Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(1,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 216) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −11.4164 | −1.02111 | −0.510557 | − | 0.859844i | \(-0.670561\pi\) | ||||
−0.510557 | + | 0.859844i | \(0.670561\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 29.8328 | 1.61082 | 0.805410 | − | 0.592718i | \(-0.201945\pi\) | ||||
0.805410 | + | 0.592718i | \(0.201945\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −66.2492 | −1.81590 | −0.907950 | − | 0.419079i | \(-0.862353\pi\) | ||||
−0.907950 | + | 0.419079i | \(0.862353\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −39.8328 | −0.849818 | −0.424909 | − | 0.905236i | \(-0.639694\pi\) | ||||
−0.424909 | + | 0.905236i | \(0.639694\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −107.416 | −1.53249 | −0.766244 | − | 0.642549i | \(-0.777877\pi\) | ||||
−0.766244 | + | 0.642549i | \(0.777877\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 70.3313 | 0.849216 | 0.424608 | − | 0.905377i | \(-0.360412\pi\) | ||||
0.424608 | + | 0.905377i | \(0.360412\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.91796 | 0.0627172 | 0.0313586 | − | 0.999508i | \(-0.490017\pi\) | ||||
0.0313586 | + | 0.999508i | \(0.490017\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.33437 | 0.0426749 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 36.6687 | 0.234800 | 0.117400 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117400 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 231.331 | 1.34027 | 0.670134 | − | 0.742240i | \(-0.266237\pi\) | ||||
0.670134 | + | 0.742240i | \(0.266237\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −340.584 | −1.64483 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −36.8359 | −0.163670 | −0.0818350 | − | 0.996646i | \(-0.526078\pi\) | ||||
−0.0818350 | + | 0.996646i | \(0.526078\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −429.325 | −1.63535 | −0.817674 | − | 0.575681i | \(-0.804737\pi\) | ||||
−0.817674 | + | 0.575681i | \(0.804737\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −74.3344 | −0.263625 | −0.131813 | − | 0.991275i | \(-0.542080\pi\) | ||||
−0.131813 | + | 0.991275i | \(0.542080\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 52.5836 | 0.163194 | 0.0815969 | − | 0.996665i | \(-0.473998\pi\) | ||||
0.0815969 | + | 0.996665i | \(0.473998\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 546.997 | 1.59474 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 288.170 | 0.746853 | 0.373427 | − | 0.927660i | \(-0.378183\pi\) | ||||
0.373427 | + | 0.927660i | \(0.378183\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 756.328 | 1.85424 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 783.745 | 1.72940 | 0.864702 | − | 0.502285i | \(-0.167507\pi\) | ||||
0.864702 | + | 0.502285i | \(0.167507\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −439.158 | −0.921777 | −0.460889 | − | 0.887458i | \(-0.652469\pi\) | ||||
−0.460889 | + | 0.887458i | \(0.652469\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 454.748 | 0.867762 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −218.337 | −0.398122 | −0.199061 | − | 0.979987i | \(-0.563789\pi\) | ||||
−0.199061 | + | 0.979987i | \(0.563789\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 790.492 | 1.32133 | 0.660663 | − | 0.750682i | \(-0.270275\pi\) | ||||
0.660663 | + | 0.750682i | \(0.270275\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1098.00 | 1.76042 | 0.880211 | − | 0.474582i | \(-0.157401\pi\) | ||||
0.880211 | + | 0.474582i | \(0.157401\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1976.40 | −2.92509 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −439.827 | −0.626384 | −0.313192 | − | 0.949690i | \(-0.601398\pi\) | ||||
−0.313192 | + | 0.949690i | \(0.601398\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 50.8452 | 0.0672408 | 0.0336204 | − | 0.999435i | \(-0.489296\pi\) | ||||
0.0336204 | + | 0.999435i | \(0.489296\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1226.31 | 1.56485 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −719.745 | −0.857222 | −0.428611 | − | 0.903489i | \(-0.640997\pi\) | ||||
−0.428611 | + | 0.903489i | \(0.640997\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1188.33 | −1.36890 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −802.930 | −0.867147 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1199.64 | −1.25573 | −0.627863 | − | 0.778324i | \(-0.716070\pi\) | ||||
−0.627863 | + | 0.778324i | \(0.716070\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 245.981 | 0.242337 | 0.121169 | − | 0.992632i | \(-0.461336\pi\) | ||||
0.121169 | + | 0.992632i | \(0.461336\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −575.820 | −0.550847 | −0.275424 | − | 0.961323i | \(-0.588818\pi\) | ||||
−0.275424 | + | 0.961323i | \(0.588818\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1015.89 | 0.917849 | 0.458924 | − | 0.888475i | \(-0.348235\pi\) | ||||
