Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, 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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1362828.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 23x^{2} + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.54739\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.54739 | −1.60775 | −0.803873 | − | 0.594801i | \(-0.797231\pi\) | ||||
−0.803873 | + | 0.594801i | \(0.797231\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 12.6788 | 1.58485 | ||||||||
\(5\) | −12.9118 | −1.15487 | −0.577434 | − | 0.816437i | \(-0.695946\pi\) | ||||
−0.577434 | + | 0.816437i | \(0.695946\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.7289 | 0.903273 | 0.451637 | − | 0.892202i | \(-0.350840\pi\) | ||||
0.451637 | + | 0.892202i | \(0.350840\pi\) | |||||||
\(8\) | −21.2762 | −0.940286 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 58.7151 | 1.85674 | ||||||||
\(11\) | −24.9280 | −0.683280 | −0.341640 | − | 0.939831i | \(-0.610982\pi\) | ||||
−0.341640 | + | 0.939831i | \(0.610982\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −76.0727 | −1.45223 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.67878 | −0.0731059 | ||||||||
\(17\) | 134.145 | 1.91383 | 0.956913 | − | 0.290376i | \(-0.0937804\pi\) | ||||
0.956913 | + | 0.290376i | \(0.0937804\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.9376 | −0.180365 | −0.0901824 | − | 0.995925i | \(-0.528745\pi\) | ||||
−0.0901824 | + | 0.995925i | \(0.528745\pi\) | |||||||
\(20\) | −163.706 | −1.83029 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 113.358 | 1.09854 | ||||||||
\(23\) | −72.0000 | −0.652741 | −0.326370 | − | 0.945242i | \(-0.605826\pi\) | ||||
−0.326370 | + | 0.945242i | \(0.605826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 41.7151 | 0.333721 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 212.101 | 1.43155 | ||||||||
\(29\) | 206.145 | 1.32001 | 0.660004 | − | 0.751262i | \(-0.270555\pi\) | ||||
0.660004 | + | 0.751262i | \(0.270555\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −249.142 | −1.44346 | −0.721728 | − | 0.692176i | \(-0.756652\pi\) | ||||
−0.721728 | + | 0.692176i | \(0.756652\pi\) | |||||||
\(32\) | 191.486 | 1.05782 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −610.012 | −3.07694 | ||||||||
\(35\) | −216.000 | −1.04316 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 293.955 | 1.30610 | 0.653052 | − | 0.757313i | \(-0.273488\pi\) | ||||
0.653052 | + | 0.757313i | \(0.273488\pi\) | |||||||
\(38\) | 67.9273 | 0.289981 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 274.715 | 1.08591 | ||||||||
\(41\) | −250.506 | −0.954208 | −0.477104 | − | 0.878847i | \(-0.658314\pi\) | ||||
−0.477104 | + | 0.878847i | \(0.658314\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 432.145 | 1.53259 | 0.766297 | − | 0.642486i | \(-0.222097\pi\) | ||||
0.766297 | + | 0.642486i | \(0.222097\pi\) | |||||||
\(44\) | −316.057 | −1.08290 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 327.412 | 1.04944 | ||||||||
\(47\) | 159.889 | 0.496217 | 0.248109 | − | 0.968732i | \(-0.420191\pi\) | ||||
0.248109 | + | 0.968732i | \(0.420191\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −63.1454 | −0.184097 | ||||||||
\(50\) | −189.695 | −0.536539 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 194.581 | 0.504298 | 0.252149 | − | 0.967688i | \(-0.418863\pi\) | ||||
0.252149 | + | 0.967688i | \(0.418863\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 321.866 | 0.789099 | ||||||||
\(56\) | −355.927 | −0.849336 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −937.424 | −2.12224 | ||||||||
\(59\) | −232.647 | −0.513358 | −0.256679 | − | 0.966497i | \(-0.582628\pi\) | ||||
−0.256679 | + | 0.966497i | \(0.582628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −185.006 | −0.388321 | −0.194160 | − | 0.980970i | \(-0.562198\pi\) | ||||
−0.194160 | + | 0.980970i | \(0.562198\pi\) | |||||||
\(62\) | 1132.94 | 2.32071 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −833.333 | −1.62760 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −39.4393 | −0.0719145 | −0.0359573 | − | 0.999353i | \(-0.511448\pi\) | ||||
−0.0359573 | + | 0.999353i | \(0.511448\pi\) | |||||||
\(68\) | 1700.80 | 3.03312 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 982.237 | 1.67714 | ||||||||
\(71\) | −920.460 | −1.53857 | −0.769286 | − | 0.638905i | \(-0.779388\pi\) | ||||
−0.769286 | + | 0.638905i | \(0.779388\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −549.078 | −0.880338 | −0.440169 | − | 0.897915i | \(-0.645082\pi\) | ||||
−0.440169 | + | 0.897915i | \(0.645082\pi\) | |||||||
\(74\) | −1336.73 | −2.09988 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −189.391 | −0.285851 | ||||||||
\(77\) | −417.018 | −0.617189 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 933.140 | 1.32894 | 0.664471 | − | 0.747314i | \(-0.268657\pi\) | ||||
0.664471 | + | 0.747314i | \(0.268657\pi\) | |||||||
\(80\) | 60.4116 | 0.0844277 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1139.15 | 1.53412 | ||||||||
\(83\) | 1095.38 | 1.44860 | 0.724301 | − | 0.689484i | \(-0.242163\pi\) | ||||
0.724301 | + | 0.689484i | \(0.242163\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1732.06 | −2.21022 | ||||||||
\(86\) | −1965.13 | −2.46402 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 530.375 | 0.642479 | ||||||||
\(89\) | 532.114 | 0.633753 | 0.316876 | − | 0.948467i | \(-0.397366\pi\) | ||||
0.316876 | + | 0.948467i | \(0.397366\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −912.872 | −1.03449 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −727.079 | −0.797792 | ||||||||
\(95\) | 192.872 | 0.208298 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −362.661 | −0.379615 | −0.189808 | − | 0.981821i | \(-0.560786\pi\) | ||||
−0.189808 | + | 0.981821i | \(0.560786\pi\) | |||||||
\(98\) | 287.147 | 0.295982 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 528.897 | 0.528897 | ||||||||
\(101\) | −1490.58 | −1.46850 | −0.734249 | − | 0.678880i | \(-0.762466\pi\) | ||||
−0.734249 | + | 0.678880i | \(0.762466\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 628.436 | 0.601181 | 0.300591 | − | 0.953753i | \(-0.402816\pi\) | ||||
0.300591 | + | 0.953753i | \(0.402816\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −884.838 | −0.810784 | ||||||||
\(107\) | −477.454 | −0.431376 | −0.215688 | − | 0.976462i | \(-0.569199\pi\) | ||||
