Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1169,1,Mod(333,1169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1169.333");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1169 = 7 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1169.f (of order \(6\), degree \(2\), 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: | \(0.583406999768\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
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 | 333.2 | ||
Root | \(0.580057 - 0.814576i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1169.333 |
Dual form | 1169.1.f.c.667.2 |
$q$-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 \(\left(\mathbb{Z}/1169\mathbb{Z}\right)^\times\).
\(n\) | \(673\) | \(836\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.841254 | − | 1.45709i | −0.841254 | − | 1.45709i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.0475819 | − | 0.998867i | \(-0.484848\pi\) | |||||||
\(3\) | 0.327068 | − | 0.566498i | 0.327068 | − | 0.566498i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(4\) | −0.915415 | + | 1.58555i | −0.915415 | + | 1.58555i | ||||
\(5\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | −1.10059 | −1.10059 | ||||||||
\(7\) | 0.235759 | + | 0.971812i | 0.235759 | + | 0.971812i | ||||
\(8\) | 1.39788 | 1.39788 | ||||||||
\(9\) | 0.286053 | + | 0.495458i | 0.286053 | + | 0.495458i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.580057 | + | 1.00469i | −0.580057 | + | 1.00469i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(12\) | 0.598806 | + | 1.03716i | 0.598806 | + | 1.03716i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 1.21769 | − | 1.16106i | 1.21769 | − | 1.16106i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.260554 | − | 0.451293i | −0.260554 | − | 0.451293i | ||||
\(17\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 0.481286 | − | 0.833612i | 0.481286 | − | 0.833612i | ||||
\(19\) | 0.142315 | + | 0.246497i | 0.142315 | + | 0.246497i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.627639 | + | 0.184291i | 0.627639 | + | 0.184291i | ||||
\(22\) | 1.95190 | 1.95190 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0.457201 | − | 0.791895i | 0.457201 | − | 0.791895i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.02837 | 1.02837 | ||||||||
\(28\) | −1.75667 | − | 0.515804i | −1.75667 | − | 0.515804i | ||||
\(29\) | 1.44747 | 1.44747 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0475819 | + | 0.0824143i | −0.0475819 | + | 0.0824143i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(32\) | 0.260554 | − | 0.451293i | 0.260554 | − | 0.451293i | ||||
\(33\) | 0.379436 | + | 0.657203i | 0.379436 | + | 0.657203i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.04743 | −1.04743 | ||||||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | 0.239446 | − | 0.414732i | 0.239446 | − | 0.414732i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | −0.259474 | − | 1.06956i | −0.259474 | − | 1.06956i | ||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | −1.06199 | − | 1.83941i | −1.06199 | − | 1.83941i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(48\) | −0.340876 | −0.340876 | ||||||||
\(49\) | −0.888835 | + | 0.458227i | −0.888835 | + | 0.458227i | ||||
\(50\) | 1.68251 | 1.68251 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | −0.865121 | − | 1.49843i | −0.865121 | − | 1.49843i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.329562 | + | 1.35847i | 0.329562 | + | 1.35847i | ||||
\(57\) | 0.186186 | 0.186186 | ||||||||
\(58\) | −1.21769 | − | 2.10910i | −1.21769 | − | 2.10910i | ||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.654861 | + | 1.13425i | 0.654861 | + | 1.13425i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(62\) | 0.160114 | 0.160114 | ||||||||
\(63\) | −0.414053 | + | 0.394798i | −0.414053 | + | 0.394798i | ||||
\(64\) | −1.39788 | −1.39788 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.638404 | − | 1.10575i | 0.638404 | − | 1.10575i | ||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0.399867 | + | 0.692590i | 0.399867 | + | 0.692590i | ||||
\(73\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.327068 | + | 0.566498i | 0.327068 | + | 0.566498i | ||||
\(76\) | −0.521109 | −0.521109 | ||||||||
\(77\) | −1.11312 | − | 0.326842i | −1.11312 | − | 0.326842i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.0502942 | − | 0.0871120i | 0.0502942 | − | 0.0871120i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | −0.866752 | + | 0.826447i | −0.866752 | + | 0.826447i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.473420 | − | 0.819988i | 0.473420 | − | 0.819988i | ||||
