Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,2,Mod(73,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.q (of order \(9\), degree \(6\), 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: | \(5.17430605098\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 505.3 | ||
Character | \(\chi\) | \(=\) | 648.505 |
Dual form | 648.2.q.a.145.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0770674 | + | 0.437071i | 0.0344656 | + | 0.195464i | 0.997179 | − | 0.0750589i | \(-0.0239145\pi\) |
−0.962714 | + | 0.270523i | \(0.912803\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.935232 | + | 0.784753i | 0.353485 | + | 0.296609i | 0.802188 | − | 0.597072i | \(-0.203669\pi\) |
−0.448703 | + | 0.893681i | \(0.648114\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.00921771 | + | 0.0522762i | −0.00277924 | + | 0.0157619i | −0.986166 | − | 0.165762i | \(-0.946992\pi\) |
0.983387 | + | 0.181524i | \(0.0581029\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.58518 | + | 0.576957i | 0.439649 | + | 0.160019i | 0.552355 | − | 0.833609i | \(-0.313729\pi\) |
−0.112706 | + | 0.993628i | \(0.535952\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.44650 | + | 4.23746i | 0.593363 | + | 1.02773i | 0.993776 | + | 0.111400i | \(0.0355335\pi\) |
−0.400413 | + | 0.916335i | \(0.631133\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.83033 | + | 3.17022i | −0.419905 | + | 0.727297i | −0.995930 | − | 0.0901352i | \(-0.971270\pi\) |
0.576024 | + | 0.817433i | \(0.304603\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.10868 | − | 4.28669i | 1.06523 | − | 0.893837i | 0.0706216 | − | 0.997503i | \(-0.477502\pi\) |
0.994612 | + | 0.103666i | \(0.0330573\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.51337 | − | 1.64273i | 0.902674 | − | 0.328547i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.444832 | + | 0.161906i | −0.0826032 | + | 0.0300651i | −0.382991 | − | 0.923752i | \(-0.625106\pi\) |
0.300388 | + | 0.953817i | \(0.402884\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.09742 | + | 5.11634i | −1.09513 | + | 0.918922i | −0.997088 | − | 0.0762601i | \(-0.975702\pi\) |
−0.0980410 | + | 0.995182i | \(0.531258\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.270917 | + | 0.469242i | −0.0457933 | + | 0.0793163i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.58110 | + | 7.93469i | 0.753128 | + | 1.30446i | 0.946300 | + | 0.323291i | \(0.104789\pi\) |
−0.193172 | + | 0.981165i | \(0.561878\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.04020 | + | 1.83448i | 0.787146 | + | 0.286498i | 0.704149 | − | 0.710052i | \(-0.251329\pi\) |
0.0829971 | + | 0.996550i | \(0.473551\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.366331 | + | 2.07757i | −0.0558649 | + | 0.316826i | −0.999916 | − | 0.0129740i | \(-0.995870\pi\) |
0.944051 | + | 0.329800i | \(0.106981\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.992456 | − | 0.832769i | −0.144765 | − | 0.121472i | 0.567529 | − | 0.823353i | \(-0.307899\pi\) |
−0.712294 | + | 0.701881i | \(0.752344\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.956715 | − | 5.42580i | −0.136674 | − | 0.775114i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.9018 | 1.63484 | 0.817420 | − | 0.576043i | \(-0.195404\pi\) | ||||
0.817420 | + | 0.576043i | \(0.195404\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0235588 | −0.00317667 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.65278 | − | 9.37338i | −0.215174 | − | 1.22031i | −0.880605 | − | 0.473851i | \(-0.842863\pi\) |
0.665431 | − | 0.746459i | \(-0.268248\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.214574 | − | 0.180049i | −0.0274734 | − | 0.0230529i | 0.628948 | − | 0.777448i | \(-0.283486\pi\) |
−0.656421 | + | 0.754395i | \(0.727930\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.130006 | + | 0.737299i | −0.0161252 | + | 0.0914507i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.43634 | − | 2.70660i | −0.908493 | − | 0.330664i | −0.154842 | − | 0.987939i | \(-0.549487\pi\) |
−0.753651 | + | 0.657275i | \(0.771709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.96200 | + | 5.13033i | 0.351525 | + | 0.608858i | 0.986517 | − | 0.163660i | \(-0.0523301\pi\) |
−0.634992 | + | 0.772519i | \(0.718997\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.57777 | + | 7.92893i | −0.535788 | + | 0.928012i | 0.463337 | + | 0.886182i | \(0.346652\pi\) |
−0.999125 | + | 0.0418294i | \(0.986681\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0496446 | + | 0.0416568i | −0.00565753 | + | 0.00474723i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.33162 | − | 3.39643i | 1.04989 | − | 0.382128i | 0.241268 | − | 0.970459i | \(-0.422437\pi\) |
0.808621 | + | 0.588330i | \(0.200214\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.6764 | + | 3.88590i | −1.17189 | + | 0.426533i | −0.853331 | − | 0.521369i | \(-0.825421\pi\) |
−0.318560 | + | 0.947903i | \(0.603199\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.66353 | + | 1.39586i | −0.180435 | + | 0.151403i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.10545 | + | 5.37880i | −0.329177 | + | 0.570152i | −0.982349 | − | 0.187058i | \(-0.940105\pi\) |
0.653172 | + | 0.757210i | \(0.273438\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.02974 | + | 1.78356i | 0.107946 | + | 0.186968i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.52667 | − | 0.555662i | −0.156633 | − | 0.0570097i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.80539 | − | 15.9101i | 0.284844 | − | 1.61543i | −0.420998 | − | 0.907062i | \(-0.638320\pi\) |
0.705842 | − | 0.708369i | \(-0.250569\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.9928 | − | 9.22402i | −1.09382 | − | 0.917824i | −0.0968259 | − | 0.995301i | \(-0.530869\pi\) |
−0.996994 | + | 0.0774773i | \(0.975313\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.03225 | − | 17.1967i | −0.298776 | − | 1.69444i | −0.651445 | − | 0.758696i | \(-0.725837\pi\) |
0.352669 | − | 0.935748i | \(-0.385274\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.5879 | −1.79696 | −0.898482 | − | 0.439010i | \(-0.855329\pi\) | ||||
