Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(19,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 91.1 | ||
Character | \(\chi\) | \(=\) | 108.91 |
Dual form | 108.5.f.a.19.1 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.99035 | + | 0.277636i | −0.997588 | + | 0.0694089i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 15.8458 | − | 2.21573i | 0.990365 | − | 0.138483i | ||||
\(5\) | 23.3466 | − | 40.4374i | 0.933862 | − | 1.61750i | 0.157212 | − | 0.987565i | \(-0.449749\pi\) |
0.776650 | − | 0.629932i | \(-0.216917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 52.4363 | − | 30.2741i | 1.07013 | − | 0.617839i | 0.141913 | − | 0.989879i | \(-0.454675\pi\) |
0.928217 | + | 0.372040i | \(0.121341\pi\) | |||||||
\(8\) | −62.6153 | + | 13.2409i | −0.978364 | + | 0.206889i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −81.9341 | + | 167.841i | −0.819341 | + | 1.67841i | ||||
\(11\) | −63.7631 | + | 36.8136i | −0.526968 | + | 0.304245i | −0.739781 | − | 0.672848i | \(-0.765071\pi\) |
0.212813 | + | 0.977093i | \(0.431737\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.5924 | − | 27.0068i | 0.0922626 | − | 0.159803i | −0.816200 | − | 0.577769i | \(-0.803923\pi\) |
0.908463 | + | 0.417966i | \(0.137257\pi\) | |||||||
\(14\) | −200.834 | + | 135.363i | −1.02466 | + | 0.690626i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 246.181 | − | 70.2201i | 0.961645 | − | 0.274297i | ||||
\(17\) | −53.8013 | −0.186164 | −0.0930819 | − | 0.995658i | \(-0.529672\pi\) | ||||
−0.0930819 | + | 0.995658i | \(0.529672\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 54.9619i | − | 0.152249i | −0.997098 | − | 0.0761245i | \(-0.975745\pi\) | ||
0.997098 | − | 0.0761245i | \(-0.0242546\pi\) | |||||||
\(20\) | 280.347 | − | 692.494i | 0.700869 | − | 1.73124i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 244.217 | − | 164.602i | 0.504580 | − | 0.340088i | ||||
\(23\) | 243.863 | + | 140.795i | 0.460990 | + | 0.266152i | 0.712460 | − | 0.701712i | \(-0.247581\pi\) |
−0.251471 | + | 0.967865i | \(0.580914\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −777.624 | − | 1346.88i | −1.24420 | − | 2.15501i | ||||
\(26\) | −54.7210 | + | 112.096i | −0.0809483 | + | 0.165822i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 763.818 | − | 595.904i | 0.974258 | − | 0.760081i | ||||
\(29\) | −223.597 | − | 387.282i | −0.265871 | − | 0.460502i | 0.701921 | − | 0.712255i | \(-0.252326\pi\) |
−0.967791 | + | 0.251753i | \(0.918993\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −240.584 | − | 138.901i | −0.250347 | − | 0.144538i | 0.369576 | − | 0.929200i | \(-0.379503\pi\) |
−0.619923 | + | 0.784663i | \(0.712836\pi\) | |||||||
\(32\) | −962.854 | + | 348.552i | −0.940287 | + | 0.340383i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 214.686 | − | 14.9372i | 0.185715 | − | 0.0129214i | ||||
\(35\) | − | 2827.19i | − | 2.30791i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1016.51 | 0.742522 | 0.371261 | − | 0.928528i | \(-0.378925\pi\) | ||||
0.371261 | + | 0.928528i | \(0.378925\pi\) | |||||||
\(38\) | 15.2594 | + | 219.317i | 0.0105674 | + | 0.151882i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −926.424 | + | 2841.13i | −0.579015 | + | 1.77571i | ||||
\(41\) | 946.158 | − | 1638.79i | 0.562854 | − | 0.974892i | −0.434392 | − | 0.900724i | \(-0.643037\pi\) |
0.997246 | − | 0.0741680i | \(-0.0236301\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −666.266 | + | 384.669i | −0.360339 | + | 0.208042i | −0.669229 | − | 0.743056i | \(-0.733376\pi\) |
0.308891 | + | 0.951098i | \(0.400042\pi\) | |||||||
\(44\) | −928.811 | + | 724.625i | −0.479758 | + | 0.374290i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1012.19 | − | 494.115i | −0.478351 | − | 0.233514i | ||||
\(47\) | −2374.81 | + | 1371.10i | −1.07506 | + | 0.620687i | −0.929560 | − | 0.368671i | \(-0.879813\pi\) |
−0.145502 | + | 0.989358i | \(0.546480\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 632.546 | − | 1095.60i | 0.263451 | − | 0.456311i | ||||
\(50\) | 3476.94 | + | 5158.64i | 1.39077 | + | 2.06346i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 187.235 | − | 462.494i | 0.0692435 | − | 0.171041i | ||||
\(53\) | 4647.69 | 1.65457 | 0.827286 | − | 0.561780i | \(-0.189883\pi\) | ||||
0.827286 | + | 0.561780i | \(0.189883\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3437.89i | 1.13649i | ||||||||
\(56\) | −2882.46 | + | 2589.93i | −0.919152 | + | 0.825870i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 999.756 | + | 1483.31i | 0.297193 | + | 0.440937i | ||||
\(59\) | 262.792 | + | 151.723i | 0.0754934 | + | 0.0435861i | 0.537272 | − | 0.843409i | \(-0.319455\pi\) |
−0.461778 | + | 0.886995i | \(0.652788\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −478.174 | − | 828.222i | −0.128507 | − | 0.222580i | 0.794591 | − | 0.607145i | \(-0.207685\pi\) |
−0.923098 | + | 0.384564i | \(0.874352\pi\) | |||||||
\(62\) | 998.577 | + | 487.469i | 0.259776 | + | 0.126813i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3745.36 | − | 1658.17i | 0.914394 | − | 0.404826i | ||||
\(65\) | −728.057 | − | 1261.03i | −0.172321 | − | 0.298469i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6010.96 | − | 3470.43i | −1.33904 | − | 0.773096i | −0.352376 | − | 0.935858i | \(-0.614626\pi\) |
−0.986665 | + | 0.162762i | \(0.947960\pi\) | |||||||
\(68\) | −852.527 | + | 119.209i | −0.184370 | + | 0.0257805i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 784.928 | + | 11281.5i | 0.160189 | + | 2.30234i | ||||
\(71\) | 5971.60i | 1.18461i | 0.805715 | + | 0.592303i | \(0.201781\pi\) | ||||
−0.805715 | + | 0.592303i | \(0.798219\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4339.17 | −0.814257 | −0.407128 | − | 0.913371i | \(-0.633470\pi\) | ||||
−0.407128 | + | 0.913371i | \(0.633470\pi\) | |||||||
\(74\) | −4056.25 | + | 282.220i | −0.740732 | + | 0.0515377i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −121.781 | − | 870.917i | −0.0210839 | − | 0.150782i | ||||
\(77\) | −2229.00 | + | 3860.75i | −0.375949 | + | 0.651163i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3294.15 | − | 1901.88i | 0.527824 | − | 0.304740i | −0.212306 | − | 0.977203i | \(-0.568097\pi\) |
0.740130 | + | 0.672464i | \(0.234764\pi\) | |||||||
\(80\) | 2907.96 | − | 11594.3i | 0.454369 | − | 1.81161i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3320.52 | + | 6802.05i | −0.493831 | + | 1.01161i | ||||
\(83\) | 2730.64 | − | 1576.53i | 0.396376 | − | 0.228848i | −0.288543 | − | 0.957467i | \(-0.593171\pi\) |
0.684919 | + | 0.728619i | \(0.259837\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1256.08 | + | 2175.59i | −0.173851 | + | 0.301119i | ||||
\(86\) | 2551.84 | − | 1719.94i | 0.345030 | − | 0.232551i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3505.10 | − | 3149.38i | 0.452622 | − | 0.406686i | ||||
\(89\) | 7132.44 | 0.900447 | 0.450224 | − | 0.892916i | \(-0.351344\pi\) | ||||
0.450224 | + | 0.892916i | \(0.351344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1888.18i | − | 0.228014i | ||||||
\(92\) | 4176.18 | + | 1690.67i | 0.493405 | + | 0.199749i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9095.67 | − | 6130.50i | 1.02939 | − | 0.693809i | ||||
\(95\) | −2222.52 | − | 1283.17i | −0.246262 | − | 0.142180i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 980.405 | + | 1698.11i | 0.104199 | + | 0.180477i | 0.913411 | − | 0.407040i | \(-0.133439\pi\) |
−0.809212 | + | 0.587517i | \(0.800106\pi\) | |||||||
\(98\) | −2219.91 | + | 4547.46i | −0.231144 | + | 0.473496i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −15306.4 | − | 19619.5i | −1.53064 | − | 1.96195i | ||||
\(101\) | −3849.96 | − | 6668.32i | −0.377410 | − | 0.653693i | 0.613275 | − | 0.789870i | \(-0.289852\pi\) |
−0.990685 | + | 0.136177i | \(0.956519\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3195.22 | + | 1844.76i | 0.301180 | + | 0.173886i | 0.642973 | − | 0.765889i | \(-0.277701\pi\) |
−0.341793 | + | 0.939775i | \(0.611034\pi\) | |||||||
\(104\) | −618.727 | + | 1897.50i | −0.0572048 | + | 0.175434i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18545.9 | + | 1290.37i | −1.65058 | + | 0.114842i | ||||
\(107\) | − | 13741.5i | − | 1.20024i | −0.799911 | − | 0.600118i | \(-0.795120\pi\) | ||
0.799911 | − | 0.600118i | \(-0.204880\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18709.9 | 1.57478 | 0.787388 | − | 0.616458i | \(-0.211433\pi\) | ||||
0.787388 | + | 0.616458i | \(0.211433\pi\) | |||||||
\(110\) | −954.480 | − | 13718.4i | −0.0788826 | − | 1.13375i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10783.0 | − | 11135.0i | 0.859613 | − | 0.887676i | ||||
\(113\) | −5000.50 | + | 8661.12i | −0.391613 | + | 0.678293i | −0.992662 | − | 0.120919i | \(-0.961416\pi\) |