0.458924 | + | 0.888475i | \(0.348235\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1471.64 | −1.29319 | −0.646595 | − | 0.762834i | \(-0.723807\pi\) | ||||
−0.646595 | + | 0.762834i | \(0.723807\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1903.57 | 1.58472 | 0.792359 | − | 0.610055i | \(-0.208853\pi\) | ||||
0.792359 | + | 0.610055i | \(0.208853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −78.9783 | −0.0640414 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3204.53 | −2.46856 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3057.96 | 2.29749 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1366.15 | 0.977539 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −230.310 | −0.160919 | −0.0804593 | − | 0.996758i | \(-0.525639\pi\) | ||||
−0.0804593 | + | 0.996758i | \(0.525639\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −794.310 | −0.529764 | −0.264882 | − | 0.964281i | \(-0.585333\pi\) | ||||
−0.264882 | + | 0.964281i | \(0.585333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2098.18 | 1.36793 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 683.076 | 0.425979 | 0.212989 | − | 0.977055i | \(-0.431680\pi\) | ||||
0.212989 | + | 0.977055i | \(0.431680\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1512.64 | −0.923025 | −0.461513 | − | 0.887134i | \(-0.652693\pi\) | ||||
−0.461513 | + | 0.887134i | \(0.652693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2638.89 | 1.54318 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −418.625 | −0.239758 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2307.14 | 1.26851 | 0.634255 | − | 0.773124i | \(-0.281307\pi\) | ||||
0.634255 | + | 0.773124i | \(0.281307\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2523.17 | −1.35982 | −0.679910 | − | 0.733296i | \(-0.737981\pi\) | ||||
−0.679910 | + | 0.733296i | \(0.737981\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2640.97 | −1.36857 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2918.98 | 1.48382 | 0.741912 | − | 0.670497i | \(-0.233919\pi\) | ||||
0.741912 | + | 0.670497i | \(0.233919\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 206.382 | 0.101026 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1096.99 | 0.527133 | 0.263567 | − | 0.964641i | \(-0.415101\pi\) | ||||
0.263567 | + | 0.964641i | \(0.415101\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −732.729 | −0.339523 | −0.169761 | − | 0.985485i | \(-0.554300\pi\) | ||||
−0.169761 | + | 0.985485i | \(0.554300\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −610.347 | −0.277809 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 722.675 | 0.317595 | 0.158798 | − | 0.987311i | \(-0.449238\pi\) | ||||
0.158798 | + | 0.987311i | \(0.449238\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 159.139 | 0.0687417 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1010.16 | −0.421806 | −0.210903 | − | 0.977507i | \(-0.567640\pi\) | ||||
−0.210903 | + | 0.977507i | \(0.567640\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4256.79 | 1.74809 | 0.874045 | − | 0.485844i | \(-0.161488\pi\) | ||||
0.874045 | + | 0.485844i | \(0.161488\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 420.534 | 0.167126 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7116.25 | 2.78284 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3429.39 | 1.29917 | 0.649585 | − | 0.760289i | \(-0.274943\pi\) | ||||
0.649585 | + | 0.760289i | \(0.274943\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 967.341 | 0.360781 | 0.180390 | − | 0.983595i | \(-0.442264\pi\) | ||||
0.180390 | + | 0.983595i | \(0.442264\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −468.413 | −0.169406 | −0.0847032 | − | 0.996406i | \(-0.526994\pi\) | ||||
−0.0847032 | + | 0.996406i | \(0.526994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2673.47 | 0.952347 | 0.476174 | − | 0.879351i | \(-0.342023\pi\) | ||||
0.476174 | + | 0.879351i | \(0.342023\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1093.93 | 0.378221 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4901.35 | 1.66988 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4659.39 | −1.54209 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2870.62 | 0.936594 | 0.468297 | − | 0.883571i | \(-0.344868\pi\) | ||||
0.468297 | + | 0.883571i | \(0.344868\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 848.631 | 0.269192 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6901.26 | 2.15893 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4278.70 | 1.30234 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1246.60 | 0.374343 | 0.187172 | − | 0.982327i | \(-0.440068\pi\) | ||||
0.187172 | + | 0.982327i | \(0.440068\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −560.461 | −0.163873 | −0.0819364 | − | 0.996638i | \(-0.526110\pi\) | ||||
−0.0819364 | + | 0.996638i | \(0.526110\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1145.38 | 0.330519 | 0.165260 | − | 0.986250i | \(-0.447154\pi\) | ||||
0.165260 | + | 0.986250i | \(0.447154\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 623.709 | 0.175367 | 0.0876836 | − | 0.996148i | \(-0.472054\pi\) | ||||
