Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2740,1,Mod(3,2740)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2740, base_ring=CyclotomicField(136))
chi = DirichletCharacter(H, H._module([68, 102, 1]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2740.3");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2740 = 2^{2} \cdot 5 \cdot 137 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2740.cd (of order \(136\), degree \(64\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.36743813461\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Coefficient field: | \(\Q(\zeta_{136})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{64} - x^{60} + x^{56} - x^{52} + x^{48} - x^{44} + x^{40} - x^{36} + x^{32} - x^{28} + x^{24} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{136}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{136} - \cdots)\) |
Embedding invariants
Embedding label | 603.1 | ||
Root | \(-0.914794 - 0.403921i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2740.603 |
Dual form | 2740.1.cd.a.827.1 |
$q$-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 \(\left(\mathbb{Z}/2740\mathbb{Z}\right)^\times\).
\(n\) | \(1097\) | \(1371\) | \(1921\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{61}{136}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.739009 | − | 0.673696i | −0.739009 | − | 0.673696i | ||||
\(3\) | 0 | 0 | 0.584041 | − | 0.811724i | \(-0.301471\pi\) | ||||
−0.584041 | + | 0.811724i | \(0.698529\pi\) | |||||||
\(4\) | 0.0922684 | + | 0.995734i | 0.0922684 | + | 0.995734i | ||||
\(5\) | −0.990410 | + | 0.138156i | −0.990410 | + | 0.138156i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.273663 | − | 0.961826i | \(-0.411765\pi\) | ||||
−0.273663 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(8\) | 0.602635 | − | 0.798017i | 0.602635 | − | 0.798017i | ||||
\(9\) | −0.317791 | − | 0.948161i | −0.317791 | − | 0.948161i | ||||
\(10\) | 0.824997 | + | 0.565136i | 0.824997 | + | 0.565136i | ||||
\(11\) | 0 | 0 | 0.638847 | − | 0.769334i | \(-0.279412\pi\) | ||||
−0.638847 | + | 0.769334i | \(0.720588\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.107475 | + | 0.926378i | 0.107475 | + | 0.926378i | 0.932472 | + | 0.361242i | \(0.117647\pi\) |
−0.824997 | + | 0.565136i | \(0.808824\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.982973 | + | 0.183750i | −0.982973 | + | 0.183750i | ||||
\(17\) | 0.220502 | − | 0.166516i | 0.220502 | − | 0.166516i | −0.486604 | − | 0.873622i | \(-0.661765\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | −0.403921 | + | 0.914794i | −0.403921 | + | 0.914794i | ||||
\(19\) | 0 | 0 | −0.914794 | − | 0.403921i | \(-0.867647\pi\) | ||||
0.914794 | + | 0.403921i | \(0.132353\pi\) | |||||||
\(20\) | −0.228951 | − | 0.973438i | −0.228951 | − | 0.973438i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.545930 | − | 0.837831i | \(-0.683824\pi\) | ||||
0.545930 | + | 0.837831i | \(0.316176\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.961826 | − | 0.273663i | 0.961826 | − | 0.273663i | ||||
\(26\) | 0.544672 | − | 0.757007i | 0.544672 | − | 0.757007i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.677943 | − | 1.04043i | −0.677943 | − | 1.04043i | −0.995734 | − | 0.0922684i | \(-0.970588\pi\) |
0.317791 | − | 0.948161i | \(-0.397059\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.690585 | − | 0.723251i | \(-0.257353\pi\) | ||||
−0.690585 | + | 0.723251i | \(0.742647\pi\) | |||||||
\(32\) | 0.850217 | + | 0.526432i | 0.850217 | + | 0.526432i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.275134 | − | 0.0254949i | −0.275134 | − | 0.0254949i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.914794 | − | 0.403921i | 0.914794 | − | 0.403921i | ||||
\(37\) | 0.0923669i | 0.0923669i | 0.998933 | + | 0.0461835i | \(0.0147059\pi\) | ||||
−0.998933 | + | 0.0461835i | \(0.985294\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.486604 | + | 0.873622i | −0.486604 | + | 0.873622i | ||||
\(41\) | −0.765163 | − | 1.84727i | −0.765163 | − | 1.84727i | −0.403921 | − | 0.914794i | \(-0.632353\pi\) |
−0.361242 | − | 0.932472i | \(-0.617647\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.723251 | − | 0.690585i | \(-0.242647\pi\) | ||||
−0.723251 | + | 0.690585i | \(0.757353\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.445738 | + | 0.895163i | 0.445738 | + | 0.895163i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.656446 | − | 0.754373i | \(-0.727941\pi\) | ||||
0.656446 | + | 0.754373i | \(0.272059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.850217 | − | 0.526432i | −0.850217 | − | 0.526432i | ||||
\(50\) | −0.895163 | − | 0.445738i | −0.895163 | − | 0.445738i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.912510 | + | 0.192492i | −0.912510 | + | 0.192492i | ||||
\(53\) | 1.93526 | + | 0.0447124i | 1.93526 | + | 0.0447124i | 0.973438 | − | 0.228951i | \(-0.0735294\pi\) |
0.961826 | + | 0.273663i | \(0.0882353\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.199927 | + | 1.22561i | −0.199927 | + | 1.22561i | ||||
\(59\) | 0 | 0 | −0.895163 | − | 0.445738i | \(-0.852941\pi\) | ||||
0.895163 | + | 0.445738i | \(0.147059\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.348448 | + | 0.116788i | 0.348448 | + | 0.116788i | 0.486604 | − | 0.873622i | \(-0.338235\pi\) |
−0.138156 | + | 0.990410i | \(0.544118\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.273663 | − | 0.961826i | −0.273663 | − | 0.961826i | ||||
\(65\) | −0.234429 | − | 0.902646i | −0.234429 | − | 0.902646i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.783885 | − | 0.620906i | \(-0.786765\pi\) | ||||
0.783885 | + | 0.620906i | \(0.213235\pi\) | |||||||
\(68\) | 0.186151 | + | 0.204198i | 0.186151 | + | 0.204198i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.884629 | − | 0.466296i | \(-0.845588\pi\) | ||||
0.884629 | + | 0.466296i | \(0.154412\pi\) | |||||||
\(72\) | −0.948161 | − | 0.317791i | −0.948161 | − | 0.317791i | ||||
\(73\) | 0.309277 | − | 0.555259i | 0.309277 | − | 0.555259i | −0.673696 | − | 0.739009i | \(-0.735294\pi\) |
0.982973 | + | 0.183750i | \(0.0588235\pi\) | |||||||
