Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(703,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.703");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 703.5 | ||
Root | \(0.581861 + 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.703 |
Dual form | 1152.3.b.i.703.4 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 5.29150i | 1.05830i | 0.848528 | + | 0.529150i | \(0.177489\pi\) | ||||
−0.848528 | + | 0.529150i | \(0.822511\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | 5.65685 | 0.514259 | 0.257130 | − | 0.966377i | \(-0.417223\pi\) | ||||
0.257130 | + | 0.966377i | \(0.417223\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.00000i | − 0.307692i | −0.988095 | − | 0.153846i | \(-0.950834\pi\) | ||||
0.988095 | − | 0.153846i | \(-0.0491660\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | −29.9333 | −1.57543 | −0.787717 | − | 0.616037i | \(-0.788737\pi\) | ||||
−0.787717 | + | 0.616037i | \(0.788737\pi\) | |||||||
\(20\) | 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 | ||||||||
\(29\) | 5.29150i | 0.182466i | 0.995830 | + | 0.0912328i | \(0.0290807\pi\) | ||||
−0.995830 | + | 0.0912328i | \(0.970919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 22.4499i | − 0.724192i | −0.932141 | − | 0.362096i | \(-0.882061\pi\) | ||||
0.932141 | − | 0.362096i | \(-0.117939\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 39.5980 | 1.13137 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 28.0000i | 0.756757i | 0.925651 | + | 0.378378i | \(0.123518\pi\) | ||||
−0.925651 | + | 0.378378i | \(0.876482\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −63.4980 | −1.54873 | −0.774366 | − | 0.632738i | \(-0.781931\pi\) | ||||
−0.774366 | + | 0.632738i | \(0.781931\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 29.9333 | 0.696122 | 0.348061 | − | 0.937472i | \(-0.386840\pi\) | ||||
0.348061 | + | 0.937472i | \(0.386840\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 67.8823i | − 1.44430i | −0.691735 | − | 0.722152i | \(-0.743153\pi\) | ||||
0.691735 | − | 0.722152i | \(-0.256847\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 47.6235i | − 0.898557i | −0.893392 | − | 0.449279i | \(-0.851681\pi\) | ||||
0.893392 | − | 0.449279i | \(-0.148319\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 29.9333i | 0.544241i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 101.823 | 1.72582 | 0.862910 | − | 0.505358i | \(-0.168639\pi\) | ||||
0.862910 | + | 0.505358i | \(0.168639\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 76.0000i | − 1.24590i | −0.782261 | − | 0.622951i | \(-0.785934\pi\) | ||||
0.782261 | − | 0.622951i | \(-0.214066\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 21.1660 | 0.325631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 59.8665 | 0.893530 | 0.446765 | − | 0.894651i | \(-0.352576\pi\) | ||||
0.446765 | + | 0.894651i | \(0.352576\pi\) | |||||||
\(68\) | 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 | \(-0.443011\pi\) | ||||
0.178082 | + | 0.984016i | \(0.443011\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 42.3320i | − 0.549767i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 127.216i | 1.61033i | 0.593048 | + | 0.805167i | \(0.297924\pi\) | ||||
−0.593048 | + | 0.805167i | \(0.702076\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 118.794 | 1.43125 | 0.715626 | − | 0.698484i | \(-0.246141\pi\) | ||||
0.715626 | + | 0.698484i | \(0.246141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 112.000i | 1.31765i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 42.3320 | 0.475641 | 0.237820 | − | 0.971309i | \(-0.423567\pi\) | ||||
0.237820 | + | 0.971309i | \(0.423567\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −29.9333 | −0.328937 | ||||||||
\(92\) | 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 | ||||||||
\(101\) | 164.037i | 1.62412i | 0.583571 | + | 0.812062i | \(0.301655\pi\) | ||||
−0.583571 | + | 0.812062i | \(0.698345\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | 101.823 | 0.951620 | 0.475810 | − | 0.879548i | \(-0.342155\pi\) | ||||
0.475810 | + | 0.879548i | \(0.342155\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 148.000i | − 1.35780i | −0.734232 | − | 0.678899i | \(-0.762457\pi\) | ||||
0.734232 | − | 0.678899i | \(-0.237543\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 119.733 | 1.04116 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | 116.413i | 0.931304i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 217.016i | − 1.70879i | −0.519625 | − | 0.854394i | \(-0.673928\pi\) | ||||
0.519625 | − | 0.854394i | \(-0.326072\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 158.392 | 1.20910 | 0.604549 | − | 0.796568i | \(-0.293353\pi\) | ||||
