Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(107,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 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("504.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bm (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.17 | ||
Character | \(\chi\) | \(=\) | 504.107 |
Dual form | 504.2.bm.c.179.17 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.830529 | − | 1.14465i | 0.587273 | − | 0.809389i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.620442 | − | 1.90133i | −0.310221 | − | 0.950665i | ||||
\(5\) | 1.88256 | − | 3.26069i | 0.841907 | − | 1.45823i | −0.0463738 | − | 0.998924i | \(-0.514767\pi\) |
0.888281 | − | 0.459301i | \(-0.151900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.23426 | − | 1.41706i | 0.844472 | − | 0.535600i | ||||
\(8\) | −2.69165 | − | 0.868922i | −0.951642 | − | 0.307210i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.16882 | − | 4.86297i | −0.685842 | − | 1.53781i | ||||
\(11\) | −1.47084 | + | 0.849192i | −0.443476 | + | 0.256041i | −0.705071 | − | 0.709137i | \(-0.749085\pi\) |
0.261595 | + | 0.965178i | \(0.415752\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.64222i | 1.56487i | 0.622733 | + | 0.782435i | \(0.286022\pi\) | ||||
−0.622733 | + | 0.782435i | \(0.713978\pi\) | |||||||
\(14\) | 0.233580 | − | 3.73436i | 0.0624270 | − | 0.998050i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.23010 | + | 2.35933i | −0.807526 | + | 0.589832i | ||||
\(17\) | 2.26012 | − | 1.30488i | 0.548158 | − | 0.316479i | −0.200220 | − | 0.979751i | \(-0.564166\pi\) |
0.748379 | + | 0.663271i | \(0.230833\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.18076 | + | 2.04513i | −0.270885 | + | 0.469186i | −0.969089 | − | 0.246713i | \(-0.920649\pi\) |
0.698204 | + | 0.715899i | \(0.253983\pi\) | |||||||
\(20\) | −7.36767 | − | 1.55630i | −1.64746 | − | 0.347999i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.249553 | + | 2.38888i | −0.0532048 | + | 0.509311i | ||||
\(23\) | −0.653873 | + | 1.13254i | −0.136342 | + | 0.236151i | −0.926109 | − | 0.377255i | \(-0.876868\pi\) |
0.789767 | + | 0.613406i | \(0.210201\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.58807 | − | 7.94677i | −0.917614 | − | 1.58935i | ||||
\(26\) | 6.45836 | + | 4.68603i | 1.26659 | + | 0.919006i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.08053 | − | 3.36886i | −0.771149 | − | 0.636655i | ||||
\(29\) | 6.80944 | 1.26448 | 0.632241 | − | 0.774772i | \(-0.282135\pi\) | ||||
0.632241 | + | 0.774772i | \(0.282135\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.75107 | + | 2.74303i | −0.853317 | + | 0.492663i | −0.861769 | − | 0.507302i | \(-0.830643\pi\) |
0.00845183 | + | 0.999964i | \(0.497310\pi\) | |||||||
\(32\) | 0.0179044 | + | 5.65683i | 0.00316508 | + | 0.999995i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.383465 | − | 3.67078i | 0.0657637 | − | 0.629533i | ||||
\(35\) | −0.414472 | − | 9.95295i | −0.0700586 | − | 1.68236i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.20109 | + | 3.00285i | 0.855054 | + | 0.493666i | 0.862353 | − | 0.506308i | \(-0.168990\pi\) |
−0.00729899 | + | 0.999973i | \(0.502323\pi\) | |||||||
\(38\) | 1.36030 | + | 3.05010i | 0.220671 | + | 0.494791i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.90048 | + | 7.14084i | −1.24918 | + | 1.12907i | ||||
\(41\) | − | 6.10456i | − | 0.953373i | −0.879073 | − | 0.476686i | \(-0.841838\pi\) | ||
0.879073 | − | 0.476686i | \(-0.158162\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.49804 | −0.990943 | −0.495471 | − | 0.868624i | \(-0.665005\pi\) | ||||
−0.495471 | + | 0.868624i | \(0.665005\pi\) | |||||||
\(44\) | 2.52717 | + | 2.26968i | 0.380985 | + | 0.342168i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.753301 | + | 1.68906i | 0.111068 | + | 0.249039i | ||||
\(47\) | 3.53360 | − | 6.12038i | 0.515429 | − | 0.892749i | −0.484411 | − | 0.874841i | \(-0.660966\pi\) |
0.999840 | − | 0.0179081i | \(-0.00570062\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.98386 | − | 6.33219i | 0.426266 | − | 0.904598i | ||||
\(50\) | −12.9068 | − | 1.34830i | −1.82530 | − | 0.190678i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.7277 | − | 3.50067i | 1.48767 | − | 0.485455i | ||||
\(53\) | −0.488913 | − | 0.846821i | −0.0671573 | − | 0.116320i | 0.830492 | − | 0.557031i | \(-0.188060\pi\) |
−0.897649 | + | 0.440711i | \(0.854726\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.39462i | 0.862251i | ||||||||
\(56\) | −7.24517 | + | 1.87284i | −0.968176 | + | 0.250269i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.65544 | − | 7.79442i | 0.742596 | − | 1.02346i | ||||
\(59\) | −6.67395 | + | 3.85320i | −0.868874 | + | 0.501645i | −0.866974 | − | 0.498354i | \(-0.833938\pi\) |
−0.00190001 | + | 0.999998i | \(0.500605\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.64484 | − | 4.41375i | −0.978822 | − | 0.565123i | −0.0769075 | − | 0.997038i | \(-0.524505\pi\) |
−0.901914 | + | 0.431915i | \(0.857838\pi\) | |||||||
\(62\) | −0.806095 | + | 7.71647i | −0.102374 | + | 0.979993i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.48995 | + | 4.67767i | 0.811244 | + | 0.584708i | ||||
\(65\) | 18.3975 | + | 10.6218i | 2.28193 | + | 1.31747i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.69828 | + | 11.6018i | 0.818325 | + | 1.41738i | 0.906916 | + | 0.421312i | \(0.138430\pi\) |
−0.0885910 | + | 0.996068i | \(0.528236\pi\) | |||||||
\(68\) | −3.88327 | − | 3.48762i | −0.470916 | − | 0.422936i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −11.7369 | − | 7.79179i | −1.40282 | − | 0.931297i | ||||
\(71\) | 9.40544 | 1.11622 | 0.558110 | − | 0.829767i | \(-0.311527\pi\) | ||||
0.558110 | + | 0.829767i | \(0.311527\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.09003 | − | 1.88798i | −0.127578 | − | 0.220971i | 0.795160 | − | 0.606400i | \(-0.207387\pi\) |
−0.922738 | + | 0.385429i | \(0.874054\pi\) | |||||||
\(74\) | 7.75687 | − | 3.45947i | 0.901717 | − | 0.402155i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.62106 | + | 0.976124i | 0.530072 | + | 0.111969i | ||||
\(77\) | −2.08289 | + | 3.98160i | −0.237368 | + | 0.453745i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0908 | + | 8.71267i | 1.69785 | + | 0.980252i | 0.947800 | + | 0.318865i | \(0.103302\pi\) |
0.750045 | + | 0.661386i | \(0.230032\pi\) | |||||||
\(80\) | 1.61217 | + | 14.9739i | 0.180246 | + | 1.67414i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.98758 | − | 5.07002i | −0.771649 | − | 0.559890i | ||||
\(83\) | 11.8864i | 1.30471i | 0.757915 | + | 0.652353i | \(0.226218\pi\) | ||||
−0.757915 | + | 0.652353i | \(0.773782\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 9.82605i | − | 1.06578i | ||||||
\(86\) | −5.39682 | + | 7.43798i | −0.581954 | + | 0.802058i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.69688 | − | 1.00768i | 0.500689 | − | 0.107419i | ||||
\(89\) | −9.58642 | − | 5.53472i | −1.01616 | − | 0.586679i | −0.103170 | − | 0.994664i | \(-0.532898\pi\) |
−0.912989 | + | 0.407984i | \(0.866232\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.99538 | + | 12.6062i | 0.838144 | + | 1.32149i | ||||
\(92\) | 2.55902 | + | 0.540552i | 0.266797 | + | 0.0563564i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.07092 | − | 9.12788i | −0.419883 | − | 0.941469i | ||||
\(95\) | 4.44570 | + | 7.70018i | 0.456119 | + | 0.790021i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.0631 | 1.52943 | 0.764715 | − | 0.644369i | \(-0.222880\pi\) | ||||
0.764715 | + | 0.644369i | \(0.222880\pi\) | |||||||
\(98\) | −4.76995 | − | 8.67454i | −0.481837 | − | 0.876261i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −12.2628 | + | 13.6539i | −1.22628 | + | 1.36539i | ||||
\(101\) | 0.777899 | + | 1.34736i | 0.0774039 | + | 0.134067i | 0.902129 | − | 0.431466i | \(-0.142004\pi\) |
−0.824725 | + | 0.565534i | \(0.808670\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.94066 | − | 4.00719i | −0.683883 | − | 0.394840i | 0.117433 | − | 0.993081i | \(-0.462533\pi\) |
−0.801317 | + | 0.598240i | \(0.795867\pi\) | |||||||
\(104\) | 4.90265 | − | 15.1869i | 0.480744 | − | 1.48919i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.37537 | − | 0.143677i | −0.133588 | − | 0.0139551i | ||||
\(107\) | −12.6257 | − | 7.28943i | −1.22057 | − | 0.704696i | −0.255530 | − | 0.966801i | \(-0.582250\pi\) |
−0.965039 | + | 0.262105i | \(0.915583\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.655188 | − | 0.378273i | 0.0627556 | − | 0.0362320i | −0.468294 | − | 0.883573i | \(-0.655131\pi\) |
0.531050 | + | 0.847341i | \(0.321798\pi\) | |||||||
\(110\) | 7.31960 | + | 5.31092i | 0.697896 | + | 0.506377i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.87358 | + | 9.84862i | −0.366019 | + | 0.930607i | ||||
\(113\) | 9.87390i | 0.928859i | 0.885610 | + | 0.464429i | \(0.153741\pi\) | ||||
