Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(1,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 169.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | 2.00000 | 0.384900 | 0.192450 | − | 0.981307i | \(-0.438357\pi\) | ||||
0.192450 | + | 0.981307i | \(0.438357\pi\) | |||||||
\(4\) | 8.00000 | 1.00000 | ||||||||
\(5\) | −17.0000 | −1.52053 | −0.760263 | − | 0.649615i | \(-0.774930\pi\) | ||||
−0.760263 | + | 0.649615i | \(0.774930\pi\) | |||||||
\(6\) | −8.00000 | −0.544331 | ||||||||
\(7\) | −20.0000 | −1.07990 | −0.539949 | − | 0.841698i | \(-0.681557\pi\) | ||||
−0.539949 | + | 0.841698i | \(0.681557\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −23.0000 | −0.851852 | ||||||||
\(10\) | 68.0000 | 2.15035 | ||||||||
\(11\) | 32.0000 | 0.877124 | 0.438562 | − | 0.898701i | \(-0.355488\pi\) | ||||
0.438562 | + | 0.898701i | \(0.355488\pi\) | |||||||
\(12\) | 16.0000 | 0.384900 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 80.0000 | 1.52721 | ||||||||
\(15\) | −34.0000 | −0.585251 | ||||||||
\(16\) | −64.0000 | −1.00000 | ||||||||
\(17\) | −13.0000 | −0.185468 | −0.0927342 | − | 0.995691i | \(-0.529561\pi\) | ||||
−0.0927342 | + | 0.995691i | \(0.529561\pi\) | |||||||
\(18\) | 92.0000 | 1.20470 | ||||||||
\(19\) | −30.0000 | −0.362235 | −0.181118 | − | 0.983461i | \(-0.557971\pi\) | ||||
−0.181118 | + | 0.983461i | \(0.557971\pi\) | |||||||
\(20\) | −136.000 | −1.52053 | ||||||||
\(21\) | −40.0000 | −0.415653 | ||||||||
\(22\) | −128.000 | −1.24044 | ||||||||
\(23\) | 78.0000 | 0.707136 | 0.353568 | − | 0.935409i | \(-0.384968\pi\) | ||||
0.353568 | + | 0.935409i | \(0.384968\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 164.000 | 1.31200 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −100.000 | −0.712778 | ||||||||
\(28\) | −160.000 | −1.07990 | ||||||||
\(29\) | 197.000 | 1.26145 | 0.630724 | − | 0.776007i | \(-0.282758\pi\) | ||||
0.630724 | + | 0.776007i | \(0.282758\pi\) | |||||||
\(30\) | 136.000 | 0.827670 | ||||||||
\(31\) | 74.0000 | 0.428735 | 0.214368 | − | 0.976753i | \(-0.431231\pi\) | ||||
0.214368 | + | 0.976753i | \(0.431231\pi\) | |||||||
\(32\) | 256.000 | 1.41421 | ||||||||
\(33\) | 64.0000 | 0.337605 | ||||||||
\(34\) | 52.0000 | 0.262292 | ||||||||
\(35\) | 340.000 | 1.64201 | ||||||||
\(36\) | −184.000 | −0.851852 | ||||||||
\(37\) | 227.000 | 1.00861 | 0.504305 | − | 0.863526i | \(-0.331749\pi\) | ||||
0.504305 | + | 0.863526i | \(0.331749\pi\) | |||||||
\(38\) | 120.000 | 0.512278 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 165.000 | 0.628504 | 0.314252 | − | 0.949340i | \(-0.398246\pi\) | ||||
0.314252 | + | 0.949340i | \(0.398246\pi\) | |||||||
\(42\) | 160.000 | 0.587822 | ||||||||
\(43\) | −156.000 | −0.553251 | −0.276625 | − | 0.960978i | \(-0.589216\pi\) | ||||
−0.276625 | + | 0.960978i | \(0.589216\pi\) | |||||||
\(44\) | 256.000 | 0.877124 | ||||||||
\(45\) | 391.000 | 1.29526 | ||||||||
\(46\) | −312.000 | −1.00004 | ||||||||
\(47\) | 162.000 | 0.502769 | 0.251384 | − | 0.967887i | \(-0.419114\pi\) | ||||
0.251384 | + | 0.967887i | \(0.419114\pi\) | |||||||
\(48\) | −128.000 | −0.384900 | ||||||||
\(49\) | 57.0000 | 0.166181 | ||||||||
\(50\) | −656.000 | −1.85545 | ||||||||
\(51\) | −26.0000 | −0.0713868 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 93.0000 | 0.241029 | 0.120514 | − | 0.992712i | \(-0.461546\pi\) | ||||
0.120514 | + | 0.992712i | \(0.461546\pi\) | |||||||
\(54\) | 400.000 | 1.00802 | ||||||||
\(55\) | −544.000 | −1.33369 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −60.0000 | −0.139424 | ||||||||
\(58\) | −788.000 | −1.78396 | ||||||||
\(59\) | 864.000 | 1.90650 | 0.953248 | − | 0.302190i | \(-0.0977178\pi\) | ||||
0.953248 | + | 0.302190i | \(0.0977178\pi\) | |||||||
\(60\) | −272.000 | −0.585251 | ||||||||
\(61\) | 145.000 | 0.304350 | 0.152175 | − | 0.988354i | \(-0.451372\pi\) | ||||
0.152175 | + | 0.988354i | \(0.451372\pi\) | |||||||
\(62\) | −296.000 | −0.606323 | ||||||||
\(63\) | 460.000 | 0.919914 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −256.000 | −0.477446 | ||||||||
\(67\) | −862.000 | −1.57179 | −0.785896 | − | 0.618359i | \(-0.787798\pi\) | ||||
−0.785896 | + | 0.618359i | \(0.787798\pi\) | |||||||
\(68\) | −104.000 | −0.185468 | ||||||||
\(69\) | 156.000 | 0.272177 | ||||||||
\(70\) | −1360.00 | −2.32216 | ||||||||
\(71\) | −654.000 | −1.09318 | −0.546588 | − | 0.837402i | \(-0.684074\pi\) | ||||
−0.546588 | + | 0.837402i | \(0.684074\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −215.000 | −0.344710 | −0.172355 | − | 0.985035i | \(-0.555138\pi\) | ||||
−0.172355 | + | 0.985035i | \(0.555138\pi\) | |||||||
\(74\) | −908.000 | −1.42639 | ||||||||
\(75\) | 328.000 | 0.504989 | ||||||||
\(76\) | −240.000 | −0.362235 | ||||||||
\(77\) | −640.000 | −0.947205 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −76.0000 | −0.108236 | −0.0541182 | − | 0.998535i | \(-0.517235\pi\) | ||||
−0.0541182 | + | 0.998535i | \(0.517235\pi\) | |||||||
\(80\) | 1088.00 | 1.52053 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | −660.000 | −0.888839 | ||||||||
\(83\) | −628.000 | −0.830505 | −0.415253 | − | 0.909706i | \(-0.636307\pi\) | ||||
−0.415253 | + | 0.909706i | \(0.636307\pi\) | |||||||
\(84\) | −320.000 | −0.415653 | ||||||||
\(85\) | 221.000 | 0.282010 | ||||||||
\(86\) | 624.000 | 0.782415 | ||||||||
\(87\) | 394.000 | 0.485531 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 266.000 | 0.316808 | 0.158404 | − | 0.987374i | \(-0.449365\pi\) | ||||
0.158404 | + | 0.987374i | \(0.449365\pi\) | |||||||
\(90\) | −1564.00 | −1.83178 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 624.000 | 0.707136 | ||||||||
\(93\) | 148.000 | 0.165020 | ||||||||
\(94\) | −648.000 | −0.711022 | ||||||||
\(95\) | 510.000 | 0.550788 | ||||||||
\(96\) | 512.000 | 0.544331 | ||||||||
\(97\) | −238.000 | −0.249126 | −0.124563 | − | 0.992212i | \(-0.539753\pi\) | ||||
−0.124563 | + | 0.992212i | \(0.539753\pi\) | |||||||
\(98\) | −228.000 | −0.235015 | ||||||||
\(99\) | −736.000 | −0.747180 | ||||||||
\(100\) | 1312.00 | 1.31200 | ||||||||
\(101\) | −819.000 | −0.806867 | −0.403433 | − | 0.915009i | \(-0.632183\pi\) | ||||
−0.403433 | + | 0.915009i | \(0.632183\pi\) | |||||||
\(102\) | 104.000 | 0.100956 | ||||||||
\(103\) | 1638.00 | 1.56696 | 0.783480 | − | 0.621417i | \(-0.213443\pi\) | ||||
0.783480 | + | 0.621417i | \(0.213443\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 680.000 | 0.632011 | ||||||||
\(106\) | −372.000 | −0.340866 | ||||||||
\(107\) | 522.000 | 0.471623 | 0.235811 | − | 0.971799i | \(-0.424225\pi\) | ||||
0.235811 | + | 0.971799i | \(0.424225\pi\) | |||||||
\(108\) | −800.000 | −0.712778 | ||||||||
\(109\) | 1634.00 | 1.43586 | 0.717930 | − | 0.696115i | \(-0.245090\pi\) | ||||
0.717930 | + | 0.696115i | \(0.245090\pi\) | |||||||
\(110\) | 2176.00 | 1.88612 | ||||||||
\(111\) | 454.000 | 0.388214 | ||||||||
\(112\) | 1280.00 | 1.07990 | ||||||||
\(113\) | 327.000 | 0.272226 | 0.136113 | − | 0.990693i | \(-0.456539\pi\) | ||||
0.136113 | + | 0.990693i | \(0.456539\pi\) | |||||||
