Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.6257832.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 19x^{2} + 42 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 63) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.05539\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.05539 | −1.43380 | −0.716899 | − | 0.697177i | \(-0.754439\pi\) | ||||
−0.716899 | + | 0.697177i | \(0.754439\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 8.44622 | 1.05578 | ||||||||
\(5\) | −9.92039 | −0.887307 | −0.443654 | − | 0.896198i | \(-0.646318\pi\) | ||||
−0.443654 | + | 0.896198i | \(0.646318\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.80961 | −0.0799740 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 40.2311 | 1.27222 | ||||||||
\(11\) | −13.5396 | −0.371122 | −0.185561 | − | 0.982633i | \(-0.559410\pi\) | ||||
−0.185561 | + | 0.982633i | \(0.559410\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.5538 | 0.395838 | 0.197919 | − | 0.980218i | \(-0.436582\pi\) | ||||
0.197919 | + | 0.980218i | \(0.436582\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −60.2311 | −0.941111 | ||||||||
\(17\) | −93.7102 | −1.33695 | −0.668473 | − | 0.743737i | \(-0.733052\pi\) | ||||
−0.668473 | + | 0.743737i | \(0.733052\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 131.908 | 1.59273 | 0.796365 | − | 0.604816i | \(-0.206753\pi\) | ||||
0.796365 | + | 0.604816i | \(0.206753\pi\) | |||||||
\(20\) | −83.7899 | −0.936799 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 54.9084 | 0.532115 | ||||||||
\(23\) | −198.278 | −1.79756 | −0.898779 | − | 0.438401i | \(-0.855545\pi\) | ||||
−0.898779 | + | 0.438401i | \(0.855545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −26.5858 | −0.212686 | ||||||||
\(26\) | −75.2429 | −0.567552 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 188.358 | 1.20611 | 0.603054 | − | 0.797700i | \(-0.293950\pi\) | ||||
0.603054 | + | 0.797700i | \(0.293950\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −83.9244 | −0.486235 | −0.243117 | − | 0.969997i | \(-0.578170\pi\) | ||||
−0.243117 | + | 0.969997i | \(0.578170\pi\) | |||||||
\(32\) | 258.738 | 1.42934 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 380.032 | 1.91691 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 80.1555 | 0.356148 | 0.178074 | − | 0.984017i | \(-0.443013\pi\) | ||||
0.178074 | + | 0.984017i | \(0.443013\pi\) | |||||||
\(38\) | −534.941 | −2.28365 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 17.9520 | 0.0709615 | ||||||||
\(41\) | −385.828 | −1.46967 | −0.734833 | − | 0.678249i | \(-0.762739\pi\) | ||||
−0.734833 | + | 0.678249i | \(0.762739\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −397.048 | −1.40812 | −0.704061 | − | 0.710139i | \(-0.748632\pi\) | ||||
−0.704061 | + | 0.710139i | \(0.748632\pi\) | |||||||
\(44\) | −114.359 | −0.391823 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 804.096 | 2.57734 | ||||||||
\(47\) | 272.277 | 0.845016 | 0.422508 | − | 0.906359i | \(-0.361150\pi\) | ||||
0.422508 | + | 0.906359i | \(0.361150\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 107.816 | 0.304949 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 156.709 | 0.417917 | ||||||||
\(53\) | −36.9996 | −0.0958922 | −0.0479461 | − | 0.998850i | \(-0.515268\pi\) | ||||
−0.0479461 | + | 0.998850i | \(0.515268\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 134.318 | 0.329299 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −763.865 | −1.72932 | ||||||||
\(59\) | 395.749 | 0.873256 | 0.436628 | − | 0.899642i | \(-0.356173\pi\) | ||||
0.436628 | + | 0.899642i | \(0.356173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.4738 | 0.0282810 | 0.0141405 | − | 0.999900i | \(-0.495499\pi\) | ||||
0.0141405 | + | 0.999900i | \(0.495499\pi\) | |||||||
\(62\) | 340.347 | 0.697162 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −567.435 | −1.10827 | ||||||||
\(65\) | −184.061 | −0.351230 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 340.522 | 0.620916 | 0.310458 | − | 0.950587i | \(-0.399518\pi\) | ||||
0.310458 | + | 0.950587i | \(0.399518\pi\) | |||||||
\(68\) | −791.498 | −1.41152 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −211.140 | −0.352925 | −0.176463 | − | 0.984307i | \(-0.556466\pi\) | ||||
−0.176463 | + | 0.984307i | \(0.556466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 486.124 | 0.779404 | 0.389702 | − | 0.920941i | \(-0.372578\pi\) | ||||
0.389702 | + | 0.920941i | \(0.372578\pi\) | |||||||
\(74\) | −325.062 | −0.510645 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1114.13 | 1.68157 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 293.741 | 0.418335 | 0.209168 | − | 0.977880i | \(-0.432925\pi\) | ||||
0.209168 | + | 0.977880i | \(0.432925\pi\) | |||||||
\(80\) | 597.516 | 0.835055 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1564.69 | 2.10720 | ||||||||
\(83\) | 889.635 | 1.17651 | 0.588253 | − | 0.808677i | \(-0.299816\pi\) | ||||
0.588253 | + | 0.808677i | \(0.299816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 929.643 | 1.18628 | ||||||||
\(86\) | 1610.19 | 2.01896 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 24.5014 | 0.0296801 | ||||||||
\(89\) | 1144.36 | 1.36295 | 0.681474 | − | 0.731843i | \(-0.261339\pi\) | ||||
0.681474 | + | 0.731843i | \(0.261339\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1674.70 | −1.89782 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1104.19 | −1.21158 | ||||||||
\(95\) | −1308.58 | −1.41324 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1384.61 | 1.44933 | 0.724667 | − | 0.689099i | \(-0.241993\pi\) | ||||
0.724667 | + | 0.689099i | \(0.241993\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −224.549 | −0.224549 | ||||||||
\(101\) | 1785.99 | 1.75953 | 0.879765 | − | 0.475409i | \(-0.157700\pi\) | ||||
0.879765 | + | 0.475409i | \(0.157700\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 489.661 | 0.468425 | 0.234212 | − | 0.972185i | \(-0.424749\pi\) | ||||
0.234212 | + | 0.972185i | \(0.424749\pi\) | |||||||
\(104\) | −33.5750 | −0.0316568 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 150.048 | 0.137490 | ||||||||
\(107\) | 282.068 | 0.254846 | 0.127423 | − | 0.991848i | \(-0.459329\pi\) | ||||
0.127423 | + | 0.991848i | \(0.459329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −287.231 | −0.252401 | −0.126201 | − | 0.992005i | \(-0.540278\pi\) | ||||
