Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(3583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.3583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.b (of order \(2\), degree \(1\), 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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.29960650073923649536.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} + 40x^{8} - 112x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | no (minimal twist has level 2016) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3583.10 | ||
Root | \(-1.38588 + 0.281691i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.3583 |
Dual form | 4032.2.b.r.3583.5 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.69614i | 0.758537i | 0.925287 | + | 0.379269i | \(0.123824\pi\) | ||||
−0.925287 | + | 0.379269i | \(0.876176\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.13578 | + | 1.56155i | −0.807249 | + | 0.590211i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.794156i | − | 0.239447i | −0.992807 | − | 0.119723i | \(-0.961799\pi\) | ||
0.992807 | − | 0.119723i | \(-0.0382008\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.87285i | − | 0.519436i | −0.965685 | − | 0.259718i | \(-0.916370\pi\) | ||
0.965685 | − | 0.259718i | \(-0.0836296\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.34475i | − | 1.05376i | −0.849940 | − | 0.526879i | \(-0.823362\pi\) | ||
0.849940 | − | 0.526879i | \(-0.176638\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.39871 | −0.550301 | −0.275150 | − | 0.961401i | \(-0.588728\pi\) | ||||
−0.275150 | + | 0.961401i | \(0.588728\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.62258i | 0.755361i | 0.925936 | + | 0.377680i | \(0.123278\pi\) | ||||
−0.925936 | + | 0.377680i | \(0.876722\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.12311 | 0.424621 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.41674 | −0.820168 | −0.410084 | − | 0.912048i | \(-0.634501\pi\) | ||||
−0.410084 | + | 0.912048i | \(0.634501\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.87285 | −0.336374 | −0.168187 | − | 0.985755i | \(-0.553791\pi\) | ||||
−0.168187 | + | 0.985755i | \(0.553791\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.64861 | − | 3.62258i | −0.447697 | − | 0.612328i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.12311 | 0.513435 | 0.256718 | − | 0.966486i | \(-0.417359\pi\) | ||||
0.256718 | + | 0.966486i | \(0.417359\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.34475i | − | 0.678537i | −0.940690 | − | 0.339268i | \(-0.889821\pi\) | ||
0.940690 | − | 0.339268i | \(-0.110179\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.876894i | − | 0.133725i | −0.997762 | − | 0.0668626i | \(-0.978701\pi\) | ||
0.997762 | − | 0.0668626i | \(-0.0212989\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.0818 | 1.76231 | 0.881155 | − | 0.472827i | \(-0.156766\pi\) | ||||
0.881155 | + | 0.472827i | \(0.156766\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.12311 | − | 6.67026i | 0.303301 | − | 0.952895i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.0736 | −1.38371 | −0.691857 | − | 0.722034i | \(-0.743207\pi\) | ||||
−0.691857 | + | 0.722034i | \(0.743207\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.34700 | 0.181629 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.78456 | −0.883275 | −0.441638 | − | 0.897194i | \(-0.645602\pi\) | ||||
−0.441638 | + | 0.897194i | \(0.645602\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.4677i | − | 1.46829i | −0.678995 | − | 0.734143i | \(-0.737584\pi\) | ||
0.678995 | − | 0.734143i | \(-0.262416\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.17662 | 0.394012 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.876894i | 0.107130i | 0.998564 | + | 0.0535648i | \(0.0170584\pi\) | ||||
−0.998564 | + | 0.0535648i | \(0.982942\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.21089i | 0.618419i | 0.950994 | + | 0.309210i | \(0.100064\pi\) | ||||
−0.950994 | + | 0.309210i | \(0.899936\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.74571i | − | 0.438402i | −0.975680 | − | 0.219201i | \(-0.929655\pi\) | ||
0.975680 | − | 0.219201i | \(-0.0703450\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.24012 | + | 1.69614i | 0.141324 | + | 0.193293i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.12311i | − | 0.351377i | −0.984446 | − | 0.175688i | \(-0.943785\pi\) | ||
0.984446 | − | 0.175688i | \(-0.0562151\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0818 | −1.32615 | −0.663074 | − | 0.748553i | \(-0.730749\pi\) | ||||
−0.663074 | + | 0.748553i | \(0.730749\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.36932 | 0.799315 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.73704i | − | 0.820124i | −0.912058 | − | 0.410062i | \(-0.865507\pi\) | ||
0.912058 | − | 0.410062i | \(-0.134493\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.92456 | + | 4.00000i | 0.306577 | + | 0.419314i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.06854i | − | 0.417424i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.3405i | − | 1.35453i | −0.735741 | − | 0.677263i | \(-0.763166\pi\) | ||
0.735741 | − | 0.677263i | \(-0.236834\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3857i | 1.03341i | 0.856163 | + | 0.516705i | \(0.172842\pi\) | ||||
