Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1340,1,Mod(19,1340)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1340, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([33, 33, 10]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1340.19");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1340 = 2^{2} \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1340.bl (of order \(66\), degree \(20\), 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: | \(0.668747116928\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{33}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{33} - \cdots)\) |
Embedding invariants
Embedding label | 1239.1 | ||
Root | \(0.723734 - 0.690079i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1340.1239 |
Dual form | 1340.1.bl.a.199.1 |
$q$-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 \(\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times\).
\(n\) | \(537\) | \(671\) | \(1141\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{16}{33}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0475819 | − | 0.998867i | −0.0475819 | − | 0.998867i | ||||
\(3\) | −1.91030 | + | 0.560914i | −1.91030 | + | 0.560914i | −0.928368 | + | 0.371662i | \(0.878788\pi\) |
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(4\) | −0.995472 | + | 0.0950560i | −0.995472 | + | 0.0950560i | ||||
\(5\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(6\) | 0.651174 | + | 1.88144i | 0.651174 | + | 1.88144i | ||||
\(7\) | 0.419102 | + | 0.216062i | 0.419102 | + | 0.216062i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(8\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(9\) | 2.49336 | − | 1.60238i | 2.49336 | − | 1.60238i | ||||
\(10\) | −0.723734 | + | 0.690079i | −0.723734 | + | 0.690079i | ||||
\(11\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(12\) | 1.84833 | − | 0.739959i | 1.84833 | − | 0.739959i | ||||
\(13\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(14\) | 0.195876 | − | 0.428908i | 0.195876 | − | 0.428908i | ||||
\(15\) | 1.67489 | + | 1.07639i | 1.67489 | + | 1.07639i | ||||
\(16\) | 0.981929 | − | 0.189251i | 0.981929 | − | 0.189251i | ||||
\(17\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(18\) | −1.71921 | − | 2.41429i | −1.71921 | − | 2.41429i | ||||
\(19\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(20\) | 0.723734 | + | 0.690079i | 0.723734 | + | 0.690079i | ||||
\(21\) | −0.921801 | − | 0.177663i | −0.921801 | − | 0.177663i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.235759 | − | 0.971812i | 0.235759 | − | 0.971812i | −0.723734 | − | 0.690079i | \(-0.757576\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(24\) | −0.827068 | − | 1.81103i | −0.827068 | − | 1.81103i | ||||
\(25\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.56046 | + | 2.95493i | −2.56046 | + | 2.95493i | ||||
\(28\) | −0.437742 | − | 0.175245i | −0.437742 | − | 0.175245i | ||||
\(29\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(30\) | 0.995472 | − | 1.72421i | 0.995472 | − | 1.72421i | ||||
\(31\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(32\) | −0.235759 | − | 0.971812i | −0.235759 | − | 0.971812i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.111165 | − | 0.458227i | −0.111165 | − | 0.458227i | ||||
\(36\) | −2.32975 | + | 1.83214i | −2.32975 | + | 1.83214i | ||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(41\) | −0.911911 | + | 1.28060i | −0.911911 | + | 1.28060i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(42\) | −0.133600 | + | 0.929210i | −0.133600 | + | 0.929210i | ||||
\(43\) | −0.481929 | − | 1.05528i | −0.481929 | − | 1.05528i | −0.981929 | − | 0.189251i | \(-0.939394\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.84380 | − | 0.835015i | −2.84380 | − | 0.835015i | ||||
\(46\) | −0.981929 | − | 0.189251i | −0.981929 | − | 0.189251i | ||||
\(47\) | −1.34378 | − | 1.28129i | −1.34378 | − | 1.28129i | −0.928368 | − | 0.371662i | \(-0.878788\pi\) |
−0.415415 | − | 0.909632i | \(-0.636364\pi\) | |||||||
\(48\) | −1.76962 | + | 0.912303i | −1.76962 | + | 0.912303i | ||||
\(49\) | −0.451093 | − | 0.633472i | −0.451093 | − | 0.633472i | ||||
\(50\) | 0.995472 | + | 0.0950560i | 0.995472 | + | 0.0950560i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(54\) | 3.07341 | + | 2.41696i | 3.07341 | + | 2.41696i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.154218 | + | 0.445585i | −0.154218 | + | 0.445585i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.21769 | + | 0.782560i | −1.21769 | + | 0.782560i | ||||
\(59\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(60\) | −1.76962 | − | 0.912303i | −1.76962 | − | 0.912303i | ||||
\(61\) | 0.428368 | + | 1.23769i | 0.428368 | + | 1.23769i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.39118 | − | 0.132842i | 1.39118 | − | 0.132842i | ||||
\(64\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.580057 | − | 0.814576i | −0.580057 | − | 0.814576i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0947329 | + | 1.98869i | 0.0947329 | + | 1.98869i | ||||
\(70\) | −0.452418 | + | 0.132842i | −0.452418 | + | 0.132842i | ||||
\(71\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(72\) | 1.94091 | + | 2.23993i | 1.94091 | + | 2.23993i | ||||
\(73\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.283341 | − | 1.97068i | −0.283341 | − | 1.97068i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(80\) | −0.786053 | − | 0.618159i | −0.786053 | − | 0.618159i | ||||
\(81\) | 2.00255 | − | 4.38497i | 2.00255 | − | 4.38497i | ||||
\(82\) | 1.32254 | + | 0.849945i | 1.32254 | + | 0.849945i | ||||
