Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2576,2,Mod(1,2576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2576.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2576 = 2^{4} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2576.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(20.5694635607\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.8580816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 12x^{3} + 10x^{2} + 20x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 644) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.604308\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2576.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.604308 | 0.348897 | 0.174449 | − | 0.984666i | \(-0.444186\pi\) | ||||
0.174449 | + | 0.984666i | \(0.444186\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.83889 | −1.71681 | −0.858403 | − | 0.512976i | \(-0.828543\pi\) | ||||
−0.858403 | + | 0.512976i | \(0.828543\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.63481 | −0.878271 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.52849 | −1.66690 | −0.833451 | − | 0.552593i | \(-0.813638\pi\) | ||||
−0.833451 | + | 0.552593i | \(0.813638\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.106323 | 0.0294887 | 0.0147444 | − | 0.999891i | \(-0.495307\pi\) | ||||
0.0147444 | + | 0.999891i | \(0.495307\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.31987 | −0.598989 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.497985 | −0.120779 | −0.0603895 | − | 0.998175i | \(-0.519234\pi\) | ||||
−0.0603895 | + | 0.998175i | \(0.519234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.82942 | −0.419699 | −0.209849 | − | 0.977734i | \(-0.567297\pi\) | ||||
−0.209849 | + | 0.977734i | \(0.567297\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.604308 | −0.131871 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.73710 | 1.94742 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.40516 | −0.655324 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.25159 | 1.34659 | 0.673293 | − | 0.739375i | \(-0.264879\pi\) | ||||
0.673293 | + | 0.739375i | \(0.264879\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.94522 | −0.708582 | −0.354291 | − | 0.935135i | \(-0.615278\pi\) | ||||
−0.354291 | + | 0.935135i | \(0.615278\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.34091 | −0.581578 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.83889 | 0.648891 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.37919 | 0.884333 | 0.442167 | − | 0.896933i | \(-0.354210\pi\) | ||||
0.442167 | + | 0.896933i | \(0.354210\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0642519 | 0.0102885 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.10229 | 0.796844 | 0.398422 | − | 0.917202i | \(-0.369558\pi\) | ||||
0.398422 | + | 0.917202i | \(0.369558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.40816 | −0.367241 | −0.183621 | − | 0.982997i | \(-0.558782\pi\) | ||||
−0.183621 | + | 0.982997i | \(0.558782\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.1148 | 1.50782 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.35338 | 1.21847 | 0.609233 | − | 0.792991i | \(-0.291477\pi\) | ||||
0.609233 | + | 0.792991i | \(0.291477\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.300936 | −0.0421395 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.25653 | −1.13412 | −0.567060 | − | 0.823676i | \(-0.691919\pi\) | ||||
−0.567060 | + | 0.823676i | \(0.691919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 21.2233 | 2.86175 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.10554 | −0.146432 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.668560 | −0.0870391 | −0.0435195 | − | 0.999053i | \(-0.513857\pi\) | ||||
−0.0435195 | + | 0.999053i | \(0.513857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.21808 | 0.412033 | 0.206017 | − | 0.978548i | \(-0.433950\pi\) | ||||
0.206017 | + | 0.978548i | \(0.433950\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.63481 | 0.331955 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.408163 | −0.0506264 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1453 | −1.36161 | −0.680806 | − | 0.732464i | \(-0.738370\pi\) | ||||
−0.680806 | + | 0.732464i | \(0.738370\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.604308 | −0.0727501 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.897708 | 0.106538 | 0.0532691 | − | 0.998580i | \(-0.483036\pi\) | ||||
0.0532691 | + | 0.998580i | \(0.483036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5755 | 1.23777 | 0.618884 | − | 0.785482i | \(-0.287585\pi\) | ||||
0.618884 | + | 0.785482i | \(0.287585\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.88421 | 0.679450 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.52849 | 0.630030 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.77011 | 0.311661 | 0.155831 | − | 0.987784i | \(-0.450195\pi\) | ||||
0.155831 | + | 0.987784i | \(0.450195\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.84667 | 0.649630 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.4362 | 1.58458 | 0.792288 | − | 0.610148i | \(-0.208890\pi\) | ||||
0.792288 | + | 0.610148i | \(0.208890\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.91171 | 0.207354 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.38219 | 0.469820 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.9762 | −1.79948 | −0.899738 | − | 0.436430i | \(-0.856243\pi\) | ||||
−0.899738 | + | 0.436430i | \(0.856243\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.106323 | −0.0111457 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.38413 | −0.247222 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.02297 | 0.720541 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2471 | 1.24350 | 0.621750 | − | 0.783216i | \(-0.286422\pi\) | ||||
0.621750 | + | 0.783216i | \(0.286422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.5665 | 1.46399 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.4782 | −1.04262 | −0.521312 | − | 0.853366i | \(-0.674557\pi\) | ||||
−0.521312 | + | 0.853366i | \(0.674557\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.67376 | −0.460519 | −0.230259 | − | 0.973129i | \(-0.573957\pi\) | ||||
−0.230259 | + | 0.973129i | \(0.573957\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.31987 | 0.226396 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.9764 | −1.73784 | −0.868921 | − | 0.494950i | \(-0.835186\pi\) | ||||
