Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −18.0000 | −1.60997 | −0.804984 | − | 0.593296i | \(-0.797826\pi\) | ||||
−0.804984 | + | 0.593296i | \(0.797826\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 72.0000 | 1.97353 | 0.986764 | − | 0.162160i | \(-0.0518462\pi\) | ||||
0.986764 | + | 0.162160i | \(0.0518462\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 34.0000 | 0.725377 | 0.362689 | − | 0.931910i | \(-0.381859\pi\) | ||||
0.362689 | + | 0.931910i | \(0.381859\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −54.0000 | −0.929516 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | 0.0856008 | 0.0428004 | − | 0.999084i | \(-0.486372\pi\) | ||||
0.0428004 | + | 0.999084i | \(0.486372\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −92.0000 | −1.11086 | −0.555428 | − | 0.831565i | \(-0.687445\pi\) | ||||
−0.555428 | + | 0.831565i | \(0.687445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −180.000 | −1.63185 | −0.815926 | − | 0.578156i | \(-0.803772\pi\) | ||||
−0.815926 | + | 0.578156i | \(0.803772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 199.000 | 1.59200 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 114.000 | 0.729975 | 0.364987 | − | 0.931012i | \(-0.381073\pi\) | ||||
0.364987 | + | 0.931012i | \(0.381073\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 56.0000 | 0.324448 | 0.162224 | − | 0.986754i | \(-0.448133\pi\) | ||||
0.162224 | + | 0.986754i | \(0.448133\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 216.000 | 1.13942 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −126.000 | −0.608511 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.0000 | 0.151069 | 0.0755347 | − | 0.997143i | \(-0.475934\pi\) | ||||
0.0755347 | + | 0.997143i | \(0.475934\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 102.000 | 0.418797 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.0228547 | 0.0114273 | − | 0.999935i | \(-0.496362\pi\) | ||||
0.0114273 | + | 0.999935i | \(0.496362\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −164.000 | −0.581622 | −0.290811 | − | 0.956780i | \(-0.593925\pi\) | ||||
−0.290811 | + | 0.956780i | \(0.593925\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −162.000 | −0.536656 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 168.000 | 0.521390 | 0.260695 | − | 0.965421i | \(-0.416048\pi\) | ||||
0.260695 | + | 0.965421i | \(0.416048\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.0000 | 0.0494217 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −654.000 | −1.69498 | −0.847489 | − | 0.530813i | \(-0.821887\pi\) | ||||
−0.847489 | + | 0.530813i | \(0.821887\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1296.00 | −3.17732 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −276.000 | −0.641353 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 492.000 | 1.08564 | 0.542822 | − | 0.839848i | \(-0.317356\pi\) | ||||
0.542822 | + | 0.839848i | \(0.317356\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 250.000 | 0.524741 | 0.262371 | − | 0.964967i | \(-0.415496\pi\) | ||||
0.262371 | + | 0.964967i | \(0.415496\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −612.000 | −1.16783 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 124.000 | 0.226105 | 0.113052 | − | 0.993589i | \(-0.463937\pi\) | ||||
0.113052 | + | 0.993589i | \(0.463937\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −540.000 | −0.942150 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36.0000 | 0.0601748 | 0.0300874 | − | 0.999547i | \(-0.490421\pi\) | ||||
0.0300874 | + | 0.999547i | \(0.490421\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1010.00 | 1.61934 | 0.809668 | − | 0.586888i | \(-0.199647\pi\) | ||||
0.809668 | + | 0.586888i | \(0.199647\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 597.000 | 0.919142 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 504.000 | 0.745924 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 56.0000 | 0.0797531 | 0.0398765 | − | 0.999205i | \(-0.487304\pi\) | ||||
0.0398765 | + | 0.999205i | \(0.487304\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −228.000 | −0.301521 | −0.150761 | − | 0.988570i | \(-0.548172\pi\) | ||||
−0.150761 | + | 0.988570i | \(0.548172\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −108.000 | −0.137815 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 342.000 | 0.421451 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 390.000 | 0.464493 | 0.232247 | − | 0.972657i | \(-0.425392\pi\) | ||||
0.232247 | + | 0.972657i | \(0.425392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 238.000 | 0.274167 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 168.000 | 0.187320 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1656.00 | 1.78844 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −70.0000 | −0.0732724 | −0.0366362 | − | 0.999329i | \(-0.511664\pi\) | ||||
−0.0366362 | + | 0.999329i | \(0.511664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 648.000 | 0.657843 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1350.00 | 1.33000 | 0.665000 | − | 0.746843i | \(-0.268431\pi\) | ||||
0.665000 | + | 0.746843i | \(0.268431\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2000.00 | 1.91326 | 0.956630 | − | 0.291305i | \(-0.0940893\pi\) | ||||
0.956630 | + | 0.291305i | \(0.0940893\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −378.000 | −0.351324 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −696.000 | −0.628830 | −0.314415 | − | 0.949286i | \(-0.601808\pi\) | ||||
−0.314415 | + | 0.949286i | \(0.601808\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1114.00 | 0.978916 | 0.489458 | − | 0.872027i | \(-0.337195\pi\) | ||||
0.489458 | + | 0.872027i | \(0.337195\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 102.000 | 0.0872199 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −462.000 | −0.384613 | −0.192307 | − | 0.981335i | \(-0.561597\pi\) | ||||
−0.192307 | + | 0.981335i | \(0.561597\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3240.00 | 2.62723 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 306.000 | 0.241792 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 42.0000 | 0.0323541 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3853.00 | 2.89482 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.0000 | 0.0131952 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1332.00 | −0.953102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1064.00 | 0.743423 | 0.371712 | − | 0.928348i | \(-0.378771\pi\) | ||||
