Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5040,2,Mod(881,5040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5040.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5040.f (of order \(2\), degree \(1\), 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: | \(40.2446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.7442857984.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.3 | ||
Root | \(3.73923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5040.881 |
Dual form | 5040.2.f.i.881.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5040\mathbb{Z}\right)^\times\).
\(n\) | \(2017\) | \(2801\) | \(3151\) | \(3601\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0951965 | − | 2.64404i | −0.0359809 | − | 0.999352i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.28808i | − | 1.59441i | −0.603705 | − | 0.797207i | \(-0.706310\pi\) | ||
0.603705 | − | 0.797207i | \(-0.293690\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.19039i | − | 0.607506i | −0.952751 | − | 0.303753i | \(-0.901760\pi\) | ||
0.952751 | − | 0.303753i | \(-0.0982397\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.04544 | −0.253555 | −0.126778 | − | 0.991931i | \(-0.540463\pi\) | ||||
−0.126778 | + | 0.991931i | \(0.540463\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.43303i | 1.47584i | 0.674889 | + | 0.737920i | \(0.264192\pi\) | ||||
−0.674889 | + | 0.737920i | \(0.735808\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.47847i | − | 1.55937i | −0.626173 | − | 0.779684i | \(-0.715380\pi\) | ||
0.626173 | − | 0.779684i | \(-0.284620\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.47847i | 1.38872i | 0.719629 | + | 0.694358i | \(0.244312\pi\) | ||||
−0.719629 | + | 0.694358i | \(0.755688\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.09768i | − | 1.63399i | −0.576643 | − | 0.816996i | \(-0.695638\pi\) | ||
0.576643 | − | 0.816996i | \(-0.304362\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0951965 | − | 2.64404i | −0.0160911 | − | 0.446924i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.855043 | −0.140568 | −0.0702841 | − | 0.997527i | \(-0.522391\pi\) | ||||
−0.0702841 | + | 0.997527i | \(0.522391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.19039 | 0.342082 | 0.171041 | − | 0.985264i | \(-0.445287\pi\) | ||||
0.171041 | + | 0.985264i | \(0.445287\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.954564 | 0.145570 | 0.0727849 | − | 0.997348i | \(-0.476811\pi\) | ||||
0.0727849 | + | 0.997348i | \(0.476811\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.0092 | 1.60585 | 0.802927 | − | 0.596077i | \(-0.203275\pi\) | ||||
0.802927 | + | 0.596077i | \(0.203275\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.98188 | + | 0.503406i | −0.997411 | + | 0.0719152i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.09768i | − | 0.425500i | −0.977107 | − | 0.212750i | \(-0.931758\pi\) | ||
0.977107 | − | 0.212750i | \(-0.0682419\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.28808i | − | 0.713044i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.7734 | −1.79314 | −0.896569 | − | 0.442904i | \(-0.853948\pi\) | ||||
−0.896569 | + | 0.442904i | \(0.853948\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.05225i | − | 1.03098i | −0.856894 | − | 0.515492i | \(-0.827609\pi\) | ||
0.856894 | − | 0.515492i | \(-0.172391\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.19039i | − | 0.271685i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.33535 | −0.651817 | −0.325908 | − | 0.945401i | \(-0.605670\pi\) | ||||
−0.325908 | + | 0.945401i | \(0.605670\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.43303i | 0.763461i | 0.924274 | + | 0.381730i | \(0.124672\pi\) | ||||
−0.924274 | + | 0.381730i | \(0.875328\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.57615i | − | 0.535598i | −0.963475 | − | 0.267799i | \(-0.913704\pi\) | ||
0.963475 | − | 0.267799i | \(-0.0862963\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.9819 | + | 0.503406i | −1.59338 | + | 0.0573684i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.6738 | −1.76344 | −0.881722 | − | 0.471769i | \(-0.843616\pi\) | ||||
−0.881722 | + | 0.471769i | \(0.843616\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.38079 | 0.480854 | 0.240427 | − | 0.970667i | \(-0.422713\pi\) | ||||
0.240427 | + | 0.970667i | \(0.422713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.04544 | −0.113393 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.28126 | 0.453813 | 0.226907 | − | 0.973917i | \(-0.427139\pi\) | ||||
0.226907 | + | 0.973917i | \(0.427139\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.79148 | + | 0.208518i | −0.607112 | + | 0.0218586i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.43303i | 0.660015i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.8593i | 1.20412i | 0.798449 | + | 0.602062i | \(0.205654\pi\) | ||||
−0.798449 | + | 0.602062i | \(0.794346\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5830 | 1.15255 | 0.576274 | − | 0.817257i | \(-0.304506\pi\) | ||||
0.576274 | + | 0.817257i | \(0.304506\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.6757i | 1.64310i | 0.570134 | + | 0.821552i | \(0.306891\pi\) | ||||
−0.570134 | + | 0.821552i | \(0.693109\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 7.00681i | − | 0.677374i | −0.940899 | − | 0.338687i | \(-0.890017\pi\) | ||
