Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(337,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(-2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.337 |
Dual form | 546.2.c.e.337.4 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 3.56155i | − | 1.59277i | −0.604787 | − | 0.796387i | \(-0.706742\pi\) | ||
0.604787 | − | 0.796387i | \(-0.293258\pi\) | |||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.56155 | −1.12626 | ||||||||
\(11\) | − | 5.56155i | − | 1.67687i | −0.545001 | − | 0.838436i | \(-0.683471\pi\) | ||
0.545001 | − | 0.838436i | \(-0.316529\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.56155 | + | 0.561553i | 0.987797 | + | 0.155747i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 3.56155i | 0.919589i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.68466 | −1.62127 | −0.810634 | − | 0.585553i | \(-0.800877\pi\) | ||||
−0.810634 | + | 0.585553i | \(0.800877\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 1.56155i | 0.358245i | 0.983827 | + | 0.179122i | \(0.0573258\pi\) | ||||
−0.983827 | + | 0.179122i | \(0.942674\pi\) | |||||||
\(20\) | 3.56155i | 0.796387i | ||||||||
\(21\) | − | 1.00000i | − | 0.218218i | ||||||
\(22\) | −5.56155 | −1.18573 | ||||||||
\(23\) | −6.68466 | −1.39385 | −0.696924 | − | 0.717145i | \(-0.745448\pi\) | ||||
−0.696924 | + | 0.717145i | \(0.745448\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −7.68466 | −1.53693 | ||||||||
\(26\) | 0.561553 | − | 3.56155i | 0.110130 | − | 0.698478i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | − | 1.00000i | − | 0.188982i | ||||||
\(29\) | 1.56155 | 0.289973 | 0.144987 | − | 0.989434i | \(-0.453686\pi\) | ||||
0.144987 | + | 0.989434i | \(0.453686\pi\) | |||||||
\(30\) | 3.56155 | 0.650248 | ||||||||
\(31\) | 6.24621i | 1.12185i | 0.827866 | + | 0.560926i | \(0.189555\pi\) | ||||
−0.827866 | + | 0.560926i | \(0.810445\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 5.56155i | 0.968142i | ||||||||
\(34\) | 6.68466i | 1.14641i | ||||||||
\(35\) | 3.56155 | 0.602012 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − | 10.6847i | − | 1.75655i | −0.478159 | − | 0.878274i | \(-0.658696\pi\) | ||
0.478159 | − | 0.878274i | \(-0.341304\pi\) | |||||||
\(38\) | 1.56155 | 0.253317 | ||||||||
\(39\) | −3.56155 | − | 0.561553i | −0.570305 | − | 0.0899204i | ||||
\(40\) | 3.56155 | 0.563131 | ||||||||
\(41\) | − | 4.00000i | − | 0.624695i | −0.949968 | − | 0.312348i | \(-0.898885\pi\) | ||
0.949968 | − | 0.312348i | \(-0.101115\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −6.43845 | −0.981854 | −0.490927 | − | 0.871201i | \(-0.663342\pi\) | ||||
−0.490927 | + | 0.871201i | \(0.663342\pi\) | |||||||
\(44\) | 5.56155i | 0.838436i | ||||||||
\(45\) | − | 3.56155i | − | 0.530925i | ||||||
\(46\) | 6.68466i | 0.985599i | ||||||||
\(47\) | 10.2462i | 1.49456i | 0.664507 | + | 0.747282i | \(0.268641\pi\) | ||||
−0.664507 | + | 0.747282i | \(0.731359\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 7.68466i | 1.08677i | ||||||||
\(51\) | 6.68466 | 0.936039 | ||||||||
\(52\) | −3.56155 | − | 0.561553i | −0.493899 | − | 0.0778734i | ||||
\(53\) | 4.87689 | 0.669893 | 0.334946 | − | 0.942237i | \(-0.391282\pi\) | ||||
0.334946 | + | 0.942237i | \(0.391282\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −19.8078 | −2.67088 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | − | 1.56155i | − | 0.206833i | ||||||
\(58\) | − | 1.56155i | − | 0.205042i | ||||||
\(59\) | − | 4.24621i | − | 0.552810i | −0.961041 | − | 0.276405i | \(-0.910857\pi\) | ||
0.961041 | − | 0.276405i | \(-0.0891431\pi\) | |||||||
\(60\) | − | 3.56155i | − | 0.459794i | ||||||
\(61\) | −1.56155 | −0.199936 | −0.0999682 | − | 0.994991i | \(-0.531874\pi\) | ||||
−0.0999682 | + | 0.994991i | \(0.531874\pi\) | |||||||
\(62\) | 6.24621 | 0.793270 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.00000 | − | 12.6847i | 0.248069 | − | 1.57334i | ||||
\(66\) | 5.56155 | 0.684580 | ||||||||
\(67\) | 1.12311i | 0.137209i | 0.997644 | + | 0.0686046i | \(0.0218547\pi\) | ||||
−0.997644 | + | 0.0686046i | \(0.978145\pi\) | |||||||
\(68\) | 6.68466 | 0.810634 | ||||||||
\(69\) | 6.68466 | 0.804738 | ||||||||
\(70\) | − | 3.56155i | − | 0.425687i | ||||||
\(71\) | − | 9.36932i | − | 1.11193i | −0.831205 | − | 0.555967i | \(-0.812348\pi\) | ||
0.831205 | − | 0.555967i | \(-0.187652\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − | 11.5616i | − | 1.35318i | −0.736361 | − | 0.676589i | \(-0.763458\pi\) | ||
0.736361 | − | 0.676589i | \(-0.236542\pi\) | |||||||
\(74\) | −10.6847 | −1.24207 | ||||||||
\(75\) | 7.68466 | 0.887348 | ||||||||
\(76\) | − | 1.56155i | − | 0.179122i | ||||||
\(77\) | 5.56155 | 0.633798 | ||||||||
\(78\) | −0.561553 | + | 3.56155i | −0.0635833 | + | 0.403266i | ||||
\(79\) | 16.0000 | 1.80014 | 0.900070 | − | 0.435745i | \(-0.143515\pi\) | ||||
0.900070 | + | 0.435745i | \(0.143515\pi\) | |||||||
\(80\) | − | 3.56155i | − | 0.398194i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.00000 | −0.441726 | ||||||||
\(83\) | 2.00000i | 0.219529i | 0.993958 | + | 0.109764i | \(0.0350096\pi\) | ||||
−0.993958 | + | 0.109764i | \(0.964990\pi\) | |||||||
\(84\) | 1.00000i | 0.109109i | ||||||||
\(85\) | 23.8078i | 2.58231i | ||||||||
\(86\) | 6.43845i | 0.694276i | ||||||||
\(87\) | −1.56155 | −0.167416 | ||||||||
\(88\) | 5.56155 | 0.592864 | ||||||||
\(89\) | 8.00000i | 0.847998i | 0.905663 | + | 0.423999i | \(0.139374\pi\) | ||||
−0.905663 | + | 0.423999i | \(0.860626\pi\) | |||||||
\(90\) | −3.56155 | −0.375421 | ||||||||
\(91\) | −0.561553 | + | 3.56155i | −0.0588667 | + | 0.373352i | ||||
\(92\) | 6.68466 | 0.696924 | ||||||||
\(93\) | − | 6.24621i | − | 0.647702i | ||||||
\(94\) | 10.2462 | 1.05682 | ||||||||
\(95\) | 5.56155 | 0.570603 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | − | 10.0000i | − | 1.01535i | −0.861550 | − | 0.507673i | \(-0.830506\pi\) | ||
0.861550 | − | 0.507673i | \(-0.169494\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | − | 5.56155i | − | 0.558957i | ||||||
\(100\) | 7.68466 | 0.768466 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | − | 6.68466i | − | 0.661880i | ||||||
\(103\) | 1.80776 | 0.178124 | 0.0890621 | − | 0.996026i | \(-0.471613\pi\) | ||||
0.0890621 | + | 0.996026i | \(0.471613\pi\) | |||||||
\(104\) | −0.561553 | + | 3.56155i | −0.0550648 | + | 0.349239i | ||||
\(105\) | −3.56155 | −0.347572 | ||||||||
\(106\) | − | 4.87689i | − | 0.473686i | ||||||
\(107\) | −4.87689 | −0.471467 | −0.235734 | − | 0.971818i | \(-0.575749\pi\) | ||||
−0.235734 | + | 0.971818i | \(0.575749\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | − | 12.9309i | − | 1.23855i | −0.785173 | − | 0.619276i | \(-0.787426\pi\) | ||
0.785173 | − | 0.619276i | \(-0.212574\pi\) | |||||||
\(110\) | 19.8078i | 1.88860i | ||||||||
\(111\) | 10.6847i | 1.01414i | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 20.2462 | 1.90460 | 0.952302 | − | 0.305158i | \(-0.0987093\pi\) | ||||
0.952302 | + | 0.305158i | \(0.0987093\pi\) | |||||||
\(114\) | −1.56155 | −0.146253 | ||||||||
\(115\) | 23.8078i | 2.22009i | ||||||||
\(116\) | −1.56155 | −0.144987 | ||||||||
\(117\) | 3.56155 | + | 0.561553i | 0.329266 | + | 0.0519156i | ||||
\(118\) | −4.24621 | −0.390895 | ||||||||
\(119\) | − | 6.68466i | − | 0.612782i | ||||||
\(120\) | −3.56155 | −0.325124 | ||||||||
\(121\) | −19.9309 | −1.81190 | ||||||||
\(122\) | 1.56155i | 0.141376i | ||||||||
\(123\) | 4.00000i | 0.360668i | ||||||||
\(124\) | − | 6.24621i | − | 0.560926i | ||||||
