Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,4,Mod(513,1024)]
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, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.513");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(60.4179558459\) |
Analytic rank: | \(0\) |
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) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 513.10 | ||
Root | \(-2.34476i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.513 |
Dual form | 1024.4.b.j.513.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 8.43597i | 1.62350i | 0.584003 | + | 0.811752i | \(0.301486\pi\) | ||||
−0.584003 | + | 0.811752i | \(0.698514\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 12.2748i | − 1.09789i | −0.835858 | − | 0.548945i | \(-0.815029\pi\) | ||||
0.835858 | − | 0.548945i | \(-0.184971\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | 25.7416i | 0.705580i | 0.935702 | + | 0.352790i | \(0.114767\pi\) | ||||
−0.935702 | + | 0.352790i | \(0.885233\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 13.2187i | − 0.282015i | −0.990009 | − | 0.141008i | \(-0.954966\pi\) | ||||
0.990009 | − | 0.141008i | \(-0.0450342\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 100.391i | 1.21217i | 0.795400 | + | 0.606085i | \(0.207261\pi\) | ||||
−0.795400 | + | 0.606085i | \(0.792739\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 13.8286i | − 0.143698i | ||||||||
\(22\) | 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 | ||||||||
\(27\) | − 144.809i | − 1.03216i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 256.105i | 1.63992i | 0.572424 | + | 0.819958i | \(0.306003\pi\) | ||||
−0.572424 | + | 0.819958i | \(0.693997\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 132.684 | 0.768733 | 0.384367 | − | 0.923180i | \(-0.374420\pi\) | ||||
0.384367 | + | 0.923180i | \(0.374420\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −217.155 | −1.14551 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 20.1214i | 0.0971753i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 247.306i | − 1.09884i | −0.835548 | − | 0.549418i | \(-0.814849\pi\) | ||||
0.835548 | − | 0.549418i | \(-0.185151\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 111.512 | 0.457853 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −198.660 | −0.756720 | −0.378360 | − | 0.925658i | \(-0.623512\pi\) | ||||
−0.378360 | + | 0.925658i | \(0.623512\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 404.064i | − 1.43300i | −0.697585 | − | 0.716502i | \(-0.745742\pi\) | ||||
0.697585 | − | 0.716502i | \(-0.254258\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 542.124i | 1.79589i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −78.3629 | −0.243200 | −0.121600 | − | 0.992579i | \(-0.538803\pi\) | ||||
−0.121600 | + | 0.992579i | \(0.538803\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −340.313 | −0.992166 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 452.264i | − 1.24176i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 743.559i | − 1.92709i | −0.267549 | − | 0.963544i | \(-0.586214\pi\) | ||||
0.267549 | − | 0.963544i | \(-0.413786\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 315.973 | 0.774650 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −846.894 | −1.96796 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 65.8036i | − 0.145202i | −0.997361 | − | 0.0726008i | \(-0.976870\pi\) | ||||
0.997361 | − | 0.0726008i | \(-0.0231299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 273.392i | − 0.573841i | −0.957954 | − | 0.286921i | \(-0.907368\pi\) | ||||
0.957954 | − | 0.286921i | \(-0.0926316\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 72.3982 | 0.144783 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −162.256 | −0.309622 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 399.066i | − 0.727667i | −0.931464 | − | 0.363834i | \(-0.881468\pi\) | ||||
0.931464 | − | 0.363834i | \(-0.118532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 211.903i | − 0.369711i | ||||||||
\(70\) | 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 | \(-0.527098\pi\) | ||||
−0.0850270 | + | 0.996379i | \(0.527098\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 216.556i | − 0.333410i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 42.1968i | − 0.0624515i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 58.9970 | 0.0840213 | 0.0420107 | − | 0.999117i | \(-0.486624\pi\) | ||||
0.0420107 | + | 0.999117i | \(0.486624\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.1298 | 0.0399586 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 580.049i | − 0.767092i | −0.923522 | − | 0.383546i | \(-0.874703\pi\) | ||||
0.923522 | − | 0.383546i | \(-0.125297\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 658.068i | 0.839735i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2160.50 | −2.66241 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 768.959 | 0.915837 | 0.457918 | − | 0.888994i | \(-0.348595\pi\) | ||||
0.457918 | + | 0.888994i | \(0.348595\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.6686i | 0.0249614i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1119.32i | 1.24804i | ||||||||
\(94\) | 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 | ||||||||
\(99\) | − 1136.89i | − 1.15416i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 428.775i | 0.422422i | 0.977440 | + | 0.211211i | \(0.0677408\pi\) | ||||
−0.977440 | + | 0.211211i | \(0.932259\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | 1030.02i | 0.930618i | 0.885148 | + | 0.465309i | \(0.154057\pi\) | ||||
−0.885148 | + | 0.465309i | \(0.845943\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 838.993i | − 0.737256i | −0.929577 | − | 0.368628i | \(-0.879828\pi\) | ||||
