Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(127,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.o (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 127.3 | ||
Root | \(1.84233 - 0.778342i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.127 |
Dual form | 1728.3.o.g.1279.3 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 1.10093 | + | 1.90686i | 0.220185 | + | 0.381372i | 0.954864 | − | 0.297043i | \(-0.0960005\pi\) |
−0.734679 | + | 0.678415i | \(0.762667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.23844 | − | 4.17912i | −1.03406 | − | 0.597017i | −0.115917 | − | 0.993259i | \(-0.536981\pi\) |
−0.918146 | + | 0.396242i | \(0.870314\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.54769 | + | 2.62561i | 0.413426 | + | 0.238692i | 0.692261 | − | 0.721648i | \(-0.256615\pi\) |
−0.278835 | + | 0.960339i | \(0.589948\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.37788 | + | 12.7789i | 0.567529 | + | 0.982990i | 0.996809 | + | 0.0798182i | \(0.0254340\pi\) |
−0.429280 | + | 0.903171i | \(0.641233\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −28.2789 | −1.66346 | −0.831732 | − | 0.555178i | \(-0.812650\pi\) | ||||
−0.831732 | + | 0.555178i | \(0.812650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 19.1376i | − | 1.00724i | −0.863925 | − | 0.503620i | \(-0.832001\pi\) | ||
0.863925 | − | 0.503620i | \(-0.167999\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.16702 | − | 1.82848i | 0.137696 | − | 0.0794990i | −0.429569 | − | 0.903034i | \(-0.641335\pi\) |
0.567266 | + | 0.823535i | \(0.308001\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.0759 | − | 17.4520i | 0.403037 | − | 0.698081i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −12.3355 | + | 21.3657i | −0.425362 | + | 0.736748i | −0.996454 | − | 0.0841375i | \(-0.973187\pi\) |
0.571092 | + | 0.820886i | \(0.306520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32.9674 | − | 19.0338i | 1.06347 | − | 0.613992i | 0.137077 | − | 0.990560i | \(-0.456229\pi\) |
0.926389 | + | 0.376568i | \(0.122896\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 18.4036i | − | 0.525817i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.21977 | 0.114048 | 0.0570239 | − | 0.998373i | \(-0.481839\pi\) | ||||
0.0570239 | + | 0.998373i | \(0.481839\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.92483 | + | 17.1903i | 0.242069 | + | 0.419276i | 0.961303 | − | 0.275492i | \(-0.0888406\pi\) |
−0.719235 | + | 0.694767i | \(0.755507\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20.1894 | + | 11.6564i | 0.469521 | + | 0.271078i | 0.716039 | − | 0.698060i | \(-0.245953\pi\) |
−0.246518 | + | 0.969138i | \(0.579286\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 25.8538 | + | 14.9267i | 0.550082 | + | 0.317590i | 0.749155 | − | 0.662395i | \(-0.230460\pi\) |
−0.199073 | + | 0.979985i | \(0.563793\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.4300 | + | 18.0654i | 0.212858 | + | 0.368681i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −32.1118 | −0.605883 | −0.302942 | − | 0.953009i | \(-0.597969\pi\) | ||||
−0.302942 | + | 0.953009i | \(0.597969\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.5624i | 0.210225i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.96159 | − | 4.59663i | 0.134942 | − | 0.0779089i | −0.431009 | − | 0.902348i | \(-0.641842\pi\) |
0.565951 | + | 0.824439i | \(0.308509\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 40.8215 | − | 70.7049i | 0.669205 | − | 1.15910i | −0.308922 | − | 0.951087i | \(-0.599968\pi\) |
0.978127 | − | 0.208009i | \(-0.0666985\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.2450 | + | 28.1372i | −0.249923 | + | 0.432879i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.86179 | − | 3.96166i | 0.102415 | − | 0.0591292i | −0.447918 | − | 0.894075i | \(-0.647834\pi\) |
0.550333 | + | 0.834946i | \(0.314501\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 62.9286i | − | 0.886318i | −0.896443 | − | 0.443159i | \(-0.853858\pi\) | ||
0.896443 | − | 0.443159i | \(-0.146142\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33.3218 | 0.456463 | 0.228232 | − | 0.973607i | \(-0.426706\pi\) | ||||
0.228232 | + | 0.973607i | \(0.426706\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.9454 | − | 38.0106i | −0.285006 | − | 0.493644i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −53.7133 | − | 31.0114i | −0.679916 | − | 0.392549i | 0.119908 | − | 0.992785i | \(-0.461740\pi\) |
−0.799823 | + | 0.600236i | \(0.795073\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 103.056 | + | 59.4995i | 1.24164 | + | 0.716861i | 0.969428 | − | 0.245376i | \(-0.0789114\pi\) |
0.272212 | + | 0.962237i | \(0.412245\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −31.1329 | − | 53.9238i | −0.366270 | − | 0.634398i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 107.361 | 1.20630 | 0.603152 | − | 0.797626i | \(-0.293911\pi\) | ||||
0.603152 | + | 0.797626i | \(0.293911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 123.332i | − | 1.35530i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 36.4927 | − | 21.0690i | 0.384133 | − | 0.221779i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.78621 | − | 3.09380i | 0.0184145 | − | 0.0318949i | −0.856671 | − | 0.515863i | \(-0.827471\pi\) |
0.875086 | + | 0.483968i | \(0.160805\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.54688 | − | 13.0716i | 0.0747216 | − | 0.129422i | −0.826244 | − | 0.563313i | \(-0.809527\pi\) |
0.900965 | + | 0.433891i | \(0.142860\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 112.813 | − | 65.1324i | 1.09527 | − | 0.632353i | 0.160294 | − | 0.987069i | \(-0.448756\pi\) |
0.934974 | + | 0.354716i | \(0.115422\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 51.2733i | − | 0.479190i | −0.970873 | − | 0.239595i | \(-0.922985\pi\) | ||
0.970873 | − | 0.239595i | \(-0.0770146\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 25.4737 | 0.233704 | 0.116852 | − | 0.993149i | \(-0.462720\pi\) | ||||
