Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [297,2,Mod(1,297)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(297, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("297.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 297 = 3^{3} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 297.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: | \(2.37155694003\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.571993\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 297.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.571993 | 0.404460 | 0.202230 | − | 0.979338i | \(-0.435181\pi\) | ||||
0.202230 | + | 0.979338i | \(0.435181\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.67282 | −0.836412 | ||||||||
\(5\) | 2.67282 | 1.19532 | 0.597662 | − | 0.801749i | \(-0.296097\pi\) | ||||
0.597662 | + | 0.801749i | \(0.296097\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.57199 | 0.972122 | 0.486061 | − | 0.873925i | \(-0.338433\pi\) | ||||
0.486061 | + | 0.873925i | \(0.338433\pi\) | |||||||
\(8\) | −2.10083 | −0.742756 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.52884 | 0.483461 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.67282 | 1.29601 | 0.648004 | − | 0.761637i | \(-0.275604\pi\) | ||||
0.648004 | + | 0.761637i | \(0.275604\pi\) | |||||||
\(14\) | 1.47116 | 0.393185 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.14399 | 0.535997 | ||||||||
\(17\) | −3.24482 | −0.786984 | −0.393492 | − | 0.919328i | \(-0.628733\pi\) | ||||
−0.393492 | + | 0.919328i | \(0.628733\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.52884 | 0.809571 | 0.404785 | − | 0.914412i | \(-0.367346\pi\) | ||||
0.404785 | + | 0.914412i | \(0.367346\pi\) | |||||||
\(20\) | −4.47116 | −0.999782 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.571993 | −0.121949 | ||||||||
\(23\) | 4.52884 | 0.944328 | 0.472164 | − | 0.881511i | \(-0.343473\pi\) | ||||
0.472164 | + | 0.881511i | \(0.343473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.14399 | 0.428797 | ||||||||
\(26\) | 2.67282 | 0.524184 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.30249 | −0.813094 | ||||||||
\(29\) | −5.91764 | −1.09888 | −0.549439 | − | 0.835534i | \(-0.685159\pi\) | ||||
−0.549439 | + | 0.835534i | \(0.685159\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.67282 | 0.839264 | 0.419632 | − | 0.907694i | \(-0.362159\pi\) | ||||
0.419632 | + | 0.907694i | \(0.362159\pi\) | |||||||
\(32\) | 5.42801 | 0.959545 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.85601 | −0.318304 | ||||||||
\(35\) | 6.87448 | 1.16200 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.3064 | −1.85877 | −0.929384 | − | 0.369114i | \(-0.879661\pi\) | ||||
−0.929384 | + | 0.369114i | \(0.879661\pi\) | |||||||
\(38\) | 2.01847 | 0.327439 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.61515 | −0.887833 | ||||||||
\(41\) | −7.06163 | −1.10284 | −0.551420 | − | 0.834227i | \(-0.685914\pi\) | ||||
−0.551420 | + | 0.834227i | \(0.685914\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.38880 | −0.364289 | −0.182145 | − | 0.983272i | \(-0.558304\pi\) | ||||
−0.182145 | + | 0.983272i | \(0.558304\pi\) | |||||||
\(44\) | 1.67282 | 0.252188 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.59046 | 0.381943 | ||||||||
\(47\) | −9.48963 | −1.38421 | −0.692103 | − | 0.721799i | \(-0.743315\pi\) | ||||
−0.692103 | + | 0.721799i | \(0.743315\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.384851 | −0.0549787 | ||||||||
\(50\) | 1.22635 | 0.173431 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.81681 | −1.08400 | ||||||||
\(53\) | −10.2017 | −1.40131 | −0.700653 | − | 0.713502i | \(-0.747108\pi\) | ||||
−0.700653 | + | 0.713502i | \(0.747108\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.67282 | −0.360403 | ||||||||
\(56\) | −5.40332 | −0.722049 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.38485 | −0.444453 | ||||||||
\(59\) | 7.96080 | 1.03641 | 0.518204 | − | 0.855257i | \(-0.326601\pi\) | ||||
0.518204 | + | 0.855257i | \(0.326601\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.16246 | 0.660985 | 0.330492 | − | 0.943809i | \(-0.392785\pi\) | ||||
0.330492 | + | 0.943809i | \(0.392785\pi\) | |||||||
\(62\) | 2.67282 | 0.339449 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.18319 | −0.147899 | ||||||||
\(65\) | 12.4896 | 1.54915 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.61515 | 0.197322 | 0.0986610 | − | 0.995121i | \(-0.468544\pi\) | ||||
0.0986610 | + | 0.995121i | \(0.468544\pi\) | |||||||
\(68\) | 5.42801 | 0.658243 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.93216 | 0.469983 | ||||||||
\(71\) | −10.2017 | −1.21071 | −0.605357 | − | 0.795954i | \(-0.706970\pi\) | ||||
−0.605357 | + | 0.795954i | \(0.706970\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.48963 | 0.993636 | 0.496818 | − | 0.867855i | \(-0.334502\pi\) | ||||
0.496818 | + | 0.867855i | \(0.334502\pi\) | |||||||
\(74\) | −6.46721 | −0.751798 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.90312 | −0.677135 | ||||||||
\(77\) | −2.57199 | −0.293106 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9361 | −1.34292 | −0.671459 | − | 0.741042i | \(-0.734332\pi\) | ||||
−0.671459 | + | 0.741042i | \(0.734332\pi\) | |||||||
\(80\) | 5.73050 | 0.640689 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.03920 | −0.446055 | ||||||||
\(83\) | 14.0185 | 1.53873 | 0.769364 | − | 0.638811i | \(-0.220573\pi\) | ||||
0.769364 | + | 0.638811i | \(0.220573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.67282 | −0.940700 | ||||||||
\(86\) | −1.36638 | −0.147340 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.10083 | 0.223949 | ||||||||
\(89\) | 13.6336 | 1.44516 | 0.722580 | − | 0.691287i | \(-0.242956\pi\) | ||||
0.722580 | + | 0.691287i | \(0.242956\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0185 | 1.25988 | ||||||||
\(92\) | −7.57595 | −0.789847 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.42801 | −0.559856 | ||||||||
\(95\) | 9.43196 | 0.967699 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.4504 | −1.26415 | −0.632075 | − | 0.774907i | \(-0.717796\pi\) | ||||
−0.632075 | + | 0.774907i | \(0.717796\pi\) | |||||||
\(98\) | −0.220132 | −0.0222367 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.58651 | −0.358651 | ||||||||
\(101\) | 9.24482 | 0.919894 | 0.459947 | − | 0.887946i | \(-0.347868\pi\) | ||||
0.459947 | + | 0.887946i | \(0.347868\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.38485 | 0.826184 | 0.413092 | − | 0.910689i | \(-0.364449\pi\) | ||||
0.413092 | + | 0.910689i | \(0.364449\pi\) | |||||||
\(104\) | −9.81681 | −0.962617 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.83528 | −0.566773 | ||||||||
\(107\) | −15.8168 | −1.52907 | −0.764534 | − | 0.644583i | \(-0.777031\pi\) | ||||