0.601050 | + | 0.799212i | \(0.294749\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11386.7 | − | 6574.14i | 0.861002 | − | 0.497099i | ||||
\(116\) | −4401.20 | − | 5641.38i | −0.327081 | − | 0.419246i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1090.76 | − | 532.469i | −0.0783366 | − | 0.0382411i | ||||
\(119\) | −2821.15 | + | 1628.79i | −0.199219 | + | 0.115019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4610.01 | + | 7984.77i | −0.314870 | + | 0.545371i | ||||
\(122\) | 2138.03 | + | 3172.14i | 0.143646 | + | 0.213124i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4120.01 | − | 1667.93i | −0.267951 | − | 0.108477i | ||||
\(125\) | −43436.1 | −2.77991 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18883.8i | 1.17080i | 0.810745 | + | 0.585400i | \(0.199063\pi\) | ||||
−0.810745 | + | 0.585400i | \(0.800937\pi\) | |||||||
\(128\) | −14484.9 | + | 7656.52i | −0.884090 | + | 0.467317i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3255.31 | + | 4829.82i | 0.192622 | + | 0.285788i | ||||
\(131\) | 25700.9 | + | 14838.4i | 1.49763 | + | 0.864660i | 0.999996 | − | 0.00272458i | \(-0.000867262\pi\) |
0.497639 | + | 0.867384i | \(0.334201\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1663.92 | − | 2882.00i | −0.0940654 | − | 0.162926i | ||||
\(134\) | 24949.4 | + | 12179.4i | 1.38947 | + | 0.678290i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3368.79 | − | 712.379i | 0.182136 | − | 0.0385153i | ||||
\(137\) | 8332.79 | + | 14432.8i | 0.443965 | + | 0.768971i | 0.997980 | − | 0.0635366i | \(-0.0202380\pi\) |
−0.554014 | + | 0.832507i | \(0.686905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3545.95 | + | 2047.25i | 0.183528 | + | 0.105960i | 0.588949 | − | 0.808170i | \(-0.299542\pi\) |
−0.405421 | + | 0.914130i | \(0.632875\pi\) | |||||||
\(140\) | −6264.28 | − | 44799.1i | −0.319606 | − | 2.28567i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1657.93 | − | 23828.8i | −0.0822222 | − | 1.18175i | ||||
\(143\) | 2296.05i | 0.112282i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20880.9 | −0.993147 | ||||||||
\(146\) | 17314.8 | − | 1204.71i | 0.812293 | − | 0.0565167i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16107.5 | − | 2252.32i | 0.735368 | − | 0.102827i | ||||
\(149\) | −2934.59 | + | 5082.86i | −0.132183 | + | 0.228947i | −0.924518 | − | 0.381139i | \(-0.875532\pi\) |
0.792335 | + | 0.610086i | \(0.208865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 28725.6 | − | 16584.7i | 1.25984 | − | 0.727369i | 0.286797 | − | 0.957991i | \(-0.407409\pi\) |
0.973043 | + | 0.230622i | \(0.0740760\pi\) | |||||||
\(152\) | 727.745 | + | 3441.46i | 0.0314987 | + | 0.148955i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7822.63 | − | 16024.6i | 0.329846 | − | 0.675687i | ||||
\(155\) | −11233.6 | + | 6485.72i | −0.467579 | + | 0.269957i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11089.2 | + | 19207.1i | −0.449886 | + | 0.779226i | −0.998378 | − | 0.0569302i | \(-0.981869\pi\) |
0.548492 | + | 0.836156i | \(0.315202\pi\) | |||||||
\(158\) | −12616.8 | + | 8503.74i | −0.505400 | + | 0.340640i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8384.79 | + | 47072.8i | −0.327531 | + | 1.83878i | ||||
\(161\) | 17049.7 | 0.657758 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 31303.8i | 1.17821i | 0.808057 | + | 0.589104i | \(0.200519\pi\) | ||||
−0.808057 | + | 0.589104i | \(0.799481\pi\) | |||||||
\(164\) | 11361.5 | − | 28064.5i | 0.422425 | − | 1.04344i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10458.5 | + | 7049.04i | −0.379536 | + | 0.255808i | ||||
\(167\) | −22551.7 | − | 13020.2i | −0.808622 | − | 0.466858i | 0.0378548 | − | 0.999283i | \(-0.487948\pi\) |
−0.846477 | + | 0.532425i | \(0.821281\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13794.3 | + | 23892.4i | 0.482975 | + | 0.836538i | ||||
\(170\) | 4408.17 | − | 9030.10i | 0.152532 | − | 0.312460i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9705.23 | + | 7571.67i | −0.328057 | + | 0.255938i | ||||
\(173\) | 7830.38 | + | 13562.6i | 0.261632 | + | 0.453160i | 0.966676 | − | 0.256004i | \(-0.0824060\pi\) |
−0.705044 | + | 0.709164i | \(0.749073\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −81551.5 | − | 47083.8i | −2.66290 | − | 1.53743i | ||||
\(176\) | −13112.2 | + | 13540.3i | −0.423302 | + | 0.437122i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −28461.0 | + | 1980.22i | −0.898276 | + | 0.0624991i | ||||
\(179\) | 36836.7i | 1.14967i | 0.818268 | + | 0.574837i | \(0.194935\pi\) | ||||
−0.818268 | + | 0.574837i | \(0.805065\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 56961.0 | 1.73868 | 0.869342 | − | 0.494211i | \(-0.164543\pi\) | ||||
0.869342 | + | 0.494211i | \(0.164543\pi\) | |||||||
\(182\) | 524.227 | + | 7534.52i | 0.0158262 | + | 0.227464i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17133.8 | − | 5586.93i | −0.506080 | − | 0.165020i | ||||
\(185\) | 23732.1 | − | 41105.2i | 0.693414 | − | 1.20103i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3430.54 | − | 1980.62i | 0.0981024 | − | 0.0566394i | ||||
\(188\) | −34592.9 | + | 26988.1i | −0.978749 | + | 0.763584i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9224.88 | + | 4503.26i | 0.255537 | + | 0.124744i | ||||
\(191\) | 33837.1 | − | 19535.9i | 0.927527 | − | 0.535508i | 0.0414986 | − | 0.999139i | \(-0.486787\pi\) |
0.886029 | + | 0.463630i | \(0.153453\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2025.97 | + | 3509.08i | −0.0543898 | + | 0.0942059i | −0.891938 | − | 0.452157i | \(-0.850655\pi\) |
0.837549 | + | 0.546363i | \(0.183988\pi\) | |||||||
\(194\) | −4383.62 | − | 6503.87i | −0.116474 | − | 0.172810i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7595.67 | − | 18762.3i | 0.197721 | − | 0.488398i | ||||
\(197\) | 44869.6 | 1.15617 | 0.578083 | − | 0.815978i | \(-0.303801\pi\) | ||||
0.578083 | + | 0.815978i | \(0.303801\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 56256.7i | − | 1.42059i | −0.703905 | − | 0.710294i | \(-0.748562\pi\) | ||
0.703905 | − | 0.710294i | \(-0.251438\pi\) | |||||||
\(200\) | 66525.1 | + | 74039.1i | 1.66313 | + | 1.85098i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17214.1 | + | 25540.1i | 0.421872 | + | 0.625921i | ||||
\(203\) | −23449.3 | − | 13538.4i | −0.569032 | − | 0.328531i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −44179.1 | − | 76520.4i | −1.05126 | − | 1.82083i | ||||
\(206\) | −13262.2 | − | 6474.13i | −0.312523 | − | 0.152562i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1942.13 | − | 7743.46i | 0.0448902 | − | 0.178982i | ||||
\(209\) | 2023.35 | + | 3504.54i | 0.0463210 | + | 0.0802303i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 63309.8 | + | 36552.0i | 1.42202 | + | 0.821005i | 0.996472 | − | 0.0839298i | \(-0.0267471\pi\) |
0.425551 | + | 0.904935i | \(0.360080\pi\) | |||||||
\(212\) | 73646.6 | − | 10298.0i | 1.63863 | − | 0.229130i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3815.13 | + | 54833.4i | 0.0833071 | + | 1.19734i | ||||
\(215\) | 35922.8i | 0.777129i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16820.4 | −0.357205 | ||||||||
\(218\) | −74659.2 | + | 5194.54i | −1.57098 | + | 0.109303i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7617.42 | + | 54476.2i | 0.157385 | + | 1.12554i | ||||
\(221\) | −838.891 | + | 1453.00i | −0.0171760 | + | 0.0297496i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −65737.1 | + | 37953.3i | −1.32191 | + | 0.763203i | −0.984032 | − | 0.177989i | \(-0.943041\pi\) |
−0.337873 | + | 0.941192i | \(0.609708\pi\) | |||||||
\(224\) | −39936.4 | + | 47426.3i | −0.795927 | + | 0.945200i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17549.1 | − | 35949.3i | 0.343589 | − | 0.703839i | ||||
\(227\) | 35712.5 | − | 20618.6i | 0.693057 | − | 0.400136i | −0.111700 | − | 0.993742i | \(-0.535629\pi\) |
0.804756 | + | 0.593606i | \(0.202296\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13792.1 | + | 23888.7i | −0.263003 | + | 0.455534i | −0.967038 | − | 0.254630i | \(-0.918046\pi\) |
0.704036 | + | 0.710165i | \(0.251379\pi\) | |||||||
\(230\) | −43611.9 | + | 29394.5i | −0.824422 | + | 0.555662i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19128.6 | + | 21289.2i | 0.355391 | + | 0.395533i | ||||
\(233\) | −49430.2 | −0.910502 | −0.455251 | − | 0.890363i | \(-0.650450\pi\) | ||||
−0.455251 | + | 0.890363i | \(0.650450\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 128042.i | 2.31855i | ||||||||
\(236\) | 4500.34 | + | 1821.91i | 0.0808019 | + | 0.0327116i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10805.2 | − | 7282.69i | 0.190756 | − | 0.128570i | ||||
\(239\) | −97042.8 | − | 56027.7i | −1.69890 | − | 0.980859i | −0.946808 | − | 0.321800i | \(-0.895712\pi\) |
