Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(2431,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4560.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.d (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: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 35x^{10} + 202x^{8} + 362x^{6} + 245x^{4} + 63x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.3 | ||
Root | \(5.32019i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.2431 |
Dual form | 4560.2.d.j.2431.10 |
$q$-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 \(\left(\mathbb{Z}/4560\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(1711\) | \(1921\) | \(2737\) | \(3041\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.21222i | − | 1.21410i | −0.794662 | − | 0.607052i | \(-0.792352\pi\) | ||
0.794662 | − | 0.607052i | \(-0.207648\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.53893i | 0.765515i | 0.923849 | + | 0.382757i | \(0.125025\pi\) | ||||
−0.923849 | + | 0.382757i | \(0.874975\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.54784i | − | 0.429293i | −0.976692 | − | 0.214646i | \(-0.931140\pi\) | ||
0.976692 | − | 0.214646i | \(-0.0688599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.67107 | −0.647829 | −0.323914 | − | 0.946086i | \(-0.604999\pi\) | ||||
−0.323914 | + | 0.946086i | \(0.604999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.05331 | + | 4.22972i | −0.241645 | + | 0.970365i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.21222i | 0.700963i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.98643i | 1.24826i | 0.781322 | + | 0.624129i | \(0.214546\pi\) | ||||
−0.781322 | + | 0.624129i | \(0.785454\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.925176i | − | 0.171801i | −0.996304 | − | 0.0859005i | \(-0.972623\pi\) | ||
0.996304 | − | 0.0859005i | \(-0.0273767\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.27279 | −0.587810 | −0.293905 | − | 0.955835i | \(-0.594955\pi\) | ||||
−0.293905 | + | 0.955835i | \(0.594955\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.53893i | − | 0.441970i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 3.21222i | − | 0.542964i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.3117i | − | 1.69522i | −0.530616 | − | 0.847612i | \(-0.678039\pi\) | ||
0.530616 | − | 0.847612i | \(-0.321961\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.54784i | 0.247852i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.19865i | − | 1.43659i | −0.695740 | − | 0.718294i | \(-0.744923\pi\) | ||
0.695740 | − | 0.718294i | \(-0.255077\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.9254i | − | 1.81861i | −0.416134 | − | 0.909303i | \(-0.636615\pi\) | ||
0.416134 | − | 0.909303i | \(-0.363385\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.08676i | 0.596115i | 0.954548 | + | 0.298058i | \(0.0963388\pi\) | ||||
−0.954548 | + | 0.298058i | \(0.903661\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.31834 | −0.474048 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.67107 | 0.374024 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.52233i | − | 0.346469i | −0.984881 | − | 0.173234i | \(-0.944578\pi\) | ||
0.984881 | − | 0.173234i | \(-0.0554218\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.53893i | 0.342349i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.05331 | − | 4.22972i | 0.139514 | − | 0.560240i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.59113 | −1.24866 | −0.624329 | − | 0.781161i | \(-0.714628\pi\) | ||||
−0.624329 | + | 0.781161i | \(0.714628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.68166 | −0.471388 | −0.235694 | − | 0.971827i | \(-0.575736\pi\) | ||||
−0.235694 | + | 0.971827i | \(0.575736\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 3.21222i | − | 0.404701i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.54784i | − | 0.191985i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.6323 | 1.78762 | 0.893812 | − | 0.448441i | \(-0.148021\pi\) | ||||
0.893812 | + | 0.448441i | \(0.148021\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 5.98643i | − | 0.720682i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.94385 | −0.942762 | −0.471381 | − | 0.881930i | \(-0.656244\pi\) | ||||
−0.471381 | + | 0.881930i | \(0.656244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.83724 | 0.917280 | 0.458640 | − | 0.888622i | \(-0.348337\pi\) | ||||
0.458640 | + | 0.888622i | \(0.348337\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.15558 | 0.929415 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.2951 | −1.83334 | −0.916672 | − | 0.399640i | \(-0.869135\pi\) | ||||
−0.916672 | + | 0.399640i | \(0.869135\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.0509i | 1.21299i | 0.795088 | + | 0.606494i | \(0.207425\pi\) | ||||
−0.795088 | + | 0.606494i | \(0.792575\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.67107 | −0.289718 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.925176i | 0.0991893i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.71016i | 0.287276i | 0.989630 | + | 0.143638i | \(0.0458801\pi\) | ||||
−0.989630 | + | 0.143638i | \(0.954120\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.97199 | −0.521206 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.27279 | 0.339372 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.05331 | + | 4.22972i | −0.108067 | + | 0.433960i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.46130i | − | 0.859115i | −0.903040 | − | 0.429557i | \(-0.858670\pi\) | ||
0.903040 | − | 0.429557i | \(-0.141330\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.53893i | 0.255172i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.3407 | −1.32745 | −0.663723 | − | 0.747978i | \(-0.731025\pi\) | ||||
−0.663723 | + | 0.747978i | \(0.731025\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.6323 | −1.44177 | −0.720883 | − | 0.693056i | \(-0.756264\pi\) | ||||
−0.720883 | + | 0.693056i | \(0.756264\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.21222i | 0.313480i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.5762 | 1.40913 | 0.704567 | − | 0.709638i | \(-0.251141\pi\) | ||||
0.704567 | + | 0.709638i | \(0.251141\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1423i | 0.971454i | 0.874111 | + | 0.485727i | \(0.161445\pi\) | ||||
−0.874111 | + | 0.485727i | \(0.838555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3117i | 0.978739i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.2216i | 1.62007i | 0.586383 | + | 0.810034i | \(0.300551\pi\) | ||||
