Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [416,2,Mod(289,416)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(416, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("416.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 416 = 2^{5} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 416.i (of order \(3\), degree \(2\), 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: | \(3.32177672409\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 11x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 321.1 | ||
Root | \(-1.65831 + 2.87228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 416.321 |
Dual form | 416.2.i.d.289.1 |
$q$-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 \(\left(\mathbb{Z}/416\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(287\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.65831 | + | 2.87228i | −0.957427 | + | 1.65831i | −0.228714 | + | 0.973494i | \(0.573452\pi\) |
−0.728714 | + | 0.684819i | \(0.759881\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.65831 | − | 2.87228i | −0.626783 | − | 1.08562i | −0.988193 | − | 0.153213i | \(-0.951038\pi\) |
0.361410 | − | 0.932407i | \(-0.382295\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.00000 | − | 6.92820i | −1.33333 | − | 2.30940i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.65831 | + | 2.87228i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | − | 3.46410i | −0.277350 | − | 0.960769i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.65831 | − | 2.87228i | −0.380443 | − | 0.658947i | 0.610683 | − | 0.791875i | \(-0.290895\pi\) |
−0.991126 | + | 0.132929i | \(0.957562\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.0000 | 2.40040 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.65831 | − | 2.87228i | 0.345782 | − | 0.598912i | −0.639713 | − | 0.768613i | \(-0.720947\pi\) |
0.985496 | + | 0.169701i | \(0.0542803\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.5831 | 3.19142 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.50000 | − | 4.33013i | 0.464238 | − | 0.804084i | −0.534928 | − | 0.844897i | \(-0.679661\pi\) |
0.999167 | + | 0.0408130i | \(0.0129948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.50000 | − | 9.52628i | −0.957427 | − | 1.65831i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.50000 | + | 7.79423i | −0.739795 | + | 1.28136i | 0.212792 | + | 0.977098i | \(0.431744\pi\) |
−0.952587 | + | 0.304266i | \(0.901589\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.6082 | + | 2.87228i | 1.85880 | + | 0.459933i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | − | 2.59808i | 0.234261 | − | 0.405751i | −0.724797 | − | 0.688963i | \(-0.758066\pi\) |
0.959058 | + | 0.283211i | \(0.0913998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.97494 | − | 8.61684i | −0.758671 | − | 1.31406i | −0.943529 | − | 0.331291i | \(-0.892516\pi\) |
0.184858 | − | 0.982765i | \(-0.440818\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.63325 | −0.967559 | −0.483779 | − | 0.875190i | \(-0.660736\pi\) | ||||
−0.483779 | + | 0.875190i | \(0.660736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.00000 | + | 3.46410i | −0.285714 | + | 0.494872i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.94987 | −1.39326 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.00000 | −1.09888 | −0.549442 | − | 0.835532i | \(-0.685160\pi\) | ||||
−0.549442 | + | 0.835532i | \(0.685160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.0000 | 1.45699 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.65831 | − | 2.87228i | −0.215894 | − | 0.373939i | 0.737655 | − | 0.675178i | \(-0.235933\pi\) |
−0.953549 | + | 0.301239i | \(0.902600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.50000 | + | 7.79423i | 0.576166 | + | 0.997949i | 0.995914 | + | 0.0903080i | \(0.0287851\pi\) |
−0.419748 | + | 0.907641i | \(0.637882\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.2665 | + | 22.9783i | −1.67142 | + | 2.89499i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.97494 | + | 8.61684i | −0.607785 | + | 1.05272i | 0.383819 | + | 0.923408i | \(0.374609\pi\) |
−0.991605 | + | 0.129307i | \(0.958725\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.50000 | + | 9.52628i | 0.662122 | + | 1.14683i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.97494 | − | 8.61684i | −0.590416 | − | 1.02263i | −0.994176 | − | 0.107766i | \(-0.965630\pi\) |
0.403760 | − | 0.914865i | \(-0.367703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.29156 | − | 14.3614i | 0.957427 | − | 1.65831i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.0000 | 1.25357 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.63325 | 0.746299 | 0.373149 | − | 0.927771i | \(-0.378278\pi\) | ||||
0.373149 | + | 0.927771i | \(0.378278\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −15.5000 | + | 26.8468i | −1.72222 | + | 2.98298i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.2665 | −1.45619 | −0.728094 | − | 0.685478i | \(-0.759593\pi\) | ||||
