Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.69180\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69180 | −1.90339 | −0.951695 | − | 0.307046i | \(-0.900659\pi\) | ||||
−0.951695 | + | 0.307046i | \(0.900659\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.24578 | 2.62289 | ||||||||
\(5\) | −3.62847 | −1.62270 | −0.811351 | − | 0.584559i | \(-0.801268\pi\) | ||||
−0.811351 | + | 0.584559i | \(0.801268\pi\) | |||||||
\(6\) | −2.69180 | −1.09892 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.73699 | −3.08899 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 9.76712 | 3.08863 | ||||||||
\(11\) | 3.79578 | 1.14447 | 0.572235 | − | 0.820090i | \(-0.306077\pi\) | ||||
0.572235 | + | 0.820090i | \(0.306077\pi\) | |||||||
\(12\) | 5.24578 | 1.51433 | ||||||||
\(13\) | 0.986924 | 0.273723 | 0.136862 | − | 0.990590i | \(-0.456298\pi\) | ||||
0.136862 | + | 0.990590i | \(0.456298\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.62847 | −0.936868 | ||||||||
\(16\) | 13.0267 | 3.25666 | ||||||||
\(17\) | 1.05753 | 0.256488 | 0.128244 | − | 0.991743i | \(-0.459066\pi\) | ||||
0.128244 | + | 0.991743i | \(0.459066\pi\) | |||||||
\(18\) | −2.69180 | −0.634463 | ||||||||
\(19\) | −2.81023 | −0.644711 | −0.322355 | − | 0.946619i | \(-0.604475\pi\) | ||||
−0.322355 | + | 0.946619i | \(0.604475\pi\) | |||||||
\(20\) | −19.0342 | −4.25617 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.2175 | −2.17837 | ||||||||
\(23\) | −5.66437 | −1.18110 | −0.590551 | − | 0.807000i | \(-0.701090\pi\) | ||||
−0.590551 | + | 0.807000i | \(0.701090\pi\) | |||||||
\(24\) | −8.73699 | −1.78343 | ||||||||
\(25\) | 8.16582 | 1.63316 | ||||||||
\(26\) | −2.65660 | −0.521002 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.21857 | −0.411977 | −0.205989 | − | 0.978554i | \(-0.566041\pi\) | ||||
−0.205989 | + | 0.978554i | \(0.566041\pi\) | |||||||
\(30\) | 9.76712 | 1.78322 | ||||||||
\(31\) | 10.4547 | 1.87773 | 0.938863 | − | 0.344291i | \(-0.111881\pi\) | ||||
0.938863 | + | 0.344291i | \(0.111881\pi\) | |||||||
\(32\) | −17.5912 | −3.10971 | ||||||||
\(33\) | 3.79578 | 0.660760 | ||||||||
\(34\) | −2.84664 | −0.488196 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.24578 | 0.874297 | ||||||||
\(37\) | −7.86953 | −1.29374 | −0.646871 | − | 0.762599i | \(-0.723923\pi\) | ||||
−0.646871 | + | 0.762599i | \(0.723923\pi\) | |||||||
\(38\) | 7.56457 | 1.22714 | ||||||||
\(39\) | 0.986924 | 0.158034 | ||||||||
\(40\) | 31.7019 | 5.01251 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.16152 | 0.634625 | 0.317313 | − | 0.948321i | \(-0.397220\pi\) | ||||
0.317313 | + | 0.948321i | \(0.397220\pi\) | |||||||
\(44\) | 19.9118 | 3.00182 | ||||||||
\(45\) | −3.62847 | −0.540901 | ||||||||
\(46\) | 15.2473 | 2.24810 | ||||||||
\(47\) | −5.08902 | −0.742309 | −0.371155 | − | 0.928571i | \(-0.621038\pi\) | ||||
−0.371155 | + | 0.928571i | \(0.621038\pi\) | |||||||
\(48\) | 13.0267 | 1.88024 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −21.9807 | −3.10854 | ||||||||
\(51\) | 1.05753 | 0.148083 | ||||||||
\(52\) | 5.17719 | 0.717946 | ||||||||
\(53\) | −9.17461 | −1.26023 | −0.630115 | − | 0.776502i | \(-0.716992\pi\) | ||||
−0.630115 | + | 0.776502i | \(0.716992\pi\) | |||||||
\(54\) | −2.69180 | −0.366307 | ||||||||
\(55\) | −13.7729 | −1.85713 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.81023 | −0.372224 | ||||||||
\(58\) | 5.97193 | 0.784153 | ||||||||
\(59\) | −7.58471 | −0.987446 | −0.493723 | − | 0.869619i | \(-0.664364\pi\) | ||||
−0.493723 | + | 0.869619i | \(0.664364\pi\) | |||||||
\(60\) | −19.0342 | −2.45730 | ||||||||
\(61\) | 5.96328 | 0.763520 | 0.381760 | − | 0.924262i | \(-0.375318\pi\) | ||||
0.381760 | + | 0.924262i | \(0.375318\pi\) | |||||||
\(62\) | −28.1420 | −3.57404 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 21.2985 | 2.66232 | ||||||||
\(65\) | −3.58103 | −0.444172 | ||||||||
\(66\) | −10.2175 | −1.25768 | ||||||||
\(67\) | −15.6363 | −1.91027 | −0.955137 | − | 0.296165i | \(-0.904292\pi\) | ||||
−0.955137 | + | 0.296165i | \(0.904292\pi\) | |||||||
\(68\) | 5.54754 | 0.672739 | ||||||||
\(69\) | −5.66437 | −0.681909 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.6213 | 1.37920 | 0.689600 | − | 0.724190i | \(-0.257786\pi\) | ||||
0.689600 | + | 0.724190i | \(0.257786\pi\) | |||||||
\(72\) | −8.73699 | −1.02966 | ||||||||
\(73\) | −3.75487 | −0.439475 | −0.219737 | − | 0.975559i | \(-0.570520\pi\) | ||||
−0.219737 | + | 0.975559i | \(0.570520\pi\) | |||||||
\(74\) | 21.1832 | 2.46250 | ||||||||
\(75\) | 8.16582 | 0.942907 | ||||||||
\(76\) | −14.7418 | −1.69101 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.65660 | −0.300801 | ||||||||
\(79\) | −4.83413 | −0.543883 | −0.271941 | − | 0.962314i | \(-0.587666\pi\) | ||||
−0.271941 | + | 0.962314i | \(0.587666\pi\) | |||||||
\(80\) | −47.2669 | −5.28460 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.69180 | −0.297259 | ||||||||
\(83\) | 7.04509 | 0.773299 | 0.386649 | − | 0.922227i | \(-0.373632\pi\) | ||||
0.386649 | + | 0.922227i | \(0.373632\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.83720 | −0.416203 | ||||||||
\(86\) | −11.2020 | −1.20794 | ||||||||
\(87\) | −2.21857 | −0.237855 | ||||||||
\(88\) | −33.1637 | −3.53526 | ||||||||
\(89\) | 9.53384 | 1.01059 | 0.505293 | − | 0.862948i | \(-0.331385\pi\) | ||||
0.505293 | + | 0.862948i | \(0.331385\pi\) | |||||||
\(90\) | 9.76712 | 1.02954 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −29.7140 | −3.09790 | ||||||||
\(93\) | 10.4547 | 1.08411 | ||||||||
\(94\) | 13.6986 | 1.41290 | ||||||||
\(95\) | 10.1968 | 1.04617 | ||||||||
\(96\) | −17.5912 | −1.79539 | ||||||||
\(97\) | 14.2834 | 1.45026 | 0.725130 | − | 0.688612i | \(-0.241779\pi\) | ||||
0.725130 | + | 0.688612i | \(0.241779\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.79578 | 0.381490 | ||||||||
\(100\) | 42.8361 | 4.28361 | ||||||||
\(101\) | 1.27838 | 0.127203 | 0.0636017 | − | 0.997975i | \(-0.479741\pi\) | ||||
0.0636017 | + | 0.997975i | \(0.479741\pi\) | |||||||
\(102\) | −2.84664 | −0.281860 | ||||||||
\(103\) | 11.9906 | 1.18147 | 0.590737 | − | 0.806864i | \(-0.298837\pi\) | ||||
0.590737 | + | 0.806864i | \(0.298837\pi\) | |||||||
\(104\) | −8.62274 | −0.845529 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.6962 | 2.39871 | ||||||||
\(107\) | −18.0089 | −1.74098 | −0.870491 | − | 0.492185i | \(-0.836198\pi\) | ||||
−0.870491 | + | 0.492185i | \(0.836198\pi\) | |||||||
\(108\) | 5.24578 | 0.504775 | ||||||||
\(109\) | −14.0107 | −1.34198 | −0.670992 | − | 0.741464i | \(-0.734132\pi\) | ||||
−0.670992 | + | 0.741464i | \(0.734132\pi\) | |||||||
\(110\) | 37.0738 | 3.53485 | ||||||||
\(111\) | −7.86953 | −0.746943 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.5638 | 1.27597 | 0.637986 | − | 0.770048i | \(-0.279768\pi\) | ||||
0.637986 | + | 0.770048i | \(0.279768\pi\) | |||||||
