Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(49,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.bb (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 49.13 | ||
Character | \(\chi\) | \(=\) | 576.49 |
Dual form | 576.2.bb.e.529.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.15652 | + | 1.28937i | 0.667717 | + | 0.744415i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.21694 | − | 0.326078i | 0.544232 | − | 0.145827i | 0.0237796 | − | 0.999717i | \(-0.492430\pi\) |
0.520452 | + | 0.853891i | \(0.325763\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707732 | − | 0.408609i | 0.267497 | − | 0.154440i | −0.360252 | − | 0.932855i | \(-0.617309\pi\) |
0.627750 | + | 0.778415i | \(0.283976\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.324925 | + | 2.98235i | −0.108308 | + | 0.994117i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.497094 | + | 1.85518i | −0.149879 | + | 0.559357i | 0.849610 | + | 0.527411i | \(0.176837\pi\) |
−0.999490 | + | 0.0319463i | \(0.989829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.116336 | + | 0.434170i | 0.0322657 | + | 0.120417i | 0.980180 | − | 0.198107i | \(-0.0634794\pi\) |
−0.947915 | + | 0.318524i | \(0.896813\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.82785 | + | 1.19196i | 0.471948 | + | 0.307764i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.62002 | 1.60559 | 0.802795 | − | 0.596255i | \(-0.203345\pi\) | ||||
0.802795 | + | 0.596255i | \(0.203345\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.18421 | + | 1.18421i | −0.271677 | + | 0.271677i | −0.829775 | − | 0.558098i | \(-0.811531\pi\) |
0.558098 | + | 0.829775i | \(0.311531\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.34535 | + | 0.439960i | 0.293580 | + | 0.0960072i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.66201 | − | 1.53691i | −0.555067 | − | 0.320468i | 0.196096 | − | 0.980585i | \(-0.437174\pi\) |
−0.751163 | + | 0.660117i | \(0.770507\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.95551 | + | 1.70637i | −0.591102 | + | 0.341273i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.22112 | + | 3.03020i | −0.812356 | + | 0.583163i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.65622 | + | 2.31943i | 1.60742 | + | 0.430707i | 0.947272 | − | 0.320430i | \(-0.103827\pi\) |
0.660147 | + | 0.751136i | \(0.270494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.61440 | − | 7.99238i | 0.828771 | − | 1.43547i | −0.0702316 | − | 0.997531i | \(-0.522374\pi\) |
0.899003 | − | 0.437943i | \(-0.144293\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.96690 | + | 1.50462i | −0.516471 | + | 0.261920i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.728028 | − | 0.728028i | 0.123059 | − | 0.123059i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.14134 | − | 2.14134i | −0.352035 | − | 0.352035i | 0.508831 | − | 0.860866i | \(-0.330078\pi\) |
−0.860866 | + | 0.508831i | \(0.830078\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.425259 | + | 0.652125i | −0.0680960 | + | 0.104424i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.15868 | − | 5.28777i | −1.43035 | − | 0.825810i | −0.433199 | − | 0.901299i | \(-0.642615\pi\) |
−0.997147 | + | 0.0754884i | \(0.975948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.66072 | + | 6.19791i | −0.253258 | + | 0.945172i | 0.715793 | + | 0.698312i | \(0.246065\pi\) |
−0.969051 | + | 0.246860i | \(0.920601\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.577065 | + | 3.73529i | 0.0860238 | + | 0.556825i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.140916 | + | 0.244074i | 0.0205547 | + | 0.0356018i | 0.876120 | − | 0.482093i | \(-0.160123\pi\) |
−0.855565 | + | 0.517695i | \(0.826790\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.16608 | + | 5.48381i | −0.452297 | + | 0.783401i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.65618 | + | 8.53562i | 1.07208 | + | 1.19523i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.83822 | + | 4.83822i | 0.664580 | + | 0.664580i | 0.956456 | − | 0.291876i | \(-0.0942794\pi\) |
−0.291876 | + | 0.956456i | \(0.594279\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.41973i | 0.326277i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.89645 | − | 0.157317i | −0.383644 | − | 0.0208372i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.15823 | − | 1.91804i | 0.931923 | − | 0.249708i | 0.239248 | − | 0.970958i | \(-0.423099\pi\) |
0.692674 | + | 0.721251i | \(0.256432\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.87829 | − | 2.64688i | −1.26479 | − | 0.338898i | −0.436755 | − | 0.899581i | \(-0.643872\pi\) |
−0.828031 | + | 0.560682i | \(0.810539\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.988656 | + | 2.24347i | 0.124559 | + | 0.282651i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.283147 | + | 0.490424i | 0.0351200 | + | 0.0608296i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.39968 | − | 5.22368i | −0.170998 | − | 0.638175i | −0.997199 | − | 0.0747982i | \(-0.976169\pi\) |
0.826200 | − | 0.563376i | \(-0.190498\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.09702 | − | 5.20977i | −0.132066 | − | 0.627182i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.27174i | − | 0.388284i | −0.980973 | − | 0.194142i | \(-0.937808\pi\) | ||
0.980973 | − | 0.194142i | \(-0.0621922\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.92262i | − | 0.576150i | −0.957608 | − | 0.288075i | \(-0.906985\pi\) | ||
0.957608 | − | 0.288075i | \(-0.0930152\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.61824 | − | 1.83729i | −0.648738 | − | 0.212152i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.406234 | + | 1.51609i | 0.0462947 | + | 0.172774i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.70232 | − | 13.3408i | −0.866578 | − | 1.50096i | −0.865472 | − | 0.500958i | \(-0.832981\pi\) |
−0.00110666 | − | 0.999999i | \(-0.500352\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.78885 | − | 1.93808i | −0.976539 | − | 0.215342i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.9241 | + | 2.92711i | 1.19908 | + | 0.321292i | 0.802468 | − | 0.596695i | \(-0.203520\pi\) |
0.396610 | + | 0.917987i | \(0.370187\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.05616 | − | 2.15864i | 0.873813 | − | 0.234138i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.02050 | + | 13.8435i | 0.752676 | + | 1.48418i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.44143i | − | 0.364790i | −0.983225 | − | 0.182395i | \(-0.941615\pi\) | ||
0.983225 | − | 0.182395i | \(-0.0583850\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.259740 | + | 0.259740i | 0.0272282 | + | 0.0272282i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.6417 | − | 3.29369i | 1.62197 | − | 0.341540i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.05497 | + | 1.82726i | −0.108238 | + | 0.187473i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.46939 | − | 7.74121i | −0.453798 | − | 0.786001i | 0.544820 | − | 0.838553i | \(-0.316598\pi\) |
−0.998618 | + | 0.0525516i | \(0.983265\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.37128 | − | 2.08530i | −0.539834 | − | 0.209581i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.78073 | − | 6.64577i | 0.177189 | − | 0.661278i | −0.818979 | − | 0.573823i | \(-0.805460\pi\) |
0.996168 | − | 0.0874556i | \(-0.0278736\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.76134 | − | 3.32631i | −0.567681 | − | 0.327751i | 0.188541 | − | 0.982065i | \(-0.439624\pi\) |
−0.756223 | + | 0.654314i | \(0.772957\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.78067 | + | 0.0967154i | 0.173776 | + | 0.00943845i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.06262 | + | 4.06262i | 0.392748 | + | 0.392748i | 0.875666 | − | 0.482918i | \(-0.160423\pi\) |
−0.482918 | + | 0.875666i | \(0.660423\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.19802 | + | 7.19802i | −0.689445 | + | 0.689445i | −0.962109 | − | 0.272664i | \(-0.912095\pi\) |
0.272664 | + | 0.962109i | \(0.412095\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.284468 | − | 5.23748i | 0.0270005 | − | 0.497119i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.45739 | − | 11.1845i | 0.607460 | − | 1.05215i | −0.384197 | − | 0.923251i | \(-0.625522\pi\) |