\(114\) | 240.000 | 0.197176 | ||||||||
\(115\) | −1326.00 | −1.07522 | ||||||||
\(116\) | 1576.00 | 1.26145 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3456.00 | −2.69619 | ||||||||
\(119\) | 260.000 | 0.200287 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −307.000 | −0.230654 | ||||||||
\(122\) | −580.000 | −0.430416 | ||||||||
\(123\) | 330.000 | 0.241911 | ||||||||
\(124\) | 592.000 | 0.428735 | ||||||||
\(125\) | −663.000 | −0.474404 | ||||||||
\(126\) | −1840.00 | −1.30095 | ||||||||
\(127\) | −2158.00 | −1.50781 | −0.753904 | − | 0.656985i | \(-0.771831\pi\) | ||||
−0.753904 | + | 0.656985i | \(0.771831\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −312.000 | −0.212946 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 730.000 | 0.486873 | 0.243437 | − | 0.969917i | \(-0.421725\pi\) | ||||
0.243437 | + | 0.969917i | \(0.421725\pi\) | |||||||
\(132\) | 512.000 | 0.337605 | ||||||||
\(133\) | 600.000 | 0.391177 | ||||||||
\(134\) | 3448.00 | 2.22285 | ||||||||
\(135\) | 1700.00 | 1.08380 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1671.00 | −1.04207 | −0.521033 | − | 0.853536i | \(-0.674453\pi\) | ||||
−0.521033 | + | 0.853536i | \(0.674453\pi\) | |||||||
\(138\) | −624.000 | −0.384916 | ||||||||
\(139\) | 912.000 | 0.556510 | 0.278255 | − | 0.960507i | \(-0.410244\pi\) | ||||
0.278255 | + | 0.960507i | \(0.410244\pi\) | |||||||
\(140\) | 2720.00 | 1.64201 | ||||||||
\(141\) | 324.000 | 0.193516 | ||||||||
\(142\) | 2616.00 | 1.54598 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1472.00 | 0.851852 | ||||||||
\(145\) | −3349.00 | −1.91806 | ||||||||
\(146\) | 860.000 | 0.487494 | ||||||||
\(147\) | 114.000 | 0.0639630 | ||||||||
\(148\) | 1816.00 | 1.00861 | ||||||||
\(149\) | 2115.00 | 1.16287 | 0.581435 | − | 0.813593i | \(-0.302492\pi\) | ||||
0.581435 | + | 0.813593i | \(0.302492\pi\) | |||||||
\(150\) | −1312.00 | −0.714162 | ||||||||
\(151\) | −514.000 | −0.277011 | −0.138506 | − | 0.990362i | \(-0.544230\pi\) | ||||
−0.138506 | + | 0.990362i | \(0.544230\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 299.000 | 0.157992 | ||||||||
\(154\) | 2560.00 | 1.33955 | ||||||||
\(155\) | −1258.00 | −0.651903 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2901.00 | 1.47468 | 0.737341 | − | 0.675521i | \(-0.236081\pi\) | ||||
0.737341 | + | 0.675521i | \(0.236081\pi\) | |||||||
\(158\) | 304.000 | 0.153069 | ||||||||
\(159\) | 186.000 | 0.0927721 | ||||||||
\(160\) | −4352.00 | −2.15035 | ||||||||
\(161\) | −1560.00 | −0.763635 | ||||||||
\(162\) | −1684.00 | −0.816713 | ||||||||
\(163\) | −2360.00 | −1.13405 | −0.567023 | − | 0.823702i | \(-0.691905\pi\) | ||||
−0.567023 | + | 0.823702i | \(0.691905\pi\) | |||||||
\(164\) | 1320.00 | 0.628504 | ||||||||
\(165\) | −1088.00 | −0.513337 | ||||||||
\(166\) | 2512.00 | 1.17451 | ||||||||
\(167\) | −280.000 | −0.129743 | −0.0648714 | − | 0.997894i | \(-0.520664\pi\) | ||||
−0.0648714 | + | 0.997894i | \(0.520664\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −884.000 | −0.398822 | ||||||||
\(171\) | 690.000 | 0.308571 | ||||||||
\(172\) | −1248.00 | −0.553251 | ||||||||
\(173\) | 1326.00 | 0.582739 | 0.291370 | − | 0.956611i | \(-0.405889\pi\) | ||||
0.291370 | + | 0.956611i | \(0.405889\pi\) | |||||||
\(174\) | −1576.00 | −0.686645 | ||||||||
\(175\) | −3280.00 | −1.41683 | ||||||||
\(176\) | −2048.00 | −0.877124 | ||||||||
\(177\) | 1728.00 | 0.733810 | ||||||||
\(178\) | −1064.00 | −0.448035 | ||||||||
\(179\) | 4264.00 | 1.78048 | 0.890241 | − | 0.455490i | \(-0.150536\pi\) | ||||
0.890241 | + | 0.455490i | \(0.150536\pi\) | |||||||
\(180\) | 3128.00 | 1.29526 | ||||||||
\(181\) | −403.000 | −0.165496 | −0.0827479 | − | 0.996571i | \(-0.526370\pi\) | ||||
−0.0827479 | + | 0.996571i | \(0.526370\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 290.000 | 0.117144 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3859.00 | −1.53362 | ||||||||
\(186\) | −592.000 | −0.233374 | ||||||||
\(187\) | −416.000 | −0.162679 | ||||||||
\(188\) | 1296.00 | 0.502769 | ||||||||
\(189\) | 2000.00 | 0.769728 | ||||||||
\(190\) | −2040.00 | −0.778932 | ||||||||
\(191\) | −1246.00 | −0.472028 | −0.236014 | − | 0.971750i | \(-0.575841\pi\) | ||||
−0.236014 | + | 0.971750i | \(0.575841\pi\) | |||||||
\(192\) | −1024.00 | −0.384900 | ||||||||
\(193\) | −267.000 | −0.0995807 | −0.0497904 | − | 0.998760i | \(-0.515855\pi\) | ||||
−0.0497904 | + | 0.998760i | \(0.515855\pi\) | |||||||
\(194\) | 952.000 | 0.352318 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 456.000 | 0.166181 | ||||||||
\(197\) | −1278.00 | −0.462202 | −0.231101 | − | 0.972930i | \(-0.574233\pi\) | ||||
−0.231101 | + | 0.972930i | \(0.574233\pi\) | |||||||
\(198\) | 2944.00 | 1.05667 | ||||||||
\(199\) | 4238.00 | 1.50967 | 0.754834 | − | 0.655916i | \(-0.227717\pi\) | ||||
0.754834 | + | 0.655916i | \(0.227717\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1724.00 | −0.604983 | ||||||||
\(202\) | 3276.00 | 1.14108 | ||||||||
\(203\) | −3940.00 | −1.36224 | ||||||||
\(204\) | −208.000 | −0.0713868 | ||||||||
\(205\) | −2805.00 | −0.955657 | ||||||||
\(206\) | −6552.00 | −2.21602 | ||||||||
\(207\) | −1794.00 | −0.602375 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −960.000 | −0.317725 | ||||||||
\(210\) | −2720.00 | −0.893799 | ||||||||
\(211\) | 3070.00 | 1.00165 | 0.500823 | − | 0.865549i | \(-0.333031\pi\) | ||||
0.500823 | + | 0.865549i | \(0.333031\pi\) | |||||||
\(212\) | 744.000 | 0.241029 | ||||||||
\(213\) | −1308.00 | −0.420764 | ||||||||
\(214\) | −2088.00 | −0.666975 | ||||||||
\(215\) | 2652.00 | 0.841232 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1480.00 | −0.462991 | ||||||||
\(218\) | −6536.00 | −2.03061 | ||||||||
\(219\) | −430.000 | −0.132679 | ||||||||
\(220\) | −4352.00 | −1.33369 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1816.00 | −0.549018 | ||||||||
\(223\) | 5378.00 | 1.61497 | 0.807483 | − | 0.589891i | \(-0.200829\pi\) | ||||
0.807483 | + | 0.589891i | \(0.200829\pi\) | |||||||
\(224\) | −5120.00 | −1.52721 | ||||||||
\(225\) | −3772.00 | −1.11763 | ||||||||
\(226\) | −1308.00 | −0.384986 | ||||||||
\(227\) | 3974.00 | 1.16195 | 0.580977 | − | 0.813920i | \(-0.302671\pi\) | ||||
0.580977 | + | 0.813920i | \(0.302671\pi\) | |||||||
\(228\) | −480.000 | −0.139424 | ||||||||
\(229\) | 6298.00 | 1.81740 | 0.908698 | − | 0.417455i | \(-0.137078\pi\) | ||||
0.908698 | + | 0.417455i | \(0.137078\pi\) | |||||||
\(230\) | 5304.00 | 1.52059 | ||||||||
\(231\) | −1280.00 | −0.364579 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4030.00 | 1.13311 | 0.566554 | − | 0.824025i | \(-0.308276\pi\) | ||||
0.566554 | + | 0.824025i | \(0.308276\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2754.00 | −0.764473 | ||||||||
\(236\) | 6912.00 | 1.90650 | ||||||||
\(237\) | −152.000 | −0.0416602 | ||||||||
\(238\) | −1040.00 | −0.283249 | ||||||||
\(239\) | 984.000 | 0.266317 | 0.133158 | − | 0.991095i | \(-0.457488\pi\) | ||||
0.133158 | + | 0.991095i | \(0.457488\pi\) | |||||||
\(240\) | 2176.00 | 0.585251 | ||||||||
