Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(287,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.287");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 287.8 | ||
Character | \(\chi\) | \(=\) | 864.287 |
Dual form | 864.2.s.a.575.8 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.398132 | + | 0.229862i | 0.178050 | + | 0.102797i | 0.586376 | − | 0.810039i | \(-0.300554\pi\) |
−0.408326 | + | 0.912836i | \(0.633887\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.28309 | − | 2.47284i | 1.61886 | − | 0.934647i | 0.631638 | − | 0.775263i | \(-0.282383\pi\) |
0.987217 | − | 0.159383i | \(-0.0509506\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.17474 | + | 2.03471i | 0.354198 | + | 0.613489i | 0.986980 | − | 0.160841i | \(-0.0514206\pi\) |
−0.632782 | + | 0.774330i | \(0.718087\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0384586 | + | 0.0666122i | −0.0106665 | + | 0.0184749i | −0.871309 | − | 0.490734i | \(-0.836729\pi\) |
0.860643 | + | 0.509209i | \(0.170062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.92857i | − | 1.43789i | −0.695068 | − | 0.718944i | \(-0.744626\pi\) | ||
0.695068 | − | 0.718944i | \(-0.255374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.59561i | 0.824889i | 0.910983 | + | 0.412444i | \(0.135325\pi\) | ||||
−0.910983 | + | 0.412444i | \(0.864675\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.41469 | + | 4.18237i | −0.503498 | + | 0.872084i | 0.496494 | + | 0.868040i | \(0.334621\pi\) |
−0.999992 | + | 0.00404388i | \(0.998713\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.39433 | − | 4.14710i | −0.478865 | − | 0.829419i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.54954 | − | 3.78138i | 1.21622 | − | 0.702184i | 0.252112 | − | 0.967698i | \(-0.418875\pi\) |
0.964107 | + | 0.265514i | \(0.0855416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.663421 | + | 0.383026i | 0.119154 | + | 0.0687935i | 0.558392 | − | 0.829577i | \(-0.311418\pi\) |
−0.439238 | + | 0.898370i | \(0.644752\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.27365 | 0.384317 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.47993 | −0.900894 | −0.450447 | − | 0.892803i | \(-0.648735\pi\) | ||||
−0.450447 | + | 0.892803i | \(0.648735\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.986492 | + | 0.569551i | 0.154064 | + | 0.0889490i | 0.575050 | − | 0.818118i | \(-0.304983\pi\) |
−0.420986 | + | 0.907067i | \(0.638316\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.79101 | − | 3.92079i | 1.03562 | − | 0.597915i | 0.117030 | − | 0.993128i | \(-0.462663\pi\) |
0.918590 | + | 0.395213i | \(0.129329\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.01076 | + | 5.21479i | 0.439165 | + | 0.760656i | 0.997625 | − | 0.0688755i | \(-0.0219411\pi\) |
−0.558461 | + | 0.829531i | \(0.688608\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.72990 | − | 15.1206i | 1.24713 | − | 2.16009i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.71390i | 1.33431i | 0.744920 | + | 0.667154i | \(0.232488\pi\) | ||||
−0.744920 | + | 0.667154i | \(0.767512\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.08011i | 0.145642i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.15776 | − | 7.20145i | 0.541294 | − | 0.937548i | −0.457536 | − | 0.889191i | \(-0.651268\pi\) |
0.998830 | − | 0.0483574i | \(-0.0153986\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.63407 | + | 4.56234i | 0.337258 | + | 0.584147i | 0.983916 | − | 0.178633i | \(-0.0571674\pi\) |
−0.646658 | + | 0.762780i | \(0.723834\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0306232 | + | 0.0176803i | −0.00379834 | + | 0.00219297i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.84450 | − | 1.06492i | −0.225342 | − | 0.130101i | 0.383079 | − | 0.923715i | \(-0.374864\pi\) |
−0.608421 | + | 0.793614i | \(0.708197\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6650 | 1.26570 | 0.632851 | − | 0.774273i | \(-0.281885\pi\) | ||||
0.632851 | + | 0.774273i | \(0.281885\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.51416 | −0.879466 | −0.439733 | − | 0.898129i | \(-0.644927\pi\) | ||||
−0.439733 | + | 0.898129i | \(0.644927\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.0630 | + | 5.80990i | 1.14679 | + | 0.662100i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.52870 | + | 1.45994i | −0.284501 | + | 0.164256i | −0.635459 | − | 0.772135i | \(-0.719189\pi\) |
0.350959 | + | 0.936391i | \(0.385856\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.44322 | + | 7.69588i | 0.487706 | + | 0.844732i | 0.999900 | − | 0.0141378i | \(-0.00450034\pi\) |
−0.512194 | + | 0.858870i | \(0.671167\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.36275 | − | 2.36035i | 0.147811 | − | 0.256016i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.71390i | − | 1.02967i | −0.857289 | − | 0.514836i | \(-0.827853\pi\) | ||
0.857289 | − | 0.514836i | \(-0.172147\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.380408i | 0.0398776i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.826493 | + | 1.43153i | −0.0847964 | + | 0.146872i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.16305 | + | 5.47856i | 0.321159 | + | 0.556263i | 0.980727 | − | 0.195381i | \(-0.0625944\pi\) |
−0.659569 | + | 0.751644i | \(0.729261\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.50085 | + | 2.59857i | −0.447851 | + | 0.258567i | −0.706922 | − | 0.707291i | \(-0.749917\pi\) |
0.259071 | + | 0.965858i | \(0.416584\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.41781 | − | 1.39593i | −0.238234 | − | 0.137545i | 0.376131 | − | 0.926567i | \(-0.377254\pi\) |
−0.614365 | + | 0.789022i | \(0.710588\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.5911 | −1.41057 | −0.705286 | − | 0.708923i | \(-0.749181\pi\) | ||||
−0.705286 | + | 0.708923i | \(0.749181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.6711 | −1.21368 | −0.606838 | − | 0.794826i | \(-0.707562\pi\) | ||||
