Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(33,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 11]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.bk (of order \(12\), degree \(4\), 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: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 33.1 | ||
Root | \(1.49418i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.33 |
Dual form | 260.2.bk.c.197.1 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{11}{12}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.51912 | + | 0.674996i | −1.45441 | + | 0.389709i | −0.897557 | − | 0.440899i | \(-0.854660\pi\) |
−0.556857 | + | 0.830608i | \(0.687993\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.14030 | − | 0.647383i | 0.957172 | − | 0.289518i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.45437 | + | 0.839682i | −0.549701 | + | 0.317370i | −0.749001 | − | 0.662568i | \(-0.769466\pi\) |
0.199300 | + | 0.979938i | \(0.436133\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.29226 | − | 1.90079i | 1.09742 | − | 0.633596i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.758596 | + | 2.83112i | 0.228725 | + | 0.853614i | 0.980878 | + | 0.194625i | \(0.0623490\pi\) |
−0.752153 | + | 0.658989i | \(0.770984\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.727792 | + | 3.53133i | 0.201853 | + | 0.979416i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.95470 | + | 3.07553i | −1.27930 | + | 0.794098i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.11795 | + | 7.90430i | −0.513679 | + | 1.91707i | −0.137597 | + | 0.990488i | \(0.543938\pi\) |
−0.376082 | + | 0.926587i | \(0.622729\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.32093 | − | 0.621891i | −0.532458 | − | 0.142672i | −0.0174347 | − | 0.999848i | \(-0.505550\pi\) |
−0.515023 | + | 0.857176i | \(0.672217\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.09695 | − | 3.09695i | 0.675811 | − | 0.675811i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.421590 | + | 1.57340i | 0.0879077 | + | 0.328076i | 0.995849 | − | 0.0910215i | \(-0.0290132\pi\) |
−0.907941 | + | 0.419098i | \(0.862347\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.16179 | − | 2.77119i | 0.832358 | − | 0.554238i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.47820 | + | 1.47820i | −0.284480 | + | 0.284480i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.41580 | − | 1.39477i | −0.448604 | − | 0.259001i | 0.258637 | − | 0.965975i | \(-0.416727\pi\) |
−0.707240 | + | 0.706973i | \(0.750060\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.32419 | + | 7.32419i | 1.31546 | + | 1.31546i | 0.917326 | + | 0.398137i | \(0.130343\pi\) |
0.398137 | + | 0.917326i | \(0.369657\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.82198 | − | 6.61987i | −0.665322 | − | 1.15237i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.56920 | + | 2.73871i | −0.434274 | + | 0.462926i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.60763 | − | 2.08286i | −0.593090 | − | 0.342421i | 0.173228 | − | 0.984882i | \(-0.444580\pi\) |
−0.766318 | + | 0.642461i | \(0.777913\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.21703 | − | 8.40459i | −0.675265 | − | 1.34581i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.77856 | − | 1.28041i | 0.746286 | − | 0.199967i | 0.134416 | − | 0.990925i | \(-0.457084\pi\) |
0.611870 | + | 0.790958i | \(0.290418\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.93456 | + | 0.786313i | 0.447516 | + | 0.119912i | 0.475537 | − | 0.879696i | \(-0.342254\pi\) |
−0.0280207 | + | 0.999607i | \(0.508920\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.81590 | − | 6.19961i | 0.866983 | − | 0.924184i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.5504i | − | 1.53894i | −0.638685 | − | 0.769469i | \(-0.720521\pi\) | ||
0.638685 | − | 0.769469i | \(-0.279479\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.08987 | + | 3.61976i | −0.298553 | + | 0.517108i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 21.3415i | − | 2.98840i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.66320 | − | 6.66320i | −0.915261 | − | 0.915261i | 0.0814188 | − | 0.996680i | \(-0.474055\pi\) |
−0.996680 | + | 0.0814188i | \(0.974055\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.45644 | + | 5.56835i | 0.466066 | + | 0.750836i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.26647 | 0.830014 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.16609 | − | 4.35192i | 0.151812 | − | 0.566572i | −0.847545 | − | 0.530724i | \(-0.821920\pi\) |
0.999357 | − | 0.0358480i | \(-0.0114132\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.16875 | − | 3.75639i | −0.277680 | − | 0.480956i | 0.693128 | − | 0.720815i | \(-0.256232\pi\) |
−0.970808 | + | 0.239859i | \(0.922899\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.19211 | + | 5.52891i | −0.402169 | + | 0.696577i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.84382 | + | 7.08696i | 0.476767 | + | 0.879030i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.47460 | + | 4.28613i | −0.302320 | + | 0.523634i | −0.976661 | − | 0.214786i | \(-0.931095\pi\) |
0.674341 | + | 0.738420i | \(0.264428\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.12407 | − | 3.67900i | −0.255708 | − | 0.442900i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.63607 | − | 6.10591i | 0.194166 | − | 0.724639i | −0.798315 | − | 0.602240i | \(-0.794275\pi\) |
0.992481 | − | 0.122398i | \(-0.0390585\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.13327 | 0.834886 | 0.417443 | − | 0.908703i | \(-0.362926\pi\) | ||||
0.417443 | + | 0.908703i | \(0.362926\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.61350 | + | 9.79014i | −0.994602 | + | 1.13047i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.48052 | − | 3.48052i | −0.396642 | − | 0.396642i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.73120i | 1.09485i | 0.836856 | + | 0.547423i | \(0.184391\pi\) | ||||
−0.836856 | + | 0.547423i | \(0.815609\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.97638 | + | 5.15523i | −0.330708 | + | 0.572804i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.67496i | 0.732672i | 0.930483 | + | 0.366336i | \(0.119388\pi\) | ||||
−0.930483 | + | 0.366336i | \(0.880612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.584050 | + | 18.2887i | 0.0633492 | + | 1.98369i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.02716 | + | 1.88292i | 0.753390 | + | 0.201870i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.578139 | + | 0.154912i | −0.0612826 | + | 0.0164206i | −0.289330 | − | 0.957229i | \(-0.593433\pi\) |
0.228047 | + | 0.973650i | \(0.426766\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.02368 | − | 4.52476i | −0.421796 | − | 0.474324i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.3943 | − | 13.5067i | −2.42588 | − | 1.40058i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.37009 | + | 0.171494i | −0.550960 | + | 0.0175949i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.03380 | + | 10.4508i | 0.612639 | + | 1.06112i | 0.990794 | + | 0.135380i | \(0.0432254\pi\) |
−0.378155 | + | 0.925742i | \(0.623441\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.87885 | + | 7.87885i | 0.791854 | + | 0.791854i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.73824 | + | 1.00357i | 0.172961 | + | 0.0998590i | 0.583981 | − | 0.811767i | \(-0.301494\pi\) |
−0.411020 | + | 0.911626i | \(0.634827\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.87986 | − | 6.87986i | 0.677892 | − | 0.677892i | −0.281631 | − | 0.959523i | \(-0.590875\pi\) |
0.959523 | + | 0.281631i | \(0.0908753\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.62350 | − | 8.63333i | 0.451208 | − | 0.842527i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.716027 | − | 2.67225i | −0.0692209 | − | 0.258336i | 0.922640 | − | 0.385662i | \(-0.126027\pi\) |
−0.991861 | + | 0.127327i | \(0.959360\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.04868 | + | 1.04868i | −0.100445 | + | 0.100445i | −0.755544 | − | 0.655098i | \(-0.772627\pi\) |
