Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(257,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 9, 17]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.cc (of order \(18\), degree \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 545.1 | ||
Root | \(-0.173648 + 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.545 |
Dual form | 912.2.cc.a.497.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.592396 | − | 1.62760i | 0.342020 | − | 0.939693i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.47178 | + | 4.28125i | −0.934246 | + | 1.61816i | −0.158272 | + | 0.987396i | \(0.550592\pi\) |
−0.775974 | + | 0.630765i | \(0.782741\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.29813 | − | 1.92836i | −0.766044 | − | 0.642788i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.08512 | + | 2.98135i | 0.300959 | + | 0.826877i | 0.994334 | + | 0.106301i | \(0.0339006\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 4.33013i | −0.114708 | + | 0.993399i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.50387 | + | 6.55926i | 1.20104 | + | 1.43135i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.69846 | + | 1.71010i | −0.939693 | + | 0.342020i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.50000 | + | 2.59808i | −0.866025 | + | 0.500000i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.66772 | + | 2.69491i | 0.838347 | + | 0.484020i | 0.856702 | − | 0.515812i | \(-0.172510\pi\) |
−0.0183550 | + | 0.999832i | \(0.505843\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.7352i | 1.92925i | 0.263620 | + | 0.964626i | \(0.415083\pi\) | ||||
−0.263620 | + | 0.964626i | \(0.584917\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.49525 | 0.879945 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0957998 | + | 0.543308i | 0.0146093 | + | 0.0828537i | 0.991241 | − | 0.132068i | \(-0.0421616\pi\) |
−0.976631 | + | 0.214921i | \(0.931050\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.71941 | − | 15.1025i | −1.24563 | − | 2.15749i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.75150 | + | 3.37895i | 0.894258 | + | 0.447553i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.762641 | − | 4.32515i | 0.0976462 | − | 0.553779i | −0.896258 | − | 0.443533i | \(-0.853725\pi\) |
0.993904 | − | 0.110246i | \(-0.0351639\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.9363 | − | 5.07239i | 1.75581 | − | 0.639062i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.42514 | − | 1.69842i | 0.174109 | − | 0.207495i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) |
0.846041 | + | 0.533118i | \(0.178980\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.4547 | + | 5.26108i | 1.69180 | + | 0.615763i | 0.994850 | − | 0.101361i | \(-0.0323196\pi\) |
0.696946 | + | 0.717124i | \(0.254542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.66025i | 1.00000i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.09879 | − | 14.0088i | 0.573659 | − | 1.57612i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
0.798677 | − | 0.601760i | \(-0.205534\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.56283 | + | 8.86327i | 0.173648 | + | 0.984808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.4461 | − | 2.72356i | −1.61919 | − | 0.285507i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.15136 | − | 6.00070i | 0.741561 | − | 0.622244i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.34002 | − | 3.98048i | −0.339128 | − | 0.404157i | 0.569346 | − | 0.822098i | \(-0.307196\pi\) |
−0.908474 | + | 0.417941i | \(0.862752\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.5783 | + | 10.1488i | −1.73204 | + | 0.999995i | −0.864507 | + | 0.502621i | \(0.832369\pi\) |
−0.867536 | + | 0.497374i | \(0.834298\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.52869 | + | 1.50384i | −0.816900 | + | 0.144041i | −0.566458 | − | 0.824090i | \(-0.691687\pi\) |
−0.250441 | + | 0.968132i | \(0.580576\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19.1001 | + | 6.95188i | 1.81290 | + | 0.659843i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.25537 | − | 8.94405i | 0.300959 | − | 0.826877i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.50000 | + | 9.52628i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.14677 | + | 11.3932i | 0.367967 | + | 1.01098i | 0.976134 | + | 0.217171i | \(0.0696829\pi\) |
−0.608167 | + | 0.793809i | \(0.708095\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.941037 | + | 0.165930i | 0.0828537 | + | 0.0146093i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.3025 | − | 12.8438i | −1.50031 | − | 1.11369i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.4179 | + | 4.88371i | −1.13809 | + | 0.414230i | −0.841223 | − | 0.540689i | \(-0.818164\pi\) |
