Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(559,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.u (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: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1231.7 | ||
Character | \(\chi\) | \(=\) | 1344.1231 |
Dual form | 1344.2.u.a.559.7 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.07201 | + | 1.07201i | −0.479420 | + | 0.479420i | −0.904946 | − | 0.425526i | \(-0.860089\pi\) |
0.425526 | + | 0.904946i | \(0.360089\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.929507 | + | 2.47710i | −0.351321 | + | 0.936255i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.12178 | − | 1.12178i | 0.338229 | − | 0.338229i | −0.517472 | − | 0.855700i | \(-0.673127\pi\) |
0.855700 | + | 0.517472i | \(0.173127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.380324 | − | 0.380324i | −0.105483 | − | 0.105483i | 0.652396 | − | 0.757879i | \(-0.273764\pi\) |
−0.757879 | + | 0.652396i | \(0.773764\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.51606i | − | 0.391444i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.93076i | 1.19588i | 0.801539 | + | 0.597942i | \(0.204015\pi\) | ||||
−0.801539 | + | 0.597942i | \(0.795985\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.00735220 | + | 0.00735220i | −0.00168671 | + | 0.00168671i | −0.707950 | − | 0.706263i | \(-0.750380\pi\) |
0.706263 | + | 0.707950i | \(0.250380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.09431 | − | 2.40883i | −0.238798 | − | 0.525651i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.62475 | −0.338783 | −0.169392 | − | 0.985549i | \(-0.554180\pi\) | ||||
−0.169392 | + | 0.985549i | \(0.554180\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.70157i | 0.540314i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.69584 | + | 3.69584i | −0.686301 | + | 0.686301i | −0.961412 | − | 0.275112i | \(-0.911285\pi\) |
0.275112 | + | 0.961412i | \(0.411285\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.21242 | −0.217757 | −0.108878 | − | 0.994055i | \(-0.534726\pi\) | ||||
−0.108878 | + | 0.994055i | \(0.534726\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.58643i | 0.276162i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.65904 | − | 3.65193i | −0.280429 | − | 0.617289i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.70001 | − | 6.70001i | −1.10148 | − | 1.10148i | −0.994233 | − | 0.107243i | \(-0.965798\pi\) |
−0.107243 | − | 0.994233i | \(-0.534202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.537859 | 0.0861264 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.08793 | −0.326080 | −0.163040 | − | 0.986619i | \(-0.552130\pi\) | ||||
−0.163040 | + | 0.986619i | \(0.552130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.89391 | − | 7.89391i | 1.20381 | − | 1.20381i | 0.230812 | − | 0.972998i | \(-0.425862\pi\) |
0.972998 | − | 0.230812i | \(-0.0741383\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.07201 | + | 1.07201i | 0.159807 | + | 0.159807i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.09637 | −0.305787 | −0.152894 | − | 0.988243i | \(-0.548859\pi\) | ||||
−0.152894 | + | 0.988243i | \(0.548859\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.27203 | − | 4.60496i | −0.753148 | − | 0.657852i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.48657 | − | 3.48657i | −0.488218 | − | 0.488218i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.28124 | − | 5.28124i | −0.725434 | − | 0.725434i | 0.244272 | − | 0.969707i | \(-0.421451\pi\) |
−0.969707 | + | 0.244272i | \(0.921451\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.40512i | 0.324307i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.0103976i | − | 0.00137719i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.39247 | − | 9.39247i | −1.22280 | − | 1.22280i | −0.966634 | − | 0.256162i | \(-0.917542\pi\) |
−0.256162 | − | 0.966634i | \(-0.582458\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.45118 | + | 2.45118i | 0.313841 | + | 0.313841i | 0.846396 | − | 0.532555i | \(-0.178768\pi\) |
−0.532555 | + | 0.846396i | \(0.678768\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.47710 | + | 0.929507i | 0.312085 | + | 0.117107i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.815426 | 0.101141 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.70113 | − | 4.70113i | −0.574334 | − | 0.574334i | 0.359002 | − | 0.933337i | \(-0.383117\pi\) |
−0.933337 | + | 0.359002i | \(0.883117\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.14887 | − | 1.14887i | 0.138308 | − | 0.138308i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.16953 | −0.613510 | −0.306755 | − | 0.951789i | \(-0.599243\pi\) | ||||
−0.306755 | + | 0.951789i | \(0.599243\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.83339 | 0.916828 | 0.458414 | − | 0.888739i | \(-0.348418\pi\) | ||||
0.458414 | + | 0.888739i | \(0.348418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.91030 | − | 1.91030i | −0.220582 | − | 0.220582i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.73605 | + | 3.82145i | 0.197842 | + | 0.435495i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.65497i | 0.523725i | 0.965105 | + | 0.261863i | \(0.0843368\pi\) | ||||
−0.965105 | + | 0.261863i | \(0.915663\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.694961 | + | 0.694961i | −0.0762819 | + | 0.0762819i | −0.744218 | − | 0.667936i | \(-0.767178\pi\) |
0.667936 | + | 0.744218i | \(0.267178\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.28584 | − | 5.28584i | −0.573330 | − | 0.573330i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 5.22671i | − | 0.560362i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.3938 | −1.73774 | −0.868869 | − | 0.495043i | \(-0.835152\pi\) | ||||
−0.868869 | + | 0.495043i | \(0.835152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.29561 | − | 0.588586i | 0.135817 | − | 0.0617006i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.857310 | − | 0.857310i | 0.0888989 | − | 0.0888989i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.0157633i | − | 0.00161728i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.8094i | − | 1.60520i | −0.596516 | − | 0.802601i | \(-0.703449\pi\) | ||
0.596516 | − | 0.802601i | \(-0.296551\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.12178 | − | 1.12178i | −0.112743 | − | 0.112743i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.6943 | + | 11.6943i | −1.16363 | + | 1.16363i | −0.179951 | + | 0.983676i | \(0.557594\pi\) |
−0.983676 | + | 0.179951i | \(0.942406\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.2578i | 1.70046i | 0.526408 | + | 0.850232i | \(0.323539\pi\) | ||||
−0.526408 | + | 0.850232i | \(0.676461\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.75542 | + | 1.40919i | 0.366492 | + | 0.137523i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.486324 | − | 0.486324i | 0.0470148 | − | 0.0470148i | −0.683209 | − | 0.730223i | \(-0.739416\pi\) |
0.730223 | + | 0.683209i | \(0.239416\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.59269 | − | 4.59269i | 0.439900 | − | 0.439900i | −0.452078 | − | 0.891978i | \(-0.649317\pi\) |
0.891978 | + | 0.452078i | \(0.149317\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.47525 | 0.899351 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.4776 | 1.55009 | 0.775043 | − | 0.631908i | \(-0.217728\pi\) | ||||
