Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,4,Mod(37,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.i (of order \(9\), degree \(6\), 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: | \(19.1166188419\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 73.6 | ||
Character | \(\chi\) | \(=\) | 324.73 |
Dual form | 324.4.i.a.253.6 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.18194 | − | 4.34817i | 0.463487 | − | 0.388912i | −0.380925 | − | 0.924606i | \(-0.624394\pi\) |
0.844412 | + | 0.535694i | \(0.179950\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.8240 | − | 6.12342i | 0.908409 | − | 0.330634i | 0.154792 | − | 0.987947i | \(-0.450529\pi\) |
0.753617 | + | 0.657313i | \(0.228307\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −45.5667 | − | 38.2350i | −1.24899 | − | 1.04803i | −0.996766 | − | 0.0803571i | \(-0.974394\pi\) |
−0.252223 | − | 0.967669i | \(-0.581162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.02544 | − | 28.5007i | −0.107216 | − | 0.608052i | −0.990312 | − | 0.138860i | \(-0.955656\pi\) |
0.883096 | − | 0.469192i | \(-0.155455\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.6698 | + | 25.4089i | 0.209291 | + | 0.362503i | 0.951491 | − | 0.307675i | \(-0.0995510\pi\) |
−0.742200 | + | 0.670178i | \(0.766218\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.7884 | − | 23.8822i | 0.166488 | − | 0.288366i | −0.770695 | − | 0.637205i | \(-0.780091\pi\) |
0.937183 | + | 0.348839i | \(0.113424\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.946050 | + | 0.344334i | 0.00857674 | + | 0.00312168i | 0.346305 | − | 0.938122i | \(-0.387436\pi\) |
−0.337728 | + | 0.941244i | \(0.609658\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.7600 | + | 78.0370i | −0.110080 | + | 0.624296i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 15.4827 | − | 87.8069i | 0.0991404 | − | 0.562253i | −0.894259 | − | 0.447549i | \(-0.852297\pi\) |
0.993400 | − | 0.114704i | \(-0.0365919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.6374 | − | 4.23566i | −0.0674238 | − | 0.0245402i | 0.308088 | − | 0.951358i | \(-0.400311\pi\) |
−0.375512 | + | 0.926818i | \(0.622533\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 60.5552 | − | 104.885i | 0.292448 | − | 0.506536i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −186.599 | − | 323.199i | −0.829100 | − | 1.43604i | −0.898745 | − | 0.438472i | \(-0.855520\pi\) |
0.0696442 | − | 0.997572i | \(-0.477814\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −38.3921 | − | 217.733i | −0.146240 | − | 0.829369i | −0.966363 | − | 0.257182i | \(-0.917206\pi\) |
0.820123 | − | 0.572187i | \(-0.193905\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −415.169 | − | 348.368i | −1.47239 | − | 1.23548i | −0.913882 | − | 0.405979i | \(-0.866931\pi\) |
−0.558505 | − | 0.829501i | \(-0.688625\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 575.029 | − | 209.294i | 1.78461 | − | 0.649545i | 0.785063 | − | 0.619416i | \(-0.212631\pi\) |
0.999546 | − | 0.0301286i | \(-0.00959170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −17.2036 | + | 14.4355i | −0.0501562 | + | 0.0420861i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 51.1253 | 0.132502 | 0.0662509 | − | 0.997803i | \(-0.478896\pi\) | ||||
0.0662509 | + | 0.997803i | \(0.478896\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −402.376 | −0.986480 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 326.874 | − | 274.280i | 0.721278 | − | 0.605224i | −0.206460 | − | 0.978455i | \(-0.566194\pi\) |
0.927739 | + | 0.373231i | \(0.121750\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 488.734 | − | 177.884i | 1.02583 | − | 0.373373i | 0.226341 | − | 0.974048i | \(-0.427324\pi\) |
0.799493 | + | 0.600675i | \(0.205101\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −149.967 | − | 125.838i | −0.286172 | − | 0.240127i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 38.0132 | + | 215.584i | 0.0693143 | + | 0.393101i | 0.999652 | + | 0.0263958i | \(0.00840303\pi\) |
−0.930337 | + | 0.366705i | \(0.880486\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 99.9846 | + | 173.178i | 0.167127 | + | 0.289472i | 0.937408 | − | 0.348232i | \(-0.113218\pi\) |
−0.770282 | + | 0.637704i | \(0.779884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −398.711 | + | 690.588i | −0.639255 | + | 1.10722i | 0.346342 | + | 0.938108i | \(0.387424\pi\) |
−0.985597 | + | 0.169113i | \(0.945910\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1000.74 | − | 364.240i | −1.48111 | − | 0.539078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 227.171 | − | 1288.35i | 0.323529 | − | 1.83482i | −0.196290 | − | 0.980546i | \(-0.562889\pi\) |
0.519819 | − | 0.854277i | \(-0.326000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.1689 | − | 63.3422i | 0.0147705 | − | 0.0837675i | −0.976531 | − | 0.215375i | \(-0.930903\pi\) |
0.991302 | + | 0.131607i | \(0.0420138\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 186.500 | + | 67.8805i | 0.237986 | + | 0.0866197i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −466.341 | + | 807.726i | −0.555416 | + | 0.962009i | 0.442455 | + | 0.896791i | \(0.354108\pi\) |
−0.997871 | + | 0.0652184i | \(0.979226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −259.070 | − | 448.722i | −0.298439 | − | 0.516911i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −32.3931 | − | 183.711i | −0.0349839 | − | 0.198403i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 915.498 | + | 768.194i | 0.958296 | + | 0.804106i | 0.980675 | − | 0.195644i | \(-0.0626797\pi\) |
−0.0223792 | + | 0.999750i | \(0.507124\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 934.108 | − | 339.987i | 0.920269 | − | 0.334951i | 0.161924 | − | 0.986803i | \(-0.448230\pi\) |
0.758346 | + | 0.651853i | \(0.226008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −252.152 | + | 211.581i | −0.241216 | + | 0.202405i | −0.755379 | − | 0.655288i | \(-0.772547\pi\) |
0.514163 | + | 0.857693i | \(0.328103\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 321.330 | 0.290319 | 0.145159 | − | 0.989408i | \(-0.453631\pi\) | ||||
