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 | 91.16 | ||
Character | \(\chi\) | \(=\) | 108.91 |
Dual form | 108.5.f.a.19.16 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.23562 | − | 3.31693i | 0.558904 | − | 0.829232i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.00404 | − | 14.8308i | −0.375253 | − | 0.926923i | ||||
\(5\) | 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 | −0.928217 | − | 0.372040i | \(-0.878659\pi\) |
−0.141913 | + | 0.989879i | \(0.545325\pi\) | |||||||
\(8\) | −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 | −0.212813 | − | 0.977093i | \(-0.568263\pi\) |
0.739781 | + | 0.672848i | \(0.234929\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.5924 | − | 27.0068i | 0.0922626 | − | 0.159803i | −0.816200 | − | 0.577769i | \(-0.803923\pi\) |
0.908463 | + | 0.417966i | \(0.137257\pi\) | |||||||
\(14\) | −16.8104 | + | 241.609i | −0.0857671 | + | 1.23270i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −183.903 | + | 178.089i | −0.718371 | + | 0.695660i | ||||
\(17\) | −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 | \(0.0242546\pi\) | ||||
−0.997098 | + | 0.0761245i | \(0.975745\pi\) | |||||||
\(20\) | −739.891 | − | 103.459i | −1.84973 | − | 0.258648i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 20.4416 | − | 293.799i | 0.0422346 | − | 0.607023i | ||||
\(23\) | −243.863 | − | 140.795i | −0.460990 | − | 0.266152i | 0.251471 | − | 0.967865i | \(-0.419086\pi\) |
−0.712460 | + | 0.701712i | \(0.752419\pi\) | |||||||
\(24\) | 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 | 0.619923 | − | 0.784663i | \(-0.287164\pi\) |
−0.369576 | + | 0.929200i | \(0.620497\pi\) | |||||||
\(32\) | 179.572 | + | 1008.13i | 0.175364 | + | 0.984504i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −120.279 | + | 178.455i | −0.104048 | + | 0.154373i | ||||
\(35\) | 2827.19i | 2.30791i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1016.51 | 0.742522 | 0.371261 | − | 0.928528i | \(-0.378925\pi\) | ||||
0.371261 | + | 0.928528i | \(0.378925\pi\) | |||||||
\(38\) | 182.305 | + | 122.874i | 0.126250 | + | 0.0850926i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1997.28 | + | 2222.87i | −1.24830 | + | 1.38930i | ||||
\(41\) | 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 | −0.308891 | − | 0.951098i | \(-0.599958\pi\) |
0.669229 | + | 0.743056i | \(0.266624\pi\) | |||||||
\(44\) | −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 | 0.145502 | − | 0.989358i | \(-0.453520\pi\) |
0.929560 | + | 0.368671i | \(0.120187\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 632.546 | − | 1095.60i | 0.263451 | − | 0.456311i | ||||
\(50\) | −6205.98 | − | 431.792i | −2.48239 | − | 0.172717i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −494.148 | − | 69.0969i | −0.182747 | − | 0.0255536i | ||||
\(53\) | 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 | ||||||
\(56\) | 3684.18 | − | 1201.32i | 1.17480 | − | 0.383074i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1784.46 | − | 124.157i | −0.530459 | − | 0.0369076i | ||||
\(59\) | −262.792 | − | 151.723i | −0.0754934 | − | 0.0435861i | 0.461778 | − | 0.886995i | \(-0.347212\pi\) |
−0.537272 | + | 0.843409i | \(0.680545\pi\) | |||||||
\(60\) | 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 | 0.986665 | − | 0.162762i | \(-0.0520403\pi\) |
0.352376 | + | 0.935858i | \(0.385374\pi\) | |||||||
\(68\) | 323.026 | + | 797.915i | 0.0698585 | + | 0.172559i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9377.58 | + | 6320.51i | 1.91379 | + | 1.28990i | ||||
\(71\) | − | 5971.60i | − | 1.18461i | −0.805715 | − | 0.592303i | \(-0.798219\pi\) | ||
0.805715 | − | 0.592303i | \(-0.201781\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4339.17 | −0.814257 | −0.407128 | − | 0.913371i | \(-0.633470\pi\) | ||||
−0.407128 | + | 0.913371i | \(0.633470\pi\) | |||||||
\(74\) | 2272.53 | − | 3371.70i | 0.414999 | − | 0.615724i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 815.127 | − | 329.993i | 0.141123 | − | 0.0571318i | ||||
\(77\) | −2229.00 | + | 3860.75i | −0.375949 | + | 0.651163i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3294.15 | + | 1901.88i | −0.527824 | + | 0.304740i | −0.740130 | − | 0.672464i | \(-0.765236\pi\) |
0.212306 | + | 0.977203i | \(0.431903\pi\) | |||||||
\(80\) | 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 | −0.684919 | − | 0.728619i | \(-0.740163\pi\) |
0.288543 | + | 0.957467i | \(0.406829\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1256.08 | + | 2175.59i | −0.173851 | + | 0.301119i | ||||
\(86\) | 213.596 | − | 3069.93i | 0.0288799 | − | 0.415080i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4479.99 | + | 1460.82i | −0.578512 | + | 0.188639i | ||||
\(89\) | 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 | ||||||||
\(92\) | −623.925 | + | 4462.02i | −0.0737152 | + | 0.527176i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 761.331 | − | 10942.3i | 0.0861624 | − | 1.23838i | ||||
\(95\) | 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 | 0.341793 | − | 0.939775i | \(-0.388966\pi\) |
−0.642973 | + | 0.765889i | \(0.722299\pi\) | |||||||
\(104\) | −1333.92 | + | 1484.58i | −0.123328 | + | 0.137258i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10390.5 | − | 15416.1i | 0.924747 | − | 1.37203i | ||||
\(107\) | 13741.5i | 1.20024i | 0.799911 | + | 0.600118i | \(0.204880\pi\) | ||||
−0.799911 | + | 0.600118i | \(0.795120\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18709.9 | 1.57478 | 0.787388 | − | 0.616458i | \(-0.211433\pi\) | ||||
