Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(3149,3150)]
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, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.3149");
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.d (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: | \(25.1528766367\) |
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: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3149.7 | ||
Root | \(-3.73923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.3149 |
Dual form | 3150.2.d.f.3149.8 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64404 | − | 0.0951965i | 0.999352 | − | 0.0359809i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 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 | ||||||||
\(13\) | 2.19039 | 0.607506 | 0.303753 | − | 0.952751i | \(-0.401760\pi\) | ||||
0.303753 | + | 0.952751i | \(0.401760\pi\) | |||||||
\(14\) | 2.64404 | − | 0.0951965i | 0.706649 | − | 0.0254423i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.04544i | 0.253555i | 0.991931 | + | 0.126778i | \(0.0404635\pi\) | ||||
−0.991931 | + | 0.126778i | \(0.959537\pi\) | |||||||
\(18\) | 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 | ||||||||
\(22\) | 5.28808i | 1.12742i | ||||||||
\(23\) | −7.47847 | −1.55937 | −0.779684 | − | 0.626173i | \(-0.784620\pi\) | ||||
−0.779684 | + | 0.626173i | \(0.784620\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.19039 | 0.429571 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.64404 | − | 0.0951965i | 0.499676 | − | 0.0179904i | ||||
\(29\) | − | 7.47847i | − | 1.38872i | −0.719629 | − | 0.694358i | \(-0.755688\pi\) | ||
0.719629 | − | 0.694358i | \(-0.244312\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.09768i | 1.63399i | 0.576643 | + | 0.816996i | \(0.304362\pi\) | ||||
−0.576643 | + | 0.816996i | \(0.695638\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.04544i | 0.179291i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.855043i | 0.140568i | 0.997527 | + | 0.0702841i | \(0.0223906\pi\) | ||||
−0.997527 | + | 0.0702841i | \(0.977609\pi\) | |||||||
\(38\) | 6.43303i | 1.04358i | ||||||||
\(39\) | 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 | ||||||||
\(43\) | − | 0.954564i | − | 0.145570i | −0.997348 | − | 0.0727849i | \(-0.976811\pi\) | ||
0.997348 | − | 0.0727849i | \(-0.0231886\pi\) | |||||||
\(44\) | 5.28808i | 0.797207i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.47847 | −1.10264 | ||||||||
\(47\) | 11.0092i | 1.60585i | 0.596077 | + | 0.802927i | \(0.296725\pi\) | ||||
−0.596077 | + | 0.802927i | \(0.703275\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98188 | − | 0.503406i | 0.997411 | − | 0.0719152i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.19039 | 0.303753 | ||||||||
\(53\) | 3.09768 | 0.425500 | 0.212750 | − | 0.977107i | \(-0.431758\pi\) | ||||
0.212750 | + | 0.977107i | \(0.431758\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.64404 | − | 0.0951965i | 0.353324 | − | 0.0127212i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 7.47847i | − | 0.981971i | ||||||
\(59\) | −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 | \(-0.172391\pi\) | |||||||
\(62\) | 9.09768i | 1.15541i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.33535i | − | 0.651817i | −0.945401 | − | 0.325908i | \(-0.894330\pi\) | ||
0.945401 | − | 0.325908i | \(-0.105670\pi\) | |||||||
\(68\) | 1.04544i | 0.126778i | ||||||||
\(69\) | 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 | ||||||||
\(73\) | 4.57615 | 0.535598 | 0.267799 | − | 0.963475i | \(-0.413704\pi\) | ||||
0.267799 | + | 0.963475i | \(0.413704\pi\) | |||||||
\(74\) | 0.855043i | 0.0993967i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.43303i | 0.737920i | ||||||||
\(77\) | 0.503406 | + | 13.9819i | 0.0573684 | + | 1.59338i | ||||
\(78\) | 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 | ||||||||
\(82\) | 2.19039 | 0.241888 | ||||||||
\(83\) | − | 4.38079i | − | 0.480854i | −0.970667 | − | 0.240427i | \(-0.922713\pi\) | ||
0.970667 | − | 0.240427i | \(-0.0772874\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 0.954564i | − | 0.102933i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.28808i | 0.563711i | ||||||||
\(89\) | −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 | ||||
\(92\) | −7.47847 | −0.779684 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.0092i | 1.13551i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.8593 | 1.20412 | 0.602062 | − | 0.798449i | \(-0.294346\pi\) | ||||
0.602062 | + | 0.798449i | \(0.294346\pi\) | |||||||
\(98\) | 6.98188 | − | 0.503406i | 0.705276 | − | 0.0508517i | ||||
\(99\) | 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 | ||||||||
\(103\) | 16.6757 | 1.64310 | 0.821552 | − | 0.570134i | \(-0.193109\pi\) | ||||
0.821552 | + | 0.570134i | \(0.193109\pi\) | |||||||
\(104\) | 2.19039 | 0.214786 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.09768 | 0.300874 | ||||||||
\(107\) | 7.00681 | 0.677374 | 0.338687 | − | 0.940899i | \(-0.390017\pi\) | ||||
0.338687 | + | 0.940899i | \(0.390017\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.28991 | 0.410899 | 0.205450 | − | 0.978668i | \(-0.434134\pi\) | ||||
0.205450 | + | 0.978668i | \(0.434134\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.64404 | − | 0.0951965i | 0.249838 | − | 0.00899522i | ||||
\(113\) | 8.09087 | 0.761125 | 0.380563 | − | 0.924755i | \(-0.375730\pi\) | ||||
0.380563 | + | 0.924755i | \(0.375730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 7.47847i | − | 0.694358i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.7734 | −1.26794 | ||||||||
