Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(1279,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.1279");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(62.7794529086\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 8x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1279.1 | ||
Root | \(-2.57794i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1279 |
Dual form | 2304.3.g.p.1279.2 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.29150 | −1.05830 | −0.529150 | − | 0.848528i | \(-0.677489\pi\) | ||||
−0.529150 | + | 0.848528i | \(0.677489\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 7.48331i | − 1.06904i | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||||
0.845154 | − | 0.534522i | \(-0.179509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.65685i | − 0.514259i | −0.966377 | − | 0.257130i | \(-0.917223\pi\) | ||||
0.966377 | − | 0.257130i | \(-0.0827768\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −0.307692 | −0.153846 | − | 0.988095i | \(-0.549166\pi\) | ||||
−0.153846 | + | 0.988095i | \(0.549166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21.1660 | 1.24506 | 0.622530 | − | 0.782596i | \(-0.286105\pi\) | ||||
0.622530 | + | 0.782596i | \(0.286105\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 29.9333i | − 1.57543i | −0.616037 | − | 0.787717i | \(-0.711263\pi\) | ||||
0.616037 | − | 0.787717i | \(-0.288737\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 22.6274i | − 0.983801i | −0.870651 | − | 0.491900i | \(-0.836302\pi\) | ||||
0.870651 | − | 0.491900i | \(-0.163698\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.120000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.29150 | 0.182466 | 0.0912328 | − | 0.995830i | \(-0.470919\pi\) | ||||
0.0912328 | + | 0.995830i | \(0.470919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.4499i | 0.724192i | 0.932141 | + | 0.362096i | \(0.117939\pi\) | ||||
−0.932141 | + | 0.362096i | \(0.882061\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 39.5980i | 1.13137i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −28.0000 | −0.756757 | −0.378378 | − | 0.925651i | \(-0.623518\pi\) | ||||
−0.378378 | + | 0.925651i | \(0.623518\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 63.4980 | 1.54873 | 0.774366 | − | 0.632738i | \(-0.218069\pi\) | ||||
0.774366 | + | 0.632738i | \(0.218069\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 29.9333i | − 0.696122i | −0.937472 | − | 0.348061i | \(-0.886840\pi\) | ||||
0.937472 | − | 0.348061i | \(-0.113160\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 67.8823i | 1.44430i | 0.691735 | + | 0.722152i | \(0.256847\pi\) | ||||
−0.691735 | + | 0.722152i | \(0.743153\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 47.6235 | 0.898557 | 0.449279 | − | 0.893392i | \(-0.351681\pi\) | ||||
0.449279 | + | 0.893392i | \(0.351681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 29.9333i | 0.544241i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 101.823i | − 1.72582i | −0.505358 | − | 0.862910i | \(-0.668639\pi\) | ||||
0.505358 | − | 0.862910i | \(-0.331361\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −76.0000 | −1.24590 | −0.622951 | − | 0.782261i | \(-0.714066\pi\) | ||||
−0.622951 | + | 0.782261i | \(0.714066\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 21.1660 | 0.325631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 59.8665i | 0.893530i | 0.894651 | + | 0.446765i | \(0.147424\pi\) | ||||
−0.894651 | + | 0.446765i | \(0.852576\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 90.5097i | − 1.27478i | −0.770540 | − | 0.637392i | \(-0.780013\pi\) | ||||
0.770540 | − | 0.637392i | \(-0.219987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −26.0000 | −0.356164 | −0.178082 | − | 0.984016i | \(-0.556989\pi\) | ||||
−0.178082 | + | 0.984016i | \(0.556989\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −42.3320 | −0.549767 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 127.216i | − 1.61033i | −0.593048 | − | 0.805167i | \(-0.702076\pi\) | ||||
0.593048 | − | 0.805167i | \(-0.297924\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 118.794i | 1.43125i | 0.698484 | + | 0.715626i | \(0.253859\pi\) | ||||
−0.698484 | + | 0.715626i | \(0.746141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −112.000 | −1.31765 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −42.3320 | −0.475641 | −0.237820 | − | 0.971309i | \(-0.576433\pi\) | ||||
−0.237820 | + | 0.971309i | \(0.576433\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 29.9333i | 0.328937i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 158.392i | 1.66728i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.0000 | 0.185567 | 0.0927835 | − | 0.995686i | \(-0.470424\pi\) | ||||
0.0927835 | + | 0.995686i | \(0.470424\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −164.037 | −1.62412 | −0.812062 | − | 0.583571i | \(-0.801655\pi\) | ||||
−0.812062 | + | 0.583571i | \(0.801655\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 22.4499i | − 0.217961i | −0.994044 | − | 0.108980i | \(-0.965241\pi\) | ||||
0.994044 | − | 0.108980i | \(-0.0347585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 101.823i | − 0.951620i | −0.879548 | − | 0.475810i | \(-0.842155\pi\) | ||||
