Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(757,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.757");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 793.2 | ||
Root | \(-1.58114 - 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.793 |
Dual form | 900.3.l.h.757.2 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | − | 1.00000i | 0.142857 | − | 0.142857i | −0.632061 | − | 0.774918i | \(-0.717791\pi\) |
0.774918 | + | 0.632061i | \(0.217791\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.8114 | 1.43740 | 0.718699 | − | 0.695321i | \(-0.244738\pi\) | ||||
0.718699 | + | 0.695321i | \(0.244738\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | + | 6.00000i | 0.461538 | + | 0.461538i | 0.899160 | − | 0.437621i | \(-0.144179\pi\) |
−0.437621 | + | 0.899160i | \(0.644179\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −15.8114 | + | 15.8114i | −0.930082 | + | 0.930082i | −0.997711 | − | 0.0676289i | \(-0.978457\pi\) |
0.0676289 | + | 0.997711i | \(0.478457\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.0000i | 0.736842i | 0.929659 | + | 0.368421i | \(0.120102\pi\) | ||||
−0.929659 | + | 0.368421i | \(0.879898\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −15.8114 | − | 15.8114i | −0.687452 | − | 0.687452i | 0.274216 | − | 0.961668i | \(-0.411582\pi\) |
−0.961668 | + | 0.274216i | \(0.911582\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 15.8114i | − | 0.545220i | −0.962125 | − | 0.272610i | \(-0.912113\pi\) | ||
0.962125 | − | 0.272610i | \(-0.0878869\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.0000 | 0.516129 | 0.258065 | − | 0.966128i | \(-0.416915\pi\) | ||||
0.258065 | + | 0.966128i | \(0.416915\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 30.0000 | − | 30.0000i | 0.810811 | − | 0.810811i | −0.173945 | − | 0.984755i | \(-0.555651\pi\) |
0.984755 | + | 0.173945i | \(0.0556514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −31.6228 | −0.771287 | −0.385644 | − | 0.922648i | \(-0.626021\pi\) | ||||
−0.385644 | + | 0.922648i | \(0.626021\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 54.0000 | + | 54.0000i | 1.25581 | + | 1.25581i | 0.953073 | + | 0.302741i | \(0.0979018\pi\) |
0.302741 | + | 0.953073i | \(0.402098\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 47.4342 | − | 47.4342i | 1.00924 | − | 1.00924i | 0.00928062 | − | 0.999957i | \(-0.497046\pi\) |
0.999957 | − | 0.00928062i | \(-0.00295415\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 47.0000i | 0.959184i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 63.2456 | + | 63.2456i | 1.19331 | + | 1.19331i | 0.976131 | + | 0.217181i | \(0.0696862\pi\) |
0.217181 | + | 0.976131i | \(0.430314\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 79.0569i | 1.33995i | 0.742384 | + | 0.669974i | \(0.233695\pi\) | ||||
−0.742384 | + | 0.669974i | \(0.766305\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 54.0000 | 0.885246 | 0.442623 | − | 0.896708i | \(-0.354048\pi\) | ||||
0.442623 | + | 0.896708i | \(0.354048\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34.0000 | − | 34.0000i | 0.507463 | − | 0.507463i | −0.406284 | − | 0.913747i | \(-0.633176\pi\) |
0.913747 | + | 0.406284i | \(0.133176\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −63.2456 | −0.890782 | −0.445391 | − | 0.895336i | \(-0.646935\pi\) | ||||
−0.445391 | + | 0.895336i | \(0.646935\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 65.0000 | + | 65.0000i | 0.890411 | + | 0.890411i | 0.994562 | − | 0.104151i | \(-0.0332124\pi\) |
−0.104151 | + | 0.994562i | \(0.533212\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.8114 | − | 15.8114i | 0.205343 | − | 0.205343i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 108.000i | 1.36709i | 0.729909 | + | 0.683544i | \(0.239562\pi\) | ||||
−0.729909 | + | 0.683544i | \(0.760438\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −47.4342 | − | 47.4342i | −0.571496 | − | 0.571496i | 0.361050 | − | 0.932546i | \(-0.382418\pi\) |
−0.932546 | + | 0.361050i | \(0.882418\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 126.491i | − | 1.42125i | −0.703572 | − | 0.710624i | \(-0.748413\pi\) | ||
0.703572 | − | 0.710624i | \(-0.251587\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | 0.131868 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 69.0000 | − | 69.0000i | 0.711340 | − | 0.711340i | −0.255475 | − | 0.966816i | \(-0.582232\pi\) |
0.966816 | + | 0.255475i | \(0.0822320\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 79.0569 | 0.782742 | 0.391371 | − | 0.920233i | \(-0.372001\pi\) | ||||
0.391371 | + | 0.920233i | \(0.372001\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 95.0000 | + | 95.0000i | 0.922330 | + | 0.922330i | 0.997194 | − | 0.0748637i | \(-0.0238522\pi\) |
−0.0748637 | + | 0.997194i | \(0.523852\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −110.680 | + | 110.680i | −1.03439 | + | 1.03439i | −0.0350027 | + | 0.999387i | \(0.511144\pi\) |
