Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1096,1,Mod(99,1096)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1096, base_ring=CyclotomicField(34))
chi = DirichletCharacter(H, H._module([17, 17, 31]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1096.99");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1096 = 2^{3} \cdot 137 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1096.u (of order \(34\), degree \(16\), 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: | \(0.546975253846\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{34})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{34}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{34} - \cdots)\) |
Embedding invariants
Embedding label | 699.1 | ||
Root | \(0.850217 - 0.526432i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1096.699 |
Dual form | 1096.1.u.a.323.1 |
$q$-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 \(\left(\mathbb{Z}/1096\mathbb{Z}\right)^\times\).
\(n\) | \(549\) | \(823\) | \(825\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{13}{34}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.850217 | − | 0.526432i | 0.850217 | − | 0.526432i | ||||
\(3\) | 0.719401 | + | 1.85699i | 0.719401 | + | 1.85699i | 0.445738 | + | 0.895163i | \(0.352941\pi\) |
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(4\) | 0.445738 | − | 0.895163i | 0.445738 | − | 0.895163i | ||||
\(5\) | 0 | 0 | 0.526432 | − | 0.850217i | \(-0.323529\pi\) | ||||
−0.526432 | + | 0.850217i | \(0.676471\pi\) | |||||||
\(6\) | 1.58923 | + | 1.20013i | 1.58923 | + | 1.20013i | ||||
\(7\) | 0 | 0 | −0.982973 | − | 0.183750i | \(-0.941176\pi\) | ||||
0.982973 | + | 0.183750i | \(0.0588235\pi\) | |||||||
\(8\) | −0.0922684 | − | 0.995734i | −0.0922684 | − | 0.995734i | ||||
\(9\) | −2.19186 | + | 1.99815i | −2.19186 | + | 1.99815i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.537235 | − | 1.07891i | 0.537235 | − | 1.07891i | −0.445738 | − | 0.895163i | \(-0.647059\pi\) |
0.982973 | − | 0.183750i | \(-0.0588235\pi\) | |||||||
\(12\) | 1.98297 | + | 0.183750i | 1.98297 | + | 0.183750i | ||||
\(13\) | 0 | 0 | 0.183750 | − | 0.982973i | \(-0.441176\pi\) | ||||
−0.183750 | + | 0.982973i | \(0.558824\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.602635 | − | 0.798017i | −0.602635 | − | 0.798017i | ||||
\(17\) | −0.111208 | + | 1.20013i | −0.111208 | + | 1.20013i | 0.739009 | + | 0.673696i | \(0.235294\pi\) |
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(18\) | −0.811670 | + | 2.85272i | −0.811670 | + | 2.85272i | ||||
\(19\) | −0.0505009 | + | 0.177492i | −0.0505009 | + | 0.177492i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) |
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.111208 | − | 1.20013i | −0.111208 | − | 1.20013i | ||||
\(23\) | 0 | 0 | 0.798017 | − | 0.602635i | \(-0.205882\pi\) | ||||
−0.798017 | + | 0.602635i | \(0.794118\pi\) | |||||||
\(24\) | 1.78269 | − | 0.887674i | 1.78269 | − | 0.887674i | ||||
\(25\) | −0.445738 | − | 0.895163i | −0.445738 | − | 0.895163i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.50467 | − | 1.74512i | −3.50467 | − | 1.74512i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.798017 | − | 0.602635i | \(-0.205882\pi\) | ||||
−0.798017 | + | 0.602635i | \(0.794118\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.961826 | − | 0.273663i | \(-0.0882353\pi\) | ||||
−0.961826 | + | 0.273663i | \(0.911765\pi\) | |||||||
\(32\) | −0.932472 | − | 0.361242i | −0.932472 | − | 0.361242i | ||||
\(33\) | 2.39002 | + | 0.221468i | 2.39002 | + | 0.221468i | ||||
\(34\) | 0.537235 | + | 1.07891i | 0.537235 | + | 1.07891i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.811670 | + | 2.85272i | 0.811670 | + | 2.85272i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0.0505009 | + | 0.177492i | 0.0505009 | + | 0.177492i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.722483i | − | 0.722483i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) | ||
0.932472 | − | 0.361242i | \(-0.117647\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.53511 | − | 0.436776i | −1.53511 | − | 0.436776i | −0.602635 | − | 0.798017i | \(-0.705882\pi\) |
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(44\) | −0.726337 | − | 0.961826i | −0.726337 | − | 0.961826i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.673696 | − | 0.739009i | \(-0.735294\pi\) | ||||
0.673696 | + | 0.739009i | \(0.264706\pi\) | |||||||
\(48\) | 1.04837 | − | 1.69318i | 1.04837 | − | 1.69318i | ||||
\(49\) | 0.932472 | + | 0.361242i | 0.932472 | + | 0.361242i | ||||
\(50\) | −0.850217 | − | 0.526432i | −0.850217 | − | 0.526432i | ||||
\(51\) | −2.30863 | + | 0.656861i | −2.30863 | + | 0.656861i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.961826 | − | 0.273663i | \(-0.911765\pi\) | ||||
0.961826 | + | 0.273663i | \(0.0882353\pi\) | |||||||
\(54\) | −3.89842 | + | 0.361242i | −3.89842 | + | 0.361242i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.365931 | + | 0.0339085i | −0.365931 | + | 0.0339085i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.25664 | + | 1.14558i | −1.25664 | + | 1.14558i | −0.273663 | + | 0.961826i | \(0.588235\pi\) |
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.739009 | − | 0.673696i | \(-0.764706\pi\) | ||||
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.982973 | + | 0.183750i | −0.982973 | + | 0.183750i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.14862 | − | 1.06989i | 2.14862 | − | 1.06989i | ||||
\(67\) | 0.365931 | − | 1.95756i | 0.365931 | − | 1.95756i | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) |
0.273663 | − | 0.961826i | \(-0.411765\pi\) | |||||||
\(68\) | 1.02474 | + | 0.634493i | 1.02474 | + | 0.634493i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.895163 | − | 0.445738i | \(-0.147059\pi\) | ||||
−0.895163 | + | 0.445738i | \(0.852941\pi\) | |||||||
\(72\) | 2.19186 | + | 1.99815i | 2.19186 | + | 1.99815i | ||||
\(73\) | 1.83319 | − | 0.342683i | 1.83319 | − | 0.342683i | 0.850217 | − | 0.526432i | \(-0.176471\pi\) |
0.982973 | + | 0.183750i | \(0.0588235\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.34164 | − | 1.47171i | 1.34164 | − | 1.47171i | ||||
