Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2144,1,Mod(47,2144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2144, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([33, 33, 50]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2144.47");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2144 = 2^{5} \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2144.bu (of order \(66\), degree \(20\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.06999538709\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 536) |
Projective image: | \(D_{33}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{33} - \cdots)\) |
Embedding invariants
Embedding label | 1711.1 | ||
Root | \(-0.786053 + 0.618159i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2144.1711 |
Dual form | 2144.1.bu.a.1327.1 |
$q$-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 \(\left(\mathbb{Z}/2144\mathbb{Z}\right)^\times\).
\(n\) | \(671\) | \(805\) | \(1409\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{7}{33}\right)\) |
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 | 0 | ||||||||
\(3\) | −1.30379 | − | 1.50465i | −1.30379 | − | 1.50465i | −0.723734 | − | 0.690079i | \(-0.757576\pi\) |
−0.580057 | − | 0.814576i | \(-0.696970\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.421801 | + | 2.93369i | −0.421801 | + | 2.93369i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0395325 | + | 0.829889i | −0.0395325 | + | 0.829889i | 0.888835 | + | 0.458227i | \(0.151515\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.341254 | − | 1.40667i | 0.341254 | − | 1.40667i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.65033 | + | 0.660694i | 1.65033 | + | 0.660694i | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.28924 | − | 2.11387i | 3.28924 | − | 2.11387i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.30024 | − | 1.02252i | 1.30024 | − | 1.02252i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.205996 | − | 0.196417i | −0.205996 | − | 0.196417i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0913090 | − | 0.0268107i | 0.0913090 | − | 0.0268107i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.723734 | − | 0.690079i | 0.723734 | − | 0.690079i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.56147 | + | 1.32053i | −2.56147 | + | 1.32053i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.15757 | − | 3.34459i | −1.15757 | − | 3.34459i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.481929 | + | 1.05528i | −0.481929 | + | 1.05528i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0224357 | + | 0.470984i | 0.0224357 | + | 0.470984i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.827068 | − | 1.81103i | 0.827068 | − | 1.81103i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.62533 | − | 1.35812i | −4.62533 | − | 1.35812i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.49547 | − | 0.770969i | 1.49547 | − | 0.770969i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.02951 | − | 1.18812i | 1.02951 | − | 1.18812i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.235759 | + | 0.408346i | −0.235759 | + | 0.408346i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.41796 | − | 0.466024i | −2.41796 | − | 0.466024i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.10181 | − | 0.708089i | 1.10181 | − | 0.708089i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.03115 | − | 0.531595i | −1.03115 | − | 0.531595i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.308319 | + | 0.0294409i | 0.308319 | + | 0.0294409i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0269638 | + | 0.566040i | −0.0269638 | + | 0.566040i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.159389 | − | 0.102433i | −0.159389 | − | 0.102433i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.186393 | − | 0.215109i | −0.186393 | − | 0.215109i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.428368 | + | 0.494363i | 0.428368 | + | 0.494363i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | 0.888835 | − | 0.458227i | \(-0.151515\pi\) |
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.98193 | − | 0.189251i | −1.98193 | − | 0.189251i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.98278 | + | 1.59446i | 3.98278 | + | 1.59446i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.928368 | + | 1.60798i | 0.928368 | + | 1.60798i | 0.786053 | + | 0.618159i | \(0.212121\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.981929 | + | 0.189251i | 0.981929 | + | 0.189251i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.63438 | + | 4.56288i | −2.63438 | + | 4.56288i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.21616 | − | 0.650724i | 2.21616 | − | 0.650724i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.10181 | − | 1.27155i | 1.10181 | − | 1.27155i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.15389 | + | 0.338812i | 1.15389 | + | 0.338812i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.283341 | + | 1.97068i | 0.283341 | + | 1.97068i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.613544 | + | 1.34347i | −0.613544 | + | 1.34347i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.514186 | − | 1.48564i | −0.514186 | − | 1.48564i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.327068 | − | 0.945001i | \(-0.393939\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.679417 | − | 0.647822i | 0.679417 | − | 0.647822i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.84380 | + | 0.835015i | −2.84380 | + | 0.835015i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.34378 | − | 1.28129i | −1.34378 | − | 1.28129i | −0.928368 | − | 0.371662i | \(-0.878788\pi\) |
