Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [959,1,Mod(202,959)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(959, base_ring=CyclotomicField(34))
chi = DirichletCharacter(H, H._module([17, 25]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("959.202");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 959 = 7 \cdot 137 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 959.r (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: | \(0.478603347115\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
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 | 748.1 | ||
Root | \(0.982973 + 0.183750i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 959.748 |
Dual form | 959.1.r.a.909.1 |
$q$-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 \(\left(\mathbb{Z}/959\mathbb{Z}\right)^\times\).
\(n\) | \(414\) | \(549\) |
\(\chi(n)\) | \(e\left(\frac{11}{34}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.658809 | + | 0.600584i | 0.658809 | + | 0.600584i | 0.932472 | − | 0.361242i | \(-0.117647\pi\) |
−0.273663 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(3\) | 0 | 0 | −0.526432 | − | 0.850217i | \(-0.676471\pi\) | ||||
0.526432 | + | 0.850217i | \(0.323529\pi\) | |||||||
\(4\) | −0.0189399 | − | 0.204394i | −0.0189399 | − | 0.204394i | ||||
\(5\) | 0 | 0 | −0.673696 | − | 0.739009i | \(-0.735294\pi\) | ||||
0.673696 | + | 0.739009i | \(0.264706\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.273663 | − | 0.961826i | 0.273663 | − | 0.961826i | ||||
\(8\) | 0.647513 | − | 0.857445i | 0.647513 | − | 0.857445i | ||||
\(9\) | −0.445738 | + | 0.895163i | −0.445738 | + | 0.895163i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.136374 | − | 1.47171i | −0.136374 | − | 1.47171i | −0.739009 | − | 0.673696i | \(-0.764706\pi\) |
0.602635 | − | 0.798017i | \(-0.294118\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.961826 | − | 0.273663i | \(-0.911765\pi\) | ||||
0.961826 | + | 0.273663i | \(0.0882353\pi\) | |||||||
\(14\) | 0.757949 | − | 0.469302i | 0.757949 | − | 0.469302i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.739781 | − | 0.138289i | 0.739781 | − | 0.138289i | ||||
\(17\) | 0 | 0 | −0.602635 | − | 0.798017i | \(-0.705882\pi\) | ||||
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(18\) | −0.831277 | + | 0.322039i | −0.831277 | + | 0.322039i | ||||
\(19\) | 0 | 0 | 0.932472 | − | 0.361242i | \(-0.117647\pi\) | ||||
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.794043 | − | 1.05148i | 0.794043 | − | 1.05148i | ||||
\(23\) | 0.0675278 | + | 0.361242i | 0.0675278 | + | 0.361242i | 1.00000 | \(0\) | ||
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0922684 | + | 0.995734i | −0.0922684 | + | 0.995734i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.201774 | − | 0.0377181i | −0.201774 | − | 0.0377181i | ||||
\(29\) | 0.247582 | + | 1.32445i | 0.247582 | + | 1.32445i | 0.850217 | + | 0.526432i | \(0.176471\pi\) |
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.361242 | − | 0.932472i | \(-0.382353\pi\) | ||||
−0.361242 | + | 0.932472i | \(0.617647\pi\) | |||||||
\(32\) | −0.343104 | − | 0.212441i | −0.343104 | − | 0.212441i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.191408 | + | 0.0741518i | 0.191408 | + | 0.0741518i | ||||
\(37\) | 0.184537 | 0.184537 | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) | ||||
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.132756 | + | 0.342683i | 0.132756 | + | 0.342683i | 0.982973 | − | 0.183750i | \(-0.0588235\pi\) |
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(44\) | −0.298226 | + | 0.0557481i | −0.298226 | + | 0.0557481i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.172468 | + | 0.278545i | −0.172468 | + | 0.278545i | ||||
\(47\) | 0 | 0 | −0.895163 | − | 0.445738i | \(-0.852941\pi\) | ||||
0.895163 | + | 0.445738i | \(0.147059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.850217 | − | 0.526432i | −0.850217 | − | 0.526432i | ||||
\(50\) | −0.658809 | + | 0.600584i | −0.658809 | + | 0.600584i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.380338 | + | 0.981767i | 0.380338 | + | 0.981767i | 0.982973 | + | 0.183750i | \(0.0588235\pi\) |
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.647513 | − | 0.857445i | −0.647513 | − | 0.857445i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.632333 | + | 1.02125i | −0.632333 | + | 1.02125i | ||||
\(59\) | 0 | 0 | 0.445738 | − | 0.895163i | \(-0.352941\pi\) | ||||
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.445738 | − | 0.895163i | \(-0.647059\pi\) | ||||
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.739009 | + | 0.673696i | 0.739009 | + | 0.673696i | ||||
\(64\) | −0.304409 | − | 1.06989i | −0.304409 | − | 1.06989i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.72198 | + | 0.489946i | 1.72198 | + | 0.489946i | 0.982973 | − | 0.183750i | \(-0.0588235\pi\) |
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.98297 | − | 0.183750i | −1.98297 | − | 0.183750i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0.478932 | + | 0.961826i | 0.478932 | + | 0.961826i | ||||
\(73\) | 0 | 0 | −0.273663 | − | 0.961826i | \(-0.588235\pi\) | ||||
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(74\) | 0.121574 | + | 0.110830i | 0.121574 | + | 0.110830i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.45285 | − | 0.271585i | −1.45285 | − | 0.271585i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.380338 | + | 0.614268i | −0.380338 | + | 0.614268i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) |
