Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(1,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1728.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 864) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1728.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −19.0000 | −1.69941 | −0.849706 | − | 0.527257i | \(-0.823220\pi\) | ||||
−0.849706 | + | 0.527257i | \(0.823220\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.0000 | 0.701934 | 0.350967 | − | 0.936388i | \(-0.385853\pi\) | ||||
0.350967 | + | 0.936388i | \(0.385853\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 65.0000 | 1.78166 | 0.890829 | − | 0.454339i | \(-0.150124\pi\) | ||||
0.890829 | + | 0.454339i | \(0.150124\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 56.0000 | 1.19474 | 0.597369 | − | 0.801966i | \(-0.296213\pi\) | ||||
0.597369 | + | 0.801966i | \(0.296213\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 108.000 | 1.54081 | 0.770407 | − | 0.637552i | \(-0.220053\pi\) | ||||
0.770407 | + | 0.637552i | \(0.220053\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −58.0000 | −0.700322 | −0.350161 | − | 0.936690i | \(-0.613873\pi\) | ||||
−0.350161 | + | 0.936690i | \(0.613873\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 66.0000 | 0.598346 | 0.299173 | − | 0.954199i | \(-0.403289\pi\) | ||||
0.299173 | + | 0.954199i | \(0.403289\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 236.000 | 1.88800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −118.000 | −0.755588 | −0.377794 | − | 0.925890i | \(-0.623317\pi\) | ||||
−0.377794 | + | 0.925890i | \(0.623317\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −145.000 | −0.840089 | −0.420045 | − | 0.907503i | \(-0.637986\pi\) | ||||
−0.420045 | + | 0.907503i | \(0.637986\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −247.000 | −1.19287 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −190.000 | −0.844211 | −0.422106 | − | 0.906547i | \(-0.638709\pi\) | ||||
−0.422106 | + | 0.906547i | \(0.638709\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 430.000 | 1.63792 | 0.818960 | − | 0.573851i | \(-0.194551\pi\) | ||||
0.818960 | + | 0.573851i | \(0.194551\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −530.000 | −1.87963 | −0.939817 | − | 0.341679i | \(-0.889004\pi\) | ||||
−0.939817 | + | 0.341679i | \(0.889004\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 74.0000 | 0.229660 | 0.114830 | − | 0.993385i | \(-0.463368\pi\) | ||||
0.114830 | + | 0.993385i | \(0.463368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −174.000 | −0.507289 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 295.000 | 0.764554 | 0.382277 | − | 0.924048i | \(-0.375140\pi\) | ||||
0.382277 | + | 0.924048i | \(0.375140\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1235.00 | −3.02777 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 628.000 | 1.38574 | 0.692870 | − | 0.721063i | \(-0.256346\pi\) | ||||
0.692870 | + | 0.721063i | \(0.256346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −360.000 | −0.755627 | −0.377814 | − | 0.925882i | \(-0.623324\pi\) | ||||
−0.377814 | + | 0.925882i | \(0.623324\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1064.00 | −2.03035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −146.000 | −0.266220 | −0.133110 | − | 0.991101i | \(-0.542496\pi\) | ||||
−0.133110 | + | 0.991101i | \(0.542496\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −388.000 | −0.648551 | −0.324276 | − | 0.945963i | \(-0.605121\pi\) | ||||
−0.324276 | + | 0.945963i | \(0.605121\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 753.000 | 1.20729 | 0.603644 | − | 0.797254i | \(-0.293715\pi\) | ||||
0.603644 | + | 0.797254i | \(0.293715\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 845.000 | 1.25061 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1136.00 | 1.61785 | 0.808924 | − | 0.587913i | \(-0.200050\pi\) | ||||
0.808924 | + | 0.587913i | \(0.200050\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 153.000 | 0.202337 | 0.101168 | − | 0.994869i | \(-0.467742\pi\) | ||||
0.101168 | + | 0.994869i | \(0.467742\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2052.00 | −2.61848 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −850.000 | −1.01236 | −0.506179 | − | 0.862429i | \(-0.668942\pi\) | ||||
−0.506179 | + | 0.862429i | \(0.668942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 728.000 | 0.838628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1102.00 | 1.19013 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 391.000 | 0.409279 | 0.204639 | − | 0.978837i | \(-0.434398\pi\) | ||||
0.204639 | + | 0.978837i | \(0.434398\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −597.000 | −0.588156 | −0.294078 | − | 0.955781i | \(-0.595012\pi\) | ||||
−0.294078 | + | 0.955781i | \(0.595012\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 252.000 | 0.241071 | 0.120535 | − | 0.992709i | \(-0.461539\pi\) | ||||
0.120535 | + | 0.992709i | \(0.461539\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −395.000 | −0.356879 | −0.178440 | − | 0.983951i | \(-0.557105\pi\) | ||||