−0.999387 | + | 0.0350027i | \(0.988856\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 46.0000i | 0.422018i | 0.977484 | + | 0.211009i | \(0.0676750\pi\) | ||||
−0.977484 | + | 0.211009i | \(0.932325\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −79.0569 | − | 79.0569i | −0.699619 | − | 0.699619i | 0.264709 | − | 0.964328i | \(-0.414724\pi\) |
−0.964328 | + | 0.264709i | \(0.914724\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 31.6228i | 0.265738i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 129.000 | 1.06612 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −35.0000 | + | 35.0000i | −0.275591 | + | 0.275591i | −0.831346 | − | 0.555755i | \(-0.812429\pi\) |
0.555755 | + | 0.831346i | \(0.312429\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 205.548 | 1.56907 | 0.784535 | − | 0.620085i | \(-0.212902\pi\) | ||||
0.784535 | + | 0.620085i | \(0.212902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.0000 | + | 14.0000i | 0.105263 | + | 0.105263i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −47.4342 | + | 47.4342i | −0.346235 | + | 0.346235i | −0.858705 | − | 0.512470i | \(-0.828730\pi\) |
0.512470 | + | 0.858705i | \(0.328730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.0000i | 0.158273i | 0.996864 | + | 0.0791367i | \(0.0252164\pi\) | ||||
−0.996864 | + | 0.0791367i | \(0.974784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 94.8683 | + | 94.8683i | 0.663415 | + | 0.663415i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 142.302i | 0.955050i | 0.878618 | + | 0.477525i | \(0.158466\pi\) | ||||
−0.878618 | + | 0.477525i | \(0.841534\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −134.000 | −0.887417 | −0.443709 | − | 0.896171i | \(-0.646337\pi\) | ||||
−0.443709 | + | 0.896171i | \(0.646337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 144.000 | − | 144.000i | 0.917197 | − | 0.917197i | −0.0796273 | − | 0.996825i | \(-0.525373\pi\) |
0.996825 | + | 0.0796273i | \(0.0253730\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −31.6228 | −0.196415 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | + | 4.00000i | 0.0245399 | + | 0.0245399i | 0.719270 | − | 0.694730i | \(-0.244476\pi\) |
−0.694730 | + | 0.719270i | \(0.744476\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 110.680 | − | 110.680i | 0.662753 | − | 0.662753i | −0.293275 | − | 0.956028i | \(-0.594745\pi\) |
0.956028 | + | 0.293275i | \(0.0947452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 97.0000i | − | 0.573964i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.8114 | − | 15.8114i | −0.0913953 | − | 0.0913953i | 0.659931 | − | 0.751326i | \(-0.270586\pi\) |
−0.751326 | + | 0.659931i | \(0.770586\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 268.794i | − | 1.50164i | −0.660507 | − | 0.750820i | \(-0.729659\pi\) | ||
0.660507 | − | 0.750820i | \(-0.270341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.0000 | 0.143646 | 0.0718232 | − | 0.997417i | \(-0.477118\pi\) | ||||
0.0718232 | + | 0.997417i | \(0.477118\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −250.000 | + | 250.000i | −1.33690 | + | 1.33690i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −347.851 | −1.82121 | −0.910604 | − | 0.413281i | \(-0.864383\pi\) | ||||
−0.910604 | + | 0.413281i | \(0.864383\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −219.000 | − | 219.000i | −1.13472 | − | 1.13472i | −0.989383 | − | 0.145332i | \(-0.953575\pi\) |
−0.145332 | − | 0.989383i | \(-0.546425\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 94.8683 | − | 94.8683i | 0.481565 | − | 0.481565i | −0.424066 | − | 0.905631i | \(-0.639398\pi\) |
0.905631 | + | 0.424066i | \(0.139398\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 66.0000i | 0.331658i | 0.986154 | + | 0.165829i | \(0.0530300\pi\) | ||||
−0.986154 | + | 0.165829i | \(0.946970\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.8114 | − | 15.8114i | −0.0778886 | − | 0.0778886i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 221.359i | 1.05914i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −106.000 | −0.502370 | −0.251185 | − | 0.967939i | \(-0.580820\pi\) | ||||
−0.251185 | + | 0.967939i | \(0.580820\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000 | − | 16.0000i | 0.0737327 | − | 0.0737327i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −189.737 | −0.858537 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 51.0000 | + | 51.0000i | 0.228700 | + | 0.228700i | 0.812149 | − | 0.583450i | \(-0.198297\pi\) |
−0.583450 | + | 0.812149i | \(0.698297\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −31.6228 | + | 31.6228i | −0.139307 | + | 0.139307i | −0.773321 | − | 0.634014i | \(-0.781406\pi\) |
0.634014 | + | 0.773321i | \(0.281406\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 366.000i | − | 1.59825i | −0.601163 | − | 0.799127i | \(-0.705296\pi\) | ||
