Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(607,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.607");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.b (of order \(2\), degree \(1\), 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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 607.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.607 |
Dual form | 1216.2.b.a.607.3 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.00000i | − | 1.15470i | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||
0.816497 | − | 0.577350i | \(-0.195913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.73205i | 0.774597i | 0.921954 | + | 0.387298i | \(0.126592\pi\) | ||||
−0.921954 | + | 0.387298i | \(0.873408\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) | ||
0.981981 | − | 0.188982i | \(-0.0605189\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.19615 | 1.56670 | 0.783349 | − | 0.621582i | \(-0.213510\pi\) | ||||
0.783349 | + | 0.621582i | \(0.213510\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46410 | 0.894427 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.73205 | + | 4.00000i | 0.397360 | + | 0.917663i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.00000i | − | 0.769800i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.3923 | 1.86651 | 0.933257 | − | 0.359211i | \(-0.116954\pi\) | ||||
0.933257 | + | 0.359211i | \(0.116954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 10.3923i | − | 1.80907i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.73205 | 0.292770 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.00000i | 1.28103i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.46410i | − | 0.541002i | −0.962720 | − | 0.270501i | \(-0.912811\pi\) | ||
0.962720 | − | 0.270501i | \(-0.0871893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.19615 | −0.792406 | −0.396203 | − | 0.918163i | \(-0.629672\pi\) | ||||
−0.396203 | + | 0.918163i | \(0.629672\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.73205i | − | 0.258199i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.00000i | − | 1.31278i | −0.754420 | − | 0.656392i | \(-0.772082\pi\) | ||
0.754420 | − | 0.656392i | \(-0.227918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.00000 | 0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 6.00000i | − | 0.840168i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00000i | 1.21356i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.00000 | − | 3.46410i | 1.05963 | − | 0.458831i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.73205i | 0.221766i | 0.993833 | + | 0.110883i | \(0.0353679\pi\) | ||||
−0.993833 | + | 0.110883i | \(0.964632\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 6.92820i | − | 0.859338i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.00000i | − | 0.244339i | −0.992509 | − | 0.122169i | \(-0.961015\pi\) | ||
0.992509 | − | 0.122169i | \(-0.0389851\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.92820 | 0.822226 | 0.411113 | − | 0.911584i | \(-0.365140\pi\) | ||||
0.411113 | + | 0.911584i | \(0.365140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0000 | −1.28745 | −0.643726 | − | 0.765256i | \(-0.722612\pi\) | ||||
−0.643726 | + | 0.765256i | \(0.722612\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 4.00000i | − | 0.461880i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.19615i | − | 0.592157i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.46410 | 0.389742 | 0.194871 | − | 0.980829i | \(-0.437571\pi\) | ||||
0.194871 | + | 0.980829i | \(0.437571\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.46410 | −0.380235 | −0.190117 | − | 0.981761i | \(-0.560887\pi\) | ||||
−0.190117 | + | 0.981761i | \(0.560887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.19615i | 0.563602i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.0000i | 1.28654i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.46410i | 0.367194i | 0.983002 | + | 0.183597i | \(0.0587741\pi\) | ||||
−0.983002 | + | 0.183597i | \(0.941226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000i | 0.419314i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 20.7846i | − | 2.15526i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.92820 | + | 3.00000i | −0.710819 | + | 0.307794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.8564i | − | 1.40690i | −0.710742 | − | 0.703452i | \(-0.751641\pi\) | ||
0.710742 | − | 0.703452i | \(-0.248359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.19615 | −0.522233 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 13.8564i | − | 1.37876i | −0.724398 | − | 0.689382i | \(-0.757882\pi\) | ||
0.724398 | − | 0.689382i | \(-0.242118\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.92820 | 0.682656 | 0.341328 | − | 0.939944i | \(-0.389123\pi\) | ||||
0.341328 | + | 0.939944i | \(0.389123\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 3.46410i | − | 0.338062i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 12.0000i | − | 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 4.00000i | − | 0.379663i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3205i | 1.62938i | 0.579899 | + | 0.814688i | \(0.303092\pi\) | ||||
−0.579899 | + | 0.814688i | \(0.696908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.00000 | 0.369800 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.00000i | − | 0.275010i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.0000 | 1.45455 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.92820 | −0.624695 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3923 | 0.922168 | 0.461084 | − | 0.887357i | \(-0.347461\pi\) | ||||
0.461084 | + | 0.887357i | \(0.347461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.3923i | 0.914991i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.73205 | 0.151330 | 0.0756650 | − | 0.997133i | \(-0.475892\pi\) | ||||