0.787388 | + | 0.616458i | \(0.211433\pi\) | |||||||
\(110\) | −11403.2 | − | 7685.80i | −0.942416 | − | 0.635190i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4251.71 | − | 14905.8i | 0.338944 | − | 1.18828i | ||||
\(113\) | −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 | ||||
\(122\) | −3816.17 | − | 265.516i | −0.256394 | − | 0.0178390i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 615.534 | − | 4402.00i | 0.0400321 | − | 0.286291i | ||||
\(125\) | −43436.1 | −2.77991 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 18883.8i | − | 1.17080i | −0.810745 | − | 0.585400i | \(-0.800937\pi\) | ||
0.810745 | − | 0.585400i | \(-0.199063\pi\) | |||||||
\(128\) | 13873.2 | − | 8716.06i | 0.846753 | − | 0.531986i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5810.41 | − | 404.269i | −0.343811 | − | 0.0239212i | ||||
\(131\) | −25700.9 | − | 14838.4i | −1.49763 | − | 0.864660i | −0.497639 | − | 0.867384i | \(-0.665799\pi\) |
−0.999996 | + | 0.00272458i | \(0.999133\pi\) | |||||||
\(132\) | 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 | 0.405421 | − | 0.914130i | \(-0.367125\pi\) |
−0.588949 | + | 0.808170i | \(0.700458\pi\) | |||||||
\(140\) | 41929.3 | − | 16974.5i | 2.13925 | − | 0.866048i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −19807.4 | − | 13350.2i | −0.982314 | − | 0.662081i | ||||
\(143\) | − | 2296.05i | − | 0.112282i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20880.9 | −0.993147 | ||||||||
\(146\) | −9700.73 | + | 14392.7i | −0.455091 | + | 0.675208i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6103.19 | − | 15075.7i | −0.278633 | − | 0.688261i | ||||
\(149\) | −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 | −0.973043 | − | 0.230622i | \(-0.925924\pi\) |
−0.286797 | + | 0.957991i | \(0.592591\pi\) | |||||||
\(152\) | 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 | \(0.315202\pi\) | |||||||
\(158\) | −1056.06 | + | 15178.3i | −0.0423033 | + | 0.608009i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 44958.6 | + | 16275.0i | 1.75620 | + | 0.635741i | ||||
\(161\) | 17049.7 | 0.657758 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 31303.8i | − | 1.17821i | −0.808057 | − | 0.589104i | \(-0.799481\pi\) | ||
0.808057 | − | 0.589104i | \(-0.200519\pi\) | |||||||
\(164\) | −29985.3 | − | 4192.86i | −1.11486 | − | 0.155891i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −875.403 | + | 12581.8i | −0.0317682 | + | 0.456592i | ||||
\(167\) | 22551.7 | + | 13020.2i | 0.808622 | + | 0.466858i | 0.846477 | − | 0.532425i | \(-0.178719\pi\) |
−0.0378548 | + | 0.999283i | \(0.512052\pi\) | |||||||
\(168\) | 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 | ||||
\(176\) | −5170.12 | + | 18125.6i | −0.166907 | + | 0.585151i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15945.4 | − | 23657.8i | 0.503264 | − | 0.746680i | ||||
\(179\) | − | 36836.7i | − | 1.14967i | −0.818268 | − | 0.574837i | \(-0.805065\pi\) | ||
0.818268 | − | 0.574837i | \(-0.194935\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 56961.0 | 1.73868 | 0.869342 | − | 0.494211i | \(-0.164543\pi\) | ||||
0.869342 | + | 0.494211i | \(0.164543\pi\) | |||||||
\(182\) | 6262.97 | + | 4221.25i | 0.189076 | + | 0.127438i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13405.3 | + | 12044.9i | 0.395952 | + | 0.355768i | ||||
\(185\) | 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 | −0.886029 | − | 0.463630i | \(-0.846547\pi\) |
−0.0414986 | + | 0.999139i | \(0.513213\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2025.97 | + | 3509.08i | −0.0543898 | + | 0.0942059i | −0.891938 | − | 0.452157i | \(-0.850655\pi\) |
0.837549 | + | 0.546363i | \(0.183988\pi\) | |||||||
\(194\) | 7824.33 | + | 544.391i | 0.207895 | + | 0.0144646i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −20046.5 | − | 2803.10i | −0.521826 | − | 0.0729670i | ||||
\(197\) | 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 | \(0.251438\pi\) | ||||
−0.703905 | + | 0.710294i | \(0.748562\pi\) | |||||||
\(200\) | 30857.2 | + | 94632.0i | 0.771430 | + | 2.36580i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −30725.4 | − | 2137.77i | −0.752999 | − | 0.0523912i | ||||
\(203\) | 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 | −0.425551 | − | 0.904935i | \(-0.639920\pi\) |
−0.996472 | + | 0.0839298i | \(0.973253\pi\) | |||||||
\(212\) | −27905.0 | − | 68928.9i | −0.620883 | − | 1.53366i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 45579.6 | + | 30720.7i | 0.995275 | + | 0.670817i | ||||
\(215\) | − | 35922.8i | − | 0.777129i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16820.4 | −0.357205 | ||||||||
\(218\) | 41828.2 | − | 62059.5i | 0.880149 | − | 1.30586i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −50986.5 | + | 20641.2i | −1.05344 | + | 0.426472i | ||||
\(221\) | −838.891 | + | 1453.00i | −0.0171760 | + | 0.0297496i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 65737.1 | − | 37953.3i | 1.32191 | − | 0.763203i | 0.337873 | − | 0.941192i | \(-0.390292\pi\) |
0.984032 | + | 0.177989i | \(0.0569591\pi\) | |||||||
\(224\) | −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 | −0.804756 | − | 0.593606i | \(-0.797704\pi\) |
0.111700 | + | 0.993742i | \(0.464371\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13792.1 | + | 23888.7i | −0.263003 | + | 0.455534i | −0.967038 | − | 0.254630i | \(-0.918046\pi\) |
0.704036 | + | 0.710165i | \(0.251379\pi\) | |||||||