0.371712 | + | 0.928348i | \(0.378771\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −492.000 | −0.335800 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −180.000 | −0.120051 | −0.0600255 | − | 0.998197i | \(-0.519118\pi\) | ||||
−0.0600255 | + | 0.998197i | \(0.519118\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −644.000 | −0.419864 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −486.000 | −0.309839 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2718.00 | −1.69500 | −0.847498 | − | 0.530799i | \(-0.821892\pi\) | ||||
−0.847498 | + | 0.530799i | \(0.821892\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1348.00 | 0.822560 | 0.411280 | − | 0.911509i | \(-0.365082\pi\) | ||||
0.411280 | + | 0.911509i | \(0.365082\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 504.000 | 0.301025 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2448.00 | 1.43155 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2052.00 | −1.17524 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −558.000 | −0.306800 | −0.153400 | − | 0.988164i | \(-0.549022\pi\) | ||||
−0.153400 | + | 0.988164i | \(0.549022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1928.00 | 1.03906 | 0.519531 | − | 0.854451i | \(-0.326107\pi\) | ||||
0.519531 | + | 0.854451i | \(0.326107\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 54.0000 | 0.0285336 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1008.00 | −0.522352 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2410.00 | 1.22509 | 0.612544 | − | 0.790436i | \(-0.290146\pi\) | ||||
0.612544 | + | 0.790436i | \(0.290146\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1962.00 | −0.978596 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1260.00 | −0.616782 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −740.000 | −0.355591 | −0.177795 | − | 0.984067i | \(-0.556896\pi\) | ||||
−0.177795 | + | 0.984067i | \(0.556896\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3888.00 | −1.83443 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3984.00 | 1.84605 | 0.923027 | − | 0.384734i | \(-0.125707\pi\) | ||||
0.923027 | + | 0.384734i | \(0.125707\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1041.00 | −0.473828 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −828.000 | −0.370285 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1038.00 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1393.00 | 0.601719 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1476.00 | 0.626796 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2568.00 | 1.07230 | 0.536149 | − | 0.844123i | \(-0.319879\pi\) | ||||
0.536149 | + | 0.844123i | \(0.319879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2698.00 | 1.10796 | 0.553980 | − | 0.832530i | \(-0.313108\pi\) | ||||
0.553980 | + | 0.832530i | \(0.313108\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 750.000 | 0.302960 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −612.000 | −0.243217 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 432.000 | 0.168936 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4116.00 | −1.55928 | −0.779642 | − | 0.626225i | \(-0.784599\pi\) | ||||
−0.779642 | + | 0.626225i | \(0.784599\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3310.00 | −1.23450 | −0.617251 | − | 0.786766i | \(-0.711754\pi\) | ||||
−0.617251 | + | 0.786766i | \(0.711754\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1836.00 | −0.674250 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1278.00 | −0.462202 | −0.231101 | − | 0.972930i | \(-0.574233\pi\) | ||||
−0.231101 | + | 0.972930i | \(0.574233\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2936.00 | 1.04587 | 0.522933 | − | 0.852374i | \(-0.324838\pi\) | ||||
0.522933 | + | 0.852374i | \(0.324838\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 372.000 | 0.130542 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 798.000 | 0.275905 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −108.000 | −0.0367954 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1620.00 | −0.543951 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6624.00 | −2.19230 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3508.00 | 1.14455 | 0.572276 | − | 0.820061i | \(-0.306060\pi\) | ||||
0.572276 | + | 0.820061i | \(0.306060\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 108.000 | 0.0347420 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2952.00 | 0.936394 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 392.000 | 0.122630 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3030.00 | 0.934924 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 204.000 | 0.0620929 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1888.00 | −0.566950 | −0.283475 | − | 0.958980i | \(-0.591487\pi\) | ||||
−0.283475 | + | 0.958980i | \(0.591487\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1791.00 | 0.530667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3564.00 | −1.04207 | −0.521037 | − | 0.853534i | \(-0.674455\pi\) | ||||
−0.521037 | + | 0.853534i | \(0.674455\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1334.00 | −0.384948 | −0.192474 | − | 0.981302i | \(-0.561651\pi\) | ||||
−0.192474 | + | 0.981302i | \(0.561651\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1512.00 | 0.430659 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2658.00 | 0.747345 | 0.373672 | − | 0.927561i | \(-0.378098\pi\) | ||||
0.373672 | + | 0.927561i | \(0.378098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3024.00 | −0.839421 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 168.000 | 0.0460455 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −588.000 | −0.159140 | −0.0795702 | − | 0.996829i | \(-0.525355\pi\) | ||||
−0.0795702 | + | 0.996829i | \(0.525355\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5690.00 | 1.52085 | 0.760426 | − | 0.649425i | \(-0.224990\pi\) | ||||
0.760426 | + | 0.649425i | \(0.224990\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −882.000 | −0.229996 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3128.00 | −0.805789 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −684.000 | −0.174083 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −180.000 | −0.0452649 | −0.0226325 | − | 0.999744i | \(-0.507205\pi\) | ||||
−0.0226325 | + | 0.999744i | \(0.507205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12960.0 | −3.22051 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −324.000 | −0.0795673 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5310.00 | 1.28883 | 0.644414 | − | 0.764677i | \(-0.277101\pi\) | ||||