\(74\) | 0.0622272 | − | 0.0682600i | 0.0622272 | − | 0.0682600i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.584041 | − | 0.811724i | \(-0.698529\pi\) | ||||
0.584041 | + | 0.811724i | \(0.301471\pi\) | |||||||
\(80\) | 0.948161 | − | 0.317791i | 0.948161 | − | 0.317791i | ||||
\(81\) | −0.798017 | + | 0.602635i | −0.798017 | + | 0.602635i | ||||
\(82\) | −0.679033 | + | 1.88063i | −0.679033 | + | 1.88063i | ||||
\(83\) | 0 | 0 | 0.251374 | − | 0.967890i | \(-0.419118\pi\) | ||||
−0.251374 | + | 0.967890i | \(0.580882\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.195383 | + | 0.195383i | −0.195383 | + | 0.195383i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.396689 | − | 1.09866i | −0.396689 | − | 1.09866i | −0.961826 | − | 0.273663i | \(-0.911765\pi\) |
0.565136 | − | 0.824997i | \(-0.308824\pi\) | |||||||
\(90\) | 0.273663 | − | 0.961826i | 0.273663 | − | 0.961826i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.861602 | − | 1.63458i | −0.861602 | − | 1.63458i | −0.769334 | − | 0.638847i | \(-0.779412\pi\) |
−0.0922684 | − | 0.995734i | \(-0.529412\pi\) | |||||||
\(98\) | 0.273663 | + | 0.961826i | 0.273663 | + | 0.961826i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.361242 | + | 0.932472i | 0.361242 | + | 0.932472i | ||||
\(101\) | −0.686841 | − | 1.55555i | −0.686841 | − | 1.55555i | −0.824997 | − | 0.565136i | \(-0.808824\pi\) |
0.138156 | − | 0.990410i | \(-0.455882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.638847 | − | 0.769334i | \(-0.720588\pi\) | ||||
0.638847 | + | 0.769334i | \(0.279412\pi\) | |||||||
\(104\) | 0.804034 | + | 0.472501i | 0.804034 | + | 0.472501i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.40005 | − | 1.33682i | −1.40005 | − | 1.33682i | ||||
\(107\) | 0 | 0 | 0.850217 | − | 0.526432i | \(-0.176471\pi\) | ||||
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.60617 | − | 1.10025i | 1.60617 | − | 1.10025i | 0.673696 | − | 0.739009i | \(-0.264706\pi\) |
0.932472 | − | 0.361242i | \(-0.117647\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.930353 | − | 1.76501i | 0.930353 | − | 1.76501i | 0.403921 | − | 0.914794i | \(-0.367647\pi\) |
0.526432 | − | 0.850217i | \(-0.323529\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.973438 | − | 0.771049i | 0.973438 | − | 0.771049i | ||||
\(117\) | 0.844201 | − | 0.396298i | 0.844201 | − | 0.396298i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.183750 | − | 0.982973i | −0.183750 | − | 0.982973i | ||||
\(122\) | −0.178827 | − | 0.321055i | −0.178827 | − | 0.321055i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.914794 | + | 0.403921i | −0.914794 | + | 0.403921i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(128\) | −0.445738 | + | 0.895163i | −0.445738 | + | 0.895163i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.434864 | + | 0.824997i | −0.434864 | + | 0.824997i | ||||
\(131\) | 0 | 0 | −0.206405 | − | 0.978467i | \(-0.566176\pi\) | ||||
0.206405 | + | 0.978467i | \(0.433824\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 0.276313i | − | 0.276313i | ||||||
\(137\) | −0.961826 | + | 0.273663i | −0.961826 | + | 0.273663i | ||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.998933 | − | 0.0461835i | \(-0.0147059\pi\) | ||||
−0.998933 | + | 0.0461835i | \(0.985294\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.486604 | + | 0.873622i | 0.486604 | + | 0.873622i | ||||
\(145\) | 0.815183 | + | 0.936790i | 0.815183 | + | 0.936790i | ||||
\(146\) | −0.602635 | + | 0.201983i | −0.602635 | + | 0.201983i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.0919729 | + | 0.00852254i | −0.0919729 | + | 0.00852254i | ||||
\(149\) | 0.822596 | − | 0.213639i | 0.822596 | − | 0.213639i | 0.183750 | − | 0.982973i | \(-0.441176\pi\) |
0.638847 | + | 0.769334i | \(0.279412\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.526432 | − | 0.850217i | \(-0.676471\pi\) | ||||
0.526432 | + | 0.850217i | \(0.323529\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.227957 | − | 0.156154i | −0.227957 | − | 0.156154i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.288627 | + | 0.614838i | 0.288627 | + | 0.614838i | 0.995734 | − | 0.0922684i | \(-0.0294118\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.914794 | − | 0.403921i | −0.914794 | − | 0.403921i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.995734 | + | 0.0922684i | 0.995734 | + | 0.0922684i | ||||
\(163\) | 0 | 0 | 0.986955 | − | 0.160996i | \(-0.0514706\pi\) | ||||
−0.986955 | + | 0.160996i | \(0.948529\pi\) | |||||||
\(164\) | 1.76879 | − | 0.932343i | 1.76879 | − | 0.932343i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.526432 | − | 0.850217i | \(-0.676471\pi\) | ||||
0.526432 | + | 0.850217i | \(0.323529\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.126813 | − | 0.0298260i | 0.126813 | − | 0.0298260i | ||||
\(170\) | 0.276018 | − | 0.0127611i | 0.276018 | − | 0.0127611i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.510366 | − | 0.197717i | −0.510366 | − | 0.197717i | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) |
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.447006 | + | 1.07917i | −0.447006 | + | 1.07917i | ||||
\(179\) | 0 | 0 | −0.656446 | − | 0.754373i | \(-0.727941\pi\) | ||||
0.656446 | + | 0.754373i | \(0.272059\pi\) | |||||||
\(180\) | −0.850217 | + | 0.526432i | −0.850217 | + | 0.526432i | ||||
\(181\) | −0.987432 | + | 1.44147i | −0.987432 | + | 1.44147i | −0.0922684 | + | 0.995734i | \(0.529412\pi\) |
−0.895163 | + | 0.445738i | \(0.852941\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0127611 | − | 0.0914812i | −0.0127611 | − | 0.0914812i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.862150 | − | 0.506653i | \(-0.169118\pi\) | ||||
−0.862150 | + | 0.506653i | \(0.830882\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.247345 | + | 1.77316i | −0.247345 | + | 1.77316i | 0.317791 | + | 0.948161i | \(0.397059\pi\) |
−0.565136 | + | 0.824997i | \(0.691176\pi\) | |||||||
\(194\) | −0.464478 | + | 1.78843i | −0.464478 | + | 1.78843i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.445738 | − | 0.895163i | 0.445738 | − | 0.895163i | ||||