0.145159 | + | 0.989408i | \(0.453631\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 379.701 | 0.333658 | 0.166829 | − | 0.985986i | \(-0.446647\pi\) | ||||
0.166829 | + | 0.985986i | \(0.446647\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1463.88 | + | 1228.34i | −1.21867 | + | 1.02259i | −0.219780 | + | 0.975549i | \(0.570534\pi\) |
−0.998893 | + | 0.0470391i | \(0.985021\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.39960 | − | 2.32926i | 0.00518927 | − | 0.00188874i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 402.394 | + | 337.648i | 0.309978 | + | 0.260102i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 383.283 | + | 2173.71i | 0.287966 | + | 1.63314i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 690.799 | + | 1196.50i | 0.494295 | + | 0.856145i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −84.0772 | + | 145.626i | −0.0587453 | + | 0.101750i | −0.893902 | − | 0.448262i | \(-0.852043\pi\) |
0.835157 | + | 0.550011i | \(0.185377\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1884.63 | − | 685.949i | −1.25695 | − | 0.457493i | −0.374207 | − | 0.927345i | \(-0.622085\pi\) |
−0.882745 | + | 0.469852i | \(0.844307\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 85.7348 | − | 486.226i | 0.0558958 | − | 0.317001i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 160.622 | − | 910.931i | 0.100167 | − | 0.568073i | −0.892874 | − | 0.450306i | \(-0.851315\pi\) |
0.993041 | − | 0.117768i | \(-0.0375738\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2389.86 | + | 869.838i | 1.45831 | + | 0.530782i | 0.944900 | − | 0.327360i | \(-0.106159\pi\) |
0.513412 | + | 0.858142i | \(0.328381\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −860.732 | + | 1490.83i | −0.503343 | + | 0.871815i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −301.569 | − | 522.332i | −0.172717 | − | 0.299154i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 353.990 | + | 2007.58i | 0.194631 | + | 1.10381i | 0.912943 | + | 0.408086i | \(0.133804\pi\) |
−0.718313 | + | 0.695720i | \(0.755085\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 631.192 | + | 529.633i | 0.340170 | + | 0.285437i | 0.796829 | − | 0.604205i | \(-0.206509\pi\) |
−0.456658 | + | 0.889642i | \(0.650954\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −78.7217 | + | 28.6523i | −0.0407940 | + | 0.0148478i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −721.515 | + | 605.423i | −0.366772 | + | 0.307758i | −0.807483 | − | 0.589891i | \(-0.799171\pi\) |
0.440711 | + | 0.897649i | \(0.354726\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.0248 | 0.00882332 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3395.63 | −1.63169 | −0.815847 | − | 0.578267i | \(-0.803729\pi\) | ||||
−0.815847 | + | 0.578267i | \(0.803729\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2218.43 | − | 1861.48i | 1.02795 | − | 0.862550i | 0.0373420 | − | 0.999303i | \(-0.488111\pi\) |
0.990605 | + | 0.136752i | \(0.0436665\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1277.47 | − | 464.961i | 0.581461 | − | 0.211634i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1595.10 | + | 1338.45i | 0.701002 | + | 0.588211i | 0.922059 | − | 0.387050i | \(-0.126506\pi\) |
−0.221056 | + | 0.975261i | \(0.570950\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 246.355 | + | 1397.15i | 0.106416 | + | 0.603513i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2179.06 | + | 3774.24i | 0.909890 | + | 1.57598i | 0.814215 | + | 0.580563i | \(0.197168\pi\) |
0.0956752 | + | 0.995413i | \(0.469499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1347.22 | + | 2333.45i | −0.553248 | + | 0.958254i | 0.444789 | + | 0.895635i | \(0.353279\pi\) |
−0.998038 | + | 0.0626187i | \(0.980055\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2372.27 | − | 863.436i | −0.942772 | − | 0.343141i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 303.053 | − | 1718.70i | 0.118510 | − | 0.672105i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 523.862 | − | 2970.97i | 0.198457 | − | 1.12551i | −0.708951 | − | 0.705258i | \(-0.750831\pi\) |
0.907408 | − | 0.420250i | \(-0.138058\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1388.37 | + | 505.325i | 0.517808 | + | 0.188467i | 0.587686 | − | 0.809089i | \(-0.300039\pi\) |
−0.0698784 | + | 0.997556i | \(0.522261\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1889.39 | + | 3272.53i | −0.683318 | + | 1.18354i | 0.290644 | + | 0.956831i | \(0.406131\pi\) |
−0.973962 | + | 0.226711i | \(0.927203\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 160.647 | + | 278.248i | 0.0572258 | + | 0.0991180i | 0.893219 | − | 0.449622i | \(-0.148441\pi\) |
−0.835993 | + | 0.548740i | \(0.815108\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −277.198 | − | 1572.07i | −0.0958399 | − | 0.543535i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1145.68 | − | 961.343i | −0.390332 | − | 0.327527i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1541.43 | + | 561.034i | −0.510157 | + | 0.185682i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 973.780 | − | 817.098i | 0.317714 | − | 0.266594i | −0.469957 | − | 0.882689i | \(-0.655731\pi\) |
0.787672 | + | 0.616095i | \(0.211286\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3666.15 | −1.16293 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −221.724 | −0.0693622 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 650.448 | − | 545.791i | 0.197981 | − | 0.166126i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4698.03 | − | 1709.94i | 1.41078 | − | 0.513481i | 0.479420 | − | 0.877585i | \(-0.340847\pi\) |
0.931358 | + | 0.364104i | \(0.118625\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 907.775 | + | 761.713i | 0.265423 | + | 0.222717i | 0.765780 | − | 0.643103i | \(-0.222353\pi\) |
−0.500356 | + | 0.865820i | \(0.666798\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 321.039 | + | 1820.70i | 0.0926412 | + | 0.525394i | 0.995445 | + | 0.0953410i | \(0.0303941\pi\) |
