Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, 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("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.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: | \(69.3862461668\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{113}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(5.81507\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-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 | ||||||||
\(5\) | 13.6301 | 1.21912 | 0.609559 | − | 0.792741i | \(-0.291347\pi\) | ||||
0.609559 | + | 0.792741i | \(0.291347\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 32.8904 | 0.901531 | 0.450765 | − | 0.892642i | \(-0.351151\pi\) | ||||
0.450765 | + | 0.892642i | \(0.351151\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 42.5206 | 0.907161 | 0.453580 | − | 0.891215i | \(-0.350147\pi\) | ||||
0.453580 | + | 0.891215i | \(0.350147\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 40.8904 | 0.703858 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.6301 | 0.365660 | 0.182830 | − | 0.983145i | \(-0.441474\pi\) | ||||
0.182830 | + | 0.983145i | \(0.441474\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −15.2603 | −0.184261 | −0.0921303 | − | 0.995747i | \(-0.529368\pi\) | ||||
−0.0921303 | + | 0.995747i | \(0.529368\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 134.671 | 1.22091 | 0.610455 | − | 0.792051i | \(-0.290987\pi\) | ||||
0.610455 | + | 0.792051i | \(0.290987\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 60.7809 | 0.486247 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −163.343 | −1.04593 | −0.522965 | − | 0.852354i | \(-0.675174\pi\) | ||||
−0.522965 | + | 0.852354i | \(0.675174\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −40.3015 | −0.233495 | −0.116748 | − | 0.993162i | \(-0.537247\pi\) | ||||
−0.116748 | + | 0.993162i | \(0.537247\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 98.6713 | 0.520499 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 351.343 | 1.56109 | 0.780546 | − | 0.625099i | \(-0.214941\pi\) | ||||
0.780546 | + | 0.625099i | \(0.214941\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 127.562 | 0.523749 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −256.754 | −0.978004 | −0.489002 | − | 0.872283i | \(-0.662639\pi\) | ||||
−0.489002 | + | 0.872283i | \(0.662639\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 188.000 | 0.666738 | 0.333369 | − | 0.942796i | \(-0.391815\pi\) | ||||
0.333369 | + | 0.942796i | \(0.391815\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 122.671 | 0.406372 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −290.082 | −0.900274 | −0.450137 | − | 0.892960i | \(-0.648625\pi\) | ||||
−0.450137 | + | 0.892960i | \(0.648625\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 76.8904 | 0.211114 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −354.904 | −0.919809 | −0.459904 | − | 0.887968i | \(-0.652116\pi\) | ||||
−0.459904 | + | 0.887968i | \(0.652116\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 448.301 | 1.09907 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −45.7809 | −0.106383 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 616.165 | 1.35962 | 0.679812 | − | 0.733386i | \(-0.262061\pi\) | ||||
0.679812 | + | 0.733386i | \(0.262061\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −394.822 | −0.828718 | −0.414359 | − | 0.910114i | \(-0.635994\pi\) | ||||
−0.414359 | + | 0.910114i | \(0.635994\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 579.562 | 1.10594 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 176.466 | 0.321773 | 0.160886 | − | 0.986973i | \(-0.448565\pi\) | ||||
0.160886 | + | 0.986973i | \(0.448565\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 404.014 | 0.704892 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 716.014 | 1.19683 | 0.598417 | − | 0.801185i | \(-0.295797\pi\) | ||||
0.598417 | + | 0.801185i | \(0.295797\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 258.657 | 0.414706 | 0.207353 | − | 0.978266i | \(-0.433515\pi\) | ||||
0.207353 | + | 0.978266i | \(0.433515\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 182.343 | 0.280735 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1011.59 | −1.44067 | −0.720334 | − | 0.693628i | \(-0.756011\pi\) | ||||
−0.720334 | + | 0.693628i | \(0.756011\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 271.835 | 0.359492 | 0.179746 | − | 0.983713i | \(-0.442472\pi\) | ||||
0.179746 | + | 0.983713i | \(0.442472\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 349.343 | 0.445783 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −490.028 | −0.603868 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1061.79 | −1.26461 | −0.632304 | − | 0.774721i | \(-0.717890\pi\) | ||||
−0.632304 | + | 0.774721i | \(0.717890\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −120.904 | −0.134809 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −208.000 | −0.224635 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1174.55 | 1.22946 | 0.614728 | − | 0.788739i | \(-0.289266\pi\) | ||||
0.614728 | + | 0.788739i | \(0.289266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 296.014 | 0.300510 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1485.33 | 1.46332 | 0.731662 | − | 0.681668i | \(-0.238745\pi\) | ||||
0.731662 | + | 0.681668i | \(0.238745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1688.96 | 1.61571 | 0.807855 | − | 0.589381i | \(-0.200628\pi\) | ||||
0.807855 | + | 0.589381i | \(0.200628\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1160.92 | −1.04888 | −0.524440 | − | 0.851447i | \(-0.675725\pi\) | ||||
−0.524440 | + | 0.851447i | \(0.675725\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1812.30 | −1.59254 | −0.796271 | − | 0.604940i | \(-0.793197\pi\) | ||||