0.0876836 | + | 0.996148i | \(0.472054\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −600.316 | −0.166639 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6265.80 | 1.69582 | 0.847910 | − | 0.530141i | \(-0.177861\pi\) | ||||
0.847910 | + | 0.530141i | \(0.177861\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −640.653 | −0.171237 | −0.0856185 | − | 0.996328i | \(-0.527287\pi\) | ||||
−0.0856185 | + | 0.996328i | \(0.527287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6244.74 | −1.62842 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2801.49 | −0.721679 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7748.91 | 1.94863 | 0.974316 | − | 0.225183i | \(-0.0722980\pi\) | ||||
0.974316 | + | 0.225183i | \(0.0722980\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −458.310 | −0.113888 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3191.76 | −0.774693 | −0.387347 | − | 0.921934i | \(-0.626608\pi\) | ||||
−0.387347 | + | 0.921934i | \(0.626608\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1098.92 | −0.263643 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3776.41 | −0.885413 | −0.442706 | − | 0.896667i | \(-0.645982\pi\) | ||||
−0.442706 | + | 0.896667i | \(0.645982\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3289.87 | −0.762623 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4065.91 | −0.921572 | −0.460786 | − | 0.887511i | \(-0.652432\pi\) | ||||
−0.460786 | + | 0.887511i | \(0.652432\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5508.17 | 1.23468 | 0.617339 | − | 0.786697i | \(-0.288211\pi\) | ||||
0.617339 | + | 0.786697i | \(0.288211\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −353.398 | −0.0774934 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8306.91 | 1.80186 | 0.900928 | − | 0.433970i | \(-0.142887\pi\) | ||||
0.900928 | + | 0.433970i | \(0.142887\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2962.67 | 0.628962 | 0.314481 | − | 0.949264i | \(-0.398169\pi\) | ||||
0.314481 | + | 0.949264i | \(0.398169\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4509.67 | −0.947250 | −0.473625 | − | 0.880727i | \(-0.657055\pi\) | ||||
−0.473625 | + | 0.880727i | \(0.657055\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12808.0 | −2.63425 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6625.28 | 1.34852 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1814.46 | 0.361781 | 0.180890 | − | 0.983503i | \(-0.442102\pi\) | ||||
0.180890 | + | 0.983503i | \(0.442102\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8947.55 | −1.76592 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −275.562 | −0.0532982 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2217.60 | −0.424653 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5013.61 | 0.941240 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4395.62 | 0.817171 | 0.408585 | − | 0.912720i | \(-0.366022\pi\) | ||||
0.408585 | + | 0.912720i | \(0.366022\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1377.23 | −0.251111 | −0.125555 | − | 0.992087i | \(-0.540071\pi\) | ||||
−0.125555 | + | 0.992087i | \(0.540071\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7347.95 | 1.32693 | 0.663467 | − | 0.748205i | \(-0.269084\pi\) | ||||
0.663467 | + | 0.748205i | \(0.269084\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2607.78 | 0.462043 | 0.231021 | − | 0.972949i | \(-0.425793\pi\) | ||||
0.231021 | + | 0.972949i | \(0.425793\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2429.28 | −0.426374 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7554.73 | −1.30141 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −212.483 | −0.0362659 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1568.72 | 0.262876 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6541.33 | −1.08624 | −0.543118 | − | 0.839656i | \(-0.682756\pi\) | ||||
−0.543118 | + | 0.839656i | \(0.682756\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2492.63 | 0.406528 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4315.66 | 0.697594 | 0.348797 | − | 0.937198i | \(-0.386590\pi\) | ||||
0.348797 | + | 0.937198i | \(0.386590\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15325.5 | −2.43379 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6085.80 | 0.958025 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3895.76 | −0.602695 | −0.301347 | − | 0.953514i | \(-0.597436\pi\) | ||||
−0.301347 | + | 0.953514i | \(0.597436\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4877.42 | 0.748087 | 0.374044 | − | 0.927411i | \(-0.377971\pi\) | ||||
0.374044 | + | 0.927411i | \(0.377971\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1739.79 | −0.262322 | −0.131161 | − | 0.991361i | \(-0.541871\pi\) | ||||
−0.131161 | + | 0.991361i | \(0.541871\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9024.58 | −1.34923 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 188.828 | 0.0277604 | 0.0138802 | − | 0.999904i | \(-0.495582\pi\) | ||||
