Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3204,1,Mod(35,3204)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3204, base_ring=CyclotomicField(88))
chi = DirichletCharacter(H, H._module([44, 44, 63]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3204.35");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3204 = 2^{2} \cdot 3^{2} \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3204.cd (of order \(88\), degree \(40\), 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: | \(1.59900430048\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Coefficient field: | \(\Q(\zeta_{88})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{40} - x^{36} + x^{32} - x^{28} + x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{88}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{88} - \cdots)\) |
Embedding invariants
Embedding label | 1475.1 | ||
Root | \(-0.349464 + 0.936950i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3204.1475 |
Dual form | 3204.1.cd.b.719.1 |
$q$-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 \(\left(\mathbb{Z}/3204\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(713\) | \(1603\) |
\(\chi(n)\) | \(e\left(\frac{7}{88}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.755750 | − | 0.654861i | 0.755750 | − | 0.654861i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(5\) | 0.550588 | + | 0.119773i | 0.550588 | + | 0.119773i | 0.479249 | − | 0.877679i | \(-0.340909\pi\) |
0.0713392 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.177553 | − | 0.984111i | \(-0.556818\pi\) | ||||
0.177553 | + | 0.984111i | \(0.443182\pi\) | |||||||
\(8\) | −0.540641 | − | 0.841254i | −0.540641 | − | 0.841254i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.494541 | − | 0.270040i | 0.494541 | − | 0.270040i | ||||
\(11\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.183863 | − | 0.109091i | 0.183863 | − | 0.109091i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.599278 | + | 0.800541i | \(0.295455\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(17\) | 1.86912 | − | 0.133682i | 1.86912 | − | 0.133682i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.778642 | − | 0.627469i | \(-0.215909\pi\) | ||||
−0.778642 | + | 0.627469i | \(0.784091\pi\) | |||||||
\(20\) | 0.196911 | − | 0.527938i | 0.196911 | − | 0.527938i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.994270 | − | 0.106895i | \(-0.965909\pi\) | ||||
0.994270 | + | 0.106895i | \(0.0340909\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.620830 | − | 0.283524i | −0.620830 | − | 0.283524i | ||||
\(26\) | 0.0675149 | − | 0.202850i | 0.0675149 | − | 0.202850i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.11946 | + | 0.777256i | 1.11946 | + | 0.777256i | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.106895 | − | 0.994270i | \(-0.534091\pi\) | ||||
0.106895 | + | 0.994270i | \(0.465909\pi\) | |||||||
\(32\) | −0.909632 | + | 0.415415i | −0.909632 | + | 0.415415i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.32505 | − | 1.32505i | 1.32505 | − | 1.32505i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.583522 | + | 0.241703i | −0.583522 | + | 0.241703i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.0713392 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.196911 | − | 0.527938i | −0.196911 | − | 0.527938i | ||||
\(41\) | −1.47925 | − | 0.877679i | −1.47925 | − | 0.877679i | −0.479249 | − | 0.877679i | \(-0.659091\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.570323 | − | 0.821421i | \(-0.693182\pi\) | ||||
0.570323 | + | 0.821421i | \(0.306818\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.800541 | − | 0.599278i | \(-0.204545\pi\) | ||||
−0.800541 | + | 0.599278i | \(0.795455\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.936950 | + | 0.349464i | −0.936950 | + | 0.349464i | ||||
\(50\) | −0.654861 | + | 0.192284i | −0.654861 | + | 0.192284i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0818140 | − | 0.197516i | −0.0818140 | − | 0.197516i | ||||
\(53\) | 1.19550 | − | 1.59700i | 1.19550 | − | 1.59700i | 0.540641 | − | 0.841254i | \(-0.318182\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.35503 | − | 0.145681i | 1.35503 | − | 0.145681i | ||||
\(59\) | 0 | 0 | 0.968937 | − | 0.247307i | \(-0.0795455\pi\) | ||||
−0.968937 | + | 0.247307i | \(0.920455\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0126746 | − | 0.354880i | −0.0126746 | − | 0.354880i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
0.977147 | − | 0.212565i | \(-0.0681818\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(65\) | 0.114299 | − | 0.0380423i | 0.114299 | − | 0.0380423i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(68\) | 0.133682 | − | 1.86912i | 0.133682 | − | 1.86912i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.212565 | − | 0.977147i | \(-0.568182\pi\) | ||||
0.212565 | + | 0.977147i | \(0.431818\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0801894 | − | 0.273100i | 0.0801894 | − | 0.273100i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(74\) | −0.282715 | + | 0.564792i | −0.282715 | + | 0.564792i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.479249 | − | 0.877679i | \(-0.659091\pi\) | ||||