−0.796271 | + | 0.604940i | \(0.793197\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1054.03 | 0.901296 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −526.000 | −0.437893 | −0.218947 | − | 0.975737i | \(-0.570262\pi\) | ||||
−0.218947 | + | 0.975737i | \(0.570262\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1835.59 | 1.48843 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 382.685 | 0.302387 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −249.219 | −0.187242 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −770.261 | −0.564651 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −875.316 | −0.626325 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 98.6574 | 0.0689325 | 0.0344662 | − | 0.999406i | \(-0.489027\pi\) | ||||
0.0344662 | + | 0.999406i | \(0.489027\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 564.000 | 0.384941 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2286.47 | −1.52496 | −0.762479 | − | 0.647013i | \(-0.776018\pi\) | ||||
−0.762479 | + | 0.647013i | \(0.776018\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 368.014 | 0.234619 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1858.49 | 1.15899 | 0.579496 | − | 0.814975i | \(-0.303250\pi\) | ||||
0.579496 | + | 0.814975i | \(0.303250\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1485.15 | 0.906250 | 0.453125 | − | 0.891447i | \(-0.350309\pi\) | ||||
0.453125 | + | 0.891447i | \(0.350309\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −870.247 | −0.519773 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1398.52 | 0.817833 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2226.38 | −1.27511 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1023.40 | −0.562685 | −0.281342 | − | 0.959607i | \(-0.590780\pi\) | ||||
−0.281342 | + | 0.959607i | \(0.590780\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1670.25 | −0.900151 | −0.450075 | − | 0.892991i | \(-0.648603\pi\) | ||||
−0.450075 | + | 0.892991i | \(0.648603\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 230.671 | 0.121887 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −549.315 | −0.284658 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1889.89 | 0.960698 | 0.480349 | − | 0.877077i | \(-0.340510\pi\) | ||||
0.480349 | + | 0.877077i | \(0.340510\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1064.71 | −0.531052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −647.478 | −0.311131 | −0.155566 | − | 0.987826i | \(-0.549720\pi\) | ||||
−0.155566 | + | 0.987826i | \(0.549720\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1344.90 | 0.634549 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2919.40 | 1.35275 | 0.676376 | − | 0.736556i | \(-0.263549\pi\) | ||||
0.676376 | + | 0.736556i | \(0.263549\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −389.000 | −0.177060 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −137.343 | −0.0614202 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1432.26 | −0.629437 | −0.314719 | − | 0.949185i | \(-0.601910\pi\) | ||||
−0.314719 | + | 0.949185i | \(0.601910\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1848.49 | 0.784979 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1566.23 | 0.653999 | 0.326999 | − | 0.945025i | \(-0.393963\pi\) | ||||
0.326999 | + | 0.945025i | \(0.393963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1564.93 | 0.642655 | 0.321327 | − | 0.946968i | \(-0.395871\pi\) | ||||
0.321327 | + | 0.946968i | \(0.395871\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1184.47 | −0.478460 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4788.85 | 1.90315 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 842.987 | 0.329654 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2251.19 | 0.852830 | 0.426415 | − | 0.904528i | \(-0.359776\pi\) | ||||
0.426415 | + | 0.904528i | \(0.359776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4972.00 | 1.85437 | 0.927183 | − | 0.374609i | \(-0.122223\pi\) | ||||
0.927183 | + | 0.374609i | \(0.122223\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1738.69 | 0.638512 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −212.602 | −0.0768895 | −0.0384448 | − | 0.999261i | \(-0.512240\pi\) | ||||
−0.0384448 | + | 0.999261i | \(0.512240\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2358.25 | 0.840059 | 0.420029 | − | 0.907511i | \(-0.362020\pi\) | ||||
0.420029 | + | 0.907511i | \(0.362020\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 529.398 | 0.185776 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3499.59 | −1.19230 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1212.04 | 0.406970 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −501.918 | −0.166117 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3081.43 | −1.00538 | −0.502688 | − | 0.864468i | \(-0.667655\pi\) | ||||
−0.502688 | + | 0.864468i | \(0.667655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2148.04 | 0.690992 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2562.47 | 0.812832 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 775.972 | 0.239431 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1089.81 | 0.331713 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5299.01 | 1.59125 | 0.795624 | − | 0.605791i | \(-0.207143\pi\) | ||||
0.795624 | + | 0.605791i | \(0.207143\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 547.028 | 0.162082 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3624.66 | −1.05981 | −0.529906 | − | 0.848057i | \(-0.677773\pi\) | ||||
−0.529906 | + | 0.848057i | \(0.677773\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6154.36 | −1.77595 | −0.887973 | − | 0.459896i | \(-0.847887\pi\) | ||||
−0.887973 | + | 0.459896i | \(0.847887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5860.41 | 1.64776 | 0.823881 | − | 0.566763i | \(-0.191804\pi\) | ||||
