Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [828,2,Mod(73,828)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(828, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("828.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 828.q (of order \(11\), degree \(10\), 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: | \(6.61161328736\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{11})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 276) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 469.2 | ||
Root | \(-0.262998 - 0.575885i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 828.469 |
Dual form | 828.2.q.c.685.2 |
$q$-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 \(\left(\mathbb{Z}/828\mathbb{Z}\right)^\times\).
\(n\) | \(415\) | \(461\) | \(649\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.149019 | + | 1.03645i | 0.0666431 | + | 0.463513i | 0.995629 | + | 0.0933976i | \(0.0297728\pi\) |
−0.928986 | + | 0.370115i | \(0.879318\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.607780 | − | 1.33085i | 0.229719 | − | 0.503015i | −0.759311 | − | 0.650728i | \(-0.774464\pi\) |
0.989030 | + | 0.147713i | \(0.0471911\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.96481 | − | 0.576921i | −0.592413 | − | 0.173948i | −0.0282350 | − | 0.999601i | \(-0.508989\pi\) |
−0.564178 | + | 0.825653i | \(0.690807\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.86365 | − | 6.27053i | −0.794235 | − | 1.73913i | −0.664112 | − | 0.747633i | \(-0.731190\pi\) |
−0.130123 | − | 0.991498i | \(-0.541537\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.54296 | + | 4.20490i | 1.58690 | + | 1.01984i | 0.973102 | + | 0.230375i | \(0.0739954\pi\) |
0.613798 | + | 0.789463i | \(0.289641\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.36057 | − | 3.44503i | 1.22980 | − | 0.790344i | 0.245939 | − | 0.969285i | \(-0.420904\pi\) |
0.983860 | + | 0.178941i | \(0.0572672\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.692970 | − | 4.74550i | 0.144494 | − | 0.989506i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.74545 | − | 1.09976i | 0.749090 | − | 0.219953i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.48875 | − | 2.24209i | −0.647845 | − | 0.416345i | 0.175033 | − | 0.984563i | \(-0.443997\pi\) |
−0.822878 | + | 0.568218i | \(0.807633\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.595921 | + | 0.687730i | −0.107031 | + | 0.123520i | −0.806737 | − | 0.590910i | \(-0.798769\pi\) |
0.699707 | + | 0.714430i | \(0.253314\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.46993 | + | 0.431610i | 0.248463 | + | 0.0729554i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.580529 | + | 4.03767i | −0.0954384 | + | 0.663789i | 0.884800 | + | 0.465970i | \(0.154295\pi\) |
−0.980239 | + | 0.197818i | \(0.936614\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.696437 | + | 4.84382i | 0.108765 | + | 0.756478i | 0.969086 | + | 0.246725i | \(0.0793543\pi\) |
−0.860321 | + | 0.509753i | \(0.829737\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.29407 | + | 2.64750i | 0.349842 | + | 0.403740i | 0.903211 | − | 0.429197i | \(-0.141203\pi\) |
−0.553369 | + | 0.832937i | \(0.686658\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.92699 | 0.281080 | 0.140540 | − | 0.990075i | \(-0.455116\pi\) | ||||
0.140540 | + | 0.990075i | \(0.455116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.18225 | + | 3.67251i | 0.454607 | + | 0.524645i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.25236 | − | 7.12168i | 0.446746 | − | 0.978238i | −0.543564 | − | 0.839368i | \(-0.682926\pi\) |
0.990311 | − | 0.138870i | \(-0.0443471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.305154 | − | 2.12240i | 0.0411470 | − | 0.286184i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00809 | − | 13.1559i | −0.782187 | − | 1.71275i | −0.697772 | − | 0.716320i | \(-0.745825\pi\) |
−0.0844153 | − | 0.996431i | \(-0.526902\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.93456 | − | 5.69479i | 0.631806 | − | 0.729143i | −0.346098 | − | 0.938198i | \(-0.612494\pi\) |
0.977904 | + | 0.209056i | \(0.0670390\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.07233 | − | 3.90245i | 0.753180 | − | 0.484039i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.68609 | − | 2.84409i | 1.18334 | − | 0.347461i | 0.369882 | − | 0.929079i | \(-0.379398\pi\) |
0.813462 | + | 0.581618i | \(0.197580\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.189483 | + | 0.0556372i | −0.0224875 | + | 0.00660292i | −0.292957 | − | 0.956126i | \(-0.594639\pi\) |
0.270469 | + | 0.962729i | \(0.412821\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.69670 | + | 4.30371i | −0.783789 | + | 0.503711i | −0.870289 | − | 0.492541i | \(-0.836068\pi\) |
0.0864999 | + | 0.996252i | \(0.472432\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.96197 | + | 2.26424i | −0.223587 | + | 0.258034i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.92232 | − | 4.20928i | −0.216277 | − | 0.473581i | 0.770133 | − | 0.637884i | \(-0.220190\pi\) |
−0.986410 | + | 0.164302i | \(0.947463\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.17882 | − | 8.19891i | 0.129393 | − | 0.899947i | −0.816933 | − | 0.576733i | \(-0.804327\pi\) |
0.946326 | − | 0.323214i | \(-0.104763\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.38314 | + | 7.40803i | −0.366953 | + | 0.803514i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.180249 | − | 0.208018i | −0.0191063 | − | 0.0220499i | 0.746116 | − | 0.665816i | \(-0.231916\pi\) |
−0.765222 | + | 0.643766i | \(0.777371\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0856 | −1.05726 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.36941 | + | 5.04257i | 0.448292 | + | 0.517357i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.04696 | + | 7.28177i | 0.106303 | + | 0.739351i | 0.971349 | + | 0.237659i | \(0.0763800\pi\) |
−0.865046 | + | 0.501693i | \(0.832711\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.03748 | + | 14.1710i | −0.202737 | + | 1.41006i | 0.593380 | + | 0.804922i | \(0.297793\pi\) |