0.604549 | + | 0.796568i | \(0.293353\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 224.000i | 1.68421i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 232.826 | 1.69946 | 0.849730 | − | 0.527218i | \(-0.176765\pi\) | ||||
0.849730 | + | 0.527218i | \(0.176765\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −179.600 | −1.29208 | −0.646042 | − | 0.763302i | \(-0.723577\pi\) | ||||
−0.646042 | + | 0.763302i | \(0.723577\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | − 248.701i | − 1.66913i | −0.550908 | − | 0.834566i | \(-0.685719\pi\) | ||||
0.550908 | − | 0.834566i | \(-0.314281\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 118.794 | 0.766413 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 236.000i | − 1.50318i | −0.659628 | − | 0.751592i | \(-0.729286\pi\) | ||||
0.659628 | − | 0.751592i | \(-0.270714\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −169.328 | −1.05173 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −269.399 | −1.65276 | −0.826378 | − | 0.563115i | \(-0.809603\pi\) | ||||
−0.826378 | + | 0.563115i | \(0.809603\pi\) | |||||||
\(164\) | 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 | ||||||||
\(173\) | − 89.9555i | − 0.519974i | −0.965612 | − | 0.259987i | \(-0.916282\pi\) | ||||
0.965612 | − | 0.259987i | \(-0.0837183\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.4499i | 0.128285i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −33.9411 | −0.189615 | −0.0948076 | − | 0.995496i | \(-0.530224\pi\) | ||||
−0.0948076 | + | 0.995496i | \(0.530224\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 228.000i | 1.25967i | 0.776730 | + | 0.629834i | \(0.216877\pi\) | ||||
−0.776730 | + | 0.629834i | \(0.783123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −148.162 | −0.800876 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 119.733 | 0.640284 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 22.6274i | − 0.118468i | −0.998244 | − | 0.0592341i | \(-0.981134\pi\) | ||||
0.998244 | − | 0.0592341i | \(-0.0188658\pi\) | |||||||
\(192\) | 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 | ||||||||
\(197\) | 121.705i | 0.617790i | 0.951096 | + | 0.308895i | \(0.0999591\pi\) | ||||
−0.951096 | + | 0.308895i | \(0.900041\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 39.5980 | 0.195064 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 336.000i | − 1.63902i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −169.328 | −0.810182 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −59.8665 | −0.283728 | −0.141864 | − | 0.989886i | \(-0.545309\pi\) | ||||
−0.141864 | + | 0.989886i | \(0.545309\pi\) | |||||||
\(212\) | 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 | ||||||||
\(221\) | − 84.6640i | − 0.383095i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 172.116i | 0.771822i | 0.922536 | + | 0.385911i | \(0.126113\pi\) | ||||
−0.922536 | + | 0.385911i | \(0.873887\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −96.1665 | −0.423641 | −0.211821 | − | 0.977309i | \(-0.567939\pi\) | ||||
−0.211821 | + | 0.977309i | \(0.567939\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 244.000i | 1.06550i | 0.846272 | + | 0.532751i | \(0.178842\pi\) | ||||
−0.846272 | + | 0.532751i | \(0.821158\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −42.3320 | −0.181682 | −0.0908412 | − | 0.995865i | \(-0.528956\pi\) | ||||
−0.0908412 | + | 0.995865i | \(0.528956\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 359.199 | 1.52851 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 67.8823i | − 0.284026i | −0.989865 | − | 0.142013i | \(-0.954642\pi\) | ||||
0.989865 | − | 0.142013i | \(-0.0453575\pi\) | |||||||
\(240\) | 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 | ||||||||
\(245\) | − 37.0405i | − 0.151186i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 119.733i | 0.484749i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −401.637 | −1.60015 | −0.800073 | − | 0.599903i | \(-0.795206\pi\) | ||||
−0.800073 | + | 0.599903i | \(0.795206\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 128.000i | − 0.505929i | ||||||||
\(254\) | 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 | ||||||||
\(259\) | 209.533 | 0.809007 | ||||||||
\(260\) | 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 | ||||||||
\(269\) | − 37.0405i | − 0.137697i | −0.997627 | − | 0.0688485i | \(-0.978067\pi\) | ||||
0.997627 | − | 0.0688485i | \(-0.0219325\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 52.3832i | 0.193296i | 0.995319 | + | 0.0966480i | \(0.0308121\pi\) | ||||