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.602635 | − | 0.798017i | −0.602635 | − | 0.798017i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.798017 | − | 0.602635i | \(-0.794118\pi\) | ||||
0.798017 | + | 0.602635i | \(0.205882\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.118349 | + | 0.305494i | −0.118349 | + | 0.305494i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.35022 | − | 0.836019i | −1.35022 | − | 0.836019i | ||||
\(89\) | 0 | 0 | −0.673696 | − | 0.739009i | \(-0.735294\pi\) | ||||
0.673696 | + | 0.739009i | \(0.264706\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.0725565 | − | 0.0206441i | 0.0725565 | − | 0.0206441i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.995734 | − | 0.0922684i | \(-0.0294118\pi\) | ||||
−0.995734 | + | 0.0922684i | \(0.970588\pi\) | |||||||
\(98\) | −0.243964 | − | 0.857445i | −0.243964 | − | 0.857445i | ||||
\(99\) | 1.37821 | + | 0.533922i | 1.37821 | + | 0.533922i | ||||
\(100\) | 0.205269 | 0.205269 | ||||||||
\(101\) | 0 | 0 | −0.932472 | − | 0.361242i | \(-0.882353\pi\) | ||||
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) | ||||
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.339063 | + | 0.875222i | −0.339063 | + | 0.875222i | ||||
\(107\) | −1.67148 | + | 1.03494i | −1.67148 | + | 1.03494i | −0.739009 | + | 0.673696i | \(0.764706\pi\) |
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.876298 | + | 0.163808i | 0.876298 | + | 0.163808i | 0.602635 | − | 0.798017i | \(-0.294118\pi\) |
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0694407 | − | 0.749385i | 0.0694407 | − | 0.749385i | ||||
\(113\) | −1.91545 | − | 0.177492i | −1.91545 | − | 0.177492i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) |
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.266020 | − | 0.0756892i | 0.266020 | − | 0.0756892i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.16437 | + | 0.217658i | −1.16437 | + | 0.217658i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.0822551 | + | 0.887674i | 0.0822551 | + | 0.887674i | ||||
\(127\) | − | 1.79033i | − | 1.79033i | −0.445738 | − | 0.895163i | \(-0.647059\pi\) | ||
0.445738 | − | 0.895163i | \(-0.352941\pi\) | |||||||
\(128\) | 0.262132 | − | 0.526432i | 0.262132 | − | 0.526432i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.183750 | − | 0.982973i | \(-0.441176\pi\) | ||||
−0.183750 | + | 0.982973i | \(0.558824\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.840204 | + | 1.35698i | 0.840204 | + | 1.35698i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.00000 | −1.00000 | ||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.739009 | − | 0.673696i | \(-0.764706\pi\) | ||||
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.19604 | − | 1.31200i | −1.19604 | − | 1.31200i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.205957 | + | 0.723865i | −0.205957 | + | 0.723865i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.00349510 | − | 0.0377181i | −0.00349510 | − | 0.0377181i | ||||
\(149\) | 0.840204 | − | 0.634493i | 0.840204 | − | 0.634493i | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) |
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.70043 | − | 1.05286i | 1.70043 | − | 1.05286i | 0.850217 | − | 0.526432i | \(-0.176471\pi\) |
0.850217 | − | 0.526432i | \(-0.176471\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.794043 | − | 1.05148i | −0.794043 | − | 1.05148i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.673696 | − | 0.739009i | \(-0.264706\pi\) | ||||
−0.673696 | + | 0.739009i | \(0.735294\pi\) | |||||||
\(158\) | −0.619490 | + | 0.176260i | −0.619490 | + | 0.176260i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.365931 | + | 0.0339085i | 0.365931 | + | 0.0339085i | ||||
\(162\) | 0.0822551 | − | 0.887674i | 0.0822551 | − | 0.887674i | ||||
\(163\) | 0.840204 | + | 1.35698i | 0.840204 | + | 1.35698i | 0.932472 | + | 0.361242i | \(0.117647\pi\) |
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.850217 | − | 0.526432i | \(-0.176471\pi\) | ||||
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.850217 | + | 0.526432i | 0.850217 | + | 0.526432i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.0675278 | − | 0.0336248i | 0.0675278 | − | 0.0336248i | ||||
\(173\) | 0 | 0 | −0.932472 | − | 0.361242i | \(-0.882353\pi\) | ||||
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.932472 | + | 0.361242i | 0.932472 | + | 0.361242i | ||||
\(176\) | −0.304409 | − | 1.06989i | −0.304409 | − | 1.06989i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.445738 | − | 0.895163i | \(-0.352941\pi\) | ||||
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.982973 | − | 0.183750i | \(-0.0588235\pi\) | ||||
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.353470 | + | 0.176007i | 0.353470 | + | 0.176007i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.42871 | + | 1.07891i | 1.42871 | + | 1.07891i | 0.982973 | + | 0.183750i | \(0.0588235\pi\) |
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.537235 | − | 0.711414i | −0.537235 | − | 0.711414i | 0.445738 | − | 0.895163i | \(-0.352941\pi\) |
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0914964 | + | 0.183750i | −0.0914964 | + | 0.183750i | ||||
\(197\) | −1.18475 | − | 0.221468i | −1.18475 | − | 0.221468i | −0.445738 | − | 0.895163i | \(-0.647059\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(198\) | 0.587313 | + | 1.17948i | 0.587313 | + | 1.17948i | ||||
\(199\) | 0 | 0 | 0.895163 | − | 0.445738i | \(-0.147059\pi\) | ||||
−0.895163 | + | 0.445738i | \(0.852941\pi\) | |||||||