0.879548 | − | 0.475810i | \(-0.157845\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −148.000 | −1.35780 | −0.678899 | − | 0.734232i | \(-0.737543\pi\) | ||||
−0.678899 | + | 0.734232i | \(0.737543\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −42.3320 | −0.374620 | −0.187310 | − | 0.982301i | \(-0.559977\pi\) | ||||
−0.187310 | + | 0.982301i | \(0.559977\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 119.733i | 1.04116i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 158.392i | − 1.33102i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 89.0000 | 0.735537 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 116.413 | 0.931304 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 217.016i | 1.70879i | 0.519625 | + | 0.854394i | \(0.326072\pi\) | ||||
−0.519625 | + | 0.854394i | \(0.673928\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 158.392i | 1.20910i | 0.796568 | + | 0.604549i | \(0.206647\pi\) | ||||
−0.796568 | + | 0.604549i | \(0.793353\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −224.000 | −1.68421 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −232.826 | −1.69946 | −0.849730 | − | 0.527218i | \(-0.823235\pi\) | ||||
−0.849730 | + | 0.527218i | \(0.823235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 179.600i | 1.29208i | 0.763302 | + | 0.646042i | \(0.223577\pi\) | ||||
−0.763302 | + | 0.646042i | \(0.776423\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.6274i | 0.158234i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −28.0000 | −0.193103 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 248.701 | 1.66913 | 0.834566 | − | 0.550908i | \(-0.185719\pi\) | ||||
0.834566 | + | 0.550908i | \(0.185719\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.4499i | 0.148675i | 0.997233 | + | 0.0743376i | \(0.0236842\pi\) | ||||
−0.997233 | + | 0.0743376i | \(0.976316\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 118.794i | − 0.766413i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −236.000 | −1.50318 | −0.751592 | − | 0.659628i | \(-0.770714\pi\) | ||||
−0.751592 | + | 0.659628i | \(0.770714\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −169.328 | −1.05173 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 269.399i | − 1.65276i | −0.563115 | − | 0.826378i | \(-0.690397\pi\) | ||||
0.563115 | − | 0.826378i | \(-0.309603\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 113.137i | − 0.677468i | −0.940882 | − | 0.338734i | \(-0.890001\pi\) | ||||
0.940882 | − | 0.338734i | \(-0.109999\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −153.000 | −0.905325 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −89.9555 | −0.519974 | −0.259987 | − | 0.965612i | \(-0.583718\pi\) | ||||
−0.259987 | + | 0.965612i | \(0.583718\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 22.4499i | − 0.128285i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 33.9411i | − 0.189615i | −0.995496 | − | 0.0948076i | \(-0.969776\pi\) | ||||
0.995496 | − | 0.0948076i | \(-0.0302236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −228.000 | −1.25967 | −0.629834 | − | 0.776730i | \(-0.716877\pi\) | ||||
−0.629834 | + | 0.776730i | \(0.716877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 148.162 | 0.800876 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 119.733i | − 0.640284i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6274i | 0.118468i | 0.998244 | + | 0.0592341i | \(0.0188658\pi\) | ||||
−0.998244 | + | 0.0592341i | \(0.981134\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 70.0000 | 0.362694 | 0.181347 | − | 0.983419i | \(-0.441954\pi\) | ||||
0.181347 | + | 0.983419i | \(0.441954\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −121.705 | −0.617790 | −0.308895 | − | 0.951096i | \(-0.599959\pi\) | ||||
−0.308895 | + | 0.951096i | \(0.599959\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 202.049i | − 1.01532i | −0.861556 | − | 0.507662i | \(-0.830510\pi\) | ||||
0.861556 | − | 0.507662i | \(-0.169490\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 39.5980i | − 0.195064i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −336.000 | −1.63902 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −169.328 | −0.810182 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 59.8665i | − 0.283728i | −0.989886 | − | 0.141864i | \(-0.954691\pi\) | ||||
0.989886 | − | 0.141864i | \(-0.0453095\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 158.392i | 0.736707i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 168.000 | 0.774194 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −84.6640 | −0.383095 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 172.116i | − 0.771822i | −0.922536 | − | 0.385911i | \(-0.873887\pi\) | ||||
0.922536 | − | 0.385911i | \(-0.126113\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 96.1665i | − 0.423641i | −0.977309 | − | 0.211821i | \(-0.932061\pi\) | ||||
0.977309 | − | 0.211821i | \(-0.0679392\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −244.000 | −1.06550 | −0.532751 | − | 0.846272i | \(-0.678842\pi\) | ||||