−0.126201 | + | 0.992005i | \(0.540278\pi\) | |||||||
\(110\) | −544.713 | −0.472149 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1895.21 | 1.57776 | 0.788879 | − | 0.614548i | \(-0.210662\pi\) | ||||
0.788879 | + | 0.614548i | \(0.210662\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1967.00 | 1.59499 | ||||||||
\(116\) | 1590.91 | 1.27338 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1604.92 | −1.25207 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1147.68 | −0.862268 | ||||||||
\(122\) | −54.6415 | −0.0405493 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −708.844 | −0.513356 | ||||||||
\(125\) | 1503.79 | 1.07603 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1222.92 | −0.854463 | −0.427231 | − | 0.904142i | \(-0.640511\pi\) | ||||
−0.427231 | + | 0.904142i | \(0.640511\pi\) | |||||||
\(128\) | 231.269 | 0.159699 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 746.439 | 0.503593 | ||||||||
\(131\) | 1190.61 | 0.794074 | 0.397037 | − | 0.917803i | \(-0.370038\pi\) | ||||
0.397037 | + | 0.917803i | \(0.370038\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1380.95 | −0.890268 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 169.579 | 0.106921 | ||||||||
\(137\) | 106.961 | 0.0667031 | 0.0333516 | − | 0.999444i | \(-0.489382\pi\) | ||||
0.0333516 | + | 0.999444i | \(0.489382\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1096.78 | −0.669262 | −0.334631 | − | 0.942349i | \(-0.608612\pi\) | ||||
−0.334631 | + | 0.942349i | \(0.608612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 856.256 | 0.506024 | ||||||||
\(143\) | −251.211 | −0.146904 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1868.58 | −1.07019 | ||||||||
\(146\) | −1971.42 | −1.11751 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 677.012 | 0.376014 | ||||||||
\(149\) | 716.662 | 0.394035 | 0.197018 | − | 0.980400i | \(-0.436874\pi\) | ||||
0.197018 | + | 0.980400i | \(0.436874\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 154.368 | 0.0831939 | 0.0415970 | − | 0.999134i | \(-0.486755\pi\) | ||||
0.0415970 | + | 0.999134i | \(0.486755\pi\) | |||||||
\(152\) | −238.702 | −0.127377 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 832.564 | 0.431439 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2093.75 | −1.06433 | −0.532163 | − | 0.846642i | \(-0.678621\pi\) | ||||
−0.532163 | + | 0.846642i | \(0.678621\pi\) | |||||||
\(158\) | −1191.24 | −0.599808 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2566.78 | −1.26826 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3007.86 | 1.44536 | 0.722680 | − | 0.691183i | \(-0.242910\pi\) | ||||
0.722680 | + | 0.691183i | \(0.242910\pi\) | |||||||
\(164\) | −3258.79 | −1.55164 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3607.82 | −1.68687 | ||||||||
\(167\) | −2230.43 | −1.03351 | −0.516754 | − | 0.856134i | \(-0.672860\pi\) | ||||
−0.516754 | + | 0.856134i | \(0.672860\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1852.76 | −0.843312 | ||||||||
\(170\) | −3770.07 | −1.70089 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3353.56 | −1.48666 | ||||||||
\(173\) | −563.170 | −0.247497 | −0.123749 | − | 0.992314i | \(-0.539492\pi\) | ||||
−0.123749 | + | 0.992314i | \(0.539492\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 815.506 | 0.349267 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4640.85 | −1.95419 | ||||||||
\(179\) | 1839.50 | 0.768104 | 0.384052 | − | 0.923312i | \(-0.374528\pi\) | ||||
0.384052 | + | 0.923312i | \(0.374528\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2324.71 | 0.954664 | 0.477332 | − | 0.878723i | \(-0.341604\pi\) | ||||
0.477332 | + | 0.878723i | \(0.341604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 358.805 | 0.143758 | ||||||||
\(185\) | −795.175 | −0.316013 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1268.80 | 0.496170 | ||||||||
\(188\) | 2299.71 | 0.892149 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5306.82 | 2.02630 | ||||||||
\(191\) | −3127.27 | −1.18472 | −0.592360 | − | 0.805673i | \(-0.701804\pi\) | ||||
−0.592360 | + | 0.805673i | \(0.701804\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3709.29 | −1.38342 | −0.691711 | − | 0.722175i | \(-0.743143\pi\) | ||||
−0.691711 | + | 0.722175i | \(0.743143\pi\) | |||||||
\(194\) | −5615.12 | −2.07805 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 851.150 | 0.307827 | 0.153913 | − | 0.988084i | \(-0.450812\pi\) | ||||
0.153913 | + | 0.988084i | \(0.450812\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3397.78 | 1.21036 | 0.605182 | − | 0.796087i | \(-0.293100\pi\) | ||||
0.605182 | + | 0.796087i | \(0.293100\pi\) | |||||||
\(200\) | 48.1098 | 0.0170094 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7242.89 | −2.52281 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3827.57 | 1.30404 | ||||||||
\(206\) | −1985.77 | −0.671627 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1117.51 | −0.372527 | ||||||||
\(209\) | −1785.99 | −0.591098 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 216.732 | 0.0707132 | 0.0353566 | − | 0.999375i | \(-0.488743\pi\) | ||||
0.0353566 | + | 0.999375i | \(0.488743\pi\) | |||||||
\(212\) | −312.507 | −0.101241 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1143.90 | −0.365398 | ||||||||
\(215\) | 3938.87 | 1.24944 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1164.84 | 0.361893 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1134.48 | 0.347667 | ||||||||
\(221\) | −1738.68 | −0.529214 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2254.86 | −0.677115 | −0.338558 | − | 0.940946i | \(-0.609939\pi\) | ||||
−0.338558 | + | 0.940946i | \(0.609939\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7685.84 | −2.26219 | ||||||||
\(227\) | −3390.80 | −0.991433 | −0.495716 | − | 0.868484i | \(-0.665094\pi\) | ||||
−0.495716 | + | 0.868484i | \(0.665094\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2587.85 | 0.746768 | 0.373384 | − | 0.927677i | \(-0.378197\pi\) | ||||
0.373384 | + | 0.927677i | \(0.378197\pi\) | |||||||
\(230\) | −7976.95 | −2.28689 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −340.853 | −0.0964574 | ||||||||
\(233\) | −954.420 | −0.268353 | −0.134176 | − | 0.990957i | \(-0.542839\pi\) | ||||
