Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,2,Mod(79,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("490.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.i (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.91266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 79.3 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.79 |
Dual form | 490.2.i.d.459.3 |
$q$-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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −2.19067 | − | 0.448288i | −0.979698 | − | 0.200480i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | −1.67303 | − | 1.48356i | −0.529059 | − | 0.469144i | ||||
\(11\) | 2.00000 | + | 3.46410i | 0.603023 | + | 1.04447i | 0.992361 | + | 0.123371i | \(0.0393705\pi\) |
−0.389338 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264i | 1.17670i | 0.808608 | + | 0.588348i | \(0.200222\pi\) | ||||
−0.808608 | + | 0.588348i | \(0.799778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.67423 | − | 2.12132i | 0.891133 | − | 0.514496i | 0.0168199 | − | 0.999859i | \(-0.494646\pi\) |
0.874313 | + | 0.485363i | \(0.161312\pi\) | |||||||
\(18\) | −2.59808 | + | 1.50000i | −0.612372 | + | 0.353553i | ||||
\(19\) | −2.82843 | + | 4.89898i | −0.648886 | + | 1.12390i | 0.334504 | + | 0.942394i | \(0.391431\pi\) |
−0.983389 | + | 0.181509i | \(0.941902\pi\) | |||||||
\(20\) | −0.707107 | − | 2.12132i | −0.158114 | − | 0.474342i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000i | 0.852803i | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.59808 | + | 1.96410i | 0.919615 | + | 0.392820i | ||||
\(26\) | −2.12132 | + | 3.67423i | −0.416025 | + | 0.720577i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.82843 | − | 4.89898i | −0.508001 | − | 0.879883i | −0.999957 | − | 0.00926296i | \(-0.997051\pi\) |
0.491957 | − | 0.870620i | \(-0.336282\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.24264 | 0.727607 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | −5.19615 | − | 3.00000i | −0.854242 | − | 0.493197i | 0.00783774 | − | 0.999969i | \(-0.497505\pi\) |
−0.862080 | + | 0.506772i | \(0.830838\pi\) | |||||||
\(38\) | −4.89898 | + | 2.82843i | −0.794719 | + | 0.458831i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.448288 | − | 2.19067i | 0.0708805 | − | 0.346375i | ||||
\(41\) | 1.41421 | 0.220863 | 0.110432 | − | 0.993884i | \(-0.464777\pi\) | ||||
0.110432 | + | 0.993884i | \(0.464777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12.0000i | − | 1.82998i | −0.403473 | − | 0.914991i | \(-0.632197\pi\) | ||
0.403473 | − | 0.914991i | \(-0.367803\pi\) | |||||||
\(44\) | −2.00000 | + | 3.46410i | −0.301511 | + | 0.522233i | ||||
\(45\) | 4.45069 | − | 5.01910i | 0.663470 | − | 0.748203i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.00000 | + | 4.00000i | 0.424264 | + | 0.565685i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.67423 | + | 2.12132i | −0.509525 | + | 0.294174i | ||||
\(53\) | −10.3923 | + | 6.00000i | −1.42749 | + | 0.824163i | −0.996922 | − | 0.0783936i | \(-0.975021\pi\) |
−0.430570 | + | 0.902557i | \(0.641688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.82843 | − | 8.48528i | −0.381385 | − | 1.14416i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.46410 | + | 2.00000i | 0.454859 | + | 0.262613i | ||||
\(59\) | 5.65685 | + | 9.79796i | 0.736460 | + | 1.27559i | 0.954080 | + | 0.299552i | \(0.0968372\pi\) |
−0.217620 | + | 0.976034i | \(0.569829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.53553 | − | 6.12372i | 0.452679 | − | 0.784063i | −0.545873 | − | 0.837868i | \(-0.683802\pi\) |
0.998551 | + | 0.0538056i | \(0.0171351\pi\) | |||||||
\(62\) | − | 5.65685i | − | 0.718421i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.90192 | − | 9.29423i | 0.235905 | − | 1.15281i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3923 | − | 6.00000i | 1.26962 | − | 0.733017i | 0.294706 | − | 0.955588i | \(-0.404778\pi\) |
0.974916 | + | 0.222571i | \(0.0714450\pi\) | |||||||
\(68\) | 3.67423 | + | 2.12132i | 0.445566 | + | 0.257248i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | −2.59808 | − | 1.50000i | −0.306186 | − | 0.176777i | ||||
\(73\) | −3.67423 | + | 2.12132i | −0.430037 | + | 0.248282i | −0.699362 | − | 0.714767i | \(-0.746533\pi\) |
0.269326 | + | 0.963049i | \(0.413199\pi\) | |||||||
\(74\) | −3.00000 | − | 5.19615i | −0.348743 | − | 0.604040i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.65685 | −0.648886 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(80\) | 1.48356 | − | 1.67303i | 0.165867 | − | 0.187051i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 1.22474 | + | 0.707107i | 0.135250 | + | 0.0780869i | ||||
\(83\) | 16.9706i | 1.86276i | 0.364047 | + | 0.931381i | \(0.381395\pi\) | ||||
−0.364047 | + | 0.931381i | \(0.618605\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | + | 3.00000i | −0.976187 | + | 0.325396i | ||||
\(86\) | 6.00000 | − | 10.3923i | 0.646997 | − | 1.12063i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.46410 | + | 2.00000i | −0.369274 | + | 0.213201i | ||||
\(89\) | 2.12132 | − | 3.67423i | 0.224860 | − | 0.389468i | −0.731418 | − | 0.681930i | \(-0.761141\pi\) |
0.956277 | + | 0.292462i | \(0.0944744\pi\) | |||||||
\(90\) | 6.36396 | − | 2.12132i | 0.670820 | − | 0.223607i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.39230 | − | 9.46410i | 0.861032 | − | 0.970996i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.24264i | − | 0.430775i | −0.976529 | − | 0.215387i | \(-0.930899\pi\) | ||
0.976529 | − | 0.215387i | \(-0.0691014\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.0000 | −1.20605 | ||||||||
\(100\) | 0.598076 | + | 4.96410i | 0.0598076 | + | 0.496410i | ||||
\(101\) | 4.94975 | + | 8.57321i | 0.492518 | + | 0.853067i | 0.999963 | − | 0.00861771i | \(-0.00274313\pi\) |
−0.507445 | + | 0.861684i | \(0.669410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.6969 | + | 8.48528i | 1.44813 | + | 0.836080i | 0.998370 | − | 0.0570688i | \(-0.0181754\pi\) |
0.449762 | + | 0.893148i | \(0.351509\pi\) | |||||||
\(104\) | −4.24264 | −0.416025 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | 10.3923 | + | 6.00000i | 1.00466 | + | 0.580042i | 0.909624 | − | 0.415432i | \(-0.136370\pi\) |
0.0950377 | + | 0.995474i | \(0.469703\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.00000 | − | 10.3923i | −0.574696 | − | 0.995402i | −0.996075 | − | 0.0885176i | \(-0.971787\pi\) |
0.421379 | − | 0.906885i | \(-0.361546\pi\) | |||||||
\(110\) | 1.79315 | − | 8.76268i | 0.170970 | − | 0.835489i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.00000 | + | 3.46410i | 0.185695 | + | 0.321634i | ||||
\(117\) | −11.0227 | − | 6.36396i | −1.01905 | − | 0.588348i | ||||
\(118\) | 11.3137i | 1.04151i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | 6.12372 | − | 3.53553i | 0.554416 | − | 0.320092i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.82843 | − | 4.89898i | 0.254000 | − | 0.439941i | ||||
\(125\) | −9.19239 | − | 6.36396i | −0.822192 | − | 0.569210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.29423 | − | 7.09808i | 0.552040 | − | 0.622542i | ||||
\(131\) | 8.48528 | − | 14.6969i | 0.741362 | − | 1.28408i | −0.210513 | − | 0.977591i | \(-0.567513\pi\) |
