Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(449,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.4 | ||
Root | \(-0.437016 - 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.449 |
Dual form | 1152.3.h.e.449.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.24264 | −0.848528 | −0.424264 | − | 0.905539i | \(-0.639467\pi\) | ||||
−0.424264 | + | 0.905539i | \(0.639467\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.6491 | 1.80702 | 0.903508 | − | 0.428571i | \(-0.140983\pi\) | ||||
0.903508 | + | 0.428571i | \(0.140983\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.8885 | 1.62623 | 0.813116 | − | 0.582102i | \(-0.197770\pi\) | ||||
0.813116 | + | 0.582102i | \(0.197770\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.0000i | 0.769231i | 0.923077 | + | 0.384615i | \(0.125666\pi\) | ||||
−0.923077 | + | 0.384615i | \(0.874334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 24.0416i | − 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.2982i | 1.33149i | 0.746181 | + | 0.665743i | \(0.231885\pi\) | ||||
−0.746181 | + | 0.665743i | \(0.768115\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 17.8885i | − 0.777763i | −0.921288 | − | 0.388881i | \(-0.872862\pi\) | ||||
0.921288 | − | 0.388881i | \(-0.127138\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | −0.280000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 15.5563 | 0.536426 | 0.268213 | − | 0.963360i | \(-0.413567\pi\) | ||||
0.268213 | + | 0.963360i | \(0.413567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −12.6491 | −0.408036 | −0.204018 | − | 0.978967i | \(-0.565400\pi\) | ||||
−0.204018 | + | 0.978967i | \(0.565400\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −53.6656 | −1.53330 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 64.0000i | 1.72973i | 0.502005 | + | 0.864865i | \(0.332596\pi\) | ||||
−0.502005 | + | 0.864865i | \(0.667404\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 12.7279i | − 0.310437i | −0.987880 | − | 0.155219i | \(-0.950392\pi\) | ||||
0.987880 | − | 0.155219i | \(-0.0496082\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 50.5964i | − 1.17666i | −0.808620 | − | 0.588331i | \(-0.799785\pi\) | ||||
0.808620 | − | 0.588331i | \(-0.200215\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 17.8885i | 0.380607i | 0.981725 | + | 0.190304i | \(0.0609473\pi\) | ||||
−0.981725 | + | 0.190304i | \(0.939053\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 111.000 | 2.26531 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 18.3848 | 0.346883 | 0.173441 | − | 0.984844i | \(-0.444511\pi\) | ||||
0.173441 | + | 0.984844i | \(0.444511\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −75.8947 | −1.37990 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 42.4264i | − 0.652714i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 75.8947i | − 1.13276i | −0.824146 | − | 0.566378i | \(-0.808344\pi\) | ||||
0.824146 | − | 0.566378i | \(-0.191656\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 125.220i | 1.76366i | 0.471568 | + | 0.881830i | \(0.343688\pi\) | ||||
−0.471568 | + | 0.881830i | \(0.656312\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 96.0000 | 1.31507 | 0.657534 | − | 0.753425i | \(-0.271599\pi\) | ||||
0.657534 | + | 0.753425i | \(0.271599\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 226.274 | 2.93863 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 63.2456 | 0.800577 | 0.400288 | − | 0.916389i | \(-0.368910\pi\) | ||||
0.400288 | + | 0.916389i | \(0.368910\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 125.220 | 1.50867 | 0.754336 | − | 0.656488i | \(-0.227959\pi\) | ||||
0.754336 | + | 0.656488i | \(0.227959\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 102.000i | 1.20000i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 55.1543i | − 0.619712i | −0.950784 | − | 0.309856i | \(-0.899719\pi\) | ||||
0.950784 | − | 0.309856i | \(-0.100281\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 126.491i | 1.39001i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 107.331i | − 1.12980i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 64.0000 | 0.659794 | 0.329897 | − | 0.944017i | \(-0.392986\pi\) | ||||
0.329897 | + | 0.944017i | \(0.392986\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −41.0122 | −0.406061 | −0.203031 | − | 0.979172i | \(-0.565079\pi\) | ||||
−0.203031 | + | 0.979172i | \(0.565079\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 139.140 | 1.35088 | 0.675438 | − | 0.737417i | \(-0.263955\pi\) | ||||
0.675438 | + | 0.737417i | \(0.263955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −143.108 | −1.33746 | −0.668731 | − | 0.743505i | \(-0.733162\pi\) | ||||
−0.668731 | + | 0.743505i | \(0.733162\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 118.000i | 1.08257i | 0.840840 | + | 0.541284i | \(0.182062\pi\) | ||||
−0.840840 | + | 0.541284i | \(0.817938\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 24.0416i | − 0.212758i | −0.994326 | − | 0.106379i | \(-0.966074\pi\) | ||||