0.775043 | + | 0.631908i | \(0.217728\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.74175 | − | 1.74175i | 0.162419 | − | 0.162419i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.380324 | + | 0.380324i | −0.0351610 | + | 0.0351610i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.2140 | − | 4.58317i | −1.11965 | − | 0.420139i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.48323i | 0.771203i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.47639 | − | 1.47639i | 0.133122 | − | 0.133122i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.25620 | − | 8.25620i | −0.738457 | − | 0.738457i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8244i | 1.04925i | 0.851335 | + | 0.524623i | \(0.175794\pi\) | ||||
−0.851335 | + | 0.524623i | \(0.824206\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.1637i | 0.982907i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.68747 | + | 9.68747i | −0.846398 | + | 0.846398i | −0.989682 | − | 0.143283i | \(-0.954234\pi\) |
0.143283 | + | 0.989682i | \(0.454234\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0113782 | − | 0.0250460i | −0.000986615 | − | 0.00217177i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.51606 | −0.130481 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.638902i | 0.0545851i | 0.999627 | + | 0.0272925i | \(0.00868856\pi\) | ||||
−0.999627 | + | 0.0272925i | \(0.991311\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.78705 | + | 8.78705i | 0.745308 | + | 0.745308i | 0.973594 | − | 0.228286i | \(-0.0733121\pi\) |
−0.228286 | + | 0.973594i | \(0.573312\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.48236 | − | 1.48236i | 0.124837 | − | 0.124837i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.853277 | −0.0713546 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.92400i | − | 0.658052i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.98409 | − | 0.471690i | 0.576038 | − | 0.0389044i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.68763 | − | 6.68763i | −0.547872 | − | 0.547872i | 0.377953 | − | 0.925825i | \(-0.376628\pi\) |
−0.925825 | + | 0.377953i | \(0.876628\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.7089 | −0.952854 | −0.476427 | − | 0.879214i | \(-0.658068\pi\) | ||||
−0.476427 | + | 0.879214i | \(0.658068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.93076 | 0.398628 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.29973 | − | 1.29973i | 0.104397 | − | 0.104397i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.87159 | + | 7.87159i | 0.628221 | + | 0.628221i | 0.947620 | − | 0.319399i | \(-0.103481\pi\) |
−0.319399 | + | 0.947620i | \(0.603481\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.46881 | 0.592315 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.51021 | − | 4.02466i | 0.119022 | − | 0.317188i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.16256 | − | 4.16256i | −0.326037 | − | 0.326037i | 0.525041 | − | 0.851077i | \(-0.324050\pi\) |
−0.851077 | + | 0.525041i | \(0.824050\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.70068 | − | 1.70068i | −0.132398 | − | 0.132398i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.10931i | − | 0.395370i | −0.980266 | − | 0.197685i | \(-0.936658\pi\) | ||
0.980266 | − | 0.197685i | \(-0.0633423\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.7107i | − | 0.977747i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.00735220 | + | 0.00735220i | 0.000562237 | + | 0.000562237i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.04872 | − | 6.04872i | −0.459876 | − | 0.459876i | 0.438739 | − | 0.898615i | \(-0.355425\pi\) |
−0.898615 | + | 0.438739i | \(0.855425\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.69205 | − | 2.51113i | −0.505871 | − | 0.189823i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.2830 | 0.998409 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.3303 | + | 11.3303i | 0.846868 | + | 0.846868i | 0.989741 | − | 0.142873i | \(-0.0456340\pi\) |
−0.142873 | + | 0.989741i | \(0.545634\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.12921 | − | 3.12921i | 0.232593 | − | 0.232593i | −0.581181 | − | 0.813774i | \(-0.697409\pi\) |
0.813774 | + | 0.581181i | \(0.197409\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.46649 | −0.256250 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.3650 | 1.05614 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.53121 | + | 5.53121i | 0.404482 | + | 0.404482i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.40883 | + | 1.09431i | −0.175217 | + | 0.0795995i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2514i | 0.814126i | 0.913400 | + | 0.407063i | \(0.133447\pi\) | ||||
−0.913400 | + | 0.407063i | \(0.866553\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6044 | 1.12323 | 0.561613 | − | 0.827400i | \(-0.310181\pi\) | ||||
0.561613 | + | 0.827400i | \(0.310181\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.576593 | + | 0.576593i | −0.0412907 | + | 0.0412907i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.75482 | + | 6.75482i | 0.481261 | + | 0.481261i | 0.905534 | − | 0.424273i | \(-0.139470\pi\) |
−0.424273 | + | 0.905534i | \(0.639470\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 22.4644i | − | 1.59246i | −0.604996 | − | 0.796229i | \(-0.706825\pi\) | ||
0.604996 | − | 0.796229i | \(-0.293175\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.64840 | 0.468942 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.71965 | − | 12.5903i | −0.401441 | − | 0.883664i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.23829 | − | 2.23829i | 0.156329 | − | 0.156329i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.62475i | 0.112928i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0164951i | 0.00114099i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.76337 | − | 3.76337i | −0.259081 | − | 0.259081i | 0.565599 | − | 0.824680i | \(-0.308645\pi\) |
−0.824680 | + | 0.565599i | \(0.808645\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.65541 | − | 3.65541i | 0.250464 | − | 0.250464i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.9248i | 1.15426i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.12695 | − | 3.00328i | 0.0765025 | − | 0.203876i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.53904 | + | 5.53904i | −0.374294 | + | 0.374294i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.87528 | − | 1.87528i | 0.126145 | − | 0.126145i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0828 | 0.943054 | 0.471527 | − | 0.881852i | \(-0.343703\pi\) | ||||
0.471527 | + | 0.881852i | \(0.343703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.70157 | 0.180105 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.0404 | + | 18.0404i | −1.19738 | + | 1.19738i | −0.222436 | + | 0.974947i | \(0.571401\pi\) |
−0.974947 | + | 0.222436i | \(0.928599\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.6213 | + | 16.6213i | −1.09837 | + | 1.09837i | −0.103767 | + | 0.994602i | \(0.533090\pi\) |
−0.994602 | + | 0.103767i | \(0.966910\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.92975 | − | 1.47460i | −0.258559 | − | 0.0970216i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.67000i | 0.633503i | 0.948509 | + | 0.316751i | \(0.102592\pi\) | ||||
−0.948509 | + | 0.316751i | \(0.897408\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.24734 | − | 2.24734i | 0.146600 | − | 0.146600i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.29156 | − | 3.29156i | −0.213810 | − | 0.213810i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.0336i | 1.42523i | 0.701553 | + | 0.712617i | \(0.252490\pi\) | ||||
