Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(415,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.415");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.m (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 10x^{12} + 88x^{10} - 752x^{8} + 1408x^{6} + 2560x^{4} - 24576x^{2} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 415.4 | ||
Root | \(-0.136762 + 1.99532i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.415 |
Dual form | 1152.3.m.e.991.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.227650 | − | 0.227650i | −0.0455300 | − | 0.0455300i | 0.683975 | − | 0.729505i | \(-0.260250\pi\) |
−0.729505 | + | 0.683975i | \(0.760250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.90219 | 0.557456 | 0.278728 | − | 0.960370i | \(-0.410087\pi\) | ||||
0.278728 | + | 0.960370i | \(0.410087\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.21045 | − | 2.21045i | 0.200950 | − | 0.200950i | −0.599457 | − | 0.800407i | \(-0.704617\pi\) |
0.800407 | + | 0.599457i | \(0.204617\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.08526 | + | 5.08526i | −0.391174 | + | 0.391174i | −0.875106 | − | 0.483932i | \(-0.839208\pi\) |
0.483932 | + | 0.875106i | \(0.339208\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −18.8341 | −1.10789 | −0.553943 | − | 0.832555i | \(-0.686877\pi\) | ||||
−0.553943 | + | 0.832555i | \(0.686877\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −11.7651 | − | 11.7651i | −0.619216 | − | 0.619216i | 0.326114 | − | 0.945330i | \(-0.394261\pi\) |
−0.945330 | + | 0.326114i | \(0.894261\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −35.4354 | −1.54067 | −0.770335 | − | 0.637640i | \(-0.779911\pi\) | ||||
−0.770335 | + | 0.637640i | \(0.779911\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 24.8964i | − | 0.995854i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 21.2499 | − | 21.2499i | 0.732755 | − | 0.732755i | −0.238410 | − | 0.971165i | \(-0.576626\pi\) |
0.971165 | + | 0.238410i | \(0.0766261\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 35.9691i | 1.16029i | 0.814512 | + | 0.580146i | \(0.197005\pi\) | ||||
−0.814512 | + | 0.580146i | \(0.802995\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.888334 | − | 0.888334i | −0.0253810 | − | 0.0253810i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.4199 | + | 34.4199i | 0.930267 | + | 0.930267i | 0.997722 | − | 0.0674555i | \(-0.0214881\pi\) |
−0.0674555 | + | 0.997722i | \(0.521488\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 44.1055i | − | 1.07574i | −0.843026 | − | 0.537872i | \(-0.819228\pi\) | ||
0.843026 | − | 0.537872i | \(-0.180772\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 28.3018 | − | 28.3018i | 0.658180 | − | 0.658180i | −0.296769 | − | 0.954949i | \(-0.595909\pi\) |
0.954949 | + | 0.296769i | \(0.0959091\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 32.8802i | 0.699579i | 0.936828 | + | 0.349790i | \(0.113747\pi\) | ||||
−0.936828 | + | 0.349790i | \(0.886253\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −33.7729 | −0.689242 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −42.1450 | − | 42.1450i | −0.795189 | − | 0.795189i | 0.187144 | − | 0.982333i | \(-0.440077\pi\) |
−0.982333 | + | 0.187144i | \(0.940077\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00642 | −0.0182985 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −66.9935 | + | 66.9935i | −1.13548 | + | 1.13548i | −0.146233 | + | 0.989250i | \(0.546715\pi\) |
−0.989250 | + | 0.146233i | \(0.953285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17.3728 | + | 17.3728i | −0.284800 | + | 0.284800i | −0.835020 | − | 0.550220i | \(-0.814544\pi\) |
0.550220 | + | 0.835020i | \(0.314544\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.31532 | 0.0356203 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −39.6756 | − | 39.6756i | −0.592174 | − | 0.592174i | 0.346044 | − | 0.938218i | \(-0.387525\pi\) |
−0.938218 | + | 0.346044i | \(0.887525\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −63.0272 | −0.887707 | −0.443853 | − | 0.896099i | \(-0.646389\pi\) | ||||
−0.443853 | + | 0.896099i | \(0.646389\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 75.4549i | − | 1.03363i | −0.856097 | − | 0.516815i | \(-0.827118\pi\) | ||
0.856097 | − | 0.516815i | \(-0.172882\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.62561 | − | 8.62561i | 0.112021 | − | 0.112021i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 59.1583i | 0.748839i | 0.927259 | + | 0.374419i | \(0.122158\pi\) | ||||
−0.927259 | + | 0.374419i | \(0.877842\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −71.2155 | − | 71.2155i | −0.858018 | − | 0.858018i | 0.133086 | − | 0.991104i | \(-0.457511\pi\) |
−0.991104 | + | 0.133086i | \(0.957511\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.28757 | + | 4.28757i | 0.0504420 | + | 0.0504420i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 150.671i | − | 1.69293i | −0.532443 | − | 0.846466i | \(-0.678726\pi\) | ||
0.532443 | − | 0.846466i | \(-0.321274\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.8437 | + | 19.8437i | −0.218062 | + | 0.218062i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.35665i | 0.0563858i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 51.5586 | 0.531532 | 0.265766 | − | 0.964038i | \(-0.414375\pi\) | ||||
0.265766 | + | 0.964038i | \(0.414375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −139.414 | − | 139.414i | −1.38034 | − | 1.38034i | −0.844010 | − | 0.536327i | \(-0.819811\pi\) |
−0.536327 | − | 0.844010i | \(-0.680189\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 67.9691 | 0.659894 | 0.329947 | − | 0.943999i | \(-0.392969\pi\) | ||||
0.329947 | + | 0.943999i | \(0.392969\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −129.801 | + | 129.801i | −1.21309 | + | 1.21309i | −0.243090 | + | 0.970004i | \(0.578161\pi\) |
