Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(251,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3150.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
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: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.2 | ||
Root | \(-3.73923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.251 |
Dual form | 3150.2.b.e.251.6 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0951965 | + | 2.64404i | −0.0359809 | + | 0.999352i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.28808i | 1.59441i | 0.603705 | + | 0.797207i | \(0.293690\pi\) | ||||
−0.603705 | + | 0.797207i | \(0.706310\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.19039i | − | 0.607506i | −0.952751 | − | 0.303753i | \(-0.901760\pi\) | ||
0.952751 | − | 0.303753i | \(-0.0982397\pi\) | |||||||
\(14\) | 2.64404 | + | 0.0951965i | 0.706649 | + | 0.0254423i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −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 | ||||||||
\(22\) | 5.28808 | 1.12742 | ||||||||
\(23\) | − | 7.47847i | − | 1.55937i | −0.626173 | − | 0.779684i | \(-0.715380\pi\) | ||
0.626173 | − | 0.779684i | \(-0.284620\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.19039 | −0.429571 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.0951965 | − | 2.64404i | 0.0179904 | − | 0.499676i | ||||
\(29\) | 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 | \(-0.304362\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.04544i | 0.179291i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.855043 | 0.140568 | 0.0702841 | − | 0.997527i | \(-0.477609\pi\) | ||||
0.0702841 | + | 0.997527i | \(0.477609\pi\) | |||||||
\(38\) | 6.43303 | 1.04358 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.19039 | −0.342082 | −0.171041 | − | 0.985264i | \(-0.554713\pi\) | ||||
−0.171041 | + | 0.985264i | \(0.554713\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.954564 | 0.145570 | 0.0727849 | − | 0.997348i | \(-0.476811\pi\) | ||||
0.0727849 | + | 0.997348i | \(0.476811\pi\) | |||||||
\(44\) | − | 5.28808i | − | 0.797207i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.47847 | −1.10264 | ||||||||
\(47\) | −11.0092 | −1.60585 | −0.802927 | − | 0.596077i | \(-0.796725\pi\) | ||||
−0.802927 | + | 0.596077i | \(0.796725\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.98188 | − | 0.503406i | −0.997411 | − | 0.0719152i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.19039i | 0.303753i | ||||||||
\(53\) | 3.09768i | 0.425500i | 0.977107 | + | 0.212750i | \(0.0682419\pi\) | ||||
−0.977107 | + | 0.212750i | \(0.931758\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.64404 | − | 0.0951965i | −0.353324 | − | 0.0127212i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.47847 | 0.981971 | ||||||||
\(59\) | −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 | \(0.172391\pi\) | ||||
−0.856894 | + | 0.515492i | \(0.827609\pi\) | |||||||
\(62\) | −9.09768 | −1.15541 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.33535 | −0.651817 | −0.325908 | − | 0.945401i | \(-0.605670\pi\) | ||||
−0.325908 | + | 0.945401i | \(0.605670\pi\) | |||||||
\(68\) | 1.04544 | 0.126778 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.43303i | − | 0.763461i | −0.924274 | − | 0.381730i | \(-0.875328\pi\) | ||
0.924274 | − | 0.381730i | \(-0.124672\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.57615i | − | 0.535598i | −0.963475 | − | 0.267799i | \(-0.913704\pi\) | ||
0.963475 | − | 0.267799i | \(-0.0862963\pi\) | |||||||
\(74\) | − | 0.855043i | − | 0.0993967i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 6.43303i | − | 0.737920i | ||||||
\(77\) | −13.9819 | − | 0.503406i | −1.59338 | − | 0.0573684i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.6738 | 1.76344 | 0.881722 | − | 0.471769i | \(-0.156384\pi\) | ||||
0.881722 | + | 0.471769i | \(0.156384\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.19039i | 0.241888i | ||||||||
\(83\) | −4.38079 | −0.480854 | −0.240427 | − | 0.970667i | \(-0.577287\pi\) | ||||
−0.240427 | + | 0.970667i | \(0.577287\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 0.954564i | − | 0.102933i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.28808 | −0.563711 | ||||||||
\(89\) | −4.28126 | −0.453813 | −0.226907 | − | 0.973917i | \(-0.572861\pi\) | ||||
−0.226907 | + | 0.973917i | \(0.572861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.79148 | + | 0.208518i | 0.607112 | + | 0.0218586i | ||||
\(92\) | 7.47847i | 0.779684i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.0092i | 1.13551i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.8593i | 1.20412i | 0.798449 | + | 0.602062i | \(0.205654\pi\) | ||||
−0.798449 | + | 0.602062i | \(0.794346\pi\) | |||||||
\(98\) | −0.503406 | + | 6.98188i | −0.0508517 | + | 0.705276i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.5830 | −1.15255 | −0.576274 | − | 0.817257i | \(-0.695494\pi\) | ||||
−0.576274 | + | 0.817257i | \(0.695494\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.6757i | − | 1.64310i | −0.570134 | − | 0.821552i | \(-0.693109\pi\) | ||
0.570134 | − | 0.821552i | \(-0.306891\pi\) | |||||||
\(104\) | 2.19039 | 0.214786 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.09768 | 0.300874 | ||||||||
\(107\) | − | 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 | ||||||||
\(112\) | −0.0951965 | + | 2.64404i | −0.00899522 | + | 0.249838i | ||||
\(113\) | 8.09087i | 0.761125i | 0.924755 | + | 0.380563i | \(0.124270\pi\) | ||||
−0.924755 | + | 0.380563i | \(0.875730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 7.47847i | − | 0.694358i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.7734i | 1.26794i | ||||||||