−0.885610 | + | 0.464429i | \(0.846259\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.46191 | + | 4.26416i | 0.229574 | + | 0.397635i | ||||
\(116\) | −4.22486 | − | 12.9470i | −0.392268 | − | 1.20210i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.13234 | + | 10.8395i | −0.104241 | + | 0.997859i | ||||
\(119\) | 3.20060 | − | 6.11817i | 0.293398 | − | 0.560852i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.05774 | + | 7.02822i | −0.368886 | + | 0.638929i | ||||
\(122\) | −11.4015 | + | 5.08491i | −1.03224 | + | 0.460366i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.16316 | + | 7.33145i | 0.733074 | + | 0.658384i | ||||
\(125\) | −15.7237 | −1.40637 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.50847i | − | 0.400062i | −0.979790 | − | 0.200031i | \(-0.935896\pi\) | ||
0.979790 | − | 0.200031i | \(-0.0641043\pi\) | |||||||
\(128\) | 10.7444 | − | 3.54377i | 0.949678 | − | 0.313228i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 27.4379 | − | 12.2370i | 2.40647 | − | 1.07325i | ||||
\(131\) | −14.0673 | − | 8.12176i | −1.22907 | − | 0.709601i | −0.262231 | − | 0.965005i | \(-0.584458\pi\) |
−0.966835 | + | 0.255404i | \(0.917792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.259961 | + | 6.24258i | 0.0225414 | + | 0.541300i | ||||
\(134\) | 18.8431 | + | 1.96843i | 1.62779 | + | 0.170046i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.21727 | + | 1.54841i | −0.618876 | + | 0.132775i | ||||
\(137\) | −3.63470 | + | 2.09849i | −0.310533 | + | 0.179286i | −0.647165 | − | 0.762350i | \(-0.724046\pi\) |
0.336632 | + | 0.941636i | \(0.390712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.70274 | −0.483700 | −0.241850 | − | 0.970314i | \(-0.577754\pi\) | ||||
−0.241850 | + | 0.970314i | \(0.577754\pi\) | |||||||
\(140\) | −18.6667 | + | 6.96327i | −1.57762 | + | 0.588504i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.81150 | − | 10.7659i | 0.655526 | − | 0.903457i | ||||
\(143\) | −4.79133 | − | 8.29882i | −0.400671 | − | 0.693982i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.8192 | − | 22.2035i | 1.06458 | − | 1.84390i | ||||
\(146\) | −3.06637 | − | 0.320326i | −0.253775 | − | 0.0265104i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.48243 | − | 11.7521i | 0.204055 | − | 0.966015i | ||||
\(149\) | 6.74195 | − | 11.6774i | 0.552322 | − | 0.956650i | −0.445784 | − | 0.895140i | \(-0.647075\pi\) |
0.998106 | − | 0.0615095i | \(-0.0195915\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.4727 | − | 10.6652i | 1.50329 | − | 0.867924i | 0.503295 | − | 0.864115i | \(-0.332121\pi\) |
0.999993 | − | 0.00380878i | \(-0.00121238\pi\) | |||||||
\(152\) | 4.95525 | − | 4.47879i | 0.401924 | − | 0.363278i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.82763 | + | 5.69102i | 0.227857 | + | 0.458595i | ||||
\(155\) | 20.6557i | 1.65910i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.97251 | − | 4.60293i | 0.636276 | − | 0.367354i | −0.146903 | − | 0.989151i | \(-0.546930\pi\) |
0.783179 | + | 0.621797i | \(0.213597\pi\) | |||||||
\(158\) | 22.5063 | − | 10.0375i | 1.79050 | − | 0.798542i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18.4789 | + | 10.5909i | 1.46088 | + | 0.837287i | ||||
\(161\) | 0.143959 | + | 3.45697i | 0.0113456 | + | 0.272448i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0600325 | − | 0.103979i | 0.00470211 | − | 0.00814429i | −0.863665 | − | 0.504067i | \(-0.831837\pi\) |
0.868367 | + | 0.495922i | \(0.165170\pi\) | |||||||
\(164\) | −11.6068 | + | 3.78753i | −0.906338 | + | 0.295756i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.6058 | + | 9.87204i | 1.05601 | + | 0.766219i | ||||
\(167\) | −12.9810 | −1.00450 | −0.502251 | − | 0.864722i | \(-0.667495\pi\) | ||||
−0.502251 | + | 0.864722i | \(0.667495\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.8346 | −1.44882 | ||||||||
\(170\) | −11.2474 | − | 8.16082i | −0.862634 | − | 0.625907i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.03166 | + | 12.3549i | 0.307411 | + | 0.942054i | ||||
\(173\) | −3.44458 | + | 5.96618i | −0.261886 | + | 0.453600i | −0.966743 | − | 0.255749i | \(-0.917678\pi\) |
0.704857 | + | 0.709350i | \(0.251011\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.5120 | − | 11.2536i | −1.62616 | − | 0.850691i | ||||
\(176\) | 2.74746 | − | 6.21318i | 0.207097 | − | 0.468336i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.2971 | + | 6.37634i | −1.07161 | + | 0.477927i | ||||
\(179\) | 13.6043 | − | 7.85445i | 1.01683 | − | 0.587070i | 0.103649 | − | 0.994614i | \(-0.466948\pi\) |
0.913185 | + | 0.407544i | \(0.133615\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.6714i | 1.16485i | 0.812886 | + | 0.582423i | \(0.197895\pi\) | ||||
−0.812886 | + | 0.582423i | \(0.802105\pi\) | |||||||
\(182\) | 21.0701 | + | 1.31791i | 1.56182 | + | 0.0976901i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.74409 | − | 2.48024i | 0.202297 | − | 0.182846i | ||||
\(185\) | 19.5827 | − | 11.3061i | 1.43975 | − | 0.831241i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.21618 | + | 3.83854i | −0.162063 | + | 0.280702i | ||||
\(188\) | −13.8292 | − | 2.92120i | −1.00860 | − | 0.213051i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.5063 | + | 1.30646i | 0.907301 | + | 0.0947805i | ||||
\(191\) | −12.0633 | + | 20.8943i | −0.872873 | + | 1.51186i | −0.0138617 | + | 0.999904i | \(0.504412\pi\) |
−0.859011 | + | 0.511957i | \(0.828921\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.80306 | − | 8.31914i | −0.345732 | − | 0.598825i | 0.639755 | − | 0.768579i | \(-0.279036\pi\) |
−0.985486 | + | 0.169754i | \(0.945703\pi\) | |||||||
\(194\) | 12.5104 | − | 17.2420i | 0.898193 | − | 1.23790i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.8909 | − | 1.74455i | −0.992206 | − | 0.124610i | ||||
\(197\) | 2.05305 | 0.146274 | 0.0731371 | − | 0.997322i | \(-0.476699\pi\) | ||||
0.0731371 | + | 0.997322i | \(0.476699\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.62103 | + | 4.97735i | −0.611128 | + | 0.352835i | −0.773407 | − | 0.633910i | \(-0.781449\pi\) |
0.162279 | + | 0.986745i | \(0.448116\pi\) | |||||||
\(200\) | 5.44435 | + | 25.3766i | 0.384974 | + | 1.79440i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.18832 | + | 0.228602i | 0.153970 | + | 0.0160844i | ||||
\(203\) | 15.2141 | − | 9.64941i | 1.06782 | − | 0.677256i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.9051 | − | 11.4922i | −1.39023 | − | 0.802651i | ||||
\(206\) | −10.3512 | + | 4.61653i | −0.721206 | + | 0.321649i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.3118 | − | 18.2249i | −0.923010 | − | 1.26367i | ||||
\(209\) | − | 4.01076i | − | 0.277430i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.9757 | −0.962128 | −0.481064 | − | 0.876685i | \(-0.659750\pi\) | ||||
−0.481064 | + | 0.876685i | \(0.659750\pi\) | |||||||
\(212\) | −1.30674 | + | 1.45499i | −0.0897476 | + | 0.0999289i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.8298 | + | 8.39787i | −1.28718 | + | 0.574066i | ||||
\(215\) | −12.2330 | + | 21.1881i | −0.834281 | + | 1.44502i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.72808 | + | 12.8612i | −0.456732 | + | 0.873076i | ||||
\(218\) | 0.111163 | − | 1.06413i | 0.00752893 | − | 0.0720718i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.1583 | − | 3.96749i | 0.819711 | − | 0.267488i | ||||
\(221\) | 7.36241 | + | 12.7521i | 0.495249 | + | 0.857796i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 15.8817i | − | 1.06352i | −0.846896 | − | 0.531759i | \(-0.821531\pi\) | ||
0.846896 | − | 0.531759i | \(-0.178469\pi\) | |||||||
\(224\) | 8.05609 | + | 12.6135i | 0.538270 | + | 0.842772i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.3022 | + | 8.20057i | 0.751808 | + | 0.545494i | ||||
\(227\) | 0.620059 | − | 0.357991i | 0.0411548 | − | 0.0237607i | −0.479281 | − | 0.877661i | \(-0.659103\pi\) |
0.520436 | + | 0.853901i | \(0.325769\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.89913 | − | 2.25117i | −0.257662 | − | 0.148761i | 0.365606 | − | 0.930770i | \(-0.380862\pi\) |
−0.623268 | + | 0.782009i | \(0.714195\pi\) | |||||||
\(230\) | 6.92565 | + | 0.723483i | 0.456664 | + | 0.0477051i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.3286 | − | 5.91687i | −1.20333 | − | 0.388462i | ||||
\(233\) | 6.69604 | + | 3.86596i | 0.438672 | + | 0.253267i | 0.703034 | − | 0.711156i | \(-0.251828\pi\) |
−0.264362 | + | 0.964423i | \(0.585161\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.3044 | − | 23.0440i | −0.867886 | − | 1.50322i | ||||
\(236\) | 11.4670 | + | 10.2987i | 0.746438 | + | 0.670387i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.34496 | − | 8.74488i | −0.281642 | − | 0.566846i | ||||
\(239\) | −21.3788 | −1.38288 | −0.691440 | − | 0.722433i | \(-0.743024\pi\) | ||||