0.0138802 | + | 0.999904i | \(0.495582\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1912.51 | −0.278833 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12535.2 | −1.79759 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6338.15 | 0.901495 | 0.450747 | − | 0.892651i | \(-0.351157\pi\) | ||||
0.450747 | + | 0.892651i | \(0.351157\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8596.93 | 1.20305 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8641.41 | −1.19956 | −0.599779 | − | 0.800166i | \(-0.704745\pi\) | ||||
−0.599779 | + | 0.800166i | \(0.704745\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1460.62 | −0.199538 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4143.88 | −0.561627 | −0.280814 | − | 0.959762i | \(-0.590604\pi\) | ||||
−0.280814 | + | 0.959762i | \(0.590604\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4193.94 | −0.559531 | −0.279766 | − | 0.960068i | \(-0.590257\pi\) | ||||
−0.279766 | + | 0.960068i | \(0.590257\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 22563.4 | 2.98685 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10870.4 | 1.41684 | 0.708422 | − | 0.705789i | \(-0.249407\pi\) | ||||
0.708422 | + | 0.705789i | \(0.249407\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −743.102 | −0.0961133 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5021.24 | 0.639610 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8890.87 | 1.12398 | 0.561990 | − | 0.827144i | \(-0.310036\pi\) | ||||
0.561990 | + | 0.827144i | \(0.310036\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15095.4 | −1.87987 | −0.939936 | − | 0.341349i | \(-0.889116\pi\) | ||||
−0.939936 | + | 0.341349i | \(0.889116\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9214.58 | −1.13898 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2440.35 | 0.297208 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1618.34 | 0.195652 | 0.0978260 | − | 0.995204i | \(-0.468811\pi\) | ||||
0.0978260 | + | 0.995204i | \(0.468811\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23381.3 | 2.78576 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −580.470 | −0.0686606 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10011.9 | −1.16733 | −0.583666 | − | 0.811994i | \(-0.698382\pi\) | ||||
−0.583666 | + | 0.811994i | \(0.698382\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7234.43 | −0.837493 | −0.418747 | − | 0.908103i | \(-0.637530\pi\) | ||||
−0.418747 | + | 0.908103i | \(0.637530\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −572.999 | −0.0653989 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13101.3 | −1.48482 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5379.03 | 0.601157 | 0.300579 | − | 0.953757i | \(-0.402820\pi\) | ||||
0.300579 | + | 0.953757i | \(0.402820\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1602.96 | −0.177906 | −0.0889530 | − | 0.996036i | \(-0.528352\pi\) | ||||
−0.0889530 | + | 0.996036i | \(0.528352\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 486.549 | 0.0532604 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6725.87 | −0.731226 | −0.365613 | − | 0.930767i | \(-0.619141\pi\) | ||||
−0.365613 | + | 0.930767i | \(0.619141\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1169.92 | −0.125473 | −0.0627367 | − | 0.998030i | \(-0.519983\pi\) | ||||
−0.0627367 | + | 0.998030i | \(0.519983\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8216.90 | 0.875322 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2996.56 | 0.314958 | 0.157479 | − | 0.987522i | \(-0.449663\pi\) | ||||
0.157479 | + | 0.987522i | \(0.449663\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28442.5 | 2.96963 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13566.4 | 1.39781 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11152.1 | −1.14151 | −0.570757 | − | 0.821119i | \(-0.693350\pi\) | ||||
−0.570757 | + | 0.821119i | \(0.693350\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2947.17 | −0.297752 | −0.148876 | − | 0.988856i | \(-0.547565\pi\) | ||||
−0.148876 | + | 0.988856i | \(0.547565\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6563.38 | −0.658804 | −0.329402 | − | 0.944190i | \(-0.606847\pi\) | ||||
−0.329402 | + | 0.944190i | \(0.606847\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2727.33 | 0.270248 | 0.135124 | − | 0.990829i | \(-0.456857\pi\) | ||||
0.135124 | + | 0.990829i | \(0.456857\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6513.62 | −0.641303 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4924.59 | 0.478717 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 375.173 | 0.0362402 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14512.1 | 1.38429 | 0.692146 | − | 0.721758i | \(-0.256665\pi\) | ||||
0.692146 | + | 0.721758i | \(0.256665\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1467.28 | 0.139090 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13695.6 | 1.28224 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14189.9 | 1.32034 | 0.660170 | − | 0.751116i | \(-0.270484\pi\) | ||||
0.660170 | + | 0.751116i | \(0.270484\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7215.91 | 0.663238 | 0.331619 | − | 0.943413i | \(-0.392405\pi\) | ||||