0.991657 | − | 0.128901i | \(-0.0411450\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.74066 | − | 1.00231i | −0.348818 | − | 0.0934655i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.33265 | + | 0.205881i | −0.123203 | + | 0.0190337i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.68520 | − | 2.70500i | 0.429491 | − | 0.247967i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.33169 | + | 3.65560i | 0.575608 | + | 0.332328i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.77433 | − | 17.9243i | −0.340320 | − | 1.61618i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.49458 | + | 7.49458i | −0.670336 | + | 0.670336i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.6917 | −1.30368 | −0.651838 | − | 0.758358i | \(-0.726002\pi\) | ||||
−0.651838 | + | 0.758358i | \(0.726002\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.91202 | + | 5.02672i | −0.872705 | + | 0.442578i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.59556 | − | 9.68678i | −0.226775 | − | 0.846338i | −0.981685 | − | 0.190509i | \(-0.938986\pi\) |
0.754910 | − | 0.655828i | \(-0.227681\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.354225 | + | 1.32198i | −0.0307152 | + | 0.114631i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.14877 | + | 5.06399i | −0.357069 | + | 0.435839i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.37032 | − | 1.36850i | 0.202510 | − | 0.116919i | −0.395316 | − | 0.918545i | \(-0.629365\pi\) |
0.597826 | + | 0.801626i | \(0.296031\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.46230 | + | 2.26747i | −0.717763 | + | 0.192324i | −0.599173 | − | 0.800619i | \(-0.704504\pi\) |
−0.118590 | + | 0.992943i | \(0.537837\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.151728 | + | 0.463968i | −0.0127778 | + | 0.0390732i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.863293 | −0.0721922 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.2904 | 0.937617 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.7323 | + | 2.25990i | −0.885182 | + | 0.186393i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.25990 | + | 2.21323i | −0.676678 | + | 0.181315i | −0.580761 | − | 0.814074i | \(-0.697245\pi\) |
−0.0959167 | + | 0.995389i | \(0.530578\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.2738 | − | 11.7051i | 1.64986 | − | 0.952546i | 0.672732 | − | 0.739886i | \(-0.265121\pi\) |
0.977126 | − | 0.212660i | \(-0.0682126\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.15101 | + | 19.7432i | −0.173899 | + | 1.59614i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.00931 | − | 11.2309i | 0.241714 | − | 0.902087i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.60365 | − | 20.9131i | −0.447220 | − | 1.66905i | −0.710008 | − | 0.704194i | \(-0.751309\pi\) |
0.262788 | − | 0.964854i | \(-0.415358\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.642736 | + | 11.8337i | −0.0509723 | + | 0.938475i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.51198 | −0.197972 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.39858 | + | 1.39858i | −0.109545 | + | 0.109545i | −0.759755 | − | 0.650210i | \(-0.774681\pi\) |
0.650210 | + | 0.759755i | \(0.274681\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.11992 | + | 2.79847i | −0.242885 | + | 0.217860i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.0385 | − | 11.5692i | −1.55063 | − | 0.895254i | −0.998091 | − | 0.0617643i | \(-0.980327\pi\) |
−0.552535 | − | 0.833490i | \(-0.686339\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0834 | − | 6.39898i | 0.852566 | − | 0.492229i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.14696 | − | 3.91652i | −0.240654 | − | 0.299504i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.95697 | + | 1.32822i | 0.376871 | + | 0.100982i | 0.442282 | − | 0.896876i | \(-0.354169\pi\) |
−0.0654105 | + | 0.997858i | \(0.520836\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.39447 | + | 2.41530i | −0.105412 | + | 0.182579i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.7517 | + | 7.01132i | 0.808147 | + | 0.527003i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.14784 | + | 3.14784i | −0.235281 | + | 0.235281i | −0.814893 | − | 0.579612i | \(-0.803204\pi\) |
0.579612 | + | 0.814893i | \(0.303204\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.82816 | − | 2.82816i | −0.210216 | − | 0.210216i | 0.594143 | − | 0.804359i | \(-0.297491\pi\) |
−0.804359 | + | 0.594143i | \(0.797491\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.01164 | − | 15.7979i | −0.592238 | − | 1.16781i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.30413 | − | 1.90764i | −0.242924 | − | 0.140253i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.29077 | + | 12.2813i | −0.240645 | + | 0.898099i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.74925 | + | 3.86936i | −0.127240 | + | 0.281454i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.50375 | + | 14.7289i | 0.615310 | + | 1.06575i | 0.990330 | + | 0.138732i | \(0.0443025\pi\) |
−0.375020 | + | 0.927017i | \(0.622364\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.70970 | + | 4.69334i | −0.195049 | + | 0.337834i | −0.946916 | − | 0.321480i | \(-0.895820\pi\) |
0.751868 | + | 0.659314i | \(0.229153\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.304871 | + | 0.932265i | −0.0218323 | + | 0.0667609i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.03915 | − | 8.03915i | −0.572766 | − | 0.572766i | 0.360135 | − | 0.932900i | \(-0.382731\pi\) |
−0.932900 | + | 0.360135i | \(0.882731\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2258i | 0.795773i | 0.917435 | + | 0.397886i | \(0.130256\pi\) | ||||
−0.917435 | + | 0.397886i | \(0.869744\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.11648 | − | 7.84599i | 0.360888 | − | 0.553414i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.07402 | − | 1.89548i | 0.496499 | − | 0.133036i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.8698 | − | 3.44845i | −0.898865 | − | 0.240850i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.44856 | − | 7.43966i | 0.378701 | − | 0.517092i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.60826 | − | 2.78559i | −0.111246 | − | 0.192683i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.84526 | + | 14.3507i | 0.264718 | + | 0.987942i | 0.962423 | + | 0.271556i | \(0.0875383\pi\) |
−0.697704 | + | 0.716386i | \(0.745795\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.21846 | − | 3.78383i | 0.289044 | − | 0.259264i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.08400i | 0.551324i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 7.54195i | − | 0.511981i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.34706 | − | 5.69311i | 0.428895 | − | 0.384705i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.770143 | + | 2.87421i | 0.0518054 | + | 0.193340i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.28003 | + | 14.3414i | 0.554472 | + | 0.960373i | 0.997944 | + | 0.0640854i | \(0.0204130\pi\) |
−0.443473 | + | 0.896288i | \(0.646254\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.12866 | − | 9.36882i | −0.275244 | − | 0.624588i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.88725 | − | 2.11338i | −0.523495 | − | 0.140270i | −0.0126123 | − | 0.999920i | \(-0.504015\pi\) |
−0.510883 | + | 0.859650i | \(0.670681\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.33776 | + | 1.16230i | −0.286647 | + | 0.0768068i | −0.399278 | − | 0.916830i | \(-0.630739\pi\) |
0.112631 | + | 0.993637i | \(0.464072\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.48497 | + | 2.27717i | −0.0977039 | + | 0.149827i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.33128i | 0.480288i | 0.970737 | + | 0.240144i | \(0.0771947\pi\) | ||||
−0.970737 | + | 0.240144i | \(0.922805\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.251073 | + | 0.251073i | 0.0163782 | + | 0.0163782i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.29329 | − | 25.3600i | 0.538707 | − | 1.64731i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.40305 | + | 5.89425i | −0.220125 | + | 0.381268i | −0.954846 | − | 0.297102i | \(-0.903980\pi\) |