0.655098 | + | 0.755544i | \(0.272627\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.4940 | + | 2.81185i | 0.996042 | + | 0.266889i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.04332 | − | 15.0899i | 0.380363 | − | 1.41953i | −0.464985 | − | 0.885319i | \(-0.653940\pi\) |
0.845348 | − | 0.534216i | \(-0.179393\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.92092 | + | 3.09462i | 0.179127 | + | 0.288574i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.10840 | + | 10.2427i | 0.842072 | + | 0.946937i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.55681 | − | 13.2742i | −0.326052 | − | 1.21684i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.08652 | − | 1.20465i | 0.189684 | − | 0.109514i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.1735 | + | 6.45102i | −1.00748 | + | 0.581669i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.11347 | − | 8.62546i | 0.636248 | − | 0.771484i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.4949 | − | 4.41981i | 1.46369 | − | 0.392194i | 0.562927 | − | 0.826507i | \(-0.309675\pi\) |
0.900762 | + | 0.434312i | \(0.143009\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.92326 | −0.697604 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.6221 | −1.45228 | −0.726139 | − | 0.687548i | \(-0.758687\pi\) | ||||
−0.726139 | + | 0.687548i | \(0.758687\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.89768 | − | 1.04438i | 0.337972 | − | 0.0905594i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.20684 | + | 4.12077i | −0.189935 | + | 0.354659i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.1199 | + | 5.84275i | −0.864605 | + | 0.499180i | −0.865552 | − | 0.500819i | \(-0.833032\pi\) |
0.000946524 | 1.00000i | \(0.499699\pi\) | ||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.95180 | + | 1.70422i | −0.250368 | + | 0.144550i | −0.619933 | − | 0.784655i | \(-0.712840\pi\) |
0.369565 | + | 0.929205i | \(0.379507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.12149 | + | 26.5778i | 0.599738 | + | 2.23825i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.44552 | + | 4.73932i | −0.789874 | + | 0.396322i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.07350 | − | 1.42127i | −0.504377 | − | 0.118030i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.82130 | − | 10.5292i | 0.232697 | − | 0.868438i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.18213 | − | 2.19240i | −0.670306 | − | 0.179608i | −0.0924136 | − | 0.995721i | \(-0.529458\pi\) |
−0.577893 | + | 0.816113i | \(0.696125\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.28831 | + | 8.28831i | −0.674493 | + | 0.674493i | −0.958749 | − | 0.284255i | \(-0.908254\pi\) |
0.284255 | + | 0.958749i | \(0.408254\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.05155 | + | 30.0488i | 0.650929 | + | 2.42930i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.4175 | + | 10.9344i | 1.63998 | + | 0.878275i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.70757 | − | 6.70757i | 0.535322 | − | 0.535322i | −0.386829 | − | 0.922151i | \(-0.626430\pi\) |
0.922151 | + | 0.386829i | \(0.126430\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.2830 | + | 12.2878i | 1.68785 | + | 0.974483i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.93430 | − | 1.93430i | −0.152444 | − | 0.152444i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.22873 | − | 12.5205i | −0.566198 | − | 0.980683i | −0.996937 | − | 0.0782070i | \(-0.975080\pi\) |
0.430739 | − | 0.902476i | \(-0.358253\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.4658 | − | 11.6942i | −0.970461 | − | 0.910396i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.61311 | − | 3.81808i | −0.511738 | − | 0.295452i | 0.221810 | − | 0.975090i | \(-0.428804\pi\) |
−0.733548 | + | 0.679638i | \(0.762137\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9406 | + | 5.14016i | −0.918510 | + | 0.395397i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.82319 | + | 2.36417i | −0.674726 | + | 0.180792i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.7032 | + | 6.08331i | 1.72609 | + | 0.462505i | 0.979277 | − | 0.202526i | \(-0.0649150\pi\) |
0.746816 | + | 0.665031i | \(0.231582\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.72588 | + | 7.52492i | −0.281650 | + | 0.568831i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.7501i | 0.883193i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.3426 | − | 21.3780i | 0.922530 | − | 1.59787i | 0.127045 | − | 0.991897i | \(-0.459451\pi\) |
0.795486 | − | 0.605973i | \(-0.207216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.35761i | − | 0.472557i | −0.971685 | − | 0.236279i | \(-0.924072\pi\) | ||
0.971685 | − | 0.236279i | \(-0.0759278\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.99888 | + | 7.99888i | 0.591294 | + | 0.591294i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.06982 | − | 2.12244i | −0.666826 | − | 0.156045i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.9847 | −1.75393 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.908637 | − | 3.39108i | 0.0660936 | − | 0.246665i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.43459 | + | 9.41299i | 0.393233 | + | 0.681100i | 0.992874 | − | 0.119169i | \(-0.0380232\pi\) |
−0.599641 | + | 0.800269i | \(0.704690\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.07014 | − | 13.9779i | 0.580901 | − | 1.00615i | −0.414471 | − | 0.910062i | \(-0.636034\pi\) |
0.995373 | − | 0.0960884i | \(-0.0306332\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.4667 | − | 15.2583i | −1.03598 | − | 1.09267i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.68699 | + | 11.5822i | −0.476428 | + | 0.825198i | −0.999635 | − | 0.0270075i | \(-0.991402\pi\) |
0.523207 | + | 0.852206i | \(0.324736\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5547 | + | 18.2812i | 0.748199 | + | 1.29592i | 0.948685 | + | 0.316223i | \(0.102415\pi\) |
−0.200485 | + | 0.979697i | \(0.564252\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.34069 | − | 12.4676i | 0.235634 | − | 0.879398i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.68464 | 0.328797 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.39865 | − | 5.83403i | 0.656430 | − | 0.407466i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.37868 | + | 4.37868i | 0.304339 | + | 0.304339i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 7.04259i | − | 0.487146i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.38134 | − | 14.5169i | 0.576995 | − | 0.999385i | −0.418826 | − | 0.908066i | \(-0.637558\pi\) |
0.995822 | − | 0.0913189i | \(-0.0291082\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.4859i | 1.12959i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.78989 | − | 0.216835i | 0.463067 | − | 0.0147880i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.8021 | − | 4.50211i | −1.14060 | − | 0.305623i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.9695 | + | 4.81492i | −1.21427 | + | 0.325362i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.4542 | − | 1.72650i | −1.98130 | − | 0.116137i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.13130 | + | 1.80786i | 0.209688 | + | 0.121063i | 0.601166 | − | 0.799124i | \(-0.294703\pi\) |
−0.391479 | + | 0.920187i | \(0.628036\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.43426 | − | 17.0342i | 0.562284 | − | 1.13561i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.24896 | − | 10.8235i | −0.414758 | − | 0.718382i | 0.580645 | − | 0.814157i | \(-0.302800\pi\) |
−0.995403 | + | 0.0957751i | \(0.969467\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.8049 | + | 19.8049i | 1.30874 | + | 1.30874i | 0.922324 | + | 0.386417i | \(0.126288\pi\) |
0.386417 | + | 0.922324i | \(0.373712\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.1172 | + | 6.41850i | 0.731456 | + | 0.422307i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.31519 | + | 8.31519i | −0.544746 | + | 0.544746i | −0.924917 | − | 0.380170i | \(-0.875865\pi\) |