−0.902803 | + | 0.430053i | \(0.858495\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1585.36 | − | 2745.93i | −0.445754 | − | 0.772068i | 0.552351 | − | 0.833612i | \(-0.313731\pi\) |
−0.998104 | + | 0.0615437i | \(0.980398\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2069.73 | − | 3584.87i | 0.574528 | − | 0.995111i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5573.01 | − | 2028.41i | −1.50832 | − | 0.548983i | −0.550119 | − | 0.835086i | \(-0.685418\pi\) |
−0.958199 | + | 0.286104i | \(0.907640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −517.453 | + | 2934.62i | −0.138307 | + | 0.784380i | 0.834192 | + | 0.551474i | \(0.185935\pi\) |
−0.972499 | + | 0.232906i | \(0.925177\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −26.3800 | + | 149.608i | −0.00687900 | + | 0.0390127i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −749.953 | − | 272.961i | −0.193192 | − | 0.0703161i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3456.30 | − | 5986.49i | 0.869162 | − | 1.50543i | 0.00630772 | − | 0.999980i | \(-0.497992\pi\) |
0.862854 | − | 0.505453i | \(-0.168674\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.9428 | − | 51.8624i | −0.00744066 | − | 0.0128876i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 882.257 | + | 5003.53i | 0.214139 | + | 1.21444i | 0.882395 | + | 0.470510i | \(0.155930\pi\) |
−0.668256 | + | 0.743931i | \(0.732959\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5118.43 | − | 4294.87i | −1.22797 | − | 1.03039i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7196.97 | − | 2619.48i | 1.68739 | − | 0.614160i | 0.693099 | − | 0.720843i | \(-0.256245\pi\) |
0.994293 | + | 0.106682i | \(0.0340228\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 264.928 | − | 222.301i | 0.0614129 | − | 0.0515316i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6884.46 | 1.56042 | 0.780210 | − | 0.625518i | \(-0.215112\pi\) | ||||
0.780210 | + | 0.625518i | \(0.215112\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3232.55 | −0.724588 | −0.362294 | − | 0.932064i | \(-0.618006\pi\) | ||||
−0.362294 | + | 0.932064i | \(0.618006\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3610.75 | − | 3029.78i | 0.791768 | − | 0.664372i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2971.80 | + | 1081.65i | −0.644615 | + | 0.234621i | −0.643580 | − | 0.765379i | \(-0.722552\pi\) |
−0.00103476 | + | 0.999999i | \(0.500329\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3251.44 | − | 2728.28i | −0.690266 | − | 0.579202i | 0.228720 | − | 0.973492i | \(-0.426546\pi\) |
−0.918986 | + | 0.394290i | \(0.870991\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −927.955 | − | 5262.69i | −0.194916 | − | 1.10542i | −0.912538 | − | 0.408991i | \(-0.865881\pi\) |
0.717623 | − | 0.696432i | \(-0.245230\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1979.18 | − | 3428.04i | −0.407063 | − | 0.705054i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2026.09 | − | 3509.30i | 0.412394 | − | 0.714288i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2133.39 | − | 776.490i | −0.425372 | − | 0.154823i | 0.120459 | − | 0.992718i | \(-0.461563\pi\) |
−0.545830 | + | 0.837896i | \(0.683786\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 501.229 | − | 2842.61i | 0.0989243 | − | 0.561028i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.05944 | − | 28.6935i | 0.000978579 | − | 0.00554980i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9118.00 | − | 3318.68i | −1.74602 | − | 0.635500i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1759.12 | − | 3046.88i | 0.330252 | − | 0.572013i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −324.386 | − | 561.853i | −0.0603052 | − | 0.104452i | 0.834297 | − | 0.551316i | \(-0.185874\pi\) |
−0.894602 | + | 0.446864i | \(0.852541\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 990.109 | + | 5615.19i | 0.180527 | + | 1.02382i | 0.931569 | + | 0.363565i | \(0.118441\pi\) |
−0.751042 | + | 0.660255i | \(0.770448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3737.23 | + | 3135.91i | 0.674890 | + | 0.566300i | 0.914508 | − | 0.404567i | \(-0.132578\pi\) |
−0.239618 | + | 0.970867i | \(0.577022\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6695.08 | + | 2436.81i | −1.18623 | + | 0.431751i | −0.858397 | − | 0.512987i | \(-0.828539\pi\) |
−0.327829 | + | 0.944737i | \(0.606317\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4062.80 | + | 3409.09i | −0.713081 | + | 0.598346i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 809.093 | 0.139378 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2293.26 | 0.391407 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8392.68 | − | 7042.30i | 1.40639 | − | 1.18010i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4873.32 | + | 1773.74i | −0.809250 | + | 0.294543i | −0.713314 | − | 0.700844i | \(-0.752807\pi\) |
−0.0959363 | + | 0.995387i | \(0.530584\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1134.38 | + | 951.855i | 0.185008 | + | 0.155240i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1266.75 | − | 7184.10i | −0.204760 | − | 1.16125i | −0.897816 | − | 0.440370i | \(-0.854847\pi\) |
0.693056 | − | 0.720884i | \(-0.256264\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 368.327 | + | 637.961i | 0.0584927 | + | 0.101312i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3271.52 | + | 5666.44i | −0.515002 | + | 0.892009i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3010.74 | + | 1095.82i | 0.465777 | + | 0.169529i | 0.564239 | − | 0.825612i | \(-0.309170\pi\) |
−0.0984612 | + | 0.995141i | \(0.531392\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −322.003 | + | 1826.17i | −0.0493881 | + | 0.280094i | −0.999493 | − | 0.0318364i | \(-0.989864\pi\) |
0.950105 | + | 0.311930i | \(0.100976\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −57.4469 | + | 325.798i | −0.00866173 | + | 0.0491231i | −0.988832 | − | 0.149033i | \(-0.952384\pi\) |