0.940899 | − | 0.338687i | \(-0.109983\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.28991 | −0.410899 | −0.205450 | − | 0.978668i | \(-0.565866\pi\) | ||||
−0.205450 | + | 0.978668i | \(0.565866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.09087i | − | 0.761125i | −0.924755 | − | 0.380563i | \(-0.875730\pi\) | ||
0.924755 | − | 0.380563i | \(-0.124270\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 7.47847i | − | 0.697371i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0995218 | + | 2.76417i | 0.00912314 | + | 0.253391i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.9638 | −1.54216 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.57118 | −0.760569 | −0.380285 | − | 0.924870i | \(-0.624174\pi\) | ||||
−0.380285 | + | 0.924870i | \(0.624174\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.90048 | −0.515527 | −0.257764 | − | 0.966208i | \(-0.582986\pi\) | ||||
−0.257764 | + | 0.966208i | \(0.582986\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.0092 | − | 0.612402i | 1.47488 | − | 0.0531020i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.86607i | − | 0.586608i | −0.956019 | − | 0.293304i | \(-0.905245\pi\) | ||
0.956019 | − | 0.293304i | \(-0.0947548\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.9115i | 1.17996i | 0.807418 | + | 0.589979i | \(0.200864\pi\) | ||||
−0.807418 | + | 0.589979i | \(0.799136\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.5830 | −0.968616 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.47847i | 0.621053i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 15.9638i | − | 1.30780i | −0.756580 | − | 0.653901i | \(-0.773131\pi\) | ||
0.756580 | − | 0.653901i | \(-0.226869\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0546 | −1.30651 | −0.653253 | − | 0.757139i | \(-0.726596\pi\) | ||||
−0.653253 | + | 0.757139i | \(0.726596\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 9.09768i | − | 0.730744i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.7665i | 1.97659i | 0.152569 | + | 0.988293i | \(0.451245\pi\) | ||||
−0.152569 | + | 0.988293i | \(0.548755\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.7734 | + | 0.711924i | −1.55836 | + | 0.0561075i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.42622 | −0.581667 | −0.290833 | − | 0.956774i | \(-0.593932\pi\) | ||||
−0.290833 | + | 0.956774i | \(0.593932\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.573779 | −0.0444003 | −0.0222002 | − | 0.999754i | \(-0.507067\pi\) | ||||
−0.0222002 | + | 0.999754i | \(0.507067\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.20218 | 0.630937 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.96375 | −0.757530 | −0.378765 | − | 0.925493i | \(-0.623651\pi\) | ||||
−0.378765 | + | 0.925493i | \(0.623651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0951965 | − | 2.64404i | −0.00719618 | − | 0.199870i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1.77336i | − | 0.132547i | −0.997801 | − | 0.0662735i | \(-0.978889\pi\) | ||
0.997801 | − | 0.0662735i | \(-0.0211110\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.0092i | − | 0.818306i | −0.912466 | − | 0.409153i | \(-0.865824\pi\) | ||
0.912466 | − | 0.409153i | \(-0.134176\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.855043 | −0.0628640 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.52834i | 0.404272i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.56697i | 0.402812i | 0.979508 | + | 0.201406i | \(0.0645510\pi\) | ||||
−0.979508 | + | 0.201406i | \(0.935449\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.47166 | −0.609803 | −0.304902 | − | 0.952384i | \(-0.598624\pi\) | ||||
−0.304902 | + | 0.952384i | \(0.598624\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.8661i | − | 0.916669i | −0.888780 | − | 0.458335i | \(-0.848446\pi\) | ||
0.888780 | − | 0.458335i | \(-0.151554\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 17.5830i | − | 1.24642i | −0.782053 | − | 0.623212i | \(-0.785828\pi\) | ||
0.782053 | − | 0.623212i | \(-0.214172\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.7734 | − | 0.711924i | 1.38782 | − | 0.0499673i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.19039 | 0.152984 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 34.0184 | 2.35310 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.954564 | 0.0651008 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.0546 | + | 0.866067i | −1.63293 | + | 0.0587925i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.28991i | 0.154036i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.8710i | 0.727979i | 0.931403 | + | 0.363989i | \(0.118586\pi\) | ||||
−0.931403 | + | 0.363989i | \(0.881414\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.0909 | 0.935244 | 0.467622 | − | 0.883929i | \(-0.345111\pi\) | ||||
0.467622 | + | 0.883929i | \(0.345111\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.5239i | − | 0.959767i | −0.877332 | − | 0.479883i | \(-0.840679\pi\) | ||
0.877332 | − | 0.479883i | \(-0.159321\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 20.6806i | − | 1.35483i | −0.735599 | − | 0.677417i | \(-0.763099\pi\) | ||
0.735599 | − | 0.677417i | \(-0.236901\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0092 | 0.718160 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.56697i | − | 0.360097i | −0.983658 | − | 0.180049i | \(-0.942375\pi\) | ||