0.116852 | + | 0.993149i | \(0.462720\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −76.1529 | − | 131.901i | −0.673919 | − | 1.16726i | −0.976783 | − | 0.214229i | \(-0.931276\pi\) |
0.302864 | − | 0.953034i | \(-0.402057\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.97330 | + | 4.02603i | 0.0606374 | + | 0.0350090i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 204.695 | + | 118.181i | 1.72013 | + | 0.993116i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −46.7124 | − | 80.9082i | −0.386053 | − | 0.668663i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 99.4176 | 0.795341 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 147.428i | − | 1.16085i | −0.814314 | − | 0.580425i | \(-0.802886\pi\) | ||
0.814314 | − | 0.580425i | \(-0.197114\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 112.889 | − | 65.1766i | 0.861750 | − | 0.497532i | −0.00284803 | − | 0.999996i | \(-0.500907\pi\) |
0.864598 | + | 0.502464i | \(0.167573\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −79.9782 | + | 138.526i | −0.601340 | + | 1.04155i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −49.9179 | + | 86.4604i | −0.364364 | + | 0.631098i | −0.988674 | − | 0.150079i | \(-0.952047\pi\) |
0.624310 | + | 0.781177i | \(0.285380\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 82.7828 | − | 47.7947i | 0.595560 | − | 0.343847i | −0.171733 | − | 0.985144i | \(-0.554937\pi\) |
0.767293 | + | 0.641297i | \(0.221603\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 77.4857i | 0.541858i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −54.3218 | −0.374633 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 34.3382 | + | 59.4755i | 0.230458 | + | 0.399164i | 0.957943 | − | 0.286959i | \(-0.0926443\pi\) |
−0.727485 | + | 0.686123i | \(0.759311\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 91.2633 | + | 52.6909i | 0.604393 | + | 0.348946i | 0.770768 | − | 0.637116i | \(-0.219873\pi\) |
−0.166375 | + | 0.986063i | \(0.553206\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 72.5894 | + | 41.9095i | 0.468319 | + | 0.270384i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 107.502 | + | 186.200i | 0.684729 | + | 1.18598i | 0.973522 | + | 0.228593i | \(0.0734125\pi\) |
−0.288794 | + | 0.957391i | \(0.593254\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −30.5657 | −0.189849 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 33.7439i | − | 0.207018i | −0.994629 | − | 0.103509i | \(-0.966993\pi\) | ||
0.994629 | − | 0.103509i | \(-0.0330071\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 131.565 | − | 75.9589i | 0.787812 | − | 0.454843i | −0.0513797 | − | 0.998679i | \(-0.516362\pi\) |
0.839192 | + | 0.543836i | \(0.183029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −24.3663 | + | 42.2036i | −0.144179 | + | 0.249726i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −59.4003 | + | 102.884i | −0.343354 | + | 0.594707i | −0.985053 | − | 0.172249i | \(-0.944896\pi\) |
0.641699 | + | 0.766957i | \(0.278230\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −145.868 | + | 84.2170i | −0.833532 | + | 0.481240i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 218.189i | 1.21894i | 0.792811 | + | 0.609468i | \(0.208617\pi\) | ||||
−0.792811 | + | 0.609468i | \(0.791383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −184.078 | −1.01701 | −0.508503 | − | 0.861060i | \(-0.669801\pi\) | ||||
−0.508503 | + | 0.861060i | \(0.669801\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.64565 | + | 8.04650i | 0.0251116 | + | 0.0434946i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −128.603 | − | 74.2492i | −0.687719 | − | 0.397055i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −215.775 | − | 124.578i | −1.12971 | − | 0.652239i | −0.185849 | − | 0.982578i | \(-0.559503\pi\) |
−0.943862 | + | 0.330339i | \(0.892837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 125.086 | + | 216.656i | 0.648115 | + | 1.12257i | 0.983573 | + | 0.180513i | \(0.0577758\pi\) |
−0.335457 | + | 0.942055i | \(0.608891\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 255.674 | 1.29784 | 0.648919 | − | 0.760858i | \(-0.275221\pi\) | ||||
0.648919 | + | 0.760858i | \(0.275221\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 309.110i | − | 1.55332i | −0.629921 | − | 0.776659i | \(-0.716913\pi\) | ||
0.629921 | − | 0.776659i | \(-0.283087\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 178.580 | − | 103.103i | 0.879702 | − | 0.507896i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.8530 | + | 37.8505i | −0.106600 | + | 0.184636i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 50.2478 | − | 87.0317i | 0.240420 | − | 0.416420i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 341.158 | − | 196.968i | 1.61686 | − | 0.933497i | 0.629140 | − | 0.777292i | \(-0.283407\pi\) |
0.987725 | − | 0.156205i | \(-0.0499261\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 51.3311i | 0.238750i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −318.177 | −1.46626 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −208.638 | − | 361.372i | −0.944064 | − | 1.63517i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 89.4002 | + | 51.6152i | 0.400898 | + | 0.231458i | 0.686871 | − | 0.726779i | \(-0.258984\pi\) |
−0.285974 | + | 0.958238i | \(0.592317\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −122.210 | − | 70.5578i | −0.538369 | − | 0.310828i | 0.206049 | − | 0.978542i | \(-0.433939\pi\) |
−0.744418 | + | 0.667714i | \(0.767273\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −105.572 | − | 182.856i | −0.461012 | − | 0.798496i | 0.538000 | − | 0.842945i | \(-0.319180\pi\) |
−0.999012 | + | 0.0444490i | \(0.985847\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 280.109 | 1.20219 | 0.601093 | − | 0.799179i | \(-0.294732\pi\) | ||||
0.601093 | + | 0.799179i | \(0.294732\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 65.7328i | 0.279714i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 339.349 | − | 195.923i | 1.41987 | − | 0.819762i | 0.423583 | − | 0.905857i | \(-0.360772\pi\) |