−0.728094 | + | 0.685478i | \(0.759593\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.29156 | + | 14.3614i | 0.888949 | + | 1.53970i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.500000 | − | 0.866025i | 0.0529999 | − | 0.0917985i | −0.838308 | − | 0.545197i | \(-0.816455\pi\) |
0.891308 | + | 0.453398i | \(0.149788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.29156 | + | 8.61684i | −0.869192 | + | 0.903291i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.50000 | − | 6.06218i | −0.355371 | − | 0.615521i | 0.631810 | − | 0.775123i | \(-0.282312\pi\) |
−0.987181 | + | 0.159602i | \(0.948979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 26.5330 | 2.66667 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.50000 | − | 12.9904i | 0.746278 | − | 1.29259i | −0.203317 | − | 0.979113i | \(-0.565172\pi\) |
0.949595 | − | 0.313478i | \(-0.101494\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.65831 | + | 2.87228i | −0.160315 | + | 0.277674i | −0.934982 | − | 0.354696i | \(-0.884584\pi\) |
0.774667 | + | 0.632370i | \(0.217918\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.0000 | −1.53252 | −0.766261 | − | 0.642529i | \(-0.777885\pi\) | ||||
−0.766261 | + | 0.642529i | \(0.777885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.9248 | − | 25.8505i | −1.41660 | − | 2.45362i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.50000 | + | 9.52628i | 0.517396 | + | 0.896157i | 0.999796 | + | 0.0202056i | \(0.00643208\pi\) |
−0.482399 | + | 0.875951i | \(0.660235\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −20.0000 | + | 20.7846i | −1.84900 | + | 1.92154i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.97494 | − | 8.61684i | 0.456052 | − | 0.789905i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.97494 | + | 8.61684i | 0.448575 | + | 0.776955i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.97494 | − | 8.61684i | 0.441454 | − | 0.764621i | −0.556343 | − | 0.830952i | \(-0.687796\pi\) |
0.997798 | + | 0.0663312i | \(0.0211294\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 33.0000 | 2.90549 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.2665 | 1.15910 | 0.579550 | − | 0.814937i | \(-0.303228\pi\) | ||||
0.579550 | + | 0.814937i | \(0.303228\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.50000 | + | 9.52628i | −0.476910 | + | 0.826033i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.50000 | + | 7.79423i | 0.384461 | + | 0.665906i | 0.991694 | − | 0.128618i | \(-0.0410540\pi\) |
−0.607233 | + | 0.794524i | \(0.707721\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.65831 | − | 2.87228i | −0.140656 | − | 0.243624i | 0.787088 | − | 0.616841i | \(-0.211588\pi\) |
−0.927744 | + | 0.373217i | \(0.878255\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.0000 | − | 19.0526i | 0.926367 | − | 1.60451i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.6082 | + | 2.87228i | 0.970725 | + | 0.240192i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.63325 | − | 11.4891i | −0.547101 | − | 0.947607i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.500000 | + | 0.866025i | 0.0409616 | + | 0.0709476i | 0.885779 | − | 0.464107i | \(-0.153625\pi\) |
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.0000 | − | 20.7846i | 0.970143 | − | 1.68034i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.00000 | −0.638470 | −0.319235 | − | 0.947676i | \(-0.603426\pi\) | ||||
−0.319235 | + | 0.947676i | \(0.603426\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.2665 | − | 22.9783i | 1.05210 | − | 1.82229i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.0000 | −0.866921 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.29156 | + | 14.3614i | 0.649445 | + | 1.12487i | 0.983256 | + | 0.182232i | \(0.0583322\pi\) |
−0.333810 | + | 0.942640i | \(0.608335\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.65831 | − | 2.87228i | 0.128324 | − | 0.222264i | −0.794703 | − | 0.606998i | \(-0.792374\pi\) |
0.923027 | + | 0.384734i | \(0.125707\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.2665 | + | 22.9783i | −1.01451 | + | 1.75719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.50000 | − | 6.06218i | −0.266100 | − | 0.460899i | 0.701751 | − | 0.712422i | \(-0.252402\pi\) |
−0.967851 | + | 0.251523i | \(0.919068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.29156 | + | 14.3614i | 0.626783 | + | 1.08562i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.0000 | 0.826811 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.65831 | + | 2.87228i | −0.123948 | + | 0.214684i | −0.921321 | − | 0.388802i | \(-0.872889\pi\) |
0.797373 | + | 0.603487i | \(0.206222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.00000 | −0.594635 | −0.297318 | − | 0.954779i | \(-0.596092\pi\) | ||||
