Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8032,2,Mod(1,8032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8032 = 2^{5} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8032.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: | \(64.1358429035\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8032.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.679540 | −0.392333 | −0.196166 | − | 0.980571i | \(-0.562849\pi\) | ||||
−0.196166 | + | 0.980571i | \(0.562849\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.36350 | −0.609778 | −0.304889 | − | 0.952388i | \(-0.598619\pi\) | ||||
−0.304889 | + | 0.952388i | \(0.598619\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.99119 | 1.13056 | 0.565282 | − | 0.824898i | \(-0.308767\pi\) | ||||
0.565282 | + | 0.824898i | \(0.308767\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.53823 | −0.846075 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.20862 | 1.26895 | 0.634473 | − | 0.772945i | \(-0.281217\pi\) | ||||
0.634473 | + | 0.772945i | \(0.281217\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.86960 | 0.518535 | 0.259267 | − | 0.965806i | \(-0.416519\pi\) | ||||
0.259267 | + | 0.965806i | \(0.416519\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.926556 | 0.239236 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.227597 | 0.0552003 | 0.0276002 | − | 0.999619i | \(-0.491213\pi\) | ||||
0.0276002 | + | 0.999619i | \(0.491213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.54048 | −0.812242 | −0.406121 | − | 0.913819i | \(-0.633119\pi\) | ||||
−0.406121 | + | 0.913819i | \(0.633119\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.03263 | −0.443557 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.07033 | 0.431693 | 0.215847 | − | 0.976427i | \(-0.430749\pi\) | ||||
0.215847 | + | 0.976427i | \(0.430749\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.14086 | −0.628171 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.76345 | 0.724276 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.12050 | −0.765157 | −0.382578 | − | 0.923923i | \(-0.624964\pi\) | ||||
−0.382578 | + | 0.923923i | \(0.624964\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.59931 | −0.466850 | −0.233425 | − | 0.972375i | \(-0.574993\pi\) | ||||
−0.233425 | + | 0.972375i | \(0.574993\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.85993 | −0.497849 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.07850 | −0.689392 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.32332 | −0.710749 | −0.355375 | − | 0.934724i | \(-0.615647\pi\) | ||||
−0.355375 | + | 0.934724i | \(0.615647\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.27047 | −0.203438 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.83717 | −1.06779 | −0.533893 | − | 0.845552i | \(-0.679271\pi\) | ||||
−0.533893 | + | 0.845552i | \(0.679271\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.66256 | −0.558536 | −0.279268 | − | 0.960213i | \(-0.590092\pi\) | ||||
−0.279268 | + | 0.960213i | \(0.590092\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.46088 | 0.515918 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.50454 | 1.09465 | 0.547325 | − | 0.836920i | \(-0.315646\pi\) | ||||
0.547325 | + | 0.836920i | \(0.315646\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.94722 | 0.278174 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.154661 | −0.0216569 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.77747 | 1.06832 | 0.534159 | − | 0.845384i | \(-0.320628\pi\) | ||||
0.534159 | + | 0.845384i | \(0.320628\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.73847 | −0.773775 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.40590 | 0.318669 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.60379 | 0.469174 | 0.234587 | − | 0.972095i | \(-0.424626\pi\) | ||||
0.234587 | + | 0.972095i | \(0.424626\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.86472 | −0.622864 | −0.311432 | − | 0.950269i | \(-0.600809\pi\) | ||||
−0.311432 | + | 0.950269i | \(0.600809\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.59231 | −0.956542 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.54921 | −0.316191 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.83449 | 0.957136 | 0.478568 | − | 0.878051i | \(-0.341156\pi\) | ||||
0.478568 | + | 0.878051i | \(0.341156\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.40687 | −0.169367 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.5925 | −1.85049 | −0.925244 | − | 0.379372i | \(-0.876140\pi\) | ||||
−0.925244 | + | 0.379372i | \(0.876140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.6380 | −1.71325 | −0.856623 | − | 0.515943i | \(-0.827442\pi\) | ||||
−0.856623 | + | 0.515943i | \(0.827442\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.13434 | 0.246452 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.5888 | 1.43463 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.78478 | −0.313312 | −0.156656 | − | 0.987653i | \(-0.550071\pi\) | ||||
−0.156656 | + | 0.987653i | \(0.550071\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.05726 | 0.561918 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.68148 | −0.404095 | −0.202047 | − | 0.979376i | \(-0.564759\pi\) | ||||
−0.202047 | + | 0.979376i | \(0.564759\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.310329 | −0.0336599 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.80004 | 0.300196 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.715053 | −0.0757954 | −0.0378977 | − | 0.999282i | \(-0.512066\pi\) | ||||
−0.0378977 | + | 0.999282i | \(0.512066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.59234 | 0.586237 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.76634 | 0.183161 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.82746 | 0.495287 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.611218 | −0.0620598 | −0.0310299 | − | 0.999518i | \(-0.509879\pi\) | ||||
−0.0310299 | + | 0.999518i | \(0.509879\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.6824 | −1.07362 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.78674 | −0.476299 | −0.238149 | − | 0.971229i | \(-0.576541\pi\) | ||||
−0.238149 | + | 0.971229i | \(0.576541\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.52719 | 0.643143 | 0.321572 | − | 0.946885i | \(-0.395789\pi\) | ||||