−0.691440 | + | 0.722433i | \(0.743024\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.25688 | + | 7.37313i | 0.274210 | + | 0.474945i | 0.969935 | − | 0.243362i | \(-0.0782504\pi\) |
−0.695726 | + | 0.718308i | \(0.744917\pi\) | |||||||
\(242\) | 4.67477 | + | 10.4818i | 0.300505 | + | 0.673798i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.64882 | + | 17.2738i | −0.233592 | + | 1.10584i | ||||
\(245\) | −15.0300 | − | 21.6502i | −0.960232 | − | 1.38318i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.5391 | − | 6.66209i | −0.734215 | − | 0.423899i | ||||
\(248\) | 15.1717 | − | 3.25497i | 0.963403 | − | 0.206691i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.0590 | + | 17.9981i | −0.825922 | + | 1.13830i | ||||
\(251\) | 0.778871i | 0.0491619i | 0.999698 | + | 0.0245810i | \(0.00782515\pi\) | ||||
−0.999698 | + | 0.0245810i | \(0.992175\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.22106i | − | 0.139637i | ||||||
\(254\) | −5.16062 | − | 3.74442i | −0.323806 | − | 0.234946i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.86715 | − | 15.2417i | 0.304197 | − | 0.952609i | ||||
\(257\) | −10.6901 | − | 6.17195i | −0.666832 | − | 0.384996i | 0.128043 | − | 0.991769i | \(-0.459130\pi\) |
−0.794875 | + | 0.606773i | \(0.792464\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.8758 | − | 0.661120i | 0.986476 | − | 0.0410800i | ||||
\(260\) | 8.78098 | − | 41.5700i | 0.544573 | − | 2.57806i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.9799 | + | 9.35676i | −1.29614 | + | 0.578062i | ||||
\(263\) | −1.01432 | − | 1.75686i | −0.0625458 | − | 0.108333i | 0.833057 | − | 0.553187i | \(-0.186589\pi\) |
−0.895603 | + | 0.444855i | \(0.853255\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.68163 | −0.226161 | ||||||||
\(266\) | 7.36146 | + | 4.88708i | 0.451360 | + | 0.299646i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 17.9029 | − | 19.9338i | 1.09359 | − | 1.21765i | ||||
\(269\) | 13.1346 | + | 22.7498i | 0.800833 | + | 1.38708i | 0.919069 | + | 0.394097i | \(0.128943\pi\) |
−0.118236 | + | 0.992986i | \(0.537724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.01591 | + | 4.05064i | 0.426186 | + | 0.246059i | 0.697720 | − | 0.716370i | \(-0.254198\pi\) |
−0.271535 | + | 0.962429i | \(0.587531\pi\) | |||||||
\(272\) | −4.22177 | + | 9.54724i | −0.255983 | + | 0.578887i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.616685 | + | 5.90331i | −0.0372553 | + | 0.356632i | ||||
\(275\) | 13.4967 | + | 7.79231i | 0.813880 | + | 0.469894i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.45693 | − | 4.88261i | 0.508127 | − | 0.293368i | −0.223936 | − | 0.974604i | \(-0.571891\pi\) |
0.732064 | + | 0.681236i | \(0.238557\pi\) | |||||||
\(278\) | −4.73630 | + | 6.52764i | −0.284064 | + | 0.391502i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.53272 | + | 27.1500i | −0.450166 | + | 1.62252i | ||||
\(281\) | − | 1.88752i | − | 0.112600i | −0.998414 | − | 0.0562999i | \(-0.982070\pi\) | ||
0.998414 | − | 0.0562999i | \(-0.0179303\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.28892 | + | 5.69657i | 0.195506 | + | 0.338626i | 0.947066 | − | 0.321038i | \(-0.104032\pi\) |
−0.751560 | + | 0.659664i | \(0.770698\pi\) | |||||||
\(284\) | −5.83553 | − | 17.8828i | −0.346275 | − | 1.06115i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.4786 | − | 1.40803i | −0.797005 | − | 0.0832585i | ||||
\(287\) | −8.65056 | − | 13.6392i | −0.510626 | − | 0.805097i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.09459 | + | 8.82408i | −0.299682 | + | 0.519064i | ||||
\(290\) | −14.7685 | − | 33.1141i | −0.867235 | − | 1.94453i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.91337 | + | 3.24388i | −0.170492 | + | 0.189834i | ||||
\(293\) | −14.1311 | −0.825545 | −0.412772 | − | 0.910834i | \(-0.635440\pi\) | ||||
−0.412772 | + | 0.910834i | \(0.635440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.0156i | 1.68935i | ||||||||
\(296\) | −11.3903 | − | 12.6020i | −0.662046 | − | 0.732474i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.76713 | − | 17.4156i | −0.449938 | − | 1.00886i | ||||
\(299\) | −6.39004 | − | 3.68929i | −0.369546 | − | 0.213357i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.5183 | + | 9.20814i | −0.836823 | + | 0.530749i | ||||
\(302\) | 3.13419 | − | 30.0025i | 0.180353 | − | 1.72645i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.01117 | − | 9.39179i | −0.0579944 | − | 0.538656i | ||||
\(305\) | −28.7838 | + | 16.6183i | −1.64815 | + | 0.951562i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.5973 | −1.00433 | −0.502167 | − | 0.864771i | \(-0.667464\pi\) | ||||
−0.502167 | + | 0.864771i | \(0.667464\pi\) | |||||||
\(308\) | 8.86264 | + | 1.48991i | 0.504996 | + | 0.0848958i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 23.6435 | + | 17.1552i | 1.34286 | + | 0.974347i | ||||
\(311\) | −5.44683 | − | 9.43418i | −0.308861 | − | 0.534963i | 0.669252 | − | 0.743035i | \(-0.266615\pi\) |
−0.978114 | + | 0.208072i | \(0.933281\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.76535 | + | 3.05768i | −0.0997835 | + | 0.172830i | −0.911595 | − | 0.411090i | \(-0.865148\pi\) |
0.811811 | + | 0.583920i | \(0.198482\pi\) | |||||||
\(314\) | 1.35267 | − | 12.9486i | 0.0763354 | − | 0.730732i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.20270 | − | 34.0982i | 0.405183 | − | 1.91818i | ||||
\(317\) | −8.09426 | + | 14.0197i | −0.454619 | + | 0.787423i | −0.998666 | − | 0.0516316i | \(-0.983558\pi\) |
0.544047 | + | 0.839055i | \(0.316891\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0156 | + | 5.78252i | −0.560767 | + | 0.323759i | ||||
\(320\) | 27.4701 | − | 12.3557i | 1.53563 | − | 0.690706i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.07658 | + | 2.70634i | 0.227179 | + | 0.150818i | ||||
\(323\) | 6.16298i | 0.342918i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 44.8374 | − | 25.8869i | 2.48713 | − | 1.43595i | ||||
\(326\) | −0.0691610 | − | 0.155074i | −0.00383048 | − | 0.00858875i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.30439 | + | 16.4313i | −0.292886 | + | 0.907269i | ||||
\(329\) | −0.777972 | − | 18.6819i | −0.0428910 | − | 1.02996i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.79835 | − | 10.0430i | 0.318706 | − | 0.552016i | −0.661512 | − | 0.749935i | \(-0.730085\pi\) |
0.980218 | + | 0.197919i | \(0.0634183\pi\) | |||||||
\(332\) | 22.6000 | − | 7.37484i | 1.24034 | − | 0.404747i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.7811 | + | 14.8587i | −0.589917 | + | 0.813033i | ||||
\(335\) | 50.4397 | 2.75581 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.81073 | 0.153110 | 0.0765550 | − | 0.997065i | \(-0.475608\pi\) | ||||
0.0765550 | + | 0.997065i | \(0.475608\pi\) | |||||||
\(338\) | −15.6427 | + | 21.5590i | −0.850851 | + | 1.17266i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −18.6826 | + | 6.09649i | −1.01320 | + | 0.330629i | ||||
\(341\) | 4.65872 | − | 8.06914i | 0.252284 | − | 0.436968i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.30639 | − | 18.3761i | −0.124533 | − | 0.992215i | ||||
\(344\) | 17.4905 | + | 5.64629i | 0.943022 | + | 0.304428i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.96836 | + | 8.89792i | 0.213340 | + | 0.478355i | ||||
\(347\) | −18.7883 | + | 10.8474i | −1.00861 | + | 0.582320i | −0.910784 | − | 0.412884i | \(-0.864522\pi\) |
−0.0978242 | + | 0.995204i | \(0.531188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.44465i | 0.398503i | 0.979948 | + | 0.199251i | \(0.0638511\pi\) | ||||
−0.979948 | + | 0.199251i | \(0.936149\pi\) | |||||||
\(350\) | −30.7478 | + | 15.2773i | −1.64354 | + | 0.816606i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.83007 | − | 8.30511i | −0.257443 | − | 0.442664i | ||||
\(353\) | 13.0365 | − | 7.52665i | 0.693865 | − | 0.400603i | −0.111193 | − | 0.993799i | \(-0.535467\pi\) |
0.805058 | + | 0.593196i | \(0.202134\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.7063 | − | 30.6682i | 0.939754 | − | 1.62770i | ||||
\(356\) | −4.57551 | + | 21.6609i | −0.242502 | + | 1.14803i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.30819 | − | 22.0955i | 0.121992 | − | 1.16778i | ||||
\(359\) | 9.01876 | − | 15.6210i | 0.475992 | − | 0.824442i | −0.523630 | − | 0.851946i | \(-0.675422\pi\) |
0.999622 | + | 0.0275035i | \(0.00875575\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.71162 | + | 11.6249i | 0.353243 | + | 0.611835i | ||||
\(362\) | 17.9383 | + | 13.0156i | 0.942814 | + | 0.684083i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 19.0079 | − | 23.0233i | 0.996282 | − | 1.20675i | ||||
\(365\) | −8.20816 | −0.429635 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.38897 | − | 1.95662i | 0.176903 | − | 0.102135i | −0.408934 | − | 0.912564i | \(-0.634099\pi\) |
0.585837 | + | 0.810429i | \(0.300766\pi\) | |||||||
\(368\) | −0.559958 | − | 5.20093i | −0.0291898 | − | 0.271117i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.32253 | − | 31.8054i | 0.172730 | − | 1.65348i | ||||