0.823881 | + | 0.566763i | \(0.191804\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3953.86 | −1.09754 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3034.77 | −0.831770 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2390.81 | −0.647066 | −0.323533 | − | 0.946217i | \(-0.604871\pi\) | ||||
−0.323533 | + | 0.946217i | \(0.604871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1652.91 | −0.441797 | −0.220899 | − | 0.975297i | \(-0.570899\pi\) | ||||
−0.220899 | + | 0.975297i | \(0.570899\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −648.877 | −0.167154 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 815.506 | 0.207553 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7586.03 | 1.90767 | 0.953836 | − | 0.300326i | \(-0.0970956\pi\) | ||||
0.953836 | + | 0.300326i | \(0.0970956\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4429.40 | 1.10069 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1048.03 | 0.257373 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −153.245 | −0.0371952 | −0.0185976 | − | 0.999827i | \(-0.505920\pi\) | ||||
−0.0185976 | + | 0.999827i | \(0.505920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1470.08 | −0.348643 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 601.245 | 0.140967 | 0.0704836 | − | 0.997513i | \(-0.477546\pi\) | ||||
0.0704836 | + | 0.997513i | \(0.477546\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4837.40 | −1.12135 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3185.38 | −0.730121 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4974.56 | 1.12753 | 0.563763 | − | 0.825937i | \(-0.309353\pi\) | ||||
0.563763 | + | 0.825937i | \(0.309353\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1830.16 | 0.410238 | 0.205119 | − | 0.978737i | \(-0.434242\pi\) | ||||
0.205119 | + | 0.978737i | \(0.434242\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1999.11 | 0.438367 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6568.33 | −1.42474 | −0.712370 | − | 0.701805i | \(-0.752378\pi\) | ||||
−0.712370 | + | 0.701805i | \(0.752378\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −362.713 | −0.0778318 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2562.99 | −0.544110 | −0.272055 | − | 0.962282i | \(-0.587703\pi\) | ||||
−0.272055 | + | 0.962282i | \(0.587703\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5547.65 | 1.16528 | 0.582639 | − | 0.812731i | \(-0.302020\pi\) | ||||
0.582639 | + | 0.812731i | \(0.302020\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −624.000 | −0.129693 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4256.10 | −0.866293 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3523.65 | 0.709827 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3783.69 | 0.754422 | 0.377211 | − | 0.926127i | \(-0.376883\pi\) | ||||
0.377211 | + | 0.926127i | \(0.376883\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8398.41 | 1.65754 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 888.042 | 0.173500 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5726.30 | 1.10756 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4455.99 | 0.844851 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5381.48 | −1.01030 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2388.25 | −0.443989 | −0.221995 | − | 0.975048i | \(-0.571257\pi\) | ||||
−0.221995 | + | 0.975048i | \(0.571257\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5066.88 | 0.932831 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1014.69 | 0.185009 | 0.0925043 | − | 0.995712i | \(-0.470513\pi\) | ||||
0.0925043 | + | 0.995712i | \(0.470513\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7801.98 | −1.40893 | −0.704463 | − | 0.709741i | \(-0.748812\pi\) | ||||
−0.704463 | + | 0.709741i | \(0.748812\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4418.31 | −0.782829 | −0.391415 | − | 0.920214i | \(-0.628014\pi\) | ||||
−0.391415 | + | 0.920214i | \(0.628014\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5372.41 | −0.942938 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3482.75 | −0.605571 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −391.123 | −0.0673768 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2584.44 | 0.441104 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5436.91 | −0.919455 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7709.04 | −1.28014 | −0.640072 | − | 0.768315i | \(-0.721095\pi\) | ||||
−0.640072 | + | 0.768315i | \(0.721095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3162.08 | 0.520364 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2405.26 | 0.392279 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1980.02 | 0.320056 | 0.160028 | − | 0.987112i | \(-0.448842\pi\) | ||||
0.160028 | + | 0.987112i | \(0.448842\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1578.00 | −0.252818 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1325.53 | −0.210503 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5506.77 | 0.859346 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5671.05 | 0.877343 | 0.438672 | − | 0.898647i | \(-0.355449\pi\) | ||||
0.438672 | + | 0.898647i | \(0.355449\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5680.52 | −0.871265 | −0.435632 | − | 0.900125i | \(-0.643475\pi\) | ||||
−0.435632 | + | 0.900125i | \(0.643475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1148.06 | 0.174583 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8078.65 | −1.21808 | −0.609041 | − | 0.793139i | \(-0.708446\pi\) | ||||
−0.609041 | + | 0.793139i | \(0.708446\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9759.37 | 1.45908 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 222.365 | 0.0326907 | 0.0163453 | − | 0.999866i | \(-0.494797\pi\) | ||||