−0.178440 | + | 0.983951i | \(0.557105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −254.000 | −0.223200 | −0.111600 | − | 0.993753i | \(-0.535598\pi\) | ||||
−0.111600 | + | 0.993753i | \(0.535598\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 862.000 | 0.717612 | 0.358806 | − | 0.933412i | \(-0.383184\pi\) | ||||
0.358806 | + | 0.933412i | \(0.383184\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1254.00 | −1.01684 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1404.00 | 1.08155 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2894.00 | 2.17431 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2109.00 | −1.50908 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1019.00 | 0.711981 | 0.355991 | − | 0.934490i | \(-0.384143\pi\) | ||||
0.355991 | + | 0.934490i | \(0.384143\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2741.00 | 1.82811 | 0.914055 | − | 0.405591i | \(-0.132934\pi\) | ||||
0.914055 | + | 0.405591i | \(0.132934\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −754.000 | −0.491580 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 750.000 | 0.467714 | 0.233857 | − | 0.972271i | \(-0.424865\pi\) | ||||
0.233857 | + | 0.972271i | \(0.424865\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3028.00 | 1.84771 | 0.923855 | − | 0.382743i | \(-0.125021\pi\) | ||||
0.923855 | + | 0.382743i | \(0.125021\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3640.00 | 2.12862 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2242.00 | 1.28405 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1677.00 | 0.922048 | 0.461024 | − | 0.887388i | \(-0.347482\pi\) | ||||
0.461024 | + | 0.887388i | \(0.347482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −573.000 | −0.308808 | −0.154404 | − | 0.988008i | \(-0.549346\pi\) | ||||
−0.154404 | + | 0.988008i | \(0.549346\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2755.00 | 1.42766 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1564.00 | 0.795037 | 0.397518 | − | 0.917594i | \(-0.369871\pi\) | ||||
0.397518 | + | 0.917594i | \(0.369871\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 858.000 | 0.419999 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1072.00 | −0.515126 | −0.257563 | − | 0.966262i | \(-0.582919\pi\) | ||||
−0.257563 | + | 0.966262i | \(0.582919\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3106.00 | −1.43922 | −0.719609 | − | 0.694379i | \(-0.755679\pi\) | ||||
−0.719609 | + | 0.694379i | \(0.755679\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 939.000 | 0.427401 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4263.00 | −1.87347 | −0.936734 | − | 0.350043i | \(-0.886167\pi\) | ||||
−0.936734 | + | 0.350043i | \(0.886167\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3068.00 | 1.32525 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 723.000 | 0.301897 | 0.150948 | − | 0.988542i | \(-0.451767\pi\) | ||||
0.150948 | + | 0.988542i | \(0.451767\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3104.00 | −1.27469 | −0.637344 | − | 0.770579i | \(-0.719967\pi\) | ||||
−0.637344 | + | 0.770579i | \(0.719967\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3610.00 | 1.43466 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7020.00 | 2.74520 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1776.00 | −0.672811 | −0.336405 | − | 0.941717i | \(-0.609211\pi\) | ||||
−0.336405 | + | 0.941717i | \(0.609211\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 957.000 | 0.356924 | 0.178462 | − | 0.983947i | \(-0.442888\pi\) | ||||
0.178462 | + | 0.983947i | \(0.442888\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1007.00 | 0.364192 | 0.182096 | − | 0.983281i | \(-0.441712\pi\) | ||||
0.182096 | + | 0.983281i | \(0.441712\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 803.000 | 0.286046 | 0.143023 | − | 0.989719i | \(-0.454318\pi\) | ||||
0.143023 | + | 0.989719i | \(0.454318\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1534.00 | −0.530373 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8170.00 | −2.78350 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3770.00 | −1.24773 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3274.00 | −1.06821 | −0.534103 | − | 0.845419i | \(-0.679351\pi\) | ||||
−0.534103 | + | 0.845419i | \(0.679351\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10070.0 | 3.19427 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1885.00 | −0.589687 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6048.00 | 1.84087 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1064.00 | −0.319510 | −0.159755 | − | 0.987157i | \(-0.551070\pi\) | ||||
−0.159755 | + | 0.987157i | \(0.551070\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1644.00 | 0.480688 | 0.240344 | − | 0.970688i | \(-0.422740\pi\) | ||||
0.240344 | + | 0.970688i | \(0.422740\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3082.00 | 0.889364 | 0.444682 | − | 0.895689i | \(-0.353317\pi\) | ||||
