Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,4,Mod(1,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.a (trivial) |
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: | yes |
Analytic conductor: | \(64.2530799963\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 363) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1089.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.00000 | −1.06066 | −0.530330 | − | 0.847791i | \(-0.677932\pi\) | ||||
−0.530330 | + | 0.847791i | \(0.677932\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.125000 | ||||||||
\(5\) | 12.0000 | 1.07331 | 0.536656 | − | 0.843801i | \(-0.319687\pi\) | ||||
0.536656 | + | 0.843801i | \(0.319687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.0000 | 0.647939 | 0.323970 | − | 0.946068i | \(-0.394982\pi\) | ||||
0.323970 | + | 0.946068i | \(0.394982\pi\) | |||||||
\(8\) | 21.0000 | 0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −36.0000 | −1.13842 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −66.0000 | −1.40809 | −0.704043 | − | 0.710158i | \(-0.748624\pi\) | ||||
−0.704043 | + | 0.710158i | \(0.748624\pi\) | |||||||
\(14\) | −36.0000 | −0.687243 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | 114.000 | 1.62642 | 0.813208 | − | 0.581974i | \(-0.197719\pi\) | ||||
0.813208 | + | 0.581974i | \(0.197719\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 42.0000 | 0.507130 | 0.253565 | − | 0.967318i | \(-0.418397\pi\) | ||||
0.253565 | + | 0.967318i | \(0.418397\pi\) | |||||||
\(20\) | 12.0000 | 0.134164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −18.0000 | −0.163185 | −0.0815926 | − | 0.996666i | \(-0.526001\pi\) | ||||
−0.0815926 | + | 0.996666i | \(0.526001\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.0000 | 0.152000 | ||||||||
\(26\) | 198.000 | 1.49350 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 12.0000 | 0.0809924 | ||||||||
\(29\) | −186.000 | −1.19101 | −0.595506 | − | 0.803351i | \(-0.703048\pi\) | ||||
−0.595506 | + | 0.803351i | \(0.703048\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −308.000 | −1.78447 | −0.892233 | − | 0.451576i | \(-0.850862\pi\) | ||||
−0.892233 | + | 0.451576i | \(0.850862\pi\) | |||||||
\(32\) | 45.0000 | 0.248592 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −342.000 | −1.72507 | ||||||||
\(35\) | 144.000 | 0.695441 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −146.000 | −0.648710 | −0.324355 | − | 0.945936i | \(-0.605147\pi\) | ||||
−0.324355 | + | 0.945936i | \(0.605147\pi\) | |||||||
\(38\) | −126.000 | −0.537892 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 252.000 | 0.996117 | ||||||||
\(41\) | −42.0000 | −0.159983 | −0.0799914 | − | 0.996796i | \(-0.525489\pi\) | ||||
−0.0799914 | + | 0.996796i | \(0.525489\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −366.000 | −1.29801 | −0.649006 | − | 0.760784i | \(-0.724815\pi\) | ||||
−0.649006 | + | 0.760784i | \(0.724815\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 54.0000 | 0.173084 | ||||||||
\(47\) | −618.000 | −1.91797 | −0.958985 | − | 0.283458i | \(-0.908518\pi\) | ||||
−0.958985 | + | 0.283458i | \(0.908518\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −199.000 | −0.580175 | ||||||||
\(50\) | −57.0000 | −0.161220 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −66.0000 | −0.176011 | ||||||||
\(53\) | 408.000 | 1.05742 | 0.528709 | − | 0.848803i | \(-0.322676\pi\) | ||||
0.528709 | + | 0.848803i | \(0.322676\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 252.000 | 0.601338 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 558.000 | 1.26326 | ||||||||
\(59\) | 132.000 | 0.291270 | 0.145635 | − | 0.989338i | \(-0.453477\pi\) | ||||
0.145635 | + | 0.989338i | \(0.453477\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 630.000 | 1.32235 | 0.661174 | − | 0.750233i | \(-0.270058\pi\) | ||||
0.661174 | + | 0.750233i | \(0.270058\pi\) | |||||||
\(62\) | 924.000 | 1.89271 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | −792.000 | −1.51132 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −452.000 | −0.824188 | −0.412094 | − | 0.911141i | \(-0.635202\pi\) | ||||
−0.412094 | + | 0.911141i | \(0.635202\pi\) | |||||||
\(68\) | 114.000 | 0.203302 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −432.000 | −0.737627 | ||||||||
\(71\) | 282.000 | 0.471370 | 0.235685 | − | 0.971830i | \(-0.424267\pi\) | ||||
0.235685 | + | 0.971830i | \(0.424267\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 684.000 | 1.09666 | 0.548330 | − | 0.836262i | \(-0.315264\pi\) | ||||
0.548330 | + | 0.836262i | \(0.315264\pi\) | |||||||
\(74\) | 438.000 | 0.688060 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 42.0000 | 0.0633912 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1272.00 | 1.81153 | 0.905767 | − | 0.423776i | \(-0.139296\pi\) | ||||
0.905767 | + | 0.423776i | \(0.139296\pi\) | |||||||
\(80\) | −852.000 | −1.19071 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 126.000 | 0.169687 | ||||||||
\(83\) | 432.000 | 0.571303 | 0.285652 | − | 0.958334i | \(-0.407790\pi\) | ||||
0.285652 | + | 0.958334i | \(0.407790\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1368.00 | 1.74565 | ||||||||
\(86\) | 1098.00 | 1.37675 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −954.000 | −1.13622 | −0.568111 | − | 0.822952i | \(-0.692326\pi\) | ||||
−0.568111 | + | 0.822952i | \(0.692326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −792.000 | −0.912353 | ||||||||
\(92\) | −18.0000 | −0.0203981 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1854.00 | 2.03431 | ||||||||
\(95\) | 504.000 | 0.544309 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 326.000 | 0.341240 | 0.170620 | − | 0.985337i | \(-0.445423\pi\) | ||||
0.170620 | + | 0.985337i | \(0.445423\pi\) | |||||||
\(98\) | 597.000 | 0.615368 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 19.0000 | 0.0190000 | ||||||||
\(101\) | −1326.00 | −1.30636 | −0.653178 | − | 0.757205i | \(-0.726565\pi\) | ||||
−0.653178 | + | 0.757205i | \(0.726565\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1564.00 | −1.49617 | −0.748085 | − | 0.663603i | \(-0.769026\pi\) | ||||
−0.748085 | + | 0.663603i | \(0.769026\pi\) | |||||||
\(104\) | −1386.00 | −1.30681 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1224.00 | −1.12156 | ||||||||
\(107\) | 84.0000 | 0.0758933 | 0.0379467 | − | 0.999280i | \(-0.487918\pi\) | ||||