−0.970004 | + | 0.243090i | \(0.921839\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −30.1323 | + | 30.1323i | −0.276443 | + | 0.276443i | −0.831687 | − | 0.555244i | \(-0.812625\pi\) |
0.555244 | + | 0.831687i | \(0.312625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.11034 | 0.0452243 | 0.0226121 | − | 0.999744i | \(-0.492802\pi\) | ||||
0.0226121 | + | 0.999744i | \(0.492802\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.06687 | + | 8.06687i | 0.0701467 | + | 0.0701467i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −73.4942 | −0.617598 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 111.228i | 0.919238i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.3589 | + | 11.3589i | −0.0908712 | + | 0.0908712i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 123.225i | − | 0.970277i | −0.874437 | − | 0.485138i | \(-0.838769\pi\) | ||
0.874437 | − | 0.485138i | \(-0.161231\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −76.2899 | − | 76.2899i | −0.582365 | − | 0.582365i | 0.353187 | − | 0.935553i | \(-0.385098\pi\) |
−0.935553 | + | 0.353187i | \(0.885098\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −45.9098 | − | 45.9098i | −0.345186 | − | 0.345186i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 73.0194i | − | 0.532988i | −0.963837 | − | 0.266494i | \(-0.914135\pi\) | ||
0.963837 | − | 0.266494i | \(-0.0858653\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.5250 | + | 16.5250i | −0.118885 | + | 0.118885i | −0.764046 | − | 0.645162i | \(-0.776790\pi\) |
0.645162 | + | 0.764046i | \(0.276790\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.4814i | 0.157213i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.67507 | −0.0667246 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.0334 | − | 22.0334i | −0.147875 | − | 0.147875i | 0.629293 | − | 0.777168i | \(-0.283344\pi\) |
−0.777168 | + | 0.629293i | \(0.783344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −161.017 | −1.06634 | −0.533168 | − | 0.846010i | \(-0.678999\pi\) | ||||
−0.533168 | + | 0.846010i | \(0.678999\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.18836 | − | 8.18836i | 0.0528281 | − | 0.0528281i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 151.888 | − | 151.888i | 0.967441 | − | 0.967441i | −0.0320455 | − | 0.999486i | \(-0.510202\pi\) |
0.999486 | + | 0.0320455i | \(0.0102022\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −138.276 | −0.858856 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 186.334 | + | 186.334i | 1.14315 | + | 1.14315i | 0.987870 | + | 0.155283i | \(0.0496290\pi\) |
0.155283 | + | 0.987870i | \(0.450371\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −199.590 | −1.19515 | −0.597576 | − | 0.801813i | \(-0.703869\pi\) | ||||
−0.597576 | + | 0.801813i | \(0.703869\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 117.280i | 0.693966i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 138.631 | − | 138.631i | 0.801333 | − | 0.801333i | −0.181971 | − | 0.983304i | \(-0.558248\pi\) |
0.983304 | + | 0.181971i | \(0.0582477\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 97.1504i | − | 0.555145i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 148.572 | + | 148.572i | 0.830010 | + | 0.830010i | 0.987518 | − | 0.157508i | \(-0.0503458\pi\) |
−0.157508 | + | 0.987518i | \(0.550346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −99.6006 | − | 99.6006i | −0.550280 | − | 0.550280i | 0.376242 | − | 0.926522i | \(-0.377216\pi\) |
−0.926522 | + | 0.376242i | \(0.877216\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 15.6714i | − | 0.0847101i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −41.6318 | + | 41.6318i | −0.222630 | + | 0.222630i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 149.517i | 0.782812i | 0.920218 | + | 0.391406i | \(0.128011\pi\) | ||||
−0.920218 | + | 0.391406i | \(0.871989\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −52.8254 | −0.273707 | −0.136853 | − | 0.990591i | \(-0.543699\pi\) | ||||
−0.136853 | + | 0.990591i | \(0.543699\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 108.072 | + | 108.072i | 0.548590 | + | 0.548590i | 0.926033 | − | 0.377443i | \(-0.123197\pi\) |
−0.377443 | + | 0.926033i | \(0.623197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.24707 | −0.0112918 | −0.00564590 | − | 0.999984i | \(-0.501797\pi\) | ||||
−0.00564590 | + | 0.999984i | \(0.501797\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 82.9212 | − | 82.9212i | 0.408479 | − | 0.408479i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.0406 | + | 10.0406i | −0.0489787 | + | 0.0489787i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −52.0124 | −0.248863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −50.4041 | − | 50.4041i | −0.238882 | − | 0.238882i | 0.577505 | − | 0.816387i | \(-0.304026\pi\) |
−0.816387 | + | 0.577505i | \(0.804026\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.8858 | −0.0599339 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 140.358i | 0.646812i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 95.7760 | − | 95.7760i | 0.433376 | − | 0.433376i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 230.340i | − | 1.03291i | −0.856313 | − | 0.516457i | \(-0.827251\pi\) | ||
0.856313 | − | 0.516457i | \(-0.172749\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.1395 | − | 12.1395i | −0.0534779 | − | 0.0534779i | 0.679862 | − | 0.733340i | \(-0.262040\pi\) |
−0.733340 | + | 0.679862i | \(0.762040\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −39.1259 | − | 39.1259i | −0.170855 | − | 0.170855i | 0.616500 | − | 0.787355i | \(-0.288550\pi\) |
−0.787355 | + | 0.616500i | \(0.788550\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 36.6784i | 0.157418i | 0.996898 | + | 0.0787090i | \(0.0250798\pi\) | ||||
