Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,2,Mod(53,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 11]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("342.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.bb (of order \(18\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.73088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 287.2 | ||
Character | \(\chi\) | \(=\) | 342.287 |
Dual form | 342.2.bb.a.143.2 |
$q$-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 \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.173648 | − | 0.984808i | 0.122788 | − | 0.696364i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.939693 | − | 0.342020i | −0.469846 | − | 0.171010i | ||||
\(5\) | −0.0466858 | − | 0.128268i | −0.0208785 | − | 0.0573633i | 0.928816 | − | 0.370542i | \(-0.120828\pi\) |
−0.949694 | + | 0.313179i | \(0.898606\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.51073 | − | 4.34872i | −0.948968 | − | 1.64366i | −0.747604 | − | 0.664145i | \(-0.768796\pi\) |
−0.201365 | − | 0.979516i | \(-0.564538\pi\) | |||||||
\(8\) | −0.500000 | + | 0.866025i | −0.176777 | + | 0.306186i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.134426 | + | 0.0237030i | −0.0425094 | + | 0.00749555i | ||||
\(11\) | 3.11116 | + | 1.79623i | 0.938049 | + | 0.541583i | 0.889348 | − | 0.457231i | \(-0.151159\pi\) |
0.0487005 | + | 0.998813i | \(0.484492\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.32138 | − | 2.76651i | −0.643835 | − | 0.767292i | 0.341136 | − | 0.940014i | \(-0.389188\pi\) |
−0.984971 | + | 0.172722i | \(0.944744\pi\) | |||||||
\(14\) | −4.71864 | + | 1.71744i | −1.26111 | + | 0.459006i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.766044 | + | 0.642788i | 0.191511 | + | 0.160697i | ||||
\(17\) | −5.05668 | − | 0.891629i | −1.22642 | − | 0.216252i | −0.477335 | − | 0.878721i | \(-0.658397\pi\) |
−0.749089 | + | 0.662470i | \(0.769508\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.27353 | − | 0.858478i | −0.980414 | − | 0.196948i | ||||
\(20\) | 0.136500i | 0.0305224i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.30918 | − | 2.75198i | 0.492320 | − | 0.586724i | ||||
\(23\) | 2.33023 | − | 6.40226i | 0.485887 | − | 1.33496i | −0.418487 | − | 0.908223i | \(-0.637440\pi\) |
0.904374 | − | 0.426740i | \(-0.140338\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.81595 | − | 3.20196i | 0.763190 | − | 0.640392i | ||||
\(26\) | −3.12759 | + | 1.80571i | −0.613370 | + | 0.354129i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.871969 | + | 4.94518i | 0.164787 | + | 0.934551i | ||||
\(29\) | 1.24964 | + | 7.08707i | 0.232053 | + | 1.31604i | 0.848733 | + | 0.528822i | \(0.177366\pi\) |
−0.616680 | + | 0.787214i | \(0.711523\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.67105 | − | 2.11948i | 0.659340 | − | 0.380670i | −0.132685 | − | 0.991158i | \(-0.542360\pi\) |
0.792025 | + | 0.610488i | \(0.209027\pi\) | |||||||
\(32\) | 0.766044 | − | 0.642788i | 0.135419 | − | 0.113630i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.75617 | + | 4.82502i | −0.301180 | + | 0.827485i | ||||
\(35\) | −0.440587 | + | 0.525071i | −0.0744727 | + | 0.0887531i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.852851i | 0.140208i | 0.997540 | + | 0.0701039i | \(0.0223331\pi\) | ||||
−0.997540 | + | 0.0701039i | \(0.977667\pi\) | |||||||
\(38\) | −1.58753 | + | 4.05953i | −0.257531 | + | 0.658542i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.134426 | + | 0.0237030i | 0.0212547 | + | 0.00374777i | ||||
\(41\) | −2.61979 | − | 2.19827i | −0.409142 | − | 0.343311i | 0.414872 | − | 0.909880i | \(-0.363826\pi\) |
−0.824015 | + | 0.566568i | \(0.808271\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.48830 | − | 1.63361i | 0.684459 | − | 0.249123i | 0.0236983 | − | 0.999719i | \(-0.492456\pi\) |
0.660761 | + | 0.750596i | \(0.270234\pi\) | |||||||
\(44\) | −2.30918 | − | 2.75198i | −0.348123 | − | 0.414876i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.90035 | − | 3.40657i | −0.869959 | − | 0.502271i | ||||
\(47\) | 6.64017 | − | 1.17084i | 0.968568 | − | 0.170785i | 0.333083 | − | 0.942898i | \(-0.391911\pi\) |
0.635486 | + | 0.772113i | \(0.280800\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.10757 | + | 15.7748i | −1.30108 | + | 2.25354i | ||||
\(50\) | −2.49068 | − | 4.31399i | −0.352236 | − | 0.610090i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.23518 | + | 3.39363i | 0.171289 | + | 0.470612i | ||||
\(53\) | 2.63008 | + | 0.957270i | 0.361269 | + | 0.131491i | 0.516276 | − | 0.856422i | \(-0.327318\pi\) |
−0.155007 | + | 0.987913i | \(0.549540\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0851519 | − | 0.482920i | 0.0114819 | − | 0.0651170i | ||||
\(56\) | 5.02147 | 0.671022 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.19640 | 0.944933 | ||||||||
\(59\) | −1.77228 | + | 10.0511i | −0.230732 | + | 1.30855i | 0.620687 | + | 0.784059i | \(0.286854\pi\) |
−0.851419 | + | 0.524487i | \(0.824257\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.59208 | + | 1.30741i | 0.459919 | + | 0.167397i | 0.561580 | − | 0.827422i | \(-0.310194\pi\) |
−0.101661 | + | 0.994819i | \(0.532416\pi\) | |||||||
\(62\) | −1.44981 | − | 3.98332i | −0.184126 | − | 0.505882i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.500000 | − | 0.866025i | −0.0625000 | − | 0.108253i | ||||
\(65\) | −0.246480 | + | 0.426916i | −0.0305721 | + | 0.0529524i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.32389 | − | 1.11507i | 0.772587 | − | 0.136228i | 0.226562 | − | 0.973997i | \(-0.427252\pi\) |
0.546025 | + | 0.837769i | \(0.316140\pi\) | |||||||
\(68\) | 4.44677 | + | 2.56734i | 0.539250 | + | 0.311336i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.440587 | + | 0.525071i | 0.0526602 | + | 0.0627579i | ||||
\(71\) | 14.3392 | − | 5.21904i | 1.70175 | − | 0.619386i | 0.705725 | − | 0.708486i | \(-0.250621\pi\) |
0.996023 | + | 0.0890999i | \(0.0283990\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.54200 | + | 2.97209i | 0.414560 | + | 0.347857i | 0.826089 | − | 0.563540i | \(-0.190561\pi\) |
−0.411529 | + | 0.911397i | \(0.635005\pi\) | |||||||
\(74\) | 0.839894 | + | 0.148096i | 0.0976357 | + | 0.0172158i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.72218 | + | 2.26834i | 0.426964 | + | 0.260196i | ||||
\(77\) | − | 18.0394i | − | 2.05578i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.45498 | − | 5.30924i | 0.501225 | − | 0.597336i | −0.454811 | − | 0.890588i | \(-0.650293\pi\) |
0.956035 | + | 0.293252i | \(0.0947375\pi\) | |||||||
\(80\) | 0.0466858 | − | 0.128268i | 0.00521963 | − | 0.0143408i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.61979 | + | 2.19827i | −0.289307 | + | 0.242758i | ||||
\(83\) | −1.38926 | + | 0.802089i | −0.152491 | + | 0.0880407i | −0.574304 | − | 0.818642i | \(-0.694727\pi\) |
0.421813 | + | 0.906683i | \(0.361394\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.121707 | + | 0.690237i | 0.0132010 | + | 0.0748667i | ||||
\(86\) | −0.829404 | − | 4.70379i | −0.0894370 | − | 0.507222i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.11116 | + | 1.79623i | −0.331650 | + | 0.191478i | ||||
\(89\) | 4.51237 | − | 3.78633i | 0.478311 | − | 0.401350i | −0.371504 | − | 0.928431i | \(-0.621158\pi\) |
0.849815 | + | 0.527081i | \(0.176713\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.20242 | + | 17.0410i | −0.650190 | + | 1.78638i | ||||
\(92\) | −4.37940 | + | 5.21917i | −0.456584 | + | 0.544136i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 6.74261i | − | 0.695447i | ||||||
\(95\) | 0.0893976 | + | 0.588236i | 0.00917200 | + | 0.0603517i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.49864 | − | 0.969559i | −0.558303 | − | 0.0984438i | −0.112625 | − | 0.993638i | \(-0.535926\pi\) |
−0.445677 | + | 0.895194i | \(0.647037\pi\) | |||||||
\(98\) | 13.9536 | + | 11.7085i | 1.40953 | + | 1.18273i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.68095 | + | 1.70373i | −0.468095 | + | 0.170373i | ||||
\(101\) | −1.83905 | − | 2.19170i | −0.182993 | − | 0.218082i | 0.666748 | − | 0.745283i | \(-0.267686\pi\) |
−0.849740 | + | 0.527201i | \(0.823241\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.24761 | − | 5.33911i | −0.911194 | − | 0.526078i | −0.0303790 | − | 0.999538i | \(-0.509671\pi\) |
−0.880815 | + | 0.473460i | \(0.843005\pi\) | |||||||
\(104\) | 3.55656 | − | 0.627117i | 0.348749 | − | 0.0614939i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.39944 | − | 2.42389i | 0.135925 | − | 0.235429i | ||||
\(107\) | −1.13008 | − | 1.95735i | −0.109249 | − | 0.189225i | 0.806217 | − | 0.591620i | \(-0.201511\pi\) |
−0.915466 | + | 0.402395i | \(0.868178\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.25449 | − | 11.6891i | −0.407507 | − | 1.11962i | −0.958497 | − | 0.285103i | \(-0.907972\pi\) |
0.550990 | − | 0.834512i | \(-0.314250\pi\) | |||||||