−0.701553 | + | 0.712617i | \(0.747510\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.30808i | 0.148676i | 0.997233 | + | 0.0743382i | \(0.0236844\pi\) | ||||
−0.997233 | + | 0.0743382i | \(0.976316\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.5883 | − | 0.715110i | 0.676461 | − | 0.0456867i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.00559243 | 0.000355838 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 0.982823i | − | 0.0622839i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.88634 | + | 1.88634i | 0.119065 | + | 0.119065i | 0.764129 | − | 0.645064i | \(-0.223169\pi\) |
−0.645064 | + | 0.764129i | \(0.723169\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.82261 | + | 1.82261i | −0.114586 | + | 0.114586i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.47531 | 0.468122 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.19078i | 0.199036i | 0.995036 | + | 0.0995178i | \(0.0317300\pi\) | ||||
−0.995036 | + | 0.0995178i | \(0.968270\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.8243 | − | 10.3689i | 1.41823 | − | 0.644291i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.69584 | + | 3.69584i | 0.228767 | + | 0.228767i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.1194 | 1.24061 | 0.620306 | − | 0.784360i | \(-0.287008\pi\) | ||||
0.620306 | + | 0.784360i | \(0.287008\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.3231 | 0.695575 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.5922 | − | 11.5922i | 0.709428 | − | 0.709428i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.4208 | − | 16.4208i | −1.00119 | − | 1.00119i | −0.999999 | − | 0.00119219i | \(-0.999621\pi\) |
−0.00119219 | − | 0.999999i | \(-0.500379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.3695 | −1.84481 | −0.922407 | − | 0.386218i | \(-0.873781\pi\) | ||||
−0.922407 | + | 0.386218i | \(0.873781\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.499944 | + | 1.33233i | −0.0302580 | + | 0.0806363i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.03056 | + | 3.03056i | 0.182750 | + | 0.182750i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.2331 | + | 20.2331i | 1.21569 | + | 1.21569i | 0.969127 | + | 0.246563i | \(0.0793011\pi\) |
0.246563 | + | 0.969127i | \(0.420699\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.21242i | 0.0725857i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.4713i | 1.69846i | 0.528026 | + | 0.849228i | \(0.322932\pi\) | ||||
−0.528026 | + | 0.849228i | \(0.677068\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.05298 | + | 6.05298i | 0.359813 | + | 0.359813i | 0.863744 | − | 0.503931i | \(-0.168114\pi\) |
−0.503931 | + | 0.863744i | \(0.668114\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0111464 | + | 0.0111464i | 0.000660253 | + | 0.000660253i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.94075 | − | 5.17201i | 0.114559 | − | 0.305294i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.31235 | −0.430138 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.1789 | + | 11.1789i | 0.655321 | + | 0.655321i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2656 | − | 11.2656i | 0.658142 | − | 0.658142i | −0.296798 | − | 0.954940i | \(-0.595919\pi\) |
0.954940 | + | 0.296798i | \(0.0959189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.1377 | 1.17246 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.58643 | 0.0920542 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.617930 | + | 0.617930i | 0.0357358 | + | 0.0357358i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.2165 | + | 26.8914i | 0.704150 | + | 1.55000i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 16.5382i | − | 0.950097i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.25540 | −0.300923 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.9262 | − | 19.9262i | 1.13725 | − | 1.13725i | 0.148305 | − | 0.988942i | \(-0.452618\pi\) |
0.988942 | − | 0.148305i | \(-0.0473818\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.2031 | − | 12.2031i | −0.694212 | − | 0.694212i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.15514i | − | 0.462436i | −0.972902 | − | 0.231218i | \(-0.925729\pi\) | ||
0.972902 | − | 0.231218i | \(-0.0742710\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.5813 | −1.61551 | −0.807754 | − | 0.589520i | \(-0.799317\pi\) | ||||
−0.807754 | + | 0.589520i | \(0.799317\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.65193 | + | 1.65904i | −0.205763 | + | 0.0934764i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.7765 | + | 12.7765i | −0.717599 | + | 0.717599i | −0.968113 | − | 0.250514i | \(-0.919400\pi\) |
0.250514 | + | 0.968113i | \(0.419400\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.29182i | 0.464253i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.687767i | 0.0383874i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0362519 | − | 0.0362519i | −0.00201711 | − | 0.00201711i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.02747 | − | 1.02747i | 0.0569938 | − | 0.0569938i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.49505i | 0.359177i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.94859 | − | 5.19292i | 0.107429 | − | 0.286295i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.1140 | − | 15.1140i | 0.830739 | − | 0.830739i | −0.156879 | − | 0.987618i | \(-0.550143\pi\) |
0.987618 | + | 0.156879i | \(0.0501432\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.70001 | + | 6.70001i | −0.367159 | + | 0.367159i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.0794 | 0.550694 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.12166 | −0.387942 | −0.193971 | − | 0.981007i | \(-0.562137\pi\) | ||||
−0.193971 | + | 0.981007i | \(0.562137\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.6515 | + | 11.6515i | −0.632820 | + | 0.632820i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.36006 | + | 1.36006i | −0.0736516 | + | 0.0736516i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.3073 | − | 8.77900i | 0.880513 | − | 0.474021i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.46321i | 0.132615i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.263964 | + | 0.263964i | −0.0141704 | + | 0.0141704i | −0.714156 | − | 0.699986i | \(-0.753190\pi\) |
0.699986 | + | 0.714156i | \(0.253190\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.37893 | + | 4.37893i | 0.234399 | + | 0.234399i | 0.814526 | − | 0.580127i | \(-0.196997\pi\) |
−0.580127 | + | 0.814526i | \(0.696997\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 0.537859i | − | 0.0287088i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.9515i | 0.902238i | 0.892464 | + | 0.451119i | \(0.148975\pi\) | ||||
−0.892464 | + | 0.451119i | \(0.851025\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.54181 | − | 5.54181i | 0.294129 | − | 0.294129i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.8774 | − | 5.39579i | 0.628617 | − | 0.285575i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.7322 | 1.56921 | 0.784603 | − | 0.619998i | \(-0.212867\pi\) | ||||
0.784603 | + | 0.619998i | \(0.212867\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9999i | 0.999994i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.99855 | − | 5.99855i | −0.314842 | − | 0.314842i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.39751 | + | 8.39751i | −0.439546 | + | 0.439546i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.27534 | −0.327570 | −0.163785 | − | 0.986496i | \(-0.552370\pi\) | ||||