−0.996898 | + | 0.0787090i | \(0.974920\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.48518 | − | 7.48518i | 0.0318518 | − | 0.0318518i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 147.098i | − | 0.615474i | −0.951471 | − | 0.307737i | \(-0.900428\pi\) | ||
0.951471 | − | 0.307737i | \(-0.0995717\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 205.488 | 0.852649 | 0.426324 | − | 0.904570i | \(-0.359808\pi\) | ||||
0.426324 | + | 0.904570i | \(0.359808\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.68839 | + | 7.68839i | 0.0313812 | + | 0.0313812i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 119.657 | 0.484442 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 55.4867 | − | 55.4867i | 0.221063 | − | 0.221063i | −0.587883 | − | 0.808946i | \(-0.700039\pi\) |
0.808946 | + | 0.587883i | \(0.200039\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −78.3282 | + | 78.3282i | −0.309598 | + | 0.309598i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 142.878 | 0.555944 | 0.277972 | − | 0.960589i | \(-0.410338\pi\) | ||||
0.277972 | + | 0.960589i | \(0.410338\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 134.313 | + | 134.313i | 0.518583 | + | 0.518583i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 242.691 | 0.922780 | 0.461390 | − | 0.887197i | \(-0.347351\pi\) | ||||
0.461390 | + | 0.887197i | \(0.347351\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.1886i | 0.0724099i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −292.665 | + | 292.665i | −1.08797 | + | 1.08797i | −0.0922353 | + | 0.995737i | \(0.529401\pi\) |
−0.995737 | + | 0.0922353i | \(0.970599\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 258.180i | 0.952694i | 0.879257 | + | 0.476347i | \(0.158039\pi\) | ||||
−0.879257 | + | 0.476347i | \(0.841961\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −55.0322 | − | 55.0322i | −0.200117 | − | 0.200117i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −63.2023 | − | 63.2023i | −0.228167 | − | 0.228167i | 0.583759 | − | 0.811927i | \(-0.301581\pi\) |
−0.811927 | + | 0.583759i | \(0.801581\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 421.406i | 1.49966i | 0.661628 | + | 0.749832i | \(0.269866\pi\) | ||||
−0.661628 | + | 0.749832i | \(0.730134\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −275.707 | + | 275.707i | −0.974229 | + | 0.974229i | −0.999676 | − | 0.0254475i | \(-0.991899\pi\) |
0.0254475 | + | 0.999676i | \(0.491899\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 172.108i | − | 0.599681i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 65.7217 | 0.227411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 181.330 | + | 181.330i | 0.618873 | + | 0.618873i | 0.945242 | − | 0.326369i | \(-0.105825\pi\) |
−0.326369 | + | 0.945242i | \(0.605825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.5021 | 0.103397 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 180.198 | − | 180.198i | 0.602669 | − | 0.602669i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 110.439 | − | 110.439i | 0.366907 | − | 0.366907i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.90985 | 0.0259339 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −279.027 | − | 279.027i | −0.908883 | − | 0.908883i | 0.0872996 | − | 0.996182i | \(-0.472176\pi\) |
−0.996182 | + | 0.0872996i | \(0.972176\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 414.511 | 1.33283 | 0.666417 | − | 0.745579i | \(-0.267827\pi\) | ||||
0.666417 | + | 0.745579i | \(0.267827\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 331.008i | − | 1.05753i | −0.848767 | − | 0.528767i | \(-0.822654\pi\) | ||
0.848767 | − | 0.528767i | \(-0.177346\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −194.563 | + | 194.563i | −0.613764 | + | 0.613764i | −0.943925 | − | 0.330161i | \(-0.892897\pi\) |
0.330161 | + | 0.943925i | \(0.392897\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 93.9437i | − | 0.294494i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 221.585 | + | 221.585i | 0.686021 | + | 0.686021i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 126.604 | + | 126.604i | 0.389552 | + | 0.389552i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 128.305i | 0.389985i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 462.054 | − | 462.054i | 1.39593 | − | 1.39593i | 0.584641 | − | 0.811292i | \(-0.301235\pi\) |
0.811292 | − | 0.584641i | \(-0.198765\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.0643i | 0.0539233i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −472.439 | −1.40190 | −0.700948 | − | 0.713212i | \(-0.747240\pi\) | ||||
−0.700948 | + | 0.713212i | \(0.747240\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 79.5078 | + | 79.5078i | 0.233161 | + | 0.233161i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −322.996 | −0.941679 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 92.8976 | − | 92.8976i | 0.267716 | − | 0.267716i | −0.560463 | − | 0.828179i | \(-0.689377\pi\) |
0.828179 | + | 0.560463i | \(0.189377\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −264.708 | + | 264.708i | −0.758475 | + | 0.758475i | −0.976045 | − | 0.217570i | \(-0.930187\pi\) |
0.217570 | + | 0.976045i | \(0.430187\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 413.360 | 1.17099 | 0.585495 | − | 0.810676i | \(-0.300900\pi\) | ||||
0.585495 | + | 0.810676i | \(0.300900\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.3481 | + | 14.3481i | 0.0404173 | + | 0.0404173i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 625.198 | 1.74150 | 0.870749 | − | 0.491728i | \(-0.163635\pi\) | ||||