−0.297318 | + | 0.954779i | \(0.596092\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.8496 | −2.20655 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.94987 | −0.727607 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −27.5000 | − | 47.6314i | −2.00033 | − | 3.46467i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.6082 | + | 20.1060i | 0.839939 | + | 1.45482i | 0.889945 | + | 0.456068i | \(0.150743\pi\) |
−0.0500060 | + | 0.998749i | \(0.515924\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.50000 | + | 11.2583i | −0.467880 | + | 0.810392i | −0.999326 | − | 0.0366998i | \(-0.988315\pi\) |
0.531446 | + | 0.847092i | \(0.321649\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.50000 | − | 11.2583i | 0.463106 | − | 0.802123i | −0.536008 | − | 0.844213i | \(-0.680068\pi\) |
0.999114 | + | 0.0420901i | \(0.0134016\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.97494 | − | 8.61684i | −0.352664 | − | 0.610832i | 0.634051 | − | 0.773291i | \(-0.281391\pi\) |
−0.986715 | + | 0.162459i | \(0.948057\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.5000 | − | 28.5788i | −1.16382 | − | 2.01580i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.5831 | −1.16391 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −26.5330 | −1.84417 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.0000 | 0.760886 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.65831 | + | 2.87228i | −0.114163 | + | 0.197736i | −0.917445 | − | 0.397863i | \(-0.869752\pi\) |
0.803282 | + | 0.595599i | \(0.203085\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 33.0000 | 2.26112 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.63325 | − | 11.4891i | 0.448233 | − | 0.776363i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.50000 | − | 7.79423i | 0.504505 | − | 0.524297i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.65831 | − | 2.87228i | 0.111049 | − | 0.192342i | −0.805145 | − | 0.593079i | \(-0.797912\pi\) |
0.916193 | + | 0.400736i | \(0.131246\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.0000 | + | 34.6410i | 1.33333 | + | 2.30940i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.65831 | − | 2.87228i | −0.110066 | − | 0.190640i | 0.805731 | − | 0.592282i | \(-0.201773\pi\) |
−0.915797 | + | 0.401642i | \(0.868440\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | 0.528655 | 0.264327 | − | 0.964433i | \(-0.414850\pi\) | ||||
0.264327 | + | 0.964433i | \(0.414850\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.2414 | + | 31.5951i | −1.20020 | + | 2.07880i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.00000 | 0.262049 | 0.131024 | − | 0.991379i | \(-0.458173\pi\) | ||||
0.131024 | + | 0.991379i | \(0.458173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.0000 | + | 19.0526i | −0.714527 | + | 1.23760i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.5330 | 1.71628 | 0.858138 | − | 0.513418i | \(-0.171621\pi\) | ||||
0.858138 | + | 0.513418i | \(0.171621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.50000 | − | 11.2583i | −0.418702 | − | 0.725213i | 0.577107 | − | 0.816668i | \(-0.304181\pi\) |
−0.995809 | + | 0.0914555i | \(0.970848\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −26.5330 | − | 45.9565i | −1.70209 | − | 2.94811i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.29156 | + | 8.61684i | −0.527579 | + | 0.548277i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.0000 | − | 38.1051i | 1.39419 | − | 2.41481i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.29156 | + | 14.3614i | 0.523359 | + | 0.906484i | 0.999630 | + | 0.0271858i | \(0.00865456\pi\) |
−0.476272 | + | 0.879298i | \(0.658012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.50000 | + | 9.52628i | 0.345782 | + | 0.598912i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.50000 | + | 11.2583i | −0.405459 | + | 0.702275i | −0.994375 | − | 0.105919i | \(-0.966222\pi\) |
0.588916 | + | 0.808194i | \(0.299555\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.8496 | 1.85477 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −40.0000 | −2.47594 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.6082 | + | 20.1060i | −0.715791 | + | 1.23979i | 0.246862 | + | 0.969051i | \(0.420601\pi\) |
−0.962653 | + | 0.270737i | \(0.912733\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.65831 | + | 2.87228i | 0.101487 | + | 0.175781i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.5000 | − | 25.1147i | −0.884081 | − | 1.53127i | −0.846764 | − | 0.531969i | \(-0.821452\pi\) |
−0.0373168 | − | 0.999303i | \(-0.511881\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9248 | − | 25.8505i | 0.906618 | − | 1.57031i | 0.0878869 | − | 0.996130i | \(-0.471989\pi\) |
0.818731 | − | 0.574178i | \(-0.194678\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.0000 | − | 38.1051i | −0.665750 | − | 2.30623i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.29156 | − | 14.3614i | 0.500000 | − | 0.866025i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.50000 | − | 4.33013i | −0.150210 | − | 0.260172i | 0.781094 | − | 0.624413i | \(-0.214662\pi\) |
−0.931305 | + | 0.364241i | \(0.881328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0000 | 1.19310 | 0.596550 | − | 0.802576i | \(-0.296538\pi\) | ||||
