Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(143,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.l (of order \(4\), 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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.3 | ||
Root | \(1.36166 - 0.381939i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.143 |
Dual form | 576.2.l.a.431.3 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(5\) | −0.763878 | + | 0.763878i | −0.341617 | + | 0.341617i | −0.856975 | − | 0.515358i | \(-0.827659\pi\) |
0.515358 | + | 0.856975i | \(0.327659\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.33620 | −0.505038 | −0.252519 | − | 0.967592i | \(-0.581259\pi\) | ||||
−0.252519 | + | 0.967592i | \(0.581259\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.95945 | + | 1.95945i | 0.590795 | + | 0.590795i | 0.937846 | − | 0.347051i | \(-0.112817\pi\) |
−0.347051 | + | 0.937846i | \(0.612817\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.18757 | − | 4.18757i | 1.16142 | − | 1.16142i | 0.177257 | − | 0.984165i | \(-0.443278\pi\) |
0.984165 | − | 0.177257i | \(-0.0567224\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.03243i | 0.978009i | 0.872281 | + | 0.489004i | \(0.162640\pi\) | ||||
−0.872281 | + | 0.489004i | \(0.837360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.26785 | + | 4.26785i | 0.979112 | + | 0.979112i | 0.999786 | − | 0.0206739i | \(-0.00658119\pi\) |
−0.0206739 | + | 0.999786i | \(0.506581\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.86408i | 1.84829i | 0.382044 | + | 0.924144i | \(0.375220\pi\) | ||||
−0.382044 | + | 0.924144i | \(0.624780\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.83298i | 0.766596i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.23934 | − | 1.23934i | −0.230140 | − | 0.230140i | 0.582611 | − | 0.812751i | \(-0.302031\pi\) |
−0.812751 | + | 0.582611i | \(0.802031\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.87835i | − | 0.516968i | −0.966016 | − | 0.258484i | \(-0.916777\pi\) | ||
0.966016 | − | 0.258484i | \(-0.0832229\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.02070 | − | 1.02070i | 0.172529 | − | 0.172529i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.434870 | + | 0.434870i | 0.0714922 | + | 0.0714922i | 0.741949 | − | 0.670457i | \(-0.233902\pi\) |
−0.670457 | + | 0.741949i | \(0.733902\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.81179 | 1.22000 | 0.609998 | − | 0.792403i | \(-0.291170\pi\) | ||||
0.609998 | + | 0.792403i | \(0.291170\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.49678 | − | 5.49678i | 0.838251 | − | 0.838251i | −0.150378 | − | 0.988629i | \(-0.548049\pi\) |
0.988629 | + | 0.150378i | \(0.0480491\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.20723 | −0.467822 | −0.233911 | − | 0.972258i | \(-0.575152\pi\) | ||||
−0.233911 | + | 0.972258i | \(0.575152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.21456 | −0.744937 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.06777 | + | 4.06777i | −0.558751 | + | 0.558751i | −0.928952 | − | 0.370201i | \(-0.879289\pi\) |
0.370201 | + | 0.928952i | \(0.379289\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.99355 | −0.403651 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.71811 | − | 4.71811i | −0.614245 | − | 0.614245i | 0.329804 | − | 0.944049i | \(-0.393017\pi\) |
−0.944049 | + | 0.329804i | \(0.893017\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.26785 | − | 3.26785i | 0.418406 | − | 0.418406i | −0.466248 | − | 0.884654i | \(-0.654395\pi\) |
0.884654 | + | 0.466248i | \(0.154395\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.39758i | 0.793522i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.44348 | + | 5.44348i | 0.665027 | + | 0.665027i | 0.956561 | − | 0.291533i | \(-0.0941654\pi\) |
−0.291533 | + | 0.956561i | \(0.594165\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.76718i | − | 0.447082i | −0.974695 | − | 0.223541i | \(-0.928238\pi\) | ||
0.974695 | − | 0.223541i | \(-0.0717616\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5357i | 1.23311i | 0.787312 | + | 0.616555i | \(0.211472\pi\) | ||||
−0.787312 | + | 0.616555i | \(0.788528\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.61822 | − | 2.61822i | −0.298374 | − | 0.298374i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.1995i | − | 1.26004i | −0.776578 | − | 0.630021i | \(-0.783046\pi\) | ||
0.776578 | − | 0.630021i | \(-0.216954\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.73306 | − | 9.73306i | 1.06834 | − | 1.06834i | 0.0708558 | − | 0.997487i | \(-0.477427\pi\) |
0.997487 | − | 0.0708558i | \(-0.0225730\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.08029 | − | 3.08029i | −0.334104 | − | 0.334104i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.64130 | 0.173977 | 0.0869886 | − | 0.996209i | \(-0.472276\pi\) | ||||
0.0869886 | + | 0.996209i | \(0.472276\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.59544 | + | 5.59544i | −0.586562 | + | 0.586562i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.52023 | −0.668962 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.70272 | −0.579024 | −0.289512 | − | 0.957174i | \(-0.593493\pi\) | ||||
−0.289512 | + | 0.957174i | \(0.593493\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.68599 | − | 6.68599i | 0.665281 | − | 0.665281i | −0.291339 | − | 0.956620i | \(-0.594101\pi\) |
0.956620 | + | 0.291339i | \(0.0941008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8784 | −1.07188 | −0.535938 | − | 0.844257i | \(-0.680042\pi\) | ||||
−0.535938 | + | 0.844257i | \(0.680042\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.31755 | − | 1.31755i | −0.127372 | − | 0.127372i | 0.640547 | − | 0.767919i | \(-0.278708\pi\) |
