066i | −0.975492 | − | 0.220033i | \(-0.929384\pi\) | ||
0.975492 | − | 0.220033i | \(-0.0706164\pi\) | |||||||
\(620\) | −8.64320 | − | 2.40954i | −0.347119 | − | 0.0967693i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.87689 | − | 5.10551i | −0.155449 | − | 0.204712i | ||||
\(623\) | 4.85394 | 0.194469 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.11492 | −0.164597 | ||||||||
\(626\) | −10.6179 | − | 13.9828i | −0.424376 | − | 0.558865i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.696723 | − | 0.194231i | −0.0278023 | − | 0.00775067i | ||||
\(629\) | 1.42270i | 0.0567267i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.7432 | −0.825773 | −0.412886 | − | 0.910783i | \(-0.635479\pi\) | ||||
−0.412886 | + | 0.910783i | \(0.635479\pi\) | |||||||
\(632\) | −34.5295 | + | 13.6949i | −1.37351 | + | 0.544756i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26.0116 | − | 19.7520i | 1.03305 | − | 0.784451i | ||||
\(635\) | − | 3.95986i | − | 0.157142i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.9360i | 1.02762i | ||||||||
\(638\) | −1.45622 | − | 1.91772i | −0.0576525 | − | 0.0759231i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.83234 | − | 16.8881i | 0.111958 | − | 0.667562i | ||||
\(641\) | 34.5310 | 1.36389 | 0.681946 | − | 0.731403i | \(-0.261134\pi\) | ||||
0.681946 | + | 0.731403i | \(0.261134\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.5300i | 0.849062i | 0.905413 | + | 0.424531i | \(0.139561\pi\) | ||||
−0.905413 | + | 0.424531i | \(0.860439\pi\) | |||||||
\(644\) | 1.82445 | − | 6.54446i | 0.0718935 | − | 0.257888i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.35316 | + | 1.02752i | −0.0532392 | + | 0.0404274i | ||||
\(647\) | −22.7527 | −0.894502 | −0.447251 | − | 0.894409i | \(-0.647597\pi\) | ||||
−0.447251 | + | 0.894409i | \(0.647597\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.340256 | 0.0133562 | ||||||||
\(650\) | −11.8765 | + | 9.01846i | −0.465835 | + | 0.353733i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.281331 | + | 0.0784288i | 0.0110178 | + | 0.00307151i | ||||
\(653\) | 35.6805i | 1.39629i | 0.715958 | + | 0.698143i | \(0.245990\pi\) | ||||
−0.715958 | + | 0.698143i | \(0.754010\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00334 | −0.156423 | ||||||||
\(656\) | −30.9646 | − | 18.7193i | −1.20896 | − | 0.730866i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.37897 | − | 8.40053i | −0.248678 | − | 0.327487i | ||||
\(659\) | 35.8589i | 1.39686i | 0.715676 | + | 0.698432i | \(0.246119\pi\) | ||||
−0.715676 | + | 0.698432i | \(0.753881\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 25.4409i | − | 0.989537i | −0.869025 | − | 0.494769i | \(-0.835253\pi\) | ||
0.869025 | − | 0.494769i | \(-0.164747\pi\) | |||||||
\(662\) | 29.7052 | − | 22.5567i | 1.15453 | − | 0.876693i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.86468 | − | 9.74416i | −0.149979 | − | 0.378147i | ||||
\(665\) | 0.878110 | 0.0340516 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.56429i | − | 0.292890i | ||||||
\(668\) | 0.218377 | − | 0.783335i | 0.00844925 | − | 0.0303082i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.3608 | + | 16.2780i | 0.477539 | + | 0.628876i | ||||
\(671\) | −19.4008 | −0.748959 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.2142 | 1.31886 | 0.659431 | − | 0.751765i | \(-0.270797\pi\) | ||||
0.659431 | + | 0.751765i | \(0.270797\pi\) | |||||||