\(241\) | −943.000 | −0.252050 | −0.126025 | − | 0.992027i | \(-0.540222\pi\) | ||||
−0.126025 | + | 0.992027i | \(0.540222\pi\) | |||||||
\(242\) | 1228.00 | 0.326194 | ||||||||
\(243\) | 3542.00 | 0.935059 | ||||||||
\(244\) | 1160.00 | 0.304350 | ||||||||
\(245\) | −969.000 | −0.252682 | ||||||||
\(246\) | −1320.00 | −0.342114 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1256.00 | −0.319662 | ||||||||
\(250\) | 2652.00 | 0.670909 | ||||||||
\(251\) | −2730.00 | −0.686518 | −0.343259 | − | 0.939241i | \(-0.611531\pi\) | ||||
−0.343259 | + | 0.939241i | \(0.611531\pi\) | |||||||
\(252\) | 3680.00 | 0.919914 | ||||||||
\(253\) | 2496.00 | 0.620246 | ||||||||
\(254\) | 8632.00 | 2.13236 | ||||||||
\(255\) | 442.000 | 0.108546 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | −1885.00 | −0.457522 | −0.228761 | − | 0.973483i | \(-0.573467\pi\) | ||||
−0.228761 | + | 0.973483i | \(0.573467\pi\) | |||||||
\(258\) | 1248.00 | 0.301151 | ||||||||
\(259\) | −4540.00 | −1.08920 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4531.00 | −1.07457 | ||||||||
\(262\) | −2920.00 | −0.688543 | ||||||||
\(263\) | 4032.00 | 0.945338 | 0.472669 | − | 0.881240i | \(-0.343291\pi\) | ||||
0.472669 | + | 0.881240i | \(0.343291\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1581.00 | −0.366491 | ||||||||
\(266\) | −2400.00 | −0.553208 | ||||||||
\(267\) | 532.000 | 0.121940 | ||||||||
\(268\) | −6896.00 | −1.57179 | ||||||||
\(269\) | 4006.00 | 0.907993 | 0.453997 | − | 0.891003i | \(-0.349998\pi\) | ||||
0.453997 | + | 0.891003i | \(0.349998\pi\) | |||||||
\(270\) | −6800.00 | −1.53272 | ||||||||
\(271\) | 4296.00 | 0.962965 | 0.481482 | − | 0.876456i | \(-0.340099\pi\) | ||||
0.481482 | + | 0.876456i | \(0.340099\pi\) | |||||||
\(272\) | 832.000 | 0.185468 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6684.00 | 1.47371 | ||||||||
\(275\) | 5248.00 | 1.15079 | ||||||||
\(276\) | 1248.00 | 0.272177 | ||||||||
\(277\) | −5551.00 | −1.20407 | −0.602035 | − | 0.798470i | \(-0.705643\pi\) | ||||
−0.602035 | + | 0.798470i | \(0.705643\pi\) | |||||||
\(278\) | −3648.00 | −0.787023 | ||||||||
\(279\) | −1702.00 | −0.365219 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5557.00 | 1.17973 | 0.589863 | − | 0.807504i | \(-0.299182\pi\) | ||||
0.589863 | + | 0.807504i | \(0.299182\pi\) | |||||||
\(282\) | −1296.00 | −0.273673 | ||||||||
\(283\) | 3120.00 | 0.655352 | 0.327676 | − | 0.944790i | \(-0.393734\pi\) | ||||
0.327676 | + | 0.944790i | \(0.393734\pi\) | |||||||
\(284\) | −5232.00 | −1.09318 | ||||||||
\(285\) | 1020.00 | 0.211999 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3300.00 | −0.678721 | ||||||||
\(288\) | −5888.00 | −1.20470 | ||||||||
\(289\) | −4744.00 | −0.965601 | ||||||||
\(290\) | 13396.0 | 2.71255 | ||||||||
\(291\) | −476.000 | −0.0958887 | ||||||||
\(292\) | −1720.00 | −0.344710 | ||||||||
\(293\) | −8301.00 | −1.65512 | −0.827559 | − | 0.561379i | \(-0.810271\pi\) | ||||
−0.827559 | + | 0.561379i | \(0.810271\pi\) | |||||||
\(294\) | −456.000 | −0.0904573 | ||||||||
\(295\) | −14688.0 | −2.89888 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3200.00 | −0.625195 | ||||||||
\(298\) | −8460.00 | −1.64455 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2624.00 | 0.504989 | ||||||||
\(301\) | 3120.00 | 0.597455 | ||||||||
\(302\) | 2056.00 | 0.391753 | ||||||||
\(303\) | −1638.00 | −0.310563 | ||||||||
\(304\) | 1920.00 | 0.362235 | ||||||||
\(305\) | −2465.00 | −0.462772 | ||||||||
\(306\) | −1196.00 | −0.223434 | ||||||||
\(307\) | −8678.00 | −1.61329 | −0.806644 | − | 0.591037i | \(-0.798719\pi\) | ||||
−0.806644 | + | 0.591037i | \(0.798719\pi\) | |||||||
\(308\) | −5120.00 | −0.947205 | ||||||||
\(309\) | 3276.00 | 0.603123 | ||||||||
\(310\) | 5032.00 | 0.921930 | ||||||||
\(311\) | 8658.00 | 1.57862 | 0.789309 | − | 0.613996i | \(-0.210439\pi\) | ||||
0.789309 | + | 0.613996i | \(0.210439\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5250.00 | −0.948075 | −0.474038 | − | 0.880505i | \(-0.657204\pi\) | ||||
−0.474038 | + | 0.880505i | \(0.657204\pi\) | |||||||
\(314\) | −11604.0 | −2.08551 | ||||||||
\(315\) | −7820.00 | −1.39875 | ||||||||
\(316\) | −608.000 | −0.108236 | ||||||||
\(317\) | −6413.00 | −1.13625 | −0.568123 | − | 0.822944i | \(-0.692330\pi\) | ||||
−0.568123 | + | 0.822944i | \(0.692330\pi\) | |||||||
\(318\) | −744.000 | −0.131200 | ||||||||
\(319\) | 6304.00 | 1.10645 | ||||||||
\(320\) | 8704.00 | 1.52053 | ||||||||
\(321\) | 1044.00 | 0.181528 | ||||||||
\(322\) | 6240.00 | 1.07994 | ||||||||
\(323\) | 390.000 | 0.0671832 | ||||||||
\(324\) | 3368.00 | 0.577503 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9440.00 | 1.60378 | ||||||||
\(327\) | 3268.00 | 0.552663 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3240.00 | −0.542939 | ||||||||
\(330\) | 4352.00 | 0.725969 | ||||||||
\(331\) | −3488.00 | −0.579208 | −0.289604 | − | 0.957147i | \(-0.593524\pi\) | ||||
−0.289604 | + | 0.957147i | \(0.593524\pi\) | |||||||
\(332\) | −5024.00 | −0.830505 | ||||||||
\(333\) | −5221.00 | −0.859186 | ||||||||
\(334\) | 1120.00 | 0.183484 | ||||||||
\(335\) | 14654.0 | 2.38995 | ||||||||
\(336\) | 2560.00 | 0.415653 | ||||||||
\(337\) | −1833.00 | −0.296290 | −0.148145 | − | 0.988966i | \(-0.547330\pi\) | ||||
−0.148145 | + | 0.988966i | \(0.547330\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 654.000 | 0.104780 | ||||||||
\(340\) | 1768.00 | 0.282010 | ||||||||
\(341\) | 2368.00 | 0.376054 | ||||||||
\(342\) | −2760.00 | −0.436385 | ||||||||
\(343\) | 5720.00 | 0.900440 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2652.00 | −0.413852 | ||||||||
\(346\) | −5304.00 | −0.824118 | ||||||||
\(347\) | 7230.00 | 1.11852 | 0.559260 | − | 0.828992i | \(-0.311085\pi\) | ||||
0.559260 | + | 0.828992i | \(0.311085\pi\) | |||||||
\(348\) | 3152.00 | 0.485531 | ||||||||
\(349\) | 5258.00 | 0.806459 | 0.403230 | − | 0.915099i | \(-0.367888\pi\) | ||||
0.403230 | + | 0.915099i | \(0.367888\pi\) | |||||||
\(350\) | 13120.0 | 2.00370 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8192.00 | 1.24044 | ||||||||
\(353\) | −3163.00 | −0.476911 | −0.238455 | − | 0.971153i | \(-0.576641\pi\) | ||||
−0.238455 | + | 0.971153i | \(0.576641\pi\) | |||||||
\(354\) | −6912.00 | −1.03776 | ||||||||
\(355\) | 11118.0 | 1.66220 | ||||||||
\(356\) | 2128.00 | 0.316808 | ||||||||
\(357\) | 520.000 | 0.0770905 | ||||||||
\(358\) | −17056.0 | −2.51798 | ||||||||
\(359\) | 10068.0 | 1.48014 | 0.740068 | − | 0.672532i | \(-0.234793\pi\) | ||||
0.740068 | + | 0.672532i | \(0.234793\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5959.00 | −0.868786 | ||||||||
\(362\) | 1612.00 | 0.234047 | ||||||||
\(363\) | −614.000 | −0.0887786 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3655.00 | 0.524141 | ||||||||
\(366\) | −1160.00 | −0.165667 | ||||||||
\(367\) | 7438.00 | 1.05793 | 0.528965 | − | 0.848644i | \(-0.322580\pi\) | ||||
0.528965 | + | 0.848644i | \(0.322580\pi\) | |||||||
\(368\) | −4992.00 | −0.707136 | ||||||||
\(369\) | −3795.00 | −0.535392 | ||||||||
\(370\) | 15436.0 | 2.16886 | ||||||||