0.0379467 | + | 0.999280i | \(0.487918\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1122.00 | −0.985946 | −0.492973 | − | 0.870045i | \(-0.664090\pi\) | ||||
−0.492973 | + | 0.870045i | \(0.664090\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −852.000 | −0.718807 | ||||||||
\(113\) | 906.000 | 0.754242 | 0.377121 | − | 0.926164i | \(-0.376914\pi\) | ||||
0.377121 | + | 0.926164i | \(0.376914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −216.000 | −0.175149 | ||||||||
\(116\) | −186.000 | −0.148876 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −396.000 | −0.308939 | ||||||||
\(119\) | 1368.00 | 1.05382 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1890.00 | −1.40256 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −308.000 | −0.223058 | ||||||||
\(125\) | −1272.00 | −0.910169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1992.00 | −1.39182 | −0.695911 | − | 0.718128i | \(-0.744999\pi\) | ||||
−0.695911 | + | 0.718128i | \(0.744999\pi\) | |||||||
\(128\) | −1659.00 | −1.14560 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2376.00 | 1.60299 | ||||||||
\(131\) | −1068.00 | −0.712302 | −0.356151 | − | 0.934428i | \(-0.615911\pi\) | ||||
−0.356151 | + | 0.934428i | \(0.615911\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 504.000 | 0.328589 | ||||||||
\(134\) | 1356.00 | 0.874183 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2394.00 | 1.50944 | ||||||||
\(137\) | 462.000 | 0.288112 | 0.144056 | − | 0.989570i | \(-0.453985\pi\) | ||||
0.144056 | + | 0.989570i | \(0.453985\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2274.00 | 1.38761 | 0.693806 | − | 0.720162i | \(-0.255932\pi\) | ||||
0.693806 | + | 0.720162i | \(0.255932\pi\) | |||||||
\(140\) | 144.000 | 0.0869302 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −846.000 | −0.499963 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2232.00 | −1.27833 | ||||||||
\(146\) | −2052.00 | −1.16318 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −146.000 | −0.0810887 | ||||||||
\(149\) | 750.000 | 0.412365 | 0.206183 | − | 0.978514i | \(-0.433896\pi\) | ||||
0.206183 | + | 0.978514i | \(0.433896\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −720.000 | −0.388032 | −0.194016 | − | 0.980998i | \(-0.562151\pi\) | ||||
−0.194016 | + | 0.980998i | \(0.562151\pi\) | |||||||
\(152\) | 882.000 | 0.470656 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3696.00 | −1.91529 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3206.00 | −1.62972 | −0.814862 | − | 0.579655i | \(-0.803187\pi\) | ||||
−0.814862 | + | 0.579655i | \(0.803187\pi\) | |||||||
\(158\) | −3816.00 | −1.92142 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 540.000 | 0.266817 | ||||||||
\(161\) | −216.000 | −0.105734 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 740.000 | 0.355591 | 0.177795 | − | 0.984067i | \(-0.443104\pi\) | ||||
0.177795 | + | 0.984067i | \(0.443104\pi\) | |||||||
\(164\) | −42.0000 | −0.0199979 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1296.00 | −0.605958 | ||||||||
\(167\) | 1968.00 | 0.911907 | 0.455953 | − | 0.890004i | \(-0.349298\pi\) | ||||
0.455953 | + | 0.890004i | \(0.349298\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2159.00 | 0.982704 | ||||||||
\(170\) | −4104.00 | −1.85154 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −366.000 | −0.162251 | ||||||||
\(173\) | −2898.00 | −1.27359 | −0.636794 | − | 0.771034i | \(-0.719740\pi\) | ||||
−0.636794 | + | 0.771034i | \(0.719740\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 228.000 | 0.0984867 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2862.00 | 1.20515 | ||||||||
\(179\) | −120.000 | −0.0501074 | −0.0250537 | − | 0.999686i | \(-0.507976\pi\) | ||||
−0.0250537 | + | 0.999686i | \(0.507976\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1150.00 | −0.472259 | −0.236129 | − | 0.971722i | \(-0.575879\pi\) | ||||
−0.236129 | + | 0.971722i | \(0.575879\pi\) | |||||||
\(182\) | 2376.00 | 0.967697 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −378.000 | −0.151449 | ||||||||
\(185\) | −1752.00 | −0.696268 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −618.000 | −0.239746 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1512.00 | −0.577326 | ||||||||
\(191\) | 1518.00 | 0.575071 | 0.287536 | − | 0.957770i | \(-0.407164\pi\) | ||||
0.287536 | + | 0.957770i | \(0.407164\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2052.00 | −0.765317 | −0.382659 | − | 0.923890i | \(-0.624991\pi\) | ||||
−0.382659 | + | 0.923890i | \(0.624991\pi\) | |||||||
\(194\) | −978.000 | −0.361940 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −199.000 | −0.0725219 | ||||||||
\(197\) | 3282.00 | 1.18697 | 0.593484 | − | 0.804846i | \(-0.297752\pi\) | ||||
0.593484 | + | 0.804846i | \(0.297752\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −704.000 | −0.250780 | −0.125390 | − | 0.992108i | \(-0.540018\pi\) | ||||
−0.125390 | + | 0.992108i | \(0.540018\pi\) | |||||||
\(200\) | 399.000 | 0.141068 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3978.00 | 1.38560 | ||||||||
\(203\) | −2232.00 | −0.771703 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −504.000 | −0.171712 | ||||||||
\(206\) | 4692.00 | 1.58693 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4686.00 | 1.56209 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1986.00 | −0.647971 | −0.323985 | − | 0.946062i | \(-0.605023\pi\) | ||||
−0.323985 | + | 0.946062i | \(0.605023\pi\) | |||||||
\(212\) | 408.000 | 0.132177 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −252.000 | −0.0804970 | ||||||||
\(215\) | −4392.00 | −1.39317 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3696.00 | −1.15623 | ||||||||
\(218\) | 3366.00 | 1.04575 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7524.00 | −2.29013 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2248.00 | −0.675055 | −0.337527 | − | 0.941316i | \(-0.609591\pi\) | ||||
−0.337527 | + | 0.941316i | \(0.609591\pi\) | |||||||
\(224\) | 540.000 | 0.161073 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2718.00 | −0.799994 | ||||||||
\(227\) | 2796.00 | 0.817520 | 0.408760 | − | 0.912642i | \(-0.365961\pi\) | ||||
0.408760 | + | 0.912642i | \(0.365961\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2198.00 | −0.634270 | −0.317135 | − | 0.948380i | \(-0.602721\pi\) | ||||
−0.317135 | + | 0.948380i | \(0.602721\pi\) | |||||||