0.870749 | + | 0.491728i | \(0.163635\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 84.1643i | − | 0.233142i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.1773 | + | 17.1773i | −0.0470611 | + | 0.0470611i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 601.904i | 1.64007i | 0.572316 | + | 0.820033i | \(0.306045\pi\) | ||||
−0.572316 | + | 0.820033i | \(0.693955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −164.458 | − | 164.458i | −0.443283 | − | 0.443283i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 493.026 | + | 493.026i | 1.32179 | + | 1.32179i | 0.912330 | + | 0.409455i | \(0.134281\pi\) |
0.409455 | + | 0.912330i | \(0.365719\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 216.122i | 0.573269i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 144.970 | − | 144.970i | 0.382506 | − | 0.382506i | −0.489498 | − | 0.872004i | \(-0.662820\pi\) |
0.872004 | + | 0.489498i | \(0.162820\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 417.764i | − | 1.09077i | −0.838187 | − | 0.545384i | \(-0.816384\pi\) | ||
0.838187 | − | 0.545384i | \(-0.183616\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.92724 | −0.0102006 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 144.751 | + | 144.751i | 0.372109 | + | 0.372109i | 0.868245 | − | 0.496136i | \(-0.165248\pi\) |
−0.496136 | + | 0.868245i | \(0.665248\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 667.392 | 1.70689 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.4674 | − | 13.4674i | 0.0340946 | − | 0.0340946i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 105.531 | − | 105.531i | 0.265822 | − | 0.265822i | −0.561592 | − | 0.827414i | \(-0.689811\pi\) |
0.827414 | + | 0.561592i | \(0.189811\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 529.383 | 1.32016 | 0.660078 | − | 0.751197i | \(-0.270523\pi\) | ||||
0.660078 | + | 0.751197i | \(0.270523\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −182.912 | − | 182.912i | −0.453876 | − | 0.453876i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 152.167 | 0.373874 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 371.204i | − | 0.907590i | −0.891106 | − | 0.453795i | \(-0.850070\pi\) | ||
0.891106 | − | 0.453795i | \(-0.149930\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −261.422 | + | 261.422i | −0.632982 | + | 0.632982i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.4244i | 0.0781311i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 124.486 | + | 124.486i | 0.297103 | + | 0.297103i | 0.839878 | − | 0.542775i | \(-0.182626\pi\) |
−0.542775 | + | 0.839878i | \(0.682626\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −51.7267 | − | 51.7267i | −0.122866 | − | 0.122866i | 0.643000 | − | 0.765866i | \(-0.277690\pi\) |
−0.765866 | + | 0.643000i | \(0.777690\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 468.899i | 1.10329i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −67.7922 | + | 67.7922i | −0.158764 | + | 0.158764i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 424.978i | 0.986029i | 0.870021 | + | 0.493014i | \(0.164105\pi\) | ||||
−0.870021 | + | 0.493014i | \(0.835895\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 283.151 | 0.653927 | 0.326964 | − | 0.945037i | \(-0.393975\pi\) | ||||
0.326964 | + | 0.945037i | \(0.393975\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 416.901 | + | 416.901i | 0.954008 | + | 0.954008i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −701.459 | −1.59786 | −0.798928 | − | 0.601427i | \(-0.794599\pi\) | ||||
−0.798928 | + | 0.601427i | \(0.794599\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 272.651 | − | 272.651i | 0.615464 | − | 0.615464i | −0.328900 | − | 0.944365i | \(-0.606678\pi\) |
0.944365 | + | 0.328900i | \(0.106678\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.3002 | + | 34.3002i | −0.0770792 | + | 0.0770792i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −614.711 | −1.36907 | −0.684534 | − | 0.728981i | \(-0.739994\pi\) | ||||
−0.684534 | + | 0.728981i | \(0.739994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −97.4931 | − | 97.4931i | −0.216171 | − | 0.216171i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.03482 | 0.0198567 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 117.859i | − | 0.257898i | −0.991651 | − | 0.128949i | \(-0.958840\pi\) | ||
0.991651 | − | 0.128949i | \(-0.0411603\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 262.235 | − | 262.235i | 0.568839 | − | 0.568839i | −0.362964 | − | 0.931803i | \(-0.618235\pi\) |
0.931803 | + | 0.362964i | \(0.118235\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 192.234i | 0.415192i | 0.978215 | + | 0.207596i | \(0.0665640\pi\) | ||||
−0.978215 | + | 0.207596i | \(0.933436\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 529.169 | + | 529.169i | 1.13312 | + | 1.13312i | 0.989655 | + | 0.143470i | \(0.0458259\pi\) |
0.143470 | + | 0.989655i | \(0.454174\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −154.822 | − | 154.822i | −0.330111 | − | 0.330111i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 125.119i | − | 0.264523i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −292.908 | + | 292.908i | −0.616649 | + | 0.616649i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.43750i | 0.00300104i | 0.999999 | + | 0.00150052i | \(0.000477630\pi\) | ||||
−0.999999 | + | 0.00150052i | \(0.999522\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −350.068 | −0.727792 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.7373 | − | 11.7373i | −0.0242006 | − | 0.0242006i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 701.238 | 1.43991 | 0.719957 | − | 0.694019i | \(-0.244162\pi\) | ||||
0.719957 | + | 0.694019i | \(0.244162\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 519.668 | − | 519.668i | 1.05839 | − | 1.05839i | 0.0602007 | − | 0.998186i | \(-0.480826\pi\) |