0.734721 | + | 0.678370i | \(0.237313\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.98687 | + | 5.17340i | 0.192401 | + | 0.333248i | 0.946045 | − | 0.324034i | \(-0.105039\pi\) |
−0.753644 | + | 0.657282i | \(0.771706\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.66558 | − | 13.5735i | −0.491747 | − | 0.870738i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.06478 | + | 7.70585i | −0.131914 | + | 0.492309i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.651915 | − | 0.376383i | −0.0414804 | − | 0.0239487i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.85985 | + | 17.4704i | 0.561470 | + | 1.10714i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.1412 | + | 16.1412i | 1.01882 | + | 1.01882i | 0.999819 | + | 0.0190030i | \(0.00604922\pi\) |
0.0190030 | + | 0.999819i | \(0.493951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.17451 | − | 4.17451i | 0.262449 | − | 0.262449i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.1004 | + | 7.89082i | 0.757755 | + | 0.494142i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.172522 | + | 0.298817i | −0.0107616 | + | 0.0186397i | −0.871356 | − | 0.490651i | \(-0.836759\pi\) |
0.860594 | + | 0.509291i | \(0.170092\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.39047 | − | 0.640524i | −0.148536 | − | 0.0398002i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.72997 | + | 25.0623i | −0.602270 | + | 1.55131i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.43128 | − | 2.55840i | 0.273244 | − | 0.157758i | −0.357117 | − | 0.934060i | \(-0.616240\pi\) |
0.630361 | + | 0.776302i | \(0.282907\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.46546 | + | 4.31018i | 0.458599 | + | 0.264772i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.43726 | − | 3.98008i | 0.271556 | − | 0.243577i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.4613 | + | 15.4613i | −0.942692 | + | 0.942692i | −0.998445 | − | 0.0557529i | \(-0.982244\pi\) |
0.0557529 | + | 0.998445i | \(0.482244\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4048 | 0.753538 | 0.376769 | − | 0.926307i | \(-0.377035\pi\) | ||||
0.376769 | + | 0.926307i | \(0.377035\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0345053 | + | 0.635294i | −0.00208836 | + | 0.0384498i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.69645 | − | 6.33123i | −0.102300 | − | 0.381787i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.42920 | + | 20.2621i | −0.326209 | + | 1.21743i | 0.586881 | + | 0.809673i | \(0.300356\pi\) |
−0.913091 | + | 0.407757i | \(0.866311\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.3368 | + | 16.3587i | 1.33727 | + | 0.979370i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.9537 | − | 6.32414i | 0.653445 | − | 0.377266i | −0.136330 | − | 0.990663i | \(-0.543531\pi\) |
0.789775 | + | 0.613397i | \(0.210197\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.2483 | − | 5.69346i | 1.26308 | − | 0.338441i | 0.435703 | − | 0.900090i | \(-0.356500\pi\) |
0.827375 | + | 0.561650i | \(0.189833\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.57610 | + | 0.753021i | −0.211830 | + | 0.0446051i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.64252 | −0.510152 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.8246 | 1.57792 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.81231 | − | 14.7155i | 0.282103 | − | 0.862641i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.111616 | + | 0.0299075i | −0.00652069 | + | 0.00174721i | −0.262078 | − | 0.965047i | \(-0.584408\pi\) |
0.255557 | + | 0.966794i | \(0.417741\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.08571 | − | 4.66828i | 0.470768 | − | 0.271798i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.52327 | − | 9.33723i | −0.204441 | − | 0.541801i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.357595 | − | 1.33456i | 0.0206802 | − | 0.0771797i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.35717 | + | 5.06504i | 0.0782262 | + | 0.291944i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.6283 | − | 5.38995i | 0.610578 | − | 0.309645i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.8844 | −0.737757 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.4426 | − | 12.4426i | 0.710135 | − | 0.710135i | −0.256428 | − | 0.966563i | \(-0.582546\pi\) |
0.966563 | + | 0.256428i | \(0.0825456\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.37427 | − | 11.2754i | −0.135068 | − | 0.641436i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.03115 | + | 1.17269i | 0.115176 | + | 0.0664969i | 0.556481 | − | 0.830860i | \(-0.312151\pi\) |
−0.441305 | + | 0.897357i | \(0.645484\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.62293 | − | 4.97845i | 0.487397 | − | 0.281399i | −0.236097 | − | 0.971729i | \(-0.575868\pi\) |
0.723494 | + | 0.690331i | \(0.242535\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.93468 | + | 2.40779i | 0.109007 | + | 0.135664i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.42985 | + | 1.18698i | 0.248805 | + | 0.0666672i | 0.381066 | − | 0.924548i | \(-0.375557\pi\) |
−0.132261 | + | 0.991215i | \(0.542224\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.60590 | + | 14.9059i | −0.481838 | + | 0.834568i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.539701 | + | 9.93669i | −0.0301232 | + | 0.554612i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.83950 | + | 7.83950i | −0.436202 | + | 0.436202i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.08468 | − | 1.08468i | −0.0601674 | − | 0.0601674i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.6055 | − | 0.956225i | −0.973588 | − | 0.0528794i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.199461 | + | 0.115159i | 0.0109967 | + | 0.00634892i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.49465 | + | 16.7743i | −0.247048 | + | 0.921997i | 0.725294 | + | 0.688439i | \(0.241704\pi\) |
−0.972343 | + | 0.233558i | \(0.924963\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.08202 | − | 5.69046i | 0.388092 | − | 0.311835i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.40666 | − | 5.90050i | −0.186126 | − | 0.322379i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.8424 | + | 25.7078i | −0.808517 | + | 1.40039i | 0.105375 | + | 0.994433i | \(0.466396\pi\) |
−0.913891 | + | 0.405959i | \(0.866937\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.8890 | − | 4.60919i | 1.18885 | − | 0.250337i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.5335 | + | 12.5335i | 0.678727 | + | 0.678727i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.8953i | 0.588290i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.03380 | − | 5.98226i | −0.163334 | − | 0.322074i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.94185 | + | 0.520318i | −0.104244 | + | 0.0279321i | −0.310564 | − | 0.950552i | \(-0.600518\pi\) |
0.206320 | + | 0.978485i | \(0.433851\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.6321 | + | 7.13604i | 1.42558 | + | 0.381984i | 0.887461 | − | 0.460883i | \(-0.152467\pi\) |
0.538122 | + | 0.842867i | \(0.319134\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.80669 | − | 1.48017i | −0.0964339 | − | 0.0790054i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.58657 | + | 2.74801i | 0.0844444 | + | 0.146262i | 0.905154 | − | 0.425083i | \(-0.139755\pi\) |
−0.820710 | + | 0.571345i | \(0.806422\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.06684 | − | 3.98150i | −0.0566220 | − | 0.211316i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.90625 | + | 2.91254i | 0.471369 | + | 0.154148i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.6997i | 1.19804i | 0.800732 | + | 0.599022i | \(0.204444\pi\) | ||||
−0.800732 | + | 0.599022i | \(0.795556\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.1953i | 0.852383i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.60932 | + | 12.3916i | 0.136954 | + | 0.650393i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.60516 | − | 5.99054i | −0.0840179 | − | 0.313559i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.94141 | + | 3.36261i | 0.101341 | + | 0.175527i | 0.912237 | − | 0.409662i | \(-0.134354\pi\) |
