Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(863,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.863");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.s (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: | \(20.6972242039\) |
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: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1727.1 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.1727 |
Dual form | 2592.2.s.h.863.1 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.275255 | − | 0.158919i | 0.123098 | − | 0.0710706i | −0.437187 | − | 0.899371i | \(-0.644025\pi\) |
0.560285 | + | 0.828300i | \(0.310692\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.25529 | − | 0.724745i | −0.474457 | − | 0.273928i | 0.243647 | − | 0.969864i | \(-0.421656\pi\) |
−0.718104 | + | 0.695936i | \(0.754990\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.548188 | + | 0.949490i | −0.165285 | + | 0.286282i | −0.936756 | − | 0.349982i | \(-0.886188\pi\) |
0.771471 | + | 0.636264i | \(0.219521\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.44949 | − | 2.51059i | −0.402016 | − | 0.696312i | 0.591953 | − | 0.805972i | \(-0.298357\pi\) |
−0.993969 | + | 0.109660i | \(0.965024\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.46410i | − | 0.840168i | −0.907485 | − | 0.420084i | \(-0.862001\pi\) | ||
0.907485 | − | 0.420084i | \(-0.137999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.89898i | 1.12390i | 0.827170 | + | 0.561951i | \(0.189949\pi\) | ||||
−0.827170 | + | 0.561951i | \(0.810051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.41421 | + | 2.44949i | 0.294884 | + | 0.510754i | 0.974958 | − | 0.222390i | \(-0.0713857\pi\) |
−0.680074 | + | 0.733144i | \(0.738052\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.44949 | + | 4.24264i | −0.489898 | + | 0.848528i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.89898 | − | 4.56048i | −1.46680 | − | 0.846859i | −0.467493 | − | 0.883997i | \(-0.654843\pi\) |
−0.999310 | + | 0.0371370i | \(0.988176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.45145 | − | 3.72474i | 1.15871 | − | 0.668984i | 0.207719 | − | 0.978189i | \(-0.433396\pi\) |
0.950996 | + | 0.309205i | \(0.100063\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.460702 | −0.0778728 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.89898 | 0.805387 | 0.402694 | − | 0.915335i | \(-0.368074\pi\) | ||||
0.402694 | + | 0.915335i | \(0.368074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.44949 | + | 4.87832i | −1.31959 | + | 0.761865i | −0.983662 | − | 0.180023i | \(-0.942383\pi\) |
−0.335926 | + | 0.941888i | \(0.609049\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.97469 | − | 3.44949i | −0.911132 | − | 0.526042i | −0.0303367 | − | 0.999540i | \(-0.509658\pi\) |
−0.880795 | + | 0.473497i | \(0.842991\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.56048 | + | 7.89898i | −0.665214 | + | 1.15218i | 0.314013 | + | 0.949419i | \(0.398326\pi\) |
−0.979227 | + | 0.202766i | \(0.935007\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.44949 | − | 4.24264i | −0.349927 | − | 0.606092i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.41761i | 0.606806i | 0.952862 | + | 0.303403i | \(0.0981228\pi\) | ||||
−0.952862 | + | 0.303403i | \(0.901877\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.348469i | 0.0469876i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.56048 | + | 7.89898i | 0.593724 | + | 1.02836i | 0.993726 | + | 0.111845i | \(0.0356761\pi\) |
−0.400002 | + | 0.916514i | \(0.630991\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | + | 3.46410i | −0.256074 | + | 0.443533i | −0.965187 | − | 0.261562i | \(-0.915762\pi\) |
0.709113 | + | 0.705095i | \(0.249096\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.797959 | − | 0.460702i | −0.0989746 | − | 0.0571430i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.41761 | + | 2.55051i | −0.539697 | + | 0.311594i | −0.744956 | − | 0.667113i | \(-0.767530\pi\) |
0.205259 | + | 0.978708i | \(0.434196\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.56388 | −0.897667 | −0.448834 | − | 0.893615i | \(-0.648160\pi\) | ||||
−0.448834 | + | 0.893615i | \(0.648160\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.89898 | 0.222259 | 0.111129 | − | 0.993806i | \(-0.464553\pi\) | ||||
0.111129 | + | 0.993806i | \(0.464553\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.37628 | − | 0.794593i | 0.156841 | − | 0.0905523i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.73205 | + | 1.00000i | 0.194871 | + | 0.112509i | 0.594261 | − | 0.804272i | \(-0.297445\pi\) |
−0.399390 | + | 0.916781i | \(0.630778\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.93709 | + | 13.7474i | −0.871209 | + | 1.50898i | −0.0104623 | + | 0.999945i | \(0.503330\pi\) |
−0.860747 | + | 0.509033i | \(0.830003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.550510 | − | 0.953512i | −0.0597112 | − | 0.103423i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 11.9494i | − | 1.26663i | −0.773893 | − | 0.633316i | \(-0.781693\pi\) | ||
0.773893 | − | 0.633316i | \(-0.218307\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.20204i | 0.440494i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.778539 | + | 1.34847i | 0.0798764 | + | 0.138350i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.50000 | − | 4.33013i | 0.253837 | − | 0.439658i | −0.710742 | − | 0.703452i | \(-0.751641\pi\) |
0.964579 | + | 0.263795i | \(0.0849741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.6237 | − | 7.86566i | −1.35561 | − | 0.782663i | −0.366582 | − | 0.930386i | \(-0.619472\pi\) |
−0.989029 | + | 0.147723i | \(0.952806\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.66025 | − | 5.00000i | 0.853320 | − | 0.492665i | −0.00844953 | − | 0.999964i | \(-0.502690\pi\) |