0.951875 | − | 0.306486i | \(-0.0991534\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.0000 | 1.03664 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.12132 | + | 3.67423i | 0.181902 | + | 0.315063i | ||||
\(137\) | −5.19615 | + | 3.00000i | −0.443937 | + | 0.256307i | −0.705266 | − | 0.708942i | \(-0.749173\pi\) |
0.261329 | + | 0.965250i | \(0.415839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.65685 | 0.479808 | 0.239904 | − | 0.970797i | \(-0.422884\pi\) | ||||
0.239904 | + | 0.970797i | \(0.422884\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.92820 | + | 4.00000i | 0.581402 | + | 0.335673i | ||||
\(143\) | −14.6969 | + | 8.48528i | −1.22902 | + | 0.709575i | ||||
\(144\) | −1.50000 | − | 2.59808i | −0.125000 | − | 0.216506i | ||||
\(145\) | −8.76268 | − | 1.79315i | −0.727701 | − | 0.148913i | ||||
\(146\) | −4.24264 | −0.351123 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 6.00000i | − | 0.493197i | ||||||
\(149\) | 5.00000 | − | 8.66025i | 0.409616 | − | 0.709476i | −0.585231 | − | 0.810867i | \(-0.698996\pi\) |
0.994847 | + | 0.101391i | \(0.0323294\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | − | 6.92820i | −0.325515 | − | 0.563809i | 0.656101 | − | 0.754673i | \(-0.272204\pi\) |
−0.981617 | + | 0.190864i | \(0.938871\pi\) | |||||||
\(152\) | −4.89898 | − | 2.82843i | −0.397360 | − | 0.229416i | ||||
\(153\) | 12.7279i | 1.02899i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | + | 12.0000i | 0.321288 | + | 0.963863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.67423 | − | 2.12132i | 0.293236 | − | 0.169300i | −0.346164 | − | 0.938174i | \(-0.612516\pi\) |
0.639400 | + | 0.768874i | \(0.279183\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.12132 | − | 0.707107i | 0.167705 | − | 0.0559017i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | 10.3923 | + | 6.00000i | 0.813988 | + | 0.469956i | 0.848339 | − | 0.529454i | \(-0.177603\pi\) |
−0.0343508 | + | 0.999410i | \(0.510936\pi\) | |||||||
\(164\) | 0.707107 | + | 1.22474i | 0.0552158 | + | 0.0956365i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.48528 | + | 14.6969i | −0.658586 | + | 1.14070i | ||||
\(167\) | − | 16.9706i | − | 1.31322i | −0.754230 | − | 0.656611i | \(-0.771989\pi\) | ||
0.754230 | − | 0.656611i | \(-0.228011\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | −9.29423 | − | 1.90192i | −0.712835 | − | 0.145871i | ||||
\(171\) | −8.48528 | − | 14.6969i | −0.648886 | − | 1.12390i | ||||
\(172\) | 10.3923 | − | 6.00000i | 0.792406 | − | 0.457496i | ||||
\(173\) | −3.67423 | − | 2.12132i | −0.279347 | − | 0.161281i | 0.353781 | − | 0.935328i | \(-0.384896\pi\) |
−0.633128 | + | 0.774047i | \(0.718229\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.67423 | − | 2.12132i | 0.275396 | − | 0.159000i | ||||
\(179\) | 10.0000 | + | 17.3205i | 0.747435 | + | 1.29460i | 0.949048 | + | 0.315130i | \(0.102048\pi\) |
−0.201613 | + | 0.979465i | \(0.564618\pi\) | |||||||
\(180\) | 6.57201 | + | 1.34486i | 0.489849 | + | 0.100240i | ||||
\(181\) | 15.5563 | 1.15629 | 0.578147 | − | 0.815933i | \(-0.303776\pi\) | ||||
0.578147 | + | 0.815933i | \(0.303776\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.0382 | + | 8.90138i | 0.738023 | + | 0.654443i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.6969 | + | 8.48528i | 1.07475 | + | 0.620505i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.0000 | − | 4.00000i | 0.870572 | − | 0.290191i | ||||
\(191\) | −4.00000 | + | 6.92820i | −0.289430 | + | 0.501307i | −0.973674 | − | 0.227946i | \(-0.926799\pi\) |
0.684244 | + | 0.729253i | \(0.260132\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.7846 | + | 12.0000i | −1.49611 | + | 0.863779i | −0.999990 | − | 0.00447566i | \(-0.998575\pi\) |
−0.496119 | + | 0.868255i | \(0.665242\pi\) | |||||||
\(194\) | 2.12132 | − | 3.67423i | 0.152302 | − | 0.263795i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000i | 0.854965i | 0.904024 | + | 0.427482i | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | −10.3923 | − | 6.00000i | −0.738549 | − | 0.426401i | ||||
\(199\) | −5.65685 | − | 9.79796i | −0.401004 | − | 0.694559i | 0.592844 | − | 0.805318i | \(-0.298005\pi\) |
−0.993847 | + | 0.110759i | \(0.964672\pi\) | |||||||
\(200\) | −1.96410 | + | 4.59808i | −0.138883 | + | 0.325133i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.89949i | 0.696526i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.09808 | − | 0.633975i | −0.216379 | − | 0.0442787i | ||||
\(206\) | 8.48528 | + | 14.6969i | 0.591198 | + | 1.02398i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.67423 | − | 2.12132i | −0.254762 | − | 0.147087i | ||||
\(209\) | −22.6274 | −1.56517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | −10.3923 | − | 6.00000i | −0.713746 | − | 0.412082i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | + | 10.3923i | 0.410152 | + | 0.710403i | ||||
\(215\) | −5.37945 | + | 26.2880i | −0.366876 | + | 1.79283i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 12.0000i | − | 0.812743i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.93426 | − | 6.69213i | 0.400087 | − | 0.451183i | ||||
\(221\) | 9.00000 | + | 15.5885i | 0.605406 | + | 1.04859i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.9706i | − | 1.13643i | −0.822879 | − | 0.568216i | \(-0.807634\pi\) | ||
0.822879 | − | 0.568216i | \(-0.192366\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.0000 | + | 9.00000i | −0.800000 | + | 0.600000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.6969 | + | 8.48528i | −0.975470 | + | 0.563188i | −0.900899 | − | 0.434028i | \(-0.857092\pi\) |
−0.0745706 | + | 0.997216i | \(0.523759\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.77817 | + | 13.4722i | −0.513996 | + | 0.890268i | 0.485872 | + | 0.874030i | \(0.338502\pi\) |
−0.999868 | + | 0.0162376i | \(0.994831\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.00000i | 0.262613i | ||||||||
\(233\) | −5.19615 | − | 3.00000i | −0.340411 | − | 0.196537i | 0.320043 | − | 0.947403i | \(-0.396303\pi\) |
−0.660454 | + | 0.750867i | \(0.729636\pi\) | |||||||
\(234\) | −6.36396 | − | 11.0227i | −0.416025 | − | 0.720577i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.65685 | + | 9.79796i | −0.368230 | + | 0.637793i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.77817 | − | 13.4722i | −0.501036 | − | 0.867820i | −0.999999 | − | 0.00119700i | \(-0.999619\pi\) |
0.498963 | − | 0.866623i | \(-0.333714\pi\) | |||||||
\(242\) | −4.33013 | + | 2.50000i | −0.278351 | + | 0.160706i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.07107 | 0.452679 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.7846 | − | 12.0000i | −1.32249 | − | 0.763542i | ||||
\(248\) | 4.89898 | − | 2.82843i | 0.311086 | − | 0.179605i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.77886 | − | 10.1075i | −0.302242 | − | 0.639257i | ||||
\(251\) | 5.65685 | 0.357057 | 0.178529 | − | 0.983935i | \(-0.442866\pi\) | ||||
0.178529 | + | 0.983935i | \(0.442866\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −11.0227 | − | 6.36396i | −0.687577 | − | 0.396973i | 0.115126 | − | 0.993351i | \(-0.463273\pi\) |