−0.752091 | − | 0.659060i | \(-0.770955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20548.3 | − | 35590.7i | −0.353787 | − | 0.612776i | 0.633123 | − | 0.774051i | \(-0.281773\pi\) |
−0.986910 | + | 0.161275i | \(0.948439\pi\) | |||||||
\(242\) | 16178.7 | − | 33142.0i | 0.276257 | − | 0.565910i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9412.18 | − | 12064.4i | −0.158092 | − | 0.202640i | ||||
\(245\) | −29535.6 | − | 51157.1i | −0.492054 | − | 0.852263i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1484.34 | − | 856.986i | −0.0243299 | − | 0.0140469i | ||||
\(248\) | 16903.4 | + | 5511.79i | 0.274834 | + | 0.0896167i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 173326. | − | 12059.4i | 2.77321 | − | 0.192951i | ||||
\(251\) | − | 50848.1i | − | 0.807099i | −0.914958 | − | 0.403550i | \(-0.867776\pi\) | ||
0.914958 | − | 0.403550i | \(-0.132224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20732.7 | −0.323902 | ||||||||
\(254\) | −5242.83 | − | 75353.2i | −0.0812640 | − | 1.16798i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 55674.3 | − | 34573.7i | 0.849522 | − | 0.527553i | ||||
\(257\) | 6405.02 | − | 11093.8i | 0.0969738 | − | 0.167964i | −0.813457 | − | 0.581625i | \(-0.802417\pi\) |
0.910431 | + | 0.413662i | \(0.135750\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 53302.2 | − | 30774.1i | 0.794595 | − | 0.458760i | ||||
\(260\) | −14330.8 | − | 18368.9i | −0.211994 | − | 0.271730i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −106675. | − | 52075.1i | −1.55404 | − | 0.758625i | ||||
\(263\) | −27445.5 | + | 15845.6i | −0.396789 | + | 0.229086i | −0.685097 | − | 0.728452i | \(-0.740240\pi\) |
0.288309 | + | 0.957537i | \(0.406907\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 108508. | − | 187941.i | 1.54514 | − | 2.67627i | ||||
\(266\) | 7439.79 | + | 11038.2i | 0.105147 | + | 0.156004i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −102938. | − | 41673.2i | −1.43320 | − | 0.580213i | ||||
\(269\) | 54892.9 | 0.758598 | 0.379299 | − | 0.925274i | \(-0.376165\pi\) | ||||
0.379299 | + | 0.925274i | \(0.376165\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 106332.i | − | 1.44785i | −0.689877 | − | 0.723927i | \(-0.742335\pi\) | ||
0.689877 | − | 0.723927i | \(-0.257665\pi\) | |||||||
\(272\) | −13244.9 | + | 3777.94i | −0.179024 | + | 0.0510643i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −37257.8 | − | 55278.5i | −0.496268 | − | 0.736301i | ||||
\(275\) | 99167.4 | + | 57254.3i | 1.31130 | + | 0.757082i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25166.6 | + | 43589.8i | 0.327993 | + | 0.568100i | 0.982113 | − | 0.188290i | \(-0.0602945\pi\) |
−0.654121 | + | 0.756390i | \(0.726961\pi\) | |||||||
\(278\) | −14718.0 | − | 7184.78i | −0.190440 | − | 0.0929660i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 37434.5 | + | 177025.i | 0.477481 | + | 2.25797i | ||||
\(281\) | −3048.20 | − | 5279.64i | −0.0386039 | − | 0.0668640i | 0.846078 | − | 0.533059i | \(-0.178958\pi\) |
−0.884682 | + | 0.466195i | \(0.845624\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −44494.8 | − | 25689.1i | −0.555567 | − | 0.320757i | 0.195797 | − | 0.980644i | \(-0.437271\pi\) |
−0.751364 | + | 0.659888i | \(0.770604\pi\) | |||||||
\(284\) | 13231.4 | + | 94625.0i | 0.164048 | + | 1.17319i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −637.465 | − | 9162.05i | −0.00779335 | − | 0.112011i | ||||
\(287\) | − | 114576.i | − | 1.39101i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −80626.4 | −0.965343 | ||||||||
\(290\) | 83322.2 | − | 5797.29i | 0.990752 | − | 0.0689332i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −68757.8 | + | 9614.43i | −0.806411 | + | 0.112761i | ||||
\(293\) | 45640.7 | − | 79051.9i | 0.531639 | − | 0.920825i | −0.467679 | − | 0.883898i | \(-0.654910\pi\) |
0.999318 | − | 0.0369270i | \(-0.0117569\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12270.6 | − | 7084.43i | 0.141001 | − | 0.0814068i | ||||
\(296\) | −63649.3 | + | 13459.6i | −0.726457 | + | 0.153620i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10298.9 | − | 21097.1i | 0.115973 | − | 0.237570i | ||||
\(299\) | 7604.82 | − | 4390.65i | 0.0850642 | − | 0.0491118i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23291.0 | + | 40341.3i | −0.257073 | + | 0.445263i | ||||
\(302\) | −110021. | + | 74154.3i | −1.20632 | + | 0.813059i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3859.43 | − | 13530.6i | −0.0417615 | − | 0.146409i | ||||
\(305\) | −44654.9 | −0.480031 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 108180.i | − | 1.14781i | −0.818923 | − | 0.573904i | \(-0.805428\pi\) | ||
0.818923 | − | 0.573904i | \(-0.194572\pi\) | |||||||
\(308\) | −26766.0 | + | 66115.6i | −0.282152 | + | 0.696952i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 43025.4 | − | 28999.2i | 0.447714 | − | 0.301760i | ||||
\(311\) | 86673.2 | + | 50040.8i | 0.896116 | + | 0.517373i | 0.875938 | − | 0.482424i | \(-0.160243\pi\) |
0.0201778 | + | 0.999796i | \(0.493577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 75895.3 | + | 131455.i | 0.774687 | + | 1.34180i | 0.934970 | + | 0.354726i | \(0.115426\pi\) |
−0.160283 | + | 0.987071i | \(0.551241\pi\) | |||||||
\(314\) | 38917.4 | − | 79722.0i | 0.394716 | − | 0.808572i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 47984.5 | − | 37435.8i | 0.480537 | − | 0.374898i | ||||
\(317\) | 56202.0 | + | 97344.7i | 0.559285 | + | 0.968710i | 0.997556 | + | 0.0698672i | \(0.0222575\pi\) |
−0.438271 | + | 0.898843i | \(0.644409\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28514.5 | + | 16462.9i | 0.280211 | + | 0.161780i | ||||
\(320\) | 20389.2 | − | 190165.i | 0.199113 | − | 1.85708i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −68034.5 | + | 4733.62i | −0.656172 | + | 0.0456543i | ||||
\(323\) | 2957.02i | 0.0283433i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −48500.0 | −0.459172 | ||||||||
\(326\) | −8691.05 | − | 124913.i | −0.0817781 | − | 1.17537i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −37544.9 | + | 115142.i | −0.348982 | + | 1.07025i | ||||
\(329\) | −83017.6 | + | 143791.i | −0.766970 | + | 1.32843i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −99528.9 | + | 57463.0i | −0.908433 | + | 0.524484i | −0.879927 | − | 0.475109i | \(-0.842408\pi\) |
−0.0285065 | + | 0.999594i | \(0.509075\pi\) | |||||||
\(332\) | 39776.0 | − | 31031.8i | 0.360865 | − | 0.281534i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 93604.0 | + | 45694.1i | 0.839076 | + | 0.409607i | ||||
\(335\) | −280670. | + | 162045.i | −2.50096 | + | 1.44393i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −61646.2 | + | 106774.i | −0.542808 | + | 0.940171i | 0.455933 | + | 0.890014i | \(0.349306\pi\) |
−0.998741 | + | 0.0501573i | \(0.984028\pi\) | |||||||
\(338\) | −61677.3 | − | 91509.1i | −0.539874 | − | 0.800997i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −15083.1 | + | 37257.1i | −0.130476 | + | 0.322294i | ||||
\(341\) | 20453.8 | 0.175900 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 68777.2i | 0.584597i | ||||||||
\(344\) | 36625.1 | − | 32908.2i | 0.309501 | − | 0.278091i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −35011.5 | − | 51945.7i | −0.292454 | − | 0.433907i | ||||
\(347\) | 82843.4 | + | 47829.7i | 0.688017 | + | 0.397227i | 0.802869 | − | 0.596156i | \(-0.203306\pi\) |
−0.114852 | + | 0.993383i | \(0.536639\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21543.6 | − | 37314.5i | −0.176875 | − | 0.306357i | 0.763934 | − | 0.645295i | \(-0.223266\pi\) |
−0.940809 | + | 0.338938i | \(0.889932\pi\) | |||||||
\(350\) | 338491. | + | 165239.i | 2.76319 | + | 1.34889i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 48563.1 | − | 57670.9i | 0.391941 | − | 0.465448i | ||||
\(353\) | −56436.9 | − | 97751.7i | −0.452912 | − | 0.784467i | 0.545653 | − | 0.838011i | \(-0.316282\pi\) |
−0.998565 | + | 0.0535440i | \(0.982948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 241476. | + | 139416.i | 1.91610 | + | 1.10626i | ||||
\(356\) | 113020. | − | 15803.6i | 0.891771 | − | 0.124697i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10227.2 | − | 146992.i | −0.0797977 | − | 1.14690i | ||||
\(359\) | 223134.i | 1.73132i | 0.500632 | + | 0.865660i | \(0.333101\pi\) | ||||
−0.500632 | + | 0.865660i | \(0.666899\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 127300. | 0.976820 | ||||||||
\(362\) | −227295. | + | 15814.4i | −1.73449 | + | 0.120680i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4183.70 | − | 29919.8i | −0.0315760 | − | 0.225817i | ||||
\(365\) | −101305. | + | 175465.i | −0.760404 | + | 1.31706i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −92257.6 | + | 53265.0i | −0.684968 | + | 0.395466i | −0.801724 | − | 0.597694i | \(-0.796084\pi\) |
0.116756 | + | 0.993161i | \(0.462750\pi\) | |||||||
