Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [152,2,Mod(9,152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(152, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("152.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 152.q (of order \(9\), degree \(6\), 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: | \(1.21372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(-0.173648 + 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 152.17 |
Dual form | 152.2.q.a.9.1 |
$q$-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 \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).
\(n\) | \(39\) | \(77\) | \(97\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{9}\right)\) |
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 | ||||||||
\(3\) | −1.17365 | − | 0.984808i | −0.677606 | − | 0.568579i | 0.237700 | − | 0.971339i | \(-0.423607\pi\) |
−0.915306 | + | 0.402760i | \(0.868051\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.76604 | − | 0.642788i | 0.789799 | − | 0.287463i | 0.0845465 | − | 0.996420i | \(-0.473056\pi\) |
0.705253 | + | 0.708956i | \(0.250834\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.03209 | − | 1.78763i | −0.390093 | − | 0.675661i | 0.602369 | − | 0.798218i | \(-0.294224\pi\) |
−0.992461 | + | 0.122557i | \(0.960890\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.113341 | − | 0.642788i | −0.0377803 | − | 0.214263i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.03209 | − | 1.78763i | 0.311187 | − | 0.538991i | −0.667433 | − | 0.744670i | \(-0.732607\pi\) |
0.978620 | + | 0.205679i | \(0.0659403\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.17365 | − | 0.984808i | 0.325511 | − | 0.273137i | −0.465357 | − | 0.885123i | \(-0.654074\pi\) |
0.790868 | + | 0.611987i | \(0.209629\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.70574 | − | 0.984808i | −0.698618 | − | 0.254276i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0603074 | − | 0.342020i | 0.0146267 | − | 0.0829521i | −0.976621 | − | 0.214970i | \(-0.931035\pi\) |
0.991247 | + | 0.132018i | \(0.0421457\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.75877 | + | 2.20718i | 0.862321 | + | 0.506362i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.549163 | + | 3.11446i | −0.119837 | + | 0.679631i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.76604 | − | 1.00676i | −0.576760 | − | 0.209924i | 0.0371361 | − | 0.999310i | \(-0.488176\pi\) |
−0.613896 | + | 0.789387i | \(0.710399\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.12449 | + | 0.943555i | −0.224897 | + | 0.188711i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.79813 | + | 4.84651i | −0.538501 | + | 0.932711i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.81908 | + | 10.3165i | 0.337794 | + | 1.91573i | 0.397686 | + | 0.917522i | \(0.369813\pi\) |
−0.0598915 | + | 0.998205i | \(0.519075\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.72668 | + | 4.72275i | 0.489726 | + | 0.848231i | 0.999930 | − | 0.0118225i | \(-0.00376331\pi\) |
−0.510204 | + | 0.860054i | \(0.670430\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.97178 | + | 1.08164i | −0.517321 | + | 0.188289i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.97178 | − | 2.49362i | −0.502323 | − | 0.421499i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.51754 | 0.907078 | 0.453539 | − | 0.891236i | \(-0.350161\pi\) | ||||
0.453539 | + | 0.891236i | \(0.350161\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.34730 | −0.375868 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.64930 | − | 6.41852i | −1.19462 | − | 1.00241i | −0.999767 | − | 0.0215727i | \(-0.993133\pi\) |
−0.194853 | − | 0.980833i | \(-0.562423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.52481 | − | 2.37484i | 0.995025 | − | 0.362159i | 0.207361 | − | 0.978265i | \(-0.433513\pi\) |
0.787664 | + | 0.616105i | \(0.211290\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.613341 | − | 1.06234i | −0.0914314 | − | 0.158364i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.897804 | + | 5.09170i | 0.130958 | + | 0.742700i | 0.977589 | + | 0.210520i | \(0.0675159\pi\) |
−0.846631 | + | 0.532180i | \(0.821373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.36959 | − | 2.37219i | 0.195655 | − | 0.338884i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.407604 | + | 0.342020i | −0.0570759 | + | 0.0478924i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.29813 | − | 2.65630i | −1.00248 | − | 0.364871i | −0.211937 | − | 0.977283i | \(-0.567977\pi\) |
−0.790539 | + | 0.612412i | \(0.790199\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.673648 | − | 3.82045i | 0.0908347 | − | 0.515149i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.23783 | − | 6.29212i | −0.296407 | − | 0.833412i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0457595 | + | 0.259515i | −0.00595737 | + | 0.0337859i | −0.987642 | − | 0.156730i | \(-0.949905\pi\) |
0.981684 | + | 0.190516i | \(0.0610160\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.97818 | + | 3.63176i | 1.27757 | + | 0.464999i | 0.889629 | − | 0.456683i | \(-0.150963\pi\) |
0.387945 | + | 0.921682i | \(0.373185\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.03209 | + | 0.866025i | −0.130031 | + | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.43969 | − | 2.49362i | 0.178572 | − | 0.309296i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.22281 | + | 6.93491i | 0.149390 | + | 0.847234i | 0.963737 | + | 0.266855i | \(0.0859844\pi\) |
−0.814347 | + | 0.580379i | \(0.802904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.25490 | + | 3.90560i | 0.271458 | + | 0.470179i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.07145 | − | 2.20983i | 0.720549 | − | 0.262258i | 0.0443900 | − | 0.999014i | \(-0.485866\pi\) |
0.676159 | + | 0.736756i | \(0.263643\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.7777 | − | 9.88263i | −1.37847 | − | 1.15667i | −0.969774 | − | 0.244003i | \(-0.921539\pi\) |
−0.408696 | − | 0.912671i | \(-0.634016\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.24897 | 0.259689 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.26083 | −0.485567 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.64930 | + | 8.09672i | 1.08563 | + | 0.910953i | 0.996376 | − | 0.0850562i | \(-0.0271070\pi\) |
0.0892549 | + | 0.996009i | \(0.471551\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.21688 | − | 2.26276i | 0.690765 | − | 0.251418i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.54963 | − | 11.3443i | −0.718915 | − | 1.24520i | −0.961430 | − | 0.275050i | \(-0.911306\pi\) |
0.242515 | − | 0.970148i | \(-0.422028\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.113341 | − | 0.642788i | −0.0122935 | − | 0.0697201i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.02481 | − | 13.8994i | 0.860350 | − | 1.49017i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.52094 | + | 2.95442i | −0.373219 | + | 0.313168i | −0.810034 | − | 0.586384i | \(-0.800551\pi\) |
0.436814 | + | 0.899552i | \(0.356107\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.97178 | − | 1.08164i | −0.311527 | − | 0.113387i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.45084 | − | 8.22811i | 0.150445 | − | 0.853215i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.05690 | + | 1.48189i | 0.826621 | + | 0.152038i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.301537 | − | 1.71010i | 0.0306164 | − | 0.173634i | −0.965665 | − | 0.259789i | \(-0.916347\pi\) |
0.996282 | + | 0.0861549i | \(0.0274580\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.26604 | − | 0.460802i | −0.127242 | − | 0.0463124i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.64930 | + | 6.41852i | −0.761134 | + | 0.638667i | −0.938422 | − | 0.345492i | \(-0.887712\pi\) |
0.177288 | + | 0.984159i | \(0.443268\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.642903 | + | 1.11354i | −0.0633472 | + | 0.109721i | −0.895960 | − | 0.444136i | \(-0.853511\pi\) |
0.832612 | + | 0.553856i | \(0.186844\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.03209 | + | 5.85327i | 0.100722 | + | 0.571220i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.337496 | − | 0.584561i | −0.0326270 | − | 0.0565116i | 0.849251 | − | 0.527990i | \(-0.177054\pi\) |