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −29.7460 | + | 5.24503i | −2.45341 | + | 0.432603i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.5885i | − | 1.26857i | −0.773099 | − | 0.634285i | \(-0.781294\pi\) | ||
0.773099 | − | 0.634285i | \(-0.218706\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.05004 | + | 5.95507i | 0.0838023 | + | 0.475267i | 0.997609 | + | 0.0691164i | \(0.0220180\pi\) |
−0.913806 | + | 0.406150i | \(0.866871\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.6348 | − | 21.8840i | −0.989630 | − | 1.71409i | −0.619210 | − | 0.785225i | \(-0.712547\pi\) |
−0.370420 | − | 0.928864i | \(-0.620786\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.24763 | − | 1.88598i | 0.172894 | − | 0.145076i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.49912 | − | 8.98703i | 0.726416 | − | 0.687255i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.29220 | − | 24.3423i | 0.324460 | − | 1.84010i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2467 | + | 14.5951i | −0.910294 | + | 1.08485i | 0.0857797 | + | 0.996314i | \(0.472662\pi\) |
−0.996073 | + | 0.0885316i | \(0.971783\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.58781 | − | 3.80347i | −0.486985 | − | 0.281161i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 25.6875i | − | 1.86849i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.70052 | − | 21.1570i | 0.554296 | − | 1.52292i | −0.273492 | − | 0.961874i | \(-0.588179\pi\) |
0.827788 | − | 0.561041i | \(-0.189599\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.7253 | + | 12.3560i | 1.04385 | + | 0.875895i | 0.992434 | − | 0.122782i | \(-0.0391815\pi\) |
0.0514178 | + | 0.998677i | \(0.483626\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.92009 | − | 3.32570i | −0.135433 | − | 0.234577i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.5510 | + | 22.1082i | 1.27710 | + | 1.52199i | 0.726359 | + | 0.687315i | \(0.241211\pi\) |
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.0752 | + | 13.3224i | −1.56644 | + | 0.904387i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.1258 | − | 20.4098i | 1.15726 | − | 1.37916i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.0483 | − | 3.35873i | 1.27557 | − | 0.224917i | 0.505471 | − | 0.862844i | \(-0.331319\pi\) |
0.770097 | + | 0.637927i | \(0.220208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.0954 | + | 5.13030i | 0.939693 | + | 0.342020i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 30.2131 | 1.99654 | 0.998268 | − | 0.0588329i | \(-0.0187379\pi\) | ||||
0.998268 | + | 0.0588329i | \(0.0187379\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.7802 | − | 16.5975i | −1.28486 | − | 1.07813i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.26904 | − | 19.9715i | −0.468240 | − | 1.28648i | −0.919150 | − | 0.393909i | \(-0.871123\pi\) |
0.450910 | − | 0.892570i | \(-0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3516 | + | 2.70691i | 0.984808 | + | 0.173648i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.4522 | + | 3.20804i | −0.855942 | + | 0.204123i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −50.2413 | − | 29.0068i | −3.12184 | − | 1.80240i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.173648 | + | 0.984808i | 0.0105484 | + | 0.0598228i | 0.989628 | − | 0.143657i | \(-0.0458861\pi\) |
−0.979079 | + | 0.203479i | \(0.934775\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.5831 | + | 23.5266i | −0.822084 | + | 1.42389i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.50000 | + | 4.33013i | 0.150210 | + | 0.260172i | 0.931305 | − | 0.364241i | \(-0.118672\pi\) |
−0.781094 | + | 0.624413i | \(0.785338\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.53028 | − | 15.1943i | −0.331089 | − | 0.909660i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.36231 | − | 4.49951i | 0.318756 | − | 0.267468i | −0.469344 | − | 0.883016i | \(-0.655509\pi\) |
0.788100 | + | 0.615547i | \(0.211065\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.95202 | − | 16.7417i | 0.173648 | − | 0.984808i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.45723 | + | 3.07818i | −0.495772 | + | 0.180446i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.56283 | − | 0.932795i | −0.147719 | − | 0.0537654i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0707 | + | 27.6691i | −0.574767 | + | 1.57916i | 0.222112 | + | 0.975021i | \(0.428705\pi\) |