\(197\) | −0.868610 | + | 0.595012i | −0.868610 | + | 0.595012i | −0.914794 | − | 0.403921i | \(-0.867647\pi\) |
0.0461835 | + | 0.998933i | \(0.485294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.656446 | − | 0.754373i | \(-0.272059\pi\) | ||||
−0.656446 | + | 0.754373i | \(0.727941\pi\) | |||||||
\(200\) | 0.361242 | − | 0.932472i | 0.361242 | − | 0.932472i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.540383 | + | 1.61228i | −0.540383 | + | 1.61228i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.01304 | + | 1.72384i | 1.01304 | + | 1.72384i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.275866 | − | 0.890856i | −0.275866 | − | 0.890856i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.739009 | − | 0.673696i | \(-0.764706\pi\) | ||||
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(212\) | 0.134042 | + | 1.93113i | 0.134042 | + | 1.93113i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.92821 | − | 0.268973i | −1.92821 | − | 0.268973i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.177955 | + | 0.186372i | 0.177955 | + | 0.186372i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.723251 | − | 0.690585i | \(-0.757353\pi\) | ||||
0.723251 | + | 0.690585i | \(0.242647\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.565136 | − | 0.824997i | −0.565136 | − | 0.824997i | ||||
\(226\) | −1.87662 | + | 0.677584i | −1.87662 | + | 0.677584i | ||||
\(227\) | 0 | 0 | 0.754373 | − | 0.656446i | \(-0.227941\pi\) | ||||
−0.754373 | + | 0.656446i | \(0.772059\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.166699 | − | 1.43686i | 0.166699 | − | 1.43686i | −0.602635 | − | 0.798017i | \(-0.705882\pi\) |
0.769334 | − | 0.638847i | \(-0.220588\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.23883 | − | 0.0859886i | −1.23883 | − | 0.0859886i | ||||
\(233\) | 0.936174 | + | 0.387776i | 0.936174 | + | 0.387776i | 0.798017 | − | 0.602635i | \(-0.205882\pi\) |
0.138156 | + | 0.990410i | \(0.455882\pi\) | |||||||
\(234\) | −0.890856 | − | 0.275866i | −0.890856 | − | 0.275866i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.0692444 | − | 0.997600i | \(-0.522059\pi\) | ||||
0.0692444 | + | 0.997600i | \(0.477941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.764411 | + | 1.30076i | −0.764411 | + | 1.30076i | 0.183750 | + | 0.982973i | \(0.441176\pi\) |
−0.948161 | + | 0.317791i | \(0.897059\pi\) | |||||||
\(242\) | −0.526432 | + | 0.850217i | −0.526432 | + | 0.850217i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.0841391 | + | 0.357738i | −0.0841391 | + | 0.357738i | ||||
\(245\) | 0.914794 | + | 0.403921i | 0.914794 | + | 0.403921i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.948161 | + | 0.317791i | 0.948161 | + | 0.317791i | ||||
\(251\) | 0 | 0 | 0.206405 | − | 0.978467i | \(-0.433824\pi\) | ||||
−0.206405 | + | 0.978467i | \(0.566176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.932472 | − | 0.361242i | 0.932472 | − | 0.361242i | ||||
\(257\) | 0.927255 | + | 1.22788i | 0.927255 | + | 1.22788i | 0.973438 | + | 0.228951i | \(0.0735294\pi\) |
−0.0461835 | + | 0.998933i | \(0.514706\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.877165 | − | 0.316715i | 0.877165 | − | 0.316715i | ||||
\(261\) | −0.771049 | + | 0.973438i | −0.771049 | + | 0.973438i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) | ||||
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.92288 | + | 0.223085i | −1.92288 | + | 0.223085i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.0588498 | + | 0.125363i | −0.0588498 | + | 0.125363i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) |
0.873622 | + | 0.486604i | \(0.161765\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.986955 | − | 0.160996i | \(-0.0514706\pi\) | ||||
−0.986955 | + | 0.160996i | \(0.948529\pi\) | |||||||
\(272\) | −0.186151 | + | 0.204198i | −0.186151 | + | 0.204198i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.895163 | + | 0.445738i | 0.895163 | + | 0.445738i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.621267 | − | 0.447006i | −0.621267 | − | 0.447006i | 0.228951 | − | 0.973438i | \(-0.426471\pi\) |
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.74538 | − | 0.972171i | 1.74538 | − | 0.972171i | 0.850217 | − | 0.526432i | \(-0.176471\pi\) |
0.895163 | − | 0.445738i | \(-0.147059\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.895163 | − | 0.445738i | \(-0.852941\pi\) | ||||
0.895163 | + | 0.445738i | \(0.147059\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.228951 | − | 0.973438i | 0.228951 | − | 0.973438i | ||||
\(289\) | −0.252769 | + | 0.888391i | −0.252769 | + | 0.888391i | ||||
\(290\) | 0.0286833 | − | 1.24148i | 0.0286833 | − | 1.24148i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.581427 | + | 0.256725i | 0.581427 | + | 0.256725i | ||||
\(293\) | −1.19141 | + | 0.461556i | −1.19141 | + | 0.461556i | −0.873622 | − | 0.486604i | \(-0.838235\pi\) |
−0.317791 | + | 0.948161i | \(0.602941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.0737104 | + | 0.0556635i | 0.0737104 | + | 0.0556635i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.751834 | − | 0.396298i | −0.751834 | − | 0.396298i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.361242 | − | 0.0675278i | −0.361242 | − | 0.0675278i | ||||
\(306\) | 0.0632619 | + | 0.268973i | 0.0632619 | + | 0.268973i | ||||
\(307\) | 0 | 0 | 0.967890 | − | 0.251374i | \(-0.0808824\pi\) | ||||
−0.967890 | + | 0.251374i | \(0.919118\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.58701 | − | 0.451543i | 1.58701 | − | 0.451543i | 0.638847 | − | 0.769334i | \(-0.279412\pi\) |
0.948161 | + | 0.317791i | \(0.102941\pi\) | |||||||
\(314\) | 0.200916 | − | 0.648818i | 0.200916 | − | 0.648818i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.0319021 | − | 0.0334111i | −0.0319021 | − | 0.0334111i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.403921 | + | 0.914794i | 0.403921 | + | 0.914794i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.673696 | − | 0.739009i | −0.673696 | − | 0.739009i | ||||
