Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(145,864)]
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([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.145");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.r (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: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.6 | ||
Root | \(-1.12494 + 0.857038i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 864.145 |
Dual form | 864.2.r.b.721.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(5\) | 1.19115 | + | 0.687709i | 0.532697 | + | 0.307553i | 0.742114 | − | 0.670274i | \(-0.233823\pi\) |
−0.209417 | + | 0.977826i | \(0.567157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.80469 | − | 3.12581i | −0.682107 | − | 1.18144i | −0.974337 | − | 0.225096i | \(-0.927730\pi\) |
0.292229 | − | 0.956348i | \(-0.405603\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.83294 | − | 1.05825i | 0.552652 | − | 0.319074i | −0.197539 | − | 0.980295i | \(-0.563295\pi\) |
0.750191 | + | 0.661221i | \(0.229961\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.887751 | − | 0.512543i | −0.246218 | − | 0.142154i | 0.371813 | − | 0.928307i | \(-0.378736\pi\) |
−0.618031 | + | 0.786154i | \(0.712069\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.808822 | −0.196168 | −0.0980841 | − | 0.995178i | \(-0.531271\pi\) | ||||
−0.0980841 | + | 0.995178i | \(0.531271\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.43122i | − | 1.70484i | −0.522858 | − | 0.852420i | \(-0.675134\pi\) | ||
0.522858 | − | 0.852420i | \(-0.324866\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.65498 | + | 2.86652i | −0.345088 | + | 0.597710i | −0.985370 | − | 0.170430i | \(-0.945484\pi\) |
0.640282 | + | 0.768140i | \(0.278818\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.55411 | − | 2.69180i | −0.310823 | − | 0.538361i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.71083 | − | 4.45185i | 1.43187 | − | 0.826688i | 0.434603 | − | 0.900622i | \(-0.356889\pi\) |
0.997263 | + | 0.0739344i | \(0.0235555\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.26436 | + | 5.65403i | −0.586296 | + | 1.01549i | 0.408417 | + | 0.912796i | \(0.366081\pi\) |
−0.994713 | + | 0.102698i | \(0.967252\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 4.96439i | − | 0.839136i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.01531i | − | 0.660113i | −0.943961 | − | 0.330057i | \(-0.892932\pi\) | ||
0.943961 | − | 0.330057i | \(-0.107068\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.45852 | − | 5.99034i | 0.540131 | − | 0.935534i | −0.458765 | − | 0.888557i | \(-0.651708\pi\) |
0.998896 | − | 0.0469764i | \(-0.0149585\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.245957 | − | 0.142003i | 0.0375081 | − | 0.0216553i | −0.481129 | − | 0.876650i | \(-0.659773\pi\) |
0.518637 | + | 0.854995i | \(0.326440\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.61351 | − | 6.25878i | −0.527084 | − | 0.912937i | −0.999502 | − | 0.0315619i | \(-0.989952\pi\) |
0.472417 | − | 0.881375i | \(-0.343381\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.01378 | + | 5.22003i | −0.430540 | + | 0.745718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.86330i | 0.530666i | 0.964157 | + | 0.265333i | \(0.0854818\pi\) | ||||
−0.964157 | + | 0.265333i | \(0.914518\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.91107 | 0.392528 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.06904 | + | 4.08131i | 0.920310 | + | 0.531341i | 0.883734 | − | 0.467989i | \(-0.155021\pi\) |
0.0365764 | + | 0.999331i | \(0.488355\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.31237 | − | 3.64445i | 0.808216 | − | 0.466624i | −0.0381201 | − | 0.999273i | \(-0.512137\pi\) |
0.846336 | + | 0.532650i | \(0.178804\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.704961 | − | 1.22103i | −0.0874396 | − | 0.151450i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.43973 | + | 1.40858i | 0.298061 | + | 0.172085i | 0.641571 | − | 0.767063i | \(-0.278283\pi\) |
−0.343511 | + | 0.939149i | \(0.611616\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.69830 | 0.557586 | 0.278793 | − | 0.960351i | \(-0.410066\pi\) | ||||
0.278793 | + | 0.960351i | \(0.410066\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.409922 | 0.0479777 | 0.0239889 | − | 0.999712i | \(-0.492363\pi\) | ||||
0.0239889 | + | 0.999712i | \(0.492363\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.61576 | − | 3.81961i | −0.753936 | − | 0.435285i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0456121 | + | 0.0790024i | 0.00513176 | + | 0.00888847i | 0.868580 | − | 0.495549i | \(-0.165033\pi\) |
−0.863448 | + | 0.504438i | \(0.831700\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.40891 | + | 1.39079i | −0.264412 | + | 0.152659i | −0.626346 | − | 0.779545i | \(-0.715450\pi\) |
0.361933 | + | 0.932204i | \(0.382117\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.963426 | − | 0.556234i | −0.104498 | − | 0.0603321i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.91934 | −0.945448 | −0.472724 | − | 0.881210i | \(-0.656729\pi\) | ||||
−0.472724 | + | 0.881210i | \(0.656729\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.69992i | 0.387857i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.11052 | − | 8.85168i | 0.524328 | − | 0.908163i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.76022 | − | 4.78084i | −0.280258 | − | 0.485421i | 0.691190 | − | 0.722673i | \(-0.257087\pi\) |
−0.971448 | + | 0.237252i | \(0.923753\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.63193 | + | 3.25160i | −0.560398 | + | 0.323546i | −0.753305 | − | 0.657671i | \(-0.771542\pi\) |
0.192907 | + | 0.981217i | \(0.438208\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.50528 | − | 2.60723i | 0.148320 | − | 0.256898i | −0.782287 | − | 0.622918i | \(-0.785947\pi\) |
0.930607 | + | 0.366021i | \(0.119280\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.447393i | − | 0.0432511i | −0.999766 | − | 0.0216256i | \(-0.993116\pi\) | ||
