Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(737,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.s (of order \(4\), degree \(2\), 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: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.3 | ||
Character | \(\chi\) | \(=\) | 4140.737 |
Dual form | 4140.2.s.a.2393.3 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.20494 | + | 0.371802i | −0.986079 | + | 0.166275i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.41792 | − | 3.41792i | −1.29185 | − | 1.29185i | −0.933639 | − | 0.358214i | \(-0.883386\pi\) |
−0.358214 | − | 0.933639i | \(-0.616614\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.26967i | − | 1.28735i | −0.765298 | − | 0.643677i | \(-0.777408\pi\) | ||
0.765298 | − | 0.643677i | \(-0.222592\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.36964 | + | 1.36964i | −0.379869 | + | 0.379869i | −0.871055 | − | 0.491186i | \(-0.836564\pi\) |
0.491186 | + | 0.871055i | \(0.336564\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.76377 | − | 3.76377i | 0.912848 | − | 0.912848i | −0.0836476 | − | 0.996495i | \(-0.526657\pi\) |
0.996495 | + | 0.0836476i | \(0.0266570\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.34766i | − | 0.768006i | −0.923332 | − | 0.384003i | \(-0.874545\pi\) | ||
0.923332 | − | 0.384003i | \(-0.125455\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.707107 | − | 0.707107i | −0.147442 | − | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.72353 | − | 1.63960i | 0.944705 | − | 0.327920i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.28737 | −0.796145 | −0.398072 | − | 0.917354i | \(-0.630321\pi\) | ||||
−0.398072 | + | 0.917354i | \(0.630321\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.17527 | 0.211085 | 0.105542 | − | 0.994415i | \(-0.466342\pi\) | ||||
0.105542 | + | 0.994415i | \(0.466342\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.80711 | + | 6.26553i | 1.48867 | + | 1.05907i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.12240 | − | 1.12240i | −0.184521 | − | 0.184521i | 0.608802 | − | 0.793322i | \(-0.291650\pi\) |
−0.793322 | + | 0.608802i | \(0.791650\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.1412i | − | 1.58378i | −0.610661 | − | 0.791892i | \(-0.709096\pi\) | ||
0.610661 | − | 0.791892i | \(-0.290904\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.84843 | − | 8.84843i | 1.34937 | − | 1.34937i | 0.463029 | − | 0.886343i | \(-0.346763\pi\) |
0.886343 | − | 0.463029i | \(-0.153237\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.85281 | + | 4.85281i | −0.707855 | + | 0.707855i | −0.966084 | − | 0.258229i | \(-0.916861\pi\) |
0.258229 | + | 0.966084i | \(0.416861\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.3644i | 2.33777i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.95219 | − | 7.95219i | −1.09232 | − | 1.09232i | −0.995281 | − | 0.0970365i | \(-0.969064\pi\) |
−0.0970365 | − | 0.995281i | \(-0.530936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.58747 | + | 9.41436i | 0.214054 | + | 1.26943i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.65152 | 0.605577 | 0.302788 | − | 0.953058i | \(-0.402082\pi\) | ||||
0.302788 | + | 0.953058i | \(0.402082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2709 | −1.57113 | −0.785566 | − | 0.618779i | \(-0.787628\pi\) | ||||
−0.785566 | + | 0.618779i | \(0.787628\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.51074 | − | 3.52920i | 0.311419 | − | 0.437744i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.27273 | + | 9.27273i | 1.13284 | + | 1.13284i | 0.989702 | + | 0.143142i | \(0.0457207\pi\) |
0.143142 | + | 0.989702i | \(0.454279\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.18378i | − | 0.852558i | −0.904592 | − | 0.426279i | \(-0.859824\pi\) | ||
0.904592 | − | 0.426279i | \(-0.140176\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.225292 | + | 0.225292i | −0.0263685 | + | 0.0263685i | −0.720168 | − | 0.693800i | \(-0.755935\pi\) |
0.693800 | + | 0.720168i | \(0.255935\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.5934 | + | 14.5934i | −1.66307 | + | 1.66307i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.6943i | 1.20321i | 0.798795 | + | 0.601603i | \(0.205471\pi\) | ||||
−0.798795 | + | 0.601603i | \(0.794529\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.70519 | − | 7.70519i | −0.845755 | − | 0.845755i | 0.143845 | − | 0.989600i | \(-0.454053\pi\) |
−0.989600 | + | 0.143845i | \(0.954053\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.89951 | + | 9.69826i | −0.748357 | + | 1.05192i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.97729 | 0.421592 | 0.210796 | − | 0.977530i | \(-0.432394\pi\) | ||||
0.210796 | + | 0.977530i | \(0.432394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.36263 | 0.981471 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.24467 | + | 7.38139i | 0.127700 | + | 0.757315i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.874011 | − | 0.874011i | −0.0887423 | − | 0.0887423i | 0.661342 | − | 0.750084i | \(-0.269987\pi\) |
−0.750084 | + | 0.661342i | \(0.769987\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.0972i | 1.30322i | 0.758556 | + | 0.651608i | \(0.225905\pi\) | ||||
−0.758556 | + | 0.651608i | \(0.774095\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7391 | − | 10.7391i | 1.05816 | − | 1.05816i | 0.0599585 | − | 0.998201i | \(-0.480903\pi\) |
0.998201 | − | 0.0599585i | \(-0.0190968\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.92524 | + | 2.92524i | −0.282794 | + | 0.282794i | −0.834222 | − | 0.551428i | \(-0.814083\pi\) |