−0.215688 | + | 0.976462i | \(0.569199\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −378.207 | −0.332345 | −0.166173 | − | 0.986097i | \(-0.553141\pi\) | ||||
−0.166173 | + | 0.986097i | \(0.553141\pi\) | |||||||
\(110\) | −1463.65 | −1.26867 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −78.2706 | −0.0660346 | ||||||||
\(113\) | −13.2732 | −0.0110499 | −0.00552495 | − | 0.999985i | \(-0.501759\pi\) | ||||
−0.00552495 | + | 0.999985i | \(0.501759\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 929.651 | 0.753830 | ||||||||
\(116\) | 2613.67 | 2.09201 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1057.94 | 0.825349 | ||||||||
\(119\) | 2244.10 | 1.72871 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −709.593 | −0.533128 | ||||||||
\(122\) | 841.294 | 0.624321 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3158.81 | −2.28766 | ||||||||
\(125\) | 1075.36 | 0.769465 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 145.988 | 0.102003 | 0.0510015 | − | 0.998699i | \(-0.483759\pi\) | ||||
0.0510015 | + | 0.998699i | \(0.483759\pi\) | |||||||
\(128\) | 2257.60 | 1.55895 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −317.163 | −0.211532 | −0.105766 | − | 0.994391i | \(-0.533729\pi\) | ||||
−0.105766 | + | 0.994391i | \(0.533729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −249.890 | −0.162919 | ||||||||
\(134\) | 179.346 | 0.115620 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2854.11 | −1.79954 | ||||||||
\(137\) | −443.149 | −0.276356 | −0.138178 | − | 0.990407i | \(-0.544125\pi\) | ||||
−0.138178 | + | 0.990407i | \(0.544125\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 785.018 | 0.479024 | 0.239512 | − | 0.970893i | \(-0.423013\pi\) | ||||
0.239512 | + | 0.970893i | \(0.423013\pi\) | |||||||
\(140\) | −2738.62 | −1.65325 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4185.69 | 2.47363 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2661.71 | −1.52444 | ||||||||
\(146\) | 2496.87 | 1.41536 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3726.99 | 2.06997 | ||||||||
\(149\) | −135.420 | −0.0744566 | −0.0372283 | − | 0.999307i | \(-0.511853\pi\) | ||||
−0.0372283 | + | 0.999307i | \(0.511853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2373.74 | −1.27929 | −0.639643 | − | 0.768672i | \(-0.720918\pi\) | ||||
−0.639643 | + | 0.768672i | \(0.720918\pi\) | |||||||
\(152\) | 317.817 | 0.169594 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1896.34 | 0.992283 | ||||||||
\(155\) | 3216.87 | 1.66700 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1166.73 | −0.593089 | −0.296544 | − | 0.955019i | \(-0.595834\pi\) | ||||
−0.296544 | + | 0.955019i | \(0.595834\pi\) | |||||||
\(158\) | −4243.35 | −2.13660 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2472.44 | −1.22165 | ||||||||
\(161\) | −1204.48 | −0.589603 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2309.19 | −1.10963 | −0.554815 | − | 0.831974i | \(-0.687211\pi\) | ||||
−0.554815 | + | 0.831974i | \(0.687211\pi\) | |||||||
\(164\) | −3176.12 | −1.51227 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4981.14 | −2.32898 | ||||||||
\(167\) | 600.788 | 0.278386 | 0.139193 | − | 0.990265i | \(-0.455549\pi\) | ||||
0.139193 | + | 0.990265i | \(0.455549\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 7876.36 | 3.55347 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5479.08 | 2.42893 | ||||||||
\(173\) | −3430.36 | −1.50755 | −0.753773 | − | 0.657135i | \(-0.771768\pi\) | ||||
−0.753773 | + | 0.657135i | \(0.771768\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 697.846 | 0.301441 | ||||||||
\(176\) | 116.633 | 0.0499519 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2419.73 | −1.01891 | ||||||||
\(179\) | −978.837 | −0.408725 | −0.204362 | − | 0.978895i | \(-0.565512\pi\) | ||||
−0.204362 | + | 0.978895i | \(0.565512\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3839.09 | −1.57656 | −0.788279 | − | 0.615318i | \(-0.789028\pi\) | ||||
−0.788279 | + | 0.615318i | \(0.789028\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1531.89 | 0.613763 | ||||||||
\(185\) | −3795.49 | −1.50838 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3343.98 | −1.30768 | ||||||||
\(188\) | 2027.20 | 0.786429 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −877.065 | −0.334890 | ||||||||
\(191\) | 487.709 | 0.184761 | 0.0923806 | − | 0.995724i | \(-0.470552\pi\) | ||||
0.0923806 | + | 0.995724i | \(0.470552\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4245.61 | 1.58345 | 0.791725 | − | 0.610878i | \(-0.209183\pi\) | ||||
0.791725 | + | 0.610878i | \(0.209183\pi\) | |||||||
\(194\) | 1649.16 | 0.610325 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −800.606 | −0.291766 | ||||||||
\(197\) | 2712.71 | 0.981079 | 0.490539 | − | 0.871419i | \(-0.336800\pi\) | ||||
0.490539 | + | 0.871419i | \(0.336800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3116.90 | 1.11031 | 0.555153 | − | 0.831748i | \(-0.312660\pi\) | ||||
0.555153 | + | 0.831748i | \(0.312660\pi\) | |||||||
\(200\) | −887.541 | −0.313793 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6778.26 | 2.36097 | ||||||||
\(203\) | 3448.58 | 1.19233 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3234.49 | 1.10198 | ||||||||
\(206\) | −2857.75 | −0.966546 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 372.366 | 0.123240 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1051.22 | −0.342981 | −0.171491 | − | 0.985186i | \(-0.554858\pi\) | ||||
−0.171491 | + | 0.985186i | \(0.554858\pi\) | |||||||
\(212\) | 2467.06 | 0.799236 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2171.17 | 0.693542 | ||||||||
\(215\) | −5579.78 | −1.76994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4167.85 | −1.30384 | ||||||||
\(218\) | 1719.85 | 0.534327 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4080.87 | 1.25060 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5496.12 | 1.65044 | 0.825218 | − | 0.564814i | \(-0.191052\pi\) | ||||
0.825218 | + | 0.564814i | \(0.191052\pi\) | |||||||
\(224\) | 3203.35 | 0.955502 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 60.3585 | 0.0177654 | ||||||||
\(227\) | 921.570 | 0.269457 | 0.134729 | − | 0.990883i | \(-0.456984\pi\) | ||||
0.134729 | + | 0.990883i | \(0.456984\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 192.941 | 0.0556764 | 0.0278382 | − | 0.999612i | \(-0.491138\pi\) | ||||
0.0278382 | + | 0.999612i | \(0.491138\pi\) | |||||||
\(230\) | −4227.49 | −1.21197 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4386.00 | −1.24119 | ||||||||