\(325\) | 0.356887 | + | 0.861602i | 0.356887 | + | 0.861602i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.93526 | − | 0.502614i | −1.93526 | − | 0.502614i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.967890 | − | 0.251374i | \(-0.919118\pi\) | ||||
0.967890 | + | 0.251374i | \(0.0808824\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.0875787 | − | 0.0293534i | 0.0875787 | − | 0.0293534i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.00852254 | − | 0.184340i | −0.00852254 | − | 0.184340i | −0.998933 | − | 0.0461835i | \(-0.985294\pi\) |
0.990410 | − | 0.138156i | \(-0.0441176\pi\) | |||||||
\(338\) | −0.113809 | − | 0.0633913i | −0.113809 | − | 0.0633913i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.212577 | − | 0.176521i | −0.212577 | − | 0.176521i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.243964 | + | 0.489946i | 0.243964 | + | 0.489946i | ||||
\(347\) | 0 | 0 | −0.873622 | − | 0.486604i | \(-0.838235\pi\) | ||||
0.873622 | + | 0.486604i | \(0.161765\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.379259 | + | 0.330027i | 0.379259 | + | 0.330027i | 0.824997 | − | 0.565136i | \(-0.191176\pi\) |
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.29577 | − | 0.211370i | −1.29577 | − | 0.211370i | −0.526432 | − | 0.850217i | \(-0.676471\pi\) |
−0.769334 | + | 0.638847i | \(0.779412\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.05737 | − | 0.496369i | 1.05737 | − | 0.496369i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.837831 | − | 0.545930i | \(-0.816176\pi\) | ||||
0.837831 | + | 0.545930i | \(0.183824\pi\) | |||||||
\(360\) | 0.982973 | + | 0.183750i | 0.982973 | + | 0.183750i | ||||
\(361\) | 0.673696 | + | 0.739009i | 0.673696 | + | 0.739009i | ||||
\(362\) | 1.70083 | − | 0.400033i | 1.70083 | − | 0.400033i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.229599 | + | 0.592663i | −0.229599 | + | 0.592663i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.982973 | − | 0.183750i | \(-0.0588235\pi\) | ||||
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.50834 | + | 1.31254i | −1.50834 | + | 1.31254i | ||||
\(370\) | −0.0521999 | + | 0.0762025i | −0.0521999 | + | 0.0762025i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.82178 | − | 0.804396i | 1.82178 | − | 0.804396i | 0.873622 | − | 0.486604i | \(-0.161765\pi\) |
0.948161 | − | 0.317791i | \(-0.102941\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.890969 | − | 0.739851i | 0.890969 | − | 0.739851i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.228951 | − | 0.973438i | \(-0.573529\pi\) | ||||
0.228951 | + | 0.973438i | \(0.426471\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.183750 | − | 0.982973i | \(-0.441176\pi\) | ||||
−0.183750 | + | 0.982973i | \(0.558824\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.37736 | − | 1.14374i | 1.37736 | − | 1.14374i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.54811 | − | 1.00875i | 1.54811 | − | 1.00875i | ||||
\(389\) | 1.51330 | + | 1.14279i | 1.51330 | + | 1.14279i | 0.948161 | + | 0.317791i | \(0.102941\pi\) |
0.565136 | + | 0.824997i | \(0.308824\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.932472 | + | 0.361242i | −0.932472 | + | 0.361242i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.04277 | + | 0.145460i | 1.04277 | + | 0.145460i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.308486 | + | 1.31160i | −0.308486 | + | 1.31160i | 0.565136 | + | 0.824997i | \(0.308824\pi\) |
−0.873622 | + | 0.486604i | \(0.838235\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.895163 | + | 0.445738i | −0.895163 | + | 0.445738i | ||||
\(401\) | −0.760267 | + | 1.83545i | −0.760267 | + | 1.83545i | −0.273663 | + | 0.961826i | \(0.588235\pi\) |
−0.486604 | + | 0.873622i | \(0.661765\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.48554 | − | 0.827439i | 1.48554 | − | 0.827439i | ||||
\(405\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.0333668 | − | 0.721712i | −0.0333668 | − | 0.721712i | −0.948161 | − | 0.317791i | \(-0.897059\pi\) |
0.914794 | − | 0.403921i | \(-0.132353\pi\) | |||||||
\(410\) | 0.412700 | − | 1.95641i | 0.412700 | − | 1.95641i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.396298 | + | 0.844201i | −0.396298 | + | 0.844201i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.990410 | − | 0.138156i | \(-0.0441176\pi\) | ||||
−0.990410 | + | 0.138156i | \(0.955882\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.297482 | − | 0.123221i | −0.297482 | − | 0.123221i | 0.228951 | − | 0.973438i | \(-0.426471\pi\) |
−0.526432 | + | 0.850217i | \(0.676471\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.20194 | − | 1.51743i | 1.20194 | − | 1.51743i | ||||
\(425\) | 0.166516 | − | 0.220502i | 0.166516 | − | 0.220502i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.339607 | − | 0.940567i | \(-0.389706\pi\) | ||||
−0.339607 | + | 0.940567i | \(0.610294\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.0632619 | + | 0.453510i | 0.0632619 | + | 0.453510i | 0.995734 | + | 0.0922684i | \(0.0294118\pi\) |
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.24376 | + | 1.49780i | 1.24376 | + | 1.49780i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.565136 | − | 0.824997i | \(-0.691176\pi\) | ||||
0.565136 | + | 0.824997i | \(0.308824\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.228951 | + | 0.973438i | −0.228951 | + | 0.973438i | ||||
\(442\) | −0.00595202 | − | 0.257618i | −0.00595202 | − | 0.257618i | ||||
\(443\) | 0 | 0 | 0.526432 | − | 0.850217i | \(-0.323529\pi\) | ||||
−0.526432 | + | 0.850217i | \(0.676471\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.544672 | + | 1.03332i | 0.544672 | + | 1.03332i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.351564 | − | 0.907490i | 0.351564 | − | 0.907490i | −0.638847 | − | 0.769334i | \(-0.720588\pi\) |
0.990410 | − | 0.138156i | \(-0.0441176\pi\) | |||||||
\(450\) | −0.138156 | + | 0.990410i | −0.138156 | + | 0.990410i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.84332 | + | 0.763530i | 1.84332 | + | 0.763530i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.15285 | − | 1.60227i | −1.15285 | − | 1.60227i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.445738 | − | 0.895163i | \(-0.647059\pi\) | |||||||