0.601163 | − | 0.799127i | \(-0.294704\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 47.4342 | + | 47.4342i | 0.203580 | + | 0.203580i | 0.801532 | − | 0.597952i | \(-0.204019\pi\) |
−0.597952 | + | 0.801532i | \(0.704019\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | 0.0165975 | 0.00829876 | − | 0.999966i | \(-0.497358\pi\) | ||||
0.00829876 | + | 0.999966i | \(0.497358\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −84.0000 | + | 84.0000i | −0.340081 | + | 0.340081i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 142.302 | 0.566942 | 0.283471 | − | 0.958981i | \(-0.408514\pi\) | ||||
0.283471 | + | 0.958981i | \(0.408514\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −250.000 | − | 250.000i | −0.988142 | − | 0.988142i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 110.680 | − | 110.680i | 0.430660 | − | 0.430660i | −0.458193 | − | 0.888853i | \(-0.651503\pi\) |
0.888853 | + | 0.458193i | \(0.151503\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 60.0000i | − | 0.231660i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 205.548 | + | 205.548i | 0.781552 | + | 0.781552i | 0.980093 | − | 0.198541i | \(-0.0636203\pi\) |
−0.198541 | + | 0.980093i | \(0.563620\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 79.0569i | 0.293892i | 0.989145 | + | 0.146946i | \(0.0469444\pi\) | ||||
−0.989145 | + | 0.146946i | \(0.953056\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −258.000 | −0.952030 | −0.476015 | − | 0.879437i | \(-0.657919\pi\) | ||||
−0.476015 | + | 0.879437i | \(0.657919\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −114.000 | + | 114.000i | −0.411552 | + | 0.411552i | −0.882279 | − | 0.470727i | \(-0.843992\pi\) |
0.470727 | + | 0.882279i | \(0.343992\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 284.605 | 1.01283 | 0.506415 | − | 0.862290i | \(-0.330971\pi\) | ||||
0.506415 | + | 0.862290i | \(0.330971\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −314.000 | − | 314.000i | −1.10954 | − | 1.10954i | −0.993211 | − | 0.116330i | \(-0.962887\pi\) |
−0.116330 | − | 0.993211i | \(-0.537113\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −31.6228 | + | 31.6228i | −0.110184 | + | 0.110184i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 211.000i | − | 0.730104i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −189.737 | − | 189.737i | −0.647565 | − | 0.647565i | 0.304839 | − | 0.952404i | \(-0.401397\pi\) |
−0.952404 | + | 0.304839i | \(0.901397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 189.737i | − | 0.634571i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 108.000 | 0.358804 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −366.000 | + | 366.000i | −1.19218 | + | 1.19218i | −0.215729 | + | 0.976453i | \(0.569213\pi\) |
−0.976453 | + | 0.215729i | \(0.930787\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 126.491 | 0.406724 | 0.203362 | − | 0.979104i | \(-0.434813\pi\) | ||||
0.203362 | + | 0.979104i | \(0.434813\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −201.000 | − | 201.000i | −0.642173 | − | 0.642173i | 0.308917 | − | 0.951089i | \(-0.400034\pi\) |
−0.951089 | + | 0.308917i | \(0.900034\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −237.171 | + | 237.171i | −0.748173 | + | 0.748173i | −0.974136 | − | 0.225963i | \(-0.927447\pi\) |
0.225963 | + | 0.974136i | \(0.427447\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 250.000i | − | 0.783699i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −221.359 | − | 221.359i | −0.685323 | − | 0.685323i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 94.8683i | − | 0.288354i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −638.000 | −1.92749 | −0.963746 | − | 0.266821i | \(-0.914027\pi\) | ||||
−0.963746 | + | 0.266821i | \(0.914027\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 291.000 | − | 291.000i | 0.863501 | − | 0.863501i | −0.128241 | − | 0.991743i | \(-0.540933\pi\) |
0.991743 | + | 0.128241i | \(0.0409333\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 252.982 | 0.741883 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 96.0000 | + | 96.0000i | 0.279883 | + | 0.279883i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −442.719 | + | 442.719i | −1.27585 | + | 1.27585i | −0.332876 | + | 0.942970i | \(0.608019\pi\) |
−0.942970 | + | 0.332876i | \(0.891981\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000i | 0.00573066i | 0.999996 | + | 0.00286533i | \(0.000912064\pi\) | ||||
−0.999996 | + | 0.00286533i | \(0.999088\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −142.302 | − | 142.302i | −0.403123 | − | 0.403123i | 0.476209 | − | 0.879332i | \(-0.342011\pi\) |
−0.879332 | + | 0.476209i | \(0.842011\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 158.114i | 0.440429i | 0.975452 | + | 0.220214i | \(0.0706757\pi\) | ||||
−0.975452 | + | 0.220214i | \(0.929324\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 165.000 | 0.457064 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −299.000 | + | 299.000i | −0.814714 | + | 0.814714i | −0.985336 | − | 0.170623i | \(-0.945422\pi\) |