−0.881878 | + | 0.471478i | \(0.843721\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.28359 | − | 3.37895i | 0.889206 | − | 0.323645i | 0.143287 | − | 0.989681i | \(-0.454233\pi\) |
0.745919 | + | 0.666037i | \(0.232011\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.47565 | − | 5.43372i | −0.614642 | − | 0.515746i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.61081 | −0.433749 | −0.216874 | − | 0.976199i | \(-0.569586\pi\) | ||||
−0.216874 | + | 0.976199i | \(0.569586\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.53209 | −0.515870 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.766044 | − | 0.642788i | −0.0708208 | − | 0.0594257i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.673648 | + | 0.245188i | −0.0617532 | + | 0.0224763i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.36959 | + | 5.83629i | 0.306326 | + | 0.530572i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.65657 | + | 15.0662i | 0.239535 | + | 1.35847i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.07785 | + | 10.5271i | −0.543619 | + | 0.941576i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.15136 | + | 6.00070i | −0.634581 | + | 0.532476i | −0.902349 | − | 0.431007i | \(-0.858158\pi\) |
0.267768 | + | 0.963483i | \(0.413714\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.99660 | − | 3.63846i | −0.880151 | − | 0.320349i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.29473 | − | 13.0141i | 0.200491 | − | 1.13704i | −0.703887 | − | 0.710312i | \(-0.748554\pi\) |
0.904378 | − | 0.426732i | \(-0.140335\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0662372 | − | 8.99730i | 0.00574349 | − | 0.780165i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.82635 | + | 10.3578i | −0.157187 | + | 0.891454i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.5599 | + | 7.48319i | 1.75655 | + | 0.639332i | 0.999895 | − | 0.0144818i | \(-0.00460986\pi\) |
0.756655 | + | 0.653814i | \(0.226832\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.7777 | + | 13.2390i | −1.33824 | + | 1.12292i | −0.356170 | + | 0.934421i | \(0.615918\pi\) |
−0.982074 | + | 0.188498i | \(0.939638\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.96064 | − | 6.86002i | 0.333546 | − | 0.577718i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.549163 | − | 3.11446i | −0.0459233 | − | 0.260444i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.84389 | + | 17.0501i | 0.817491 | + | 1.41594i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.94356 | + | 1.43534i | −0.325260 | + | 0.118385i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.23783 | + | 5.23416i | 0.511023 | + | 0.428799i | 0.861489 | − | 0.507776i | \(-0.169532\pi\) |
−0.350466 | + | 0.936575i | \(0.613977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.226682 | −0.0183261 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.85117 | + | 6.58791i | 0.630621 | + | 0.529154i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.07145 | − | 1.84586i | 0.404746 | − | 0.147315i | −0.131622 | − | 0.991300i | \(-0.542018\pi\) |
0.536367 | + | 0.843985i | \(0.319796\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.94949 | + | 10.3048i | 0.471825 | + | 0.817226i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.05509 | + | 5.98373i | 0.0831530 | + | 0.471584i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2442 | − | 19.4756i | 0.880715 | − | 1.52544i | 0.0301685 | − | 0.999545i | \(-0.490396\pi\) |
0.850547 | − | 0.525899i | \(-0.176271\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.55303 | + | 3.82045i | −0.354453 | + | 0.297422i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.6532 | − | 6.06126i | −1.28866 | − | 0.469034i | −0.395374 | − | 0.918520i | \(-0.629385\pi\) |
−0.893287 | + | 0.449486i | \(0.851607\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.84982 | + | 10.4909i | −0.142294 | + | 0.806990i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.992726 | − | 2.66625i | 0.0759157 | − | 0.203894i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.32888 | + | 18.8790i | −0.253090 | + | 1.43534i | 0.547839 | + | 0.836584i | \(0.315451\pi\) |
−0.800928 | + | 0.598760i | \(0.795660\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.84730 | + | 1.03633i | 0.215235 | + | 0.0783393i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.309278 | − | 0.259515i | 0.0232467 | − | 0.0195063i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.27332 | + | 3.93750i | −0.169916 | + | 0.294303i | −0.938390 | − | 0.345578i | \(-0.887683\pi\) |
0.768474 | + | 0.639881i | \(0.221016\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.63429 | − | 14.9398i | −0.195805 | − | 1.11046i | −0.911268 | − | 0.411814i | \(-0.864895\pi\) |
0.715463 | − | 0.698651i | \(-0.246216\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.13429 | − | 14.0890i | −0.601304 | − | 1.04149i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.74422 | − | 3.54661i | 0.716409 | − | 0.260752i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.549163 | − | 0.460802i | −0.0401588 | − | 0.0336972i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.5517 | 0.840262 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6459 | −0.987382 | −0.493691 | − | 0.869637i | \(-0.664353\pi\) | ||||
−0.493691 | + | 0.869637i | \(0.664353\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.15136 | − | 6.00070i | −0.514766 | − | 0.431940i | 0.348037 | − | 0.937481i | \(-0.386849\pi\) |
−0.862803 | + | 0.505541i | \(0.831293\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.14543 | + | 1.50881i | −0.296860 | + | 0.108048i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.32295 | − | 4.02346i | −0.165503 | − | 0.286660i | 0.771331 | − | 0.636435i | \(-0.219591\pi\) |
−0.936834 | + | 0.349775i | \(0.886258\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.0748553 | + | 0.424525i | 0.00530635 | + | 0.0300938i | 0.987346 | − | 0.158581i | \(-0.0506919\pi\) |
−0.982040 | + | 0.188675i | \(0.939581\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.39440 | − | 9.34337i | 0.380492 | − | 0.659031i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.5646 | − | 13.8994i | 1.16261 | − | 0.975546i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.6348 | − | 6.41852i | −1.23166 | − | 0.448289i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.333626 | + | 1.89209i | −0.0231886 | + | 0.131509i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.82501 | − | 4.44129i | 0.541267 | − | 0.307210i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.01842 | − | 17.1183i | 0.207796 | − | 1.17847i | −0.685182 | − | 0.728372i | \(-0.740277\pi\) |
0.892978 | − | 0.450100i | \(-0.148612\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.30200 | − | 3.38565i | −0.637363 | − | 0.231981i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.99660 | − | 8.38814i | 0.681762 | − | 0.572066i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.62836 | − | 9.74860i | 0.382078 | − | 0.661778i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.09034 | + | 23.1975i | 0.276399 | + | 1.56754i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.266044 | − | 0.460802i | −0.0178961 | − | 0.0309969i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.4410 | − | 4.52817i | 0.833113 | − | 0.303228i | 0.109977 | − | 0.993934i | \(-0.464922\pi\) |
0.723136 | + | 0.690706i | \(0.242700\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.733956 | + | 0.615862i | 0.0489304 | + | 0.0410575i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.77425 | −0.515995 | −0.257998 | − | 0.966146i | \(-0.583063\pi\) | ||||
−0.257998 | + | 0.966146i | \(0.583063\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.73917 | 0.181009 | 0.0905047 | − | 0.995896i | \(-0.471152\pi\) | ||||
0.0905047 | + | 0.995896i | \(0.471152\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.00072 | + | 4.19610i | 0.329023 | + | 0.276083i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.76604 | − | 0.642788i | 0.115697 | − | 0.0421104i | −0.283523 | − | 0.958966i | \(-0.591503\pi\) |
