Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,4,Mod(1,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, 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("1024.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.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: | \(60.4179558459\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 36x^{8} + 405x^{6} - 1380x^{4} + 420x^{2} - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 16) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.34476\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.1 |
$q$-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 | ||||||||
\(3\) | 8.43597 | 1.62350 | 0.811752 | − | 0.584003i | \(-0.198514\pi\) | ||||
0.811752 | + | 0.584003i | \(0.198514\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −12.2748 | −1.09789 | −0.548945 | − | 0.835858i | \(-0.684971\pi\) | ||||
−0.548945 | + | 0.835858i | \(0.684971\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.63924 | −0.0885109 | −0.0442554 | − | 0.999020i | \(-0.514092\pi\) | ||||
−0.0442554 | + | 0.999020i | \(0.514092\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 44.1656 | 1.63576 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −25.7416 | −0.705580 | −0.352790 | − | 0.935702i | \(-0.614767\pi\) | ||||
−0.352790 | + | 0.935702i | \(0.614767\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.2187 | 0.282015 | 0.141008 | − | 0.990009i | \(-0.454966\pi\) | ||||
0.141008 | + | 0.990009i | \(0.454966\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −103.550 | −1.78243 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −53.6113 | −0.764862 | −0.382431 | − | 0.923984i | \(-0.624913\pi\) | ||||
−0.382431 | + | 0.923984i | \(0.624913\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 100.391 | 1.21217 | 0.606085 | − | 0.795400i | \(-0.292739\pi\) | ||||
0.606085 | + | 0.795400i | \(0.292739\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −13.8286 | −0.143698 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −25.1189 | −0.227724 | −0.113862 | − | 0.993497i | \(-0.536322\pi\) | ||||
−0.113862 | + | 0.993497i | \(0.536322\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.6706 | 0.205365 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 144.809 | 1.03216 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −256.105 | −1.63992 | −0.819958 | − | 0.572424i | \(-0.806003\pi\) | ||||
−0.819958 | + | 0.572424i | \(0.806003\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −132.684 | −0.768733 | −0.384367 | − | 0.923180i | \(-0.625580\pi\) | ||||
−0.384367 | + | 0.923180i | \(0.625580\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −217.155 | −1.14551 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 20.1214 | 0.0971753 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −247.306 | −1.09884 | −0.549418 | − | 0.835548i | \(-0.685151\pi\) | ||||
−0.549418 | + | 0.835548i | \(0.685151\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 111.512 | 0.457853 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 198.660 | 0.756720 | 0.378360 | − | 0.925658i | \(-0.376488\pi\) | ||||
0.378360 | + | 0.925658i | \(0.376488\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 404.064 | 1.43300 | 0.716502 | − | 0.697585i | \(-0.245742\pi\) | ||||
0.716502 | + | 0.697585i | \(0.245742\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −542.124 | −1.79589 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 78.3629 | 0.243200 | 0.121600 | − | 0.992579i | \(-0.461197\pi\) | ||||
0.121600 | + | 0.992579i | \(0.461197\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −340.313 | −0.992166 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −452.264 | −1.24176 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −743.559 | −1.92709 | −0.963544 | − | 0.267549i | \(-0.913786\pi\) | ||||
−0.963544 | + | 0.267549i | \(0.913786\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 315.973 | 0.774650 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 846.894 | 1.96796 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 65.8036 | 0.145202 | 0.0726008 | − | 0.997361i | \(-0.476870\pi\) | ||||
0.0726008 | + | 0.997361i | \(0.476870\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 273.392 | 0.573841 | 0.286921 | − | 0.957954i | \(-0.407368\pi\) | ||||
0.286921 | + | 0.957954i | \(0.407368\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −72.3982 | −0.144783 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −162.256 | −0.309622 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −399.066 | −0.727667 | −0.363834 | − | 0.931464i | \(-0.618532\pi\) | ||||
−0.363834 | + | 0.931464i | \(0.618532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −211.903 | −0.369711 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −727.536 | −1.21609 | −0.608046 | − | 0.793901i | \(-0.708047\pi\) | ||||
−0.608046 | + | 0.793901i | \(0.708047\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 106.065 | 0.170054 | 0.0850270 | − | 0.996379i | \(-0.472902\pi\) | ||||
0.0850270 | + | 0.996379i | \(0.472902\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 216.556 | 0.333410 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 42.1968 | 0.0624515 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −58.9970 | −0.0840213 | −0.0420107 | − | 0.999117i | \(-0.513376\pi\) | ||||
−0.0420107 | + | 0.999117i | \(0.513376\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.1298 | 0.0399586 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −580.049 | −0.767092 | −0.383546 | − | 0.923522i | \(-0.625297\pi\) | ||||
−0.383546 | + | 0.923522i | \(0.625297\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 658.068 | 0.839735 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2160.50 | −2.66241 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −768.959 | −0.915837 | −0.457918 | − | 0.888994i | \(-0.651405\pi\) | ||||
−0.457918 | + | 0.888994i | \(0.651405\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.6686 | −0.0249614 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1119.32 | −1.24804 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1232.28 | −1.33083 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −809.953 | −0.847817 | −0.423908 | − | 0.905705i | \(-0.639342\pi\) | ||||
−0.423908 | + | 0.905705i | \(0.639342\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1136.89 | −1.15416 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 428.775 | 0.422422 | 0.211211 | − | 0.977440i | \(-0.432259\pi\) | ||||
0.211211 | + | 0.977440i | \(0.432259\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −962.201 | −0.920471 | −0.460235 | − | 0.887797i | \(-0.652235\pi\) | ||||