−0.868921 | + | 0.494950i | \(0.835186\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.79138 | 0.458931 | 0.229466 | − | 0.973317i | \(-0.426302\pi\) | ||||
0.229466 | + | 0.973317i | \(0.426302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.25069 | 0.308542 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.62988 | −0.811831 | −0.405915 | − | 0.913911i | \(-0.633047\pi\) | ||||
−0.405915 | + | 0.913911i | \(0.633047\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.83889 | 0.357979 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.280141 | −0.0258991 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.497985 | 0.0456502 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.5642 | 1.77856 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.08336 | 0.278017 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −18.1852 | −1.62654 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4198 | 1.36829 | 0.684144 | − | 0.729347i | \(-0.260176\pi\) | ||||
0.684144 | + | 0.729347i | \(0.260176\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.45527 | −0.128130 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.4194 | −1.17246 | −0.586230 | − | 0.810144i | \(-0.699389\pi\) | ||||
−0.586230 | + | 0.810144i | \(0.699389\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.82942 | 0.158631 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.0721 | 1.12506 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.825394 | −0.0705182 | −0.0352591 | − | 0.999378i | \(-0.511226\pi\) | ||||
−0.0352591 | + | 0.999378i | \(0.511226\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.6573 | −1.07357 | −0.536787 | − | 0.843718i | \(-0.680362\pi\) | ||||
−0.536787 | + | 0.843718i | \(0.680362\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.04801 | 0.425119 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.587806 | −0.0491548 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −27.8381 | −2.31183 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.604308 | 0.0498425 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.6738 | 1.20212 | 0.601060 | − | 0.799204i | \(-0.294745\pi\) | ||||
0.601060 | + | 0.799204i | \(0.294745\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.5334 | 0.857198 | 0.428599 | − | 0.903495i | \(-0.359007\pi\) | ||||
0.428599 | + | 0.903495i | \(0.359007\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.31210 | 0.106077 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.1453 | 1.21650 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.8536 | 1.90372 | 0.951861 | − | 0.306531i | \(-0.0991683\pi\) | ||||
0.951861 | + | 0.306531i | \(0.0991683\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.98948 | −0.395692 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.40089 | 0.579682 | 0.289841 | − | 0.957075i | \(-0.406398\pi\) | ||||
0.289841 | + | 0.957075i | \(0.406398\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.8254 | 0.998456 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.5973 | 1.28434 | 0.642168 | − | 0.766564i | \(-0.278035\pi\) | ||||
0.642168 | + | 0.766564i | \(0.278035\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9887 | −0.999130 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.82019 | 0.368609 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.19955 | −0.699429 | −0.349714 | − | 0.936856i | \(-0.613721\pi\) | ||||
−0.349714 | + | 0.936856i | \(0.613721\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.73710 | −0.736056 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.404016 | −0.0303677 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.9507 | −0.967977 | −0.483989 | − | 0.875074i | \(-0.660812\pi\) | ||||
−0.483989 | + | 0.875074i | \(0.660812\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.7676 | 1.17200 | 0.585999 | − | 0.810312i | \(-0.300702\pi\) | ||||
0.585999 | + | 0.810312i | \(0.300702\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.94471 | 0.143757 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.6501 | −1.51823 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.75310 | 0.201327 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.40516 | 0.247689 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.7348 | −0.921455 | −0.460728 | − | 0.887542i | \(-0.652412\pi\) | ||||
−0.460728 | + | 0.887542i | \(0.652412\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.4100 | −0.965270 | −0.482635 | − | 0.875822i | \(-0.660320\pi\) | ||||
−0.482635 | + | 0.875822i | \(0.660320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.246656 | −0.0176634 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.7841 | −0.839583 | −0.419792 | − | 0.907621i | \(-0.637897\pi\) | ||||
−0.419792 | + | 0.907621i | \(0.637897\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.3266 | 1.58269 | 0.791345 | − | 0.611369i | \(-0.209381\pi\) | ||||
0.791345 | + | 0.611369i | \(0.209381\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.73517 | −0.475062 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.25159 | −0.508962 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.5872 | −1.36803 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.63481 | 0.183132 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.1140 | 0.699597 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.36428 | −0.162764 | −0.0813820 | − | 0.996683i | \(-0.525933\pi\) | ||||
−0.0813820 | + | 0.996683i | \(0.525933\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.542492 | 0.0371709 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.24468 | 0.630482 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.94522 | 0.267819 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.39085 | 0.431854 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.0529473 | −0.00356162 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.97119 | 0.533790 | 0.266895 | − | 0.963726i | \(-0.414002\pi\) | ||||
0.266895 | + | 0.963726i | \(0.414002\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.6554 | −1.71036 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.68182 | −0.443488 | −0.221744 | − | 0.975105i | \(-0.571175\pi\) | ||||
−0.221744 | + | 0.975105i | \(0.571175\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.08478 | 0.0716846 | 0.0358423 | − | 0.999357i | \(-0.488589\pi\) | ||||