\(368\) | 69921.2 | + | 17536.9i | 0.516313 | + | 0.129496i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −83287.1 | + | 170613.i | −0.608379 | + | 1.24626i | ||||
\(371\) | 243708. | − | 140705.i | 1.77061 | − | 1.02226i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −71440.5 | + | 123739.i | −0.513484 | + | 0.889380i | 0.486394 | + | 0.873740i | \(0.338312\pi\) |
−0.999878 | + | 0.0156403i | \(0.995021\pi\) | |||||||
\(374\) | −13139.2 | + | 8855.83i | −0.0939345 | + | 0.0633120i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 130545. | − | 117296.i | 0.923389 | − | 0.829677i | ||||
\(377\) | −13945.7 | −0.0981197 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 95242.7i | − | 0.663061i | −0.943445 | − | 0.331530i | \(-0.892435\pi\) | ||
0.943445 | − | 0.331530i | \(-0.107565\pi\) | |||||||
\(380\) | −38060.8 | − | 15408.4i | −0.263579 | − | 0.106707i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −129598. | + | 87349.4i | −0.888121 | + | 0.598595i | ||||
\(383\) | −46899.6 | − | 27077.5i | −0.319721 | − | 0.184591i | 0.331547 | − | 0.943439i | \(-0.392429\pi\) |
−0.651268 | + | 0.758848i | \(0.725763\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 104079. | + | 180270.i | 0.702169 | + | 1.21619i | ||||
\(386\) | 7110.07 | − | 14564.9i | 0.0477199 | − | 0.0977538i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19297.9 | + | 24735.7i | 0.128188 | + | 0.164309i | ||||
\(389\) | 6513.23 | + | 11281.2i | 0.0430425 | + | 0.0745518i | 0.886744 | − | 0.462261i | \(-0.152962\pi\) |
−0.843702 | + | 0.536813i | \(0.819628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13120.2 | − | 7574.94i | −0.0858196 | − | 0.0495480i | ||||
\(392\) | −25100.3 | + | 76977.0i | −0.163346 | + | 0.500943i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −179046. | + | 12457.4i | −1.15338 | + | 0.0802481i | ||||
\(395\) | − | 177609.i | − | 1.13834i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 54407.2 | 0.345204 | 0.172602 | − | 0.984992i | \(-0.444783\pi\) | ||||
0.172602 | + | 0.984992i | \(0.444783\pi\) | |||||||
\(398\) | 15618.9 | + | 224484.i | 0.0986014 | + | 1.41716i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −286015. | − | 276972.i | −1.78759 | − | 1.73108i | ||||
\(401\) | 25211.2 | − | 43667.1i | 0.156785 | − | 0.271560i | −0.776922 | − | 0.629596i | \(-0.783220\pi\) |
0.933708 | + | 0.358036i | \(0.116554\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7502.54 | + | 4331.59i | −0.0461953 | + | 0.0266709i | ||||
\(404\) | −75781.0 | − | 97134.7i | −0.464299 | − | 0.595130i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 97329.6 | + | 47512.8i | 0.590463 | + | 0.288243i | ||||
\(407\) | −64816.0 | + | 37421.6i | −0.391285 | + | 0.225909i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20416.9 | + | 35363.2i | −0.122052 | + | 0.211400i | −0.920577 | − | 0.390562i | \(-0.872281\pi\) |
0.798525 | + | 0.601962i | \(0.205614\pi\) | |||||||
\(410\) | 197535. | + | 293078.i | 1.17510 | + | 1.74347i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 54718.4 | + | 22152.0i | 0.322358 | + | 0.130503i | ||||
\(413\) | 18373.2 | 0.107717 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 147226.i | − | 0.854850i | ||||||
\(416\) | −5599.92 | + | 31438.3i | −0.0323590 | + | 0.181666i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9046.86 | − | 13422.6i | −0.0517780 | − | 0.0768217i | ||||
\(419\) | −28866.9 | − | 16666.3i | −0.164427 | − | 0.0949318i | 0.415529 | − | 0.909580i | \(-0.363597\pi\) |
−0.579955 | + | 0.814648i | \(0.696930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4180.31 | − | 7240.51i | −0.0235855 | − | 0.0408512i | 0.853992 | − | 0.520287i | \(-0.174175\pi\) |
−0.877577 | + | 0.479435i | \(0.840842\pi\) | |||||||
\(422\) | −262777. | − | 128278.i | −1.47558 | − | 0.720324i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −291017. | + | 61539.7i | −1.61877 | + | 0.342313i | ||||
\(425\) | 41837.2 | + | 72464.1i | 0.231625 | + | 0.401186i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −50147.4 | − | 28952.6i | −0.275038 | − | 0.158793i | ||||
\(428\) | −30447.4 | − | 217746.i | −0.166212 | − | 1.18867i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9973.45 | − | 143345.i | −0.0539397 | − | 0.775255i | ||||
\(431\) | − | 88445.3i | − | 0.476124i | −0.971250 | − | 0.238062i | \(-0.923488\pi\) | ||
0.971250 | − | 0.238062i | \(-0.0765122\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 119092. | 0.635195 | 0.317598 | − | 0.948226i | \(-0.397124\pi\) | ||||
0.317598 | + | 0.948226i | \(0.397124\pi\) | |||||||
\(434\) | 67119.5 | − | 4669.95i | 0.356344 | − | 0.0247932i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 296474. | − | 41456.1i | 1.55960 | − | 0.218080i | ||||
\(437\) | 7738.34 | − | 13403.2i | 0.0405214 | − | 0.0701852i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 103483. | − | 59746.2i | 0.536960 | − | 0.310014i | −0.206886 | − | 0.978365i | \(-0.566333\pi\) |
0.743846 | + | 0.668351i | \(0.233000\pi\) | |||||||
\(440\) | −45520.7 | − | 215264.i | −0.235128 | − | 1.11190i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2944.07 | − | 6030.90i | 0.0150696 | − | 0.0308700i | ||||
\(443\) | 176414. | − | 101853.i | 0.898930 | − | 0.518998i | 0.0220772 | − | 0.999756i | \(-0.492972\pi\) |
0.876853 | + | 0.480759i | \(0.159639\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 166518. | − | 288418.i | 0.840894 | − | 1.45647i | ||||
\(446\) | 251777. | − | 169698.i | 1.26574 | − | 0.853114i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 146193. | − | 200336.i | 0.728402 | − | 0.998165i | ||||
\(449\) | −77156.2 | −0.382717 | −0.191359 | − | 0.981520i | \(-0.561289\pi\) | ||||
−0.191359 | + | 0.981520i | \(0.561289\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 139326.i | 0.684982i | ||||||||
\(452\) | −60046.4 | + | 148322.i | −0.293907 | + | 0.725989i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −136781. | + | 92190.7i | −0.663612 | + | 0.447276i | ||||
\(455\) | −76353.2 | − | 44082.6i | −0.368812 | − | 0.212934i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −140420. | − | 243215.i | −0.672353 | − | 1.16455i | −0.977235 | − | 0.212159i | \(-0.931951\pi\) |
0.304882 | − | 0.952390i | \(-0.401383\pi\) | |||||||
\(458\) | 48403.1 | − | 99153.4i | 0.230750 | − | 0.472690i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 165866. | − | 129403.i | 0.783866 | − | 0.611544i | ||||
\(461\) | −200811. | − | 347814.i | −0.944898 | − | 1.63661i | −0.755956 | − | 0.654623i | \(-0.772827\pi\) |
−0.188942 | − | 0.981988i | \(-0.560506\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 51806.1 | + | 29910.3i | 0.241668 | + | 0.139527i | 0.615943 | − | 0.787791i | \(-0.288775\pi\) |
−0.374275 | + | 0.927318i | \(0.622108\pi\) | |||||||
\(464\) | −82240.4 | − | 79640.5i | −0.381988 | − | 0.369912i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 197244. | − | 13723.6i | 0.908306 | − | 0.0631969i | ||||
\(467\) | 208473.i | 0.955909i | 0.878385 | + | 0.477955i | \(0.158622\pi\) | ||||
−0.878385 | + | 0.477955i | \(0.841378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −420257. | −1.91060 | ||||||||
\(470\) | −35548.9 | − | 510931.i | −0.160928 | − | 2.31295i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18463.8 | − | 6020.59i | −0.0828775 | − | 0.0270243i | ||||
\(473\) | 28322.1 | − | 49055.4i | 0.126591 | − | 0.219263i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −74027.3 | + | 42739.7i | −0.328099 | + | 0.189428i | ||||
\(476\) | −41094.5 | + | 32060.4i | −0.181372 | + | 0.141500i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 402790. | + | 196628.i | 1.76288 | + | 0.860575i | ||||
\(479\) | −138667. | + | 80059.3i | −0.604368 | + | 0.348932i | −0.770758 | − | 0.637128i | \(-0.780122\pi\) |
0.166390 | + | 0.986060i | \(0.446789\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15849.9 | − | 27452.8i | 0.0685070 | − | 0.118658i | ||||
\(482\) | 91876.1 | + | 136314.i | 0.395466 | + | 0.586743i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −55357.4 | + | 136740.i | −0.236312 | + | 0.583720i | ||||
\(485\) | 91556.4 | 0.389229 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 371960.i | − | 1.56834i | −0.620549 | − | 0.784168i | \(-0.713090\pi\) | ||
0.620549 | − | 0.784168i | \(-0.286910\pi\) | |||||||
\(488\) | 40907.4 | + | 45527.9i | 0.171776 | + | 0.191178i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 132060. | + | 195935.i | 0.550022 | + | 0.816055i | ||||
\(491\) | −57863.4 | − | 33407.4i | −0.240016 | − | 0.138574i | 0.375168 | − | 0.926957i | \(-0.377585\pi\) |
−0.615184 | + | 0.788383i | \(0.710918\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12029.8 | + | 20836.3i | 0.0494955 | + | 0.0857288i | ||||
