Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(13,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.13");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.i (of order \(9\), degree \(6\), 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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 13.4 | ||
Character | \(\chi\) | \(=\) | 108.13 |
Dual form | 108.4.i.a.25.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.716497 | − | 5.14652i | −0.137890 | − | 0.990448i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.52940 | + | 6.31792i | 0.673450 | + | 0.565092i | 0.914084 | − | 0.405524i | \(-0.132911\pi\) |
−0.240634 | + | 0.970616i | \(0.577355\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 24.9076 | + | 9.06562i | 1.34488 | + | 0.489497i | 0.911347 | − | 0.411639i | \(-0.135044\pi\) |
0.433536 | + | 0.901136i | \(0.357266\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −25.9733 | + | 7.37493i | −0.961973 | + | 0.273146i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.0456 | − | 14.3030i | 0.467223 | − | 0.392046i | −0.378558 | − | 0.925578i | \(-0.623580\pi\) |
0.845780 | + | 0.533531i | \(0.179135\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.5975 | − | 77.1153i | 0.290098 | − | 1.64522i | −0.396389 | − | 0.918083i | \(-0.629737\pi\) |
0.686487 | − | 0.727142i | \(-0.259152\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 27.1205 | − | 43.2769i | 0.466832 | − | 0.744937i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 32.2518 | − | 55.8618i | 0.460130 | − | 0.796969i | −0.538837 | − | 0.842410i | \(-0.681136\pi\) |
0.998967 | + | 0.0454411i | \(0.0144693\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 35.2151 | + | 60.9943i | 0.425205 | + | 0.736477i | 0.996440 | − | 0.0843100i | \(-0.0268686\pi\) |
−0.571234 | + | 0.820787i | \(0.693535\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 28.8101 | − | 134.683i | 0.299375 | − | 1.39953i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −112.980 | + | 41.1215i | −1.02426 | + | 0.372801i | −0.798894 | − | 0.601472i | \(-0.794581\pi\) |
−0.225369 | + | 0.974274i | \(0.572359\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.93023 | − | 27.9607i | −0.0394419 | − | 0.223686i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 56.5650 | + | 128.388i | 0.403183 | + | 0.915119i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 30.3150 | + | 171.925i | 0.194116 | + | 1.10089i | 0.913672 | + | 0.406452i | \(0.133234\pi\) |
−0.719556 | + | 0.694434i | \(0.755655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 139.932 | − | 50.9312i | 0.810728 | − | 0.295081i | 0.0968036 | − | 0.995304i | \(-0.469138\pi\) |
0.713925 | + | 0.700223i | \(0.246916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −85.8237 | − | 77.4776i | −0.452727 | − | 0.408700i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 130.263 | + | 225.623i | 0.629100 | + | 1.08963i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 144.919 | − | 251.008i | 0.643908 | − | 1.11528i | −0.340644 | − | 0.940192i | \(-0.610645\pi\) |
0.984553 | − | 0.175090i | \(-0.0560215\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −406.617 | − | 14.7269i | −1.66951 | − | 0.0604664i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −76.1146 | + | 431.667i | −0.289929 | + | 1.64427i | 0.397197 | + | 0.917733i | \(0.369983\pi\) |
−0.687126 | + | 0.726538i | \(0.741128\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −76.4782 | + | 64.1728i | −0.271228 | + | 0.227588i | −0.768249 | − | 0.640151i | \(-0.778872\pi\) |
0.497021 | + | 0.867739i | \(0.334427\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −242.157 | − | 108.568i | −0.802193 | − | 0.359653i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −290.224 | − | 105.633i | −0.900712 | − | 0.327832i | −0.150174 | − | 0.988660i | \(-0.547983\pi\) |
−0.750538 | + | 0.660827i | \(0.770206\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 275.449 | + | 231.129i | 0.803057 | + | 0.673845i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −310.602 | − | 125.960i | −0.852804 | − | 0.345841i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −533.670 | −1.38312 | −0.691558 | − | 0.722321i | \(-0.743075\pi\) | ||||
−0.691558 | + | 0.722321i | \(0.743075\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 218.708 | 0.536193 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 288.677 | − | 224.937i | 0.670810 | − | 0.522696i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 320.392 | + | 268.841i | 0.706975 | + | 0.593222i | 0.923748 | − | 0.383000i | \(-0.125109\pi\) |
−0.216774 | + | 0.976222i | \(0.569553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −87.3117 | − | 31.7789i | −0.183264 | − | 0.0667027i | 0.248758 | − | 0.968566i | \(-0.419978\pi\) |
−0.432022 | + | 0.901863i | \(0.642200\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −713.789 | − | 51.7720i | −1.42744 | − | 0.103534i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 589.589 | − | 494.724i | 1.12507 | − | 0.944045i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −80.8767 | + | 458.675i | −0.147473 | + | 0.836359i | 0.817876 | + | 0.575395i | \(0.195152\pi\) |
−0.965349 | + | 0.260964i | \(0.915960\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 292.583 | + | 551.992i | 0.510475 | + | 0.963073i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −451.994 | + | 782.877i | −0.755519 | + | 1.30860i | 0.189597 | + | 0.981862i | \(0.439282\pi\) |
−0.945116 | + | 0.326735i | \(0.894051\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −86.0801 | − | 149.095i | −0.138012 | − | 0.239045i | 0.788732 | − | 0.614738i | \(-0.210738\pi\) |
−0.926744 | + | 0.375693i | \(0.877405\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −140.368 | + | 45.4073i | −0.216111 | + | 0.0699091i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 554.231 | − | 201.723i | 0.820265 | − | 0.298552i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −27.8206 | − | 157.779i | −0.0396211 | − | 0.224702i | 0.958567 | − | 0.284866i | \(-0.0919490\pi\) |
−0.998189 | + | 0.0601633i | \(0.980838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 620.221 | − | 383.102i | 0.850783 | − | 0.525517i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 103.082 | + | 584.607i | 0.136322 | + | 0.773120i | 0.973930 | + | 0.226849i | \(0.0728423\pi\) |
−0.837608 | + | 0.546272i | \(0.816047\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 595.767 | − | 216.841i | 0.760235 | − | 0.276703i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 863.095 | − | 279.201i | 1.06360 | − | 0.344063i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −818.257 | − | 1417.26i | −0.974551 | − | 1.68797i | −0.681408 | − | 0.731904i | \(-0.738632\pi\) |
−0.293143 | − | 0.956068i | \(-0.594701\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1037.78 | − | 1797.48i | 1.19548 | − | 2.07063i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −362.379 | − | 683.672i | −0.404053 | − | 0.762295i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −120.209 | + | 681.737i | −0.129823 | + | 0.736260i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −323.876 | + | 271.765i | −0.339017 | + | 0.284469i | −0.796362 | − | 0.604820i | \(-0.793245\pi\) |
0.457345 | + | 0.889289i | \(0.348800\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −337.247 | + | 497.205i | −0.342370 | + | 0.504758i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 743.112 | + | 270.471i | 0.732103 | + | 0.266464i | 0.681055 | − | 0.732233i | \(-0.261522\pi\) |
0.0510481 | + | 0.998696i | \(0.483744\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 696.301 | + | 584.266i | 0.666103 | + | 0.558927i | 0.911909 | − | 0.410392i | \(-0.134608\pi\) |
−0.245806 | + | 0.969319i | \(0.579053\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1067.84 | − | 832.060i | 0.992478 | − | 0.773340i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 225.538 | 0.203772 | 0.101886 | − | 0.994796i | \(-0.467512\pi\) | ||||
0.101886 | + | 0.994796i | \(0.467512\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1916.33 | −1.68396 | −0.841979 | − | 0.539510i | \(-0.818610\pi\) | ||||