\(458\) | −1.09120 | + | 0.949551i | −1.09120 | + | 0.949551i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.658809 | + | 0.600584i | −0.658809 | + | 0.600584i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) |
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.206405 | − | 0.978467i | \(-0.566176\pi\) | ||||
0.206405 | + | 0.978467i | \(0.433824\pi\) | |||||||
\(464\) | 0.857578 | + | 0.898142i | 0.857578 | + | 0.898142i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.430598 | − | 0.917266i | −0.430598 | − | 0.917266i | ||||
\(467\) | 0 | 0 | −0.990410 | − | 0.138156i | \(-0.955882\pi\) | ||||
0.990410 | + | 0.138156i | \(0.0441176\pi\) | |||||||
\(468\) | 0.472501 | + | 0.804034i | 0.472501 | + | 0.804034i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.572616 | − | 1.84915i | −0.572616 | − | 1.84915i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.0461835 | − | 0.998933i | \(-0.485294\pi\) | ||||
−0.0461835 | + | 0.998933i | \(0.514706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0855667 | + | 0.00992711i | −0.0855667 | + | 0.00992711i | ||||
\(482\) | 1.44123 | − | 0.446296i | 1.44123 | − | 0.446296i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.961826 | − | 0.273663i | 0.961826 | − | 0.273663i | ||||
\(485\) | 1.07917 | + | 1.49987i | 1.07917 | + | 1.49987i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.445738 | − | 0.895163i | \(-0.647059\pi\) | ||||
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(488\) | 0.303186 | − | 0.207687i | 0.303186 | − | 0.207687i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.403921 | − | 0.914794i | −0.403921 | − | 0.914794i | ||||
\(491\) | 0 | 0 | 0.251374 | − | 0.967890i | \(-0.419118\pi\) | ||||
−0.251374 | + | 0.967890i | \(0.580882\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.322736 | − | 0.116529i | −0.322736 | − | 0.116529i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.526432 | − | 0.850217i | \(-0.323529\pi\) | ||||
−0.526432 | + | 0.850217i | \(0.676471\pi\) | |||||||
\(500\) | −0.486604 | − | 0.873622i | −0.486604 | − | 0.873622i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.620906 | − | 0.783885i | \(-0.713235\pi\) | ||||
0.620906 | + | 0.783885i | \(0.286765\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.895163 | + | 1.44574i | 0.895163 | + | 1.44574i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.719210 | − | 1.29123i | 0.719210 | − | 1.29123i | −0.228951 | − | 0.973438i | \(-0.573529\pi\) |
0.948161 | − | 0.317791i | \(-0.102941\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.932472 | − | 0.361242i | −0.932472 | − | 0.361242i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.141970 | − | 1.53210i | 0.141970 | − | 1.53210i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.861602 | − | 0.356887i | −0.861602 | − | 0.356887i | ||||
\(521\) | −0.203895 | + | 0.107475i | −0.203895 | + | 0.107475i | −0.565136 | − | 0.824997i | \(-0.691176\pi\) |
0.361242 | + | 0.932472i | \(0.382353\pi\) | |||||||
\(522\) | 1.22561 | − | 0.199927i | 1.22561 | − | 0.199927i | ||||
\(523\) | 0 | 0 | −0.995734 | − | 0.0922684i | \(-0.970588\pi\) | ||||
0.995734 | + | 0.0922684i | \(0.0294118\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.403921 | + | 0.914794i | −0.403921 | + | 0.914794i | ||||
\(530\) | 1.57132 | + | 1.13058i | 1.57132 | + | 1.13058i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.62903 | − | 0.907364i | 1.62903 | − | 0.907364i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.127947 | − | 0.0529974i | 0.127947 | − | 0.0529974i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.907490 | + | 1.62926i | 0.907490 | + | 1.62926i | 0.769334 | + | 0.638847i | \(0.220588\pi\) |
0.138156 | + | 0.990410i | \(0.455882\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.275134 | − | 0.0254949i | 0.275134 | − | 0.0254949i | ||||
\(545\) | −1.43876 | + | 1.31160i | −1.43876 | + | 1.31160i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(548\) | −0.361242 | − | 0.932472i | −0.361242 | − | 0.932472i | ||||
\(549\) | − | 0.367499i | − | 0.367499i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.157976 | + | 0.748886i | 0.157976 | + | 0.748886i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.711414 | + | 1.42871i | −0.711414 | + | 1.42871i | 0.183750 | + | 0.982973i | \(0.441176\pi\) |
−0.895163 | + | 0.445738i | \(0.852941\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.94480 | − | 0.457413i | −1.94480 | − | 0.457413i | ||||
\(563\) | 0 | 0 | −0.486604 | − | 0.873622i | \(-0.661765\pi\) | ||||
0.486604 | + | 0.873622i | \(0.338235\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.677584 | + | 1.87662i | −0.677584 | + | 1.87662i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.08268 | + | 0.857578i | −1.08268 | + | 0.857578i | −0.990410 | − | 0.138156i | \(-0.955882\pi\) |
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.978467 | − | 0.206405i | \(-0.933824\pi\) | ||||
0.978467 | + | 0.206405i | \(0.0661765\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.824997 | + | 0.565136i | −0.824997 | + | 0.565136i | ||||
\(577\) | 0.373684 | − | 1.77146i | 0.373684 | − | 1.77146i | −0.228951 | − | 0.973438i | \(-0.573529\pi\) |
0.602635 | − | 0.798017i | \(-0.294118\pi\) | |||||||
\(578\) | 0.785304 | − | 0.486240i | 0.785304 | − | 0.486240i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.857578 | + | 0.898142i | −0.857578 | + | 0.898142i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.256725 | − | 0.581427i | −0.256725 | − | 0.581427i | ||||
\(585\) | −0.781354 | + | 0.509130i | −0.781354 | + | 0.509130i | ||||
\(586\) | 1.19141 | + | 0.461556i | 1.19141 | + | 0.461556i | ||||
\(587\) | 0 | 0 | −0.273663 | − | 0.961826i | \(-0.588235\pi\) | ||||
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.0169724 | − | 0.0907942i | −0.0169724 | − | 0.0907942i | ||||