0.983658 | − | 0.180049i | \(-0.0576255\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.3839i | − | 0.733303i | −0.930358 | − | 0.366651i | \(-0.880504\pi\) | ||
0.930358 | − | 0.366651i | \(-0.119496\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.98188 | + | 0.503406i | −0.446056 | + | 0.0321614i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.0909 | 0.896581 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.71874 | −0.108486 | −0.0542428 | − | 0.998528i | \(-0.517275\pi\) | ||||
−0.0542428 | + | 0.998528i | \(0.517275\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −39.5467 | −2.48628 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.18779 | 0.136471 | 0.0682354 | − | 0.997669i | \(-0.478263\pi\) | ||||
0.0682354 | + | 0.997669i | \(0.478263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0813970 | + | 2.26077i | 0.00505777 | + | 0.140477i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 17.3876i | − | 1.07217i | −0.844166 | − | 0.536083i | \(-0.819904\pi\) | ||
0.844166 | − | 0.536083i | \(-0.180096\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.09768i | − | 0.190289i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.3445 | 1.24043 | 0.620214 | − | 0.784433i | \(-0.287046\pi\) | ||||
0.620214 | + | 0.784433i | \(0.287046\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.47847i | 0.0898106i | 0.998991 | + | 0.0449053i | \(0.0142986\pi\) | ||||
−0.998991 | + | 0.0449053i | \(0.985701\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 5.28808i | − | 0.318883i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.7642 | 0.646756 | 0.323378 | − | 0.946270i | \(-0.395181\pi\) | ||||
0.323378 | + | 0.946270i | \(0.395181\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.42806i | 0.144846i | 0.997374 | + | 0.0724230i | \(0.0230731\pi\) | ||||
−0.997374 | + | 0.0724230i | \(0.976927\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 24.5898i | − | 1.46171i | −0.682532 | − | 0.730855i | \(-0.739121\pi\) | ||
0.682532 | − | 0.730855i | \(-0.260879\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.208518 | − | 5.79148i | −0.0123084 | − | 0.341860i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9071 | −0.935710 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.6707 | 0.740230 | 0.370115 | − | 0.928986i | \(-0.379318\pi\) | ||||
0.370115 | + | 0.928986i | \(0.379318\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.7734 | −0.801916 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.3808 | −0.947325 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0908711 | − | 2.52390i | −0.00523773 | − | 0.145475i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8.05225i | − | 0.461070i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.866067i | 0.0494291i | 0.999695 | + | 0.0247145i | \(0.00786768\pi\) | ||||
−0.999695 | + | 0.0247145i | \(0.992132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.71009 | 0.550608 | 0.275304 | − | 0.961357i | \(-0.411221\pi\) | ||||
0.275304 | + | 0.961357i | \(0.411221\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5.80096i | − | 0.327889i | −0.986470 | − | 0.163945i | \(-0.947578\pi\) | ||
0.986470 | − | 0.163945i | \(-0.0524219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.1591i | 1.58157i | 0.612092 | + | 0.790787i | \(0.290328\pi\) | ||||
−0.612092 | + | 0.790787i | \(0.709672\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.5467 | 2.21419 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.72532i | − | 0.374207i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.19039i | − | 0.121501i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.04804 | − | 29.1087i | −0.0577801 | − | 1.60482i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.5830 | 1.07638 | 0.538189 | − | 0.842824i | \(-0.319109\pi\) | ||||
0.538189 | + | 0.842824i | \(0.319109\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.33535 | −0.291501 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.3992 | −1.54700 | −0.773500 | − | 0.633796i | \(-0.781496\pi\) | ||||
−0.773500 | + | 0.633796i | \(0.781496\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −48.1092 | −2.60526 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.99567 | + | 18.4124i | 0.107756 | + | 0.994177i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.5898i | 0.675855i | 0.941172 | + | 0.337927i | \(0.109726\pi\) | ||||
−0.941172 | + | 0.337927i | \(0.890274\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.9956i | 1.12387i | 0.827183 | + | 0.561933i | \(0.189942\pi\) | ||||
−0.827183 | + | 0.561933i | \(0.810058\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.1363 | −0.805624 | −0.402812 | − | 0.915283i | \(-0.631967\pi\) | ||||
−0.402812 | + | 0.915283i | \(0.631967\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.43303i | 0.341430i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 33.1909i | − | 1.75175i | −0.482538 | − | 0.875875i | \(-0.660285\pi\) | ||
0.482538 | − | 0.875875i | \(-0.339715\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.3839 | −1.17810 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 4.57615i | − | 0.239527i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 11.6825i | − | 0.609821i | −0.952381 | − | 0.304910i | \(-0.901373\pi\) | ||