0.998186 | − | 0.0602007i | \(-0.0191741\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −400.222 | + | 400.222i | −0.811809 | + | 0.811809i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −245.944 | −0.494858 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −359.284 | − | 359.284i | −0.720009 | − | 0.720009i | 0.248598 | − | 0.968607i | \(-0.420030\pi\) |
−0.968607 | + | 0.248598i | \(0.920030\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −174.376 | −0.346671 | −0.173335 | − | 0.984863i | \(-0.555454\pi\) | ||||
−0.173335 | + | 0.984863i | \(0.555454\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 63.4752i | 0.125693i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 314.247 | − | 314.247i | 0.617381 | − | 0.617381i | −0.327478 | − | 0.944859i | \(-0.606199\pi\) |
0.944859 | + | 0.327478i | \(0.106199\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 294.440i | − | 0.576203i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.4732 | − | 15.4732i | −0.0300450 | − | 0.0300450i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 72.6801 | + | 72.6801i | 0.140580 | + | 0.140580i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 468.678i | 0.899575i | 0.893136 | + | 0.449787i | \(0.148500\pi\) | ||||
−0.893136 | + | 0.449787i | \(0.851500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 417.239 | − | 417.239i | 0.797780 | − | 0.797780i | −0.184965 | − | 0.982745i | \(-0.559217\pi\) |
0.982745 | + | 0.184965i | \(0.0592173\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 677.443i | − | 1.28547i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 726.667 | 1.37366 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 224.288 | + | 224.288i | 0.420803 | + | 0.420803i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 59.0984 | 0.110464 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −74.6533 | + | 74.6533i | −0.138503 | + | 0.138503i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 163.152 | − | 163.152i | 0.301574 | − | 0.301574i | −0.540055 | − | 0.841629i | \(-0.681597\pi\) |
0.841629 | + | 0.540055i | \(0.181597\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.7192 | 0.0251729 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 595.267 | + | 595.267i | 1.08824 | + | 1.08824i | 0.995710 | + | 0.0925300i | \(0.0294954\pi\) |
0.0925300 | + | 0.995710i | \(0.470505\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −500.015 | −0.907468 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 230.847i | 0.417445i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −370.177 | + | 370.177i | −0.664590 | + | 0.664590i | −0.956459 | − | 0.291868i | \(-0.905723\pi\) |
0.291868 | + | 0.956459i | \(0.405723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 287.843i | 0.514926i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −426.543 | − | 426.543i | −0.757625 | − | 0.757625i | 0.218264 | − | 0.975890i | \(-0.429960\pi\) |
−0.975890 | + | 0.218264i | \(0.929960\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.16337 | − | 1.16337i | −0.00205906 | − | 0.00205906i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 291.547i | − | 0.512385i | −0.966626 | − | 0.256192i | \(-0.917532\pi\) | ||
0.966626 | − | 0.256192i | \(-0.0824680\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −569.328 | + | 569.328i | −0.997071 | + | 0.997071i | −0.999996 | − | 0.00292477i | \(-0.999069\pi\) |
0.00292477 | + | 0.999996i | \(0.499069\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 882.212i | 1.53428i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −360.847 | −0.625385 | −0.312692 | − | 0.949854i | \(-0.601231\pi\) | ||||
−0.312692 | + | 0.949854i | \(0.601231\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −277.897 | − | 277.897i | −0.478308 | − | 0.478308i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −186.319 | −0.319586 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −373.439 | + | 373.439i | −0.636183 | + | 0.636183i | −0.949612 | − | 0.313429i | \(-0.898522\pi\) |
0.313429 | + | 0.949612i | \(0.398522\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 423.180 | − | 423.180i | 0.718472 | − | 0.718472i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −608.053 | −1.02538 | −0.512692 | − | 0.858572i | \(-0.671352\pi\) | ||||
−0.512692 | + | 0.858572i | \(0.671352\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.7309 | + | 16.7309i | 0.0281192 | + | 0.0281192i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −211.563 | −0.353194 | −0.176597 | − | 0.984283i | \(-0.556509\pi\) | ||||
−0.176597 | + | 0.984283i | \(0.556509\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 343.381i | 0.571349i | 0.958327 | + | 0.285674i | \(0.0922176\pi\) | ||||
−0.958327 | + | 0.285674i | \(0.907782\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.3210 | − | 25.3210i | 0.0418529 | − | 0.0418529i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1006.23i | − | 1.65771i | −0.559461 | − | 0.828856i | \(-0.688992\pi\) | ||
0.559461 | − | 0.828856i | \(-0.311008\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −167.204 | − | 167.204i | −0.273657 | − | 0.273657i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −380.705 | − | 380.705i | −0.621052 | − | 0.621052i | 0.324748 | − | 0.945801i | \(-0.394720\pi\) |
−0.945801 | + | 0.324748i | \(0.894720\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 693.808i | − | 1.12449i | −0.826972 | − | 0.562243i | \(-0.809939\pi\) | ||
0.826972 | − | 0.562243i | \(-0.190061\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 619.279 | − | 619.279i | 1.00045 | − | 1.00045i | 0.000450619 | − | 1.00000i | \(-0.499857\pi\) |
1.00000 | 0.000450619i | \(-0.000143436\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 587.947i | − | 0.943736i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −617.237 | −0.987579 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −648.266 | − | 648.266i | −1.03063 | − | 1.03063i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1007.91 | −1.59732 | −0.798661 | − | 0.601781i | \(-0.794458\pi\) | ||||
