Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1944,1,Mod(43,1944)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1944, base_ring=CyclotomicField(162))
chi = DirichletCharacter(H, H._module([81, 81, 130]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1944.43");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1944 = 2^{3} \cdot 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1944.bh (of order \(162\), degree \(54\), 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: | \(0.970182384559\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Coefficient field: | \(\Q(\zeta_{162})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{54} - x^{27} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{81}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{81} + \cdots)\) |
Embedding invariants
Embedding label | 355.1 | ||
Root | \(0.431386 + 0.902167i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1944.355 |
Dual form | 1944.1.bh.a.115.1 |
$q$-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 \(\left(\mathbb{Z}/1944\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(973\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{37}{81}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.135331 | − | 0.990800i | −0.135331 | − | 0.990800i | ||||
\(3\) | −0.360178 | − | 0.932884i | −0.360178 | − | 0.932884i | ||||
\(4\) | −0.963371 | + | 0.268173i | −0.963371 | + | 0.268173i | ||||
\(5\) | 0 | 0 | 0.0193913 | − | 0.999812i | \(-0.493827\pi\) | ||||
−0.0193913 | + | 0.999812i | \(0.506173\pi\) | |||||||
\(6\) | −0.875558 | + | 0.483113i | −0.875558 | + | 0.483113i | ||||
\(7\) | 0 | 0 | 0.996993 | − | 0.0774924i | \(-0.0246914\pi\) | ||||
−0.996993 | + | 0.0774924i | \(0.975309\pi\) | |||||||
\(8\) | 0.396080 | + | 0.918216i | 0.396080 | + | 0.918216i | ||||
\(9\) | −0.740544 | + | 0.672008i | −0.740544 | + | 0.672008i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.938848 | + | 1.07580i | 0.938848 | + | 1.07580i | 0.996993 | + | 0.0774924i | \(0.0246914\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(12\) | 0.597159 | + | 0.802123i | 0.597159 | + | 0.802123i | ||||
\(13\) | 0 | 0 | 0.466044 | − | 0.884762i | \(-0.345679\pi\) | ||||
−0.466044 | + | 0.884762i | \(0.654321\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.856167 | − | 0.516699i | 0.856167 | − | 0.516699i | ||||
\(17\) | 0.906963 | + | 0.214954i | 0.906963 | + | 0.214954i | 0.657521 | − | 0.753436i | \(-0.271605\pi\) |
0.249441 | + | 0.968390i | \(0.419753\pi\) | |||||||
\(18\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(19\) | 1.34676 | + | 1.42748i | 1.34676 | + | 1.42748i | 0.813552 | + | 0.581492i | \(0.197531\pi\) |
0.533204 | + | 0.845986i | \(0.320988\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.938848 | − | 1.07580i | 0.938848 | − | 1.07580i | ||||
\(23\) | 0 | 0 | 0.565607 | − | 0.824675i | \(-0.308642\pi\) | ||||
−0.565607 | + | 0.824675i | \(0.691358\pi\) | |||||||
\(24\) | 0.713930 | − | 0.700217i | 0.713930 | − | 0.700217i | ||||
\(25\) | −0.999248 | − | 0.0387754i | −0.999248 | − | 0.0387754i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.893633 | + | 0.448799i | 0.893633 | + | 0.448799i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.952248 | − | 0.305326i | \(-0.0987654\pi\) | ||||
−0.952248 | + | 0.305326i | \(0.901235\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.910363 | − | 0.413811i | \(-0.864198\pi\) | ||||
0.910363 | + | 0.413811i | \(0.135802\pi\) | |||||||
\(32\) | −0.627812 | − | 0.778365i | −0.627812 | − | 0.778365i | ||||
\(33\) | 0.665445 | − | 1.26332i | 0.665445 | − | 1.26332i | ||||
\(34\) | 0.0902362 | − | 0.927709i | 0.0902362 | − | 0.927709i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.533204 | − | 0.845986i | 0.533204 | − | 0.845986i | ||||
\(37\) | 0 | 0 | 0.893633 | − | 0.448799i | \(-0.148148\pi\) | ||||
−0.893633 | + | 0.448799i | \(0.851852\pi\) | |||||||
\(38\) | 1.23209 | − | 1.52755i | 1.23209 | − | 1.52755i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.56180 | − | 1.21049i | −1.56180 | − | 1.21049i | −0.875558 | − | 0.483113i | \(-0.839506\pi\) |
−0.686242 | − | 0.727374i | \(-0.740741\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.569364 | + | 1.47469i | 0.569364 | + | 1.47469i | 0.856167 | + | 0.516699i | \(0.172840\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(44\) | −1.19296 | − | 0.784622i | −1.19296 | − | 0.784622i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.910363 | − | 0.413811i | \(-0.135802\pi\) | ||||
−0.910363 | + | 0.413811i | \(0.864198\pi\) | |||||||
\(48\) | −0.790393 | − | 0.612601i | −0.790393 | − | 0.612601i | ||||
\(49\) | 0.987990 | − | 0.154519i | 0.987990 | − | 0.154519i | ||||
\(50\) | 0.0968109 | + | 0.995303i | 0.0968109 | + | 0.995303i | ||||
\(51\) | −0.126141 | − | 0.923512i | −0.126141 | − | 0.923512i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(54\) | 0.323734 | − | 0.946148i | 0.323734 | − | 0.946148i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.846600 | − | 1.77051i | 0.846600 | − | 1.77051i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.68024 | − | 0.329988i | −1.68024 | − | 0.329988i | −0.740544 | − | 0.672008i | \(-0.765432\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.963371 | − | 0.268173i | \(-0.913580\pi\) | ||||
0.963371 | + | 0.268173i | \(0.0864198\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.686242 | + | 0.727374i | −0.686242 | + | 0.727374i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.34175 | − | 0.488357i | −1.34175 | − | 0.488357i | ||||
\(67\) | 1.89877 | + | 0.608816i | 1.89877 | + | 0.608816i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
0.925724 | + | 0.378200i | \(0.123457\pi\) | |||||||
\(68\) | −0.931386 | + | 0.0361420i | −0.931386 | + | 0.0361420i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(72\) | −0.910363 | − | 0.413811i | −0.910363 | − | 0.413811i | ||||
\(73\) | 0.420545 | + | 0.0491546i | 0.420545 | + | 0.0491546i | 0.323734 | − | 0.946148i | \(-0.395062\pi\) |
0.0968109 | + | 0.995303i | \(0.469136\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.323734 | + | 0.946148i | 0.323734 | + | 0.946148i | ||||
\(76\) | −1.68024 | − | 1.01403i | −1.68024 | − | 1.01403i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.925724 | − | 0.378200i | \(-0.876543\pi\) | ||||