−0.606838 | + | 0.794826i | \(0.707562\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.5820 | − | 9.57360i | −1.55990 | − | 0.900608i | −0.997265 | − | 0.0739025i | \(-0.976455\pi\) |
−0.562634 | − | 0.826706i | \(-0.690212\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.92273 | + | 1.11009i | −0.179296 | + | 0.103517i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.6604 | − | 25.3926i | −1.34392 | − | 2.32773i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.73996 | − | 4.74576i | 0.249088 | − | 0.431432i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 4.50008i | − | 0.402499i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2364i | 0.997071i | 0.866869 | + | 0.498535i | \(0.166129\pi\) | ||||
−0.866869 | + | 0.498535i | \(0.833871\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.54434 | + | 13.0672i | −0.659152 | + | 1.14168i | 0.321684 | + | 0.946847i | \(0.395751\pi\) |
−0.980836 | + | 0.194837i | \(0.937582\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.89137 | + | 15.4003i | 0.770979 | + | 1.33538i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.11622 | − | 1.79915i | 0.266237 | − | 0.153712i | −0.360939 | − | 0.932589i | \(-0.617544\pi\) |
0.627176 | + | 0.778877i | \(0.284211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.13766 | − | 3.54358i | −0.520590 | − | 0.300563i | 0.216586 | − | 0.976264i | \(-0.430508\pi\) |
−0.737176 | + | 0.675701i | \(0.763841\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.180716 | −0.0151122 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.47678 | 0.288731 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.985645 | − | 0.569062i | −0.0807472 | − | 0.0466194i | 0.459083 | − | 0.888393i | \(-0.348178\pi\) |
−0.539830 | + | 0.841774i | \(0.681511\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.68181 | − | 5.58979i | 0.787894 | − | 0.454891i | −0.0513265 | − | 0.998682i | \(-0.516345\pi\) |
0.839221 | + | 0.543791i | \(0.183012\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.176086 | + | 0.304990i | 0.0141436 | + | 0.0244974i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.18986 | + | 14.1853i | −0.653622 | + | 1.13211i | 0.328615 | + | 0.944464i | \(0.393418\pi\) |
−0.982237 | + | 0.187643i | \(0.939915\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.8846i | 1.88237i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.04520i | 0.316845i | 0.987371 | + | 0.158422i | \(0.0506408\pi\) | ||||
−0.987371 | + | 0.158422i | \(0.949359\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.58072 | − | 2.73790i | 0.122320 | − | 0.211865i | −0.798362 | − | 0.602178i | \(-0.794300\pi\) |
0.920682 | + | 0.390313i | \(0.127633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.49704 | + | 11.2532i | 0.499772 | + | 0.865631i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.4056 | + | 10.0491i | −1.32333 | + | 0.764022i | −0.984258 | − | 0.176739i | \(-0.943445\pi\) |
−0.339068 | + | 0.940762i | \(0.610112\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.5102 | − | 11.8416i | −1.55043 | − | 0.895140i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.1699 | −0.760135 | −0.380067 | − | 0.924959i | \(-0.624099\pi\) | ||||
−0.380067 | + | 0.924959i | \(0.624099\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.0572 | 1.11920 | 0.559598 | − | 0.828764i | \(-0.310956\pi\) | ||||
0.559598 | + | 0.828764i | \(0.310956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.18174 | − | 1.25963i | −0.160404 | − | 0.0926095i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0629 | − | 6.96454i | 0.882129 | − | 0.509297i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.41193 | + | 2.44554i | 0.102164 | + | 0.176953i | 0.912576 | − | 0.408907i | \(-0.134090\pi\) |
−0.810412 | + | 0.585860i | \(0.800757\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.95170 | + | 15.5048i | −0.644357 | + | 1.11606i | 0.340092 | + | 0.940392i | \(0.389542\pi\) |
−0.984450 | + | 0.175668i | \(0.943792\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.65685i | − | 0.403034i | −0.979485 | − | 0.201517i | \(-0.935413\pi\) | ||
0.979485 | − | 0.201517i | \(-0.0645872\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.78022i | 0.480637i | 0.970694 | + | 0.240319i | \(0.0772519\pi\) | ||||
−0.970694 | + | 0.240319i | \(0.922748\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.7015 | − | 32.3919i | 1.31259 | − | 2.27347i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.261836 | + | 0.453514i | 0.0182874 | + | 0.0316748i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.31603 | + | 4.22391i | −0.506060 | + | 0.292174i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.2250 | − | 8.21281i | −0.979289 | − | 0.565393i | −0.0772337 | − | 0.997013i | \(-0.524609\pi\) |
−0.902055 | + | 0.431620i | \(0.857942\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.60496 | 0.245856 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.78865 | 0.257191 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.394915 | + | 0.228004i | 0.0265649 | + | 0.0153372i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.5026 | + | 7.79574i | −0.904202 | + | 0.522041i | −0.878561 | − | 0.477630i | \(-0.841496\pi\) |
−0.0256409 | + | 0.999671i | \(0.508163\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.25723 | − | 3.90964i | −0.149818 | − | 0.259492i | 0.781342 | − | 0.624103i | \(-0.214535\pi\) |
−0.931160 | + | 0.364611i | \(0.881202\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.77842 | − | 4.81237i | 0.183603 | − | 0.318010i | −0.759502 | − | 0.650505i | \(-0.774557\pi\) |
0.943105 | + | 0.332495i | \(0.107890\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.32613i | − | 0.0868780i | −0.999056 | − | 0.0434390i | \(-0.986169\pi\) | ||
0.999056 | − | 0.0434390i | \(-0.0138314\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.76824i | 0.180580i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.1286 | + | 21.0073i | −0.784534 | + | 1.35885i | 0.144744 | + | 0.989469i | \(0.453764\pi\) |