0.861770 | + | 0.507300i | \(0.169356\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.66025 | −0.837218 | −0.418609 | − | 0.908166i | \(-0.637482\pi\) | ||||
−0.418609 | + | 0.908166i | \(0.637482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.89898 | −0.469237 | −0.234619 | − | 0.972088i | \(-0.575384\pi\) | ||||
−0.234619 | + | 0.972088i | \(0.575384\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.2474 | + | 7.07107i | −1.15214 | + | 0.665190i | −0.949409 | − | 0.314044i | \(-0.898316\pi\) |
−0.202735 | + | 0.979234i | \(0.564983\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.778539 | + | 0.449490i | 0.0725991 | + | 0.0419151i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.51059 | + | 4.34847i | −0.230145 | + | 0.398624i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.89898 | + | 8.48528i | 0.445362 | + | 0.771389i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.14626i | 0.281410i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.2474i | − | 1.35299i | −0.736446 | − | 0.676496i | \(-0.763498\pi\) | ||
0.736446 | − | 0.676496i | \(-0.236502\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.50170 | − | 2.60102i | −0.131204 | − | 0.227252i | 0.792937 | − | 0.609304i | \(-0.208551\pi\) |
−0.924141 | + | 0.382052i | \(0.875218\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.55051 | − | 6.14966i | 0.307868 | − | 0.533244i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.24745 | − | 5.33902i | −0.790063 | − | 0.456143i | 0.0499218 | − | 0.998753i | \(-0.484103\pi\) |
−0.839985 | + | 0.542610i | \(0.817436\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.3205 | + | 10.0000i | −1.46911 | + | 0.848189i | −0.999400 | − | 0.0346338i | \(-0.988974\pi\) |
−0.469706 | + | 0.882823i | \(0.655640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.17837 | 0.265789 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.89898 | −0.240747 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.27526 | + | 1.89097i | −0.268319 | + | 0.154914i | −0.628124 | − | 0.778114i | \(-0.716177\pi\) |
0.359804 | + | 0.933028i | \(0.382843\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.9367 | + | 8.62372i | 1.21553 | + | 0.701789i | 0.963959 | − | 0.266049i | \(-0.0857184\pi\) |
0.251574 | + | 0.967838i | \(0.419052\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.18386 | − | 2.05051i | 0.0950901 | − | 0.164701i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.89898 | + | 11.9494i | 0.550599 | + | 0.953665i | 0.998231 | + | 0.0594472i | \(0.0189338\pi\) |
−0.447633 | + | 0.894217i | \(0.647733\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.09978i | − | 0.323108i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000i | 0.469956i | 0.972001 | + | 0.234978i | \(0.0755019\pi\) | ||||
−0.972001 | + | 0.234978i | \(0.924498\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.4887 | + | 19.8990i | 0.889021 | + | 1.53983i | 0.841035 | + | 0.540981i | \(0.181947\pi\) |
0.0479862 | + | 0.998848i | \(0.484720\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.29796 | − | 3.98018i | 0.176766 | − | 0.306168i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.62372 | − | 2.66951i | −0.351535 | − | 0.202959i | 0.313826 | − | 0.949481i | \(-0.398389\pi\) |
−0.665361 | + | 0.746522i | \(0.731722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.14966 | − | 3.55051i | 0.464871 | − | 0.268393i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.66025 | 0.647298 | 0.323649 | − | 0.946177i | \(-0.395090\pi\) | ||||
0.323649 | + | 0.946177i | \(0.395090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.79796 | −0.728277 | −0.364138 | − | 0.931345i | \(-0.618636\pi\) | ||||
−0.364138 | + | 0.931345i | \(0.618636\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.34847 | − | 0.778539i | 0.0991414 | − | 0.0572393i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.28913 | + | 1.89898i | 0.240525 | + | 0.138867i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.80312 | + | 15.2474i | −0.636971 | + | 1.10327i | 0.349123 | + | 0.937077i | \(0.386480\pi\) |
−0.986094 | + | 0.166190i | \(0.946854\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.05051 | − | 1.81954i | −0.0756174 | − | 0.130973i | 0.825737 | − | 0.564055i | \(-0.190759\pi\) |
−0.901355 | + | 0.433082i | \(0.857426\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.2672i | − | 0.874003i | −0.899461 | − | 0.437002i | \(-0.856040\pi\) | ||
0.899461 | − | 0.437002i | \(-0.143960\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20.3485i | − | 1.44246i | −0.692693 | − | 0.721232i | \(-0.743576\pi\) | ||
0.692693 | − | 0.721232i | \(-0.256424\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.61037 | + | 11.4495i | 0.463957 | + | 0.803597i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.55051 | + | 2.68556i | −0.108292 | + | 0.187568i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.65153 | − | 2.68556i | −0.321753 | − | 0.185764i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.6773 | + | 14.2474i | −1.69886 | + | 0.980835i | −0.752007 | + | 0.659155i | \(0.770914\pi\) |
−0.946848 | + | 0.321680i | \(0.895752\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.19275 | −0.149544 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.7980 | −0.733013 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.69694 | + | 5.02118i | −0.585019 | + | 0.337761i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.174973 | + | 0.101021i | 0.0117170 | + | 0.00676483i | 0.505847 | − | 0.862623i | \(-0.331180\pi\) |
−0.494130 | + | 0.869388i | \(0.664513\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.83183 | + | 10.1010i | −0.387072 | + | 0.670428i | −0.992054 | − | 0.125811i | \(-0.959847\pi\) |
0.604982 | + | 0.796239i | \(0.293180\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | − | 1.73205i | −0.0660819 | − | 0.114457i | 0.831092 | − | 0.556136i | \(-0.187717\pi\) |