\(200\) | 0.794043 | + | 0.723865i | 0.794043 | + | 0.723865i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.34164 | + | 0.124322i | 1.34164 | + | 0.124322i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.353470 | − | 0.100571i | −0.353470 | − | 0.100571i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.25664 | − | 1.14558i | −1.25664 | − | 1.14558i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) |
−0.273663 | − | 0.961826i | \(-0.588235\pi\) | |||||||
\(212\) | 0.193463 | − | 0.0963333i | 0.193463 | − | 0.0963333i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.72275 | − | 0.322039i | −1.72275 | − | 0.322039i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.478932 | + | 0.634209i | 0.478932 | + | 0.634209i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.361242 | − | 0.932472i | \(-0.382353\pi\) | ||||
−0.361242 | + | 0.932472i | \(0.617647\pi\) | |||||||
\(224\) | −0.298226 | + | 0.271869i | −0.298226 | + | 0.271869i | ||||
\(225\) | −0.850217 | − | 0.526432i | −0.850217 | − | 0.526432i | ||||
\(226\) | −1.15531 | − | 1.26732i | −1.15531 | − | 1.26732i | ||||
\(227\) | 0 | 0 | −0.895163 | − | 0.445738i | \(-0.852941\pi\) | ||||
0.895163 | + | 0.445738i | \(0.147059\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.961826 | − | 0.273663i | \(-0.0882353\pi\) | ||||
−0.961826 | + | 0.273663i | \(0.911765\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.29596 | + | 0.645309i | 1.29596 | + | 0.645309i | ||||
\(233\) | − | 0.722483i | − | 0.722483i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) | ||
0.932472 | − | 0.361242i | \(-0.117647\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.646741 | − | 0.322039i | 0.646741 | − | 0.322039i | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) |
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.798017 | − | 0.602635i | \(-0.205882\pi\) | ||||
−0.798017 | + | 0.602635i | \(0.794118\pi\) | |||||||
\(242\) | −0.897818 | − | 0.555905i | −0.897818 | − | 0.555905i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.183750 | − | 0.982973i | \(-0.558824\pi\) | ||||
0.183750 | + | 0.982973i | \(0.441176\pi\) | |||||||
\(252\) | 0.123702 | − | 0.163808i | 0.123702 | − | 0.163808i | ||||
\(253\) | 0.522435 | − | 0.148646i | 0.522435 | − | 0.148646i | ||||
\(254\) | 1.07524 | − | 1.17948i | 1.07524 | − | 1.17948i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.548373 | + | 0.212441i | −0.548373 | + | 0.212441i | ||||
\(257\) | 0 | 0 | −0.602635 | − | 0.798017i | \(-0.705882\pi\) | ||||
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0505009 | − | 0.177492i | 0.0505009 | − | 0.177492i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.29596 | − | 0.368731i | −1.29596 | − | 0.368731i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.172075 | + | 1.85699i | 0.172075 | + | 1.85699i | 0.445738 | + | 0.895163i | \(0.352941\pi\) |
−0.273663 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.0675278 | − | 0.361242i | 0.0675278 | − | 0.361242i | ||||
\(269\) | 0 | 0 | −0.673696 | − | 0.739009i | \(-0.735294\pi\) | ||||
0.673696 | + | 0.739009i | \(0.264706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.526432 | − | 0.850217i | \(-0.676471\pi\) | ||||
0.526432 | + | 0.850217i | \(0.323529\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.658809 | − | 0.600584i | −0.658809 | − | 0.600584i | ||||
\(275\) | 1.47802 | 1.47802 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.709310 | + | 1.14558i | 0.709310 | + | 1.14558i | 0.982973 | + | 0.183750i | \(0.0588235\pi\) |
−0.273663 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.465346 | − | 1.63552i | 0.465346 | − | 1.63552i | −0.273663 | − | 0.961826i | \(-0.588235\pi\) |
0.739009 | − | 0.673696i | \(-0.235294\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.445738 | − | 0.895163i | \(-0.352941\pi\) | ||||
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(284\) | 0.408787i | 0.408787i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.343104 | − | 0.212441i | 0.343104 | − | 0.212441i | ||||
\(289\) | −0.273663 | + | 0.961826i | −0.273663 | + | 0.961826i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.932472 | − | 0.361242i | \(-0.117647\pi\) | ||||
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.119490 | − | 0.158230i | 0.119490 | − | 0.158230i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.934600 | + | 0.0866035i | 0.934600 | + | 0.0866035i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.365931 | − | 0.0339085i | 0.365931 | − | 0.0339085i | ||||
\(302\) | 1.75260 | + | 0.327617i | 1.75260 | + | 0.327617i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.798017 | − | 0.602635i | \(-0.205882\pi\) | ||||
−0.798017 | + | 0.602635i | \(0.794118\pi\) | |||||||
\(308\) | −0.0279934 | + | 0.302097i | −0.0279934 | + | 0.302097i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.273663 | − | 0.961826i | \(-0.588235\pi\) | ||||
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.132756 | + | 0.0661046i | 0.132756 | + | 0.0661046i | ||||
\(317\) | 0.719401 | + | 1.85699i | 0.719401 | + | 1.85699i | 0.445738 | + | 0.895163i | \(0.352941\pi\) |
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.91545 | − | 0.544991i | 1.91545 | − | 0.544991i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.220714 | + | 0.242112i | 0.220714 | + | 0.242112i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.151696 | + | 0.138289i | −0.151696 | + | 0.138289i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.261444 | + | 1.39860i | −0.261444 | + | 1.39860i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.58923 | − | 1.20013i | −1.58923 | − | 1.20013i | −0.850217 | − | 0.526432i | \(-0.823529\pi\) |