\(371\) | −2.29236 | − | 1.19920i | −0.119013 | − | 0.0622594i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.8513 | − | 9.15178i | −0.820752 | − | 0.473861i | 0.0299239 | − | 0.999552i | \(-0.490473\pi\) |
−0.850676 | + | 0.525691i | \(0.823807\pi\) | |||||||
\(374\) | 2.55318 | + | 5.72478i | 0.132022 | + | 0.296021i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.8293 | + | 13.4035i | −0.764765 | + | 0.691232i | ||||
\(377\) | 38.4203i | 1.97875i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.8073 | 1.32563 | 0.662816 | − | 0.748783i | \(-0.269361\pi\) | ||||
0.662816 | + | 0.748783i | \(0.269361\pi\) | |||||||
\(380\) | 11.8823 | − | 13.2302i | 0.609548 | − | 0.678697i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.8977 | + | 31.1616i | 0.711068 | + | 1.59437i | ||||
\(383\) | 7.37665 | − | 12.7767i | 0.376929 | − | 0.652860i | −0.613685 | − | 0.789551i | \(-0.710313\pi\) |
0.990614 | + | 0.136691i | \(0.0436467\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.06159 | + | 14.2873i | 0.461822 | + | 0.728147i | ||||
\(386\) | −13.5116 | − | 1.41148i | −0.687721 | − | 0.0718423i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.34580 | − | 28.6400i | −0.474461 | − | 1.45397i | ||||
\(389\) | −8.70264 | − | 15.0734i | −0.441242 | − | 0.764253i | 0.556540 | − | 0.830821i | \(-0.312128\pi\) |
−0.997782 | + | 0.0665677i | \(0.978795\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.41290i | 0.172598i | ||||||||
\(392\) | −13.5337 | + | 14.4513i | −0.683554 | + | 0.729900i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.70512 | − | 2.35003i | 0.0859028 | − | 0.118393i | ||||
\(395\) | 56.8186 | − | 32.8042i | 2.85886 | − | 1.65056i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.0273 | − | 5.78926i | −0.503255 | − | 0.290554i | 0.226802 | − | 0.973941i | \(-0.427173\pi\) |
−0.730057 | + | 0.683387i | \(0.760506\pi\) | |||||||
\(398\) | −1.46270 | + | 14.0019i | −0.0733184 | + | 0.701851i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 33.5690 | + | 14.8441i | 1.67845 | + | 0.742207i | ||||
\(401\) | −31.1453 | − | 17.9818i | −1.55532 | − | 0.897967i | −0.997694 | − | 0.0678773i | \(-0.978377\pi\) |
−0.557630 | − | 0.830089i | \(-0.688289\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.4768 | − | 26.8065i | −0.770953 | − | 1.33533i | ||||
\(404\) | 2.07914 | − | 2.31500i | 0.103441 | − | 0.115176i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.59055 | − | 25.4289i | 0.0789378 | − | 1.26201i | ||||
\(407\) | −10.2000 | −0.505595 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.1615 | + | 21.0644i | 0.601349 | + | 1.04157i | 0.992617 | + | 0.121290i | \(0.0387031\pi\) |
−0.391268 | + | 0.920277i | \(0.627964\pi\) | |||||||
\(410\) | −29.6863 | + | 13.2397i | −1.46610 | + | 0.653863i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.31272 | + | 15.6827i | −0.163206 | + | 0.772631i | ||||
\(413\) | −9.45111 | + | 18.0665i | −0.465059 | + | 0.888993i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38.7580 | + | 22.3769i | 1.90256 | + | 1.09844i | ||||
\(416\) | −31.9170 | + | 0.101021i | −1.56486 | + | 0.00495294i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.59092 | − | 3.33106i | −0.224549 | − | 0.162927i | ||||
\(419\) | 6.92954i | 0.338530i | 0.985571 | + | 0.169265i | \(0.0541394\pi\) | ||||
−0.985571 | + | 0.169265i | \(0.945861\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.6192i | 0.615024i | 0.951544 | + | 0.307512i | \(0.0994965\pi\) | ||||
−0.951544 | + | 0.307512i | \(0.900504\pi\) | |||||||
\(422\) | −11.6072 | + | 15.9973i | −0.565032 | + | 0.778736i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.580159 | + | 2.70417i | 0.0281750 | + | 0.131326i | ||||
\(425\) | −20.7391 | − | 11.9737i | −1.00600 | − | 0.580812i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.3352 | + | 0.971750i | −1.12927 | + | 0.0470263i | ||||
\(428\) | −6.02612 | + | 28.5282i | −0.291284 | + | 1.37896i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.0931 | + | 31.5998i | 0.679630 | + | 1.52388i | ||||
\(431\) | 11.1759 | + | 19.3571i | 0.538322 | + | 0.932401i | 0.998995 | + | 0.0448306i | \(0.0142748\pi\) |
−0.460673 | + | 0.887570i | \(0.652392\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.2813 | −1.55134 | −0.775671 | − | 0.631138i | \(-0.782588\pi\) | ||||
−0.775671 | + | 0.631138i | \(0.782588\pi\) | |||||||
\(434\) | 9.13370 | + | 18.3829i | 0.438432 | + | 0.882408i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.12573 | − | 1.01103i | −0.0539126 | − | 0.0484196i | ||||
\(437\) | −1.54413 | − | 2.67451i | −0.0738658 | − | 0.127939i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.42798 | + | 1.40180i | 0.115881 | + | 0.0669041i | 0.556820 | − | 0.830633i | \(-0.312021\pi\) |
−0.440939 | + | 0.897537i | \(0.645355\pi\) | |||||||
\(440\) | 5.55643 | − | 17.2121i | 0.264892 | − | 0.820554i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.7113 | + | 2.16359i | 0.985137 | + | 0.102912i | ||||
\(443\) | 16.2066 | + | 9.35689i | 0.769999 | + | 0.444559i | 0.832874 | − | 0.553462i | \(-0.186694\pi\) |
−0.0628752 | + | 0.998021i | \(0.520027\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −36.0940 | + | 20.8389i | −1.71102 | + | 0.987859i | ||||
\(446\) | −18.1790 | − | 13.1902i | −0.860799 | − | 0.624575i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 21.1288 | + | 1.25446i | 0.998242 | + | 0.0592678i | ||||
\(449\) | 13.8950i | 0.655747i | 0.944722 | + | 0.327874i | \(0.106332\pi\) | ||||
−0.944722 | + | 0.327874i | \(0.893668\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.18395 | + | 8.97886i | 0.244103 | + | 0.422798i | ||||
\(452\) | 18.7735 | − | 6.12618i | 0.883033 | − | 0.288151i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.105203 | − | 1.00707i | 0.00493742 | − | 0.0472642i | ||||
\(455\) | 56.1567 | − | 2.33854i | 2.63267 | − | 0.109633i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.88922 | − | 5.00428i | 0.135152 | − | 0.234090i | −0.790503 | − | 0.612458i | \(-0.790181\pi\) |
0.925656 | + | 0.378367i | \(0.123514\pi\) | |||||||
\(458\) | −5.81514 | + | 2.59348i | −0.271724 | + | 0.121185i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.58009 | − | 7.32656i | 0.306798 | − | 0.341603i | ||||
\(461\) | 15.4222 | 0.718285 | 0.359142 | − | 0.933283i | \(-0.383069\pi\) | ||||
0.359142 | + | 0.933283i | \(0.383069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.5902i | 0.538644i | 0.963050 | + | 0.269322i | \(0.0867996\pi\) | ||||
−0.963050 | + | 0.269322i | \(0.913200\pi\) | |||||||
\(464\) | −21.9952 | + | 16.0657i | −1.02110 | + | 0.745831i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.98642 | − | 4.45382i | 0.462612 | − | 0.206319i | ||||
\(467\) | −1.98153 | − | 1.14404i | −0.0916943 | − | 0.0529397i | 0.453452 | − | 0.891281i | \(-0.350192\pi\) |
−0.545146 | + | 0.838341i | \(0.683526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.4061 | + | 16.4295i | 1.45020 | + | 0.758643i | ||||
\(470\) | −37.4270 | − | 3.90978i | −1.72638 | − | 0.180345i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.3121 | − | 4.57234i | 0.980967 | − | 0.210459i | ||||
\(473\) | 9.55761 | − | 5.51809i | 0.439459 | − | 0.253722i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.6696 | 0.994270 | ||||||||
\(476\) | −13.6184 | − | 2.28942i | −0.624200 | − | 0.104935i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.7557 | + | 24.4712i | −0.812129 | + | 1.11929i | ||||
\(479\) | −9.42948 | − | 16.3323i | −0.430844 | − | 0.746244i | 0.566102 | − | 0.824335i | \(-0.308451\pi\) |
−0.996946 | + | 0.0780912i | \(0.975117\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.9427 | + | 29.3457i | −0.772522 | + | 1.33805i | ||||
\(482\) | 11.9751 | + | 1.25097i | 0.545451 | + | 0.0569802i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.8806 | + | 3.35451i | 0.721843 | + | 0.152478i | ||||
\(485\) | 28.3573 | − | 49.1162i | 1.28764 | − | 2.23025i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.9019 | − | 15.5318i | 1.21904 | − | 0.703813i | 0.254327 | − | 0.967118i | \(-0.418146\pi\) |
0.964713 | + | 0.263305i | \(0.0848126\pi\) | |||||||
\(488\) | 16.7420 | + | 18.5230i | 0.757876 | + | 0.838499i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −37.2647 | − | 0.777026i | −1.68345 | − | 0.0351025i | ||||
\(491\) | − | 7.52948i | − | 0.339801i | −0.985461 | − | 0.169900i | \(-0.945655\pi\) | ||
0.985461 | − | 0.169900i | \(-0.0543446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.3901 | − | 8.88549i | 0.693136 | − | 0.400182i | ||||
\(494\) | −17.2093 | + | 7.67514i | −0.774283 | + | 0.345321i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.87474 | − | 20.0696i | 0.398487 | − | 0.901151i | ||||