\(88\) | −0.810848 | + | 1.40443i | −0.810848 | + | 1.40443i | ||||
\(89\) | −0.981929 | − | 1.70075i | −0.981929 | − | 1.70075i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.327068 | − | 0.945001i | \(-0.606061\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.0311250 | + | 0.0539102i | 0.0311250 | + | 0.0539102i | ||||
\(94\) | −1.56199 | + | 2.70544i | −1.56199 | + | 2.70544i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.170438 | − | 0.295207i | −0.170438 | − | 0.295207i | ||||
\(97\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(98\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(99\) | −0.663708 | −0.663708 | ||||||||
\(100\) | −0.915415 | − | 1.58555i | −0.915415 | − | 1.58555i | ||||
\(101\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.235759 | − | 0.408346i | −0.235759 | − | 0.408346i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(108\) | −0.941386 | + | 1.63053i | −0.941386 | + | 1.63053i | ||||
\(109\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.377144 | − | 0.359606i | 0.377144 | − | 0.359606i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | −0.156630 | − | 0.271291i | −0.156630 | − | 0.271291i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.32503 | + | 2.29503i | −1.32503 | + | 2.29503i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.172932 | − | 0.299527i | −0.172932 | − | 0.299527i | ||||
\(122\) | 1.10181 | − | 1.90839i | 1.10181 | − | 1.90839i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.0871144 | − | 0.150887i | −0.0871144 | − | 0.150887i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.923582 | + | 0.271188i | 0.923582 | + | 0.271188i | ||||
\(127\) | −1.99094 | −1.99094 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(128\) | 0.915415 | + | 1.58555i | 0.915415 | + | 1.58555i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(132\) | −1.38937 | −1.38937 | ||||||||
\(133\) | −0.205996 | + | 0.196417i | −0.205996 | + | 0.196417i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.995472 | − | 1.72421i | 0.995472 | − | 1.72421i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.580057 | − | 0.814576i | \(-0.303030\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.21456 | −1.21456 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.149065 | − | 0.258188i | 0.149065 | − | 0.258188i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0311250 | + | 0.653395i | −0.0311250 | + | 0.653395i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0.550294 | − | 0.953137i | 0.550294 | − | 0.953137i | ||||
\(151\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(152\) | 0.198939 | + | 0.344572i | 0.198939 | + | 0.344572i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.460178 | + | 1.89688i | 0.460178 | + | 1.89688i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.888835 | − | 1.53951i | 0.888835 | − | 1.53951i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.169241 | −0.169241 | ||||||||
\(163\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 1.00000 | ||||||||
\(168\) | 0.877362 | + | 0.257617i | 0.877362 | + | 0.257617i | ||||
\(169\) | 1.00000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0814192 | + | 0.141022i | −0.0814192 | + | 0.141022i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.995472 | + | 1.72421i | 0.995472 | + | 1.72421i | 0.580057 | + | 0.814576i | \(0.303030\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(174\) | −1.59307 | −1.59307 | ||||||||
\(175\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(176\) | 0.604545 | 0.604545 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.65210 | + | 2.86152i | −1.65210 | + | 2.86152i | ||||
\(179\) | −0.928368 | + | 1.60798i | −0.928368 | + | 1.60798i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.85674 | 1.85674 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.856736 | 0.856736 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.0523681 | − | 0.0907042i | 0.0523681 | − | 0.0907042i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.39937 | 3.39937 | ||||||||
\(189\) | 0.242448 | + | 0.999383i | 0.242448 | + | 0.999383i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.888835 | + | 1.53951i | 0.888835 | + | 1.53951i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(192\) | −0.457201 | + | 0.791895i | −0.457201 | + | 0.791895i | ||||