\(494\) | 6160.99 | + | 3007.57i | 0.0252462 | + | 0.0123243i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −68980.8 | − | 17301.0i | −0.280391 | − | 0.0703246i | ||||
\(497\) | 180785. | + | 313129.i | 0.731896 | + | 1.26768i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 288151. | + | 166364.i | 1.15723 | + | 0.668127i | 0.950638 | − | 0.310301i | \(-0.100430\pi\) |
0.206591 | + | 0.978427i | \(0.433763\pi\) | |||||||
\(500\) | −688282. | + | 96242.7i | −2.75313 | + | 0.384971i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14117.2 | + | 202902.i | 0.0560199 | + | 0.805153i | ||||
\(503\) | 12673.0i | 0.0500892i | 0.999686 | + | 0.0250446i | \(0.00797278\pi\) | ||||
−0.999686 | + | 0.0250446i | \(0.992027\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −359533. | −1.40980 | ||||||||
\(506\) | 82730.6 | − | 5756.12i | 0.323121 | − | 0.0224817i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 41841.5 | + | 299230.i | 0.162136 | + | 1.15952i | ||||
\(509\) | −19452.7 | + | 33693.0i | −0.0750834 | + | 0.130048i | −0.901123 | − | 0.433564i | \(-0.857256\pi\) |
0.826039 | + | 0.563613i | \(0.190589\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −227530. | + | 131365.i | −0.871360 | + | 0.503080i | ||||
\(512\) | −212561. | + | 153419.i | −0.810856 | + | 0.585245i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22478.3 | + | 46046.5i | −0.0850817 | + | 0.174289i | ||||
\(515\) | 149195. | − | 86137.5i | 0.562521 | − | 0.324772i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 100950. | − | 174851.i | 0.377682 | − | 0.654164i | ||||
\(518\) | −204151. | + | 137598.i | −0.760837 | + | 0.512805i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 62284.7 | + | 69319.7i | 0.230343 | + | 0.256360i | ||||
\(521\) | −28001.3 | −0.103158 | −0.0515790 | − | 0.998669i | \(-0.516425\pi\) | ||||
−0.0515790 | + | 0.998669i | \(0.516425\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 306435.i | 1.12030i | 0.828391 | + | 0.560151i | \(0.189257\pi\) | ||||
−0.828391 | + | 0.560151i | \(0.810743\pi\) | |||||||
\(524\) | 440130. | + | 178181.i | 1.60295 | + | 0.648932i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 105118. | − | 70849.6i | 0.379931 | − | 0.256074i | ||||
\(527\) | 12943.7 | + | 7473.06i | 0.0466056 | + | 0.0269077i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −100274. | − | 173680.i | −0.358326 | − | 0.620638i | ||||
\(530\) | −380805. | + | 780076.i | −1.35566 | + | 2.77706i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −32752.0 | − | 41980.9i | −0.115722 | − | 0.148330i | ||||
\(533\) | −29505.7 | − | 51105.4i | −0.103861 | − | 0.179892i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −555671. | − | 320817.i | −1.94138 | − | 1.12086i | ||||
\(536\) | 422330. | + | 137711.i | 1.47002 | + | 0.479336i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −219042. | + | 15240.2i | −0.756768 | + | 0.0526534i | ||||
\(539\) | 93145.3i | 0.320615i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 387269. | 1.32318 | 0.661590 | − | 0.749866i | \(-0.269882\pi\) | ||||
0.661590 | + | 0.749866i | \(0.269882\pi\) | |||||||
\(542\) | 29521.5 | + | 424302.i | 0.100494 | + | 1.44436i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 51802.8 | − | 18752.6i | 0.175047 | − | 0.0633669i | ||||
\(545\) | 436812. | − | 756581.i | 1.47062 | − | 2.54720i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 220183. | − | 127123.i | 0.735883 | − | 0.424862i | −0.0846877 | − | 0.996408i | \(-0.526989\pi\) |
0.820570 | + | 0.571545i | \(0.193656\pi\) | |||||||
\(548\) | 164019. | + | 210237.i | 0.546177 | + | 0.700080i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −411609. | − | 200933.i | −1.36069 | − | 0.664240i | ||||
\(551\) | −21285.8 | + | 12289.3i | −0.0701109 | + | 0.0404786i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 115156. | − | 199455.i | 0.376560 | − | 0.652221i | ||||
\(554\) | −112526. | − | 166951.i | −0.366633 | − | 0.543965i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 60724.6 | + | 24583.6i | 0.196433 | + | 0.0795235i | ||||
\(557\) | 154243. | 0.497159 | 0.248580 | − | 0.968611i | \(-0.420036\pi\) | ||||
0.248580 | + | 0.968611i | \(0.420036\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23991.6i | 0.0767779i | ||||||||
\(560\) | −198525. | − | 696000.i | −0.633053 | − | 2.21939i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13629.2 | + | 20221.4i | 0.0431518 | + | 0.0640232i | ||||
\(563\) | −188653. | − | 108919.i | −0.595177 | − | 0.343626i | 0.171965 | − | 0.985103i | \(-0.444988\pi\) |
−0.767142 | + | 0.641477i | \(0.778322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 233489. | + | 404415.i | 0.731425 | + | 1.26686i | ||||
\(566\) | 184682. | + | 90155.2i | 0.576490 | + | 0.281422i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −79069.4 | − | 373914.i | −0.245082 | − | 1.15898i | ||||
\(569\) | 112165. | + | 194275.i | 0.346443 | + | 0.600057i | 0.985615 | − | 0.169007i | \(-0.0540561\pi\) |
−0.639172 | + | 0.769064i | \(0.720723\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 227168. | + | 131156.i | 0.696748 | + | 0.402268i | 0.806135 | − | 0.591732i | \(-0.201555\pi\) |
−0.109387 | + | 0.993999i | \(0.534889\pi\) | |||||||
\(572\) | 5087.42 | + | 36382.8i | 0.0155491 | + | 0.111200i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 31810.5 | + | 457201.i | 0.0965488 | + | 1.38766i | ||||
\(575\) | − | 437941.i | − | 1.32458i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 450994. | 1.35462 | 0.677312 | − | 0.735696i | \(-0.263145\pi\) | ||||
0.677312 | + | 0.735696i | \(0.263145\pi\) | |||||||
\(578\) | 321728. | − | 22384.8i | 0.963015 | − | 0.0670034i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −330876. | + | 46266.4i | −0.983578 | + | 0.137534i | ||||
\(581\) | 95456.3 | − | 165335.i | 0.282782 | − | 0.489794i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −296351. | + | 171099.i | −0.871907 | + | 0.503396i | ||||
\(584\) | 271699. | − | 57454.6i | 0.796640 | − | 0.168461i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −160175. | + | 328117.i | −0.466443 | + | 0.955505i | ||||
\(587\) | −307738. | + | 177673.i | −0.893111 | + | 0.515638i | −0.874959 | − | 0.484197i | \(-0.839112\pi\) |
−0.0181523 | + | 0.999835i | \(0.505778\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7634.26 | + | 13222.9i | −0.0220058 | + | 0.0381151i | ||||
\(590\) | −46997.1 | + | 31676.1i | −0.135010 | + | 0.0909972i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 250246. | − | 71379.7i | 0.714043 | − | 0.203672i | ||||
\(593\) | −89819.5 | −0.255424 | −0.127712 | − | 0.991811i | \(-0.540763\pi\) | ||||
−0.127712 | + | 0.991811i | \(0.540763\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 152106.i | 0.429649i | ||||||||
\(596\) | −35238.8 | + | 87044.4i | −0.0992038 | + | 0.245046i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −29126.9 | + | 19631.6i | −0.0814502 | + | 0.0548976i | ||||
\(599\) | −357687. | − | 206511.i | −0.996896 | − | 0.575558i | −0.0895677 | − | 0.995981i | \(-0.528549\pi\) |
−0.907328 | + | 0.420422i | \(0.861882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −129317. | − | 223984.i | −0.358020 | − | 0.620110i | 0.629610 | − | 0.776912i | \(-0.283215\pi\) |
−0.987630 | + | 0.156802i | \(0.949882\pi\) | |||||||
\(602\) | 81739.3 | − | 167442.i | 0.225548 | − | 0.462032i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 418434. | − | 326447.i | 1.14697 | − | 0.894828i | ||||
\(605\) | 215256. | + | 372834.i | 0.588090 | + | 1.01860i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −267430. | − | 154401.i | −0.725825 | − | 0.419055i | 0.0910678 | − | 0.995845i | \(-0.470972\pi\) |
−0.816893 | + | 0.576789i | \(0.804305\pi\) | |||||||
\(608\) | 19157.1 | + | 52920.3i | 0.0518229 | + | 0.143158i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 178189. | − | 12397.8i | 0.478873 | − | 0.0333184i | ||||
\(611\) | 85514.7i | 0.229065i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −464349. | −1.23573 | −0.617865 | − | 0.786284i | \(-0.712002\pi\) | ||||
−0.617865 | + | 0.786284i | \(0.712002\pi\) | |||||||
\(614\) | 30034.6 | + | 431675.i | 0.0796681 | + | 1.14504i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 88449.9 | − | 271256.i | 0.233097 | − | 0.714855i | ||||
\(617\) | −253688. | + | 439401.i | −0.666392 | + | 1.15423i | 0.312513 | + | 0.949913i | \(0.398829\pi\) |
−0.978906 | + | 0.204312i | \(0.934504\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −244884. | + | 141384.i | −0.639115 | + | 0.368993i | −0.784273 | − | 0.620415i | \(-0.786964\pi\) |
0.145159 | + | 0.989408i | \(0.453631\pi\) | |||||||
\(620\) | −163635. | + | 127662.i | −0.425690 | + | 0.332108i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −359750. | − | 175617.i | −0.929865 | − | 0.453927i | ||||
