Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,4,Mod(1133,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.1133");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.f (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: | \(133.816331893\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1133.6 | ||
Character | \(\chi\) | \(=\) | 2268.1133 |
Dual form | 2268.4.f.a.1133.5 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −16.5975 | −1.48452 | −0.742262 | − | 0.670110i | \(-0.766247\pi\) | ||||
−0.742262 | + | 0.670110i | \(0.766247\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.9446 | + | 14.1537i | −0.644948 | + | 0.764227i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 53.4353i | 1.46467i | 0.680945 | + | 0.732334i | \(0.261569\pi\) | ||||
−0.680945 | + | 0.732334i | \(0.738431\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 12.7565i | − | 0.272155i | −0.990698 | − | 0.136077i | \(-0.956550\pi\) | ||
0.990698 | − | 0.136077i | \(-0.0434496\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 96.7463 | 1.38026 | 0.690130 | − | 0.723686i | \(-0.257553\pi\) | ||||
0.690130 | + | 0.723686i | \(0.257553\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 54.6996i | 0.660471i | 0.943899 | + | 0.330235i | \(0.107128\pi\) | ||||
−0.943899 | + | 0.330235i | \(0.892872\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 64.2853i | 0.582800i | 0.956601 | + | 0.291400i | \(0.0941211\pi\) | ||||
−0.956601 | + | 0.291400i | \(0.905879\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 150.476 | 1.20381 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 130.148i | − | 0.833375i | −0.909050 | − | 0.416688i | \(-0.863191\pi\) | ||
0.909050 | − | 0.416688i | \(-0.136809\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 220.107i | 1.27524i | 0.770353 | + | 0.637618i | \(0.220080\pi\) | ||||
−0.770353 | + | 0.637618i | \(0.779920\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 198.250 | − | 234.915i | 0.957440 | − | 1.13451i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 279.735 | 1.24292 | 0.621462 | − | 0.783445i | \(-0.286539\pi\) | ||||
0.621462 | + | 0.783445i | \(0.286539\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −370.617 | −1.41172 | −0.705861 | − | 0.708351i | \(-0.749440\pi\) | ||||
−0.705861 | + | 0.708351i | \(0.749440\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 307.751 | 1.09143 | 0.545717 | − | 0.837970i | \(-0.316258\pi\) | ||||
0.545717 | + | 0.837970i | \(0.316258\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 327.365 | 1.01598 | 0.507990 | − | 0.861363i | \(-0.330389\pi\) | ||||
0.507990 | + | 0.861363i | \(0.330389\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −57.6532 | − | 338.120i | −0.168085 | − | 0.985772i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 451.749i | 1.17080i | 0.810744 | + | 0.585401i | \(0.199063\pi\) | ||||
−0.810744 | + | 0.585401i | \(0.800937\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 886.892i | − | 2.17434i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 517.477 | 1.14186 | 0.570930 | − | 0.820998i | \(-0.306583\pi\) | ||||
0.570930 | + | 0.820998i | \(0.306583\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 270.790i | − | 0.568378i | −0.958768 | − | 0.284189i | \(-0.908276\pi\) | ||
0.958768 | − | 0.284189i | \(-0.0917243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 211.725i | 0.404020i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 741.763 | 1.35255 | 0.676274 | − | 0.736650i | \(-0.263594\pi\) | ||||
0.676274 | + | 0.736650i | \(0.263594\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 914.198i | 1.52810i | 0.645155 | + | 0.764051i | \(0.276793\pi\) | ||||
−0.645155 | + | 0.764051i | \(0.723207\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 337.210i | − | 0.540650i | −0.962769 | − | 0.270325i | \(-0.912869\pi\) | ||
0.962769 | − | 0.270325i | \(-0.0871311\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −756.306 | − | 638.264i | −1.11934 | − | 0.944635i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 997.165 | 1.42012 | 0.710062 | − | 0.704139i | \(-0.248667\pi\) | ||||
0.710062 | + | 0.704139i | \(0.248667\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 34.0541 | 0.0450352 | 0.0225176 | − | 0.999746i | \(-0.492832\pi\) | ||||
0.0225176 | + | 0.999746i | \(0.492832\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1605.74 | −2.04903 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 208.953 | 0.248865 | 0.124433 | − | 0.992228i | \(-0.460289\pi\) | ||||
0.124433 | + | 0.992228i | \(0.460289\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 180.551 | + | 152.371i | 0.207988 | + | 0.175526i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 907.875i | − | 0.980484i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1271.26i | − | 1.33069i | −0.746536 | − | 0.665345i | \(-0.768285\pi\) | ||
0.746536 | − | 0.665345i | \(-0.231715\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −614.247 | −0.605148 | −0.302574 | − | 0.953126i | \(-0.597846\pi\) | ||||
−0.302574 | + | 0.953126i | \(0.597846\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1043.17i | 0.997926i | 0.866623 | + | 0.498963i | \(0.166286\pi\) | ||||
−0.866623 | + | 0.498963i | \(0.833714\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1128.83i | 1.01989i | 0.860207 | + | 0.509945i | \(0.170334\pi\) | ||||
