Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [228,3,Mod(5,228)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(228, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 9, 16]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("228.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 228 = 2^{2} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 228.s (of order \(18\), degree \(6\), 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: | \(6.21255002741\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 101.1 | ||
Root | \(-0.766044 + 0.642788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 228.101 |
Dual form | 228.3.s.a.149.1 |
$q$-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 \(\left(\mathbb{Z}/228\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) | \(115\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{9}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 2.81908 | + | 1.02606i | 0.939693 | + | 0.342020i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.30928 | − | 5.73184i | 0.472754 | − | 0.818834i | −0.526760 | − | 0.850014i | \(-0.676593\pi\) |
0.999514 | + | 0.0311803i | \(0.00992661\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.89440 | + | 5.78509i | 0.766044 | + | 0.642788i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.4128 | − | 5.97378i | 1.26252 | − | 0.459521i | 0.377909 | − | 0.925843i | \(-0.376643\pi\) |
0.884615 | + | 0.466321i | \(0.154421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.50000 | + | 18.1865i | 0.289474 | + | 0.957186i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 15.2103 | − | 12.7630i | 0.724301 | − | 0.607761i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.4923 | + | 8.55050i | −0.939693 | + | 0.342020i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.5000 | + | 23.3827i | 0.500000 | + | 0.866025i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.25893 | − | 7.37669i | 0.137385 | − | 0.237958i | −0.789121 | − | 0.614238i | \(-0.789464\pi\) |
0.926506 | + | 0.376280i | \(0.122797\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −24.6165 | −0.665310 | −0.332655 | − | 0.943049i | \(-0.607944\pi\) | ||||
−0.332655 | + | 0.943049i | \(0.607944\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 52.3985 | 1.34355 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.2063 | − | 69.2254i | −0.283868 | − | 1.60989i | −0.709302 | − | 0.704904i | \(-0.750990\pi\) |
0.425435 | − | 0.904989i | \(-0.360121\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.59736 | + | 4.49876i | 0.0530074 | + | 0.0918115i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.15555 | + | 56.9126i | −0.0553606 | + | 0.998466i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.3557 | + | 81.4153i | −0.235340 | + | 1.33468i | 0.606557 | + | 0.795040i | \(0.292550\pi\) |
−0.841897 | + | 0.539638i | \(0.818561\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 55.9747 | − | 20.3731i | 0.888487 | − | 0.323383i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −102.343 | − | 85.8759i | −1.52751 | − | 1.28173i | −0.813433 | − | 0.581659i | \(-0.802404\pi\) |
−0.714073 | − | 0.700071i | \(-0.753152\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −120.723 | − | 43.9397i | −1.65375 | − | 0.601914i | −0.664384 | − | 0.747392i | \(-0.731306\pi\) |
−0.989362 | + | 0.145478i | \(0.953528\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.0000 | −1.00000 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −103.122 | − | 37.5335i | −1.30535 | − | 0.475107i | −0.406612 | − | 0.913601i | \(-0.633290\pi\) |
−0.898734 | + | 0.438494i | \(0.855512\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 14.0655 | + | 79.7694i | 0.173648 | + | 0.984808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.0739 | − | 113.844i | 0.220592 | − | 1.25104i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.5752 | − | 16.4255i | 0.210486 | − | 0.176619i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −129.462 | + | 108.631i | −1.33465 | + | 1.11991i | −0.351690 | + | 0.936117i | \(0.614393\pi\) |
−0.982965 | + | 0.183792i | \(0.941163\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.2709 | + | 29.9140i | 0.167678 | + | 0.290427i | 0.937603 | − | 0.347707i | \(-0.113040\pi\) |
−0.769925 | + | 0.638135i | \(0.779706\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.3290 | + | 69.9214i | 0.113110 | + | 0.641480i | 0.987668 | + | 0.156560i | \(0.0500404\pi\) |