\(371\) | −1860.00 | −0.260287 | ||||||||
\(372\) | 1184.00 | 0.165020 | ||||||||
\(373\) | −9683.00 | −1.34415 | −0.672073 | − | 0.740485i | \(-0.734596\pi\) | ||||
−0.672073 | + | 0.740485i | \(0.734596\pi\) | |||||||
\(374\) | 1664.00 | 0.230063 | ||||||||
\(375\) | −1326.00 | −0.182598 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −8000.00 | −1.08856 | ||||||||
\(379\) | 1062.00 | 0.143935 | 0.0719674 | − | 0.997407i | \(-0.477072\pi\) | ||||
0.0719674 | + | 0.997407i | \(0.477072\pi\) | |||||||
\(380\) | 4080.00 | 0.550788 | ||||||||
\(381\) | −4316.00 | −0.580355 | ||||||||
\(382\) | 4984.00 | 0.667549 | ||||||||
\(383\) | 3532.00 | 0.471219 | 0.235609 | − | 0.971848i | \(-0.424291\pi\) | ||||
0.235609 | + | 0.971848i | \(0.424291\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10880.0 | 1.44025 | ||||||||
\(386\) | 1068.00 | 0.140828 | ||||||||
\(387\) | 3588.00 | 0.471288 | ||||||||
\(388\) | −1904.00 | −0.249126 | ||||||||
\(389\) | −11063.0 | −1.44194 | −0.720972 | − | 0.692964i | \(-0.756304\pi\) | ||||
−0.720972 | + | 0.692964i | \(0.756304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1014.00 | −0.131151 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1460.00 | 0.187398 | ||||||||
\(394\) | 5112.00 | 0.653652 | ||||||||
\(395\) | 1292.00 | 0.164576 | ||||||||
\(396\) | −5888.00 | −0.747180 | ||||||||
\(397\) | 5986.00 | 0.756747 | 0.378374 | − | 0.925653i | \(-0.376483\pi\) | ||||
0.378374 | + | 0.925653i | \(0.376483\pi\) | |||||||
\(398\) | −16952.0 | −2.13499 | ||||||||
\(399\) | 1200.00 | 0.150564 | ||||||||
\(400\) | −10496.0 | −1.31200 | ||||||||
\(401\) | −5935.00 | −0.739102 | −0.369551 | − | 0.929211i | \(-0.620488\pi\) | ||||
−0.369551 | + | 0.929211i | \(0.620488\pi\) | |||||||
\(402\) | 6896.00 | 0.855575 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6552.00 | −0.806867 | ||||||||
\(405\) | −7157.00 | −0.878109 | ||||||||
\(406\) | 15760.0 | 1.92649 | ||||||||
\(407\) | 7264.00 | 0.884676 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15089.0 | 1.82421 | 0.912106 | − | 0.409954i | \(-0.134455\pi\) | ||||
0.912106 | + | 0.409954i | \(0.134455\pi\) | |||||||
\(410\) | 11220.0 | 1.35150 | ||||||||
\(411\) | −3342.00 | −0.401092 | ||||||||
\(412\) | 13104.0 | 1.56696 | ||||||||
\(413\) | −17280.0 | −2.05882 | ||||||||
\(414\) | 7176.00 | 0.851887 | ||||||||
\(415\) | 10676.0 | 1.26281 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1824.00 | 0.214201 | ||||||||
\(418\) | 3840.00 | 0.449331 | ||||||||
\(419\) | −10814.0 | −1.26086 | −0.630428 | − | 0.776248i | \(-0.717120\pi\) | ||||
−0.630428 | + | 0.776248i | \(0.717120\pi\) | |||||||
\(420\) | 5440.00 | 0.632011 | ||||||||
\(421\) | 6535.00 | 0.756524 | 0.378262 | − | 0.925699i | \(-0.376522\pi\) | ||||
0.378262 | + | 0.925699i | \(0.376522\pi\) | |||||||
\(422\) | −12280.0 | −1.41654 | ||||||||
\(423\) | −3726.00 | −0.428284 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2132.00 | −0.243335 | ||||||||
\(426\) | 5232.00 | 0.595050 | ||||||||
\(427\) | −2900.00 | −0.328667 | ||||||||
\(428\) | 4176.00 | 0.471623 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10608.0 | −1.18968 | ||||||||
\(431\) | −1980.00 | −0.221284 | −0.110642 | − | 0.993860i | \(-0.535291\pi\) | ||||
−0.110642 | + | 0.993860i | \(0.535291\pi\) | |||||||
\(432\) | 6400.00 | 0.712778 | ||||||||
\(433\) | −6929.00 | −0.769022 | −0.384511 | − | 0.923120i | \(-0.625630\pi\) | ||||
−0.384511 | + | 0.923120i | \(0.625630\pi\) | |||||||
\(434\) | 5920.00 | 0.654767 | ||||||||
\(435\) | −6698.00 | −0.738263 | ||||||||
\(436\) | 13072.0 | 1.43586 | ||||||||
\(437\) | −2340.00 | −0.256150 | ||||||||
\(438\) | 1720.00 | 0.187636 | ||||||||
\(439\) | −4576.00 | −0.497496 | −0.248748 | − | 0.968568i | \(-0.580019\pi\) | ||||
−0.248748 | + | 0.968568i | \(0.580019\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1311.00 | −0.141561 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8812.00 | −0.945081 | −0.472540 | − | 0.881309i | \(-0.656663\pi\) | ||||
−0.472540 | + | 0.881309i | \(0.656663\pi\) | |||||||
\(444\) | 3632.00 | 0.388214 | ||||||||
\(445\) | −4522.00 | −0.481715 | ||||||||
\(446\) | −21512.0 | −2.28391 | ||||||||
\(447\) | 4230.00 | 0.447589 | ||||||||
\(448\) | 10240.0 | 1.07990 | ||||||||
\(449\) | −1918.00 | −0.201595 | −0.100797 | − | 0.994907i | \(-0.532139\pi\) | ||||
−0.100797 | + | 0.994907i | \(0.532139\pi\) | |||||||
\(450\) | 15088.0 | 1.58057 | ||||||||
\(451\) | 5280.00 | 0.551276 | ||||||||
\(452\) | 2616.00 | 0.272226 | ||||||||
\(453\) | −1028.00 | −0.106622 | ||||||||
\(454\) | −15896.0 | −1.64325 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11761.0 | 1.20384 | 0.601922 | − | 0.798555i | \(-0.294402\pi\) | ||||
0.601922 | + | 0.798555i | \(0.294402\pi\) | |||||||
\(458\) | −25192.0 | −2.57019 | ||||||||
\(459\) | 1300.00 | 0.132198 | ||||||||
\(460\) | −10608.0 | −1.07522 | ||||||||
\(461\) | −901.000 | −0.0910277 | −0.0455138 | − | 0.998964i | \(-0.514493\pi\) | ||||
−0.0455138 | + | 0.998964i | \(0.514493\pi\) | |||||||
\(462\) | 5120.00 | 0.515593 | ||||||||
\(463\) | −1372.00 | −0.137715 | −0.0688577 | − | 0.997626i | \(-0.521935\pi\) | ||||
−0.0688577 | + | 0.997626i | \(0.521935\pi\) | |||||||
\(464\) | −12608.0 | −1.26145 | ||||||||
\(465\) | −2516.00 | −0.250918 | ||||||||
\(466\) | −16120.0 | −1.60246 | ||||||||
\(467\) | −6396.00 | −0.633772 | −0.316886 | − | 0.948464i | \(-0.602637\pi\) | ||||
−0.316886 | + | 0.948464i | \(0.602637\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17240.0 | 1.69738 | ||||||||
\(470\) | 11016.0 | 1.08113 | ||||||||
\(471\) | 5802.00 | 0.567605 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4992.00 | −0.485269 | ||||||||
\(474\) | 608.000 | 0.0589164 | ||||||||
\(475\) | −4920.00 | −0.475253 | ||||||||
\(476\) | 2080.00 | 0.200287 | ||||||||
\(477\) | −2139.00 | −0.205321 | ||||||||
\(478\) | −3936.00 | −0.376629 | ||||||||
\(479\) | −3270.00 | −0.311921 | −0.155960 | − | 0.987763i | \(-0.549847\pi\) | ||||
−0.155960 | + | 0.987763i | \(0.549847\pi\) | |||||||
\(480\) | −8704.00 | −0.827670 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3772.00 | 0.356452 | ||||||||
\(483\) | −3120.00 | −0.293923 | ||||||||
\(484\) | −2456.00 | −0.230654 | ||||||||
\(485\) | 4046.00 | 0.378803 | ||||||||
\(486\) | −14168.0 | −1.32237 | ||||||||
\(487\) | −19920.0 | −1.85351 | −0.926757 | − | 0.375661i | \(-0.877416\pi\) | ||||
−0.926757 | + | 0.375661i | \(0.877416\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4720.00 | −0.436494 | ||||||||
\(490\) | 3876.00 | 0.357347 | ||||||||
\(491\) | 6552.00 | 0.602215 | 0.301108 | − | 0.953590i | \(-0.402644\pi\) | ||||
0.301108 | + | 0.953590i | \(0.402644\pi\) | |||||||
\(492\) | 2640.00 | 0.241911 | ||||||||
\(493\) | −2561.00 | −0.233959 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12512.0 | 1.13611 | ||||||||
\(496\) | −4736.00 | −0.428735 | ||||||||
\(497\) | 13080.0 | 1.18052 | ||||||||
\(498\) | 5024.00 | 0.452070 | ||||||||
\(499\) | −1746.00 | −0.156637 | −0.0783183 | − | 0.996928i | \(-0.524955\pi\) | ||||