0.551428 | + | 0.834222i | \(0.314083\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.50341i | 0.910262i | 0.890425 | + | 0.455131i | \(0.150408\pi\) | ||||
−0.890425 | + | 0.455131i | \(0.849592\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.58874 | − | 8.58874i | −0.807960 | − | 0.807960i | 0.176365 | − | 0.984325i | \(-0.443566\pi\) |
−0.984325 | + | 0.176365i | \(0.943566\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.82203 | + | 1.29623i | 0.169905 | + | 0.120874i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −25.7285 | −2.35853 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.23006 | −0.657278 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.80549 | + | 5.37144i | −0.877030 | + | 0.480436i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.92710 | − | 4.92710i | −0.437210 | − | 0.437210i | 0.453862 | − | 0.891072i | \(-0.350046\pi\) |
−0.891072 | + | 0.453862i | \(0.850046\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.1467i | 1.32337i | 0.749782 | + | 0.661685i | \(0.230158\pi\) | ||||
−0.749782 | + | 0.661685i | \(0.769842\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.4420 | + | 11.4420i | −0.992151 | + | 0.992151i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.98387 | + | 7.98387i | −0.682108 | + | 0.682108i | −0.960475 | − | 0.278366i | \(-0.910207\pi\) |
0.278366 | + | 0.960475i | \(0.410207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.1601i | 0.946590i | 0.880904 | + | 0.473295i | \(0.156936\pi\) | ||||
−0.880904 | + | 0.473295i | \(0.843064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.84790 | + | 5.84790i | 0.489026 | + | 0.489026i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.45340 | − | 1.59405i | 0.785062 | − | 0.132379i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.250755 | 0.0205426 | 0.0102713 | − | 0.999947i | \(-0.496730\pi\) | ||||
0.0102713 | + | 0.999947i | \(0.496730\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.15636 | 0.338240 | 0.169120 | − | 0.985596i | \(-0.445908\pi\) | ||||
0.169120 | + | 0.985596i | \(0.445908\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.59140 | + | 0.436967i | −0.208146 | + | 0.0350980i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.45615 | − | 8.45615i | −0.674874 | − | 0.674874i | 0.283961 | − | 0.958836i | \(-0.408351\pi\) |
−0.958836 | + | 0.283961i | \(0.908351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.83367i | 0.380947i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.29491 | − | 2.29491i | 0.179751 | − | 0.179751i | −0.611496 | − | 0.791247i | \(-0.709432\pi\) |
0.791247 | + | 0.611496i | \(0.209432\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.9321 | + | 13.9321i | −1.07810 | + | 1.07810i | −0.0814162 | + | 0.996680i | \(0.525944\pi\) |
−0.996680 | + | 0.0814162i | \(0.974056\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.24819i | 0.711399i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.28865 | − | 9.28865i | −0.706203 | − | 0.706203i | 0.259532 | − | 0.965735i | \(-0.416432\pi\) |
−0.965735 | + | 0.259532i | \(0.916432\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.7487 | − | 10.5406i | −1.64405 | − | 0.796796i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.4124 | −0.927749 | −0.463874 | − | 0.885901i | \(-0.653541\pi\) | ||||
−0.463874 | + | 0.885901i | \(0.653541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.1507 | 1.64645 | 0.823225 | − | 0.567715i | \(-0.192173\pi\) | ||||
0.823225 | + | 0.567715i | \(0.192173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.89212 | + | 2.05751i | 0.212633 | + | 0.151271i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.0700 | − | 16.0700i | −1.17516 | − | 1.17516i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.43431i | − | 0.176141i | −0.996114 | − | 0.0880703i | \(-0.971930\pi\) | ||
0.996114 | − | 0.0880703i | \(-0.0280700\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.2690 | + | 12.2690i | −0.883144 | + | 0.883144i | −0.993853 | − | 0.110709i | \(-0.964688\pi\) |
0.110709 | + | 0.993853i | \(0.464688\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.9955 | − | 10.9955i | 0.783395 | − | 0.783395i | −0.197007 | − | 0.980402i | \(-0.563122\pi\) |
0.980402 | + | 0.197007i | \(0.0631221\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.8224i | 1.05073i | 0.850877 | + | 0.525365i | \(0.176071\pi\) | ||||
−0.850877 | + | 0.525365i | \(0.823929\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.6539 | + | 14.6539i | 1.02850 | + | 1.02850i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.77050 | + | 22.3607i | 0.263343 | + | 1.56174i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.2934 | −0.988695 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0744 | −0.693549 | −0.346774 | − | 0.937949i | \(-0.612723\pi\) | ||||
−0.346774 | + | 0.937949i | \(0.612723\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.2204 | + | 22.8001i | −1.10622 | + | 1.55495i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.01698 | − | 4.01698i | −0.272691 | − | 0.272691i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3100i | 0.693525i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.5428 | − | 17.5428i | 1.17475 | − | 1.17475i | 0.193687 | − | 0.981063i | \(-0.437955\pi\) |
0.981063 | − | 0.193687i | \(-0.0620447\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.09202 | + | 3.09202i | −0.205225 | + | 0.205225i | −0.802234 | − | 0.597009i | \(-0.796355\pi\) |
0.597009 | + | 0.802234i | \(0.296355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.02242i | 0.265809i | 0.991129 | + | 0.132905i | \(0.0424304\pi\) | ||||