0.0358423 | + | 0.999357i | \(0.488589\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.34091 | 0.219816 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.2370 | 1.65333 | 0.826667 | − | 0.562692i | \(-0.190234\pi\) | ||||
0.826667 | + | 0.562692i | \(0.190234\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −32.0677 | −2.09187 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.67400 | 0.108738 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.83670 | 0.183491 | 0.0917454 | − | 0.995782i | \(-0.470755\pi\) | ||||
0.0917454 | + | 0.995782i | \(0.470755\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.71466 | 0.239282 | 0.119641 | − | 0.992817i | \(-0.461826\pi\) | ||||
0.119641 | + | 0.992817i | \(0.461826\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.7487 | 0.881978 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.83889 | −0.245258 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.194510 | −0.0123764 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.72389 | 0.552854 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.5962 | −1.61562 | −0.807810 | − | 0.589443i | \(-0.799347\pi\) | ||||
−0.807810 | + | 0.589443i | \(0.799347\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.52849 | 0.347573 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.15526 | 0.0723453 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.17237 | −0.572157 | −0.286078 | − | 0.958206i | \(-0.592352\pi\) | ||||
−0.286078 | + | 0.958206i | \(0.592352\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.37919 | −0.334247 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.1066 | −1.18267 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.48642 | −0.214982 | −0.107491 | − | 0.994206i | \(-0.534282\pi\) | ||||
−0.107491 | + | 0.994206i | \(0.534282\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 31.6959 | 1.94707 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.2589 | −0.627832 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.24389 | −0.136813 | −0.0684063 | − | 0.997658i | \(-0.521791\pi\) | ||||
−0.0684063 | + | 0.997658i | \(0.521791\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0288129 | 0.00175026 | 0.000875131 | − | 1.00000i | \(-0.499721\pi\) | ||||
0.000875131 | 1.00000i | \(0.499721\pi\) | ||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0642519 | −0.00388870 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −53.8315 | −3.24616 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.91898 | 0.415721 | 0.207861 | − | 0.978158i | \(-0.433350\pi\) | ||||
0.207861 | + | 0.978158i | \(0.433350\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.3949 | 0.622327 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.5561 | 1.94214 | 0.971068 | − | 0.238803i | \(-0.0767552\pi\) | ||||
0.971068 | + | 0.238803i | \(0.0767552\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.22755 | −0.0729704 | −0.0364852 | − | 0.999334i | \(-0.511616\pi\) | ||||
−0.0364852 | + | 0.999334i | \(0.511616\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.24403 | 0.251395 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.10229 | −0.301179 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7520 | −0.985412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.40099 | 0.433854 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 34.0388 | 1.98857 | 0.994284 | − | 0.106768i | \(-0.0340502\pi\) | ||||
0.994284 | + | 0.106768i | \(0.0340502\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.56653 | 0.149429 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.8254 | 1.09236 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.106323 | −0.00614882 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.40816 | 0.138804 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.33208 | −0.363769 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.3539 | −0.707381 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.25612 | 0.471202 | 0.235601 | − | 0.971850i | \(-0.424294\pi\) | ||||
0.235601 | + | 0.971850i | \(0.424294\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.82439 | −0.160674 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.0844 | −1.42240 | −0.711202 | − | 0.702988i | \(-0.751849\pi\) | ||||
−0.711202 | + | 0.702988i | \(0.751849\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.1377 | 0.742588 | 0.371294 | − | 0.928515i | \(-0.378914\pi\) | ||||
0.371294 | + | 0.928515i | \(0.378914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.1148 | −0.569902 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.0697 | −1.63272 | −0.816359 | − | 0.577545i | \(-0.804011\pi\) | ||||
−0.816359 | + | 0.577545i | \(0.804011\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −40.0903 | −2.24463 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.8633 | −0.606329 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.911026 | 0.0506908 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.03528 | 0.0574270 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.89547 | 0.160120 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.35338 | −0.460537 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.1357 | 1.43655 | 0.718273 | − | 0.695762i | \(-0.244933\pi\) | ||||
0.718273 | + | 0.695762i | \(0.244933\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.1732 | −0.776684 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 42.7855 | 2.33762 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.04308 | −0.438134 | −0.219067 | − | 0.975710i | \(-0.570301\pi\) | ||||
−0.219067 | + | 0.975710i | \(0.570301\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.21510 | −0.283245 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.8111 | 1.18114 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.31987 | 0.124898 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.3941 | 0.665350 | 0.332675 | − | 0.943042i | \(-0.392049\pi\) | ||||
0.332675 | + | 0.943042i | \(0.392049\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.8977 | 0.797456 | 0.398728 | − | 0.917069i | \(-0.369452\pi\) | ||||
0.398728 | + | 0.917069i | \(0.369452\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.362047 | −0.0193247 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.35298 | 0.231686 | 0.115843 | − | 0.993268i | \(-0.463043\pi\) | ||||
0.115843 | + | 0.993268i | \(0.463043\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.44620 | −0.182906 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.300936 | 0.0159272 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.2673 | −1.86134 | −0.930668 | − | 0.365865i | \(-0.880773\pi\) | ||||