0.929577 | − | 0.368628i | \(-0.120172\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 308.330i | 0.250017i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 583.810i | 0.461310i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 87.8821 | 0.0676986 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 668.370 | 0.502157 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1675.89i | − 1.22854i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1219.25i | − 0.872423i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2365.81 | −1.65301 | −0.826504 | − | 0.562931i | \(-0.809674\pi\) | ||||
−0.826504 | + | 0.562931i | \(0.809674\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3408.67 | 2.32649 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 570.570i | − 0.380541i | −0.981732 | − | 0.190271i | \(-0.939063\pi\) | ||||
0.981732 | − | 0.190271i | \(-0.0609365\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 164.565i | − 0.107290i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1777.50 | −1.13320 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 856.850 | 0.534348 | 0.267174 | − | 0.963648i | \(-0.413910\pi\) | ||||
0.267174 | + | 0.963648i | \(0.413910\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2389.08i | − 1.45783i | −0.684603 | − | 0.728916i | \(-0.740024\pi\) | ||||
0.684603 | − | 0.728916i | \(-0.259976\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 661.067i | − 0.394836i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 340.269 | 0.198984 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3143.64 | 1.80045 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2870.87i | − 1.61078i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 45.5671i | − 0.0250537i | −0.999922 | − | 0.0125269i | \(-0.996012\pi\) | ||||
0.999922 | − | 0.0125269i | \(-0.00398753\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | − 1628.67i | − 0.843986i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2694.94i | − 1.36994i | −0.728573 | − | 0.684968i | \(-0.759816\pi\) | ||||
0.728573 | − | 0.684968i | \(-0.240184\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6272.64 | 3.12863 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 41.1761 | 0.0201561 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1003.85i | − 0.482377i | −0.970478 | − | 0.241189i | \(-0.922463\pi\) | ||||
0.970478 | − | 0.241189i | \(-0.0775372\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2665.54i | 1.25765i | ||||||||
\(166\) | 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 | ||||||||
\(171\) | − 4433.82i | − 1.98282i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1843.49i | − 0.810162i | −0.914281 | − | 0.405081i | \(-0.867243\pi\) | ||||
0.914281 | − | 0.405081i | \(-0.132757\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 42.0803 | 0.0181770 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 555.117 | 0.235735 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1530.67i | − 0.639149i | −0.947561 | − | 0.319575i | \(-0.896460\pi\) | ||||
0.947561 | − | 0.319575i | \(-0.103540\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4163.35i | 1.70972i | 0.518860 | + | 0.854859i | \(0.326357\pi\) | ||||
−0.518860 | + | 0.854859i | \(0.673643\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2306.33 | 0.931633 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3035.64 | −1.20640 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1380.04i | − 0.539672i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 237.377i | 0.0913577i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −430.650 | −0.163145 | −0.0815726 | − | 0.996667i | \(-0.525994\pi\) | ||||
−0.0815726 | + | 0.996667i | \(0.525994\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2266.98 | −0.845497 | −0.422749 | − | 0.906247i | \(-0.638935\pi\) | ||||
−0.422749 | + | 0.906247i | \(0.638935\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1368.79i | − 0.502672i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1469.95i | 0.531621i | 0.964025 | + | 0.265810i | \(0.0856395\pi\) | ||||
−0.964025 | + | 0.265810i | \(0.914360\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | − 419.819i | − 0.145150i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2438.51i | 0.830796i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1109.39 | 0.372503 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2584.22 | −0.855283 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3749.79i | 1.22344i | 0.791074 | + | 0.611720i | \(0.209522\pi\) | ||||
−0.791074 | + | 0.611720i | \(0.790478\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 6137.47i | − 1.97433i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4959.80 | −1.57328 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −217.501 | −0.0680413 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 894.760i | − 0.276083i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 708.670i | 0.215703i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3690.85 | 1.10833 | 0.554165 | − | 0.832407i | \(-0.313038\pi\) | ||||
0.554165 | + | 0.832407i | \(0.313038\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1133.76 | 0.335928 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2418.90i | 0.707259i | 0.935385 | + | 0.353630i | \(0.115053\pi\) | ||||
−0.935385 | + | 0.353630i | \(0.884947\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 129.827i | 0.0374637i | 0.999825 | + | 0.0187318i | \(0.00596288\pi\) | ||||
−0.999825 | + | 0.0187318i | \(0.994037\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 355.971 | 0.101390 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4259.71 | −1.19769 | −0.598847 | − | 0.800863i | \(-0.704374\pi\) | ||||