−0.860207 | + | 0.509945i | \(0.829666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1555.72 | 1.36707 | 0.683535 | − | 0.729918i | \(-0.260442\pi\) | ||||
0.683535 | + | 0.729918i | \(0.260442\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 258.461i | − | 0.215168i | −0.994196 | − | 0.107584i | \(-0.965689\pi\) | ||
0.994196 | − | 0.107584i | \(-0.0343115\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1066.97i | − | 0.865180i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1155.60 | + | 1369.32i | −0.890195 | + | 1.05483i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1524.33 | −1.14526 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −422.841 | −0.302560 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −586.759 | −0.409972 | −0.204986 | − | 0.978765i | \(-0.565715\pi\) | ||||
−0.204986 | + | 0.978765i | \(0.565715\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2264.86 | −1.51055 | −0.755275 | − | 0.655408i | \(-0.772497\pi\) | ||||
−0.755275 | + | 0.655408i | \(0.772497\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −774.200 | − | 653.364i | −0.504749 | − | 0.425969i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1910.69i | 1.19154i | 0.803154 | + | 0.595772i | \(0.203154\pi\) | ||||
−0.803154 | + | 0.595772i | \(0.796846\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1697.17i | 1.03563i | 0.855494 | + | 0.517813i | \(0.173254\pi\) | ||||
−0.855494 | + | 0.517813i | \(0.826746\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 681.647 | 0.398617 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2160.13i | 1.23717i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 161.997i | 0.0890695i | 0.999008 | + | 0.0445347i | \(0.0141805\pi\) | ||||
−0.999008 | + | 0.0445347i | \(0.985819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3072.80 | −1.65603 | −0.828017 | − | 0.560703i | \(-0.810531\pi\) | ||||
−0.828017 | + | 0.560703i | \(0.810531\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3653.21i | − | 1.89312i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1013.64i | − | 0.515271i | −0.966242 | − | 0.257636i | \(-0.917057\pi\) | ||
0.966242 | − | 0.257636i | \(-0.0829434\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −909.873 | − | 767.862i | −0.445391 | − | 0.375876i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1297.23 | 0.623356 | 0.311678 | − | 0.950188i | \(-0.399109\pi\) | ||||
0.311678 | + | 0.950188i | \(0.399109\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1432.47 | −0.663758 | −0.331879 | − | 0.943322i | \(-0.607683\pi\) | ||||
−0.331879 | + | 0.943322i | \(0.607683\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2034.27 | 0.925932 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1975.32 | −0.868096 | −0.434048 | − | 0.900890i | \(-0.642915\pi\) | ||||
−0.434048 | + | 0.900890i | \(0.642915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1797.38 | + | 2129.79i | −0.776394 | + | 0.919984i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2310.07i | 0.964595i | 0.876007 | + | 0.482298i | \(0.160198\pi\) | ||||
−0.876007 | + | 0.482298i | \(0.839802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 423.545i | − | 0.173933i | −0.996211 | − | 0.0869665i | \(-0.972283\pi\) | ||
0.996211 | − | 0.0869665i | \(-0.0277173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4642.90 | −1.84515 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5169.67i | 2.02162i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2344.54i | 0.888192i | 0.895979 | + | 0.444096i | \(0.146475\pi\) | ||||
−0.895979 | + | 0.444096i | \(0.853525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4050.71 | 1.51076 | 0.755380 | − | 0.655287i | \(-0.227452\pi\) | ||||
0.755380 | + | 0.655287i | \(0.227452\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3659.21i | 1.32339i | 0.749773 | + | 0.661695i | \(0.230163\pi\) | ||||
−0.749773 | + | 0.661695i | \(0.769837\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 557.050i | − | 0.198433i | −0.995066 | − | 0.0992166i | \(-0.968366\pi\) | ||
0.995066 | − | 0.0992166i | \(-0.0316337\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1842.07 | + | 1554.57i | 0.636888 | + | 0.537483i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6151.30 | 2.09573 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2922.89 | −0.967371 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4390.07 | −1.43235 | −0.716173 | − | 0.697923i | \(-0.754108\pi\) | ||||
−0.716173 | + | 0.697923i | \(0.754108\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5107.89 | −1.62026 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3115.32 | − | 2629.08i | −0.974569 | − | 0.822460i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1234.14i | − | 0.375644i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2507.72i | 0.753047i | 0.926407 | + | 0.376523i | \(0.122881\pi\) | ||||
−0.926407 | + | 0.376523i | \(0.877119\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2689.69 | 0.786435 | 0.393218 | − | 0.919445i | \(-0.371362\pi\) | ||||
0.393218 | + | 0.919445i | \(0.371362\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4113.08i | 1.18690i | 0.804871 | + | 0.593449i | \(0.202234\pi\) | ||||