\(119\) | 0.0995218 | − | 2.76417i | 0.00912314 | − | 0.253391i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.9638 | −1.54216 | ||||||||
\(122\) | 8.05225 | 0.729016 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.09768i | 0.816996i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.57118 | −0.760569 | −0.380285 | − | 0.924870i | \(-0.624174\pi\) | ||||
−0.380285 | + | 0.924870i | \(0.624174\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 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 | ||||
\(134\) | 5.33535i | 0.460904i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 1.04544i | − | 0.0896454i | ||||||
\(137\) | 6.86607i | 0.586608i | 0.956019 | + | 0.293304i | \(0.0947548\pi\) | ||||
−0.956019 | + | 0.293304i | \(0.905245\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | −6.43303 | −0.539848 | ||||||||
\(143\) | 11.5830 | 0.968616 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.57615 | −0.378725 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.855043 | −0.0702841 | ||||||||
\(149\) | − | 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 | \(-0.273404\pi\) | ||||
0.653253 | + | 0.757139i | \(0.273404\pi\) | |||||||
\(152\) | −6.43303 | −0.521788 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.503406 | + | 13.9819i | −0.0405656 | + | 1.12669i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.7665i | 1.97659i | 0.152569 | + | 0.988293i | \(0.451245\pi\) | ||||
−0.152569 | + | 0.988293i | \(0.548755\pi\) | |||||||
\(158\) | − | 15.6738i | − | 1.24694i | ||||||
\(159\) | 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 | \(0.593932\pi\) | |||||||
\(164\) | 2.19039 | 0.171041 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.38079i | 0.340015i | ||||||||
\(167\) | 0.573779 | 0.0444003 | 0.0222002 | − | 0.999754i | \(-0.492933\pi\) | ||||
0.0222002 | + | 0.999754i | \(0.492933\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.20218 | 0.630937 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.954564 | −0.0727849 | ||||||||
\(173\) | −9.96375 | −0.757530 | −0.378765 | − | 0.925493i | \(-0.623651\pi\) | ||||
−0.378765 | + | 0.925493i | \(0.623651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.28808i | 0.398604i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.28126i | 0.320894i | ||||||||
\(179\) | 1.77336i | 0.132547i | 0.997801 | + | 0.0662735i | \(0.0211110\pi\) | ||||
−0.997801 | + | 0.0662735i | \(0.978889\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0092i | 0.818306i | 0.912466 | + | 0.409153i | \(0.134176\pi\) | ||||
−0.912466 | + | 0.409153i | \(0.865824\pi\) | |||||||
\(182\) | 0.208518 | − | 5.79148i | 0.0154564 | − | 0.429293i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.47847 | 0.551320 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.52834i | − | 0.404272i | ||||||
\(188\) | 11.0092 | 0.802927 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 5.56697i | − | 0.402812i | −0.979508 | − | 0.201406i | \(-0.935449\pi\) | ||
0.979508 | − | 0.201406i | \(-0.0645510\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.47166 | 0.609803 | 0.304902 | − | 0.952384i | \(-0.401376\pi\) | ||||
0.304902 | + | 0.952384i | \(0.401376\pi\) | |||||||
\(194\) | 11.8593 | 0.851445 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.98188 | + | 0.503406i | 0.498705 | + | 0.0359576i | ||||
\(197\) | 12.8661i | 0.916669i | 0.888780 | + | 0.458335i | \(0.151554\pi\) | ||||
−0.888780 | + | 0.458335i | \(0.848446\pi\) | |||||||
\(198\) | 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 | ||||||||
\(202\) | 11.5830i | 0.814975i | ||||||||
\(203\) | −19.7734 | − | 0.711924i | −1.38782 | − | 0.0499673i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.6757 | −1.16185 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 2.19039i | − | 0.151876i | ||||||
\(209\) | −34.0184 | −2.35310 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | − | 3.09768i | − | 0.212750i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.00681 | −0.478976 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.0546 | + | 0.866067i | 1.63293 | + | 0.0587925i | ||||
\(218\) | 4.28991i | 0.290550i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.28991i | 0.154036i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.8710i | − | 0.727979i | −0.931403 | − | 0.363989i | \(-0.881414\pi\) | ||
0.931403 | − | 0.363989i | \(-0.118586\pi\) | |||||||
\(224\) | 2.64404 | + | 0.0951965i | 0.176662 | + | 0.00636058i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.09087 | 0.538197 | ||||||||
\(227\) | −14.0909 | −0.935244 | −0.467622 | − | 0.883929i | \(-0.654889\pi\) | ||||
−0.467622 | + | 0.883929i | \(0.654889\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.5239i | 0.959767i | 0.877332 | + | 0.479883i | \(0.159321\pi\) | ||||
−0.877332 | + | 0.479883i | \(0.840679\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.47847 | −0.490986 | ||||||||
\(233\) | 20.6806i | 1.35483i | 0.735599 | + | 0.677417i | \(0.236901\pi\) | ||||
−0.735599 | + | 0.677417i | \(0.763099\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.7734 | 0.896569 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.76417 | − | 0.0995218i | −0.179175 | − | 0.00645104i | ||||
\(239\) | 5.56697i | 0.360097i | 0.983658 | + | 0.180049i | \(0.0576255\pi\) | ||||
−0.983658 | + | 0.180049i | \(0.942375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3839i | 0.733303i | 0.930358 | + | 0.366651i | \(0.119496\pi\) | ||||
−0.930358 | + | 0.366651i | \(0.880504\pi\) | |||||||
