Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,5,Mod(255,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.255");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.c (of order \(2\), degree \(1\), not 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: | \(26.4627105495\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 128) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 255.2 | ||
Root | \(2.44949i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.255 |
Dual form | 256.5.c.f.255.1 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 9.79796i | 1.08866i | 0.838870 | + | 0.544331i | \(0.183216\pi\) | ||||
−0.838870 | + | 0.544331i | \(0.816784\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.00000 | 0.320000 | 0.160000 | − | 0.987117i | \(-0.448851\pi\) | ||||
0.160000 | + | 0.987117i | \(0.448851\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 78.3837i | − 1.59967i | −0.600222 | − | 0.799833i | \(-0.704921\pi\) | ||||
0.600222 | − | 0.799833i | \(-0.295079\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −15.0000 | −0.185185 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 107.778i | 0.890724i | 0.895351 | + | 0.445362i | \(0.146925\pi\) | ||||
−0.895351 | + | 0.445362i | \(0.853075\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −216.000 | −1.27811 | −0.639053 | − | 0.769162i | \(-0.720674\pi\) | ||||
−0.639053 | + | 0.769162i | \(0.720674\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 78.3837i | 0.348372i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −162.000 | −0.560554 | −0.280277 | − | 0.959919i | \(-0.590426\pi\) | ||||
−0.280277 | + | 0.959919i | \(0.590426\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 440.908i | 1.22135i | 0.791880 | + | 0.610676i | \(0.209102\pi\) | ||||
−0.791880 | + | 0.610676i | \(0.790898\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 768.000 | 1.74150 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 705.453i | 1.33356i | 0.745255 | + | 0.666780i | \(0.232328\pi\) | ||||
−0.745255 | + | 0.666780i | \(0.767672\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −561.000 | −0.897600 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 646.665i | 0.887058i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1304.00 | −1.55054 | −0.775268 | − | 0.631633i | \(-0.782385\pi\) | ||||
−0.775268 | + | 0.631633i | \(0.782385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 627.069i | − 0.652518i | −0.945280 | − | 0.326259i | \(-0.894212\pi\) | ||||
0.945280 | − | 0.326259i | \(-0.105788\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1056.00 | −0.969697 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 627.069i | − 0.511893i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1512.00 | 1.10446 | 0.552228 | − | 0.833693i | \(-0.313778\pi\) | ||||
0.552228 | + | 0.833693i | \(0.313778\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 2116.36i | − 1.39143i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1890.00 | −1.12433 | −0.562165 | − | 0.827025i | \(-0.690032\pi\) | ||||
−0.562165 | + | 0.827025i | \(0.690032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2909.99i | − 1.57382i | −0.617068 | − | 0.786910i | \(-0.711679\pi\) | ||||
0.617068 | − | 0.786910i | \(-0.288321\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −120.000 | −0.0592593 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1410.91i | 0.638708i | 0.947635 | + | 0.319354i | \(0.103466\pi\) | ||||
−0.947635 | + | 0.319354i | \(0.896534\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3743.00 | −1.55893 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 1587.27i | − 0.610253i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1976.00 | −0.703453 | −0.351727 | − | 0.936103i | \(-0.614405\pi\) | ||||
−0.351727 | + | 0.936103i | \(0.614405\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 862.220i | 0.285032i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4320.00 | −1.32964 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2263.33i | 0.650195i | 0.945681 | + | 0.325097i | \(0.105397\pi\) | ||||
−0.945681 | + | 0.325097i | \(0.894603\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2376.00 | 0.638538 | 0.319269 | − | 0.947664i | \(-0.396563\pi\) | ||||
0.319269 | + | 0.947664i | \(0.396563\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1175.76i | 0.296235i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1728.00 | −0.408994 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1675.45i | − 0.373235i | −0.982433 | − | 0.186617i | \(-0.940248\pi\) | ||||
0.982433 | − | 0.186617i | \(-0.0597525\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6912.00 | −1.45180 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7759.98i | 1.53937i | 0.638422 | + | 0.769687i | \(0.279588\pi\) | ||||
−0.638422 | + | 0.769687i | \(0.720412\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2750.00 | −0.516044 | −0.258022 | − | 0.966139i | \(-0.583071\pi\) | ||||
−0.258022 | + | 0.966139i | \(0.583071\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 5496.65i | − 0.977183i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8448.00 | 1.42486 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 7995.13i | − 1.28107i | −0.767931 | − | 0.640533i | \(-0.778713\pi\) | ||||
0.767931 | − | 0.640533i | \(-0.221287\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7551.00 | −1.15089 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9337.45i | 1.35542i | 0.735332 | + | 0.677708i | \(0.237026\pi\) | ||||
−0.735332 | + | 0.677708i | \(0.762974\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1296.00 | −0.179377 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 12776.5i | − 1.68801i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2430.00 | −0.306779 | −0.153390 | − | 0.988166i | \(-0.549019\pi\) | ||||
−0.153390 | + | 0.988166i | \(0.549019\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16930.9i | 2.04454i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6144.00 | 0.710371 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3527.27i | 0.390833i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7454.00 | 0.792220 | 0.396110 | − | 0.918203i | \(-0.370360\pi\) | ||||
0.396110 | + | 0.918203i | \(0.370360\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 1616.66i | − 0.164949i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1496.00 | −0.146652 | −0.0733261 | − | 0.997308i | \(-0.523361\pi\) | ||||
−0.0733261 | + | 0.997308i | \(0.523361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2586.66i | − 0.243818i | −0.992541 | − | 0.121909i | \(-0.961098\pi\) | ||||