\(83\) | 1.74555 | − | 0.336426i | 1.74555 | − | 0.336426i | 0.786053 | − | 0.618159i | \(-0.212121\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(84\) | 0.934515 | + | 0.0892353i | 0.934515 | + | 0.0892353i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.03115 | + | 0.531595i | −1.03115 | + | 0.531595i | ||||
\(87\) | 2.08568 | + | 1.98869i | 2.08568 | + | 1.98869i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(90\) | −0.698756 | + | 2.88031i | −0.698756 | + | 2.88031i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.21590 | + | 1.40323i | −1.21590 | + | 1.40323i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.995472 | + | 1.72421i | 0.995472 | + | 1.72421i | ||||
\(97\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(98\) | −0.611291 | + | 0.480724i | −0.611291 | + | 0.480724i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0475819 | − | 0.998867i | 0.0475819 | − | 0.998867i | ||||
\(101\) | 0.0800569 | − | 1.68060i | 0.0800569 | − | 1.68060i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.580057 | − | 0.814576i | \(-0.303030\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.0748038 | − | 0.0588264i | 0.0748038 | − | 0.0588264i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.469383 | + | 0.812995i | 0.469383 | + | 0.812995i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.186393 | + | 0.215109i | −0.186393 | + | 0.215109i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(108\) | 2.26798 | − | 3.18493i | 2.26798 | − | 3.18493i | ||||
\(109\) | −0.0135432 | + | 0.0941952i | −0.0135432 | + | 0.0941952i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.452418 | + | 0.132842i | 0.452418 | + | 0.132842i | ||||
\(113\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.888835 | + | 0.458227i | −0.888835 | + | 0.458227i | ||||
\(116\) | 0.839614 | + | 1.17907i | 0.839614 | + | 1.17907i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.827068 | + | 1.81103i | −0.827068 | + | 1.81103i | ||||
\(121\) | −0.786053 | − | 0.618159i | −0.786053 | − | 0.618159i | ||||
\(122\) | 1.21590 | − | 0.486774i | 1.21590 | − | 0.486774i | ||||
\(123\) | 1.02371 | − | 2.95783i | 1.02371 | − | 2.95783i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(126\) | −0.198887 | − | 1.38329i | −0.198887 | − | 1.38329i | ||||
\(127\) | −0.581419 | − | 0.299742i | −0.581419 | − | 0.299742i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(128\) | 0.327068 | + | 0.945001i | 0.327068 | + | 0.945001i | ||||
\(129\) | 1.51255 | + | 1.74557i | 1.51255 | + | 1.74557i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.786053 | + | 0.618159i | −0.786053 | + | 0.618159i | ||||
\(135\) | 3.90993 | 3.90993 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(138\) | 1.98193 | − | 0.189251i | 1.98193 | − | 0.189251i | ||||
\(139\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(140\) | 0.154218 | + | 0.445585i | 0.154218 | + | 0.445585i | ||||
\(141\) | 3.28572 | + | 1.69391i | 3.28572 | + | 1.69391i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.14504 | − | 2.04530i | 2.14504 | − | 2.04530i | ||||
\(145\) | −0.473420 | + | 1.36786i | −0.473420 | + | 1.36786i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.21705 | + | 0.957095i | 1.21705 | + | 0.957095i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.32254 | − | 0.849945i | −1.32254 | − | 0.849945i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(150\) | −1.95496 | + | 0.376789i | −1.95496 | + | 0.376789i | ||||
\(151\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.580057 | + | 0.814576i | −0.580057 | + | 0.814576i | ||||
\(161\) | 0.308779 | − | 0.356349i | 0.308779 | − | 0.356349i | ||||
\(162\) | −4.47528 | − | 1.79163i | −4.47528 | − | 1.79163i | ||||
\(163\) | 0.415415 | + | 0.719520i | 0.415415 | + | 0.719520i | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) |
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(164\) | 0.786053 | − | 1.36148i | 0.786053 | − | 1.36148i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.419102 | − | 1.72756i | −0.419102 | − | 1.72756i | ||||
\(167\) | 0.0913090 | − | 1.91681i | 0.0913090 | − | 1.91681i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
0.327068 | − | 0.945001i | \(-0.393939\pi\) | |||||||
\(168\) | 0.0446683 | − | 0.937702i | 0.0446683 | − | 0.937702i | ||||
\(169\) | 0.235759 | + | 0.971812i | 0.235759 | + | 0.971812i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.580057 | + | 1.00469i | 0.580057 | + | 1.00469i | ||||
\(173\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(174\) | 1.88720 | − | 2.17794i | 1.88720 | − | 2.17794i | ||||
\(175\) | −0.273507 | + | 0.384087i | −0.273507 | + | 0.384087i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.396666 | + | 1.63508i | −0.396666 | + | 1.63508i | ||||
\(179\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(180\) | 2.91030 | + | 0.560914i | 2.91030 | + | 0.560914i | ||||
\(181\) | 0.601300 | + | 0.573338i | 0.601300 | + | 0.573338i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.51255 | − | 2.12407i | −1.51255 | − | 2.12407i | ||||
\(184\) | 0.995472 | + | 0.0950560i | 0.995472 | + | 0.0950560i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.45949 | + | 1.14776i | 1.45949 | + | 1.14776i | ||||
\(189\) | −1.71154 | + | 0.685198i | −1.71154 | + | 0.685198i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(192\) | 1.67489 | − | 1.07639i | 1.67489 | − | 1.07639i | ||||
\(193\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.509266 | + | 0.587724i | 0.509266 | + | 0.587724i | ||||
\(197\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(200\) | −1.00000 | −1.00000 | ||||||||
\(201\) | 1.56499 | + | 1.23072i | 1.56499 | + | 1.23072i | ||||
