Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,4,Mod(1,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, 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("124.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.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: | \(7.31623684071\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.841724.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 16x^{2} + 11x + 7 \) |
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 | 1.4 | ||
Root | \(-3.81863\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 124.1 |
$q$-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 | ||||||||
\(3\) | 4.12869 | 0.794567 | 0.397284 | − | 0.917696i | \(-0.369953\pi\) | ||||
0.397284 | + | 0.917696i | \(0.369953\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.8920 | −0.974210 | −0.487105 | − | 0.873343i | \(-0.661947\pi\) | ||||
−0.487105 | + | 0.873343i | \(0.661947\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −29.9908 | −1.61935 | −0.809676 | − | 0.586878i | \(-0.800357\pi\) | ||||
−0.809676 | + | 0.586878i | \(0.800357\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.95389 | −0.368663 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.75411 | 0.130311 | 0.0651554 | − | 0.997875i | \(-0.479246\pi\) | ||||
0.0651554 | + | 0.997875i | \(0.479246\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −75.3498 | −1.60756 | −0.803780 | − | 0.594927i | \(-0.797181\pi\) | ||||
−0.803780 | + | 0.594927i | \(0.797181\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −44.9697 | −0.774076 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 111.675 | 1.59325 | 0.796625 | − | 0.604473i | \(-0.206616\pi\) | ||||
0.796625 | + | 0.604473i | \(0.206616\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 90.8213 | 1.09662 | 0.548311 | − | 0.836274i | \(-0.315271\pi\) | ||||
0.548311 | + | 0.836274i | \(0.315271\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −123.823 | −1.28668 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −42.3266 | −0.383727 | −0.191863 | − | 0.981422i | \(-0.561453\pi\) | ||||
−0.191863 | + | 0.981422i | \(0.561453\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.36432 | −0.0509145 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −152.571 | −1.08749 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −202.535 | −1.29689 | −0.648446 | − | 0.761261i | \(-0.724581\pi\) | ||||
−0.648446 | + | 0.761261i | \(0.724581\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −31.0000 | −0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 19.6283 | 0.103541 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 326.660 | 1.57759 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 334.906 | 1.48806 | 0.744030 | − | 0.668147i | \(-0.232912\pi\) | ||||
0.744030 | + | 0.668147i | \(0.232912\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −311.096 | −1.27731 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −367.314 | −1.39914 | −0.699571 | − | 0.714563i | \(-0.746626\pi\) | ||||
−0.699571 | + | 0.714563i | \(0.746626\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 82.6879 | 0.293251 | 0.146625 | − | 0.989192i | \(-0.453159\pi\) | ||||
0.146625 | + | 0.989192i | \(0.453159\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 108.418 | 0.359155 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −276.578 | −0.858363 | −0.429182 | − | 0.903218i | \(-0.641198\pi\) | ||||
−0.429182 | + | 0.903218i | \(0.641198\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 556.448 | 1.62230 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 461.073 | 1.26594 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 581.851 | 1.50799 | 0.753994 | − | 0.656882i | \(-0.228125\pi\) | ||||
0.753994 | + | 0.656882i | \(0.228125\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −51.7818 | −0.126950 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 374.973 | 0.871341 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −630.494 | −1.39124 | −0.695621 | − | 0.718409i | \(-0.744871\pi\) | ||||
−0.695621 | + | 0.718409i | \(0.744871\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 527.474 | 1.10715 | 0.553574 | − | 0.832800i | \(-0.313263\pi\) | ||||
0.553574 | + | 0.832800i | \(0.313263\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 298.525 | 0.596994 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 820.710 | 1.56610 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −684.749 | −1.24859 | −0.624294 | − | 0.781189i | \(-0.714613\pi\) | ||||
−0.624294 | + | 0.781189i | \(0.714613\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −174.754 | −0.304897 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −230.564 | −0.385393 | −0.192696 | − | 0.981258i | \(-0.561723\pi\) | ||||
−0.192696 | + | 0.981258i | \(0.561723\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 802.656 | 1.28690 | 0.643451 | − | 0.765488i | \(-0.277502\pi\) | ||||
0.643451 | + | 0.765488i | \(0.277502\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −26.2763 | −0.0404550 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −142.580 | −0.211019 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −455.003 | −0.647998 | −0.323999 | − | 0.946057i | \(-0.605027\pi\) | ||||
−0.323999 | + | 0.946057i | \(0.605027\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −361.165 | −0.495425 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −214.005 | −0.283013 | −0.141507 | − | 0.989937i | \(-0.545195\pi\) | ||||
−0.141507 | + | 0.989937i | \(0.545195\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1216.37 | −1.55216 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −836.206 | −1.03047 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −340.002 | −0.404946 | −0.202473 | − | 0.979288i | \(-0.564898\pi\) | ||||
−0.202473 | + | 0.979288i | \(0.564898\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2259.80 | 2.60320 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −127.989 | −0.142709 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −989.226 | −1.06834 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −995.113 | −1.04163 | −0.520817 | − | 0.853669i | \(-0.674373\pi\) | ||||
−0.520817 | + | 0.853669i | \(0.674373\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −47.3219 | −0.0480407 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −585.825 | −0.577146 | −0.288573 | − | 0.957458i | \(-0.593181\pi\) | ||||
−0.288573 | + | 0.957458i | \(0.593181\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 492.440 | 0.471083 | 0.235542 | − | 0.971864i | \(-0.424314\pi\) | ||||