0.331619 | + | 0.943413i | \(0.392405\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3938.82 | −0.359829 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23582.6 | 2.12842 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13032.6 | 1.16917 | 0.584587 | − | 0.811331i | \(-0.301257\pi\) | ||||
0.584587 | + | 0.811331i | \(0.301257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9502.84 | 0.842367 | 0.421184 | − | 0.906975i | \(-0.361615\pi\) | ||||
0.421184 | + | 0.906975i | \(0.361615\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2808.22 | −0.247454 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3794.30 | 0.330411 | 0.165206 | − | 0.986259i | \(-0.447171\pi\) | ||||
0.165206 | + | 0.986259i | \(0.447171\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32756.3 | 2.83572 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6573.80 | 0.562478 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3483.62 | −0.296343 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14811.2 | −1.24547 | −0.622735 | − | 0.782432i | \(-0.713979\pi\) | ||||
−0.622735 | + | 0.782432i | \(0.713979\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −345.532 | −0.0288892 | −0.0144446 | − | 0.999896i | \(-0.504598\pi\) | ||||
−0.0144446 | + | 0.999896i | \(0.504598\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24848.8 | −2.05395 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12119.1 | −0.996067 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17101.2 | 1.38975 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11597.8 | −0.937229 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36238.1 | −2.89589 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5474.45 | 0.435056 | 0.217528 | − | 0.976054i | \(-0.430201\pi\) | ||||
0.217528 | + | 0.976054i | \(0.430201\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16800.9 | 1.32049 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 977.278 | 0.0763901 | 0.0381951 | − | 0.999270i | \(-0.487839\pi\) | ||||
0.0381951 | + | 0.999270i | \(0.487839\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2578.96 | 0.199396 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13121.3 | −1.00899 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18833.3 | −1.43266 | −0.716330 | − | 0.697762i | \(-0.754179\pi\) | ||||
−0.716330 | + | 0.697762i | \(0.754179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2960.95 | 0.224033 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20967.0 | 1.56954 | 0.784772 | − | 0.619784i | \(-0.212780\pi\) | ||||
0.784772 | + | 0.619784i | \(0.212780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21732.0 | −1.61818 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13488.7 | −0.993804 | −0.496902 | − | 0.867807i | \(-0.665529\pi\) | ||||
−0.496902 | + | 0.867807i | \(0.665529\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2248.90 | −0.164822 | −0.0824110 | − | 0.996598i | \(-0.526262\pi\) | ||||
−0.0824110 | + | 0.996598i | \(0.526262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.9030 | 0.00267645 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1968.87 | −0.142054 | −0.0710270 | − | 0.997474i | \(-0.522628\pi\) | ||||
−0.0710270 | + | 0.997474i | \(0.522628\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1516.86 | 0.108313 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19091.1 | −1.35621 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4107.66 | −0.288827 | −0.144413 | − | 0.989517i | \(-0.546129\pi\) | ||||
−0.144413 | + | 0.989517i | \(0.546129\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16269.8 | 1.13818 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7497.21 | 0.519180 | 0.259590 | − | 0.965719i | \(-0.416413\pi\) | ||||
0.259590 | + | 0.965719i | \(0.416413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36584.3 | 2.52069 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27107.1 | −1.84903 | −0.924513 | − | 0.381151i | \(-0.875528\pi\) | ||||
−0.924513 | + | 0.381151i | \(0.875528\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6802.17 | 0.461674 | 0.230837 | − | 0.972992i | \(-0.425854\pi\) | ||||
0.230837 | + | 0.972992i | \(0.425854\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −34910.9 | −2.34600 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16992.4 | −1.13625 | −0.568123 | − | 0.822943i | \(-0.692330\pi\) | ||||
−0.568123 | + | 0.822943i | \(0.692330\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2094.55 | −0.138685 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13766.6 | 0.907062 | 0.453531 | − | 0.891241i | \(-0.350164\pi\) | ||||
0.453531 | + | 0.891241i | \(0.350164\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17356.0 | 1.13246 | 0.566229 | − | 0.824248i | \(-0.308402\pi\) | ||||
0.566229 | + | 0.824248i | \(0.308402\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2924.89 | 0.189922 | 0.0949608 | − | 0.995481i | \(-0.469727\pi\) | ||||