\(110\) | −0.460797 | − | 0.167716i | −0.0439353 | − | 0.0159911i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.871969 | − | 4.94518i | 0.0823933 | − | 0.467276i | ||||
\(113\) | −10.8537 | −1.02103 | −0.510514 | − | 0.859869i | \(-0.670545\pi\) | ||||
−0.510514 | + | 0.859869i | \(0.670545\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.929994 | −0.0867224 | ||||||||
\(116\) | 1.24964 | − | 7.08707i | 0.116026 | − | 0.658018i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.59067 | + | 3.49072i | 0.882893 | + | 0.321347i | ||||
\(119\) | 8.81853 | + | 24.2287i | 0.808393 | + | 2.22104i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.952858 | + | 1.65040i | 0.0866235 | + | 0.150036i | ||||
\(122\) | 1.91131 | − | 3.31048i | 0.173042 | − | 0.299717i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.17456 | + | 0.736088i | −0.374887 | + | 0.0661027i | ||||
\(125\) | −1.17992 | − | 0.681229i | −0.105536 | − | 0.0609310i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.4784 | + | 12.4876i | 0.929805 | + | 1.10810i | 0.993914 | + | 0.110156i | \(0.0351351\pi\) |
−0.0641088 | + | 0.997943i | \(0.520420\pi\) | |||||||
\(128\) | −0.939693 | + | 0.342020i | −0.0830579 | + | 0.0302306i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.377629 | + | 0.316868i | 0.0331203 | + | 0.0277912i | ||||
\(131\) | −13.3343 | − | 2.35120i | −1.16503 | − | 0.205425i | −0.442499 | − | 0.896769i | \(-0.645908\pi\) |
−0.722526 | + | 0.691344i | \(0.757019\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.99641 | + | 20.7398i | 0.606666 | + | 1.79837i | ||||
\(134\) | − | 6.42145i | − | 0.554729i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.30051 | − | 3.93340i | 0.283017 | − | 0.337286i | ||||
\(137\) | −0.996983 | + | 2.73919i | −0.0851780 | + | 0.234025i | −0.974968 | − | 0.222346i | \(-0.928629\pi\) |
0.889790 | + | 0.456370i | \(0.150851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.7330 | − | 12.3625i | 1.24964 | − | 1.04857i | 0.252930 | − | 0.967485i | \(-0.418606\pi\) |
0.996707 | − | 0.0810850i | \(-0.0258385\pi\) | |||||||
\(140\) | 0.593601 | − | 0.342716i | 0.0501684 | − | 0.0289647i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.64977 | − | 15.0276i | −0.222364 | − | 1.26109i | ||||
\(143\) | −2.25289 | − | 12.7768i | −0.188396 | − | 1.06845i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.850705 | − | 0.491155i | 0.0706472 | − | 0.0407882i | ||||
\(146\) | 3.54200 | − | 2.97209i | 0.293138 | − | 0.245972i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.291692 | − | 0.801417i | 0.0239769 | − | 0.0658761i | ||||
\(149\) | −8.33690 | + | 9.93553i | −0.682985 | + | 0.813950i | −0.990488 | − | 0.137597i | \(-0.956062\pi\) |
0.307503 | + | 0.951547i | \(0.400507\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.19318i | − | 0.341236i | −0.985337 | − | 0.170618i | \(-0.945424\pi\) | ||
0.985337 | − | 0.170618i | \(-0.0545764\pi\) | |||||||
\(152\) | 2.88023 | − | 3.27174i | 0.233617 | − | 0.265373i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −17.7653 | − | 3.13251i | −1.43157 | − | 0.252425i | ||||
\(155\) | −0.443248 | − | 0.371929i | −0.0356025 | − | 0.0298741i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.46975 | + | 2.35480i | −0.516342 | + | 0.187933i | −0.587030 | − | 0.809565i | \(-0.699703\pi\) |
0.0706875 | + | 0.997499i | \(0.477481\pi\) | |||||||
\(158\) | −4.45498 | − | 5.30924i | −0.354419 | − | 0.422380i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.118213 | − | 0.0682501i | −0.00934552 | − | 0.00539564i | ||||
\(161\) | −33.6922 | + | 5.94085i | −2.65532 | + | 0.468204i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.75667 | − | 4.77469i | 0.215919 | − | 0.373983i | −0.737637 | − | 0.675197i | \(-0.764059\pi\) |
0.953556 | + | 0.301214i | \(0.0973919\pi\) | |||||||
\(164\) | 1.70995 | + | 2.96171i | 0.133524 | + | 0.231271i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.548661 | + | 1.50743i | 0.0425844 | + | 0.117000i | ||||
\(167\) | −2.77319 | − | 1.00936i | −0.214596 | − | 0.0781064i | 0.232485 | − | 0.972600i | \(-0.425314\pi\) |
−0.447081 | + | 0.894493i | \(0.647536\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.00736016 | + | 0.0417415i | −0.000566166 | + | 0.00321089i | ||||
\(170\) | 0.700885 | 0.0537554 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.77635 | −0.364193 | ||||||||
\(173\) | −2.31080 | + | 13.1052i | −0.175687 | + | 0.996368i | 0.761662 | + | 0.647975i | \(0.224384\pi\) |
−0.937348 | + | 0.348393i | \(0.886727\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −23.5053 | − | 8.55522i | −1.77683 | − | 0.646714i | ||||
\(176\) | 1.22869 | + | 3.37580i | 0.0926161 | + | 0.254461i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.94524 | − | 5.10131i | −0.220755 | − | 0.382359i | ||||
\(179\) | −10.3499 | + | 17.9266i | −0.773590 | + | 1.33990i | 0.161994 | + | 0.986792i | \(0.448207\pi\) |
−0.935584 | + | 0.353105i | \(0.885126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.3567 | − | 3.94209i | 1.66176 | − | 0.293013i | 0.737663 | − | 0.675169i | \(-0.235929\pi\) |
0.924098 | + | 0.382156i | \(0.124818\pi\) | |||||||
\(182\) | 15.7051 | + | 9.06733i | 1.16414 | + | 0.672115i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.37940 | + | 5.21917i | 0.322854 | + | 0.384762i | ||||
\(185\) | 0.109394 | − | 0.0398160i | 0.00804278 | − | 0.00292733i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.1305 | − | 11.8569i | −1.03333 | − | 0.867065i | ||||
\(188\) | −6.64017 | − | 1.17084i | −0.484284 | − | 0.0853924i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.594823 | + | 0.0141067i | 0.0431530 | + | 0.00102341i | ||||
\(191\) | − | 2.42275i | − | 0.175304i | −0.996151 | − | 0.0876518i | \(-0.972064\pi\) | ||
0.996151 | − | 0.0876518i | \(-0.0279363\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.0355 | + | 15.5351i | −0.938313 | + | 1.11824i | 0.0544947 | + | 0.998514i | \(0.482645\pi\) |
−0.992807 | + | 0.119723i | \(0.961799\pi\) | |||||||
\(194\) | −1.90966 | + | 5.24675i | −0.137106 | + | 0.376694i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.9536 | − | 11.7085i | 0.996687 | − | 0.836319i | ||||
\(197\) | −13.7220 | + | 7.92240i | −0.977652 | + | 0.564448i | −0.901560 | − | 0.432653i | \(-0.857577\pi\) |
−0.0760915 | + | 0.997101i | \(0.524244\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.80369 | − | 21.5718i | −0.269636 | − | 1.52918i | −0.755500 | − | 0.655148i | \(-0.772606\pi\) |
0.485864 | − | 0.874034i | \(-0.338505\pi\) | |||||||
\(200\) | 0.865005 | + | 4.90569i | 0.0611651 | + | 0.346885i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.47775 | + | 1.43053i | −0.174334 | + | 0.100652i | ||||
\(203\) | 27.6822 | − | 23.2281i | 1.94291 | − | 1.63029i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.159660 | + | 0.438663i | −0.0111512 | + | 0.0306376i | ||||
\(206\) | −6.86383 | + | 8.17999i | −0.478226 | + | 0.569927i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 3.61142i | − | 0.250407i | ||||||
\(209\) | −11.7536 | − | 10.3471i | −0.813012 | − | 0.715722i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.74189 | + | 0.307143i | 0.119917 | + | 0.0211446i | 0.233284 | − | 0.972409i | \(-0.425053\pi\) |
−0.113368 | + | 0.993553i | \(0.536164\pi\) | |||||||
\(212\) | −2.14406 | − | 1.79908i | −0.147255 | − | 0.123561i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.12385 | + | 0.773020i | −0.145184 | + | 0.0528425i | ||||
\(215\) | −0.419080 | − | 0.499440i | −0.0285810 | − | 0.0340615i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.4341 | − | 10.6429i | −1.25139 | − | 0.722488i | ||||
\(218\) | −12.2503 | + | 2.16006i | −0.829697 | + | 0.146298i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.245185 | + | 0.424673i | −0.0165304 | + | 0.0286315i | ||||
\(221\) | 9.27176 | + | 16.0592i | 0.623686 | + | 1.08026i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.45660 | + | 6.74945i | 0.164506 | + | 0.451977i | 0.994367 | − | 0.105994i | \(-0.0338024\pi\) |
−0.829861 | + | 0.557971i | \(0.811580\pi\) | |||||||
\(224\) | −4.71864 | − | 1.71744i | −0.315277 | − | 0.114752i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.88472 | + | 10.6888i | −0.125370 | + | 0.711008i | ||||
\(227\) | 23.5253 | 1.56143 | 0.780714 | − | 0.624889i | \(-0.214856\pi\) | ||||
0.780714 | + | 0.624889i | \(0.214856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.534218 | −0.0353021 | −0.0176511 | − | 0.999844i | \(-0.505619\pi\) | ||||
−0.0176511 | + | 0.999844i | \(0.505619\pi\) | |||||||
\(230\) | −0.161492 | + | 0.915866i | −0.0106485 | + | 0.0603904i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.76240 | − | 2.46131i | −0.443974 | − | 0.161593i | ||||
\(233\) | −9.67989 | − | 26.5953i | −0.634151 | − | 1.74231i | −0.669364 | − | 0.742935i | \(-0.733433\pi\) |