0.235542 | + | 0.971864i | \(0.424314\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1348.68 | 1.25350 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1883.39 | −1.70163 | −0.850813 | − | 0.525469i | \(-0.823890\pi\) | ||||
−0.850813 | + | 0.525469i | \(0.823890\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1176.96 | −1.03424 | −0.517122 | − | 0.855912i | \(-0.672997\pi\) | ||||
−0.517122 | + | 0.855912i | \(0.672997\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1382.72 | 1.18236 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1946.32 | 1.62031 | 0.810154 | − | 0.586218i | \(-0.199384\pi\) | ||||
0.810154 | + | 0.586218i | \(0.199384\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 461.022 | 0.373831 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 750.024 | 0.592647 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3349.23 | −2.58003 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1308.40 | −0.983019 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1516.53 | −1.11171 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1430.82 | 1.02381 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 487.162 | 0.340383 | 0.170191 | − | 0.985411i | \(-0.445561\pi\) | ||||
0.170191 | + | 0.985411i | \(0.445561\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 341.393 | 0.233008 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −453.362 | −0.302370 | −0.151185 | − | 0.988506i | \(-0.548309\pi\) | ||||
−0.151185 | + | 0.988506i | \(0.548309\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2723.80 | −1.77582 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1661.81 | 1.05945 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −869.263 | −0.542089 | −0.271044 | − | 0.962567i | \(-0.587369\pi\) | ||||
−0.271044 | + | 0.962567i | \(0.587369\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −291.016 | −0.177580 | −0.0887900 | − | 0.996050i | \(-0.528300\pi\) | ||||
−0.0887900 | + | 0.996050i | \(0.528300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1141.91 | −0.682027 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −358.221 | −0.209482 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2206.01 | 1.26344 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2297.41 | 1.28903 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 815.345 | 0.448293 | 0.224147 | − | 0.974555i | \(-0.428041\pi\) | ||||
0.224147 | + | 0.974555i | \(0.428041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2288.65 | 1.23343 | 0.616715 | − | 0.787187i | \(-0.288463\pi\) | ||||
0.616715 | + | 0.787187i | \(0.288463\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1111.60 | −0.587372 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 337.652 | 0.174973 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 851.521 | 0.432858 | 0.216429 | − | 0.976298i | \(-0.430559\pi\) | ||||
0.216429 | + | 0.976298i | \(0.430559\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2402.28 | 1.19820 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1269.41 | 0.621388 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2400.93 | −1.15371 | −0.576857 | − | 0.816845i | \(-0.695721\pi\) | ||||
−0.576857 | + | 0.816845i | \(0.695721\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −213.791 | −0.100870 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −820.836 | −0.380349 | −0.190174 | − | 0.981750i | \(-0.560905\pi\) | ||||
−0.190174 | + | 0.981750i | \(0.560905\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3480.59 | 1.58425 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −904.025 | −0.404284 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −744.786 | −0.327312 | −0.163656 | − | 0.986517i | \(-0.552329\pi\) | ||||
−0.163656 | + | 0.986517i | \(0.552329\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 190.871 | 0.0824485 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2603.12 | −1.10544 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.4598 | 0.00520275 | 0.00260137 | − | 0.999997i | \(-0.499172\pi\) | ||||
0.00260137 | + | 0.999997i | \(0.499172\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −806.271 | −0.331103 | −0.165552 | − | 0.986201i | \(-0.552940\pi\) | ||||
−0.165552 | + | 0.986201i | \(0.552940\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2177.78 | 0.879704 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3647.80 | −1.44968 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 530.917 | 0.207618 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4575.74 | 1.76104 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2065.90 | −0.782633 | −0.391317 | − | 0.920256i | \(-0.627980\pi\) | ||||
−0.391317 | + | 0.920256i | \(0.627980\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −32.4222 | −0.0120922 | −0.00604611 | − | 0.999982i | \(-0.501925\pi\) | ||||
−0.00604611 | + | 0.999982i | \(0.501925\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3388.46 | 1.24437 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −776.177 | −0.280712 | −0.140356 | − | 0.990101i | \(-0.544825\pi\) | ||||
−0.140356 | + | 0.990101i | \(0.544825\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1682.12 | 0.599208 | 0.299604 | − | 0.954064i | \(-0.403146\pi\) | ||||
0.299604 | + | 0.954064i | \(0.403146\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2827.12 | −0.992088 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6074.19 | 2.10012 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4000.79 | 1.36306 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 421.315 | 0.141466 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 431.775 | 0.142902 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1826.70 | 0.595996 | 0.297998 | − | 0.954566i | \(-0.403681\pi\) | ||||
0.297998 | + | 0.954566i | \(0.403681\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −951.927 | −0.306220 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −900.637 | −0.285688 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 929.715 | 0.290844 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3313.92 | 1.02253 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8414.72 | −2.56125 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6174.56 | 1.85417 | 0.927083 | − | 0.374856i | \(-0.122308\pi\) | ||||
0.927083 | + | 0.374856i | \(0.122308\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 63.3497 | 0.0187703 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4255.39 | −1.24423 | −0.622115 | − | 0.782926i | \(-0.713726\pi\) | ||||
