Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.27492 | −1.91180 | −0.955901 | − | 0.293691i | \(-0.905116\pi\) | ||||
−0.955901 | + | 0.293691i | \(0.905116\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.27492 | 1.35185 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −4.27492 | −1.10378 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.54983 | −1.50264 | −0.751318 | − | 0.659941i | \(-0.770581\pi\) | ||||
−0.751318 | + | 0.659941i | \(0.770581\pi\) | |||||||
\(20\) | −4.27492 | −0.955901 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −4.00000 | −0.852803 | ||||||||
\(23\) | −5.27492 | −1.09990 | −0.549948 | − | 0.835199i | \(-0.685353\pi\) | ||||
−0.549948 | + | 0.835199i | \(0.685353\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 13.2749 | 2.65498 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 8.27492 | 1.53661 | 0.768307 | − | 0.640082i | \(-0.221100\pi\) | ||||
0.768307 | + | 0.640082i | \(0.221100\pi\) | |||||||
\(30\) | 4.27492 | 0.780490 | ||||||||
\(31\) | 1.27492 | 0.228982 | 0.114491 | − | 0.993424i | \(-0.463476\pi\) | ||||
0.114491 | + | 0.993424i | \(0.463476\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.00000 | 0.696311 | ||||||||
\(34\) | −3.00000 | −0.514496 | ||||||||
\(35\) | 4.27492 | 0.722593 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.274917 | −0.0451961 | −0.0225981 | − | 0.999745i | \(-0.507194\pi\) | ||||
−0.0225981 | + | 0.999745i | \(0.507194\pi\) | |||||||
\(38\) | 6.54983 | 1.06252 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.27492 | 0.675924 | ||||||||
\(41\) | −8.27492 | −1.29232 | −0.646162 | − | 0.763200i | \(-0.723627\pi\) | ||||
−0.646162 | + | 0.763200i | \(0.723627\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | −11.8248 | −1.80326 | −0.901629 | − | 0.432511i | \(-0.857628\pi\) | ||||
−0.901629 | + | 0.432511i | \(0.857628\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | −4.27492 | −0.637267 | ||||||||
\(46\) | 5.27492 | 0.777744 | ||||||||
\(47\) | 6.54983 | 0.955392 | 0.477696 | − | 0.878525i | \(-0.341472\pi\) | ||||
0.477696 | + | 0.878525i | \(0.341472\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −13.2749 | −1.87736 | ||||||||
\(51\) | 3.00000 | 0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.54983 | −0.487607 | −0.243804 | − | 0.969825i | \(-0.578395\pi\) | ||||
−0.243804 | + | 0.969825i | \(0.578395\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −17.0997 | −2.30572 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −6.54983 | −0.867547 | ||||||||
\(58\) | −8.27492 | −1.08655 | ||||||||
\(59\) | 11.8248 | 1.53945 | 0.769726 | − | 0.638375i | \(-0.220393\pi\) | ||||
0.769726 | + | 0.638375i | \(0.220393\pi\) | |||||||
\(60\) | −4.27492 | −0.551889 | ||||||||
\(61\) | −9.00000 | −1.15233 | −0.576166 | − | 0.817333i | \(-0.695452\pi\) | ||||
−0.576166 | + | 0.817333i | \(0.695452\pi\) | |||||||
\(62\) | −1.27492 | −0.161915 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | 2.72508 | 0.332922 | 0.166461 | − | 0.986048i | \(-0.446766\pi\) | ||||
0.166461 | + | 0.986048i | \(0.446766\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | −5.27492 | −0.635025 | ||||||||
\(70\) | −4.27492 | −0.510950 | ||||||||
\(71\) | −5.27492 | −0.626018 | −0.313009 | − | 0.949750i | \(-0.601337\pi\) | ||||
−0.313009 | + | 0.949750i | \(0.601337\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −5.72508 | −0.670070 | −0.335035 | − | 0.942206i | \(-0.608748\pi\) | ||||
−0.335035 | + | 0.942206i | \(0.608748\pi\) | |||||||
\(74\) | 0.274917 | 0.0319585 | ||||||||
\(75\) | 13.2749 | 1.53286 | ||||||||
\(76\) | −6.54983 | −0.751318 | ||||||||
\(77\) | −4.00000 | −0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | −4.27492 | −0.477950 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.27492 | 0.913812 | ||||||||
\(83\) | 11.8248 | 1.29794 | 0.648968 | − | 0.760816i | \(-0.275201\pi\) | ||||
0.648968 | + | 0.760816i | \(0.275201\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −12.8248 | −1.39104 | ||||||||
\(86\) | 11.8248 | 1.27510 | ||||||||
\(87\) | 8.27492 | 0.887164 | ||||||||
\(88\) | −4.00000 | −0.426401 | ||||||||
\(89\) | −0.725083 | −0.0768586 | −0.0384293 | − | 0.999261i | \(-0.512235\pi\) | ||||
−0.0384293 | + | 0.999261i | \(0.512235\pi\) | |||||||
\(90\) | 4.27492 | 0.450616 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.27492 | −0.549948 | ||||||||
\(93\) | 1.27492 | 0.132203 | ||||||||
\(94\) | −6.54983 | −0.675564 | ||||||||
\(95\) | 28.0000 | 2.87274 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 0.549834 | 0.0558272 | 0.0279136 | − | 0.999610i | \(-0.491114\pi\) | ||||
0.0279136 | + | 0.999610i | \(0.491114\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 13.2749 | 1.32749 | ||||||||
\(101\) | 1.72508 | 0.171652 | 0.0858261 | − | 0.996310i | \(-0.472647\pi\) | ||||
0.0858261 | + | 0.996310i | \(0.472647\pi\) | |||||||
\(102\) | −3.00000 | −0.297044 | ||||||||
\(103\) | 5.27492 | 0.519753 | 0.259877 | − | 0.965642i | \(-0.416318\pi\) | ||||
0.259877 | + | 0.965642i | \(0.416318\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.27492 | 0.417189 | ||||||||
\(106\) | 3.54983 | 0.344790 | ||||||||
\(107\) | 2.54983 | 0.246502 | 0.123251 | − | 0.992376i | \(-0.460668\pi\) | ||||
0.123251 | + | 0.992376i | \(0.460668\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 4.54983 | 0.435795 | 0.217898 | − | 0.975972i | \(-0.430080\pi\) | ||||
0.217898 | + | 0.975972i | \(0.430080\pi\) | |||||||
\(110\) | 17.0997 | 1.63039 | ||||||||
\(111\) | −0.274917 | −0.0260940 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 14.8248 | 1.39460 | 0.697298 | − | 0.716782i | \(-0.254386\pi\) | ||||
0.697298 | + | 0.716782i | \(0.254386\pi\) | |||||||
\(114\) | 6.54983 | 0.613448 | ||||||||
\(115\) | 22.5498 | 2.10278 | ||||||||
\(116\) | 8.27492 | 0.768307 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.8248 | −1.08856 | ||||||||
\(119\) | −3.00000 | −0.275010 | ||||||||
\(120\) | 4.27492 | 0.390245 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 9.00000 | 0.814822 | ||||||||