0.0163453 | + | 0.999866i | \(0.494797\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6626.12 | −0.966048 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −747.657 | −0.108104 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3525.54 | 0.505576 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10963.7 | −1.55941 | −0.779703 | − | 0.626150i | \(-0.784630\pi\) | ||||
−0.779703 | + | 0.626150i | \(0.784630\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2310.78 | −0.326001 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13881.3 | −1.92694 | −0.963470 | − | 0.267815i | \(-0.913698\pi\) | ||||
−0.963470 | + | 0.267815i | \(0.913698\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2625.95 | −0.361609 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6945.42 | −0.948826 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7909.27 | 1.07196 | 0.535979 | − | 0.844232i | \(-0.319943\pi\) | ||||
0.535979 | + | 0.844232i | \(0.319943\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 295.972 | 0.0397982 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4329.15 | 0.577570 | 0.288785 | − | 0.957394i | \(-0.406749\pi\) | ||||
0.288785 | + | 0.957394i | \(0.406749\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1692.00 | 0.222246 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6914.58 | −0.901242 | −0.450621 | − | 0.892715i | \(-0.648797\pi\) | ||||
−0.450621 | + | 0.892715i | \(0.648797\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3451.65 | 0.446438 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6859.40 | −0.880435 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13788.1 | −1.75634 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −142.434 | −0.0180065 | −0.00900325 | − | 0.999959i | \(-0.502866\pi\) | ||||
−0.00900325 | + | 0.999959i | \(0.502866\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10229.3 | 1.27389 | 0.636944 | − | 0.770910i | \(-0.280198\pi\) | ||||
0.636944 | + | 0.770910i | \(0.280198\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1713.64 | −0.211818 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1104.04 | 0.135457 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11555.8 | 1.40737 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5552.47 | 0.671277 | 0.335638 | − | 0.941991i | \(-0.391048\pi\) | ||||
0.335638 | + | 0.941991i | \(0.391048\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5575.48 | 0.669144 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3705.16 | 0.438262 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4455.45 | 0.523224 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11571.1 | 1.34913 | 0.674563 | − | 0.738217i | \(-0.264332\pi\) | ||||
0.674563 | + | 0.738217i | \(0.264332\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2150.80 | −0.248987 | −0.124494 | − | 0.992220i | \(-0.539731\pi\) | ||||
−0.124494 | + | 0.992220i | \(0.539731\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2610.74 | −0.300091 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1557.82 | 0.177801 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4195.56 | 0.472176 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16771.5 | 1.87438 | 0.937188 | − | 0.348825i | \(-0.113419\pi\) | ||||
0.937188 | + | 0.348825i | \(0.113419\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11983.6 | −1.33001 | −0.665007 | − | 0.746837i | \(-0.731571\pi\) | ||||
−0.665007 | + | 0.746837i | \(0.731571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6679.15 | −0.736186 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2055.12 | −0.224965 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3542.96 | 0.385185 | 0.192592 | − | 0.981279i | \(-0.438311\pi\) | ||||
0.192592 | + | 0.981279i | \(0.438311\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6522.07 | 0.699488 | 0.349744 | − | 0.936845i | \(-0.386269\pi\) | ||||
0.349744 | + | 0.936845i | \(0.386269\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14472.4 | −1.54170 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3070.20 | −0.324866 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15612.5 | −1.64098 | −0.820491 | − | 0.571660i | \(-0.806300\pi\) | ||||
−0.820491 | + | 0.571660i | \(0.806300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8444.74 | −0.881701 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5010.74 | −0.519702 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4059.04 | −0.415479 | −0.207739 | − | 0.978184i | \(-0.566611\pi\) | ||||
−0.207739 | + | 0.978184i | \(0.566611\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 692.014 | 0.0703713 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14452.5 | −1.46013 | −0.730067 | − | 0.683375i | \(-0.760511\pi\) | ||||
−0.730067 | + | 0.683375i | \(0.760511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7970.34 | −0.800028 | −0.400014 | − | 0.916509i | \(-0.630995\pi\) | ||||
−0.400014 | + | 0.916509i | \(0.630995\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1647.94 | −0.164347 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6695.51 | 0.663450 | 0.331725 | − | 0.943376i | \(-0.392369\pi\) | ||||
0.331725 | + | 0.943376i | \(0.392369\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5669.67 | 0.554659 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6183.40 | 0.601085 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −927.534 | −0.0895962 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3194.14 | −0.306603 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1434.68 | −0.136852 | −0.0684261 | − | 0.997656i | \(-0.521798\pi\) | ||||
−0.0684261 | + | 0.997656i | \(0.521798\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14939.3 | 1.41616 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16009.3 | 1.49885 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5522.46 | −0.513853 | −0.256927 | − | 0.966431i | \(-0.582710\pi\) | ||||