−0.841979 | + | 0.539510i | \(0.818610\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1395.65 | − | 565.984i | −1.19342 | − | 0.483971i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −496.602 | − | 416.698i | −0.413419 | − | 0.346900i | 0.412234 | − | 0.911078i | \(-0.364749\pi\) |
−0.825653 | + | 0.564178i | \(0.809193\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1110.48 | − | 404.180i | −0.900456 | − | 0.327739i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 215.548 | + | 2103.22i | 0.170320 | + | 1.66190i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1309.74 | − | 1099.00i | 1.00894 | − | 0.846597i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −145.148 | + | 823.172i | −0.109051 | + | 0.618462i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2276.12 | + | 82.4366i | 1.66854 | + | 0.0604313i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 753.840 | − | 1305.69i | 0.539404 | − | 0.934275i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −180.673 | − | 312.934i | −0.126237 | − | 0.218649i | 0.795979 | − | 0.605324i | \(-0.206957\pi\) |
−0.922216 | + | 0.386676i | \(0.873623\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 385.063 | + | 347.617i | 0.262813 | + | 0.237255i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −659.456 | + | 240.022i | −0.439824 | + | 0.160083i | −0.552434 | − | 0.833556i | \(-0.686301\pi\) |
0.112611 | + | 0.993639i | \(0.464079\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 324.171 | + | 1838.47i | 0.211348 | + | 1.19861i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −385.243 | + | 1324.06i | −0.245603 | + | 0.844122i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −490.451 | − | 2781.48i | −0.305854 | − | 1.73459i | −0.619456 | − | 0.785031i | \(-0.712647\pi\) |
0.313602 | − | 0.949555i | \(-0.398464\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −928.816 | + | 338.061i | −0.566771 | + | 0.206288i | −0.609482 | − | 0.792800i | \(-0.708623\pi\) |
0.0427113 | + | 0.999087i | \(0.486400\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −335.696 | + | 1569.33i | −0.200502 | + | 0.937313i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −871.200 | − | 1508.96i | −0.509464 | − | 0.882418i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −857.954 | + | 1486.02i | −0.491374 | + | 0.851085i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 992.150 | − | 1583.20i | 0.556674 | − | 0.888302i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −339.478 | + | 1925.27i | −0.186652 | + | 1.05855i | 0.737163 | + | 0.675715i | \(0.236165\pi\) |
−0.923815 | + | 0.382840i | \(0.874946\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2176.29 | + | 1826.12i | −1.17287 | + | 0.984156i | −1.00000 | 0.000788384i | \(-0.999749\pi\) | |
−0.172872 | + | 0.984944i | \(0.555305\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −425.708 | + | 1688.77i | −0.224944 | + | 0.892345i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1375.38 | + | 500.599i | 0.712733 | + | 0.259413i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 544.235 | + | 456.668i | 0.276654 | + | 0.232140i | 0.770548 | − | 0.637382i | \(-0.219983\pi\) |
−0.493894 | + | 0.869522i | \(0.664427\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 382.373 | + | 2746.54i | 0.190718 | + | 1.36990i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3186.86 | −1.56000 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1340.84 | 0.644311 | 0.322156 | − | 0.946687i | \(-0.395593\pi\) | ||||
0.322156 | + | 0.946687i | \(0.395593\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −156.704 | − | 1125.59i | −0.0739357 | − | 0.531071i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1287.33 | + | 1080.20i | 0.596508 | + | 0.500530i | 0.890321 | − | 0.455333i | \(-0.150480\pi\) |
−0.293813 | + | 0.955863i | \(0.594924\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3697.37 | − | 1345.73i | −1.68292 | − | 0.612531i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1364.48 | − | 1324.51i | −0.610201 | − | 0.592328i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −118.475 | + | 99.4124i | −0.0520664 | + | 0.0436889i | −0.668450 | − | 0.743758i | \(-0.733042\pi\) |
0.616383 | + | 0.787446i | \(0.288597\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 130.681 | − | 741.130i | 0.0564490 | − | 0.320138i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1154.03 | − | 1841.53i | 0.490071 | − | 0.782021i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −426.813 | + | 739.262i | −0.178221 | + | 0.308687i | −0.941271 | − | 0.337652i | \(-0.890367\pi\) |
0.763050 | + | 0.646339i | \(0.223701\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −985.862 | − | 1707.56i | −0.404854 | − | 0.701228i | 0.589451 | − | 0.807804i | \(-0.299344\pi\) |
−0.994304 | + | 0.106577i | \(0.966011\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −100.992 | + | 472.121i | −0.0407953 | + | 0.190711i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2677.00 | − | 974.349i | 1.06388 | − | 0.387219i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −249.238 | − | 1413.50i | −0.0974656 | − | 0.552755i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 244.983 | + | 3710.62i | 0.0942850 | + | 1.42809i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −887.225 | − | 5031.70i | −0.336112 | − | 1.90618i | −0.415970 | − | 0.909378i | \(-0.636558\pi\) |
0.0798581 | − | 0.996806i | \(-0.474553\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 456.904 | − | 166.299i | 0.170408 | − | 0.0620233i | −0.255408 | − | 0.966833i | \(-0.582210\pi\) |
0.425815 | + | 0.904810i | \(0.359987\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2968.54 | − | 2679.86i | −1.09016 | − | 0.984147i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1019.37 | + | 1765.60i | 0.368665 | + | 0.638546i | 0.989357 | − | 0.145508i | \(-0.0464817\pi\) |
−0.620692 | + | 0.784054i | \(0.713148\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2237.59 | − | 3875.62i | 0.797079 | − | 1.38058i | −0.124432 | − | 0.992228i | \(-0.539711\pi\) |
0.921511 | − | 0.388353i | \(-0.126956\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2418.53 | + | 87.5942i | 0.848705 | + | 0.0307384i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −803.533 | + | 4557.06i | −0.277817 | + | 1.57558i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3300.34 | + | 2769.31i | −1.12442 | + | 0.943498i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2631.20 | − | 1901.28i | 0.883484 | − | 0.638397i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1472.66 | + | 536.006i | 0.487399 | + | 0.177399i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3003.60 | + | 2520.32i | 0.979983 | + | 0.822304i | 0.984087 | − | 0.177688i | \(-0.0568618\pi\) |
−0.00410365 | + | 0.999992i | \(0.501306\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4352.94 | + | 1765.27i | 1.40028 | + | 0.567860i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −981.273 | −0.311266 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3947.10 | 1.23478 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −705.644 | + | 549.839i | −0.217731 | + | 0.169656i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3869.25 | − | 3246.69i | −1.17771 | − | 0.988217i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1464.87 | + | 533.169i | 0.439888 | + | 0.160106i | 0.552464 | − | 0.833537i | \(-0.313688\pi\) |
−0.112576 | + | 0.993643i | \(0.535910\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 334.263 | + | 689.871i | 0.0990408 | + | 0.204406i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −195.605 | + | 164.132i | −0.0571927 | + | 0.0479904i | −0.670936 | − | 0.741515i | \(-0.734107\pi\) |
0.613743 | + | 0.789506i | \(0.289663\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −897.549 | + | 5090.25i | −0.259003 | + | 1.46888i | 0.526581 | + | 0.850125i | \(0.323474\pi\) |
−0.785584 | + | 0.618755i | \(0.787637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1435.28 | − | 2707.82i | −0.408807 | − | 0.771263i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2015.27 | − | 3490.54i | 0.566629 | − | 0.981430i | −0.430268 | − | 0.902701i | \(-0.641581\pi\) |