\(497\) | 21.0142 | − | 13.3281i | 0.942617 | − | 0.597848i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.883277 | + | 1.52988i | −0.0395409 | + | 0.0684869i | −0.885119 | − | 0.465366i | \(-0.845923\pi\) |
0.845578 | + | 0.533852i | \(0.179256\pi\) | |||||||
\(500\) | 9.75562 | + | 29.8959i | 0.436285 | + | 1.33698i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.891534 | + | 0.646876i | 0.0397911 | + | 0.0288715i | ||||
\(503\) | −16.9584 | −0.756136 | −0.378068 | − | 0.925778i | \(-0.623411\pi\) | ||||
−0.378068 | + | 0.925778i | \(0.623411\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.85777 | 0.260667 | ||||||||
\(506\) | −2.54233 | − | 1.84465i | −0.113020 | − | 0.0820048i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.57209 | + | 2.79724i | −0.380325 | + | 0.124108i | ||||
\(509\) | −5.13114 | + | 8.88739i | −0.227434 | + | 0.393927i | −0.957047 | − | 0.289934i | \(-0.906367\pi\) |
0.729613 | + | 0.683860i | \(0.239700\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.11079 | − | 2.67361i | −0.226088 | − | 0.118273i | ||||
\(512\) | −13.4041 | − | 18.2299i | −0.592385 | − | 0.805655i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.9432 | + | 7.11046i | −0.703224 | + | 0.313629i | ||||
\(515\) | −26.1324 | + | 15.0876i | −1.15153 | + | 0.664837i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0028i | 0.527884i | ||||||||
\(518\) | 12.4286 | − | 18.7213i | 0.546081 | − | 0.822568i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −40.2902 | − | 44.5762i | −1.76684 | − | 1.95480i | ||||
\(521\) | −32.7368 | + | 18.9006i | −1.43423 | + | 0.828051i | −0.997440 | − | 0.0715138i | \(-0.977217\pi\) |
−0.436787 | + | 0.899565i | \(0.643884\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.6691 | − | 34.0679i | 0.860070 | − | 1.48968i | −0.0117911 | − | 0.999930i | \(-0.503753\pi\) |
0.871861 | − | 0.489754i | \(-0.162913\pi\) | |||||||
\(524\) | −6.71420 | + | 31.7856i | −0.293311 | + | 1.38856i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.85341 | − | 0.298080i | −0.124415 | − | 0.0129969i | ||||
\(527\) | −7.15864 | + | 12.3991i | −0.311835 | + | 0.540114i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6449 | + | 18.4375i | 0.462822 | + | 0.801631i | ||||
\(530\) | −3.05770 | + | 4.21417i | −0.132818 | + | 0.183052i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.7079 | − | 4.36742i | 0.507602 | − | 0.189352i | ||||
\(533\) | 34.4433 | 1.49190 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −47.5372 | + | 27.4456i | −2.05521 | + | 1.18658i | ||||
\(536\) | −7.94839 | − | 37.0481i | −0.343318 | − | 1.60024i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 36.9493 | + | 3.85988i | 1.59300 | + | 0.166411i | ||||
\(539\) | 0.988451 | + | 11.8475i | 0.0425756 | + | 0.510309i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.8385 | − | 7.41231i | −0.551970 | − | 0.318680i | 0.197946 | − | 0.980213i | \(-0.436573\pi\) |
−0.749916 | + | 0.661533i | \(0.769906\pi\) | |||||||
\(542\) | 10.4635 | − | 4.66658i | 0.449445 | − | 0.200447i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.42193 | + | 12.7617i | 0.318213 | + | 0.547154i | ||||
\(545\) | − | 2.84849i | − | 0.122016i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.2017 | −0.692736 | −0.346368 | − | 0.938099i | \(-0.612585\pi\) | ||||
−0.346368 | + | 0.938099i | \(0.612585\pi\) | |||||||
\(548\) | 6.24505 | + | 5.60876i | 0.266775 | + | 0.239595i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 20.1288 | − | 8.97721i | 0.858297 | − | 0.382790i | ||||
\(551\) | −8.04030 | + | 13.9262i | −0.342528 | + | 0.593277i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46.0632 | − | 1.91822i | 1.95881 | − | 0.0815708i | ||||
\(554\) | 1.43485 | − | 13.7354i | 0.0609611 | − | 0.583560i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.53822 | + | 10.8428i | 0.150054 | + | 0.459837i | ||||
\(557\) | 1.17534 | + | 2.03574i | 0.0498006 | + | 0.0862572i | 0.889851 | − | 0.456251i | \(-0.150808\pi\) |
−0.840051 | + | 0.542508i | \(0.817475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 36.6634i | − | 1.55070i | ||||||
\(560\) | 24.8211 | + | 31.1712i | 1.04888 | + | 1.31722i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.16054 | − | 1.56764i | −0.0911370 | − | 0.0661268i | ||||
\(563\) | −6.40537 | + | 3.69814i | −0.269954 | + | 0.155858i | −0.628867 | − | 0.777513i | \(-0.716481\pi\) |
0.358913 | + | 0.933371i | \(0.383148\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.1957 | + | 18.5882i | 1.35449 | + | 0.782012i | ||||
\(566\) | 9.25211 | + | 0.966515i | 0.388895 | + | 0.0406257i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −25.3161 | − | 8.17260i | −1.06224 | − | 0.342914i | ||||
\(569\) | −30.2952 | − | 17.4909i | −1.27004 | − | 0.733258i | −0.295045 | − | 0.955483i | \(-0.595334\pi\) |
−0.974995 | + | 0.222226i | \(0.928668\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4081 | + | 28.4197i | 0.686659 | + | 1.18933i | 0.972912 | + | 0.231174i | \(0.0742567\pi\) |
−0.286254 | + | 0.958154i | \(0.592410\pi\) | |||||||
\(572\) | −12.8061 | + | 14.2588i | −0.535448 | + | 0.596191i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22.7966 | − | 1.42591i | −0.951513 | − | 0.0595162i | ||||
\(575\) | 12.0001 | 0.500437 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.58139 | + | 7.93520i | 0.190726 | + | 0.330347i | 0.945491 | − | 0.325648i | \(-0.105583\pi\) |
−0.754765 | + | 0.655995i | \(0.772249\pi\) | |||||||
\(578\) | 5.86927 | + | 13.1602i | 0.244130 | + | 0.547391i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −50.1697 | − | 10.5975i | −2.08318 | − | 0.440038i | ||||
\(581\) | 16.8438 | + | 26.5574i | 0.698800 | + | 1.10179i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.43823 | + | 0.830362i | 0.0595653 | + | 0.0343901i | ||||
\(584\) | 1.29346 | + | 6.02893i | 0.0535237 | + | 0.249479i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.7363 | + | 16.1751i | −0.484820 | + | 0.668187i | ||||
\(587\) | − | 17.4528i | − | 0.720354i | −0.932884 | − | 0.360177i | \(-0.882716\pi\) | ||
0.932884 | − | 0.360177i | \(-0.117284\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 12.9554i | − | 0.533819i | ||||||
\(590\) | 33.2126 | + | 24.0983i | 1.36734 | + | 0.992111i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −23.8848 | + | 2.57155i | −0.981658 | + | 0.105690i | ||||
\(593\) | −17.0385 | − | 9.83721i | −0.699689 | − | 0.403966i | 0.107542 | − | 0.994200i | \(-0.465702\pi\) |
−0.807232 | + | 0.590235i | \(0.799035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.9241 | − | 21.9540i | −0.570834 | − | 0.900025i | ||||
\(596\) | −26.3856 | − | 5.57352i | −1.08079 | − | 0.228300i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.53006 | + | 4.25029i | −0.389713 | + | 0.173807i | ||||
\(599\) | 2.68048 | + | 4.64273i | 0.109521 | + | 0.189697i | 0.915576 | − | 0.402144i | \(-0.131735\pi\) |
−0.806055 | + | 0.591841i | \(0.798402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.4609 | 0.508291 | 0.254145 | − | 0.967166i | \(-0.418206\pi\) | ||||
0.254145 | + | 0.967166i | \(0.418206\pi\) | |||||||
\(602\) | −1.51782 | + | 24.2660i | −0.0618616 | + | 0.989010i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −31.7393 | − | 28.5055i | −1.29146 | − | 1.15987i | ||||
\(605\) | 15.2779 | + | 26.4621i | 0.621135 | + | 1.07584i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.6807 | − | 6.16649i | −0.433515 | − | 0.250290i | 0.267328 | − | 0.963606i | \(-0.413859\pi\) |
−0.700843 | + | 0.713315i | \(0.747193\pi\) | |||||||
\(608\) | −11.5901 | − | 6.64273i | −0.470041 | − | 0.269398i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.88363 | + | 46.7493i | −0.197732 | + | 1.89282i | ||||
\(611\) | 34.5325 | + | 19.9373i | 1.39704 | + | 0.806579i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.55744 | + | 2.05389i | −0.143683 | + | 0.0829557i | −0.570118 | − | 0.821563i | \(-0.693103\pi\) |
0.426435 | + | 0.904518i | \(0.359769\pi\) | |||||||
\(614\) | −14.6151 | + | 20.1428i | −0.589818 | + | 0.812896i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.06612 | − | 8.90720i | 0.365284 | − | 0.358881i | ||||
\(617\) | 36.1255i | 1.45436i | 0.686447 | + | 0.727180i | \(0.259169\pi\) | ||||
−0.686447 | + | 0.727180i | \(0.740831\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.802674 | − | 1.39027i | −0.0322622 | − | 0.0558798i | 0.849443 | − | 0.527680i | \(-0.176938\pi\) |
−0.881706 | + | 0.471800i | \(0.843604\pi\) | |||||||
\(620\) | 39.2732 | − | 12.8156i | 1.57725 | − | 0.514689i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.3226 | − | 1.60066i | −0.614379 | − | 0.0641807i | ||||
\(623\) | −29.2616 | + | 1.21855i | −1.17234 | + | 0.0488201i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.66043 | + | 11.5362i | −0.266417 | + | 0.461448i | ||||
\(626\) | 2.03379 | + | 4.56020i | 0.0812866 | + | 0.182262i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.6982 | − | 12.3025i | −0.546616 | − | 0.490924i | ||||