−0.929277 | + | 0.369383i | \(0.879569\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.00711 | − | 5.20846i | −0.193705 | − | 0.335507i | 0.752770 | − | 0.658283i | \(-0.228717\pi\) |
−0.946475 | + | 0.322777i | \(0.895384\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.95131 | − | 4.01334i | 0.444103 | − | 0.256403i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.239511 | − | 0.138282i | −0.0152397 | − | 0.00879867i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.7656 | −0.805760 | −0.402880 | − | 0.915253i | \(-0.631991\pi\) | ||||
−0.402880 | + | 0.915253i | \(0.631991\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.3466 | −0.713352 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.4638 | + | 6.61864i | 0.715094 | + | 0.412860i | 0.812944 | − | 0.582342i | \(-0.197863\pi\) |
−0.0978505 | + | 0.995201i | \(0.531197\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.4710 | + | 13.5510i | −1.45842 | + | 0.842018i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.76791 | − | 6.52622i | −0.232340 | − | 0.402424i | 0.726157 | − | 0.687529i | \(-0.241305\pi\) |
−0.958496 | + | 0.285105i | \(0.907971\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.23286 | + | 3.86742i | −0.137163 | + | 0.237574i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.40793i | 0.390699i | 0.980734 | + | 0.195349i | \(0.0625840\pi\) | ||||
−0.980734 | + | 0.195349i | \(0.937416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.53211i | 0.336051i | 0.985783 | + | 0.168026i | \(0.0537392\pi\) | ||||
−0.985783 | + | 0.168026i | \(0.946261\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.62543 | − | 9.74353i | 0.339226 | − | 0.587557i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.1627 | − | 17.6023i | −0.610616 | − | 1.05762i | −0.991137 | − | 0.132846i | \(-0.957588\pi\) |
0.380520 | − | 0.924773i | \(-0.375745\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.20013 | + | 3.57965i | −0.369869 | + | 0.213544i | −0.673401 | − | 0.739277i | \(-0.735167\pi\) |
0.303532 | + | 0.952821i | \(0.401834\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.4042 | + | 6.00686i | 0.618465 | + | 0.357071i | 0.776271 | − | 0.630399i | \(-0.217109\pi\) |
−0.157806 | + | 0.987470i | \(0.550442\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.63364 | 0.332543 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.1479 | −1.06752 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.6573 | − | 11.9265i | −1.20681 | − | 0.696752i | −0.244749 | − | 0.969586i | \(-0.578706\pi\) |
−0.962061 | + | 0.272834i | \(0.912039\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.31067 | − | 1.91142i | 0.192755 | − | 0.111287i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.185731 | − | 0.321696i | −0.0107411 | − | 0.0186042i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.3910 | − | 33.5862i | 1.11768 | − | 1.93588i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.42188i | 0.138677i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.1729i | 0.751818i | 0.926657 | + | 0.375909i | \(0.122669\pi\) | ||||
−0.926657 | + | 0.375909i | \(0.877331\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.14825 | − | 1.98883i | 0.0651114 | − | 0.112776i | −0.831632 | − | 0.555327i | \(-0.812593\pi\) |
0.896743 | + | 0.442551i | \(0.145926\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.36557 | + | 7.56139i | 0.246757 | + | 0.427395i | 0.962624 | − | 0.270841i | \(-0.0873018\pi\) |
−0.715867 | + | 0.698236i | \(0.753968\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.23728 | + | 2.44640i | −0.237990 | + | 0.137403i | −0.614252 | − | 0.789110i | \(-0.710542\pi\) |
0.376263 | + | 0.926513i | \(0.377209\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.3880 | + | 8.88428i | 0.861564 | + | 0.497424i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.3168 | 1.18610 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.368330 | 0.0204313 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.7907 | + | 14.8903i | 1.42189 | + | 0.820927i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.14019 | + | 1.81299i | −0.172601 | + | 0.0996511i | −0.583812 | − | 0.811889i | \(-0.698439\pi\) |
0.411211 | + | 0.911540i | \(0.365106\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.489571 | − | 0.847962i | −0.0267481 | − | 0.0463291i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.75655 | + | 8.23858i | −0.259106 | + | 0.448784i | −0.966003 | − | 0.258532i | \(-0.916761\pi\) |
0.706897 | + | 0.707317i | \(0.250094\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.79983i | 0.0974661i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 51.7308i | − | 2.79320i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.42602 | + | 4.20199i | −0.130236 | + | 0.225575i | −0.923767 | − | 0.382954i | \(-0.874907\pi\) |
0.793532 | + | 0.608529i | \(0.208240\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.40121 | + | 7.62312i | 0.235591 | + | 0.408056i | 0.959444 | − | 0.281898i | \(-0.0909640\pi\) |
−0.723853 | + | 0.689954i | \(0.757631\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.5392 | − | 9.54894i | 0.880295 | − | 0.508239i | 0.00953954 | − | 0.999954i | \(-0.496963\pi\) |
0.870756 | + | 0.491716i | \(0.163630\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.24608 | + | 2.45148i | 0.225359 | + | 0.130111i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.99319 | 0.263531 | 0.131765 | − | 0.991281i | \(-0.457935\pi\) | ||||
0.131765 | + | 0.991281i | \(0.457935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.07161 | 0.319558 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.99163 | − | 1.72722i | −0.156589 | − | 0.0904067i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.30108 | − | 3.06058i | 0.276714 | − | 0.159761i | −0.355221 | − | 0.934782i | \(-0.615594\pi\) |
0.631935 | + | 0.775021i | \(0.282261\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.0210 | + | 41.6055i | 1.24711 | + | 2.16005i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.06426 | + | 3.57540i | −0.106883 | + | 0.185127i | −0.914506 | − | 0.404572i | \(-0.867420\pi\) |