−0.856163 | + | 0.516705i | \(0.827158\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.4677 | 1.12994 | 0.564972 | − | 0.825110i | \(-0.308887\pi\) | ||||
0.564972 | + | 0.825110i | \(0.308887\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13.6962i | − | 1.32406i | −0.749478 | − | 0.662030i | \(-0.769695\pi\) | ||
0.749478 | − | 0.662030i | \(-0.230305\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.24621 | 0.789844 | 0.394922 | − | 0.918715i | \(-0.370772\pi\) | ||||
0.394922 | + | 0.918715i | \(0.370772\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.65685 | 0.532152 | 0.266076 | − | 0.963952i | \(-0.414273\pi\) | ||||
0.266076 | + | 0.963952i | \(0.414273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.14441 | −0.572969 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.78456 | + | 9.27944i | 0.621940 | + | 0.850645i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3693 | 0.942665 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0818i | 1.08063i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.1231i | − | 0.987016i | −0.869741 | − | 0.493508i | \(-0.835714\pi\) | ||
0.869741 | − | 0.493508i | \(-0.164286\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.78456 | 0.592770 | 0.296385 | − | 0.955069i | \(-0.404219\pi\) | ||||
0.296385 | + | 0.955069i | \(0.404219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.12311 | − | 3.74571i | 0.444230 | − | 0.324794i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.1472 | 1.72129 | 0.860645 | − | 0.509205i | \(-0.170061\pi\) | ||||
0.860645 | + | 0.509205i | \(0.170061\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.0862 | 1.44924 | 0.724618 | − | 0.689151i | \(-0.242016\pi\) | ||||
0.724618 | + | 0.689151i | \(0.242016\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.48734 | −0.124377 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.49141i | − | 0.622128i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0736 | 0.825261 | 0.412630 | − | 0.910899i | \(-0.364610\pi\) | ||||
0.412630 | + | 0.910899i | \(0.364610\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1231i | 0.905185i | 0.891717 | + | 0.452593i | \(0.149501\pi\) | ||||
−0.891717 | + | 0.452593i | \(0.850499\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.17662i | − | 0.255152i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 18.9591i | − | 1.51310i | −0.653936 | − | 0.756550i | \(-0.726883\pi\) | ||
0.653936 | − | 0.756550i | \(-0.273117\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.65685 | − | 7.73704i | −0.445823 | − | 0.609764i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.12311i | − | 0.557925i | −0.960302 | − | 0.278962i | \(-0.910010\pi\) | ||
0.960302 | − | 0.278962i | \(-0.0899905\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.49242 | 0.730186 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.60109i | 0.273786i | 0.990586 | + | 0.136893i | \(0.0437116\pi\) | ||||
−0.990586 | + | 0.136893i | \(0.956288\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.53448 | + | 3.31534i | −0.342775 | + | 0.250616i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.1764i | 1.20908i | 0.796574 | + | 0.604541i | \(0.206643\pi\) | ||||
−0.796574 | + | 0.604541i | \(0.793357\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.87285i | − | 0.139208i | −0.997575 | − | 0.0696040i | \(-0.977826\pi\) | ||
0.997575 | − | 0.0696040i | \(-0.0221736\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.29723i | 0.389460i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.45041 | −0.252319 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.9363i | 1.08075i | 0.841424 | + | 0.540376i | \(0.181718\pi\) | ||||
−0.841424 | + | 0.540376i | \(0.818282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.3693 | 0.962344 | 0.481172 | − | 0.876626i | \(-0.340211\pi\) | ||||
0.481172 | + | 0.876626i | \(0.340211\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.41674 | −0.314680 | −0.157340 | − | 0.987545i | \(-0.550292\pi\) | ||||
−0.157340 | + | 0.987545i | \(0.550292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.06897 | 0.642882 | 0.321441 | − | 0.946930i | \(-0.395833\pi\) | ||||
0.321441 | + | 0.946930i | \(0.395833\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.43318 | − | 6.89697i | 0.662079 | − | 0.484072i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.36932 | 0.514695 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.90495i | 0.131768i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 21.3693i | − | 1.47112i | −0.677457 | − | 0.735562i | \(-0.736918\pi\) | ||
0.677457 | − | 0.735562i | \(-0.263082\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.48734 | 0.101436 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | − | 2.92456i | 0.271538 | − | 0.198532i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.13709 | −0.547360 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.8147 | −0.858134 | −0.429067 | − | 0.903273i | \(-0.641158\pi\) | ||||
−0.429067 | + | 0.903273i | \(0.641158\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.8664 | −1.25220 | −0.626102 | − | 0.779741i | \(-0.715351\pi\) | ||||
−0.626102 | + | 0.779741i | \(0.715351\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 18.9591i | − | 1.25285i | −0.779481 | − | 0.626426i | \(-0.784517\pi\) | ||