\(230\) | −3650.43 | + | 52466.3i | −0.0690063 | + | 0.991801i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8872.66 | + | 27210.4i | 0.164846 | + | 0.505544i | ||||
\(233\) | −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 | ||||||
\(236\) | −672.355 | + | 4808.36i | −0.0120719 | + | 0.0863323i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 904.420 | − | 12998.9i | 0.0159667 | − | 0.229484i | ||||
\(239\) | 97042.8 | + | 56027.7i | 1.69890 | + | 0.980859i | 0.946808 | + | 0.321800i | \(0.104288\pi\) |
0.752091 | + | 0.659060i | \(0.229045\pi\) | |||||||
\(240\) | 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 | ||||
\(248\) | −13225.0 | − | 11882.9i | −0.215027 | − | 0.193205i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −97106.5 | + | 144075.i | −1.55370 | + | 2.30519i | ||||
\(251\) | 50848.1i | 0.807099i | 0.914958 | + | 0.403550i | \(0.132224\pi\) | ||||
−0.914958 | + | 0.403550i | \(0.867776\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20732.7 | −0.323902 | ||||||||
\(254\) | −62636.4 | − | 42217.0i | −0.970865 | − | 0.654365i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2104.60 | − | 65502.2i | 0.0321137 | − | 0.999484i | ||||
\(257\) | 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 | −0.288309 | − | 0.957537i | \(-0.593093\pi\) |
0.685097 | + | 0.728452i | \(0.259760\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 108508. | − | 187941.i | 1.54514 | − | 2.67627i | ||||
\(266\) | −13279.3 | − | 923.929i | −0.187677 | − | 0.0130580i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15379.1 | − | 109984.i | 0.214121 | − | 1.53129i | ||||
\(269\) | 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 | \(0.257665\pi\) | ||||
−0.689877 | + | 0.723927i | \(0.742335\pi\) | |||||||
\(272\) | 9894.23 | − | 9581.43i | 0.133735 | − | 0.129507i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 66501.5 | + | 4626.96i | 0.885789 | + | 0.0616303i | ||||
\(275\) | −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 | 0.751364 | − | 0.659888i | \(-0.229396\pi\) |
−0.195797 | + | 0.980644i | \(0.562729\pi\) | |||||||
\(284\) | −88563.4 | + | 35853.7i | −1.09804 | + | 0.444527i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7615.83 | − | 5133.08i | −0.0931076 | − | 0.0627547i | ||||
\(287\) | 114576.i | 1.39101i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −80626.4 | −0.965343 | ||||||||
\(290\) | −46681.7 | + | 69260.5i | −0.555074 | + | 0.823550i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 26052.6 | + | 64353.3i | 0.305552 | + | 0.754753i | ||||
\(293\) | 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 | ||||
\(302\) | −9209.03 | + | 132358.i | −0.100972 | + | 1.45123i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9788.11 | − | 10107.7i | −0.105914 | − | 0.109371i | ||||
\(305\) | −44654.9 | −0.480031 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 108180.i | 1.14781i | 0.818923 | + | 0.573904i | \(0.194572\pi\) | ||||
−0.818923 | + | 0.573904i | \(0.805428\pi\) | |||||||
\(308\) | 70640.8 | + | 9877.73i | 0.744654 | + | 0.104125i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3601.33 | − | 51760.6i | 0.0374749 | − | 0.538612i | ||||
\(311\) | −86673.2 | − | 50040.8i | −0.896116 | − | 0.517373i | −0.0201778 | − | 0.999796i | \(-0.506423\pi\) |
−0.875938 | + | 0.482424i | \(0.839757\pi\) | |||||||
\(312\) | 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 | ||||
\(320\) | 154493. | − | 112740.i | 1.50872 | − | 1.10098i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 38116.7 | − | 56552.8i | 0.367624 | − | 0.545434i | ||||
\(323\) | − | 2957.02i | − | 0.0283433i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −48500.0 | −0.459172 | ||||||||
\(326\) | −103832. | − | 69983.3i | −0.977008 | − | 0.658505i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −80943.1 | + | 90085.6i | −0.752371 | + | 0.837351i | ||||
\(329\) | −83017.6 | + | 143791.i | −0.766970 | + | 1.32843i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 99528.9 | − | 57463.0i | 0.908433 | − | 0.524484i | 0.0285065 | − | 0.999594i | \(-0.490925\pi\) |
0.879927 | + | 0.475109i | \(0.157592\pi\) | |||||||
\(332\) | 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 | \(0.984028\pi\) | |||||||
\(338\) | 110088. | + | 7659.55i | 0.963621 | + | 0.0670456i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 39807.2 | + | 5566.25i | 0.344353 | + | 0.0481509i | ||||
\(341\) | 20453.8 | 0.175900 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 68777.2i | − | 0.584597i | ||||||
\(344\) | −46811.9 | + | 15264.2i | −0.395584 | + | 0.128990i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 62492.0 | + | 4347.99i | 0.522002 | + | 0.0363192i | ||||
\(347\) | −82843.4 | − | 47829.7i | −0.688017 | − | 0.397227i | 0.114852 | − | 0.993383i | \(-0.463361\pi\) |
−0.802869 | + | 0.596156i | \(0.796694\pi\) | |||||||
\(348\) | 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 | ||||
\(356\) | −42823.5 | − | 105780.i | −0.337895 | − | 0.834645i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −122185. | − | 82352.8i | −0.953348 | − | 0.642558i | ||||
\(359\) | − | 223134.i | − | 1.73132i | −0.500632 | − | 0.865660i | \(-0.666899\pi\) | ||
0.500632 | − | 0.865660i | \(-0.333101\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 127300. | 0.976820 | ||||||||
\(362\) | 127343. | − | 188936.i | 0.971758 | − | 1.44177i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 28003.2 | − | 11336.7i | 0.211351 | − | 0.0855628i | ||||