0.952381 | − | 0.304910i | \(-0.0986265\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.19039 | + | 0.294888i | −0.425224 | + | 0.0153098i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.8550 | 0.665609 | 0.332804 | − | 0.942996i | \(-0.392005\pi\) | ||||
0.332804 | + | 0.942996i | \(0.392005\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.3808 | 0.843653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0751 | −1.28802 | −0.644010 | − | 0.765017i | \(-0.722730\pi\) | ||||
−0.644010 | + | 0.765017i | \(0.722730\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.0092 | 1.17571 | 0.587857 | − | 0.808965i | \(-0.299972\pi\) | ||||
0.587857 | + | 0.808965i | \(0.299972\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.9819 | + | 0.503406i | −0.712582 | + | 0.0256560i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.1591i | 0.515088i | 0.966267 | + | 0.257544i | \(0.0829132\pi\) | ||||
−0.966267 | + | 0.257544i | \(0.917087\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.81826i | 0.395386i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.6738 | −0.788636 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.9141i | 0.698329i | 0.937061 | + | 0.349164i | \(0.113535\pi\) | ||||
−0.937061 | + | 0.349164i | \(0.886465\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 14.6197i | − | 0.730075i | −0.930993 | − | 0.365038i | \(-0.881056\pi\) | ||
0.930993 | − | 0.365038i | \(-0.118944\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.9275 | −0.992660 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.52153i | 0.224124i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0000i | 0.593362i | 0.954977 | + | 0.296681i | \(0.0958798\pi\) | ||||
−0.954977 | + | 0.296681i | \(0.904120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.31117 | + | 36.4173i | 0.0645187 | + | 1.79198i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.38079 | 0.215044 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.60743 | −0.127381 | −0.0636906 | − | 0.997970i | \(-0.520287\pi\) | ||||
−0.0636906 | + | 0.997970i | \(0.520287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.852443 | 0.0415455 | 0.0207728 | − | 0.999784i | \(-0.493387\pi\) | ||||
0.0207728 | + | 0.999784i | \(0.493387\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.04544 | −0.0507111 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.2905 | + | 0.766545i | −1.03032 | + | 0.0370957i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.2476i | − | 0.975293i | −0.873041 | − | 0.487647i | \(-0.837855\pi\) | ||
0.873041 | − | 0.487647i | \(-0.162145\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 30.6444i | − | 1.47268i | −0.676614 | − | 0.736338i | \(-0.736553\pi\) | ||
0.676614 | − | 0.736338i | \(-0.263447\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 48.1092 | 2.30138 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 22.6308i | − | 1.08011i | −0.841630 | − | 0.540054i | \(-0.818404\pi\) | ||
0.841630 | − | 0.540054i | \(-0.181596\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.3083i | 1.72506i | 0.506007 | + | 0.862529i | \(0.331121\pi\) | ||||
−0.506007 | + | 0.862529i | \(0.668879\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.28126 | 0.202951 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.6764i | 1.21175i | 0.795561 | + | 0.605873i | \(0.207176\pi\) | ||||
−0.795561 | + | 0.605873i | \(0.792824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 11.5830i | − | 0.545421i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.79148 | + | 0.208518i | −0.271509 | + | 0.00977546i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.3477 | 1.18571 | 0.592857 | − | 0.805308i | \(-0.298000\pi\) | ||||
0.592857 | + | 0.805308i | \(0.298000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.7253 | −0.592677 | −0.296339 | − | 0.955083i | \(-0.595766\pi\) | ||||
−0.296339 | + | 0.955083i | \(0.595766\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.2655 | 0.988289 | 0.494145 | − | 0.869380i | \(-0.335481\pi\) | ||||
0.494145 | + | 0.869380i | \(0.335481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.1424 | 0.608156 | 0.304078 | − | 0.952647i | \(-0.401652\pi\) | ||||
0.304078 | + | 0.952647i | \(0.401652\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.507906 | + | 14.1069i | 0.0234529 | + | 0.651395i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.04781i | − | 0.232099i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.43303i | 0.295168i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.2899 | 1.20122 | 0.600608 | − | 0.799543i | \(-0.294925\pi\) | ||||
0.600608 | + | 0.799543i | \(0.294925\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.87288i | 0.0853959i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.8593i | 0.538501i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.5381 | −1.79164 | −0.895820 | − | 0.444416i | \(-0.853411\pi\) | ||||
−0.895820 | + | 0.444416i | \(0.853411\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.62105i | 0.208545i | 0.994549 | + | 0.104273i | \(0.0332514\pi\) | ||||
−0.994549 | + | 0.104273i | \(0.966749\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.81826i | − | 0.352117i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.0092 | − | 0.612402i | 0.762966 | − | 0.0274700i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.0152 | −1.38843 | −0.694216 | − | 0.719766i | \(-0.744249\pi\) | ||||