\(230\) | 648.000 | 0.185773 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3906.00 | −1.10535 | ||||||||
\(233\) | −5802.00 | −1.63134 | −0.815669 | − | 0.578519i | \(-0.803631\pi\) | ||||
−0.815669 | + | 0.578519i | \(0.803631\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7416.00 | −2.05858 | ||||||||
\(236\) | 132.000 | 0.0364088 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4104.00 | −1.11774 | ||||||||
\(239\) | −1104.00 | −0.298794 | −0.149397 | − | 0.988777i | \(-0.547733\pi\) | ||||
−0.149397 | + | 0.988777i | \(0.547733\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5208.00 | 1.39202 | 0.696010 | − | 0.718032i | \(-0.254957\pi\) | ||||
0.696010 | + | 0.718032i | \(0.254957\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 630.000 | 0.165294 | ||||||||
\(245\) | −2388.00 | −0.622709 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2772.00 | −0.714082 | ||||||||
\(248\) | −6468.00 | −1.65612 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3816.00 | 0.965380 | ||||||||
\(251\) | 2880.00 | 0.724239 | 0.362119 | − | 0.932132i | \(-0.382053\pi\) | ||||
0.362119 | + | 0.932132i | \(0.382053\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 5976.00 | 1.47625 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | −3762.00 | −0.913102 | −0.456551 | − | 0.889697i | \(-0.650915\pi\) | ||||
−0.456551 | + | 0.889697i | \(0.650915\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1752.00 | −0.420324 | ||||||||
\(260\) | −792.000 | −0.188914 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3204.00 | 0.755511 | ||||||||
\(263\) | 1920.00 | 0.450161 | 0.225080 | − | 0.974340i | \(-0.427736\pi\) | ||||
0.225080 | + | 0.974340i | \(0.427736\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4896.00 | 1.13494 | ||||||||
\(266\) | −1512.00 | −0.348521 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −452.000 | −0.103023 | ||||||||
\(269\) | 6144.00 | 1.39259 | 0.696294 | − | 0.717756i | \(-0.254831\pi\) | ||||
0.696294 | + | 0.717756i | \(0.254831\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5904.00 | −1.32340 | −0.661702 | − | 0.749767i | \(-0.730166\pi\) | ||||
−0.661702 | + | 0.749767i | \(0.730166\pi\) | |||||||
\(272\) | −8094.00 | −1.80430 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1386.00 | −0.305589 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3630.00 | −0.787385 | −0.393692 | − | 0.919242i | \(-0.628802\pi\) | ||||
−0.393692 | + | 0.919242i | \(0.628802\pi\) | |||||||
\(278\) | −6822.00 | −1.47179 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3024.00 | 0.645423 | ||||||||
\(281\) | −1842.00 | −0.391048 | −0.195524 | − | 0.980699i | \(-0.562641\pi\) | ||||
−0.195524 | + | 0.980699i | \(0.562641\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2382.00 | −0.500336 | −0.250168 | − | 0.968202i | \(-0.580486\pi\) | ||||
−0.250168 | + | 0.968202i | \(0.580486\pi\) | |||||||
\(284\) | 282.000 | 0.0589212 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −504.000 | −0.103659 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8083.00 | 1.64523 | ||||||||
\(290\) | 6696.00 | 1.35587 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 684.000 | 0.137082 | ||||||||
\(293\) | −2238.00 | −0.446230 | −0.223115 | − | 0.974792i | \(-0.571623\pi\) | ||||
−0.223115 | + | 0.974792i | \(0.571623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1584.00 | 0.312624 | ||||||||
\(296\) | −3066.00 | −0.602053 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2250.00 | −0.437379 | ||||||||
\(299\) | 1188.00 | 0.229779 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4392.00 | −0.841032 | ||||||||
\(302\) | 2160.00 | 0.411570 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2982.00 | −0.562597 | ||||||||
\(305\) | 7560.00 | 1.41929 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −558.000 | −0.103735 | −0.0518677 | − | 0.998654i | \(-0.516517\pi\) | ||||
−0.0518677 | + | 0.998654i | \(0.516517\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11088.0 | 2.03147 | ||||||||
\(311\) | 4062.00 | 0.740627 | 0.370313 | − | 0.928907i | \(-0.379250\pi\) | ||||
0.370313 | + | 0.928907i | \(0.379250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3098.00 | −0.559455 | −0.279727 | − | 0.960079i | \(-0.590244\pi\) | ||||
−0.279727 | + | 0.960079i | \(0.590244\pi\) | |||||||
\(314\) | 9618.00 | 1.72858 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1272.00 | 0.226442 | ||||||||
\(317\) | 3600.00 | 0.637843 | 0.318921 | − | 0.947781i | \(-0.396679\pi\) | ||||
0.318921 | + | 0.947781i | \(0.396679\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 5196.00 | 0.907704 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 648.000 | 0.112148 | ||||||||
\(323\) | 4788.00 | 0.824803 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1254.00 | −0.214029 | ||||||||
\(326\) | −2220.00 | −0.377161 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −882.000 | −0.148477 | ||||||||
\(329\) | −7416.00 | −1.24273 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4156.00 | −0.690134 | −0.345067 | − | 0.938578i | \(-0.612144\pi\) | ||||
−0.345067 | + | 0.938578i | \(0.612144\pi\) | |||||||
\(332\) | 432.000 | 0.0714129 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5904.00 | −0.967223 | ||||||||
\(335\) | −5424.00 | −0.884611 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2748.00 | 0.444193 | 0.222097 | − | 0.975025i | \(-0.428710\pi\) | ||||
0.222097 | + | 0.975025i | \(0.428710\pi\) | |||||||
\(338\) | −6477.00 | −1.04231 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1368.00 | 0.218207 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6504.00 | −1.02386 | ||||||||
\(344\) | −7686.00 | −1.20466 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8694.00 | 1.35084 | ||||||||
\(347\) | −696.000 | −0.107675 | −0.0538375 | − | 0.998550i | \(-0.517145\pi\) | ||||
−0.0538375 | + | 0.998550i | \(0.517145\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3246.00 | −0.497864 | −0.248932 | − | 0.968521i | \(-0.580080\pi\) | ||||
−0.248932 | + | 0.968521i | \(0.580080\pi\) | |||||||
\(350\) | −684.000 | −0.104461 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10926.0 | 1.64740 | 0.823700 | − | 0.567026i | \(-0.191906\pi\) | ||||
0.823700 | + | 0.567026i | \(0.191906\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3384.00 | 0.505927 | ||||||||
\(356\) | −954.000 | −0.142028 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 360.000 | 0.0531469 | ||||||||