\(674\) | −3.26795 | − | 4.30359i | −0.125877 | − | 0.165768i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.15471 | − | 4.14204i | 0.0444120 | − | 0.159309i | ||||
\(677\) | − | 37.9103i | − | 1.45701i | −0.685040 | − | 0.728505i | \(-0.740215\pi\) | ||
0.685040 | − | 0.728505i | \(-0.259785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.88837 | 0.379481 | ||||||||
\(680\) | 1.89621 | + | 4.78098i | 0.0727164 | + | 0.183342i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.40008 | + | 3.34121i | −0.168488 | + | 0.127942i | ||||
\(683\) | − | 30.3542i | − | 1.16147i | −0.814092 | − | 0.580736i | \(-0.802765\pi\) | ||
0.814092 | − | 0.580736i | \(-0.197235\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7.38671i | − | 0.282232i | ||||||
\(686\) | 6.77960 | + | 8.92812i | 0.258846 | + | 0.340877i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −17.3584 | + | 28.7135i | −0.661785 | + | 1.09469i | ||||
\(689\) | −11.9565 | −0.455506 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.50694i | 0.133410i | 0.997773 | + | 0.0667052i | \(0.0212487\pi\) | ||||
−0.997773 | + | 0.0667052i | \(0.978751\pi\) | |||||||
\(692\) | −24.3642 | − | 6.79222i | −0.926189 | − | 0.258201i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.6545 | − | 25.5557i | 1.27751 | − | 0.970081i | ||||
\(695\) | 15.6402 | 0.593268 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.8678 | 0.411647 | ||||||||
\(698\) | −14.3058 | + | 10.8631i | −0.541481 | + | 0.411175i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.844143 | + | 3.02801i | −0.0319056 | + | 0.114448i | ||||
\(701\) | − | 13.2168i | − | 0.499190i | −0.968350 | − | 0.249595i | \(-0.919703\pi\) | ||
0.968350 | − | 0.249595i | \(-0.0802975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.18418 | 0.0446621 | ||||||||
\(704\) | −7.22692 | − | 7.67759i | −0.272375 | − | 0.289360i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.5339 | + | 25.7244i | 0.735167 | + | 0.968149i | ||||
\(707\) | − | 1.14710i | − | 0.0431411i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 23.2882i | − | 0.874605i | −0.899314 | − | 0.437302i | \(-0.855934\pi\) | ||
0.899314 | − | 0.437302i | \(-0.144066\pi\) | |||||||
\(710\) | 11.8256 | − | 8.97978i | 0.443805 | − | 0.337005i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 21.9972 | − | 8.72441i | 0.824379 | − | 0.326961i | ||||
\(713\) | −17.3558 | −0.649979 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 7.76457i | − | 0.290378i | ||||||
\(716\) | 10.7038 | + | 2.98399i | 0.400020 | + | 0.111517i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 30.2763 | + | 39.8711i | 1.12990 | + | 1.48798i | ||||
\(719\) | −0.192843 | −0.00719184 | −0.00359592 | − | 0.999994i | \(-0.501145\pi\) | ||||
−0.00359592 | + | 0.999994i | \(0.501145\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.33932 | −0.0498789 | ||||||||
\(722\) | 0.855255 | + | 1.12629i | 0.0318293 | + | 0.0419163i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.5970 | − | 4.90567i | −0.653988 | − | 0.182318i | ||||
\(725\) | 3.49987i | 0.129982i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.5604 | 0.540014 | 0.270007 | − | 0.962858i | \(-0.412974\pi\) | ||||
0.270007 | + | 0.962858i | \(0.412974\pi\) | |||||||
\(728\) | −2.35476 | − | 5.93713i | −0.0872731 | − | 0.220045i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 26.0709 | − | 19.7970i | 0.964926 | − | 0.732720i | ||||
\(731\) | − | 10.0777i | − | 0.372739i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.0856i | 1.07430i | 0.843487 | + | 0.537150i | \(0.180499\pi\) | ||||