−0.256927 | + | 0.966431i | \(0.582710\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1942.43 | −0.179632 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2340.34 | −0.215108 | −0.107554 | − | 0.994199i | \(-0.534302\pi\) | ||||
−0.107554 | + | 0.994199i | \(0.534302\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4186.50 | −0.382455 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4034.71 | 0.366357 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17693.0 | −1.58727 | −0.793637 | − | 0.608392i | \(-0.791815\pi\) | ||||
−0.793637 | + | 0.608392i | \(0.791815\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8758.19 | 0.781012 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17042.9 | −1.51074 | −0.755371 | − | 0.655297i | \(-0.772543\pi\) | ||||
−0.755371 | + | 0.655297i | \(0.772543\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20245.2 | 1.78396 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1167.00 | −0.102225 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6252.35 | −0.544460 | −0.272230 | − | 0.962232i | \(-0.587761\pi\) | ||||
−0.272230 | + | 0.962232i | \(0.587761\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −412.028 | −0.0354610 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23020.8 | 1.96974 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9540.93 | −0.811624 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4296.78 | −0.363406 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9375.13 | −0.788353 | −0.394177 | − | 0.919035i | \(-0.628970\pi\) | ||||
−0.394177 | + | 0.919035i | \(0.628970\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13852.2 | −1.15816 | −0.579078 | − | 0.815272i | \(-0.696587\pi\) | ||||
−0.579078 | + | 0.815272i | \(0.696587\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1032.93 | −0.0853800 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5969.36 | 0.490619 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5545.48 | 0.453208 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10917.3 | −0.887207 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15823.5 | −1.27871 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4698.70 | 0.377586 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4303.77 | −0.342022 | −0.171011 | − | 0.985269i | \(-0.554703\pi\) | ||||
−0.171011 | + | 0.985269i | \(0.554703\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4694.80 | 0.371037 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24702.0 | −1.94150 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18406.3 | −1.43875 | −0.719377 | − | 0.694620i | \(-0.755573\pi\) | ||||
−0.719377 | + | 0.694620i | \(0.755573\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3553.40 | −0.276239 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2492.66 | 0.192724 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14366.6 | 1.09879 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5473.81 | 0.416397 | 0.208198 | − | 0.978087i | \(-0.433240\pi\) | ||||
0.208198 | + | 0.978087i | \(0.433240\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7993.87 | 0.604838 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2528.96 | 0.190326 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7361.93 | 0.551098 | 0.275549 | − | 0.961287i | \(-0.411140\pi\) | ||||
0.275549 | + | 0.961287i | \(0.411140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7169.46 | −0.533843 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5628.42 | −0.414685 | −0.207342 | − | 0.978268i | \(-0.566481\pi\) | ||||
−0.207342 | + | 0.978268i | \(0.566481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15398.8 | −1.12858 | −0.564291 | − | 0.825576i | \(-0.690851\pi\) | ||||
−0.564291 | + | 0.825576i | \(0.690851\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6753.58 | 0.492382 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8185.44 | 0.593663 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23587.9 | −1.70187 | −0.850933 | − | 0.525274i | \(-0.823963\pi\) | ||||
−0.850933 | + | 0.525274i | \(0.823963\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14916.0 | 1.07062 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11673.0 | −0.829236 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5216.06 | 0.368645 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10358.1 | −0.728324 | −0.364162 | − | 0.931336i | \(-0.618645\pi\) | ||||
−0.364162 | + | 0.931336i | \(0.618645\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 615.012 | 0.0430240 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −637.805 | −0.0443922 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4159.31 | −0.288031 | −0.144015 | − | 0.989575i | \(-0.546001\pi\) | ||||
−0.144015 | + | 0.989575i | \(0.546001\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7074.74 | 0.485008 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12888.3 | −0.879137 | −0.439568 | − | 0.898209i | \(-0.644869\pi\) | ||||
−0.439568 | + | 0.898209i | \(0.644869\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2768.82 | −0.187924 | −0.0939620 | − | 0.995576i | \(-0.529953\pi\) | ||||
−0.0939620 | + | 0.995576i | \(0.529953\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1588.20 | 0.107258 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3396.89 | −0.228270 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26084.0 | 1.74418 | 0.872090 | − | 0.489345i | \(-0.162764\pi\) | ||||
0.872090 | + | 0.489345i | \(0.162764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12334.5 | −0.816693 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7507.98 | 0.494689 | 0.247344 | − | 0.968928i | \(-0.420442\pi\) | ||||