0.779481 | − | 0.626426i | \(-0.215483\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.9706 | −1.11178 | −0.555889 | − | 0.831256i | \(-0.687622\pi\) | ||||
−0.555889 | + | 0.831256i | \(0.687622\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.4924i | 1.33678i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.7012i | − | 1.27437i | −0.770712 | − | 0.637183i | \(-0.780099\pi\) | ||
0.770712 | − | 0.637183i | \(-0.219901\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.59482i | − | 0.618057i | −0.951053 | − | 0.309028i | \(-0.899996\pi\) | ||
0.951053 | − | 0.309028i | \(-0.100004\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.3137 | + | 3.60109i | 0.722806 | + | 0.230065i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.49242i | 0.285846i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.29723 | 0.334358 | 0.167179 | − | 0.985927i | \(-0.446534\pi\) | ||||
0.167179 | + | 0.985927i | \(0.446534\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.87689 | 0.180869 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.5216i | 0.905833i | 0.891553 | + | 0.452916i | \(0.149616\pi\) | ||||
−0.891553 | + | 0.452916i | \(0.850384\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.67026 | + | 4.87689i | −0.414470 | + | 0.303035i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 20.5931i | − | 1.26983i | −0.772583 | − | 0.634914i | \(-0.781036\pi\) | ||
0.772583 | − | 0.634914i | \(-0.218964\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 17.0862i | − | 1.04960i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 19.0752i | − | 1.16303i | −0.813535 | − | 0.581517i | \(-0.802460\pi\) | ||
0.813535 | − | 0.581517i | \(-0.197540\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.2134 | −0.924147 | −0.462074 | − | 0.886842i | \(-0.652894\pi\) | ||||
−0.462074 | + | 0.886842i | \(0.652894\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.68608i | − | 0.101674i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.36932 | 0.0822743 | 0.0411371 | − | 0.999154i | \(-0.486902\pi\) | ||||
0.0411371 | + | 0.999154i | \(0.486902\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.65685 | 0.337460 | 0.168730 | − | 0.985662i | \(-0.446033\pi\) | ||||
0.168730 | + | 0.985662i | \(0.446033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.14441 | 0.365247 | 0.182624 | − | 0.983183i | \(-0.441541\pi\) | ||||
0.182624 | + | 0.983183i | \(0.441541\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.78456 | + | 9.27944i | 0.400480 | + | 0.547748i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.87689 | −0.110406 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 25.8597i | − | 1.51074i | −0.655298 | − | 0.755371i | \(-0.727457\pi\) | ||
0.655298 | − | 0.755371i | \(-0.272543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 11.5076i | − | 0.669997i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.78456 | 0.392361 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.36932 | + | 1.87285i | 0.0789261 | + | 0.107949i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.4508 | 1.11375 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.2306 | −1.32584 | −0.662921 | − | 0.748689i | \(-0.730684\pi\) | ||||
−0.662921 | + | 0.748689i | \(0.730684\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.6509 | −1.45453 | −0.727265 | − | 0.686357i | \(-0.759209\pi\) | ||||
−0.727265 | + | 0.686357i | \(0.759209\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.5538 | 0.705093 | 0.352547 | − | 0.935794i | \(-0.385316\pi\) | ||||
0.352547 | + | 0.935794i | \(0.385316\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.50758i | 0.196387i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.4218i | 0.579884i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.97626i | − | 0.220563i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.8040 | + | 18.8664i | −1.42262 | + | 1.04014i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.6155i | 0.638447i | 0.947679 | + | 0.319224i | \(0.103422\pi\) | ||||
−0.947679 | + | 0.319224i | \(0.896578\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.48734 | −0.0812619 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.24621 | 0.449200 | 0.224600 | − | 0.974451i | \(-0.427892\pi\) | ||||
0.224600 | + | 0.974451i | \(0.427892\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.48734i | 0.0805438i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.88148 | + | 17.5616i | 0.317570 | + | 0.948235i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.8434i | 1.81681i | 0.418095 | + | 0.908403i | \(0.362698\pi\) | ||||
−0.418095 | + | 0.908403i | \(0.637302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.2134i | − | 0.814354i | −0.913349 | − | 0.407177i | \(-0.866513\pi\) | ||
0.913349 | − | 0.407177i | \(-0.133487\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 0.952473i | − | 0.0506950i | −0.999679 | − | 0.0253475i | \(-0.991931\pi\) | ||
0.999679 | − | 0.0253475i | \(-0.00806923\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.83841 | −0.469094 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.51450i | 0.238266i | 0.992878 | + | 0.119133i | \(0.0380115\pi\) | ||||