−0.796117 | + | 0.605143i | \(0.793116\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.85204 | + | 1.13106i | 0.379553 | + | 0.111447i | 0.465943 | − | 0.884815i | \(-0.345715\pi\) |
−0.0863903 | + | 0.996261i | \(0.527533\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.52969 | + | 9.84379i | −0.824596 | + | 0.951635i | −0.999457 | − | 0.0329585i | \(-0.989507\pi\) |
0.174861 | + | 0.984593i | \(0.444053\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.98252 | − | 1.91675i | −0.285674 | − | 0.183592i | 0.389954 | − | 0.920834i | \(-0.372491\pi\) |
−0.675628 | + | 0.737243i | \(0.736127\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.6873 | + | 4.31258i | −1.38166 | + | 0.405693i | −0.886348 | − | 0.463019i | \(-0.846766\pi\) |
−0.495316 | + | 0.868713i | \(0.664948\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.02173 | + | 0.0110588i | 0.468278 | + | 0.00103124i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.57279 | − | 6.15206i | 0.877536 | − | 0.563958i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.72614 | − | 3.67997i | −0.520558 | − | 0.334542i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.87290 | + | 8.48047i | 0.346403 | + | 0.758517i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.2206 | − | 3.88193i | −1.17314 | − | 0.344466i | −0.363616 | − | 0.931549i | \(-0.618458\pi\) |
−0.809527 | + | 0.587083i | \(0.800276\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.99409 | − | 8.74584i | 0.348966 | − | 0.764128i | −0.651022 | − | 0.759059i | \(-0.725659\pi\) |
0.999987 | − | 0.00506875i | \(-0.00161344\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.32678 | − | 9.22796i | −0.115046 | − | 0.800165i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.53079 | −0.301656 | −0.150828 | − | 0.988560i | \(-0.548194\pi\) | ||||
−0.150828 | + | 0.988560i | \(0.548194\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.28333 | 0.193670 | 0.0968349 | − | 0.995300i | \(-0.469128\pi\) | ||||
0.0968349 | + | 0.995300i | \(0.469128\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00894 | + | 13.9725i | 0.167996 | + | 1.16844i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.80391 | − | 3.95002i | 0.149807 | − | 0.328031i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.9656 | − | 3.80706i | −1.06219 | − | 0.311886i | −0.296456 | − | 0.955047i | \(-0.595805\pi\) |
−0.765732 | + | 0.643160i | \(0.777623\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.959780 | − | 2.10162i | −0.0781058 | − | 0.171028i | 0.866551 | − | 0.499089i | \(-0.166332\pi\) |
−0.944656 | + | 0.328061i | \(0.893605\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.801598 | − | 0.515156i | −0.0643859 | − | 0.0413783i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1745 | + | 6.53877i | −0.812015 | + | 0.521851i | −0.879516 | − | 0.475869i | \(-0.842134\pi\) |
0.0675010 | + | 0.997719i | \(0.478497\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.89439 | − | 3.80646i | −0.464543 | − | 0.299991i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.7606 | − | 6.09585i | 1.62609 | − | 0.477464i | 0.663447 | − | 0.748224i | \(-0.269093\pi\) |
0.962647 | + | 0.270759i | \(0.0872748\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.66020 | + | 2.99493i | 0.360617 | + | 0.231755i | 0.708385 | − | 0.705826i | \(-0.249424\pi\) |
−0.347768 | + | 0.937581i | \(0.613060\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −22.6058 | + | 26.0885i | −1.73891 | + | 2.00681i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5327 | + | 3.09267i | 0.800783 | + | 0.235131i | 0.656422 | − | 0.754394i | \(-0.272069\pi\) |
0.144361 | + | 0.989525i | \(0.453887\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.812787 | − | 5.65306i | 0.0614409 | − | 0.427331i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.69832 | + | 18.7672i | 0.201682 | + | 1.40273i | 0.799293 | + | 0.600942i | \(0.205208\pi\) |
−0.597611 | + | 0.801786i | \(0.703883\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9386 | + | 12.6238i | 0.813060 | + | 0.938322i | 0.999021 | − | 0.0442355i | \(-0.0140852\pi\) |
−0.185961 | + | 0.982557i | \(0.559540\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.27134 | −0.314035 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.4298 | − | 12.0366i | −0.762701 | − | 0.880204i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.20633 | + | 9.21058i | −0.304359 | + | 0.666454i | −0.998578 | − | 0.0533102i | \(-0.983023\pi\) |
0.694219 | + | 0.719764i | \(0.255750\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.01479 | + | 14.0132i | −0.145028 | + | 1.00869i | 0.779180 | + | 0.626801i | \(0.215636\pi\) |
−0.924207 | + | 0.381891i | \(0.875273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.5317 | + | 23.0613i | 0.750356 | + | 1.64305i | 0.765725 | + | 0.643168i | \(0.222380\pi\) |
−0.0153688 | + | 0.999882i | \(0.504892\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.66657 | + | 10.0018i | −0.614357 | + | 0.709005i | −0.974625 | − | 0.223843i | \(-0.928140\pi\) |
0.360269 | + | 0.932849i | \(0.382685\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.10428 | + | 3.28032i | −0.358251 | + | 0.230234i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.91658 | + | 1.44364i | −0.343389 | + | 0.100828i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.5200 | + | 3.67621i | −0.866028 | + | 0.254289i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.09064 | + | 0.700911i | −0.0750826 | + | 0.0482527i | −0.577644 | − | 0.816289i | \(-0.696028\pi\) |
0.502561 | + | 0.864542i | \(0.332391\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.40213 | + | 2.77221i | −0.163824 | + | 0.189063i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.553078 | + | 1.21107i | 0.0375454 | + | 0.0822129i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.63019 | − | 53.0692i | 0.513262 | − | 3.56982i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.04981 | + | 11.0575i | −0.338160 | + | 0.740468i | −0.999958 | − | 0.00921525i | \(-0.997067\pi\) |
0.661797 | + | 0.749683i | \(0.269794\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.4515 | − | 17.8319i | −1.02555 | − | 1.18355i | −0.982840 | − | 0.184460i | \(-0.940946\pi\) |