0.996287 | + | 0.0860949i | \(0.0274388\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.6786 | + | 41.0125i | −0.0982514 | + | 0.170176i | −0.910961 | − | 0.412493i | \(-0.864658\pi\) |
0.812710 | + | 0.582669i | \(0.197992\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22.9654 | + | 39.7772i | −0.0937363 | + | 0.162356i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 244.557 | − | 141.195i | 0.990107 | − | 0.571639i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 389.416i | − | 1.55146i | −0.631065 | − | 0.775730i | \(-0.717382\pi\) | ||
0.631065 | − | 0.775730i | \(-0.282618\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.2035 | 0.0759030 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 32.5409 | + | 56.3625i | 0.126618 | + | 0.219310i | 0.922364 | − | 0.386321i | \(-0.126254\pi\) |
−0.795746 | + | 0.605631i | \(0.792921\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −30.5445 | − | 17.6349i | −0.117933 | − | 0.0680884i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 124.773 | + | 72.0378i | 0.474423 | + | 0.273908i | 0.718089 | − | 0.695951i | \(-0.245017\pi\) |
−0.243667 | + | 0.969859i | \(0.578350\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.3527 | − | 61.2327i | −0.133406 | − | 0.231067i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −72.4113 | −0.269187 | −0.134593 | − | 0.990901i | \(-0.542973\pi\) | ||||
−0.134593 | + | 0.990901i | \(0.542973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 35.4695i | 0.130884i | 0.997856 | + | 0.0654419i | \(0.0208457\pi\) | ||||
−0.997856 | + | 0.0654419i | \(0.979154\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 91.6443 | − | 52.9109i | 0.333252 | − | 0.192403i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 166.922 | − | 289.118i | 0.602607 | − | 1.04375i | −0.389818 | − | 0.920892i | \(-0.627462\pi\) |
0.992425 | − | 0.122854i | \(-0.0392047\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.5385 | − | 35.5737i | 0.0730906 | − | 0.126597i | −0.827164 | − | 0.561961i | \(-0.810047\pi\) |
0.900254 | + | 0.435364i | \(0.143380\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −218.583 | + | 126.199i | −0.772378 | + | 0.445933i | −0.833722 | − | 0.552184i | \(-0.813795\pi\) |
0.0613442 | + | 0.998117i | \(0.480461\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 165.908i | − | 0.578077i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 510.695 | 1.76711 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.3415 | + | 35.2325i | 0.0694248 | + | 0.120247i | 0.898648 | − | 0.438670i | \(-0.144550\pi\) |
−0.829223 | + | 0.558917i | \(0.811217\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.5302 | + | 10.1211i | 0.0594245 | + | 0.0343088i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 46.7317 | + | 26.9806i | 0.156293 | + | 0.0902361i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −97.4266 | − | 168.748i | −0.323677 | − | 0.560624i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 179.766 | 0.589396 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 136.830i | − | 0.445701i | −0.974853 | − | 0.222850i | \(-0.928464\pi\) | ||
0.974853 | − | 0.222850i | \(-0.0715361\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −371.260 | + | 214.347i | −1.19376 | + | 0.689219i | −0.959158 | − | 0.282871i | \(-0.908713\pi\) |
−0.234605 | + | 0.972091i | \(0.575380\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.98705 | − | 10.3699i | 0.0191280 | − | 0.0331306i | −0.856303 | − | 0.516474i | \(-0.827244\pi\) |
0.875431 | + | 0.483343i | \(0.160578\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.5266 | + | 40.7493i | −0.0742164 | + | 0.128547i | −0.900745 | − | 0.434348i | \(-0.856979\pi\) |
0.826529 | + | 0.562894i | \(0.190312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −112.196 | + | 64.7763i | −0.351711 | + | 0.203061i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 541.189i | 1.67551i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 297.356 | 0.914941 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −124.761 | − | 216.092i | −0.379213 | − | 0.656816i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −73.1501 | − | 42.2332i | −0.220997 | − | 0.127593i | 0.385415 | − | 0.922743i | \(-0.374058\pi\) |
−0.606412 | + | 0.795151i | \(0.707392\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.1086 | + | 8.72297i | 0.0451004 | + | 0.0260387i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −252.558 | − | 437.443i | −0.749430 | − | 1.29805i | −0.948096 | − | 0.317983i | \(-0.896994\pi\) |
0.198667 | − | 0.980067i | \(-0.436339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 199.901 | 0.586219 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 235.200i | 0.685714i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −424.751 | + | 245.230i | −1.22407 | + | 0.706715i | −0.965782 | − | 0.259354i | \(-0.916490\pi\) |
−0.258284 | + | 0.966069i | \(0.583157\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −186.972 | + | 323.845i | −0.535736 | + | 0.927923i | 0.463391 | + | 0.886154i | \(0.346633\pi\) |
−0.999127 | + | 0.0417686i | \(0.986701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −297.026 | + | 514.465i | −0.841434 | + | 1.45741i | 0.0472483 | + | 0.998883i | \(0.484955\pi\) |
−0.888682 | + | 0.458523i | \(0.848379\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 119.996 | − | 69.2796i | 0.338016 | − | 0.195154i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 410.893i | 1.14455i | 0.820062 | + | 0.572274i | \(0.193939\pi\) | ||||
−0.820062 | + | 0.572274i | \(0.806061\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.24690 | −0.0145343 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.6848 | + | 63.5400i | 0.100506 | + | 0.174082i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −466.176 | − | 269.147i | −1.27023 | − | 0.733370i | −0.295203 | − | 0.955435i | \(-0.595387\pi\) |