\(114\) | 7.56457 | 0.708487 | ||||||||
\(115\) | 20.5530 | 1.91658 | ||||||||
\(116\) | −11.6381 | −1.08057 | ||||||||
\(117\) | 0.986924 | 0.0912411 | ||||||||
\(118\) | 20.4165 | 1.87949 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 31.7019 | 2.89398 | ||||||||
\(121\) | 3.40793 | 0.309812 | ||||||||
\(122\) | −16.0519 | −1.45328 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 54.8433 | 4.92507 | ||||||||
\(125\) | −11.4871 | −1.02744 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.6460 | 1.12215 | 0.561076 | − | 0.827764i | \(-0.310387\pi\) | ||||
0.561076 | + | 0.827764i | \(0.310387\pi\) | |||||||
\(128\) | −22.1491 | −1.95772 | ||||||||
\(129\) | 4.16152 | 0.366401 | ||||||||
\(130\) | 9.63940 | 0.845431 | ||||||||
\(131\) | 21.8687 | 1.91068 | 0.955340 | − | 0.295509i | \(-0.0954893\pi\) | ||||
0.955340 | + | 0.295509i | \(0.0954893\pi\) | |||||||
\(132\) | 19.9118 | 1.73310 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 42.0897 | 3.63599 | ||||||||
\(135\) | −3.62847 | −0.312289 | ||||||||
\(136\) | −9.23959 | −0.792288 | ||||||||
\(137\) | −4.28037 | −0.365697 | −0.182848 | − | 0.983141i | \(-0.558532\pi\) | ||||
−0.182848 | + | 0.983141i | \(0.558532\pi\) | |||||||
\(138\) | 15.2473 | 1.29794 | ||||||||
\(139\) | 0.0145030 | 0.00123013 | 0.000615064 | − | 1.00000i | \(-0.499804\pi\) | ||||
0.000615064 | 1.00000i | \(0.499804\pi\) | ||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.08902 | −0.428572 | ||||||||
\(142\) | −31.2823 | −2.62515 | ||||||||
\(143\) | 3.74614 | 0.313268 | ||||||||
\(144\) | 13.0267 | 1.08555 | ||||||||
\(145\) | 8.05001 | 0.668517 | ||||||||
\(146\) | 10.1074 | 0.836491 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −41.2818 | −3.39335 | ||||||||
\(149\) | −14.7596 | −1.20915 | −0.604577 | − | 0.796547i | \(-0.706658\pi\) | ||||
−0.604577 | + | 0.796547i | \(0.706658\pi\) | |||||||
\(150\) | −21.9807 | −1.79472 | ||||||||
\(151\) | −6.86221 | −0.558438 | −0.279219 | − | 0.960227i | \(-0.590076\pi\) | ||||
−0.279219 | + | 0.960227i | \(0.590076\pi\) | |||||||
\(152\) | 24.5529 | 1.99151 | ||||||||
\(153\) | 1.05753 | 0.0854958 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −37.9347 | −3.04699 | ||||||||
\(156\) | 5.17719 | 0.414507 | ||||||||
\(157\) | 4.17576 | 0.333262 | 0.166631 | − | 0.986019i | \(-0.446711\pi\) | ||||
0.166631 | + | 0.986019i | \(0.446711\pi\) | |||||||
\(158\) | 13.0125 | 1.03522 | ||||||||
\(159\) | −9.17461 | −0.727594 | ||||||||
\(160\) | 63.8290 | 5.04613 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.69180 | −0.211488 | ||||||||
\(163\) | −23.5210 | −1.84231 | −0.921155 | − | 0.389195i | \(-0.872753\pi\) | ||||
−0.921155 | + | 0.389195i | \(0.872753\pi\) | |||||||
\(164\) | 5.24578 | 0.409627 | ||||||||
\(165\) | −13.7729 | −1.07222 | ||||||||
\(166\) | −18.9640 | −1.47189 | ||||||||
\(167\) | −15.7070 | −1.21544 | −0.607722 | − | 0.794150i | \(-0.707917\pi\) | ||||
−0.607722 | + | 0.794150i | \(0.707917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0260 | −0.925076 | ||||||||
\(170\) | 10.3290 | 0.792196 | ||||||||
\(171\) | −2.81023 | −0.214904 | ||||||||
\(172\) | 21.8304 | 1.66455 | ||||||||
\(173\) | −5.89269 | −0.448013 | −0.224006 | − | 0.974588i | \(-0.571914\pi\) | ||||
−0.224006 | + | 0.974588i | \(0.571914\pi\) | |||||||
\(174\) | 5.97193 | 0.452731 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 49.4463 | 3.72715 | ||||||||
\(177\) | −7.58471 | −0.570102 | ||||||||
\(178\) | −25.6632 | −1.92354 | ||||||||
\(179\) | 4.67222 | 0.349218 | 0.174609 | − | 0.984638i | \(-0.444134\pi\) | ||||
0.174609 | + | 0.984638i | \(0.444134\pi\) | |||||||
\(180\) | −19.0342 | −1.41872 | ||||||||
\(181\) | −13.2354 | −0.983776 | −0.491888 | − | 0.870658i | \(-0.663693\pi\) | ||||
−0.491888 | + | 0.870658i | \(0.663693\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.96328 | 0.440818 | ||||||||
\(184\) | 49.4895 | 3.64841 | ||||||||
\(185\) | 28.5544 | 2.09936 | ||||||||
\(186\) | −28.1420 | −2.06348 | ||||||||
\(187\) | 4.01413 | 0.293542 | ||||||||
\(188\) | −26.6959 | −1.94700 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −27.4478 | −1.99127 | ||||||||
\(191\) | 18.4336 | 1.33381 | 0.666903 | − | 0.745145i | \(-0.267620\pi\) | ||||
0.666903 | + | 0.745145i | \(0.267620\pi\) | |||||||
\(192\) | 21.2985 | 1.53709 | ||||||||
\(193\) | 11.4648 | 0.825254 | 0.412627 | − | 0.910900i | \(-0.364611\pi\) | ||||
0.412627 | + | 0.910900i | \(0.364611\pi\) | |||||||
\(194\) | −38.4481 | −2.76041 | ||||||||
\(195\) | −3.58103 | −0.256443 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.88305 | 0.205408 | 0.102704 | − | 0.994712i | \(-0.467250\pi\) | ||||
0.102704 | + | 0.994712i | \(0.467250\pi\) | |||||||
\(198\) | −10.2175 | −0.726124 | ||||||||
\(199\) | 18.6674 | 1.32330 | 0.661650 | − | 0.749813i | \(-0.269856\pi\) | ||||
0.661650 | + | 0.749813i | \(0.269856\pi\) | |||||||
\(200\) | −71.3446 | −5.04483 | ||||||||
\(201\) | −15.6363 | −1.10290 | ||||||||
\(202\) | −3.44114 | −0.242118 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.54754 | 0.388406 | ||||||||
\(205\) | −3.62847 | −0.253424 | ||||||||
\(206\) | −32.2764 | −2.24880 | ||||||||
\(207\) | −5.66437 | −0.393701 | ||||||||
\(208\) | 12.8563 | 0.891425 | ||||||||
\(209\) | −10.6670 | −0.737852 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.09415 | −0.213010 | −0.106505 | − | 0.994312i | \(-0.533966\pi\) | ||||
−0.106505 | + | 0.994312i | \(0.533966\pi\) | |||||||
\(212\) | −48.1280 | −3.30544 | ||||||||
\(213\) | 11.6213 | 0.796282 | ||||||||
\(214\) | 48.4762 | 3.31377 | ||||||||
\(215\) | −15.1000 | −1.02981 | ||||||||
\(216\) | −8.73699 | −0.594477 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 37.7141 | 2.55432 | ||||||||
\(219\) | −3.75487 | −0.253731 | ||||||||
\(220\) | −72.2495 | −4.87106 | ||||||||
\(221\) | 1.04370 | 0.0702066 | ||||||||
\(222\) | 21.1832 | 1.42172 | ||||||||
\(223\) | 20.2026 | 1.35286 | 0.676432 | − | 0.736505i | \(-0.263525\pi\) | ||||
0.676432 | + | 0.736505i | \(0.263525\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.16582 | 0.544388 | ||||||||
\(226\) | −36.5109 | −2.42867 | ||||||||
\(227\) | −23.1892 | −1.53912 | −0.769559 | − | 0.638575i | \(-0.779524\pi\) | ||||
−0.769559 | + | 0.638575i | \(0.779524\pi\) | |||||||
\(228\) | −14.7418 | −0.976302 | ||||||||
\(229\) | −14.8334 | −0.980219 | −0.490109 | − | 0.871661i | \(-0.663043\pi\) | ||||
−0.490109 | + | 0.871661i | \(0.663043\pi\) | |||||||
\(230\) | −55.3245 | −3.64799 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.3836 | 1.27259 | ||||||||
\(233\) | 23.8864 | 1.56485 | 0.782426 | − | 0.622744i | \(-0.213982\pi\) | ||||
0.782426 | + | 0.622744i | \(0.213982\pi\) | |||||||
\(234\) | −2.65660 | −0.173667 | ||||||||
\(235\) | 18.4654 | 1.20455 | ||||||||
\(236\) | −39.7877 | −2.58996 | ||||||||