−0.897173 | + | 0.441679i | \(0.854383\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.2207i | 0.866119i | 0.901365 | + | 0.433059i | \(0.142566\pi\) | ||||
−0.901365 | + | 0.433059i | \(0.857434\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.89898i | 0.189109i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.5352 | − | 18.2474i | −0.681463 | − | 1.18033i | −0.974534 | − | 0.224239i | \(-0.928011\pi\) |
0.293071 | − | 0.956091i | \(-0.405323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.89898 | − | 17.1455i | 0.637649 | − | 1.10444i | −0.348298 | − | 0.937384i | \(-0.613240\pi\) |
0.985947 | − | 0.167057i | \(-0.0534264\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.34847 | − | 0.778539i | −0.0861505 | − | 0.0497390i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.2993 | − | 7.10102i | 0.782588 | − | 0.451827i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3205 | −1.09326 | −0.546630 | − | 0.837374i | \(-0.684090\pi\) | ||||
−0.546630 | + | 0.837374i | \(0.684090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.10102 | −0.194959 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.1010 | − | 5.83183i | 0.630084 | − | 0.363779i | −0.150700 | − | 0.988579i | \(-0.548153\pi\) |
0.780785 | + | 0.624800i | \(0.214820\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.14966 | − | 3.55051i | −0.382122 | − | 0.220618i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.4422 | − | 21.5505i | 0.767218 | − | 1.32886i | −0.171847 | − | 0.985124i | \(-0.554974\pi\) |
0.939066 | − | 0.343738i | \(-0.111693\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.702041 | + | 1.21597i | 0.0431260 | + | 0.0746965i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 10.3923i | − | 0.633630i | −0.948487 | − | 0.316815i | \(-0.897387\pi\) | ||
0.948487 | − | 0.316815i | \(-0.102613\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.5505i | − | 0.762389i | −0.924495 | − | 0.381195i | \(-0.875513\pi\) | ||
0.924495 | − | 0.381195i | \(-0.124487\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.68556 | − | 4.65153i | −0.161946 | − | 0.280498i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.89898 | − | 11.9494i | 0.414520 | − | 0.717969i | −0.580858 | − | 0.814005i | \(-0.697283\pi\) |
0.995378 | + | 0.0960358i | \(0.0306163\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.797959 | + | 0.460702i | 0.0476022 | + | 0.0274832i | 0.523612 | − | 0.851957i | \(-0.324584\pi\) |
−0.476010 | + | 0.879440i | \(0.657917\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.68556 | + | 1.55051i | −0.159640 | + | 0.0921683i | −0.577692 | − | 0.816255i | \(-0.696046\pi\) |
0.418052 | + | 0.908423i | \(0.362713\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.1421 | 0.834784 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.20204 | + | 3.00340i | −0.303906 | + | 0.175460i | −0.644196 | − | 0.764860i | \(-0.722808\pi\) |
0.340290 | + | 0.940321i | \(0.389475\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.51059 | + | 1.44949i | 0.146172 | + | 0.0843926i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.09978 | − | 7.10102i | 0.237096 | − | 0.410663i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.00000 | + | 8.66025i | 0.288195 | + | 0.499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.27135i | 0.0727972i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0000i | 1.02731i | 0.857996 | + | 0.513657i | \(0.171710\pi\) | ||||
−0.857996 | + | 0.513657i | \(0.828290\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.04989 | − | 3.55051i | −0.116238 | − | 0.201331i | 0.802036 | − | 0.597276i | \(-0.203750\pi\) |
−0.918274 | + | 0.395945i | \(0.870417\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.7474 | + | 25.5433i | −0.833575 | + | 1.44379i | 0.0616102 | + | 0.998100i | \(0.480376\pi\) |
−0.895185 | + | 0.445694i | \(0.852957\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.6237 | + | 14.7939i | 1.43917 | + | 0.830906i | 0.997792 | − | 0.0664143i | \(-0.0211559\pi\) |
0.441380 | + | 0.897320i | \(0.354489\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.66025 | − | 5.00000i | 0.484881 | − | 0.279946i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.9706 | 0.944267 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.2020 | 0.787787 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.4495 | − | 6.61037i | 0.631231 | − | 0.364441i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.603566 | − | 0.348469i | −0.0331750 | − | 0.0191536i | 0.483321 | − | 0.875443i | \(-0.339430\pi\) |
−0.516496 | + | 0.856290i | \(0.672764\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.810647 | + | 1.40408i | −0.0442904 | + | 0.0767132i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.10102 | − | 3.63907i | −0.114450 | − | 0.198233i | 0.803110 | − | 0.595831i | \(-0.203177\pi\) |
−0.917560 | + | 0.397598i | \(0.869844\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.16744i | 0.442292i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2474i | 0.931275i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.74094 | − | 4.74745i | −0.147141 | − | 0.254856i | 0.783028 | − | 0.621986i | \(-0.213674\pi\) |
−0.930170 | + | 0.367130i | \(0.880341\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.4495 | + | 21.5631i | −0.666406 | + | 1.15425i | 0.312496 | + | 0.949919i | \(0.398835\pi\) |
−0.978902 | + | 0.204330i | \(0.934498\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.2474 | − | 7.07107i | −0.651866 | − | 0.376355i | 0.137305 | − | 0.990529i | \(-0.456156\pi\) |
−0.789171 | + | 0.614174i | \(0.789489\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.08200 | + | 1.20204i | −0.110501 | + | 0.0637977i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.2911 | −1.80981 | −0.904907 | − | 0.425610i | \(-0.860060\pi\) | ||||