0.380170 | + | 0.924917i | \(0.375865\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.83016 | − | 22.5811i | −0.445550 | − | 1.47303i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.56852 | − | 24.5140i | −0.426671 | − | 1.59236i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.12430 | − | 1.12430i | 0.0727249 | − | 0.0727249i | −0.669809 | − | 0.742534i | \(-0.733624\pi\) |
0.742534 | + | 0.669809i | \(0.233624\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0900 | + | 5.91899i | 1.42294 | + | 0.381275i | 0.886525 | − | 0.462680i | \(-0.153112\pi\) |
0.536414 | + | 0.843955i | \(0.319779\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.64126 | − | 21.0535i | 0.361887 | − | 1.35058i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.12958 | + | 9.10032i | −0.136054 | + | 0.581398i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.506950 | − | 8.64858i | 0.0322565 | − | 0.550296i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.50557 | − | 16.8150i | −0.285529 | − | 1.06561i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.8530 | − | 7.42069i | 0.811275 | − | 0.468390i | −0.0361238 | − | 0.999347i | \(-0.511501\pi\) |
0.847398 | + | 0.530958i | \(0.178168\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.13466 | + | 2.38714i | −0.259944 | + | 0.150079i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.8161 | − | 45.6772i | −0.865198 | − | 2.86042i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.44452 | + | 2.26270i | −0.526754 | + | 0.141143i | −0.512389 | − | 0.858753i | \(-0.671239\pi\) |
−0.0143653 | + | 0.999897i | \(0.504573\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.99577 | 0.434696 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.6046 | −0.656409 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.7547 | − | 4.75737i | 1.09480 | − | 0.293352i | 0.334157 | − | 0.942517i | \(-0.391548\pi\) |
0.760647 | + | 0.649166i | \(0.224882\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.5749 | − | 9.94763i | −1.14105 | − | 0.611078i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.35184 | − | 0.780483i | 0.0827310 | − | 0.0477648i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.29173 | − | 5.36458i | 0.566526 | − | 0.327084i | −0.189234 | − | 0.981932i | \(-0.560601\pi\) |
0.755761 | + | 0.654848i | \(0.227267\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.32705 | + | 23.6129i | 0.384341 | + | 1.43438i | 0.839204 | + | 0.543817i | \(0.183022\pi\) |
−0.454863 | + | 0.890562i | \(0.650312\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.1903 | + | 8.68244i | 0.798314 | + | 0.525485i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.0027 | + | 9.68031i | 0.663487 | + | 0.583745i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.99634 | − | 26.1107i | 0.420369 | − | 1.56884i | −0.353463 | − | 0.935448i | \(-0.614996\pi\) |
0.773832 | − | 0.633390i | \(-0.218337\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 38.0349 | + | 10.1914i | 2.27709 | + | 0.610144i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.7650 | + | 20.7650i | −1.23874 | + | 1.23874i | −0.278218 | + | 0.960518i | \(0.589744\pi\) |
−0.960518 | + | 0.278218i | \(0.910256\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.09550 | + | 11.5526i | 0.184008 | + | 0.686729i | 0.994841 | + | 0.101450i | \(0.0323483\pi\) |
−0.810832 | + | 0.585279i | \(0.800985\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.4121 | − | 4.05680i | 0.794466 | − | 0.240304i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.87467 | + | 5.87467i | −0.346771 | + | 0.346771i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −43.2698 | − | 24.9819i | −2.54528 | − | 1.46952i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.2541 | − | 22.2541i | −1.30456 | − | 1.30456i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.86338 | + | 10.1557i | 0.342542 | + | 0.593301i | 0.984904 | − | 0.173101i | \(-0.0553786\pi\) |
−0.642362 | + | 0.766402i | \(0.722045\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.321564 | − | 10.0693i | −0.0187222 | − | 0.586260i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.30633 | − | 3.06361i | −0.307904 | − | 0.177769i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.24936 | + | 2.63388i | −0.303578 | + | 0.152321i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.92820 | + | 1.32051i | −0.284057 | + | 0.0761127i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.05623 | − | 1.35481i | −0.290473 | − | 0.0778319i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.07360 | − | 6.63579i | −0.405033 | − | 0.379964i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.5100i | 0.999348i | 0.866214 | + | 0.499674i | \(0.166547\pi\) | ||||
−0.866214 | + | 0.499674i | \(0.833453\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.6873 | + | 21.9750i | −0.721755 | + | 1.25012i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 18.3218i | − | 1.03893i | −0.854491 | − | 0.519467i | \(-0.826131\pi\) | ||
0.854491 | − | 0.519467i | \(-0.173869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.75747 | + | 4.75747i | 0.268908 | + | 0.268908i | 0.828660 | − | 0.559752i | \(-0.189104\pi\) |
−0.559752 | + | 0.828660i | \(0.689104\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.25278 | + | 13.9001i | −0.183273 | + | 0.783179i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.5858 | 1.60554 | 0.802768 | − | 0.596291i | \(-0.203359\pi\) | ||||
0.802768 | + | 0.596291i | \(0.203359\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.11613 | − | 7.89749i | 0.118480 | − | 0.442174i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.60751 | + | 6.24839i | 0.201352 | + | 0.348751i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.83123 | − | 17.0282i | 0.547024 | − | 0.947474i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.8149 | + | 12.6798i | 0.710844 | + | 0.703350i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.93390 | − | 3.34960i | 0.106945 | − | 0.185234i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.85900 | + | 15.3442i | 0.488413 | + | 0.845955i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.56323 | + | 20.7622i | −0.305783 | + | 1.14120i | 0.626487 | + | 0.779432i | \(0.284492\pi\) |
−0.932270 | + | 0.361764i | \(0.882175\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.8363 | −0.867825 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.52162 | + | 10.7756i | −0.137771 | + | 0.588736i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5568 | + | 12.5568i | 0.684010 | + | 0.684010i | 0.960901 | − | 0.276891i | \(-0.0893042\pi\) |
−0.276891 | + | 0.960901i | \(0.589304\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 40.7424i | 2.21282i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.1795 | + | 26.2917i | −0.822018 | + | 1.42378i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.7748i | − | 1.01375i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.92788 | − | 6.49909i | −0.372985 | − | 0.349899i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.96312 | − | 1.06192i | −0.212751 | − | 0.0570066i | 0.150869 | − | 0.988554i | \(-0.451793\pi\) |
−0.363620 | + | 0.931547i | \(0.618459\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.89219 | + | 0.507011i | −0.101287 | + | 0.0271397i | −0.309106 | − | 0.951027i | \(-0.600030\pi\) |
0.207820 | + | 0.978167i | \(0.433363\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.29586 | − | 4.14420i | −0.336048 | − | 0.221201i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.69208 | − | 1.55427i | −0.143285 | − | 0.0827256i | 0.426644 | − | 0.904420i | \(-0.359696\pi\) |
−0.569929 | + | 0.821694i | \(0.693029\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.451167 | − | 14.1277i | −0.0239455 | − | 0.749819i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.9201 | + | 31.0385i | 0.948430 | + | 1.64273i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.98593 | + | 6.98593i | 0.368703 | + | 0.368703i | 0.867004 | − | 0.498301i | \(-0.166043\pi\) |