0.170623 | + | 0.985336i | \(0.445422\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 126.491 | 0.340946 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −316.000 | − | 316.000i | −0.847185 | − | 0.847185i | 0.142596 | − | 0.989781i | \(-0.454455\pi\) |
−0.989781 | + | 0.142596i | \(0.954455\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 94.8683 | − | 94.8683i | 0.251640 | − | 0.251640i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 286.000i | − | 0.754617i | −0.926088 | − | 0.377309i | \(-0.876850\pi\) | ||
0.926088 | − | 0.377309i | \(-0.123150\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 142.302 | + | 142.302i | 0.371547 | + | 0.371547i | 0.868040 | − | 0.496493i | \(-0.165379\pi\) |
−0.496493 | + | 0.868040i | \(0.665379\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 332.039i | − | 0.853571i | −0.904353 | − | 0.426786i | \(-0.859646\pi\) | ||
0.904353 | − | 0.426786i | \(-0.140354\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 500.000 | 1.27877 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 116.000 | − | 116.000i | 0.292191 | − | 0.292191i | −0.545754 | − | 0.837945i | \(-0.683757\pi\) |
0.837945 | + | 0.545754i | \(0.183757\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −379.473 | −0.946318 | −0.473159 | − | 0.880977i | \(-0.656886\pi\) | ||||
−0.473159 | + | 0.880977i | \(0.656886\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 96.0000 | + | 96.0000i | 0.238213 | + | 0.238213i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 474.342 | − | 474.342i | 1.16546 | − | 1.16546i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 156.000i | − | 0.381418i | −0.981647 | − | 0.190709i | \(-0.938921\pi\) | ||
0.981647 | − | 0.190709i | \(-0.0610787\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 79.0569 | + | 79.0569i | 0.191421 | + | 0.191421i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 142.302i | 0.339624i | 0.985476 | + | 0.169812i | \(0.0543161\pi\) | ||||
−0.985476 | + | 0.169812i | \(0.945684\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −142.000 | −0.337292 | −0.168646 | − | 0.985677i | \(-0.553939\pi\) | ||||
−0.168646 | + | 0.985677i | \(0.553939\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 54.0000 | − | 54.0000i | 0.126464 | − | 0.126464i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −600.833 | −1.39404 | −0.697022 | − | 0.717050i | \(-0.745492\pi\) | ||||
−0.697022 | + | 0.717050i | \(0.745492\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.0000 | + | 31.0000i | 0.0715935 | + | 0.0715935i | 0.741997 | − | 0.670403i | \(-0.233879\pi\) |
−0.670403 | + | 0.741997i | \(0.733879\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 221.359 | − | 221.359i | 0.506543 | − | 0.506543i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 766.000i | 1.74487i | 0.488726 | + | 0.872437i | \(0.337462\pi\) | ||||
−0.488726 | + | 0.872437i | \(0.662538\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 94.8683 | + | 94.8683i | 0.214150 | + | 0.214150i | 0.806028 | − | 0.591878i | \(-0.201613\pi\) |
−0.591878 | + | 0.806028i | \(0.701613\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 411.096i | 0.915582i | 0.889060 | + | 0.457791i | \(0.151359\pi\) | ||||
−0.889060 | + | 0.457791i | \(0.848641\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −500.000 | −1.10865 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −195.000 | + | 195.000i | −0.426696 | + | 0.426696i | −0.887501 | − | 0.460805i | \(-0.847561\pi\) |
0.460805 | + | 0.887501i | \(0.347561\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −268.794 | −0.583066 | −0.291533 | − | 0.956561i | \(-0.594165\pi\) | ||||
−0.291533 | + | 0.956561i | \(0.594165\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 295.000 | + | 295.000i | 0.637149 | + | 0.637149i | 0.949851 | − | 0.312702i | \(-0.101234\pi\) |
−0.312702 | + | 0.949851i | \(0.601234\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 363.662 | − | 363.662i | 0.778719 | − | 0.778719i | −0.200894 | − | 0.979613i | \(-0.564385\pi\) |
0.979613 | + | 0.200894i | \(0.0643846\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 68.0000i | − | 0.144989i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 853.815 | + | 853.815i | 1.80511 | + | 1.80511i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 505.964i | 1.05629i | 0.849153 | + | 0.528147i | \(0.177113\pi\) | ||||
−0.849153 | + | 0.528147i | \(0.822887\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 360.000 | 0.748441 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 129.000 | − | 129.000i | 0.264887 | − | 0.264887i | −0.562149 | − | 0.827036i | \(-0.690025\pi\) |
0.827036 | + | 0.562149i | \(0.190025\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 173.925 | 0.354227 | 0.177113 | − | 0.984190i | \(-0.443324\pi\) | ||||