0.0949608 | + | 0.995481i | \(0.469727\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21472.0 | −1.38083 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16263.3 | −1.04085 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3956.78 | 0.250822 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6158.40 | −0.388530 | −0.194265 | − | 0.980949i | \(-0.562232\pi\) | ||||
−0.194265 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2629.31 | 0.164316 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21788.4 | −1.35524 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11814.2 | −0.727979 | −0.363990 | − | 0.931403i | \(-0.618586\pi\) | ||||
−0.363990 | + | 0.931403i | \(0.618586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16914.7 | −1.03741 | −0.518703 | − | 0.854954i | \(-0.673585\pi\) | ||||
−0.518703 | + | 0.854954i | \(0.673585\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28652.4 | −1.74103 | −0.870513 | − | 0.492145i | \(-0.836213\pi\) | ||||
−0.870513 | + | 0.492145i | \(0.836213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −51922.5 | −3.14042 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5498.48 | −0.329513 | −0.164757 | − | 0.986334i | \(-0.552684\pi\) | ||||
−0.164757 | + | 0.986334i | \(0.552684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9068.16 | 0.540950 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18785.1 | 1.11042 | 0.555209 | − | 0.831711i | \(-0.312638\pi\) | ||||
0.555209 | + | 0.831711i | \(0.312638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17304.5 | 1.01825 | 0.509127 | − | 0.860691i | \(-0.329968\pi\) | ||||
0.509127 | + | 0.860691i | \(0.329968\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23953.7 | −1.39682 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 253.673 | 0.0147260 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29093.9 | 1.67385 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13711.5 | −0.785346 | −0.392673 | − | 0.919678i | \(-0.628450\pi\) | ||||
−0.392673 | + | 0.919678i | \(0.628450\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30566.9 | −1.73527 | −0.867637 | − | 0.497198i | \(-0.834362\pi\) | ||||
−0.867637 | + | 0.497198i | \(0.834362\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35788.8 | −2.02275 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4445.72 | −0.249064 | −0.124532 | − | 0.992216i | \(-0.539743\pi\) | ||||
−0.124532 | + | 0.992216i | \(0.539743\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7798.27 | −0.434973 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11478.6 | −0.634690 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12198.7 | −0.671580 | −0.335790 | − | 0.941937i | \(-0.609003\pi\) | ||||
−0.335790 | + | 0.941937i | \(0.609003\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17268.9 | 0.942515 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46116.6 | 2.50615 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21613.4 | 1.16452 | 0.582258 | − | 0.813004i | \(-0.302169\pi\) | ||||
0.582258 | + | 0.813004i | \(0.302169\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2590.72 | −0.138991 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7338.32 | 0.390362 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4924.85 | 0.260870 | 0.130435 | − | 0.991457i | \(-0.458363\pi\) | ||||
0.130435 | + | 0.991457i | \(0.458363\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1600.34 | 0.0840578 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −30126.7 | −1.57577 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −205.354 | −0.0106515 | −0.00532573 | − | 0.999986i | \(-0.501695\pi\) | ||||
−0.00532573 | + | 0.999986i | \(0.501695\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17178.3 | −0.887316 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 195.605 | 0.0100201 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15796.0 | −0.805836 | −0.402918 | − | 0.915236i | \(-0.632004\pi\) | ||||
−0.402918 | + | 0.915236i | \(0.632004\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7984.73 | 0.404003 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32125.3 | −1.61880 | −0.809398 | − | 0.587261i | \(-0.800206\pi\) | ||||
−0.809398 | + | 0.587261i | \(0.800206\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14464.7 | 0.722949 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28938.9 | 1.44051 | 0.720255 | − | 0.693710i | \(-0.244025\pi\) | ||||
0.720255 | + | 0.693710i | \(0.244025\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36108.5 | 1.78289 | 0.891447 | − | 0.453124i | \(-0.149691\pi\) | ||||
0.891447 | + | 0.453124i | \(0.149691\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26339.2 | −1.29529 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30306.9 | 1.47849 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23231.7 | 1.12881 | 0.564405 | − | 0.825498i | \(-0.309106\pi\) | ||||
0.564405 | + | 0.825498i | \(0.309106\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28805.5 | 1.38853 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22762.6 | −1.09289 | −0.546447 | − | 0.837494i | \(-0.684020\pi\) | ||||