0.996896 | − | 0.0787281i | \(-0.0250859\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1517.83 | − | 2628.96i | −0.421329 | − | 0.729764i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −792.077 | + | 256.227i | −0.217092 | + | 0.0702268i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5365.88 | − | 1953.02i | 1.45226 | − | 0.528579i | 0.509037 | − | 0.860745i | \(-0.330002\pi\) |
0.943221 | + | 0.332166i | \(0.107779\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −438.520 | − | 2486.97i | −0.117210 | − | 0.664730i | −0.985632 | − | 0.168905i | \(-0.945977\pi\) |
0.868422 | − | 0.495825i | \(-0.165134\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2416.03 | − | 2917.49i | −0.637812 | − | 0.770192i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 613.710 | + | 3480.52i | 0.160035 | + | 0.907602i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5182.43 | − | 1886.25i | 1.33502 | − | 0.485908i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2934.83 | − | 949.383i | 0.746938 | − | 0.241625i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −289.705 | − | 501.784i | −0.0728526 | − | 0.126184i | 0.827298 | − | 0.561764i | \(-0.189877\pi\) |
−0.900150 | + | 0.435579i | \(0.856544\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1337.66 | + | 2316.90i | −0.332403 | + | 0.575740i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1542.84 | − | 2910.76i | −0.378889 | − | 0.714819i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −614.801 | + | 3486.71i | −0.149223 | + | 0.846284i | 0.814657 | + | 0.579944i | \(0.196925\pi\) |
−0.963879 | + | 0.266340i | \(0.914186\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5885.13 | − | 4938.21i | 1.41191 | − | 1.18473i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2055.32 | − | 4241.88i | −0.487436 | − | 1.00600i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2173.81 | + | 791.204i | 0.509670 | + | 0.185505i | 0.584038 | − | 0.811726i | \(-0.301472\pi\) |
−0.0743683 | + | 0.997231i | \(0.523694\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4018.21 | − | 3371.68i | −0.931460 | − | 0.781587i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6707.69 | + | 5226.64i | −1.53747 | + | 1.19800i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −595.561 | −0.134989 | −0.0674944 | − | 0.997720i | \(-0.521500\pi\) | ||||
−0.0674944 | + | 0.997720i | \(0.521500\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −498.234 | −0.111681 | −0.0558406 | − | 0.998440i | \(-0.517784\pi\) | ||||
−0.0558406 | + | 0.998440i | \(0.517784\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9994.35 | − | 4053.05i | −2.21570 | − | 0.898541i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −483.961 | − | 406.091i | −0.106123 | − | 0.0890481i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8126.82 | + | 2957.92i | 1.76279 | + | 0.641604i | 0.999987 | − | 0.00502614i | \(-0.00159988\pi\) |
0.762804 | + | 0.646630i | \(0.223822\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3258.88 | + | 2354.84i | −0.699298 | + | 0.505307i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1183.18 | + | 992.805i | −0.251183 | + | 0.210768i | −0.759682 | − | 0.650295i | \(-0.774645\pi\) |
0.508498 | + | 0.861063i | \(0.330201\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1007.68 | − | 5714.81i | 0.211661 | − | 1.20039i | −0.674946 | − | 0.737867i | \(-0.735833\pi\) |
0.886607 | − | 0.462523i | \(-0.153056\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3594.70 | + | 130.193i | 0.747128 | + | 0.0270595i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5809.16 | + | 10061.8i | −1.19479 | + | 2.06943i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 376.139 | + | 651.493i | 0.0765600 | + | 0.132606i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1630.70 | + | 1472.12i | 0.328499 | + | 0.296553i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3902.90 | + | 1420.54i | −0.778191 | + | 0.283238i | −0.700418 | − | 0.713733i | \(-0.747003\pi\) |
−0.0777730 | + | 0.996971i | \(0.524781\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 713.846 | + | 4048.42i | 0.140887 | + | 0.799011i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2800.51 | + | 1379.40i | 0.547146 | + | 0.269498i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1634.84 | + | 9271.66i | 0.316206 | + | 1.79329i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2486.65 | + | 905.067i | −0.476174 | + | 0.173313i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 859.544 | − | 4018.23i | 0.162969 | − | 0.761852i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −456.629 | − | 790.904i | −0.0857261 | − | 0.148482i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3125.08 | + | 5412.80i | −0.580970 | + | 1.00627i | 0.414395 | + | 0.910097i | \(0.363993\pi\) |
−0.995365 | + | 0.0961718i | \(0.969340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2508.04 | − | 4002.15i | 0.461739 | − | 0.736810i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −893.683 | + | 5068.33i | −0.162946 | + | 0.924111i | 0.788212 | + | 0.615404i | \(0.211007\pi\) |
−0.951157 | + | 0.308707i | \(0.900104\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4309.20 | − | 3615.85i | 0.778180 | − | 0.652971i | −0.164610 | − | 0.986359i | \(-0.552636\pi\) |
0.942790 | + | 0.333388i | \(0.108192\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5047.31 | − | 4899.47i | −0.902806 | − | 0.876362i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2826.93 | − | 1028.92i | −0.500872 | − | 0.182302i | 0.0792143 | − | 0.996858i | \(-0.474759\pi\) |
−0.580086 | + | 0.814555i | \(0.696981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2975.78 | + | 2496.98i | 0.522294 | + | 0.438257i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −161.597 | − | 1160.73i | −0.0280981 | − | 0.201825i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4543.01 | 0.782599 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2223.24 | −0.379456 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1373.05 | + | 9862.44i | 0.232201 | + | 1.66787i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6271.14 | − | 5262.11i | −1.05088 | − | 0.881792i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4837.44 | − | 1760.69i | −0.803293 | − | 0.292375i | −0.0924426 | − | 0.995718i | \(-0.529467\pi\) |
−0.710850 | + | 0.703343i | \(0.751690\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1912.87 | + | 7588.26i | −0.314788 | + | 1.24875i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3506.82 | + | 2942.57i | −0.571935 | + | 0.479910i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 935.450 | − | 5305.20i | 0.151208 | − | 0.857545i | −0.810963 | − | 0.585098i | \(-0.801056\pi\) |
0.962171 | − | 0.272447i | \(-0.0878328\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1788.73 | + | 2854.33i | −0.286580 | + | 0.457304i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1656.77 | − | 2869.60i | 0.263105 | − | 0.455712i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 219.637 | + | 380.422i | 0.0345751 | + | 0.0598859i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1284.47 | + | 6004.68i | −0.200445 | + | 0.937047i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9458.09 | − | 3442.46i | 1.46322 | − | 0.532568i | 0.516969 | − | 0.856004i | \(-0.327060\pi\) |
0.946250 | + | 0.323436i | \(0.104838\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 197.712 | + | 1121.28i | 0.0303246 | + | 0.171979i | 0.996209 | − | 0.0869952i | \(-0.0277265\pi\) |
−0.965884 | + | 0.258975i | \(0.916615\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10669.8 | − | 2616.27i | 1.62254 | − | 0.397852i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 910.038 | + | 5161.08i | 0.137214 | + | 0.778177i | 0.973293 | + | 0.229568i | \(0.0737314\pi\) |
−0.836079 | + | 0.548609i | \(0.815158\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8349.40 | + | 3038.93i | −1.24828 | + | 0.454337i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6594.44 | − | 5953.15i | −0.977632 | − | 0.882560i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 324.335 | + | 561.764i | 0.0476817 | + | 0.0825871i | 0.888881 | − | 0.458138i | \(-0.151483\pi\) |