0.177113 | + | 0.984190i | \(0.443324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 250.000 | + | 250.000i | 0.507099 | + | 0.507099i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −63.2456 | + | 63.2456i | −0.127255 | + | 0.127255i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 226.000i | 0.452906i | 0.974022 | + | 0.226453i | \(0.0727129\pi\) | ||||
−0.974022 | + | 0.226453i | \(0.927287\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −521.776 | − | 521.776i | −1.03733 | − | 1.03733i | −0.999276 | − | 0.0380519i | \(-0.987885\pi\) |
−0.0380519 | − | 0.999276i | \(-0.512115\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 964.495i | − | 1.89488i | −0.319931 | − | 0.947441i | \(-0.603660\pi\) | ||
0.319931 | − | 0.947441i | \(-0.396340\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 130.000 | 0.254403 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 750.000 | − | 750.000i | 1.45068 | − | 1.45068i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 94.8683 | 0.182089 | 0.0910445 | − | 0.995847i | \(-0.470979\pi\) | ||||
0.0910445 | + | 0.995847i | \(0.470979\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 54.0000 | + | 54.0000i | 0.103250 | + | 0.103250i | 0.756845 | − | 0.653594i | \(-0.226740\pi\) |
−0.653594 | + | 0.756845i | \(0.726740\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −252.982 | + | 252.982i | −0.480042 | + | 0.480042i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 29.0000i | − | 0.0548204i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −189.737 | − | 189.737i | −0.355979 | − | 0.355979i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 743.135i | 1.37873i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 634.000 | 1.17190 | 0.585952 | − | 0.810346i | \(-0.300721\pi\) | ||||
0.585952 | + | 0.810346i | \(0.300721\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −330.000 | + | 330.000i | −0.603291 | + | 0.603291i | −0.941184 | − | 0.337894i | \(-0.890286\pi\) |
0.337894 | + | 0.941184i | \(0.390286\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 221.359 | 0.401741 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 108.000 | + | 108.000i | 0.195298 | + | 0.195298i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −569.210 | + | 569.210i | −1.02192 | + | 1.02192i | −0.0221667 | + | 0.999754i | \(0.507056\pi\) |
−0.999754 | + | 0.0221667i | \(0.992944\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 648.000i | 1.15921i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −379.473 | − | 379.473i | −0.674020 | − | 0.674020i | 0.284620 | − | 0.958640i | \(-0.408132\pi\) |
−0.958640 | + | 0.284620i | \(0.908132\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 695.701i | − | 1.22267i | −0.791371 | − | 0.611337i | \(-0.790632\pi\) | ||
0.791371 | − | 0.611337i | \(-0.209368\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 494.000 | 0.865149 | 0.432574 | − | 0.901598i | \(-0.357605\pi\) | ||||
0.432574 | + | 0.901598i | \(0.357605\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 299.000 | − | 299.000i | 0.518198 | − | 0.518198i | −0.398828 | − | 0.917026i | \(-0.630583\pi\) |
0.917026 | + | 0.398828i | \(0.130583\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −94.8683 | −0.163285 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1000.00 | + | 1000.00i | 1.71527 | + | 1.71527i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 47.4342 | − | 47.4342i | 0.0808078 | − | 0.0808078i | −0.665548 | − | 0.746355i | \(-0.731802\pi\) |
0.746355 | + | 0.665548i | \(0.231802\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 224.000i | 0.380306i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −300.416 | − | 300.416i | −0.506604 | − | 0.506604i | 0.406878 | − | 0.913482i | \(-0.366617\pi\) |
−0.913482 | + | 0.406878i | \(0.866617\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 917.061i | − | 1.53099i | −0.643444 | − | 0.765493i | \(-0.722495\pi\) | ||
0.643444 | − | 0.765493i | \(-0.277505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −574.000 | −0.955075 | −0.477537 | − | 0.878611i | \(-0.658471\pi\) | ||||
−0.477537 | + | 0.878611i | \(0.658471\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 765.000 | − | 765.000i | 1.26030 | − | 1.26030i | 0.309347 | − | 0.950949i | \(-0.399889\pi\) |
0.950949 | − | 0.309347i | \(-0.100111\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 569.210 | 0.931604 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 540.000 | + | 540.000i | 0.880914 | + | 0.880914i | 0.993627 | − | 0.112714i | \(-0.0359544\pi\) |
−0.112714 | + | 0.993627i | \(0.535954\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −332.039 | + | 332.039i | −0.538151 | + | 0.538151i | −0.922986 | − | 0.384835i | \(-0.874258\pi\) |
0.384835 | + | 0.922986i | \(0.374258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 174.000i | − | 0.281099i | −0.990074 | − | 0.140549i | \(-0.955113\pi\) | ||