0.994326 | − | 0.106379i | \(-0.0339256\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 75.8947i | 0.659954i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 304.105i | − 2.55551i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 199.000 | 1.64463 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 135.765 | 1.08612 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −63.2456 | −0.497996 | −0.248998 | − | 0.968504i | \(-0.580101\pi\) | ||||
−0.248998 | + | 0.968504i | \(0.580101\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 107.331 | 0.819323 | 0.409661 | − | 0.912238i | \(-0.365647\pi\) | ||||
0.409661 | + | 0.912238i | \(0.365647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 320.000i | 2.40602i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 123.037i | − 0.898077i | −0.893512 | − | 0.449039i | \(-0.851767\pi\) | ||||
0.893512 | − | 0.449039i | \(-0.148233\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 126.491i | 0.910008i | 0.890489 | + | 0.455004i | \(0.150362\pi\) | ||||
−0.890489 | + | 0.455004i | \(0.849638\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 178.885i | 1.25095i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −66.0000 | −0.455172 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −199.404 | −1.33828 | −0.669141 | − | 0.743135i | \(-0.733338\pi\) | ||||
−0.669141 | + | 0.743135i | \(0.733338\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −37.9473 | −0.251307 | −0.125653 | − | 0.992074i | \(-0.540103\pi\) | ||||
−0.125653 | + | 0.992074i | \(0.540103\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 53.6656 | 0.346230 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 256.000i | − 1.63057i | −0.579058 | − | 0.815287i | \(-0.696579\pi\) | ||||
0.579058 | − | 0.815287i | \(-0.303421\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 226.274i | − 1.40543i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 101.193i | − 0.620815i | −0.950604 | − | 0.310408i | \(-0.899534\pi\) | ||||
0.950604 | − | 0.310408i | \(-0.100466\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 214.663i | 1.28540i | 0.766116 | + | 0.642702i | \(0.222187\pi\) | ||||
−0.766116 | + | 0.642702i | \(0.777813\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 69.0000 | 0.408284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 173.948 | 1.00548 | 0.502741 | − | 0.864437i | \(-0.332325\pi\) | ||||
0.502741 | + | 0.864437i | \(0.332325\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −88.5438 | −0.505964 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −250.440 | −1.39910 | −0.699552 | − | 0.714582i | \(-0.746617\pi\) | ||||
−0.699552 | + | 0.714582i | \(0.746617\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 218.000i | 1.20442i | 0.798338 | + | 0.602210i | \(0.205713\pi\) | ||||
−0.798338 | + | 0.602210i | \(0.794287\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 271.529i | − 1.46772i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 430.070i | − 2.29984i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 71.5542i | 0.374629i | 0.982300 | + | 0.187315i | \(0.0599784\pi\) | ||||
−0.982300 | + | 0.187315i | \(0.940022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −30.0000 | −0.155440 | −0.0777202 | − | 0.996975i | \(-0.524764\pi\) | ||||
−0.0777202 | + | 0.996975i | \(0.524764\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −131.522 | −0.667624 | −0.333812 | − | 0.942640i | \(-0.608335\pi\) | ||||
−0.333812 | + | 0.942640i | \(0.608335\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.6491 | −0.0635634 | −0.0317817 | − | 0.999495i | \(-0.510118\pi\) | ||||
−0.0317817 | + | 0.999495i | \(0.510118\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 196.774 | 0.969330 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 54.0000i | 0.263415i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 452.548i | 2.16530i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 126.491i | − 0.599484i | −0.954020 | − | 0.299742i | \(-0.903099\pi\) | ||||
0.954020 | − | 0.299742i | \(-0.0969006\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 214.663i | 0.998430i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −160.000 | −0.737327 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 240.416 | 1.08786 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.6491 | −0.0567225 | −0.0283612 | − | 0.999598i | \(-0.509029\pi\) | ||||
−0.0283612 | + | 0.999598i | \(0.509029\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −196.774 | −0.866846 | −0.433423 | − | 0.901191i | \(-0.642694\pi\) | ||||
−0.433423 | + | 0.901191i | \(0.642694\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 58.0000i | − 0.253275i | −0.991949 | − | 0.126638i | \(-0.959581\pi\) | ||||
0.991949 | − | 0.126638i | \(-0.0404185\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 349.311i | 1.49919i | 0.661898 | + | 0.749594i | \(0.269751\pi\) | ||||
−0.661898 | + | 0.749594i | \(0.730249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 75.8947i | − 0.322956i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 321.994i | − 1.34725i | −0.739071 | − | 0.673627i | \(-0.764735\pi\) | ||||
