Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3120,2,Mod(1,3120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3120.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3120.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: | \(24.9133254306\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1560) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3120.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.56155 | 0.968176 | 0.484088 | − | 0.875019i | \(-0.339151\pi\) | ||||
0.484088 | + | 0.875019i | \(0.339151\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.43845 | 0.433708 | 0.216854 | − | 0.976204i | \(-0.430420\pi\) | ||||
0.216854 | + | 0.976204i | \(0.430420\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.68466 | 1.37873 | 0.689366 | − | 0.724413i | \(-0.257889\pi\) | ||||
0.689366 | + | 0.724413i | \(0.257889\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.12311 | 1.17532 | 0.587661 | − | 0.809108i | \(-0.300049\pi\) | ||||
0.587661 | + | 0.809108i | \(0.300049\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.56155 | 0.558977 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.43845 | 0.299937 | 0.149968 | − | 0.988691i | \(-0.452083\pi\) | ||||
0.149968 | + | 0.988691i | \(0.452083\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.12311 | −0.201716 | −0.100858 | − | 0.994901i | \(-0.532159\pi\) | ||||
−0.100858 | + | 0.994901i | \(0.532159\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.43845 | 0.250402 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.56155 | 0.432981 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.8078 | −1.77679 | −0.888393 | − | 0.459084i | \(-0.848178\pi\) | ||||
−0.888393 | + | 0.459084i | \(0.848178\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.68466 | −1.51249 | −0.756245 | − | 0.654289i | \(-0.772968\pi\) | ||||
−0.756245 | + | 0.654289i | \(0.772968\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.24621 | −0.952538 | −0.476269 | − | 0.879300i | \(-0.658011\pi\) | ||||
−0.476269 | + | 0.879300i | \(0.658011\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.12311 | 0.163822 | 0.0819109 | − | 0.996640i | \(-0.473898\pi\) | ||||
0.0819109 | + | 0.996640i | \(0.473898\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.438447 | −0.0626353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.68466 | 0.796011 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.561553 | −0.0771352 | −0.0385676 | − | 0.999256i | \(-0.512279\pi\) | ||||
−0.0385676 | + | 0.999256i | \(0.512279\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.43845 | 0.193960 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.12311 | 0.678572 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.00000 | 1.04151 | 0.520756 | − | 0.853706i | \(-0.325650\pi\) | ||||
0.520756 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.68466 | 0.215698 | 0.107849 | − | 0.994167i | \(-0.465604\pi\) | ||||
0.107849 | + | 0.994167i | \(0.465604\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.56155 | 0.322725 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.24621 | −0.274418 | −0.137209 | − | 0.990542i | \(-0.543813\pi\) | ||||
−0.137209 | + | 0.990542i | \(0.543813\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.43845 | 0.173169 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.68466 | 0.912001 | 0.456001 | − | 0.889979i | \(-0.349281\pi\) | ||||
0.456001 | + | 0.889979i | \(0.349281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.246211 | −0.0288168 | −0.0144084 | − | 0.999896i | \(-0.504587\pi\) | ||||
−0.0144084 | + | 0.999896i | \(0.504587\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.68466 | 0.419906 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.80776 | 0.990951 | 0.495475 | − | 0.868622i | \(-0.334994\pi\) | ||||
0.495475 | + | 0.868622i | \(0.334994\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.68466 | 0.616588 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.31534 | −0.245426 | −0.122713 | − | 0.992442i | \(-0.539159\pi\) | ||||
−0.122713 | + | 0.992442i | \(0.539159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.56155 | 0.268524 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.12311 | −0.116461 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.12311 | 0.525620 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.80776 | 0.285085 | 0.142543 | − | 0.989789i | \(-0.454472\pi\) | ||||
0.142543 | + | 0.989789i | \(0.454472\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.43845 | 0.144569 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.12311 | −0.708776 | −0.354388 | − | 0.935099i | \(-0.615311\pi\) | ||||
−0.354388 | + | 0.935099i | \(0.615311\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.24621 | 0.221326 | 0.110663 | − | 0.993858i | \(-0.464703\pi\) | ||||
0.110663 | + | 0.993858i | \(0.464703\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.56155 | 0.249982 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.80776 | −0.464784 | −0.232392 | − | 0.972622i | \(-0.574655\pi\) | ||||
−0.232392 | + | 0.972622i | \(0.574655\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.87689 | −0.467122 | −0.233561 | − | 0.972342i | \(-0.575038\pi\) | ||||
−0.233561 | + | 0.972342i | \(0.575038\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.8078 | −1.02583 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.43845 | 0.134136 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.5616 | 1.33486 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.93087 | −0.811897 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.68466 | −0.873236 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.36932 | −0.653921 | −0.326961 | − | 0.945038i | \(-0.606024\pi\) | ||||
−0.326961 | + | 0.945038i | \(0.606024\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.24621 | −0.549948 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.87689 | 0.600837 | 0.300419 | − | 0.953807i | \(-0.402874\pi\) | ||||