0.807623 | + | 0.589699i | \(0.200754\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.581706i | 0.0299594i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 28.0527i | − | 1.44097i | −0.693470 | − | 0.720485i | \(-0.743919\pi\) | ||
0.693470 | − | 0.720485i | \(-0.256081\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.13318 | + | 14.0871i | −0.415586 | + | 0.719816i | −0.995490 | − | 0.0948689i | \(-0.969757\pi\) |
0.579904 | + | 0.814685i | \(0.303090\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.67095 | + | 4.62622i | 0.136124 | + | 0.235774i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.3063 | − | 18.0747i | 1.58729 | − | 0.916424i | 0.593542 | − | 0.804803i | \(-0.297729\pi\) |
0.993751 | − | 0.111621i | \(-0.0356042\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.7955 | + | 14.3157i | 1.25396 | + | 0.723974i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.34234 | −0.0675405 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.9550 | 1.65396 | 0.826982 | − | 0.562229i | \(-0.190056\pi\) | ||||
0.826982 | + | 0.562229i | \(0.190056\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.54505 | + | 3.77879i | 0.326844 | + | 0.188704i | 0.654439 | − | 0.756115i | \(-0.272905\pi\) |
−0.327595 | + | 0.944818i | \(0.606238\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0510285 | + | 0.0294613i | −0.00254191 | + | 0.00146757i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.43750 | − | 11.1501i | −0.319095 | − | 0.552689i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.05684 | + | 7.02666i | −0.200598 | + | 0.347446i | −0.948721 | − | 0.316114i | \(-0.897622\pi\) |
0.748123 | + | 0.663560i | \(0.230955\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 41.1259i | − | 2.02367i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.08530i | 0.200540i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.99038 | + | 10.3756i | −0.292649 | + | 0.506883i | −0.974435 | − | 0.224668i | \(-0.927870\pi\) |
0.681786 | + | 0.731552i | \(0.261203\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.5646 | − | 21.7626i | −0.612363 | − | 1.06064i | −0.990841 | − | 0.135034i | \(-0.956886\pi\) |
0.378478 | − | 0.925610i | \(-0.376448\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.5863 | + | 14.1949i | −1.19261 | + | 0.688555i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.5639 | + | 13.0273i | 1.09194 | + | 0.630433i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.7211 | 0.901763 | 0.450881 | − | 0.892584i | \(-0.351110\pi\) | ||||
0.450881 | + | 0.892584i | \(0.351110\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.06315 | −0.0991487 | −0.0495744 | − | 0.998770i | \(-0.515786\pi\) | ||||
−0.0495744 | + | 0.998770i | \(0.515786\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.0382 | − | 8.68228i | −0.719372 | − | 0.415330i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.4517 | − | 12.9625i | 1.07156 | − | 0.618665i | 0.142952 | − | 0.989730i | \(-0.454340\pi\) |
0.928607 | + | 0.371065i | \(0.121007\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.25888 | − | 12.5727i | −0.344880 | − | 0.597349i | 0.640452 | − | 0.767998i | \(-0.278747\pi\) |
−0.985332 | + | 0.170649i | \(0.945414\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.23286 | − | 3.86742i | 0.105848 | − | 0.183333i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 14.4797i | − | 0.683341i | −0.939820 | − | 0.341670i | \(-0.889007\pi\) | ||
0.939820 | − | 0.341670i | \(-0.110993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.67630i | 0.126022i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0874413 | + | 0.151453i | −0.00409931 | + | 0.00710021i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.7269 | − | 22.0437i | −0.595341 | − | 1.03116i | −0.993499 | − | 0.113844i | \(-0.963684\pi\) |
0.398158 | − | 0.917317i | \(-0.369650\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.81422 | − | 1.04744i | 0.0844966 | − | 0.0487841i | −0.457156 | − | 0.889386i | \(-0.651132\pi\) |
0.541653 | + | 0.840602i | \(0.317799\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.82478 | + | 2.78559i | 0.224226 | + | 0.129457i | 0.607906 | − | 0.794009i | \(-0.292010\pi\) |
−0.383679 | + | 0.923466i | \(0.625343\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.0574 | −1.80736 | −0.903680 | − | 0.428208i | \(-0.859145\pi\) | ||||
−0.903680 | + | 0.428208i | \(0.859145\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.5336 | −0.486395 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.9554 | + | 9.21184i | 0.733629 | + | 0.423561i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.9113 | − | 8.60906i | 0.684179 | − | 0.395011i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.8390 | + | 27.4340i | 0.723703 | + | 1.25349i | 0.959506 | + | 0.281689i | \(0.0908947\pi\) |
−0.235803 | + | 0.971801i | \(0.575772\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.210750 | − | 0.365030i | 0.00960938 | − | 0.0166439i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.90825i | 0.132057i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.3903i | 1.51306i | 0.653961 | + | 0.756528i | \(0.273106\pi\) | ||||
−0.653961 | + | 0.756528i | \(0.726894\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.52060 | + | 16.4902i | −0.429659 | + | 0.744190i | −0.996843 | − | 0.0794005i | \(-0.974699\pi\) |
0.567184 | + | 0.823591i | \(0.308033\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.4182 | − | 38.8294i | −1.00966 | − | 1.74879i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 45.6791 | − | 26.3729i | 2.04899 | − | 1.18298i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.8684 | + | 10.8937i | 0.844664 | + | 0.487667i | 0.858847 | − | 0.512232i | \(-0.171181\pi\) |
−0.0141827 | + | 0.999899i | \(0.504515\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.6101 | −0.963547 | −0.481774 | − | 0.876296i | \(-0.660007\pi\) | ||||