0.0756650 | + | 0.997133i | \(0.475892\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | − | 1.73205i | 0.346844 | − | 0.150188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.92820 | 0.596285 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.00000 | −0.768922 | −0.384461 | − | 0.923141i | \(-0.625613\pi\) | ||||
−0.384461 | + | 0.923141i | \(0.625613\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.73205 | 0.146911 | 0.0734553 | − | 0.997299i | \(-0.476597\pi\) | ||||
0.0734553 | + | 0.997299i | \(0.476597\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.0000 | −1.51587 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.7846 | −1.73810 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 10.3923i | − | 0.863034i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 12.0000i | − | 0.989743i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.0526i | 1.56085i | 0.625252 | + | 0.780423i | \(0.284996\pi\) | ||||
−0.625252 | + | 0.780423i | \(0.715004\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.8564 | −1.12762 | −0.563809 | − | 0.825905i | \(-0.690665\pi\) | ||||
−0.563809 | + | 0.825905i | \(0.690665\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.0000i | 1.44579i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 12.0000i | − | 0.951662i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.3205 | 1.35665 | 0.678323 | − | 0.734763i | \(-0.262707\pi\) | ||||
0.678323 | + | 0.734763i | \(0.262707\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18.0000 | 1.40130 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.3205 | −1.34030 | −0.670151 | − | 0.742225i | \(-0.733770\pi\) | ||||
−0.670151 | + | 0.742225i | \(0.733770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.73205 | − | 4.00000i | −0.132453 | − | 0.305888i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.00000i | − | 0.151186i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000i | 0.448461i | 0.974536 | + | 0.224231i | \(0.0719869\pi\) | ||||
−0.974536 | + | 0.224231i | \(0.928013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.46410 | 0.256074 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.46410i | 0.254686i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.5885 | 1.13994 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.00000 | −0.290957 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00000i | 0.651217i | 0.945505 | + | 0.325609i | \(0.105569\pi\) | ||||
−0.945505 | + | 0.325609i | \(0.894431\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.3205i | 1.24676i | 0.781920 | + | 0.623379i | \(0.214240\pi\) | ||||
−0.781920 | + | 0.623379i | \(0.785760\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.8564 | −0.992278 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.7846i | 1.48084i | 0.672143 | + | 0.740421i | \(0.265374\pi\) | ||||
−0.672143 | + | 0.740421i | \(0.734626\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 19.0000i | − | 1.34687i | −0.739244 | − | 0.673437i | \(-0.764817\pi\) | ||
0.739244 | − | 0.673437i | \(-0.235183\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.00000i | 0.421117i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | 0.419058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.00000 | + | 20.7846i | 0.622543 | + | 1.43770i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000i | 0.275371i | 0.990476 | + | 0.137686i | \(0.0439664\pi\) | ||||
−0.990476 | + | 0.137686i | \(0.956034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 13.8564i | − | 0.949425i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 9.00000i | − | 0.613795i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 10.3923i | − | 0.705476i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.0000i | 1.48662i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3923 | 0.695920 | 0.347960 | − | 0.937509i | \(-0.386874\pi\) | ||||
0.347960 | + | 0.937509i | \(0.386874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.0000i | 1.59294i | 0.604681 | + | 0.796468i | \(0.293301\pi\) | ||||
−0.604681 | + | 0.796468i | \(0.706699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.9808i | 1.71686i | 0.512933 | + | 0.858429i | \(0.328559\pi\) | ||||
−0.512933 | + | 0.858429i | \(0.671441\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.3923 | −0.683763 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.00000 | −0.589610 | −0.294805 | − | 0.955557i | \(-0.595255\pi\) | ||||
−0.294805 | + | 0.955557i | \(0.595255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.5885 | 1.01688 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 6.92820i | − | 0.450035i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.00000i | − | 0.582162i | −0.956698 | − | 0.291081i | \(-0.905985\pi\) | ||
0.956698 | − | 0.291081i | \(-0.0940149\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3.46410i | − | 0.223142i | −0.993756 | − | 0.111571i | \(-0.964412\pi\) | ||
0.993756 | − | 0.111571i | \(-0.0355883\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0000i | 0.641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.3923i | 0.663940i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.92820 | − | 16.0000i | −0.440831 | − | 1.01806i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.92820i | 0.439057i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.1244 | −0.765283 | −0.382641 | − | 0.923897i | \(-0.624985\pi\) | ||||
−0.382641 | + | 0.923897i | \(0.624985\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.3923 | 0.650791 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.7128i | 1.72868i | 0.502910 | + | 0.864339i | \(0.332263\pi\) | ||||