\(76\) | 0.136374 | + | 0.124322i | 0.136374 | + | 0.124322i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.361242 | − | 0.932472i | \(-0.382353\pi\) | ||||
−0.361242 | + | 0.932472i | \(0.617647\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.445738 | − | 4.81028i | 0.445738 | − | 4.81028i | ||||
\(82\) | −0.380338 | − | 0.614268i | −0.380338 | − | 0.614268i | ||||
\(83\) | −0.365931 | + | 0.0339085i | −0.365931 | + | 0.0339085i | −0.273663 | − | 0.961826i | \(-0.588235\pi\) |
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.53511 | + | 0.436776i | −1.53511 | + | 0.436776i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.12388 | − | 0.435393i | −1.12388 | − | 0.435393i | ||||
\(89\) | −1.01267 | + | 1.63552i | −1.01267 | + | 1.63552i | −0.273663 | + | 0.961826i | \(0.588235\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.99147i | − | 1.99147i | ||||||
\(97\) | 1.60263 | + | 0.798017i | 1.60263 | + | 0.798017i | 1.00000 | \(0\) | ||
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(98\) | 0.982973 | − | 0.183750i | 0.982973 | − | 0.183750i | ||||
\(99\) | 0.978281 | + | 3.43830i | 0.978281 | + | 3.43830i | ||||
\(100\) | −1.00000 | −1.00000 | ||||||||
\(101\) | 0 | 0 | −0.273663 | − | 0.961826i | \(-0.588235\pi\) | ||||
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(102\) | −1.61704 | + | 1.77381i | −1.61704 | + | 1.77381i | ||||
\(103\) | 0 | 0 | −0.445738 | − | 0.895163i | \(-0.647059\pi\) | ||||
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.83319 | − | 0.710182i | 1.83319 | − | 0.710182i | 0.850217 | − | 0.526432i | \(-0.176471\pi\) |
0.982973 | − | 0.183750i | \(-0.0588235\pi\) | |||||||
\(108\) | −3.12433 | + | 2.35939i | −3.12433 | + | 2.35939i | ||||
\(109\) | 0 | 0 | 0.602635 | − | 0.798017i | \(-0.294118\pi\) | ||||
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.646741 | + | 0.322039i | −0.646741 | + | 0.322039i | −0.739009 | − | 0.673696i | \(-0.764706\pi\) |
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(114\) | −0.293271 | + | 0.221468i | −0.293271 | + | 0.221468i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.465346 | + | 1.63552i | −0.465346 | + | 1.63552i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.272797 | − | 0.361242i | −0.272797 | − | 0.361242i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.34164 | − | 0.519755i | 1.34164 | − | 0.519755i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | −0.739009 | + | 0.673696i | −0.739009 | + | 0.673696i | ||||
\(129\) | −0.293271 | − | 3.16489i | −0.293271 | − | 3.16489i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.27366 | − | 0.961826i | −1.27366 | − | 0.961826i | −0.273663 | − | 0.961826i | \(-0.588235\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(132\) | 1.26357 | − | 2.04074i | 1.26357 | − | 2.04074i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.719401 | − | 1.85699i | −0.719401 | − | 1.85699i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.20527 | 1.20527 | ||||||||
\(137\) | 0.273663 | + | 0.961826i | 0.273663 | + | 0.961826i | ||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.156896 | − | 0.0971461i | 0.156896 | − | 0.0971461i | −0.445738 | − | 0.895163i | \(-0.647059\pi\) |
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.91545 | + | 0.544991i | 2.91545 | + | 0.544991i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.37821 | − | 1.25640i | 1.37821 | − | 1.25640i | ||||
\(147\) | 1.99147i | 1.99147i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.995734 | − | 0.0922684i | \(-0.970588\pi\) | ||||
0.995734 | + | 0.0922684i | \(0.0294118\pi\) | |||||||
\(150\) | 0.365931 | − | 1.95756i | 0.365931 | − | 1.95756i | ||||
\(151\) | 0 | 0 | 0.932472 | − | 0.361242i | \(-0.117647\pi\) | ||||
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(152\) | 0.181395 | + | 0.0339085i | 0.181395 | + | 0.0339085i | ||||
\(153\) | −2.15428 | − | 2.85272i | −2.15428 | − | 2.85272i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.526432 | − | 0.850217i | \(-0.676471\pi\) | ||||
0.526432 | + | 0.850217i | \(0.323529\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.15331 | − | 4.32444i | −2.15331 | − | 4.32444i | ||||
\(163\) | 0.646741 | + | 1.66943i | 0.646741 | + | 1.66943i | 0.739009 | + | 0.673696i | \(0.235294\pi\) |
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(164\) | −0.646741 | − | 0.322039i | −0.646741 | − | 0.322039i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.293271 | + | 0.221468i | −0.293271 | + | 0.221468i | ||||
\(167\) | 0 | 0 | 0.932472 | − | 0.361242i | \(-0.117647\pi\) | ||||
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.932472 | − | 0.361242i | −0.932472 | − | 0.361242i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.243964 | − | 0.489946i | −0.243964 | − | 0.489946i | ||||
\(172\) | −1.07524 | + | 1.17948i | −1.07524 | + | 1.17948i | ||||
\(173\) | 0 | 0 | −0.273663 | − | 0.961826i | \(-0.588235\pi\) | ||||
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.18475 | + | 0.221468i | −1.18475 | + | 0.221468i | ||||
\(177\) | −3.03135 | − | 1.50943i | −3.03135 | − | 1.50943i | ||||
\(178\) | 1.92365i | 1.92365i | ||||||||
\(179\) | −0.486734 | − | 0.533922i | −0.486734 | − | 0.533922i | 0.445738 | − | 0.895163i | \(-0.352941\pi\) |
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.602635 | − | 0.798017i | \(-0.705882\pi\) | ||||
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.23509 | + | 0.764734i | 1.23509 | + | 0.764734i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.995734 | − | 0.0922684i | \(-0.0294118\pi\) | ||||
−0.995734 | + | 0.0922684i | \(0.970588\pi\) | |||||||
\(192\) | −1.04837 | − | 1.69318i | −1.04837 | − | 1.69318i | ||||
\(193\) | −0.0822551 | + | 0.887674i | −0.0822551 | + | 0.887674i | 0.850217 | + | 0.526432i | \(0.176471\pi\) |
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(194\) | 1.78269 | − | 0.165190i | 1.78269 | − | 0.165190i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.739009 | − | 0.673696i | 0.739009 | − | 0.673696i | ||||
\(197\) | 0 | 0 | 0.602635 | − | 0.798017i | \(-0.294118\pi\) | ||||