−0.460235 | + | 0.887797i | \(0.652235\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 169.743 | 0.157764 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1030.02 | −0.930618 | −0.465309 | − | 0.885148i | \(-0.654057\pi\) | ||||
−0.465309 | + | 0.885148i | \(0.654057\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 838.993 | 0.737256 | 0.368628 | − | 0.929577i | \(-0.379828\pi\) | ||||
0.368628 | + | 0.929577i | \(0.379828\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2086.27 | −1.78396 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −351.938 | −0.292987 | −0.146493 | − | 0.989212i | \(-0.546799\pi\) | ||||
−0.146493 | + | 0.989212i | \(0.546799\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 308.330 | 0.250017 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 583.810 | 0.461310 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 87.8821 | 0.0676986 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −668.370 | −0.502157 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1675.89 | 1.22854 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1219.25 | 0.872423 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2365.81 | 1.65301 | 0.826504 | − | 0.562931i | \(-0.190326\pi\) | ||||
0.826504 | + | 0.562931i | \(0.190326\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3408.67 | 2.32649 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −570.570 | −0.380541 | −0.190271 | − | 0.981732i | \(-0.560937\pi\) | ||||
−0.190271 | + | 0.981732i | \(0.560937\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −164.565 | −0.107290 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1777.50 | −1.13320 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −856.850 | −0.534348 | −0.267174 | − | 0.963648i | \(-0.586090\pi\) | ||||
−0.267174 | + | 0.963648i | \(0.586090\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2389.08 | 1.45783 | 0.728916 | − | 0.684603i | \(-0.240024\pi\) | ||||
0.728916 | + | 0.684603i | \(0.240024\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 661.067 | 0.394836 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −340.269 | −0.198984 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3143.64 | 1.80045 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2870.87 | −1.61078 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −45.5671 | −0.0250537 | −0.0125269 | − | 0.999922i | \(-0.503988\pi\) | ||||
−0.0125269 | + | 0.999922i | \(0.503988\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1077.06 | −0.580460 | −0.290230 | − | 0.956957i | \(-0.593732\pi\) | ||||
−0.290230 | + | 0.956957i | \(0.593732\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2367.78 | −1.25113 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1628.67 | 0.843986 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2694.94 | 1.36994 | 0.684968 | − | 0.728573i | \(-0.259816\pi\) | ||||
0.684968 | + | 0.728573i | \(0.259816\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6272.64 | −3.12863 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 41.1761 | 0.0201561 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1003.85 | −0.482377 | −0.241189 | − | 0.970478i | \(-0.577537\pi\) | ||||
−0.241189 | + | 0.970478i | \(0.577537\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2665.54 | 1.25765 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3460.66 | 1.60356 | 0.801778 | − | 0.597623i | \(-0.203888\pi\) | ||||
0.801778 | + | 0.597623i | \(0.203888\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2022.27 | −0.920467 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4433.82 | 1.98282 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1843.49 | 0.810162 | 0.405081 | − | 0.914281i | \(-0.367243\pi\) | ||||
0.405081 | + | 0.914281i | \(0.367243\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −42.0803 | −0.0181770 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 555.117 | 0.235735 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1530.67 | −0.639149 | −0.319575 | − | 0.947561i | \(-0.603540\pi\) | ||||
−0.319575 | + | 0.947561i | \(0.603540\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4163.35 | 1.70972 | 0.854859 | − | 0.518860i | \(-0.173643\pi\) | ||||
0.854859 | + | 0.518860i | \(0.173643\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2306.33 | 0.931633 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3035.64 | 1.20640 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1380.04 | 0.539672 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −237.377 | −0.0913577 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 430.650 | 0.163145 | 0.0815726 | − | 0.996667i | \(-0.474006\pi\) | ||||
0.0815726 | + | 0.996667i | \(0.474006\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2266.98 | −0.845497 | −0.422749 | − | 0.906247i | \(-0.638935\pi\) | ||||
−0.422749 | + | 0.906247i | \(0.638935\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1368.79 | −0.502672 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1469.95 | 0.531621 | 0.265810 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265810 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4989.44 | −1.77735 | −0.888674 | − | 0.458540i | \(-0.848373\pi\) | ||||
−0.888674 | + | 0.458540i | \(0.848373\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3366.51 | −1.18137 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 419.819 | 0.145150 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2438.51 | −0.830796 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1109.39 | −0.372503 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2584.22 | −0.855283 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3749.79 | 1.22344 | 0.611720 | − | 0.791074i | \(-0.290478\pi\) | ||||
0.611720 | + | 0.791074i | \(0.290478\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6137.47 | −1.97433 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4959.80 | −1.57328 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 217.501 | 0.0680413 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 894.760 | 0.276083 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −708.670 | −0.215703 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3690.85 | −1.10833 | −0.554165 | − | 0.832407i | \(-0.686962\pi\) | ||||
−0.554165 | + | 0.832407i | \(0.686962\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1133.76 | 0.335928 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2418.90 | 0.707259 | 0.353630 | − | 0.935385i | \(-0.384947\pi\) | ||||
0.353630 | + | 0.935385i | \(0.384947\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 129.827 | 0.0374637 | 0.0187318 | − | 0.999825i | \(-0.494037\pi\) | ||||
0.0187318 | + | 0.999825i | \(0.494037\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 355.971 | 0.101390 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4259.71 | 1.19769 | 0.598847 | − | 0.800863i | \(-0.295626\pi\) | ||||