−0.498301 | + | 0.867004i | \(0.666043\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.4545 | − | 6.61327i | −0.602870 | − | 0.348067i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.44305 | + | 4.44305i | −0.233200 | + | 0.233200i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.2673 | − | 4.61795i | 0.799130 | − | 0.241715i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.336651 | + | 1.25640i | 0.0175731 | + | 0.0655835i | 0.974156 | − | 0.225878i | \(-0.0725251\pi\) |
−0.956583 | + | 0.291462i | \(0.905858\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.2985 | − | 13.2985i | 0.692291 | − | 0.692291i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.2857 | + | 4.09580i | 0.793596 | + | 0.212644i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.233395 | + | 0.871043i | −0.0120847 | + | 0.0451009i | −0.971705 | − | 0.236198i | \(-0.924099\pi\) |
0.959620 | + | 0.281299i | \(0.0907653\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0975 | + | 26.5301i | −0.624714 | + | 1.37001i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.16718 | − | 9.54611i | 0.163118 | − | 0.491650i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.97268 | + | 14.8263i | 0.204063 | + | 0.761574i | 0.989733 | + | 0.142928i | \(0.0456517\pi\) |
−0.785670 | + | 0.618646i | \(0.787682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −38.5694 | + | 22.2680i | −1.97597 | + | 1.14083i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.0835 | + | 6.39904i | −0.566339 | + | 0.326976i | −0.755686 | − | 0.654935i | \(-0.772696\pi\) |
0.189347 | + | 0.981910i | \(0.439363\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.70259 | − | 5.19614i | −0.494490 | − | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.1560 | − | 2.98923i | 0.567089 | − | 0.151951i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.5057 | −0.836870 | −0.418435 | − | 0.908247i | \(-0.637421\pi\) | ||||
−0.418435 | + | 0.908247i | \(0.637421\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.3295 | −0.674103 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 41.8730 | − | 11.2198i | 2.11221 | − | 0.565966i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.29981 | + | 20.8277i | 0.316978 | + | 1.04796i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.12829 | − | 4.11552i | 0.357759 | − | 0.206552i | −0.310338 | − | 0.950626i | \(-0.600442\pi\) |
0.668097 | + | 0.744074i | \(0.267109\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.11377 | + | 5.26184i | −0.456259 | + | 0.263422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.17051 | − | 26.7607i | −0.358078 | − | 1.33637i | −0.876566 | − | 0.481281i | \(-0.840172\pi\) |
0.518488 | − | 0.855085i | \(-0.326495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.5337 | + | 31.1946i | −1.02285 | + | 1.55392i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.03294 | + | 12.9606i | −0.150708 | + | 0.644018i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.16010 | − | 11.7937i | 0.156640 | − | 0.584590i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.8703 | − | 4.78835i | −0.883632 | − | 0.236768i | −0.211658 | − | 0.977344i | \(-0.567886\pi\) |
−0.671973 | + | 0.740575i | \(0.734553\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.5495 | − | 21.5495i | 1.06296 | − | 1.06296i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.95830 | + | 7.30846i | 0.0963615 | + | 0.359626i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.32125 | + | 14.2864i | 0.212122 | + | 0.701293i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.28558 | − | 6.28558i | 0.307806 | − | 0.307806i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.72308 | + | 2.14952i | 0.181884 | + | 0.105011i | 0.588178 | − | 0.808732i | \(-0.299846\pi\) |
−0.406293 | + | 0.913743i | \(0.633179\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.99925 | + | 6.99925i | 0.341123 | + | 0.341123i | 0.856789 | − | 0.515667i | \(-0.172456\pi\) |
−0.515667 | + | 0.856789i | \(0.672456\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.0541 | − | 34.7347i | −0.975064 | − | 1.68886i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.0898 | + | 38.7653i | 0.634951 | + | 1.88039i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.30834 | + | 3.64212i | 0.305282 | + | 0.176255i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.5954 | − | 18.3146i | 0.994354 | − | 0.884237i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.26467 | − | 0.338868i | 0.0609171 | − | 0.0163227i | −0.228232 | − | 0.973607i | \(-0.573294\pi\) |
0.289149 | + | 0.957284i | \(0.406628\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0767 | − | 2.70003i | −0.484253 | − | 0.129755i | 0.00842905 | − | 0.999964i | \(-0.497317\pi\) |
−0.492682 | + | 0.870209i | \(0.663984\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.2592 | − | 0.519238i | 0.779570 | − | 0.0248956i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 3.91393i | − | 0.187228i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.6918 | − | 23.7150i | 0.653476 | − | 1.13185i | −0.328798 | − | 0.944400i | \(-0.606643\pi\) |
0.982274 | − | 0.187453i | \(-0.0600232\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.8896i | 0.756647i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.05524 | − | 2.05524i | −0.0976474 | − | 0.0976474i | 0.656595 | − | 0.754243i | \(-0.271996\pi\) |
−0.754243 | + | 0.656595i | \(0.771996\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.13711 | + | 0.705835i | −0.0539040 | + | 0.0334598i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.0916 | 1.04490 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.73279 | − | 6.46685i | 0.0817753 | − | 0.305190i | −0.912909 | − | 0.408164i | \(-0.866169\pi\) |
0.994684 | + | 0.102974i | \(0.0328359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.24999 | + | 12.5574i | 0.341389 | + | 0.591303i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.2847 | − | 26.4738i | 0.718136 | − | 1.24385i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.5411 | − | 7.07949i | −0.541057 | − | 0.331892i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.2163 | − | 19.4272i | 0.524677 | − | 0.908768i | −0.474910 | − | 0.880034i | \(-0.657519\pi\) |
0.999587 | − | 0.0287333i | \(-0.00914734\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.55340 | − | 14.8149i | −0.399239 | − | 0.691502i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.83936 | − | 25.5248i | 0.318541 | − | 1.18881i | −0.602107 | − | 0.798416i | \(-0.705672\pi\) |
0.920647 | − | 0.390395i | \(-0.127662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.6621 | −0.913777 | −0.456888 | − | 0.889524i | \(-0.651036\pi\) | ||||
−0.456888 | + | 0.889524i | \(0.651036\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −58.8149 | − | 13.7634i | −2.72747 | − | 0.638261i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.598955 | + | 0.598955i | 0.0277163 | + | 0.0277163i | 0.720829 | − | 0.693113i | \(-0.243761\pi\) |
−0.693113 | + | 0.720829i | \(0.743761\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 8.31151i | − | 0.383790i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.3696 | + | 21.4247i | −0.569960 | + | 0.987200i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.90458i | 0.409433i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.3826 | + | 3.84355i | −0.522269 | + | 0.176354i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −34.6023 | − | 9.27167i | −1.58433 | − | 0.424520i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.1500 | − | 4.05942i | 0.692220 | − | 0.185480i | 0.104477 | − | 0.994527i | \(-0.466683\pi\) |
0.587743 | + | 0.809048i | \(0.300017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.72968 | − | 14.2556i | 0.215655 | − | 0.650000i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.17838 | + | 3.56709i | 0.281126 | + | 0.162308i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.6798 | + | 18.4618i | 0.893616 | + | 0.838307i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.5156 | − | 19.9455i | −0.521820 | − | 0.903818i | −0.999678 | − | 0.0253810i | \(-0.991920\pi\) |
0.477858 | − | 0.878437i | \(-0.341413\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 26.6613 | + | 26.6613i | 1.20567 | + | 1.20567i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.0505 | − | 14.4629i | −1.13051 | − | 0.652702i | −0.186449 | − | 0.982465i | \(-0.559698\pi\) |