\(233\) | −913.779 | −0.256926 | −0.128463 | − | 0.991714i | \(-0.541004\pi\) | ||||
−0.128463 | + | 0.991714i | \(0.541004\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2064.46 | −0.573066 | ||||||||
\(236\) | −2949.68 | −0.813594 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10204.8 | −2.77932 | ||||||||
\(239\) | 1976.86 | 0.535032 | 0.267516 | − | 0.963553i | \(-0.413797\pi\) | ||||
0.267516 | + | 0.963553i | \(0.413797\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3904.45 | 1.04360 | 0.521800 | − | 0.853068i | \(-0.325261\pi\) | ||||
0.521800 | + | 0.853068i | \(0.325261\pi\) | |||||||
\(242\) | 3226.80 | 0.857134 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2345.65 | −0.615429 | ||||||||
\(245\) | 815.322 | 0.212608 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5300.80 | 1.35726 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4890.08 | −1.23710 | ||||||||
\(251\) | 942.035 | 0.236895 | 0.118448 | − | 0.992960i | \(-0.462208\pi\) | ||||
0.118448 | + | 0.992960i | \(0.462208\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1794.82 | 0.446005 | ||||||||
\(254\) | −663.866 | −0.163995 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3599.54 | −0.878794 | ||||||||
\(257\) | 812.616 | 0.197236 | 0.0986179 | − | 0.995125i | \(-0.468558\pi\) | ||||
0.0986179 | + | 0.995125i | \(0.468558\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4917.52 | 1.17977 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1442.26 | 0.340089 | ||||||||
\(263\) | 2608.29 | 0.611536 | 0.305768 | − | 0.952106i | \(-0.401087\pi\) | ||||
0.305768 | + | 0.952106i | \(0.401087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2512.40 | −0.582398 | ||||||||
\(266\) | 1136.35 | 0.261932 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −500.042 | −0.113974 | ||||||||
\(269\) | 4791.02 | 1.08592 | 0.542962 | − | 0.839757i | \(-0.317303\pi\) | ||||
0.542962 | + | 0.839757i | \(0.317303\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3663.62 | −0.821214 | −0.410607 | − | 0.911812i | \(-0.634683\pi\) | ||||
−0.410607 | + | 0.911812i | \(0.634683\pi\) | |||||||
\(272\) | −627.637 | −0.139912 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2015.17 | 0.444311 | ||||||||
\(275\) | −1039.88 | −0.228025 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −624.326 | −0.135423 | −0.0677114 | − | 0.997705i | \(-0.521570\pi\) | ||||
−0.0677114 | + | 0.997705i | \(0.521570\pi\) | |||||||
\(278\) | −3569.78 | −0.770149 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4595.67 | 0.980871 | ||||||||
\(281\) | −5535.12 | −1.17508 | −0.587540 | − | 0.809195i | \(-0.699904\pi\) | ||||
−0.587540 | + | 0.809195i | \(0.699904\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 175.151 | 0.0367903 | 0.0183952 | − | 0.999831i | \(-0.494144\pi\) | ||||
0.0183952 | + | 0.999831i | \(0.494144\pi\) | |||||||
\(284\) | −11670.3 | −2.43840 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4190.69 | −0.861911 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13082.0 | 2.66273 | ||||||||
\(290\) | 12103.8 | 2.45091 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6961.64 | −1.39520 | ||||||||
\(293\) | 7774.33 | 1.55011 | 0.775054 | − | 0.631895i | \(-0.217723\pi\) | ||||
0.775054 | + | 0.631895i | \(0.217723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3003.90 | 0.592861 | ||||||||
\(296\) | −6254.25 | −1.22811 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 615.808 | 0.119707 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7229.30 | 1.38435 | ||||||||
\(302\) | 10794.3 | 2.05677 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 69.8899 | 0.0131857 | ||||||||
\(305\) | 2388.76 | 0.448459 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8022.85 | 1.49149 | 0.745746 | − | 0.666230i | \(-0.232093\pi\) | ||||
0.745746 | + | 0.666230i | \(0.232093\pi\) | |||||||
\(308\) | −5287.27 | −0.978150 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14628.4 | −2.68012 | ||||||||
\(311\) | 9264.87 | 1.68927 | 0.844635 | − | 0.535343i | \(-0.179818\pi\) | ||||
0.844635 | + | 0.535343i | \(0.179818\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7423.57 | 1.34059 | 0.670296 | − | 0.742094i | \(-0.266167\pi\) | ||||
0.670296 | + | 0.742094i | \(0.266167\pi\) | |||||||
\(314\) | 5305.56 | 0.953536 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11831.1 | 2.10617 | ||||||||
\(317\) | −2641.04 | −0.467935 | −0.233968 | − | 0.972244i | \(-0.575171\pi\) | ||||
−0.233968 | + | 0.972244i | \(0.575171\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5138.80 | −0.901936 | ||||||||
\(320\) | 10759.8 | 1.87967 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5477.23 | 0.947932 | ||||||||
\(323\) | −2003.82 | −0.345187 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10500.8 | 1.78400 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5329.84 | 0.897229 | ||||||||
\(329\) | 2674.76 | 0.448220 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10779.5 | 1.79001 | 0.895007 | − | 0.446052i | \(-0.147170\pi\) | ||||
0.895007 | + | 0.446052i | \(0.147170\pi\) | |||||||
\(332\) | 13888.1 | 2.29581 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2732.02 | −0.447573 | ||||||||
\(335\) | 509.233 | 0.0830518 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −313.465 | −0.0506693 | −0.0253346 | − | 0.999679i | \(-0.508065\pi\) | ||||
−0.0253346 | + | 0.999679i | \(0.508065\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −21960.4 | −3.50286 | ||||||||
\(341\) | 6210.61 | 0.986286 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6794.35 | −1.06956 | ||||||||
\(344\) | −9194.43 | −1.44108 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15599.2 | 2.42375 | ||||||||
\(347\) | 2849.23 | 0.440792 | 0.220396 | − | 0.975410i | \(-0.429265\pi\) | ||||
0.220396 | + | 0.975410i | \(0.429265\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6466.94 | 0.991883 | 0.495941 | − | 0.868356i | \(-0.334823\pi\) | ||||
0.495941 | + | 0.868356i | \(0.334823\pi\) | |||||||
\(350\) | −3173.38 | −0.484641 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4773.38 | −0.722789 | ||||||||
\(353\) | 2773.10 | 0.418122 | 0.209061 | − | 0.977903i | \(-0.432959\pi\) | ||||
0.209061 | + | 0.977903i | \(0.432959\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11884.8 | 1.77685 | ||||||||
\(356\) | 6746.56 | 1.00440 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4451.16 | 0.657126 | ||||||||
\(359\) | 1467.11 | 0.215685 | 0.107843 | − | 0.994168i | \(-0.465606\pi\) | ||||