−0.532751 | + | 0.846272i | \(0.678842\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 42.3320 | 0.181682 | 0.0908412 | − | 0.995865i | \(-0.471044\pi\) | ||||
0.0908412 | + | 0.995865i | \(0.471044\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 359.199i | − 1.52851i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 67.8823i | 0.284026i | 0.989865 | + | 0.142013i | \(0.0453575\pi\) | ||||
−0.989865 | + | 0.142013i | \(0.954642\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −166.000 | −0.688797 | −0.344398 | − | 0.938824i | \(-0.611917\pi\) | ||||
−0.344398 | + | 0.938824i | \(0.611917\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 37.0405 | 0.151186 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 119.733i | 0.484749i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 401.637i | 1.60015i | 0.599903 | + | 0.800073i | \(0.295206\pi\) | ||||
−0.599903 | + | 0.800073i | \(0.704794\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −128.000 | −0.505929 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 423.320 | 1.64716 | 0.823580 | − | 0.567200i | \(-0.191973\pi\) | ||||
0.823580 | + | 0.567200i | \(0.191973\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 209.533i | 0.809007i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 271.529i | 1.03243i | 0.856459 | + | 0.516215i | \(0.172659\pi\) | ||||
−0.856459 | + | 0.516215i | \(0.827341\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −252.000 | −0.950943 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −37.0405 | −0.137697 | −0.0688485 | − | 0.997627i | \(-0.521933\pi\) | ||||
−0.0688485 | + | 0.997627i | \(0.521933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 52.3832i | − 0.193296i | −0.995319 | − | 0.0966480i | \(-0.969188\pi\) | ||||
0.995319 | − | 0.0966480i | \(-0.0308121\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 16.9706i | − 0.0617111i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −372.000 | −1.34296 | −0.671480 | − | 0.741023i | \(-0.734341\pi\) | ||||
−0.671480 | + | 0.741023i | \(0.734341\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −84.6640 | −0.301296 | −0.150648 | − | 0.988588i | \(-0.548136\pi\) | ||||
−0.150648 | + | 0.988588i | \(0.548136\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 475.176i | − 1.65566i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 159.000 | 0.550173 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −291.033 | −0.993285 | −0.496643 | − | 0.867955i | \(-0.665434\pi\) | ||||
−0.496643 | + | 0.867955i | \(0.665434\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 538.799i | 1.82644i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 90.5097i | 0.302708i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −224.000 | −0.744186 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 402.154 | 1.31854 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 179.600i | − 0.585015i | −0.956263 | − | 0.292507i | \(-0.905510\pi\) | ||||
0.956263 | − | 0.292507i | \(-0.0944896\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 135.765i | 0.436542i | 0.975888 | + | 0.218271i | \(0.0700416\pi\) | ||||
−0.975888 | + | 0.218271i | \(0.929958\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 470.000 | 1.50160 | 0.750799 | − | 0.660531i | \(-0.229669\pi\) | ||||
0.750799 | + | 0.660531i | \(0.229669\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 386.280 | 1.21855 | 0.609274 | − | 0.792960i | \(-0.291461\pi\) | ||||
0.609274 | + | 0.792960i | \(0.291461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 29.9333i | − 0.0938347i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 633.568i | − 1.96151i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0000 | −0.0369231 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 507.984 | 1.54403 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 119.733i | 0.361731i | 0.983508 | + | 0.180866i | \(0.0578899\pi\) | ||||
−0.983508 | + | 0.180866i | \(0.942110\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 316.784i | − 0.945623i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −42.0000 | −0.124629 | −0.0623145 | − | 0.998057i | \(-0.519848\pi\) | ||||
−0.0623145 | + | 0.998057i | \(0.519848\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 126.996 | 0.372422 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 314.299i | − 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 164.049i | 0.472763i | 0.971660 | + | 0.236382i | \(0.0759615\pi\) | ||||
−0.971660 | + | 0.236382i | \(0.924038\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −284.000 | −0.813754 | −0.406877 | − | 0.913483i | \(-0.633382\pi\) | ||||
−0.406877 | + | 0.913483i | \(0.633382\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −211.660 | −0.599604 | −0.299802 | − | 0.954001i | \(-0.596921\pi\) | ||||
−0.299802 | + | 0.954001i | \(0.596921\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 478.932i | 1.34910i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 452.548i | 1.26058i | 0.776360 | + | 0.630290i | \(0.217064\pi\) | ||||
−0.776360 | + | 0.630290i | \(0.782936\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −535.000 | −1.48199 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 137.579 | 0.376929 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 561.249i | 1.52929i | 0.644453 | + | 0.764644i | \(0.277085\pi\) | ||||