−0.764534 | + | 0.644583i | \(0.777031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.14399 | −0.492705 | −0.246352 | − | 0.969180i | \(-0.579232\pi\) | ||||
−0.246352 | + | 0.969180i | \(0.579232\pi\) | |||||||
\(110\) | −1.52884 | −0.145769 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.51432 | 0.521054 | ||||||||
\(113\) | −8.18319 | −0.769810 | −0.384905 | − | 0.922956i | \(-0.625766\pi\) | ||||
−0.384905 | + | 0.922956i | \(0.625766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.1048 | 1.12878 | ||||||||
\(116\) | 9.89917 | 0.919115 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.55352 | 0.419186 | ||||||||
\(119\) | −8.34565 | −0.765044 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.95289 | 0.267342 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.81681 | −0.701970 | ||||||||
\(125\) | −7.63362 | −0.682772 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.8168 | 1.58099 | 0.790493 | − | 0.612471i | \(-0.209824\pi\) | ||||
0.790493 | + | 0.612471i | \(0.209824\pi\) | |||||||
\(128\) | −11.5328 | −1.01936 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.14399 | 0.626569 | ||||||||
\(131\) | 4.20166 | 0.367101 | 0.183550 | − | 0.983010i | \(-0.441241\pi\) | ||||
0.183550 | + | 0.983010i | \(0.441241\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.07615 | 0.787002 | ||||||||
\(134\) | 0.923855 | 0.0798089 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.81681 | 0.584537 | ||||||||
\(137\) | −0.489634 | −0.0418323 | −0.0209161 | − | 0.999781i | \(-0.506658\pi\) | ||||
−0.0209161 | + | 0.999781i | \(0.506658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.81286 | −0.323402 | −0.161701 | − | 0.986840i | \(-0.551698\pi\) | ||||
−0.161701 | + | 0.986840i | \(0.551698\pi\) | |||||||
\(140\) | −11.4998 | −0.971911 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.83528 | −0.489686 | ||||||||
\(143\) | −4.67282 | −0.390761 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.8168 | −1.31351 | ||||||||
\(146\) | 4.85601 | 0.401887 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.9137 | 1.55470 | ||||||||
\(149\) | 9.16246 | 0.750618 | 0.375309 | − | 0.926900i | \(-0.377537\pi\) | ||||
0.375309 | + | 0.926900i | \(0.377537\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0185 | 1.30356 | 0.651782 | − | 0.758406i | \(-0.274022\pi\) | ||||
0.651782 | + | 0.758406i | \(0.274022\pi\) | |||||||
\(152\) | −7.41349 | −0.601313 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.47116 | −0.118550 | ||||||||
\(155\) | 12.4896 | 1.00319 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.79834 | −0.223332 | −0.111666 | − | 0.993746i | \(-0.535619\pi\) | ||||
−0.111666 | + | 0.993746i | \(0.535619\pi\) | |||||||
\(158\) | −6.82738 | −0.543157 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14.5081 | 1.14697 | ||||||||
\(161\) | 11.6481 | 0.918002 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.05767 | 0.396148 | 0.198074 | − | 0.980187i | \(-0.436531\pi\) | ||||
0.198074 | + | 0.980187i | \(0.436531\pi\) | |||||||
\(164\) | 11.8129 | 0.922429 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.01847 | 0.622354 | ||||||||
\(167\) | −9.65209 | −0.746901 | −0.373451 | − | 0.927650i | \(-0.621825\pi\) | ||||
−0.373451 | + | 0.927650i | \(0.621825\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.83528 | 0.679637 | ||||||||
\(170\) | −4.96080 | −0.380476 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.99605 | 0.304696 | ||||||||
\(173\) | 20.8824 | 1.58766 | 0.793829 | − | 0.608141i | \(-0.208084\pi\) | ||||
0.793829 | + | 0.608141i | \(0.208084\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.51432 | 0.416843 | ||||||||
\(176\) | −2.14399 | −0.161609 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.79834 | 0.584510 | ||||||||
\(179\) | −5.56804 | −0.416175 | −0.208087 | − | 0.978110i | \(-0.566724\pi\) | ||||
−0.208087 | + | 0.978110i | \(0.566724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.7490 | −1.98824 | −0.994118 | − | 0.108306i | \(-0.965457\pi\) | ||||
−0.994118 | + | 0.108306i | \(0.965457\pi\) | |||||||
\(182\) | 6.87448 | 0.509571 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.51432 | −0.701405 | ||||||||
\(185\) | −30.2201 | −2.22183 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.24482 | 0.237285 | ||||||||
\(188\) | 15.8745 | 1.15777 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.39502 | 0.391396 | ||||||||
\(191\) | 8.51037 | 0.615788 | 0.307894 | − | 0.951421i | \(-0.400376\pi\) | ||||
0.307894 | + | 0.951421i | \(0.400376\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.52884 | −0.397974 | −0.198987 | − | 0.980002i | \(-0.563765\pi\) | ||||
−0.198987 | + | 0.980002i | \(0.563765\pi\) | |||||||
\(194\) | −7.12156 | −0.511298 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.643787 | 0.0459848 | ||||||||
\(197\) | 14.9753 | 1.06695 | 0.533474 | − | 0.845817i | \(-0.320886\pi\) | ||||
0.533474 | + | 0.845817i | \(0.320886\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.0968776 | 0.00686747 | 0.00343373 | − | 0.999994i | \(-0.498907\pi\) | ||||
0.00343373 | + | 0.999994i | \(0.498907\pi\) | |||||||
\(200\) | −4.50415 | −0.318492 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.28797 | 0.372060 | ||||||||
\(203\) | −15.2201 | −1.06824 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.8745 | −1.31825 | ||||||||
\(206\) | 4.79608 | 0.334159 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.0185 | 0.694656 | ||||||||
\(209\) | −3.52884 | −0.244095 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.19771 | 0.564353 | 0.282177 | − | 0.959362i | \(-0.408944\pi\) | ||||
0.282177 | + | 0.959362i | \(0.408944\pi\) | |||||||
\(212\) | 17.0656 | 1.17207 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.04711 | −0.618448 | ||||||||
\(215\) | −6.38485 | −0.435443 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0185 | 0.815867 | ||||||||
\(218\) | −2.94233 | −0.199279 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.47116 | 0.301446 | ||||||||
\(221\) | −15.1625 | −1.01994 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.73050 | −0.249813 | −0.124906 | − | 0.992169i | \(-0.539863\pi\) | ||||
−0.124906 | + | 0.992169i | \(0.539863\pi\) | |||||||
\(224\) | 13.9608 | 0.932795 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.68073 | −0.311357 | ||||||||
\(227\) | 18.3849 | 1.22025 | 0.610123 | − | 0.792307i | \(-0.291120\pi\) | ||||
0.610123 | + | 0.792307i | \(0.291120\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.5081 | −1.81779 | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(230\) | 6.92385 | 0.456545 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.4320 | 0.816198 | ||||||||
\(233\) | 5.61515 | 0.367861 | 0.183930 | − | 0.982939i | \(-0.441118\pi\) | ||||