0.999766 | − | 0.0216256i | \(-0.00688417\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.36497i | − | 0.897002i | −0.893782 | − | 0.448501i | \(-0.851958\pi\) | ||
0.893782 | − | 0.448501i | \(-0.148042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.66349 | + | 9.80944i | −0.532776 | + | 0.922795i | 0.466492 | + | 0.884526i | \(0.345518\pi\) |
−0.999267 | + | 0.0382692i | \(0.987816\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.94266 | + | 2.27629i | −0.367655 | + | 0.212266i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.45967 | + | 2.52822i | 0.133808 | + | 0.231762i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.26022 | + | 5.64687i | −0.296384 | + | 0.513351i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1522i | − | 0.997483i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8341 | 1.05011 | 0.525053 | − | 0.851069i | \(-0.324045\pi\) | ||||
0.525053 | + | 0.851069i | \(0.324045\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.40891 | + | 1.39079i | 0.210468 | + | 0.121514i | 0.601529 | − | 0.798851i | \(-0.294559\pi\) |
−0.391061 | + | 0.920365i | \(0.627892\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.2286 | + | 13.4110i | −2.01417 | + | 1.16288i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.17841 | + | 14.1654i | 0.698729 | + | 1.21023i | 0.968907 | + | 0.247424i | \(0.0795840\pi\) |
−0.270178 | + | 0.962810i | \(0.587083\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.22979 | − | 0.710017i | −0.104309 | − | 0.0602229i | 0.446938 | − | 0.894565i | \(-0.352514\pi\) |
−0.551247 | + | 0.834342i | \(0.685848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.16959 | −0.181430 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.2463 | 1.01700 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.91390 | + | 2.83704i | 0.402563 | + | 0.232420i | 0.687589 | − | 0.726100i | \(-0.258669\pi\) |
−0.285027 | + | 0.958520i | \(0.592002\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.07318 | − | 12.2511i | −0.575607 | − | 0.996981i | −0.995975 | − | 0.0896271i | \(-0.971432\pi\) |
0.420368 | − | 0.907354i | \(-0.361901\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.77665 | + | 4.48985i | −0.624636 | + | 0.360634i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.6713 | + | 10.7799i | 1.49013 | + | 0.860328i | 0.999936 | − | 0.0112838i | \(-0.00359181\pi\) |
0.490196 | + | 0.871612i | \(0.336925\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.9469 | 0.941548 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.9239i | 1.16893i | 0.811418 | + | 0.584466i | \(0.198696\pi\) | ||||
−0.811418 | + | 0.584466i | \(0.801304\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.0234 | + | 19.0931i | −0.853019 | + | 1.47747i | 0.0254524 | + | 0.999676i | \(0.491897\pi\) |
−0.878471 | + | 0.477796i | \(0.841436\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.97460 | − | 10.3483i | −0.459585 | − | 0.796024i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.9052 | + | 6.29612i | −0.829107 | + | 0.478685i | −0.853547 | − | 0.521016i | \(-0.825553\pi\) |
0.0244397 | + | 0.999701i | \(0.492220\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.60937 | + | 9.71572i | −0.424029 | + | 0.734439i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1116i | 0.905264i | 0.891697 | + | 0.452632i | \(0.149515\pi\) | ||||
−0.891697 | + | 0.452632i | \(0.850485\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6790i | 1.31407i | 0.753862 | + | 0.657033i | \(0.228189\pi\) | ||||
−0.753862 | + | 0.657033i | \(0.771811\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.76137 | − | 4.78283i | 0.203020 | − | 0.351640i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.48252 | + | 0.855935i | −0.108413 | + | 0.0625922i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.72173 | + | 16.8385i | 0.703440 | + | 1.21839i | 0.967252 | + | 0.253820i | \(0.0816870\pi\) |
−0.263812 | + | 0.964574i | \(0.584980\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.159120 | − | 0.275604i | 0.0114537 | − | 0.0198384i | −0.860242 | − | 0.509886i | \(-0.829687\pi\) |
0.871695 | + | 0.490048i | \(0.163021\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.5066i | 1.74602i | 0.487701 | + | 0.873011i | \(0.337836\pi\) | ||||
−0.487701 | + | 0.873011i | \(0.662164\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.13579 | 0.505843 | 0.252921 | − | 0.967487i | \(-0.418609\pi\) | ||||
0.252921 | + | 0.967487i | \(0.418609\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −27.8313 | − | 16.0684i | −1.95337 | − | 1.12778i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.23922 | − | 4.75692i | 0.575452 | − | 0.332237i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.86408 | − | 13.6210i | −0.543970 | − | 0.942183i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.00175 | + | 4.04246i | 0.482020 | + | 0.278294i | 0.721258 | − | 0.692667i | \(-0.243564\pi\) |
−0.239238 | + | 0.970961i | \(0.576898\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.390628 | 0.0266406 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.5646 | 1.59967 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.718032 | + | 0.414556i | 0.0483001 | + | 0.0278861i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.11236 | + | 3.65872i | 0.141454 | + | 0.245006i | 0.928044 | − | 0.372469i | \(-0.121489\pi\) |
−0.786590 | + | 0.617475i | \(0.788156\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.09451 | − | 0.631913i | 0.0726449 | − | 0.0419415i | −0.463238 | − | 0.886234i | \(-0.653312\pi\) |
0.535882 | + | 0.844293i | \(0.319979\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.29196 | − | 3.63267i | −0.415785 | − | 0.240053i | 0.277487 | − | 0.960729i | \(-0.410498\pi\) |
−0.693272 | + | 0.720676i | \(0.743832\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.91061 | 0.387217 | 0.193608 | − | 0.981079i | \(-0.437981\pi\) | ||||