−0.586383 | + | 0.810034i | \(0.699449\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.98643i | 0.558238i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.54784i | − | 0.143098i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.58004i | 0.786531i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.55386 | 0.413987 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.19865i | 0.829414i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.4696 | −1.81638 | −0.908191 | − | 0.418557i | \(-0.862536\pi\) | ||||
−0.908191 | + | 0.418557i | \(0.862536\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.9254i | 1.04997i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 19.6268i | − | 1.71481i | −0.514646 | − | 0.857403i | \(-0.672077\pi\) | ||
0.514646 | − | 0.857403i | \(-0.327923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.5868 | + | 3.38345i | 1.17812 | + | 0.293382i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.0819 | −1.54484 | −0.772420 | − | 0.635112i | \(-0.780954\pi\) | ||||
−0.772420 | + | 0.635112i | \(0.780954\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.978154i | − | 0.0829659i | −0.999139 | − | 0.0414830i | \(-0.986792\pi\) | ||
0.999139 | − | 0.0414830i | \(-0.0132082\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.08676i | − | 0.344167i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.92984 | 0.328630 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.925176i | − | 0.0768317i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.31834 | 0.273692 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4894 | 1.02317 | 0.511587 | − | 0.859232i | \(-0.329058\pi\) | ||||
0.511587 | + | 0.859232i | \(0.329058\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.14498 | 0.581451 | 0.290725 | − | 0.956807i | \(-0.406103\pi\) | ||||
0.290725 | + | 0.956807i | \(0.406103\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.67107 | −0.215943 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.27279 | −0.262877 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24.2739 | −1.93727 | −0.968635 | − | 0.248487i | \(-0.920067\pi\) | ||||
−0.968635 | + | 0.248487i | \(0.920067\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.52233i | 0.200034i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.2297 | 1.51551 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.2689i | − | 1.19595i | −0.801514 | − | 0.597976i | \(-0.795972\pi\) | ||
0.801514 | − | 0.597976i | \(-0.204028\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 2.53893i | − | 0.197655i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.4754 | −1.12014 | −0.560071 | − | 0.828445i | \(-0.689226\pi\) | ||||
−0.560071 | + | 0.828445i | \(0.689226\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.6042 | 0.815708 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.05331 | + | 4.22972i | −0.0805483 | + | 0.323455i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 17.7746i | − | 1.35138i | −0.737186 | − | 0.675690i | \(-0.763846\pi\) | ||
0.737186 | − | 0.675690i | \(-0.236154\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.21222i | − | 0.242821i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.59113 | 0.720913 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.6372 | −1.91622 | −0.958109 | − | 0.286404i | \(-0.907540\pi\) | ||||
−0.958109 | + | 0.286404i | \(0.907540\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.28875i | 0.170121i | 0.996376 | + | 0.0850607i | \(0.0271084\pi\) | ||||
−0.996376 | + | 0.0850607i | \(0.972892\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.68166 | 0.272156 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 10.3117i | − | 0.758128i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.78164i | − | 0.495922i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.21222i | 0.233654i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.12456i | 0.587872i | 0.955825 | + | 0.293936i | \(0.0949653\pi\) | ||||
−0.955825 | + | 0.293936i | \(0.905035\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 7.21598i | − | 0.519417i | −0.965687 | − | 0.259709i | \(-0.916373\pi\) | ||
0.965687 | − | 0.259709i | \(-0.0836266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.54784i | 0.110843i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.319681 | 0.0227763 | 0.0113882 | − | 0.999935i | \(-0.496375\pi\) | ||||
0.0113882 | + | 0.999935i | \(0.496375\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 18.2126i | − | 1.29106i | −0.763735 | − | 0.645530i | \(-0.776637\pi\) | ||
0.763735 | − | 0.645530i | \(-0.223363\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.6323 | −1.03209 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.97187 | −0.208584 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 9.19865i | − | 0.642461i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.98643i | 0.416086i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.7389 | − | 2.67427i | −0.742829 | − | 0.184983i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.7936 | −1.01844 | −0.509218 | − | 0.860638i | \(-0.670065\pi\) | ||||
−0.509218 | + | 0.860638i | \(0.670065\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.94385 | 0.544304 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 11.9254i | − | 0.813306i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.5129i | 0.713662i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.83724 | −0.529592 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.13437i | 0.278108i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7598 | 1.45714 | 0.728571 | − | 0.684970i | \(-0.240185\pi\) | ||||
0.728571 | + | 0.684970i | \(0.240185\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.41229 | 0.0937370 | 0.0468685 | − | 0.998901i | \(-0.485076\pi\) | ||||
0.0468685 | + | 0.998901i | \(0.485076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.9705 | −1.12144 | −0.560722 | − | 0.828004i | \(-0.689476\pi\) | ||||
−0.560722 | + | 0.828004i | \(0.689476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.15558 | −0.536598 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.281071 | −0.0184135 | −0.00920677 | − | 0.999958i | \(-0.502931\pi\) | ||||
−0.00920677 | + | 0.999958i | \(0.502931\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.08676i | 0.266591i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.2951 | 1.05848 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.10518i | 0.394911i | 0.980312 | + | 0.197455i | \(0.0632678\pi\) | ||||