−0.843487 | + | 0.537150i | \(0.819501\pi\) | |||||||
\(734\) | 14.7231 | + | 19.3890i | 0.543439 | + | 0.715660i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.49484 | − | 32.9375i | −0.128822 | − | 1.21409i | ||||
\(737\) | 12.5853 | 0.463584 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 28.8090i | − | 1.05975i | −0.848074 | − | 0.529877i | \(-0.822238\pi\) | ||
0.848074 | − | 0.529877i | \(-0.177762\pi\) | |||||||
\(740\) | 0.962615 | − | 3.45298i | 0.0353864 | − | 0.126934i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.00724 | + | 1.52420i | −0.0736879 | + | 0.0559552i | ||||
\(743\) | −42.2025 | −1.54826 | −0.774129 | − | 0.633027i | \(-0.781812\pi\) | ||||
−0.774129 | + | 0.633027i | \(0.781812\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.6431 | 0.463208 | ||||||||
\(746\) | 22.9208 | − | 17.4050i | 0.839191 | − | 0.637242i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.05060 | + | 0.850440i | 0.111541 | + | 0.0310952i | ||||
\(749\) | − | 8.72538i | − | 0.318818i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.64036 | 0.0963483 | 0.0481741 | − | 0.998839i | \(-0.484660\pi\) | ||||
0.0481741 | + | 0.998839i | \(0.484660\pi\) | |||||||
\(752\) | −44.0073 | − | 26.6042i | −1.60478 | − | 0.970155i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.30054 | − | 5.66343i | −0.156617 | − | 0.206250i | ||||
\(755\) | − | 8.85344i | − | 0.322210i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 4.51764i | − | 0.164197i | −0.996624 | − | 0.0820983i | \(-0.973838\pi\) | ||
0.996624 | − | 0.0820983i | \(-0.0261621\pi\) | |||||||
\(758\) | −4.76158 | + | 3.61572i | −0.172948 | + | 0.131329i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.97943 | − | 1.57830i | 0.144349 | − | 0.0572511i | ||||
\(761\) | 23.5124 | 0.852323 | 0.426162 | − | 0.904647i | \(-0.359866\pi\) | ||||
0.426162 | + | 0.904647i | \(0.359866\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.77428i | 0.281448i | ||||||||
\(764\) | 2.94067 | − | 10.5484i | 0.106390 | − | 0.381628i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.30693 | + | 10.9395i | 0.300142 | + | 0.395259i | ||||
\(767\) | 1.00485 | 0.0362830 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.6727 | −1.07002 | −0.535012 | − | 0.844845i | \(-0.679693\pi\) | ||||
−0.535012 | + | 0.844845i | \(0.679693\pi\) | |||||||
\(770\) | −0.989819 | − | 1.30350i | −0.0356706 | − | 0.0469750i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.11403 | + | 32.6928i | −0.328021 | + | 1.17664i | ||||
\(773\) | − | 10.1647i | − | 0.365598i | −0.983150 | − | 0.182799i | \(-0.941484\pi\) | ||
0.983150 | − | 0.182799i | \(-0.0585158\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.03023 | 0.288454 | ||||||||
\(776\) | 44.8123 | − | 17.7732i | 1.60867 | − | 0.638022i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.1491 | + | 19.0970i | −0.901638 | + | 0.684662i | ||||
\(779\) | − | 9.04577i | − | 0.324098i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 9.14285i | − | 0.327157i | ||||||
\(782\) | 6.01643 | + | 7.92309i | 0.215147 | + | 0.283329i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22.8095 | + | 13.7893i | 0.814625 | + | 0.492473i | ||||
\(785\) | −0.547372 | −0.0195365 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 18.8481i | − | 0.671863i | −0.941886 | − | 0.335931i | \(-0.890949\pi\) | ||
0.941886 | − | 0.335931i | \(-0.109051\pi\) | |||||||