0.321572 | + | 0.946885i | \(0.395789\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.77151 | 0.270471 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.75917 | −0.846781 | −0.423391 | − | 0.905947i | \(-0.639160\pi\) | ||||
−0.423391 | + | 0.905947i | \(0.639160\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.55359 | 0.244590 | 0.122295 | − | 0.992494i | \(-0.460975\pi\) | ||||
0.122295 | + | 0.992494i | \(0.460975\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.93787 | 0.278850 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.75811 | 0.353533 | 0.176767 | − | 0.984253i | \(-0.443436\pi\) | ||||
0.176767 | + | 0.984253i | \(0.443436\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.82290 | −0.263237 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.74548 | −0.438719 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.680785 | 0.0624075 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.71249 | 0.610226 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.64613 | 0.418927 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1001 | 0.992822 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.60626 | 0.763682 | 0.381841 | − | 0.924228i | \(-0.375290\pi\) | ||||
0.381841 | + | 0.924228i | \(0.375290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.48886 | 0.219132 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.96398 | −0.171594 | −0.0857968 | − | 0.996313i | \(-0.527344\pi\) | ||||
−0.0857968 | + | 0.996313i | \(0.527344\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.5903 | −0.918291 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.13148 | −0.441647 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.5122 | 1.92335 | 0.961674 | − | 0.274195i | \(-0.0884113\pi\) | ||||
0.961674 | + | 0.274195i | \(0.0884113\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.338030 | 0.0286713 | 0.0143357 | − | 0.999897i | \(-0.495437\pi\) | ||||
0.0143357 | + | 0.999897i | \(0.495437\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.09964 | −0.429467 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.86845 | 0.657993 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.61831 | 0.466576 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.32321 | −0.109137 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.3561 | −1.33995 | −0.669973 | − | 0.742385i | \(-0.733695\pi\) | ||||
−0.669973 | + | 0.742385i | \(0.733695\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.69657 | −0.544959 | −0.272479 | − | 0.962162i | \(-0.587844\pi\) | ||||
−0.272479 | + | 0.962162i | \(0.587844\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.577692 | −0.0467036 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.54417 | 0.284675 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.6728 | 1.72968 | 0.864840 | − | 0.502047i | \(-0.167420\pi\) | ||||
0.864840 | + | 0.502047i | \(0.167420\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.28510 | −0.419136 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.19275 | 0.488057 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1372 | 0.794003 | 0.397002 | − | 0.917818i | \(-0.370051\pi\) | ||||
0.397002 | + | 0.917818i | \(0.370051\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.89952 | 0.303577 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.1348 | −1.63546 | −0.817731 | − | 0.575600i | \(-0.804768\pi\) | ||||
−0.817731 | + | 0.575600i | \(0.804768\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.50458 | −0.731122 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.98654 | 0.687218 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.3989 | 1.17076 | 0.585380 | − | 0.810759i | \(-0.300945\pi\) | ||||
0.585380 | + | 0.810759i | \(0.300945\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.39490 | −0.710188 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.44892 | −0.184072 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.01859 | −0.225620 | −0.112810 | − | 0.993617i | \(-0.535985\pi\) | ||||
−0.112810 | + | 0.993617i | \(0.535985\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.68158 | 0.273650 | 0.136825 | − | 0.990595i | \(-0.456310\pi\) | ||||
0.136825 | + | 0.990595i | \(0.456310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.30577 | 0.244370 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.89487 | 0.433399 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.957868 | 0.0700463 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.2572 | 0.818840 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.1589 | −1.74808 | −0.874040 | − | 0.485854i | \(-0.838509\pi\) | ||||
−0.874040 | + | 0.485854i | \(0.838509\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.0374 | −1.01043 | −0.505216 | − | 0.862993i | \(-0.668587\pi\) | ||||
−0.505216 | + | 0.862993i | \(0.668587\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.73229 | 0.124052 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.7083 | 1.04793 | 0.523963 | − | 0.851741i | \(-0.324453\pi\) | ||||
0.523963 | + | 0.851741i | \(0.324453\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.25012 | −0.230395 | −0.115197 | − | 0.993343i | \(-0.536750\pi\) | ||||
−0.115197 | + | 0.993343i | \(0.536750\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.32385 | −0.375516 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.3252 | −0.865059 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.32251 | 0.651112 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.25496 | −0.365245 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.9005 | −1.03069 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.19360 | 0.495228 | 0.247614 | − | 0.968859i | \(-0.420354\pi\) | ||||
0.247614 | + | 0.968859i | \(0.420354\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.5957 | 0.726007 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.99392 | 0.340583 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.77503 | −0.527804 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.94710 | 0.672162 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.425516 | 0.0286233 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.6736 | −1.25048 | −0.625239 | − | 0.780433i | \(-0.714998\pi\) | ||||
−0.625239 | + | 0.780433i | \(0.714998\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.97220 | 0.531480 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.5440 | −1.49630 | −0.748148 | − | 0.663531i | \(-0.769057\pi\) | ||||