\(119\) | 0.0995218 | + | 2.76417i | 0.00912314 | + | 0.253391i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.9638 | −1.54216 | ||||||||
\(122\) | − | 8.05225i | − | 0.729016i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.09768i | 0.816996i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.57118i | − | 0.760569i | −0.924870 | − | 0.380285i | \(-0.875826\pi\) | ||
0.924870 | − | 0.380285i | \(-0.124174\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.90048 | 0.515527 | 0.257764 | − | 0.966208i | \(-0.417014\pi\) | ||||
0.257764 | + | 0.966208i | \(0.417014\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.612402 | + | 17.0092i | 0.0531020 | + | 1.47488i | ||||
\(134\) | − | 5.33535i | − | 0.460904i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.04544i | 0.0896454i | ||||||||
\(137\) | −6.86607 | −0.586608 | −0.293304 | − | 0.956019i | \(-0.594755\pi\) | ||||
−0.293304 | + | 0.956019i | \(0.594755\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | − | 6.43303i | − | 0.539848i | ||||||
\(143\) | 11.5830i | 0.968616i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.57615 | 0.378725 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.855043i | 0.0702841i | ||||||||
\(149\) | 15.9638i | 1.30780i | 0.756580 | + | 0.653901i | \(0.226869\pi\) | ||||
−0.756580 | + | 0.653901i | \(0.773131\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0546 | 1.30651 | 0.653253 | − | 0.757139i | \(-0.273404\pi\) | ||||
0.653253 | + | 0.757139i | \(0.273404\pi\) | |||||||
\(152\) | 6.43303i | 0.521788i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.503406 | + | 13.9819i | 0.0405656 | + | 1.12669i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.7665 | 1.97659 | 0.988293 | − | 0.152569i | \(-0.0487548\pi\) | ||||
0.988293 | + | 0.152569i | \(0.0487548\pi\) | |||||||
\(158\) | −15.6738 | −1.24694 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.7734 | + | 0.711924i | −1.55836 | + | 0.0561075i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.42622i | 0.581667i | 0.956774 | + | 0.290833i | \(0.0939325\pi\) | ||||
−0.956774 | + | 0.290833i | \(0.906068\pi\) | |||||||
\(164\) | 2.19039 | 0.171041 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 4.38079i | − | 0.340015i | ||||||
\(167\) | − | 0.573779i | − | 0.0444003i | −0.999754 | − | 0.0222002i | \(-0.992933\pi\) | ||
0.999754 | − | 0.0222002i | \(-0.00706711\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.20218 | −0.630937 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 0.954564i | − | 0.0727849i | ||||||
\(173\) | − | 9.96375i | − | 0.757530i | −0.925493 | − | 0.378765i | \(-0.876349\pi\) | ||
0.925493 | − | 0.378765i | \(-0.123651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.28808i | 0.398604i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.28126 | −0.320894 | ||||||||
\(179\) | − | 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 | \(-0.134176\pi\) | |||||||
\(182\) | 5.79148 | − | 0.208518i | 0.429293 | − | 0.0154564i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.47847 | −0.551320 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.52834 | −0.404272 | ||||||||
\(188\) | 11.0092i | 0.802927i | ||||||||
\(189\) | 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 | ||||||||
\(193\) | − | 8.47166i | − | 0.609803i | −0.952384 | − | 0.304902i | \(-0.901376\pi\) | ||
0.952384 | − | 0.304902i | \(-0.0986236\pi\) | |||||||
\(194\) | 11.8593 | 0.851445 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.98188 | − | 0.503406i | 0.498705 | − | 0.0359576i | ||||
\(197\) | −12.8661 | −0.916669 | −0.458335 | − | 0.888780i | \(-0.651554\pi\) | ||||
−0.458335 | + | 0.888780i | \(0.651554\pi\) | |||||||
\(198\) | 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 | ||||||||
\(202\) | 11.5830 | 0.814975 | ||||||||
\(203\) | −0.711924 | − | 19.7734i | −0.0499673 | − | 1.38782i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.6757 | 1.16185 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.19039 | 0.151876 | ||||||||
\(209\) | −34.0184 | −2.35310 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 3.09768 | 0.212750 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.00681 | 0.478976 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.866067 | + | 24.0546i | 0.0587925 | + | 1.63293i | ||||
\(218\) | 4.28991 | 0.290550 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.28991i | 0.154036i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.8710 | 0.727979 | 0.363989 | − | 0.931403i | \(-0.381414\pi\) | ||||
0.363989 | + | 0.931403i | \(0.381414\pi\) | |||||||
\(224\) | 2.64404 | − | 0.0951965i | 0.176662 | − | 0.00636058i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.09087 | 0.538197 | ||||||||
\(227\) | 14.0909i | 0.935244i | 0.883929 | + | 0.467622i | \(0.154889\pi\) | ||||
−0.883929 | + | 0.467622i | \(0.845111\pi\) | |||||||
\(228\) | 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 | ||||||||
\(232\) | − | 7.47847i | − | 0.490986i | ||||||
\(233\) | 20.6806 | 1.35483 | 0.677417 | − | 0.735599i | \(-0.263099\pi\) | ||||
0.677417 | + | 0.735599i | \(0.263099\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.7734 | −0.896569 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.0995218 | + | 2.76417i | 0.00645104 | + | 0.179175i | ||||
\(239\) | − | 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 | \(-0.119496\pi\) | |||||||
\(242\) | −16.9638 | −1.09047 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.05225i | − | 0.515492i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.0909i | 0.896581i | ||||||||
\(248\) | 9.09768i | 0.577703i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.71874 | 0.108486 | 0.0542428 | − | 0.998528i | \(-0.482725\pi\) | ||||