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(198\) | 2.64178 | + | 2.40830i | 2.64178 | + | 2.40830i | ||||
\(199\) | 0 | 0 | 0.673696 | − | 0.739009i | \(-0.264706\pi\) | ||||
−0.673696 | + | 0.739009i | \(0.735294\pi\) | |||||||
\(200\) | −0.850217 | + | 0.526432i | −0.850217 | + | 0.526432i | ||||
\(201\) | 3.89842 | − | 0.728741i | 3.89842 | − | 0.728741i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.441046 | + | 2.35939i | −0.441046 | + | 2.35939i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.164368 | + | 0.149841i | 0.164368 | + | 0.149841i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.44574 | + | 0.895163i | −1.44574 | + | 0.895163i | −0.445738 | + | 0.895163i | \(0.647059\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.18475 | − | 1.56886i | 1.18475 | − | 1.56886i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.41430 | + | 3.65074i | −1.41430 | + | 3.65074i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.95516 | + | 3.15769i | 1.95516 | + | 3.15769i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.961826 | − | 0.273663i | \(-0.0882353\pi\) | ||||
−0.961826 | + | 0.273663i | \(0.911765\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.76566 | + | 1.07142i | 2.76566 | + | 1.07142i | ||||
\(226\) | −0.380338 | + | 0.614268i | −0.380338 | + | 0.614268i | ||||
\(227\) | −0.247582 | − | 0.271585i | −0.247582 | − | 0.271585i | 0.602635 | − | 0.798017i | \(-0.294118\pi\) |
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(228\) | −0.132756 | + | 0.342683i | −0.132756 | + | 0.342683i | ||||
\(229\) | 0 | 0 | −0.183750 | − | 0.982973i | \(-0.558824\pi\) | ||||
0.183750 | + | 0.982973i | \(0.441176\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.79033i | 1.79033i | 0.445738 | + | 0.895163i | \(0.352941\pi\) | ||||
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.465346 | + | 1.63552i | 0.465346 | + | 1.63552i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.673696 | − | 0.739009i | \(-0.264706\pi\) | ||||
−0.673696 | + | 0.739009i | \(0.735294\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.78269 | − | 0.165190i | −1.78269 | − | 0.165190i | −0.850217 | − | 0.526432i | \(-0.823529\pi\) |
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(242\) | −0.422106 | − | 0.163525i | −0.422106 | − | 0.163525i | ||||
\(243\) | 5.48764 | − | 1.56137i | 5.48764 | − | 1.56137i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.867072 | − | 1.14819i | 0.867072 | − | 1.14819i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.326219 | − | 0.655137i | −0.326219 | − | 0.655137i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.27366 | + | 0.961826i | −1.27366 | + | 0.961826i | −0.273663 | + | 0.961826i | \(0.588235\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.273663 | + | 0.961826i | −0.273663 | + | 0.961826i | ||||
\(257\) | −0.172075 | + | 1.85699i | −0.172075 | + | 1.85699i | 0.273663 | + | 0.961826i | \(0.411765\pi\) |
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(258\) | −1.91545 | − | 2.53646i | −1.91545 | − | 2.53646i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.58923 | − | 0.147263i | −1.58923 | − | 0.147263i | ||||
\(263\) | 0 | 0 | 0.445738 | − | 0.895163i | \(-0.352941\pi\) | ||||
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(264\) | − | 2.40026i | − | 2.40026i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.76566 | − | 0.703924i | −3.76566 | − | 0.703924i | ||||
\(268\) | −1.58923 | − | 1.20013i | −1.58923 | − | 1.20013i | ||||
\(269\) | 0 | 0 | 0.526432 | − | 0.850217i | \(-0.323529\pi\) | ||||
−0.526432 | + | 0.850217i | \(0.676471\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.361242 | − | 0.932472i | \(-0.617647\pi\) | ||||
0.361242 | + | 0.932472i | \(0.382353\pi\) | |||||||
\(272\) | 1.02474 | − | 0.634493i | 1.02474 | − | 0.634493i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.739009 | + | 0.673696i | 0.739009 | + | 0.673696i | ||||
\(275\) | −1.20527 | −1.20527 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.361242 | − | 0.932472i | \(-0.617647\pi\) | ||||
0.361242 | + | 0.932472i | \(0.382353\pi\) | |||||||
\(278\) | 0.0822551 | − | 0.165190i | 0.0822551 | − | 0.165190i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.181395 | + | 0.0339085i | 0.181395 | + | 0.0339085i | 0.273663 | − | 0.961826i | \(-0.411765\pi\) |
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.09227 | − | 0.995734i | 1.09227 | − | 0.995734i | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) |
1.00000 | \(0\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.76566 | − | 1.07142i | 2.76566 | − | 1.07142i | ||||
\(289\) | −0.444966 | − | 0.0831786i | −0.444966 | − | 0.0831786i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.328972 | + | 3.55017i | −0.328972 | + | 3.55017i | ||||
\(292\) | 0.510366 | − | 1.79375i | 0.510366 | − | 1.79375i | ||||
\(293\) | 0 | 0 | 0.273663 | − | 0.961826i | \(-0.411765\pi\) | ||||
−0.273663 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(294\) | 1.04837 | + | 1.69318i | 1.04837 | + | 1.69318i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.76566 | + | 2.84370i | −3.76566 | + | 2.84370i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.719401 | − | 1.85699i | −0.719401 | − | 1.85699i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.172075 | − | 0.0666624i | 0.172075 | − | 0.0666624i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.33337 | − | 1.29135i | −3.33337 | − | 1.29135i | ||||
\(307\) | 1.98297 | + | 0.183750i | 1.98297 | + | 0.183750i | 1.00000 | \(0\) | ||
0.982973 | + | 0.183750i | \(0.0588235\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.538007 | − | 0.100571i | 0.538007 | − | 0.100571i | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) |
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.961826 | − | 0.273663i | \(-0.911765\pi\) | ||||
0.961826 | + | 0.273663i | \(0.0882353\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.63760 | + | 2.89331i | 2.63760 | + | 2.89331i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.207397 | − | 0.0803461i | −0.207397 | − | 0.0803461i | ||||