−0.644453 | + | 0.764644i | \(0.722915\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 356.382i | − 0.960598i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 84.0000 | 0.225201 | 0.112601 | − | 0.993640i | \(-0.464082\pi\) | ||||
0.112601 | + | 0.993640i | \(0.464082\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.1660 | −0.0561433 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 448.999i | 1.18469i | 0.805683 | + | 0.592347i | \(0.201798\pi\) | ||||
−0.805683 | + | 0.592347i | \(0.798202\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 158.392i | − 0.413556i | −0.978388 | − | 0.206778i | \(-0.933702\pi\) | ||||
0.978388 | − | 0.206778i | \(-0.0662978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 224.000 | 0.581818 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 714.353 | 1.83638 | 0.918191 | − | 0.396137i | \(-0.129650\pi\) | ||||
0.918191 | + | 0.396137i | \(0.129650\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 478.932i | − 1.22489i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 673.166i | 1.70422i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 244.000 | 0.614610 | 0.307305 | − | 0.951611i | \(-0.400573\pi\) | ||||
0.307305 | + | 0.951611i | \(0.400573\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 232.826 | 0.580614 | 0.290307 | − | 0.956934i | \(-0.406243\pi\) | ||||
0.290307 | + | 0.956934i | \(0.406243\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 89.7998i | − 0.222828i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 158.392i | 0.389169i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 418.000 | 1.02200 | 0.511002 | − | 0.859579i | \(-0.329274\pi\) | ||||
0.511002 | + | 0.859579i | \(0.329274\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −761.976 | −1.84498 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 628.598i | − 1.51470i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 152.735i | 0.364523i | 0.983250 | + | 0.182261i | \(0.0583417\pi\) | ||||
−0.983250 | + | 0.182261i | \(0.941658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −212.000 | −0.503563 | −0.251781 | − | 0.967784i | \(-0.581016\pi\) | ||||
−0.251781 | + | 0.967784i | \(0.581016\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 63.4980 | 0.149407 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 568.732i | 1.33192i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 746.705i | − 1.73249i | −0.499616 | − | 0.866247i | \(-0.666526\pi\) | ||||
0.499616 | − | 0.866247i | \(-0.333474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −466.000 | −1.07621 | −0.538106 | − | 0.842877i | \(-0.680860\pi\) | ||||
−0.538106 | + | 0.842877i | \(0.680860\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −677.312 | −1.54991 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 381.649i | − 0.869360i | −0.900585 | − | 0.434680i | \(-0.856861\pi\) | ||||
0.900585 | − | 0.434680i | \(-0.143139\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 254.558i | 0.574624i | 0.957837 | + | 0.287312i | \(0.0927617\pi\) | ||||
−0.957837 | + | 0.287312i | \(0.907238\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 224.000 | 0.503371 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −571.482 | −1.27279 | −0.636395 | − | 0.771364i | \(-0.719575\pi\) | ||||
−0.636395 | + | 0.771364i | \(0.719575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 359.199i | − 0.796450i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 158.392i | − 0.348114i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −542.000 | −1.18600 | −0.592998 | − | 0.805204i | \(-0.702056\pi\) | ||||
−0.592998 | + | 0.805204i | \(0.702056\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −174.620 | −0.378784 | −0.189392 | − | 0.981902i | \(-0.560652\pi\) | ||||
−0.189392 | + | 0.981902i | \(0.560652\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 336.749i | 0.727320i | 0.931532 | + | 0.363660i | \(0.118473\pi\) | ||||
−0.931532 | + | 0.363660i | \(0.881527\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 526.087i | − 1.12653i | −0.826278 | − | 0.563263i | \(-0.809546\pi\) | ||||
0.826278 | − | 0.563263i | \(-0.190454\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 448.000 | 0.955224 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −169.328 | −0.357987 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 89.7998i | − 0.189052i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 181.019i | 0.377911i | 0.981986 | + | 0.188955i | \(0.0605102\pi\) | ||||
−0.981986 | + | 0.188955i | \(0.939490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 112.000 | 0.232848 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −95.2470 | −0.196386 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 651.048i | 1.33686i | 0.743777 | + | 0.668428i | \(0.233032\pi\) | ||||
−0.743777 | + | 0.668428i | \(0.766968\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 248.902i | − 0.506928i | −0.967345 | − | 0.253464i | \(-0.918430\pi\) | ||||