\(242\) | 16.9638i | 1.09047i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.05225i | − | 0.515492i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.0909 | 0.896581 | ||||||||
\(248\) | 9.09768 | 0.577703 | ||||||||
\(249\) | 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 | ||||||||
\(254\) | 8.57118i | 0.537804i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 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 | ||||||||
\(262\) | 5.90048i | 0.364533i | ||||||||
\(263\) | − | 17.3876i | − | 1.07217i | −0.844166 | − | 0.536083i | \(-0.819904\pi\) | ||
0.844166 | − | 0.536083i | \(-0.180096\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.612402 | + | 17.0092i | −0.0375488 | + | 1.04290i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.33535 | 0.325908 | ||||||||
\(269\) | −20.3445 | −1.24043 | −0.620214 | − | 0.784433i | \(-0.712954\pi\) | ||||
−0.620214 | + | 0.784433i | \(0.712954\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.47847i | 0.0898106i | 0.998991 | + | 0.0449053i | \(0.0142986\pi\) | ||||
−0.998991 | + | 0.0449053i | \(0.985701\pi\) | |||||||
\(272\) | −1.04544 | −0.0633888 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.86607 | 0.414794 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.7642 | −0.646756 | −0.323378 | − | 0.946270i | \(-0.604819\pi\) | ||||
−0.323378 | + | 0.946270i | \(0.604819\pi\) | |||||||
\(278\) | 13.9115 | 0.834356 | ||||||||
\(279\) | 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 | \(0.260879\pi\) | ||||
−0.682532 | + | 0.730855i | \(0.739121\pi\) | |||||||
\(284\) | 6.43303i | 0.381730i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 11.5830i | − | 0.684915i | ||||||
\(287\) | 0.208518 | − | 5.79148i | 0.0123084 | − | 0.341860i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9071 | −0.935710 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.57615i | 0.267799i | ||||||||
\(293\) | 12.6707 | 0.740230 | 0.370115 | − | 0.928986i | \(-0.379318\pi\) | ||||
0.370115 | + | 0.928986i | \(0.379318\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.855043i | 0.0496983i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.9638 | −0.924755 | ||||||||
\(299\) | −16.3808 | −0.947325 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0908711 | + | 2.52390i | −0.00523773 | + | 0.145475i | ||||
\(302\) | − | 16.0546i | − | 0.923840i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.43303i | 0.368960i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 0.866067i | − | 0.0494291i | −0.999695 | − | 0.0247145i | \(-0.992132\pi\) | ||
0.999695 | − | 0.0247145i | \(-0.00786768\pi\) | |||||||
\(308\) | 13.9819 | + | 0.503406i | 0.796691 | + | 0.0286842i | ||||
\(309\) | 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 | \(-0.0524219\pi\) | |||||||
\(314\) | 24.7665 | 1.39766 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.6738 | −0.881722 | ||||||||
\(317\) | − | 28.1591i | − | 1.58157i | −0.612092 | − | 0.790787i | \(-0.709672\pi\) | ||
0.612092 | − | 0.790787i | \(-0.290328\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −39.5467 | −2.21419 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.711924 | − | 19.7734i | 0.0396740 | − | 1.10193i | ||||
\(323\) | − | 6.72532i | − | 0.374207i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.42622i | 0.411300i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 2.19039i | − | 0.120944i | ||||||
\(329\) | 1.04804 | − | 29.1087i | 0.0577801 | − | 1.60482i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.5830 | −1.07638 | −0.538189 | − | 0.842824i | \(-0.680891\pi\) | ||||
−0.538189 | + | 0.842824i | \(0.680891\pi\) | |||||||
\(332\) | 4.38079 | 0.240427 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 0.573779i | − | 0.0313958i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.3992 | 1.54700 | 0.773500 | − | 0.633796i | \(-0.218504\pi\) | ||||
0.773500 | + | 0.633796i | \(0.218504\pi\) | |||||||
\(338\) | − | 8.20218i | − | 0.446140i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 48.1092 | 2.60526 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.99567 | − | 18.4124i | 0.107756 | − | 0.994177i | ||||
\(344\) | 0.954564i | 0.0514667i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.96375i | 0.535655i | ||||||||
\(347\) | 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 | \(-0.810058\pi\) | ||
0.827183 | − | 0.561933i | \(-0.189942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.28808 | 0.281855 | ||||||||
\(353\) | −15.1363 | −0.805624 | −0.402812 | − | 0.915283i | \(-0.631967\pi\) | ||||
−0.402812 | + | 0.915283i | \(0.631967\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.28126 | 0.226907 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.77336 | 0.0937249 | ||||||||
\(359\) | 33.1909i | 1.75175i | 0.482538 | + | 0.875875i | \(0.339715\pi\) | ||||
−0.482538 | + | 0.875875i | \(0.660285\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.3839 | −1.17810 | ||||||||
\(362\) | 11.0092 | 0.578630 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.79148 | − | 0.208518i | −0.303556 | − | 0.0109293i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.6825i | 0.609821i | 0.952381 | + | 0.304910i | \(0.0986265\pi\) | ||||
−0.952381 | + | 0.304910i | \(0.901373\pi\) | |||||||
\(368\) | − | 7.47847i | − | 0.389842i | ||||||
\(369\) | 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 | \(-0.607995\pi\) | ||||
−0.332804 | + | 0.942996i | \(0.607995\pi\) | |||||||
\(374\) | −5.52834 | −0.285864 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 11.0092i | − | 0.567755i | ||||||
\(377\) | 16.3808 | 0.843653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.0751 | 1.28802 | 0.644010 | − | 0.765017i | \(-0.277270\pi\) | ||||