−0.481774 | + | 0.876296i | \(0.660007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.38924 | −0.106320 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.5799 | − | 13.0365i | −1.00084 | − | 0.577834i | −0.0923421 | − | 0.995727i | \(-0.529435\pi\) |
−0.908496 | + | 0.417893i | \(0.862769\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.1838 | + | 18.5813i | −1.42373 | + | 0.821989i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.641740 | − | 1.11153i | −0.0282784 | − | 0.0489797i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.07373 | + | 12.2521i | −0.311102 | + | 0.538845i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 0.184295i | − | 0.00807410i | −0.999992 | − | 0.00403705i | \(-0.998715\pi\) | ||
0.999992 | − | 0.00403705i | \(-0.00128504\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 28.9997i | − | 1.26807i | −0.773304 | − | 0.634035i | \(-0.781397\pi\) | ||
0.773304 | − | 0.634035i | \(-0.218603\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.27080 | − | 3.93314i | 0.0989175 | − | 0.171330i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.161471 | − | 0.279677i | −0.00702050 | − | 0.0121599i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0758781 | + | 0.0438083i | −0.00328665 | + | 0.00189755i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.80918 | − | 3.35393i | −0.251153 | − | 0.145003i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41.0215 | 1.76692 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.1108 | 1.72450 | 0.862249 | − | 0.506484i | \(-0.169055\pi\) | ||||
0.862249 | + | 0.506484i | \(0.169055\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.04479 | − | 2.91261i | −0.216095 | − | 0.124763i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.7795 | − | 10.2650i | 0.760198 | − | 0.438901i | −0.0691687 | − | 0.997605i | \(-0.522035\pi\) |
0.829367 | + | 0.558704i | \(0.188701\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.5963 | + | 23.5496i | 0.579224 | + | 1.00325i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.22042 | + | 12.5061i | −0.307043 | + | 0.531815i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.23121i | 0.0521682i | 0.999660 | + | 0.0260841i | \(0.00830378\pi\) | ||||
−0.999660 | + | 0.0260841i | \(0.991696\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.603152i | 0.0255106i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.8990 | − | 18.8776i | 0.459337 | − | 0.795595i | −0.539589 | − | 0.841928i | \(-0.681420\pi\) |
0.998926 | + | 0.0463337i | \(0.0147538\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.40121 | − | 7.62312i | −0.185160 | − | 0.320707i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.3575 | + | 8.28931i | −0.601898 | + | 0.347506i | −0.769788 | − | 0.638300i | \(-0.779638\pi\) |
0.167890 | + | 0.985806i | \(0.446305\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.452356 | + | 0.261168i | 0.0189305 | + | 0.0109295i | 0.509435 | − | 0.860509i | \(-0.329854\pi\) |
−0.490505 | + | 0.871438i | \(0.663188\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.1262 | 0.964431 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.5966 | 1.44028 | 0.720139 | − | 0.693830i | \(-0.244078\pi\) | ||||
0.720139 | + | 0.693830i | \(0.244078\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.0614 | + | 21.9747i | 1.57905 | + | 0.911666i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.7650 | + | 11.4113i | −0.818583 | + | 0.472609i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.942362 | − | 1.63222i | −0.0388955 | − | 0.0673689i | 0.845922 | − | 0.533306i | \(-0.179051\pi\) |
−0.884818 | + | 0.465937i | \(0.845717\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.37721 | + | 2.38540i | −0.0567470 | + | 0.0982887i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.7478i | 1.09840i | 0.835691 | + | 0.549199i | \(0.185067\pi\) | ||||
−0.835691 | + | 0.549199i | \(0.814933\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 13.4795i | − | 0.552605i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.7506 | − | 20.3527i | 0.480118 | − | 0.831589i | −0.519622 | − | 0.854396i | \(-0.673927\pi\) |
0.999740 | + | 0.0228075i | \(0.00726050\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.49651 | − | 14.7164i | −0.346580 | − | 0.600294i | 0.639060 | − | 0.769157i | \(-0.279324\pi\) |
−0.985640 | + | 0.168863i | \(0.945990\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.18174 | − | 1.25963i | 0.0887002 | − | 0.0512111i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.5877 | − | 9.57694i | −0.673276 | − | 0.388716i | 0.124041 | − | 0.992277i | \(-0.460415\pi\) |
−0.797317 | + | 0.603561i | \(0.793748\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.463158 | −0.0187374 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.5441 | −0.668211 | −0.334106 | − | 0.942536i | \(-0.608434\pi\) | ||||
−0.334106 | + | 0.942536i | \(0.608434\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.4744 | − | 15.8624i | −1.10608 | − | 0.638595i | −0.168268 | − | 0.985741i | \(-0.553817\pi\) |
−0.937811 | + | 0.347146i | \(0.887151\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.46158 | − | 4.88529i | 0.340099 | − | 0.196356i | −0.320217 | − | 0.947344i | \(-0.603756\pi\) |
0.660316 | + | 0.750988i | \(0.270422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.0210 | − | 41.6055i | −0.962379 | − | 1.66689i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.9372 | + | 18.9439i | −0.437490 | + | 0.757754i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.4881i | 1.29539i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 23.9365i | − | 0.952896i | −0.879203 | − | 0.476448i | \(-0.841924\pi\) | ||
0.879203 | − | 0.476448i | \(-0.158076\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.58282 | + | 4.47358i | −0.102496 | + | 0.177529i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.671479 | + | 1.16304i | 0.0266050 | + | 0.0460811i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.947835 | + | 0.547233i | −0.0374372 | + | 0.0216144i | −0.518602 | − | 0.855016i | \(-0.673547\pi\) |