−0.810897 | + | 0.585189i | \(0.801020\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.7459 | − | 25.5963i | 0.975871 | − | 1.33249i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.40110 | + | 1.44722i | 0.280411 | + | 0.0751359i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.36176 | − | 1.16873i | 0.225843 | − | 0.0605145i | −0.144123 | − | 0.989560i | \(-0.546036\pi\) |
0.369966 | + | 0.929045i | \(0.379369\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.3309 | − | 0.995622i | −0.946602 | − | 0.0514137i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.02810i | 0.207458i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.6109 | − | 14.6109i | −0.750509 | − | 0.750509i | 0.224065 | − | 0.974574i | \(-0.428067\pi\) |
−0.974574 | + | 0.224065i | \(0.928067\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.9912 | − | 18.9429i | −0.870487 | − | 0.970476i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.4164 | + | 24.9699i | −0.736643 | + | 1.27590i | 0.217355 | + | 0.976093i | \(0.430257\pi\) |
−0.953999 | + | 0.299811i | \(0.903076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.988724 | + | 1.71252i | 0.0503901 | + | 0.0872781i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.9447 | − | 6.96672i | −0.912182 | − | 0.354138i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.0510254 | − | 0.190429i | 0.00258709 | − | 0.00965514i | −0.964620 | − | 0.263643i | \(-0.915076\pi\) |
0.967207 | + | 0.253988i | \(0.0817425\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.6225 | − | 10.1744i | −0.891210 | − | 0.514540i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.48797 | − | 14.5496i | 0.478605 | − | 0.733929i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.7234 | − | 13.7234i | −0.690499 | − | 0.690499i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.98504 | + | 9.98504i | −0.501135 | + | 0.501135i | −0.911791 | − | 0.410656i | \(-0.865300\pi\) |
0.410656 | + | 0.911791i | \(0.365300\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.11419 | + | 1.07218i | −0.105842 | + | 0.0536759i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.396741 | − | 0.687175i | 0.0198123 | − | 0.0343159i | −0.855949 | − | 0.517060i | \(-0.827026\pi\) |
0.875762 | + | 0.482744i | \(0.160360\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00687 | + | 1.07364i | 0.199596 | + | 0.0534817i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.3275 | + | 0.507321i | −0.562866 | + | 0.0252090i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.03702 | − | 2.90813i | 0.249676 | − | 0.144150i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.225551 | − | 0.130222i | −0.0111528 | − | 0.00643907i | 0.494413 | − | 0.869227i | \(-0.335383\pi\) |
−0.505566 | + | 0.862788i | \(0.668716\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.50582 | + | 1.47350i | 0.222256 | + | 0.0726826i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.28238 | − | 4.28238i | 0.210722 | − | 0.210722i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.2485 | 0.699429 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.7104 | − | 8.28863i | −0.622431 | − | 0.405896i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.985334 | + | 3.67732i | 0.0481367 | + | 0.179649i | 0.985809 | − | 0.167873i | \(-0.0536899\pi\) |
−0.937672 | + | 0.347522i | \(0.887023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.208895 | + | 0.779608i | −0.0101809 | + | 0.0379958i | −0.970829 | − | 0.239771i | \(-0.922928\pi\) |
0.960649 | + | 0.277767i | \(0.0895943\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.773700 | + | 0.340955i | −0.0376186 | + | 0.0165778i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.5655 | + | 11.2962i | −0.949068 | + | 0.547945i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.07272 | + | 2.16308i | −0.390666 | + | 0.104679i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.998415 | − | 1.11310i | −0.0482039 | − | 0.0537409i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.6515 | −1.23559 | −0.617796 | − | 0.786339i | \(-0.711974\pi\) | ||||
−0.617796 | + | 0.786339i | \(0.711974\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.0987 | −1.11005 | −0.555026 | − | 0.831833i | \(-0.687292\pi\) | ||||
−0.555026 | + | 0.831833i | \(0.687292\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.0576 | + | 14.5575i | 0.626063 | + | 0.697977i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.97241 | − | 1.33235i | 0.237863 | − | 0.0637351i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.88493 | − | 4.55237i | 0.376327 | − | 0.217273i | −0.299892 | − | 0.953973i | \(-0.596951\pi\) |
0.676219 | + | 0.736701i | \(0.263617\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.3259 | − | 11.2242i | −0.729805 | − | 0.534485i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.31445 | − | 27.2979i | 0.347520 | − | 1.29696i | −0.542120 | − | 0.840301i | \(-0.682378\pi\) |
0.889640 | − | 0.456662i | \(-0.150955\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.12217 | − | 4.18801i | −0.0531961 | − | 0.198531i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.4064 | − | 8.09038i | −0.586803 | − | 0.382662i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.90915 | 0.278870 | 0.139435 | − | 0.990231i | \(-0.455471\pi\) | ||||
0.139435 | + | 0.990231i | \(0.455471\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.3625 | − | 14.3625i | 0.676302 | − | 0.676302i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 38.5392 | + | 12.6032i | 1.81073 | + | 0.592149i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.400784 | + | 0.231393i | 0.0187890 | + | 0.0108478i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.70096 | + | 2.71410i | −0.219902 | + | 0.126960i | −0.605905 | − | 0.795537i | \(-0.707189\pi\) |
0.386003 | + | 0.922497i | \(0.373855\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.9439 | + | 20.0600i | −1.30431 | + | 0.936320i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.1830 | − | 6.74777i | −1.17289 | − | 0.314275i | −0.380787 | − | 0.924663i | \(-0.624347\pi\) |
−0.792103 | + | 0.610388i | \(0.791014\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.87708 | − | 17.1076i | 0.459027 | − | 0.795057i | −0.539883 | − | 0.841740i | \(-0.681532\pi\) |
0.998910 | + | 0.0466825i | \(0.0148649\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.9611 | − | 9.10865i | 0.832924 | − | 0.422404i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.1348 | + | 16.1348i | −0.746628 | + | 0.746628i | −0.973844 | − | 0.227217i | \(-0.927037\pi\) |
0.227217 | + | 0.973844i | \(0.427037\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.12504 | − | 3.12504i | −0.144301 | − | 0.144301i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.4839 | − | 31.4116i | 0.943848 | − | 1.44737i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.6727 | − | 6.16188i | −0.490731 | − | 0.283324i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.47925 | − | 5.52065i | 0.0678728 | − | 0.253305i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.0013 | + | 12.8572i | −0.732650 | + | 0.588691i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.1996 | − | 19.3982i | −0.511721 | − | 0.886327i | −0.999908 | − | 0.0135877i | \(-0.995675\pi\) |
0.488187 | − | 0.872739i | \(-0.337659\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.680593 | − | 1.17882i | 0.0310324 | − | 0.0537496i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.90516 | − | 3.23886i | −0.132189 | − | 0.147373i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.96322 | − | 7.96322i | −0.361591 | − | 0.361591i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8.27717i | − | 0.375074i | −0.982258 | − | 0.187537i | \(-0.939950\pi\) | ||
0.982258 | − | 0.187537i | \(-0.0600505\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.42076 | − | 0.185795i | −0.154692 | − | 0.00840194i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.7589 | + | 9.31362i | −1.56865 | + | 0.420318i | −0.935388 | − | 0.353622i | \(-0.884950\pi\) |
−0.633259 | + | 0.773940i | \(0.718283\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 57.3043 | + | 15.3546i | 2.58086 | + | 0.691538i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.21649 | − | 0.786232i | −0.324357 | − | 0.0353385i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.33686 | − | 2.31551i | −0.0599664 | − | 0.103865i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.44528 | + | 27.7862i | 0.333297 | + | 1.24388i | 0.905704 | + | 0.423911i | \(0.139343\pi\) |