−0.904907 | + | 0.425610i | \(0.860060\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00000 | −0.263158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.522704 | − | 0.301783i | 0.0273596 | − | 0.0157961i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.40496 | + | 4.27526i | 0.386536 | + | 0.223167i | 0.680658 | − | 0.732601i | \(-0.261694\pi\) |
−0.294122 | + | 0.955768i | \(0.595027\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.20164 | − | 5.54541i | 0.166221 | − | 0.287903i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.2474 | − | 29.8735i | −0.893039 | − | 1.54679i | −0.836213 | − | 0.548405i | \(-0.815235\pi\) |
−0.0568261 | − | 0.998384i | \(-0.518098\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.4415i | 1.36180i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000i | 0.410932i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.87492 | + | 3.24745i | 0.0958037 | + | 0.165937i | 0.909944 | − | 0.414732i | \(-0.136125\pi\) |
−0.814140 | + | 0.580669i | \(0.802791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.252551 | − | 0.437432i | 0.0128712 | − | 0.0222936i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.7702 | + | 16.0331i | 1.40800 | + | 0.812911i | 0.995195 | − | 0.0979078i | \(-0.0312150\pi\) |
0.412807 | + | 0.910818i | \(0.364548\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.48528 | − | 4.89898i | 0.429119 | − | 0.247752i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.635674 | 0.0319843 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.69694 | 0.436487 | 0.218243 | − | 0.975894i | \(-0.429967\pi\) | ||||
0.218243 | + | 0.975894i | \(0.429967\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.5959 | − | 11.3137i | 0.978573 | − | 0.564980i | 0.0767343 | − | 0.997052i | \(-0.475551\pi\) |
0.901839 | + | 0.432072i | \(0.142217\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.7026 | − | 10.7980i | −0.931644 | − | 0.537885i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.68556 | + | 4.65153i | −0.133118 | + | 0.230568i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50000 | + | 6.06218i | 0.173064 | + | 0.299755i | 0.939490 | − | 0.342578i | \(-0.111300\pi\) |
−0.766426 | + | 0.642333i | \(0.777967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 13.2207i | − | 0.650550i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.04541i | 0.247669i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.0458 | − | 22.5959i | −0.637327 | − | 1.10388i | −0.986017 | − | 0.166645i | \(-0.946707\pi\) |
0.348690 | − | 0.937238i | \(-0.386627\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.8990 | − | 25.8058i | 0.726132 | − | 1.25770i | −0.232375 | − | 0.972626i | \(-0.574650\pi\) |
0.958506 | − | 0.285071i | \(-0.0920171\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.6969 | + | 8.48528i | 0.712906 | + | 0.411597i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.02118 | − | 2.89898i | 0.242992 | − | 0.140291i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.3629 | 1.31802 | 0.659011 | − | 0.752133i | \(-0.270975\pi\) | ||||
0.659011 | + | 0.752133i | \(0.270975\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.3939 | 1.55675 | 0.778375 | − | 0.627799i | \(-0.216044\pi\) | ||||
0.778375 | + | 0.627799i | \(0.216044\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.0000 | + | 6.92820i | −0.574038 | + | 0.331421i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.6688 | − | 9.62372i | −0.795557 | − | 0.459315i | 0.0463579 | − | 0.998925i | \(-0.485239\pi\) |
−0.841915 | + | 0.539610i | \(0.818572\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.3171 | − | 24.7980i | 0.680226 | − | 1.17819i | −0.294685 | − | 0.955594i | \(-0.595215\pi\) |
0.974912 | − | 0.222592i | \(-0.0714518\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.89898 | − | 3.28913i | −0.0900203 | − | 0.155920i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.3417i | 1.05437i | 0.849751 | + | 0.527185i | \(0.176752\pi\) | ||||
−0.849751 | + | 0.527185i | \(0.823248\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 10.6969i | − | 0.503699i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.667783 | + | 1.15663i | 0.0313061 | + | 0.0542238i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5000 | + | 21.6506i | −0.584725 | + | 1.01277i | 0.410184 | + | 0.912003i | \(0.365464\pi\) |
−0.994910 | + | 0.100771i | \(0.967869\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.62372 | + | 0.937458i | 0.0756244 | + | 0.0436618i | 0.537335 | − | 0.843369i | \(-0.319431\pi\) |
−0.461711 | + | 0.887030i | \(0.652764\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.4220 | − | 13.5227i | 1.08851 | − | 0.628453i | 0.155333 | − | 0.987862i | \(-0.450355\pi\) |
0.933180 | + | 0.359409i | \(0.117022\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.174973 | 0.00809677 | 0.00404838 | − | 0.999992i | \(-0.498711\pi\) | ||||
0.00404838 | + | 0.999992i | \(0.498711\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.39388 | 0.341418 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.55051 | − | 3.78194i | 0.301193 | − | 0.173894i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.7846 | − | 12.0000i | −0.953663 | − | 0.550598i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.0458 | − | 22.5959i | 0.596076 | − | 1.03243i | −0.397318 | − | 0.917681i | \(-0.630059\pi\) |
0.993394 | − | 0.114753i | \(-0.0366076\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.10102 | − | 12.2993i | −0.323779 | − | 0.560801i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.58919i | − | 0.0721612i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 3.79796i | − | 0.172102i | −0.996291 | − | 0.0860510i | \(-0.972575\pi\) | ||
0.996291 | − | 0.0860510i | \(-0.0274248\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.15855 | + | 12.3990i | 0.323061 | + | 0.559558i | 0.981118 | − | 0.193410i | \(-0.0619548\pi\) |