0.399220 | + | 0.916855i | \(0.369281\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.85844 | + | 8.41507i | 0.316930 | + | 0.548938i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.35117 | − | 19.0054i | −0.217682 | − | 1.23453i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.40167 | − | 16.2842i | 0.608144 | − | 1.05334i | −0.383402 | − | 0.923581i | \(-0.625248\pi\) |
0.991546 | − | 0.129754i | \(-0.0414189\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.91013 | + | 7.47649i | −0.573952 | + | 0.481603i | −0.882955 | − | 0.469458i | \(-0.844449\pi\) |
0.309003 | + | 0.951061i | \(0.400005\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.25150 | + | 2.27536i | 0.401034 | + | 0.145964i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.893933 | − | 5.06975i | 0.0571113 | − | 0.323894i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.58512 | − | 1.11121i | 0.419001 | − | 0.0707048i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.48499 | + | 19.7643i | −0.220852 | + | 1.25251i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.60354 | + | 2.76746i | 0.479931 | + | 0.174681i | 0.570646 | − | 0.821196i | \(-0.306693\pi\) |
−0.0907147 | + | 0.995877i | \(0.528915\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.65451 | + | 3.90560i | −0.292627 | + | 0.245543i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.500000 | + | 0.866025i | −0.0313112 | + | 0.0542326i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.72756 | − | 9.79747i | −0.107762 | − | 0.611150i | −0.990081 | − | 0.140497i | \(-0.955130\pi\) |
0.882319 | − | 0.470652i | \(-0.155981\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.69459 | − | 9.86332i | −0.353845 | − | 0.612877i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.42514 | − | 2.33856i | 0.397706 | − | 0.144753i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.4722 | + | 10.4655i | 0.769072 | + | 0.645328i | 0.940471 | − | 0.339874i | \(-0.110384\pi\) |
−0.171399 | + | 0.985202i | \(0.554829\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.5963 | −0.896642 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.04189 | 0.430957 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.9101 | − | 9.15469i | −0.665202 | − | 0.558171i | 0.246439 | − | 0.969158i | \(-0.420740\pi\) |
−0.911641 | + | 0.410987i | \(0.865184\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.9440 | + | 8.71491i | −1.45450 | + | 0.529393i | −0.943843 | − | 0.330394i | \(-0.892819\pi\) |
−0.510653 | + | 0.859787i | \(0.670596\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.42262 | + | 4.19610i | 0.146624 | + | 0.253959i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.526159 | + | 2.98400i | 0.0317286 | + | 0.179942i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.62836 | + | 9.74860i | −0.338175 | + | 0.585736i | −0.984090 | − | 0.177673i | \(-0.943143\pi\) |
0.645914 | + | 0.763410i | \(0.276476\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.72668 | − | 2.28796i | 0.163242 | − | 0.136976i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.15018 | − | 0.782601i | −0.128269 | − | 0.0466860i | 0.277088 | − | 0.960844i | \(-0.410631\pi\) |
−0.405357 | + | 0.914158i | \(0.632853\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.35117 | + | 7.66285i | −0.0803185 | + | 0.455509i | 0.917950 | + | 0.396695i | \(0.129843\pi\) |
−0.998269 | + | 0.0588139i | \(0.981268\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.99660 | − | 9.67372i | −0.473677 | − | 0.573021i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.57919 | + | 20.2986i | −0.211273 | + | 1.19819i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8614 | + | 5.77309i | 0.933026 | + | 0.339594i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.03802 | + | 1.71010i | −0.119471 | + | 0.100248i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.04664 | − | 3.54488i | 0.119566 | − | 0.207094i | −0.800030 | − | 0.599960i | \(-0.795183\pi\) |
0.919596 | + | 0.392866i | \(0.128516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0859997 | + | 0.487728i | 0.00500709 | + | 0.0283966i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.77584 | + | 10.0041i | 0.335148 | + | 0.580494i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.23783 | + | 1.54244i | −0.245080 | + | 0.0892018i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.9795 | − | 9.21291i | −0.632849 | − | 0.531023i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.2986 | 0.878882 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.9564 | 1.14270 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.0608 | − | 10.9593i | −0.745418 | − | 0.625480i | 0.188869 | − | 0.982002i | \(-0.439518\pi\) |
−0.934287 | + | 0.356523i | \(0.883962\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.85117 | − | 0.673770i | 0.105309 | − | 0.0383294i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.03209 | − | 15.6440i | −0.512163 | − | 0.887092i | −0.999901 | − | 0.0141018i | \(-0.995511\pi\) |
0.487738 | − | 0.872990i | \(-0.337822\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.550507 | − | 3.12208i | −0.0311165 | − | 0.176470i | 0.965289 | − | 0.261185i | \(-0.0841133\pi\) |
−0.996405 | + | 0.0847146i | \(0.973002\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.26604 | + | 2.19285i | −0.0713335 | + | 0.123553i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.7777 | + | 9.88263i | −0.661499 | + | 0.555064i | −0.910536 | − | 0.413430i | \(-0.864330\pi\) |
0.249037 | + | 0.968494i | \(0.419886\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.3195 | + | 7.39571i | 1.13768 | + | 0.414080i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.179578 | + | 1.01844i | −0.0100231 | + | 0.0568436i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.981582 | − | 1.15247i | 0.0546167 | − | 0.0641249i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.390530 | + | 2.21480i | −0.0216627 | + | 0.122855i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.2233 | − | 5.17685i | −0.786549 | − | 0.286280i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.17546 | − | 6.86002i | 0.450728 | − | 0.378205i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8550 | + | 22.2656i | −0.706577 | + | 1.22383i | 0.259543 | + | 0.965732i | \(0.416428\pi\) |
−0.966119 | + | 0.258095i | \(0.916905\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.625362 | − | 3.54661i | −0.0342697 | − | 0.194353i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.61721 | + | 11.4613i | 0.361537 | + | 0.626200i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.7028 | + | 11.9028i | −1.78144 | + | 0.648389i | −0.781742 | + | 0.623602i | \(0.785669\pi\) |
−0.999693 | + | 0.0247877i | \(0.992109\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.41147 | + | 4.54077i | 0.293911 | + | 0.246621i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.2567 | 0.609585 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1034 | −1.08548 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.49273 | + | 5.44804i | 0.349557 | + | 0.293313i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.608593 | − | 0.221510i | 0.0326710 | − | 0.0118913i | −0.325633 | − | 0.945496i | \(-0.605577\pi\) |
0.358304 | + | 0.933605i | \(0.383355\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.50000 | − | 9.52628i | −0.294408 | − | 0.509930i | 0.680439 | − | 0.732805i | \(-0.261789\pi\) |
−0.974847 | + | 0.222875i | \(0.928456\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.48886 | + | 8.44372i | 0.0794692 | + | 0.450692i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.69253 | + | 15.0559i | −0.462657 | + | 0.801345i | −0.999092 | − | 0.0425961i | \(-0.986437\pi\) |
0.536436 | + | 0.843941i | \(0.319770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.30200 | − | 7.80531i | 0.493699 | − | 0.414263i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.03209 | + | 0.375650i | 0.0546239 | + | 0.0198815i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.18361 | + | 18.0552i | −0.168025 | + | 0.952914i | 0.777866 | + | 0.628430i | \(0.216302\pi\) |