−0.802704 | + | 0.596378i | \(0.796606\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.00000 | − | 3.00000i | 0.558156 | − | 0.186052i | ||||
\(261\) | −6.00000 | + | 10.3923i | −0.371391 | + | 0.643268i | ||||
\(262\) | 14.6969 | − | 8.48528i | 0.907980 | − | 0.524222i | ||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.4558 | − | 8.48528i | 1.56374 | − | 0.521247i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.3923 | + | 6.00000i | 0.634811 | + | 0.366508i | ||||
\(269\) | −10.6066 | − | 18.3712i | −0.646696 | − | 1.12011i | −0.983907 | − | 0.178681i | \(-0.942817\pi\) |
0.337211 | − | 0.941429i | \(-0.390516\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.65685 | + | 9.79796i | −0.343629 | + | 0.595184i | −0.985104 | − | 0.171961i | \(-0.944990\pi\) |
0.641474 | + | 0.767144i | \(0.278323\pi\) | |||||||
\(272\) | 4.24264i | 0.257248i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | 2.39230 | + | 19.8564i | 0.144261 | + | 1.19739i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.3923 | + | 6.00000i | −0.624413 | + | 0.360505i | −0.778585 | − | 0.627539i | \(-0.784062\pi\) |
0.154172 | + | 0.988044i | \(0.450729\pi\) | |||||||
\(278\) | 4.89898 | + | 2.82843i | 0.293821 | + | 0.169638i | ||||
\(279\) | 16.9706 | 1.01600 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0000 | 0.954480 | 0.477240 | − | 0.878773i | \(-0.341637\pi\) | ||||
0.477240 | + | 0.878773i | \(0.341637\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(284\) | 4.00000 | + | 6.92820i | 0.237356 | + | 0.411113i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.9706 | −1.00349 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 3.00000i | − | 0.176777i | ||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | −6.69213 | − | 5.93426i | −0.392975 | − | 0.348471i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.67423 | − | 2.12132i | −0.215018 | − | 0.124141i | ||||
\(293\) | − | 4.24264i | − | 0.247858i | −0.992291 | − | 0.123929i | \(-0.960451\pi\) | ||
0.992291 | − | 0.123929i | \(-0.0395495\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | − | 24.0000i | −0.465778 | − | 1.39733i | ||||
\(296\) | 3.00000 | − | 5.19615i | 0.174371 | − | 0.302020i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.66025 | − | 5.00000i | 0.501675 | − | 0.289642i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 8.00000i | − | 0.460348i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.82843 | − | 4.89898i | −0.162221 | − | 0.280976i | ||||
\(305\) | −10.4904 | + | 11.8301i | −0.600677 | + | 0.677391i | ||||
\(306\) | −6.36396 | + | 11.0227i | −0.363803 | + | 0.630126i | ||||
\(307\) | 16.9706i | 0.968561i | 0.874913 | + | 0.484281i | \(0.160919\pi\) | ||||
−0.874913 | + | 0.484281i | \(0.839081\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.53590 | + | 12.3923i | −0.144029 | + | 0.703836i | ||||
\(311\) | 8.48528 | + | 14.6969i | 0.481156 | + | 0.833387i | 0.999766 | − | 0.0216240i | \(-0.00688367\pi\) |
−0.518610 | + | 0.855011i | \(0.673550\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0227 | − | 6.36396i | −0.623040 | − | 0.359712i | 0.155012 | − | 0.987913i | \(-0.450459\pi\) |
−0.778052 | + | 0.628200i | \(0.783792\pi\) | |||||||
\(314\) | 4.24264 | 0.239426 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.3923 | + | 6.00000i | 0.583690 | + | 0.336994i | 0.762598 | − | 0.646872i | \(-0.223923\pi\) |
−0.178908 | + | 0.983866i | \(0.557257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | + | 13.8564i | 0.447914 | + | 0.775810i | ||||
\(320\) | 2.19067 | + | 0.448288i | 0.122462 | + | 0.0250600i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(325\) | −8.33298 | + | 19.5080i | −0.462230 | + | 1.08211i | ||||
\(326\) | 6.00000 | + | 10.3923i | 0.332309 | + | 0.575577i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.41421i | 0.0780869i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.00000 | + | 10.3923i | −0.329790 | + | 0.571213i | −0.982470 | − | 0.186421i | \(-0.940311\pi\) |
0.652680 | + | 0.757634i | \(0.273645\pi\) | |||||||
\(332\) | −14.6969 | + | 8.48528i | −0.806599 | + | 0.465690i | ||||
\(333\) | 15.5885 | − | 9.00000i | 0.854242 | − | 0.493197i | ||||
\(334\) | 8.48528 | − | 14.6969i | 0.464294 | − | 0.804181i | ||||
\(335\) | −25.4558 | + | 8.48528i | −1.39080 | + | 0.463600i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000i | 0.980522i | 0.871576 | + | 0.490261i | \(0.163099\pi\) | ||||
−0.871576 | + | 0.490261i | \(0.836901\pi\) | |||||||
\(338\) | −4.33013 | − | 2.50000i | −0.235528 | − | 0.135982i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.09808 | − | 6.29423i | −0.384947 | − | 0.341352i | ||||
\(341\) | 11.3137 | − | 19.5959i | 0.612672 | − | 1.06118i | ||||
\(342\) | − | 16.9706i | − | 0.917663i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.0000 | 0.646997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.12132 | − | 3.67423i | −0.114043 | − | 0.197528i | ||||
\(347\) | 10.3923 | − | 6.00000i | 0.557888 | − | 0.322097i | −0.194409 | − | 0.980921i | \(-0.562279\pi\) |
0.752297 | + | 0.658824i | \(0.228946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0416 | −1.28692 | −0.643459 | − | 0.765480i | \(-0.722502\pi\) | ||||
−0.643459 | + | 0.765480i | \(0.722502\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.46410 | − | 2.00000i | −0.184637 | − | 0.106600i | ||||
\(353\) | 18.3712 | − | 10.6066i | 0.977799 | − | 0.564532i | 0.0761940 | − | 0.997093i | \(-0.475723\pi\) |
0.901605 | + | 0.432561i | \(0.142390\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.5254 | − | 3.58630i | −0.930150 | − | 0.190341i | ||||
\(356\) | 4.24264 | 0.224860 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.0000i | 1.05703i | ||||||||
\(359\) | 8.00000 | − | 13.8564i | 0.422224 | − | 0.731313i | −0.573933 | − | 0.818902i | \(-0.694583\pi\) |
0.996157 | + | 0.0875892i | \(0.0279163\pi\) | |||||||
\(360\) | 5.01910 | + | 4.45069i | 0.264530 | + | 0.234572i | ||||
\(361\) | −6.50000 | − | 11.2583i | −0.342105 | − | 0.592544i | ||||
\(362\) | 13.4722 | + | 7.77817i | 0.708083 | + | 0.408812i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.00000 | − | 3.00000i | 0.471082 | − | 0.157027i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.6969 | − | 8.48528i | 0.767174 | − | 0.442928i | −0.0646916 | − | 0.997905i | \(-0.520606\pi\) |
0.831866 | + | 0.554977i | \(0.187273\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.12132 | + | 3.67423i | −0.110432 | + | 0.191273i | ||||
\(370\) | 4.24264 | + | 12.7279i | 0.220564 | + | 0.661693i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.3923 | − | 6.00000i | −0.538093 | − | 0.310668i | 0.206213 | − | 0.978507i | \(-0.433886\pi\) |
−0.744306 | + | 0.667839i | \(0.767219\pi\) | |||||||
\(374\) | 8.48528 | + | 14.6969i | 0.438763 | + | 0.759961i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.9706i | 0.874028i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 12.3923 | + | 2.53590i | 0.635712 | + | 0.130089i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.92820 | + | 4.00000i | −0.354478 | + | 0.204658i | ||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.0000 | −1.22157 | ||||||||
\(387\) | 31.1769 | + | 18.0000i | 1.58481 | + | 0.914991i | ||||