\(629\) | 15.6734 | 0.624940 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.98270i | 0.357596i | 0.983886 | + | 0.178798i | \(0.0572208\pi\) | ||||
−0.983886 | + | 0.178798i | \(0.942779\pi\) | |||||||
\(632\) | −33.0485 | − | 36.5642i | −1.31460 | − | 1.45444i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.32507 | + | 20.9088i | 0.370346 | + | 0.830396i | ||||
\(635\) | −14.7007 | − | 8.48748i | −0.583381 | − | 0.336815i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.7276 | + | 16.8356i | 1.41558 | + | 0.667050i | ||||
\(638\) | −1.69931 | + | 16.2669i | −0.0672764 | + | 0.644014i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.67180 | − | 41.7055i | 0.342783 | − | 1.64855i | ||||
\(641\) | 34.1214 | − | 19.7000i | 1.34772 | − | 0.778104i | 0.359790 | − | 0.933033i | \(-0.382848\pi\) |
0.987926 | + | 0.154929i | \(0.0495149\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.0002 | 1.57745 | 0.788726 | − | 0.614745i | \(-0.210741\pi\) | ||||
0.788726 | + | 0.614745i | \(0.210741\pi\) | |||||||
\(644\) | 6.48353 | − | 2.41856i | 0.255487 | − | 0.0953048i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.05445 | + | 5.11854i | 0.277554 | + | 0.201386i | ||||
\(647\) | −19.8854 | − | 34.4425i | −0.781775 | − | 1.35407i | −0.930907 | − | 0.365257i | \(-0.880981\pi\) |
0.149132 | − | 0.988817i | \(-0.452352\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.54422 | − | 11.3349i | 0.256883 | − | 0.444935i | ||||
\(650\) | 7.60739 | − | 72.8229i | 0.298386 | − | 2.85635i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.234946 | − | 0.0496284i | −0.00920118 | − | 0.00194360i | ||||
\(653\) | 1.64003 | − | 2.84061i | 0.0641792 | − | 0.111162i | −0.832150 | − | 0.554550i | \(-0.812890\pi\) |
0.896330 | + | 0.443388i | \(0.146224\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −52.9651 | + | 30.5794i | −2.06952 | + | 1.19484i | ||||
\(656\) | 14.4027 | + | 19.7184i | 0.562330 | + | 0.769873i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −22.0303 | − | 14.6253i | −0.858831 | − | 0.570155i | ||||
\(659\) | 16.7484i | 0.652425i | 0.945297 | + | 0.326212i | \(0.105772\pi\) | ||||
−0.945297 | + | 0.326212i | \(0.894228\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.50164 | + | 2.59902i | −0.175093 | + | 0.101090i | −0.584985 | − | 0.811044i | \(-0.698900\pi\) |
0.409892 | + | 0.912134i | \(0.365566\pi\) | |||||||
\(662\) | −6.68005 | − | 14.9781i | −0.259628 | − | 0.582141i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.3284 | − | 31.9941i | 0.400819 | − | 1.24161i | ||||
\(665\) | 20.8445 | + | 10.9044i | 0.808315 | + | 0.422854i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.45251 | + | 7.71197i | −0.172402 | + | 0.298609i | ||||
\(668\) | 8.05397 | + | 24.6812i | 0.311618 | + | 0.954945i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 41.8916 | − | 57.7357i | 1.61841 | − | 2.23052i | ||||
\(671\) | 14.9925 | 0.578779 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.9571 | −1.15476 | −0.577380 | − | 0.816475i | \(-0.695925\pi\) | ||||
−0.577380 | + | 0.816475i | \(0.695925\pi\) | |||||||
\(674\) | 2.33439 | − | 3.21729i | 0.0899174 | − | 0.123926i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.6858 | + | 35.8108i | 0.449453 | + | 1.37734i | ||||
\(677\) | 15.2704 | − | 26.4492i | 0.586891 | − | 1.01652i | −0.407746 | − | 0.913095i | \(-0.633685\pi\) |
0.994637 | − | 0.103429i | \(-0.0329816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.6550 | − | 21.3454i | 1.29156 | − | 0.819162i | ||||
\(680\) | −8.53807 | + | 26.4483i | −0.327420 | + | 1.01425i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.36713 | − | 12.0343i | −0.205518 | − | 0.460815i | ||||
\(683\) | 11.1942 | − | 6.46296i | 0.428333 | − | 0.247298i | −0.270303 | − | 0.962775i | \(-0.587124\pi\) |
0.698636 | + | 0.715477i | \(0.253791\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.8022i | 0.603770i | ||||||||
\(686\) | −22.9497 | − | 12.6219i | −0.876223 | − | 0.481906i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.9894 | − | 15.3310i | 0.800212 | − | 0.584489i | ||||
\(689\) | 4.77795 | − | 2.75855i | 0.182025 | − | 0.105092i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.33676 | + | 14.4397i | −0.317145 | + | 0.549312i | −0.979891 | − | 0.199533i | \(-0.936058\pi\) |
0.662746 | + | 0.748844i | \(0.269391\pi\) | |||||||
\(692\) | 13.4808 | + | 2.84761i | 0.512464 | + | 0.108250i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.18774 | + | 30.5151i | −0.121005 | + | 1.15834i | ||||
\(695\) | −10.7358 | + | 18.5949i | −0.407231 | + | 0.705344i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.96571 | − | 13.7970i | −0.301723 | − | 0.522599i | ||||
\(698\) | 8.52151 | + | 6.18300i | 0.322544 | + | 0.234030i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.04980 | + | 47.8837i | −0.304254 | + | 1.80983i | ||||
\(701\) | 24.5914 | 0.928805 | 0.464403 | − | 0.885624i | \(-0.346269\pi\) | ||||
0.464403 | + | 0.885624i | \(0.346269\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.2825 | + | 7.09128i | −0.463242 | + | 0.267453i | ||||
\(704\) | −13.5179 | − | 1.36890i | −0.509477 | − | 0.0515925i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.21186 | − | 21.1734i | 0.0832444 | − | 0.796870i | ||||
\(707\) | 3.64733 | + | 1.90803i | 0.137172 | + | 0.0717587i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.59843 | + | 2.65490i | 0.172698 | + | 0.0997070i | 0.583857 | − | 0.811856i | \(-0.301543\pi\) |
−0.411160 | + | 0.911563i | \(0.634876\pi\) | |||||||
\(710\) | −20.3987 | − | 45.7384i | −0.765551 | − | 1.71653i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20.9940 | + | 23.2274i | 0.786785 | + | 0.870483i | ||||
\(713\) | − | 7.17437i | − | 0.268682i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.0799 | −1.34931 | ||||||||
\(716\) | −23.3746 | − | 20.9930i | −0.873549 | − | 0.784547i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.3902 | − | 23.2970i | −0.387757 | − | 0.869436i | ||||
\(719\) | 5.16456 | − | 8.94528i | 0.192606 | − | 0.333603i | −0.753507 | − | 0.657439i | \(-0.771640\pi\) |
0.946113 | + | 0.323837i | \(0.104973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.1857 | + | 0.882240i | −0.788997 | + | 0.0328563i | ||||
\(722\) | 18.8806 | + | 1.97235i | 0.702663 | + | 0.0734031i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 29.7965 | − | 9.72319i | 1.10738 | − | 0.361360i | ||||
\(725\) | −31.2422 | − | 54.1131i | −1.16031 | − | 2.00971i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 28.6727i | − | 1.06341i | −0.846929 | − | 0.531706i | \(-0.821551\pi\) | ||
0.846929 | − | 0.531706i | \(-0.178449\pi\) | |||||||
\(728\) | −10.5670 | − | 40.8788i | −0.391638 | − | 1.51507i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.81712 | + | 9.39546i | −0.252313 | + | 0.347742i | ||||
\(731\) | −14.6863 | + | 8.47916i | −0.543193 | + | 0.313613i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.6091 | − | 19.4042i | −1.24138 | − | 0.716710i | −0.272004 | − | 0.962296i | \(-0.587686\pi\) |
−0.969375 | + | 0.245586i | \(0.921020\pi\) | |||||||
\(734\) | 0.574993 | − | 5.50421i | 0.0212234 | − | 0.203164i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.41830 | − | 3.67857i | −0.236582 | − | 0.135594i | ||||
\(737\) | −19.7042 | − | 11.3763i | −0.725815 | − | 0.419050i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.59773 | − | 9.69556i | −0.205916 | − | 0.356657i | 0.744508 | − | 0.667613i | \(-0.232684\pi\) |
−0.950424 | + | 0.310956i | \(0.899351\pi\) | |||||||
\(740\) | −33.6466 | − | 30.2184i | −1.23687 | − | 1.11085i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.27654 | + | 1.62797i | −0.120285 | + | 0.0597648i | ||||
\(743\) | 6.68201 | 0.245139 | 0.122570 | − | 0.992460i | \(-0.460887\pi\) | ||||
0.122570 | + | 0.992460i | \(0.460887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.3843 | − | 43.9668i | −0.930007 | − | 1.61082i | ||||
\(746\) | −23.6406 | + | 10.5434i | −0.865543 | + | 0.386021i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.67335 | + | 1.83210i | 0.317129 | + | 0.0669883i | ||||
\(749\) | −38.5387 | + | 1.60487i | −1.40817 | + | 0.0586407i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.2883 | + | 24.9925i | 1.57961 | + | 0.911990i | 0.994913 | + | 0.100741i | \(0.0321215\pi\) |
0.584701 | + | 0.811249i | \(0.301212\pi\) | |||||||
\(752\) | 3.02607 | + | 28.1064i | 0.110349 | + | 1.02493i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 43.9778 | + | 31.9092i | 1.60158 | + | 1.16207i | ||||
\(755\) | − | 80.3117i | − | 2.92284i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 32.8378i | − | 1.19351i | −0.802424 | − | 0.596755i | \(-0.796457\pi\) | ||
0.802424 | − | 0.596755i | \(-0.203543\pi\) | |||||||
\(758\) | 21.4337 | − | 29.5403i | 0.778507 | − | 1.07295i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.27541 | − | 24.5891i | −0.191359 | − | 0.891942i | ||||