0.644010 | + | 0.765017i | \(0.277270\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.56697 | −0.284831 | ||||||||
\(383\) | −23.0092 | −1.17571 | −0.587857 | − | 0.808965i | \(-0.700028\pi\) | ||||
−0.587857 | + | 0.808965i | \(0.700028\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 8.47166i | − | 0.431196i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 11.8593i | − | 0.602062i | ||||||
\(389\) | 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 | ||||||||
\(392\) | 0.503406 | − | 6.98188i | 0.0254258 | − | 0.352638i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.8661 | 0.648183 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.9141i | 0.698329i | 0.937061 | + | 0.349164i | \(0.113535\pi\) | ||||
−0.937061 | + | 0.349164i | \(0.886465\pi\) | |||||||
\(398\) | −17.5830 | −0.881354 | ||||||||
\(399\) | 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 | ||||||||
\(404\) | 11.5830 | 0.576274 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.711924 | + | 19.7734i | −0.0353322 | + | 0.981335i | ||||
\(407\) | 4.52153i | 0.224124i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.0000i | − | 0.593362i | −0.954977 | − | 0.296681i | \(-0.904120\pi\) | ||
0.954977 | − | 0.296681i | \(-0.0958798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.6757i | 0.821552i | ||||||||
\(413\) | 1.31117 | − | 36.4173i | 0.0645187 | − | 1.79198i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.19039 | −0.107393 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 34.0184i | 1.66389i | ||||||||
\(419\) | −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 | \(0.493387\pi\) | |||||||
\(422\) | − | 4.00000i | − | 0.194717i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.09768 | −0.150437 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.2905 | − | 0.766545i | −1.03032 | − | 0.0370957i | ||||
\(428\) | 7.00681i | 0.338687i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.2476i | 0.975293i | 0.873041 | + | 0.487647i | \(0.162145\pi\) | ||||
−0.873041 | + | 0.487647i | \(0.837855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 30.6444i | − | 1.47268i | −0.676614 | − | 0.736338i | \(-0.736553\pi\) | ||
0.676614 | − | 0.736338i | \(-0.263447\pi\) | |||||||
\(434\) | 0.866067 | − | 24.0546i | 0.0415726 | − | 1.15466i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.28991 | 0.205450 | ||||||||
\(437\) | 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 | ||||||||
\(442\) | 2.28991 | 0.108920 | ||||||||
\(443\) | 36.3083i | 1.72506i | 0.506007 | + | 0.862529i | \(0.331121\pi\) | ||||
−0.506007 | + | 0.862529i | \(0.668879\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.8710 | −0.514759 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.0951965 | − | 2.64404i | 0.00449761 | − | 0.124919i | ||||
\(449\) | 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 | ||||||
\(452\) | − | 8.09087i | − | 0.380563i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.0909i | 0.661317i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.3477 | −1.18571 | −0.592857 | − | 0.805308i | \(-0.702000\pi\) | ||||
−0.592857 | + | 0.805308i | \(0.702000\pi\) | |||||||
\(458\) | 14.5239 | 0.678657 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.7253 | 0.592677 | 0.296339 | − | 0.955083i | \(-0.404234\pi\) | ||||
0.296339 | + | 0.955083i | \(0.404234\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.2655 | 0.988289 | 0.494145 | − | 0.869380i | \(-0.335481\pi\) | ||||
0.494145 | + | 0.869380i | \(0.335481\pi\) | |||||||
\(464\) | 7.47847i | 0.347179i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.6806 | 0.958013 | ||||||||
\(467\) | −13.1424 | −0.608156 | −0.304078 | − | 0.952647i | \(-0.598348\pi\) | ||||
−0.304078 | + | 0.952647i | \(0.598348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.507906 | − | 14.1069i | 0.0234529 | − | 0.651395i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 13.7734i | − | 0.633970i | ||||||
\(473\) | 5.04781i | 0.232099i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.0995218 | + | 2.76417i | −0.00456157 | + | 0.126696i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.56697 | 0.254627 | ||||||||
\(479\) | 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 | ||||||
\(482\) | 11.3839 | 0.518523 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.9638 | 0.771080 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.5381 | −1.79164 | −0.895820 | − | 0.444416i | \(-0.853411\pi\) | ||||
−0.895820 | + | 0.444416i | \(0.853411\pi\) | |||||||
\(488\) | −8.05225 | −0.364508 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.62105i | − | 0.208545i | −0.994549 | − | 0.104273i | \(-0.966749\pi\) | ||
0.994549 | − | 0.104273i | \(-0.0332514\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.81826i | − | 0.352117i | ||||||
\(494\) | − | 14.0909i | − | 0.633978i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 9.09768i | − | 0.408498i | ||||||
\(497\) | 17.0092 | + | 0.612402i | 0.762966 | + | 0.0274700i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.0152 | 1.38843 | 0.694216 | − | 0.719766i | \(-0.255751\pi\) | ||||
0.694216 | + | 0.719766i | \(0.255751\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.71874i | 0.0767109i | ||||||||
\(503\) | 28.3385 | 1.26355 | 0.631775 | − | 0.775152i | \(-0.282327\pi\) | ||||
0.631775 | + | 0.775152i | \(0.282327\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 39.5467i | − | 1.75807i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.57118 | 0.380285 | ||||||||
\(509\) | 22.3808 | 0.992011 | 0.496005 | − | 0.868319i | \(-0.334800\pi\) | ||||