0.598847 | + | 0.800863i | \(0.295626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −961.889 | −0.267007 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −497.697 | −0.136409 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5053.12 | −1.36761 | −0.683806 | − | 0.729664i | \(-0.739676\pi\) | ||||
−0.683806 | + | 0.729664i | \(0.739676\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −48.8379 | −0.0130536 | −0.00652681 | − | 0.999979i | \(-0.502078\pi\) | ||||
−0.00652681 | + | 0.999979i | \(0.502078\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3664.09 | −0.967291 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4177.27 | 1.08929 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1327.03 | 0.341850 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4893.28 | −1.24538 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3683.69 | −0.926345 | −0.463172 | − | 0.886268i | \(-0.653289\pi\) | ||||
−0.463172 | + | 0.886268i | \(0.653289\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 646.602 | 0.160678 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5551.44 | 1.36331 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 739.054 | 0.179381 | 0.0896905 | − | 0.995970i | \(-0.471412\pi\) | ||||
0.0896905 | + | 0.995970i | \(0.471412\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 405.396 | 0.0972589 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11311.0 | −2.68251 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2448.30 | −0.574025 | −0.287012 | − | 0.957927i | \(-0.592662\pi\) | ||||
−0.287012 | + | 0.957927i | \(0.592662\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9127.03 | 2.11573 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6486.91 | −1.48686 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1173.73 | 0.266035 | 0.133018 | − | 0.991114i | \(-0.457533\pi\) | ||||
0.133018 | + | 0.991114i | \(0.457533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1404.85 | 0.314902 | 0.157451 | − | 0.987527i | \(-0.449672\pi\) | ||||
0.157451 | + | 0.987527i | \(0.449672\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −182.796 | −0.0405249 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −660.801 | −0.144901 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3175.88 | −0.688881 | −0.344440 | − | 0.938808i | \(-0.611931\pi\) | ||||
−0.344440 | + | 0.938808i | \(0.611931\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5860.07 | −1.25747 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6045.97 | 1.28353 | 0.641766 | − | 0.766900i | \(-0.278202\pi\) | ||||
0.641766 | + | 0.766900i | \(0.278202\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3478.45 | 0.730644 | 0.365322 | − | 0.930881i | \(-0.380959\pi\) | ||||
0.365322 | + | 0.930881i | \(0.380959\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10395.4 | −2.16061 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −325.653 | −0.0669780 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2038.82 | −0.414986 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6832.74 | −1.37643 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2619.82 | 0.522360 | 0.261180 | − | 0.965290i | \(-0.415888\pi\) | ||||
0.261180 | + | 0.965290i | \(0.415888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −807.725 | −0.159415 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3727.60 | −0.728275 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −332.039 | −0.0642217 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −662.360 | −0.126837 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3617.13 | 0.685804 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3355.83 | −0.630015 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2980.24 | 0.554044 | 0.277022 | − | 0.960864i | \(-0.410653\pi\) | ||||
0.277022 | + | 0.960864i | \(0.410653\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8117.10 | −1.49439 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5294.90 | 0.965422 | 0.482711 | − | 0.875780i | \(-0.339652\pi\) | ||||
0.482711 | + | 0.875780i | \(0.339652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4005.87 | 0.723403 | 0.361702 | − | 0.932294i | \(-0.382196\pi\) | ||||
0.361702 | + | 0.932294i | \(0.382196\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 888.673 | 0.158956 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1144.44 | 0.202770 | 0.101385 | − | 0.994847i | \(-0.467673\pi\) | ||||
0.101385 | + | 0.994847i | \(0.467673\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6592.56 | 1.15709 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8689.25 | −1.51086 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5382.08 | −0.927143 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 339.331 | 0.0579159 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7077.72 | 1.19694 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −128.456 | −0.0215259 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5981.64 | 0.993295 | 0.496648 | − | 0.867952i | \(-0.334564\pi\) | ||||
0.496648 | + | 0.867952i | \(0.334564\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10922.4 | −1.79744 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4898.46 | 0.798899 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10002.6 | −1.61684 | −0.808419 | − | 0.588607i | \(-0.799677\pi\) | ||||
−0.808419 | + | 0.588607i | \(0.799677\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2968.94 | −0.475665 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3415.50 | 0.542403 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1120.12 | 0.176328 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2601.06 | 0.405903 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9064.38 | −1.40231 | −0.701155 | − | 0.713009i | \(-0.747332\pi\) | ||||
−0.701155 | + | 0.713009i | \(0.747332\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7782.74 | −1.19370 | −0.596849 | − | 0.802354i | \(-0.703581\pi\) | ||||
−0.596849 | + | 0.802354i | \(0.703581\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1914.18 | 0.291086 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1411.35 | −0.212800 | −0.106400 | − | 0.994323i | \(-0.533932\pi\) | ||||
−0.106400 | + | 0.994323i | \(0.533932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8930.35 | 1.33514 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 741.371 | 0.109909 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2160.73 | 0.317658 | 0.158829 | − | 0.987306i | \(-0.449228\pi\) | ||||