−0.134176 | + | 0.990957i | \(0.542839\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2701.10 | −0.749788 | ||||||||
\(236\) | 3342.58 | 0.921964 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 199.504 | 0.0539951 | 0.0269976 | − | 0.999635i | \(-0.491405\pi\) | ||||
0.0269976 | + | 0.999635i | \(0.491405\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4794.43 | 1.28148 | 0.640739 | − | 0.767759i | \(-0.278628\pi\) | ||||
0.640739 | + | 0.767759i | \(0.278628\pi\) | |||||||
\(242\) | 4654.29 | 1.23632 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 113.803 | 0.0298585 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2447.40 | 0.630463 | ||||||||
\(248\) | 151.870 | 0.0388862 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6098.46 | −1.54280 | ||||||||
\(251\) | 6249.73 | 1.57163 | 0.785816 | − | 0.618460i | \(-0.212243\pi\) | ||||
0.785816 | + | 0.618460i | \(0.212243\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2684.61 | 0.667114 | ||||||||
\(254\) | 4959.43 | 1.22513 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3601.59 | 0.879294 | ||||||||
\(257\) | −3837.85 | −0.931512 | −0.465756 | − | 0.884913i | \(-0.654218\pi\) | ||||
−0.465756 | + | 0.884913i | \(0.654218\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1554.62 | −0.370821 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4828.38 | −1.13854 | ||||||||
\(263\) | 207.203 | 0.0485806 | 0.0242903 | − | 0.999705i | \(-0.492267\pi\) | ||||
0.0242903 | + | 0.999705i | \(0.492267\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 367.051 | 0.0850858 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2876.12 | 0.655549 | ||||||||
\(269\) | 4804.08 | 1.08888 | 0.544442 | − | 0.838798i | \(-0.316741\pi\) | ||||
0.544442 | + | 0.838798i | \(0.316741\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3215.75 | 0.720823 | 0.360411 | − | 0.932793i | \(-0.382636\pi\) | ||||
0.360411 | + | 0.932793i | \(0.382636\pi\) | |||||||
\(272\) | 5644.27 | 1.25821 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −433.771 | −0.0956388 | ||||||||
\(275\) | 359.961 | 0.0789326 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2054.39 | 0.445619 | 0.222810 | − | 0.974862i | \(-0.428477\pi\) | ||||
0.222810 | + | 0.974862i | \(0.428477\pi\) | |||||||
\(278\) | 4447.87 | 0.959587 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1768.61 | 0.375468 | 0.187734 | − | 0.982220i | \(-0.439886\pi\) | ||||
0.187734 | + | 0.982220i | \(0.439886\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2340.53 | 0.491625 | 0.245813 | − | 0.969317i | \(-0.420945\pi\) | ||||
0.245813 | + | 0.969317i | \(0.420945\pi\) | |||||||
\(284\) | −1783.34 | −0.372611 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1018.76 | 0.210631 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3868.61 | 0.787423 | ||||||||
\(290\) | 7577.84 | 1.53443 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4105.91 | 0.822877 | ||||||||
\(293\) | −3633.47 | −0.724470 | −0.362235 | − | 0.932087i | \(-0.617986\pi\) | ||||
−0.362235 | + | 0.932087i | \(0.617986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3925.98 | −0.774846 | ||||||||
\(296\) | −145.050 | −0.0284826 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2906.35 | −0.564967 | ||||||||
\(299\) | −3678.81 | −0.711542 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −626.023 | −0.119283 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7944.99 | −1.49894 | ||||||||
\(305\) | −133.665 | −0.0250939 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5954.32 | 1.10694 | 0.553471 | − | 0.832868i | \(-0.313303\pi\) | ||||
0.553471 | + | 0.832868i | \(0.313303\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3376.37 | −0.618597 | ||||||||
\(311\) | 1180.09 | 0.215167 | 0.107584 | − | 0.994196i | \(-0.465689\pi\) | ||||
0.107584 | + | 0.994196i | \(0.465689\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9746.25 | −1.76003 | −0.880017 | − | 0.474943i | \(-0.842469\pi\) | ||||
−0.880017 | + | 0.474943i | \(0.842469\pi\) | |||||||
\(314\) | 8490.97 | 1.52603 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2481.00 | 0.441669 | ||||||||
\(317\) | 8591.91 | 1.52230 | 0.761151 | − | 0.648574i | \(-0.224634\pi\) | ||||
0.761151 | + | 0.648574i | \(0.224634\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2550.29 | −0.447614 | ||||||||
\(320\) | 5629.18 | 0.983377 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12361.2 | −2.12939 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −493.267 | −0.0841892 | ||||||||
\(326\) | −12198.0 | −2.07235 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 698.197 | 0.117535 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5251.20 | −0.872000 | −0.436000 | − | 0.899947i | \(-0.643605\pi\) | ||||
−0.436000 | + | 0.899947i | \(0.643605\pi\) | |||||||
\(332\) | 7514.05 | 1.24213 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9045.28 | 1.48184 | ||||||||
\(335\) | −3378.11 | −0.550943 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8496.45 | −1.37339 | −0.686693 | − | 0.726947i | \(-0.740938\pi\) | ||||
−0.686693 | + | 0.726947i | \(0.740938\pi\) | |||||||
\(338\) | 7513.66 | 1.20914 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7851.97 | 1.25245 | ||||||||
\(341\) | 1136.30 | 0.180453 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 718.500 | 0.112613 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2283.88 | 0.354861 | ||||||||
\(347\) | −5830.15 | −0.901956 | −0.450978 | − | 0.892535i | \(-0.648925\pi\) | ||||
−0.450978 | + | 0.892535i | \(0.648925\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1811.13 | 0.277786 | 0.138893 | − | 0.990307i | \(-0.455646\pi\) | ||||
0.138893 | + | 0.990307i | \(0.455646\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3503.21 | −0.530459 | ||||||||
\(353\) | 3327.76 | 0.501753 | 0.250876 | − | 0.968019i | \(-0.419281\pi\) | ||||
0.250876 | + | 0.968019i | \(0.419281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2094.59 | 0.313153 | ||||||||
\(356\) | 9665.55 | 1.43897 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7459.89 | −1.10131 | ||||||||
\(359\) | −870.861 | −0.128029 | −0.0640143 | − | 0.997949i | \(-0.520390\pi\) | ||||
−0.0640143 | + | 0.997949i | \(0.520390\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10540.8 | 1.53679 | ||||||||