\(123\) | −8.27492 | −0.746124 | ||||||||
\(124\) | 1.27492 | 0.114491 | ||||||||
\(125\) | −35.3746 | −3.16400 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −11.8248 | −1.04111 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.72508 | −0.238092 | −0.119046 | − | 0.992889i | \(-0.537984\pi\) | ||||
−0.119046 | + | 0.992889i | \(0.537984\pi\) | |||||||
\(132\) | 4.00000 | 0.348155 | ||||||||
\(133\) | 6.54983 | 0.567943 | ||||||||
\(134\) | −2.72508 | −0.235411 | ||||||||
\(135\) | −4.27492 | −0.367926 | ||||||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | −22.8248 | −1.95005 | −0.975025 | − | 0.222095i | \(-0.928711\pi\) | ||||
−0.975025 | + | 0.222095i | \(0.928711\pi\) | |||||||
\(138\) | 5.27492 | 0.449031 | ||||||||
\(139\) | −9.09967 | −0.771824 | −0.385912 | − | 0.922536i | \(-0.626113\pi\) | ||||
−0.385912 | + | 0.922536i | \(0.626113\pi\) | |||||||
\(140\) | 4.27492 | 0.361296 | ||||||||
\(141\) | 6.54983 | 0.551596 | ||||||||
\(142\) | 5.27492 | 0.442661 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −35.3746 | −2.93770 | ||||||||
\(146\) | 5.72508 | 0.473811 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −0.274917 | −0.0225981 | ||||||||
\(149\) | 1.00000 | 0.0819232 | 0.0409616 | − | 0.999161i | \(-0.486958\pi\) | ||||
0.0409616 | + | 0.999161i | \(0.486958\pi\) | |||||||
\(150\) | −13.2749 | −1.08389 | ||||||||
\(151\) | −13.0997 | −1.06604 | −0.533018 | − | 0.846104i | \(-0.678942\pi\) | ||||
−0.533018 | + | 0.846104i | \(0.678942\pi\) | |||||||
\(152\) | 6.54983 | 0.531262 | ||||||||
\(153\) | 3.00000 | 0.242536 | ||||||||
\(154\) | 4.00000 | 0.322329 | ||||||||
\(155\) | −5.45017 | −0.437768 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.72508 | −0.297294 | −0.148647 | − | 0.988890i | \(-0.547492\pi\) | ||||
−0.148647 | + | 0.988890i | \(0.547492\pi\) | |||||||
\(158\) | 8.00000 | 0.636446 | ||||||||
\(159\) | −3.54983 | −0.281520 | ||||||||
\(160\) | 4.27492 | 0.337962 | ||||||||
\(161\) | 5.27492 | 0.415722 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 13.2749 | 1.03977 | 0.519886 | − | 0.854236i | \(-0.325974\pi\) | ||||
0.519886 | + | 0.854236i | \(0.325974\pi\) | |||||||
\(164\) | −8.27492 | −0.646162 | ||||||||
\(165\) | −17.0997 | −1.33121 | ||||||||
\(166\) | −11.8248 | −0.917779 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 12.8248 | 0.983614 | ||||||||
\(171\) | −6.54983 | −0.500878 | ||||||||
\(172\) | −11.8248 | −0.901629 | ||||||||
\(173\) | −4.54983 | −0.345918 | −0.172959 | − | 0.984929i | \(-0.555333\pi\) | ||||
−0.172959 | + | 0.984929i | \(0.555333\pi\) | |||||||
\(174\) | −8.27492 | −0.627320 | ||||||||
\(175\) | −13.2749 | −1.00349 | ||||||||
\(176\) | 4.00000 | 0.301511 | ||||||||
\(177\) | 11.8248 | 0.888803 | ||||||||
\(178\) | 0.725083 | 0.0543473 | ||||||||
\(179\) | 1.45017 | 0.108390 | 0.0541952 | − | 0.998530i | \(-0.482741\pi\) | ||||
0.0541952 | + | 0.998530i | \(0.482741\pi\) | |||||||
\(180\) | −4.27492 | −0.318634 | ||||||||
\(181\) | −16.8248 | −1.25057 | −0.625287 | − | 0.780395i | \(-0.715018\pi\) | ||||
−0.625287 | + | 0.780395i | \(0.715018\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.00000 | −0.665299 | ||||||||
\(184\) | 5.27492 | 0.388872 | ||||||||
\(185\) | 1.17525 | 0.0864060 | ||||||||
\(186\) | −1.27492 | −0.0934815 | ||||||||
\(187\) | 12.0000 | 0.877527 | ||||||||
\(188\) | 6.54983 | 0.477696 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −28.0000 | −2.03133 | ||||||||
\(191\) | 6.72508 | 0.486610 | 0.243305 | − | 0.969950i | \(-0.421768\pi\) | ||||
0.243305 | + | 0.969950i | \(0.421768\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 24.8248 | 1.78692 | 0.893462 | − | 0.449138i | \(-0.148269\pi\) | ||||
0.893462 | + | 0.449138i | \(0.148269\pi\) | |||||||
\(194\) | −0.549834 | −0.0394758 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 21.8248 | 1.55495 | 0.777475 | − | 0.628914i | \(-0.216500\pi\) | ||||
0.777475 | + | 0.628914i | \(0.216500\pi\) | |||||||
\(198\) | −4.00000 | −0.284268 | ||||||||
\(199\) | 11.8248 | 0.838234 | 0.419117 | − | 0.907932i | \(-0.362340\pi\) | ||||
0.419117 | + | 0.907932i | \(0.362340\pi\) | |||||||
\(200\) | −13.2749 | −0.938678 | ||||||||
\(201\) | 2.72508 | 0.192213 | ||||||||
\(202\) | −1.72508 | −0.121376 | ||||||||
\(203\) | −8.27492 | −0.580785 | ||||||||
\(204\) | 3.00000 | 0.210042 | ||||||||
\(205\) | 35.3746 | 2.47067 | ||||||||
\(206\) | −5.27492 | −0.367521 | ||||||||
\(207\) | −5.27492 | −0.366632 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −26.1993 | −1.81225 | ||||||||
\(210\) | −4.27492 | −0.294997 | ||||||||
\(211\) | 21.0997 | 1.45256 | 0.726281 | − | 0.687398i | \(-0.241247\pi\) | ||||
0.726281 | + | 0.687398i | \(0.241247\pi\) | |||||||
\(212\) | −3.54983 | −0.243804 | ||||||||
\(213\) | −5.27492 | −0.361431 | ||||||||
\(214\) | −2.54983 | −0.174303 | ||||||||
\(215\) | 50.5498 | 3.44747 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −1.27492 | −0.0865470 | ||||||||
\(218\) | −4.54983 | −0.308154 | ||||||||
\(219\) | −5.72508 | −0.386865 | ||||||||
\(220\) | −17.0997 | −1.15286 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.274917 | 0.0184512 | ||||||||
\(223\) | −10.7251 | −0.718205 | −0.359102 | − | 0.933298i | \(-0.616917\pi\) | ||||
−0.359102 | + | 0.933298i | \(0.616917\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 13.2749 | 0.884994 | ||||||||
\(226\) | −14.8248 | −0.986128 | ||||||||
\(227\) | 21.0997 | 1.40043 | 0.700217 | − | 0.713930i | \(-0.253087\pi\) | ||||
0.700217 | + | 0.713930i | \(0.253087\pi\) | |||||||
\(228\) | −6.54983 | −0.433773 | ||||||||
\(229\) | −12.7251 | −0.840897 | −0.420449 | − | 0.907316i | \(-0.638127\pi\) | ||||
−0.420449 | + | 0.907316i | \(0.638127\pi\) | |||||||
\(230\) | −22.5498 | −1.48689 | ||||||||
\(231\) | −4.00000 | −0.263181 | ||||||||
\(232\) | −8.27492 | −0.543275 | ||||||||
\(233\) | 7.45017 | 0.488077 | 0.244038 | − | 0.969766i | \(-0.421528\pi\) | ||||