\(365\) | −101305. | + | 175465.i | −0.760404 | + | 1.31706i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 92257.6 | − | 53265.0i | 0.684968 | − | 0.395466i | −0.116756 | − | 0.993161i | \(-0.537250\pi\) |
0.801724 | + | 0.597694i | \(0.203916\pi\) | |||||||
\(368\) | 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 | \(0.995021\pi\) | |||||||
\(374\) | −1099.78 | + | 15806.8i | −0.00786256 | + | 0.113006i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −166854. | + | 54407.1i | −1.18022 | + | 0.384840i | ||||
\(377\) | −13945.7 | −0.0981197 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 95242.7i | 0.663061i | 0.943445 | + | 0.331530i | \(0.107565\pi\) | ||||
−0.943445 | + | 0.331530i | \(0.892435\pi\) | |||||||
\(380\) | 5686.32 | − | 40665.8i | 0.0393789 | − | 0.281619i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10847.7 | + | 155910.i | −0.0743381 | + | 1.06843i | ||||
\(383\) | 46899.6 | + | 27077.5i | 0.319721 | + | 0.184591i | 0.651268 | − | 0.758848i | \(-0.274237\pi\) |
−0.331547 | + | 0.943439i | \(0.607571\pi\) | |||||||
\(384\) | 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 | ||||
\(392\) | −54113.9 | + | 60226.0i | −0.352157 | + | 0.391933i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 100311. | − | 148829.i | 0.646185 | − | 0.958730i | ||||
\(395\) | 177609.i | 1.13834i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 54407.2 | 0.345204 | 0.172602 | − | 0.984992i | \(-0.444783\pi\) | ||||
0.172602 | + | 0.984992i | \(0.444783\pi\) | |||||||
\(398\) | 186599. | + | 125768.i | 1.17800 | + | 0.793972i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 382872. | + | 109210.i | 2.39295 | + | 0.682560i | ||||
\(401\) | 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 | \(0.205614\pi\) | |||||||
\(410\) | −352580. | − | 24531.4i | −2.09744 | − | 0.145933i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8174.97 | + | 58463.5i | −0.0481606 | + | 0.344422i | ||||
\(413\) | 18373.2 | 0.107717 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 147226.i | 0.854850i | ||||||||
\(416\) | 30026.4 | + | 10869.5i | 0.173507 | + | 0.0628091i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16147.7 | + | 1123.51i | 0.0924186 | + | 0.00643018i | ||||
\(419\) | 28866.9 | + | 16666.3i | 0.164427 | + | 0.0949318i | 0.579955 | − | 0.814648i | \(-0.303070\pi\) |
−0.415529 | + | 0.909580i | \(0.636403\pi\) | |||||||
\(420\) | 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 | ||||
\(428\) | 203797. | − | 82504.6i | 1.11253 | − | 0.450392i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −119153. | − | 80309.6i | −0.644421 | − | 0.434341i | ||||
\(431\) | 88445.3i | 0.476124i | 0.971250 | + | 0.238062i | \(0.0765122\pi\) | ||||
−0.971250 | + | 0.238062i | \(0.923488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 119092. | 0.635195 | 0.317598 | − | 0.948226i | \(-0.397124\pi\) | ||||
0.317598 | + | 0.948226i | \(0.397124\pi\) | |||||||
\(434\) | −37604.0 | + | 55792.2i | −0.199643 | + | 0.296206i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −112335. | − | 277482.i | −0.590939 | − | 1.45970i | ||||
\(437\) | 7738.34 | − | 13403.2i | 0.0405214 | − | 0.0701852i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −103483. | + | 59746.2i | −0.536960 | + | 0.310014i | −0.743846 | − | 0.668351i | \(-0.767000\pi\) |
0.206886 | + | 0.978365i | \(0.433667\pi\) | |||||||
\(440\) | −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 | −0.876853 | − | 0.480759i | \(-0.840361\pi\) |
−0.0220772 | + | 0.999756i | \(0.507028\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 166518. | − | 288418.i | 0.840894 | − | 1.45647i | ||||
\(446\) | 21074.4 | − | 302894.i | 0.105946 | − | 1.52272i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −246592. | + | 26439.2i | −1.22864 | + | 0.131732i | ||||
\(449\) | −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 | ||||||
\(452\) | 158474. | + | 22159.5i | 0.775679 | + | 0.108463i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11448.9 | + | 164551.i | −0.0555461 | + | 0.798343i | ||||
\(455\) | 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 | 0.374275 | − | 0.927318i | \(-0.377892\pi\) |
−0.615943 | + | 0.787791i | \(0.711225\pi\) | |||||||
\(464\) | 110091. | + | 31402.1i | 0.511347 | + | 0.145855i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −110507. | + | 163957.i | −0.508883 | + | 0.755018i | ||||
\(467\) | − | 208473.i | − | 0.955909i | −0.878385 | − | 0.477955i | \(-0.841378\pi\) | ||
0.878385 | − | 0.477955i | \(-0.158622\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −420257. | −1.91060 | ||||||||
\(470\) | −424705. | − | 286252.i | −1.92261 | − | 1.29584i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14445.9 | + | 12979.8i | 0.0648425 | + | 0.0582619i | ||||
\(473\) | 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 | −0.166390 | − | 0.986060i | \(-0.553211\pi\) |
0.770758 | + | 0.637128i | \(0.219878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15849.9 | − | 27452.8i | 0.0685070 | − | 0.118658i | ||||
\(482\) | −163990. | − | 11409.9i | −0.705867 | − | 0.0491119i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 146099. | + | 20429.1i | 0.623672 | + | 0.0872083i | ||||
\(485\) | 91556.4 | 0.389229 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 371960.i | 1.56834i | 0.620549 | + | 0.784168i | \(0.286910\pi\) | ||||
−0.620549 | + | 0.784168i | \(0.713090\pi\) | |||||||