0.992541 | − | 0.121909i | \(-0.0389015\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6144.00 | 0.557279 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1067.98i | − 0.0932813i | −0.998912 | − | 0.0466406i | \(-0.985148\pi\) | ||||
0.998912 | − | 0.0466406i | \(-0.0148516\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14904.0 | −1.25444 | −0.627220 | − | 0.778842i | \(-0.715807\pi\) | ||||
−0.627220 | + | 0.778842i | \(0.715807\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14814.5i | 1.20238i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −702.000 | −0.0549769 | −0.0274884 | − | 0.999622i | \(-0.508751\pi\) | ||||
−0.0274884 | + | 0.999622i | \(0.508751\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5643.62i | 0.426739i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3240.00 | 0.236686 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12698.2i | 0.896699i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3025.00 | 0.206612 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 18518.1i | − 1.22402i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9488.00 | −0.607232 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3448.88i | − 0.213831i | −0.994268 | − | 0.106916i | \(-0.965903\pi\) | ||||
0.994268 | − | 0.106916i | \(-0.0340974\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 28512.0 | 1.71336 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 9592.20i | − 0.558954i | −0.960152 | − | 0.279477i | \(-0.909839\pi\) | ||||
0.960152 | − | 0.279477i | \(-0.0901610\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34560.0 | 1.95376 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5173.32i | 0.283859i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 32670.0 | 1.74064 | 0.870318 | − | 0.492490i | \(-0.163913\pi\) | ||||
0.870318 | + | 0.492490i | \(0.163913\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1322.72i | 0.0684605i | 0.999414 | + | 0.0342302i | \(0.0108979\pi\) | ||||
−0.999414 | + | 0.0342302i | \(0.989102\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13824.0 | −0.695337 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 23280.0i | − 1.13844i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10432.0 | −0.496171 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 36673.8i | − 1.69715i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 872.000 | 0.0392775 | 0.0196388 | − | 0.999807i | \(-0.493748\pi\) | ||||
0.0196388 | + | 0.999807i | \(0.493748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9484.42i | 0.415965i | 0.978133 | + | 0.207983i | \(0.0666898\pi\) | ||||
−0.978133 | + | 0.207983i | \(0.933310\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2430.00 | 0.103806 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 5016.55i | − 0.208806i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −28728.0 | −1.16548 | −0.582742 | − | 0.812657i | \(-0.698020\pi\) | ||||
−0.582742 | + | 0.812657i | \(0.698020\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 19360.8i | − 0.765823i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 55296.0 | 2.13325 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 31128.1i | 1.17160i | 0.810457 | + | 0.585798i | \(0.199219\pi\) | ||||
−0.810457 | + | 0.585798i | \(0.800781\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8448.00 | −0.310303 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 54319.9i | − 1.94772i | −0.227155 | − | 0.973859i | \(-0.572942\pi\) | ||||
0.227155 | − | 0.973859i | \(-0.427058\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18095.0 | 0.633556 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 6613.62i | − 0.226176i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25256.0 | 0.843864 | 0.421932 | − | 0.906628i | \(-0.361352\pi\) | ||||
0.421932 | + | 0.906628i | \(0.361352\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 43973.2i | 1.43586i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22176.0 | −0.707843 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8945.54i | 0.279190i | 0.990209 | + | 0.139595i | \(0.0445801\pi\) | ||||
−0.990209 | + | 0.139595i | \(0.955420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 36072.0 | 1.10107 | 0.550533 | − | 0.834814i | \(-0.314425\pi\) | ||||
0.550533 | + | 0.834814i | \(0.314425\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23280.0i | 0.695152i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12096.0 | 0.353426 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 17460.0i | − 0.499298i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 50688.0 | 1.41900 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 31039.9i | 0.850852i | 0.904993 | + | 0.425426i | \(0.139876\pi\) | ||||
−0.904993 | + | 0.425426i | \(0.860124\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 41374.0 | 1.11074 | 0.555371 | − | 0.831603i | \(-0.312576\pi\) | ||||
0.555371 | + | 0.831603i | \(0.312576\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 16930.9i | − 0.445256i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −67640.0 | −1.74289 | −0.871447 | − | 0.490489i | \(-0.836818\pi\) | ||||
−0.871447 | + | 0.490489i | \(0.836818\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25004.4i | 0.631408i | 0.948858 | + | 0.315704i | \(0.102241\pi\) | ||||
−0.948858 | + | 0.315704i | \(0.897759\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16416.0 | 0.406327 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 102212.i | 2.48034i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15120.0 | −0.359786 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 10581.8i | − 0.246955i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −47520.0 | −1.08789 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26189.9i | 0.588260i | 0.955765 | + | 0.294130i | \(0.0950299\pi\) | ||||
−0.955765 | + | 0.294130i | \(0.904970\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −76032.0 | −1.67586 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 23280.0i | − 0.503623i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −49152.0 | −1.04381 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 26944.4i | − 0.561798i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 34992.0 | 0.716447 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 20693.3i | − 0.416121i | −0.978116 | − | 0.208061i | \(-0.933285\pi\) | ||||
0.978116 | − | 0.208061i | \(-0.0667151\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8415.00 | 0.166222 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 77923.2i | 1.51222i | 0.654445 | + | 0.756110i | \(0.272902\pi\) | ||||
−0.654445 | + | 0.756110i | \(0.727098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14472.0 | 0.275967 | 0.137984 | − | 0.990435i | \(-0.455938\pi\) | ||||