−0.658057 | + | 0.752968i | \(0.728621\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.7980 | + | 27.3629i | −0.711504 | + | 1.23236i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.49490 | + | 5.48188i | 0.425904 | + | 0.245896i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.9029 | − | 7.44949i | 0.577613 | − | 0.333485i | −0.182571 | − | 0.983193i | \(-0.558442\pi\) |
0.760184 | + | 0.649708i | \(0.225109\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.1127 | 1.38725 | 0.693623 | − | 0.720338i | \(-0.256013\pi\) | ||||
0.693623 | + | 0.720338i | \(0.256013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.00000 | −0.222497 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.1186 | − | 13.3475i | 1.02471 | − | 0.591619i | 0.109249 | − | 0.994014i | \(-0.465155\pi\) |
0.915466 | + | 0.402395i | \(0.131822\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.38378 | − | 1.37628i | −0.105452 | − | 0.0608828i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.58919 | − | 2.75255i | 0.0700279 | − | 0.121292i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.00000 | − | 8.66025i | −0.219900 | − | 0.380878i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 21.7060i | − | 0.950958i | −0.879727 | − | 0.475479i | \(-0.842275\pi\) | ||
0.879727 | − | 0.475479i | \(-0.157725\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.3939i | 1.19785i | 0.800805 | + | 0.598925i | \(0.204405\pi\) | ||||
−0.800805 | + | 0.598925i | \(0.795595\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.9029 | − | 22.3485i | −0.562059 | − | 0.973515i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.50000 | − | 12.9904i | 0.326087 | − | 0.564799i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.4949 | + | 14.1421i | 1.06099 | + | 0.612564i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.38378 | + | 1.37628i | −0.103060 | + | 0.0595016i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.37113 | 0.231351 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0000 | −0.859867 | −0.429934 | − | 0.902861i | \(-0.641463\pi\) | ||||
−0.429934 | + | 0.902861i | \(0.641463\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.34847 | + | 0.778539i | −0.0577621 | + | 0.0333489i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.6096 | + | 11.8990i | 0.881204 | + | 0.508764i | 0.871055 | − | 0.491185i | \(-0.163436\pi\) |
0.0101491 | + | 0.999948i | \(0.496769\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.3417 | − | 38.6969i | 0.951788 | − | 1.64855i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.44949 | − | 2.51059i | −0.0616386 | − | 0.106761i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.5529i | 0.531886i | 0.963989 | + | 0.265943i | \(0.0856832\pi\) | ||||
−0.963989 | + | 0.265943i | \(0.914317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.0000i | 0.845910i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.4012 | − | 19.7474i | −0.480503 | − | 0.832256i | 0.519247 | − | 0.854624i | \(-0.326213\pi\) |
−0.999750 | + | 0.0223687i | \(0.992879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.24745 | + | 3.89270i | −0.0945509 | + | 0.163767i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.10102 | − | 4.09978i | −0.297690 | − | 0.171872i | 0.343715 | − | 0.939074i | \(-0.388315\pi\) |
−0.641405 | + | 0.767203i | \(0.721648\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.1455 | + | 9.89898i | −0.717518 | + | 0.414259i | −0.813839 | − | 0.581091i | \(-0.802626\pi\) |
0.0963203 | + | 0.995350i | \(0.469293\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.8564 | −0.577852 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.79796 | −0.158111 | −0.0790556 | − | 0.996870i | \(-0.525190\pi\) | ||||
−0.0790556 | + | 0.996870i | \(0.525190\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.9268 | − | 11.5047i | 0.826702 | − | 0.477297i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.19448 | − | 2.42168i | −0.173718 | − | 0.100296i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.5441 | − | 19.9949i | 0.476474 | − | 0.825278i | −0.523162 | − | 0.852233i | \(-0.675248\pi\) |
0.999637 | + | 0.0269553i | \(0.00858119\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.2474 | + | 31.6055i | 0.751873 | + | 1.30228i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.13534i | 0.334078i | 0.985950 | + | 0.167039i | \(0.0534206\pi\) | ||||
−0.985950 | + | 0.167039i | \(0.946579\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.59592i | 0.0654263i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.7600 | − | 22.1010i | −0.521361 | − | 0.903023i | −0.999691 | − | 0.0248434i | \(-0.992091\pi\) |
0.478331 | − | 0.878180i | \(-0.341242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.15153 | + | 8.92271i | −0.210135 | + | 0.363965i | −0.951757 | − | 0.306854i | \(-0.900724\pi\) |
0.741621 | + | 0.670819i | \(0.234057\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.69694 | + | 1.55708i | 0.109646 | + | 0.0633042i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.6096 | + | 11.8990i | −0.836519 | + | 0.482965i | −0.856080 | − | 0.516844i | \(-0.827107\pi\) |
0.0195602 | + | 0.999809i | \(0.493773\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.4415 | 1.06971 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.0000 | 1.21169 | 0.605844 | − | 0.795583i | \(-0.292835\pi\) | ||||
0.605844 | + | 0.795583i | \(0.292835\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.2474 | − | 13.9993i | 0.976166 | − | 0.563589i | 0.0750552 | − | 0.997179i | \(-0.476087\pi\) |
0.901110 | + | 0.433590i | \(0.142753\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.7026 | + | 10.7980i | 0.751722 | + | 0.434007i | 0.826316 | − | 0.563207i | \(-0.190433\pi\) |
−0.0745941 | + | 0.997214i | \(0.523766\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.66025 | + | 15.0000i | −0.346966 | + | 0.600962i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.7474 | − | 20.3472i | −0.469898 | − | 0.813887i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 16.9706i | − | 0.676661i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 45.7423i | − | 1.82097i | −0.413538 | − | 0.910487i | \(-0.635707\pi\) | ||