−0.622115 | + | 0.782926i | \(0.713726\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3459.92 | −0.998420 | −0.499210 | − | 0.866481i | \(-0.666376\pi\) | ||||
−0.499210 | + | 0.866481i | \(0.666376\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −588.668 | −0.167669 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2248.39 | −0.632177 | −0.316088 | − | 0.948730i | \(-0.602370\pi\) | ||||
−0.316088 | + | 0.948730i | \(0.602370\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3012.49 | 0.836226 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1878.57 | −0.514878 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3876.19 | −1.04908 | −0.524540 | − | 0.851386i | \(-0.675763\pi\) | ||||
−0.524540 | + | 0.851386i | \(0.675763\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2935.28 | 0.784556 | 0.392278 | − | 0.919847i | \(-0.371687\pi\) | ||||
0.392278 | + | 0.919847i | \(0.371687\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2628.28 | 0.693846 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6060.84 | −1.58046 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6843.37 | −1.76289 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −883.561 | −0.224873 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3810.36 | −0.958199 | −0.479099 | − | 0.877761i | \(-0.659037\pi\) | ||||
−0.479099 | + | 0.877761i | \(0.659037\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −201.226 | −0.0500038 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5022.01 | −1.23330 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5898.77 | 1.43173 | 0.715866 | − | 0.698238i | \(-0.246032\pi\) | ||||
0.715866 | + | 0.698238i | \(0.246032\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10044.1 | −2.40969 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2016.01 | 0.478115 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4054.69 | −0.950657 | −0.475328 | − | 0.879808i | \(-0.657671\pi\) | ||||
−0.475328 | + | 0.879808i | \(0.657671\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6337.52 | −1.46910 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1403.77 | −0.321757 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3047.31 | −0.690697 | −0.345349 | − | 0.938474i | \(-0.612239\pi\) | ||||
−0.345349 | + | 0.938474i | \(0.612239\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1252.70 | 0.280798 | 0.140399 | − | 0.990095i | \(-0.455162\pi\) | ||||
0.140399 | + | 0.990095i | \(0.455162\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9330.03 | 2.06842 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −30.2567 | −0.00663472 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −813.610 | −0.176480 | −0.0882402 | − | 0.996099i | \(-0.528124\pi\) | ||||
−0.0882402 | + | 0.996099i | \(0.528124\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 308.571 | 0.0662138 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5237.25 | 1.11184 | 0.555922 | − | 0.831234i | \(-0.312365\pi\) | ||||
0.555922 | + | 0.831234i | \(0.312365\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1857.01 | 0.390062 | 0.195031 | − | 0.980797i | \(-0.437519\pi\) | ||||
0.195031 | + | 0.980797i | \(0.437519\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4084.21 | −0.848869 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11016.0 | 2.26570 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7558.39 | 1.53845 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4108.52 | −0.827648 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1879.24 | 0.374698 | 0.187349 | − | 0.982293i | \(-0.440011\pi\) | ||||
0.187349 | + | 0.982293i | \(0.440011\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6867.34 | 1.35536 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −725.341 | −0.141712 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3189.30 | 0.616864 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2479.88 | −0.474876 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2418.69 | −0.458582 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5745.24 | −1.07860 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10205.3 | −1.89723 | −0.948613 | − | 0.316439i | \(-0.897513\pi\) | ||||
−0.948613 | + | 0.316439i | \(0.897513\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2033.13 | 0.374307 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 679.582 | 0.123909 | 0.0619543 | − | 0.998079i | \(-0.480267\pi\) | ||||
0.0619543 | + | 0.998079i | \(0.480267\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −506.236 | −0.0914190 | −0.0457095 | − | 0.998955i | \(-0.514555\pi\) | ||||
−0.0457095 | + | 0.998955i | \(0.514555\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3251.54 | −0.581598 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 104.454 | 0.0185070 | 0.00925352 | − | 0.999957i | \(-0.497054\pi\) | ||||
0.00925352 | + | 0.999957i | \(0.497054\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −962.875 | −0.168999 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7775.93 | −1.35206 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10142.5 | 1.74720 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 479.550 | 0.0818482 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4859.32 | −0.821777 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8294.80 | 1.38999 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8147.05 | 1.35288 | 0.676439 | − | 0.736499i | \(-0.263522\pi\) | ||||
0.676439 | + | 0.736499i | \(0.263522\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3333.62 | −0.548592 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7458.29 | 1.21639 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1397.48 | 0.225893 | 0.112946 | − | 0.993601i | \(-0.463971\pi\) | ||||
0.112946 | + | 0.993601i | \(0.463971\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8035.77 | 1.28744 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −147.378 | −0.0234045 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6401.49 | −1.00772 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1903.42 | 0.297034 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7205.65 | 1.11475 | 0.557377 | − | 0.830260i | \(-0.311808\pi\) | ||||
0.557377 | + | 0.830260i | \(0.311808\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10772.5 | −1.65227 | −0.826134 | − | 0.563474i | \(-0.809464\pi\) | ||||
−0.826134 | + | 0.563474i | \(0.809464\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11496.2 | 1.74821 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10072.5 | 1.51871 | 0.759356 | − | 0.650675i | \(-0.225514\pi\) | ||||