0.967345 | − | 0.253464i | \(-0.0815699\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 112.000 | 0.227181 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −677.312 | −1.36280 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 239.466i | 0.479892i | 0.970786 | + | 0.239946i | \(0.0771297\pi\) | ||||
−0.970786 | + | 0.239946i | \(0.922870\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 950.352i | 1.88937i | 0.327984 | + | 0.944683i | \(0.393631\pi\) | ||||
−0.327984 | + | 0.944683i | \(0.606369\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 868.000 | 1.71881 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 428.612 | 0.842066 | 0.421033 | − | 0.907045i | \(-0.361668\pi\) | ||||
0.421033 | + | 0.907045i | \(0.361668\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 194.566i | 0.380756i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 118.794i | 0.230668i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 384.000 | 0.742747 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −698.478 | −1.34065 | −0.670325 | − | 0.742068i | \(-0.733845\pi\) | ||||
−0.670325 | + | 0.742068i | \(0.733845\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 868.065i | − 1.65978i | −0.557928 | − | 0.829890i | \(-0.688403\pi\) | ||||
0.557928 | − | 0.829890i | \(-0.311597\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 475.176i | 0.901662i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0000 | 0.0321361 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −253.992 | −0.476533 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 538.799i | 1.00710i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 39.5980i | 0.0734656i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 556.000 | 1.02773 | 0.513863 | − | 0.857872i | \(-0.328214\pi\) | ||||
0.513863 | + | 0.857872i | \(0.328214\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 783.142 | 1.43696 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 448.999i | − 0.820839i | −0.911897 | − | 0.410419i | \(-0.865382\pi\) | ||||
0.911897 | − | 0.410419i | \(-0.134618\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 158.392i | − 0.287463i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −952.000 | −1.72152 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 799.017 | 1.43450 | 0.717250 | − | 0.696816i | \(-0.245400\pi\) | ||||
0.717250 | + | 0.696816i | \(0.245400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 119.733i | 0.214191i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 220.617i | 0.391860i | 0.980618 | + | 0.195930i | \(0.0627726\pi\) | ||||
−0.980618 | + | 0.195930i | \(0.937227\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 224.000 | 0.396460 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −529.150 | −0.929965 | −0.464983 | − | 0.885320i | \(-0.653939\pi\) | ||||
−0.464983 | + | 0.885320i | \(0.653939\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 897.998i | − 1.57268i | −0.617797 | − | 0.786338i | \(-0.711975\pi\) | ||||
0.617797 | − | 0.786338i | \(-0.288025\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 67.8823i | − 0.118056i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 586.000 | 1.01560 | 0.507799 | − | 0.861476i | \(-0.330459\pi\) | ||||
0.507799 | + | 0.861476i | \(0.330459\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 888.972 | 1.53007 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 269.399i | − 0.462091i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 45.2548i | − 0.0770951i | −0.999257 | − | 0.0385476i | \(-0.987727\pi\) | ||||
0.999257 | − | 0.0385476i | \(-0.0122731\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 672.000 | 1.14092 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −296.324 | −0.499703 | −0.249852 | − | 0.968284i | \(-0.580382\pi\) | ||||
−0.249852 | + | 0.968284i | \(0.580382\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 838.131i | 1.40862i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1154.00i | − 1.92654i | −0.268532 | − | 0.963271i | \(-0.586539\pi\) | ||||
0.268532 | − | 0.963271i | \(-0.413461\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 634.000 | 1.05491 | 0.527454 | − | 0.849583i | \(-0.323147\pi\) | ||||
0.527454 | + | 0.849583i | \(0.323147\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −470.944 | −0.778419 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 800.715i | − 1.31913i | −0.751646 | − | 0.659567i | \(-0.770740\pi\) | ||||
0.751646 | − | 0.659567i | \(-0.229260\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 271.529i | − 0.444401i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1140.00 | 1.85971 | 0.929853 | − | 0.367931i | \(-0.119934\pi\) | ||||
0.929853 | + | 0.367931i | \(0.119934\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −592.648 | −0.960532 | −0.480266 | − | 0.877123i | \(-0.659460\pi\) | ||||
−0.480266 | + | 0.877123i | \(0.659460\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 359.199i | 0.580289i | 0.956983 | + | 0.290145i | \(0.0937034\pi\) | ||||
−0.956983 | + | 0.290145i | \(0.906297\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 316.784i | 0.508481i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −691.000 | −1.10560 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −592.648 | −0.942207 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 291.849i | 0.462519i | 0.972892 | + | 0.231259i | \(0.0742846\pi\) | ||||