−0.0783183 | + | 0.996928i | \(0.524955\pi\) | |||||||
\(500\) | −5304.00 | −0.474404 | ||||||||
\(501\) | −560.000 | −0.0499380 | ||||||||
\(502\) | 10920.0 | 0.970883 | ||||||||
\(503\) | 14692.0 | 1.30235 | 0.651177 | − | 0.758926i | \(-0.274276\pi\) | ||||
0.651177 | + | 0.758926i | \(0.274276\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13923.0 | 1.22686 | ||||||||
\(506\) | −9984.00 | −0.877160 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17264.0 | −1.50781 | ||||||||
\(509\) | −8077.00 | −0.703353 | −0.351677 | − | 0.936122i | \(-0.614388\pi\) | ||||
−0.351677 | + | 0.936122i | \(0.614388\pi\) | |||||||
\(510\) | −1768.00 | −0.153507 | ||||||||
\(511\) | 4300.00 | 0.372252 | ||||||||
\(512\) | −16384.0 | −1.41421 | ||||||||
\(513\) | 3000.00 | 0.258193 | ||||||||
\(514\) | 7540.00 | 0.647033 | ||||||||
\(515\) | −27846.0 | −2.38260 | ||||||||
\(516\) | −2496.00 | −0.212946 | ||||||||
\(517\) | 5184.00 | 0.440990 | ||||||||
\(518\) | 18160.0 | 1.54036 | ||||||||
\(519\) | 2652.00 | 0.224296 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11247.0 | 0.945758 | 0.472879 | − | 0.881127i | \(-0.343215\pi\) | ||||
0.472879 | + | 0.881127i | \(0.343215\pi\) | |||||||
\(522\) | 18124.0 | 1.51967 | ||||||||
\(523\) | 2732.00 | 0.228417 | 0.114208 | − | 0.993457i | \(-0.463567\pi\) | ||||
0.114208 | + | 0.993457i | \(0.463567\pi\) | |||||||
\(524\) | 5840.00 | 0.486873 | ||||||||
\(525\) | −6560.00 | −0.545337 | ||||||||
\(526\) | −16128.0 | −1.33691 | ||||||||
\(527\) | −962.000 | −0.0795168 | ||||||||
\(528\) | −4096.00 | −0.337605 | ||||||||
\(529\) | −6083.00 | −0.499959 | ||||||||
\(530\) | 6324.00 | 0.518296 | ||||||||
\(531\) | −19872.0 | −1.62405 | ||||||||
\(532\) | 4800.00 | 0.391177 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2128.00 | −0.172449 | ||||||||
\(535\) | −8874.00 | −0.717115 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8528.00 | 0.685308 | ||||||||
\(538\) | −16024.0 | −1.28410 | ||||||||
\(539\) | 1824.00 | 0.145761 | ||||||||
\(540\) | 13600.0 | 1.08380 | ||||||||
\(541\) | 18375.0 | 1.46026 | 0.730132 | − | 0.683306i | \(-0.239458\pi\) | ||||
0.730132 | + | 0.683306i | \(0.239458\pi\) | |||||||
\(542\) | −17184.0 | −1.36184 | ||||||||
\(543\) | −806.000 | −0.0636994 | ||||||||
\(544\) | −3328.00 | −0.262292 | ||||||||
\(545\) | −27778.0 | −2.18326 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10346.0 | −0.808708 | −0.404354 | − | 0.914603i | \(-0.632504\pi\) | ||||
−0.404354 | + | 0.914603i | \(0.632504\pi\) | |||||||
\(548\) | −13368.0 | −1.04207 | ||||||||
\(549\) | −3335.00 | −0.259261 | ||||||||
\(550\) | −20992.0 | −1.62746 | ||||||||
\(551\) | −5910.00 | −0.456941 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1520.00 | 0.116884 | ||||||||
\(554\) | 22204.0 | 1.70281 | ||||||||
\(555\) | −7718.00 | −0.590290 | ||||||||
\(556\) | 7296.00 | 0.556510 | ||||||||
\(557\) | −345.000 | −0.0262444 | −0.0131222 | − | 0.999914i | \(-0.504177\pi\) | ||||
−0.0131222 | + | 0.999914i | \(0.504177\pi\) | |||||||
\(558\) | 6808.00 | 0.516498 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −21760.0 | −1.64201 | ||||||||
\(561\) | −832.000 | −0.0626151 | ||||||||
\(562\) | −22228.0 | −1.66838 | ||||||||
\(563\) | −8580.00 | −0.642280 | −0.321140 | − | 0.947032i | \(-0.604066\pi\) | ||||
−0.321140 | + | 0.947032i | \(0.604066\pi\) | |||||||
\(564\) | 2592.00 | 0.193516 | ||||||||
\(565\) | −5559.00 | −0.413927 | ||||||||
\(566\) | −12480.0 | −0.926808 | ||||||||
\(567\) | −8420.00 | −0.623645 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19682.0 | −1.45011 | −0.725055 | − | 0.688691i | \(-0.758186\pi\) | ||||
−0.725055 | + | 0.688691i | \(0.758186\pi\) | |||||||
\(570\) | −4080.00 | −0.299811 | ||||||||
\(571\) | 26624.0 | 1.95128 | 0.975639 | − | 0.219382i | \(-0.0704042\pi\) | ||||
0.975639 | + | 0.219382i | \(0.0704042\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2492.00 | −0.181684 | ||||||||
\(574\) | 13200.0 | 0.959856 | ||||||||
\(575\) | 12792.0 | 0.927762 | ||||||||
\(576\) | 11776.0 | 0.851852 | ||||||||
\(577\) | 14101.0 | 1.01739 | 0.508694 | − | 0.860948i | \(-0.330129\pi\) | ||||
0.508694 | + | 0.860948i | \(0.330129\pi\) | |||||||
\(578\) | 18976.0 | 1.36557 | ||||||||
\(579\) | −534.000 | −0.0383286 | ||||||||
\(580\) | −26792.0 | −1.91806 | ||||||||
\(581\) | 12560.0 | 0.896862 | ||||||||
\(582\) | 1904.00 | 0.135607 | ||||||||
\(583\) | 2976.00 | 0.211412 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33204.0 | 2.34069 | ||||||||
\(587\) | −1408.00 | −0.0990023 | −0.0495012 | − | 0.998774i | \(-0.515763\pi\) | ||||
−0.0495012 | + | 0.998774i | \(0.515763\pi\) | |||||||
\(588\) | 912.000 | 0.0639630 | ||||||||
\(589\) | −2220.00 | −0.155303 | ||||||||
\(590\) | 58752.0 | 4.09963 | ||||||||
\(591\) | −2556.00 | −0.177902 | ||||||||
\(592\) | −14528.0 | −1.00861 | ||||||||
\(593\) | 1241.00 | 0.0859389 | 0.0429694 | − | 0.999076i | \(-0.486318\pi\) | ||||
0.0429694 | + | 0.999076i | \(0.486318\pi\) | |||||||
\(594\) | 12800.0 | 0.884159 | ||||||||
\(595\) | −4420.00 | −0.304542 | ||||||||
\(596\) | 16920.0 | 1.16287 | ||||||||
\(597\) | 8476.00 | 0.581071 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11078.0 | 0.755651 | 0.377825 | − | 0.925877i | \(-0.376672\pi\) | ||||
0.377825 | + | 0.925877i | \(0.376672\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13817.0 | −0.937782 | −0.468891 | − | 0.883256i | \(-0.655346\pi\) | ||||
−0.468891 | + | 0.883256i | \(0.655346\pi\) | |||||||
\(602\) | −12480.0 | −0.844928 | ||||||||
\(603\) | 19826.0 | 1.33893 | ||||||||
\(604\) | −4112.00 | −0.277011 | ||||||||
\(605\) | 5219.00 | 0.350715 | ||||||||
\(606\) | 6552.00 | 0.439203 | ||||||||
\(607\) | 8270.00 | 0.552997 | 0.276498 | − | 0.961014i | \(-0.410826\pi\) | ||||
0.276498 | + | 0.961014i | \(0.410826\pi\) | |||||||
\(608\) | −7680.00 | −0.512278 | ||||||||
\(609\) | −7880.00 | −0.524325 | ||||||||
\(610\) | 9860.00 | 0.654459 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2392.00 | 0.157992 | ||||||||
\(613\) | −22273.0 | −1.46753 | −0.733767 | − | 0.679402i | \(-0.762239\pi\) | ||||
−0.733767 | + | 0.679402i | \(0.762239\pi\) | |||||||
\(614\) | 34712.0 | 2.28153 | ||||||||
\(615\) | −5610.00 | −0.367833 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18989.0 | 1.23901 | 0.619504 | − | 0.784993i | \(-0.287334\pi\) | ||||
0.619504 | + | 0.784993i | \(0.287334\pi\) | |||||||
\(618\) | −13104.0 | −0.852945 | ||||||||
\(619\) | −72.0000 | −0.00467516 | −0.00233758 | − | 0.999997i | \(-0.500744\pi\) | ||||
−0.00233758 | + | 0.999997i | \(0.500744\pi\) | |||||||
\(620\) | −10064.0 | −0.651903 | ||||||||
\(621\) | −7800.00 | −0.504031 | ||||||||
\(622\) | −34632.0 | −2.23250 | ||||||||
\(623\) | −5320.00 | −0.342121 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9229.00 | −0.590656 | ||||||||
\(626\) | 21000.0 | 1.34078 | ||||||||
\(627\) | −1920.00 | −0.122293 | ||||||||
\(628\) | 23208.0 | 1.47468 | ||||||||
\(629\) | −2951.00 | −0.187065 | ||||||||
\(630\) | 31280.0 | 1.97813 | ||||||||