−0.0427099 | − | 0.999088i | \(-0.513599\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.4803 | 1.02296 | 0.511482 | − | 0.859294i | \(-0.329097\pi\) | ||||
0.511482 | + | 0.859294i | \(0.329097\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.18474 | + | 9.44569i | 0.536200 | + | 0.618808i | 0.957612 | − | 0.288062i | \(-0.0930108\pi\) |
−0.421412 | + | 0.906869i | \(0.638465\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.287157 | + | 1.99722i | 0.0187320 | + | 0.130284i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.97190 | − | 20.6700i | 0.192236 | − | 1.33703i | −0.633837 | − | 0.773467i | \(-0.718521\pi\) |
0.826073 | − | 0.563564i | \(-0.190570\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.47491 | − | 0.726700i | −0.159423 | − | 0.0468109i | 0.201047 | − | 0.979582i | \(-0.435566\pi\) |
−0.360470 | + | 0.932771i | \(0.617384\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.33215 | + | 3.84551i | −0.212883 | + | 0.245680i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −36.9530 | − | 23.7482i | −2.35126 | − | 1.51106i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.05809 | − | 1.77882i | 0.382383 | − | 0.112278i | −0.0848910 | − | 0.996390i | \(-0.527054\pi\) |
0.467274 | + | 0.884112i | \(0.345236\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.09934 | + | 8.92423i | −0.257723 | + | 0.561062i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.3497 | + | 6.65137i | −0.645599 | + | 0.414901i | −0.822056 | − | 0.569407i | \(-0.807173\pi\) |
0.176457 | + | 0.984308i | \(0.443536\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.02071 | + | 3.22661i | 0.311972 | + | 0.200492i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.94567 | − | 6.45011i | −0.181638 | − | 0.397731i | 0.796809 | − | 0.604231i | \(-0.206520\pi\) |
−0.978447 | + | 0.206500i | \(0.933793\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.86590 | + | 2.30964i | 0.483199 | + | 0.141880i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.22048 | − | 13.6209i | 0.379269 | − | 0.830484i | −0.619689 | − | 0.784848i | \(-0.712741\pi\) |
0.998958 | − | 0.0456362i | \(-0.0145315\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.61485 | − | 18.1867i | −0.158841 | − | 1.10476i | −0.900774 | − | 0.434288i | \(-0.857000\pi\) |
0.741933 | − | 0.670474i | \(-0.233909\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.99358 | −0.482031 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.9414 | 0.837657 | 0.418829 | − | 0.908065i | \(-0.362441\pi\) | ||||
0.418829 | + | 0.908065i | \(0.362441\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.10403 | − | 7.67872i | −0.0658611 | − | 0.458074i | −0.995889 | − | 0.0905846i | \(-0.971126\pi\) |
0.930028 | − | 0.367490i | \(-0.119783\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.5340 | + | 29.6354i | −0.804514 | + | 1.76164i | −0.175128 | + | 0.984546i | \(0.556034\pi\) |
−0.629385 | + | 0.777093i | \(0.716693\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.86970 | + | 2.01713i | 0.405506 | + | 0.119067i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.0670 | + | 39.5612i | 1.06277 | + | 2.32713i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.0543 | − | 11.6028i | −1.05475 | − | 0.677844i | −0.106155 | − | 0.994350i | \(-0.533854\pi\) |
−0.948591 | + | 0.316506i | \(0.897490\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.7401 | − | 8.18754i | 0.741755 | − | 0.476697i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.7412 | + | 9.24419i | −1.83564 | + | 0.534605i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.91772 | − | 1.44397i | 0.283453 | − | 0.0832293i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.63768 | + | 4.26578i | 0.380073 | + | 0.244258i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.82498 | − | 3.26020i | 0.161230 | − | 0.186070i | −0.669386 | − | 0.742915i | \(-0.733443\pi\) |
0.830616 | + | 0.556845i | \(0.187988\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.4182 | + | 3.64631i | 0.704171 | + | 0.206763i | 0.614165 | − | 0.789178i | \(-0.289493\pi\) |
0.0900065 | + | 0.995941i | \(0.471311\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.525717 | + | 3.65644i | −0.0297153 | + | 0.206674i | −0.999270 | − | 0.0382000i | \(-0.987838\pi\) |
0.969555 | + | 0.244874i | \(0.0787467\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.66225 | + | 18.5164i | 0.149527 | + | 1.03998i | 0.916996 | + | 0.398897i | \(0.130607\pi\) |
−0.767469 | + | 0.641087i | \(0.778484\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.56124 | + | 6.41801i | 0.311370 | + | 0.359340i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 49.5600 | 2.75759 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.6218 | − | 20.3366i | −0.977480 | − | 1.12807i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.17118 | − | 2.56454i | 0.0645695 | − | 0.141387i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.646147 | − | 4.49405i | 0.0355154 | − | 0.247015i | −0.964328 | − | 0.264710i | \(-0.914724\pi\) |
0.999843 | + | 0.0176950i | \(0.00563279\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.39116 | + | 9.61529i | 0.239914 | + | 0.525339i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8054 | − | 17.0864i | 0.806503 | − | 0.930754i | −0.192216 | − | 0.981353i | \(-0.561567\pi\) |
0.998719 | + | 0.0505986i | \(0.0161129\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.56764 | − | 1.00746i | 0.0848924 | − | 0.0545570i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.6483 | − | 4.88839i | 0.898924 | − | 0.263948i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.3095 | − | 5.08253i | 0.929222 | − | 0.272844i | 0.218111 | − | 0.975924i | \(-0.430010\pi\) |
0.711111 | + | 0.703080i | \(0.248192\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.22571 | + | 2.71570i | −0.226197 | + | 0.145368i | −0.648831 | − | 0.760932i | \(-0.724742\pi\) |
0.422634 | + | 0.906300i | \(0.361106\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.32044 | − | 9.60230i | 0.442852 | − | 0.511079i | −0.489810 | − | 0.871829i | \(-0.662934\pi\) |