−0.804871 | + | 0.593449i | \(0.797766\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 2621.07i | − | 0.736960i | −0.929636 | − | 0.368480i | \(-0.879878\pi\) | ||
0.929636 | − | 0.368480i | \(-0.120122\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5433.43 | −1.50825 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5133.90i | 1.38948i | 0.719263 | + | 0.694738i | \(0.244480\pi\) | ||||
−0.719263 | + | 0.694738i | \(0.755520\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 656.905i | − | 0.175581i | −0.996139 | − | 0.0877903i | \(-0.972019\pi\) | ||
0.996139 | − | 0.0877903i | \(-0.0279806\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 956.897 | + | 5611.94i | 0.249526 | + | 1.46340i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 697.774 | 0.179750 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1807.27 | 0.454479 | 0.227239 | − | 0.973839i | \(-0.427030\pi\) | ||||
0.227239 | + | 0.973839i | \(0.427030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3435.10 | −0.853609 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2089.43 | 0.507140 | 0.253570 | − | 0.967317i | \(-0.418395\pi\) | ||||
0.253570 | + | 0.967317i | \(0.418395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3341.32 | + | 3959.28i | −0.801620 | + | 0.949875i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4872.09i | − | 1.14230i | −0.820844 | − | 0.571152i | \(-0.806497\pi\) | ||
0.820844 | − | 0.571152i | \(-0.193503\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 7497.90i | − | 1.73808i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4640.31 | −1.05176 | −0.525882 | − | 0.850557i | \(-0.676265\pi\) | ||||
−0.525882 | + | 0.850557i | \(0.676265\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5685.82i | 1.27450i | 0.770658 | + | 0.637249i | \(0.219928\pi\) | ||||
−0.770658 | + | 0.637249i | \(0.780072\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8040.75i | 1.76318i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5015.19 | −1.08785 | −0.543923 | − | 0.839135i | \(-0.683062\pi\) | ||||
−0.543923 | + | 0.839135i | \(0.683062\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5105.90i | 1.08396i | 0.840392 | + | 0.541979i | \(0.182325\pi\) | ||||
−0.840392 | + | 0.541979i | \(0.817675\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 6350.15i | − | 1.33384i | −0.745129 | − | 0.666921i | \(-0.767612\pi\) | ||
0.745129 | − | 0.666921i | \(-0.232388\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4426.87 | − | 5245.59i | 0.910486 | − | 1.07888i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4446.84 | 0.905117 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1524.59 | −0.303986 | −0.151993 | − | 0.988382i | \(-0.548569\pi\) | ||||
−0.151993 | + | 0.988382i | \(0.548569\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8588.81 | −1.69512 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 820.054 | 0.158612 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3675.96 | + | 4355.81i | −0.703917 | + | 0.834102i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4494.43i | 0.843771i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 633.080i | − | 0.117693i | −0.998267 | − | 0.0588466i | \(-0.981258\pi\) | ||
0.998267 | − | 0.0588466i | \(-0.0187423\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4444.71 | 0.810407 | 0.405204 | − | 0.914226i | \(-0.367201\pi\) | ||||
0.405204 | + | 0.914226i | \(0.367201\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10268.7i | − | 1.85438i | −0.374593 | − | 0.927189i | \(-0.622218\pi\) | ||
0.374593 | − | 0.927189i | \(-0.377782\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1877.40i | 0.332635i | 0.986072 | + | 0.166318i | \(0.0531877\pi\) | ||||
−0.986072 | + | 0.166318i | \(0.946812\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6954.50 | 1.22062 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5291.98i | 0.911621i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1919.55i | − | 0.327623i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3910.24 | + | 4633.42i | −0.655254 | + | 0.776440i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3098.06 | −0.514455 | −0.257228 | − | 0.966351i | \(-0.582809\pi\) | ||||
−0.257228 | + | 0.966351i | \(0.582809\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12311.4 | −2.00789 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10890.2 | 1.76032 | 0.880158 | − | 0.474681i | \(-0.157436\pi\) | ||||
0.880158 | + | 0.474681i | \(0.157436\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11761.5 | −1.86780 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5474.29 | + | 3222.70i | 0.861760 | + | 0.507317i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3725.99i | 0.576430i | 0.957566 | + | 0.288215i | \(0.0930619\pi\) | ||||
−0.957566 | + | 0.288215i | \(0.906938\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 611.863i | − | 0.0938460i | −0.998899 | − | 0.0469230i | \(-0.985058\pi\) | ||
0.998899 | − | 0.0469230i | \(-0.0149415\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5184.79 | −0.781752 | −0.390876 | − | 0.920443i | \(-0.627828\pi\) | ||||
−0.390876 | + | 0.920443i | \(0.627828\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 15173.4i | − | 2.26850i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 10228.9i | − | 1.50379i | −0.659280 | − | 0.751897i | \(-0.729139\pi\) | ||