0.0542428 | + | 0.998528i | \(0.482725\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 39.5467i | − | 2.48628i | ||||||
\(254\) | − | 8.57118i | − | 0.537804i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 2.18779i | − | 0.136471i | −0.997669 | − | 0.0682354i | \(-0.978263\pi\) | ||
0.997669 | − | 0.0682354i | \(-0.0217369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0813970 | + | 2.26077i | 0.00505777 | + | 0.140477i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.90048 | 0.364533 | ||||||||
\(263\) | −17.3876 | −1.07217 | −0.536083 | − | 0.844166i | \(-0.680096\pi\) | ||||
−0.536083 | + | 0.844166i | \(0.680096\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.612402 | + | 17.0092i | 0.0375488 | + | 1.04290i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 5.33535i | − | 0.325908i | ||||||
\(269\) | −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 | \(-0.985701\pi\) | ||
0.998991 | − | 0.0449053i | \(-0.0142986\pi\) | |||||||
\(272\) | 1.04544i | 0.0633888i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.86607 | −0.414794 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 10.7642i | − | 0.646756i | −0.946270 | − | 0.323378i | \(-0.895181\pi\) | ||
0.946270 | − | 0.323378i | \(-0.104819\pi\) | |||||||
\(278\) | 13.9115i | 0.834356i | ||||||||
\(279\) | 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 | ||||||||
\(283\) | −24.5898 | −1.46171 | −0.730855 | − | 0.682532i | \(-0.760879\pi\) | ||||
−0.730855 | + | 0.682532i | \(0.760879\pi\) | |||||||
\(284\) | − | 6.43303i | − | 0.381730i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.5830i | 0.684915i | ||||||||
\(287\) | 5.79148 | − | 0.208518i | 0.341860 | − | 0.0123084i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.9071 | 0.935710 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.57615 | 0.267799 | ||||||||
\(293\) | 12.6707i | 0.740230i | 0.928986 | + | 0.370115i | \(0.120682\pi\) | ||||
−0.928986 | + | 0.370115i | \(0.879318\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.855043i | 0.0496983i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.9638i | 0.924755i | ||||||||
\(299\) | −16.3808 | −0.947325 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0908711 | − | 2.52390i | −0.00523773 | − | 0.145475i | ||||
\(302\) | 16.0546 | 0.923840 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.43303i | 0.368960i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.866067 | −0.0494291 | −0.0247145 | − | 0.999695i | \(-0.507868\pi\) | ||||
−0.0247145 | + | 0.999695i | \(0.507868\pi\) | |||||||
\(308\) | 0.503406 | + | 13.9819i | 0.0286842 | + | 0.796691i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.71009 | −0.550608 | −0.275304 | − | 0.961357i | \(-0.588779\pi\) | ||||
−0.275304 | + | 0.961357i | \(0.588779\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.80096 | 0.327889 | 0.163945 | − | 0.986470i | \(-0.447578\pi\) | ||||
0.163945 | + | 0.986470i | \(0.447578\pi\) | |||||||
\(314\) | 24.7665 | 1.39766 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.6738 | −0.881722 | ||||||||
\(317\) | 28.1591 | 1.58157 | 0.790787 | − | 0.612092i | \(-0.209672\pi\) | ||||
0.790787 | + | 0.612092i | \(0.209672\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.5467 | 2.21419 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −19.7734 | + | 0.711924i | −1.10193 | + | 0.0396740i | ||||
\(323\) | −6.72532 | −0.374207 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.42622i | 0.411300i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.19039 | 0.120944 | ||||||||
\(329\) | 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 | \(0.680891\pi\) | |||||||
\(332\) | − | 4.38079i | − | 0.240427i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 0.573779i | − | 0.0313958i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.3992i | 1.54700i | 0.633796 | + | 0.773500i | \(0.281496\pi\) | ||||
−0.633796 | + | 0.773500i | \(0.718504\pi\) | |||||||
\(338\) | −8.20218 | −0.446140 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −48.1092 | −2.60526 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4124 | − | 1.99567i | 0.994177 | − | 0.107756i | ||||
\(344\) | − | 0.954564i | − | 0.0514667i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 9.96375i | − | 0.535655i | ||||||
\(347\) | −12.5898 | −0.675855 | −0.337927 | − | 0.941172i | \(-0.609726\pi\) | ||||
−0.337927 | + | 0.941172i | \(0.609726\pi\) | |||||||
\(348\) | 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 | ||||||||
\(352\) | 5.28808i | 0.281855i | ||||||||
\(353\) | − | 15.1363i | − | 0.805624i | −0.915283 | − | 0.402812i | \(-0.868033\pi\) | ||
0.915283 | − | 0.402812i | \(-0.131967\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.28126 | −0.226907 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 1.77336i | − | 0.0937249i | ||||||
\(359\) | − | 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 | ||||||||
\(362\) | − | 11.0092i | − | 0.578630i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.79148 | − | 0.208518i | 0.303556 | − | 0.0109293i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.6825 | 0.609821 | 0.304910 | − | 0.952381i | \(-0.401373\pi\) | ||||
0.304910 | + | 0.952381i | \(0.401373\pi\) | |||||||
\(368\) | −7.47847 | −0.389842 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.19039 | − | 0.294888i | 0.425224 | − | 0.0153098i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.8550i | 0.665609i | 0.942996 | + | 0.332804i | \(0.107995\pi\) | ||||
−0.942996 | + | 0.332804i | \(0.892005\pi\) | |||||||