−0.991129 | + | 0.132905i | \(0.957570\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.85064 | − | 4.85064i | −0.317776 | − | 0.317776i | 0.530136 | − | 0.847912i | \(-0.322141\pi\) |
−0.847912 | + | 0.530136i | \(0.822141\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.89587 | − | 12.5044i | 0.580303 | − | 0.815699i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.2005 | 1.50072 | 0.750359 | − | 0.661031i | \(-0.229881\pi\) | ||||
0.750359 | + | 0.661031i | \(0.229881\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.7481 | 1.40092 | 0.700458 | − | 0.713694i | \(-0.252979\pi\) | ||||
0.700458 | + | 0.713694i | \(0.252979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.08431 | − | 36.0825i | −0.388712 | − | 2.30523i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.58508 | + | 4.58508i | 0.291742 | + | 0.291742i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 23.3240i | − | 1.47220i | −0.676875 | − | 0.736098i | \(-0.736666\pi\) | ||
0.676875 | − | 0.736098i | \(-0.263334\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.01911 | + | 3.01911i | −0.189810 | + | 0.189810i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.84479 | + | 3.84479i | −0.239831 | + | 0.239831i | −0.816780 | − | 0.576949i | \(-0.804243\pi\) |
0.576949 | + | 0.816780i | \(0.304243\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.67252i | 0.476747i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.16327 | − | 5.16327i | −0.318381 | − | 0.318381i | 0.529764 | − | 0.848145i | \(-0.322280\pi\) |
−0.848145 | + | 0.529764i | \(0.822280\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.4907 | + | 14.5775i | 1.25874 | + | 0.895487i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.73810 | −0.410829 | −0.205415 | − | 0.978675i | \(-0.565854\pi\) | ||||
−0.205415 | + | 0.978675i | \(0.565854\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.0070 | 1.70131 | 0.850653 | − | 0.525727i | \(-0.176207\pi\) | ||||
0.850653 | + | 0.525727i | \(0.176207\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.00055 | − | 20.1679i | −0.422149 | − | 1.21617i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.9659 | − | 18.9659i | −1.13955 | − | 1.13955i | −0.988531 | − | 0.151020i | \(-0.951744\pi\) |
−0.151020 | − | 0.988531i | \(-0.548256\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 28.7383i | − | 1.71438i | −0.514999 | − | 0.857191i | \(-0.672208\pi\) | ||
0.514999 | − | 0.857191i | \(-0.327792\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.9490 | + | 20.9490i | −1.24529 | + | 1.24529i | −0.287515 | + | 0.957776i | \(0.592829\pi\) |
−0.957776 | + | 0.287515i | \(0.907171\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −34.6617 | + | 34.6617i | −2.04602 | + | 2.04602i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 11.3319i | − | 0.666582i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.15026 | − | 3.15026i | −0.184040 | − | 0.184040i | 0.609074 | − | 0.793114i | \(-0.291541\pi\) |
−0.793114 | + | 0.609074i | \(0.791541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.2563 | + | 1.72944i | −0.597147 | + | 0.100692i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.93696 | 0.112017 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −60.4865 | −3.48638 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27.0567 | − | 4.56235i | 1.54926 | − | 0.261239i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.73372 | − | 5.73372i | −0.327241 | − | 0.327241i | 0.524296 | − | 0.851536i | \(-0.324329\pi\) |
−0.851536 | + | 0.524296i | \(0.824329\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.19062i | 0.237628i | 0.992916 | + | 0.118814i | \(0.0379093\pi\) | ||||
−0.992916 | + | 0.118814i | \(0.962091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.2983 | + | 18.2983i | −1.03428 | + | 1.03428i | −0.0348889 | + | 0.999391i | \(0.511108\pi\) |
−0.999391 | + | 0.0348889i | \(0.988892\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.3760 | − | 14.3760i | 0.807436 | − | 0.807436i | −0.176809 | − | 0.984245i | \(-0.556578\pi\) |
0.984245 | + | 0.176809i | \(0.0565775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.3056i | 1.02492i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.5998 | − | 12.5998i | −0.701073 | − | 0.701073i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.22386 | + | 8.71518i | −0.234298 | + | 0.483431i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.1730 | 1.82889 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.6622 | −1.13570 | −0.567849 | − | 0.823133i | \(-0.692224\pi\) | ||||
−0.567849 | + | 0.823133i | \(0.692224\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.8934 | − | 16.9982i | −1.30544 | − | 0.928711i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.7908 | − | 17.7908i | −0.969128 | − | 0.969128i | 0.0304099 | − | 0.999538i | \(-0.490319\pi\) |
−0.999538 | + | 0.0304099i | \(0.990319\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5.01801i | − | 0.271741i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 32.0068 | − | 32.0068i | 1.72821 | − | 1.72821i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.0764 | − | 17.0764i | 0.916707 | − | 0.916707i | −0.0800810 | − | 0.996788i | \(-0.525518\pi\) |
0.996788 | + | 0.0800810i | \(0.0255179\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.50127i | − | 0.187419i | −0.995600 | − | 0.0937094i | \(-0.970128\pi\) | ||
0.995600 | − | 0.0937094i | \(-0.0298725\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.6060 | + | 25.6060i | 1.36287 | + | 1.36287i | 0.870240 | + | 0.492629i | \(0.163964\pi\) |
0.492629 | + | 0.870240i | \(0.336036\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.67094 | + | 15.8398i | 0.141759 | + | 0.840690i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.9666 | 1.21213 | 0.606066 | − | 0.795414i | \(-0.292747\pi\) | ||||