\(125\) | 9.56155i | 0.855211i | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 10.2462 | 0.909204 | 0.454602 | − | 0.890695i | \(-0.349781\pi\) | ||||
0.454602 | + | 0.890695i | \(0.349781\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 6.43845 | 0.566874 | ||||||||
\(130\) | −12.6847 | − | 2.00000i | −1.11252 | − | 0.175412i | ||||
\(131\) | −1.56155 | −0.136434 | −0.0682168 | − | 0.997671i | \(-0.521731\pi\) | ||||
−0.0682168 | + | 0.997671i | \(0.521731\pi\) | |||||||
\(132\) | − | 5.56155i | − | 0.484071i | ||||||
\(133\) | −1.56155 | −0.135404 | ||||||||
\(134\) | 1.12311 | 0.0970215 | ||||||||
\(135\) | 3.56155i | 0.306530i | ||||||||
\(136\) | − | 6.68466i | − | 0.573205i | ||||||
\(137\) | − | 6.68466i | − | 0.571109i | −0.958362 | − | 0.285554i | \(-0.907822\pi\) | ||
0.958362 | − | 0.285554i | \(-0.0921777\pi\) | |||||||
\(138\) | − | 6.68466i | − | 0.569036i | ||||||
\(139\) | 10.2462 | 0.869072 | 0.434536 | − | 0.900654i | \(-0.356912\pi\) | ||||
0.434536 | + | 0.900654i | \(0.356912\pi\) | |||||||
\(140\) | −3.56155 | −0.301006 | ||||||||
\(141\) | − | 10.2462i | − | 0.862887i | ||||||
\(142\) | −9.36932 | −0.786256 | ||||||||
\(143\) | 3.12311 | − | 19.8078i | 0.261167 | − | 1.65641i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − | 5.56155i | − | 0.461862i | ||||||
\(146\) | −11.5616 | −0.956841 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 10.6847i | 0.878274i | ||||||||
\(149\) | − | 10.0000i | − | 0.819232i | −0.912258 | − | 0.409616i | \(-0.865663\pi\) | ||
0.912258 | − | 0.409616i | \(-0.134337\pi\) | |||||||
\(150\) | − | 7.68466i | − | 0.627450i | ||||||
\(151\) | − | 16.6847i | − | 1.35778i | −0.734241 | − | 0.678889i | \(-0.762462\pi\) | ||
0.734241 | − | 0.678889i | \(-0.237538\pi\) | |||||||
\(152\) | −1.56155 | −0.126659 | ||||||||
\(153\) | −6.68466 | −0.540423 | ||||||||
\(154\) | − | 5.56155i | − | 0.448163i | ||||||
\(155\) | 22.2462 | 1.78686 | ||||||||
\(156\) | 3.56155 | + | 0.561553i | 0.285152 | + | 0.0449602i | ||||
\(157\) | −11.8078 | −0.942362 | −0.471181 | − | 0.882037i | \(-0.656172\pi\) | ||||
−0.471181 | + | 0.882037i | \(0.656172\pi\) | |||||||
\(158\) | − | 16.0000i | − | 1.27289i | ||||||
\(159\) | −4.87689 | −0.386763 | ||||||||
\(160\) | −3.56155 | −0.281565 | ||||||||
\(161\) | − | 6.68466i | − | 0.526825i | ||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 9.12311i | − | 0.714577i | −0.933994 | − | 0.357288i | \(-0.883701\pi\) | ||
0.933994 | − | 0.357288i | \(-0.116299\pi\) | |||||||
\(164\) | 4.00000i | 0.312348i | ||||||||
\(165\) | 19.8078 | 1.54203 | ||||||||
\(166\) | 2.00000 | 0.155230 | ||||||||
\(167\) | 11.8078i | 0.913712i | 0.889541 | + | 0.456856i | \(0.151025\pi\) | ||||
−0.889541 | + | 0.456856i | \(0.848975\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 12.3693 | + | 4.00000i | 0.951486 | + | 0.307692i | ||||
\(170\) | 23.8078 | 1.82597 | ||||||||
\(171\) | 1.56155i | 0.119415i | ||||||||
\(172\) | 6.43845 | 0.490927 | ||||||||
\(173\) | −3.75379 | −0.285395 | −0.142698 | − | 0.989766i | \(-0.545578\pi\) | ||||
−0.142698 | + | 0.989766i | \(0.545578\pi\) | |||||||
\(174\) | 1.56155i | 0.118381i | ||||||||
\(175\) | − | 7.68466i | − | 0.580906i | ||||||
\(176\) | − | 5.56155i | − | 0.419218i | ||||||
\(177\) | 4.24621i | 0.319165i | ||||||||
\(178\) | 8.00000 | 0.599625 | ||||||||
\(179\) | 11.1231 | 0.831380 | 0.415690 | − | 0.909506i | \(-0.363540\pi\) | ||||
0.415690 | + | 0.909506i | \(0.363540\pi\) | |||||||
\(180\) | 3.56155i | 0.265462i | ||||||||
\(181\) | −13.3693 | −0.993733 | −0.496867 | − | 0.867827i | \(-0.665516\pi\) | ||||
−0.496867 | + | 0.867827i | \(0.665516\pi\) | |||||||
\(182\) | 3.56155 | + | 0.561553i | 0.264000 | + | 0.0416251i | ||||
\(183\) | 1.56155 | 0.115433 | ||||||||
\(184\) | − | 6.68466i | − | 0.492800i | ||||||
\(185\) | −38.0540 | −2.79778 | ||||||||
\(186\) | −6.24621 | −0.457994 | ||||||||
\(187\) | 37.1771i | 2.71866i | ||||||||
\(188\) | − | 10.2462i | − | 0.747282i | ||||||
\(189\) | − | 1.00000i | − | 0.0727393i | ||||||
\(190\) | − | 5.56155i | − | 0.403477i | ||||||
\(191\) | −24.0540 | −1.74048 | −0.870242 | − | 0.492624i | \(-0.836038\pi\) | ||||
−0.870242 | + | 0.492624i | \(0.836038\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 12.0000i | 0.863779i | 0.901927 | + | 0.431889i | \(0.142153\pi\) | ||||
−0.901927 | + | 0.431889i | \(0.857847\pi\) | |||||||
\(194\) | −10.0000 | −0.717958 | ||||||||
\(195\) | −2.00000 | + | 12.6847i | −0.143223 | + | 0.908367i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | −5.56155 | −0.395242 | ||||||||
\(199\) | 4.93087 | 0.349540 | 0.174770 | − | 0.984609i | \(-0.444082\pi\) | ||||
0.174770 | + | 0.984609i | \(0.444082\pi\) | |||||||
\(200\) | − | 7.68466i | − | 0.543387i | ||||||
\(201\) | − | 1.12311i | − | 0.0792178i | ||||||
\(202\) | − | 6.00000i | − | 0.422159i | ||||||
\(203\) | 1.56155i | 0.109600i | ||||||||
\(204\) | −6.68466 | −0.468020 | ||||||||
\(205\) | −14.2462 | −0.994999 | ||||||||
\(206\) | − | 1.80776i | − | 0.125953i | ||||||
\(207\) | −6.68466 | −0.464616 | ||||||||
\(208\) | 3.56155 | + | 0.561553i | 0.246949 | + | 0.0389367i | ||||
\(209\) | 8.68466 | 0.600730 | ||||||||
\(210\) | 3.56155i | 0.245770i | ||||||||
\(211\) | 7.80776 | 0.537509 | 0.268754 | − | 0.963209i | \(-0.413388\pi\) | ||||
0.268754 | + | 0.963209i | \(0.413388\pi\) | |||||||
\(212\) | −4.87689 | −0.334946 | ||||||||
\(213\) | 9.36932i | 0.641975i | ||||||||
\(214\) | 4.87689i | 0.333378i | ||||||||
\(215\) | 22.9309i | 1.56387i | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −6.24621 | −0.424020 | ||||||||
\(218\) | −12.9309 | −0.875789 | ||||||||
\(219\) | 11.5616i | 0.781257i | ||||||||
\(220\) | 19.8078 | 1.33544 | ||||||||
\(221\) | −23.8078 | − | 3.75379i | −1.60148 | − | 0.252507i | ||||
\(222\) | 10.6847 | 0.717107 | ||||||||
\(223\) | 1.75379i | 0.117442i | 0.998274 | + | 0.0587212i | \(0.0187023\pi\) | ||||
−0.998274 | + | 0.0587212i | \(0.981298\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −7.68466 | −0.512311 | ||||||||
\(226\) | − | 20.2462i | − | 1.34676i | ||||||
\(227\) | 17.6155i | 1.16918i | 0.811328 | + | 0.584592i | \(0.198745\pi\) | ||||
−0.811328 | + | 0.584592i | \(0.801255\pi\) | |||||||
\(228\) | 1.56155i | 0.103416i | ||||||||
\(229\) | − | 2.00000i | − | 0.132164i | −0.997814 | − | 0.0660819i | \(-0.978950\pi\) | ||
0.997814 | − | 0.0660819i | \(-0.0210498\pi\) | |||||||
\(230\) | 23.8078 | 1.56984 | ||||||||
\(231\) | −5.56155 | −0.365923 | ||||||||
\(232\) | 1.56155i | 0.102521i | ||||||||
\(233\) | 2.00000 | 0.131024 | 0.0655122 | − | 0.997852i | \(-0.479132\pi\) | ||||
0.0655122 | + | 0.997852i | \(0.479132\pi\) | |||||||
\(234\) | 0.561553 | − | 3.56155i | 0.0367099 | − | 0.232826i | ||||
\(235\) | 36.4924 | 2.38050 | ||||||||
\(236\) | 4.24621i | 0.276405i | ||||||||
\(237\) | −16.0000 | −1.03931 | ||||||||
\(238\) | −6.68466 | −0.433302 | ||||||||
\(239\) | − | 14.2462i | − | 0.921511i | −0.887527 | − | 0.460755i | \(-0.847579\pi\) | ||
0.887527 | − | 0.460755i | \(-0.152421\pi\) | |||||||
\(240\) | 3.56155i | 0.229897i | ||||||||
\(241\) | − | 6.00000i | − | 0.386494i | −0.981150 | − | 0.193247i | \(-0.938098\pi\) | ||
0.981150 | − | 0.193247i | \(-0.0619019\pi\) | |||||||
\(242\) | 19.9309i | 1.28120i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.56155 | 0.0999682 | ||||||||
\(245\) | 3.56155i | 0.227539i | ||||||||
\(246\) | 4.00000 | 0.255031 | ||||||||
\(247\) | −0.876894 | + | 5.56155i | −0.0557955 | + | 0.353873i | ||||
\(248\) | −6.24621 | −0.396635 | ||||||||