−0.841200 | + | 0.540725i | \(0.818150\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 949.293 | − | 1644.22i | 0.138401 | − | 0.239718i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4340.47 | + | 157.203i | 0.627591 | + | 0.0227301i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 293.839 | − | 1666.44i | 0.0421376 | − | 0.238974i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4084.64 | + | 3427.42i | −0.580971 | + | 0.487493i | −0.885266 | − | 0.465085i | \(-0.846024\pi\) |
0.304295 | + | 0.952578i | \(0.401579\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1206.57 | − | 11773.2i | −0.170221 | − | 1.66094i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13292.4 | − | 4838.04i | −1.86013 | − | 0.677032i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5635.34 | − | 4728.61i | −0.782270 | − | 0.656403i | 0.161549 | − | 0.986865i | \(-0.448351\pi\) |
−0.943819 | + | 0.330462i | \(0.892795\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7259.88 | − | 2944.13i | −0.999729 | − | 0.405424i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13670.3 | 1.86752 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12285.0 | 1.66501 | 0.832507 | − | 0.554015i | \(-0.186905\pi\) | ||||
0.832507 | + | 0.554015i | \(0.186905\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1481.07 | + | 1154.05i | −0.199153 | + | 0.155181i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9861.87 | − | 8275.10i | −1.31571 | − | 1.10401i | −0.987195 | − | 0.159517i | \(-0.949006\pi\) |
−0.328518 | − | 0.944498i | \(-0.606549\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5447.50 | + | 1982.73i | 0.721117 | + | 0.262465i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1513.12 | − | 2230.80i | 0.198750 | − | 0.293018i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3905.60 | − | 3277.18i | 0.509053 | − | 0.427146i | −0.351743 | − | 0.936097i | \(-0.614411\pi\) |
0.860796 | + | 0.508951i | \(0.169966\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1346.70 | + | 7637.53i | −0.174183 | + | 0.987843i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1707.78 | + | 3221.92i | 0.219201 | + | 0.413549i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 787.359 | − | 1363.75i | 0.100295 | − | 0.173715i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3842.87 | + | 6656.05i | 0.485814 | + | 0.841455i | 0.999867 | − | 0.0163035i | \(-0.00518981\pi\) |
−0.514053 | + | 0.857759i | \(0.671856\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9229.44 | − | 2985.61i | 1.15802 | − | 0.374605i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10580.7 | − | 3851.08i | 1.31765 | − | 0.479585i | 0.414944 | − | 0.909847i | \(-0.363801\pi\) |
0.902704 | + | 0.430262i | \(0.141579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2024.84 | − | 11483.4i | −0.250284 | − | 1.41943i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7090.30 | + | 1033.98i | 0.869925 | + | 0.126861i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1119.92 | − | 6351.37i | −0.136394 | − | 0.773527i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9890.09 | − | 3599.70i | 1.19568 | − | 0.435192i | 0.333966 | − | 0.942585i | \(-0.391613\pi\) |
0.861715 | + | 0.507393i | \(0.169391\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13963.6 | + | 4517.04i | −1.67584 | + | 0.542115i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5542.98 | + | 9600.73i | 0.660417 | + | 1.14388i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2917.35 | + | 5053.01i | −0.345078 | + | 0.597692i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2405.33 | + | 4537.95i | 0.282469 | + | 0.532912i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −605.417 | + | 3433.49i | −0.0705884 | + | 0.400327i | 0.928957 | + | 0.370187i | \(0.120706\pi\) |
−0.999546 | + | 0.0301399i | \(0.990405\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6215.42 | − | 5215.36i | 0.719527 | − | 0.603755i | −0.207727 | − | 0.978187i | \(-0.566607\pi\) |
0.927255 | + | 0.374432i | \(0.122162\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8317.09 | + | 603.249i | 0.956006 | + | 0.0693403i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1720.95 | − | 626.373i | −0.196419 | − | 0.0714907i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1886.63 | − | 1583.07i | −0.213818 | − | 0.179415i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7141.69 | + | 5564.81i | −0.803739 | + | 0.626274i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3793.19 | −0.423925 | −0.211962 | − | 0.977278i | \(-0.567985\pi\) | ||||
−0.211962 | + | 0.977278i | \(0.567985\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13262.0 | −1.47190 | −0.735948 | − | 0.677038i | \(-0.763263\pi\) | ||||
−0.735948 | + | 0.677038i | \(0.763263\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8262.55 | + | 3350.75i | 0.910710 | + | 0.369324i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6486.79 | − | 5443.07i | −0.710081 | − | 0.595829i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9674.73 | − | 3521.31i | −1.05182 | − | 0.382832i | −0.242471 | − | 0.970159i | \(-0.577958\pi\) |
−0.809350 | + | 0.587327i | \(0.800180\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8858.86 | − | 3971.75i | −0.956577 | − | 0.428869i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6433.59 | − | 5398.43i | 0.689998 | − | 0.578977i | −0.228910 | − | 0.973447i | \(-0.573516\pi\) |
0.918909 | + | 0.394470i | \(0.129072\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2793.16 | − | 15840.8i | 0.297547 | − | 1.68748i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10151.7 | + | 367.674i | 1.07418 | + | 0.0389047i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5426.60 | − | 9399.15i | 0.570373 | − | 0.987914i | −0.426155 | − | 0.904650i | \(-0.640132\pi\) |
0.996528 | − | 0.0832641i | \(-0.0265345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4876.71 | + | 8446.71i | 0.509169 | + | 0.881907i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10957.5 | + | 9891.88i | 1.13648 | + | 1.02596i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19170.2 | − | 6977.38i | 1.97519 | − | 0.718911i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2521.85 | + | 14302.1i | 0.258134 | + | 1.46395i | 0.787899 | + | 0.615805i | \(0.211169\pi\) |
−0.529765 | + | 0.848144i | \(0.677720\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8996.29 | + | 980.917i | 0.914839 | + | 0.0997501i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1197.28 | − | 6790.14i | −0.120961 | − | 0.686005i | −0.983625 | − | 0.180227i | \(-0.942317\pi\) |
0.862664 | − | 0.505778i | \(-0.168794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16976.9 | + | 6179.10i | −1.70407 | + | 0.620231i | −0.996279 | − | 0.0861899i | \(-0.972531\pi\) |
−0.707792 | + | 0.706421i | \(0.750309\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1590.88 | − | 7437.12i | 0.158657 | − | 0.741695i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4432.93 | + | 7678.07i | 0.439254 | + | 0.760811i | 0.997632 | − | 0.0687761i | \(-0.0219094\pi\) |
−0.558378 | + | 0.829587i | \(0.688576\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6172.61 | + | 10691.3i | −0.607729 | + | 1.05262i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1960.30 | − | 3128.12i | 0.191775 | − | 0.306021i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −385.756 | + | 2187.73i | −0.0374991 | + | 0.212668i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1531.83 | − | 1285.36i | 0.147969 | − | 0.124160i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13861.1 | − | 3935.78i | 1.33052 | − | 0.377792i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13232.7 | − | 4816.31i | −1.26225 | − | 0.459422i | −0.377727 | − | 0.925917i | \(-0.623294\pi\) |
−0.884524 | + | 0.466495i | \(0.845516\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17386.0 | − | 14588.6i | −1.64809 | − | 1.38291i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2283.38 | + | 16401.2i | 0.215108 | + | 1.54510i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4155.58 | −0.389062 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19389.4 | −1.80414 | −0.902072 | − | 0.431586i | \(-0.857954\pi\) | ||||