−0.598847 | + | 0.800863i | \(0.704374\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 961.889i | 0.267007i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 497.697i | 0.136409i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5053.12 | 1.36761 | 0.683806 | − | 0.729664i | \(-0.260324\pi\) | ||||
0.683806 | + | 0.729664i | \(0.260324\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −48.8379 | −0.0130536 | −0.00652681 | − | 0.999979i | \(-0.502078\pi\) | ||||
−0.00652681 | + | 0.999979i | \(0.502078\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 3664.09i | − 0.967291i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4177.27i | 1.08929i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1327.03 | 0.341850 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4893.28 | 1.24538 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3683.69i | 0.926345i | 0.886268 | + | 0.463172i | \(0.153289\pi\) | ||||
−0.886268 | + | 0.463172i | \(0.846711\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 646.602i | − 0.160678i | ||||||||
\(254\) | 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 | ||||||||
\(259\) | 405.396i | 0.0972589i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 11311.0i | − 2.68251i | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 6486.91i | 1.48686i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1173.73i | − 0.266035i | −0.991114 | − | 0.133018i | \(-0.957533\pi\) | ||||
0.991114 | − | 0.133018i | \(-0.0424667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1404.85 | −0.314902 | −0.157451 | − | 0.987527i | \(-0.550328\pi\) | ||||
−0.157451 | + | 0.987527i | \(0.550328\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −182.796 | −0.0405249 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 660.801i | − 0.144901i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3175.88i | − 0.688881i | −0.938808 | − | 0.344440i | \(-0.888069\pi\) | ||||
0.938808 | − | 0.344440i | \(-0.111931\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5860.07 | −1.25747 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6045.97 | −1.28353 | −0.641766 | − | 0.766900i | \(-0.721798\pi\) | ||||
−0.641766 | + | 0.766900i | \(0.721798\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3478.45i | − 0.730644i | −0.930881 | − | 0.365322i | \(-0.880959\pi\) | ||||
0.930881 | − | 0.365322i | \(-0.119041\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10395.4i | 2.16061i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 325.653 | 0.0669780 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2038.82 | −0.414986 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 6832.74i | − 1.37643i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2619.82i | 0.522360i | 0.965290 | + | 0.261180i | \(0.0841116\pi\) | ||||
−0.965290 | + | 0.261180i | \(0.915888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −807.725 | −0.159415 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3727.60 | 0.728275 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 332.039i | 0.0642217i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 662.360i | 0.126837i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3617.13 | −0.685804 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3355.83 | −0.630015 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2980.24i | 0.554044i | 0.960864 | + | 0.277022i | \(0.0893475\pi\) | ||||
−0.960864 | + | 0.277022i | \(0.910653\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 8117.10i | − 1.49439i | ||||||||
\(310\) | 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 | \(-0.617804\pi\) | ||||
−0.361702 | + | 0.932294i | \(0.617804\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 888.673i | − 0.158956i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1144.44i | − 0.202770i | −0.994847 | − | 0.101385i | \(-0.967673\pi\) | ||||
0.994847 | − | 0.101385i | \(-0.0323274\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6592.56 | −1.15709 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8689.25 | −1.51086 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 5382.08i | − 0.927143i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 339.331i | 0.0579159i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7077.72 | 1.19694 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 128.456 | 0.0215259 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 5981.64i | − 0.993295i | −0.867952 | − | 0.496648i | \(-0.834564\pi\) | ||||
0.867952 | − | 0.496648i | \(-0.165436\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10922.4i | 1.79744i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 2968.94i | − 0.475665i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3415.50i | 0.542403i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1120.12 | 0.176328 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2601.06 | −0.405903 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9064.38i | 1.40231i | 0.713009 | + | 0.701155i | \(0.247332\pi\) | ||||
−0.713009 | + | 0.701155i | \(0.752668\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7782.74i | 1.19370i | 0.802354 | + | 0.596849i | \(0.203581\pi\) | ||||
−0.802354 | + | 0.596849i | \(0.796419\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 8930.35i | 1.33514i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 741.371i | 0.109909i | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 5638.35i | 0.815253i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1301.92i | 0.186701i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10757.7 | −1.53010 | −0.765052 | − | 0.643969i | \(-0.777287\pi\) | ||||