\(388\) | 3.67423 | − | 2.12132i | 0.186531 | − | 0.107694i | ||||
\(389\) | −10.0000 | − | 17.3205i | −0.507020 | − | 0.878185i | −0.999967 | − | 0.00812520i | \(-0.997414\pi\) |
0.492947 | − | 0.870059i | \(-0.335920\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.00000 | + | 10.3923i | −0.302276 | + | 0.523557i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.00000 | − | 10.3923i | −0.301511 | − | 0.522233i | ||||
\(397\) | 25.7196 | + | 14.8492i | 1.29083 | + | 0.745262i | 0.978802 | − | 0.204810i | \(-0.0656577\pi\) |
0.312030 | + | 0.950072i | \(0.398991\pi\) | |||||||
\(398\) | − | 11.3137i | − | 0.567105i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | + | 3.00000i | −0.200000 | + | 0.150000i | ||||
\(401\) | 4.00000 | − | 6.92820i | 0.199750 | − | 0.345978i | −0.748697 | − | 0.662912i | \(-0.769320\pi\) |
0.948447 | + | 0.316934i | \(0.102654\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.7846 | − | 12.0000i | 1.03536 | − | 0.597763i | ||||
\(404\) | −4.94975 | + | 8.57321i | −0.246259 | + | 0.426533i | ||||
\(405\) | 6.36396 | + | 19.0919i | 0.316228 | + | 0.948683i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 24.0000i | − | 1.18964i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.94975 | + | 8.57321i | 0.244749 | + | 0.423918i | 0.962061 | − | 0.272834i | \(-0.0879610\pi\) |
−0.717312 | + | 0.696752i | \(0.754628\pi\) | |||||||
\(410\) | −2.36603 | − | 2.09808i | −0.116850 | − | 0.103617i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.9706i | 0.836080i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.60770 | − | 37.1769i | 0.373447 | − | 1.82494i | ||||
\(416\) | −2.12132 | − | 3.67423i | −0.104006 | − | 0.180144i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −19.5959 | − | 11.3137i | −0.958468 | − | 0.553372i | ||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 10.3923 | + | 6.00000i | 0.505889 | + | 0.292075i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | − | 10.3923i | −0.291386 | − | 0.504695i | ||||
\(425\) | 21.0609 | − | 2.53742i | 1.02160 | − | 0.123083i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.0000i | 0.580042i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.8028 | + | 20.0764i | −0.858526 | + | 0.968170i | ||||
\(431\) | −8.00000 | − | 13.8564i | −0.385346 | − | 0.667440i | 0.606471 | − | 0.795106i | \(-0.292585\pi\) |
−0.991817 | + | 0.127666i | \(0.959251\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.6985i | − | 1.42722i | −0.700544 | − | 0.713609i | \(-0.747059\pi\) | ||
0.700544 | − | 0.713609i | \(-0.252941\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.00000 | − | 10.3923i | 0.287348 | − | 0.497701i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.7990 | − | 34.2929i | 0.944954 | − | 1.63671i | 0.189111 | − | 0.981956i | \(-0.439439\pi\) |
0.755843 | − | 0.654753i | \(-0.227227\pi\) | |||||||
\(440\) | 8.48528 | − | 2.82843i | 0.404520 | − | 0.134840i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.0000i | 0.856173i | ||||||||
\(443\) | 10.3923 | + | 6.00000i | 0.493753 | + | 0.285069i | 0.726130 | − | 0.687557i | \(-0.241317\pi\) |
−0.232377 | + | 0.972626i | \(0.574650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.29423 | + | 7.09808i | −0.298375 | + | 0.336481i | ||||
\(446\) | 8.48528 | − | 14.6969i | 0.401790 | − | 0.695920i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | −14.8923 | + | 1.79423i | −0.702030 | + | 0.0845807i | ||||
\(451\) | 2.82843 | + | 4.89898i | 0.133185 | + | 0.230684i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16.9706 | −0.796468 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.7846 | − | 12.0000i | −0.972263 | − | 0.561336i | −0.0723376 | − | 0.997380i | \(-0.523046\pi\) |
−0.899925 | + | 0.436044i | \(0.856379\pi\) | |||||||
\(458\) | −13.4722 | + | 7.77817i | −0.629514 | + | 0.363450i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.2132 | 0.987997 | 0.493999 | − | 0.869463i | \(-0.335535\pi\) | ||||
0.493999 | + | 0.869463i | \(0.335535\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.0000i | − | 1.11537i | −0.830051 | − | 0.557687i | \(-0.811689\pi\) | ||
0.830051 | − | 0.557687i | \(-0.188311\pi\) | |||||||
\(464\) | −2.00000 | + | 3.46410i | −0.0928477 | + | 0.160817i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | − | 5.19615i | −0.138972 | − | 0.240707i | ||||
\(467\) | −14.6969 | − | 8.48528i | −0.680093 | − | 0.392652i | 0.119797 | − | 0.992798i | \(-0.461776\pi\) |
−0.799890 | + | 0.600146i | \(0.795109\pi\) | |||||||
\(468\) | − | 12.7279i | − | 0.588348i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.79796 | + | 5.65685i | −0.450988 | + | 0.260378i | ||||
\(473\) | 41.5692 | − | 24.0000i | 1.91135 | − | 1.10352i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.6274 | + | 16.9706i | −1.03822 | + | 0.778663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 36.0000i | − | 1.64833i | ||||||
\(478\) | 6.92820 | + | 4.00000i | 0.316889 | + | 0.182956i | ||||
\(479\) | 8.48528 | + | 14.6969i | 0.387702 | + | 0.671520i | 0.992140 | − | 0.125132i | \(-0.0399355\pi\) |
−0.604438 | + | 0.796652i | \(0.706602\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.7279 | − | 22.0454i | 0.580343 | − | 1.00518i | ||||
\(482\) | − | 15.5563i | − | 0.708572i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.00000 | −0.227273 | ||||||||
\(485\) | −1.90192 | + | 9.29423i | −0.0863619 | + | 0.422029i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.7846 | + | 12.0000i | −0.941841 | + | 0.543772i | −0.890537 | − | 0.454911i | \(-0.849671\pi\) |
−0.0513038 | + | 0.998683i | \(0.516338\pi\) | |||||||
\(488\) | 6.12372 | + | 3.53553i | 0.277208 | + | 0.160046i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.00000 | −0.180517 | −0.0902587 | − | 0.995918i | \(-0.528769\pi\) | ||||
−0.0902587 | + | 0.995918i | \(0.528769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.6969 | − | 8.48528i | 0.661917 | − | 0.382158i | ||||
\(494\) | −12.0000 | − | 20.7846i | −0.539906 | − | 0.935144i | ||||
\(495\) | 26.2880 | + | 5.37945i | 1.18156 | + | 0.241788i | ||||
\(496\) | 5.65685 | 0.254000 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.00000 | − | 3.46410i | 0.0895323 | − | 0.155074i | −0.817781 | − | 0.575529i | \(-0.804796\pi\) |
0.907314 | + | 0.420455i | \(0.138129\pi\) | |||||||
\(500\) | 0.915158 | − | 11.1428i | 0.0409271 | − | 0.498322i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.89898 | + | 2.82843i | 0.218652 | + | 0.126239i | ||||
\(503\) | − | 33.9411i | − | 1.51336i | −0.653785 | − | 0.756680i | \(-0.726820\pi\) | ||
0.653785 | − | 0.756680i | \(-0.273180\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.00000 | − | 21.0000i | −0.311496 | − | 0.934488i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.36396 | + | 11.0227i | −0.282078 | + | 0.488573i | −0.971896 | − | 0.235409i | \(-0.924357\pi\) |
0.689819 | + | 0.723982i | \(0.257690\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.36396 | − | 11.0227i | −0.280702 | − | 0.486191i | ||||
\(515\) | −28.3923 | − | 25.1769i | −1.25111 | − | 1.10943i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.29423 | + | 1.90192i | 0.407579 | + | 0.0834049i | ||||
\(521\) | 6.36396 | + | 11.0227i | 0.278810 | + | 0.482913i | 0.971089 | − | 0.238716i | \(-0.0767266\pi\) |