\(362\) | −9427.61 | −1.36880 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4822.54 | −0.691570 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1174.72 | 0.167084 | 0.0835418 | − | 0.996504i | \(-0.473377\pi\) | ||||
0.0835418 | + | 0.996504i | \(0.473377\pi\) | |||||||
\(368\) | 11942.5 | 1.69170 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3224.75 | 0.453099 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3628.33 | 0.503667 | 0.251834 | − | 0.967771i | \(-0.418966\pi\) | ||||
0.251834 | + | 0.967771i | \(0.418966\pi\) | |||||||
\(374\) | −5145.48 | −0.711408 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −492.715 | −0.0675793 | ||||||||
\(377\) | 3494.75 | 0.477424 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7321.99 | 0.992362 | 0.496181 | − | 0.868219i | \(-0.334735\pi\) | ||||
0.496181 | + | 0.868219i | \(0.334735\pi\) | |||||||
\(380\) | −11052.6 | −1.49207 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12682.3 | 1.69865 | ||||||||
\(383\) | −7354.89 | −0.981247 | −0.490623 | − | 0.871372i | \(-0.663231\pi\) | ||||
−0.490623 | + | 0.871372i | \(0.663231\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15042.6 | 1.98355 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11694.7 | 1.53018 | ||||||||
\(389\) | 9069.62 | 1.18213 | 0.591064 | − | 0.806624i | \(-0.298708\pi\) | ||||
0.591064 | + | 0.806624i | \(0.298708\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18580.7 | 2.40324 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3451.75 | −0.441362 | ||||||||
\(395\) | −2914.03 | −0.371192 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7376.83 | 0.932575 | 0.466288 | − | 0.884633i | \(-0.345591\pi\) | ||||
0.466288 | + | 0.884633i | \(0.345591\pi\) | |||||||
\(398\) | −13779.4 | −1.73542 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1601.29 | 0.200161 | ||||||||
\(401\) | −2853.51 | −0.355356 | −0.177678 | − | 0.984089i | \(-0.556858\pi\) | ||||
−0.177678 | + | 0.984089i | \(0.556858\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1557.12 | −0.192470 | ||||||||
\(404\) | 15084.9 | 1.85767 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1085.27 | −0.132175 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11260.1 | 1.36130 | 0.680652 | − | 0.732607i | \(-0.261696\pi\) | ||||
0.680652 | + | 0.732607i | \(0.261696\pi\) | |||||||
\(410\) | −15522.3 | −1.86974 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4135.79 | 0.494553 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8825.53 | −1.04392 | ||||||||
\(416\) | 4800.56 | 0.565786 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7242.89 | 0.847515 | ||||||||
\(419\) | −9221.47 | −1.07517 | −0.537587 | − | 0.843208i | \(-0.680664\pi\) | ||||
−0.537587 | + | 0.843208i | \(0.680664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8520.28 | −0.986349 | −0.493175 | − | 0.869930i | \(-0.664164\pi\) | ||||
−0.493175 | + | 0.869930i | \(0.664164\pi\) | |||||||
\(422\) | −878.936 | −0.101388 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 66.9547 | 0.00766889 | ||||||||
\(425\) | 2491.36 | 0.284350 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2382.41 | 0.269061 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15973.7 | −1.79144 | ||||||||
\(431\) | 9162.10 | 1.02395 | 0.511976 | − | 0.859000i | \(-0.328914\pi\) | ||||
0.511976 | + | 0.859000i | \(0.328914\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10976.2 | −1.21820 | −0.609100 | − | 0.793093i | \(-0.708469\pi\) | ||||
−0.609100 | + | 0.793093i | \(0.708469\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2426.02 | −0.266480 | ||||||||
\(437\) | −26154.6 | −2.86303 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3983.18 | 0.433045 | 0.216523 | − | 0.976278i | \(-0.430528\pi\) | ||||
0.216523 | + | 0.976278i | \(0.430528\pi\) | |||||||
\(440\) | −243.063 | −0.0263354 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7051.03 | 0.758786 | ||||||||
\(443\) | 4524.45 | 0.485244 | 0.242622 | − | 0.970121i | \(-0.421993\pi\) | ||||
0.242622 | + | 0.970121i | \(0.421993\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11352.5 | −1.20935 | ||||||||
\(446\) | 9144.35 | 0.970847 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2076.49 | −0.218253 | −0.109127 | − | 0.994028i | \(-0.534805\pi\) | ||||
−0.109127 | + | 0.994028i | \(0.534805\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5223.96 | 0.545425 | ||||||||
\(452\) | 16007.4 | 1.66576 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13751.0 | 1.42151 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1847.59 | −0.189117 | −0.0945587 | − | 0.995519i | \(-0.530144\pi\) | ||||
−0.0945587 | + | 0.995519i | \(0.530144\pi\) | |||||||
\(458\) | −10494.7 | −1.07071 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16613.7 | 1.68395 | ||||||||
\(461\) | 876.945 | 0.0885974 | 0.0442987 | − | 0.999018i | \(-0.485895\pi\) | ||||
0.0442987 | + | 0.999018i | \(0.485895\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16245.2 | 1.63062 | 0.815310 | − | 0.579025i | \(-0.196566\pi\) | ||||
0.815310 | + | 0.579025i | \(0.196566\pi\) | |||||||
\(464\) | −11345.0 | −1.13508 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3870.55 | 0.384763 | ||||||||
\(467\) | −18961.8 | −1.87890 | −0.939449 | − | 0.342689i | \(-0.888662\pi\) | ||||
−0.939449 | + | 0.342689i | \(0.888662\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10954.0 | 1.07505 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −716.149 | −0.0698378 | ||||||||
\(473\) | 5375.87 | 0.522585 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3506.89 | −0.338752 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −809.067 | −0.0774181 | ||||||||
\(479\) | −8377.76 | −0.799143 | −0.399572 | − | 0.916702i | \(-0.630841\pi\) | ||||
−0.399572 | + | 0.916702i | \(0.630841\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1487.19 | 0.140977 | ||||||||
\(482\) | −19443.3 | −1.83738 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9693.55 | −0.910364 | ||||||||
\(485\) | −13735.8 | −1.28600 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4558.85 | −0.424191 | −0.212096 | − | 0.977249i | \(-0.568029\pi\) | ||||
−0.212096 | + | 0.977249i | \(0.568029\pi\) | |||||||
\(488\) | −24.3822 | −0.00226175 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15809.9 | 1.45314 | 0.726570 | − | 0.687092i | \(-0.241113\pi\) | ||||