−0.898482 | + | 0.439010i | \(0.855329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.45278 | 0.139151 | 0.0695753 | − | 0.997577i | \(-0.477836\pi\) | ||||
0.0695753 | + | 0.997577i | \(0.477836\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.276022 | − | 1.56540i | −0.0259659 | − | 0.147260i | 0.969068 | − | 0.246792i | \(-0.0793765\pi\) |
−0.995034 | + | 0.0995321i | \(0.968265\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.26730 | + | 1.90249i | 0.211427 | + | 0.177408i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.03732 | + | 5.88291i | −0.0950905 | + | 0.539285i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3340 | + | 3.76126i | 0.939452 | + | 0.341933i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.17536 | + | 3.76783i | 0.194570 | + | 0.337005i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.87831 | − | 10.1815i | 0.521616 | − | 0.903465i | −0.478068 | − | 0.878323i | \(-0.658663\pi\) |
0.999684 | − | 0.0251425i | \(-0.00800395\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.11753 | − | 4.29412i | 0.447121 | − | 0.375179i | −0.391245 | − | 0.920286i | \(-0.627956\pi\) |
0.838366 | + | 0.545107i | \(0.183511\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.19962 | + | 1.52854i | −0.364153 | + | 0.132541i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.2681 | + | 4.46524i | −1.04814 | + | 0.381491i | −0.807960 | − | 0.589238i | \(-0.799428\pi\) |
−0.240178 | + | 0.970729i | \(0.577206\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.5772 | + | 13.9099i | −1.40606 | + | 1.17983i | −0.447729 | + | 0.894169i | \(0.647767\pi\) |
−0.958332 | + | 0.285656i | \(0.907788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0447728 | + | 0.0775488i | −0.00374409 | + | 0.00648496i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.105046 | − | 0.181945i | −0.00872362 | − | 0.0151097i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.48430 | − | 3.08803i | −0.695061 | − | 0.252981i | −0.0297602 | − | 0.999557i | \(-0.509474\pi\) |
−0.665301 | + | 0.746576i | \(0.731697\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.09988 | − | 6.23773i | 0.0895069 | − | 0.507619i | −0.906786 | − | 0.421592i | \(-0.861472\pi\) |
0.996293 | − | 0.0860275i | \(-0.0274173\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.70612 | − | 2.27070i | −0.217361 | − | 0.182387i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.93460 | − | 22.3142i | −0.314015 | − | 1.78087i | −0.577688 | − | 0.816257i | \(-0.696045\pi\) |
0.263673 | − | 0.964612i | \(-0.415066\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.14180 | 0.641664 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.49680 | −0.195565 | −0.0977823 | − | 0.995208i | \(-0.531175\pi\) | ||||
−0.0977823 | + | 0.995208i | \(0.531175\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.435926 | − | 2.47226i | −0.0337329 | − | 0.191309i | 0.963285 | − | 0.268482i | \(-0.0865218\pi\) |
−0.997018 | + | 0.0771726i | \(0.975411\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.77867 | − | 6.52708i | −0.598359 | − | 0.502083i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.38044 | − | 13.5001i | 0.180982 | − | 1.02640i | −0.750029 | − | 0.661405i | \(-0.769961\pi\) |
0.931011 | − | 0.364992i | \(-0.118928\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.51019 | + | 2.00555i | 0.416531 | + | 0.151605i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.96977 | + | 3.41174i | 0.147227 | + | 0.255005i | 0.930202 | − | 0.367049i | \(-0.119632\pi\) |
−0.782974 | + | 0.622054i | \(0.786298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.98124 | + | 6.89571i | −0.295923 | + | 0.512554i | −0.975199 | − | 0.221329i | \(-0.928961\pi\) |
0.679276 | + | 0.733883i | \(0.262294\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.11497 | + | 2.61377i | −0.229017 | + | 0.192168i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.244069 | + | 0.0888340i | −0.0178481 | + | 0.00649619i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2633 | − | 4.09951i | 0.814985 | − | 0.296630i | 0.0993039 | − | 0.995057i | \(-0.468338\pi\) |
0.715682 | + | 0.698427i | \(0.246116\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.55375 | + | 5.49925i | −0.471749 | + | 0.395845i | −0.847432 | − | 0.530904i | \(-0.821853\pi\) |
0.375683 | + | 0.926748i | \(0.377408\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.14032 | + | 7.17125i | −0.294986 | + | 0.510930i | −0.974982 | − | 0.222286i | \(-0.928648\pi\) |
0.679996 | + | 0.733216i | \(0.261982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.75733 | − | 6.50789i | −0.266350 | − | 0.461332i | 0.701566 | − | 0.712604i | \(-0.252484\pi\) |
−0.967916 | + | 0.251272i | \(0.919151\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.543077 | − | 0.197664i | −0.0381165 | − | 0.0138733i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.413364 | + | 2.34430i | −0.0288706 | + | 0.163733i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.148855 | − | 0.124905i | −0.0102965 | − | 0.00863983i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.539398 | − | 3.05908i | −0.0371337 | − | 0.210596i | 0.960595 | − | 0.277951i | \(-0.0896551\pi\) |
−0.997729 | + | 0.0673549i | \(0.978544\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.936276 | −0.0638535 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.71757 | −0.659672 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.43330 | + | 8.12865i | 0.0964142 | + | 0.546792i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2343 | + | 8.58764i | 0.685343 | + | 0.575071i | 0.917562 | − | 0.397593i | \(-0.130154\pi\) |
−0.232219 | + | 0.972663i | \(0.574599\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.28119 | + | 12.9372i | −0.151408 | + | 0.858675i | 0.810589 | + | 0.585615i | \(0.199147\pi\) |
−0.961997 | + | 0.273060i | \(0.911964\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.24176 | + | 3.36373i | 0.610713 | + | 0.222281i | 0.628815 | − | 0.777555i | \(-0.283540\pi\) |