0.247344 | + | 0.968928i | \(0.420442\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10498.8 | −0.688376 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13414.4 | −0.875275 | −0.437638 | − | 0.899151i | \(-0.644185\pi\) | ||||
−0.437638 | + | 0.899151i | \(0.644185\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19775.5 | −1.28408 | −0.642038 | − | 0.766673i | \(-0.721911\pi\) | ||||
−0.642038 | + | 0.766673i | \(0.721911\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3636.13 | 0.234964 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19528.3 | −1.24981 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1505.75 | −0.0959075 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9004.96 | 0.570829 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12474.1 | 0.786984 | 0.393492 | − | 0.919328i | \(-0.371267\pi\) | ||||
0.393492 | + | 0.919328i | \(0.371267\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9244.28 | −0.580454 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1344.71 | 0.0840368 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6444.13 | 0.398945 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8075.38 | −0.497595 | −0.248797 | − | 0.968556i | \(-0.580035\pi\) | ||||
−0.248797 | + | 0.968556i | \(0.580035\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17525.2 | −1.07485 | −0.537423 | − | 0.843313i | \(-0.680602\pi\) | ||||
−0.537423 | + | 0.843313i | \(0.680602\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7687.40 | 0.469289 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3190.19 | −0.193848 | −0.0969238 | − | 0.995292i | \(-0.530900\pi\) | ||||
−0.0969238 | + | 0.995292i | \(0.530900\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20265.9 | 1.22574 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6581.37 | 0.394409 | 0.197204 | − | 0.980362i | \(-0.436814\pi\) | ||||
0.197204 | + | 0.980362i | \(0.436814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31164.9 | −1.85910 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2327.92 | 0.138235 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14239.0 | −0.841686 | −0.420843 | − | 0.907134i | \(-0.638266\pi\) | ||||
−0.420843 | + | 0.907134i | \(0.638266\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24996.2 | 1.47086 | 0.735431 | − | 0.677600i | \(-0.236980\pi\) | ||||
0.735431 | + | 0.677600i | \(0.236980\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3269.43 | 0.191514 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21997.6 | −1.27699 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15897.0 | 0.918707 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12985.9 | −0.747115 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23298.9 | 1.33448 | 0.667242 | − | 0.744841i | \(-0.267475\pi\) | ||||
0.667242 | + | 0.744841i | \(0.267475\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1641.08 | 0.0935783 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16825.4 | −0.955172 | −0.477586 | − | 0.878585i | \(-0.658488\pi\) | ||||
−0.477586 | + | 0.878585i | \(0.658488\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10874.0 | −0.611882 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10039.3 | −0.562436 | −0.281218 | − | 0.959644i | \(-0.590738\pi\) | ||||
−0.281218 | + | 0.959644i | \(0.590738\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25331.5 | 1.41295 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18463.1 | −1.02534 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15090.7 | −0.834414 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35180.7 | −1.93681 | −0.968405 | − | 0.249382i | \(-0.919773\pi\) | ||||
−0.968405 | + | 0.249382i | \(0.919773\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20242.8 | 1.10483 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6580.63 | −0.357617 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17581.2 | 0.951336 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14725.4 | −0.793395 | −0.396697 | − | 0.917949i | \(-0.629844\pi\) | ||||
−0.396697 | + | 0.917949i | \(0.629844\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5361.59 | −0.287648 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11861.6 | −0.633664 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6264.80 | −0.331847 | −0.165923 | − | 0.986139i | \(-0.553060\pi\) | ||||
−0.165923 | + | 0.986139i | \(0.553060\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9104.31 | −0.480222 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5427.45 | −0.285077 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19062.0 | 0.997035 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7172.43 | −0.373584 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6764.99 | −0.350892 | −0.175446 | − | 0.984489i | \(-0.556137\pi\) | ||||
−0.175446 | + | 0.984489i | \(0.556137\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4958.72 | −0.255072 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9928.11 | −0.508580 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30930.1 | 1.57790 | 0.788950 | − | 0.614458i | \(-0.210625\pi\) | ||||
0.788950 | + | 0.614458i | \(0.210625\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4818.47 | 0.243800 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31046.2 | 1.56441 | 0.782207 | − | 0.623018i | \(-0.214094\pi\) | ||||
0.782207 | + | 0.623018i | \(0.214094\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5804.05 | 0.290088 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26261.8 | −1.30725 | −0.653625 | − | 0.756819i | \(-0.726752\pi\) | ||||
−0.653625 | + | 0.756819i | \(0.726752\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1946.63 | −0.0965064 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21911.5 | 1.08191 | 0.540953 | − | 0.841053i | \(-0.318064\pi\) | ||||