−0.874558 | + | 0.484921i | \(0.838849\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −69.3958 | − | 25.2580i | −0.625187 | − | 0.227549i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 147.715 | + | 53.7640i | 1.26252 | + | 0.459521i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −60.5000 | + | 104.789i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 237.742 | − | 86.5311i | 1.87199 | − | 0.681347i | 0.905674 | − | 0.423976i | \(-0.139366\pi\) |
0.966313 | − | 0.257371i | \(-0.0828564\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 36.6189 | − | 207.676i | 0.283868 | − | 1.60989i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 122.443 | + | 28.6592i | 0.920626 | + | 0.215483i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 260.049 | − | 94.6500i | 1.87085 | − | 0.680936i | 0.902878 | − | 0.429898i | \(-0.141450\pi\) |
0.967977 | − | 0.251038i | \(-0.0807719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.70616 | + | 15.3474i | 0.0184093 | + | 0.104404i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 227.000 | 1.50331 | 0.751656 | − | 0.659556i | \(-0.229256\pi\) | ||||
0.751656 | + | 0.659556i | \(0.229256\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.5367 | + | 207.210i | 0.232718 | + | 1.31981i | 0.847367 | + | 0.531007i | \(0.178186\pi\) |
−0.614650 | + | 0.788800i | \(0.710703\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −72.7734 | − | 126.047i | −0.446462 | − | 0.773295i | 0.551690 | − | 0.834049i | \(-0.313983\pi\) |
−0.998153 | + | 0.0607535i | \(0.980650\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 104.233 | − | 87.4619i | 0.616764 | − | 0.517526i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −67.2915 | + | 157.203i | −0.393518 | + | 0.919317i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −28.7325 | + | 162.950i | −0.164186 | + | 0.931144i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −239.772 | − | 201.193i | −1.32471 | − | 1.11156i | −0.985284 | − | 0.170927i | \(-0.945324\pi\) |
−0.339423 | − | 0.940634i | \(-0.610232\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −124.007 | + | 214.786i | −0.677634 | + | 1.17370i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 178.701 | 0.945508 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 308.460 | + | 112.270i | 1.59824 | + | 0.581710i | 0.979065 | − | 0.203546i | \(-0.0652466\pi\) |
0.619171 | + | 0.785256i | \(0.287469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 178.753 | + | 149.992i | 0.898259 | + | 0.753728i | 0.969849 | − | 0.243706i | \(-0.0783631\pi\) |
−0.0715907 | + | 0.997434i | \(0.522808\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −200.399 | − | 347.101i | −0.997009 | − | 1.72687i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −288.455 | + | 242.043i | −1.36709 | + | 1.14712i | −0.393365 | + | 0.919382i | \(0.628689\pi\) |
−0.973722 | + | 0.227740i | \(0.926866\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −28.1880 | − | 48.8230i | −0.129899 | − | 0.224991i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −295.244 | − | 247.739i | −1.34815 | − | 1.13123i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −37.8715 | − | 214.780i | −0.169828 | − | 0.963140i | −0.943946 | − | 0.330099i | \(-0.892918\pi\) |
0.774119 | − | 0.633041i | \(-0.218193\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −211.431 | − | 76.9545i | −0.939693 | − | 0.342020i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 313.839 | 1.37048 | 0.685238 | − | 0.728319i | \(-0.259698\pi\) | ||||
0.685238 | + | 0.728319i | \(0.259698\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −252.198 | − | 211.620i | −1.06413 | − | 0.892909i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −127.850 | + | 46.5337i | −0.530499 | + | 0.193086i | −0.593361 | − | 0.804936i | \(-0.702199\pi\) |
0.0628623 | + | 0.998022i | \(0.479977\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −42.1965 | + | 239.308i | −0.173648 | + | 0.984808i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 198.913 | + | 265.636i | 0.805315 | + | 1.07545i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −81.4628 | + | 141.098i | −0.314528 | + | 0.544779i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 51.9208 | + | 294.458i | 0.191590 | + | 1.08656i | 0.917192 | + | 0.398445i | \(0.130450\pi\) |
−0.725603 | + | 0.688114i | \(0.758439\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 173.401 | − | 300.339i | 0.635169 | − | 1.10014i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −203.500 | − | 352.472i | −0.734657 | − | 1.27246i | −0.954874 | − | 0.297012i | \(-0.904010\pi\) |
0.220217 | − | 0.975451i | \(-0.429324\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 72.0376 | − | 26.2195i | 0.258199 | − | 0.0939768i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 45.1966 | − | 37.9245i | 0.159705 | − | 0.134009i | −0.559433 | − | 0.828876i | \(-0.688981\pi\) |