0.990074 | − | 0.140549i | \(-0.0448868\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −126.491 | − | 126.491i | −0.203035 | − | 0.203035i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 948.683i | 1.50824i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −236.000 | −0.374010 | −0.187005 | − | 0.982359i | \(-0.559878\pi\) | ||||
−0.187005 | + | 0.982359i | \(0.559878\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −282.000 | + | 282.000i | −0.442700 | + | 0.442700i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 695.701 | 1.08534 | 0.542669 | − | 0.839947i | \(-0.317414\pi\) | ||||
0.542669 | + | 0.839947i | \(0.317414\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −540.000 | − | 540.000i | −0.839813 | − | 0.839813i | 0.149021 | − | 0.988834i | \(-0.452388\pi\) |
−0.988834 | + | 0.149021i | \(0.952388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 110.680 | − | 110.680i | 0.171066 | − | 0.171066i | −0.616382 | − | 0.787448i | \(-0.711402\pi\) |
0.787448 | + | 0.616382i | \(0.211402\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1250.00i | 1.92604i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 521.776 | + | 521.776i | 0.799044 | + | 0.799044i | 0.982945 | − | 0.183901i | \(-0.0588725\pi\) |
−0.183901 | + | 0.982945i | \(0.558872\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.8114i | 0.0239930i | 0.999928 | + | 0.0119965i | \(0.00381870\pi\) | ||||
−0.999928 | + | 0.0119965i | \(0.996181\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 878.000 | 1.32829 | 0.664145 | − | 0.747604i | \(-0.268796\pi\) | ||||
0.664145 | + | 0.747604i | \(0.268796\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −250.000 | + | 250.000i | −0.374813 | + | 0.374813i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 853.815 | 1.27245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 425.000 | + | 425.000i | 0.631501 | + | 0.631501i | 0.948444 | − | 0.316944i | \(-0.102657\pi\) |
−0.316944 | + | 0.948444i | \(0.602657\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.8114 | + | 15.8114i | −0.0233551 | + | 0.0233551i | −0.718688 | − | 0.695333i | \(-0.755257\pi\) |
0.695333 | + | 0.718688i | \(0.255257\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 138.000i | − | 0.203240i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 521.776 | + | 521.776i | 0.763947 | + | 0.763947i | 0.977033 | − | 0.213086i | \(-0.0683516\pi\) |
−0.213086 | + | 0.977033i | \(0.568352\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 758.947i | 1.10152i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 318.000 | 0.460203 | 0.230101 | − | 0.973167i | \(-0.426094\pi\) | ||||
0.230101 | + | 0.973167i | \(0.426094\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 500.000 | − | 500.000i | 0.717360 | − | 0.717360i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −173.925 | −0.248110 | −0.124055 | − | 0.992275i | \(-0.539590\pi\) | ||||
−0.124055 | + | 0.992275i | \(0.539590\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 420.000 | + | 420.000i | 0.597440 | + | 0.597440i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 79.0569 | − | 79.0569i | 0.111820 | − | 0.111820i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 734.000i | 1.03526i | 0.855604 | + | 0.517630i | \(0.173186\pi\) | ||||
−0.855604 | + | 0.517630i | \(0.826814\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −252.982 | − | 252.982i | −0.354814 | − | 0.354814i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 442.719i | − | 0.615743i | −0.951428 | − | 0.307871i | \(-0.900383\pi\) | ||
0.951428 | − | 0.307871i | \(-0.0996166\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 190.000 | 0.263523 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 429.000 | − | 429.000i | 0.590096 | − | 0.590096i | −0.347561 | − | 0.937657i | \(-0.612990\pi\) |
0.937657 | + | 0.347561i | \(0.112990\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1707.63 | −2.33602 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.0000 | + | 50.0000i | 0.0682128 | + | 0.0682128i | 0.740390 | − | 0.672177i | \(-0.234641\pi\) |
−0.672177 | + | 0.740390i | \(0.734641\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 537.587 | − | 537.587i | 0.729426 | − | 0.729426i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 278.000i | − | 0.376184i | −0.982151 | − | 0.188092i | \(-0.939770\pi\) | ||
0.982151 | − | 0.188092i | \(-0.0602303\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.8114 | + | 15.8114i | 0.0212805 | + | 0.0212805i | 0.717667 | − | 0.696386i | \(-0.245210\pi\) |
−0.696386 | + | 0.717667i | \(0.745210\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 221.359i | 0.295540i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.0000 | 0.0639148 | 0.0319574 | − | 0.999489i | \(-0.489826\pi\) | ||||
0.0319574 | + | 0.999489i | \(0.489826\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −414.000 | + | 414.000i | −0.546896 | + | 0.546896i | −0.925542 | − | 0.378646i | \(-0.876390\pi\) |
