Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1920,2,Mod(289,1920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1920, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 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("1920.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1920 = 2^{7} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1920.bl (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.3312771881\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 289.18 | ||
Character | \(\chi\) | \(=\) | 1920.289 |
Dual form | 1920.2.bl.a.1249.18 |
$q$-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 \(\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(641\) | \(901\) | \(1537\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.06370 | + | 0.860885i | 0.922917 | + | 0.385000i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707398 | 0.267371 | 0.133686 | − | 0.991024i | \(-0.457319\pi\) | ||||
0.133686 | + | 0.991024i | \(0.457319\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.79993 | + | 1.79993i | −0.542699 | + | 0.542699i | −0.924319 | − | 0.381621i | \(-0.875366\pi\) |
0.381621 | + | 0.924319i | \(0.375366\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.86348 | + | 3.86348i | −1.07154 | + | 1.07154i | −0.0742996 | + | 0.997236i | \(0.523672\pi\) |
−0.997236 | + | 0.0742996i | \(0.976328\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.06800 | − | 0.850522i | 0.533955 | − | 0.219604i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.244884i | − | 0.0593932i | −0.999559 | − | 0.0296966i | \(-0.990546\pi\) | ||
0.999559 | − | 0.0296966i | \(-0.00945410\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.53863 | − | 1.53863i | −0.352986 | − | 0.352986i | 0.508233 | − | 0.861219i | \(-0.330299\pi\) |
−0.861219 | + | 0.508233i | \(0.830299\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500206 | − | 0.500206i | 0.109154 | − | 0.109154i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.92280 | 1.44350 | 0.721752 | − | 0.692152i | \(-0.243337\pi\) | ||||
0.721752 | + | 0.692152i | \(0.243337\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.51775 | + | 3.55323i | 0.703551 | + | 0.710645i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.89882 | + | 4.89882i | 0.909688 | + | 0.909688i | 0.996247 | − | 0.0865591i | \(-0.0275871\pi\) |
−0.0865591 | + | 0.996247i | \(0.527587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.60734 | 1.36632 | 0.683159 | − | 0.730270i | \(-0.260606\pi\) | ||||
0.683159 | + | 0.730270i | \(0.260606\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.54548i | 0.443112i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.45986 | + | 0.608988i | 0.246761 | + | 0.102938i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.47863 | + | 8.47863i | 1.39388 | + | 1.39388i | 0.816420 | + | 0.577459i | \(0.195956\pi\) |
0.577459 | + | 0.816420i | \(0.304044\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.46378i | 0.874905i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.12118i | 0.331272i | 0.986187 | + | 0.165636i | \(0.0529677\pi\) | ||||
−0.986187 | + | 0.165636i | \(0.947032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.684507 | + | 0.684507i | 0.104386 | + | 0.104386i | 0.757371 | − | 0.652985i | \(-0.226483\pi\) |
−0.652985 | + | 0.757371i | \(0.726483\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.860885 | − | 2.06370i | 0.128333 | − | 0.307639i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.47342i | − | 0.652515i | −0.945281 | − | 0.326258i | \(-0.894212\pi\) | ||
0.945281 | − | 0.326258i | \(-0.105788\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.49959 | −0.928513 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.173159 | − | 0.173159i | −0.0242472 | − | 0.0242472i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.47026 | − | 1.47026i | −0.201956 | − | 0.201956i | 0.598881 | − | 0.800838i | \(-0.295612\pi\) |
−0.800838 | + | 0.598881i | \(0.795612\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.26405 | + | 2.16499i | −0.709804 | + | 0.291927i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.17595 | −0.288212 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.86121 | + | 5.86121i | −0.763065 | + | 0.763065i | −0.976875 | − | 0.213810i | \(-0.931413\pi\) |
0.213810 | + | 0.976875i | \(0.431413\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0537432 | − | 0.0537432i | −0.00688112 | − | 0.00688112i | 0.703658 | − | 0.710539i | \(-0.251549\pi\) |
−0.710539 | + | 0.703658i | \(0.751549\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.707398i | − | 0.0891237i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.2991 | + | 4.64706i | −1.40148 | + | 0.576397i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.85550 | − | 7.85550i | 0.959702 | − | 0.959702i | −0.0395170 | − | 0.999219i | \(-0.512582\pi\) |
0.999219 | + | 0.0395170i | \(0.0125819\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.89516 | − | 4.89516i | 0.589308 | − | 0.589308i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.08595i | − | 0.247557i | −0.992310 | − | 0.123778i | \(-0.960499\pi\) | ||
0.992310 | − | 0.123778i | \(-0.0395012\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.69951 | 1.13524 | 0.567621 | − | 0.823290i | \(-0.307864\pi\) | ||||
0.567621 | + | 0.823290i | \(0.307864\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.99994 | + | 0.0250827i | 0.577343 | + | 0.00289630i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.27326 | + | 1.27326i | −0.145102 | + | 0.145102i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.34690 | −0.826591 | −0.413295 | − | 0.910597i | \(-0.635622\pi\) | ||||
−0.413295 | + | 0.910597i | \(0.635622\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.80291 | − | 6.80291i | 0.746716 | − | 0.746716i | −0.227145 | − | 0.973861i | \(-0.572939\pi\) |
0.973861 | + | 0.227145i | \(0.0729391\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.210817 | − | 0.505369i | 0.0228663 | − | 0.0548149i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.92797 | 0.742757 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.07483i | − | 0.325931i | −0.986632 | − | 0.162966i | \(-0.947894\pi\) | ||
0.986632 | − | 0.162966i | \(-0.0521060\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.73301 | + | 2.73301i | −0.286498 | + | 0.286498i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.37920 | − | 5.37920i | 0.557797 | − | 0.557797i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.85069 | − | 4.49986i | −0.189877 | − | 0.461676i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.39922i | − | 0.142070i | −0.997474 | − | 0.0710348i | \(-0.977370\pi\) | ||
0.997474 | − | 0.0710348i | \(-0.0226301\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.79993 | + | 1.79993i | 0.180900 | + | 0.180900i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.7916 | + | 11.7916i | −1.17331 | + | 1.17331i | −0.191895 | + | 0.981415i | \(0.561463\pi\) |
−0.981415 | + | 0.191895i | \(0.938537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.29240 | 0.225877 | 0.112938 | − | 0.993602i | \(-0.463974\pi\) | ||||
0.112938 | + | 0.993602i | \(0.463974\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.46290 | − | 0.601657i | 0.142764 | − | 0.0587157i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.49009 | − | 9.49009i | −0.917442 | − | 0.917442i | 0.0794010 | − | 0.996843i | \(-0.474699\pi\) |
−0.996843 | + | 0.0794010i | \(0.974699\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.9058 | − | 11.9058i | −1.14037 | − | 1.14037i | −0.988383 | − | 0.151984i | \(-0.951434\pi\) |
−0.151984 | − | 0.988383i | \(-0.548566\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.9906 | 1.13810 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.92806i | 0.745809i | 0.927870 | + | 0.372904i | \(0.121638\pi\) | ||||