0.444682 | + | 0.895689i | \(0.353317\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2766.00 | −0.777711 | −0.388856 | − | 0.921299i | \(-0.627129\pi\) | ||||
−0.388856 | + | 0.921299i | \(0.627129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1406.00 | −0.390286 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 798.000 | 0.215976 | 0.107988 | − | 0.994152i | \(-0.465559\pi\) | ||||
0.107988 | + | 0.994152i | \(0.465559\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3554.00 | −0.949931 | −0.474965 | − | 0.880005i | \(-0.657539\pi\) | ||||
−0.474965 | + | 0.880005i | \(0.657539\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3306.00 | 0.862092 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3248.00 | −0.836702 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2400.00 | 0.603532 | 0.301766 | − | 0.953382i | \(-0.402424\pi\) | ||||
0.301766 | + | 0.953382i | \(0.402424\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4290.00 | 1.06605 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1904.00 | −0.462133 | −0.231067 | − | 0.972938i | \(-0.574222\pi\) | ||||
−0.231067 | + | 0.972938i | \(0.574222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2470.00 | −0.592580 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6642.00 | 1.55727 | 0.778637 | − | 0.627474i | \(-0.215911\pi\) | ||||
0.778637 | + | 0.627474i | \(0.215911\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5605.00 | −1.29929 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5034.00 | 1.14100 | 0.570499 | − | 0.821298i | \(-0.306750\pi\) | ||||
0.570499 | + | 0.821298i | \(0.306750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5973.00 | 1.33887 | 0.669435 | − | 0.742870i | \(-0.266536\pi\) | ||||
0.669435 | + | 0.742870i | \(0.266536\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15340.0 | 3.36377 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5456.00 | 1.18346 | 0.591732 | − | 0.806135i | \(-0.298445\pi\) | ||||
0.591732 | + | 0.806135i | \(0.298445\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1908.00 | −0.405060 | −0.202530 | − | 0.979276i | \(-0.564916\pi\) | ||||
−0.202530 | + | 0.979276i | \(0.564916\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6518.00 | −1.36910 | −0.684549 | − | 0.728967i | \(-0.740001\pi\) | ||||
−0.684549 | + | 0.728967i | \(0.740001\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5590.00 | 1.14971 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6751.00 | 1.37411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4818.00 | −0.960650 | −0.480325 | − | 0.877090i | \(-0.659481\pi\) | ||||
−0.480325 | + | 0.877090i | \(0.659481\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11932.0 | −2.35494 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3696.00 | 0.714867 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6890.00 | −1.31938 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6840.00 | 1.28412 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8172.00 | −1.51922 | −0.759610 | − | 0.650379i | \(-0.774610\pi\) | ||||
−0.759610 | + | 0.650379i | \(0.774610\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8118.00 | −1.48016 | −0.740080 | − | 0.672519i | \(-0.765212\pi\) | ||||
−0.740080 | + | 0.672519i | \(0.765212\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4187.00 | −0.756113 | −0.378056 | − | 0.925783i | \(-0.623407\pi\) | ||||
−0.378056 | + | 0.925783i | \(0.623407\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3117.00 | −0.552265 | −0.276133 | − | 0.961120i | \(-0.589053\pi\) | ||||
−0.276133 | + | 0.961120i | \(0.589053\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7670.00 | −1.34620 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6264.00 | −1.07907 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13216.0 | 2.25567 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 962.000 | 0.161206 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1322.00 | −0.219528 | −0.109764 | − | 0.993958i | \(-0.535009\pi\) | ||||
−0.109764 | + | 0.993958i | \(0.535009\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2774.00 | 0.452417 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3362.00 | 0.543442 | 0.271721 | − | 0.962376i | \(-0.412407\pi\) | ||||
0.271721 | + | 0.962376i | \(0.412407\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9425.00 | −1.49675 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6721.00 | −1.05802 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3631.00 | 0.561736 | 0.280868 | − | 0.959746i | \(-0.409378\pi\) | ||||
0.280868 | + | 0.959746i | \(0.409378\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10454.0 | 1.60341 | 0.801705 | − | 0.597720i | \(-0.203927\pi\) | ||||
0.801705 | + | 0.597720i | \(0.203927\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −406.000 | −0.0612159 | −0.0306079 | − | 0.999531i | \(-0.509744\pi\) | ||||
−0.0306079 | + | 0.999531i | \(0.509744\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7372.00 | 1.10216 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4366.00 | 0.641863 | 0.320931 | − | 0.947102i | \(-0.396004\pi\) | ||||