0.107843 | + | 0.994168i | \(0.465606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6635.87 | −0.967469 | ||||||||
\(362\) | 17457.8 | 2.53471 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7089.59 | 1.01667 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4648.22 | 0.661130 | 0.330565 | − | 0.943783i | \(-0.392761\pi\) | ||||
0.330565 | + | 0.943783i | \(0.392761\pi\) | |||||||
\(368\) | 336.872 | 0.0477192 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17259.6 | 2.42509 | ||||||||
\(371\) | 3255.12 | 0.455519 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1763.72 | 0.244831 | 0.122416 | − | 0.992479i | \(-0.460936\pi\) | ||||
0.122416 | + | 0.992479i | \(0.460936\pi\) | |||||||
\(374\) | 15206.4 | 2.10242 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3401.84 | −0.466586 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1930.47 | 0.261640 | 0.130820 | − | 0.991406i | \(-0.458239\pi\) | ||||
0.130820 | + | 0.991406i | \(0.458239\pi\) | |||||||
\(380\) | 2445.38 | 0.330120 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2217.81 | −0.297049 | ||||||||
\(383\) | 8845.93 | 1.18017 | 0.590086 | − | 0.807340i | \(-0.299094\pi\) | ||||
0.590086 | + | 0.807340i | \(0.299094\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5384.46 | 0.712772 | ||||||||
\(386\) | −19306.5 | −2.54579 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4598.10 | −0.601632 | ||||||||
\(389\) | 1598.08 | 0.208292 | 0.104146 | − | 0.994562i | \(-0.466789\pi\) | ||||
0.104146 | + | 0.994562i | \(0.466789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9658.47 | −1.24923 | ||||||||
\(392\) | 1343.50 | 0.173104 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12335.8 | −1.57733 | ||||||||
\(395\) | −12048.5 | −1.53475 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3578.82 | 0.452433 | 0.226217 | − | 0.974077i | \(-0.427364\pi\) | ||||
0.226217 | + | 0.974077i | \(0.427364\pi\) | |||||||
\(398\) | −14173.7 | −1.78509 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −195.176 | −0.0243970 | ||||||||
\(401\) | 3485.99 | 0.434120 | 0.217060 | − | 0.976158i | \(-0.430353\pi\) | ||||
0.217060 | + | 0.976158i | \(0.430353\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −18898.8 | −2.32735 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15682.0 | −1.91696 | ||||||||
\(407\) | −7327.71 | −0.892435 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14709.1 | 1.77828 | 0.889139 | − | 0.457637i | \(-0.151304\pi\) | ||||
0.889139 | + | 0.457637i | \(0.151304\pi\) | |||||||
\(410\) | −14708.5 | −1.77171 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7967.80 | 0.952780 | ||||||||
\(413\) | −3891.92 | −0.463702 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14143.4 | −1.67294 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1693.29 | −0.198138 | ||||||||
\(419\) | −3709.01 | −0.432451 | −0.216226 | − | 0.976343i | \(-0.569375\pi\) | ||||
−0.216226 | + | 0.976343i | \(0.569375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 794.029 | 0.0919207 | 0.0459603 | − | 0.998943i | \(-0.485365\pi\) | ||||
0.0459603 | + | 0.998943i | \(0.485365\pi\) | |||||||
\(422\) | 4780.32 | 0.551427 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4139.96 | −0.474185 | ||||||||
\(425\) | 5595.89 | 0.638684 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3094.94 | −0.350760 | ||||||||
\(428\) | −6053.53 | −0.683664 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 25373.5 | 2.84562 | ||||||||
\(431\) | −2891.52 | −0.323155 | −0.161577 | − | 0.986860i | \(-0.551658\pi\) | ||||
−0.161577 | + | 0.986860i | \(0.551658\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5560.94 | 0.617186 | 0.308593 | − | 0.951194i | \(-0.400142\pi\) | ||||
0.308593 | + | 0.951194i | \(0.400142\pi\) | |||||||
\(434\) | 18952.9 | 2.09624 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4795.20 | −0.526717 | ||||||||
\(437\) | 1075.51 | 0.117731 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15127.2 | 1.64460 | 0.822302 | − | 0.569051i | \(-0.192689\pi\) | ||||
0.822302 | + | 0.569051i | \(0.192689\pi\) | |||||||
\(440\) | −6848.11 | −0.741979 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2357.89 | −0.252883 | −0.126441 | − | 0.991974i | \(-0.540356\pi\) | ||||
−0.126441 | + | 0.991974i | \(0.540356\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6870.56 | −0.731901 | ||||||||
\(446\) | −24993.0 | −2.65348 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −13940.7 | −1.47017 | ||||||||
\(449\) | 7165.06 | 0.753096 | 0.376548 | − | 0.926397i | \(-0.377111\pi\) | ||||
0.376548 | + | 0.926397i | \(0.377111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6244.63 | 0.651992 | ||||||||
\(452\) | −168.288 | −0.0175124 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4190.74 | −0.433219 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8020.96 | 0.821017 | 0.410508 | − | 0.911857i | \(-0.365351\pi\) | ||||
0.410508 | + | 0.911857i | \(0.365351\pi\) | |||||||
\(458\) | −877.378 | −0.0895135 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11786.8 | 1.19471 | ||||||||
\(461\) | 4146.59 | 0.418928 | 0.209464 | − | 0.977816i | \(-0.432828\pi\) | ||||
0.209464 | + | 0.977816i | \(0.432828\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7118.21 | 0.714495 | 0.357248 | − | 0.934010i | \(-0.383715\pi\) | ||||
0.357248 | + | 0.934010i | \(0.383715\pi\) | |||||||
\(464\) | −964.509 | −0.0965004 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4155.31 | 0.413071 | ||||||||
\(467\) | 2128.22 | 0.210883 | 0.105441 | − | 0.994426i | \(-0.466374\pi\) | ||||
0.105441 | + | 0.994426i | \(0.466374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −659.774 | −0.0649585 | ||||||||
\(470\) | 9387.91 | 0.921344 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4949.86 | 0.482703 | ||||||||
\(473\) | −10772.5 | −1.04719 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −623.125 | −0.0601915 | ||||||||
\(476\) | 28452.4 | 2.73974 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8989.57 | −0.860196 | ||||||||
\(479\) | 3715.30 | 0.354397 | 0.177199 | − | 0.984175i | \(-0.443296\pi\) | ||||
0.177199 | + | 0.984175i | \(0.443296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −17755.0 | −1.67784 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8996.77 | −0.844926 | ||||||||
\(485\) | 4682.62 | 0.438405 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8139.28 | −0.757343 | −0.378671 | − | 0.925531i | \(-0.623619\pi\) | ||||
−0.378671 | + | 0.925531i | \(0.623619\pi\) | |||||||