\(193\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | −0.698939 | − | 1.21060i | −0.698939 | − | 1.21060i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.0871144 | − | 1.82876i | 0.0871144 | − | 1.82876i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0.558347 | + | 0.967085i | 0.558347 | + | 0.967085i | ||||
\(199\) | 0.995472 | − | 1.72421i | 0.995472 | − | 1.72421i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.580057 | − | 0.814576i | \(-0.303030\pi\) | |||||||
\(200\) | −0.698939 | + | 1.21060i | −0.698939 | + | 1.21060i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.341254 | + | 1.40667i | 0.341254 | + | 1.40667i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.330203 | −0.330203 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.77767 | −1.77767 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.396666 | + | 0.687046i | −0.396666 | + | 0.687046i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.43754 | 1.43754 | ||||||||
\(217\) | −0.0913090 | − | 0.0268107i | −0.0913090 | − | 0.0268107i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.96386 | 1.96386 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(224\) | 0.500000 | + | 0.146813i | 0.500000 | + | 0.146813i | ||||
\(225\) | −0.572106 | −0.572106 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | −0.170438 | + | 0.295207i | −0.170438 | + | 0.295207i | ||||
\(229\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.549222 | + | 0.523682i | −0.549222 | + | 0.523682i | ||||
\(232\) | 2.02338 | 2.02338 | ||||||||
\(233\) | −0.0475819 | − | 0.0824143i | −0.0475819 | − | 0.0824143i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.654136 | −0.654136 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(242\) | −0.290959 | + | 0.503956i | −0.290959 | + | 0.503956i | ||||
\(243\) | 0.481286 | + | 0.833612i | 0.481286 | + | 0.833612i | ||||
\(244\) | −2.39788 | −2.39788 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.0665137 | + | 0.115205i | −0.0665137 | + | 0.115205i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(252\) | −0.246941 | − | 1.01790i | −0.246941 | − | 1.01790i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.67489 | + | 2.90099i | 1.67489 | + | 2.90099i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.841254 | − | 1.45709i | 0.841254 | − | 1.45709i | ||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.414053 | + | 0.717160i | 0.414053 | + | 0.717160i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.654861 | − | 1.13425i | 0.654861 | − | 1.13425i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(264\) | 0.530405 | + | 0.918689i | 0.530405 | + | 0.918689i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.459493 | + | 0.134919i | 0.459493 | + | 0.134919i | ||||
\(267\) | −1.28463 | −1.28463 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.34978 | −3.34978 | ||||||||
\(275\) | −0.580057 | − | 1.00469i | −0.580057 | − | 1.00469i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.0544438 | −0.0544438 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(282\) | 1.02175 | + | 1.76972i | 1.02175 | + | 1.76972i | ||||
\(283\) | −0.580057 | + | 1.00469i | −0.580057 | + | 1.00469i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.298129 | 0.298129 | ||||||||
\(289\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.271738 | − | 0.470664i | 0.271738 | − | 0.470664i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.0951638 | 0.0951638 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(294\) | 0.978242 | − | 0.504319i | 0.978242 | − | 0.504319i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.596514 | + | 1.03319i | −0.596514 | + | 1.03319i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.19761 | −1.19761 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.0741615 | − | 0.128451i | 0.0741615 | − | 0.128451i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 1.53719 | − | 1.46571i | 1.53719 | − | 1.46571i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(314\) | −2.99094 | −2.99094 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.327068 | + | 0.566498i | 0.327068 | + | 0.566498i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.839614 | + | 1.45425i | −0.839614 | + | 1.45425i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.308437 | −0.308437 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.0920801 | + | 0.159487i | 0.0920801 | + | 0.159487i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.34378 | − | 1.28129i | 1.34378 | − | 1.28129i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.841254 | − | 1.45709i | −0.841254 | − | 1.45709i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.0803645 | − | 0.331267i | −0.0803645 | − | 0.331267i | ||||