0.496005 | + | 0.868319i | \(0.334800\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0995 | + | 0.435633i | 0.535251 | + | 0.0192713i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 2.18779i | − | 0.0964994i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 58.2174i | − | 2.56040i | ||||||
\(518\) | 2.26077 | + | 0.0813970i | 0.0993323 | + | 0.00357638i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.5896 | 1.25253 | 0.626265 | − | 0.779610i | \(-0.284583\pi\) | ||||
0.626265 | + | 0.779610i | \(0.284583\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.51472i | 0.153688i | 0.997043 | + | 0.0768440i | \(0.0244843\pi\) | ||||
−0.997043 | + | 0.0768440i | \(0.975516\pi\) | |||||||
\(524\) | 5.90048 | 0.257764 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.3876 | −0.758135 | ||||||||
\(527\) | 9.51104i | 0.414307i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −32.9275 | −1.43163 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 17.0092 | + | 0.612402i | 0.737442 | + | 0.0265510i | ||||
\(533\) | 4.79782i | 0.207817i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 5.33535i | − | 0.230452i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.3445i | 0.877115i | ||||||||
\(539\) | 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 | \(0.272486\pi\) | |||||||
\(542\) | 1.47847 | 0.0635057 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.04544i | 0.0448227i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.86369 | 0.293470 | 0.146735 | − | 0.989176i | \(-0.453123\pi\) | ||||
0.146735 | + | 0.989176i | \(0.453123\pi\) | |||||||
\(548\) | − | 6.86607i | − | 0.293304i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −48.1092 | −2.04952 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.49209 | + | 41.4422i | −0.0634503 | + | 1.76230i | ||||
\(554\) | 10.7642i | 0.457326i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 13.9115i | − | 0.589979i | ||||||
\(557\) | 1.81826i | 0.0770421i | 0.999258 | + | 0.0385210i | \(0.0122647\pi\) | ||||
−0.999258 | + | 0.0385210i | \(0.987735\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.09087i | − | 0.0884344i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.42806 | 0.102422 | ||||||||
\(563\) | −34.0184 | −1.43370 | −0.716852 | − | 0.697226i | \(-0.754418\pi\) | ||||
−0.716852 | + | 0.697226i | \(0.754418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.5898 | 1.03359 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.43303 | 0.269924 | ||||||||
\(569\) | − | 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 | \(-0.427294\pi\) | ||||
0.226431 | + | 0.974027i | \(0.427294\pi\) | |||||||
\(572\) | −11.5830 | −0.484308 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.79148 | − | 0.208518i | −0.241732 | − | 0.00870336i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 39.1523i | − | 1.62993i | −0.579509 | − | 0.814966i | \(-0.696756\pi\) | ||
0.579509 | − | 0.814966i | \(-0.303244\pi\) | |||||||
\(578\) | 15.9071i | 0.661647i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.417035 | − | 11.5830i | 0.0173015 | − | 0.480542i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.3808 | −0.678423 | ||||||||
\(584\) | 4.57615 | 0.189363 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 12.6707i | − | 0.523422i | ||||||
\(587\) | −5.52834 | −0.228179 | −0.114090 | − | 0.993470i | \(-0.536395\pi\) | ||||
−0.114090 | + | 0.993470i | \(0.536395\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 58.5257 | 2.41151 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.855043 | 0.0351420 | ||||||||
\(593\) | 18.6830 | 0.767220 | 0.383610 | − | 0.923495i | \(-0.374681\pi\) | ||||
0.383610 | + | 0.923495i | \(0.374681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.9638i | 0.653901i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.3808i | 0.669860i | ||||||||
\(599\) | 4.06587i | 0.166127i | 0.996544 | + | 0.0830635i | \(0.0264704\pi\) | ||||
−0.996544 | + | 0.0830635i | \(0.973530\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.1161i | 1.02451i | 0.858835 | + | 0.512253i | \(0.171189\pi\) | ||||
−0.858835 | + | 0.512253i | \(0.828811\pi\) | |||||||
\(602\) | 2.52390 | + | 0.0908711i | 0.102867 | + | 0.00370363i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.0546 | −0.653253 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 31.4336i | − | 1.27585i | −0.770099 | − | 0.637925i | \(-0.779793\pi\) | ||
0.770099 | − | 0.637925i | \(-0.220207\pi\) | |||||||
\(608\) | 6.43303 | 0.260894 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.1144i | 0.975566i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.4532 | −1.59350 | −0.796751 | − | 0.604308i | \(-0.793450\pi\) | ||||
−0.796751 | + | 0.604308i | \(0.793450\pi\) | |||||||
\(614\) | −0.866067 | −0.0349516 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.503406 | − | 13.9819i | 0.0202828 | − | 0.563346i | ||||
\(617\) | 39.7421i | 1.59996i | 0.600029 | + | 0.799978i | \(0.295156\pi\) | ||||
−0.600029 | + | 0.799978i | \(0.704844\pi\) | |||||||
\(618\) | 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 | ||||||||
\(622\) | − | 9.71009i | − | 0.389339i | ||||||
\(623\) | 0.407561 | − | 11.3198i | 0.0163286 | − | 0.453519i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.80096 | −0.231853 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 24.7665i | − | 0.988293i | ||||||
\(629\) | −0.893892 | −0.0356418 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.3083 | −0.649223 | −0.324611 | − | 0.945847i | \(-0.605233\pi\) | ||||
−0.324611 | + | 0.945847i | \(0.605233\pi\) | |||||||
\(632\) | 15.6738i | 0.623472i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.1591 | −1.11834 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.10266 | + | 15.2931i | −0.0436889 | + | 0.605933i | ||||