\(324\) | −4.10731 | − | 2.54314i | −4.10731 | − | 2.54314i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.42871 | + | 1.07891i | 1.42871 | + | 1.07891i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.719401 | + | 0.0666624i | −0.719401 | + | 0.0666624i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) | ||||
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(332\) | −0.132756 | + | 0.342683i | −0.132756 | + | 0.342683i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.58561 | − | 0.981767i | 1.58561 | − | 0.981767i | 0.602635 | − | 0.798017i | \(-0.294118\pi\) |
0.982973 | − | 0.183750i | \(-0.0588235\pi\) | |||||||
\(338\) | −0.982973 | + | 0.183750i | −0.982973 | + | 0.183750i | ||||
\(339\) | −1.06329 | − | 0.969315i | −1.06329 | − | 0.969315i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.465346 | − | 0.288130i | −0.465346 | − | 0.288130i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.293271 | + | 1.56886i | −0.293271 | + | 1.56886i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.45285 | + | 0.271585i | −1.45285 | + | 0.271585i | −0.850217 | − | 0.526432i | \(-0.823529\pi\) |
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.673696 | − | 0.739009i | \(-0.264706\pi\) | ||||
−0.673696 | + | 0.739009i | \(0.735294\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.890705 | + | 0.811985i | −0.890705 | + | 0.811985i | ||||
\(353\) | 0.132756 | − | 0.342683i | 0.132756 | − | 0.342683i | −0.850217 | − | 0.526432i | \(-0.823529\pi\) |
0.982973 | + | 0.183750i | \(0.0588235\pi\) | |||||||
\(354\) | −3.37192 | + | 0.312454i | −3.37192 | + | 0.312454i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.01267 | + | 1.63552i | 1.01267 | + | 1.63552i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.694903 | − | 0.197717i | −0.694903 | − | 0.197717i | ||||
\(359\) | 0 | 0 | −0.798017 | − | 0.602635i | \(-0.794118\pi\) | ||||
0.798017 | + | 0.602635i | \(0.205882\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.821264 | + | 0.508505i | 0.821264 | + | 0.508505i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.474571 | − | 0.766459i | 0.474571 | − | 0.766459i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.602635 | − | 0.798017i | \(-0.705882\pi\) | ||||
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.44363 | + | 1.58358i | 1.44363 | + | 1.58358i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.273663 | − | 0.961826i | \(-0.588235\pi\) | ||||
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(374\) | 1.45267 | 1.45267 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.831277 | − | 0.322039i | −0.831277 | − | 0.322039i | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.602635 | − | 0.798017i | \(-0.294118\pi\) | ||||
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(384\) | −1.78269 | − | 0.887674i | −1.78269 | − | 0.887674i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.397365 | + | 0.798017i | 0.397365 | + | 0.798017i | ||||
\(387\) | 4.23748 | − | 2.11001i | 4.23748 | − | 2.11001i | ||||
\(388\) | 1.42871 | − | 1.07891i | 1.42871 | − | 1.07891i | ||||
\(389\) | 0 | 0 | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) | ||||
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.273663 | − | 0.961826i | 0.273663 | − | 0.961826i | ||||
\(393\) | 0.869825 | − | 3.05712i | 0.869825 | − | 3.05712i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.51390 | + | 0.656861i | 3.51390 | + | 0.656861i | ||||
\(397\) | 0 | 0 | 0.932472 | − | 0.361242i | \(-0.117647\pi\) | ||||
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.445738 | + | 0.895163i | −0.445738 | + | 0.895163i | ||||
\(401\) | 1.34739i | 1.34739i | 0.739009 | + | 0.673696i | \(0.235294\pi\) | ||||
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(402\) | 2.93087 | − | 2.67184i | 2.93087 | − | 2.67184i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.867072 | + | 2.23817i | 0.867072 | + | 2.23817i | ||||
\(409\) | 0.757949 | − | 0.469302i | 0.757949 | − | 0.469302i | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) |
0.850217 | + | 0.526432i | \(0.176471\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.58923 | + | 1.20013i | −1.58923 | + | 1.20013i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.293271 | + | 0.221468i | 0.293271 | + | 0.221468i | ||||
\(418\) | 0.218629 | + | 0.0408689i | 0.218629 | + | 0.0408689i | ||||
\(419\) | −0.0822551 | − | 0.887674i | −0.0822551 | − | 0.887674i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) |
0.850217 | − | 0.526432i | \(-0.176471\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | −0.757949 | + | 1.52217i | −0.757949 | + | 1.52217i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.12388 | − | 0.435393i | 1.12388 | − | 0.435393i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.181395 | − | 1.95756i | 0.181395 | − | 1.95756i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.526432 | − | 0.850217i | \(-0.676471\pi\) | ||||
0.526432 | + | 0.850217i | \(0.323529\pi\) | |||||||
\(432\) | 0.719401 | + | 3.84846i | 0.719401 | + | 3.84846i | ||||
\(433\) | −0.0822551 | − | 0.887674i | −0.0822551 | − | 0.887674i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) |
0.850217 | − | 0.526432i | \(-0.176471\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 3.32462 | + | 1.65546i | 3.32462 | + | 1.65546i | ||||
\(439\) | 0 | 0 | 0.602635 | − | 0.798017i | \(-0.294118\pi\) | ||||
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.76566 | + | 1.07142i | −2.76566 | + | 1.07142i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.831277 | + | 0.322039i | 0.831277 | + | 0.322039i | 0.739009 | − | 0.673696i | \(-0.235294\pi\) |
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.243964 | − | 0.857445i | −0.243964 | − | 0.857445i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) |
0.739009 | − | 0.673696i | \(-0.235294\pi\) | |||||||
\(450\) | 2.91545 | − | 0.544991i | 2.91545 | − | 0.544991i | ||||
\(451\) | −0.779497 | − | 0.388143i | −0.779497 | − | 0.388143i | ||||
\(452\) | 0.722483i | 0.722483i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.353470 | − | 0.100571i | −0.353470 | − | 0.100571i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0675278 | + | 0.361242i | 0.0675278 | + | 0.361242i | ||||