−0.767919 | + | 0.640547i | \(0.778708\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.51516 | + | 3.51516i | −0.336691 | + | 0.336691i | −0.855120 | − | 0.518429i | \(-0.826517\pi\) |
0.518429 | + | 0.855120i | \(0.326517\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.3139i | − | 1.53469i | −0.641236 | − | 0.767344i | \(-0.721578\pi\) | ||
0.641236 | − | 0.767344i | \(-0.278422\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.77107 | − | 6.77107i | −0.631406 | − | 0.631406i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.38815i | − | 0.493931i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 3.32115i | − | 0.301922i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.74732 | − | 6.74732i | −0.603499 | − | 0.603499i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.7416i | 1.84052i | 0.391303 | + | 0.920262i | \(0.372024\pi\) | ||||
−0.391303 | + | 0.920262i | \(0.627976\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.43621 | + | 9.43621i | −0.824446 | + | 0.824446i | −0.986742 | − | 0.162296i | \(-0.948110\pi\) |
0.162296 | + | 0.986742i | \(0.448110\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.70272 | − | 5.70272i | −0.494489 | − | 0.494489i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.8211 | −1.09538 | −0.547692 | − | 0.836680i | \(-0.684494\pi\) | ||||
−0.547692 | + | 0.836680i | \(0.684494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.44348 | + | 1.44348i | −0.122435 | + | 0.122435i | −0.765669 | − | 0.643235i | \(-0.777592\pi\) |
0.643235 | + | 0.765669i | \(0.277592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.4106 | 1.37232 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.89341 | 0.157239 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.42073 | − | 6.42073i | 0.526007 | − | 0.526007i | −0.393372 | − | 0.919379i | \(-0.628692\pi\) |
0.919379 | + | 0.393372i | \(0.128692\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.205945 | −0.0167596 | −0.00837978 | − | 0.999965i | \(-0.502667\pi\) | ||||
−0.00837978 | + | 0.999965i | \(0.502667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.19871 | + | 2.19871i | 0.176605 | + | 0.176605i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.26785 | + | 1.26785i | −0.101186 | + | 0.101186i | −0.755887 | − | 0.654702i | \(-0.772794\pi\) |
0.654702 | + | 0.755887i | \(0.272794\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11.8442i | − | 0.933456i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.169186 | − | 0.169186i | −0.0132517 | − | 0.0132517i | 0.700450 | − | 0.713702i | \(-0.252983\pi\) |
−0.713702 | + | 0.700450i | \(0.752983\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 10.4503i | − | 0.808671i | −0.914611 | − | 0.404335i | \(-0.867503\pi\) | ||
0.914611 | − | 0.404335i | \(-0.132497\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 22.0714i | − | 1.69780i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.974085 | − | 0.974085i | −0.0740583 | − | 0.0740583i | 0.669107 | − | 0.743166i | \(-0.266677\pi\) |
−0.743166 | + | 0.669107i | \(0.766677\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.12165i | − | 0.387160i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.59560 | − | 6.59560i | 0.492979 | − | 0.492979i | −0.416265 | − | 0.909243i | \(-0.636661\pi\) |
0.909243 | + | 0.416265i | \(0.136661\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.1876 | + | 10.1876i | 0.757236 | + | 0.757236i | 0.975818 | − | 0.218583i | \(-0.0701433\pi\) |
−0.218583 | + | 0.975818i | \(0.570143\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.664376 | −0.0488459 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.90133 | + | 7.90133i | −0.577803 | + | 0.577803i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.2297 | −1.02962 | −0.514812 | − | 0.857303i | \(-0.672138\pi\) | ||||
−0.514812 | + | 0.857303i | \(0.672138\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.53570 | 0.470450 | 0.235225 | − | 0.971941i | \(-0.424417\pi\) | ||||
0.235225 | + | 0.971941i | \(0.424417\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.07713 | + | 9.07713i | −0.646718 | + | 0.646718i | −0.952198 | − | 0.305480i | \(-0.901183\pi\) |
0.305480 | + | 0.952198i | \(0.401183\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0865 | 0.715011 | 0.357505 | − | 0.933911i | \(-0.383627\pi\) | ||||
0.357505 | + | 0.933911i | \(0.383627\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.65601 | + | 1.65601i | 0.116229 | + | 0.116229i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.96725 | + | 5.96725i | −0.416771 | + | 0.416771i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.7252i | 1.15691i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.9792 | − | 17.9792i | −1.23774 | − | 1.23774i | −0.960923 | − | 0.276815i | \(-0.910721\pi\) |
−0.276815 | − | 0.960923i | \(-0.589279\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.39773i | 0.572721i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.84607i | 0.261088i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.8861 | + | 16.8861i | 1.13588 | + | 1.13588i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00861i | 0.268437i | 0.990952 | + | 0.134218i | \(0.0428523\pi\) | ||||
−0.990952 | + | 0.134218i | \(0.957148\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.7915 | + | 13.7915i | −0.915373 | + | 0.915373i | −0.996688 | − | 0.0813152i | \(-0.974088\pi\) |
0.0813152 | + | 0.996688i | \(0.474088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.47840 | + | 3.47840i | 0.229859 | + | 0.229859i | 0.812634 | − | 0.582775i | \(-0.198033\pi\) |
−0.582775 | + | 0.812634i | \(0.698033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.23973 | −0.212241 | −0.106121 | − | 0.994353i | \(-0.533843\pi\) | ||||