0.300419 | + | 0.953807i | \(0.402874\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.1231 | 1.13792 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.246211 | −0.0210352 | −0.0105176 | − | 0.999945i | \(-0.503348\pi\) | ||||
−0.0105176 | + | 0.999945i | \(0.503348\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.43845 | 0.461283 | 0.230642 | − | 0.973039i | \(-0.425918\pi\) | ||||
0.230642 | + | 0.973039i | \(0.425918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.12311 | 0.0945826 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.43845 | 0.120289 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.438447 | −0.0361625 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.5616 | −1.35678 | −0.678388 | − | 0.734704i | \(-0.737321\pi\) | ||||
−0.678388 | + | 0.734704i | \(0.737321\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | −0.325515 | −0.162758 | − | 0.986666i | \(-0.552039\pi\) | ||||
−0.162758 | + | 0.986666i | \(0.552039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.68466 | 0.459577 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.12311 | −0.0902100 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.4924 | −1.79509 | −0.897545 | − | 0.440922i | \(-0.854651\pi\) | ||||
−0.897545 | + | 0.440922i | \(0.854651\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.561553 | −0.0445340 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.68466 | 0.290392 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.43845 | −0.739276 | −0.369638 | − | 0.929176i | \(-0.620518\pi\) | ||||
−0.369638 | + | 0.929176i | \(0.620518\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.43845 | 0.111983 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.2462 | 1.72146 | 0.860732 | − | 0.509059i | \(-0.170006\pi\) | ||||
0.860732 | + | 0.509059i | \(0.170006\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.12311 | 0.391774 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.0000 | 1.06440 | 0.532200 | − | 0.846619i | \(-0.321365\pi\) | ||||
0.532200 | + | 0.846619i | \(0.321365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.56155 | 0.193635 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.00000 | 0.601317 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.8769 | 1.11195 | 0.555976 | − | 0.831199i | \(-0.312345\pi\) | ||||
0.555976 | + | 0.831199i | \(0.312345\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.9309 | 1.48145 | 0.740725 | − | 0.671808i | \(-0.234482\pi\) | ||||
0.740725 | + | 0.671808i | \(0.234482\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.68466 | 0.124534 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.8078 | −0.794603 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.17708 | 0.597967 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.56155 | 0.186326 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.6847 | 1.56090 | 0.780448 | − | 0.625221i | \(-0.214991\pi\) | ||||
0.780448 | + | 0.625221i | \(0.214991\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.3693 | −1.23751 | −0.618756 | − | 0.785583i | \(-0.712363\pi\) | ||||
−0.618756 | + | 0.785583i | \(0.712363\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.2462 | −1.29344 | −0.646720 | − | 0.762728i | \(-0.723860\pi\) | ||||
−0.646720 | + | 0.762728i | \(0.723860\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.24621 | −0.158436 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.12311 | −0.359572 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.68466 | −0.676406 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.43845 | 0.0999790 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.36932 | 0.509746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.68466 | 0.526544 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.24621 | −0.425988 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.87689 | −0.195296 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.246211 | −0.0166374 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.68466 | 0.382392 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.2462 | −0.953997 | −0.476998 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476998 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.630683 | −0.0418599 | −0.0209300 | − | 0.999781i | \(-0.506663\pi\) | ||||
−0.0209300 | + | 0.999781i | \(0.506663\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.68466 | 0.242433 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.31534 | 0.413732 | 0.206866 | − | 0.978369i | \(-0.433674\pi\) | ||||
0.206866 | + | 0.978369i | \(0.433674\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.12311 | 0.0732633 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.80776 | 0.572126 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.6847 | 1.01456 | 0.507278 | − | 0.861782i | \(-0.330652\pi\) | ||||
0.507278 | + | 0.861782i | \(0.330652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.2462 | 1.81950 | 0.909749 | − | 0.415158i | \(-0.136274\pi\) | ||||
0.909749 | + | 0.415158i | \(0.136274\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.438447 | −0.0280114 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.12311 | 0.325975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.00000 | 0.506979 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.4924 | 1.54595 | 0.772974 | − | 0.634438i | \(-0.218768\pi\) | ||||
0.772974 | + | 0.634438i | \(0.218768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.06913 | 0.130085 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.68466 | 0.355987 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.4924 | −1.15353 | −0.576763 | − | 0.816912i | \(-0.695684\pi\) | ||||
−0.576763 | + | 0.816912i | \(0.695684\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.6847 | −1.72024 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.49242 | 0.277015 | 0.138507 | − | 0.990361i | \(-0.455770\pi\) | ||||