0.320931 | + | 0.947102i | \(0.396004\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3495.00 | −0.509549 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14307.0 | −2.05168 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9939.00 | 1.41366 | 0.706828 | − | 0.707386i | \(-0.250126\pi\) | ||||
0.706828 | + | 0.707386i | \(0.250126\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3835.00 | 0.536667 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5500.00 | 0.763483 | 0.381742 | − | 0.924269i | \(-0.375324\pi\) | ||||
0.381742 | + | 0.924269i | \(0.375324\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6608.00 | −0.902730 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11060.0 | 1.49898 | 0.749491 | − | 0.662015i | \(-0.230298\pi\) | ||||
0.749491 | + | 0.662015i | \(0.230298\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12668.0 | 1.69009 | 0.845045 | − | 0.534695i | \(-0.179573\pi\) | ||||
0.845045 | + | 0.534695i | \(0.179573\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16055.0 | −2.12529 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5925.00 | 0.772261 | 0.386130 | − | 0.922444i | \(-0.373811\pi\) | ||||
0.386130 | + | 0.922444i | \(0.373811\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7128.00 | 0.921940 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21584.0 | −2.74939 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6296.00 | 0.795937 | 0.397969 | − | 0.917399i | \(-0.369715\pi\) | ||||
0.397969 | + | 0.917399i | \(0.369715\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −292.000 | −0.0363636 | −0.0181818 | − | 0.999835i | \(-0.505788\pi\) | ||||
−0.0181818 | + | 0.999835i | \(0.505788\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8120.00 | −1.00369 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12350.0 | −1.50410 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7649.00 | −0.924740 | −0.462370 | − | 0.886687i | \(-0.653001\pi\) | ||||
−0.462370 | + | 0.886687i | \(0.653001\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8164.00 | 0.972698 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2907.00 | −0.343853 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15644.0 | 1.82401 | 0.912004 | − | 0.410181i | \(-0.134535\pi\) | ||||
0.912004 | + | 0.410181i | \(0.134535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14192.0 | −1.64294 | −0.821468 | − | 0.570255i | \(-0.806844\pi\) | ||||
−0.821468 | + | 0.570255i | \(0.806844\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25488.0 | 2.90906 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4680.00 | −0.530401 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13158.0 | 1.47053 | 0.735265 | − | 0.677780i | \(-0.237058\pi\) | ||||
0.735265 | + | 0.677780i | \(0.237058\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7307.00 | −0.810975 | −0.405487 | − | 0.914101i | \(-0.632898\pi\) | ||||
−0.405487 | + | 0.914101i | \(0.632898\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3828.00 | −0.419034 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11671.0 | 1.26885 | 0.634426 | − | 0.772983i | \(-0.281236\pi\) | ||||
0.634426 | + | 0.772983i | \(0.281236\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9924.00 | 1.06434 | 0.532171 | − | 0.846637i | \(-0.321376\pi\) | ||||
0.532171 | + | 0.846637i | \(0.321376\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16150.0 | 1.72041 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3794.00 | 0.398775 | 0.199387 | − | 0.979921i | \(-0.436105\pi\) | ||||
0.199387 | + | 0.979921i | \(0.436105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27950.0 | 2.91821 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13832.0 | −1.42517 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4033.00 | −0.412814 | −0.206407 | − | 0.978466i | \(-0.566177\pi\) | ||||
−0.206407 | + | 0.978466i | \(0.566177\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16365.0 | 1.65335 | 0.826675 | − | 0.562680i | \(-0.190230\pi\) | ||||
0.826675 | + | 0.562680i | \(0.190230\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2743.00 | −0.275330 | −0.137665 | − | 0.990479i | \(-0.543960\pi\) | ||||
−0.137665 | + | 0.990479i | \(0.543960\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2551.00 | −0.252776 | −0.126388 | − | 0.991981i | \(-0.540338\pi\) | ||||
−0.126388 | + | 0.991981i | \(0.540338\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1898.00 | −0.186869 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34450.0 | −3.34886 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13688.0 | −1.32221 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6906.00 | 0.658754 | 0.329377 | − | 0.944198i | \(-0.393161\pi\) | ||||
0.329377 | + | 0.944198i | \(0.393161\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10640.0 | −1.00861 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7429.00 | −0.695533 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10648.0 | 0.990774 | 0.495387 | − | 0.868672i | \(-0.335026\pi\) | ||||