−0.0181024 | + | 0.999836i | \(0.505762\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.1999 | − | 22.8629i | −0.864756 | − | 1.49780i | −0.867289 | − | 0.497805i | \(-0.834140\pi\) |
0.00253310 | − | 0.999997i | \(-0.499194\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.287493 | − | 0.497953i | 0.0187540 | − | 0.0324829i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.8363 | − | 9.93187i | 0.765630 | − | 0.642440i | −0.173956 | − | 0.984753i | \(-0.555655\pi\) |
0.939586 | + | 0.342314i | \(0.111211\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.24187 | + | 1.54391i | −0.273243 | + | 0.0994522i | −0.475007 | − | 0.879982i | \(-0.657555\pi\) |
0.201765 | + | 0.979434i | \(0.435332\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.29773 | − | 0.836305i | 0.146796 | − | 0.0534295i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.73047 | + | 3.96933i | −0.300992 | + | 0.252563i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.29663 | − | 7.44198i | 0.271201 | − | 0.469733i | −0.697969 | − | 0.716128i | \(-0.745913\pi\) |
0.969170 | + | 0.246395i | \(0.0792459\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.177002 | + | 0.306576i | 0.0111280 | + | 0.0192743i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.48529 | − | 0.540602i | −0.0926499 | − | 0.0337218i | 0.295279 | − | 0.955411i | \(-0.404587\pi\) |
−0.387929 | + | 0.921689i | \(0.626810\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.94239 | + | 11.0158i | −0.120694 | + | 0.684489i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.8949 | + | 18.3720i | 1.35010 | + | 1.13286i | 0.978907 | + | 0.204308i | \(0.0654942\pi\) |
0.371189 | + | 0.928557i | \(0.378950\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.917242 | + | 5.20194i | 0.0563457 | + | 0.319552i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.7693 | 1.20536 | 0.602678 | − | 0.797984i | \(-0.294100\pi\) | ||||
0.602678 | + | 0.797984i | \(0.294100\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.6042 | 0.947890 | 0.473945 | − | 0.880555i | \(-0.342830\pi\) | ||||
0.473945 | + | 0.880555i | \(0.342830\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0442729 | + | 0.251084i | 0.00266976 | + | 0.0151409i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.09930 | − | 5.11792i | −0.366471 | − | 0.307506i | 0.440892 | − | 0.897560i | \(-0.354662\pi\) |
−0.807364 | + | 0.590054i | \(0.799106\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.539642 | − | 3.06046i | 0.0321923 | − | 0.182572i | −0.964472 | − | 0.264186i | \(-0.914897\pi\) |
0.996664 | + | 0.0816146i | \(0.0260077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.8942 | + | 7.24091i | 1.18259 | + | 0.430428i | 0.857116 | − | 0.515123i | \(-0.172254\pi\) |
0.325474 | + | 0.945551i | \(0.394476\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.27414 | + | 5.67098i | 0.193266 | + | 0.334747i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.47071 | + | 6.01145i | −0.204159 | + | 0.353614i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.9909 | + | 17.6135i | −1.22630 | + | 1.02899i | −0.227831 | + | 0.973701i | \(0.573163\pi\) |
−0.998470 | + | 0.0552880i | \(0.982392\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.96946 | − | 1.44476i | 0.231111 | − | 0.0841174i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.5714 | − | 3.84768i | 0.611360 | − | 0.222517i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.97298 | + | 1.65553i | −0.113721 | + | 0.0954230i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0621575 | − | 0.107660i | 0.00355913 | − | 0.00616460i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.06815 | − | 5.31419i | −0.175108 | − | 0.303297i | 0.765090 | − | 0.643923i | \(-0.222694\pi\) |
−0.940199 | + | 0.340626i | \(0.889361\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.7023 | + | 7.53500i | 1.17392 | + | 0.427271i | 0.854050 | − | 0.520191i | \(-0.174139\pi\) |
0.319867 | + | 0.947462i | \(0.396362\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.01293 | + | 11.4159i | −0.113778 | + | 0.645264i | 0.873571 | + | 0.486697i | \(0.161799\pi\) |
−0.987348 | + | 0.158567i | \(0.949313\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.93161 | − | 5.81631i | −0.389318 | − | 0.326677i | 0.427029 | − | 0.904238i | \(-0.359560\pi\) |
−0.816347 | + | 0.577561i | \(0.804005\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.00436348 | − | 0.0247465i | −0.000244308 | − | 0.00138554i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.9116 | −0.996625 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.10228 | 0.449433 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.274658 | − | 1.55767i | −0.0151424 | − | 0.0858769i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.3760 | + | 9.54559i | 0.625281 | + | 0.524673i | 0.899458 | − | 0.437006i | \(-0.143961\pi\) |
−0.274178 | + | 0.961679i | \(0.588406\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.609879 | − | 3.45880i | 0.0333213 | − | 0.188974i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.8302 | + | 10.8573i | 1.62496 | + | 0.591436i | 0.984317 | − | 0.176406i | \(-0.0564472\pi\) |
0.640639 | + | 0.767842i | \(0.278669\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.211259 | − | 0.365911i | −0.0114403 | − | 0.0198152i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.63617 | − | 13.2262i | 0.412314 | − | 0.714150i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.5612 | + | 20.6093i | −1.31851 | + | 1.10637i | −0.331897 | + | 0.943316i | \(0.607689\pi\) |
−0.986618 | + | 0.163050i | \(0.947867\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.0107 | + | 8.37522i | −1.23174 | + | 0.448315i | −0.874192 | − | 0.485581i | \(-0.838608\pi\) |
−0.357545 | + | 0.933896i | \(0.616386\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.0675 | − | 6.94001i | 1.01486 | − | 0.369379i | 0.219563 | − | 0.975598i | \(-0.429537\pi\) |
0.795298 | + | 0.606219i | \(0.207314\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.01405 | + | 1.68998i | −0.106894 | + | 0.0896951i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.61062 | − | 14.9140i | 0.454451 | − | 0.787133i | −0.544205 | − | 0.838952i | \(-0.683169\pi\) |