−0.572407 | + | 0.819969i | \(0.693990\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.25795 | − | 39.2170i | −0.368938 | − | 1.75209i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 15.6106i | − | 0.696044i | −0.937486 | − | 0.348022i | \(-0.886854\pi\) | ||
0.937486 | − | 0.348022i | \(-0.113146\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 8.66815i | − | 0.385728i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.0687 | + | 6.88995i | 0.935696 | + | 0.305994i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.65858 | + | 9.92195i | 0.117839 | + | 0.439783i | 0.999484 | − | 0.0321319i | \(-0.0102297\pi\) |
−0.881644 | + | 0.471915i | \(0.843563\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.01143 | − | 3.48390i | −0.0889804 | − | 0.154119i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.41030 | − | 8.58710i | 0.0622664 | − | 0.379130i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.09583 | − | 2.16927i | −0.356745 | − | 0.0955896i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.522849 | + | 0.140097i | −0.0229949 | + | 0.00616145i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.02028 | + | 7.92745i | 0.176471 | + | 0.347977i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.2775i | 0.932185i | 0.884736 | + | 0.466092i | \(0.154339\pi\) | ||||
−0.884736 | + | 0.466092i | \(0.845661\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.96994 | + | 2.96994i | 0.129867 | + | 0.129867i | 0.769052 | − | 0.639186i | \(-0.220729\pi\) |
−0.639186 | + | 0.769052i | \(0.720729\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.72694 | + | 0.995354i | −0.206300 | + | 0.0434408i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.5474 | − | 52.9097i | 1.33067 | − | 2.30478i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.77581 | − | 11.7360i | −0.294600 | − | 0.510263i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.39439 | + | 21.9716i | 0.147304 | + | 0.953486i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.23031 | − | 4.59158i | 0.0532906 | − | 0.198883i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.26869 | + | 3.61923i | 0.271019 | + | 0.156473i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.69926 | − | 0.418177i | −0.332248 | − | 0.0180457i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.59960 | − | 8.59960i | −0.370411 | − | 0.370411i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.1934 | + | 15.1934i | −0.653214 | + | 0.653214i | −0.953765 | − | 0.300552i | \(-0.902829\pi\) |
0.300552 | + | 0.953765i | \(0.402829\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.375709 | − | 6.91736i | 0.0161232 | − | 0.296853i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.41244 | + | 11.1067i | −0.274679 | + | 0.475757i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.6172 | − | 9.00771i | −1.43737 | − | 0.385142i | −0.545757 | − | 0.837943i | \(-0.683758\pi\) |
−0.891611 | + | 0.452802i | \(0.850425\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.1036 | − | 28.6005i | 0.473892 | − | 1.22064i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.9975 | + | 7.50410i | −0.553712 | + | 0.319686i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.9023 | − | 6.29447i | −0.463615 | − | 0.267668i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.36165 | − | 6.46645i | −0.0577987 | − | 0.274486i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.3686 | − | 15.3686i | 0.651189 | − | 0.651189i | −0.302091 | − | 0.953279i | \(-0.597685\pi\) |
0.953279 | + | 0.302091i | \(0.0976845\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.88415 | −0.121986 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.6409 | + | 9.96058i | −0.829241 | + | 0.420536i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.11840 | + | 15.3701i | 0.173570 | + | 0.647772i | 0.996791 | + | 0.0800506i | \(0.0255082\pi\) |
−0.823221 | + | 0.567721i | \(0.807825\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.21123 | − | 15.7165i | 0.177168 | − | 0.661199i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.01206 | + | 2.21956i | −0.294479 | + | 0.0932128i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.4673 | − | 21.0544i | 1.52879 | − | 0.882647i | 0.529376 | − | 0.848387i | \(-0.322426\pi\) |
0.999413 | − | 0.0342597i | \(-0.0109073\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.8497 | − | 10.1418i | 1.58396 | − | 0.424421i | 0.643813 | − | 0.765183i | \(-0.277352\pi\) |
0.940150 | + | 0.340762i | \(0.110685\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.15622 | + | 27.9987i | −0.382506 | + | 1.16966i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.4901 | 0.437469 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.5220 | 0.562927 | 0.281463 | − | 0.959572i | \(-0.409180\pi\) | ||||
0.281463 | + | 0.959572i | \(0.409180\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.18525 | + | 1.93414i | −0.381726 | + | 0.0803803i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.92739 | − | 2.39209i | 0.370371 | − | 0.0992405i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3808 | + | 6.57071i | −0.471345 | + | 0.272131i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.55462 | + | 0.685092i | −0.0642756 | + | 0.0283251i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.32769 | + | 31.0793i | −0.343720 | + | 1.28278i | 0.550380 | + | 0.834915i | \(0.314483\pi\) |
−0.894100 | + | 0.447867i | \(0.852184\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00024 | + | 14.9291i | 0.164827 | + | 0.615143i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.06797 | − | 19.6628i | 0.0439303 | − | 0.808821i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.2071 | −0.994066 | −0.497033 | − | 0.867732i | \(-0.665577\pi\) | ||||
−0.497033 | + | 0.867732i | \(0.665577\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.81956 | − | 4.81956i | 0.197583 | − | 0.197583i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.4741 | + | 12.9828i | −0.592386 | + | 0.531351i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.5549 | + | 19.3729i | 1.37102 | + | 0.791557i | 0.991056 | − | 0.133445i | \(-0.0426041\pi\) |
0.379961 | + | 0.925003i | \(0.375937\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.4630 | + | 12.3917i | −0.875493 | + | 0.505466i | −0.869170 | − | 0.494514i | \(-0.835346\pi\) |
−0.00632336 | + | 0.999980i | \(0.502013\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.0337 | − | 2.47704i | 0.652941 | − | 0.100873i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.89730 | + | 2.38402i | 0.361727 | + | 0.0969244i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.85399 | + | 10.1394i | −0.237606 | + | 0.411546i | −0.960027 | − | 0.279908i | \(-0.909696\pi\) |
0.722421 | + | 0.691454i | \(0.243029\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.6252 | + | 6.92884i | 0.430555 | + | 0.280771i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0895759 | + | 0.0895759i | −0.00362385 | + | 0.00362385i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.6378 | − | 24.6378i | −0.995112 | − | 0.995112i | 0.00487577 | − | 0.999988i | \(-0.498448\pi\) |
−0.999988 | + | 0.00487577i | \(0.998448\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.4378 | − | 20.5820i | −0.420895 | − | 0.829948i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.72698 | + | 2.72912i | 0.190301 | + | 0.109870i | 0.592123 | − | 0.805847i | \(-0.298290\pi\) |
−0.401822 | + | 0.915718i | \(0.631623\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.43389 | − | 16.5475i | 0.178213 | − | 0.665101i | −0.817769 | − | 0.575547i | \(-0.804789\pi\) |
0.995982 | − | 0.0895538i | \(-0.0285441\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.8938 | − | 1.57893i | 0.637797 | − | 0.0633602i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.40620 | − | 2.43561i | −0.0563381 | − | 0.0975805i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.85520 | − | 3.21329i | 0.0742078 | − | 0.128532i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.73166 | − | 5.29522i | 0.0691557 | − | 0.211471i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.1757 | − | 14.1757i | −0.565223 | − | 0.565223i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.04281i | 0.200751i | 0.994950 | + | 0.100376i | \(0.0320045\pi\) | ||||