\(788\) | 45.7991 | + | 12.7678i | 1.63152 | + | 0.454833i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −22.3883 | + | 17.0006i | −0.796540 | + | 0.604855i | ||||
\(791\) | −2.84115 | −0.101020 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −57.2947 | −2.03459 | ||||||||
\(794\) | 26.9421 | − | 20.4586i | 0.956140 | − | 0.726049i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.43896 | − | 33.8583i | 0.334555 | − | 1.20008i | ||||
\(797\) | − | 13.9098i | − | 0.492709i | −0.969180 | − | 0.246355i | \(-0.920767\pi\) | ||
0.969180 | − | 0.246355i | \(-0.0792328\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.4455 | 0.546423 | ||||||||
\(800\) | 1.61700 | + | 15.2396i | 0.0571697 | + | 0.538802i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.1320 | − | 18.6105i | −0.499018 | − | 0.657161i | ||||
\(803\) | − | 20.1565i | − | 0.711308i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 5.14157i | − | 0.181217i | ||||||
\(806\) | −12.9944 | + | 9.86732i | −0.457707 | + | 0.347562i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.06178 | − | 5.19844i | −0.0725332 | − | 0.182881i | ||||
\(809\) | −19.7630 | −0.694831 | −0.347415 | − | 0.937711i | \(-0.612941\pi\) | ||||
−0.347415 | + | 0.937711i | \(0.612941\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.1099i | 1.05730i | 0.848839 | + | 0.528651i | \(0.177302\pi\) | ||||
−0.848839 | + | 0.528651i | \(0.822698\pi\) | |||||||
\(812\) | −1.44394 | − | 0.402538i | −0.0506722 | − | 0.0141263i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.33482 | − | 1.75784i | −0.0467855 | − | 0.0616123i | ||||
\(815\) | 0.221024 | 0.00774213 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.38816 | −0.293465 | ||||||||
\(818\) | −13.7036 | − | 18.0464i | −0.479135 | − | 0.630978i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26.3769 | − | 7.35330i | −0.921120 | − | 0.256788i | ||||
\(821\) | − | 26.1788i | − | 0.913645i | −0.889558 | − | 0.456823i | \(-0.848987\pi\) | ||
0.889558 | − | 0.456823i | \(-0.151013\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.9817 | 1.46339 | 0.731696 | − | 0.681631i | \(-0.238729\pi\) | ||||
0.731696 | + | 0.681631i | \(0.238729\pi\) | |||||||
\(824\) | −6.06955 | + | 2.40728i | −0.211443 | + | 0.0838615i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.168692 | − | 0.128097i | 0.00586956 | − | 0.00445707i | ||||
\(827\) | 20.6394i | 0.717703i | 0.933395 | + | 0.358851i | \(0.116832\pi\) | ||||
−0.933395 | + | 0.358851i | \(0.883168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 36.6292i | − | 1.27218i | −0.771613 | − | 0.636092i | \(-0.780550\pi\) | ||
0.771613 | − | 0.636092i | \(-0.219450\pi\) | |||||||
\(830\) | −4.79754 | − | 6.31793i | −0.166525 | − | 0.219299i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −21.3426 | − | 22.6736i | −0.739923 | − | 0.786065i | ||||
\(833\) | −8.00558 | −0.277377 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 0.615418i | − | 0.0212974i | ||||||
\(836\) | 0.707861 | − | 2.53915i | 0.0244819 | − | 0.0878184i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.3598 | − | 10.9042i | 0.496051 | − | 0.376678i | ||||
\(839\) | −3.71855 | −0.128379 | −0.0641893 | − | 0.997938i | \(-0.520446\pi\) | ||||
−0.0641893 | + | 0.997938i | \(0.520446\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.3311 | 0.942450 | ||||||||
\(842\) | −2.13200 | + | 1.61894i | −0.0734736 | + | 0.0557924i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 33.2913 | + | 9.28089i | 1.14593 | + | 0.319461i | ||||
\(845\) | − | 3.25414i | − | 0.111946i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.37399 | 0.184652 | ||||||||