−0.163785 | + | 0.986496i | \(0.552370\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.08793i | 0.108693i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.9911 | − | 8.17320i | 0.934052 | − | 0.424332i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.151895 | + | 0.151895i | 0.00786483 | + | 0.00786483i | 0.711028 | − | 0.703163i | \(-0.248230\pi\) |
−0.703163 | + | 0.711028i | \(0.748230\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.6760 | 0.602947 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.81123 | 0.144786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.6234 | + | 12.6234i | −0.648420 | + | 0.648420i | −0.952611 | − | 0.304191i | \(-0.901614\pi\) |
0.304191 | + | 0.952611i | \(0.401614\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.36112 | − | 8.36112i | −0.428353 | − | 0.428353i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.5769 | −1.10253 | −0.551263 | − | 0.834331i | \(-0.685854\pi\) | ||||
−0.551263 | + | 0.834331i | \(0.685854\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.95773 | − | 2.23558i | −0.303634 | − | 0.113936i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.89391 | − | 7.89391i | −0.401270 | − | 0.401270i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.93088 | − | 4.93088i | −0.250006 | − | 0.250006i | 0.570967 | − | 0.820973i | \(-0.306568\pi\) |
−0.820973 | + | 0.570967i | \(0.806568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.01123i | − | 0.405146i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 13.7002i | − | 0.691081i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.99020 | − | 4.99020i | −0.251084 | − | 0.251084i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.5942 | + | 21.5942i | 1.08378 | + | 1.08378i | 0.996153 | + | 0.0876282i | \(0.0279287\pi\) |
0.0876282 | + | 0.996153i | \(0.472071\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0257558 | + | 0.00966463i | 0.00128940 | + | 0.000483837i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.58725 | −0.428827 | −0.214414 | − | 0.976743i | \(-0.568784\pi\) | ||||
−0.214414 | + | 0.976743i | \(0.568784\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.461112 | + | 0.461112i | 0.0229696 | + | 0.0229696i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.07201 | − | 1.07201i | 0.0532688 | − | 0.0532688i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.0318 | −0.745101 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.59158 | 0.325933 | 0.162966 | − | 0.986632i | \(-0.447894\pi\) | ||||
0.162966 | + | 0.986632i | \(0.447894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.451772 | − | 0.451772i | −0.0222843 | − | 0.0222843i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 31.9965 | − | 14.5357i | 1.57444 | − | 0.715256i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.49002i | − | 0.0731421i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.4268 | −0.608542 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.50670 | + | 3.50670i | −0.171313 | + | 0.171313i | −0.787556 | − | 0.616243i | \(-0.788654\pi\) |
0.616243 | + | 0.787556i | \(0.288654\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.7198 | + | 12.7198i | 0.619924 | + | 0.619924i | 0.945512 | − | 0.325588i | \(-0.105562\pi\) |
−0.325588 | + | 0.945512i | \(0.605562\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.09637i | 0.101929i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.3208 | −0.646152 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.35019 | + | 3.79342i | −0.404094 | + | 0.183576i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.603358 | − | 0.603358i | 0.0291304 | − | 0.0291304i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 35.1089i | − | 1.69114i | −0.533867 | − | 0.845568i | \(-0.679262\pi\) | ||
0.533867 | − | 0.845568i | \(-0.320738\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.6070i | − | 1.32671i | −0.748306 | − | 0.663353i | \(-0.769133\pi\) | ||
0.748306 | − | 0.663353i | \(-0.230867\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.60311 | + | 5.60311i | 0.268649 | + | 0.268649i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0119455 | − | 0.0119455i | 0.000571429 | − | 0.000571429i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.3491i | 0.875753i | 0.899035 | + | 0.437877i | \(0.144269\pi\) | ||||
−0.899035 | + | 0.437877i | \(0.855731\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.60496 | + | 5.27203i | −0.219284 | + | 0.251049i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.7001 | + | 14.7001i | −0.698421 | + | 0.698421i | −0.964070 | − | 0.265649i | \(-0.914414\pi\) |
0.265649 | + | 0.964070i | \(0.414414\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.5744 | − | 17.5744i | 0.833105 | − | 0.833105i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.45774 | 0.447336 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.70106 | −0.269050 | −0.134525 | − | 0.990910i | \(-0.542951\pi\) | ||||
−0.134525 | + | 0.990910i | \(0.542951\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.34219 | + | 2.34219i | −0.110290 | + | 0.110290i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.27942 | − | 8.27942i | 0.389001 | − | 0.389001i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.757944 | + | 2.01989i | −0.0355330 | + | 0.0946939i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.58548i | 0.401612i | 0.979631 | + | 0.200806i | \(0.0643561\pi\) | ||||
−0.979631 | + | 0.200806i | \(0.935644\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.48657 | + | 3.48657i | −0.162739 | + | 0.162739i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.5957 | − | 21.5957i | −1.00581 | − | 1.00581i | −0.999983 | − | 0.00582709i | \(-0.998145\pi\) |
−0.00582709 | − | 0.999983i | \(-0.501855\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.5950i | − | 1.05008i | −0.851078 | − | 0.525039i | \(-0.824051\pi\) | ||
0.851078 | − | 0.525039i | \(-0.175949\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.83810i | 0.0852398i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.33529 | − | 7.33529i | 0.339437 | − | 0.339437i | −0.516719 | − | 0.856155i | \(-0.672847\pi\) |
0.856155 | + | 0.516719i | \(0.172847\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0149 | − | 7.27542i | 0.739499 | − | 0.335948i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.1321 | −0.512940 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 17.7104i | − | 0.814326i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0198625 | − | 0.0198625i | −0.000911353 | − | 0.000911353i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.28124 | + | 5.28124i | −0.241811 | + | 0.241811i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.2356 | 1.38150 | 0.690749 | − | 0.723095i | \(-0.257281\pi\) | ||||
0.690749 | + | 0.723095i | \(0.257281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.09635i | 0.232374i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.77798 | + | 3.91375i | 0.0809010 | + | 0.178082i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.9479 | + | 16.9479i | 0.769565 | + | 0.769565i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.2232 | −0.735144 | −0.367572 | − | 0.929995i | \(-0.619811\pi\) | ||||
−0.367572 | + | 0.929995i | \(0.619811\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.88675 | 0.266208 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.8388 | + | 14.8388i | −0.669668 | + | 0.669668i | −0.957639 | − | 0.287971i | \(-0.907019\pi\) |