\(374\) | −5.52834 | −0.285864 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.0092i | 0.567755i | ||||||||
\(377\) | − | 16.3808i | − | 0.843653i | ||||||
\(378\) | 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 | ||||||||
\(382\) | − | 5.56697i | − | 0.284831i | ||||||
\(383\) | − | 23.0092i | − | 1.17571i | −0.808965 | − | 0.587857i | \(-0.799972\pi\) | ||
0.808965 | − | 0.587857i | \(-0.200028\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 8.47166i | − | 0.431196i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.8593 | 0.602062 | ||||||||
\(389\) | − | 10.1591i | − | 0.515088i | −0.966267 | − | 0.257544i | \(-0.917087\pi\) | ||
0.966267 | − | 0.257544i | \(-0.0829132\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.81826i | − | 0.395386i | ||||||
\(392\) | 6.98188 | − | 0.503406i | 0.352638 | − | 0.0254258i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.8661 | −0.648183 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.9141 | 0.698329 | 0.349164 | − | 0.937061i | \(-0.386465\pi\) | ||||
0.349164 | + | 0.937061i | \(0.386465\pi\) | |||||||
\(398\) | − | 17.5830i | − | 0.881354i | ||||||
\(399\) | 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 | ||||||||
\(403\) | 19.9275i | 0.992660i | ||||||||
\(404\) | 11.5830 | 0.576274 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.711924 | − | 19.7734i | −0.0353322 | − | 0.981335i | ||||
\(407\) | −4.52153 | −0.224124 | ||||||||
\(408\) | 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 | ||||||||
\(412\) | 16.6757 | 0.821552 | ||||||||
\(413\) | −36.4173 | + | 1.31117i | −1.79198 | + | 0.0645187i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.19039 | 0.107393 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −34.0184 | −1.66389 | ||||||||
\(419\) | −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 | \(0.493387\pi\) | |||||||
\(422\) | 4.00000 | 0.194717 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.09768 | 0.150437 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.766545 | − | 21.2905i | −0.0370957 | − | 1.03032i | ||||
\(428\) | 7.00681 | 0.338687 | ||||||||
\(429\) | 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 | ||||||||
\(433\) | 30.6444 | 1.47268 | 0.736338 | − | 0.676614i | \(-0.236553\pi\) | ||||
0.736338 | + | 0.676614i | \(0.236553\pi\) | |||||||
\(434\) | 0.866067 | + | 24.0546i | 0.0415726 | + | 1.15466i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.28991 | 0.205450 | ||||||||
\(437\) | − | 48.1092i | − | 2.30138i | ||||||
\(438\) | 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 | ||||||||
\(442\) | 2.28991i | 0.108920i | ||||||||
\(443\) | 36.3083 | 1.72506 | 0.862529 | − | 0.506007i | \(-0.168879\pi\) | ||||
0.862529 | + | 0.506007i | \(0.168879\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.8710 | 0.514759 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.64404 | − | 0.0951965i | 0.124919 | − | 0.00449761i | ||||
\(449\) | − | 25.6764i | − | 1.21175i | −0.795561 | − | 0.605873i | \(-0.792824\pi\) | ||
0.795561 | − | 0.605873i | \(-0.207176\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.5830i | 0.545421i | ||||||||
\(452\) | 8.09087 | 0.380563 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.0909i | 0.661317i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 25.3477i | − | 1.18571i | −0.805308 | − | 0.592857i | \(-0.798000\pi\) | ||
0.805308 | − | 0.592857i | \(-0.202000\pi\) | |||||||
\(458\) | 14.5239i | 0.678657i | ||||||||
\(459\) | 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 | ||||||||
\(463\) | − | 21.2655i | − | 0.988289i | −0.869380 | − | 0.494145i | \(-0.835481\pi\) | ||
0.869380 | − | 0.494145i | \(-0.164519\pi\) | |||||||
\(464\) | − | 7.47847i | − | 0.347179i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.6806 | 0.958013 | ||||||||
\(467\) | 13.1424i | 0.608156i | 0.952647 | + | 0.304078i | \(0.0983483\pi\) | ||||
−0.952647 | + | 0.304078i | \(0.901652\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.507906 | − | 14.1069i | −0.0234529 | − | 0.651395i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.7734 | −0.633970 | ||||||||
\(473\) | 5.04781 | 0.232099 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.0995218 | + | 2.76417i | 0.00456157 | + | 0.126696i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 5.56697i | − | 0.254627i | ||||||
\(479\) | 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 | ||||||||
\(482\) | − | 11.3839i | − | 0.518523i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.9638 | −0.771080 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 39.5381i | − | 1.79164i | −0.444416 | − | 0.895820i | \(-0.646589\pi\) | ||
0.444416 | − | 0.895820i | \(-0.353411\pi\) | |||||||
\(488\) | − | 8.05225i | − | 0.364508i | ||||||
\(489\) | 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 | ||||||||
\(493\) | 7.81826 | 0.352117 | ||||||||
\(494\) | 14.0909i | 0.633978i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.09768i | 0.408498i | ||||||||
\(497\) | −0.612402 | − | 17.0092i | −0.0274700 | − | 0.762966i | ||||
\(498\) | 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 | ||||||||
\(502\) | 1.71874 | 0.0767109 | ||||||||
\(503\) | 28.3385i | 1.26355i | 0.775152 | + | 0.631775i | \(0.217673\pi\) | ||||
−0.775152 | + | 0.631775i | \(0.782327\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 39.5467i | − | 1.75807i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 8.57118i | − | 0.380285i | ||||||
\(509\) | 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 | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 2.18779i | − | 0.0964994i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −58.2174 | −2.56040 | ||||||||