0.495387 | + | 0.868672i | \(0.335026\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9899.00 | 0.909849 | 0.454924 | − | 0.890530i | \(-0.349666\pi\) | ||||
0.454924 | + | 0.890530i | \(0.349666\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12744.0 | −1.16422 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5044.00 | −0.455240 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2382.00 | 0.213693 | 0.106847 | − | 0.994276i | \(-0.465925\pi\) | ||||
0.106847 | + | 0.994276i | \(0.465925\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6450.00 | −0.571752 | −0.285876 | − | 0.958267i | \(-0.592285\pi\) | ||||
−0.285876 | + | 0.958267i | \(0.592285\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11343.0 | 0.999519 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4839.00 | 0.421385 | 0.210692 | − | 0.977552i | \(-0.432428\pi\) | ||||
0.210692 | + | 0.977552i | \(0.432428\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9789.00 | 0.847436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4788.00 | −0.409679 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4810.00 | 0.409175 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7656.00 | −0.643792 | −0.321896 | − | 0.946775i | \(-0.604320\pi\) | ||||
−0.321896 | + | 0.946775i | \(0.604320\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9756.00 | −0.815679 | −0.407839 | − | 0.913054i | \(-0.633718\pi\) | ||||
−0.407839 | + | 0.913054i | \(0.633718\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15660.0 | −1.29442 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7811.00 | −0.641982 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24080.0 | 1.95689 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7505.00 | 0.606485 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11310.0 | −0.903815 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12452.0 | 0.989562 | 0.494781 | − | 0.869018i | \(-0.335248\pi\) | ||||
0.494781 | + | 0.869018i | \(0.335248\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4826.00 | 0.379308 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21708.0 | 1.69683 | 0.848416 | − | 0.529330i | \(-0.177557\pi\) | ||||
0.848416 | + | 0.529330i | \(0.177557\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6844.00 | 0.529155 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14768.0 | 1.13562 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18941.0 | 1.44085 | 0.720427 | − | 0.693531i | \(-0.243946\pi\) | ||||
0.720427 | + | 0.693531i | \(0.243946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29680.0 | −2.24567 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9561.00 | −0.715716 | −0.357858 | − | 0.933776i | \(-0.616493\pi\) | ||||
−0.357858 | + | 0.933776i | \(0.616493\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16378.0 | −1.21952 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11932.0 | 0.879113 | 0.439557 | − | 0.898215i | \(-0.355136\pi\) | ||||
0.439557 | + | 0.898215i | \(0.355136\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16016.0 | 1.17382 | 0.586908 | − | 0.809654i | \(-0.300345\pi\) | ||||
0.586908 | + | 0.809654i | \(0.300345\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15576.0 | 1.12968 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15918.0 | 1.14848 | 0.574242 | − | 0.818686i | \(-0.305297\pi\) | ||||
0.574242 | + | 0.818686i | \(0.305297\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1989.00 | 0.142027 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19175.0 | 1.36217 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19527.0 | −1.37302 | −0.686512 | − | 0.727118i | \(-0.740859\pi\) | ||||
−0.686512 | + | 0.727118i | \(0.740859\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8410.00 | 0.588333 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14658.0 | 1.01506 | 0.507531 | − | 0.861633i | \(-0.330558\pi\) | ||||
0.507531 | + | 0.861633i | \(0.330558\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26676.0 | −1.83800 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2086.00 | −0.142290 | −0.0711449 | − | 0.997466i | \(-0.522665\pi\) | ||||
−0.0711449 | + | 0.997466i | \(0.522665\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21125.0 | −1.43379 | −0.716894 | − | 0.697182i | \(-0.754437\pi\) | ||||
−0.716894 | + | 0.697182i | \(0.754437\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −54986.0 | −3.69504 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −184.000 | −0.0123037 | −0.00615184 | − | 0.999981i | \(-0.501958\pi\) | ||||
−0.00615184 | + | 0.999981i | \(0.501958\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4144.00 | 0.274383 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26658.0 | 1.75645 | 0.878227 | − | 0.478244i | \(-0.158726\pi\) | ||||
0.878227 | + | 0.478244i | \(0.158726\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4386.00 | 0.286181 | 0.143091 | − | 0.989710i | \(-0.454296\pi\) | ||||