−0.927870 | + | 0.372904i | \(0.878362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.2866 | + | 5.95974i | 1.33223 | + | 0.555748i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.86348 | + | 3.86348i | 0.357179 | + | 0.357179i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.173231i | − | 0.0158800i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.52052i | 0.410956i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.49990 | + | 1.49990i | 0.135241 | + | 0.135241i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.20068 | + | 10.3612i | 0.375721 | + | 0.926733i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.4466i | 1.72561i | 0.505536 | + | 0.862806i | \(0.331295\pi\) | ||||
−0.505536 | + | 0.862806i | \(0.668705\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.968040 | 0.0852311 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.354049 | + | 0.354049i | 0.0309334 | + | 0.0309334i | 0.722404 | − | 0.691471i | \(-0.243037\pi\) |
−0.691471 | + | 0.722404i | \(0.743037\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.08842 | − | 1.08842i | −0.0943783 | − | 0.0943783i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.850522 | − | 2.06800i | −0.0732013 | − | 0.177985i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.30033 | −0.623709 | −0.311854 | − | 0.950130i | \(-0.600950\pi\) | ||||
−0.311854 | + | 0.950130i | \(0.600950\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.85519 | − | 8.85519i | 0.751087 | − | 0.751087i | −0.223595 | − | 0.974682i | \(-0.571779\pi\) |
0.974682 | + | 0.223595i | \(0.0717793\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.16319 | − | 3.16319i | −0.266388 | − | 0.266388i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 13.9080i | − | 1.16304i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.89239 | + | 14.3270i | 0.489337 | + | 1.18980i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.59590 | + | 4.59590i | −0.379064 | + | 0.379064i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.41385 | + | 5.41385i | −0.443520 | + | 0.443520i | −0.893193 | − | 0.449673i | \(-0.851540\pi\) |
0.449673 | + | 0.893193i | \(0.351540\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 0.341548i | − | 0.0277948i | −0.999903 | − | 0.0138974i | \(-0.995576\pi\) | ||
0.999903 | − | 0.0138974i | \(-0.00442382\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.244884 | −0.0197977 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.6993 | + | 6.54904i | 1.26100 | + | 0.526032i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.86465 | − | 2.86465i | 0.228624 | − | 0.228624i | −0.583494 | − | 0.812118i | \(-0.698315\pi\) |
0.812118 | + | 0.583494i | \(0.198315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.07927 | −0.164897 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.89717 | 0.385951 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.94216 | − | 5.94216i | 0.465426 | − | 0.465426i | −0.435003 | − | 0.900429i | \(-0.643253\pi\) |
0.900429 | + | 0.435003i | \(0.143253\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.19137 | + | 5.25312i | −0.170598 | + | 0.408955i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.4595 | 1.11891 | 0.559454 | − | 0.828861i | \(-0.311011\pi\) | ||||
0.559454 | + | 0.828861i | \(0.311011\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 16.8529i | − | 1.29638i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.53863 | + | 1.53863i | −0.117662 | + | 0.117662i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.65096 | − | 6.65096i | 0.505663 | − | 0.505663i | −0.407529 | − | 0.913192i | \(-0.633610\pi\) |
0.913192 | + | 0.407529i | \(0.133610\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.48845 | + | 2.51354i | 0.188109 | + | 0.190006i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.28901i | 0.623040i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.2660 | − | 17.2660i | −1.29052 | − | 1.29052i | −0.934466 | − | 0.356052i | \(-0.884123\pi\) |
−0.356052 | − | 0.934466i | \(-0.615877\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.12242 | + | 5.12242i | −0.380746 | + | 0.380746i | −0.871371 | − | 0.490625i | \(-0.836769\pi\) |
0.490625 | + | 0.871371i | \(0.336769\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.0760044 | −0.00561841 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.1983 | + | 24.7965i | 0.749791 | + | 1.82308i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.440774 | + | 0.440774i | 0.0322326 | + | 0.0322326i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.500206 | − | 0.500206i | −0.0363846 | − | 0.0363846i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.8040 | −1.28825 | −0.644124 | − | 0.764921i | \(-0.722778\pi\) | ||||
−0.644124 | + | 0.764921i | \(0.722778\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 17.2222i | − | 1.23968i | −0.784727 | − | 0.619842i | \(-0.787197\pi\) | ||
0.784727 | − | 0.619842i | \(-0.212803\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.70369 | + | 11.2756i | −0.336838 | + | 0.807465i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0764 | + | 10.0764i | 0.717915 | + | 0.717915i | 0.968178 | − | 0.250263i | \(-0.0805171\pi\) |
−0.250263 | + | 0.968178i | \(0.580517\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.74179i | − | 0.407025i | −0.979072 | − | 0.203513i | \(-0.934764\pi\) | ||
0.979072 | − | 0.203513i | \(-0.0652358\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 11.1094i | − | 0.783593i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.46541 | + | 3.46541i | 0.243224 | + | 0.243224i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.82609 | + | 4.37748i | −0.127540 | + | 0.305737i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.92280i | − | 0.481168i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.53885 | 0.383130 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.73318 | + | 9.73318i | 0.670060 | + | 0.670060i | 0.957730 | − | 0.287670i | \(-0.0928806\pi\) |
−0.287670 | + | 0.957730i | \(0.592881\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.47499 | − | 1.47499i | −0.101065 | − | 0.101065i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.823339 | + | 2.00190i | 0.0561512 | + | 0.136529i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.38141 | 0.365314 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.85859 | − | 6.85859i | 0.463460 | − | 0.463460i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.946104 | + | 0.946104i | 0.0636419 | + | 0.0636419i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 22.1037i | − | 1.48017i | −0.672511 | − | 0.740087i | \(-0.734784\pi\) | ||
0.672511 | − | 0.740087i | \(-0.265216\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.55323 | − | 3.51775i | 0.236882 | − | 0.234517i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.35387 | + | 5.35387i | −0.355349 | + | 0.355349i | −0.862095 | − | 0.506746i | \(-0.830848\pi\) |
0.506746 | + | 0.862095i | \(0.330848\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.3018 | − | 18.3018i | 1.20942 | − | 1.20942i | 0.238204 | − | 0.971215i | \(-0.423441\pi\) |
0.971215 | − | 0.238204i | \(-0.0765587\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.80067i | 0.118475i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.0546 | −0.789721 | −0.394861 | − | 0.918741i | \(-0.629207\pi\) | ||||
−0.394861 | + | 0.918741i | \(0.629207\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.85110 | − | 9.23182i | 0.251218 | − | 0.602217i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.19504 | + | 5.19504i | −0.337454 | + | 0.337454i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.9193 | −1.80595 | −0.902974 | − | 0.429695i | \(-0.858621\pi\) | ||||