0.739071 | − | 0.673627i | \(-0.235265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 160.000 | 0.663900 | 0.331950 | − | 0.943297i | \(-0.392293\pi\) | ||||
0.331950 | + | 0.943297i | \(0.392293\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −470.933 | −1.92218 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −252.982 | −1.02422 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 53.6656 | 0.213807 | 0.106904 | − | 0.994269i | \(-0.465906\pi\) | ||||
0.106904 | + | 0.994269i | \(0.465906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 320.000i | − 1.26482i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 179.605i | − 0.698853i | −0.936964 | − | 0.349426i | \(-0.886377\pi\) | ||||
0.936964 | − | 0.349426i | \(-0.113623\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 809.543i | 3.12565i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 250.440i | − 0.952242i | −0.879380 | − | 0.476121i | \(-0.842042\pi\) | ||||
0.879380 | − | 0.476121i | \(-0.157958\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −78.0000 | −0.294340 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 369.110 | 1.37216 | 0.686078 | − | 0.727528i | \(-0.259331\pi\) | ||||
0.686078 | + | 0.727528i | \(0.259331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 341.526 | 1.26024 | 0.630122 | − | 0.776496i | \(-0.283005\pi\) | ||||
0.630122 | + | 0.776496i | \(0.283005\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −125.220 | −0.455345 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 230.000i | − 0.830325i | −0.909747 | − | 0.415162i | \(-0.863725\pi\) | ||||
0.909747 | − | 0.415162i | \(-0.136275\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 352.139i | 1.25316i | 0.779355 | + | 0.626582i | \(0.215547\pi\) | ||||
−0.779355 | + | 0.626582i | \(0.784453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 404.772i | 1.43029i | 0.698977 | + | 0.715144i | \(0.253639\pi\) | ||||
−0.698977 | + | 0.715144i | \(0.746361\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 160.997i | − 0.560965i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −289.000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.24264 | −0.0144800 | −0.00724000 | − | 0.999974i | \(-0.502305\pi\) | ||||
−0.00724000 | + | 0.999974i | \(0.502305\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 178.885 | 0.598279 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 640.000i | − 2.12625i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 379.473i | − 1.23607i | −0.786151 | − | 0.618035i | \(-0.787929\pi\) | ||||
0.786151 | − | 0.618035i | \(-0.212071\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 35.7771i | − 0.115039i | −0.998344 | − | 0.0575194i | \(-0.981681\pi\) | ||||
0.998344 | − | 0.0575194i | \(-0.0183191\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −430.000 | −1.37380 | −0.686901 | − | 0.726751i | \(-0.741029\pi\) | ||||
−0.686901 | + | 0.726751i | \(0.741029\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −287.085 | −0.905632 | −0.452816 | − | 0.891604i | \(-0.649581\pi\) | ||||
−0.452816 | + | 0.891604i | \(0.649581\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 278.280 | 0.872352 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 608.210 | 1.88300 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 70.0000i | − 0.215385i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 226.274i | 0.687763i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.2982i | 0.0764297i | 0.999270 | + | 0.0382148i | \(0.0121671\pi\) | ||||
−0.999270 | + | 0.0382148i | \(0.987833\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 321.994i | 0.961175i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 224.000 | 0.664688 | 0.332344 | − | 0.943158i | \(-0.392160\pi\) | ||||
0.332344 | + | 0.943158i | \(0.392160\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −226.274 | −0.663561 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 784.245 | 2.28643 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −375.659 | −1.08259 | −0.541296 | − | 0.840832i | \(-0.682066\pi\) | ||||
−0.541296 | + | 0.840832i | \(0.682066\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 320.000i | − 0.916905i | −0.888719 | − | 0.458453i | \(-0.848404\pi\) | ||||
0.888719 | − | 0.458453i | \(-0.151596\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 179.605i | 0.508796i | 0.967100 | + | 0.254398i | \(0.0818774\pi\) | ||||
−0.967100 | + | 0.254398i | \(0.918123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 531.263i | − 1.49651i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 482.991i | − 1.34538i | −0.739925 | − | 0.672689i | \(-0.765139\pi\) | ||||
0.739925 | − | 0.672689i | \(-0.234861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −279.000 | −0.772853 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −407.294 | −1.11587 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −720.999 | −1.96458 | −0.982288 | − | 0.187378i | \(-0.940001\pi\) | ||||