0.606066 | + | 0.795414i | \(0.292747\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.79317 | 0.410167 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.412992 | − | 0.580521i | 0.0216170 | − | 0.0303858i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.62630 | + | 1.62630i | 0.0848920 | + | 0.0848920i | 0.748278 | − | 0.663386i | \(-0.230881\pi\) |
−0.663386 | + | 0.748278i | \(0.730881\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 54.3600i | 2.82223i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.89347 | − | 8.89347i | 0.460487 | − | 0.460487i | −0.438328 | − | 0.898815i | \(-0.644429\pi\) |
0.898815 | + | 0.438328i | \(0.144429\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.87214 | − | 5.87214i | 0.302431 | − | 0.302431i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5853i | 0.749196i | 0.927187 | + | 0.374598i | \(0.122219\pi\) | ||||
−0.927187 | + | 0.374598i | \(0.877781\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.06119 | − | 9.06119i | −0.463005 | − | 0.463005i | 0.436634 | − | 0.899639i | \(-0.356170\pi\) |
−0.899639 | + | 0.436634i | \(0.856170\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.7517 | − | 37.6034i | 1.36339 | − | 1.91645i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.01516 | −0.304981 | −0.152490 | − | 0.988305i | \(-0.548729\pi\) | ||||
−0.152490 | + | 0.988305i | \(0.548729\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.32277 | −0.269184 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.97617 | − | 23.5804i | −0.200063 | − | 1.18646i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.87141 | + | 8.87141i | 0.445243 | + | 0.445243i | 0.893770 | − | 0.448526i | \(-0.148051\pi\) |
−0.448526 | + | 0.893770i | \(0.648051\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.87130i | 0.243261i | 0.992575 | + | 0.121631i | \(0.0388123\pi\) | ||||
−0.992575 | + | 0.121631i | \(0.961188\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.60969 | + | 1.60969i | −0.0801846 | + | 0.0801846i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.79225 | + | 4.79225i | −0.237543 | + | 0.237543i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.9407i | 1.33213i | 0.745893 | + | 0.666065i | \(0.232023\pi\) | ||||
−0.745893 | + | 0.666065i | \(0.767977\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.8985 | − | 15.8985i | −0.782316 | − | 0.782316i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.8543 | + | 14.1247i | 0.974609 | + | 0.693354i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.6331 | 1.05685 | 0.528423 | − | 0.848981i | \(-0.322783\pi\) | ||||
0.528423 | + | 0.848981i | \(0.322783\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.8620 | 1.30917 | 0.654587 | − | 0.755987i | \(-0.272842\pi\) | ||||
0.654587 | + | 0.755987i | \(0.272842\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.6072 | − | 23.9493i | 0.563031 | − | 1.16171i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 41.9411 | + | 41.9411i | 2.02967 | + | 2.02967i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.3927i | 1.07862i | 0.842107 | + | 0.539310i | \(0.181315\pi\) | ||||
−0.842107 | + | 0.539310i | \(0.818685\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.7684 | − | 10.7684i | 0.517497 | − | 0.517497i | −0.399316 | − | 0.916813i | \(-0.630752\pi\) |
0.916813 | + | 0.399316i | \(0.130752\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.36715 | + | 2.36715i | −0.113236 | + | 0.113236i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.34035i | 0.111699i | 0.998439 | + | 0.0558495i | \(0.0177867\pi\) | ||||
−0.998439 | + | 0.0558495i | \(0.982213\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.7252 | + | 20.7252i | 0.984682 | + | 0.984682i | 0.999884 | − | 0.0152022i | \(-0.00483920\pi\) |
−0.0152022 | + | 0.999884i | \(0.504839\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.76970 | + | 1.47876i | −0.415724 | + | 0.0701001i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.9780 | −1.27317 | −0.636584 | − | 0.771207i | \(-0.719653\pi\) | ||||
−0.636584 | + | 0.771207i | \(0.719653\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.2994 | −2.03889 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.6441 | + | 3.48104i | −0.967808 | + | 0.163194i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.8386 | + | 21.8386i | 1.02157 | + | 1.02157i | 0.999762 | + | 0.0218045i | \(0.00694112\pi\) |
0.0218045 | + | 0.999762i | \(0.493059\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.84937i | 0.412156i | 0.978536 | + | 0.206078i | \(0.0660701\pi\) | ||||
−0.978536 | + | 0.206078i | \(0.933930\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.78554 | − | 6.78554i | 0.315351 | − | 0.315351i | −0.531628 | − | 0.846978i | \(-0.678419\pi\) |
0.846978 | + | 0.531628i | \(0.178419\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.50861 | − | 8.50861i | 0.393732 | − | 0.393732i | −0.482284 | − | 0.876015i | \(-0.660193\pi\) |
0.876015 | + | 0.482284i | \(0.160193\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 63.3870i | − | 2.92694i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −37.7798 | − | 37.7798i | −1.73712 | − | 1.73712i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.48883 | − | 15.8128i | −0.251845 | − | 0.725539i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.97105 | 0.272824 | 0.136412 | − | 0.990652i | \(-0.456443\pi\) | ||||
0.136412 | + | 0.990652i | \(0.456443\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.07455 | 0.140187 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.25210 | + | 1.60218i | 0.102263 | + | 0.0727514i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.2838 | + | 20.2838i | 0.919148 | + | 0.919148i | 0.996967 | − | 0.0778196i | \(-0.0247958\pi\) |