0.980171 | + | 0.198156i | \(0.0634952\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1271.12 | + | 462.651i | 0.190040 | + | 0.0691689i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2668.13 | + | 4621.33i | −0.392251 | + | 0.679399i | −0.992746 | − | 0.120229i | \(-0.961637\pi\) |
0.600495 | + | 0.799629i | \(0.294970\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3049.26 | + | 5281.47i | 0.444563 | + | 0.770006i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 936.693 | + | 5312.25i | 0.134325 | + | 0.761797i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1992.63 | + | 1672.02i | 0.283418 | + | 0.237816i | 0.773403 | − | 0.633915i | \(-0.218553\pi\) |
−0.489984 | + | 0.871731i | \(0.662998\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 860.130 | − | 313.062i | 0.120366 | − | 0.0438096i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4976.72 | − | 4175.97i | 0.690844 | − | 0.579687i | −0.228308 | − | 0.973589i | \(-0.573319\pi\) |
0.919153 | + | 0.393902i | \(0.128875\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2580.37 | −0.352508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5410.32 | 0.733271 | 0.366635 | − | 0.930365i | \(-0.380510\pi\) | ||||
0.366635 | + | 0.930365i | \(0.380510\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6463.74 | − | 5423.72i | 0.862354 | − | 0.723601i | −0.100120 | − | 0.994975i | \(-0.531923\pi\) |
0.962474 | + | 0.271374i | \(0.0874781\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6769.57 | + | 2463.92i | −0.896128 | + | 0.326164i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8970.57 | − | 7527.21i | −1.16922 | − | 0.981091i | −0.169229 | − | 0.985577i | \(-0.554128\pi\) |
−0.999990 | + | 0.00448556i | \(0.998572\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.12924 | + | 29.0894i | 0.000663419 | + | 0.00376244i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4424.78 | − | 7663.95i | −0.563633 | − | 0.976241i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6759.21 | − | 11707.3i | 0.854496 | − | 1.48003i | −0.0226159 | − | 0.999744i | \(-0.507199\pi\) |
0.877112 | − | 0.480286i | \(-0.159467\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6064.01 | − | 2207.12i | −0.755168 | − | 0.274859i | −0.0643893 | − | 0.997925i | \(-0.520510\pi\) |
−0.690779 | + | 0.723066i | \(0.742732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −62.2364 | + | 352.960i | −0.00769284 | + | 0.0436283i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3854.82 | + | 21861.7i | −0.469475 | + | 2.66252i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5073.67 | + | 1846.66i | 0.613390 | + | 0.223256i | 0.629986 | − | 0.776606i | \(-0.283061\pi\) |
−0.0165958 | + | 0.999862i | \(0.505283\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3819.79 | − | 6616.07i | 0.455108 | − | 0.788270i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −217.546 | − | 376.800i | −0.0257323 | − | 0.0445696i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1598.37 | + | 9064.78i | 0.186361 | + | 1.05691i | 0.924194 | + | 0.381923i | \(0.124738\pi\) |
−0.737833 | + | 0.674983i | \(0.764151\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6648.55 | + | 5578.80i | 0.769669 | + | 0.645829i | 0.940624 | − | 0.339450i | \(-0.110241\pi\) |
−0.170955 | + | 0.985279i | \(0.554685\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2184.69 | + | 795.162i | −0.249348 | + | 0.0907553i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7133.18 | − | 5985.45i | 0.808428 | − | 0.678351i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13477.8 | −1.50628 | −0.753138 | − | 0.657862i | \(-0.771461\pi\) | ||||
−0.753138 | + | 0.657862i | \(0.771461\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12659.9 | 1.40507 | 0.702533 | − | 0.711651i | \(-0.252052\pi\) | ||||
0.702533 | + | 0.711651i | \(0.252052\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.2680 | − | 17.8460i | 0.00232811 | − | 0.00195352i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8751.79 | + | 3185.39i | −0.951480 | + | 0.346311i | −0.770689 | − | 0.637211i | \(-0.780088\pi\) |
−0.180791 | + | 0.983522i | \(0.557866\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3512.25 | + | 2947.12i | 0.376686 | + | 0.316077i | 0.811400 | − | 0.584492i | \(-0.198706\pi\) |
−0.434714 | + | 0.900569i | \(0.643150\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1095.58 | + | 6213.32i | 0.116709 | + | 0.661887i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −530.524 | − | 918.895i | −0.0557616 | − | 0.0965820i | 0.836797 | − | 0.547513i | \(-0.184425\pi\) |
−0.892559 | + | 0.450931i | \(0.851092\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6575.61 | + | 11389.3i | −0.686548 | + | 1.18914i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3293.61 | − | 1198.77i | −0.339355 | − | 0.123515i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2136.23 | + | 12115.2i | −0.218662 | + | 1.24009i | 0.655775 | + | 0.754956i | \(0.272342\pi\) |
−0.874437 | + | 0.485139i | \(0.838769\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.2863 | − | 171.762i | 0.00305981 | − | 0.0173531i | −0.983240 | − | 0.182318i | \(-0.941640\pi\) |
0.986299 | + | 0.164965i | \(0.0527511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8366.64 | + | 3045.21i | 0.839808 | + | 0.305665i | 0.725878 | − | 0.687824i | \(-0.241434\pi\) |
0.113930 | + | 0.993489i | \(0.463656\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1326.26 | + | 2297.15i | −0.131418 | + | 0.227622i | −0.924223 | − | 0.381853i | \(-0.875286\pi\) |
0.792806 | + | 0.609475i | \(0.208620\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1959.64 | + | 3394.20i | 0.192938 | + | 0.334179i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5598.02 | + | 31748.0i | 0.544181 | + | 3.08620i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1673.97 | + | 1404.63i | 0.161699 | + | 0.135681i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18164.9 | + | 6611.48i | −1.73272 | + | 0.630660i | −0.998819 | − | 0.0485928i | \(-0.984526\pi\) |