0.244038 | + | 0.969766i | \(0.421528\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −28.0000 | −1.82652 | ||||||||
\(236\) | 11.8248 | 0.769726 | ||||||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | 3.00000 | 0.194461 | ||||||||
\(239\) | 5.27492 | 0.341206 | 0.170603 | − | 0.985340i | \(-0.445428\pi\) | ||||
0.170603 | + | 0.985340i | \(0.445428\pi\) | |||||||
\(240\) | −4.27492 | −0.275945 | ||||||||
\(241\) | 15.7251 | 1.01294 | 0.506471 | − | 0.862257i | \(-0.330950\pi\) | ||||
0.506471 | + | 0.862257i | \(0.330950\pi\) | |||||||
\(242\) | −5.00000 | −0.321412 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −9.00000 | −0.576166 | ||||||||
\(245\) | −4.27492 | −0.273114 | ||||||||
\(246\) | 8.27492 | 0.527589 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.27492 | −0.0809573 | ||||||||
\(249\) | 11.8248 | 0.749363 | ||||||||
\(250\) | 35.3746 | 2.23729 | ||||||||
\(251\) | 13.2749 | 0.837905 | 0.418953 | − | 0.908008i | \(-0.362397\pi\) | ||||
0.418953 | + | 0.908008i | \(0.362397\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −21.0997 | −1.32652 | ||||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | −12.8248 | −0.803117 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.0000 | 0.935674 | 0.467837 | − | 0.883815i | \(-0.345033\pi\) | ||||
0.467837 | + | 0.883815i | \(0.345033\pi\) | |||||||
\(258\) | 11.8248 | 0.736177 | ||||||||
\(259\) | 0.274917 | 0.0170825 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.27492 | 0.512205 | ||||||||
\(262\) | 2.72508 | 0.168356 | ||||||||
\(263\) | 21.0997 | 1.30106 | 0.650531 | − | 0.759480i | \(-0.274547\pi\) | ||||
0.650531 | + | 0.759480i | \(0.274547\pi\) | |||||||
\(264\) | −4.00000 | −0.246183 | ||||||||
\(265\) | 15.1752 | 0.932208 | ||||||||
\(266\) | −6.54983 | −0.401596 | ||||||||
\(267\) | −0.725083 | −0.0443743 | ||||||||
\(268\) | 2.72508 | 0.166461 | ||||||||
\(269\) | −18.0000 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(270\) | 4.27492 | 0.260163 | ||||||||
\(271\) | −25.2749 | −1.53534 | −0.767671 | − | 0.640844i | \(-0.778584\pi\) | ||||
−0.767671 | + | 0.640844i | \(0.778584\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.8248 | 1.37889 | ||||||||
\(275\) | 53.0997 | 3.20203 | ||||||||
\(276\) | −5.27492 | −0.317513 | ||||||||
\(277\) | 14.8248 | 0.890733 | 0.445366 | − | 0.895348i | \(-0.353073\pi\) | ||||
0.445366 | + | 0.895348i | \(0.353073\pi\) | |||||||
\(278\) | 9.09967 | 0.545762 | ||||||||
\(279\) | 1.27492 | 0.0763273 | ||||||||
\(280\) | −4.27492 | −0.255475 | ||||||||
\(281\) | 20.8248 | 1.24230 | 0.621150 | − | 0.783691i | \(-0.286666\pi\) | ||||
0.621150 | + | 0.783691i | \(0.286666\pi\) | |||||||
\(282\) | −6.54983 | −0.390037 | ||||||||
\(283\) | −9.45017 | −0.561754 | −0.280877 | − | 0.959744i | \(-0.590625\pi\) | ||||
−0.280877 | + | 0.959744i | \(0.590625\pi\) | |||||||
\(284\) | −5.27492 | −0.313009 | ||||||||
\(285\) | 28.0000 | 1.65858 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.27492 | 0.488453 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 35.3746 | 2.07727 | ||||||||
\(291\) | 0.549834 | 0.0322319 | ||||||||
\(292\) | −5.72508 | −0.335035 | ||||||||
\(293\) | 18.2749 | 1.06763 | 0.533816 | − | 0.845601i | \(-0.320757\pi\) | ||||
0.533816 | + | 0.845601i | \(0.320757\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −50.5498 | −2.94313 | ||||||||
\(296\) | 0.274917 | 0.0159792 | ||||||||
\(297\) | 4.00000 | 0.232104 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 13.2749 | 0.766428 | ||||||||
\(301\) | 11.8248 | 0.681567 | ||||||||
\(302\) | 13.0997 | 0.753801 | ||||||||
\(303\) | 1.72508 | 0.0991034 | ||||||||
\(304\) | −6.54983 | −0.375659 | ||||||||
\(305\) | 38.4743 | 2.20303 | ||||||||
\(306\) | −3.00000 | −0.171499 | ||||||||
\(307\) | 1.45017 | 0.0827653 | 0.0413827 | − | 0.999143i | \(-0.486824\pi\) | ||||
0.0413827 | + | 0.999143i | \(0.486824\pi\) | |||||||
\(308\) | −4.00000 | −0.227921 | ||||||||
\(309\) | 5.27492 | 0.300080 | ||||||||
\(310\) | 5.45017 | 0.309549 | ||||||||
\(311\) | −2.54983 | −0.144588 | −0.0722939 | − | 0.997383i | \(-0.523032\pi\) | ||||
−0.0722939 | + | 0.997383i | \(0.523032\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.6495 | 0.997609 | 0.498804 | − | 0.866715i | \(-0.333773\pi\) | ||||
0.498804 | + | 0.866715i | \(0.333773\pi\) | |||||||
\(314\) | 3.72508 | 0.210219 | ||||||||
\(315\) | 4.27492 | 0.240864 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 7.54983 | 0.424041 | 0.212020 | − | 0.977265i | \(-0.431996\pi\) | ||||
0.212020 | + | 0.977265i | \(0.431996\pi\) | |||||||
\(318\) | 3.54983 | 0.199065 | ||||||||
\(319\) | 33.0997 | 1.85323 | ||||||||
\(320\) | −4.27492 | −0.238975 | ||||||||
\(321\) | 2.54983 | 0.142318 | ||||||||
\(322\) | −5.27492 | −0.293960 | ||||||||
\(323\) | −19.6495 | −1.09333 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.2749 | −0.735230 | ||||||||
\(327\) | 4.54983 | 0.251606 | ||||||||
\(328\) | 8.27492 | 0.456906 | ||||||||
\(329\) | −6.54983 | −0.361104 | ||||||||
\(330\) | 17.0997 | 0.941306 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 11.8248 | 0.648968 | ||||||||
\(333\) | −0.274917 | −0.0150654 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.6495 | −0.636480 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 0.274917 | 0.0149757 | 0.00748785 | − | 0.999972i | \(-0.497617\pi\) | ||||
0.00748785 | + | 0.999972i | \(0.497617\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.8248 | 0.805170 | ||||||||
\(340\) | −12.8248 | −0.695520 | ||||||||
\(341\) | 5.09967 | 0.276163 | ||||||||
\(342\) | 6.54983 | 0.354174 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 11.8248 | 0.637548 | ||||||||
\(345\) | 22.5498 | 1.21404 | ||||||||
\(346\) | 4.54983 | 0.244601 | ||||||||
\(347\) | 30.5498 | 1.64000 | 0.820001 | − | 0.572363i | \(-0.193973\pi\) | ||||
0.820001 | + | 0.572363i | \(0.193973\pi\) | |||||||
\(348\) | 8.27492 | 0.443582 | ||||||||
\(349\) | 34.9244 | 1.86946 | 0.934731 | − | 0.355357i | \(-0.115641\pi\) | ||||
0.934731 | + | 0.355357i | \(0.115641\pi\) | |||||||