−0.975032 | + | 0.222064i | \(0.928721\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 232.440 | + | 134.199i | 0.626522 | + | 0.361722i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 74.9606 | + | 129.836i | 0.200967 | + | 0.348085i | 0.948840 | − | 0.315757i | \(-0.102258\pi\) |
−0.747873 | + | 0.663841i | \(0.768925\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −364.039 | −0.965621 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 184.361i | 0.486442i | 0.969971 | + | 0.243221i | \(0.0782040\pi\) | ||||
−0.969971 | + | 0.243221i | \(0.921796\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −180.514 | + | 104.220i | −0.471315 | + | 0.272114i | −0.716790 | − | 0.697289i | \(-0.754389\pi\) |
0.245475 | + | 0.969403i | \(0.421056\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 48.3206 | − | 83.6937i | 0.125508 | − | 0.217386i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −150.914 | + | 261.390i | −0.387953 | + | 0.671954i | −0.992174 | − | 0.124863i | \(-0.960151\pi\) |
0.604221 | + | 0.796816i | \(0.293484\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −89.5597 | + | 51.7073i | −0.229053 | + | 0.132244i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 136.565i | − | 0.345734i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 246.672 | 0.621341 | 0.310670 | − | 0.950518i | \(-0.399447\pi\) | ||||
0.310670 | + | 0.950518i | \(0.399447\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −377.516 | − | 653.877i | −0.941437 | − | 1.63062i | −0.762734 | − | 0.646713i | \(-0.776143\pi\) |
−0.178703 | − | 0.983903i | \(-0.557190\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 486.460 | + | 280.858i | 1.20710 | + | 0.696917i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.1902 | + | 11.0794i | 0.0471503 | + | 0.0272222i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 130.730 | + | 226.432i | 0.319634 | + | 0.553622i | 0.980412 | − | 0.196959i | \(-0.0631067\pi\) |
−0.660778 | + | 0.750582i | \(0.729773\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −76.8394 | −0.186052 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 262.018i | 0.631369i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 340.246 | − | 196.441i | 0.812043 | − | 0.468833i | −0.0356217 | − | 0.999365i | \(-0.511341\pi\) |
0.847665 | + | 0.530532i | \(0.178008\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −102.451 | + | 177.450i | −0.243351 | + | 0.421496i | −0.961667 | − | 0.274221i | \(-0.911580\pi\) |
0.718316 | + | 0.695717i | \(0.244913\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −284.936 | + | 493.524i | −0.670438 | + | 1.16123i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −590.968 | + | 341.196i | −1.38400 | + | 0.799053i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 462.725i | − | 1.07361i | −0.843707 | − | 0.536803i | \(-0.819632\pi\) | ||
0.843707 | − | 0.536803i | \(-0.180368\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 190.574 | 0.440126 | 0.220063 | − | 0.975486i | \(-0.429374\pi\) | ||||
0.220063 | + | 0.975486i | \(0.429374\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −34.9926 | − | 60.6090i | −0.0800747 | − | 0.138693i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 379.279 | + | 218.977i | 0.863962 | + | 0.498809i | 0.865337 | − | 0.501190i | \(-0.167104\pi\) |
−0.00137479 | + | 0.999999i | \(0.500438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −721.993 | − | 416.843i | −1.62978 | − | 0.940954i | −0.984157 | − | 0.177297i | \(-0.943265\pi\) |
−0.645623 | − | 0.763657i | \(-0.723402\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 118.196 | + | 204.722i | 0.265610 | + | 0.460050i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 480.789 | 1.07080 | 0.535399 | − | 0.844599i | \(-0.320161\pi\) | ||||
0.535399 | + | 0.844599i | \(0.320161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 104.235i | 0.231119i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 235.177 | − | 135.779i | 0.516872 | − | 0.298416i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 109.313 | − | 189.336i | 0.239197 | − | 0.414302i | −0.721287 | − | 0.692636i | \(-0.756449\pi\) |
0.960484 | + | 0.278334i | \(0.0897824\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −358.474 | + | 620.894i | −0.777600 | + | 1.34684i | 0.155722 | + | 0.987801i | \(0.450230\pi\) |
−0.933322 | + | 0.359042i | \(0.883104\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.6250 | + | 15.3719i | −0.0575053 | + | 0.0332007i | −0.528477 | − | 0.848948i | \(-0.677237\pi\) |
0.470972 | + | 0.882148i | \(0.343903\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 458.639i | − | 0.982096i | −0.871133 | − | 0.491048i | \(-0.836614\pi\) | ||
0.871133 | − | 0.491048i | \(-0.163386\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −66.2249 | −0.141204 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 61.2101 | + | 106.019i | 0.129408 | + | 0.224142i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −333.989 | − | 192.829i | −0.703135 | − | 0.405955i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −570.477 | − | 329.365i | −1.19098 | − | 0.687610i | −0.232448 | − | 0.972609i | \(-0.574674\pi\) |
−0.958528 | + | 0.284999i | \(0.908007\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.1329 | + | 53.9238i | 0.0647254 | + | 0.112108i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.86593 | 0.0162184 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 715.589i | 1.46938i | 0.678402 | + | 0.734691i | \(0.262673\pi\) | ||||
−0.678402 | + | 0.734691i | \(0.737327\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −574.179 | + | 331.502i | −1.16941 | + | 0.675157i | −0.953540 | − | 0.301266i | \(-0.902591\pi\) |
−0.215866 | + | 0.976423i | \(0.569258\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 348.834 | − | 604.198i | 0.707574 | − | 1.22555i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −262.986 | + | 455.505i | −0.529147 | + | 0.916509i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −458.706 | + | 264.834i | −0.919251 | + | 0.530730i | −0.883396 | − | 0.468627i | \(-0.844749\pi\) |