\(202\) | −1.68251 | −1.68251 | ||||||||
\(203\) | −0.0324750 | − | 0.681734i | −0.0324750 | − | 0.681734i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.56499 | − | 0.149438i | 1.56499 | − | 0.149438i | ||||
\(206\) | −0.0623191 | − | 0.0719200i | −0.0623191 | − | 0.0719200i | ||||
\(207\) | −0.969383 | − | 2.80085i | −0.969383 | − | 2.80085i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.789740 | − | 0.507535i | 0.789740 | − | 0.507535i | ||||
\(211\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.223734 | + | 0.175946i | 0.223734 | + | 0.175946i | ||||
\(215\) | −0.481929 | + | 1.05528i | −0.481929 | + | 1.05528i | ||||
\(216\) | −3.28924 | − | 2.11387i | −3.28924 | − | 2.11387i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.0947329 | + | 0.00904590i | 0.0947329 | + | 0.00904590i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.25667 | − | 0.368991i | −1.25667 | − | 0.368991i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(224\) | 0.111165 | − | 0.458227i | 0.111165 | − | 0.458227i | ||||
\(225\) | 1.23123 | + | 2.69602i | 1.23123 | + | 2.69602i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.975950 | + | 1.37053i | −0.975950 | + | 1.37053i | −0.0475819 | + | 0.998867i | \(0.515152\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.607279 | − | 0.243118i | −0.607279 | − | 0.243118i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(230\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.13779 | − | 0.894765i | 1.13779 | − | 0.894765i | ||||
\(233\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0883470 | + | 1.85463i | −0.0883470 | + | 1.85463i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | 1.84833 | + | 0.739959i | 1.84833 | + | 0.739959i | ||||
\(241\) | −0.0623191 | + | 0.0719200i | −0.0623191 | + | 0.0719200i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(242\) | −0.580057 | + | 0.814576i | −0.580057 | + | 0.814576i | ||||
\(243\) | −0.809430 | + | 5.62971i | −0.809430 | + | 5.62971i | ||||
\(244\) | −0.544078 | − | 1.19136i | −0.544078 | − | 1.19136i | ||||
\(245\) | −0.183343 | + | 0.755750i | −0.183343 | + | 0.755750i | ||||
\(246\) | −3.00319 | − | 0.881816i | −3.00319 | − | 0.881816i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.14580 | + | 1.62177i | −3.14580 | + | 1.62177i | ||||
\(250\) | −0.580057 | − | 0.814576i | −0.580057 | − | 0.814576i | ||||
\(251\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(252\) | −1.37226 | + | 0.264481i | −1.37226 | + | 0.264481i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.271738 | + | 0.595023i | −0.271738 | + | 0.595023i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.928368 | − | 0.371662i | 0.928368 | − | 0.371662i | ||||
\(257\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(258\) | 1.67162 | − | 1.59389i | 1.67162 | − | 1.59389i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.81318 | − | 1.96583i | −3.81318 | − | 1.96583i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.28605 | + | 1.48418i | 1.28605 | + | 1.48418i | 0.786053 | + | 0.618159i | \(0.212121\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.34978 | 3.34978 | ||||||||
\(268\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(269\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(270\) | −0.186042 | − | 3.90550i | −0.186042 | − | 3.90550i | ||||
\(271\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.283341 | − | 1.97068i | −0.283341 | − | 1.97068i | ||||
\(277\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.437742 | − | 0.175245i | 0.437742 | − | 0.175245i | ||||
\(281\) | −1.45949 | − | 1.14776i | −1.45949 | − | 1.14776i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(282\) | 1.53565 | − | 3.36260i | 1.53565 | − | 3.36260i | ||||
\(283\) | −1.65210 | − | 1.06174i | −1.65210 | − | 1.06174i | −0.928368 | − | 0.371662i | \(-0.878788\pi\) |
−0.723734 | − | 0.690079i | \(-0.757576\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.658873 | + | 0.339672i | −0.658873 | + | 0.339672i | ||||
\(288\) | −2.14504 | − | 2.04530i | −2.14504 | − | 2.04530i | ||||
\(289\) | 0.981929 | + | 0.189251i | 0.981929 | + | 0.189251i | ||||
\(290\) | 1.38884 | + | 0.407799i | 1.38884 | + | 0.407799i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(294\) | 0.898102 | − | 1.26121i | 0.898102 | − | 1.26121i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.786053 | + | 1.36148i | −0.786053 | + | 1.36148i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.469383 | + | 1.93482i | 0.469383 | + | 1.93482i | ||||
\(301\) | 0.0260280 | − | 0.546395i | 0.0260280 | − | 0.546395i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.789740 | + | 3.25535i | 0.789740 | + | 3.25535i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.654861 | − | 1.13425i | 0.654861 | − | 1.13425i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.264241 | + | 0.105786i | 0.264241 | + | 0.105786i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.109901 | + | 0.154334i | −0.109901 | + | 0.154334i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.01143 | − | 0.964394i | −1.01143 | − | 0.964394i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(321\) | 0.235408 | − | 0.515472i | 0.235408 | − | 0.515472i | ||||
\(322\) | −0.370638 | − | 0.291473i | −0.370638 | − | 0.291473i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.57666 | + | 4.55546i | −1.57666 | + | 4.55546i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | ||||
\(327\) | −0.0269638 | − | 0.187537i | −0.0269638 | − | 0.187537i | ||||
\(328\) | −1.39734 | − | 0.720381i | −1.39734 | − | 0.720381i | ||||