−0.796879 | + | 0.604139i | \(0.793517\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.10488 | + | 34.6225i | 0.347295 | + | 1.96961i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.95858 | + | 8.35624i | 0.562892 | + | 0.472323i | 0.879279 | − | 0.476308i | \(-0.158025\pi\) |
−0.316387 | + | 0.948630i | \(0.602470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.1968 | − | 12.1521i | −0.565617 | − | 0.674077i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.60472 | + | 14.7721i | −0.144041 | + | 0.816900i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.32279 | + | 3.65046i | −0.347532 | + | 0.200648i | −0.663598 | − | 0.748090i | \(-0.730971\pi\) |
0.316066 | + | 0.948737i | \(0.397638\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.6297 | − | 26.9690i | 1.24010 | − | 1.47789i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.6052 | − | 5.39652i | 1.66717 | − | 0.293967i | 0.741122 | − | 0.671370i | \(-0.234294\pi\) |
0.926049 | + | 0.377403i | \(0.123183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 51.6049 | 2.78640 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.77110 | − | 9.99583i | 0.308920 | − | 0.535065i | −0.669207 | − | 0.743076i | \(-0.733366\pi\) |
0.978126 | + | 0.208012i | \(0.0666992\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.6288 | − | 10.5968i | −0.674077 | − | 0.565617i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5000 | − | 4.33013i | −0.973684 | − | 0.227901i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.2467 | + | 14.5951i | 0.642788 | + | 0.766044i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.1370 | − | 7.32926i | 1.05114 | − | 0.382584i | 0.242048 | − | 0.970264i | \(-0.422181\pi\) |
0.809093 | + | 0.587680i | \(0.199959\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00000 | − | 3.46410i | −0.310668 | − | 0.179364i | 0.336557 | − | 0.941663i | \(-0.390737\pi\) |
−0.647225 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.26158i | 0.0648029i | 0.999475 | + | 0.0324014i | \(0.0103155\pi\) | ||||
−0.999475 | + | 0.0324014i | \(0.989684\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.0000 | 1.07586 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.827534 | − | 1.43333i | 0.0420659 | − | 0.0728603i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.2028 | + | 16.9522i | −1.01395 | + | 0.850805i | −0.988855 | − | 0.148880i | \(-0.952433\pi\) |
−0.0250943 | + | 0.999685i | \(0.507989\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −31.1544 | + | 20.5528i | −1.55967 | + | 1.02893i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.96942 | + | 16.8404i | −0.147917 | + | 0.838880i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.90673 | − | 10.6146i | 0.440409 | − | 0.524859i | −0.499486 | − | 0.866322i | \(-0.666478\pi\) |
0.939895 | + | 0.341463i | \(0.110922\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.7320i | 1.21113i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.4403 | + | 34.1795i | −0.606304 | + | 1.66581i | 0.131927 | + | 0.991259i | \(0.457883\pi\) |
−0.738231 | + | 0.674548i | \(0.764339\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.6320 | + | 13.9559i | 0.804878 | + | 0.675373i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.7952 | + | 6.66431i | 1.81632 | + | 0.320266i | 0.975325 | − | 0.220774i | \(-0.0708584\pi\) |
0.840996 | + | 0.541041i | \(0.181970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.2046 | − | 25.2706i | −1.01204 | − | 1.20610i | −0.978412 | − | 0.206666i | \(-0.933739\pi\) |
−0.0336266 | − | 0.999434i | \(-0.510706\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.08466 | + | 51.5216i | −0.432603 | + | 2.45341i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.3717 | − | 9.23454i | −1.19207 | − | 0.433877i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.6144 | 1.10464 | 0.552318 | − | 0.833633i | \(-0.313743\pi\) | ||||
0.552318 | + | 0.833633i | \(0.313743\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.0266 | + | 29.4910i | −0.791294 | + | 1.37056i | 0.133871 | + | 0.990999i | \(0.457259\pi\) |
−0.925166 | + | 0.379563i | \(0.876074\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.74872 | + | 10.2995i | 0.173100 | + | 0.475588i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.3145 | + | 1.81872i | 0.475267 | + | 0.0838023i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.05572 | − | 21.2000i | −0.231972 | − | 0.972722i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.9867 | + | 12.7341i | −1.59526 | + | 0.580626i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.5000 | + | 19.9186i | 1.56334 | + | 0.902597i | 0.996915 | + | 0.0784867i | \(0.0250088\pi\) |