0.540953 | + | 0.841053i | \(0.318064\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13949.1 | −0.685979 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2446.52 | 0.119831 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22265.8 | −1.08188 | −0.540938 | − | 0.841062i | \(-0.681931\pi\) | ||||
−0.540938 | + | 0.841062i | \(0.681931\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22758.1 | 1.10140 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22765.7 | −1.09739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 246.869 | 0.0118528 | 0.00592642 | − | 0.999982i | \(-0.498114\pi\) | ||||
0.00592642 | + | 0.999982i | \(0.498114\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13288.2 | 0.635482 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6297.54 | 0.299981 | 0.149991 | − | 0.988687i | \(-0.452076\pi\) | ||||
0.149991 | + | 0.988687i | \(0.452076\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3144.08 | 0.148594 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26199.7 | 1.23340 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38562.6 | −1.80833 | −0.904163 | − | 0.427187i | \(-0.859505\pi\) | ||||
−0.904163 | + | 0.427187i | \(0.859505\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −459.735 | −0.0214747 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33338.8 | 1.55125 | 0.775623 | − | 0.631196i | \(-0.217436\pi\) | ||||
0.775623 | + | 0.631196i | \(0.217436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2449.56 | −0.113536 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3918.14 | 0.180208 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23550.0 | 1.07898 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4410.25 | −0.201289 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25759.5 | 1.17120 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29492.7 | 1.33583 | 0.667917 | − | 0.744235i | \(-0.267186\pi\) | ||||
0.667917 | + | 0.744235i | \(0.267186\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1803.74 | 0.0813874 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16788.1 | −0.751780 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14512.2 | −0.647414 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17821.6 | 0.792062 | 0.396031 | − | 0.918237i | \(-0.370387\pi\) | ||||
0.396031 | + | 0.918237i | \(0.370387\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7434.85 | −0.329194 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9556.15 | −0.421536 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8507.35 | 0.373870 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14923.7 | 0.650977 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23280.4 | −1.01174 | −0.505869 | − | 0.862611i | \(-0.668828\pi\) | ||||
−0.505869 | + | 0.862611i | \(0.668828\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29822.4 | −1.29125 | −0.645627 | − | 0.763653i | \(-0.723404\pi\) | ||||
−0.645627 | + | 0.763653i | \(0.723404\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5490.49 | 0.236851 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8825.22 | −0.379306 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2868.93 | −0.122854 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40215.0 | 1.70952 | 0.854758 | − | 0.519027i | \(-0.173706\pi\) | ||||
0.854758 | + | 0.519027i | \(0.173706\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2077.68 | 0.0879991 | 0.0439996 | − | 0.999032i | \(-0.485990\pi\) | ||||
0.0439996 | + | 0.999032i | \(0.485990\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5997.33 | 0.253091 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25858.4 | 1.08728 | 0.543642 | − | 0.839317i | \(-0.317045\pi\) | ||||
0.543642 | + | 0.839317i | \(0.317045\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27781.4 | 1.16392 | 0.581958 | − | 0.813219i | \(-0.302287\pi\) | ||||
0.581958 | + | 0.813219i | \(0.302287\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19705.0 | −0.822574 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39791.8 | 1.64916 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1088.14 | −0.0449362 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5199.25 | 0.213943 | 0.106971 | − | 0.994262i | \(-0.465885\pi\) | ||||
0.106971 | + | 0.994262i | \(0.465885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2291.81 | 0.0939691 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7688.96 | −0.314142 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5302.13 | −0.215856 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16642.9 | 0.672773 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47315.8 | 1.90595 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23538.6 | 0.944839 | 0.472420 | − | 0.881374i | \(-0.343381\pi\) | ||||
0.472420 | + | 0.881374i | \(0.343381\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1872.00 | −0.0748784 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12563.3 | −0.500762 | −0.250381 | − | 0.968147i | \(-0.580556\pi\) | ||||
−0.250381 | + | 0.968147i | \(0.580556\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3807.37 | −0.151229 | −0.0756145 | − | 0.997137i | \(-0.524092\pi\) | ||||
−0.0756145 | + | 0.997137i | \(0.524092\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30845.9 | −1.21669 | −0.608347 | − | 0.793671i | \(-0.708167\pi\) | ||||
−0.608347 | + | 0.793671i | \(0.708167\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19521.9 | −0.767358 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12768.3 | −0.500154 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33271.6 | −1.29881 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7503.44 | 0.291899 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10570.9 | 0.409819 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18058.9 | 0.695331 | 0.347666 | − | 0.937619i | \(-0.386974\pi\) | ||||