0.726570 | + | 0.687092i | \(0.241113\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17651.1 | −1.61250 | ||||||||
\(494\) | −9925.17 | −0.903957 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5054.86 | 0.457601 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13386.1 | 1.20089 | 0.600444 | − | 0.799667i | \(-0.294990\pi\) | ||||
0.600444 | + | 0.799667i | \(0.294990\pi\) | |||||||
\(500\) | 12701.3 | 1.13604 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25345.1 | −2.25340 | ||||||||
\(503\) | 5720.55 | 0.507091 | 0.253545 | − | 0.967323i | \(-0.418403\pi\) | ||||
0.253545 | + | 0.967323i | \(0.418403\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17717.7 | −1.56124 | ||||||||
\(506\) | −10887.1 | −0.956507 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10329.1 | −0.902123 | ||||||||
\(509\) | −15293.2 | −1.33175 | −0.665873 | − | 0.746065i | \(-0.731941\pi\) | ||||
−0.665873 | + | 0.746065i | \(0.731941\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16456.0 | −1.42043 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15564.0 | 1.33560 | ||||||||
\(515\) | −4857.63 | −0.415637 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3686.53 | −0.313604 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 333.078 | 0.0280893 | ||||||||
\(521\) | 4368.69 | 0.367363 | 0.183681 | − | 0.982986i | \(-0.441199\pi\) | ||||
0.183681 | + | 0.982986i | \(0.441199\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2422.17 | −0.202512 | −0.101256 | − | 0.994860i | \(-0.532286\pi\) | ||||
−0.101256 | + | 0.994860i | \(0.532286\pi\) | |||||||
\(524\) | 10056.1 | 0.838366 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −840.291 | −0.0696548 | ||||||||
\(527\) | 7864.58 | 0.650069 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27147.2 | 2.23122 | ||||||||
\(530\) | −1488.54 | −0.121996 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7158.57 | −0.581749 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2798.23 | −0.226127 | ||||||||
\(536\) | −616.210 | −0.0496571 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19482.4 | −1.56124 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13162.5 | 1.04603 | 0.523014 | − | 0.852324i | \(-0.324807\pi\) | ||||
0.523014 | + | 0.852324i | \(0.324807\pi\) | |||||||
\(542\) | −13041.1 | −1.03351 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −24246.4 | −1.91095 | ||||||||
\(545\) | 2849.45 | 0.223958 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12112.4 | 0.946778 | 0.473389 | − | 0.880853i | \(-0.343031\pi\) | ||||
0.473389 | + | 0.880853i | \(0.343031\pi\) | |||||||
\(548\) | 903.420 | 0.0704237 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1459.78 | −0.113173 | ||||||||
\(551\) | 24846.0 | 1.92101 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8331.38 | −0.638928 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9263.63 | −0.706592 | ||||||||
\(557\) | −8359.65 | −0.635924 | −0.317962 | − | 0.948103i | \(-0.602998\pi\) | ||||
−0.317962 | + | 0.948103i | \(0.602998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7366.74 | −0.557388 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7172.42 | −0.538346 | ||||||||
\(563\) | 13638.4 | 1.02094 | 0.510471 | − | 0.859895i | \(-0.329471\pi\) | ||||
0.510471 | + | 0.859895i | \(0.329471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18801.3 | −1.39996 | ||||||||
\(566\) | −9491.76 | −0.704891 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 382.080 | 0.0282249 | ||||||||
\(569\) | 15491.3 | 1.14135 | 0.570677 | − | 0.821175i | \(-0.306681\pi\) | ||||
0.570677 | + | 0.821175i | \(0.306681\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4648.15 | −0.340664 | −0.170332 | − | 0.985387i | \(-0.554484\pi\) | ||||
−0.170332 | + | 0.985387i | \(0.554484\pi\) | |||||||
\(572\) | −2121.78 | −0.155098 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5271.38 | 0.382316 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5479.06 | −0.395314 | −0.197657 | − | 0.980271i | \(-0.563333\pi\) | ||||
−0.197657 | + | 0.980271i | \(0.563333\pi\) | |||||||
\(578\) | −15688.7 | −1.12901 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15782.5 | −1.12988 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 500.960 | 0.0355877 | ||||||||
\(584\) | −879.692 | −0.0623321 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14735.2 | 1.03874 | ||||||||
\(587\) | 4408.22 | 0.309960 | 0.154980 | − | 0.987918i | \(-0.450469\pi\) | ||||
0.154980 | + | 0.987918i | \(0.450469\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11070.3 | −0.774441 | ||||||||
\(590\) | 15921.4 | 1.11097 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4827.86 | −0.335175 | ||||||||
\(593\) | 2815.26 | 0.194956 | 0.0974779 | − | 0.995238i | \(-0.468922\pi\) | ||||
0.0974779 | + | 0.995238i | \(0.468922\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6053.09 | 0.416014 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14919.0 | 1.02021 | ||||||||
\(599\) | 19719.1 | 1.34507 | 0.672537 | − | 0.740064i | \(-0.265205\pi\) | ||||
0.672537 | + | 0.740064i | \(0.265205\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13982.8 | −0.949033 | −0.474517 | − | 0.880247i | \(-0.657377\pi\) | ||||
−0.474517 | + | 0.880247i | \(0.657377\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1303.83 | 0.0878343 | ||||||||
\(605\) | 11385.4 | 0.765097 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13388.3 | 0.895245 | 0.447622 | − | 0.894223i | \(-0.352271\pi\) | ||||
0.447622 | + | 0.894223i | \(0.352271\pi\) | |||||||
\(608\) | 34129.7 | 2.27655 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 542.065 | 0.0359797 | ||||||||
\(611\) | 5051.77 | 0.334489 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27791.9 | −1.83116 | −0.915582 | − | 0.402131i | \(-0.868269\pi\) | ||||
−0.915582 | + | 0.402131i | \(0.868269\pi\) | |||||||
\(614\) | −24147.1 | −1.58713 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19107.2 | −1.24672 | −0.623361 | − | 0.781935i | \(-0.714233\pi\) | ||||
−0.623361 | + | 0.781935i | \(0.714233\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1092.94 | 0.0709675 | 0.0354837 | − | 0.999370i | \(-0.488703\pi\) | ||||
0.0354837 | + | 0.999370i | \(0.488703\pi\) | |||||||