−0.765052 | + | 0.643969i | \(0.777287\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8773.95 | 1.23782 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1218.87i | 0.170568i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1989.79i | 0.276213i | 0.990417 | + | 0.138107i | \(0.0441016\pi\) | ||||
−0.990417 | + | 0.138107i | \(0.955898\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10285.5 | 1.41638 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3385.37 | 0.462481 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1622.04i | 0.219838i | 0.993941 | + | 0.109919i | \(0.0350591\pi\) | ||||
−0.993941 | + | 0.109919i | \(0.964941\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 19957.9i | − 2.68366i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9042.17 | 1.20635 | 0.603176 | − | 0.797608i | \(-0.293902\pi\) | ||||
0.603176 | + | 0.797608i | \(0.293902\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −517.957 | −0.0685650 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17845.7i | 2.34406i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 3642.08i | − 0.474706i | −0.971423 | − | 0.237353i | \(-0.923720\pi\) | ||||
0.971423 | − | 0.237353i | \(-0.0762799\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1346.66 | 0.174178 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4813.31 | 0.617810 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 724.176i | − 0.0922462i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 10071.3i | − 1.27320i | −0.771192 | − | 0.636602i | \(-0.780339\pi\) | ||||
0.771192 | − | 0.636602i | \(-0.219661\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − 1753.90i | − 0.216794i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 357.562i | − 0.0438702i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6366.06 | 0.775317 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9440.21 | −1.14129 | −0.570646 | − | 0.821196i | \(-0.693307\pi\) | ||||
−0.570646 | + | 0.821196i | \(0.693307\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7228.36i | 0.867515i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 107.868i | 0.0128519i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7119.98 | −0.842183 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20154.2 | 2.36680 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4604.25i | 0.536831i | 0.963303 | + | 0.268416i | \(0.0865000\pi\) | ||||
−0.963303 | + | 0.268416i | \(0.913500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13347.4i | 1.54516i | 0.634917 | + | 0.772580i | \(0.281034\pi\) | ||||
−0.634917 | + | 0.772580i | \(0.718966\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3460.95 | 0.397818 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1376.23 | 0.157076 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 448.157i | 0.0507912i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2870.50i | 0.323052i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10617.7 | 1.18663 | 0.593314 | − | 0.804971i | \(-0.297819\pi\) | ||||
0.593314 | + | 0.804971i | \(0.297819\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −706.479 | −0.0784093 | −0.0392046 | − | 0.999231i | \(-0.512482\pi\) | ||||
−0.0392046 | + | 0.999231i | \(0.512482\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26519.7i | 2.92303i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 2521.71i | − 0.276041i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | − 4422.21i | − 0.474279i | −0.971476 | − | 0.237139i | \(-0.923790\pi\) | ||||
0.971476 | − | 0.237139i | \(-0.0762098\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 9438.81i | − 1.00549i | ||||||||
\(446\) | 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 | ||||||||
\(451\) | − 5113.83i | − 0.533927i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 9086.01i | − 0.942379i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 265.978 | 0.0274049 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6833.10 | 0.699429 | 0.349715 | − | 0.936856i | \(-0.386279\pi\) | ||||
0.349715 | + | 0.936856i | \(0.386279\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7763.38i | 0.789463i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 8451.19i | − 0.853821i | −0.904294 | − | 0.426910i | \(-0.859602\pi\) | ||||
0.904294 | − | 0.426910i | \(-0.140398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4273.38 | 0.428943 | 0.214472 | − | 0.976730i | \(-0.431197\pi\) | ||||
0.214472 | + | 0.976730i | \(0.431197\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13739.4 | 1.37021 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17317.9i | 1.71601i | 0.513643 | + | 0.858004i | \(0.328296\pi\) | ||||
−0.513643 | + | 0.858004i | \(0.671704\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 654.167i | 0.0644065i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22734.5 | 2.22410 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10401.3 | 1.01110 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2577.09i | − 0.248937i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32839.7i | 3.15226i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4067.97 | −0.388038 | −0.194019 | − | 0.980998i | \(-0.562152\pi\) | ||||
−0.194019 | + | 0.980998i | \(0.562152\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3269.06 | −0.309888 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 347.360i | 0.0327235i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9942.00i | 0.930811i | ||||||||
\(486\) | 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 | ||||||||
\(491\) | 19228.6i | 1.76736i | 0.468091 | + | 0.883680i | \(0.344942\pi\) | ||||