0.659280 | − | 0.751897i | \(-0.270861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3866.96 | 0.563778 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5596.83i | 0.802607i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 9972.52i | − | 1.41842i | −0.704996 | − | 0.709212i | \(-0.749051\pi\) | ||
0.704996 | − | 0.709212i | \(-0.250949\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6393.91 | − | 5395.96i | −0.894759 | − | 0.755106i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8460.91 | 1.17450 | 0.587251 | − | 0.809405i | \(-0.300210\pi\) | ||||
0.587251 | + | 0.809405i | \(0.300210\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1660.23 | −0.226807 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.71044 | −0.000231819 | −0.000115910 | − | 1.00000i | \(-0.500037\pi\) | ||||
−0.000115910 | 1.00000i | \(0.500037\pi\) | ||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2556.55 | 0.341080 | 0.170540 | − | 0.985351i | \(-0.445449\pi\) | ||||
0.170540 | + | 0.985351i | \(0.445449\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12552.8 | + | 10593.6i | 1.66169 | + | 1.40233i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2380.29i | 0.310245i | 0.987895 | + | 0.155123i | \(0.0495773\pi\) | ||||
−0.987895 | + | 0.155123i | \(0.950423\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6219.36i | 0.804415i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16550.4 | −2.10821 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12885.5i | 1.62898i | 0.580177 | + | 0.814491i | \(0.302983\pi\) | ||||
−0.580177 | + | 0.814491i | \(0.697017\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 7376.69i | − | 0.918640i | −0.888271 | − | 0.459320i | \(-0.848093\pi\) | ||
0.888271 | − | 0.459320i | \(-0.151907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2807.79 | 0.347061 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14947.7i | 1.82047i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6777.29i | − | 0.819353i | −0.912231 | − | 0.409676i | \(-0.865642\pi\) | ||
0.912231 | − | 0.409676i | \(-0.134358\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6181.06 | + | 7324.20i | −0.736440 | + | 0.872641i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −565.212 | −0.0668558 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5415.30 | 0.631395 | 0.315698 | − | 0.948860i | \(-0.397761\pi\) | ||||
0.315698 | + | 0.948860i | \(0.397761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 818.272 | 0.0947271 | 0.0473636 | − | 0.998878i | \(-0.484918\pi\) | ||||
0.0473636 | + | 0.998878i | \(0.484918\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14558.0 | 1.66157 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3832.67 | + | 3234.47i | 0.434370 | + | 0.366574i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10300.0i | 1.15113i | 0.817757 | + | 0.575564i | \(0.195217\pi\) | ||||
−0.817757 | + | 0.575564i | \(0.804783\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 16119.3i | − | 1.78902i | −0.447047 | − | 0.894511i | \(-0.647524\pi\) | ||
0.447047 | − | 0.894511i | \(-0.352476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3516.38 | −0.384922 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9460.41i | 1.02852i | 0.857634 | + | 0.514260i | \(0.171934\pi\) | ||||
−0.857634 | + | 0.514260i | \(0.828066\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3842.11i | 0.412063i | 0.978545 | + | 0.206032i | \(0.0660550\pi\) | ||||
−0.978545 | + | 0.206032i | \(0.933945\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3468.10 | −0.369446 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15663.0i | − | 1.64628i | −0.567837 | − | 0.823141i | \(-0.692220\pi\) | ||
0.567837 | − | 0.823141i | \(-0.307780\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 19804.0i | − | 2.06770i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2996.69 | − | 2528.98i | −0.308763 | − | 0.260572i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4953.18 | 0.507002 | 0.253501 | − | 0.967335i | \(-0.418418\pi\) | ||||
0.253501 | + | 0.967335i | \(0.418418\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3510.43 | 0.354657 | 0.177329 | − | 0.984152i | \(-0.443254\pi\) | ||||
0.177329 | + | 0.984152i | \(0.443254\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14173.5 | 1.42268 | 0.711338 | − | 0.702850i | \(-0.248090\pi\) | ||||
0.711338 | + | 0.702850i | \(0.248090\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1922.47 | −0.190495 | −0.0952474 | − | 0.995454i | \(-0.530364\pi\) | ||||
−0.0952474 | + | 0.995454i | \(0.530364\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8860.05 | + | 10498.7i | −0.872323 | + | 1.03365i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16444.8i | 1.59859i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8230.99i | 0.795081i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17113.0 | −1.63238 | −0.816192 | − | 0.577781i | \(-0.803919\pi\) | ||||
−0.816192 | + | 0.577781i | \(0.803919\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 3568.44i | − | 0.338268i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21099.7i | 1.97544i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3067.21 | 0.285397 | 0.142699 | − | 0.989766i | \(-0.454422\pi\) | ||||
