Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3288,1,Mod(35,3288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3288, base_ring=CyclotomicField(136))
chi = DirichletCharacter(H, H._module([68, 68, 68, 117]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3288.35");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3288 = 2^{3} \cdot 3 \cdot 137 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3288.cj (of order \(136\), degree \(64\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.64092576154\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Coefficient field: | \(\Q(\zeta_{136})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{64} - x^{60} + x^{56} - x^{52} + x^{48} - x^{44} + x^{40} - x^{36} + x^{32} - x^{28} + x^{24} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{136}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{136} - \cdots)\) |
Embedding invariants
Embedding label | 1691.1 | ||
Root | \(0.948161 + 0.317791i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3288.1691 |
Dual form | 3288.1.cj.b.35.1 |
$q$-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 \(\left(\mathbb{Z}/3288\mathbb{Z}\right)^\times\).
\(n\) | \(823\) | \(1097\) | \(1645\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(e\left(\frac{19}{136}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.948161 | + | 0.317791i | −0.948161 | + | 0.317791i | ||||
\(3\) | 0.228951 | − | 0.973438i | 0.228951 | − | 0.973438i | ||||
\(4\) | 0.798017 | − | 0.602635i | 0.798017 | − | 0.602635i | ||||
\(5\) | 0 | 0 | 0.997600 | − | 0.0692444i | \(-0.0220588\pi\) | ||||
−0.997600 | + | 0.0692444i | \(0.977941\pi\) | |||||||
\(6\) | 0.0922684 | + | 0.995734i | 0.0922684 | + | 0.995734i | ||||
\(7\) | 0 | 0 | 0.914794 | − | 0.403921i | \(-0.132353\pi\) | ||||
−0.914794 | + | 0.403921i | \(0.867647\pi\) | |||||||
\(8\) | −0.565136 | + | 0.824997i | −0.565136 | + | 0.824997i | ||||
\(9\) | −0.895163 | − | 0.445738i | −0.895163 | − | 0.445738i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.265765 | − | 1.90520i | 0.265765 | − | 1.90520i | −0.138156 | − | 0.990410i | \(-0.544118\pi\) |
0.403921 | − | 0.914794i | \(-0.367647\pi\) | |||||||
\(12\) | −0.403921 | − | 0.914794i | −0.403921 | − | 0.914794i | ||||
\(13\) | 0 | 0 | −0.0230979 | − | 0.999733i | \(-0.507353\pi\) | ||||
0.0230979 | + | 0.999733i | \(0.492647\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.273663 | − | 0.961826i | 0.273663 | − | 0.961826i | ||||
\(17\) | 1.44147 | − | 0.987432i | 1.44147 | − | 0.987432i | 0.445738 | − | 0.895163i | \(-0.352941\pi\) |
0.995734 | − | 0.0922684i | \(-0.0294118\pi\) | |||||||
\(18\) | 0.990410 | + | 0.138156i | 0.990410 | + | 0.138156i | ||||
\(19\) | 0.377767 | + | 1.60617i | 0.377767 | + | 1.60617i | 0.739009 | + | 0.673696i | \(0.235294\pi\) |
−0.361242 | + | 0.932472i | \(0.617647\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.353470 | + | 1.89090i | 0.353470 | + | 1.89090i | ||||
\(23\) | 0 | 0 | 0.993337 | − | 0.115243i | \(-0.0367647\pi\) | ||||
−0.993337 | + | 0.115243i | \(0.963235\pi\) | |||||||
\(24\) | 0.673696 | + | 0.739009i | 0.673696 | + | 0.739009i | ||||
\(25\) | 0.990410 | − | 0.138156i | 0.990410 | − | 0.138156i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.638847 | + | 0.769334i | −0.638847 | + | 0.769334i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.783885 | − | 0.620906i | \(-0.786765\pi\) | ||||
0.783885 | + | 0.620906i | \(0.213235\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.811724 | − | 0.584041i | \(-0.801471\pi\) | ||||
0.811724 | + | 0.584041i | \(0.198529\pi\) | |||||||
\(32\) | 0.0461835 | + | 0.998933i | 0.0461835 | + | 0.998933i | ||||
\(33\) | −1.79375 | − | 0.694903i | −1.79375 | − | 0.694903i | ||||
\(34\) | −1.05295 | + | 1.39433i | −1.05295 | + | 1.39433i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.982973 | + | 0.183750i | −0.982973 | + | 0.183750i | ||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | −0.868610 | − | 1.40285i | −0.868610 | − | 1.40285i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.785192 | − | 0.325237i | −0.785192 | − | 0.325237i | −0.0461835 | − | 0.998933i | \(-0.514706\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0371073 | + | 0.227480i | −0.0371073 | + | 0.227480i | −0.998933 | − | 0.0461835i | \(-0.985294\pi\) |
0.961826 | + | 0.273663i | \(0.0882353\pi\) | |||||||
\(44\) | −0.936057 | − | 1.68054i | −0.936057 | − | 1.68054i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.884629 | − | 0.466296i | \(-0.845588\pi\) | ||||
0.884629 | + | 0.466296i | \(0.154412\pi\) | |||||||
\(48\) | −0.873622 | − | 0.486604i | −0.873622 | − | 0.486604i | ||||
\(49\) | 0.673696 | − | 0.739009i | 0.673696 | − | 0.739009i | ||||
\(50\) | −0.895163 | + | 0.445738i | −0.895163 | + | 0.445738i | ||||
\(51\) | −0.631178 | − | 1.62926i | −0.631178 | − | 1.62926i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.811724 | − | 0.584041i | \(-0.198529\pi\) | ||||
−0.811724 | + | 0.584041i | \(0.801471\pi\) | |||||||
\(54\) | 0.361242 | − | 0.932472i | 0.361242 | − | 0.932472i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.64999 | 1.64999 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.78269 | − | 0.165190i | −1.78269 | − | 0.165190i | −0.850217 | − | 0.526432i | \(-0.823529\pi\) |
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.638847 | − | 0.769334i | \(-0.279412\pi\) | ||||
−0.638847 | + | 0.769334i | \(0.720588\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.361242 | − | 0.932472i | −0.361242 | − | 0.932472i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.92160 | + | 0.0888409i | 1.92160 | + | 0.0888409i | ||||
\(67\) | −0.789689 | − | 0.754023i | −0.789689 | − | 0.754023i | 0.183750 | − | 0.982973i | \(-0.441176\pi\) |
−0.973438 | + | 0.228951i | \(0.926471\pi\) | |||||||
\(68\) | 0.555259 | − | 1.65667i | 0.555259 | − | 1.65667i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.251374 | − | 0.967890i | \(-0.419118\pi\) | ||||
−0.251374 | + | 0.967890i | \(0.580882\pi\) | |||||||
\(72\) | 0.873622 | − | 0.486604i | 0.873622 | − | 0.486604i | ||||
\(73\) | 0.0861296 | − | 0.0333668i | 0.0861296 | − | 0.0333668i | −0.317791 | − | 0.948161i | \(-0.602941\pi\) |
0.403921 | + | 0.914794i | \(0.367647\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0922684 | − | 0.995734i | 0.0922684 | − | 0.995734i | ||||
\(76\) | 1.26940 | + | 1.05409i | 1.26940 | + | 1.05409i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.339607 | − | 0.940567i | \(-0.389706\pi\) | ||||