−0.0778196 | + | 0.996967i | \(0.524796\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 25.3494i | − | 1.14400i | −0.820253 | − | 0.572001i | \(-0.806167\pi\) | ||
0.820253 | − | 0.572001i | \(-0.193833\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.1367 | + | 16.1367i | −0.726759 | + | 0.726759i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.5536 | + | 24.5536i | −1.10138 | + | 1.10138i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 22.8057i | − | 1.02092i | −0.859901 | − | 0.510461i | \(-0.829475\pi\) | ||
0.859901 | − | 0.510461i | \(-0.170525\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.65002 | − | 3.65002i | −0.162746 | − | 0.162746i | 0.621036 | − | 0.783782i | \(-0.286712\pi\) |
−0.783782 | + | 0.621036i | \(0.786712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.86954 | − | 28.8784i | −0.216692 | − | 1.28507i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.6901 | −0.828425 | −0.414212 | − | 0.910180i | \(-0.635943\pi\) | ||||
−0.414212 | + | 0.910180i | \(0.635943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.54006 | 0.0681285 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.6863 | + | 27.6720i | −0.867484 | + | 1.21937i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.7199 | + | 20.7199i | 0.911259 | + | 0.911259i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.1355i | 0.444046i | 0.975041 | + | 0.222023i | \(0.0712659\pi\) | ||||
−0.975041 | + | 0.222023i | \(0.928734\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.892711 | − | 0.892711i | 0.0390355 | − | 0.0390355i | −0.687320 | − | 0.726355i | \(-0.741213\pi\) |
0.726355 | + | 0.687320i | \(0.241213\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.42344 | − | 4.42344i | 0.192688 | − | 0.192688i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.8897 | + | 13.8897i | 0.601631 | + | 0.601631i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.36238 | − | 7.53759i | 0.231836 | − | 0.325879i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 69.8705 | 3.00954 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.3981 | 0.447048 | 0.223524 | − | 0.974698i | \(-0.428244\pi\) | ||||
0.223524 | + | 0.974698i | \(0.428244\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.53338 | − | 20.9545i | −0.151354 | − | 0.897590i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.93355 | − | 5.93355i | −0.253700 | − | 0.253700i | 0.568786 | − | 0.822486i | \(-0.307413\pi\) |
−0.822486 | + | 0.568786i | \(0.807413\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.3527i | 0.611444i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.5524 | − | 36.5524i | 1.55437 | − | 1.55437i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.48712 | + | 1.48712i | −0.0630112 | + | 0.0630112i | −0.737910 | − | 0.674899i | \(-0.764187\pi\) |
0.674899 | + | 0.737910i | \(0.264187\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.2383i | 1.02517i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.34390 | + | 1.34390i | 0.0566386 | + | 0.0566386i | 0.734859 | − | 0.678220i | \(-0.237248\pi\) |
−0.678220 | + | 0.734859i | \(0.737248\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.1310 | + | 15.7443i | 0.931056 | + | 0.662370i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.59881 | 0.150870 | 0.0754351 | − | 0.997151i | \(-0.475965\pi\) | ||||
0.0754351 | + | 0.997151i | \(0.475965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.1665 | −1.51352 | −0.756760 | − | 0.653693i | \(-0.773219\pi\) | ||||
−0.756760 | + | 0.653693i | \(0.773219\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.49941 | − | 2.18067i | −0.187638 | − | 0.0909400i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.91060 | − | 6.91060i | −0.287692 | − | 0.287692i | 0.548475 | − | 0.836167i | \(-0.315209\pi\) |
−0.836167 | + | 0.548475i | \(0.815209\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 52.6715i | 2.18518i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −33.9532 | + | 33.9532i | −1.40620 | + | 1.40620i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.0170 | + | 16.0170i | −0.661094 | + | 0.661094i | −0.955638 | − | 0.294544i | \(-0.904832\pi\) |
0.294544 | + | 0.955638i | \(0.404832\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 3.93440i | − | 0.162114i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.91800 | − | 5.91800i | −0.243023 | − | 0.243023i | 0.575076 | − | 0.818100i | \(-0.304972\pi\) |
−0.818100 | + | 0.575076i | \(0.804972\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 56.7299 | − | 9.56591i | 2.32570 | − | 0.392164i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.5141 | 0.838184 | 0.419092 | − | 0.907944i | \(-0.362348\pi\) | ||||
0.419092 | + | 0.907944i | \(0.362348\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.4713 | −0.916625 | −0.458312 | − | 0.888791i | \(-0.651546\pi\) | ||||
−0.458312 | + | 0.888791i | \(0.651546\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.9418 | − | 2.68815i | 0.648128 | − | 0.109289i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.64464 | − | 9.64464i | −0.391464 | − | 0.391464i | 0.483745 | − | 0.875209i | \(-0.339276\pi\) |
−0.875209 | + | 0.483745i | \(0.839276\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 13.2932i | − | 0.537784i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.7423 | + | 26.7423i | −1.08011 | + | 1.08011i | −0.0836136 | + | 0.996498i | \(0.526646\pi\) |