0.158829 | + | 0.987306i | \(0.449228\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3219.31 | 0.469355 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5638.35 | −0.815253 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1301.92 | −0.186701 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10757.7 | 1.53010 | 0.765052 | − | 0.643969i | \(-0.222713\pi\) | ||||
0.765052 | + | 0.643969i | \(0.222713\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8773.95 | 1.23782 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1218.87 | 0.170568 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1989.79 | 0.276213 | 0.138107 | − | 0.990417i | \(-0.455898\pi\) | ||||
0.138107 | + | 0.990417i | \(0.455898\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10285.5 | 1.41638 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3385.37 | −0.462481 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1622.04 | −0.219838 | −0.109919 | − | 0.993941i | \(-0.535059\pi\) | ||||
−0.109919 | + | 0.993941i | \(0.535059\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19957.9 | 2.68366 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9042.17 | −1.20635 | −0.603176 | − | 0.797608i | \(-0.706098\pi\) | ||||
−0.603176 | + | 0.797608i | \(0.706098\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −517.957 | −0.0685650 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17845.7 | 2.34406 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3642.08 | −0.474706 | −0.237353 | − | 0.971423i | \(-0.576280\pi\) | ||||
−0.237353 | + | 0.971423i | \(0.576280\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1346.66 | 0.174178 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4813.31 | −0.617810 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 724.176 | 0.0922462 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10071.3 | 1.27320 | 0.636602 | − | 0.771192i | \(-0.280339\pi\) | ||||
0.636602 | + | 0.771192i | \(0.280339\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1388.27 | −0.174186 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3025.14 | 0.376729 | 0.188365 | − | 0.982099i | \(-0.439681\pi\) | ||||
0.188365 | + | 0.982099i | \(0.439681\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1753.90 | −0.216794 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −357.562 | −0.0438702 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6366.06 | 0.775317 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9440.21 | 1.14129 | 0.570646 | − | 0.821196i | \(-0.306693\pi\) | ||||
0.570646 | + | 0.821196i | \(0.306693\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7228.36 | −0.867515 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −107.868 | −0.0128519 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7119.98 | 0.842183 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20154.2 | 2.36680 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4604.25 | 0.536831 | 0.268416 | − | 0.963303i | \(-0.413500\pi\) | ||||
0.268416 | + | 0.963303i | \(0.413500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13347.4 | 1.54516 | 0.772580 | − | 0.634917i | \(-0.218966\pi\) | ||||
0.772580 | + | 0.634917i | \(0.218966\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3460.95 | 0.397818 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1376.23 | −0.157076 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −448.157 | −0.0507912 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2870.50 | −0.323052 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10617.7 | −1.18663 | −0.593314 | − | 0.804971i | \(-0.702181\pi\) | ||||
−0.593314 | + | 0.804971i | \(0.702181\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −706.479 | −0.0784093 | −0.0392046 | − | 0.999231i | \(-0.512482\pi\) | ||||
−0.0392046 | + | 0.999231i | \(0.512482\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26519.7 | 2.92303 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2521.71 | −0.276041 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13611.8 | −1.47985 | −0.739926 | − | 0.672688i | \(-0.765140\pi\) | ||||
−0.739926 | + | 0.672688i | \(0.765140\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15030.1 | −1.62295 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4422.21 | 0.474279 | 0.237139 | − | 0.971476i | \(-0.423790\pi\) | ||||
0.237139 | + | 0.971476i | \(0.423790\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9438.81 | 1.00549 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −384.403 | −0.0406748 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5231.76 | −0.549893 | −0.274947 | − | 0.961460i | \(-0.588660\pi\) | ||||
−0.274947 | + | 0.961460i | \(0.588660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5113.83 | −0.533927 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9086.01 | −0.942379 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 265.978 | 0.0274049 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6833.10 | −0.699429 | −0.349715 | − | 0.936856i | \(-0.613721\pi\) | ||||
−0.349715 | + | 0.936856i | \(0.613721\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7763.38 | −0.789463 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8451.19 | 0.853821 | 0.426910 | − | 0.904294i | \(-0.359602\pi\) | ||||
0.426910 | + | 0.904294i | \(0.359602\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4273.38 | −0.428943 | −0.214472 | − | 0.976730i | \(-0.568803\pi\) | ||||
−0.214472 | + | 0.976730i | \(0.568803\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13739.4 | 1.37021 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17317.9 | 1.71601 | 0.858004 | − | 0.513643i | \(-0.171704\pi\) | ||||
0.858004 | + | 0.513643i | \(0.171704\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 654.167 | 0.0644065 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22734.5 | 2.22410 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10401.3 | −1.01110 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2577.09 | 0.248937 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32839.7 | −3.15226 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4067.97 | 0.388038 | 0.194019 | − | 0.980998i | \(-0.437848\pi\) | ||||
0.194019 | + | 0.980998i | \(0.437848\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3269.06 | −0.309888 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 347.360 | 0.0327235 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9942.00 | 0.930811 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16174.3 | 1.50499 | 0.752493 | − | 0.658600i | \(-0.228851\pi\) | ||||
0.752493 | + | 0.658600i | \(0.228851\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8468.44 | −0.783141 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19228.6 | −1.76736 | −0.883680 | − | 0.468091i | \(-0.844942\pi\) | ||||