\(488\) | 3936.23 | 0.365133 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3707.59 | −0.341820 | ||||||||
\(491\) | −18081.7 | −1.66194 | −0.830972 | − | 0.556315i | \(-0.812215\pi\) | ||||
−0.830972 | + | 0.556315i | \(0.812215\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27653.4 | 2.52626 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1165.68 | 0.105525 | ||||||||
\(497\) | −15398.3 | −1.38975 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11031.5 | 0.989659 | 0.494829 | − | 0.868990i | \(-0.335231\pi\) | ||||
0.494829 | + | 0.868990i | \(0.335231\pi\) | |||||||
\(500\) | 13634.2 | 1.21948 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4283.80 | −0.380868 | ||||||||
\(503\) | −8016.14 | −0.710581 | −0.355290 | − | 0.934756i | \(-0.615618\pi\) | ||||
−0.355290 | + | 0.934756i | \(0.615618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19246.1 | 1.69592 | ||||||||
\(506\) | −8161.74 | −0.717063 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1850.95 | 0.161659 | ||||||||
\(509\) | −20173.9 | −1.75676 | −0.878382 | − | 0.477959i | \(-0.841377\pi\) | ||||
−0.878382 | + | 0.477959i | \(0.841377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9185.44 | −0.795186 | ||||||||
\(512\) | −1692.30 | −0.146074 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3695.29 | −0.317105 | ||||||||
\(515\) | −8114.25 | −0.694285 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3985.72 | −0.339056 | ||||||||
\(518\) | −22361.9 | −1.89677 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9746.95 | −0.819619 | −0.409810 | − | 0.912171i | \(-0.634405\pi\) | ||||
−0.409810 | + | 0.912171i | \(0.634405\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18929.3 | −1.58264 | −0.791320 | − | 0.611402i | \(-0.790606\pi\) | ||||
−0.791320 | + | 0.611402i | \(0.790606\pi\) | |||||||
\(524\) | −4021.24 | −0.335245 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11860.9 | −0.983195 | ||||||||
\(527\) | −33421.2 | −2.76252 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 11424.9 | 0.936349 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3168.30 | −0.258201 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6164.80 | 0.498182 | ||||||||
\(536\) | 839.120 | 0.0676203 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −21786.6 | −1.74589 | ||||||||
\(539\) | 1574.09 | 0.125790 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11366.8 | −0.903321 | −0.451661 | − | 0.892190i | \(-0.649168\pi\) | ||||
−0.451661 | + | 0.892190i | \(0.649168\pi\) | |||||||
\(542\) | 16659.9 | 1.32030 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 25687.0 | 2.02449 | ||||||||
\(545\) | 4883.34 | 0.383815 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17495.4 | 1.36755 | 0.683775 | − | 0.729693i | \(-0.260337\pi\) | ||||
0.683775 | + | 0.729693i | \(0.260337\pi\) | |||||||
\(548\) | −5618.59 | −0.437983 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4728.72 | 0.366606 | ||||||||
\(551\) | −3079.33 | −0.238083 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15610.4 | 1.20040 | ||||||||
\(554\) | 2839.05 | 0.217725 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9953.06 | 0.759180 | ||||||||
\(557\) | 11873.1 | 0.903192 | 0.451596 | − | 0.892223i | \(-0.350855\pi\) | ||||
0.451596 | + | 0.892223i | \(0.350855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1010.62 | 0.0762613 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25170.4 | 1.88923 | ||||||||
\(563\) | 2829.31 | 0.211796 | 0.105898 | − | 0.994377i | \(-0.466228\pi\) | ||||
0.105898 | + | 0.994377i | \(0.466228\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 171.381 | 0.0127612 | ||||||||
\(566\) | −796.481 | −0.0591495 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19583.9 | 1.44670 | ||||||||
\(569\) | −16136.8 | −1.18891 | −0.594453 | − | 0.804130i | \(-0.702632\pi\) | ||||
−0.594453 | + | 0.804130i | \(0.702632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17840.5 | −1.30754 | −0.653769 | − | 0.756695i | \(-0.726813\pi\) | ||||
−0.653769 | + | 0.756695i | \(0.726813\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 19056.7 | 1.38573 | ||||||||
\(575\) | −3003.49 | −0.217833 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8516.17 | 0.614442 | 0.307221 | − | 0.951638i | \(-0.400601\pi\) | ||||
0.307221 | + | 0.951638i | \(0.400601\pi\) | |||||||
\(578\) | −59488.9 | −4.28099 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −33747.3 | −2.41600 | ||||||||
\(581\) | 18324.5 | 1.30848 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4850.53 | −0.344577 | ||||||||
\(584\) | 11682.3 | 0.827770 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −35352.9 | −2.49218 | ||||||||
\(587\) | 20688.3 | 1.45468 | 0.727340 | − | 0.686277i | \(-0.240756\pi\) | ||||
0.727340 | + | 0.686277i | \(0.240756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3721.59 | 0.260349 | ||||||||
\(590\) | −13659.9 | −0.953169 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1375.35 | −0.0954839 | ||||||||
\(593\) | −11435.9 | −0.791933 | −0.395966 | − | 0.918265i | \(-0.629590\pi\) | ||||
−0.395966 | + | 0.918265i | \(0.629590\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28975.4 | −1.99643 | ||||||||
\(596\) | −1716.96 | −0.118002 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1260.80 | −0.0860016 | −0.0430008 | − | 0.999075i | \(-0.513692\pi\) | ||||
−0.0430008 | + | 0.999075i | \(0.513692\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6261.10 | 0.424951 | 0.212476 | − | 0.977166i | \(-0.431847\pi\) | ||||
0.212476 | + | 0.977166i | \(0.431847\pi\) | |||||||
\(602\) | −32874.5 | −2.22569 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −30096.1 | −2.02747 | ||||||||
\(605\) | 9162.14 | 0.615692 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3230.33 | 0.216005 | 0.108003 | − | 0.994151i | \(-0.465555\pi\) | ||||
0.108003 | + | 0.994151i | \(0.465555\pi\) | |||||||
\(608\) | −2860.35 | −0.190794 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10862.6 | −0.721009 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14868.5 | 0.979660 | 0.489830 | − | 0.871818i | \(-0.337059\pi\) | ||||
0.489830 | + | 0.871818i | \(0.337059\pi\) | |||||||
\(614\) | −36483.0 | −2.39794 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8872.57 | 0.580334 | ||||||||
\(617\) | 19952.8 | 1.30190 | 0.650949 | − | 0.759121i | \(-0.274371\pi\) | ||||
0.650949 | + | 0.759121i | \(0.274371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8316.48 | 0.540012 | 0.270006 | − | 0.962859i | \(-0.412974\pi\) | ||||