−0.945891 | + | 0.324485i | \(0.894809\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.25671 | + | 16.5926i | 0.487195 | + | 0.873293i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.79292 | − | 10.1681i | 0.0941038 | − | 0.533689i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.1523 | − | 9.88263i | −1.42122 | − | 0.517280i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.06077 | − | 7.60289i | 0.472969 | − | 0.396868i | −0.374907 | − | 0.927062i | \(-0.622326\pi\) |
0.847876 | + | 0.530194i | \(0.177881\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.25877 | + | 5.64436i | −0.169645 | + | 0.293833i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.78383 | + | 15.7879i | 0.144529 | + | 0.819667i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.13041 | − | 1.95794i | −0.0585307 | − | 0.101378i | 0.835275 | − | 0.549832i | \(-0.185308\pi\) |
−0.893806 | + | 0.448454i | \(0.851975\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.5005 | − | 6.36965i | 0.903720 | − | 0.328927i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.2947 | + | 10.3165i | 0.633211 | + | 0.531327i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.4243 | −0.638192 | −0.319096 | − | 0.947722i | \(-0.603379\pi\) | ||||
−0.319096 | + | 0.947722i | \(0.603379\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.3027 | 0.732750 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.8418 | + | 12.4538i | 0.758382 | + | 0.636358i | 0.937705 | − | 0.347432i | \(-0.112946\pi\) |
−0.179323 | + | 0.983790i | \(0.557391\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.52481 | + | 2.73881i | −0.383500 | + | 0.139583i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.26604 | − | 3.92490i | −0.115190 | − | 0.199514i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.81908 | + | 21.6591i | 0.193635 | + | 1.09816i | 0.914349 | + | 0.404926i | \(0.132703\pi\) |
−0.720714 | + | 0.693232i | \(0.756186\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.511144 | + | 0.885328i | −0.0258497 | + | 0.0447730i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.5096 | + | 13.0141i | −0.782353 | + | 0.656472i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.2456 | + | 8.09672i | 1.11930 | + | 0.407390i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.0234708 | + | 0.133109i | −0.00117796 | + | 0.00668056i | −0.985391 | − | 0.170307i | \(-0.945524\pi\) |
0.984213 | + | 0.176987i | \(0.0566352\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.93835 | + | 10.4944i | −0.447477 | + | 0.525379i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.64203 | − | 37.6688i | 0.331687 | − | 1.88109i | −0.126083 | − | 0.992020i | \(-0.540241\pi\) |
0.457770 | − | 0.889071i | \(-0.348648\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.85117 | + | 2.85759i | 0.391094 | + | 0.142347i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.52481 | − | 7.99227i | 0.473292 | − | 0.397139i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.69459 | − | 9.86332i | 0.282270 | − | 0.488907i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.21600 | − | 18.2389i | −0.159021 | − | 0.901854i | −0.955017 | − | 0.296552i | \(-0.904163\pi\) |
0.795996 | − | 0.605302i | \(-0.206948\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.7606 | − | 29.0302i | −0.826739 | − | 1.43195i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.511144 | − | 0.186041i | 0.0251518 | − | 0.00915450i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.8589 | − | 15.8245i | −0.925747 | − | 0.776794i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.5553 | 1.54527 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.2567 | −0.989605 | −0.494803 | − | 0.869005i | \(-0.664760\pi\) | ||||
−0.494803 | + | 0.869005i | \(0.664760\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.95883 | − | 1.64365i | −0.0954673 | − | 0.0801066i | 0.593805 | − | 0.804609i | \(-0.297625\pi\) |
−0.689272 | + | 0.724503i | \(0.742070\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.17112 | − | 1.15419i | 0.154185 | − | 0.0561188i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.254900 | + | 0.441500i | 0.0123645 | + | 0.0214159i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.80612 | − | 21.5856i | −0.184191 | − | 1.04460i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.42262 | + | 4.19610i | −0.116965 | + | 0.202590i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.43036 | − | 6.23481i | 0.357908 | − | 0.300320i | −0.446048 | − | 0.895009i | \(-0.647169\pi\) |
0.803956 | + | 0.594689i | \(0.202725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.22890 | + | 1.17522i | 0.155171 | + | 0.0564777i | 0.418438 | − | 0.908245i | \(-0.362578\pi\) |
−0.263267 | + | 0.964723i | \(0.584800\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.23783 | − | 29.7052i | 0.251135 | − | 1.42425i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.17483 | − | 9.88933i | −0.391055 | − | 0.473071i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.61974 | − | 37.5424i | 0.315943 | − | 1.79180i | −0.250940 | − | 0.968003i | \(-0.580740\pi\) |
0.566883 | − | 0.823798i | \(-0.308149\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.68004 | − | 0.611486i | −0.0800021 | − | 0.0291184i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.64930 | + | 3.06213i | −0.173383 | + | 0.145486i | −0.725350 | − | 0.688380i | \(-0.758322\pi\) |
0.551967 | + | 0.833866i | \(0.313878\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.31908 | + | 7.48086i | −0.204744 | + | 0.354627i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.16637 | − | 12.2861i | −0.102466 | − | 0.581113i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.14590 | − | 5.44885i | −0.148464 | − | 0.257147i | 0.782196 | − | 0.623033i | \(-0.214100\pi\) |
−0.930660 | + | 0.365885i | \(0.880766\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.3687 | + | 7.04963i | −0.912037 | + | 0.331954i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.7784 | + | 15.7569i | 0.882285 | + | 0.740325i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.94356 | −0.278639 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.6459 | 1.66744 | 0.833722 | − | 0.552184i | \(-0.186205\pi\) | ||||
0.833722 | + | 0.552184i | \(0.186205\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.48886 | + | 1.24930i | 0.0694938 | + | 0.0583122i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.3282 | − | 10.6746i | 1.36595 | − | 0.497165i | 0.448060 | − | 0.894003i | \(-0.352115\pi\) |
0.917888 | + | 0.396839i | \(0.129893\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.94831 | − | 5.10662i | −0.137020 | − | 0.237325i | 0.789348 | − | 0.613947i | \(-0.210419\pi\) |
−0.926367 | + | 0.376622i | \(0.877086\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.72668 | − | 15.4638i | −0.126447 | − | 0.717116i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.7267 | + | 28.9715i | −0.774019 | + | 1.34064i | 0.161326 | + | 0.986901i | \(0.448423\pi\) |
−0.935344 | + | 0.353738i | \(0.884910\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.1350 | − | 9.34337i | 0.514167 | − | 0.431437i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.76991 | − | 2.82802i | −0.358019 | − | 0.130308i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.48886 | − | 14.1150i | 0.114438 | − | 0.649008i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.30928 | + | 1.06467i | −0.289490 | + | 0.0488502i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.880263 | + | 4.99222i | −0.0403045 | + | 0.228578i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.2545 | − | 8.82791i | −1.10822 | − | 0.403358i | −0.277877 | − | 0.960617i | \(-0.589631\pi\) |
−0.830339 | + | 0.557259i | \(0.811853\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.47565 | − | 5.43372i | 0.295264 | − | 0.247756i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.65451 | − | 8.06186i | 0.211788 | − | 0.366827i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.566704 | − | 3.21394i | −0.0257327 | − | 0.145937i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.8996 | + | 29.2710i | 0.765795 | + | 1.32640i | 0.939825 | + | 0.341655i | \(0.110987\pi\) |