0.644414 | + | 0.764677i | \(0.277101\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 238.000 | 0.0570988 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1026.00 | 0.243325 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 828.000 | 0.194132 | 0.0970659 | − | 0.995278i | \(-0.469054\pi\) | ||||
0.0970659 | + | 0.995278i | \(0.469054\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11772.0 | 2.72886 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1170.00 | 0.268175 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4134.00 | 0.937005 | 0.468503 | − | 0.883462i | \(-0.344794\pi\) | ||||
0.468503 | + | 0.883462i | \(0.344794\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2968.00 | −0.665288 | −0.332644 | − | 0.943052i | \(-0.607941\pi\) | ||||
−0.332644 | + | 0.943052i | \(0.607941\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 714.000 | 0.158290 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14328.0 | 3.14186 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4786.00 | 1.03813 | 0.519067 | − | 0.854734i | \(-0.326280\pi\) | ||||
0.519067 | + | 0.854734i | \(0.326280\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 504.000 | 0.108149 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4398.00 | −0.933675 | −0.466838 | − | 0.884343i | \(-0.654607\pi\) | ||||
−0.466838 | + | 0.884343i | \(0.654607\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4772.00 | −1.00235 | −0.501177 | − | 0.865345i | \(-0.667099\pi\) | ||||
−0.501177 | + | 0.865345i | \(0.667099\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4968.00 | 1.03256 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 42.0000 | 0.00863826 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4877.00 | −0.992673 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −210.000 | −0.0423038 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6522.00 | −1.30041 | −0.650204 | − | 0.759760i | \(-0.725316\pi\) | ||||
−0.650204 | + | 0.759760i | \(0.725316\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8856.00 | −1.74785 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1944.00 | 0.379806 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6120.00 | −1.18371 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1148.00 | −0.219833 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4050.00 | 0.767876 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4500.00 | −0.844817 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6244.00 | 1.16079 | 0.580397 | − | 0.814333i | \(-0.302897\pi\) | ||||
0.580397 | + | 0.814333i | \(0.302897\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6000.00 | 1.10462 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −528.000 | −0.0962705 | −0.0481353 | − | 0.998841i | \(-0.515328\pi\) | ||||
−0.0481353 | + | 0.998841i | \(0.515328\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5830.00 | −1.05281 | −0.526407 | − | 0.850232i | \(-0.676461\pi\) | ||||
−0.526407 | + | 0.850232i | \(0.676461\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1134.00 | −0.202837 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5046.00 | −0.894043 | −0.447021 | − | 0.894523i | \(-0.647515\pi\) | ||||
−0.447021 | + | 0.894523i | \(0.647515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8208.00 | 1.44063 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2088.00 | −0.363055 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −552.000 | −0.0950901 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6766.00 | 1.15480 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3342.00 | 0.565177 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1176.00 | 0.197067 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5020.00 | 0.833608 | 0.416804 | − | 0.908996i | \(-0.363150\pi\) | ||||
0.416804 | + | 0.908996i | \(0.363150\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 306.000 | 0.0503564 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2232.00 | −0.364021 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7486.00 | −1.21005 | −0.605027 | − | 0.796205i | \(-0.706838\pi\) | ||||
−0.605027 | + | 0.796205i | \(0.706838\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1386.00 | −0.222057 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4032.00 | 0.640308 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9720.00 | 1.51683 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10032.0 | 1.55201 | 0.776003 | − | 0.630729i | \(-0.217244\pi\) | ||||
0.776003 | + | 0.630729i | \(0.217244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5942.00 | −0.911370 | −0.455685 | − | 0.890141i | \(-0.650606\pi\) | ||||
−0.455685 | + | 0.890141i | \(0.650606\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 918.000 | 0.139599 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −90.0000 | −0.0135700 | −0.00678501 | − | 0.999977i | \(-0.502160\pi\) | ||||
−0.00678501 | + | 0.999977i | \(0.502160\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −648.000 | −0.0968796 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 126.000 | 0.0186796 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10596.0 | 1.55776 | 0.778880 | − | 0.627174i | \(-0.215788\pi\) | ||||
0.778880 | + | 0.627174i | \(0.215788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1605.00 | 0.233999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11559.0 | 1.67132 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18180.0 | −2.60708 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4016.00 | 0.571208 | 0.285604 | − | 0.958348i | \(-0.407806\pi\) | ||||
0.285604 | + | 0.958348i | \(0.407806\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 54.0000 | 0.00761823 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4578.00 | −0.640641 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3278.00 | −0.455036 | −0.227518 | − | 0.973774i | \(-0.573061\pi\) | ||||
−0.227518 | + | 0.973774i | \(0.573061\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3996.00 | −0.550273 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3876.00 | 0.529507 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4628.00 | −0.627241 | −0.313621 | − | 0.949548i | \(-0.601542\pi\) | ||||
−0.313621 | + | 0.949548i | \(0.601542\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3192.00 | 0.429216 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2880.00 | −0.384233 | −0.192116 | − | 0.981372i | \(-0.561535\pi\) | ||||