−0.106121 | + | 0.994353i | \(0.533843\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.44993 | − | 2.44993i | 0.159816 | − | 0.159816i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.2484 | 1.56850 | 0.784249 | − | 0.620446i | \(-0.213048\pi\) | ||||
0.784249 | + | 0.620446i | \(0.213048\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5596 | 1.06670 | 0.533348 | − | 0.845896i | \(-0.320934\pi\) | ||||
0.533348 | + | 0.845896i | \(0.320934\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.98329 | − | 3.98329i | 0.254483 | − | 0.254483i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 35.7438 | 2.27432 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.3957 | − | 11.3957i | −0.719287 | − | 0.719287i | 0.249172 | − | 0.968459i | \(-0.419842\pi\) |
−0.968459 | + | 0.249172i | \(0.919842\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.3687 | + | 17.3687i | −1.09196 | + | 1.09196i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3.54316i | − | 0.221016i | −0.993875 | − | 0.110508i | \(-0.964752\pi\) | ||
0.993875 | − | 0.110508i | \(-0.0352478\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.581076 | − | 0.581076i | −0.0361063 | − | 0.0361063i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 21.0534i | − | 1.29821i | −0.760701 | − | 0.649103i | \(-0.775145\pi\) | ||
0.760701 | − | 0.649103i | \(-0.224855\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.21456i | − | 0.381757i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.4077 | + | 20.4077i | 1.24428 | + | 1.24428i | 0.958208 | + | 0.286072i | \(0.0923496\pi\) |
0.286072 | + | 0.958208i | \(0.407650\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.06279i | 0.307543i | 0.988106 | + | 0.153771i | \(0.0491419\pi\) | ||||
−0.988106 | + | 0.153771i | \(0.950858\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.51052 | + | 7.51052i | −0.452901 | + | 0.452901i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.86642 | − | 5.86642i | −0.352479 | − | 0.352479i | 0.508552 | − | 0.861031i | \(-0.330181\pi\) |
−0.861031 | + | 0.508552i | \(0.830181\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.77316 | −0.284743 | −0.142371 | − | 0.989813i | \(-0.545473\pi\) | ||||
−0.142371 | + | 0.989813i | \(0.545473\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.0779 | − | 10.0779i | 0.599066 | − | 0.599066i | −0.340998 | − | 0.940064i | \(-0.610765\pi\) |
0.940064 | + | 0.340998i | \(0.110765\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.4381 | −0.616144 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.739481 | 0.0434989 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.7829 | + | 11.7829i | −0.688364 | + | 0.688364i | −0.961870 | − | 0.273506i | \(-0.911817\pi\) |
0.273506 | + | 0.961870i | \(0.411817\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.20811 | 0.419673 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 37.1189 | + | 37.1189i | 2.14664 | + | 2.14664i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.34482 | + | 7.34482i | −0.423348 | + | 0.423348i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.99248i | 0.285869i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.31322 | + | 4.31322i | 0.246169 | + | 0.246169i | 0.819396 | − | 0.573228i | \(-0.194309\pi\) |
−0.573228 | + | 0.819396i | \(0.694309\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.4434i | 1.55617i | 0.628156 | + | 0.778087i | \(0.283810\pi\) | ||||
−0.628156 | + | 0.778087i | \(0.716190\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 18.8568i | − | 1.06585i | −0.846162 | − | 0.532926i | \(-0.821092\pi\) | ||
0.846162 | − | 0.532926i | \(-0.178908\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.154552 | + | 0.154552i | 0.00868053 | + | 0.00868053i | 0.711434 | − | 0.702753i | \(-0.248046\pi\) |
−0.702753 | + | 0.711434i | \(0.748046\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.85685i | − | 0.271931i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.2098 | + | 17.2098i | −0.957580 | + | 0.957580i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.0509 | + | 16.0509i | 0.890342 | + | 0.890342i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.28551 | 0.236268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.3132 | − | 16.3132i | 0.896656 | − | 0.896656i | −0.0984829 | − | 0.995139i | \(-0.531399\pi\) |
0.995139 | + | 0.0984829i | \(0.0313990\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.31631 | −0.454369 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.89341 | 0.103141 | 0.0515704 | − | 0.998669i | \(-0.483577\pi\) | ||||
0.0515704 | + | 0.998669i | \(0.483577\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.63998 | − | 5.63998i | 0.305422 | − | 0.305422i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.3211 | 0.881259 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.7630 | − | 19.7630i | −1.06093 | − | 1.06093i | −0.998019 | − | 0.0629131i | \(-0.979961\pi\) |
−0.0629131 | − | 0.998019i | \(-0.520039\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.1008 | − | 18.1008i | 0.968915 | − | 0.968915i | −0.0306158 | − | 0.999531i | \(-0.509747\pi\) |
0.999531 | + | 0.0306158i | \(0.00974685\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.3695i | 1.03093i | 0.856910 | + | 0.515466i | \(0.172381\pi\) | ||||
−0.856910 | + | 0.515466i | \(0.827619\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.87766 | + | 2.87766i | 0.152730 | + | 0.152730i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 7.09236i | − | 0.374321i | −0.982329 | − | 0.187160i | \(-0.940072\pi\) | ||