0.138507 | + | 0.990361i | \(0.455770\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.561553 | −0.0344959 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.31534 | −0.141697 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.87689 | −0.297349 | −0.148675 | − | 0.988886i | \(-0.547501\pi\) | ||||
−0.148675 | + | 0.988886i | \(0.547501\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.3693 | −1.17660 | −0.588301 | − | 0.808642i | \(-0.700203\pi\) | ||||
−0.588301 | + | 0.808642i | \(0.700203\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.56155 | 0.155032 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.43845 | 0.0867416 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4924 | 0.630429 | 0.315214 | − | 0.949021i | \(-0.397924\pi\) | ||||
0.315214 | + | 0.949021i | \(0.397924\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.12311 | −0.0672386 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.2462 | 1.20779 | 0.603894 | − | 0.797065i | \(-0.293615\pi\) | ||||
0.603894 | + | 0.797065i | \(0.293615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.7386 | 1.11390 | 0.556948 | − | 0.830547i | \(-0.311972\pi\) | ||||
0.556948 | + | 0.830547i | \(0.311972\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.12311 | 0.303467 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.8078 | −1.46436 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.3153 | 0.900902 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.80776 | 0.164594 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.6155 | 1.37963 | 0.689817 | − | 0.723984i | \(-0.257691\pi\) | ||||
0.689817 | + | 0.723984i | \(0.257691\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.43845 | 0.0834672 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.43845 | 0.0831875 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | −0.922225 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.12311 | −0.409212 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.68466 | 0.0964633 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.43845 | −0.538681 | −0.269340 | − | 0.963045i | \(-0.586806\pi\) | ||||
−0.269340 | + | 0.963045i | \(0.586806\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.24621 | 0.127782 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.7386 | −1.28939 | −0.644695 | − | 0.764440i | \(-0.723016\pi\) | ||||
−0.644695 | + | 0.764440i | \(0.723016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.7386 | 1.39831 | 0.699155 | − | 0.714970i | \(-0.253560\pi\) | ||||
0.699155 | + | 0.714970i | \(0.253560\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.56155 | 0.144327 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.1231 | 0.624736 | 0.312368 | − | 0.949961i | \(-0.398878\pi\) | ||||
0.312368 | + | 0.949961i | \(0.398878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.87689 | −0.161075 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.80776 | −0.268343 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.1231 | 1.62045 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.87689 | −0.269693 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.87689 | 0.158608 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.2462 | −1.44262 | −0.721311 | − | 0.692611i | \(-0.756460\pi\) | ||||
−0.721311 | + | 0.692611i | \(0.756460\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.8078 | −0.592262 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.24621 | −0.122724 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.1231 | −0.605914 | −0.302957 | − | 0.953004i | \(-0.597974\pi\) | ||||
−0.302957 | + | 0.953004i | \(0.597974\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.00000 | 0.108625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.61553 | −0.0874858 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.0540 | −1.02882 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.43845 | 0.0774434 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −31.0540 | −1.66706 | −0.833532 | − | 0.552471i | \(-0.813685\pi\) | ||||
−0.833532 | + | 0.552471i | \(0.813685\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.3693 | −1.35799 | −0.678994 | − | 0.734144i | \(-0.737584\pi\) | ||||
−0.678994 | + | 0.734144i | \(0.737584\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.2462 | 0.651800 | 0.325900 | − | 0.945404i | \(-0.394333\pi\) | ||||
0.325900 | + | 0.945404i | \(0.394333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.68466 | 0.407859 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.5616 | 0.770679 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.2462 | −0.751886 | −0.375943 | − | 0.926643i | \(-0.622681\pi\) | ||||
−0.375943 | + | 0.926643i | \(0.622681\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.24621 | 0.381380 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.93087 | −0.468749 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.246211 | −0.0128873 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.24621 | 0.117251 | 0.0586256 | − | 0.998280i | \(-0.481328\pi\) | ||||
0.0586256 | + | 0.998280i | \(0.481328\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.68466 | −0.504163 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.43845 | −0.0746805 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.1231 | −1.19727 | −0.598635 | − | 0.801022i | \(-0.704290\pi\) | ||||
−0.598635 | + | 0.801022i | \(0.704290\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.87689 | −0.147776 | −0.0738881 | − | 0.997267i | \(-0.523541\pi\) | ||||
−0.0738881 | + | 0.997267i | \(0.523541\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.36932 | −0.377542 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.3693 | −1.39851 | −0.699253 | − | 0.714874i | \(-0.746484\pi\) | ||||
−0.699253 | + | 0.714874i | \(0.746484\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.68466 | 0.187788 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.24621 | −0.317513 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.8617 | −1.10843 | −0.554217 | − | 0.832372i | \(-0.686982\pi\) | ||||