0.0352132 | − | 0.999380i | \(-0.488789\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.460183 | − | 0.797061i | −0.0300190 | − | 0.0519945i | ||||
\(236\) | 5.10309 | − | 8.83881i | 0.332183 | − | 0.575358i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 25.3919 | − | 4.47728i | 1.64592 | − | 0.290219i | ||||
\(239\) | −10.4910 | − | 6.05698i | −0.678606 | − | 0.391794i | 0.120723 | − | 0.992686i | \(-0.461479\pi\) |
−0.799330 | + | 0.600893i | \(0.794812\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.3500 | + | 14.7182i | 0.795536 | + | 0.948083i | 0.999523 | − | 0.0308903i | \(-0.00983426\pi\) |
−0.203986 | + | 0.978974i | \(0.565390\pi\) | |||||||
\(242\) | 1.79079 | − | 0.651793i | 0.115116 | − | 0.0418989i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.92829 | − | 2.45713i | −0.187465 | − | 0.157302i | ||||
\(245\) | 2.44860 | + | 0.431754i | 0.156435 | + | 0.0275837i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.54548 | + | 13.8156i | 0.480108 | + | 0.879066i | ||||
\(248\) | 4.23896i | 0.269174i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.875771 | + | 1.04370i | −0.0553886 | + | 0.0660096i | ||||
\(251\) | 9.67564 | − | 26.5836i | 0.610721 | − | 1.67794i | −0.117900 | − | 0.993025i | \(-0.537616\pi\) |
0.728621 | − | 0.684917i | \(-0.240161\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.7496 | − | 15.7328i | 1.17878 | − | 0.989112i | ||||
\(254\) | 14.1175 | − | 8.15073i | 0.885809 | − | 0.511422i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.173648 | + | 0.984808i | 0.0108530 | + | 0.0615505i | ||||
\(257\) | 1.22863 | + | 6.96791i | 0.0766398 | + | 0.434646i | 0.998849 | + | 0.0479557i | \(0.0152706\pi\) |
−0.922210 | + | 0.386690i | \(0.873618\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.70881 | − | 2.14128i | 0.230454 | − | 0.133053i | ||||
\(260\) | 0.377629 | − | 0.316868i | 0.0234196 | − | 0.0196513i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.63096 | + | 12.7235i | −0.286102 | + | 0.786058i | ||||
\(263\) | −7.85486 | + | 9.36106i | −0.484352 | + | 0.577228i | −0.951772 | − | 0.306808i | \(-0.900739\pi\) |
0.467420 | + | 0.884035i | \(0.345184\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.382046i | − | 0.0234689i | ||||||
\(266\) | 21.6396 | − | 3.28869i | 1.32681 | − | 0.201643i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.32389 | − | 1.11507i | −0.386293 | − | 0.0681139i | ||||
\(269\) | 19.3684 | + | 16.2520i | 1.18091 | + | 0.990901i | 0.999973 | + | 0.00740578i | \(0.00235735\pi\) |
0.180937 | + | 0.983495i | \(0.442087\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.498930 | + | 0.181596i | −0.0303078 | + | 0.0110311i | −0.357130 | − | 0.934055i | \(-0.616245\pi\) |
0.326822 | + | 0.945086i | \(0.394022\pi\) | |||||||
\(272\) | −3.30051 | − | 3.93340i | −0.200123 | − | 0.238497i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.52445 | + | 1.45749i | 0.152508 | + | 0.0880503i | ||||
\(275\) | 17.6235 | − | 3.10749i | 1.06273 | − | 0.187389i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.63747 | + | 9.76438i | −0.338722 | + | 0.586685i | −0.984193 | − | 0.177101i | \(-0.943328\pi\) |
0.645470 | + | 0.763785i | \(0.276661\pi\) | |||||||
\(278\) | −9.61628 | − | 16.6559i | −0.576746 | − | 0.998954i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.234431 | − | 0.644095i | −0.0140099 | − | 0.0384920i | ||||
\(281\) | 28.9491 | + | 10.5366i | 1.72696 | + | 0.628562i | 0.998407 | − | 0.0564289i | \(-0.0179714\pi\) |
0.728552 | + | 0.684990i | \(0.240194\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.170286 | − | 0.965738i | 0.0101224 | − | 0.0574072i | −0.979328 | − | 0.202278i | \(-0.935166\pi\) |
0.989451 | + | 0.144871i | \(0.0462767\pi\) | |||||||
\(284\) | −15.2594 | −0.905481 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.9739 | −0.767161 | ||||||||
\(287\) | −2.98204 | + | 16.9120i | −0.176024 | + | 0.998283i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.80020 | + | 3.20301i | 0.517659 | + | 0.188412i | ||||
\(290\) | −0.335970 | − | 0.923069i | −0.0197288 | − | 0.0542045i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.31188 | − | 4.00429i | −0.135292 | − | 0.234333i | ||||
\(293\) | 10.7790 | − | 18.6698i | 0.629717 | − | 1.09070i | −0.357892 | − | 0.933763i | \(-0.616504\pi\) |
0.987608 | − | 0.156938i | \(-0.0501623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.37198 | − | 0.241917i | 0.0798798 | − | 0.0140850i | ||||
\(296\) | −0.738590 | − | 0.426425i | −0.0429297 | − | 0.0247855i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.33690 | + | 9.93553i | 0.482944 | + | 0.575550i | ||||
\(299\) | −23.1213 | + | 8.41545i | −1.33714 | + | 0.486678i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.3730 | − | 15.4168i | −1.05900 | − | 0.888610i | ||||
\(302\) | −4.12948 | − | 0.728138i | −0.237625 | − | 0.0418996i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.72189 | − | 3.40460i | −0.156111 | − | 0.195267i | ||||
\(305\) | − | 0.521787i | − | 0.0298775i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.67412 | + | 4.37864i | −0.209693 | + | 0.249902i | −0.860632 | − | 0.509228i | \(-0.829931\pi\) |
0.650939 | + | 0.759130i | \(0.274375\pi\) | |||||||
\(308\) | −6.16983 | + | 16.9515i | −0.351559 | + | 0.965900i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.443248 | + | 0.371929i | −0.0251748 | + | 0.0211242i | ||||
\(311\) | −14.6645 | + | 8.46656i | −0.831548 | + | 0.480094i | −0.854382 | − | 0.519645i | \(-0.826064\pi\) |
0.0228345 | + | 0.999739i | \(0.492731\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.72542 | + | 9.78537i | 0.0975268 | + | 0.553102i | 0.993944 | + | 0.109890i | \(0.0350499\pi\) |
−0.896417 | + | 0.443212i | \(0.853839\pi\) | |||||||
\(314\) | 1.19556 | + | 6.78037i | 0.0674694 | + | 0.382638i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.00218 | + | 3.46536i | −0.337649 | + | 0.194942i | ||||
\(317\) | 22.2580 | − | 18.6767i | 1.25013 | − | 1.04899i | 0.253471 | − | 0.967343i | \(-0.418428\pi\) |
0.996662 | − | 0.0816425i | \(-0.0260166\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.84215 | + | 24.2936i | −0.495065 | + | 1.36018i | ||||
\(320\) | −0.0877406 | + | 0.104565i | −0.00490485 | + | 0.00584537i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 34.2120i | 1.90656i | ||||||||
\(323\) | 20.8444 | + | 8.15144i | 1.15981 | + | 0.453558i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.7165 | − | 3.12390i | −0.982736 | − | 0.173283i | ||||
\(326\) | −4.22346 | − | 3.54391i | −0.233916 | − | 0.196279i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.21365 | − | 1.16967i | 0.177444 | − | 0.0645844i | ||||
\(329\) | −21.7634 | − | 25.9366i | −1.19985 | − | 1.42993i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.09963 | + | 4.09897i | 0.390231 | + | 0.225300i | 0.682260 | − | 0.731109i | \(-0.260997\pi\) |
−0.292029 | + | 0.956409i | \(0.594330\pi\) | |||||||
\(332\) | 1.57981 | − | 0.278563i | 0.0867031 | − | 0.0152881i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.47558 | + | 2.55578i | −0.0807402 | + | 0.139846i | ||||
\(335\) | −0.438264 | − | 0.759096i | −0.0239449 | − | 0.0414738i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.164795 | − | 0.452771i | −0.00897697 | − | 0.0246640i | 0.935123 | − | 0.354323i | \(-0.115289\pi\) |
−0.944100 | + | 0.329659i | \(0.893066\pi\) | |||||||
\(338\) | 0.0398293 | + | 0.0144967i | 0.00216643 | + | 0.000788516i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.121707 | − | 0.690237i | 0.00660051 | − | 0.0374334i | ||||
\(341\) | 15.2283 | 0.824657 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 56.3165 | 3.04081 | ||||||||
\(344\) | −0.829404 | + | 4.70379i | −0.0447185 | + | 0.253611i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.5048 | + | 4.55138i | 0.672263 | + | 0.244684i | ||||
\(347\) | 3.16613 | + | 8.69887i | 0.169967 | + | 0.466980i | 0.995206 | − | 0.0978040i | \(-0.0311818\pi\) |
−0.825239 | + | 0.564784i | \(0.808960\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.1245 | − | 17.5361i | −0.541951 | − | 0.938686i | −0.998792 | − | 0.0491379i | \(-0.984353\pi\) |
0.456841 | − | 0.889548i | \(-0.348981\pi\) | |||||||
\(350\) | −12.5069 | + | 21.6626i | −0.668521 | + | 1.15791i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.53788 | − | 0.623823i | 0.188569 | − | 0.0332499i | ||||
\(353\) | 8.44596 | + | 4.87628i | 0.449533 | + | 0.259538i | 0.707633 | − | 0.706580i | \(-0.249763\pi\) |
−0.258100 | + | 0.966118i | \(0.583096\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.33887 | − | 1.59561i | −0.0710600 | − | 0.0846860i | ||||
\(356\) | −5.53525 | + | 2.01466i | −0.293367 | + | 0.106777i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.8570 | + | 13.3056i | 0.838069 | + | 0.703223i | ||||
\(359\) | 1.37537 | + | 0.242514i | 0.0725891 | + | 0.0127994i | 0.209825 | − | 0.977739i | \(-0.432711\pi\) |