0.183930 | + | 0.982939i | \(0.441118\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.3641 | −1.65457 | ||||||||
\(236\) | −13.3170 | −0.866863 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.77365 | −0.309430 | ||||||||
\(239\) | −17.4504 | −1.12877 | −0.564387 | − | 0.825510i | \(-0.690888\pi\) | ||||
−0.564387 | + | 0.825510i | \(0.690888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0784065 | −0.00505060 | −0.00252530 | − | 0.999997i | \(-0.500804\pi\) | ||||
−0.00252530 | + | 0.999997i | \(0.500804\pi\) | |||||||
\(242\) | 0.571993 | 0.0367691 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.63588 | −0.552856 | ||||||||
\(245\) | −1.02864 | −0.0657173 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.4896 | 1.04921 | ||||||||
\(248\) | −9.81681 | −0.623368 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.36638 | −0.276154 | ||||||||
\(251\) | −5.94233 | −0.375076 | −0.187538 | − | 0.982257i | \(-0.560051\pi\) | ||||
−0.187538 | + | 0.982257i | \(0.560051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.52884 | −0.284726 | ||||||||
\(254\) | 10.1911 | 0.639446 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.23030 | −0.264394 | ||||||||
\(257\) | 18.7098 | 1.16708 | 0.583542 | − | 0.812083i | \(-0.301667\pi\) | ||||
0.583542 | + | 0.812083i | \(0.301667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.0801 | −1.80695 | ||||||||
\(260\) | −20.8930 | −1.29573 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.40332 | 0.148478 | ||||||||
\(263\) | −1.42405 | −0.0878109 | −0.0439055 | − | 0.999036i | \(-0.513980\pi\) | ||||
−0.0439055 | + | 0.999036i | \(0.513980\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.2672 | −1.67501 | ||||||||
\(266\) | 5.19149 | 0.318311 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.70186 | −0.165042 | ||||||||
\(269\) | 8.67282 | 0.528791 | 0.264396 | − | 0.964414i | \(-0.414828\pi\) | ||||
0.264396 | + | 0.964414i | \(0.414828\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.3681 | 1.54100 | 0.770500 | − | 0.637440i | \(-0.220006\pi\) | ||||
0.770500 | + | 0.637440i | \(0.220006\pi\) | |||||||
\(272\) | −6.95684 | −0.421821 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.280067 | −0.0169195 | ||||||||
\(275\) | −2.14399 | −0.129287 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.69129 | 0.402041 | 0.201020 | − | 0.979587i | \(-0.435574\pi\) | ||||
0.201020 | + | 0.979587i | \(0.435574\pi\) | |||||||
\(278\) | −2.18093 | −0.130803 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −14.4421 | −0.863082 | ||||||||
\(281\) | −7.16641 | −0.427512 | −0.213756 | − | 0.976887i | \(-0.568570\pi\) | ||||
−0.213756 | + | 0.976887i | \(0.568570\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.3272 | −0.792218 | −0.396109 | − | 0.918203i | \(-0.629640\pi\) | ||||
−0.396109 | + | 0.918203i | \(0.629640\pi\) | |||||||
\(284\) | 17.0656 | 1.01266 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.67282 | −0.158047 | ||||||||
\(287\) | −18.1625 | −1.07210 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.47116 | −0.380657 | ||||||||
\(290\) | −9.04711 | −0.531265 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.2017 | −0.831089 | ||||||||
\(293\) | −3.81681 | −0.222980 | −0.111490 | − | 0.993766i | \(-0.535562\pi\) | ||||
−0.111490 | + | 0.993766i | \(0.535562\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.2778 | 1.23884 | ||||||||
\(296\) | 23.7529 | 1.38061 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.24086 | 0.303595 | ||||||||
\(299\) | 21.1625 | 1.22386 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.14399 | −0.354133 | ||||||||
\(302\) | 9.16246 | 0.527240 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.56578 | 0.433927 | ||||||||
\(305\) | 13.7983 | 0.790091 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.05372 | −0.174285 | −0.0871425 | − | 0.996196i | \(-0.527774\pi\) | ||||
−0.0871425 | + | 0.996196i | \(0.527774\pi\) | |||||||
\(308\) | 4.30249 | 0.245157 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.14399 | 0.405751 | ||||||||
\(311\) | 11.0185 | 0.624800 | 0.312400 | − | 0.949951i | \(-0.398867\pi\) | ||||
0.312400 | + | 0.949951i | \(0.398867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.63362 | −0.318431 | −0.159216 | − | 0.987244i | \(-0.550896\pi\) | ||||
−0.159216 | + | 0.987244i | \(0.550896\pi\) | |||||||
\(314\) | −1.60063 | −0.0903288 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.9670 | 1.12323 | ||||||||
\(317\) | −28.4112 | −1.59573 | −0.797867 | − | 0.602834i | \(-0.794038\pi\) | ||||
−0.797867 | + | 0.602834i | \(0.794038\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.91764 | 0.331324 | ||||||||
\(320\) | −3.16246 | −0.176787 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.66266 | 0.371295 | ||||||||
\(323\) | −11.4504 | −0.637119 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.0185 | 0.555725 | ||||||||
\(326\) | 2.89296 | 0.160226 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.8353 | 0.819141 | ||||||||
\(329\) | −24.4073 | −1.34562 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.9977 | −1.70379 | −0.851895 | − | 0.523713i | \(-0.824547\pi\) | ||||
−0.851895 | + | 0.523713i | \(0.824547\pi\) | |||||||
\(332\) | −23.4504 | −1.28701 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.52093 | −0.302092 | ||||||||
\(335\) | 4.31701 | 0.235863 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.45043 | 0.405851 | 0.202925 | − | 0.979194i | \(-0.434955\pi\) | ||||
0.202925 | + | 0.979194i | \(0.434955\pi\) | |||||||
\(338\) | 5.05372 | 0.274886 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.5081 | 0.786812 | ||||||||
\(341\) | −4.67282 | −0.253048 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.9938 | −1.02557 | ||||||||
\(344\) | 5.01847 | 0.270578 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.9446 | 0.642145 | ||||||||
\(347\) | 20.8930 | 1.12159 | 0.560796 | − | 0.827954i | \(-0.310495\pi\) | ||||
0.560796 | + | 0.827954i | \(0.310495\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.9114 | −1.44054 | −0.720268 | − | 0.693696i | \(-0.755981\pi\) | ||||
−0.720268 | + | 0.693696i | \(0.755981\pi\) | |||||||
\(350\) | 3.15415 | 0.168597 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.42801 | −0.289314 | ||||||||
\(353\) | 11.8353 | 0.629928 | 0.314964 | − | 0.949104i | \(-0.398007\pi\) | ||||
0.314964 | + | 0.949104i | \(0.398007\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.2672 | −1.44719 | ||||||||
\(356\) | −22.8066 | −1.20875 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.18488 | −0.168326 | ||||||||
\(359\) | 2.83754 | 0.149760 | 0.0748799 | − | 0.997193i | \(-0.476143\pi\) | ||||
0.0748799 | + | 0.997193i | \(0.476143\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.54731 | −0.344595 | ||||||||