−0.192116 | + | 0.981372i | \(0.561535\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9072.00 | −1.20091 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1476.00 | −0.193874 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7974.00 | −1.03933 | −0.519663 | − | 0.854371i | \(-0.673943\pi\) | ||||
−0.519663 | + | 0.854371i | \(0.673943\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1080.00 | −0.139688 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −540.000 | −0.0693114 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1008.00 | −0.128400 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12346.0 | 1.56078 | 0.780388 | − | 0.625296i | \(-0.215022\pi\) | ||||
0.780388 | + | 0.625296i | \(0.215022\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1932.00 | −0.242408 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9738.00 | 1.21270 | 0.606350 | − | 0.795198i | \(-0.292633\pi\) | ||||
0.606350 | + | 0.795198i | \(0.292633\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1904.00 | 0.235347 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1458.00 | −0.178885 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2448.00 | 0.298140 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −430.000 | −0.0519857 | −0.0259928 | − | 0.999662i | \(-0.508275\pi\) | ||||
−0.0259928 | + | 0.999662i | \(0.508275\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8154.00 | −0.978606 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3444.00 | 0.410335 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4104.00 | 0.485440 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4044.00 | 0.474905 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1812.00 | 0.211270 | 0.105635 | − | 0.994405i | \(-0.466313\pi\) | ||||
0.105635 | + | 0.994405i | \(0.466313\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10690.0 | 1.23753 | 0.618763 | − | 0.785577i | \(-0.287634\pi\) | ||||
0.618763 | + | 0.785577i | \(0.287634\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1512.00 | 0.173797 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1194.00 | 0.136276 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1750.00 | 0.198334 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7344.00 | 0.826507 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4116.00 | −0.460002 | −0.230001 | − | 0.973190i | \(-0.573873\pi\) | ||||
−0.230001 | + | 0.973190i | \(0.573873\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9938.00 | 1.10298 | 0.551489 | − | 0.834182i | \(-0.314060\pi\) | ||||
0.551489 | + | 0.834182i | \(0.314060\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6156.00 | −0.678523 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16560.0 | 1.81275 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1784.00 | 0.193954 | 0.0969769 | − | 0.995287i | \(-0.469083\pi\) | ||||
0.0969769 | + | 0.995287i | \(0.469083\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11712.0 | 1.25610 | 0.628052 | − | 0.778172i | \(-0.283853\pi\) | ||||
0.628052 | + | 0.778172i | \(0.283853\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7020.00 | −0.747820 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1674.00 | −0.177131 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7650.00 | 0.804066 | 0.402033 | − | 0.915625i | \(-0.368304\pi\) | ||||
0.402033 | + | 0.915625i | \(0.368304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 432.000 | 0.0451044 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5784.00 | 0.599903 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4284.00 | −0.441400 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3674.00 | 0.376067 | 0.188033 | − | 0.982163i | \(-0.439789\pi\) | ||||
0.188033 | + | 0.982163i | \(0.439789\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 162.000 | 0.0164739 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3102.00 | 0.313394 | 0.156697 | − | 0.987647i | \(-0.449915\pi\) | ||||
0.156697 | + | 0.987647i | \(0.449915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8984.00 | 0.901775 | 0.450888 | − | 0.892581i | \(-0.351108\pi\) | ||||
0.450888 | + | 0.892581i | \(0.351108\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3024.00 | −0.301580 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3612.00 | −0.357909 | −0.178954 | − | 0.983857i | \(-0.557271\pi\) | ||||
−0.178954 | + | 0.983857i | \(0.557271\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 868.000 | 0.0854595 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7230.00 | 0.707305 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11808.0 | −1.14785 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18308.0 | −1.76848 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5886.00 | −0.564993 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9288.00 | −0.885970 | −0.442985 | − | 0.896529i | \(-0.646080\pi\) | ||||
−0.442985 | + | 0.896529i | \(0.646080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1156.00 | 0.109582 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3780.00 | −0.356099 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1260.00 | 0.117966 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5848.00 | −0.544144 | −0.272072 | − | 0.962277i | \(-0.587709\pi\) | ||||
−0.272072 | + | 0.962277i | \(0.587709\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2220.00 | −0.205300 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5952.00 | 0.547067 | 0.273534 | − | 0.961862i | \(-0.411808\pi\) | ||||
0.273534 | + | 0.961862i | \(0.411808\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 684.000 | 0.0624864 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11664.0 | −1.05911 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 252.000 | 0.0227440 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10748.0 | −0.964222 | −0.482111 | − | 0.876110i | \(-0.660130\pi\) | ||||
−0.482111 | + | 0.876110i | \(0.660130\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11952.0 | 1.06582 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16488.0 | −1.46156 | −0.730779 | − | 0.682614i | \(-0.760843\pi\) | ||||
−0.730779 | + | 0.682614i | \(0.760843\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24300.0 | −2.14126 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3123.00 | −0.273565 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14058.0 | −1.22418 | −0.612092 | − | 0.790786i | \(-0.709672\pi\) | ||||