0.596550 | + | 0.802576i | \(0.296538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.6082 | − | 20.1060i | 0.690035 | − | 1.19518i | −0.281791 | − | 0.959476i | \(-0.590928\pi\) |
0.971826 | − | 0.235700i | \(-0.0757383\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.94987 | −0.587323 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.2164 | 1.36097 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.50000 | − | 6.06218i | −0.204472 | − | 0.354156i | 0.745492 | − | 0.666514i | \(-0.232214\pi\) |
−0.949964 | + | 0.312358i | \(0.898881\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −27.5000 | + | 47.6314i | −1.59571 | + | 2.76385i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.6082 | − | 2.87228i | −0.671319 | − | 0.166108i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.5000 | + | 28.5788i | −0.951044 | + | 1.64726i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.8747 | + | 43.0842i | 1.42901 | + | 2.47512i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.2665 | 0.757159 | 0.378580 | − | 0.925569i | \(-0.376413\pi\) | ||||
0.378580 | + | 0.925569i | \(0.376413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.5330 | 1.50455 | 0.752274 | − | 0.658850i | \(-0.228957\pi\) | ||||
0.752274 | + | 0.658850i | \(0.228957\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.00000 | 0.226093 | 0.113047 | − | 0.993590i | \(-0.463939\pi\) | ||||
0.113047 | + | 0.993590i | \(0.463939\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.29156 | + | 14.3614i | 0.464238 | + | 0.804084i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.50000 | − | 9.52628i | −0.306980 | − | 0.531705i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.97494 | − | 8.61684i | 0.276813 | − | 0.479454i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.00000 | + | 17.3205i | 0.277350 | + | 0.960769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.5330 | − | 45.9565i | 1.46728 | − | 2.54140i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.0000 | + | 19.0526i | 0.606450 | + | 1.05040i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.97494 | − | 8.61684i | −0.273447 | − | 0.473625i | 0.696295 | − | 0.717756i | \(-0.254831\pi\) |
−0.969742 | + | 0.244131i | \(0.921497\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 72.0000 | 3.94558 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.0000 | −0.653682 | −0.326841 | − | 0.945079i | \(-0.605984\pi\) | ||||
−0.326841 | + | 0.945079i | \(0.605984\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −36.4829 | −1.98148 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.94987 | −0.537243 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.29156 | + | 14.3614i | 0.445114 | + | 0.770961i | 0.998060 | − | 0.0622565i | \(-0.0198297\pi\) |
−0.552946 | + | 0.833217i | \(0.686496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.500000 | + | 0.866025i | −0.0267644 | + | 0.0463573i | −0.879097 | − | 0.476642i | \(-0.841854\pi\) |
0.852333 | + | 0.523000i | \(0.175187\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.5831 | − | 57.4456i | −0.885142 | − | 3.06622i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.5000 | + | 26.8468i | −0.824982 | + | 1.42891i | 0.0769515 | + | 0.997035i | \(0.475481\pi\) |
−0.901933 | + | 0.431875i | \(0.857852\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.5000 | + | 28.5788i | 0.873273 | + | 1.51255i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.5330 | −1.40036 | −0.700179 | − | 0.713967i | \(-0.746897\pi\) | ||||
−0.700179 | + | 0.713967i | \(0.746897\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.00000 | − | 6.92820i | 0.210526 | − | 0.364642i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.6082 | + | 20.1060i | −0.605942 | + | 1.04952i | 0.385959 | + | 0.922516i | \(0.373870\pi\) |
−0.991902 | + | 0.127007i | \(0.959463\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −24.0000 | −1.24939 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.2665 | + | 22.9783i | 0.688762 | + | 1.19297i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.50000 | − | 11.2583i | −0.336557 | − | 0.582934i | 0.647225 | − | 0.762299i | \(-0.275929\pi\) |
−0.983783 | + | 0.179364i | \(0.942596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.5000 | − | 4.33013i | −0.901296 | − | 0.223013i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9248 | + | 25.8505i | −0.766636 | + | 1.32785i | 0.172741 | + | 0.984967i | \(0.444738\pi\) |
−0.939377 | + | 0.342885i | \(0.888596\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.5000 | + | 28.5788i | 0.845321 | + | 1.46414i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.65831 | − | 2.87228i | −0.0847358 | − | 0.146767i | 0.820543 | − | 0.571585i | \(-0.193671\pi\) |