\(362\) | −15.3002 | −0.804162 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −20.1048 | −1.05378 | ||||||||
\(365\) | 22.6913 | 1.18772 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.22239 | 0.272607 | 0.136303 | − | 0.990667i | \(-0.456478\pi\) | ||||
0.136303 | + | 0.990667i | \(0.456478\pi\) | |||||||
\(368\) | 9.70977 | 0.506157 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −17.2857 | −0.898641 | ||||||||
\(371\) | −26.2386 | −1.36224 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.3434 | 1.77823 | 0.889117 | − | 0.457681i | \(-0.151320\pi\) | ||||
0.889117 | + | 0.457681i | \(0.151320\pi\) | |||||||
\(374\) | 1.85601 | 0.0959722 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.9361 | 1.02813 | ||||||||
\(377\) | −27.6521 | −1.42416 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.1625 | −1.60071 | −0.800354 | − | 0.599528i | \(-0.795355\pi\) | ||||
−0.800354 | + | 0.599528i | \(0.795355\pi\) | |||||||
\(380\) | −15.7780 | −0.809395 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.86787 | 0.249062 | ||||||||
\(383\) | 14.7776 | 0.755100 | 0.377550 | − | 0.925989i | \(-0.376767\pi\) | ||||
0.377550 | + | 0.925989i | \(0.376767\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.87448 | −0.350356 | ||||||||
\(386\) | −3.16246 | −0.160965 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 20.8274 | 1.05735 | ||||||||
\(389\) | 1.63362 | 0.0828278 | 0.0414139 | − | 0.999142i | \(-0.486814\pi\) | ||||
0.0414139 | + | 0.999142i | \(0.486814\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.6952 | −0.743171 | ||||||||
\(392\) | 0.808506 | 0.0408357 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.56578 | 0.431538 | ||||||||
\(395\) | −31.9031 | −1.60522 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.9216 | 0.598328 | 0.299164 | − | 0.954202i | \(-0.403292\pi\) | ||||
0.299164 | + | 0.954202i | \(0.403292\pi\) | |||||||
\(398\) | 0.0554133 | 0.00277762 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.59668 | 0.229834 | ||||||||
\(401\) | 17.1809 | 0.857975 | 0.428987 | − | 0.903311i | \(-0.358870\pi\) | ||||
0.428987 | + | 0.903311i | \(0.358870\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.8353 | 1.08769 | ||||||||
\(404\) | −15.4649 | −0.769410 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.70581 | −0.432062 | ||||||||
\(407\) | 11.3064 | 0.560440 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.7490 | 1.66878 | 0.834390 | − | 0.551175i | \(-0.185820\pi\) | ||||
0.834390 | + | 0.551175i | \(0.185820\pi\) | |||||||
\(410\) | −10.7961 | −0.533180 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.0264 | −0.691030 | ||||||||
\(413\) | 20.4751 | 1.00751 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 37.4689 | 1.83928 | ||||||||
\(416\) | 25.3641 | 1.24358 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.01847 | −0.0987266 | ||||||||
\(419\) | 7.91369 | 0.386609 | 0.193304 | − | 0.981139i | \(-0.438079\pi\) | ||||
0.193304 | + | 0.981139i | \(0.438079\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.85601 | 0.480353 | 0.240176 | − | 0.970729i | \(-0.422795\pi\) | ||||
0.240176 | + | 0.970729i | \(0.422795\pi\) | |||||||
\(422\) | 4.68903 | 0.228259 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 21.4320 | 1.04083 | ||||||||
\(425\) | −6.95684 | −0.337456 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.2778 | 0.642558 | ||||||||
\(428\) | 26.4587 | 1.27893 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.65209 | −0.176119 | ||||||||
\(431\) | 17.2857 | 0.832623 | 0.416312 | − | 0.909222i | \(-0.363323\pi\) | ||||
0.416312 | + | 0.909222i | \(0.363323\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.5450 | 1.13150 | 0.565751 | − | 0.824576i | \(-0.308586\pi\) | ||||
0.565751 | + | 0.824576i | \(0.308586\pi\) | |||||||
\(434\) | 6.87448 | 0.329986 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.60498 | 0.412104 | ||||||||
\(437\) | 15.9815 | 0.764500 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.388804 | 0.0185566 | 0.00927829 | − | 0.999957i | \(-0.497047\pi\) | ||||
0.00927829 | + | 0.999957i | \(0.497047\pi\) | |||||||
\(440\) | 5.61515 | 0.267692 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.67282 | −0.412524 | ||||||||
\(443\) | −13.7490 | −0.653233 | −0.326617 | − | 0.945157i | \(-0.605909\pi\) | ||||
−0.326617 | + | 0.945157i | \(0.605909\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.4403 | 1.72743 | ||||||||
\(446\) | −2.13382 | −0.101039 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.04316 | −0.143776 | ||||||||
\(449\) | 37.9691 | 1.79187 | 0.895936 | − | 0.444182i | \(-0.146506\pi\) | ||||
0.895936 | + | 0.444182i | \(0.146506\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.06163 | 0.332519 | ||||||||
\(452\) | 13.6890 | 0.643878 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.5160 | 0.493541 | ||||||||
\(455\) | 32.1233 | 1.50596 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.7384 | −0.829768 | −0.414884 | − | 0.909874i | \(-0.636178\pi\) | ||||
−0.414884 | + | 0.909874i | \(0.636178\pi\) | |||||||
\(458\) | −15.7345 | −0.735223 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −20.2492 | −0.944122 | ||||||||
\(461\) | −26.7882 | −1.24765 | −0.623825 | − | 0.781564i | \(-0.714422\pi\) | ||||
−0.623825 | + | 0.781564i | \(0.714422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.0577 | 1.62927 | 0.814634 | − | 0.579975i | \(-0.196938\pi\) | ||||
0.814634 | + | 0.579975i | \(0.196938\pi\) | |||||||
\(464\) | −12.6873 | −0.588995 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.21183 | 0.148785 | ||||||||
\(467\) | 16.0841 | 0.744281 | 0.372141 | − | 0.928176i | \(-0.378624\pi\) | ||||
0.372141 | + | 0.928176i | \(0.378624\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.15415 | 0.191821 | ||||||||
\(470\) | −14.5081 | −0.669209 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16.7243 | −0.769798 | ||||||||
\(473\) | 2.38880 | 0.109837 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.56578 | 0.347142 | ||||||||
\(476\) | 13.9608 | 0.639892 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.98153 | −0.456545 | ||||||||
\(479\) | −42.3249 | −1.93387 | −0.966937 | − | 0.255014i | \(-0.917920\pi\) | ||||
−0.966937 | + | 0.255014i | \(0.917920\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −52.8330 | −2.40898 | ||||||||
\(482\) | −0.0448480 | −0.00204277 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.67282 | −0.0760374 | ||||||||
\(485\) | −33.2778 | −1.51107 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.3664 | 1.10415 | 0.552073 | − | 0.833796i | \(-0.313837\pi\) | ||||
0.552073 | + | 0.833796i | \(0.313837\pi\) | |||||||
\(488\) | −10.8454 | −0.490950 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.588374 | −0.0265800 | ||||||||