\(337\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(338\) | −0.841254 | − | 1.45709i | −0.841254 | − | 1.45709i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.0552004 | − | 0.0956100i | −0.0552004 | − | 0.0956100i | ||||
\(342\) | 0.273977 | 0.273977 | ||||||||
\(343\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.67489 | − | 2.90099i | 1.67489 | − | 2.90099i | ||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0.866752 | + | 1.50126i | 0.866752 | + | 1.50126i | ||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0.396666 | + | 1.63508i | 0.396666 | + | 1.63508i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.302273 | + | 0.523552i | 0.302273 | + | 0.523552i | ||||
\(353\) | −0.235759 | + | 0.408346i | −0.235759 | + | 0.408346i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.59549 | 3.59549 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.12397 | 3.12397 | ||||||||
\(359\) | −0.0475819 | − | 0.0824143i | −0.0475819 | − | 0.0824143i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.459493 | − | 0.795865i | 0.459493 | − | 0.795865i | ||||
\(362\) | −1.56199 | − | 2.70544i | −1.56199 | − | 2.70544i | ||||
\(363\) | −0.226242 | −0.226242 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.720732 | − | 1.24834i | −0.720732 | − | 1.24834i | ||||
\(367\) | 0.786053 | − | 1.36148i | 0.786053 | − | 1.36148i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.928368 | − | 0.371662i | \(-0.121212\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.113969 | −0.113969 | ||||||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.29774 | − | 2.24776i | −1.29774 | − | 2.24776i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.25223 | − | 1.19400i | 1.25223 | − | 1.19400i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.651174 | + | 1.12787i | −0.651174 | + | 1.12787i | ||||
\(382\) | 1.49547 | − | 2.59023i | 1.49547 | − | 2.59023i | ||||
\(383\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(384\) | 1.19761 | 1.19761 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.760554 | + | 1.31732i | −0.760554 | + | 1.31732i | ||||
\(389\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.24248 | + | 0.640544i | −1.24248 | + | 0.640544i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.607569 | − | 1.05234i | 0.607569 | − | 1.05234i | ||||
\(397\) | −0.981929 | − | 1.70075i | −0.981929 | − | 1.70075i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.327068 | − | 0.945001i | \(-0.606061\pi\) | |||||||
\(398\) | −3.34978 | −3.34978 | ||||||||
\(399\) | 0.0438951 | + | 0.180938i | 0.0438951 | + | 0.180938i | ||||
\(400\) | 0.521109 | 0.521109 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.76256 | − | 1.68060i | 1.76256 | − | 1.68060i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.995472 | − | 1.72421i | 0.995472 | − | 1.72421i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.580057 | − | 0.814576i | \(-0.303030\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.651174 | − | 1.12787i | −0.651174 | − | 1.12787i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.277784 | + | 0.481137i | 0.277784 | + | 0.481137i | ||||
\(419\) | −1.77767 | −1.77767 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.471518 | 0.471518 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(422\) | 1.49547 | + | 2.59023i | 1.49547 | + | 2.59023i | ||||
\(423\) | 0.531125 | − | 0.919936i | 0.531125 | − | 0.919936i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.947890 | + | 0.903811i | −0.947890 | + | 0.903811i | ||||
\(428\) | 0.863269 | 0.863269 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.981929 | + | 1.70075i | −0.981929 | + | 1.70075i | −0.327068 | + | 0.945001i | \(0.606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(432\) | −0.267947 | − | 0.464097i | −0.267947 | − | 0.464097i | ||||
\(433\) | −1.57211 | −1.57211 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(434\) | 0.0377483 | + | 0.155600i | 0.0377483 | + | 0.155600i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.481286 | − | 0.309304i | −0.481286 | − | 0.309304i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.65210 | − | 2.86152i | −1.65210 | − | 2.86152i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.329562 | − | 1.35847i | −0.329562 | − | 1.35847i | ||||