−0.930668 | + | 0.365865i | \(0.880773\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6532 | −0.823853 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.8228 | 0.620536 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40.5982 | −2.12501 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.4520 | 0.545592 | 0.272796 | − | 0.962072i | \(-0.412052\pi\) | ||||
0.272796 | + | 0.962072i | \(0.412052\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.4436 | −0.699845 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.25653 | 0.428657 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.2827 | 0.739531 | 0.369766 | − | 0.929125i | \(-0.379438\pi\) | ||||
0.369766 | + | 0.929125i | \(0.379438\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.9895 | −0.567494 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.771012 | 0.0397091 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6910 | −1.11419 | −0.557096 | − | 0.830448i | \(-0.688084\pi\) | ||||
−0.557096 | + | 0.830448i | \(0.688084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.31832 | 0.477392 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.9913 | 1.68578 | 0.842888 | − | 0.538089i | \(-0.180854\pi\) | ||||
0.842888 | + | 0.538089i | \(0.180854\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.2233 | −1.08164 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.34506 | 0.322537 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.3987 | −1.59197 | −0.795987 | − | 0.605313i | \(-0.793048\pi\) | ||||
−0.795987 | + | 0.605313i | \(0.793048\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.497985 | 0.0251842 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.10946 | −0.409068 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.6341 | −0.535062 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.75917 | −0.289044 | −0.144522 | − | 0.989502i | \(-0.546165\pi\) | ||||
−0.144522 | + | 0.989502i | \(0.546165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.10554 | 0.0553460 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.7917 | 1.18810 | 0.594051 | − | 0.804427i | \(-0.297528\pi\) | ||||
0.594051 | + | 0.804427i | \(0.297528\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.419468 | −0.0208952 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.4447 | −1.11529 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.7388 | −1.47410 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.8809 | 1.27973 | 0.639865 | − | 0.768487i | \(-0.278990\pi\) | ||||
0.639865 | + | 0.768487i | \(0.278990\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.498792 | −0.0246036 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.668560 | 0.0328977 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −55.4189 | −2.72041 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.64888 | −0.374567 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.5322 | 0.563383 | 0.281691 | − | 0.959505i | \(-0.409105\pi\) | ||||
0.281691 | + | 0.959505i | \(0.409105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.41123 | −0.117516 | −0.0587580 | − | 0.998272i | \(-0.518714\pi\) | ||||
−0.0587580 | + | 0.998272i | \(0.518714\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.0096 | −1.07014 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.84893 | −0.235208 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.21808 | −0.155734 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.355216 | −0.0171500 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.0144 | 1.30124 | 0.650620 | − | 0.759404i | \(-0.274509\pi\) | ||||
0.650620 | + | 0.759404i | \(0.274509\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.4550 | −1.17523 | −0.587617 | − | 0.809139i | \(-0.699934\pi\) | ||||
−0.587617 | + | 0.809139i | \(0.699934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.8228 | −0.806590 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.82942 | 0.0875133 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.3451 | 0.827835 | 0.413918 | − | 0.910314i | \(-0.364160\pi\) | ||||
0.413918 | + | 0.910314i | \(0.364160\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.63481 | −0.125467 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.9547 | 1.13812 | 0.569061 | − | 0.822296i | \(-0.307307\pi\) | ||||
0.569061 | + | 0.822296i | \(0.307307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 65.1699 | 3.08935 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.86747 | 0.419417 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.5180 | 1.34585 | 0.672923 | − | 0.739712i | \(-0.265038\pi\) | ||||
0.672923 | + | 0.739712i | \(0.265038\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.2080 | −1.32826 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.36543 | 0.299074 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.408163 | 0.0191350 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.68686 | 0.172464 | 0.0862319 | − | 0.996275i | \(-0.472517\pi\) | ||||
0.0862319 | + | 0.996275i | \(0.472517\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.69572 | 0.0791493 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.3634 | 1.50731 | 0.753656 | − | 0.657269i | \(-0.228288\pi\) | ||||
0.753656 | + | 0.657269i | \(0.228288\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.33664 | −0.155067 | −0.0775333 | − | 0.996990i | \(-0.524704\pi\) | ||||
−0.0775333 | + | 0.996990i | \(0.524704\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.15240 | 0.424433 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.8817 | 1.15139 | 0.575694 | − | 0.817665i | \(-0.304732\pi\) | ||||
0.575694 | + | 0.817665i | \(0.304732\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.1453 | 0.514641 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.4149 | 0.664203 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.3135 | 0.612156 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.8133 | −0.817330 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.7544 | 0.996065 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.8584 | −0.678898 | −0.339449 | − | 0.940625i | \(-0.610241\pi\) | ||||
−0.339449 | + | 0.940625i | \(0.610241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.571932 | 0.0260779 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.604308 | 0.0274970 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −47.0151 | −2.13485 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.76114 | 0.125119 | 0.0625597 | − | 0.998041i | \(-0.480074\pi\) | ||||