−0.995319 | + | 0.0966480i | \(0.969188\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.9706 | −0.0617111 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 372.000i | 1.34296i | 0.741023 | + | 0.671480i | \(0.234341\pi\) | ||||
−0.741023 | + | 0.671480i | \(0.765659\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 84.6640 | 0.301296 | 0.150648 | − | 0.988588i | \(-0.451864\pi\) | ||||
0.150648 | + | 0.988588i | \(0.451864\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 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 | ||||||||
\(293\) | 291.033i | 0.993285i | 0.867955 | + | 0.496643i | \(0.165434\pi\) | ||||
−0.867955 | + | 0.496643i | \(0.834566\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 538.799i | 1.82644i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −90.5097 | −0.302708 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 224.000i | − 0.744186i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 402.154 | 1.31854 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −179.600 | −0.585015 | −0.292507 | − | 0.956263i | \(-0.594490\pi\) | ||||
−0.292507 | + | 0.956263i | \(0.594490\pi\) | |||||||
\(308\) | 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 | \(-0.770331\pi\) | ||||
−0.750799 | + | 0.660531i | \(0.770331\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 386.280i | 1.21855i | 0.792960 | + | 0.609274i | \(0.208539\pi\) | ||||
−0.792960 | + | 0.609274i | \(0.791461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.9333i | 0.0938347i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −633.568 | −1.96151 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.0000i | 0.0369231i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −507.984 | −1.54403 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −119.733 | −0.361731 | −0.180866 | − | 0.983508i | \(-0.557890\pi\) | ||||
−0.180866 | + | 0.983508i | \(0.557890\pi\) | |||||||
\(332\) | 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 | ||||||||
\(341\) | − 126.996i | − 0.372422i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 314.299i | − 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −164.049 | −0.472763 | −0.236382 | − | 0.971660i | \(-0.575962\pi\) | ||||
−0.236382 | + | 0.971660i | \(0.575962\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 284.000i | − 0.813754i | −0.913483 | − | 0.406877i | \(-0.866618\pi\) | ||||
0.913483 | − | 0.406877i | \(-0.133382\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 478.932 | 1.34910 | ||||||||
\(356\) | 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 | ||||||||
\(365\) | 137.579i | 0.376929i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 561.249i | − 1.52929i | −0.644453 | − | 0.764644i | \(-0.722915\pi\) | ||||
0.644453 | − | 0.764644i | \(-0.277085\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −356.382 | −0.960598 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 84.0000i | − 0.225201i | −0.993640 | − | 0.112601i | \(-0.964082\pi\) | ||||
0.993640 | − | 0.112601i | \(-0.0359180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.1660 | 0.0561433 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −448.999 | −1.18469 | −0.592347 | − | 0.805683i | \(-0.701798\pi\) | ||||
−0.592347 | + | 0.805683i | \(0.701798\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 158.392i | 0.413556i | 0.978388 | + | 0.206778i | \(0.0662978\pi\) | ||||
−0.978388 | + | 0.206778i | \(0.933702\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 224.000 | 0.581818 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 714.353i | − 1.83638i | −0.396137 | − | 0.918191i | \(-0.629650\pi\) | ||||
0.396137 | − | 0.918191i | \(-0.370350\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 478.932i | − 1.22489i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −673.166 | −1.70422 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 244.000i | 0.614610i | 0.951611 | + | 0.307305i | \(0.0994271\pi\) | ||||
−0.951611 | + | 0.307305i | \(0.900573\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | −89.7998 | −0.222828 | ||||||||
\(404\) | 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 | \(-0.670726\pi\) | ||||
−0.511002 | + | 0.859579i | \(0.670726\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 761.976i | − 1.84498i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 628.598i | 1.51470i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 152.735 | 0.364523 | 0.182261 | − | 0.983250i | \(-0.441658\pi\) | ||||
0.182261 | + | 0.983250i | \(0.441658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 212.000i | 0.503563i | 0.967784 | + | 0.251781i | \(0.0810164\pi\) | ||||