−0.902974 | + | 0.429695i | \(0.858621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.7118 | 0.883253 | 0.441626 | − | 0.897199i | \(-0.354402\pi\) | ||||
0.441626 | + | 0.897199i | \(0.354402\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.4132 | − | 5.59540i | −0.856940 | − | 0.357477i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.8889 | 0.756474 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 9.62077i | − | 0.609691i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.07173 | − | 9.07173i | 0.572602 | − | 0.572602i | −0.360252 | − | 0.932855i | \(-0.617309\pi\) |
0.932855 | + | 0.360252i | \(0.117309\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.4605 | + | 12.4605i | −0.783388 | + | 0.783388i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.208279 | − | 0.506420i | −0.0130430 | − | 0.0317132i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 9.23416i | − | 0.576011i | −0.957629 | − | 0.288006i | \(-0.907008\pi\) | ||
0.957629 | − | 0.288006i | \(-0.0929922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.99776 | + | 5.99776i | 0.372683 | + | 0.372683i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.89882 | − | 4.89882i | 0.303229 | − | 0.303229i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.5516 | −1.14394 | −0.571971 | − | 0.820274i | \(-0.693821\pi\) | ||||
−0.571971 | + | 0.820274i | \(0.693821\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.76846 | − | 4.29992i | −0.108636 | − | 0.264142i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.17423 | − | 2.17423i | −0.133061 | − | 0.133061i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.3977 | − | 14.3977i | −0.877844 | − | 0.877844i | 0.115467 | − | 0.993311i | \(-0.463163\pi\) |
−0.993311 | + | 0.115467i | \(0.963163\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.2974 | 1.17224 | 0.586118 | − | 0.810226i | \(-0.300656\pi\) | ||||
0.586118 | + | 0.810226i | \(0.300656\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.86507i | 0.233924i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.7272 | − | 0.0638476i | −0.767482 | − | 0.00385016i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.52269 | − | 3.52269i | −0.211658 | − | 0.211658i | 0.593314 | − | 0.804971i | \(-0.297819\pi\) |
−0.804971 | + | 0.593314i | \(0.797819\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 7.60734i | − | 0.455439i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.2076i | 1.74238i | 0.490945 | + | 0.871191i | \(0.336652\pi\) | ||||
−0.490945 | + | 0.871191i | \(0.663348\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.84279 | + | 9.84279i | 0.585093 | + | 0.585093i | 0.936298 | − | 0.351205i | \(-0.114228\pi\) |
−0.351205 | + | 0.936298i | \(0.614228\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.49052 | − | 1.87325i | −0.265996 | − | 0.110961i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.50052i | 0.0885726i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9400 | 0.996472 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.989400 | − | 0.989400i | −0.0579997 | − | 0.0579997i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.8238 | − | 11.8238i | −0.690755 | − | 0.690755i | 0.271643 | − | 0.962398i | \(-0.412433\pi\) |
−0.962398 | + | 0.271643i | \(0.912433\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.1416 | + | 7.04998i | −0.998025 | + | 0.410466i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.54548 | 0.147704 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −26.7461 | + | 26.7461i | −1.54677 | + | 1.54677i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.484219 | + | 0.484219i | 0.0279099 | + | 0.0279099i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.6759i | 0.958004i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.0646434 | − | 0.157177i | −0.00370147 | − | 0.00899992i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.6232 | + | 16.6232i | −0.948733 | + | 0.948733i | −0.998748 | − | 0.0500151i | \(-0.984073\pi\) |
0.0500151 | + | 0.998748i | \(0.484073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.62097 | − | 1.62097i | 0.0922139 | − | 0.0922139i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.8069i | 0.782920i | 0.920195 | + | 0.391460i | \(0.128030\pi\) | ||||
−0.920195 | + | 0.391460i | \(0.871970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.40380 | −0.418488 | −0.209244 | − | 0.977864i | \(-0.567100\pi\) | ||||
−0.209244 | + | 0.977864i | \(0.567100\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.608988 | − | 1.45986i | 0.0343126 | − | 0.0822538i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.80712 | + | 1.80712i | −0.101498 | + | 0.101498i | −0.756032 | − | 0.654534i | \(-0.772865\pi\) |
0.654534 | + | 0.756032i | \(0.272865\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.6350 | −0.987372 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.4210 | −0.749088 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.376786 | + | 0.376786i | −0.0209650 | + | 0.0209650i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.3186 | − | 0.137046i | −1.51536 | − | 0.00760197i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.8373 | −0.931106 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3.16449i | − | 0.174464i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.82711 | − | 5.82711i | 0.320287 | − | 0.320287i | −0.528590 | − | 0.848877i | \(-0.677279\pi\) |
0.848877 | + | 0.528590i | \(0.177279\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.47863 | − | 8.47863i | 0.464626 | − | 0.464626i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.9741 | − | 9.44875i | 1.25521 | − | 0.516240i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 25.5357i | − | 1.39102i | −0.718516 | − | 0.695510i | \(-0.755178\pi\) | ||
0.718516 | − | 0.695510i | \(-0.244822\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.60598 | + | 5.60598i | 0.304475 | + | 0.304475i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.6927 | + | 13.6927i | −0.741499 | + | 0.741499i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.54958 | −0.515629 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.3163 | − | 5.88799i | 0.770766 | − | 0.316999i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.6028 | − | 17.6028i | −0.944970 | − | 0.944970i | 0.0535933 | − | 0.998563i | \(-0.482933\pi\) |
−0.998563 | + | 0.0535933i | \(0.982933\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.07562 | + | 5.07562i | 0.271692 | + | 0.271692i | 0.829781 | − | 0.558089i | \(-0.188465\pi\) |
−0.558089 | + | 0.829781i | \(0.688465\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.46378 | 0.291635 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 0.171535i | − | 0.00912990i | −0.999990 | − | 0.00456495i | \(-0.998547\pi\) | ||
0.999990 | − | 0.00456495i | \(-0.00145307\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.79576 | − | 4.30479i | 0.0953093 | − | 0.228474i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.122492 | − | 0.122492i | −0.00648299 | − | 0.00648299i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 17.1694i | − | 0.906169i | −0.891468 | − | 0.453084i | \(-0.850324\pi\) | ||
0.891468 | − | 0.453084i | \(-0.149676\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 14.2652i | − | 0.750802i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.19649 | + | 3.19649i | 0.167772 | + | 0.167772i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.0169 | + | 8.35016i | 1.04773 | + | 0.437068i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.3124i | 1.21690i | 0.793593 | + | 0.608450i | \(0.208208\pi\) | ||||
−0.793593 | + | 0.608450i | \(0.791792\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.12118 | 0.110424 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.04006 | − | 1.04006i | −0.0539973 | − | 0.0539973i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.11817 | − | 1.11817i | −0.0578964 | − | 0.0578964i | 0.677566 | − | 0.735462i | \(-0.263035\pi\) |