0.925724 | + | 0.378200i | \(0.123457\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.0968109 | − | 0.995303i | 0.0968109 | − | 0.995303i | ||||
\(82\) | −0.987990 | + | 1.71125i | −0.987990 | + | 1.71125i | ||||
\(83\) | 0.0919145 | − | 0.0712391i | 0.0919145 | − | 0.0712391i | −0.565607 | − | 0.824675i | \(-0.691358\pi\) |
0.657521 | + | 0.753436i | \(0.271605\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.38407 | − | 0.763697i | 1.38407 | − | 0.763697i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.615959 | + | 1.28817i | −0.615959 | + | 1.28817i | ||||
\(89\) | −0.819590 | + | 1.10090i | −0.819590 | + | 1.10090i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(97\) | −0.0353063 | − | 1.82038i | −0.0353063 | − | 1.82038i | −0.431386 | − | 0.902167i | \(-0.641975\pi\) |
0.396080 | − | 0.918216i | \(-0.370370\pi\) | |||||||
\(98\) | −0.286803 | − | 0.957990i | −0.286803 | − | 0.957990i | ||||
\(99\) | −1.41820 | − | 0.165764i | −1.41820 | − | 0.165764i | ||||
\(100\) | 0.973045 | − | 0.230616i | 0.973045 | − | 0.230616i | ||||
\(101\) | 0 | 0 | 0.713930 | − | 0.700217i | \(-0.246914\pi\) | ||||
−0.713930 | + | 0.700217i | \(0.753086\pi\) | |||||||
\(102\) | −0.897946 | + | 0.249960i | −0.897946 | + | 0.249960i | ||||
\(103\) | 0 | 0 | −0.323734 | − | 0.946148i | \(-0.604938\pi\) | ||||
0.323734 | + | 0.946148i | \(0.395062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.257188 | − | 1.45859i | −0.257188 | − | 1.45859i | −0.790393 | − | 0.612601i | \(-0.790123\pi\) |
0.533204 | − | 0.845986i | \(-0.320988\pi\) | |||||||
\(108\) | −0.981255 | − | 0.192712i | −0.981255 | − | 0.192712i | ||||
\(109\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.285318 | + | 0.738993i | −0.285318 | + | 0.738993i | 0.713930 | + | 0.700217i | \(0.246914\pi\) |
−0.999248 | + | 0.0387754i | \(0.987654\pi\) | |||||||
\(114\) | −1.86880 | − | 0.599206i | −1.86880 | − | 0.599206i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.0995634 | + | 1.70944i | −0.0995634 | + | 1.70944i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.140580 | + | 1.02923i | −0.140580 | + | 1.02923i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.566717 | + | 1.89297i | −0.566717 | + | 1.89297i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(128\) | 0.813552 | + | 0.581492i | 0.813552 | + | 0.581492i | ||||
\(129\) | 1.17064 | − | 1.06230i | 1.17064 | − | 1.06230i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.971639 | − | 0.694486i | 0.971639 | − | 0.694486i | 0.0193913 | − | 0.999812i | \(-0.493827\pi\) |
0.952248 | + | 0.305326i | \(0.0987654\pi\) | |||||||
\(132\) | −0.302283 | + | 1.39550i | −0.302283 | + | 1.39550i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.346252 | − | 1.96369i | 0.346252 | − | 1.96369i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.161855 | + | 0.917927i | 0.161855 | + | 0.917927i | ||||
\(137\) | 0.867579 | − | 1.37651i | 0.867579 | − | 1.37651i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
0.925724 | − | 0.378200i | \(-0.123457\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.193040 | + | 0.0150042i | 0.193040 | + | 0.0150042i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.0193913 | + | 0.999812i | \(0.493827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.286803 | + | 0.957990i | −0.286803 | + | 0.957990i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.00821044 | − | 0.423328i | −0.00821044 | − | 0.423328i | ||||
\(147\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.533204 | − | 0.845986i | \(-0.679012\pi\) | ||||
0.533204 | + | 0.845986i | \(0.320988\pi\) | |||||||
\(150\) | 0.893633 | − | 0.448799i | 0.893633 | − | 0.448799i | ||||
\(151\) | 0 | 0 | 0.323734 | − | 0.946148i | \(-0.395062\pi\) | ||||
−0.323734 | + | 0.946148i | \(0.604938\pi\) | |||||||
\(152\) | −0.777311 | + | 1.80201i | −0.777311 | + | 1.80201i | ||||
\(153\) | −0.816096 | + | 0.450303i | −0.816096 | + | 0.450303i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.875558 | − | 0.483113i | \(-0.160494\pi\) | ||||
−0.875558 | + | 0.483113i | \(0.839506\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.999248 | + | 0.0387754i | −0.999248 | + | 0.0387754i | ||||
\(163\) | 0.993238 | + | 1.72034i | 0.993238 | + | 1.72034i | 0.597159 | + | 0.802123i | \(0.296296\pi\) |
0.396080 | + | 0.918216i | \(0.370370\pi\) | |||||||
\(164\) | 1.82921 | + | 0.747315i | 1.82921 | + | 0.747315i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.0830226 | − | 0.0814280i | −0.0830226 | − | 0.0814280i | ||||
\(167\) | 0 | 0 | −0.856167 | − | 0.516699i | \(-0.827160\pi\) | ||||
0.856167 | + | 0.516699i | \(0.172840\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.565607 | − | 0.824675i | −0.565607 | − | 0.824675i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.95661 | − | 0.152080i | −1.95661 | − | 0.152080i | ||||
\(172\) | −0.943980 | − | 1.26798i | −0.943980 | − | 1.26798i | ||||
\(173\) | 0 | 0 | 0.981255 | − | 0.192712i | \(-0.0617284\pi\) | ||||
−0.981255 | + | 0.192712i | \(0.938272\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.35968 | + | 0.435963i | 1.35968 | + | 0.435963i | ||||
\(177\) | 0.297344 | + | 1.68632i | 0.297344 | + | 1.68632i | ||||
\(178\) | 1.20169 | + | 0.663064i | 1.20169 | + | 0.663064i | ||||
\(179\) | −1.33549 | + | 1.41553i | −1.33549 | + | 1.41553i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.286803 | − | 0.957990i | \(-0.407407\pi\) | ||||
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.620252 | + | 1.17752i | 0.620252 | + | 1.17752i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.211704 | − | 0.977334i | \(-0.432099\pi\) | ||||
−0.211704 | + | 0.977334i | \(0.567901\pi\) | |||||||
\(192\) | 0.925724 | + | 0.378200i | 0.925724 | + | 0.378200i | ||||
\(193\) | −0.0697382 | − | 0.716972i | −0.0697382 | − | 0.716972i | −0.963371 | − | 0.268173i | \(-0.913580\pi\) |
0.893633 | − | 0.448799i | \(-0.148148\pi\) | |||||||
\(194\) | −1.79886 | + | 0.281336i | −1.79886 | + | 0.281336i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.910363 | + | 0.413811i | −0.910363 | + | 0.413811i | ||||
\(197\) | 0 | 0 | −0.893633 | − | 0.448799i | \(-0.851852\pi\) | ||||
0.893633 | + | 0.448799i | \(0.148148\pi\) | |||||||
\(198\) | 0.0276881 | + | 1.42759i | 0.0276881 | + | 1.42759i | ||||