\(620\) | 7032.02 | 0.455504 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4785.75 | −0.308507 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11595.0 | −0.742078 | ||||||||
\(626\) | 39524.9 | 2.52353 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17684.3 | −1.12369 | ||||||||
\(629\) | −7511.40 | −0.476151 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19235.2 | 1.21353 | 0.606767 | − | 0.794879i | \(-0.292466\pi\) | ||||
0.606767 | + | 0.794879i | \(0.292466\pi\) | |||||||
\(632\) | −531.556 | −0.0334560 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −34843.6 | −2.18267 | ||||||||
\(635\) | 12131.9 | 0.758171 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10342.4 | 0.641788 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2294.28 | −0.141702 | ||||||||
\(641\) | −19950.7 | −1.22933 | −0.614667 | − | 0.788787i | \(-0.710710\pi\) | ||||
−0.614667 | + | 0.788787i | \(0.710710\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 688.125 | 0.0422037 | 0.0211019 | − | 0.999777i | \(-0.493283\pi\) | ||||
0.0211019 | + | 0.999777i | \(0.493283\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 50129.4 | 3.05312 | ||||||||
\(647\) | 10966.2 | 0.666345 | 0.333173 | − | 0.942866i | \(-0.391881\pi\) | ||||
0.333173 | + | 0.942866i | \(0.391881\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5358.28 | −0.324085 | ||||||||
\(650\) | 2000.39 | 0.120710 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 25405.0 | 1.52598 | ||||||||
\(653\) | −12925.1 | −0.774575 | −0.387287 | − | 0.921959i | \(-0.626588\pi\) | ||||
−0.387287 | + | 0.921959i | \(0.626588\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11811.3 | −0.704588 | ||||||||
\(656\) | 23238.9 | 1.38312 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11779.0 | −0.696273 | −0.348137 | − | 0.937444i | \(-0.613185\pi\) | ||||
−0.348137 | + | 0.937444i | \(0.613185\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25040.1 | −1.47344 | −0.736721 | − | 0.676196i | \(-0.763627\pi\) | ||||
−0.736721 | + | 0.676196i | \(0.763627\pi\) | |||||||
\(662\) | 21295.7 | 1.25027 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1609.89 | −0.0940900 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37347.2 | −2.16805 | ||||||||
\(668\) | −18838.7 | −1.09116 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13699.6 | 0.789941 | ||||||||
\(671\) | −182.430 | −0.0104957 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4104.64 | 0.235100 | 0.117550 | − | 0.993067i | \(-0.462496\pi\) | ||||
0.117550 | + | 0.993067i | \(0.462496\pi\) | |||||||
\(674\) | 34456.5 | 1.96916 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15648.8 | −0.890350 | ||||||||
\(677\) | 12153.4 | 0.689945 | 0.344973 | − | 0.938613i | \(-0.387888\pi\) | ||||
0.344973 | + | 0.938613i | \(0.387888\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1682.29 | −0.0948717 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4608.16 | −0.258733 | ||||||||
\(683\) | −20414.0 | −1.14366 | −0.571830 | − | 0.820372i | \(-0.693766\pi\) | ||||
−0.571830 | + | 0.820372i | \(0.693766\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1061.10 | −0.0591862 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 23914.6 | 1.32520 | ||||||||
\(689\) | −686.483 | −0.0379578 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16093.5 | 0.886001 | 0.443000 | − | 0.896521i | \(-0.353914\pi\) | ||||
0.443000 | + | 0.896521i | \(0.353914\pi\) | |||||||
\(692\) | −4756.66 | −0.261302 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23643.6 | 1.29322 | ||||||||
\(695\) | 10880.5 | 0.593841 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36156.1 | 1.96486 | ||||||||
\(698\) | −7344.83 | −0.398290 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20803.0 | 1.12085 | 0.560426 | − | 0.828204i | \(-0.310637\pi\) | ||||
0.560426 | + | 0.828204i | \(0.310637\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10573.2 | 0.567248 | ||||||||
\(704\) | 7682.84 | 0.411304 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13495.4 | −0.719412 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 141.492 | 0.00749484 | 0.00374742 | − | 0.999993i | \(-0.498807\pi\) | ||||
0.00374742 | + | 0.999993i | \(0.498807\pi\) | |||||||
\(710\) | −8494.40 | −0.448999 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2070.85 | −0.109000 | ||||||||
\(713\) | 16640.4 | 0.874035 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2492.11 | 0.130349 | ||||||||
\(716\) | 15536.8 | 0.810947 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3531.68 | 0.183567 | ||||||||
\(719\) | −6664.46 | −0.345678 | −0.172839 | − | 0.984950i | \(-0.555294\pi\) | ||||
−0.172839 | + | 0.984950i | \(0.555294\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −42747.2 | −2.20345 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19635.0 | 1.00791 | ||||||||
\(725\) | −5007.64 | −0.256523 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4837.23 | −0.246772 | −0.123386 | − | 0.992359i | \(-0.539375\pi\) | ||||
−0.123386 | + | 0.992359i | \(0.539375\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 19557.3 | 0.991572 | ||||||||
\(731\) | 37207.5 | 1.88258 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31602.5 | −1.59245 | −0.796225 | − | 0.605001i | \(-0.793173\pi\) | ||||
−0.796225 | + | 0.605001i | \(0.793173\pi\) | |||||||
\(734\) | −4763.93 | −0.239564 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −51302.0 | −2.56932 | ||||||||
\(737\) | −4610.53 | −0.230436 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8227.58 | −0.409549 | −0.204774 | − | 0.978809i | \(-0.565646\pi\) | ||||
−0.204774 | + | 0.978809i | \(0.565646\pi\) | |||||||
\(740\) | −6716.22 | −0.333639 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37020.3 | 1.82792 | 0.913959 | − | 0.405805i | \(-0.133009\pi\) | ||||
0.913959 | + | 0.405805i | \(0.133009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7109.57 | −0.349630 | ||||||||
\(746\) | −14714.3 | −0.722158 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10716.6 | 0.523846 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25149.9 | −1.22202 | −0.611008 | − | 0.791625i | \(-0.709236\pi\) | ||||
−0.611008 | + | 0.791625i | \(0.709236\pi\) | |||||||
\(752\) | −16399.6 | −0.795254 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −14172.6 | −0.684529 | ||||||||