0.193608 | + | 0.981079i | \(0.437981\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 9.94017i | − | 0.648425i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.96266 | − | 10.3276i | 0.385692 | − | 0.668039i | −0.606173 | − | 0.795333i | \(-0.707296\pi\) |
0.991865 | + | 0.127294i | \(0.0406293\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.80170 | + | 3.12063i | 0.116057 | + | 0.201017i | 0.918202 | − | 0.396113i | \(-0.129641\pi\) |
−0.802145 | + | 0.597130i | \(0.796308\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.17972 | + | 4.14521i | −0.458695 | + | 0.264828i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.80882 | + | 6.59707i | −0.242350 | + | 0.419762i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.641516i | 0.0404922i | 0.999795 | + | 0.0202461i | \(0.00644497\pi\) | ||||
−0.999795 | + | 0.0202461i | \(0.993555\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.00554i | 0.440434i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.99885 | − | 3.46212i | 0.124685 | − | 0.215961i | −0.796925 | − | 0.604079i | \(-0.793541\pi\) |
0.921610 | + | 0.388118i | \(0.126875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.5511 | + | 7.24638i | −0.779887 | + | 0.450268i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.64671 | − | 9.78039i | −0.348191 | − | 0.603085i | 0.637737 | − | 0.770254i | \(-0.279871\pi\) |
−0.985928 | + | 0.167169i | \(0.946537\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.65683 | + | 4.60176i | −0.163208 | + | 0.282684i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 24.2695i | − | 1.47974i | −0.672750 | − | 0.739870i | \(-0.734887\pi\) | ||
0.672750 | − | 0.739870i | \(-0.265113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.2330 | −0.743102 | −0.371551 | − | 0.928413i | \(-0.621174\pi\) | ||||
−0.371551 | + | 0.928413i | \(0.621174\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.69719 | − | 3.28928i | −0.343554 | − | 0.198351i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.9249 | + | 6.30750i | −0.656414 | + | 0.378981i | −0.790909 | − | 0.611933i | \(-0.790392\pi\) |
0.134495 | + | 0.990914i | \(0.457059\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.54364 | − | 16.5301i | −0.569326 | − | 0.986101i | −0.996633 | − | 0.0819947i | \(-0.973871\pi\) |
0.427307 | − | 0.904107i | \(-0.359462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.01045 | + | 0.583382i | 0.0600649 | + | 0.0346785i | 0.529732 | − | 0.848165i | \(-0.322293\pi\) |
−0.469667 | + | 0.882844i | \(0.655626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.9662 | −1.47371 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3458 | −0.961518 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.11446 | − | 1.22079i | −0.123528 | − | 0.0713191i | 0.436963 | − | 0.899480i | \(-0.356054\pi\) |
−0.560491 | + | 0.828161i | \(0.689388\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.61351 | + | 9.72288i | 0.326831 | + | 0.566088i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.93843 | − | 1.69650i | 0.169934 | − | 0.0981112i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.887751 | − | 0.512543i | −0.0511691 | − | 0.0295425i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.0253 | 0.574046 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.7452i | − | 0.898626i | −0.893374 | − | 0.449313i | \(-0.851669\pi\) | ||
0.893374 | − | 0.449313i | \(-0.148331\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.90129 | − | 17.1495i | 0.561451 | − | 0.972461i | −0.435919 | − | 0.899986i | \(-0.643577\pi\) |
0.997370 | − | 0.0724757i | \(-0.0230900\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.2557 | + | 28.1557i | 0.918828 | + | 1.59146i | 0.801198 | + | 0.598399i | \(0.204196\pi\) |
0.117630 | + | 0.993057i | \(0.462470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.9271 | − | 8.04083i | 0.782225 | − | 0.451618i | −0.0549932 | − | 0.998487i | \(-0.517514\pi\) |
0.837218 | + | 0.546869i | \(0.184180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.42233 | − | 16.3200i | 0.527549 | − | 0.913742i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.01054i | 0.334435i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.18620i | 0.176739i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.0425 | + | 22.5903i | −0.719056 | + | 1.24544i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.7569 | − | 10.2520i | 0.976010 | − | 0.563499i | 0.0749465 | − | 0.997188i | \(-0.476121\pi\) |
0.901063 | + | 0.433688i | \(0.142788\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.93739 | + | 3.35565i | 0.105851 | + | 0.183339i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.21760 | − | 10.7692i | 0.338694 | − | 0.586635i | −0.645493 | − | 0.763766i | \(-0.723348\pi\) |
0.984187 | + | 0.177131i | \(0.0566815\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.8180i | 0.748287i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.50988 | −0.189515 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.1550 | + | 13.9459i | 1.29671 | + | 0.748654i | 0.979834 | − | 0.199814i | \(-0.0640339\pi\) |
0.316873 | + | 0.948468i | \(0.397367\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.0103 | − | 15.0171i | 1.39230 | − | 0.803846i | 0.398732 | − | 0.917068i | \(-0.369450\pi\) |
0.993570 | + | 0.113222i | \(0.0361171\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.48011 | + | 16.4200i | 0.504575 | + | 0.873950i | 0.999986 | + | 0.00529122i | \(0.00168426\pi\) |
−0.495411 | + | 0.868659i | \(0.664982\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.59637 | + | 3.23107i | 0.297024 | + | 0.171487i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.6420 | 1.51167 | 0.755833 | − | 0.654765i | \(-0.227232\pi\) | ||||
0.755833 | + | 0.654765i | \(0.227232\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −36.2231 | −1.90648 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.488277 | + | 0.281907i | 0.0255576 | + | 0.0147557i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.77148 | − | 9.99650i | −0.301269 | − | 0.521813i | 0.675155 | − | 0.737676i | \(-0.264077\pi\) |