\(491\) | 22.8560 | 1.03148 | 0.515739 | − | 0.856746i | \(-0.327518\pi\) | ||||
0.515739 | + | 0.856746i | \(0.327518\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.2017 | 0.864799 | ||||||||
\(494\) | 9.43196 | 0.424364 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.0185 | 0.449843 | ||||||||
\(497\) | −26.2386 | −1.17696 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.0841 | 0.943852 | 0.471926 | − | 0.881638i | \(-0.343559\pi\) | ||||
0.471926 | + | 0.881638i | \(0.343559\pi\) | |||||||
\(500\) | 12.7697 | 0.571078 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.39897 | −0.151703 | ||||||||
\(503\) | 26.8930 | 1.19910 | 0.599549 | − | 0.800338i | \(-0.295347\pi\) | ||||
0.599549 | + | 0.800338i | \(0.295347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.7098 | 1.09957 | ||||||||
\(506\) | −2.59046 | −0.115160 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −29.8044 | −1.32236 | ||||||||
\(509\) | −30.9898 | −1.37360 | −0.686800 | − | 0.726846i | \(-0.740985\pi\) | ||||
−0.686800 | + | 0.726846i | \(0.740985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.8353 | 0.965936 | ||||||||
\(512\) | 20.6459 | 0.912428 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.7019 | 0.472039 | ||||||||
\(515\) | 22.4112 | 0.987557 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.48963 | 0.417354 | ||||||||
\(518\) | −16.6336 | −0.730839 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −26.2386 | −1.15064 | ||||||||
\(521\) | −9.48737 | −0.415649 | −0.207825 | − | 0.978166i | \(-0.566638\pi\) | ||||
−0.207825 | + | 0.978166i | \(0.566638\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.1664 | 0.663181 | 0.331590 | − | 0.943423i | \(-0.392415\pi\) | ||||
0.331590 | + | 0.943423i | \(0.392415\pi\) | |||||||
\(524\) | −7.02864 | −0.307047 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.814549 | −0.0355160 | ||||||||
\(527\) | −15.1625 | −0.660487 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.48963 | −0.108245 | ||||||||
\(530\) | −15.5967 | −0.677476 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −15.1828 | −0.658257 | ||||||||
\(533\) | −32.9977 | −1.42929 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −42.2755 | −1.82773 | ||||||||
\(536\) | −3.39315 | −0.146562 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.96080 | 0.213875 | ||||||||
\(539\) | 0.384851 | 0.0165767 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.4112 | −1.39347 | −0.696734 | − | 0.717330i | \(-0.745364\pi\) | ||||
−0.696734 | + | 0.717330i | \(0.745364\pi\) | |||||||
\(542\) | 14.5104 | 0.623274 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.6129 | −0.755146 | ||||||||
\(545\) | −13.7490 | −0.588941 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.7345 | 0.758270 | 0.379135 | − | 0.925341i | \(-0.376222\pi\) | ||||
0.379135 | + | 0.925341i | \(0.376222\pi\) | |||||||
\(548\) | 0.819071 | 0.0349890 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.22635 | −0.0522916 | ||||||||
\(551\) | −20.8824 | −0.889620 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.6996 | −1.30548 | ||||||||
\(554\) | 3.82738 | 0.162610 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.37824 | 0.270498 | ||||||||
\(557\) | −5.64814 | −0.239319 | −0.119660 | − | 0.992815i | \(-0.538180\pi\) | ||||
−0.119660 | + | 0.992815i | \(0.538180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.1625 | −0.472122 | ||||||||
\(560\) | 14.7388 | 0.622828 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.09914 | −0.172912 | ||||||||
\(563\) | −17.9506 | −0.756529 | −0.378264 | − | 0.925698i | \(-0.623479\pi\) | ||||
−0.378264 | + | 0.925698i | \(0.623479\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.8722 | −0.920171 | ||||||||
\(566\) | −7.62306 | −0.320421 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.4320 | 0.899265 | ||||||||
\(569\) | 34.4218 | 1.44304 | 0.721518 | − | 0.692395i | \(-0.243445\pi\) | ||||
0.721518 | + | 0.692395i | \(0.243445\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.5882 | −1.15453 | −0.577265 | − | 0.816557i | \(-0.695880\pi\) | ||||
−0.577265 | + | 0.816557i | \(0.695880\pi\) | |||||||
\(572\) | 7.81681 | 0.326837 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.3888 | −0.433620 | ||||||||
\(575\) | 9.70977 | 0.404925 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.0577 | −0.418706 | −0.209353 | − | 0.977840i | \(-0.567136\pi\) | ||||
−0.209353 | + | 0.977840i | \(0.567136\pi\) | |||||||
\(578\) | −3.70146 | −0.153961 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 26.4587 | 1.09864 | ||||||||
\(581\) | 36.0554 | 1.49583 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.2017 | 0.422510 | ||||||||
\(584\) | −17.8353 | −0.738029 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.18319 | −0.0901867 | ||||||||
\(587\) | 18.3720 | 0.758295 | 0.379147 | − | 0.925336i | \(-0.376217\pi\) | ||||
0.379147 | + | 0.925336i | \(0.376217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.4896 | 0.679444 | ||||||||
\(590\) | 12.1708 | 0.501062 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.2409 | −0.996293 | ||||||||
\(593\) | −13.8208 | −0.567551 | −0.283775 | − | 0.958891i | \(-0.591587\pi\) | ||||
−0.283775 | + | 0.958891i | \(0.591587\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.3064 | −0.914475 | ||||||||
\(596\) | −15.3272 | −0.627826 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.1048 | 0.495001 | ||||||||
\(599\) | 8.24086 | 0.336713 | 0.168356 | − | 0.985726i | \(-0.446154\pi\) | ||||
0.168356 | + | 0.985726i | \(0.446154\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.75123 | −0.356970 | −0.178485 | − | 0.983943i | \(-0.557120\pi\) | ||||
−0.178485 | + | 0.983943i | \(0.557120\pi\) | |||||||
\(602\) | −3.51432 | −0.143233 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −26.7961 | −1.09032 | ||||||||
\(605\) | 2.67282 | 0.108666 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.4504 | 1.03300 | 0.516501 | − | 0.856287i | \(-0.327234\pi\) | ||||
0.516501 | + | 0.856287i | \(0.327234\pi\) | |||||||
\(608\) | 19.1546 | 0.776820 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.89256 | 0.319560 | ||||||||
\(611\) | −44.3434 | −1.79394 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.7512 | 0.757355 | 0.378678 | − | 0.925529i | \(-0.376379\pi\) | ||||
0.378678 | + | 0.925529i | \(0.376379\pi\) | |||||||
\(614\) | −1.74671 | −0.0704914 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.40332 | 0.217706 | ||||||||
\(617\) | −2.34791 | −0.0945232 | −0.0472616 | − | 0.998883i | \(-0.515049\pi\) | ||||
−0.0472616 | + | 0.998883i | \(0.515049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.85375 | 0.154895 | 0.0774477 | − | 0.996996i | \(-0.475323\pi\) | ||||
0.0774477 | + | 0.996996i | \(0.475323\pi\) | |||||||