−0.0358546 | + | 0.999357i | \(0.511415\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 68.3537i | 0.135892i | 0.997689 | + | 0.0679460i | \(0.0216446\pi\) | ||||
−0.997689 | + | 0.0679460i | \(0.978355\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.2342 | 0.0658103 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −400.473 | − | 693.640i | −0.786784 | − | 1.36275i | −0.927927 | − | 0.372761i | \(-0.878411\pi\) |
0.141143 | − | 0.989989i | \(-0.454922\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −241.198 | − | 139.256i | −0.472012 | − | 0.272516i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 248.396 | + | 143.412i | 0.482323 | + | 0.278469i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 78.3834 | + | 135.764i | 0.151612 | + | 0.262600i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 208.227 | 0.399668 | 0.199834 | − | 0.979830i | \(-0.435960\pi\) | ||||
0.199834 | + | 0.979830i | \(0.435960\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 30.5350i | − | 0.0583843i | −0.999574 | − | 0.0291921i | \(-0.990707\pi\) | ||
0.999574 | − | 0.0291921i | \(-0.00929347\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −932.283 | + | 538.254i | −1.76904 | + | 1.02135i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −257.813 | + | 446.546i | −0.487360 | + | 0.844132i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −146.448 | + | 253.656i | −0.274762 | + | 0.475903i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 97.7710 | − | 56.4481i | 0.182749 | − | 0.105510i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 109.541i | 0.203230i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −526.091 | −0.972442 | −0.486221 | − | 0.873836i | \(-0.661625\pi\) | ||||
−0.486221 | + | 0.873836i | \(0.661625\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.0446 | + | 48.5747i | 0.0514580 | + | 0.0891279i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 823.276 | + | 475.318i | 1.50507 | + | 0.868955i | 0.999983 | + | 0.00588962i | \(0.00187474\pi\) |
0.505092 | + | 0.863066i | \(0.331459\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 408.888 | + | 236.071i | 0.742083 | + | 0.428442i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 259.201 | + | 448.949i | 0.468717 | + | 0.811842i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 978.257 | 1.75630 | 0.878148 | − | 0.478390i | \(-0.158779\pi\) | ||||
0.878148 | + | 0.478390i | \(0.158779\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 343.997i | 0.615379i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −925.131 | + | 534.125i | −1.64322 | + | 0.948712i | −0.663538 | + | 0.748143i | \(0.730946\pi\) |
−0.979680 | + | 0.200569i | \(0.935721\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 167.677 | − | 290.426i | 0.296774 | − | 0.514028i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 481.775 | − | 834.459i | 0.846705 | − | 1.46654i | −0.0374271 | − | 0.999299i | \(-0.511916\pi\) |
0.884132 | − | 0.467237i | \(-0.154750\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −243.132 | + | 140.372i | −0.425800 | + | 0.245836i | −0.697556 | − | 0.716531i | \(-0.745729\pi\) |
0.271756 | + | 0.962366i | \(0.412396\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 73.6944i | − | 0.128164i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −552.228 | −0.957068 | −0.478534 | − | 0.878069i | \(-0.658832\pi\) | ||||
−0.478534 | + | 0.878069i | \(0.658832\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −497.311 | − | 861.367i | −0.855956 | − | 1.48256i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −146.034 | − | 84.3130i | −0.250488 | − | 0.144619i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −141.476 | − | 81.6811i | −0.241015 | − | 0.139150i | 0.374628 | − | 0.927175i | \(-0.377770\pi\) |
−0.615643 | + | 0.788025i | \(0.711104\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −364.260 | − | 630.917i | −0.618438 | − | 1.07117i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 818.460 | 1.38020 | 0.690101 | − | 0.723713i | \(-0.257566\pi\) | ||||
0.690101 | + | 0.723713i | \(0.257566\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 520.433i | 0.874677i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −398.849 | + | 230.275i | −0.665857 | + | 0.384433i | −0.794505 | − | 0.607257i | \(-0.792270\pi\) |
0.128648 | + | 0.991690i | \(0.458936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 162.324 | − | 281.153i | 0.270090 | − | 0.467809i | −0.698795 | − | 0.715322i | \(-0.746280\pi\) |
0.968885 | + | 0.247513i | \(0.0796132\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 102.854 | − | 178.148i | 0.170006 | − | 0.294459i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −764.054 | + | 441.127i | −1.25874 | + | 0.726733i | −0.972829 | − | 0.231524i | \(-0.925629\pi\) |
−0.285909 | + | 0.958257i | \(0.592295\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 440.510i | 0.720966i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.4869 | −0.0317895 | −0.0158947 | − | 0.999874i | \(-0.505060\pi\) | ||||
−0.0158947 | + | 0.999874i | \(0.505060\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 48.3314 | + | 83.7124i | 0.0783329 | + | 0.135677i | 0.902531 | − | 0.430625i | \(-0.141707\pi\) |
−0.824198 | + | 0.566302i | \(0.808374\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −363.937 | − | 210.119i | −0.587944 | − | 0.339449i | 0.176340 | − | 0.984329i | \(-0.443574\pi\) |
−0.764284 | + | 0.644880i | \(0.776907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −777.127 | − | 448.674i | −1.24739 | − | 0.720184i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −142.447 | − | 246.725i | −0.227915 | − | 0.394760i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −119.330 | −0.189714 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 483.230i | − | 0.765816i | −0.923787 | − | 0.382908i | \(-0.874923\pi\) | ||