−0.748148 | + | 0.663531i | \(0.769057\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.97996 | −0.263003 | −0.131502 | − | 0.991316i | \(-0.541980\pi\) | ||||
−0.131502 | + | 0.991316i | \(0.541980\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.55459 | −0.562850 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.3681 | −0.875773 | −0.437886 | − | 0.899030i | \(-0.644273\pi\) | ||||
−0.437886 | + | 0.899030i | \(0.644273\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2325 | −0.667493 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.89237 | 0.122923 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.7495 | −1.73028 | −0.865140 | − | 0.501530i | \(-0.832771\pi\) | ||||
−0.865140 | + | 0.501530i | \(0.832771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.5753 | 0.938877 | 0.469438 | − | 0.882965i | \(-0.344456\pi\) | ||||
0.469438 | + | 0.882965i | \(0.344456\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7270 | −0.944734 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.65504 | −0.169624 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.61930 | −0.421176 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.50171 | 0.158540 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.71323 | 0.547796 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.210881 | 0.0132059 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.3840 | 0.710112 | 0.355056 | − | 0.934845i | \(-0.384462\pi\) | ||||
0.355056 | + | 0.934845i | \(0.384462\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.9319 | −0.803548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.4587 | 0.647380 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.792727 | 0.0488817 | 0.0244408 | − | 0.999701i | \(-0.492219\pi\) | ||||
0.0244408 | + | 0.999701i | \(0.492219\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.6046 | −0.651436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.485907 | 0.0297370 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.65585 | 0.222901 | 0.111451 | − | 0.993770i | \(-0.464450\pi\) | ||||
0.111451 | + | 0.993770i | \(0.464450\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.58681 | −0.339375 | −0.169687 | − | 0.985498i | \(-0.554276\pi\) | ||||
−0.169687 | + | 0.985498i | \(0.554276\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.80022 | −0.230000 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.2187 | −0.797116 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.90053 | 0.534781 | 0.267390 | − | 0.963588i | \(-0.413839\pi\) | ||||
0.267390 | + | 0.963588i | \(0.413839\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.59764 | 0.394990 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00303 | 0.119490 | 0.0597452 | − | 0.998214i | \(-0.480971\pi\) | ||||
0.0597452 | + | 0.998214i | \(0.480971\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.9941 | 1.66408 | 0.832039 | − | 0.554717i | \(-0.187173\pi\) | ||||
0.832039 | + | 0.554717i | \(0.187173\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.28045 | −0.194317 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.4513 | −1.20720 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9482 | −0.996953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.415347 | 0.0243481 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.5569 | −1.43463 | −0.717316 | − | 0.696748i | \(-0.754629\pi\) | ||||
−0.717316 | + | 0.696748i | \(0.754629\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.91378 | −0.286092 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.8389 | 0.919067 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.87069 | 0.223848 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.9554 | −0.631460 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.25279 | 0.186868 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.63307 | 0.379808 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.2155 | −0.868393 | −0.434197 | − | 0.900818i | \(-0.642968\pi\) | ||||
−0.434197 | + | 0.900818i | \(0.642968\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.43549 | −0.252326 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.1508 | −1.08594 | −0.542971 | − | 0.839751i | \(-0.682701\pi\) | ||||
−0.542971 | + | 0.839751i | \(0.682701\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.62198 | −0.374296 | −0.187148 | − | 0.982332i | \(-0.559924\pi\) | ||||
−0.187148 | + | 0.982332i | \(0.559924\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.3522 | 0.583278 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.74674 | −0.547432 | −0.273716 | − | 0.961811i | \(-0.588253\pi\) | ||||
−0.273716 | + | 0.961811i | \(0.588253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.3416 | −0.970943 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.95221 | 0.332220 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.805802 | −0.0448360 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.87216 | −0.325729 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.73527 | −0.0959605 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.4475 | 1.23757 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.9147 | −0.874754 | −0.437377 | − | 0.899278i | \(-0.644092\pi\) | ||||
−0.437377 | + | 0.899278i | \(0.644092\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.9736 | 0.601347 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.6824 | −0.583640 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 36.5040 | 1.98850 | 0.994249 | − | 0.107097i | \(-0.0341554\pi\) | ||||
0.994249 | + | 0.107097i | \(0.0341554\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.55379 | −0.138703 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.9395 | −0.592408 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.1138 | −0.816070 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.91828 | 0.103276 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.5077 | 1.15459 | 0.577296 | − | 0.816535i | \(-0.304108\pi\) | ||||
0.577296 | + | 0.816535i | \(0.304108\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.1242 | 1.29134 | 0.645669 | − | 0.763618i | \(-0.276579\pi\) | ||||
0.645669 | + | 0.763618i | \(0.276579\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.03615 | 0.375562 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.8474 | −1.42894 | −0.714470 | − | 0.699666i | \(-0.753332\pi\) | ||||