\(631\) | 23380.0 | 1.47503 | 0.737514 | − | 0.675331i | \(-0.235999\pi\) | ||||
0.737514 | + | 0.675331i | \(0.235999\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6140.00 | 0.385534 | ||||||||
\(634\) | 25652.0 | 1.60689 | ||||||||
\(635\) | 36686.0 | 2.29266 | ||||||||
\(636\) | 1488.00 | 0.0927721 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25216.0 | −1.56475 | ||||||||
\(639\) | 15042.0 | 0.931224 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6383.00 | 0.393313 | 0.196656 | − | 0.980472i | \(-0.436992\pi\) | ||||
0.196656 | + | 0.980472i | \(0.436992\pi\) | |||||||
\(642\) | −4176.00 | −0.256719 | ||||||||
\(643\) | 17104.0 | 1.04901 | 0.524507 | − | 0.851406i | \(-0.324250\pi\) | ||||
0.524507 | + | 0.851406i | \(0.324250\pi\) | |||||||
\(644\) | −12480.0 | −0.763635 | ||||||||
\(645\) | 5304.00 | 0.323790 | ||||||||
\(646\) | −1560.00 | −0.0950114 | ||||||||
\(647\) | 6994.00 | 0.424981 | 0.212490 | − | 0.977163i | \(-0.431843\pi\) | ||||
0.212490 | + | 0.977163i | \(0.431843\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27648.0 | 1.67223 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2960.00 | −0.178205 | ||||||||
\(652\) | −18880.0 | −1.13405 | ||||||||
\(653\) | −5250.00 | −0.314622 | −0.157311 | − | 0.987549i | \(-0.550283\pi\) | ||||
−0.157311 | + | 0.987549i | \(0.550283\pi\) | |||||||
\(654\) | −13072.0 | −0.781584 | ||||||||
\(655\) | −12410.0 | −0.740304 | ||||||||
\(656\) | −10560.0 | −0.628504 | ||||||||
\(657\) | 4945.00 | 0.293642 | ||||||||
\(658\) | 12960.0 | 0.767832 | ||||||||
\(659\) | −4340.00 | −0.256544 | −0.128272 | − | 0.991739i | \(-0.540943\pi\) | ||||
−0.128272 | + | 0.991739i | \(0.540943\pi\) | |||||||
\(660\) | −8704.00 | −0.513337 | ||||||||
\(661\) | 4179.00 | 0.245907 | 0.122953 | − | 0.992412i | \(-0.460763\pi\) | ||||
0.122953 | + | 0.992412i | \(0.460763\pi\) | |||||||
\(662\) | 13952.0 | 0.819124 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10200.0 | −0.594796 | ||||||||
\(666\) | 20884.0 | 1.21507 | ||||||||
\(667\) | 15366.0 | 0.892015 | ||||||||
\(668\) | −2240.00 | −0.129743 | ||||||||
\(669\) | 10756.0 | 0.621601 | ||||||||
\(670\) | −58616.0 | −3.37990 | ||||||||
\(671\) | 4640.00 | 0.266953 | ||||||||
\(672\) | −10240.0 | −0.587822 | ||||||||
\(673\) | 22867.0 | 1.30974 | 0.654872 | − | 0.755740i | \(-0.272722\pi\) | ||||
0.654872 | + | 0.755740i | \(0.272722\pi\) | |||||||
\(674\) | 7332.00 | 0.419018 | ||||||||
\(675\) | −16400.0 | −0.935165 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5410.00 | 0.307124 | 0.153562 | − | 0.988139i | \(-0.450925\pi\) | ||||
0.153562 | + | 0.988139i | \(0.450925\pi\) | |||||||
\(678\) | −2616.00 | −0.148181 | ||||||||
\(679\) | 4760.00 | 0.269031 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7948.00 | 0.447236 | ||||||||
\(682\) | −9472.00 | −0.531821 | ||||||||
\(683\) | 13578.0 | 0.760685 | 0.380342 | − | 0.924846i | \(-0.375806\pi\) | ||||
0.380342 | + | 0.924846i | \(0.375806\pi\) | |||||||
\(684\) | 5520.00 | 0.308571 | ||||||||
\(685\) | 28407.0 | 1.58449 | ||||||||
\(686\) | −22880.0 | −1.27341 | ||||||||
\(687\) | 12596.0 | 0.699516 | ||||||||
\(688\) | 9984.00 | 0.553251 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 10608.0 | 0.585275 | ||||||||
\(691\) | −12744.0 | −0.701599 | −0.350799 | − | 0.936451i | \(-0.614090\pi\) | ||||
−0.350799 | + | 0.936451i | \(0.614090\pi\) | |||||||
\(692\) | 10608.0 | 0.582739 | ||||||||
\(693\) | 14720.0 | 0.806878 | ||||||||
\(694\) | −28920.0 | −1.58183 | ||||||||
\(695\) | −15504.0 | −0.846187 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2145.00 | −0.116568 | ||||||||
\(698\) | −21032.0 | −1.14051 | ||||||||
\(699\) | 8060.00 | 0.436133 | ||||||||
\(700\) | −26240.0 | −1.41683 | ||||||||
\(701\) | 16406.0 | 0.883946 | 0.441973 | − | 0.897028i | \(-0.354279\pi\) | ||||
0.441973 | + | 0.897028i | \(0.354279\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6810.00 | −0.365354 | ||||||||
\(704\) | −16384.0 | −0.877124 | ||||||||
\(705\) | −5508.00 | −0.294246 | ||||||||
\(706\) | 12652.0 | 0.674454 | ||||||||
\(707\) | 16380.0 | 0.871334 | ||||||||
\(708\) | 13824.0 | 0.733810 | ||||||||
\(709\) | −709.000 | −0.0375558 | −0.0187779 | − | 0.999824i | \(-0.505978\pi\) | ||||
−0.0187779 | + | 0.999824i | \(0.505978\pi\) | |||||||
\(710\) | −44472.0 | −2.35071 | ||||||||
\(711\) | 1748.00 | 0.0922013 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5772.00 | 0.303174 | ||||||||
\(714\) | −2080.00 | −0.109022 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 34112.0 | 1.78048 | ||||||||
\(717\) | 1968.00 | 0.102505 | ||||||||
\(718\) | −40272.0 | −2.09323 | ||||||||
\(719\) | −7644.00 | −0.396486 | −0.198243 | − | 0.980153i | \(-0.563523\pi\) | ||||
−0.198243 | + | 0.980153i | \(0.563523\pi\) | |||||||
\(720\) | −25024.0 | −1.29526 | ||||||||
\(721\) | −32760.0 | −1.69216 | ||||||||
\(722\) | 23836.0 | 1.22865 | ||||||||
\(723\) | −1886.00 | −0.0970140 | ||||||||
\(724\) | −3224.00 | −0.165496 | ||||||||
\(725\) | 32308.0 | 1.65502 | ||||||||
\(726\) | 2456.00 | 0.125552 | ||||||||
\(727\) | −15808.0 | −0.806446 | −0.403223 | − | 0.915102i | \(-0.632110\pi\) | ||||
−0.403223 | + | 0.915102i | \(0.632110\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4283.00 | −0.217599 | ||||||||
\(730\) | −14620.0 | −0.741247 | ||||||||
\(731\) | 2028.00 | 0.102611 | ||||||||
\(732\) | 2320.00 | 0.117144 | ||||||||
\(733\) | 2583.00 | 0.130157 | 0.0650786 | − | 0.997880i | \(-0.479270\pi\) | ||||
0.0650786 | + | 0.997880i | \(0.479270\pi\) | |||||||
\(734\) | −29752.0 | −1.49614 | ||||||||
\(735\) | −1938.00 | −0.0972574 | ||||||||
\(736\) | 19968.0 | 1.00004 | ||||||||
\(737\) | −27584.0 | −1.37866 | ||||||||
\(738\) | 15180.0 | 0.757159 | ||||||||
\(739\) | −4076.00 | −0.202893 | −0.101447 | − | 0.994841i | \(-0.532347\pi\) | ||||
−0.101447 | + | 0.994841i | \(0.532347\pi\) | |||||||
\(740\) | −30872.0 | −1.53362 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7440.00 | 0.368101 | ||||||||
\(743\) | 34056.0 | 1.68155 | 0.840776 | − | 0.541383i | \(-0.182099\pi\) | ||||
0.840776 | + | 0.541383i | \(0.182099\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35955.0 | −1.76817 | ||||||||
\(746\) | 38732.0 | 1.90091 | ||||||||
\(747\) | 14444.0 | 0.707468 | ||||||||
\(748\) | −3328.00 | −0.162679 | ||||||||
\(749\) | −10440.0 | −0.509305 | ||||||||
\(750\) | 5304.00 | 0.258233 | ||||||||
\(751\) | −364.000 | −0.0176865 | −0.00884324 | − | 0.999961i | \(-0.502815\pi\) | ||||
−0.00884324 | + | 0.999961i | \(0.502815\pi\) | |||||||
\(752\) | −10368.0 | −0.502769 | ||||||||
\(753\) | −5460.00 | −0.264241 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8738.00 | 0.421203 | ||||||||
\(756\) | 16000.0 | 0.769728 | ||||||||
\(757\) | −6914.00 | −0.331960 | −0.165980 | − | 0.986129i | \(-0.553079\pi\) | ||||
−0.165980 | + | 0.986129i | \(0.553079\pi\) | |||||||
\(758\) | −4248.00 | −0.203554 | ||||||||
\(759\) | 4992.00 | 0.238733 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13982.0 | −0.666028 | −0.333014 | − | 0.942922i | \(-0.608066\pi\) | ||||