\(623\) | 373999. | − | 215929.i | 0.963595 | − | 0.556332i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −528069. | + | 914643.i | −1.35186 | + | 2.34149i | ||||
\(626\) | −339346. | − | 503479.i | −0.865951 | − | 1.28479i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −133161. | + | 328924.i | −0.337642 | + | 0.834019i | ||||
\(629\) | −54689.8 | −0.138231 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 403620.i | 1.01371i | 0.862031 | + | 0.506855i | \(0.169192\pi\) | ||||
−0.862031 | + | 0.506855i | \(0.830808\pi\) | |||||||
\(632\) | −181082. | + | 162704.i | −0.453357 | + | 0.407347i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −251292. | − | 372836.i | −0.625173 | − | 0.927554i | ||||
\(635\) | 763614. | + | 440873.i | 1.89377 | + | 1.09337i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19725.8 | − | 34166.1i | −0.0486134 | − | 0.0842008i | ||||
\(638\) | −118354. | − | 57776.0i | −0.290764 | − | 0.141940i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −28563.4 | + | 764487.i | −0.0697350 | + | 1.86642i | ||||
\(641\) | −181028. | − | 313549.i | −0.440584 | − | 0.763114i | 0.557149 | − | 0.830413i | \(-0.311895\pi\) |
−0.997733 | + | 0.0672990i | \(0.978562\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −346651. | − | 200139.i | −0.838437 | − | 0.484072i | 0.0182957 | − | 0.999833i | \(-0.494176\pi\) |
−0.856733 | + | 0.515761i | \(0.827509\pi\) | |||||||
\(644\) | 270167. | − | 37777.6i | 0.651420 | − | 0.0910883i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −820.975 | − | 11799.6i | −0.00196727 | − | 0.0282749i | ||||
\(647\) | 98990.1i | 0.236474i | 0.992985 | + | 0.118237i | \(0.0377242\pi\) | ||||
−0.992985 | + | 0.118237i | \(0.962276\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22341.9 | −0.0530434 | ||||||||
\(650\) | 193532. | − | 13465.3i | 0.458064 | − | 0.0318706i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 69360.7 | + | 496035.i | 0.163162 | + | 1.16686i | ||||
\(653\) | −269165. | + | 466208.i | −0.631237 | + | 1.09333i | 0.356062 | + | 0.934462i | \(0.384119\pi\) |
−0.987299 | + | 0.158872i | \(0.949214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.20006e6 | − | 692852.i | 2.79717 | − | 1.61495i | ||||
\(656\) | 117850. | − | 469879.i | 0.273856 | − | 1.09189i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 291348. | − | 596824.i | 0.672915 | − | 1.37846i | ||||
\(659\) | −126219. | + | 72872.6i | −0.290639 | + | 0.167801i | −0.638230 | − | 0.769846i | \(-0.720333\pi\) |
0.347591 | + | 0.937646i | \(0.387000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 126176. | − | 218543.i | 0.288784 | − | 0.500189i | −0.684736 | − | 0.728792i | \(-0.740082\pi\) |
0.973520 | + | 0.228603i | \(0.0734157\pi\) | |||||||
\(662\) | 381201. | − | 256930.i | 0.869838 | − | 0.586273i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −150105. | + | 134871.i | −0.340454 | + | 0.305903i | ||||
\(665\) | −155388. | −0.351377 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 125925.i | − | 0.283049i | ||||||
\(668\) | −386199. | − | 156348.i | −0.865483 | − | 0.350380i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.07498e6 | − | 724541.i | 2.39471 | − | 1.61404i | ||||
\(671\) | 60979.7 | + | 35206.7i | 0.135438 | + | 0.0781951i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −327332. | − | 566956.i | −0.722701 | − | 1.25175i | −0.959913 | − | 0.280297i | \(-0.909567\pi\) |
0.237213 | − | 0.971458i | \(-0.423766\pi\) | |||||||
\(674\) | 216346. | − | 443182.i | 0.476243 | − | 0.975580i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 271520. | + | 348030.i | 0.594168 | + | 0.761594i | ||||
\(677\) | −106756. | − | 184907.i | −0.232924 | − | 0.403437i | 0.725743 | − | 0.687966i | \(-0.241496\pi\) |
−0.958667 | + | 0.284529i | \(0.908163\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 102818. | + | 59361.8i | 0.223012 | + | 0.128756i | ||||
\(680\) | 49842.9 | − | 152857.i | 0.107792 | − | 0.330572i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −81617.9 | + | 5678.71i | −0.175476 | + | 0.0122090i | ||||
\(683\) | 885039.i | 1.89724i | 0.316425 | + | 0.948618i | \(0.397517\pi\) | ||||
−0.316425 | + | 0.948618i | \(0.602483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 778168. | 1.65841 | ||||||||
\(686\) | −19095.0 | − | 274445.i | −0.0405762 | − | 0.583187i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −137011. | + | 141484.i | −0.289453 | + | 0.298902i | ||||
\(689\) | 72468.6 | − | 125519.i | 0.152655 | − | 0.264406i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 382656. | − | 220927.i | 0.801406 | − | 0.462692i | −0.0425567 | − | 0.999094i | \(-0.513550\pi\) |
0.843963 | + | 0.536402i | \(0.180217\pi\) | |||||||
\(692\) | 154130. | + | 197561.i | 0.321866 | + | 0.412562i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −343854. | − | 167857.i | −0.713929 | − | 0.348514i | ||||
\(695\) | 165571. | − | 95592.6i | 0.342780 | − | 0.197904i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50904.6 | + | 88169.3i | −0.104783 | + | 0.181490i | ||||
\(698\) | 96326.3 | + | 142917.i | 0.197712 | + | 0.293341i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.39658e6 | − | 565386.i | −2.85015 | − | 1.15385i | ||||
\(701\) | −340679. | −0.693281 | −0.346640 | − | 0.937998i | \(-0.612678\pi\) | ||||
−0.346640 | + | 0.937998i | \(0.612678\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 55869.5i | − | 0.113048i | ||||||
\(704\) | −177772. | + | 243610.i | −0.358690 | + | 0.491530i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 252343. | + | 374395.i | 0.506269 | + | 0.751139i | ||||
\(707\) | −403755. | − | 233108.i | −0.807755 | − | 0.466357i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 292720. | + | 507006.i | 0.582318 | + | 1.00860i | 0.995204 | + | 0.0978214i | \(0.0311874\pi\) |
−0.412886 | + | 0.910783i | \(0.635479\pi\) | |||||||
\(710\) | −1.00228e6 | − | 489278.i | −1.98826 | − | 0.970597i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −446600. | + | 94440.0i | −0.880966 | + | 0.186293i | ||||
\(713\) | −39113.0 | − | 67745.8i | −0.0769383 | − | 0.133261i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 92846.3 | + | 53604.8i | 0.181615 | + | 0.104856i | ||||
\(716\) | 81620.2 | + | 583709.i | 0.159210 | + | 1.13860i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −61950.0 | − | 890385.i | −0.120169 | − | 1.72715i | ||||
\(719\) | 306988.i | 0.593832i | 0.954904 | + | 0.296916i | \(0.0959581\pi\) | ||||
−0.954904 | + | 0.296916i | \(0.904042\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 223394. | 0.429735 | ||||||||
\(722\) | −507973. | + | 35343.1i | −0.974464 | + | 0.0678000i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 902595. | − | 126210.i | 1.72193 | − | 0.240778i | ||||
\(725\) | −347749. | + | 602319.i | −0.661592 | + | 1.14591i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −488481. | + | 282025.i | −0.924227 | + | 0.533603i | −0.884981 | − | 0.465627i | \(-0.845829\pi\) |
−0.0392459 | + | 0.999230i | \(0.512496\pi\) | |||||||
\(728\) | 25001.2 | + | 118229.i | 0.0471736 | + | 0.223081i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 355526. | − | 728293.i | 0.667154 | − | 1.36666i | ||||
\(731\) | 35846.0 | − | 20695.7i | 0.0670821 | − | 0.0387298i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −290960. | + | 503957.i | −0.541533 | + | 0.937963i | 0.457283 | + | 0.889321i | \(0.348823\pi\) |
−0.998816 | + | 0.0486418i | \(0.984511\pi\) | |||||||
\(734\) | 353352. | − | 238160.i | 0.655867 | − | 0.442055i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −283879. | − | 50565.6i | −0.524056 | − | 0.0933469i | ||||
\(737\) | 511037. | 0.940843 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 193774.i | 0.354818i | 0.984137 | + | 0.177409i | \(0.0567715\pi\) | ||||
−0.984137 | + | 0.177409i | \(0.943228\pi\) | |||||||
\(740\) | 284977. | − | 703930.i | 0.520411 | − | 1.28548i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −933417. | + | 629124.i | −1.69538 | + | 1.14269i | ||||
\(743\) | −76480.8 | − | 44156.2i | −0.138540 | − | 0.0799861i | 0.429128 | − | 0.903244i | \(-0.358821\pi\) |
−0.567668 | + | 0.823258i | \(0.692154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 137025. | + | 237334.i | 0.246881 | + | 0.427610i | ||||
\(746\) | 250719. | − | 513595.i | 0.450514 | − | 0.922875i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 49971.3 | − | 38985.8i | 0.0893135 | − | 0.0696792i | ||||
\(749\) | −416012. | − | 720554.i | −0.741553 | − | 1.28441i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 474180. | + | 273768.i | 0.840743 | + | 0.485403i | 0.857517 | − | 0.514456i | \(-0.172006\pi\) |
−0.0167738 | + | 0.999859i | \(0.505340\pi\) | |||||||
\(752\) | −488355. | + | 504298.i | −0.863575 | + | 0.891767i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 55648.1 | − | 3871.81i | 0.0978831 | − | 0.00681038i | ||||