−0.554217 | + | 0.832372i | \(0.686982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.17708 | 0.413533 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.87689 | 0.346893 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.80776 | 0.443167 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.1922 | 0.662099 | 0.331050 | − | 0.943613i | \(-0.392597\pi\) | ||||
0.331050 | + | 0.943613i | \(0.392597\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.1231 | 0.656977 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.2462 | 0.611547 | 0.305773 | − | 0.952104i | \(-0.401085\pi\) | ||||
0.305773 | + | 0.952104i | \(0.401085\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.12311 | −0.0559459 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.5464 | −0.770606 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.4924 | 0.716604 | 0.358302 | − | 0.933606i | \(-0.383356\pi\) | ||||
0.358302 | + | 0.933606i | \(0.383356\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.246211 | −0.0121447 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.4924 | 1.00837 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.43845 | 0.266322 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.12311 | −0.445693 | −0.222846 | − | 0.974854i | \(-0.571535\pi\) | ||||
−0.222846 | + | 0.974854i | \(0.571535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.8617 | −1.84527 | −0.922634 | − | 0.385676i | \(-0.873968\pi\) | ||||
−0.922634 | + | 0.385676i | \(0.873968\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.12311 | 0.0546073 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.68466 | 0.275746 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.31534 | 0.208834 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.43845 | 0.0694489 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.2462 | −1.45691 | −0.728454 | − | 0.685094i | \(-0.759761\pi\) | ||||
−0.728454 | + | 0.685094i | \(0.759761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.6307 | 0.510878 | 0.255439 | − | 0.966825i | \(-0.417780\pi\) | ||||
0.255439 | + | 0.966825i | \(0.417780\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.00000 | −0.0958927 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.36932 | 0.352522 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.9309 | 1.04670 | 0.523352 | − | 0.852117i | \(-0.324681\pi\) | ||||
0.523352 | + | 0.852117i | \(0.324681\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.438447 | −0.0208784 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.6847 | 0.745201 | 0.372600 | − | 0.927992i | \(-0.378466\pi\) | ||||
0.372600 | + | 0.927992i | \(0.378466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.31534 | −0.109758 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.5616 | −0.783335 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.68466 | −0.0795039 | −0.0397520 | − | 0.999210i | \(-0.512657\pi\) | ||||
−0.0397520 | + | 0.999210i | \(0.512657\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.9309 | −0.655979 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.00000 | −0.187936 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.56155 | 0.120087 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.4384 | −1.47063 | −0.735314 | − | 0.677726i | \(-0.762965\pi\) | ||||
−0.735314 | + | 0.677726i | \(0.762965\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.68466 | 0.265337 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.4384 | −0.532742 | −0.266371 | − | 0.963871i | \(-0.585825\pi\) | ||||
−0.266371 | + | 0.963871i | \(0.585825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.5616 | 0.490837 | 0.245418 | − | 0.969417i | \(-0.421075\pi\) | ||||
0.245418 | + | 0.969417i | \(0.421075\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.12311 | −0.0520828 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.1771 | 0.933684 | 0.466842 | − | 0.884341i | \(-0.345392\pi\) | ||||
0.466842 | + | 0.884341i | \(0.345392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.75379 | −0.265685 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.4924 | −1.03640 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.98485 | −0.413124 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.12311 | 0.235064 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.561553 | −0.0257117 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.5464 | 1.62416 | 0.812078 | − | 0.583549i | \(-0.198336\pi\) | ||||
0.812078 | + | 0.583549i | \(0.198336\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.8078 | −0.492792 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.68466 | 0.167658 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.80776 | 0.127494 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.68466 | 0.348225 | 0.174113 | − | 0.984726i | \(-0.444294\pi\) | ||||
0.174113 | + | 0.984726i | \(0.444294\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.43845 | −0.426821 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.4924 | 1.82740 | 0.913699 | − | 0.406392i | \(-0.133213\pi\) | ||||
0.913699 | + | 0.406392i | \(0.133213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.3693 | −0.512048 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.43845 | 0.0646534 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.6847 | 0.882978 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.8617 | −0.889134 | −0.444567 | − | 0.895746i | \(-0.646642\pi\) | ||||
−0.444567 | + | 0.895746i | \(0.646642\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.2462 | 0.993887 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.7386 | 1.37057 | 0.685284 | − | 0.728276i | \(-0.259678\pi\) | ||||
0.685284 | + | 0.728276i | \(0.259678\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.12311 | −0.316974 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.3153 | −1.34370 | −0.671852 | − | 0.740685i | \(-0.734501\pi\) | ||||