\(593\) | −1.22895 | + | 0.973438i | −1.22895 | + | 0.973438i | −0.228951 | + | 0.973438i | \(0.573529\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.288627 | + | 0.799375i | 0.288627 | + | 0.799375i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.999733 | − | 0.0230979i | \(-0.00735294\pi\) | ||||
−0.999733 | + | 0.0230979i | \(0.992647\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.42763 | − | 1.36315i | 1.42763 | − | 1.36315i | 0.602635 | − | 0.798017i | \(-0.294118\pi\) |
0.824997 | − | 0.565136i | \(-0.191176\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.317791 | + | 0.948161i | 0.317791 | + | 0.948161i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.317791 | − | 0.948161i | \(-0.602941\pi\) | ||||
0.317791 | + | 0.948161i | \(0.397059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.221468 | + | 0.293271i | 0.221468 | + | 0.293271i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.134455 | − | 0.241393i | 0.134455 | − | 0.241393i | ||||
\(613\) | 1.73474 | + | 0.581427i | 1.73474 | + | 0.581427i | 0.995734 | − | 0.0922684i | \(-0.0294118\pi\) |
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.811985 | − | 0.890705i | −0.811985 | − | 0.890705i | 0.183750 | − | 0.982973i | \(-0.441176\pi\) |
−0.995734 | + | 0.0922684i | \(0.970588\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.466296 | − | 0.884629i | \(-0.345588\pi\) | ||||
−0.466296 | + | 0.884629i | \(0.654412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.850217 | − | 0.526432i | 0.850217 | − | 0.526432i | ||||
\(626\) | −1.47701 | − | 0.735466i | −1.47701 | − | 0.735466i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.585584 | + | 0.344126i | −0.585584 | + | 0.344126i | ||||
\(629\) | 0.0153805 | + | 0.0203671i | 0.0153805 | + | 0.0203671i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.506653 | − | 0.862150i | \(-0.669118\pi\) | ||||
0.506653 | + | 0.862150i | \(0.330882\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.00106703 | + | 0.0461835i | 0.00106703 | + | 0.0461835i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.396298 | − | 0.844201i | 0.396298 | − | 0.844201i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.317791 | − | 0.948161i | 0.317791 | − | 0.948161i | ||||
\(641\) | −1.63417 | − | 1.11943i | −1.63417 | − | 1.11943i | −0.895163 | − | 0.445738i | \(-0.852941\pi\) |
−0.739009 | − | 0.673696i | \(-0.764706\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.0692444 | − | 0.997600i | \(-0.477941\pi\) | ||||
−0.0692444 | + | 0.997600i | \(0.522059\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.403921 | − | 0.914794i | \(-0.632353\pi\) | ||||
0.403921 | + | 0.914794i | \(0.367647\pi\) | |||||||
\(648\) | 1.00000i | 1.00000i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.316715 | − | 0.877165i | 0.316715 | − | 0.877165i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.61228 | + | 0.998285i | 1.61228 | + | 0.998285i | 0.973438 | + | 0.228951i | \(0.0735294\pi\) |
0.638847 | + | 0.769334i | \(0.279412\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.09157 | + | 1.67521i | 1.09157 | + | 1.67521i | ||||
\(657\) | −0.624761 | − | 0.116788i | −0.624761 | − | 0.116788i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.584041 | − | 0.811724i | \(-0.301471\pi\) | ||||
−0.584041 | + | 0.811724i | \(0.698529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.463756 | + | 1.49761i | 0.463756 | + | 1.49761i | 0.824997 | + | 0.565136i | \(0.191176\pi\) |
−0.361242 | + | 0.932472i | \(0.617647\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.0844967 | − | 0.0373089i | −0.0844967 | − | 0.0373089i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.433444 | − | 0.254719i | −0.433444 | − | 0.254719i | 0.273663 | − | 0.961826i | \(-0.411765\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(674\) | −0.117891 | + | 0.141970i | −0.117891 | + | 0.141970i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.0413996 | + | 0.123520i | 0.0413996 | + | 0.123520i | ||||
\(677\) | −0.890705 | + | 1.17948i | −0.890705 | + | 1.17948i | 0.0922684 | + | 0.995734i | \(0.470588\pi\) |
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.0381744 | + | 0.273663i | 0.0381744 | + | 0.273663i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.739009 | − | 0.673696i | \(-0.764706\pi\) | ||||
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.914794 | − | 0.403921i | 0.914794 | − | 0.403921i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.166571 | + | 1.79759i | 0.166571 | + | 1.79759i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.978467 | − | 0.206405i | \(-0.0661765\pi\) | ||||
−0.978467 | + | 0.206405i | \(0.933824\pi\) | |||||||
\(692\) | 0.149783 | − | 0.526432i | 0.149783 | − | 0.526432i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.476319 | − | 0.279915i | −0.476319 | − | 0.279915i | ||||
\(698\) | −0.0579382 | − | 0.499398i | −0.0579382 | − | 0.499398i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.181395 | + | 0.0339085i | −0.181395 | + | 0.0339085i | −0.273663 | − | 0.961826i | \(-0.588235\pi\) |
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.815183 | + | 1.02916i | 0.815183 | + | 1.02916i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.388362 | − | 1.25414i | −0.388362 | − | 1.25414i | −0.914794 | − | 0.403921i | \(-0.867647\pi\) |
0.526432 | − | 0.850217i | \(-0.323529\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.11581 | − | 0.345526i | −1.11581 | − | 0.345526i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.995734 | − | 0.0922684i | \(-0.970588\pi\) | ||||
0.995734 | + | 0.0922684i | \(0.0294118\pi\) | |||||||
\(720\) | −0.602635 | − | 0.798017i | −0.602635 | − | 0.798017i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 1.00000i | − | 1.00000i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.52643 | − | 0.850217i | −1.52643 | − | 0.850217i | ||||
\(725\) | −0.936790 | − | 0.815183i | −0.936790 | − | 0.815183i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.0692444 | − | 0.997600i | \(-0.477941\pi\) | ||||
−0.0692444 | + | 0.997600i | \(0.522059\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.824997 | + | 0.565136i | 0.824997 | + | 0.565136i | ||||