0.0625597 | + | 0.998041i | \(0.480074\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.47242 | 0.202250 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.4760 | 1.19485 | 0.597423 | − | 0.801927i | \(-0.296191\pi\) | ||||
0.597423 | + | 0.801927i | \(0.296191\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.61118 | −0.162639 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −55.9194 | −2.51339 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.897708 | −0.0402677 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.5058 | 1.05226 | 0.526132 | − | 0.850403i | \(-0.323642\pi\) | ||||
0.526132 | + | 0.850403i | \(0.323642\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.0299 | 0.448101 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.9285 | 0.843979 | 0.421989 | − | 0.906601i | \(-0.361332\pi\) | ||||
0.421989 | + | 0.906601i | \(0.361332\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 40.2248 | 1.78998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.84917 | −0.348594 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.7910 | −1.54208 | −0.771041 | − | 0.636785i | \(-0.780264\pi\) | ||||
−0.771041 | + | 0.636785i | \(0.780264\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5755 | −0.467832 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.22949 | 0.275039 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.9421 | 0.790621 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −46.1816 | −2.03106 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.55936 | −0.244029 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.2804 | −1.19518 | −0.597588 | − | 0.801803i | \(-0.703874\pi\) | ||||
−0.597588 | + | 0.801803i | \(0.703874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 44.6189 | 1.95105 | 0.975525 | − | 0.219888i | \(-0.0705692\pi\) | ||||
0.975525 | + | 0.219888i | \(0.0705692\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.88421 | −0.256808 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.96466 | 0.0855818 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.76153 | 0.0764439 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.542492 | 0.0234979 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 69.0094 | 2.98354 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.82618 | −0.337725 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.52849 | −0.238129 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −44.9839 | −1.93401 | −0.967004 | − | 0.254759i | \(-0.918004\pi\) | ||||
−0.967004 | + | 0.254759i | \(0.918004\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.52849 | 0.408907 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.3936 | −0.787896 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.9736 | −1.19607 | −0.598033 | − | 0.801472i | \(-0.704051\pi\) | ||||
−0.598033 | + | 0.801472i | \(0.704051\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.47905 | −0.361877 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.2662 | −0.565161 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.77011 | −0.117797 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.4790 | −0.529706 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.8945 | 0.885327 | 0.442663 | − | 0.896688i | \(-0.354034\pi\) | ||||
0.442663 | + | 0.896688i | \(0.354034\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.256043 | −0.0108295 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.66372 | 0.0702424 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.1140 | 0.931992 | 0.465996 | − | 0.884787i | \(-0.345696\pi\) | ||||
0.465996 | + | 0.884787i | \(0.345696\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.1292 | 1.39376 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.84667 | −0.245537 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.3090 | 1.10293 | 0.551465 | − | 0.834198i | \(-0.314069\pi\) | ||||
0.551465 | + | 0.834198i | \(0.314069\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.7899 | −1.16297 | −0.581486 | − | 0.813556i | \(-0.697529\pi\) | ||||
−0.581486 | + | 0.813556i | \(0.697529\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.69572 | −0.321493 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.73710 | −0.406065 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.4669 | 0.435744 | 0.217872 | − | 0.975977i | \(-0.430088\pi\) | ||||
0.217872 | + | 0.975977i | \(0.430088\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.10374 | −0.336780 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.4362 | −0.598913 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.6461 | 1.89047 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.07543 | 0.0444637 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.8082 | −0.900123 | −0.450061 | − | 0.892998i | \(-0.648598\pi\) | ||||
−0.450061 | + | 0.892998i | \(0.648598\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.21748 | 0.297391 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.12123 | −0.292928 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.4823 | −0.882171 | −0.441086 | − | 0.897465i | \(-0.645406\pi\) | ||||
−0.441086 | + | 0.897465i | \(0.645406\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.91171 | −0.0783725 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.4921 | 0.552197 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.6127 | 0.923932 | 0.461966 | − | 0.886898i | \(-0.347144\pi\) | ||||
0.461966 | + | 0.886898i | \(0.347144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.2833 | 1.43923 | 0.719617 | − | 0.694371i | \(-0.244317\pi\) | ||||
0.719617 | + | 0.694371i | \(0.244317\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 29.3657 | 1.19586 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −75.1048 | −3.05345 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.4081 | −0.544219 | −0.272109 | − | 0.962266i | \(-0.587721\pi\) | ||||
−0.272109 | + | 0.962266i | \(0.587721\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.38219 | −0.177575 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.888157 | 0.0359310 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.9863 | −0.968796 | −0.484398 | − | 0.874848i | \(-0.660961\pi\) | ||||
−0.484398 | + | 0.874848i | \(0.660961\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.8367 | −0.477301 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.8338 | −1.52313 | −0.761566 | − | 0.648087i | \(-0.775569\pi\) | ||||