−0.905279 | + | 0.424818i | \(0.860338\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −39.7995 | + | 68.9348i | −2.02312 | + | 3.50415i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.0000 | −0.507020 | −0.253510 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253510 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.94987 | 0.503187 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.0000 | + | 38.1051i | −1.10975 | + | 1.92215i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.50000 | − | 4.33013i | −0.125471 | − | 0.217323i | 0.796446 | − | 0.604710i | \(-0.206711\pi\) |
−0.921917 | + | 0.387387i | \(0.873378\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.2414 | − | 31.5951i | −0.913214 | − | 1.58173i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.50000 | − | 9.52628i | 0.274657 | − | 0.475720i | −0.695392 | − | 0.718631i | \(-0.744769\pi\) |
0.970049 | + | 0.242911i | \(0.0781024\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.9248 | − | 25.8505i | −0.739795 | − | 1.28136i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.50000 | − | 11.2583i | −0.321404 | − | 0.556689i | 0.659374 | − | 0.751815i | \(-0.270822\pi\) |
−0.980778 | + | 0.195127i | \(0.937488\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29.8496 | −1.47237 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.50000 | + | 9.52628i | −0.270637 | + | 0.468758i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.0000 | 0.538672 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.29156 | − | 14.3614i | 0.405069 | − | 0.701601i | −0.589260 | − | 0.807943i | \(-0.700581\pi\) |
0.994330 | + | 0.106343i | \(0.0339141\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.5330 | + | 45.9565i | 1.29008 | + | 2.23448i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.50000 | − | 12.9904i | −0.363803 | − | 0.630126i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.9248 | − | 25.8505i | 0.722262 | − | 1.25099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −27.5000 | + | 28.5788i | −1.32771 | + | 1.37980i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.29156 | + | 14.3614i | −0.399390 | + | 0.691765i | −0.993651 | − | 0.112508i | \(-0.964112\pi\) |
0.594260 | + | 0.804273i | \(0.297445\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.5000 | − | 18.1865i | −0.504598 | − | 0.873989i | −0.999986 | − | 0.00531724i | \(-0.998307\pi\) |
0.495388 | − | 0.868672i | \(-0.335026\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.0000 | −0.526201 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.29156 | + | 14.3614i | −0.395735 | + | 0.685433i | −0.993195 | − | 0.116466i | \(-0.962843\pi\) |
0.597460 | + | 0.801899i | \(0.296177\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 32.0000 | 1.52381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.2665 | −0.630310 | −0.315155 | − | 0.949040i | \(-0.602057\pi\) | ||||
−0.315155 | + | 0.949040i | \(0.602057\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.31662 | −0.156871 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.50000 | + | 2.59808i | 0.0707894 | + | 0.122611i | 0.899247 | − | 0.437440i | \(-0.144115\pi\) |
−0.828458 | + | 0.560051i | \(0.810782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.97494 | + | 8.61684i | 0.234261 | + | 0.405751i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.500000 | − | 0.866025i | 0.0233890 | − | 0.0405110i | −0.854094 | − | 0.520119i | \(-0.825888\pi\) |
0.877483 | + | 0.479608i | \(0.159221\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.8747 | + | 43.0842i | 1.16105 | + | 2.01100i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.50000 | + | 2.59808i | 0.0698620 | + | 0.121004i | 0.898840 | − | 0.438276i | \(-0.144411\pi\) |
−0.828978 | + | 0.559281i | \(0.811077\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.5330 | −1.23309 | −0.616547 | − | 0.787318i | \(-0.711469\pi\) | ||||
−0.616547 | + | 0.787318i | \(0.711469\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.8997 | 0.920851 | 0.460425 | − | 0.887698i | \(-0.347697\pi\) | ||||
0.460425 | + | 0.887698i | \(0.347697\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.0000 | 1.52380 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.2665 | − | 22.9783i | 0.611288 | − | 1.05878i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.0000 | 1.51734 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.29156 | + | 14.3614i | 0.380443 | + | 0.658947i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.0000 | + | 55.4256i | 1.46518 | + | 2.53777i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.97494 | − | 8.61684i | 0.227311 | − | 0.393714i | −0.729700 | − | 0.683768i | \(-0.760340\pi\) |
0.957010 | + | 0.290054i | \(0.0936734\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.5000 | + | 7.79423i | 1.43628 | + | 0.355386i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.2414 | − | 31.5951i | 0.830014 | − | 1.43763i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.97494 | − | 8.61684i | −0.225436 | − | 0.390466i | 0.731014 | − | 0.682362i | \(-0.239047\pi\) |