0.923787 | − | 0.382908i | \(-0.125077\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 281.124 | − | 162.307i | 0.442715 | − | 0.255602i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −153.903 | + | 266.568i | −0.241606 | + | 0.418475i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.2967 | − | 78.4562i | 0.0706657 | − | 0.122397i | −0.828528 | − | 0.559948i | \(-0.810821\pi\) |
0.899193 | + | 0.437552i | \(0.144154\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 453.773 | − | 261.986i | 0.705713 | − | 0.407444i | −0.103759 | − | 0.994602i | \(-0.533087\pi\) |
0.809472 | + | 0.587159i | \(0.199754\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 31.3018i | − | 0.0483799i | −0.999707 | − | 0.0241900i | \(-0.992299\pi\) | ||
0.999707 | − | 0.0241900i | \(-0.00770066\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.2758 | 0.0743848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 445.115 | + | 770.961i | 0.681646 | + | 1.18065i | 0.974478 | + | 0.224481i | \(0.0720688\pi\) |
−0.292833 | + | 0.956164i | \(0.594598\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 248.565 | + | 143.509i | 0.379489 | + | 0.219098i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.1783 | − | 23.7743i | −0.0624860 | − | 0.0360763i | 0.468432 | − | 0.883500i | \(-0.344819\pi\) |
−0.530918 | + | 0.847423i | \(0.678153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.8421 | + | 43.0278i | 0.0375826 | + | 0.0650950i | 0.884205 | − | 0.467099i | \(-0.154701\pi\) |
−0.846622 | + | 0.532194i | \(0.821368\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −352.200 | −0.529624 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 90.2207i | 0.135263i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 371.287 | − | 214.362i | 0.553333 | − | 0.319467i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.4365 | + | 28.4688i | −0.0244227 | + | 0.0423013i | −0.877978 | − | 0.478700i | \(-0.841108\pi\) |
0.853556 | + | 0.521002i | \(0.174441\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 457.417 | − | 792.269i | 0.675653 | − | 1.17026i | −0.300625 | − | 0.953742i | \(-0.597195\pi\) |
0.976278 | − | 0.216522i | \(-0.0694714\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.8587 | + | 14.9296i | −0.0380836 | + | 0.0219876i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 870.646i | − | 1.27474i | −0.770559 | − | 0.637369i | \(-0.780023\pi\) | ||
0.770559 | − | 0.637369i | \(-0.219977\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −219.824 | −0.320910 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −236.917 | − | 410.352i | −0.343856 | − | 0.595577i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −800.188 | − | 461.988i | −1.15801 | − | 0.668580i | −0.207187 | − | 0.978301i | \(-0.566431\pi\) |
−0.950827 | + | 0.309722i | \(0.899764\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 182.275 | + | 105.237i | 0.262267 | + | 0.151420i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −280.663 | − | 486.123i | −0.402673 | − | 0.697450i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1191.44 | 1.69963 | 0.849815 | − | 0.527082i | \(-0.176714\pi\) | ||||
0.849815 | + | 0.527082i | \(0.176714\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 80.7561i | − | 0.114874i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −109.255 | + | 63.0786i | −0.154534 | + | 0.0892201i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −655.954 | + | 1136.15i | −0.925182 | + | 1.60246i | −0.133914 | + | 0.990993i | \(0.542754\pi\) |
−0.791268 | + | 0.611469i | \(0.790579\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 69.6056 | − | 120.560i | 0.0976236 | − | 0.169089i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −147.754 | + | 85.3059i | −0.206649 | + | 0.119309i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 245.763i | − | 0.341813i | −0.985287 | − | 0.170906i | \(-0.945330\pi\) | ||
0.985287 | − | 0.170906i | \(-0.0546695\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1088.78 | −1.51010 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 248.583 | + | 430.559i | 0.342873 | + | 0.593874i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1041.96 | + | 601.573i | 1.43323 | + | 0.827473i | 0.997365 | − | 0.0725411i | \(-0.0231108\pi\) |
0.435860 | + | 0.900014i | \(0.356444\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −570.934 | − | 329.629i | −0.781032 | − | 0.450929i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 510.693 | + | 884.546i | 0.696716 | + | 1.20675i | 0.969599 | + | 0.244700i | \(0.0786896\pi\) |
−0.272883 | + | 0.962047i | \(0.587977\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 41.6070 | 0.0564546 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 259.300i | 0.350879i | 0.984490 | + | 0.175439i | \(0.0561346\pi\) | ||||
−0.984490 | + | 0.175439i | \(0.943865\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −100.270 | + | 57.8907i | −0.134953 | + | 0.0779149i | −0.565956 | − | 0.824435i | \(-0.691493\pi\) |
0.431004 | + | 0.902350i | \(0.358160\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −75.6076 | + | 130.956i | −0.101487 | + | 0.175780i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −214.277 | + | 371.139i | −0.286084 | + | 0.495513i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −543.581 | + | 313.837i | −0.723809 | + | 0.417891i | −0.816153 | − | 0.577836i | \(-0.803897\pi\) |
0.0923438 | + | 0.995727i | \(0.470564\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 232.035i | 0.307331i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.5546 | −0.0654618 | −0.0327309 | − | 0.999464i | \(-0.510420\pi\) | ||||
−0.0327309 | + | 0.999464i | \(0.510420\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.0738 | + | 22.6446i | 0.0171798 | + | 0.0297563i | 0.874488 | − | 0.485048i | \(-0.161198\pi\) |
−0.857308 | + | 0.514804i | \(0.827865\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −184.390 | − | 106.458i | −0.241664 | − | 0.139525i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 117.479 | + | 67.8267i | 0.153167 | + | 0.0884312i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 93.5875 | + | 162.098i | 0.121700 | + | 0.210791i | 0.920438 | − | 0.390888i | \(-0.127832\pi\) |