−0.733905 | + | 0.679252i | \(0.762304\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8273.67 | + | 6942.43i | −0.784297 | + | 0.658103i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8084.29 | 0.756884 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6386.49 | 0.594249 | 0.297125 | − | 0.954839i | \(-0.403972\pi\) | ||||
0.297125 | + | 0.954839i | \(0.403972\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13082.9 | − | 10977.9i | 1.20249 | − | 1.00901i | 0.202936 | − | 0.979192i | \(-0.434952\pi\) |
0.999555 | − | 0.0298176i | \(-0.00949265\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2458.20 | − | 894.712i | 0.224568 | − | 0.0817359i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2742.58 | + | 2301.30i | 0.247528 | + | 0.207701i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1145.21 | − | 6494.83i | −0.102739 | − | 0.582662i | −0.992099 | − | 0.125455i | \(-0.959961\pi\) |
0.889360 | − | 0.457207i | \(-0.151150\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3417.70 | + | 5919.63i | 0.302958 | + | 0.524738i | 0.976805 | − | 0.214133i | \(-0.0686925\pi\) |
−0.673847 | + | 0.738871i | \(0.735359\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3362.17 | − | 5823.45i | 0.296267 | − | 0.513149i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 435.292 | + | 158.433i | 0.0379056 | + | 0.0137965i | 0.360903 | − | 0.932603i | \(-0.382468\pi\) |
−0.322998 | + | 0.946400i | \(0.604691\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2479.14 | + | 14059.9i | −0.214620 | + | 1.21717i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −386.650 | + | 2192.80i | −0.0330831 | + | 0.187624i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34204.5 | − | 12449.4i | −2.90970 | − | 1.05904i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5085.58 | − | 8808.49i | 0.427646 | − | 0.740704i | −0.569018 | − | 0.822325i | \(-0.692676\pi\) |
0.996663 | + | 0.0816212i | \(0.0260098\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4957.61 | + | 8586.84i | 0.414496 | + | 0.717928i | 0.995375 | − | 0.0960616i | \(-0.0306246\pi\) |
−0.580879 | + | 0.813990i | \(0.697291\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −63.0949 | − | 357.829i | −0.00521529 | − | 0.0295774i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9319.69 | − | 7820.15i | −0.765981 | − | 0.642734i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6012.60 | + | 2188.41i | −0.488620 | + | 0.177843i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1665.11 | − | 1397.19i | 0.134559 | − | 0.112908i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1335.85 | 0.106752 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12272.1 | 0.975264 | 0.487632 | − | 0.873049i | \(-0.337861\pi\) | ||||
0.487632 | + | 0.873049i | \(0.337861\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1967.59 | − | 1651.00i | 0.154646 | − | 0.129764i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17044.4 | − | 6203.64i | 1.33229 | − | 0.484915i | 0.424915 | − | 0.905233i | \(-0.360304\pi\) |
0.907377 | + | 0.420318i | \(0.138082\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1883.54 | − | 1580.48i | −0.145629 | − | 0.122197i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4067.21 | − | 23066.3i | −0.312758 | − | 1.77374i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1502.66 | − | 2602.69i | −0.114309 | − | 0.197988i | 0.803195 | − | 0.595717i | \(-0.203132\pi\) |
−0.917503 | + | 0.397729i | \(0.869799\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7842.33 | + | 13583.3i | −0.593373 | + | 1.02775i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2205.13 | − | 802.602i | −0.165071 | − | 0.0600811i | 0.258163 | − | 0.966101i | \(-0.416883\pi\) |
−0.423234 | + | 0.906020i | \(0.639105\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2244.71 | + | 12730.4i | −0.167143 | + | 0.947913i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3585.08 | − | 20332.0i | 0.264138 | − | 1.49800i | −0.507341 | − | 0.861745i | \(-0.669372\pi\) |
0.771479 | − | 0.636255i | \(-0.219517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10022.8 | + | 3648.01i | 0.734575 | + | 0.267363i | 0.682100 | − | 0.731259i | \(-0.261067\pi\) |
0.0524748 | + | 0.998622i | \(0.483289\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.8885 | + | 69.0889i | −0.00289298 | + | 0.00501079i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5276.40 | − | 9138.99i | −0.380692 | − | 0.659378i | 0.610469 | − | 0.792040i | \(-0.290981\pi\) |
−0.991161 | + | 0.132662i | \(0.957648\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −199.965 | − | 1134.06i | −0.0142787 | − | 0.0809788i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2329.61 | − | 1954.78i | −0.165493 | − | 0.138865i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5519.40 | − | 2008.90i | 0.388092 | − | 0.141254i | −0.140602 | − | 0.990066i | \(-0.544904\pi\) |
0.528695 | + | 0.848812i | \(0.322682\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −261.618 | + | 219.524i | −0.0183018 | + | 0.0153571i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10619.0 | 0.735360 | 0.367680 | − | 0.929952i | \(-0.380152\pi\) | ||||
0.367680 | + | 0.929952i | \(0.380152\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3553.33 | 0.244828 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 291.282 | − | 244.414i | 0.0198689 | − | 0.0166719i | −0.632799 | − | 0.774316i | \(-0.718094\pi\) |
0.652668 | + | 0.757644i | \(0.273650\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2760.03 | + | 1004.57i | −0.187327 | + | 0.0681816i | −0.433981 | − | 0.900922i | \(-0.642891\pi\) |
0.246653 | + | 0.969104i | \(0.420669\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11437.8 | + | 9597.45i | 0.768616 | + | 0.644945i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4004.42 | + | 22710.2i | 0.267766 | + | 1.51858i | 0.761040 | + | 0.648705i | \(0.224689\pi\) |
−0.493274 | + | 0.869874i | \(0.664200\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8854.79 | − | 15336.9i | −0.586295 | − | 1.01549i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7919.71 | − | 13717.3i | 0.521818 | − | 0.903814i | −0.477860 | − | 0.878436i | \(-0.658588\pi\) |