0.413538 | − | 0.910487i | \(-0.364293\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.42310 | − | 4.19694i | −0.0961579 | − | 0.166550i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.10102 | + | 12.2993i | −0.281353 | + | 0.487317i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.2474 | + | 24.3916i | 1.66867 | + | 0.963409i | 0.968354 | + | 0.249580i | \(0.0802926\pi\) |
0.700320 | + | 0.713829i | \(0.253041\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.3840 | − | 18.6969i | 1.27710 | − | 0.737335i | 0.300788 | − | 0.953691i | \(-0.402750\pi\) |
0.976315 | + | 0.216356i | \(0.0694171\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.7846 | −0.817127 | −0.408564 | − | 0.912730i | \(-0.633970\pi\) | ||||
−0.408564 | + | 0.912730i | \(0.633970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.0000 | −0.392534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.0732 | + | 9.27987i | −0.628993 | + | 0.363150i | −0.780362 | − | 0.625328i | \(-0.784965\pi\) |
0.151369 | + | 0.988477i | \(0.451632\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.826701 | − | 0.477296i | −0.0323019 | − | 0.0186495i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.9118 | − | 24.0959i | 0.541926 | − | 0.938644i | −0.456867 | − | 0.889535i | \(-0.651029\pi\) |
0.998793 | − | 0.0491088i | \(-0.0156381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.24745 | + | 3.89270i | 0.0874156 | + | 0.151408i | 0.906418 | − | 0.422382i | \(-0.138806\pi\) |
−0.819002 | + | 0.573790i | \(0.805473\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.25697i | − | 0.0875215i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 25.7980i | − | 0.998901i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.19275 | − | 3.79796i | −0.0846503 | − | 0.146619i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.2980 | − | 31.6930i | 0.705334 | − | 1.22168i | −0.261236 | − | 0.965275i | \(-0.584130\pi\) |
0.966571 | − | 0.256400i | \(-0.0825365\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.49490 | − | 5.48188i | −0.364919 | − | 0.210686i | 0.306318 | − | 0.951929i | \(-0.400903\pi\) |
−0.671236 | + | 0.741244i | \(0.734236\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.27647 | + | 3.62372i | −0.240869 | + | 0.139066i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.3923 | −0.397650 | −0.198825 | − | 0.980035i | \(-0.563713\pi\) | ||||
−0.198825 | + | 0.980035i | \(0.563713\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.39388 | −0.129673 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.0908 | − | 6.40329i | 0.422526 | − | 0.243946i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.46410 | + | 2.00000i | 0.131781 | + | 0.0760836i | 0.564441 | − | 0.825473i | \(-0.309092\pi\) |
−0.432660 | + | 0.901557i | \(0.642425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.17837 | + | 5.50510i | −0.120563 | + | 0.208820i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.8990 | + | 29.2699i | 0.640094 | + | 1.10868i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.7087i | 1.46201i | 0.682374 | + | 0.731003i | \(0.260948\pi\) | ||||
−0.682374 | + | 0.731003i | \(0.739052\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000i | 0.905177i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.4012 | + | 19.7474i | 0.428786 | + | 0.742679i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.0000 | − | 34.6410i | 0.751116 | − | 1.30097i | −0.196167 | − | 0.980571i | \(-0.562849\pi\) |
0.947282 | − | 0.320400i | \(-0.103817\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.2474 | + | 10.5352i | 0.683372 | + | 0.394545i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.874863 | − | 0.505103i | 0.0327180 | − | 0.0188898i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.92820 | 0.258378 | 0.129189 | − | 0.991620i | \(-0.458763\pi\) | ||||
0.129189 | + | 0.991620i | \(0.458763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4949 | −0.539818 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.6969 | − | 22.3417i | 1.43717 | − | 0.829749i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.27647 | − | 3.62372i | −0.232782 | − | 0.134396i | 0.379073 | − | 0.925367i | \(-0.376243\pi\) |
−0.611855 | + | 0.790970i | \(0.709576\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.9494 | + | 20.6969i | −0.441964 | + | 0.765504i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.24745 | − | 3.89270i | −0.0830114 | − | 0.143780i | 0.821531 | − | 0.570164i | \(-0.193120\pi\) |
−0.904542 | + | 0.426384i | \(0.859787\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 5.59264i | − | 0.206007i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 19.3939i | − | 0.713415i | −0.934216 | − | 0.356708i | \(-0.883899\pi\) | ||
0.934216 | − | 0.356708i | \(-0.116101\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.7313 | + | 27.2474i | 0.577126 | + | 0.999612i | 0.995807 | + | 0.0914785i | \(0.0291593\pi\) |
−0.418681 | + | 0.908133i | \(0.637507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.601021 | + | 1.04100i | −0.0220197 | + | 0.0381392i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.8712 | + | 6.27647i | 0.397224 | + | 0.229337i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.3461 | + | 23.8712i | −1.50874 | + | 0.871071i | −0.508792 | + | 0.860890i | \(0.669908\pi\) |
−0.999948 | + | 0.0101819i | \(0.996759\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.48188 | 0.199506 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.3939 | −1.43179 | −0.715897 | − | 0.698205i | \(-0.753982\pi\) | ||||
−0.715897 | + | 0.698205i | \(0.753982\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.7980 | + | 26.4415i | −1.66017 | + | 0.958502i | −0.687545 | + | 0.726142i | \(0.741312\pi\) |