−0.339607 | + | 0.940567i | \(0.610294\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.602635 | + | 0.798017i | 0.602635 | + | 0.798017i | ||||
\(82\) | 0.847846 | + | 0.0588498i | 0.847846 | + | 0.0588498i | ||||
\(83\) | −1.67521 | + | 1.09157i | −1.67521 | + | 1.09157i | −0.824997 | + | 0.565136i | \(0.808824\pi\) |
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.0371073 | − | 0.227480i | −0.0371073 | − | 0.227480i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.42160 | + | 1.29596i | 1.42160 | + | 1.29596i | ||||
\(89\) | 1.29577 | − | 1.48906i | 1.29577 | − | 1.48906i | 0.526432 | − | 0.850217i | \(-0.323529\pi\) |
0.769334 | − | 0.638847i | \(-0.220588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.982973 | + | 0.183750i | 0.982973 | + | 0.183750i | ||||
\(97\) | −0.873622 | − | 0.513396i | −0.873622 | − | 0.513396i | − | 1.00000i | \(-0.5\pi\) | |
−0.873622 | + | 0.486604i | \(0.838235\pi\) | |||||||
\(98\) | −0.403921 | + | 0.914794i | −0.403921 | + | 0.914794i | ||||
\(99\) | −1.08713 | + | 1.58701i | −1.08713 | + | 1.58701i | ||||
\(100\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(101\) | 0 | 0 | −0.973438 | − | 0.228951i | \(-0.926471\pi\) | ||||
0.973438 | + | 0.228951i | \(0.0735294\pi\) | |||||||
\(102\) | 1.11622 | + | 1.34421i | 1.11622 | + | 1.34421i | ||||
\(103\) | 0 | 0 | −0.798017 | − | 0.602635i | \(-0.794118\pi\) | ||||
0.798017 | + | 0.602635i | \(0.205882\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.86295 | + | 0.0861296i | 1.86295 | + | 0.0861296i | 0.948161 | − | 0.317791i | \(-0.102941\pi\) |
0.914794 | + | 0.403921i | \(0.132353\pi\) | |||||||
\(108\) | −0.0461835 | + | 0.998933i | −0.0461835 | + | 0.998933i | ||||
\(109\) | 0 | 0 | −0.873622 | − | 0.486604i | \(-0.838235\pi\) | ||||
0.873622 | + | 0.486604i | \(0.161765\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.953083 | + | 1.62182i | 0.953083 | + | 1.62182i | 0.769334 | + | 0.638847i | \(0.220588\pi\) |
0.183750 | + | 0.982973i | \(0.441176\pi\) | |||||||
\(114\) | −1.56446 | + | 0.524354i | −1.56446 | + | 0.524354i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.74277 | − | 0.409896i | 1.74277 | − | 0.409896i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.59735 | − | 0.739009i | −2.59735 | − | 0.739009i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.496369 | + | 0.689873i | −0.496369 | + | 0.689873i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(128\) | 0.638847 | + | 0.769334i | 0.638847 | + | 0.769334i | ||||
\(129\) | 0.212941 | + | 0.0882033i | 0.212941 | + | 0.0882033i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.180675 | − | 1.55732i | 0.180675 | − | 1.55732i | −0.526432 | − | 0.850217i | \(-0.676471\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(132\) | −1.85022 | + | 0.526432i | −1.85022 | + | 0.526432i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.988373 | + | 0.463978i | 0.988373 | + | 0.463978i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.74724i | 1.74724i | ||||||||
\(137\) | −0.973438 | − | 0.228951i | −0.973438 | − | 0.228951i | ||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.116788 | − | 0.348448i | −0.116788 | − | 0.348448i | 0.873622 | − | 0.486604i | \(-0.161765\pi\) |
−0.990410 | + | 0.138156i | \(0.955882\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.673696 | + | 0.739009i | −0.673696 | + | 0.739009i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.0710610 | + | 0.0590083i | −0.0710610 | + | 0.0590083i | ||||
\(147\) | −0.565136 | − | 0.824997i | −0.565136 | − | 0.824997i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.206405 | − | 0.978467i | \(-0.566176\pi\) | ||||
0.206405 | + | 0.978467i | \(0.433824\pi\) | |||||||
\(150\) | 0.228951 | + | 0.973438i | 0.228951 | + | 0.973438i | ||||
\(151\) | 0 | 0 | −0.673696 | − | 0.739009i | \(-0.735294\pi\) | ||||
0.673696 | + | 0.739009i | \(0.264706\pi\) | |||||||
\(152\) | −1.53857 | − | 0.596047i | −1.53857 | − | 0.596047i | ||||
\(153\) | −1.73049 | + | 0.241393i | −1.73049 | + | 0.241393i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.656446 | − | 0.754373i | \(-0.727941\pi\) | ||||
0.656446 | + | 0.754373i | \(0.272059\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.824997 | − | 0.565136i | −0.824997 | − | 0.565136i | ||||
\(163\) | 0.472868 | − | 0.170737i | 0.472868 | − | 0.170737i | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) |
0.565136 | + | 0.824997i | \(0.308824\pi\) | |||||||
\(164\) | −0.822596 | + | 0.213639i | −0.822596 | + | 0.213639i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.24148 | − | 1.56735i | 1.24148 | − | 1.56735i | ||||
\(167\) | 0 | 0 | 0.0461835 | − | 0.998933i | \(-0.485294\pi\) | ||||
−0.0461835 | + | 0.998933i | \(0.514706\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.998933 | + | 0.0461835i | −0.998933 | + | 0.0461835i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.377767 | − | 1.60617i | 0.377767 | − | 1.60617i | ||||
\(172\) | 0.107475 | + | 0.203895i | 0.107475 | + | 0.203895i | ||||
\(173\) | 0 | 0 | 0.228951 | − | 0.973438i | \(-0.426471\pi\) | ||||
−0.228951 | + | 0.973438i | \(0.573529\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.75974 | − | 0.777003i | −1.75974 | − | 0.777003i | ||||
\(177\) | −0.568950 | + | 1.69752i | −0.568950 | + | 1.69752i | ||||
\(178\) | −0.755383 | + | 1.82366i | −0.755383 | + | 1.82366i | ||||
\(179\) | −0.648818 | + | 0.200916i | −0.648818 | + | 0.200916i | −0.602635 | − | 0.798017i | \(-0.705882\pi\) |
−0.0461835 | + | 0.998933i | \(0.514706\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.873622 | − | 0.486604i | \(-0.161765\pi\) | ||||
−0.873622 | + | 0.486604i | \(0.838235\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.49817 | − | 3.00872i | −1.49817 | − | 3.00872i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.545930 | − | 0.837831i | \(-0.683824\pi\) | ||||
0.545930 | + | 0.837831i | \(0.316176\pi\) | |||||||
\(192\) | −0.990410 | + | 0.138156i | −0.990410 | + | 0.138156i | ||||
\(193\) | 1.94709 | + | 0.363975i | 1.94709 | + | 0.363975i | 0.998933 | + | 0.0461835i | \(0.0147059\pi\) |
0.948161 | + | 0.317791i | \(0.102941\pi\) | |||||||
\(194\) | 0.991487 | + | 0.209152i | 0.991487 | + | 0.209152i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.0922684 | − | 0.995734i | 0.0922684 | − | 0.995734i | ||||
\(197\) | 0 | 0 | 0.961826 | − | 0.273663i | \(-0.0882353\pi\) | ||||
−0.961826 | + | 0.273663i | \(0.911765\pi\) | |||||||