0.142699 | + | 0.989766i | \(0.454422\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8626.73i | − | 0.792910i | −0.918054 | − | 0.396455i | \(-0.870240\pi\) | ||
0.918054 | − | 0.396455i | \(-0.129760\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12591.3i | − | 1.15027i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12939.3 | − | 10919.7i | −1.16782 | − | 0.985546i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12284.4 | −1.10205 | −0.551026 | − | 0.834488i | \(-0.685764\pi\) | ||||
−0.551026 | + | 0.834488i | \(0.685764\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3977.87 | −0.352613 | −0.176307 | − | 0.984335i | \(-0.556415\pi\) | ||||
−0.176307 | + | 0.984335i | \(0.556415\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10195.0 | 0.898356 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16724.6 | −1.45640 | −0.728199 | − | 0.685365i | \(-0.759642\pi\) | ||||
−0.728199 | + | 0.685365i | \(0.759642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4772.76 | + | 4027.84i | 0.413179 | + | 0.348691i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 17313.9i | − | 1.48144i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17492.9i | 1.48808i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9088.77 | 0.764273 | 0.382137 | − | 0.924106i | \(-0.375188\pi\) | ||||
0.382137 | + | 0.924106i | \(0.375188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13218.7i | 1.10519i | 0.833450 | + | 0.552596i | \(0.186363\pi\) | ||||
−0.833450 | + | 0.552596i | \(0.813637\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21294.5i | 1.76016i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8034.41 | 0.660344 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4727.76i | 0.384207i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 18735.7i | − | 1.51405i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18067.6 | − | 3080.72i | 1.44383 | − | 0.246189i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20011.9 | −1.59035 | −0.795174 | − | 0.606382i | \(-0.792620\pi\) | ||||
−0.795174 | + | 0.606382i | \(0.792620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25821.0 | −2.02945 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17451.2 | −1.36409 | −0.682046 | − | 0.731309i | \(-0.738910\pi\) | ||||
−0.682046 | + | 0.731309i | \(0.738910\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7119.04 | 0.550420 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11910.7 | + | 14113.6i | −0.915906 | + | 1.08530i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 15169.7i | − | 1.15397i | −0.816754 | − | 0.576986i | \(-0.804229\pi\) | ||
0.816754 | − | 0.576986i | \(-0.195771\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3925.82i | − | 0.297039i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6977.24 | −0.522301 | −0.261151 | − | 0.965298i | \(-0.584102\pi\) | ||||
−0.261151 | + | 0.965298i | \(0.584102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4289.81i | 0.319422i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20039.6i | 1.47645i | 0.674552 | + | 0.738227i | \(0.264337\pi\) | ||||
−0.674552 | + | 0.738227i | \(0.735663\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16655.4 | −1.22068 | −0.610339 | − | 0.792140i | \(-0.708967\pi\) | ||||
−0.610339 | + | 0.792140i | \(0.708967\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9673.40i | 0.701580i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8678.08i | 0.626123i | 0.949733 | + | 0.313062i | \(0.101355\pi\) | ||||
−0.949733 | + | 0.313062i | \(0.898645\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −406.763 | + | 481.991i | −0.0290454 | + | 0.0344171i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24139.4 | −1.71484 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11883.7 | −0.835593 | −0.417796 | − | 0.908541i | \(-0.637197\pi\) | ||||
−0.417796 | + | 0.908541i | \(0.637197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12039.7 | −0.842256 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12702.9 | −0.879675 | −0.439838 | − | 0.898077i | \(-0.644964\pi\) | ||||
−0.439838 | + | 0.898077i | \(0.644964\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19180.0 | − | 22727.2i | 1.32152 | − | 1.56592i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 23873.0i | − | 1.62842i | −0.580572 | − | 0.814209i | \(-0.697171\pi\) | ||
0.580572 | − | 0.814209i | \(-0.302829\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10411.4i | − | 0.706640i | −0.935503 | − | 0.353320i | \(-0.885053\pi\) | ||
0.935503 | − | 0.353320i | \(-0.114947\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25300.1 | 1.70016 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15527.0i | 1.03826i | 0.854696 | + | 0.519129i | \(0.173744\pi\) | ||||
−0.854696 | + | 0.519129i | \(0.826256\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4176.03i | − | 0.276504i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9275.88 | −0.611173 | −0.305587 | − | 0.952164i | \(-0.598853\pi\) | ||||
−0.305587 | + | 0.952164i | \(0.598853\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3102.94i | − | 0.202463i | −0.994863 | − | 0.101232i | \(-0.967722\pi\) | ||
0.994863 | − | 0.101232i | \(-0.0322783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6765.73i | − | 0.439318i | −0.975577 | − | 0.219659i | \(-0.929506\pi\) | ||