\(199\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(200\) | −0.360178 | − | 0.932884i | −0.360178 | − | 0.932884i | ||||
\(201\) | −0.115940 | − | 1.99061i | −0.115940 | − | 1.99061i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.369181 | + | 0.855857i | 0.369181 | + | 0.855857i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.271282 | + | 2.78903i | −0.271282 | + | 2.78903i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.12207 | − | 1.39114i | −1.12207 | − | 1.39114i | −0.910363 | − | 0.413811i | \(-0.864198\pi\) |
−0.211704 | − | 0.977334i | \(-0.567901\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.41036 | + | 0.452215i | −1.41036 | + | 0.452215i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.0581448 | + | 0.998308i | −0.0581448 | + | 0.998308i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.105615 | − | 0.410024i | −0.105615 | − | 0.410024i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.249441 | − | 0.968390i | \(-0.580247\pi\) | ||||
0.249441 | + | 0.968390i | \(0.419753\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(226\) | 0.770807 | + | 0.182685i | 0.770807 | + | 0.182685i | ||||
\(227\) | 1.58515 | − | 0.956642i | 1.58515 | − | 0.956642i | 0.597159 | − | 0.802123i | \(-0.296296\pi\) |
0.987990 | − | 0.154519i | \(-0.0493827\pi\) | |||||||
\(228\) | −0.340786 | + | 1.93270i | −0.340786 | + | 1.93270i | ||||
\(229\) | 0 | 0 | −0.211704 | − | 0.977334i | \(-0.567901\pi\) | ||||
0.211704 | + | 0.977334i | \(0.432099\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.73928 | − | 0.203292i | 1.73928 | − | 0.203292i | 0.813552 | − | 0.581492i | \(-0.197531\pi\) |
0.925724 | + | 0.378200i | \(0.123457\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.70718 | − | 0.132693i | 1.70718 | − | 0.132693i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.963371 | − | 0.268173i | \(-0.0864198\pi\) | ||||
−0.963371 | + | 0.268173i | \(0.913580\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.116760 | + | 0.854835i | 0.116760 | + | 0.854835i | 0.952248 | + | 0.305326i | \(0.0987654\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(242\) | 1.03878 | 1.03878 | ||||||||
\(243\) | −0.963371 | + | 0.268173i | −0.963371 | + | 0.268173i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.95225 | + | 0.305326i | 1.95225 | + | 0.305326i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.0995634 | − | 0.0600868i | −0.0995634 | − | 0.0600868i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.107204 | − | 0.248527i | −0.107204 | − | 0.248527i | 0.856167 | − | 0.516699i | \(-0.172840\pi\) |
−0.963371 | + | 0.268173i | \(0.913580\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.466044 | − | 0.884762i | 0.466044 | − | 0.884762i | ||||
\(257\) | 0.182652 | + | 0.843216i | 0.182652 | + | 0.843216i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
−0.790393 | + | 0.612601i | \(0.790123\pi\) | |||||||
\(258\) | −1.21095 | − | 1.01611i | −1.21095 | − | 1.01611i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.819590 | − | 0.868715i | −0.819590 | − | 0.868715i | ||||
\(263\) | 0 | 0 | −0.249441 | − | 0.968390i | \(-0.580247\pi\) | ||||
0.249441 | + | 0.968390i | \(0.419753\pi\) | |||||||
\(264\) | 1.42357 | + | 0.110648i | 1.42357 | + | 0.110648i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.32221 | + | 0.368062i | 1.32221 | + | 0.368062i | ||||
\(268\) | −1.99249 | − | 0.0773175i | −1.99249 | − | 0.0773175i | ||||
\(269\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(272\) | 0.887578 | − | 0.284590i | 0.887578 | − | 0.284590i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.48126 | − | 0.673313i | −1.48126 | − | 0.673313i | ||||
\(275\) | −0.896427 | − | 1.11140i | −0.896427 | − | 1.11140i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.0968109 | − | 0.995303i | \(-0.469136\pi\) | ||||
−0.0968109 | + | 0.995303i | \(0.530864\pi\) | |||||||
\(278\) | −0.0112581 | − | 0.193294i | −0.0112581 | − | 0.193294i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.12207 | + | 1.39114i | −1.12207 | + | 1.39114i | −0.211704 | + | 0.977334i | \(0.567901\pi\) |
−0.910363 | + | 0.413811i | \(0.864198\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.54686 | + | 0.631963i | −1.54686 | + | 0.631963i | −0.981255 | − | 0.192712i | \(-0.938272\pi\) |
−0.565607 | + | 0.824675i | \(0.691358\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.987990 | + | 0.154519i | 0.987990 | + | 0.154519i | ||||
\(289\) | −0.117257 | − | 0.0588886i | −0.117257 | − | 0.0588886i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.68549 | + | 0.688598i | −1.68549 | + | 0.688598i | ||||
\(292\) | −0.418323 | + | 0.0654245i | −0.418323 | + | 0.0654245i | ||||
\(293\) | 0 | 0 | −0.0968109 | − | 0.995303i | \(-0.530864\pi\) | ||||
0.0968109 | + | 0.995303i | \(0.469136\pi\) | |||||||
\(294\) | −0.790393 | + | 0.612601i | −0.790393 | + | 0.612601i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.356167 | + | 1.38272i | 0.356167 | + | 1.38272i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.565607 | − | 0.824675i | −0.565607 | − | 0.824675i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.89063 | + | 0.526292i | 1.89063 | + | 0.526292i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.556604 | + | 0.747649i | 0.556604 | + | 0.747649i | ||||
\(307\) | 1.20169 | − | 1.27372i | 1.20169 | − | 1.27372i | 0.249441 | − | 0.968390i | \(-0.419753\pi\) |
0.952248 | − | 0.305326i | \(-0.0987654\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.999248 | − | 0.0387754i | \(-0.0123457\pi\) | ||||
−0.999248 | + | 0.0387754i | \(0.987654\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.23209 | − | 0.241974i | 1.23209 | − | 0.241974i | 0.466044 | − | 0.884762i | \(-0.345679\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.565607 | − | 0.824675i | \(-0.691358\pi\) | ||||
0.565607 | + | 0.824675i | \(0.308642\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.26806 | + | 0.765277i | −1.26806 | + | 0.765277i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.914615 | + | 1.58416i | 0.914615 | + | 1.58416i | ||||
\(324\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.57010 | − | 1.21692i | 1.57010 | − | 1.21692i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.492891 | − | 1.91352i | 0.492891 | − | 1.91352i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.839516 | + | 1.75570i | −0.839516 | + | 1.75570i | −0.211704 | + | 0.977334i | \(0.567901\pi\) |