0.137984 | + | 0.990435i | \(0.455938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 82773.2i | 1.55119i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2754.00 | 0.0507285 | 0.0253643 | − | 0.999678i | \(-0.491925\pi\) | ||||
0.0253643 | + | 0.999678i | \(0.491925\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11287.2i | 0.204387i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 78336.0 | 1.39465 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 91708.9i | − 1.60552i | −0.596302 | − | 0.802760i | \(-0.703364\pi\) | ||||
0.596302 | − | 0.802760i | \(-0.296636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −97570.0 | −1.67990 | −0.839948 | − | 0.542667i | \(-0.817414\pi\) | ||||
−0.839948 | + | 0.542667i | \(0.817414\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 21604.5i | − 0.365874i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −29944.0 | −0.498859 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 95236.2i | − 1.56102i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −91488.0 | −1.47559 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 67811.7i | − 1.07636i | −0.842830 | − | 0.538179i | \(-0.819112\pi\) | ||||
0.842830 | − | 0.538179i | \(-0.180888\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −76032.0 | −1.18783 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 12698.2i | − 0.195281i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 80514.0 | 1.21900 | 0.609502 | − | 0.792785i | \(-0.291369\pi\) | ||||
0.609502 | + | 0.792785i | \(0.291369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 118516.i | − 1.76676i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19560.0 | 0.287136 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 14814.5i | − 0.214179i | −0.994249 | − | 0.107089i | \(-0.965847\pi\) | ||||
0.994249 | − | 0.107089i | \(-0.0341531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15808.0 | −0.225105 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 23809.0i | − 0.333979i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 44872.0 | 0.620113 | 0.310057 | − | 0.950718i | \(-0.399652\pi\) | ||||
0.310057 | + | 0.950718i | \(0.399652\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 91395.4i | 1.24447i | 0.782829 | + | 0.622237i | \(0.213776\pi\) | ||||
−0.782829 | + | 0.622237i | \(0.786224\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −165888. | −2.22582 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 60463.2i | − 0.799513i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 90504.0 | 1.17953 | 0.589764 | − | 0.807576i | \(-0.299221\pi\) | ||||
0.589764 | + | 0.807576i | \(0.299221\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9406.04i | 0.120837i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23166.0 | −0.293385 | −0.146693 | − | 0.989182i | \(-0.546863\pi\) | ||||
−0.146693 | + | 0.989182i | \(0.546863\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 70809.8i | 0.884140i | 0.896981 | + | 0.442070i | \(0.145756\pi\) | ||||
−0.896981 | + | 0.442070i | \(0.854244\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −34560.0 | −0.425485 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 148145.i | 1.79855i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −57277.0 | −0.685780 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 73034.0i | 0.862460i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 37768.0 | 0.439935 | 0.219968 | − | 0.975507i | \(-0.429405\pi\) | ||||
0.219968 | + | 0.975507i | \(0.429405\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18106.6i | 0.208062i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −69696.0 | −0.790123 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 152378.i | − 1.70443i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −228096. | −2.51759 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 14657.7i | − 0.159655i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19008.0 | 0.204332 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 38535.4i | 0.408868i | 0.978880 | + | 0.204434i | \(0.0655353\pi\) | ||||
−0.978880 | + | 0.204434i | \(0.934465\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25344.0 | 0.265435 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 85359.8i | 0.882537i | 0.897375 | + | 0.441268i | \(0.145471\pi\) | ||||
−0.897375 | + | 0.441268i | \(0.854529\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −93602.0 | −0.955425 | −0.477712 | − | 0.878516i | \(-0.658534\pi\) | ||||
−0.477712 | + | 0.878516i | \(0.658534\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9406.04i | 0.0947951i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 49192.0 | 0.489526 | 0.244763 | − | 0.969583i | \(-0.421290\pi\) | ||||
0.244763 | + | 0.969583i | \(0.421290\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 140542.i | − 1.38110i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10464.0 | 0.101552 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 71427.1i | − 0.684633i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 121176. | 1.14723 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 146029.i | − 1.36566i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 110592. | 1.02172 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16490.0i | 0.150509i | 0.997164 | + | 0.0752547i | \(0.0239770\pi\) | ||||
−0.997164 | + | 0.0752547i | \(0.976023\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22680.0 | −0.204529 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 13403.6i | − 0.119435i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −93758.0 | −0.825560 | −0.412780 | − | 0.910831i | \(-0.635442\pi\) | ||||
−0.412780 | + | 0.910831i | \(0.635442\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 6878.17i | − 0.0598513i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 67584.0 | 0.581213 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 105191.i | 0.894108i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −55296.0 | −0.464575 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 220405.i | 1.83047i | 0.402920 | + | 0.915235i | \(0.367995\pi\) | ||||
−0.402920 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −48600.0 | −0.399012 | −0.199506 | − | 0.979897i | \(-0.563934\pi\) | ||||
−0.199506 | + | 0.979897i | \(0.563934\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 139680.i | − 1.13375i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 108162. | 0.868011 | 0.434006 | − | 0.900910i | \(-0.357100\pi\) | ||||
0.434006 | + | 0.900910i | \(0.357100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 62079.9i | 0.492600i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −124416. | −0.976202 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 50087.2i | 0.388631i | 0.980939 | + | 0.194316i | \(0.0622486\pi\) | ||||