0.378646 | + | 0.925542i | \(0.376390\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1170.04 | −1.53751 | −0.768753 | − | 0.639545i | \(-0.779123\pi\) | ||||
−0.768753 | + | 0.639545i | \(0.779123\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.0000 | + | 46.0000i | 0.0602883 | + | 0.0602883i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −474.342 | + | 474.342i | −0.618438 | + | 0.618438i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1154.00i | − | 1.50065i | −0.661069 | − | 0.750325i | \(-0.729897\pi\) | ||
0.661069 | − | 0.750325i | \(-0.270103\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −711.512 | − | 711.512i | −0.920456 | − | 0.920456i | 0.0766055 | − | 0.997061i | \(-0.475592\pi\) |
−0.997061 | + | 0.0766055i | \(0.975592\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 442.719i | − | 0.568317i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1000.00 | −1.28041 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 446.000 | − | 446.000i | 0.566709 | − | 0.566709i | −0.364496 | − | 0.931205i | \(-0.618759\pi\) |
0.931205 | + | 0.364496i | \(0.118759\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −158.114 | −0.199891 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 324.000 | + | 324.000i | 0.408575 | + | 0.408575i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1090.99 | − | 1090.99i | 1.36887 | − | 1.36887i | 0.506804 | − | 0.862061i | \(-0.330827\pi\) |
0.862061 | − | 0.506804i | \(-0.169173\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1500.00i | 1.87735i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1027.74 | + | 1027.74i | 1.27988 | + | 1.27988i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1075.17i | − | 1.32902i | −0.747281 | − | 0.664508i | \(-0.768641\pi\) | ||
0.747281 | − | 0.664508i | \(-0.231359\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 386.000 | 0.475956 | 0.237978 | − | 0.971271i | \(-0.423515\pi\) | ||||
0.237978 | + | 0.971271i | \(0.423515\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −756.000 | + | 756.000i | −0.925337 | + | 0.925337i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 300.416 | 0.365915 | 0.182958 | − | 0.983121i | \(-0.441433\pi\) | ||||
0.182958 | + | 0.983121i | \(0.441433\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −281.000 | − | 281.000i | −0.341434 | − | 0.341434i | 0.515472 | − | 0.856906i | \(-0.327616\pi\) |
−0.856906 | + | 0.515472i | \(0.827616\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 379.473 | − | 379.473i | 0.458855 | − | 0.458855i | −0.439424 | − | 0.898280i | \(-0.644818\pi\) |
0.898280 | + | 0.439424i | \(0.144818\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 458.000i | − | 0.552473i | −0.961090 | − | 0.276236i | \(-0.910913\pi\) | ||
0.961090 | − | 0.276236i | \(-0.0890873\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −743.135 | − | 743.135i | −0.892119 | − | 0.892119i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 347.851i | 0.414601i | 0.978277 | + | 0.207301i | \(0.0664678\pi\) | ||||
−0.978277 | + | 0.207301i | \(0.933532\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 591.000 | 0.702735 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 129.000 | − | 129.000i | 0.152302 | − | 0.152302i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −948.683 | −1.11479 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −304.000 | − | 304.000i | −0.356389 | − | 0.356389i | 0.506091 | − | 0.862480i | \(-0.331090\pi\) |
−0.862480 | + | 0.506091i | \(0.831090\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −47.4342 | + | 47.4342i | −0.0553491 | + | 0.0553491i | −0.734240 | − | 0.678890i | \(-0.762461\pi\) |
0.678890 | + | 0.734240i | \(0.262461\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1082.00i | − | 1.25960i | −0.776756 | − | 0.629802i | \(-0.783136\pi\) | ||
0.776756 | − | 0.629802i | \(-0.216864\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 648.267 | + | 648.267i | 0.751178 | + | 0.751178i | 0.974699 | − | 0.223521i | \(-0.0717551\pi\) |
−0.223521 | + | 0.974699i | \(0.571755\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1707.63i | 1.96505i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 408.000 | 0.468427 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −84.0000 | + | 84.0000i | −0.0957811 | + | 0.0957811i | −0.753374 | − | 0.657593i | \(-0.771575\pi\) |
0.657593 | + | 0.753374i | \(0.271575\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 822.192 | 0.933249 | 0.466624 | − | 0.884456i | \(-0.345470\pi\) | ||||
0.466624 | + | 0.884456i | \(0.345470\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1096.00 | − | 1096.00i | −1.24122 | − | 1.24122i | −0.959494 | − | 0.281729i | \(-0.909092\pi\) |
−0.281729 | − | 0.959494i | \(-0.590908\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1185.85 | + | 1185.85i | −1.33693 | + | 1.33693i | −0.437906 | + | 0.899021i | \(0.644280\pi\) |