0.719138 | + | 0.694867i | \(0.244537\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 50.1843 | − | 284.609i | 0.173648 | − | 0.984808i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −476.424 | + | 173.404i | −1.63720 | + | 0.595891i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −437.183 | − | 159.122i | −1.45243 | − | 0.528643i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −574.152 | − | 208.974i | −1.87020 | − | 0.680698i | −0.968870 | − | 0.247571i | \(-0.920368\pi\) |
−0.901333 | − | 0.433127i | \(-0.857410\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.9943 | + | 102.051i | 0.0582341 | + | 0.330262i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 458.861 | + | 385.030i | 1.46601 | + | 1.23013i | 0.919747 | + | 0.392513i | \(0.128394\pi\) |
0.546262 | + | 0.837615i | \(0.316050\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −334.496 | + | 280.676i | −1.02922 | + | 0.863618i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −36.9871 | + | 209.764i | −0.113110 | + | 0.641480i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −316.789 | − | 548.694i | −0.957065 | − | 1.65769i | −0.729570 | − | 0.683906i | \(-0.760280\pi\) |
−0.227495 | − | 0.973779i | \(-0.573054\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −169.716 | − | 142.408i | −0.509657 | − | 0.427653i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 95.1000 | + | 539.339i | 0.282196 | + | 1.60041i | 0.715134 | + | 0.698988i | \(0.246366\pi\) |
−0.432938 | + | 0.901424i | \(0.642523\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 358.691 | 1.04575 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 348.145 | − | 603.005i | 0.997550 | − | 1.72781i | 0.438187 | − | 0.898884i | \(-0.355621\pi\) |
0.559362 | − | 0.828923i | \(-0.311046\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 361.256 | + | 303.130i | 1.02922 | + | 0.863618i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −300.500 | + | 200.052i | −0.832410 | + | 0.554160i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −278.074 | + | 233.332i | −0.766044 | + | 0.642788i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 608.915 | − | 221.627i | 1.65917 | − | 0.603888i | 0.668937 | − | 0.743319i | \(-0.266749\pi\) |
0.990232 | + | 0.139431i | \(0.0445272\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −349.000 | + | 604.486i | −0.935657 | + | 1.62061i | −0.162198 | + | 0.986758i | \(0.551858\pi\) |
−0.773458 | + | 0.633847i | \(0.781475\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 179.698 | 0.474137 | 0.237068 | − | 0.971493i | \(-0.423813\pi\) | ||||
0.237068 | + | 0.971493i | \(0.423813\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 759.000 | 1.99213 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 316.320 | − | 547.882i | 0.817364 | − | 1.41572i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 581.276 | − | 487.748i | 1.46417 | − | 1.22858i | 0.542821 | − | 0.839848i | \(-0.317356\pi\) |
0.921349 | − | 0.388736i | \(-0.127088\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 315.771 | + | 206.427i | 0.791406 | + | 0.517360i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.8344 | − | 146.514i | 0.0641052 | − | 0.363559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 479.544 | + | 402.385i | 1.17248 | + | 0.983827i | 0.999999 | − | 0.00118660i | \(-0.000377706\pi\) |
0.172479 | + | 0.985013i | \(0.444822\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 830.215 | 1.99092 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −788.402 | − | 286.955i | −1.87269 | − | 0.681603i | −0.965190 | − | 0.261548i | \(-0.915767\pi\) |
−0.907499 | − | 0.420055i | \(-0.862011\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 419.152 | + | 351.711i | 0.981622 | + | 0.823678i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 135.720 | − | 769.706i | 0.313441 | − | 1.77761i | −0.267390 | − | 0.963588i | \(-0.586161\pi\) |
0.580831 | − | 0.814024i | \(-0.302728\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −671.066 | + | 563.091i | −1.52862 | + | 1.28267i | −0.721107 | + | 0.692824i | \(0.756366\pi\) |
−0.807517 | + | 0.589844i | \(0.799189\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.11849 | + | 46.0422i | −0.0184093 | + | 0.104404i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 639.931 | + | 232.916i | 1.41265 | + | 0.514163i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 622.735 | 1.36266 | 0.681329 | − | 0.731977i | \(-0.261402\pi\) | ||||
0.681329 | + | 0.731977i | \(0.261402\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 420.932 | − | 729.075i | 0.909140 | − | 1.57468i | 0.0938775 | − | 0.995584i | \(-0.470074\pi\) |