−0.994950 | + | 0.100376i | \(0.967996\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.0562 | + | 21.5548i | −0.558682 | + | 0.856726i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.8789 | + | 4.79063i | −0.709502 | + | 0.190111i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.74923 | − | 0.736654i | −0.108929 | − | 0.0291873i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.75747 | + | 1.06307i | 0.385999 | + | 0.0420544i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.2406 | + | 17.7373i | 0.404480 | + | 0.700579i | 0.994261 | − | 0.106984i | \(-0.0341193\pi\) |
−0.589781 | + | 0.807563i | \(0.700786\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.7731 | + | 40.2059i | 0.424851 | + | 1.58557i | 0.764248 | + | 0.644922i | \(0.223110\pi\) |
−0.339397 | + | 0.940643i | \(0.610223\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.4232 | + | 9.34931i | −0.410414 | + | 0.368129i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 9.07428i | − | 0.356747i | −0.983963 | − | 0.178373i | \(-0.942917\pi\) | ||
0.983963 | − | 0.178373i | \(-0.0570835\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.2332i | 0.558704i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.72432 | − | 8.72241i | 0.381126 | − | 0.341858i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.05224 | − | 30.0514i | −0.315109 | − | 1.17600i | −0.923888 | − | 0.382662i | \(-0.875007\pi\) |
0.608780 | − | 0.793339i | \(-0.291659\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.31729 | − | 10.9419i | −0.246837 | − | 0.427534i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6810 | + | 1.59948i | 0.572760 | + | 0.0624018i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.3336 | + | 3.30479i | 0.480450 | + | 0.128736i | 0.490912 | − | 0.871209i | \(-0.336664\pi\) |
−0.0104620 | + | 0.999945i | \(0.503330\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.7191 | − | 11.4466i | 1.66158 | − | 0.445219i | 0.698759 | − | 0.715357i | \(-0.253736\pi\) |
0.962822 | + | 0.270137i | \(0.0870692\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.81522 | + | 4.31708i | −0.109334 | + | 0.167661i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.72428i | 0.0668647i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.4782 | − | 19.4782i | −0.754198 | − | 0.754198i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.91533 | + | 27.2621i | −0.344686 | + | 1.05401i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.82087 | − | 17.0102i | 0.379131 | − | 0.656673i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.9683 | − | 29.3899i | −0.654079 | − | 1.13290i | −0.982124 | − | 0.188236i | \(-0.939723\pi\) |
0.328045 | − | 0.944662i | \(-0.393610\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.30495 | − | 16.1586i | 0.281168 | − | 0.621944i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.7072 | − | 39.9599i | 0.411512 | − | 1.53578i | −0.380210 | − | 0.924900i | \(-0.624148\pi\) |
0.791721 | − | 0.610882i | \(-0.209185\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.32626 | − | 3.65247i | −0.242780 | − | 0.140169i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.39684 | − | 12.6137i | −0.245127 | − | 0.483359i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.0872426 | − | 0.0872426i | −0.00333824 | − | 0.00333824i | 0.705436 | − | 0.708774i | \(-0.250751\pi\) |
−0.708774 | + | 0.705436i | \(0.750751\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.43830 | − | 2.43830i | 0.0931625 | − | 0.0931625i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.51533 | − | 4.24873i | −0.248575 | − | 0.162099i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.53775 | + | 2.66347i | −0.0585837 | + | 0.101470i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.5322 | + | 3.62594i | 0.514789 | + | 0.137937i | 0.506855 | − | 0.862031i | \(-0.330808\pi\) |
0.00793395 | + | 0.999969i | \(0.497475\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.65350 | + | 0.718918i | −0.176772 | + | 0.0273094i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.55874 | + | 5.51874i | −0.362584 | + | 0.209338i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −60.6306 | − | 35.0051i | −2.29655 | − | 1.32591i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.45270 | + | 8.47877i | −0.357534 | + | 0.320696i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.7257 | − | 10.7257i | 0.405103 | − | 0.405103i | −0.474924 | − | 0.880027i | \(-0.657525\pi\) |
0.880027 | + | 0.474924i | \(0.157525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.07161 | 0.191279 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0333540 | + | 0.614096i | −0.00125618 | + | 0.0231282i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.45524 | − | 5.43104i | −0.0547300 | − | 0.204255i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.7081 | + | 39.9633i | −0.402153 | + | 1.50085i | 0.407095 | + | 0.913386i | \(0.366542\pi\) |
−0.809247 | + | 0.587468i | \(0.800125\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42.2896 | − | 18.6363i | 1.58599 | − | 0.698914i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.5671 | + | 14.1839i | −0.920047 | + | 0.531189i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.05057 | + | 0.281501i | −0.0392893 | + | 0.0105275i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.5355 | + | 2.42905i | −0.430802 | + | 0.0907144i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.2734 | 1.27818 | 0.639091 | − | 0.769131i | \(-0.279311\pi\) | ||||
0.639091 | + | 0.769131i | \(0.279311\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.43664 | −0.202471 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.21604 | + | 9.83430i | −0.119606 | + | 0.365742i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −29.5413 | + | 7.91558i | −1.09714 | + | 0.293977i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.8380 | + | 16.6496i | −1.06954 | + | 0.617501i | −0.928057 | − | 0.372439i | \(-0.878522\pi\) |
−0.141487 | + | 0.989940i | \(0.545188\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.63576 | − | 25.5817i | 0.319843 | − | 0.947471i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.9940 | + | 41.0302i | −0.406629 | + | 1.51756i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.71001 | − | 36.2382i | −0.358647 | − | 1.33849i | −0.875832 | − | 0.482616i | \(-0.839687\pi\) |
0.517185 | − | 0.855874i | \(-0.326980\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.3236 | + | 6.24972i | −0.454563 | + | 0.230524i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.3866 | 0.382597 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.57380 | − | 8.57380i | 0.315392 | − | 0.315392i | −0.531602 | − | 0.846994i | \(-0.678410\pi\) |
0.846994 | + | 0.531602i | \(0.178410\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.268657 | − | 1.27585i | −0.00986936 | − | 0.0468696i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.3476 | + | 5.97418i | 0.379616 | + | 0.219172i | 0.677651 | − | 0.735383i | \(-0.262998\pi\) |
−0.298035 | + | 0.954555i | \(0.596331\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.33012 | + | 5.38674i | −0.341829 | + | 0.197355i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.2792 | + | 31.6285i | −0.449272 | + | 1.15723i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.53526 | + | 1.21522i | 0.165715 | + | 0.0444032i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.2293 | + | 21.1818i | −0.446254 | + | 0.772934i | −0.998139 | − | 0.0609863i | \(-0.980575\pi\) |
0.551885 | + | 0.833920i | \(0.313909\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.14429 | + | 39.4795i | −0.0781421 | + | 1.43871i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.8552 | − | 20.8552i | 0.758999 | − | 0.758999i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.77221 | + | 5.77221i | 0.209794 | + | 0.209794i | 0.804180 | − | 0.594386i | \(-0.202605\pi\) |
−0.594386 | + | 0.804180i | \(0.702605\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.2104 | + | 0.554566i | 0.370613 | + | 0.0201295i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.8368 | + | 20.6904i | 1.29908 | + | 0.750025i | 0.980246 | − | 0.197784i | \(-0.0633746\pi\) |