−0.761566 | + | 0.648087i | \(0.775569\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.4917 | 1.62750 | 0.813749 | − | 0.581216i | \(-0.197423\pi\) | ||||
0.813749 | + | 0.581216i | \(0.197423\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.40516 | 0.136644 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.9762 | 0.680138 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.1257 | 0.845027 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.11194 | 0.244087 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.67875 | −0.106809 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.3532 | −1.08892 | −0.544458 | − | 0.838788i | \(-0.683264\pi\) | ||||
−0.544458 | + | 0.838788i | \(0.683264\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.42876 | −0.0567879 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −59.1951 | −2.34908 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.106323 | 0.00421268 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.36529 | −0.0935695 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.4456 | −1.59750 | −0.798752 | − | 0.601661i | \(-0.794506\pi\) | ||||
−0.798752 | + | 0.601661i | \(0.794506\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.9045 | 0.824395 | 0.412197 | − | 0.911095i | \(-0.364761\pi\) | ||||
0.412197 | + | 0.911095i | \(0.364761\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.58663 | 0.219973 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.03117 | 0.158482 | 0.0792408 | − | 0.996856i | \(-0.474750\pi\) | ||||
0.0792408 | + | 0.996856i | \(0.474750\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.69612 | 0.145086 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.38413 | 0.0934412 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.1107 | −1.64792 | −0.823960 | − | 0.566648i | \(-0.808240\pi\) | ||||
−0.823960 | + | 0.566648i | \(0.808240\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 51.5157 | 2.01289 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.8644 | −1.08710 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.1364 | −1.36872 | −0.684361 | − | 0.729144i | \(-0.739919\pi\) | ||||
−0.684361 | + | 0.729144i | \(0.739919\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.65893 | 0.375689 | 0.187844 | − | 0.982199i | \(-0.439850\pi\) | ||||
0.187844 | + | 0.982199i | \(0.439850\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0319965 | −0.00124264 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.02297 | −0.272339 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.25159 | −0.280783 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.81705 | 0.186238 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.7911 | −0.686819 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.9398 | −1.80940 | −0.904698 | − | 0.426054i | \(-0.859903\pi\) | ||||
−0.904698 | + | 0.426054i | \(0.859903\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −33.1564 | −1.27619 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.4968 | −0.787755 | −0.393878 | − | 0.919163i | \(-0.628867\pi\) | ||||
−0.393878 | + | 0.919163i | \(0.628867\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.2471 | −0.469999 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.03787 | −0.154732 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.2648 | −0.737147 | −0.368574 | − | 0.929599i | \(-0.620154\pi\) | ||||
−0.368574 | + | 0.929599i | \(0.620154\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.16860 | 0.121066 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.655544 | 0.0250105 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.877860 | −0.0334438 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.1176 | −0.727267 | −0.363634 | − | 0.931542i | \(-0.618464\pi\) | ||||
−0.363634 | + | 0.931542i | \(0.618464\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.5665 | −0.553337 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 48.5899 | 1.84312 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.54086 | −0.0962421 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.2509 | 0.576844 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.9164 | −0.601153 | −0.300577 | − | 0.953758i | \(-0.597179\pi\) | ||||
−0.300577 | + | 0.953758i | \(0.597179\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.84083 | −0.371154 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.3788 | −0.729847 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.4782 | 0.394075 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.7591 | −1.71852 | −0.859259 | − | 0.511541i | \(-0.829075\pi\) | ||||
−0.859259 | + | 0.511541i | \(0.829075\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.29871 | −0.273723 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.94522 | 0.147750 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.25653 | 0.0843893 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.71424 | 0.0640194 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 49.6642 | 1.85216 | 0.926080 | − | 0.377326i | \(-0.123156\pi\) | ||||
0.926080 | + | 0.377326i | \(0.123156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.67376 | 0.174060 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.24480 | 0.0834850 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 70.6095 | 2.62237 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.8348 | −1.32904 | −0.664520 | − | 0.747271i | \(-0.731364\pi\) | ||||
−0.664520 | + | 0.747271i | \(0.731364\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.23158 | −0.341911 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.19923 | 0.0443551 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.9548 | 0.478497 | 0.239249 | − | 0.970958i | \(-0.423099\pi\) | ||||
0.239249 | + | 0.970958i | \(0.423099\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.31987 | −0.0855698 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 61.6165 | 2.26967 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.6560 | 1.64270 | 0.821348 | − | 0.570427i | \(-0.193222\pi\) | ||||
0.821348 | + | 0.570427i | \(0.193222\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.117544 | −0.00431809 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.1471 | −0.702438 | −0.351219 | − | 0.936293i | \(-0.614233\pi\) | ||||