−0.137236 | + | 0.990538i | \(0.543822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.5260 | + | 7.33745i | 0.922423 | + | 0.386182i | ||||
\(362\) | − | 22.7016i | − | 1.19317i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.6567 | − | 13.8920i | 0.610979 | − | 0.728136i | ||||
\(365\) | 0.215864 | − | 0.593080i | 0.0112988 | − | 0.0310432i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.38029 | + | 6.19280i | −0.385248 | + | 0.323262i | −0.814759 | − | 0.579800i | \(-0.803131\pi\) |
0.429510 | + | 0.903062i | \(0.358686\pi\) | |||||||
\(368\) | 5.90035 | − | 3.40657i | 0.307577 | − | 0.177580i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.0202151 | − | 0.114646i | −0.00105093 | − | 0.00596014i | ||||
\(371\) | −2.44053 | − | 13.8409i | −0.126706 | − | 0.718585i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.1885 | − | 10.5011i | 0.941765 | − | 0.543728i | 0.0512520 | − | 0.998686i | \(-0.483679\pi\) |
0.890513 | + | 0.454957i | \(0.150346\pi\) | |||||||
\(374\) | −14.1305 | + | 11.8569i | −0.730673 | + | 0.613107i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.30611 | + | 6.33598i | −0.118928 | + | 0.326753i | ||||
\(377\) | 16.7056 | − | 19.9089i | 0.860381 | − | 1.02536i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.87543i | 0.147701i | 0.997269 | + | 0.0738506i | \(0.0235288\pi\) | ||||
−0.997269 | + | 0.0738506i | \(0.976471\pi\) | |||||||
\(380\) | 0.117182 | − | 0.583337i | 0.00601132 | − | 0.0299245i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.38594 | − | 0.420705i | −0.122075 | − | 0.0215252i | ||||
\(383\) | −2.77066 | − | 2.32486i | −0.141574 | − | 0.118795i | 0.569250 | − | 0.822164i | \(-0.307234\pi\) |
−0.710824 | + | 0.703369i | \(0.751678\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.31388 | + | 0.842183i | −0.117926 | + | 0.0429216i | ||||
\(386\) | 13.0355 | + | 15.5351i | 0.663487 | + | 0.790713i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.83543 | + | 2.79173i | 0.245482 | + | 0.141729i | ||||
\(389\) | −3.28260 | + | 0.578811i | −0.166434 | + | 0.0293469i | −0.256244 | − | 0.966612i | \(-0.582485\pi\) |
0.0898099 | + | 0.995959i | \(0.471374\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.4917 | + | 30.2964i | −0.884591 | + | 1.53216i | ||||
\(392\) | −9.10757 | − | 15.7748i | −0.460002 | − | 0.796747i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.41924 | + | 14.8892i | 0.273017 | + | 0.750109i | ||||
\(395\) | −0.888991 | − | 0.323566i | −0.0447300 | − | 0.0162804i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.36071 | + | 7.71696i | −0.0682920 | + | 0.387303i | 0.931434 | + | 0.363909i | \(0.118558\pi\) |
−0.999726 | + | 0.0233937i | \(0.992553\pi\) | |||||||
\(398\) | −21.9046 | −1.09798 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.98137 | 0.249068 | ||||||||
\(401\) | −1.60123 | + | 9.08105i | −0.0799618 | + | 0.453486i | 0.918369 | + | 0.395726i | \(0.129507\pi\) |
−0.998330 | + | 0.0577600i | \(0.981604\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.3855 | − | 5.23588i | −0.716591 | − | 0.260818i | ||||
\(404\) | 0.978539 | + | 2.68851i | 0.0486842 | + | 0.133759i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.0682 | − | 31.2951i | −0.896712 | − | 1.55315i | ||||
\(407\) | −1.53191 | + | 2.65335i | −0.0759341 | + | 0.131522i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.6709 | + | 6.46607i | −1.81326 | + | 0.319727i | −0.974434 | − | 0.224673i | \(-0.927868\pi\) |
−0.838826 | + | 0.544400i | \(0.816757\pi\) | |||||||
\(410\) | 0.404274 | + | 0.233408i | 0.0199657 | + | 0.0115272i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.86383 | + | 8.17999i | 0.338157 | + | 0.402999i | ||||
\(413\) | 48.1593 | − | 17.5285i | 2.36976 | − | 0.862523i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.167741 | + | 0.140751i | 0.00823409 | + | 0.00690922i | ||||
\(416\) | −3.55656 | − | 0.627117i | −0.174375 | − | 0.0307470i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.2309 | + | 9.77827i | −0.598231 | + | 0.478271i | ||||
\(419\) | 7.44965i | 0.363939i | 0.983304 | + | 0.181970i | \(0.0582472\pi\) | ||||
−0.983304 | + | 0.181970i | \(0.941753\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.4503 | − | 29.1388i | 1.19164 | − | 1.42014i | 0.308370 | − | 0.951267i | \(-0.400217\pi\) |
0.883267 | − | 0.468870i | \(-0.155339\pi\) | |||||||
\(422\) | 0.604953 | − | 1.66210i | 0.0294487 | − | 0.0809095i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.14406 | + | 1.79908i | −0.104125 | + | 0.0873710i | ||||
\(425\) | −22.1510 | + | 12.7889i | −1.07448 | + | 0.620352i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.33320 | − | 18.9035i | −0.161305 | − | 0.914806i | ||||
\(428\) | 0.392472 | + | 2.22582i | 0.0189709 | + | 0.107589i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.564625 | + | 0.325986i | −0.0272286 | + | 0.0157204i | ||||
\(431\) | −26.0302 | + | 21.8420i | −1.25383 | + | 1.05209i | −0.257522 | + | 0.966272i | \(0.582906\pi\) |
−0.996311 | + | 0.0858183i | \(0.972650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.158394 | + | 0.435184i | −0.00761193 | + | 0.0209136i | −0.943440 | − | 0.331542i | \(-0.892431\pi\) |
0.935828 | + | 0.352456i | \(0.114653\pi\) | |||||||
\(434\) | −13.6823 | + | 16.3059i | −0.656770 | + | 0.782708i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.4393i | 0.595735i | ||||||||
\(437\) | −15.4545 | + | 25.3598i | −0.739289 | + | 1.21312i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.4342 | − | 3.07412i | −0.832089 | − | 0.146720i | −0.258653 | − | 0.965970i | \(-0.583279\pi\) |
−0.573436 | + | 0.819250i | \(0.694390\pi\) | |||||||
\(440\) | 0.375645 | + | 0.315204i | 0.0179082 | + | 0.0150268i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.4252 | − | 6.34226i | 0.828833 | − | 0.301670i | ||||
\(443\) | −19.7271 | − | 23.5099i | −0.937264 | − | 1.11699i | −0.992949 | − | 0.118539i | \(-0.962179\pi\) |
0.0556857 | − | 0.998448i | \(-0.482266\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.696330 | − | 0.402026i | −0.0330092 | − | 0.0190579i | ||||
\(446\) | 7.07350 | − | 1.24725i | 0.334940 | − | 0.0590589i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.51073 | + | 4.34872i | −0.118621 | + | 0.205458i | ||||
\(449\) | 2.84947 | + | 4.93543i | 0.134475 | + | 0.232917i | 0.925397 | − | 0.379000i | \(-0.123732\pi\) |
−0.790922 | + | 0.611917i | \(0.790399\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.20199 | − | 11.5449i | −0.197864 | − | 0.543627i | ||||
\(452\) | 10.1991 | + | 3.71218i | 0.479726 | + | 0.174606i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.08512 | − | 23.1679i | 0.191724 | − | 1.08732i | ||||
\(455\) | 2.47538 | 0.116048 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.1284 | 1.22224 | 0.611118 | − | 0.791540i | \(-0.290720\pi\) | ||||
0.611118 | + | 0.791540i | \(0.290720\pi\) | |||||||
\(458\) | −0.0927660 | + | 0.526102i | −0.00433467 | + | 0.0245831i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.873909 | + | 0.318077i | 0.0407462 | + | 0.0148304i | ||||
\(461\) | 5.02602 | + | 13.8089i | 0.234085 | + | 0.643143i | 1.00000 | 0.000201404i | \(6.41089e-5\pi\) | |
−0.765915 | + | 0.642942i | \(0.777714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.76150 | + | 11.7113i | 0.314233 | + | 0.544268i | 0.979274 | − | 0.202539i | \(-0.0649192\pi\) |
−0.665041 | + | 0.746807i | \(0.731586\pi\) | |||||||
\(464\) | −3.59820 | + | 6.23226i | −0.167042 | + | 0.289326i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.8721 | + | 4.91461i | −1.29115 | + | 0.227665i | ||||
\(467\) | 1.81507 | + | 1.04793i | 0.0839913 | + | 0.0484924i | 0.541407 | − | 0.840760i | \(-0.317892\pi\) |
−0.457416 | + | 0.889253i | \(0.651225\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.7268 | − | 24.7012i | −0.957073 | − | 1.14059i | ||||
\(470\) | −0.864862 | + | 0.314784i | −0.0398931 | + | 0.0145199i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.81839 | − | 6.56041i | −0.359871 | − | 0.301967i | ||||
\(473\) | 16.8981 | + | 2.97960i | 0.776977 | + | 0.137002i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.0564 | + | 10.4078i | −0.874366 | + | 0.477541i | ||||
\(476\) | − | 25.7837i | − | 1.18179i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.78671 | + | 9.27984i | −0.356156 | + | 0.424450i | ||||
\(479\) | 6.33708 | − | 17.4110i | 0.289549 | − | 0.795528i | −0.706581 | − | 0.707632i | \(-0.749763\pi\) |
0.996130 | − | 0.0878961i | \(-0.0280143\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.35942 | − | 1.97979i | 0.107580 | − | 0.0902706i | ||||
\(482\) | 16.6392 | − | 9.60663i | 0.757894 | − | 0.437570i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.330924 | − | 1.87676i | −0.0150420 | − | 0.0853075i | ||||
\(485\) | 0.132345 | + | 0.750566i | 0.00600947 | + | 0.0340814i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.6299 | − | 14.2201i | 1.11609 | − | 0.644374i | 0.175688 | − | 0.984446i | \(-0.443785\pi\) |