0.998656 | + | 0.0518195i | \(0.0165020\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.79982 | + | 4.84943i | 0.147359 | + | 0.255233i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.81830 | − | 1.38975i | −0.199859 | − | 0.0727428i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.632469 | + | 3.58691i | −0.0330146 | + | 0.187235i | −0.996855 | − | 0.0792442i | \(-0.974749\pi\) |
0.963841 | + | 0.266479i | \(0.0858604\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.1310 | + | 9.33998i | 0.577891 | + | 0.484908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.18473 | − | 6.71895i | −0.0613431 | − | 0.347894i | −0.999995 | − | 0.00302919i | \(-0.999036\pi\) |
0.938652 | − | 0.344865i | \(-0.112075\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.798550 | −0.0411274 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.12744 | 0.109279 | 0.0546396 | − | 0.998506i | \(-0.482599\pi\) | ||||
0.0546396 | + | 0.998506i | \(0.482599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.68105 | + | 20.8763i | 0.188093 | + | 1.06673i | 0.921917 | + | 0.387388i | \(0.126623\pi\) |
−0.733824 | + | 0.679340i | \(0.762266\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0220330 | − | 0.0184878i | −0.00112290 | − | 0.000942228i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.229463 | − | 1.30135i | 0.0116342 | − | 0.0659811i | −0.978438 | − | 0.206541i | \(-0.933779\pi\) |
0.990072 | + | 0.140560i | \(0.0448904\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.6631 | + | 11.1604i | 1.55070 | + | 0.564408i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.20364 | + | 3.81682i | 0.110877 | + | 0.192045i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7027 | − | 20.2696i | 0.587340 | − | 1.01730i | −0.407239 | − | 0.913322i | \(-0.633508\pi\) |
0.994579 | − | 0.103981i | \(-0.0331582\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.3865 | − | 20.4627i | 1.21780 | − | 1.02186i | 0.218866 | − | 0.975755i | \(-0.429764\pi\) |
0.998937 | − | 0.0461030i | \(-0.0146802\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.6174 | + | 4.59236i | −0.628517 | + | 0.228762i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.457023 | + | 0.166343i | −0.0226538 | + | 0.00824530i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.5058 | + | 11.3327i | −0.667820 | + | 0.560368i | −0.912419 | − | 0.409257i | \(-0.865788\pi\) |
0.244599 | + | 0.969624i | \(0.421344\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.81006 | − | 10.0633i | 0.285894 | − | 0.495183i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.52122 | − | 4.36688i | −0.123762 | − | 0.214362i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.78294 | + | 1.74085i | 0.233662 | + | 0.0850459i | 0.456197 | − | 0.889879i | \(-0.349211\pi\) |
−0.222536 | + | 0.974925i | \(0.571433\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.06322 | + | 28.7150i | −0.246766 | + | 1.39948i | 0.569588 | + | 0.821930i | \(0.307103\pi\) |
−0.816355 | + | 0.577551i | \(0.804008\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.0030 | + | 15.1063i | 0.873272 | + | 0.732763i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0593826 | − | 0.336775i | −0.00287373 | − | 0.0162977i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.9171 | −0.574024 | −0.287012 | − | 0.957927i | \(-0.592662\pi\) | ||||
−0.287012 | + | 0.957927i | \(0.592662\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.2817 | −1.69553 | −0.847765 | − | 0.530373i | \(-0.822052\pi\) | ||||
−0.847765 | + | 0.530373i | \(0.822052\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.23919 | + | 24.0417i | 0.202788 | + | 1.15007i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.5157 | − | 13.8583i | −0.788253 | − | 0.661423i | 0.157060 | − | 0.987589i | \(-0.449799\pi\) |
−0.945312 | + | 0.326167i | \(0.894243\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.74502 | − | 9.89647i | 0.0829082 | − | 0.470196i | −0.914880 | − | 0.403725i | \(-0.867715\pi\) |
0.997788 | − | 0.0664703i | \(-0.0211738\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.59025 | − | 0.942772i | −0.122789 | − | 0.0446917i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.1303 | − | 36.5987i | −0.997200 | − | 1.72720i | −0.563358 | − | 0.826213i | \(-0.690491\pi\) |
−0.433843 | − | 0.900989i | \(-0.642843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.142359 | + | 0.246573i | −0.00670341 | + | 0.0116107i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.700184 | + | 0.587524i | −0.0328251 | + | 0.0275435i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.45512 | − | 2.71344i | 0.348736 | − | 0.126929i | −0.161713 | − | 0.986838i | \(-0.551702\pi\) |
0.510448 | + | 0.859908i | \(0.329479\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.3655 | − | 8.50436i | 1.08824 | − | 0.396087i | 0.265272 | − | 0.964174i | \(-0.414538\pi\) |
0.822969 | + | 0.568086i | \(0.192316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.41524 | − | 7.90032i | 0.437563 | − | 0.367159i | −0.397233 | − | 0.917718i | \(-0.630030\pi\) |
0.834797 | + | 0.550559i | \(0.185585\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.30296 | − | 7.45295i | 0.199117 | − | 0.344881i | −0.749125 | − | 0.662429i | \(-0.769526\pi\) |
0.948242 | + | 0.317547i | \(0.102859\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.83069 | − | 8.36699i | −0.223060 | − | 0.386352i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.105231 | − | 0.0383008i | −0.00483851 | − | 0.00176107i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.05312 | + | 17.3151i | −0.140087 | + | 0.794471i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.21251 | − | 4.37381i | −0.238166 | − | 0.199845i | 0.515891 | − | 0.856654i | \(-0.327461\pi\) |
−0.754056 | + | 0.656810i | \(0.771905\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.68387 | + | 15.2210i | 0.122374 | + | 0.694017i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.17007 | 0.325576 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.6682 | −0.619364 | −0.309682 | − | 0.950840i | \(-0.600223\pi\) | ||||