\(359\) | 1584.00 | 0.232870 | 0.116435 | − | 0.993198i | \(-0.462853\pi\) | ||||
0.116435 | + | 0.993198i | \(0.462853\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5095.00 | −0.742820 | ||||||||
\(362\) | 3450.00 | 0.500906 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −792.000 | −0.114044 | ||||||||
\(365\) | 8208.00 | 1.17706 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −232.000 | −0.0329981 | −0.0164990 | − | 0.999864i | \(-0.505252\pi\) | ||||
−0.0164990 | + | 0.999864i | \(0.505252\pi\) | |||||||
\(368\) | 1278.00 | 0.181034 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5256.00 | 0.738504 | ||||||||
\(371\) | 4896.00 | 0.685142 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10806.0 | −1.50004 | −0.750018 | − | 0.661417i | \(-0.769955\pi\) | ||||
−0.750018 | + | 0.661417i | \(0.769955\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12978.0 | −1.78002 | ||||||||
\(377\) | 12276.0 | 1.67705 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 164.000 | 0.0222272 | 0.0111136 | − | 0.999938i | \(-0.496462\pi\) | ||||
0.0111136 | + | 0.999938i | \(0.496462\pi\) | |||||||
\(380\) | 504.000 | 0.0680386 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4554.00 | −0.609955 | ||||||||
\(383\) | −8058.00 | −1.07505 | −0.537526 | − | 0.843247i | \(-0.680641\pi\) | ||||
−0.537526 | + | 0.843247i | \(0.680641\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6156.00 | 0.811741 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 326.000 | 0.0426550 | ||||||||
\(389\) | 708.000 | 0.0922803 | 0.0461401 | − | 0.998935i | \(-0.485308\pi\) | ||||
0.0461401 | + | 0.998935i | \(0.485308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2052.00 | −0.265407 | ||||||||
\(392\) | −4179.00 | −0.538447 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9846.00 | −1.25897 | ||||||||
\(395\) | 15264.0 | 1.94434 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −286.000 | −0.0361560 | −0.0180780 | − | 0.999837i | \(-0.505755\pi\) | ||||
−0.0180780 | + | 0.999837i | \(0.505755\pi\) | |||||||
\(398\) | 2112.00 | 0.265992 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1349.00 | −0.168625 | ||||||||
\(401\) | 5262.00 | 0.655291 | 0.327646 | − | 0.944801i | \(-0.393745\pi\) | ||||
0.327646 | + | 0.944801i | \(0.393745\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20328.0 | 2.51268 | ||||||||
\(404\) | −1326.00 | −0.163294 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6696.00 | 0.818515 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2280.00 | −0.275645 | −0.137822 | − | 0.990457i | \(-0.544010\pi\) | ||||
−0.137822 | + | 0.990457i | \(0.544010\pi\) | |||||||
\(410\) | 1512.00 | 0.182128 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1564.00 | −0.187021 | ||||||||
\(413\) | 1584.00 | 0.188725 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5184.00 | 0.613187 | ||||||||
\(416\) | −2970.00 | −0.350039 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4272.00 | −0.498093 | −0.249046 | − | 0.968492i | \(-0.580117\pi\) | ||||
−0.249046 | + | 0.968492i | \(0.580117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10150.0 | 1.17501 | 0.587507 | − | 0.809219i | \(-0.300110\pi\) | ||||
0.587507 | + | 0.809219i | \(0.300110\pi\) | |||||||
\(422\) | 5958.00 | 0.687277 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8568.00 | 0.981365 | ||||||||
\(425\) | 2166.00 | 0.247215 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7560.00 | 0.856801 | ||||||||
\(428\) | 84.0000 | 0.00948667 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13176.0 | 1.47768 | ||||||||
\(431\) | −13056.0 | −1.45913 | −0.729565 | − | 0.683911i | \(-0.760278\pi\) | ||||
−0.729565 | + | 0.683911i | \(0.760278\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13682.0 | 1.51851 | 0.759255 | − | 0.650793i | \(-0.225563\pi\) | ||||
0.759255 | + | 0.650793i | \(0.225563\pi\) | |||||||
\(434\) | 11088.0 | 1.22636 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1122.00 | −0.123243 | ||||||||
\(437\) | −756.000 | −0.0827560 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7020.00 | −0.763203 | −0.381602 | − | 0.924327i | \(-0.624627\pi\) | ||||
−0.381602 | + | 0.924327i | \(0.624627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22572.0 | 2.42905 | ||||||||
\(443\) | 8916.00 | 0.956235 | 0.478117 | − | 0.878296i | \(-0.341319\pi\) | ||||
0.478117 | + | 0.878296i | \(0.341319\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11448.0 | −1.21952 | ||||||||
\(446\) | 6744.00 | 0.716004 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5196.00 | 0.547964 | ||||||||
\(449\) | −10110.0 | −1.06263 | −0.531314 | − | 0.847175i | \(-0.678302\pi\) | ||||
−0.531314 | + | 0.847175i | \(0.678302\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 906.000 | 0.0942802 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8388.00 | −0.867111 | ||||||||
\(455\) | −9504.00 | −0.979240 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1824.00 | 0.186703 | 0.0933513 | − | 0.995633i | \(-0.470242\pi\) | ||||
0.0933513 | + | 0.995633i | \(0.470242\pi\) | |||||||
\(458\) | 6594.00 | 0.672745 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −216.000 | −0.0218936 | ||||||||
\(461\) | −17118.0 | −1.72942 | −0.864712 | − | 0.502267i | \(-0.832499\pi\) | ||||
−0.864712 | + | 0.502267i | \(0.832499\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 596.000 | 0.0598239 | 0.0299120 | − | 0.999553i | \(-0.490477\pi\) | ||||
0.0299120 | + | 0.999553i | \(0.490477\pi\) | |||||||
\(464\) | 13206.0 | 1.32128 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17406.0 | 1.73029 | ||||||||
\(467\) | −5856.00 | −0.580264 | −0.290132 | − | 0.956987i | \(-0.593699\pi\) | ||||
−0.290132 | + | 0.956987i | \(0.593699\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5424.00 | −0.534024 | ||||||||
\(470\) | 22248.0 | 2.18345 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2772.00 | 0.270321 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 798.000 | 0.0770837 | ||||||||
\(476\) | 1368.00 | 0.131727 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3312.00 | 0.316919 | ||||||||
\(479\) | −3264.00 | −0.311349 | −0.155674 | − | 0.987808i | \(-0.549755\pi\) | ||||
−0.155674 | + | 0.987808i | \(0.549755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9636.00 | 0.913438 | ||||||||
\(482\) | −15624.0 | −1.47646 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3912.00 | 0.366257 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9920.00 | −0.923035 | −0.461518 | − | 0.887131i | \(-0.652695\pi\) | ||||