−0.972892 | + | 0.231259i | \(0.925715\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1148.34i | − 1.80841i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.0000 | 0.0439560 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −486.818 | −0.759467 | −0.379733 | − | 0.925096i | \(-0.623984\pi\) | ||||
−0.379733 | + | 0.925096i | \(0.623984\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 808.198i | − 1.25692i | −0.777843 | − | 0.628459i | \(-0.783686\pi\) | ||||
0.777843 | − | 0.628459i | \(-0.216314\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 294.156i | 0.454647i | 0.973819 | + | 0.227323i | \(0.0729974\pi\) | ||||
−0.973819 | + | 0.227323i | \(0.927003\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −576.000 | −0.887519 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 79.3725 | 0.121551 | 0.0607753 | − | 0.998151i | \(-0.480643\pi\) | ||||
0.0607753 | + | 0.998151i | \(0.480643\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 838.131i | − 1.27959i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1040.86i | 1.57946i | 0.613457 | + | 0.789728i | \(0.289778\pi\) | ||||
−0.613457 | + | 0.789728i | \(0.710222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 548.000 | 0.829047 | 0.414523 | − | 0.910039i | \(-0.363948\pi\) | ||||
0.414523 | + | 0.910039i | \(0.363948\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1185.30 | 1.78240 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 119.733i | − 0.179510i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 429.921i | 0.640717i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 334.000 | 0.496285 | 0.248143 | − | 0.968724i | \(-0.420180\pi\) | ||||
0.248143 | + | 0.968724i | \(0.420180\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 79.3725 | 0.117242 | 0.0586208 | − | 0.998280i | \(-0.481330\pi\) | ||||
0.0586208 | + | 0.998280i | \(0.481330\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 134.700i | − 0.198379i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 627.911i | 0.919342i | 0.888089 | + | 0.459671i | \(0.152033\pi\) | ||||
−0.888089 | + | 0.459671i | \(0.847967\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1232.00 | 1.79854 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −190.494 | −0.276479 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 748.331i | − 1.08297i | −0.840711 | − | 0.541484i | \(-0.817863\pi\) | ||||
0.840711 | − | 0.541484i | \(-0.182137\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 950.352i | − 1.36741i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1344.00 | 1.92826 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −121.705 | −0.173616 | −0.0868078 | − | 0.996225i | \(-0.527667\pi\) | ||||
−0.0868078 | + | 0.996225i | \(0.527667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 838.131i | 1.19222i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1227.54i | 1.73626i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00000 | −0.00564175 | −0.00282087 | − | 0.999996i | \(-0.500898\pi\) | ||||
−0.00282087 | + | 0.999996i | \(0.500898\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 507.984 | 0.712460 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 119.733i | − 0.167459i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 316.784i | 0.440589i | 0.975433 | + | 0.220295i | \(0.0707019\pi\) | ||||
−0.975433 | + | 0.220295i | \(0.929298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −168.000 | −0.233010 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.8745 | 0.0218959 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1174.88i | − 1.61607i | −0.589137 | − | 0.808033i | \(-0.700532\pi\) | ||||
0.589137 | − | 0.808033i | \(-0.299468\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 633.568i | − 0.866714i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1212.00 | 1.65348 | 0.826739 | − | 0.562585i | \(-0.190193\pi\) | ||||
0.826739 | + | 0.562585i | \(0.190193\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 338.656 | 0.459506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1257.20i | 1.70121i | 0.525802 | + | 0.850607i | \(0.323765\pi\) | ||||
−0.525802 | + | 0.850607i | \(0.676235\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1018.23i | − 1.37044i | −0.728338 | − | 0.685218i | \(-0.759707\pi\) | ||||
0.728338 | − | 0.685218i | \(-0.240293\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1316.00 | −1.76644 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −761.976 | −1.01732 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 411.582i | 0.548046i | 0.961723 | + | 0.274023i | \(0.0883544\pi\) | ||||
−0.961723 | + | 0.274023i | \(0.911646\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 118.794i | − 0.157343i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1020.00 | 1.34742 | 0.673712 | − | 0.738994i | \(-0.264699\pi\) | ||||
0.673712 | + | 0.738994i | \(0.264699\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 529.150 | 0.695335 | 0.347668 | − | 0.937618i | \(-0.386974\pi\) | ||||