−0.902072 | + | 0.431586i | \(0.857954\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −960.709 | − | 6900.66i | −0.0888441 | − | 0.638157i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13194.3 | − | 11071.3i | −1.21273 | − | 1.01760i | −0.999173 | − | 0.0406697i | \(-0.987051\pi\) |
−0.213556 | − | 0.976931i | \(-0.568505\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10581.8 | + | 3851.45i | 0.966691 | + | 0.351847i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5680.57 | + | 1612.96i | −0.515803 | + | 0.146459i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18355.3 | + | 15402.0i | −1.65664 | + | 1.39009i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2323.05 | + | 13174.7i | −0.208405 | + | 1.18192i | 0.683585 | + | 0.729871i | \(0.260420\pi\) |
−0.891991 | + | 0.452054i | \(0.850691\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4636.90 | − | 7399.24i | 0.413496 | − | 0.659828i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6922.31 | − | 11989.8i | 0.613620 | − | 1.06282i | −0.377005 | − | 0.926211i | \(-0.623046\pi\) |
0.990625 | − | 0.136609i | \(-0.0436205\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3886.38 | + | 6731.40i | 0.342458 | + | 0.593155i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4276.67 | + | 19992.8i | −0.374623 | + | 1.75130i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14055.9 | + | 5115.94i | −1.22400 | + | 0.445501i | −0.871540 | − | 0.490324i | \(-0.836878\pi\) |
−0.352464 | + | 0.935825i | \(0.614656\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −792.407 | − | 4493.96i | −0.0685989 | − | 0.389044i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5838.98 | + | 7971.33i | −0.502529 | + | 0.686048i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1551.39 | + | 8798.34i | 0.132742 | + | 0.752818i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6457.91 | + | 2350.49i | −0.549359 | + | 0.199950i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 596.514 | + | 538.505i | 0.0504510 | + | 0.0455448i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3924.43 | − | 6797.31i | −0.330004 | − | 0.571584i | 0.652508 | − | 0.757782i | \(-0.273717\pi\) |
−0.982512 | + | 0.186198i | \(0.940384\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7321.97 | − | 12682.0i | 0.612175 | − | 1.06032i | −0.378698 | − | 0.925520i | \(-0.623628\pi\) |
0.990873 | − | 0.134798i | \(-0.0430385\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3907.87 | − | 141.535i | −0.324864 | − | 0.0117659i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1667.96 | − | 9459.49i | 0.137870 | − | 0.781901i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1753.12 | − | 1471.05i | 0.144088 | − | 0.120905i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10304.3 | − | 4619.81i | −0.842126 | − | 0.377556i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32253.2 | + | 11739.2i | 2.62109 | + | 0.953998i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1698.17 | + | 1424.93i | 0.137230 | + | 0.115150i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4110.43 | + | 1666.92i | 0.330313 | + | 0.133953i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8001.03 | 0.639385 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12240.4 | −0.972745 | −0.486372 | − | 0.873752i | \(-0.661680\pi\) | ||||
−0.486372 | + | 0.873752i | \(0.661680\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8081.64 | + | 6297.22i | −0.638704 | + | 0.497679i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14428.8 | − | 12107.2i | −1.13406 | − | 0.951591i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13010.6 | + | 4735.49i | 1.01699 | + | 0.370155i | 0.796114 | − | 0.605146i | \(-0.206885\pi\) |
0.220879 | + | 0.975301i | \(0.429108\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2502.14 | + | 181.483i | 0.194515 | + | 0.0141084i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9418.91 | + | 7903.41i | −0.728238 | + | 0.611064i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 737.416 | − | 4182.09i | 0.0567054 | − | 0.321593i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6932.57 | − | 13079.1i | −0.530218 | − | 1.00032i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2049.36 | + | 3549.59i | −0.155896 | + | 0.270020i | −0.933385 | − | 0.358877i | \(-0.883160\pi\) |
0.777489 | + | 0.628897i | \(0.216493\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3908.79 | + | 6770.22i | 0.295750 | + | 0.512254i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7096.01 | + | 2295.47i | −0.534035 | + | 0.172754i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19726.1 | − | 7179.71i | 1.47665 | − | 0.537458i | 0.526755 | − | 0.850017i | \(-0.323408\pi\) |
0.949898 | + | 0.312559i | \(0.101186\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1106.45 | − | 6274.97i | −0.0823869 | − | 0.467239i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18921.3 | − | 3919.46i | 1.40144 | − | 0.290303i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3207.06 | + | 18188.1i | 0.236286 | + | 1.34005i | 0.839888 | + | 0.542760i | \(0.182621\pi\) |
−0.603602 | + | 0.797286i | \(0.706268\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8850.02 | − | 3221.15i | 0.648620 | − | 0.236078i | 0.00330448 | − | 0.999995i | \(-0.498948\pi\) |
0.645315 | + | 0.763916i | \(0.276726\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25260.0 | + | 8171.32i | −1.84163 | + | 0.595745i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1706.81 | + | 2956.28i | 0.123789 | + | 0.214409i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6534.09 | + | 11317.4i | −0.471435 | + | 0.816549i | −0.999466 | − | 0.0326762i | \(-0.989597\pi\) |
0.528031 | + | 0.849225i | \(0.322930\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1183.23 | − | 2232.31i | −0.0849283 | − | 0.160227i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2732.30 | + | 15495.7i | −0.195103 | + | 1.10649i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9096.74 | + | 7633.07i | −0.646223 | + | 0.542246i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11665.0 | + | 17197.8i | −0.824424 | + | 1.21545i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2383.29 | − | 867.448i | −0.167579 | − | 0.0609939i | 0.256868 | − | 0.966446i | \(-0.417309\pi\) |
−0.424447 | + | 0.905453i | \(0.639532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8034.24 | + | 6741.53i | 0.562046 | + | 0.471613i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8356.30 | − | 6511.24i | 0.581611 | − | 0.453192i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8431.98 | 0.583912 | 0.291956 | − | 0.956432i | \(-0.405694\pi\) | ||||
0.291956 | + | 0.956432i | \(0.405694\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16804.9 | 1.15787 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21549.2 | − | 8738.93i | −1.47730 | − | 0.599097i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −285.369 | − | 239.453i | −0.0194655 | − | 0.0163335i | 0.633003 | − | 0.774149i | \(-0.281822\pi\) |
−0.652468 | + | 0.757816i | \(0.726267\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3783.87 | + | 1377.22i | 0.256818 | + | 0.0934740i | 0.467221 | − | 0.884141i | \(-0.345255\pi\) |
−0.210403 | + | 0.977615i | \(0.567478\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1282.06 | − | 12509.7i | −0.0865831 | − | 0.844836i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6293.61 | + | 5280.96i | −0.422928 | + | 0.354879i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −240.592 | + | 1364.47i | −0.0160879 | + | 0.0912388i | −0.991795 | − | 0.127842i | \(-0.959195\pi\) |
0.975707 | + | 0.219081i | \(0.0703060\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24028.7 | + | 870.273i | 1.59884 | + | 0.0579068i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12092.2 | + | 20944.3i | −0.800652 | + | 1.38677i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6625.82 | − | 11476.3i | −0.436565 | − | 0.756153i | 0.560857 | − | 0.827913i | \(-0.310472\pi\) |
−0.997422 | + | 0.0717601i | \(0.977138\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16617.0 | + | 15001.0i | 1.08953 | + | 0.983577i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5742.14 | − | 2089.97i | 0.374667 | − | 0.136368i | −0.147821 | − | 0.989014i | \(-0.547226\pi\) |