\(198\) | 0.526432 | − | 1.85022i | 0.526432 | − | 1.85022i | ||||
\(199\) | 0 | 0 | 0.295806 | − | 0.955248i | \(-0.404412\pi\) | ||||
−0.295806 | + | 0.955248i | \(0.595588\pi\) | |||||||
\(200\) | −0.445738 | + | 0.895163i | −0.445738 | + | 0.895163i | ||||
\(201\) | −0.914794 | + | 0.596079i | −0.914794 | + | 0.596079i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.48554 | − | 0.919806i | −1.48554 | − | 0.919806i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.16048 | − | 0.292861i | 3.16048 | − | 0.292861i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.283304 | + | 0.568950i | −0.283304 | + | 0.568950i | −0.990410 | − | 0.138156i | \(-0.955882\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.79375 | + | 0.510366i | −1.79375 | + | 0.510366i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.273663 | − | 0.961826i | −0.273663 | − | 0.961826i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.0127611 | − | 0.0914812i | −0.0127611 | − | 0.0914812i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.986955 | − | 0.160996i | \(-0.0514706\pi\) | ||||
−0.986955 | + | 0.160996i | \(0.948529\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.948161 | − | 0.317791i | −0.948161 | − | 0.317791i | ||||
\(226\) | −1.41908 | − | 1.23486i | −1.41908 | − | 1.23486i | ||||
\(227\) | 0.0215409 | − | 0.0408661i | 0.0215409 | − | 0.0408661i | −0.873622 | − | 0.486604i | \(-0.838235\pi\) |
0.895163 | + | 0.445738i | \(0.147059\pi\) | |||||||
\(228\) | 1.31672 | − | 0.994344i | 1.31672 | − | 0.994344i | ||||
\(229\) | 0 | 0 | −0.690585 | − | 0.723251i | \(-0.742647\pi\) | ||||
0.690585 | + | 0.723251i | \(0.257353\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.740791 | + | 1.78843i | −0.740791 | + | 1.78843i | −0.138156 | + | 0.990410i | \(0.544118\pi\) |
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.52217 | + | 0.942485i | −1.52217 | + | 0.942485i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.466296 | − | 0.884629i | \(-0.654412\pi\) | ||||
0.466296 | + | 0.884629i | \(0.345588\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.941347 | − | 1.44467i | 0.941347 | − | 1.44467i | 0.0461835 | − | 0.998933i | \(-0.485294\pi\) |
0.895163 | − | 0.445738i | \(-0.147059\pi\) | |||||||
\(242\) | 2.69755 | − | 0.124715i | 2.69755 | − | 0.124715i | ||||
\(243\) | 0.914794 | − | 0.403921i | 0.914794 | − | 0.403921i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.251402 | − | 0.811852i | 0.251402 | − | 0.811852i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.679033 | + | 1.88063i | 0.679033 | + | 1.88063i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.143110 | + | 1.23354i | 0.143110 | + | 1.23354i | 0.850217 | + | 0.526432i | \(0.176471\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.850217 | − | 0.526432i | −0.850217 | − | 0.526432i | ||||
\(257\) | 0.761460 | + | 1.11159i | 0.761460 | + | 1.11159i | 0.990410 | + | 0.138156i | \(0.0441176\pi\) |
−0.228951 | + | 0.973438i | \(0.573529\pi\) | |||||||
\(258\) | −0.229933 | − | 0.0159599i | −0.229933 | − | 0.0159599i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.323596 | + | 1.53401i | 0.323596 | + | 1.53401i | ||||
\(263\) | 0 | 0 | −0.990410 | − | 0.138156i | \(-0.955882\pi\) | ||||
0.990410 | + | 0.138156i | \(0.0441176\pi\) | |||||||
\(264\) | 1.58701 | − | 1.08713i | 1.58701 | − | 1.08713i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.15285 | − | 1.60227i | −1.15285 | − | 1.60227i | ||||
\(268\) | −1.08459 | − | 0.125829i | −1.08459 | − | 0.125829i | ||||
\(269\) | 0 | 0 | −0.0692444 | − | 0.997600i | \(-0.522059\pi\) | ||||
0.0692444 | + | 0.997600i | \(0.477941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.424943 | − | 0.905220i | \(-0.360294\pi\) | ||||
−0.424943 | + | 0.905220i | \(0.639706\pi\) | |||||||
\(272\) | −0.555259 | − | 1.65667i | −0.555259 | − | 1.65667i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.995734 | − | 0.0922684i | 0.995734 | − | 0.0922684i | ||||
\(275\) | − | 1.92365i | − | 1.92365i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.905220 | − | 0.424943i | \(-0.860294\pi\) | ||||
0.905220 | + | 0.424943i | \(0.139706\pi\) | |||||||
\(278\) | 0.221468 | + | 0.293271i | 0.221468 | + | 0.293271i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.794087 | + | 1.79844i | 0.794087 | + | 1.79844i | 0.565136 | + | 0.824997i | \(0.308824\pi\) |
0.228951 | + | 0.973438i | \(0.426471\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.982973 | + | 1.18375i | 0.982973 | + | 1.18375i | 0.982973 | + | 0.183750i | \(0.0588235\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.403921 | − | 0.914794i | 0.403921 | − | 0.914794i | ||||
\(289\) | 0.741580 | − | 1.91424i | 0.741580 | − | 1.91424i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.699775 | + | 0.732875i | −0.699775 | + | 0.732875i | ||||
\(292\) | 0.0486249 | − | 0.0785319i | 0.0486249 | − | 0.0785319i | ||||
\(293\) | 0 | 0 | 0.973438 | − | 0.228951i | \(-0.0735294\pi\) | ||||
−0.973438 | + | 0.228951i | \(0.926471\pi\) | |||||||
\(294\) | 0.798017 | + | 0.602635i | 0.798017 | + | 0.602635i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.29596 | + | 1.42160i | 1.29596 | + | 1.42160i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.526432 | − | 0.850217i | −0.526432 | − | 0.850217i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.64823 | + | 0.0762025i | 1.64823 | + | 0.0762025i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.56407 | − | 0.778814i | 1.56407 | − | 0.778814i | ||||
\(307\) | −1.40392 | − | 0.914794i | −1.40392 | − | 0.914794i | −0.403921 | − | 0.914794i | \(-0.632353\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.184956 | + | 0.418885i | −0.184956 | + | 0.418885i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) |
0.798017 | + | 0.602635i | \(0.205882\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.986955 | − | 0.160996i | \(-0.948529\pi\) | ||||
0.986955 | + | 0.160996i | \(0.0514706\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.510366 | − | 1.79375i | 0.510366 | − | 1.79375i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.13052 | + | 1.94223i | 2.13052 | + | 1.94223i | ||||
\(324\) | 0.961826 | + | 0.273663i | 0.961826 | + | 0.273663i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.394096 | + | 0.312159i | −0.394096 | + | 0.312159i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.712061 | − | 0.463978i | 0.712061 | − | 0.463978i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.381387 | − | 1.80797i | 0.381387 | − | 1.80797i | −0.183750 | − | 0.982973i | \(-0.558824\pi\) |