\(518\) | 0.0813970 | + | 2.26077i | 0.00357638 | + | 0.0993323i | ||||
\(519\) | 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 | ||||||||
\(523\) | −3.51472 | −0.153688 | −0.0768440 | − | 0.997043i | \(-0.524484\pi\) | ||||
−0.0768440 | + | 0.997043i | \(0.524484\pi\) | |||||||
\(524\) | 5.90048 | 0.257764 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.3876 | −0.758135 | ||||||||
\(527\) | −9.51104 | −0.414307 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.9275 | 1.43163 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.612402 | + | 17.0092i | 0.0265510 | + | 0.737442i | ||||
\(533\) | 4.79782 | 0.207817 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 5.33535i | − | 0.230452i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.3445 | −0.877115 | ||||||||
\(539\) | 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 | \(0.272486\pi\) | |||||||
\(542\) | − | 1.47847i | − | 0.0635057i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.04544i | 0.0448227i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.86369i | 0.293470i | 0.989176 | + | 0.146735i | \(0.0468765\pi\) | ||||
−0.989176 | + | 0.146735i | \(0.953123\pi\) | |||||||
\(548\) | −6.86607 | −0.293304 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 48.1092 | 2.04952 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.4422 | + | 1.49209i | −1.76230 | + | 0.0634503i | ||||
\(554\) | − | 10.7642i | − | 0.457326i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.9115i | 0.589979i | ||||||||
\(557\) | −1.81826 | −0.0770421 | −0.0385210 | − | 0.999258i | \(-0.512265\pi\) | ||||
−0.0385210 | + | 0.999258i | \(0.512265\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.09087i | − | 0.0884344i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.42806i | 0.102422i | ||||||||
\(563\) | − | 34.0184i | − | 1.43370i | −0.697226 | − | 0.716852i | \(-0.745582\pi\) | ||
0.697226 | − | 0.716852i | \(-0.254418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −24.5898 | −1.03359 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.43303i | − | 0.269924i | ||||||
\(569\) | 5.10871i | 0.214168i | 0.994250 | + | 0.107084i | \(0.0341514\pi\) | ||||
−0.994250 | + | 0.107084i | \(0.965849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.8214 | 0.452861 | 0.226431 | − | 0.974027i | \(-0.427294\pi\) | ||||
0.226431 | + | 0.974027i | \(0.427294\pi\) | |||||||
\(572\) | 11.5830i | 0.484308i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.79148 | − | 0.208518i | 0.241732 | − | 0.00870336i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.1523 | −1.62993 | −0.814966 | − | 0.579509i | \(-0.803244\pi\) | ||||
−0.814966 | + | 0.579509i | \(0.803244\pi\) | |||||||
\(578\) | 15.9071 | 0.661647 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.417035 | − | 11.5830i | −0.0173015 | − | 0.480542i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.3808i | 0.678423i | ||||||||
\(584\) | 4.57615 | 0.189363 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.6707i | 0.523422i | ||||||||
\(587\) | 5.52834i | 0.228179i | 0.993470 | + | 0.114090i | \(0.0363951\pi\) | ||||
−0.993470 | + | 0.114090i | \(0.963605\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −58.5257 | −2.41151 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.855043i | 0.0351420i | ||||||||
\(593\) | 18.6830i | 0.767220i | 0.923495 | + | 0.383610i | \(0.125319\pi\) | ||||
−0.923495 | + | 0.383610i | \(0.874681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.9638i | 0.653901i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.3808 | −0.669860 | ||||||||
\(599\) | − | 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 | \(-0.171189\pi\) | |||||||
\(602\) | −0.0908711 | − | 2.52390i | −0.00370363 | − | 0.102867i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.0546 | 0.653253 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.4336 | −1.27585 | −0.637925 | − | 0.770099i | \(-0.720207\pi\) | ||||
−0.637925 | + | 0.770099i | \(0.720207\pi\) | |||||||
\(608\) | 6.43303i | 0.260894i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.1144i | 0.975566i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.4532i | 1.59350i | 0.604308 | + | 0.796751i | \(0.293450\pi\) | ||||
−0.604308 | + | 0.796751i | \(0.706550\pi\) | |||||||
\(614\) | −0.866067 | −0.0349516 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.503406 | + | 13.9819i | 0.0202828 | + | 0.563346i | ||||
\(617\) | −39.7421 | −1.59996 | −0.799978 | − | 0.600029i | \(-0.795156\pi\) | ||||
−0.799978 | + | 0.600029i | \(0.795156\pi\) | |||||||
\(618\) | 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 | ||||||||
\(622\) | −9.71009 | −0.389339 | ||||||||
\(623\) | −11.3198 | + | 0.407561i | −0.453519 | + | 0.0163286i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.80096 | 0.231853 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.7665 | 0.988293 | ||||||||
\(629\) | −0.893892 | −0.0356418 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.3083 | −0.649223 | −0.324611 | − | 0.945847i | \(-0.605233\pi\) | ||||
−0.324611 | + | 0.945847i | \(0.605233\pi\) | |||||||
\(632\) | −15.6738 | −0.623472 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.1591 | 1.11834 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.2931 | − | 1.10266i | 0.605933 | − | 0.0436889i | ||||
\(638\) | 39.5467 | 1.56567 | ||||||||
\(639\) | 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 | ||||||||
\(643\) | −14.3992 | −0.567847 | −0.283924 | − | 0.958847i | \(-0.591636\pi\) | ||||
−0.283924 | + | 0.958847i | \(0.591636\pi\) | |||||||