\(730\) | 0.568950 | − | 0.283304i | 0.568950 | − | 0.283304i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.251402 | − | 0.535539i | 0.251402 | − | 0.535539i | −0.739009 | − | 0.673696i | \(-0.764706\pi\) |
0.990410 | + | 0.138156i | \(0.0441176\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.99893 | + | 0.0461835i | 1.99893 | + | 0.0461835i | ||||
\(739\) | 0 | 0 | −0.506653 | − | 0.862150i | \(-0.669118\pi\) | ||||
0.506653 | + | 0.862150i | \(0.330882\pi\) | |||||||
\(740\) | 0.0899135 | − | 0.0211475i | 0.0899135 | − | 0.0211475i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.160996 | − | 0.986955i | \(-0.448529\pi\) | ||||
−0.160996 | + | 0.986955i | \(0.551471\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.785192 | + | 0.325237i | −0.785192 | + | 0.325237i | ||||
\(746\) | −1.88823 | − | 0.632872i | −1.88823 | − | 0.632872i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.466296 | − | 0.884629i | \(-0.345588\pi\) | ||||
−0.466296 | + | 0.884629i | \(0.654412\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.15687 | − | 0.0534853i | −1.15687 | − | 0.0534853i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.40140 | + | 0.469701i | 1.40140 | + | 0.469701i | 0.914794 | − | 0.403921i | \(-0.132353\pi\) |
0.486604 | + | 0.873622i | \(0.338235\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.581427 | − | 1.73474i | 0.581427 | − | 1.73474i | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) |
0.673696 | − | 0.739009i | \(-0.264706\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.247345 | + | 0.123163i | 0.247345 | + | 0.123163i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.27962 | + | 1.22182i | −1.27962 | + | 1.22182i | −0.317791 | + | 0.948161i | \(0.602941\pi\) |
−0.961826 | + | 0.273663i | \(0.911765\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.78842 | − | 0.0826835i | −1.78842 | − | 0.0826835i | ||||
\(773\) | 0.418885 | + | 1.78099i | 0.418885 | + | 1.78099i | 0.602635 | + | 0.798017i | \(0.294118\pi\) |
−0.183750 | + | 0.982973i | \(0.558824\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.82366 | − | 0.297482i | −1.82366 | − | 0.297482i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.348448 | − | 1.86403i | −0.348448 | − | 1.86403i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.932472 | + | 0.361242i | 0.932472 | + | 0.361242i | ||||
\(785\) | −0.370803 | − | 0.569067i | −0.370803 | − | 0.569067i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.656446 | − | 0.754373i | \(-0.272059\pi\) | ||||
−0.656446 | + | 0.754373i | \(0.727941\pi\) | |||||||
\(788\) | −0.672619 | − | 0.810004i | −0.672619 | − | 0.810004i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.0707405 | + | 0.335346i | −0.0707405 | + | 0.335346i | ||||
\(794\) | 1.11159 | − | 0.761460i | 1.11159 | − | 0.761460i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.172075 | − | 1.85699i | 0.172075 | − | 1.85699i | −0.273663 | − | 0.961826i | \(-0.588235\pi\) |
0.445738 | − | 0.895163i | \(-0.352941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.961826 | + | 0.273663i | 0.961826 | + | 0.273663i | ||||
\(801\) | −0.915642 | + | 0.725270i | −0.915642 | + | 0.725270i | ||||
\(802\) | 1.79838 | − | 0.844224i | 1.79838 | − | 0.844224i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.65527 | − | 0.389315i | −1.65527 | − | 0.389315i | ||||
\(809\) | −0.0362122 | − | 0.0286833i | −0.0362122 | − | 0.0286833i | 0.602635 | − | 0.798017i | \(-0.294118\pi\) |
−0.638847 | + | 0.769334i | \(0.720588\pi\) | |||||||
\(810\) | −0.998933 | + | 0.0461835i | −0.998933 | + | 0.0461835i | ||||
\(811\) | 0 | 0 | −0.769334 | − | 0.638847i | \(-0.779412\pi\) | ||||
0.769334 | + | 0.638847i | \(0.220588\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.461556 | + | 0.555831i | −0.461556 | + | 0.555831i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.62301 | + | 1.16777i | −1.62301 | + | 1.16777i | ||||
\(821\) | − | 1.27769i | − | 1.27769i | −0.769334 | − | 0.638847i | \(-0.779412\pi\) | ||
0.769334 | − | 0.638847i | \(-0.220588\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.339607 | − | 0.940567i | \(-0.610294\pi\) | ||||
0.339607 | + | 0.940567i | \(0.389706\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.802895 | − | 1.44147i | −0.802895 | − | 1.44147i | −0.895163 | − | 0.445738i | \(-0.852941\pi\) |
0.0922684 | − | 0.995734i | \(-0.470588\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.861602 | − | 0.356887i | 0.861602 | − | 0.356887i | ||||
\(833\) | −0.275134 | + | 0.0254949i | −0.275134 | + | 0.0254949i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.138156 | − | 0.990410i | \(-0.455882\pi\) | ||||
−0.138156 | + | 0.990410i | \(0.544118\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.218965 | + | 0.495909i | −0.218965 | + | 0.495909i | ||||
\(842\) | 0.136828 | + | 0.291473i | 0.136828 | + | 0.291473i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.121476 | + | 0.0470600i | −0.121476 | + | 0.0470600i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.91053 | + | 0.311653i | −1.91053 | + | 0.311653i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.271608 | + | 0.0507723i | −0.271608 | + | 0.0507723i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.321906 | + | 0.00743733i | −0.321906 | + | 0.00743733i | −0.183750 | − | 0.982973i | \(-0.558824\pi\) |
−0.138156 | + | 0.990410i | \(0.544118\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.49869 | + | 1.30415i | 1.49869 | + | 1.30415i | 0.824997 | + | 0.565136i | \(0.191176\pi\) |
0.673696 | + | 0.739009i | \(0.264706\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.532788 | + | 0.125311i | 0.532788 | + | 0.125311i | ||||
\(866\) | 0.258777 | − | 0.377767i | 0.258777 | − | 0.377767i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.0899135 | − | 1.94480i | 0.0899135 | − | 1.94480i | ||||
\(873\) | −1.27604 | + | 1.33639i | −1.27604 | + | 1.33639i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.130258 | − | 0.0470318i | −0.130258 | − | 0.0470318i | 0.273663 | − | 0.961826i | \(-0.411765\pi\) |
−0.403921 | + | 0.914794i | \(0.632353\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.831277 | − | 1.66943i | 0.831277 | − | 1.66943i | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) |