\(755\) | − | 1.54879e6i | − | 2.71705i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45164.0 | −0.0788135 | −0.0394068 | − | 0.999223i | \(-0.512547\pi\) | ||||
−0.0394068 | + | 0.999223i | \(0.512547\pi\) | |||||||
\(758\) | 26442.8 | + | 380052.i | 0.0460223 | + | 0.661462i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 156154. | + | 50918.0i | 0.270350 | + | 0.0881545i | ||||
\(761\) | −100185. | + | 173525.i | −0.172995 | + | 0.299636i | −0.939465 | − | 0.342644i | \(-0.888678\pi\) |
0.766471 | + | 0.642279i | \(0.222011\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 981079. | − | 566426.i | 1.68521 | − | 0.972959i | ||||
\(764\) | 492891. | − | 384536.i | 0.844432 | − | 0.658795i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 194663. | + | 95027.7i | 0.331762 | + | 0.161954i | ||||
\(767\) | 8195.11 | − | 4731.45i | 0.0139304 | − | 0.00804273i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −212834. | + | 368639.i | −0.359905 | + | 0.623374i | −0.987945 | − | 0.154807i | \(-0.950524\pi\) |
0.628039 | + | 0.778181i | \(0.283858\pi\) | |||||||
\(770\) | −465362. | − | 690446.i | −0.784891 | − | 1.16452i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24328.0 | + | 60093.2i | −0.0408198 | + | 0.100830i | ||||
\(773\) | −199528. | −0.333922 | −0.166961 | − | 0.985964i | \(-0.553395\pi\) | ||||
−0.166961 | + | 0.985964i | \(0.553395\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 432051.i | 0.719335i | ||||||||
\(776\) | −83872.9 | − | 93346.4i | −0.139283 | − | 0.155015i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −29122.2 | − | 43207.9i | −0.0481132 | − | 0.0713844i | ||||
\(779\) | −90071.2 | − | 52002.6i | −0.148426 | − | 0.0856940i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −219836. | − | 380768.i | −0.360411 | − | 0.624249i | ||||
\(782\) | 54457.2 | + | 26584.1i | 0.0890517 | + | 0.0434718i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 78787.6 | − | 314134.i | 0.128182 | − | 0.511073i | ||||
\(785\) | 517791. | + | 896841.i | 0.840263 | + | 1.45538i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −899924. | − | 519571.i | −1.45297 | − | 0.838872i | −0.454320 | − | 0.890839i | \(-0.650118\pi\) |
−0.998649 | + | 0.0519669i | \(0.983451\pi\) | |||||||
\(788\) | 710997. | − | 99418.9i | 1.14503 | − | 0.160109i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 49310.7 | + | 708724.i | 0.0790109 | + | 1.13559i | ||||
\(791\) | 605543.i | 0.967815i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29823.5 | −0.0474255 | ||||||||
\(794\) | −217104. | + | 15105.4i | −0.344371 | + | 0.0239602i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −124650. | − | 891434.i | −0.196727 | − | 1.40690i | ||||
\(797\) | 12577.0 | − | 21783.9i | 0.0197997 | − | 0.0342941i | −0.855956 | − | 0.517049i | \(-0.827030\pi\) |
0.875755 | + | 0.482755i | \(0.160364\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 127768. | − | 73766.9i | 0.200138 | − | 0.115549i | ||||
\(800\) | 1.21820e6 | + | 1.02581e6i | 1.90343 | + | 1.60283i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −88478.1 | + | 181247.i | −0.137558 | + | 0.281787i | ||||
\(803\) | 276679. | − | 159741.i | 0.429087 | − | 0.247734i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 398053. | − | 689448.i | 0.614255 | − | 1.06392i | ||||
\(806\) | 28735.2 | − | 19367.6i | 0.0442327 | − | 0.0298129i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 329361. | + | 366562.i | 0.504486 | + | 0.561468i | ||||
\(809\) | −975055. | −1.48981 | −0.744907 | − | 0.667168i | \(-0.767506\pi\) | ||||
−0.744907 | + | 0.667168i | \(0.767506\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 240015.i | 0.364919i | 0.983213 | + | 0.182460i | \(0.0584059\pi\) | ||||
−0.983213 | + | 0.182460i | \(0.941594\pi\) | |||||||
\(812\) | −401571. | − | 162571.i | −0.609046 | − | 0.246564i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 248249. | − | 167320.i | 0.374662 | − | 0.252523i | ||||
\(815\) | 1.26584e6 | + | 730836.i | 1.90575 | + | 1.10028i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21142.1 | + | 36619.3i | 0.0316741 | + | 0.0548612i | ||||
\(818\) | 71652.7 | − | 146780.i | 0.107084 | − | 0.219361i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −869603. | − | 1.11464e6i | −1.29328 | − | 1.65770i | ||||
\(821\) | −406806. | − | 704608.i | −0.603533 | − | 1.04535i | −0.992282 | − | 0.124005i | \(-0.960426\pi\) |
0.388749 | − | 0.921344i | \(-0.372907\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24117.0 | − | 13924.0i | −0.0356061 | − | 0.0205572i | 0.482091 | − | 0.876121i | \(-0.339877\pi\) |
−0.517697 | + | 0.855564i | \(0.673211\pi\) | |||||||
\(824\) | −224496. | − | 73202.6i | −0.330639 | − | 0.107813i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −73315.4 | + | 5101.04i | −0.107457 | + | 0.00747651i | ||||
\(827\) | − | 1.05969e6i | − | 1.54941i | −0.632323 | − | 0.774705i | \(-0.717898\pi\) | ||
0.632323 | − | 0.774705i | \(-0.282102\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −904280. | −1.31581 | −0.657906 | − | 0.753100i | \(-0.728558\pi\) | ||||
−0.657906 | + | 0.753100i | \(0.728558\pi\) | |||||||
\(830\) | 40875.3 | + | 587486.i | 0.0593342 | + | 0.852788i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13617.2 | − | 127005.i | 0.0196717 | − | 0.183474i | ||||
\(833\) | −34031.8 | + | 58944.9i | −0.0490451 | + | 0.0849486i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.05301e6 | + | 607954.i | −1.51028 | + | 0.871963i | ||||
\(836\) | 39826.7 | + | 51049.2i | 0.0569852 | + | 0.0730426i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 119816. | + | 58490.0i | 0.170619 | + | 0.0832902i | ||||
\(839\) | −308829. | + | 178303.i | −0.438727 | + | 0.253299i | −0.703058 | − | 0.711133i | \(-0.748182\pi\) |
0.264330 | + | 0.964432i | \(0.414849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 253649. | − | 439333.i | 0.358625 | − | 0.621157i | ||||
\(842\) | 18691.1 | + | 27731.6i | 0.0263640 | + | 0.0391156i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.08419e6 | + | 438919.i | 1.52202 | + | 0.616168i | ||||
\(845\) | 1.28819e6 | 1.80413 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 558256.i | 0.778156i | ||||||||
\(848\) | 1.14417e6 | − | 326362.i | 1.59111 | − | 0.453845i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −187064. | − | 277542.i | −0.258912 | − | 0.384141i | ||||
\(851\) | 247890. | + | 143120.i | 0.342295 | + | 0.197624i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 93966.4 | + | 162755.i | 0.129144 | + | 0.223684i | 0.923345 | − | 0.383971i | \(-0.125444\pi\) |
−0.794201 | + | 0.607655i | \(0.792110\pi\) | |||||||
\(854\) | 208144. | + | 101608.i | 0.285396 | + | 0.139320i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 181950. | + | 860429.i | 0.248316 | + | 1.17427i | ||||
\(857\) | 424830. | + | 735827.i | 0.578434 | + | 1.00188i | 0.995659 | + | 0.0930735i | \(0.0296692\pi\) |
−0.417226 | + | 0.908803i | \(0.636998\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.04585e6 | − | 603819.i | −1.41736 | − | 0.818315i | −0.421297 | − | 0.906923i | \(-0.638425\pi\) |
−0.996067 | + | 0.0886072i | \(0.971758\pi\) | |||||||
\(860\) | 79595.2 | + | 569227.i | 0.107619 | + | 0.769641i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24555.6 | + | 352928.i | 0.0330473 | + | 0.474976i | ||||
\(863\) | 77194.2i | 0.103648i | 0.998656 | + | 0.0518242i | \(0.0165036\pi\) | ||||
−0.998656 | + | 0.0518242i | \(0.983496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 731250. | 0.977313 | ||||||||
\(866\) | −475220. | + | 33064.2i | −0.633664 | + | 0.0440882i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −266534. | + | 37269.5i | −0.353763 | + | 0.0494668i | ||||
\(869\) | −140030. | + | 242539.i | −0.185431 | + | 0.321176i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −187450. | + | 108224.i | −0.247087 | + | 0.142656i | ||||
\(872\) | −1.17153e6 | + | 247736.i | −1.54070 | + | 0.325804i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −27157.5 | + | 55631.9i | −0.0355522 | + | 0.0728285i | ||||
\(875\) | −2.27763e6 | + | 1.31499e6i | −2.97487 | + | 1.71754i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −71455.2 | + | 123764.i | −0.0929040 | + | 0.160914i | −0.908732 | − | 0.417380i | \(-0.862948\pi\) |
0.815828 | + | 0.578295i | \(0.196282\pi\) | |||||||
\(878\) | −396348. | + | 267139.i | −0.514147 | + | 0.346536i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 241409. | + | 846343.i | 0.311737 | + | 1.09290i | ||||
\(881\) | 305226. | 0.393250 | 0.196625 | − | 0.980479i | \(-0.437002\pi\) | ||||
0.196625 | + | 0.980479i | \(0.437002\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 902045.i | − | 1.15693i | −0.815707 | − | 0.578465i | \(-0.803652\pi\) | ||
0.815707 | − | 0.578465i | \(-0.196348\pi\) | |||||||