−0.735462 | + | 0.677566i | \(0.763035\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.2968 | + | 4.35614i | 0.531724 | + | 0.224950i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −37.8529 | −1.94953 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3707 | + | 22.3707i | −1.14910 | + | 1.14910i | −0.162375 | + | 0.986729i | \(0.551915\pi\) |
−0.986729 | + | 0.162375i | \(0.948085\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.7509 | + | 13.7509i | 0.704478 | + | 0.704478i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.1168i | 1.64109i | 0.571579 | + | 0.820547i | \(0.306331\pi\) | ||||
−0.571579 | + | 0.820547i | \(0.693669\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.72378 | + | 1.53151i | −0.189781 | + | 0.0780528i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.684507 | − | 0.684507i | 0.0347955 | − | 0.0347955i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.7409 | − | 22.7409i | 1.15301 | − | 1.15301i | 0.167062 | − | 0.985946i | \(-0.446572\pi\) |
0.985946 | − | 0.167062i | \(-0.0534280\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.69529i | − | 0.0857342i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.500701 | 0.0252570 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.1618 | − | 6.32484i | −0.762874 | − | 0.318237i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.6530 | − | 21.6530i | 1.08673 | − | 1.08673i | 0.0908707 | − | 0.995863i | \(-0.471035\pi\) |
0.995863 | − | 0.0908707i | \(-0.0289650\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.53926 | −0.0770596 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1600 | 0.856931 | 0.428466 | − | 0.903558i | \(-0.359054\pi\) | ||||
0.428466 | + | 0.903558i | \(0.359054\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.3908 | + | 29.3908i | −1.46406 | + | 1.46406i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.06370 | − | 0.860885i | −0.102546 | − | 0.0427777i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −30.5218 | −1.51291 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 17.9588i | − | 0.888006i | −0.896025 | − | 0.444003i | \(-0.853558\pi\) | ||
0.896025 | − | 0.444003i | \(-0.146442\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.16211 | + | 5.16211i | −0.254628 | + | 0.254628i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.14621 | + | 4.14621i | −0.204022 | + | 0.204022i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.8957 | − | 8.18267i | 0.976642 | − | 0.401671i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 12.5231i | − | 0.613260i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.4031 | − | 23.4031i | −1.14332 | − | 1.14332i | −0.987840 | − | 0.155476i | \(-0.950309\pi\) |
−0.155476 | − | 0.987840i | \(-0.549691\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.0016 | − | 27.0016i | 1.31598 | − | 1.31598i | 0.399043 | − | 0.916932i | \(-0.369342\pi\) |
0.916932 | − | 0.399043i | \(-0.130658\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.47342 | −0.217505 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.870129 | − | 0.861442i | 0.0422075 | − | 0.0417861i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0380178 | − | 0.0380178i | −0.00183981 | − | 0.00183981i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.83441 | − | 9.83441i | −0.474810 | − | 0.474810i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.4043 | −1.36819 | −0.684093 | − | 0.729395i | \(-0.739802\pi\) | ||||
−0.684093 | + | 0.729395i | \(0.739802\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.04564i | 0.194421i | 0.995264 | + | 0.0972106i | \(0.0309920\pi\) | ||||
−0.995264 | + | 0.0972106i | \(0.969008\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.2973 | + | 5.96419i | 0.685503 | + | 0.285961i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.6516 | − | 10.6516i | −0.509537 | − | 0.509537i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.4690i | 0.499660i | 0.968290 | + | 0.249830i | \(0.0803748\pi\) | ||||
−0.968290 | + | 0.249830i | \(0.919625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.49959i | 0.309504i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.81582 | + | 1.81582i | 0.0862722 | + | 0.0862722i | 0.748926 | − | 0.662654i | \(-0.230570\pi\) |
−0.662654 | + | 0.748926i | \(0.730570\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.64707 | − | 6.34554i | 0.125483 | − | 0.300807i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.65634i | 0.362132i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.2064 | −1.04799 | −0.523993 | − | 0.851723i | \(-0.675558\pi\) | ||||
−0.523993 | + | 0.851723i | \(0.675558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.81797 | − | 3.81797i | −0.179781 | − | 0.179781i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.241511 | − | 0.241511i | −0.0113472 | − | 0.0113472i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.99294 | + | 3.28732i | −0.374715 | + | 0.154112i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.2280 | 0.572000 | 0.286000 | − | 0.958230i | \(-0.407674\pi\) | ||||
0.286000 | + | 0.958230i | \(0.407674\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.173159 | + | 0.173159i | −0.00808238 | + | 0.00808238i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.723447 | − | 0.723447i | −0.0336943 | − | 0.0336943i | 0.690059 | − | 0.723753i | \(-0.257585\pi\) |
−0.723753 | + | 0.690059i | \(0.757585\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.42343i | 0.252048i | 0.992027 | + | 0.126024i | \(0.0402217\pi\) | ||||
−0.992027 | + | 0.126024i | \(0.959778\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.7320 | − | 6.47021i | 0.729552 | − | 0.300049i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.3242 | − | 13.3242i | 0.616571 | − | 0.616571i | −0.328079 | − | 0.944650i | \(-0.606401\pi\) |
0.944650 | + | 0.328079i | \(0.106401\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.55696 | − | 5.55696i | 0.256597 | − | 0.256597i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 4.05122i | − | 0.186671i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.46413 | −0.113301 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0545788 | − | 10.8796i | 0.00250425 | − | 0.499191i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.47026 | + | 1.47026i | −0.0673188 | + | 0.0673188i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.25963 | −0.0575541 | −0.0287771 | − | 0.999586i | \(-0.509161\pi\) | ||||
−0.0287771 | + | 0.999586i | \(0.509161\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −65.5140 | −2.98718 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.46282 | − | 3.46282i | 0.157564 | − | 0.157564i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.20457 | − | 2.88758i | 0.0546967 | − | 0.131118i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.8116 | 0.716491 | 0.358246 | − | 0.933627i | \(-0.383375\pi\) | ||||
0.358246 | + | 0.933627i | \(0.383375\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 8.40349i | − | 0.380019i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.6008 | − | 15.6008i | 0.704054 | − | 0.704054i | −0.261224 | − | 0.965278i | \(-0.584126\pi\) |
0.965278 | + | 0.261224i | \(0.0841263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.19964 | − | 1.19964i | 0.0540292 | − | 0.0540292i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.16499 | + | 5.26405i | 0.0973090 | + | 0.236601i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.47560i | − | 0.0661896i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.6650 | − | 25.6650i | −1.14892 | − | 1.14892i | −0.986765 | − | 0.162159i | \(-0.948154\pi\) |