\(249\) | − | 2.00000i | − | 0.126745i | ||||||
\(250\) | 9.56155 | 0.604726 | ||||||||
\(251\) | 22.0540 | 1.39203 | 0.696017 | − | 0.718025i | \(-0.254954\pi\) | ||||
0.696017 | + | 0.718025i | \(0.254954\pi\) | |||||||
\(252\) | − | 1.00000i | − | 0.0629941i | ||||||
\(253\) | 37.1771i | 2.33730i | ||||||||
\(254\) | − | 10.2462i | − | 0.642904i | ||||||
\(255\) | − | 23.8078i | − | 1.49090i | ||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.0000 | −1.62184 | −0.810918 | − | 0.585160i | \(-0.801032\pi\) | ||||
−0.810918 | + | 0.585160i | \(0.801032\pi\) | |||||||
\(258\) | − | 6.43845i | − | 0.400840i | ||||||
\(259\) | 10.6847 | 0.663912 | ||||||||
\(260\) | −2.00000 | + | 12.6847i | −0.124035 | + | 0.786669i | ||||
\(261\) | 1.56155 | 0.0966577 | ||||||||
\(262\) | 1.56155i | 0.0964731i | ||||||||
\(263\) | −23.3693 | −1.44101 | −0.720507 | − | 0.693448i | \(-0.756091\pi\) | ||||
−0.720507 | + | 0.693448i | \(0.756091\pi\) | |||||||
\(264\) | −5.56155 | −0.342290 | ||||||||
\(265\) | − | 17.3693i | − | 1.06699i | ||||||
\(266\) | 1.56155i | 0.0957449i | ||||||||
\(267\) | − | 8.00000i | − | 0.489592i | ||||||
\(268\) | − | 1.12311i | − | 0.0686046i | ||||||
\(269\) | 31.3693 | 1.91262 | 0.956311 | − | 0.292353i | \(-0.0944382\pi\) | ||||
0.956311 | + | 0.292353i | \(0.0944382\pi\) | |||||||
\(270\) | 3.56155 | 0.216749 | ||||||||
\(271\) | 8.00000i | 0.485965i | 0.970031 | + | 0.242983i | \(0.0781258\pi\) | ||||
−0.970031 | + | 0.242983i | \(0.921874\pi\) | |||||||
\(272\) | −6.68466 | −0.405317 | ||||||||
\(273\) | 0.561553 | − | 3.56155i | 0.0339867 | − | 0.215555i | ||||
\(274\) | −6.68466 | −0.403835 | ||||||||
\(275\) | 42.7386i | 2.57724i | ||||||||
\(276\) | −6.68466 | −0.402369 | ||||||||
\(277\) | −10.8769 | −0.653529 | −0.326765 | − | 0.945106i | \(-0.605958\pi\) | ||||
−0.326765 | + | 0.945106i | \(0.605958\pi\) | |||||||
\(278\) | − | 10.2462i | − | 0.614527i | ||||||
\(279\) | 6.24621i | 0.373951i | ||||||||
\(280\) | 3.56155i | 0.212843i | ||||||||
\(281\) | − | 6.00000i | − | 0.357930i | −0.983855 | − | 0.178965i | \(-0.942725\pi\) | ||
0.983855 | − | 0.178965i | \(-0.0572749\pi\) | |||||||
\(282\) | −10.2462 | −0.610153 | ||||||||
\(283\) | −4.87689 | −0.289901 | −0.144951 | − | 0.989439i | \(-0.546302\pi\) | ||||
−0.144951 | + | 0.989439i | \(0.546302\pi\) | |||||||
\(284\) | 9.36932i | 0.555967i | ||||||||
\(285\) | −5.56155 | −0.329438 | ||||||||
\(286\) | −19.8078 | − | 3.12311i | −1.17126 | − | 0.184673i | ||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 27.6847 | 1.62851 | ||||||||
\(290\) | −5.56155 | −0.326586 | ||||||||
\(291\) | 10.0000i | 0.586210i | ||||||||
\(292\) | 11.5616i | 0.676589i | ||||||||
\(293\) | 7.75379i | 0.452981i | 0.974013 | + | 0.226491i | \(0.0727253\pi\) | ||||
−0.974013 | + | 0.226491i | \(0.927275\pi\) | |||||||
\(294\) | − | 1.00000i | − | 0.0583212i | ||||||
\(295\) | −15.1231 | −0.880501 | ||||||||
\(296\) | 10.6847 | 0.621033 | ||||||||
\(297\) | 5.56155i | 0.322714i | ||||||||
\(298\) | −10.0000 | −0.579284 | ||||||||
\(299\) | −23.8078 | − | 3.75379i | −1.37684 | − | 0.217087i | ||||
\(300\) | −7.68466 | −0.443674 | ||||||||
\(301\) | − | 6.43845i | − | 0.371106i | ||||||
\(302\) | −16.6847 | −0.960094 | ||||||||
\(303\) | −6.00000 | −0.344691 | ||||||||
\(304\) | 1.56155i | 0.0895612i | ||||||||
\(305\) | 5.56155i | 0.318454i | ||||||||
\(306\) | 6.68466i | 0.382136i | ||||||||
\(307\) | − | 26.2462i | − | 1.49795i | −0.662598 | − | 0.748975i | \(-0.730546\pi\) | ||
0.662598 | − | 0.748975i | \(-0.269454\pi\) | |||||||
\(308\) | −5.56155 | −0.316899 | ||||||||
\(309\) | −1.80776 | −0.102840 | ||||||||
\(310\) | − | 22.2462i | − | 1.26350i | ||||||
\(311\) | −0.492423 | −0.0279227 | −0.0139614 | − | 0.999903i | \(-0.504444\pi\) | ||||
−0.0139614 | + | 0.999903i | \(0.504444\pi\) | |||||||
\(312\) | 0.561553 | − | 3.56155i | 0.0317917 | − | 0.201633i | ||||
\(313\) | 32.2462 | 1.82266 | 0.911332 | − | 0.411673i | \(-0.135055\pi\) | ||||
0.911332 | + | 0.411673i | \(0.135055\pi\) | |||||||
\(314\) | 11.8078i | 0.666351i | ||||||||
\(315\) | 3.56155 | 0.200671 | ||||||||
\(316\) | −16.0000 | −0.900070 | ||||||||
\(317\) | 3.36932i | 0.189240i | 0.995513 | + | 0.0946198i | \(0.0301636\pi\) | ||||
−0.995513 | + | 0.0946198i | \(0.969836\pi\) | |||||||
\(318\) | 4.87689i | 0.273483i | ||||||||
\(319\) | − | 8.68466i | − | 0.486248i | ||||||
\(320\) | 3.56155i | 0.199097i | ||||||||
\(321\) | 4.87689 | 0.272202 | ||||||||
\(322\) | −6.68466 | −0.372521 | ||||||||
\(323\) | − | 10.4384i | − | 0.580811i | ||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −27.3693 | − | 4.31534i | −1.51818 | − | 0.239372i | ||||
\(326\) | −9.12311 | −0.505282 | ||||||||
\(327\) | 12.9309i | 0.715079i | ||||||||
\(328\) | 4.00000 | 0.220863 | ||||||||
\(329\) | −10.2462 | −0.564892 | ||||||||
\(330\) | − | 19.8078i | − | 1.09038i | ||||||
\(331\) | 1.12311i | 0.0617315i | 0.999524 | + | 0.0308657i | \(0.00982643\pi\) | ||||
−0.999524 | + | 0.0308657i | \(0.990174\pi\) | |||||||
\(332\) | − | 2.00000i | − | 0.109764i | ||||||
\(333\) | − | 10.6847i | − | 0.585516i | ||||||
\(334\) | 11.8078 | 0.646092 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | − | 1.00000i | − | 0.0545545i | ||||||
\(337\) | 20.0540 | 1.09241 | 0.546205 | − | 0.837652i | \(-0.316072\pi\) | ||||
0.546205 | + | 0.837652i | \(0.316072\pi\) | |||||||
\(338\) | 4.00000 | − | 12.3693i | 0.217571 | − | 0.672802i | ||||
\(339\) | −20.2462 | −1.09962 | ||||||||
\(340\) | − | 23.8078i | − | 1.29116i | ||||||
\(341\) | 34.7386 | 1.88120 | ||||||||
\(342\) | 1.56155 | 0.0844391 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | − | 6.43845i | − | 0.347138i | ||||||
\(345\) | − | 23.8078i | − | 1.28177i | ||||||
\(346\) | 3.75379i | 0.201805i | ||||||||
\(347\) | −24.4924 | −1.31482 | −0.657411 | − | 0.753532i | \(-0.728348\pi\) | ||||
−0.657411 | + | 0.753532i | \(0.728348\pi\) | |||||||
\(348\) | 1.56155 | 0.0837080 | ||||||||
\(349\) | − | 3.36932i | − | 0.180355i | −0.995926 | − | 0.0901777i | \(-0.971256\pi\) | ||
0.995926 | − | 0.0901777i | \(-0.0287435\pi\) | |||||||
\(350\) | −7.68466 | −0.410762 | ||||||||
\(351\) | −3.56155 | − | 0.561553i | −0.190102 | − | 0.0299735i | ||||
\(352\) | −5.56155 | −0.296432 | ||||||||
\(353\) | 18.2462i | 0.971148i | 0.874196 | + | 0.485574i | \(0.161389\pi\) | ||||
−0.874196 | + | 0.485574i | \(0.838611\pi\) | |||||||
\(354\) | 4.24621 | 0.225684 | ||||||||
\(355\) | −33.3693 | −1.77106 | ||||||||
\(356\) | − | 8.00000i | − | 0.423999i | ||||||
\(357\) | 6.68466i | 0.353790i | ||||||||
\(358\) | − | 11.1231i | − | 0.587874i | ||||||
\(359\) | − | 23.6155i | − | 1.24638i | −0.782071 | − | 0.623190i | \(-0.785836\pi\) | ||
0.782071 | − | 0.623190i | \(-0.214164\pi\) | |||||||
\(360\) | 3.56155 | 0.187710 | ||||||||
\(361\) | 16.5616 | 0.871661 | ||||||||
\(362\) | 13.3693i | 0.702676i | ||||||||
\(363\) | 19.9309 | 1.04610 | ||||||||
\(364\) | 0.561553 | − | 3.56155i | 0.0294334 | − | 0.186676i | ||||
\(365\) | −41.1771 | −2.15531 | ||||||||
\(366\) | − | 1.56155i | − | 0.0816237i | ||||||
\(367\) | 0.630683 | 0.0329214 | 0.0164607 | − | 0.999865i | \(-0.494760\pi\) | ||||
0.0164607 | + | 0.999865i | \(0.494760\pi\) | |||||||
\(368\) | −6.68466 | −0.348462 | ||||||||
\(369\) | − | 4.00000i | − | 0.208232i | ||||||
\(370\) | 38.0540i | 1.97833i | ||||||||
\(371\) | 4.87689i | 0.253196i | ||||||||
\(372\) | 6.24621i | 0.323851i | ||||||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | 37.1771 | 1.92238 | ||||||||
\(375\) | − | 9.56155i | − | 0.493756i | ||||||