−0.956450 | + | 0.291896i | \(0.905714\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −55.0000 | −2.48719 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.29156 | − | 14.3614i | 0.374193 | − | 0.648121i | −0.616013 | − | 0.787736i | \(-0.711253\pi\) |
0.990206 | + | 0.139615i | \(0.0445864\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.0000 | 0.675566 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.5000 | + | 28.5788i | −0.740126 | + | 1.28194i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.2665 | −0.593890 | −0.296945 | − | 0.954895i | \(-0.595968\pi\) | ||||
−0.296945 | + | 0.954895i | \(0.595968\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.50000 | + | 9.52628i | 0.245722 | + | 0.425603i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.65831 | − | 2.87228i | −0.0739405 | − | 0.128069i | 0.826685 | − | 0.562666i | \(-0.190224\pi\) |
−0.900625 | + | 0.434597i | \(0.856891\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.65831 | − | 43.0842i | −0.0736482 | − | 1.91344i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.5000 | − | 33.7750i | 0.864322 | − | 1.49705i | −0.00339621 | − | 0.999994i | \(-0.501081\pi\) |
0.867719 | − | 0.497056i | \(-0.165586\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.63325 | + | 11.4891i | 0.293438 | + | 0.508249i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.5000 | − | 47.6314i | −1.21415 | − | 2.10298i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.0000 | − | 19.0526i | 0.483779 | − | 0.837931i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.2164 | 1.01909 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0000 | −0.525730 | −0.262865 | − | 0.964833i | \(-0.584667\pi\) | ||||
−0.262865 | + | 0.964833i | \(0.584667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.29156 | − | 14.3614i | 0.362565 | − | 0.627980i | −0.625817 | − | 0.779970i | \(-0.715235\pi\) |
0.988382 | + | 0.151989i | \(0.0485679\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −55.0000 | −2.40040 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.00000 | + | 10.3923i | 0.260870 | + | 0.451839i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.2665 | + | 22.9783i | −0.575717 | + | 0.997171i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.5000 | − | 2.59808i | −0.454805 | − | 0.112535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.50000 | − | 9.52628i | −0.237343 | − | 0.411089i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.63325 | − | 11.4891i | −0.285714 | − | 0.494872i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.2665 | − | 22.9783i | 0.569320 | − | 0.986091i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.2665 | −0.567235 | −0.283617 | − | 0.958938i | \(-0.591535\pi\) | ||||
−0.283617 | + | 0.958938i | \(0.591535\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.0000 | − | 62.3538i | 1.53644 | − | 2.66120i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.5831 | −0.706465 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.0000 | − | 19.0526i | −0.467768 | − | 0.810197i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.5000 | − | 32.0429i | 0.783870 | − | 1.35770i | −0.145802 | − | 0.989314i | \(-0.546576\pi\) |
0.929672 | − | 0.368389i | \(-0.120091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.8747 | + | 25.8505i | −1.05209 | + | 1.09336i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.5000 | − | 28.5788i | 0.696631 | − | 1.20660i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.65831 | − | 2.87228i | −0.0698895 | − | 0.121052i | 0.828963 | − | 0.559303i | \(-0.188931\pi\) |
−0.898853 | + | 0.438251i | \(0.855598\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 102.815 | 4.31784 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.50000 | + | 12.9904i | −0.314416 | + | 0.544585i | −0.979313 | − | 0.202350i | \(-0.935142\pi\) |
0.664897 | + | 0.746935i | \(0.268475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.2665 | 0.555186 | 0.277593 | − | 0.960699i | \(-0.410463\pi\) | ||||
0.277593 | + | 0.960699i | \(0.410463\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −77.0000 | −3.21672 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.29156 | + | 14.3614i | −0.345782 | + | 0.598912i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.0000 | 0.832611 | 0.416305 | − | 0.909225i | \(-0.363325\pi\) | ||||
0.416305 | + | 0.909225i | \(0.363325\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.5581 | − | 37.3397i | −0.895922 | − | 1.55178i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.0000 | + | 38.1051i | 0.912714 | + | 1.58087i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.2665 | − | 22.9783i | 0.549442 | − | 0.951662i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.5581 | − | 37.3397i | 0.889796 | − | 1.54117i | 0.0496808 | − | 0.998765i | \(-0.484180\pi\) |
0.840116 | − | 0.542407i | \(-0.182487\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.5581 | + | 37.3397i | 0.886780 | + | 1.53595i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.0000 | −1.47834 | −0.739171 | − | 0.673517i | \(-0.764783\pi\) | ||||