0.270006 | + | 0.962859i | \(0.412974\pi\) | |||||||
\(620\) | 40786.0 | 2.64194 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −42131.0 | −2.71592 | ||||||||
\(623\) | 8901.66 | 0.572452 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19099.2 | −1.22235 | ||||||||
\(626\) | −33757.9 | −2.15533 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14792.7 | −0.939955 | ||||||||
\(629\) | 39432.6 | 2.49965 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12605.9 | −0.795299 | −0.397649 | − | 0.917537i | \(-0.630174\pi\) | ||||
−0.397649 | + | 0.917537i | \(0.630174\pi\) | |||||||
\(632\) | −19853.7 | −1.24959 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12009.8 | 0.752321 | ||||||||
\(635\) | −1884.98 | −0.117800 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 23368.1 | 1.45008 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −29149.8 | −1.80038 | ||||||||
\(641\) | 9224.04 | 0.568374 | 0.284187 | − | 0.958769i | \(-0.408276\pi\) | ||||
0.284187 | + | 0.958769i | \(0.408276\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4439.16 | 0.272260 | 0.136130 | − | 0.990691i | \(-0.456533\pi\) | ||||
0.136130 | + | 0.990691i | \(0.456533\pi\) | |||||||
\(644\) | −15271.3 | −0.934431 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9112.13 | 0.554972 | ||||||||
\(647\) | 9601.15 | 0.583401 | 0.291700 | − | 0.956510i | \(-0.405779\pi\) | ||||
0.291700 | + | 0.956510i | \(0.405779\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5799.44 | 0.350767 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −29277.7 | −1.75859 | ||||||||
\(653\) | −27112.8 | −1.62482 | −0.812410 | − | 0.583087i | \(-0.801845\pi\) | ||||
−0.812410 | + | 0.583087i | \(0.801845\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4095.15 | 0.244291 | ||||||||
\(656\) | 1172.06 | 0.0697583 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12163.2 | −0.720624 | ||||||||
\(659\) | −5587.26 | −0.330271 | −0.165136 | − | 0.986271i | \(-0.552806\pi\) | ||||
−0.165136 | + | 0.986271i | \(0.552806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3060.13 | −0.180069 | −0.0900343 | − | 0.995939i | \(-0.528698\pi\) | ||||
−0.0900343 | + | 0.995939i | \(0.528698\pi\) | |||||||
\(662\) | −49018.6 | −2.87789 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −23305.6 | −1.36210 | ||||||||
\(665\) | 3226.53 | 0.188150 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14842.5 | −0.861623 | ||||||||
\(668\) | 7617.26 | 0.441199 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2315.68 | −0.133526 | ||||||||
\(671\) | 4611.83 | 0.265332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4121.55 | 0.236069 | 0.118034 | − | 0.993010i | \(-0.462341\pi\) | ||||
0.118034 | + | 0.993010i | \(0.462341\pi\) | |||||||
\(674\) | 1425.45 | 0.0814633 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22889.5 | −1.29943 | −0.649715 | − | 0.760178i | \(-0.725112\pi\) | ||||
−0.649715 | + | 0.760178i | \(0.725112\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6066.91 | −0.342896 | ||||||||
\(680\) | 36851.8 | 2.07824 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −28242.1 | −1.58570 | ||||||||
\(683\) | 19297.9 | 1.08113 | 0.540566 | − | 0.841301i | \(-0.318210\pi\) | ||||
0.540566 | + | 0.841301i | \(0.318210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5721.87 | 0.319155 | ||||||||
\(686\) | 30896.6 | 1.71959 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2021.91 | −0.112042 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30317.8 | −1.66910 | −0.834548 | − | 0.550935i | \(-0.814271\pi\) | ||||
−0.834548 | + | 0.550935i | \(0.814271\pi\) | |||||||
\(692\) | −43492.8 | −2.38923 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12956.6 | −0.708682 | ||||||||
\(695\) | −10136.0 | −0.553210 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33604.3 | −1.82619 | ||||||||
\(698\) | −29407.7 | −1.59470 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8847.84 | 0.477738 | ||||||||
\(701\) | −9606.16 | −0.517574 | −0.258787 | − | 0.965934i | \(-0.583323\pi\) | ||||
−0.258787 | + | 0.965934i | \(0.583323\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4390.99 | −0.235575 | ||||||||
\(704\) | 20773.4 | 1.11211 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12610.4 | −0.672235 | ||||||||
\(707\) | −24935.7 | −1.32646 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23398.8 | −1.23944 | −0.619718 | − | 0.784825i | \(-0.712753\pi\) | ||||
−0.619718 | + | 0.784825i | \(0.712753\pi\) | |||||||
\(710\) | −54044.9 | −2.85672 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11321.4 | −0.595909 | ||||||||
\(713\) | 17938.2 | 0.942203 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12410.5 | −0.647766 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6671.51 | −0.346767 | ||||||||
\(719\) | 23588.7 | 1.22352 | 0.611758 | − | 0.791045i | \(-0.290463\pi\) | ||||
0.611758 | + | 0.791045i | \(0.290463\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10513.0 | 0.543031 | ||||||||
\(722\) | 30175.9 | 1.55544 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −48674.9 | −2.49861 | ||||||||
\(725\) | 8599.38 | 0.440514 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15733.5 | 0.802644 | 0.401322 | − | 0.915937i | \(-0.368551\pi\) | ||||
0.401322 | + | 0.915937i | \(0.368551\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −32239.2 | −1.63455 | ||||||||
\(731\) | 57970.3 | 2.93312 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17297.1 | −0.871598 | −0.435799 | − | 0.900044i | \(-0.643534\pi\) | ||||
−0.435799 | + | 0.900044i | \(0.643534\pi\) | |||||||
\(734\) | −21137.3 | −1.06293 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13787.0 | −0.690484 | ||||||||
\(737\) | 983.144 | 0.0491378 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38749.2 | 1.92884 | 0.964419 | − | 0.264377i | \(-0.0851663\pi\) | ||||
0.964419 | + | 0.264377i | \(0.0851663\pi\) | |||||||
\(740\) | −48122.2 | −2.39055 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14802.3 | −0.732359 | ||||||||
\(743\) | 3139.76 | 0.155029 | 0.0775144 | − | 0.996991i | \(-0.475302\pi\) | ||||
0.0775144 | + | 0.996991i | \(0.475302\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1748.52 | 0.0859876 | ||||||||
\(746\) | −8020.33 | −0.393626 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −42397.6 | −2.07247 | ||||||||
\(749\) | −7987.25 | −0.389650 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40628.6 | 1.97411 | 0.987055 | − | 0.160380i | \(-0.0512721\pi\) | ||||