−0.174031 | + | 0.984740i | \(0.555679\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −32.3764 | + | 11.7841i | −1.46411 | + | 0.532894i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.12907 | − | 4.30380i | −0.231472 | − | 0.194228i | 0.519673 | − | 0.854365i | \(-0.326054\pi\) |
−0.751145 | + | 0.660137i | \(0.770498\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.63816 | 0.163854 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.53209 | −0.113809 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.2166 | − | 8.57277i | −0.458279 | − | 0.384541i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.15018 | + | 1.14657i | −0.141021 | + | 0.0513276i | −0.411567 | − | 0.911380i | \(-0.635018\pi\) |
0.270545 | + | 0.962707i | \(0.412796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.5758 | + | 23.5140i | 0.606522 | + | 1.05053i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.95424 | − | 22.4256i | −0.176311 | − | 0.999909i | −0.936620 | − | 0.350347i | \(-0.886064\pi\) |
0.760309 | − | 0.649562i | \(-0.225047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.38326 | + | 16.2523i | −0.417549 | + | 0.723217i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.5025 | − | 10.4909i | 0.555257 | − | 0.465916i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.9937 | + | 13.8286i | 1.68404 | + | 0.612940i | 0.993855 | − | 0.110693i | \(-0.0353070\pi\) |
0.690185 | + | 0.723633i | \(0.257529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.51090 | + | 31.2538i | −0.243788 | + | 1.38259i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −21.2147 | + | 12.0409i | −0.936650 | + | 0.531620i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.419625 | + | 2.37981i | −0.0184909 | + | 0.104867i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.0287 | + | 3.65014i | 0.441061 | + | 0.160533i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.4991 | − | 18.8790i | 0.987602 | − | 0.828696i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.80541 | − | 10.0553i | 0.254340 | − | 0.440529i | −0.710376 | − | 0.703822i | \(-0.751475\pi\) |
0.964716 | + | 0.263293i | \(0.0848086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.96198 | + | 11.1269i | 0.0857915 | + | 0.486548i | 0.997183 | + | 0.0750072i | \(0.0238980\pi\) |
−0.911392 | + | 0.411540i | \(0.864991\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.32114 | − | 4.02033i | −0.101303 | − | 0.175461i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.77972 | − | 0.647763i | 0.0775256 | − | 0.0282170i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.9816 | − | 9.21464i | −0.477460 | − | 0.400637i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.171999 | 0.00746413 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.2986 | −0.662656 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.971782 | − | 0.815422i | −0.0420138 | − | 0.0352537i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.54576 | − | 2.38246i | 0.282470 | − | 0.102811i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.82707 | − | 4.89662i | −0.121770 | − | 0.210913i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.48457 | + | 14.0907i | 0.106820 | + | 0.605808i | 0.990478 | + | 0.137673i | \(0.0439625\pi\) |
−0.883657 | + | 0.468134i | \(0.844926\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.6211 | + | 20.1283i | −0.498708 | + | 0.863788i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.2233 | − | 11.9347i | 0.609258 | − | 0.511228i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.1657 | + | 12.0713i | 1.41806 | + | 0.516132i | 0.933485 | − | 0.358617i | \(-0.116752\pi\) |
0.484576 | + | 0.874749i | \(0.338974\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.20352 | − | 6.82548i | 0.0513648 | − | 0.291304i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.9329 | + | 42.7924i | −0.678764 | + | 1.82302i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.51501 | − | 25.6059i | 0.191998 | − | 1.08887i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.9290 | − | 5.43372i | −0.633701 | − | 0.230648i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.4277 | + | 18.8191i | −0.950291 | + | 0.797389i | −0.979347 | − | 0.202189i | \(-0.935194\pi\) |
0.0290556 | + | 0.999578i | \(0.490750\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.31908 | − | 9.21291i | 0.224973 | − | 0.389665i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.190722 | + | 1.08164i | 0.00805230 | + | 0.0456669i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.96791 | − | 10.3367i | −0.251517 | − | 0.435641i | 0.712426 | − | 0.701747i | \(-0.247596\pi\) |
−0.963944 | + | 0.266106i | \(0.914263\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.14290 | + | 2.96377i | −0.342575 | + | 0.124687i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.4614 | − | 8.77812i | −0.439336 | − | 0.368646i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.5526 | −0.861611 | −0.430805 | − | 0.902445i | \(-0.641770\pi\) | ||||
−0.430805 | + | 0.902445i | \(0.641770\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.7202 | 1.45299 | 0.726497 | − | 0.687169i | \(-0.241147\pi\) | ||||
0.726497 | + | 0.687169i | \(0.241147\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0155 | + | 13.4386i | 0.669056 | + | 0.561405i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.06031 | − | 1.47783i | 0.169327 | − | 0.0616298i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.66756 | + | 8.08444i | 0.194313 | + | 0.336560i | 0.946675 | − | 0.322190i | \(-0.104419\pi\) |
−0.752362 | + | 0.658750i | \(0.771086\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.48364 | + | 14.0854i | 0.103217 | + | 0.585370i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.5196 | + | 23.4166i | −0.560888 | + | 0.971486i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.2808 | + | 10.3048i | −0.508619 | + | 0.426782i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.76604 | − | 0.642788i | −0.0730170 | − | 0.0265760i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.59240 | + | 31.7161i | −0.230823 | + | 1.30906i | 0.620412 | + | 0.784276i | \(0.286966\pi\) |
−0.851235 | + | 0.524785i | \(0.824146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.174992 | + | 23.7700i | −0.00721043 | + | 0.979426i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.23601 | + | 7.00979i | −0.0508429 | + | 0.288344i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.0920 | − | 9.49671i | −1.07147 | − | 0.389983i | −0.254743 | − | 0.967009i | \(-0.581991\pi\) |
−0.816726 | + | 0.577026i | \(0.804213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.03209 | + | 0.866025i | −0.0423115 | + | 0.0355036i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.330222 | − | 0.571962i | 0.0135151 | − | 0.0234088i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.32383 | − | 24.5216i | −0.176667 | − | 1.00193i | −0.936202 | − | 0.351461i | \(-0.885685\pi\) |
0.759536 | − | 0.650466i | \(-0.225426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.86959 | − | 13.6305i | −0.321007 | − | 0.556001i | 0.659689 | − | 0.751539i | \(-0.270688\pi\) |
−0.980696 | + | 0.195538i | \(0.937355\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.31908 | − | 1.57202i | 0.175886 | − | 0.0640174i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.70233 | + | 8.14122i | 0.394456 | + | 0.330988i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.16756 | 0.169156 | 0.0845779 | − | 0.996417i | \(-0.473046\pi\) | ||||
0.0845779 | + | 0.996417i | \(0.473046\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −33.1293 | −1.34247 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.06805 | + | 5.09170i | 0.245487 | + | 0.205988i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.8252 | + | 5.03195i | −0.558393 | + | 0.203239i | −0.605772 | − | 0.795638i | \(-0.707136\pi\) |
0.0473784 | + | 0.998877i | \(0.484913\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.3760 | + | 24.8999i | 0.579696 | + | 1.00406i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.53091 | − | 31.3673i | −0.222666 | − | 1.26280i | −0.867097 | − | 0.498139i | \(-0.834017\pi\) |