−0.627812 | + | 0.778365i | \(0.716049\pi\) | |||||||
\(332\) | −0.0694434 | + | 0.0932786i | −0.0694434 | + | 0.0932786i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.144318 | − | 0.228977i | −0.144318 | − | 0.228977i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.910363 | + | 0.413811i | \(0.864198\pi\) | |||||||
\(338\) | −0.740544 | + | 0.672008i | −0.740544 | + | 0.672008i | ||||
\(339\) | 0.792160 | 0.792160 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.114110 | + | 1.95919i | 0.114110 | + | 1.95919i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.12857 | + | 1.10689i | −1.12857 | + | 1.10689i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.31109 | + | 0.101906i | 1.31109 | + | 0.101906i | 0.713930 | − | 0.700217i | \(-0.246914\pi\) |
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.533204 | − | 0.845986i | \(-0.320988\pi\) | ||||
−0.533204 | + | 0.845986i | \(0.679012\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.247945 | − | 1.40617i | 0.247945 | − | 1.40617i | ||||
\(353\) | −1.41036 | − | 1.27984i | −1.41036 | − | 1.27984i | −0.910363 | − | 0.413811i | \(-0.864198\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(354\) | 1.63057 | − | 0.522820i | 1.63057 | − | 0.522820i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.494338 | − | 1.28037i | 0.494338 | − | 1.28037i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.58325 | + | 1.13164i | 1.58325 | + | 1.13164i | ||||
\(359\) | 0 | 0 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.165797 | + | 2.84662i | −0.165797 | + | 2.84662i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.01078 | − | 0.239560i | 1.01078 | − | 0.239560i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.987990 | − | 0.154519i | \(-0.950617\pi\) | ||||
0.987990 | + | 0.154519i | \(0.0493827\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.97004 | − | 0.153123i | 1.97004 | − | 0.153123i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.360178 | − | 0.932884i | \(-0.382716\pi\) | ||||
−0.360178 | + | 0.932884i | \(0.617284\pi\) | |||||||
\(374\) | 1.08275 | − | 0.773902i | 1.08275 | − | 0.773902i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.218037 | − | 1.23655i | −0.218037 | − | 1.23655i | −0.875558 | − | 0.483113i | \(-0.839506\pi\) |
0.657521 | − | 0.753436i | \(-0.271605\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.323734 | − | 0.946148i | \(-0.604938\pi\) | ||||
0.323734 | + | 0.946148i | \(0.395062\pi\) | |||||||
\(384\) | 0.249441 | − | 0.968390i | 0.249441 | − | 0.968390i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.700938 | + | 0.166125i | −0.700938 | + | 0.166125i | ||||
\(387\) | −1.41264 | − | 0.709455i | −1.41264 | − | 0.709455i | ||||
\(388\) | 0.522190 | + | 1.74424i | 0.522190 | + | 1.74424i | ||||
\(389\) | 0 | 0 | −0.0193913 | − | 0.999812i | \(-0.506173\pi\) | ||||
0.0193913 | + | 0.999812i | \(0.493827\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.533204 | + | 0.845986i | 0.533204 | + | 0.845986i | ||||
\(393\) | −0.997837 | − | 0.656288i | −0.997837 | − | 0.656288i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.41071 | − | 0.220631i | 1.41071 | − | 0.220631i | ||||
\(397\) | 0 | 0 | 0.597159 | − | 0.802123i | \(-0.296296\pi\) | ||||
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.875558 | + | 0.483113i | −0.875558 | + | 0.483113i | ||||
\(401\) | 0.161505 | − | 0.627001i | 0.161505 | − | 0.627001i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
0.996993 | − | 0.0774924i | \(-0.0246914\pi\) | |||||||
\(402\) | −1.95661 | + | 0.384266i | −1.95661 | + | 0.384266i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.798022 | − | 0.481609i | 0.798022 | − | 0.481609i | ||||
\(409\) | 0.761341 | + | 0.746718i | 0.761341 | + | 0.746718i | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) |
−0.211704 | + | 0.977334i | \(0.567901\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.59660 | − | 0.313563i | −1.59660 | − | 0.313563i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0555313 | − | 0.185488i | −0.0555313 | − | 0.185488i | ||||
\(418\) | 2.80008 | − | 0.108656i | 2.80008 | − | 0.108656i | ||||
\(419\) | −1.89162 | − | 0.606523i | −1.89162 | − | 0.606523i | −0.981255 | − | 0.192712i | \(-0.938272\pi\) |
−0.910363 | − | 0.413811i | \(-0.864198\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.875558 | − | 0.483113i | \(-0.839506\pi\) | ||||
0.875558 | + | 0.483113i | \(0.160494\pi\) | |||||||
\(422\) | −1.22650 | + | 1.30001i | −1.22650 | + | 1.30001i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.897946 | − | 0.249960i | −0.897946 | − | 0.249960i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.638921 | + | 1.33619i | 0.638921 | + | 1.33619i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(432\) | 0.996993 | − | 0.0774924i | 0.996993 | − | 0.0774924i | ||||
\(433\) | −1.53094 | − | 1.28461i | −1.53094 | − | 1.28461i | −0.790393 | − | 0.612601i | \(-0.790123\pi\) |
−0.740544 | − | 0.672008i | \(-0.765432\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.391959 | + | 0.160133i | −0.391959 | + | 0.160133i | ||||
\(439\) | 0 | 0 | 0.910363 | − | 0.413811i | \(-0.135802\pi\) | ||||
−0.910363 | + | 0.413811i | \(0.864198\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.627812 | + | 0.778365i | −0.627812 | + | 0.778365i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.259456 | + | 0.672008i | 0.259456 | + | 0.672008i | 1.00000 | \(0\) | ||
−0.740544 | + | 0.672008i | \(0.765432\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.173027 | − | 0.0868973i | 0.173027 | − | 0.0868973i | −0.360178 | − | 0.932884i | \(-0.617284\pi\) |
0.533204 | + | 0.845986i | \(0.320988\pi\) | |||||||
\(450\) | −0.740544 | − | 0.672008i | −0.740544 | − | 0.672008i | ||||
\(451\) | −0.164051 | − | 2.81665i | −0.164051 | − | 2.81665i | ||||
\(452\) | 0.0766897 | − | 0.788439i | 0.0766897 | − | 0.788439i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.16236 | − | 1.44110i | −1.16236 | − | 1.44110i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.96103 | + | 0.0760971i | 1.96103 | + | 0.0760971i | ||||