0.347668 | + | 0.937618i | \(0.386974\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1107.53i | 1.45155i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 407.294i | 0.531022i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 262.000 | 0.340702 | 0.170351 | − | 0.985383i | \(-0.445510\pi\) | ||||
0.170351 | + | 0.985383i | \(0.445510\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 851.932 | 1.10211 | 0.551056 | − | 0.834469i | \(-0.314225\pi\) | ||||
0.551056 | + | 0.834469i | \(0.314225\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 67.3498i | 0.0869030i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1900.70i | − 2.43993i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −512.000 | −0.655570 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1248.79 | 1.59082 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 568.732i | − 0.722658i | −0.932438 | − | 0.361329i | \(-0.882323\pi\) | ||||
0.932438 | − | 0.361329i | \(-0.117677\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 316.784i | 0.400485i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 304.000 | 0.383354 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −894.264 | −1.12204 | −0.561019 | − | 0.827803i | \(-0.689590\pi\) | ||||
−0.561019 | + | 0.827803i | \(0.689590\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1436.80i | 1.79824i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 147.078i | 0.183161i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 896.000 | 1.11304 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 105.830 | 0.130816 | 0.0654079 | − | 0.997859i | \(-0.479165\pi\) | ||||
0.0654079 | + | 0.997859i | \(0.479165\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 987.798i | 1.21800i | 0.793170 | + | 0.609000i | \(0.208429\pi\) | ||||
−0.793170 | + | 0.609000i | \(0.791571\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1425.53i | 1.74911i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −896.000 | −1.09670 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1010.68 | −1.23103 | −0.615516 | − | 0.788125i | \(-0.711052\pi\) | ||||
−0.615516 | + | 0.788125i | \(0.711052\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 830.648i | 1.00929i | 0.863326 | + | 0.504646i | \(0.168377\pi\) | ||||
−0.863326 | + | 0.504646i | \(0.831623\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 328.098i | 0.396732i | 0.980128 | + | 0.198366i | \(0.0635635\pi\) | ||||
−0.980128 | + | 0.198366i | \(0.936437\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1164.00 | 1.40410 | 0.702051 | − | 0.712127i | \(-0.252268\pi\) | ||||
0.702051 | + | 0.712127i | \(0.252268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −148.162 | −0.177866 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 598.665i | 0.716964i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 995.606i | − 1.18666i | −0.804960 | − | 0.593329i | \(-0.797813\pi\) | ||||
0.804960 | − | 0.593329i | \(-0.202187\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −813.000 | −0.966706 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 809.600 | 0.958106 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 666.015i | − 0.786322i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 633.568i | 0.744498i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 276.000 | 0.323564 | 0.161782 | − | 0.986827i | \(-0.448276\pi\) | ||||
0.161782 | + | 0.986827i | \(0.448276\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −275.158 | −0.321071 | −0.160536 | − | 0.987030i | \(-0.551322\pi\) | ||||
−0.160536 | + | 0.987030i | \(0.551322\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 628.598i | 0.731779i | 0.930658 | + | 0.365890i | \(0.119235\pi\) | ||||
−0.930658 | + | 0.365890i | \(0.880765\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 294.156i | − 0.340853i | −0.985370 | − | 0.170427i | \(-0.945485\pi\) | ||||
0.985370 | − | 0.170427i | \(-0.0545146\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 476.000 | 0.550289 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −719.644 | −0.828129 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 239.466i | − 0.274932i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 871.156i | − 0.995606i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 340.000 | 0.387685 | 0.193843 | − | 0.981033i | \(-0.437905\pi\) | ||||
0.193843 | + | 0.981033i | \(0.437905\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 761.976 | 0.864899 | 0.432450 | − | 0.901658i | \(-0.357649\pi\) | ||||
0.432450 | + | 0.901658i | \(0.357649\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 89.7998i | 0.101699i | 0.998706 | + | 0.0508493i | \(0.0161928\pi\) | ||||
−0.998706 | + | 0.0508493i | \(0.983807\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 859.842i | − 0.969382i | −0.874685 | − | 0.484691i | \(-0.838932\pi\) | ||||
0.874685 | − | 0.484691i | \(-0.161068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1624.00 | 1.82677 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2031.94 | 2.27541 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 179.600i | 0.200670i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 118.794i | 0.132140i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1008.00 | 1.11876 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1206.46 | 1.33311 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 448.999i | − 0.495037i | −0.968883 | − | 0.247519i | \(-0.920385\pi\) | ||||