0.287971 | + | 0.957639i | \(0.407019\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.2233 | − | 18.2233i | −0.820736 | − | 0.820736i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.40512 | 0.108102 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.80511 | − | 12.8054i | 0.215539 | − | 0.574402i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.1057 | + | 16.1057i | 0.720990 | + | 0.720990i | 0.968807 | − | 0.247817i | \(-0.0797132\pi\) |
−0.247817 | + | 0.968807i | \(0.579713\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.61283 | + | 3.61283i | 0.161409 | + | 0.161409i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 6.58635i | − | 0.293671i | −0.989161 | − | 0.146835i | \(-0.953091\pi\) | ||
0.989161 | − | 0.146835i | \(-0.0469088\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 25.0729i | − | 1.11573i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.98783 | + | 8.98783i | 0.399163 | + | 0.399163i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.6237 | + | 22.6237i | 1.00278 | + | 1.00278i | 0.999996 | + | 0.00278262i | \(0.000885738\pi\) |
0.00278262 | + | 0.999996i | \(0.499114\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.28119 | + | 19.4041i | −0.322101 | + | 0.858385i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.0103976 | −0.000459064 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.5006 | − | 18.5006i | −0.815236 | − | 0.815236i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.35166 | + | 2.35166i | −0.103426 | + | 0.103426i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.55419 | 0.375487 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.23960 | −0.185740 | −0.0928701 | − | 0.995678i | \(-0.529604\pi\) | ||||
−0.0928701 | + | 0.995678i | \(0.529604\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.3026 | − | 10.3026i | −0.450501 | − | 0.450501i | 0.445020 | − | 0.895521i | \(-0.353197\pi\) |
−0.895521 | + | 0.445020i | \(0.853197\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.50763 | − | 2.95636i | 0.284016 | − | 0.129026i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 5.97814i | − | 0.260412i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.3602 | −0.885226 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.39247 | + | 9.39247i | −0.407599 | + | 0.407599i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.794090 | + | 0.794090i | 0.0343959 | + | 0.0343959i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.04269i | 0.0450796i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.0235 | −0.691465 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.0798 | + | 0.748305i | −0.477240 | + | 0.0322318i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.0207 | − | 12.0207i | 0.516810 | − | 0.516810i | −0.399795 | − | 0.916605i | \(-0.630919\pi\) |
0.916605 | + | 0.399795i | \(0.130919\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.42537i | 0.189911i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.84687i | 0.421794i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.7257 | − | 23.7257i | −1.01444 | − | 1.01444i | −0.999894 | − | 0.0145455i | \(-0.995370\pi\) |
−0.0145455 | − | 0.999894i | \(-0.504630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.45118 | − | 2.45118i | 0.104614 | − | 0.104614i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 0.0543451i | − | 0.00231518i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.5308 | − | 4.32683i | −0.490341 | − | 0.183996i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.1576 | + | 10.1576i | −0.431167 | + | 0.431167i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.791262 | + | 0.791262i | −0.0335269 | + | 0.0335269i | −0.723671 | − | 0.690145i | \(-0.757547\pi\) |
0.690145 | + | 0.723671i | \(0.257547\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.00449 | −0.253963 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.82231 | −0.330258 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.1409 | + | 27.1409i | −1.14385 | + | 1.14385i | −0.156114 | + | 0.987739i | \(0.549897\pi\) |
−0.987739 | + | 0.156114i | \(0.950103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.6643 | + | 17.6643i | −0.743142 | + | 0.743142i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.929507 | − | 2.47710i | 0.0390356 | − | 0.104028i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 46.0744i | − | 1.93154i | −0.259403 | − | 0.965769i | \(-0.583526\pi\) | ||
0.259403 | − | 0.965769i | \(-0.416474\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.3445 | + | 27.3445i | −1.14433 | + | 1.14433i | −0.156684 | + | 0.987649i | \(0.550080\pi\) |
−0.987649 | + | 0.156684i | \(0.949920\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.95597 | − | 7.95597i | −0.332365 | − | 0.332365i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 4.38937i | − | 0.183049i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.45943i | 0.268910i | 0.990920 | + | 0.134455i | \(0.0429283\pi\) | ||||
−0.990920 | + | 0.134455i | \(0.957072\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.0339 | + | 11.0339i | −0.458555 | + | 0.458555i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.07552 | − | 2.36746i | −0.0446199 | − | 0.0982187i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.8488 | −0.490725 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 0.815426i | − | 0.0337137i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.6920 | + | 21.6920i | 0.895325 | + | 0.895325i | 0.995018 | − | 0.0996934i | \(-0.0317862\pi\) |
−0.0996934 | + | 0.995018i | \(0.531786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.00891395 | − | 0.00891395i | 0.000367293 | − | 0.000367293i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.55275 | −0.392948 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.5016i | 1.37575i | 0.725831 | + | 0.687873i | \(0.241456\pi\) | ||||
−0.725831 | + | 0.687873i | \(0.758544\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.0068 | − | 8.18032i | 0.738206 | − | 0.335361i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.8847 | + | 15.8847i | 0.650118 | + | 0.650118i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.91644 | −0.119162 | −0.0595812 | − | 0.998223i | \(-0.518977\pi\) | ||||
−0.0595812 | + | 0.998223i | \(0.518977\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.37362 | 0.178404 | 0.0892018 | − | 0.996014i | \(-0.471568\pi\) | ||||
0.0892018 | + | 0.996014i | \(0.471568\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.70113 | + | 4.70113i | −0.191445 | + | 0.191445i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.09415 | − | 9.09415i | −0.369730 | − | 0.369730i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.8679 | −1.21230 | −0.606150 | − | 0.795350i | \(-0.707287\pi\) | ||||
−0.606150 | + | 0.795350i | \(0.707287\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.9471 | + | 4.85827i | 0.524642 | + | 0.196867i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.797300 | + | 0.797300i | 0.0322553 | + | 0.0322553i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.86096 | + | 4.86096i | 0.196333 | + | 0.196333i | 0.798426 | − | 0.602093i | \(-0.205666\pi\) |
−0.602093 | + | 0.798426i | \(0.705666\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.16542i | 0.127642i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.74665i | − | 0.150835i | −0.997152 | − | 0.0754173i | \(-0.975971\pi\) | ||
0.997152 | − | 0.0754173i | \(-0.0240289\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.0497 | + | 19.0497i | 0.765671 | + | 0.765671i | 0.977341 | − | 0.211670i | \(-0.0678903\pi\) |