\(237\) | −4.83413 | −0.314011 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.1844 | 1.11156 | 0.555782 | − | 0.831328i | \(-0.312419\pi\) | ||||
0.555782 | + | 0.831328i | \(0.312419\pi\) | |||||||
\(240\) | −47.2669 | −3.05106 | ||||||||
\(241\) | 6.16967 | 0.397423 | 0.198712 | − | 0.980058i | \(-0.436324\pi\) | ||||
0.198712 | + | 0.980058i | \(0.436324\pi\) | |||||||
\(242\) | −9.17345 | −0.589692 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 31.2821 | 2.00263 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.69180 | −0.171623 | ||||||||
\(247\) | −2.77348 | −0.176472 | ||||||||
\(248\) | −91.3429 | −5.80028 | ||||||||
\(249\) | 7.04509 | 0.446464 | ||||||||
\(250\) | 30.9209 | 1.95561 | ||||||||
\(251\) | −21.2207 | −1.33944 | −0.669720 | − | 0.742614i | \(-0.733586\pi\) | ||||
−0.669720 | + | 0.742614i | \(0.733586\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.5007 | −1.35174 | ||||||||
\(254\) | −34.0405 | −2.13589 | ||||||||
\(255\) | −3.83720 | −0.240295 | ||||||||
\(256\) | 17.0238 | 1.06399 | ||||||||
\(257\) | 23.2708 | 1.45159 | 0.725796 | − | 0.687910i | \(-0.241472\pi\) | ||||
0.725796 | + | 0.687910i | \(0.241472\pi\) | |||||||
\(258\) | −11.2020 | −0.697404 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −18.7853 | −1.16501 | ||||||||
\(261\) | −2.21857 | −0.137326 | ||||||||
\(262\) | −58.8662 | −3.63677 | ||||||||
\(263\) | −30.5369 | −1.88299 | −0.941493 | − | 0.337033i | \(-0.890577\pi\) | ||||
−0.941493 | + | 0.337033i | \(0.890577\pi\) | |||||||
\(264\) | −33.1637 | −2.04108 | ||||||||
\(265\) | 33.2898 | 2.04498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.53384 | 0.583462 | ||||||||
\(268\) | −82.0244 | −5.01044 | ||||||||
\(269\) | −4.54700 | −0.277235 | −0.138618 | − | 0.990346i | \(-0.544266\pi\) | ||||
−0.138618 | + | 0.990346i | \(0.544266\pi\) | |||||||
\(270\) | 9.76712 | 0.594408 | ||||||||
\(271\) | −21.0582 | −1.27919 | −0.639597 | − | 0.768711i | \(-0.720899\pi\) | ||||
−0.639597 | + | 0.768711i | \(0.720899\pi\) | |||||||
\(272\) | 13.7760 | 0.835294 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.5219 | 0.696063 | ||||||||
\(275\) | 30.9956 | 1.86911 | ||||||||
\(276\) | −29.7140 | −1.78857 | ||||||||
\(277\) | −1.16773 | −0.0701620 | −0.0350810 | − | 0.999384i | \(-0.511169\pi\) | ||||
−0.0350810 | + | 0.999384i | \(0.511169\pi\) | |||||||
\(278\) | −0.0390392 | −0.00234141 | ||||||||
\(279\) | 10.4547 | 0.625909 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.8177 | −1.00326 | −0.501631 | − | 0.865082i | \(-0.667266\pi\) | ||||
−0.501631 | + | 0.865082i | \(0.667266\pi\) | |||||||
\(282\) | 13.6986 | 0.815740 | ||||||||
\(283\) | 32.2924 | 1.91958 | 0.959791 | − | 0.280715i | \(-0.0905717\pi\) | ||||
0.959791 | + | 0.280715i | \(0.0905717\pi\) | |||||||
\(284\) | 60.9630 | 3.61749 | ||||||||
\(285\) | 10.1968 | 0.604008 | ||||||||
\(286\) | −10.0839 | −0.596271 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −17.5912 | −1.03657 | ||||||||
\(289\) | −15.8816 | −0.934214 | ||||||||
\(290\) | −21.6690 | −1.27245 | ||||||||
\(291\) | 14.2834 | 0.837309 | ||||||||
\(292\) | −19.6972 | −1.15269 | ||||||||
\(293\) | −22.4014 | −1.30871 | −0.654353 | − | 0.756189i | \(-0.727059\pi\) | ||||
−0.654353 | + | 0.756189i | \(0.727059\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.5209 | 1.60233 | ||||||||
\(296\) | 68.7560 | 3.99636 | ||||||||
\(297\) | 3.79578 | 0.220253 | ||||||||
\(298\) | 39.7299 | 2.30149 | ||||||||
\(299\) | −5.59030 | −0.323295 | ||||||||
\(300\) | 42.8361 | 2.47314 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.4717 | 1.06293 | ||||||||
\(303\) | 1.27838 | 0.0734409 | ||||||||
\(304\) | −36.6079 | −2.09961 | ||||||||
\(305\) | −21.6376 | −1.23897 | ||||||||
\(306\) | −2.84664 | −0.162732 | ||||||||
\(307\) | −15.5675 | −0.888481 | −0.444241 | − | 0.895907i | \(-0.646526\pi\) | ||||
−0.444241 | + | 0.895907i | \(0.646526\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.9906 | 0.682124 | ||||||||
\(310\) | 102.113 | 5.79961 | ||||||||
\(311\) | −20.2286 | −1.14706 | −0.573531 | − | 0.819184i | \(-0.694427\pi\) | ||||
−0.573531 | + | 0.819184i | \(0.694427\pi\) | |||||||
\(312\) | −8.62274 | −0.488167 | ||||||||
\(313\) | −13.2244 | −0.747490 | −0.373745 | − | 0.927532i | \(-0.621926\pi\) | ||||
−0.373745 | + | 0.927532i | \(0.621926\pi\) | |||||||
\(314\) | −11.2403 | −0.634328 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −25.3588 | −1.42654 | ||||||||
\(317\) | −17.4307 | −0.979004 | −0.489502 | − | 0.872002i | \(-0.662821\pi\) | ||||
−0.489502 | + | 0.872002i | \(0.662821\pi\) | |||||||
\(318\) | 24.6962 | 1.38489 | ||||||||
\(319\) | −8.42118 | −0.471496 | ||||||||
\(320\) | −77.2812 | −4.32015 | ||||||||
\(321\) | −18.0089 | −1.00516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.97189 | −0.165360 | ||||||||
\(324\) | 5.24578 | 0.291432 | ||||||||
\(325\) | 8.05904 | 0.447035 | ||||||||
\(326\) | 63.3139 | 3.50663 | ||||||||
\(327\) | −14.0107 | −0.774795 | ||||||||
\(328\) | −8.73699 | −0.482420 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 37.0738 | 2.04085 | ||||||||
\(331\) | 20.7539 | 1.14074 | 0.570369 | − | 0.821389i | \(-0.306800\pi\) | ||||
0.570369 | + | 0.821389i | \(0.306800\pi\) | |||||||
\(332\) | 36.9570 | 2.02828 | ||||||||
\(333\) | −7.86953 | −0.431248 | ||||||||
\(334\) | 42.2801 | 2.31346 | ||||||||
\(335\) | 56.7358 | 3.09981 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.56654 | −0.194282 | −0.0971409 | − | 0.995271i | \(-0.530970\pi\) | ||||
−0.0971409 | + | 0.995271i | \(0.530970\pi\) | |||||||
\(338\) | 32.3715 | 1.76078 | ||||||||
\(339\) | 13.5638 | 0.736682 | ||||||||
\(340\) | −20.1291 | −1.09165 | ||||||||
\(341\) | 39.6839 | 2.14900 | ||||||||
\(342\) | 7.56457 | 0.409045 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −36.3591 | −1.96035 | ||||||||
\(345\) | 20.5530 | 1.10654 | ||||||||
\(346\) | 15.8619 | 0.852743 | ||||||||
\(347\) | 11.9328 | 0.640586 | 0.320293 | − | 0.947319i | \(-0.396219\pi\) | ||||
0.320293 | + | 0.947319i | \(0.396219\pi\) | |||||||
\(348\) | −11.6381 | −0.623868 | ||||||||
\(349\) | −6.91055 | −0.369913 | −0.184957 | − | 0.982747i | \(-0.559214\pi\) | ||||
−0.184957 | + | 0.982747i | \(0.559214\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.986924 | 0.0526781 | ||||||||
\(352\) | −66.7721 | −3.55897 | ||||||||
\(353\) | 3.75498 | 0.199858 | 0.0999288 | − | 0.994995i | \(-0.468139\pi\) | ||||
0.0999288 | + | 0.994995i | \(0.468139\pi\) | |||||||
\(354\) | 20.4165 | 1.08513 | ||||||||
\(355\) | −42.1677 | −2.23803 | ||||||||
\(356\) | 50.0125 | 2.65066 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.5767 | −0.664698 | ||||||||
\(359\) | 9.38283 | 0.495207 | 0.247603 | − | 0.968861i | \(-0.420357\pi\) | ||||
0.247603 | + | 0.968861i | \(0.420357\pi\) | |||||||
\(360\) | 31.7019 | 1.67084 | ||||||||
\(361\) | −11.1026 | −0.584348 | ||||||||
\(362\) | 35.6269 | 1.87251 | ||||||||