0.739009 | − | 0.673696i | \(-0.235294\pi\) | |||||||
\(882\) | 0.824997 | − | 0.565136i | 0.824997 | − | 0.565136i | ||||
\(883\) | 0 | 0 | −0.445738 | − | 0.895163i | \(-0.647059\pi\) | ||||
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(884\) | −0.169158 | + | 0.194392i | −0.169158 | + | 0.194392i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.317791 | − | 0.948161i | \(-0.397059\pi\) | ||||
−0.317791 | + | 0.948161i | \(0.602941\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.293625 | − | 1.13058i | 0.293625 | − | 1.13058i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.871181 | + | 0.433797i | −0.871181 | + | 0.433797i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.769334 | − | 0.638847i | 0.769334 | − | 0.638847i | ||||
\(901\) | 0.434175 | − | 0.312392i | 0.434175 | − | 0.312392i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.847846 | − | 1.80609i | −0.847846 | − | 1.80609i | ||||
\(905\) | 0.778814 | − | 1.56407i | 0.778814 | − | 1.56407i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.206405 | − | 0.978467i | \(-0.566176\pi\) | ||||
0.206405 | + | 0.978467i | \(0.433824\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.25664 | + | 1.14558i | −1.25664 | + | 1.14558i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.940567 | − | 0.339607i | \(-0.110294\pi\) | ||||
−0.940567 | + | 0.339607i | \(0.889706\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.227480 | + | 1.96076i | −0.227480 | + | 1.96076i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.44612 | + | 0.0334111i | 1.44612 | + | 0.0334111i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.955248 | − | 0.295806i | \(-0.904412\pi\) | ||||
0.955248 | + | 0.295806i | \(0.0955882\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.891477 | 0.891477 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0252774 | + | 0.0888409i | 0.0252774 | + | 0.0888409i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.0286833 | − | 1.24148i | −0.0286833 | − | 1.24148i | ||||
\(929\) | −0.352279 | + | 1.49780i | −0.352279 | + | 1.49780i | 0.445738 | + | 0.895163i | \(0.352941\pi\) |
−0.798017 | + | 0.602635i | \(0.794118\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.299742 | + | 0.967959i | −0.299742 | + | 0.967959i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.192492 | − | 0.912510i | 0.192492 | − | 0.912510i | ||||
\(937\) | −0.265765 | − | 1.90520i | −0.265765 | − | 1.90520i | −0.403921 | − | 0.914794i | \(-0.632353\pi\) |
0.138156 | − | 0.990410i | \(-0.455882\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.84706 | + | 0.715555i | −1.84706 | + | 0.715555i | −0.873622 | + | 0.486604i | \(0.838235\pi\) |
−0.973438 | + | 0.228951i | \(0.926471\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.506653 | − | 0.862150i | \(-0.330882\pi\) | ||||
−0.506653 | + | 0.862150i | \(0.669118\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.547620 | + | 0.226831i | 0.547620 | + | 0.226831i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.988373 | − | 1.51684i | 0.988373 | − | 1.51684i | 0.138156 | − | 0.990410i | \(-0.455882\pi\) |
0.850217 | − | 0.526432i | \(-0.176471\pi\) | |||||||
\(954\) | −0.822596 | + | 1.75231i | −0.822596 | + | 1.75231i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.0461835 | − | 0.998933i | −0.0461835 | − | 0.998933i | ||||
\(962\) | 0.0699224 | + | 0.0503097i | 0.0699224 | + | 0.0503097i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.36575 | − | 0.641131i | −1.36575 | − | 0.641131i | ||||
\(965\) | − | 1.79033i | − | 1.79033i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.798017 | − | 0.602635i | \(-0.794118\pi\) | ||||
0.798017 | + | 0.602635i | \(0.205882\pi\) | |||||||
\(968\) | −0.895163 | − | 0.445738i | −0.895163 | − | 0.445738i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.212941 | − | 1.83545i | 0.212941 | − | 1.83545i | ||||
\(971\) | 0 | 0 | −0.251374 | − | 0.967890i | \(-0.580882\pi\) | ||||
0.251374 | + | 0.967890i | \(0.419118\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.363975 | − | 0.0507723i | −0.363975 | − | 0.0507723i | ||||
\(977\) | 1.75974 | + | 0.777003i | 1.75974 | + | 0.777003i | 0.990410 | + | 0.138156i | \(0.0441176\pi\) |
0.769334 | + | 0.638847i | \(0.220588\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.317791 | + | 0.948161i | −0.317791 | + | 0.948161i | ||||
\(981\) | −1.55364 | − | 1.17325i | −1.55364 | − | 1.17325i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.884629 | − | 0.466296i | \(-0.845588\pi\) | ||||
0.884629 | + | 0.466296i | \(0.154412\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.778076 | − | 0.709310i | 0.778076 | − | 0.709310i | ||||
\(986\) | 0.159999 | + | 0.303542i | 0.159999 | + | 0.303542i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.228951 | − | 0.973438i | \(-0.573529\pi\) | ||||
0.228951 | + | 0.973438i | \(0.426471\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.10257 | + | 0.486834i | −1.10257 | + | 0.486834i | −0.873622 | − | 0.486604i | \(-0.838235\pi\) |
−0.228951 | + | 0.973438i | \(0.573529\pi\) | |||||||
\(998\) | 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 | 2740.1.cd.a.603.1 | yes | 64 | |
4.3 | odd | 2 | CM | 2740.1.cd.a.603.1 | yes | 64 | |
5.2 | odd | 4 | 2740.1.bw.a.2247.1 | yes | 64 | ||
20.7 | even | 4 | 2740.1.bw.a.2247.1 | yes | 64 | ||
137.5 | odd | 136 | 2740.1.bw.a.1923.1 | ✓ | 64 | ||
548.279 | even | 136 | 2740.1.bw.a.1923.1 | ✓ | 64 | ||
685.142 | even | 136 | inner | 2740.1.cd.a.827.1 | yes | 64 | |
2740.827 | odd | 136 | inner | 2740.1.cd.a.827.1 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2740.1.bw.a.1923.1 | ✓ | 64 | 137.5 | odd | 136 | ||
2740.1.bw.a.1923.1 | ✓ | 64 | 548.279 | even | 136 | ||
2740.1.bw.a.2247.1 | yes | 64 | 5.2 | odd | 4 | ||
2740.1.bw.a.2247.1 | yes | 64 | 20.7 | even | 4 | ||
2740.1.cd.a.603.1 | yes | 64 | 1.1 | even | 1 | trivial | |
2740.1.cd.a.603.1 | yes | 64 | 4.3 | odd | 2 | CM | |
2740.1.cd.a.827.1 | yes | 64 | 685.142 | even | 136 | inner | |
2740.1.cd.a.827.1 | yes | 64 | 2740.827 | odd | 136 | inner |