−0.694216 | + | 0.719766i | \(0.744249\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.3385 | −1.26355 | −0.631775 | − | 0.775152i | \(-0.717673\pi\) | ||||
−0.631775 | + | 0.775152i | \(0.717673\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.5830 | 0.515435 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.3808 | −0.992011 | −0.496005 | − | 0.868319i | \(-0.665200\pi\) | ||||
−0.496005 | + | 0.868319i | \(0.665200\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0995 | + | 0.435633i | −0.535251 | + | 0.0192713i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.6757i | 0.734818i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 58.2174i | − | 2.56040i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.5896 | −1.25253 | −0.626265 | − | 0.779610i | \(-0.715417\pi\) | ||||
−0.626265 | + | 0.779610i | \(0.715417\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.51472i | − | 0.153688i | −0.997043 | − | 0.0768440i | \(-0.975516\pi\) | ||
0.997043 | − | 0.0768440i | \(-0.0244843\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.51104i | 0.414307i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −32.9275 | −1.43163 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.79782i | − | 0.207817i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 7.00681i | − | 0.302931i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.66205 | + | 36.9207i | 0.114663 | + | 1.59029i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.4900 | 1.31087 | 0.655434 | − | 0.755252i | \(-0.272486\pi\) | ||||
0.655434 | + | 0.755252i | \(0.272486\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.28991 | −0.183760 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.86369 | 0.293470 | 0.146735 | − | 0.989176i | \(-0.453123\pi\) | ||||
0.146735 | + | 0.989176i | \(0.453123\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −48.1092 | −2.04952 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.49209 | + | 41.4422i | 0.0634503 | + | 1.76230i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.81826i | − | 0.0770421i | −0.999258 | − | 0.0385210i | \(-0.987735\pi\) | ||
0.999258 | − | 0.0385210i | \(-0.0122647\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.09087i | − | 0.0884344i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.0184 | 1.43370 | 0.716852 | − | 0.697226i | \(-0.245582\pi\) | ||||
0.716852 | + | 0.697226i | \(0.245582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 8.09087i | − | 0.340386i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 5.10871i | − | 0.214168i | −0.994250 | − | 0.107084i | \(-0.965849\pi\) | ||
0.994250 | − | 0.107084i | \(-0.0341514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.8214 | −0.452861 | −0.226431 | − | 0.974027i | \(-0.572706\pi\) | ||||
−0.226431 | + | 0.974027i | \(0.572706\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 7.47847i | − | 0.311874i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 39.1523i | − | 1.62993i | −0.579509 | − | 0.814966i | \(-0.696756\pi\) | ||
0.579509 | − | 0.814966i | \(-0.303244\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.417035 | − | 11.5830i | −0.0173015 | − | 0.480542i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.3808 | −0.678423 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.52834 | 0.228179 | 0.114090 | − | 0.993470i | \(-0.463605\pi\) | ||||
0.114090 | + | 0.993470i | \(0.463605\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 58.5257 | 2.41151 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.6830 | 0.767220 | 0.383610 | − | 0.923495i | \(-0.374681\pi\) | ||||
0.383610 | + | 0.923495i | \(0.374681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0995218 | + | 2.76417i | 0.00407999 | + | 0.113320i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 4.06587i | − | 0.166127i | −0.996544 | − | 0.0830635i | \(-0.973530\pi\) | ||
0.996544 | − | 0.0830635i | \(-0.0264704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 25.1161i | − | 1.02451i | −0.858835 | − | 0.512253i | \(-0.828811\pi\) | ||
0.858835 | − | 0.512253i | \(-0.171189\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.9638 | −0.689675 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.4336i | 1.27585i | 0.770099 | + | 0.637925i | \(0.220207\pi\) | ||||
−0.770099 | + | 0.637925i | \(0.779793\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 24.1144i | − | 0.975566i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.4532 | 1.59350 | 0.796751 | − | 0.604308i | \(-0.206550\pi\) | ||||
0.796751 | + | 0.604308i | \(0.206550\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 39.7421i | − | 1.59996i | −0.600029 | − | 0.799978i | \(-0.704844\pi\) | ||
0.600029 | − | 0.799978i | \(-0.295156\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.7776i | − | 0.593961i | −0.954884 | − | 0.296980i | \(-0.904020\pi\) | ||
0.954884 | − | 0.296980i | \(-0.0959796\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.407561 | − | 11.3198i | −0.0163286 | − | 0.453519i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.893892 | 0.0356418 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.3083 | 0.649223 | 0.324611 | − | 0.945847i | \(-0.394767\pi\) | ||||