\(488\) | 18974.6 | + | 58190.8i | 0.0796771 | + | 0.244351i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −235715. | − | 16400.2i | −0.981735 | − | 0.0683059i | ||||
\(491\) | 57863.4 | + | 33407.4i | 0.240016 | + | 0.138574i | 0.615184 | − | 0.788383i | \(-0.289082\pi\) |
−0.375168 | + | 0.926957i | \(0.622415\pi\) | |||||||
\(492\) | 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 | −0.206591 | − | 0.978427i | \(-0.566237\pi\) |
−0.950638 | + | 0.310301i | \(0.899570\pi\) | |||||||
\(500\) | 260792. | + | 644191.i | 1.04317 | + | 2.57676i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 168659. | + | 113677.i | 0.669273 | + | 0.451091i | ||||
\(503\) | − | 12673.0i | − | 0.0500892i | −0.999686 | − | 0.0250446i | \(-0.992027\pi\) | ||
0.999686 | − | 0.0250446i | \(-0.00797278\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −359533. | −1.40980 | ||||||||
\(506\) | −46350.3 | + | 68768.8i | −0.181030 | + | 0.268590i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −280062. | + | 113379.i | −1.08524 | + | 0.439346i | ||||
\(509\) | −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 | ||||
\(518\) | −17087.9 | + | 245599.i | −0.0636840 | + | 0.915306i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 28890.3 | + | 88600.0i | 0.106843 | + | 0.327663i | ||||
\(521\) | −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 | \(-0.810743\pi\) | ||
0.828391 | − | 0.560151i | \(-0.189257\pi\) | |||||||
\(524\) | −65755.8 | + | 470255.i | −0.239481 | + | 1.71266i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8798.63 | − | 126459.i | 0.0318012 | − | 0.457067i | ||||
\(527\) | −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 | ||||
\(536\) | −330426. | − | 296893.i | −1.15013 | − | 1.03340i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 122719. | − | 182076.i | 0.423983 | − | 0.629054i | ||||
\(539\) | − | 93145.3i | − | 0.320615i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 387269. | 1.32318 | 0.661590 | − | 0.749866i | \(-0.269882\pi\) | ||||
0.661590 | + | 0.749866i | \(0.269882\pi\) | |||||||
\(542\) | 352695. | + | 237717.i | 1.20061 | + | 0.809211i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9661.23 | − | 54238.9i | −0.0326464 | − | 0.183279i | ||||
\(545\) | 436812. | − | 756581.i | 1.47062 | − | 2.54720i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −220183. | + | 127123.i | −0.735883 | + | 0.424862i | −0.820570 | − | 0.571545i | \(-0.806344\pi\) |
0.0846877 | + | 0.996408i | \(0.473011\pi\) | |||||||
\(548\) | 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 | ||||
\(554\) | 200847. | + | 13974.3i | 0.654404 | + | 0.0455312i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9072.31 | + | 64880.9i | −0.0293473 | + | 0.209878i | ||||
\(557\) | 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 | ||||||
\(560\) | −503491. | − | 519928.i | −1.60552 | − | 1.65793i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24326.8 | − | 1692.58i | −0.0770216 | − | 0.00535891i | ||||
\(563\) | 188653. | + | 108919.i | 0.595177 | + | 0.343626i | 0.767142 | − | 0.641477i | \(-0.221678\pi\) |
−0.171965 | + | 0.985103i | \(0.555012\pi\) | |||||||
\(564\) | 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 | 0.109387 | − | 0.993999i | \(-0.465111\pi\) |
−0.806135 | + | 0.591732i | \(0.798445\pi\) | |||||||
\(572\) | −34052.2 | + | 13785.6i | −0.104076 | + | 0.0421340i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 380042. | + | 256149.i | 1.15347 | + | 0.777443i | ||||
\(575\) | 437941.i | 1.32458i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 450994. | 1.35462 | 0.677312 | − | 0.735696i | \(-0.263145\pi\) | ||||
0.677312 | + | 0.735696i | \(0.263145\pi\) | |||||||
\(578\) | −180250. | + | 267432.i | −0.539534 | + | 0.800494i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 125370. | + | 309680.i | 0.372681 | + | 0.920570i | ||||
\(581\) | 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 | 0.0181523 | − | 0.999835i | \(-0.494222\pi\) |
0.874959 | + | 0.484197i | \(0.160888\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7634.26 | + | 13222.9i | −0.0220058 | + | 0.0381151i | ||||
\(590\) | −3933.78 | + | 56538.8i | −0.0113007 | + | 0.162421i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −186940. | + | 181030.i | −0.533406 | + | 0.516543i | ||||
\(593\) | −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 | ||||||
\(596\) | 93002.0 | + | 13004.5i | 0.261818 | + | 0.0366101i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2438.00 | + | 35040.5i | −0.00681759 | + | 0.0979868i | ||||
\(599\) | 357687. | + | 206511.i | 0.996896 | + | 0.575558i | 0.907328 | − | 0.420422i | \(-0.138118\pi\) |
0.0895677 | + | 0.995981i | \(0.471451\pi\) | |||||||
\(600\) | 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 | 0.816893 | − | 0.576789i | \(-0.195695\pi\) |
−0.0910678 | + | 0.995845i | \(0.529028\pi\) | |||||||
\(608\) | −55408.8 | + | 9869.63i | −0.149890 | + | 0.0266989i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −99831.1 | + | 148117.i | −0.268291 | + | 0.398057i | ||||
\(611\) | − | 85514.7i | − | 0.229065i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −464349. | −1.23573 | −0.617865 | − | 0.786284i | \(-0.712002\pi\) | ||||
−0.617865 | + | 0.786284i | \(0.712002\pi\) | |||||||
\(614\) | 358825. | + | 241848.i | 0.951800 | + | 0.641515i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 190689. | − | 212228.i | 0.502534 | − | 0.559295i | ||||
\(617\) | −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 | −0.145159 | − | 0.989408i | \(-0.546369\pi\) |