−0.351219 | + | 0.936293i | \(0.614233\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −56.3310 | −2.06381 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −38.0366 | −1.39169 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.9764 | 0.656843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.13072 | −0.187223 | −0.0936113 | − | 0.995609i | \(-0.529841\pi\) | ||||
−0.0936113 | + | 0.995609i | \(0.529841\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.4680 | −0.563685 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.4367 | −1.47164 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.5986 | −1.51193 | −0.755963 | − | 0.654615i | \(-0.772831\pi\) | ||||
−0.755963 | + | 0.654615i | \(0.772831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.34091 | 0.121267 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.0221 | 1.63205 | 0.816024 | − | 0.578018i | \(-0.196174\pi\) | ||||
0.816024 | + | 0.578018i | \(0.196174\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.79138 | −0.173460 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.03700 | −0.182113 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.0710834 | −0.00256667 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.3467 | 0.877963 | 0.438982 | − | 0.898496i | \(-0.355339\pi\) | ||||
0.438982 | + | 0.898496i | \(0.355339\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.54293 | −0.199624 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.9581 | 1.04155 | 0.520775 | − | 0.853694i | \(-0.325643\pi\) | ||||
0.520775 | + | 0.853694i | \(0.325643\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38.4150 | −1.37991 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.25069 | −0.116618 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.33426 | −0.334435 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.96297 | −0.177589 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.6928 | −0.882450 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −91.5713 | −3.26832 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.3643 | 0.369447 | 0.184723 | − | 0.982791i | \(-0.440861\pi\) | ||||
0.184723 | + | 0.982791i | \(0.440861\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.10687 | −0.0750065 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.62988 | 0.306843 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.342157 | 0.0121503 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.1541 | 0.679326 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.0652 | 1.02954 | 0.514772 | − | 0.857327i | \(-0.327877\pi\) | ||||
0.514772 | + | 0.857327i | \(0.327877\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.15986 | −0.147165 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 44.7292 | 1.58043 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −58.4665 | −2.06324 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.83889 | −0.135303 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.35600 | −0.0477336 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.1570 | 1.13058 | 0.565291 | − | 0.824892i | \(-0.308764\pi\) | ||||
0.565291 | + | 0.824892i | \(0.308764\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.5270 | −0.510113 | −0.255056 | − | 0.966926i | \(-0.582094\pi\) | ||||
−0.255056 | + | 0.966926i | \(0.582094\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0174119 | 0.000610662 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.4112 | −0.995202 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.40555 | 0.154131 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.280141 | 0.00978893 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.201239 | 0.00702329 | 0.00351164 | − | 0.999994i | \(-0.498882\pi\) | ||||
0.00351164 | + | 0.999994i | \(0.498882\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.3719 | 0.779836 | 0.389918 | − | 0.920850i | \(-0.372503\pi\) | ||||
0.389918 | + | 0.920850i | \(0.372503\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −32.5308 | −1.13258 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.19173 | −0.319628 | −0.159814 | − | 0.987147i | \(-0.551089\pi\) | ||||
−0.159814 | + | 0.987147i | \(0.551089\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.8345 | −0.376296 | −0.188148 | − | 0.982141i | \(-0.560249\pi\) | ||||
−0.188148 | + | 0.982141i | \(0.560249\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.18120 | 0.145044 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.497985 | −0.0172541 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −63.7152 | −2.20495 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.4341 | 0.464350 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.77829 | 0.337584 | 0.168792 | − | 0.985652i | \(-0.446013\pi\) | ||||
0.168792 | + | 0.985652i | \(0.446013\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.5856 | 0.813296 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.6739 | 0.677606 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 49.8622 | 1.71531 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.5642 | −0.672234 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.741820 | −0.0254592 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.37919 | −0.184396 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.927467 | 0.0317559 | 0.0158779 | − | 0.999874i | \(-0.494946\pi\) | ||||
0.0158779 | + | 0.999874i | \(0.494946\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.5042 | −0.632830 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.66044 | −0.0908789 | −0.0454394 | − | 0.998967i | \(-0.514469\pi\) | ||||
−0.0454394 | + | 0.998967i | \(0.514469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.4822 | −1.27888 | −0.639438 | − | 0.768843i | \(-0.720833\pi\) | ||||
−0.639438 | + | 0.768843i | \(0.720833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.08336 | −0.105080 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.1751 | 0.482528 | 0.241264 | − | 0.970460i | \(-0.422438\pi\) | ||||
0.241264 | + | 0.970460i | \(0.422438\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.3161 | 1.20078 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.1234 | −0.343808 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.3145 | −0.519509 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.18500 | −0.0401522 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −32.2687 | −1.09213 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.1852 | 0.614773 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.13991 | −0.139795 | −0.0698974 | − | 0.997554i | \(-0.522267\pi\) | ||||