−0.798738 | + | 0.601679i | \(0.794499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −877.069 | −1.13463 | −0.567315 | − | 0.823501i | \(-0.692018\pi\) | ||||
−0.567315 | + | 0.823501i | \(0.692018\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 767.131i | − | 0.989847i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 328.981 | − | 189.937i | 0.422312 | − | 0.243822i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 165.226 | − | 286.179i | 0.211557 | − | 0.366427i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −236.704 | + | 409.984i | −0.301534 | + | 0.522272i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 577.106 | − | 333.192i | 0.733298 | − | 0.423370i | −0.0863293 | − | 0.996267i | \(-0.527514\pi\) |
0.819628 | + | 0.572897i | \(0.194180\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1273.01i | 1.60936i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1204.70 | 1.51917 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 90.8816 | + | 157.412i | 0.114030 | + | 0.197505i | 0.917391 | − | 0.397986i | \(-0.130291\pi\) |
−0.803362 | + | 0.595491i | \(0.796957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −731.118 | − | 422.111i | −0.915041 | − | 0.528299i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 151.537 | + | 87.4900i | 0.188714 | + | 0.108954i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −33.6505 | − | 58.2844i | −0.0418019 | − | 0.0724030i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −114.921 | −0.142053 | −0.0710266 | − | 0.997474i | \(-0.522628\pi\) | ||||
−0.0710266 | + | 0.997474i | \(0.522628\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1378.48i | 1.69973i | 0.526997 | + | 0.849867i | \(0.323318\pi\) | ||||
−0.526997 | + | 0.849867i | \(0.676682\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 64.3449 | − | 37.1496i | 0.0789508 | − | 0.0455823i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 223.075 | − | 386.377i | 0.273041 | − | 0.472921i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −160.807 | + | 278.526i | −0.195867 | + | 0.339252i | −0.947184 | − | 0.320689i | \(-0.896085\pi\) |
0.751317 | + | 0.659941i | \(0.229419\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 56.6805 | − | 32.7245i | 0.0688706 | − | 0.0397625i | −0.465169 | − | 0.885222i | \(-0.654007\pi\) |
0.534040 | + | 0.845459i | \(0.320673\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 778.406i | 0.941240i | 0.882336 | + | 0.470620i | \(0.155970\pi\) | ||||
−0.882336 | + | 0.470620i | \(0.844030\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 81.3426 | 0.0981214 | 0.0490607 | − | 0.998796i | \(-0.484377\pi\) | ||||
0.0490607 | + | 0.998796i | \(0.484377\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −294.950 | − | 510.869i | −0.354082 | − | 0.613288i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 289.686 | + | 167.250i | 0.346929 | + | 0.200299i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −553.733 | − | 319.698i | −0.659992 | − | 0.381046i | 0.132282 | − | 0.991212i | \(-0.457769\pi\) |
−0.792274 | + | 0.610166i | \(0.791103\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 116.171 | + | 201.214i | 0.138135 | + | 0.239256i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −107.302 | −0.126984 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 780.866i | 0.921920i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.3641 | − | 7.71575i | 0.0157040 | − | 0.00906668i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.8069 | − | 67.2155i | 0.0454946 | − | 0.0787989i | −0.842381 | − | 0.538882i | \(-0.818847\pi\) |
0.887876 | + | 0.460083i | \(0.152180\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −436.010 | + | 755.192i | −0.508763 | + | 0.881204i | 0.491185 | + | 0.871055i | \(0.336564\pi\) |
−0.999948 | + | 0.0101489i | \(0.996769\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −136.909 | + | 79.0444i | −0.159382 | + | 0.0920191i | −0.577570 | − | 0.816342i | \(-0.695999\pi\) |
0.418188 | + | 0.908361i | \(0.362665\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 685.963i | − | 0.794859i | −0.917633 | − | 0.397429i | \(-0.869902\pi\) | ||
0.917633 | − | 0.397429i | \(-0.130098\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −261.581 | −0.302406 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −162.848 | − | 282.060i | −0.187396 | − | 0.324580i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 101.251 | + | 58.4573i | 0.116247 | + | 0.0671151i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −719.629 | − | 415.478i | −0.822433 | − | 0.474832i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −458.905 | − | 794.847i | −0.523267 | − | 0.906325i | −0.999633 | − | 0.0270780i | \(-0.991380\pi\) |
0.476366 | − | 0.879247i | \(-0.341954\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 657.430 | 0.746231 | 0.373116 | − | 0.927785i | \(-0.378289\pi\) | ||||
0.373116 | + | 0.927785i | \(0.378289\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 618.879i | − | 0.700882i | −0.936585 | − | 0.350441i | \(-0.886032\pi\) | ||
0.936585 | − | 0.350441i | \(-0.113968\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 110.844 | − | 63.9959i | 0.124965 | − | 0.0721487i | −0.436214 | − | 0.899843i | \(-0.643681\pi\) |
0.561180 | + | 0.827694i | \(0.310348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −616.119 | + | 1067.15i | −0.693047 | + | 1.20039i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 285.661 | − | 494.780i | 0.319890 | − | 0.554065i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −416.056 | + | 240.210i | −0.464867 | + | 0.268391i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 939.164i | 1.04468i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 908.086 | 1.00786 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −202.656 | − | 351.011i | −0.223930 | − | 0.387858i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.7946 | + | 7.96431i | 0.0152090 | + | 0.00878094i | 0.507585 | − | 0.861602i | \(-0.330538\pi\) |