0.566429 | + | 0.824110i | \(0.308325\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −43.1031 | + | 7.60024i | −1.94919 | + | 0.343695i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.29648 | + | 35.7091i | 0.281869 | + | 1.59856i | 0.716258 | + | 0.697835i | \(0.245853\pi\) |
−0.434389 | + | 0.900725i | \(0.643036\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.73813 | − | 4.77547i | −0.0771931 | − | 0.212086i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −58.2529 | + | 48.8800i | −2.57696 | + | 2.16232i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.00000 | − | 20.7846i | −0.397360 | − | 0.917663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.4800 | − | 30.3659i | 1.11416 | − | 1.32781i | 0.174908 | − | 0.984585i | \(-0.444037\pi\) |
0.939254 | − | 0.343222i | \(-0.111518\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −37.0767 | − | 21.4063i | −1.61816 | − | 0.934246i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6129 | − | 7.86646i | −0.939693 | − | 0.342020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.9281 | + | 29.3082i | 1.50168 | + | 1.26006i | 0.878274 | + | 0.478157i | \(0.158695\pi\) |
0.623404 | + | 0.781900i | \(0.285749\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.5000 | + | 28.5788i | 0.708083 | + | 1.22644i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.9131 | + | 6.33245i | 1.53553 | + | 0.270756i | 0.876517 | − | 0.481371i | \(-0.159861\pi\) |
0.659018 | + | 0.752128i | \(0.270972\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.0931 | + | 8.46913i | −0.430764 | + | 0.361453i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 47.3722 | + | 56.4560i | 2.01447 | + | 2.40075i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.51584 | + | 0.875168i | −0.0641130 | + | 0.0370157i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −41.8089 | − | 15.2172i | −1.75581 | − | 0.639062i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.2036 | 1.72432 | 0.862158 | − | 0.506640i | \(-0.169113\pi\) | ||||
0.862158 | + | 0.506640i | \(0.169113\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.5000 | − | 30.3109i | 0.728535 | − | 1.26186i | −0.228968 | − | 0.973434i | \(-0.573535\pi\) |
0.957503 | − | 0.288425i | \(-0.0931316\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.8733 | − | 25.0667i | −1.24149 | − | 1.04174i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.0032 | + | 18.8644i | −0.576990 | + | 0.777292i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28.8338 | − | 16.6472i | 1.18009 | − | 0.681326i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.9232 | − | 9.19329i | −0.649523 | − | 0.375002i | 0.138751 | − | 0.990327i | \(-0.455691\pi\) |
−0.788273 | + | 0.615325i | \(0.789025\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.55035 | + | 1.15500i | −0.266751 | + | 0.0470353i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 49.1579i | − | 1.99526i | −0.0688294 | − | 0.997628i | \(-0.521926\pi\) | ||
0.0688294 | − | 0.997628i | \(-0.478074\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.42498 | + | 36.4379i | 0.259503 | + | 1.47171i | 0.784245 | + | 0.620451i | \(0.213051\pi\) |
−0.524742 | + | 0.851261i | \(0.675838\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.51872 | + | 14.7549i | 0.342396 | + | 0.593048i | 0.984877 | − | 0.173254i | \(-0.0554281\pi\) |
−0.642481 | + | 0.766302i | \(0.722095\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.1511 | − | 16.0697i | 0.766044 | − | 0.642788i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.14636 | − | 17.8439i | 0.125255 | − | 0.710355i | −0.855901 | − | 0.517139i | \(-0.826997\pi\) |
0.981156 | − | 0.193216i | \(-0.0618918\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 46.9727 | − | 17.0967i | 1.86700 | − | 0.679532i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.5641 | − | 42.3836i | 1.40910 | − | 1.67930i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.3008 | + | 9.20875i | 0.997767 | + | 0.363157i | 0.788723 | − | 0.614749i | \(-0.210743\pi\) |
0.209044 | + | 0.977906i | \(0.432965\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.01392 | + | 45.4492i | 0.314090 | + | 1.78129i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −23.0736 | − | 39.9646i | −0.900186 | − | 1.55917i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.1147 | + | 6.01535i | 1.32691 | + | 0.233970i | 0.791783 | − | 0.610802i | \(-0.209153\pi\) |
0.535126 | + | 0.844772i | \(0.320264\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.81749 | − | 32.9926i | 0.224917 | − | 1.27557i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.0862 | + | 15.0609i | −1.00555 | + | 0.580554i | −0.909886 | − | 0.414859i | \(-0.863831\pi\) |