−0.612092 | + | 0.790786i | \(0.709672\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7070.00 | 0.612052 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2484.00 | −0.213784 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36000.0 | −3.08029 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12096.0 | 1.02898 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3114.00 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14466.0 | −1.21644 | −0.608222 | − | 0.793767i | \(-0.708117\pi\) | ||||
−0.608222 | + | 0.793767i | \(0.708117\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18524.0 | −1.54875 | −0.774377 | − | 0.632725i | \(-0.781936\pi\) | ||||
−0.774377 | + | 0.632725i | \(0.781936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4179.00 | 0.347403 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 336.000 | 0.0277730 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20233.0 | 1.66294 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4428.00 | 0.361881 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 204.000 | 0.0165783 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12528.0 | 1.01240 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7704.00 | 0.619092 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3528.00 | 0.281933 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4358.00 | −0.346331 | −0.173165 | − | 0.984893i | \(-0.555400\pi\) | ||||
−0.173165 | + | 0.984893i | \(0.555400\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8094.00 | 0.639681 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20052.0 | −1.57602 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2140.00 | 0.167276 | 0.0836378 | − | 0.996496i | \(-0.473346\pi\) | ||||
0.0836378 | + | 0.996496i | \(0.473346\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2250.00 | 0.174914 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10488.0 | −0.810896 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 392.000 | 0.0301438 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1836.00 | −0.140421 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2022.00 | −0.153815 | −0.0769074 | − | 0.997038i | \(-0.524505\pi\) | ||||
−0.0769074 | + | 0.997038i | \(0.524505\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5576.00 | −0.421896 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1296.00 | 0.0975350 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7356.00 | −0.550654 | −0.275327 | − | 0.961351i | \(-0.588786\pi\) | ||||
−0.275327 | + | 0.961351i | \(0.588786\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8316.00 | 0.619215 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11202.0 | 0.825329 | 0.412665 | − | 0.910883i | \(-0.364598\pi\) | ||||
0.412665 | + | 0.910883i | \(0.364598\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10564.0 | 0.774238 | 0.387119 | − | 0.922030i | \(-0.373470\pi\) | ||||
0.387119 | + | 0.922030i | \(0.373470\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12348.0 | −0.900253 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −35820.0 | −2.59791 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18574.0 | −1.34011 | −0.670057 | − | 0.742310i | \(-0.733730\pi\) | ||||
−0.670057 | + | 0.742310i | \(0.733730\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9930.00 | −0.712740 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1596.00 | −0.113964 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −47088.0 | −3.34509 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5508.00 | −0.389278 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13188.0 | −0.927303 | −0.463652 | − | 0.886018i | \(-0.653461\pi\) | ||||
−0.463652 | + | 0.886018i | \(0.653461\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5152.00 | −0.360415 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3834.00 | −0.266852 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22506.0 | −1.55853 | −0.779267 | − | 0.626692i | \(-0.784408\pi\) | ||||
−0.779267 | + | 0.626692i | \(0.784408\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −756.000 | −0.0520890 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8808.00 | 0.603832 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10596.0 | 0.722773 | 0.361386 | − | 0.932416i | \(-0.382304\pi\) | ||||
0.361386 | + | 0.932416i | \(0.382304\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14618.0 | 0.992148 | 0.496074 | − | 0.868280i | \(-0.334775\pi\) | ||||
0.496074 | + | 0.868280i | \(0.334775\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1116.00 | 0.0753682 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −69354.0 | −4.66056 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5168.00 | 0.345573 | 0.172786 | − | 0.984959i | \(-0.444723\pi\) | ||||
0.172786 | + | 0.984959i | \(0.444723\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2394.00 | 0.159294 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5712.00 | 0.378204 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5726.00 | −0.377277 | −0.188639 | − | 0.982047i | \(-0.560407\pi\) | ||||
−0.188639 | + | 0.982047i | \(0.560407\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −324.000 | −0.0212438 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7806.00 | −0.509332 | −0.254666 | − | 0.967029i | \(-0.581965\pi\) | ||||
−0.254666 | + | 0.967029i | \(0.581965\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18052.0 | 1.17217 | 0.586083 | − | 0.810251i | \(-0.300669\pi\) | ||||
0.586083 | + | 0.810251i | \(0.300669\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4860.00 | −0.314050 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2730.00 | 0.175562 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −899.000 | −0.0575360 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19872.0 | −1.26573 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 204.000 | 0.0129317 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6208.00 | −0.391659 | −0.195829 | − | 0.980638i | \(-0.562740\pi\) | ||||
−0.195829 | + | 0.980638i | \(0.562740\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10524.0 | 0.660808 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19152.0 | −1.19689 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1666.00 | 0.103625 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 324.000 | 0.0200583 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21510.0 | −1.32542 | −0.662710 | − | 0.748876i | \(-0.730594\pi\) | ||||