−0.492376 | + | 0.870382i | \(0.663872\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.9255 | − | 25.3604i | −0.0482168 | − | 0.0278380i | 0.475698 | − | 0.879609i | \(-0.342196\pi\) |
−0.523915 | + | 0.851771i | \(0.675529\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 312.445 | + | 541.170i | 0.342218 | + | 0.592738i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1089.52 | −1.18814 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1065.04i | 1.15892i | 0.815002 | + | 0.579458i | \(0.196736\pi\) | ||||
−0.815002 | + | 0.579458i | \(0.803264\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 804.156 | − | 464.279i | 0.871241 | − | 0.503011i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.5181 | − | 73.6434i | 0.0459655 | − | 0.0796145i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −171.699 | + | 297.392i | −0.184822 | + | 0.320121i | −0.943516 | − | 0.331326i | \(-0.892504\pi\) |
0.758695 | + | 0.651446i | \(0.225837\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 345.727 | − | 199.606i | 0.371351 | − | 0.214399i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 326.971i | − | 0.349702i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −267.742 | −0.285744 | −0.142872 | − | 0.989741i | \(-0.545634\pi\) | ||||
−0.142872 | + | 0.989741i | \(0.545634\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −610.126 | − | 1056.77i | −0.648380 | − | 1.12303i | −0.983510 | − | 0.180855i | \(-0.942113\pi\) |
0.335130 | − | 0.942172i | \(-0.391220\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 62.8642 | + | 36.2946i | 0.0666640 | + | 0.0384885i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1395.84 | + | 805.888i | 1.47396 | + | 0.850991i | 0.999570 | − | 0.0293240i | \(-0.00933547\pi\) |
0.474390 | + | 0.880315i | \(0.342669\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 245.845 | + | 425.815i | 0.259056 | + | 0.448699i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −242.459 | −0.254416 | −0.127208 | − | 0.991876i | \(-0.540602\pi\) | ||||
−0.127208 | + | 0.991876i | \(0.540602\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 548.603i | − | 0.574453i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 722.656 | − | 417.226i | 0.753552 | − | 0.435063i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 244.068 | − | 422.739i | 0.253973 | − | 0.439895i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −275.421 | + | 477.043i | −0.285411 | + | 0.494346i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1543.81 | − | 891.320i | 1.59650 | − | 0.921737i | 0.604340 | − | 0.796726i | \(-0.293437\pi\) |
0.992155 | − | 0.125011i | \(-0.0398966\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 645.136i | − | 0.664404i | −0.943208 | − | 0.332202i | \(-0.892208\pi\) | ||
0.943208 | − | 0.332202i | \(-0.107792\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −798.958 | −0.821129 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 689.779 | + | 1194.73i | 0.706017 | + | 1.22286i | 0.966323 | + | 0.257331i | \(0.0828431\pi\) |
−0.260306 | + | 0.965526i | \(0.583824\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 488.244 | + | 281.888i | 0.498717 | + | 0.287935i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 639.804 | + | 369.391i | 0.650869 | + | 0.375779i | 0.788789 | − | 0.614664i | \(-0.210708\pi\) |
−0.137920 | + | 0.990443i | \(0.544042\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 281.478 | + | 487.534i | 0.285764 | + | 0.494959i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 85.2536 | 0.0862018 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1533.69i | − | 1.54762i | −0.633416 | − | 0.773811i | \(-0.718348\pi\) | ||
0.633416 | − | 0.773811i | \(-0.281652\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 589.430 | − | 340.307i | 0.592391 | − | 0.342017i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 871.274 | − | 1509.09i | 0.873896 | − | 1.51363i | 0.0159621 | − | 0.999873i | \(-0.494919\pi\) |
0.857934 | − | 0.513760i | \(-0.171748\pi\) | |||||||
\(998\) | 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 | 1728.3.o.g.127.3 | 16 | ||
3.2 | odd | 2 | 576.3.o.g.511.5 | 16 | |||
4.3 | odd | 2 | inner | 1728.3.o.g.127.4 | 16 | ||
8.3 | odd | 2 | 108.3.f.c.19.7 | 16 | |||
8.5 | even | 2 | 108.3.f.c.19.1 | 16 | |||
9.4 | even | 3 | inner | 1728.3.o.g.1279.4 | 16 | ||
9.5 | odd | 6 | 576.3.o.g.319.4 | 16 | |||
12.11 | even | 2 | 576.3.o.g.511.4 | 16 | |||
24.5 | odd | 2 | 36.3.f.c.7.8 | yes | 16 | ||
24.11 | even | 2 | 36.3.f.c.7.2 | ✓ | 16 | ||
36.23 | even | 6 | 576.3.o.g.319.5 | 16 | |||
36.31 | odd | 6 | inner | 1728.3.o.g.1279.3 | 16 | ||
72.5 | odd | 6 | 36.3.f.c.31.2 | yes | 16 | ||
72.11 | even | 6 | 324.3.d.i.163.4 | 8 | |||
72.13 | even | 6 | 108.3.f.c.91.7 | 16 | |||
72.29 | odd | 6 | 324.3.d.i.163.3 | 8 | |||
72.43 | odd | 6 | 324.3.d.g.163.5 | 8 | |||
72.59 | even | 6 | 36.3.f.c.31.8 | yes | 16 | ||
72.61 | even | 6 | 324.3.d.g.163.6 | 8 | |||
72.67 | odd | 6 | 108.3.f.c.91.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.2 | ✓ | 16 | 24.11 | even | 2 | ||
36.3.f.c.7.8 | yes | 16 | 24.5 | odd | 2 | ||
36.3.f.c.31.2 | yes | 16 | 72.5 | odd | 6 | ||
36.3.f.c.31.8 | yes | 16 | 72.59 | even | 6 | ||
108.3.f.c.19.1 | 16 | 8.5 | even | 2 | |||
108.3.f.c.19.7 | 16 | 8.3 | odd | 2 | |||
108.3.f.c.91.1 | 16 | 72.67 | odd | 6 | |||
108.3.f.c.91.7 | 16 | 72.13 | even | 6 | |||
324.3.d.g.163.5 | 8 | 72.43 | odd | 6 | |||
324.3.d.g.163.6 | 8 | 72.61 | even | 6 | |||
324.3.d.i.163.3 | 8 | 72.29 | odd | 6 | |||
324.3.d.i.163.4 | 8 | 72.11 | even | 6 | |||
576.3.o.g.319.4 | 16 | 9.5 | odd | 6 | |||
576.3.o.g.319.5 | 16 | 36.23 | even | 6 | |||
576.3.o.g.511.4 | 16 | 12.11 | even | 2 | |||
576.3.o.g.511.5 | 16 | 3.2 | odd | 2 | |||
1728.3.o.g.127.3 | 16 | 1.1 | even | 1 | trivial | ||
1728.3.o.g.127.4 | 16 | 4.3 | odd | 2 | inner | ||
1728.3.o.g.1279.3 | 16 | 36.31 | odd | 6 | inner | ||
1728.3.o.g.1279.4 | 16 | 9.4 | even | 3 | inner |