−0.671852 | + | 0.740685i | \(0.734501\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.630683 | −0.0278998 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.12311 | 0.226191 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.24621 | 0.0989799 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.61553 | 0.0710508 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.0000 | 0.614532 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.2462 | −1.32257 | −0.661287 | − | 0.750133i | \(-0.729990\pi\) | ||||
−0.661287 | + | 0.750133i | \(0.729990\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.56155 | 0.111795 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.38447 | −0.278112 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.9309 | −0.910038 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.00000 | 0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.68466 | −0.419489 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.80776 | −0.207858 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.8769 | 0.641985 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.630683 | −0.0271654 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.0000 | −1.46177 | −0.730887 | − | 0.682498i | \(-0.760893\pi\) | ||||
−0.730887 | + | 0.682498i | \(0.760893\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.9309 | 0.855315 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.87689 | −0.208903 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.7386 | −1.82737 | −0.913686 | − | 0.406421i | \(-0.866777\pi\) | ||||
−0.913686 | + | 0.406421i | \(0.866777\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.68466 | 0.0718995 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.2462 | −0.436503 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.5616 | 0.959415 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.8078 | −0.458764 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.0000 | −1.44063 | −0.720313 | − | 0.693649i | \(-0.756002\pi\) | ||||
−0.720313 | + | 0.693649i | \(0.756002\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.24621 | −0.264187 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.17708 | 0.345237 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.4384 | 0.903523 | 0.451761 | − | 0.892139i | \(-0.350796\pi\) | ||||
0.451761 | + | 0.892139i | \(0.350796\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | 0.0841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.56155 | 0.107575 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.12311 | 0.298616 | 0.149308 | − | 0.988791i | \(-0.452295\pi\) | ||||
0.149308 | + | 0.988791i | \(0.452295\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.4384 | −0.897171 | −0.448586 | − | 0.893740i | \(-0.648072\pi\) | ||||
−0.448586 | + | 0.893740i | \(0.648072\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.00000 | −0.334205 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.43845 | 0.0599874 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.5464 | 1.39655 | 0.698277 | − | 0.715827i | \(-0.253950\pi\) | ||||
0.698277 | + | 0.715827i | \(0.253950\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.6847 | 0.901184 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.4924 | 0.850169 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.807764 | −0.0334542 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.36932 | −0.304164 | −0.152082 | − | 0.988368i | \(-0.548598\pi\) | ||||
−0.152082 | + | 0.988368i | \(0.548598\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.75379 | −0.237081 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.3693 | −0.714478 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.6155 | 1.46255 | 0.731277 | − | 0.682080i | \(-0.238925\pi\) | ||||
0.731277 | + | 0.682080i | \(0.238925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.5616 | 0.596965 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.2462 | −0.746768 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.7386 | −1.25595 | −0.627973 | − | 0.778235i | \(-0.716115\pi\) | ||||
−0.627973 | + | 0.778235i | \(0.716115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.561553 | 0.0229062 | 0.0114531 | − | 0.999934i | \(-0.496354\pi\) | ||||
0.0114531 | + | 0.999934i | \(0.496354\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.24621 | −0.0914728 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.93087 | −0.363091 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.7386 | 0.922933 | 0.461466 | − | 0.887158i | \(-0.347324\pi\) | ||||
0.461466 | + | 0.887158i | \(0.347324\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.12311 | −0.207599 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.12311 | 0.0454360 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.9309 | −0.966559 | −0.483279 | − | 0.875466i | \(-0.660554\pi\) | ||||
−0.483279 | + | 0.875466i | \(0.660554\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.68466 | −0.390523 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.2462 | −0.654048 | −0.327024 | − | 0.945016i | \(-0.606046\pi\) | ||||
−0.327024 | + | 0.945016i | \(0.606046\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.3693 | −1.26084 | −0.630420 | − | 0.776255i | \(-0.717117\pi\) | ||||
−0.630420 | + | 0.776255i | \(0.717117\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.43845 | 0.0577229 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.93087 | −0.237615 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.36932 | 0.294302 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −61.4384 | −2.44971 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.75379 | −0.388292 | −0.194146 | − | 0.980973i | \(-0.562194\pi\) | ||||
−0.194146 | + | 0.980973i | \(0.562194\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.36932 | −0.292442 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.438447 | −0.0173719 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.68466 | 0.304000 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.3693 | 1.00203 | 0.501014 | − | 0.865439i | \(-0.332961\pi\) | ||||