−0.468091 | + | 0.883680i | \(0.655058\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 13730.1i | − 1.25431i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13955.1 | −1.26714 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1192.61 | 0.107637 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 20713.6i | − 1.85825i | −0.369762 | − | 0.929127i | \(-0.620561\pi\) | ||||
0.369762 | − | 0.929127i | \(-0.379439\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29194.0i | 2.60338i | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 17059.8i | 1.49438i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 19029.8i | − 1.65714i | −0.559889 | − | 0.828568i | \(-0.689156\pi\) | ||||
0.559889 | − | 0.828568i | \(-0.310844\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 173.866 | 0.0150516 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14537.5 | 1.25116 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11810.8i | 1.01058i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2017.19i | − 0.171597i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15551.6 | 1.31530 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10607.1 | −0.891950 | −0.445975 | − | 0.895045i | \(-0.647143\pi\) | ||||
−0.445975 | + | 0.895045i | \(0.647143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5519.88i | 0.461506i | 0.973012 | + | 0.230753i | \(0.0741190\pi\) | ||||
−0.973012 | + | 0.230753i | \(0.925881\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 354.989i | 0.0295104i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7113.36 | −0.587975 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11536.0 | −0.948142 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2906.25i | 0.237515i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2626.02i | 0.213407i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12643.3 | 1.02172 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12912.7 | 1.03766 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 8760.20i | − 0.700053i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 13481.4i | − 1.07137i | −0.844419 | − | 0.535683i | \(-0.820054\pi\) | ||||
0.844419 | − | 0.535683i | \(-0.179946\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −35121.9 | −2.77573 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10298.5 | −0.809427 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1743.55i | 0.136287i | 0.997676 | + | 0.0681434i | \(0.0217075\pi\) | ||||
−0.997676 | + | 0.0681434i | \(0.978292\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12074.5i | 0.938668i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25710.6 | −1.98786 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −96.7105 | −0.00743680 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 25608.5i | − 1.95860i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 4086.47i | − 0.310861i | −0.987847 | − | 0.155430i | \(-0.950324\pi\) | ||||
0.987847 | − | 0.155430i | \(-0.0496764\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5341.19 | −0.404129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11642.0 | 0.876159 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 99.1014i | 0.00741852i | 0.999993 | + | 0.00370926i | \(0.00118070\pi\) | ||||
−0.999993 | + | 0.00370926i | \(0.998819\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4319.96i | 0.321668i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −47.7509 | −0.00353677 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8915.23 | −0.656847 | −0.328423 | − | 0.944531i | \(-0.606517\pi\) | ||||
−0.328423 | + | 0.944531i | \(0.606517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 6995.13i | − 0.512674i | −0.966587 | − | 0.256337i | \(-0.917484\pi\) | ||||
0.966587 | − | 0.256337i | \(-0.0825157\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 3632.95i | − 0.264867i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | − 19124.2i | − 1.37267i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 950.842i | 0.0678960i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19140.4 | 1.35972 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7166.15 | 0.506468 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11229.2i | 0.789573i | 0.918773 | + | 0.394787i | \(0.129181\pi\) | ||||
−0.918773 | + | 0.394787i | \(0.870819\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13320.2i | 0.931835i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | − 1078.73i | − 0.0743257i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 42090.8i | − 2.88553i | ||||||||
\(598\) | 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 | \(-0.632751\pi\) | ||||
−0.405063 | + | 0.914289i | \(0.632751\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17625.0i | 1.19029i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 8204.11i | − 0.551313i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3850.00 | −0.257441 | −0.128721 | − | 0.991681i | \(-0.541087\pi\) | ||||
−0.128721 | + | 0.991681i | \(0.541087\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3541.58 | 0.235652 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1035.85i | 0.0685861i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8938.34i | 0.588933i | 0.955662 | + | 0.294467i | \(0.0951420\pi\) | ||||
−0.955662 | + | 0.294467i | \(0.904858\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20571.2 | −1.34880 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2585.09 | 0.168674 | 0.0843370 | − | 0.996437i | \(-0.473123\pi\) | ||||
0.0843370 | + | 0.996437i | \(0.473123\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10359.1i | 0.672648i | 0.941746 | + | 0.336324i | \(0.109184\pi\) | ||||