−0.976424 | + | 0.215863i | \(0.930744\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0759 | − | 6.97205i | 0.626952 | − | 0.361971i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.4301 | − | 11.2180i | −1.00605 | − | 0.580846i | −0.0960206 | − | 0.995379i | \(-0.530611\pi\) |
−0.910034 | + | 0.414533i | \(0.863945\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.12706 | −0.470068 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.6668i | 1.16431i | 0.813077 | + | 0.582157i | \(0.197791\pi\) | ||||
−0.813077 | + | 0.582157i | \(0.802209\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.94277 | + | 3.36498i | −0.0992709 | + | 0.171942i | −0.911383 | − | 0.411559i | \(-0.864984\pi\) |
0.812112 | + | 0.583501i | \(0.198318\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.25356 | − | 9.09944i | −0.267746 | − | 0.463750i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.9463 | + | 6.89722i | −0.605703 | + | 0.349703i | −0.771282 | − | 0.636494i | \(-0.780384\pi\) |
0.165579 | + | 0.986197i | \(0.447051\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.33859 | − | 2.31850i | 0.0676953 | − | 0.117252i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.125471i | 0.00631315i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 23.7680i | − | 1.19288i | −0.802657 | − | 0.596441i | \(-0.796581\pi\) | ||
0.802657 | − | 0.596441i | \(-0.203419\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.47782 | − | 7.75581i | 0.223612 | − | 0.387307i | −0.732290 | − | 0.680992i | \(-0.761549\pi\) |
0.955902 | + | 0.293686i | \(0.0948820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.79587 | − | 3.34625i | 0.288713 | − | 0.166688i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.24920 | − | 7.35983i | −0.210625 | − | 0.364813i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.4170 | − | 18.0429i | 0.515090 | − | 0.892162i | −0.484757 | − | 0.874649i | \(-0.661092\pi\) |
0.999847 | − | 0.0175128i | \(-0.00557480\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 29.4619i | − | 1.44973i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.82582 | −0.187802 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.74372 | + | 5.04819i | 0.427159 | + | 0.246620i | 0.698135 | − | 0.715966i | \(-0.254013\pi\) |
−0.270977 | + | 0.962586i | \(0.587347\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.2218 | − | 11.6751i | 0.985551 | − | 0.569008i | 0.0816096 | − | 0.996664i | \(-0.473994\pi\) |
0.903941 | + | 0.427656i | \(0.140661\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.25700 | + | 2.17719i | 0.0609735 | + | 0.105609i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.7837 | − | 13.1542i | −1.10258 | − | 0.636575i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.40348 | −0.308445 | −0.154222 | − | 0.988036i | \(-0.549287\pi\) | ||||
−0.154222 | + | 0.988036i | \(0.549287\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.82857 | −0.472331 | −0.236166 | − | 0.971713i | \(-0.575891\pi\) | ||||
−0.236166 | + | 0.971713i | \(0.575891\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.3017 | + | 12.2986i | 1.01900 | + | 0.588320i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.3831 | + | 21.4482i | 0.591015 | + | 1.02367i | 0.994096 | + | 0.108504i | \(0.0346061\pi\) |
−0.403081 | + | 0.915164i | \(0.632061\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.5518 | − | 13.5976i | 1.11898 | − | 0.646044i | 0.177840 | − | 0.984059i | \(-0.443089\pi\) |
0.941140 | + | 0.338016i | \(0.109756\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.6242 | − | 6.13391i | −0.503637 | − | 0.290775i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.6861 | −1.54255 | −0.771276 | − | 0.636501i | \(-0.780381\pi\) | ||||
−0.771276 | + | 0.636501i | \(0.780381\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 14.6399i | − | 0.689367i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.54447 | + | 4.40714i | −0.119286 | + | 0.206610i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.3779 | − | 17.9750i | −0.485456 | − | 0.840834i | 0.514404 | − | 0.857548i | \(-0.328013\pi\) |
−0.999860 | + | 0.0167133i | \(0.994680\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.4695 | − | 18.7463i | 1.51226 | − | 0.873101i | 0.512359 | − | 0.858771i | \(-0.328772\pi\) |
0.999897 | − | 0.0143300i | \(-0.00456153\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.97597 | − | 13.8148i | 0.370675 | − | 0.642028i | −0.618995 | − | 0.785395i | \(-0.712460\pi\) |
0.989670 | + | 0.143367i | \(0.0457931\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 27.0476i | − | 1.25161i | −0.779979 | − | 0.625806i | \(-0.784770\pi\) | ||
0.779979 | − | 0.625806i | \(-0.215230\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 10.1682i | − | 0.469523i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.300550 | − | 0.520568i | 0.0138193 | − | 0.0239357i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.0034 | + | 11.5490i | −0.917818 | + | 0.529903i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.6550 | + | 23.6511i | 0.623912 | + | 1.08065i | 0.988750 | + | 0.149577i | \(0.0477910\pi\) |
−0.364838 | + | 0.931071i | \(0.618876\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.05802 | + | 3.56460i | −0.0938377 | + | 0.162532i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 7.59291i | − | 0.344776i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.1126 | −0.866073 | −0.433036 | − | 0.901376i | \(-0.642558\pi\) | ||||
−0.433036 | + | 0.901376i | \(0.642558\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.1131 | + | 6.41614i | 0.501526 | + | 0.289556i | 0.729344 | − | 0.684147i | \(-0.239826\pi\) |
−0.227817 | + | 0.973704i | \(0.573159\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.23669 | + | 3.60076i | −0.280886 | + | 0.162170i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.47896 | − | 14.6860i | −0.380334 | − | 0.658757i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.3846 | − | 8.88232i | −0.688711 | − | 0.397627i | 0.114418 | − | 0.993433i | \(-0.463500\pi\) |