−0.980312 | + | 0.197455i | \(0.936732\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.30218i | 0.148296i | 0.997247 | + | 0.0741481i | \(0.0236237\pi\) | ||||
−0.997247 | + | 0.0741481i | \(0.976376\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.31834 | −0.212001 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.54692 | + | 1.63034i | 0.416570 | + | 0.103736i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 11.0509i | − | 0.700319i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 13.8121i | − | 0.871814i | −0.899992 | − | 0.435907i | \(-0.856428\pi\) | ||
0.899992 | − | 0.435907i | \(-0.143572\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.1991 | −0.955559 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.67107 | 0.167269 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2.47301i | − | 0.154262i | −0.997021 | − | 0.0771311i | \(-0.975424\pi\) | ||
0.997021 | − | 0.0771311i | \(-0.0245760\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −33.1233 | −2.05818 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 0.925176i | − | 0.0572670i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.2851i | 1.49748i | 0.662862 | + | 0.748742i | \(0.269342\pi\) | ||||
−0.662862 | + | 0.748742i | \(0.730658\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.52233i | − | 0.154945i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2.71016i | − | 0.165859i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 17.7800i | − | 1.08407i | −0.840357 | − | 0.542033i | \(-0.817655\pi\) | ||
0.840357 | − | 0.542033i | \(-0.182345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5298i | 0.761129i | 0.924754 | + | 0.380564i | \(0.124270\pi\) | ||||
−0.924754 | + | 0.380564i | \(0.875730\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.97199 | 0.300918 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.53893i | 0.153103i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.337218 | 0.0202615 | 0.0101307 | − | 0.999949i | \(-0.496775\pi\) | ||||
0.0101307 | + | 0.999949i | \(0.496775\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.27279 | −0.195937 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.9732i | 1.48977i | 0.667190 | + | 0.744887i | \(0.267497\pi\) | ||||
−0.667190 | + | 0.744887i | \(0.732503\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.2093i | 1.79576i | 0.440243 | + | 0.897879i | \(0.354892\pi\) | ||||
−0.440243 | + | 0.897879i | \(0.645108\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.05331 | − | 4.22972i | 0.0623925 | − | 0.250547i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29.5481 | −1.74417 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.86541 | −0.580318 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.46130i | 0.496010i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.55233i | 0.207529i | 0.994602 | + | 0.103765i | \(0.0330889\pi\) | ||||
−0.994602 | + | 0.103765i | \(0.966911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.59113 | −0.558417 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.53893i | − | 0.147323i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.26601 | 0.535867 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −38.3070 | −2.20798 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.3407 | 0.766401 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.68166 | −0.210811 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.5146 | −0.999611 | −0.499806 | − | 0.866138i | \(-0.666595\pi\) | ||||
−0.499806 | + | 0.866138i | \(0.666595\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.6323 | 0.832405 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 23.1622i | − | 1.31341i | −0.754148 | − | 0.656705i | \(-0.771950\pi\) | ||
0.754148 | − | 0.656705i | \(-0.228050\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.3068 | −1.60000 | −0.799998 | − | 0.600003i | \(-0.795166\pi\) | ||||
−0.799998 | + | 0.600003i | \(0.795166\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 3.21222i | − | 0.180988i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 30.4729i | − | 1.71153i | −0.517365 | − | 0.855765i | \(-0.673087\pi\) | ||
0.517365 | − | 0.855765i | \(-0.326913\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.34895 | 0.131516 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.5762 | −0.813564 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.81345 | − | 11.2979i | 0.156544 | − | 0.628630i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.54784i | − | 0.0858585i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 10.1423i | − | 0.560869i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.1276 | 0.723746 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3547 | 0.843970 | 0.421985 | − | 0.906603i | \(-0.361334\pi\) | ||||
0.421985 | + | 0.906603i | \(0.361334\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 10.3117i | − | 0.565075i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.6323 | 0.799450 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.1023i | 1.04057i | 0.853993 | + | 0.520285i | \(0.174174\pi\) | ||||
−0.853993 | + | 0.520285i | \(0.825826\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 17.2216i | − | 0.935346i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 8.30936i | − | 0.449977i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 11.8263i | − | 0.638560i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 5.98643i | − | 0.322299i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 4.94300i | − | 0.265354i | −0.991159 | − | 0.132677i | \(-0.957643\pi\) | ||
0.991159 | − | 0.132677i | \(-0.0423573\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.1725 | −1.29392 | −0.646961 | − | 0.762523i | \(-0.723960\pi\) | ||||
−0.646961 | + | 0.762523i | \(0.723960\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.54784i | 0.0826174i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.8335 | 1.58788 | 0.793939 | − | 0.607998i | \(-0.208027\pi\) | ||||
0.793939 | + | 0.607998i | \(0.208027\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.94385 | −0.421616 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 8.58004i | − | 0.454104i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.0003i | 1.10835i | 0.832399 | + | 0.554176i | \(0.186967\pi\) | ||||
−0.832399 | + | 0.554176i | \(0.813033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7811 | − | 8.91038i | −0.883215 | − | 0.468967i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.55386 | −0.239016 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.83724 | 0.410220 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.70124i | 0.193203i | 0.995323 | + | 0.0966017i | \(0.0307973\pi\) | ||||