−0.714470 | + | 0.699666i | \(0.753332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.2604 | 1.12839 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.462621 | −0.0244845 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.8590 | −0.995338 | −0.497669 | − | 0.867367i | \(-0.665811\pi\) | ||||
−0.497669 | + | 0.867367i | \(0.665811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.46499 | −0.340263 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.56140 | −0.239412 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.9589 | 1.04470 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.2398 | 1.10871 | 0.554353 | − | 0.832282i | \(-0.312966\pi\) | ||||
0.554353 | + | 0.832282i | \(0.312966\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.3543 | 0.903427 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.2639 | 1.20780 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.3452 | −1.26055 | −0.630273 | − | 0.776374i | \(-0.717057\pi\) | ||||
−0.630273 | + | 0.776374i | \(0.717057\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.54296 | −0.389517 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.70369 | −0.396760 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6765 | 0.599782 | 0.299891 | − | 0.953973i | \(-0.403050\pi\) | ||||
0.299891 | + | 0.953973i | \(0.403050\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.84830 | −0.299618 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.3577 | −0.580350 | −0.290175 | − | 0.956974i | \(-0.593713\pi\) | ||||
−0.290175 | + | 0.956974i | \(0.593713\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.1649 | −0.874802 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.29641 | 0.472563 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.6374 | −1.70548 | −0.852742 | − | 0.522332i | \(-0.825062\pi\) | ||||
−0.852742 | + | 0.522332i | \(0.825062\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.471200 | 0.0238296 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.33460 | 0.0673218 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.79706 | 0.191051 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.44145 | −0.0723442 | −0.0361721 | − | 0.999346i | \(-0.511516\pi\) | ||||
−0.0361721 | + | 0.999346i | \(0.511516\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.19650 | 0.360276 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.4372 | −0.870772 | −0.435386 | − | 0.900244i | \(-0.643388\pi\) | ||||
−0.435386 | + | 0.900244i | \(0.643388\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.85968 | −0.242078 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.89560 | −0.342645 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.1952 | −0.901903 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.0268 | −0.594687 | −0.297343 | − | 0.954771i | \(-0.596101\pi\) | ||||
−0.297343 | + | 0.954771i | \(0.596101\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.2980 | −0.754592 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.7796 | 0.530431 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.01971 | 0.246408 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.229705 | −0.0112487 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.31694 | −0.162043 | −0.0810215 | − | 0.996712i | \(-0.525818\pi\) | ||||
−0.0810215 | + | 0.996712i | \(0.525818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.05446 | −0.246339 | −0.123170 | − | 0.992386i | \(-0.539306\pi\) | ||||
−0.123170 | + | 0.992386i | \(0.539306\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.0482 | −0.926156 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.714849 | −0.0346753 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.5513 | −0.704187 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.34693 | −0.258152 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.2555 | −1.21651 | −0.608257 | − | 0.793740i | \(-0.708131\pi\) | ||||
−0.608257 | + | 0.793740i | \(0.708131\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.14271 | −0.295200 | −0.147600 | − | 0.989047i | \(-0.547155\pi\) | ||||
−0.147600 | + | 0.989047i | \(0.547155\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.81787 | −0.183053 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.32996 | −0.350640 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.3925 | 0.543737 | 0.271868 | − | 0.962334i | \(-0.412359\pi\) | ||||
0.271868 | + | 0.962334i | \(0.412359\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.94248 | −0.235356 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.6474 | 0.553385 | 0.276693 | − | 0.960959i | \(-0.410762\pi\) | ||||
0.276693 | + | 0.960959i | \(0.410762\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.974978 | 0.0462184 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.1147 | 0.525705 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.07118 | −0.286517 | −0.143258 | − | 0.989685i | \(-0.545758\pi\) | ||||
−0.143258 | + | 0.989685i | \(0.545758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.7750 | −1.35496 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.55059 | 0.213805 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.62518 | −0.357474 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.35362 | −0.297210 | −0.148605 | − | 0.988897i | \(-0.547478\pi\) | ||||
−0.148605 | + | 0.988897i | \(0.547478\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.856548 | 0.0399802 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.9227 | −1.30049 | −0.650246 | − | 0.759724i | \(-0.725334\pi\) | ||||
−0.650246 | + | 0.759724i | \(0.725334\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.52184 | 0.256622 | 0.128311 | − | 0.991734i | \(-0.459044\pi\) | ||||
0.128311 | + | 0.991734i | \(0.459044\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.40841 | −0.111687 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.0946 | −0.883592 | −0.441796 | − | 0.897115i | \(-0.645659\pi\) | ||||
−0.441796 | + | 0.897115i | \(0.645659\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.4345 | 1.08210 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.7276 | −0.678610 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.4143 | −0.708752 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.1201 | 0.510227 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.7410 | −0.903877 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.7312 | 0.627393 | 0.313696 | − | 0.949523i | \(-0.398433\pi\) | ||||