−0.415415 | − | 0.909632i | \(-0.636364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.981929 | − | 0.189251i | −0.981929 | − | 0.189251i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.41542 | − | 0.909632i | 1.41542 | − | 0.909632i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
1.00000 | \(0\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.36271 | + | 5.17362i | 2.36271 | + | 5.17362i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.10983 | − | 1.24499i | −3.10983 | − | 1.24499i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.437742 | + | 1.80440i | −0.437742 | + | 1.80440i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.0913090 | + | 1.91681i | −0.0913090 | + | 1.91681i | 0.235759 | + | 0.971812i | \(0.424242\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.12998 | −3.12998 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.771316 | + | 0.308788i | −0.771316 | + | 0.308788i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.44091 | − | 0.137591i | −1.44091 | − | 0.137591i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | −0.928368 | − | 0.371662i | \(-0.878788\pi\) |
0.786053 | − | 0.618159i | \(-0.212121\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.973420 | − | 0.501833i | −0.973420 | − | 0.501833i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.921801 | − | 0.177663i | 0.921801 | − | 0.177663i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.62424 | + | 2.81327i | 1.62424 | + | 2.81327i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.0552004 | − | 0.0775182i | −0.0552004 | − | 0.0775182i | 0.786053 | − | 0.618159i | \(-0.212121\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.16413 | − | 1.34347i | 1.16413 | − | 1.34347i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
0.928368 | − | 0.371662i | \(-0.121212\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.50196 | − | 0.734641i | −2.50196 | − | 0.734641i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.49256 | − | 2.09600i | 1.49256 | − | 2.09600i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.419102 | + | 1.72756i | 0.419102 | + | 1.72756i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.50842 | + | 1.18624i | 1.50842 | + | 1.18624i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.544537 | + | 2.24461i | 0.544537 | + | 2.24461i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.580057 | − | 0.814576i | 0.580057 | − | 0.814576i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.947890 | + | 0.903811i | −0.947890 | + | 0.903811i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.56335 | + | 1.49065i | 1.56335 | + | 1.49065i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.357685 | − | 0.502299i | −0.357685 | − | 0.502299i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.663116 | − | 0.521480i | 0.663116 | − | 0.521480i | ||||
\(370\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.279486 | − | 0.0538665i | 0.279486 | − | 0.0538665i | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) |
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0401402 | + | 0.279181i | 0.0401402 | + | 0.279181i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.0806472 | + | 0.560914i | −0.0806472 | + | 0.560914i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.21590 | + | 0.486774i | −1.21590 | + | 0.486774i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.185343 | − | 1.28909i | 0.185343 | − | 1.28909i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.283341 | − | 1.97068i | −0.283341 | − | 1.97068i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.111165 | + | 0.458227i | −0.111165 | + | 0.458227i | 0.888835 | + | 0.458227i | \(0.151515\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.42131 | − | 0.273935i | 1.42131 | − | 0.273935i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.651174 | − | 0.0621796i | 0.651174 | − | 0.0621796i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 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 | ||||||||