0.784273 | + | 0.620415i | \(0.213036\pi\) | |||||||
\(620\) | −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 | ||||
\(626\) | 605698. | + | 42142.5i | 1.54564 | + | 0.107540i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 351437. | + | 49141.5i | 0.891103 | + | 0.124603i | ||||
\(629\) | −54689.8 | −0.138231 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 403620.i | − | 1.01371i | −0.862031 | − | 0.506855i | \(-0.830808\pi\) | ||
0.862031 | − | 0.506855i | \(-0.169192\pi\) | |||||||
\(632\) | 231447. | − | 75469.2i | 0.579452 | − | 0.188945i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 448531. | + | 31207.3i | 1.11587 | + | 0.0776387i | ||||
\(635\) | −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 | 0.856733 | − | 0.515761i | \(-0.172491\pi\) |
−0.0182957 | + | 0.999833i | \(0.505824\pi\) | |||||||
\(644\) | −102367. | − | 252861.i | −0.246825 | − | 0.609691i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9808.24 | − | 6610.77i | −0.0235031 | − | 0.0158412i | ||||
\(647\) | − | 98990.1i | − | 0.236474i | −0.992985 | − | 0.118237i | \(-0.962276\pi\) | ||
0.992985 | − | 0.118237i | \(-0.0377242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22341.9 | −0.0530434 | ||||||||
\(650\) | −108427. | + | 160871.i | −0.256633 | + | 0.380760i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −464259. | + | 187949.i | −1.09211 | + | 0.442125i | ||||
\(653\) | −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 | −0.347591 | − | 0.937646i | \(-0.613000\pi\) |
0.638230 | + | 0.769846i | \(0.279667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 126176. | − | 218543.i | 0.288784 | − | 0.500189i | −0.684736 | − | 0.728792i | \(-0.740082\pi\) |
0.973520 | + | 0.228603i | \(0.0734157\pi\) | |||||||
\(662\) | 31907.6 | − | 458595.i | 0.0728077 | − | 1.04644i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 191854. | − | 62559.0i | 0.435146 | − | 0.141891i | ||||
\(665\) | −155388. | −0.351377 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 125925.i | 0.283049i | ||||||||
\(668\) | 57698.5 | − | 412632.i | 0.129304 | − | 0.924720i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 89979.0 | − | 1.29323e6i | 0.200443 | − | 2.88090i | ||||
\(671\) | −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 | ||||
\(680\) | 107456. | − | 119594.i | 0.232388 | − | 0.258637i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 45726.9 | − | 67843.8i | 0.0983111 | − | 0.145862i | ||||
\(683\) | − | 885039.i | − | 1.89724i | −0.316425 | − | 0.948618i | \(-0.602483\pi\) | ||
0.316425 | − | 0.948618i | \(-0.397517\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 778168. | 1.65841 | ||||||||
\(686\) | −228129. | − | 153759.i | −0.484767 | − | 0.326733i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −54023.0 | + | 189397.i | −0.114131 | + | 0.400124i | ||||
\(689\) | 72468.6 | − | 125519.i | 0.152655 | − | 0.264406i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −382656. | + | 220927.i | −0.801406 | + | 0.462692i | −0.843963 | − | 0.536402i | \(-0.819783\pi\) |
0.0425567 | + | 0.999094i | \(0.486450\pi\) | |||||||
\(692\) | 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 | ||||
\(698\) | −171933. | − | 11962.5i | −0.352897 | − | 0.0245534i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 208650. | − | 1.49216e6i | 0.425816 | − | 3.04523i | ||||
\(701\) | −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 | ||||||||
\(704\) | 299859. | − | 32150.4i | 0.605022 | − | 0.0648695i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −450407. | − | 31337.8i | −0.903640 | − | 0.0628723i | ||||
\(707\) | 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 | ||||
\(716\) | −546317. | + | 221169.i | −1.06566 | + | 0.431419i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −740121. | − | 498843.i | −1.43567 | − | 0.967642i | ||||
\(719\) | − | 306988.i | − | 0.593832i | −0.954904 | − | 0.296916i | \(-0.904042\pi\) | ||
0.954904 | − | 0.296916i | \(-0.0959581\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 223394. | 0.429735 | ||||||||
\(722\) | 284594. | − | 422246.i | 0.545949 | − | 0.810011i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −341996. | − | 844775.i | −0.652446 | − | 1.61163i | ||||
\(725\) | −347749. | + | 602319.i | −0.661592 | + | 1.14591i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 488481. | − | 282025.i | 0.924227 | − | 0.533603i | 0.0392459 | − | 0.999230i | \(-0.487504\pi\) |
0.884981 | + | 0.465627i | \(0.154171\pi\) | |||||||
\(728\) | 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 | \(0.984511\pi\) | |||||||
\(734\) | 29576.5 | − | 425092.i | 0.0548978 | − | 0.789025i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 98148.4 | − | 271129.i | 0.181187 | − | 0.500519i | ||||
\(737\) | 511037. | 0.940843 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 193774.i | − | 0.354818i | −0.984137 | − | 0.177409i | \(-0.943228\pi\) | ||
0.984137 | − | 0.177409i | \(-0.0567715\pi\) | |||||||
\(740\) | −752109. | − | 105168.i | −1.37346 | − | 0.192052i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −78129.4 | + | 1.12292e6i | −0.141908 | + | 2.03959i | ||||
\(743\) | 76480.8 | + | 44156.2i | 0.138540 | + | 0.0799861i | 0.567668 | − | 0.823258i | \(-0.307846\pi\) |
−0.429128 | + | 0.903244i | \(0.641179\pi\) | |||||||
\(744\) | 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 | 0.0167738 | − | 0.999859i | \(-0.494660\pi\) |