−0.944064 | + | 0.329762i | \(0.893031\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.1412 | − | 16.1412i | 0.726963 | − | 0.726963i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21.9638 | + | 11.7625i | 0.987197 | + | 0.528685i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.74757 | + | 10.2541i | 0.123245 | + | 0.459957i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.5783 | + | 16.5783i | −0.742147 | + | 0.742147i | −0.972991 | − | 0.230844i | \(-0.925851\pi\) |
0.230844 | + | 0.972991i | \(0.425851\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.2364 | + | 5.15438i | 0.859419 | + | 0.230281i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.86494 | + | 18.1562i | −0.216917 | + | 0.809545i | 0.768566 | + | 0.639771i | \(0.220971\pi\) |
−0.985483 | + | 0.169775i | \(0.945696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.37005 | + | 1.02264i | 0.194464 | + | 0.0455070i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 26.6103 | − | 21.0085i | 1.18180 | − | 0.933022i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.12866 | + | 26.6045i | 0.315972 | + | 1.17922i | 0.923081 | + | 0.384606i | \(0.125663\pi\) |
−0.607109 | + | 0.794619i | \(0.707671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.3744 | + | 5.98968i | −0.458937 | + | 0.264968i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.35009 | − | 2.51152i | 0.192061 | − | 0.110886i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.2711 | − | 19.1789i | 0.452598 | − | 0.845122i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.8695 | − | 8.00350i | 1.31366 | − | 0.351994i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −61.2983 | −2.69069 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.4504 | 0.545463 | 0.272731 | − | 0.962090i | \(-0.412073\pi\) | ||||
0.272731 | + | 0.962090i | \(0.412073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.3767 | + | 3.31632i | −0.541194 | + | 0.145012i | −0.519052 | − | 0.854742i | \(-0.673715\pi\) |
−0.0221413 | + | 0.999755i | \(0.507048\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.30663 | − | 21.4711i | 0.187957 | − | 0.937076i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −73.4049 | + | 42.3803i | −3.19757 | + | 1.84612i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.6207 | − | 10.1733i | 0.766119 | − | 0.442319i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.43299 | − | 16.5442i | −0.192376 | − | 0.717955i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.99936 | + | 15.9428i | 0.346491 | + | 0.690560i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.26248 | − | 5.25588i | −0.141049 | − | 0.227231i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.6624 | + | 62.1850i | −0.719037 | + | 2.68348i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.8333 | − | 3.17073i | −0.509697 | − | 0.136573i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7555 | − | 14.7555i | 0.634390 | − | 0.634390i | −0.314776 | − | 0.949166i | \(-0.601929\pi\) |
0.949166 | + | 0.314776i | \(0.101929\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.29136 | + | 16.0156i | 0.184160 | + | 0.687294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.56560 | + | 2.92339i | −0.0670628 | + | 0.125224i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.8130 | + | 12.8130i | −0.547845 | + | 0.547845i | −0.925817 | − | 0.377972i | \(-0.876621\pi\) |
0.377972 | + | 0.925817i | \(0.376621\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.2802 | − | 8.24467i | −0.609463 | − | 0.351874i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.73952 | + | 4.73952i | 0.201910 | + | 0.201910i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.17111 | − | 14.1528i | −0.347471 | − | 0.601837i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.2806 | − | 0.775401i | 1.03065 | − | 0.0329139i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.635888 | + | 0.367130i | 0.0269435 | + | 0.0155558i | 0.513411 | − | 0.858143i | \(-0.328382\pi\) |
−0.486468 | + | 0.873699i | \(0.661715\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.640983 | + | 10.9352i | −0.0271107 | + | 0.462509i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 60.4202 | − | 16.1896i | 2.55094 | − | 0.683524i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.0579 | − | 5.64244i | −0.887483 | − | 0.237800i | −0.213850 | − | 0.976866i | \(-0.568600\pi\) |
−0.673633 | + | 0.739066i | \(0.735267\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.11499 | − | 34.9144i | −0.0469081 | − | 1.46886i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 9.99684i | − | 0.419828i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.9881 | − | 22.4960i | 0.544487 | − | 0.943080i | −0.454152 | − | 0.890924i | \(-0.650058\pi\) |
0.998639 | − | 0.0521554i | \(-0.0166091\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.75018i | 0.366184i | 0.983096 | + | 0.183092i | \(0.0586106\pi\) | ||||
−0.983096 | + | 0.183092i | \(0.941389\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.0441 | − | 20.0441i | −0.837354 | − | 0.837354i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.11475 | + | 5.37984i | 0.255003 | + | 0.224355i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.98223 | 0.332304 | 0.166152 | − | 0.986100i | \(-0.446866\pi\) | ||||
0.166152 | + | 0.986100i | \(0.446866\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.8946 | + | 40.6593i | −0.452765 | + | 1.68974i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.60484 | − | 9.70787i | −0.232528 | − | 0.402750i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.8096 | − | 23.9190i | 0.571937 | − | 0.990623i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 26.1257 | + | 16.0258i | 1.08016 | + | 0.662587i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.91804 | + | 10.2503i | −0.244264 | + | 0.423077i | −0.961924 | − | 0.273316i | \(-0.911880\pi\) |
0.717661 | + | 0.696393i | \(0.245213\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.4441 | − | 21.5538i | −0.512749 | − | 0.888108i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.02738 | − | 33.6906i | 0.371337 | − | 1.38585i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.65756 | −0.232328 | −0.116164 | − | 0.993230i | \(-0.537060\pi\) | ||||
−0.116164 | + | 0.993230i | \(0.537060\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.2061 | − | 26.1082i | −0.664387 | − | 1.07033i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −38.9281 | − | 38.9281i | −1.59322 | − | 1.59322i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 21.5444i | − | 0.880281i | −0.897929 | − | 0.440141i | \(-0.854929\pi\) | ||
0.897929 | − | 0.440141i | \(-0.145071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.2202 | − | 19.4339i | 0.457680 | − | 0.792725i | −0.541158 | − | 0.840921i | \(-0.682014\pi\) |
0.998838 | + | 0.0481961i | \(0.0153473\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.8148i | 0.766196i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.68591 | − | 3.92910i | 0.149854 | − | 0.159741i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.0372 | + | 4.56512i | 0.691521 | + | 0.185292i | 0.587429 | − | 0.809275i | \(-0.300140\pi\) |
0.104091 | + | 0.994568i | \(0.466807\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.8012 | + | 3.16211i | −0.478207 | + | 0.128135i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.2571 | − | 7.67852i | 1.50726 | − | 0.310640i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.63937 | − | 0.946493i | −0.0662137 | − | 0.0382285i | 0.466528 | − | 0.884507i | \(-0.345505\pi\) |
−0.532741 | + | 0.846278i | \(0.678838\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −19.7384 | + | 21.0407i | −0.795928 | + | 0.848441i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.77906 | + | 4.81348i | 0.111881 | + | 0.193783i | 0.916529 | − | 0.399969i | \(-0.130979\pi\) |
−0.804648 | + | 0.593753i | \(0.797646\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.0772 | − | 29.0772i | −1.16871 | − | 1.16871i | −0.982512 | − | 0.186200i | \(-0.940383\pi\) |