0.522489 | + | 0.852646i | \(0.325004\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 158.970 | + | 901.563i | 0.0103224 | + | 0.0585410i | 0.989534 | − | 0.144301i | \(-0.0460933\pi\) |
−0.979211 | + | 0.202842i | \(0.934982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11670.2 | − | 12179.3i | −0.754122 | − | 0.787016i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7532.44 | − | 42718.6i | −0.484399 | − | 2.74716i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10590.2 | − | 3854.53i | 0.677774 | − | 0.246690i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1703.40 | − | 7963.14i | 0.108497 | − | 0.507204i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9347.83 | − | 16190.9i | −0.592563 | − | 1.02635i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3125.11 | − | 5412.85i | 0.197161 | − | 0.341493i | −0.750446 | − | 0.660932i | \(-0.770161\pi\) |
0.947607 | + | 0.319439i | \(0.103495\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10818.8 | − | 17263.9i | 0.679319 | − | 1.08401i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 616.735 | − | 3497.68i | 0.0385423 | − | 0.218585i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21569.0 | − | 18098.5i | 1.34159 | − | 1.12573i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5966.10 | − | 23667.3i | 0.369351 | − | 1.46520i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7732.55 | + | 2814.42i | 0.476470 | + | 0.173421i | 0.569081 | − | 0.822281i | \(-0.307299\pi\) |
−0.0926108 | + | 0.995702i | \(0.529521\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1394.39 | − | 1170.03i | −0.0855201 | − | 0.0717599i | 0.599025 | − | 0.800730i | \(-0.295555\pi\) |
−0.684545 | + | 0.728970i | \(0.739999\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 703.080 | + | 5050.14i | 0.0429205 | + | 0.308293i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14438.2 | −0.877318 | −0.438659 | − | 0.898654i | \(-0.644546\pi\) | ||||
−0.438659 | + | 0.898654i | \(0.644546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9306.51 | 0.562885 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2828.08 | − | 20313.8i | −0.170263 | − | 1.22298i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15367.0 | + | 12894.4i | 0.920914 | + | 0.772739i | 0.974164 | − | 0.225842i | \(-0.0725134\pi\) |
−0.0532495 | + | 0.998581i | \(0.516958\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6481.75 | − | 2359.16i | −0.386661 | − | 0.140733i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3335.35 | + | 3237.65i | 0.198058 | + | 0.192257i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14421.1 | − | 12100.7i | 0.852451 | − | 0.715291i | −0.107877 | − | 0.994164i | \(-0.534405\pi\) |
0.960328 | + | 0.278873i | \(0.0899608\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 387.406 | − | 2197.09i | 0.0227963 | − | 0.129284i | −0.971286 | − | 0.237916i | \(-0.923536\pi\) |
0.994082 | + | 0.108632i | \(0.0346469\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13936.8 | + | 22239.4i | −0.816382 | + | 1.30273i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9174.47 | + | 15890.6i | −0.534993 | + | 0.926636i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10494.8 | − | 18177.6i | −0.609237 | − | 1.05523i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1694.39 | − | 7920.99i | 0.0979206 | − | 0.457763i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1942.82 | + | 707.127i | −0.111776 | + | 0.0406831i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2561.47 | − | 14526.8i | −0.146712 | − | 0.832048i | −0.965976 | − | 0.258631i | \(-0.916729\pi\) |
0.819264 | − | 0.573417i | \(-0.194382\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3310.94 | − | 2214.58i | 0.188797 | − | 0.126280i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 666.714 | + | 3781.13i | 0.0378492 | + | 0.214654i | 0.997867 | − | 0.0652871i | \(-0.0207963\pi\) |
−0.960017 | + | 0.279941i | \(0.909685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10530.7 | + | 3832.86i | −0.595185 | + | 0.216630i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 984.857 | + | 889.083i | 0.0554182 | + | 0.0500290i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6452.62 | + | 11176.3i | 0.361497 | + | 0.626132i | 0.988207 | − | 0.153121i | \(-0.0489323\pi\) |
−0.626710 | + | 0.779252i | \(0.715599\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13880.4 | − | 24041.5i | 0.774222 | − | 1.34099i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26840.2 | + | 972.098i | 1.49056 | + | 0.0539852i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7256.57 | + | 41154.1i | −0.401239 | + | 2.27554i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5853.56 | + | 4911.72i | −0.322257 | + | 0.270406i | −0.789536 | − | 0.613704i | \(-0.789679\pi\) |
0.467279 | + | 0.884110i | \(0.345234\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12907.5 | + | 9326.83i | −0.707525 | + | 0.511251i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9129.27 | − | 3322.78i | −0.498263 | − | 0.181353i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21658.9 | + | 18174.0i | 1.17703 | + | 0.987644i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19408.1 | − | 7870.63i | −1.05019 | − | 0.425887i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16562.4 | 0.892373 | 0.446187 | − | 0.894940i | \(-0.352782\pi\) | ||||
0.446187 | + | 0.894940i | \(0.352782\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20413.4 | 1.09517 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12442.5 | + | 9695.18i | −0.664695 | + | 0.517932i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16057.1 | + | 13473.5i | 0.854159 | + | 0.716725i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 866.193 | + | 315.268i | 0.0458823 | + | 0.0166998i | 0.364859 | − | 0.931063i | \(-0.381117\pi\) |
−0.318977 | + | 0.947762i | \(0.603339\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1886.20 | + | 3892.85i | 0.0994908 | + | 0.205335i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13715.2 | + | 11508.4i | −0.720392 | + | 0.604481i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2973.89 | − | 16865.8i | 0.155548 | − | 0.882159i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13895.9 | − | 26216.2i | −0.723781 | − | 1.36550i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1108.55 | − | 1920.06i | 0.0574992 | − | 0.0995915i | −0.835843 | − | 0.548969i | \(-0.815021\pi\) |
0.893342 | + | 0.449377i | \(0.148354\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12046.4 | + | 20865.0i | 0.622237 | + | 1.07775i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12485.0 | + | 4038.76i | −0.642218 | + | 0.207750i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4657.69 | − | 1695.26i | 0.238596 | − | 0.0868420i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2305.90 | + | 13077.4i | 0.117636 | + | 0.667145i | 0.985411 | + | 0.170189i | \(0.0544378\pi\) |
−0.867776 | + | 0.496956i | \(0.834451\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13283.8 | + | 14524.5i | −0.674887 | + | 0.737921i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1118.25 | + | 6341.90i | 0.0565799 | + | 0.320880i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18468.5 | − | 6721.99i | 0.930628 | − | 0.338721i | 0.168169 | − | 0.985758i | \(-0.446214\pi\) |
0.762458 | + | 0.647037i | \(0.223992\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17472.8 | − | 5652.25i | 0.876865 | − | 0.283655i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5181.82 | + | 8975.18i | 0.258989 | + | 0.448582i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6917.27 | − | 11981.1i | 0.344325 | − | 0.596388i | −0.640906 | − | 0.767619i | \(-0.721441\pi\) |
0.985231 | + | 0.171231i | \(0.0547746\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13420.8 | − | 25320.0i | −0.665352 | − | 1.25527i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3872.43 | + | 21961.6i | −0.191206 | + | 1.08438i | 0.726514 | + | 0.687152i | \(0.241139\pi\) |