\(457\) | −1.66750 | + | 0.534661i | −1.66750 | + | 0.534661i | −0.981255 | − | 0.192712i | \(-0.938272\pi\) |
−0.686242 | + | 0.727374i | \(0.740741\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.714020 | + | 0.599134i | 0.714020 | + | 0.599134i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.999248 | − | 0.0387754i | \(-0.987654\pi\) | ||||
0.999248 | + | 0.0387754i | \(0.0123457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.565607 | − | 0.824675i | \(-0.308642\pi\) | ||||
−0.565607 | + | 0.824675i | \(0.691358\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.436800 | − | 1.69576i | −0.436800 | − | 1.69576i | ||||
\(467\) | −0.444319 | − | 0.470951i | −0.444319 | − | 0.470951i | 0.466044 | − | 0.884762i | \(-0.345679\pi\) |
−0.910363 | + | 0.413811i | \(0.864198\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.362508 | − | 1.67352i | −0.362508 | − | 1.67352i | ||||
\(473\) | −1.05193 | + | 1.99703i | −1.05193 | + | 1.99703i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.29039 | − | 1.47863i | −1.29039 | − | 1.47863i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.996993 | − | 0.0774924i | \(-0.0246914\pi\) | ||||
−0.996993 | + | 0.0774924i | \(0.975309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.831170 | − | 0.231372i | 0.831170 | − | 0.231372i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.140580 | − | 1.02923i | −0.140580 | − | 1.02923i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.396080 | + | 0.918216i | 0.396080 | + | 0.918216i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.24713 | − | 1.54620i | 1.24713 | − | 1.54620i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.0369307 | − | 1.90414i | 0.0369307 | − | 1.90414i | −0.286803 | − | 0.957990i | \(-0.592593\pi\) |
0.323734 | − | 0.946148i | \(-0.395062\pi\) | |||||||
\(492\) | 0.0383169 | − | 1.97561i | 0.0383169 | − | 1.97561i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.0460600 | + | 0.106779i | −0.0460600 | + | 0.106779i | ||||
\(499\) | −0.931386 | + | 1.76819i | −0.931386 | + | 1.76819i | −0.431386 | + | 0.902167i | \(0.641975\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.231732 | + | 0.139851i | −0.231732 | + | 0.139851i | ||||
\(503\) | 0 | 0 | −0.973045 | − | 0.230616i | \(-0.925926\pi\) | ||||
0.973045 | + | 0.230616i | \(0.0740741\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.565607 | + | 0.824675i | −0.565607 | + | 0.824675i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.565607 | − | 0.824675i | \(-0.308642\pi\) | ||||
−0.565607 | + | 0.824675i | \(0.691358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(513\) | 0.562854 | + | 1.88006i | 0.562854 | + | 1.88006i | ||||
\(514\) | 0.810741 | − | 0.295085i | 0.810741 | − | 0.295085i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.842882 | + | 1.33732i | −0.842882 | + | 1.33732i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.107652 | − | 1.84832i | −0.107652 | − | 1.84832i | −0.431386 | − | 0.902167i | \(-0.641975\pi\) |
0.323734 | − | 0.946148i | \(-0.395062\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.707900 | − | 0.355521i | 0.707900 | − | 0.355521i | −0.0581448 | − | 0.998308i | \(-0.518519\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(524\) | −0.749807 | + | 0.929615i | −0.749807 | + | 0.929615i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.0830226 | − | 1.42544i | −0.0830226 | − | 1.42544i | ||||
\(529\) | −0.360178 | − | 0.932884i | −0.360178 | − | 0.932884i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.46604 | − | 0.884762i | 1.46604 | − | 0.884762i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.185740 | − | 1.35986i | 0.185740 | − | 1.35986i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.193040 | + | 1.98462i | 0.193040 | + | 1.98462i | ||||
\(537\) | 1.80154 | + | 0.736011i | 1.80154 | + | 0.736011i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.09380 | + | 0.917810i | 1.09380 | + | 0.917810i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.402089 | − | 0.840899i | −0.402089 | − | 0.840899i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.02735 | − | 0.285982i | −1.02735 | − | 0.285982i | −0.286803 | − | 0.957990i | \(-0.592593\pi\) |
−0.740544 | + | 0.672008i | \(0.765432\pi\) | |||||||
\(548\) | −0.466659 | + | 1.55875i | −0.466659 | + | 1.55875i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.979857 | + | 1.03859i | −0.979857 | + | 1.03859i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.189992 | + | 0.0373133i | −0.189992 | + | 0.0373133i | ||||
\(557\) | 0 | 0 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.875088 | − | 1.00274i | 0.875088 | − | 1.00274i | ||||
\(562\) | 1.53020 | + | 0.923479i | 1.53020 | + | 0.923479i | ||||
\(563\) | 0.138232 | + | 0.135577i | 0.138232 | + | 0.135577i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.627812 | + | 0.778365i | \(0.716049\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.835488 | + | 1.44711i | 0.835488 | + | 1.44711i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.0306535 | + | 0.0237583i | −0.0306535 | + | 0.0237583i | −0.627812 | − | 0.778365i | \(-0.716049\pi\) |
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.369444 | + | 1.43427i | −0.369444 | + | 1.43427i | 0.466044 | + | 0.884762i | \(0.345679\pi\) |
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.0193913 | − | 0.999812i | 0.0193913 | − | 0.999812i | ||||
\(577\) | 0.644463 | − | 1.49403i | 0.644463 | − | 1.49403i | −0.211704 | − | 0.977334i | \(-0.567901\pi\) |
0.856167 | − | 0.516699i | \(-0.172840\pi\) | |||||||
\(578\) | −0.0424783 | + | 0.124148i | −0.0424783 | + | 0.124148i | ||||
\(579\) | −0.643733 | + | 0.323295i | −0.643733 | + | 0.323295i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.910363 | + | 1.57679i | 0.910363 | + | 1.57679i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.121435 | + | 0.405620i | 0.121435 | + | 0.405620i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.615959 | + | 0.604128i | −0.615959 | + | 0.604128i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.323734 | + | 0.946148i | \(0.395062\pi\) | |||||||
\(588\) | 0.713930 | + | 0.700217i | 0.713930 | + | 0.700217i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.0996057 | − | 0.564892i | −0.0996057 | − | 0.564892i | −0.993238 | − | 0.116093i | \(-0.962963\pi\) |