\(644\) | −19.7734 | + | 0.711924i | −0.779179 | + | 0.0280537i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.72532 | −0.264604 | ||||||||
\(647\) | 31.7708i | 1.24904i | 0.781010 | + | 0.624519i | \(0.214705\pi\) | ||||
−0.781010 | + | 0.624519i | \(0.785295\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 72.8346i | − | 2.85901i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.42622i | 0.290833i | ||||||||
\(653\) | 20.7389 | 0.811578 | 0.405789 | − | 0.913967i | \(-0.366997\pi\) | ||||
0.405789 | + | 0.913967i | \(0.366997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.19039 | 0.0855205 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.04804 | + | 29.1087i | 0.0408567 | + | 1.13478i | ||||
\(659\) | 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 | \(0.775067\pi\) | |||||||
\(662\) | −19.5830 | −0.761114 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 4.38079i | − | 0.170007i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 55.9275i | 2.16552i | ||||||||
\(668\) | − | 0.573779i | − | 0.0222002i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.5809 | 1.64382 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 18.6943i | − | 0.720611i | −0.932834 | − | 0.360306i | \(-0.882672\pi\) | ||
0.932834 | − | 0.360306i | \(-0.117328\pi\) | |||||||
\(674\) | 28.3992i | 1.09389i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.20218 | −0.315468 | ||||||||
\(677\) | − | 36.5861i | − | 1.40612i | −0.711131 | − | 0.703059i | \(-0.751817\pi\) | ||
0.711131 | − | 0.703059i | \(-0.248183\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.3563 | − | 1.12896i | 1.20335 | − | 0.0433255i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −48.1092 | −1.84220 | ||||||||
\(683\) | −36.9207 | −1.41273 | −0.706365 | − | 0.707847i | \(-0.749666\pi\) | ||||
−0.706365 | + | 0.707847i | \(0.749666\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.4124 | − | 1.99567i | 0.702990 | − | 0.0761952i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 0.954564i | − | 0.0363924i | ||||||
\(689\) | 6.78514 | 0.258493 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 5.20823i | − | 0.198130i | −0.995081 | − | 0.0990652i | \(-0.968415\pi\) | ||
0.995081 | − | 0.0990652i | \(-0.0315852\pi\) | |||||||
\(692\) | − | 9.96375i | − | 0.378765i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.5898 | −0.477901 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.28991i | 0.0867367i | ||||||||
\(698\) | − | 20.9956i | − | 0.794694i | ||||||
\(699\) | 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 | ||||||||
\(703\) | −5.50052 | −0.207456 | ||||||||
\(704\) | 5.28808i | 0.199302i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 15.1363i | − | 0.569662i | ||||||
\(707\) | 30.6258 | − | 1.10266i | 1.15180 | − | 0.0414697i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.09087 | 0.153636 | 0.0768179 | − | 0.997045i | \(-0.475524\pi\) | ||||
0.0768179 | + | 0.997045i | \(0.475524\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.28126 | −0.160447 | ||||||||
\(713\) | − | 68.0367i | − | 2.54800i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 1.77336i | − | 0.0662735i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 33.1909i | − | 1.23867i | ||||||
\(719\) | 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 | ||||
\(722\) | −22.3839 | −0.833043 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 11.0092i | − | 0.409153i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.7849 | −1.51263 | −0.756314 | − | 0.654208i | \(-0.773002\pi\) | ||||
−0.756314 | + | 0.654208i | \(0.773002\pi\) | |||||||
\(728\) | 5.79148 | − | 0.208518i | 0.214647 | − | 0.00772818i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.997936 | 0.0369100 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.2481 | −1.44966 | −0.724832 | − | 0.688926i | \(-0.758083\pi\) | ||||
−0.724832 | + | 0.688926i | \(0.758083\pi\) | |||||||
\(734\) | 11.6825 | 0.431208 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.47847 | −0.275660 | ||||||||
\(737\) | 28.2137 | 1.03927 | ||||||||
\(738\) | 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 | ||||||||
\(742\) | 8.19039 | − | 0.294888i | 0.300679 | − | 0.0108257i | ||||
\(743\) | 35.7185 | 1.31039 | 0.655193 | − | 0.755462i | \(-0.272588\pi\) | ||||
0.655193 | + | 0.755462i | \(0.272588\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.8550i | 0.470657i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.52834 | −0.202136 | ||||||||
\(749\) | 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 | \(0.553345\pi\) | |||||||
\(752\) | 11.0092i | 0.401464i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 16.3808i | − | 0.596553i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 48.2027i | − | 1.75196i | −0.482350 | − | 0.875979i | \(-0.660217\pi\) | ||
0.482350 | − | 0.875979i | \(-0.339783\pi\) | |||||||
\(758\) | −25.0751 | −0.910767 | ||||||||
\(759\) | 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 | ||||||||
\(763\) | 11.3427 | − | 0.408385i | 0.410633 | − | 0.0147845i | ||||
\(764\) | − | 5.56697i | − | 0.201406i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 23.0092i | − | 0.831356i | ||||||
\(767\) | −30.1691 | −1.08934 | ||||||||
\(768\) | 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 | ||||||||
\(772\) | − | 8.47166i | − | 0.304902i | ||||||
\(773\) | 12.2726i | 0.441415i | 0.975340 | + | 0.220708i | \(0.0708367\pi\) | ||||
−0.975340 | + | 0.220708i | \(0.929163\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.8593 | 0.425722 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 10.1591i | − | 0.364222i | ||||||
\(779\) | 14.0909i | 0.504858i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.0184 | 1.21727 | ||||||||