−0.662710 | + | 0.748876i | \(0.730594\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11140.0 | 0.683233 | 0.341616 | − | 0.939839i | \(-0.389026\pi\) | ||||
0.341616 | + | 0.939839i | \(0.389026\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8856.00 | 0.540627 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9312.00 | 0.565831 | 0.282915 | − | 0.959145i | \(-0.408698\pi\) | ||||
0.282915 | + | 0.959145i | \(0.408698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35424.0 | 2.14255 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1176.00 | 0.0708004 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4878.00 | −0.292329 | −0.146165 | − | 0.989260i | \(-0.546693\pi\) | ||||
−0.146165 | + | 0.989260i | \(0.546693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3240.00 | 0.193278 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9090.00 | 0.539779 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9744.00 | 0.575982 | 0.287991 | − | 0.957633i | \(-0.407013\pi\) | ||||
0.287991 | + | 0.957633i | \(0.407013\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2990.00 | −0.175942 | −0.0879709 | − | 0.996123i | \(-0.528038\pi\) | ||||
−0.0879709 | + | 0.996123i | \(0.528038\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 612.000 | 0.0358493 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11592.0 | 0.675968 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20520.0 | −1.19121 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5664.00 | −0.327329 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18000.0 | 1.03559 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33266.0 | 1.90536 | 0.952682 | − | 0.303969i | \(-0.0983118\pi\) | ||||
0.952682 | + | 0.303969i | \(0.0983118\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5373.00 | 0.306381 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5370.00 | −0.304854 | −0.152427 | − | 0.988315i | \(-0.548709\pi\) | ||||
−0.152427 | + | 0.988315i | \(0.548709\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −490.000 | −0.0276944 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10692.0 | −0.601642 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −384.000 | −0.0215130 | −0.0107565 | − | 0.999942i | \(-0.503424\pi\) | ||||
−0.0107565 | + | 0.999942i | \(0.503424\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48924.0 | 2.72889 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4002.00 | −0.222250 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22236.0 | −1.22950 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14524.0 | 0.799593 | 0.399797 | − | 0.916604i | \(-0.369081\pi\) | ||||
0.399797 | + | 0.916604i | \(0.369081\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4536.00 | 0.248641 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24264.0 | −1.32430 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.0000 | 0.00195638 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7974.00 | 0.431480 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24750.0 | −1.33352 | −0.666758 | − | 0.745274i | \(-0.732318\pi\) | ||||
−0.666758 | + | 0.745274i | \(0.732318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3128.00 | −0.167816 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9072.00 | −0.484640 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9450.00 | 0.502693 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1042.00 | 0.0551948 | 0.0275974 | − | 0.999619i | \(-0.491214\pi\) | ||||
0.0275974 | + | 0.999619i | \(0.491214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 504.000 | 0.0265844 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10080.0 | −0.529452 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −44064.0 | −2.30476 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1764.00 | −0.0918798 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36960.0 | −1.91707 | −0.958536 | − | 0.284970i | \(-0.908016\pi\) | ||||
−0.958536 | + | 0.284970i | \(0.908016\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14000.0 | 0.723145 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17070.0 | 0.878064 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22686.0 | 1.16212 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16288.0 | −0.830933 | −0.415467 | − | 0.909608i | \(-0.636382\pi\) | ||||
−0.415467 | + | 0.909608i | \(0.636382\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −984.000 | −0.0497874 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7810.00 | 0.393546 | 0.196773 | − | 0.980449i | \(-0.436954\pi\) | ||||
0.196773 | + | 0.980449i | \(0.436954\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2646.00 | −0.132788 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8928.00 | 0.446224 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36700.0 | 1.82684 | 0.913418 | − | 0.407024i | \(-0.133433\pi\) | ||||
0.913418 | + | 0.407024i | \(0.133433\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9384.00 | −0.465222 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29508.0 | 1.45699 | 0.728495 | − | 0.685051i | \(-0.240220\pi\) | ||||
0.728495 | + | 0.685051i | \(0.240220\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10044.0 | 0.493938 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2052.00 | −0.100507 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4872.00 | −0.237676 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15136.0 | −0.735447 | −0.367723 | − | 0.929935i | \(-0.619863\pi\) | ||||
−0.367723 | + | 0.929935i | \(0.619863\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −540.000 | −0.0261337 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34704.0 | −1.67286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3422.00 | −0.164299 | −0.0821497 | − | 0.996620i | \(-0.526179\pi\) | ||||
−0.0821497 | + | 0.996620i | \(0.526179\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −38880.0 | −1.85936 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31446.0 | 1.49792 | 0.748960 | − | 0.662616i | \(-0.230554\pi\) | ||||
0.748960 | + | 0.662616i | \(0.230554\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7798.00 | 0.369995 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −972.000 | −0.0459382 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16728.0 | 0.787501 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18718.0 | −0.877748 | −0.438874 | − | 0.898549i | \(-0.644623\pi\) | ||||
−0.438874 | + | 0.898549i | \(0.644623\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15930.0 | 0.744105 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1686.00 | 0.0784492 | 0.0392246 | − | 0.999230i | \(-0.487511\pi\) | ||||