0.815262 | − | 0.579092i | \(-0.196593\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −830.908 | + | 302.426i | −1.77166 | + | 0.644831i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −109.610 | + | 621.629i | −0.232718 | + | 1.31981i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −284.712 | − | 380.216i | −0.599393 | − | 0.800455i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −404.026 | + | 147.053i | −0.839970 | + | 0.305724i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 174.500 | − | 302.243i | 0.358316 | − | 0.620622i | −0.629363 | − | 0.777111i | \(-0.716684\pi\) |
0.987680 | + | 0.156489i | \(0.0500176\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −75.8218 | − | 430.007i | −0.155055 | − | 0.879359i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 171.394 | + | 972.024i | 0.343475 | + | 1.94794i | 0.317423 | + | 0.948284i | \(0.397182\pi\) |
0.0260521 | + | 0.999661i | \(0.491706\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 383.582 | − | 139.613i | 0.756573 | − | 0.275370i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −651.363 | + | 546.558i | −1.27468 | + | 1.06959i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −351.000 | + | 374.123i | −0.684211 | + | 0.729285i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −753.658 | − | 632.394i | −1.44103 | − | 1.20917i | −0.938815 | − | 0.344423i | \(-0.888075\pi\) |
−0.502214 | − | 0.864743i | \(-0.667481\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −248.196 | + | 429.888i | −0.472754 | + | 0.818834i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −497.097 | − | 180.929i | −0.939693 | − | 0.342020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −827.821 | − | 694.624i | −1.53017 | − | 1.28396i | −0.797265 | − | 0.603629i | \(-0.793721\pi\) |
−0.732902 | − | 0.680334i | \(-0.761835\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −469.500 | − | 813.198i | −0.864641 | − | 1.49760i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.9606 | + | 141.559i | −0.0456319 | + | 0.258791i | −0.999086 | − | 0.0427471i | \(-0.986389\pi\) |
0.953454 | + | 0.301538i | \(0.0975001\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −569.969 | + | 478.261i | −1.03820 | + | 0.871149i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −556.396 | + | 466.872i | −1.00614 | + | 0.844253i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −613.877 | − | 1063.27i | −1.09817 | − | 1.90209i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 503.772 | + | 183.358i | 0.888487 | + | 0.323383i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −215.566 | −0.377523 | −0.188761 | − | 0.982023i | \(-0.560447\pi\) | ||||
−0.188761 | + | 0.982023i | \(0.560447\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 516.500 | − | 894.604i | 0.895147 | − | 1.55044i | 0.0615251 | − | 0.998106i | \(-0.480404\pi\) |
0.833622 | − | 0.552335i | \(-0.186263\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 754.376 | + | 632.996i | 1.30289 | + | 1.09326i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 157.581 | + | 36.8834i | 0.267539 | + | 0.0626204i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 350.019 | + | 606.251i | 0.586297 | + | 1.01550i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −486.520 | + | 842.678i | −0.809518 | + | 1.40213i | 0.103680 | + | 0.994611i | \(0.466938\pi\) |
−0.913198 | + | 0.407516i | \(0.866395\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −208.793 | − | 1184.13i | −0.346258 | − | 1.96372i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1072.96 | 1.76764 | 0.883819 | − | 0.467830i | \(-0.154964\pi\) | ||||
0.883819 | + | 0.467830i | \(0.154964\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 170.696 | + | 968.066i | 0.278460 | + | 1.57923i | 0.727751 | + | 0.685841i | \(0.240566\pi\) |
−0.449291 | + | 0.893386i | \(0.648323\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −309.071 | − | 535.326i | −0.499306 | − | 0.864824i | 0.500693 | − | 0.865625i | \(-0.333078\pi\) |
−1.00000 | 0.000800838i | \(0.999745\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 478.778 | − | 401.742i | 0.766044 | − | 0.642788i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.4341 | + | 166.929i | −0.0466467 | + | 0.264546i | −0.999208 | − | 0.0398015i | \(-0.987327\pi\) |
0.952561 | + | 0.304348i | \(0.0984386\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1061.53 | + | 386.365i | −1.67698 | + | 0.610371i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 69.5047 | + | 58.3213i | 0.109112 | + | 0.0915562i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −123.534 | − | 44.9626i | −0.192121 | − | 0.0699263i | 0.244168 | − | 0.969733i | \(-0.421485\pi\) |