−0.461518 | + | 0.887131i | \(0.652695\pi\) | |||||||
\(488\) | 13230.0 | 1.22724 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7164.00 | 0.660483 | ||||||||
\(491\) | 10620.0 | 0.976118 | 0.488059 | − | 0.872811i | \(-0.337705\pi\) | ||||
0.488059 | + | 0.872811i | \(0.337705\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21204.0 | −1.93708 | ||||||||
\(494\) | 8316.00 | 0.757398 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21868.0 | 1.97964 | ||||||||
\(497\) | 3384.00 | 0.305419 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 52.0000 | 0.00466501 | 0.00233250 | − | 0.999997i | \(-0.499258\pi\) | ||||
0.00233250 | + | 0.999997i | \(0.499258\pi\) | |||||||
\(500\) | −1272.00 | −0.113771 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8640.00 | −0.768171 | ||||||||
\(503\) | −8568.00 | −0.759499 | −0.379750 | − | 0.925089i | \(-0.623990\pi\) | ||||
−0.379750 | + | 0.925089i | \(0.623990\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15912.0 | −1.40213 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1992.00 | −0.173978 | ||||||||
\(509\) | 21096.0 | 1.83706 | 0.918530 | − | 0.395351i | \(-0.129377\pi\) | ||||
0.918530 | + | 0.395351i | \(0.129377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8208.00 | 0.710569 | ||||||||
\(512\) | 8733.00 | 0.753804 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11286.0 | 0.968491 | ||||||||
\(515\) | −18768.0 | −1.60586 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 5256.00 | 0.445821 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −16632.0 | −1.40262 | ||||||||
\(521\) | −15762.0 | −1.32542 | −0.662712 | − | 0.748874i | \(-0.730595\pi\) | ||||
−0.662712 | + | 0.748874i | \(0.730595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23778.0 | 1.98803 | 0.994015 | − | 0.109247i | \(-0.0348438\pi\) | ||||
0.994015 | + | 0.109247i | \(0.0348438\pi\) | |||||||
\(524\) | −1068.00 | −0.0890378 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5760.00 | −0.477468 | ||||||||
\(527\) | −35112.0 | −2.90228 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11843.0 | −0.973371 | ||||||||
\(530\) | −14688.0 | −1.20378 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 504.000 | 0.0410736 | ||||||||
\(533\) | 2772.00 | 0.225270 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1008.00 | 0.0814573 | ||||||||
\(536\) | −9492.00 | −0.764910 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18432.0 | −1.47706 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5478.00 | 0.435338 | 0.217669 | − | 0.976023i | \(-0.430155\pi\) | ||||
0.217669 | + | 0.976023i | \(0.430155\pi\) | |||||||
\(542\) | 17712.0 | 1.40368 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5130.00 | 0.404314 | ||||||||
\(545\) | −13464.0 | −1.05823 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6714.00 | −0.524808 | −0.262404 | − | 0.964958i | \(-0.584515\pi\) | ||||
−0.262404 | + | 0.964958i | \(0.584515\pi\) | |||||||
\(548\) | 462.000 | 0.0360140 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7812.00 | −0.603997 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15264.0 | 1.17376 | ||||||||
\(554\) | 10890.0 | 0.835148 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2274.00 | 0.173452 | ||||||||
\(557\) | 7218.00 | 0.549078 | 0.274539 | − | 0.961576i | \(-0.411475\pi\) | ||||
0.274539 | + | 0.961576i | \(0.411475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24156.0 | 1.82771 | ||||||||
\(560\) | −10224.0 | −0.771505 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5526.00 | 0.414769 | ||||||||
\(563\) | −552.000 | −0.0413215 | −0.0206608 | − | 0.999787i | \(-0.506577\pi\) | ||||
−0.0206608 | + | 0.999787i | \(0.506577\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10872.0 | 0.809537 | ||||||||
\(566\) | 7146.00 | 0.530687 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5922.00 | 0.437468 | ||||||||
\(569\) | −5766.00 | −0.424821 | −0.212411 | − | 0.977180i | \(-0.568131\pi\) | ||||
−0.212411 | + | 0.977180i | \(0.568131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17070.0 | 1.25106 | 0.625532 | − | 0.780199i | \(-0.284882\pi\) | ||||
0.625532 | + | 0.780199i | \(0.284882\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1512.00 | 0.109947 | ||||||||
\(575\) | −342.000 | −0.0248041 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26170.0 | 1.88817 | 0.944083 | − | 0.329709i | \(-0.106951\pi\) | ||||
0.944083 | + | 0.329709i | \(0.106951\pi\) | |||||||
\(578\) | −24249.0 | −1.74503 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2232.00 | −0.159791 | ||||||||
\(581\) | 5184.00 | 0.370170 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 14364.0 | 1.01779 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6714.00 | 0.473298 | ||||||||
\(587\) | −27996.0 | −1.96852 | −0.984258 | − | 0.176739i | \(-0.943445\pi\) | ||||
−0.984258 | + | 0.176739i | \(0.943445\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12936.0 | −0.904955 | ||||||||
\(590\) | −4752.00 | −0.331588 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10366.0 | 0.719662 | ||||||||
\(593\) | 28398.0 | 1.96655 | 0.983277 | − | 0.182118i | \(-0.0582954\pi\) | ||||
0.983277 | + | 0.182118i | \(0.0582954\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16416.0 | 1.13108 | ||||||||
\(596\) | 750.000 | 0.0515456 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3564.00 | −0.243717 | ||||||||
\(599\) | −13482.0 | −0.919632 | −0.459816 | − | 0.888014i | \(-0.652085\pi\) | ||||
−0.459816 | + | 0.888014i | \(0.652085\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4488.00 | 0.304608 | 0.152304 | − | 0.988334i | \(-0.451331\pi\) | ||||
0.152304 | + | 0.988334i | \(0.451331\pi\) | |||||||
\(602\) | 13176.0 | 0.892049 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −720.000 | −0.0485039 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −600.000 | −0.0401207 | −0.0200603 | − | 0.999799i | \(-0.506386\pi\) | ||||
−0.0200603 | + | 0.999799i | \(0.506386\pi\) | |||||||
\(608\) | 1890.00 | 0.126068 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −22680.0 | −1.50539 | ||||||||
\(611\) | 40788.0 | 2.70066 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1674.00 | −0.110297 | −0.0551486 | − | 0.998478i | \(-0.517563\pi\) | ||||
−0.0551486 | + | 0.998478i | \(0.517563\pi\) | |||||||