0.313696 | + | 0.949523i | \(0.398433\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.08290 | −0.368548 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.20822 | −0.191481 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.833399 | 0.0378427 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.1790 | −0.914397 | −0.457199 | − | 0.889365i | \(-0.651147\pi\) | ||||
−0.457199 | + | 0.889365i | \(0.651147\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.88860 | −0.311513 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.6305 | 0.479747 | 0.239873 | − | 0.970804i | \(-0.422894\pi\) | ||||
0.239873 | + | 0.970804i | \(0.422894\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.937812 | −0.0422369 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.5655 | 0.654672 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −46.6401 | −2.09210 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.16748 | 0.276094 | 0.138047 | − | 0.990426i | \(-0.455917\pi\) | ||||
0.138047 | + | 0.990426i | \(0.455917\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.3620 | 0.641645 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.3841 | −0.685943 | −0.342972 | − | 0.939346i | \(-0.611433\pi\) | ||||
−0.342972 | + | 0.939346i | \(0.611433\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.52675 | 0.290436 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.45875 | 0.286843 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.7461 | −0.919554 | −0.459777 | − | 0.888034i | \(-0.652071\pi\) | ||||
−0.459777 | + | 0.888034i | \(0.652071\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −43.7850 | −1.93693 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.3244 | −0.588287 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.89985 | −0.392174 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.5838 | 1.38905 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.4642 | −0.459327 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0882 | 0.573406 | 0.286703 | − | 0.958020i | \(-0.407441\pi\) | ||||
0.286703 | + | 0.958020i | \(0.407441\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.5058 | 1.55256 | 0.776279 | − | 0.630389i | \(-0.217105\pi\) | ||||
0.776279 | + | 0.630389i | \(0.217105\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.38421 | 0.278630 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.591595 | −0.0257703 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.7137 | −0.813641 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.14723 | −0.396956 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.7828 | −0.553684 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.9432 | 0.516348 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.05125 | 0.0885180 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.19511 | 0.352988 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.598123 | −0.0257153 | −0.0128577 | − | 0.999917i | \(-0.504093\pi\) | ||||
−0.0128577 | + | 0.999917i | \(0.504093\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.50178 | −0.107362 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.48183 | −0.149145 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.85299 | −0.293013 | −0.146506 | − | 0.989210i | \(-0.546803\pi\) | ||||
−0.146506 | + | 0.989210i | \(0.546803\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.3478 | 0.526989 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.5885 | 0.621493 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.32981 | −0.354220 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.00580 | −0.170037 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.9715 | −1.01571 | −0.507853 | − | 0.861444i | \(-0.669561\pi\) | ||||
−0.507853 | + | 0.861444i | \(0.669561\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.84754 | −0.289620 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.650910 | −0.0274814 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.17913 | 0.386854 | 0.193427 | − | 0.981115i | \(-0.438040\pi\) | ||||
0.193427 | + | 0.981115i | \(0.438040\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.12420 | −0.215577 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.1272 | 0.635284 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 45.9680 | 1.92708 | 0.963540 | − | 0.267566i | \(-0.0862192\pi\) | ||||
0.963540 | + | 0.267566i | \(0.0862192\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.73574 | 0.365579 | 0.182790 | − | 0.983152i | \(-0.441487\pi\) | ||||
0.182790 | + | 0.983152i | \(0.441487\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.4170 | 0.685829 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.50260 | −0.271177 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.25261 | 0.343561 | 0.171780 | − | 0.985135i | \(-0.445048\pi\) | ||||
0.171780 | + | 0.985135i | \(0.445048\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.53896 | 0.396426 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.0120 | −0.456855 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.7324 | 1.35564 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.47048 | 0.267521 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.7878 | 0.486533 | 0.243266 | − | 0.969960i | \(-0.421781\pi\) | ||||
0.243266 | + | 0.969960i | \(0.421781\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.20281 | 0.379195 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.99490 | −0.411135 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.0021 | 1.80695 | 0.903476 | − | 0.428639i | \(-0.141007\pi\) | ||||
0.903476 | + | 0.428639i | \(0.141007\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.928254 | −0.0380547 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.20858 | 0.0903914 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.7252 | 1.29626 | 0.648129 | − | 0.761531i | \(-0.275552\pi\) | ||||
0.648129 | + | 0.761531i | \(0.275552\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.9575 | −1.75227 | −0.876137 | − | 0.482062i | \(-0.839888\pi\) | ||||
−0.876137 | + | 0.482062i | \(0.839888\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.8857 | −0.809809 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.15251 | −0.372102 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.0420 | 1.66584 | 0.832922 | − | 0.553391i | \(-0.186666\pi\) | ||||
0.832922 | + | 0.553391i | \(0.186666\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.37546 | 0.339391 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.0305 | 0.567614 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.4336 | 0.704137 | 0.352069 | − | 0.935974i | \(-0.385478\pi\) | ||||