−0.803129 | + | 0.595805i | \(0.796833\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.0108 | −1.07059 | −0.535294 | − | 0.844666i | \(-0.679799\pi\) | ||||
−0.535294 | + | 0.844666i | \(0.679799\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.94461 | −0.398030 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.91916 | − | 3.99478i | −0.306686 | − | 0.177065i | 0.338756 | − | 0.940874i | \(-0.389994\pi\) |
−0.645443 | + | 0.763809i | \(0.723327\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.739780 | − | 1.28134i | −0.0327259 | − | 0.0566830i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.58602 | − | 2.07039i | 0.158019 | − | 0.0912324i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.2467 | − | 7.64798i | −0.582589 | − | 0.336358i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.9809 | 1.62016 | 0.810082 | − | 0.586317i | \(-0.199423\pi\) | ||||
0.810082 | + | 0.586317i | \(0.199423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 18.4217i | − | 0.805526i | −0.915304 | − | 0.402763i | \(-0.868050\pi\) | ||
0.915304 | − | 0.402763i | \(-0.131950\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.64028 | − | 4.57311i | 0.115013 | − | 0.199208i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.02206 | + | 10.4305i | 0.261828 | + | 0.453500i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.14061 | + | 3.54529i | −0.265980 | + | 0.153563i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.307676 | − | 0.532911i | 0.0133020 | − | 0.0230397i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.7573i | 0.549497i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 13.5032i | − | 0.580549i | −0.956943 | − | 0.290275i | \(-0.906253\pi\) | ||
0.956943 | − | 0.290275i | \(-0.0937467\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.44038 | − | 11.1551i | 0.275875 | − | 0.477830i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.2252 | − | 18.6052i | 1.37785 | − | 0.795501i | 0.385948 | − | 0.922520i | \(-0.373874\pi\) |
0.991900 | + | 0.127019i | \(0.0405410\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33.0827 | − | 57.3009i | −1.40937 | − | 2.44110i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.164631 | − | 0.285149i | 0.00700082 | − | 0.0121258i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.9602i | 0.718628i | 0.933217 | + | 0.359314i | \(0.116989\pi\) | ||||
−0.933217 | + | 0.359314i | \(0.883011\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.291131 | −0.0123135 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.0083 | − | 14.4385i | −1.05397 | − | 0.608512i | −0.130214 | − | 0.991486i | \(-0.541566\pi\) |
−0.923759 | + | 0.382974i | \(0.874900\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.4921 | + | 7.78966i | −0.567616 | + | 0.327713i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.20060 | − | 3.81154i | −0.0922538 | − | 0.159788i | 0.816205 | − | 0.577762i | \(-0.196074\pi\) |
−0.908459 | + | 0.417974i | \(0.862740\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.6730 | + | 16.5544i | 1.19993 | + | 0.692779i | 0.960539 | − | 0.278144i | \(-0.0897193\pi\) |
0.239390 | + | 0.970924i | \(0.423053\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.2881 | 0.429045 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.4122 | 0.475097 | 0.237548 | − | 0.971376i | \(-0.423656\pi\) | ||||
0.237548 | + | 0.971376i | \(0.423656\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.69466 | + | 5.01986i | 0.360715 | + | 0.208259i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.08834 | + | 7.08121i | 0.169322 | + | 0.293274i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.5512 | + | 13.0200i | −0.930788 | + | 0.537391i | −0.887061 | − | 0.461653i | \(-0.847257\pi\) |
−0.0437275 | + | 0.999043i | \(0.513923\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.0164 | + | 24.2582i | 1.73125 | + | 0.999540i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.75114 | −0.236171 | −0.118086 | − | 0.993003i | \(-0.537676\pi\) | ||||
−0.118086 | + | 0.993003i | \(0.537676\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.01531i | 0.164612i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.10409 | + | 14.0367i | −0.331124 | + | 0.573524i | −0.982733 | − | 0.185032i | \(-0.940761\pi\) |
0.651608 | + | 0.758556i | \(0.274095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.78181 | + | 16.9426i | 0.399008 | + | 0.691102i | 0.993604 | − | 0.112922i | \(-0.0360212\pi\) |
−0.594596 | + | 0.804025i | \(0.702688\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.76680 | + | 4.48416i | −0.315765 | + | 0.182307i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.82627 | − | 6.62730i | 0.155304 | − | 0.268994i | −0.777866 | − | 0.628430i | \(-0.783698\pi\) |
0.933170 | + | 0.359437i | \(0.117031\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.40831i | 0.299708i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.6512i | 1.11682i | 0.829565 | + | 0.558410i | \(0.188588\pi\) | ||||
−0.829565 | + | 0.558410i | \(0.811412\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.6938 | − | 21.9863i | 0.511034 | − | 0.885136i | −0.488885 | − | 0.872348i | \(-0.662596\pi\) |
0.999918 | − | 0.0127878i | \(-0.00407059\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.8583 | − | 11.4652i | 0.798171 | − | 0.460824i | −0.0446605 | − | 0.999002i | \(-0.514221\pi\) |
0.842831 | + | 0.538178i | \(0.180887\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.0966 | + | 27.8801i | 0.644897 | + | 1.11699i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.101100 | + | 0.175110i | −0.00404398 | + | 0.00700439i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.24767i | 0.129493i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.2785 | −0.926701 | −0.463350 | − | 0.886175i | \(-0.653353\pi\) | ||||
−0.463350 | + | 0.886175i | \(0.653353\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.0961 | + | 8.13841i | 0.559388 | + | 0.322963i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.35098 | − | 3.08939i | 0.212013 | − | 0.122406i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.4170 | + | 30.1672i | 0.687932 | + | 1.19153i | 0.972506 | + | 0.232879i | \(0.0748146\pi\) |