\(848\) | −6.35684 | + | 10.5152i | −0.218295 | + | 0.361093i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.78370 | − | 3.66588i | −0.0954801 | − | 0.125739i | ||||
\(851\) | − | 6.93367i | − | 0.237683i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 49.7965i | − | 1.70500i | −0.522726 | − | 0.852501i | \(-0.675085\pi\) | ||
0.522726 | − | 0.852501i | \(-0.324915\pi\) | |||||||
\(854\) | −9.61854 | + | 7.30387i | −0.329140 | + | 0.249933i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.6829 | − | 39.5418i | −0.536030 | − | 1.35151i | ||||
\(857\) | −35.6409 | −1.21747 | −0.608735 | − | 0.793374i | \(-0.708323\pi\) | ||||
−0.608735 | + | 0.793374i | \(0.708323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.5752i | 1.48677i | 0.668866 | + | 0.743383i | \(0.266780\pi\) | ||||
−0.668866 | + | 0.743383i | \(0.733220\pi\) | |||||||
\(860\) | −6.81873 | + | 24.4593i | −0.232517 | + | 0.834056i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31.8297 | + | 41.9169i | 1.08412 | + | 1.42769i | ||||
\(863\) | 43.6579 | 1.48613 | 0.743067 | − | 0.669217i | \(-0.233370\pi\) | ||||
0.743067 | + | 0.669217i | \(0.233370\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.1415 | −0.650829 | ||||||||
\(866\) | 30.8161 | + | 40.5820i | 1.04717 | + | 1.37903i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.923598 | + | 3.31302i | −0.0313490 | + | 0.112451i | ||||
\(869\) | 17.3093i | 0.587179i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.1669 | 1.25935 | ||||||||
\(872\) | 13.9734 | + | 35.2316i | 0.473199 | + | 1.19309i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.59475 | − | 5.00775i | 0.223071 | − | 0.169390i | ||||
\(875\) | 6.76947i | 0.228850i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.23078i | 0.176631i | 0.996093 | + | 0.0883154i | \(0.0281483\pi\) | ||||
−0.996093 | + | 0.0883154i | \(0.971852\pi\) | |||||||
\(878\) | 15.9239 | + | 20.9703i | 0.537405 | + | 0.707713i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.82858 | − | 4.12815i | −0.230191 | − | 0.139160i | ||||
\(881\) | 22.0358 | 0.742405 | 0.371203 | − | 0.928552i | \(-0.378946\pi\) | ||||
0.371203 | + | 0.928552i | \(0.378946\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.9658i | 1.91705i | 0.285008 | + | 0.958525i | \(0.408004\pi\) | ||||
−0.285008 | + | 0.958525i | \(0.591996\pi\) | |||||||
\(884\) | 9.00907 | + | 2.51153i | 0.303008 | + | 0.0844720i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.55542 | − | 1.94047i | 0.0858510 | − | 0.0651912i | ||||
\(887\) | −3.28694 | −0.110365 | −0.0551823 | − | 0.998476i | \(-0.517574\pi\) | ||||
−0.0551823 | + | 0.998476i | \(0.517574\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.51785 | −0.0509071 | ||||||||
\(890\) | 14.2625 | − | 10.8303i | 0.478082 | − | 0.363033i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.23153 | + | 22.3530i | −0.208647 | + | 0.748434i | ||||
\(893\) | − | 12.8560i | − | 0.430210i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.40932 | 0.281092 | ||||||||
\(896\) | −6.47337 | − | 1.08566i | −0.216260 | − | 0.0362695i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.212881 | + | 0.280345i | 0.00710392 | + | 0.00935522i | ||||
\(899\) | 3.82929i | 0.127714i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.69057i | − | 0.122951i | ||||||
\(902\) | −13.4279 | + | 10.1965i | −0.447101 | + | 0.339508i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.8756 | + | 5.10665i | −0.428235 | + | 0.169845i | ||||