0.644431 | − | 0.764662i | \(-0.277094\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.6334 | − | 18.4176i | 0.427393 | − | 0.740266i | −0.569248 | − | 0.822166i | \(-0.692765\pi\) |
0.996641 | + | 0.0819000i | \(0.0260988\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.6190 | − | 10.5886i | 0.506384 | − | 0.424907i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.91534 | + | 3.24492i | 0.357186 | + | 0.130005i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.69253 | + | 15.2701i | −0.107701 | + | 0.610805i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.5576 | − | 2.49362i | −0.541439 | − | 0.0995856i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.332748 | − | 1.88711i | 0.0132675 | − | 0.0752440i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.696814 | + | 0.253620i | 0.0277397 | + | 0.0100964i | 0.355853 | − | 0.934542i | \(-0.384190\pi\) |
−0.328113 | + | 0.944638i | \(0.606413\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.4008 | + | 17.1183i | −0.810859 | + | 0.680391i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.77244 | + | 15.1943i | −0.348124 | + | 0.602968i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.728741 | − | 4.13290i | −0.0288738 | − | 0.163751i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.10859 | − | 3.65219i | −0.0834147 | − | 0.144478i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.3282 | − | 8.49076i | 0.921407 | − | 0.335365i | 0.162609 | − | 0.986691i | \(-0.448009\pi\) |
0.758798 | + | 0.651326i | \(0.225787\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.6202 | + | 29.8889i | 1.40472 | + | 1.17870i | 0.958956 | + | 0.283554i | \(0.0915137\pi\) |
0.445768 | + | 0.895149i | \(0.352931\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.9932 | −0.787231 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.2918 | −0.443926 | −0.221963 | − | 0.975055i | \(-0.571246\pi\) | ||||
−0.221963 | + | 0.975055i | \(0.571246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.416689 | + | 0.349643i | 0.0163565 | + | 0.0137247i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.2062 | + | 5.89858i | −0.635171 | + | 0.231183i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.11081 | − | 14.0483i | −0.317401 | − | 0.549754i | 0.662544 | − | 0.749023i | \(-0.269477\pi\) |
−0.979945 | + | 0.199269i | \(0.936143\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.31268 | − | 24.4584i | −0.168510 | − | 0.955670i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.01754 | + | 8.69064i | −0.195753 | + | 0.339054i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.0608 | − | 14.3157i | 0.664593 | − | 0.557660i | −0.246866 | − | 0.969050i | \(-0.579401\pi\) |
0.911460 | + | 0.411389i | \(0.134956\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.2836 | + | 4.10689i | 0.438881 | + | 0.159739i | 0.552004 | − | 0.833841i | \(-0.313863\pi\) |
−0.113123 | + | 0.993581i | \(0.536086\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.141559 | + | 0.802823i | −0.00549771 | + | 0.0311790i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.66637 | − | 15.9322i | −0.219733 | − | 0.617824i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.35457 | − | 30.3673i | 0.207330 | − | 1.17583i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.0608 | − | 6.93755i | −0.736932 | − | 0.268221i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.7906 | − | 14.0890i | 0.648194 | − | 0.543900i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0175 | + | 19.0829i | −0.424695 | + | 0.735593i | −0.996392 | − | 0.0848716i | \(-0.972952\pi\) |
0.571697 | + | 0.820465i | \(0.306285\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.42649 | − | 8.09002i | −0.0549056 | − | 0.311385i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.03714 | − | 6.99253i | −0.155160 | − | 0.268745i | 0.777957 | − | 0.628317i | \(-0.216256\pi\) |
−0.933117 | + | 0.359572i | \(0.882923\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.36824 | + | 1.22594i | −0.129261 | + | 0.0470472i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.12424 | + | 7.65614i | 0.349642 | + | 0.293384i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.0933 | 0.883640 | 0.441820 | − | 0.897104i | \(-0.354333\pi\) | ||||
0.441820 | + | 0.897104i | \(0.354333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.1198 | 1.57111 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.21482 | − | 2.69756i | −0.122653 | − | 0.102918i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.1814 | + | 4.06969i | −0.425977 | + | 0.155043i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.8746 | + | 24.0316i | 0.527816 | + | 0.914204i | 0.999474 | + | 0.0324228i | \(0.0103223\pi\) |
−0.471658 | + | 0.881781i | \(0.656344\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.482926 | + | 2.73881i | 0.0183448 | + | 0.104039i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.3542 | + | 33.5224i | −0.734145 | + | 1.27158i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.65657 | + | 2.22913i | −0.100625 | + | 0.0844343i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.70574 | − | 0.984808i | −0.102340 | − | 0.0372489i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.678863 | + | 3.85002i | −0.0256403 | + | 0.145413i | −0.994940 | − | 0.100468i | \(-0.967966\pi\) |
0.969300 | + | 0.245881i | \(0.0790772\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.7392 | + | 12.1782i | 0.782193 | + | 0.459310i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.58512 | − | 14.6610i | 0.0973613 | − | 0.552164i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.3687 | + | 7.04963i | 0.728435 | + | 0.265129i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.9675 | − | 26.8239i | 1.20056 | − | 1.00739i | 0.200951 | − | 0.979601i | \(-0.435597\pi\) |
0.999614 | − | 0.0277921i | \(-0.00884763\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.11081 | − | 7.12014i | 0.154168 | − | 0.267026i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.78746 | − | 15.8084i | −0.104391 | − | 0.592031i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.97178 | − | 5.14728i | −0.111138 | − | 0.192497i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.0710 | + | 9.85305i | −1.01099 | + | 0.367969i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.47494 | − | 6.27222i | −0.278768 | − | 0.233914i | 0.492674 | − | 0.870214i | \(-0.336020\pi\) |
−0.771442 | + | 0.636300i | \(0.780464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.65413 | 0.0988451 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.8203 | 0.662743 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.7797 | − | 9.88435i | −0.437488 | − | 0.367096i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.3828 | − | 10.3305i | 1.05266 | − | 0.383137i | 0.242995 | − | 0.970028i | \(-0.421870\pi\) |
0.809667 | + | 0.586890i | \(0.199648\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.0201 | − | 26.0155i | −0.556299 | − | 0.963538i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.418748 | − | 2.37484i | −0.0154880 | − | 0.0878366i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.76083 | − | 6.51395i | 0.138909 | − | 0.240598i | −0.788175 | − | 0.615452i | \(-0.788974\pi\) |
0.927084 | + | 0.374853i | \(0.122307\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.04189 | + | 5.06975i | −0.222858 | + | 0.187000i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.6591 | + | 4.97151i | 0.503139 | + | 0.183128i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.654210 | − | 3.71021i | 0.0240655 | − | 0.136482i | −0.970408 | − | 0.241472i | \(-0.922370\pi\) |
0.994473 | + | 0.104990i | \(0.0334809\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.82295 | − | 5.18091i | −0.324119 | − | 0.190325i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.52822 | + | 25.6808i | −0.166124 | + | 0.942137i | 0.781774 | + | 0.623563i | \(0.214315\pi\) |
−0.947898 | + | 0.318575i | \(0.896796\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.3807 | + | 5.23416i | 0.526869 | + | 0.191765i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.54963 | + | 5.49579i | −0.239638 | + | 0.201081i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.696652 | + | 1.20664i | −0.0254551 | + | 0.0440896i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.51098 | − | 31.2543i | −0.201099 | − | 1.14049i | −0.903462 | − | 0.428668i | \(-0.858983\pi\) |