−0.992878 | + | 0.119133i | \(0.961988\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.2462 | −0.697169 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.35324 | 0.332544 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.6638 | −0.974242 | −0.487121 | − | 0.873334i | \(-0.661953\pi\) | ||||
−0.487121 | + | 0.873334i | \(0.661953\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.5150 | − | 15.7304i | 1.11700 | − | 0.816684i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.27190i | 0.426025i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.8769i | − | 0.866908i | −0.901176 | − | 0.433454i | \(-0.857295\pi\) | ||
0.901176 | − | 0.433454i | \(-0.142705\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.6762 | −1.15870 | −0.579351 | − | 0.815078i | \(-0.696694\pi\) | ||||
−0.579351 | + | 0.815078i | \(0.696694\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.87689 | + | 2.10341i | −0.146620 | + | 0.107200i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.2107 | −0.923318 | −0.461659 | − | 0.887057i | \(-0.652746\pi\) | ||||
−0.461659 | + | 0.887057i | \(0.652746\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.7392 | 0.795967 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.29723 | 0.266532 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.5539i | 1.43308i | 0.697546 | + | 0.716540i | \(0.254275\pi\) | ||||
−0.697546 | + | 0.716540i | \(0.745725\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.8141 | −1.88835 | −0.944174 | − | 0.329447i | \(-0.893138\pi\) | ||||
−0.944174 | + | 0.329447i | \(0.893138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.50758i | 0.174725i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.48023i | − | 0.122941i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 20.8319i | − | 1.03007i | −0.857168 | − | 0.515037i | \(-0.827778\pi\) | ||
0.857168 | − | 0.515037i | \(-0.172222\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.4903 | − | 10.5945i | 0.713023 | − | 0.521319i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 20.4924i | − | 1.00593i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.2454 | 1.77070 | 0.885351 | − | 0.464923i | \(-0.153918\pi\) | ||||
0.885351 | + | 0.464923i | \(0.153918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.12311 | −0.152211 | −0.0761054 | − | 0.997100i | \(-0.524249\pi\) | ||||
−0.0761054 | + | 0.997100i | \(0.524249\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 9.22437i | − | 0.447448i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.9074 | + | 24.4924i | 0.866599 | + | 1.18527i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 39.1520i | − | 1.88589i | −0.332954 | − | 0.942943i | \(-0.608045\pi\) | ||
0.332954 | − | 0.942943i | \(-0.391955\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.4268i | 1.46222i | 0.682261 | + | 0.731108i | \(0.260997\pi\) | ||||
−0.682261 | + | 0.731108i | \(0.739003\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 8.68951i | − | 0.415676i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.5604 | 0.790384 | 0.395192 | − | 0.918599i | \(-0.370678\pi\) | ||||
0.395192 | + | 0.918599i | \(0.370678\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 16.1764i | − | 0.768564i | −0.923216 | − | 0.384282i | \(-0.874449\pi\) | ||
0.923216 | − | 0.384282i | \(-0.125551\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.1231 | 0.622095 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.4903 | −0.683841 | −0.341920 | − | 0.939729i | \(-0.611077\pi\) | ||||
−0.341920 | + | 0.939729i | \(0.611077\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.45041 | −0.162474 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.78456 | + | 4.96046i | −0.318065 | + | 0.232550i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.75379 | 0.175595 | 0.0877974 | − | 0.996138i | \(-0.472017\pi\) | ||||
0.0877974 | + | 0.996138i | \(0.472017\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.48071i | 0.394986i | 0.980304 | + | 0.197493i | \(0.0632799\pi\) | ||||
−0.980304 | + | 0.197493i | \(0.936720\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 39.6155i | − | 1.84109i | −0.390637 | − | 0.920545i | \(-0.627745\pi\) | ||
0.390637 | − | 0.920545i | \(-0.372255\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.29723 | −0.245126 | −0.122563 | − | 0.992461i | \(-0.539111\pi\) | ||||
−0.122563 | + | 0.992461i | \(0.539111\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.36932 | − | 1.87285i | −0.0632292 | − | 0.0864803i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.696391 | −0.0320201 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.09271 | −0.233669 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.6762 | −1.03610 | −0.518052 | − | 0.855349i | \(-0.673343\pi\) | ||||
−0.518052 | + | 0.855349i | \(0.673343\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 5.84912i | − | 0.266697i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.6274 | 1.02746 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.6155i | 1.43264i | 0.697774 | + | 0.716318i | \(0.254174\pi\) | ||||
−0.697774 | + | 0.716318i | \(0.745826\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.2550i | 1.45565i | 0.685763 | + | 0.727825i | \(0.259469\pi\) | ||||
−0.685763 | + | 0.727825i | \(0.740531\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.1896i | 0.864258i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.13709 | − | 11.1293i | −0.364998 | − | 0.499218i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 25.8617i | − | 1.15773i | −0.815423 | − | 0.578865i | \(-0.803496\pi\) | ||