\(755\) | −1531.39 | −0.0738186 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20460.8 | 0.982377 | 0.491189 | − | 0.871053i | \(-0.336563\pi\) | ||||
0.491189 | + | 0.871053i | \(0.336563\pi\) | |||||||
\(758\) | −29693.6 | −1.42285 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2368.02 | 0.113023 | ||||||||
\(761\) | 32659.1 | 1.55571 | 0.777853 | − | 0.628447i | \(-0.216309\pi\) | ||||
0.777853 | + | 0.628447i | \(0.216309\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −26413.7 | −1.25080 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29827.0 | 1.40691 | ||||||||
\(767\) | 7342.64 | 0.345668 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11005.3 | −0.516075 | −0.258037 | − | 0.966135i | \(-0.583076\pi\) | ||||
−0.258037 | + | 0.966135i | \(0.583076\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −31329.5 | −1.46059 | ||||||||
\(773\) | −3038.18 | −0.141366 | −0.0706829 | − | 0.997499i | \(-0.522518\pi\) | ||||
−0.0706829 | + | 0.997499i | \(0.522518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2231.20 | 0.103415 | ||||||||
\(776\) | −2505.59 | −0.115909 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36780.9 | −1.69493 | ||||||||
\(779\) | −50894.0 | −2.34078 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2858.75 | 0.130979 | ||||||||
\(782\) | −75352.0 | −3.44576 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20770.8 | 0.944384 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12306.8 | −0.557419 | −0.278710 | − | 0.960375i | \(-0.589907\pi\) | ||||
−0.278710 | + | 0.960375i | \(0.589907\pi\) | |||||||
\(788\) | 7189.00 | 0.324997 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11817.5 | 0.532214 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 249.990 | 0.0111947 | ||||||||
\(794\) | −29915.9 | −1.33712 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28698.4 | 1.27788 | ||||||||
\(797\) | 3007.06 | 0.133646 | 0.0668228 | − | 0.997765i | \(-0.478714\pi\) | ||||
0.0668228 | + | 0.997765i | \(0.478714\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25515.2 | −1.12974 | ||||||||
\(800\) | −6878.74 | −0.304000 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11572.1 | 0.509508 | ||||||||
\(803\) | −6581.92 | −0.289254 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6314.72 | 0.275963 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3231.94 | −0.140717 | ||||||||
\(809\) | −10585.0 | −0.460009 | −0.230005 | − | 0.973190i | \(-0.573874\pi\) | ||||
−0.230005 | + | 0.973190i | \(0.573874\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18217.8 | −0.788796 | −0.394398 | − | 0.918940i | \(-0.629047\pi\) | ||||
−0.394398 | + | 0.918940i | \(0.629047\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4401.22 | 0.189512 | ||||||||
\(815\) | −29839.1 | −1.28248 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −52374.0 | −2.24276 | ||||||||
\(818\) | −45663.9 | −1.95184 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 32328.5 | 1.37678 | ||||||||
\(821\) | −25596.5 | −1.08809 | −0.544047 | − | 0.839055i | \(-0.683109\pi\) | ||||
−0.544047 | + | 0.839055i | \(0.683109\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43778.9 | 1.85424 | 0.927118 | − | 0.374769i | \(-0.122278\pi\) | ||||
0.927118 | + | 0.374769i | \(0.122278\pi\) | |||||||
\(824\) | −886.094 | −0.0374618 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2735.78 | 0.115033 | 0.0575166 | − | 0.998345i | \(-0.481682\pi\) | ||||
0.0575166 | + | 0.998345i | \(0.481682\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31144.2 | −1.30480 | −0.652402 | − | 0.757873i | \(-0.726239\pi\) | ||||
−0.652402 | + | 0.757873i | \(0.726239\pi\) | |||||||
\(830\) | 35791.0 | 1.49677 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10528.1 | −0.438696 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22126.8 | 0.917039 | ||||||||
\(836\) | −15084.9 | −0.624068 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 37396.7 | 1.54158 | ||||||||
\(839\) | −14977.3 | −0.616300 | −0.308150 | − | 0.951338i | \(-0.599710\pi\) | ||||
−0.308150 | + | 0.951338i | \(0.599710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11089.6 | 0.454698 | ||||||||
\(842\) | 34553.1 | 1.41423 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1830.57 | 0.0746574 | ||||||||
\(845\) | 18380.1 | 0.748277 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2228.53 | 0.0902452 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10103.4 | −0.407700 | ||||||||
\(851\) | −15893.1 | −0.640198 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42861.7 | 1.72047 | 0.860233 | − | 0.509901i | \(-0.170318\pi\) | ||||
0.860233 | + | 0.509901i | \(0.170318\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −510.432 | −0.0203811 | ||||||||
\(857\) | −9390.00 | −0.374278 | −0.187139 | − | 0.982333i | \(-0.559921\pi\) | ||||
−0.187139 | + | 0.982333i | \(0.559921\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33561.2 | 1.33305 | 0.666526 | − | 0.745482i | \(-0.267781\pi\) | ||||
0.666526 | + | 0.745482i | \(0.267781\pi\) | |||||||
\(860\) | 33268.6 | 1.31913 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37155.9 | −1.46814 | ||||||||
\(863\) | 25691.6 | 1.01339 | 0.506693 | − | 0.862127i | \(-0.330868\pi\) | ||||
0.506693 | + | 0.862127i | \(0.330868\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5586.87 | 0.219606 | ||||||||
\(866\) | 44512.7 | 1.74665 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3977.14 | −0.155254 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6317.97 | 0.245782 | ||||||||
\(872\) | 519.775 | 0.0201856 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 106067. | 4.10500 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5351.52 | −0.206052 | −0.103026 | − | 0.994679i | \(-0.532853\pi\) | ||||
−0.103026 | + | 0.994679i | \(0.532853\pi\) | |||||||
\(878\) | −16153.4 | −0.620900 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8090.14 | −0.309907 | ||||||||
\(881\) | −34212.7 | −1.30835 | −0.654174 | − | 0.756344i | \(-0.726984\pi\) | ||||
−0.654174 | + | 0.756344i | \(0.726984\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17149.2 | 0.653587 | 0.326794 | − | 0.945096i | \(-0.394032\pi\) | ||||
0.326794 | + | 0.945096i | \(0.394032\pi\) | |||||||
\(884\) | −14685.3 | −0.558732 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18348.4 | −0.695742 | ||||||||