0.932662 | + | 0.360750i | \(0.117479\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.0859014 | − | 0.188098i | −0.00455917 | − | 0.00998320i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.759247 | − | 5.28068i | 0.0400715 | − | 0.278703i | −0.959927 | − | 0.280249i | \(-0.909583\pi\) |
0.999999 | + | 0.00154569i | \(0.000492007\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.97460 | − | 19.6516i | 0.472348 | − | 1.03430i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.45849 | − | 6.29944i | −0.285711 | − | 0.329728i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.47822 | −0.0771624 | −0.0385812 | − | 0.999255i | \(-0.512284\pi\) | ||||
−0.0385812 | + | 0.999255i | \(0.512284\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.50119 | − | 8.65683i | −0.389442 | − | 0.449440i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.50047 | − | 17.3912i | −0.129470 | − | 0.900480i | −0.946228 | − | 0.323501i | \(-0.895140\pi\) |
0.816758 | − | 0.576980i | \(-0.195769\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.06848 | + | 28.2969i | −0.209537 | + | 1.45736i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.96855 | + | 1.45890i | 0.255218 | + | 0.0749386i | 0.406839 | − | 0.913500i | \(-0.366631\pi\) |
−0.151621 | + | 0.988439i | \(0.548449\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.1398 | + | 20.9345i | −0.926901 | + | 1.06970i | 0.0704902 | + | 0.997512i | \(0.477544\pi\) |
−0.997391 | + | 0.0721881i | \(0.977002\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.63913 | − | 1.69607i | −0.134503 | − | 0.0864395i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.15517 | − | 1.51370i | 0.261378 | − | 0.0767474i | −0.148418 | − | 0.988925i | \(-0.547418\pi\) |
0.409796 | + | 0.912177i | \(0.365600\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.4884 | − | 28.1357i | 1.23843 | − | 1.42289i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.07624 | − | 2.61964i | 0.205098 | − | 0.131808i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.4469 | − | 19.5670i | −1.52808 | − | 0.982040i | −0.990298 | − | 0.138959i | \(-0.955624\pi\) |
−0.537786 | − | 0.843081i | \(-0.680739\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.81908 | + | 8.36262i | 0.190716 | + | 0.417609i | 0.980700 | − | 0.195518i | \(-0.0626387\pi\) |
−0.789984 | + | 0.613127i | \(0.789911\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.01894 | + | 1.76732i | 0.299825 | + | 0.0880365i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.47005 | − | 7.59834i | 0.172004 | − | 0.376636i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.120756 | + | 0.839879i | 0.00597102 | + | 0.0415293i | 0.992589 | − | 0.121519i | \(-0.0387765\pi\) |
−0.986618 | + | 0.163048i | \(0.947867\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.1602 | −1.04122 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.67340 | 0.425760 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.51724 | + | 24.4629i | 0.171828 | + | 1.19509i | 0.875018 | + | 0.484090i | \(0.160849\pi\) |
−0.703190 | + | 0.711002i | \(0.748242\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.50485 | − | 14.2436i | 0.317027 | − | 0.694192i | −0.682293 | − | 0.731079i | \(-0.739017\pi\) |
0.999319 | + | 0.0368873i | \(0.0117443\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.1307 | + | 8.55355i | 1.41305 | + | 0.414908i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.57980 | − | 10.0284i | −0.221632 | − | 0.485306i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.59612 | + | 3.59641i | 0.269555 | + | 0.173233i | 0.668435 | − | 0.743771i | \(-0.266964\pi\) |
−0.398880 | + | 0.917003i | \(0.630601\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0259 | − | 10.9419i | 0.818214 | − | 0.525834i | −0.0632987 | − | 0.997995i | \(-0.520162\pi\) |
0.881513 | + | 0.472160i | \(0.156526\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.6337 | − | 27.8259i | −0.604351 | − | 1.33109i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.95674 | + | 1.16180i | −0.188845 | + | 0.0554498i | −0.374787 | − | 0.927111i | \(-0.622284\pi\) |
0.185943 | + | 0.982561i | \(0.440466\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.8064 | − | 16.5847i | −1.22610 | − | 0.787965i | −0.242819 | − | 0.970072i | \(-0.578072\pi\) |
−0.983279 | + | 0.182106i | \(0.941708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.188739 | − | 0.217817i | 0.00894710 | − | 0.0103255i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.7635 | + | 6.39035i | 1.02709 | + | 0.301579i | 0.751525 | − | 0.659704i | \(-0.229318\pi\) |
0.275560 | + | 0.961284i | \(0.411137\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.42614 | − | 9.91899i | 0.0671541 | − | 0.467067i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.50294 | − | 10.4532i | −0.0704591 | − | 0.490054i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.4108 | + | 21.2472i | 0.861222 | + | 0.993903i | 0.999994 | + | 0.00357885i | \(0.00113919\pi\) |
−0.138772 | + | 0.990324i | \(0.544315\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.98643 | 0.232241 | 0.116121 | − | 0.993235i | \(-0.462954\pi\) | ||||
0.116121 | + | 0.993235i | \(0.462954\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.2211 | + | 19.8742i | 0.800333 | + | 0.923634i | 0.998400 | − | 0.0565546i | \(-0.0180115\pi\) |
−0.198066 | + | 0.980189i | \(0.563466\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.8145 | + | 32.4393i | −0.685534 | + | 1.50111i | 0.171137 | + | 0.985247i | \(0.445256\pi\) |
−0.856671 | + | 0.515863i | \(0.827471\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.10194 | − | 14.6193i | 0.0970588 | − | 0.675059i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.98002 | − | 6.52533i | −0.137021 | − | 0.300035i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.2890 | − | 18.7985i | 0.747392 | − | 0.862536i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.6477 | − | 22.9094i | 1.62878 | − | 1.04676i | 0.678863 | − | 0.734265i | \(-0.262473\pi\) |