\(614\) | 1674.00 | 0.110028 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18834.0 | 1.22890 | 0.614448 | − | 0.788958i | \(-0.289379\pi\) | ||||
0.614448 | + | 0.788958i | \(0.289379\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7436.00 | 0.482840 | 0.241420 | − | 0.970421i | \(-0.422387\pi\) | ||||
0.241420 | + | 0.970421i | \(0.422387\pi\) | |||||||
\(620\) | −3696.00 | −0.239411 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12186.0 | −0.785553 | ||||||||
\(623\) | −11448.0 | −0.736203 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17639.0 | −1.12890 | ||||||||
\(626\) | 9294.00 | 0.593391 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3206.00 | −0.203715 | ||||||||
\(629\) | −16644.0 | −1.05507 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23852.0 | −1.50481 | −0.752403 | − | 0.658703i | \(-0.771106\pi\) | ||||
−0.752403 | + | 0.658703i | \(0.771106\pi\) | |||||||
\(632\) | 26712.0 | 1.68124 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10800.0 | −0.676534 | ||||||||
\(635\) | −23904.0 | −1.49386 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13134.0 | 0.816936 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19908.0 | −1.22958 | ||||||||
\(641\) | −10998.0 | −0.677683 | −0.338842 | − | 0.940843i | \(-0.610035\pi\) | ||||
−0.338842 | + | 0.940843i | \(0.610035\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16724.0 | 1.02571 | 0.512854 | − | 0.858476i | \(-0.328588\pi\) | ||||
0.512854 | + | 0.858476i | \(0.328588\pi\) | |||||||
\(644\) | −216.000 | −0.0132168 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14364.0 | −0.874836 | ||||||||
\(647\) | −26226.0 | −1.59359 | −0.796793 | − | 0.604252i | \(-0.793472\pi\) | ||||
−0.796793 | + | 0.604252i | \(0.793472\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3762.00 | 0.227012 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 740.000 | 0.0444488 | ||||||||
\(653\) | 1884.00 | 0.112904 | 0.0564522 | − | 0.998405i | \(-0.482021\pi\) | ||||
0.0564522 | + | 0.998405i | \(0.482021\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12816.0 | −0.764523 | ||||||||
\(656\) | 2982.00 | 0.177481 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22248.0 | 1.31811 | ||||||||
\(659\) | 22584.0 | 1.33497 | 0.667487 | − | 0.744622i | \(-0.267370\pi\) | ||||
0.667487 | + | 0.744622i | \(0.267370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2266.00 | 0.133339 | 0.0666696 | − | 0.997775i | \(-0.478763\pi\) | ||||
0.0666696 | + | 0.997775i | \(0.478763\pi\) | |||||||
\(662\) | 12468.0 | 0.731998 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9072.00 | 0.530214 | ||||||||
\(665\) | 6048.00 | 0.352679 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3348.00 | 0.194355 | ||||||||
\(668\) | 1968.00 | 0.113988 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16272.0 | 0.938272 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23604.0 | 1.35196 | 0.675979 | − | 0.736921i | \(-0.263721\pi\) | ||||
0.675979 | + | 0.736921i | \(0.263721\pi\) | |||||||
\(674\) | −8244.00 | −0.471138 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2159.00 | 0.122838 | ||||||||
\(677\) | 6594.00 | 0.374340 | 0.187170 | − | 0.982328i | \(-0.440069\pi\) | ||||
0.187170 | + | 0.982328i | \(0.440069\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3912.00 | 0.221103 | ||||||||
\(680\) | 28728.0 | 1.62010 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16368.0 | −0.916990 | −0.458495 | − | 0.888697i | \(-0.651611\pi\) | ||||
−0.458495 | + | 0.888697i | \(0.651611\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5544.00 | 0.309234 | ||||||||
\(686\) | 19512.0 | 1.08596 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 25986.0 | 1.43998 | ||||||||
\(689\) | −26928.0 | −1.48893 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11860.0 | −0.652931 | −0.326466 | − | 0.945209i | \(-0.605858\pi\) | ||||
−0.326466 | + | 0.945209i | \(0.605858\pi\) | |||||||
\(692\) | −2898.00 | −0.159199 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2088.00 | 0.114207 | ||||||||
\(695\) | 27288.0 | 1.48934 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4788.00 | −0.260199 | ||||||||
\(698\) | 9738.00 | 0.528064 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 228.000 | 0.0123108 | ||||||||
\(701\) | 28698.0 | 1.54623 | 0.773116 | − | 0.634265i | \(-0.218697\pi\) | ||||
0.773116 | + | 0.634265i | \(0.218697\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6132.00 | −0.328980 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −32778.0 | −1.74733 | ||||||||
\(707\) | −15912.0 | −0.846439 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10766.0 | −0.570276 | −0.285138 | − | 0.958486i | \(-0.592039\pi\) | ||||
−0.285138 | + | 0.958486i | \(0.592039\pi\) | |||||||
\(710\) | −10152.0 | −0.536617 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −20034.0 | −1.05450 | ||||||||
\(713\) | 5544.00 | 0.291198 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −120.000 | −0.00626342 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4752.00 | −0.246996 | ||||||||
\(719\) | 20226.0 | 1.04910 | 0.524550 | − | 0.851380i | \(-0.324234\pi\) | ||||
0.524550 | + | 0.851380i | \(0.324234\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18768.0 | −0.969427 | ||||||||
\(722\) | 15285.0 | 0.787879 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1150.00 | −0.0590323 | ||||||||
\(725\) | −3534.00 | −0.181034 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29576.0 | −1.50882 | −0.754411 | − | 0.656403i | \(-0.772077\pi\) | ||||
−0.754411 | + | 0.656403i | \(0.772077\pi\) | |||||||
\(728\) | −16632.0 | −0.846735 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −24624.0 | −1.24846 | ||||||||
\(731\) | −41724.0 | −2.11111 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16878.0 | 0.850482 | 0.425241 | − | 0.905080i | \(-0.360189\pi\) | ||||
0.425241 | + | 0.905080i | \(0.360189\pi\) | |||||||
\(734\) | 696.000 | 0.0349998 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −810.000 | −0.0405666 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6726.00 | −0.334804 | −0.167402 | − | 0.985889i | \(-0.553538\pi\) | ||||
−0.167402 | + | 0.985889i | \(0.553538\pi\) | |||||||
\(740\) | −1752.00 | −0.0870335 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14688.0 | −0.726703 | ||||||||
\(743\) | −20592.0 | −1.01675 | −0.508376 | − | 0.861135i | \(-0.669754\pi\) | ||||