−0.967784 | + | 0.251781i | \(0.918984\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −63.4980 | −0.149407 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −568.732 | −1.33192 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 746.705i | 1.73249i | 0.499616 | + | 0.866247i | \(0.333474\pi\) | ||||
−0.499616 | + | 0.866247i | \(0.666526\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | 677.312i | 1.54991i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | −254.558 | −0.574624 | −0.287312 | − | 0.957837i | \(-0.592762\pi\) | ||||
−0.287312 | + | 0.957837i | \(0.592762\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 224.000i | 0.503371i | ||||||||
\(446\) | 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 | ||||||||
\(451\) | −359.199 | −0.796450 | ||||||||
\(452\) | 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 | \(-0.297944\pi\) | ||||
0.592998 | + | 0.805204i | \(0.297944\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 174.620i | − 0.378784i | −0.981902 | − | 0.189392i | \(-0.939348\pi\) | ||||
0.981902 | − | 0.189392i | \(-0.0606517\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 336.749i | − 0.727320i | −0.931532 | − | 0.363660i | \(-0.881527\pi\) | ||||
0.931532 | − | 0.363660i | \(-0.118473\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −526.087 | −1.12653 | −0.563263 | − | 0.826278i | \(-0.690454\pi\) | ||||
−0.563263 | + | 0.826278i | \(0.690454\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 448.000i | − 0.955224i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 169.328 | 0.357987 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 89.7998 | 0.189052 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 181.019i | − 0.377911i | −0.981986 | − | 0.188955i | \(-0.939490\pi\) | ||||
0.981986 | − | 0.188955i | \(-0.0605102\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 112.000 | 0.232848 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 95.2470i | 0.196386i | ||||||||
\(486\) | 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 | ||||||||
\(491\) | 248.902 | 0.506928 | 0.253464 | − | 0.967345i | \(-0.418430\pi\) | ||||
0.253464 | + | 0.967345i | \(0.418430\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 112.000i | 0.227181i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −677.312 | −1.36280 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 239.466 | 0.479892 | 0.239946 | − | 0.970786i | \(-0.422870\pi\) | ||||
0.239946 | + | 0.970786i | \(0.422870\pi\) | |||||||
\(500\) | 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 | ||||||||
\(509\) | 428.612i | 0.842066i | 0.907045 | + | 0.421033i | \(0.138332\pi\) | ||||
−0.907045 | + | 0.421033i | \(0.861668\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 194.566i | − 0.380756i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 118.794 | 0.230668 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 384.000i | − 0.742747i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 698.478 | 1.34065 | 0.670325 | − | 0.742068i | \(-0.266155\pi\) | ||||
0.670325 | + | 0.742068i | \(0.266155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 868.065 | 1.65978 | 0.829890 | − | 0.557928i | \(-0.188403\pi\) | ||||
0.829890 | + | 0.557928i | \(0.188403\pi\) | |||||||
\(524\) | 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 | ||||||||
\(533\) | 253.992i | 0.476533i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 538.799i | 1.00710i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −39.5980 | −0.0734656 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 556.000i | 1.02773i | 0.857872 | + | 0.513863i | \(0.171786\pi\) | ||||
−0.857872 | + | 0.513863i | \(0.828214\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 783.142 | 1.43696 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −448.999 | −0.820839 | −0.410419 | − | 0.911897i | \(-0.634618\pi\) | ||||
−0.410419 | + | 0.911897i | \(0.634618\pi\) | |||||||
\(548\) | 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 | ||||||||
\(557\) | 799.017i | 1.43450i | 0.696816 | + | 0.717250i | \(0.254600\pi\) | ||||
−0.696816 | + | 0.717250i | \(0.745400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 119.733i | − 0.214191i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 220.617 | 0.391860 | 0.195930 | − | 0.980618i | \(-0.437227\pi\) | ||||
0.195930 | + | 0.980618i | \(0.437227\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 224.000i | − 0.396460i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 529.150 | 0.929965 | 0.464983 | − | 0.885320i | \(-0.346061\pi\) | ||||
0.464983 | + | 0.885320i | \(0.346061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 897.998 | 1.57268 | 0.786338 | − | 0.617797i | \(-0.211975\pi\) | ||||