−0.798661 | + | 0.601781i | \(0.794458\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28.0522 | + | 28.0522i | −0.0441767 | + | 0.0441767i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 171.744 | − | 171.744i | 0.269613 | − | 0.269613i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 511.481 | 0.797943 | 0.398971 | − | 0.916963i | \(-0.369367\pi\) | ||||
0.398971 | + | 0.916963i | \(0.369367\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 497.727 | + | 497.727i | 0.774071 | + | 0.774071i | 0.978815 | − | 0.204745i | \(-0.0656365\pi\) |
−0.204745 | + | 0.978815i | \(0.565636\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −59.8694 | −0.0925339 | −0.0462669 | − | 0.998929i | \(-0.514732\pi\) | ||||
−0.0462669 | + | 0.998929i | \(0.514732\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 296.172i | 0.456351i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 489.952 | − | 489.952i | 0.750310 | − | 0.750310i | −0.224227 | − | 0.974537i | \(-0.571986\pi\) |
0.974537 | + | 0.224227i | \(0.0719858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.7348i | 0.0530302i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 234.984 | + | 234.984i | 0.356577 | + | 0.356577i | 0.862549 | − | 0.505973i | \(-0.168866\pi\) |
−0.505973 | + | 0.862549i | \(0.668866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −305.060 | − | 305.060i | −0.461512 | − | 0.461512i | 0.437639 | − | 0.899151i | \(-0.355815\pi\) |
−0.899151 | + | 0.437639i | \(0.855815\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.9027i | 0.0314326i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −752.998 | + | 752.998i | −1.12893 | + | 1.12893i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 76.8036i | 0.114461i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 458.738 | 0.681632 | 0.340816 | − | 0.940130i | \(-0.389297\pi\) | ||||
0.340816 | + | 0.940130i | \(0.389297\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 171.344 | + | 171.344i | 0.253094 | + | 0.253094i | 0.822238 | − | 0.569144i | \(-0.192725\pi\) |
−0.569144 | + | 0.822238i | \(0.692725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 201.192 | 0.296306 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −769.447 | + | 769.447i | −1.12657 | + | 1.12657i | −0.135838 | + | 0.990731i | \(0.543373\pi\) |
−0.990731 | + | 0.135838i | \(0.956627\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.6229 | + | 16.6229i | −0.0242670 | + | 0.0242670i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 428.636 | 0.622114 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.7951 | − | 44.7951i | −0.0648264 | − | 0.0648264i | 0.673950 | − | 0.738777i | \(-0.264596\pi\) |
−0.738777 | + | 0.673950i | \(0.764596\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.52381 | 0.0108256 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 830.686i | 1.19180i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.7012 | − | 31.7012i | 0.0452229 | − | 0.0452229i | −0.684134 | − | 0.729357i | \(-0.739820\pi\) |
0.729357 | + | 0.684134i | \(0.239820\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 809.907i | − | 1.15207i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −544.021 | − | 544.021i | −0.769478 | − | 0.769478i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −256.706 | − | 256.706i | −0.362068 | − | 0.362068i | 0.502506 | − | 0.864574i | \(-0.332411\pi\) |
−0.864574 | + | 0.502506i | \(0.832411\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1274.58i | − | 1.78763i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.11789 | − | 5.11789i | 0.00715789 | − | 0.00715789i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1368.29i | 1.90305i | 0.307574 | + | 0.951524i | \(0.400483\pi\) | ||||
−0.307574 | + | 0.951524i | \(0.599517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 265.229 | 0.367862 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −529.045 | − | 529.045i | −0.729717 | − | 0.729717i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.5336 | 0.0516281 | 0.0258141 | − | 0.999667i | \(-0.491782\pi\) | ||||
0.0258141 | + | 0.999667i | \(0.491782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −533.037 | + | 533.037i | −0.729189 | + | 0.729189i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 385.216 | − | 385.216i | 0.525534 | − | 0.525534i | −0.393704 | − | 0.919237i | \(-0.628806\pi\) |
0.919237 | + | 0.393704i | \(0.128806\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −175.402 | −0.237995 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 889.039 | + | 889.039i | 1.20303 | + | 1.20303i | 0.973240 | + | 0.229790i | \(0.0738040\pi\) |
0.229790 | + | 0.973240i | \(0.426196\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −506.252 | −0.681362 | −0.340681 | − | 0.940179i | \(-0.610658\pi\) | ||||
−0.340681 | + | 0.940179i | \(0.610658\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0318i | 0.0134655i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −506.509 | + | 506.509i | −0.676247 | + | 0.676247i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 456.844i | 0.608314i | 0.952622 | + | 0.304157i | \(0.0983748\pi\) | ||||
−0.952622 | + | 0.304157i | \(0.901625\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36.6554 | + | 36.6554i | 0.0485502 | + | 0.0485502i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 221.708 | + | 221.708i | 0.292877 | + | 0.292877i | 0.838216 | − | 0.545339i | \(-0.183599\pi\) |
−0.545339 | + | 0.838216i | \(0.683599\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 205.900i | − | 0.270566i | −0.990807 | − | 0.135283i | \(-0.956806\pi\) | ||