−0.692279 | + | 0.721630i | \(0.743393\pi\) | |||||||
\(522\) | −10.3923 | + | 6.00000i | −0.454859 | + | 0.262613i | ||||
\(523\) | −29.3939 | − | 16.9706i | −1.28530 | − | 0.742071i | −0.307492 | − | 0.951551i | \(-0.599490\pi\) |
−0.977813 | + | 0.209480i | \(0.932823\pi\) | |||||||
\(524\) | 16.9706 | 0.741362 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.7846 | − | 12.0000i | −0.905392 | − | 0.522728i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5000 | − | 19.9186i | −0.500000 | − | 0.866025i | ||||
\(530\) | 26.2880 | + | 5.37945i | 1.14188 | + | 0.233668i | ||||
\(531\) | −33.9411 | −1.47292 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000i | 0.259889i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.0764 | − | 17.8028i | −0.867978 | − | 0.769681i | ||||
\(536\) | 6.00000 | + | 10.3923i | 0.259161 | + | 0.448879i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 21.2132i | − | 0.914566i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.0000 | − | 25.9808i | 0.644900 | − | 1.11700i | −0.339424 | − | 0.940633i | \(-0.610232\pi\) |
0.984325 | − | 0.176367i | \(-0.0564345\pi\) | |||||||
\(542\) | −9.79796 | + | 5.65685i | −0.420858 | + | 0.242983i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.12132 | + | 3.67423i | −0.0909509 | + | 0.157532i | ||||
\(545\) | 8.48528 | + | 25.4558i | 0.363470 | + | 1.09041i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000i | 0.513083i | 0.966533 | + | 0.256541i | \(0.0825830\pi\) | ||||
−0.966533 | + | 0.256541i | \(0.917417\pi\) | |||||||
\(548\) | −5.19615 | − | 3.00000i | −0.221969 | − | 0.128154i | ||||
\(549\) | 10.6066 | + | 18.3712i | 0.452679 | + | 0.784063i | ||||
\(550\) | −7.85641 | + | 18.3923i | −0.334998 | + | 0.784251i | ||||
\(551\) | −11.3137 | + | 19.5959i | −0.481980 | + | 0.834814i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −12.0000 | −0.509831 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.82843 | + | 4.89898i | 0.119952 | + | 0.207763i | ||||
\(557\) | 10.3923 | − | 6.00000i | 0.440336 | − | 0.254228i | −0.263404 | − | 0.964686i | \(-0.584845\pi\) |
0.703740 | + | 0.710457i | \(0.251512\pi\) | |||||||
\(558\) | 14.6969 | + | 8.48528i | 0.622171 | + | 0.359211i | ||||
\(559\) | 50.9117 | 2.15333 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.8564 | + | 8.00000i | 0.584497 | + | 0.337460i | ||||
\(563\) | 29.3939 | − | 16.9706i | 1.23880 | − | 0.715224i | 0.269954 | − | 0.962873i | \(-0.412991\pi\) |
0.968850 | + | 0.247649i | \(0.0796580\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.00000i | 0.335673i | ||||||||
\(569\) | −4.00000 | + | 6.92820i | −0.167689 | + | 0.290445i | −0.937607 | − | 0.347697i | \(-0.886964\pi\) |
0.769918 | + | 0.638143i | \(0.220297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.00000 | − | 3.46410i | −0.0836974 | − | 0.144968i | 0.821138 | − | 0.570730i | \(-0.193340\pi\) |
−0.904835 | + | 0.425762i | \(0.860006\pi\) | |||||||
\(572\) | −14.6969 | − | 8.48528i | −0.614510 | − | 0.354787i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | −18.3712 | + | 10.6066i | −0.764802 | + | 0.441559i | −0.831017 | − | 0.556247i | \(-0.812241\pi\) |
0.0662152 | + | 0.997805i | \(0.478908\pi\) | |||||||
\(578\) | 0.866025 | − | 0.500000i | 0.0360219 | − | 0.0207973i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.82843 | − | 8.48528i | −0.117444 | − | 0.352332i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −41.5692 | − | 24.0000i | −1.72162 | − | 0.993978i | ||||
\(584\) | −2.12132 | − | 3.67423i | −0.0877809 | − | 0.152041i | ||||
\(585\) | 21.2942 | + | 18.8827i | 0.880408 | + | 0.780703i | ||||
\(586\) | 2.12132 | − | 3.67423i | 0.0876309 | − | 0.151781i | ||||
\(587\) | 16.9706i | 0.700450i | 0.936666 | + | 0.350225i | \(0.113895\pi\) | ||||
−0.936666 | + | 0.350225i | \(0.886105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.0000 | 1.31854 | ||||||||
\(590\) | 5.07180 | − | 24.7846i | 0.208803 | − | 1.02037i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.19615 | − | 3.00000i | 0.213561 | − | 0.123299i | ||||
\(593\) | 11.0227 | + | 6.36396i | 0.452648 | + | 0.261337i | 0.708948 | − | 0.705261i | \(-0.249170\pi\) |
−0.256300 | + | 0.966597i | \(0.582503\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.0000 | 0.409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.00000 | + | 13.8564i | 0.326871 | + | 0.566157i | 0.981889 | − | 0.189456i | \(-0.0606724\pi\) |
−0.655018 | + | 0.755613i | \(0.727339\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.8701 | −1.09605 | −0.548026 | − | 0.836461i | \(-0.684621\pi\) | ||||
−0.548026 | + | 0.836461i | \(0.684621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 36.0000i | 1.46603i | ||||||||
\(604\) | 4.00000 | − | 6.92820i | 0.162758 | − | 0.281905i | ||||
\(605\) | 7.41782 | − | 8.36516i | 0.301577 | − | 0.340092i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.6969 | + | 8.48528i | 0.596530 | + | 0.344407i | 0.767675 | − | 0.640839i | \(-0.221413\pi\) |
−0.171145 | + | 0.985246i | \(0.554747\pi\) | |||||||
\(608\) | − | 5.65685i | − | 0.229416i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.0000 | + | 5.00000i | −0.607332 | + | 0.202444i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −11.0227 | + | 6.36396i | −0.445566 | + | 0.257248i | ||||
\(613\) | 5.19615 | − | 3.00000i | 0.209871 | − | 0.121169i | −0.391381 | − | 0.920229i | \(-0.628002\pi\) |
0.601251 | + | 0.799060i | \(0.294669\pi\) | |||||||
\(614\) | −8.48528 | + | 14.6969i | −0.342438 | + | 0.593120i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 42.0000i | − | 1.69086i | −0.534089 | − | 0.845428i | \(-0.679345\pi\) | ||
0.534089 | − | 0.845428i | \(-0.320655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.6274 | + | 39.1918i | 0.909473 | + | 1.57525i | 0.814798 | + | 0.579745i | \(0.196848\pi\) |
0.0946744 | + | 0.995508i | \(0.469819\pi\) | |||||||
\(620\) | −8.39230 | + | 9.46410i | −0.337043 | + | 0.380087i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.9706i | 0.680458i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2846 | + | 18.0622i | 0.691384 | + | 0.722487i | ||||
\(626\) | −6.36396 | − | 11.0227i | −0.254355 | − | 0.440556i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.67423 | + | 2.12132i | 0.146618 | + | 0.0846499i | ||||
\(629\) | −25.4558 | −1.01499 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0000 | 0.955425 | 0.477712 | − | 0.878516i | \(-0.341466\pi\) | ||||
0.477712 | + | 0.878516i | \(0.341466\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.00000 | + | 10.3923i | 0.238290 | + | 0.412731i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.0000i | 0.633446i | ||||||||
\(639\) | −12.0000 | + | 20.7846i | −0.474713 | + | 0.822226i | ||||
\(640\) | 1.67303 | + | 1.48356i | 0.0661324 | + | 0.0586430i | ||||
\(641\) | 20.0000 | + | 34.6410i | 0.789953 | + | 1.36824i | 0.925995 | + | 0.377535i | \(0.123228\pi\) |
−0.136043 | + | 0.990703i | \(0.543438\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | + | 20.7846i | −0.472134 | + | 0.817760i | ||||
\(647\) | −14.6969 | + | 8.48528i | −0.577796 | + | 0.333591i | −0.760257 | − | 0.649622i | \(-0.774927\pi\) |