\(329\) | −0.286343 | − | 0.827333i | −0.286343 | − | 0.827333i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(332\) | −1.70566 | + | 0.500828i | −1.70566 | + | 0.500828i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.91899 | −1.91899 | ||||||||
\(335\) | −0.235759 | + | 0.971812i | −0.235759 | + | 0.971812i | ||||
\(336\) | −0.938766 | −0.938766 | ||||||||
\(337\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(338\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.119289 | − | 0.829672i | −0.119289 | − | 0.829672i | ||||
\(344\) | 0.975950 | − | 0.627205i | 0.975950 | − | 0.627205i | ||||
\(345\) | 1.44091 | − | 1.37391i | 1.44091 | − | 1.37391i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.21590 | − | 0.486774i | 1.21590 | − | 0.486774i | 0.327068 | − | 0.945001i | \(-0.393939\pi\) |
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(348\) | −2.26527 | − | 1.78143i | −2.26527 | − | 1.78143i | ||||
\(349\) | 0.481929 | − | 1.05528i | 0.481929 | − | 1.05528i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(350\) | 0.396666 | + | 0.254922i | 0.396666 | + | 0.254922i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.65210 | + | 0.318417i | 1.65210 | + | 0.318417i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(360\) | 0.421801 | − | 2.93369i | 0.421801 | − | 2.93369i | ||||
\(361\) | 0.580057 | − | 0.814576i | 0.580057 | − | 0.814576i | ||||
\(362\) | 0.544078 | − | 0.627899i | 0.544078 | − | 0.627899i | ||||
\(363\) | 1.84833 | + | 0.739959i | 1.84833 | + | 0.739959i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.04970 | + | 1.61190i | −2.04970 | + | 1.61190i | ||||
\(367\) | −0.0224357 | − | 0.0924813i | −0.0224357 | − | 0.0924813i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(368\) | 0.0475819 | − | 0.998867i | 0.0475819 | − | 0.998867i | ||||
\(369\) | −0.221708 | + | 4.65422i | −0.221708 | + | 4.65422i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.30379 | + | 1.50465i | −1.30379 | + | 1.50465i | ||||
\(376\) | 1.07701 | − | 1.51245i | 1.07701 | − | 1.51245i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.765860 | + | 1.67700i | 0.765860 | + | 1.67700i | ||||
\(379\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.27881 | + | 0.246471i | 1.27881 | + | 0.246471i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.65033 | − | 0.850806i | 1.65033 | − | 0.850806i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | |||||||
\(384\) | −1.15486 | − | 1.62177i | −1.15486 | − | 1.62177i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.89258 | − | 1.85895i | −2.89258 | − | 1.85895i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.0748038 | − | 0.0588264i | −0.0748038 | − | 0.0588264i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.562827 | − | 0.536654i | 0.562827 | − | 0.536654i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.0475819 | + | 0.998867i | 0.0475819 | + | 0.998867i | ||||
\(401\) | 0.471518 | 0.471518 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(402\) | 1.15486 | − | 1.62177i | 1.15486 | − | 1.62177i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.0800569 | + | 1.68060i | 0.0800569 | + | 1.68060i | ||||
\(405\) | −4.62533 | + | 1.35812i | −4.62533 | + | 1.35812i | ||||
\(406\) | −0.679417 | + | 0.0648764i | −0.679417 | + | 0.0648764i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.738471 | − | 0.380708i | −0.738471 | − | 0.380708i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(410\) | −0.223734 | − | 1.55610i | −0.223734 | − | 1.55610i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.0688733 | + | 0.0656706i | −0.0688733 | + | 0.0656706i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.75155 | + | 1.10155i | −2.75155 | + | 1.10155i | ||||
\(415\) | −1.39734 | − | 1.09888i | −1.39734 | − | 1.09888i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(420\) | −0.544537 | − | 0.764696i | −0.544537 | − | 0.764696i | ||||
\(421\) | 1.70566 | − | 0.879330i | 1.70566 | − | 0.879330i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.40365 | − | 1.04147i | −5.40365 | − | 1.04147i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0878875 | + | 0.611271i | −0.0878875 | + | 0.611271i | ||||
\(428\) | 0.165101 | − | 0.231852i | 0.165101 | − | 0.231852i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.07701 | + | 0.431171i | 1.07701 | + | 0.431171i | ||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | −1.95496 | + | 3.38610i | −1.95496 | + | 3.38610i | ||||
\(433\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.137123 | − | 2.87856i | 0.137123 | − | 2.87856i | ||||
\(436\) | 0.00452808 | − | 0.0950560i | 0.00452808 | − | 0.0950560i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.13980 | − | 0.856647i | −2.13980 | − | 0.856647i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.839614 | + | 1.17907i | −0.839614 | + | 1.17907i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(446\) | −0.308779 | + | 1.27280i | −0.308779 | + | 1.27280i | ||||
\(447\) | 3.00319 | + | 0.881816i | 3.00319 | + | 0.881816i | ||||
\(448\) | −0.462997 | − | 0.0892353i | −0.462997 | − | 0.0892353i | ||||
\(449\) | 1.34378 | + | 1.28129i | 1.34378 | + | 1.28129i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(450\) | 2.63438 | − | 1.35812i | 2.63438 | − | 1.35812i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(458\) | −0.213947 | + | 0.618159i | −0.213947 | + | 0.618159i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(461\) | 0.252989 | + | 1.75958i | 0.252989 | + | 1.75958i | 0.580057 | + | 0.814576i | \(0.303030\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.271738 | + | 0.785135i | 0.271738 | + | 0.785135i | 0.995472 | + | 0.0950560i | \(0.0303030\pi\) |