−0.996498 | + | 0.0836136i | \(0.973354\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.28593 | − | 4.28593i | 0.172545 | − | 0.172545i | −0.615551 | − | 0.788097i | \(-0.711067\pi\) |
0.788097 | + | 0.615551i | \(0.211067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.08175i | 0.123866i | 0.998080 | + | 0.0619330i | \(0.0197265\pi\) | ||||
−0.998080 | + | 0.0619330i | \(0.980274\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.5941 | − | 13.5941i | −0.544636 | − | 0.544636i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.6234 | − | 15.4894i | 0.784937 | − | 0.619576i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.44887 | −0.336879 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.7808 | 1.34479 | 0.672396 | − | 0.740192i | \(-0.265265\pi\) | ||||
0.672396 | + | 0.740192i | \(0.265265\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.6959 | + | 9.03207i | 0.503820 | + | 0.358427i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.4133 | − | 22.4133i | −0.888047 | − | 0.888047i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.27083i | 0.247683i | 0.992302 | + | 0.123841i | \(0.0395214\pi\) | ||||
−0.992302 | + | 0.123841i | \(0.960479\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.401964 | − | 0.401964i | 0.0158519 | − | 0.0158519i | −0.699136 | − | 0.714988i | \(-0.746432\pi\) |
0.714988 | + | 0.699136i | \(0.246432\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.0254 | + | 18.0254i | −0.708650 | + | 0.708650i | −0.966251 | − | 0.257602i | \(-0.917068\pi\) |
0.257602 | + | 0.966251i | \(0.417068\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 19.8604i | − | 0.779591i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.4282 | + | 10.4282i | 0.408087 | + | 0.408087i | 0.881071 | − | 0.472984i | \(-0.156823\pi\) |
−0.472984 | + | 0.881071i | \(0.656823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.63155 | − | 33.3975i | −0.220043 | − | 1.30495i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.7163 | −1.35235 | −0.676177 | − | 0.736740i | \(-0.736364\pi\) | ||||
−0.676177 | + | 0.736740i | \(0.736364\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.16381 | 0.0841626 | 0.0420813 | − | 0.999114i | \(-0.486601\pi\) | ||||
0.0420813 | + | 0.999114i | \(0.486601\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.9749 | − | 29.4832i | 0.813370 | − | 1.14331i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.03163 | + | 3.03163i | 0.117385 | + | 0.117385i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 52.3928i | 2.02260i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.4973 | + | 24.4973i | −0.944301 | + | 0.944301i | −0.998529 | − | 0.0542280i | \(-0.982730\pi\) |
0.0542280 | + | 0.998529i | \(0.482730\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.3472 | + | 17.3472i | −0.666707 | + | 0.666707i | −0.956952 | − | 0.290245i | \(-0.906263\pi\) |
0.290245 | + | 0.956952i | \(0.406263\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.97460i | 0.229284i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.2852 | + | 28.2852i | 1.08230 | + | 1.08230i | 0.996294 | + | 0.0860078i | \(0.0274110\pi\) |
0.0860078 | + | 0.996294i | \(0.472589\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6356 | − | 20.5724i | 0.559196 | − | 0.786030i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.7832 | 0.829875 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.15648 | 0.158120 | 0.0790600 | − | 0.996870i | \(-0.474808\pi\) | ||||
0.0790600 | + | 0.996870i | \(0.474808\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.14935 | − | 24.6074i | −0.157394 | − | 0.933413i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38.1690 | − | 38.1690i | −1.44575 | − | 1.44575i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.46884i | 0.0932469i | 0.998913 | + | 0.0466235i | \(0.0148461\pi\) | ||||
−0.998913 | + | 0.0466235i | \(0.985154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.75740 | + | 3.75740i | −0.141713 | + | 0.141713i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 44.7651 | − | 44.7651i | 1.68356 | − | 1.68356i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.8058i | 1.15694i | 0.815705 | + | 0.578468i | \(0.196349\pi\) | ||||
−0.815705 | + | 0.578468i | \(0.803651\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.831041 | − | 0.831041i | −0.0311227 | − | 0.0311227i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.0685 | − | 10.7200i | −0.563531 | − | 0.400906i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.6337 | 0.806803 | 0.403401 | − | 0.915023i | \(-0.367828\pi\) | ||||
0.403401 | + | 0.915023i | \(0.367828\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −73.4111 | −2.73397 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.2515 | + | 7.02958i | −0.752122 | + | 0.261072i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.2014 | − | 17.2014i | −0.637964 | − | 0.637964i | 0.312089 | − | 0.950053i | \(-0.398971\pi\) |
−0.950053 | + | 0.312089i | \(0.898971\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 66.6068i | − | 2.46354i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.5444 | − | 24.5444i | 0.906568 | − | 0.906568i | −0.0894254 | − | 0.995994i | \(-0.528503\pi\) |
0.995994 | + | 0.0894254i | \(0.0285031\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.5915 | − | 39.5915i | 1.45837 | − | 1.45837i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.7299i | 1.31435i | 0.753740 | + | 0.657173i | \(0.228248\pi\) | ||||
−0.753740 | + | 0.657173i | \(0.771752\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.2253 | − | 19.2253i | −0.705308 | − | 0.705308i | 0.260237 | − | 0.965545i | \(-0.416199\pi\) |