0.479249 | + | 0.877679i | \(0.340909\pi\) | |||||||
\(80\) | −0.494541 | − | 0.270040i | −0.494541 | − | 0.270040i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.69270 | + | 0.305397i | −1.69270 | + | 0.305397i | ||||
\(83\) | 0 | 0 | −0.447617 | − | 0.894225i | \(-0.647727\pi\) | ||||
0.447617 | + | 0.894225i | \(0.352273\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.04513 | + | 0.150267i | 1.04513 | + | 0.150267i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.212565 | + | 0.977147i | 0.212565 | + | 0.977147i | ||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.34692 | + | 0.865611i | −1.34692 | + | 0.865611i | −0.997452 | − | 0.0713392i | \(-0.977273\pi\) |
−0.349464 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(98\) | −0.479249 | + | 0.877679i | −0.479249 | + | 0.877679i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.368991 | + | 0.574161i | −0.368991 | + | 0.574161i | ||||
\(101\) | 1.79036 | + | 0.741593i | 1.79036 | + | 0.741593i | 0.989821 | + | 0.142315i | \(0.0454545\pi\) |
0.800541 | + | 0.599278i | \(0.204545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.627469 | − | 0.778642i | \(-0.284091\pi\) | ||||
−0.627469 | + | 0.778642i | \(0.715909\pi\) | |||||||
\(104\) | −0.191177 | − | 0.0956962i | −0.191177 | − | 0.0956962i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.142315 | − | 1.98982i | −0.142315 | − | 1.98982i | ||||
\(107\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.85483 | − | 0.691814i | −1.85483 | − | 0.691814i | −0.977147 | − | 0.212565i | \(-0.931818\pi\) |
−0.877679 | − | 0.479249i | \(-0.840909\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.599278 | + | 1.80054i | 0.599278 | + | 1.80054i | 0.599278 | + | 0.800541i | \(0.295455\pi\) |
1.00000i | \(0.500000\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.928661 | − | 0.997452i | 0.928661 | − | 0.997452i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(122\) | −0.241976 | − | 0.259900i | −0.241976 | − | 0.259900i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.758940 | − | 0.568136i | −0.758940 | − | 0.568136i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.984111 | − | 0.177553i | \(-0.943182\pi\) | ||||
0.984111 | + | 0.177553i | \(0.0568182\pi\) | |||||||
\(128\) | 0.281733 | + | 0.959493i | 0.281733 | + | 0.959493i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.0614688 | − | 0.103600i | 0.0614688 | − | 0.103600i | ||||
\(131\) | 0 | 0 | −0.599278 | − | 0.800541i | \(-0.704545\pi\) | ||||
0.599278 | + | 0.800541i | \(0.295455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.12299 | − | 1.50013i | −1.12299 | − | 1.50013i | ||||
\(137\) | −0.0364255 | + | 0.0613918i | −0.0364255 | + | 0.0613918i | −0.877679 | − | 0.479249i | \(-0.840909\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.523268 | + | 0.562029i | 0.523268 | + | 0.562029i | ||||
\(146\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.156199 | + | 0.611980i | 0.156199 | + | 0.611980i | ||||
\(149\) | −0.436506 | + | 0.628688i | −0.436506 | + | 0.628688i | −0.977147 | − | 0.212565i | \(-0.931818\pi\) |
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.681418 | − | 0.731895i | \(-0.261364\pi\) | ||||
−0.681418 | + | 0.731895i | \(0.738636\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.30638 | − | 0.0934345i | −1.30638 | − | 0.0934345i | −0.599278 | − | 0.800541i | \(-0.704545\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.550588 | + | 0.119773i | −0.550588 | + | 0.119773i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.894225 | − | 0.447617i | \(-0.852273\pi\) | ||||
0.894225 | + | 0.447617i | \(0.147727\pi\) | |||||||
\(164\) | −1.07926 | + | 1.33929i | −1.07926 | + | 1.33929i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.457344 | + | 0.837564i | −0.457344 | + | 0.837564i | ||||
\(170\) | 0.888260 | − | 0.570850i | 0.888260 | − | 0.570850i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.229843 | − | 1.05657i | 0.229843 | − | 1.05657i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.936950 | − | 0.349464i | \(-0.113636\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.800541 | + | 0.599278i | 0.800541 | + | 0.599278i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.10521 | + | 0.282089i | 1.10521 | + | 0.282089i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
0.349464 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.350230 | + | 0.0631884i | −0.350230 | + | 0.0631884i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.510270 | − | 0.860014i | \(-0.670455\pi\) | ||||
0.510270 | + | 0.860014i | \(0.329545\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.735364 | + | 1.46907i | −0.735364 | + | 1.46907i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(194\) | −0.451077 | + | 1.53623i | −0.451077 | + | 1.53623i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.212565 | + | 0.977147i | 0.212565 | + | 0.977147i | ||||