\(350\) | 13.2749 | 0.709574 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.00000 | −0.213201 | ||||||||
\(353\) | 19.5498 | 1.04053 | 0.520266 | − | 0.854004i | \(-0.325833\pi\) | ||||
0.520266 | + | 0.854004i | \(0.325833\pi\) | |||||||
\(354\) | −11.8248 | −0.628478 | ||||||||
\(355\) | 22.5498 | 1.19682 | ||||||||
\(356\) | −0.725083 | −0.0384293 | ||||||||
\(357\) | −3.00000 | −0.158777 | ||||||||
\(358\) | −1.45017 | −0.0766436 | ||||||||
\(359\) | 1.09967 | 0.0580383 | 0.0290192 | − | 0.999579i | \(-0.490762\pi\) | ||||
0.0290192 | + | 0.999579i | \(0.490762\pi\) | |||||||
\(360\) | 4.27492 | 0.225308 | ||||||||
\(361\) | 23.9003 | 1.25791 | ||||||||
\(362\) | 16.8248 | 0.884289 | ||||||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.4743 | 1.28104 | ||||||||
\(366\) | 9.00000 | 0.470438 | ||||||||
\(367\) | 13.2749 | 0.692945 | 0.346473 | − | 0.938060i | \(-0.387379\pi\) | ||||
0.346473 | + | 0.938060i | \(0.387379\pi\) | |||||||
\(368\) | −5.27492 | −0.274974 | ||||||||
\(369\) | −8.27492 | −0.430775 | ||||||||
\(370\) | −1.17525 | −0.0610983 | ||||||||
\(371\) | 3.54983 | 0.184298 | ||||||||
\(372\) | 1.27492 | 0.0661014 | ||||||||
\(373\) | 26.8248 | 1.38893 | 0.694466 | − | 0.719525i | \(-0.255640\pi\) | ||||
0.694466 | + | 0.719525i | \(0.255640\pi\) | |||||||
\(374\) | −12.0000 | −0.620505 | ||||||||
\(375\) | −35.3746 | −1.82674 | ||||||||
\(376\) | −6.54983 | −0.337782 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 28.0000 | 1.43637 | ||||||||
\(381\) | 8.00000 | 0.409852 | ||||||||
\(382\) | −6.72508 | −0.344085 | ||||||||
\(383\) | −22.1993 | −1.13433 | −0.567167 | − | 0.823603i | \(-0.691960\pi\) | ||||
−0.567167 | + | 0.823603i | \(0.691960\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 17.0997 | 0.871480 | ||||||||
\(386\) | −24.8248 | −1.26355 | ||||||||
\(387\) | −11.8248 | −0.601086 | ||||||||
\(388\) | 0.549834 | 0.0279136 | ||||||||
\(389\) | −24.6495 | −1.24978 | −0.624890 | − | 0.780713i | \(-0.714856\pi\) | ||||
−0.624890 | + | 0.780713i | \(0.714856\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.8248 | −0.800292 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −2.72508 | −0.137462 | ||||||||
\(394\) | −21.8248 | −1.09952 | ||||||||
\(395\) | 34.1993 | 1.72076 | ||||||||
\(396\) | 4.00000 | 0.201008 | ||||||||
\(397\) | −23.2749 | −1.16813 | −0.584067 | − | 0.811705i | \(-0.698540\pi\) | ||||
−0.584067 | + | 0.811705i | \(0.698540\pi\) | |||||||
\(398\) | −11.8248 | −0.592721 | ||||||||
\(399\) | 6.54983 | 0.327902 | ||||||||
\(400\) | 13.2749 | 0.663746 | ||||||||
\(401\) | 2.27492 | 0.113604 | 0.0568020 | − | 0.998385i | \(-0.481910\pi\) | ||||
0.0568020 | + | 0.998385i | \(0.481910\pi\) | |||||||
\(402\) | −2.72508 | −0.135915 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.72508 | 0.0858261 | ||||||||
\(405\) | −4.27492 | −0.212422 | ||||||||
\(406\) | 8.27492 | 0.410677 | ||||||||
\(407\) | −1.09967 | −0.0545086 | ||||||||
\(408\) | −3.00000 | −0.148522 | ||||||||
\(409\) | 29.9244 | 1.47967 | 0.739834 | − | 0.672790i | \(-0.234904\pi\) | ||||
0.739834 | + | 0.672790i | \(0.234904\pi\) | |||||||
\(410\) | −35.3746 | −1.74703 | ||||||||
\(411\) | −22.8248 | −1.12586 | ||||||||
\(412\) | 5.27492 | 0.259877 | ||||||||
\(413\) | −11.8248 | −0.581858 | ||||||||
\(414\) | 5.27492 | 0.259248 | ||||||||
\(415\) | −50.5498 | −2.48139 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.09967 | −0.445613 | ||||||||
\(418\) | 26.1993 | 1.28145 | ||||||||
\(419\) | −22.3746 | −1.09307 | −0.546535 | − | 0.837436i | \(-0.684053\pi\) | ||||
−0.546535 | + | 0.837436i | \(0.684053\pi\) | |||||||
\(420\) | 4.27492 | 0.208595 | ||||||||
\(421\) | −8.27492 | −0.403295 | −0.201647 | − | 0.979458i | \(-0.564630\pi\) | ||||
−0.201647 | + | 0.979458i | \(0.564630\pi\) | |||||||
\(422\) | −21.0997 | −1.02712 | ||||||||
\(423\) | 6.54983 | 0.318464 | ||||||||
\(424\) | 3.54983 | 0.172395 | ||||||||
\(425\) | 39.8248 | 1.93178 | ||||||||
\(426\) | 5.27492 | 0.255571 | ||||||||
\(427\) | 9.00000 | 0.435541 | ||||||||
\(428\) | 2.54983 | 0.123251 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −50.5498 | −2.43773 | ||||||||
\(431\) | 13.2749 | 0.639430 | 0.319715 | − | 0.947514i | \(-0.396413\pi\) | ||||
0.319715 | + | 0.947514i | \(0.396413\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −10.2749 | −0.493781 | −0.246891 | − | 0.969043i | \(-0.579409\pi\) | ||||
−0.246891 | + | 0.969043i | \(0.579409\pi\) | |||||||
\(434\) | 1.27492 | 0.0611980 | ||||||||
\(435\) | −35.3746 | −1.69608 | ||||||||
\(436\) | 4.54983 | 0.217898 | ||||||||
\(437\) | 34.5498 | 1.65274 | ||||||||
\(438\) | 5.72508 | 0.273555 | ||||||||
\(439\) | 13.0997 | 0.625213 | 0.312607 | − | 0.949883i | \(-0.398798\pi\) | ||||
0.312607 | + | 0.949883i | \(0.398798\pi\) | |||||||
\(440\) | 17.0997 | 0.815195 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.5498 | 1.64151 | 0.820756 | − | 0.571279i | \(-0.193552\pi\) | ||||
0.820756 | + | 0.571279i | \(0.193552\pi\) | |||||||
\(444\) | −0.274917 | −0.0130470 | ||||||||
\(445\) | 3.09967 | 0.146938 | ||||||||
\(446\) | 10.7251 | 0.507847 | ||||||||
\(447\) | 1.00000 | 0.0472984 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 19.0997 | 0.901369 | 0.450685 | − | 0.892683i | \(-0.351180\pi\) | ||||
0.450685 | + | 0.892683i | \(0.351180\pi\) | |||||||
\(450\) | −13.2749 | −0.625786 | ||||||||
\(451\) | −33.0997 | −1.55860 | ||||||||
\(452\) | 14.8248 | 0.697298 | ||||||||
\(453\) | −13.0997 | −0.615476 | ||||||||
\(454\) | −21.0997 | −0.990257 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.54983 | 0.306724 | ||||||||
\(457\) | 17.0000 | 0.795226 | 0.397613 | − | 0.917553i | \(-0.369839\pi\) | ||||
0.397613 | + | 0.917553i | \(0.369839\pi\) | |||||||
\(458\) | 12.7251 | 0.594604 | ||||||||
\(459\) | 3.00000 | 0.140028 | ||||||||
\(460\) | 22.5498 | 1.05139 | ||||||||
\(461\) | 19.3746 | 0.902364 | 0.451182 | − | 0.892432i | \(-0.351002\pi\) | ||||
0.451182 | + | 0.892432i | \(0.351002\pi\) | |||||||
\(462\) | 4.00000 | 0.186097 | ||||||||