\(441\) | 1.71921 | + | 2.41429i | 1.71921 | + | 2.41429i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.04758 | − | 0.998867i | −1.04758 | − | 0.998867i | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.271738 | + | 0.785135i | −0.271738 | + | 0.785135i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.171148 | − | 0.163189i | 0.171148 | − | 0.163189i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.911911 | + | 1.28060i | −0.911911 | + | 1.28060i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.85104 | − | 5.34823i | −1.85104 | − | 5.34823i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.653077 | + | 0.513585i | 0.653077 | + | 0.513585i | 0.888835 | − | 0.458227i | \(-0.151515\pi\) |
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.0186403 | + | 0.0768363i | 0.0186403 | + | 0.0768363i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0845850 | + | 1.77566i | 0.0845850 | + | 1.77566i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.20906 | − | 3.49334i | 1.20906 | − | 3.49334i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | −0.981929 | − | 0.189251i | \(-0.939394\pi\) |
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.981929 | − | 1.70075i | 0.981929 | − | 1.70075i | 0.327068 | − | 0.945001i | \(-0.393939\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.995472 | − | 1.72421i | −0.995472 | − | 1.72421i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.82496 | − | 1.31540i | 6.82496 | − | 1.31540i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.279486 | − | 1.94387i | −0.279486 | − | 1.94387i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.0475819 | − | 0.998867i | \(-0.484848\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.651174 | − | 0.0621796i | −0.651174 | − | 0.0621796i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.928368 | − | 0.371662i | 0.928368 | − | 0.371662i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.89258 | − | 1.85895i | −2.89258 | − | 1.85895i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.34978 | −3.34978 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.544078 | + | 0.627899i | 0.544078 | + | 0.627899i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.0800569 | + | 1.68060i | −0.0800569 | + | 1.68060i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.994632 | − | 2.17794i | −0.994632 | − | 2.17794i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.65210 | + | 1.06174i | −1.65210 | + | 1.06174i | −0.723734 | + | 0.690079i | \(0.757576\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.370638 | + | 0.291473i | −0.370638 | + | 0.291473i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.42131 | − | 0.273935i | −1.42131 | − | 0.273935i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.13779 | − | 1.08488i | −1.13779 | − | 1.08488i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.66583 | − | 1.07639i | 3.66583 | − | 1.07639i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.419102 | − | 0.216062i | 0.419102 | − | 0.216062i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.154218 | − | 0.445585i | −0.154218 | − | 0.445585i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.45949 | − | 1.14776i | −1.45949 | − | 1.14776i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.94091 | − | 2.23993i | 1.94091 | − | 2.23993i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.581419 | + | 0.299742i | −0.581419 | + | 0.299742i | −0.723734 | − | 0.690079i | \(-0.757576\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.82140 | − | 0.828437i | 2.82140 | − | 0.828437i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.56499 | + | 2.71064i | −1.56499 | + | 2.71064i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.975950 | + | 0.627205i | −0.975950 | + | 0.627205i | −0.928368 | − | 0.371662i | \(-0.878788\pi\) |
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.856711 | − | 0.441665i | −0.856711 | − | 0.441665i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.39118 | − | 0.132842i | −1.39118 | − | 0.132842i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.0475819 | − | 0.998867i | 0.0475819 | − | 0.998867i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.888835 | − | 0.458227i | \(-0.151515\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.28605 | − | 1.48418i | −1.28605 | − | 1.48418i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.28924 | + | 2.11387i | 3.28924 | + | 2.11387i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.175894 | + | 3.69247i | −0.175894 | + | 3.69247i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.651174 | − | 0.0621796i | −0.651174 | − | 0.0621796i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.16413 | − | 0.600149i | −1.16413 | − | 0.600149i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.346590 | + | 0.222740i | −0.346590 | + | 0.222740i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.995472 | + | 1.72421i | 0.995472 | + | 1.72421i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.21409 | − | 0.943741i | −3.21409 | − | 0.943741i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.70149 | − | 5.91543i | 2.70149 | − | 5.91543i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.00655425 | − | 0.137591i | −0.00655425 | − | 0.137591i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.481929 | − | 0.676774i | 0.481929 | − | 0.676774i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.911911 | + | 0.717135i | 0.911911 | + | 0.717135i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.63099 | + | 4.71245i | 1.63099 | + | 4.71245i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.28572 | − | 1.69391i | 3.28572 | − | 1.69391i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.82318 | + | 0.351390i | 1.82318 | + | 0.351390i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00319 | − | 2.36173i | 3.00319 | − | 2.36173i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.210191 | − | 0.460254i | −0.210191 | − | 0.460254i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.308779 | − | 1.27280i | 0.308779 | − | 1.27280i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