−0.995323 | + | 0.0966017i | \(0.969203\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 9.19865i | − | 0.478863i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.10227 | −0.420649 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 17.7289i | − | 0.917967i | −0.888445 | − | 0.458983i | \(-0.848214\pi\) | ||
0.888445 | − | 0.458983i | \(-0.151786\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.43202 | −0.0737528 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.78792 | 0.348672 | 0.174336 | − | 0.984686i | \(-0.444222\pi\) | ||||
0.174336 | + | 0.984686i | \(0.444222\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.4696 | 1.04869 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.8106 | 1.06337 | 0.531686 | − | 0.846941i | \(-0.321559\pi\) | ||||
0.531686 | + | 0.846941i | \(0.321559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.15558 | 0.415647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 11.9254i | − | 0.606202i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.55535 | −0.383072 | −0.191536 | − | 0.981486i | \(-0.561347\pi\) | ||||
−0.191536 | + | 0.981486i | \(0.561347\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15.9901i | − | 0.808657i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.6268i | 0.990043i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.2951 | −0.819896 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.03143 | 0.403086 | 0.201543 | − | 0.979480i | \(-0.435404\pi\) | ||||
0.201543 | + | 0.979480i | \(0.435404\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.5868 | − | 3.38345i | −0.680190 | − | 0.169384i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 28.1366i | − | 1.40508i | −0.711646 | − | 0.702538i | \(-0.752050\pi\) | ||
0.711646 | − | 0.702538i | \(-0.247950\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.06574i | 0.252342i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.1805 | 1.29772 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.71758i | − | 0.332163i | −0.986112 | − | 0.166081i | \(-0.946889\pi\) | ||
0.986112 | − | 0.166081i | \(-0.0531115\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.0819 | 0.891914 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.8088i | 1.51600i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.0509i | 0.542465i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.978154i | 0.0479004i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.6853i | 1.10825i | 0.832433 | + | 0.554125i | \(0.186947\pi\) | ||||
−0.832433 | + | 0.554125i | \(0.813053\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.23308i | 0.449993i | 0.974360 | + | 0.224996i | \(0.0722370\pi\) | ||||
−0.974360 | + | 0.224996i | \(0.927763\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.08676i | 0.198705i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.67107 | −0.129566 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.8263i | 0.572315i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.92984 | −0.189734 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.8019 | −0.905657 | −0.452829 | − | 0.891598i | \(-0.649585\pi\) | ||||
−0.452829 | + | 0.891598i | \(0.649585\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.5862i | 1.46988i | 0.678134 | + | 0.734938i | \(0.262789\pi\) | ||||
−0.678134 | + | 0.734938i | \(0.737211\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.925176i | 0.0443588i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.3209 | − | 6.30554i | −1.21126 | − | 0.301635i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.7175 | −0.750154 | −0.375077 | − | 0.926994i | \(-0.622384\pi\) | ||||
−0.375077 | + | 0.926994i | \(0.622384\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.31834 | −0.158016 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 18.4828i | − | 0.878146i | −0.898451 | − | 0.439073i | \(-0.855307\pi\) | ||
0.898451 | − | 0.439073i | \(-0.144693\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.71016i | 0.128474i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.4894 | −0.590730 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 38.2554i | − | 1.80538i | −0.430287 | − | 0.902692i | \(-0.641587\pi\) | ||
0.430287 | − | 0.902692i | \(-0.358413\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.3547 | 1.09973 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.14498 | −0.335701 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.97199 | −0.233090 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.4936 | −0.958652 | −0.479326 | − | 0.877637i | \(-0.659119\pi\) | ||||
−0.479326 | + | 0.877637i | \(0.659119\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.67107 | 0.124675 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.4120 | 1.50958 | 0.754788 | − | 0.655969i | \(-0.227740\pi\) | ||||
0.754788 | + | 0.655969i | \(0.227740\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.8208i | − | 0.781729i | −0.920448 | − | 0.390864i | \(-0.872176\pi\) | ||
0.920448 | − | 0.390864i | \(-0.127824\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.27279 | 0.151772 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.42141i | 0.297148i | 0.988901 | + | 0.148574i | \(0.0474682\pi\) | ||||
−0.988901 | + | 0.148574i | \(0.952532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 47.0022i | − | 2.17036i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.2739 | 1.11848 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.2777 | 1.39217 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.05331 | + | 4.22972i | −0.0483290 | + | 0.194073i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2.52233i | − | 0.115490i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.3372i | 0.929232i | 0.885512 | + | 0.464616i | \(0.153808\pi\) | ||||
−0.885512 | + | 0.464616i | \(0.846192\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.9607 | −0.727747 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19.2297 | −0.874982 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 8.46130i | − | 0.384208i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.8567 | 1.57951 | 0.789755 | − | 0.613423i | \(-0.210208\pi\) | ||||
0.789755 | + | 0.613423i | \(0.210208\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.2689i | 0.690484i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9.84278i | − | 0.444198i | −0.975024 | − | 0.222099i | \(-0.928709\pi\) | ||