0.949921 | − | 0.312490i | \(-0.101163\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.9807 | − | 7.92226i | 1.23022 | − | 0.361224i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.39115 | + | 2.17024i | −0.335615 | + | 0.0985454i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.0812 | + | 16.1187i | −1.13654 | + | 0.730407i | −0.966914 | − | 0.255102i | \(-0.917891\pi\) |
−0.169622 | + | 0.985509i | \(0.554255\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.55804 | − | 9.87650i | 0.386219 | − | 0.445720i | −0.529034 | − | 0.848601i | \(-0.677446\pi\) |
0.915253 | + | 0.402880i | \(0.131991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.3990 | − | 29.3397i | −0.603461 | − | 1.32140i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.0411190 | + | 0.285989i | −0.00184444 | + | 0.0128284i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.02701 | + | 19.7664i | −0.404104 | + | 0.884865i | 0.592733 | + | 0.805399i | \(0.298049\pi\) |
−0.996838 | + | 0.0794664i | \(0.974678\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.9282 | − | 13.7659i | −0.531852 | − | 0.613790i | 0.424706 | − | 0.905331i | \(-0.360377\pi\) |
−0.956558 | + | 0.291541i | \(0.905832\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.9911 | −0.667094 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.994643 | − | 1.14788i | −0.0440868 | − | 0.0508788i | 0.733278 | − | 0.679929i | \(-0.237989\pi\) |
−0.777365 | + | 0.629050i | \(0.783444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.65748 | + | 11.5280i | 0.0733226 | + | 0.509970i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.598260 | + | 4.16099i | −0.0263625 | + | 0.183355i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.78617 | − | 1.11172i | −0.166515 | − | 0.0488933i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.68764 | − | 11.1801i | 0.424423 | − | 0.489810i | −0.502756 | − | 0.864428i | \(-0.667681\pi\) |
0.927179 | + | 0.374618i | \(0.122226\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.4684 | + | 10.5836i | 0.720114 | + | 0.462789i | 0.848677 | − | 0.528912i | \(-0.177400\pi\) |
−0.128563 | + | 0.991701i | \(0.541036\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.79092 | + | 1.99399i | −0.295817 | + | 0.0868597i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0396 | − | 6.57698i | −0.958243 | − | 0.285956i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.3790 | − | 18.2381i | 1.22923 | − | 0.789978i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.4736 | − | 7.37366i | −0.496049 | − | 0.318791i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.13378 | − | 9.05171i | −0.178054 | − | 0.389885i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.35451 | + | 0.397719i | 0.0582349 | + | 0.0170993i | 0.310720 | − | 0.950501i | \(-0.399430\pi\) |
−0.252485 | + | 0.967601i | \(0.581248\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.54216 | − | 3.37686i | 0.0660589 | − | 0.144649i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.19234 | + | 22.2032i | 0.136494 | + | 0.949340i | 0.936829 | + | 0.349787i | \(0.113746\pi\) |
−0.800335 | + | 0.599553i | \(0.795345\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.4258 | −1.12578 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.77028 | −0.287902 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.95373 | + | 34.4539i | 0.209896 | + | 1.45986i | 0.773490 | + | 0.633808i | \(0.218509\pi\) |
−0.563594 | + | 0.826052i | \(0.690582\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0318 | − | 21.9665i | 0.424299 | − | 0.929086i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.9036 | − | 13.1849i | −1.89246 | − | 0.555677i | −0.992910 | − | 0.118865i | \(-0.962074\pi\) |
−0.899553 | − | 0.436812i | \(-0.856107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.65844 | − | 14.5799i | −0.280123 | − | 0.613383i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.35168 | + | 4.72464i | 0.308198 | + | 0.198067i | 0.685592 | − | 0.727986i | \(-0.259543\pi\) |
−0.377394 | + | 0.926053i | \(0.623180\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.5741 | − | 10.6516i | 0.693606 | − | 0.445754i | −0.145760 | − | 0.989320i | \(-0.546563\pi\) |
0.839366 | + | 0.543566i | \(0.182926\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.62344 | − | 18.5361i | −0.109405 | − | 0.773011i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.5543 | − | 4.86079i | 0.689165 | − | 0.202357i | 0.0816453 | − | 0.996661i | \(-0.473983\pi\) |
0.607520 | + | 0.794304i | \(0.292164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.1951 | − | 6.55198i | −0.422963 | − | 0.271822i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.4989 | + | 12.1164i | −0.434821 | + | 0.501810i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.4307 | + | 6.58626i | 0.925815 | + | 0.271844i | 0.709684 | − | 0.704520i | \(-0.248838\pi\) |
0.216131 | + | 0.976364i | \(0.430656\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.825228 | + | 5.73959i | −0.0340029 | + | 0.236496i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.08335 | + | 14.4900i | 0.0855529 | + | 0.595034i | 0.986826 | + | 0.161783i | \(0.0517244\pi\) |
−0.901273 | + | 0.433251i | \(0.857366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.80280 | + | 9.00491i | 0.319884 | + | 0.369166i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.2295 | 0.744838 | 0.372419 | − | 0.928065i | \(-0.378528\pi\) | ||||
0.372419 | + | 0.928065i | \(0.378528\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.2399 | + | 25.6662i | 0.907185 | + | 1.04695i | 0.998691 | + | 0.0511429i | \(0.0162864\pi\) |
−0.0915063 | + | 0.995804i | \(0.529168\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.96079 | − | 6.48322i | 0.120373 | − | 0.263580i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.97050 | + | 48.4809i | −0.282924 | + | 1.96778i | −0.0332604 | + | 0.999447i | \(0.510589\pi\) |
−0.249664 | + | 0.968333i | \(0.580320\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.51822 | − | 12.0832i | −0.223243 | − | 0.488835i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.5055 | + | 15.5862i | −0.545482 | + | 0.629519i | −0.959824 | − | 0.280601i | \(-0.909466\pi\) |