0.501014 | + | 0.865439i | \(0.332961\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.80776 | 0.347344 | 0.173672 | − | 0.984804i | \(-0.444437\pi\) | ||||
0.173672 | + | 0.984804i | \(0.444437\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.24621 | −0.245944 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.6847 | −0.459371 | −0.229686 | − | 0.973265i | \(-0.573770\pi\) | ||||
−0.229686 | + | 0.973265i | \(0.573770\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.5076 | 0.451712 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.87689 | −0.112754 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.2462 | 1.57496 | 0.787478 | − | 0.616343i | \(-0.211386\pi\) | ||||
0.787478 | + | 0.616343i | \(0.211386\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.87689 | 0.268702 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.246211 | −0.00960562 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.4924 | 0.954089 | 0.477045 | − | 0.878879i | \(-0.341708\pi\) | ||||
0.477045 | + | 0.878879i | \(0.341708\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.1231 | −1.52171 | −0.760856 | − | 0.648920i | \(-0.775221\pi\) | ||||
−0.760856 | + | 0.648920i | \(0.775221\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.68466 | 0.220774 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.1231 | 0.508892 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.87689 | −0.111394 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.2462 | −0.550790 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.42329 | 0.0935502 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0000 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586968\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.9309 | 1.38094 | 0.690468 | − | 0.723363i | \(-0.257405\pi\) | ||||
0.690468 | + | 0.723363i | \(0.257405\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.19224 | 0.276013 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.630683 | −0.0241678 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.4924 | 1.09023 | 0.545116 | − | 0.838361i | \(-0.316486\pi\) | ||||
0.545116 | + | 0.838361i | \(0.316486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.246211 | −0.00940725 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.0000 | −0.381524 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.561553 | −0.0213935 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.1231 | −1.41223 | −0.706115 | − | 0.708097i | \(-0.749554\pi\) | ||||
−0.706115 | + | 0.708097i | \(0.749554\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.68466 | 0.139969 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.43845 | 0.206292 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −55.0540 | −2.08532 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.31534 | 0.238868 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.36932 | 0.202796 | 0.101398 | − | 0.994846i | \(-0.467668\pi\) | ||||
0.101398 | + | 0.994846i | \(0.467668\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −55.3693 | −2.08829 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.12311 | 0.0422986 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.2462 | −0.686219 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.87689 | 0.333379 | 0.166689 | − | 0.986009i | \(-0.446692\pi\) | ||||
0.166689 | + | 0.986009i | \(0.446692\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.80776 | 0.330317 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.61553 | −0.0605020 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.43845 | 0.0537949 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.6847 | 0.585754 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.2462 | −0.978819 | −0.489409 | − | 0.872054i | \(-0.662788\pi\) | ||||
−0.489409 | + | 0.872054i | \(0.662788\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.75379 | 0.214282 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.2462 | 1.05049 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.3693 | 1.75683 | 0.878415 | − | 0.477898i | \(-0.158601\pi\) | ||||
0.878415 | + | 0.477898i | \(0.158601\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.5076 | −1.31330 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.4233 | 1.19758 | 0.598791 | − | 0.800905i | \(-0.295648\pi\) | ||||
0.598791 | + | 0.800905i | \(0.295648\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.438447 | −0.0161724 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.23106 | −0.119017 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.8617 | 1.02491 | 0.512455 | − | 0.858714i | \(-0.328736\pi\) | ||||
0.512455 | + | 0.858714i | \(0.328736\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.12311 | 0.188202 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.1231 | 0.628186 | 0.314093 | − | 0.949392i | \(-0.398300\pi\) | ||||
0.314093 | + | 0.949392i | \(0.398300\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.5616 | −0.606768 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.00000 | 0.292705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.3153 | −0.449993 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.6847 | 0.718303 | 0.359152 | − | 0.933279i | \(-0.383066\pi\) | ||||
0.359152 | + | 0.933279i | \(0.383066\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.4924 | 0.892553 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.00000 | −0.145575 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.1231 | −0.840424 | −0.420212 | − | 0.907426i | \(-0.638044\pi\) | ||||
−0.420212 | + | 0.907426i | \(0.638044\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.06913 | 0.0751047 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.4924 | −0.380350 | −0.190175 | − | 0.981750i | \(-0.560906\pi\) | ||||