0.759356 | + | 0.650675i | \(0.225514\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2511.30 | 0.375453 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −13828.0 | −2.05001 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9359.95 | −1.37604 | −0.688021 | − | 0.725691i | \(-0.741520\pi\) | ||||
−0.688021 | + | 0.725691i | \(0.741520\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1389.51 | 0.202582 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5401.98 | −0.781075 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8742.53 | −1.25371 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12168.9 | 1.73083 | 0.865413 | − | 0.501060i | \(-0.167056\pi\) | ||||
0.865413 | + | 0.501060i | \(0.167056\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3656.21 | 0.515812 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17450.2 | −2.44196 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10713.1 | 1.48715 | 0.743573 | − | 0.668655i | \(-0.233130\pi\) | ||||
0.743573 | + | 0.668655i | \(0.233130\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5907.42 | 0.813487 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15261.0 | 2.08483 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11273.6 | −1.52793 | −0.763964 | − | 0.645259i | \(-0.776749\pi\) | ||||
−0.763964 | + | 0.645259i | \(0.776749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2011.34 | 0.270457 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13371.9 | 1.78400 | 0.891999 | − | 0.452038i | \(-0.149303\pi\) | ||||
0.891999 | + | 0.452038i | \(0.149303\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1552.98 | 0.205577 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −823.066 | −0.108111 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4121.34 | 0.537173 | 0.268586 | − | 0.963256i | \(-0.413444\pi\) | ||||
0.268586 | + | 0.963256i | \(0.413444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4726.84 | −0.611373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1871.79 | −0.240253 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4955.89 | 0.631286 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7854.41 | −0.992951 | −0.496475 | − | 0.868051i | \(-0.665373\pi\) | ||||
−0.496475 | + | 0.868051i | \(0.665373\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11245.8 | −1.41101 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2013.90 | 0.250796 | 0.125398 | − | 0.992106i | \(-0.459979\pi\) | ||||
0.125398 | + | 0.992106i | \(0.459979\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2335.84 | 0.288726 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3933.81 | 0.482648 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1592.18 | 0.193910 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3894.04 | −0.470777 | −0.235389 | − | 0.971901i | \(-0.575636\pi\) | ||||
−0.235389 | + | 0.971901i | \(0.575636\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3588.92 | −0.430726 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18909.0 | 2.25291 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2330.94 | 0.275714 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1201.51 | −0.141099 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1355.84 | 0.158084 | 0.0790418 | − | 0.996871i | \(-0.474814\pi\) | ||||
0.0790418 | + | 0.996871i | \(0.474814\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5451.46 | −0.631088 | −0.315544 | − | 0.948911i | \(-0.602187\pi\) | ||||
−0.315544 | + | 0.948911i | \(0.602187\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2753.03 | 0.316446 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −710.738 | −0.0811196 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15819.4 | −1.79286 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1478.99 | −0.166448 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13618.0 | −1.52194 | −0.760970 | − | 0.648787i | \(-0.775276\pi\) | ||||
−0.760970 | + | 0.648787i | \(0.775276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17611.2 | 1.95460 | 0.977299 | − | 0.211867i | \(-0.0679543\pi\) | ||||
0.977299 | + | 0.211867i | \(0.0679543\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9107.95 | 1.00389 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3844.16 | −0.420804 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11551.7 | 1.25588 | 0.627939 | − | 0.778262i | \(-0.283899\pi\) | ||||
0.627939 | + | 0.778262i | \(0.283899\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5538.83 | −0.598081 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10596.2 | −1.13644 | −0.568219 | − | 0.822878i | \(-0.692367\pi\) | ||||
−0.568219 | + | 0.822878i | \(0.692367\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3703.30 | 0.394502 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3366.31 | 0.356199 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6897.92 | −0.725018 | −0.362509 | − | 0.931980i | \(-0.618080\pi\) | ||||
−0.362509 | + | 0.931980i | \(0.618080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1746.25 | −0.182323 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9449.14 | 0.980043 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24613.8 | −2.53607 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11429.2 | 1.16989 | 0.584943 | − | 0.811075i | \(-0.301117\pi\) | ||||
0.584943 | + | 0.811075i | \(0.301117\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17038.5 | −1.73265 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7635.92 | −0.771454 | −0.385727 | − | 0.922613i | \(-0.626049\pi\) | ||||
−0.385727 | + | 0.922613i | \(0.626049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8531.66 | −0.856372 | −0.428186 | − | 0.903691i | \(-0.640847\pi\) | ||||
−0.428186 | + | 0.903691i | \(0.640847\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1394.06 | 0.139028 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8529.80 | −0.845208 | −0.422604 | − | 0.906314i | \(-0.638884\pi\) | ||||
−0.422604 | + | 0.906314i | \(0.638884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20536.2 | 2.02190 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3515.67 | 0.343935 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 393.108 | 0.0382138 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −578.016 | −0.0558341 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5791.68 | −0.555938 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2957.05 | −0.282069 | −0.141034 | − | 0.990005i | \(-0.545043\pi\) | ||||