\(376\) | −10.2462 | −0.528408 | ||||||||
\(377\) | 5.56155 | + | 0.876894i | 0.286435 | + | 0.0451624i | ||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 18.8769i | 0.969641i | 0.874614 | + | 0.484820i | \(0.161115\pi\) | ||||
−0.874614 | + | 0.484820i | \(0.838885\pi\) | |||||||
\(380\) | −5.56155 | −0.285302 | ||||||||
\(381\) | −10.2462 | −0.524929 | ||||||||
\(382\) | 24.0540i | 1.23071i | ||||||||
\(383\) | − | 17.5616i | − | 0.897353i | −0.893694 | − | 0.448677i | \(-0.851895\pi\) | ||
0.893694 | − | 0.448677i | \(-0.148105\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | − | 19.8078i | − | 1.00950i | ||||||
\(386\) | 12.0000 | 0.610784 | ||||||||
\(387\) | −6.43845 | −0.327285 | ||||||||
\(388\) | 10.0000i | 0.507673i | ||||||||
\(389\) | 27.1231 | 1.37520 | 0.687598 | − | 0.726092i | \(-0.258665\pi\) | ||||
0.687598 | + | 0.726092i | \(0.258665\pi\) | |||||||
\(390\) | 12.6847 | + | 2.00000i | 0.642313 | + | 0.101274i | ||||
\(391\) | 44.6847 | 2.25980 | ||||||||
\(392\) | − | 1.00000i | − | 0.0505076i | ||||||
\(393\) | 1.56155 | 0.0787699 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | − | 56.9848i | − | 2.86722i | ||||||
\(396\) | 5.56155i | 0.279479i | ||||||||
\(397\) | − | 15.3693i | − | 0.771364i | −0.922632 | − | 0.385682i | \(-0.873966\pi\) | ||
0.922632 | − | 0.385682i | \(-0.126034\pi\) | |||||||
\(398\) | − | 4.93087i | − | 0.247162i | ||||||
\(399\) | 1.56155 | 0.0781754 | ||||||||
\(400\) | −7.68466 | −0.384233 | ||||||||
\(401\) | 30.9848i | 1.54731i | 0.633608 | + | 0.773655i | \(0.281573\pi\) | ||||
−0.633608 | + | 0.773655i | \(0.718427\pi\) | |||||||
\(402\) | −1.12311 | −0.0560154 | ||||||||
\(403\) | −3.50758 | + | 22.2462i | −0.174725 | + | 1.10816i | ||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | − | 3.56155i | − | 0.176975i | ||||||
\(406\) | 1.56155 | 0.0774986 | ||||||||
\(407\) | −59.4233 | −2.94550 | ||||||||
\(408\) | 6.68466i | 0.330940i | ||||||||
\(409\) | − | 13.8078i | − | 0.682750i | −0.939927 | − | 0.341375i | \(-0.889107\pi\) | ||
0.939927 | − | 0.341375i | \(-0.110893\pi\) | |||||||
\(410\) | 14.2462i | 0.703570i | ||||||||
\(411\) | 6.68466i | 0.329730i | ||||||||
\(412\) | −1.80776 | −0.0890621 | ||||||||
\(413\) | 4.24621 | 0.208942 | ||||||||
\(414\) | 6.68466i | 0.328533i | ||||||||
\(415\) | 7.12311 | 0.349660 | ||||||||
\(416\) | 0.561553 | − | 3.56155i | 0.0275324 | − | 0.174619i | ||||
\(417\) | −10.2462 | −0.501759 | ||||||||
\(418\) | − | 8.68466i | − | 0.424781i | ||||||
\(419\) | −20.6847 | −1.01051 | −0.505256 | − | 0.862970i | \(-0.668602\pi\) | ||||
−0.505256 | + | 0.862970i | \(0.668602\pi\) | |||||||
\(420\) | 3.56155 | 0.173786 | ||||||||
\(421\) | 10.0000i | 0.487370i | 0.969854 | + | 0.243685i | \(0.0783563\pi\) | ||||
−0.969854 | + | 0.243685i | \(0.921644\pi\) | |||||||
\(422\) | − | 7.80776i | − | 0.380076i | ||||||
\(423\) | 10.2462i | 0.498188i | ||||||||
\(424\) | 4.87689i | 0.236843i | ||||||||
\(425\) | 51.3693 | 2.49178 | ||||||||
\(426\) | 9.36932 | 0.453945 | ||||||||
\(427\) | − | 1.56155i | − | 0.0755688i | ||||||
\(428\) | 4.87689 | 0.235734 | ||||||||
\(429\) | −3.12311 | + | 19.8078i | −0.150785 | + | 0.956328i | ||||
\(430\) | 22.9309 | 1.10582 | ||||||||
\(431\) | − | 29.8617i | − | 1.43839i | −0.694809 | − | 0.719195i | \(-0.744511\pi\) | ||
0.694809 | − | 0.719195i | \(-0.255489\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 23.3693 | 1.12306 | 0.561529 | − | 0.827457i | \(-0.310213\pi\) | ||||
0.561529 | + | 0.827457i | \(0.310213\pi\) | |||||||
\(434\) | 6.24621i | 0.299828i | ||||||||
\(435\) | 5.56155i | 0.266656i | ||||||||
\(436\) | 12.9309i | 0.619276i | ||||||||
\(437\) | − | 10.4384i | − | 0.499339i | ||||||
\(438\) | 11.5616 | 0.552432 | ||||||||
\(439\) | −8.93087 | −0.426247 | −0.213124 | − | 0.977025i | \(-0.568364\pi\) | ||||
−0.213124 | + | 0.977025i | \(0.568364\pi\) | |||||||
\(440\) | − | 19.8078i | − | 0.944298i | ||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | −3.75379 | + | 23.8078i | −0.178550 | + | 1.13242i | ||||
\(443\) | 6.63068 | 0.315033 | 0.157517 | − | 0.987516i | \(-0.449651\pi\) | ||||
0.157517 | + | 0.987516i | \(0.449651\pi\) | |||||||
\(444\) | − | 10.6847i | − | 0.507071i | ||||||
\(445\) | 28.4924 | 1.35067 | ||||||||
\(446\) | 1.75379 | 0.0830443 | ||||||||
\(447\) | 10.0000i | 0.472984i | ||||||||
\(448\) | − | 1.00000i | − | 0.0472456i | ||||||
\(449\) | 9.31534i | 0.439618i | 0.975543 | + | 0.219809i | \(0.0705434\pi\) | ||||
−0.975543 | + | 0.219809i | \(0.929457\pi\) | |||||||
\(450\) | 7.68466i | 0.362258i | ||||||||
\(451\) | −22.2462 | −1.04753 | ||||||||
\(452\) | −20.2462 | −0.952302 | ||||||||
\(453\) | 16.6847i | 0.783914i | ||||||||
\(454\) | 17.6155 | 0.826738 | ||||||||
\(455\) | 12.6847 | + | 2.00000i | 0.594666 | + | 0.0937614i | ||||
\(456\) | 1.56155 | 0.0731264 | ||||||||
\(457\) | 16.0000i | 0.748448i | 0.927338 | + | 0.374224i | \(0.122091\pi\) | ||||
−0.927338 | + | 0.374224i | \(0.877909\pi\) | |||||||
\(458\) | −2.00000 | −0.0934539 | ||||||||
\(459\) | 6.68466 | 0.312013 | ||||||||
\(460\) | − | 23.8078i | − | 1.11004i | ||||||
\(461\) | − | 36.9309i | − | 1.72004i | −0.510259 | − | 0.860021i | \(-0.670450\pi\) | ||
0.510259 | − | 0.860021i | \(-0.329550\pi\) | |||||||
\(462\) | 5.56155i | 0.258747i | ||||||||
\(463\) | 30.5464i | 1.41961i | 0.704397 | + | 0.709806i | \(0.251217\pi\) | ||||
−0.704397 | + | 0.709806i | \(0.748783\pi\) | |||||||
\(464\) | 1.56155 | 0.0724933 | ||||||||
\(465\) | −22.2462 | −1.03164 | ||||||||
\(466\) | − | 2.00000i | − | 0.0926482i | ||||||
\(467\) | 1.56155 | 0.0722600 | 0.0361300 | − | 0.999347i | \(-0.488497\pi\) | ||||
0.0361300 | + | 0.999347i | \(0.488497\pi\) | |||||||
\(468\) | −3.56155 | − | 0.561553i | −0.164633 | − | 0.0259578i | ||||
\(469\) | −1.12311 | −0.0518602 | ||||||||
\(470\) | − | 36.4924i | − | 1.68327i | ||||||
\(471\) | 11.8078 | 0.544073 | ||||||||
\(472\) | 4.24621 | 0.195448 | ||||||||
\(473\) | 35.8078i | 1.64644i | ||||||||
\(474\) | 16.0000i | 0.734904i | ||||||||
\(475\) | − | 12.0000i | − | 0.550598i | ||||||
\(476\) | 6.68466i | 0.306391i | ||||||||
\(477\) | 4.87689 | 0.223298 | ||||||||
\(478\) | −14.2462 | −0.651607 | ||||||||
\(479\) | − | 12.3002i | − | 0.562010i | −0.959706 | − | 0.281005i | \(-0.909332\pi\) | ||
0.959706 | − | 0.281005i | \(-0.0906677\pi\) | |||||||
\(480\) | 3.56155 | 0.162562 | ||||||||
\(481\) | 6.00000 | − | 38.0540i | 0.273576 | − | 1.73511i | ||||
\(482\) | −6.00000 | −0.273293 | ||||||||
\(483\) | 6.68466i | 0.304162i | ||||||||
\(484\) | 19.9309 | 0.905949 | ||||||||
\(485\) | −35.6155 | −1.61722 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 13.7538i | 0.623244i | 0.950206 | + | 0.311622i | \(0.100872\pi\) | ||||
−0.950206 | + | 0.311622i | \(0.899128\pi\) | |||||||
\(488\) | − | 1.56155i | − | 0.0706882i | ||||||
\(489\) | 9.12311i | 0.412561i | ||||||||
\(490\) | 3.56155 | 0.160895 | ||||||||
\(491\) | −10.2462 | −0.462405 | −0.231203 | − | 0.972906i | \(-0.574266\pi\) | ||||
−0.231203 | + | 0.972906i | \(0.574266\pi\) | |||||||
\(492\) | − | 4.00000i | − | 0.180334i | ||||||
\(493\) | −10.4384 | −0.470124 | ||||||||
\(494\) | 5.56155 | + | 0.876894i | 0.250226 | + | 0.0394533i | ||||
\(495\) | −19.8078 | −0.890293 | ||||||||
\(496\) | 6.24621i | 0.280463i | ||||||||
\(497\) | 9.36932 | 0.420271 | ||||||||
\(498\) | −2.00000 | −0.0896221 | ||||||||
\(499\) | 1.50758i | 0.0674884i | 0.999431 | + | 0.0337442i | \(0.0107432\pi\) | ||||
−0.999431 | + | 0.0337442i | \(0.989257\pi\) | |||||||