0.352069 | + | 0.935974i | \(0.385478\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.33502 | −0.255453 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.1336 | −0.568998 | −0.284499 | − | 0.958676i | \(-0.591827\pi\) | ||||
−0.284499 | + | 0.958676i | \(0.591827\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.8743 | −1.36153 | −0.680763 | − | 0.732504i | \(-0.738351\pi\) | ||||
−0.680763 | + | 0.732504i | \(0.738351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.79157 | 0.312665 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.13886 | −0.0856916 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.569256 | 0.0227702 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.1255 | 0.404374 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.983974 | −0.0392336 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.0157 | −0.876432 | −0.438216 | − | 0.898870i | \(-0.644389\pi\) | ||||
−0.438216 | + | 0.898870i | \(0.644389\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.88834 | −0.194294 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.7347 | −0.465676 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.64053 | 0.144243 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 39.5773 | 1.56565 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.67040 | −0.302962 | −0.151481 | − | 0.988460i | \(-0.548404\pi\) | ||||
−0.151481 | + | 0.988460i | \(0.548404\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.7858 | 0.938019 | 0.469009 | − | 0.883193i | \(-0.344611\pi\) | ||||
0.469009 | + | 0.883193i | \(0.344611\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.39357 | −0.133622 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.8081 | −1.56502 | −0.782509 | − | 0.622639i | \(-0.786060\pi\) | ||||
−0.782509 | + | 0.622639i | \(0.786060\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.1670 | 0.595356 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.28345 | 0.207075 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.5966 | −1.07994 | −0.539968 | − | 0.841685i | \(-0.681564\pi\) | ||||
−0.539968 | + | 0.841685i | \(0.681564\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.67789 | 0.104634 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 37.1545 | 1.44953 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.37969 | 0.287472 | 0.143736 | − | 0.989616i | \(-0.454088\pi\) | ||||
0.143736 | + | 0.989616i | \(0.454088\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.752600 | 0.0292727 | 0.0146364 | − | 0.999893i | \(-0.495341\pi\) | ||||
0.0146364 | + | 0.999893i | \(0.495341\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.289155 | −0.0112299 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.4399 | 0.559954 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.53078 | −0.330313 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.6895 | 0.490603 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.4738 | −0.790381 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.9415 | 0.575953 | 0.287977 | − | 0.957637i | \(-0.407017\pi\) | ||||
0.287977 | + | 0.957637i | \(0.407017\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.8204 | −0.454969 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.3094 | −1.35705 | −0.678525 | − | 0.734577i | \(-0.737381\pi\) | ||||
−0.678525 | + | 0.734577i | \(0.737381\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.82827 | −0.0701626 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.3195 | 0.587046 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.29495 | 0.279133 | 0.139567 | − | 0.990213i | \(-0.455429\pi\) | ||||
0.139567 | + | 0.990213i | \(0.455429\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.6955 | −1.17281 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.70454 | 0.103185 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.5408 | 0.553960 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.9939 | −1.14102 | −0.570510 | − | 0.821290i | \(-0.693255\pi\) | ||||
−0.570510 | + | 0.821290i | \(0.693255\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −31.9532 | −1.21380 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.460905 | −0.0174831 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.55612 | −0.0589421 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.08415 | 0.343594 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.52887 | −0.284362 | −0.142181 | − | 0.989841i | \(-0.545411\pi\) | ||||
−0.142181 | + | 0.989841i | \(0.545411\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.3066 | 0.577301 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.95338 | 0.261879 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.3181 | −0.538486 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.23645 | 0.159103 | 0.0795517 | − | 0.996831i | \(-0.474651\pi\) | ||||
0.0795517 | + | 0.996831i | \(0.474651\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.06840 | 0.265086 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.38143 | −0.201536 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.7287 | −0.401229 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.1773 | 0.678845 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.0902 | −0.786530 | −0.393265 | − | 0.919425i | \(-0.628655\pi\) | ||||
−0.393265 | + | 0.919425i | \(0.628655\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.5241 | 0.727114 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.90449 | −0.368352 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.9419 | 0.480650 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.04832 | 0.0759678 | 0.0379839 | − | 0.999278i | \(-0.487906\pi\) | ||||
0.0379839 | + | 0.999278i | \(0.487906\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.16423 | −0.191268 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.833588 | −0.0308314 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.5788 | −0.427673 | −0.213837 | − | 0.976869i | \(-0.568596\pi\) | ||||
−0.213837 | + | 0.976869i | \(0.568596\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.80421 | 0.0665492 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.9724 | 1.21455 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.40400 | −0.309146 | −0.154573 | − | 0.987981i | \(-0.549400\pi\) | ||||