−0.982288 | + | 0.187378i | \(0.940001\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 232.551 | 0.626822 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 256.000i | 0.686327i | 0.939276 | + | 0.343164i | \(0.111499\pi\) | ||||
−0.939276 | + | 0.343164i | \(0.888501\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 155.563i | 0.412635i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.2982i | 0.0667499i | 0.999443 | + | 0.0333750i | \(0.0106256\pi\) | ||||
−0.999443 | + | 0.0333750i | \(0.989374\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 679.765i | 1.77484i | 0.460959 | + | 0.887421i | \(0.347505\pi\) | ||||
−0.460959 | + | 0.887421i | \(0.652495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −960.000 | −2.49351 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −765.090 | −1.96681 | −0.983406 | − | 0.181421i | \(-0.941930\pi\) | ||||
−0.983406 | + | 0.181421i | \(0.941930\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −430.070 | −1.09992 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −268.328 | −0.679312 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 64.0000i | 0.161209i | 0.996746 | + | 0.0806045i | \(0.0256851\pi\) | ||||
−0.996746 | + | 0.0806045i | \(0.974315\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 337.997i | 0.842885i | 0.906855 | + | 0.421443i | \(0.138476\pi\) | ||||
−0.906855 | + | 0.421443i | \(0.861524\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 126.491i | − 0.313874i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1144.87i | 2.81294i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −640.000 | −1.56479 | −0.782396 | − | 0.622781i | \(-0.786003\pi\) | ||||
−0.782396 | + | 0.622781i | \(0.786003\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −531.263 | −1.28015 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −232.551 | −0.555014 | −0.277507 | − | 0.960724i | \(-0.589508\pi\) | ||||
−0.277507 | + | 0.960724i | \(0.589508\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 518.000i | − 1.23040i | −0.788370 | − | 0.615202i | \(-0.789074\pi\) | ||||
0.788370 | − | 0.615202i | \(-0.210926\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 168.291i | 0.395980i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 697.653i | − 1.61868i | −0.587337 | − | 0.809342i | \(-0.699824\pi\) | ||||
0.587337 | − | 0.809342i | \(-0.300176\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 290.000 | 0.669746 | 0.334873 | − | 0.942263i | \(-0.391307\pi\) | ||||
0.334873 | + | 0.942263i | \(0.391307\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 452.548 | 1.03558 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.9473 | −0.0864404 | −0.0432202 | − | 0.999066i | \(-0.513762\pi\) | ||||
−0.0432202 | + | 0.999066i | \(0.513762\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −697.653 | −1.57484 | −0.787419 | − | 0.616418i | \(-0.788583\pi\) | ||||
−0.787419 | + | 0.616418i | \(0.788583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 234.000i | 0.525843i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 722.663i | − 1.60949i | −0.593617 | − | 0.804747i | \(-0.702301\pi\) | ||||
0.593617 | − | 0.804747i | \(-0.297699\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 227.684i | − 0.504843i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 536.656i | − 1.17946i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 64.0000 | 0.140044 | 0.0700219 | − | 0.997545i | \(-0.477693\pi\) | ||||
0.0700219 | + | 0.997545i | \(0.477693\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −581.242 | −1.26083 | −0.630414 | − | 0.776259i | \(-0.717115\pi\) | ||||
−0.630414 | + | 0.776259i | \(0.717115\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 63.2456 | 0.136599 | 0.0682997 | − | 0.997665i | \(-0.478243\pi\) | ||||
0.0682997 | + | 0.997665i | \(0.478243\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 160.997 | 0.344747 | 0.172374 | − | 0.985032i | \(-0.444856\pi\) | ||||
0.172374 | + | 0.985032i | \(0.444856\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 960.000i | − 2.04691i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 905.097i | − 1.91352i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 177.088i | − 0.372816i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 304.105i | − 0.634875i | −0.948279 | − | 0.317438i | \(-0.897178\pi\) | ||||
0.948279 | − | 0.317438i | \(-0.102822\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −640.000 | −1.33056 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −271.529 | −0.559854 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −771.596 | −1.58439 | −0.792193 | − | 0.610271i | \(-0.791061\pi\) | ||||
−0.792193 | + | 0.610271i | \(0.791061\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −107.331 | −0.218597 | −0.109299 | − | 0.994009i | \(-0.534860\pi\) | ||||
−0.109299 | + | 0.994009i | \(0.534860\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 374.000i | − 0.758621i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1583.92i | 3.18696i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 708.350i | 1.41954i | 0.704434 | + | 0.709770i | \(0.251201\pi\) | ||||