−0.186200 | − | 0.982512i | \(-0.559617\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.94900 | − | 1.70260i | −0.118339 | − | 0.0683232i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.710753 | − | 0.710753i | 0.0284757 | − | 0.0284757i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.64102 | − | 23.0662i | 0.385641 | − | 0.922649i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.75372 | + | 17.7411i | 0.189845 | + | 0.708512i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.1044 | − | 24.1044i | 0.961104 | − | 0.961104i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.87343 | + | 0.501983i | 0.0745799 | + | 0.0199836i | 0.295916 | − | 0.955214i | \(-0.404375\pi\) |
−0.221336 | + | 0.975198i | \(0.571042\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.3147 | + | 42.2272i | −0.449720 | + | 1.67838i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.4429 | − | 20.1383i | 1.28746 | − | 0.799162i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.3036 | − | 4.74559i | −0.566728 | − | 0.188027i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.21966 | − | 23.2121i | −0.246046 | − | 0.918256i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.7660 | + | 10.8346i | −0.741213 | + | 0.427939i | −0.822510 | − | 0.568751i | \(-0.807427\pi\) |
0.0812974 | + | 0.996690i | \(0.474094\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.2163 | + | 21.4869i | −1.46767 | + | 0.847359i | −0.999345 | − | 0.0361975i | \(-0.988475\pi\) |
−0.468324 | + | 0.883557i | \(0.655142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.9582 | + | 5.12938i | −0.667728 | + | 0.201969i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.70951 | + | 2.60165i | −0.381720 | + | 0.102282i | −0.444576 | − | 0.895741i | \(-0.646646\pi\) |
0.0628562 | + | 0.998023i | \(0.479979\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.2054 | 0.518357 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 45.3653 | 1.77801 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.62853 | − | 1.24021i | 0.181128 | − | 0.0485332i | −0.167115 | − | 0.985937i | \(-0.553445\pi\) |
0.348243 | + | 0.937404i | \(0.386778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −35.5763 | + | 10.7608i | −1.39008 | + | 0.420461i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.4846 | − | 13.5588i | 0.916220 | − | 0.528980i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.9239 | − | 17.8539i | 1.20462 | − | 0.695490i | 0.243045 | − | 0.970015i | \(-0.421854\pi\) |
0.961580 | + | 0.274525i | \(0.0885205\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.365777 | − | 1.36510i | −0.0142271 | − | 0.0530961i | 0.958447 | − | 0.285269i | \(-0.0920830\pi\) |
−0.972674 | + | 0.232173i | \(0.925416\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 75.3639 | − | 15.5322i | 2.92689 | − | 0.603219i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.66611 | − | 4.75859i | 0.297279 | − | 0.184530i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.17604 | − | 4.38904i | 0.0455364 | − | 0.169944i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.10842 | − | 2.44059i | −0.352152 | − | 0.0943588i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.98956 | − | 8.98956i | 0.347038 | − | 0.347038i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.1843 | − | 45.4726i | −0.469672 | − | 1.75284i | −0.640915 | − | 0.767611i | \(-0.721445\pi\) |
0.171243 | − | 0.985229i | \(-0.445222\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.05559 | + | 10.2484i | −0.0791198 | + | 0.394459i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.45570 | + | 8.45570i | −0.324979 | + | 0.324979i | −0.850673 | − | 0.525695i | \(-0.823805\pi\) |
0.525695 | + | 0.850673i | \(0.323805\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.5508 | − | 10.1329i | −0.673537 | − | 0.388867i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.0477 | + | 23.0477i | 0.883189 | + | 0.883189i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.2209 | + | 26.3633i | 0.582411 | + | 1.00877i | 0.995193 | + | 0.0979355i | \(0.0312239\pi\) |
−0.412782 | + | 0.910830i | \(0.635443\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.8772 | + | 19.0567i | −0.683055 | + | 0.728120i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −63.2589 | − | 36.5226i | −2.41348 | − | 1.39342i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.6806 | − | 28.3794i | 0.711673 | − | 1.08117i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.23292 | − | 1.67011i | 0.237111 | − | 0.0635338i | −0.138306 | − | 0.990389i | \(-0.544166\pi\) |
0.375418 | + | 0.926856i | \(0.377499\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.0745 | − | 4.84305i | −0.686594 | − | 0.183972i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.21445 | + | 5.55849i | −0.197795 | + | 0.210845i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.4831i | 1.53340i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.3342 | − | 26.5597i | 0.579994 | − | 1.00458i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.4703i | − | 0.508766i | −0.967104 | − | 0.254383i | \(-0.918128\pi\) | ||
0.967104 | − | 0.254383i | \(-0.0818724\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.07773 | + | 7.07773i | 0.266942 | + | 0.266942i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 32.4481 | + | 52.2741i | 1.22207 | + | 1.96876i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.37072 | −0.126769 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.38408 | + | 5.16546i | −0.0519802 | + | 0.193993i | −0.987034 | − | 0.160514i | \(-0.948685\pi\) |
0.935053 | + | 0.354507i | \(0.115351\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.4969 | + | 32.0376i | 0.693689 | + | 1.20151i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.43605 | + | 14.6117i | −0.315933 | + | 0.547211i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.1481 | + | 16.2584i | −0.641303 | + | 0.608031i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.07335 | + | 3.59114i | −0.0774305 | + | 0.134114i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.75667 | + | 11.7029i | 0.251981 | + | 0.436444i | 0.964071 | − | 0.265644i | \(-0.0855845\pi\) |
−0.712090 | + | 0.702088i | \(0.752251\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.22898 | + | 15.7828i | −0.157495 | + | 0.587781i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −59.6425 | −2.21813 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.9192 | + | 0.889929i | −0.516947 | + | 0.0330511i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.2005 | + | 19.2005i | 0.712108 | + | 0.712108i | 0.966976 | − | 0.254868i | \(-0.0820319\pi\) |
−0.254868 | + | 0.966976i | \(0.582032\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 38.9858i | 1.44392i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.4305 | + | 21.5303i | −0.459759 | + | 0.796326i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0351i | 0.518399i | 0.965824 | + | 0.259199i | \(0.0834587\pi\) | ||||
−0.965824 | + | 0.259199i | \(0.916541\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.778008 | − | 24.3622i | −0.0286973 | − | 0.898615i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.0118 | − | 3.75444i | −0.516130 | − | 0.138297i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.2162 | + | 5.41692i | −0.743666 | + | 0.199265i | −0.610707 | − | 0.791857i | \(-0.709115\pi\) |
−0.132959 | + | 0.991122i | \(0.542448\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.56069 | + | 22.1290i | 0.167541 | + | 0.812929i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.2529 | + | 9.38363i | 0.596262 | + | 0.344252i | 0.767570 | − | 0.640966i | \(-0.221466\pi\) |
−0.171308 | + | 0.985218i | \(0.554799\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.9316 | + | 0.604579i | −0.693599 | + | 0.0221501i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.6877 | + | 21.9757i | 0.464218 | + | 0.804049i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.28521 | + | 3.28521i | 0.120039 | + | 0.120039i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.6911 | − | 13.6781i | −0.864502 | − | 0.499121i | 0.00101517 | − | 0.999999i | \(-0.499677\pi\) |