\(457\) | 0.576554 | − | 1.48826i | 0.576554 | − | 1.48826i | −0.273663 | − | 0.961826i | \(-0.588235\pi\) |
0.850217 | − | 0.526432i | \(-0.176471\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.48411 | − | 4.01198i | 2.48411 | − | 4.01198i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.850217 | − | 0.526432i | \(-0.823529\pi\) | ||||
0.850217 | + | 0.526432i | \(0.176471\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.798017 | − | 0.602635i | \(-0.794118\pi\) | ||||
0.798017 | + | 0.602635i | \(0.205882\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.942485 | + | 1.52217i | 0.942485 | + | 1.52217i | ||||
\(467\) | 0.172075 | − | 1.85699i | 0.172075 | − | 1.85699i | −0.273663 | − | 0.961826i | \(-0.588235\pi\) |
0.445738 | − | 0.895163i | \(-0.352941\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.25664 | + | 1.14558i | 1.25664 | + | 1.14558i | ||||
\(473\) | −1.29596 | + | 1.42160i | −1.29596 | + | 1.42160i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.181395 | − | 0.0339085i | 0.181395 | − | 0.0339085i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.850217 | − | 0.526432i | \(-0.823529\pi\) | ||||
0.850217 | + | 0.526432i | \(0.176471\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.60263 | + | 0.798017i | −1.60263 | + | 0.798017i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.444966 | + | 0.0831786i | −0.444966 | + | 0.0831786i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.84373 | − | 4.21638i | 3.84373 | − | 4.21638i | ||||
\(487\) | 0 | 0 | −0.739009 | − | 0.673696i | \(-0.764706\pi\) | ||||
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.63485 | + | 2.40198i | −2.63485 | + | 2.40198i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.04837 | − | 0.0971461i | 1.04837 | − | 0.0971461i | 0.445738 | − | 0.895163i | \(-0.352941\pi\) |
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(492\) | 0.132756 | − | 1.43267i | 0.132756 | − | 1.43267i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.622242 | − | 0.385276i | −0.622242 | − | 0.385276i | ||||
\(499\) | 1.37821 | + | 0.533922i | 1.37821 | + | 0.533922i | 0.932472 | − | 0.361242i | \(-0.117647\pi\) |
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.576554 | + | 1.48826i | −0.576554 | + | 1.48826i | ||||
\(503\) | 0 | 0 | −0.183750 | − | 0.982973i | \(-0.558824\pi\) | ||||
0.183750 | + | 0.982973i | \(0.441176\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.99147i | − | 1.99147i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.982973 | − | 0.183750i | \(-0.0588235\pi\) | ||||
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.273663 | + | 0.961826i | 0.273663 | + | 0.961826i | ||||
\(513\) | 0.486734 | − | 0.533922i | 0.486734 | − | 0.533922i | ||||
\(514\) | 0.831277 | + | 1.66943i | 0.831277 | + | 1.66943i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.96382 | − | 1.14819i | −2.96382 | − | 1.14819i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.646741 | − | 0.322039i | −0.646741 | − | 0.322039i | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.658809 | − | 1.32307i | −0.658809 | − | 1.32307i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) |
0.273663 | − | 0.961826i | \(-0.411765\pi\) | |||||||
\(524\) | −1.42871 | + | 0.711414i | −1.42871 | + | 0.711414i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.26357 | − | 2.04074i | −1.26357 | − | 2.04074i | ||||
\(529\) | 0.273663 | − | 0.961826i | 0.273663 | − | 0.961826i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.465346 | − | 5.02188i | 0.465346 | − | 5.02188i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.57220 | + | 1.38388i | −3.57220 | + | 1.38388i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.98297 | − | 0.183750i | −1.98297 | − | 0.183750i | ||||
\(537\) | 0.641330 | − | 1.28796i | 0.641330 | − | 1.28796i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.890705 | − | 0.811985i | 0.890705 | − | 0.811985i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.982973 | − | 0.183750i | \(-0.941176\pi\) | ||||
0.982973 | + | 0.183750i | \(0.0588235\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.537235 | − | 1.07891i | 0.537235 | − | 1.07891i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.86494 | 1.86494 | 0.932472 | − | 0.361242i | \(-0.117647\pi\) | ||||
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(548\) | 0.982973 | + | 0.183750i | 0.982973 | + | 0.183750i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.02474 | + | 0.634493i | −1.02474 | + | 0.634493i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0170269 | − | 0.183750i | −0.0170269 | − | 0.183750i | ||||
\(557\) | 0 | 0 | 0.739009 | − | 0.673696i | \(-0.235294\pi\) | ||||
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.531579 | + | 2.84370i | −0.531579 | + | 2.84370i | ||||
\(562\) | 0.172075 | − | 0.0666624i | 0.172075 | − | 0.0666624i | ||||
\(563\) | 1.93247 | + | 0.361242i | 1.93247 | + | 0.361242i | 1.00000 | \(0\) | ||
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.404479 | − | 1.42160i | 0.404479 | − | 1.42160i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.247582 | − | 1.32445i | −0.247582 | − | 1.32445i | −0.850217 | − | 0.526432i | \(-0.823529\pi\) |
0.602635 | − | 0.798017i | \(-0.294118\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.293271 | + | 0.221468i | −0.293271 | + | 0.221468i | −0.739009 | − | 0.673696i | \(-0.764706\pi\) |
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.78738 | − | 2.36688i | 1.78738 | − | 2.36688i | ||||
\(577\) | −1.07524 | + | 0.811985i | −1.07524 | + | 0.811985i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) |
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(578\) | −0.422106 | + | 0.163525i | −0.422106 | + | 0.163525i | ||||
\(579\) | −1.70757 | + | 0.485847i | −1.70757 | + | 0.485847i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.58923 | + | 3.19160i | 1.58923 | + | 3.19160i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.510366 | − | 1.79375i | −0.510366 | − | 1.79375i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.538007 | + | 0.100571i | −0.538007 | + | 0.100571i | −0.445738 | − | 0.895163i | \(-0.647059\pi\) |