\(905\) | −13.8249 | −0.459555 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 0.0491571i | − | 0.00163223i | −1.00000 | 0.000816117i | \(-0.999740\pi\) | |||
1.00000 | 0.000816117i | \(-0.000259778\pi\) | ||||||||
\(908\) | 52.8804 | + | 14.7419i | 1.75490 | + | 0.489228i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.92315 | − | 3.84952i | −0.0969014 | − | 0.127610i | ||||
\(911\) | −32.4990 | −1.07674 | −0.538370 | − | 0.842708i | \(-0.680960\pi\) | ||||
−0.538370 | + | 0.842708i | \(0.680960\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.88466 | −0.161659 | ||||||||
\(914\) | 5.97624 | + | 7.87017i | 0.197676 | + | 0.260322i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −42.1296 | − | 11.7448i | −1.39200 | − | 0.388059i | ||||
\(917\) | 1.53452i | 0.0506742i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.8145 | −0.653619 | −0.326810 | − | 0.945090i | \(-0.605974\pi\) | ||||
−0.326810 | + | 0.945090i | \(0.605974\pi\) | |||||||
\(920\) | −9.24139 | − | 23.3006i | −0.304680 | − | 0.768200i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −38.4769 | + | 29.2175i | −1.26717 | + | 0.962229i | ||||
\(923\) | − | 27.0008i | − | 0.888742i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.20809i | 0.105481i | ||||||||
\(926\) | −29.5329 | − | 38.8922i | −0.970513 | − | 1.27808i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.26717 | + | 0.771084i | −0.238557 | + | 0.0253121i | ||||
\(929\) | −43.9293 | −1.44127 | −0.720637 | − | 0.693313i | \(-0.756150\pi\) | ||||
−0.720637 | + | 0.693313i | \(0.756150\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.66341i | 0.218385i | ||||||||
\(932\) | −11.9218 | + | 42.7643i | −0.390510 | + | 1.40079i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 44.6571 | − | 33.9105i | 1.46122 | − | 1.10959i | ||||
\(935\) | 2.39666 | 0.0783793 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.9026 | −0.780863 | −0.390431 | − | 0.920632i | \(-0.627674\pi\) | ||||
−0.390431 | + | 0.920632i | \(0.627674\pi\) | |||||||
\(938\) | 6.23953 | − | 4.73801i | 0.203728 | − | 0.154701i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −37.4872 | − | 10.4506i | −1.22270 | − | 0.340862i | ||||
\(941\) | 20.4109i | 0.665375i | 0.943037 | + | 0.332688i | \(0.107955\pi\) | ||||
−0.943037 | + | 0.332688i | \(0.892045\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −52.9654 | −1.72479 | ||||||||
\(944\) | 0.534242 | − | 0.883718i | 0.0173881 | − | 0.0287626i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.45527 | + | 12.4517i | 0.307417 | + | 0.404841i | ||||
\(947\) | 2.72706i | 0.0886176i | 0.999018 | + | 0.0443088i | \(0.0141085\pi\) | ||||
−0.999018 | + | 0.0443088i | \(0.985891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 59.5265i | − | 1.93231i | ||||||
\(950\) | −3.05128 | + | 2.31700i | −0.0989967 | + | 0.0751734i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.83260 | − | 0.726835i | 0.0593947 | − | 0.0235569i | ||||
\(953\) | 32.7679 | 1.06146 | 0.530729 | − | 0.847542i | \(-0.321918\pi\) | ||||
0.530729 | + | 0.847542i | \(0.321918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 8.28723i | − | 0.268168i | ||||||
\(956\) | 11.3511 | − | 40.7174i | 0.367122 | − | 1.31690i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.2675 | − | 28.0074i | −0.687123 | − | 0.904879i | ||||
\(959\) | −2.83139 | −0.0914305 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2139 | −0.716578 | ||||||||