0.815423 | − | 0.578865i | \(-0.196504\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0818 | −0.538700 | −0.269350 | − | 0.963042i | \(-0.586809\pi\) | ||||
−0.269350 | + | 0.963042i | \(0.586809\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.6155 | −0.783881 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 44.7261i | − | 1.98245i | −0.132191 | − | 0.991224i | \(-0.542201\pi\) | ||
0.132191 | − | 0.991224i | \(-0.457799\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.84912 | + | 8.00000i | 0.258750 | + | 0.353899i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.4508i | 0.857104i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.59482i | − | 0.421980i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.1293i | 0.487584i | 0.969828 | + | 0.243792i | \(0.0783915\pi\) | ||||
−0.969828 | + | 0.243792i | \(0.921609\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.0216 | 1.75002 | 0.875011 | − | 0.484103i | \(-0.160854\pi\) | ||||
0.875011 | + | 0.484103i | \(0.160854\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.13709i | 0.354457i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.87689 | 0.429430 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.13709 | −0.352456 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.2306 | 1.00435 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.29723 | − | 1.68608i | −0.228168 | − | 0.0726244i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.6155 | −1.35926 | −0.679629 | − | 0.733556i | \(-0.737859\pi\) | ||||
−0.679629 | + | 0.733556i | \(0.737859\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.9867i | 0.599126i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 39.1231i | − | 1.67278i | −0.548132 | − | 0.836392i | \(-0.684661\pi\) | ||
0.548132 | − | 0.836392i | \(-0.315339\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.5945 | 0.451339 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.87689 | + | 6.67026i | 0.207387 | + | 0.283648i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.5345 | −1.75987 | −0.879936 | − | 0.475092i | \(-0.842415\pi\) | ||||
−0.879936 | + | 0.475092i | \(0.842415\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.64229 | −0.0694616 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.6762 | 0.955690 | 0.477845 | − | 0.878444i | \(-0.341418\pi\) | ||||
0.477845 | + | 0.878444i | \(0.341418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.59482i | 0.403657i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.4903 | −0.607466 | −0.303733 | − | 0.952757i | \(-0.598233\pi\) | ||||
−0.303733 | + | 0.952757i | \(0.598233\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.8769i | 1.04107i | 0.853842 | + | 0.520533i | \(0.174267\pi\) | ||||
−0.853842 | + | 0.520533i | \(0.825733\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.69113i | 0.320742i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.9182i | 1.57855i | 0.614037 | + | 0.789277i | \(0.289544\pi\) | ||||
−0.614037 | + | 0.789277i | \(0.710456\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.8040 | − | 18.8664i | 1.07053 | − | 0.782708i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.00000i | 0.331326i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.1636 | −0.997338 | −0.498669 | − | 0.866793i | \(-0.666178\pi\) | ||||
−0.498669 | + | 0.866793i | \(0.666178\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.49242 | 0.185107 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.3062i | 0.874939i | 0.899233 | + | 0.437470i | \(0.144125\pi\) | ||||
−0.899233 | + | 0.437470i | \(0.855875\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.7392 | + | 11.5076i | −0.645246 | + | 0.471765i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 41.4367i | − | 1.69306i | −0.532342 | − | 0.846529i | \(-0.678688\pi\) | ||
0.532342 | − | 0.846529i | \(-0.321312\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.3405i | 0.544171i | 0.962273 | + | 0.272086i | \(0.0877134\pi\) | ||||
−0.962273 | + | 0.272086i | \(0.912287\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.5878i | 0.715047i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.4957 | −1.60308 | −0.801541 | − | 0.597940i | \(-0.795986\pi\) | ||||
−0.801541 | + | 0.597940i | \(0.795986\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 22.6274i | − | 0.915407i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.2311 | −1.66531 | −0.832653 | − | 0.553795i | \(-0.813179\pi\) | ||||
−0.832653 | + | 0.553795i | \(0.813179\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.3137 | 0.455473 | 0.227736 | − | 0.973723i | \(-0.426868\pi\) | ||||
0.227736 | + | 0.973723i | \(0.426868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.7673 | 1.75916 | 0.879578 | − | 0.475755i | \(-0.157825\pi\) | ||||
0.879578 | + | 0.475755i | \(0.157825\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0818 | + | 16.5246i | 0.484047 | + | 0.662044i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.87689 | −0.395076 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 13.5691i | − | 0.541037i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14.6307i | − | 0.582438i | −0.956656 | − | 0.291219i | \(-0.905939\pi\) | ||