−0.502910 | + | 0.864339i | \(0.667737\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.00000i | − | 0.124274i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.00000i | 0.184988i | 0.995713 | + | 0.0924940i | \(0.0294839\pi\) | ||||
−0.995713 | + | 0.0924940i | \(0.970516\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.3923i | 0.638394i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.92820 | 0.423999 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.0000i | 1.70088i | 0.526073 | + | 0.850439i | \(0.323664\pi\) | ||||
−0.526073 | + | 0.850439i | \(0.676336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.00000 | 0.484182 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.3923 | 0.626680 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.19615i | − | 0.312207i | −0.987741 | − | 0.156103i | \(-0.950107\pi\) | ||
0.987741 | − | 0.156103i | \(-0.0498933\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.3923 | −0.622171 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.7128i | 1.65321i | 0.562784 | + | 0.826604i | \(0.309730\pi\) | ||||
−0.562784 | + | 0.826604i | \(0.690270\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.9808 | −1.54440 | −0.772198 | − | 0.635382i | \(-0.780843\pi\) | ||||
−0.772198 | + | 0.635382i | \(0.780843\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.00000 | + | 13.8564i | 0.355409 | + | 0.820783i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.46410 | −0.204479 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.7128 | −1.62455 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.0000 | 1.40209 | 0.701047 | − | 0.713115i | \(-0.252716\pi\) | ||||
0.701047 | + | 0.713115i | \(0.252716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 20.7846i | − | 1.20605i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.19615i | 0.299501i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −27.7128 | −1.59206 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.00000 | −0.171780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.0000i | − | 1.25561i | −0.778372 | − | 0.627803i | \(-0.783954\pi\) | ||
0.778372 | − | 0.627803i | \(-0.216046\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 13.8564i | − | 0.788263i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 33.0000i | − | 1.87126i | −0.352985 | − | 0.935629i | \(-0.614833\pi\) | ||
0.352985 | − | 0.935629i | \(-0.385167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.73205 | −0.0975900 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.0000 | −1.34797 | −0.673987 | − | 0.738743i | \(-0.735420\pi\) | ||||
−0.673987 | + | 0.738743i | \(0.735420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −31.1769 | −1.74557 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0000 | −1.33955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.19615 | + | 12.0000i | 0.289122 | + | 0.667698i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.00000 | −0.443760 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 28.0000i | 1.54840i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.00000 | −0.496186 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 26.0000i | − | 1.42909i | −0.699590 | − | 0.714545i | \(-0.746634\pi\) | ||
0.699590 | − | 0.714545i | \(-0.253366\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.46410 | 0.189264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 27.7128i | − | 1.50961i | −0.655947 | − | 0.754807i | \(-0.727731\pi\) | ||
0.655947 | − | 0.754807i | \(-0.272269\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 34.6410 | 1.88144 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 54.0000 | 2.92426 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.0000i | − | 0.701934i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.5885 | −0.836832 | −0.418416 | − | 0.908255i | \(-0.637415\pi\) | ||||
−0.418416 | + | 0.908255i | \(0.637415\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.66025i | − | 0.463573i | −0.972767 | − | 0.231786i | \(-0.925543\pi\) | ||
0.972767 | − | 0.231786i | \(-0.0744570\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.0000i | 0.854017i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.0000 | −1.59674 | −0.798369 | − | 0.602168i | \(-0.794304\pi\) | ||||
−0.798369 | + | 0.602168i | \(0.794304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0000i | 0.636894i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.00000 | −0.317554 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 15.0000i | − | 0.791670i | −0.918322 | − | 0.395835i | \(-0.870455\pi\) | ||
0.918322 | − | 0.395835i | \(-0.129545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0000 | + | 13.8564i | −0.684211 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 32.0000i | − | 1.67956i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 19.0526i | − | 0.997257i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000i | 0.417597i | 0.977959 | + | 0.208798i | \(0.0669552\pi\) | ||||
−0.977959 | + | 0.208798i | \(0.933045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.46410i | 0.180334i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 6.00000i | − | 0.311504i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.0000 | −0.828449 | −0.414224 | − | 0.910175i | \(-0.635947\pi\) | ||||
−0.414224 | + | 0.910175i | \(0.635947\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.2487 | 1.25220 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000i | 1.02733i | 0.857991 | + | 0.513665i | \(0.171713\pi\) | ||||
−0.857991 | + | 0.513665i | \(0.828287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 20.7846i | − | 1.06483i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.1769 | −1.59307 | −0.796533 | − | 0.604595i | \(-0.793335\pi\) | ||||