−0.739009 | − | 0.673696i | \(-0.764706\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0822551 | + | 0.165190i | −0.0822551 | + | 0.165190i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.09227 | − | 0.995734i | −1.09227 | − | 0.995734i | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0.243964 | + | 0.857445i | 0.243964 | + | 0.857445i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.739009 | + | 0.673696i | −0.739009 | + | 0.673696i | ||||
\(344\) | 0.379793 | + | 0.108060i | 0.379793 | + | 0.108060i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.149783 | − | 0.526432i | −0.149783 | − | 0.526432i | 0.850217 | − | 0.526432i | \(-0.176471\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.895163 | − | 0.445738i | \(-0.147059\pi\) | ||||
−0.895163 | + | 0.445738i | \(0.852941\pi\) | |||||||
\(350\) | 0.397365 | + | 0.798017i | 0.397365 | + | 0.798017i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.265861 | + | 0.533922i | −0.265861 | + | 0.533922i | ||||
\(353\) | 0 | 0 | 0.526432 | − | 0.850217i | \(-0.323529\pi\) | ||||
−0.526432 | + | 0.850217i | \(0.676471\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.247582 | + | 1.32445i | −0.247582 | + | 1.32445i | 0.602635 | + | 0.798017i | \(0.294118\pi\) |
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.739009 | − | 0.673696i | 0.739009 | − | 0.673696i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.982973 | − | 0.183750i | \(-0.0588235\pi\) | ||||
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(368\) | 0.0999115 | + | 0.257901i | 0.0999115 | + | 0.257901i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.04837 | − | 0.0971461i | 1.04837 | − | 0.0971461i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.510366 | − | 0.197717i | −0.510366 | − | 0.197717i | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) |
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.44574 | + | 0.895163i | 1.44574 | + | 0.895163i | 1.00000 | \(0\) | ||
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.293271 | + | 1.56886i | 0.293271 | + | 1.56886i | ||||
\(383\) | 0 | 0 | −0.982973 | − | 0.183750i | \(-0.941176\pi\) | ||||
0.982973 | + | 0.183750i | \(0.0588235\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.0733285 | − | 0.791341i | 0.0733285 | − | 0.791341i | ||||
\(387\) | −0.365931 | − | 0.0339085i | −0.365931 | − | 0.0339085i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.329838 | + | 0.436776i | −0.329838 | + | 0.436776i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) |
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.00191 | + | 0.388143i | −1.00191 | + | 0.388143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.647513 | − | 0.857445i | −0.647513 | − | 0.857445i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0830271 | − | 0.291810i | 0.0830271 | − | 0.291810i | ||||
\(397\) | 0 | 0 | 0.850217 | − | 0.526432i | \(-0.176471\pi\) | ||||
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.0694407 | + | 0.749385i | 0.0694407 | + | 0.749385i | ||||
\(401\) | − | 1.92365i | − | 1.92365i | −0.273663 | − | 0.961826i | \(-0.588235\pi\) | ||
0.273663 | − | 0.961826i | \(-0.411765\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.809222 | + | 0.887674i | 0.809222 | + | 0.887674i | ||||
\(407\) | −0.0251661 | − | 0.271585i | −0.0251661 | − | 0.271585i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.739009 | − | 0.673696i | \(-0.764706\pi\) | ||||
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.172468 | − | 0.278545i | −0.172468 | − | 0.278545i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.602635 | − | 0.798017i | \(-0.294118\pi\) | ||||
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.99147i | 1.99147i | 0.0922684 | + | 0.995734i | \(0.470588\pi\) | ||||
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(422\) | −0.139869 | − | 1.50943i | −0.139869 | − | 1.50943i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.08809 | + | 0.309587i | 1.08809 | + | 0.309587i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.243192 | + | 0.322039i | 0.243192 | + | 0.322039i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.20614 | − | 1.32307i | 1.20614 | − | 1.32307i | 0.273663 | − | 0.961826i | \(-0.411765\pi\) |
0.932472 | − | 0.361242i | \(-0.117647\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 0.602635 | − | 0.798017i | \(-0.294118\pi\) | ||||
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.0168844 | − | 0.182212i | 0.0168844 | − | 0.182212i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.982973 | − | 0.183750i | \(-0.941176\pi\) | ||||
0.982973 | + | 0.183750i | \(0.0588235\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.850217 | − | 0.526432i | 0.850217 | − | 0.526432i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.465346 | − | 0.288130i | −0.465346 | − | 0.288130i | 0.273663 | − | 0.961826i | \(-0.411765\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.11235 | −1.11235 | ||||||||
\(449\) | −1.58561 | − | 0.614268i | −1.58561 | − | 0.614268i | −0.602635 | − | 0.798017i | \(-0.705882\pi\) |
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(450\) | −0.243964 | − | 0.857445i | −0.243964 | − | 0.857445i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.394867i | 0.394867i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.850217 | − | 0.526432i | \(-0.823529\pi\) | ||||