−0.883680 | + | 0.468091i | \(0.844942\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13730.1 | 1.25431 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13955.1 | 1.26714 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1192.61 | 0.107637 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20713.6 | −1.85825 | −0.929127 | − | 0.369762i | \(-0.879439\pi\) | ||||
−0.929127 | + | 0.369762i | \(0.879439\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29194.0 | 2.60338 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9828.84 | −0.871265 | −0.435632 | − | 0.900125i | \(-0.643475\pi\) | ||||
−0.435632 | + | 0.900125i | \(0.643475\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5263.12 | −0.463774 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17059.8 | −1.49438 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19029.8 | 1.65714 | 0.828568 | − | 0.559889i | \(-0.189156\pi\) | ||||
0.828568 | + | 0.559889i | \(0.189156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −173.866 | −0.0150516 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14537.5 | 1.25116 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11810.8 | 1.01058 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2017.19 | −0.171597 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15551.6 | 1.31530 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10607.1 | 0.891950 | 0.445975 | − | 0.895045i | \(-0.352857\pi\) | ||||
0.445975 | + | 0.895045i | \(0.352857\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5519.88 | −0.461506 | −0.230753 | − | 0.973012i | \(-0.574119\pi\) | ||||
−0.230753 | + | 0.973012i | \(0.574119\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −354.989 | −0.0295104 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7113.36 | 0.587975 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11536.0 | −0.948142 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2906.25 | 0.237515 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2626.02 | 0.213407 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12643.3 | 1.02172 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12912.7 | −1.03766 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8760.20 | 0.700053 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13481.4 | 1.07137 | 0.535683 | − | 0.844419i | \(-0.320054\pi\) | ||||
0.535683 | + | 0.844419i | \(0.320054\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35121.9 | 2.77573 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10298.5 | −0.809427 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1743.55 | 0.136287 | 0.0681434 | − | 0.997676i | \(-0.478292\pi\) | ||||
0.0681434 | + | 0.997676i | \(0.478292\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12074.5 | 0.938668 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25710.6 | −1.98786 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 96.7105 | 0.00743680 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 25608.5 | 1.95860 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4086.47 | 0.310861 | 0.155430 | − | 0.987847i | \(-0.450324\pi\) | ||||
0.155430 | + | 0.987847i | \(0.450324\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5341.19 | 0.404129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11642.0 | 0.876159 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 99.1014 | 0.00741852 | 0.00370926 | − | 0.999993i | \(-0.498819\pi\) | ||||
0.00370926 | + | 0.999993i | \(0.498819\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4319.96 | 0.321668 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −47.7509 | −0.00353677 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8915.23 | 0.656847 | 0.328423 | − | 0.944531i | \(-0.393483\pi\) | ||||
0.328423 | + | 0.944531i | \(0.393483\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6995.13 | 0.512674 | 0.256337 | − | 0.966587i | \(-0.417484\pi\) | ||||
0.256337 | + | 0.966587i | \(0.417484\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3632.95 | 0.264867 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −644.818 | −0.0467665 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17911.5 | 1.29232 | 0.646159 | − | 0.763203i | \(-0.276374\pi\) | ||||
0.646159 | + | 0.763203i | \(0.276374\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19124.2 | −1.37267 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 950.842 | 0.0678960 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19140.4 | 1.35972 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7166.15 | −0.506468 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11229.2 | −0.789573 | −0.394787 | − | 0.918773i | \(-0.629181\pi\) | ||||
−0.394787 | + | 0.918773i | \(0.629181\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13320.2 | −0.931835 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12400.4 | 0.863088 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7006.26 | 0.485181 | 0.242591 | − | 0.970129i | \(-0.422003\pi\) | ||||
0.242591 | + | 0.970129i | \(0.422003\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1078.73 | −0.0743257 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −42090.8 | −2.88553 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8502.74 | 0.579987 | 0.289994 | − | 0.957029i | \(-0.406347\pi\) | ||||
0.289994 | + | 0.957029i | \(0.406347\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11936.2 | 0.810127 | 0.405063 | − | 0.914289i | \(-0.367249\pi\) | ||||
0.405063 | + | 0.914289i | \(0.367249\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17625.0 | −1.19029 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8204.11 | 0.551313 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3850.00 | 0.257441 | 0.128721 | − | 0.991681i | \(-0.458913\pi\) | ||||
0.128721 | + | 0.991681i | \(0.458913\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3541.58 | 0.235652 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1035.85 | 0.0685861 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8938.34 | 0.588933 | 0.294467 | − | 0.955662i | \(-0.404858\pi\) | ||||
0.294467 | + | 0.955662i | \(0.404858\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20571.2 | −1.34880 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2585.09 | −0.168674 | −0.0843370 | − | 0.996437i | \(-0.526877\pi\) | ||||
−0.0843370 | + | 0.996437i | \(0.526877\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10359.1 | −0.672648 | −0.336324 | − | 0.941746i | \(-0.609184\pi\) | ||||
−0.336324 | + | 0.941746i | \(0.609184\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3637.44 | −0.235049 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1260.51 | 0.0810615 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18174.8 | −1.16319 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21800.4 | −1.38855 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13258.4 | 0.840458 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14411.5 | −0.909210 | −0.454605 | − | 0.890693i | \(-0.650220\pi\) | ||||