0.324611 | + | 0.945847i | \(0.394767\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.57118 | −0.340137 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.10266 | + | 15.2931i | 0.0436889 | + | 0.605933i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.5289i | − | 0.494861i | −0.968906 | − | 0.247430i | \(-0.920414\pi\) | ||
0.968906 | − | 0.247430i | \(-0.0795862\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 14.3992i | − | 0.567847i | −0.958847 | − | 0.283924i | \(-0.908364\pi\) | ||
0.958847 | − | 0.283924i | \(-0.0916362\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.7708 | 1.24904 | 0.624519 | − | 0.781010i | \(-0.285295\pi\) | ||||
0.624519 | + | 0.781010i | \(0.285295\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 72.8346i | 2.85901i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 20.7389i | − | 0.811578i | −0.913967 | − | 0.405789i | \(-0.866997\pi\) | ||
0.913967 | − | 0.405789i | \(-0.133003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.90048 | −0.230551 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.44038i | 0.0950638i | 0.998870 | + | 0.0475319i | \(0.0151356\pi\) | ||||
−0.998870 | + | 0.0475319i | \(0.984864\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.3863i | 1.29858i | 0.760542 | + | 0.649288i | \(0.224933\pi\) | ||||
−0.760542 | + | 0.649288i | \(0.775067\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.0092 | − | 0.612402i | 0.659588 | − | 0.0237479i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 55.9275 | 2.16552 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.5809 | −1.64382 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.6943 | −0.720611 | −0.360306 | − | 0.932834i | \(-0.617328\pi\) | ||||
−0.360306 | + | 0.932834i | \(0.617328\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.5861 | 1.40612 | 0.703059 | − | 0.711131i | \(-0.251817\pi\) | ||||
0.703059 | + | 0.711131i | \(0.251817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.3563 | − | 1.12896i | 1.20335 | − | 0.0433255i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 36.9207i | − | 1.41273i | −0.707847 | − | 0.706365i | \(-0.750334\pi\) | ||
0.707847 | − | 0.706365i | \(-0.249666\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.86607i | − | 0.262339i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.78514 | −0.258493 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.20823i | 0.198130i | 0.995081 | + | 0.0990652i | \(0.0315852\pi\) | ||||
−0.995081 | + | 0.0990652i | \(0.968415\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.9115i | 0.527693i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.28991 | −0.0867367 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.2831i | − | 0.501696i | −0.968027 | − | 0.250848i | \(-0.919291\pi\) | ||
0.968027 | − | 0.250848i | \(-0.0807094\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.50052i | − | 0.207456i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.10266 | − | 30.6258i | −0.0414697 | − | 1.15180i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.09087 | −0.153636 | −0.0768179 | − | 0.997045i | \(-0.524476\pi\) | ||||
−0.0768179 | + | 0.997045i | \(0.524476\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −68.0367 | −2.54800 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.5830 | −0.433178 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.1817 | 0.603477 | 0.301739 | − | 0.953391i | \(-0.402433\pi\) | ||||
0.301739 | + | 0.953391i | \(0.402433\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.0911 | − | 1.58747i | 1.64204 | − | 0.0591203i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.47847i | 0.277743i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.7849i | 1.51263i | 0.654208 | + | 0.756314i | \(0.273002\pi\) | ||||
−0.654208 | + | 0.756314i | \(0.726998\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.997936 | −0.0369100 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.2481i | 1.44966i | 0.688926 | + | 0.724832i | \(0.258083\pi\) | ||||
−0.688926 | + | 0.724832i | \(0.741917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.2137i | 1.03927i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.7305 | 0.615442 | 0.307721 | − | 0.951477i | \(-0.400434\pi\) | ||||
0.307721 | + | 0.951477i | \(0.400434\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.7185i | 1.31039i | 0.755462 | + | 0.655193i | \(0.227412\pi\) | ||||
−0.755462 | + | 0.655193i | \(0.772588\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 15.9638i | − | 0.584867i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.5263 | + | 0.667024i | −0.676935 | + | 0.0243725i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.14236 | 0.333609 | 0.166805 | − | 0.985990i | \(-0.446655\pi\) | ||||
0.166805 | + | 0.985990i | \(0.446655\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.0546 | −0.584288 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.2027 | 1.75196 | 0.875979 | − | 0.482350i | \(-0.160217\pi\) | ||||
0.875979 | + | 0.482350i | \(0.160217\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.61056 | −0.348383 | −0.174191 | − | 0.984712i | \(-0.555731\pi\) | ||||
−0.174191 | + | 0.984712i | \(0.555731\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.408385 | + | 11.3427i | 0.0147845 | + | 0.410633i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.1691i | 1.08934i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 33.2931i | − | 1.20058i | −0.799783 | − | 0.600289i | \(-0.795052\pi\) | ||