\(363\) | 3.40793 | 0.178870 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.6245 | 0.713136 | ||||||||
\(366\) | −16.0519 | −0.839049 | ||||||||
\(367\) | −26.7028 | −1.39388 | −0.696938 | − | 0.717132i | \(-0.745455\pi\) | ||||
−0.696938 | + | 0.717132i | \(0.745455\pi\) | |||||||
\(368\) | −73.7877 | −3.84645 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −76.8626 | −3.99590 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 54.8433 | 2.84349 | ||||||||
\(373\) | 6.05227 | 0.313375 | 0.156687 | − | 0.987648i | \(-0.449919\pi\) | ||||
0.156687 | + | 0.987648i | \(0.449919\pi\) | |||||||
\(374\) | −10.8052 | −0.558725 | ||||||||
\(375\) | −11.4871 | −0.593190 | ||||||||
\(376\) | 44.4627 | 2.29299 | ||||||||
\(377\) | −2.18956 | −0.112768 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.68737 | −0.240774 | −0.120387 | − | 0.992727i | \(-0.538414\pi\) | ||||
−0.120387 | + | 0.992727i | \(0.538414\pi\) | |||||||
\(380\) | 53.4904 | 2.74400 | ||||||||
\(381\) | 12.6460 | 0.647875 | ||||||||
\(382\) | −49.6194 | −2.53875 | ||||||||
\(383\) | −34.5205 | −1.76391 | −0.881957 | − | 0.471330i | \(-0.843774\pi\) | ||||
−0.881957 | + | 0.471330i | \(0.843774\pi\) | |||||||
\(384\) | −22.1491 | −1.13029 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −30.8609 | −1.57078 | ||||||||
\(387\) | 4.16152 | 0.211542 | ||||||||
\(388\) | 74.9277 | 3.80388 | ||||||||
\(389\) | 1.71421 | 0.0869137 | 0.0434569 | − | 0.999055i | \(-0.486163\pi\) | ||||
0.0434569 | + | 0.999055i | \(0.486163\pi\) | |||||||
\(390\) | 9.63940 | 0.488110 | ||||||||
\(391\) | −5.99021 | −0.302938 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.8687 | 1.10313 | ||||||||
\(394\) | −7.76058 | −0.390972 | ||||||||
\(395\) | 17.5405 | 0.882560 | ||||||||
\(396\) | 19.9118 | 1.00061 | ||||||||
\(397\) | 14.5925 | 0.732377 | 0.366189 | − | 0.930541i | \(-0.380662\pi\) | ||||
0.366189 | + | 0.930541i | \(0.380662\pi\) | |||||||
\(398\) | −50.2490 | −2.51876 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 106.373 | 5.31866 | ||||||||
\(401\) | 10.9102 | 0.544829 | 0.272415 | − | 0.962180i | \(-0.412178\pi\) | ||||
0.272415 | + | 0.962180i | \(0.412178\pi\) | |||||||
\(402\) | 42.0897 | 2.09924 | ||||||||
\(403\) | 10.3180 | 0.513978 | ||||||||
\(404\) | 6.70609 | 0.333641 | ||||||||
\(405\) | −3.62847 | −0.180300 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.8710 | −1.48065 | ||||||||
\(408\) | −9.23959 | −0.457428 | ||||||||
\(409\) | −14.5454 | −0.719224 | −0.359612 | − | 0.933102i | \(-0.617091\pi\) | ||||
−0.359612 | + | 0.933102i | \(0.617091\pi\) | |||||||
\(410\) | 9.76712 | 0.482364 | ||||||||
\(411\) | −4.28037 | −0.211135 | ||||||||
\(412\) | 62.9003 | 3.09888 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 15.2473 | 0.749365 | ||||||||
\(415\) | −25.5629 | −1.25483 | ||||||||
\(416\) | −17.3611 | −0.851199 | ||||||||
\(417\) | 0.0145030 | 0.000710215 0 | ||||||||
\(418\) | 28.7134 | 1.40442 | ||||||||
\(419\) | −18.6549 | −0.911353 | −0.455676 | − | 0.890146i | \(-0.650603\pi\) | ||||
−0.455676 | + | 0.890146i | \(0.650603\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.2812 | −1.47582 | −0.737909 | − | 0.674900i | \(-0.764187\pi\) | ||||
−0.737909 | + | 0.674900i | \(0.764187\pi\) | |||||||
\(422\) | 8.32884 | 0.405441 | ||||||||
\(423\) | −5.08902 | −0.247436 | ||||||||
\(424\) | 80.1584 | 3.89284 | ||||||||
\(425\) | 8.63555 | 0.418886 | ||||||||
\(426\) | −31.2823 | −1.51563 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −94.4705 | −4.56640 | ||||||||
\(429\) | 3.74614 | 0.180865 | ||||||||
\(430\) | 40.6460 | 1.96013 | ||||||||
\(431\) | 12.4541 | 0.599895 | 0.299948 | − | 0.953956i | \(-0.403031\pi\) | ||||
0.299948 | + | 0.953956i | \(0.403031\pi\) | |||||||
\(432\) | 13.0267 | 0.626745 | ||||||||
\(433\) | −6.80377 | −0.326968 | −0.163484 | − | 0.986546i | \(-0.552273\pi\) | ||||
−0.163484 | + | 0.986546i | \(0.552273\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.05001 | 0.385968 | ||||||||
\(436\) | −73.4972 | −3.51988 | ||||||||
\(437\) | 15.9182 | 0.761469 | ||||||||
\(438\) | 10.1074 | 0.482948 | ||||||||
\(439\) | −23.6472 | −1.12862 | −0.564310 | − | 0.825563i | \(-0.690858\pi\) | ||||
−0.564310 | + | 0.825563i | \(0.690858\pi\) | |||||||
\(440\) | 120.333 | 5.73667 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.80942 | −0.133631 | ||||||||
\(443\) | 14.4599 | 0.687009 | 0.343505 | − | 0.939151i | \(-0.388386\pi\) | ||||
0.343505 | + | 0.939151i | \(0.388386\pi\) | |||||||
\(444\) | −41.2818 | −1.95915 | ||||||||
\(445\) | −34.5933 | −1.63988 | ||||||||
\(446\) | −54.3812 | −2.57503 | ||||||||
\(447\) | −14.7596 | −0.698105 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.7644 | −0.696777 | −0.348388 | − | 0.937350i | \(-0.613271\pi\) | ||||
−0.348388 | + | 0.937350i | \(0.613271\pi\) | |||||||
\(450\) | −21.9807 | −1.03618 | ||||||||
\(451\) | 3.79578 | 0.178736 | ||||||||
\(452\) | 71.1525 | 3.34673 | ||||||||
\(453\) | −6.86221 | −0.322415 | ||||||||
\(454\) | 62.4205 | 2.92954 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 24.5529 | 1.14980 | ||||||||
\(457\) | −7.93084 | −0.370989 | −0.185495 | − | 0.982645i | \(-0.559389\pi\) | ||||
−0.185495 | + | 0.982645i | \(0.559389\pi\) | |||||||
\(458\) | 39.9285 | 1.86574 | ||||||||
\(459\) | 1.05753 | 0.0493610 | ||||||||
\(460\) | 107.817 | 5.02697 | ||||||||
\(461\) | 9.83013 | 0.457835 | 0.228917 | − | 0.973446i | \(-0.426481\pi\) | ||||
0.228917 | + | 0.973446i | \(0.426481\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.47631 | −0.300980 | −0.150490 | − | 0.988612i | \(-0.548085\pi\) | ||||
−0.150490 | + | 0.988612i | \(0.548085\pi\) | |||||||
\(464\) | −28.9005 | −1.34167 | ||||||||
\(465\) | −37.9347 | −1.75918 | ||||||||
\(466\) | −64.2975 | −2.97852 | ||||||||
\(467\) | 2.17951 | 0.100856 | 0.0504278 | − | 0.998728i | \(-0.483942\pi\) | ||||
0.0504278 | + | 0.998728i | \(0.483942\pi\) | |||||||
\(468\) | 5.17719 | 0.239315 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −49.7050 | −2.29272 | ||||||||
\(471\) | 4.17576 | 0.192409 | ||||||||
\(472\) | 66.2676 | 3.05021 | ||||||||
\(473\) | 15.7962 | 0.726310 | ||||||||
\(474\) | 13.0125 | 0.597685 | ||||||||
\(475\) | −22.9478 | −1.05292 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.17461 | −0.420076 | ||||||||
\(478\) | −46.2569 | −2.11574 | ||||||||
\(479\) | −23.3346 | −1.06619 | −0.533093 | − | 0.846057i | \(-0.678970\pi\) | ||||
−0.533093 | + | 0.846057i | \(0.678970\pi\) | |||||||
\(480\) | 63.8290 | 2.91338 | ||||||||
\(481\) | −7.76663 | −0.354128 | ||||||||
\(482\) | −16.6075 | −0.756451 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.8772 | 0.812602 | ||||||||
\(485\) | −51.8270 | −2.35334 | ||||||||
\(486\) | −2.69180 | −0.122102 | ||||||||
\(487\) | −0.181820 | −0.00823903 | −0.00411952 | − | 0.999992i | \(-0.501311\pi\) | ||||