\(197\) | 0.715720 | + | 0.888154i | 0.715720 | + | 0.888154i | 0.997452 | − | 0.0713392i | \(-0.0227273\pi\) |
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.0713392 | − | 0.997452i | \(-0.477273\pi\) | ||||
−0.0713392 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(200\) | 0.0971309 | + | 0.675560i | 0.0971309 | + | 0.675560i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.83871 | − | 0.611980i | 1.83871 | − | 0.611980i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.709335 | − | 0.660414i | −0.709335 | − | 0.660414i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.207149 | + | 0.0528717i | −0.207149 | + | 0.0528717i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.731895 | − | 0.681418i | \(-0.238636\pi\) | ||||
−0.731895 | + | 0.681418i | \(0.761364\pi\) | |||||||
\(212\) | −1.41061 | − | 1.41061i | −1.41061 | − | 1.41061i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.85483 | + | 0.691814i | −1.85483 | + | 0.691814i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.329079 | − | 0.228483i | 0.329079 | − | 0.228483i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.63201 | + | 0.968315i | 1.63201 | + | 0.968315i | ||||
\(227\) | 0 | 0 | −0.349464 | − | 0.936950i | \(-0.613636\pi\) | ||||
0.349464 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.158952 | − | 0.881010i | 0.158952 | − | 0.881010i | −0.800541 | − | 0.599278i | \(-0.795455\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.0486428 | − | 1.36197i | 0.0486428 | − | 1.36197i | ||||
\(233\) | 0.587486 | − | 0.587486i | 0.587486 | − | 0.587486i | −0.349464 | − | 0.936950i | \(-0.613636\pi\) |
0.936950 | + | 0.349464i | \(0.113636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.999363 | − | 0.0356923i | \(-0.0113636\pi\) | ||||
−0.999363 | + | 0.0356923i | \(0.988636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.241703 | − | 0.726200i | 0.241703 | − | 0.726200i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
0.997452 | − | 0.0713392i | \(-0.0227273\pi\) | |||||||
\(242\) | 0.909632 | + | 0.415415i | 0.909632 | + | 0.415415i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.353072 | − | 0.0379591i | −0.353072 | − | 0.0379591i | ||||
\(245\) | −0.557730 | + | 0.0801894i | −0.557730 | + | 0.0801894i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.945619 | + | 0.0676320i | −0.945619 | + | 0.0676320i | ||||
\(251\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(257\) | −1.14952 | + | 0.627683i | −1.14952 | + | 0.627683i | −0.936950 | − | 0.349464i | \(-0.886364\pi\) |
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.0213887 | − | 0.118549i | −0.0213887 | − | 0.118549i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.849507 | − | 0.736102i | 0.849507 | − | 0.736102i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.37491 | + | 1.19136i | −1.37491 | + | 1.19136i | −0.415415 | + | 0.909632i | \(0.636364\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(272\) | −1.83107 | − | 0.398326i | −1.83107 | − | 0.398326i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.0126746 | + | 0.0702505i | 0.0126746 | + | 0.0702505i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.373128 | − | 0.203743i | 0.373128 | − | 0.203743i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.794635 | − | 0.640357i | −0.794635 | − | 0.640357i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−0.936950 | + | 0.349464i | \(0.886364\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.48594 | − | 0.357424i | 2.48594 | − | 0.357424i | ||||
\(290\) | 0.763511 | + | 0.0820859i | 0.763511 | + | 0.0820859i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.258908 | − | 0.118239i | −0.258908 | − | 0.118239i | ||||
\(293\) | −0.462264 | + | 1.38888i | −0.462264 | + | 1.38888i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.518809 | + | 0.360215i | 0.518809 | + | 0.360215i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.0818140 | + | 0.760982i | 0.0818140 | + | 0.760982i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0355266 | − | 0.196911i | 0.0355266 | − | 0.196911i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.349464 | − | 0.936950i | \(-0.613636\pi\) | ||||
0.349464 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.64179 | + | 1.13992i | −1.64179 | + | 1.13992i | −0.800541 | + | 0.599278i | \(0.795455\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(314\) | −1.04849 | + | 0.784887i | −1.04849 | + | 0.784887i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.407910 | − | 0.119773i | 0.407910 | − | 0.119773i | −0.0713392 | − | 0.997452i | \(-0.522727\pi\) |
0.479249 | + | 0.877679i | \(0.340909\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.337672 | + | 0.451077i | −0.337672 | + | 0.451077i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.145077 | + | 0.0155974i | −0.145077 | + | 0.0155974i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.0613918 | + | 1.71893i | 0.0613918 | + | 1.71893i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.977147 | + | 1.21257i | 0.977147 | + | 1.21257i | 0.977147 | + | 0.212565i | \(0.0681818\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 0.202850 | + | 0.932485i | 0.202850 | + | 0.932485i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.297475 | − | 1.01311i | 0.297475 | − | 1.01311i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.518203 | − | 0.949018i | −0.518203 | − | 0.949018i | ||||