\(500\) | − | 9.56155i | − | 0.427606i | ||||||
\(501\) | − | 11.8078i | − | 0.527532i | ||||||
\(502\) | − | 22.0540i | − | 0.984317i | ||||||
\(503\) | 35.6155 | 1.58802 | 0.794009 | − | 0.607906i | \(-0.207990\pi\) | ||||
0.794009 | + | 0.607906i | \(0.207990\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | − | 21.3693i | − | 0.950922i | ||||||
\(506\) | 37.1771 | 1.65272 | ||||||||
\(507\) | −12.3693 | − | 4.00000i | −0.549341 | − | 0.177646i | ||||
\(508\) | −10.2462 | −0.454602 | ||||||||
\(509\) | − | 2.68466i | − | 0.118995i | −0.998228 | − | 0.0594977i | \(-0.981050\pi\) | ||
0.998228 | − | 0.0594977i | \(-0.0189499\pi\) | |||||||
\(510\) | −23.8078 | −1.05423 | ||||||||
\(511\) | 11.5616 | 0.511453 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 1.56155i | − | 0.0689442i | ||||||
\(514\) | 26.0000i | 1.14681i | ||||||||
\(515\) | − | 6.43845i | − | 0.283712i | ||||||
\(516\) | −6.43845 | −0.283437 | ||||||||
\(517\) | 56.9848 | 2.50619 | ||||||||
\(518\) | − | 10.6847i | − | 0.469457i | ||||||
\(519\) | 3.75379 | 0.164773 | ||||||||
\(520\) | 12.6847 | + | 2.00000i | 0.556259 | + | 0.0877058i | ||||
\(521\) | 8.05398 | 0.352851 | 0.176426 | − | 0.984314i | \(-0.443547\pi\) | ||||
0.176426 | + | 0.984314i | \(0.443547\pi\) | |||||||
\(522\) | − | 1.56155i | − | 0.0683473i | ||||||
\(523\) | −8.49242 | −0.371348 | −0.185674 | − | 0.982611i | \(-0.559447\pi\) | ||||
−0.185674 | + | 0.982611i | \(0.559447\pi\) | |||||||
\(524\) | 1.56155 | 0.0682168 | ||||||||
\(525\) | 7.68466i | 0.335386i | ||||||||
\(526\) | 23.3693i | 1.01895i | ||||||||
\(527\) | − | 41.7538i | − | 1.81882i | ||||||
\(528\) | 5.56155i | 0.242036i | ||||||||
\(529\) | 21.6847 | 0.942811 | ||||||||
\(530\) | −17.3693 | −0.754475 | ||||||||
\(531\) | − | 4.24621i | − | 0.184270i | ||||||
\(532\) | 1.56155 | 0.0677019 | ||||||||
\(533\) | 2.24621 | − | 14.2462i | 0.0972942 | − | 0.617072i | ||||
\(534\) | −8.00000 | −0.346194 | ||||||||
\(535\) | 17.3693i | 0.750941i | ||||||||
\(536\) | −1.12311 | −0.0485108 | ||||||||
\(537\) | −11.1231 | −0.479997 | ||||||||
\(538\) | − | 31.3693i | − | 1.35243i | ||||||
\(539\) | 5.56155i | 0.239553i | ||||||||
\(540\) | − | 3.56155i | − | 0.153265i | ||||||
\(541\) | 6.19224i | 0.266225i | 0.991101 | + | 0.133113i | \(0.0424972\pi\) | ||||
−0.991101 | + | 0.133113i | \(0.957503\pi\) | |||||||
\(542\) | 8.00000 | 0.343629 | ||||||||
\(543\) | 13.3693 | 0.573732 | ||||||||
\(544\) | 6.68466i | 0.286602i | ||||||||
\(545\) | −46.0540 | −1.97274 | ||||||||
\(546\) | −3.56155 | − | 0.561553i | −0.152420 | − | 0.0240322i | ||||
\(547\) | 28.9848 | 1.23930 | 0.619651 | − | 0.784877i | \(-0.287274\pi\) | ||||
0.619651 | + | 0.784877i | \(0.287274\pi\) | |||||||
\(548\) | 6.68466i | 0.285554i | ||||||||
\(549\) | −1.56155 | −0.0666455 | ||||||||
\(550\) | 42.7386 | 1.82238 | ||||||||
\(551\) | 2.43845i | 0.103881i | ||||||||
\(552\) | 6.68466i | 0.284518i | ||||||||
\(553\) | 16.0000i | 0.680389i | ||||||||
\(554\) | 10.8769i | 0.462115i | ||||||||
\(555\) | 38.0540 | 1.61530 | ||||||||
\(556\) | −10.2462 | −0.434536 | ||||||||
\(557\) | − | 16.2462i | − | 0.688374i | −0.938901 | − | 0.344187i | \(-0.888155\pi\) | ||
0.938901 | − | 0.344187i | \(-0.111845\pi\) | |||||||
\(558\) | 6.24621 | 0.264423 | ||||||||
\(559\) | −22.9309 | − | 3.61553i | −0.969872 | − | 0.152921i | ||||
\(560\) | 3.56155 | 0.150503 | ||||||||
\(561\) | − | 37.1771i | − | 1.56962i | ||||||
\(562\) | −6.00000 | −0.253095 | ||||||||
\(563\) | 38.0540 | 1.60378 | 0.801892 | − | 0.597469i | \(-0.203827\pi\) | ||||
0.801892 | + | 0.597469i | \(0.203827\pi\) | |||||||
\(564\) | 10.2462i | 0.431443i | ||||||||
\(565\) | − | 72.1080i | − | 3.03360i | ||||||
\(566\) | 4.87689i | 0.204991i | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 9.36932 | 0.393128 | ||||||||
\(569\) | −18.0000 | −0.754599 | −0.377300 | − | 0.926091i | \(-0.623147\pi\) | ||||
−0.377300 | + | 0.926091i | \(0.623147\pi\) | |||||||
\(570\) | 5.56155i | 0.232948i | ||||||||
\(571\) | −18.2462 | −0.763580 | −0.381790 | − | 0.924249i | \(-0.624692\pi\) | ||||
−0.381790 | + | 0.924249i | \(0.624692\pi\) | |||||||
\(572\) | −3.12311 | + | 19.8078i | −0.130584 | + | 0.828204i | ||||
\(573\) | 24.0540 | 1.00487 | ||||||||
\(574\) | − | 4.00000i | − | 0.166957i | ||||||
\(575\) | 51.3693 | 2.14225 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − | 7.75379i | − | 0.322794i | −0.986890 | − | 0.161397i | \(-0.948400\pi\) | ||
0.986890 | − | 0.161397i | \(-0.0516000\pi\) | |||||||
\(578\) | − | 27.6847i | − | 1.15153i | ||||||
\(579\) | − | 12.0000i | − | 0.498703i | ||||||
\(580\) | 5.56155i | 0.230931i | ||||||||
\(581\) | −2.00000 | −0.0829740 | ||||||||
\(582\) | 10.0000 | 0.414513 | ||||||||
\(583\) | − | 27.1231i | − | 1.12332i | ||||||
\(584\) | 11.5616 | 0.478420 | ||||||||
\(585\) | 2.00000 | − | 12.6847i | 0.0826898 | − | 0.524446i | ||||
\(586\) | 7.75379 | 0.320306 | ||||||||
\(587\) | 37.1231i | 1.53223i | 0.642701 | + | 0.766117i | \(0.277814\pi\) | ||||
−0.642701 | + | 0.766117i | \(0.722186\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −9.75379 | −0.401898 | ||||||||
\(590\) | 15.1231i | 0.622608i | ||||||||
\(591\) | − | 6.00000i | − | 0.246807i | ||||||
\(592\) | − | 10.6847i | − | 0.439137i | ||||||
\(593\) | 28.0000i | 1.14982i | 0.818216 | + | 0.574911i | \(0.194963\pi\) | ||||
−0.818216 | + | 0.574911i | \(0.805037\pi\) | |||||||
\(594\) | 5.56155 | 0.228193 | ||||||||
\(595\) | −23.8078 | −0.976023 | ||||||||
\(596\) | 10.0000i | 0.409616i | ||||||||
\(597\) | −4.93087 | −0.201807 | ||||||||
\(598\) | −3.75379 | + | 23.8078i | −0.153504 | + | 0.973572i | ||||
\(599\) | 30.3002 | 1.23803 | 0.619016 | − | 0.785378i | \(-0.287532\pi\) | ||||
0.619016 | + | 0.785378i | \(0.287532\pi\) | |||||||
\(600\) | 7.68466i | 0.313725i | ||||||||
\(601\) | −31.8617 | −1.29967 | −0.649834 | − | 0.760076i | \(-0.725161\pi\) | ||||
−0.649834 | + | 0.760076i | \(0.725161\pi\) | |||||||
\(602\) | −6.43845 | −0.262412 | ||||||||
\(603\) | 1.12311i | 0.0457364i | ||||||||
\(604\) | 16.6847i | 0.678889i | ||||||||
\(605\) | 70.9848i | 2.88594i | ||||||||
\(606\) | 6.00000i | 0.243733i | ||||||||
\(607\) | −28.5464 | −1.15866 | −0.579331 | − | 0.815092i | \(-0.696686\pi\) | ||||
−0.579331 | + | 0.815092i | \(0.696686\pi\) | |||||||
\(608\) | 1.56155 | 0.0633293 | ||||||||
\(609\) | − | 1.56155i | − | 0.0632773i | ||||||
\(610\) | 5.56155 | 0.225181 | ||||||||
\(611\) | −5.75379 | + | 36.4924i | −0.232773 | + | 1.47633i | ||||
\(612\) | 6.68466 | 0.270211 | ||||||||
\(613\) | 1.80776i | 0.0730149i | 0.999333 | + | 0.0365075i | \(0.0116233\pi\) | ||||
−0.999333 | + | 0.0365075i | \(0.988377\pi\) | |||||||
\(614\) | −26.2462 | −1.05921 | ||||||||
\(615\) | 14.2462 | 0.574463 | ||||||||
\(616\) | 5.56155i | 0.224081i | ||||||||
\(617\) | − | 6.19224i | − | 0.249290i | −0.992201 | − | 0.124645i | \(-0.960221\pi\) | ||
0.992201 | − | 0.124645i | \(-0.0397792\pi\) | |||||||
\(618\) | 1.80776i | 0.0727189i | ||||||||
\(619\) | 30.9309i | 1.24322i | 0.783328 | + | 0.621608i | \(0.213520\pi\) | ||||
−0.783328 | + | 0.621608i | \(0.786480\pi\) | |||||||
\(620\) | −22.2462 | −0.893429 | ||||||||
\(621\) | 6.68466 | 0.268246 | ||||||||
\(622\) | 0.492423i | 0.0197443i | ||||||||
\(623\) | −8.00000 | −0.320513 | ||||||||
\(624\) | −3.56155 | − | 0.561553i | −0.142576 | − | 0.0224801i | ||||
\(625\) | −4.36932 | −0.174773 | ||||||||
\(626\) | − | 32.2462i | − | 1.28882i | ||||||
\(627\) | −8.68466 | −0.346832 | ||||||||
\(628\) | 11.8078 | 0.471181 | ||||||||