−0.796533 | + | 0.604595i | \(0.793335\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.00000 | 0.458682 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.19615 | 0.264135 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 5.19615i | − | 0.263455i | −0.991286 | − | 0.131728i | \(-0.957948\pi\) | ||
0.991286 | − | 0.131728i | \(-0.0420524\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3.46410i | − | 0.174741i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.00000i | 0.301893i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 25.9808i | − | 1.30394i | −0.758246 | − | 0.651969i | \(-0.773943\pi\) | ||
0.758246 | − | 0.651969i | \(-0.226057\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.46410 | − | 8.00000i | −0.173422 | − | 0.400501i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3923i | 0.518967i | 0.965748 | + | 0.259483i | \(0.0835523\pi\) | ||||
−0.965748 | + | 0.259483i | \(0.916448\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −41.5692 | −2.07071 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 19.0526i | − | 0.946729i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.3923 | 0.515127 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.2487i | 1.19902i | 0.800367 | + | 0.599511i | \(0.204638\pi\) | ||||
−0.800367 | + | 0.599511i | \(0.795362\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.0000i | 0.887875i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 6.00000i | − | 0.294528i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3.46410i | − | 0.169638i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.3923 | −0.507697 | −0.253849 | − | 0.967244i | \(-0.581697\pi\) | ||||
−0.253849 | + | 0.967244i | \(0.581697\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.00000i | 0.437595i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00000 | 0.291043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.73205 | 0.0838198 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 41.5692i | 2.00698i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.7128 | −1.33488 | −0.667440 | − | 0.744664i | \(-0.732610\pi\) | ||||
−0.667440 | + | 0.744664i | \(0.732610\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.3923i | − | 0.499422i | −0.968320 | − | 0.249711i | \(-0.919664\pi\) | ||
0.968320 | − | 0.249711i | \(-0.0803357\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.7846 | −0.996546 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.3923 | 0.495998 | 0.247999 | − | 0.968760i | \(-0.420227\pi\) | ||||
0.247999 | + | 0.968760i | \(0.420227\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.73205 | −0.0822922 | −0.0411461 | − | 0.999153i | \(-0.513101\pi\) | ||||
−0.0411461 | + | 0.999153i | \(0.513101\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | −0.284427 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 38.1051 | 1.80231 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.92820i | − | 0.326962i | −0.986546 | − | 0.163481i | \(-0.947728\pi\) | ||
0.986546 | − | 0.163481i | \(-0.0522723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 18.0000i | − | 0.847587i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 27.7128i | 1.30206i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.92820 | −0.324799 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.0000 | −1.35656 | −0.678281 | − | 0.734802i | \(-0.737275\pi\) | ||||
−0.678281 | + | 0.734802i | \(0.737275\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 12.0000i | − | 0.560112i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 22.5167i | − | 1.04871i | −0.851501 | − | 0.524353i | \(-0.824307\pi\) | ||
0.851501 | − | 0.524353i | \(-0.175693\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.0000i | 1.16185i | 0.813958 | + | 0.580924i | \(0.197309\pi\) | ||||
−0.813958 | + | 0.580924i | \(0.802691\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 36.0000 | 1.66946 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.5885 | −0.721348 | −0.360674 | − | 0.932692i | \(-0.617453\pi\) | ||||
−0.360674 | + | 0.932692i | \(0.617453\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.00000 | −0.0923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.0000 | −1.24146 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.46410 | + | 8.00000i | 0.158944 | + | 0.367065i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.0000i | 1.09659i | 0.836286 | + | 0.548294i | \(0.184723\pi\) | ||||
−0.836286 | + | 0.548294i | \(0.815277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | −0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.0000 | 1.08978 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.7128 | 1.25579 | 0.627894 | − | 0.778299i | \(-0.283917\pi\) | ||||
0.627894 | + | 0.778299i | \(0.283917\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 34.6410i | − | 1.56652i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.2487 | 1.09433 | 0.547165 | − | 0.837025i | \(-0.315707\pi\) | ||||
0.547165 | + | 0.837025i | \(0.315707\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0000 | −0.810679 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 9.00000i | − | 0.404520i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6.92820i | − | 0.310772i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.3731 | 1.62828 | 0.814141 | − | 0.580667i | \(-0.197208\pi\) | ||||
0.814141 | + | 0.580667i | \(0.197208\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 34.6410i | 1.54765i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000i | 1.07011i | 0.844818 | + | 0.535054i | \(0.179709\pi\) | ||||
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000 | 1.06799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 6.00000i | − | 0.266469i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.0000 | 1.06378 | 0.531891 | − | 0.846813i | \(-0.321482\pi\) | ||||