0.143091 | + | 0.989710i | \(0.454296\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15000.0 | 0.973992 | 0.486996 | − | 0.873404i | \(-0.338093\pi\) | ||||
0.486996 | + | 0.873404i | \(0.338093\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11050.0 | −0.710608 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10571.0 | 0.676544 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20520.0 | −1.30077 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19877.0 | 1.25403 | 0.627013 | − | 0.779008i | \(-0.284277\pi\) | ||||
0.627013 | + | 0.779008i | \(0.284277\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19361.0 | −1.20995 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9744.00 | −0.606077 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11146.0 | −0.686803 | −0.343401 | − | 0.939189i | \(-0.611579\pi\) | ||||
−0.343401 | + | 0.939189i | \(0.611579\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23052.0 | 1.41381 | 0.706907 | − | 0.707307i | \(-0.250090\pi\) | ||||
0.706907 | + | 0.707307i | \(0.250090\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13896.0 | −0.844371 | −0.422186 | − | 0.906509i | \(-0.638737\pi\) | ||||
−0.422186 | + | 0.906509i | \(0.638737\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40820.0 | 2.46891 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7583.00 | −0.454434 | −0.227217 | − | 0.973844i | \(-0.572963\pi\) | ||||
−0.227217 | + | 0.973844i | \(0.572963\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −52079.0 | −3.10671 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12591.0 | 0.744273 | 0.372136 | − | 0.928178i | \(-0.378625\pi\) | ||||
0.372136 | + | 0.928178i | \(0.378625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30098.0 | −1.77107 | −0.885534 | − | 0.464574i | \(-0.846208\pi\) | ||||
−0.885534 | + | 0.464574i | \(0.846208\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14326.0 | 0.835396 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7788.00 | −0.452103 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23400.0 | −1.34627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 173.000 | 0.00990886 | 0.00495443 | − | 0.999988i | \(-0.498423\pi\) | ||||
0.00495443 | + | 0.999988i | \(0.498423\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12934.0 | 0.734260 | 0.367130 | − | 0.930170i | \(-0.380340\pi\) | ||||
0.367130 | + | 0.930170i | \(0.380340\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5083.00 | 0.287287 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4164.00 | −0.233281 | −0.116641 | − | 0.993174i | \(-0.537213\pi\) | ||||
−0.116641 | + | 0.993174i | \(0.537213\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14250.0 | −0.794839 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16520.0 | 0.913442 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22660.0 | −1.24751 | −0.623753 | − | 0.781621i | \(-0.714393\pi\) | ||||
−0.623753 | + | 0.781621i | \(0.714393\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −57532.0 | −3.14002 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46440.0 | 2.52373 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27231.0 | 1.46719 | 0.733595 | − | 0.679587i | \(-0.237841\pi\) | ||||
0.733595 | + | 0.679587i | \(0.237841\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11020.0 | 0.591219 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7761.00 | −0.412846 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32140.0 | −1.70246 | −0.851229 | − | 0.524794i | \(-0.824142\pi\) | ||||
−0.851229 | + | 0.524794i | \(0.824142\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9570.00 | −0.502664 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −69160.0 | −3.61739 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4028.00 | 0.208928 | 0.104464 | − | 0.994529i | \(-0.466687\pi\) | ||||
0.104464 | + | 0.994529i | \(0.466687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3276.00 | 0.169216 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −27848.0 | −1.42655 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27963.0 | −1.42653 | −0.713267 | − | 0.700892i | \(-0.752785\pi\) | ||||
−0.713267 | + | 0.700892i | \(0.752785\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −57240.0 | −2.89617 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16142.0 | −0.813395 | −0.406697 | − | 0.913563i | \(-0.633320\pi\) | ||||
−0.406697 | + | 0.913563i | \(0.633320\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9490.00 | −0.474313 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8404.00 | −0.418330 | −0.209165 | − | 0.977880i | \(-0.567075\pi\) | ||||
−0.209165 | + | 0.977880i | \(0.567075\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24912.0 | −1.23006 | −0.615029 | − | 0.788505i | \(-0.710856\pi\) | ||||
−0.615029 | + | 0.788505i | \(0.710856\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31863.0 | −1.56694 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5135.00 | −0.250506 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12685.0 | −0.616354 | −0.308177 | − | 0.951329i | \(-0.599719\pi\) | ||||