−0.965545 | + | 0.260237i | \(0.916199\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.552899 | + | 0.0932310i | −0.0202567 | + | 0.00341572i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.9965 | 0.730656 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.8862 | −0.944601 | −0.472301 | − | 0.881438i | \(-0.656576\pi\) | ||||
−0.472301 | + | 0.881438i | \(0.656576\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.16452 | + | 1.54534i | −0.333531 | + | 0.0562407i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.2623 | + | 12.2623i | 0.445683 | + | 0.445683i | 0.893916 | − | 0.448234i | \(-0.147947\pi\) |
−0.448234 | + | 0.893916i | \(0.647947\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 32.6802i | − | 1.18466i | −0.805697 | − | 0.592328i | \(-0.798209\pi\) | ||
0.805697 | − | 0.592328i | \(-0.201791\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.4819 | − | 32.4819i | 1.17592 | − | 1.17592i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.37090 | + | 6.37090i | −0.230040 | + | 0.230040i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 28.8429i | − | 1.04010i | −0.854135 | − | 0.520051i | \(-0.825913\pi\) | ||
0.854135 | − | 0.520051i | \(-0.174087\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.7783 | + | 18.7783i | 0.675410 | + | 0.675410i | 0.958958 | − | 0.283548i | \(-0.0915115\pi\) |
−0.283548 | + | 0.958958i | \(0.591511\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.55142 | − | 1.92697i | 0.199413 | − | 0.0692189i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.9492 | −1.21636 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.6723 | −1.09754 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.7893 | + | 15.5013i | 0.777694 | + | 0.553265i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.1501 | − | 18.1501i | −0.646980 | − | 0.646980i | 0.305282 | − | 0.952262i | \(-0.401249\pi\) |
−0.952262 | + | 0.305282i | \(0.901249\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 58.7113i | 2.08753i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.8067 | − | 16.8067i | 0.596824 | − | 0.596824i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.17940 | − | 3.17940i | 0.112620 | − | 0.112620i | −0.648551 | − | 0.761171i | \(-0.724625\pi\) |
0.761171 | + | 0.648551i | \(0.224625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.5297i | 1.29233i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.961924 | + | 0.961924i | 0.0339456 | + | 0.0339456i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.79717 | − | 10.6580i | −0.0633418 | − | 0.375644i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.71067 | 0.0601440 | 0.0300720 | − | 0.999548i | \(-0.490426\pi\) | ||||
0.0300720 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.8731 | −1.32991 | −0.664953 | − | 0.746885i | \(-0.731548\pi\) | ||||
−0.664953 | + | 0.746885i | \(0.731548\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.20689 | + | 5.91340i | −0.147361 | + | 0.207137i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.6215 | − | 29.6215i | −1.03633 | − | 1.03633i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 22.4969i | − | 0.785148i | −0.919720 | − | 0.392574i | \(-0.871585\pi\) | ||
0.919720 | − | 0.392574i | \(-0.128415\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.38947 | − | 4.38947i | 0.153007 | − | 0.153007i | −0.626452 | − | 0.779460i | \(-0.715494\pi\) |
0.779460 | + | 0.626452i | \(0.215494\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.4863 | + | 21.4863i | −0.747152 | + | 0.747152i | −0.973943 | − | 0.226792i | \(-0.927176\pi\) |
0.226792 | + | 0.973943i | \(0.427176\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.9243i | 1.14351i | 0.820425 | + | 0.571755i | \(0.193737\pi\) | ||||
−0.820425 | + | 0.571755i | \(0.806263\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 61.5918 | + | 61.5918i | 2.13403 | + | 2.13403i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.5394 | − | 35.8994i | 0.883829 | − | 1.24235i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.9008 | 1.48110 | 0.740550 | − | 0.672002i | \(-0.234565\pi\) | ||||
0.740550 | + | 0.672002i | \(0.234565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.6185 | −0.366153 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.43849 | − | 20.3917i | −0.118288 | − | 0.701496i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.7118 | + | 24.7118i | 0.849107 | + | 0.849107i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.58731i | 0.0544122i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.30459 | − | 1.30459i | 0.0446684 | − | 0.0446684i | −0.684420 | − | 0.729088i | \(-0.739944\pi\) |
0.729088 | + | 0.684420i | \(0.239944\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.0277 | − | 20.0277i | 0.684132 | − | 0.684132i | −0.276797 | − | 0.960929i | \(-0.589273\pi\) |
0.960929 | + | 0.276797i | \(0.0892728\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 25.4308i | − | 0.867689i | −0.900988 | − | 0.433844i | \(-0.857157\pi\) | ||
0.900988 | − | 0.433844i | \(-0.142843\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.93715 | + | 7.93715i | 0.270184 | + | 0.270184i | 0.829174 | − | 0.558990i | \(-0.188811\pi\) |
−0.558990 | + | 0.829174i | \(0.688811\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.9345 | + | 17.0274i | 0.813796 | + | 0.578949i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.6612 | 1.54895 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.4006 | −0.860665 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 51.8736 | + | 15.1553i | 1.75365 | + | 0.512341i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.3803 | − | 38.3803i | −1.29601 | − | 1.29601i | −0.931005 | − | 0.365006i | \(-0.881067\pi\) |