−0.980939 | + | 0.194316i | \(0.937751\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −64079.0 | −0.491701 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29638.8i | 0.224930i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22000.0 | −0.165134 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 61296.0i | − 0.455093i | −0.973767 | − | 0.227547i | \(-0.926930\pi\) | ||||
0.973767 | − | 0.227547i | \(-0.0730704\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28350.0 | 0.208209 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 154886.i | 1.12529i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −54648.0 | −0.392787 | −0.196393 | − | 0.980525i | \(-0.562923\pi\) | ||||
−0.196393 | + | 0.980525i | \(0.562923\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 92963.0i | − 0.661070i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 281664. | 1.98175 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 103790.i | − 0.722564i | −0.932457 | − | 0.361282i | \(-0.882339\pi\) | ||||
0.932457 | − | 0.361282i | \(-0.117661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 33792.0 | 0.232790 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 124160.i | 0.846415i | 0.906033 | + | 0.423207i | \(0.139096\pi\) | ||||
−0.906033 | + | 0.423207i | \(0.860904\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 67584.0 | 0.455955 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 43649.9i | 0.291448i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −129112. | −0.853233 | −0.426616 | − | 0.904433i | \(-0.640295\pi\) | ||||
−0.426616 | + | 0.904433i | \(0.640295\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 114283.i | − 0.747532i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 93984.0 | 0.608512 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 63961.1i | − 0.409941i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 232200. | 1.47327 | 0.736633 | − | 0.676293i | \(-0.236415\pi\) | ||||
0.736633 | + | 0.676293i | \(0.236415\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 338617.i | 2.12698i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 151902. | 0.944658 | 0.472329 | − | 0.881422i | \(-0.343413\pi\) | ||||
0.472329 | + | 0.881422i | \(0.343413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 135447.i | 0.833987i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −60408.0 | −0.368285 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 162960.i | 0.983765i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28450.0 | −0.170073 | −0.0850366 | − | 0.996378i | \(-0.527101\pi\) | ||||
−0.0850366 | + | 0.996378i | \(0.527101\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 320099.i | 1.89496i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 177408. | 1.04010 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 74699.6i | 0.433733i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12960.0 | −0.0745303 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 291382.i | − 1.65972i | −0.557974 | − | 0.829858i | \(-0.688421\pi\) | ||||
0.557974 | − | 0.829858i | \(-0.311579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 119880. | 0.676367 | 0.338184 | − | 0.941080i | \(-0.390188\pi\) | ||||
0.338184 | + | 0.941080i | \(0.390188\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 21163.6i | − 0.118279i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 90882.0 | 0.503153 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 186240.i | − 1.02145i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 228096. | 1.23938 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 170720.i | − 0.919028i | −0.888170 | − | 0.459514i | \(-0.848024\pi\) | ||||
0.888170 | − | 0.459514i | \(-0.151976\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 215518. | 1.14950 | 0.574748 | − | 0.818330i | \(-0.305100\pi\) | ||||
0.574748 | + | 0.818330i | \(0.305100\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 102212.i | − 0.540163i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −311040. | −1.62875 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 75169.9i | − 0.390045i | −0.980799 | − | 0.195023i | \(-0.937522\pi\) | ||||
0.980799 | − | 0.195023i | \(-0.0624781\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 56145.0 | 0.288691 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 185270.i | − 0.944054i | −0.881584 | − | 0.472027i | \(-0.843523\pi\) | ||||
0.881584 | − | 0.472027i | \(-0.156477\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19440.0 | −0.0981694 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8543.82i | 0.0427599i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 177822. | 0.882049 | 0.441025 | − | 0.897495i | \(-0.354615\pi\) | ||||
0.441025 | + | 0.897495i | \(0.354615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 203700.i | − 1.00147i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −92928.0 | −0.452846 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 135447.i | 0.654254i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 203294. | 0.973402 | 0.486701 | − | 0.873569i | \(-0.338200\pi\) | ||||
0.486701 | + | 0.873569i | \(0.338200\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 104760.i | − 0.497244i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −286648. | −1.34880 | −0.674399 | − | 0.738367i | \(-0.735597\pi\) | ||||
−0.674399 | + | 0.738367i | \(0.735597\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 332817.i | − 1.55254i | −0.630399 | − | 0.776271i | \(-0.717109\pi\) | ||||
0.630399 | − | 0.776271i | \(-0.282891\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 49152.0 | 0.227319 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 58738.8i | − 0.269334i | −0.990891 | − | 0.134667i | \(-0.957004\pi\) | ||||
0.990891 | − | 0.134667i | \(-0.0429965\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −131328. | −0.597051 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 281476.i | − 1.26882i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 313632. | 1.40184 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 247349.i | − 1.09629i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29640.0 | 0.130269 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 186240.i | − 0.811710i | −0.913937 | − | 0.405855i | \(-0.866974\pi\) | ||||
0.913937 | − | 0.405855i | \(-0.133026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −326592. | −1.41161 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 541788.i | 2.32239i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 59632.0 | 0.253510 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 363308.i | 1.53185i | 0.642927 | + | 0.765927i | \(0.277720\pi\) | ||||