−0.211670 | + | 0.977341i | \(0.567890\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.14887 | − | 1.14887i | −0.0461026 | − | 0.0461026i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.2381 | − | 40.6090i | 0.610503 | − | 1.62697i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.19369 | 0.167748 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0116638 | − | 0.0116638i | −0.000465806 | − | 0.000465806i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.0361 | − | 33.0361i | 1.31724 | − | 1.31724i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.4844 | −1.13395 | −0.566974 | − | 0.823736i | \(-0.691886\pi\) | ||||
−0.566974 | + | 0.823736i | \(0.691886\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.32221 | 0.211539 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.6759 | − | 12.6759i | −0.503029 | − | 0.503029i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.253703 | + | 3.75646i | 0.0100521 | + | 0.148836i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.16953i | 0.204503i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.3813 | −0.923506 | −0.461753 | − | 0.887009i | \(-0.652779\pi\) | ||||
−0.461753 | + | 0.887009i | \(0.652779\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.17454 | + | 4.17454i | −0.164628 | + | 0.164628i | −0.784613 | − | 0.619985i | \(-0.787138\pi\) |
0.619985 | + | 0.784613i | \(0.287138\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.9676 | − | 11.9676i | −0.471225 | − | 0.471225i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 17.1525i | − | 0.674335i | −0.941445 | − | 0.337168i | \(-0.890531\pi\) | ||
0.941445 | − | 0.337168i | \(-0.109469\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.0725 | −0.827169 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.32677 | + | 2.92052i | 0.0520000 | + | 0.114464i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.83742 | − | 6.83742i | 0.267569 | − | 0.267569i | −0.560551 | − | 0.828120i | \(-0.689411\pi\) |
0.828120 | + | 0.560551i | \(0.189411\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 20.7702i | − | 0.811560i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 7.83339i | − | 0.305609i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.8182 | + | 18.8182i | 0.733054 | + | 0.733054i | 0.971224 | − | 0.238170i | \(-0.0765475\pi\) |
−0.238170 | + | 0.971224i | \(0.576547\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.9718 | + | 23.9718i | −0.932396 | + | 0.932396i | −0.997855 | − | 0.0654588i | \(-0.979149\pi\) |
0.0654588 | + | 0.997855i | \(0.479149\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.65205i | 0.102997i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0390473 | + | 0.0146521i | 0.00151419 | + | 0.000568185i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.00481 | − | 6.00481i | 0.232507 | − | 0.232507i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.95804 | + | 9.95804i | −0.385000 | + | 0.385000i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.49935 | 0.212300 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.36157 | 0.129579 | 0.0647896 | − | 0.997899i | \(-0.479362\pi\) | ||||
0.0647896 | + | 0.997899i | \(0.479362\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.91030 | + | 1.91030i | −0.0735274 | + | 0.0735274i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.3331 | + | 16.3331i | −0.627731 | + | 0.627731i | −0.947497 | − | 0.319766i | \(-0.896396\pi\) |
0.319766 | + | 0.947497i | \(0.396396\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.1615 | + | 14.6950i | 1.50288 | + | 0.563941i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 25.5130i | − | 0.977659i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.36376 | − | 6.36376i | 0.243503 | − | 0.243503i | −0.574795 | − | 0.818298i | \(-0.694918\pi\) |
0.818298 | + | 0.574795i | \(0.194918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.684912 | − | 0.684912i | −0.0261691 | − | 0.0261691i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 23.5061i | − | 0.896814i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.01717i | 0.153042i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.76023 | − | 5.76023i | 0.219129 | − | 0.219129i | −0.589002 | − | 0.808131i | \(-0.700479\pi\) |
0.808131 | + | 0.589002i | \(0.200479\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.82145 | − | 1.73605i | 0.145165 | − | 0.0659472i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.8397 | −0.714631 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10.2951i | − | 0.389954i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.83772 | − | 6.83772i | −0.258626 | − | 0.258626i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.52774 | + | 2.52774i | −0.0954714 | + | 0.0954714i | −0.753229 | − | 0.657758i | \(-0.771505\pi\) |
0.657758 | + | 0.753229i | \(0.271505\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0985197 | 0.00371574 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.17822i | 0.119699i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.0980 | − | 39.8379i | −0.680645 | − | 1.49826i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.4224 | − | 25.4224i | −0.954759 | − | 0.954759i | 0.0442613 | − | 0.999020i | \(-0.485907\pi\) |
−0.999020 | + | 0.0442613i | \(0.985907\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.65497 | 0.174575 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.96988 | 0.0737724 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.914726 | − | 0.914726i | 0.0342088 | − | 0.0342088i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.5801 | − | 15.5801i | −0.581849 | − | 0.581849i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.26294 | −0.308156 | −0.154078 | − | 0.988059i | \(-0.549241\pi\) | ||||
−0.154078 | + | 0.988059i | \(0.549241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.7493 | − | 16.0413i | −1.59207 | − | 0.597408i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.63206 | − | 1.63206i | −0.0606969 | − | 0.0606969i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.98457 | − | 9.98457i | −0.370818 | − | 0.370818i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.21095i | − | 0.119087i | −0.998226 | − | 0.0595437i | \(-0.981035\pi\) | ||
0.998226 | − | 0.0595437i | \(-0.0189646\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.9230 | + | 38.9230i | 1.43962 | + | 1.43962i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.97638 | + | 9.97638i | 0.368486 | + | 0.368486i | 0.866925 | − | 0.498439i | \(-0.166093\pi\) |
−0.498439 | + | 0.866925i | \(0.666093\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.98139 | + | 7.99271i | −0.257512 | + | 0.294815i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.5472 | −0.388513 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.7848 | − | 14.7848i | −0.543868 | − | 0.543868i | 0.380793 | − | 0.924660i | \(-0.375651\pi\) |
−0.924660 | + | 0.380793i | \(0.875651\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.00395445 | + | 0.00395445i | −0.000145270 | + | 0.000145270i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.4950 | 0.898634 | 0.449317 | − | 0.893372i | \(-0.351667\pi\) | ||||
0.449317 | + | 0.893372i | \(0.351667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.3385 | 0.525322 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.694961 | + | 0.694961i | 0.0254273 | + | 0.0254273i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.752631 | + | 1.65672i | 0.0275006 | + | 0.0605351i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 9.30768i | − | 0.339642i | −0.985475 | − | 0.169821i | \(-0.945681\pi\) | ||