0.565136 | − | 0.824997i | \(-0.308824\pi\) | |||||||
\(332\) | −0.679033 | + | 1.88063i | −0.679033 | + | 1.88063i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.78842 | + | 0.890525i | 1.78842 | + | 0.890525i | 0.914794 | + | 0.403921i | \(0.132353\pi\) |
0.873622 | + | 0.486604i | \(0.161765\pi\) | |||||||
\(338\) | 0.932472 | − | 0.361242i | 0.932472 | − | 0.361242i | ||||
\(339\) | 1.79695 | − | 0.556451i | 1.79695 | − | 0.556451i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.152242 | + | 1.64296i | 0.152242 | + | 1.64296i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.166699 | − | 0.159170i | −0.166699 | − | 0.159170i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.0666624 | − | 0.172075i | −0.0666624 | − | 0.172075i | 0.895163 | − | 0.445738i | \(-0.147059\pi\) |
−0.961826 | + | 0.273663i | \(0.911765\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.955248 | − | 0.295806i | \(-0.904412\pi\) | ||||
0.955248 | + | 0.295806i | \(0.0955882\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.91545 | + | 0.177492i | 1.91545 | + | 0.177492i | ||||
\(353\) | −1.36053 | − | 0.491242i | −1.36053 | − | 0.491242i | −0.445738 | − | 0.895163i | \(-0.647059\pi\) |
−0.914794 | + | 0.403921i | \(0.867647\pi\) | |||||||
\(354\) | − | 1.79033i | − | 1.79033i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.136682 | − | 1.96917i | 0.136682 | − | 1.96917i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.551334 | − | 0.396689i | 0.551334 | − | 0.396689i | ||||
\(359\) | 0 | 0 | −0.620906 | − | 0.783885i | \(-0.713235\pi\) | ||||
0.620906 | + | 0.783885i | \(0.286765\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.54190 | + | 0.767777i | −1.54190 | + | 0.767777i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.31404 | + | 2.35916i | −1.31404 | + | 2.35916i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.486604 | − | 0.873622i | \(-0.661765\pi\) | ||||
0.486604 | + | 0.873622i | \(0.338235\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.557905 | + | 0.641131i | 0.557905 | + | 0.641131i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.526432 | − | 0.850217i | \(-0.676471\pi\) | ||||
0.526432 | + | 0.850217i | \(0.323529\pi\) | |||||||
\(374\) | 2.37665 | + | 2.37665i | 2.37665 | + | 2.37665i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.0737104 | + | 1.59433i | 0.0737104 | + | 1.59433i | 0.638847 | + | 0.769334i | \(0.279412\pi\) |
−0.565136 | + | 0.824997i | \(0.691176\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.486604 | − | 0.873622i | \(-0.338235\pi\) | ||||
−0.486604 | + | 0.873622i | \(0.661765\pi\) | |||||||
\(384\) | 0.895163 | − | 0.445738i | 0.895163 | − | 0.445738i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.96183 | + | 0.273663i | −1.96183 | + | 0.273663i | ||||
\(387\) | 0.134613 | − | 0.187091i | 0.134613 | − | 0.187091i | ||||
\(388\) | −1.00656 | + | 0.116777i | −1.00656 | + | 0.116777i | ||||
\(389\) | 0 | 0 | −0.183750 | − | 0.982973i | \(-0.558824\pi\) | ||||
0.183750 | + | 0.982973i | \(0.441176\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.228951 | + | 0.973438i | 0.228951 | + | 0.973438i | ||||
\(393\) | −1.47459 | − | 0.532426i | −1.47459 | − | 0.532426i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0888409 | + | 1.92160i | 0.0888409 | + | 1.92160i | ||||
\(397\) | 0 | 0 | 0.739009 | − | 0.673696i | \(-0.235294\pi\) | ||||
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.138156 | − | 0.990410i | 0.138156 | − | 0.990410i | ||||
\(401\) | −1.76507 | + | 0.731115i | −1.76507 | + | 0.731115i | −0.769334 | + | 0.638847i | \(0.779412\pi\) |
−0.995734 | + | 0.0922684i | \(0.970588\pi\) | |||||||
\(402\) | 0.677943 | − | 0.855892i | 0.677943 | − | 0.855892i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.70083 | + | 0.400033i | 1.70083 | + | 0.400033i | ||||
\(409\) | −1.14279 | + | 0.383024i | −1.14279 | + | 0.383024i | −0.824997 | − | 0.565136i | \(-0.808824\pi\) |
−0.317791 | + | 0.948161i | \(0.602941\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.445738 | + | 0.895163i | −0.445738 | + | 0.895163i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.365931 | + | 0.0339085i | −0.365931 | + | 0.0339085i | ||||
\(418\) | −2.90357 | + | 1.28205i | −2.90357 | + | 1.28205i | ||||
\(419\) | 0.681142 | − | 0.994344i | 0.681142 | − | 0.994344i | −0.317791 | − | 0.948161i | \(-0.602941\pi\) |
0.998933 | − | 0.0461835i | \(-0.0147059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(422\) | 0.0878098 | − | 0.629488i | 0.0878098 | − | 0.629488i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.29123 | − | 1.17711i | 1.29123 | − | 1.17711i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.53857 | − | 1.05395i | 1.53857 | − | 1.05395i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.754373 | − | 0.656446i | \(-0.227941\pi\) | ||||
−0.754373 | + | 0.656446i | \(0.772059\pi\) | |||||||
\(432\) | 0.565136 | + | 0.824997i | 0.565136 | + | 0.824997i | ||||
\(433\) | 0.0507723 | + | 0.271608i | 0.0507723 | + | 0.271608i | 0.998933 | − | 0.0461835i | \(-0.0147059\pi\) |
−0.948161 | + | 0.317791i | \(0.897059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0.0411715 | + | 0.0826835i | 0.0411715 | + | 0.0826835i | ||||
\(439\) | 0 | 0 | 0.486604 | − | 0.873622i | \(-0.338235\pi\) | ||||
−0.486604 | + | 0.873622i | \(0.661765\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.932472 | + | 0.361242i | −0.932472 | + | 0.361242i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0127611 | + | 0.276018i | 0.0127611 | + | 0.276018i | 0.995734 | + | 0.0922684i | \(0.0294118\pi\) |
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.840204 | + | 1.35698i | 0.840204 | + | 1.35698i | 0.932472 | + | 0.361242i | \(0.117647\pi\) |
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(450\) | 1.00000 | 1.00000 | ||||||||
\(451\) | −0.828320 | + | 1.40952i | −0.828320 | + | 1.40952i | ||||
\(452\) | 1.73794 | + | 0.719879i | 1.73794 | + | 0.719879i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.00743733 | + | 0.0455932i | −0.00743733 | + | 0.0455932i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.932472 | + | 1.36124i | −0.932472 | + | 1.36124i | ||||
\(457\) | 1.79838 | − | 0.844224i | 1.79838 | − | 0.844224i | 0.850217 | − | 0.526432i | \(-0.176471\pi\) |
0.948161 | − | 0.317791i | \(-0.102941\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.161215 | + | 1.73979i | −0.161215 | + | 1.73979i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.895163 | − | 0.445738i | \(-0.147059\pi\) | ||||