0.893633 | − | 0.448799i | \(-0.148148\pi\) | |||||||
\(594\) | 1.32180 | − | 0.540016i | 1.32180 | − | 0.540016i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.360178 | − | 0.932884i | \(-0.382716\pi\) | ||||
−0.360178 | + | 0.932884i | \(0.617284\pi\) | |||||||
\(600\) | −0.740544 | + | 0.672008i | −0.740544 | + | 0.672008i | ||||
\(601\) | −1.56750 | − | 1.12039i | −1.56750 | − | 1.12039i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.627812 | − | 0.778365i | \(-0.716049\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.81525 | + | 0.825133i | −1.81525 | + | 0.825133i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.135331 | − | 0.990800i | \(-0.456790\pi\) | ||||
−0.135331 | + | 0.990800i | \(0.543210\pi\) | |||||||
\(608\) | 0.265589 | − | 1.94446i | 0.265589 | − | 1.94446i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.665445 | − | 0.652664i | 0.665445 | − | 0.652664i | ||||
\(613\) | 0 | 0 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
−0.835488 | + | 0.549509i | \(0.814815\pi\) | |||||||
\(614\) | −1.42462 | − | 1.01826i | −1.42462 | − | 1.01826i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.48126 | + | 1.05874i | −1.48126 | + | 1.05874i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.981255 | + | 0.192712i | \(0.938272\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.533455 | + | 0.484085i | 0.533455 | + | 0.484085i | 0.893633 | − | 0.448799i | \(-0.148148\pi\) |
−0.360178 | + | 0.932884i | \(0.617284\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.996993 | + | 0.0774924i | 0.996993 | + | 0.0774924i | ||||
\(626\) | −0.406488 | − | 1.18801i | −0.406488 | − | 1.18801i | ||||
\(627\) | 2.69955 | − | 0.751470i | 2.69955 | − | 0.751470i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.286803 | − | 0.957990i | \(-0.592593\pi\) | ||||
0.286803 | + | 0.957990i | \(0.407407\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.893633 | + | 1.54782i | −0.893633 | + | 1.54782i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.567291 | + | 1.18639i | −0.567291 | + | 1.18639i | 0.396080 | + | 0.918216i | \(0.370370\pi\) |
−0.963371 | + | 0.268173i | \(0.913580\pi\) | |||||||
\(642\) | 0.929845 | + | 1.15283i | 0.929845 | + | 1.15283i | ||||
\(643\) | −0.436800 | + | 0.241016i | −0.436800 | + | 0.241016i | −0.686242 | − | 0.727374i | \(-0.740741\pi\) |
0.249441 | + | 0.968390i | \(0.419753\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.44581 | − | 1.12059i | 1.44581 | − | 1.12059i | ||||
\(647\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(648\) | 0.952248 | − | 0.305326i | 0.952248 | − | 0.305326i | ||||
\(649\) | −1.22249 | − | 2.11741i | −1.22249 | − | 2.11741i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.41820 | − | 1.39097i | −1.41820 | − | 1.39097i | ||||
\(653\) | 0 | 0 | −0.856167 | − | 0.516699i | \(-0.827160\pi\) | ||||
0.856167 | + | 0.516699i | \(0.172840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.96262 | − | 0.229397i | −1.96262 | − | 0.229397i | ||||
\(657\) | −0.344464 | + | 0.246208i | −0.344464 | + | 0.246208i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.75376 | + | 0.344428i | −1.75376 | + | 0.344428i | −0.963371 | − | 0.268173i | \(-0.913580\pi\) |
−0.790393 | + | 0.612601i | \(0.790123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.999248 | − | 0.0387754i | \(-0.0123457\pi\) | ||||
−0.999248 | + | 0.0387754i | \(0.987654\pi\) | |||||||
\(662\) | 1.85316 | + | 0.594192i | 1.85316 | + | 0.594192i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.101818 | + | 0.0561810i | 0.101818 | + | 0.0561810i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.778747 | − | 1.47842i | −0.778747 | − | 1.47842i | −0.875558 | − | 0.483113i | \(-0.839506\pi\) |
0.0968109 | − | 0.995303i | \(-0.469136\pi\) | |||||||
\(674\) | −0.207340 | + | 0.173979i | −0.207340 | + | 0.173979i | ||||
\(675\) | −0.875558 | − | 0.483113i | −0.875558 | − | 0.483113i | ||||
\(676\) | 0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | ||||
\(677\) | 0 | 0 | 0.211704 | − | 0.977334i | \(-0.432099\pi\) | ||||
−0.211704 | + | 0.977334i | \(0.567901\pi\) | |||||||
\(678\) | −0.107204 | − | 0.784872i | −0.107204 | − | 0.784872i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.46337 | − | 1.13420i | −1.46337 | − | 1.13420i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.01089 | − | 0.507688i | −1.01089 | − | 0.507688i | −0.135331 | − | 0.990800i | \(-0.543210\pi\) |
−0.875558 | + | 0.483113i | \(0.839506\pi\) | |||||||
\(684\) | 1.92572 | − | 0.378200i | 1.92572 | − | 0.378200i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.24944 | + | 0.968390i | 1.24944 | + | 0.968390i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.861662 | − | 1.06829i | 0.861662 | − | 1.06829i | −0.135331 | − | 0.990800i | \(-0.543210\pi\) |
0.996993 | − | 0.0774924i | \(-0.0246914\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.0764629 | − | 1.31282i | −0.0764629 | − | 1.31282i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.15629 | − | 1.43358i | −1.15629 | − | 1.43358i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.816096 | − | 1.54932i | −0.816096 | − | 1.54932i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.42679 | − | 0.0553658i | −1.42679 | − | 0.0553658i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.07720 | + | 1.57059i | −1.07720 | + | 1.57059i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.738677 | − | 1.54481i | −0.738677 | − | 1.54481i | ||||
\(709\) | 0 | 0 | −0.249441 | − | 0.968390i | \(-0.580247\pi\) | ||||
0.249441 | + | 0.968390i | \(0.419753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.33549 | − | 0.316516i | −1.33549 | − | 0.316516i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.906963 | − | 1.72183i | 0.906963 | − | 1.72183i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.993238 | − | 0.116093i | \(-0.0370370\pi\) | ||||
−0.993238 | + | 0.116093i | \(0.962963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.84287 | − | 0.220966i | 2.84287 | − | 0.220966i | ||||
\(723\) | 0.755407 | − | 0.416816i | 0.755407 | − | 0.416816i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.374146 | − | 0.969063i | −0.374146 | − | 0.969063i | ||||
\(727\) | 0 | 0 | −0.135331 | − | 0.990800i | \(-0.543210\pi\) | ||||