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(588\) | 1.78269 | + | 0.887674i | 1.78269 | + | 0.887674i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.193463 | + | 1.03494i | 0.193463 | + | 1.03494i | 0.932472 | + | 0.361242i | \(0.117647\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(594\) | −1.70462 | + | 4.40013i | −1.70462 | + | 4.40013i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.961826 | − | 0.273663i | \(-0.0882353\pi\) | ||||
−0.961826 | + | 0.273663i | \(0.911765\pi\) | |||||||
\(600\) | −1.58923 | − | 1.20013i | −1.58923 | − | 1.20013i | ||||
\(601\) | −0.353470 | − | 0.100571i | −0.353470 | − | 0.100571i | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) |
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.10942 | + | 5.02188i | 3.10942 | + | 5.02188i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.739009 | − | 0.673696i | \(-0.235294\pi\) | ||||
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(608\) | 0.111208 | − | 0.147263i | 0.111208 | − | 0.147263i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.51390 | + | 0.656861i | −3.51390 | + | 0.656861i | ||||
\(613\) | 0 | 0 | −0.739009 | − | 0.673696i | \(-0.764706\pi\) | ||||
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(614\) | 1.78269 | − | 0.887674i | 1.78269 | − | 0.887674i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.465346 | + | 0.288130i | 0.465346 | + | 0.288130i | 0.739009 | − | 0.673696i | \(-0.235294\pi\) |
−0.273663 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.20614 | + | 0.600584i | −1.20614 | + | 0.600584i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) |
−0.273663 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.602635 | + | 0.798017i | −0.602635 | + | 0.798017i | ||||
\(626\) | 0.404479 | − | 0.368731i | 0.404479 | − | 0.368731i | ||||
\(627\) | −0.160007 | + | 0.413025i | −0.160007 | + | 0.413025i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.995734 | − | 0.0922684i | \(-0.0294118\pi\) | ||||
−0.995734 | + | 0.0922684i | \(0.970588\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.70237 | − | 2.04074i | −2.70237 | − | 2.04074i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.890705 | − | 1.17948i | −0.890705 | − | 1.17948i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) |
0.0922684 | − | 0.995734i | \(-0.470588\pi\) | |||||||
\(642\) | 3.76566 | + | 1.07142i | 3.76566 | + | 1.07142i | ||||
\(643\) | −0.907732 | − | 0.995734i | −0.907732 | − | 0.995734i | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.218629 | + | 0.0408689i | −0.218629 | + | 0.0408689i | ||||
\(647\) | 0 | 0 | −0.273663 | − | 0.961826i | \(-0.588235\pi\) | ||||
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(648\) | −4.83089 | −4.83089 | ||||||||
\(649\) | 0.560867 | + | 1.97124i | 0.560867 | + | 1.97124i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.78269 | + | 0.165190i | 1.78269 | + | 0.165190i | ||||
\(653\) | 0 | 0 | −0.932472 | − | 0.361242i | \(-0.882353\pi\) | ||||
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.576554 | + | 0.435393i | −0.576554 | + | 0.435393i | ||||
\(657\) | −3.33337 | + | 4.41409i | −3.33337 | + | 4.41409i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.132756 | + | 0.342683i | 0.132756 | + | 0.342683i | 0.982973 | − | 0.183750i | \(-0.0588235\pi\) |
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.895163 | − | 0.445738i | \(-0.147059\pi\) | ||||
−0.895163 | + | 0.445738i | \(0.852941\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.0675278 | + | 0.361242i | 0.0675278 | + | 0.361242i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.58923 | − | 0.147263i | −1.58923 | − | 0.147263i | −0.739009 | − | 0.673696i | \(-0.764706\pi\) |
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(674\) | 0.831277 | − | 1.66943i | 0.831277 | − | 1.66943i | ||||
\(675\) | 3.91512i | 3.91512i | ||||||||
\(676\) | −0.739009 | + | 0.673696i | −0.739009 | + | 0.673696i | ||||
\(677\) | 0 | 0 | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) | ||||
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(678\) | −1.41430 | − | 0.264379i | −1.41430 | − | 0.264379i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.326219 | − | 0.655137i | 0.326219 | − | 0.655137i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.58561 | + | 0.981767i | −1.58561 | + | 0.981767i | −0.602635 | + | 0.798017i | \(0.705882\pi\) |
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(684\) | −0.547326 | −0.547326 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.576554 | + | 1.48826i | 0.576554 | + | 1.48826i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.602635 | − | 0.798017i | \(-0.294118\pi\) | ||||
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.09227 | + | 0.995734i | −1.09227 | + | 0.995734i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.867072 | + | 0.0803461i | 0.867072 | + | 0.0803461i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.32462 | + | 1.28796i | −3.32462 | + | 1.28796i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.602635 | − | 0.798017i | \(-0.705882\pi\) | ||||
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.329838 | + | 1.15926i | −0.329838 | + | 1.15926i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.0675278 | − | 0.361242i | −0.0675278 | − | 0.361242i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.70237 | + | 2.04074i | −2.70237 | + | 2.04074i | ||||
\(709\) | 0 | 0 | 0.895163 | − | 0.445738i | \(-0.147059\pi\) | ||||
−0.895163 | + | 0.445738i | \(0.852941\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.72198 | + | 0.857445i | 1.72198 | + | 0.857445i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.694903 | + | 0.197717i | −0.694903 | + | 0.197717i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.445738 | − | 0.895163i | \(-0.647059\pi\) | ||||
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.965946 | 0.965946 | ||||||||
\(723\) | −0.975712 | − | 3.42927i | −0.975712 | − | 3.42927i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 0.901486i | − | 0.901486i | ||||||