−0.508376 | + | 0.861135i | \(0.669754\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9000.00 | 0.442597 | ||||||||
\(746\) | 32418.0 | 1.59103 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1008.00 | 0.0491743 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8764.00 | 0.425836 | 0.212918 | − | 0.977070i | \(-0.431703\pi\) | ||||
0.212918 | + | 0.977070i | \(0.431703\pi\) | |||||||
\(752\) | 43878.0 | 2.12775 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −36828.0 | −1.77878 | ||||||||
\(755\) | −8640.00 | −0.416479 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11810.0 | −0.567030 | −0.283515 | − | 0.958968i | \(-0.591501\pi\) | ||||
−0.283515 | + | 0.958968i | \(0.591501\pi\) | |||||||
\(758\) | −492.000 | −0.0235755 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10584.0 | 0.505161 | ||||||||
\(761\) | 29346.0 | 1.39789 | 0.698943 | − | 0.715177i | \(-0.253654\pi\) | ||||
0.698943 | + | 0.715177i | \(0.253654\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13464.0 | −0.638833 | ||||||||
\(764\) | 1518.00 | 0.0718839 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24174.0 | 1.14026 | ||||||||
\(767\) | −8712.00 | −0.410133 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15684.0 | 0.735474 | 0.367737 | − | 0.929930i | \(-0.380133\pi\) | ||||
0.367737 | + | 0.929930i | \(0.380133\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2052.00 | −0.0956646 | ||||||||
\(773\) | 25632.0 | 1.19265 | 0.596325 | − | 0.802743i | \(-0.296627\pi\) | ||||
0.596325 | + | 0.802743i | \(0.296627\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5852.00 | −0.271239 | ||||||||
\(776\) | 6846.00 | 0.316697 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2124.00 | −0.0978780 | ||||||||
\(779\) | −1764.00 | −0.0811320 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 6156.00 | 0.281507 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 14129.0 | 0.643632 | ||||||||
\(785\) | −38472.0 | −1.74920 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37854.0 | −1.71455 | −0.857274 | − | 0.514860i | \(-0.827844\pi\) | ||||
−0.857274 | + | 0.514860i | \(0.827844\pi\) | |||||||
\(788\) | 3282.00 | 0.148371 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −45792.0 | −2.06229 | ||||||||
\(791\) | 10872.0 | 0.488703 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41580.0 | −1.86198 | ||||||||
\(794\) | 858.000 | 0.0383492 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −704.000 | −0.0313475 | ||||||||
\(797\) | 23484.0 | 1.04372 | 0.521861 | − | 0.853031i | \(-0.325238\pi\) | ||||
0.521861 | + | 0.853031i | \(0.325238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −70452.0 | −3.11942 | ||||||||
\(800\) | 855.000 | 0.0377860 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15786.0 | −0.695041 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2592.00 | −0.113486 | ||||||||
\(806\) | −60984.0 | −2.66510 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −27846.0 | −1.21240 | ||||||||
\(809\) | −9054.00 | −0.393476 | −0.196738 | − | 0.980456i | \(-0.563035\pi\) | ||||
−0.196738 | + | 0.980456i | \(0.563035\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9858.00 | −0.426833 | −0.213416 | − | 0.976961i | \(-0.568459\pi\) | ||||
−0.213416 | + | 0.976961i | \(0.568459\pi\) | |||||||
\(812\) | −2232.00 | −0.0964629 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8880.00 | 0.381660 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15372.0 | −0.658260 | ||||||||
\(818\) | 6840.00 | 0.292366 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −504.000 | −0.0214640 | ||||||||
\(821\) | 18210.0 | 0.774097 | 0.387048 | − | 0.922059i | \(-0.373495\pi\) | ||||
0.387048 | + | 0.922059i | \(0.373495\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41240.0 | 1.74670 | 0.873351 | − | 0.487091i | \(-0.161942\pi\) | ||||
0.873351 | + | 0.487091i | \(0.161942\pi\) | |||||||
\(824\) | −32844.0 | −1.38856 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4752.00 | −0.200173 | ||||||||
\(827\) | −37680.0 | −1.58436 | −0.792178 | − | 0.610290i | \(-0.791053\pi\) | ||||
−0.792178 | + | 0.610290i | \(0.791053\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11626.0 | −0.487078 | −0.243539 | − | 0.969891i | \(-0.578308\pi\) | ||||
−0.243539 | + | 0.969891i | \(0.578308\pi\) | |||||||
\(830\) | −15552.0 | −0.650383 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −28578.0 | −1.19082 | ||||||||
\(833\) | −22686.0 | −0.943605 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23616.0 | 0.978761 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12816.0 | 0.528307 | ||||||||
\(839\) | −12150.0 | −0.499958 | −0.249979 | − | 0.968251i | \(-0.580424\pi\) | ||||
−0.249979 | + | 0.968251i | \(0.580424\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10207.0 | 0.418508 | ||||||||
\(842\) | −30450.0 | −1.24629 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1986.00 | −0.0809964 | ||||||||
\(845\) | 25908.0 | 1.05475 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −28968.0 | −1.17307 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6498.00 | −0.262211 | ||||||||
\(851\) | 2628.00 | 0.105860 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41022.0 | 1.64662 | 0.823310 | − | 0.567592i | \(-0.192125\pi\) | ||||
0.823310 | + | 0.567592i | \(0.192125\pi\) | |||||||
\(854\) | −22680.0 | −0.908775 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1764.00 | 0.0704349 | ||||||||
\(857\) | 9234.00 | 0.368060 | 0.184030 | − | 0.982921i | \(-0.441086\pi\) | ||||
0.184030 | + | 0.982921i | \(0.441086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30004.0 | −1.19176 | −0.595881 | − | 0.803073i | \(-0.703197\pi\) | ||||
−0.595881 | + | 0.803073i | \(0.703197\pi\) | |||||||
\(860\) | −4392.00 | −0.174146 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 39168.0 | 1.54764 | ||||||||
\(863\) | −14958.0 | −0.590007 | −0.295004 | − | 0.955496i | \(-0.595321\pi\) | ||||
−0.295004 | + | 0.955496i | \(0.595321\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34776.0 | −1.36696 | ||||||||
\(866\) | −41046.0 | −1.61062 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3696.00 | −0.144528 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29832.0 | 1.16053 | ||||||||
\(872\) | −23562.0 | −0.915034 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2268.00 | 0.0877760 | ||||||||
\(875\) | −15264.0 | −0.589734 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3714.00 | 0.143002 | 0.0715011 | − | 0.997441i | \(-0.477221\pi\) | ||||