0.414343 | + | 0.910121i | \(0.364012\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.7181 | − | 14.6000i | 0.914597 | − | 0.587776i | 0.00351174 | − | 0.999994i | \(-0.498882\pi\) |
0.911085 | + | 0.412218i | \(0.135246\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.2222 | + | 7.69954i | −1.05396 | + | 0.309471i | −0.762416 | − | 0.647087i | \(-0.775987\pi\) |
−0.291544 | + | 0.956557i | \(0.594169\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.386393 | + | 0.113455i | −0.0154805 | + | 0.00454549i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.20704 | − | 5.27435i | 0.328282 | − | 0.210974i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.7764 | + | 23.9772i | −0.828408 | + | 0.956034i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.7273 | + | 36.6276i | 0.665903 | + | 1.45812i | 0.876918 | + | 0.480640i | \(0.159596\pi\) |
−0.211015 | + | 0.977483i | \(0.567677\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.05329 | − | 14.2810i | 0.0814825 | − | 0.566723i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.9157 | − | 30.4712i | 0.551361 | − | 1.20731i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.25845 | − | 2.60639i | −0.0892035 | − | 0.102946i | 0.709393 | − | 0.704813i | \(-0.248969\pi\) |
−0.798596 | + | 0.601867i | \(0.794424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.4827 | −0.926065 | −0.463033 | − | 0.886341i | \(-0.653239\pi\) | ||||
−0.463033 | + | 0.886341i | \(0.653239\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.6644 | + | 29.6183i | 1.00897 | + | 1.16442i | 0.986348 | + | 0.164672i | \(0.0526565\pi\) |
0.0226236 | + | 0.999744i | \(0.492798\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.21487 | + | 29.3150i | 0.165448 | + | 1.15072i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.626064 | + | 4.35437i | −0.0244998 | + | 0.170400i | −0.998398 | − | 0.0565867i | \(-0.981978\pi\) |
0.973898 | + | 0.226987i | \(0.0728873\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.65980 | + | 2.83637i | 0.377439 | + | 0.110826i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.1304 | − | 11.6911i | 0.394623 | − | 0.455419i | −0.523317 | − | 0.852138i | \(-0.675306\pi\) |
0.917940 | + | 0.396719i | \(0.129851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.5003 | − | 13.8174i | −0.836264 | − | 0.537434i | 0.0509984 | − | 0.998699i | \(-0.483760\pi\) |
−0.887263 | + | 0.461264i | \(0.847396\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.36657 | − | 2.75027i | 0.363220 | − | 0.106651i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.0574 | + | 15.0022i | −0.505586 | + | 0.580887i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.9809 | + | 8.34233i | −0.501123 | + | 0.322052i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.8361 | − | 8.89193i | −0.533343 | − | 0.342759i | 0.246087 | − | 0.969248i | \(-0.420855\pi\) |
−0.779430 | + | 0.626489i | \(0.784491\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.6868 | − | 40.9185i | −0.718193 | − | 1.57262i | −0.816419 | − | 0.577460i | \(-0.804044\pi\) |
0.0982256 | − | 0.995164i | \(-0.468683\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.3273 | + | 3.03236i | 0.396325 | + | 0.116371i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.20603 | + | 4.83054i | −0.0844115 | + | 0.184836i | −0.947131 | − | 0.320848i | \(-0.896032\pi\) |
0.862719 | + | 0.505683i | \(0.168760\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.526153 | − | 3.65948i | −0.0201033 | − | 0.139821i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −53.9703 | −2.05611 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.2506 | −0.846454 | −0.423227 | − | 0.906024i | \(-0.639103\pi\) | ||||
−0.423227 | + | 0.906024i | \(0.639103\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.340259 | + | 2.36655i | 0.0129068 | + | 0.0897685i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.8110 | + | 34.6214i | −0.598886 | + | 1.31138i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.8621 | + | 8.76829i | 1.12787 | + | 0.331174i | 0.791872 | − | 0.610687i | \(-0.209107\pi\) |
0.336003 | + | 0.941861i | \(0.390925\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.7979 | + | 23.6441i | 0.407251 | + | 0.891756i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.6212 | + | 11.3244i | 0.662712 | + | 0.425899i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.2880 | − | 12.3956i | 0.724376 | − | 0.465528i | −0.125781 | − | 0.992058i | \(-0.540144\pi\) |
0.850157 | + | 0.526530i | \(0.176507\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.85067 | + | 3.30452i | 0.106758 | + | 0.123755i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.1824 | + | 4.16433i | −0.530391 | + | 0.155737i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.6336 | − | 24.8283i | −1.44079 | − | 0.925939i | −0.999593 | − | 0.0285287i | \(-0.990918\pi\) |
−0.441197 | − | 0.897410i | \(-0.645446\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.84647 | − | 4.43907i | 0.143250 | − | 0.165320i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.5327 | − | 4.56082i | −0.576871 | − | 0.169385i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.94326 | + | 20.4708i | −0.109159 | + | 0.759221i | 0.859555 | + | 0.511043i | \(0.170741\pi\) |
−0.968715 | + | 0.248178i | \(0.920168\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.87753 | + | 26.9688i | 0.143416 | + | 0.997477i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.5114 | − | 29.4417i | −0.942284 | − | 1.08745i | −0.996041 | − | 0.0888999i | \(-0.971665\pi\) |
0.0537563 | − | 0.998554i | \(-0.482881\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.6722 | −0.761469 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.0924 | − | 22.0338i | −0.702324 | − | 0.810525i | 0.286740 | − | 0.958008i | \(-0.407428\pi\) |
−0.989065 | + | 0.147483i | \(0.952883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.03328 | − | 2.26256i | 0.0379073 | − | 0.0830054i | −0.889731 | − | 0.456485i | \(-0.849108\pi\) |