−0.190175 | + | 0.981750i | \(0.560906\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.4924 | −0.452256 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.68466 | 0.205529 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.00000 | 0.288863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.6155 | −0.563110 | −0.281555 | − | 0.959545i | \(-0.590850\pi\) | ||||
−0.281555 | + | 0.959545i | \(0.590850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.4924 | −0.665988 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.8769 | −0.463150 | −0.231575 | − | 0.972817i | \(-0.574388\pi\) | ||||
−0.231575 | + | 0.972817i | \(0.574388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.12311 | −0.0403431 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −27.6847 | −0.993182 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −49.6155 | −1.77766 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.0540 | 0.395542 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.4924 | −0.802789 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.7386 | −1.09571 | −0.547857 | − | 0.836572i | \(-0.684556\pi\) | ||||
−0.547857 | + | 0.836572i | \(0.684556\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.49242 | 0.159934 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.12311 | 0.182157 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.68466 | 0.0598240 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.561553 | −0.0199162 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.4233 | −0.723430 | −0.361715 | − | 0.932289i | \(-0.617809\pi\) | ||||
−0.361715 | + | 0.932289i | \(0.617809\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.38447 | 0.225866 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.31534 | −0.0818086 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.354162 | −0.0124981 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.68466 | 0.129867 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.87689 | −0.171675 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.4924 | 0.509526 | 0.254763 | − | 0.967003i | \(-0.418002\pi\) | ||||
0.254763 | + | 0.967003i | \(0.418002\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.9848 | 0.877337 | 0.438668 | − | 0.898649i | \(-0.355450\pi\) | ||||
0.438668 | + | 0.898649i | \(0.355450\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.3693 | −0.679312 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.43845 | −0.330614 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | −1.11954 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.56155 | 0.0895079 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.6847 | −1.59441 | −0.797203 | − | 0.603712i | \(-0.793688\pi\) | ||||
−0.797203 | + | 0.603712i | \(0.793688\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.4924 | 1.55091 | 0.775454 | − | 0.631404i | \(-0.217521\pi\) | ||||
0.775454 | + | 0.631404i | \(0.217521\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.43845 | 0.0500803 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.3693 | −1.64719 | −0.823596 | − | 0.567177i | \(-0.808036\pi\) | ||||
−0.823596 | + | 0.567177i | \(0.808036\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.0000 | 1.04194 | 0.520972 | − | 0.853574i | \(-0.325570\pi\) | ||||
0.520972 | + | 0.853574i | \(0.325570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.4924 | 0.363978 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.49242 | −0.0863573 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.2462 | 0.769862 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.12311 | −0.0388202 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.1922 | 0.386399 | 0.193199 | − | 0.981160i | \(-0.438114\pi\) | ||||
0.193199 | + | 0.981160i | \(0.438114\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.2462 | 0.697317 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.8769 | −0.786059 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.7386 | 0.643108 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.5464 | −0.532924 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.4384 | −1.21339 | −0.606695 | − | 0.794935i | \(-0.707505\pi\) | ||||
−0.606695 | + | 0.794935i | \(0.707505\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.12311 | 0.175207 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 51.7926 | 1.76920 | 0.884601 | − | 0.466349i | \(-0.154431\pi\) | ||||
0.884601 | + | 0.466349i | \(0.154431\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.8078 | −1.80178 | −0.900889 | − | 0.434050i | \(-0.857084\pi\) | ||||
−0.900889 | + | 0.434050i | \(0.857084\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −24.8078 | −0.845446 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.8617 | 1.90156 | 0.950778 | − | 0.309873i | \(-0.100287\pi\) | ||||
0.950778 | + | 0.309873i | \(0.100287\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0000 | 0.476014 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.3153 | 0.520136 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.6695 | 0.429783 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.24621 | −0.0761100 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.80776 | 0.0950284 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.56155 | 0.0865963 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.0000 | −1.14810 | −0.574049 | − | 0.818821i | \(-0.694628\pi\) | ||||
−0.574049 | + | 0.818821i | \(0.694628\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.6155 | 0.796532 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.24621 | −0.277822 | −0.138911 | − | 0.990305i | \(-0.544360\pi\) | ||||
−0.138911 | + | 0.990305i | \(0.544360\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.492423 | 0.0165713 | 0.00828567 | − | 0.999966i | \(-0.497363\pi\) | ||||
0.00828567 | + | 0.999966i | \(0.497363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.00000 | 0.268917 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.0540 | 0.371156 | 0.185578 | − | 0.982630i | \(-0.440584\pi\) | ||||