−0.895163 | + | 0.445738i | \(0.852941\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.620906 | − | 0.783885i | \(-0.713235\pi\) | ||||
0.620906 | + | 0.783885i | \(0.286765\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.134042 | − | 1.93113i | 0.134042 | − | 1.93113i | ||||
\(467\) | −0.271585 | + | 1.45285i | −0.271585 | + | 1.45285i | 0.526432 | + | 0.850217i | \(0.323529\pi\) |
−0.798017 | + | 0.602635i | \(0.794118\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.14374 | − | 1.37736i | 1.14374 | − | 1.37736i | ||||
\(473\) | 0.423533 | + | 0.131153i | 0.423533 | + | 0.131153i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.596047 | + | 1.53857i | 0.596047 | + | 1.53857i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.317791 | − | 0.948161i | \(-0.397059\pi\) | ||||
−0.317791 | + | 0.948161i | \(0.602941\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.433444 | + | 1.66893i | −0.433444 | + | 1.66893i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.51808 | + | 0.975509i | −2.51808 | + | 0.975509i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.739009 | + | 0.673696i | −0.739009 | + | 0.673696i | ||||
\(487\) | 0 | 0 | −0.769334 | − | 0.638847i | \(-0.779412\pi\) | ||||
0.769334 | + | 0.638847i | \(0.220588\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0579382 | − | 0.499398i | −0.0579382 | − | 0.499398i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.311413 | − | 1.47626i | 0.311413 | − | 1.47626i | −0.486604 | − | 0.873622i | \(-0.661765\pi\) |
0.798017 | − | 0.602635i | \(-0.205882\pi\) | |||||||
\(492\) | 0.0196306 | + | 0.849659i | 0.0196306 | + | 0.849659i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.24148 | − | 1.56735i | −1.24148 | − | 1.56735i | ||||
\(499\) | −0.136374 | − | 0.124322i | −0.136374 | − | 0.124322i | 0.602635 | − | 0.798017i | \(-0.294118\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.527700 | − | 1.12411i | −0.527700 | − | 1.12411i | ||||
\(503\) | 0 | 0 | 0.723251 | − | 0.690585i | \(-0.242647\pi\) | ||||
−0.723251 | + | 0.690585i | \(0.757353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.183750 | + | 0.982973i | −0.183750 | + | 0.982973i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.403921 | − | 0.914794i | \(-0.367647\pi\) | ||||
−0.403921 | + | 0.914794i | \(0.632353\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.973438 | + | 0.228951i | 0.973438 | + | 0.228951i | ||||
\(513\) | −1.47701 | − | 0.735466i | −1.47701 | − | 0.735466i | ||||
\(514\) | −1.07524 | − | 0.811985i | −1.07524 | − | 0.811985i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.223085 | − | 0.0579382i | 0.223085 | − | 0.0579382i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.455097 | − | 1.75231i | −0.455097 | − | 1.75231i | −0.638847 | − | 0.769334i | \(-0.720588\pi\) |
0.183750 | − | 0.982973i | \(-0.441176\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.275134 | + | 1.97237i | 0.275134 | + | 1.97237i | 0.228951 | + | 0.973438i | \(0.426471\pi\) |
0.0461835 | + | 0.998933i | \(0.485294\pi\) | |||||||
\(524\) | −0.794316 | − | 1.35165i | −0.794316 | − | 1.35165i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.15926 | + | 1.53511i | −1.15926 | + | 1.53511i | ||||
\(529\) | 0.973438 | − | 0.228951i | 0.973438 | − | 0.228951i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.52217 | + | 0.942485i | 1.52217 | + | 0.942485i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.60227 | + | 1.15285i | 1.60227 | + | 1.15285i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.06835 | − | 0.225365i | 1.06835 | − | 0.225365i | ||||
\(537\) | 0.0470318 | + | 0.677584i | 0.0470318 | + | 0.677584i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.22892 | − | 1.47993i | −1.22892 | − | 1.47993i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.403921 | − | 0.914794i | \(-0.632353\pi\) | ||||
0.403921 | + | 0.914794i | \(0.367647\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.05295 | + | 1.39433i | 1.05295 | + | 1.39433i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.47802i | 1.47802i | 0.673696 | + | 0.739009i | \(0.264706\pi\) | ||||
−0.673696 | + | 0.739009i | \(0.735294\pi\) | |||||||
\(548\) | −0.914794 | + | 0.403921i | −0.914794 | + | 0.403921i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.611320 | + | 1.82393i | 0.611320 | + | 1.82393i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.303186 | − | 0.207687i | −0.303186 | − | 0.207687i | ||||
\(557\) | 0 | 0 | 0.769334 | − | 0.638847i | \(-0.220588\pi\) | ||||
−0.769334 | + | 0.638847i | \(0.779412\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.27181 | + | 0.769523i | −3.27181 | + | 0.769523i | ||||
\(562\) | −1.32445 | − | 1.45285i | −1.32445 | − | 1.45285i | ||||
\(563\) | −0.673696 | − | 0.260991i | −0.673696 | − | 0.260991i | − | 1.00000i | \(-0.5\pi\) | |
−0.673696 | + | 0.739009i | \(0.735294\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.30820 | − | 0.810004i | −1.30820 | − | 0.810004i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.0408661 | + | 1.76879i | −0.0408661 | + | 1.76879i | 0.445738 | + | 0.895163i | \(0.352941\pi\) |
−0.486604 | + | 0.873622i | \(0.661765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.159170 | − | 1.37197i | −0.159170 | − | 1.37197i | −0.798017 | − | 0.602635i | \(-0.794118\pi\) |
0.638847 | − | 0.769334i | \(-0.279412\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.0922684 | + | 0.995734i | −0.0922684 | + | 0.995734i | ||||
\(577\) | 0.367336 | − | 0.463756i | 0.367336 | − | 0.463756i | −0.565136 | − | 0.824997i | \(-0.691176\pi\) |
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(578\) | −0.0948084 | + | 2.05067i | −0.0948084 | + | 2.05067i | ||||
\(579\) | 0.800095 | − | 1.81204i | 0.800095 | − | 1.81204i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.430598 | − | 0.917266i | 0.430598 | − | 0.917266i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.0211475 | + | 0.0899135i | −0.0211475 | + | 0.0899135i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.963154 | + | 0.425274i | 0.963154 | + | 0.425274i | 0.824997 | − | 0.565136i | \(-0.191176\pi\) |
0.138156 | + | 0.990410i | \(0.455882\pi\) | |||||||
\(588\) | −0.948161 | − | 0.317791i | −0.948161 | − | 0.317791i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.37786 | + | 1.44303i | 1.37786 | + | 1.44303i | 0.739009 | + | 0.673696i | \(0.235294\pi\) |
0.638847 | + | 0.769334i | \(0.279412\pi\) | |||||||