0.481165 | + | 0.876630i | \(0.340214\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.4240 | − | 17.5653i | −1.19981 | − | 0.692708i | −0.239294 | − | 0.970947i | \(-0.576916\pi\) |
−0.960512 | + | 0.278239i | \(0.910249\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.2369 | 1.46393 | 0.731966 | − | 0.681341i | \(-0.238603\pi\) | ||||
0.731966 | + | 0.681341i | \(0.238603\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.5372 | 0.766901 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.6290 | + | 20.5704i | 1.39427 | + | 0.804982i | 0.993784 | − | 0.111322i | \(-0.0355085\pi\) |
0.400484 | + | 0.916304i | \(0.368842\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.00729 | + | 3.46831i | −0.234724 | + | 0.135518i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.31389 | + | 16.1321i | 0.362818 | + | 0.628419i | 0.988423 | − | 0.151721i | \(-0.0484815\pi\) |
−0.625606 | + | 0.780139i | \(0.715148\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.50846 | + | 2.61273i | −0.0586722 | + | 0.101623i | −0.893870 | − | 0.448327i | \(-0.852020\pi\) |
0.835197 | + | 0.549950i | \(0.185353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.17514i | 0.317019i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.5234i | 1.41419i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.18869 | + | 10.7191i | −0.238912 | + | 0.413808i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.1646 | − | 24.5337i | −0.546004 | − | 0.945706i | −0.998543 | − | 0.0539618i | \(-0.982815\pi\) |
0.452539 | − | 0.891744i | \(-0.350518\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.8629 | + | 12.6226i | −0.840260 | + | 0.485124i | −0.857353 | − | 0.514730i | \(-0.827892\pi\) |
0.0170927 | + | 0.999854i | \(0.494559\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.0952 | + | 15.6434i | 1.03982 | + | 0.600340i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.12320 | −0.349089 | −0.174545 | − | 0.984649i | \(-0.555845\pi\) | ||||
−0.174545 | + | 0.984649i | \(0.555845\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.65423 | 0.0632047 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.647065 | − | 0.373583i | −0.0246512 | − | 0.0142324i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.6272 | + | 23.4561i | −1.54553 | + | 0.892313i | −0.547058 | + | 0.837095i | \(0.684252\pi\) |
−0.998474 | + | 0.0552184i | \(0.982415\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.62907 | − | 2.82163i | −0.0617941 | − | 0.107030i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.37662 | − | 5.84848i | 0.127899 | − | 0.221527i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.2915i | − | 0.539783i | −0.962891 | − | 0.269892i | \(-0.913012\pi\) | ||
0.962891 | − | 0.269892i | \(-0.0869879\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 19.7037i | − | 0.743138i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.8517 | + | 22.2598i | −0.483337 | + | 0.837165i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.4700 | + | 35.4551i | 0.768768 | + | 1.33155i | 0.938231 | + | 0.346009i | \(0.112463\pi\) |
−0.169463 | + | 0.985537i | \(0.554203\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.20391 | + | 1.84978i | −0.119988 | + | 0.0692748i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0719487 | − | 0.0415396i | −0.00269073 | − | 0.00155349i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −51.0710 | −1.90463 | −0.952313 | − | 0.305123i | \(-0.901303\pi\) | ||||
−0.952313 | + | 0.305123i | \(0.901303\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.8076 | −0.514222 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −31.3635 | − | 18.1077i | −1.16481 | − | 0.672503i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.0591 | + | 13.3132i | −0.855213 | + | 0.493758i | −0.862406 | − | 0.506216i | \(-0.831044\pi\) |
0.00719304 | + | 0.999974i | \(0.497710\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.2447 | − | 40.2610i | −0.859736 | − | 1.48911i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.7287 | + | 37.6352i | −0.802567 | + | 1.39009i | 0.115354 | + | 0.993324i | \(0.463200\pi\) |
−0.917921 | + | 0.396763i | \(0.870134\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 5.00405i | − | 0.184326i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.24313i | 0.0825150i | 0.999149 | + | 0.0412575i | \(0.0131364\pi\) | ||||
−0.999149 | + | 0.0412575i | \(0.986864\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.4331 | − | 38.8553i | 0.822991 | − | 1.42546i | −0.0804542 | − | 0.996758i | \(-0.525637\pi\) |
0.903445 | − | 0.428704i | \(-0.141030\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.261611 | − | 0.453124i | −0.00958470 | − | 0.0166012i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −62.4949 | + | 36.0814i | −2.28351 | + | 1.31839i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.6400 | + | 14.2259i | 0.899128 | + | 0.519112i | 0.876917 | − | 0.480642i | \(-0.159596\pi\) |
0.0222105 | + | 0.999753i | \(0.492930\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.13952 | 0.187046 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.8913 | −0.650269 | −0.325135 | − | 0.945668i | \(-0.605410\pi\) | ||||
−0.325135 | + | 0.945668i | \(0.605410\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.80178 | + | 2.77231i | 0.174064 | + | 0.100496i | 0.584501 | − | 0.811393i | \(-0.301290\pi\) |
−0.410437 | + | 0.911889i | \(0.634624\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −54.2716 | + | 31.3337i | −1.96476 | + | 1.13436i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.319803 | + | 0.553915i | 0.0115474 | + | 0.0200007i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.3305 | − | 19.6250i | 0.408589 | − | 0.707696i | −0.586143 | − | 0.810207i | \(-0.699354\pi\) |
0.994732 | + | 0.102511i | \(0.0326878\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 20.9941i | − | 0.755105i | −0.925988 | − | 0.377552i | \(-0.876766\pi\) | ||