−0.00411952 | + | 0.999992i | \(0.501311\pi\) | |||||||
\(488\) | −52.1011 | −2.35851 | ||||||||
\(489\) | −23.5210 | −1.06366 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.2932 | 0.870688 | 0.435344 | − | 0.900264i | \(-0.356627\pi\) | ||||
0.435344 | + | 0.900264i | \(0.356627\pi\) | |||||||
\(492\) | 5.24578 | 0.236498 | ||||||||
\(493\) | −2.34619 | −0.105667 | ||||||||
\(494\) | 7.46565 | 0.335896 | ||||||||
\(495\) | −13.7729 | −0.619045 | ||||||||
\(496\) | 136.190 | 6.11512 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −18.9640 | −0.849795 | ||||||||
\(499\) | 9.27958 | 0.415411 | 0.207706 | − | 0.978191i | \(-0.433400\pi\) | ||||
0.207706 | + | 0.978191i | \(0.433400\pi\) | |||||||
\(500\) | −60.2587 | −2.69485 | ||||||||
\(501\) | −15.7070 | −0.701737 | ||||||||
\(502\) | 57.1219 | 2.54948 | ||||||||
\(503\) | 19.7484 | 0.880537 | 0.440269 | − | 0.897866i | \(-0.354883\pi\) | ||||
0.440269 | + | 0.897866i | \(0.354883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.63856 | −0.206413 | ||||||||
\(506\) | 57.8755 | 2.57288 | ||||||||
\(507\) | −12.0260 | −0.534093 | ||||||||
\(508\) | 66.3383 | 2.94328 | ||||||||
\(509\) | 10.5926 | 0.469510 | 0.234755 | − | 0.972055i | \(-0.424571\pi\) | ||||
0.234755 | + | 0.972055i | \(0.424571\pi\) | |||||||
\(510\) | 10.3290 | 0.457375 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.52644 | −0.0674599 | ||||||||
\(513\) | −2.81023 | −0.124075 | ||||||||
\(514\) | −62.6403 | −2.76294 | ||||||||
\(515\) | −43.5077 | −1.91718 | ||||||||
\(516\) | 21.8304 | 0.961030 | ||||||||
\(517\) | −19.3168 | −0.849551 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.89269 | −0.258660 | ||||||||
\(520\) | 31.2874 | 1.37204 | ||||||||
\(521\) | 27.2068 | 1.19195 | 0.595976 | − | 0.803002i | \(-0.296765\pi\) | ||||
0.595976 | + | 0.803002i | \(0.296765\pi\) | |||||||
\(522\) | 5.97193 | 0.261384 | ||||||||
\(523\) | −43.2412 | −1.89081 | −0.945403 | − | 0.325904i | \(-0.894331\pi\) | ||||
−0.945403 | + | 0.325904i | \(0.894331\pi\) | |||||||
\(524\) | 114.719 | 5.01150 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 82.1992 | 3.58406 | ||||||||
\(527\) | 11.0561 | 0.481613 | ||||||||
\(528\) | 49.4463 | 2.15187 | ||||||||
\(529\) | 9.08504 | 0.395002 | ||||||||
\(530\) | −89.6095 | −3.89239 | ||||||||
\(531\) | −7.58471 | −0.329149 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.986924 | 0.0427484 | ||||||||
\(534\) | −25.6632 | −1.11055 | ||||||||
\(535\) | 65.3446 | 2.82510 | ||||||||
\(536\) | 136.614 | 5.90082 | ||||||||
\(537\) | 4.67222 | 0.201621 | ||||||||
\(538\) | 12.2396 | 0.527687 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −19.0342 | −0.819100 | ||||||||
\(541\) | 11.1859 | 0.480919 | 0.240459 | − | 0.970659i | \(-0.422702\pi\) | ||||
0.240459 | + | 0.970659i | \(0.422702\pi\) | |||||||
\(542\) | 56.6844 | 2.43480 | ||||||||
\(543\) | −13.2354 | −0.567983 | ||||||||
\(544\) | −18.6031 | −0.797601 | ||||||||
\(545\) | 50.8375 | 2.17764 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.4215 | 1.47176 | 0.735878 | − | 0.677115i | \(-0.236770\pi\) | ||||
0.735878 | + | 0.677115i | \(0.236770\pi\) | |||||||
\(548\) | −22.4539 | −0.959183 | ||||||||
\(549\) | 5.96328 | 0.254507 | ||||||||
\(550\) | −83.4340 | −3.55764 | ||||||||
\(551\) | 6.23468 | 0.265606 | ||||||||
\(552\) | 49.4895 | 2.10641 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.14329 | 0.133546 | ||||||||
\(555\) | 28.5544 | 1.21207 | ||||||||
\(556\) | 0.0760796 | 0.00322649 | ||||||||
\(557\) | 37.0851 | 1.57134 | 0.785672 | − | 0.618643i | \(-0.212317\pi\) | ||||
0.785672 | + | 0.618643i | \(0.212317\pi\) | |||||||
\(558\) | −28.1420 | −1.19135 | ||||||||
\(559\) | 4.10710 | 0.173712 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.01413 | 0.169477 | ||||||||
\(562\) | 45.2699 | 1.90960 | ||||||||
\(563\) | 0.795779 | 0.0335381 | 0.0167690 | − | 0.999859i | \(-0.494662\pi\) | ||||
0.0167690 | + | 0.999859i | \(0.494662\pi\) | |||||||
\(564\) | −26.6959 | −1.12410 | ||||||||
\(565\) | −49.2157 | −2.07052 | ||||||||
\(566\) | −86.9246 | −3.65371 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −101.536 | −4.26034 | ||||||||
\(569\) | 11.2518 | 0.471701 | 0.235850 | − | 0.971789i | \(-0.424212\pi\) | ||||
0.235850 | + | 0.971789i | \(0.424212\pi\) | |||||||
\(570\) | −27.4478 | −1.14966 | ||||||||
\(571\) | −39.0794 | −1.63542 | −0.817711 | − | 0.575629i | \(-0.804757\pi\) | ||||
−0.817711 | + | 0.575629i | \(0.804757\pi\) | |||||||
\(572\) | 19.6514 | 0.821668 | ||||||||
\(573\) | 18.4336 | 0.770073 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −46.2542 | −1.92893 | ||||||||
\(576\) | 21.2985 | 0.887439 | ||||||||
\(577\) | −11.3745 | −0.473527 | −0.236763 | − | 0.971567i | \(-0.576087\pi\) | ||||
−0.236763 | + | 0.971567i | \(0.576087\pi\) | |||||||
\(578\) | 42.7502 | 1.77817 | ||||||||
\(579\) | 11.4648 | 0.476461 | ||||||||
\(580\) | 42.2286 | 1.75345 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −38.4481 | −1.59372 | ||||||||
\(583\) | −34.8248 | −1.44229 | ||||||||
\(584\) | 32.8063 | 1.35753 | ||||||||
\(585\) | −3.58103 | −0.148057 | ||||||||
\(586\) | 60.3002 | 2.49098 | ||||||||
\(587\) | −1.19831 | −0.0494595 | −0.0247297 | − | 0.999694i | \(-0.507873\pi\) | ||||
−0.0247297 | + | 0.999694i | \(0.507873\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.3802 | −1.21059 | ||||||||
\(590\) | −74.0808 | −3.04986 | ||||||||
\(591\) | 2.88305 | 0.118593 | ||||||||
\(592\) | −102.514 | −4.21329 | ||||||||
\(593\) | 24.6608 | 1.01270 | 0.506349 | − | 0.862329i | \(-0.330995\pi\) | ||||
0.506349 | + | 0.862329i | \(0.330995\pi\) | |||||||
\(594\) | −10.2175 | −0.419228 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −77.4256 | −3.17148 | ||||||||
\(597\) | 18.6674 | 0.764008 | ||||||||
\(598\) | 15.0480 | 0.615357 | ||||||||
\(599\) | −25.4843 | −1.04126 | −0.520630 | − | 0.853783i | \(-0.674303\pi\) | ||||
−0.520630 | + | 0.853783i | \(0.674303\pi\) | |||||||
\(600\) | −71.3446 | −2.91263 | ||||||||
\(601\) | −0.495078 | −0.0201947 | −0.0100973 | − | 0.999949i | \(-0.503214\pi\) | ||||
−0.0100973 | + | 0.999949i | \(0.503214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.6363 | −0.636758 | ||||||||
\(604\) | −35.9976 | −1.46472 | ||||||||
\(605\) | −12.3656 | −0.502732 | ||||||||
\(606\) | −3.44114 | −0.139787 | ||||||||
\(607\) | −47.8430 | −1.94189 | −0.970943 | − | 0.239309i | \(-0.923079\pi\) | ||||
−0.970943 | + | 0.239309i | \(0.923079\pi\) | |||||||
\(608\) | 49.4352 | 2.00486 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 58.2441 | 2.35823 | ||||||||
\(611\) | −5.02247 | −0.203187 | ||||||||
\(612\) | 5.54754 | 0.224246 | ||||||||
\(613\) | −38.3710 | −1.54979 | −0.774895 | − | 0.632090i | \(-0.782197\pi\) | ||||
−0.774895 | + | 0.632090i | \(0.782197\pi\) | |||||||
\(614\) | 41.9044 | 1.69113 | ||||||||