0.940399 | + | 0.340072i | \(0.110452\pi\) | |||||||
\(488\) | −2.92829 | + | 2.45713i | −0.132558 | + | 0.111229i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.850389 | − | 2.33642i | 0.0384166 | − | 0.105549i | ||||
\(491\) | 0.594649 | − | 0.708675i | 0.0268361 | − | 0.0319821i | −0.752459 | − | 0.658639i | \(-0.771133\pi\) |
0.779296 | + | 0.626657i | \(0.215577\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 36.9512i | − | 1.66420i | ||||||
\(494\) | 14.9160 | − | 5.03179i | 0.671102 | − | 0.226391i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.17456 | + | 0.736088i | 0.187443 | + | 0.0330513i | ||||
\(497\) | −58.6980 | − | 49.2535i | −2.63297 | − | 2.20932i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.3488 | − | 9.22619i | 1.13477 | − | 0.413021i | 0.294746 | − | 0.955576i | \(-0.404765\pi\) |
0.840020 | + | 0.542555i | \(0.182543\pi\) | |||||||
\(500\) | 0.875771 | + | 1.04370i | 0.0391657 | + | 0.0466758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24.4996 | − | 14.1448i | −1.09347 | − | 0.631315i | ||||
\(503\) | 20.8654 | − | 3.67913i | 0.930340 | − | 0.164044i | 0.312114 | − | 0.950045i | \(-0.398963\pi\) |
0.618226 | + | 0.786000i | \(0.287852\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.195267 | + | 0.338213i | −0.00868928 | + | 0.0150503i | ||||
\(506\) | −12.2379 | − | 21.1967i | −0.544043 | − | 0.942310i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.57543 | − | 15.3184i | −0.247370 | − | 0.679642i | ||||
\(509\) | 34.0484 | + | 12.3926i | 1.50917 | + | 0.549292i | 0.958416 | − | 0.285376i | \(-0.0921186\pi\) |
0.550753 | + | 0.834669i | \(0.314341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.03177 | − | 22.8653i | 0.178355 | − | 1.01150i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.07540 | 0.312082 | ||||||||
\(515\) | −0.253106 | + | 1.43543i | −0.0111532 | + | 0.0632528i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.7617 | + | 8.28458i | 1.00106 | + | 0.364355i | ||||
\(518\) | −1.46472 | − | 4.02429i | −0.0643562 | − | 0.176817i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.246480 | − | 0.426916i | −0.0108089 | − | 0.0187215i | ||||
\(521\) | −15.4645 | + | 26.7854i | −0.677514 | + | 1.17349i | 0.298213 | + | 0.954499i | \(0.403609\pi\) |
−0.975727 | + | 0.218989i | \(0.929724\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.4570 | + | 6.60468i | −1.63788 | + | 0.288803i | −0.915387 | − | 0.402575i | \(-0.868115\pi\) |
−0.722494 | + | 0.691378i | \(0.757004\pi\) | |||||||
\(524\) | 11.7260 | + | 6.77001i | 0.512253 | + | 0.295749i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.85486 | + | 9.36106i | 0.342488 | + | 0.408162i | ||||
\(527\) | −20.4531 | + | 7.44432i | −0.890951 | + | 0.324280i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.9399 | − | 15.0534i | −0.779996 | − | 0.654494i | ||||
\(530\) | −0.376242 | − | 0.0663416i | −0.0163429 | − | 0.00288170i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.518946 | − | 21.8819i | 0.0224992 | − | 0.948702i | ||||
\(533\) | 12.3507i | 0.534968i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.198308 | + | 0.236334i | −0.00857358 | + | 0.0102176i | ||||
\(536\) | −2.19627 | + | 6.03419i | −0.0948642 | + | 0.260637i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.3684 | − | 16.2520i | 0.835029 | − | 0.700672i | ||||
\(539\) | −56.6702 | + | 32.7185i | −2.44096 | + | 1.40929i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.56860 | + | 31.5811i | 0.239413 | + | 1.35778i | 0.833118 | + | 0.553095i | \(0.186553\pi\) |
−0.593706 | + | 0.804682i | \(0.702336\pi\) | |||||||
\(542\) | 0.0921985 | + | 0.522884i | 0.00396026 | + | 0.0224598i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.44677 | + | 2.56734i | −0.190654 | + | 0.110074i | ||||
\(545\) | −1.30072 | + | 1.09143i | −0.0557166 | + | 0.0467518i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.117215 | + | 0.322046i | −0.00501176 | + | 0.0137697i | −0.942173 | − | 0.335126i | \(-0.891221\pi\) |
0.937162 | + | 0.348896i | \(0.113443\pi\) | |||||||
\(548\) | 1.87371 | − | 2.23301i | 0.0800411 | − | 0.0953893i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 17.8953i | − | 0.763059i | ||||||
\(551\) | 0.743715 | − | 31.3596i | 0.0316833 | − | 1.33596i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −34.2737 | − | 6.04337i | −1.45746 | − | 0.256990i | ||||
\(554\) | 8.63710 | + | 7.24739i | 0.366955 | + | 0.307912i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.0727 | + | 6.57792i | −0.766453 | + | 0.278966i | ||||
\(557\) | 10.0448 | + | 11.9709i | 0.425611 | + | 0.507223i | 0.935651 | − | 0.352928i | \(-0.114814\pi\) |
−0.510040 | + | 0.860151i | \(0.670369\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.9384 | − | 8.62471i | −0.631829 | − | 0.364786i | ||||
\(560\) | −0.675018 | + | 0.119024i | −0.0285247 | + | 0.00502968i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.4035 | − | 26.6796i | 0.649757 | − | 1.12541i | ||||
\(563\) | 3.43337 | + | 5.94678i | 0.144699 | + | 0.250627i | 0.929261 | − | 0.369424i | \(-0.120445\pi\) |
−0.784561 | + | 0.620051i | \(0.787112\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.506713 | + | 1.39218i | 0.0213176 | + | 0.0585695i | ||||
\(566\) | −0.921496 | − | 0.335397i | −0.0387334 | − | 0.0140978i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.64977 | + | 15.0276i | −0.111182 | + | 0.630545i | ||||
\(569\) | 24.4652 | 1.02563 | 0.512817 | − | 0.858498i | \(-0.328602\pi\) | ||||
0.512817 | + | 0.858498i | \(0.328602\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.07578 | −0.379810 | −0.189905 | − | 0.981803i | \(-0.560818\pi\) | ||||
−0.189905 | + | 0.981803i | \(0.560818\pi\) | |||||||
\(572\) | −2.25289 | + | 12.7768i | −0.0941980 | + | 0.534224i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16.1372 | + | 5.87347i | 0.673555 | + | 0.245154i | ||||
\(575\) | −11.6077 | − | 31.8920i | −0.484076 | − | 1.32999i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.184936 | + | 0.320318i | 0.00769897 | + | 0.0133350i | 0.869849 | − | 0.493318i | \(-0.164216\pi\) |
−0.862150 | + | 0.506653i | \(0.830883\pi\) | |||||||
\(578\) | 4.68249 | − | 8.11031i | 0.194766 | − | 0.337344i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.967386 | + | 0.170576i | −0.0401685 | + | 0.00708279i | ||||
\(581\) | 6.97612 | + | 4.02766i | 0.289418 | + | 0.167096i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.46311 | + | 7.70243i | 0.267675 | + | 0.319002i | ||||
\(584\) | −4.34491 | + | 1.58142i | −0.179794 | + | 0.0654395i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.5144 | − | 13.8572i | −0.682204 | − | 0.572437i | ||||
\(587\) | 5.26876 | + | 0.929025i | 0.217465 | + | 0.0383449i | 0.281319 | − | 0.959614i | \(-0.409228\pi\) |
−0.0638540 | + | 0.997959i | \(0.520339\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.5079 | + | 5.90614i | −0.721398 | + | 0.243358i | ||||
\(590\) | − | 1.39315i | − | 0.0573549i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.548202 | + | 0.653321i | −0.0225310 | + | 0.0268513i | ||||
\(593\) | −9.96880 | + | 27.3891i | −0.409370 | + | 1.12473i | 0.548154 | + | 0.836378i | \(0.315331\pi\) |
−0.957523 | + | 0.288356i | \(0.906891\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.69607 | − | 2.26227i | 0.110528 | − | 0.0927442i | ||||
\(596\) | 11.2323 | − | 6.48496i | 0.460092 | − | 0.265634i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.27264 | + | 24.2313i | 0.174721 | + | 0.990893i | ||||
\(599\) | −0.982727 | − | 5.57332i | −0.0401531 | − | 0.227720i | 0.958127 | − | 0.286344i | \(-0.0924399\pi\) |
−0.998280 | + | 0.0586238i | \(0.981329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.28297 | − | 5.35952i | 0.378660 | − | 0.218620i | −0.298575 | − | 0.954386i | \(-0.596511\pi\) |
0.677235 | + | 0.735767i | \(0.263178\pi\) | |||||||
\(602\) | −18.3730 | + | 15.4168i | −0.748829 | + | 0.628342i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.43415 | + | 3.94030i | −0.0583548 | + | 0.160329i | ||||
\(605\) | 0.167209 | − | 0.199272i | 0.00679800 | − | 0.00810154i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.58035i | 0.104733i | 0.998628 | + | 0.0523665i | \(0.0166764\pi\) | ||||
−0.998628 | + | 0.0523665i | \(0.983324\pi\) | |||||||
\(608\) | −3.82553 | + | 2.08934i | −0.155146 | + | 0.0847338i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.513860 | − | 0.0906074i | −0.0208056 | − | 0.00366859i | ||||
\(611\) | −18.6535 | − | 15.6521i | −0.754640 | − | 0.633218i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.40442 | + | 2.69499i | −0.299062 | + | 0.108850i | −0.487193 | − | 0.873294i | \(-0.661979\pi\) |
0.188131 | + | 0.982144i | \(0.439757\pi\) | |||||||
\(614\) | 3.67412 | + | 4.37864i | 0.148275 | + | 0.176708i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.6226 | + | 9.01969i | 0.629451 | + | 0.363414i | ||||