−0.154573 | + | 0.987981i | \(0.549400\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.49808 | 0.165241 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.0904 | −1.69089 | −0.845447 | − | 0.534060i | \(-0.820666\pi\) | ||||
−0.845447 | + | 0.534060i | \(0.820666\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.3017 | 0.817070 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.34442 | 0.341894 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.2004 | −0.957340 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.5479 | −1.11471 | −0.557354 | − | 0.830275i | \(-0.688183\pi\) | ||||
−0.557354 | + | 0.830275i | \(0.688183\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.679540 | 0.0247638 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.13080 | 0.332304 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.5569 | 0.529079 | 0.264540 | − | 0.964375i | \(-0.414780\pi\) | ||||
0.264540 | + | 0.964375i | \(0.414780\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.92099 | −0.214918 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.6971 | 1.62027 | 0.810135 | − | 0.586244i | \(-0.199394\pi\) | ||||
0.810135 | + | 0.586244i | \(0.199394\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.63828 | 0.276524 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.787685 | 0.0284788 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.73766 | 0.243283 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.8380 | −0.535073 | −0.267537 | − | 0.963548i | \(-0.586210\pi\) | ||||
−0.267537 | + | 0.963548i | \(0.586210\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.73586 | −0.278600 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.6561 | 1.49826 | 0.749132 | − | 0.662421i | \(-0.230471\pi\) | ||||
0.749132 | + | 0.662421i | \(0.230471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.16406 | 0.293262 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.78773 | 0.315258 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.2069 | 0.867301 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −65.6229 | −2.34817 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.5073 | −0.554184 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.5510 | −1.05472 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.4389 | 1.33455 | 0.667276 | − | 0.744811i | \(-0.267460\pi\) | ||||
0.667276 | + | 0.744811i | \(0.267460\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.538690 | −0.0191779 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.2412 | 0.399692 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.09510 | −0.322976 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.20626 | 0.255580 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.94145 | 0.245879 | 0.122939 | − | 0.992414i | \(-0.460768\pi\) | ||||
0.122939 | + | 0.992414i | \(0.460768\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.70801 | 0.0604250 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.81496 | 0.0641286 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −61.6057 | −2.17402 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.44384 | −0.297606 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.48430 | −0.0874515 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.2665 | 1.20474 | 0.602372 | − | 0.798215i | \(-0.294222\pi\) | ||||
0.602372 | + | 0.798215i | \(0.294222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.8888 | 0.452589 | 0.226294 | − | 0.974059i | \(-0.427339\pi\) | ||||
0.226294 | + | 0.974059i | \(0.427339\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.79646 | 0.133148 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.8221 | −0.484165 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.9672 | 0.453666 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.1946 | −0.496000 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.5118 | −1.58837 | −0.794186 | − | 0.607675i | \(-0.792102\pi\) | ||||
−0.794186 | + | 0.607675i | \(0.792102\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.59330 | 0.0903969 | 0.0451984 | − | 0.998978i | \(-0.485608\pi\) | ||||
0.0451984 | + | 0.998978i | \(0.485608\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.98262 | 0.312735 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.9105 | −0.553262 | −0.276631 | − | 0.960976i | \(-0.589218\pi\) | ||||
−0.276631 | + | 0.960976i | \(0.589218\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.3558 | 0.984837 | 0.492418 | − | 0.870359i | \(-0.336113\pi\) | ||||
0.492418 | + | 0.870359i | \(0.336113\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.04827 | −0.209812 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.443181 | 0.0153553 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.8174 | 0.997268 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.78237 | −0.338128 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.35538 | −0.253936 | −0.126968 | − | 0.991907i | \(-0.540525\pi\) | ||||
−0.126968 | + | 0.991907i | \(0.540525\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.0215 | −0.414535 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.36114 | −0.0468800 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.9595 | 0.445822 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.0783 | 0.689899 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.0231 | −0.652872 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.95069 | −0.306826 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.0336 | −0.891373 | −0.445686 | − | 0.895189i | \(-0.647040\pi\) | ||||
−0.445686 | + | 0.895189i | \(0.647040\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.2532 | −0.419050 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.2591 | −1.64850 | −0.824250 | − | 0.566226i | \(-0.808403\pi\) | ||||
−0.824250 | + | 0.566226i | \(0.808403\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.1397 | −0.994234 | −0.497117 | − | 0.867684i | \(-0.665608\pi\) | ||||
−0.497117 | + | 0.867684i | \(0.665608\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.8975 | 0.473624 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.04525 | −0.137702 | −0.0688510 | − | 0.997627i | \(-0.521933\pi\) | ||||
−0.0688510 | + | 0.997627i | \(0.521933\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.9965 | −0.713903 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.5170 | 0.391137 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.7201 | −0.397577 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.6474 | 0.496308 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.55141 | 0.0525073 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.2025 | 1.12245 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.1319 | 0.342128 | 0.171064 | − | 0.985260i | \(-0.445279\pi\) | ||||