\(347\) | 0 | 0 | −0.877679 | − | 0.479249i | \(-0.840909\pi\) | ||||
0.877679 | + | 0.479249i | \(0.159091\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.44053 | + | 0.259900i | −1.44053 | + | 0.259900i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.599278 | + | 0.800541i | \(0.704545\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.479249 | − | 0.122321i | −0.479249 | − | 0.122321i | − | 1.00000i | \(-0.5\pi\) | |
−0.479249 | + | 0.877679i | \(0.659091\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.997452 | − | 0.0713392i | 0.997452 | − | 0.0713392i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.247307 | − | 0.968937i | \(-0.420455\pi\) | ||||
−0.247307 | + | 0.968937i | \(0.579545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.212565 | − | 0.977147i | 0.212565 | − | 0.977147i | ||||
\(362\) | 1.01999 | − | 0.510572i | 1.01999 | − | 0.510572i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.0768614 | − | 0.140761i | 0.0768614 | − | 0.140761i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.223306 | + | 0.277106i | −0.223306 | + | 0.277106i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.0498610 | + | 0.697148i | 0.0498610 | + | 0.697148i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.290619 | + | 0.0207855i | 0.290619 | + | 0.0207855i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.106895 | − | 0.994270i | \(-0.465909\pi\) | ||||
−0.106895 | + | 0.994270i | \(0.534091\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.681418 | − | 0.731895i | \(-0.261364\pi\) | ||||
−0.681418 | + | 0.731895i | \(0.738636\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.406285 | + | 1.59181i | 0.406285 | + | 1.59181i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.665114 | + | 1.45640i | 0.665114 | + | 1.45640i | ||||
\(389\) | 1.36197 | + | 1.46286i | 1.36197 | + | 1.46286i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.800541 | + | 0.599278i | 0.800541 | + | 0.599278i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.12252 | + | 0.202525i | 1.12252 | + | 0.202525i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.794635 | − | 1.33929i | 0.794635 | − | 1.33929i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.936950 | − | 0.349464i | \(-0.113636\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.515804 | + | 0.446947i | 0.515804 | + | 0.446947i | ||||
\(401\) | −1.49611 | − | 1.29639i | −1.49611 | − | 1.29639i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.654861 | − | 0.755750i | \(-0.727273\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.988839 | − | 1.66660i | 0.988839 | − | 1.66660i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.865611 | + | 0.647988i | 0.865611 | + | 0.647988i | 0.936950 | − | 0.349464i | \(-0.113636\pi\) |
−0.0713392 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(410\) | −0.968559 | − | 0.0345922i | −0.968559 | − | 0.0345922i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.121929 | + | 0.175612i | −0.121929 | + | 0.175612i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.948826 | − | 0.315800i | \(-0.897727\pi\) | ||||
0.948826 | + | 0.315800i | \(0.102273\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.396309 | − | 1.19072i | −0.396309 | − | 1.19072i | −0.936950 | − | 0.349464i | \(-0.886364\pi\) |
0.540641 | − | 0.841254i | \(-0.318182\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.98982 | − | 0.142315i | −1.98982 | − | 0.142315i | ||||
\(425\) | −1.19831 | − | 0.446947i | −1.19831 | − | 0.446947i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.627469 | − | 0.778642i | \(-0.284091\pi\) | ||||
−0.627469 | + | 0.778642i | \(0.715909\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.75320 | + | 0.726200i | 1.75320 | + | 0.726200i | 0.997452 | + | 0.0713392i | \(0.0227273\pi\) |
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.948742 | + | 1.73749i | −0.948742 | + | 1.73749i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.894225 | − | 0.447617i | \(-0.147727\pi\) | ||||
−0.894225 | + | 0.447617i | \(0.852273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.0990763 | − | 0.388177i | 0.0990763 | − | 0.388177i | ||||
\(443\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.563465i | 0.563465i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.141226 | + | 0.0203052i | 0.141226 | + | 0.0203052i | 0.212565 | − | 0.977147i | \(-0.431818\pi\) |
−0.0713392 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.86750 | − | 0.336934i | 1.86750 | − | 0.336934i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.741593 | + | 1.79036i | −0.741593 | + | 1.79036i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.599278 | + | 0.800541i | \(0.704545\pi\) | |||||||