−0.857517 | + | 0.514456i | \(0.827994\pi\) | |||||||
\(752\) | −192557. | + | 675077.i | −0.340506 | + | 1.19376i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −31177.1 | + | 46256.8i | −0.0548395 | + | 0.0813640i | ||||
\(755\) | 1.54879e6i | 2.71705i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45164.0 | −0.0788135 | −0.0394068 | − | 0.999223i | \(-0.512547\pi\) | ||||
−0.0394068 | + | 0.999223i | \(0.512547\pi\) | |||||||
\(758\) | 315913. | + | 212926.i | 0.549831 | + | 0.370587i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −122173. | − | 109774.i | −0.211519 | − | 0.190052i | ||||
\(761\) | −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 | \(0.283858\pi\) | |||||||
\(770\) | 830625. | + | 57792.1i | 1.40095 | + | 0.0974736i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 64206.2 | + | 8977.98i | 0.107731 | + | 0.0150641i | ||||
\(773\) | −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 | ||||||
\(776\) | −38903.9 | − | 119309.i | −0.0646055 | − | 0.198130i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 51980.2 | + | 3616.61i | 0.0858774 | + | 0.00597506i | ||||
\(779\) | 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 | 0.998649 | − | 0.0519669i | \(-0.0165490\pi\) |
0.454320 | + | 0.890839i | \(0.349882\pi\) | |||||||
\(788\) | −269399. | − | 665451.i | −0.433854 | − | 1.07168i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 589118. | + | 397066.i | 0.943948 | + | 0.636222i | ||||
\(791\) | − | 605543.i | − | 0.967815i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29823.5 | −0.0474255 | ||||||||
\(794\) | 121634. | − | 180465.i | 0.192936 | − | 0.286254i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 834330. | − | 337768.i | 1.31677 | − | 0.533079i | ||||
\(797\) | 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 | ||||
\(806\) | 2405.21 | − | 34569.2i | 0.00370239 | − | 0.0532131i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 152772. | + | 468516.i | 0.234002 | + | 0.717632i | ||||
\(809\) | −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 | \(-0.941594\pi\) | ||
0.983213 | − | 0.182460i | \(-0.0584059\pi\) | |||||||
\(812\) | 59995.0 | − | 429056.i | 0.0909919 | − | 0.650731i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20779.1 | − | 298650.i | 0.0313601 | − | 0.450728i | ||||
\(815\) | −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 | 0.517697 | − | 0.855564i | \(-0.326789\pi\) |
−0.482091 | + | 0.876121i | \(0.660123\pi\) | |||||||
\(824\) | 175643. | + | 157818.i | 0.258688 | + | 0.232435i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 41075.3 | − | 60942.5i | 0.0602034 | − | 0.0893223i | ||||
\(827\) | 1.05969e6i | 1.54941i | 0.632323 | + | 0.774705i | \(0.282102\pi\) | ||||
−0.632323 | + | 0.774705i | \(0.717898\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −904280. | −1.31581 | −0.657906 | − | 0.753100i | \(-0.728558\pi\) | ||||
−0.657906 | + | 0.753100i | \(0.728558\pi\) | |||||||
\(830\) | 488340. | + | 329142.i | 0.708869 | + | 0.477779i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 103181. | − | 75295.3i | 0.149057 | − | 0.108773i | ||||
\(833\) | −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 | −0.264330 | − | 0.964432i | \(-0.585151\pi\) |
0.703058 | + | 0.711133i | \(0.251818\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 253649. | − | 439333.i | 0.358625 | − | 0.621157i | ||||
\(842\) | −33361.8 | − | 2321.21i | −0.0470571 | − | 0.00327408i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −161978. | + | 1.15839e6i | −0.227390 | + | 1.62619i | ||||
\(845\) | 1.28819e6 | 1.80413 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 558256.i | − | 0.778156i | ||||||
\(848\) | −854725. | + | 827703.i | −1.18860 | + | 1.15102i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 333890. | + | 23231.0i | 0.462132 | + | 0.0321536i | ||||
\(851\) | −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 | 0.996067 | − | 0.0886072i | \(-0.0282416\pi\) |
0.421297 | + | 0.906923i | \(0.361575\pi\) | |||||||
\(860\) | −532762. | + | 215682.i | −0.720339 | + | 0.291620i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 293367. | + | 197730.i | 0.394818 | + | 0.266108i | ||||
\(863\) | − | 77194.2i | − | 0.103648i | −0.998656 | − | 0.0518242i | \(-0.983496\pi\) | ||
0.998656 | − | 0.0518242i | \(-0.0165036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 731250. | 0.977313 | ||||||||
\(866\) | 266244. | − | 395020.i | 0.355013 | − | 0.526725i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 100991. | + | 249460.i | 0.134042 | + | 0.331101i | ||||
\(869\) | −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 | \(0.196282\pi\) | |||||||
\(878\) | −33175.3 | + | 476817.i | −0.0430354 | + | 0.618533i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 612250. | + | 632238.i | 0.790612 | + | 0.816423i | ||||
\(881\) | 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 | \(0.196348\pi\) | ||||
−0.815707 | + | 0.578465i | \(0.803652\pi\) | |||||||
\(884\) | 26585.9 | + | 3717.51i | 0.0340209 | + | 0.00475716i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −56555.9 | + | 812857.i | −0.0720461 | + | 1.03549i | ||||
\(887\) | 797270. | + | 460304.i | 1.01335 | + | 0.585056i | 0.912170 | − | 0.409813i | \(-0.134406\pi\) |
0.101177 | + | 0.994868i | \(0.467739\pi\) | |||||||
\(888\) | 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 | ||||
\(896\) | −463589. | + | 877037.i | −0.577453 | + | 1.09245i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −172492. | + | 255922.i | −0.213902 | + | 0.317362i | ||||