0.182461 | + | 0.983213i | \(0.441594\pi\) | |||||||
\(648\) | 7.79423 | − | 4.50000i | 0.306186 | − | 0.176777i | ||||
\(649\) | −22.6274 | + | 39.1918i | −0.888204 | + | 1.53841i | ||||
\(650\) | −16.9706 | + | 12.7279i | −0.665640 | + | 0.499230i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.0000i | 0.469956i | ||||||||
\(653\) | 15.5885 | + | 9.00000i | 0.610023 | + | 0.352197i | 0.772975 | − | 0.634437i | \(-0.218768\pi\) |
−0.162951 | + | 0.986634i | \(0.552101\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.1769 | + | 28.3923i | −0.983743 | + | 1.10938i | ||||
\(656\) | −0.707107 | + | 1.22474i | −0.0276079 | + | 0.0478183i | ||||
\(657\) | − | 12.7279i | − | 0.496564i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.0000 | −0.779089 | −0.389545 | − | 0.921008i | \(-0.627368\pi\) | ||||
−0.389545 | + | 0.921008i | \(0.627368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0208 | − | 20.8207i | −0.467556 | − | 0.809830i | 0.531757 | − | 0.846897i | \(-0.321532\pi\) |
−0.999313 | + | 0.0370669i | \(0.988199\pi\) | |||||||
\(662\) | −10.3923 | + | 6.00000i | −0.403908 | + | 0.233197i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.9706 | −0.658586 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.0000 | 0.697486 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 14.6969 | − | 8.48528i | 0.568642 | − | 0.328305i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −26.2880 | − | 5.37945i | −1.01560 | − | 0.207826i | ||||
\(671\) | 28.2843 | 1.09190 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0000i | 0.693849i | 0.937893 | + | 0.346925i | \(0.112774\pi\) | ||||
−0.937893 | + | 0.346925i | \(0.887226\pi\) | |||||||
\(674\) | −9.00000 | + | 15.5885i | −0.346667 | + | 0.600445i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.50000 | − | 4.33013i | −0.0961538 | − | 0.166543i | ||||
\(677\) | −18.3712 | − | 10.6066i | −0.706062 | − | 0.407645i | 0.103540 | − | 0.994625i | \(-0.466983\pi\) |
−0.809601 | + | 0.586981i | \(0.800317\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.00000 | − | 9.00000i | −0.115045 | − | 0.345134i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19.5959 | − | 11.3137i | 0.750366 | − | 0.433224i | ||||
\(683\) | 10.3923 | − | 6.00000i | 0.397650 | − | 0.229584i | −0.287819 | − | 0.957685i | \(-0.592930\pi\) |
0.685470 | + | 0.728101i | \(0.259597\pi\) | |||||||
\(684\) | 8.48528 | − | 14.6969i | 0.324443 | − | 0.561951i | ||||
\(685\) | 12.7279 | − | 4.24264i | 0.486309 | − | 0.162103i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.3923 | + | 6.00000i | 0.396203 | + | 0.228748i | ||||
\(689\) | −25.4558 | − | 44.0908i | −0.969790 | − | 1.67973i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.82843 | + | 4.89898i | −0.107598 | + | 0.186366i | −0.914797 | − | 0.403914i | \(-0.867649\pi\) |
0.807198 | + | 0.590280i | \(0.200983\pi\) | |||||||
\(692\) | − | 4.24264i | − | 0.161281i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | −12.3923 | − | 2.53590i | −0.470067 | − | 0.0961921i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.19615 | − | 3.00000i | 0.196818 | − | 0.113633i | ||||
\(698\) | −20.8207 | − | 12.0208i | −0.788074 | − | 0.454995i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.0000 | −1.66186 | −0.830929 | − | 0.556379i | \(-0.812190\pi\) | ||||
−0.830929 | + | 0.556379i | \(0.812190\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.3939 | − | 16.9706i | 1.10861 | − | 0.640057i | ||||
\(704\) | −2.00000 | − | 3.46410i | −0.0753778 | − | 0.130558i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.2132 | 0.798369 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.0000 | + | 38.1051i | −0.826227 | + | 1.43107i | 0.0747503 | + | 0.997202i | \(0.476184\pi\) |
−0.900978 | + | 0.433865i | \(0.857149\pi\) | |||||||
\(710\) | −13.3843 | − | 11.8685i | −0.502302 | − | 0.445417i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.67423 | + | 2.12132i | 0.137698 | + | 0.0794998i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.0000 | − | 12.0000i | 1.34632 | − | 0.448775i | ||||
\(716\) | −10.0000 | + | 17.3205i | −0.373718 | + | 0.647298i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.8564 | − | 8.00000i | 0.517116 | − | 0.298557i | ||||
\(719\) | 2.82843 | − | 4.89898i | 0.105483 | − | 0.182701i | −0.808453 | − | 0.588561i | \(-0.799695\pi\) |
0.913935 | + | 0.405860i | \(0.133028\pi\) | |||||||
\(720\) | 2.12132 | + | 6.36396i | 0.0790569 | + | 0.237171i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 13.0000i | − | 0.483810i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.77817 | + | 13.4722i | 0.289074 | + | 0.500690i | ||||
\(725\) | 18.3923 | + | 7.85641i | 0.683073 | + | 0.291780i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9706i | 0.629403i | 0.949191 | + | 0.314702i | \(0.101904\pi\) | ||||
−0.949191 | + | 0.314702i | \(0.898096\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 9.29423 | + | 1.90192i | 0.343995 | + | 0.0703934i | ||||
\(731\) | −25.4558 | − | 44.0908i | −0.941518 | − | 1.63076i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.0227 | − | 6.36396i | −0.407133 | − | 0.235058i | 0.282424 | − | 0.959290i | \(-0.408861\pi\) |
−0.689557 | + | 0.724231i | \(0.742195\pi\) | |||||||
\(734\) | 16.9706 | 0.626395 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 41.5692 | + | 24.0000i | 1.53122 | + | 0.884051i | ||||
\(738\) | −3.67423 | + | 2.12132i | −0.135250 | + | 0.0780869i | ||||
\(739\) | 10.0000 | + | 17.3205i | 0.367856 | + | 0.637145i | 0.989230 | − | 0.146369i | \(-0.0467586\pi\) |
−0.621374 | + | 0.783514i | \(0.713425\pi\) | |||||||
\(740\) | −2.68973 | + | 13.1440i | −0.0988763 | + | 0.483184i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.8356 | + | 16.7303i | −0.543536 | + | 0.612952i | ||||
\(746\) | −6.00000 | − | 10.3923i | −0.219676 | − | 0.380489i | ||||
\(747\) | −44.0908 | − | 25.4558i | −1.61320 | − | 0.931381i | ||||
\(748\) | 16.9706i | 0.620505i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.48528 | + | 14.6969i | −0.309016 | + | 0.535231i | ||||
\(755\) | 5.65685 | + | 16.9706i | 0.205874 | + | 0.617622i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000i | 1.52652i | 0.646094 | + | 0.763258i | \(0.276401\pi\) | ||||
−0.646094 | + | 0.763258i | \(0.723599\pi\) | |||||||
\(758\) | −17.3205 | − | 10.0000i | −0.629109 | − | 0.363216i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.46410 | + | 8.39230i | 0.343299 | + | 0.304421i | ||||
\(761\) | −23.3345 | + | 40.4166i | −0.845876 | + | 1.46510i | 0.0389826 | + | 0.999240i | \(0.487588\pi\) |
−0.884858 | + | 0.465860i | \(0.845745\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 5.70577 | − | 27.8827i | 0.206293 | − | 1.00810i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −41.5692 | + | 24.0000i | −1.50098 | + | 0.866590i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.07107 | 0.254989 | 0.127495 | − | 0.991839i | \(-0.459306\pi\) | ||||
0.127495 | + | 0.991839i | \(0.459306\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.7846 | − | 12.0000i | −0.748054 | − | 0.431889i | ||||
\(773\) | −33.0681 | + | 19.0919i | −1.18938 | + | 0.686687i | −0.958165 | − | 0.286216i | \(-0.907602\pi\) |
−0.231212 | + | 0.972903i | \(0.574269\pi\) | |||||||