0.702363 | − | 0.711819i | \(-0.252128\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.19846 | − | 10.7361i | −0.225885 | − | 0.391244i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.2567 | + | 10.2846i | −1.02837 | + | 0.374295i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.8195 | + | 12.4351i | 0.538626 | + | 0.451960i | 0.871068 | − | 0.491163i | \(-0.163428\pi\) |
−0.332442 | + | 0.943124i | \(0.607873\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.30903 | 0.337896 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.1284 | 0.439653 | 0.219826 | − | 0.975539i | \(-0.429451\pi\) | ||||
0.219826 | + | 0.975539i | \(0.429451\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.6218 | − | 13.1082i | −0.565547 | − | 0.474550i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.400330 | + | 0.145708i | −0.0144740 | + | 0.00526809i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.201867 | + | 0.349643i | 0.00728898 | + | 0.0126249i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.71806 | − | 26.7575i | −0.170138 | − | 0.964899i | −0.943608 | − | 0.331066i | \(-0.892592\pi\) |
0.773470 | − | 0.633833i | \(-0.218519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.62108 | + | 13.2001i | −0.274467 | + | 0.475390i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.99660 | − | 8.38814i | 0.359553 | − | 0.301700i | −0.445060 | − | 0.895501i | \(-0.646818\pi\) |
0.804612 | + | 0.593800i | \(0.202373\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.52229 | − | 2.73789i | −0.270209 | − | 0.0983479i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.03003 | + | 17.1842i | −0.108702 | + | 0.616478i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.5851 | − | 41.0091i | −0.522566 | − | 1.46931i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.31592 | − | 13.1343i | 0.0828702 | − | 0.469980i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −55.0890 | − | 20.0508i | −1.96872 | − | 0.716556i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.76991 | − | 6.51973i | 0.277320 | − | 0.232699i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.5942 | − | 35.6702i | 0.734104 | − | 1.27151i | −0.221011 | − | 0.975271i | \(-0.570936\pi\) |
0.955115 | − | 0.296234i | \(-0.0957310\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.33157 | − | 24.5655i | −0.154208 | − | 0.874556i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.75877 | + | 8.24243i | 0.169202 | + | 0.293067i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.2875 | − | 5.56418i | 0.542873 | − | 0.197590i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.1309 | + | 14.3745i | 0.607570 | + | 0.509812i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.20676 | −0.149011 | −0.0745055 | − | 0.997221i | \(-0.523738\pi\) | ||||
−0.0745055 | + | 0.997221i | \(0.523738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.79561 | 0.0635240 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.29813 | + | 1.92836i | 0.0812005 | + | 0.0681354i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29.8221 | + | 10.8543i | −1.05240 | + | 0.383042i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.70961 | + | 9.88933i | 0.201237 | + | 0.348553i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.78905 | + | 21.4888i | 0.133381 | + | 0.756440i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.4263 | − | 28.4512i | 0.577519 | − | 1.00029i | −0.418244 | − | 0.908335i | \(-0.637354\pi\) |
0.995763 | − | 0.0919574i | \(-0.0293124\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.9215 | + | 21.7507i | −0.910227 | + | 0.763771i | −0.972162 | − | 0.234309i | \(-0.924717\pi\) |
0.0619354 | + | 0.998080i | \(0.480273\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 36.6844 | + | 13.3520i | 1.28658 | + | 0.468276i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.33915 | − | 41.6224i | 0.257079 | − | 1.45797i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.7670 | + | 5.47497i | 1.04141 | + | 0.191545i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.358441 | + | 2.03282i | −0.0125249 | + | 0.0710324i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.22446 | − | 0.445667i | −0.0427340 | − | 0.0155539i | 0.320565 | − | 0.947227i | \(-0.396127\pi\) |
−0.363299 | + | 0.931673i | \(0.618350\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.9188 | − | 34.3350i | 1.42634 | − | 1.19684i | 0.478503 | − | 0.878086i | \(-0.341180\pi\) |
0.947837 | − | 0.318755i | \(-0.103265\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.32114 | − | 4.02033i | 0.0808116 | − | 0.139970i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.74211 | − | 43.9077i | −0.269219 | − | 1.52682i | −0.756745 | − | 0.653710i | \(-0.773211\pi\) |
0.487525 | − | 0.873109i | \(-0.337900\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.677052 | − | 1.17269i | −0.0235150 | − | 0.0407291i | 0.854028 | − | 0.520226i | \(-0.174152\pi\) |
−0.877543 | + | 0.479497i | \(0.840819\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.2062 | − | 5.89858i | 0.562187 | − | 0.204619i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.728741 | − | 0.611486i | −0.0252494 | − | 0.0211867i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.3063 | −1.15261 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.5185 | −1.05487 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.0094 | + | 27.6982i | 1.13961 | + | 0.956247i | 0.999426 | − | 0.0338785i | \(-0.0107859\pi\) |
0.140185 | + | 0.990125i | \(0.455230\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −75.8701 | + | 27.6145i | −2.61621 | + | 0.952223i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.75284 | + | 3.03601i | 0.0603710 | + | 0.104566i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.47653 | + | 19.7164i | 0.119596 | + | 0.678264i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.95542 | − | 12.0471i | 0.238991 | − | 0.413945i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.13223 | − | 7.66285i | 0.313417 | − | 0.262988i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.2618 | − | 5.55483i | −0.523167 | − | 0.190417i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.00387 | + | 39.7209i | −0.239808 | + | 1.36002i | 0.592440 | + | 0.805615i | \(0.298165\pi\) |
−0.832248 | + | 0.554404i | \(0.812946\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0393628 | − | 5.34684i | 0.00134618 | − | 0.182858i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.72344 | + | 26.7880i | −0.161350 | + | 0.915059i | 0.791399 | + | 0.611300i | \(0.209353\pi\) |
−0.952749 | + | 0.303759i | \(0.901758\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.1116 | + | 5.86414i | 0.549720 | + | 0.200082i | 0.601922 | − | 0.798555i | \(-0.294402\pi\) |
−0.0522020 | + | 0.998637i | \(0.516624\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.1909 | − | 20.2986i | 0.824425 | − | 0.691775i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.1117 | + | 33.1025i | −0.650571 | + | 1.12682i | 0.332413 | + | 0.943134i | \(0.392137\pi\) |
−0.982984 | + | 0.183689i | \(0.941196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.25624 | + | 35.4809i | 0.212719 | + | 1.20639i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.9304 | − | 22.3960i | −0.439138 | − | 0.760609i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.4329 | − | 8.89284i | 0.828829 | − | 0.301669i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.26470 | + | 6.93491i | 0.280039 | + | 0.234980i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.13341 | −0.0383600 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25.0915 | 0.848248 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.37030 | + | 4.50622i | 0.181342 | + | 0.152164i | 0.728940 | − | 0.684577i | \(-0.240013\pi\) |
−0.547598 | + | 0.836742i | \(0.684458\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.89306 | + | 2.14490i | −0.198768 | + | 0.0723456i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.2743 | + | 24.7237i | 0.480912 | + | 0.832964i | 0.999760 | − | 0.0219027i | \(-0.00697240\pi\) |