\(899\) | − | 124232.i | − | 0.153714i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −250052. | −0.308022 | ||||||||
\(902\) | −462135. | − | 311480.i | −0.568010 | − | 0.382839i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 427789. | − | 476108.i | 0.523471 | − | 0.582597i | ||||
\(905\) | 1.32984e6 | − | 2.30336e6i | 1.62369 | − | 2.81232i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 426945. | − | 246497.i | 0.518988 | − | 0.299638i | −0.217533 | − | 0.976053i | \(-0.569801\pi\) |
0.736520 | + | 0.676415i | \(0.236468\pi\) | |||||||
\(908\) | 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 | −0.620404 | − | 0.784283i | \(-0.713031\pi\) |
0.369007 | + | 0.929427i | \(0.379698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −116076. | + | 201049.i | −0.139252 | + | 0.241191i | ||||
\(914\) | −1.12065e6 | − | 77971.3i | −1.34146 | − | 0.0933345i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 437096. | + | 61119.2i | 0.520937 | + | 0.0728428i | ||||
\(917\) | 1.79688e6 | 2.13688 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 155183.i | − | 0.183744i | −0.995771 | − | 0.0918719i | \(-0.970715\pi\) | ||
0.995771 | − | 0.0918719i | \(-0.0292850\pi\) | |||||||
\(920\) | 800032. | − | 260871.i | 0.945218 | − | 0.308213i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.60261e6 | − | 111504.i | −1.88524 | − | 0.131169i | ||||
\(923\) | −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 | ||||
\(932\) | 296781. | + | 733088.i | 0.341668 | + | 0.843965i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −691491. | − | 466066.i | −0.792671 | − | 0.534262i | ||||
\(935\) | 184963.i | 0.211574i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −237273. | −0.270252 | −0.135126 | − | 0.990828i | \(-0.543144\pi\) | ||||
−0.135126 | + | 0.990828i | \(0.543144\pi\) | |||||||
\(938\) | −939533. | + | 1.39396e6i | −1.06784 | + | 1.58433i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.89896e6 | + | 768768.i | −2.14911 | + | 0.870040i | ||||
\(941\) | 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 | −0.906102 | − | 0.423060i | \(-0.860956\pi\) |
−0.0866700 | + | 0.996237i | \(0.527623\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −67658.0 | + | 117187.i | −0.0751254 | + | 0.130121i | ||||
\(950\) | 23732.1 | − | 341093.i | 0.0262960 | − | 0.377942i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −198214. | + | 64632.6i | −0.218705 | + | 0.0713145i | ||||
\(953\) | −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 | ||||||||
\(956\) | 248284. | − | 1.77561e6i | 0.271665 | − | 1.94282i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 44454.6 | − | 638930.i | 0.0484380 | − | 0.696181i | ||||
\(959\) | −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 | 0.548642 | − | 0.836058i | \(-0.315145\pi\) |
−0.449726 | + | 0.893166i | \(0.648479\pi\) | |||||||
\(968\) | 394383. | − | 438928.i | 0.420889 | − | 0.468428i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 204685. | − | 303686.i | 0.217542 | − | 0.322761i | ||||
\(971\) | − | 689120.i | − | 0.730897i | −0.930832 | − | 0.365448i | \(-0.880916\pi\) | ||
0.930832 | − | 0.365448i | \(-0.119084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 247915. | 0.261865 | ||||||||
\(974\) | 1.23377e6 | + | 831561.i | 1.30051 | + | 0.876549i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 235435. | + | 67154.9i | 0.247156 | + | 0.0704982i | ||||
\(977\) | −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 | −0.664853 | − | 0.746974i | \(-0.731506\pi\) |
0.314472 | + | 0.949267i | \(0.398173\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.04755e6 | − | 1.81441e6i | 1.07970 | − | 1.87009i | ||||
\(986\) | 96006.6 | + | 6679.82i | 0.0987523 | + | 0.00687086i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3797.70 | − | 27159.3i | 0.00389051 | − | 0.0278231i | ||||
\(989\) | −216637. | −0.221483 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 462949.i | − | 0.471396i | −0.971826 | − | 0.235698i | \(-0.924262\pi\) | ||
0.971826 | − | 0.235698i | \(-0.0757376\pi\) | |||||||
\(992\) | −96828.4 | + | 267483.i | −0.0983964 | + | 0.271814i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.44279e6 | + | 100385.i | 1.46026 | + | 0.101600i | ||||
\(995\) | 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.91.16 | 44 | ||
3.2 | odd | 2 | 36.5.f.a.31.7 | yes | 44 | ||
4.3 | odd | 2 | inner | 108.5.f.a.91.1 | 44 | ||
9.2 | odd | 6 | 36.5.f.a.7.22 | yes | 44 | ||
9.4 | even | 3 | 324.5.d.e.163.16 | 22 | |||
9.5 | odd | 6 | 324.5.d.f.163.7 | 22 | |||
9.7 | even | 3 | inner | 108.5.f.a.19.1 | 44 | ||
12.11 | even | 2 | 36.5.f.a.31.22 | yes | 44 | ||
36.7 | odd | 6 | inner | 108.5.f.a.19.16 | 44 | ||
36.11 | even | 6 | 36.5.f.a.7.7 | ✓ | 44 | ||
36.23 | even | 6 | 324.5.d.f.163.8 | 22 | |||
36.31 | odd | 6 | 324.5.d.e.163.15 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.7 | ✓ | 44 | 36.11 | even | 6 | ||
36.5.f.a.7.22 | yes | 44 | 9.2 | odd | 6 | ||
36.5.f.a.31.7 | yes | 44 | 3.2 | odd | 2 | ||
36.5.f.a.31.22 | yes | 44 | 12.11 | even | 2 | ||
108.5.f.a.19.1 | 44 | 9.7 | even | 3 | inner | ||
108.5.f.a.19.16 | 44 | 36.7 | odd | 6 | inner | ||
108.5.f.a.91.1 | 44 | 4.3 | odd | 2 | inner | ||
108.5.f.a.91.16 | 44 | 1.1 | even | 1 | trivial | ||
324.5.d.e.163.15 | 22 | 36.31 | odd | 6 | |||
324.5.d.e.163.16 | 22 | 9.4 | even | 3 | |||
324.5.d.f.163.7 | 22 | 9.5 | odd | 6 | |||
324.5.d.f.163.8 | 22 | 36.23 | even | 6 |