0.531891 | + | 0.846813i | \(0.321482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0000i | 0.486611i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.0000 | − | 6.92820i | 0.706417 | − | 0.305888i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.0000i | 0.528783i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 46.7654i | − | 2.05674i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 17.3205i | − | 0.758825i | −0.925228 | − | 0.379413i | \(-0.876126\pi\) | ||
0.925228 | − | 0.379413i | \(-0.123874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8.00000i | − | 0.349816i | −0.984585 | − | 0.174908i | \(-0.944037\pi\) | ||
0.984585 | − | 0.174908i | \(-0.0559627\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.00000 | −0.174574 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 31.1769 | 1.35809 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.8564i | 0.600188i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.7846 | 0.898597 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0000 | 0.517838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.1769 | 1.34288 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.66025i | 0.372333i | 0.982518 | + | 0.186167i | \(0.0596065\pi\) | ||||
−0.982518 | + | 0.186167i | \(0.940394\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 40.0000i | − | 1.71656i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 24.2487i | − | 1.03870i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.00000i | − | 0.342055i | −0.985266 | − | 0.171028i | \(-0.945291\pi\) | ||
0.985266 | − | 0.171028i | \(-0.0547087\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 1.73205i | − | 0.0739221i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.3923 | − | 24.0000i | −0.442727 | − | 1.02243i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.46410i | − | 0.147309i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.92820 | 0.294086 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.66025i | 0.366947i | 0.983025 | + | 0.183473i | \(0.0587341\pi\) | ||||
−0.983025 | + | 0.183473i | \(0.941266\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.7846 | 0.879095 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 31.1769i | − | 1.31629i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 30.0000i | − | 1.26435i | −0.774826 | − | 0.632175i | \(-0.782163\pi\) | ||
0.774826 | − | 0.632175i | \(-0.217837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.0000 | −1.26211 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.0000i | 0.461957i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.7128i | 1.16178i | 0.813982 | + | 0.580891i | \(0.197296\pi\) | ||||
−0.813982 | + | 0.580891i | \(0.802704\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.46410 | −0.144968 | −0.0724841 | − | 0.997370i | \(-0.523093\pi\) | ||||
−0.0724841 | + | 0.997370i | \(0.523093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.0000 | 0.751961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.0000 | 1.20729 | 0.603643 | − | 0.797255i | \(-0.293715\pi\) | ||||
0.603643 | + | 0.797255i | \(0.293715\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34.6410 | 1.43963 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.46410i | 0.143715i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.1769 | 1.29122 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.92820i | 0.286446i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.9090 | −1.35830 | −0.679149 | − | 0.734000i | \(-0.737651\pi\) | ||||
−0.679149 | + | 0.734000i | \(0.737651\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0000 | + | 41.5692i | 0.741677 | + | 1.71283i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 41.5692 | 1.70993 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00000 | −0.246390 | −0.123195 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.19615 | 0.213021 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −38.0000 | −1.55524 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.1051 | −1.55693 | −0.778466 | − | 0.627686i | \(-0.784002\pi\) | ||||
−0.778466 | + | 0.627686i | \(0.784002\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 41.5692i | − | 1.69564i | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||
0.530281 | − | 0.847822i | \(-0.322086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.00000i | 0.0814463i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.7128i | 1.12669i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.92820 | 0.281207 | 0.140604 | − | 0.990066i | \(-0.455096\pi\) | ||||
0.140604 | + | 0.990066i | \(0.455096\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.0000 | 0.486265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.0000i | 1.45640i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 39.8372i | − | 1.60901i | −0.593947 | − | 0.804504i | \(-0.702431\pi\) | ||
0.593947 | − | 0.804504i | \(-0.297569\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 12.0000i | − | 0.483887i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00000 | −0.120775 | −0.0603877 | − | 0.998175i | \(-0.519234\pi\) | ||||
−0.0603877 | + | 0.998175i | \(0.519234\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.2487 | 0.974638 | 0.487319 | − | 0.873224i | \(-0.337975\pi\) | ||||
0.487319 | + | 0.873224i | \(0.337975\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.46410 | 0.138786 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 41.5692 | − | 18.0000i | 1.66011 | − | 0.718851i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.00000i | − | 0.278666i | −0.990246 | − | 0.139333i | \(-0.955504\pi\) | ||
0.990246 | − | 0.139333i | \(-0.0444958\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.00000 | 0.317971 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.0000i | 0.714308i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.0000 | −0.950915 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.92820 | −0.274075 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.6410i | 1.36824i | 0.729370 | + | 0.684119i | \(0.239813\pi\) | ||||