−0.642927 | + | 0.765927i | \(0.722280\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −304992. | −1.27547 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 107533.i | 0.446043i | 0.974813 | + | 0.223022i | \(0.0715921\pi\) | ||||
−0.974813 | + | 0.223022i | \(0.928408\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 211248. | 0.869158 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 12933.3i | − 0.0527836i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 608256. | 2.46249 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 385089.i | − 1.54654i | −0.634079 | − | 0.773268i | \(-0.718621\pi\) | ||||
0.634079 | − | 0.773268i | \(-0.281379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 532224. | 2.12041 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 210930.i | − 0.833688i | −0.908978 | − | 0.416844i | \(-0.863136\pi\) | ||||
0.908978 | − | 0.416844i | \(-0.136864\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11968.0 | −0.0469287 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 177294.i | 0.689729i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −171512. | −0.662001 | −0.331001 | − | 0.943630i | \(-0.607386\pi\) | ||||
−0.331001 | + | 0.943630i | \(0.607386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 215555.i | 0.825499i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −285120. | −1.08341 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 20693.3i | − 0.0780216i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −152064. | −0.568912 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 247457.i | 0.918683i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 184734. | 0.680568 | 0.340284 | − | 0.940323i | \(-0.389477\pi\) | ||||
0.340284 | + | 0.940323i | \(0.389477\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 420009.i | 1.53552i | 0.640738 | + | 0.767760i | \(0.278629\pi\) | ||||
−0.640738 | + | 0.767760i | \(0.721371\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −430848. | −1.56317 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 101585.i | 0.365771i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −217823. | −0.778381 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 33949.9i | − 0.120406i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 408240. | 1.43701 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 8543.82i | − 0.0298500i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −87648.0 | −0.303944 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 403411.i | − 1.38858i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −230904. | −0.788927 | −0.394464 | − | 0.918912i | \(-0.629070\pi\) | ||||
−0.394464 | + | 0.918912i | \(0.629070\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 353432.i | 1.19869i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −119232. | −0.401421 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 39769.9i | − 0.132917i | −0.997789 | − | 0.0664584i | \(-0.978830\pi\) | ||||
0.997789 | − | 0.0664584i | \(-0.0211700\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −35640.0 | −0.118248 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 574944.i | − 1.89375i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −626688. | −2.04928 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 118516.i | 0.384761i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23144.0 | 0.0745981 | 0.0372991 | − | 0.999304i | \(-0.488125\pi\) | ||||
0.0372991 | + | 0.999304i | \(0.488125\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 628559.i | 2.01151i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 171072. | 0.543567 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 491123.i | 1.54943i | 0.632308 | + | 0.774717i | \(0.282108\pi\) | ||||
−0.632308 | + | 0.774717i | \(0.717892\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5616.00 | −0.0175926 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 591875.i | 1.84104i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 127710. | 0.394458 | 0.197229 | − | 0.980357i | \(-0.436806\pi\) | ||||
0.197229 | + | 0.980357i | \(0.436806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39064.5i | 0.119815i | 0.998204 | + | 0.0599073i | \(0.0190805\pi\) | ||||
−0.998204 | + | 0.0599073i | \(0.980919\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −304128. | −0.926290 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 395759.i | − 1.19700i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −270718. | −0.813140 | −0.406570 | − | 0.913620i | \(-0.633275\pi\) | ||||
−0.406570 | + | 0.913620i | \(0.633275\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 405381.i | 1.20922i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 731904. | 2.16821 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 212968.i | − 0.626582i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 25920.0 | 0.0757396 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 273353.i | 0.793319i | 0.917966 | + | 0.396660i | \(0.129831\pi\) | ||||
−0.917966 | + | 0.396660i | \(0.870169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 276480. | 0.796954 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 662734.i | − 1.89742i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −62910.0 | −0.178900 | −0.0894500 | − | 0.995991i | \(-0.528511\pi\) | ||||
−0.0894500 | + | 0.995991i | \(0.528511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 101585.i | 0.286944i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −244992. | −0.687390 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 261723.i | − 0.729438i | −0.931118 | − | 0.364719i | \(-0.881165\pi\) | ||||
0.931118 | − | 0.364719i | \(-0.118835\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −203902. | −0.564511 | −0.282256 | − | 0.959339i | \(-0.591083\pi\) | ||||
−0.282256 | + | 0.959339i | \(0.591083\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25131.8i | 0.0691176i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24200.0 | 0.0661157 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 369657.i | − 1.00328i | −0.865077 | − | 0.501640i | \(-0.832730\pi\) | ||||
0.865077 | − | 0.501640i | \(-0.167270\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.00147e6 | −2.70025 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 304756.i | − 0.816337i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −222264. | −0.591491 | −0.295746 | − | 0.955267i | \(-0.595568\pi\) | ||||
−0.295746 | + | 0.955267i | \(0.595568\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 148145.i | − 0.391685i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −363582. | −0.955063 | −0.477532 | − | 0.878615i | \(-0.658468\pi\) | ||||
−0.477532 | + | 0.878615i | \(0.658468\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 317718.i | 0.829203i | 0.910003 | + | 0.414602i | \(0.136079\pi\) | ||||