\(884\) | −10073.5 | + | 24882.8i | −0.0128906 | + | 0.0318416i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −675677. | + | 455407.i | −0.860739 | + | 0.580140i | ||||
\(887\) | −797270. | − | 460304.i | −1.01335 | − | 0.585056i | −0.101177 | − | 0.994868i | \(-0.532261\pi\) |
−0.912170 | + | 0.409813i | \(0.865594\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 571692. | + | 990199.i | 0.723367 | + | 1.25291i | ||||
\(890\) | −584391. | + | 1.19712e6i | −0.737774 | + | 1.51132i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −957564. | + | 747057.i | −1.20348 | + | 0.938911i | ||||
\(893\) | 75358.1 | + | 130524.i | 0.0944990 | + | 0.163677i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.48958e6 | + | 860011.i | 1.85960 | + | 1.07364i | ||||
\(896\) | −527742. | + | 839998.i | −0.657364 | + | 1.04631i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 307881. | − | 21421.3i | 0.381794 | − | 0.0265640i | ||||
\(899\) | 124232.i | 0.153714i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −250052. | −0.308022 | ||||||||
\(902\) | −38681.9 | − | 555960.i | −0.0475439 | − | 0.683330i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 198427. | − | 608530.i | 0.242808 | − | 0.744638i | ||||
\(905\) | 1.32984e6 | − | 2.30336e6i | 1.62369 | − | 2.81232i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −426945. | + | 246497.i | −0.518988 | + | 0.299638i | −0.736520 | − | 0.676415i | \(-0.763532\pi\) |
0.217533 | + | 0.976053i | \(0.430199\pi\) | |||||||
\(908\) | 520209. | − | 405849.i | 0.630967 | − | 0.492258i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 316915. | + | 154707.i | 0.382702 | + | 0.186821i | ||||
\(911\) | 208640. | − | 120458.i | 0.251397 | − | 0.145144i | −0.369007 | − | 0.929427i | \(-0.620302\pi\) |
0.620404 | + | 0.784283i | \(0.286969\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −116076. | + | 201049.i | −0.139252 | + | 0.241191i | ||||
\(914\) | 627851. | + | 931528.i | 0.751561 | + | 1.11507i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −165617. | + | 409095.i | −0.197385 | + | 0.487566i | ||||
\(917\) | 1.79688e6 | 2.13688 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 155183.i | 0.183744i | 0.995771 | + | 0.0918719i | \(0.0292850\pi\) | ||||
−0.995771 | + | 0.0918719i | \(0.970715\pi\) | |||||||
\(920\) | −625937. | + | 562413.i | −0.739529 | + | 0.664476i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 897871. | + | 1.33215e6i | 1.05621 | + | 1.56708i | ||||
\(923\) | 161274. | + | 93111.4i | 0.189304 | + | 0.109295i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −790464. | − | 1.36912e6i | −0.923844 | − | 1.60015i | ||||
\(926\) | −215029. | − | 104969.i | −0.250769 | − | 0.122417i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 350279. | + | 294961.i | 0.406742 | + | 0.342506i | ||||
\(929\) | −352354. | − | 610296.i | −0.408271 | − | 0.707145i | 0.586425 | − | 0.810003i | \(-0.300535\pi\) |
−0.994696 | + | 0.102858i | \(0.967201\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −60216.4 | − | 34765.9i | −0.0694729 | − | 0.0401102i | ||||
\(932\) | −783263. | + | 109524.i | −0.901729 | + | 0.126089i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −57879.6 | − | 831882.i | −0.0663486 | − | 0.953604i | ||||
\(935\) | − | 184963.i | − | 0.211574i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −237273. | −0.270252 | −0.135126 | − | 0.990828i | \(-0.543144\pi\) | ||||
−0.135126 | + | 0.990828i | \(0.543144\pi\) | |||||||
\(938\) | 1.67697e6 | − | 116678.i | 1.90599 | − | 0.132612i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 283706. | + | 2.02893e6i | 0.321079 | + | 2.29621i | ||||
\(941\) | 57476.2 | − | 99551.7i | 0.0649096 | − | 0.112427i | −0.831744 | − | 0.555159i | \(-0.812657\pi\) |
0.896654 | + | 0.442732i | \(0.145991\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 461467. | − | 266428.i | 0.518940 | − | 0.299610i | ||||
\(944\) | 75348.5 | + | 18898.1i | 0.0845534 | + | 0.0212067i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −99395.8 | + | 203612.i | −0.111067 | + | 0.227520i | ||||
\(947\) | 890326. | − | 514030.i | 0.992772 | − | 0.573177i | 0.0866700 | − | 0.996237i | \(-0.472377\pi\) |
0.906102 | + | 0.423060i | \(0.139044\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −67658.0 | + | 117187.i | −0.0751254 | + | 0.130121i | ||||
\(950\) | 283529. | − | 191099.i | 0.314159 | − | 0.211744i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 155080. | − | 139342.i | 0.171113 | − | 0.153747i | ||||
\(953\) | −837599. | −0.922253 | −0.461127 | − | 0.887334i | \(-0.652555\pi\) | ||||
−0.461127 | + | 0.887334i | \(0.652555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.82438e6i | − | 2.00036i | ||||||
\(956\) | −1.66187e6 | − | 672785.i | −1.81836 | − | 0.736140i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 531102. | − | 357964.i | 0.578692 | − | 0.390039i | ||||
\(959\) | 873882. | + | 504536.i | 0.950201 | + | 0.548599i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −423174. | − | 732958.i | −0.458218 | − | 0.793656i | ||||
\(962\) | −55624.7 | + | 113947.i | −0.0601059 | + | 0.123126i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −404464. | − | 518435.i | −0.435237 | − | 0.557879i | ||||
\(965\) | 94598.6 | + | 163850.i | 0.101585 | + | 0.175951i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −92494.4 | − | 53401.7i | −0.0989151 | − | 0.0571087i | 0.449726 | − | 0.893166i | \(-0.351521\pi\) |
−0.548642 | + | 0.836058i | \(0.684855\pi\) | |||||||
\(968\) | 182932. | − | 561010.i | 0.195226 | − | 0.598714i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −365342. | + | 25419.3i | −0.388290 | + | 0.0270159i | ||||
\(971\) | 689120.i | 0.730897i | 0.930832 | + | 0.365448i | \(0.119084\pi\) | ||||
−0.930832 | + | 0.365448i | \(0.880916\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 247915. | 0.261865 | ||||||||
\(974\) | 103269. | + | 1.48425e6i | 0.108856 | + | 1.56455i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −175875. | − | 170315.i | −0.184631 | − | 0.178794i | ||||
\(977\) | −293734. | + | 508762.i | −0.307726 | + | 0.532998i | −0.977865 | − | 0.209239i | \(-0.932901\pi\) |
0.670138 | + | 0.742236i | \(0.266235\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −454787. | + | 262571.i | −0.474507 | + | 0.273957i | ||||
\(980\) | −581366. | − | 745184.i | −0.605337 | − | 0.775910i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 240170. | + | 117243.i | 0.249056 | + | 0.121580i | ||||
\(983\) | 338570. | − | 195474.i | 0.350382 | − | 0.202293i | −0.314472 | − | 0.949267i | \(-0.601827\pi\) |
0.664853 | + | 0.746974i | \(0.268494\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.04755e6 | − | 1.81441e6i | 1.07970 | − | 1.87009i | ||||
\(986\) | −53788.2 | − | 79804.3i | −0.0553265 | − | 0.0820866i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25419.5 | − | 10290.8i | −0.0260408 | − | 0.0105423i | ||||
\(989\) | −216637. | −0.221483 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 462949.i | 0.471396i | 0.971826 | + | 0.235698i | \(0.0757376\pi\) | ||||
−0.971826 | + | 0.235698i | \(0.924262\pi\) | |||||||
\(992\) | 280061. | + | 49885.5i | 0.284596 | + | 0.0506934i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −808332. | − | 1.19930e6i | −0.818120 | − | 1.21382i | ||||
\(995\) | −2.27488e6 | − | 1.31340e6i | −2.29780 | − | 1.32663i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −386642. | − | 669683.i | −0.388972 | − | 0.673720i | 0.603339 | − | 0.797485i | \(-0.293836\pi\) |
−0.992312 | + | 0.123765i | \(0.960503\pi\) | |||||||
\(998\) | −1.19601e6 | − | 583851.i | −1.20081 | − | 0.586193i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.5.f.a.91.1 | 44 | ||
3.2 | odd | 2 | 36.5.f.a.31.22 | yes | 44 | ||
4.3 | odd | 2 | inner | 108.5.f.a.91.16 | 44 | ||
9.2 | odd | 6 | 36.5.f.a.7.7 | ✓ | 44 | ||
9.4 | even | 3 | 324.5.d.e.163.15 | 22 | |||
9.5 | odd | 6 | 324.5.d.f.163.8 | 22 | |||
9.7 | even | 3 | inner | 108.5.f.a.19.16 | 44 | ||
12.11 | even | 2 | 36.5.f.a.31.7 | yes | 44 | ||
36.7 | odd | 6 | inner | 108.5.f.a.19.1 | 44 | ||
36.11 | even | 6 | 36.5.f.a.7.22 | yes | 44 | ||
36.23 | even | 6 | 324.5.d.f.163.7 | 22 | |||
36.31 | odd | 6 | 324.5.d.e.163.16 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.7 | ✓ | 44 | 9.2 | odd | 6 | ||
36.5.f.a.7.22 | yes | 44 | 36.11 | even | 6 | ||
36.5.f.a.31.7 | yes | 44 | 12.11 | even | 2 | ||
36.5.f.a.31.22 | yes | 44 | 3.2 | odd | 2 | ||
108.5.f.a.19.1 | 44 | 36.7 | odd | 6 | inner | ||
108.5.f.a.19.16 | 44 | 9.7 | even | 3 | inner | ||
108.5.f.a.91.1 | 44 | 1.1 | even | 1 | trivial | ||
108.5.f.a.91.16 | 44 | 4.3 | odd | 2 | inner | ||
324.5.d.e.163.15 | 22 | 9.4 | even | 3 | |||
324.5.d.e.163.16 | 22 | 36.31 | odd | 6 | |||
324.5.d.f.163.7 | 22 | 36.23 | even | 6 | |||
324.5.d.f.163.8 | 22 | 9.5 | odd | 6 |