0.982329 | − | 0.187160i | \(-0.0599284\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.4291i | 0.917322i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.04799 | − | 8.04799i | −0.421251 | − | 0.421251i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.65735i | 0.0865130i | 0.999064 | + | 0.0432565i | \(0.0137733\pi\) | ||||
−0.999064 | + | 0.0432565i | \(0.986227\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.43537 | − | 5.43537i | 0.282190 | − | 0.282190i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.48241 | − | 3.48241i | −0.180312 | − | 0.180312i | 0.611180 | − | 0.791492i | \(-0.290695\pi\) |
−0.791492 | + | 0.611180i | \(0.790695\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.3797 | −0.534579 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.1548 | + | 19.1548i | −0.983917 | + | 0.983917i | −0.999873 | − | 0.0159558i | \(-0.994921\pi\) |
0.0159558 | + | 0.999873i | \(0.494921\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.2907 | 0.781319 | 0.390660 | − | 0.920535i | \(-0.372247\pi\) | ||||
0.390660 | + | 0.920535i | \(0.372247\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.7144 | − | 22.7144i | 1.15166 | − | 1.15166i | 0.165445 | − | 0.986219i | \(-0.447094\pi\) |
0.986219 | − | 0.165445i | \(-0.0529060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.7438 | −1.80764 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.55505 | + | 8.55505i | 0.430451 | + | 0.430451i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.45854 | − | 7.45854i | 0.374334 | − | 0.374334i | −0.494719 | − | 0.869053i | \(-0.664729\pi\) |
0.869053 | + | 0.494719i | \(0.164729\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 11.5911i | − | 0.578834i | −0.957203 | − | 0.289417i | \(-0.906539\pi\) | ||
0.957203 | − | 0.289417i | \(-0.0934615\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0533 | − | 12.0533i | −0.600417 | − | 0.600417i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.70421i | 0.0844745i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.4659i | − | 0.616398i | −0.951322 | − | 0.308199i | \(-0.900274\pi\) | ||
0.951322 | − | 0.308199i | \(-0.0997262\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.30435 | + | 6.30435i | 0.310217 | + | 0.310217i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.8697i | 0.729927i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.4096 | − | 14.4096i | 0.703953 | − | 0.703953i | −0.261304 | − | 0.965257i | \(-0.584152\pi\) |
0.965257 | + | 0.261304i | \(0.0841525\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.83630 | − | 5.83630i | −0.284444 | − | 0.284444i | 0.550434 | − | 0.834878i | \(-0.314462\pi\) |
−0.834878 | + | 0.550434i | \(0.814462\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.4562 | −0.749738 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.36652 | + | 4.36652i | −0.211311 | + | 0.211311i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.4510 | 0.888755 | 0.444377 | − | 0.895840i | \(-0.353425\pi\) | ||||
0.444377 | + | 0.895840i | \(0.353425\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.58166 | 0.316295 | 0.158147 | − | 0.987416i | \(-0.449448\pi\) | ||||
0.158147 | + | 0.987416i | \(0.449448\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −37.8306 | + | 37.8306i | −1.80968 | + | 1.80968i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.68747 | −0.175993 | −0.0879966 | − | 0.996121i | \(-0.528046\pi\) | ||||
−0.0879966 | + | 0.996121i | \(0.528046\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.31861 | − | 3.31861i | −0.157672 | − | 0.157672i | 0.623862 | − | 0.781534i | \(-0.285563\pi\) |
−0.781534 | + | 0.623862i | \(0.785563\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.25375 | + | 1.25375i | −0.0594335 | + | 0.0594335i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.3555i | − | 0.960635i | −0.877095 | − | 0.480318i | \(-0.840521\pi\) | ||
0.877095 | − | 0.480318i | \(-0.159479\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.3068 | + | 15.3068i | 0.720768 | + | 0.720768i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 8.54847i | − | 0.400758i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0239i | 0.468897i | 0.972129 | + | 0.234448i | \(0.0753284\pi\) | ||||
−0.972129 | + | 0.234448i | \(0.924672\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.4043 | − | 16.4043i | −0.764026 | − | 0.764026i | 0.213021 | − | 0.977048i | \(-0.431670\pi\) |
−0.977048 | + | 0.213021i | \(0.931670\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 0.997833i | − | 0.0463732i | −0.999731 | − | 0.0231866i | \(-0.992619\pi\) | ||
0.999731 | − | 0.0231866i | \(-0.00738119\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.73306 | − | 9.73306i | 0.450392 | − | 0.450392i | −0.445092 | − | 0.895485i | \(-0.646829\pi\) |
0.895485 | + | 0.445092i | \(0.146829\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.27361 | − | 7.27361i | −0.335864 | − | 0.335864i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.5413 | 0.990469 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.3586 | + | 16.3586i | −0.750584 | + | 0.750584i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.0669 | −1.69363 | −0.846816 | − | 0.531886i | \(-0.821483\pi\) | ||||
−0.846816 | + | 0.531886i | \(0.821483\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.64210 | 0.166065 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.35618 | − | 4.35618i | 0.197804 | − | 0.197804i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.1866 | −1.50383 | −0.751914 | − | 0.659261i | \(-0.770869\pi\) | ||||
−0.751914 | + | 0.659261i | \(0.770869\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.2580 | − | 10.2580i | −0.462936 | − | 0.462936i | 0.436681 | − | 0.899617i | \(-0.356154\pi\) |