−0.309682 | + | 0.950840i | \(0.600223\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.78778 | − | 15.8103i | −0.125811 | − | 0.713508i | −0.980823 | − | 0.194900i | \(-0.937562\pi\) |
0.855012 | − | 0.518608i | \(-0.173549\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.77435 | − | 1.48886i | −0.0799127 | − | 0.0670547i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.25589 | + | 7.12249i | −0.0563342 | + | 0.319487i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.99466 | + | 2.18188i | 0.268358 | + | 0.0976743i | 0.472694 | − | 0.881226i | \(-0.343281\pi\) |
−0.204336 | + | 0.978901i | \(0.565504\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.62821 | + | 6.28424i | 0.161774 | + | 0.280200i | 0.935505 | − | 0.353314i | \(-0.114945\pi\) |
−0.773731 | + | 0.633514i | \(0.781612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.18437 | − | 5.51549i | 0.141702 | − | 0.245436i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.6070 | + | 15.6131i | −0.824741 | + | 0.692040i | −0.954077 | − | 0.299561i | \(-0.903160\pi\) |
0.129336 | + | 0.991601i | \(0.458715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5035 | + | 3.82298i | −0.464649 | + | 0.169118i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.28250 | − | 2.65061i | 0.320905 | − | 0.116800i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0526822 | − | 0.0442056i | 0.00231696 | − | 0.00194416i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.2398 | + | 22.9320i | −0.580046 | + | 1.00467i | 0.415428 | + | 0.909626i | \(0.363632\pi\) |
−0.995473 | + | 0.0950422i | \(0.969701\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.95994 | − | 15.5191i | −0.391791 | − | 0.678601i | 0.600895 | − | 0.799328i | \(-0.294811\pi\) |
−0.992686 | + | 0.120726i | \(0.961478\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.5976 | − | 13.3204i | −1.59422 | − | 0.580248i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.72898 | − | 21.1481i | 0.162130 | − | 0.919483i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.93118 | + | 5.81595i | 0.300223 | + | 0.251917i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.43252 | − | 8.12425i | −0.0619334 | − | 0.351242i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.292459 | 0.0125971 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.1015 | 1.76709 | 0.883547 | − | 0.468343i | \(-0.155149\pi\) | ||||
0.883547 | + | 0.468343i | \(0.155149\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.111962 | + | 0.634966i | 0.00479591 | + | 0.0271990i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.7775 | − | 18.2735i | −0.931139 | − | 0.781319i | 0.0448824 | − | 0.998992i | \(-0.485709\pi\) |
−0.976022 | + | 0.217674i | \(0.930153\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.300911 | − | 1.70655i | 0.0128193 | − | 0.0727016i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.3926 | + | 4.14656i | 0.484462 | + | 0.176330i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.94115 | − | 10.2904i | −0.251735 | − | 0.436017i | 0.712269 | − | 0.701907i | \(-0.247668\pi\) |
−0.964003 | + | 0.265890i | \(0.914334\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.77937 | + | 3.08195i | −0.0752591 | + | 0.130353i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.2029 | + | 11.9177i | −0.598582 | + | 0.502270i | −0.890989 | − | 0.454024i | \(-0.849988\pi\) |
0.292408 | + | 0.956294i | \(0.405544\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.662917 | − | 0.241282i | 0.0278891 | − | 0.0101508i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.8144 | + | 9.39569i | −1.08220 | + | 0.393888i | −0.820725 | − | 0.571323i | \(-0.806430\pi\) |
−0.261472 | + | 0.965211i | \(0.584208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.74026 | + | 8.17305i | −0.407617 | + | 0.342032i | −0.823429 | − | 0.567419i | \(-0.807942\pi\) |
0.415812 | + | 0.909451i | \(0.363497\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.0155 | − | 27.7396i | 0.667892 | − | 1.15682i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.9550 | − | 32.8311i | −0.789109 | − | 1.36678i | −0.926514 | − | 0.376261i | \(-0.877209\pi\) |
0.137405 | − | 0.990515i | \(-0.456124\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.0344 | − | 4.74414i | −0.540759 | − | 0.196820i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.109707 | + | 0.622182i | −0.00454362 | + | 0.0257681i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.3606 | − | 22.9583i | −1.12929 | − | 0.947590i | −0.130258 | − | 0.991480i | \(-0.541580\pi\) |
−0.999036 | + | 0.0438900i | \(0.986025\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.05965 | − | 28.6947i | −0.208479 | − | 1.18234i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.5452 | −0.802624 | −0.401312 | − | 0.915941i | \(-0.631446\pi\) | ||||
−0.401312 | + | 0.915941i | \(0.631446\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.65119 | −0.108688 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.43167 | + | 25.1332i | 0.181073 | + | 1.02692i | 0.930898 | + | 0.365280i | \(0.119027\pi\) |
−0.749825 | + | 0.661637i | \(0.769862\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.5383 | + | 9.68176i | 0.470656 | + | 0.394927i | 0.847034 | − | 0.531539i | \(-0.178386\pi\) |
−0.376378 | + | 0.926466i | \(0.622831\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.847524 | + | 4.80655i | −0.0344568 | + | 0.195414i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.5353 | − | 9.29408i | −1.03645 | − | 0.377235i | −0.232914 | − | 0.972497i | \(-0.574826\pi\) |
−0.803532 | + | 0.595262i | \(0.797048\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.09275 | − | 1.89269i | −0.0442078 | − | 0.0765701i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.98720 | − | 6.90604i | 0.161042 | − | 0.278932i | −0.774201 | − | 0.632940i | \(-0.781848\pi\) |
0.935243 | + | 0.354008i | \(0.115181\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.33313 | − | 5.31412i | 0.254962 | − | 0.213939i | −0.506343 | − | 0.862332i | \(-0.669003\pi\) |