−0.333014 | + | 0.942922i | \(0.608066\pi\) | |||||||
\(762\) | 17264.0 | 0.820746 | ||||||||
\(763\) | −32680.0 | −1.55058 | ||||||||
\(764\) | −9968.00 | −0.472028 | ||||||||
\(765\) | −5083.00 | −0.240230 | ||||||||
\(766\) | −14128.0 | −0.666404 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 8192.00 | 0.384900 | ||||||||
\(769\) | 18066.0 | 0.847174 | 0.423587 | − | 0.905855i | \(-0.360771\pi\) | ||||
0.423587 | + | 0.905855i | \(0.360771\pi\) | |||||||
\(770\) | −43520.0 | −2.03682 | ||||||||
\(771\) | −3770.00 | −0.176100 | ||||||||
\(772\) | −2136.00 | −0.0995807 | ||||||||
\(773\) | −14434.0 | −0.671610 | −0.335805 | − | 0.941931i | \(-0.609008\pi\) | ||||
−0.335805 | + | 0.941931i | \(0.609008\pi\) | |||||||
\(774\) | −14352.0 | −0.666501 | ||||||||
\(775\) | 12136.0 | 0.562501 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9080.00 | −0.419232 | ||||||||
\(778\) | 44252.0 | 2.03922 | ||||||||
\(779\) | −4950.00 | −0.227666 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20928.0 | −0.958851 | ||||||||
\(782\) | 4056.00 | 0.185476 | ||||||||
\(783\) | −19700.0 | −0.899132 | ||||||||
\(784\) | −3648.00 | −0.166181 | ||||||||
\(785\) | −49317.0 | −2.24229 | ||||||||
\(786\) | −5840.00 | −0.265020 | ||||||||
\(787\) | 15398.0 | 0.697433 | 0.348716 | − | 0.937228i | \(-0.386618\pi\) | ||||
0.348716 | + | 0.937228i | \(0.386618\pi\) | |||||||
\(788\) | −10224.0 | −0.462202 | ||||||||
\(789\) | 8064.00 | 0.363861 | ||||||||
\(790\) | −5168.00 | −0.232746 | ||||||||
\(791\) | −6540.00 | −0.293977 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −23944.0 | −1.07020 | ||||||||
\(795\) | −3162.00 | −0.141062 | ||||||||
\(796\) | 33904.0 | 1.50967 | ||||||||
\(797\) | −36842.0 | −1.63740 | −0.818702 | − | 0.574219i | \(-0.805306\pi\) | ||||
−0.818702 | + | 0.574219i | \(0.805306\pi\) | |||||||
\(798\) | −4800.00 | −0.212930 | ||||||||
\(799\) | −2106.00 | −0.0932477 | ||||||||
\(800\) | 41984.0 | 1.85545 | ||||||||
\(801\) | −6118.00 | −0.269874 | ||||||||
\(802\) | 23740.0 | 1.04525 | ||||||||
\(803\) | −6880.00 | −0.302354 | ||||||||
\(804\) | −13792.0 | −0.604983 | ||||||||
\(805\) | 26520.0 | 1.16113 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8012.00 | 0.349487 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41511.0 | 1.80402 | 0.902008 | − | 0.431719i | \(-0.142093\pi\) | ||||
0.902008 | + | 0.431719i | \(0.142093\pi\) | |||||||
\(810\) | 28628.0 | 1.24183 | ||||||||
\(811\) | −23066.0 | −0.998714 | −0.499357 | − | 0.866396i | \(-0.666430\pi\) | ||||
−0.499357 | + | 0.866396i | \(0.666430\pi\) | |||||||
\(812\) | −31520.0 | −1.36224 | ||||||||
\(813\) | 8592.00 | 0.370645 | ||||||||
\(814\) | −29056.0 | −1.25112 | ||||||||
\(815\) | 40120.0 | 1.72435 | ||||||||
\(816\) | 1664.00 | 0.0713868 | ||||||||
\(817\) | 4680.00 | 0.200407 | ||||||||
\(818\) | −60356.0 | −2.57983 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22440.0 | −0.955657 | ||||||||
\(821\) | −28838.0 | −1.22589 | −0.612943 | − | 0.790127i | \(-0.710015\pi\) | ||||
−0.612943 | + | 0.790127i | \(0.710015\pi\) | |||||||
\(822\) | 13368.0 | 0.567229 | ||||||||
\(823\) | 27456.0 | 1.16289 | 0.581443 | − | 0.813587i | \(-0.302488\pi\) | ||||
0.581443 | + | 0.813587i | \(0.302488\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10496.0 | 0.442938 | ||||||||
\(826\) | 69120.0 | 2.91161 | ||||||||
\(827\) | 33572.0 | 1.41162 | 0.705812 | − | 0.708399i | \(-0.250582\pi\) | ||||
0.705812 | + | 0.708399i | \(0.250582\pi\) | |||||||
\(828\) | −14352.0 | −0.602375 | ||||||||
\(829\) | −45799.0 | −1.91878 | −0.959388 | − | 0.282090i | \(-0.908972\pi\) | ||||
−0.959388 | + | 0.282090i | \(0.908972\pi\) | |||||||
\(830\) | −42704.0 | −1.78588 | ||||||||
\(831\) | −11102.0 | −0.463447 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −741.000 | −0.0308213 | ||||||||
\(834\) | −7296.00 | −0.302925 | ||||||||
\(835\) | 4760.00 | 0.197277 | ||||||||
\(836\) | −7680.00 | −0.317725 | ||||||||
\(837\) | −7400.00 | −0.305593 | ||||||||
\(838\) | 43256.0 | 1.78312 | ||||||||
\(839\) | −32286.0 | −1.32853 | −0.664265 | − | 0.747497i | \(-0.731255\pi\) | ||||
−0.664265 | + | 0.747497i | \(0.731255\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14420.0 | 0.591250 | ||||||||
\(842\) | −26140.0 | −1.06989 | ||||||||
\(843\) | 11114.0 | 0.454077 | ||||||||
\(844\) | 24560.0 | 1.00165 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14904.0 | 0.605686 | ||||||||
\(847\) | 6140.00 | 0.249083 | ||||||||
\(848\) | −5952.00 | −0.241029 | ||||||||
\(849\) | 6240.00 | 0.252245 | ||||||||
\(850\) | 8528.00 | 0.344127 | ||||||||
\(851\) | 17706.0 | 0.713224 | ||||||||
\(852\) | −10464.0 | −0.420764 | ||||||||
\(853\) | −20937.0 | −0.840409 | −0.420205 | − | 0.907429i | \(-0.638042\pi\) | ||||
−0.420205 | + | 0.907429i | \(0.638042\pi\) | |||||||
\(854\) | 11600.0 | 0.464805 | ||||||||
\(855\) | −11730.0 | −0.469190 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7189.00 | −0.286548 | −0.143274 | − | 0.989683i | \(-0.545763\pi\) | ||||
−0.143274 | + | 0.989683i | \(0.545763\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32498.0 | −1.29082 | −0.645412 | − | 0.763835i | \(-0.723314\pi\) | ||||
−0.645412 | + | 0.763835i | \(0.723314\pi\) | |||||||
\(860\) | 21216.0 | 0.841232 | ||||||||
\(861\) | −6600.00 | −0.261240 | ||||||||
\(862\) | 7920.00 | 0.312942 | ||||||||
\(863\) | −8428.00 | −0.332436 | −0.166218 | − | 0.986089i | \(-0.553156\pi\) | ||||
−0.166218 | + | 0.986089i | \(0.553156\pi\) | |||||||
\(864\) | −25600.0 | −1.00802 | ||||||||
\(865\) | −22542.0 | −0.886071 | ||||||||
\(866\) | 27716.0 | 1.08756 | ||||||||
\(867\) | −9488.00 | −0.371660 | ||||||||
\(868\) | −11840.0 | −0.462991 | ||||||||
\(869\) | −2432.00 | −0.0949367 | ||||||||
\(870\) | 26792.0 | 1.04406 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5474.00 | 0.212219 | ||||||||
\(874\) | 9360.00 | 0.362250 | ||||||||
\(875\) | 13260.0 | 0.512308 | ||||||||
\(876\) | −3440.00 | −0.132679 | ||||||||
\(877\) | 6847.00 | 0.263634 | 0.131817 | − | 0.991274i | \(-0.457919\pi\) | ||||
0.131817 | + | 0.991274i | \(0.457919\pi\) | |||||||
\(878\) | 18304.0 | 0.703565 | ||||||||
\(879\) | −16602.0 | −0.637055 | ||||||||
\(880\) | 34816.0 | 1.33369 | ||||||||
\(881\) | 29731.0 | 1.13696 | 0.568481 | − | 0.822697i | \(-0.307531\pi\) | ||||
0.568481 | + | 0.822697i | \(0.307531\pi\) | |||||||
\(882\) | 5244.00 | 0.200198 | ||||||||
\(883\) | −23738.0 | −0.904697 | −0.452348 | − | 0.891841i | \(-0.649414\pi\) | ||||
−0.452348 | + | 0.891841i | \(0.649414\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29376.0 | −1.11578 | ||||||||
\(886\) | 35248.0 | 1.33655 | ||||||||
\(887\) | 27588.0 | 1.04432 | 0.522161 | − | 0.852847i | \(-0.325126\pi\) | ||||
0.522161 | + | 0.852847i | \(0.325126\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43160.0 | 1.62828 | ||||||||
\(890\) | 18088.0 | 0.681248 | ||||||||
\(891\) | 13472.0 | 0.506542 | ||||||||
\(892\) | 43024.0 | 1.61497 | ||||||||
\(893\) | −4860.00 | −0.182121 | ||||||||
\(894\) | −16920.0 | −0.632986 | ||||||||