\(594\) | −1.68054 | − | 0.936057i | −1.68054 | − | 0.936057i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.986955 | − | 0.160996i | \(-0.0514706\pi\) | ||||
−0.986955 | + | 0.160996i | \(0.948529\pi\) | |||||||
\(600\) | 0.769334 | + | 0.638847i | 0.769334 | + | 0.638847i | ||||
\(601\) | 0.806661 | + | 1.12113i | 0.806661 | + | 1.12113i | 0.990410 | + | 0.138156i | \(0.0441176\pi\) |
−0.183750 | + | 0.982973i | \(0.558824\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.370803 | + | 1.02697i | 0.370803 | + | 1.02697i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) | ||||
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(608\) | −1.58701 | + | 0.451543i | −1.58701 | + | 0.451543i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.23549 | + | 1.23549i | −1.23549 | + | 1.23549i | ||||
\(613\) | 0 | 0 | 0.995734 | − | 0.0922684i | \(-0.0294118\pi\) | ||||
−0.995734 | + | 0.0922684i | \(0.970588\pi\) | |||||||
\(614\) | 1.62186 | + | 0.421217i | 1.62186 | + | 0.421217i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.434164 | − | 0.145517i | −0.434164 | − | 0.145517i | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) |
−0.526432 | + | 0.850217i | \(0.676471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.572616 | − | 0.148716i | −0.572616 | − | 0.148716i | −0.0461835 | − | 0.998933i | \(-0.514706\pi\) |
−0.526432 | + | 0.850217i | \(0.676471\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.961826 | − | 0.273663i | 0.961826 | − | 0.273663i | ||||
\(626\) | 0.0422498 | − | 0.455948i | 0.0422498 | − | 0.455948i | ||||
\(627\) | 0.438510 | − | 3.14358i | 0.438510 | − | 3.14358i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.545930 | − | 0.837831i | \(-0.683824\pi\) | ||||
0.545930 | + | 0.837831i | \(0.316176\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.488975 | + | 0.406040i | 0.488975 | + | 0.406040i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.34421 | − | 0.748723i | 1.34421 | − | 0.748723i | 0.361242 | − | 0.932472i | \(-0.382353\pi\) |
0.982973 | + | 0.183750i | \(0.0588235\pi\) | |||||||
\(642\) | 0.0861296 | + | 1.86295i | 0.0861296 | + | 1.86295i | ||||
\(643\) | −0.890856 | + | 0.275866i | −0.890856 | + | 0.275866i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.183750 | + | 0.982973i | \(0.558824\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.63730 | − | 1.16448i | −2.63730 | − | 1.16448i | ||||
\(647\) | 0 | 0 | 0.850217 | − | 0.526432i | \(-0.176471\pi\) | ||||
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(648\) | −0.998933 | + | 0.0461835i | −0.998933 | + | 0.0461835i | ||||
\(649\) | −0.788497 | + | 3.35249i | −0.788497 | + | 3.35249i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.274465 | − | 0.421217i | 0.274465 | − | 0.421217i | ||||
\(653\) | 0 | 0 | 0.998933 | − | 0.0461835i | \(-0.0147059\pi\) | ||||
−0.998933 | + | 0.0461835i | \(0.985294\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.527700 | + | 0.666213i | −0.527700 | + | 0.666213i | ||||
\(657\) | −0.0919729 | − | 0.00852254i | −0.0919729 | − | 0.00852254i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.29908 | + | 0.469056i | −1.29908 | + | 0.469056i | −0.895163 | − | 0.445738i | \(-0.852941\pi\) |
−0.403921 | + | 0.914794i | \(0.632353\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.862150 | − | 0.506653i | \(-0.169118\pi\) | ||||
−0.862150 | + | 0.506653i | \(0.830882\pi\) | |||||||
\(662\) | 0.212941 | + | 1.83545i | 0.212941 | + | 1.83545i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.0461835 | − | 1.99893i | 0.0461835 | − | 1.99893i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.256316 | + | 1.21507i | 0.256316 | + | 1.21507i | 0.895163 | + | 0.445738i | \(0.147059\pi\) |
−0.638847 | + | 0.769334i | \(0.720588\pi\) | |||||||
\(674\) | −1.97871 | − | 0.276018i | −1.97871 | − | 0.276018i | ||||
\(675\) | −0.526432 | + | 0.850217i | −0.526432 | + | 0.850217i | ||||
\(676\) | −0.769334 | + | 0.638847i | −0.769334 | + | 0.638847i | ||||
\(677\) | 0 | 0 | −0.824997 | − | 0.565136i | \(-0.808824\pi\) | ||||
0.824997 | + | 0.565136i | \(0.191176\pi\) | |||||||
\(678\) | −1.52696 | + | 1.09866i | −1.52696 | + | 1.09866i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.0348488 | − | 0.0303251i | −0.0348488 | − | 0.0303251i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.634905 | + | 1.89430i | 0.634905 | + | 1.89430i | 0.361242 | + | 0.932472i | \(0.382353\pi\) |
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(684\) | −0.666468 | − | 1.50941i | −0.666468 | − | 1.50941i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.208641 | + | 0.0979435i | 0.208641 | + | 0.0979435i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.0882033 | − | 0.760267i | 0.0882033 | − | 0.760267i | −0.873622 | − | 0.486604i | \(-0.838235\pi\) |
0.961826 | − | 0.273663i | \(-0.0882353\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.117891 | + | 0.141970i | 0.117891 | + | 0.141970i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.45298 | + | 0.306503i | −1.45298 | + | 0.306503i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.57132 | + | 1.13058i | 1.57132 | + | 1.13058i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.961826 | − | 0.273663i | \(-0.911765\pi\) | ||||
0.961826 | + | 0.273663i | \(0.0882353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.87256 | + | 0.440421i | −1.87256 | + | 0.440421i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.44612 | + | 0.0334111i | 1.44612 | + | 0.0334111i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.568950 | + | 1.69752i | 0.568950 | + | 1.69752i | ||||
\(709\) | 0 | 0 | −0.506653 | − | 0.862150i | \(-0.669118\pi\) | ||||
0.506653 | + | 0.862150i | \(0.330882\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.496189 | + | 1.91053i | 0.496189 | + | 1.91053i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.396689 | + | 0.551334i | −0.396689 | + | 0.551334i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.798017 | − | 0.602635i | \(-0.794118\pi\) | ||||
0.798017 | + | 0.602635i | \(0.205882\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.21798 | − | 1.21798i | 1.21798 | − | 1.21798i | ||||
\(723\) | −1.19078 | − | 1.24710i | −1.19078 | − | 1.24710i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.496203 | − | 2.65445i | 0.496203 | − | 2.65445i | ||||
\(727\) | 0 | 0 | −0.295806 | − | 0.955248i | \(-0.595588\pi\) | ||||