0.850217 | + | 0.526432i | \(0.176471\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.739009 | − | 0.673696i | \(-0.235294\pi\) | ||||
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.293271 | − | 1.56886i | 0.293271 | − | 1.56886i | −0.445738 | − | 0.895163i | \(-0.647059\pi\) |
0.739009 | − | 0.673696i | \(-0.235294\pi\) | |||||||
\(464\) | 0.366314 | + | 0.945564i | 0.366314 | + | 0.945564i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.433912 | − | 0.475979i | 0.433912 | − | 0.475979i | ||||
\(467\) | 0 | 0 | −0.602635 | − | 0.798017i | \(-0.705882\pi\) | ||||
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.942485 | − | 1.52217i | 0.942485 | − | 1.52217i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.486226 | − | 0.242112i | 0.486226 | − | 0.242112i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.04837 | − | 0.0971461i | −1.04837 | − | 0.0971461i | ||||
\(478\) | 0.619490 | + | 0.176260i | 0.619490 | + | 0.176260i | ||||
\(479\) | 0 | 0 | 0.739009 | − | 0.673696i | \(-0.235294\pi\) | ||||
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.0665409 | + | 0.233867i | 0.0665409 | + | 0.233867i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.831277 | − | 1.66943i | −0.831277 | − | 1.66943i | −0.739009 | − | 0.673696i | \(-0.764706\pi\) |
−0.0922684 | − | 0.995734i | \(-0.529412\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.07524 | − | 0.811985i | −1.07524 | − | 0.811985i | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) |
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.719401 | + | 1.85699i | −0.719401 | + | 1.85699i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.44574 | − | 0.895163i | −1.44574 | − | 0.895163i | −0.445738 | − | 0.895163i | \(-0.647059\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.961826 | − | 0.273663i | \(-0.0882353\pi\) | ||||
−0.961826 | + | 0.273663i | \(0.911765\pi\) | |||||||
\(504\) | 1.05617 | − | 0.197433i | 1.05617 | − | 0.197433i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.433459 | + | 0.215837i | 0.433459 | + | 0.215837i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.365931 | + | 0.0339085i | −0.365931 | + | 0.0339085i | ||||
\(509\) | 0 | 0 | −0.273663 | − | 0.961826i | \(-0.588235\pi\) | ||||
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.03723 | − | 0.401827i | −1.03723 | − | 0.401827i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.139869 | − | 0.0866035i | 0.139869 | − | 0.0866035i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.995734 | − | 0.0922684i | \(-0.0294118\pi\) | ||||
−0.995734 | + | 0.0922684i | \(0.970588\pi\) | |||||||
\(522\) | −0.632333 | − | 1.02125i | −0.632333 | − | 1.02125i | ||||
\(523\) | 0 | 0 | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) | ||||
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.00191 | + | 1.32675i | −1.00191 | + | 1.32675i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.806537 | − | 0.312454i | 0.806537 | − | 0.312454i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.53511 | − | 1.15926i | 1.53511 | − | 1.15926i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.658809 | + | 1.32307i | −0.658809 | + | 1.32307i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.329838 | − | 1.15926i | 0.329838 | − | 1.15926i | −0.602635 | − | 0.798017i | \(-0.705882\pi\) |
0.932472 | − | 0.361242i | \(-0.117647\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.86494 | 1.86494 | 0.932472 | − | 0.361242i | \(-0.117647\pi\) | ||||
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(548\) | 0.0189399 | + | 0.204394i | 0.0189399 | + | 0.204394i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.973732 | + | 0.887674i | 0.973732 | + | 0.887674i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.486734 | + | 0.533922i | 0.486734 | + | 0.533922i | ||||
\(554\) | −0.220714 | + | 1.18072i | −0.220714 | + | 1.18072i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.831277 | + | 1.66943i | −0.831277 | + | 1.66943i | −0.0922684 | + | 0.995734i | \(0.529412\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.28884 | − | 0.798017i | 1.28884 | − | 0.798017i | ||||
\(563\) | 0 | 0 | 0.273663 | − | 0.961826i | \(-0.411765\pi\) | ||||
−0.273663 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.932472 | + | 0.361242i | −0.932472 | + | 0.361242i | ||||
\(568\) | −1.44156 | + | 1.58131i | −1.44156 | + | 1.58131i | ||||
\(569\) | 1.85022 | − | 0.526432i | 1.85022 | − | 0.526432i | 0.850217 | − | 0.526432i | \(-0.176471\pi\) |
1.00000 | \(0\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.132756 | − | 0.710182i | −0.132756 | − | 0.710182i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) |
0.850217 | − | 0.526432i | \(-0.176471\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.365931 | + | 0.0339085i | −0.365931 | + | 0.0339085i | ||||
\(576\) | 1.09341 | + | 0.204394i | 1.09341 | + | 0.204394i | ||||
\(577\) | 0 | 0 | −0.183750 | − | 0.982973i | \(-0.558824\pi\) | ||||
0.183750 | + | 0.982973i | \(0.441176\pi\) | |||||||
\(578\) | −0.757949 | + | 0.469302i | −0.757949 | + | 0.469302i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.39301 | − | 0.693637i | 1.39301 | − | 0.693637i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 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 | ||||||||
\(592\) | 0.136517 | − | 0.0255194i | 0.136517 | − | 0.0255194i | ||||
\(593\) | 0 | 0 | 0.961826 | − | 0.273663i | \(-0.0882353\pi\) | ||||
−0.961826 | + | 0.273663i | \(0.911765\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.145600 | − | 0.159715i | −0.145600 | − | 0.159715i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.380338 | − | 0.981767i | 0.380338 | − | 0.981767i | −0.602635 | − | 0.798017i | \(-0.705882\pi\) |