−0.454605 | + | 0.890693i | \(0.650220\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 31633.1 | 1.98626 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −29039.9 | −1.81482 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4498.48 | −0.279806 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −32132.1 | −1.98924 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25724.0 | −1.58508 | −0.792542 | − | 0.609818i | \(-0.791243\pi\) | ||||
−0.792542 | + | 0.609818i | \(0.791243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11081.4 | 0.679640 | 0.339820 | − | 0.940491i | \(-0.389634\pi\) | ||||
0.339820 | + | 0.940491i | \(0.389634\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −41840.8 | −2.55423 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1247.43 | −0.0757981 | −0.0378991 | − | 0.999282i | \(-0.512067\pi\) | ||||
−0.0378991 | + | 0.999282i | \(0.512067\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1693.89 | −0.102451 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1834.84 | 0.110465 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11741.1 | −0.703621 | −0.351811 | − | 0.936071i | \(-0.614434\pi\) | ||||
−0.351811 | + | 0.936071i | \(0.614434\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7003.63 | 0.417793 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4684.42 | 0.278168 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2398.73 | 0.141792 | 0.0708961 | − | 0.997484i | \(-0.477414\pi\) | ||||
0.0708961 | + | 0.997484i | \(0.477414\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12428.5 | −0.731337 | −0.365669 | − | 0.930745i | \(-0.619160\pi\) | ||||
−0.365669 | + | 0.930745i | \(0.619160\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5978.32 | −0.350194 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2020.00 | 0.117793 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6433.09 | 0.373449 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −31135.9 | −1.79938 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7037.56 | −0.404891 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23869.3 | −1.36716 | −0.683578 | − | 0.729878i | \(-0.739577\pi\) | ||||
−0.683578 | + | 0.729878i | \(0.739577\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3717.32 | 0.211970 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8009.12 | 0.454676 | 0.227338 | − | 0.973816i | \(-0.426998\pi\) | ||||
0.227338 | + | 0.973816i | \(0.426998\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1327.71 | 0.0750410 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20405.8 | 1.14824 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12944.0 | 0.725167 | 0.362583 | − | 0.931951i | \(-0.381895\pi\) | ||||
0.362583 | + | 0.931951i | \(0.381895\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10517.7 | 0.586655 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1095.21 | 0.0608224 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9828.85 | −0.543468 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24123.5 | 1.32807 | 0.664037 | − | 0.747699i | \(-0.268842\pi\) | ||||
0.664037 | + | 0.747699i | \(0.268842\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1863.65 | 0.102156 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29325.4 | −1.60054 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10650.4 | −0.578787 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35934.8 | 1.94446 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10918.3 | −0.588274 | −0.294137 | − | 0.955763i | \(-0.595032\pi\) | ||||
−0.294137 | + | 0.955763i | \(0.595032\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24827.3 | −1.33198 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8114.47 | −0.433487 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −702.866 | −0.0373890 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6473.79 | −0.342917 | −0.171459 | − | 0.985191i | \(-0.554848\pi\) | ||||
−0.171459 | + | 0.985191i | \(0.554848\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2605.64 | −0.137439 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3332.88 | 0.175059 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4176.74 | 0.218463 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −42628.0 | −2.22032 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30210.0 | −1.56696 | −0.783479 | − | 0.621418i | \(-0.786557\pi\) | ||||
−0.783479 | + | 0.621418i | \(0.786557\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1577.28 | 0.0814717 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −411.995 | −0.0211926 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6574.37 | −0.336781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20721.3 | 1.05710 | 0.528549 | − | 0.848903i | \(-0.322736\pi\) | ||||
0.528549 | + | 0.848903i | \(0.322736\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −31696.7 | −1.61036 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21662.4 | −1.09605 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19629.0 | −0.989107 | −0.494553 | − | 0.869147i | \(-0.664668\pi\) | ||||
−0.494553 | + | 0.869147i | \(0.664668\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 35239.3 | 1.76847 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10272.6 | 0.513428 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12436.5 | −0.619058 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11194.8 | 0.554995 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7669.27 | −0.378678 | −0.189339 | − | 0.981912i | \(-0.560635\pi\) | ||||
−0.189339 | + | 0.981912i | \(0.560635\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 559.327 | 0.0275062 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −25618.2 | −1.25478 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1688.46 | 0.0823698 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26531.8 | −1.28916 | −0.644580 | − | 0.764537i | \(-0.722968\pi\) | ||||
−0.644580 | + | 0.764537i | \(0.722968\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31075.5 | −1.50392 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13220.6 | 0.637282 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −112.316 | −0.00539258 | −0.00269629 | − | 0.999996i | \(-0.500858\pi\) | ||||
−0.00269629 | + | 0.999996i | \(0.500858\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5454.71 | 0.260861 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36991.3 | 1.76207 | 0.881033 | − | 0.473055i | \(-0.156849\pi\) | ||||