0.975024 | − | 0.222099i | \(-0.0712909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.47121i | 0.111298i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.53893i | 0.114116i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.5174i | 1.14461i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 30.0869i | − | 1.34687i | −0.739245 | − | 0.673437i | \(-0.764817\pi\) | ||
0.739245 | − | 0.673437i | \(-0.235183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.4754 | 0.646714 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.61248i | 0.161072i | 0.996752 | + | 0.0805362i | \(0.0256632\pi\) | ||||
−0.996752 | + | 0.0805362i | \(0.974337\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.3407 | −0.593652 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.6042 | −0.470949 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 23.6635i | − | 1.04886i | −0.851452 | − | 0.524432i | \(-0.824278\pi\) | ||
0.851452 | − | 0.524432i | \(-0.175722\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 25.1749i | − | 1.11367i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.05331 | − | 4.22972i | 0.0465046 | − | 0.186747i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.6323 | −0.644778 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.3760 | −0.456335 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.7746i | 0.780220i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.9835i | 0.656438i | 0.944602 | + | 0.328219i | \(0.106448\pi\) | ||||
−0.944602 | + | 0.328219i | \(0.893552\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.41765 | −0.193170 | −0.0965852 | − | 0.995325i | \(-0.530792\pi\) | ||||
−0.0965852 | + | 0.995325i | \(0.530792\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.21222i | 0.140193i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.74183 | 0.380800 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.8374 | −0.558146 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.59113 | −0.416219 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.2380 | −0.616716 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.5762 | 0.630184 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.6372 | 1.10633 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 8.42501i | − | 0.362891i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.1358 | −0.779717 | −0.389859 | − | 0.920875i | \(-0.627476\pi\) | ||||
−0.389859 | + | 0.920875i | \(0.627476\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 2.28875i | − | 0.0982196i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.1423i | 0.434447i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.4794 | −1.17493 | −0.587466 | − | 0.809249i | \(-0.699874\pi\) | ||||
−0.587466 | + | 0.809249i | \(0.699874\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.68166 | −0.157129 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.91324 | + | 0.974494i | 0.166710 | + | 0.0415148i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 52.3435i | 2.22587i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.3117i | 0.437705i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.2719 | 0.604718 | 0.302359 | − | 0.953194i | \(-0.402226\pi\) | ||||
0.302359 | + | 0.953194i | \(0.402226\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.4586 | −0.780714 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.78164i | 0.286321i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.1877 | −0.429358 | −0.214679 | − | 0.976685i | \(-0.568871\pi\) | ||||
−0.214679 | + | 0.976685i | \(0.568871\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.2216i | 0.724516i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3.21222i | − | 0.134900i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.9875i | 0.628308i | 0.949372 | + | 0.314154i | \(0.101721\pi\) | ||||
−0.949372 | + | 0.314154i | \(0.898279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 11.3338i | − | 0.474303i | −0.971473 | − | 0.237151i | \(-0.923786\pi\) | ||
0.971473 | − | 0.237151i | \(-0.0762138\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 8.12456i | − | 0.339408i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.98643i | 0.249651i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.05725 | −0.293797 | −0.146899 | − | 0.989152i | \(-0.546929\pi\) | ||||
−0.146899 | + | 0.989152i | \(0.546929\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.21598i | 0.299886i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.4977 | 1.47269 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.40401 | 0.265227 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 1.54784i | − | 0.0639951i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 6.81923i | − | 0.281460i | −0.990048 | − | 0.140730i | \(-0.955055\pi\) | ||
0.990048 | − | 0.140730i | \(-0.0449449\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.44725 | − | 13.8430i | 0.142041 | − | 0.570390i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.319681 | −0.0131499 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.6470 | 1.42278 | 0.711391 | − | 0.702796i | \(-0.248065\pi\) | ||||
0.711391 | + | 0.702796i | \(0.248065\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.58004i | 0.351747i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.2126i | 0.745394i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.55670 | 0.390476 | 0.195238 | − | 0.980756i | \(-0.437452\pi\) | ||||
0.195238 | + | 0.980756i | \(0.437452\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.3033i | − | 0.542654i | −0.962487 | − | 0.271327i | \(-0.912538\pi\) | ||
0.962487 | − | 0.271327i | \(-0.0874624\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.6323 | 0.595875 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.55386 | 0.185141 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.2367 | −1.30845 | −0.654224 | − | 0.756301i | \(-0.727004\pi\) | ||||
−0.654224 | + | 0.756301i | \(0.727004\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.97187 | 0.120426 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.32564 | 0.255908 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.8868 | 0.883998 | 0.441999 | − | 0.897015i | \(-0.354269\pi\) | ||||
0.441999 | + | 0.897015i | \(0.354269\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.19865i | 0.370925i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.9822 | −0.764196 | −0.382098 | − | 0.924122i | \(-0.624798\pi\) | ||||
−0.382098 | + | 0.924122i | \(0.624798\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.97762i | 0.280454i | 0.990119 | + | 0.140227i | \(0.0447833\pi\) | ||||