0.925988 | − | 0.377552i | \(-0.123234\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.66836i | − | 0.131771i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.04788 | + | 3.54704i | −0.0733730 | + | 0.127086i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.5286 | + | 21.7002i | 0.448309 | + | 0.776494i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.52130 | + | 3.76507i | −0.232755 | + | 0.134381i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.4280 | + | 6.59793i | 0.407363 | + | 0.235191i | 0.689656 | − | 0.724137i | \(-0.257762\pi\) |
−0.282293 | + | 0.959328i | \(0.591095\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −94.6960 | −3.36700 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.405210 | −0.0143894 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.2431 | + | 24.9664i | 1.53175 | + | 0.884356i | 0.999281 | + | 0.0379066i | \(0.0120689\pi\) |
0.532469 | + | 0.846450i | \(0.321264\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.9162 | − | 17.8495i | 1.09374 | − | 0.631470i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.82719 | − | 15.2891i | −0.311505 | − | 0.539542i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.49016 | + | 9.50923i | −0.193503 | + | 0.335156i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 38.4167i | − | 1.35066i | −0.737516 | − | 0.675329i | \(-0.764001\pi\) | ||
0.737516 | − | 0.675329i | \(-0.235999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.98092i | − | 0.315363i | −0.987490 | − | 0.157681i | \(-0.949598\pi\) | ||
0.987490 | − | 0.157681i | \(-0.0504019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.929838 | + | 1.61053i | −0.0325708 | + | 0.0564143i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.0976 | + | 24.4178i | 0.493214 | + | 0.854271i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.8738 | − | 28.2173i | 1.70571 | − | 0.984792i | 0.765984 | − | 0.642859i | \(-0.222252\pi\) |
0.939725 | − | 0.341932i | \(-0.111081\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.6509 | − | 20.5831i | −1.24271 | − | 0.717481i | −0.273068 | − | 0.961995i | \(-0.588038\pi\) |
−0.969646 | + | 0.244514i | \(0.921372\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.24168 | 0.217044 | 0.108522 | − | 0.994094i | \(-0.465388\pi\) | ||||
0.108522 | + | 0.994094i | \(0.465388\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.2083 | −1.15337 | −0.576686 | − | 0.816966i | \(-0.695654\pi\) | ||||
−0.576686 | + | 0.816966i | \(0.695654\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −89.6437 | − | 51.7558i | −3.10597 | − | 1.79323i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.25868 | − | 0.726697i | 0.0435583 | − | 0.0251484i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.9352 | + | 20.6724i | 0.412049 | + | 0.713690i | 0.995114 | − | 0.0987356i | \(-0.0314798\pi\) |
−0.583064 | + | 0.812426i | \(0.698146\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0976 | − | 24.4178i | 0.486125 | − | 0.841994i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.97369i | 0.205501i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 27.1020i | − | 0.931235i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.2323 | − | 22.9191i | 0.453599 | − | 0.785656i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.5841 | + | 33.9206i | 0.670545 | + | 1.16142i | 0.977750 | + | 0.209775i | \(0.0672731\pi\) |
−0.307205 | + | 0.951644i | \(0.599394\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.87557 | + | 5.12431i | −0.303184 | + | 0.175043i | −0.643872 | − | 0.765133i | \(-0.722673\pi\) |
0.340689 | + | 0.940176i | \(0.389340\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.6163 | − | 7.86135i | −0.464581 | − | 0.268226i | 0.249388 | − | 0.968404i | \(-0.419771\pi\) |
−0.713968 | + | 0.700178i | \(0.753104\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.0370 | 1.09055 | 0.545276 | − | 0.838257i | \(-0.316425\pi\) | ||||
0.545276 | + | 0.838257i | \(0.316425\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.23966 | −0.314158 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.94113 | − | 3.43011i | −0.201539 | − | 0.116359i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.141874 | − | 0.0819110i | 0.00480722 | − | 0.00277545i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.1280 | − | 19.2742i | −0.376194 | − | 0.651588i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.3684 | + | 31.8149i | −0.620255 | + | 1.07431i | 0.369183 | + | 0.929357i | \(0.379638\pi\) |
−0.989438 | + | 0.144957i | \(0.953696\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.9995i | 1.51607i | 0.652213 | + | 0.758036i | \(0.273841\pi\) | ||||
−0.652213 | + | 0.758036i | \(0.726159\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 28.0715i | − | 0.944680i | −0.881416 | − | 0.472340i | \(-0.843409\pi\) | ||
0.881416 | − | 0.472340i | \(-0.156591\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.4625 | + | 23.3177i | −0.452025 | + | 0.782930i | −0.998512 | − | 0.0545375i | \(-0.982632\pi\) |
0.546487 | + | 0.837468i | \(0.315965\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.7859 | + | 48.1266i | 0.931909 | + | 1.61411i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.7503 | + | 10.8255i | −0.627456 | + | 0.362262i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.04897 | − | 2.33767i | −0.135342 | − | 0.0781398i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.79347 | 0.193223 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 57.5895 | 1.91859 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.99477 | + | 3.46108i | 0.199273 | + | 0.115050i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.49526 | + | 3.17269i | −0.182467 | + | 0.105347i | −0.588451 | − | 0.808533i | \(-0.700262\pi\) |
0.405984 | + | 0.913880i | \(0.366929\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.6552 | + | 20.1874i | 0.386154 | + | 0.668838i | 0.991929 | − | 0.126798i | \(-0.0404701\pi\) |