−0.941746 | + | 0.336324i | \(0.890816\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3637.44i | 0.235049i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1260.51 | −0.0810615 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18174.8 | −1.16319 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 21800.4i | − 1.38855i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13258.4i | 0.840458i | ||||||||
\(630\) | 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 | ||||||||
\(635\) | 29039.9i | 1.81482i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4498.48i | 0.279806i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 11081.4i | 0.679640i | 0.940491 | + | 0.339820i | \(0.110366\pi\) | ||||
−0.940491 | + | 0.339820i | \(0.889634\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 41840.8i | − 2.55423i | ||||||||
\(646\) | 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 | ||||||||
\(651\) | − 1834.84i | − 0.110465i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11741.1i | 0.703621i | 0.936071 | + | 0.351811i | \(0.114434\pi\) | ||||
−0.936071 | + | 0.351811i | \(0.885566\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7003.63 | −0.417793 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4684.42 | 0.278168 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2398.73i | 0.141792i | 0.997484 | + | 0.0708961i | \(0.0225859\pi\) | ||||
−0.997484 | + | 0.0708961i | \(0.977414\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 12428.5i | − 0.731337i | −0.930745 | − | 0.365669i | \(-0.880840\pi\) | ||||
0.930745 | − | 0.365669i | \(-0.119160\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5978.32 | −0.350194 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2020.00 | −0.117793 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6433.09i | − 0.373449i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 31135.9i | 1.79938i | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 3717.32i | 0.211970i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8009.12i | 0.454676i | 0.973816 | + | 0.227338i | \(0.0730022\pi\) | ||||
−0.973816 | + | 0.227338i | \(0.926998\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1327.71 | 0.0750410 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20405.8 | −1.14824 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 12944.0i | − 0.725167i | −0.931951 | − | 0.362583i | \(-0.881895\pi\) | ||||
0.931951 | − | 0.362583i | \(-0.118105\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 10517.7i | − 0.586655i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1095.21 | −0.0608224 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9828.85 | −0.543468 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24123.5i | 1.32807i | 0.747699 | + | 0.664037i | \(0.231158\pi\) | ||||
−0.747699 | + | 0.664037i | \(0.768842\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1863.65i | 0.102156i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29325.4 | −1.60054 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10650.4 | 0.578787 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 35934.8i | − 1.94446i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10918.3i | 0.588274i | 0.955763 | + | 0.294137i | \(0.0950322\pi\) | ||||
−0.955763 | + | 0.294137i | \(0.904968\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24827.3 | 1.33198 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8114.47 | −0.433487 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 702.866i | − 0.0373890i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 6473.79i | − 0.342917i | −0.985191 | − | 0.171459i | \(-0.945152\pi\) | ||||
0.985191 | − | 0.171459i | \(-0.0548480\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2605.64 | −0.137439 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3332.88 | −0.175059 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 4176.74i | − 0.218463i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 42628.0i | 2.22032i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30210.0 | 1.56696 | 0.783479 | − | 0.621418i | \(-0.213443\pi\) | ||||
0.783479 | + | 0.621418i | \(0.213443\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1577.28 | 0.0814717 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 411.995i | − 0.0211926i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 6574.37i | − 0.336781i | ||||||||
\(726\) | 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 | ||||||||
\(731\) | 21662.4i | 1.09605i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19629.0i | 0.989107i | 0.869147 | + | 0.494553i | \(0.164668\pi\) | ||||
−0.869147 | + | 0.494553i | \(0.835332\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −35239.3 | −1.76847 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10272.6 | 0.513428 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 12436.5i | − 0.619058i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) | ||||
0.950890 | − | 0.309529i | \(-0.100171\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11194.8i | 0.554995i | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 25618.2i | 1.25478i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1688.46i | − 0.0823698i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26531.8 | 1.28916 | 0.644580 | − | 0.764537i | \(-0.277032\pi\) | ||||
0.644580 | + | 0.764537i | \(0.277032\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31075.5 | −1.50392 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13220.6i | 0.637282i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 112.316i | − 0.00539258i | −0.999996 | − | 0.00269629i | \(-0.999142\pi\) | ||||
0.999996 | − | 0.00269629i | \(-0.000858257\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5454.71 | 0.260861 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36991.3 | −1.76207 | −0.881033 | − | 0.473055i | \(-0.843151\pi\) | ||||