−0.990119 | + | 0.140227i | \(0.955217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 5.98643i | − | 0.240227i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.70561 | 0.348783 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.7389 | + | 2.67427i | 0.428872 | + | 0.106800i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.5431i | 1.09822i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.7974i | 1.18622i | 0.805123 | + | 0.593109i | \(0.202100\pi\) | ||||
−0.805123 | + | 0.593109i | \(0.797900\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.7936 | 0.587994 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.4696 | −0.812310 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.13624i | 0.203505i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.94385 | −0.314254 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.0432i | 1.42362i | 0.702372 | + | 0.711810i | \(0.252124\pi\) | ||||
−0.702372 | + | 0.711810i | \(0.747876\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.79655i | − | 0.0708491i | −0.999372 | − | 0.0354245i | \(-0.988722\pi\) | ||
0.999372 | − | 0.0354245i | \(-0.0112783\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.9254i | 0.469562i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.72893i | − | 0.0679713i | −0.999422 | − | 0.0339857i | \(-0.989180\pi\) | ||
0.999422 | − | 0.0339857i | \(-0.0108201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 24.3512i | − | 0.955866i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 10.5129i | − | 0.412033i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.4671 | 0.605274 | 0.302637 | − | 0.953106i | \(-0.402133\pi\) | ||||
0.302637 | + | 0.953106i | \(0.402133\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 19.6268i | − | 0.766884i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.83724 | 0.305760 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.7171 | −1.35239 | −0.676193 | − | 0.736724i | \(-0.736372\pi\) | ||||
−0.676193 | + | 0.736724i | \(0.736372\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.1807i | 1.56285i | 0.624000 | + | 0.781424i | \(0.285506\pi\) | ||||
−0.624000 | + | 0.781424i | \(0.714494\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 4.13437i | − | 0.160566i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.5868 | + | 3.38345i | 0.526873 | + | 0.131204i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.53850 | 0.214452 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.7598 | −0.841282 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 9.34746i | − | 0.360855i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 8.94691i | − | 0.344878i | −0.985020 | − | 0.172439i | \(-0.944835\pi\) | ||
0.985020 | − | 0.172439i | \(-0.0551648\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.4341i | 1.55401i | 0.629495 | + | 0.777005i | \(0.283262\pi\) | ||||
−0.629495 | + | 0.777005i | \(0.716738\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.1795 | −1.04305 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.41229 | −0.0541191 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.3252 | 1.61953 | 0.809765 | − | 0.586755i | \(-0.199595\pi\) | ||||
0.809765 | + | 0.586755i | \(0.199595\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0819 | −0.690874 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.9705 | 0.647466 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.90415 | −0.148736 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.8439i | 0.450562i | 0.974294 | + | 0.225281i | \(0.0723300\pi\) | ||||
−0.974294 | + | 0.225281i | \(0.927670\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.15558 | 0.309805 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.978154i | − | 0.0371035i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.5702i | 0.930662i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.281071 | 0.0106311 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.57075 | −0.285943 | −0.142972 | − | 0.989727i | \(-0.545666\pi\) | ||||
−0.142972 | + | 0.989727i | \(0.545666\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.6154 | + | 10.8613i | 1.64499 | + | 0.409643i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 4.08676i | − | 0.153916i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 42.8531i | 1.61166i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.7826 | −0.592728 | −0.296364 | − | 0.955075i | \(-0.595774\pi\) | ||||
−0.296364 | + | 0.955075i | \(0.595774\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.2951 | −0.611115 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 19.5923i | − | 0.733738i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.92984 | 0.146968 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 6.10518i | − | 0.228002i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.52963i | 0.206220i | 0.994670 | + | 0.103110i | \(0.0328794\pi\) | ||||
−0.994670 | + | 0.103110i | \(0.967121\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.0022i | 1.75045i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 2.30218i | − | 0.0856188i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 0.925176i | − | 0.0343602i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 49.6316i | − | 1.84073i | −0.391056 | − | 0.920367i | \(-0.627890\pi\) | ||
0.391056 | − | 0.920367i | \(-0.372110\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.8535i | 1.17815i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.1979 | −1.55862 | −0.779308 | − | 0.626641i | \(-0.784429\pi\) | ||||
−0.779308 | + | 0.626641i | \(0.784429\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.31834 | 0.122399 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 37.1504i | 1.36845i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 11.8402i | − | 0.435547i | −0.975999 | − | 0.217774i | \(-0.930121\pi\) | ||
0.975999 | − | 0.217774i | \(-0.0698794\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.54692 | − | 1.63034i | −0.240507 | − | 0.0598922i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.2273 | 0.815440 | 0.407720 | − | 0.913107i | \(-0.366324\pi\) | ||||
0.407720 | + | 0.913107i | \(0.366324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.4894 | 0.457577 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.0509i | 0.404330i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 46.8219i | − | 1.71083i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.2573 | 0.520257 | 0.260129 | − | 0.965574i | \(-0.416235\pi\) | ||||