\(620\) | −20.8930 | −0.839081 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.30249 | 0.252707 | ||||||||
\(623\) | 35.0656 | 1.40487 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1233 | −1.24493 | ||||||||
\(626\) | −3.22239 | −0.128793 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.68113 | 0.186797 | ||||||||
\(629\) | 36.6873 | 1.46282 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.5081 | 0.657177 | 0.328589 | − | 0.944473i | \(-0.393427\pi\) | ||||
0.328589 | + | 0.944473i | \(0.393427\pi\) | |||||||
\(632\) | 25.0757 | 0.997460 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.2510 | −0.645411 | ||||||||
\(635\) | 47.6212 | 1.88979 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.79834 | −0.0712528 | ||||||||
\(638\) | 3.38485 | 0.134008 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −30.8251 | −1.21847 | ||||||||
\(641\) | −8.34791 | −0.329723 | −0.164861 | − | 0.986317i | \(-0.552718\pi\) | ||||
−0.164861 | + | 0.986317i | \(0.552718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.4689 | 0.610034 | 0.305017 | − | 0.952347i | \(-0.401338\pi\) | ||||
0.305017 | + | 0.952347i | \(0.401338\pi\) | |||||||
\(644\) | −19.4853 | −0.767828 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.54957 | −0.257689 | ||||||||
\(647\) | −23.4610 | −0.922347 | −0.461173 | − | 0.887310i | \(-0.652571\pi\) | ||||
−0.461173 | + | 0.887310i | \(0.652571\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.96080 | −0.312489 | ||||||||
\(650\) | 5.73050 | 0.224769 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.46060 | −0.331343 | ||||||||
\(653\) | −16.5759 | −0.648667 | −0.324333 | − | 0.945943i | \(-0.605140\pi\) | ||||
−0.324333 | + | 0.945943i | \(0.605140\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.2303 | 0.438804 | ||||||||
\(656\) | −15.1400 | −0.591119 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.9608 | −0.544249 | ||||||||
\(659\) | −41.7305 | −1.62559 | −0.812795 | − | 0.582550i | \(-0.802055\pi\) | ||||
−0.812795 | + | 0.582550i | \(0.802055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.5266 | 1.07066 | 0.535330 | − | 0.844643i | \(-0.320187\pi\) | ||||
0.535330 | + | 0.844643i | \(0.320187\pi\) | |||||||
\(662\) | −17.7305 | −0.689115 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −29.4504 | −1.14290 | ||||||||
\(665\) | 24.2589 | 0.940721 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.8000 | −1.03770 | ||||||||
\(668\) | 16.1462 | 0.624717 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.46930 | 0.0953974 | ||||||||
\(671\) | −5.16246 | −0.199294 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.22013 | 0.316863 | 0.158431 | − | 0.987370i | \(-0.449356\pi\) | ||||
0.158431 | + | 0.987370i | \(0.449356\pi\) | |||||||
\(674\) | 4.26160 | 0.164151 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.7799 | −0.568456 | ||||||||
\(677\) | 15.9546 | 0.613184 | 0.306592 | − | 0.951841i | \(-0.400811\pi\) | ||||
0.306592 | + | 0.951841i | \(0.400811\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.0224 | −1.22891 | ||||||||
\(680\) | 18.2201 | 0.698710 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.67282 | −0.102348 | ||||||||
\(683\) | 9.37429 | 0.358697 | 0.179349 | − | 0.983786i | \(-0.442601\pi\) | ||||
0.179349 | + | 0.983786i | \(0.442601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.30871 | −0.0500031 | ||||||||
\(686\) | −10.8643 | −0.414802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.12156 | −0.195258 | ||||||||
\(689\) | −47.6706 | −1.81610 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.6050 | −0.859934 | −0.429967 | − | 0.902845i | \(-0.641475\pi\) | ||||
−0.429967 | + | 0.902845i | \(0.641475\pi\) | |||||||
\(692\) | −34.9326 | −1.32794 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.9506 | 0.453640 | ||||||||
\(695\) | −10.1911 | −0.386570 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.9137 | 0.867918 | ||||||||
\(698\) | −15.3932 | −0.582640 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.22448 | −0.348653 | ||||||||
\(701\) | 38.2162 | 1.44341 | 0.721703 | − | 0.692203i | \(-0.243360\pi\) | ||||
0.721703 | + | 0.692203i | \(0.243360\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.8986 | −1.50480 | ||||||||
\(704\) | 1.18319 | 0.0445931 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.76970 | 0.254781 | ||||||||
\(707\) | 23.7776 | 0.894249 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.8824 | 1.19737 | 0.598684 | − | 0.800985i | \(-0.295690\pi\) | ||||
0.598684 | + | 0.800985i | \(0.295690\pi\) | |||||||
\(710\) | −15.5967 | −0.585333 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −28.6419 | −1.07340 | ||||||||
\(713\) | 21.1625 | 0.792540 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.4896 | −0.467086 | ||||||||
\(716\) | 9.31435 | 0.348094 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.62306 | 0.0605719 | ||||||||
\(719\) | 21.4320 | 0.799277 | 0.399639 | − | 0.916673i | \(-0.369136\pi\) | ||||
0.399639 | + | 0.916673i | \(0.369136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.5658 | 0.803152 | ||||||||
\(722\) | −3.74502 | −0.139375 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 44.7463 | 1.66298 | ||||||||
\(725\) | −12.6873 | −0.471196 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.19110 | 0.229615 | 0.114808 | − | 0.993388i | \(-0.463375\pi\) | ||||
0.114808 | + | 0.993388i | \(0.463375\pi\) | |||||||
\(728\) | −25.2488 | −0.935782 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.9793 | 0.480384 | ||||||||
\(731\) | 7.75123 | 0.286690 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.7384 | −0.433568 | −0.216784 | − | 0.976220i | \(-0.569557\pi\) | ||||
−0.216784 | + | 0.976220i | \(0.569557\pi\) | |||||||
\(734\) | 2.98717 | 0.110259 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.5826 | 0.906125 | ||||||||
\(737\) | −1.61515 | −0.0594948 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.1378 | −1.03506 | −0.517532 | − | 0.855664i | \(-0.673149\pi\) | ||||
−0.517532 | + | 0.855664i | \(0.673149\pi\) | |||||||
\(740\) | 50.5530 | 1.85836 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.0083 | −0.550972 | ||||||||
\(743\) | −14.0784 | −0.516487 | −0.258243 | − | 0.966080i | \(-0.583144\pi\) | ||||
−0.258243 | + | 0.966080i | \(0.583144\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.4896 | 0.897231 | ||||||||
\(746\) | 19.6442 | 0.719225 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.42801 | −0.198468 | ||||||||
\(749\) | −40.6807 | −1.48644 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.7753 | 0.721613 | 0.360806 | − | 0.932641i | \(-0.382502\pi\) | ||||
0.360806 | + | 0.932641i | \(0.382502\pi\) | |||||||
\(752\) | −20.3456 | −0.741929 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.8168 | −0.576014 | ||||||||