\(761\) | 28.7157 | + | 16.5790i | 1.04094 | + | 0.600988i | 0.920100 | − | 0.391683i | \(-0.128107\pi\) |
0.120842 | + | 0.992672i | \(0.461440\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.927825 | − | 1.77360i | 0.0335895 | − | 0.0642088i | ||||
\(764\) | 47.2116 | + | 9.97268i | 1.70806 | + | 0.360799i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.49835 | − | 19.0551i | −0.307058 | − | 0.688490i | ||||
\(767\) | −21.7406 | − | 37.6559i | −0.785008 | − | 1.35967i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.1183 | −1.73519 | −0.867596 | − | 0.497270i | \(-0.834336\pi\) | ||||
−0.867596 | + | 0.497270i | \(0.834336\pi\) | |||||||
\(770\) | 23.8798 | + | 1.49366i | 0.860569 | + | 0.0538277i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.8374 | + | 14.2937i | −0.462028 | + | 0.514443i | ||||
\(773\) | −14.2293 | − | 24.6458i | −0.511791 | − | 0.886449i | −0.999907 | − | 0.0136695i | \(-0.995649\pi\) |
0.488115 | − | 0.872779i | \(-0.337685\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.5965 | + | 25.1704i | 1.56603 | + | 0.904148i | ||||
\(776\) | −40.5447 | − | 13.0887i | −1.45547 | − | 0.469857i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.4816 | − | 2.55745i | −0.877707 | − | 0.0916890i | ||||
\(779\) | 12.4847 | + | 7.20802i | 0.447309 | + | 0.258254i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.8339 | + | 7.98703i | −0.495017 | + | 0.285798i | ||||
\(782\) | 3.90657 | + | 2.83451i | 0.139699 | + | 0.101362i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.30152 | + | 27.4935i | 0.189340 | + | 0.981912i | ||||
\(785\) | − | 34.6612i | − | 1.23711i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.0597 | − | 19.1559i | −0.394234 | − | 0.682834i | 0.598769 | − | 0.800922i | \(-0.295657\pi\) |
−0.993003 | + | 0.118088i | \(0.962323\pi\) | |||||||
\(788\) | −1.27380 | − | 3.90353i | −0.0453773 | − | 0.139058i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.64020 | − | 92.2823i | 0.342983 | − | 3.28326i | ||||
\(791\) | 13.9920 | + | 22.0609i | 0.497497 | + | 0.784395i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.9033 | − | 43.1339i | 0.884344 | − | 1.53173i | ||||
\(794\) | −14.9546 | + | 6.66957i | −0.530720 | + | 0.236694i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.8124 | + | 13.3033i | 0.525013 | + | 0.471521i | ||||
\(797\) | −25.7820 | −0.913247 | −0.456623 | − | 0.889660i | \(-0.650941\pi\) | ||||
−0.456623 | + | 0.889660i | \(0.650941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 18.4437i | − | 0.652490i | ||||||
\(800\) | 44.8714 | − | 26.0962i | 1.58644 | − | 0.922640i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −46.4499 | + | 20.7161i | −1.64020 | + | 0.731510i | ||||
\(803\) | 3.20652 | + | 1.85128i | 0.113156 | + | 0.0653304i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.5431 | + | 6.03856i | 0.406842 | + | 0.212831i | ||||
\(806\) | −43.5380 | − | 4.54816i | −1.53356 | − | 0.160202i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.923080 | − | 4.30256i | −0.0324738 | − | 0.151363i | ||||
\(809\) | 2.56573 | − | 1.48132i | 0.0902062 | − | 0.0520806i | −0.454218 | − | 0.890890i | \(-0.650081\pi\) |
0.544425 | + | 0.838810i | \(0.316748\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.9174 | −1.82307 | −0.911533 | − | 0.411228i | \(-0.865100\pi\) | ||||
−0.911533 | + | 0.411228i | \(0.865100\pi\) | |||||||
\(812\) | −27.7862 | − | 22.9401i | −0.975103 | − | 0.805039i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.47139 | + | 11.6754i | −0.296922 | + | 0.409223i | ||||
\(815\) | −0.226030 | − | 0.391495i | −0.00791747 | − | 0.0137135i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.67262 | − | 13.2894i | 0.268431 | − | 0.464936i | ||||
\(818\) | 34.2118 | + | 3.57391i | 1.19619 | + | 0.124959i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.50053 | + | 44.9764i | −0.331773 | + | 1.57064i | ||||
\(821\) | −10.7741 | + | 18.6612i | −0.376017 | + | 0.651281i | −0.990479 | − | 0.137666i | \(-0.956040\pi\) |
0.614462 | + | 0.788947i | \(0.289373\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.0162 | − | 17.3299i | 1.04630 | − | 0.604082i | 0.124689 | − | 0.992196i | \(-0.460207\pi\) |
0.921611 | + | 0.388114i | \(0.126873\pi\) | |||||||
\(824\) | 15.1999 | + | 16.8168i | 0.529513 | + | 0.585843i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.8303 | + | 25.8229i | 0.446425 | + | 0.898495i | ||||
\(827\) | − | 40.6029i | − | 1.41190i | −0.708260 | − | 0.705951i | \(-0.750520\pi\) | ||
0.708260 | − | 0.705951i | \(-0.249480\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.2837 | + | 16.3296i | −0.982334 | + | 0.567151i | −0.902974 | − | 0.429695i | \(-0.858621\pi\) |
−0.0793604 | + | 0.996846i | \(0.525288\pi\) | |||||||
\(830\) | 57.8034 | − | 25.7796i | 2.00639 | − | 0.894823i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −26.3924 | + | 36.6177i | −0.914992 | + | 1.26949i | ||||
\(833\) | −1.51886 | − | 18.2050i | −0.0526256 | − | 0.630767i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.4376 | + | 42.3271i | −0.845697 | + | 1.46479i | ||||
\(836\) | −7.62578 | + | 2.48844i | −0.263743 | + | 0.0860647i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.93189 | + | 5.75519i | 0.274002 | + | 0.198810i | ||||
\(839\) | 35.4704 | 1.22458 | 0.612288 | − | 0.790635i | \(-0.290249\pi\) | ||||
0.612288 | + | 0.790635i | \(0.290249\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.3685 | 0.598913 | ||||||||
\(842\) | 14.4446 | + | 10.4807i | 0.497794 | + | 0.361187i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.67112 | + | 26.5724i | 0.298472 | + | 0.914661i | ||||
\(845\) | −35.4573 | + | 61.4138i | −1.21977 | + | 2.11270i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.893370 | + | 21.4530i | 0.0306965 | + | 0.737133i | ||||
\(848\) | 3.57717 | + | 1.58182i | 0.122840 | + | 0.0543198i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −30.9302 | + | 13.7945i | −1.06090 | + | 0.473147i | ||||
\(851\) | −6.80170 | + | 3.92697i | −0.233159 | + | 0.134615i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.87597i | 0.0984714i | 0.998787 | + | 0.0492357i | \(0.0156786\pi\) | ||||
−0.998787 | + | 0.0492357i | \(0.984321\pi\) | |||||||
\(854\) | −18.2682 | + | 27.5176i | −0.625126 | + | 0.941634i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27.6499 | + | 30.5913i | 0.945055 | + | 1.04559i | ||||
\(857\) | 5.76468 | − | 3.32824i | 0.196918 | − | 0.113691i | −0.398299 | − | 0.917256i | \(-0.630399\pi\) |
0.595217 | + | 0.803565i | \(0.297066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.2685 | − | 17.7855i | 0.350355 | − | 0.606833i | −0.635956 | − | 0.771725i | \(-0.719394\pi\) |
0.986312 | + | 0.164892i | \(0.0527276\pi\) | |||||||
\(860\) | 47.8754 | + | 10.1129i | 1.63254 | + | 0.344847i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31.4390 | + | 3.28425i | 1.07082 | + | 0.111862i | ||||
\(863\) | −15.7546 | + | 27.2877i | −0.536292 | + | 0.928886i | 0.462807 | + | 0.886459i | \(0.346842\pi\) |
−0.999100 | + | 0.0424266i | \(0.986491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.9692 | + | 22.4634i | 0.440968 | + | 0.763778i | ||||
\(866\) | −26.8106 | + | 36.9508i | −0.911061 | + | 1.25564i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 28.6278 | + | 4.81267i | 0.971690 | + | 0.163353i | ||||
\(869\) | −29.5949 | −1.00394 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −65.4596 | + | 37.7931i | −2.21801 | + | 1.28057i | ||||
\(872\) | −2.09223 | + | 0.448871i | −0.0708517 | + | 0.0152007i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.34383 | − | 0.453775i | −0.146932 | − | 0.0153492i | ||||
\(875\) | −35.1308 | + | 22.2815i | −1.18764 | + | 0.753251i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.3067 | − | 27.8899i | −1.63120 | − | 0.941774i | −0.983723 | − | 0.179689i | \(-0.942491\pi\) |
−0.647477 | − | 0.762085i | \(-0.724176\pi\) | |||||||
\(878\) | 3.62107 | − | 1.61495i | 0.122205 | − | 0.0545020i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15.0870 | − | 20.6553i | −0.508583 | − | 0.696290i | ||||
\(881\) | 21.9485i | 0.739464i | 0.929138 | + | 0.369732i | \(0.120550\pi\) | ||||
−0.929138 | + | 0.369732i | \(0.879450\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.4287 | 1.12497 | 0.562483 | − | 0.826809i | \(-0.309846\pi\) | ||||
0.562483 | + | 0.826809i | \(0.309846\pi\) | |||||||
\(884\) | 19.6779 | − | 21.9103i | 0.661840 | − | 0.736922i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.1704 | − | 10.7797i | 0.812021 | − | 0.362151i | ||||
\(887\) | −6.18309 | + | 10.7094i | −0.207608 | + | 0.359587i | −0.950960 | − | 0.309313i | \(-0.899901\pi\) |
0.743353 | + | 0.668900i | \(0.233234\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.38880 | − | 10.0731i | −0.214273 | − | 0.337841i | ||||