\(617\) | −15.0528 | + | 2.65421i | −0.606001 | + | 0.106854i | −0.468225 | − | 0.883609i | \(-0.655106\pi\) |
−0.137776 | + | 0.990463i | \(0.543995\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.8851 | + | 41.3701i | −0.960021 | + | 1.66281i | −0.237587 | + | 0.971366i | \(0.576357\pi\) |
−0.722434 | + | 0.691440i | \(0.756977\pi\) | |||||||
\(620\) | 0.289310 | + | 0.501099i | 0.0116189 | + | 0.0201246i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.79147 | + | 15.9119i | 0.232217 | + | 0.638010i | ||||
\(623\) | −27.7951 | − | 10.1166i | −1.11359 | − | 0.405312i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.29273 | − | 24.3453i | 0.171709 | − | 0.973812i | ||||
\(626\) | 9.93632 | 0.397135 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.88497 | 0.274740 | ||||||||
\(629\) | 0.760426 | − | 4.31259i | 0.0303202 | − | 0.171954i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.99316 | − | 2.90927i | −0.318202 | − | 0.115816i | 0.177981 | − | 0.984034i | \(-0.443043\pi\) |
−0.496183 | + | 0.868218i | \(0.665266\pi\) | |||||||
\(632\) | 2.37045 | + | 6.51275i | 0.0942913 | + | 0.259063i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.5279 | − | 25.1630i | −0.576975 | − | 0.999350i | ||||
\(635\) | 1.11258 | − | 1.92704i | 0.0441512 | − | 0.0764721i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 64.7832 | − | 11.4230i | 2.56681 | − | 0.452597i | ||||
\(638\) | 22.3891 | + | 12.9264i | 0.886394 | + | 0.511760i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.0877406 | + | 0.104565i | 0.00346825 | + | 0.00413330i | ||||
\(641\) | −0.712852 | + | 0.259457i | −0.0281559 | + | 0.0102479i | −0.356060 | − | 0.934463i | \(-0.615880\pi\) |
0.327904 | + | 0.944711i | \(0.393658\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.6624 | + | 20.6942i | 0.972591 | + | 0.816101i | 0.982955 | − | 0.183845i | \(-0.0588546\pi\) |
−0.0103641 | + | 0.999946i | \(0.503299\pi\) | |||||||
\(644\) | 33.6922 | + | 5.94085i | 1.32766 | + | 0.234102i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.6472 | − | 19.1122i | 0.458253 | − | 0.751961i | ||||
\(647\) | 9.88512i | 0.388624i | 0.980940 | + | 0.194312i | \(0.0622474\pi\) | ||||
−0.980940 | + | 0.194312i | \(0.937753\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.5680 | + | 28.0872i | −0.925123 | + | 1.10252i | ||||
\(650\) | −6.15289 | + | 16.9049i | −0.241336 | + | 0.663065i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.22346 | + | 3.54391i | −0.165404 | + | 0.138790i | ||||
\(653\) | 18.2549 | − | 10.5395i | 0.714368 | − | 0.412441i | −0.0983080 | − | 0.995156i | \(-0.531343\pi\) |
0.812676 | + | 0.582715i | \(0.198010\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.320939 | + | 1.82014i | 0.0125401 | + | 0.0711186i | ||||
\(656\) | −0.593858 | − | 3.36794i | −0.0231863 | − | 0.131496i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −29.3217 | + | 16.9289i | −1.14308 | + | 0.659957i | ||||
\(659\) | 3.22064 | − | 2.70244i | 0.125458 | − | 0.105272i | −0.577900 | − | 0.816108i | \(-0.696128\pi\) |
0.703358 | + | 0.710836i | \(0.251683\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.34653 | + | 3.69957i | −0.0523741 | + | 0.143897i | −0.963121 | − | 0.269068i | \(-0.913284\pi\) |
0.910747 | + | 0.412964i | \(0.135507\pi\) | |||||||
\(662\) | 5.26954 | − | 6.27999i | 0.204806 | − | 0.244079i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1.60418i | − | 0.0622542i | ||||||
\(665\) | 2.33362 | − | 1.86567i | 0.0904939 | − | 0.0723475i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.2852 | + | 8.51398i | 1.86961 | + | 0.329663i | ||||
\(668\) | 2.26072 | + | 1.89697i | 0.0874699 | + | 0.0733960i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.823668 | + | 0.299790i | −0.0318211 | + | 0.0115819i | ||||
\(671\) | 8.82712 | + | 10.5198i | 0.340767 | + | 0.406111i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0889 | + | 17.3719i | 1.15984 | + | 0.669636i | 0.951266 | − | 0.308370i | \(-0.0997835\pi\) |
0.208577 | + | 0.978006i | \(0.433117\pi\) | |||||||
\(674\) | −0.474509 | + | 0.0836688i | −0.0182774 | + | 0.00322280i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.0211927 | − | 0.0367069i | 0.000815105 | − | 0.00141180i | ||||
\(677\) | 3.64635 | + | 6.31567i | 0.140141 | + | 0.242731i | 0.927549 | − | 0.373700i | \(-0.121911\pi\) |
−0.787409 | + | 0.616431i | \(0.788578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.58929 | + | 26.3464i | 0.368003 | + | 1.01108i | ||||
\(680\) | −0.658616 | − | 0.239717i | −0.0252568 | − | 0.00919272i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.64436 | − | 14.9969i | 0.101258 | − | 0.574262i | ||||
\(683\) | −23.0454 | −0.881809 | −0.440904 | − | 0.897554i | \(-0.645342\pi\) | ||||
−0.440904 | + | 0.897554i | \(0.645342\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.397896 | 0.0152028 | ||||||||
\(686\) | 9.77926 | − | 55.4609i | 0.373374 | − | 2.11751i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.48830 | + | 1.63361i | 0.171115 | + | 0.0622807i | ||||
\(689\) | −3.45711 | − | 9.49833i | −0.131705 | − | 0.361858i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.3725 | + | 23.1619i | 0.508714 | + | 0.881119i | 0.999949 | + | 0.0100920i | \(0.00321243\pi\) |
−0.491235 | + | 0.871027i | \(0.663454\pi\) | |||||||
\(692\) | 6.65367 | − | 11.5245i | 0.252935 | − | 0.438096i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.11650 | − | 1.60749i | 0.346058 | − | 0.0610193i | ||||
\(695\) | −2.27353 | − | 1.31262i | −0.0862399 | − | 0.0497907i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.2874 | + | 13.4518i | 0.427541 | + | 0.509523i | ||||
\(698\) | −19.0278 | + | 6.92555i | −0.720212 | + | 0.262136i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 19.1617 | + | 16.0785i | 0.724243 | + | 0.607712i | ||||
\(701\) | −22.5009 | − | 3.96751i | −0.849846 | − | 0.149851i | −0.268271 | − | 0.963343i | \(-0.586452\pi\) |
−0.581575 | + | 0.813493i | \(0.697563\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.732153 | − | 3.64468i | 0.0276137 | − | 0.137462i | ||||
\(704\) | − | 3.59245i | − | 0.135396i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.26882 | − | 7.47089i | 0.235930 | − | 0.281171i | ||||
\(707\) | −4.91370 | + | 13.5003i | −0.184799 | + | 0.507731i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.5025 | + | 13.0081i | −0.582208 | + | 0.488531i | −0.885672 | − | 0.464312i | \(-0.846302\pi\) |
0.303463 | + | 0.952843i | \(0.401857\pi\) | |||||||
\(710\) | −1.80386 | + | 1.04146i | −0.0676976 | + | 0.0390852i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.02287 | + | 5.80100i | 0.0383338 | + | 0.217402i | ||||
\(713\) | −5.01507 | − | 28.4419i | −0.187816 | − | 1.06516i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.53367 | + | 0.885467i | −0.0573562 | + | 0.0331146i | ||||
\(716\) | 15.8570 | − | 13.3056i | 0.592604 | − | 0.497254i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.477660 | − | 1.31236i | 0.0178261 | − | 0.0489769i | ||||
\(719\) | 14.9828 | − | 17.8557i | 0.558762 | − | 0.665907i | −0.410522 | − | 0.911851i | \(-0.634653\pi\) |
0.969284 | + | 0.245944i | \(0.0790978\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 53.6204i | 1.99693i | ||||||||
\(722\) | 10.2693 | − | 15.9856i | 0.382185 | − | 0.594924i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.3567 | − | 3.94209i | −0.830880 | − | 0.146507i | ||||
\(725\) | 27.4611 | + | 23.0426i | 1.01988 | + | 0.855780i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.1905 | + | 8.07667i | −0.822999 | + | 0.299547i | −0.718982 | − | 0.695028i | \(-0.755392\pi\) |
−0.104017 | + | 0.994576i | \(0.533170\pi\) | |||||||
\(728\) | −11.6567 | − | 13.8920i | −0.432027 | − | 0.514870i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.546586 | − | 0.315572i | −0.0202301 | − | 0.0116798i | ||||
\(731\) | −24.1525 | + | 4.25873i | −0.893311 | + | 0.157515i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.0248 | − | 32.9519i | 0.702697 | − | 1.21711i | −0.264819 | − | 0.964298i | \(-0.585312\pi\) |
0.967516 | − | 0.252809i | \(-0.0813544\pi\) | |||||||
\(734\) | 4.81714 | + | 8.34354i | 0.177804 | + | 0.307966i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.33023 | − | 6.40226i | −0.0858935 | − | 0.235990i | ||||
\(737\) | 21.6775 | + | 7.88998i | 0.798502 | + | 0.290631i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.653731 | + | 3.70749i | −0.0240479 | + | 0.136382i | −0.994468 | − | 0.105040i | \(-0.966503\pi\) |
0.970420 | + | 0.241423i | \(0.0776140\pi\) | |||||||
\(740\) | −0.116414 | −0.00427947 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.0544 | −0.515955 | ||||||||
\(743\) | −7.46064 | + | 42.3114i | −0.273704 | + | 1.55225i | 0.469343 | + | 0.883016i | \(0.344491\pi\) |
−0.743047 | + | 0.669239i | \(0.766620\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.66363 | + | 0.605511i | 0.0609506 | + | 0.0221842i | ||||