−0.899617 | + | 0.436681i | \(0.856154\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.99757 | − | 4.99757i | 0.225079 | − | 0.225079i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.03372i | 0.225793i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.19733 | − | 4.19733i | −0.187898 | − | 0.187898i | 0.606889 | − | 0.794787i | \(-0.292417\pi\) |
−0.794787 | + | 0.606889i | \(0.792417\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.0655i | 0.939266i | 0.882862 | + | 0.469633i | \(0.155614\pi\) | ||||
−0.882862 | + | 0.469633i | \(0.844386\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.2146i | 0.454542i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.6424 | − | 22.6424i | −1.00361 | − | 1.00361i | −0.999993 | − | 0.00361481i | \(-0.998849\pi\) |
−0.00361481 | − | 0.999993i | \(-0.501151\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 14.0779i | − | 0.622768i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.30973 | − | 8.30973i | 0.366171 | − | 0.366171i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.28439 | − | 6.28439i | −0.276387 | − | 0.276387i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.3351 | 1.67949 | 0.839746 | − | 0.542980i | \(-0.182704\pi\) | ||||
0.839746 | + | 0.542980i | \(0.182704\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.39811 | − | 5.39811i | 0.236043 | − | 0.236043i | −0.579166 | − | 0.815209i | \(-0.696622\pi\) |
0.815209 | + | 0.579166i | \(0.196622\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.6068 | 0.505599 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −55.5719 | −2.41617 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.7124 | − | 32.7124i | 1.41693 | − | 1.41693i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.01289 | 0.0870249 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.2176 | − | 10.2176i | −0.440105 | − | 0.440105i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.51516 | − | 5.51516i | 0.237115 | − | 0.237115i | −0.578539 | − | 0.815654i | \(-0.696377\pi\) |
0.815654 | + | 0.578539i | \(0.196377\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 5.37030i | − | 0.230038i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.2535 | + | 23.2535i | 0.994247 | + | 0.994247i | 0.999984 | − | 0.00573636i | \(-0.00182595\pi\) |
−0.00573636 | + | 0.999984i | \(0.501826\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.5787i | − | 0.450666i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.9648i | 0.636369i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.9066 | − | 26.9066i | −1.14007 | − | 1.14007i | −0.988437 | − | 0.151635i | \(-0.951546\pi\) |
−0.151635 | − | 0.988437i | \(-0.548454\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 46.0362i | − | 1.94712i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.4144 | − | 21.4144i | 0.902508 | − | 0.902508i | −0.0931446 | − | 0.995653i | \(-0.529692\pi\) |
0.995653 | + | 0.0931446i | \(0.0296919\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.4619 | + | 12.4619i | 0.524275 | + | 0.524275i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.54807 | 0.0648986 | 0.0324493 | − | 0.999473i | \(-0.489669\pi\) | ||||
0.0324493 | + | 0.999473i | \(0.489669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.3384 | − | 12.3384i | 0.516345 | − | 0.516345i | −0.400119 | − | 0.916463i | \(-0.631031\pi\) |
0.916463 | + | 0.400119i | \(0.131031\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33.9759 | −1.41689 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.9648 | −1.03930 | −0.519650 | − | 0.854380i | \(-0.673937\pi\) | ||||
−0.519650 | + | 0.854380i | \(0.673937\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.0054 | + | 13.0054i | −0.539553 | + | 0.539553i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.9411 | −0.660215 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.99426 | − | 3.99426i | −0.164861 | − | 0.164861i | 0.619855 | − | 0.784716i | \(-0.287191\pi\) |
−0.784716 | + | 0.619855i | \(0.787191\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.2844 | − | 12.2844i | 0.506169 | − | 0.506169i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 21.0442i | − | 0.864183i | −0.901830 | − | 0.432092i | \(-0.857776\pi\) | ||
0.901830 | − | 0.432092i | \(-0.142224\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.11589 | + | 4.11589i | 0.168735 | + | 0.168735i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 12.7718i | − | 0.521840i | −0.965360 | − | 0.260920i | \(-0.915974\pi\) | ||
0.965360 | − | 0.260920i | \(-0.0840259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.2967i | 1.80690i | 0.428691 | + | 0.903451i | \(0.358975\pi\) | ||||
−0.428691 | + | 0.903451i | \(0.641025\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.53695 | + | 2.53695i | 0.103142 | + | 0.103142i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.8784i | 1.09096i | 0.838124 | + | 0.545479i | \(0.183652\pi\) | ||||
−0.838124 | + | 0.545479i | \(0.816348\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.4305 | + | 13.4305i | −0.543339 | + | 0.543339i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.6602 | − | 27.6602i | −1.11719 | − | 1.11719i | −0.992153 | − | 0.125033i | \(-0.960096\pi\) |
−0.125033 | − | 0.992153i | \(-0.539904\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.6148 | −0.789661 | −0.394831 | − | 0.918754i | \(-0.629197\pi\) | ||||
−0.394831 | + | 0.918754i | \(0.629197\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.7854 | − | 11.7854i | 0.473697 | − | 0.473697i | −0.429412 | − | 0.903109i | \(-0.641279\pi\) |
0.903109 | + | 0.429412i | \(0.141279\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.19311 | −0.0878651 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.85665 | −0.354266 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.75359 | + | 1.75359i | −0.0699200 | + | 0.0699200i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.8195 | −0.749193 | −0.374596 | − | 0.927188i | \(-0.622219\pi\) | ||||