−0.141034 | + | 0.990005i | \(0.545043\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25235.1 | −2.39214 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5241.01 | 0.493735 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10838.8 | 1.01477 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13582.8 | −1.26385 | −0.631927 | − | 0.775028i | \(-0.717736\pi\) | ||||
−0.631927 | + | 0.775028i | \(0.717736\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9912.71 | −0.916704 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9271.49 | −0.852172 | −0.426086 | − | 0.904683i | \(-0.640108\pi\) | ||||
−0.426086 | + | 0.904683i | \(0.640108\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22618.2 | −2.06627 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 515.430 | 0.0468018 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6914.79 | 0.624086 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17511.3 | 1.57097 | 0.785483 | − | 0.618883i | \(-0.212414\pi\) | ||||
0.785483 | + | 0.618883i | \(0.212414\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3388.98 | −0.302213 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10035.8 | 0.889607 | 0.444804 | − | 0.895628i | \(-0.353273\pi\) | ||||
0.444804 | + | 0.895628i | \(0.353273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6380.81 | 0.562262 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14370.3 | 1.25879 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5524.96 | 0.481119 | 0.240559 | − | 0.970634i | \(-0.422669\pi\) | ||||
0.240559 | + | 0.970634i | \(0.422669\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24072.3 | −2.08394 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13856.7 | −1.19257 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5363.66 | −0.458934 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1314.88 | −0.111854 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3074.99 | −0.260072 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9697.79 | 0.815485 | 0.407743 | − | 0.913097i | \(-0.366316\pi\) | ||||
0.407743 | + | 0.913097i | \(0.366316\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1395.38 | 0.116665 | 0.0583323 | − | 0.998297i | \(-0.481422\pi\) | ||||
0.0583323 | + | 0.998297i | \(0.481422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 788.048 | 0.0655109 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3461.94 | −0.286156 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10375.5 | −0.852754 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6275.87 | 0.512899 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27677.1 | 2.24920 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20513.9 | 1.65774 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 51.4428 | 0.00413393 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2645.42 | 0.211403 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5935.90 | −0.471727 | −0.235863 | − | 0.971786i | \(-0.575792\pi\) | ||||
−0.235863 | + | 0.971786i | \(0.575792\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3328.85 | −0.263084 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12819.5 | 1.00757 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2930.48 | 0.229065 | 0.114532 | − | 0.993420i | \(-0.463463\pi\) | ||||
0.114532 | + | 0.993420i | \(0.463463\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5250.41 | −0.408164 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18394.5 | −1.42220 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13645.9 | 1.04934 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15060.6 | −1.15187 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12687.7 | 0.965162 | 0.482581 | − | 0.875851i | \(-0.339699\pi\) | ||||
0.482581 | + | 0.875851i | \(0.339699\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6230.52 | −0.471418 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2192.00 | 0.164966 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23865.7 | 1.78654 | 0.893269 | − | 0.449522i | \(-0.148406\pi\) | ||||
0.893269 | + | 0.449522i | \(0.148406\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21199.4 | −1.57852 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10831.6 | 0.802268 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12451.1 | −0.917356 | −0.458678 | − | 0.888603i | \(-0.651677\pi\) | ||||
−0.458678 | + | 0.888603i | \(0.651677\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8498.58 | −0.622863 | −0.311431 | − | 0.950269i | \(-0.600808\pi\) | ||||
−0.311431 | + | 0.950269i | \(0.600808\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8529.45 | −0.621855 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 269.380 | 0.0195373 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14527.9 | 1.04819 | 0.524094 | − | 0.851661i | \(-0.324404\pi\) | ||||
0.524094 | + | 0.851661i | \(0.324404\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −133.861 | −0.00960808 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6418.18 | 0.458298 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2766.18 | 0.196507 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8169.26 | −0.577363 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24367.2 | 1.71336 | 0.856681 | − | 0.515847i | \(-0.172523\pi\) | ||||
0.856681 | + | 0.515847i | \(0.172523\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2815.46 | −0.196959 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3204.60 | −0.223045 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27008.9 | −1.87036 | −0.935179 | − | 0.354177i | \(-0.884761\pi\) | ||||
−0.935179 | + | 0.354177i | \(0.884761\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36479.9 | 2.51349 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6944.96 | 0.476111 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20539.1 | 1.40101 | 0.700504 | − | 0.713648i | \(-0.252958\pi\) | ||||
0.700504 | + | 0.713648i | \(0.252958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9748.76 | −0.661664 | −0.330832 | − | 0.943690i | \(-0.607329\pi\) | ||||
−0.330832 | + | 0.943690i | \(0.607329\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6815.92 | 0.460308 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14251.1 | 0.957667 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15825.2 | −1.05819 | −0.529097 | − | 0.848561i | \(-0.677469\pi\) | ||||
−0.529097 | + | 0.848561i | \(0.677469\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25078.5 | 1.66869 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20840.1 | 1.37987 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8498.46 | −0.559950 | −0.279975 | − | 0.960007i | \(-0.590326\pi\) | ||||