−0.910003 | + | 0.414602i | \(0.863921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −456192. | −1.18294 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 190472.i | 0.490745i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 274721. | 0.703286 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 465599.i | − 1.18434i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −244944. | −0.619107 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 348415.i | 0.875062i | 0.899203 | + | 0.437531i | \(0.144147\pi\) | ||||
−0.899203 | + | 0.437531i | \(0.855853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −256608. | −0.640417 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 27591.1i | − 0.0684259i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 808488. | 1.99248 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 116400.i | − 0.285069i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 67230.0 | 0.163624 | 0.0818120 | − | 0.996648i | \(-0.473929\pi\) | ||||
0.0818120 | + | 0.996648i | \(0.473929\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 74513.5i | 0.180224i | 0.995932 | + | 0.0901121i | \(0.0287225\pi\) | ||||
−0.995932 | + | 0.0901121i | \(0.971277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 228096. | 0.548275 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 380239.i | 0.908340i | 0.890915 | + | 0.454170i | \(0.150064\pi\) | ||||
−0.890915 | + | 0.454170i | \(0.849936\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −243936. | −0.579144 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 481589.i | − 1.13636i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 89288.0 | 0.209395 | 0.104698 | − | 0.994504i | \(-0.466613\pi\) | ||||
0.104698 | + | 0.994504i | \(0.466613\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 76737.6i | − 0.178865i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 41250.0 | 0.0955638 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 223149.i | − 0.513834i | −0.966433 | − | 0.256917i | \(-0.917293\pi\) | ||||
0.966433 | − | 0.256917i | \(-0.0827068\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −560088. | −1.28190 | −0.640949 | − | 0.767584i | \(-0.721459\pi\) | ||||
−0.640949 | + | 0.767584i | \(0.721459\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 342850.i | 0.779969i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 276480. | 0.625202 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 919911.i | − 2.06773i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 202752. | 0.453015 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 256079.i | 0.568761i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −810722. | −1.78995 | −0.894977 | − | 0.446112i | \(-0.852808\pi\) | ||||
−0.894977 | + | 0.446112i | \(0.852808\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 362779.i | − 0.796223i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −655768. | −1.43078 | −0.715390 | − | 0.698725i | \(-0.753751\pi\) | ||||
−0.715390 | + | 0.698725i | \(0.753751\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 584272.i | − 1.26729i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −763488. | −1.64630 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 189208.i | 0.405601i | 0.979220 | + | 0.202800i | \(0.0650043\pi\) | ||||
−0.979220 | + | 0.202800i | \(0.934996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 261360. | 0.557004 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 141796.i | 0.300435i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 426816. | 0.899088 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 569389.i | 1.19248i | 0.802804 | + | 0.596242i | \(0.203340\pi\) | ||||
−0.802804 | + | 0.596242i | \(0.796660\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −126720. | −0.263863 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10581.8i | 0.0219073i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 306180. | 0.630248 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26983.6i | 0.0552262i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −519224. | −1.05662 | −0.528310 | − | 0.849052i | \(-0.677174\pi\) | ||||
−0.528310 | + | 0.849052i | \(0.677174\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 666653.i | 1.34893i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −110592. | −0.222508 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 117262.i | 0.234595i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −919512. | −1.82922 | −0.914608 | − | 0.404342i | \(-0.867501\pi\) | ||||
−0.914608 | + | 0.404342i | \(0.867501\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 119927.i | 0.237234i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 442368. | 0.870171 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 186240.i | − 0.364301i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 898560. | 1.74787 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 656071.i | 1.26909i | 0.772885 | + | 0.634546i | \(0.218813\pi\) | ||||
−0.772885 | + | 0.634546i | \(0.781187\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −202752. | −0.390027 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 955987.i | − 1.82884i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 731544. | 1.39176 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 488722.i | − 0.924684i | −0.886702 | − | 0.462342i | \(-0.847009\pi\) | ||||
0.886702 | − | 0.462342i | \(-0.152991\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −399951. | −0.752578 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 471419.i | 0.882211i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 706536. | 1.31500 | 0.657501 | − | 0.753454i | \(-0.271614\pi\) | ||||
0.657501 | + | 0.753454i | \(0.271614\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 293390.i | − 0.543089i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 180576. | 0.332449 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 172748.i | − 0.316318i | −0.987414 | − | 0.158159i | \(-0.949444\pi\) | ||||
0.987414 | − | 0.158159i | \(-0.0505558\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 933120. | 1.69942 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 250436.i | 0.453648i | 0.973936 | + | 0.226824i | \(0.0728342\pi\) | ||||
−0.973936 | + | 0.226824i | \(0.927166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6976.00 | 0.0125688 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 140062.i | − 0.251003i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −83712.0 | −0.149219 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 536301.i | − 0.950887i | −0.879746 | − | 0.475443i | \(-0.842288\pi\) | ||||