0.347666 | + | 0.937619i | \(0.386974\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11351.1 | 0.435565 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51388.8 | 1.96519 | 0.982596 | − | 0.185756i | \(-0.0594734\pi\) | ||||
0.982596 | + | 0.185756i | \(0.0594734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25852.4 | −0.985281 | −0.492640 | − | 0.870233i | \(-0.663968\pi\) | ||||
−0.492640 | + | 0.870233i | \(0.663968\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25195.2 | 0.956982 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33982.4 | −1.28638 | −0.643189 | − | 0.765707i | \(-0.722389\pi\) | ||||
−0.643189 | + | 0.765707i | \(0.722389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2664.13 | 0.100170 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4426.74 | 0.165885 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21348.0 | 0.797301 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17178.9 | 0.639450 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6582.95 | 0.244220 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9096.25 | −0.336337 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21330.3 | 0.783471 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1730.58 | 0.0633550 | 0.0316775 | − | 0.999498i | \(-0.489915\pi\) | ||||
0.0316775 | + | 0.999498i | \(0.489915\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13368.0 | 0.487775 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.2017 | 0.00208033 | 0.00104016 | − | 0.999999i | \(-0.499669\pi\) | ||||
0.00104016 | + | 0.999999i | \(0.499669\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8940.78 | 0.324093 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16144.4 | −0.583299 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44264.3 | 1.58884 | 0.794420 | − | 0.607369i | \(-0.207775\pi\) | ||||
0.794420 | + | 0.607369i | \(0.207775\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7164.75 | −0.256337 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30445.3 | 1.08572 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21354.9 | 0.759076 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15200.6 | 0.538570 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37811.9 | 1.33538 | 0.667690 | − | 0.744440i | \(-0.267283\pi\) | ||||
0.667690 | + | 0.744440i | \(0.267283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3044.06 | 0.106815 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11490.0 | 0.401887 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40391.3 | 1.40824 | 0.704122 | − | 0.710079i | \(-0.251341\pi\) | ||||
0.704122 | + | 0.710079i | \(0.251341\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23405.9 | −0.813444 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4662.49 | 0.161523 | 0.0807613 | − | 0.996733i | \(-0.474265\pi\) | ||||
0.0807613 | + | 0.996733i | \(0.474265\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34577.4 | −1.19405 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27594.1 | −0.946874 | −0.473437 | − | 0.880828i | \(-0.656987\pi\) | ||||
−0.473437 | + | 0.880828i | \(0.656987\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10998.3 | 0.376205 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13254.9 | −0.451967 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32317.6 | −1.09850 | −0.549249 | − | 0.835659i | \(-0.685086\pi\) | ||||
−0.549249 | + | 0.835659i | \(0.685086\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30684.1 | 1.03970 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16117.2 | −0.544406 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28166.8 | −0.945480 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10448.3 | −0.349627 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 67769.1 | 2.26069 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10669.7 | 0.354825 | 0.177413 | − | 0.984137i | \(-0.443227\pi\) | ||||
0.177413 | + | 0.984137i | \(0.443227\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1173.37 | −0.0389000 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11821.9 | 0.390715 | 0.195358 | − | 0.980732i | \(-0.437413\pi\) | ||||
0.195358 | + | 0.980732i | \(0.437413\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7753.31 | 0.254672 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32994.5 | −1.08044 | −0.540219 | − | 0.841525i | \(-0.681659\pi\) | ||||
−0.540219 | + | 0.841525i | \(0.681659\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34922.9 | −1.14008 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16310.7 | −0.530847 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52785.2 | 1.71270 | 0.856351 | − | 0.516395i | \(-0.172726\pi\) | ||||
0.856351 | + | 0.516395i | \(0.172726\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2897.79 | −0.0937374 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25318.2 | 0.814026 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 999.387 | 0.0320349 | 0.0160174 | − | 0.999872i | \(-0.494901\pi\) | ||||
0.0160174 | + | 0.999872i | \(0.494901\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23127.1 | −0.739091 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32143.3 | 1.02413 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12363.2 | −0.392724 | −0.196362 | − | 0.980531i | \(-0.562913\pi\) | ||||
−0.196362 | + | 0.980531i | \(0.562913\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9486.25 | 0.300432 |
(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 | 1176.4.a.v.1.2 | yes | 2 | |
4.3 | odd | 2 | 2352.4.a.bs.1.2 | 2 | |||
7.6 | odd | 2 | 1176.4.a.q.1.1 | ✓ | 2 | ||
28.27 | even | 2 | 2352.4.a.by.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.4.a.q.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
1176.4.a.v.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
2352.4.a.bs.1.2 | 2 | 4.3 | odd | 2 | |||
2352.4.a.by.1.1 | 2 | 28.27 | even | 2 |