−0.162159 | − | 0.986765i | \(-0.551846\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.2244 | − | 10.2244i | 0.456792 | − | 0.456792i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.72004 | 0.210456 | 0.105228 | − | 0.994448i | \(-0.466443\pi\) | ||||
0.105228 | + | 0.994448i | \(0.466443\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.4857 | + | 14.1832i | −1.53459 | + | 0.631144i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.9168 | − | 11.9168i | −0.529244 | − | 0.529244i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.8862 | + | 11.8862i | 0.526848 | + | 0.526848i | 0.919631 | − | 0.392783i | \(-0.128488\pi\) |
−0.392783 | + | 0.919631i | \(0.628488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.86141 | 0.303531 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.17595i | 0.0960706i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.73084 | + | 1.97349i | 0.208466 | + | 0.0869625i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.05183 | + | 8.05183i | 0.354119 | + | 0.354119i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9.40587i | − | 0.412872i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.01467i | − | 0.219696i | −0.993948 | − | 0.109848i | \(-0.964964\pi\) | ||
0.993948 | − | 0.109848i | \(-0.0350365\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.9502 | − | 18.9502i | −0.828635 | − | 0.828635i | 0.158693 | − | 0.987328i | \(-0.449272\pi\) |
−0.987328 | + | 0.158693i | \(0.949272\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.53694 | + | 0.0177435i | 0.154365 | + | 0.000774388i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.86292i | − | 0.0811499i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.9252 | 1.08370 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.86121 | + | 5.86121i | 0.254355 | + | 0.254355i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.19512 | − | 8.19512i | −0.354970 | − | 0.354970i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.4149 | − | 27.7546i | −0.493508 | − | 1.19994i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.4178 | −1.05370 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.6988 | − | 11.6988i | 0.503903 | − | 0.503903i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.8366 | + | 22.8366i | 0.981822 | + | 0.981822i | 0.999838 | − | 0.0180153i | \(-0.00573475\pi\) |
−0.0180153 | + | 0.999838i | \(0.505735\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.24419i | 0.310878i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.3205 | − | 34.8195i | −0.613423 | − | 1.49150i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.00963023 | − | 0.00963023i | 0.000411759 | − | 0.000411759i | −0.706901 | − | 0.707313i | \(-0.749907\pi\) |
0.707313 | + | 0.706901i | \(0.249907\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0537432 | + | 0.0537432i | −0.00229371 | + | 0.00229371i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 15.0749i | − | 0.642214i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.19718 | −0.221006 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.7450 | + | 10.3225i | 1.05037 | + | 0.438167i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.6660 | + | 25.6660i | −1.08750 | + | 1.08750i | −0.0917192 | + | 0.995785i | \(0.529236\pi\) |
−0.995785 | + | 0.0917192i | \(0.970764\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.28916 | −0.223707 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.623348 | 0.0263178 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.16719 | − | 6.16719i | 0.259916 | − | 0.259916i | −0.565104 | − | 0.825020i | \(-0.691164\pi\) |
0.825020 | + | 0.565104i | \(0.191164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.82515 | + | 16.3612i | −0.287136 | + | 0.688319i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.707398 | −0.0297079 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 4.05892i | − | 0.170159i | −0.996374 | − | 0.0850794i | \(-0.972886\pi\) | ||
0.996374 | − | 0.0850794i | \(-0.0271144\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9113 | − | 12.9113i | 0.540323 | − | 0.540323i | −0.383301 | − | 0.923624i | \(-0.625213\pi\) |
0.923624 | + | 0.383301i | \(0.125213\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.5893 | + | 12.5893i | −0.525925 | + | 0.525925i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.3527 | + | 24.5983i | 1.01558 | + | 1.02582i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.4193i | 0.433761i | 0.976198 | + | 0.216880i | \(0.0695882\pi\) | ||||
−0.976198 | + | 0.216880i | \(0.930412\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.1780 | − | 12.1780i | −0.506099 | − | 0.506099i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.81236 | − | 4.81236i | 0.199650 | − | 0.199650i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.29274 | 0.219203 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.64706 | + | 11.2991i | 0.192132 | + | 0.467160i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.7728 | + | 27.7728i | 1.14631 | + | 1.14631i | 0.987273 | + | 0.159033i | \(0.0508376\pi\) |
0.159033 | + | 0.987273i | \(0.449162\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.7049 | − | 11.7049i | −0.482291 | − | 0.482291i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.2502 | 0.586175 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.4466i | − | 1.04496i | −0.852650 | − | 0.522482i | \(-0.825006\pi\) | ||
0.852650 | − | 0.522482i | \(-0.174994\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.149132 | − | 0.357497i | 0.00611380 | − | 0.0146559i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.06006 | − | 4.06006i | −0.166167 | − | 0.166167i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.32051i | 0.0539544i | 0.999636 | + | 0.0269772i | \(0.00858816\pi\) | ||||
−0.999636 | + | 0.0269772i | \(0.991412\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.8236i | 0.971787i | 0.874018 | + | 0.485893i | \(0.161506\pi\) | ||||
−0.874018 | + | 0.485893i | \(0.838494\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.85550 | − | 7.85550i | −0.319901 | − | 0.319901i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.89165 | + | 9.32902i | −0.158218 | + | 0.379279i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.20300i | 0.0488283i | 0.999702 | + | 0.0244141i | \(0.00777203\pi\) | ||||
−0.999702 | + | 0.0244141i | \(0.992228\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.90083 | 0.198592 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.2830 | + | 17.2830i | 0.699193 | + | 0.699193i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.84340 | + | 4.84340i | 0.195623 | + | 0.195623i | 0.798121 | − | 0.602498i | \(-0.205828\pi\) |
−0.602498 | + | 0.798121i | \(0.705828\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.80411 | + | 4.38659i | 0.0727486 | + | 0.176884i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.9719 | 1.08585 | 0.542924 | − | 0.839782i | \(-0.317317\pi\) | ||||
0.542924 | + | 0.839782i | \(0.317317\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.9202 | + | 19.9202i | −0.800660 | + | 0.800660i | −0.983199 | − | 0.182539i | \(-0.941568\pi\) |
0.182539 | + | 0.983199i | \(0.441568\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.89516 | − | 4.89516i | −0.196436 | − | 0.196436i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.17513i | − | 0.0871446i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.250824 | + | 24.9987i | −0.0100330 | + | 0.999950i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.91656 | − | 3.91656i | 0.156412 | − | 0.156412i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.07628 | − | 2.07628i | 0.0827868 | − | 0.0827868i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 12.7975i | − | 0.509462i | −0.967012 | − | 0.254731i | \(-0.918013\pi\) | ||