\(629\) | 71.4233i | 2.84783i | ||||||||
\(630\) | − | 3.56155i | − | 0.141896i | ||||||
\(631\) | − | 12.6847i | − | 0.504968i | −0.967601 | − | 0.252484i | \(-0.918752\pi\) | ||
0.967601 | − | 0.252484i | \(-0.0812476\pi\) | |||||||
\(632\) | 16.0000i | 0.636446i | ||||||||
\(633\) | −7.80776 | −0.310331 | ||||||||
\(634\) | 3.36932 | 0.133813 | ||||||||
\(635\) | − | 36.4924i | − | 1.44816i | ||||||
\(636\) | 4.87689 | 0.193381 | ||||||||
\(637\) | −3.56155 | − | 0.561553i | −0.141114 | − | 0.0222495i | ||||
\(638\) | −8.68466 | −0.343829 | ||||||||
\(639\) | − | 9.36932i | − | 0.370644i | ||||||
\(640\) | 3.56155 | 0.140783 | ||||||||
\(641\) | 30.1080 | 1.18919 | 0.594596 | − | 0.804024i | \(-0.297312\pi\) | ||||
0.594596 | + | 0.804024i | \(0.297312\pi\) | |||||||
\(642\) | − | 4.87689i | − | 0.192476i | ||||||
\(643\) | 0.192236i | 0.00758105i | 0.999993 | + | 0.00379052i | \(0.00120656\pi\) | ||||
−0.999993 | + | 0.00379052i | \(0.998793\pi\) | |||||||
\(644\) | 6.68466i | 0.263412i | ||||||||
\(645\) | − | 22.9309i | − | 0.902902i | ||||||
\(646\) | −10.4384 | −0.410695 | ||||||||
\(647\) | 10.6307 | 0.417935 | 0.208968 | − | 0.977923i | \(-0.432990\pi\) | ||||
0.208968 | + | 0.977923i | \(0.432990\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −23.6155 | −0.926991 | ||||||||
\(650\) | −4.31534 | + | 27.3693i | −0.169262 | + | 1.07351i | ||||
\(651\) | 6.24621 | 0.244808 | ||||||||
\(652\) | 9.12311i | 0.357288i | ||||||||
\(653\) | −29.5616 | −1.15683 | −0.578416 | − | 0.815742i | \(-0.696329\pi\) | ||||
−0.578416 | + | 0.815742i | \(0.696329\pi\) | |||||||
\(654\) | 12.9309 | 0.505637 | ||||||||
\(655\) | 5.56155i | 0.217308i | ||||||||
\(656\) | − | 4.00000i | − | 0.156174i | ||||||
\(657\) | − | 11.5616i | − | 0.451059i | ||||||
\(658\) | 10.2462i | 0.399439i | ||||||||
\(659\) | 12.8769 | 0.501613 | 0.250806 | − | 0.968037i | \(-0.419304\pi\) | ||||
0.250806 | + | 0.968037i | \(0.419304\pi\) | |||||||
\(660\) | −19.8078 | −0.771016 | ||||||||
\(661\) | 44.7386i | 1.74013i | 0.492936 | + | 0.870066i | \(0.335924\pi\) | ||||
−0.492936 | + | 0.870066i | \(0.664076\pi\) | |||||||
\(662\) | 1.12311 | 0.0436507 | ||||||||
\(663\) | 23.8078 | + | 3.75379i | 0.924617 | + | 0.145785i | ||||
\(664\) | −2.00000 | −0.0776151 | ||||||||
\(665\) | 5.56155i | 0.215668i | ||||||||
\(666\) | −10.6847 | −0.414022 | ||||||||
\(667\) | −10.4384 | −0.404178 | ||||||||
\(668\) | − | 11.8078i | − | 0.456856i | ||||||
\(669\) | − | 1.75379i | − | 0.0678054i | ||||||
\(670\) | − | 4.00000i | − | 0.154533i | ||||||
\(671\) | 8.68466i | 0.335268i | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 37.8078 | 1.45738 | 0.728691 | − | 0.684843i | \(-0.240129\pi\) | ||||
0.728691 | + | 0.684843i | \(0.240129\pi\) | |||||||
\(674\) | − | 20.0540i | − | 0.772450i | ||||||
\(675\) | 7.68466 | 0.295783 | ||||||||
\(676\) | −12.3693 | − | 4.00000i | −0.475743 | − | 0.153846i | ||||
\(677\) | 31.3693 | 1.20562 | 0.602810 | − | 0.797884i | \(-0.294048\pi\) | ||||
0.602810 | + | 0.797884i | \(0.294048\pi\) | |||||||
\(678\) | 20.2462i | 0.777551i | ||||||||
\(679\) | 10.0000 | 0.383765 | ||||||||
\(680\) | −23.8078 | −0.912986 | ||||||||
\(681\) | − | 17.6155i | − | 0.675029i | ||||||
\(682\) | − | 34.7386i | − | 1.33021i | ||||||
\(683\) | − | 0.684658i | − | 0.0261977i | −0.999914 | − | 0.0130989i | \(-0.995830\pi\) | ||
0.999914 | − | 0.0130989i | \(-0.00416962\pi\) | |||||||
\(684\) | − | 1.56155i | − | 0.0597075i | ||||||
\(685\) | −23.8078 | −0.909648 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 2.00000i | 0.0763048i | ||||||||
\(688\) | −6.43845 | −0.245463 | ||||||||
\(689\) | 17.3693 | + | 2.73863i | 0.661718 | + | 0.104334i | ||||
\(690\) | −23.8078 | −0.906346 | ||||||||
\(691\) | − | 36.4924i | − | 1.38824i | −0.719861 | − | 0.694119i | \(-0.755794\pi\) | ||
0.719861 | − | 0.694119i | \(-0.244206\pi\) | |||||||
\(692\) | 3.75379 | 0.142698 | ||||||||
\(693\) | 5.56155 | 0.211266 | ||||||||
\(694\) | 24.4924i | 0.929720i | ||||||||
\(695\) | − | 36.4924i | − | 1.38424i | ||||||
\(696\) | − | 1.56155i | − | 0.0591905i | ||||||
\(697\) | 26.7386i | 1.01280i | ||||||||
\(698\) | −3.36932 | −0.127531 | ||||||||
\(699\) | −2.00000 | −0.0756469 | ||||||||
\(700\) | 7.68466i | 0.290453i | ||||||||
\(701\) | −3.61553 | −0.136557 | −0.0682783 | − | 0.997666i | \(-0.521751\pi\) | ||||
−0.0682783 | + | 0.997666i | \(0.521751\pi\) | |||||||
\(702\) | −0.561553 | + | 3.56155i | −0.0211944 | + | 0.134422i | ||||
\(703\) | 16.6847 | 0.629274 | ||||||||
\(704\) | 5.56155i | 0.209609i | ||||||||
\(705\) | −36.4924 | −1.37438 | ||||||||
\(706\) | 18.2462 | 0.686705 | ||||||||
\(707\) | 6.00000i | 0.225653i | ||||||||
\(708\) | − | 4.24621i | − | 0.159582i | ||||||
\(709\) | − | 31.7538i | − | 1.19254i | −0.802784 | − | 0.596269i | \(-0.796649\pi\) | ||
0.802784 | − | 0.596269i | \(-0.203351\pi\) | |||||||
\(710\) | 33.3693i | 1.25233i | ||||||||
\(711\) | 16.0000 | 0.600047 | ||||||||
\(712\) | −8.00000 | −0.299813 | ||||||||
\(713\) | − | 41.7538i | − | 1.56369i | ||||||
\(714\) | 6.68466 | 0.250167 | ||||||||
\(715\) | −70.5464 | − | 11.1231i | −2.63829 | − | 0.415981i | ||||
\(716\) | −11.1231 | −0.415690 | ||||||||
\(717\) | 14.2462i | 0.532035i | ||||||||
\(718\) | −23.6155 | −0.881324 | ||||||||
\(719\) | 13.7538 | 0.512930 | 0.256465 | − | 0.966554i | \(-0.417442\pi\) | ||||
0.256465 | + | 0.966554i | \(0.417442\pi\) | |||||||
\(720\) | − | 3.56155i | − | 0.132731i | ||||||
\(721\) | 1.80776i | 0.0673247i | ||||||||
\(722\) | − | 16.5616i | − | 0.616357i | ||||||
\(723\) | 6.00000i | 0.223142i | ||||||||
\(724\) | 13.3693 | 0.496867 | ||||||||
\(725\) | −12.0000 | −0.445669 | ||||||||
\(726\) | − | 19.9309i | − | 0.739704i | ||||||
\(727\) | −48.9309 | −1.81475 | −0.907373 | − | 0.420327i | \(-0.861915\pi\) | ||||
−0.907373 | + | 0.420327i | \(0.861915\pi\) | |||||||
\(728\) | −3.56155 | − | 0.561553i | −0.132000 | − | 0.0208125i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 41.1771i | 1.52403i | ||||||||
\(731\) | 43.0388 | 1.59185 | ||||||||
\(732\) | −1.56155 | −0.0577167 | ||||||||
\(733\) | 22.8769i | 0.844977i | 0.906368 | + | 0.422489i | \(0.138843\pi\) | ||||
−0.906368 | + | 0.422489i | \(0.861157\pi\) | |||||||
\(734\) | − | 0.630683i | − | 0.0232789i | ||||||
\(735\) | − | 3.56155i | − | 0.131370i | ||||||
\(736\) | 6.68466i | 0.246400i | ||||||||
\(737\) | 6.24621 | 0.230082 | ||||||||
\(738\) | −4.00000 | −0.147242 | ||||||||
\(739\) | 17.6155i | 0.647998i | 0.946057 | + | 0.323999i | \(0.105027\pi\) | ||||
−0.946057 | + | 0.323999i | \(0.894973\pi\) | |||||||
\(740\) | 38.0540 | 1.39889 | ||||||||
\(741\) | 0.876894 | − | 5.56155i | 0.0322135 | − | 0.204309i | ||||
\(742\) | 4.87689 | 0.179036 | ||||||||
\(743\) | 16.0000i | 0.586983i | 0.955962 | + | 0.293492i | \(0.0948173\pi\) | ||||
−0.955962 | + | 0.293492i | \(0.905183\pi\) | |||||||
\(744\) | 6.24621 | 0.228997 | ||||||||
\(745\) | −35.6155 | −1.30485 | ||||||||
\(746\) | 6.00000i | 0.219676i | ||||||||
\(747\) | 2.00000i | 0.0731762i | ||||||||
\(748\) | − | 37.1771i | − | 1.35933i | ||||||
\(749\) | − | 4.87689i | − | 0.178198i | ||||||
\(750\) | −9.56155 | −0.349139 | ||||||||
\(751\) | 2.24621 | 0.0819654 | 0.0409827 | − | 0.999160i | \(-0.486951\pi\) | ||||
0.0409827 | + | 0.999160i | \(0.486951\pi\) | |||||||
\(752\) | 10.2462i | 0.373641i | ||||||||
\(753\) | −22.0540 | −0.803692 | ||||||||
\(754\) | 0.876894 | − | 5.56155i | 0.0319346 | − | 0.202540i | ||||
\(755\) | −59.4233 | −2.16264 | ||||||||