0.295806 | + | 0.955248i | \(0.404412\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.183750 | − | 0.982973i | −0.183750 | − | 0.982973i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.171131 | + | 0.364546i | 0.171131 | + | 0.364546i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.656446 | − | 0.754373i | \(-0.272059\pi\) | ||||
−0.656446 | + | 0.754373i | \(0.727941\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.64644 | + | 1.30413i | −1.64644 | + | 1.30413i | ||||
\(738\) | −0.732729 | − | 0.430598i | −0.732729 | − | 0.430598i | ||||
\(739\) | 0.116030 | − | 0.0756052i | 0.116030 | − | 0.0756052i | −0.486604 | − | 0.873622i | \(-0.661765\pi\) |
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.339607 | − | 0.940567i | \(-0.389706\pi\) | ||||
−0.339607 | + | 0.940567i | \(0.610294\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.98614 | − | 0.230425i | 1.98614 | − | 0.230425i | ||||
\(748\) | −3.00872 | − | 1.49817i | −3.00872 | − | 1.49817i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.251374 | − | 0.967890i | \(-0.419118\pi\) | ||||
−0.251374 | + | 0.967890i | \(0.580882\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.23354 | + | 0.143110i | 1.23354 | + | 0.143110i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) | ||||
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(758\) | −0.576554 | − | 1.48826i | −0.576554 | − | 1.48826i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.461556 | − | 0.555831i | 0.461556 | − | 0.555831i | −0.486604 | − | 0.873622i | \(-0.661765\pi\) |
0.948161 | + | 0.317791i | \(0.102941\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(769\) | 1.22468 | − | 0.881170i | 1.22468 | − | 0.881170i | 0.228951 | − | 0.973438i | \(-0.426471\pi\) |
0.995734 | + | 0.0922684i | \(0.0294118\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.25640 | − | 0.486734i | 1.25640 | − | 0.486734i | ||||
\(772\) | 1.77316 | − | 0.882928i | 1.77316 | − | 0.882928i | ||||
\(773\) | 0 | 0 | 0.673696 | − | 0.739009i | \(-0.264706\pi\) | ||||
−0.673696 | + | 0.739009i | \(0.735294\pi\) | |||||||
\(774\) | −0.0681792 | + | 0.220171i | −0.0681792 | + | 0.220171i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.917266 | − | 0.430598i | 0.917266 | − | 0.430598i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.225766 | − | 1.38401i | 0.225766 | − | 1.38401i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.526432 | − | 0.850217i | −0.526432 | − | 0.850217i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.56735 | + | 0.0362122i | 1.56735 | + | 0.0362122i | ||||
\(787\) | 1.71245 | − | 0.902646i | 1.71245 | − | 0.902646i | 0.739009 | − | 0.673696i | \(-0.235294\pi\) |
0.973438 | − | 0.228951i | \(-0.0735294\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.694903 | − | 1.79375i | −0.694903 | − | 1.79375i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.990410 | − | 0.138156i | \(-0.0441176\pi\) | ||||
−0.990410 | + | 0.138156i | \(0.955882\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.183750 | + | 0.982973i | 0.183750 | + | 0.982973i | ||||
\(801\) | −1.82366 | + | 0.755383i | −1.82366 | + | 0.755383i | ||||
\(802\) | 1.44123 | − | 1.25414i | 1.44123 | − | 1.25414i | ||||
\(803\) | −0.0406803 | − | 0.172962i | −0.0406803 | − | 0.172962i | ||||
\(804\) | −0.370803 | + | 1.02697i | −0.370803 | + | 1.02697i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.0303251 | − | 1.31254i | −0.0303251 | − | 1.31254i | −0.769334 | − | 0.638847i | \(-0.779412\pi\) |
0.739009 | − | 0.673696i | \(-0.235294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.261989 | + | 1.87814i | −0.261989 | + | 1.87814i | 0.183750 | + | 0.982973i | \(0.441176\pi\) |
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.73979 | + | 0.161215i | −1.73979 | + | 0.161215i | ||||
\(817\) | −0.379388 | + | 0.0263337i | −0.379388 | + | 0.0263337i | ||||
\(818\) | 0.961826 | − | 0.726337i | 0.961826 | − | 0.726337i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0.138156 | − | 0.990410i | 0.138156 | − | 0.990410i | ||||
\(823\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.87256 | − | 0.440421i | −1.87256 | − | 0.440421i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.80609 | − | 0.125363i | 1.80609 | − | 0.125363i | 0.873622 | − | 0.486604i | \(-0.161765\pi\) |
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.914794 | − | 0.403921i | \(-0.132353\pi\) | ||||
−0.914794 | + | 0.403921i | \(0.867647\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.241393 | − | 1.73049i | 0.241393 | − | 1.73049i | ||||
\(834\) | 0.336186 | − | 0.148441i | 0.336186 | − | 0.148441i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.34563 | − | 2.13832i | 2.34563 | − | 2.13832i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.329838 | + | 1.15926i | −0.329838 | + | 1.15926i | ||||
\(839\) | 0 | 0 | 0.824997 | − | 0.565136i | \(-0.191176\pi\) | ||||
−0.824997 | + | 0.565136i | \(0.808824\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.228951 | + | 0.973438i | 0.228951 | + | 0.973438i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.93247 | − | 0.361242i | 1.93247 | − | 0.361242i | ||||
\(844\) | 0.116788 | + | 0.624761i | 0.116788 | + | 0.624761i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.37736 | − | 0.685843i | 1.37736 | − | 0.685843i | ||||
\(850\) | −0.850217 | + | 1.52643i | −0.850217 | + | 1.52643i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.811724 | − | 0.584041i | \(-0.801471\pi\) | ||||
0.811724 | + | 0.584041i | \(0.198529\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.12388 | + | 1.48826i | −1.12388 | + | 1.48826i | ||||
\(857\) | 1.48234 | − | 0.781354i | 1.48234 | − | 0.781354i | 0.486604 | − | 0.873622i | \(-0.338235\pi\) |
0.995734 | + | 0.0922684i | \(0.0294118\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.952750 | + | 0.952750i | 0.952750 | + | 0.952750i | 0.998933 | − | 0.0461835i | \(-0.0147059\pi\) |
−0.0461835 | + | 0.998933i | \(0.514706\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(864\) | −0.798017 | − | 0.602635i | −0.798017 | − | 0.602635i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.134455 | − | 0.241393i | −0.134455 | − | 0.241393i | ||||
\(867\) | −1.69361 | − | 1.16015i | −1.69361 | − | 1.16015i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.553195 | + | 0.848980i | 0.553195 | + | 0.848980i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.0653133 | − | 0.0653133i | −0.0653133 | − | 0.0653133i | ||||
\(877\) | 0 | 0 | 0.0692444 | − | 0.997600i | \(-0.477941\pi\) | ||||