0.879746 | − | 0.475443i | \(-0.157712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 664416. | 1.17179 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 75875.4i | 0.133109i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −470232. | −0.820579 | −0.410290 | − | 0.911955i | \(-0.634572\pi\) | ||||
−0.410290 | + | 0.911955i | \(0.634572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 744958.i | − 1.29315i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 691038. | 1.19325 | 0.596627 | − | 0.802519i | \(-0.296507\pi\) | ||||
0.596627 | + | 0.802519i | \(0.296507\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.16823e6i | 2.00669i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19440.0 | 0.0332180 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 488879.i | − 0.831018i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 304030. | 0.514119 | 0.257060 | − | 0.966396i | \(-0.417246\pi\) | ||||
0.257060 | + | 0.966396i | \(0.417246\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 788873.i | 1.32708i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −533720. | −0.893212 | −0.446606 | − | 0.894731i | \(-0.647367\pi\) | ||||
−0.446606 | + | 0.894731i | \(0.647367\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 351786.i | 0.585700i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.16122e6 | 1.92341 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 833316.i | − 1.37320i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −836352. | −1.37116 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 843252.i | − 1.37541i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −229824. | −0.372955 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.17467e6i | 1.89656i | 0.317442 | + | 0.948278i | \(0.397176\pi\) | ||||
−0.317442 | + | 0.948278i | \(0.602824\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 145152. | 0.233168 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 55025.3i | 0.0879447i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −513216. | −0.816120 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 154886.i | − 0.245063i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −552376. | −0.869597 | −0.434799 | − | 0.900528i | \(-0.643180\pi\) | ||||
−0.434799 | + | 0.900528i | \(0.643180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 228567.i | − 0.358030i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36450.0 | 0.0568110 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 296388.i | − 0.459653i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 442368. | 0.682640 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 439654.i | 0.675094i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −803682. | −1.22797 | −0.613984 | − | 0.789318i | \(-0.710434\pi\) | ||||
−0.613984 | + | 0.789318i | \(0.710434\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 68869.9i | − 0.104710i | −0.998629 | − | 0.0523549i | \(-0.983327\pi\) | ||||
0.998629 | − | 0.0523549i | \(-0.0166727\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −895488. | −1.35481 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 249025.i | 0.374910i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.28304e6 | 1.92219 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 253963.i | − 0.378619i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 867592. | 1.28715 | 0.643575 | − | 0.765383i | \(-0.277450\pi\) | ||||
0.643575 | + | 0.765383i | \(0.277450\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30177.7i | 0.0445540i | 0.999752 | + | 0.0222770i | \(0.00709158\pi\) | ||||
−0.999752 | + | 0.0222770i | \(0.992908\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 592416. | 0.870400 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 864680.i | 1.26428i | 0.774853 | + | 0.632141i | \(0.217824\pi\) | ||||
−0.774853 | + | 0.632141i | \(0.782176\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 449928. | 0.654687 | 0.327344 | − | 0.944905i | \(-0.393847\pi\) | ||||
0.327344 | + | 0.944905i | \(0.393847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 886754.i | 1.28411i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 606366. | 0.873866 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 434559.i | − 0.623269i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 405504. | 0.578821 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 800689.i | 1.13747i | 0.822521 | + | 0.568735i | \(0.192567\pi\) | ||||
−0.822521 | + | 0.568735i | \(0.807433\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 993135. | 1.40416 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 226980.i | − 0.319398i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 144760. | 0.202738 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 237111.i | − 0.330510i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −693792. | −0.962529 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.06665e6i | 1.47286i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 121608. | 0.167134 | 0.0835669 | − | 0.996502i | \(-0.473369\pi\) | ||||
0.0835669 | + | 0.996502i | \(0.473369\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 52909.0i | − 0.0723764i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.26473e6 | 1.72202 | 0.861009 | − | 0.508590i | \(-0.169833\pi\) | ||||
0.861009 | + | 0.508590i | \(0.169833\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 967088.i | 1.31063i | 0.755356 | + | 0.655314i | \(0.227464\pi\) | ||||
−0.755356 | + | 0.655314i | \(0.772536\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.45152e6 | −1.95802 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 428915.i | 0.575904i | 0.957645 | + | 0.287952i | \(0.0929744\pi\) | ||||
−0.957645 | + | 0.287952i | \(0.907026\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 202048. | 0.270036 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 561198.i | − 0.746582i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 861696. | 1.14108 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 361897.i | 0.477034i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −111810. | −0.146707 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 743704.i | 0.971369i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 519048. | 0.674852 | 0.337426 | − | 0.941352i | \(-0.390444\pi\) | ||||
0.337426 | + | 0.941352i | \(0.390444\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 370049.i | 0.478941i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 434754. | 0.560134 | 0.280067 | − | 0.959980i | \(-0.409643\pi\) | ||||
0.280067 | + | 0.959980i | \(0.409643\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 474329.i | − 0.608357i | −0.952615 | − | 0.304178i | \(-0.901618\pi\) | ||||
0.952615 | − | 0.304178i | \(-0.0983819\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −177408. | −0.226510 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 298407.i | − 0.379281i | −0.981854 | − | 0.189641i | \(-0.939268\pi\) | ||||