0.799783 | − | 0.600289i | \(-0.204948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.2726 | 0.441415 | 0.220708 | − | 0.975340i | \(-0.429163\pi\) | ||||
0.220708 | + | 0.975340i | \(0.429163\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 9.09768i | − | 0.326798i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.0909i | 0.504858i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.0184 | 1.21727 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.7665i | 0.883956i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.4286i | 0.763847i | 0.924194 | + | 0.381923i | \(0.124738\pi\) | ||||
−0.924194 | + | 0.381923i | \(0.875262\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.3926 | + | 0.770222i | −0.760632 | + | 0.0273859i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.6376 | −0.626329 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.96375 | 0.352934 | 0.176467 | − | 0.984307i | \(-0.443533\pi\) | ||||
0.176467 | + | 0.984307i | \(0.443533\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.5094 | −0.407173 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.1990 | −0.853966 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.7734 | + | 0.711924i | −0.696919 | + | 0.0250920i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 32.6234i | − | 1.14698i | −0.819213 | − | 0.573489i | \(-0.805589\pi\) | ||
0.819213 | − | 0.573489i | \(-0.194411\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 56.6914i | − | 1.99071i | −0.0962936 | − | 0.995353i | \(-0.530699\pi\) | ||
0.0962936 | − | 0.995353i | \(-0.469301\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.42622 | −0.260129 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.14075i | 0.214837i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.3198i | 1.58167i | 0.612027 | + | 0.790837i | \(0.290354\pi\) | ||||
−0.612027 | + | 0.790837i | \(0.709646\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.6462 | −1.03340 | −0.516701 | − | 0.856166i | \(-0.672840\pi\) | ||||
−0.516701 | + | 0.856166i | \(0.672840\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 42.1129i | − | 1.46441i | −0.681084 | − | 0.732205i | \(-0.738491\pi\) | ||
0.681084 | − | 0.732205i | \(-0.261509\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 33.3936i | − | 1.15981i | −0.814684 | − | 0.579905i | \(-0.803090\pi\) | ||
0.814684 | − | 0.579905i | \(-0.196910\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.29910 | − | 0.526279i | 0.252899 | − | 0.0182345i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.573779 | −0.0198564 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.4385 | 1.43062 | 0.715309 | − | 0.698809i | \(-0.246286\pi\) | ||||
0.715309 | + | 0.698809i | \(0.246286\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9275 | −0.928535 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.20218 | 0.282164 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.61489 | + | 44.8528i | 0.0554882 | + | 1.54116i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.39441i | 0.219198i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.4866i | 1.04384i | 0.852994 | + | 0.521920i | \(0.174784\pi\) | ||||
−0.852994 | + | 0.521920i | \(0.825216\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.22718 | 0.178557 | 0.0892785 | − | 0.996007i | \(-0.471544\pi\) | ||||
0.0892785 | + | 0.996007i | \(0.471544\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.2728i | 1.47645i | 0.674555 | + | 0.738224i | \(0.264335\pi\) | ||||
−0.674555 | + | 0.738224i | \(0.735665\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.9259i | 1.05273i | 0.850259 | + | 0.526365i | \(0.176445\pi\) | ||||
−0.850259 | + | 0.526365i | \(0.823555\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.96375 | −0.338778 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 82.8844i | 2.81166i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.6865i | 0.395982i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.0951965 | − | 2.64404i | −0.00321823 | − | 0.0893848i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.79836 | 0.0607262 | 0.0303631 | − | 0.999539i | \(-0.490334\pi\) | ||||
0.0303631 | + | 0.999539i | \(0.490334\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.6289 | −0.661316 | −0.330658 | − | 0.943751i | \(-0.607271\pi\) | ||||
−0.330658 | + | 0.943751i | \(0.607271\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.5013 | 1.76681 | 0.883404 | − | 0.468611i | \(-0.155246\pi\) | ||||
0.883404 | + | 0.468611i | \(0.155246\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.1720 | −1.31527 | −0.657633 | − | 0.753338i | \(-0.728442\pi\) | ||||
−0.657633 | + | 0.753338i | \(0.728442\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.815946 | + | 22.6625i | 0.0273659 | + | 0.760077i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 70.8225i | 2.36998i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.77336i | − | 0.0592768i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 68.0367 | 2.26915 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.23843i | 0.107888i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 11.0092i | − | 0.365958i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.0822 | 1.56334 | 0.781669 | − | 0.623693i | \(-0.214369\pi\) | ||||
0.781669 | + | 0.623693i | \(0.214369\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.6504i | 1.34681i | 0.739274 | + | 0.673405i | \(0.235169\pi\) | ||||