−0.865517 | + | 0.500879i | \(0.833010\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.3693 | + | 27.3693i | −0.997393 | + | 0.997393i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.3738 | + | 23.1052i | −0.450328 | + | 0.840884i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.85135 | + | 14.3734i | 0.139980 | + | 0.522412i | 0.999928 | + | 0.0120297i | \(0.00382926\pi\) |
−0.859948 | + | 0.510382i | \(0.829504\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.80437 | − | 8.80437i | 0.319579 | − | 0.319579i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.9406 | − | 10.7020i | −1.44784 | − | 0.387949i | −0.552571 | − | 0.833466i | \(-0.686353\pi\) |
−0.895274 | + | 0.445517i | \(0.853020\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.644613 | − | 2.40573i | 0.0233366 | − | 0.0870933i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 36.6858 | + | 59.1011i | 1.32638 | + | 2.13680i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.2168 | + | 0.950571i | 0.585553 | + | 0.0343231i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.79043 | + | 21.6102i | 0.208808 | + | 0.779283i | 0.988255 | + | 0.152815i | \(0.0488337\pi\) |
−0.779447 | + | 0.626469i | \(0.784500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.7454 | − | 11.4000i | 0.711114 | − | 0.410562i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.2861 | + | 9.98015i | −0.621739 | + | 0.358961i | −0.777546 | − | 0.628827i | \(-0.783536\pi\) |
0.155807 | + | 0.987788i | \(0.450202\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 50.7785 | + | 10.1850i | 1.82402 | + | 0.365857i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.6232 | + | 4.72212i | −0.632228 | + | 0.169405i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.8870 | −0.425895 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.5277 | 0.662973 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.63280 | − | 1.50930i | 0.201300 | − | 0.0539381i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0139 | − | 18.6986i | 0.357410 | − | 0.667381i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.4716 | − | 17.0155i | 1.05055 | − | 0.606536i | 0.127747 | − | 0.991807i | \(-0.459225\pi\) |
0.922803 | + | 0.385271i | \(0.125892\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −41.5151 | + | 23.9687i | −1.47798 | + | 0.853310i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.79020 | + | 25.3414i | 0.241432 | + | 0.901036i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.6867 | − | 10.3924i | 0.415005 | − | 0.369047i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 53.5070 | + | 12.5213i | 1.89770 | + | 0.444084i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.34638 | + | 16.2209i | −0.153957 | + | 0.574574i | 0.845236 | + | 0.534394i | \(0.179460\pi\) |
−0.999192 | + | 0.0401804i | \(0.987207\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 83.3937 | + | 22.3453i | 2.95026 | + | 0.790519i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.60893 | + | 1.60893i | −0.0568487 | + | 0.0568487i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.41127 | + | 20.1951i | 0.190959 | + | 0.712670i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.39223 | − | 2.88776i | −0.190051 | − | 0.101780i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.7859 | + | 19.7859i | −0.696496 | + | 0.696496i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.82165 | + | 5.67053i | 0.345311 | + | 0.199365i | 0.662618 | − | 0.748957i | \(-0.269445\pi\) |
−0.317307 | + | 0.948323i | \(0.602779\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.6282 | − | 28.6282i | −1.00527 | − | 1.00527i | −0.999986 | − | 0.00528760i | \(-0.998317\pi\) |
−0.00528760 | − | 0.999986i | \(-0.501683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.8772 | − | 55.2129i | −1.11798 | − | 1.93640i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.5772 | − | 22.1180i | −0.825875 | − | 0.774759i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.32191 | − | 3.64995i | −0.221175 | − | 0.127696i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −21.8476 | − | 7.24853i | −0.763417 | − | 0.253284i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.2420 | − | 5.15587i | 0.671550 | − | 0.179941i | 0.0930969 | − | 0.995657i | \(-0.470323\pi\) |
0.578453 | + | 0.815716i | \(0.303657\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.55765 | − | 1.48917i | −0.193728 | − | 0.0519092i | 0.160651 | − | 0.987011i | \(-0.448641\pi\) |
−0.354378 | + | 0.935102i | \(0.615307\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −34.2512 | − | 16.9591i | −1.19247 | − | 0.590439i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.7588i | 0.547985i | 0.961732 | + | 0.273993i | \(0.0883444\pi\) | ||||
−0.961732 | + | 0.273993i | \(0.911656\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.86690 | − | 13.6259i | 0.273229 | − | 0.473246i | −0.696458 | − | 0.717598i | \(-0.745242\pi\) |
0.969687 | + | 0.244352i | \(0.0785751\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 70.4984i | 2.44556i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.1854 | − | 24.1854i | −0.837975 | − | 0.837975i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.6258 | − | 3.89064i | −0.575360 | − | 0.134641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.6533 | −0.748447 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.629782 | − | 2.35038i | 0.0217425 | − | 0.0811441i | −0.954202 | − | 0.299163i | \(-0.903293\pi\) |
0.975945 | + | 0.218019i | \(0.0699593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.6093 | − | 18.3758i | −0.365837 | − | 0.633648i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38.2932 | − | 66.3258i | 1.31889 | − | 2.28438i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.2289 | + | 18.7316i | −0.764698 | + | 0.644388i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.02305 | + | 3.50403i | −0.0695128 | + | 0.120400i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.5959 | − | 27.0128i | −0.535249 | − | 0.927078i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.75623 | − | 6.55434i | 0.0602028 | − | 0.224680i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.0234 | −1.13070 | −0.565350 | − | 0.824851i | \(-0.691259\pi\) | ||||
−0.565350 | + | 0.824851i | \(0.691259\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.3538 | + | 10.7720i | −0.593486 | + | 0.368395i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.7686 | + | 10.7686i | 0.367849 | + | 0.367849i | 0.866692 | − | 0.498843i | \(-0.166242\pi\) |
−0.498843 | + | 0.866692i | \(0.666242\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 15.3788i | − | 0.524717i | −0.964970 | − | 0.262359i | \(-0.915500\pi\) | ||
0.964970 | − | 0.262359i | \(-0.0845003\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.8336 | − | 18.7644i | 0.369208 | − | 0.639488i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 21.4239i | − | 0.729278i | −0.931149 | − | 0.364639i | \(-0.881192\pi\) | ||
0.931149 | − | 0.364639i | \(-0.118808\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 52.5300 | − | 1.67754i | 1.78607 | − | 0.0570382i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 125.864 | + | 33.7253i | 4.27458 | + | 1.14537i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.5502 | + | 7.38204i | −0.934575 | + | 0.250419i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.9368 | − | 5.61922i | −0.573880 | − | 0.190400i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 39.7297 | + | 22.9379i | 1.34465 | + | 0.776331i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.10300 | + | 18.5177i | −0.104900 | + | 0.626012i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.869538 | − | 1.50608i | −0.0293622 | − | 0.0508568i | 0.850971 | − | 0.525213i | \(-0.176014\pi\) |
−0.880333 | + | 0.474356i | \(0.842681\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.6256 | − | 21.6256i | −0.729413 | − | 0.729413i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.2860 | − | 14.5989i | −0.851908 | − | 0.491849i | 0.00938605 | − | 0.999956i | \(-0.497012\pi\) |