\(895\) | −72488.0 | −2.70727 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7672.00 | 0.285098 | ||||||||
\(899\) | 14578.0 | 0.540827 | ||||||||
\(900\) | −30176.0 | −1.11763 | ||||||||
\(901\) | −1209.00 | −0.0447033 | ||||||||
\(902\) | −21120.0 | −0.779622 | ||||||||
\(903\) | 6240.00 | 0.229960 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6851.00 | 0.251641 | ||||||||
\(906\) | 4112.00 | 0.150786 | ||||||||
\(907\) | −37128.0 | −1.35922 | −0.679611 | − | 0.733572i | \(-0.737852\pi\) | ||||
−0.679611 | + | 0.733572i | \(0.737852\pi\) | |||||||
\(908\) | 31792.0 | 1.16195 | ||||||||
\(909\) | 18837.0 | 0.687331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20516.0 | 0.746131 | 0.373066 | − | 0.927805i | \(-0.378307\pi\) | ||||
0.373066 | + | 0.927805i | \(0.378307\pi\) | |||||||
\(912\) | 3840.00 | 0.139424 | ||||||||
\(913\) | −20096.0 | −0.728456 | ||||||||
\(914\) | −47044.0 | −1.70249 | ||||||||
\(915\) | −4930.00 | −0.178121 | ||||||||
\(916\) | 50384.0 | 1.81740 | ||||||||
\(917\) | −14600.0 | −0.525774 | ||||||||
\(918\) | −5200.00 | −0.186956 | ||||||||
\(919\) | −21006.0 | −0.753998 | −0.376999 | − | 0.926214i | \(-0.623044\pi\) | ||||
−0.376999 | + | 0.926214i | \(0.623044\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17356.0 | −0.620955 | ||||||||
\(922\) | 3604.00 | 0.128733 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −10240.0 | −0.364579 | ||||||||
\(925\) | 37228.0 | 1.32330 | ||||||||
\(926\) | 5488.00 | 0.194759 | ||||||||
\(927\) | −37674.0 | −1.33482 | ||||||||
\(928\) | 50432.0 | 1.78396 | ||||||||
\(929\) | −20427.0 | −0.721408 | −0.360704 | − | 0.932680i | \(-0.617464\pi\) | ||||
−0.360704 | + | 0.932680i | \(0.617464\pi\) | |||||||
\(930\) | 10064.0 | 0.354851 | ||||||||
\(931\) | −1710.00 | −0.0601965 | ||||||||
\(932\) | 32240.0 | 1.13311 | ||||||||
\(933\) | 17316.0 | 0.607610 | ||||||||
\(934\) | 25584.0 | 0.896289 | ||||||||
\(935\) | 7072.00 | 0.247357 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33191.0 | 1.15721 | 0.578603 | − | 0.815609i | \(-0.303598\pi\) | ||||
0.578603 | + | 0.815609i | \(0.303598\pi\) | |||||||
\(938\) | −68960.0 | −2.40045 | ||||||||
\(939\) | −10500.0 | −0.364914 | ||||||||
\(940\) | −22032.0 | −0.764473 | ||||||||
\(941\) | 36422.0 | 1.26177 | 0.630884 | − | 0.775877i | \(-0.282692\pi\) | ||||
0.630884 | + | 0.775877i | \(0.282692\pi\) | |||||||
\(942\) | −23208.0 | −0.802715 | ||||||||
\(943\) | 12870.0 | 0.444438 | ||||||||
\(944\) | −55296.0 | −1.90650 | ||||||||
\(945\) | −34000.0 | −1.17039 | ||||||||
\(946\) | 19968.0 | 0.686275 | ||||||||
\(947\) | 39630.0 | 1.35988 | 0.679938 | − | 0.733270i | \(-0.262007\pi\) | ||||
0.679938 | + | 0.733270i | \(0.262007\pi\) | |||||||
\(948\) | −1216.00 | −0.0416602 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 19680.0 | 0.672109 | ||||||||
\(951\) | −12826.0 | −0.437341 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 57642.0 | 1.95929 | 0.979647 | − | 0.200727i | \(-0.0643305\pi\) | ||||
0.979647 | + | 0.200727i | \(0.0643305\pi\) | |||||||
\(954\) | 8556.00 | 0.290368 | ||||||||
\(955\) | 21182.0 | 0.717731 | ||||||||
\(956\) | 7872.00 | 0.266317 | ||||||||
\(957\) | 12608.0 | 0.425871 | ||||||||
\(958\) | 13080.0 | 0.441123 | ||||||||
\(959\) | 33420.0 | 1.12533 | ||||||||
\(960\) | 17408.0 | 0.585251 | ||||||||
\(961\) | −24315.0 | −0.816186 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12006.0 | −0.401753 | ||||||||
\(964\) | −7544.00 | −0.252050 | ||||||||
\(965\) | 4539.00 | 0.151415 | ||||||||
\(966\) | 12480.0 | 0.415670 | ||||||||
\(967\) | −2162.00 | −0.0718979 | −0.0359489 | − | 0.999354i | \(-0.511445\pi\) | ||||
−0.0359489 | + | 0.999354i | \(0.511445\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 780.000 | 0.0258588 | ||||||||
\(970\) | −16184.0 | −0.535708 | ||||||||
\(971\) | −19758.0 | −0.653001 | −0.326501 | − | 0.945197i | \(-0.605870\pi\) | ||||
−0.326501 | + | 0.945197i | \(0.605870\pi\) | |||||||
\(972\) | 28336.0 | 0.935059 | ||||||||
\(973\) | −18240.0 | −0.600974 | ||||||||
\(974\) | 79680.0 | 2.62126 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9280.00 | −0.304350 | ||||||||
\(977\) | 12489.0 | 0.408965 | 0.204482 | − | 0.978870i | \(-0.434449\pi\) | ||||
0.204482 | + | 0.978870i | \(0.434449\pi\) | |||||||
\(978\) | 18880.0 | 0.617296 | ||||||||
\(979\) | 8512.00 | 0.277880 | ||||||||
\(980\) | −7752.00 | −0.252682 | ||||||||
\(981\) | −37582.0 | −1.22314 | ||||||||
\(982\) | −26208.0 | −0.851661 | ||||||||
\(983\) | 28658.0 | 0.929856 | 0.464928 | − | 0.885349i | \(-0.346080\pi\) | ||||
0.464928 | + | 0.885349i | \(0.346080\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21726.0 | 0.702790 | ||||||||
\(986\) | 10244.0 | 0.330868 | ||||||||
\(987\) | −6480.00 | −0.208977 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12168.0 | −0.391223 | ||||||||
\(990\) | −50048.0 | −1.60670 | ||||||||
\(991\) | −42794.0 | −1.37174 | −0.685871 | − | 0.727723i | \(-0.740579\pi\) | ||||
−0.685871 | + | 0.727723i | \(0.740579\pi\) | |||||||
\(992\) | 18944.0 | 0.606323 | ||||||||
\(993\) | −6976.00 | −0.222937 | ||||||||
\(994\) | −52320.0 | −1.66951 | ||||||||
\(995\) | −72046.0 | −2.29549 | ||||||||
\(996\) | −10048.0 | −0.319662 | ||||||||
\(997\) | −52583.0 | −1.67033 | −0.835166 | − | 0.549998i | \(-0.814628\pi\) | ||||
−0.835166 | + | 0.549998i | \(0.814628\pi\) | |||||||
\(998\) | 6984.00 | 0.221518 | ||||||||
\(999\) | −22700.0 | −0.718915 |
(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 | 169.4.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 1521.4.a.k.1.1 | 1 | |||
13.2 | odd | 12 | 169.4.e.c.147.1 | 4 | |||
13.3 | even | 3 | 169.4.c.d.22.1 | 2 | |||
13.4 | even | 6 | 13.4.c.a.3.1 | ✓ | 2 | ||
13.5 | odd | 4 | 169.4.b.c.168.2 | 2 | |||
13.6 | odd | 12 | 169.4.e.c.23.2 | 4 | |||
13.7 | odd | 12 | 169.4.e.c.23.1 | 4 | |||
13.8 | odd | 4 | 169.4.b.c.168.1 | 2 | |||
13.9 | even | 3 | 169.4.c.d.146.1 | 2 | |||
13.10 | even | 6 | 13.4.c.a.9.1 | yes | 2 | ||
13.11 | odd | 12 | 169.4.e.c.147.2 | 4 | |||
13.12 | even | 2 | 169.4.a.d.1.1 | 1 | |||
39.17 | odd | 6 | 117.4.g.c.55.1 | 2 | |||
39.23 | odd | 6 | 117.4.g.c.100.1 | 2 | |||
39.38 | odd | 2 | 1521.4.a.b.1.1 | 1 | |||
52.23 | odd | 6 | 208.4.i.b.113.1 | 2 | |||
52.43 | odd | 6 | 208.4.i.b.81.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.c.a.3.1 | ✓ | 2 | 13.4 | even | 6 | ||
13.4.c.a.9.1 | yes | 2 | 13.10 | even | 6 | ||
117.4.g.c.55.1 | 2 | 39.17 | odd | 6 | |||
117.4.g.c.100.1 | 2 | 39.23 | odd | 6 | |||
169.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
169.4.a.d.1.1 | 1 | 13.12 | even | 2 | |||
169.4.b.c.168.1 | 2 | 13.8 | odd | 4 | |||
169.4.b.c.168.2 | 2 | 13.5 | odd | 4 | |||
169.4.c.d.22.1 | 2 | 13.3 | even | 3 | |||
169.4.c.d.146.1 | 2 | 13.9 | even | 3 | |||
169.4.e.c.23.1 | 4 | 13.7 | odd | 12 | |||
169.4.e.c.23.2 | 4 | 13.6 | odd | 12 | |||
169.4.e.c.147.1 | 4 | 13.2 | odd | 12 | |||
169.4.e.c.147.2 | 4 | 13.11 | odd | 12 | |||
208.4.i.b.81.1 | 2 | 52.43 | odd | 6 | |||
208.4.i.b.113.1 | 2 | 52.23 | odd | 6 | |||
1521.4.a.b.1.1 | 1 | 39.38 | odd | 2 | |||
1521.4.a.k.1.1 | 1 | 3.2 | odd | 2 |