0.881033 | + | 0.473055i | \(0.156849\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1375.31 | −0.0652552 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 29064.0 | 1.37361 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 869.835 | 0.0409490 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26637.0 | 1.24910 | 0.624548 | − | 0.780987i | \(-0.285283\pi\) | ||||
0.624548 | + | 0.780987i | \(0.285283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6234.64 | 0.291226 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27921.7 | −1.29919 | −0.649596 | − | 0.760280i | \(-0.725062\pi\) | ||||
−0.649596 | + | 0.760280i | \(0.725062\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3406.07 | −0.157871 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3419.91 | 0.157900 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19943.7 | 0.917273 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18727.9 | 0.858051 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −37086.2 | −1.69266 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33079.9 | −1.50404 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40839.8 | −1.84979 | −0.924893 | − | 0.380229i | \(-0.875845\pi\) | ||||
−0.924893 | + | 0.380229i | \(0.875845\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20653.8 | −0.931931 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 576.912 | 0.0259325 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3613.88 | 0.161832 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 76995.4 | 3.43490 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23555.1 | −1.04688 | −0.523440 | − | 0.852062i | \(-0.675352\pi\) | ||||
−0.523440 | + | 0.852062i | \(0.675352\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4201.14 | −0.186015 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33961.5 | −1.49809 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2730.28 | −0.119987 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −505.428 | −0.0221292 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9901.55 | 0.431910 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34940.4 | 1.51847 | 0.759233 | − | 0.650819i | \(-0.225574\pi\) | ||||
0.759233 | + | 0.650819i | \(0.225574\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21451.0 | 0.928789 | 0.464395 | − | 0.885628i | \(-0.346272\pi\) | ||||
0.464395 | + | 0.885628i | \(0.346272\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11851.3 | 0.511244 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12322.0 | 0.529597 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40564.3 | 1.73705 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −957.008 | −0.0408310 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12318.6 | 0.523656 | 0.261828 | − | 0.965115i | \(-0.415675\pi\) | ||||
0.261828 | + | 0.965115i | \(0.415675\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24493.5 | 1.03741 | 0.518707 | − | 0.854952i | \(-0.326414\pi\) | ||||
0.518707 | + | 0.854952i | \(0.326414\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5574.50 | −0.235248 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37233.4 | 1.56558 | 0.782789 | − | 0.622287i | \(-0.213796\pi\) | ||||
0.782789 | + | 0.622287i | \(0.213796\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12881.0 | 0.539658 | 0.269829 | − | 0.962908i | \(-0.413033\pi\) | ||||
0.269829 | + | 0.962908i | \(0.413033\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26791.6 | −1.11840 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18244.6 | 0.758870 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −42478.9 | −1.76053 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19213.8 | −0.793459 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1394.89 | −0.0573982 | −0.0286991 | − | 0.999588i | \(-0.509136\pi\) | ||||
−0.0286991 | + | 0.999588i | \(0.509136\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41200.9 | 1.68932 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 51003.7 | 2.08382 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24822.9 | 1.01057 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1095.62 | 0.0444463 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29344.1 | 1.18620 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6212.08 | 0.250232 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21615.8 | 0.867658 | 0.433829 | − | 0.900995i | \(-0.357162\pi\) | ||||
0.433829 | + | 0.900995i | \(0.357162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −54424.2 | −2.17692 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2273.70 | −0.0906277 | −0.0453139 | − | 0.998973i | \(-0.514429\pi\) | ||||
−0.0453139 | + | 0.998973i | \(0.514429\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30652.1 | −1.21750 | −0.608752 | − | 0.793361i | \(-0.708329\pi\) | ||||
−0.608752 | + | 0.793361i | \(0.708329\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2747.20 | −0.108739 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23721.7 | −0.935686 | −0.467843 | − | 0.883812i | \(-0.654969\pi\) | ||||
−0.467843 | + | 0.883812i | \(0.654969\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22628.5 | −0.889469 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17199.5 | −0.673731 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1518.68 | 0.0592838 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5275.12 | −0.205213 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −35772.1 | −1.38683 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1998.65 | −0.0772189 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31720.2 | −1.22134 | −0.610670 | − | 0.791885i | \(-0.709100\pi\) | ||||
−0.610670 | + | 0.791885i | \(0.709100\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22100.7 | 0.848054 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24603.0 | −0.940859 | −0.470429 | − | 0.882438i | \(-0.655901\pi\) | ||||
−0.470429 | + | 0.882438i | \(0.655901\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33215.2 | −1.26589 | −0.632945 | − | 0.774197i | \(-0.718154\pi\) | ||||
−0.632945 | + | 0.774197i | \(0.718154\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6813.95 | −0.258812 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39722.9 | −1.50368 | −0.751841 | − | 0.659345i | \(-0.770834\pi\) | ||||
−0.751841 | + | 0.659345i | \(0.770834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3878.15 | −0.146309 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −749.848 | −0.0281940 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7866.92 | 0.294800 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18788.7 | 0.701716 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2801.07 | −0.104264 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33981.1 | 1.26066 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39863.2 | 1.47396 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5587.65 | −0.205920 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −51104.2 | −1.87708 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6456.50 | −0.236367 | −0.118183 | − | 0.992992i | \(-0.537707\pi\) | ||||