−0.365006 | − | 0.931005i | \(-0.618933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.3146i | 1.32454i | 0.749264 | + | 0.662272i | \(0.230407\pi\) | ||||
−0.749264 | + | 0.662272i | \(0.769593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.4985 | − | 12.4985i | 0.420608 | − | 0.420608i | −0.464805 | − | 0.885413i | \(-0.653876\pi\) |
0.885413 | + | 0.464805i | \(0.153876\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.6349 | − | 30.6349i | 1.02862 | − | 1.02862i | 0.0290398 | − | 0.999578i | \(-0.490755\pi\) |
0.999578 | − | 0.0290398i | \(-0.00924496\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.6809i | 1.12962i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.2455 | + | 16.2455i | 0.543636 | + | 0.543636i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.3687 | − | 4.61496i | 0.914834 | − | 0.154261i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.03882 | −0.168054 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −59.8604 | −1.99424 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −48.8410 | + | 8.23567i | −1.62353 | + | 0.273763i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.5458 | + | 15.5458i | 0.516190 | + | 0.516190i | 0.916416 | − | 0.400226i | \(-0.131068\pi\) |
−0.400226 | + | 0.916416i | \(0.631068\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 16.9576i | − | 0.561830i | −0.959733 | − | 0.280915i | \(-0.909362\pi\) | ||
0.959733 | − | 0.280915i | \(-0.0906379\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.8986 | + | 32.8986i | −1.08878 | + | 1.08878i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 51.7701 | − | 51.7701i | 1.70960 | − | 1.70960i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 23.4546i | − | 0.773695i | −0.922144 | − | 0.386847i | \(-0.873564\pi\) | ||
0.922144 | − | 0.386847i | \(-0.126436\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.83917 | + | 9.83917i | 0.323860 | + | 0.323860i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.14195 | − | 3.46138i | −0.234826 | − | 0.113810i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.7528 | 0.680878 | 0.340439 | − | 0.940267i | \(-0.389424\pi\) | ||||
0.340439 | + | 0.940267i | \(0.389424\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 54.7825 | 1.79542 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 41.4083 | + | 29.4586i | 1.35420 | + | 0.963400i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.0717 | + | 16.0717i | 0.525039 | + | 0.525039i | 0.919089 | − | 0.394050i | \(-0.128926\pi\) |
−0.394050 | + | 0.919089i | \(0.628926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 41.8188i | − | 1.36325i | −0.731700 | − | 0.681627i | \(-0.761273\pi\) | ||
0.731700 | − | 0.681627i | \(-0.238727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.17089 | + | 7.17089i | −0.233516 | + | 0.233516i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.8172 | − | 31.8172i | 1.03392 | − | 1.03392i | 0.0345160 | − | 0.999404i | \(-0.489011\pi\) |
0.999404 | − | 0.0345160i | \(-0.0109890\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 0.617138i | − | 0.0200332i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.7060 | − | 23.7060i | −0.767914 | − | 0.767914i | 0.209825 | − | 0.977739i | \(-0.432710\pi\) |
−0.977739 | + | 0.209825i | \(0.932710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.905081 | + | 5.36751i | 0.0292877 | + | 0.173689i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 54.5765 | 1.76237 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6187 | −0.955443 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.4908 | − | 31.6141i | 0.724005 | − | 1.01769i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.79750 | + | 2.79750i | 0.0899614 | + | 0.0899614i | 0.750655 | − | 0.660694i | \(-0.229738\pi\) |
−0.660694 | + | 0.750655i | \(0.729738\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.0193i | 1.34846i | 0.738520 | + | 0.674231i | \(0.235525\pi\) | ||||
−0.738520 | + | 0.674231i | \(0.764475\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.1445 | − | 38.1445i | 1.22286 | − | 1.22286i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.9684 | − | 18.9684i | 0.606853 | − | 0.606853i | −0.335270 | − | 0.942122i | \(-0.608827\pi\) |
0.942122 | + | 0.335270i | \(0.108827\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 16.9817i | − | 0.542738i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.3002 | + | 33.3002i | 1.06211 | + | 1.06211i | 0.997939 | + | 0.0641732i | \(0.0204410\pi\) |
0.0641732 | + | 0.997939i | \(0.479559\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.1562 | + | 28.3325i | −0.642231 | + | 0.902749i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.5136 | −0.397908 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.9998 | 1.27064 | 0.635318 | − | 0.772250i | \(-0.280869\pi\) | ||||
0.635318 | + | 0.772250i | \(0.280869\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.51098 | − | 32.6824i | −0.174710 | − | 1.03610i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.72877 | − | 2.72877i | −0.0864211 | − | 0.0864211i | 0.662575 | − | 0.748996i | \(-0.269464\pi\) |
−0.748996 | + | 0.662575i | \(0.769464\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4140.2.s.a.737.3 | ✓ | 44 | |
3.2 | odd | 2 | inner | 4140.2.s.a.737.20 | yes | 44 | |
5.3 | odd | 4 | inner | 4140.2.s.a.2393.20 | yes | 44 | |
15.8 | even | 4 | inner | 4140.2.s.a.2393.3 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.s.a.737.3 | ✓ | 44 | 1.1 | even | 1 | trivial | |
4140.2.s.a.737.20 | yes | 44 | 3.2 | odd | 2 | inner | |
4140.2.s.a.2393.3 | yes | 44 | 15.8 | even | 4 | inner | |
4140.2.s.a.2393.20 | yes | 44 | 5.3 | odd | 4 | inner |