−0.0956642 | + | 0.995414i | \(0.530497\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.7001 | − | 19.9024i | 0.642788 | − | 0.766044i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.2973 | − | 4.46059i | 0.970820 | − | 0.171182i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.8981 | − | 49.1746i | 0.682855 | − | 1.87613i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.5000 | − | 35.5070i | 0.779857 | − | 1.35075i | −0.152167 | − | 0.988355i | \(-0.548625\pi\) |
0.932024 | − | 0.362397i | \(-0.118041\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −50.8149 | − | 5.86759i | −1.91652 | − | 0.221300i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.2904 | + | 15.0285i | −1.55070 | + | 0.564407i | −0.968581 | − | 0.248700i | \(-0.919997\pi\) |
−0.582115 | + | 0.813107i | \(0.697775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −38.7318 | + | 22.3618i | −1.45256 | + | 0.838633i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 100.343i | − | 3.73697i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36.8117 | −1.36904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.00480 | + | 22.7124i | 0.148530 | + | 0.842355i | 0.964465 | + | 0.264211i | \(0.0851117\pi\) |
−0.815935 | + | 0.578144i | \(0.803777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5000 | − | 23.3827i | 0.500000 | − | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.5000 | + | 37.2391i | 0.794121 | + | 1.37546i | 0.923396 | + | 0.383849i | \(0.125402\pi\) |
−0.129275 | + | 0.991609i | \(0.541265\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.09652 | + | 1.75919i | −0.0771216 | + | 0.0647127i | −0.680534 | − | 0.732717i | \(-0.738252\pi\) |
0.603412 | + | 0.797430i | \(0.293807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.74763 | + | 23.7951i | −0.100937 | + | 0.874136i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.9839 | + | 36.9251i | −1.13062 | + | 1.34742i | −0.200698 | + | 0.979653i | \(0.564321\pi\) |
−0.929919 | + | 0.367764i | \(0.880123\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.0096 | + | 17.4740i | 1.74494 | + | 0.635105i | 0.999505 | − | 0.0314762i | \(-0.0100208\pi\) |
0.745432 | + | 0.666581i | \(0.232243\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.6427 | − | 40.2306i | 0.530103 | − | 1.45645i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.0795 | − | 35.3089i | −1.51743 | − | 1.27327i | −0.847432 | − | 0.530904i | \(-0.821852\pi\) |
−0.669994 | − | 0.742367i | \(-0.733703\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.5397 | − | 4.67966i | −0.953333 | − | 0.168098i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −76.9741 | + | 64.5890i | −2.76143 | + | 2.31712i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.2397 | − | 27.2738i | 1.68391 | − | 0.972208i | 0.724897 | − | 0.688858i | \(-0.241887\pi\) |
0.959017 | − | 0.283350i | \(-0.0914459\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.7223 | − | 2.41962i | 0.487295 | − | 0.0859232i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.3643 | − | 50.4555i | −0.644857 | − | 1.77173i | −0.635901 | − | 0.771771i | \(-0.719371\pi\) |
−0.00895645 | − | 0.999960i | \(-0.502851\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.70574 | + | 0.300767i | 0.0598228 | + | 0.0105484i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.40049 | + | 0.143172i | −0.0839826 | + | 0.00500894i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 30.2452 | + | 36.0448i | 1.05685 | + | 1.25951i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.1656 | + | 16.0749i | −1.53951 | + | 0.560337i | −0.965929 | − | 0.258808i | \(-0.916670\pi\) |
−0.573586 | + | 0.819146i | \(0.694448\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.5657 | − | 8.40949i | −0.505886 | − | 0.292074i | 0.225255 | − | 0.974300i | \(-0.427679\pi\) |
−0.731141 | + | 0.682226i | \(0.761012\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.52869 | − | 1.50384i | 0.295857 | − | 0.0521675i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.0063 | −0.968040 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.03580 | − | 28.5594i | −0.173648 | − | 0.984808i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.1896 | − | 47.0938i | −0.934246 | − | 1.61816i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.14677 | − | 11.3932i | −0.142317 | − | 0.391012i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.4473 | + | 31.4220i | −1.28217 | + | 1.07587i | −0.289229 | + | 0.957260i | \(0.593399\pi\) |