\(615\) | −3.62847 | −0.146314 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.52594 | −0.383500 | −0.191750 | − | 0.981444i | \(-0.561416\pi\) | ||||
−0.191750 | + | 0.981444i | \(0.561416\pi\) | |||||||
\(618\) | −32.2764 | −1.29835 | ||||||||
\(619\) | −33.0989 | −1.33036 | −0.665179 | − | 0.746684i | \(-0.731645\pi\) | ||||
−0.665179 | + | 0.746684i | \(0.731645\pi\) | |||||||
\(620\) | −198.997 | −7.99192 | ||||||||
\(621\) | −5.66437 | −0.227303 | ||||||||
\(622\) | 54.4515 | 2.18330 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 12.8563 | 0.514665 | ||||||||
\(625\) | 0.851461 | 0.0340584 | ||||||||
\(626\) | 35.5976 | 1.42276 | ||||||||
\(627\) | −10.6670 | −0.425999 | ||||||||
\(628\) | 21.9051 | 0.874110 | ||||||||
\(629\) | −8.32223 | −0.331829 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.62134 | −0.303401 | −0.151700 | − | 0.988427i | \(-0.548475\pi\) | ||||
−0.151700 | + | 0.988427i | \(0.548475\pi\) | |||||||
\(632\) | 42.2358 | 1.68005 | ||||||||
\(633\) | −3.09415 | −0.122982 | ||||||||
\(634\) | 46.9199 | 1.86343 | ||||||||
\(635\) | −45.8857 | −1.82092 | ||||||||
\(636\) | −48.1280 | −1.90840 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.6681 | 0.897440 | ||||||||
\(639\) | 11.6213 | 0.459733 | ||||||||
\(640\) | 80.3673 | 3.17680 | ||||||||
\(641\) | −33.7943 | −1.33479 | −0.667397 | − | 0.744702i | \(-0.732592\pi\) | ||||
−0.667397 | + | 0.744702i | \(0.732592\pi\) | |||||||
\(642\) | 48.4762 | 1.91320 | ||||||||
\(643\) | 6.60324 | 0.260406 | 0.130203 | − | 0.991487i | \(-0.458437\pi\) | ||||
0.130203 | + | 0.991487i | \(0.458437\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.1000 | −0.594560 | ||||||||
\(646\) | 7.99972 | 0.314745 | ||||||||
\(647\) | −12.2008 | −0.479663 | −0.239832 | − | 0.970815i | \(-0.577092\pi\) | ||||
−0.239832 | + | 0.970815i | \(0.577092\pi\) | |||||||
\(648\) | −8.73699 | −0.343221 | ||||||||
\(649\) | −28.7899 | −1.13010 | ||||||||
\(650\) | −21.6933 | −0.850881 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −123.386 | −4.83218 | ||||||||
\(653\) | −37.3586 | −1.46195 | −0.730977 | − | 0.682402i | \(-0.760936\pi\) | ||||
−0.730977 | + | 0.682402i | \(0.760936\pi\) | |||||||
\(654\) | 37.7141 | 1.47474 | ||||||||
\(655\) | −79.3501 | −3.10046 | ||||||||
\(656\) | 13.0267 | 0.508605 | ||||||||
\(657\) | −3.75487 | −0.146492 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.0668 | 0.664829 | 0.332414 | − | 0.943133i | \(-0.392137\pi\) | ||||
0.332414 | + | 0.943133i | \(0.392137\pi\) | |||||||
\(660\) | −72.2495 | −2.81231 | ||||||||
\(661\) | 9.34986 | 0.363668 | 0.181834 | − | 0.983329i | \(-0.441797\pi\) | ||||
0.181834 | + | 0.983329i | \(0.441797\pi\) | |||||||
\(662\) | −55.8653 | −2.17127 | ||||||||
\(663\) | 1.04370 | 0.0405338 | ||||||||
\(664\) | −61.5528 | −2.38871 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 21.1832 | 0.820832 | ||||||||
\(667\) | 12.5668 | 0.486587 | ||||||||
\(668\) | −82.3955 | −3.18798 | ||||||||
\(669\) | 20.2026 | 0.781076 | ||||||||
\(670\) | −152.721 | −5.90014 | ||||||||
\(671\) | 22.6353 | 0.873825 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.36902 | 0.284055 | 0.142027 | − | 0.989863i | \(-0.454638\pi\) | ||||
0.142027 | + | 0.989863i | \(0.454638\pi\) | |||||||
\(674\) | 9.60040 | 0.369794 | ||||||||
\(675\) | 8.16582 | 0.314302 | ||||||||
\(676\) | −63.0857 | −2.42637 | ||||||||
\(677\) | 18.2593 | 0.701762 | 0.350881 | − | 0.936420i | \(-0.385882\pi\) | ||||
0.350881 | + | 0.936420i | \(0.385882\pi\) | |||||||
\(678\) | −36.5109 | −1.40219 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 33.5256 | 1.28565 | ||||||||
\(681\) | −23.1892 | −0.888610 | ||||||||
\(682\) | −106.821 | −4.09039 | ||||||||
\(683\) | 5.22095 | 0.199774 | 0.0998870 | − | 0.994999i | \(-0.468152\pi\) | ||||
0.0998870 | + | 0.994999i | \(0.468152\pi\) | |||||||
\(684\) | −14.7418 | −0.563668 | ||||||||
\(685\) | 15.5312 | 0.593417 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.8334 | −0.565929 | ||||||||
\(688\) | 54.2107 | 2.06676 | ||||||||
\(689\) | −9.05464 | −0.344954 | ||||||||
\(690\) | −55.3245 | −2.10617 | ||||||||
\(691\) | −1.84487 | −0.0701823 | −0.0350912 | − | 0.999384i | \(-0.511172\pi\) | ||||
−0.0350912 | + | 0.999384i | \(0.511172\pi\) | |||||||
\(692\) | −30.9117 | −1.17509 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.1207 | −1.21928 | ||||||||
\(695\) | −0.0526237 | −0.00199613 | ||||||||
\(696\) | 19.3836 | 0.734733 | ||||||||
\(697\) | 1.05753 | 0.0400566 | ||||||||
\(698\) | 18.6018 | 0.704089 | ||||||||
\(699\) | 23.8864 | 0.903468 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.6724 | −1.15848 | −0.579240 | − | 0.815157i | \(-0.696651\pi\) | ||||
−0.579240 | + | 0.815157i | \(0.696651\pi\) | |||||||
\(702\) | −2.65660 | −0.100267 | ||||||||
\(703\) | 22.1152 | 0.834090 | ||||||||
\(704\) | 80.8445 | 3.04694 | ||||||||
\(705\) | 18.4654 | 0.695446 | ||||||||
\(706\) | −10.1077 | −0.380407 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −39.7877 | −1.49531 | ||||||||
\(709\) | −29.3623 | −1.10273 | −0.551363 | − | 0.834266i | \(-0.685892\pi\) | ||||
−0.551363 | + | 0.834266i | \(0.685892\pi\) | |||||||
\(710\) | 113.507 | 4.25984 | ||||||||
\(711\) | −4.83413 | −0.181294 | ||||||||
\(712\) | −83.2971 | −3.12169 | ||||||||
\(713\) | −59.2195 | −2.21779 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.5928 | −0.508341 | ||||||||
\(716\) | 24.5094 | 0.915961 | ||||||||
\(717\) | 17.1844 | 0.641762 | ||||||||
\(718\) | −25.2567 | −0.942572 | ||||||||
\(719\) | 13.0625 | 0.487148 | 0.243574 | − | 0.969882i | \(-0.421680\pi\) | ||||
0.243574 | + | 0.969882i | \(0.421680\pi\) | |||||||
\(720\) | −47.2669 | −1.76153 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 29.8860 | 1.11224 | ||||||||
\(723\) | 6.16967 | 0.229452 | ||||||||
\(724\) | −69.4298 | −2.58034 | ||||||||
\(725\) | −18.1164 | −0.672826 | ||||||||
\(726\) | −9.17345 | −0.340459 | ||||||||
\(727\) | −18.2556 | −0.677064 | −0.338532 | − | 0.940955i | \(-0.609930\pi\) | ||||
−0.338532 | + | 0.940955i | \(0.609930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −36.6743 | −1.35738 | ||||||||
\(731\) | 4.40091 | 0.162773 | ||||||||
\(732\) | 31.2821 | 1.15622 | ||||||||
\(733\) | 21.0158 | 0.776235 | 0.388117 | − | 0.921610i | \(-0.373126\pi\) | ||||
0.388117 | + | 0.921610i | \(0.373126\pi\) | |||||||
\(734\) | 71.8786 | 2.65309 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 99.6427 | 3.67288 | ||||||||
\(737\) | −59.3518 | −2.18625 | ||||||||
\(738\) | −2.69180 | −0.0990865 | ||||||||
\(739\) | 42.2094 | 1.55270 | 0.776348 | − | 0.630304i | \(-0.217070\pi\) | ||||
0.776348 | + | 0.630304i | \(0.217070\pi\) | |||||||
\(740\) | 149.790 | 5.50639 | ||||||||
\(741\) | −2.77348 | −0.101886 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −52.7446 | −1.93501 | −0.967505 | − | 0.252852i | \(-0.918632\pi\) | ||||
−0.967505 | + | 0.252852i | \(0.918632\pi\) | |||||||