−0.899021 | + | 0.437906i | \(0.855720\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 70.0000i | 0.0787402i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 664.078 | + | 664.078i | 0.743649 | + | 0.743649i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 252.982i | − | 0.281404i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2000.00 | −2.21976 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −280.000 | + | 280.000i | −0.308710 | + | 0.308710i | −0.844409 | − | 0.535699i | \(-0.820048\pi\) |
0.535699 | + | 0.844409i | \(0.320048\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 980.306 | 1.07608 | 0.538038 | − | 0.842920i | \(-0.319166\pi\) | ||||
0.538038 | + | 0.842920i | \(0.319166\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −750.000 | − | 750.000i | −0.821468 | − | 0.821468i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 205.548 | − | 205.548i | 0.224153 | − | 0.224153i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 896.000i | − | 0.974973i | −0.873131 | − | 0.487486i | \(-0.837914\pi\) | ||
0.873131 | − | 0.487486i | \(-0.162086\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −379.473 | − | 379.473i | −0.411130 | − | 0.411130i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 411.096i | 0.442515i | 0.975215 | + | 0.221257i | \(0.0710161\pi\) | ||||
−0.975215 | + | 0.221257i | \(0.928984\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −658.000 | −0.706767 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −289.000 | + | 289.000i | −0.308431 | + | 0.308431i | −0.844301 | − | 0.535870i | \(-0.819984\pi\) |
0.535870 | + | 0.844301i | \(0.319984\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1280.72 | 1.36102 | 0.680511 | − | 0.732737i | \(-0.261758\pi\) | ||||
0.680511 | + | 0.732737i | \(0.261758\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 500.000 | + | 500.000i | 0.530223 | + | 0.530223i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 158.114 | − | 158.114i | 0.166963 | − | 0.166963i | −0.618680 | − | 0.785643i | \(-0.712332\pi\) |
0.785643 | + | 0.618680i | \(0.212332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 780.000i | 0.821918i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −142.302 | − | 142.302i | −0.149321 | − | 0.149321i | 0.628494 | − | 0.777814i | \(-0.283672\pi\) |
−0.777814 | + | 0.628494i | \(0.783672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 94.8683i | 0.0989242i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −705.000 | −0.733611 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 365.000 | − | 365.000i | 0.377456 | − | 0.377456i | −0.492728 | − | 0.870184i | \(-0.664000\pi\) |
0.870184 | + | 0.492728i | \(0.164000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −395.285 | −0.407090 | −0.203545 | − | 0.979066i | \(-0.565246\pi\) | ||||
−0.203545 | + | 0.979066i | \(0.565246\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.0000 | + | 22.0000i | 0.0226105 | + | 0.0226105i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −142.302 | + | 142.302i | −0.145653 | + | 0.145653i | −0.776173 | − | 0.630520i | \(-0.782842\pi\) |
0.630520 | + | 0.776173i | \(0.282842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2000.00i | − | 2.04290i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −932.872 | − | 932.872i | −0.949005 | − | 0.949005i | 0.0497564 | − | 0.998761i | \(-0.484156\pi\) |
−0.998761 | + | 0.0497564i | \(0.984156\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1707.63i | − | 1.72662i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1714.00 | 1.72957 | 0.864783 | − | 0.502146i | \(-0.167456\pi\) | ||||
0.864783 | + | 0.502146i | \(0.167456\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1270.00 | + | 1270.00i | −1.27382 | + | 1.27382i | −0.329755 | + | 0.944067i | \(0.606966\pi\) |
−0.944067 | + | 0.329755i | \(0.893034\pi\) | |||||||
\(998\) | 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 | 900.3.l.h.793.2 | 4 | ||
3.2 | odd | 2 | inner | 900.3.l.h.793.1 | 4 | ||
5.2 | odd | 4 | inner | 900.3.l.h.757.2 | 4 | ||
5.3 | odd | 4 | 180.3.l.c.37.2 | yes | 4 | ||
5.4 | even | 2 | 180.3.l.c.73.2 | yes | 4 | ||
15.2 | even | 4 | inner | 900.3.l.h.757.1 | 4 | ||
15.8 | even | 4 | 180.3.l.c.37.1 | ✓ | 4 | ||
15.14 | odd | 2 | 180.3.l.c.73.1 | yes | 4 | ||
20.3 | even | 4 | 720.3.bh.h.577.2 | 4 | |||
20.19 | odd | 2 | 720.3.bh.h.433.2 | 4 | |||
60.23 | odd | 4 | 720.3.bh.h.577.1 | 4 | |||
60.59 | even | 2 | 720.3.bh.h.433.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.l.c.37.1 | ✓ | 4 | 15.8 | even | 4 | ||
180.3.l.c.37.2 | yes | 4 | 5.3 | odd | 4 | ||
180.3.l.c.73.1 | yes | 4 | 15.14 | odd | 2 | ||
180.3.l.c.73.2 | yes | 4 | 5.4 | even | 2 | ||
720.3.bh.h.433.1 | 4 | 60.59 | even | 2 | |||
720.3.bh.h.433.2 | 4 | 20.19 | odd | 2 | |||
720.3.bh.h.577.1 | 4 | 60.23 | odd | 4 | |||
720.3.bh.h.577.2 | 4 | 20.3 | even | 4 | |||
900.3.l.h.757.1 | 4 | 15.2 | even | 4 | inner | ||
900.3.l.h.757.2 | 4 | 5.2 | odd | 4 | inner | ||
900.3.l.h.793.1 | 4 | 3.2 | odd | 2 | inner | ||
900.3.l.h.793.2 | 4 | 1.1 | even | 1 | trivial |