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(464\) | −0.947890 | − | 1.09392i | −0.947890 | − | 1.09392i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.0311250 | + | 0.653395i | 0.0311250 | + | 0.653395i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.0671040 | − | 0.466718i | −0.0671040 | − | 0.466718i | ||||
\(470\) | 1.85674 | 1.85674 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(480\) | 0.651174 | − | 1.88144i | 0.651174 | − | 1.88144i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.0748038 | + | 0.0588264i | 0.0748038 | + | 0.0588264i | ||||
\(483\) | −0.389977 | + | 0.853931i | −0.389977 | + | 0.853931i | ||||
\(484\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.66185 | + | 0.540641i | 5.66185 | + | 0.540641i | ||||
\(487\) | 1.03115 | + | 1.44805i | 1.03115 | + | 1.44805i | 0.888835 | + | 0.458227i | \(0.151515\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(488\) | −1.16413 | + | 0.600149i | −1.16413 | + | 0.600149i | ||||
\(489\) | −1.19715 | − | 1.14148i | −1.19715 | − | 1.14148i | ||||
\(490\) | 0.763617 | + | 0.147175i | 0.763617 | + | 0.147175i | ||||
\(491\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(492\) | −0.737920 | + | 3.04175i | −0.737920 | + | 3.04175i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.76962 | + | 3.06507i | 1.76962 | + | 3.06507i | ||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | −0.786053 | + | 0.618159i | −0.786053 | + | 0.618159i | ||||
\(501\) | 0.900739 | + | 3.71290i | 0.900739 | + | 3.71290i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.0748038 | − | 1.57033i | 0.0748038 | − | 1.57033i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(504\) | 0.329476 | + | 1.35812i | 0.329476 | + | 1.35812i | ||||
\(505\) | −1.32254 | + | 1.04006i | −1.32254 | + | 1.04006i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.995472 | − | 1.72421i | −0.995472 | − | 1.72421i | ||||
\(508\) | 0.607279 | + | 0.243118i | 0.607279 | + | 0.243118i | ||||
\(509\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.0934441 | − | 0.0180099i | −0.0934441 | − | 0.0180099i | ||||
\(516\) | −1.67162 | − | 1.59389i | −1.67162 | − | 1.59389i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(522\) | −1.78217 | + | 3.90240i | −1.78217 | + | 3.90240i | ||||
\(523\) | 0.911911 | + | 0.717135i | 0.911911 | + | 0.717135i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.307040 | − | 0.887134i | 0.307040 | − | 0.887134i | ||||
\(526\) | 1.42131 | − | 1.35522i | 1.42131 | − | 1.35522i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.159389 | − | 3.34598i | −0.159389 | − | 3.34598i | ||||
\(535\) | 0.284630 | 0.284630 | ||||||||
\(536\) | 0.723734 | − | 0.690079i | 0.723734 | − | 0.690079i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.0395325 | − | 0.829889i | −0.0395325 | − | 0.829889i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.89223 | + | 0.371662i | −3.89223 | + | 0.371662i | ||||
\(541\) | −0.759713 | − | 0.876756i | −0.759713 | − | 0.876756i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.47025 | − | 0.757969i | −1.47025 | − | 0.757969i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0800569 | − | 0.0514495i | 0.0800569 | − | 0.0514495i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.213947 | + | 0.618159i | −0.213947 | + | 0.618159i | 0.786053 | + | 0.618159i | \(0.212121\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.05132 | + | 2.39959i | 3.05132 | + | 2.39959i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.95496 | + | 0.376789i | −1.95496 | + | 0.376789i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.195876 | − | 0.428908i | −0.195876 | − | 0.428908i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.07701 | + | 1.51245i | −1.07701 | + | 1.51245i | ||||
\(563\) | 0.759713 | − | 0.876756i | 0.759713 | − | 0.876756i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(564\) | −3.43186 | − | 1.37391i | −3.43186 | − | 1.37391i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.981929 | + | 1.70075i | −0.981929 | + | 1.70075i | ||||
\(567\) | 1.78670 | − | 1.40507i | 1.78670 | − | 1.40507i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.0913090 | + | 1.91681i | −0.0913090 | + | 1.91681i | 0.235759 | + | 0.971812i | \(0.424242\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.370638 | + | 0.641964i | 0.370638 | + | 0.641964i | ||||
\(575\) | 0.928368 | + | 0.371662i | 0.928368 | + | 0.371662i | ||||
\(576\) | −1.94091 | + | 2.23993i | −1.94091 | + | 2.23993i | ||||
\(577\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(578\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.341254 | − | 1.40667i | 0.341254 | − | 1.40667i | ||||
\(581\) | 0.804250 | + | 0.236149i | 0.804250 | + | 0.236149i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.279486 | − | 0.0538665i | 0.279486 | − | 0.0538665i | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) |
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(588\) | −1.30251 | − | 0.837074i | −1.30251 | − | 0.837074i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.39734 | + | 0.720381i | 1.39734 | + | 0.720381i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(600\) | 1.91030 | − | 0.560914i | 1.91030 | − | 0.560914i | ||||
\(601\) | 0.0552004 | + | 1.15880i | 0.0552004 | + | 1.15880i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(602\) | −0.547014 | −0.547014 | ||||||||
\(603\) | −2.75155 | − | 1.10155i | −2.75155 | − | 1.10155i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.0475819 | + | 0.998867i | 0.0475819 | + | 0.998867i | ||||
\(606\) | 3.21409 | − | 0.943741i | 3.21409 | − | 0.943741i | ||||