\(458\) | −0.456811 | − | 0.769914i | −0.456811 | − | 0.769914i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.304632 | − | 1.03748i | 0.304632 | − | 1.03748i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.212565 | − | 0.977147i | \(-0.568182\pi\) | ||||
0.212565 | + | 0.977147i | \(0.431818\pi\) | |||||||
\(464\) | −0.855137 | − | 1.06116i | −0.855137 | − | 1.06116i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.0592707 | − | 0.828713i | 0.0592707 | − | 0.828713i | ||||
\(467\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0809203 | + | 0.108097i | −0.0809203 | + | 0.108097i | ||||
\(482\) | −0.292893 | − | 0.707107i | −0.292893 | − | 0.707107i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(485\) | −0.845273 | + | 0.315271i | −0.845273 | + | 0.315271i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.800541 | − | 0.599278i | \(-0.204545\pi\) | ||||
−0.800541 | + | 0.599278i | \(0.795455\pi\) | |||||||
\(488\) | −0.291692 | + | 0.202525i | −0.291692 | + | 0.202525i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.368991 | + | 0.425839i | −0.368991 | + | 0.425839i | ||||
\(491\) | 0 | 0 | −0.570323 | − | 0.821421i | \(-0.693182\pi\) | ||||
0.570323 | + | 0.821421i | \(0.306818\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.19632 | + | 1.30314i | 2.19632 | + | 1.30314i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.0356923 | − | 0.999363i | \(-0.488636\pi\) | ||||
−0.0356923 | + | 0.999363i | \(0.511364\pi\) | |||||||
\(500\) | −0.670361 | + | 0.670361i | −0.670361 | + | 0.670361i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.106895 | − | 0.994270i | \(-0.534091\pi\) | ||||
0.106895 | + | 0.994270i | \(0.465909\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.896930 | + | 0.622749i | 0.896930 | + | 0.622749i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.258908 | − | 0.118239i | −0.258908 | − | 0.118239i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.989821 | − | 0.142315i | 0.989821 | − | 0.142315i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.457701 | + | 1.22714i | −0.457701 | + | 1.22714i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.0937978 | − | 0.0755870i | −0.0937978 | − | 0.0755870i | ||||
\(521\) | −1.71017 | + | 1.01469i | −1.71017 | + | 1.01469i | −0.800541 | + | 0.599278i | \(0.795455\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.977147 | + | 0.212565i | 0.977147 | + | 0.212565i | ||||
\(530\) | 0.159970 | − | 1.11262i | 0.159970 | − | 1.11262i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.367725 | −0.367725 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.258908 | + | 1.80075i | −0.258908 | + | 1.80075i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.291692 | − | 1.61674i | −0.291692 | − | 1.61674i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.64468 | + | 0.898064i | −1.64468 | + | 0.898064i | ||||
\(545\) | −0.938384 | − | 0.603063i | −0.938384 | − | 0.603063i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.860014 | − | 0.510270i | \(-0.170455\pi\) | ||||
−0.860014 | + | 0.510270i | \(0.829545\pi\) | |||||||
\(548\) | 0.0555831 | + | 0.0447917i | 0.0555831 | + | 0.0447917i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.148568 | − | 0.398326i | 0.148568 | − | 0.398326i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.97715 | + | 0.212565i | 1.97715 | + | 0.212565i | 1.00000 | \(0\) | ||
0.977147 | + | 0.212565i | \(0.0681818\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.01989 | + | 0.0364255i | −1.01989 | + | 0.0364255i | ||||
\(563\) | 0 | 0 | −0.821421 | − | 0.570323i | \(-0.806818\pi\) | ||||
0.821421 | + | 0.570323i | \(0.193182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.114299 | + | 1.06313i | 0.114299 | + | 1.06313i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.0407123 | − | 1.13992i | 0.0407123 | − | 1.13992i | −0.800541 | − | 0.599278i | \(-0.795455\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.05382 | + | 1.51779i | 1.05382 | + | 1.51779i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
0.212565 | + | 0.977147i | \(0.431818\pi\) | |||||||
\(578\) | 1.64468 | − | 1.89806i | 1.64468 | − | 1.89806i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.630778 | − | 0.437957i | 0.630778 | − | 0.437957i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.273100 | + | 0.0801894i | −0.273100 | + | 0.0801894i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.560168 | + | 1.35236i | 0.560168 | + | 1.35236i | ||||
\(587\) | 0 | 0 | 0.599278 | − | 0.800541i | \(-0.295455\pi\) | ||||
−0.599278 | + | 0.800541i | \(0.704545\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.627980 | − | 0.0675149i | 0.627980 | − | 0.0675149i | ||||
\(593\) | −1.59181 | + | 0.406285i | −1.59181 | + | 0.406285i | −0.936950 | − | 0.349464i | \(-0.886364\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.560168 | + | 0.521535i | 0.560168 | + | 0.521535i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.948826 | − | 0.315800i | \(-0.102273\pi\) | ||||