\(727\) | 0 | 0 | −0.673696 | − | 0.739009i | \(-0.735294\pi\) | ||||
0.673696 | + | 0.739009i | \(0.264706\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.93600 | + | 5.21211i | 3.93600 | + | 5.21211i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.694903 | − | 1.79375i | 0.694903 | − | 1.79375i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.526432 | − | 0.850217i | \(-0.323529\pi\) | ||||
−0.526432 | + | 0.850217i | \(0.676471\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.91545 | − | 1.44648i | −1.91545 | − | 1.44648i | ||||
\(738\) | 2.06104 | + | 0.586418i | 2.06104 | + | 0.586418i | ||||
\(739\) | 1.04837 | − | 0.0971461i | 1.04837 | − | 0.0971461i | 0.445738 | − | 0.895163i | \(-0.352941\pi\) |
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.361242 | − | 0.932472i | \(-0.382353\pi\) | ||||
−0.361242 | + | 0.932472i | \(0.617647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.734316 | − | 0.805507i | 0.734316 | − | 0.805507i | ||||
\(748\) | 1.23509 | − | 0.764734i | 1.23509 | − | 0.764734i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.895163 | − | 0.445738i | \(-0.147059\pi\) | ||||
−0.895163 | + | 0.445738i | \(0.852941\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.70237 | − | 1.67324i | −2.70237 | − | 1.67324i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.739009 | − | 0.673696i | \(-0.764706\pi\) | ||||
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(758\) | −0.876298 | + | 0.163808i | −0.876298 | + | 0.163808i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.45285 | + | 1.32445i | 1.45285 | + | 1.32445i | 0.850217 | + | 0.526432i | \(0.176471\pi\) |
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.98297 | + | 0.183750i | −1.98297 | + | 0.183750i | ||||
\(769\) | 1.01267 | + | 0.288130i | 1.01267 | + | 0.288130i | 0.739009 | − | 0.673696i | \(-0.235294\pi\) |
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.57220 | + | 1.01638i | −3.57220 | + | 1.01638i | ||||
\(772\) | 0.757949 | + | 0.469302i | 0.757949 | + | 0.469302i | ||||
\(773\) | 0 | 0 | −0.932472 | − | 0.361242i | \(-0.882353\pi\) | ||||
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(774\) | 2.49200 | − | 4.02472i | 2.49200 | − | 4.02472i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.646741 | − | 1.66943i | 0.646741 | − | 1.66943i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.128235 | + | 0.0364860i | 0.128235 | + | 0.0364860i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.273663 | − | 0.961826i | −0.273663 | − | 0.961826i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.869825 | − | 3.05712i | −0.869825 | − | 3.05712i | ||||
\(787\) | 1.20614 | − | 1.32307i | 1.20614 | − | 1.32307i | 0.273663 | − | 0.961826i | \(-0.411765\pi\) |
0.932472 | − | 0.361242i | \(-0.117647\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.33337 | − | 1.29135i | 3.33337 | − | 1.29135i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.445738 | − | 0.895163i | \(-0.647059\pi\) | ||||
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.0922684 | + | 0.995734i | 0.0922684 | + | 0.995734i | ||||
\(801\) | −1.04837 | − | 5.60830i | −1.04837 | − | 5.60830i | ||||
\(802\) | 0.709310 | + | 1.14558i | 0.709310 | + | 1.14558i | ||||
\(803\) | 0.615129 | − | 2.16195i | 0.615129 | − | 2.16195i | ||||
\(804\) | 1.08533 | − | 3.81455i | 1.08533 | − | 3.81455i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.193463 | − | 1.03494i | 0.193463 | − | 1.03494i | −0.739009 | − | 0.673696i | \(-0.764706\pi\) |
0.932472 | − | 0.361242i | \(-0.117647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.757949 | + | 1.52217i | −0.757949 | + | 1.52217i | 0.0922684 | + | 0.995734i | \(0.470588\pi\) |
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.91545 | + | 1.44648i | 1.91545 | + | 1.44648i | ||||
\(817\) | 0.155048 | − | 0.250412i | 0.155048 | − | 0.250412i | ||||
\(818\) | 0.397365 | − | 0.798017i | 0.397365 | − | 0.798017i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | −0.719401 | + | 1.85699i | −0.719401 | + | 1.85699i | ||||
\(823\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.867072 | − | 2.23817i | −0.867072 | − | 2.23817i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.380338 | + | 0.614268i | −0.380338 | + | 0.614268i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) |
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.982973 | − | 0.183750i | \(-0.941176\pi\) | ||||
0.982973 | + | 0.183750i | \(0.0588235\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.537235 | + | 1.07891i | −0.537235 | + | 1.07891i | ||||
\(834\) | 0.365931 | + | 0.0339085i | 0.365931 | + | 0.0339085i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.207397 | − | 0.0803461i | 0.207397 | − | 0.0803461i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.537235 | − | 0.711414i | −0.537235 | − | 0.711414i | ||||
\(839\) | 0 | 0 | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) | ||||
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.273663 | − | 0.961826i | 0.273663 | − | 0.961826i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.0675278 | + | 0.361242i | 0.0675278 | + | 0.361242i | ||||
\(844\) | 0.156896 | + | 1.69318i | 0.156896 | + | 1.69318i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.63485 | + | 1.31200i | 2.63485 | + | 1.31200i | ||||
\(850\) | 0.726337 | − | 0.961826i | 0.726337 | − | 0.961826i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.961826 | − | 0.273663i | \(-0.0882353\pi\) | ||||
−0.961826 | + | 0.273663i | \(0.911765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.876298 | − | 1.75984i | −0.876298 | − | 1.75984i | ||||
\(857\) | 1.34164 | − | 1.47171i | 1.34164 | − | 1.47171i | 0.602635 | − | 0.798017i | \(-0.294118\pi\) |
0.739009 | − | 0.673696i | \(-0.235294\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.86494 | −1.86494 | −0.932472 | − | 0.361242i | \(-0.882353\pi\) | ||||
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 2.63760 | + | 2.89331i | 2.63760 | + | 2.89331i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.537235 | − | 0.711414i | −0.537235 | − | 0.711414i | ||||