0.0392246 | + | 0.999230i | \(0.487511\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11144.0 | 0.516522 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 714.000 | 0.0329660 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −552.000 | −0.0253883 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2592.00 | 0.118757 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3078.00 | 0.140484 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −43380.0 | −1.97235 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5492.00 | −0.248753 | −0.124377 | − | 0.992235i | \(-0.539693\pi\) | ||||
−0.124377 | + | 0.992235i | \(0.539693\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2484.00 | 0.112082 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3234.00 | −0.145370 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8500.00 | 0.380635 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35316.0 | 1.57551 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17310.0 | 0.769325 | 0.384662 | − | 0.923057i | \(-0.374318\pi\) | ||||
0.384662 | + | 0.923057i | \(0.374318\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1008.00 | 0.0446314 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3510.00 | 0.154831 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 72720.0 | 3.19581 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22680.0 | 0.993000 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12402.0 | 0.540980 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35754.0 | 1.55382 | 0.776912 | − | 0.629609i | \(-0.216785\pi\) | ||||
0.776912 | + | 0.629609i | \(0.216785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33644.0 | −1.45672 | −0.728360 | − | 0.685194i | \(-0.759717\pi\) | ||||
−0.728360 | + | 0.685194i | \(0.759717\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8904.00 | −0.384104 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13320.0 | 0.572490 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15088.0 | 0.646098 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2142.00 | 0.0913889 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28734.0 | −1.22147 | −0.610733 | − | 0.791837i | \(-0.709125\pi\) | ||||
−0.610733 | + | 0.791837i | \(0.709125\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28672.0 | −1.21439 | −0.607195 | − | 0.794553i | \(-0.707705\pi\) | ||||
−0.607195 | + | 0.794553i | \(0.707705\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 42984.0 | 1.81395 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15912.0 | 0.669062 | 0.334531 | − | 0.942385i | \(-0.391422\pi\) | ||||
0.334531 | + | 0.942385i | \(0.391422\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17534.0 | −0.734597 | −0.367299 | − | 0.930103i | \(-0.619717\pi\) | ||||
−0.367299 | + | 0.930103i | \(0.619717\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14358.0 | 0.599366 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 294.000 | 0.0122287 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −71712.0 | −2.97209 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1512.00 | 0.0624401 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40656.0 | 1.67295 | 0.836473 | − | 0.548009i | \(-0.184614\pi\) | ||||
0.836473 | + | 0.548009i | \(0.184614\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11393.0 | −0.467137 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13194.0 | −0.539058 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18738.0 | 0.762848 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26971.0 | 1.09414 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14316.0 | −0.578709 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6120.00 | −0.246523 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23870.0 | −0.958140 | −0.479070 | − | 0.877777i | \(-0.659026\pi\) | ||||
−0.479070 | + | 0.877777i | \(0.659026\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14904.0 | 0.596147 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29610.0 | −1.18023 | −0.590116 | − | 0.807319i | \(-0.700918\pi\) | ||||
−0.590116 | + | 0.807319i | \(0.700918\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45484.0 | 1.80663 | 0.903314 | − | 0.428979i | \(-0.141127\pi\) | ||||
0.903314 | + | 0.428979i | \(0.141127\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 126.000 | 0.00498730 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46164.0 | 1.82090 | 0.910452 | − | 0.413614i | \(-0.135734\pi\) | ||||
0.910452 | + | 0.413614i | \(0.135734\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18684.0 | −0.734422 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14631.0 | −0.573120 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4032.00 | 0.157395 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4216.00 | 0.164011 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −630.000 | −0.0244241 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9324.00 | −0.360239 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2986.00 | 0.114972 | 0.0574858 | − | 0.998346i | \(-0.481692\pi\) | ||||
0.0574858 | + | 0.998346i | \(0.481692\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19566.0 | −0.750790 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6534.00 | 0.249871 | 0.124935 | − | 0.992165i | \(-0.460128\pi\) | ||||
0.124935 | + | 0.992165i | \(0.460128\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29756.0 | −1.13405 | −0.567027 | − | 0.823699i | \(-0.691906\pi\) | ||||
−0.567027 | + | 0.823699i | \(0.691906\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26568.0 | −1.00912 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29952.0 | 1.13381 | 0.566905 | − | 0.823783i | \(-0.308141\pi\) | ||||
0.566905 | + | 0.823783i | \(0.308141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7448.00 | 0.280988 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5832.00 | 0.219281 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15456.0 | −0.579188 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46224.0 | −1.72637 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18360.0 | −0.683414 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6384.00 | 0.236839 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3924.00 | −0.145091 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3444.00 | −0.126920 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −48564.0 | −1.78378 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36268.0 | 1.32774 | 0.663869 | − | 0.747848i | \(-0.268913\pi\) | ||||