0.967012 | − | 0.254731i | \(-0.0819870\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.7648 | 0.547101 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.7413 | + | 40.1321i | −0.664360 | + | 1.59260i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.1110 | − | 25.1110i | 0.994934 | − | 0.994934i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.08595 | −0.0825190 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.9406 | 0.432129 | 0.216064 | − | 0.976379i | \(-0.430678\pi\) | ||||
0.216064 | + | 0.976379i | \(0.430678\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.2613 | + | 18.2613i | −0.720157 | + | 0.720157i | −0.968637 | − | 0.248480i | \(-0.920069\pi\) |
0.248480 | + | 0.968637i | \(0.420069\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.99775 | + | 0.833371i | 0.0786612 | + | 0.0328140i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.5055 | 0.413014 | 0.206507 | − | 0.978445i | \(-0.433790\pi\) | ||||
0.206507 | + | 0.978445i | \(0.433790\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 21.0995i | − | 0.828228i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.80523 | − | 3.80523i | 0.149139 | − | 0.149139i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.1836 | − | 11.1836i | 0.437648 | − | 0.437648i | −0.453572 | − | 0.891220i | \(-0.649850\pi\) |
0.891220 | + | 0.453572i | \(0.149850\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.425857 | + | 1.03545i | 0.0166396 | + | 0.0404583i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 9.69951i | − | 0.378414i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.60687 | − | 2.60687i | −0.101549 | − | 0.101549i | 0.654507 | − | 0.756056i | \(-0.272876\pi\) |
−0.756056 | + | 0.654507i | \(0.772876\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.9084 | + | 15.9084i | −0.618766 | + | 0.618766i | −0.945215 | − | 0.326449i | \(-0.894148\pi\) |
0.326449 | + | 0.945215i | \(0.394148\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.33799 | 0.0519634 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.30918 | − | 3.18319i | −0.0507677 | − | 0.123439i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.9135 | + | 33.9135i | 1.31314 | + | 1.31314i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.6297 | − | 15.6297i | −0.604278 | − | 0.604278i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.193468 | 0.00746874 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.1091i | 1.04498i | 0.852645 | + | 0.522490i | \(0.174997\pi\) | ||||
−0.852645 | + | 0.522490i | \(0.825003\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.0250827 | − | 4.99994i | 0.000965434 | − | 0.192448i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.0637 | − | 11.0637i | −0.425211 | − | 0.425211i | 0.461782 | − | 0.886993i | \(-0.347210\pi\) |
−0.886993 | + | 0.461782i | \(0.847210\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 0.989807i | − | 0.0379853i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.57152i | 0.290141i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.4289 | − | 17.4289i | −0.666898 | − | 0.666898i | 0.290098 | − | 0.956997i | \(-0.406312\pi\) |
−0.956997 | + | 0.290098i | \(0.906312\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.0657 | − | 6.28474i | −0.575631 | − | 0.240128i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 25.8827i | − | 0.987487i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.3607 | 0.432807 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.0352 | − | 26.0352i | −0.990426 | − | 0.990426i | 0.00952887 | − | 0.999955i | \(-0.496967\pi\) |
−0.999955 | + | 0.00952887i | \(0.996967\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.27326 | + | 1.27326i | 0.0483673 | + | 0.0483673i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.8978 | − | 10.6512i | 0.982359 | − | 0.404023i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.519443 | 0.0196753 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.52387 | + | 8.52387i | −0.322402 | + | 0.322402i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.08057 | − | 2.08057i | −0.0785822 | − | 0.0785822i | 0.666723 | − | 0.745305i | \(-0.267696\pi\) |
−0.745305 | + | 0.666723i | \(0.767696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 26.0910i | − | 0.984039i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.80474 | − | 9.25102i | −0.143295 | − | 0.348414i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.34137 | + | 8.34137i | −0.313709 | + | 0.313709i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.27484 | − | 3.27484i | 0.122989 | − | 0.122989i | −0.642933 | − | 0.765922i | \(-0.722283\pi\) |
0.765922 | + | 0.642933i | \(0.222283\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.34690i | 0.275530i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 52.6641 | 1.97229 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.9732 | − | 28.7019i | 0.447771 | − | 1.07339i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.7419 | + | 19.7419i | −0.737275 | + | 0.737275i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.03220 | −0.0757882 | −0.0378941 | − | 0.999282i | \(-0.512065\pi\) | ||||
−0.0378941 | + | 0.999282i | \(0.512065\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.62164 | 0.0603930 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.69568 | − | 9.69568i | 0.360586 | − | 0.360586i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.173772 | + | 34.6394i | −0.00645375 | + | 1.28648i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.37077 | −0.236279 | −0.118139 | − | 0.992997i | \(-0.537693\pi\) | ||||
−0.118139 | + | 0.992997i | \(0.537693\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.167625 | − | 0.167625i | 0.00619984 | − | 0.00619984i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.95026 | + | 6.95026i | −0.256714 | + | 0.256714i | −0.823716 | − | 0.567002i | \(-0.808103\pi\) |
0.567002 | + | 0.823716i | \(0.308103\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.4411 | + | 5.52804i | −0.495784 | + | 0.203905i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.2787i | 1.04166i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.0483355 | − | 0.0483355i | −0.00177805 | − | 0.00177805i | 0.706217 | − | 0.707995i | \(-0.250400\pi\) |
−0.707995 | + | 0.706217i | \(0.750400\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.40674 | − | 8.40674i | 0.308829 | − | 0.308829i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.148848 | 0.00546069 | 0.00273035 | − | 0.999996i | \(-0.499131\pi\) | ||||
0.00273035 | + | 0.999996i | \(0.499131\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.8333 | + | 6.51188i | −0.580087 | + | 0.238577i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.80291 | − | 6.80291i | −0.248905 | − | 0.248905i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.71327 | − | 6.71327i | −0.245297 | − | 0.245297i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.69304 | 0.0617798 | 0.0308899 | − | 0.999523i | \(-0.490166\pi\) | ||||
0.0308899 | + | 0.999523i | \(0.490166\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 12.8294i | − | 0.467528i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.294034 | − | 0.704855i | 0.0107010 | − | 0.0256523i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.6876 | − | 26.6876i | −0.969977 | − | 0.969977i | 0.0295851 | − | 0.999562i | \(-0.490581\pi\) |
−0.999562 | + | 0.0295851i | \(0.990581\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17.6219i | 0.639633i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 17.1363i | − | 0.621189i | −0.950542 | − | 0.310595i | \(-0.899472\pi\) | ||