0.0715011 | + | 0.997441i | \(0.477221\pi\) | |||||||
\(878\) | 21060.0 | 0.809500 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45390.0 | −1.73579 | −0.867893 | − | 0.496751i | \(-0.834526\pi\) | ||||
−0.867893 | + | 0.496751i | \(0.834526\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23452.0 | 0.893797 | 0.446898 | − | 0.894585i | \(-0.352529\pi\) | ||||
0.446898 | + | 0.894585i | \(0.352529\pi\) | |||||||
\(884\) | −7524.00 | −0.286266 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26748.0 | −1.01424 | ||||||||
\(887\) | −27072.0 | −1.02479 | −0.512395 | − | 0.858750i | \(-0.671242\pi\) | ||||
−0.512395 | + | 0.858750i | \(0.671242\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23904.0 | −0.901816 | ||||||||
\(890\) | 34344.0 | 1.29350 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2248.00 | −0.0843818 | ||||||||
\(893\) | −25956.0 | −0.972659 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1440.00 | −0.0537809 | ||||||||
\(896\) | −19908.0 | −0.742276 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30330.0 | 1.12709 | ||||||||
\(899\) | 57288.0 | 2.12532 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46512.0 | 1.71980 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19026.0 | 0.699995 | ||||||||
\(905\) | −13800.0 | −0.506881 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29716.0 | −1.08788 | −0.543938 | − | 0.839125i | \(-0.683067\pi\) | ||||
−0.543938 | + | 0.839125i | \(0.683067\pi\) | |||||||
\(908\) | 2796.00 | 0.102190 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 28512.0 | 1.03864 | ||||||||
\(911\) | −17094.0 | −0.621679 | −0.310839 | − | 0.950462i | \(-0.600610\pi\) | ||||
−0.310839 | + | 0.950462i | \(0.600610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −5472.00 | −0.198028 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2198.00 | −0.0792838 | ||||||||
\(917\) | −12816.0 | −0.461528 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24840.0 | 0.891617 | 0.445808 | − | 0.895128i | \(-0.352916\pi\) | ||||
0.445808 | + | 0.895128i | \(0.352916\pi\) | |||||||
\(920\) | −4536.00 | −0.162552 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 51354.0 | 1.83433 | ||||||||
\(923\) | −18612.0 | −0.663729 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2774.00 | −0.0986038 | ||||||||
\(926\) | −1788.00 | −0.0634528 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8370.00 | −0.296076 | ||||||||
\(929\) | −10578.0 | −0.373577 | −0.186788 | − | 0.982400i | \(-0.559808\pi\) | ||||
−0.186788 | + | 0.982400i | \(0.559808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8358.00 | −0.294224 | ||||||||
\(932\) | −5802.00 | −0.203917 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17568.0 | 0.615463 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38208.0 | −1.33212 | −0.666062 | − | 0.745896i | \(-0.732022\pi\) | ||||
−0.666062 | + | 0.745896i | \(0.732022\pi\) | |||||||
\(938\) | 16272.0 | 0.566418 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7416.00 | −0.257323 | ||||||||
\(941\) | 2154.00 | 0.0746210 | 0.0373105 | − | 0.999304i | \(-0.488121\pi\) | ||||
0.0373105 | + | 0.999304i | \(0.488121\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 756.000 | 0.0261068 | ||||||||
\(944\) | −9372.00 | −0.323128 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6564.00 | −0.225239 | −0.112620 | − | 0.993638i | \(-0.535924\pi\) | ||||
−0.112620 | + | 0.993638i | \(0.535924\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45144.0 | −1.54419 | ||||||||
\(950\) | −2394.00 | −0.0817596 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 28728.0 | 0.978025 | ||||||||
\(953\) | 36162.0 | 1.22917 | 0.614587 | − | 0.788849i | \(-0.289323\pi\) | ||||
0.614587 | + | 0.788849i | \(0.289323\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18216.0 | 0.617231 | ||||||||
\(956\) | −1104.00 | −0.0373493 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9792.00 | 0.330235 | ||||||||
\(959\) | 5544.00 | 0.186679 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 65073.0 | 2.18432 | ||||||||
\(962\) | −28908.0 | −0.968848 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5208.00 | 0.174002 | ||||||||
\(965\) | −24624.0 | −0.821424 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37728.0 | −1.25465 | −0.627327 | − | 0.778756i | \(-0.715851\pi\) | ||||
−0.627327 | + | 0.778756i | \(0.715851\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11736.0 | −0.388474 | ||||||||
\(971\) | −24156.0 | −0.798355 | −0.399178 | − | 0.916874i | \(-0.630704\pi\) | ||||
−0.399178 | + | 0.916874i | \(0.630704\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27288.0 | 0.899089 | ||||||||
\(974\) | 29760.0 | 0.979027 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −44730.0 | −1.46698 | ||||||||
\(977\) | 23742.0 | 0.777455 | 0.388728 | − | 0.921353i | \(-0.372915\pi\) | ||||
0.388728 | + | 0.921353i | \(0.372915\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2388.00 | −0.0778386 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −31860.0 | −1.03533 | ||||||||
\(983\) | −11562.0 | −0.375148 | −0.187574 | − | 0.982250i | \(-0.560062\pi\) | ||||
−0.187574 | + | 0.982250i | \(0.560062\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 39384.0 | 1.27399 | ||||||||
\(986\) | 63612.0 | 2.05458 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2772.00 | −0.0892602 | ||||||||
\(989\) | 6588.00 | 0.211816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52180.0 | 1.67261 | 0.836303 | − | 0.548268i | \(-0.184713\pi\) | ||||
0.836303 | + | 0.548268i | \(0.184713\pi\) | |||||||
\(992\) | −13860.0 | −0.443604 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10152.0 | −0.323946 | ||||||||
\(995\) | −8448.00 | −0.269165 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15714.0 | 0.499165 | 0.249582 | − | 0.968354i | \(-0.419707\pi\) | ||||
0.249582 | + | 0.968354i | \(0.419707\pi\) | |||||||
\(998\) | −156.000 | −0.00494799 | ||||||||
\(999\) | 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 | 1089.4.a.c.1.1 | 1 | ||
3.2 | odd | 2 | 363.4.a.f.1.1 | yes | 1 | ||
11.10 | odd | 2 | 1089.4.a.i.1.1 | 1 | |||
33.32 | even | 2 | 363.4.a.b.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.4.a.b.1.1 | ✓ | 1 | 33.32 | even | 2 | ||
363.4.a.f.1.1 | yes | 1 | 3.2 | odd | 2 | ||
1089.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1089.4.a.i.1.1 | 1 | 11.10 | odd | 2 |