−0.279975 | + | 0.960007i | \(0.590326\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16518.0 | 1.08304 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6035.14 | 0.393785 | 0.196893 | − | 0.980425i | \(-0.436915\pi\) | ||||
0.196893 | + | 0.980425i | \(0.436915\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12286.8 | −0.797815 | −0.398908 | − | 0.916991i | \(-0.630611\pi\) | ||||
−0.398908 | + | 0.916991i | \(0.630611\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6457.83 | 0.417301 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10196.9 | 0.655749 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14789.0 | −0.946493 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1782.67 | 0.113545 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 37400.7 | 2.37085 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4932.61 | 0.311195 | 0.155597 | − | 0.987821i | \(-0.450270\pi\) | ||||
0.155597 | + | 0.987821i | \(0.450270\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7541.88 | 0.473559 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5306.17 | −0.331604 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −41928.3 | −2.60794 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2295.01 | 0.142080 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10027.0 | −0.617852 | −0.308926 | − | 0.951086i | \(-0.599970\pi\) | ||||
−0.308926 | + | 0.951086i | \(0.599970\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12963.5 | 0.795071 | 0.397535 | − | 0.917587i | \(-0.369866\pi\) | ||||
0.397535 | + | 0.917587i | \(0.369866\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3718.45 | −0.226998 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30692.4 | −1.86498 | −0.932490 | − | 0.361196i | \(-0.882369\pi\) | ||||
−0.932490 | + | 0.361196i | \(0.882369\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2997.44 | −0.181294 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3838.51 | 0.231095 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23445.6 | −1.40505 | −0.702524 | − | 0.711660i | \(-0.747944\pi\) | ||||
−0.702524 | + | 0.711660i | \(0.747944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4938.02 | 0.294572 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7989.55 | −0.474432 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6039.31 | −0.356993 | −0.178496 | − | 0.983941i | \(-0.557123\pi\) | ||||
−0.178496 | + | 0.983941i | \(0.557123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6549.05 | 0.385369 | 0.192684 | − | 0.981261i | \(-0.438281\pi\) | ||||
0.192684 | + | 0.981261i | \(0.438281\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −34741.8 | −2.03508 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 29667.7 | 1.73002 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8572.64 | 0.497652 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25492.9 | 1.47326 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2507.67 | 0.144273 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1144.93 | 0.0655778 | 0.0327889 | − | 0.999462i | \(-0.489561\pi\) | ||||
0.0327889 | + | 0.999462i | \(0.489561\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 971.012 | 0.0553693 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19501.4 | −1.10709 | −0.553544 | − | 0.832820i | \(-0.686725\pi\) | ||||
−0.553544 | + | 0.832820i | \(0.686725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29844.2 | 1.68677 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17569.2 | −0.988624 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10787.3 | −0.604338 | −0.302169 | − | 0.953254i | \(-0.597711\pi\) | ||||
−0.302169 | + | 0.953254i | \(0.597711\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9468.01 | 0.528108 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14285.0 | −0.793312 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −43842.3 | −2.42418 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16050.0 | −0.883603 | −0.441801 | − | 0.897113i | \(-0.645660\pi\) | ||||
−0.441801 | + | 0.897113i | \(0.645660\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1419.22 | 0.0777948 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3169.74 | 0.173000 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41020.0 | −2.22918 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9282.93 | −0.502307 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8234.20 | 0.443654 | 0.221827 | − | 0.975086i | \(-0.428798\pi\) | ||||
0.221827 | + | 0.975086i | \(0.428798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30416.6 | 1.63184 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12437.6 | 0.664438 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17569.4 | 0.934603 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18749.0 | −0.993136 | −0.496568 | − | 0.867998i | \(-0.665407\pi\) | ||||
−0.496568 | + | 0.867998i | \(0.665407\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4529.05 | 0.238892 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1312.13 | 0.0689194 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3901.75 | 0.204080 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16003.6 | −0.833564 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2057.31 | 0.106710 | 0.0533551 | − | 0.998576i | \(-0.483008\pi\) | ||||
0.0533551 | + | 0.998576i | \(0.483008\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14768.7 | −0.762849 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12118.9 | 0.623382 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1289.00 | 0.0660306 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5762.61 | 0.293980 | 0.146990 | − | 0.989138i | \(-0.453042\pi\) | ||||
0.146990 | + | 0.989138i | \(0.453042\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20602.8 | 1.04673 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9234.20 | 0.467222 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28273.9 | 1.42472 | 0.712361 | − | 0.701813i | \(-0.247626\pi\) | ||||
0.712361 | + | 0.701813i | \(0.247626\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −25023.3 | −1.25578 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3255.37 | −0.162705 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33535.1 | −1.66929 | −0.834647 | − | 0.550785i | \(-0.814328\pi\) | ||||
−0.834647 | + | 0.550785i | \(0.814328\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −28254.2 | −1.40073 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28870.0 | −1.42549 | −0.712743 | − | 0.701425i | \(-0.752547\pi\) | ||||