\(463\) | 10.5498 | 0.490292 | 0.245146 | − | 0.969486i | \(-0.421164\pi\) | ||||
0.245146 | + | 0.969486i | \(0.421164\pi\) | |||||||
\(464\) | 8.27492 | 0.384153 | ||||||||
\(465\) | −5.45017 | −0.252745 | ||||||||
\(466\) | −7.45017 | −0.345122 | ||||||||
\(467\) | −8.17525 | −0.378305 | −0.189153 | − | 0.981948i | \(-0.560574\pi\) | ||||
−0.189153 | + | 0.981948i | \(0.560574\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.72508 | −0.125833 | ||||||||
\(470\) | 28.0000 | 1.29154 | ||||||||
\(471\) | −3.72508 | −0.171643 | ||||||||
\(472\) | −11.8248 | −0.544278 | ||||||||
\(473\) | −47.2990 | −2.17481 | ||||||||
\(474\) | 8.00000 | 0.367452 | ||||||||
\(475\) | −86.9485 | −3.98947 | ||||||||
\(476\) | −3.00000 | −0.137505 | ||||||||
\(477\) | −3.54983 | −0.162536 | ||||||||
\(478\) | −5.27492 | −0.241269 | ||||||||
\(479\) | −20.0000 | −0.913823 | −0.456912 | − | 0.889512i | \(-0.651044\pi\) | ||||
−0.456912 | + | 0.889512i | \(0.651044\pi\) | |||||||
\(480\) | 4.27492 | 0.195122 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −15.7251 | −0.716258 | ||||||||
\(483\) | 5.27492 | 0.240017 | ||||||||
\(484\) | 5.00000 | 0.227273 | ||||||||
\(485\) | −2.35050 | −0.106731 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 1.09967 | 0.0498308 | 0.0249154 | − | 0.999690i | \(-0.492068\pi\) | ||||
0.0249154 | + | 0.999690i | \(0.492068\pi\) | |||||||
\(488\) | 9.00000 | 0.407411 | ||||||||
\(489\) | 13.2749 | 0.600313 | ||||||||
\(490\) | 4.27492 | 0.193121 | ||||||||
\(491\) | 25.0997 | 1.13273 | 0.566366 | − | 0.824154i | \(-0.308349\pi\) | ||||
0.566366 | + | 0.824154i | \(0.308349\pi\) | |||||||
\(492\) | −8.27492 | −0.373062 | ||||||||
\(493\) | 24.8248 | 1.11805 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.0997 | −0.768573 | ||||||||
\(496\) | 1.27492 | 0.0572455 | ||||||||
\(497\) | 5.27492 | 0.236612 | ||||||||
\(498\) | −11.8248 | −0.529880 | ||||||||
\(499\) | 31.8248 | 1.42467 | 0.712336 | − | 0.701839i | \(-0.247637\pi\) | ||||
0.712336 | + | 0.701839i | \(0.247637\pi\) | |||||||
\(500\) | −35.3746 | −1.58200 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.2749 | −0.592489 | ||||||||
\(503\) | −21.0997 | −0.940788 | −0.470394 | − | 0.882457i | \(-0.655888\pi\) | ||||
−0.470394 | + | 0.882457i | \(0.655888\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −7.37459 | −0.328165 | ||||||||
\(506\) | 21.0997 | 0.937995 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.00000 | 0.354943 | ||||||||
\(509\) | 13.1752 | 0.583983 | 0.291991 | − | 0.956421i | \(-0.405682\pi\) | ||||
0.291991 | + | 0.956421i | \(0.405682\pi\) | |||||||
\(510\) | 12.8248 | 0.567890 | ||||||||
\(511\) | 5.72508 | 0.253263 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.54983 | −0.289182 | ||||||||
\(514\) | −15.0000 | −0.661622 | ||||||||
\(515\) | −22.5498 | −0.993664 | ||||||||
\(516\) | −11.8248 | −0.520556 | ||||||||
\(517\) | 26.1993 | 1.15225 | ||||||||
\(518\) | −0.274917 | −0.0120792 | ||||||||
\(519\) | −4.54983 | −0.199716 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.8248 | −0.912349 | −0.456174 | − | 0.889890i | \(-0.650781\pi\) | ||||
−0.456174 | + | 0.889890i | \(0.650781\pi\) | |||||||
\(522\) | −8.27492 | −0.362183 | ||||||||
\(523\) | −26.1993 | −1.14562 | −0.572809 | − | 0.819689i | \(-0.694146\pi\) | ||||
−0.572809 | + | 0.819689i | \(0.694146\pi\) | |||||||
\(524\) | −2.72508 | −0.119046 | ||||||||
\(525\) | −13.2749 | −0.579365 | ||||||||
\(526\) | −21.0997 | −0.919989 | ||||||||
\(527\) | 3.82475 | 0.166609 | ||||||||
\(528\) | 4.00000 | 0.174078 | ||||||||
\(529\) | 4.82475 | 0.209772 | ||||||||
\(530\) | −15.1752 | −0.659171 | ||||||||
\(531\) | 11.8248 | 0.513151 | ||||||||
\(532\) | 6.54983 | 0.283971 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.725083 | 0.0313774 | ||||||||
\(535\) | −10.9003 | −0.471262 | ||||||||
\(536\) | −2.72508 | −0.117706 | ||||||||
\(537\) | 1.45017 | 0.0625793 | ||||||||
\(538\) | 18.0000 | 0.776035 | ||||||||
\(539\) | 4.00000 | 0.172292 | ||||||||
\(540\) | −4.27492 | −0.183963 | ||||||||
\(541\) | −25.3746 | −1.09094 | −0.545469 | − | 0.838131i | \(-0.683649\pi\) | ||||
−0.545469 | + | 0.838131i | \(0.683649\pi\) | |||||||
\(542\) | 25.2749 | 1.08565 | ||||||||
\(543\) | −16.8248 | −0.722019 | ||||||||
\(544\) | −3.00000 | −0.128624 | ||||||||
\(545\) | −19.4502 | −0.833154 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.90033 | 0.124009 | 0.0620046 | − | 0.998076i | \(-0.480251\pi\) | ||||
0.0620046 | + | 0.998076i | \(0.480251\pi\) | |||||||
\(548\) | −22.8248 | −0.975025 | ||||||||
\(549\) | −9.00000 | −0.384111 | ||||||||
\(550\) | −53.0997 | −2.26418 | ||||||||
\(551\) | −54.1993 | −2.30897 | ||||||||
\(552\) | 5.27492 | 0.224515 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | −14.8248 | −0.629843 | ||||||||
\(555\) | 1.17525 | 0.0498865 | ||||||||
\(556\) | −9.09967 | −0.385912 | ||||||||
\(557\) | 35.1993 | 1.49144 | 0.745722 | − | 0.666257i | \(-0.232105\pi\) | ||||
0.745722 | + | 0.666257i | \(0.232105\pi\) | |||||||
\(558\) | −1.27492 | −0.0539715 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.27492 | 0.180648 | ||||||||
\(561\) | 12.0000 | 0.506640 | ||||||||
\(562\) | −20.8248 | −0.878439 | ||||||||
\(563\) | 24.0000 | 1.01148 | 0.505740 | − | 0.862686i | \(-0.331220\pi\) | ||||
0.505740 | + | 0.862686i | \(0.331220\pi\) | |||||||
\(564\) | 6.54983 | 0.275798 | ||||||||
\(565\) | −63.3746 | −2.66619 | ||||||||
\(566\) | 9.45017 | 0.397220 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 5.27492 | 0.221331 | ||||||||
\(569\) | 4.90033 | 0.205433 | 0.102716 | − | 0.994711i | \(-0.467247\pi\) | ||||
0.102716 | + | 0.994711i | \(0.467247\pi\) | |||||||
\(570\) | −28.0000 | −1.17279 | ||||||||
\(571\) | −14.7251 | −0.616226 | −0.308113 | − | 0.951350i | \(-0.599697\pi\) | ||||
−0.308113 | + | 0.951350i | \(0.599697\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.72508 | 0.280944 | ||||||||
\(574\) | −8.27492 | −0.345388 | ||||||||