0.927638 | + | 0.373480i | \(0.121835\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.01369 | − | 14.0055i | 0.0737759 | − | 0.513123i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.91646 | + | 17.3346i | 0.289261 | + | 0.633393i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.6256 | − | 20.3411i | 0.643169 | − | 0.742256i | −0.336763 | − | 0.941589i | \(-0.609332\pi\) |
0.979932 | + | 0.199333i | \(0.0638775\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.03520 | − | 1.30794i | 0.0740684 | − | 0.0476009i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.4648 | + | 4.24725i | −0.525733 | + | 0.154369i | −0.533820 | − | 0.845598i | \(-0.679244\pi\) |
0.00808709 | + | 0.999967i | \(0.497426\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.3488 | − | 5.68132i | 0.701394 | − | 0.205948i | 0.0884574 | − | 0.996080i | \(-0.471806\pi\) |
0.612937 | + | 0.790132i | \(0.289988\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.36364 | + | 2.80434i | −0.157974 | + | 0.101524i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −65.2892 | + | 75.3478i | −2.35746 | + | 2.72065i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.8841 | − | 28.2123i | −0.464613 | − | 1.01736i | −0.986412 | − | 0.164293i | \(-0.947466\pi\) |
0.521798 | − | 0.853069i | \(-0.325261\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.11398 | − | 14.7030i | 0.0760344 | − | 0.528831i | −0.915833 | − | 0.401559i | \(-0.868469\pi\) |
0.991868 | − | 0.127273i | \(-0.0406223\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.47565 | + | 3.23123i | −0.0530070 | + | 0.116069i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.4204 | + | 23.5664i | 0.731637 | + | 0.844354i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.404396 | 0.0144704 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.29328 | − | 9.57095i | −0.296000 | − | 0.341602i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.39324 | + | 23.6005i | 0.120956 | + | 0.841268i | 0.956477 | + | 0.291809i | \(0.0942571\pi\) |
−0.835521 | + | 0.549459i | \(0.814834\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.18724 | + | 22.1677i | −0.113325 | + | 0.788194i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.8402 | − | 14.6344i | −1.76988 | − | 0.519683i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.00998140 | + | 0.0115191i | −0.000353559 | + | 0.000408029i | −0.755926 | − | 0.654657i | \(-0.772813\pi\) |
0.755573 | + | 0.655065i | \(0.227359\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.6082 | + | 8.10279i | 0.446046 | + | 0.286656i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.6407 | − | 4.59251i | 0.551947 | − | 0.162066i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.06682 | − | 6.67646i | 0.108091 | − | 0.235314i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.8969 | − | 18.5709i | 1.01596 | − | 0.652917i | 0.0770303 | − | 0.997029i | \(-0.475456\pi\) |
0.938929 | + | 0.344111i | \(0.111820\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.9953 | − | 19.2768i | −1.05328 | − | 0.676899i | −0.105041 | − | 0.994468i | \(-0.533497\pi\) |
−0.948235 | + | 0.317568i | \(0.897134\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.41174 | + | 20.6088i | 0.329679 | + | 0.721896i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.4182 | + | 6.28896i | 0.749329 | + | 0.220023i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.4238 | + | 31.5837i | −0.503393 | + | 1.10228i | 0.471958 | + | 0.881621i | \(0.343547\pi\) |
−0.975352 | + | 0.220657i | \(0.929180\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.76747 | + | 26.2033i | 0.131326 | + | 0.913390i | 0.943829 | + | 0.330434i | \(0.107195\pi\) |
−0.812504 | + | 0.582956i | \(0.801896\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.7194 | 0.894351 | 0.447176 | − | 0.894446i | \(-0.352430\pi\) | ||||
0.447176 | + | 0.894446i | \(0.352430\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.78348 | 0.0966741 | 0.0483371 | − | 0.998831i | \(-0.484608\pi\) | ||||
0.0483371 | + | 0.998831i | \(0.484608\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.37877 | + | 37.4102i | 0.186363 | + | 1.29618i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.40963 | + | 5.27635i | −0.0833887 | + | 0.182596i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.0523 | − | 11.7604i | −1.38276 | − | 0.406014i | −0.496030 | − | 0.868306i | \(-0.665209\pi\) |
−0.886728 | + | 0.462291i | \(0.847028\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.90258 | − | 10.7352i | −0.169054 | − | 0.370178i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30.4080 | − | 19.5420i | −1.04607 | − | 0.672267i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.37773 | + | 5.38404i | −0.287862 | + | 0.184998i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.7585 | + | 5.55289i | 0.643032 | + | 0.190350i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.9788 | − | 7.62807i | 0.889498 | − | 0.261180i | 0.195110 | − | 0.980781i | \(-0.437493\pi\) |
0.694388 | + | 0.719601i | \(0.255675\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.7373 | − | 17.1830i | −0.913330 | − | 0.586961i | −0.00261458 | − | 0.999997i | \(-0.500832\pi\) |
−0.910715 | + | 0.413035i | \(0.864469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.1980 | + | 11.7692i | −0.347952 | + | 0.401558i | −0.902567 | − | 0.430549i | \(-0.858320\pi\) |
0.554615 | + | 0.832107i | \(0.312866\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.00864 | + | 0.883417i | 0.102415 | + | 0.0300719i | 0.332539 | − | 0.943090i | \(-0.392095\pi\) |
−0.230123 | + | 0.973161i | \(0.573913\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.63582 | + | 11.3774i | −0.0556197 | + | 0.386843i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.34856 | + | 9.37947i | 0.0457469 | + | 0.318177i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.5715 | − | 52.5924i | −1.54413 | − | 1.78202i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.6401 | 0.461121 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.94937 | + | 5.71188i | 0.167128 | + | 0.192877i | 0.833136 | − | 0.553069i | \(-0.186543\pi\) |