\(755\) | 42.8145 | 1.55818 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.73276 | 0.0629782 | 0.0314891 | − | 0.999504i | \(-0.489975\pi\) | ||||
0.0314891 | + | 0.999504i | \(0.489975\pi\) | |||||||
\(758\) | −17.8247 | −0.647423 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.8149 | −0.718764 | ||||||||
\(761\) | −29.6151 | −1.07355 | −0.536774 | − | 0.843726i | \(-0.680357\pi\) | ||||
−0.536774 | + | 0.843726i | \(0.680357\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.2303 | −0.478969 | ||||||||
\(764\) | −14.2363 | −0.515053 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.45269 | 0.305408 | ||||||||
\(767\) | 37.1994 | 1.34319 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.90086 | −0.320973 | −0.160487 | − | 0.987038i | \(-0.551306\pi\) | ||||
−0.160487 | + | 0.987038i | \(0.551306\pi\) | |||||||
\(770\) | −3.93216 | −0.141705 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.24877 | 0.332871 | ||||||||
\(773\) | 33.3227 | 1.19853 | 0.599266 | − | 0.800550i | \(-0.295459\pi\) | ||||
0.599266 | + | 0.800550i | \(0.295459\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.0185 | 0.359874 | ||||||||
\(776\) | 26.1562 | 0.938954 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.934420 | 0.0335006 | ||||||||
\(779\) | −24.9193 | −0.892828 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.2017 | 0.365044 | ||||||||
\(782\) | −8.40558 | −0.300583 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.825115 | −0.0294684 | ||||||||
\(785\) | −7.47947 | −0.266954 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.3355 | −1.01005 | −0.505025 | − | 0.863104i | \(-0.668517\pi\) | ||||
−0.505025 | + | 0.863104i | \(0.668517\pi\) | |||||||
\(788\) | −25.0511 | −0.892407 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18.2484 | −0.649248 | ||||||||
\(791\) | −21.0471 | −0.748349 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.1233 | 0.856642 | ||||||||
\(794\) | 6.81907 | 0.242000 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.162059 | −0.00574403 | ||||||||
\(797\) | 13.5288 | 0.479216 | 0.239608 | − | 0.970870i | \(-0.422981\pi\) | ||||
0.239608 | + | 0.970870i | \(0.422981\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.7921 | 1.08935 | ||||||||
\(800\) | 11.6376 | 0.411450 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.82738 | 0.347017 | ||||||||
\(803\) | −8.48963 | −0.299593 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 31.1334 | 1.09731 | ||||||||
\(806\) | 12.4896 | 0.439929 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −19.4218 | −0.683256 | ||||||||
\(809\) | 39.1849 | 1.37767 | 0.688834 | − | 0.724920i | \(-0.258123\pi\) | ||||
0.688834 | + | 0.724920i | \(0.258123\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.2263 | −0.394210 | −0.197105 | − | 0.980382i | \(-0.563154\pi\) | ||||
−0.197105 | + | 0.980382i | \(0.563154\pi\) | |||||||
\(812\) | 25.4606 | 0.893492 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.46721 | 0.226676 | ||||||||
\(815\) | 13.5183 | 0.473524 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.42970 | −0.294918 | ||||||||
\(818\) | 19.3042 | 0.674955 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 31.5737 | 1.10260 | ||||||||
\(821\) | 16.8291 | 0.587339 | 0.293669 | − | 0.955907i | \(-0.405124\pi\) | ||||
0.293669 | + | 0.955907i | \(0.405124\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.0448 | 0.907866 | 0.453933 | − | 0.891036i | \(-0.350020\pi\) | ||||
0.453933 | + | 0.891036i | \(0.350020\pi\) | |||||||
\(824\) | −17.6151 | −0.613653 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.7116 | 0.407500 | ||||||||
\(827\) | −50.0139 | −1.73916 | −0.869578 | − | 0.493796i | \(-0.835609\pi\) | ||||
−0.869578 | + | 0.493796i | \(0.835609\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.99774 | −0.347236 | −0.173618 | − | 0.984813i | \(-0.555546\pi\) | ||||
−0.173618 | + | 0.984813i | \(0.555546\pi\) | |||||||
\(830\) | 21.4320 | 0.743914 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.52884 | −0.191678 | ||||||||
\(833\) | 1.24877 | 0.0432673 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.7983 | −0.892788 | ||||||||
\(836\) | 5.90312 | 0.204164 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.52658 | 0.156368 | ||||||||
\(839\) | −28.4583 | −0.982491 | −0.491245 | − | 0.871021i | \(-0.663458\pi\) | ||||
−0.491245 | + | 0.871021i | \(0.663458\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.01847 | 0.207533 | ||||||||
\(842\) | 5.63757 | 0.194284 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.7133 | −0.472032 | ||||||||
\(845\) | 23.6151 | 0.812386 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.57199 | 0.0883747 | ||||||||
\(848\) | −21.8722 | −0.751095 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.97927 | −0.136488 | ||||||||
\(851\) | −51.2050 | −1.75529 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.20166 | −0.0753834 | −0.0376917 | − | 0.999289i | \(-0.512000\pi\) | ||||
−0.0376917 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(854\) | 7.59482 | 0.259889 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33.2284 | 1.13572 | ||||||||
\(857\) | 24.1272 | 0.824170 | 0.412085 | − | 0.911145i | \(-0.364801\pi\) | ||||
0.412085 | + | 0.911145i | \(0.364801\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6728 | −0.432391 | −0.216196 | − | 0.976350i | \(-0.569365\pi\) | ||||
−0.216196 | + | 0.976350i | \(0.569365\pi\) | |||||||
\(860\) | 10.6807 | 0.364210 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.88731 | 0.336763 | ||||||||
\(863\) | −28.2488 | −0.961599 | −0.480800 | − | 0.876830i | \(-0.659654\pi\) | ||||
−0.480800 | + | 0.876830i | \(0.659654\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 55.8149 | 1.89777 | ||||||||
\(866\) | 13.4676 | 0.457648 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −20.1048 | −0.682401 | ||||||||
\(869\) | 11.9361 | 0.404905 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.54731 | 0.255731 | ||||||||
\(872\) | 10.8066 | 0.365959 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.14133 | 0.309210 | ||||||||
\(875\) | −19.6336 | −0.663738 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.23820 | 0.109346 | 0.0546732 | − | 0.998504i | \(-0.482588\pi\) | ||||
0.0546732 | + | 0.998504i | \(0.482588\pi\) | |||||||
\(878\) | 0.222393 | 0.00750540 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.73050 | −0.193175 | ||||||||
\(881\) | 8.29854 | 0.279585 | 0.139792 | − | 0.990181i | \(-0.455356\pi\) | ||||
0.139792 | + | 0.990181i | \(0.455356\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.9872 | 0.975496 | 0.487748 | − | 0.872984i | \(-0.337818\pi\) | ||||
0.487748 | + | 0.872984i | \(0.337818\pi\) | |||||||