0.786338 | + | 0.617797i | \(0.211975\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | − 888.972i | − 1.53007i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 269.399i | − 0.462091i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.2548 | 0.0770951 | 0.0385476 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385476 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 672.000i | 1.14092i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | 838.131 | 1.40862 | ||||||||
\(596\) | 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 | \(-0.676853\pi\) | ||||
−0.527454 | + | 0.849583i | \(0.676853\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 470.944i | − 0.778419i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 800.715i | 1.31913i | 0.751646 | + | 0.659567i | \(0.229260\pi\) | ||||
−0.751646 | + | 0.659567i | \(0.770740\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −271.529 | −0.444401 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1140.00i | − 1.85971i | −0.367931 | − | 0.929853i | \(-0.619934\pi\) | ||||
0.367931 | − | 0.929853i | \(-0.380066\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 592.648 | 0.960532 | 0.480266 | − | 0.877123i | \(-0.340540\pi\) | ||||
0.480266 | + | 0.877123i | \(0.340540\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −359.199 | −0.580289 | −0.290145 | − | 0.956983i | \(-0.593703\pi\) | ||||
−0.290145 | + | 0.956983i | \(0.593703\pi\) | |||||||
\(620\) | 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 | ||||||||
\(629\) | 592.648i | 0.942207i | ||||||||
\(630\) | 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 | ||||||||
\(635\) | 1148.34 | 1.80841 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.0000i | 0.0439560i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | −808.198 | −1.25692 | −0.628459 | − | 0.777843i | \(-0.716314\pi\) | ||||
−0.628459 | + | 0.777843i | \(0.716314\pi\) | |||||||
\(644\) | 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 | ||||||||
\(653\) | 79.3725i | 0.121551i | 0.998151 | + | 0.0607753i | \(0.0193573\pi\) | ||||
−0.998151 | + | 0.0607753i | \(0.980643\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 838.131i | 1.27959i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1040.86 | 1.57946 | 0.789728 | − | 0.613457i | \(-0.210222\pi\) | ||||
0.789728 | + | 0.613457i | \(0.210222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 548.000i | − 0.829047i | −0.910039 | − | 0.414523i | \(-0.863948\pi\) | ||||
0.910039 | − | 0.414523i | \(-0.136052\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1185.30 | −1.78240 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 119.733 | 0.179510 | ||||||||
\(668\) | 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 | ||||||||
\(677\) | − 79.3725i | − 0.117242i | −0.998280 | − | 0.0586208i | \(-0.981330\pi\) | ||||
0.998280 | − | 0.0586208i | \(-0.0186703\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 134.700i | − 0.198379i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −627.911 | −0.919342 | −0.459671 | − | 0.888089i | \(-0.652033\pi\) | ||||
−0.459671 | + | 0.888089i | \(0.652033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1232.00i | 1.79854i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −190.494 | −0.276479 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −748.331 | −1.08297 | −0.541484 | − | 0.840711i | \(-0.682137\pi\) | ||||
−0.541484 | + | 0.840711i | \(0.682137\pi\) | |||||||
\(692\) | 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 | ||||||||
\(701\) | − 121.705i | − 0.173616i | −0.996225 | − | 0.0868078i | \(-0.972333\pi\) | ||||
0.996225 | − | 0.0868078i | \(-0.0276666\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 838.131i | − 1.19222i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1227.54 | 1.73626 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.00000i | 0.00564175i | 0.999996 | + | 0.00282087i | \(0.000897913\pi\) | ||||
−0.999996 | + | 0.00282087i | \(0.999102\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −507.984 | −0.712460 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 119.733 | 0.167459 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 316.784i | − 0.440589i | −0.975433 | − | 0.220295i | \(-0.929298\pi\) | ||||
0.975433 | − | 0.220295i | \(-0.0707019\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −168.000 | −0.233010 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 15.8745i | − 0.0218959i | ||||||||
\(726\) | 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 | ||||||||
\(731\) | 633.568 | 0.866714 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1212.00i | 1.65348i | 0.562585 | + | 0.826739i | \(0.309807\pi\) | ||||