−0.739171 | + | 0.673517i | \(0.764783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33.0000 | 1.35060 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.1662 | −1.35514 | −0.677568 | − | 0.735460i | \(-0.736966\pi\) | ||||
−0.677568 | + | 0.735460i | \(0.736966\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.5000 | + | 25.1147i | −0.591467 | + | 1.02445i | 0.402568 | + | 0.915390i | \(0.368118\pi\) |
−0.994035 | + | 0.109061i | \(0.965216\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 79.5990 | 3.24152 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.97494 | − | 8.61684i | −0.201926 | − | 0.349747i | 0.747223 | − | 0.664574i | \(-0.231387\pi\) |
−0.949149 | + | 0.314827i | \(0.898054\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.5000 | − | 47.6314i | 1.11436 | − | 1.93012i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.63325 | + | 22.9783i | 0.268353 | + | 0.929601i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.50000 | − | 6.06218i | 0.141364 | − | 0.244849i | −0.786647 | − | 0.617403i | \(-0.788185\pi\) |
0.928010 | + | 0.372554i | \(0.121518\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.50000 | + | 14.7224i | 0.342197 | + | 0.592703i | 0.984840 | − | 0.173463i | \(-0.0554956\pi\) |
−0.642643 | + | 0.766165i | \(0.722162\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.7995 | −1.59968 | −0.799838 | − | 0.600215i | \(-0.795082\pi\) | ||||
−0.799838 | + | 0.600215i | \(0.795082\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.5000 | − | 47.6314i | 1.10354 | − | 1.91138i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.31662 | −0.132878 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.2414 | + | 31.5951i | −0.728493 | + | 1.26179i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.0000 | −1.07656 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.97494 | − | 8.61684i | −0.198049 | − | 0.343031i | 0.749847 | − | 0.661612i | \(-0.230127\pi\) |
−0.947896 | + | 0.318580i | \(0.896794\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.50000 | − | 9.52628i | −0.218605 | − | 0.378636i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.0000 | + | 3.46410i | 0.554700 | + | 0.137253i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −39.7995 | + | 68.9348i | −1.57444 | + | 2.72702i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | − | 18.1865i | −0.414725 | − | 0.718325i | 0.580674 | − | 0.814136i | \(-0.302789\pi\) |
−0.995400 | + | 0.0958109i | \(0.969456\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.2414 | − | 31.5951i | −0.719372 | − | 1.24599i | −0.961249 | − | 0.275682i | \(-0.911096\pi\) |
0.241877 | − | 0.970307i | \(-0.422237\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.97494 | − | 8.61684i | 0.195585 | − | 0.338763i | −0.751507 | − | 0.659725i | \(-0.770673\pi\) |
0.947092 | + | 0.320962i | \(0.104006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.0000 | 0.431788 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.50000 | − | 12.9904i | 0.293498 | − | 0.508353i | −0.681137 | − | 0.732156i | \(-0.738514\pi\) |
0.974634 | + | 0.223803i | \(0.0718474\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.0000 | + | 27.7128i | 0.624219 | + | 1.08118i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.5581 | + | 37.3397i | 0.839783 | + | 1.45455i | 0.890076 | + | 0.455812i | \(0.150651\pi\) |
−0.0502932 | + | 0.998734i | \(0.516016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.50000 | + | 14.7224i | −0.330612 | + | 0.572636i | −0.982632 | − | 0.185565i | \(-0.940588\pi\) |
0.652020 | + | 0.758202i | \(0.273922\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.94987 | + | 34.4674i | 0.386421 | + | 1.33860i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.29156 | − | 14.3614i | −0.321051 | − | 0.556076i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.50000 | + | 9.52628i | 0.212642 | + | 0.368307i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.8496 | −1.15233 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.5000 | − | 42.4352i | 0.944406 | − | 1.63576i | 0.187469 | − | 0.982271i | \(-0.439972\pi\) |
0.756937 | − | 0.653488i | \(-0.226695\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −82.9156 | −3.19142 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.0000 | −0.922395 | −0.461197 | − | 0.887298i | \(-0.652580\pi\) | ||||
−0.461197 | + | 0.887298i | \(0.652580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.6082 | + | 20.1060i | −0.445481 | + | 0.771596i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.0000 | 0.421521 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.9248 | − | 25.8505i | −0.571082 | − | 0.989143i | −0.996455 | − | 0.0841251i | \(-0.973190\pi\) |
0.425373 | − | 0.905018i | \(-0.360143\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.2665 | + | 22.9783i | −0.506149 | + | 0.876675i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.00000 | + | 27.7128i | 0.304776 | + | 1.05577i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.6082 | − | 20.1060i | 0.441596 | − | 0.764867i | −0.556212 | − | 0.831041i | \(-0.687746\pi\) |