−0.546447 | + | 0.837494i | \(0.684020\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40518.6 | 1.93009 | 0.965044 | − | 0.262088i | \(-0.0844112\pi\) | ||||
0.965044 | + | 0.262088i | \(0.0844112\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43903.2 | −2.08310 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31218.8 | −1.46968 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27401.1 | −1.28493 | −0.642464 | − | 0.766316i | \(-0.722088\pi\) | ||||
−0.642464 | + | 0.766316i | \(0.722088\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35698.4 | −1.66104 | −0.830520 | − | 0.556989i | \(-0.811957\pi\) | ||||
−0.830520 | + | 0.556989i | \(0.811957\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1234.01 | 0.0571959 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30195.0 | −1.38876 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52369.5 | −2.39940 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33324.3 | −1.51515 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9566.36 | −0.433296 | −0.216648 | − | 0.976250i | \(-0.569512\pi\) | ||||
−0.216648 | + | 0.976250i | \(0.569512\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56789.0 | 2.55270 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17492.9 | 0.783343 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5306.01 | −0.235820 | −0.117910 | − | 0.993024i | \(-0.537619\pi\) | ||||
−0.117910 | + | 0.993024i | \(0.537619\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5648.34 | −0.250093 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −72741.4 | −3.19675 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2356.14 | −0.103159 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9362.75 | −0.406893 | −0.203447 | − | 0.979086i | \(-0.565214\pi\) | ||||
−0.203447 | + | 0.979086i | \(0.565214\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32610.2 | 1.41196 | 0.705981 | − | 0.708231i | \(-0.250507\pi\) | ||||
0.705981 | + | 0.708231i | \(0.250507\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12523.7 | −0.538263 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5228.03 | −0.223875 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18930.7 | 0.804732 | 0.402366 | − | 0.915479i | \(-0.368188\pi\) | ||||
0.402366 | + | 0.915479i | \(0.368188\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40673.1 | −1.72269 | −0.861346 | − | 0.508018i | \(-0.830378\pi\) | ||||
−0.861346 | + | 0.508018i | \(0.830378\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30770.2 | 1.29382 | 0.646908 | − | 0.762568i | \(-0.276062\pi\) | ||||
0.646908 | + | 0.762568i | \(0.276062\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10464.9 | −0.438434 | −0.219217 | − | 0.975676i | \(-0.570350\pi\) | ||||
−0.219217 | + | 0.975676i | \(0.570350\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −58756.4 | −2.44393 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8365.13 | 0.346691 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22716.4 | 0.934752 | 0.467376 | − | 0.884059i | \(-0.345200\pi\) | ||||
0.467376 | + | 0.884059i | \(0.345200\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23044.4 | −0.944869 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6967.97 | 0.283675 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 91227.5 | 3.70084 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −254.829 | −0.0102649 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10181.2 | 0.408671 | 0.204335 | − | 0.978901i | \(-0.434497\pi\) | ||||
0.204335 | + | 0.978901i | \(0.434497\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3885.59 | −0.154877 | −0.0774384 | − | 0.996997i | \(-0.524674\pi\) | ||||
−0.0774384 | + | 0.996997i | \(0.524674\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17734.9 | −0.704433 | −0.352217 | − | 0.935919i | \(-0.614572\pi\) | ||||
−0.352217 | + | 0.935919i | \(0.614572\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19658.7 | 0.775421 | 0.387711 | − | 0.921781i | \(-0.373266\pi\) | ||||
0.387711 | + | 0.921781i | \(0.373266\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8250.35 | −0.324301 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29138.2 | 1.13745 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8697.00 | 0.338331 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40756.2 | 1.57464 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5586.82 | −0.215112 | −0.107556 | − | 0.994199i | \(-0.534303\pi\) | ||||
−0.107556 | + | 0.994199i | \(0.534303\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8050.03 | 0.307846 | 0.153923 | − | 0.988083i | \(-0.450809\pi\) | ||||
0.153923 | + | 0.988083i | \(0.450809\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2326.88 | −0.0886815 | −0.0443408 | − | 0.999016i | \(-0.514119\pi\) | ||||
−0.0443408 | + | 0.999016i | \(0.514119\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19343.5 | −0.732233 | −0.366116 | − | 0.930569i | \(-0.619313\pi\) | ||||