\(890\) | −6.12394 | + | 58.6223i | −0.205275 | + | 1.96502i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30.1963 | + | 9.85367i | −1.01105 | + | 0.329925i | ||||
\(893\) | 8.34466 | + | 14.4534i | 0.279243 | + | 0.483664i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 59.1460i | − | 1.97703i | ||||||
\(896\) | 18.9840 | − | 23.1432i | 0.634211 | − | 0.773160i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.9049 | + | 11.5402i | 0.530755 | + | 0.385103i | ||||
\(899\) | −32.3521 | + | 18.6785i | −1.07900 | + | 0.622963i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.21000 | − | 1.27594i | −0.0736257 | − | 0.0425078i | ||||
\(902\) | 14.5831 | + | 1.52341i | 0.485563 | + | 0.0507240i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.57965 | − | 26.5771i | 0.285355 | − | 0.883941i | ||||
\(905\) | 51.0996 | + | 29.5024i | 1.69861 | + | 0.980692i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.85914 | − | 11.8804i | −0.227754 | − | 0.394481i | 0.729388 | − | 0.684100i | \(-0.239805\pi\) |
−0.957142 | + | 0.289619i | \(0.906471\pi\) | |||||||
\(908\) | −1.06537 | − | 0.956823i | −0.0353555 | − | 0.0317533i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 43.9630 | − | 66.2219i | 1.45736 | − | 2.19524i | ||||
\(911\) | 9.02706 | 0.299080 | 0.149540 | − | 0.988756i | \(-0.452221\pi\) | ||||
0.149540 | + | 0.988756i | \(0.452221\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0939 | − | 17.4831i | −0.334058 | − | 0.578606i | ||||
\(914\) | −3.32856 | − | 7.46335i | −0.110099 | − | 0.246866i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.86102 | + | 8.81025i | −0.0614899 | + | 0.291099i | ||||
\(917\) | −42.9391 | + | 1.78812i | −1.41797 | + | 0.0590489i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.8104 | − | 21.8298i | −1.24725 | − | 0.720100i | −0.276689 | − | 0.960959i | \(-0.589237\pi\) |
−0.970560 | + | 0.240860i | \(0.922571\pi\) | |||||||
\(920\) | −2.92138 | − | 13.6168i | −0.0963151 | − | 0.448933i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.8086 | − | 17.6530i | 0.421829 | − | 0.581372i | ||||
\(923\) | 53.0675i | 1.74674i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 55.1092i | − | 1.81198i | ||||||
\(926\) | 13.2668 | + | 9.62603i | 0.435973 | + | 0.316331i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.121919 | + | 38.5198i | 0.00400218 | + | 1.26447i | ||||
\(929\) | 43.0944 | + | 24.8806i | 1.41388 | + | 0.816304i | 0.995751 | − | 0.0920830i | \(-0.0293525\pi\) |
0.418129 | + | 0.908387i | \(0.362686\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.42695 | + | 13.5792i | 0.308956 | + | 0.445039i | ||||
\(932\) | 3.19596 | − | 15.1300i | 0.104687 | − | 0.495599i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.95524 | + | 1.31800i | −0.0966984 | + | 0.0431263i | ||||
\(935\) | 8.34421 | + | 14.4526i | 0.272885 | + | 0.472650i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.5415 | 1.32443 | 0.662216 | − | 0.749313i | \(-0.269616\pi\) | ||||
0.662216 | + | 0.749313i | \(0.269616\pi\) | |||||||
\(938\) | 44.8897 | − | 22.3038i | 1.46570 | − | 0.728246i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −35.5595 | + | 39.5935i | −1.15982 | + | 1.29140i | ||||
\(941\) | 27.1914 | + | 47.0968i | 0.886414 | + | 1.53531i | 0.844085 | + | 0.536209i | \(0.180144\pi\) |
0.0423286 | + | 0.999104i | \(0.486522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.91367 | + | 3.99161i | 0.225140 | + | 0.129985i | ||||
\(944\) | 12.4666 | − | 28.1923i | 0.405752 | − | 0.917581i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.62160 | − | 15.5230i | 0.0527229 | − | 0.504698i | ||||
\(947\) | −12.3501 | − | 7.13032i | −0.401323 | − | 0.231704i | 0.285732 | − | 0.958310i | \(-0.407763\pi\) |
−0.687055 | + | 0.726606i | \(0.741097\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.6524 | − | 6.15016i | 0.345791 | − | 0.199643i | ||||
\(950\) | 17.9972 | − | 24.8041i | 0.583908 | − | 0.804751i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.9311 | + | 13.6869i | −0.451509 | + | 0.443595i | ||||
\(953\) | − | 3.31610i | − | 0.107419i | −0.998557 | − | 0.0537095i | \(-0.982896\pi\) | ||
0.998557 | − | 0.0537095i | \(-0.0171045\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.4200 | + | 78.6697i | 1.46976 | + | 2.54569i | ||||
\(956\) | 13.2643 | + | 40.6482i | 0.428998 | + | 1.31466i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.5263 | − | 2.77105i | −0.857025 | − | 0.0895285i | ||||
\(959\) | −5.14717 | + | 9.83919i | −0.166211 | + | 0.317724i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.451578 | + | 0.782157i | −0.0145670 | + | 0.0252309i | ||||
\(962\) | 19.5191 | + | 43.7659i | 0.629319 | + | 1.41107i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.3776 | − | 12.6683i | 0.366448 | − | 0.408019i | ||||
\(965\) | −36.1682 | −1.16430 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.6637i | 0.600185i | 0.953910 | + | 0.300092i | \(0.0970175\pi\) | ||||
−0.953910 | + | 0.300092i | \(0.902982\pi\) | |||||||
\(968\) | 17.0290 | − | 15.3916i | 0.547333 | − | 0.494706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −32.6693 | − | 73.2516i | −1.04895 | − | 2.35197i | ||||
\(971\) | 4.93811 | + | 2.85102i | 0.158472 | + | 0.0914936i | 0.577139 | − | 0.816646i | \(-0.304169\pi\) |
−0.418667 | + | 0.908140i | \(0.637503\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.7414 | + | 8.08115i | −0.408471 | + | 0.259070i | ||||
\(974\) | 4.56434 | − | 43.6928i | 0.146251 | − | 1.40001i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 35.1071 | − | 3.77981i | 1.12375 | − | 0.120989i | ||||
\(977\) | −3.52730 | + | 2.03649i | −0.112848 | + | 0.0651530i | −0.555362 | − | 0.831609i | \(-0.687420\pi\) |
0.442514 | + | 0.896762i | \(0.354087\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.8002 | 0.600856 | ||||||||
\(980\) | −31.8389 | + | 42.0097i | −1.01705 | + | 1.34195i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.61861 | − | 6.25345i | −0.275031 | − | 0.199556i | ||||
\(983\) | −13.6318 | − | 23.6109i | −0.434786 | − | 0.753071i | 0.562492 | − | 0.826803i | \(-0.309843\pi\) |
−0.997278 | + | 0.0737313i | \(0.976509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.86500 | − | 6.69438i | 0.123149 | − | 0.213301i | ||||
\(986\) | 2.61118 | − | 24.9959i | 0.0831570 | − | 0.796033i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.50750 | + | 26.0730i | −0.175217 | + | 0.829494i | ||||
\(989\) | 4.24890 | − | 7.35930i | 0.135107 | − | 0.234012i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.91978 | + | 4.57249i | −0.251580 | + | 0.145250i | −0.620488 | − | 0.784216i | \(-0.713065\pi\) |
0.368907 | + | 0.929466i | \(0.379732\pi\) | |||||||
\(992\) | −15.6019 | − | 26.8268i | −0.495361 | − | 0.851753i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.19693 | − | 35.1233i | 0.0696823 | − | 1.11404i | ||||
\(995\) | 37.4807i | 1.18822i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.5025 | − | 23.3841i | 1.28273 | − | 0.740583i | 0.305381 | − | 0.952230i | \(-0.401216\pi\) |
0.977346 | + | 0.211647i | \(0.0678827\pi\) | |||||||
\(998\) | 1.01759 | + | 2.28165i | 0.0322112 | + | 0.0722245i | ||||
\(999\) | 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 | 504.2.bm.c.107.17 | yes | 48 | |
3.2 | odd | 2 | inner | 504.2.bm.c.107.8 | ✓ | 48 | |
4.3 | odd | 2 | 2016.2.bu.c.1871.23 | 48 | |||
7.4 | even | 3 | inner | 504.2.bm.c.179.15 | yes | 48 | |
8.3 | odd | 2 | inner | 504.2.bm.c.107.10 | yes | 48 | |
8.5 | even | 2 | 2016.2.bu.c.1871.1 | 48 | |||
12.11 | even | 2 | 2016.2.bu.c.1871.2 | 48 | |||
21.11 | odd | 6 | inner | 504.2.bm.c.179.10 | yes | 48 | |
24.5 | odd | 2 | 2016.2.bu.c.1871.24 | 48 | |||
24.11 | even | 2 | inner | 504.2.bm.c.107.15 | yes | 48 | |
28.11 | odd | 6 | 2016.2.bu.c.431.24 | 48 | |||
56.11 | odd | 6 | inner | 504.2.bm.c.179.8 | yes | 48 | |
56.53 | even | 6 | 2016.2.bu.c.431.2 | 48 | |||
84.11 | even | 6 | 2016.2.bu.c.431.1 | 48 | |||
168.11 | even | 6 | inner | 504.2.bm.c.179.17 | yes | 48 | |
168.53 | odd | 6 | 2016.2.bu.c.431.23 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bm.c.107.8 | ✓ | 48 | 3.2 | odd | 2 | inner | |
504.2.bm.c.107.10 | yes | 48 | 8.3 | odd | 2 | inner | |
504.2.bm.c.107.15 | yes | 48 | 24.11 | even | 2 | inner | |
504.2.bm.c.107.17 | yes | 48 | 1.1 | even | 1 | trivial | |
504.2.bm.c.179.8 | yes | 48 | 56.11 | odd | 6 | inner | |
504.2.bm.c.179.10 | yes | 48 | 21.11 | odd | 6 | inner | |
504.2.bm.c.179.15 | yes | 48 | 7.4 | even | 3 | inner | |
504.2.bm.c.179.17 | yes | 48 | 168.11 | even | 6 | inner | |
2016.2.bu.c.431.1 | 48 | 84.11 | even | 6 | |||
2016.2.bu.c.431.2 | 48 | 56.53 | even | 6 | |||
2016.2.bu.c.431.23 | 48 | 168.53 | odd | 6 | |||
2016.2.bu.c.431.24 | 48 | 28.11 | odd | 6 | |||
2016.2.bu.c.1871.1 | 48 | 8.5 | even | 2 | |||
2016.2.bu.c.1871.2 | 48 | 12.11 | even | 2 | |||
2016.2.bu.c.1871.23 | 48 | 4.3 | odd | 2 | |||
2016.2.bu.c.1871.24 | 48 | 24.5 | odd | 2 |