0.975577 | − | 0.219659i | \(-0.0704945\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2495.86 | + | 2957.46i | −0.160505 | + | 0.190190i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11791.4 | −0.754652 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27063.3 | 1.71556 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4096.60 | −0.258452 | −0.129226 | − | 0.991615i | \(-0.541249\pi\) | ||||
−0.129226 | + | 0.991615i | \(0.541249\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9738.72 | 0.608613 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4313.22 | + | 735.452i | −0.268283 | + | 0.0457452i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17478.5i | 1.07700i | 0.842624 | + | 0.538502i | \(0.181010\pi\) | ||||
−0.842624 | + | 0.538502i | \(0.818990\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10352.1i | 0.634908i | 0.948274 | + | 0.317454i | \(0.102828\pi\) | ||||
−0.948274 | + | 0.317454i | \(0.897172\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13536.7 | 0.822539 | 0.411269 | − | 0.911514i | \(-0.365086\pi\) | ||||
0.411269 | + | 0.911514i | \(0.365086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27651.6i | 1.67245i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 23295.9i | − | 1.39608i | −0.716060 | − | 0.698039i | \(-0.754056\pi\) | ||
0.716060 | − | 0.698039i | \(-0.245944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37591.0 | 2.24245 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1192.51i | − | 0.0704909i | −0.999379 | − | 0.0352454i | \(-0.988779\pi\) | ||
0.999379 | − | 0.0352454i | \(-0.0112213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 12612.5i | − | 0.742162i | −0.928601 | − | 0.371081i | \(-0.878987\pi\) | ||
0.928601 | − | 0.371081i | \(-0.121013\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12849.8 | + | 10844.2i | 0.749312 | + | 0.632361i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8366.60 | 0.485691 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14469.7 | 0.832486 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25648.0 | 1.46903 | 0.734515 | − | 0.678592i | \(-0.237410\pi\) | ||||
0.734515 | + | 0.678592i | \(0.237410\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14099.7 | 0.800439 | 0.400220 | − | 0.916419i | \(-0.368934\pi\) | ||||
0.400220 | + | 0.916419i | \(0.368934\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17993.0 | + | 15184.7i | 1.01695 | + | 0.858225i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6066.68i | 0.339875i | 0.985455 | + | 0.169938i | \(0.0543567\pi\) | ||||
−0.985455 | + | 0.169938i | \(0.945643\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 31712.7i | − | 1.76888i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5762.73 | 0.318640 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 31595.8i | − | 1.73945i | −0.493537 | − | 0.869725i | \(-0.664296\pi\) | ||
0.493537 | − | 0.869725i | \(-0.335704\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 28168.7i | − | 1.53741i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35855.8 | −1.94854 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14828.2i | 0.798936i | 0.916747 | + | 0.399468i | \(0.130805\pi\) | ||||
−0.916747 | + | 0.399468i | \(0.869195\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15301.4i | 0.820914i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7336.94 | − | 8693.86i | 0.390288 | − | 0.462470i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21027.1 | −1.11381 | −0.556903 | − | 0.830578i | \(-0.688011\pi\) | ||||
−0.556903 | + | 0.830578i | \(0.688011\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14149.6 | −0.743207 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11313.6 | −0.591756 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36268.4 | −1.88120 | −0.940601 | − | 0.339514i | \(-0.889738\pi\) | ||||
−0.940601 | + | 0.339514i | \(0.889738\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14764.7 | − | 12460.2i | −0.762642 | − | 0.643610i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 19584.2i | − | 1.00323i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23568.7i | 1.20236i | 0.799115 | + | 0.601178i | \(0.205302\pi\) | ||||
−0.799115 | + | 0.601178i | \(0.794698\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29773.8 | 1.50646 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18430.9i | 0.928734i | 0.885643 | + | 0.464367i | \(0.153718\pi\) | ||||
−0.885643 | + | 0.464367i | \(0.846282\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39636.3i | 1.98104i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2029.42 | −0.101020 | −0.0505098 | − | 0.998724i | \(-0.516085\pi\) | ||||
−0.0505098 | + | 0.998724i | \(0.516085\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1839.15i | − | 0.0908101i | −0.998969 | − | 0.0454050i | \(-0.985542\pi\) | ||
0.998969 | − | 0.0454050i | \(-0.0144578\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 2688.75i | − | 0.132226i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15977.1 | − | 13483.4i | −0.779427 | − | 0.657776i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2182.60 | −0.106051 | −0.0530254 | − | 0.998593i | \(-0.516886\pi\) | ||||
−0.0530254 | + | 0.998593i | \(0.516886\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 51000.8 | 2.45842 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14605.5 | 0.701250 | 0.350625 | − | 0.936516i | \(-0.385969\pi\) | ||||