−0.284574 | + | 0.958654i | \(0.591852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.0047 | − | 19.6326i | −1.34102 | − | 0.774236i | −0.354059 | − | 0.935223i | \(-0.615199\pi\) |
−0.986956 | + | 0.160987i | \(0.948532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.5092 | 1.74984 | 0.874918 | − | 0.484271i | \(-0.160915\pi\) | ||||
0.874918 | + | 0.484271i | \(0.160915\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.2762 | 0.678149 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.7763 | − | 9.10843i | −0.617373 | − | 0.356440i | 0.158473 | − | 0.987363i | \(-0.449343\pi\) |
−0.775845 | + | 0.630923i | \(0.782676\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.91291 | + | 3.31326i | 0.0747437 | + | 0.129460i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.2085 | + | 20.9050i | −1.41048 | + | 0.814343i | −0.995434 | − | 0.0954566i | \(-0.969569\pi\) |
−0.415049 | + | 0.909799i | \(0.636236\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.78973 | + | 5.65210i | 0.380776 | + | 0.219841i | 0.678156 | − | 0.734918i | \(-0.262779\pi\) |
−0.297380 | + | 0.954759i | \(0.596113\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −36.8915 | −1.43059 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.4710i | 1.14112i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.71346 | − | 13.3601i | 0.297775 | − | 0.515761i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.6390 | + | 30.5517i | 0.679934 | + | 1.17768i | 0.975000 | + | 0.222203i | \(0.0713249\pi\) |
−0.295066 | + | 0.955477i | \(0.595342\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.5026 | − | 10.1051i | 0.672679 | − | 0.388372i | −0.124412 | − | 0.992231i | \(-0.539704\pi\) |
0.797091 | + | 0.603859i | \(0.206371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.96266 | + | 17.2558i | −0.382332 | + | 0.662218i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 43.6659i | − | 1.67083i | −0.549621 | − | 0.835414i | \(-0.685228\pi\) | ||
0.549621 | − | 0.835414i | \(-0.314772\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.4975i | 0.859584i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.98011 | − | 3.42965i | 0.0754362 | − | 0.130659i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.91193 | − | 4.56796i | 0.300984 | − | 0.173773i | −0.341901 | − | 0.939736i | \(-0.611071\pi\) |
0.642885 | + | 0.765963i | \(0.277737\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.976570 | − | 1.69147i | −0.0370434 | − | 0.0641611i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.79733 | + | 4.84512i | −0.105956 | + | 0.183522i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.8665i | 1.69458i | 0.531127 | + | 0.847292i | \(0.321769\pi\) | ||||
−0.531127 | + | 0.847292i | \(0.678231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.8387 | −1.12539 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.3277 | + | 11.7362i | 0.764504 | + | 0.441386i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.1529 | + | 13.3673i | −0.869525 | + | 0.502021i | −0.867190 | − | 0.497977i | \(-0.834077\pi\) |
−0.00233491 | + | 0.999997i | \(0.500743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.8049 | − | 18.7147i | −0.404647 | − | 0.700870i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.58430 | − | 1.49205i | −0.0966474 | − | 0.0557994i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.4738 | −1.39754 | −0.698768 | − | 0.715348i | \(-0.746268\pi\) | ||||
−0.698768 | + | 0.715348i | \(0.746268\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8662 | −0.404680 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.9670 | − | 13.8374i | −0.890112 | − | 0.513907i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.18140 | + | 15.9027i | 0.340519 | + | 0.589797i | 0.984529 | − | 0.175220i | \(-0.0560638\pi\) |
−0.644010 | + | 0.765017i | \(0.722730\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.198936 | + | 0.114856i | −0.00735790 | + | 0.00424808i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.6508 | − | 20.5830i | −1.31679 | − | 0.760249i | −0.333580 | − | 0.942722i | \(-0.608257\pi\) |
−0.983211 | + | 0.182472i | \(0.941590\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.96251 | 0.219632 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.1004i | 1.65905i | 0.558473 | + | 0.829523i | \(0.311387\pi\) | ||||
−0.558473 | + | 0.829523i | \(0.688613\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.7217 | + | 37.6231i | −0.796893 | + | 1.38026i | 0.124737 | + | 0.992190i | \(0.460191\pi\) |
−0.921630 | + | 0.388070i | \(0.873142\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.90212 | + | 6.75867i | 0.142963 | + | 0.247618i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.39846 | + | 0.807404i | −0.0510988 | + | 0.0295019i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.3394 | − | 26.5686i | 0.559742 | − | 0.969501i | −0.437776 | − | 0.899084i | \(-0.644234\pi\) |
0.997518 | − | 0.0704172i | \(-0.0224330\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 19.4571i | − | 0.708118i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.84137i | 0.103271i | 0.998666 | + | 0.0516357i | \(0.0164435\pi\) | ||||
−0.998666 | + | 0.0516357i | \(0.983557\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.52480 | + | 11.3013i | −0.236524 | + | 0.409672i | −0.959714 | − | 0.280977i | \(-0.909342\pi\) |
0.723191 | + | 0.690649i | \(0.242675\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.2731 | + | 16.9008i | −1.05976 | + | 0.611851i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.18370 | − | 7.24637i | −0.151065 | − | 0.261651i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.7846 | − | 23.8756i | 0.497084 | − | 0.860975i | −0.502910 | − | 0.864339i | \(-0.667737\pi\) |
0.999994 | + | 0.00336360i | \(0.00107067\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.7109i | 0.565082i | 0.959255 | + | 0.282541i | \(0.0911774\pi\) | ||||