0.999678 | − | 0.0253787i | \(-0.00807915\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7369.88 | − | 2682.42i | −0.480875 | − | 0.175024i | 0.0901973 | − | 0.995924i | \(-0.471250\pi\) |
−0.571072 | + | 0.820900i | \(0.693472\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3859.29 | − | 21887.1i | 0.250594 | − | 1.42119i | −0.556539 | − | 0.830821i | \(-0.687871\pi\) |
0.807133 | − | 0.590369i | \(-0.201018\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2899.66 | + | 16444.8i | −0.186472 | + | 1.05754i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −525.504 | − | 191.268i | −0.0336323 | − | 0.0122411i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5474.75 | − | 9482.54i | 0.347047 | − | 0.601103i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2964.46 | − | 5134.59i | −0.187026 | − | 0.323938i | 0.757232 | − | 0.653146i | \(-0.226551\pi\) |
−0.944257 | + | 0.329209i | \(0.893218\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 197.523 | + | 1120.21i | 0.0123440 | + | 0.0700065i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 497.879 | + | 417.770i | 0.0309681 | + | 0.0259853i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3853.21 | + | 1402.45i | −0.237430 | + | 0.0864175i | −0.457995 | − | 0.888955i | \(-0.651432\pi\) |
0.220565 | + | 0.975372i | \(0.429210\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 237.689 | − | 199.444i | 0.0145778 | − | 0.0122322i | −0.635470 | − | 0.772126i | \(-0.719193\pi\) |
0.650047 | + | 0.759894i | \(0.274749\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17190.2 | −1.04454 | −0.522268 | − | 0.852781i | \(-0.674914\pi\) | ||||
−0.522268 | + | 0.852781i | \(0.674914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25381.7 | −1.53516 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5085.19 | − | 4266.98i | 0.304746 | − | 0.255712i | −0.477571 | − | 0.878593i | \(-0.658482\pi\) |
0.782316 | + | 0.622881i | \(0.214038\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12748.7 | + | 4640.13i | −0.760506 | + | 0.276802i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1245.58 | + | 1045.16i | 0.0736279 | + | 0.0617812i | 0.678859 | − | 0.734269i | \(-0.262475\pi\) |
−0.605231 | + | 0.796050i | \(0.706919\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1371.31 | − | 7777.07i | −0.0806924 | − | 0.457629i | −0.998203 | − | 0.0599185i | \(-0.980916\pi\) |
0.917511 | − | 0.397711i | \(-0.130195\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1669.92 | − | 2892.39i | −0.0973785 | − | 0.168665i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.8823 | − | 77.7385i | 0.00260547 | − | 0.00451281i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29071.4 | − | 10581.1i | −1.67256 | − | 0.608763i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2739.40 | − | 15535.9i | 0.156904 | − | 0.889846i | −0.800121 | − | 0.599839i | \(-0.795231\pi\) |
0.957025 | − | 0.290007i | \(-0.0936576\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5133.84 | − | 29115.5i | 0.291447 | − | 1.65288i | −0.389856 | − | 0.920876i | \(-0.627475\pi\) |
0.681303 | − | 0.732002i | \(-0.261414\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20106.3 | + | 7318.09i | 1.13639 | + | 0.413612i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12777.3 | + | 22131.0i | −0.715829 | + | 1.23985i | 0.246810 | + | 0.969064i | \(0.420618\pi\) |
−0.962639 | + | 0.270788i | \(0.912716\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3128.55 | − | 5418.80i | −0.174505 | − | 0.302251i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −256.927 | − | 1457.11i | −0.0142063 | − | 0.0805680i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16424.3 | − | 13781.6i | −0.904212 | − | 0.758724i | 0.0667969 | − | 0.997767i | \(-0.478722\pi\) |
−0.971009 | + | 0.239042i | \(0.923166\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16166.3 | − | 5884.06i | 0.882336 | − | 0.321144i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4969.13 | − | 4169.60i | 0.270042 | − | 0.226592i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11587.1 | 0.624308 | 0.312154 | − | 0.950031i | \(-0.398949\pi\) | ||||
0.312154 | + | 0.950031i | \(0.398949\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10291.6 | −0.552142 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13633.5 | − | 11439.9i | 0.725235 | − | 0.608544i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8347.62 | − | 3038.29i | 0.442174 | − | 0.160938i | −0.111332 | − | 0.993783i | \(-0.535512\pi\) |
0.553506 | + | 0.832845i | \(0.313289\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.55107 | − | 8.01430i | −0.000501669 | − | 0.000420951i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2022.12 | + | 11468.0i | 0.105766 | + | 0.599831i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4391.89 | + | 7606.97i | 0.227802 | + | 0.394565i | 0.957156 | − | 0.289571i | \(-0.0935127\pi\) |
−0.729354 | + | 0.684136i | \(0.760179\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2946.60 | + | 5103.66i | −0.152201 | + | 0.263620i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6639.15 | + | 2416.45i | 0.340099 | + | 0.123786i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2189.91 | − | 12419.6i | 0.111718 | − | 0.633587i | −0.876604 | − | 0.481212i | \(-0.840197\pi\) |
0.988323 | − | 0.152375i | \(-0.0486921\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2761.19 | − | 15659.5i | 0.139707 | − | 0.792320i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5389.52 | + | 1961.62i | 0.271578 | + | 0.0988462i | 0.474219 | − | 0.880407i | \(-0.342730\pi\) |
−0.202642 | + | 0.979253i | \(0.564953\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6510.71 | − | 11276.9i | 0.325407 | − | 0.563622i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6949.01 | − | 12036.0i | −0.345904 | − | 0.599124i | 0.639613 | − | 0.768697i | \(-0.279095\pi\) |
−0.985518 | + | 0.169573i | \(0.945761\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2458.80 | − | 13944.6i | −0.121406 | − | 0.688528i | −0.983378 | − | 0.181572i | \(-0.941882\pi\) |