−0.992941 | + | 0.118609i | \(0.962157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.10917 | + | 45.9894i | −0.276681 | + | 1.56914i | 0.456889 | + | 0.889524i | \(0.348964\pi\) |
−0.733571 | + | 0.679613i | \(0.762148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.5000 | − | 14.7224i | −0.866025 | − | 0.500000i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.61004 | + | 2.40586i | 0.223973 | + | 0.0815194i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.5885i | 0.527589i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.6095 | − | 31.8969i | 0.392026 | − | 1.07708i | −0.574049 | − | 0.818821i | \(-0.694628\pi\) |
0.966075 | − | 0.258261i | \(-0.0831496\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.67049 | + | 8.11451i | 0.325438 | + | 0.273075i | 0.790838 | − | 0.612026i | \(-0.209645\pi\) |
−0.465400 | + | 0.885100i | \(0.654090\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −59.0269 | − | 10.4080i | −1.97970 | − | 0.349074i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.03643 | + | 3.61867i | −0.101046 | + | 0.120422i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −56.2893 | + | 9.92533i | −1.86906 | + | 0.329565i | −0.989304 | − | 0.145868i | \(-0.953403\pi\) |
−0.879752 | + | 0.475433i | \(0.842292\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.9372 | − | 51.8528i | 0.987538 | − | 1.71047i | 0.357472 | − | 0.933924i | \(-0.383639\pi\) |
0.630065 | − | 0.776542i | \(-0.283028\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.0683 | + | 32.7822i | 1.28734 | + | 1.08021i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.0684 | − | 55.1373i | −0.659843 | − | 1.81290i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 59.9680 | + | 10.5740i | 1.96961 | + | 0.347295i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 69.7553 | − | 30.2049i | 2.28614 | − | 0.989926i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.7720 | − | 14.8398i | 1.33196 | − | 0.484795i | 0.424691 | − | 0.905338i | \(-0.360383\pi\) |
0.907273 | + | 0.420543i | \(0.138160\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.5000 | − | 11.2583i | 0.636358 | − | 0.367402i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.8034i | 1.58423i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.974937 | − | 1.68864i | −0.0314496 | − | 0.0544723i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.2610 | + | 14.4837i | −0.555078 | + | 0.465766i | −0.876656 | − | 0.481117i | \(-0.840231\pi\) |
0.321578 | + | 0.946883i | \(0.395787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.2577 | − | 69.5167i | 0.392963 | − | 2.22860i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.8192 | + | 9.39743i | −0.826877 | + | 0.300959i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.5000 | + | 12.9904i | 0.718370 | + | 0.414751i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.1457 | + | 33.3700i | −0.385820 | + | 1.06003i | 0.583044 | + | 0.812440i | \(0.301861\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.19588 | + | 12.4535i | 0.0696842 | + | 0.395199i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.8350 | − | 20.8391i | −0.786533 | − | 0.659980i | 0.158352 | − | 0.987383i | \(-0.449382\pi\) |
−0.944885 | + | 0.327403i | \(0.893827\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.4889 | − | 52.8083i | −0.964626 | − | 1.67078i |
(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 | 912.2.cc.a.545.1 | 6 | ||
3.2 | odd | 2 | CM | 912.2.cc.a.545.1 | 6 | ||
4.3 | odd | 2 | 57.2.j.a.32.1 | ✓ | 6 | ||
12.11 | even | 2 | 57.2.j.a.32.1 | ✓ | 6 | ||
19.3 | odd | 18 | inner | 912.2.cc.a.497.1 | 6 | ||
57.41 | even | 18 | inner | 912.2.cc.a.497.1 | 6 | ||
76.3 | even | 18 | 57.2.j.a.41.1 | yes | 6 | ||
76.15 | even | 18 | 1083.2.d.a.1082.4 | 6 | |||
76.23 | odd | 18 | 1083.2.d.a.1082.1 | 6 | |||
228.23 | even | 18 | 1083.2.d.a.1082.1 | 6 | |||
228.155 | odd | 18 | 57.2.j.a.41.1 | yes | 6 | ||
228.167 | odd | 18 | 1083.2.d.a.1082.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.2.j.a.32.1 | ✓ | 6 | 4.3 | odd | 2 | ||
57.2.j.a.32.1 | ✓ | 6 | 12.11 | even | 2 | ||
57.2.j.a.41.1 | yes | 6 | 76.3 | even | 18 | ||
57.2.j.a.41.1 | yes | 6 | 228.155 | odd | 18 | ||
912.2.cc.a.497.1 | 6 | 19.3 | odd | 18 | inner | ||
912.2.cc.a.497.1 | 6 | 57.41 | even | 18 | inner | ||
912.2.cc.a.545.1 | 6 | 1.1 | even | 1 | trivial | ||
912.2.cc.a.545.1 | 6 | 3.2 | odd | 2 | CM | ||
1083.2.d.a.1082.1 | 6 | 76.23 | odd | 18 | |||
1083.2.d.a.1082.1 | 6 | 228.23 | even | 18 | |||
1083.2.d.a.1082.4 | 6 | 76.15 | even | 18 | |||
1083.2.d.a.1082.4 | 6 | 228.167 | odd | 18 |