\(774\) | 18.0000 | + | 31.1769i | 0.646997 | + | 1.12063i | ||||
\(775\) | −3.38323 | − | 28.0812i | −0.121529 | − | 1.00871i | ||||
\(776\) | 4.24264 | 0.152302 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 20.0000i | − | 0.717035i | ||||||
\(779\) | −4.00000 | + | 6.92820i | −0.143315 | + | 0.248229i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | + | 27.7128i | 0.572525 | + | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.00000 | + | 3.00000i | −0.321224 | + | 0.107075i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.0908 | − | 25.4558i | 1.57167 | − | 0.907403i | 0.575703 | − | 0.817659i | \(-0.304728\pi\) |
0.995965 | − | 0.0897439i | \(-0.0286049\pi\) | |||||||
\(788\) | −10.3923 | + | 6.00000i | −0.370211 | + | 0.213741i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 12.0000i | − | 0.426401i | ||||||
\(793\) | 25.9808 | + | 15.0000i | 0.922604 | + | 0.532666i | ||||
\(794\) | 14.8492 | + | 25.7196i | 0.526980 | + | 0.912756i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.65685 | − | 9.79796i | 0.200502 | − | 0.347279i | ||||
\(797\) | 4.24264i | 0.150282i | 0.997173 | + | 0.0751410i | \(0.0239407\pi\) | ||||
−0.997173 | + | 0.0751410i | \(0.976059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.96410 | + | 0.598076i | −0.175507 | + | 0.0211452i | ||||
\(801\) | 6.36396 | + | 11.0227i | 0.224860 | + | 0.389468i | ||||
\(802\) | 6.92820 | − | 4.00000i | 0.244643 | − | 0.141245i | ||||
\(803\) | −14.6969 | − | 8.48528i | −0.518644 | − | 0.299439i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.0000 | 0.845364 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.57321 | + | 4.94975i | −0.301605 | + | 0.174132i | ||||
\(809\) | −13.0000 | − | 22.5167i | −0.457056 | − | 0.791644i | 0.541748 | − | 0.840541i | \(-0.317763\pi\) |
−0.998804 | + | 0.0488972i | \(0.984429\pi\) | |||||||
\(810\) | −4.03459 | + | 19.7160i | −0.141761 | + | 0.692751i | ||||
\(811\) | −45.2548 | −1.58911 | −0.794556 | − | 0.607191i | \(-0.792296\pi\) | ||||
−0.794556 | + | 0.607191i | \(0.792296\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0000 | − | 20.7846i | 0.420600 | − | 0.728500i | ||||
\(815\) | −20.0764 | − | 17.8028i | −0.703245 | − | 0.623604i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 58.7878 | + | 33.9411i | 2.05672 | + | 1.18745i | ||||
\(818\) | 9.89949i | 0.346128i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.00000 | − | 3.00000i | −0.0349215 | − | 0.104765i | ||||
\(821\) | −5.00000 | + | 8.66025i | −0.174501 | + | 0.302245i | −0.939989 | − | 0.341206i | \(-0.889165\pi\) |
0.765487 | + | 0.643451i | \(0.222498\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.7846 | + | 12.0000i | −0.724506 | + | 0.418294i | −0.816409 | − | 0.577474i | \(-0.804038\pi\) |
0.0919029 | + | 0.995768i | \(0.470705\pi\) | |||||||
\(824\) | −8.48528 | + | 14.6969i | −0.295599 | + | 0.511992i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000i | 1.25184i | 0.779886 | + | 0.625921i | \(0.215277\pi\) | ||||
−0.779886 | + | 0.625921i | \(0.784723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.77817 | − | 13.4722i | −0.270147 | − | 0.467909i | 0.698752 | − | 0.715364i | \(-0.253739\pi\) |
−0.968899 | + | 0.247455i | \(0.920406\pi\) | |||||||
\(830\) | 25.1769 | − | 28.3923i | 0.873903 | − | 0.985511i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4.24264i | − | 0.147087i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.60770 | + | 37.1769i | −0.263275 | + | 1.28656i | ||||
\(836\) | −11.3137 | − | 19.5959i | −0.391293 | − | 0.677739i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.6274 | 0.781185 | 0.390593 | − | 0.920564i | \(-0.372270\pi\) | ||||
0.390593 | + | 0.920564i | \(0.372270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | −5.19615 | − | 3.00000i | −0.179071 | − | 0.103387i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.00000 | + | 10.3923i | 0.206529 | + | 0.357718i | ||||
\(845\) | 10.9534 | + | 2.24144i | 0.376807 | + | 0.0771078i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 12.0000i | − | 0.412082i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 19.5080 | + | 8.33298i | 0.669118 | + | 0.285819i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 46.6690i | − | 1.59792i | −0.601386 | − | 0.798959i | \(-0.705384\pi\) | ||
0.601386 | − | 0.798959i | \(-0.294616\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.0000 | + | 36.0000i | 0.410391 | + | 1.23117i | ||||
\(856\) | −6.00000 | + | 10.3923i | −0.205076 | + | 0.355202i | ||||
\(857\) | 11.0227 | − | 6.36396i | 0.376528 | − | 0.217389i | −0.299778 | − | 0.954009i | \(-0.596913\pi\) |
0.676307 | + | 0.736620i | \(0.263579\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.82843 | + | 4.89898i | −0.0965047 | + | 0.167151i | −0.910236 | − | 0.414091i | \(-0.864100\pi\) |
0.813731 | + | 0.581242i | \(0.197433\pi\) | |||||||
\(860\) | −25.4558 | + | 8.48528i | −0.868037 | + | 0.289346i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 16.0000i | − | 0.544962i | ||||||
\(863\) | −20.7846 | − | 12.0000i | −0.707516 | − | 0.408485i | 0.102624 | − | 0.994720i | \(-0.467276\pi\) |
−0.810141 | + | 0.586235i | \(0.800609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.09808 | + | 6.29423i | 0.241342 | + | 0.214010i | ||||
\(866\) | 14.8492 | − | 25.7196i | 0.504598 | − | 0.873989i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.4558 | + | 44.0908i | 0.862538 | + | 1.49396i | ||||
\(872\) | 10.3923 | − | 6.00000i | 0.351928 | − | 0.203186i | ||||
\(873\) | 11.0227 | + | 6.36396i | 0.373062 | + | 0.215387i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.5885 | − | 9.00000i | −0.526385 | − | 0.303908i | 0.213158 | − | 0.977018i | \(-0.431625\pi\) |
−0.739543 | + | 0.673109i | \(0.764958\pi\) | |||||||
\(878\) | 34.2929 | − | 19.7990i | 1.15733 | − | 0.668184i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.76268 | + | 1.79315i | 0.295390 | + | 0.0604471i | ||||
\(881\) | 32.5269 | 1.09586 | 0.547930 | − | 0.836524i | \(-0.315416\pi\) | ||||
0.547930 | + | 0.836524i | \(0.315416\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 12.0000i | − | 0.403832i | −0.979403 | − | 0.201916i | \(-0.935283\pi\) | ||
0.979403 | − | 0.201916i | \(-0.0647168\pi\) | |||||||
\(884\) | −9.00000 | + | 15.5885i | −0.302703 | + | 0.524297i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.00000 | + | 10.3923i | 0.201574 | + | 0.349136i | ||||
\(887\) | 14.6969 | + | 8.48528i | 0.493475 | + | 0.284908i | 0.726015 | − | 0.687679i | \(-0.241370\pi\) |
−0.232540 | + | 0.972587i | \(0.574704\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9.00000 | + | 3.00000i | −0.301681 | + | 0.100560i | ||||
\(891\) | 18.0000 | − | 31.1769i | 0.603023 | − | 1.04447i | ||||
\(892\) | 14.6969 | − | 8.48528i | 0.492090 | − | 0.284108i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.1421 | − | 42.4264i | −0.472719 | − | 1.41816i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.73205 | + | 1.00000i | 0.0577993 | + | 0.0333704i | ||||
\(899\) | −11.3137 | − | 19.5959i | −0.377333 | − | 0.653560i | ||||
\(900\) | −13.7942 | − | 5.89230i | −0.459808 | − | 0.196410i | ||||
\(901\) | −25.4558 | + | 44.0908i | −0.848057 | + | 1.46888i | ||||