\(575\) | −70.0241 | −2.92021 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −9.37459 | −0.390269 | −0.195135 | − | 0.980776i | \(-0.562514\pi\) | ||||
−0.195135 | + | 0.980776i | \(0.562514\pi\) | |||||||
\(578\) | 8.00000 | 0.332756 | ||||||||
\(579\) | 24.8248 | 1.03168 | ||||||||
\(580\) | −35.3746 | −1.46885 | ||||||||
\(581\) | −11.8248 | −0.490573 | ||||||||
\(582\) | −0.549834 | −0.0227914 | ||||||||
\(583\) | −14.1993 | −0.588076 | ||||||||
\(584\) | 5.72508 | 0.236906 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.2749 | −0.754930 | ||||||||
\(587\) | −8.92442 | −0.368350 | −0.184175 | − | 0.982893i | \(-0.558961\pi\) | ||||
−0.184175 | + | 0.982893i | \(0.558961\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −8.35050 | −0.344076 | ||||||||
\(590\) | 50.5498 | 2.08110 | ||||||||
\(591\) | 21.8248 | 0.897750 | ||||||||
\(592\) | −0.274917 | −0.0112990 | ||||||||
\(593\) | −4.45017 | −0.182746 | −0.0913732 | − | 0.995817i | \(-0.529126\pi\) | ||||
−0.0913732 | + | 0.995817i | \(0.529126\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 12.8248 | 0.525764 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 11.8248 | 0.483955 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.7251 | −0.438215 | −0.219108 | − | 0.975701i | \(-0.570315\pi\) | ||||
−0.219108 | + | 0.975701i | \(0.570315\pi\) | |||||||
\(600\) | −13.2749 | −0.541946 | ||||||||
\(601\) | −7.72508 | −0.315113 | −0.157556 | − | 0.987510i | \(-0.550362\pi\) | ||||
−0.157556 | + | 0.987510i | \(0.550362\pi\) | |||||||
\(602\) | −11.8248 | −0.481941 | ||||||||
\(603\) | 2.72508 | 0.110974 | ||||||||
\(604\) | −13.0997 | −0.533018 | ||||||||
\(605\) | −21.3746 | −0.869000 | ||||||||
\(606\) | −1.72508 | −0.0700767 | ||||||||
\(607\) | 14.7251 | 0.597673 | 0.298836 | − | 0.954304i | \(-0.403402\pi\) | ||||
0.298836 | + | 0.954304i | \(0.403402\pi\) | |||||||
\(608\) | 6.54983 | 0.265631 | ||||||||
\(609\) | −8.27492 | −0.335317 | ||||||||
\(610\) | −38.4743 | −1.55778 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 3.00000 | 0.121268 | ||||||||
\(613\) | −29.3746 | −1.18643 | −0.593214 | − | 0.805045i | \(-0.702141\pi\) | ||||
−0.593214 | + | 0.805045i | \(0.702141\pi\) | |||||||
\(614\) | −1.45017 | −0.0585239 | ||||||||
\(615\) | 35.3746 | 1.42644 | ||||||||
\(616\) | 4.00000 | 0.161165 | ||||||||
\(617\) | −39.9244 | −1.60730 | −0.803648 | − | 0.595105i | \(-0.797111\pi\) | ||||
−0.803648 | + | 0.595105i | \(0.797111\pi\) | |||||||
\(618\) | −5.27492 | −0.212188 | ||||||||
\(619\) | 15.6495 | 0.629007 | 0.314503 | − | 0.949256i | \(-0.398162\pi\) | ||||
0.314503 | + | 0.949256i | \(0.398162\pi\) | |||||||
\(620\) | −5.45017 | −0.218884 | ||||||||
\(621\) | −5.27492 | −0.211675 | ||||||||
\(622\) | 2.54983 | 0.102239 | ||||||||
\(623\) | 0.725083 | 0.0290498 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 84.8488 | 3.39395 | ||||||||
\(626\) | −17.6495 | −0.705416 | ||||||||
\(627\) | −26.1993 | −1.04630 | ||||||||
\(628\) | −3.72508 | −0.148647 | ||||||||
\(629\) | −0.824752 | −0.0328850 | ||||||||
\(630\) | −4.27492 | −0.170317 | ||||||||
\(631\) | 29.0997 | 1.15844 | 0.579220 | − | 0.815171i | \(-0.303357\pi\) | ||||
0.579220 | + | 0.815171i | \(0.303357\pi\) | |||||||
\(632\) | 8.00000 | 0.318223 | ||||||||
\(633\) | 21.0997 | 0.838637 | ||||||||
\(634\) | −7.54983 | −0.299842 | ||||||||
\(635\) | −34.1993 | −1.35716 | ||||||||
\(636\) | −3.54983 | −0.140760 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −33.0997 | −1.31043 | ||||||||
\(639\) | −5.27492 | −0.208673 | ||||||||
\(640\) | 4.27492 | 0.168981 | ||||||||
\(641\) | 18.8248 | 0.743533 | 0.371766 | − | 0.928326i | \(-0.378752\pi\) | ||||
0.371766 | + | 0.928326i | \(0.378752\pi\) | |||||||
\(642\) | −2.54983 | −0.100634 | ||||||||
\(643\) | 32.7492 | 1.29150 | 0.645751 | − | 0.763548i | \(-0.276545\pi\) | ||||
0.645751 | + | 0.763548i | \(0.276545\pi\) | |||||||
\(644\) | 5.27492 | 0.207861 | ||||||||
\(645\) | 50.5498 | 1.99040 | ||||||||
\(646\) | 19.6495 | 0.773099 | ||||||||
\(647\) | 9.45017 | 0.371524 | 0.185762 | − | 0.982595i | \(-0.440525\pi\) | ||||
0.185762 | + | 0.982595i | \(0.440525\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 47.2990 | 1.85665 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.27492 | −0.0499679 | ||||||||
\(652\) | 13.2749 | 0.519886 | ||||||||
\(653\) | 33.4743 | 1.30995 | 0.654974 | − | 0.755651i | \(-0.272679\pi\) | ||||
0.654974 | + | 0.755651i | \(0.272679\pi\) | |||||||
\(654\) | −4.54983 | −0.177913 | ||||||||
\(655\) | 11.6495 | 0.455184 | ||||||||
\(656\) | −8.27492 | −0.323081 | ||||||||
\(657\) | −5.72508 | −0.223357 | ||||||||
\(658\) | 6.54983 | 0.255339 | ||||||||
\(659\) | −13.4502 | −0.523944 | −0.261972 | − | 0.965075i | \(-0.584373\pi\) | ||||
−0.261972 | + | 0.965075i | \(0.584373\pi\) | |||||||
\(660\) | −17.0997 | −0.665604 | ||||||||
\(661\) | −9.90033 | −0.385078 | −0.192539 | − | 0.981289i | \(-0.561672\pi\) | ||||
−0.192539 | + | 0.981289i | \(0.561672\pi\) | |||||||
\(662\) | 4.00000 | 0.155464 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.8248 | −0.458889 | ||||||||
\(665\) | −28.0000 | −1.08579 | ||||||||
\(666\) | 0.274917 | 0.0106528 | ||||||||
\(667\) | −43.6495 | −1.69012 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.7251 | −0.414656 | ||||||||
\(670\) | 11.6495 | 0.450060 | ||||||||
\(671\) | −36.0000 | −1.38976 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −18.0997 | −0.697691 | −0.348845 | − | 0.937180i | \(-0.613426\pi\) | ||||
−0.348845 | + | 0.937180i | \(0.613426\pi\) | |||||||
\(674\) | −0.274917 | −0.0105894 | ||||||||
\(675\) | 13.2749 | 0.510952 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.6495 | −1.29326 | −0.646628 | − | 0.762806i | \(-0.723821\pi\) | ||||
−0.646628 | + | 0.762806i | \(0.723821\pi\) | |||||||
\(678\) | −14.8248 | −0.569341 | ||||||||
\(679\) | −0.549834 | −0.0211007 | ||||||||
\(680\) | 12.8248 | 0.491807 | ||||||||
\(681\) | 21.0997 | 0.808541 | ||||||||
\(682\) | −5.09967 | −0.195276 | ||||||||
\(683\) | 4.35050 | 0.166467 | 0.0832336 | − | 0.996530i | \(-0.473475\pi\) | ||||