−0.704434 | + | 0.709770i | \(0.748799\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 482.991i | − 0.960220i | −0.877208 | − | 0.480110i | \(-0.840597\pi\) | ||||
0.877208 | − | 0.480110i | \(-0.159403\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 174.000 | 0.344554 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 241.831 | 0.475109 | 0.237555 | − | 0.971374i | \(-0.423654\pi\) | ||||
0.237555 | + | 0.971374i | \(0.423654\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1214.31 | 2.37635 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −590.322 | −1.14626 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 320.000i | 0.618956i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 284.257i | 0.545599i | 0.962071 | + | 0.272799i | \(0.0879495\pi\) | ||||
−0.962071 | + | 0.272799i | \(0.912050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 278.280i | 0.532085i | 0.963961 | + | 0.266042i | \(0.0857161\pi\) | ||||
−0.963961 | + | 0.266042i | \(0.914284\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 304.105i | 0.577050i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 209.000 | 0.395085 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 127.279 | 0.238798 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 607.157 | 1.13487 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1985.63 | 3.68391 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 662.000i | 1.22366i | 0.790989 | + | 0.611830i | \(0.209566\pi\) | ||||
−0.790989 | + | 0.611830i | \(0.790434\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 500.632i | − 0.918590i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 151.789i | − 0.277494i | −0.990328 | − | 0.138747i | \(-0.955692\pi\) | ||||
0.990328 | − | 0.138747i | \(-0.0443075\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 393.548i | 0.714243i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 800.000 | 1.44665 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −400.222 | −0.718532 | −0.359266 | − | 0.933235i | \(-0.616973\pi\) | ||||
−0.359266 | + | 0.933235i | \(0.616973\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 505.964 | 0.905124 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 268.328 | 0.476604 | 0.238302 | − | 0.971191i | \(-0.423409\pi\) | ||||
0.238302 | + | 0.971191i | \(0.423409\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 102.000i | 0.180531i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 578.413i | 1.01654i | 0.861197 | + | 0.508272i | \(0.169715\pi\) | ||||
−0.861197 | + | 0.508272i | \(0.830285\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 50.5964i | − 0.0886102i | −0.999018 | − | 0.0443051i | \(-0.985893\pi\) | ||||
0.999018 | − | 0.0443051i | \(-0.0141074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 125.220i | 0.217774i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.0000 | −0.0519931 | −0.0259965 | − | 0.999662i | \(-0.508276\pi\) | ||||
−0.0259965 | + | 0.999662i | \(0.508276\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1583.92 | 2.72619 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 328.877 | 0.564111 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 286.217 | 0.487592 | 0.243796 | − | 0.969826i | \(-0.421607\pi\) | ||||
0.243796 | + | 0.969826i | \(0.421607\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 320.000i | − 0.543294i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 250.316i | 0.422118i | 0.977473 | + | 0.211059i | \(0.0676912\pi\) | ||||
−0.977473 | + | 0.211059i | \(0.932309\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1290.21i | 2.16842i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 482.991i | 0.806328i | 0.915128 | + | 0.403164i | \(0.132090\pi\) | ||||
−0.915128 | + | 0.403164i | \(0.867910\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 658.000 | 1.09484 | 0.547421 | − | 0.836857i | \(-0.315610\pi\) | ||||
0.547421 | + | 0.836857i | \(0.315610\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −844.285 | −1.39551 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −164.438 | −0.270904 | −0.135452 | − | 0.990784i | \(-0.543249\pi\) | ||||
−0.135452 | + | 0.990784i | \(0.543249\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −178.885 | −0.292775 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 576.000i | − 0.939641i | −0.882762 | − | 0.469821i | \(-0.844319\pi\) | ||||
0.882762 | − | 0.469821i | \(-0.155681\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 193.747i | 0.314015i | 0.987597 | + | 0.157008i | \(0.0501847\pi\) | ||||
−0.987597 | + | 0.157008i | \(0.949815\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 556.561i | − 0.899129i | −0.893248 | − | 0.449565i | \(-0.851579\pi\) | ||||
0.893248 | − | 0.449565i | \(-0.148421\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 697.653i | − 1.11983i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −401.000 | −0.641600 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1538.66 | 2.44621 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −518.614 | −0.821891 | −0.410946 | − | 0.911660i | \(-0.634801\pi\) | ||||