−0.366116 | + | 0.930569i | \(0.619313\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6870.78 | −0.259211 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3698.27 | 0.138587 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11532.4 | 0.430712 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8482.63 | 0.314696 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30954.2 | −1.14454 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −48597.2 | −1.78500 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −299.317 | −0.0109577 | −0.00547886 | − | 0.999985i | \(-0.501744\pi\) | ||||
−0.00547886 | + | 0.999985i | \(0.501744\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21022.5 | −0.764551 | −0.382275 | − | 0.924048i | \(-0.624859\pi\) | ||||
−0.382275 | + | 0.924048i | \(0.624859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3368.46 | −0.122103 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23696.5 | −0.853356 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18375.8 | 0.659587 | 0.329794 | − | 0.944053i | \(-0.393021\pi\) | ||||
0.329794 | + | 0.944053i | \(0.393021\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31487.5 | −1.12289 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −196.496 | −0.00698461 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29548.0 | 1.04353 | 0.521764 | − | 0.853090i | \(-0.325274\pi\) | ||||
0.521764 | + | 0.853090i | \(0.325274\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38471.0 | 1.35428 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −81242.1 | −2.84160 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36751.2 | 1.28133 | 0.640667 | − | 0.767819i | \(-0.278658\pi\) | ||||
0.640667 | + | 0.767819i | \(0.278658\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26024.7 | 0.901575 | 0.450788 | − | 0.892631i | \(-0.351143\pi\) | ||||
0.450788 | + | 0.892631i | \(0.351143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2970.05 | −0.102564 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40238.6 | −1.38076 | −0.690379 | − | 0.723448i | \(-0.742556\pi\) | ||||
−0.690379 | + | 0.723448i | \(0.742556\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43736.3 | −1.49604 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52396.4 | 1.78099 | 0.890496 | − | 0.454991i | \(-0.150357\pi\) | ||||
0.890496 | + | 0.454991i | \(0.150357\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39151.3 | −1.32660 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20378.1 | 0.686176 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23723.2 | 0.796319 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11043.6 | −0.368399 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9007.03 | 0.299531 | 0.149765 | − | 0.988722i | \(-0.452148\pi\) | ||||
0.149765 | + | 0.988722i | \(0.452148\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1110.63 | 0.0367062 | 0.0183531 | − | 0.999832i | \(-0.494158\pi\) | ||||
0.0183531 | + | 0.999832i | \(0.494158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45126.3 | −1.48683 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27544.4 | 0.901969 | 0.450984 | − | 0.892532i | \(-0.351073\pi\) | ||||
0.450984 | + | 0.892532i | \(0.351073\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47682.5 | 1.55663 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8657.48 | −0.280906 | −0.140453 | − | 0.990087i | \(-0.544856\pi\) | ||||
−0.140453 | + | 0.990087i | \(0.544856\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5347.60 | 0.172983 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −514.242 | −0.0165338 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54045.9 | 1.73242 | 0.866208 | − | 0.499683i | \(-0.166550\pi\) | ||||
0.866208 | + | 0.499683i | \(0.166550\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30521.4 | −0.972456 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32591.1 | 1.03528 | 0.517638 | − | 0.855600i | \(-0.326811\pi\) | ||||
0.517638 | + | 0.855600i | \(0.326811\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1728.4.a.br.1.1 | 2 | ||
3.2 | odd | 2 | 1728.4.a.bj.1.2 | 2 | |||
4.3 | odd | 2 | 1728.4.a.bq.1.1 | 2 | |||
8.3 | odd | 2 | 216.4.a.f.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 432.4.a.p.1.2 | 2 | |||
12.11 | even | 2 | 1728.4.a.bi.1.2 | 2 | |||
24.5 | odd | 2 | 432.4.a.r.1.1 | 2 | |||
24.11 | even | 2 | 216.4.a.g.1.1 | yes | 2 | ||
72.11 | even | 6 | 648.4.i.o.433.2 | 4 | |||
72.43 | odd | 6 | 648.4.i.r.433.1 | 4 | |||
72.59 | even | 6 | 648.4.i.o.217.2 | 4 | |||
72.67 | odd | 6 | 648.4.i.r.217.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.4.a.f.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
216.4.a.g.1.1 | yes | 2 | 24.11 | even | 2 | ||
432.4.a.p.1.2 | 2 | 8.5 | even | 2 | |||
432.4.a.r.1.1 | 2 | 24.5 | odd | 2 | |||
648.4.i.o.217.2 | 4 | 72.59 | even | 6 | |||
648.4.i.o.433.2 | 4 | 72.11 | even | 6 | |||
648.4.i.r.217.1 | 4 | 72.67 | odd | 6 | |||
648.4.i.r.433.1 | 4 | 72.43 | odd | 6 | |||
1728.4.a.bi.1.2 | 2 | 12.11 | even | 2 | |||
1728.4.a.bj.1.2 | 2 | 3.2 | odd | 2 | |||
1728.4.a.bq.1.1 | 2 | 4.3 | odd | 2 | |||
1728.4.a.br.1.1 | 2 | 1.1 | even | 1 | trivial |