−0.374596 | + | 0.927188i | \(0.622219\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.8441 | − | 15.8441i | −0.628753 | − | 0.628753i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.8363 | + | 21.8363i | −0.865186 | + | 0.865186i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.9718i | 0.709845i | 0.934896 | + | 0.354923i | \(0.115493\pi\) | ||||
−0.934896 | + | 0.354923i | \(0.884507\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.92589 | + | 9.92589i | 0.391439 | + | 0.391439i | 0.875200 | − | 0.483761i | \(-0.160730\pi\) |
−0.483761 | + | 0.875200i | \(0.660730\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.6801i | 0.537820i | 0.963165 | + | 0.268910i | \(0.0866635\pi\) | ||||
−0.963165 | + | 0.268910i | \(0.913337\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 18.4897i | − | 0.725786i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.1940 | + | 31.1940i | 1.22071 | + | 1.22071i | 0.967378 | + | 0.253336i | \(0.0815278\pi\) |
0.253336 | + | 0.967378i | \(0.418472\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 14.4162i | − | 0.563288i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.2397 | − | 27.2397i | 1.06111 | − | 1.06111i | 0.0631026 | − | 0.998007i | \(-0.479900\pi\) |
0.998007 | − | 0.0631026i | \(-0.0200995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0770 | − | 12.0770i | −0.469740 | − | 0.469740i | 0.432091 | − | 0.901830i | \(-0.357776\pi\) |
−0.901830 | + | 0.432091i | \(0.857776\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.71237 | 0.337851 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.9856 | − | 10.9856i | 0.425365 | − | 0.425365i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.8064 | 0.494384 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.0108 | 0.424434 | 0.212217 | − | 0.977223i | \(-0.431932\pi\) | ||||
0.212217 | + | 0.977223i | \(0.431932\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.26708 | − | 5.26708i | 0.202430 | − | 0.202430i | −0.598610 | − | 0.801040i | \(-0.704280\pi\) |
0.801040 | + | 0.598610i | \(0.204280\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.62000 | 0.292429 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.0080 | − | 16.0080i | −0.612528 | − | 0.612528i | 0.331076 | − | 0.943604i | \(-0.392588\pi\) |
−0.943604 | + | 0.331076i | \(0.892588\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.79379 | − | 9.79379i | 0.374201 | − | 0.374201i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.0681i | 1.29789i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.63348 | − | 7.63348i | −0.290391 | − | 0.290391i | 0.546843 | − | 0.837235i | \(-0.315829\pi\) |
−0.837235 | + | 0.546843i | \(0.815829\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 2.20529i | − | 0.0836514i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.5005i | 1.19317i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.3494 | − | 18.3494i | −0.693049 | − | 0.693049i | 0.269853 | − | 0.962902i | \(-0.413025\pi\) |
−0.962902 | + | 0.269853i | \(0.913025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.71192i | 0.139998i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.93385 | + | 8.93385i | −0.335992 | + | 0.335992i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.8774 | + | 19.8774i | 0.746511 | + | 0.746511i | 0.973822 | − | 0.227311i | \(-0.0729934\pi\) |
−0.227311 | + | 0.973822i | \(0.572993\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.5140 | 0.955505 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.5357 | + | 12.5357i | −0.468809 | + | 0.468809i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.1176 | 0.601083 | 0.300542 | − | 0.953769i | \(-0.402833\pi\) | ||||
0.300542 | + | 0.953769i | \(0.402833\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.5357 | 0.541338 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.75038 | − | 4.75038i | 0.176425 | − | 0.176425i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.4536 | −0.610229 | −0.305115 | − | 0.952316i | \(-0.598695\pi\) | ||||
−0.305115 | + | 0.952316i | \(0.598695\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.1654 | + | 22.1654i | 0.819816 | + | 0.819816i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.5995 | − | 24.5995i | 0.908602 | − | 0.908602i | −0.0875578 | − | 0.996159i | \(-0.527906\pi\) |
0.996159 | + | 0.0875578i | \(0.0279063\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.3324i | 0.785790i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.06707 | − | 3.06707i | −0.112824 | − | 0.112824i | 0.648441 | − | 0.761265i | \(-0.275421\pi\) |
−0.761265 | + | 0.648441i | \(0.775421\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.16681i | 0.0428061i | 0.999771 | + | 0.0214031i | \(0.00681333\pi\) | ||||
−0.999771 | + | 0.0214031i | \(0.993187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.80931i | 0.359385i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.76051 | + | 1.76051i | 0.0643278 | + | 0.0643278i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2.12809i | − | 0.0776552i | −0.999246 | − | 0.0388276i | \(-0.987638\pi\) | ||
0.999246 | − | 0.0388276i | \(-0.0123623\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.157317 | − | 0.157317i | 0.00572534 | − | 0.00572534i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.1573 | + | 19.1573i | 0.696282 | + | 0.696282i | 0.963607 | − | 0.267324i | \(-0.0861395\pi\) |
−0.267324 | + | 0.963607i | \(0.586140\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.2848 | −0.372824 | −0.186412 | − | 0.982472i | \(-0.559686\pi\) | ||||