0.185578 | + | 0.982630i | \(0.440584\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.8769 | −0.633111 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.43845 | 0.0481898 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.75379 | 0.192543 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.8769 | 0.497280 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.43845 | 0.0480284 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.24621 | 0.0749153 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.19224 | −0.106349 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.0000 | −0.532447 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.9309 | 0.662525 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.8769 | 1.29089 | 0.645443 | − | 0.763808i | \(-0.276673\pi\) | ||||
0.645443 | + | 0.763808i | \(0.276673\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.12311 | −0.236259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.2462 | −1.13463 | −0.567314 | − | 0.823502i | \(-0.692017\pi\) | ||||
−0.567314 | + | 0.823502i | \(0.692017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.5076 | 0.380845 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.68466 | 0.0556931 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.6155 | 0.581716 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.8078 | 1.08223 | 0.541114 | − | 0.840949i | \(-0.318003\pi\) | ||||
0.541114 | + | 0.840949i | \(0.318003\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.43845 | −0.311007 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.68466 | 0.252944 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.8078 | −0.355357 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.24621 | 0.0737753 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.3002 | −1.15816 | −0.579081 | − | 0.815270i | \(-0.696588\pi\) | ||||
−0.579081 | + | 0.815270i | \(0.696588\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.24621 | −0.0736166 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.7386 | −0.744429 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.17708 | 0.267419 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.2462 | −1.57614 | −0.788068 | − | 0.615589i | \(-0.788918\pi\) | ||||
−0.788068 | + | 0.615589i | \(0.788918\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.7386 | 0.807315 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.5464 | −1.61517 | −0.807583 | − | 0.589754i | \(-0.799225\pi\) | ||||
−0.807583 | + | 0.589754i | \(0.799225\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.9309 | −0.453652 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.56155 | 0.0833273 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.26137 | 0.0409889 | 0.0204944 | − | 0.999790i | \(-0.493476\pi\) | ||||
0.0204944 | + | 0.999790i | \(0.493476\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.246211 | −0.00799236 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.1231 | 0.360691 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.19224 | 0.297766 | 0.148883 | − | 0.988855i | \(-0.452432\pi\) | ||||
0.148883 | + | 0.988855i | \(0.452432\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | −0.258874 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.87689 | −0.0929968 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.630683 | −0.0203658 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7386 | −0.959311 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.80776 | −0.154928 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.6847 | 0.698054 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.7538 | 0.828186 | 0.414093 | − | 0.910235i | \(-0.364099\pi\) | ||||
0.414093 | + | 0.910235i | \(0.364099\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29.1231 | 0.935569 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.4924 | −0.785999 | −0.393000 | − | 0.919539i | \(-0.628563\pi\) | ||||
−0.393000 | + | 0.919539i | \(0.628563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.9309 | 0.446603 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.00000 | 0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.8617 | 0.443476 | 0.221738 | − | 0.975106i | \(-0.428827\pi\) | ||||
0.221738 | + | 0.975106i | \(0.428827\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.33050 | −0.106443 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.87689 | −0.155707 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.9848 | −0.414152 | −0.207076 | − | 0.978325i | \(-0.566395\pi\) | ||||
−0.207076 | + | 0.978325i | \(0.566395\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.3693 | −0.553432 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.87689 | 0.0915726 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.98485 | −0.285701 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.05398 | −0.0970127 | −0.0485064 | − | 0.998823i | \(-0.515446\pi\) | ||||
−0.0485064 | + | 0.998823i | \(0.515446\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.2462 | −0.832898 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.2462 | −0.578444 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.1231 | 0.605635 | 0.302817 | − | 0.953049i | \(-0.402073\pi\) | ||||
0.302817 | + | 0.953049i | \(0.402073\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.8078 | −0.341943 |
(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 | 3120.2.a.bg.1.2 | 2 | ||
3.2 | odd | 2 | 9360.2.a.ci.1.2 | 2 | |||
4.3 | odd | 2 | 1560.2.a.o.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 4680.2.a.y.1.1 | 2 | |||
20.19 | odd | 2 | 7800.2.a.bd.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.a.o.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
3120.2.a.bg.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4680.2.a.y.1.1 | 2 | 12.11 | even | 2 | |||
7800.2.a.bd.1.2 | 2 | 20.19 | odd | 2 | |||
9360.2.a.ci.1.2 | 2 | 3.2 | odd | 2 |