−0.712743 | + | 0.701425i | \(0.752547\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8880.74 | −0.436732 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2130.18 | 0.104336 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 56484.3 | 2.75553 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33907.3 | 1.64753 | 0.823765 | − | 0.566931i | \(-0.191869\pi\) | ||||
0.823765 | + | 0.566931i | \(0.191869\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15731.8 | −0.761354 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24928.0 | −1.20162 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23317.4 | 1.11953 | 0.559765 | − | 0.828651i | \(-0.310891\pi\) | ||||
0.559765 | + | 0.828651i | \(0.310891\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −830.799 | −0.0397314 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10183.9 | 0.485109 | 0.242554 | − | 0.970138i | \(-0.422015\pi\) | ||||
0.242554 | + | 0.970138i | \(0.422015\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35298.1 | 1.67481 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12107.6 | 0.572224 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47507.6 | 2.23650 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17775.1 | 0.833533 | 0.416766 | − | 0.909014i | \(-0.363163\pi\) | ||||
0.416766 | + | 0.909014i | \(0.363163\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24354.2 | 1.13761 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42778.7 | −1.99048 | −0.995241 | − | 0.0974480i | \(-0.968932\pi\) | ||||
−0.995241 | + | 0.0974480i | \(0.968932\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 197.294 | 0.00914452 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −41469.0 | −1.91466 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33360.0 | −1.53433 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1096.13 | −0.0502208 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30901.1 | 1.41036 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9274.77 | −0.421695 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2161.84 | −0.0979178 | −0.0489589 | − | 0.998801i | \(-0.515590\pi\) | ||||
−0.0489589 | + | 0.998801i | \(0.515590\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16740.6 | −0.755361 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −58371.8 | −2.62385 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39745.0 | −1.77981 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26165.7 | −1.16730 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28610.2 | −1.27155 | −0.635775 | − | 0.771874i | \(-0.719320\pi\) | ||||
−0.635775 | + | 0.771874i | \(0.719320\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30887.0 | −1.36759 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3384.35 | 0.149288 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3815.92 | 0.167697 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13826.4 | −0.605363 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12581.4 | −0.548805 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10133.1 | −0.440371 | −0.220185 | − | 0.975458i | \(-0.570666\pi\) | ||||
−0.220185 | + | 0.975458i | \(0.570666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24819.3 | −1.07463 | −0.537315 | − | 0.843382i | \(-0.680561\pi\) | ||||
−0.537315 | + | 0.843382i | \(0.680561\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5172.02 | 0.223113 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26150.9 | 1.12396 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7509.82 | 0.321586 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22493.8 | −0.959704 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11489.8 | 0.488426 | 0.244213 | − | 0.969722i | \(-0.421470\pi\) | ||||
0.244213 | + | 0.969722i | \(0.421470\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13011.0 | −0.551077 | −0.275539 | − | 0.961290i | \(-0.588856\pi\) | ||||
−0.275539 | + | 0.961290i | \(0.588856\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −124.921 | −0.00527173 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21913.5 | −0.921411 | −0.460706 | − | 0.887553i | \(-0.652404\pi\) | ||||
−0.460706 | + | 0.887553i | \(0.652404\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32815.2 | 1.37481 | 0.687407 | − | 0.726273i | \(-0.258749\pi\) | ||||
0.687407 | + | 0.726273i | \(0.258749\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3359.15 | −0.140226 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 62141.6 | 2.58473 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8940.55 | 0.370539 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4729.71 | 0.195320 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8028.93 | 0.330381 | 0.165190 | − | 0.986262i | \(-0.447176\pi\) | ||||
0.165190 | + | 0.986262i | \(0.447176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16631.5 | 0.681927 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21623.0 | 0.883436 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −37910.6 | −1.54339 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39239.9 | 1.59185 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7667.02 | 0.309931 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14175.4 | −0.571008 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23398.3 | 0.939204 | 0.469602 | − | 0.882878i | \(-0.344397\pi\) | ||||
0.469602 | + | 0.882878i | \(0.344397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9846.64 | 0.393857 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30105.8 | −1.19999 | −0.599996 | − | 0.800003i | \(-0.704831\pi\) | ||||
−0.599996 | + | 0.800003i | \(0.704831\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18957.5 | −0.752995 | −0.376497 | − | 0.926418i | \(-0.622872\pi\) | ||||
−0.376497 | + | 0.926418i | \(0.622872\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 45481.9 | 1.80025 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22648.6 | −0.893358 | −0.446679 | − | 0.894694i | \(-0.647393\pi\) | ||||
−0.446679 | + | 0.894694i | \(0.647393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8112.21 | 0.318871 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31206.3 | 1.22240 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2163.13 | −0.0844411 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 51595.7 | 2.00718 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9905.25 | 0.384011 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −42911.5 | −1.65791 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2662.53 | −0.102517 | −0.0512585 | − | 0.998685i | \(-0.516323\pi\) | ||||