\(756\) | 1.00000i | 0.0363696i | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 18.8769 | 0.685640 | ||||||||
\(759\) | − | 37.1771i | − | 1.34944i | ||||||
\(760\) | 5.56155i | 0.201739i | ||||||||
\(761\) | 39.1231i | 1.41821i | 0.705102 | + | 0.709106i | \(0.250901\pi\) | ||||
−0.705102 | + | 0.709106i | \(0.749099\pi\) | |||||||
\(762\) | 10.2462i | 0.371181i | ||||||||
\(763\) | 12.9309 | 0.468129 | ||||||||
\(764\) | 24.0540 | 0.870242 | ||||||||
\(765\) | 23.8078i | 0.860772i | ||||||||
\(766\) | −17.5616 | −0.634525 | ||||||||
\(767\) | 2.38447 | − | 15.1231i | 0.0860983 | − | 0.546064i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 8.43845i | 0.304298i | 0.988358 | + | 0.152149i | \(0.0486194\pi\) | ||||
−0.988358 | + | 0.152149i | \(0.951381\pi\) | |||||||
\(770\) | −19.8078 | −0.713822 | ||||||||
\(771\) | 26.0000 | 0.936367 | ||||||||
\(772\) | − | 12.0000i | − | 0.431889i | ||||||
\(773\) | − | 12.9309i | − | 0.465091i | −0.972586 | − | 0.232546i | \(-0.925295\pi\) | ||
0.972586 | − | 0.232546i | \(-0.0747055\pi\) | |||||||
\(774\) | 6.43845i | 0.231425i | ||||||||
\(775\) | − | 48.0000i | − | 1.72421i | ||||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | −10.6847 | −0.383310 | ||||||||
\(778\) | − | 27.1231i | − | 0.972410i | ||||||
\(779\) | 6.24621 | 0.223794 | ||||||||
\(780\) | 2.00000 | − | 12.6847i | 0.0716115 | − | 0.454184i | ||||
\(781\) | −52.1080 | −1.86457 | ||||||||
\(782\) | − | 44.6847i | − | 1.59792i | ||||||
\(783\) | −1.56155 | −0.0558053 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 42.0540i | 1.50097i | ||||||||
\(786\) | − | 1.56155i | − | 0.0556987i | ||||||
\(787\) | − | 17.0691i | − | 0.608449i | −0.952600 | − | 0.304224i | \(-0.901603\pi\) | ||
0.952600 | − | 0.304224i | \(-0.0983973\pi\) | |||||||
\(788\) | − | 6.00000i | − | 0.213741i | ||||||
\(789\) | 23.3693 | 0.831970 | ||||||||
\(790\) | −56.9848 | −2.02743 | ||||||||
\(791\) | 20.2462i | 0.719872i | ||||||||
\(792\) | 5.56155 | 0.197621 | ||||||||
\(793\) | −5.56155 | − | 0.876894i | −0.197497 | − | 0.0311394i | ||||
\(794\) | −15.3693 | −0.545437 | ||||||||
\(795\) | 17.3693i | 0.616026i | ||||||||
\(796\) | −4.93087 | −0.174770 | ||||||||
\(797\) | 3.75379 | 0.132966 | 0.0664830 | − | 0.997788i | \(-0.478822\pi\) | ||||
0.0664830 | + | 0.997788i | \(0.478822\pi\) | |||||||
\(798\) | − | 1.56155i | − | 0.0552784i | ||||||
\(799\) | − | 68.4924i | − | 2.42309i | ||||||
\(800\) | 7.68466i | 0.271694i | ||||||||
\(801\) | 8.00000i | 0.282666i | ||||||||
\(802\) | 30.9848 | 1.09411 | ||||||||
\(803\) | −64.3002 | −2.26910 | ||||||||
\(804\) | 1.12311i | 0.0396089i | ||||||||
\(805\) | −23.8078 | −0.839113 | ||||||||
\(806\) | 22.2462 | + | 3.50758i | 0.783589 | + | 0.123549i | ||||
\(807\) | −31.3693 | −1.10425 | ||||||||
\(808\) | 6.00000i | 0.211079i | ||||||||
\(809\) | −55.3693 | −1.94668 | −0.973341 | − | 0.229364i | \(-0.926335\pi\) | ||||
−0.973341 | + | 0.229364i | \(0.926335\pi\) | |||||||
\(810\) | −3.56155 | −0.125140 | ||||||||
\(811\) | 2.05398i | 0.0721248i | 0.999350 | + | 0.0360624i | \(0.0114815\pi\) | ||||
−0.999350 | + | 0.0360624i | \(0.988518\pi\) | |||||||
\(812\) | − | 1.56155i | − | 0.0547998i | ||||||
\(813\) | − | 8.00000i | − | 0.280572i | ||||||
\(814\) | 59.4233i | 2.08279i | ||||||||
\(815\) | −32.4924 | −1.13816 | ||||||||
\(816\) | 6.68466 | 0.234010 | ||||||||
\(817\) | − | 10.0540i | − | 0.351744i | ||||||
\(818\) | −13.8078 | −0.482777 | ||||||||
\(819\) | −0.561553 | + | 3.56155i | −0.0196222 | + | 0.124451i | ||||
\(820\) | 14.2462 | 0.497499 | ||||||||
\(821\) | 30.8769i | 1.07761i | 0.842430 | + | 0.538806i | \(0.181124\pi\) | ||||
−0.842430 | + | 0.538806i | \(0.818876\pi\) | |||||||
\(822\) | 6.68466 | 0.233154 | ||||||||
\(823\) | −30.7386 | −1.07148 | −0.535741 | − | 0.844383i | \(-0.679968\pi\) | ||||
−0.535741 | + | 0.844383i | \(0.679968\pi\) | |||||||
\(824\) | 1.80776i | 0.0629764i | ||||||||
\(825\) | − | 42.7386i | − | 1.48797i | ||||||
\(826\) | − | 4.24621i | − | 0.147745i | ||||||
\(827\) | − | 22.0540i | − | 0.766892i | −0.923563 | − | 0.383446i | \(-0.874737\pi\) | ||
0.923563 | − | 0.383446i | \(-0.125263\pi\) | |||||||
\(828\) | 6.68466 | 0.232308 | ||||||||
\(829\) | 42.0540 | 1.46059 | 0.730297 | − | 0.683129i | \(-0.239381\pi\) | ||||
0.730297 | + | 0.683129i | \(0.239381\pi\) | |||||||
\(830\) | − | 7.12311i | − | 0.247247i | ||||||
\(831\) | 10.8769 | 0.377315 | ||||||||
\(832\) | −3.56155 | − | 0.561553i | −0.123475 | − | 0.0194683i | ||||
\(833\) | 6.68466 | 0.231610 | ||||||||
\(834\) | 10.2462i | 0.354797i | ||||||||
\(835\) | 42.0540 | 1.45534 | ||||||||
\(836\) | −8.68466 | −0.300365 | ||||||||
\(837\) | − | 6.24621i | − | 0.215901i | ||||||
\(838\) | 20.6847i | 0.714540i | ||||||||
\(839\) | − | 25.7538i | − | 0.889120i | −0.895749 | − | 0.444560i | \(-0.853360\pi\) | ||
0.895749 | − | 0.444560i | \(-0.146640\pi\) | |||||||
\(840\) | − | 3.56155i | − | 0.122885i | ||||||
\(841\) | −26.5616 | −0.915916 | ||||||||
\(842\) | 10.0000 | 0.344623 | ||||||||
\(843\) | 6.00000i | 0.206651i | ||||||||
\(844\) | −7.80776 | −0.268754 | ||||||||
\(845\) | 14.2462 | − | 44.0540i | 0.490085 | − | 1.51550i | ||||
\(846\) | 10.2462 | 0.352272 | ||||||||
\(847\) | − | 19.9309i | − | 0.684833i | ||||||
\(848\) | 4.87689 | 0.167473 | ||||||||
\(849\) | 4.87689 | 0.167375 | ||||||||
\(850\) | − | 51.3693i | − | 1.76195i | ||||||
\(851\) | 71.4233i | 2.44836i | ||||||||
\(852\) | − | 9.36932i | − | 0.320988i | ||||||
\(853\) | − | 10.8769i | − | 0.372418i | −0.982510 | − | 0.186209i | \(-0.940380\pi\) | ||
0.982510 | − | 0.186209i | \(-0.0596201\pi\) | |||||||
\(854\) | −1.56155 | −0.0534352 | ||||||||
\(855\) | 5.56155 | 0.190201 | ||||||||
\(856\) | − | 4.87689i | − | 0.166689i | ||||||
\(857\) | −38.0000 | −1.29806 | −0.649028 | − | 0.760765i | \(-0.724824\pi\) | ||||
−0.649028 | + | 0.760765i | \(0.724824\pi\) | |||||||
\(858\) | 19.8078 | + | 3.12311i | 0.676226 | + | 0.106621i | ||||
\(859\) | 0.384472 | 0.0131180 | 0.00655901 | − | 0.999978i | \(-0.497912\pi\) | ||||
0.00655901 | + | 0.999978i | \(0.497912\pi\) | |||||||
\(860\) | − | 22.9309i | − | 0.781936i | ||||||
\(861\) | −4.00000 | −0.136320 | ||||||||
\(862\) | −29.8617 | −1.01709 | ||||||||
\(863\) | 42.7386i | 1.45484i | 0.686192 | + | 0.727420i | \(0.259281\pi\) | ||||
−0.686192 | + | 0.727420i | \(0.740719\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 13.3693i | 0.454570i | ||||||||
\(866\) | − | 23.3693i | − | 0.794122i | ||||||
\(867\) | −27.6847 | −0.940220 | ||||||||
\(868\) | 6.24621 | 0.212010 | ||||||||
\(869\) | − | 88.9848i | − | 3.01860i | ||||||
\(870\) | 5.56155 | 0.188554 | ||||||||
\(871\) | −0.630683 | + | 4.00000i | −0.0213699 | + | 0.135535i | ||||
\(872\) | 12.9309 | 0.437895 | ||||||||
\(873\) | − | 10.0000i | − | 0.338449i | ||||||
\(874\) | −10.4384 | −0.353086 | ||||||||
\(875\) | −9.56155 | −0.323239 | ||||||||
\(876\) | − | 11.5616i | − | 0.390629i | ||||||
\(877\) | 22.9848i | 0.776143i | 0.921629 | + | 0.388072i | \(0.126859\pi\) | ||||
−0.921629 | + | 0.388072i | \(0.873141\pi\) | |||||||
\(878\) | 8.93087i | 0.301402i | ||||||||
\(879\) | − | 7.75379i | − | 0.261529i | ||||||
\(880\) | −19.8078 | −0.667720 | ||||||||
\(881\) | 14.3002 | 0.481786 | 0.240893 | − | 0.970552i | \(-0.422560\pi\) | ||||
0.240893 | + | 0.970552i | \(0.422560\pi\) | |||||||
\(882\) | 1.00000i | 0.0336718i | ||||||||
\(883\) | −14.4384 | −0.485892 | −0.242946 | − | 0.970040i | \(-0.578114\pi\) | ||||
−0.242946 | + | 0.970040i | \(0.578114\pi\) | |||||||
\(884\) | 23.8078 | + | 3.75379i | 0.800742 | + | 0.126254i | ||||