0.260129 | + | 0.965574i | \(0.416235\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.8121i | 0.503342i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.14498 | 0.260033 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.3860 | 0.922669 | 0.461335 | − | 0.887226i | \(-0.347371\pi\) | ||||
0.461335 | + | 0.887226i | \(0.347371\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.1991 | 0.551692 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.7027 | 0.750470 | 0.375235 | − | 0.926930i | \(-0.377562\pi\) | ||||
0.375235 | + | 0.926930i | \(0.377562\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.5792 | 1.17945 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.67107 | −0.0965726 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.8455i | 0.536040i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.80505 | −0.281457 | −0.140729 | − | 0.990048i | \(-0.544944\pi\) | ||||
−0.140729 | + | 0.990048i | \(0.544944\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.47301i | 0.0890634i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 8.05834i | − | 0.289838i | −0.989443 | − | 0.144919i | \(-0.953708\pi\) | ||
0.989443 | − | 0.144919i | \(-0.0462922\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.27279 | −0.117562 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 33.1233 | 1.18829 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.9077 | + | 9.68899i | 1.39401 | + | 0.347144i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 20.1688i | − | 0.721698i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.925176i | 0.0330631i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.2739 | −0.866374 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.0475 | 1.49883 | 0.749417 | − | 0.662099i | \(-0.230334\pi\) | ||||
0.749417 | + | 0.662099i | \(0.230334\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 24.2851i | − | 0.864572i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 55.3194 | 1.96693 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.69861i | 0.202364i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.52233i | 0.0894578i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 34.5098i | − | 1.22240i | −0.791477 | − | 0.611199i | \(-0.790687\pi\) | ||
0.791477 | − | 0.611199i | \(-0.209313\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 10.9160i | − | 0.386181i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.71016i | 0.0957586i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.8982i | 0.702191i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.2297 | 0.677758 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.7800i | 0.625886i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.5441 | 1.49577 | 0.747886 | − | 0.663828i | \(-0.231069\pi\) | ||||
0.747886 | + | 0.663828i | \(0.231069\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.649193 | −0.0227963 | −0.0113981 | − | 0.999935i | \(-0.503628\pi\) | ||||
−0.0113981 | + | 0.999935i | \(0.503628\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 12.5298i | − | 0.439438i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 15.2689i | − | 0.534846i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.4411 | + | 12.5611i | 1.76471 | + | 0.439457i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.97199 | −0.173735 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.1750 | −1.08802 | −0.544008 | − | 0.839080i | \(-0.683094\pi\) | ||||
−0.544008 | + | 0.839080i | \(0.683094\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 12.1123i | − | 0.422207i | −0.977464 | − | 0.211103i | \(-0.932294\pi\) | ||
0.977464 | − | 0.211103i | \(-0.0677057\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.53893i | − | 0.0883940i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.573827 | 0.0199539 | 0.00997696 | − | 0.999950i | \(-0.496824\pi\) | ||||
0.00997696 | + | 0.999950i | \(0.496824\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.66481i | − | 0.127284i | −0.997973 | − | 0.0636421i | \(-0.979728\pi\) | ||
0.997973 | − | 0.0636421i | \(-0.0202716\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.337218 | −0.0116980 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.86350 | 0.307102 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.4754 | −0.500942 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.27279 | 0.113124 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −54.6910 | −1.88814 | −0.944071 | − | 0.329742i | \(-0.893038\pi\) | ||||
−0.944071 | + | 0.329742i | \(0.893038\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1440 | 0.970484 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 24.9732i | − | 0.860122i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.6042 | 0.364796 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 14.6280i | − | 0.502623i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 30.2093i | − | 1.03678i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 61.7300 | 2.11608 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.337218 | 0.0115461 | 0.00577306 | − | 0.999983i | \(-0.498162\pi\) | ||||
0.00577306 | + | 0.999983i | \(0.498162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.05331 | + | 4.22972i | −0.0360223 | + | 0.144653i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.8699i | 1.66936i | 0.550732 | + | 0.834682i | \(0.314349\pi\) | ||||
−0.550732 | + | 0.834682i | \(0.685651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 17.5842i | − | 0.599964i | −0.953945 | − | 0.299982i | \(-0.903019\pi\) | ||
0.953945 | − | 0.299982i | \(-0.0969807\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.5481 | 1.00700 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.17839 | 0.142234 | 0.0711170 | − | 0.997468i | \(-0.477344\pi\) | ||||
0.0711170 | + | 0.997468i | \(0.477344\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 17.7746i | − | 0.604356i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.86541 | 0.335047 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 41.3721i | − | 1.40345i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 22.6485i | − | 0.767414i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 8.46130i | − | 0.286372i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 3.21222i | − | 0.108593i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 28.9762i | − | 0.978457i | −0.872156 | − | 0.489229i | \(-0.837278\pi\) | ||
0.872156 | − | 0.489229i | \(-0.162722\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 3.55233i | − | 0.119817i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.9701 | −0.538047 | −0.269024 | − | 0.963134i | \(-0.586701\pi\) | ||||