−0.0698974 | + | 0.997554i | \(0.522267\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.5699 | 0.693806 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.9906 | 1.07779 | 0.538896 | − | 0.842372i | \(-0.318842\pi\) | ||||
0.538896 | + | 0.842372i | \(0.318842\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.9333 | 1.04099 | 0.520495 | − | 0.853865i | \(-0.325747\pi\) | ||||
0.520495 | + | 0.853865i | \(0.325747\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.55097 | 0.0521354 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.9581 | −0.938740 | −0.469370 | − | 0.883002i | \(-0.655519\pi\) | ||||
−0.469370 | + | 0.883002i | \(0.655519\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.4198 | −0.517164 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32.3233 | −1.08287 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.2819 | −0.511389 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 49.7162 | 1.66183 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0642519 | −0.00214531 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.6091 | −0.954167 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.11162 | 0.136978 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.45527 | 0.0484284 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −60.5302 | −2.01209 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.4224 | 1.07657 | 0.538284 | − | 0.842763i | \(-0.319073\pi\) | ||||
0.538284 | + | 0.842763i | \(0.319073\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.6082 | 0.915706 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.5349 | 0.746613 | 0.373306 | − | 0.927708i | \(-0.378224\pi\) | ||||
0.373306 | + | 0.927708i | \(0.378224\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −79.8102 | −2.64133 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.46555 | −0.246803 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.4194 | 0.443148 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.8810 | −1.24958 | −0.624790 | − | 0.780793i | \(-0.714815\pi\) | ||||
−0.624790 | + | 0.780793i | \(0.714815\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.98924 | 0.164401 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.0954471 | 0.00314168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 52.3777 | 1.72217 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.3145 | 0.404460 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 55.2532 | 1.81280 | 0.906399 | − | 0.422423i | \(-0.138820\pi\) | ||||
0.906399 | + | 0.422423i | \(0.138820\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.82942 | −0.0599570 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.1587 | −0.496273 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.5689 | −0.345639 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.0702 | −0.492323 | −0.246162 | − | 0.969229i | \(-0.579169\pi\) | ||||
−0.246162 | + | 0.969229i | \(0.579169\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.93923 | 0.259087 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.2068 | 0.430529 | 0.215265 | − | 0.976556i | \(-0.430939\pi\) | ||||
0.215265 | + | 0.976556i | \(0.430939\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.10229 | −0.166154 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.0721 | −0.425234 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.9948 | −0.747230 | −0.373615 | − | 0.927584i | \(-0.621882\pi\) | ||||
−0.373615 | + | 0.927584i | \(0.621882\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.12442 | 0.0365002 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.5671 | −0.569651 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.8303 | −0.674758 | −0.337379 | − | 0.941369i | \(-0.609540\pi\) | ||||
−0.337379 | + | 0.941369i | \(0.609540\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.8874 | 1.58196 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24.2269 | −0.783145 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.825394 | 0.0266534 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4353 | −0.497912 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 47.3644 | 1.52630 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 51.4794 | 1.65718 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.93655 | −0.255222 | −0.127611 | − | 0.991824i | \(-0.540731\pi\) | ||||
−0.127611 | + | 0.991824i | \(0.540731\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.550540 | 0.0176859 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.2326 | −0.360470 | −0.180235 | − | 0.983624i | \(-0.557686\pi\) | ||||
−0.180235 | + | 0.983624i | \(0.557686\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.6573 | 0.405773 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.625627 | 0.0200361 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.9955 | 0.415762 | 0.207881 | − | 0.978154i | \(-0.433343\pi\) | ||||
0.207881 | + | 0.978154i | \(0.433343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 93.8529 | 2.99955 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.6244 | −0.403066 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.1117 | 1.24747 | 0.623735 | − | 0.781636i | \(-0.285614\pi\) | ||||
0.623735 | + | 0.781636i | \(0.285614\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 45.2379 | 1.44140 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.04801 | −0.160680 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.40816 | 0.0765751 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.1445 | 0.798741 | 0.399371 | − | 0.916790i | \(-0.369229\pi\) | ||||
0.399371 | + | 0.916790i | \(0.369229\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.7940 | 0.501207 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −85.7095 | −2.71717 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.1007 | 1.27000 | 0.635001 | − | 0.772511i | \(-0.280999\pi\) | ||||
0.635001 | + | 0.772511i | \(0.280999\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.3170 | −0.579525 |
(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 | 2576.2.a.bc.1.4 | 5 | ||
4.3 | odd | 2 | 644.2.a.c.1.2 | ✓ | 5 | ||
12.11 | even | 2 | 5796.2.a.s.1.5 | 5 | |||
28.27 | even | 2 | 4508.2.a.g.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
644.2.a.c.1.2 | ✓ | 5 | 4.3 | odd | 2 | ||
2576.2.a.bc.1.4 | 5 | 1.1 | even | 1 | trivial | ||
4508.2.a.g.1.4 | 5 | 28.27 | even | 2 | |||
5796.2.a.s.1.5 | 5 | 12.11 | even | 2 |