−0.861294 | + | 0.508107i | \(0.830346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.5752 | + | 11.5752i | −0.389535 | + | 0.389535i | −0.874522 | − | 0.484986i | \(-0.838825\pi\) |
0.484986 | + | 0.874522i | \(0.338825\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.60682 | + | 25.1488i | 0.255700 | + | 0.845368i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.3273 | − | 46.0060i | −0.413909 | − | 1.54473i | −0.787011 | − | 0.616939i | \(-0.788372\pi\) |
0.373102 | − | 0.927791i | \(-0.378294\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.2785 | + | 20.2785i | −0.680121 | + | 0.680121i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.8529 | − | 4.51573i | −0.564595 | − | 0.151283i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.56121 | + | 24.4868i | −0.219563 | + | 0.819419i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.5772 | − | 53.7459i | 0.420408 | − | 1.79653i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.4459 | − | 10.1784i | 0.382167 | − | 0.339846i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.47828 | − | 27.9093i | −0.249415 | − | 0.930828i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 66.7803 | − | 38.5556i | 2.22477 | − | 1.28447i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.5234 | − | 6.65302i | 0.383474 | − | 0.221399i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.11581 | − | 13.6072i | −0.136814 | − | 0.452319i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.8833 | − | 7.47130i | 0.925848 | − | 0.248080i | 0.235765 | − | 0.971810i | \(-0.424240\pi\) |
0.690083 | + | 0.723730i | \(0.257574\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.63030 | 0.253081 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.5759 | 0.681711 | 0.340855 | − | 0.940116i | \(-0.389283\pi\) | ||||
0.340855 | + | 0.940116i | \(0.389283\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.8976 | + | 5.06359i | −0.625419 | + | 0.167581i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.2984 | + | 11.9417i | 0.737161 | + | 0.394780i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.1747 | − | 13.9573i | 0.798319 | − | 0.460909i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.7438 | + | 26.4102i | −1.50895 | + | 0.871193i | −0.509004 | + | 0.860764i | \(0.669986\pi\) |
−0.999946 | + | 0.0104288i | \(0.996680\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.8192 | − | 44.1097i | −0.389455 | − | 1.45346i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.7527 | + | 1.33369i | 0.748916 | + | 0.0438989i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.7862 | + | 1.32897i | −0.683446 | + | 0.0436962i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.57313 | − | 35.7274i | 0.314423 | − | 1.17344i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.13051 | + | 0.302919i | 0.0370908 | + | 0.00993846i | 0.277317 | − | 0.960779i | \(-0.410555\pi\) |
−0.240226 | + | 0.970717i | \(0.577222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.10153 | − | 7.10153i | 0.232743 | − | 0.232743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.3671 | + | 46.1548i | 0.404882 | + | 1.51104i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −51.3345 | + | 15.5273i | −1.67882 | + | 0.507796i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.3677 | − | 19.3677i | 0.632716 | − | 0.632716i | −0.316033 | − | 0.948748i | \(-0.602351\pi\) |
0.948748 | + | 0.316033i | \(0.102351\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.1959 | − | 8.77336i | −0.495900 | − | 0.286308i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.4168 | − | 10.4168i | −0.339576 | − | 0.339576i | 0.516631 | − | 0.856208i | \(-0.327186\pi\) |
−0.856208 | + | 0.516631i | \(0.827186\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.02919 | + | 6.97877i | 0.131209 | + | 0.227260i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.250567 | − | 7.84617i | −0.00815096 | − | 0.255236i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.2039 | + | 11.0874i | 0.624044 | + | 0.360292i | 0.778442 | − | 0.627717i | \(-0.216010\pi\) |
−0.154398 | + | 0.988009i | \(0.549344\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.19154 | + | 25.1899i | 0.168524 | + | 0.817700i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −72.0109 | + | 19.2953i | −2.33511 | + | 0.625692i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.0516447 | − | 0.0138381i | −0.00167293 | − | 0.000448262i | 0.257982 | − | 0.966150i | \(-0.416942\pi\) |
−0.259655 | + | 0.965701i | \(0.583609\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.7255 | + | 16.6284i | 0.573583 | + | 0.538082i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.3231i | 0.689277i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.81211 | − | 16.9951i | 0.316850 | − | 0.548800i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 76.2875i | 2.46089i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.43672 | − | 7.43672i | −0.239645 | − | 0.239645i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.22350 | − | 35.1414i | 0.264724 | − | 1.13124i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.7090 | −0.794586 | −0.397293 | − | 0.917692i | \(-0.630050\pi\) | ||||
−0.397293 | + | 0.917692i | \(0.630050\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.2721 | + | 49.5321i | −0.426360 | + | 1.59120i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.3866 | − | 35.3107i | −0.654238 | − | 1.13317i | −0.982084 | − | 0.188442i | \(-0.939656\pi\) |
0.327846 | − | 0.944731i | \(-0.393677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.86201 | − | 4.95714i | 0.0917517 | − | 0.158919i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −40.8411 | − | 23.2920i | −1.30796 | − | 0.745940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.3789 | − | 23.1729i | 0.428029 | − | 0.741368i | −0.568669 | − | 0.822567i | \(-0.692541\pi\) |
0.996698 | + | 0.0811984i | \(0.0258747\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.877148 | − | 1.51926i | −0.0280338 | − | 0.0485559i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.45921 | + | 5.44585i | −0.0465890 | + | 0.173873i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.8407 | −1.33451 | −0.667256 | − | 0.744829i | \(-0.732531\pi\) | ||||
−0.667256 | + | 0.744829i | \(0.732531\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.81407 | + | 29.1185i | −0.217114 | + | 0.927792i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −32.6742 | − | 32.6742i | −1.04003 | − | 1.04003i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.94873i | 0.157361i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.77839 | − | 13.4726i | 0.247089 | − | 0.427970i | −0.715628 | − | 0.698482i | \(-0.753859\pi\) |
0.962717 | + | 0.270511i | \(0.0871927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 56.0577i | − | 1.77894i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.4251 | + | 32.2944i | 1.09135 | + | 1.02380i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.4062 | − | 11.6306i | −1.37469 | − | 0.368346i | −0.505498 | − | 0.862828i | \(-0.668691\pi\) |
−0.869188 | + | 0.494481i | \(0.835358\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.41170 | − | 2.25391i | 0.266134 | − | 0.0713105i |
(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 | 260.2.bk.c.33.1 | yes | 20 | |
5.2 | odd | 4 | 260.2.bf.c.137.5 | yes | 20 | ||
5.3 | odd | 4 | 1300.2.bn.d.657.1 | 20 | |||
5.4 | even | 2 | 1300.2.bs.d.293.5 | 20 | |||
13.2 | odd | 12 | 260.2.bf.c.93.5 | ✓ | 20 | ||
65.2 | even | 12 | inner | 260.2.bk.c.197.1 | yes | 20 | |
65.28 | even | 12 | 1300.2.bs.d.457.5 | 20 | |||
65.54 | odd | 12 | 1300.2.bn.d.93.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.c.93.5 | ✓ | 20 | 13.2 | odd | 12 | ||
260.2.bf.c.137.5 | yes | 20 | 5.2 | odd | 4 | ||
260.2.bk.c.33.1 | yes | 20 | 1.1 | even | 1 | trivial | |
260.2.bk.c.197.1 | yes | 20 | 65.2 | even | 12 | inner | |
1300.2.bn.d.93.1 | 20 | 65.54 | odd | 12 | |||
1300.2.bn.d.657.1 | 20 | 5.3 | odd | 4 | |||
1300.2.bs.d.293.5 | 20 | 5.4 | even | 2 | |||
1300.2.bs.d.457.5 | 20 | 65.28 | even | 12 |