0.663869 | + | 0.747848i | \(0.268913\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12150.0 | 0.443333 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23604.0 | −0.858436 | −0.429218 | − | 0.903201i | \(-0.641211\pi\) | ||||
−0.429218 | + | 0.903201i | \(0.641211\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16416.0 | −0.595061 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13500.0 | −0.487755 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1260.00 | −0.0453750 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34184.0 | 1.22701 | 0.613507 | − | 0.789689i | \(-0.289758\pi\) | ||||
0.613507 | + | 0.789689i | \(0.289758\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18732.0 | 0.670185 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1224.00 | 0.0436495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6766.00 | 0.240502 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18000.0 | 0.637754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53922.0 | −1.90433 | −0.952165 | − | 0.305583i | \(-0.901149\pi\) | ||||
−0.952165 | + | 0.305583i | \(0.901149\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4508.00 | −0.158694 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1584.00 | −0.0555818 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7776.00 | −0.271981 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40538.0 | 1.41336 | 0.706680 | − | 0.707533i | \(-0.250192\pi\) | ||||
0.706680 | + | 0.707533i | \(0.250192\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17490.0 | −0.607843 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3606.00 | 0.124923 | 0.0624613 | − | 0.998047i | \(-0.480105\pi\) | ||||
0.0624613 | + | 0.998047i | \(0.480105\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1080.00 | −0.0372955 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3402.00 | −0.117108 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14064.0 | −0.482596 | −0.241298 | − | 0.970451i | \(-0.577573\pi\) | ||||
−0.241298 | + | 0.970451i | \(0.577573\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34340.0 | 1.17463 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15138.0 | −0.516176 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33066.0 | 1.12394 | 0.561969 | − | 0.827158i | \(-0.310044\pi\) | ||||
0.561969 | + | 0.827158i | \(0.310044\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 74088.0 | 2.51040 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24624.0 | 0.831746 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19026.0 | −0.640648 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26655.0 | −0.894733 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6264.00 | −0.209610 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 59580.0 | 1.98751 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26368.0 | −0.876875 | −0.438437 | − | 0.898762i | \(-0.644468\pi\) | ||||
−0.438437 | + | 0.898762i | \(0.644468\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1656.00 | −0.0549003 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55884.0 | −1.84696 | −0.923482 | − | 0.383641i | \(-0.874670\pi\) | ||||
−0.923482 | + | 0.383641i | \(0.874670\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9436.00 | 0.310899 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20298.0 | 0.666724 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51126.0 | −1.67417 | −0.837086 | − | 0.547072i | \(-0.815743\pi\) | ||||
−0.837086 | + | 0.547072i | \(0.815743\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28080.0 | 0.916691 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10026.0 | 0.326305 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14184.0 | −0.460223 | −0.230112 | − | 0.973164i | \(-0.573909\pi\) | ||||
−0.230112 | + | 0.973164i | \(0.573909\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23004.0 | 0.744130 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3528.00 | 0.113777 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29520.0 | 0.949122 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51680.0 | 1.65658 | 0.828289 | − | 0.560301i | \(-0.189314\pi\) | ||||
0.828289 | + | 0.560301i | \(0.189314\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15060.0 | 0.481284 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −52848.0 | −1.68381 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52094.0 | −1.65480 | −0.827399 | − | 0.561615i | \(-0.810180\pi\) | ||||
−0.827399 | + | 0.561615i | \(0.810180\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 918.000 | 0.0290733 |
(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 | 1344.4.a.o.1.1 | 1 | ||
4.3 | odd | 2 | 1344.4.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 336.4.a.l.1.1 | 1 | |||
8.5 | even | 2 | 42.4.a.a.1.1 | ✓ | 1 | ||
24.5 | odd | 2 | 126.4.a.a.1.1 | 1 | |||
24.11 | even | 2 | 1008.4.a.b.1.1 | 1 | |||
40.13 | odd | 4 | 1050.4.g.a.799.1 | 2 | |||
40.29 | even | 2 | 1050.4.a.g.1.1 | 1 | |||
40.37 | odd | 4 | 1050.4.g.a.799.2 | 2 | |||
56.5 | odd | 6 | 294.4.e.b.67.1 | 2 | |||
56.13 | odd | 2 | 294.4.a.i.1.1 | 1 | |||
56.27 | even | 2 | 2352.4.a.a.1.1 | 1 | |||
56.37 | even | 6 | 294.4.e.c.67.1 | 2 | |||
56.45 | odd | 6 | 294.4.e.b.79.1 | 2 | |||
56.53 | even | 6 | 294.4.e.c.79.1 | 2 | |||
168.5 | even | 6 | 882.4.g.o.361.1 | 2 | |||
168.53 | odd | 6 | 882.4.g.w.667.1 | 2 | |||
168.101 | even | 6 | 882.4.g.o.667.1 | 2 | |||
168.125 | even | 2 | 882.4.a.g.1.1 | 1 | |||
168.149 | odd | 6 | 882.4.g.w.361.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.a.a.1.1 | ✓ | 1 | 8.5 | even | 2 | ||
126.4.a.a.1.1 | 1 | 24.5 | odd | 2 | |||
294.4.a.i.1.1 | 1 | 56.13 | odd | 2 | |||
294.4.e.b.67.1 | 2 | 56.5 | odd | 6 | |||
294.4.e.b.79.1 | 2 | 56.45 | odd | 6 | |||
294.4.e.c.67.1 | 2 | 56.37 | even | 6 | |||
294.4.e.c.79.1 | 2 | 56.53 | even | 6 | |||
336.4.a.l.1.1 | 1 | 8.3 | odd | 2 | |||
882.4.a.g.1.1 | 1 | 168.125 | even | 2 | |||
882.4.g.o.361.1 | 2 | 168.5 | even | 6 | |||
882.4.g.o.667.1 | 2 | 168.101 | even | 6 | |||
882.4.g.w.361.1 | 2 | 168.149 | odd | 6 | |||
882.4.g.w.667.1 | 2 | 168.53 | odd | 6 | |||
1008.4.a.b.1.1 | 1 | 24.11 | even | 2 | |||
1050.4.a.g.1.1 | 1 | 40.29 | even | 2 | |||
1050.4.g.a.799.1 | 2 | 40.13 | odd | 4 | |||
1050.4.g.a.799.2 | 2 | 40.37 | odd | 4 | |||
1344.4.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
1344.4.a.o.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2352.4.a.a.1.1 | 1 | 56.27 | even | 2 |