−0.436289 | + | 0.899807i | \(0.643707\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.3687 | − | 166.558i | −0.0451133 | − | 0.255850i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −578.120 | − | 1001.33i | −0.879939 | − | 1.52410i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.1851 | − | 120.147i | 0.0320500 | − | 0.181765i | −0.964580 | − | 0.263790i | \(-0.915028\pi\) |
0.996630 | + | 0.0820248i | \(0.0261387\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 113.615 | − | 644.341i | 0.169828 | − | 0.963140i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 423.723 | + | 733.910i | 0.629604 | + | 1.09051i | 0.987631 | + | 0.156795i | \(0.0501161\pi\) |
−0.358027 | + | 0.933711i | \(0.616551\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −517.080 | − | 433.882i | −0.766044 | − | 0.642788i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 194.232 | + | 1101.54i | 0.286056 | + | 1.62230i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 884.737 | + | 322.018i | 1.28783 | + | 0.468731i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −509.500 | + | 882.480i | −0.737337 | + | 1.27711i | 0.216353 | + | 0.976315i | \(0.430584\pi\) |
−0.953690 | + | 0.300790i | \(0.902750\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −135.391 | − | 447.688i | −0.192590 | − | 0.636826i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1139.77 | − | 414.844i | 1.60758 | − | 0.585111i | 0.626620 | − | 0.779325i | \(-0.284438\pi\) |
0.980959 | + | 0.194214i | \(0.0622158\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −493.832 | − | 855.343i | −0.694560 | − | 1.20301i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 228.616 | 0.317082 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −408.166 | −0.564545 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −220.055 | − | 1247.99i | −0.302689 | − | 1.71663i | −0.634188 | − | 0.773179i | \(-0.718666\pi\) |
0.331499 | − | 0.943455i | \(-0.392446\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −364.500 | + | 631.333i | −0.500000 | + | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 708.500 | + | 1227.16i | 0.966576 | + | 1.67416i | 0.705321 | + | 0.708888i | \(0.250803\pi\) |
0.261255 | + | 0.965270i | \(0.415864\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1097.48 | − | 920.893i | 1.48508 | − | 1.24613i | 0.584543 | − | 0.811363i | \(-0.301274\pi\) |
0.900541 | − | 0.434771i | \(-0.143171\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 288.192 | + | 952.947i | 0.388923 | + | 1.28603i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 839.361 | + | 704.308i | 1.11766 | + | 0.937827i | 0.998484 | − | 0.0550467i | \(-0.0175308\pi\) |
0.119174 | + | 0.992873i | \(0.461975\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −158.401 | − | 57.6533i | −0.209248 | − | 0.0761602i | 0.235269 | − | 0.971930i | \(-0.424403\pi\) |
−0.444518 | + | 0.895770i | \(0.646625\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 441.578 | + | 160.721i | 0.578739 | + | 0.210644i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −120.429 | − | 101.052i | −0.156605 | − | 0.131407i | 0.561118 | − | 0.827736i | \(-0.310371\pi\) |
−0.717723 | + | 0.696328i | \(0.754816\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.9778 | + | 209.711i | −0.0477133 | + | 0.270595i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −374.425 | + | 314.180i | −0.481885 | + | 0.404349i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −231.141 | − | 400.347i | −0.293698 | − | 0.508700i | 0.680983 | − | 0.732299i | \(-0.261553\pi\) |
−0.974681 | + | 0.223599i | \(0.928219\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 250.739 | + | 1422.01i | 0.316191 | + | 1.79321i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 237.742 | − | 86.5311i | 0.293147 | − | 0.106697i | −0.191260 | − | 0.981539i | \(-0.561257\pi\) |
0.484407 | + | 0.874843i | \(0.339035\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −155.762 | + | 883.373i | −0.191590 | + | 1.08656i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1191.84 | − | 602.730i | 1.45880 | − | 0.737736i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 796.998 | − | 668.760i | 0.973135 | − | 0.816557i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1523.24 | − | 554.415i | 1.85084 | − | 0.673651i | 0.866037 | − | 0.499980i | \(-0.166659\pi\) |
0.984804 | − | 0.173670i | \(-0.0555627\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 487.692 | − | 844.707i | 0.588289 | − | 1.01895i | −0.406167 | − | 0.913799i | \(-0.633135\pi\) |