0.0832336 | + | 0.996530i | \(0.473475\pi\) | |||||||
\(684\) | −6.54983 | −0.250439 | ||||||||
\(685\) | 97.5739 | 3.72811 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −12.7251 | −0.485492 | ||||||||
\(688\) | −11.8248 | −0.450814 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −22.5498 | −0.858458 | ||||||||
\(691\) | −8.00000 | −0.304334 | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||||
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | −4.54983 | −0.172959 | ||||||||
\(693\) | −4.00000 | −0.151947 | ||||||||
\(694\) | −30.5498 | −1.15966 | ||||||||
\(695\) | 38.9003 | 1.47557 | ||||||||
\(696\) | −8.27492 | −0.313660 | ||||||||
\(697\) | −24.8248 | −0.940305 | ||||||||
\(698\) | −34.9244 | −1.32191 | ||||||||
\(699\) | 7.45017 | 0.281791 | ||||||||
\(700\) | −13.2749 | −0.501745 | ||||||||
\(701\) | 14.9244 | 0.563688 | 0.281844 | − | 0.959460i | \(-0.409054\pi\) | ||||
0.281844 | + | 0.959460i | \(0.409054\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.80066 | 0.0679133 | ||||||||
\(704\) | 4.00000 | 0.150756 | ||||||||
\(705\) | −28.0000 | −1.05454 | ||||||||
\(706\) | −19.5498 | −0.735768 | ||||||||
\(707\) | −1.72508 | −0.0648784 | ||||||||
\(708\) | 11.8248 | 0.444401 | ||||||||
\(709\) | 47.3746 | 1.77919 | 0.889595 | − | 0.456750i | \(-0.150987\pi\) | ||||
0.889595 | + | 0.456750i | \(0.150987\pi\) | |||||||
\(710\) | −22.5498 | −0.846280 | ||||||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 0.725083 | 0.0271736 | ||||||||
\(713\) | −6.72508 | −0.251856 | ||||||||
\(714\) | 3.00000 | 0.112272 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.45017 | 0.0541952 | ||||||||
\(717\) | 5.27492 | 0.196995 | ||||||||
\(718\) | −1.09967 | −0.0410393 | ||||||||
\(719\) | −8.00000 | −0.298350 | −0.149175 | − | 0.988811i | \(-0.547662\pi\) | ||||
−0.149175 | + | 0.988811i | \(0.547662\pi\) | |||||||
\(720\) | −4.27492 | −0.159317 | ||||||||
\(721\) | −5.27492 | −0.196448 | ||||||||
\(722\) | −23.9003 | −0.889478 | ||||||||
\(723\) | 15.7251 | 0.584822 | ||||||||
\(724\) | −16.8248 | −0.625287 | ||||||||
\(725\) | 109.849 | 4.07968 | ||||||||
\(726\) | −5.00000 | −0.185567 | ||||||||
\(727\) | 19.8248 | 0.735259 | 0.367630 | − | 0.929972i | \(-0.380169\pi\) | ||||
0.367630 | + | 0.929972i | \(0.380169\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −24.4743 | −0.905833 | ||||||||
\(731\) | −35.4743 | −1.31206 | ||||||||
\(732\) | −9.00000 | −0.332650 | ||||||||
\(733\) | 32.6495 | 1.20594 | 0.602968 | − | 0.797765i | \(-0.293984\pi\) | ||||
0.602968 | + | 0.797765i | \(0.293984\pi\) | |||||||
\(734\) | −13.2749 | −0.489986 | ||||||||
\(735\) | −4.27492 | −0.157683 | ||||||||
\(736\) | 5.27492 | 0.194436 | ||||||||
\(737\) | 10.9003 | 0.401519 | ||||||||
\(738\) | 8.27492 | 0.304604 | ||||||||
\(739\) | 49.2749 | 1.81261 | 0.906304 | − | 0.422627i | \(-0.138892\pi\) | ||||
0.906304 | + | 0.422627i | \(0.138892\pi\) | |||||||
\(740\) | 1.17525 | 0.0432030 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.54983 | −0.130319 | ||||||||
\(743\) | 4.17525 | 0.153175 | 0.0765875 | − | 0.997063i | \(-0.475598\pi\) | ||||
0.0765875 | + | 0.997063i | \(0.475598\pi\) | |||||||
\(744\) | −1.27492 | −0.0467407 | ||||||||
\(745\) | −4.27492 | −0.156621 | ||||||||
\(746\) | −26.8248 | −0.982124 | ||||||||
\(747\) | 11.8248 | 0.432645 | ||||||||
\(748\) | 12.0000 | 0.438763 | ||||||||
\(749\) | −2.54983 | −0.0931689 | ||||||||
\(750\) | 35.3746 | 1.29170 | ||||||||
\(751\) | −18.5498 | −0.676893 | −0.338447 | − | 0.940986i | \(-0.609901\pi\) | ||||
−0.338447 | + | 0.940986i | \(0.609901\pi\) | |||||||
\(752\) | 6.54983 | 0.238848 | ||||||||
\(753\) | 13.2749 | 0.483765 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 56.0000 | 2.03805 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | −26.0000 | −0.944986 | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | −20.0000 | −0.726433 | ||||||||
\(759\) | −21.0997 | −0.765869 | ||||||||
\(760\) | −28.0000 | −1.01567 | ||||||||
\(761\) | −20.1993 | −0.732225 | −0.366113 | − | 0.930571i | \(-0.619312\pi\) | ||||
−0.366113 | + | 0.930571i | \(0.619312\pi\) | |||||||
\(762\) | −8.00000 | −0.289809 | ||||||||
\(763\) | −4.54983 | −0.164715 | ||||||||
\(764\) | 6.72508 | 0.243305 | ||||||||
\(765\) | −12.8248 | −0.463680 | ||||||||
\(766\) | 22.1993 | 0.802095 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −41.6495 | −1.50192 | −0.750960 | − | 0.660348i | \(-0.770409\pi\) | ||||
−0.750960 | + | 0.660348i | \(0.770409\pi\) | |||||||
\(770\) | −17.0997 | −0.616229 | ||||||||
\(771\) | 15.0000 | 0.540212 | ||||||||
\(772\) | 24.8248 | 0.893462 | ||||||||
\(773\) | 20.9003 | 0.751733 | 0.375866 | − | 0.926674i | \(-0.377345\pi\) | ||||
0.375866 | + | 0.926674i | \(0.377345\pi\) | |||||||
\(774\) | 11.8248 | 0.425032 | ||||||||
\(775\) | 16.9244 | 0.607943 | ||||||||
\(776\) | −0.549834 | −0.0197379 | ||||||||
\(777\) | 0.274917 | 0.00986260 | ||||||||
\(778\) | 24.6495 | 0.883728 | ||||||||
\(779\) | 54.1993 | 1.94189 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.0997 | −0.755006 | ||||||||
\(782\) | 15.8248 | 0.565892 | ||||||||
\(783\) | 8.27492 | 0.295721 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 15.9244 | 0.568367 | ||||||||
\(786\) | 2.72508 | 0.0972005 | ||||||||
\(787\) | −21.0997 | −0.752122 | −0.376061 | − | 0.926595i | \(-0.622722\pi\) | ||||
−0.376061 | + | 0.926595i | \(0.622722\pi\) | |||||||
\(788\) | 21.8248 | 0.777475 | ||||||||
\(789\) | 21.0997 | 0.751168 | ||||||||
\(790\) | −34.1993 | −1.21676 | ||||||||
\(791\) | −14.8248 | −0.527107 | ||||||||
\(792\) | −4.00000 | −0.142134 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 23.2749 | 0.825996 | ||||||||
\(795\) | 15.1752 | 0.538211 | ||||||||
\(796\) | 11.8248 | 0.419117 | ||||||||
\(797\) | 16.5498 | 0.586225 | 0.293113 | − | 0.956078i | \(-0.405309\pi\) | ||||
0.293113 | + | 0.956078i | \(0.405309\pi\) | |||||||
\(798\) | −6.54983 | −0.231862 | ||||||||
\(799\) | 19.6495 | 0.695149 | ||||||||
\(800\) | −13.2749 | −0.469339 | ||||||||