−0.186412 | + | 0.982472i | \(0.559686\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.69697 | − | 4.69697i | 0.170042 | − | 0.170042i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −39.5147 | −1.42679 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.2860 | −0.551226 | −0.275613 | − | 0.961269i | \(-0.588881\pi\) | ||||
−0.275613 | + | 0.961269i | \(0.588881\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.6903 | + | 23.6903i | −0.852081 | + | 0.852081i | −0.990389 | − | 0.138308i | \(-0.955834\pi\) |
0.138308 | + | 0.990389i | \(0.455834\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.0327 | 0.396305 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.3396 | + | 33.3396i | 1.19451 | + | 1.19451i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.38158 | − | 7.38158i | 0.264134 | − | 0.264134i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.93697i | − | 0.0691333i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.3220 | + | 29.3220i | 1.04522 | + | 1.04522i | 0.998928 | + | 0.0462895i | \(0.0147397\pi\) |
0.0462895 | + | 0.998928i | \(0.485260\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.7988i | 0.775075i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 27.3687i | − | 0.971890i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.41153 | + | 3.41153i | 0.120843 | + | 0.120843i | 0.764942 | − | 0.644099i | \(-0.222768\pi\) |
−0.644099 | + | 0.764942i | \(0.722768\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 12.9329i | − | 0.457534i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.6441 | + | 20.6441i | −0.728516 | + | 0.728516i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.04754 | + | 9.04754i | 0.318884 | + | 0.318884i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.15877 | 0.322005 | 0.161003 | − | 0.986954i | \(-0.448527\pi\) | ||||
0.161003 | + | 0.986954i | \(0.448527\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.91014 | − | 8.91014i | 0.312877 | − | 0.312877i | −0.533146 | − | 0.846023i | \(-0.678990\pi\) |
0.846023 | + | 0.533146i | \(0.178990\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.258474 | 0.00905397 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.9189 | 1.64148 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.0618 | + | 27.0618i | −0.944464 | + | 0.944464i | −0.998537 | − | 0.0540734i | \(-0.982779\pi\) |
0.0540734 | + | 0.998537i | \(0.482779\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.6286 | −0.405348 | −0.202674 | − | 0.979246i | \(-0.564963\pi\) | ||||
−0.202674 | + | 0.979246i | \(0.564963\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.57283 | + | 8.57283i | 0.298107 | + | 0.298107i | 0.840272 | − | 0.542165i | \(-0.182395\pi\) |
−0.542165 | + | 0.840272i | \(0.682395\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.5629 | − | 19.5629i | 0.679447 | − | 0.679447i | −0.280428 | − | 0.959875i | \(-0.590476\pi\) |
0.959875 | + | 0.280428i | \(0.0904763\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 21.0274i | − | 0.728555i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.98277 | + | 7.98277i | 0.276255 | + | 0.276255i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.8018i | 0.511015i | 0.966807 | + | 0.255508i | \(0.0822426\pi\) | ||||
−0.966807 | + | 0.255508i | \(0.917757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 25.9281i | − | 0.894071i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.8599 | + | 16.8599i | 0.579997 | + | 0.579997i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.43773i | 0.152482i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.85473 | + | 3.85473i | −0.132138 | + | 0.132138i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.2550 | − | 27.2550i | −0.933192 | − | 0.933192i | 0.0647119 | − | 0.997904i | \(-0.479387\pi\) |
−0.997904 | + | 0.0647119i | \(0.979387\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.7462 | −0.981951 | −0.490976 | − | 0.871173i | \(-0.663360\pi\) | ||||
−0.490976 | + | 0.871173i | \(0.663360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.2578 | + | 29.2578i | −0.998264 | + | 0.998264i | −0.999998 | − | 0.00173461i | \(-0.999448\pi\) |
0.00173461 | + | 0.999998i | \(0.499448\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.6816 | 1.38482 | 0.692408 | − | 0.721506i | \(-0.256550\pi\) | ||||
0.692408 | + | 0.721506i | \(0.256550\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.48816 | 0.0505991 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.9448 | − | 21.9448i | 0.744427 | − | 0.744427i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.5899 | 1.54475 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.01580 | + | 9.01580i | 0.304790 | + | 0.304790i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.9577 | + | 28.9577i | −0.977831 | + | 0.977831i | −0.999760 | − | 0.0219281i | \(-0.993020\pi\) |
0.0219281 | + | 0.999760i | \(0.493020\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 17.2311i | − | 0.580531i | −0.956946 | − | 0.290266i | \(-0.906256\pi\) | ||
0.956946 | − | 0.290266i | \(-0.0937437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.8129 | − | 24.8129i | −0.835019 | − | 0.835019i | 0.153179 | − | 0.988198i | \(-0.451049\pi\) |
−0.988198 | + | 0.153179i | \(0.951049\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.0606i | 1.31153i | 0.754967 | + | 0.655763i | \(0.227653\pi\) | ||||
−0.754967 | + | 0.655763i | \(0.772347\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 27.7151i | − | 0.929534i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.6880 | − | 13.6880i | −0.458050 | − | 0.458050i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.0765i | 0.336819i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.56727 | + | 3.56727i | −0.118975 | + | 0.118975i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.4030 | − | 16.4030i | −0.546463 | − | 0.546463i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.5641 | −0.517369 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.366518 | + | 0.366518i | −0.0121700 | + | 0.0121700i | −0.713166 | − | 0.700996i | \(-0.752739\pi\) |