\(449\) | 1.85674 | 1.85674 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(450\) | 0.481286 | + | 0.833612i | 0.481286 | + | 0.833612i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.260266 | 0.260266 | ||||||||
\(457\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(458\) | −1.21769 | + | 2.10910i | −1.21769 | + | 2.10910i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(462\) | 1.22509 | + | 0.359718i | 1.22509 | + | 0.359718i | ||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | −0.377144 | − | 0.653233i | −0.377144 | − | 0.653233i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.0800569 | + | 0.138663i | −0.0800569 | + | 0.138663i | ||||
\(467\) | −0.235759 | − | 0.408346i | −0.235759 | − | 0.408346i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.581419 | − | 1.00705i | −0.581419 | − | 1.00705i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.284630 | −0.284630 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.550294 | + | 0.953137i | 0.550294 | + | 0.953137i | ||||
\(479\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.633218 | 0.633218 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.809768 | − | 1.40256i | 0.809768 | − | 1.40256i | ||||
\(487\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(488\) | 0.915415 | + | 1.58555i | 0.915415 | + | 1.58555i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.0495907 | 0.0495907 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.327068 | − | 0.566498i | 0.327068 | − | 0.566498i | ||||
\(502\) | 1.61435 | + | 2.79614i | 1.61435 | + | 2.79614i | ||||
\(503\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(504\) | −0.578795 | + | 0.551880i | −0.578795 | + | 0.551880i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.327068 | − | 0.566498i | 0.327068 | − | 0.566498i | ||||
\(508\) | 1.82254 | − | 3.15673i | 1.82254 | − | 3.15673i | ||||
\(509\) | −0.415415 | − | 0.719520i | −0.415415 | − | 0.719520i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −1.00000 | ||||||||
\(513\) | 0.146352 | + | 0.253490i | 0.146352 | + | 0.253490i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.15402 | 2.15402 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.30235 | 1.30235 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0.696647 | − | 1.20663i | 0.696647 | − | 1.20663i | ||||
\(523\) | 0.888835 | + | 1.53951i | 0.888835 | + | 1.53951i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.473420 | + | 0.451405i | −0.473420 | + | 0.451405i | ||||
\(526\) | −2.20362 | −2.20362 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.197727 | − | 0.342474i | 0.197727 | − | 0.342474i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.122856 | − | 0.506419i | −0.122856 | − | 0.506419i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.08070 | + | 1.87183i | 1.08070 | + | 1.87183i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.607279 | + | 1.05184i | 0.607279 | + | 1.05184i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.0552004 | − | 1.15880i | 0.0552004 | − | 1.15880i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.607279 | − | 1.05184i | 0.607279 | − | 1.05184i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 1.82254 | + | 3.15673i | 1.82254 | + | 3.15673i | ||||
\(549\) | −0.374650 | + | 0.648913i | −0.374650 | + | 0.648913i | ||||
\(550\) | −0.975950 | + | 1.69039i | −0.975950 | + | 1.69039i | ||||
\(551\) | 0.205996 | + | 0.356796i | 0.205996 | + | 0.356796i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.415415 | + | 0.719520i | −0.415415 | + | 0.719520i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(558\) | 0.0458011 | + | 0.0793298i | 0.0458011 | + | 0.0793298i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.10181 | + | 1.90839i | 1.10181 | + | 1.90839i | ||||
\(563\) | 0.786053 | − | 1.36148i | 0.786053 | − | 1.36148i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.928368 | − | 0.371662i | \(-0.121212\pi\) | |||||||
\(564\) | 1.11182 | − | 1.92574i | 1.11182 | − | 1.92574i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.95190 | 1.95190 | ||||||||
\(567\) | 0.0965138 | + | 0.0283390i | 0.0965138 | + | 0.0283390i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.16284 | 1.16284 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.399867 | − | 0.692590i | −0.399867 | − | 0.692590i | ||||
\(577\) | −0.841254 | + | 1.45709i | −0.841254 | + | 1.45709i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(578\) | −0.841254 | + | 1.45709i | −0.841254 | + | 1.45709i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.914402 | −0.914402 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.0800569 | − | 0.138663i | −0.0800569 | − | 0.138663i | ||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | −1.00750 | − | 0.647478i | −1.00750 | − | 0.647478i | ||||