0.350625 | + | 0.936516i | \(0.385969\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17942.2 | 0.854671 | 0.427336 | − | 0.904093i | \(-0.359452\pi\) | ||||
0.427336 | + | 0.904093i | \(0.359452\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18582.4 | + | 22019.1i | −0.881688 | + | 1.04475i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6601.19i | − | 0.310763i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5311.86i | − | 0.249091i | −0.992214 | − | 0.124545i | \(-0.960253\pi\) | ||
0.992214 | − | 0.124545i | \(-0.0397472\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21593.6 | −1.00475 | −0.502373 | − | 0.864651i | \(-0.667540\pi\) | ||||
−0.502373 | + | 0.864651i | \(0.667540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33120.8i | 1.53514i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 20272.6i | − | 0.932401i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48850.5 | −2.23817 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16823.9i | 0.764932i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34701.8i | 1.57177i | 0.618371 | + | 0.785887i | \(0.287793\pi\) | ||||
−0.618371 | + | 0.785887i | \(0.712207\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3658.18 | + | 3087.22i | 0.164437 | + | 0.138772i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3454.33 | −0.154687 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11120.7 | 0.494248 | 0.247124 | − | 0.968984i | \(-0.420515\pi\) | ||||
0.247124 | + | 0.968984i | \(0.420515\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31671.3 | 1.40232 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18018.9 | 0.791873 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15101.6 | + | 12744.6i | 0.661194 | + | 0.557996i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 39619.1i | − | 1.72180i | −0.508777 | − | 0.860898i | \(-0.669902\pi\) | ||
0.508777 | − | 0.860898i | \(-0.330098\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2483.62i | − | 0.107536i | −0.998553 | − | 0.0537679i | \(-0.982877\pi\) | ||
0.998553 | − | 0.0537679i | \(-0.0171231\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21530.8 | −0.925387 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16833.9i | 0.720860i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 4898.20i | − | 0.208220i | −0.994566 | − | 0.104110i | \(-0.966801\pi\) | ||
0.994566 | − | 0.104110i | \(-0.0331994\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15936.4 | 0.674980 | 0.337490 | − | 0.941329i | \(-0.390422\pi\) | ||||
0.337490 | + | 0.941329i | \(0.390422\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11183.9i | 0.470256i | 0.971964 | + | 0.235128i | \(0.0755509\pi\) | ||||
−0.971964 | + | 0.235128i | \(0.924449\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6180.21i | 0.258924i | 0.991584 | + | 0.129462i | \(0.0413250\pi\) | ||||
−0.991584 | + | 0.129462i | \(0.958675\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5577.73 | − | 32711.8i | −0.232001 | − | 1.36062i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23775.3 | 0.985364 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20319.4 | 0.836119 | 0.418059 | − | 0.908420i | \(-0.362710\pi\) | ||||
0.418059 | + | 0.908420i | \(0.362710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7450.49 | 0.305486 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33763.8 | −1.37457 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18207.6 | − | 21574.9i | 0.738630 | − | 0.875235i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17982.8i | 0.724376i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 25093.0i | − | 1.00723i | −0.863927 | − | 0.503616i | \(-0.832003\pi\) | ||
0.863927 | − | 0.503616i | \(-0.167997\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16363.5 | −0.652236 | −0.326118 | − | 0.945329i | \(-0.605741\pi\) | ||||
−0.326118 | + | 0.945329i | \(0.605741\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 35461.8i | − | 1.40855i | −0.709929 | − | 0.704273i | \(-0.751273\pi\) | ||
0.709929 | − | 0.704273i | \(-0.248727\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 33166.4i | − | 1.30822i | −0.756398 | − | 0.654111i | \(-0.773043\pi\) | ||
0.756398 | − | 0.654111i | \(-0.226957\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32785.3 | 1.28871 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 53283.9i | 2.08001i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 9462.28i | − | 0.368102i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5050.67 | − | 5984.76i | 0.195136 | − | 0.231225i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11235.9 | 0.432621 | 0.216311 | − | 0.976325i | \(-0.430598\pi\) | ||||
0.216311 | + | 0.976325i | \(0.430598\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25537.5 | 0.976597 | 0.488298 | − | 0.872677i | \(-0.337618\pi\) | ||||
0.488298 | + | 0.872677i | \(0.337618\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17936.9 | 0.683606 | 0.341803 | − | 0.939772i | \(-0.388962\pi\) | ||||
0.341803 | + | 0.939772i | \(0.388962\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5293.97 | 0.200399 | 0.100200 | − | 0.994967i | \(-0.468052\pi\) | ||||