−0.729370 | + | 0.684119i | \(0.760187\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.19615 | −0.204916 | −0.102458 | − | 0.994737i | \(-0.532671\pi\) | ||||
−0.102458 | + | 0.994737i | \(0.532671\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.0000 | −0.708749 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.00000i | 0.353827i | 0.984226 | + | 0.176913i | \(0.0566112\pi\) | ||||
−0.984226 | + | 0.176913i | \(0.943389\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.7846 | −0.814613 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.66025i | 0.338902i | 0.985539 | + | 0.169451i | \(0.0541994\pi\) | ||||
−0.985539 | + | 0.169451i | \(0.945801\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.00000i | 0.117220i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.0000 | 0.429151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.0000 | −1.55582 | −0.777910 | − | 0.628376i | \(-0.783720\pi\) | ||||
−0.777910 | + | 0.628376i | \(0.783720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.0000i | 0.932083i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.00000 | + | 6.92820i | 0.116335 | + | 0.268664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 20.7846i | − | 0.803579i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.00000i | 0.347441i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 13.8564i | − | 0.534125i | −0.963679 | − | 0.267063i | \(-0.913947\pi\) | ||
0.963679 | − | 0.267063i | \(-0.0860531\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 8.00000i | − | 0.307920i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.00000 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.8564 | −0.531760 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.0000 | 1.83936 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 24.0000i | − | 0.918334i | −0.888350 | − | 0.459167i | \(-0.848148\pi\) | ||
0.888350 | − | 0.459167i | \(-0.151852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 15.5885i | − | 0.595604i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 51.9615 | 1.98246 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.0000 | −0.914327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.19615 | 0.197671 | 0.0988355 | − | 0.995104i | \(-0.468488\pi\) | ||||
0.0988355 | + | 0.995104i | \(0.468488\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.19615i | 0.197386i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.00000i | 0.113796i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10.3923i | − | 0.393637i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.0000i | 0.680823i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.7128i | − | 1.04670i | −0.852118 | − | 0.523349i | \(-0.824682\pi\) | ||
0.852118 | − | 0.523349i | \(-0.175318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.46410 | + | 8.00000i | 0.130651 | + | 0.301726i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 31.1769i | − | 1.17419i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.8564 | −0.521124 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.8564i | 0.520388i | 0.965556 | + | 0.260194i | \(0.0837866\pi\) | ||||
−0.965556 | + | 0.260194i | \(0.916213\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.46410 | −0.129914 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 36.0000i | − | 1.34632i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.0000 | −0.672222 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 51.0000i | − | 1.90198i | −0.309223 | − | 0.950990i | \(-0.600069\pi\) | ||
0.309223 | − | 0.950990i | \(-0.399931\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 6.92820i | − | 0.258020i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.92820 | −0.257663 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.0000 | −0.445669 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.0000i | 1.59478i | 0.603463 | + | 0.797391i | \(0.293787\pi\) | ||||
−0.603463 | + | 0.797391i | \(0.706213\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.5885 | −0.576560 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20.7846 | 0.766652 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 10.3923i | − | 0.382805i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.5885 | −0.573431 | −0.286715 | − | 0.958016i | \(-0.592563\pi\) | ||||
−0.286715 | + | 0.958016i | \(0.592563\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −32.0000 | + | 13.8564i | −1.17555 | + | 0.509028i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.2487 | −0.889599 | −0.444799 | − | 0.895630i | \(-0.646725\pi\) | ||||
−0.444799 | + | 0.895630i | \(0.646725\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.0000 | −1.20903 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.46410 | 0.126745 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.7128 | −1.01125 | −0.505627 | − | 0.862752i | \(-0.668739\pi\) | ||||
−0.505627 | + | 0.862752i | \(0.668739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.2487i | 0.883672i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 24.0000i | − | 0.873449i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.1244i | 0.440667i | 0.975425 | + | 0.220334i | \(0.0707146\pi\) | ||||
−0.975425 | + | 0.220334i | \(0.929285\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.0000 | 0.978749 | 0.489375 | − | 0.872074i | \(-0.337225\pi\) | ||||
0.489375 | + | 0.872074i | \(0.337225\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0000i | 0.506834i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 5.19615i | − | 0.187867i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.0000 | −0.829401 | −0.414701 | − | 0.909958i | \(-0.636114\pi\) | ||||