\(746\) | −7.18320 | − | 19.7357i | −0.262996 | − | 0.722575i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.22305 | + | 15.9748i | 0.337228 | + | 0.584097i | ||||
\(749\) | −5.67466 | + | 9.82879i | −0.207347 | + | 0.359136i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.98396 | + | 1.40779i | −0.291339 | + | 0.0513709i | −0.317407 | − | 0.948289i | \(-0.602812\pi\) |
0.0260686 | + | 0.999660i | \(0.491701\pi\) | |||||||
\(752\) | 5.83927 | + | 3.37130i | 0.212936 | + | 0.122939i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.7056 | − | 19.9089i | −0.608381 | − | 0.725040i | ||||
\(755\) | −0.537851 | + | 0.195762i | −0.0195744 | + | 0.00712450i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.2362 | − | 22.8539i | −0.989917 | − | 0.830639i | −0.00436167 | − | 0.999990i | \(-0.501388\pi\) |
−0.985556 | + | 0.169351i | \(0.945833\pi\) | |||||||
\(758\) | 2.83175 | + | 0.499314i | 0.102854 | + | 0.0181359i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.554126 | − | 0.216697i | −0.0201003 | − | 0.00786044i | ||||
\(761\) | 39.5085i | 1.43218i | 0.698007 | + | 0.716091i | \(0.254071\pi\) | ||||
−0.698007 | + | 0.716091i | \(0.745929\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40.1508 | + | 47.8499i | −1.45356 | + | 1.73228i | ||||
\(764\) | −0.828628 | + | 2.27664i | −0.0299787 | + | 0.0823658i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.77066 | + | 2.32486i | −0.100108 | + | 0.0840006i | ||||
\(767\) | 31.9207 | − | 18.4294i | 1.15259 | − | 0.665448i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.64622 | − | 32.0213i | −0.203608 | − | 1.15472i | −0.899615 | − | 0.436684i | \(-0.856153\pi\) |
0.696007 | − | 0.718035i | \(-0.254958\pi\) | |||||||
\(770\) | 0.427588 | + | 2.42497i | 0.0154092 | + | 0.0873898i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.5626 | − | 10.1398i | 0.632093 | − | 0.364939i | ||||
\(773\) | 17.3760 | − | 14.5802i | 0.624970 | − | 0.524412i | −0.274391 | − | 0.961618i | \(-0.588476\pi\) |
0.899361 | + | 0.437206i | \(0.144032\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.22204 | − | 19.8424i | 0.259423 | − | 0.712760i | ||||
\(776\) | 3.58898 | − | 4.27719i | 0.128837 | − | 0.153542i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.33324i | 0.119502i | ||||||||
\(779\) | 9.30858 | + | 11.6434i | 0.333514 | + | 0.417167i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 53.9860 | + | 9.51919i | 1.93177 | + | 0.340623i | ||||
\(782\) | 26.7988 | + | 22.4868i | 0.958322 | + | 0.804128i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −17.1166 | + | 6.22995i | −0.611309 | + | 0.222498i | ||||
\(785\) | 0.604091 | + | 0.719927i | 0.0215609 | + | 0.0256953i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.3080 | + | 7.10603i | 0.438733 | + | 0.253303i | 0.703060 | − | 0.711131i | \(-0.251817\pi\) |
−0.264327 | + | 0.964433i | \(0.585150\pi\) | |||||||
\(788\) | 15.6041 | − | 2.75142i | 0.555872 | − | 0.0980153i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.473022 | + | 0.819298i | −0.0168294 | + | 0.0291493i | ||||
\(791\) | 27.2507 | + | 47.1996i | 0.968924 | + | 1.67823i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.72162 | − | 12.9725i | −0.167670 | − | 0.460668i | ||||
\(794\) | 7.36344 | + | 2.68007i | 0.261319 | + | 0.0951122i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.80369 | + | 21.5718i | −0.134818 | + | 0.764591i | ||||
\(797\) | −24.9960 | −0.885405 | −0.442702 | − | 0.896669i | \(-0.645980\pi\) | ||||
−0.442702 | + | 0.896669i | \(0.645980\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.6212 | −1.22481 | ||||||||
\(800\) | 0.865005 | − | 4.90569i | 0.0305826 | − | 0.173442i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.66503 | + | 3.15381i | 0.305973 | + | 0.111365i | ||||
\(803\) | 5.68117 | + | 15.6089i | 0.200484 | + | 0.550825i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.33497 | + | 4.04428i | 0.0822968 | + | 0.142542i | ||||
\(806\) | −7.65435 | + | 13.2577i | −0.269613 | + | 0.466983i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.81759 | − | 0.496817i | 0.0991225 | − | 0.0174780i | ||||
\(809\) | −35.0162 | − | 20.2166i | −1.23110 | − | 0.710778i | −0.263844 | − | 0.964565i | \(-0.584990\pi\) |
−0.967260 | + | 0.253787i | \(0.918324\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.6165 | + | 19.8028i | 0.583485 | + | 0.695370i | 0.974340 | − | 0.225082i | \(-0.0722650\pi\) |
−0.390855 | + | 0.920452i | \(0.627821\pi\) | |||||||
\(812\) | −33.9572 | + | 12.3594i | −1.19166 | + | 0.433730i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.34703 | + | 1.96939i | 0.0822632 | + | 0.0690271i | ||||
\(815\) | −0.741138 | − | 0.130683i | −0.0259609 | − | 0.00457761i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.5833 | + | 3.12816i | −0.720118 | + | 0.109440i | ||||
\(818\) | 37.2366i | 1.30195i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.300063 | − | 0.357602i | 0.0104787 | − | 0.0124880i | ||||
\(821\) | 15.3364 | − | 42.1365i | 0.535245 | − | 1.47057i | −0.317506 | − | 0.948256i | \(-0.602845\pi\) |
0.852751 | − | 0.522318i | \(-0.174932\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.2702 | − | 19.5260i | 0.811148 | − | 0.680634i | −0.139733 | − | 0.990189i | \(-0.544624\pi\) |
0.950882 | + | 0.309555i | \(0.100180\pi\) | |||||||
\(824\) | 9.24761 | − | 5.33911i | 0.322156 | − | 0.185997i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.89947 | − | 50.4714i | −0.309652 | − | 1.75613i | ||||
\(827\) | −6.19896 | − | 35.1560i | −0.215559 | − | 1.22250i | −0.879934 | − | 0.475096i | \(-0.842413\pi\) |
0.664375 | − | 0.747399i | \(-0.268698\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.76319 | + | 4.48208i | −0.269627 | + | 0.155669i | −0.628718 | − | 0.777633i | \(-0.716420\pi\) |
0.359091 | + | 0.933302i | \(0.383087\pi\) | |||||||
\(830\) | 0.167741 | − | 0.140751i | 0.00582238 | − | 0.00488555i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.23518 | + | 3.39363i | −0.0428222 | + | 0.117653i | ||||
\(833\) | 60.1193 | − | 71.6474i | 2.08301 | − | 2.48244i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.402834i | 0.0139406i | ||||||||
\(836\) | 7.50584 | + | 13.7430i | 0.259595 | + | 0.475313i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.33647 | + | 1.29362i | 0.253434 | + | 0.0446873i | ||||
\(839\) | −30.1991 | − | 25.3400i | −1.04259 | − | 0.874835i | −0.0502927 | − | 0.998735i | \(-0.516015\pi\) |
−0.992295 | + | 0.123900i | \(0.960460\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.4139 | + | 7.79401i | −0.738409 | + | 0.268759i | ||||
\(842\) | −24.4503 | − | 29.1388i | −0.842614 | − | 1.00419i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.53180 | − | 0.884382i | −0.0527266 | − | 0.0304417i | ||||
\(845\) | 0.00569773 | − | 0.00100466i | 0.000196008 | − | 3.45614e-5i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.78475 | − | 8.28743i | 0.164406 | − | 0.284759i | ||||
\(848\) | 1.39944 | + | 2.42389i | 0.0480568 | + | 0.0832369i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.74811 | + | 24.0352i | 0.300058 | + | 0.824401i | ||||
\(851\) | 5.46017 | + | 1.98734i | 0.187172 | + | 0.0681251i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.570307 | + | 3.23437i | −0.0195270 | + | 0.110743i | −0.993013 | − | 0.118002i | \(-0.962351\pi\) |
0.973486 | + | 0.228745i | \(0.0734622\pi\) | |||||||
\(854\) | −19.1951 | −0.656844 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.26016 | 0.0772506 | ||||||||
\(857\) | 4.32778 | − | 24.5441i | 0.147834 | − | 0.838409i | −0.817213 | − | 0.576335i | \(-0.804482\pi\) |
0.965048 | − | 0.262074i | \(-0.0844066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.2154 | + | 5.17397i | 0.485022 | + | 0.176534i | 0.572945 | − | 0.819594i | \(-0.305801\pi\) |
−0.0879233 | + | 0.996127i | \(0.528023\pi\) | |||||||
\(860\) | 0.222988 | + | 0.612654i | 0.00760382 | + | 0.0208913i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.9900 | + | 29.4276i | 0.578683 | + | 1.00231i | ||||
\(863\) | 12.2712 | − | 21.2544i | 0.417717 | − | 0.723508i | −0.577992 | − | 0.816042i | \(-0.696164\pi\) |
0.995709 | + | 0.0925347i | \(0.0294969\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.78886 | − | 0.315424i | 0.0608230 | − | 0.0107247i | ||||
\(866\) | 0.401068 | + | 0.231557i | 0.0136288 | + | 0.00786861i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.6823 | + | 16.3059i | 0.464406 | + | 0.553458i | ||||
\(869\) | 23.3967 | − | 8.51572i | 0.793680 | − | 0.288876i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.7650 | − | 14.9066i | −0.601945 | − | 0.505091i | ||||
\(872\) | 12.2503 | + | 2.16006i | 0.414848 | + | 0.0731490i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 22.2908 | + | 19.6234i | 0.753999 | + | 0.663771i | ||||
\(875\) | 6.84154i | 0.231286i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.39656 | + | 5.23962i | −0.148461 | + | 0.176929i | −0.835150 | − | 0.550022i | \(-0.814619\pi\) |