−0.118183 | + | 0.992992i | \(0.537707\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18937.1 | 0.690983 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2013.95 | −0.0732438 | −0.0366219 | − | 0.999329i | \(-0.511660\pi\) | ||||
−0.0366219 | + | 0.999329i | \(0.511660\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14931.4 | 0.541245 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28309.7 | −1.02283 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 935.303 | 0.0336820 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37746.5 | 1.35489 | 0.677443 | − | 0.735575i | \(-0.263088\pi\) | ||||
0.677443 | + | 0.735575i | \(0.263088\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25141.2 | 0.899492 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9617.05 | −0.342957 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6348.50 | −0.225662 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −42496.2 | −1.50567 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45643.5 | 1.61197 | 0.805983 | − | 0.591939i | \(-0.201637\pi\) | ||||
0.805983 | + | 0.591939i | \(0.201637\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34164.3 | −1.20267 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 44667.6 | 1.56737 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16939.7 | −0.592501 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47317.5 | −1.64973 | −0.824864 | − | 0.565331i | \(-0.808748\pi\) | ||||
−0.824864 | + | 0.565331i | \(0.808748\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33793.4 | 1.17445 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21318.9 | −0.738550 | −0.369275 | − | 0.929320i | \(-0.620394\pi\) | ||||
−0.369275 | + | 0.929320i | \(0.620394\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4990.14 | −0.172324 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2913.75 | 0.100301 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20601.8 | 0.706937 | 0.353468 | − | 0.935446i | \(-0.385002\pi\) | ||||
0.353468 | + | 0.935446i | \(0.385002\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1402.03 | 0.0479578 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9654.45 | 0.329198 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42987.2 | −1.46117 | −0.730583 | − | 0.682824i | \(-0.760752\pi\) | ||||
−0.730583 | + | 0.682824i | \(0.760752\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5286.14 | −0.179116 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 55614.6 | 1.87854 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1404.59 | 0.0472956 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12186.0 | −0.409049 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45491.6 | −1.52227 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27826.7 | 0.928264 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44030.7 | −1.46425 | −0.732126 | − | 0.681170i | \(-0.761472\pi\) | ||||
−0.732126 | + | 0.681170i | \(0.761472\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −45403.1 | −1.50522 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50487.1 | −1.66860 | −0.834298 | − | 0.551313i | \(-0.814127\pi\) | ||||
−0.834298 | + | 0.551313i | \(0.814127\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3916.28 | −0.129034 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2862.58 | 0.0940267 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49515.3 | 1.62143 | 0.810714 | − | 0.585442i | \(-0.199079\pi\) | ||||
0.810714 | + | 0.585442i | \(0.199079\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19794.2 | 0.646196 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37054.6 | 1.20598 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40046.2 | −1.29936 | −0.649682 | − | 0.760206i | \(-0.725098\pi\) | ||||
−0.649682 | + | 0.760206i | \(0.725098\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18043.3 | −0.583662 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1083.65 | −0.0349473 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10149.7 | −0.326330 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18673.2 | −0.598560 | −0.299280 | − | 0.954165i | \(-0.596746\pi\) | ||||
−0.299280 | + | 0.954165i | \(0.596746\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 50460.9 | 1.61262 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 61244.4 | 1.95133 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31087.3 | −0.987508 | −0.493754 | − | 0.869602i | \(-0.664376\pi\) | ||||
−0.493754 | + | 0.869602i | \(0.664376\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35812.1 | −1.13418 |
(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 | 1024.4.a.m.1.10 | 10 | ||
4.3 | odd | 2 | 1024.4.a.n.1.1 | 10 | |||
8.3 | odd | 2 | 1024.4.a.n.1.10 | 10 | |||
8.5 | even | 2 | inner | 1024.4.a.m.1.1 | 10 | ||
16.3 | odd | 4 | 1024.4.b.j.513.1 | 10 | |||
16.5 | even | 4 | 1024.4.b.k.513.1 | 10 | |||
16.11 | odd | 4 | 1024.4.b.j.513.10 | 10 | |||
16.13 | even | 4 | 1024.4.b.k.513.10 | 10 | |||
32.3 | odd | 8 | 16.4.e.a.13.2 | yes | 10 | ||
32.5 | even | 8 | 128.4.e.a.97.1 | 10 | |||
32.11 | odd | 8 | 16.4.e.a.5.2 | ✓ | 10 | ||
32.13 | even | 8 | 128.4.e.a.33.1 | 10 | |||
32.19 | odd | 8 | 128.4.e.b.33.5 | 10 | |||
32.21 | even | 8 | 64.4.e.a.49.5 | 10 | |||
32.27 | odd | 8 | 128.4.e.b.97.5 | 10 | |||
32.29 | even | 8 | 64.4.e.a.17.5 | 10 | |||
96.11 | even | 8 | 144.4.k.a.37.4 | 10 | |||
96.29 | odd | 8 | 576.4.k.a.145.1 | 10 | |||
96.35 | even | 8 | 144.4.k.a.109.4 | 10 | |||
96.53 | odd | 8 | 576.4.k.a.433.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.2 | ✓ | 10 | 32.11 | odd | 8 | ||
16.4.e.a.13.2 | yes | 10 | 32.3 | odd | 8 | ||
64.4.e.a.17.5 | 10 | 32.29 | even | 8 | |||
64.4.e.a.49.5 | 10 | 32.21 | even | 8 | |||
128.4.e.a.33.1 | 10 | 32.13 | even | 8 | |||
128.4.e.a.97.1 | 10 | 32.5 | even | 8 | |||
128.4.e.b.33.5 | 10 | 32.19 | odd | 8 | |||
128.4.e.b.97.5 | 10 | 32.27 | odd | 8 | |||
144.4.k.a.37.4 | 10 | 96.11 | even | 8 | |||
144.4.k.a.109.4 | 10 | 96.35 | even | 8 | |||
576.4.k.a.145.1 | 10 | 96.29 | odd | 8 | |||
576.4.k.a.433.1 | 10 | 96.53 | odd | 8 | |||
1024.4.a.m.1.1 | 10 | 8.5 | even | 2 | inner | ||
1024.4.a.m.1.10 | 10 | 1.1 | even | 1 | trivial | ||
1024.4.a.n.1.1 | 10 | 4.3 | odd | 2 | |||
1024.4.a.n.1.10 | 10 | 8.3 | odd | 2 | |||
1024.4.b.j.513.1 | 10 | 16.3 | odd | 4 | |||
1024.4.b.j.513.10 | 10 | 16.11 | odd | 4 | |||
1024.4.b.k.513.1 | 10 | 16.5 | even | 4 | |||
1024.4.b.k.513.10 | 10 | 16.13 | even | 4 |