−0.410946 | + | 0.911660i | \(0.634801\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 268.328 | 0.422564 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1110.00i | 1.74254i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 861.256i | − 1.34361i | −0.740727 | − | 0.671807i | \(-0.765519\pi\) | ||||
0.740727 | − | 0.671807i | \(-0.234481\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 303.579i | − 0.472129i | −0.971737 | − | 0.236064i | \(-0.924142\pi\) | ||||
0.971737 | − | 0.236064i | \(-0.0758576\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 268.328i | − 0.414727i | −0.978264 | − | 0.207363i | \(-0.933512\pi\) | ||||
0.978264 | − | 0.207363i | \(-0.0664882\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 490.732 | 0.751504 | 0.375752 | − | 0.926720i | \(-0.377384\pi\) | ||||
0.375752 | + | 0.926720i | \(0.377384\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −455.368 | −0.695218 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −643.988 | −0.977219 | −0.488610 | − | 0.872502i | \(-0.662496\pi\) | ||||
−0.488610 | + | 0.872502i | \(0.662496\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 640.000i | 0.968230i | 0.875004 | + | 0.484115i | \(0.160858\pi\) | ||||
−0.875004 | + | 0.484115i | \(0.839142\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 1357.65i | − 2.04157i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 278.280i | − 0.417212i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 830.000 | 1.23328 | 0.616642 | − | 0.787244i | \(-0.288493\pi\) | ||||
0.616642 | + | 0.787244i | \(0.288493\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −230.517 | −0.340498 | −0.170249 | − | 0.985401i | \(-0.554457\pi\) | ||||
−0.170249 | + | 0.985401i | \(0.554457\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 809.543 | 1.19226 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1055.42 | −1.54528 | −0.772638 | − | 0.634846i | \(-0.781063\pi\) | ||||
−0.772638 | + | 0.634846i | \(0.781063\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 522.000i | 0.762044i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 183.848i | 0.266833i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 809.543i | − 1.17155i | −0.810473 | − | 0.585776i | \(-0.800790\pi\) | ||||
0.810473 | − | 0.585776i | \(-0.199210\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 536.656i | − 0.772167i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −306.000 | −0.439024 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 196.576 | 0.280422 | 0.140211 | − | 0.990122i | \(-0.455222\pi\) | ||||
0.140211 | + | 0.990122i | \(0.455222\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1619.09 | −2.30311 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −518.768 | −0.733759 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 698.000i | − 0.984485i | −0.870458 | − | 0.492243i | \(-0.836177\pi\) | ||||
0.870458 | − | 0.492243i | \(-0.163823\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 226.274i | 0.317355i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 758.947i | − 1.06146i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1234.31i | 1.71670i | 0.513062 | + | 0.858352i | \(0.328511\pi\) | ||||
−0.513062 | + | 0.858352i | \(0.671489\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1760.00 | 2.44105 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −108.894 | −0.150199 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −468.017 | −0.643765 | −0.321882 | − | 0.946780i | \(-0.604316\pi\) | ||||
−0.321882 | + | 0.946780i | \(0.604316\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1216.42 | −1.66405 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1130.00i | 1.54161i | 0.637071 | + | 0.770805i | \(0.280146\pi\) | ||||
−0.637071 | + | 0.770805i | \(0.719854\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1357.65i | − 1.84212i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.5964i | 0.0684661i | 0.999414 | + | 0.0342330i | \(0.0108988\pi\) | ||||
−0.999414 | + | 0.0342330i | \(0.989101\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 143.108i | 0.192609i | 0.995352 | + | 0.0963044i | \(0.0307022\pi\) | ||||
−0.995352 | + | 0.0963044i | \(0.969298\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 846.000 | 1.13557 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1810.19 | −2.41681 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −771.596 | −1.02742 | −0.513712 | − | 0.857963i | \(-0.671730\pi\) | ||||
−0.513712 | + | 0.857963i | \(0.671730\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 160.997 | 0.213241 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 90.0000i | − 0.118890i | −0.998232 | − | 0.0594452i | \(-0.981067\pi\) | ||||
0.998232 | − | 0.0594452i | \(-0.0189331\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 1076.22i | − 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1492.60i | 1.95622i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −482.000 | −0.626788 | −0.313394 | − | 0.949623i | \(-0.601466\pi\) | ||||