0.700996 | + | 0.713166i | \(0.252739\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.8950 | 0.626018 | 0.313009 | − | 0.949750i | \(-0.398663\pi\) | ||||
0.313009 | + | 0.949750i | \(0.398663\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.1428 | 1.26234 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.6087 | − | 12.6087i | 0.416376 | − | 0.416376i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.5805 | 1.80045 | 0.900223 | − | 0.435429i | \(-0.143403\pi\) | ||||
0.900223 | + | 0.435429i | \(0.143403\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.7753 | − | 15.7753i | −0.519250 | − | 0.519250i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.66685 | + | 1.66685i | −0.0548057 | + | 0.0548057i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.2118i | 0.695938i | 0.937506 | + | 0.347969i | \(0.113129\pi\) | ||||
−0.937506 | + | 0.347969i | \(0.886871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.2550 | − | 22.2550i | −0.729377 | − | 0.729377i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 12.0713i | − | 0.394774i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.7395i | − | 0.514186i | −0.966387 | − | 0.257093i | \(-0.917235\pi\) | ||
0.966387 | − | 0.257093i | \(-0.0827647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.43393 | + | 1.43393i | 0.0467447 | + | 0.0467447i | 0.730093 | − | 0.683348i | \(-0.239477\pi\) |
−0.683348 | + | 0.730093i | \(0.739477\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 69.2443i | 2.25491i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.5461 | + | 28.5461i | −0.927623 | + | 0.927623i | −0.997552 | − | 0.0699288i | \(-0.977723\pi\) |
0.0699288 | + | 0.997552i | \(0.477723\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.1189 | + | 44.1189i | 1.43216 | + | 1.43216i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.6986 | 0.476136 | 0.238068 | − | 0.971249i | \(-0.423486\pi\) | ||||
0.238068 | + | 0.971249i | \(0.423486\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.8697 | − | 10.8697i | 0.351737 | − | 0.351737i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.1317 | 0.553210 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.7151 | 0.732745 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.99248 | + | 4.99248i | −0.160714 | + | 0.160714i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.34054 | 0.236056 | 0.118028 | − | 0.993010i | \(-0.462343\pi\) | ||||
0.118028 | + | 0.993010i | \(0.462343\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.48251 | + | 3.48251i | 0.111759 | + | 0.111759i | 0.760775 | − | 0.649016i | \(-0.224819\pi\) |
−0.649016 | + | 0.760775i | \(0.724819\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.92879 | − | 1.92879i | 0.0618341 | − | 0.0618341i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 9.95013i | − | 0.318333i | −0.987252 | − | 0.159166i | \(-0.949119\pi\) | ||
0.987252 | − | 0.159166i | \(-0.0508806\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.21603 | + | 3.21603i | 0.102785 | + | 0.102785i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.7648i | 0.598505i | 0.954174 | + | 0.299253i | \(0.0967373\pi\) | ||||
−0.954174 | + | 0.299253i | \(0.903263\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 13.8676i | − | 0.441859i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.7239 | + | 48.7239i | 1.54933 | + | 1.54933i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3.18227i | − | 0.101088i | −0.998722 | − | 0.0505441i | \(-0.983904\pi\) | ||
0.998722 | − | 0.0505441i | \(-0.0160955\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.70483 | + | 7.70483i | −0.244259 | + | 0.244259i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.9944 | + | 26.9944i | 0.854923 | + | 0.854923i | 0.990735 | − | 0.135812i | \(-0.0433643\pi\) |
−0.135812 | + | 0.990735i | \(0.543364\pi\) | |||||||
\(998\) | 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 | 576.2.l.a.143.3 | 16 | ||
3.2 | odd | 2 | inner | 576.2.l.a.143.6 | 16 | ||
4.3 | odd | 2 | 144.2.l.a.107.7 | yes | 16 | ||
8.3 | odd | 2 | 1152.2.l.a.287.6 | 16 | |||
8.5 | even | 2 | 1152.2.l.b.287.6 | 16 | |||
12.11 | even | 2 | 144.2.l.a.107.2 | yes | 16 | ||
16.3 | odd | 4 | inner | 576.2.l.a.431.6 | 16 | ||
16.5 | even | 4 | 1152.2.l.a.863.3 | 16 | |||
16.11 | odd | 4 | 1152.2.l.b.863.3 | 16 | |||
16.13 | even | 4 | 144.2.l.a.35.2 | ✓ | 16 | ||
24.5 | odd | 2 | 1152.2.l.b.287.3 | 16 | |||
24.11 | even | 2 | 1152.2.l.a.287.3 | 16 | |||
48.5 | odd | 4 | 1152.2.l.a.863.6 | 16 | |||
48.11 | even | 4 | 1152.2.l.b.863.6 | 16 | |||
48.29 | odd | 4 | 144.2.l.a.35.7 | yes | 16 | ||
48.35 | even | 4 | inner | 576.2.l.a.431.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.l.a.35.2 | ✓ | 16 | 16.13 | even | 4 | ||
144.2.l.a.35.7 | yes | 16 | 48.29 | odd | 4 | ||
144.2.l.a.107.2 | yes | 16 | 12.11 | even | 2 | ||
144.2.l.a.107.7 | yes | 16 | 4.3 | odd | 2 | ||
576.2.l.a.143.3 | 16 | 1.1 | even | 1 | trivial | ||
576.2.l.a.143.6 | 16 | 3.2 | odd | 2 | inner | ||
576.2.l.a.431.3 | 16 | 48.35 | even | 4 | inner | ||
576.2.l.a.431.6 | 16 | 16.3 | odd | 4 | inner | ||
1152.2.l.a.287.3 | 16 | 24.11 | even | 2 | |||
1152.2.l.a.287.6 | 16 | 8.3 | odd | 2 | |||
1152.2.l.a.863.3 | 16 | 16.5 | even | 4 | |||
1152.2.l.a.863.6 | 16 | 48.5 | odd | 4 | |||
1152.2.l.b.287.3 | 16 | 24.5 | odd | 2 | |||
1152.2.l.b.287.6 | 16 | 8.5 | even | 2 | |||
1152.2.l.b.863.3 | 16 | 16.11 | odd | 4 | |||
1152.2.l.b.863.6 | 16 | 48.11 | even | 4 |