\(589\) | −0.0270865 | −0.0270865 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(594\) | 2.00728 | 2.00728 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.651174 | − | 1.12787i | −0.651174 | − | 1.12787i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.959493 | − | 1.66189i | 0.959493 | − | 1.66189i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(600\) | 0.457201 | + | 0.791895i | 0.457201 | + | 0.791895i | ||||
\(601\) | 0.471518 | 0.471518 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(608\) | 0.148323 | 0.148323 | ||||||||
\(609\) | 0.908487 | + | 0.266756i | 0.908487 | + | 0.266756i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.888835 | − | 1.53951i | 0.888835 | − | 1.53951i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.55601 | − | 0.456885i | −1.55601 | − | 0.456885i | ||||
\(617\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.68251 | −1.68251 | ||||||||
\(623\) | 1.42131 | − | 1.35522i | 1.42131 | − | 1.35522i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.107999 | + | 0.187059i | −0.107999 | + | 0.187059i | ||||
\(628\) | 1.62731 | + | 2.81858i | 1.62731 | + | 2.81858i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.654136 | −0.654136 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.581419 | + | 1.00705i | −0.581419 | + | 1.00705i | ||||
\(634\) | 0.550294 | − | 0.953137i | 0.550294 | − | 0.953137i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.82531 | 2.82531 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 0.259474 | + | 0.449421i | 0.259474 | + | 0.449421i | ||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(648\) | 0.0703051 | − | 0.121772i | 0.0703051 | − | 0.121772i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0450525 | + | 0.0429575i | −0.0450525 | + | 0.0429575i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.888835 | + | 1.53951i | 0.888835 | + | 1.53951i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.99743 | − | 0.880124i | −2.99743 | − | 0.880124i | ||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −0.915415 | + | 1.58555i | −0.915415 | + | 1.58555i | ||||
\(669\) | 0.642315 | − | 1.11252i | 0.642315 | − | 1.11252i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.51943 | −1.51943 | ||||||||
\(672\) | 0.246703 | − | 0.235231i | 0.246703 | − | 0.235231i | ||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0.239446 | + | 0.414732i | 0.239446 | + | 0.414732i | ||||
\(675\) | −0.514186 | + | 0.890596i | −0.514186 | + | 0.890596i | ||||
\(676\) | −0.915415 | + | 1.58555i | −0.915415 | + | 1.58555i | ||||
\(677\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.195876 | + | 0.807410i | 0.195876 | + | 0.807410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.0928751 | + | 0.160864i | −0.0928751 | + | 0.160864i | ||||
\(683\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(684\) | −0.149065 | − | 0.258188i | −0.149065 | − | 0.258188i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.550294 | + | 1.58997i | −0.550294 | + | 1.58997i | ||||
\(687\) | −0.946841 | −0.946841 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | −3.64508 | −3.64508 | ||||||||
\(693\) | −0.156475 | − | 0.644999i | −0.156475 | − | 0.644999i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.661784 | − | 1.14624i | 0.661784 | − | 1.14624i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.0622501 | −0.0622501 | ||||||||
\(700\) | 1.32503 | − | 1.26342i | 1.32503 | − | 1.26342i | ||||
\(701\) | 1.96386 | 1.96386 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.810848 | − | 1.40443i | 0.810848 | − | 1.40443i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.793332 | 0.793332 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.37262 | − | 2.37744i | −1.37262 | − | 2.37744i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.69968 | − | 2.94394i | −1.69968 | − | 2.94394i | ||||
\(717\) | −0.213947 | + | 0.370567i | −0.213947 | + | 0.370567i | ||||
\(718\) | −0.0800569 | + | 0.138663i | −0.0800569 | + | 0.138663i | ||||
\(719\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.54620 | −1.54620 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.69968 | + | 2.94394i | −1.69968 | + | 2.94394i | ||||
\(725\) | −0.723734 | + | 1.25354i | −0.723734 | + | 1.25354i | ||||