0.761306 | + | 0.648393i | \(0.224559\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.23620 | + | 0.813909i | −0.0898803 | + | 0.0327137i | −0.386569 | − | 0.922261i | \(-0.626340\pi\) |
0.296689 | + | 0.954974i | \(0.404118\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.12535 | + | 2.59342i | −0.285471 | + | 0.103903i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.9175 | − | 14.1955i | 0.676700 | − | 0.567819i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.4153 | + | 38.8244i | −0.893756 | + | 1.54803i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.96183 | + | 15.5224i | 0.356765 | + | 0.617935i | 0.987418 | − | 0.158130i | \(-0.0505464\pi\) |
−0.630653 | + | 0.776065i | \(0.717213\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.90308 | + | 1.78458i | 0.194573 | + | 0.0708187i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.61389 | − | 9.15284i | 0.0639447 | − | 0.362649i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.6588 | + | 13.9784i | 0.657985 | + | 0.552115i | 0.909482 | − | 0.415743i | \(-0.136479\pi\) |
−0.251497 | + | 0.967858i | \(0.580923\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.96011 | − | 11.1163i | −0.0772991 | − | 0.438385i | −0.998754 | − | 0.0499002i | \(-0.984110\pi\) |
0.921455 | − | 0.388485i | \(-0.127001\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.1713 | −1.65792 | −0.828962 | − | 0.559306i | \(-0.811068\pi\) | ||||
−0.828962 | + | 0.559306i | \(0.811068\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.505240 | 0.0198324 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.45235 | − | 25.2505i | −0.174234 | − | 0.988130i | −0.939024 | − | 0.343851i | \(-0.888269\pi\) |
0.764790 | − | 0.644279i | \(-0.222842\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.27123 | + | 1.90579i | 0.0887443 | + | 0.0744653i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.39623 | − | 19.2610i | 0.132298 | − | 0.750302i | −0.844405 | − | 0.535706i | \(-0.820046\pi\) |
0.976703 | − | 0.214596i | \(-0.0688434\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0405 | − | 6.20222i | −0.662797 | − | 0.241238i | −0.0113536 | − | 0.999936i | \(-0.503614\pi\) |
−0.651444 | + | 0.758697i | \(0.725836\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.991732 | − | 1.71773i | −0.0384577 | − | 0.0666107i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.57847 | + | 2.73398i | −0.0611184 | + | 0.105860i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0113902 | − | 0.00955748i | 0.000439712 | − | 0.000368963i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.9708 | − | 12.3643i | 1.30948 | − | 0.476610i | 0.409405 | − | 0.912353i | \(-0.365736\pi\) |
0.900071 | + | 0.435742i | \(0.143514\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.70097 | + | 3.16689i | −0.334405 | + | 0.121714i | −0.503765 | − | 0.863841i | \(-0.668052\pi\) |
0.169360 | + | 0.985554i | \(0.445830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.1092 | − | 12.6782i | 0.579839 | − | 0.486543i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.3685 | − | 17.9588i | 0.396741 | − | 0.687175i | −0.596581 | − | 0.802553i | \(-0.703474\pi\) |
0.993322 | + | 0.115378i | \(0.0368078\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.89710 | − | 5.01792i | −0.110692 | − | 0.191725i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.8665 | + | 6.86683i | 0.718755 | + | 0.261606i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.63048 | − | 43.2746i | 0.290277 | − | 1.64624i | −0.395525 | − | 0.918455i | \(-0.629437\pi\) |
0.685802 | − | 0.727788i | \(-0.259452\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.35719 | − | 6.17342i | −0.279074 | − | 0.234171i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.55729 | + | 25.8457i | 0.172620 | + | 0.978975i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.3552 | 1.33535 | 0.667673 | − | 0.744455i | \(-0.267291\pi\) | ||||
0.667673 | + | 0.744455i | \(0.267291\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.5396 | −1.26497 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.04220 | − | 17.2532i | −0.114414 | − | 0.648873i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.0176 | + | 12.6013i | 0.563999 | + | 0.473251i | 0.879648 | − | 0.475625i | \(-0.157778\pi\) |
−0.315650 | + | 0.948876i | \(0.602222\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.21759 | + | 52.2755i | −0.345201 | + | 1.95773i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0373449 | − | 0.0135924i | −0.00139662 | − | 0.000508328i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.20116 | + | 12.4728i | 0.268558 | + | 0.465156i | 0.968490 | − | 0.249054i | \(-0.0801196\pi\) |
−0.699932 | + | 0.714210i | \(0.746786\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.6593 | − | 18.4625i | 0.396974 | − | 0.687580i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.74172 | + | 1.46148i | −0.0646860 | + | 0.0542780i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.7163 | + | 12.6357i | −1.28755 | + | 0.468632i | −0.892924 | − | 0.450208i | \(-0.851350\pi\) |
−0.394631 | + | 0.918840i | \(0.629128\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.69983 | + | 3.53045i | −0.358761 | + | 0.130578i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.41038 | − | 5.37895i | 0.236773 | − | 0.198676i | −0.516679 | − | 0.856179i | \(-0.672832\pi\) |
0.753452 | + | 0.657503i | \(0.228387\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.210037 | − | 0.363795i | 0.00773681 | − | 0.0134006i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.4109 | + | 19.7642i | 0.419755 | + | 0.727037i | 0.995915 | − | 0.0903001i | \(-0.0287826\pi\) |
−0.576159 | + | 0.817337i | \(0.695449\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.4756 | − | 14.7319i | −1.48491 | − | 0.540461i | −0.532803 | − | 0.846240i | \(-0.678861\pi\) |
−0.952103 | + | 0.305778i | \(0.901083\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.695826 | − | 3.94623i | 0.0254931 | − | 0.144579i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.3840 | − | 14.5869i | −0.635199 | − | 0.532995i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.58064 | + | 31.6494i | 0.203640 | + | 1.15490i | 0.899565 | + | 0.436787i | \(0.143884\pi\) |