0.987055 | + | 0.160380i | \(0.0512721\pi\) | |||||||
\(752\) | −748.086 | −0.0362764 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30649.3 | 1.47741 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24004.9 | 1.15254 | 0.576271 | − | 0.817259i | \(-0.304507\pi\) | ||||
0.576271 | + | 0.817259i | \(0.304507\pi\) | |||||||
\(758\) | −8778.62 | −0.420651 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4103.60 | −0.195859 | ||||||||
\(761\) | −29540.1 | −1.40713 | −0.703566 | − | 0.710630i | \(-0.748410\pi\) | ||||
−0.703566 | + | 0.710630i | \(0.748410\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6326.97 | −0.300199 | ||||||||
\(764\) | 6183.56 | 0.292818 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −40225.9 | −1.89742 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7585.63 | 0.355715 | 0.177857 | − | 0.984056i | \(-0.443083\pi\) | ||||
0.177857 | + | 0.984056i | \(0.443083\pi\) | |||||||
\(770\) | −24485.2 | −1.14596 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 53829.2 | 2.50953 | ||||||||
\(773\) | −3284.29 | −0.152817 | −0.0764086 | − | 0.997077i | \(-0.524345\pi\) | ||||
−0.0764086 | + | 0.997077i | \(0.524345\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10393.0 | −0.481712 | ||||||||
\(776\) | 7716.07 | 0.356947 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7267.08 | −0.334881 | ||||||||
\(779\) | 3741.98 | 0.172106 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22945.3 | 1.05128 | ||||||||
\(782\) | 43920.8 | 2.00845 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 295.443 | 0.0134586 | ||||||||
\(785\) | 15064.6 | 0.684939 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41624.1 | −1.88531 | −0.942654 | − | 0.333772i | \(-0.891679\pi\) | ||||
−0.942654 | + | 0.333772i | \(0.891679\pi\) | |||||||
\(788\) | 34393.8 | 1.55486 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 54789.4 | 2.46749 | ||||||||
\(791\) | −222.046 | −0.00998108 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −16274.3 | −0.727398 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 39518.4 | 1.75967 | ||||||||
\(797\) | 30333.3 | 1.34813 | 0.674066 | − | 0.738671i | \(-0.264546\pi\) | ||||
0.674066 | + | 0.738671i | \(0.264546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21448.4 | 0.949674 | ||||||||
\(800\) | 7987.87 | 0.353017 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15852.2 | −0.697954 | ||||||||
\(803\) | 13687.4 | 0.601518 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15552.0 | 0.680914 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 31714.0 | 1.38081 | ||||||||
\(809\) | 24853.9 | 1.08012 | 0.540060 | − | 0.841627i | \(-0.318402\pi\) | ||||
0.540060 | + | 0.841627i | \(0.318402\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17383.5 | −0.752674 | −0.376337 | − | 0.926483i | \(-0.622816\pi\) | ||||
−0.376337 | + | 0.926483i | \(0.622816\pi\) | |||||||
\(812\) | 43723.7 | 1.88966 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 33322.0 | 1.43481 | ||||||||
\(815\) | 29815.8 | 1.28148 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6455.23 | −0.276426 | ||||||||
\(818\) | −66887.8 | −2.85902 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 41009.4 | 1.74648 | ||||||||
\(821\) | 31169.4 | 1.32499 | 0.662496 | − | 0.749065i | \(-0.269497\pi\) | ||||
0.662496 | + | 0.749065i | \(0.269497\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5512.79 | 0.233492 | 0.116746 | − | 0.993162i | \(-0.462754\pi\) | ||||
0.116746 | + | 0.993162i | \(0.462754\pi\) | |||||||
\(824\) | −13370.8 | −0.565282 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17698.1 | 0.745516 | ||||||||
\(827\) | 13335.8 | 0.560738 | 0.280369 | − | 0.959892i | \(-0.409543\pi\) | ||||
0.280369 | + | 0.959892i | \(0.409543\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28338.5 | −1.18726 | −0.593628 | − | 0.804739i | \(-0.702305\pi\) | ||||
−0.593628 | + | 0.804739i | \(0.702305\pi\) | |||||||
\(830\) | 64315.5 | 2.68967 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8470.66 | −0.352330 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7757.27 | −0.321499 | ||||||||
\(836\) | 4721.15 | 0.195316 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16866.3 | 0.695272 | ||||||||
\(839\) | 27149.5 | 1.11717 | 0.558585 | − | 0.829447i | \(-0.311344\pi\) | ||||
0.558585 | + | 0.829447i | \(0.311344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18106.9 | 0.742421 | ||||||||
\(842\) | −3610.76 | −0.147785 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13328.2 | −0.543573 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11870.7 | −0.481560 | ||||||||
\(848\) | −910.404 | −0.0368672 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −25446.7 | −1.02684 | ||||||||
\(851\) | −21164.7 | −0.852547 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7978.22 | 0.320245 | 0.160123 | − | 0.987097i | \(-0.448811\pi\) | ||||
0.160123 | + | 0.987097i | \(0.448811\pi\) | |||||||
\(854\) | 14073.9 | 0.563933 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10158.4 | 0.405616 | ||||||||
\(857\) | 13614.4 | 0.542657 | 0.271329 | − | 0.962487i | \(-0.412537\pi\) | ||||
0.271329 | + | 0.962487i | \(0.412537\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35007.7 | −1.39051 | −0.695255 | − | 0.718763i | \(-0.744709\pi\) | ||||
−0.695255 | + | 0.718763i | \(0.744709\pi\) | |||||||
\(860\) | −70744.8 | −2.80509 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13148.9 | 0.519551 | ||||||||
\(863\) | 24461.5 | 0.964867 | 0.482434 | − | 0.875933i | \(-0.339753\pi\) | ||||
0.482434 | + | 0.875933i | \(0.339753\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44292.2 | 1.74102 | ||||||||
\(866\) | −25287.8 | −0.992278 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −52843.3 | −2.06638 | ||||||||
\(869\) | −23261.3 | −0.908040 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8046.82 | 0.312500 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4890.77 | −0.189282 | ||||||||
\(875\) | 17989.5 | 0.695037 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43121.6 | −1.66034 | −0.830168 | − | 0.557514i | \(-0.811755\pi\) | ||||
−0.830168 | + | 0.557514i | \(0.811755\pi\) | |||||||
\(878\) | −68789.3 | −2.64411 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1505.94 | −0.0576878 | ||||||||
\(881\) | 40824.5 | 1.56120 | 0.780598 | − | 0.625034i | \(-0.214915\pi\) | ||||
0.780598 | + | 0.625034i | \(0.214915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8262.14 | 0.314885 | 0.157442 | − | 0.987528i | \(-0.449675\pi\) | ||||