\(638\) | 39.5467i | 1.56567i | ||||||||
\(639\) | 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 | \(0.0916362\pi\) | ||||
−0.958847 | + | 0.283924i | \(0.908364\pi\) | |||||||
\(644\) | −19.7734 | − | 0.711924i | −0.779179 | − | 0.0280537i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.72532 | −0.264604 | ||||||||
\(647\) | −31.7708 | −1.24904 | −0.624519 | − | 0.781010i | \(-0.714705\pi\) | ||||
−0.624519 | + | 0.781010i | \(0.714705\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 72.8346i | − | 2.85901i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.42622 | 0.290833 | ||||||||
\(653\) | 20.7389i | 0.811578i | 0.913967 | + | 0.405789i | \(0.133003\pi\) | ||||
−0.913967 | + | 0.405789i | \(0.866997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.19039 | −0.0855205 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −29.1087 | − | 1.04804i | −1.13478 | − | 0.0408567i | ||||
\(659\) | − | 2.44038i | − | 0.0950638i | −0.998870 | − | 0.0475319i | \(-0.984864\pi\) | ||
0.998870 | − | 0.0475319i | \(-0.0151356\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 33.3863i | − | 1.29858i | −0.760542 | − | 0.649288i | \(-0.775067\pi\) | ||
0.760542 | − | 0.649288i | \(-0.224933\pi\) | |||||||
\(662\) | 19.5830i | 0.761114i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 4.38079i | − | 0.170007i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 55.9275 | 2.16552 | ||||||||
\(668\) | −0.573779 | −0.0222002 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.5809 | −1.64382 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.6943 | 0.720611 | 0.360306 | − | 0.932834i | \(-0.382672\pi\) | ||||
0.360306 | + | 0.932834i | \(0.382672\pi\) | |||||||
\(674\) | − | 28.3992i | − | 1.09389i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.20218 | −0.315468 | ||||||||
\(677\) | 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 | ||||||||
\(682\) | − | 48.1092i | − | 1.84220i | ||||||
\(683\) | − | 36.9207i | − | 1.41273i | −0.707847 | − | 0.706365i | \(-0.750334\pi\) | ||
0.707847 | − | 0.706365i | \(-0.249666\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.4124 | − | 1.99567i | −0.702990 | − | 0.0761952i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.954564 | 0.0363924 | ||||||||
\(689\) | 6.78514 | 0.258493 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.20823i | 0.198130i | 0.995081 | + | 0.0990652i | \(0.0315852\pi\) | ||||
−0.995081 | + | 0.0990652i | \(0.968415\pi\) | |||||||
\(692\) | 9.96375 | 0.378765 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.5898 | 0.477901 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.28991 | 0.0867367 | ||||||||
\(698\) | −20.9956 | −0.794694 | ||||||||
\(699\) | 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 | ||||||||
\(704\) | − | 5.28808i | − | 0.199302i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.1363i | 0.569662i | ||||||||
\(707\) | 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 | ||||||||
\(712\) | − | 4.28126i | − | 0.160447i | ||||||
\(713\) | −68.0367 | −2.54800 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 1.77336i | − | 0.0662735i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 33.1909 | 1.23867 | ||||||||
\(719\) | 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 | ||||
\(722\) | 22.3839i | 0.833043i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 11.0092i | − | 0.409153i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 40.7849i | − | 1.51263i | −0.654208 | − | 0.756314i | \(-0.726998\pi\) | ||
0.654208 | − | 0.756314i | \(-0.273002\pi\) | |||||||
\(728\) | −0.208518 | + | 5.79148i | −0.00772818 | + | 0.214647i | ||||
\(729\) | 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 | \(0.741917\pi\) | |||||||
\(734\) | 11.6825 | 0.431208 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.47847 | −0.275660 | ||||||||
\(737\) | − | 28.2137i | − | 1.03927i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.7305 | −0.615442 | −0.307721 | − | 0.951477i | \(-0.599566\pi\) | ||||
−0.307721 | + | 0.951477i | \(0.599566\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.294888 | + | 8.19039i | −0.0108257 | + | 0.300679i | ||||
\(743\) | 35.7185i | 1.31039i | 0.755462 | + | 0.655193i | \(0.227412\pi\) | ||||
−0.755462 | + | 0.655193i | \(0.772588\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.8550i | 0.470657i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.52834i | 0.202136i | ||||||||
\(749\) | 18.5263 | + | 0.667024i | 0.676935 | + | 0.0243725i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.14236 | −0.333609 | −0.166805 | − | 0.985990i | \(-0.553345\pi\) | ||||
−0.166805 | + | 0.985990i | \(0.553345\pi\) | |||||||
\(752\) | −11.0092 | −0.401464 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 16.3808i | − | 0.596553i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.2027 | −1.75196 | −0.875979 | − | 0.482350i | \(-0.839783\pi\) | ||||
−0.875979 | + | 0.482350i | \(0.839783\pi\) | |||||||
\(758\) | − | 25.0751i | − | 0.910767i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.61056 | 0.348383 | 0.174191 | − | 0.984712i | \(-0.444269\pi\) | ||||
0.174191 | + | 0.984712i | \(0.444269\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.408385 | − | 11.3427i | 0.0147845 | − | 0.410633i | ||||
\(764\) | 5.56697i | 0.201406i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.0092i | 0.831356i | ||||||||
\(767\) | 30.1691i | 1.08934i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.2931i | 1.20058i | 0.799783 | + | 0.600289i | \(0.204948\pi\) | ||||