−0.948826 | + | 0.315800i | \(0.897727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.215109 | − | 1.49611i | −0.215109 | − | 1.49611i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
0.540641 | − | 0.841254i | \(-0.318182\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.119773 | + | 0.550588i | 0.119773 | + | 0.550588i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.102100 | − | 0.172080i | −0.102100 | − | 0.172080i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.398174 | − | 0.729202i | −0.398174 | − | 0.729202i | 0.599278 | − | 0.800541i | \(-0.295455\pi\) |
−0.997452 | + | 0.0713392i | \(0.977273\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.697067 | − | 1.39256i | −0.697067 | − | 1.39256i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.212565 | − | 0.977147i | \(-0.431818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.0971309 | + | 0.112095i | 0.0971309 | + | 0.112095i | ||||
\(626\) | −0.494298 | + | 1.93664i | −0.494298 | + | 1.93664i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.278401 | + | 1.27979i | −0.278401 | + | 1.27979i | ||||
\(629\) | −1.05836 | + | 0.529779i | −1.05836 | + | 0.529779i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.229843 | − | 0.357643i | 0.229843 | − | 0.357643i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.134147 | + | 0.166466i | −0.134147 | + | 0.166466i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.0401971 | + | 0.562029i | 0.0401971 | + | 0.562029i | ||||
\(641\) | 1.47696 | − | 0.321292i | 1.47696 | − | 0.321292i | 0.599278 | − | 0.800541i | \(-0.295455\pi\) |
0.877679 | + | 0.479249i | \(0.159091\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.936950 | − | 0.349464i | \(-0.886364\pi\) | ||||
0.936950 | + | 0.349464i | \(0.113636\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.315800 | − | 0.948826i | \(-0.602273\pi\) | ||||
0.315800 | + | 0.948826i | \(0.397727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.0994280 | + | 0.106793i | −0.0994280 | + | 0.106793i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.469302 | − | 1.83871i | −0.469302 | − | 1.83871i | −0.540641 | − | 0.841254i | \(-0.681818\pi\) |
0.0713392 | − | 0.997452i | \(-0.477273\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.17206 | + | 1.25888i | 1.17206 | + | 1.25888i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.800541 | − | 0.599278i | \(-0.795455\pi\) | ||||
0.800541 | + | 0.599278i | \(0.204545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.93695 | − | 0.349464i | −1.93695 | − | 0.349464i | −0.936950 | − | 0.349464i | \(-0.886364\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.562029 | − | 1.91410i | −0.562029 | − | 1.91410i | −0.349464 | − | 0.936950i | \(-0.613636\pi\) |
−0.212565 | − | 0.977147i | \(-0.568182\pi\) | |||||||
\(674\) | 1.53254 | + | 0.276501i | 1.53254 | + | 0.276501i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.763951 | + | 0.571887i | 0.763951 | + | 0.571887i | ||||
\(677\) | −0.764879 | − | 0.0273177i | −0.764879 | − | 0.0273177i | −0.349464 | − | 0.936950i | \(-0.613636\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.438627 | − | 0.960459i | −0.438627 | − | 0.960459i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.570323 | − | 0.821421i | \(-0.306818\pi\) | ||||
−0.570323 | + | 0.821421i | \(0.693182\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.0274085 | + | 0.0294388i | −0.0274085 | + | 0.0294388i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0455898 | − | 0.424047i | 0.0455898 | − | 0.424047i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.997452 | − | 0.0713392i | \(-0.977273\pi\) | ||||
0.997452 | + | 0.0713392i | \(0.0227273\pi\) | |||||||
\(692\) | −1.01311 | − | 0.377869i | −1.01311 | − | 0.377869i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.88223 | − | 1.44274i | −2.88223 | − | 1.44274i | ||||
\(698\) | −0.918482 | + | 1.13977i | −0.918482 | + | 1.13977i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.05657 | − | 1.64406i | 1.05657 | − | 1.64406i | 0.349464 | − | 0.936950i | \(-0.386364\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.442295 | + | 0.221397i | −0.442295 | + | 0.221397i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.491779 | − | 1.92677i | 0.491779 | − | 1.92677i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.349464 | − | 0.936950i | \(-0.386364\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.984111 | − | 0.177553i | \(-0.0568182\pi\) | ||||
−0.984111 | + | 0.177553i | \(0.943182\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.479249 | − | 0.877679i | −0.479249 | − | 0.877679i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.436506 | − | 1.05382i | 0.436506 | − | 1.05382i | ||||
\(725\) | −0.474625 | − | 0.799938i | −0.474625 | − | 0.799938i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.447617 | − | 0.894225i | \(-0.352273\pi\) | ||||
−0.447617 | + | 0.894225i | \(0.647727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.0340910 | − | 0.156714i | −0.0340910 | − | 0.156714i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.0771377 | + | 1.07853i | −0.0771377 | + | 1.07853i | 0.800541 | + | 0.599278i | \(0.204545\pi\) |