−0.0512585 | + | 0.998685i | \(0.516323\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7758.81 | 0.297723 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23475.1 | 0.897726 | 0.448863 | − | 0.893601i | \(-0.351829\pi\) | ||||
0.448863 | + | 0.893601i | \(0.351829\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4188.29 | −0.159623 | −0.0798115 | − | 0.996810i | \(-0.525432\pi\) | ||||
−0.0798115 | + | 0.996810i | \(0.525432\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28353.1 | 1.07693 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27258.1 | 1.03183 | 0.515917 | − | 0.856638i | \(-0.327451\pi\) | ||||
0.515917 | + | 0.856638i | \(0.327451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14610.4 | −0.551199 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1717.02 | −0.0645593 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25119.2 | −0.941301 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −135.712 | −0.00506857 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13167.7 | 0.490140 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6278.59 | 0.232929 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 64978.4 | 2.40260 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10238.6 | −0.377321 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8781.91 | 0.322564 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15800.6 | 0.578447 | 0.289223 | − | 0.957262i | \(-0.406603\pi\) | ||||
0.289223 | + | 0.957262i | \(0.406603\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5831.24 | 0.212772 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8688.47 | 0.315985 | 0.157992 | − | 0.987440i | \(-0.449498\pi\) | ||||
0.157992 | + | 0.987440i | \(0.449498\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1017.40 | −0.0368797 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23720.3 | −0.857017 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13596.7 | 0.489643 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4601.95 | 0.165184 | 0.0825922 | − | 0.996583i | \(-0.473680\pi\) | ||||
0.0825922 | + | 0.996583i | \(0.473680\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −42134.6 | −1.50747 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17372.9 | 0.619542 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2131.45 | −0.0757639 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4901.69 | −0.173671 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27866.0 | −0.984126 | −0.492063 | − | 0.870560i | \(-0.663757\pi\) | ||||
−0.492063 | + | 0.870560i | \(0.663757\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50537.4 | 1.77905 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2805.79 | 0.0984537 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5782.75 | −0.202263 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38874.6 | 1.35536 | 0.677682 | − | 0.735355i | \(-0.262985\pi\) | ||||
0.677682 | + | 0.735355i | \(0.262985\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2090.09 | −0.0726386 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13340.3 | 0.462147 | 0.231074 | − | 0.972936i | \(-0.425776\pi\) | ||||
0.231074 | + | 0.972936i | \(0.425776\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15547.2 | 0.536888 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −49838.9 | −1.71562 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13866.9 | −0.475833 | −0.237917 | − | 0.971286i | \(-0.576464\pi\) | ||||
−0.237917 | + | 0.971286i | \(0.576464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −60480.0 | −2.06877 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 431.259 | 0.0147051 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21776.9 | −0.740213 | −0.370107 | − | 0.928989i | \(-0.620679\pi\) | ||||
−0.370107 | + | 0.928989i | \(0.620679\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22501.7 | 0.762449 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3975.42 | −0.134281 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26069.9 | 0.877832 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 961.000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18747.0 | 0.627326 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 353.142 | 0.0117804 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16969.3 | −0.564319 | −0.282160 | − | 0.959368i | \(-0.591051\pi\) | ||||
−0.282160 | + | 0.959368i | \(0.591051\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 41875.3 | 1.38826 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15787.3 | −0.521768 | −0.260884 | − | 0.965370i | \(-0.584014\pi\) | ||||
−0.260884 | + | 0.965370i | \(0.584014\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8727.79 | 0.287564 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1979.92 | 0.0650339 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33954.1 | −1.11186 | −0.555930 | − | 0.831229i | \(-0.687638\pi\) | ||||
−0.555930 | + | 0.831229i | \(0.687638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1616.41 | −0.0527688 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11715.4 | 0.381287 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48246.8 | 1.56545 | 0.782723 | − | 0.622370i | \(-0.213830\pi\) | ||||
0.782723 | + | 0.622370i | \(0.213830\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8454.13 | 0.273473 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 34246.7 | 1.10444 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3499.90 | −0.112528 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5908.32 | −0.189388 | −0.0946942 | − | 0.995506i | \(-0.530187\pi\) | ||||
−0.0946942 | + | 0.995506i | \(0.530187\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33636.7 | 1.07495 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18321.6 | −0.583754 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20202.1 | −0.641732 | −0.320866 | − | 0.947125i | \(-0.603974\pi\) | ||||
−0.320866 | + | 0.947125i | \(0.603974\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −51097.0 | −1.61826 |
(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 | 124.4.a.a.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 1116.4.a.g.1.3 | 4 | |||
4.3 | odd | 2 | 496.4.a.h.1.1 | 4 | |||
8.3 | odd | 2 | 1984.4.a.k.1.4 | 4 | |||
8.5 | even | 2 | 1984.4.a.p.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.4.a.a.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
496.4.a.h.1.1 | 4 | 4.3 | odd | 2 | |||
1116.4.a.g.1.3 | 4 | 3.2 | odd | 2 | |||
1984.4.a.k.1.4 | 4 | 8.3 | odd | 2 | |||
1984.4.a.p.1.1 | 4 | 8.5 | even | 2 |