0.100200 | + | 0.994967i | \(0.468052\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7008.60 | − | 8304.80i | 0.264411 | − | 0.313312i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17906.7i | 0.671026i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 38341.3i | − | 1.43196i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28646.4 | 1.06275 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43705.0i | 1.61601i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7029.78i | 0.258208i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13540.8 | 0.495715 | 0.247857 | − | 0.968797i | \(-0.420274\pi\) | ||||
0.247857 | + | 0.968797i | \(0.420274\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 27141.4i | − | 0.987084i | −0.869722 | − | 0.493542i | \(-0.835702\pi\) | ||
0.869722 | − | 0.493542i | \(-0.164298\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1819.69i | 0.0659617i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27052.9 | − | 32056.2i | 0.974226 | − | 1.15440i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32872.5 | −1.17994 | −0.589969 | − | 0.807426i | \(-0.700860\pi\) | ||||
−0.589969 | + | 0.807426i | \(0.700860\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11662.0 | 0.415881 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42093.5 | 1.49624 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23656.4 | 0.835459 | 0.417729 | − | 0.908572i | \(-0.362826\pi\) | ||||
0.417729 | + | 0.908572i | \(0.362826\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18495.0 | − | 3153.61i | 0.651074 | − | 0.111015i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 85803.5i | − | 3.00115i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26716.0i | − | 0.931456i | −0.884928 | − | 0.465728i | \(-0.845793\pi\) | ||
0.884928 | − | 0.465728i | \(-0.154207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39531.9 | 1.36950 | 0.684752 | − | 0.728776i | \(-0.259910\pi\) | ||||
0.684752 | + | 0.728776i | \(0.259910\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 23825.2i | − | 0.822751i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 45015.8i | − | 1.54469i | −0.635206 | − | 0.772343i | \(-0.719085\pi\) | ||
0.635206 | − | 0.772343i | \(-0.280915\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4301.61 | −0.147140 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9240.19i | 0.314081i | 0.987592 | + | 0.157040i | \(0.0501953\pi\) | ||||
−0.987592 | + | 0.157040i | \(0.949805\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 38913.4i | − | 1.31854i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27043.3 | − | 22822.5i | −0.910610 | − | 0.768484i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18655.9 | −0.626225 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −67231.6 | −2.24276 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24783.6 | −0.824186 | −0.412093 | − | 0.911142i | \(-0.635202\pi\) | ||||
−0.412093 | + | 0.911142i | \(0.635202\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37516.1 | 1.23991 | 0.619953 | − | 0.784639i | \(-0.287152\pi\) | ||||
0.619953 | + | 0.784639i | \(0.287152\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24021.2 | − | 20272.0i | −0.791454 | − | 0.667925i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 16367.8i | − | 0.535981i | −0.963422 | − | 0.267991i | \(-0.913640\pi\) | ||
0.963422 | − | 0.267991i | \(-0.0863596\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11165.5i | 0.364505i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29516.2 | 0.957700 | 0.478850 | − | 0.877897i | \(-0.341054\pi\) | ||||
0.478850 | + | 0.877897i | \(0.341054\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 60733.6i | − | 1.96460i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19783.9i | 0.636087i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13893.1 | −0.445336 | −0.222668 | − | 0.974894i | \(-0.571477\pi\) | ||||
−0.222668 | + | 0.974894i | \(0.571477\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9245.62i | 0.294579i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19790.8i | 0.628667i | 0.949313 | + | 0.314333i | \(0.101781\pi\) | ||||
−0.949313 | + | 0.314333i | \(0.898219\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2268.4.f.a.1133.6 | 48 | ||
3.2 | odd | 2 | inner | 2268.4.f.a.1133.43 | 48 | ||
7.6 | odd | 2 | inner | 2268.4.f.a.1133.44 | 48 | ||
9.2 | odd | 6 | 756.4.x.a.125.3 | 48 | |||
9.4 | even | 3 | 756.4.x.a.629.22 | 48 | |||
9.5 | odd | 6 | 252.4.x.a.209.17 | yes | 48 | ||
9.7 | even | 3 | 252.4.x.a.41.8 | ✓ | 48 | ||
21.20 | even | 2 | inner | 2268.4.f.a.1133.5 | 48 | ||
63.13 | odd | 6 | 756.4.x.a.629.3 | 48 | |||
63.20 | even | 6 | 756.4.x.a.125.22 | 48 | |||
63.34 | odd | 6 | 252.4.x.a.41.17 | yes | 48 | ||
63.41 | even | 6 | 252.4.x.a.209.8 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.8 | ✓ | 48 | 9.7 | even | 3 | ||
252.4.x.a.41.17 | yes | 48 | 63.34 | odd | 6 | ||
252.4.x.a.209.8 | yes | 48 | 63.41 | even | 6 | ||
252.4.x.a.209.17 | yes | 48 | 9.5 | odd | 6 | ||
756.4.x.a.125.3 | 48 | 9.2 | odd | 6 | |||
756.4.x.a.125.22 | 48 | 63.20 | even | 6 | |||
756.4.x.a.629.3 | 48 | 63.13 | odd | 6 | |||
756.4.x.a.629.22 | 48 | 9.4 | even | 3 | |||
2268.4.f.a.1133.5 | 48 | 21.20 | even | 2 | inner | ||
2268.4.f.a.1133.6 | 48 | 1.1 | even | 1 | trivial | ||
2268.4.f.a.1133.43 | 48 | 3.2 | odd | 2 | inner | ||
2268.4.f.a.1133.44 | 48 | 7.6 | odd | 2 | inner |