\(726\) | 0.190327 | + | 0.329656i | 0.190327 | + | 0.329656i | ||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.730242 | 0.730242 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.784269 | + | 1.35839i | −0.784269 | + | 1.35839i | ||||
\(733\) | 0.786053 | + | 1.36148i | 0.786053 | + | 1.36148i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(734\) | −2.64508 | −2.64508 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(744\) | 0.0435090 | + | 0.0753598i | 0.0435090 | + | 0.0753598i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.341254 | − | 0.325385i | 0.341254 | − | 0.325385i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(752\) | −0.483780 | + | 0.837932i | −0.483780 | + | 0.837932i | ||||
\(753\) | −0.627639 | + | 1.08710i | −0.627639 | + | 1.08710i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.80651 | − | 0.530438i | −1.80651 | − | 0.530438i | ||||
\(757\) | 1.16011 | 1.16011 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.654861 | + | 1.13425i | 0.654861 | + | 1.13425i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(762\) | 2.19121 | 2.19121 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.25461 | −3.25461 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.21769 | + | 2.10910i | −1.21769 | + | 2.10910i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.550294 | − | 0.953137i | −0.550294 | − | 0.953137i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.0475819 | − | 0.0824143i | −0.0475819 | − | 0.0824143i | ||||
\(776\) | 1.16140 | 1.16140 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.48853 | 1.48853 | ||||||||
\(784\) | 0.438384 | + | 0.281733i | 0.438384 | + | 0.281733i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.428368 | − | 0.741955i | −0.428368 | − | 0.741955i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.927783 | −0.927783 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.65210 | + | 2.86152i | −1.65210 | + | 2.86152i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.82254 | + | 3.15673i | 1.82254 | + | 3.15673i | ||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0.226717 | − | 0.216174i | 0.226717 | − | 0.216174i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.260554 | + | 0.451293i | 0.260554 | + | 0.451293i | ||||
\(801\) | 0.561767 | − | 0.973010i | 0.561767 | − | 0.973010i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.415415 | + | 0.719520i | −0.415415 | + | 0.719520i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | −2.54272 | − | 0.746610i | −2.54272 | − | 0.746610i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −3.34978 | −3.34978 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | −1.09560 | + | 1.89764i | −1.09560 | + | 1.89764i | ||||
\(823\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.758872 | −0.758872 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.302273 | − | 0.523552i | 0.302273 | − | 0.523552i | ||||
\(837\) | −0.0489319 | + | 0.0847525i | −0.0489319 | + | 0.0847525i | ||||
\(838\) | 1.49547 | + | 2.59023i | 1.49547 | + | 2.59023i | ||||
\(839\) | 1.96386 | 1.96386 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.09516 | 1.09516 | ||||||||
\(842\) | −0.396666 | − | 0.687046i | −0.396666 | − | 0.687046i | ||||
\(843\) | −0.428368 | + | 0.741955i | −0.428368 | + | 0.741955i | ||||
\(844\) | 1.62731 | − | 2.81858i | 1.62731 | − | 2.81858i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.78724 | −1.78724 | ||||||||
\(847\) | 0.250314 | − | 0.238674i | 0.250314 | − | 0.238674i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.379436 | + | 0.657203i | 0.379436 | + | 0.657203i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.99094 | −1.99094 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(854\) | 2.11435 | + | 0.620830i | 2.11435 | + | 0.620830i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.329562 | − | 0.570818i | −0.329562 | − | 0.570818i | ||||
\(857\) | 0.142315 | − | 0.246497i | 0.142315 | − | 0.246497i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.959493 | + | 1.66189i | 0.959493 | + | 1.66189i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.30420 | 3.30420 | ||||||||
\(863\) | −0.415415 | − | 0.719520i | −0.415415 | − | 0.719520i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(864\) | 0.267947 | − | 0.464097i | 0.267947 | − | 0.464097i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.32254 | + | 2.29071i | 1.32254 | + | 2.29071i | ||||
\(867\) | −0.654136 | −0.654136 | ||||||||