\(887\) | 4020.87 | 0.152207 | 0.0761035 | − | 0.997100i | \(-0.475752\pi\) | ||||
0.0761035 | + | 0.997100i | \(0.475752\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 46039.0 | 1.73397 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19045.1 | −0.714883 | ||||||||
\(893\) | 35915.7 | 1.34588 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18248.5 | −0.681544 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8420.99 | 0.312931 | ||||||||
\(899\) | −15807.8 | −0.586452 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3467.24 | 0.128203 | ||||||||
\(902\) | −21185.2 | −0.782030 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3429.59 | −0.126180 | ||||||||
\(905\) | −23062.0 | −0.847080 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22967.2 | −0.840810 | −0.420405 | − | 0.907337i | \(-0.638112\pi\) | ||||
−0.420405 | + | 0.907337i | \(0.638112\pi\) | |||||||
\(908\) | −28639.4 | −1.04673 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9860.77 | 0.358619 | 0.179309 | − | 0.983793i | \(-0.442614\pi\) | ||||
0.179309 | + | 0.983793i | \(0.442614\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12045.3 | −0.436628 | ||||||||
\(914\) | 7492.71 | 0.271156 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21857.5 | 0.788421 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5271.55 | −0.189219 | −0.0946096 | − | 0.995514i | \(-0.530160\pi\) | ||||
−0.0946096 | + | 0.995514i | \(0.530160\pi\) | |||||||
\(920\) | −3559.49 | −0.127558 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3556.36 | −0.127031 | ||||||||
\(923\) | −3917.44 | −0.139701 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2131.00 | −0.0757478 | ||||||||
\(926\) | −65880.6 | −2.33798 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 48735.3 | 1.72394 | ||||||||
\(929\) | −14902.6 | −0.526307 | −0.263153 | − | 0.964754i | \(-0.584762\pi\) | ||||
−0.263153 | + | 0.964754i | \(0.584762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8061.24 | −0.283321 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 76897.4 | 2.69396 | ||||||||
\(935\) | −12587.0 | −0.440255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21934.8 | −0.764757 | −0.382378 | − | 0.924006i | \(-0.624895\pi\) | ||||
−0.382378 | + | 0.924006i | \(0.624895\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −22814.1 | −0.791610 | ||||||||
\(941\) | 14521.5 | 0.503069 | 0.251535 | − | 0.967848i | \(-0.419065\pi\) | ||||
0.251535 | + | 0.967848i | \(0.419065\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 76501.3 | 2.64181 | ||||||||
\(944\) | −23836.4 | −0.821831 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21801.3 | −0.749282 | ||||||||
\(947\) | 1943.73 | 0.0666979 | 0.0333489 | − | 0.999444i | \(-0.489383\pi\) | ||||
0.0333489 | + | 0.999444i | \(0.489383\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9019.43 | 0.308517 | ||||||||
\(950\) | 14221.8 | 0.485702 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16904.1 | −0.574583 | −0.287292 | − | 0.957843i | \(-0.592755\pi\) | ||||
−0.287292 | + | 0.957843i | \(0.592755\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31023.8 | 1.05121 | ||||||||
\(956\) | 1685.05 | 0.0570068 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33975.1 | 1.14581 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22747.7 | −0.763576 | ||||||||
\(962\) | −6031.13 | −0.202133 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 40494.8 | 1.35296 | ||||||||
\(965\) | 36797.6 | 1.22752 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26699.3 | 0.887891 | 0.443946 | − | 0.896054i | \(-0.353578\pi\) | ||||
0.443946 | + | 0.896054i | \(0.353578\pi\) | |||||||
\(968\) | 2076.85 | 0.0689591 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 55704.2 | 1.84387 | ||||||||
\(971\) | 11089.5 | 0.366507 | 0.183253 | − | 0.983066i | \(-0.441337\pi\) | ||||
0.183253 | + | 0.983066i | \(0.441337\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 18487.9 | 0.608205 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −811.541 | −0.0266156 | ||||||||
\(977\) | 51891.9 | 1.69925 | 0.849625 | − | 0.527387i | \(-0.176828\pi\) | ||||
0.849625 | + | 0.527387i | \(0.176828\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15494.2 | −0.505820 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −64115.5 | −2.08351 | ||||||||
\(983\) | 24560.7 | 0.796911 | 0.398456 | − | 0.917188i | \(-0.369546\pi\) | ||||
0.398456 | + | 0.917188i | \(0.369546\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8443.74 | −0.273137 | ||||||||
\(986\) | 71582.0 | 2.31200 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20671.3 | 0.665629 | ||||||||
\(989\) | 78725.9 | 2.53118 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18507.5 | −0.593250 | −0.296625 | − | 0.954994i | \(-0.595861\pi\) | ||||
−0.296625 | + | 0.954994i | \(0.595861\pi\) | |||||||
\(992\) | −21714.4 | −0.694993 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33707.4 | −1.07397 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42966.2 | −1.36485 | −0.682424 | − | 0.730957i | \(-0.739074\pi\) | ||||
−0.682424 | + | 0.730957i | \(0.739074\pi\) | |||||||
\(998\) | −54285.8 | −1.72183 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.4.a.w.1.1 | 4 | ||
3.2 | odd | 2 | inner | 441.4.a.w.1.4 | 4 | ||
7.2 | even | 3 | 63.4.e.d.46.4 | yes | 8 | ||
7.3 | odd | 6 | 441.4.e.x.226.4 | 8 | |||
7.4 | even | 3 | 63.4.e.d.37.4 | yes | 8 | ||
7.5 | odd | 6 | 441.4.e.x.361.4 | 8 | |||
7.6 | odd | 2 | 441.4.a.v.1.1 | 4 | |||
21.2 | odd | 6 | 63.4.e.d.46.1 | yes | 8 | ||
21.5 | even | 6 | 441.4.e.x.361.1 | 8 | |||
21.11 | odd | 6 | 63.4.e.d.37.1 | ✓ | 8 | ||
21.17 | even | 6 | 441.4.e.x.226.1 | 8 | |||
21.20 | even | 2 | 441.4.a.v.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.e.d.37.1 | ✓ | 8 | 21.11 | odd | 6 | ||
63.4.e.d.37.4 | yes | 8 | 7.4 | even | 3 | ||
63.4.e.d.46.1 | yes | 8 | 21.2 | odd | 6 | ||
63.4.e.d.46.4 | yes | 8 | 7.2 | even | 3 | ||
441.4.a.v.1.1 | 4 | 7.6 | odd | 2 | |||
441.4.a.v.1.4 | 4 | 21.20 | even | 2 | |||
441.4.a.w.1.1 | 4 | 1.1 | even | 1 | trivial | ||
441.4.a.w.1.4 | 4 | 3.2 | odd | 2 | inner | ||
441.4.e.x.226.1 | 8 | 21.17 | even | 6 | |||
441.4.e.x.226.4 | 8 | 7.3 | odd | 6 | |||
441.4.e.x.361.1 | 8 | 21.5 | even | 6 | |||
441.4.e.x.361.4 | 8 | 7.5 | odd | 6 |