0.982973 | − | 0.183750i | \(-0.0588235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.361242 | − | 0.932472i | \(-0.617647\pi\) | ||||
0.361242 | + | 0.932472i | \(0.382353\pi\) | |||||||
\(602\) | 0.261444 | + | 0.197433i | 0.261444 | + | 0.197433i | ||||
\(603\) | −1.20614 | + | 1.32307i | −1.20614 | + | 1.32307i | ||||
\(604\) | −0.247405 | − | 0.327617i | −0.247405 | − | 0.327617i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.445738 | − | 0.895163i | \(-0.352941\pi\) | ||||
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.876298 | + | 1.75984i | 0.876298 | + | 1.75984i | 0.602635 | + | 0.798017i | \(0.294118\pi\) |
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.17361 | + | 1.06989i | −1.17361 | + | 1.06989i | ||||
\(617\) | −1.37821 | + | 1.25640i | −1.37821 | + | 1.25640i | −0.445738 | + | 0.895163i | \(0.647059\pi\) |
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.995734 | − | 0.0922684i | \(-0.970588\pi\) | ||||
0.995734 | + | 0.0922684i | \(0.0294118\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.982973 | − | 0.183750i | −0.982973 | − | 0.183750i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.58923 | − | 1.20013i | −1.58923 | − | 1.20013i | −0.850217 | − | 0.526432i | \(-0.823529\pi\) |
−0.739009 | − | 0.673696i | \(-0.764706\pi\) | |||||||
\(632\) | 0.280427 | + | 0.723865i | 0.280427 | + | 0.723865i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.641330 | + | 1.65546i | −0.641330 | + | 1.65546i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.58923 | + | 0.791341i | 1.58923 | + | 0.791341i | ||||
\(639\) | 1.04837 | − | 1.69318i | 1.04837 | − | 1.69318i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.67148 | − | 0.312454i | 1.67148 | − | 0.312454i | 0.739009 | − | 0.673696i | \(-0.235294\pi\) |
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.895163 | − | 0.445738i | \(-0.852941\pi\) | ||||
0.895163 | + | 0.445738i | \(0.147059\pi\) | |||||||
\(644\) | − | 0.0754363i | − | 0.0754363i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.932472 | − | 0.361242i | \(-0.882353\pi\) | ||||
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(648\) | −1.07447 | −1.07447 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.261444 | − | 0.197433i | 0.261444 | − | 0.197433i | ||||
\(653\) | −1.44574 | − | 0.895163i | −1.44574 | − | 0.895163i | −0.445738 | − | 0.895163i | \(-0.647059\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.840204 | − | 1.35698i | −0.840204 | − | 1.35698i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) |
0.0922684 | − | 0.995734i | \(-0.470588\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.995734 | − | 0.0922684i | \(-0.970588\pi\) | ||||
0.995734 | + | 0.0922684i | \(0.0294118\pi\) | |||||||
\(662\) | −0.326219 | − | 1.74512i | −0.326219 | − | 1.74512i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.153401 | + | 0.0594279i | −0.153401 | + | 0.0594279i | ||||
\(667\) | −0.461728 | + | 0.178874i | −0.461728 | + | 0.178874i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.07524 | + | 0.811985i | −1.07524 | + | 0.811985i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) |
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(674\) | −0.121574 | − | 1.31200i | −0.121574 | − | 1.31200i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.0914964 | − | 0.183750i | 0.0914964 | − | 0.183750i | ||||
\(677\) | 0 | 0 | 0.602635 | − | 0.798017i | \(-0.294118\pi\) | ||||
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.45285 | − | 1.32445i | −1.45285 | − | 1.32445i | −0.850217 | − | 0.526432i | \(-0.823529\pi\) |
−0.602635 | − | 0.798017i | \(-0.705882\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.891477 | −0.891477 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.145600 | + | 0.235151i | 0.145600 | + | 0.235151i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.183750 | − | 0.982973i | \(-0.441176\pi\) | ||||
−0.183750 | + | 0.982973i | \(0.558824\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.890705 | − | 1.17948i | 0.890705 | − | 1.17948i | ||||
\(694\) | 0.217488 | − | 0.436776i | 0.217488 | − | 0.436776i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.0561746 | − | 0.197433i | 0.0561746 | − | 0.197433i | ||||
\(701\) | 0.181395 | − | 0.0339085i | 0.181395 | − | 0.0339085i | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) |
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.53305 | + | 0.593907i | −1.53305 | + | 0.593907i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.34164 | − | 0.124322i | −1.34164 | − | 0.124322i | −0.602635 | − | 0.798017i | \(-0.705882\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.380338 | − | 0.614268i | −0.380338 | − | 0.614268i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.958553 | + | 0.723865i | −0.958553 | + | 0.723865i | ||||
\(719\) | 0 | 0 | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) | ||||
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.891477 | 0.891477 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.34164 | + | 0.124322i | −1.34164 | + | 0.124322i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.895163 | − | 0.445738i | \(-0.852941\pi\) | ||||
0.895163 | + | 0.445738i | \(0.147059\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.982973 | − | 0.183750i | 0.982973 | − | 0.183750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.673696 | − | 0.739009i | \(-0.735294\pi\) | ||||