−0.881033 | + | 0.473055i | \(0.843151\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1375.31i | 0.0652552i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 29064.0i | − 1.37361i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 6234.64i | 0.291226i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 27921.7i | − 1.29919i | −0.760280 | − | 0.649596i | \(-0.774938\pi\) | ||||
0.760280 | − | 0.649596i | \(-0.225062\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3406.07 | −0.157871 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3419.91 | −0.157900 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 19943.7i | − 0.917273i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 18727.9i | − 0.858051i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 37086.2 | 1.69266 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33079.9 | −1.50404 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 40839.8i | − 1.84979i | −0.380229 | − | 0.924893i | \(-0.624155\pi\) | ||||
0.380229 | − | 0.924893i | \(-0.375845\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 20653.8i | − 0.931931i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 576.912 | 0.0259325 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3613.88 | −0.161832 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 76995.4i | − 3.43490i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23555.1i | 1.04688i | 0.852062 | + | 0.523440i | \(0.175352\pi\) | ||||
−0.852062 | + | 0.523440i | \(0.824648\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4201.14 | 0.186015 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33961.5 | −1.49809 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2730.28i | − 0.119987i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 505.428i | − 0.0221292i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9901.55 | 0.431910 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34940.4 | −1.51847 | −0.759233 | − | 0.650819i | \(-0.774426\pi\) | ||||
−0.759233 | + | 0.650819i | \(0.774426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 21451.0i | − 0.928789i | −0.885628 | − | 0.464395i | \(-0.846272\pi\) | ||||
0.885628 | − | 0.464395i | \(-0.153728\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 11851.3i | − 0.511244i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12322.0 | −0.529597 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40564.3 | 1.73705 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 957.008i | − 0.0408310i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12318.6i | 0.523656i | 0.965115 | + | 0.261828i | \(0.0843252\pi\) | ||||
−0.965115 | + | 0.261828i | \(0.915675\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | − 37233.4i | − 1.56558i | −0.622287 | − | 0.782789i | \(-0.713796\pi\) | ||||
0.622287 | − | 0.782789i | \(-0.286204\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 12881.0i | − 0.539658i | −0.962908 | − | 0.269829i | \(-0.913033\pi\) | ||||
0.962908 | − | 0.269829i | \(-0.0869671\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26791.6 | 1.11840 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18244.6 | 0.758870 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 42478.9i | − 1.76053i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 19213.8i | − 0.793459i | ||||||||
\(838\) | 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 | ||||||||
\(843\) | − 51003.7i | − 2.08382i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 24822.9i | − 1.01057i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1095.62 | −0.0444463 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29344.1 | 1.18620 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6212.08i | 0.250232i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21615.8i | 0.867658i | 0.900995 | + | 0.433829i | \(0.142838\pi\) | ||||
−0.900995 | + | 0.433829i | \(0.857162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −54424.2 | −2.17692 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2273.70 | 0.0906277 | 0.0453139 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453139 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30652.1i | 1.21750i | 0.793361 | + | 0.608752i | \(0.208329\pi\) | ||||
−0.793361 | + | 0.608752i | \(0.791671\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2747.20i | 0.108739i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23721.7 | 0.935686 | 0.467843 | − | 0.883812i | \(-0.345031\pi\) | ||||
0.467843 | + | 0.883812i | \(0.345031\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22628.5 | −0.889469 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 17199.5i | − 0.673731i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1518.68i | 0.0592838i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5275.12 | −0.205213 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35772.1 | 1.38683 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1998.65i | 0.0772189i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31720.2i | 1.22134i | 0.791885 | + | 0.610670i | \(0.209100\pi\) | ||||
−0.791885 | + | 0.610670i | \(0.790900\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − 33215.2i | − 1.26589i | −0.774197 | − | 0.632945i | \(-0.781846\pi\) | ||||
0.774197 | − | 0.632945i | \(-0.218154\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 6813.95i | − 0.258812i | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 749.848i | 0.0281940i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 7866.92i | − 0.294800i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18788.7 | −0.701716 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2801.07 | −0.104264 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33981.1i | 1.26066i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39863.2i | 1.47396i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5587.65 | −0.205920 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 51104.2 | 1.87708 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6456.50i | 0.236367i | 0.992992 | + | 0.118183i | \(0.0377071\pi\) | ||||