0.997808 | + | 0.0661734i | \(0.0210790\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −44.0000 | − | 76.2102i | −1.67142 | − | 2.89499i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | 0.340899 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.63325 | + | 11.4891i | −0.250893 | + | 0.434559i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.0000 | −1.20862 | −0.604312 | − | 0.796748i | \(-0.706552\pi\) | ||||
−0.604312 | + | 0.796748i | \(0.706552\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.8496 | 1.12580 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −49.7494 | −1.87102 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.5000 | − | 25.1147i | −0.544559 | − | 0.943204i | −0.998635 | − | 0.0522406i | \(-0.983364\pi\) |
0.454076 | − | 0.890963i | \(-0.349970\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −26.5330 | − | 45.9565i | −0.995065 | − | 1.72350i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −44.0000 | + | 76.2102i | −1.64321 | + | 2.84612i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.9248 | − | 25.8505i | −0.556602 | − | 0.964062i | −0.997777 | − | 0.0666413i | \(-0.978772\pi\) |
0.441175 | − | 0.897421i | \(-0.354562\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 43.1161 | 1.60351 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.5000 | + | 21.6506i | −0.464238 | + | 0.804084i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.5330 | −0.984054 | −0.492027 | − | 0.870580i | \(-0.663744\pi\) | ||||
−0.492027 | + | 0.870580i | \(0.663744\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 83.0000 | 3.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.9248 | − | 25.8505i | 0.552014 | − | 0.956116i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.0000 | 0.664845 | 0.332423 | − | 0.943131i | \(-0.392134\pi\) | ||||
0.332423 | + | 0.943131i | \(0.392134\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.5000 | − | 28.5788i | −0.607785 | − | 1.05272i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.97494 | + | 8.61684i | −0.183006 | + | 0.316976i | −0.942903 | − | 0.333068i | \(-0.891916\pi\) |
0.759897 | + | 0.650044i | \(0.225249\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.0000 | − | 38.1051i | −0.404095 | − | 1.39983i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.5581 | + | 37.3397i | −0.790889 | + | 1.36986i | 0.134529 | + | 0.990910i | \(0.457048\pi\) |
−0.925417 | + | 0.378949i | \(0.876285\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 53.0660 | + | 91.9130i | 1.94158 | + | 3.36292i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.0000 | 0.401931 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.9248 | − | 25.8505i | 0.544614 | − | 0.943299i | −0.454017 | − | 0.890993i | \(-0.650009\pi\) |
0.998631 | − | 0.0523063i | \(-0.0166572\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −55.0000 | −2.00431 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.50000 | − | 6.06218i | 0.127210 | − | 0.220334i | −0.795385 | − | 0.606105i | \(-0.792731\pi\) |
0.922595 | + | 0.385771i | \(0.126065\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −36.4829 | −1.32424 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.5000 | + | 23.3827i | 0.489375 | + | 0.847622i | 0.999925 | − | 0.0122260i | \(-0.00389175\pi\) |
−0.510551 | + | 0.859848i | \(0.670558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.5330 | + | 45.9565i | 0.960559 | + | 1.66374i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.29156 | + | 8.61684i | −0.299391 | + | 0.311136i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.5000 | − | 23.3827i | 0.486822 | − | 0.843201i | −0.513063 | − | 0.858351i | \(-0.671489\pi\) |
0.999885 | + | 0.0151499i | \(0.00482254\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.5581 | − | 37.3397i | −0.776395 | − | 1.34475i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.5000 | − | 18.1865i | −0.377659 | − | 0.654124i | 0.613062 | − | 0.790034i | \(-0.289937\pi\) |
−0.990721 | + | 0.135910i | \(0.956604\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −49.5000 | + | 85.7365i | −1.77580 | + | 3.07578i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.94987 | −0.356491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.0000 | 1.18083 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 41.4578 | − | 71.8070i | 1.48158 | − | 2.56617i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.97494 | − | 8.61684i | −0.177337 | − | 0.307157i | 0.763630 | − | 0.645654i | \(-0.223415\pi\) |
−0.940968 | + | 0.338496i | \(0.890082\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38.5000 | − | 66.6840i | −1.37064 | − | 2.37401i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.2414 | − | 31.5951i | 0.648591 | − | 1.12339i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.5000 | − | 23.3827i | 0.798998 | − | 0.830344i |