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.731895 | − | 0.681418i | \(-0.761364\pi\) | ||||
0.731895 | + | 0.681418i | \(0.238636\pi\) | |||||||
\(740\) | 0.0127023 | + | 0.355657i | 0.0127023 | + | 0.355657i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.994270 | − | 0.106895i | \(-0.0340909\pi\) | ||||
−0.994270 | + | 0.106895i | \(0.965909\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.315635 | + | 0.293867i | −0.315635 | + | 0.293867i | ||||
\(746\) | 0.494217 | + | 0.494217i | 0.494217 | + | 0.494217i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.233247 | − | 0.174606i | 0.233247 | − | 0.174606i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.27979 | − | 1.47696i | 1.27979 | − | 1.47696i | 0.479249 | − | 0.877679i | \(-0.340909\pi\) |
0.800541 | − | 0.599278i | \(-0.204545\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.0498610 | + | 0.133682i | 0.0498610 | + | 0.133682i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.635768 | − | 0.290345i | 0.635768 | − | 0.290345i | −0.0713392 | − | 0.997452i | \(-0.522727\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.34946 | + | 0.936950i | 1.34946 | + | 0.936950i | ||||
\(773\) | −1.01989 | + | 0.0364255i | −1.01989 | + | 0.0364255i | −0.540641 | − | 0.841254i | \(-0.681818\pi\) |
−0.479249 | + | 0.877679i | \(0.659091\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.45640 | + | 0.665114i | 1.45640 | + | 0.665114i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.98727 | + | 0.213654i | 1.98727 | + | 0.213654i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.997452 | − | 0.0713392i | 0.997452 | − | 0.0713392i | ||||
\(785\) | −0.708089 | − | 0.207914i | −0.708089 | − | 0.207914i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.778642 | − | 0.627469i | \(-0.784091\pi\) | ||||
0.778642 | + | 0.627469i | \(0.215909\pi\) | |||||||
\(788\) | 0.980971 | − | 0.582037i | 0.980971 | − | 0.582037i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.0410445 | − | 0.0638665i | −0.0410445 | − | 0.0638665i | ||||
\(794\) | −0.276501 | − | 1.53254i | −0.276501 | − | 1.53254i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.136408 | − | 0.948742i | 0.136408 | − | 0.948742i | −0.800541 | − | 0.599278i | \(-0.795455\pi\) |
0.936950 | − | 0.349464i | \(-0.113636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.682507 | 0.682507 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.97964 | −1.97964 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.344076 | − | 1.90708i | −0.344076 | − | 1.90708i | ||||
\(809\) | −0.949018 | − | 1.47670i | −0.949018 | − | 1.47670i | −0.877679 | − | 0.479249i | \(-0.840909\pi\) |
−0.0713392 | − | 0.997452i | \(-0.522727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.877679 | − | 0.479249i | \(-0.159091\pi\) | ||||
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.07853 | − | 0.0771377i | 1.07853 | − | 0.0771377i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.754641 | + | 0.608128i | −0.754641 | + | 0.608128i | ||||
\(821\) | 0.613435 | − | 1.64468i | 0.613435 | − | 1.64468i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.755750 | − | 0.654861i | \(-0.227273\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.315800 | − | 0.948826i | \(-0.397727\pi\) | ||||
−0.315800 | + | 0.948826i | \(0.602273\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.84658 | − | 0.0659508i | 1.84658 | − | 0.0659508i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
0.936950 | + | 0.349464i | \(0.113636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.0228531 | + | 0.212565i | 0.0228531 | + | 0.212565i | ||||
\(833\) | −1.70456 | + | 0.778446i | −1.70456 | + | 0.778446i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.177553 | − | 0.984111i | \(-0.443182\pi\) | ||||
−0.177553 | + | 0.984111i | \(0.556818\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.299603 | + | 0.803267i | 0.299603 | + | 0.803267i | ||||
\(842\) | −1.07926 | − | 0.640357i | −1.07926 | − | 0.640357i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.352126 | + | 0.406375i | −0.352126 | + | 0.406375i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.59700 | + | 1.19550i | −1.59700 | + | 1.19550i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.19831 | + | 0.446947i | −1.19831 | + | 0.446947i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.30896 | + | 1.21868i | −1.30896 | + | 1.21868i | −0.349464 | + | 0.936950i | \(0.613636\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.994270 | − | 0.106895i | \(-0.0340909\pi\) | ||||
−0.994270 | + | 0.106895i | \(0.965909\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.731895 | − | 0.681418i | \(-0.761364\pi\) | ||||
0.731895 | + | 0.681418i | \(0.238636\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.253098 | − | 0.554206i | 0.253098 | − | 0.554206i | ||||