0.318836 | + | 0.947810i | \(0.396708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.15309 | + | 8.03544i | −0.0779471 | + | 0.290902i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.82018 | + | 24.7277i | 0.138119 | + | 0.894032i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.66551 | + | 2.88475i | 0.0601382 | + | 0.104162i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.7893 | − | 34.2761i | 0.713622 | − | 1.23603i | −0.249867 | − | 0.968280i | \(-0.580387\pi\) |
0.963489 | − | 0.267749i | \(-0.0862798\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.584809 | + | 0.123144i | −0.0210614 | + | 0.00443491i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.1627 | + | 34.1627i | 1.22875 | + | 1.22875i | 0.964439 | + | 0.264307i | \(0.0851433\pi\) |
0.264307 | + | 0.964439i | \(0.414857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.4954i | 1.13135i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.93875 | − | 3.82297i | −0.0695524 | − | 0.137148i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.1076 | − | 4.58398i | 0.612945 | − | 0.164238i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.06965 | + | 1.62636i | 0.217189 | + | 0.0581957i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −43.5673 | + | 16.4395i | −1.55697 | + | 0.587500i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.6386 | − | 23.6228i | −0.486783 | − | 0.843132i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.0877 | − | 37.6477i | −0.359586 | − | 1.34199i | −0.874614 | − | 0.484820i | \(-0.838885\pi\) |
0.515028 | − | 0.857174i | \(-0.327782\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.42357 | + | 2.75470i | 0.299887 | + | 0.0980698i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 10.5542i | − | 0.375264i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.59678i | − | 0.163237i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.07655 | + | 14.6105i | 0.109114 | + | 0.518181i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.736732 | + | 2.74952i | 0.0260964 | + | 0.0973931i | 0.977746 | − | 0.209793i | \(-0.0672791\pi\) |
−0.951649 | + | 0.307186i | \(0.900612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.932866 | + | 1.61577i | 0.0330024 | + | 0.0571619i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.2635 | + | 1.11821i | 0.362645 | + | 0.0395099i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.13235 | + | 2.44701i | 0.322274 | + | 0.0863529i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.05693 | + | 0.819102i | −0.107743 | + | 0.0288696i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.8165 | − | 2.05397i | −1.33121 | − | 0.0723030i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 14.8679i | − | 0.522727i | −0.965240 | − | 0.261364i | \(-0.915828\pi\) | ||
0.965240 | − | 0.261364i | \(-0.0841722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.8984 | − | 11.8984i | −0.417808 | − | 0.417808i | 0.466640 | − | 0.884447i | \(-0.345464\pi\) |
−0.884447 | + | 0.466640i | \(0.845464\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.3464 | + | 15.9943i | 0.503150 | + | 0.560945i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.24594 | + | 2.15803i | −0.0436433 | + | 0.0755925i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.37299 | − | 9.30628i | −0.187977 | − | 0.325586i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.859033 | + | 0.690240i | −0.0300170 | + | 0.0241190i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.0740 | + | 48.7927i | −0.456285 | + | 1.70288i | 0.227999 | + | 0.973661i | \(0.426782\pi\) |
−0.684283 | + | 0.729216i | \(0.739885\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.3773 | − | 8.30076i | −0.501163 | − | 0.289346i | 0.228031 | − | 0.973654i | \(-0.426771\pi\) |
−0.729194 | + | 0.684307i | \(0.760105\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.20129 | − | 9.50953i | 0.215901 | − | 0.331079i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.8935 | − | 19.8935i | −0.691764 | − | 0.691764i | 0.270856 | − | 0.962620i | \(-0.412693\pi\) |
−0.962620 | + | 0.270856i | \(0.912693\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.51982 | − | 4.51982i | 0.156980 | − | 0.156980i | −0.624247 | − | 0.781227i | \(-0.714594\pi\) |
0.781227 | + | 0.624247i | \(0.214594\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32.4042 | + | 16.4332i | −1.12409 | + | 0.570063i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.9595 | + | 36.3029i | −0.726203 | + | 1.25782i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.1581 | − | 7.54494i | −0.974452 | − | 0.261104i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.74056 | + | 47.7194i | 0.163858 | + | 1.64942i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.34046 | − | 3.08332i | 0.184373 | − | 0.106448i | −0.404972 | − | 0.914329i | \(-0.632719\pi\) |
0.589346 | + | 0.807881i | \(0.299386\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44.4356 | + | 25.6549i | 1.53226 | + | 0.884653i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.8223 | + | 6.80937i | 0.717159 | + | 0.234527i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.4012 | − | 11.4012i | 0.392214 | − | 0.392214i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.97485 | 0.205298 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.9150 | + | 20.8122i | 1.09532 | + | 0.714272i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.40922 | + | 8.99133i | 0.0825869 | + | 0.308219i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.75721 | − | 28.9503i | 0.265602 | − | 0.991240i | −0.696279 | − | 0.717771i | \(-0.745162\pi\) |
0.961881 | − | 0.273468i | \(-0.0881709\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.10675 | − | 3.74001i | −0.174647 | − | 0.127906i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.97997 | + | 1.14314i | −0.0676345 | + | 0.0390488i | −0.533436 | − | 0.845840i | \(-0.679099\pi\) |
0.465801 | + | 0.884889i | \(0.345766\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.9566 | + | 3.73966i | −0.476193 | + | 0.127595i | −0.488929 | − | 0.872323i | \(-0.662612\pi\) |
0.0127366 | + | 0.999919i | \(0.495946\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.99524 | − | 11.1434i | −0.340637 | − | 0.379765i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.8654 | 1.62936 | 0.814678 | − | 0.579913i | \(-0.196913\pi\) | ||||
0.814678 | + | 0.579913i | \(0.196913\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.46544 | 0.219831 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.0232 | + | 34.5867i | 1.05360 | + | 1.17463i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.5783 | − | 7.65754i | 0.969454 | − | 0.259764i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.10513 | − | 1.21540i | 0.0713298 | − | 0.0411823i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.5392 | − | 10.8140i | 0.830528 | − | 0.365998i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.24180 | + | 8.36650i | −0.0757866 | + | 0.282839i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.06187 | + | 7.69500i | 0.0696244 | + | 0.259842i | 0.991961 | − | 0.126546i | \(-0.0403892\pi\) |
−0.922336 | + | 0.386388i | \(0.873723\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.167648 | − | 0.109326i | −0.00565463 | − | 0.00368746i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.0782 | 0.373234 | 0.186617 | − | 0.982433i | \(-0.440248\pi\) | ||||
0.186617 | + | 0.982433i | \(0.440248\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.5689 | + | 24.5689i | −0.826808 | + | 0.826808i | −0.987074 | − | 0.160266i | \(-0.948765\pi\) |
0.160266 | + | 0.987074i | \(0.448765\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.3704 | + | 5.02647i | 0.516670 | + | 0.168963i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.4338 | + | 9.48806i | 0.551793 | + | 0.318578i | 0.749845 | − | 0.661614i | \(-0.230128\pi\) |