−0.666007 | + | 0.745945i | \(0.731998\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.06153 | − | 19.8420i | 0.305291 | − | 0.668493i | −0.693351 | − | 0.720600i | \(-0.743866\pi\) |
0.998642 | + | 0.0521069i | \(0.0165937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.282773 | + | 1.96673i | −0.00951608 | + | 0.0661858i | −0.994026 | − | 0.109142i | \(-0.965190\pi\) |
0.984510 | + | 0.175328i | \(0.0560986\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.13496 | + | 13.4337i | 0.205992 | + | 0.451059i | 0.984226 | − | 0.176915i | \(-0.0566118\pi\) |
−0.778234 | + | 0.627974i | \(0.783884\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.2015 | + | 15.2354i | −0.442765 | + | 0.510978i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.3297 | − | 6.63852i | 0.345672 | − | 0.222150i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.0491 | + | 5.59333i | −0.636742 | + | 0.186964i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.62097 | − | 1.06321i | 0.120766 | − | 0.0354601i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51.2260 | − | 32.9210i | 1.70659 | − | 1.09676i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.4539 | + | 13.2185i | −0.380739 | + | 0.439397i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.30569 | + | 7.23846i | 0.109764 | + | 0.240349i | 0.956541 | − | 0.291599i | \(-0.0941873\pi\) |
−0.846777 | + | 0.531948i | \(0.821460\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.07719 | − | 28.3575i | 0.135083 | − | 0.939524i | −0.803705 | − | 0.595029i | \(-0.797141\pi\) |
0.938788 | − | 0.344496i | \(-0.111950\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.04629 | + | 15.4292i | −0.233198 | + | 0.510633i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.21190 | − | 10.6311i | −0.304204 | − | 0.351070i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.7887 | −1.11458 | −0.557292 | − | 0.830316i | \(-0.688160\pi\) | ||||
−0.557292 | + | 0.830316i | \(0.688160\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.891487 | + | 1.02883i | 0.0293437 | + | 0.0338644i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.26614 | + | 15.7613i | 0.0745101 | + | 0.518229i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.77544 | + | 33.2139i | −0.156677 | + | 1.08971i | 0.748026 | + | 0.663670i | \(0.231002\pi\) |
−0.904703 | + | 0.426043i | \(0.859907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.7106 | + | 8.72382i | 0.973726 | + | 0.285912i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.9211 | − | 12.6036i | 0.357157 | − | 0.412182i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.4646 | + | 11.8665i | 0.603212 | + | 0.387661i | 0.806306 | − | 0.591499i | \(-0.201463\pi\) |
−0.203094 | + | 0.979159i | \(0.565100\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.4102 | − | 9.22286i | 1.02394 | − | 0.300657i | 0.273697 | − | 0.961816i | \(-0.411754\pi\) |
0.750245 | + | 0.661159i | \(0.229935\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.4690 | + | 0.0516832i | 0.764255 | + | 0.00168304i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.9781 | + | 17.3378i | −0.876672 | + | 0.563403i | −0.899787 | − | 0.436330i | \(-0.856278\pi\) |
0.0231147 | + | 0.999733i | \(0.492642\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.1635 | + | 29.6675i | 1.49853 | + | 0.963048i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.1659 | + | 22.2603i | 0.329307 | + | 0.721081i | 0.999783 | − | 0.0208504i | \(-0.00663737\pi\) |
−0.670476 | + | 0.741931i | \(0.733910\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.1731 | − | 2.98709i | −0.329194 | − | 0.0966600i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.14594 | + | 4.69896i | −0.0692962 | + | 0.151737i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.29391 | + | 29.8648i | 0.138513 | + | 0.963381i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.8242 | −0.477207 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.6787 | 0.568508 | 0.284254 | − | 0.958749i | \(-0.408254\pi\) | ||||
0.284254 | + | 0.958749i | \(0.408254\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.739698 | + | 5.14471i | 0.0237380 | + | 0.165102i | 0.998242 | − | 0.0592682i | \(-0.0188767\pi\) |
−0.974504 | + | 0.224370i | \(0.927968\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.38777 | − | 3.03878i | 0.0444897 | − | 0.0974189i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.4267 | − | 6.58506i | −0.717492 | − | 0.210675i | −0.0974469 | − | 0.995241i | \(-0.531068\pi\) |
−0.620045 | + | 0.784566i | \(0.712886\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.234145 | + | 0.512706i | 0.00748330 | + | 0.0163862i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.1221 | − | 18.0730i | −0.896956 | − | 0.576438i | 0.00893018 | − | 0.999960i | \(-0.497157\pi\) |
−0.905886 | + | 0.423522i | \(0.860794\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.3324 | + | 14.3522i | −0.711569 | + | 0.457298i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.1534 | − | 9.05188i | 0.450053 | − | 0.287833i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.861200 | + | 0.252871i | −0.0273569 | + | 0.00803271i | −0.295382 | − | 0.955379i | \(-0.595447\pi\) |
0.268025 | + | 0.963412i | \(0.413629\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.6578 | − | 7.49199i | −0.369576 | − | 0.237512i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.7655 | + | 37.8134i | −1.03770 | + | 1.19756i | −0.0577428 | + | 0.998331i | \(0.518390\pi\) |
−0.979952 | + | 0.199232i | \(0.936155\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 828.2.q.c.469.2 | 20 | ||
3.2 | odd | 2 | 276.2.i.a.193.1 | yes | 20 | ||
23.18 | even | 11 | inner | 828.2.q.c.685.2 | 20 | ||
69.8 | odd | 22 | 6348.2.a.s.1.7 | 10 | |||
69.38 | even | 22 | 6348.2.a.t.1.4 | 10 | |||
69.41 | odd | 22 | 276.2.i.a.133.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.a.133.1 | ✓ | 20 | 69.41 | odd | 22 | ||
276.2.i.a.193.1 | yes | 20 | 3.2 | odd | 2 | ||
828.2.q.c.469.2 | 20 | 1.1 | even | 1 | trivial | ||
828.2.q.c.685.2 | 20 | 23.18 | even | 11 | inner | ||
6348.2.a.s.1.7 | 10 | 69.8 | odd | 22 | |||
6348.2.a.t.1.4 | 10 | 69.38 | even | 22 |