−0.313394 | + | 0.949623i | \(0.601466\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1262.89 | 1.63376 | 0.816878 | − | 0.576811i | \(-0.195703\pi\) | ||||
0.816878 | + | 0.576811i | \(0.195703\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 88.5438 | 0.114250 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 321.994 | 0.413342 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2240.00i | 2.86812i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1086.12i | 1.38359i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 531.263i | − 0.675048i | −0.941317 | − | 0.337524i | \(-0.890411\pi\) | ||||
0.941317 | − | 0.337524i | \(-0.109589\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 304.105i | − 0.384457i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 603.869 | 0.757678 | 0.378839 | − | 0.925463i | \(-0.376323\pi\) | ||||
0.378839 | + | 0.925463i | \(0.376323\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 430.070 | 0.538260 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1717.30 | 2.13861 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 960.000i | 1.19255i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 168.291i | 0.208024i | 0.994576 | + | 0.104012i | \(0.0331680\pi\) | ||||
−0.994576 | + | 0.104012i | \(0.966832\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 632.456i | 0.779847i | 0.920847 | + | 0.389923i | \(0.127498\pi\) | ||||
−0.920847 | + | 0.389923i | \(0.872502\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 429.325i | 0.526779i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1280.00 | 1.56671 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 479.418 | 0.583944 | 0.291972 | − | 0.956427i | \(-0.405689\pi\) | ||||
0.291972 | + | 0.956427i | \(0.405689\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −746.298 | −0.906801 | −0.453401 | − | 0.891307i | \(-0.649789\pi\) | ||||
−0.453401 | + | 0.891307i | \(0.649789\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −679.765 | −0.821965 | −0.410982 | − | 0.911643i | \(-0.634814\pi\) | ||||
−0.410982 | + | 0.911643i | \(0.634814\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 598.000i | 0.721351i | 0.932691 | + | 0.360676i | \(0.117454\pi\) | ||||
−0.932691 | + | 0.360676i | \(0.882546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 2668.62i | − 3.20363i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 910.736i | − 1.09070i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1234.31i | 1.47117i | 0.677434 | + | 0.735584i | \(0.263092\pi\) | ||||
−0.677434 | + | 0.735584i | \(0.736908\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −599.000 | −0.712247 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −292.742 | −0.346440 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2517.17 | 2.97187 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1144.87 | 1.34532 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 256.000i | 0.300117i | 0.988677 | + | 0.150059i | \(0.0479462\pi\) | ||||
−0.988677 | + | 0.150059i | \(0.952054\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 371.938i | 0.434000i | 0.976172 | + | 0.217000i | \(0.0696272\pi\) | ||||
−0.976172 | + | 0.217000i | \(0.930373\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 860.140i | − 1.00133i | −0.865642 | − | 0.500663i | \(-0.833089\pi\) | ||||
0.865642 | − | 0.500663i | \(-0.166911\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 572.433i | − 0.663306i | −0.943401 | − | 0.331653i | \(-0.892394\pi\) | ||||
0.943401 | − | 0.331653i | \(-0.107606\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −738.000 | −0.853179 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1131.37 | 1.30192 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 758.947 | 0.871351 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1717.30 | 1.96263 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 704.000i | − 0.802737i | −0.915917 | − | 0.401368i | \(-0.868535\pi\) | ||||
0.915917 | − | 0.401368i | \(-0.131465\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 69.2965i | 0.0786566i | 0.999226 | + | 0.0393283i | \(0.0125218\pi\) | ||||
−0.999226 | + | 0.0393283i | \(0.987478\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 556.561i | − 0.630307i | −0.949041 | − | 0.315153i | \(-0.897944\pi\) | ||||
0.949041 | − | 0.315153i | \(-0.102056\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1609.97i | − 1.81507i | −0.419974 | − | 0.907536i | \(-0.637961\pi\) | ||||
0.419974 | − | 0.907536i | \(-0.362039\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −800.000 | −0.899888 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −452.548 | −0.506773 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1062.53 | 1.18718 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −196.774 | −0.218881 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 442.000i | − 0.490566i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 924.896i | − 1.02198i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1770.88i | 1.95245i | 0.216751 | + | 0.976227i | \(0.430454\pi\) | ||||