0.135331 | + | 0.990800i | \(0.456790\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.597159 | + | 0.802123i | 0.597159 | + | 0.802123i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.199401 | + | 1.45987i | 0.199401 | + | 1.45987i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.963371 | − | 0.268173i | \(-0.0864198\pi\) | ||||
−0.963371 | + | 0.268173i | \(0.913580\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.12769 | + | 2.61428i | 1.12769 | + | 2.61428i | ||||
\(738\) | −0.418323 | − | 1.93119i | −0.418323 | − | 1.93119i | ||||
\(739\) | 1.91371 | − | 0.223681i | 1.91371 | − | 0.223681i | 0.925724 | − | 0.378200i | \(-0.123457\pi\) |
0.987990 | + | 0.154519i | \(0.0493827\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.211704 | − | 0.977334i | \(-0.567901\pi\) | ||||
0.211704 | + | 0.977334i | \(0.432099\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0201935 | + | 0.114523i | −0.0201935 | + | 0.114523i | ||||
\(748\) | −0.913312 | − | 0.968054i | −0.913312 | − | 0.968054i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.657521 | − | 0.753436i | \(-0.271605\pi\) | ||||
−0.657521 | + | 0.753436i | \(0.728395\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.193234 | + | 0.189523i | −0.193234 | + | 0.189523i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(758\) | −1.19567 | + | 0.383375i | −1.19567 | + | 0.383375i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.17990 | + | 1.46285i | 1.17990 | + | 1.46285i | 0.856167 | + | 0.516699i | \(0.172840\pi\) |
0.323734 | + | 0.946148i | \(0.395062\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.993238 | − | 0.116093i | −0.993238 | − | 0.116093i | ||||
\(769\) | 0.733321 | − | 0.299595i | 0.733321 | − | 0.299595i | 0.0193913 | − | 0.999812i | \(-0.493827\pi\) |
0.713930 | + | 0.700217i | \(0.246914\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.720836 | − | 0.474101i | 0.720836 | − | 0.474101i | ||||
\(772\) | 0.259456 | + | 0.672008i | 0.259456 | + | 0.672008i | ||||
\(773\) | 0 | 0 | −0.835488 | − | 0.549509i | \(-0.814815\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(774\) | −0.511754 | + | 1.49566i | −0.511754 | + | 1.49566i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.65752 | − | 0.753436i | 1.65752 | − | 0.753436i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.375421 | − | 3.85967i | −0.375421 | − | 3.85967i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.515212 | + | 1.07747i | −0.515212 | + | 1.07747i | ||||
\(787\) | 0.0501657 | + | 0.104913i | 0.0501657 | + | 0.104913i | 0.925724 | − | 0.378200i | \(-0.123457\pi\) |
−0.875558 | + | 0.483113i | \(0.839506\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.409515 | − | 1.36787i | −0.409515 | − | 1.36787i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.999248 | − | 0.0387754i | \(-0.0123457\pi\) | ||||
−0.999248 | + | 0.0387754i | \(0.987654\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.597159 | + | 0.802123i | 0.597159 | + | 0.802123i | ||||
\(801\) | −0.132871 | − | 1.36604i | −0.132871 | − | 1.36604i | ||||
\(802\) | −0.643090 | − | 0.0751664i | −0.643090 | − | 0.0751664i | ||||
\(803\) | 0.341947 | + | 0.498571i | 0.341947 | + | 0.498571i | ||||
\(804\) | 0.645521 | + | 1.88661i | 0.645521 | + | 1.88661i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.211704 | + | 0.366682i | 0.211704 | + | 0.366682i | 0.952248 | − | 0.305326i | \(-0.0987654\pi\) |
−0.740544 | + | 0.672008i | \(0.765432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.565607 | − | 0.979660i | 0.565607 | − | 0.979660i | −0.431386 | − | 0.902167i | \(-0.641975\pi\) |
0.996993 | − | 0.0774924i | \(-0.0246914\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.585176 | − | 0.725504i | −0.585176 | − | 0.725504i | ||||
\(817\) | −1.33829 | + | 2.79880i | −1.33829 | + | 2.79880i | ||||
\(818\) | 0.636815 | − | 0.855391i | 0.636815 | − | 0.855391i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.323734 | − | 0.946148i | \(-0.395062\pi\) | ||||
−0.323734 | + | 0.946148i | \(0.604938\pi\) | |||||||
\(822\) | −0.0946077 | + | 1.62435i | −0.0946077 | + | 1.62435i | ||||
\(823\) | 0 | 0 | −0.533204 | − | 0.845986i | \(-0.679012\pi\) | ||||
0.533204 | + | 0.845986i | \(0.320988\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.713930 | + | 1.23656i | −0.713930 | + | 1.23656i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.439408 | − | 1.46773i | −0.439408 | − | 1.46773i | −0.835488 | − | 0.549509i | \(-0.814815\pi\) |
0.396080 | − | 0.918216i | \(-0.370370\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.973045 | − | 0.230616i | \(-0.0740741\pi\) | ||||
−0.973045 | + | 0.230616i | \(0.925926\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.929284 | + | 0.0722297i | 0.929284 | + | 0.0722297i | ||||
\(834\) | −0.176266 | + | 0.0801228i | −0.176266 | + | 0.0801228i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.486595 | − | 2.75962i | −0.486595 | − | 2.75962i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.344948 | + | 1.95630i | −0.344948 | + | 1.95630i | ||||
\(839\) | 0 | 0 | −0.740544 | − | 0.672008i | \(-0.765432\pi\) | ||||
0.740544 | + | 0.672008i | \(0.234568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.813552 | − | 0.581492i | 0.813552 | − | 0.581492i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.70192 | + | 0.545699i | 1.70192 | + | 0.545699i | ||||
\(844\) | 1.45403 | + | 1.03928i | 1.45403 | + | 1.03928i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.14669 | + | 1.21542i | 1.14669 | + | 1.21542i | ||||
\(850\) | −0.126141 | + | 0.923512i | −0.126141 | + | 0.923512i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.987990 | − | 0.154519i | \(-0.950617\pi\) | ||||
0.987990 | + | 0.154519i | \(0.0493827\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.23743 | − | 0.813871i | 1.23743 | − | 0.813871i | ||||
\(857\) | 0.282544 | + | 0.201950i | 0.282544 | + | 0.201950i | 0.713930 | − | 0.700217i | \(-0.246914\pi\) |
−0.431386 | + | 0.902167i | \(0.641975\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.693969 | − | 1.79743i | 0.693969 | − | 1.79743i | 0.0968109 | − | 0.995303i | \(-0.469136\pi\) |
0.597159 | − | 0.802123i | \(-0.296296\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(864\) | −0.211704 | − | 0.977334i | −0.211704 | − | 0.977334i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.06561 | + | 1.69070i | −1.06561 | + | 1.69070i | ||||