\(962\) | −3.94202 | − | 5.19128i | −0.127096 | − | 0.167374i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.26119 | − | 33.2206i | 0.298283 | − | 1.06996i | ||||
\(965\) | 25.6847i | 0.826818i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.4163 | 1.17107 | 0.585535 | − | 0.810647i | \(-0.300885\pi\) | ||||
0.585535 | + | 0.810647i | \(0.300885\pi\) | |||||||
\(968\) | 24.3539 | − | 9.65913i | 0.782764 | − | 0.310456i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 29.0554 | − | 22.0633i | 0.932914 | − | 0.708411i | ||||
\(971\) | 6.40329i | 0.205491i | 0.994708 | + | 0.102746i | \(0.0327628\pi\) | ||||
−0.994708 | + | 0.102746i | \(0.967237\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 5.99505i | − | 0.192192i | ||||||
\(974\) | 33.9810 | + | 44.7499i | 1.08882 | + | 1.43388i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −30.4616 | + | 50.3880i | −0.975051 | + | 1.61288i | ||||
\(977\) | −11.6473 | −0.372629 | −0.186315 | − | 0.982490i | \(-0.559654\pi\) | ||||
−0.186315 | + | 0.982490i | \(0.559654\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 11.0270i | − | 0.352424i | ||||||
\(980\) | 19.4301 | + | 5.41668i | 0.620670 | + | 0.173029i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.89203 | + | 2.95543i | −0.124200 | + | 0.0943115i | ||||
\(983\) | 34.7061 | 1.10695 | 0.553477 | − | 0.832864i | \(-0.313301\pi\) | ||||
0.553477 | + | 0.832864i | \(0.313301\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.9815 | 1.14646 | ||||||||
\(986\) | 1.74811 | − | 1.32743i | 0.0556712 | − | 0.0422741i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.09046 | − | 7.49866i | 0.0665065 | − | 0.238564i | ||||
\(989\) | 49.1150i | 1.56176i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.30503 | 0.104988 | 0.0524939 | − | 0.998621i | \(-0.483283\pi\) | ||||
0.0524939 | + | 0.998621i | \(0.483283\pi\) | |||||||
\(992\) | 1.76920 | + | 16.6741i | 0.0561723 | + | 0.529402i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.44203 | − | 4.53285i | −0.109175 | − | 0.143773i | ||||
\(995\) | − | 26.6003i | − | 0.843288i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 15.9009i | − | 0.503586i | −0.967781 | − | 0.251793i | \(-0.918980\pi\) | ||
0.967781 | − | 0.251793i | \(-0.0810203\pi\) | |||||||
\(998\) | −19.8045 | + | 15.0386i | −0.626899 | + | 0.476038i | ||||
\(999\) | 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 | 1368.2.g.b.685.5 | 16 | ||
3.2 | odd | 2 | 152.2.c.b.77.12 | yes | 16 | ||
4.3 | odd | 2 | 5472.2.g.b.2737.10 | 16 | |||
8.3 | odd | 2 | 5472.2.g.b.2737.7 | 16 | |||
8.5 | even | 2 | inner | 1368.2.g.b.685.6 | 16 | ||
12.11 | even | 2 | 608.2.c.b.305.5 | 16 | |||
24.5 | odd | 2 | 152.2.c.b.77.11 | ✓ | 16 | ||
24.11 | even | 2 | 608.2.c.b.305.12 | 16 | |||
48.5 | odd | 4 | 4864.2.a.bo.1.6 | 8 | |||
48.11 | even | 4 | 4864.2.a.bn.1.3 | 8 | |||
48.29 | odd | 4 | 4864.2.a.bq.1.3 | 8 | |||
48.35 | even | 4 | 4864.2.a.bp.1.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.11 | ✓ | 16 | 24.5 | odd | 2 | ||
152.2.c.b.77.12 | yes | 16 | 3.2 | odd | 2 | ||
608.2.c.b.305.5 | 16 | 12.11 | even | 2 | |||
608.2.c.b.305.12 | 16 | 24.11 | even | 2 | |||
1368.2.g.b.685.5 | 16 | 1.1 | even | 1 | trivial | ||
1368.2.g.b.685.6 | 16 | 8.5 | even | 2 | inner | ||
4864.2.a.bn.1.3 | 8 | 48.11 | even | 4 | |||
4864.2.a.bo.1.6 | 8 | 48.5 | odd | 4 | |||
4864.2.a.bp.1.6 | 8 | 48.35 | even | 4 | |||
4864.2.a.bq.1.3 | 8 | 48.29 | odd | 4 | |||
5472.2.g.b.2737.7 | 16 | 8.3 | odd | 2 | |||
5472.2.g.b.2737.10 | 16 | 4.3 | odd | 2 |