0.985475 | − | 0.169821i | \(-0.0543190\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.66769 | −0.0972159 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.5521 | − | 12.5521i | 0.456817 | − | 0.456817i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.71911 | + | 4.71911i | 0.171519 | + | 0.171519i | 0.787647 | − | 0.616127i | \(-0.211299\pi\) |
−0.616127 | + | 0.787647i | \(0.711299\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 2.57755i | − | 0.0935593i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.21468 | 0.225282 | 0.112641 | − | 0.993636i | \(-0.464069\pi\) | ||||
0.112641 | + | 0.993636i | \(0.464069\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.10761 | + | 15.6455i | 0.257313 | + | 0.566405i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.28584 | + | 5.28584i | −0.191110 | + | 0.191110i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.14436i | 0.257968i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.6035i | 1.31995i | 0.751286 | + | 0.659977i | \(0.229434\pi\) | ||||
−0.751286 | + | 0.659977i | \(0.770566\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.25622 | − | 2.25622i | −0.0812559 | − | 0.0812559i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.9532 | − | 14.9532i | 0.537831 | − | 0.537831i | −0.385061 | − | 0.922891i | \(-0.625819\pi\) |
0.922891 | + | 0.385061i | \(0.125819\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.27543i | − | 0.117657i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.80731 | + | 23.4711i | −0.315961 | + | 0.842022i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0153509 | − | 0.0153509i | 0.000550003 | − | 0.000550003i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.79906 | + | 5.79906i | −0.207507 | + | 0.207507i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.22671 | −0.186787 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.8769 | −0.602363 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.5199 | + | 28.5199i | −1.01662 | + | 1.01662i | −0.0167646 | + | 0.999859i | \(0.505337\pi\) |
−0.999859 | + | 0.0167646i | \(0.994663\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.2265 | + | 14.2265i | −0.506478 | + | 0.506478i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.3161 | + | 40.8167i | −0.544577 | + | 1.45128i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.86448i | − | 0.0662097i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.00667 | + | 8.00667i | −0.283967 | + | 0.283967i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.0556 | + | 30.0556i | 1.06462 | + | 1.06462i | 0.997762 | + | 0.0668612i | \(0.0212985\pi\) |
0.0668612 | + | 0.997762i | \(0.478702\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 10.3367i | − | 0.365686i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.3938i | 0.579246i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.78731 | − | 8.78731i | 0.310098 | − | 0.310098i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.69552 | + | 5.93347i | 0.0950047 | + | 0.209127i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.2225 | 0.817469 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 42.1631i | − | 1.48238i | −0.671297 | − | 0.741188i | \(-0.734263\pi\) | ||
0.671297 | − | 0.741188i | \(-0.265737\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.2514 | − | 25.2514i | −0.886696 | − | 0.886696i | 0.107508 | − | 0.994204i | \(-0.465713\pi\) |
−0.994204 | + | 0.107508i | \(0.965713\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.4745 | − | 21.4745i | 0.753142 | − | 0.753142i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.92465 | 0.312617 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.116075i | 0.00406096i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.588586 | − | 1.29561i | −0.0205669 | − | 0.0452724i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.8479 | + | 20.8479i | 0.727597 | + | 0.727597i | 0.970140 | − | 0.242544i | \(-0.0779818\pi\) |
−0.242544 | + | 0.970140i | \(0.577982\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.9417 | −0.799696 | −0.399848 | − | 0.916582i | \(-0.630937\pi\) | ||||
−0.399848 | + | 0.916582i | \(0.630937\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.28586 | −0.149214 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.6173 | + | 16.6173i | −0.577841 | + | 0.577841i | −0.934308 | − | 0.356467i | \(-0.883981\pi\) |
0.356467 | + | 0.934308i | \(0.383981\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.4650 | − | 37.4650i | −1.30121 | − | 1.30121i | −0.927573 | − | 0.373641i | \(-0.878109\pi\) |
−0.373641 | − | 0.927573i | \(-0.621891\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.6139 | −0.992606 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.7059 | − | 25.9951i | 0.786714 | − | 0.900677i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.47725 | + | 5.47725i | 0.189548 | + | 0.189548i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.857310 | − | 0.857310i | −0.0296330 | − | 0.0296330i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 46.1798i | − | 1.59431i | −0.603778 | − | 0.797153i | \(-0.706339\pi\) | ||
0.603778 | − | 0.797153i | \(-0.293661\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.68150i | 0.0579827i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.1323 | − | 20.1323i | −0.693392 | − | 0.693392i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.6261 | + | 13.6261i | 0.468751 | + | 0.468751i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.0138 | − | 7.88523i | −0.722043 | − | 0.270940i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.56021 | −0.293786 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.8858 | + | 10.8858i | 0.373162 | + | 0.373162i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.7966 | + | 12.7966i | −0.438147 | + | 0.438147i | −0.891388 | − | 0.453241i | \(-0.850268\pi\) |
0.453241 | + | 0.891388i | \(0.350268\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0157633 | −0.000539095 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.6120 | 1.72887 | 0.864437 | − | 0.502741i | \(-0.167675\pi\) | ||||
0.864437 | + | 0.502741i | \(0.167675\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.5878 | + | 18.5878i | 0.634209 | + | 0.634209i | 0.949121 | − | 0.314912i | \(-0.101975\pi\) |
−0.314912 | + | 0.949121i | \(0.601975\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.28485 | + | 5.02948i | 0.0778674 | + | 0.171404i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 11.9291i | − | 0.406072i | −0.979171 | − | 0.203036i | \(-0.934919\pi\) | ||
0.979171 | − | 0.203036i | \(-0.0650809\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.9686 | 0.440947 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.17061 | − | 5.17061i | 0.175603 | − | 0.175603i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.22184 | + | 5.22184i | 0.177139 | + | 0.177139i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.57590i | 0.121165i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.8094 | −0.535067 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.1256 | − | 12.7772i | 0.950819 | − | 0.431949i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.656007 | − | 0.656007i | 0.0221518 | − | 0.0221518i | −0.695944 | − | 0.718096i | \(-0.745014\pi\) |
0.718096 | + | 0.695944i | \(0.245014\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.9319i | 0.537371i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.1066i | 0.845862i | 0.906162 | + | 0.422931i | \(0.138999\pi\) | ||||
−0.906162 | + | 0.422931i | \(0.861001\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.0181 | − | 23.0181i | −0.774622 | − | 0.774622i | 0.204289 | − | 0.978911i | \(-0.434512\pi\) |