−0.198052 | + | 0.980192i | \(0.563461\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.3978 | + | 6.00315i | −0.348730 | + | 0.201339i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.96437 | − | 15.3415i | 0.266816 | − | 0.513959i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.455909 | − | 0.122160i | −0.0152564 | − | 0.00408795i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.80429 | + | 4.85718i | −0.0937371 | + | 0.162357i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.13430 | − | 1.08238i | 0.0712623 | − | 0.0361395i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.4810 | − | 58.4810i | 1.95045 | − | 1.95045i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0291 | + | 32.0291i | 1.06704 | + | 1.06704i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.96109 | + | 7.60771i | −0.165095 | + | 0.253169i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.36391 | − | 2.51950i | −0.145061 | − | 0.0837511i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.22799 | − | 19.5111i | 0.173593 | − | 0.647856i | −0.823195 | − | 0.567759i | \(-0.807810\pi\) |
0.996787 | − | 0.0800968i | \(-0.0255229\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.2414 | + | 7.47013i | 0.638197 | + | 0.247769i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.3761 | + | 21.4361i | 0.410040 | + | 0.710209i | 0.994894 | − | 0.100929i | \(-0.0321815\pi\) |
−0.584854 | + | 0.811139i | \(0.698848\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.8606 | + | 18.8112i | −0.359434 | + | 0.622558i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.9010 | − | 16.6127i | −0.492613 | − | 0.549198i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.79507 | − | 5.79507i | −0.191370 | − | 0.191370i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.93718i | 0.0968887i | 0.998826 | + | 0.0484444i | \(0.0154264\pi\) | ||||
−0.998826 | + | 0.0484444i | \(0.984574\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.4331 | + | 1.65294i | 1.00281 | + | 0.0544663i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.42049 | − | 0.380619i | 0.0467560 | − | 0.0125282i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.98268 | + | 2.67485i | 0.328229 | + | 0.0879486i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.7922 | − | 16.1015i | 0.387308 | − | 0.528844i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.2758 | + | 33.3867i | 0.632420 | + | 1.09538i | 0.987056 | + | 0.160379i | \(0.0512715\pi\) |
−0.354636 | + | 0.935004i | \(0.615395\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.74468 | − | 10.2433i | −0.0899533 | − | 0.335710i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.837047 | + | 3.97513i | 0.0274037 | + | 0.130140i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.0187i | 0.523866i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.8118i | 1.00658i | 0.864119 | + | 0.503288i | \(0.167877\pi\) | ||||
−0.864119 | + | 0.503288i | \(0.832123\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.3916 | + | 5.36043i | 0.534920 | + | 0.174931i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.42341 | − | 31.4366i | −0.274595 | − | 1.02480i | −0.956112 | − | 0.293001i | \(-0.905346\pi\) |
0.681517 | − | 0.731802i | \(-0.261321\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.2536 | + | 28.1521i | 0.529292 | + | 0.916760i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.867025 | + | 5.27917i | −0.0282043 | + | 0.171731i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.37173 | − | 2.51115i | −0.304540 | − | 0.0816013i | 0.103313 | − | 0.994649i | \(-0.467056\pi\) |
−0.407853 | + | 0.913048i | \(0.633722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.13726 | − | 0.572676i | 0.0693783 | − | 0.0185898i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.59277 | + | 7.08446i | 0.116503 | + | 0.229729i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 12.8416i | − | 0.415980i | −0.978131 | − | 0.207990i | \(-0.933308\pi\) | ||
0.978131 | − | 0.207990i | \(-0.0666921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.1513 | + | 15.1513i | 0.490286 | + | 0.490286i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29.1720 | + | 6.14277i | −0.942997 | + | 0.198567i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.11837 | − | 1.93707i | 0.0361139 | − | 0.0625512i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0854 | − | 46.9133i | −0.873723 | − | 1.51333i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.4362 | + | 10.7961i | −0.432975 | + | 0.347900i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.76715 | + | 6.59508i | −0.0568865 | + | 0.212303i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.9080 | − | 20.7315i | −1.15472 | − | 0.666680i | −0.204690 | − | 0.978827i | \(-0.565619\pi\) |
−0.950034 | + | 0.312147i | \(0.898952\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19.1745 | − | 1.04144i | −0.615974 | − | 0.0334560i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.88730 | + | 1.88730i | 0.0605663 | + | 0.0605663i | 0.736741 | − | 0.676175i | \(-0.236364\pi\) |
−0.676175 | + | 0.736741i | \(0.736364\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.06253 | + | 5.06253i | −0.162297 | + | 0.162297i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.144096 | − | 2.65301i | 0.00461475 | − | 0.0849644i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.70999 | − | 16.8182i | 0.310650 | − | 0.538062i | −0.667853 | − | 0.744293i | \(-0.732787\pi\) |
0.978503 | + | 0.206231i | \(0.0661199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.38446 | + | 1.71071i | 0.204048 | + | 0.0546746i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.1282 | − | 23.8058i | −0.610717 | − | 0.760062i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.6919 | − | 15.4106i | 0.851339 | − | 0.491521i | −0.00976322 | − | 0.999952i | \(-0.503108\pi\) |
0.861103 | + | 0.508431i | \(0.169774\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.4046 | − | 7.16177i | −0.395242 | − | 0.228193i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.0821989 | + | 0.390362i | 0.00261642 | + | 0.0124254i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.9465 | − | 13.9465i | 0.443473 | − | 0.443473i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.7024 | −0.625869 | −0.312934 | − | 0.949775i | \(-0.601312\pi\) | ||||
−0.312934 | + | 0.949775i | \(0.601312\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.8263 | + | 13.6045i | −0.851307 | + | 0.431726i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.66047 | + | 13.6611i | 0.116045 | + | 0.433085i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.25836 | − | 4.69625i | 0.0398526 | − | 0.148732i | −0.943133 | − | 0.332417i | \(-0.892136\pi\) |
0.982985 | + | 0.183685i | \(0.0588026\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.5276 | + | 2.55017i | 0.491271 | + | 0.0806839i |
(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 | 576.2.bb.e.49.13 | 72 | ||
3.2 | odd | 2 | 1728.2.bc.e.1009.7 | 72 | |||
4.3 | odd | 2 | 144.2.x.e.85.13 | yes | 72 | ||
9.2 | odd | 6 | 1728.2.bc.e.1585.12 | 72 | |||
9.7 | even | 3 | inner | 576.2.bb.e.241.6 | 72 | ||
12.11 | even | 2 | 432.2.y.e.37.6 | 72 | |||
16.3 | odd | 4 | 144.2.x.e.13.1 | ✓ | 72 | ||
16.13 | even | 4 | inner | 576.2.bb.e.337.6 | 72 | ||
36.7 | odd | 6 | 144.2.x.e.133.1 | yes | 72 | ||
36.11 | even | 6 | 432.2.y.e.181.18 | 72 | |||
48.29 | odd | 4 | 1728.2.bc.e.145.12 | 72 | |||
48.35 | even | 4 | 432.2.y.e.253.18 | 72 | |||
144.29 | odd | 12 | 1728.2.bc.e.721.7 | 72 | |||
144.61 | even | 12 | inner | 576.2.bb.e.529.13 | 72 | ||
144.83 | even | 12 | 432.2.y.e.397.6 | 72 | |||
144.115 | odd | 12 | 144.2.x.e.61.13 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.e.13.1 | ✓ | 72 | 16.3 | odd | 4 | ||
144.2.x.e.61.13 | yes | 72 | 144.115 | odd | 12 | ||
144.2.x.e.85.13 | yes | 72 | 4.3 | odd | 2 | ||
144.2.x.e.133.1 | yes | 72 | 36.7 | odd | 6 | ||
432.2.y.e.37.6 | 72 | 12.11 | even | 2 | |||
432.2.y.e.181.18 | 72 | 36.11 | even | 6 | |||
432.2.y.e.253.18 | 72 | 48.35 | even | 4 | |||
432.2.y.e.397.6 | 72 | 144.83 | even | 12 | |||
576.2.bb.e.49.13 | 72 | 1.1 | even | 1 | trivial | ||
576.2.bb.e.241.6 | 72 | 9.7 | even | 3 | inner | ||
576.2.bb.e.337.6 | 72 | 16.13 | even | 4 | inner | ||
576.2.bb.e.529.13 | 72 | 144.61 | even | 12 | inner | ||
1728.2.bc.e.145.12 | 72 | 48.29 | odd | 4 | |||
1728.2.bc.e.721.7 | 72 | 144.29 | odd | 12 | |||
1728.2.bc.e.1009.7 | 72 | 3.2 | odd | 2 | |||
1728.2.bc.e.1585.12 | 72 | 9.2 | odd | 6 |