−0.917720 | + | 0.397229i | \(0.869972\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14719.8 | + | 12351.4i | −0.723881 | + | 0.607408i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6988.82 | − | 14423.9i | −0.342312 | − | 0.706485i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5617.60 | + | 2044.64i | 0.274049 | + | 0.0997457i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18445.2 | + | 15477.4i | 0.896238 | + | 0.752033i | 0.969451 | − | 0.245283i | \(-0.0788810\pi\) |
−0.0732136 | + | 0.997316i | \(0.523325\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2374.87 | + | 1850.50i | −0.114933 | + | 0.0895563i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27923.4 | −1.34601 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15873.5 | 0.762132 | 0.381066 | − | 0.924548i | \(-0.375557\pi\) | ||||
0.381066 | + | 0.924548i | \(0.375557\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12882.4 | + | 5224.25i | 0.616075 | + | 0.249839i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21981.7 | − | 18444.8i | −1.04709 | − | 0.878613i | −0.0543053 | − | 0.998524i | \(-0.517294\pi\) |
−0.992785 | + | 0.119912i | \(0.961739\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −47731.2 | − | 17372.7i | −2.26473 | − | 0.824293i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13874.8 | + | 10025.8i | −0.655746 | + | 0.473836i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25088.3 | − | 21051.6i | 1.18108 | − | 0.991040i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2217.08 | + | 12573.7i | −0.103966 | + | 0.589620i | 0.887662 | + | 0.460495i | \(0.152328\pi\) |
−0.991628 | + | 0.129125i | \(0.958783\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18384.9 | + | 665.865i | 0.858776 | + | 0.0311032i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3017.93 | − | 5227.21i | 0.140424 | − | 0.243221i | −0.787233 | − | 0.616656i | \(-0.788487\pi\) |
0.927656 | + | 0.373435i | \(0.121820\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2113.97 | − | 3661.51i | −0.0979821 | − | 0.169710i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −29631.3 | − | 26749.7i | −1.36810 | − | 1.23506i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29009.7 | + | 10558.7i | −1.33425 | + | 0.485626i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3492.95 | + | 19809.5i | 0.160035 | + | 0.907605i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20358.3 | + | 13617.0i | −0.929178 | + | 0.621497i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1212.58 | + | 6876.87i | 0.0551321 | + | 0.312670i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20849.4 | − | 7588.56i | 0.944346 | − | 0.343714i | 0.176465 | − | 0.984307i | \(-0.443534\pi\) |
0.767881 | + | 0.640593i | \(0.221311\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2514.41 | − | 11754.5i | 0.113454 | − | 0.530380i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8591.51 | − | 14880.9i | −0.386194 | − | 0.668907i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3637.86 | + | 6300.95i | −0.162905 | + | 0.282161i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14473.4 | + | 23095.6i | −0.645682 | + | 1.03033i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2619.80 | − | 14857.6i | 0.116434 | − | 0.660332i | −0.869596 | − | 0.493764i | \(-0.835621\pi\) |
0.986030 | − | 0.166567i | \(-0.0532684\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15261.1 | + | 12805.6i | −0.675717 | + | 0.566994i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31705.0 | + | 30776.3i | 1.39855 | + | 1.35759i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3599.79 | − | 1310.22i | −0.158199 | − | 0.0575798i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23995.1 | − | 20134.3i | −1.05058 | − | 0.881542i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 426.718 | + | 3065.06i | 0.0186136 | + | 0.133699i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4962.96 | −0.215684 | −0.107842 | − | 0.994168i | \(-0.534394\pi\) | ||||
−0.107842 | + | 0.994168i | \(0.534394\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18808.2 | −0.814358 | −0.407179 | − | 0.913348i | \(-0.633488\pi\) | ||||
−0.407179 | + | 0.913348i | \(0.633488\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 356.984 | + | 2564.17i | 0.0153997 | + | 0.110614i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10095.7 | + | 8471.32i | 0.433912 | + | 0.364095i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6607.37 | − | 2404.88i | −0.282941 | − | 0.102982i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13698.2 | + | 54340.1i | −0.584435 | + | 2.31843i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10726.0 | − | 9000.16i | 0.455955 | − | 0.382592i | −0.385685 | − | 0.922630i | \(-0.626035\pi\) |
0.841640 | + | 0.540039i | \(0.181590\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6387.96 | + | 36227.9i | −0.270559 | + | 1.53442i | 0.482165 | + | 0.876081i | \(0.339851\pi\) |
−0.752724 | + | 0.658336i | \(0.771260\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1743.20 | + | 2781.68i | −0.0735641 | + | 0.117389i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10316.7 | − | 17869.0i | 0.433791 | − | 0.751349i | −0.563405 | − | 0.826181i | \(-0.690509\pi\) |
0.997196 | + | 0.0748324i | \(0.0238422\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19800.1 | − | 34294.7i | −0.829535 | − | 1.43680i | −0.898403 | − | 0.439171i | \(-0.855272\pi\) |
0.0688680 | − | 0.997626i | \(-0.478061\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9400.14 | − | 43944.1i | 0.392403 | − | 1.83442i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21795.0 | − | 7932.73i | 0.906545 | − | 0.329955i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2868.23 | + | 16266.5i | 0.118873 | + | 0.674163i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14454.2 | + | 15084.7i | 0.596906 | + | 0.622942i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3742.81 | + | 21226.5i | 0.154012 | + | 0.873446i | 0.959683 | + | 0.281083i | \(0.0906937\pi\) |
−0.805671 | + | 0.592363i | \(0.798195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5721.07 | + | 2082.30i | −0.234576 | + | 0.0853786i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5957.23 | + | 5377.91i | 0.243390 | + | 0.219721i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19336.7 | − | 33492.2i | −0.787223 | − | 1.36351i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11077.8 | + | 19187.4i | −0.449397 | + | 0.778378i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30133.4 | − | 1091.37i | −1.21811 | − | 0.0441175i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6051.23 | + | 34318.3i | −0.243753 | + | 1.38239i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10060.5 | + | 8441.78i | −0.403828 | + | 0.338852i | −0.821971 | − | 0.569529i | \(-0.807126\pi\) |
0.418143 | + | 0.908381i | \(0.362681\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1905.55 | − | 18593.5i | −0.0762205 | − | 0.743723i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6420.15 | − | 2336.74i | −0.255902 | − | 0.0931408i | 0.210884 | − | 0.977511i | \(-0.432366\pi\) |
−0.466786 | + | 0.884370i | \(0.654588\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2844.30 | + | 2386.65i | 0.112976 | + | 0.0947979i | 0.697525 | − | 0.716560i | \(-0.254284\pi\) |
−0.584550 | + | 0.811358i | \(0.698729\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 55945.3 | + | 22687.7i | 2.21441 | + | 0.898020i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28016.1 | −1.10507 | −0.552537 | − | 0.833488i | \(-0.686340\pi\) | ||||
−0.552537 | + | 0.833488i | \(0.686340\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1520.13 | −0.0597524 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3083.41 | − | 2402.60i | 0.120782 | − | 0.0941137i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2730.92 | − | 2291.52i | −0.106606 | − | 0.0894527i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34271.1 | + | 12473.7i | 1.33322 | + | 0.485251i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6407.88 | − | 9447.18i | 0.248424 | − | 0.366253i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30613.2 | − | 25687.5i | 1.18276 | − | 0.992454i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4156.37 | − | 23571.9i | 0.160035 | − | 0.907602i | −0.794003 | − | 0.607914i | \(-0.792006\pi\) |