\(866\) | 1.80054 | − | 0.599278i | 1.80054 | − | 0.599278i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.420803 | + | 1.93440i | 0.420803 | + | 1.93440i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.877679 | − | 1.47925i | −0.877679 | − | 1.47925i | −0.877679 | − | 0.479249i | \(-0.840909\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.613435 | + | 0.334961i | 0.613435 | + | 0.334961i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 0.984111 | − | 0.177553i | \(-0.0568182\pi\) | ||||
−0.984111 | + | 0.177553i | \(0.943182\pi\) | |||||||
\(884\) | −0.179325 | − | 0.358246i | −0.179325 | − | 0.358246i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.968937 | − | 0.247307i | \(-0.920455\pi\) | ||||
0.968937 | + | 0.247307i | \(0.0795455\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.368991 | + | 0.425839i | 0.368991 | + | 0.425839i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.120029 | − | 0.0771377i | 0.120029 | − | 0.0771377i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.02105 | − | 3.14482i | 2.02105 | − | 3.14482i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.19072 | − | 1.47759i | 1.19072 | − | 1.47759i | ||||
\(905\) | 0.574731 | + | 0.287690i | 0.574731 | + | 0.287690i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.0713392 | − | 0.997452i | \(-0.522727\pi\) | ||||
0.0713392 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.997452 | − | 0.0713392i | \(-0.977273\pi\) | ||||
0.997452 | + | 0.0713392i | \(0.0227273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.611980 | + | 1.83871i | 0.611980 | + | 1.83871i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.849422 | − | 0.282715i | −0.849422 | − | 0.282715i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.570323 | − | 0.821421i | \(-0.306818\pi\) | ||||
−0.570323 | + | 0.821421i | \(0.693182\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.449181 | − | 0.983568i | −0.449181 | − | 0.983568i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.430796 | + | 0.0153859i | 0.430796 | + | 0.0153859i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.34118 | − | 0.241976i | −1.34118 | − | 0.241976i | ||||
\(929\) | 0.270040 | + | 0.919672i | 0.270040 | + | 0.919672i | 0.977147 | + | 0.212565i | \(0.0681818\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.497898 | − | 0.665114i | −0.497898 | − | 0.665114i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.959493 | − | 1.28173i | −0.959493 | − | 1.28173i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.76003 | + | 0.317545i | 1.76003 | + | 0.317545i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
0.800541 | + | 0.599278i | \(0.204545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0150489 | − | 0.0589609i | −0.0150489 | − | 0.0589609i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.83871 | + | 0.611980i | 1.83871 | + | 0.611980i | 0.997452 | + | 0.0713392i | \(0.0227273\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.977147 | + | 0.212565i | −0.977147 | + | 0.212565i | ||||
\(962\) | 0.00963291 | + | 0.134686i | 0.00963291 | + | 0.134686i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.684410 | − | 0.342591i | −0.684410 | − | 0.342591i | ||||
\(965\) | −0.580838 | + | 0.720776i | −0.580838 | + | 0.720776i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(968\) | 0.540641 | − | 0.841254i | 0.540641 | − | 0.841254i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.432356 | + | 0.791802i | −0.432356 | + | 0.791802i | ||||
\(971\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.0878201 | + | 0.344076i | −0.0878201 | + | 0.344076i | ||||
\(977\) | 1.14952 | + | 1.32661i | 1.14952 | + | 1.32661i | 0.936950 | + | 0.349464i | \(0.113636\pi\) |
0.212565 | + | 0.977147i | \(0.431818\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.563465i | 0.563465i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.287690 | + | 0.574731i | 0.287690 | + | 0.574731i | ||||
\(986\) | 2.51324 | − | 0.453438i | 2.51324 | − | 0.453438i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.254771 | − | 1.17116i | −0.254771 | − | 1.17116i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(998\) | 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 | 3204.1.cd.b.1475.1 | yes | 40 | |
3.2 | odd | 2 | 3204.1.cd.a.1475.1 | yes | 40 | ||
4.3 | odd | 2 | CM | 3204.1.cd.b.1475.1 | yes | 40 | |
12.11 | even | 2 | 3204.1.cd.a.1475.1 | yes | 40 | ||
89.7 | odd | 88 | 3204.1.cd.a.719.1 | ✓ | 40 | ||
267.185 | even | 88 | inner | 3204.1.cd.b.719.1 | yes | 40 | |
356.7 | even | 88 | 3204.1.cd.a.719.1 | ✓ | 40 | ||
1068.719 | odd | 88 | inner | 3204.1.cd.b.719.1 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3204.1.cd.a.719.1 | ✓ | 40 | 89.7 | odd | 88 | ||
3204.1.cd.a.719.1 | ✓ | 40 | 356.7 | even | 88 | ||
3204.1.cd.a.1475.1 | yes | 40 | 3.2 | odd | 2 | ||
3204.1.cd.a.1475.1 | yes | 40 | 12.11 | even | 2 | ||
3204.1.cd.b.719.1 | yes | 40 | 267.185 | even | 88 | inner | |
3204.1.cd.b.719.1 | yes | 40 | 1068.719 | odd | 88 | inner | |
3204.1.cd.b.1475.1 | yes | 40 | 1.1 | even | 1 | trivial | |
3204.1.cd.b.1475.1 | yes | 40 | 4.3 | odd | 2 | CM |