−0.0692444 | + | 0.997600i | \(0.522059\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.275134 | + | 0.0254949i | 0.275134 | + | 0.0254949i | 0.228951 | − | 0.973438i | \(-0.426471\pi\) |
0.0461835 | + | 0.998933i | \(0.485294\pi\) | |||||||
\(882\) | 0.769334 | − | 0.638847i | 0.769334 | − | 0.638847i | ||||
\(883\) | 1.25594 | − | 1.51247i | 1.25594 | − | 1.51247i | 0.486604 | − | 0.873622i | \(-0.338235\pi\) |
0.769334 | − | 0.638847i | \(-0.220588\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.0998157 | − | 0.257654i | −0.0998157 | − | 0.257654i | ||||
\(887\) | 0 | 0 | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) | ||||
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.68054 | − | 0.936057i | 1.68054 | − | 0.936057i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.22788 | − | 1.01962i | −1.22788 | − | 1.01962i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.948161 | + | 0.317791i | −0.948161 | + | 0.317791i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.337448 | − | 1.59968i | 0.337448 | − | 1.59968i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.87662 | − | 0.130258i | −1.87662 | − | 0.130258i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.13389 | + | 0.898142i | −1.13389 | + | 0.898142i | −0.995734 | − | 0.0922684i | \(-0.970588\pi\) |
−0.138156 | + | 0.990410i | \(0.544118\pi\) | |||||||
\(908\) | −0.00743733 | − | 0.0455932i | −0.00743733 | − | 0.0455932i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.656446 | − | 0.754373i | \(-0.272059\pi\) | ||||
−0.656446 | + | 0.754373i | \(0.727941\pi\) | |||||||
\(912\) | 0.451543 | − | 1.58701i | 0.451543 | − | 1.58701i | ||||
\(913\) | 1.63445 | + | 3.48173i | 1.63445 | + | 3.48173i | ||||
\(914\) | −1.43686 | + | 1.37197i | −1.43686 | + | 1.37197i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.400033 | − | 1.70083i | −0.400033 | − | 1.70083i | ||||
\(919\) | 0 | 0 | −0.862150 | − | 0.506653i | \(-0.830882\pi\) | ||||
0.862150 | + | 0.506653i | \(0.169118\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.21192 | + | 1.15719i | −1.21192 | + | 1.15719i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.94480 | − | 0.0899135i | −1.94480 | − | 0.0899135i | −0.961826 | − | 0.273663i | \(-0.911765\pi\) |
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.44147 | + | 0.802895i | 1.44147 | + | 0.802895i | ||||
\(932\) | 0.486604 | + | 1.87362i | 0.486604 | + | 1.87362i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.204198 | − | 1.46384i | −0.204198 | − | 1.46384i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.25594 | + | 0.234776i | −1.25594 | + | 0.234776i | −0.769334 | − | 0.638847i | \(-0.779412\pi\) |
−0.486604 | + | 0.873622i | \(0.661765\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.365413 | + | 0.275947i | 0.365413 | + | 0.275947i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.526432 | − | 0.850217i | \(-0.323529\pi\) | ||||
−0.526432 | + | 0.850217i | \(0.676471\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −0.646741 | + | 1.66943i | −0.646741 | + | 1.66943i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.443257 | + | 0.0102410i | −0.443257 | + | 0.0102410i | ||||
\(947\) | 1.95224 | − | 0.411819i | 1.95224 | − | 0.411819i | 0.961826 | − | 0.273663i | \(-0.0882353\pi\) |
0.990410 | − | 0.138156i | \(-0.0441176\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.05409 | − | 1.26940i | −1.05409 | − | 1.26940i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.134613 | − | 1.16030i | 0.134613 | − | 1.16030i | −0.739009 | − | 0.673696i | \(-0.764706\pi\) |
0.873622 | − | 0.486604i | \(-0.161765\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.317791 | + | 0.948161i | 0.317791 | + | 0.948161i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.62926 | − | 0.907490i | −1.62926 | − | 0.907490i | ||||
\(964\) | −0.119398 | − | 1.72016i | −0.119398 | − | 1.72016i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.824997 | − | 0.565136i | \(-0.808824\pi\) | ||||
0.824997 | + | 0.565136i | \(0.191176\pi\) | |||||||
\(968\) | 2.07754 | − | 1.72516i | 2.07754 | − | 1.72516i | ||||
\(969\) | 2.37842 | − | 1.62926i | 2.37842 | − | 1.62926i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.394336 | + | 1.86936i | 0.394336 | + | 1.86936i | 0.486604 | + | 0.873622i | \(0.338235\pi\) |
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(972\) | 0.486604 | − | 0.873622i | 0.486604 | − | 0.873622i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.20239 | − | 0.744488i | −1.20239 | − | 0.744488i | −0.228951 | − | 0.973438i | \(-0.573529\pi\) |
−0.973438 | + | 0.228951i | \(0.926471\pi\) | |||||||
\(978\) | 0.213639 | + | 0.455097i | 0.213639 | + | 0.455097i | ||||
\(979\) | −2.49260 | − | 2.86444i | −2.49260 | − | 2.86444i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.173873 | + | 1.49869i | 0.173873 | + | 1.49869i | ||||
\(983\) | 0 | 0 | 0.862150 | − | 0.506653i | \(-0.169118\pi\) | ||||
−0.862150 | + | 0.506653i | \(0.830882\pi\) | |||||||
\(984\) | −0.288627 | − | 0.799375i | −0.288627 | − | 0.799375i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.998933 | − | 0.0461835i | \(-0.0147059\pi\) | ||||
−0.998933 | + | 0.0461835i | \(0.985294\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.67263 | − | 0.785192i | −1.67263 | − | 0.785192i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.67521 | + | 1.09157i | 1.67521 | + | 1.09157i | ||||
\(997\) | 0 | 0 | 0.850217 | − | 0.526432i | \(-0.176471\pi\) | ||||
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(998\) | 0.168813 | + | 0.0745383i | 0.168813 | + | 0.0745383i | ||||
\(999\) | 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 | 3288.1.cj.b.1691.1 | yes | 64 | |
3.2 | odd | 2 | 3288.1.cj.a.1691.1 | yes | 64 | ||
8.3 | odd | 2 | CM | 3288.1.cj.b.1691.1 | yes | 64 | |
24.11 | even | 2 | 3288.1.cj.a.1691.1 | yes | 64 | ||
137.35 | odd | 136 | 3288.1.cj.a.35.1 | ✓ | 64 | ||
411.35 | even | 136 | inner | 3288.1.cj.b.35.1 | yes | 64 | |
1096.35 | even | 136 | 3288.1.cj.a.35.1 | ✓ | 64 | ||
3288.35 | odd | 136 | inner | 3288.1.cj.b.35.1 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3288.1.cj.a.35.1 | ✓ | 64 | 137.35 | odd | 136 | ||
3288.1.cj.a.35.1 | ✓ | 64 | 1096.35 | even | 136 | ||
3288.1.cj.a.1691.1 | yes | 64 | 3.2 | odd | 2 | ||
3288.1.cj.a.1691.1 | yes | 64 | 24.11 | even | 2 | ||
3288.1.cj.b.35.1 | yes | 64 | 411.35 | even | 136 | inner | |
3288.1.cj.b.35.1 | yes | 64 | 3288.35 | odd | 136 | inner | |
3288.1.cj.b.1691.1 | yes | 64 | 1.1 | even | 1 | trivial | |
3288.1.cj.b.1691.1 | yes | 64 | 8.3 | odd | 2 | CM |