0.950542 | − | 0.310595i | \(-0.100528\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.42212 | − | 8.42212i | −0.304901 | − | 0.304901i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.505369 | − | 0.210817i | −0.0182716 | − | 0.00762211i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 45.2893i | − | 1.63530i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.6406 | −0.924622 | −0.462311 | − | 0.886718i | \(-0.652980\pi\) | ||||
−0.462311 | + | 0.886718i | \(0.652980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.52954 | − | 6.52954i | −0.235156 | − | 0.235156i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.4452 | + | 27.4452i | 0.987137 | + | 0.987137i | 0.999918 | − | 0.0127818i | \(-0.00406868\pi\) |
−0.0127818 | + | 0.999918i | \(0.504069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.7607 | + | 27.0306i | 0.961274 | + | 0.970967i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.48212 | 0.304294 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.26371 | − | 3.26371i | 0.116934 | − | 0.116934i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.75456 | + | 3.75456i | 0.134349 | + | 0.134349i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 6.92797i | − | 0.247586i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.37792 | − | 3.44565i | 0.299021 | − | 0.122981i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.65912 | + | 9.65912i | −0.344310 | + | 0.344310i | −0.857985 | − | 0.513675i | \(-0.828284\pi\) |
0.513675 | + | 0.857985i | \(0.328284\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.1180 | + | 13.1180i | −0.467012 | + | 0.467012i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.60829i | 0.199408i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.415271 | 0.0147467 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.29099 | − | 1.79001i | −0.152186 | − | 0.0634851i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.9978 | + | 11.9978i | −0.424984 | + | 0.424984i | −0.886916 | − | 0.461931i | \(-0.847157\pi\) |
0.461931 | + | 0.886916i | \(0.347157\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.09547 | −0.0387549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.07483 | −0.108644 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.4584 | + | 17.4584i | −0.616094 | + | 0.616094i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.1063 | + | 4.21590i | 0.356201 | + | 0.148591i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.3614 | −0.716756 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 36.2916i | − | 1.27594i | −0.770060 | − | 0.637972i | \(-0.779774\pi\) | ||
0.770060 | − | 0.637972i | \(-0.220226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.0781 | + | 17.0781i | −0.599693 | + | 0.599693i | −0.940231 | − | 0.340538i | \(-0.889391\pi\) |
0.340538 | + | 0.940231i | \(0.389391\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.6453 | − | 13.6453i | 0.478563 | − | 0.478563i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.3784 | − | 7.14735i | 0.608738 | − | 0.250361i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.10641i | − | 0.0736939i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.73301 | + | 2.73301i | 0.0954992 | + | 0.0954992i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.9249 | + | 21.9249i | −0.765183 | + | 0.765183i | −0.977254 | − | 0.212071i | \(-0.931979\pi\) |
0.212071 | + | 0.977254i | \(0.431979\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.38382 | −0.152810 | −0.0764052 | − | 0.997077i | \(-0.524344\pi\) | ||||
−0.0764052 | + | 0.997077i | \(0.524344\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.04467 | + | 8.95438i | −0.314895 | + | 0.311751i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.5889 | − | 21.5889i | −0.750718 | − | 0.750718i | 0.223895 | − | 0.974613i | \(-0.428123\pi\) |
−0.974613 | + | 0.223895i | \(0.928123\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.88066 | − | 7.88066i | −0.273707 | − | 0.273707i | 0.556884 | − | 0.830590i | \(-0.311997\pi\) |
−0.830590 | + | 0.556884i | \(0.811997\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.98183 | −0.172818 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.59165i | 0.0551473i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.8401 | + | 12.4480i | 1.03266 | + | 0.430779i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.37920 | − | 5.37920i | −0.185932 | − | 0.185932i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 6.03706i | − | 0.208423i | −0.994555 | − | 0.104211i | \(-0.966768\pi\) | ||
0.994555 | − | 0.104211i | \(-0.0332318\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.9968i | 0.655063i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.6529 | + | 20.6529i | 0.711324 | + | 0.711324i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.5084 | − | 34.7794i | 0.499105 | − | 1.19645i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.19781i | 0.109878i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.9198 | 0.477727 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 58.6959 | + | 58.6959i | 2.01207 | + | 2.01207i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.6685 | + | 12.6685i | 0.433763 | + | 0.433763i | 0.889906 | − | 0.456144i | \(-0.150770\pi\) |
−0.456144 | + | 0.889906i | \(0.650770\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.49986 | + | 1.85069i | −0.153892 | + | 0.0632924i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.79580 | 0.163821 | 0.0819106 | − | 0.996640i | \(-0.473898\pi\) | ||||
0.0819106 | + | 0.996640i | \(0.473898\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.0244 | − | 34.0244i | 1.16090 | − | 1.16090i | 0.176616 | − | 0.984280i | \(-0.443485\pi\) |
0.984280 | − | 0.176616i | \(-0.0565152\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.06102 | + | 1.06102i | 0.0361596 | + | 0.0361596i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.20297i | 0.279232i | 0.990206 | + | 0.139616i | \(0.0445869\pi\) | ||||
−0.990206 | + | 0.139616i | \(0.955413\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.4513 | − | 7.99990i | 0.661365 | − | 0.272005i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.9784 | − | 11.9784i | 0.406808 | − | 0.406808i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.2239 | − | 13.2239i | 0.448590 | − | 0.448590i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60.6991i | 2.05671i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.39922 | −0.0473565 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.97155 | + | 7.32948i | 0.100457 | + | 0.247782i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.9525 | − | 23.9525i | 0.808817 | − | 0.808817i | −0.175638 | − | 0.984455i | \(-0.556199\pi\) |
0.984455 | + | 0.175638i | \(0.0561987\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.7214 | −0.563999 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.4850 | 0.925993 | 0.462997 | − | 0.886360i | \(-0.346774\pi\) | ||||
0.462997 | + | 0.886360i | \(0.346774\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.9566 | − | 22.9566i | 0.772550 | − | 0.772550i | −0.206001 | − | 0.978552i | \(-0.566045\pi\) |
0.978552 | + | 0.206001i | \(0.0660452\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.13588 | + | 17.1061i | −0.239870 | + | 0.575014i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.52038 | 0.286086 | 0.143043 | − | 0.989716i | \(-0.454311\pi\) | ||||
0.143043 | + | 0.989716i | \(0.454311\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.7565i | 0.461379i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.79993 | − | 1.79993i | 0.0602998 | − | 0.0602998i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.88294 | + | 6.88294i | −0.230329 | + | 0.230329i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.7678 | − | 50.4958i | −0.694192 | − | 1.68789i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 37.8247i | 1.26293i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.2670 | + | 37.2670i | 1.24292 | + | 1.24292i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.360044 | + | 0.360044i | −0.0119948 | + | 0.0119948i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.684789 | 0.0227883 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.9810 | + | 6.16134i | −0.497984 | + | 0.204810i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.1812 | + | 21.1812i | 0.703312 | + | 0.703312i | 0.965120 | − | 0.261808i | \(-0.0843188\pi\) |