−0.972630 | + | 0.232361i | \(0.925355\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.14966 | + | 3.55051i | 0.222633 | + | 0.128537i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.2207 | − | 22.8990i | 0.477373 | − | 0.826834i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.74745 | − | 9.95487i | −0.207258 | − | 0.358982i | 0.743592 | − | 0.668634i | \(-0.233121\pi\) |
−0.950850 | + | 0.309652i | \(0.899787\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.2911i | 1.23336i | 0.787212 | + | 0.616682i | \(0.211524\pi\) | ||||
−0.787212 | + | 0.616682i | \(0.788476\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.4949i | 1.31094i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.8988 | − | 41.3939i | −0.856262 | − | 1.48309i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.14643 | − | 7.18182i | 0.148371 | − | 0.256986i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.79796 | + | 2.19275i | 0.135555 | + | 0.0782627i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.4770 | + | 17.5959i | −1.08639 | + | 0.627227i | −0.932613 | − | 0.360879i | \(-0.882477\pi\) |
−0.153776 | + | 0.988106i | \(0.549143\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.4989 | 0.728856 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.5959 | 0.411783 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.27526 | + | 3.62302i | −0.222281 | + | 0.128334i | −0.607006 | − | 0.794697i | \(-0.707630\pi\) |
0.384725 | + | 0.923031i | \(0.374296\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.3629 | + | 15.7980i | 0.968029 | + | 0.558892i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.04100 | + | 1.80306i | −0.0367360 | + | 0.0636287i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.651531 | − | 1.12848i | −0.0229634 | − | 0.0397738i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 11.9494i | − | 0.420118i | −0.977689 | − | 0.210059i | \(-0.932634\pi\) | ||
0.977689 | − | 0.210059i | \(-0.0673656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24.4949i | − | 0.860132i | −0.902797 | − | 0.430066i | \(-0.858490\pi\) | ||
0.902797 | − | 0.430066i | \(-0.141510\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.953512 | + | 1.65153i | 0.0334001 | + | 0.0578506i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.8990 | − | 29.2699i | 0.591220 | − | 1.02402i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.8990 | − | 11.4887i | −0.694479 | − | 0.400958i | 0.110809 | − | 0.993842i | \(-0.464656\pi\) |
−0.805288 | + | 0.592884i | \(0.797989\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.6790 | + | 14.8258i | −0.895113 | + | 0.516794i | −0.875611 | − | 0.483016i | \(-0.839541\pi\) |
−0.0195015 | + | 0.999810i | \(0.506208\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.6206 | 0.577955 | 0.288978 | − | 0.957336i | \(-0.406685\pi\) | ||||
0.288978 | + | 0.957336i | \(0.406685\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.5959 | −1.30576 | −0.652880 | − | 0.757461i | \(-0.726439\pi\) | ||||
−0.652880 | + | 0.757461i | \(0.726439\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.6969 | + | 8.48528i | −0.509219 | + | 0.293998i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.32464 | + | 3.65153i | 0.218873 | + | 0.126366i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.58919 | − | 2.75255i | 0.0548648 | − | 0.0950286i | −0.837289 | − | 0.546761i | \(-0.815861\pi\) |
0.892153 | + | 0.451733i | \(0.149194\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0959 | + | 46.9315i | 0.934342 | + | 1.61833i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1.46075i | − | 0.0502515i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 14.2020i | − | 0.487988i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.92820 | + | 12.0000i | 0.237496 | + | 0.411355i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.00000 | + | 8.66025i | −0.171197 | + | 0.296521i | −0.938839 | − | 0.344358i | \(-0.888097\pi\) |
0.767642 | + | 0.640879i | \(0.221430\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.1010 | + | 5.83183i | 0.345044 | + | 0.199211i | 0.662500 | − | 0.749062i | \(-0.269495\pi\) |
−0.317456 | + | 0.948273i | \(0.602829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.2911 | − | 19.7980i | 1.17000 | − | 0.675498i | 0.216317 | − | 0.976323i | \(-0.430596\pi\) |
0.953679 | + | 0.300826i | \(0.0972622\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.92820 | −0.235839 | −0.117919 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117919 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.69694 | −0.0576976 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.89898 | + | 1.09638i | −0.0644185 | + | 0.0371920i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.8066 | + | 7.39388i | 0.433934 | + | 0.250532i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.28024 | − | 3.94949i | 0.0770861 | − | 0.133517i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.10102 | + | 14.0314i | 0.273552 | + | 0.473806i | 0.969769 | − | 0.244026i | \(-0.0784681\pi\) |
−0.696217 | + | 0.717832i | \(0.745135\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.27815i | − | 0.245207i | −0.992456 | − | 0.122604i | \(-0.960876\pi\) | ||
0.992456 | − | 0.122604i | \(-0.0391244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 52.8990i | − | 1.78019i | −0.455773 | − | 0.890096i | \(-0.650637\pi\) | ||
0.455773 | − | 0.890096i | \(-0.349363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.6595 | − | 39.2474i | −0.760832 | − | 1.31780i | −0.942422 | − | 0.334426i | \(-0.891458\pi\) |
0.181590 | − | 0.983374i | \(-0.441876\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.0505 | + | 19.1400i | −0.370622 | + | 0.641937i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −38.6969 | − | 22.3417i | −1.29494 | − | 0.747636i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.38378 | − | 1.37628i | 0.0796810 | − | 0.0460038i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −67.9465 | −2.26614 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.3031 | 0.509819 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.69694 | + | 1.55708i | −0.0896493 | + | 0.0517590i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.89270 | + | 2.24745i | 0.129255 | + | 0.0746253i | 0.563233 | − | 0.826298i | \(-0.309557\pi\) |