0.673696 | + | 0.739009i | \(0.264706\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.0535734 | − | 0.138289i | 0.0535734 | − | 0.138289i | ||||
\(737\) | 0.486226 | − | 2.60108i | 0.486226 | − | 2.60108i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.576554 | − | 0.435393i | −0.576554 | − | 0.435393i | 0.273663 | − | 0.961826i | \(-0.411765\pi\) |
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.749022 | + | 0.565635i | 0.749022 | + | 0.565635i | ||||
\(743\) | −0.840204 | + | 1.35698i | −0.840204 | + | 1.35698i | 0.0922684 | + | 0.995734i | \(0.470588\pi\) |
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.217488 | − | 0.436776i | −0.217488 | − | 0.436776i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.538007 | + | 1.89090i | 0.538007 | + | 1.89090i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.91545 | − | 0.177492i | −1.91545 | − | 0.177492i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) |
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.0822551 | + | 0.165190i | 0.0822551 | + | 0.165190i | 0.932472 | − | 0.361242i | \(-0.117647\pi\) |
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(758\) | 0.414845 | + | 1.45803i | 0.414845 | + | 1.45803i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.445738 | − | 0.895163i | \(-0.647059\pi\) | ||||
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.397365 | − | 0.798017i | 0.397365 | − | 0.798017i | ||||
\(764\) | 0.193463 | − | 0.312454i | 0.193463 | − | 0.312454i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | −0.361242 | − | 0.932472i | \(-0.617647\pi\) | ||||
0.361242 | + | 0.932472i | \(0.382353\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.135233 | + | 0.123281i | −0.135233 | + | 0.123281i | ||||
\(773\) | 0 | 0 | −0.850217 | − | 0.526432i | \(-0.823529\pi\) | ||||
0.850217 | + | 0.526432i | \(0.176471\pi\) | |||||||
\(774\) | −0.220714 | − | 0.242112i | −0.220714 | − | 0.242112i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.479620 | + | 0.0896566i | −0.479620 | + | 0.0896566i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.94343i | 2.94343i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.701774 | − | 0.271869i | −0.701774 | − | 0.271869i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.895163 | − | 0.445738i | \(-0.147059\pi\) | ||||
−0.895163 | + | 0.445738i | \(0.852941\pi\) | |||||||
\(788\) | −0.0228276 | + | 0.246349i | −0.0228276 | + | 0.246349i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.694903 | + | 1.79375i | −0.694903 | + | 1.79375i | ||||
\(792\) | 1.35022 | − | 0.836019i | 1.35022 | − | 0.836019i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.0922684 | − | 0.995734i | \(-0.470588\pi\) | ||||
−0.0922684 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.243192 | − | 0.322039i | 0.243192 | − | 0.322039i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.15531 | − | 1.26732i | 1.15531 | − | 1.26732i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.53511 | − | 0.436776i | −1.53511 | − | 0.436776i | −0.602635 | − | 0.798017i | \(-0.705882\pi\) |
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.0922684 | − | 0.995734i | \(-0.529412\pi\) | ||||
0.0922684 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(812\) | − | 0.276578i | − | 0.276578i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.146530 | − | 0.194037i | 0.146530 | − | 0.194037i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.70043 | 1.70043 | 0.850217 | − | 0.526432i | \(-0.176471\pi\) | ||||
0.850217 | + | 0.526432i | \(0.176471\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.70043 | −1.70043 | −0.850217 | − | 0.526432i | \(-0.823529\pi\) | ||||
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.247582 | + | 0.271585i | 0.247582 | + | 0.271585i | 0.850217 | − | 0.526432i | \(-0.176471\pi\) |
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(828\) | −0.0138614 | + | 0.0741518i | −0.0138614 | + | 0.0741518i | ||||
\(829\) | 0 | 0 | 0.273663 | − | 0.961826i | \(-0.411765\pi\) | ||||
−0.273663 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.602635 | − | 0.798017i | \(-0.705882\pi\) | ||||
0.602635 | + | 0.798017i | \(0.294118\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.760397 | + | 0.294579i | −0.760397 | + | 0.294579i | ||||
\(842\) | −1.19604 | + | 1.31200i | −1.19604 | + | 1.31200i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.210348 | + | 0.278545i | −0.210348 | + | 0.278545i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.109295 | + | 1.17948i | −0.109295 | + | 1.17948i | ||||
\(848\) | 0.417135 | + | 0.673696i | 0.417135 | + | 0.673696i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0124614 | + | 0.0666624i | 0.0124614 | + | 0.0666624i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.361242 | − | 0.932472i | \(-0.382353\pi\) | ||||
−0.361242 | + | 0.932472i | \(0.617647\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.194903 | + | 2.10334i | −0.194903 | + | 2.10334i | ||||
\(857\) | 0 | 0 | 0.895163 | − | 0.445738i | \(-0.147059\pi\) | ||||
−0.895163 | + | 0.445738i | \(0.852941\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.58923 | − | 0.147263i | 1.58923 | − | 0.147263i | ||||
\(863\) | − | 0.722483i | − | 0.722483i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) | ||
0.932472 | − | 0.361242i | \(-0.117647\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.955894 | + | 0.475979i | 0.955894 | + | 0.475979i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.707870 | − | 0.645309i | 0.707870 | − | 0.645309i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.739009 | − | 0.673696i | \(-0.764706\pi\) | ||||