\(607\) | 1.84833 | − | 0.176494i | 1.84833 | − | 0.176494i | 0.888835 | − | 0.458227i | \(-0.151515\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.444431 | + | 1.28410i | 0.444431 | + | 1.28410i | ||||
\(610\) | −1.16413 | − | 0.600149i | −1.16413 | − | 0.600149i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(614\) | 0.0930932 | − | 0.268975i | 0.0930932 | − | 0.268975i | ||||
\(615\) | −2.90577 | + | 1.16329i | −2.90577 | + | 1.16329i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(618\) | 0.159389 | + | 0.102433i | 0.159389 | + | 0.102433i | ||||
\(619\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.26798 | + | 3.18493i | 2.26798 | + | 3.18493i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.574161 | − | 0.547462i | −0.574161 | − | 0.547462i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −0.915176 | + | 1.05617i | −0.915176 | + | 1.05617i | ||||
\(631\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.154218 | + | 0.635697i | 0.154218 | + | 0.635697i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(641\) | −0.981929 | − | 1.70075i | −0.981929 | − | 1.70075i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.327068 | − | 0.945001i | \(-0.606061\pi\) | |||||||
\(642\) | −0.526089 | − | 0.210614i | −0.526089 | − | 0.210614i | ||||
\(643\) | 0.947890 | − | 1.09392i | 0.947890 | − | 1.09392i | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) |
0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | |||||||
\(644\) | −0.273507 | + | 0.384087i | −0.273507 | + | 0.384087i | ||||
\(645\) | 0.328708 | − | 2.28621i | 0.328708 | − | 2.28621i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.437742 | + | 1.80440i | −0.437742 | + | 1.80440i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(648\) | 4.62533 | + | 1.35812i | 4.62533 | + | 1.35812i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.481929 | − | 0.676774i | −0.481929 | − | 0.676774i | ||||
\(653\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(654\) | −0.186042 | + | 0.0358566i | −0.186042 | + | 0.0358566i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.653077 | + | 1.43004i | −0.653077 | + | 1.43004i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.812771 | + | 0.325385i | −0.812771 | + | 0.325385i | ||||
\(659\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | −0.654861 | + | 0.755750i | \(0.727273\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.581419 | + | 1.67990i | 0.581419 | + | 1.67990i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.38884 | + | 0.407799i | −1.38884 | + | 0.407799i | ||||
\(668\) | 0.0913090 | + | 1.91681i | 0.0913090 | + | 1.91681i | ||||
\(669\) | 2.60758 | 2.60758 | ||||||||
\(670\) | 0.981929 | + | 0.189251i | 0.981929 | + | 0.189251i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.0446683 | + | 0.937702i | 0.0446683 | + | 0.937702i | ||||
\(673\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.56046 | − | 2.95493i | −2.56046 | − | 2.95493i | ||||
\(676\) | −0.327068 | − | 0.945001i | −0.327068 | − | 0.945001i | ||||
\(677\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.09560 | − | 3.16554i | 1.09560 | − | 3.16554i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.223734 | − | 0.175946i | −0.223734 | − | 0.175946i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.823056 | + | 0.158631i | −0.823056 | + | 0.158631i | ||||
\(687\) | 1.29645 | + | 0.123796i | 1.29645 | + | 0.123796i | ||||
\(688\) | −0.672932 | − | 0.945001i | −0.672932 | − | 0.945001i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.44091 | − | 1.37391i | −1.44091 | − | 1.37391i | ||||
\(691\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.544078 | − | 1.19136i | −0.544078 | − | 1.19136i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.67162 | + | 2.34747i | −1.67162 | + | 2.34747i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.07701 | − | 0.431171i | −1.07701 | − | 0.431171i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.235759 | − | 0.408346i | 0.235759 | − | 0.408346i | ||||
\(701\) | 0.786053 | − | 0.618159i | 0.786053 | − | 0.618159i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.871520 | − | 3.59245i | −0.871520 | − | 3.59245i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.396666 | − | 0.687046i | 0.396666 | − | 0.687046i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.928368 | − | 0.371662i | −0.928368 | − | 0.371662i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.239446 | − | 1.66538i | 0.239446 | − | 1.66538i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(720\) | −2.95044 | − | 0.281733i | −2.95044 | − | 0.281733i | ||||
\(721\) | 0.0440606 | − | 0.00849198i | 0.0440606 | − | 0.00849198i | ||||
\(722\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(723\) | 0.0787070 | − | 0.172344i | 0.0787070 | − | 0.172344i | ||||
\(724\) | −0.653077 | − | 0.513585i | −0.653077 | − | 0.513585i | ||||
\(725\) | 1.34378 | − | 0.537970i | 1.34378 | − | 0.537970i | ||||
\(726\) | 0.651174 | − | 1.88144i | 0.651174 | − | 1.88144i | ||||
\(727\) | 1.13779 | − | 1.08488i | 1.13779 | − | 1.08488i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.925488 | − | 6.43691i | −0.925488 | − | 6.43691i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.70760 | + | 1.97068i | 1.70760 | + | 1.97068i | ||||
\(733\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(734\) | −0.0913090 | + | 0.0268107i | −0.0913090 | + | 0.0268107i | ||||
\(735\) | −0.0736710 | − | 1.54655i | −0.0736710 | − | 1.54655i | ||||
\(736\) | −1.00000 | −1.00000 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 4.65950 | 4.65950 | ||||||||