−0.414701 | + | 0.909958i | \(0.636114\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 55.4256 | 1.99611 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0000 | 0.863220 | 0.431610 | − | 0.902060i | \(-0.357946\pi\) | ||||
0.431610 | + | 0.902060i | \(0.357946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.7846 | 0.746605 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.00000 | −0.143499 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.8564 | − | 6.00000i | 0.496457 | − | 0.214972i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.0000i | 0.857690i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 4.00000i | − | 0.142585i | −0.997455 | − | 0.0712923i | \(-0.977288\pi\) | ||
0.997455 | − | 0.0712923i | \(-0.0227123\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.00000 | 0.213606 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.3205 | 0.615846 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.92820i | − | 0.246028i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.7846 | 0.737154 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.0000 | −1.48772 | −0.743858 | − | 0.668338i | \(-0.767006\pi\) | ||||
−0.743858 | + | 0.668338i | \(0.767006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 27.0000i | − | 0.955191i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.46410i | − | 0.122398i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −57.1577 | −2.01705 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 12.0000i | − | 0.422420i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.0000 | 0.738321 | 0.369160 | − | 0.929366i | \(-0.379645\pi\) | ||||
0.369160 | + | 0.929366i | \(0.379645\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 40.0000i | − | 1.40459i | −0.711886 | − | 0.702295i | \(-0.752159\pi\) | ||
0.711886 | − | 0.702295i | \(-0.247841\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 56.0000 | 1.96401 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.0000i | 1.05085i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.00000 | − | 20.7846i | −0.314870 | − | 0.727161i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 4.00000i | − | 0.139771i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 22.5167i | − | 0.785837i | −0.919573 | − | 0.392918i | \(-0.871465\pi\) | ||
0.919573 | − | 0.392918i | \(-0.128535\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.0000i | 1.01088i | 0.862863 | + | 0.505438i | \(0.168669\pi\) | ||||
−0.862863 | + | 0.505438i | \(0.831331\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 20.7846i | − | 0.723627i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.0000i | 0.625921i | 0.949766 | + | 0.312961i | \(0.101321\pi\) | ||||
−0.949766 | + | 0.312961i | \(0.898679\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.0000 | 0.694629 | 0.347314 | − | 0.937749i | \(-0.387094\pi\) | ||||
0.347314 | + | 0.937749i | \(0.387094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.3923 | −0.360505 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | 0.623663 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 30.0000i | − | 1.03819i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 41.5692i | − | 1.43684i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.7846 | −0.717564 | −0.358782 | − | 0.933421i | \(-0.616808\pi\) | ||||
−0.358782 | + | 0.933421i | \(0.616808\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 55.4256 | 1.90896 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.19615i | 0.178753i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 16.0000i | − | 0.549767i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 51.9615i | 1.78331i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 55.4256i | − | 1.89774i | −0.315671 | − | 0.948869i | \(-0.602230\pi\) | ||
0.315671 | − | 0.948869i | \(-0.397770\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.92820 | − | 3.00000i | 0.236940 | − | 0.102598i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 41.5692i | − | 1.41998i | −0.704213 | − | 0.709989i | \(-0.748700\pi\) | ||
0.704213 | − | 0.709989i | \(-0.251300\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.6936 | −1.83200 | −0.916001 | − | 0.401177i | \(-0.868601\pi\) | ||||
−0.916001 | + | 0.401177i | \(0.868601\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.92820i | 0.236113i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.2487 | −0.825436 | −0.412718 | − | 0.910859i | \(-0.635420\pi\) | ||||
−0.412718 | + | 0.910859i | \(0.635420\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.0000i | 0.543388i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.0000 | 0.610608 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000i | 0.271070i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.8564i | 0.468968i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.1244 | 0.409878 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.0000 | 1.75592 | 0.877958 | − | 0.478738i | \(-0.158906\pi\) | ||||
0.877958 | + | 0.478738i | \(0.158906\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 48.0000i | − | 1.61900i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.0000 | −1.71823 | −0.859117 | − | 0.511780i | \(-0.828986\pi\) | ||||
−0.859117 | + | 0.511780i | \(0.828986\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.66025 | −0.291441 | −0.145720 | − | 0.989326i | \(-0.546550\pi\) | ||||
−0.145720 | + | 0.989326i | \(0.546550\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.92820 | 0.232626 | 0.116313 | − | 0.993213i | \(-0.462892\pi\) | ||||