0.981854 | − | 0.189641i | \(-0.0607323\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −270336. | −0.342058 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 813828.i | − 1.02513i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −622080. | −0.780088 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 71564.3i | 0.0893409i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.49299e6 | 1.85555 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 817698.i | 1.01175i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 320112. | 0.394323 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 2.23488e6i | − 2.74080i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 288576. | 0.352341 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 693549.i | − 0.843067i | −0.906813 | − | 0.421534i | \(-0.861492\pi\) | ||||
0.906813 | − | 0.421534i | \(-0.138508\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22440.0 | 0.0271578 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.13296e6i | 1.36514i | 0.730821 | + | 0.682570i | \(0.239138\pi\) | ||||
−0.730821 | + | 0.682570i | \(0.760862\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.00637e6 | −1.20730 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 186240.i | 0.222449i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −751872. | −0.894139 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 526817.i | 0.623776i | 0.950119 | + | 0.311888i | \(0.100961\pi\) | ||||
−0.950119 | + | 0.311888i | \(0.899039\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −377568. | −0.445119 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.67616e6i | − 1.96748i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −848232. | −0.991360 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38799.9i | 0.0451514i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −371682. | −0.430666 | −0.215333 | − | 0.976541i | \(-0.569084\pi\) | ||||
−0.215333 | + | 0.976541i | \(0.569084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.65032e6i | − 1.90401i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −836352. | −0.960784 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 139680.i | − 0.159775i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 532418. | 0.606420 | 0.303210 | − | 0.952924i | \(-0.401942\pi\) | ||||
0.303210 | + | 0.952924i | \(0.401942\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 917109.i | − 1.04013i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 614600. | 0.694086 | 0.347043 | − | 0.937849i | \(-0.387186\pi\) | ||||
0.347043 | + | 0.937849i | \(0.387186\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.33331e6i | − 1.49936i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 405504. | 0.454079 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 583988.i | − 0.651184i | −0.945510 | − | 0.325592i | \(-0.894436\pi\) | ||||
0.945510 | − | 0.325592i | \(-0.105564\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 594000. | 0.659560 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 481981.i | 0.532929i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −604962. | −0.666104 | −0.333052 | − | 0.942908i | \(-0.608079\pi\) | ||||
−0.333052 | + | 0.942908i | \(0.608079\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 248319.i | 0.272273i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.37702e6 | 1.50355 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2.56079e6i | − 2.78444i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 530305. | 0.574221 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16019.7i | 0.0172743i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 330992. | 0.355437 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.39405e6i | − 1.49082i | −0.666604 | − | 0.745412i | \(-0.732253\pi\) | ||||
0.666604 | − | 0.745412i | \(-0.267747\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 699840. | 0.745334 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 662175.i | 0.702319i | 0.936316 | + | 0.351160i | \(0.114213\pi\) | ||||
−0.936316 | + | 0.351160i | \(0.885787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 103680. | 0.109514 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.18728e6i | 1.24894i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −815778. | −0.854639 | −0.427320 | − | 0.904101i | \(-0.640542\pi\) | ||||
−0.427320 | + | 0.904101i | \(0.640542\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 261899.i | − 0.273256i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 223560. | 0.232304 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.23384e6i | 1.27688i | 0.769671 | + | 0.638441i | \(0.220420\pi\) | ||||
−0.769671 | + | 0.638441i | \(0.779580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −541120. | −0.557726 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.08358e6i | 1.11231i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.05286e6 | 2.09878 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 417315.i | 0.424929i | 0.977169 | + | 0.212464i | \(0.0681490\pi\) | ||||
−0.977169 | + | 0.212464i | \(0.931851\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −161568. | −0.163854 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 200035.i | 0.202051i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.80252e6 | −1.81338 | −0.906692 | − | 0.421793i | \(-0.861401\pi\) | ||||
−0.906692 | + | 0.421793i | \(0.861401\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 977758.i | 0.979716i |
(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 | 256.5.c.f.255.2 | 2 | ||
4.3 | odd | 2 | inner | 256.5.c.f.255.1 | 2 | ||
8.3 | odd | 2 | 256.5.c.c.255.2 | 2 | |||
8.5 | even | 2 | 256.5.c.c.255.1 | 2 | |||
16.3 | odd | 4 | 128.5.d.c.63.3 | yes | 4 | ||
16.5 | even | 4 | 128.5.d.c.63.4 | yes | 4 | ||
16.11 | odd | 4 | 128.5.d.c.63.2 | yes | 4 | ||
16.13 | even | 4 | 128.5.d.c.63.1 | ✓ | 4 | ||
48.5 | odd | 4 | 1152.5.b.i.703.2 | 4 | |||
48.11 | even | 4 | 1152.5.b.i.703.1 | 4 | |||
48.29 | odd | 4 | 1152.5.b.i.703.4 | 4 | |||
48.35 | even | 4 | 1152.5.b.i.703.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.5.d.c.63.1 | ✓ | 4 | 16.13 | even | 4 | ||
128.5.d.c.63.2 | yes | 4 | 16.11 | odd | 4 | ||
128.5.d.c.63.3 | yes | 4 | 16.3 | odd | 4 | ||
128.5.d.c.63.4 | yes | 4 | 16.5 | even | 4 | ||
256.5.c.c.255.1 | 2 | 8.5 | even | 2 | |||
256.5.c.c.255.2 | 2 | 8.3 | odd | 2 | |||
256.5.c.f.255.1 | 2 | 4.3 | odd | 2 | inner | ||
256.5.c.f.255.2 | 2 | 1.1 | even | 1 | trivial | ||
1152.5.b.i.703.1 | 4 | 48.11 | even | 4 | |||
1152.5.b.i.703.2 | 4 | 48.5 | odd | 4 | |||
1152.5.b.i.703.3 | 4 | 48.35 | even | 4 | |||
1152.5.b.i.703.4 | 4 | 48.29 | odd | 4 |