\(782\) | − | 7.81826i | − | 0.279580i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.98188 | − | 0.503406i | 0.249353 | − | 0.0179788i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.4286 | −0.763847 | −0.381923 | − | 0.924194i | \(-0.624738\pi\) | ||||
−0.381923 | + | 0.924194i | \(0.624738\pi\) | |||||||
\(788\) | −12.8661 | −0.458335 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.3926 | − | 0.770222i | 0.760632 | − | 0.0273859i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 17.6376i | − | 0.626329i | ||||||
\(794\) | 13.9141 | 0.493793 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 17.5830i | − | 0.623212i | ||||||
\(797\) | − | 9.96375i | − | 0.352934i | −0.984307 | − | 0.176467i | \(-0.943533\pi\) | ||
0.984307 | − | 0.176467i | \(-0.0564669\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.5094 | −0.407173 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 14.6197i | − | 0.516241i | ||||||
\(803\) | 24.1990i | 0.853966i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19.9275i | 0.701916i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.5830 | 0.407487 | ||||||||
\(809\) | 32.6234i | 1.14698i | 0.819213 | + | 0.573489i | \(0.194411\pi\) | ||||
−0.819213 | + | 0.573489i | \(0.805589\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 56.6914i | 1.99071i | 0.0962936 | + | 0.995353i | \(0.469301\pi\) | ||||
−0.0962936 | + | 0.995353i | \(0.530699\pi\) | |||||||
\(812\) | −0.711924 | − | 19.7734i | −0.0249836 | − | 0.693909i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.52153 | −0.158480 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.14075 | 0.214837 | ||||||||
\(818\) | − | 12.0000i | − | 0.419570i | ||||||
\(819\) | 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 | ||||||||
\(823\) | 29.6462i | 1.03340i | 0.856166 | + | 0.516701i | \(0.172840\pi\) | ||||
−0.856166 | + | 0.516701i | \(0.827160\pi\) | |||||||
\(824\) | 16.6757 | 0.580925 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36.4173 | + | 1.31117i | −1.26712 | + | 0.0456216i | ||||
\(827\) | 42.1129 | 1.46441 | 0.732205 | − | 0.681084i | \(-0.238491\pi\) | ||||
0.732205 | + | 0.681084i | \(0.238491\pi\) | |||||||
\(828\) | 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 | ||||||||
\(832\) | 2.19039 | 0.0759382 | ||||||||
\(833\) | 0.526279 | + | 7.29910i | 0.0182345 | + | 0.252899i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −34.0184 | −1.17655 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.60743 | −0.0900721 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 0.852443 | 0.0293771 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −44.8528 | + | 1.61489i | −1.54116 | + | 0.0554882i | ||||
\(848\) | 3.09768 | 0.106375 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 6.39441i | − | 0.219198i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.4866 | −1.04384 | −0.521920 | − | 0.852994i | \(-0.674784\pi\) | ||||
−0.521920 | + | 0.852994i | \(0.674784\pi\) | |||||||
\(854\) | −0.766545 | − | 21.2905i | −0.0262306 | − | 0.728544i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.00681 | 0.239488 | ||||||||
\(857\) | − | 5.22718i | − | 0.178557i | −0.996007 | − | 0.0892785i | \(-0.971544\pi\) | ||
0.996007 | − | 0.0892785i | \(-0.0284561\pi\) | |||||||
\(858\) | 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 | ||||||||
\(862\) | 20.2476i | 0.689636i | ||||||||
\(863\) | 30.9259 | 1.05273 | 0.526365 | − | 0.850259i | \(-0.323555\pi\) | ||||
0.526365 | + | 0.850259i | \(0.323555\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30.6444 | 1.04134 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.866067 | + | 24.0546i | 0.0293962 | + | 0.816467i | ||||
\(869\) | − | 82.8844i | − | 2.81166i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 11.6865i | − | 0.395982i | ||||||
\(872\) | 4.28991 | 0.145275 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 48.1092i | − | 1.62732i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.79836i | − | 0.0607262i | −0.999539 | − | 0.0303631i | \(-0.990334\pi\) | ||
0.999539 | − | 0.0303631i | \(-0.00966636\pi\) | |||||||
\(878\) | − | 22.6308i | − | 0.763752i | ||||||
\(879\) | 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 | ||||||||
\(883\) | − | 52.5013i | − | 1.76681i | −0.468611 | − | 0.883404i | \(-0.655246\pi\) | ||
0.468611 | − | 0.883404i | \(-0.344754\pi\) | |||||||
\(884\) | 2.28991i | 0.0770182i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.3083 | 1.21980 | ||||||||
\(887\) | − | 39.1720i | − | 1.31527i | −0.753338 | − | 0.657633i | \(-0.771558\pi\) | ||
0.753338 | − | 0.657633i | \(-0.228442\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.815946 | − | 22.6625i | −0.0273659 | − | 0.760077i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.8710 | 0.363989 | ||||||||
\(893\) | −70.8225 | −2.36998 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.64404 | − | 0.0951965i | 0.0883311 | − | 0.00318029i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 25.6764i | − | 0.856834i | ||||||
\(899\) | 68.0367 | 2.26915 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.23843i | 0.107888i | ||||||||
\(902\) | 11.5830i | 0.385671i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.09087 | 0.269098 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.0822i | 1.56334i | 0.623693 | + | 0.781669i | \(0.285631\pi\) | ||||
−0.623693 | + | 0.781669i | \(0.714369\pi\) | |||||||
\(908\) | 14.0909i | 0.467622i | ||||||||
\(909\) | 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 | ||||||||
\(913\) | 23.1659 | 0.766680 | ||||||||