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.445738 | − | 0.895163i | \(-0.352941\pi\) | ||||
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(882\) | 0.876298 | + | 0.163808i | 0.876298 | + | 0.163808i | ||||
\(883\) | 0.876298 | + | 1.75984i | 0.876298 | + | 1.75984i | 0.602635 | + | 0.798017i | \(0.294118\pi\) |
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.133528 | − | 0.469302i | −0.133528 | − | 0.469302i | ||||
\(887\) | 0 | 0 | −0.445738 | − | 0.895163i | \(-0.647059\pi\) | ||||
0.445738 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.72198 | − | 0.489946i | −1.72198 | − | 0.489946i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.09227 | + | 0.995734i | −1.09227 | + | 0.995734i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.434600 | − | 0.396190i | −0.434600 | − | 0.396190i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.675694 | − | 1.35698i | −0.675694 | − | 1.35698i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.0914964 | + | 0.183750i | −0.0914964 | + | 0.183750i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.39246 | + | 1.52746i | −1.39246 | + | 1.52746i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.353470 | + | 1.89090i | −0.353470 | + | 1.89090i | 0.0922684 | + | 0.995734i | \(0.470588\pi\) |
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.709310 | + | 0.778076i | 0.709310 | + | 0.778076i | 0.982973 | − | 0.183750i | \(-0.0588235\pi\) |
−0.273663 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.58923 | − | 0.147263i | 1.58923 | − | 0.147263i | 0.739009 | − | 0.673696i | \(-0.235294\pi\) |
0.850217 | + | 0.526432i | \(0.176471\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0170269 | + | 0.183750i | −0.0170269 | + | 0.183750i | ||||
\(926\) | 1.13544 | − | 0.857445i | 1.13544 | − | 0.857445i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.196421 | − | 0.507020i | 0.196421 | − | 0.507020i | ||||
\(929\) | 0 | 0 | 0.850217 | − | 0.526432i | \(-0.176471\pi\) | ||||
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.147671 | + | 0.0136837i | −0.147671 | + | 0.0136837i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.602635 | − | 0.798017i | \(-0.294118\pi\) | ||||
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(938\) | 1.53511 | − | 0.436776i | 1.53511 | − | 0.436776i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.932472 | − | 0.361242i | \(-0.117647\pi\) | ||||
−0.932472 | + | 0.361242i | \(0.882353\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.465739 | + | 0.132514i | 0.465739 | + | 0.132514i | ||||
\(947\) | 0.293271 | − | 0.221468i | 0.293271 | − | 0.221468i | −0.445738 | − | 0.895163i | \(-0.647059\pi\) |
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.982973 | − | 0.183750i | \(-0.941176\pi\) | ||||
0.982973 | + | 0.183750i | \(0.0588235\pi\) | |||||||
\(954\) | −0.632333 | − | 0.693637i | −0.632333 | − | 0.693637i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.0780718 | − | 0.126090i | −0.0780718 | − | 0.126090i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.273663 | + | 0.961826i | −0.273663 | + | 0.961826i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.739009 | − | 0.673696i | −0.739009 | − | 0.673696i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.181395 | − | 1.95756i | −0.181395 | − | 1.95756i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.18475 | + | 1.56886i | −1.18475 | + | 1.56886i | −0.445738 | + | 0.895163i | \(0.647059\pi\) |
−0.739009 | + | 0.673696i | \(0.764706\pi\) | |||||||
\(968\) | −0.567313 | + | 1.13932i | −0.567313 | + | 1.13932i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.798017 | − | 0.602635i | \(-0.205882\pi\) | ||||
−0.798017 | + | 0.602635i | \(0.794118\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.454980 | − | 1.59909i | 0.454980 | − | 1.59909i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.12388 | − | 0.435393i | 1.12388 | − | 0.435393i | 0.273663 | − | 0.961826i | \(-0.411765\pi\) |
0.850217 | + | 0.526432i | \(0.176471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.537235 | + | 0.711414i | −0.537235 | + | 0.711414i | ||||
\(982\) | −0.220714 | − | 1.18072i | −0.220714 | − | 1.18072i | ||||
\(983\) | 0 | 0 | −0.995734 | − | 0.0922684i | \(-0.970588\pi\) | ||||
0.995734 | + | 0.0922684i | \(0.0294118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.114827 | + | 0.0710976i | −0.114827 | + | 0.0710976i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.67148 | + | 1.03494i | 1.67148 | + | 1.03494i | 0.932472 | + | 0.361242i | \(0.117647\pi\) |
0.739009 | + | 0.673696i | \(0.235294\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.58923 | + | 0.791341i | −1.58923 | + | 0.791341i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.932472 | − | 0.361242i | \(-0.882353\pi\) | ||||
0.932472 | + | 0.361242i | \(0.117647\pi\) | |||||||
\(998\) | −0.414845 | − | 1.45803i | −0.414845 | − | 1.45803i | ||||
\(999\) | 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 | 959.1.r.a.748.1 | ✓ | 16 | |
7.6 | odd | 2 | CM | 959.1.r.a.748.1 | ✓ | 16 | |
137.87 | even | 34 | inner | 959.1.r.a.909.1 | yes | 16 | |
959.909 | odd | 34 | inner | 959.1.r.a.909.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
959.1.r.a.748.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
959.1.r.a.748.1 | ✓ | 16 | 7.6 | odd | 2 | CM | |
959.1.r.a.909.1 | yes | 16 | 137.87 | even | 34 | inner | |
959.1.r.a.909.1 | yes | 16 | 959.909 | odd | 34 | inner |