−0.799783 | + | 0.600289i | \(0.795052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.47166 | −0.304902 | ||||||||
\(773\) | 12.2726 | 0.441415 | 0.220708 | − | 0.975340i | \(-0.429163\pi\) | ||||
0.220708 | + | 0.975340i | \(0.429163\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11.8593 | −0.425722 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.1591 | 0.364222 | ||||||||
\(779\) | − | 14.0909i | − | 0.504858i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.0184 | 1.21727 | ||||||||
\(782\) | 7.81826 | 0.279580 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.98188 | − | 0.503406i | −0.249353 | − | 0.0179788i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 21.4286i | − | 0.763847i | −0.924194 | − | 0.381923i | \(-0.875262\pi\) | ||
0.924194 | − | 0.381923i | \(-0.124738\pi\) | |||||||
\(788\) | − | 12.8661i | − | 0.458335i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.3926 | − | 0.770222i | −0.760632 | − | 0.0273859i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.6376 | 0.626329 | ||||||||
\(794\) | 13.9141 | 0.493793 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.5830i | 0.623212i | ||||||||
\(797\) | 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 | ||||||||
\(802\) | −14.6197 | −0.516241 | ||||||||
\(803\) | 24.1990 | 0.853966 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19.9275i | 0.701916i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 11.5830i | − | 0.407487i | ||||||
\(809\) | − | 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 | \(-0.469301\pi\) | |||||||
\(812\) | 19.7734 | + | 0.711924i | 0.693909 | + | 0.0249836i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.52153 | 0.158480 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.14075i | 0.214837i | ||||||||
\(818\) | −12.0000 | −0.419570 | ||||||||
\(819\) | 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 | \(0.672840\pi\) | |||||||
\(824\) | 16.6757 | 0.580925 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36.4173 | − | 1.31117i | −1.26712 | − | 0.0456216i | ||||
\(827\) | − | 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 | \(0.196910\pi\) | ||||
−0.814684 | + | 0.579905i | \(0.803090\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.19039i | 0.0759382i | ||||||||
\(833\) | 7.29910 | + | 0.526279i | 0.252899 | + | 0.0182345i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 34.0184 | 1.17655 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.60743i | 0.0900721i | ||||||||
\(839\) | 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 | ||||||||
\(842\) | − | 0.852443i | − | 0.0293771i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.00000 | −0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.61489 | − | 44.8528i | 0.0554882 | − | 1.54116i | ||||
\(848\) | 3.09768i | 0.106375i | ||||||||
\(849\) | 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 | \(0.825216\pi\) | |||||||
\(854\) | −0.766545 | + | 21.2905i | −0.0262306 | + | 0.728544i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.00681 | 0.239488 | ||||||||
\(857\) | 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 | ||||||||
\(862\) | 20.2476 | 0.689636 | ||||||||
\(863\) | 30.9259i | 1.05273i | 0.850259 | + | 0.526365i | \(0.176445\pi\) | ||||
−0.850259 | + | 0.526365i | \(0.823555\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30.6444 | −1.04134 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −24.0546 | − | 0.866067i | −0.816467 | − | 0.0293962i | ||||
\(869\) | 82.8844i | 2.81166i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.6865i | 0.395982i | ||||||||
\(872\) | − | 4.28991i | − | 0.145275i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 48.1092i | − | 1.62732i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.79836 | −0.0607262 | −0.0303631 | − | 0.999539i | \(-0.509666\pi\) | ||||
−0.0303631 | + | 0.999539i | \(0.509666\pi\) | |||||||
\(878\) | −22.6308 | −0.763752 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.6289 | 0.661316 | 0.330658 | − | 0.943751i | \(-0.392729\pi\) | ||||
0.330658 | + | 0.943751i | \(0.392729\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.5013 | 1.76681 | 0.883404 | − | 0.468611i | \(-0.155246\pi\) | ||||
0.883404 | + | 0.468611i | \(0.155246\pi\) | |||||||
\(884\) | − | 2.28991i | − | 0.0770182i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.3083 | 1.21980 | ||||||||
\(887\) | 39.1720 | 1.31527 | 0.657633 | − | 0.753338i | \(-0.271558\pi\) | ||||
0.657633 | + | 0.753338i | \(0.271558\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.815946 | − | 22.6625i | 0.0273659 | − | 0.760077i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.8710i | 0.363989i | ||||||||
\(893\) | − | 70.8225i | − | 2.36998i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.64404 | − | 0.0951965i | −0.0883311 | − | 0.00318029i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.6764 | 0.856834 | ||||||||
\(899\) | 68.0367 | 2.26915 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.23843i | − | 0.107888i | ||||||
\(902\) | −11.5830 | −0.385671 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.09087 | −0.269098 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.0822 | 1.56334 | 0.781669 | − | 0.623693i | \(-0.214369\pi\) | ||||
0.781669 | + | 0.623693i | \(0.214369\pi\) | |||||||
\(908\) | 14.0909 | 0.467622 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 40.6504i | − | 1.34681i | −0.739274 | − | 0.673405i | \(-0.764831\pi\) | ||
0.739274 | − | 0.673405i | \(-0.235169\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23.1659i | − | 0.766680i | ||||||
\(914\) | 25.3477i | 0.838426i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 14.5239i | − | 0.479883i | ||||||