−0.308177 | + | 0.951329i | \(0.599719\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10887.0 | 0.524793 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3702.00 | 0.177743 | 0.0888715 | − | 0.996043i | \(-0.471674\pi\) | ||||
0.0888715 | + | 0.996043i | \(0.471674\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12024.0 | 0.572759 | 0.286380 | − | 0.958116i | \(-0.407548\pi\) | ||||
0.286380 | + | 0.958116i | \(0.407548\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3302.00 | −0.156672 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35168.0 | 1.65560 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18215.0 | −0.854161 | −0.427080 | − | 0.904214i | \(-0.640458\pi\) | ||||
−0.427080 | + | 0.904214i | \(0.640458\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24774.0 | −1.15273 | −0.576364 | − | 0.817193i | \(-0.695529\pi\) | ||||
−0.576364 | + | 0.817193i | \(0.695529\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34220.0 | −1.58609 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24940.0 | −1.14707 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25220.0 | −1.15550 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29716.0 | −1.35109 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1152.00 | 0.0521784 | 0.0260892 | − | 0.999660i | \(-0.491695\pi\) | ||||
0.0260892 | + | 0.999660i | \(0.491695\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11206.0 | 0.503716 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20160.0 | −0.902778 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30729.0 | 1.36572 | 0.682859 | − | 0.730550i | \(-0.260736\pi\) | ||||
0.682859 | + | 0.730550i | \(0.260736\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7992.00 | 0.353863 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 48945.0 | 2.15097 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16302.0 | −0.713752 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27982.0 | −1.21606 | −0.608031 | − | 0.793913i | \(-0.708041\pi\) | ||||
−0.608031 | + | 0.793913i | \(0.708041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33394.0 | −1.44590 | −0.722948 | − | 0.690902i | \(-0.757213\pi\) | ||||
−0.722948 | + | 0.690902i | \(0.757213\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20368.0 | 0.875411 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30740.0 | 1.31635 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15650.0 | 0.665273 | 0.332636 | − | 0.943055i | \(-0.392062\pi\) | ||||
0.332636 | + | 0.943055i | \(0.392062\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16555.0 | 0.701180 | 0.350590 | − | 0.936529i | \(-0.385981\pi\) | ||||
0.350590 | + | 0.936529i | \(0.385981\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27952.0 | −1.17532 | −0.587658 | − | 0.809109i | \(-0.699950\pi\) | ||||
−0.587658 | + | 0.809109i | \(0.699950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31130.0 | −1.30421 | −0.652105 | − | 0.758129i | \(-0.726114\pi\) | ||||
−0.652105 | + | 0.758129i | \(0.726114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18792.0 | −0.781638 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 59014.0 | 2.44582 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10396.0 | −0.427783 | −0.213891 | − | 0.976857i | \(-0.568614\pi\) | ||||
−0.213891 | + | 0.976857i | \(0.568614\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10465.0 | −0.429087 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17841.0 | −0.726330 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37622.0 | 1.52622 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12540.0 | −0.505130 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 690.000 | 0.0276965 | 0.0138483 | − | 0.999904i | \(-0.495592\pi\) | ||||
0.0138483 | + | 0.999904i | \(0.495592\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10436.0 | 0.415971 | 0.207985 | − | 0.978132i | \(-0.433309\pi\) | ||||
0.207985 | + | 0.978132i | \(0.433309\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29584.0 | 1.17508 | 0.587540 | − | 0.809195i | \(-0.300097\pi\) | ||||
0.587540 | + | 0.809195i | \(0.300097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30988.0 | −1.22230 | −0.611149 | − | 0.791515i | \(-0.709293\pi\) | ||||
−0.611149 | + | 0.791515i | \(0.709293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 80997.0 | 3.18379 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 73840.0 | 2.88245 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8176.00 | −0.318063 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27417.0 | −1.05927 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24182.0 | 0.931092 | 0.465546 | − | 0.885024i | \(-0.345858\pi\) | ||||
0.465546 | + | 0.885024i | \(0.345858\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13272.0 | −0.507543 | −0.253771 | − | 0.967264i | \(-0.581671\pi\) | ||||
−0.253771 | + | 0.967264i | \(0.581671\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16606.0 | 0.632884 | 0.316442 | − | 0.948612i | \(-0.397512\pi\) | ||||