\(868\) | 0.126095 | − | 0.120232i | 0.126095 | − | 0.120232i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.237662 | + | 0.411642i | 0.237662 | + | 0.411642i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.142315 | + | 0.246497i | 0.142315 | + | 0.246497i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.0311250 | − | 0.0539102i | 0.0311250 | − | 0.0539102i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −0.0458011 | + | 0.961482i | −0.0458011 | + | 0.961482i | ||||
\(883\) | 1.44747 | 1.44747 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.469383 | − | 1.93482i | −0.469383 | − | 1.93482i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0583469 | + | 0.101060i | 0.0583469 | + | 0.101060i | ||||
\(892\) | −1.79774 | + | 3.11378i | −1.79774 | + | 3.11378i | ||||
\(893\) | 0.264241 | − | 0.457679i | 0.264241 | − | 0.457679i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.32503 | + | 1.26342i | −1.32503 | + | 1.26342i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.56199 | − | 2.70544i | −1.56199 | − | 2.70544i | ||||
\(899\) | −0.0688733 | + | 0.119292i | −0.0688733 | + | 0.119292i | ||||
\(900\) | 0.523715 | − | 0.907100i | 0.523715 | − | 0.907100i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.327068 | − | 0.566498i | 0.327068 | − | 0.566498i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.57211 | −1.57211 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(912\) | −0.0485117 | − | 0.0840247i | −0.0485117 | − | 0.0840247i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.65007 | 2.65007 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.239446 | + | 0.414732i | 0.239446 | + | 0.414732i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.327555 | − | 1.35020i | −0.327555 | − | 1.35020i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.377144 | − | 0.653233i | 0.377144 | − | 0.653233i | ||||
\(929\) | −0.841254 | − | 1.45709i | −0.841254 | − | 1.45709i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.0475819 | − | 0.998867i | \(-0.484848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(932\) | 0.174229 | 0.174229 | ||||||||
\(933\) | −0.327068 | − | 0.566498i | −0.327068 | − | 0.566498i | ||||
\(934\) | −0.396666 | + | 0.687046i | −0.396666 | + | 0.687046i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | −0.978242 | + | 1.69436i | −0.978242 | + | 1.69436i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.981929 | − | 1.70075i | −0.981929 | − | 1.70075i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.327068 | − | 0.945001i | \(-0.606061\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.239446 | + | 0.414732i | 0.239446 | + | 0.414732i | ||||
\(951\) | 0.427894 | 0.427894 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.598806 | − | 1.03716i | 0.598806 | − | 1.03716i | ||||
\(957\) | 0.549222 | + | 0.951280i | 0.549222 | + | 0.951280i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.91030 | + | 0.560914i | 1.91030 | + | 0.560914i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.495472 | + | 0.858183i | 0.495472 | + | 0.858183i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.134879 | − | 0.233618i | 0.134879 | − | 0.233618i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.0951638 | 0.0951638 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(968\) | −0.241738 | − | 0.418702i | −0.241738 | − | 0.418702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(972\) | −1.76231 | −1.76231 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.341254 | − | 0.591068i | 0.341254 | − | 0.591068i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.27830 | 2.27830 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.841254 | + | 1.45709i | 0.841254 | + | 1.45709i | ||||
\(983\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.286343 | − | 1.18032i | −0.286343 | − | 1.18032i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(992\) | 0.0247953 | + | 0.0429468i | 0.0247953 | + | 0.0429468i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.959493 | − | 1.66189i | 0.959493 | − | 1.66189i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(998\) | 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 | 1169.1.f.c.333.2 | ✓ | 20 | |
7.2 | even | 3 | inner | 1169.1.f.c.667.2 | yes | 20 | |
167.166 | odd | 2 | CM | 1169.1.f.c.333.2 | ✓ | 20 | |
1169.667 | odd | 6 | inner | 1169.1.f.c.667.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1169.1.f.c.333.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1169.1.f.c.333.2 | ✓ | 20 | 167.166 | odd | 2 | CM | |
1169.1.f.c.667.2 | yes | 20 | 7.2 | even | 3 | inner | |
1169.1.f.c.667.2 | yes | 20 | 1169.667 | odd | 6 | inner |