\(914\) | − | 25.3477i | − | 0.838426i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.5239i | 0.479883i | ||||||||
\(917\) | 15.6011 | − | 0.561705i | 0.515193 | − | 0.0185491i | ||||
\(918\) | 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 | ||||||||
\(922\) | −12.7253 | −0.419086 | ||||||||
\(923\) | − | 14.0909i | − | 0.463807i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 21.2655i | − | 0.698826i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 7.47847i | − | 0.245493i | ||||||
\(929\) | −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 | ||||
\(932\) | 20.6806 | 0.677417 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.1424i | 0.430031i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.0682 | 1.43965 | 0.719823 | − | 0.694157i | \(-0.244223\pi\) | ||||
0.719823 | + | 0.694157i | \(0.244223\pi\) | |||||||
\(938\) | −0.507906 | − | 14.1069i | −0.0165837 | − | 0.460606i | ||||
\(939\) | 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 | ||||||||
\(943\) | −16.3808 | −0.533432 | ||||||||
\(944\) | −13.7734 | −0.448285 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.04781 | 0.164118 | ||||||||
\(947\) | 30.9244 | 1.00491 | 0.502453 | − | 0.864604i | \(-0.332431\pi\) | ||||
0.502453 | + | 0.864604i | \(0.332431\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0236 | 0.325379 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.0995218 | + | 2.76417i | 0.00322552 | + | 0.0895873i | ||||
\(953\) | −31.8414 | −1.03144 | −0.515722 | − | 0.856756i | \(-0.672476\pi\) | ||||
−0.515722 | + | 0.856756i | \(0.672476\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 5.56697i | − | 0.180049i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.2899 | 0.849389 | ||||||||
\(959\) | −18.1541 | + | 0.653625i | −0.586228 | + | 0.0211067i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −51.7678 | −1.66993 | ||||||||
\(962\) | 1.87288i | 0.0603841i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 11.3839i | − | 0.366651i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 32.6804i | − | 1.05093i | −0.850815 | − | 0.525466i | \(-0.823891\pi\) | ||
0.850815 | − | 0.525466i | \(-0.176109\pi\) | |||||||
\(968\) | −16.9638 | −0.545236 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.2419 | 0.617501 | 0.308751 | − | 0.951143i | \(-0.400089\pi\) | ||||
0.308751 | + | 0.951143i | \(0.400089\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.32433 | + | 36.7825i | 0.0424559 | + | 1.17919i | ||||
\(974\) | − | 39.5381i | − | 1.26688i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 8.05225i | − | 0.257746i | ||||||
\(977\) | 2.48528 | 0.0795112 | 0.0397556 | − | 0.999209i | \(-0.487342\pi\) | ||||
0.0397556 | + | 0.999209i | \(0.487342\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 22.6397i | − | 0.723566i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 4.62105i | − | 0.147464i | ||||||
\(983\) | − | 49.4135i | − | 1.57605i | −0.615645 | − | 0.788024i | \(-0.711104\pi\) | ||
0.615645 | − | 0.788024i | \(-0.288896\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.81826 | 0.248984 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.0909i | 0.448290i | ||||||||
\(989\) | 7.13868i | 0.226997i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.0526 | −1.81233 | −0.906167 | − | 0.422920i | \(-0.861005\pi\) | ||||
−0.906167 | + | 0.422920i | \(0.861005\pi\) | |||||||
\(992\) | 9.09768i | 0.288852i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.612402 | − | 17.0092i | −0.0194242 | − | 0.539499i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.6794 | −0.528240 | −0.264120 | − | 0.964490i | \(-0.585082\pi\) | ||||
−0.264120 | + | 0.964490i | \(0.585082\pi\) | |||||||
\(998\) | −31.0152 | −0.981770 | ||||||||
\(999\) | 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.d.f.3149.7 | 8 | ||
3.2 | odd | 2 | 3150.2.d.c.3149.7 | 8 | |||
5.2 | odd | 4 | 630.2.b.b.251.7 | yes | 8 | ||
5.3 | odd | 4 | 3150.2.b.f.251.2 | 8 | |||
5.4 | even | 2 | 3150.2.d.a.3149.2 | 8 | |||
7.6 | odd | 2 | 3150.2.d.d.3149.1 | 8 | |||
15.2 | even | 4 | 630.2.b.a.251.3 | ✓ | 8 | ||
15.8 | even | 4 | 3150.2.b.e.251.6 | 8 | |||
15.14 | odd | 2 | 3150.2.d.d.3149.2 | 8 | |||
20.7 | even | 4 | 5040.2.f.i.881.3 | 8 | |||
21.20 | even | 2 | 3150.2.d.a.3149.1 | 8 | |||
35.13 | even | 4 | 3150.2.b.e.251.2 | 8 | |||
35.27 | even | 4 | 630.2.b.a.251.7 | yes | 8 | ||
35.34 | odd | 2 | 3150.2.d.c.3149.8 | 8 | |||
60.47 | odd | 4 | 5040.2.f.f.881.3 | 8 | |||
105.62 | odd | 4 | 630.2.b.b.251.3 | yes | 8 | ||
105.83 | odd | 4 | 3150.2.b.f.251.6 | 8 | |||
105.104 | even | 2 | inner | 3150.2.d.f.3149.8 | 8 | ||
140.27 | odd | 4 | 5040.2.f.f.881.4 | 8 | |||
420.167 | even | 4 | 5040.2.f.i.881.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.b.a.251.3 | ✓ | 8 | 15.2 | even | 4 | ||
630.2.b.a.251.7 | yes | 8 | 35.27 | even | 4 | ||
630.2.b.b.251.3 | yes | 8 | 105.62 | odd | 4 | ||
630.2.b.b.251.7 | yes | 8 | 5.2 | odd | 4 | ||
3150.2.b.e.251.2 | 8 | 35.13 | even | 4 | |||
3150.2.b.e.251.6 | 8 | 15.8 | even | 4 | |||
3150.2.b.f.251.2 | 8 | 5.3 | odd | 4 | |||
3150.2.b.f.251.6 | 8 | 105.83 | odd | 4 | |||
3150.2.d.a.3149.1 | 8 | 21.20 | even | 2 | |||
3150.2.d.a.3149.2 | 8 | 5.4 | even | 2 | |||
3150.2.d.c.3149.7 | 8 | 3.2 | odd | 2 | |||
3150.2.d.c.3149.8 | 8 | 35.34 | odd | 2 | |||
3150.2.d.d.3149.1 | 8 | 7.6 | odd | 2 | |||
3150.2.d.d.3149.2 | 8 | 15.14 | odd | 2 | |||
3150.2.d.f.3149.7 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.d.f.3149.8 | 8 | 105.104 | even | 2 | inner | ||
5040.2.f.f.881.3 | 8 | 60.47 | odd | 4 | |||
5040.2.f.f.881.4 | 8 | 140.27 | odd | 4 | |||
5040.2.f.i.881.3 | 8 | 20.7 | even | 4 | |||
5040.2.f.i.881.4 | 8 | 420.167 | even | 4 |