\(867\) | −0.0127029 | + | 0.130597i | −0.0127029 | + | 0.130597i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.24946 | + | 1.32435i | 1.24946 | + | 1.32435i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.211704 | + | 0.366682i | 0.211704 | + | 0.366682i | ||||
\(877\) | 0 | 0 | 0.740544 | − | 0.672008i | \(-0.234568\pi\) | ||||
−0.740544 | + | 0.672008i | \(0.765432\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.770807 | − | 1.78693i | 0.770807 | − | 1.78693i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.597159 | − | 0.802123i | \(-0.296296\pi\) | |||||||
\(882\) | 0.856167 | + | 0.516699i | 0.856167 | + | 0.516699i | ||||
\(883\) | 0.636815 | − | 0.855391i | 0.636815 | − | 0.855391i | −0.360178 | − | 0.932884i | \(-0.617284\pi\) |
0.996993 | + | 0.0774924i | \(0.0246914\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.630713 | − | 0.348013i | 0.630713 | − | 0.348013i | ||||
\(887\) | 0 | 0 | 0.249441 | − | 0.968390i | \(-0.419753\pi\) | ||||
−0.249441 | + | 0.968390i | \(0.580247\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.16164 | − | 0.830289i | 1.16164 | − | 0.830289i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.109514 | − | 0.159675i | −0.109514 | − | 0.159675i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.565607 | + | 0.824675i | −0.565607 | + | 0.824675i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −2.76853 | + | 0.543722i | −2.76853 | + | 0.543722i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.791564 | + | 0.0307163i | −0.791564 | + | 0.0307163i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.755407 | + | 0.416816i | 0.755407 | + | 0.416816i | 0.813552 | − | 0.581492i | \(-0.197531\pi\) |
−0.0581448 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(908\) | −1.27054 | + | 1.34669i | −1.27054 | + | 1.34669i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.963371 | − | 0.268173i | \(-0.913580\pi\) | ||||
0.963371 | + | 0.268173i | \(0.0864198\pi\) | |||||||
\(912\) | −0.189992 | − | 1.95329i | −0.189992 | − | 1.95329i | ||||
\(913\) | 0.162933 | + | 0.0319990i | 0.162933 | + | 0.0319990i | ||||
\(914\) | 0.755407 | + | 1.57980i | 0.755407 | + | 1.57980i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.496993 | − | 0.788533i | 0.496993 | − | 0.788533i | ||||
\(919\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.62105 | − | 0.662272i | −1.62105 | − | 0.662272i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.125088 | − | 0.323987i | −0.125088 | − | 0.323987i | 0.856167 | − | 0.516699i | \(-0.172840\pi\) |
−0.981255 | + | 0.192712i | \(0.938272\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.55115 | + | 1.20224i | 1.55115 | + | 1.20224i | ||||
\(932\) | −1.62105 | + | 0.662272i | −1.62105 | + | 0.662272i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.406488 | + | 0.503966i | −0.406488 | + | 0.503966i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.0333522 | + | 0.572636i | 0.0333522 | + | 0.572636i | 0.973045 | + | 0.230616i | \(0.0740741\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.669504 | − | 1.06224i | −0.669504 | − | 1.06224i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.910363 | − | 0.413811i | \(-0.864198\pi\) | ||||
0.910363 | + | 0.413811i | \(0.135802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1.60907 | + | 0.585653i | −1.60907 | + | 0.585653i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.12102 | + | 0.771987i | 2.12102 | + | 0.771987i | ||||
\(947\) | 0.423089 | + | 0.0164178i | 0.423089 | + | 0.0164178i | 0.249441 | − | 0.968390i | \(-0.419753\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.29039 | + | 1.47863i | −1.29039 | + | 1.47863i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.36836 | − | 1.45037i | −1.36836 | − | 1.45037i | −0.740544 | − | 0.672008i | \(-0.765432\pi\) |
−0.627812 | − | 0.778365i | \(-0.716049\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.657521 | + | 0.753436i | 0.657521 | + | 0.753436i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.17064 | + | 0.907315i | 1.17064 | + | 0.907315i | ||||
\(964\) | −0.341727 | − | 0.792211i | −0.341727 | − | 0.792211i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.0193913 | − | 0.999812i | \(-0.493827\pi\) | ||||
−0.0193913 | + | 0.999812i | \(0.506173\pi\) | |||||||
\(968\) | −1.00073 | + | 0.278573i | −1.00073 | + | 0.278573i | ||||
\(969\) | 1.14841 | − | 1.42381i | 1.14841 | − | 1.42381i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(972\) | 0.856167 | − | 0.516699i | 0.856167 | − | 0.516699i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.000752047 | − | 0.0387754i | 0.000752047 | − | 0.0387754i | −0.999248 | − | 0.0387754i | \(-0.987654\pi\) |
1.00000 | \(0\) | |||||||||
\(978\) | −1.70076 | − | 1.02641i | −1.70076 | − | 1.02641i | ||||
\(979\) | −1.95382 | + | 0.151863i | −1.95382 | + | 0.151863i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.89162 | + | 0.221098i | −1.89162 | + | 0.221098i | ||||
\(983\) | 0 | 0 | −0.657521 | − | 0.753436i | \(-0.728395\pi\) | ||||
0.657521 | + | 0.753436i | \(0.271605\pi\) | |||||||
\(984\) | −1.96262 | + | 0.229397i | −1.96262 | + | 0.229397i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.686242 | − | 0.727374i | \(-0.740741\pi\) | ||||
0.686242 | + | 0.727374i | \(0.259259\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.94024 | + | 0.150807i | 1.94024 | + | 0.150807i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.112030 | + | 0.0311857i | 0.112030 | + | 0.0311857i | ||||
\(997\) | 0 | 0 | −0.999248 | − | 0.0387754i | \(-0.987654\pi\) | ||||
0.999248 | + | 0.0387754i | \(0.0123457\pi\) | |||||||
\(998\) | 1.87797 | + | 0.683526i | 1.87797 | + | 0.683526i | ||||
\(999\) | 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 | 1944.1.bh.a.355.1 | yes | 54 | |
8.3 | odd | 2 | CM | 1944.1.bh.a.355.1 | yes | 54 | |
243.115 | even | 81 | inner | 1944.1.bh.a.115.1 | ✓ | 54 | |
1944.115 | odd | 162 | inner | 1944.1.bh.a.115.1 | ✓ | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1944.1.bh.a.115.1 | ✓ | 54 | 243.115 | even | 81 | inner | |
1944.1.bh.a.115.1 | ✓ | 54 | 1944.115 | odd | 162 | inner | |
1944.1.bh.a.355.1 | yes | 54 | 1.1 | even | 1 | trivial | |
1944.1.bh.a.355.1 | yes | 54 | 8.3 | odd | 2 | CM |