−0.605775 | + | 0.795636i | \(0.707137\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.4393 | + | 18.0813i | −0.345489 | + | 0.598405i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 74.6238i | 2.46430i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.2387i | 0.535664i | 0.963466 | + | 0.267832i | \(0.0863072\pi\) | ||||
−0.963466 | + | 0.267832i | \(0.913693\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.410161 | + | 0.710419i | −0.0135006 | + | 0.0233837i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.1207 | + | 22.7258i | 0.431407 | + | 0.747219i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.64731 | + | 2.10577i | −0.119664 | + | 0.0690882i | −0.558637 | − | 0.829412i | \(-0.688676\pi\) |
0.438973 | + | 0.898500i | \(0.355342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 54.3678 | + | 31.3893i | 1.78183 | + | 1.02874i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.40352 | 0.209418 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.9154 | 1.40198 | 0.700992 | − | 0.713169i | \(-0.252741\pi\) | ||||
0.700992 | + | 0.713169i | \(0.252741\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.89739 | + | 3.40486i | 0.192249 | + | 0.110995i | 0.593035 | − | 0.805177i | \(-0.297929\pi\) |
−0.400786 | + | 0.916172i | \(0.631263\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.76415 | + | 2.75058i | −0.155142 | + | 0.0895713i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.8163 | − | 41.2511i | −0.773927 | − | 1.34048i | −0.935395 | − | 0.353603i | \(-0.884956\pi\) |
0.161468 | − | 0.986878i | \(-0.448377\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.288984 | − | 0.500535i | 0.00938081 | − | 0.0162480i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 56.0644i | − | 1.81610i | −0.418859 | − | 0.908051i | \(-0.637570\pi\) | ||
0.418859 | − | 0.908051i | \(-0.362430\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.29820i | 0.0420088i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.89804 | − | 15.4119i | 0.287333 | − | 0.497675i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.2066 | − | 26.3386i | −0.490535 | − | 0.849631i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.12792 | + | 4.11531i | −0.229456 | + | 0.132476i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.10910 | − | 3.52709i | −0.196455 | − | 0.113424i | 0.398546 | − | 0.917149i | \(-0.369515\pi\) |
−0.595001 | + | 0.803725i | \(0.702848\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.2137 | 1.06588 | 0.532939 | − | 0.846153i | \(-0.321087\pi\) | ||||
0.532939 | + | 0.846153i | \(0.321087\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.0509 | −1.12368 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.7166 | + | 6.76456i | 0.374846 | + | 0.216418i | 0.675574 | − | 0.737293i | \(-0.263896\pi\) |
−0.300727 | + | 0.953710i | \(0.597229\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.7650 | − | 11.4113i | 0.631692 | − | 0.364708i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.59692 | − | 7.96210i | −0.146619 | − | 0.253952i | 0.783357 | − | 0.621572i | \(-0.213506\pi\) |
−0.929976 | + | 0.367621i | \(0.880172\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.30029 | − | 2.25218i | 0.0414308 | − | 0.0717603i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.8700i | 1.20420i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.2577i | 0.929402i | 0.885468 | + | 0.464701i | \(0.153838\pi\) | ||||
−0.885468 | + | 0.464701i | \(0.846162\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.55851 | + | 2.69943i | −0.0494082 | + | 0.0855775i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.1497 | − | 43.5606i | −0.796500 | − | 1.37958i | −0.921883 | − | 0.387469i | \(-0.873349\pi\) |
0.125383 | − | 0.992108i | \(-0.459984\pi\) | |||||||
\(998\) | 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 | 864.2.s.a.287.8 | 24 | ||
3.2 | odd | 2 | 288.2.s.a.95.10 | yes | 24 | ||
4.3 | odd | 2 | inner | 864.2.s.a.287.7 | 24 | ||
8.3 | odd | 2 | 1728.2.s.g.1151.6 | 24 | |||
8.5 | even | 2 | 1728.2.s.g.1151.5 | 24 | |||
9.2 | odd | 6 | inner | 864.2.s.a.575.7 | 24 | ||
9.4 | even | 3 | 2592.2.c.c.2591.10 | 24 | |||
9.5 | odd | 6 | 2592.2.c.c.2591.16 | 24 | |||
9.7 | even | 3 | 288.2.s.a.191.3 | yes | 24 | ||
12.11 | even | 2 | 288.2.s.a.95.3 | ✓ | 24 | ||
24.5 | odd | 2 | 576.2.s.g.383.3 | 24 | |||
24.11 | even | 2 | 576.2.s.g.383.10 | 24 | |||
36.7 | odd | 6 | 288.2.s.a.191.10 | yes | 24 | ||
36.11 | even | 6 | inner | 864.2.s.a.575.8 | 24 | ||
36.23 | even | 6 | 2592.2.c.c.2591.15 | 24 | |||
36.31 | odd | 6 | 2592.2.c.c.2591.9 | 24 | |||
72.5 | odd | 6 | 5184.2.c.m.5183.10 | 24 | |||
72.11 | even | 6 | 1728.2.s.g.575.5 | 24 | |||
72.13 | even | 6 | 5184.2.c.m.5183.16 | 24 | |||
72.29 | odd | 6 | 1728.2.s.g.575.6 | 24 | |||
72.43 | odd | 6 | 576.2.s.g.191.3 | 24 | |||
72.59 | even | 6 | 5184.2.c.m.5183.9 | 24 | |||
72.61 | even | 6 | 576.2.s.g.191.10 | 24 | |||
72.67 | odd | 6 | 5184.2.c.m.5183.15 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.s.a.95.3 | ✓ | 24 | 12.11 | even | 2 | ||
288.2.s.a.95.10 | yes | 24 | 3.2 | odd | 2 | ||
288.2.s.a.191.3 | yes | 24 | 9.7 | even | 3 | ||
288.2.s.a.191.10 | yes | 24 | 36.7 | odd | 6 | ||
576.2.s.g.191.3 | 24 | 72.43 | odd | 6 | |||
576.2.s.g.191.10 | 24 | 72.61 | even | 6 | |||
576.2.s.g.383.3 | 24 | 24.5 | odd | 2 | |||
576.2.s.g.383.10 | 24 | 24.11 | even | 2 | |||
864.2.s.a.287.7 | 24 | 4.3 | odd | 2 | inner | ||
864.2.s.a.287.8 | 24 | 1.1 | even | 1 | trivial | ||
864.2.s.a.575.7 | 24 | 9.2 | odd | 6 | inner | ||
864.2.s.a.575.8 | 24 | 36.11 | even | 6 | inner | ||
1728.2.s.g.575.5 | 24 | 72.11 | even | 6 | |||
1728.2.s.g.575.6 | 24 | 72.29 | odd | 6 | |||
1728.2.s.g.1151.5 | 24 | 8.5 | even | 2 | |||
1728.2.s.g.1151.6 | 24 | 8.3 | odd | 2 | |||
2592.2.c.c.2591.9 | 24 | 36.31 | odd | 6 | |||
2592.2.c.c.2591.10 | 24 | 9.4 | even | 3 | |||
2592.2.c.c.2591.15 | 24 | 36.23 | even | 6 | |||
2592.2.c.c.2591.16 | 24 | 9.5 | odd | 6 | |||
5184.2.c.m.5183.9 | 24 | 72.59 | even | 6 | |||
5184.2.c.m.5183.10 | 24 | 72.5 | odd | 6 | |||
5184.2.c.m.5183.15 | 24 | 72.67 | odd | 6 | |||
5184.2.c.m.5183.16 | 24 | 72.13 | even | 6 |