\(902\) | 5.65685i | 0.188353i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −34.0788 | − | 6.97372i | −1.13282 | − | 0.231814i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.3923 | − | 6.00000i | 0.345071 | − | 0.199227i | −0.317441 | − | 0.948278i | \(-0.602824\pi\) |
0.662512 | + | 0.749051i | \(0.269490\pi\) | |||||||
\(908\) | −14.6969 | − | 8.48528i | −0.487735 | − | 0.281594i | ||||
\(909\) | −29.6985 | −0.985037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0000 | −1.32526 | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −58.7878 | + | 33.9411i | −1.94559 | + | 1.12329i | ||||
\(914\) | −12.0000 | − | 20.7846i | −0.396925 | − | 0.687494i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.5563 | −0.513996 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0000 | − | 41.5692i | 0.791687 | − | 1.37124i | −0.133235 | − | 0.991084i | \(-0.542536\pi\) |
0.924922 | − | 0.380158i | \(-0.124130\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.3712 | + | 10.6066i | 0.605022 | + | 0.349310i | ||||
\(923\) | 33.9411i | 1.11719i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.0000 | − | 24.0000i | −0.591836 | − | 0.789115i | ||||
\(926\) | 12.0000 | − | 20.7846i | 0.394344 | − | 0.683025i | ||||
\(927\) | −44.0908 | + | 25.4558i | −1.44813 | + | 0.836080i | ||||
\(928\) | −3.46410 | + | 2.00000i | −0.113715 | + | 0.0656532i | ||||
\(929\) | 14.8492 | − | 25.7196i | 0.487188 | − | 0.843834i | −0.512704 | − | 0.858566i | \(-0.671356\pi\) |
0.999891 | + | 0.0147316i | \(0.00468937\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 6.00000i | − | 0.196537i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.48528 | − | 14.6969i | −0.277647 | − | 0.480899i | ||||
\(935\) | −28.3923 | − | 25.1769i | −0.928528 | − | 0.823373i | ||||
\(936\) | 6.36396 | − | 11.0227i | 0.208013 | − | 0.360288i | ||||
\(937\) | − | 4.24264i | − | 0.138601i | −0.997596 | − | 0.0693005i | \(-0.977923\pi\) | ||
0.997596 | − | 0.0693005i | \(-0.0220767\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.7487 | + | 42.8661i | 0.806786 | + | 1.39739i | 0.915079 | + | 0.403275i | \(0.132128\pi\) |
−0.108293 | + | 0.994119i | \(0.534538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −11.3137 | −0.368230 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 48.0000 | 1.56061 | ||||||||
\(947\) | −10.3923 | − | 6.00000i | −0.337705 | − | 0.194974i | 0.321552 | − | 0.946892i | \(-0.395796\pi\) |
−0.659256 | + | 0.751918i | \(0.729129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.00000 | − | 15.5885i | −0.292152 | − | 0.506023i | ||||
\(950\) | −28.0812 | + | 3.38323i | −0.911074 | + | 0.109766i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 24.0000i | − | 0.777436i | −0.921357 | − | 0.388718i | \(-0.872918\pi\) | ||
0.921357 | − | 0.388718i | \(-0.127082\pi\) | |||||||
\(954\) | 18.0000 | − | 31.1769i | 0.582772 | − | 1.00939i | ||||
\(955\) | 11.8685 | − | 13.3843i | 0.384056 | − | 0.433105i | ||||
\(956\) | 4.00000 | + | 6.92820i | 0.129369 | + | 0.224074i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.9706i | 0.548294i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.500000 | + | 0.866025i | −0.0161290 | + | 0.0279363i | ||||
\(962\) | 22.0454 | − | 12.7279i | 0.710772 | − | 0.410365i | ||||
\(963\) | −31.1769 | + | 18.0000i | −1.00466 | + | 0.580042i | ||||
\(964\) | 7.77817 | − | 13.4722i | 0.250518 | − | 0.433910i | ||||
\(965\) | 50.9117 | − | 16.9706i | 1.63891 | − | 0.546302i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.0000i | 0.771788i | 0.922543 | + | 0.385894i | \(0.126107\pi\) | ||||
−0.922543 | + | 0.385894i | \(0.873893\pi\) | |||||||
\(968\) | −4.33013 | − | 2.50000i | −0.139176 | − | 0.0803530i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.29423 | + | 7.09808i | −0.202096 | + | 0.227905i | ||||
\(971\) | 22.6274 | − | 39.1918i | 0.726148 | − | 1.25773i | −0.232351 | − | 0.972632i | \(-0.574642\pi\) |
0.958500 | − | 0.285094i | \(-0.0920248\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −24.0000 | −0.769010 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.53553 | + | 6.12372i | 0.113170 | + | 0.196016i | ||||
\(977\) | 25.9808 | − | 15.0000i | 0.831198 | − | 0.479893i | −0.0230645 | − | 0.999734i | \(-0.507342\pi\) |
0.854263 | + | 0.519841i | \(0.174009\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.9706 | 0.542382 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.0000 | 1.14939 | ||||||||
\(982\) | −3.46410 | − | 2.00000i | −0.110544 | − | 0.0638226i | ||||
\(983\) | −14.6969 | + | 8.48528i | −0.468760 | + | 0.270638i | −0.715720 | − | 0.698387i | \(-0.753901\pi\) |
0.246961 | + | 0.969025i | \(0.420568\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.37945 | − | 26.2880i | 0.171404 | − | 0.837607i | ||||
\(986\) | 16.9706 | 0.540453 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 24.0000i | − | 0.763542i | ||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 20.0764 | + | 17.8028i | 0.638070 | + | 0.565809i | ||||
\(991\) | −24.0000 | − | 41.5692i | −0.762385 | − | 1.32049i | −0.941618 | − | 0.336683i | \(-0.890695\pi\) |
0.179233 | − | 0.983807i | \(-0.442638\pi\) | |||||||
\(992\) | 4.89898 | + | 2.82843i | 0.155543 | + | 0.0898027i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.00000 | + | 24.0000i | 0.253617 | + | 0.760851i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.0681 | + | 19.0919i | −1.04728 | + | 0.604646i | −0.921886 | − | 0.387461i | \(-0.873352\pi\) |
−0.125392 | + | 0.992107i | \(0.540019\pi\) | |||||||
\(998\) | 3.46410 | − | 2.00000i | 0.109654 | − | 0.0633089i | ||||
\(999\) | 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 | 490.2.i.d.79.3 | 8 | ||
5.4 | even | 2 | inner | 490.2.i.d.79.2 | 8 | ||
7.2 | even | 3 | 490.2.c.g.99.2 | yes | 4 | ||
7.3 | odd | 6 | inner | 490.2.i.d.459.1 | 8 | ||
7.4 | even | 3 | inner | 490.2.i.d.459.2 | 8 | ||
7.5 | odd | 6 | 490.2.c.g.99.1 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 490.2.i.d.79.4 | 8 | ||
35.2 | odd | 12 | 2450.2.a.bo.1.2 | 2 | |||
35.4 | even | 6 | inner | 490.2.i.d.459.3 | 8 | ||
35.9 | even | 6 | 490.2.c.g.99.4 | yes | 4 | ||
35.12 | even | 12 | 2450.2.a.bo.1.1 | 2 | |||
35.19 | odd | 6 | 490.2.c.g.99.3 | yes | 4 | ||
35.23 | odd | 12 | 2450.2.a.bi.1.1 | 2 | |||
35.24 | odd | 6 | inner | 490.2.i.d.459.4 | 8 | ||
35.33 | even | 12 | 2450.2.a.bi.1.2 | 2 | |||
35.34 | odd | 2 | inner | 490.2.i.d.79.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
490.2.c.g.99.1 | ✓ | 4 | 7.5 | odd | 6 | ||
490.2.c.g.99.2 | yes | 4 | 7.2 | even | 3 | ||
490.2.c.g.99.3 | yes | 4 | 35.19 | odd | 6 | ||
490.2.c.g.99.4 | yes | 4 | 35.9 | even | 6 | ||
490.2.i.d.79.1 | 8 | 35.34 | odd | 2 | inner | ||
490.2.i.d.79.2 | 8 | 5.4 | even | 2 | inner | ||
490.2.i.d.79.3 | 8 | 1.1 | even | 1 | trivial | ||
490.2.i.d.79.4 | 8 | 7.6 | odd | 2 | inner | ||
490.2.i.d.459.1 | 8 | 7.3 | odd | 6 | inner | ||
490.2.i.d.459.2 | 8 | 7.4 | even | 3 | inner | ||
490.2.i.d.459.3 | 8 | 35.4 | even | 6 | inner | ||
490.2.i.d.459.4 | 8 | 35.24 | odd | 6 | inner | ||
2450.2.a.bi.1.1 | 2 | 35.23 | odd | 12 | |||
2450.2.a.bi.1.2 | 2 | 35.33 | even | 12 | |||
2450.2.a.bo.1.1 | 2 | 35.12 | even | 12 | |||
2450.2.a.bo.1.2 | 2 | 35.2 | odd | 12 |