0.990807 | − | 0.135283i | \(-0.0431943\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −117.582 | + | 117.582i | −0.154105 | + | 0.154105i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 681.359i | − | 0.888342i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 900.133 | 1.17052 | 0.585262 | − | 0.810844i | \(-0.300992\pi\) | ||||
0.585262 | + | 0.810844i | \(0.300992\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −870.407 | − | 870.407i | −1.12601 | − | 1.12601i | −0.990819 | − | 0.135193i | \(-0.956835\pi\) |
−0.135193 | − | 0.990819i | \(-0.543165\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 895.498 | 1.15548 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −518.907 | + | 518.907i | −0.666119 | + | 0.666119i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −139.318 | + | 139.318i | −0.178385 | + | 0.178385i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −69.1547 | −0.0880951 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1005.24 | − | 1005.24i | −1.27730 | − | 1.27730i | −0.942171 | − | 0.335133i | \(-0.891219\pi\) |
−0.335133 | − | 0.942171i | \(-0.608781\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.9415 | 0.0252106 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 176.691i | − | 0.222813i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 434.779 | − | 434.779i | 0.545520 | − | 0.545520i | −0.379622 | − | 0.925142i | \(-0.623946\pi\) |
0.925142 | + | 0.379622i | \(0.123946\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 619.268i | − | 0.775054i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −166.789 | − | 166.789i | −0.207708 | − | 0.207708i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 31.4785 | + | 31.4785i | 0.0391037 | + | 0.0391037i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 50.0002i | − | 0.0618049i | −0.999522 | − | 0.0309024i | \(-0.990162\pi\) | ||
0.999522 | − | 0.0309024i | \(-0.00983812\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.9957 | − | 36.9957i | 0.0456173 | − | 0.0456173i | −0.683930 | − | 0.729547i | \(-0.739731\pi\) |
0.729547 | + | 0.683930i | \(0.239731\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 84.8378i | − | 0.104096i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −665.947 | −0.815112 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −297.373 | − | 297.373i | −0.362208 | − | 0.362208i | 0.502417 | − | 0.864625i | \(-0.332444\pi\) |
−0.864625 | + | 0.502417i | \(0.832444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −345.052 | −0.419262 | −0.209631 | − | 0.977781i | \(-0.567226\pi\) | ||||
−0.209631 | + | 0.977781i | \(0.567226\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −426.416 | + | 426.416i | −0.515618 | + | 0.515618i | −0.916242 | − | 0.400624i | \(-0.868793\pi\) |
0.400624 | + | 0.916242i | \(0.368793\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −897.159 | + | 897.159i | −1.08222 | + | 1.08222i | −0.0859157 | + | 0.996302i | \(0.527382\pi\) |
−0.996302 | + | 0.0859157i | \(0.972618\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 636.080 | 0.763602 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.4367 | + | 45.4367i | 0.0544152 | + | 0.0544152i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −708.037 | −0.843906 | −0.421953 | − | 0.906618i | \(-0.638655\pi\) | ||||
−0.421953 | + | 0.906618i | \(0.638655\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 62.1159i | − | 0.0738595i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.6989 | − | 26.6989i | 0.0315963 | − | 0.0315963i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 434.033i | 0.512435i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1219.68 | − | 1219.68i | −1.43323 | − | 1.43323i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −795.484 | − | 795.484i | −0.932572 | − | 0.932572i | 0.0652942 | − | 0.997866i | \(-0.479201\pi\) |
−0.997866 | + | 0.0652942i | \(0.979201\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1447.28i | − | 1.68877i | −0.535735 | − | 0.844386i | \(-0.679966\pi\) | ||
0.535735 | − | 0.844386i | \(-0.320034\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 99.6061 | − | 99.6061i | 0.115956 | − | 0.115956i | −0.646748 | − | 0.762704i | \(-0.723871\pi\) |
0.762704 | + | 0.646748i | \(0.223871\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 549.773i | 0.637049i | 0.947915 | + | 0.318525i | \(0.103187\pi\) | ||||
−0.947915 | + | 0.318525i | \(0.896813\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −63.1185 | −0.0729694 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 130.766 | + | 130.766i | 0.150479 | + | 0.150479i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 403.522 | 0.463286 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −44.3246 | + | 44.3246i | −0.0506567 | + | 0.0506567i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 165.469 | − | 165.469i | 0.188677 | − | 0.188677i | −0.606447 | − | 0.795124i | \(-0.707406\pi\) |
0.795124 | + | 0.606447i | \(0.207406\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1046.60 | −1.18796 | −0.593982 | − | 0.804479i | \(-0.702445\pi\) | ||||
−0.593982 | + | 0.804479i | \(0.702445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −338.581 | − | 338.581i | −0.383444 | − | 0.383444i | 0.488897 | − | 0.872341i | \(-0.337399\pi\) |
−0.872341 | + | 0.488897i | \(0.837399\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1486.13 | −1.67546 | −0.837728 | − | 0.546088i | \(-0.816117\pi\) | ||||
−0.837728 | + | 0.546088i | \(0.816117\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 480.848i | − | 0.540887i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 386.840 | − | 386.840i | 0.433191 | − | 0.433191i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 67.6447i | − | 0.0755807i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 764.339 | + | 764.339i | 0.850210 | + | 0.850210i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 793.761 | + | 793.761i | 0.880978 | + | 0.880978i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45.3482i | 0.0501085i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 66.8336 | − | 66.8336i | 0.0736864 | − | 0.0736864i | −0.669303 | − | 0.742989i | \(-0.733407\pi\) |