0.954037 | − | 0.299688i | \(-0.0968825\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10107.3 | + | 19068.5i | 0.387838 | + | 0.731702i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6076.95 | − | 10525.6i | 0.232392 | − | 0.402515i | −0.726119 | − | 0.687569i | \(-0.758678\pi\) |
0.958512 | + | 0.285054i | \(0.0920114\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14612.5 | − | 25309.6i | −0.556909 | − | 0.964595i | −0.997752 | − | 0.0670105i | \(-0.978654\pi\) |
0.440843 | − | 0.897584i | \(-0.354679\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20323.8 | − | 6574.50i | 0.771951 | − | 0.249717i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31069.7 | + | 11308.4i | −1.17612 | + | 0.428072i | −0.854830 | − | 0.518909i | \(-0.826338\pi\) |
−0.321290 | + | 0.946981i | \(0.604116\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1663.17 | − | 9432.33i | −0.0627459 | − | 0.355850i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5092.55 | − | 15401.2i | 0.191478 | − | 0.579080i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3777.25 | − | 21421.9i | −0.141546 | − | 0.802750i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7884.24 | + | 2869.63i | −0.294459 | + | 0.107174i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 46545.4 | − | 15056.9i | 1.73256 | − | 0.560462i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12998.4 | + | 22513.9i | 0.482226 | + | 0.835239i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17211.8 | + | 29811.7i | −0.636414 | + | 1.10230i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6439.62 | + | 12149.1i | 0.237317 | + | 0.447727i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3365.29 | − | 19085.5i | 0.123609 | − | 0.701021i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5150.43 | − | 4321.72i | 0.188553 | − | 0.158214i | −0.543625 | − | 0.839328i | \(-0.682949\pi\) |
0.732177 | + | 0.681114i | \(0.238504\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21295.7 | − | 1544.61i | −0.777046 | − | 0.0563601i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7244.57 | + | 2636.81i | 0.263472 | + | 0.0958961i | 0.470379 | − | 0.882465i | \(-0.344117\pi\) |
−0.206906 | + | 0.978361i | \(0.566340\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10118.7 | + | 8490.62i | 0.366792 | + | 0.307775i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3743.23 | + | 2916.73i | −0.135243 | + | 0.105381i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18601.4 | −0.669871 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22717.1 | 0.815418 | 0.407709 | − | 0.913112i | \(-0.366328\pi\) | ||||
0.407709 | + | 0.913112i | \(0.366328\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30096.2 | + | 12205.0i | 1.07677 | + | 0.436666i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 54225.8 | + | 45500.8i | 1.93376 | + | 1.62262i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7732.85 | − | 2814.53i | −0.274870 | − | 0.100044i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22394.1 | − | 10040.1i | −0.793441 | − | 0.355729i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29601.6 | − | 24838.7i | 1.04542 | − | 0.877213i | 0.0528166 | − | 0.998604i | \(-0.483180\pi\) |
0.992605 | + | 0.121392i | \(0.0387357\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4397.60 | + | 24940.0i | −0.154807 | + | 0.877955i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26724.6 | + | 967.911i | 0.937752 | + | 0.0339635i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7053.75 | − | 12217.4i | 0.246719 | − | 0.427330i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15175.5 | − | 26284.7i | −0.529095 | − | 0.916419i | −0.999424 | − | 0.0339279i | \(-0.989198\pi\) |
0.470330 | − | 0.882491i | \(-0.344135\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21696.5 | − | 19586.6i | −0.754036 | − | 0.680708i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22898.9 | + | 8334.50i | −0.793285 | + | 0.288732i | −0.706701 | − | 0.707512i | \(-0.749817\pi\) |
−0.0865842 | + | 0.996245i | \(0.527595\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9151.35 | − | 51899.9i | −0.316022 | − | 1.79225i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −21598.8 | + | 29486.5i | −0.743503 | + | 1.01502i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1088.11 | + | 6170.97i | 0.0373377 | + | 0.211752i | 0.997769 | − | 0.0667655i | \(-0.0212679\pi\) |
−0.960431 | + | 0.278518i | \(0.910157\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12668.0 | + | 4610.77i | −0.433319 | + | 0.157715i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3269.86 | + | 15286.1i | −0.111496 | + | 0.521225i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3531.00 | − | 6115.87i | −0.120021 | − | 0.207883i | 0.799755 | − | 0.600327i | \(-0.204963\pi\) |
−0.919776 | + | 0.392444i | \(0.871630\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25109.6 | − | 43491.1i | 0.850814 | − | 1.47365i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10718.6 | − | 17104.0i | 0.362051 | − | 0.577736i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12999.9 | − | 73726.3i | 0.437737 | − | 2.48253i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5834.18 | + | 4895.46i | −0.195837 | + | 0.164327i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5857.96 | + | 1663.33i | −0.196023 | + | 0.0556593i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4490.88 | + | 1634.55i | 0.149810 | + | 0.0545263i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8819.45 | + | 7400.40i | 0.293293 | + | 0.246102i | 0.777546 | − | 0.628826i | \(-0.216464\pi\) |
−0.484253 | + | 0.874928i | \(0.660909\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3255.05 | − | 23380.7i | −0.107913 | − | 0.775124i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25765.5 | −0.851549 | −0.425774 | − | 0.904829i | \(-0.639998\pi\) | ||||
−0.425774 | + | 0.904829i | \(0.639998\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26199.3 | −0.863218 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1592.94 | + | 11441.9i | 0.0523231 | + | 0.375831i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12494.6 | + | 10484.2i | 0.409149 | + | 0.343317i | 0.824017 | − | 0.566565i | \(-0.191728\pi\) |
−0.414868 | + | 0.909882i | \(0.636172\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34218.8 | − | 12454.6i | −1.11710 | − | 0.406590i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 49773.4 | − | 14132.8i | 1.61992 | − | 0.459966i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14280.0 | − | 11982.4i | 0.463338 | − | 0.388787i | −0.381019 | − | 0.924567i | \(-0.624427\pi\) |
0.844358 | + | 0.535780i | \(0.179982\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3479.67 | + | 19734.2i | −0.112560 | + | 0.638358i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22588.3 | + | 36044.8i | −0.728463 | + | 1.16243i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6001.65 | − | 10395.2i | 0.192964 | − | 0.334223i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3160.07 | + | 5473.39i | 0.101294 | + | 0.175447i | 0.912218 | − | 0.409705i | \(-0.134368\pi\) |
−0.810924 | + | 0.585152i | \(0.801035\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5595.38 | + | 26157.5i | −0.178816 | + | 0.835935i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41333.6 | − | 15044.2i | 1.31695 | − | 0.479330i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5035.77 | + | 28559.3i | 0.159964 | + | 0.907203i | 0.954106 | + | 0.299470i | \(0.0968099\pi\) |
−0.794141 | + | 0.607733i | \(0.792079\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40423.7 | + | 4407.62i | 1.28023 | + | 0.139591i |
(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 | 108.4.i.a.13.4 | ✓ | 54 | |
3.2 | odd | 2 | 324.4.i.a.253.3 | 54 | |||
27.2 | odd | 18 | 324.4.i.a.73.3 | 54 | |||
27.25 | even | 9 | inner | 108.4.i.a.25.4 | yes | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.i.a.13.4 | ✓ | 54 | 1.1 | even | 1 | trivial | |
108.4.i.a.25.4 | yes | 54 | 27.25 | even | 9 | inner | |
324.4.i.a.73.3 | 54 | 27.2 | odd | 18 | |||
324.4.i.a.253.3 | 54 | 3.2 | odd | 2 |