−0.562585 | + | 0.826739i | \(0.690193\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 338.656 | 0.459506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1257.20 | 1.70121 | 0.850607 | − | 0.525802i | \(-0.176235\pi\) | ||||
0.850607 | + | 0.525802i | \(0.176235\pi\) | |||||||
\(740\) | 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 | ||||||||
\(749\) | − 761.976i | − 1.01732i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 411.582i | − 0.548046i | −0.961723 | − | 0.274023i | \(-0.911646\pi\) | ||||
0.961723 | − | 0.274023i | \(-0.0883544\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −118.794 | −0.157343 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1020.00i | − 1.34742i | −0.738994 | − | 0.673712i | \(-0.764699\pi\) | ||||
0.738994 | − | 0.673712i | \(-0.235301\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −529.150 | −0.695335 | −0.347668 | − | 0.937618i | \(-0.613026\pi\) | ||||
−0.347668 | + | 0.937618i | \(0.613026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1107.53 | −1.45155 | ||||||||
\(764\) | 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 | ||||||||
\(773\) | − 851.932i | − 1.10211i | −0.834469 | − | 0.551056i | \(-0.814225\pi\) | ||||
0.834469 | − | 0.551056i | \(-0.185775\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 67.3498i | 0.0869030i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1900.70 | 2.43993 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 512.000i | − 0.655570i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1248.79 | 1.59082 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −568.732 | −0.722658 | −0.361329 | − | 0.932438i | \(-0.617677\pi\) | ||||
−0.361329 | + | 0.932438i | \(0.617677\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | − 894.264i | − 1.12204i | −0.827803 | − | 0.561019i | \(-0.810410\pi\) | ||||
0.827803 | − | 0.561019i | \(-0.189590\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1436.80i | − 1.79824i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 147.078 | 0.183161 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 896.000i | − 1.11304i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −105.830 | −0.130816 | −0.0654079 | − | 0.997859i | \(-0.520835\pi\) | ||||
−0.0654079 | + | 0.997859i | \(0.520835\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −987.798 | −1.21800 | −0.609000 | − | 0.793170i | \(-0.708429\pi\) | ||||
−0.609000 | + | 0.793170i | \(0.708429\pi\) | |||||||
\(812\) | 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 | ||||||||
\(821\) | 1010.68i | 1.23103i | 0.788125 | + | 0.615516i | \(0.211052\pi\) | ||||
−0.788125 | + | 0.615516i | \(0.788948\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | −328.098 | −0.396732 | −0.198366 | − | 0.980128i | \(-0.563563\pi\) | ||||
−0.198366 | + | 0.980128i | \(0.563563\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1164.00i | 1.40410i | 0.712127 | + | 0.702051i | \(0.247732\pi\) | ||||
−0.712127 | + | 0.702051i | \(0.752268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −148.162 | −0.177866 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 598.665 | 0.716964 | ||||||||
\(836\) | 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 | ||||||||
\(845\) | 809.600i | 0.958106i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 666.015i | 0.786322i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 633.568 | 0.744498 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 276.000i | − 0.323564i | −0.986827 | − | 0.161782i | \(-0.948276\pi\) | ||||
0.986827 | − | 0.161782i | \(-0.0517241\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 275.158 | 0.321071 | 0.160536 | − | 0.987030i | \(-0.448678\pi\) | ||||
0.160536 | + | 0.987030i | \(0.448678\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −628.598 | −0.731779 | −0.365890 | − | 0.930658i | \(-0.619235\pi\) | ||||
−0.365890 | + | 0.930658i | \(0.619235\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 294.156i | 0.340853i | 0.985370 | + | 0.170427i | \(0.0545146\pi\) | ||||
−0.985370 | + | 0.170427i | \(0.945485\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 476.000 | 0.550289 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 719.644i | 0.828129i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 239.466i | − 0.274932i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 871.156 | 0.995606 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 340.000i | 0.387685i | 0.981033 | + | 0.193843i | \(0.0620951\pi\) | ||||
−0.981033 | + | 0.193843i | \(0.937905\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 89.7998 | 0.101699 | 0.0508493 | − | 0.998706i | \(-0.483807\pi\) | ||||
0.0508493 | + | 0.998706i | \(0.483807\pi\) | |||||||
\(884\) | 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 | ||||||||