0.956656 | − | 0.291219i | \(-0.0940609\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.8664 | 0.748688 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.4924 | − | 3.97626i | −0.494968 | − | 0.157545i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.4609 | 1.24263 | 0.621315 | − | 0.783561i | \(-0.286599\pi\) | ||||
0.621315 | + | 0.783561i | \(0.286599\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.7909 | −0.662170 | −0.331085 | − | 0.943601i | \(-0.607415\pi\) | ||||
−0.331085 | + | 0.943601i | \(0.607415\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.1636 | 0.949968 | 0.474984 | − | 0.879994i | \(-0.342454\pi\) | ||||
0.474984 | + | 0.879994i | \(0.342454\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.38800i | 0.211497i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.7010 | 1.27969 | 0.639845 | − | 0.768504i | \(-0.278999\pi\) | ||||
0.639845 | + | 0.768504i | \(0.278999\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.5076i | 0.449638i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.794156i | 0.0309359i | 0.999880 | + | 0.0154680i | \(0.00492380\pi\) | ||||
−0.999880 | + | 0.0154680i | \(0.995076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.2134i | 0.591732i | 0.955229 | + | 0.295866i | \(0.0956082\pi\) | ||||
−0.955229 | + | 0.295866i | \(0.904392\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.35324 | + | 8.68951i | 0.246368 | + | 0.336965i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 16.0000i | − | 0.619522i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.10712 | −0.351576 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.6155 | −0.447746 | −0.223873 | − | 0.974618i | \(-0.571870\pi\) | ||||
−0.223873 | + | 0.974618i | \(0.571870\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.3471i | 1.05103i | 0.850783 | + | 0.525516i | \(0.176128\pi\) | ||||
−0.850783 | + | 0.525516i | \(0.823872\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.8319 | + | 28.4924i | 0.799456 | + | 1.09344i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.0784i | 1.11266i | 0.830963 | + | 0.556328i | \(0.187790\pi\) | ||||
−0.830963 | + | 0.556328i | \(0.812210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.1725i | 1.30566i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.8664i | 0.718751i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.3405 | −0.507498 | −0.253749 | − | 0.967270i | \(-0.581664\pi\) | ||||
−0.253749 | + | 0.967270i | \(0.581664\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.9807i | 1.09930i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.8769 | −0.715013 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.24012 | 0.0468385 | 0.0234193 | − | 0.999726i | \(-0.492545\pi\) | ||||
0.0234193 | + | 0.999726i | \(0.492545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.49141 | −0.282544 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.2177 | − | 22.1815i | −0.609931 | − | 0.834220i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.00000 | 0.225335 | 0.112667 | − | 0.993633i | \(-0.464061\pi\) | ||||
0.112667 | + | 0.993633i | \(0.464061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.78456i | − | 0.254084i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.52273i | − | 0.0943448i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.48734 | −0.0554683 | −0.0277341 | − | 0.999615i | \(-0.508829\pi\) | ||||
−0.0277341 | + | 0.999615i | \(0.508829\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.4924 | + | 17.9074i | −0.912145 | + | 0.666906i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.37720 | −0.348261 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.72197 | 0.286392 | 0.143196 | − | 0.989694i | \(-0.454262\pi\) | ||||
0.143196 | + | 0.989694i | \(0.454262\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.80989 | −0.140914 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.2134i | 0.561919i | 0.959720 | + | 0.280960i | \(0.0906527\pi\) | ||||
−0.959720 | + | 0.280960i | \(0.909347\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.696391 | 0.0256519 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.8769i | 0.620827i | 0.950602 | + | 0.310413i | \(0.100467\pi\) | ||||
−0.950602 | + | 0.310413i | \(0.899533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 33.4952i | − | 1.22882i | −0.788988 | − | 0.614409i | \(-0.789394\pi\) | ||
0.788988 | − | 0.614409i | \(-0.210606\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.0862i | 0.625991i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.3873 | + | 29.2520i | 0.781475 | + | 1.06885i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 25.3693i | − | 0.925740i | −0.886426 | − | 0.462870i | \(-0.846820\pi\) | ||
0.886426 | − | 0.462870i | \(-0.153180\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.8664 | −0.686617 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.9848 | −1.27155 | −0.635773 | − | 0.771876i | \(-0.719319\pi\) | ||||
−0.635773 | + | 0.771876i | \(0.719319\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 0.534864i | − | 0.0193888i | −0.999953 | − | 0.00969440i | \(-0.996914\pi\) | ||
0.999953 | − | 0.00969440i | \(-0.00308587\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.6121 | + | 12.8769i | −0.637600 | + | 0.466175i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.7065i | 0.458805i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.10341i | 0.0758510i | 0.999281 | + | 0.0379255i | \(0.0120750\pi\) | ||||