−0.739274 | + | 0.673405i | \(0.764831\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23.1659i | − | 0.766680i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.561705 | + | 15.6011i | 0.0185491 | + | 0.515193i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.4900 | −1.46759 | −0.733795 | − | 0.679371i | \(-0.762253\pi\) | ||||
−0.733795 | + | 0.679371i | \(0.762253\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.0909 | 0.463807 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.855043 | −0.0281136 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 53.7371 | 1.76306 | 0.881529 | − | 0.472131i | \(-0.156515\pi\) | ||||
0.881529 | + | 0.472131i | \(0.156515\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.23843 | − | 44.9146i | −0.106135 | − | 1.47202i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.52834i | 0.180796i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.0682i | 1.43965i | 0.694157 | + | 0.719823i | \(0.255777\pi\) | ||||
−0.694157 | + | 0.719823i | \(0.744223\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.0362 | 0.653163 | 0.326582 | − | 0.945169i | \(-0.394103\pi\) | ||||
0.326582 | + | 0.945169i | \(0.394103\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 16.3808i | − | 0.533432i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 30.9244i | − | 1.00491i | −0.864604 | − | 0.502453i | \(-0.832431\pi\) | ||
0.864604 | − | 0.502453i | \(-0.167569\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.0236 | −0.325379 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.8414i | 1.03144i | 0.856756 | + | 0.515722i | \(0.172476\pi\) | ||||
−0.856756 | + | 0.515722i | \(0.827524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.56697i | 0.180143i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.1541 | + | 0.653625i | −0.586228 | + | 0.0211067i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −51.7678 | −1.66993 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.47166 | −0.272712 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.6804 | −1.05093 | −0.525466 | − | 0.850815i | \(-0.676109\pi\) | ||||
−0.525466 | + | 0.850815i | \(0.676109\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.2419 | −0.617501 | −0.308751 | − | 0.951143i | \(-0.599911\pi\) | ||||
−0.308751 | + | 0.951143i | \(0.599911\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.7825 | − | 1.32433i | 1.17919 | − | 0.0424559i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.48528i | 0.0795112i | 0.999209 | + | 0.0397556i | \(0.0126579\pi\) | ||||
−0.999209 | + | 0.0397556i | \(0.987342\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 22.6397i | − | 0.723566i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.4135 | 1.57605 | 0.788024 | − | 0.615645i | \(-0.211104\pi\) | ||||
0.788024 | + | 0.615645i | \(0.211104\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 12.8661i | − | 0.409947i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 7.13868i | − | 0.226997i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.0526 | 1.81233 | 0.906167 | − | 0.422920i | \(-0.138995\pi\) | ||||
0.906167 | + | 0.422920i | \(0.138995\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 17.5830i | − | 0.557417i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 16.6794i | − | 0.528240i | −0.964490 | − | 0.264120i | \(-0.914918\pi\) | ||
0.964490 | − | 0.264120i | \(-0.0850816\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5040.2.f.i.881.3 | 8 | ||
3.2 | odd | 2 | 5040.2.f.f.881.3 | 8 | |||
4.3 | odd | 2 | 630.2.b.b.251.7 | yes | 8 | ||
7.6 | odd | 2 | 5040.2.f.f.881.4 | 8 | |||
12.11 | even | 2 | 630.2.b.a.251.3 | ✓ | 8 | ||
20.3 | even | 4 | 3150.2.d.f.3149.7 | 8 | |||
20.7 | even | 4 | 3150.2.d.a.3149.2 | 8 | |||
20.19 | odd | 2 | 3150.2.b.f.251.2 | 8 | |||
21.20 | even | 2 | inner | 5040.2.f.i.881.4 | 8 | ||
28.27 | even | 2 | 630.2.b.a.251.7 | yes | 8 | ||
60.23 | odd | 4 | 3150.2.d.c.3149.7 | 8 | |||
60.47 | odd | 4 | 3150.2.d.d.3149.2 | 8 | |||
60.59 | even | 2 | 3150.2.b.e.251.6 | 8 | |||
84.83 | odd | 2 | 630.2.b.b.251.3 | yes | 8 | ||
140.27 | odd | 4 | 3150.2.d.c.3149.8 | 8 | |||
140.83 | odd | 4 | 3150.2.d.d.3149.1 | 8 | |||
140.139 | even | 2 | 3150.2.b.e.251.2 | 8 | |||
420.83 | even | 4 | 3150.2.d.a.3149.1 | 8 | |||
420.167 | even | 4 | 3150.2.d.f.3149.8 | 8 | |||
420.419 | odd | 2 | 3150.2.b.f.251.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.b.a.251.3 | ✓ | 8 | 12.11 | even | 2 | ||
630.2.b.a.251.7 | yes | 8 | 28.27 | even | 2 | ||
630.2.b.b.251.3 | yes | 8 | 84.83 | odd | 2 | ||
630.2.b.b.251.7 | yes | 8 | 4.3 | odd | 2 | ||
3150.2.b.e.251.2 | 8 | 140.139 | even | 2 | |||
3150.2.b.e.251.6 | 8 | 60.59 | even | 2 | |||
3150.2.b.f.251.2 | 8 | 20.19 | odd | 2 | |||
3150.2.b.f.251.6 | 8 | 420.419 | odd | 2 | |||
3150.2.d.a.3149.1 | 8 | 420.83 | even | 4 | |||
3150.2.d.a.3149.2 | 8 | 20.7 | even | 4 | |||
3150.2.d.c.3149.7 | 8 | 60.23 | odd | 4 | |||
3150.2.d.c.3149.8 | 8 | 140.27 | odd | 4 | |||
3150.2.d.d.3149.1 | 8 | 140.83 | odd | 4 | |||
3150.2.d.d.3149.2 | 8 | 60.47 | odd | 4 | |||
3150.2.d.f.3149.7 | 8 | 20.3 | even | 4 | |||
3150.2.d.f.3149.8 | 8 | 420.167 | even | 4 | |||
5040.2.f.f.881.3 | 8 | 3.2 | odd | 2 | |||
5040.2.f.f.881.4 | 8 | 7.6 | odd | 2 | |||
5040.2.f.i.881.3 | 8 | 1.1 | even | 1 | trivial | ||
5040.2.f.i.881.4 | 8 | 21.20 | even | 2 | inner |