0.861972 | − | 0.506956i | \(-0.169230\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10563.6 | + | 8863.95i | 0.519492 | + | 0.435906i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5406.04 | − | 1967.64i | 0.263728 | − | 0.0959892i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8216.97 | + | 6894.86i | −0.399256 | + | 0.335016i | −0.820206 | − | 0.572068i | \(-0.806141\pi\) |
0.420950 | + | 0.907084i | \(0.361697\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5573.74 | 0.268674 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12941.7 | −0.621366 | −0.310683 | − | 0.950514i | \(-0.600558\pi\) | ||||
−0.310683 | + | 0.950514i | \(0.600558\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16885.2 | − | 14168.4i | 0.804323 | − | 0.674907i | −0.144923 | − | 0.989443i | \(-0.546293\pi\) |
0.949245 | + | 0.314536i | \(0.101849\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6388.07 | − | 2325.07i | 0.303098 | − | 0.110319i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9459.87 | − | 7937.77i | −0.445340 | − | 0.373685i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2620.50 | − | 14861.6i | −0.122884 | − | 0.696908i | −0.982542 | − | 0.186039i | \(-0.940435\pi\) |
0.859659 | − | 0.510869i | \(-0.170676\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16889.2 | + | 29253.0i | 0.785852 | + | 1.36113i | 0.928489 | + | 0.371360i | \(0.121108\pi\) |
−0.142637 | + | 0.989775i | \(0.545558\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 490.669 | − | 849.864i | 0.0227424 | − | 0.0393910i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5729.31 | − | 2085.30i | −0.263509 | − | 0.0959095i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2065.51 | − | 11714.1i | 0.0946347 | − | 0.536700i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1106.37 | + | 6274.53i | −0.0503032 | + | 0.285284i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25567.2 | − | 9305.71i | −1.15803 | − | 0.421490i | −0.309640 | − | 0.950854i | \(-0.600208\pi\) |
−0.848395 | + | 0.529364i | \(0.822431\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17106.6 | + | 29629.5i | −0.768952 | + | 1.33186i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7525.94 | − | 13035.3i | −0.337016 | − | 0.583729i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2911.06 | − | 16509.5i | −0.129379 | − | 0.733746i | −0.978610 | − | 0.205724i | \(-0.934045\pi\) |
0.849231 | − | 0.528022i | \(-0.177066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13753.5 | + | 11540.5i | 0.608965 | + | 0.510982i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 44572.6 | − | 16223.1i | 1.95882 | − | 0.712952i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 93.4036 | − | 78.3749i | 0.00408950 | − | 0.00343150i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8398.15 | −0.364973 | −0.182487 | − | 0.983208i | \(-0.558415\pi\) | ||||
−0.182487 | + | 0.983208i | \(0.558415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38336.5 | −1.65990 | −0.829949 | − | 0.557839i | \(-0.811631\pi\) | ||||
−0.829949 | + | 0.557839i | \(0.811631\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17596.0 | + | 14764.8i | −0.756269 | + | 0.634585i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14044.3 | + | 5111.72i | −0.601406 | + | 0.218894i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21752.9 | − | 18252.8i | −0.924703 | − | 0.775918i | 0.0501561 | − | 0.998741i | \(-0.484028\pi\) |
−0.974859 | + | 0.222824i | \(0.928473\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4570.67 | + | 25921.6i | 0.193589 | + | 1.09790i | 0.914414 | + | 0.404780i | \(0.132652\pi\) |
−0.720825 | + | 0.693117i | \(0.756237\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8653.68 | + | 14988.6i | 0.363867 | + | 0.630236i | 0.988594 | − | 0.150608i | \(-0.0481230\pi\) |
−0.624727 | + | 0.780843i | \(0.714790\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3848.42 | + | 6665.66i | −0.161232 | + | 0.279262i | −0.935311 | − | 0.353827i | \(-0.884880\pi\) |
0.774079 | + | 0.633089i | \(0.218213\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −619.164 | − | 225.357i | −0.0257536 | − | 0.00937354i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3401.74 | − | 19292.2i | 0.140984 | − | 0.799562i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2024.34 | + | 11480.6i | −0.0832992 | + | 0.472413i | 0.914411 | + | 0.404786i | \(0.132654\pi\) |
−0.997711 | + | 0.0676272i | \(0.978457\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15447.8 | + | 5622.55i | 0.633393 | + | 0.230536i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4598.05 | − | 7964.05i | 0.187192 | − | 0.324227i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19758.9 | + | 34223.4i | 0.801562 | + | 1.38835i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −65.2437 | − | 370.015i | −0.00262811 | − | 0.0149048i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16135.3 | + | 13539.1i | 0.647668 | + | 0.543458i | 0.906362 | − | 0.422501i | \(-0.138848\pi\) |
−0.258694 | + | 0.965959i | \(0.583292\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10298.8 | + | 3748.45i | −0.410501 | + | 0.149410i | −0.539012 | − | 0.842298i | \(-0.681202\pi\) |
0.128511 | + | 0.991708i | \(0.458980\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5778.78 | + | 4848.97i | −0.229534 | + | 0.192602i | −0.750300 | − | 0.661098i | \(-0.770091\pi\) |
0.520766 | + | 0.853699i | \(0.325646\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26268.2 | 1.03613 | 0.518065 | − | 0.855341i | \(-0.326652\pi\) | ||||
0.518065 | + | 0.855341i | \(0.326652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14085.5 | 0.553668 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −59611.6 | + | 50020.1i | −2.32703 | + | 1.95261i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5953.26 | − | 2166.81i | 0.231594 | − | 0.0842934i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18948.6 | + | 15899.8i | 0.732093 | + | 0.614299i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8371.42 | + | 47476.7i | 0.322329 | + | 1.82802i | 0.527814 | + | 0.849360i | \(0.323012\pi\) |