−0.999281 | + | 0.0379255i | \(0.987925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.7779i | 0.495558i | 0.968817 | + | 0.247779i | \(0.0797007\pi\) | ||||
−0.968817 | + | 0.247779i | \(0.920299\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.97626 | −0.142832 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.4218i | 0.373399i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.13826 | 0.148079 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.1573 | 1.14774 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.4096 | −1.61868 | −0.809338 | − | 0.587343i | \(-0.800174\pi\) | ||||
−0.809338 | + | 0.587343i | \(0.800174\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0818 | + | 8.83348i | −0.429579 | + | 0.314082i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.4773 | −0.762680 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.5625i | 0.728361i | 0.931328 | + | 0.364181i | \(0.118651\pi\) | ||||
−0.931328 | + | 0.364181i | \(0.881349\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 52.4924i | − | 1.85705i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.97467 | −0.104974 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.1231 | − | 9.59482i | 0.462529 | − | 0.338173i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.7645 | 1.08162 | 0.540811 | − | 0.841144i | \(-0.318117\pi\) | ||||
0.540811 | + | 0.841144i | \(0.318117\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.3234 | 0.994567 | 0.497284 | − | 0.867588i | \(-0.334331\pi\) | ||||
0.497284 | + | 0.867588i | \(0.334331\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0818 | 0.423207 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.10341i | 0.0735891i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.11313 | −0.178449 | −0.0892247 | − | 0.996012i | \(-0.528439\pi\) | ||||
−0.0892247 | + | 0.996012i | \(0.528439\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.8617i | 1.31978i | 0.751363 | + | 0.659889i | \(0.229397\pi\) | ||||
−0.751363 | + | 0.659889i | \(0.770603\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 38.6083i | − | 1.34254i | −0.741212 | − | 0.671271i | \(-0.765749\pi\) | ||
0.741212 | − | 0.671271i | \(-0.234251\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.9591i | 0.658476i | 0.944247 | + | 0.329238i | \(0.106792\pi\) | ||||
−0.944247 | + | 0.329238i | \(0.893208\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.9807 | − | 9.22437i | −1.00412 | − | 0.319606i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.5945 | 0.365761 | 0.182881 | − | 0.983135i | \(-0.441458\pi\) | ||||
0.182881 | + | 0.983135i | \(0.441458\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.49242 | −0.327325 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.1005i | 0.553874i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.1466 | + | 16.1922i | −0.760965 | + | 0.556372i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3137i | 0.387829i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.4505i | 0.905648i | 0.891600 | + | 0.452824i | \(0.149583\pi\) | ||||
−0.891600 | + | 0.452824i | \(0.850417\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 48.8620i | − | 1.66910i | −0.550936 | − | 0.834548i | \(-0.685729\pi\) | ||
0.550936 | − | 0.834548i | \(-0.314271\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.295294 | −0.0100753 | −0.00503765 | − | 0.999987i | \(-0.501604\pi\) | ||||
−0.00503765 | + | 0.999987i | \(0.501604\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.2500i | 0.893560i | 0.894644 | + | 0.446780i | \(0.147429\pi\) | ||||
−0.894644 | + | 0.446780i | \(0.852571\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.10795 | −0.207677 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.48023 | −0.0841361 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.64229 | 0.0556470 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.8664 | − | 25.8040i | −0.637799 | − | 0.872336i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.24621 | −0.278455 | −0.139227 | − | 0.990260i | \(-0.544462\pi\) | ||||
−0.139227 | + | 0.990260i | \(0.544462\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 45.4697i | − | 1.53191i | −0.642891 | − | 0.765957i | \(-0.722265\pi\) | ||
0.642891 | − | 0.765957i | \(-0.277735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 49.8617i | − | 1.67798i | −0.544146 | − | 0.838991i | \(-0.683146\pi\) | ||
0.544146 | − | 0.838991i | \(-0.316854\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.5945 | 0.355727 | 0.177863 | − | 0.984055i | \(-0.443081\pi\) | ||||
0.177863 | + | 0.984055i | \(0.443081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.3693 | + | 23.7565i | 0.582548 | + | 0.796767i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.9807 | −0.969801 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.4375 | −0.917133 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.27190 | 0.275883 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.7673i | 1.45810i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.17662 | 0.105595 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.1080i | 1.86303i | 0.363698 | + | 0.931517i | \(0.381514\pi\) | ||||