0.742989 | + | 0.669303i | \(0.233407\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 227.208i | − | 0.249406i | −0.992194 | − | 0.124703i | \(-0.960202\pi\) | ||
0.992194 | − | 0.124703i | \(-0.0397977\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −314.837 | −0.344838 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −297.698 | − | 297.698i | −0.324643 | − | 0.324643i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1375.00 | −1.49619 | −0.748097 | − | 0.663589i | \(-0.769032\pi\) | ||||
−0.748097 | + | 0.663589i | \(0.769032\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 320.509 | − | 320.509i | 0.347247 | − | 0.347247i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 856.929 | − | 856.929i | 0.926410 | − | 0.926410i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1788.04 | −1.92470 | −0.962348 | − | 0.271822i | \(-0.912374\pi\) | ||||
−0.962348 | + | 0.271822i | \(0.912374\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 397.342 | + | 397.342i | 0.426790 | + | 0.426790i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.9549 | 0.0202727 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 768.834i | − | 0.820527i | −0.911967 | − | 0.410263i | \(-0.865437\pi\) | ||
0.911967 | − | 0.410263i | \(-0.134563\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1016.85 | − | 1016.85i | 1.08061 | − | 1.08061i | 0.0841571 | − | 0.996453i | \(-0.473180\pi\) |
0.996453 | − | 0.0841571i | \(-0.0268197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1562.90i | 1.65737i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 476.431 | + | 476.431i | 0.503095 | + | 0.503095i | 0.912398 | − | 0.409304i | \(-0.134228\pi\) |
−0.409304 | + | 0.912398i | \(0.634228\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 383.708 | + | 383.708i | 0.404329 | + | 0.404329i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 577.529i | 0.606011i | 0.952989 | + | 0.303006i | \(0.0979901\pi\) | ||||
−0.952989 | + | 0.303006i | \(0.902010\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.0375 | − | 34.0375i | 0.0356414 | − | 0.0356414i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 284.936i | − | 0.297118i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −332.773 | −0.346278 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.0257 | + | 12.0257i | 0.0124619 | + | 0.0124619i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 864.047 | 0.893534 | 0.446767 | − | 0.894650i | \(-0.352575\pi\) | ||||
0.446767 | + | 0.894650i | \(0.352575\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 898.515 | − | 898.515i | 0.925350 | − | 0.925350i | −0.0720505 | − | 0.997401i | \(-0.522954\pi\) |
0.997401 | + | 0.0720505i | \(0.0229543\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −64.4836 | + | 64.4836i | −0.0662730 | + | 0.0662730i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 538.131 | 0.550799 | 0.275400 | − | 0.961330i | \(-0.411190\pi\) | ||||
0.275400 | + | 0.961330i | \(0.411190\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −333.051 | − | 333.051i | −0.340195 | − | 0.340195i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −759.452 | −0.772586 | −0.386293 | − | 0.922376i | \(-0.626245\pi\) | ||||
−0.386293 | + | 0.922376i | \(0.626245\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 49.2052i | − | 0.0499546i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1002.88 | + | 1002.88i | −1.01404 | + | 1.01404i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 514.565i | − | 0.519238i | −0.965711 | − | 0.259619i | \(-0.916403\pi\) | ||
0.965711 | − | 0.259619i | \(-0.0835969\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.511545 | + | 0.511545i | 0.000514115 | + | 0.000514115i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1249.59 | + | 1249.59i | 1.25335 | + | 1.25335i | 0.954208 | + | 0.299145i | \(0.0967013\pi\) |
0.299145 | + | 0.954208i | \(0.403299\pi\) | |||||||
\(998\) | 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.m.e.415.4 | 16 | ||
3.2 | odd | 2 | inner | 1152.3.m.e.415.5 | 16 | ||
4.3 | odd | 2 | 1152.3.m.d.415.4 | 16 | |||
8.3 | odd | 2 | 576.3.m.b.271.5 | 16 | |||
8.5 | even | 2 | 144.3.m.b.91.8 | yes | 16 | ||
12.11 | even | 2 | 1152.3.m.d.415.5 | 16 | |||
16.3 | odd | 4 | inner | 1152.3.m.e.991.4 | 16 | ||
16.5 | even | 4 | 576.3.m.b.559.5 | 16 | |||
16.11 | odd | 4 | 144.3.m.b.19.8 | yes | 16 | ||
16.13 | even | 4 | 1152.3.m.d.991.4 | 16 | |||
24.5 | odd | 2 | 144.3.m.b.91.1 | yes | 16 | ||
24.11 | even | 2 | 576.3.m.b.271.4 | 16 | |||
48.5 | odd | 4 | 576.3.m.b.559.4 | 16 | |||
48.11 | even | 4 | 144.3.m.b.19.1 | ✓ | 16 | ||
48.29 | odd | 4 | 1152.3.m.d.991.5 | 16 | |||
48.35 | even | 4 | inner | 1152.3.m.e.991.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.m.b.19.1 | ✓ | 16 | 48.11 | even | 4 | ||
144.3.m.b.19.8 | yes | 16 | 16.11 | odd | 4 | ||
144.3.m.b.91.1 | yes | 16 | 24.5 | odd | 2 | ||
144.3.m.b.91.8 | yes | 16 | 8.5 | even | 2 | ||
576.3.m.b.271.4 | 16 | 24.11 | even | 2 | |||
576.3.m.b.271.5 | 16 | 8.3 | odd | 2 | |||
576.3.m.b.559.4 | 16 | 48.5 | odd | 4 | |||
576.3.m.b.559.5 | 16 | 16.5 | even | 4 | |||
1152.3.m.d.415.4 | 16 | 4.3 | odd | 2 | |||
1152.3.m.d.415.5 | 16 | 12.11 | even | 2 | |||
1152.3.m.d.991.4 | 16 | 16.13 | even | 4 | |||
1152.3.m.d.991.5 | 16 | 48.29 | odd | 4 | |||
1152.3.m.e.415.4 | 16 | 1.1 | even | 1 | trivial | ||
1152.3.m.e.415.5 | 16 | 3.2 | odd | 2 | inner | ||
1152.3.m.e.991.4 | 16 | 16.3 | odd | 4 | inner | ||
1152.3.m.e.991.5 | 16 | 48.35 | even | 4 | inner |