−0.959255 | + | 0.282541i | \(0.908823\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.2927 | 0.728936 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −44.5155 | − | 25.7011i | −1.59494 | − | 0.920836i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.61171 | − | 4.97197i | 0.308151 | − | 0.177911i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.8268 | + | 25.6808i | 0.529193 | + | 0.916589i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.2138 | + | 7.05164i | 0.435375 | + | 0.251364i | 0.701634 | − | 0.712538i | \(-0.252454\pi\) |
−0.266259 | + | 0.963902i | \(0.585788\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.8832 | 1.45364 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.47175 | −0.265329 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.7555 | − | 13.1379i | −0.806040 | − | 0.465367i | 0.0395390 | − | 0.999218i | \(-0.487411\pi\) |
−0.845579 | + | 0.533851i | \(0.820744\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.92269 | + | 5.06224i | 0.103397 | + | 0.179089i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.751362 | − | 0.433799i | 0.0265150 | − | 0.0153084i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.2305 | + | 8.21599i | 0.501560 | + | 0.289576i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.5390 | 1.31980 | 0.659901 | − | 0.751353i | \(-0.270598\pi\) | ||||
0.659901 | + | 0.751353i | \(0.270598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 37.7228i | − | 1.32463i | −0.749227 | − | 0.662314i | \(-0.769575\pi\) | ||
0.749227 | − | 0.662314i | \(-0.230425\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.2633 | + | 17.7766i | −0.359508 | + | 0.622686i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.05526 | − | 1.82776i | −0.0369188 | − | 0.0639453i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.06427 | + | 0.614456i | −0.0371432 | + | 0.0214446i | −0.518457 | − | 0.855104i | \(-0.673493\pi\) |
0.481313 | + | 0.876549i | \(0.340160\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.4937 | − | 30.2999i | 0.609791 | − | 1.05619i | −0.381484 | − | 0.924376i | \(-0.624587\pi\) |
0.991275 | − | 0.131813i | \(-0.0420799\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.7311i | 1.69455i | 0.531157 | + | 0.847273i | \(0.321757\pi\) | ||||
−0.531157 | + | 0.847273i | \(0.678243\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.9573i | 1.00573i | 0.864366 | + | 0.502863i | \(0.167720\pi\) | ||||
−0.864366 | + | 0.502863i | \(0.832280\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.43761 | − | 4.22207i | 0.0844583 | − | 0.146286i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.2610 | + | 15.1618i | −0.908801 | + | 0.524696i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.66037 | + | 13.2681i | 0.264465 | + | 0.458067i | 0.967423 | − | 0.253164i | \(-0.0814712\pi\) |
−0.702958 | + | 0.711231i | \(0.748138\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.1380 | − | 43.5402i | 0.866826 | − | 1.50139i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 16.4351i | − | 0.565386i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.5347 | 0.808662 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.5100 | + | 6.64528i | 0.394556 | + | 0.227797i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.67204 | − | 3.27476i | 0.194207 | − | 0.112126i | −0.399743 | − | 0.916627i | \(-0.630901\pi\) |
0.593951 | + | 0.804502i | \(0.297567\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.71094 | + | 11.6237i | 0.229241 | + | 0.397058i | 0.957583 | − | 0.288156i | \(-0.0930421\pi\) |
−0.728342 | + | 0.685214i | \(0.759709\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.57865 | + | 1.48878i | 0.0879824 | + | 0.0507967i | 0.543346 | − | 0.839509i | \(-0.317157\pi\) |
−0.455363 | + | 0.890306i | \(0.650491\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.3897 | −0.830236 | −0.415118 | − | 0.909768i | \(-0.636260\pi\) | ||||
−0.415118 | + | 0.909768i | \(0.636260\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.3196 | −0.588884 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.167208 | + | 0.0965378i | 0.00567216 | + | 0.00327482i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.44392 | − | 2.50094i | −0.0489252 | − | 0.0847410i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −34.8596 | + | 20.1262i | −1.17847 | + | 0.680390i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.38552 | + | 2.53198i | 0.148088 | + | 0.0854988i | 0.572213 | − | 0.820105i | \(-0.306085\pi\) |
−0.424125 | + | 0.905604i | \(0.639418\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.2318 | −0.951154 | −0.475577 | − | 0.879674i | \(-0.657761\pi\) | ||||
−0.475577 | + | 0.879674i | \(0.657761\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0994i | 0.945619i | 0.881165 | + | 0.472809i | \(0.156760\pi\) | ||||
−0.881165 | + | 0.472809i | \(0.843240\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.666005 | − | 1.15356i | 0.0223623 | − | 0.0387326i | −0.854628 | − | 0.519241i | \(-0.826215\pi\) |
0.876990 | + | 0.480509i | \(0.159548\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.3568 | − | 36.9911i | −0.716285 | − | 1.24064i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −46.5104 | + | 26.8528i | −1.55641 | + | 0.898594i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.32926 | + | 14.4267i | −0.278417 | + | 0.482232i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.1297i | 1.93873i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.12473i | − | 0.104100i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.1580 | + | 21.0582i | −0.404145 | + | 0.699999i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.778677 | + | 0.449569i | −0.0258555 | + | 0.0149277i | −0.512872 | − | 0.858465i | \(-0.671418\pi\) |
0.487017 | + | 0.873393i | \(0.338085\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.53390 | + | 13.0491i | 0.249609 | + | 0.432336i | 0.963417 | − | 0.268005i | \(-0.0863645\pi\) |