0.316442 | + | 0.948612i | \(0.397512\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20088.0 | 0.760416 | 0.380208 | − | 0.924901i | \(-0.375852\pi\) | ||||
0.380208 | + | 0.924901i | \(0.375852\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13247.0 | 0.499764 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4292.00 | −0.160836 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13737.0 | −0.513047 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17110.0 | 0.634761 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31860.0 | 1.17804 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 58976.0 | 2.16622 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10234.0 | −0.374658 | −0.187329 | − | 0.982297i | \(-0.559983\pi\) | ||||
−0.187329 | + | 0.982297i | \(0.559983\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3966.00 | −0.144236 | −0.0721182 | − | 0.997396i | \(-0.522976\pi\) | ||||
−0.0721182 | + | 0.997396i | \(0.522976\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9945.00 | 0.360494 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 35633.0 | 1.28321 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24999.0 | 0.897324 | 0.448662 | − | 0.893701i | \(-0.351901\pi\) | ||||
0.448662 | + | 0.893701i | \(0.351901\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21728.0 | −0.774849 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44840.0 | −1.59387 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45444.0 | −1.60492 | −0.802459 | − | 0.596707i | \(-0.796475\pi\) | ||||
−0.802459 | + | 0.596707i | \(0.796475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10092.0 | 0.355265 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −133380. | −4.66523 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5579.00 | 0.194512 | 0.0972561 | − | 0.995259i | \(-0.468993\pi\) | ||||
0.0972561 | + | 0.995259i | \(0.468993\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9119.00 | −0.315910 | −0.157955 | − | 0.987446i | \(-0.550490\pi\) | ||||
−0.157955 | + | 0.987446i | \(0.550490\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28380.0 | 0.980042 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7785.00 | −0.267137 | −0.133568 | − | 0.991040i | \(-0.542644\pi\) | ||||
−0.133568 | + | 0.991040i | \(0.542644\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42168.0 | 1.44239 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31980.0 | −1.08702 | −0.543512 | − | 0.839401i | \(-0.682906\pi\) | ||||
−0.543512 | + | 0.839401i | \(0.682906\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33744.0 | 1.14338 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9750.00 | 0.328304 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8766.00 | −0.294250 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18183.0 | −0.606561 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13395.0 | −0.445454 | −0.222727 | − | 0.974881i | \(-0.571496\pi\) | ||||
−0.222727 | + | 0.974881i | \(0.571496\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4615.00 | −0.152526 | −0.0762628 | − | 0.997088i | \(-0.524299\pi\) | ||||
−0.0762628 | + | 0.997088i | \(0.524299\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39364.0 | 1.29697 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47782.0 | 1.56467 | 0.782335 | − | 0.622859i | \(-0.214029\pi\) | ||||
0.782335 | + | 0.622859i | \(0.214029\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −55250.0 | −1.80367 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15798.0 | −0.512592 | −0.256296 | − | 0.966598i | \(-0.582502\pi\) | ||||
−0.256296 | + | 0.966598i | \(0.582502\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19133.0 | −0.618912 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34980.0 | −1.12467 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13435.0 | −0.430653 | −0.215326 | − | 0.976542i | \(-0.569082\pi\) | ||||
−0.215326 | + | 0.976542i | \(0.569082\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15257.0 | −0.486110 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31536.0 | −1.00176 | −0.500880 | − | 0.865517i | \(-0.666990\pi\) | ||||
−0.500880 | + | 0.865517i | \(0.666990\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.4.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 1728.4.a.bf.1.1 | 1 | |||
4.3 | odd | 2 | 1728.4.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 864.4.a.c.1.1 | yes | 1 | ||
8.5 | even | 2 | 864.4.a.d.1.1 | yes | 1 | ||
12.11 | even | 2 | 1728.4.a.be.1.1 | 1 | |||
24.5 | odd | 2 | 864.4.a.b.1.1 | yes | 1 | ||
24.11 | even | 2 | 864.4.a.a.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.4.a.a.1.1 | ✓ | 1 | 24.11 | even | 2 | ||
864.4.a.b.1.1 | yes | 1 | 24.5 | odd | 2 | ||
864.4.a.c.1.1 | yes | 1 | 8.3 | odd | 2 | ||
864.4.a.d.1.1 | yes | 1 | 8.5 | even | 2 | ||
1728.4.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
1728.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1728.4.a.be.1.1 | 1 | 12.11 | even | 2 | |||
1728.4.a.bf.1.1 | 1 | 3.2 | odd | 2 |