\(893\) | 2031.94i | 2.27541i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 179.600i | − 0.200670i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 118.794 | 0.132140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1008.00i | − 1.11876i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1206.46 | −1.33311 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 448.999 | 0.495037 | 0.247519 | − | 0.968883i | \(-0.420385\pi\) | ||||
0.247519 | + | 0.968883i | \(0.420385\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 248.902i | − 0.273218i | −0.990625 | − | 0.136609i | \(-0.956380\pi\) | ||||
0.990625 | − | 0.136609i | \(-0.0436204\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 672.000 | 0.736035 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1185.30i | − 1.29258i | ||||||||
\(918\) | 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 | ||||||||
\(923\) | −362.039 | −0.392241 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 84.0000i | − 0.0908108i | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 209.533 | 0.225062 | ||||||||
\(932\) | 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 | \(-0.286240\pi\) | ||||
0.622199 | + | 0.782860i | \(0.286240\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 418.029i | 0.444239i | 0.975019 | + | 0.222119i | \(0.0712975\pi\) | ||||
−0.975019 | + | 0.222119i | \(0.928703\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1436.80i | 1.52364i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 893.783 | 0.943805 | 0.471902 | − | 0.881651i | \(-0.343567\pi\) | ||||
0.471902 | + | 0.881651i | \(0.343567\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 104.000i | − 0.109589i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1291.13 | 1.35480 | 0.677401 | − | 0.735614i | \(-0.263106\pi\) | ||||
0.677401 | + | 0.735614i | \(0.263106\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 119.733 | 0.125375 | ||||||||
\(956\) | 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 | ||||||||
\(965\) | 370.405i | 0.383840i | ||||||||
\(966\) | 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 | ||||||||
\(971\) | −514.774 | −0.530148 | −0.265074 | − | 0.964228i | \(-0.585396\pi\) | ||||
−0.265074 | + | 0.964228i | \(0.585396\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1344.00i | 1.38129i | ||||||||
\(974\) | 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 | ||||||||
\(979\) | 239.466 | 0.244603 | ||||||||
\(980\) | 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 | ||||||||
\(989\) | − 677.312i | − 0.684846i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 486.415i | 0.490833i | 0.969418 | + | 0.245416i | \(0.0789247\pi\) | ||||
−0.969418 | + | 0.245416i | \(0.921075\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1069.15 | 1.07452 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1244.00i | 1.24774i | 0.781527 | + | 0.623872i | \(0.214441\pi\) | ||||
−0.781527 | + | 0.623872i | \(0.785559\pi\) | |||||||
\(998\) | 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 | 1152.3.b.i.703.5 | yes | 8 | |
3.2 | odd | 2 | inner | 1152.3.b.i.703.1 | ✓ | 8 | |
4.3 | odd | 2 | inner | 1152.3.b.i.703.7 | yes | 8 | |
8.3 | odd | 2 | inner | 1152.3.b.i.703.4 | yes | 8 | |
8.5 | even | 2 | inner | 1152.3.b.i.703.2 | yes | 8 | |
12.11 | even | 2 | inner | 1152.3.b.i.703.3 | yes | 8 | |
16.3 | odd | 4 | 2304.3.g.w.1279.3 | 4 | |||
16.5 | even | 4 | 2304.3.g.p.1279.2 | 4 | |||
16.11 | odd | 4 | 2304.3.g.p.1279.1 | 4 | |||
16.13 | even | 4 | 2304.3.g.w.1279.4 | 4 | |||
24.5 | odd | 2 | inner | 1152.3.b.i.703.6 | yes | 8 | |
24.11 | even | 2 | inner | 1152.3.b.i.703.8 | yes | 8 | |
48.5 | odd | 4 | 2304.3.g.p.1279.4 | 4 | |||
48.11 | even | 4 | 2304.3.g.p.1279.3 | 4 | |||
48.29 | odd | 4 | 2304.3.g.w.1279.2 | 4 | |||
48.35 | even | 4 | 2304.3.g.w.1279.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.b.i.703.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
1152.3.b.i.703.2 | yes | 8 | 8.5 | even | 2 | inner | |
1152.3.b.i.703.3 | yes | 8 | 12.11 | even | 2 | inner | |
1152.3.b.i.703.4 | yes | 8 | 8.3 | odd | 2 | inner | |
1152.3.b.i.703.5 | yes | 8 | 1.1 | even | 1 | trivial | |
1152.3.b.i.703.6 | yes | 8 | 24.5 | odd | 2 | inner | |
1152.3.b.i.703.7 | yes | 8 | 4.3 | odd | 2 | inner | |
1152.3.b.i.703.8 | yes | 8 | 24.11 | even | 2 | inner | |
2304.3.g.p.1279.1 | 4 | 16.11 | odd | 4 | |||
2304.3.g.p.1279.2 | 4 | 16.5 | even | 4 | |||
2304.3.g.p.1279.3 | 4 | 48.11 | even | 4 | |||
2304.3.g.p.1279.4 | 4 | 48.5 | odd | 4 | |||
2304.3.g.w.1279.1 | 4 | 48.35 | even | 4 | |||
2304.3.g.w.1279.2 | 4 | 48.29 | odd | 4 | |||
2304.3.g.w.1279.3 | 4 | 16.3 | odd | 4 | |||
2304.3.g.w.1279.4 | 4 | 16.13 | even | 4 |