0.157442 | + | 0.987528i | \(0.449675\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10722.3 | 0.406571 | ||||||||
\(887\) | 40858.6 | 1.54667 | 0.773336 | − | 0.633997i | \(-0.218587\pi\) | ||||
0.773336 | + | 0.633997i | \(0.218587\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2442.22 | 0.0921365 | ||||||||
\(890\) | 31243.2 | 1.17671 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 69684.1 | 2.61569 | ||||||||
\(893\) | −2388.37 | −0.0895001 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12638.6 | 0.472023 | ||||||||
\(896\) | 37767.1 | 1.40816 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −32582.3 | −1.21079 | ||||||||
\(899\) | −51359.4 | −1.90537 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26102.2 | 0.965139 | ||||||||
\(902\) | −28396.8 | −1.04824 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 282.404 | 0.0103901 | ||||||||
\(905\) | 49569.6 | 1.82072 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32729.3 | −1.19819 | −0.599095 | − | 0.800678i | \(-0.704473\pi\) | ||||
−0.599095 | + | 0.800678i | \(0.704473\pi\) | |||||||
\(908\) | 11684.4 | 0.427048 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11065.9 | −0.402447 | −0.201223 | − | 0.979545i | \(-0.564492\pi\) | ||||
−0.201223 | + | 0.979545i | \(0.564492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27305.7 | −0.989801 | ||||||||
\(914\) | −36474.5 | −1.31999 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2446.26 | 0.0882386 | ||||||||
\(917\) | −5305.77 | −0.191071 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50682.2 | 1.81921 | 0.909604 | − | 0.415477i | \(-0.136385\pi\) | ||||
0.909604 | + | 0.415477i | \(0.136385\pi\) | |||||||
\(920\) | −19779.5 | −0.708816 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18856.2 | −0.673531 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12262.3 | 0.435874 | ||||||||
\(926\) | −32369.3 | −1.14873 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 39474.0 | 1.39633 | ||||||||
\(929\) | −41045.5 | −1.44958 | −0.724790 | − | 0.688970i | \(-0.758063\pi\) | ||||
−0.724790 | + | 0.688970i | \(0.758063\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 943.243 | 0.0332047 | ||||||||
\(932\) | −11585.6 | −0.407188 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9677.86 | −0.339046 | ||||||||
\(935\) | 43176.9 | 1.51020 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −788.985 | −0.0275080 | −0.0137540 | − | 0.999905i | \(-0.504378\pi\) | ||||
−0.0137540 | + | 0.999905i | \(0.504378\pi\) | |||||||
\(938\) | 3000.25 | 0.104437 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −26174.8 | −0.908222 | ||||||||
\(941\) | 25676.2 | 0.889499 | 0.444750 | − | 0.895655i | \(-0.353293\pi\) | ||||
0.444750 | + | 0.895655i | \(0.353293\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18036.5 | 0.622851 | ||||||||
\(944\) | 1088.51 | 0.0375295 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 48986.9 | 1.68362 | ||||||||
\(947\) | 679.352 | 0.0233115 | 0.0116557 | − | 0.999932i | \(-0.496290\pi\) | ||||
0.0116557 | + | 0.999932i | \(0.496290\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2833.60 | 0.0967726 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −47746.0 | −1.62548 | ||||||||
\(953\) | 20238.4 | 0.687917 | 0.343958 | − | 0.938985i | \(-0.388232\pi\) | ||||
0.343958 | + | 0.938985i | \(0.388232\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6297.21 | −0.213375 | ||||||||
\(956\) | 25064.2 | 0.847944 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16894.9 | −0.569781 | ||||||||
\(959\) | −7413.38 | −0.249625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32280.6 | 1.08357 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 49503.6 | 1.65395 | ||||||||
\(965\) | −54818.6 | −1.82868 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6161.63 | −0.204906 | −0.102453 | − | 0.994738i | \(-0.532669\pi\) | ||||
−0.102453 | + | 0.994738i | \(0.532669\pi\) | |||||||
\(968\) | 15097.5 | 0.501293 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21293.7 | −0.704845 | ||||||||
\(971\) | 48569.5 | 1.60522 | 0.802610 | − | 0.596504i | \(-0.203444\pi\) | ||||
0.802610 | + | 0.596504i | \(0.203444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13132.4 | 0.432689 | ||||||||
\(974\) | 37012.5 | 1.21761 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 865.602 | 0.0283886 | ||||||||
\(977\) | 44595.8 | 1.46033 | 0.730167 | − | 0.683269i | \(-0.239442\pi\) | ||||
0.730167 | + | 0.683269i | \(0.239442\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13264.6 | −0.433031 | ||||||||
\(980\) | 10337.3 | 0.336951 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 82224.4 | 2.67198 | ||||||||
\(983\) | 29599.0 | 0.960389 | 0.480195 | − | 0.877162i | \(-0.340566\pi\) | ||||
0.480195 | + | 0.877162i | \(0.340566\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35026.0 | −1.13302 | ||||||||
\(986\) | −125751. | −4.06159 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31114.5 | −1.00039 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5718.45 | 0.183302 | 0.0916511 | − | 0.995791i | \(-0.470786\pi\) | ||||
0.0916511 | + | 0.995791i | \(0.470786\pi\) | |||||||
\(992\) | −47707.2 | −1.52692 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 70021.9 | 2.23437 | ||||||||
\(995\) | −40244.8 | −1.28226 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1491.44 | −0.0473766 | −0.0236883 | − | 0.999719i | \(-0.507541\pi\) | ||||
−0.0236883 | + | 0.999719i | \(0.507541\pi\) | |||||||
\(998\) | −50164.8 | −1.59112 | ||||||||
\(999\) | 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 | 1521.4.a.w.1.1 | 4 | ||
3.2 | odd | 2 | 507.4.a.l.1.4 | 4 | |||
13.5 | odd | 4 | 117.4.b.e.64.4 | 4 | |||
13.8 | odd | 4 | 117.4.b.e.64.1 | 4 | |||
13.12 | even | 2 | inner | 1521.4.a.w.1.4 | 4 | ||
39.5 | even | 4 | 39.4.b.b.25.1 | ✓ | 4 | ||
39.8 | even | 4 | 39.4.b.b.25.4 | yes | 4 | ||
39.38 | odd | 2 | 507.4.a.l.1.1 | 4 | |||
156.47 | odd | 4 | 624.4.c.c.337.4 | 4 | |||
156.83 | odd | 4 | 624.4.c.c.337.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.b.b.25.1 | ✓ | 4 | 39.5 | even | 4 | ||
39.4.b.b.25.4 | yes | 4 | 39.8 | even | 4 | ||
117.4.b.e.64.1 | 4 | 13.8 | odd | 4 | |||
117.4.b.e.64.4 | 4 | 13.5 | odd | 4 | |||
507.4.a.l.1.1 | 4 | 39.38 | odd | 2 | |||
507.4.a.l.1.4 | 4 | 3.2 | odd | 2 | |||
624.4.c.c.337.1 | 4 | 156.83 | odd | 4 | |||
624.4.c.c.337.4 | 4 | 156.47 | odd | 4 | |||
1521.4.a.w.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1521.4.a.w.1.4 | 4 | 13.12 | even | 2 | inner |