\(744\) | −91.3429 | −3.34879 | ||||||||
\(745\) | 53.5548 | 1.96210 | ||||||||
\(746\) | −16.2915 | −0.596474 | ||||||||
\(747\) | 7.04509 | 0.257766 | ||||||||
\(748\) | 21.0572 | 0.769929 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 30.9209 | 1.12907 | ||||||||
\(751\) | −26.7511 | −0.976160 | −0.488080 | − | 0.872799i | \(-0.662303\pi\) | ||||
−0.488080 | + | 0.872799i | \(0.662303\pi\) | |||||||
\(752\) | −66.2929 | −2.41745 | ||||||||
\(753\) | −21.2207 | −0.773326 | ||||||||
\(754\) | 5.89384 | 0.214641 | ||||||||
\(755\) | 24.8993 | 0.906179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.6901 | 1.69698 | 0.848489 | − | 0.529212i | \(-0.177512\pi\) | ||||
0.848489 | + | 0.529212i | \(0.177512\pi\) | |||||||
\(758\) | 12.6175 | 0.458287 | ||||||||
\(759\) | −21.5007 | −0.780425 | ||||||||
\(760\) | −89.0896 | −3.23162 | ||||||||
\(761\) | 39.3776 | 1.42744 | 0.713718 | − | 0.700433i | \(-0.247010\pi\) | ||||
0.713718 | + | 0.700433i | \(0.247010\pi\) | |||||||
\(762\) | −34.0405 | −1.23316 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 96.6984 | 3.49843 | ||||||||
\(765\) | −3.83720 | −0.138734 | ||||||||
\(766\) | 92.9222 | 3.35742 | ||||||||
\(767\) | −7.48553 | −0.270287 | ||||||||
\(768\) | 17.0238 | 0.614293 | ||||||||
\(769\) | −40.4050 | −1.45704 | −0.728520 | − | 0.685025i | \(-0.759791\pi\) | ||||
−0.728520 | + | 0.685025i | \(0.759791\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.2708 | 0.838077 | ||||||||
\(772\) | 60.1418 | 2.16455 | ||||||||
\(773\) | −16.5528 | −0.595364 | −0.297682 | − | 0.954665i | \(-0.596214\pi\) | ||||
−0.297682 | + | 0.954665i | \(0.596214\pi\) | |||||||
\(774\) | −11.2020 | −0.402646 | ||||||||
\(775\) | 85.3715 | 3.06663 | ||||||||
\(776\) | −124.794 | −4.47984 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.61430 | −0.165431 | ||||||||
\(779\) | −2.81023 | −0.100687 | ||||||||
\(780\) | −18.7853 | −0.672621 | ||||||||
\(781\) | 44.1120 | 1.57845 | ||||||||
\(782\) | 16.1244 | 0.576609 | ||||||||
\(783\) | −2.21857 | −0.0792851 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.1516 | −0.540785 | ||||||||
\(786\) | −58.8662 | −2.09969 | ||||||||
\(787\) | −41.3752 | −1.47487 | −0.737433 | − | 0.675420i | \(-0.763962\pi\) | ||||
−0.737433 | + | 0.675420i | \(0.763962\pi\) | |||||||
\(788\) | 15.1238 | 0.538764 | ||||||||
\(789\) | −30.5369 | −1.08714 | ||||||||
\(790\) | −47.2156 | −1.67985 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −33.1637 | −1.17842 | ||||||||
\(793\) | 5.88530 | 0.208993 | ||||||||
\(794\) | −39.2801 | −1.39400 | ||||||||
\(795\) | 33.2898 | 1.18067 | ||||||||
\(796\) | 97.9253 | 3.47087 | ||||||||
\(797\) | −30.5376 | −1.08170 | −0.540849 | − | 0.841119i | \(-0.681897\pi\) | ||||
−0.540849 | + | 0.841119i | \(0.681897\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.38176 | −0.190393 | ||||||||
\(800\) | −143.646 | −5.07866 | ||||||||
\(801\) | 9.53384 | 0.336862 | ||||||||
\(802\) | −29.3680 | −1.03702 | ||||||||
\(803\) | −14.2527 | −0.502965 | ||||||||
\(804\) | −82.0244 | −2.89278 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27.7741 | −0.978299 | ||||||||
\(807\) | −4.54700 | −0.160062 | ||||||||
\(808\) | −11.1692 | −0.392930 | ||||||||
\(809\) | −23.0463 | −0.810264 | −0.405132 | − | 0.914258i | \(-0.632774\pi\) | ||||
−0.405132 | + | 0.914258i | \(0.632774\pi\) | |||||||
\(810\) | 9.76712 | 0.343182 | ||||||||
\(811\) | −16.0147 | −0.562352 | −0.281176 | − | 0.959656i | \(-0.590725\pi\) | ||||
−0.281176 | + | 0.959656i | \(0.590725\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.0582 | −0.738543 | ||||||||
\(814\) | 80.4067 | 2.81825 | ||||||||
\(815\) | 85.3455 | 2.98952 | ||||||||
\(816\) | 13.7760 | 0.482257 | ||||||||
\(817\) | −11.6948 | −0.409150 | ||||||||
\(818\) | 39.1533 | 1.36896 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.0342 | −0.664702 | ||||||||
\(821\) | 26.8925 | 0.938553 | 0.469277 | − | 0.883051i | \(-0.344515\pi\) | ||||
0.469277 | + | 0.883051i | \(0.344515\pi\) | |||||||
\(822\) | 11.5219 | 0.401872 | ||||||||
\(823\) | −49.1148 | −1.71203 | −0.856017 | − | 0.516947i | \(-0.827068\pi\) | ||||
−0.856017 | + | 0.516947i | \(0.827068\pi\) | |||||||
\(824\) | −104.762 | −3.64956 | ||||||||
\(825\) | 30.9956 | 1.07913 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.37580 | −0.186935 | −0.0934675 | − | 0.995622i | \(-0.529795\pi\) | ||||
−0.0934675 | + | 0.995622i | \(0.529795\pi\) | |||||||
\(828\) | −29.7140 | −1.03263 | ||||||||
\(829\) | 24.9271 | 0.865754 | 0.432877 | − | 0.901453i | \(-0.357498\pi\) | ||||
0.432877 | + | 0.901453i | \(0.357498\pi\) | |||||||
\(830\) | 68.8102 | 2.38844 | ||||||||
\(831\) | −1.16773 | −0.0405081 | ||||||||
\(832\) | 21.0200 | 0.728739 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.0390392 | −0.00135182 | ||||||||
\(835\) | 56.9924 | 1.97230 | ||||||||
\(836\) | −55.9567 | −1.93530 | ||||||||
\(837\) | 10.4547 | 0.361369 | ||||||||
\(838\) | 50.2153 | 1.73466 | ||||||||
\(839\) | −12.8146 | −0.442408 | −0.221204 | − | 0.975228i | \(-0.570999\pi\) | ||||
−0.221204 | + | 0.975228i | \(0.570999\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0780 | −0.830275 | ||||||||
\(842\) | 81.5110 | 2.80906 | ||||||||
\(843\) | −16.8177 | −0.579233 | ||||||||
\(844\) | −16.2312 | −0.558702 | ||||||||
\(845\) | 43.6359 | 1.50112 | ||||||||
\(846\) | 13.6986 | 0.470968 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −119.514 | −4.10414 | ||||||||
\(849\) | 32.2924 | 1.10827 | ||||||||
\(850\) | −23.2452 | −0.797303 | ||||||||
\(851\) | 44.5759 | 1.52804 | ||||||||
\(852\) | 60.9630 | 2.08856 | ||||||||
\(853\) | −55.5740 | −1.90282 | −0.951409 | − | 0.307930i | \(-0.900364\pi\) | ||||
−0.951409 | + | 0.307930i | \(0.900364\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.1968 | 0.348724 | ||||||||
\(856\) | 157.343 | 5.37788 | ||||||||
\(857\) | −18.9766 | −0.648228 | −0.324114 | − | 0.946018i | \(-0.605066\pi\) | ||||
−0.324114 | + | 0.946018i | \(0.605066\pi\) | |||||||
\(858\) | −10.0839 | −0.344257 | ||||||||
\(859\) | 6.24592 | 0.213108 | 0.106554 | − | 0.994307i | \(-0.466018\pi\) | ||||
0.106554 | + | 0.994307i | \(0.466018\pi\) | |||||||
\(860\) | −79.2110 | −2.70107 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.5241 | −1.14183 | ||||||||
\(863\) | −33.6361 | −1.14499 | −0.572494 | − | 0.819909i | \(-0.694024\pi\) | ||||
−0.572494 | + | 0.819909i | \(0.694024\pi\) | |||||||
\(864\) | −17.5912 | −0.598463 | ||||||||
\(865\) | 21.3815 | 0.726991 | ||||||||
\(866\) | 18.3144 | 0.622348 | ||||||||
\(867\) | −15.8816 | −0.539369 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.3493 | −0.622457 | ||||||||
\(870\) | −21.6690 | −0.734648 | ||||||||
\(871\) | −15.4318 | −0.522887 | ||||||||
\(872\) | 122.412 | 4.14538 | ||||||||
\(873\) | 14.2834 | 0.483420 | ||||||||