0.116313 | + | 0.993213i | \(0.462892\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 10.3923i | − | 0.348547i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −57.1577 | −1.91485 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.0000 | − | 15.5885i | 1.20469 | − | 0.521648i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.3923 | −0.347376 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −62.3538 | −2.07962 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0000 | 0.599667 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.3923 | 0.345834 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 34.6410i | 1.15151i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.0000i | 0.332045i | 0.986122 | + | 0.166022i | \(0.0530924\pi\) | ||||
−0.986122 | + | 0.166022i | \(0.946908\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.8564i | 0.459588i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.8564 | 0.459083 | 0.229542 | − | 0.973299i | \(-0.426277\pi\) | ||||
0.229542 | + | 0.973299i | \(0.426277\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | −0.595713 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.00000i | 0.198354i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1.73205i | − | 0.0571974i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16.0000i | − | 0.527791i | −0.964551 | − | 0.263896i | \(-0.914993\pi\) | ||
0.964551 | − | 0.263896i | \(-0.0850075\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −44.0000 | −1.44985 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.7128 | −0.912178 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | 0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.92820 | −0.227552 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.00000 | −0.196854 | −0.0984268 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984268 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.3923 | + | 24.0000i | 0.340594 | + | 0.786568i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −66.0000 | −2.16074 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27.0000i | 0.882994i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.0000 | −0.555366 | −0.277683 | − | 0.960673i | \(-0.589566\pi\) | ||||
−0.277683 | + | 0.960673i | \(0.589566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 28.0000i | − | 0.913745i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.0000 | −1.17357 | −0.586783 | − | 0.809744i | \(-0.699606\pi\) | ||||
−0.586783 | + | 0.809744i | \(0.699606\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 6.92820i | − | 0.225374i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.2487 | 0.787977 | 0.393989 | − | 0.919115i | \(-0.371095\pi\) | ||||
0.393989 | + | 0.919115i | \(0.371095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.0000 | 1.42830 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.0000i | 1.55651i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.3923i | 0.336640i | 0.985732 | + | 0.168320i | \(0.0538342\pi\) | ||||
−0.985732 | + | 0.168320i | \(0.946166\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.5885 | −0.504431 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 62.3538i | 2.01561i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.00000i | 0.290625i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 77.0000 | 2.48387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.0000i | 0.386695i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30.0000 | −0.965734 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.0000i | 1.67221i | 0.548572 | + | 0.836104i | \(0.315172\pi\) | ||||
−0.548572 | + | 0.836104i | \(0.684828\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.0000 | − | 10.3923i | 0.770991 | − | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.0000i | 1.54039i | 0.637806 | + | 0.770197i | \(0.279842\pi\) | ||||
−0.637806 | + | 0.770197i | \(0.720158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.73205i | − | 0.0555270i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.0000i | 0.512410i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.1769i | 0.997438i | 0.866764 | + | 0.498719i | \(0.166196\pi\) | ||||
−0.866764 | + | 0.498719i | \(0.833804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000i | 0.575282i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.6410 | −1.10488 | −0.552438 | − | 0.833554i | \(-0.686303\pi\) | ||||
−0.552438 | + | 0.833554i | \(0.686303\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0000 | −1.14706 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.0000i | 0.572946i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.1051 | −1.21045 | −0.605224 | − | 0.796055i | \(-0.706917\pi\) | ||||
−0.605224 | + | 0.796055i | \(0.706917\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −52.0000 | −1.65017 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.9090 | 1.04328 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.3731i | 1.15195i | 0.817469 | + | 0.575973i | \(0.195377\pi\) | ||||
−0.817469 | + | 0.575973i | \(0.804623\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 8.00000i | − | 0.253109i |
(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 | 1216.2.b.a.607.2 | yes | 4 | |
4.3 | odd | 2 | inner | 1216.2.b.a.607.4 | yes | 4 | |
8.3 | odd | 2 | 1216.2.b.b.607.1 | yes | 4 | ||
8.5 | even | 2 | 1216.2.b.b.607.3 | yes | 4 | ||
19.18 | odd | 2 | 1216.2.b.b.607.4 | yes | 4 | ||
76.75 | even | 2 | 1216.2.b.b.607.2 | yes | 4 | ||
152.37 | odd | 2 | inner | 1216.2.b.a.607.1 | ✓ | 4 | |
152.75 | even | 2 | inner | 1216.2.b.a.607.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.b.a.607.1 | ✓ | 4 | 152.37 | odd | 2 | inner | |
1216.2.b.a.607.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1216.2.b.a.607.3 | yes | 4 | 152.75 | even | 2 | inner | |
1216.2.b.a.607.4 | yes | 4 | 4.3 | odd | 2 | inner | |
1216.2.b.b.607.1 | yes | 4 | 8.3 | odd | 2 | ||
1216.2.b.b.607.2 | yes | 4 | 76.75 | even | 2 | ||
1216.2.b.b.607.3 | yes | 4 | 8.5 | even | 2 | ||
1216.2.b.b.607.4 | yes | 4 | 19.18 | odd | 2 |