\(885\) | 15.1231 | 0.508358 | ||||||||
\(886\) | − | 6.63068i | − | 0.222762i | ||||||
\(887\) | −37.8617 | −1.27127 | −0.635636 | − | 0.771989i | \(-0.719262\pi\) | ||||
−0.635636 | + | 0.771989i | \(0.719262\pi\) | |||||||
\(888\) | −10.6847 | −0.358554 | ||||||||
\(889\) | 10.2462i | 0.343647i | ||||||||
\(890\) | − | 28.4924i | − | 0.955068i | ||||||
\(891\) | − | 5.56155i | − | 0.186319i | ||||||
\(892\) | − | 1.75379i | − | 0.0587212i | ||||||
\(893\) | −16.0000 | −0.535420 | ||||||||
\(894\) | 10.0000 | 0.334450 | ||||||||
\(895\) | − | 39.6155i | − | 1.32420i | ||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 23.8078 | + | 3.75379i | 0.794918 | + | 0.125335i | ||||
\(898\) | 9.31534 | 0.310857 | ||||||||
\(899\) | 9.75379i | 0.325307i | ||||||||
\(900\) | 7.68466 | 0.256155 | ||||||||
\(901\) | −32.6004 | −1.08608 | ||||||||
\(902\) | 22.2462i | 0.740718i | ||||||||
\(903\) | 6.43845i | 0.214258i | ||||||||
\(904\) | 20.2462i | 0.673379i | ||||||||
\(905\) | 47.6155i | 1.58279i | ||||||||
\(906\) | 16.6847 | 0.554311 | ||||||||
\(907\) | −24.4924 | −0.813258 | −0.406629 | − | 0.913593i | \(-0.633296\pi\) | ||||
−0.406629 | + | 0.913593i | \(0.633296\pi\) | |||||||
\(908\) | − | 17.6155i | − | 0.584592i | ||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 2.00000 | − | 12.6847i | 0.0662994 | − | 0.420492i | ||||
\(911\) | −4.43845 | −0.147052 | −0.0735262 | − | 0.997293i | \(-0.523425\pi\) | ||||
−0.0735262 | + | 0.997293i | \(0.523425\pi\) | |||||||
\(912\) | − | 1.56155i | − | 0.0517082i | ||||||
\(913\) | 11.1231 | 0.368121 | ||||||||
\(914\) | 16.0000 | 0.529233 | ||||||||
\(915\) | − | 5.56155i | − | 0.183859i | ||||||
\(916\) | 2.00000i | 0.0660819i | ||||||||
\(917\) | − | 1.56155i | − | 0.0515670i | ||||||
\(918\) | − | 6.68466i | − | 0.220627i | ||||||
\(919\) | −17.8617 | −0.589204 | −0.294602 | − | 0.955620i | \(-0.595187\pi\) | ||||
−0.294602 | + | 0.955620i | \(0.595187\pi\) | |||||||
\(920\) | −23.8078 | −0.784919 | ||||||||
\(921\) | 26.2462i | 0.864842i | ||||||||
\(922\) | −36.9309 | −1.21625 | ||||||||
\(923\) | 5.26137 | − | 33.3693i | 0.173180 | − | 1.09836i | ||||
\(924\) | 5.56155 | 0.182962 | ||||||||
\(925\) | 82.1080i | 2.69969i | ||||||||
\(926\) | 30.5464 | 1.00382 | ||||||||
\(927\) | 1.80776 | 0.0593748 | ||||||||
\(928\) | − | 1.56155i | − | 0.0512605i | ||||||
\(929\) | 40.8769i | 1.34113i | 0.741852 | + | 0.670564i | \(0.233948\pi\) | ||||
−0.741852 | + | 0.670564i | \(0.766052\pi\) | |||||||
\(930\) | 22.2462i | 0.729482i | ||||||||
\(931\) | − | 1.56155i | − | 0.0511778i | ||||||
\(932\) | −2.00000 | −0.0655122 | ||||||||
\(933\) | 0.492423 | 0.0161212 | ||||||||
\(934\) | − | 1.56155i | − | 0.0510956i | ||||||
\(935\) | 132.408 | 4.33021 | ||||||||
\(936\) | −0.561553 | + | 3.56155i | −0.0183549 | + | 0.116413i | ||||
\(937\) | −19.8617 | −0.648855 | −0.324427 | − | 0.945911i | \(-0.605172\pi\) | ||||
−0.324427 | + | 0.945911i | \(0.605172\pi\) | |||||||
\(938\) | 1.12311i | 0.0366707i | ||||||||
\(939\) | −32.2462 | −1.05232 | ||||||||
\(940\) | −36.4924 | −1.19025 | ||||||||
\(941\) | 26.4924i | 0.863628i | 0.901963 | + | 0.431814i | \(0.142126\pi\) | ||||
−0.901963 | + | 0.431814i | \(0.857874\pi\) | |||||||
\(942\) | − | 11.8078i | − | 0.384718i | ||||||
\(943\) | 26.7386i | 0.870730i | ||||||||
\(944\) | − | 4.24621i | − | 0.138202i | ||||||
\(945\) | −3.56155 | −0.115857 | ||||||||
\(946\) | 35.8078 | 1.16421 | ||||||||
\(947\) | − | 27.8078i | − | 0.903631i | −0.892111 | − | 0.451815i | \(-0.850777\pi\) | ||
0.892111 | − | 0.451815i | \(-0.149223\pi\) | |||||||
\(948\) | 16.0000 | 0.519656 | ||||||||
\(949\) | 6.49242 | − | 41.1771i | 0.210753 | − | 1.33666i | ||||
\(950\) | −12.0000 | −0.389331 | ||||||||
\(951\) | − | 3.36932i | − | 0.109258i | ||||||
\(952\) | 6.68466 | 0.216651 | ||||||||
\(953\) | 0.738634 | 0.0239267 | 0.0119633 | − | 0.999928i | \(-0.496192\pi\) | ||||
0.0119633 | + | 0.999928i | \(0.496192\pi\) | |||||||
\(954\) | − | 4.87689i | − | 0.157895i | ||||||
\(955\) | 85.6695i | 2.77220i | ||||||||
\(956\) | 14.2462i | 0.460755i | ||||||||
\(957\) | 8.68466i | 0.280735i | ||||||||
\(958\) | −12.3002 | −0.397401 | ||||||||
\(959\) | 6.68466 | 0.215859 | ||||||||
\(960\) | − | 3.56155i | − | 0.114949i | ||||||
\(961\) | −8.01515 | −0.258553 | ||||||||
\(962\) | −38.0540 | − | 6.00000i | −1.22691 | − | 0.193448i | ||||
\(963\) | −4.87689 | −0.157156 | ||||||||
\(964\) | 6.00000i | 0.193247i | ||||||||
\(965\) | 42.7386 | 1.37581 | ||||||||
\(966\) | 6.68466 | 0.215075 | ||||||||
\(967\) | − | 2.93087i | − | 0.0942504i | −0.998889 | − | 0.0471252i | \(-0.984994\pi\) | ||
0.998889 | − | 0.0471252i | \(-0.0150060\pi\) | |||||||
\(968\) | − | 19.9309i | − | 0.640602i | ||||||
\(969\) | 10.4384i | 0.335331i | ||||||||
\(970\) | 35.6155i | 1.14355i | ||||||||
\(971\) | 4.00000 | 0.128366 | 0.0641831 | − | 0.997938i | \(-0.479556\pi\) | ||||
0.0641831 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 10.2462i | 0.328478i | ||||||||
\(974\) | 13.7538 | 0.440700 | ||||||||
\(975\) | 27.3693 | + | 4.31534i | 0.876520 | + | 0.138202i | ||||
\(976\) | −1.56155 | −0.0499841 | ||||||||
\(977\) | 46.7926i | 1.49703i | 0.663119 | + | 0.748514i | \(0.269232\pi\) | ||||
−0.663119 | + | 0.748514i | \(0.730768\pi\) | |||||||
\(978\) | 9.12311 | 0.291725 | ||||||||
\(979\) | 44.4924 | 1.42198 | ||||||||
\(980\) | − | 3.56155i | − | 0.113770i | ||||||
\(981\) | − | 12.9309i | − | 0.412851i | ||||||
\(982\) | 10.2462i | 0.326970i | ||||||||
\(983\) | 2.43845i | 0.0777744i | 0.999244 | + | 0.0388872i | \(0.0123813\pi\) | ||||
−0.999244 | + | 0.0388872i | \(0.987619\pi\) | |||||||
\(984\) | −4.00000 | −0.127515 | ||||||||
\(985\) | 21.3693 | 0.680883 | ||||||||
\(986\) | 10.4384i | 0.332428i | ||||||||
\(987\) | 10.2462 | 0.326140 | ||||||||
\(988\) | 0.876894 | − | 5.56155i | 0.0278977 | − | 0.176937i | ||||
\(989\) | 43.0388 | 1.36855 | ||||||||
\(990\) | 19.8078i | 0.629532i | ||||||||
\(991\) | −30.2462 | −0.960803 | −0.480401 | − | 0.877049i | \(-0.659509\pi\) | ||||
−0.480401 | + | 0.877049i | \(0.659509\pi\) | |||||||
\(992\) | 6.24621 | 0.198317 | ||||||||
\(993\) | − | 1.12311i | − | 0.0356407i | ||||||
\(994\) | − | 9.36932i | − | 0.297177i | ||||||
\(995\) | − | 17.5616i | − | 0.556739i | ||||||
\(996\) | 2.00000i | 0.0633724i | ||||||||
\(997\) | −34.6307 | −1.09676 | −0.548382 | − | 0.836228i | \(-0.684756\pi\) | ||||
−0.548382 | + | 0.836228i | \(0.684756\pi\) | |||||||
\(998\) | 1.50758 | 0.0477215 | ||||||||
\(999\) | 10.6847i | 0.338048i |
(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 | 546.2.c.e.337.1 | ✓ | 4 | |
3.2 | odd | 2 | 1638.2.c.h.883.4 | 4 | |||
4.3 | odd | 2 | 4368.2.h.n.337.1 | 4 | |||
7.6 | odd | 2 | 3822.2.c.h.883.2 | 4 | |||
13.5 | odd | 4 | 7098.2.a.bg.1.1 | 2 | |||
13.8 | odd | 4 | 7098.2.a.bv.1.2 | 2 | |||
13.12 | even | 2 | inner | 546.2.c.e.337.4 | yes | 4 | |
39.38 | odd | 2 | 1638.2.c.h.883.1 | 4 | |||
52.51 | odd | 2 | 4368.2.h.n.337.4 | 4 | |||
91.90 | odd | 2 | 3822.2.c.h.883.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.c.e.337.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
546.2.c.e.337.4 | yes | 4 | 13.12 | even | 2 | inner | |
1638.2.c.h.883.1 | 4 | 39.38 | odd | 2 | |||
1638.2.c.h.883.4 | 4 | 3.2 | odd | 2 | |||
3822.2.c.h.883.2 | 4 | 7.6 | odd | 2 | |||
3822.2.c.h.883.3 | 4 | 91.90 | odd | 2 | |||
4368.2.h.n.337.1 | 4 | 4.3 | odd | 2 | |||
4368.2.h.n.337.4 | 4 | 52.51 | odd | 2 | |||
7098.2.a.bg.1.1 | 2 | 13.5 | odd | 4 | |||
7098.2.a.bv.1.2 | 2 | 13.8 | odd | 4 |