−0.205485 | + | 0.978660i | \(0.565877\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8868.20 | + | 15360.2i | 0.339134 | + | 0.587398i | 0.984270 | − | 0.176670i | \(-0.0565326\pi\) |
−0.645136 | + | 0.764068i | \(0.723199\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17748.2 | − | 30740.7i | 0.676413 | − | 1.17158i | −0.299640 | − | 0.954052i | \(-0.596867\pi\) |
0.976054 | − | 0.217530i | \(-0.0698000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2797.75 | + | 1018.30i | 0.105907 | + | 0.0385469i | 0.394430 | − | 0.918926i | \(-0.370942\pi\) |
−0.288523 | + | 0.957473i | \(0.593164\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −522.783 | + | 2964.85i | −0.0197228 | + | 0.111854i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2930.34 | − | 16618.8i | 0.109810 | − | 0.622762i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27702.8 | + | 10083.0i | 1.03464 | + | 0.376578i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −552.099 | + | 956.264i | −0.0204822 | + | 0.0354763i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 749.998 | + | 1299.03i | 0.0277315 | + | 0.0480323i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3165.02 | + | 17949.7i | 0.116253 | + | 0.659303i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3444.78 | − | 2890.51i | −0.126110 | − | 0.105819i | 0.577551 | − | 0.816354i | \(-0.304008\pi\) |
−0.703661 | + | 0.710535i | \(0.748453\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3923.42 | − | 1428.01i | 0.142688 | − | 0.0519342i | −0.269689 | − | 0.962947i | \(-0.586921\pi\) |
0.412377 | + | 0.911013i | \(0.364699\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2930.82 | + | 2459.25i | −0.106239 | + | 0.0891449i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35907.3 | −1.29309 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25666.6 | −0.921287 | −0.460643 | − | 0.887585i | \(-0.652381\pi\) | ||||
−0.460643 | + | 0.887585i | \(0.652381\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4433.24 | − | 3719.93i | 0.158095 | − | 0.132658i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27789.1 | − | 10114.4i | 0.987785 | − | 0.359524i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20279.1 | + | 17016.2i | 0.716185 | + | 0.600950i | 0.926327 | − | 0.376720i | \(-0.122948\pi\) |
−0.210142 | + | 0.977671i | \(0.567393\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 107.542 | + | 609.903i | 0.00378578 | + | 0.0214702i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5902.78 | − | 10223.9i | −0.206462 | − | 0.357602i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17460.8 | + | 30243.1i | −0.608774 | + | 1.05443i | 0.382669 | + | 0.923885i | \(0.375005\pi\) |
−0.991443 | + | 0.130542i | \(0.958328\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46488.1 | − | 16920.3i | −1.61049 | − | 0.586169i | −0.628950 | − | 0.777446i | \(-0.716515\pi\) |
−0.981536 | + | 0.191276i | \(0.938737\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.6519 | − | 219.206i | 0.00133476 | − | 0.00756980i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4727.28 | + | 26809.7i | −0.162213 | + | 0.919956i | 0.789678 | + | 0.613521i | \(0.210247\pi\) |
−0.951891 | + | 0.306435i | \(0.900864\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21685.9 | + | 7893.04i | 0.741787 | + | 0.269988i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15252.7 | + | 26418.4i | −0.518450 | + | 0.897982i | 0.481320 | + | 0.876545i | \(0.340158\pi\) |
−0.999770 | + | 0.0214371i | \(0.993176\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10203.7 | − | 17673.3i | −0.345741 | − | 0.598841i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2875.72 | − | 16309.0i | −0.0968320 | − | 0.549161i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22703.7 | − | 19050.7i | −0.762101 | − | 0.639478i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9391.68 | − | 3418.29i | 0.313294 | − | 0.114030i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11428.8 | − | 9589.87i | 0.380066 | − | 0.318914i | −0.432662 | − | 0.901556i | \(-0.642426\pi\) |
0.812728 | + | 0.582643i | \(0.197981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16017.3 | −0.529373 | −0.264686 | − | 0.964335i | \(-0.585268\pi\) | ||||
−0.264686 | + | 0.964335i | \(0.585268\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45533.3 | 1.50024 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21806.5 | + | 18297.8i | −0.714075 | + | 0.599180i | −0.925739 | − | 0.378163i | \(-0.876556\pi\) |
0.211664 | + | 0.977342i | \(0.432112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 52133.1 | − | 18974.9i | 1.70192 | − | 0.619448i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18350.6 | − | 15398.0i | −0.595417 | − | 0.499614i | 0.294552 | − | 0.955635i | \(-0.404830\pi\) |
−0.889969 | + | 0.456022i | \(0.849274\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4438.76 | + | 25173.5i | 0.143584 | + | 0.814307i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −272.816 | − | 472.530i | −0.00877152 | − | 0.0151927i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8682.28 | + | 15038.1i | −0.278306 | + | 0.482041i | −0.970964 | − | 0.239226i | \(-0.923106\pi\) |
0.692658 | + | 0.721267i | \(0.256440\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2042.33 | + | 743.348i | 0.0650716 | + | 0.0236841i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3733.89 | + | 21175.9i | −0.118609 | + | 0.672667i | 0.866290 | + | 0.499541i | \(0.166498\pi\) |
−0.984900 | + | 0.173126i | \(0.944613\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 324.4.i.a.73.6 | 54 | ||
3.2 | odd | 2 | 108.4.i.a.25.8 | yes | 54 | ||
27.13 | even | 9 | inner | 324.4.i.a.253.6 | 54 | ||
27.14 | odd | 18 | 108.4.i.a.13.8 | ✓ | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.i.a.13.8 | ✓ | 54 | 27.14 | odd | 18 | ||
108.4.i.a.25.8 | yes | 54 | 3.2 | odd | 2 | ||
324.4.i.a.73.6 | 54 | 1.1 | even | 1 | trivial | ||
324.4.i.a.253.6 | 54 | 27.13 | even | 9 | inner |