−0.433978 | + | 0.900923i | \(0.642891\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.460702 | + | 0.797959i | −0.0152637 | + | 0.0264376i | −0.873556 | − | 0.486723i | \(-0.838192\pi\) |
0.858293 | + | 0.513161i | \(0.171525\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.70204 | − | 15.0724i | −0.287996 | − | 0.498823i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.35340i | 0.143762i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.75255i | 0.0907983i | 0.998969 | + | 0.0453991i | \(0.0144560\pi\) | ||||
−0.998969 | + | 0.0453991i | \(0.985544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.9638 | + | 18.9898i | 0.360877 | + | 0.625057i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0000 | + | 20.7846i | −0.394558 | + | 0.683394i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.1010 | + | 7.56388i | 0.429831 | + | 0.248163i | 0.699274 | − | 0.714853i | \(-0.253507\pi\) |
−0.269444 | + | 0.963016i | \(0.586840\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.7846 | − | 12.0000i | 0.681188 | − | 0.393284i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.20713 | 0.0394775 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.0000 | −0.490029 | −0.245014 | − | 0.969519i | \(-0.578793\pi\) | ||||
−0.245014 | + | 0.969519i | \(0.578793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.9722 | − | 20.7686i | 1.17266 | − | 0.677036i | 0.218355 | − | 0.975869i | \(-0.429931\pi\) |
0.954305 | + | 0.298834i | \(0.0965976\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.8988 | − | 13.7980i | −0.778251 | − | 0.449323i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.5441 | + | 19.9949i | −0.375132 | + | 0.649747i | −0.990347 | − | 0.138612i | \(-0.955736\pi\) |
0.615215 | + | 0.788359i | \(0.289069\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.75255 | − | 4.76756i | −0.0893516 | − | 0.154762i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 10.7423i | − | 0.347976i | −0.984748 | − | 0.173988i | \(-0.944335\pi\) | ||
0.984748 | − | 0.173988i | \(-0.0556653\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.59592i | 0.181080i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.73885 | + | 13.4041i | 0.249901 | + | 0.432840i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.2474 | − | 21.2132i | 0.395079 | − | 0.684297i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.578317 | − | 0.333891i | −0.0186167 | − | 0.0107483i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.6495 | + | 24.6237i | −1.37152 | + | 0.791846i | −0.991119 | − | 0.132977i | \(-0.957546\pi\) |
−0.380398 | + | 0.924823i | \(0.624213\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.3383 | 0.620595 | 0.310298 | − | 0.950639i | \(-0.399571\pi\) | ||||
0.310298 | + | 0.950639i | \(0.399571\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.9898 | 0.929370 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.2474 | + | 15.7313i | −0.871723 | + | 0.503290i | −0.867920 | − | 0.496703i | \(-0.834544\pi\) |
−0.00380265 | + | 0.999993i | \(0.501210\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.3458 | + | 6.55051i | 0.362614 | + | 0.209355i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.2665 | + | 45.4949i | −0.837771 | + | 1.45106i | 0.0539833 | + | 0.998542i | \(0.482808\pi\) |
−0.891754 | + | 0.452520i | \(0.850525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.94949 | − | 3.37662i | −0.0621159 | − | 0.107588i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 19.5133i | − | 0.620486i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.75255i | 0.278034i | 0.990290 | + | 0.139017i | \(0.0443943\pi\) | ||||
−0.990290 | + | 0.139017i | \(0.955606\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.23375 | − | 5.60102i | −0.102517 | − | 0.177564i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.3485 | − | 52.5651i | 0.961146 | − | 1.66475i | 0.241514 | − | 0.970397i | \(-0.422356\pi\) |
0.719632 | − | 0.694356i | \(-0.244311\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2592.2.s.h.1727.1 | 8 | ||
3.2 | odd | 2 | 2592.2.s.a.1727.3 | 8 | |||
4.3 | odd | 2 | inner | 2592.2.s.h.1727.2 | 8 | ||
9.2 | odd | 6 | 864.2.c.a.863.4 | yes | 8 | ||
9.4 | even | 3 | 2592.2.s.a.863.4 | 8 | |||
9.5 | odd | 6 | inner | 2592.2.s.h.863.2 | 8 | ||
9.7 | even | 3 | 864.2.c.a.863.6 | yes | 8 | ||
12.11 | even | 2 | 2592.2.s.a.1727.4 | 8 | |||
36.7 | odd | 6 | 864.2.c.a.863.5 | yes | 8 | ||
36.11 | even | 6 | 864.2.c.a.863.3 | ✓ | 8 | ||
36.23 | even | 6 | inner | 2592.2.s.h.863.1 | 8 | ||
36.31 | odd | 6 | 2592.2.s.a.863.3 | 8 | |||
72.11 | even | 6 | 1728.2.c.g.1727.5 | 8 | |||
72.29 | odd | 6 | 1728.2.c.g.1727.6 | 8 | |||
72.43 | odd | 6 | 1728.2.c.g.1727.3 | 8 | |||
72.61 | even | 6 | 1728.2.c.g.1727.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.c.a.863.3 | ✓ | 8 | 36.11 | even | 6 | ||
864.2.c.a.863.4 | yes | 8 | 9.2 | odd | 6 | ||
864.2.c.a.863.5 | yes | 8 | 36.7 | odd | 6 | ||
864.2.c.a.863.6 | yes | 8 | 9.7 | even | 3 | ||
1728.2.c.g.1727.3 | 8 | 72.43 | odd | 6 | |||
1728.2.c.g.1727.4 | 8 | 72.61 | even | 6 | |||
1728.2.c.g.1727.5 | 8 | 72.11 | even | 6 | |||
1728.2.c.g.1727.6 | 8 | 72.29 | odd | 6 | |||
2592.2.s.a.863.3 | 8 | 36.31 | odd | 6 | |||
2592.2.s.a.863.4 | 8 | 9.4 | even | 3 | |||
2592.2.s.a.1727.3 | 8 | 3.2 | odd | 2 | |||
2592.2.s.a.1727.4 | 8 | 12.11 | even | 2 | |||
2592.2.s.h.863.1 | 8 | 36.23 | even | 6 | inner | ||
2592.2.s.h.863.2 | 8 | 9.5 | odd | 6 | inner | ||
2592.2.s.h.1727.1 | 8 | 1.1 | even | 1 | trivial | ||
2592.2.s.h.1727.2 | 8 | 4.3 | odd | 2 | inner |