\(874\) | −42.8485 | −1.44937 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −19.6972 | −0.665508 | ||||||||
\(877\) | −12.4187 | −0.419351 | −0.209676 | − | 0.977771i | \(-0.567241\pi\) | ||||
−0.209676 | + | 0.977771i | \(0.567241\pi\) | |||||||
\(878\) | 63.6535 | 2.14820 | ||||||||
\(879\) | −22.4014 | −0.755582 | ||||||||
\(880\) | −179.414 | −6.04806 | ||||||||
\(881\) | 20.7551 | 0.699258 | 0.349629 | − | 0.936888i | \(-0.386308\pi\) | ||||
0.349629 | + | 0.936888i | \(0.386308\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.14363 | −0.206750 | −0.103375 | − | 0.994642i | \(-0.532964\pi\) | ||||
−0.103375 | + | 0.994642i | \(0.532964\pi\) | |||||||
\(884\) | 5.47500 | 0.184144 | ||||||||
\(885\) | 27.5209 | 0.925106 | ||||||||
\(886\) | −38.9231 | −1.30765 | ||||||||
\(887\) | 15.6800 | 0.526482 | 0.263241 | − | 0.964730i | \(-0.415209\pi\) | ||||
0.263241 | + | 0.964730i | \(0.415209\pi\) | |||||||
\(888\) | 68.7560 | 2.30730 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 93.1182 | 3.12133 | ||||||||
\(891\) | 3.79578 | 0.127163 | ||||||||
\(892\) | 105.978 | 3.54841 | ||||||||
\(893\) | 14.3013 | 0.478575 | ||||||||
\(894\) | 39.7299 | 1.32877 | ||||||||
\(895\) | −16.9530 | −0.566677 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.59030 | −0.186655 | ||||||||
\(898\) | 39.7429 | 1.32624 | ||||||||
\(899\) | −23.1945 | −0.773581 | ||||||||
\(900\) | 42.8361 | 1.42787 | ||||||||
\(901\) | −9.70238 | −0.323233 | ||||||||
\(902\) | −10.2175 | −0.340205 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −118.506 | −3.94146 | ||||||||
\(905\) | 48.0241 | 1.59638 | ||||||||
\(906\) | 18.4717 | 0.613680 | ||||||||
\(907\) | −51.5516 | −1.71174 | −0.855871 | − | 0.517190i | \(-0.826978\pi\) | ||||
−0.855871 | + | 0.517190i | \(0.826978\pi\) | |||||||
\(908\) | −121.645 | −4.03694 | ||||||||
\(909\) | 1.27838 | 0.0424011 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.3620 | −0.840280 | −0.420140 | − | 0.907459i | \(-0.638019\pi\) | ||||
−0.420140 | + | 0.907459i | \(0.638019\pi\) | |||||||
\(912\) | −36.6079 | −1.21221 | ||||||||
\(913\) | 26.7416 | 0.885017 | ||||||||
\(914\) | 21.3482 | 0.706137 | ||||||||
\(915\) | −21.6376 | −0.715317 | ||||||||
\(916\) | −77.8128 | −2.57101 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.84664 | −0.0939533 | ||||||||
\(919\) | −14.9540 | −0.493288 | −0.246644 | − | 0.969106i | \(-0.579328\pi\) | ||||
−0.246644 | + | 0.969106i | \(0.579328\pi\) | |||||||
\(920\) | −179.571 | −5.92029 | ||||||||
\(921\) | −15.5675 | −0.512965 | ||||||||
\(922\) | −26.4607 | −0.871438 | ||||||||
\(923\) | 11.4694 | 0.377519 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −64.2611 | −2.11289 | ||||||||
\(926\) | 17.4329 | 0.572882 | ||||||||
\(927\) | 11.9906 | 0.393825 | ||||||||
\(928\) | 39.0271 | 1.28113 | ||||||||
\(929\) | 22.0282 | 0.722722 | 0.361361 | − | 0.932426i | \(-0.382312\pi\) | ||||
0.361361 | + | 0.932426i | \(0.382312\pi\) | |||||||
\(930\) | 102.113 | 3.34841 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 125.303 | 4.10443 | ||||||||
\(933\) | −20.2286 | −0.662256 | ||||||||
\(934\) | −5.86680 | −0.191967 | ||||||||
\(935\) | −14.5652 | −0.476332 | ||||||||
\(936\) | −8.62274 | −0.281843 | ||||||||
\(937\) | 15.4016 | 0.503149 | 0.251575 | − | 0.967838i | \(-0.419052\pi\) | ||||
0.251575 | + | 0.967838i | \(0.419052\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.2244 | −0.431564 | ||||||||
\(940\) | 96.8652 | 3.15940 | ||||||||
\(941\) | 21.8930 | 0.713692 | 0.356846 | − | 0.934163i | \(-0.383852\pi\) | ||||
0.356846 | + | 0.934163i | \(0.383852\pi\) | |||||||
\(942\) | −11.2403 | −0.366229 | ||||||||
\(943\) | −5.66437 | −0.184457 | ||||||||
\(944\) | −98.8034 | −3.21578 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −42.5202 | −1.38245 | ||||||||
\(947\) | −24.2765 | −0.788881 | −0.394441 | − | 0.918921i | \(-0.629062\pi\) | ||||
−0.394441 | + | 0.918921i | \(0.629062\pi\) | |||||||
\(948\) | −25.3588 | −0.823616 | ||||||||
\(949\) | −3.70577 | −0.120294 | ||||||||
\(950\) | 61.7709 | 2.00411 | ||||||||
\(951\) | −17.4307 | −0.565228 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.1321 | 0.846503 | 0.423251 | − | 0.906012i | \(-0.360889\pi\) | ||||
0.423251 | + | 0.906012i | \(0.360889\pi\) | |||||||
\(954\) | 24.6962 | 0.799569 | ||||||||
\(955\) | −66.8857 | −2.16437 | ||||||||
\(956\) | 90.1455 | 2.91551 | ||||||||
\(957\) | −8.42118 | −0.272218 | ||||||||
\(958\) | 62.8121 | 2.02937 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −77.2812 | −2.49424 | ||||||||
\(961\) | 78.3015 | 2.52586 | ||||||||
\(962\) | 20.9062 | 0.674043 | ||||||||
\(963\) | −18.0089 | −0.580327 | ||||||||
\(964\) | 32.3647 | 1.04240 | ||||||||
\(965\) | −41.5997 | −1.33914 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.4692 | −0.722561 | −0.361280 | − | 0.932457i | \(-0.617660\pi\) | ||||
−0.361280 | + | 0.932457i | \(0.617660\pi\) | |||||||
\(968\) | −29.7750 | −0.957005 | ||||||||
\(969\) | −2.97189 | −0.0954708 | ||||||||
\(970\) | 139.508 | 4.47933 | ||||||||
\(971\) | −6.12283 | −0.196491 | −0.0982454 | − | 0.995162i | \(-0.531323\pi\) | ||||
−0.0982454 | + | 0.995162i | \(0.531323\pi\) | |||||||
\(972\) | 5.24578 | 0.168258 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.489422 | 0.0156821 | ||||||||
\(975\) | 8.05904 | 0.258096 | ||||||||
\(976\) | 77.6816 | 2.48653 | ||||||||
\(977\) | 6.50369 | 0.208071 | 0.104036 | − | 0.994574i | \(-0.466824\pi\) | ||||
0.104036 | + | 0.994574i | \(0.466824\pi\) | |||||||
\(978\) | 63.3139 | 2.02456 | ||||||||
\(979\) | 36.1884 | 1.15658 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.0107 | −0.447328 | ||||||||
\(982\) | −51.9333 | −1.65726 | ||||||||
\(983\) | −45.8232 | −1.46153 | −0.730766 | − | 0.682628i | \(-0.760837\pi\) | ||||
−0.730766 | + | 0.682628i | \(0.760837\pi\) | |||||||
\(984\) | −8.73699 | −0.278525 | ||||||||
\(985\) | −10.4611 | −0.333317 | ||||||||
\(986\) | 6.31547 | 0.201125 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.5491 | −0.462868 | ||||||||
\(989\) | −23.5724 | −0.749557 | ||||||||
\(990\) | 37.0738 | 1.17828 | ||||||||
\(991\) | 23.9854 | 0.761920 | 0.380960 | − | 0.924591i | \(-0.375594\pi\) | ||||
0.380960 | + | 0.924591i | \(0.375594\pi\) | |||||||
\(992\) | −183.911 | −5.83918 | ||||||||
\(993\) | 20.7539 | 0.658605 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −67.7343 | −2.14732 | ||||||||
\(996\) | 36.9570 | 1.17103 | ||||||||
\(997\) | −9.44196 | −0.299030 | −0.149515 | − | 0.988759i | \(-0.547771\pi\) | ||||
−0.149515 | + | 0.988759i | \(0.547771\pi\) | |||||||
\(998\) | −24.9788 | −0.790689 | ||||||||
\(999\) | −7.86953 | −0.248981 |
(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 | 6027.2.a.bm.1.2 | yes | 16 | |
7.6 | odd | 2 | 6027.2.a.bl.1.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bl.1.2 | ✓ | 16 | 7.6 | odd | 2 | ||
6027.2.a.bm.1.2 | yes | 16 | 1.1 | even | 1 | trivial |