0.171064 | + | 0.985260i | \(0.445279\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.6874 | 0.562853 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.0262 | −0.775773 | −0.387886 | − | 0.921707i | \(-0.626795\pi\) | ||||
−0.387886 | + | 0.921707i | \(0.626795\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.3915 | 1.05641 | 0.528204 | − | 0.849117i | \(-0.322866\pi\) | ||||
0.528204 | + | 0.849117i | \(0.322866\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.33911 | 0.112243 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.76122 | −0.294173 | −0.147087 | − | 0.989124i | \(-0.546990\pi\) | ||||
−0.147087 | + | 0.989124i | \(0.546990\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.7430 | 0.863392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.2841 | 0.713044 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.5697 | −0.889121 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.11585 | 0.137578 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.63029 | −0.0878229 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.7104 | 0.357213 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.77013 | 0.0589715 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.44465 | 0.247743 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.01986 | −0.166866 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.8893 | 0.760028 | 0.380014 | − | 0.924981i | \(-0.375919\pi\) | ||||
0.380014 | + | 0.924981i | \(0.375919\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.1498 | 0.402985 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.8379 | −0.756654 | −0.378327 | − | 0.925672i | \(-0.623501\pi\) | ||||
−0.378327 | + | 0.925672i | \(0.623501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.4939 | −0.512775 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.50744 | −0.149011 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.87464 | −0.193998 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.5651 | −1.43708 | −0.718540 | − | 0.695486i | \(-0.755189\pi\) | ||||
−0.718540 | + | 0.695486i | \(0.755189\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.3395 | 0.340699 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.1518 | −0.959543 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.5789 | 0.446472 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.5675 | −0.544147 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.0815 | 0.363573 | 0.181787 | − | 0.983338i | \(-0.441812\pi\) | ||||
0.181787 | + | 0.983338i | \(0.441812\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.89409 | −0.225945 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.0137 | 0.426051 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.30606 | −0.0427127 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.4013 | 0.927829 | 0.463915 | − | 0.885880i | \(-0.346444\pi\) | ||||
0.463915 | + | 0.885880i | \(0.346444\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.49990 | 0.146849 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.8076 | −1.10210 | −0.551048 | − | 0.834473i | \(-0.685772\pi\) | ||||
−0.551048 | + | 0.834473i | \(0.685772\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.1552 | −0.460956 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.3492 | −0.499310 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.7460 | 0.771641 | 0.385820 | − | 0.922574i | \(-0.373918\pi\) | ||||
0.385820 | + | 0.922574i | \(0.373918\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.3672 | −0.888378 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.62330 | 0.214775 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.0896 | −0.521193 | −0.260596 | − | 0.965448i | \(-0.583919\pi\) | ||||
−0.260596 | + | 0.965448i | \(0.583919\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.9408 | 1.06594 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.7843 | 0.380933 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 67.3383 | 2.17447 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.2436 | −0.782051 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.2328 | 0.716440 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.1400 | 0.616139 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.7350 | 0.763267 | 0.381633 | − | 0.924314i | \(-0.375362\pi\) | ||||
0.381633 | + | 0.924314i | \(0.375362\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.547575 | 0.0175906 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.0347 | −0.707128 | −0.353564 | − | 0.935410i | \(-0.615030\pi\) | ||||
−0.353564 | + | 0.935410i | \(0.615030\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.01111 | 0.0324148 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.99037 | 0.127794 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.54883 | 0.241508 | 0.120754 | − | 0.992682i | \(-0.461469\pi\) | ||||
0.120754 | + | 0.992682i | \(0.461469\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.00939 | −0.0961804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.48159 | −0.206941 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.6908 | 0.436669 | 0.218334 | − | 0.975874i | \(-0.429938\pi\) | ||||
0.218334 | + | 0.975874i | \(0.429938\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.0549 | −0.639001 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.2540 | −0.485540 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.58271 | −0.241116 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.4502 | 0.903751 | 0.451876 | − | 0.892081i | \(-0.350755\pi\) | ||||
0.451876 | + | 0.892081i | \(0.350755\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.8147 | 0.343194 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.43155 | 0.140490 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.5032 | −0.997716 | −0.498858 | − | 0.866684i | \(-0.666247\pi\) | ||||
−0.498858 | + | 0.866684i | \(0.666247\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.2706 | −0.514778 |
(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 | 8032.2.a.h.1.14 | ✓ | 30 | |
4.3 | odd | 2 | 8032.2.a.i.1.17 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8032.2.a.h.1.14 | ✓ | 30 | 1.1 | even | 1 | trivial | |
8032.2.a.i.1.17 | yes | 30 | 4.3 | odd | 2 |