−0.713808 | + | 0.700341i | \(0.753031\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.94360 | + | 5.09846i | −0.0974188 | + | 0.168734i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 10.0397i | − | 0.331541i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.4761 | 0.939339 | 0.469670 | − | 0.882842i | \(-0.344373\pi\) | ||||
0.469670 | + | 0.882842i | \(0.344373\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.17092 | − | 2.40808i | −0.137288 | − | 0.0792630i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.8084 | + | 6.24025i | −0.355379 | + | 0.205178i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.12086 | − | 3.67344i | −0.0695833 | − | 0.120522i | 0.829135 | − | 0.559049i | \(-0.188834\pi\) |
−0.898718 | + | 0.438527i | \(0.855500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.7912 | + | 22.3961i | 1.27133 | + | 0.734002i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.35454 | −0.0770016 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.1569 | −0.495155 | −0.247578 | − | 0.968868i | \(-0.579634\pi\) | ||||
−0.247578 | + | 0.968868i | \(0.579634\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.9463 | + | 21.3310i | 1.20442 | + | 0.695370i | 0.961534 | − | 0.274686i | \(-0.0885738\pi\) |
0.242882 | + | 0.970056i | \(0.421907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.4476 | + | 19.8278i | 0.372785 | + | 0.645683i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.7629 | − | 14.2969i | 0.804686 | − | 0.464585i | −0.0404213 | − | 0.999183i | \(-0.512870\pi\) |
0.845107 | + | 0.534597i | \(0.179537\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.363908 | − | 0.210103i | −0.0118130 | − | 0.00682022i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.1424 | 0.911622 | 0.455811 | − | 0.890077i | \(-0.349349\pi\) | ||||
0.455811 | + | 0.890077i | \(0.349349\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.7429i | 0.865380i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.5189 | − | 51.1283i | 0.953216 | − | 1.65102i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.81204 | − | 10.0668i | −0.187485 | − | 0.324734i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.379071 | − | 0.218857i | 0.0122027 | − | 0.00704525i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.99023 | − | 12.1074i | 0.224791 | − | 0.389349i | −0.731466 | − | 0.681878i | \(-0.761164\pi\) |
0.956257 | + | 0.292529i | \(0.0944969\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 17.5426i | − | 0.562969i | −0.959566 | − | 0.281484i | \(-0.909173\pi\) | ||
0.959566 | − | 0.281484i | \(-0.0908268\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.12543i | 0.164314i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.7380 | + | 39.3834i | −0.727454 | + | 1.25999i | 0.230502 | + | 0.973072i | \(0.425963\pi\) |
−0.957956 | + | 0.286916i | \(0.907370\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.3486 | + | 9.43888i | −0.522504 | + | 0.301668i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.04836 | − | 8.74402i | −0.161018 | − | 0.278891i | 0.774216 | − | 0.632921i | \(-0.218144\pi\) |
−0.935234 | + | 0.354030i | \(0.884811\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.8534 | + | 29.1909i | −0.536994 | + | 0.930100i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.940054i | 0.0298920i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.6057 | 0.559263 | 0.279631 | − | 0.960107i | \(-0.409788\pi\) | ||||
0.279631 | + | 0.960107i | \(0.409788\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.49978 | + | 4.90735i | 0.269461 | + | 0.155573i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.1168 | − | 15.0786i | 0.827128 | − | 0.477543i | −0.0257404 | − | 0.999669i | \(-0.508194\pi\) |
0.852868 | + | 0.522126i | \(0.174861\pi\) | |||||||
\(998\) | 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.r.b.145.6 | 16 | ||
3.2 | odd | 2 | 288.2.r.b.49.3 | 16 | |||
4.3 | odd | 2 | 216.2.n.b.37.5 | 16 | |||
8.3 | odd | 2 | 216.2.n.b.37.7 | 16 | |||
8.5 | even | 2 | inner | 864.2.r.b.145.3 | 16 | ||
9.2 | odd | 6 | 288.2.r.b.241.6 | 16 | |||
9.4 | even | 3 | 2592.2.d.k.1297.3 | 8 | |||
9.5 | odd | 6 | 2592.2.d.j.1297.6 | 8 | |||
9.7 | even | 3 | inner | 864.2.r.b.721.3 | 16 | ||
12.11 | even | 2 | 72.2.n.b.13.4 | yes | 16 | ||
24.5 | odd | 2 | 288.2.r.b.49.6 | 16 | |||
24.11 | even | 2 | 72.2.n.b.13.2 | ✓ | 16 | ||
36.7 | odd | 6 | 216.2.n.b.181.7 | 16 | |||
36.11 | even | 6 | 72.2.n.b.61.2 | yes | 16 | ||
36.23 | even | 6 | 648.2.d.j.325.8 | 8 | |||
36.31 | odd | 6 | 648.2.d.k.325.1 | 8 | |||
72.5 | odd | 6 | 2592.2.d.j.1297.3 | 8 | |||
72.11 | even | 6 | 72.2.n.b.61.4 | yes | 16 | ||
72.13 | even | 6 | 2592.2.d.k.1297.6 | 8 | |||
72.29 | odd | 6 | 288.2.r.b.241.3 | 16 | |||
72.43 | odd | 6 | 216.2.n.b.181.5 | 16 | |||
72.59 | even | 6 | 648.2.d.j.325.7 | 8 | |||
72.61 | even | 6 | inner | 864.2.r.b.721.6 | 16 | ||
72.67 | odd | 6 | 648.2.d.k.325.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.n.b.13.2 | ✓ | 16 | 24.11 | even | 2 | ||
72.2.n.b.13.4 | yes | 16 | 12.11 | even | 2 | ||
72.2.n.b.61.2 | yes | 16 | 36.11 | even | 6 | ||
72.2.n.b.61.4 | yes | 16 | 72.11 | even | 6 | ||
216.2.n.b.37.5 | 16 | 4.3 | odd | 2 | |||
216.2.n.b.37.7 | 16 | 8.3 | odd | 2 | |||
216.2.n.b.181.5 | 16 | 72.43 | odd | 6 | |||
216.2.n.b.181.7 | 16 | 36.7 | odd | 6 | |||
288.2.r.b.49.3 | 16 | 3.2 | odd | 2 | |||
288.2.r.b.49.6 | 16 | 24.5 | odd | 2 | |||
288.2.r.b.241.3 | 16 | 72.29 | odd | 6 | |||
288.2.r.b.241.6 | 16 | 9.2 | odd | 6 | |||
648.2.d.j.325.7 | 8 | 72.59 | even | 6 | |||
648.2.d.j.325.8 | 8 | 36.23 | even | 6 | |||
648.2.d.k.325.1 | 8 | 36.31 | odd | 6 | |||
648.2.d.k.325.2 | 8 | 72.67 | odd | 6 | |||
864.2.r.b.145.3 | 16 | 8.5 | even | 2 | inner | ||
864.2.r.b.145.6 | 16 | 1.1 | even | 1 | trivial | ||
864.2.r.b.721.3 | 16 | 9.7 | even | 3 | inner | ||
864.2.r.b.721.6 | 16 | 72.61 | even | 6 | inner | ||
2592.2.d.j.1297.3 | 8 | 72.5 | odd | 6 | |||
2592.2.d.j.1297.6 | 8 | 9.5 | odd | 6 | |||
2592.2.d.k.1297.3 | 8 | 9.4 | even | 3 | |||
2592.2.d.k.1297.6 | 8 | 72.13 | even | 6 |