−0.695925 | + | 0.718115i | \(0.745005\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.81109 | 0.102306 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.7136 | 0.643812 | 0.321906 | − | 0.946772i | \(-0.395677\pi\) | ||||
0.321906 | + | 0.946772i | \(0.395677\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.69487 | − | 15.2834i | −0.0976891 | − | 0.554022i | −0.993890 | − | 0.110374i | \(-0.964795\pi\) |
0.896201 | − | 0.443648i | \(-0.146316\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.35868 | + | 1.14007i | 0.0491876 | + | 0.0412733i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.78809 | − | 15.8121i | 0.100672 | − | 0.570940i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.4690 | − | 7.45012i | −0.738132 | − | 0.268658i | −0.0545293 | − | 0.998512i | \(-0.517366\pi\) |
−0.683603 | + | 0.729854i | \(0.739588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.242952 | + | 0.420805i | 0.00873837 | + | 0.0151353i | 0.870362 | − | 0.492413i | \(-0.163885\pi\) |
−0.861623 | + | 0.507549i | \(0.830552\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.1151 | + | 33.1084i | −0.686636 | + | 1.18929i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.0409 | + | 12.6208i | −0.538896 | + | 0.452188i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.295497 | + | 0.107552i | −0.0105737 | + | 0.00384852i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.44967 | − | 3.43940i | 0.337273 | − | 0.122757i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.1001 | − | 9.31412i | 0.395677 | − | 0.332012i | −0.423143 | − | 0.906063i | \(-0.639073\pi\) |
0.818820 | + | 0.574051i | \(0.194629\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.970306 | − | 1.68062i | 0.0345001 | − | 0.0597559i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.236257 | − | 0.409210i | −0.00838974 | − | 0.0145315i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.8020 | + | 15.2147i | 1.48070 | + | 0.538931i | 0.950983 | − | 0.309242i | \(-0.100075\pi\) |
0.529718 | + | 0.848174i | \(0.322298\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.10078 | − | 6.24286i | 0.0389430 | − | 0.220857i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.372298 | − | 0.312395i | −0.0131381 | − | 0.0110242i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.627467 | + | 3.55854i | 0.0221153 | + | 0.125422i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.9692 | −0.842713 | −0.421357 | − | 0.906895i | \(-0.638446\pi\) | ||||
−0.421357 | + | 0.906895i | \(0.638446\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.274670 | −0.00964497 | −0.00482249 | − | 0.999988i | \(-0.501535\pi\) | ||||
−0.00482249 | + | 0.999988i | \(0.501535\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.192422 | − | 1.09128i | −0.00674025 | − | 0.0382259i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.91583 | − | 4.96397i | −0.206969 | − | 0.173667i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.00229 | − | 45.3833i | 0.279282 | − | 1.58389i | −0.445741 | − | 0.895162i | \(-0.647060\pi\) |
0.725023 | − | 0.688725i | \(-0.241829\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.2491 | − | 8.46198i | −0.810413 | − | 0.294966i | −0.0966186 | − | 0.995321i | \(-0.530803\pi\) |
−0.713794 | + | 0.700355i | \(0.753025\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.3668 | + | 42.2045i | 0.847316 | + | 1.46759i | 0.883594 | + | 0.468253i | \(0.155116\pi\) |
−0.0362782 | + | 0.999342i | \(0.511550\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.832320 | − | 1.44162i | 0.0289077 | − | 0.0500695i | −0.851210 | − | 0.524826i | \(-0.824130\pi\) |
0.880117 | + | 0.474756i | \(0.157464\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.6510 | − | 17.3283i | 0.715515 | − | 0.600388i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.04696 | − | 0.381061i | 0.0362314 | − | 0.0131872i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.81480 | + | 3.57230i | −0.338845 | + | 0.123329i | −0.505838 | − | 0.862629i | \(-0.668816\pi\) |
0.166993 | + | 0.985958i | \(0.446594\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.0436 | + | 18.4968i | −0.760125 | + | 0.637821i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.25332 | − | 3.90286i | 0.0775164 | − | 0.134262i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.71301 | + | 11.6273i | 0.230662 | + | 0.399518i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 57.4170 | + | 20.8981i | 1.96823 | + | 0.716376i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.70797 | + | 55.0566i | −0.332395 | + | 1.88510i | 0.119184 | + | 0.992872i | \(0.461972\pi\) |
−0.451579 | + | 0.892231i | \(0.649139\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.5858 | + | 18.1126i | 0.737356 | + | 0.618715i | 0.932126 | − | 0.362134i | \(-0.117952\pi\) |
−0.194770 | + | 0.980849i | \(0.562396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.12084 | − | 12.0279i | −0.0723622 | − | 0.410386i | −0.999375 | − | 0.0353561i | \(-0.988743\pi\) |
0.927013 | − | 0.375030i | \(-0.122368\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.3682 | 1.57839 | 0.789196 | − | 0.614141i | \(-0.210498\pi\) | ||||
0.789196 | + | 0.614141i | \(0.210498\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.08398 | 0.206861 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.0915364 | + | 0.519129i | 0.00310516 | + | 0.0176102i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.2263 | − | 8.58089i | −0.346505 | − | 0.290752i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.922352 | + | 5.23092i | −0.0311812 | + | 0.176837i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.3989 | − | 18.3437i | −1.70185 | − | 0.619423i | −0.705817 | − | 0.708394i | \(-0.749420\pi\) |
−0.996034 | + | 0.0889709i | \(0.971642\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.75309 | + | 16.8929i | 0.328590 | + | 0.569135i | 0.982232 | − | 0.187669i | \(-0.0600932\pi\) |