0.994457 | − | 0.105148i | \(-0.0335317\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −212.024 | − | 1202.45i | −0.255144 | − | 1.44699i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 229.982 | 0.274770 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 146.038 | + | 828.223i | 0.173648 | + | 0.984808i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 400.423 | + | 693.552i | 0.472754 | + | 0.818834i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 166.326 | − | 60.5376i | 0.195908 | − | 0.0713046i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1170.82 | − | 982.434i | 1.37259 | − | 1.15174i | 0.400727 | − | 0.916198i | \(-0.368758\pi\) |
0.971864 | − | 0.235543i | \(-0.0756867\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −173.777 | + | 985.539i | −0.202302 | + | 1.14731i | 0.699328 | + | 0.714801i | \(0.253483\pi\) |
−0.901630 | + | 0.432509i | \(0.857629\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 433.500 | − | 750.844i | 0.500000 | − | 0.866025i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2192.74 | − | 798.092i | −2.51750 | − | 0.916294i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1521.00 | −1.74227 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.90293 | + | 0.692610i | 0.00216982 | + | 0.000789750i | 0.343105 | − | 0.939297i | \(-0.388521\pi\) |
−0.340935 | + | 0.940087i | \(0.610744\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1348.61 | + | 1131.62i | 1.52731 | + | 1.28156i | 0.814397 | + | 0.580308i | \(0.197068\pi\) |
0.712911 | + | 0.701255i | \(0.247377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 290.773 | − | 1649.06i | 0.327079 | − | 1.85496i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1069.18 | − | 897.152i | −1.18404 | − | 0.993524i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 289.472 | + | 1641.67i | 0.319153 | + | 1.81000i | 0.547928 | + | 0.836526i | \(0.315417\pi\) |
−0.228775 | + | 0.973479i | \(0.573472\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −852.741 | + | 1476.99i | −0.927901 | + | 1.60717i | −0.141072 | + | 0.989999i | \(0.545055\pi\) |
−0.786828 | + | 0.617172i | \(0.788278\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1404.16 | − | 1178.23i | −1.52460 | − | 1.27929i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 578.298 | − | 210.483i | 0.625187 | − | 0.227549i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −53.9830 | + | 306.153i | −0.0582341 | + | 0.330262i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −67.5314 | + | 71.9802i | −0.0725364 | + | 0.0773150i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −594.711 | + | 216.457i | −0.634697 | + | 0.231011i | −0.639274 | − | 0.768979i | \(-0.720765\pi\) |
0.00457754 | + | 0.999990i | \(0.498543\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 898.500 | + | 1556.25i | 0.956869 | + | 1.65735i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2243.90 | −2.36449 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 444.223 | + | 769.417i | 0.462251 | + | 0.800642i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1480.14 | + | 1241.98i | −1.53065 | + | 1.28437i | −0.737475 | + | 0.675374i | \(0.763982\pi\) |
−0.793175 | + | 0.608994i | \(0.791573\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 318.055 | − | 1803.78i | 0.326881 | − | 1.85383i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1230.96 | + | 448.033i | −1.26252 | + | 0.459521i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −319.500 | + | 553.390i | −0.325688 | + | 0.564108i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1826.18 | − | 664.674i | −1.84276 | − | 0.670710i | −0.988573 | − | 0.150745i | \(-0.951833\pi\) |
−0.854188 | − | 0.519965i | \(-0.825945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −330.059 | − | 1871.86i | −0.332385 | − | 1.88505i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1418.48 | − | 1190.24i | −1.42275 | − | 1.19383i | −0.949850 | − | 0.312707i | \(-0.898764\pi\) |
−0.472896 | − | 0.881118i | \(-0.656791\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −332.322 | − | 575.599i | −0.332655 | − | 0.576176i |
(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 | 228.3.s.a.101.1 | ✓ | 6 | |
3.2 | odd | 2 | CM | 228.3.s.a.101.1 | ✓ | 6 | |
19.16 | even | 9 | inner | 228.3.s.a.149.1 | yes | 6 | |
57.35 | odd | 18 | inner | 228.3.s.a.149.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.3.s.a.101.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
228.3.s.a.101.1 | ✓ | 6 | 3.2 | odd | 2 | CM | |
228.3.s.a.149.1 | yes | 6 | 19.16 | even | 9 | inner | |
228.3.s.a.149.1 | yes | 6 | 57.35 | odd | 18 | inner |