−0.518848 | + | 0.854866i | \(0.673639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.67206 | + | 15.1540i | 0.0899218 | + | 0.509972i | 0.996186 | + | 0.0872594i | \(0.0278109\pi\) |
−0.906264 | + | 0.422713i | \(0.861078\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.379385 | − | 0.657115i | 0.0127529 | − | 0.0220887i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.4277 | + | 28.8882i | −1.15597 | + | 0.969972i | −0.999842 | − | 0.0177648i | \(-0.994345\pi\) |
−0.156126 | + | 0.987737i | \(0.549901\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.1079 | + | 6.59073i | 0.607319 | + | 0.221046i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.37140 | − | 13.4489i | 0.0794448 | − | 0.450554i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.86366 | + | 21.1201i | −0.263147 | + | 0.706758i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.48380 | + | 8.41507i | −0.0495981 | + | 0.281285i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.49273 | + | 2.36316i | 0.216786 | + | 0.0789036i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −43.7622 | + | 36.7209i | −1.45955 | + | 1.22471i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.34864 | + | 2.33591i | −0.0449297 | + | 0.0778206i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.81315 | + | 21.6254i | 0.126894 | + | 0.719649i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.2554 | − | 24.6910i | −0.473864 | − | 0.820757i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.4420 | + | 15.4476i | −1.40926 | + | 0.512930i | −0.930913 | − | 0.365240i | \(-0.880987\pi\) |
−0.478349 | + | 0.878170i | \(0.658765\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.99273 | + | 4.18939i | 0.165598 | + | 0.138953i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.2336 | 1.56492 | 0.782460 | − | 0.622701i | \(-0.213965\pi\) | ||||
0.782460 | + | 0.622701i | \(0.213965\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.0392 | −0.894867 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.4217 | − | 19.6532i | −0.774299 | − | 0.649714i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.6327 | + | 9.32954i | −0.846466 | + | 0.308088i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.3375 | − | 31.7615i | −0.604898 | − | 1.04771i | −0.992068 | − | 0.125706i | \(-0.959880\pi\) |
0.387169 | − | 0.922009i | \(-0.373453\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.53596 | + | 25.7247i | 0.149465 | + | 0.847658i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.94949 | − | 8.57277i | 0.162915 | − | 0.282176i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.20439 | + | 5.20610i | −0.203999 | + | 0.171176i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.788638 | + | 0.287041i | 0.0259023 | + | 0.00942765i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.55463 | + | 8.81672i | −0.0510056 | + | 0.289267i | −0.999632 | − | 0.0271316i | \(-0.991363\pi\) |
0.948626 | + | 0.316399i | \(0.102474\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.3838 | − | 5.89360i | 0.340316 | − | 0.193155i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.80587 | + | 27.2555i | −0.157337 | + | 0.892304i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.26604 | − | 0.460802i | −0.0414041 | − | 0.0150699i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.75949 | − | 2.31548i | 0.0901485 | − | 0.0756435i | −0.596600 | − | 0.802539i | \(-0.703482\pi\) |
0.686748 | + | 0.726895i | \(0.259038\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.42855 | + | 4.20637i | −0.0792527 | + | 0.137270i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.62654 | + | 26.2384i | 0.150821 | + | 0.855349i | 0.962507 | + | 0.271255i | \(0.0874387\pi\) |
−0.811686 | + | 0.584093i | \(0.801450\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.6964 | + | 25.4549i | 0.478581 | + | 0.828926i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20.4008 | − | 7.42528i | 0.663638 | − | 0.241544i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.9857 | + | 32.7129i | 1.26686 | + | 1.06303i | 0.994915 | + | 0.100713i | \(0.0321125\pi\) |
0.271949 | + | 0.962312i | \(0.412332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.5553 | −0.764638 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.5553 | 0.763833 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.8391 | + | 26.7162i | 1.03137 | + | 0.865423i | 0.991013 | − | 0.133762i | \(-0.0427058\pi\) |
0.0403576 | + | 0.999185i | \(0.487150\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.0993 | + | 8.77141i | −0.779834 | + | 0.283836i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.5646 | − | 28.6908i | −0.535459 | − | 0.927442i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.84246 | − | 44.4768i | −0.253246 | − | 1.43623i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.630415 | − | 1.09191i | 0.0203360 | − | 0.0352229i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.337496 | + | 0.283193i | −0.0108757 | + | 0.00912576i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.4868 | − | 6.00070i | −0.530729 | − | 0.193169i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.79503 | + | 49.8791i | −0.282829 | + | 1.60400i | 0.430109 | + | 0.902777i | \(0.358475\pi\) |
−0.712938 | + | 0.701227i | \(0.752636\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.28699 | + | 0.385920i | −0.0734687 | + | 0.0123975i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.52822 | + | 14.3382i | −0.0811344 | + | 0.460136i | 0.916990 | + | 0.398911i | \(0.130612\pi\) |
−0.998124 | + | 0.0612249i | \(0.980499\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.9504 | + | 14.5408i | 1.28075 | + | 0.466156i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.63950 | − | 2.21480i | 0.0845316 | − | 0.0709305i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.51548 | − | 11.2851i | 0.208449 | − | 0.361044i | −0.742777 | − | 0.669539i | \(-0.766492\pi\) |
0.951226 | + | 0.308495i | \(0.0998252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.64749 | + | 9.34337i | 0.0526540 | + | 0.298616i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.22416 | − | 5.58440i | −0.102939 | − | 0.178296i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.39141 | + | 3.41819i | −0.299539 | + | 0.109023i | −0.487418 | − | 0.873169i | \(-0.662061\pi\) |
0.187878 | + | 0.982192i | \(0.439839\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.68866 | − | 5.61245i | −0.213119 | − | 0.178828i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.3509 | −0.520455 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.4388 | −0.649917 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.5337 | − | 34.0118i | −1.28760 | − | 1.08042i | −0.992149 | − | 0.125063i | \(-0.960087\pi\) |
−0.295448 | − | 0.955359i | \(-0.595469\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 37.0146 | − | 13.4722i | 1.17462 | − | 0.427528i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.405078 | + | 0.701615i | 0.0128418 | + | 0.0222427i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.28430 | − | 41.3113i | −0.230696 | − | 1.30834i | −0.851491 | − | 0.524370i | \(-0.824301\pi\) |
0.620795 | − | 0.783973i | \(-0.286810\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.4388 | + | 26.7408i | −0.488462 | + | 0.846042i |
(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 | 152.2.q.a.17.1 | yes | 6 | |
4.3 | odd | 2 | 304.2.u.d.17.1 | 6 | |||
19.3 | odd | 18 | 2888.2.a.p.1.3 | 3 | |||
19.9 | even | 9 | inner | 152.2.q.a.9.1 | ✓ | 6 | |
19.16 | even | 9 | 2888.2.a.q.1.1 | 3 | |||
76.3 | even | 18 | 5776.2.a.bm.1.1 | 3 | |||
76.35 | odd | 18 | 5776.2.a.bl.1.3 | 3 | |||
76.47 | odd | 18 | 304.2.u.d.161.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.q.a.9.1 | ✓ | 6 | 19.9 | even | 9 | inner | |
152.2.q.a.17.1 | yes | 6 | 1.1 | even | 1 | trivial | |
304.2.u.d.17.1 | 6 | 4.3 | odd | 2 | |||
304.2.u.d.161.1 | 6 | 76.47 | odd | 18 | |||
2888.2.a.p.1.3 | 3 | 19.3 | odd | 18 | |||
2888.2.a.q.1.1 | 3 | 19.16 | even | 9 | |||
5776.2.a.bl.1.3 | 3 | 76.35 | odd | 18 | |||
5776.2.a.bm.1.1 | 3 | 76.3 | even | 18 |