0.968883 | − | 0.247519i | \(-0.0796152\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 248.902i | 0.273218i | 0.990625 | + | 0.136609i | \(0.0436204\pi\) | ||||
−0.990625 | + | 0.136609i | \(0.956380\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 672.000 | 0.736035 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1185.30 | 1.29258 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 710.915i | 0.773574i | 0.922169 | + | 0.386787i | \(0.126415\pi\) | ||||
−0.922169 | + | 0.386787i | \(0.873585\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 362.039i | 0.392241i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −84.0000 | −0.0908108 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 910.138 | 0.979697 | 0.489848 | − | 0.871808i | \(-0.337052\pi\) | ||||
0.489848 | + | 0.871808i | \(0.337052\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 209.533i | 0.225062i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 633.568i | 0.677612i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1166.00 | −1.24440 | −0.622199 | − | 0.782860i | \(-0.713760\pi\) | ||||
−0.622199 | + | 0.782860i | \(0.713760\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 418.029 | 0.444239 | 0.222119 | − | 0.975019i | \(-0.428703\pi\) | ||||
0.222119 | + | 0.975019i | \(0.428703\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1436.80i | − 1.52364i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 893.783i | 0.943805i | 0.881651 | + | 0.471902i | \(0.156433\pi\) | ||||
−0.881651 | + | 0.471902i | \(0.843567\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 104.000 | 0.109589 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1291.13 | −1.35480 | −0.677401 | − | 0.735614i | \(-0.736894\pi\) | ||||
−0.677401 | + | 0.735614i | \(0.736894\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 119.733i | − 0.125375i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1742.31i | 1.81680i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 457.000 | 0.475546 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −370.405 | −0.383840 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1070.11i | − 1.10663i | −0.832971 | − | 0.553316i | \(-0.813362\pi\) | ||||
0.832971 | − | 0.553316i | \(-0.186638\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 514.774i | 0.530148i | 0.964228 | + | 0.265074i | \(0.0853964\pi\) | ||||
−0.964228 | + | 0.265074i | \(0.914604\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1344.00 | 1.38129 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1206.46 | −1.23486 | −0.617432 | − | 0.786624i | \(-0.711827\pi\) | ||||
−0.617432 | + | 0.786624i | \(0.711827\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 239.466i | 0.244603i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 950.352i | 0.966787i | 0.875403 | + | 0.483393i | \(0.160596\pi\) | ||||
−0.875403 | + | 0.483393i | \(0.839404\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 644.000 | 0.653807 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −677.312 | −0.684846 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 486.415i | − 0.490833i | −0.969418 | − | 0.245416i | \(-0.921075\pi\) | ||||
0.969418 | − | 0.245416i | \(-0.0789247\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1069.15i | 1.07452i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1244.00 | −1.24774 | −0.623872 | − | 0.781527i | \(-0.714441\pi\) | ||||
−0.623872 | + | 0.781527i | \(0.714441\pi\) | |||||||
\(998\) | 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 | 2304.3.g.p.1279.1 | 4 | ||
3.2 | odd | 2 | inner | 2304.3.g.p.1279.3 | 4 | ||
4.3 | odd | 2 | inner | 2304.3.g.p.1279.2 | 4 | ||
8.3 | odd | 2 | 2304.3.g.w.1279.4 | 4 | |||
8.5 | even | 2 | 2304.3.g.w.1279.3 | 4 | |||
12.11 | even | 2 | inner | 2304.3.g.p.1279.4 | 4 | ||
16.3 | odd | 4 | 1152.3.b.i.703.5 | yes | 8 | ||
16.5 | even | 4 | 1152.3.b.i.703.4 | yes | 8 | ||
16.11 | odd | 4 | 1152.3.b.i.703.2 | yes | 8 | ||
16.13 | even | 4 | 1152.3.b.i.703.7 | yes | 8 | ||
24.5 | odd | 2 | 2304.3.g.w.1279.1 | 4 | |||
24.11 | even | 2 | 2304.3.g.w.1279.2 | 4 | |||
48.5 | odd | 4 | 1152.3.b.i.703.8 | yes | 8 | ||
48.11 | even | 4 | 1152.3.b.i.703.6 | yes | 8 | ||
48.29 | odd | 4 | 1152.3.b.i.703.3 | yes | 8 | ||
48.35 | even | 4 | 1152.3.b.i.703.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.b.i.703.1 | ✓ | 8 | 48.35 | even | 4 | ||
1152.3.b.i.703.2 | yes | 8 | 16.11 | odd | 4 | ||
1152.3.b.i.703.3 | yes | 8 | 48.29 | odd | 4 | ||
1152.3.b.i.703.4 | yes | 8 | 16.5 | even | 4 | ||
1152.3.b.i.703.5 | yes | 8 | 16.3 | odd | 4 | ||
1152.3.b.i.703.6 | yes | 8 | 48.11 | even | 4 | ||
1152.3.b.i.703.7 | yes | 8 | 16.13 | even | 4 | ||
1152.3.b.i.703.8 | yes | 8 | 48.5 | odd | 4 | ||
2304.3.g.p.1279.1 | 4 | 1.1 | even | 1 | trivial | ||
2304.3.g.p.1279.2 | 4 | 4.3 | odd | 2 | inner | ||
2304.3.g.p.1279.3 | 4 | 3.2 | odd | 2 | inner | ||
2304.3.g.p.1279.4 | 4 | 12.11 | even | 2 | inner | ||
2304.3.g.w.1279.1 | 4 | 24.5 | odd | 2 | |||
2304.3.g.w.1279.2 | 4 | 24.11 | even | 2 | |||
2304.3.g.w.1279.3 | 4 | 8.5 | even | 2 | |||
2304.3.g.w.1279.4 | 4 | 8.3 | odd | 2 |