0.888835 | − | 0.458227i | \(-0.151515\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.05132 | + | 3.52141i | 3.05132 | + | 3.52141i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.391751 | −0.391751 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | 1.00000 | \(0\) | ||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.56199 | + | 0.625325i | −1.56199 | + | 0.625325i | −0.981929 | − | 0.189251i | \(-0.939394\pi\) |
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.168404 | + | 0.0160806i | 0.168404 | + | 0.0160806i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.47025 | + | 0.757969i | 1.47025 | + | 0.757969i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.815816 | + | 0.157236i | −0.815816 | + | 0.157236i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.67162 | + | 2.34747i | 1.67162 | + | 2.34747i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.30379 | + | 1.50465i | −1.30379 | + | 1.50465i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.84125 | + | 0.540641i | 1.84125 | + | 0.540641i | 1.00000 | \(0\) | ||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.839614 | + | 1.17907i | −0.839614 | + | 1.17907i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.514051 | + | 2.11895i | 0.514051 | + | 2.11895i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.09852 | − | 0.863884i | −1.09852 | − | 0.863884i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.271738 | − | 0.785135i | −0.271738 | − | 0.785135i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.165101 | − | 0.231852i | 0.165101 | − | 0.231852i | −0.723734 | − | 0.690079i | \(-0.757576\pi\) |
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.30994 | − | 3.78482i | 1.30994 | − | 3.78482i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.91030 | + | 0.182411i | −1.91030 | + | 0.182411i | −0.981929 | − | 0.189251i | \(-0.939394\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.580699 | + | 1.27155i | 0.580699 | + | 1.27155i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.0446683 | + | 0.184125i | −0.0446683 | + | 0.184125i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.279486 | + | 1.94387i | −0.279486 | + | 1.94387i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.65033 | − | 0.660694i | 1.65033 | − | 0.660694i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.53924 | −3.53924 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.223734 | + | 1.55610i | −0.223734 | + | 1.55610i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.0135432 | − | 0.0941952i | −0.0135432 | − | 0.0941952i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.981929 | − | 0.189251i | 0.981929 | − | 0.189251i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.61257 | + | 3.53103i | 1.61257 | + | 3.53103i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.09974 | + | 0.486967i | −5.09974 | + | 0.486967i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.0748038 | − | 0.0588264i | 0.0748038 | − | 0.0588264i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.975950 | + | 1.37053i | 0.975950 | + | 1.37053i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.945307 | + | 0.901349i | 0.945307 | + | 0.901349i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.05296 | − | 2.88298i | 2.05296 | − | 2.88298i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(998\) | 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 | 2144.1.bu.a.1711.1 | 20 | ||
4.3 | odd | 2 | 536.1.ba.a.371.1 | ✓ | 20 | ||
8.3 | odd | 2 | CM | 2144.1.bu.a.1711.1 | 20 | ||
8.5 | even | 2 | 536.1.ba.a.371.1 | ✓ | 20 | ||
67.54 | even | 33 | inner | 2144.1.bu.a.1327.1 | 20 | ||
268.255 | odd | 66 | 536.1.ba.a.523.1 | yes | 20 | ||
536.389 | even | 66 | 536.1.ba.a.523.1 | yes | 20 | ||
536.523 | odd | 66 | inner | 2144.1.bu.a.1327.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
536.1.ba.a.371.1 | ✓ | 20 | 4.3 | odd | 2 | ||
536.1.ba.a.371.1 | ✓ | 20 | 8.5 | even | 2 | ||
536.1.ba.a.523.1 | yes | 20 | 268.255 | odd | 66 | ||
536.1.ba.a.523.1 | yes | 20 | 536.389 | even | 66 | ||
2144.1.bu.a.1327.1 | 20 | 67.54 | even | 33 | inner | ||
2144.1.bu.a.1327.1 | 20 | 536.523 | odd | 66 | inner | ||
2144.1.bu.a.1711.1 | 20 | 1.1 | even | 1 | trivial | ||
2144.1.bu.a.1711.1 | 20 | 8.3 | odd | 2 | CM |