\(884\) | 25.3641 | 0.853088 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.86432 | −0.264207 | ||||||||
\(887\) | 30.5002 | 1.02410 | 0.512048 | − | 0.858957i | \(-0.328887\pi\) | ||||
0.512048 | + | 0.858957i | \(0.328887\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.8247 | 1.53691 | ||||||||
\(890\) | 20.8436 | 0.698679 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.24047 | 0.208946 | ||||||||
\(893\) | −33.4874 | −1.12061 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.8824 | −0.497463 | ||||||||
\(896\) | −29.6623 | −0.990947 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.7181 | 0.724741 | ||||||||
\(899\) | −27.6521 | −0.922249 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.1025 | 1.10280 | ||||||||
\(902\) | 4.03920 | 0.134491 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.1915 | 0.571781 | ||||||||
\(905\) | −71.4953 | −2.37658 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.9322 | 0.396201 | 0.198100 | − | 0.980182i | \(-0.436523\pi\) | ||||
0.198100 | + | 0.980182i | \(0.436523\pi\) | |||||||
\(908\) | −30.7546 | −1.02063 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 18.3743 | 0.609102 | ||||||||
\(911\) | 15.4403 | 0.511559 | 0.255779 | − | 0.966735i | \(-0.417668\pi\) | ||||
0.255779 | + | 0.966735i | \(0.417668\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.0185 | −0.463944 | ||||||||
\(914\) | −10.1462 | −0.335608 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46.0162 | 1.52042 | ||||||||
\(917\) | 10.8066 | 0.356867 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.3289 | −0.868509 | −0.434255 | − | 0.900790i | \(-0.642988\pi\) | ||||
−0.434255 | + | 0.900790i | \(0.642988\pi\) | |||||||
\(920\) | −25.4301 | −0.838405 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.3227 | −0.504625 | ||||||||
\(923\) | −47.6706 | −1.56910 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.2409 | −0.797035 | ||||||||
\(926\) | 20.0528 | 0.658974 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −32.1210 | −1.05442 | ||||||||
\(929\) | 43.3747 | 1.42308 | 0.711539 | − | 0.702647i | \(-0.247999\pi\) | ||||
0.711539 | + | 0.702647i | \(0.247999\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.35808 | −0.0445091 | ||||||||
\(932\) | −9.39315 | −0.307683 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.19997 | 0.301032 | ||||||||
\(935\) | 8.67282 | 0.283632 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0554 | 0.851193 | 0.425597 | − | 0.904913i | \(-0.360064\pi\) | ||||
0.425597 | + | 0.904913i | \(0.360064\pi\) | |||||||
\(938\) | 2.37615 | 0.0775840 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 42.4297 | 1.38390 | ||||||||
\(941\) | −26.2505 | −0.855741 | −0.427870 | − | 0.903840i | \(-0.640736\pi\) | ||||
−0.427870 | + | 0.903840i | \(0.640736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.9810 | −1.04144 | ||||||||
\(944\) | 17.0678 | 0.555511 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.36638 | 0.0444248 | ||||||||
\(947\) | −9.10252 | −0.295792 | −0.147896 | − | 0.989003i | \(-0.547250\pi\) | ||||
−0.147896 | + | 0.989003i | \(0.547250\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.6706 | 1.28776 | ||||||||
\(950\) | 4.32757 | 0.140405 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 17.5328 | 0.568241 | ||||||||
\(953\) | 28.3888 | 0.919604 | 0.459802 | − | 0.888022i | \(-0.347920\pi\) | ||||
0.459802 | + | 0.888022i | \(0.347920\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.7467 | 0.736066 | ||||||||
\(956\) | 29.1915 | 0.944120 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.2096 | −0.782176 | ||||||||
\(959\) | −1.25934 | −0.0406661 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.16472 | −0.295636 | ||||||||
\(962\) | −30.2201 | −0.974336 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.131160 | 0.00422438 | ||||||||
\(965\) | −14.7776 | −0.475708 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.2241 | 1.55078 | 0.775391 | − | 0.631481i | \(-0.217553\pi\) | ||||
0.775391 | + | 0.631481i | \(0.217553\pi\) | |||||||
\(968\) | −2.10083 | −0.0675232 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.0347 | −0.611167 | ||||||||
\(971\) | −19.0946 | −0.612775 | −0.306388 | − | 0.951907i | \(-0.599120\pi\) | ||||
−0.306388 | + | 0.951907i | \(0.599120\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.80664 | −0.314387 | ||||||||
\(974\) | 13.9374 | 0.446583 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.0682 | 0.354286 | ||||||||
\(977\) | 14.4033 | 0.460803 | 0.230402 | − | 0.973096i | \(-0.425996\pi\) | ||||
0.230402 | + | 0.973096i | \(0.425996\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.6336 | −0.435732 | ||||||||
\(980\) | 1.72073 | 0.0549667 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.0735 | 0.417192 | ||||||||
\(983\) | 22.1312 | 0.705874 | 0.352937 | − | 0.935647i | \(-0.385183\pi\) | ||||
0.352937 | + | 0.935647i | \(0.385183\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.0264 | 1.27535 | ||||||||
\(986\) | 10.9832 | 0.349777 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27.5843 | −0.877572 | ||||||||
\(989\) | −10.8185 | −0.344008 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.3826 | −1.56869 | −0.784345 | − | 0.620325i | \(-0.787001\pi\) | ||||
−0.784345 | + | 0.620325i | \(0.787001\pi\) | |||||||
\(992\) | 25.3641 | 0.805312 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15.0083 | −0.476035 | ||||||||
\(995\) | 0.258937 | 0.00820884 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.7361 | −0.656720 | −0.328360 | − | 0.944553i | \(-0.606496\pi\) | ||||
−0.328360 | + | 0.944553i | \(0.606496\pi\) | |||||||
\(998\) | 12.0599 | 0.381751 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 297.2.a.h.1.2 | yes | 3 | |
3.2 | odd | 2 | 297.2.a.g.1.2 | ✓ | 3 | ||
4.3 | odd | 2 | 4752.2.a.bg.1.3 | 3 | |||
5.4 | even | 2 | 7425.2.a.bm.1.2 | 3 | |||
9.2 | odd | 6 | 891.2.e.t.595.2 | 6 | |||
9.4 | even | 3 | 891.2.e.q.298.2 | 6 | |||
9.5 | odd | 6 | 891.2.e.t.298.2 | 6 | |||
9.7 | even | 3 | 891.2.e.q.595.2 | 6 | |||
11.10 | odd | 2 | 3267.2.a.t.1.2 | 3 | |||
12.11 | even | 2 | 4752.2.a.bo.1.1 | 3 | |||
15.14 | odd | 2 | 7425.2.a.bn.1.2 | 3 | |||
33.32 | even | 2 | 3267.2.a.w.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
297.2.a.g.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
297.2.a.h.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
891.2.e.q.298.2 | 6 | 9.4 | even | 3 | |||
891.2.e.q.595.2 | 6 | 9.7 | even | 3 | |||
891.2.e.t.298.2 | 6 | 9.5 | odd | 6 | |||
891.2.e.t.595.2 | 6 | 9.2 | odd | 6 | |||
3267.2.a.t.1.2 | 3 | 11.10 | odd | 2 | |||
3267.2.a.w.1.2 | 3 | 33.32 | even | 2 | |||
4752.2.a.bg.1.3 | 3 | 4.3 | odd | 2 | |||
4752.2.a.bo.1.1 | 3 | 12.11 | even | 2 | |||
7425.2.a.bm.1.2 | 3 | 5.4 | even | 2 | |||
7425.2.a.bn.1.2 | 3 | 15.14 | odd | 2 |