−0.653642 | + | 0.756804i | \(0.726760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.0023 | + | 22.5206i | −0.437561 | + | 0.757879i | −0.997501 | − | 0.0706549i | \(-0.977491\pi\) |
0.559939 | + | 0.828534i | \(0.310824\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.4775 | − | 31.4474i | 1.25837 | − | 1.05590i | 0.262519 | − | 0.964927i | \(-0.415447\pi\) |
0.995853 | − | 0.0909726i | \(-0.0289976\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.4876 | − | 4.90908i | 0.452359 | − | 0.164645i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.45658 | − | 1.62206i | 0.149134 | − | 0.0542802i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.33937 | + | 1.12386i | −0.0447701 | + | 0.0375666i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.88396 | − | 3.26312i | 0.0628337 | − | 0.108831i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.1178 | + | 50.4334i | 0.970053 | + | 1.68018i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.32074 | − | 1.20865i | −0.110385 | − | 0.0401769i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.30165 | − | 13.0533i | 0.0764251 | − | 0.433428i | −0.922455 | − | 0.386106i | \(-0.873820\pi\) |
0.998880 | − | 0.0473225i | \(-0.0150688\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.1404 | − | 36.1991i | −1.42930 | − | 1.19933i | −0.946123 | − | 0.323808i | \(-0.895037\pi\) |
−0.483181 | − | 0.875520i | \(-0.660519\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.104728 | − | 0.593943i | −0.00346599 | − | 0.0196566i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.15591 | 0.269332 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.0776 | 1.12412 | 0.562059 | − | 0.827097i | \(-0.310010\pi\) | ||||
0.562059 | + | 0.827097i | \(0.310010\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.73531 | + | 9.84143i | 0.0571184 | + | 0.323935i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.7108 | + | 28.2867i | 1.10840 | + | 0.930061i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.23618 | + | 24.0246i | −0.138985 | + | 0.788221i | 0.833017 | + | 0.553247i | \(0.186612\pi\) |
−0.972002 | + | 0.234974i | \(0.924500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.9521 | + | 6.89799i | 0.621129 | + | 0.226072i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.0576366 | − | 0.0998295i | −0.00188492 | − | 0.00326477i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.5275 | + | 21.6983i | −0.409256 | + | 0.708853i | −0.994807 | − | 0.101783i | \(-0.967545\pi\) |
0.585550 | + | 0.810636i | \(0.300878\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.7342 | − | 30.8236i | 1.19750 | − | 1.00482i | 0.197802 | − | 0.980242i | \(-0.436620\pi\) |
0.999698 | − | 0.0245796i | \(-0.00782472\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.6126 | − | 12.2340i | 1.09458 | − | 0.398394i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.9322 | + | 6.89077i | −0.615215 | + | 0.223920i | −0.630783 | − | 0.775959i | \(-0.717266\pi\) |
0.0155686 | + | 0.999879i | \(0.495044\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.8312 | + | 9.92758i | −0.384058 | + | 0.322263i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.6941 | + | 21.9868i | −0.411201 | + | 0.712221i | −0.995021 | − | 0.0996619i | \(-0.968224\pi\) |
0.583820 | + | 0.811883i | \(0.301557\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.65981 | + | 4.60693i | 0.0860696 | + | 0.149077i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.9777 | − | 5.45143i | −0.483654 | − | 0.176036i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.61847 | − | 31.8639i | 0.181241 | − | 1.02787i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.90864 | − | 2.44064i | −0.0936325 | − | 0.0785670i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.52956 | + | 25.6884i | 0.145661 | + | 0.826084i | 0.966834 | + | 0.255405i | \(0.0822088\pi\) |
−0.821173 | + | 0.570679i | \(0.806680\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.3981 | 1.55317 | 0.776584 | − | 0.630014i | \(-0.216951\pi\) | ||||
0.776584 | + | 0.630014i | \(0.216951\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.4194 | −0.846968 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.00721 | − | 34.0686i | −0.192188 | − | 1.08995i | −0.916367 | − | 0.400339i | \(-0.868892\pi\) |
0.724179 | − | 0.689612i | \(-0.242219\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.252558 | − | 0.211921i | −0.00807179 | − | 0.00677304i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.67463 | + | 9.49730i | −0.0534124 | + | 0.302917i | −0.999797 | − | 0.0201239i | \(-0.993594\pi\) |
0.946385 | + | 0.323041i | \(0.104705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.45343 | − | 1.25694i | −0.110035 | − | 0.0400496i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.03442 | + | 12.1840i | 0.223681 | + | 0.387428i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.9282 | + | 20.6602i | −0.378910 | + | 0.656292i | −0.990904 | − | 0.134571i | \(-0.957034\pi\) |
0.611994 | + | 0.790863i | \(0.290368\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.55484 | − | 2.14377i | 0.0809939 | − | 0.0679620i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.20493 | − | 1.53047i | 0.133172 | − | 0.0484705i | −0.274575 | − | 0.961566i | \(-0.588537\pi\) |
0.407746 | + | 0.913095i | \(0.366315\pi\) | |||||||
\(998\) | 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 | 648.2.q.a.505.3 | 24 | ||
3.2 | odd | 2 | 216.2.q.a.169.4 | ✓ | 24 | ||
12.11 | even | 2 | 432.2.u.e.385.1 | 24 | |||
27.2 | odd | 18 | 5832.2.a.h.1.5 | 12 | |||
27.4 | even | 9 | inner | 648.2.q.a.145.3 | 24 | ||
27.23 | odd | 18 | 216.2.q.a.193.4 | yes | 24 | ||
27.25 | even | 9 | 5832.2.a.i.1.8 | 12 | |||
108.23 | even | 18 | 432.2.u.e.193.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.q.a.169.4 | ✓ | 24 | 3.2 | odd | 2 | ||
216.2.q.a.193.4 | yes | 24 | 27.23 | odd | 18 | ||
432.2.u.e.193.1 | 24 | 108.23 | even | 18 | |||
432.2.u.e.385.1 | 24 | 12.11 | even | 2 | |||
648.2.q.a.145.3 | 24 | 27.4 | even | 9 | inner | ||
648.2.q.a.505.3 | 24 | 1.1 | even | 1 | trivial | ||
5832.2.a.h.1.5 | 12 | 27.2 | odd | 18 | |||
5832.2.a.i.1.8 | 12 | 27.25 | even | 9 |