−0.269024 | + | 0.963134i | \(0.586701\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 34.4453i | − | 1.15918i | −0.814909 | − | 0.579589i | \(-0.803213\pi\) | ||
0.814909 | − | 0.579589i | \(-0.196787\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.59113 | 0.322402 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.13999 | −0.139007 | −0.0695036 | − | 0.997582i | \(-0.522142\pi\) | ||||
−0.0695036 | + | 0.997582i | \(0.522142\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 65.7527i | 2.20528i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.53893i | 0.0850572i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.2859 | − | 4.30461i | −0.578449 | − | 0.144048i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.6372 | −0.856959 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.26601 | −0.309383 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.02790i | 0.100986i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.73731i | 0.224452i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 38.3070 | 1.27478 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.28875i | 0.0760806i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.7881 | 0.756665 | 0.378333 | − | 0.925670i | \(-0.376498\pi\) | ||||
0.378333 | + | 0.925670i | \(0.376498\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.3407 | −0.442482 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.2496 | 0.704030 | 0.352015 | − | 0.935994i | \(-0.385497\pi\) | ||||
0.352015 | + | 0.935994i | \(0.385497\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.0573 | −0.928561 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.68166 | 0.121712 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −63.0457 | −2.08195 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 37.4400i | − | 1.23503i | −0.786558 | − | 0.617516i | \(-0.788139\pi\) | ||
0.786558 | − | 0.617516i | \(-0.211861\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.5146 | 0.577126 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.2958i | 0.404721i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 10.3117i | − | 0.339045i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.6323 | −0.480589 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.2199 | −0.729012 | −0.364506 | − | 0.931201i | \(-0.618762\pi\) | ||||
−0.364506 | + | 0.931201i | \(0.618762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.49523 | − | 14.0357i | 0.114551 | − | 0.460000i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.1622i | 0.758297i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 6.78164i | − | 0.221783i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.44618 | 0.210587 | 0.105294 | − | 0.994441i | \(-0.466422\pi\) | ||||
0.105294 | + | 0.994441i | \(0.466422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.3068 | 0.923758 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.11955i | 0.232091i | 0.993244 | + | 0.116045i | \(0.0370218\pi\) | ||||
−0.993244 | + | 0.116045i | \(0.962978\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55.0671 | 1.79323 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.21222i | 0.104493i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 30.9148i | − | 1.00460i | −0.864694 | − | 0.502299i | \(-0.832488\pi\) | ||
0.864694 | − | 0.502299i | \(-0.167512\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 12.1308i | − | 0.393781i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.4729i | 0.988152i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 9.97245i | − | 0.323039i | −0.986870 | − | 0.161520i | \(-0.948360\pi\) | ||
0.986870 | − | 0.161520i | \(-0.0516395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.12456i | 0.262905i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.34895 | −0.0759309 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 58.0830i | 1.87560i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.2889 | −0.654479 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.5762 | 0.469711 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 7.21598i | − | 0.232291i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 35.2362i | − | 1.13312i | −0.824020 | − | 0.566561i | \(-0.808274\pi\) | ||
0.824020 | − | 0.566561i | \(-0.191726\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.81345 | + | 11.2979i | −0.0903810 | + | 0.362940i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.0751 | 0.419600 | 0.209800 | − | 0.977744i | \(-0.432719\pi\) | ||||
0.209800 | + | 0.977744i | \(0.432719\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.14204 | −0.100729 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.54784i | 0.0495704i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.04169i | 0.289269i | 0.989485 | + | 0.144635i | \(0.0462007\pi\) | ||||
−0.989485 | + | 0.144635i | \(0.953799\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.88088 | −0.219914 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.1423i | 0.323818i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.8593 | 1.81353 | 0.906764 | − | 0.421638i | \(-0.138545\pi\) | ||||
0.906764 | + | 0.421638i | \(0.138545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.319681 | 0.0101859 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.1276 | −0.417855 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 71.3906 | 2.27009 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.0365 | −0.827077 | −0.413539 | − | 0.910487i | \(-0.635707\pi\) | ||||
−0.413539 | + | 0.910487i | \(0.635707\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.3547 | −0.487266 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 18.2126i | − | 0.577379i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.19864 | 0.259654 | 0.129827 | − | 0.991537i | \(-0.458558\pi\) | ||||
0.129827 | + | 0.991537i | \(0.458558\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.3117i | 0.326246i |
(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 | 4560.2.d.j.2431.3 | ✓ | 12 | |
4.3 | odd | 2 | 4560.2.d.l.2431.10 | yes | 12 | ||
19.18 | odd | 2 | 4560.2.d.l.2431.3 | yes | 12 | ||
76.75 | even | 2 | inner | 4560.2.d.j.2431.10 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4560.2.d.j.2431.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
4560.2.d.j.2431.10 | yes | 12 | 76.75 | even | 2 | inner | |
4560.2.d.l.2431.3 | yes | 12 | 19.18 | odd | 2 | ||
4560.2.d.l.2431.10 | yes | 12 | 4.3 | odd | 2 |