−0.363698 | + | 0.931517i | \(0.618486\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.21089i | 0.172645i | 0.996267 | + | 0.0863223i | \(0.0275115\pi\) | ||||
−0.996267 | + | 0.0863223i | \(0.972489\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.59482i | 0.317542i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.4903 | + | 10.5945i | −0.478513 | + | 0.349860i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 8.38447i | − | 0.276578i | −0.990392 | − | 0.138289i | \(-0.955840\pi\) | ||
0.990392 | − | 0.138289i | \(-0.0441603\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.75924 | 0.321229 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.63068 | 0.218016 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 8.15465i | − | 0.267545i | −0.991012 | − | 0.133773i | \(-0.957291\pi\) | ||
0.991012 | − | 0.133773i | \(-0.0427092\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.09271 | + | 16.0000i | −0.166907 | + | 0.524379i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 5.85238i | − | 0.191393i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.7673i | 1.42982i | 0.699219 | + | 0.714908i | \(0.253531\pi\) | ||||
−0.699219 | + | 0.714908i | \(0.746469\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 27.7647i | − | 0.905102i | −0.891738 | − | 0.452551i | \(-0.850514\pi\) | ||
0.891738 | − | 0.452551i | \(-0.149486\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.7392 | 0.512540 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 53.0986i | − | 1.72547i | −0.505653 | − | 0.862737i | \(-0.668749\pi\) | ||
0.505653 | − | 0.862737i | \(-0.331251\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.01515 | −0.227722 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.48023 | −0.0803426 | −0.0401713 | − | 0.999193i | \(-0.512790\pi\) | ||||
−0.0401713 | + | 0.999193i | \(0.512790\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.3341 | −0.819791 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43.0299 | + | 31.4609i | −1.38951 | + | 1.01593i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.4924 | −0.886852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.6762i | 0.729974i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.6307i | − | 0.727754i | −0.931447 | − | 0.363877i | \(-0.881453\pi\) | ||
0.931447 | − | 0.363877i | \(-0.118547\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.4355 | −1.04090 | −0.520452 | − | 0.853891i | \(-0.674237\pi\) | ||||
−0.520452 | + | 0.853891i | \(0.674237\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.4924 | + | 26.6811i | −1.16989 | + | 0.855355i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.8436 | 0.666845 | 0.333423 | − | 0.942777i | \(-0.391796\pi\) | ||||
0.333423 | + | 0.942777i | \(0.391796\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.14441 | −0.196376 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.3018 | 1.63627 | 0.818137 | − | 0.575023i | \(-0.195007\pi\) | ||||
0.818137 | + | 0.575023i | \(0.195007\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 7.49141i | − | 0.238696i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.17662 | 0.101011 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.6307i | 0.464759i | 0.972625 | + | 0.232379i | \(0.0746511\pi\) | ||||
−0.972625 | + | 0.232379i | \(0.925349\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.3823i | 0.487650i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.6573i | 0.970927i | 0.874257 | + | 0.485464i | \(0.161349\pi\) | ||||
−0.874257 | + | 0.485464i | \(0.838651\pi\) | |||||||
\(998\) | 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 | 4032.2.b.r.3583.10 | 16 | ||
3.2 | odd | 2 | inner | 4032.2.b.r.3583.6 | 16 | ||
4.3 | odd | 2 | inner | 4032.2.b.r.3583.11 | 16 | ||
7.6 | odd | 2 | inner | 4032.2.b.r.3583.8 | 16 | ||
8.3 | odd | 2 | 2016.2.b.d.1567.7 | yes | 16 | ||
8.5 | even | 2 | 2016.2.b.d.1567.6 | yes | 16 | ||
12.11 | even | 2 | inner | 4032.2.b.r.3583.7 | 16 | ||
21.20 | even | 2 | inner | 4032.2.b.r.3583.12 | 16 | ||
24.5 | odd | 2 | 2016.2.b.d.1567.10 | yes | 16 | ||
24.11 | even | 2 | 2016.2.b.d.1567.11 | yes | 16 | ||
28.27 | even | 2 | inner | 4032.2.b.r.3583.5 | 16 | ||
56.13 | odd | 2 | 2016.2.b.d.1567.12 | yes | 16 | ||
56.27 | even | 2 | 2016.2.b.d.1567.9 | yes | 16 | ||
84.83 | odd | 2 | inner | 4032.2.b.r.3583.9 | 16 | ||
168.83 | odd | 2 | 2016.2.b.d.1567.5 | ✓ | 16 | ||
168.125 | even | 2 | 2016.2.b.d.1567.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2016.2.b.d.1567.5 | ✓ | 16 | 168.83 | odd | 2 | ||
2016.2.b.d.1567.6 | yes | 16 | 8.5 | even | 2 | ||
2016.2.b.d.1567.7 | yes | 16 | 8.3 | odd | 2 | ||
2016.2.b.d.1567.8 | yes | 16 | 168.125 | even | 2 | ||
2016.2.b.d.1567.9 | yes | 16 | 56.27 | even | 2 | ||
2016.2.b.d.1567.10 | yes | 16 | 24.5 | odd | 2 | ||
2016.2.b.d.1567.11 | yes | 16 | 24.11 | even | 2 | ||
2016.2.b.d.1567.12 | yes | 16 | 56.13 | odd | 2 | ||
4032.2.b.r.3583.5 | 16 | 28.27 | even | 2 | inner | ||
4032.2.b.r.3583.6 | 16 | 3.2 | odd | 2 | inner | ||
4032.2.b.r.3583.7 | 16 | 12.11 | even | 2 | inner | ||
4032.2.b.r.3583.8 | 16 | 7.6 | odd | 2 | inner | ||
4032.2.b.r.3583.9 | 16 | 84.83 | odd | 2 | inner | ||
4032.2.b.r.3583.10 | 16 | 1.1 | even | 1 | trivial | ||
4032.2.b.r.3583.11 | 16 | 4.3 | odd | 2 | inner | ||
4032.2.b.r.3583.12 | 16 | 21.20 | even | 2 | inner |