0.686689 | + | 0.726952i | \(0.259064\pi\) | |||||||
\(878\) | −6.05484 | + | 16.6355i | −0.204341 | + | 0.561422i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.375645 | − | 0.315204i | 0.0126630 | − | 0.0106255i | ||||
\(881\) | 46.2511 | − | 26.7031i | 1.55824 | − | 0.899649i | 0.560812 | − | 0.827943i | \(-0.310489\pi\) |
0.997426 | − | 0.0717059i | \(-0.0228443\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.286000 | + | 1.62199i | 0.00962468 | + | 0.0545843i | 0.989242 | − | 0.146289i | \(-0.0467331\pi\) |
−0.979617 | + | 0.200874i | \(0.935622\pi\) | |||||||
\(884\) | −3.22005 | − | 18.2618i | −0.108302 | − | 0.614211i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.5783 | + | 15.3450i | −0.892915 | + | 0.515524i | ||||
\(887\) | 15.2850 | − | 12.8257i | 0.513221 | − | 0.430644i | −0.349040 | − | 0.937108i | \(-0.613492\pi\) |
0.862261 | + | 0.506464i | \(0.169048\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.9968 | − | 76.9207i | 0.938984 | − | 2.57984i | ||||
\(890\) | −0.516835 | + | 0.615940i | −0.0173243 | + | 0.0206463i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 7.18262i | − | 0.240492i | ||||||
\(893\) | −29.3821 | − | 0.696818i | −0.983234 | − | 0.0233181i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.78261 | + | 0.490648i | 0.0930122 | + | 0.0164006i | ||||
\(896\) | 3.84667 | + | 3.22774i | 0.128508 | + | 0.107831i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.35526 | − | 1.94915i | 0.178707 | − | 0.0650441i | ||||
\(899\) | 19.6084 | + | 23.3684i | 0.653977 | + | 0.779380i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.4459 | − | 7.18566i | −0.414634 | − | 0.239389i | ||||
\(902\) | −12.0992 | + | 2.13341i | −0.402858 | + | 0.0710347i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.42684 | − | 9.39956i | 0.180494 | − | 0.312625i | ||||
\(905\) | −1.54939 | − | 2.68361i | −0.0515033 | − | 0.0892063i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.7415 | − | 32.2595i | −0.389870 | − | 1.07116i | −0.967060 | − | 0.254549i | \(-0.918073\pi\) |
0.577190 | − | 0.816610i | \(-0.304149\pi\) | |||||||
\(908\) | −22.1065 | − | 8.04612i | −0.733631 | − | 0.267020i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.429846 | − | 2.43778i | 0.0142492 | − | 0.0808115i | ||||
\(911\) | −23.9136 | −0.792294 | −0.396147 | − | 0.918187i | \(-0.629653\pi\) | ||||
−0.396147 | + | 0.918187i | \(0.629653\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.76293 | −0.190725 | ||||||||
\(914\) | 4.53715 | − | 25.7315i | 0.150076 | − | 0.851121i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.502001 | + | 0.182713i | 0.0165866 | + | 0.00603702i | ||||
\(917\) | 23.2542 | + | 63.8905i | 0.767922 | + | 2.10985i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.86047 | + | 11.8827i | 0.226306 | + | 0.391974i | 0.956710 | − | 0.291041i | \(-0.0940017\pi\) |
−0.730404 | + | 0.683015i | \(0.760668\pi\) | |||||||
\(920\) | 0.464997 | − | 0.805399i | 0.0153305 | − | 0.0265532i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.4718 | − | 2.55178i | 0.476605 | − | 0.0840383i | ||||
\(923\) | −47.7252 | − | 27.5542i | −1.57089 | − | 0.906956i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.73079 | + | 3.25443i | 0.0897880 | + | 0.107005i | ||||
\(926\) | 12.7075 | − | 4.62514i | 0.417593 | − | 0.151991i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.51276 | + | 4.62576i | 0.180965 | + | 0.151848i | ||||
\(929\) | 16.3896 | + | 2.88993i | 0.537725 | + | 0.0948155i | 0.435914 | − | 0.899988i | \(-0.356425\pi\) |
0.101811 | + | 0.994804i | \(0.467536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 52.4637 | − | 59.5953i | 1.71943 | − | 1.95316i | ||||
\(932\) | 28.3021i | 0.927066i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.34719 | − | 1.60552i | 0.0440815 | − | 0.0525342i | ||||
\(935\) | −0.861171 | + | 2.36605i | −0.0281633 | + | 0.0773781i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.7481 | + | 28.3181i | −1.10250 | + | 0.925110i | −0.997591 | − | 0.0693710i | \(-0.977901\pi\) |
−0.104913 | + | 0.994481i | \(0.533456\pi\) | |||||||
\(938\) | −27.9251 | + | 16.1226i | −0.911786 | + | 0.526420i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.159820 | + | 0.906384i | 0.00521275 | + | 0.0295630i | ||||
\(941\) | 8.23823 | + | 46.7213i | 0.268559 | + | 1.52307i | 0.758706 | + | 0.651433i | \(0.225832\pi\) |
−0.490147 | + | 0.871640i | \(0.663057\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.1786 | + | 11.6501i | −0.657105 | + | 0.379380i | ||||
\(944\) | −7.81839 | + | 6.56041i | −0.254467 | + | 0.213523i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.86866 | − | 16.1240i | 0.190807 | − | 0.524237i | ||||
\(947\) | −35.3270 | + | 42.1011i | −1.14797 | + | 1.36810i | −0.229169 | + | 0.973387i | \(0.573601\pi\) |
−0.918804 | + | 0.394714i | \(0.870844\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 16.6983i | − | 0.542051i | ||||||
\(950\) | 6.94054 | + | 20.5741i | 0.225181 | + | 0.667513i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −25.3919 | − | 4.47728i | −0.822958 | − | 0.145110i | ||||
\(953\) | 13.5273 | + | 11.3507i | 0.438191 | + | 0.367686i | 0.835032 | − | 0.550201i | \(-0.185449\pi\) |
−0.396841 | + | 0.917888i | \(0.629893\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.310761 | + | 0.113108i | −0.0100560 | + | 0.00366008i | ||||
\(956\) | 7.78671 | + | 9.27984i | 0.251840 | + | 0.300131i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.0461 | − | 9.26419i | −0.518424 | − | 0.299312i | ||||
\(959\) | 14.4151 | − | 2.54177i | 0.465488 | − | 0.0820782i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.51559 | + | 11.2853i | −0.210180 | + | 0.364043i | ||||
\(962\) | −1.54000 | − | 2.66736i | −0.0496517 | − | 0.0859992i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.57132 | − | 18.0546i | −0.211648 | − | 0.581498i | ||||
\(965\) | 2.60122 | + | 0.946768i | 0.0837363 | + | 0.0304775i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.05432 | + | 28.6645i | −0.162536 | + | 0.921787i | 0.789033 | + | 0.614351i | \(0.210582\pi\) |
−0.951569 | + | 0.307436i | \(0.900529\pi\) | |||||||
\(968\) | −1.90572 | −0.0612520 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.762144 | 0.0244710 | ||||||||
\(971\) | −0.732840 | + | 4.15614i | −0.0235180 | + | 0.133377i | −0.994306 | − | 0.106561i | \(-0.966016\pi\) |
0.970788 | + | 0.239938i | \(0.0771271\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −90.7515 | − | 33.0308i | −2.90936 | − | 1.05892i | ||||
\(974\) | −9.72711 | − | 26.7250i | −0.311677 | − | 0.856325i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.91131 | + | 3.31048i | 0.0611795 | + | 0.105966i | ||||
\(977\) | −27.0378 | + | 46.8308i | −0.865016 | + | 1.49825i | 0.00201614 | + | 0.999998i | \(0.499358\pi\) |
−0.867032 | + | 0.498253i | \(0.833975\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.8398 | − | 3.67462i | 0.666043 | − | 0.117441i | ||||
\(980\) | −2.15326 | − | 1.24318i | −0.0687834 | − | 0.0397121i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.594649 | − | 0.708675i | −0.0189760 | − | 0.0226147i | ||||
\(983\) | 9.02234 | − | 3.28386i | 0.287768 | − | 0.104739i | −0.194103 | − | 0.980981i | \(-0.562180\pi\) |
0.481871 | + | 0.876242i | \(0.339957\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.65681 | + | 1.39023i | 0.0527905 | + | 0.0442965i | ||||
\(986\) | −36.3899 | − | 6.41651i | −1.15889 | − | 0.204343i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.36522 | − | 15.5631i | −0.0752476 | − | 0.495129i | ||||
\(989\) | − | 32.5419i | − | 1.03477i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.68306 | + | 11.5398i | −0.307593 | + | 0.366575i | −0.897591 | − | 0.440830i | \(-0.854684\pi\) |
0.589998 | + | 0.807405i | \(0.299129\pi\) | |||||||
\(992\) | 1.44981 | − | 3.98332i | 0.0460315 | − | 0.126471i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −58.6980 | + | 49.2535i | −1.86179 | + | 1.56223i | ||||
\(995\) | −2.58939 | + | 1.49499i | −0.0820893 | + | 0.0473943i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.478914 | − | 2.71605i | −0.0151674 | − | 0.0860183i | 0.976284 | − | 0.216492i | \(-0.0694614\pi\) |
−0.991452 | + | 0.130473i | \(0.958350\pi\) | |||||||
\(998\) | −4.68426 | − | 26.5658i | −0.148278 | − | 0.840924i | ||||
\(999\) | 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 | 342.2.bb.a.287.2 | yes | 24 | |
3.2 | odd | 2 | 342.2.bb.b.287.3 | yes | 24 | ||
19.10 | odd | 18 | 342.2.bb.b.143.3 | yes | 24 | ||
57.29 | even | 18 | inner | 342.2.bb.a.143.2 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
342.2.bb.a.143.2 | ✓ | 24 | 57.29 | even | 18 | inner | |
342.2.bb.a.287.2 | yes | 24 | 1.1 | even | 1 | trivial | |
342.2.bb.b.143.3 | yes | 24 | 19.10 | odd | 18 | ||
342.2.bb.b.287.3 | yes | 24 | 3.2 | odd | 2 |