−0.261808 | + | 0.965120i | \(0.584319\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.7916 | + | 11.7916i | 0.391104 | + | 0.391104i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.3002 | −0.407525 | −0.203763 | − | 0.979020i | \(-0.565317\pi\) | ||||
−0.203763 | + | 0.979020i | \(0.565317\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.4895i | 0.810484i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.156851 | − | 0.0654311i | −0.00518532 | − | 0.00216308i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.250454 | + | 0.250454i | 0.00827070 | + | 0.00827070i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.59430i | − | 0.118565i | −0.998241 | − | 0.0592826i | \(-0.981119\pi\) | ||
0.998241 | − | 0.0592826i | \(-0.0188813\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.5087i | 0.774638i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.05902 | + | 8.05902i | 0.265266 | + | 0.265266i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.300757 | + | 59.9522i | −0.00988882 | + | 1.97122i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2.29240i | − | 0.0752923i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.8527 | −1.17629 | −0.588145 | − | 0.808756i | \(-0.700142\pi\) | ||||
−0.588145 | + | 0.808756i | \(0.700142\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.0005 | + | 10.0005i | 0.327752 | + | 0.327752i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.76298 | + | 9.76298i | 0.319626 | + | 0.319626i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.530171 | + | 1.28908i | 0.0173385 | + | 0.0421575i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.7563 | 1.33145 | 0.665725 | − | 0.746198i | \(-0.268123\pi\) | ||||
0.665725 | + | 0.746198i | \(0.268123\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.23528 | + | 5.23528i | −0.170847 | + | 0.170847i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.2143 | − | 36.2143i | −1.18055 | − | 1.18055i | −0.979602 | − | 0.200950i | \(-0.935597\pi\) |
−0.200950 | − | 0.979602i | \(-0.564403\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.6845i | 0.478193i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.601657 | − | 1.46290i | −0.0195719 | − | 0.0475880i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.5242 | − | 36.5242i | 1.18688 | − | 1.18688i | 0.208951 | − | 0.977926i | \(-0.432995\pi\) |
0.977926 | − | 0.208951i | \(-0.0670050\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.4738 | + | 37.4738i | −1.21645 | + | 1.21645i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.55566i | 0.0828729i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.0927 | −0.521294 | −0.260647 | − | 0.965434i | \(-0.583936\pi\) | ||||
−0.260647 | + | 0.965434i | \(0.583936\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.7421 | − | 15.3272i | −1.18895 | − | 0.495975i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.4699 | + | 12.4699i | −0.403093 | + | 0.403093i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.16423 | −0.166762 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.8716 | 0.866826 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.49009 | + | 9.49009i | −0.305814 | + | 0.305814i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.8264 | − | 35.5416i | 0.477278 | − | 1.14413i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.3561 | 0.686767 | 0.343384 | − | 0.939195i | \(-0.388427\pi\) | ||||
0.343384 | + | 0.939195i | \(0.388427\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.532856i | 0.0171178i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0626 | − | 20.0626i | 0.643839 | − | 0.643839i | −0.307658 | − | 0.951497i | \(-0.599545\pi\) |
0.951497 | + | 0.307658i | \(0.0995454\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.26414 | − | 6.26414i | 0.200819 | − | 0.200819i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −19.4140 | + | 19.2202i | −0.621747 | + | 0.615540i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.7769i | 0.888661i | 0.895863 | + | 0.444331i | \(0.146558\pi\) | ||||
−0.895863 | + | 0.444331i | \(0.853442\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.53447 | + | 5.53447i | 0.176882 | + | 0.176882i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.9058 | + | 11.9058i | −0.380122 | + | 0.380122i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.428090 | −0.0136540 | −0.00682698 | − | 0.999977i | \(-0.502173\pi\) | ||||
−0.00682698 | + | 0.999977i | \(0.502173\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.1201 | + | 29.4694i | 0.386179 | + | 0.938973i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.23763 | − | 2.23763i | −0.0712245 | − | 0.0712245i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.73871 | + | 4.73871i | 0.150682 | + | 0.150682i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.82267 | −0.184963 | −0.0924816 | − | 0.995714i | \(-0.529480\pi\) | ||||
−0.0924816 | + | 0.995714i | \(0.529480\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.24078i | − | 0.261513i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.94303 | − | 11.8494i | 0.156704 | − | 0.375650i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.1044 | + | 20.1044i | 0.636713 | + | 0.636713i | 0.949743 | − | 0.313030i | \(-0.101344\pi\) |
−0.313030 | + | 0.949743i | \(0.601344\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 11.9906i | − | 0.379366i |
(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 | 1920.2.bl.a.289.18 | 48 | ||
4.3 | odd | 2 | 1920.2.bl.b.289.7 | 48 | |||
5.4 | even | 2 | inner | 1920.2.bl.a.289.7 | 48 | ||
8.3 | odd | 2 | 960.2.bl.a.529.15 | 48 | |||
8.5 | even | 2 | 240.2.bl.a.109.5 | ✓ | 48 | ||
16.3 | odd | 4 | 960.2.bl.a.49.9 | 48 | |||
16.5 | even | 4 | inner | 1920.2.bl.a.1249.7 | 48 | ||
16.11 | odd | 4 | 1920.2.bl.b.1249.18 | 48 | |||
16.13 | even | 4 | 240.2.bl.a.229.20 | yes | 48 | ||
20.19 | odd | 2 | 1920.2.bl.b.289.18 | 48 | |||
24.5 | odd | 2 | 720.2.bm.h.109.20 | 48 | |||
40.19 | odd | 2 | 960.2.bl.a.529.9 | 48 | |||
40.29 | even | 2 | 240.2.bl.a.109.20 | yes | 48 | ||
48.29 | odd | 4 | 720.2.bm.h.469.5 | 48 | |||
80.19 | odd | 4 | 960.2.bl.a.49.15 | 48 | |||
80.29 | even | 4 | 240.2.bl.a.229.5 | yes | 48 | ||
80.59 | odd | 4 | 1920.2.bl.b.1249.7 | 48 | |||
80.69 | even | 4 | inner | 1920.2.bl.a.1249.18 | 48 | ||
120.29 | odd | 2 | 720.2.bm.h.109.5 | 48 | |||
240.29 | odd | 4 | 720.2.bm.h.469.20 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.bl.a.109.5 | ✓ | 48 | 8.5 | even | 2 | ||
240.2.bl.a.109.20 | yes | 48 | 40.29 | even | 2 | ||
240.2.bl.a.229.5 | yes | 48 | 80.29 | even | 4 | ||
240.2.bl.a.229.20 | yes | 48 | 16.13 | even | 4 | ||
720.2.bm.h.109.5 | 48 | 120.29 | odd | 2 | |||
720.2.bm.h.109.20 | 48 | 24.5 | odd | 2 | |||
720.2.bm.h.469.5 | 48 | 48.29 | odd | 4 | |||
720.2.bm.h.469.20 | 48 | 240.29 | odd | 4 | |||
960.2.bl.a.49.9 | 48 | 16.3 | odd | 4 | |||
960.2.bl.a.49.15 | 48 | 80.19 | odd | 4 | |||
960.2.bl.a.529.9 | 48 | 40.19 | odd | 2 | |||
960.2.bl.a.529.15 | 48 | 8.3 | odd | 2 | |||
1920.2.bl.a.289.7 | 48 | 5.4 | even | 2 | inner | ||
1920.2.bl.a.289.18 | 48 | 1.1 | even | 1 | trivial | ||
1920.2.bl.a.1249.7 | 48 | 16.5 | even | 4 | inner | ||
1920.2.bl.a.1249.18 | 48 | 80.69 | even | 4 | inner | ||
1920.2.bl.b.289.7 | 48 | 4.3 | odd | 2 | |||
1920.2.bl.b.289.18 | 48 | 20.19 | odd | 2 | |||
1920.2.bl.b.1249.7 | 48 | 80.59 | odd | 4 | |||
1920.2.bl.b.1249.18 | 48 | 16.11 | odd | 4 |