−0.978911 | + | 0.204289i | \(0.934512\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.2395 | + | 14.2395i | −0.478657 | + | 0.478657i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.2156i | 1.18243i | 0.806516 | + | 0.591213i | \(0.201351\pi\) | ||||
−0.806516 | + | 0.591213i | \(0.798649\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.2902 | − | 10.9909i | −0.982362 | − | 0.368622i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.12178 | + | 1.12178i | −0.0375810 | + | 0.0375810i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.0154129 | − | 0.0154129i | 0.000515774 | − | 0.000515774i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.2925 | −0.812010 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.873886 | −0.0291782 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.48091 | − | 4.48091i | 0.149447 | − | 0.149447i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.0405 | − | 26.0405i | 0.867535 | − | 0.867535i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.6535 | − | 10.3767i | −0.920252 | − | 0.345316i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.70912i | 0.223019i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.59277 | + | 1.59277i | −0.0528870 | + | 0.0528870i | −0.733056 | − | 0.680169i | \(-0.761907\pi\) |
0.680169 | + | 0.733056i | \(0.261907\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.6943 | + | 11.6943i | 0.387876 | + | 0.387876i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.7779i | 0.655273i | 0.944804 | + | 0.327636i | \(0.106252\pi\) | ||||
−0.944804 | + | 0.327636i | \(0.893748\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.55918i | 0.0516014i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.71613 | − | 3.71613i | 0.122851 | − | 0.122851i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.9922 | − | 33.0014i | −0.495088 | − | 1.08980i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.7184 | −0.452528 | −0.226264 | − | 0.974066i | \(-0.572651\pi\) | ||||
−0.226264 | + | 0.974066i | \(0.572651\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.1799i | 0.928558i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.96609 | + | 1.96609i | 0.0647148 | + | 0.0647148i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.1005 | − | 18.1005i | 0.595142 | − | 0.595142i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.2578 | 0.566821 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 37.2406i | − | 1.22182i | −0.791698 | − | 0.610912i | \(-0.790803\pi\) | ||
0.791698 | − | 0.610912i | \(-0.209197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0726176 | − | 0.00490444i | 0.00237995 | − | 0.000160736i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.76655 | + | 5.76655i | 0.188789 | + | 0.188789i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.8591 | −0.387833 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.5853 | 0.443813 | 0.221906 | − | 0.975068i | \(-0.428772\pi\) | ||||
0.221906 | + | 0.975068i | \(0.428772\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.2100 | − | 20.2100i | 0.659528 | − | 0.659528i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.5023 | − | 18.5023i | −0.603158 | − | 0.603158i | 0.337991 | − | 0.941149i | \(-0.390253\pi\) |
−0.941149 | + | 0.337991i | \(0.890253\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.39236 | 0.110471 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.40919 | − | 3.75542i | 0.0458409 | − | 0.122164i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.34969 | − | 1.34969i | −0.0438590 | − | 0.0438590i | 0.684837 | − | 0.728696i | \(-0.259873\pi\) |
−0.728696 | + | 0.684837i | \(0.759873\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.97922 | − | 2.97922i | −0.0967097 | − | 0.0967097i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 18.0687i | − | 0.585917i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.8779i | 1.38895i | 0.719516 | + | 0.694476i | \(0.244364\pi\) | ||||
−0.719516 | + | 0.694476i | \(0.755636\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.0617 | − | 12.0617i | −0.390308 | − | 0.390308i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.86320 | − | 5.86320i | −0.189530 | − | 0.189530i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.58262 | − | 0.593864i | −0.0511055 | − | 0.0191769i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5300 | −0.952582 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.486324 | − | 0.486324i | −0.0156716 | − | 0.0156716i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.7281 | + | 16.7281i | −0.538496 | + | 0.538496i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.9878 | 1.67181 | 0.835907 | − | 0.548871i | \(-0.184942\pi\) | ||||
0.835907 | + | 0.548871i | \(0.184942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0512679 | 0.00164696 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.444804 | − | 0.444804i | −0.0142744 | − | 0.0142744i | 0.699934 | − | 0.714208i | \(-0.253213\pi\) |
−0.714208 | + | 0.699934i | \(0.753213\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.9340 | + | 13.5988i | −0.959641 | + | 0.435956i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.45306i | 0.0465353i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.31426 | −0.265997 | −0.132998 | − | 0.991116i | \(-0.542461\pi\) | ||||
−0.132998 | + | 0.991116i | \(0.542461\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.3902 | + | 18.3902i | −0.587752 | + | 0.587752i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.59269 | − | 4.59269i | −0.146633 | − | 0.146633i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 20.8780i | − | 0.665903i | −0.942944 | − | 0.332952i | \(-0.891955\pi\) | ||
0.942944 | − | 0.332952i | \(-0.108045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.4825 | −0.461452 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.29409 | + | 5.04981i | 0.0730215 | + | 0.160737i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.8256 | + | 12.8256i | −0.407831 | + | 0.407831i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.7988i | 1.16895i | 0.811411 | + | 0.584476i | \(0.198700\pi\) | ||||
−0.811411 | + | 0.584476i | \(0.801300\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.3744i | 0.678296i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.0821 | + | 24.0821i | 0.763455 | + | 0.763455i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.9272 | − | 14.9272i | 0.472748 | − | 0.472748i | −0.430055 | − | 0.902803i | \(-0.641506\pi\) |
0.902803 | + | 0.430055i | \(0.141506\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 9.47525i | − | 0.299784i |
(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 | 1344.2.u.a.1231.7 | 64 | ||
4.3 | odd | 2 | 336.2.u.a.139.32 | yes | 64 | ||
7.6 | odd | 2 | inner | 1344.2.u.a.1231.26 | 64 | ||
16.3 | odd | 4 | inner | 1344.2.u.a.559.26 | 64 | ||
16.13 | even | 4 | 336.2.u.a.307.31 | yes | 64 | ||
28.27 | even | 2 | 336.2.u.a.139.31 | ✓ | 64 | ||
112.13 | odd | 4 | 336.2.u.a.307.32 | yes | 64 | ||
112.83 | even | 4 | inner | 1344.2.u.a.559.7 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.u.a.139.31 | ✓ | 64 | 28.27 | even | 2 | ||
336.2.u.a.139.32 | yes | 64 | 4.3 | odd | 2 | ||
336.2.u.a.307.31 | yes | 64 | 16.13 | even | 4 | ||
336.2.u.a.307.32 | yes | 64 | 112.13 | odd | 4 | ||
1344.2.u.a.559.7 | 64 | 112.83 | even | 4 | inner | ||
1344.2.u.a.559.26 | 64 | 16.3 | odd | 4 | inner | ||
1344.2.u.a.1231.7 | 64 | 1.1 | even | 1 | trivial | ||
1344.2.u.a.1231.26 | 64 | 7.6 | odd | 2 | inner |