−0.216751 | + | 0.976227i | \(0.569546\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 858.650i | − 0.942536i | −0.881990 | − | 0.471268i | \(-0.843797\pi\) | ||||
0.881990 | − | 0.471268i | \(-0.156203\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2240.00 | 2.45345 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1357.65 | 1.48053 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.9473 | −0.0412920 | −0.0206460 | − | 0.999787i | \(-0.506572\pi\) | ||||
−0.0206460 | + | 0.999787i | \(0.506572\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1252.20 | −1.35666 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 448.000i | − 0.484324i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 948.937i | 1.02146i | 0.859741 | + | 0.510731i | \(0.170625\pi\) | ||||
−0.859741 | + | 0.510731i | \(0.829375\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2808.10i | 3.01622i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1824.63i | 1.95148i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1810.00 | 1.93170 | 0.965848 | − | 0.259108i | \(-0.0834284\pi\) | ||||
0.965848 | + | 0.259108i | \(0.0834284\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 550.129 | 0.584622 | 0.292311 | − | 0.956323i | \(-0.405576\pi\) | ||||
0.292311 | + | 0.956323i | \(0.405576\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −227.684 | −0.241446 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 214.663 | 0.226676 | 0.113338 | − | 0.993556i | \(-0.463846\pi\) | ||||
0.113338 | + | 0.993556i | \(0.463846\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 960.000i | 1.01159i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 80.6102i | 0.0845857i | 0.999105 | + | 0.0422929i | \(0.0134662\pi\) | ||||
−0.999105 | + | 0.0422929i | \(0.986534\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 303.579i | − 0.317883i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1556.30i | − 1.62284i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −801.000 | −0.833507 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 127.279 | 0.131896 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 341.526 | 0.353181 | 0.176590 | − | 0.984284i | \(-0.443493\pi\) | ||||
0.176590 | + | 0.984284i | \(0.443493\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1198.53 | −1.23433 | −0.617164 | − | 0.786835i | \(-0.711718\pi\) | ||||
−0.617164 | + | 0.786835i | \(0.711718\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1600.00i | 1.64440i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 428.507i | − 0.438594i | −0.975658 | − | 0.219297i | \(-0.929624\pi\) | ||||
0.975658 | − | 0.219297i | \(-0.0703764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 986.631i | − 1.00779i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1466.86i | − 1.49223i | −0.665818 | − | 0.746114i | \(-0.731917\pi\) | ||||
0.665818 | − | 0.746114i | \(-0.268083\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 558.000 | 0.566497 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −905.097 | −0.915163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −973.982 | −0.982827 | −0.491413 | − | 0.870926i | \(-0.663520\pi\) | ||||
−0.491413 | + | 0.870926i | \(0.663520\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 53.6656 | 0.0539353 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 896.000i | − 0.898696i | −0.893357 | − | 0.449348i | \(-0.851656\pi\) | ||||
0.893357 | − | 0.449348i | \(-0.148344\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1152.3.h.e.449.4 | yes | 8 | |
3.2 | odd | 2 | inner | 1152.3.h.e.449.8 | yes | 8 | |
4.3 | odd | 2 | inner | 1152.3.h.e.449.2 | yes | 8 | |
8.3 | odd | 2 | inner | 1152.3.h.e.449.5 | yes | 8 | |
8.5 | even | 2 | inner | 1152.3.h.e.449.7 | yes | 8 | |
12.11 | even | 2 | inner | 1152.3.h.e.449.6 | yes | 8 | |
16.3 | odd | 4 | 2304.3.e.f.1025.4 | 4 | |||
16.5 | even | 4 | 2304.3.e.k.1025.1 | 4 | |||
16.11 | odd | 4 | 2304.3.e.k.1025.2 | 4 | |||
16.13 | even | 4 | 2304.3.e.f.1025.3 | 4 | |||
24.5 | odd | 2 | inner | 1152.3.h.e.449.3 | yes | 8 | |
24.11 | even | 2 | inner | 1152.3.h.e.449.1 | ✓ | 8 | |
48.5 | odd | 4 | 2304.3.e.k.1025.3 | 4 | |||
48.11 | even | 4 | 2304.3.e.k.1025.4 | 4 | |||
48.29 | odd | 4 | 2304.3.e.f.1025.1 | 4 | |||
48.35 | even | 4 | 2304.3.e.f.1025.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.h.e.449.1 | ✓ | 8 | 24.11 | even | 2 | inner | |
1152.3.h.e.449.2 | yes | 8 | 4.3 | odd | 2 | inner | |
1152.3.h.e.449.3 | yes | 8 | 24.5 | odd | 2 | inner | |
1152.3.h.e.449.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1152.3.h.e.449.5 | yes | 8 | 8.3 | odd | 2 | inner | |
1152.3.h.e.449.6 | yes | 8 | 12.11 | even | 2 | inner | |
1152.3.h.e.449.7 | yes | 8 | 8.5 | even | 2 | inner | |
1152.3.h.e.449.8 | yes | 8 | 3.2 | odd | 2 | inner | |
2304.3.e.f.1025.1 | 4 | 48.29 | odd | 4 | |||
2304.3.e.f.1025.2 | 4 | 48.35 | even | 4 | |||
2304.3.e.f.1025.3 | 4 | 16.13 | even | 4 | |||
2304.3.e.f.1025.4 | 4 | 16.3 | odd | 4 | |||
2304.3.e.k.1025.1 | 4 | 16.5 | even | 4 | |||
2304.3.e.k.1025.2 | 4 | 16.11 | odd | 4 | |||
2304.3.e.k.1025.3 | 4 | 48.5 | odd | 4 | |||
2304.3.e.k.1025.4 | 4 | 48.11 | even | 4 |