\(739\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.271738 | + | 0.785135i | 0.271738 | + | 0.785135i | 0.995472 | + | 0.0950560i | \(0.0303030\pi\) |
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.223734 | + | 1.55610i | 0.223734 | + | 1.55610i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.81318 | − | 3.63586i | 3.81318 | − | 3.63586i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.124594 | + | 0.0498801i | −0.124594 | + | 0.0498801i | ||||
\(750\) | 1.56499 | + | 1.23072i | 1.56499 | + | 1.23072i | ||||
\(751\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(752\) | −1.56199 | − | 1.00383i | −1.56199 | − | 1.00383i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.63866 | − | 0.844787i | 1.63866 | − | 0.844787i | ||||
\(757\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.345139 | + | 0.755750i | 0.345139 | + | 0.755750i | 1.00000 | \(0\) | ||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(762\) | 0.185343 | − | 1.28909i | 0.185343 | − | 1.28909i | ||||
\(763\) | −0.0260280 | + | 0.0365512i | −0.0260280 | + | 0.0365512i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.56499 | + | 1.23072i | −1.56499 | + | 1.23072i | ||||
\(769\) | −0.469383 | − | 1.93482i | −0.469383 | − | 1.93482i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(774\) | −1.71921 | + | 2.97775i | −1.71921 | + | 2.97775i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.0552004 | + | 0.0775182i | −0.0552004 | + | 0.0775182i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.55722 | + | 1.07107i | 5.55722 | + | 1.07107i | ||||
\(784\) | −0.562827 | − | 0.536654i | −0.562827 | − | 0.536654i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.651174 | − | 0.0621796i | −0.651174 | − | 0.0621796i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.28924 | − | 2.11387i | −3.28924 | − | 2.11387i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.995472 | − | 0.0950560i | 0.995472 | − | 0.0950560i | ||||
\(801\) | −4.78471 | + | 1.40492i | −4.78471 | + | 1.40492i | ||||
\(802\) | −0.0224357 | − | 0.470984i | −0.0224357 | − | 0.470984i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.67489 | − | 1.07639i | −1.67489 | − | 1.07639i | ||||
\(805\) | −0.471518 | −0.471518 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.58713 | + | 0.466024i | −1.58713 | + | 0.466024i | ||||
\(808\) | 1.67489 | − | 0.159932i | 1.67489 | − | 0.159932i | ||||
\(809\) | 0.428368 | + | 0.494363i | 0.428368 | + | 0.494363i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 1.57666 | + | 4.55546i | 1.57666 | + | 4.55546i | ||||
\(811\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(812\) | 0.0971309 | + | 0.675560i | 0.0971309 | + | 0.675560i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.271738 | − | 0.785135i | 0.271738 | − | 0.785135i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.345139 | + | 0.755750i | −0.345139 | + | 0.755750i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.54370 | + | 0.297523i | −1.54370 | + | 0.297523i | ||||
\(821\) | 1.30379 | + | 0.124497i | 1.30379 | + | 0.124497i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.28656 | − | 0.663268i | 1.28656 | − | 0.663268i | 0.327068 | − | 0.945001i | \(-0.393939\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(824\) | 0.0688733 | + | 0.0656706i | 0.0688733 | + | 0.0656706i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.370638 | − | 1.52779i | 0.370638 | − | 1.52779i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.786053 | − | 0.618159i | \(-0.212121\pi\) | |||||||
\(828\) | 1.23123 | + | 2.69602i | 1.23123 | + | 2.69602i | ||||
\(829\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(830\) | −1.03115 | + | 1.44805i | −1.03115 | + | 1.44805i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.50842 | + | 1.18624i | −1.50842 | + | 1.18624i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(840\) | −0.737920 | + | 0.580306i | −0.737920 | + | 0.580306i | ||||
\(841\) | −0.547582 | + | 0.948440i | −0.547582 | + | 0.948440i | ||||
\(842\) | −0.959493 | − | 1.66189i | −0.959493 | − | 1.66189i | ||||
\(843\) | 3.43186 | + | 1.37391i | 3.43186 | + | 1.37391i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.580057 | − | 0.814576i | 0.580057 | − | 0.814576i | ||||
\(846\) | −0.783173 | + | 5.44709i | −0.783173 | + | 5.44709i | ||||
\(847\) | −0.195876 | − | 0.428908i | −0.195876 | − | 0.428908i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.75155 | + | 1.10155i | 3.75155 | + | 1.10155i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(854\) | 0.614761 | + | 0.0587025i | 0.614761 | + | 0.0587025i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(857\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(860\) | 0.379436 | − | 1.09631i | 0.379436 | − | 1.09631i | ||||
\(861\) | 1.06812 | − | 1.01845i | 1.06812 | − | 1.01845i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.279486 | + | 1.94387i | 0.279486 | + | 1.94387i | 0.327068 | + | 0.945001i | \(0.393939\pi\) |
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(864\) | 3.47528 | + | 1.79163i | 3.47528 | + | 1.79163i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.98193 | + | 0.189251i | −1.98193 | + | 0.189251i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.88183 | −2.88183 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.0951638 | −0.0951638 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.469383 | − | 0.0448206i | 0.469383 | − | 0.0448206i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.723734 | + | 0.690079i | −0.723734 | + | 0.690079i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(882\) | −0.753861 | + | 2.17814i | −0.753861 | + | 2.17814i | ||||