\(917\) | 0.561705 | − | 15.6011i | 0.0185491 | − | 0.515193i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.4900 | 1.46759 | 0.733795 | − | 0.679371i | \(-0.237747\pi\) | ||||
0.733795 | + | 0.679371i | \(0.237747\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 12.7253i | − | 0.419086i | ||||||
\(923\) | −14.0909 | −0.463807 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 21.2655i | − | 0.698826i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.47847 | 0.245493 | ||||||||
\(929\) | −53.7371 | −1.76306 | −0.881529 | − | 0.472131i | \(-0.843485\pi\) | ||||
−0.881529 | + | 0.472131i | \(0.843485\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.23843 | − | 44.9146i | 0.106135 | − | 1.47202i | ||||
\(932\) | − | 20.6806i | − | 0.677417i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.1424i | 0.430031i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.0682i | 1.43965i | 0.694157 | + | 0.719823i | \(0.255777\pi\) | ||||
−0.694157 | + | 0.719823i | \(0.744223\pi\) | |||||||
\(938\) | −14.1069 | − | 0.507906i | −0.460606 | − | 0.0165837i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.0362 | −0.653163 | −0.326582 | − | 0.945169i | \(-0.605897\pi\) | ||||
−0.326582 | + | 0.945169i | \(0.605897\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.3808i | 0.533432i | ||||||||
\(944\) | −13.7734 | −0.448285 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.04781 | 0.164118 | ||||||||
\(947\) | − | 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 | ||||||||
\(952\) | 2.76417 | + | 0.0995218i | 0.0895873 | + | 0.00322552i | ||||
\(953\) | − | 31.8414i | − | 1.03144i | −0.856756 | − | 0.515722i | \(-0.827524\pi\) | ||
0.856756 | − | 0.515722i | \(-0.172476\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 5.56697i | − | 0.180049i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 26.2899i | − | 0.849389i | ||||||
\(959\) | −18.1541 | − | 0.653625i | −0.586228 | − | 0.0211067i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −51.7678 | −1.66993 | ||||||||
\(962\) | −1.87288 | −0.0603841 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 11.3839i | − | 0.366651i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.6804 | −1.05093 | −0.525466 | − | 0.850815i | \(-0.676109\pi\) | ||||
−0.525466 | + | 0.850815i | \(0.676109\pi\) | |||||||
\(968\) | − | 16.9638i | − | 0.545236i | ||||||
\(969\) | 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 | ||||
\(974\) | 39.5381i | 1.26688i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.05225i | 0.257746i | ||||||||
\(977\) | − | 2.48528i | − | 0.0795112i | −0.999209 | − | 0.0397556i | \(-0.987342\pi\) | ||
0.999209 | − | 0.0397556i | \(-0.0126579\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 22.6397i | − | 0.723566i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.62105 | −0.147464 | ||||||||
\(983\) | −49.4135 | −1.57605 | −0.788024 | − | 0.615645i | \(-0.788896\pi\) | ||||
−0.788024 | + | 0.615645i | \(0.788896\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.81826 | −0.248984 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.0909 | −0.448290 | ||||||||
\(989\) | − | 7.13868i | − | 0.226997i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.0526 | −1.81233 | −0.906167 | − | 0.422920i | \(-0.861005\pi\) | ||||
−0.906167 | + | 0.422920i | \(0.861005\pi\) | |||||||
\(992\) | −9.09768 | −0.288852 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.612402 | − | 17.0092i | 0.0194242 | − | 0.539499i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 16.6794i | − | 0.528240i | −0.964490 | − | 0.264120i | \(-0.914918\pi\) | ||
0.964490 | − | 0.264120i | \(-0.0850816\pi\) | |||||||
\(998\) | − | 31.0152i | − | 0.981770i | ||||||
\(999\) | 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 | 3150.2.b.e.251.2 | 8 | ||
3.2 | odd | 2 | 3150.2.b.f.251.6 | 8 | |||
5.2 | odd | 4 | 3150.2.d.d.3149.1 | 8 | |||
5.3 | odd | 4 | 3150.2.d.c.3149.8 | 8 | |||
5.4 | even | 2 | 630.2.b.a.251.7 | yes | 8 | ||
7.6 | odd | 2 | 3150.2.b.f.251.2 | 8 | |||
15.2 | even | 4 | 3150.2.d.a.3149.1 | 8 | |||
15.8 | even | 4 | 3150.2.d.f.3149.8 | 8 | |||
15.14 | odd | 2 | 630.2.b.b.251.3 | yes | 8 | ||
20.19 | odd | 2 | 5040.2.f.f.881.4 | 8 | |||
21.20 | even | 2 | inner | 3150.2.b.e.251.6 | 8 | ||
35.13 | even | 4 | 3150.2.d.a.3149.2 | 8 | |||
35.27 | even | 4 | 3150.2.d.f.3149.7 | 8 | |||
35.34 | odd | 2 | 630.2.b.b.251.7 | yes | 8 | ||
60.59 | even | 2 | 5040.2.f.i.881.4 | 8 | |||
105.62 | odd | 4 | 3150.2.d.c.3149.7 | 8 | |||
105.83 | odd | 4 | 3150.2.d.d.3149.2 | 8 | |||
105.104 | even | 2 | 630.2.b.a.251.3 | ✓ | 8 | ||
140.139 | even | 2 | 5040.2.f.i.881.3 | 8 | |||
420.419 | odd | 2 | 5040.2.f.f.881.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.b.a.251.3 | ✓ | 8 | 105.104 | even | 2 | ||
630.2.b.a.251.7 | yes | 8 | 5.4 | even | 2 | ||
630.2.b.b.251.3 | yes | 8 | 15.14 | odd | 2 | ||
630.2.b.b.251.7 | yes | 8 | 35.34 | odd | 2 | ||
3150.2.b.e.251.2 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.b.e.251.6 | 8 | 21.20 | even | 2 | inner | ||
3150.2.b.f.251.2 | 8 | 7.6 | odd | 2 | |||
3150.2.b.f.251.6 | 8 | 3.2 | odd | 2 | |||
3150.2.d.a.3149.1 | 8 | 15.2 | even | 4 | |||
3150.2.d.a.3149.2 | 8 | 35.13 | even | 4 | |||
3150.2.d.c.3149.7 | 8 | 105.62 | odd | 4 | |||
3150.2.d.c.3149.8 | 8 | 5.3 | odd | 4 | |||
3150.2.d.d.3149.1 | 8 | 5.2 | odd | 4 | |||
3150.2.d.d.3149.2 | 8 | 105.83 | odd | 4 | |||
3150.2.d.f.3149.7 | 8 | 35.27 | even | 4 | |||
3150.2.d.f.3149.8 | 8 | 15.8 | even | 4 | |||
5040.2.f.f.881.3 | 8 | 420.419 | odd | 2 | |||
5040.2.f.f.881.4 | 8 | 20.19 | odd | 2 | |||
5040.2.f.i.881.3 | 8 | 140.139 | even | 2 | |||
5040.2.f.i.881.4 | 8 | 60.59 | even | 2 |