\(867\) | −0.165648 | − | 0.886136i | −0.165648 | − | 0.886136i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.10731 | + | 1.45315i | −5.10731 | + | 1.45315i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.69813 | − | 0.342683i | 3.69813 | − | 0.342683i | ||||
\(877\) | 0 | 0 | −0.526432 | − | 0.850217i | \(-0.676471\pi\) | ||||
0.526432 | + | 0.850217i | \(0.323529\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.658809 | + | 0.600584i | −0.658809 | + | 0.600584i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) |
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(882\) | −1.78738 | + | 2.36688i | −1.78738 | + | 2.36688i | ||||
\(883\) | −0.136374 | − | 0.124322i | −0.136374 | − | 0.124322i | 0.602635 | − | 0.798017i | \(-0.294118\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.876298 | − | 0.163808i | 0.876298 | − | 0.163808i | ||||
\(887\) | 0 | 0 | −0.739009 | − | 0.673696i | \(-0.764706\pi\) | ||||
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.95041 | − | 3.06516i | −4.95041 | − | 3.06516i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.658809 | − | 0.600584i | −0.658809 | − | 0.600584i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 2.19186 | − | 1.99815i | 2.19186 | − | 1.99815i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −0.867072 | + | 0.0803461i | −0.867072 | + | 0.0803461i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.380338 | + | 0.614268i | 0.380338 | + | 0.614268i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.293271 | + | 0.221468i | 0.293271 | + | 0.221468i | 0.739009 | − | 0.673696i | \(-0.235294\pi\) |
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(908\) | −0.353470 | + | 0.100571i | −0.353470 | + | 0.100571i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.526432 | − | 0.850217i | \(-0.323529\pi\) | ||||
−0.526432 | + | 0.850217i | \(0.676471\pi\) | |||||||
\(912\) | 0.247582 | + | 0.271585i | 0.247582 | + | 0.271585i | ||||
\(913\) | −0.160007 | + | 0.413025i | −0.160007 | + | 0.413025i | ||||
\(914\) | −0.293271 | − | 1.56886i | −0.293271 | − | 1.56886i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 4.71877i | − | 4.71877i | ||||||
\(919\) | 0 | 0 | −0.895163 | − | 0.445738i | \(-0.852941\pi\) | ||||
0.895163 | + | 0.445738i | \(0.147059\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.08533 | + | 3.81455i | 1.08533 | + | 3.81455i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.510366 | + | 0.197717i | −0.510366 | + | 0.197717i | −0.602635 | − | 0.798017i | \(-0.705882\pi\) |
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.111208 | + | 0.147263i | −0.111208 | + | 0.147263i | ||||
\(932\) | 1.60263 | + | 0.798017i | 1.60263 | + | 0.798017i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.831277 | − | 1.66943i | −0.831277 | − | 1.66943i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.136374 | − | 1.47171i | −0.136374 | − | 1.47171i | −0.739009 | − | 0.673696i | \(-0.764706\pi\) |
0.602635 | − | 0.798017i | \(-0.294118\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.573802 | + | 0.926722i | 0.573802 | + | 0.926722i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.273663 | − | 0.961826i | \(-0.411765\pi\) | ||||
−0.273663 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 1.67148 | + | 0.312454i | 1.67148 | + | 0.312454i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.353470 | + | 1.89090i | −0.353470 | + | 1.89090i | ||||
\(947\) | −1.04837 | − | 0.0971461i | −1.04837 | − | 0.0971461i | −0.445738 | − | 0.895163i | \(-0.647059\pi\) |
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.136374 | − | 0.124322i | 0.136374 | − | 0.124322i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.53511 | + | 1.15926i | 1.53511 | + | 1.15926i | 0.932472 | + | 0.361242i | \(0.117647\pi\) |
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.850217 | − | 0.526432i | 0.850217 | − | 0.526432i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.59905 | + | 5.21960i | −2.59905 | + | 5.21960i | ||||
\(964\) | −0.942485 | + | 1.52217i | −0.942485 | + | 1.52217i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) | ||||
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(968\) | −0.334530 | + | 0.304965i | −0.334530 | + | 0.304965i | ||||
\(969\) | − | 0.442935i | − | 0.442935i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.34164 | + | 0.124322i | 1.34164 | + | 0.124322i | 0.739009 | − | 0.673696i | \(-0.235294\pi\) |
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(972\) | 1.04837 | − | 5.60830i | 1.04837 | − | 5.60830i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.547326 | − | 1.92365i | 0.547326 | − | 1.92365i | 0.273663 | − | 0.961826i | \(-0.411765\pi\) |
0.273663 | − | 0.961826i | \(-0.411765\pi\) | |||||||
\(978\) | −0.975712 | + | 3.42927i | −0.975712 | + | 3.42927i | ||||
\(979\) | 1.22054 | + | 1.97124i | 1.22054 | + | 1.97124i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.840204 | − | 0.634493i | 0.840204 | − | 0.634493i | ||||
\(983\) | 0 | 0 | 0.895163 | − | 0.445738i | \(-0.147059\pi\) | ||||
−0.895163 | + | 0.445738i | \(0.852941\pi\) | |||||||
\(984\) | −0.641330 | − | 1.28796i | −0.641330 | − | 1.28796i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.932472 | − | 0.361242i | \(-0.882353\pi\) | ||||
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.731863 | −0.731863 | ||||||||
\(997\) | 0 | 0 | −0.273663 | − | 0.961826i | \(-0.588235\pi\) | ||||
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(998\) | 1.45285 | − | 0.271585i | 1.45285 | − | 0.271585i | ||||
\(999\) | 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 | 1096.1.u.a.699.1 | yes | 16 | |
8.3 | odd | 2 | CM | 1096.1.u.a.699.1 | yes | 16 | |
137.49 | even | 34 | inner | 1096.1.u.a.323.1 | ✓ | 16 | |
1096.323 | odd | 34 | inner | 1096.1.u.a.323.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1096.1.u.a.323.1 | ✓ | 16 | 137.49 | even | 34 | inner | |
1096.1.u.a.323.1 | ✓ | 16 | 1096.323 | odd | 34 | inner | |
1096.1.u.a.699.1 | yes | 16 | 1.1 | even | 1 | trivial | |
1096.1.u.a.699.1 | yes | 16 | 8.3 | odd | 2 | CM |