−0.992992 | + | 0.118183i | \(0.962293\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 18937.1i | − 0.690983i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2013.95 | 0.0732438 | 0.0366219 | − | 0.999329i | \(-0.488340\pi\) | ||||
0.0366219 | + | 0.999329i | \(0.488340\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14931.4 | 0.541245 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 28309.7i | − 1.02283i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 935.303i | 0.0336820i | ||||||||
\(918\) | 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 | ||||||||
\(923\) | 9617.05i | 0.342957i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6348.50i | 0.225662i | ||||||||
\(926\) | 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 | ||||||||
\(931\) | − 34164.3i | − 1.20267i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 44667.6i | 1.56737i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16939.7 | −0.592501 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47317.5 | 1.64973 | 0.824864 | − | 0.565331i | \(-0.191252\pi\) | ||||
0.824864 | + | 0.565331i | \(0.191252\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 33793.4i | − 1.17445i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21318.9i | 0.738550i | 0.929320 | + | 0.369275i | \(0.120394\pi\) | ||||
−0.929320 | + | 0.369275i | \(0.879606\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4990.14 | 0.172324 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2913.75 | 0.100301 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20601.8i | 0.706937i | 0.935446 | + | 0.353468i | \(0.114998\pi\) | ||||
−0.935446 | + | 0.353468i | \(0.885002\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1402.03i | 0.0479578i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9654.45 | 0.329198 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42987.2 | 1.46117 | 0.730583 | − | 0.682824i | \(-0.239248\pi\) | ||||
0.730583 | + | 0.682824i | \(0.239248\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5286.14i | 0.179116i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 55614.6i | − 1.87854i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1404.59 | −0.0472956 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12186.0 | −0.409049 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 45491.6i | − 1.52227i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27826.7i | 0.928264i | ||||||||
\(966\) | 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 | ||||||||
\(971\) | 50487.1i | 1.66860i | 0.551313 | + | 0.834298i | \(0.314127\pi\) | ||||
−0.551313 | + | 0.834298i | \(0.685873\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3916.28i | 0.129034i | ||||||||
\(974\) | 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 | ||||||||
\(979\) | 19794.2i | 0.646196i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37054.6i | 1.20598i | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 1083.65i | 0.0349473i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10149.7i | 0.326330i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18673.2 | 0.598560 | 0.299280 | − | 0.954165i | \(-0.403254\pi\) | ||||
0.299280 | + | 0.954165i | \(0.403254\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 50460.9 | 1.61262 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 61244.4i | 1.95133i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 31087.3i | − 0.987508i | −0.869602 | − | 0.493754i | \(-0.835624\pi\) | ||||
0.869602 | − | 0.493754i | \(-0.164376\pi\) | |||||||
\(998\) | 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.b.j.513.10 | 10 | ||
4.3 | odd | 2 | 1024.4.b.k.513.1 | 10 | |||
8.3 | odd | 2 | 1024.4.b.k.513.10 | 10 | |||
8.5 | even | 2 | inner | 1024.4.b.j.513.1 | 10 | ||
16.3 | odd | 4 | 1024.4.a.m.1.10 | 10 | |||
16.5 | even | 4 | 1024.4.a.n.1.10 | 10 | |||
16.11 | odd | 4 | 1024.4.a.m.1.1 | 10 | |||
16.13 | even | 4 | 1024.4.a.n.1.1 | 10 | |||
32.3 | odd | 8 | 64.4.e.a.49.5 | 10 | |||
32.5 | even | 8 | 16.4.e.a.13.2 | yes | 10 | ||
32.11 | odd | 8 | 128.4.e.a.33.1 | 10 | |||
32.13 | even | 8 | 128.4.e.b.97.5 | 10 | |||
32.19 | odd | 8 | 128.4.e.a.97.1 | 10 | |||
32.21 | even | 8 | 128.4.e.b.33.5 | 10 | |||
32.27 | odd | 8 | 64.4.e.a.17.5 | 10 | |||
32.29 | even | 8 | 16.4.e.a.5.2 | ✓ | 10 | ||
96.5 | odd | 8 | 144.4.k.a.109.4 | 10 | |||
96.29 | odd | 8 | 144.4.k.a.37.4 | 10 | |||
96.35 | even | 8 | 576.4.k.a.433.1 | 10 | |||
96.59 | even | 8 | 576.4.k.a.145.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.2 | ✓ | 10 | 32.29 | even | 8 | ||
16.4.e.a.13.2 | yes | 10 | 32.5 | even | 8 | ||
64.4.e.a.17.5 | 10 | 32.27 | odd | 8 | |||
64.4.e.a.49.5 | 10 | 32.3 | odd | 8 | |||
128.4.e.a.33.1 | 10 | 32.11 | odd | 8 | |||
128.4.e.a.97.1 | 10 | 32.19 | odd | 8 | |||
128.4.e.b.33.5 | 10 | 32.21 | even | 8 | |||
128.4.e.b.97.5 | 10 | 32.13 | even | 8 | |||
144.4.k.a.37.4 | 10 | 96.29 | odd | 8 | |||
144.4.k.a.109.4 | 10 | 96.5 | odd | 8 | |||
576.4.k.a.145.1 | 10 | 96.59 | even | 8 | |||
576.4.k.a.433.1 | 10 | 96.35 | even | 8 | |||
1024.4.a.m.1.1 | 10 | 16.11 | odd | 4 | |||
1024.4.a.m.1.10 | 10 | 16.3 | odd | 4 | |||
1024.4.a.n.1.1 | 10 | 16.13 | even | 4 | |||
1024.4.a.n.1.10 | 10 | 16.5 | even | 4 | |||
1024.4.b.j.513.1 | 10 | 8.5 | even | 2 | inner | ||
1024.4.b.j.513.10 | 10 | 1.1 | even | 1 | trivial | ||
1024.4.b.k.513.1 | 10 | 4.3 | odd | 2 | |||
1024.4.b.k.513.10 | 10 | 8.3 | odd | 2 |