\(883\) | 0.264241 | − | 0.105786i | 0.264241 | − | 0.105786i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.21769 | + | 0.782560i | 1.21769 | + | 0.782560i | ||||
\(887\) | −1.42131 | + | 0.273935i | −1.42131 | + | 0.273935i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.178911 | − | 0.251245i | −0.178911 | − | 0.251245i | ||||
\(890\) | 1.49547 | − | 0.770969i | 1.49547 | − | 0.770969i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.28605 | + | 0.247866i | 1.28605 | + | 0.247866i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0.737920 | − | 3.04175i | 0.737920 | − | 3.04175i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.0671040 | + | 0.466718i | −0.0671040 | + | 0.466718i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.21590 | − | 1.40323i | 1.21590 | − | 1.40323i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.48193 | − | 2.56678i | −1.48193 | − | 2.56678i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.256759 | + | 1.05838i | 0.256759 | + | 1.05838i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.0395325 | − | 0.829889i | 0.0395325 | − | 0.829889i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.02951 | + | 0.809616i | −1.02951 | + | 0.809616i | −0.981929 | − | 0.189251i | \(-0.939394\pi\) |
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(908\) | 0.841254 | − | 1.45709i | 0.841254 | − | 1.45709i | ||||
\(909\) | −2.49336 | − | 4.31862i | −2.49336 | − | 4.31862i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.614761 | + | 2.53408i | −0.614761 | + | 2.53408i | ||||
\(916\) | 0.627639 | + | 0.184291i | 0.627639 | + | 0.184291i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(920\) | −0.580057 | − | 0.814576i | −0.580057 | − | 0.814576i | ||||
\(921\) | −0.564116 | − | 0.0538665i | −0.564116 | − | 0.0538665i | ||||
\(922\) | 1.74555 | − | 0.336426i | 1.74555 | − | 0.336426i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.771316 | − | 0.308788i | 0.771316 | − | 0.308788i | ||||
\(927\) | 0.0922502 | − | 0.266539i | 0.0922502 | − | 0.266539i | ||||
\(928\) | −1.04758 | + | 0.998867i | −1.04758 | + | 0.998867i | ||||
\(929\) | −1.49547 | + | 0.961081i | −1.49547 | + | 0.961081i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.651174 | − | 0.0621796i | 0.651174 | − | 0.0621796i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | −0.462997 | + | 0.0892353i | −0.462997 | + | 0.0892353i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.0883470 | − | 1.85463i | −0.0883470 | − | 1.85463i | ||||
\(941\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.02951 | + | 1.18812i | 1.02951 | + | 1.18812i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.63866 | + | 0.844787i | 1.63866 | + | 0.844787i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.975950 | + | 0.627205i | −0.975950 | + | 0.627205i | −0.928368 | − | 0.371662i | \(-0.878788\pi\) |
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.91030 | − | 0.560914i | −1.91030 | − | 0.560914i | ||||
\(961\) | 0.235759 | − | 0.971812i | 0.235759 | − | 0.971812i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.120057 | + | 0.835015i | −0.120057 | + | 0.835015i | ||||
\(964\) | 0.0552004 | − | 0.0775182i | 0.0552004 | − | 0.0775182i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.871520 | + | 0.348904i | 0.871520 | + | 0.348904i | ||||
\(967\) | −0.142315 | − | 0.246497i | −0.142315 | − | 0.246497i | 0.786053 | − | 0.618159i | \(-0.212121\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(968\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(972\) | 0.270627 | − | 5.68116i | 0.270627 | − | 5.68116i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.39734 | − | 1.09888i | 1.39734 | − | 1.09888i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.654861 | + | 1.13425i | 0.654861 | + | 1.13425i | ||||
\(977\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(978\) | −1.08323 | + | 1.25011i | −1.08323 | + | 1.25011i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.110674 | − | 0.769755i | 0.110674 | − | 0.769755i | ||||
\(981\) | 0.117169 | + | 0.256564i | 0.117169 | + | 0.256564i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.84125 | − | 0.540641i | −1.84125 | − | 0.540641i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(984\) | 3.07341 | + | 0.592352i | 3.07341 | + | 0.592352i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.01106 | + | 1.41984i | 1.01106 | + | 1.41984i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.13915 | + | 0.219553i | −1.13915 | + | 0.219553i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.97740 | − | 1.91346i | 2.97740 | − | 1.91346i | ||||
\(997\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(998\) | 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 | 1340.1.bl.a.1239.1 | yes | 20 | |
4.3 | odd | 2 | 1340.1.bl.b.1239.1 | yes | 20 | ||
5.4 | even | 2 | 1340.1.bl.b.1239.1 | yes | 20 | ||
20.19 | odd | 2 | CM | 1340.1.bl.a.1239.1 | yes | 20 | |
67.65 | even | 33 | inner | 1340.1.bl.a.199.1 | ✓ | 20 | |
268.199 | odd | 66 | 1340.1.bl.b.199.1 | yes | 20 | ||
335.199 | even | 66 | 1340.1.bl.b.199.1 | yes | 20 | ||
1340.199 | odd | 66 | inner | 1340.1.bl.a.199.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1340.1.bl.a.199.1 | ✓ | 20 | 67.65 | even | 33 | inner | |
1340.1.bl.a.199.1 | ✓ | 20 | 1340.199 | odd | 66 | inner | |
1340.1.bl.a.1239.1 | yes | 20 | 1.1 | even | 1 | trivial | |
1340.1.bl.a.1239.1 | yes | 20 | 20.19 | odd | 2 | CM | |
1340.1.bl.b.199.1 | yes | 20 | 268.199 | odd | 66 | ||
1340.1.bl.b.199.1 | yes | 20 | 335.199 | even | 66 | ||
1340.1.bl.b.1239.1 | yes | 20 | 4.3 | odd | 2 | ||
1340.1.bl.b.1239.1 | yes | 20 | 5.4 | even | 2 |