\(801\) | −0.725083 | −0.0256195 | ||||||||
\(802\) | −2.27492 | −0.0803301 | ||||||||
\(803\) | −22.9003 | −0.808135 | ||||||||
\(804\) | 2.72508 | 0.0961063 | ||||||||
\(805\) | −22.5498 | −0.794777 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.0000 | −0.633630 | ||||||||
\(808\) | −1.72508 | −0.0606882 | ||||||||
\(809\) | 9.72508 | 0.341916 | 0.170958 | − | 0.985278i | \(-0.445314\pi\) | ||||
0.170958 | + | 0.985278i | \(0.445314\pi\) | |||||||
\(810\) | 4.27492 | 0.150205 | ||||||||
\(811\) | −5.09967 | −0.179074 | −0.0895368 | − | 0.995984i | \(-0.528539\pi\) | ||||
−0.0895368 | + | 0.995984i | \(0.528539\pi\) | |||||||
\(812\) | −8.27492 | −0.290393 | ||||||||
\(813\) | −25.2749 | −0.886430 | ||||||||
\(814\) | 1.09967 | 0.0385434 | ||||||||
\(815\) | −56.7492 | −1.98784 | ||||||||
\(816\) | 3.00000 | 0.105021 | ||||||||
\(817\) | 77.4502 | 2.70964 | ||||||||
\(818\) | −29.9244 | −1.04628 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 35.3746 | 1.23533 | ||||||||
\(821\) | −15.2749 | −0.533098 | −0.266549 | − | 0.963821i | \(-0.585883\pi\) | ||||
−0.266549 | + | 0.963821i | \(0.585883\pi\) | |||||||
\(822\) | 22.8248 | 0.796105 | ||||||||
\(823\) | −6.90033 | −0.240530 | −0.120265 | − | 0.992742i | \(-0.538374\pi\) | ||||
−0.120265 | + | 0.992742i | \(0.538374\pi\) | |||||||
\(824\) | −5.27492 | −0.183760 | ||||||||
\(825\) | 53.0997 | 1.84869 | ||||||||
\(826\) | 11.8248 | 0.411436 | ||||||||
\(827\) | −5.09967 | −0.177333 | −0.0886664 | − | 0.996061i | \(-0.528261\pi\) | ||||
−0.0886664 | + | 0.996061i | \(0.528261\pi\) | |||||||
\(828\) | −5.27492 | −0.183316 | ||||||||
\(829\) | −44.8248 | −1.55683 | −0.778414 | − | 0.627751i | \(-0.783976\pi\) | ||||
−0.778414 | + | 0.627751i | \(0.783976\pi\) | |||||||
\(830\) | 50.5498 | 1.75461 | ||||||||
\(831\) | 14.8248 | 0.514265 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.00000 | 0.103944 | ||||||||
\(834\) | 9.09967 | 0.315096 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −26.1993 | −0.906123 | ||||||||
\(837\) | 1.27492 | 0.0440676 | ||||||||
\(838\) | 22.3746 | 0.772917 | ||||||||
\(839\) | 20.7492 | 0.716341 | 0.358170 | − | 0.933656i | \(-0.383401\pi\) | ||||
0.358170 | + | 0.933656i | \(0.383401\pi\) | |||||||
\(840\) | −4.27492 | −0.147499 | ||||||||
\(841\) | 39.4743 | 1.36118 | ||||||||
\(842\) | 8.27492 | 0.285172 | ||||||||
\(843\) | 20.8248 | 0.717243 | ||||||||
\(844\) | 21.0997 | 0.726281 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.54983 | −0.225188 | ||||||||
\(847\) | −5.00000 | −0.171802 | ||||||||
\(848\) | −3.54983 | −0.121902 | ||||||||
\(849\) | −9.45017 | −0.324329 | ||||||||
\(850\) | −39.8248 | −1.36598 | ||||||||
\(851\) | 1.45017 | 0.0497110 | ||||||||
\(852\) | −5.27492 | −0.180716 | ||||||||
\(853\) | 14.4502 | 0.494764 | 0.247382 | − | 0.968918i | \(-0.420430\pi\) | ||||
0.247382 | + | 0.968918i | \(0.420430\pi\) | |||||||
\(854\) | −9.00000 | −0.307974 | ||||||||
\(855\) | 28.0000 | 0.957580 | ||||||||
\(856\) | −2.54983 | −0.0871515 | ||||||||
\(857\) | −36.8248 | −1.25791 | −0.628955 | − | 0.777442i | \(-0.716517\pi\) | ||||
−0.628955 | + | 0.777442i | \(0.716517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.6495 | −0.943389 | −0.471694 | − | 0.881762i | \(-0.656357\pi\) | ||||
−0.471694 | + | 0.881762i | \(0.656357\pi\) | |||||||
\(860\) | 50.5498 | 1.72374 | ||||||||
\(861\) | 8.27492 | 0.282008 | ||||||||
\(862\) | −13.2749 | −0.452145 | ||||||||
\(863\) | −35.2990 | −1.20159 | −0.600796 | − | 0.799402i | \(-0.705150\pi\) | ||||
−0.600796 | + | 0.799402i | \(0.705150\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 19.4502 | 0.661325 | ||||||||
\(866\) | 10.2749 | 0.349156 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | −1.27492 | −0.0432735 | ||||||||
\(869\) | −32.0000 | −1.08553 | ||||||||
\(870\) | 35.3746 | 1.19931 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −4.54983 | −0.154077 | ||||||||
\(873\) | 0.549834 | 0.0186091 | ||||||||
\(874\) | −34.5498 | −1.16867 | ||||||||
\(875\) | 35.3746 | 1.19588 | ||||||||
\(876\) | −5.72508 | −0.193433 | ||||||||
\(877\) | 3.72508 | 0.125787 | 0.0628936 | − | 0.998020i | \(-0.479967\pi\) | ||||
0.0628936 | + | 0.998020i | \(0.479967\pi\) | |||||||
\(878\) | −13.0997 | −0.442092 | ||||||||
\(879\) | 18.2749 | 0.616398 | ||||||||
\(880\) | −17.0997 | −0.576430 | ||||||||
\(881\) | 1.54983 | 0.0522152 | 0.0261076 | − | 0.999659i | \(-0.491689\pi\) | ||||
0.0261076 | + | 0.999659i | \(0.491689\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 58.0241 | 1.95267 | 0.976333 | − | 0.216273i | \(-0.0693900\pi\) | ||||
0.976333 | + | 0.216273i | \(0.0693900\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −50.5498 | −1.69921 | ||||||||
\(886\) | −34.5498 | −1.16072 | ||||||||
\(887\) | 46.5498 | 1.56299 | 0.781495 | − | 0.623911i | \(-0.214457\pi\) | ||||
0.781495 | + | 0.623911i | \(0.214457\pi\) | |||||||
\(888\) | 0.274917 | 0.00922562 | ||||||||
\(889\) | −8.00000 | −0.268311 | ||||||||
\(890\) | −3.09967 | −0.103901 | ||||||||
\(891\) | 4.00000 | 0.134005 | ||||||||
\(892\) | −10.7251 | −0.359102 | ||||||||
\(893\) | −42.9003 | −1.43560 | ||||||||
\(894\) | −1.00000 | −0.0334450 | ||||||||
\(895\) | −6.19934 | −0.207221 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.0997 | −0.637364 | ||||||||
\(899\) | 10.5498 | 0.351857 | ||||||||
\(900\) | 13.2749 | 0.442497 | ||||||||
\(901\) | −10.6495 | −0.354786 | ||||||||
\(902\) | 33.0997 | 1.10210 | ||||||||
\(903\) | 11.8248 | 0.393503 | ||||||||
\(904\) | −14.8248 | −0.493064 | ||||||||
\(905\) | 71.9244 | 2.39085 | ||||||||
\(906\) | 13.0997 | 0.435207 | ||||||||
\(907\) | −39.8248 | −1.32236 | −0.661180 | − | 0.750228i | \(-0.729944\pi\) | ||||
−0.661180 | + | 0.750228i | \(0.729944\pi\) | |||||||
\(908\) | 21.0997 | 0.700217 | ||||||||
\(909\) | 1.72508 | 0.0572174 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.0997 | −0.831589 | −0.415795 | − | 0.909459i | \(-0.636496\pi\) | ||||
−0.415795 | + | 0.909459i | \(0.636496\pi\) | |||||||
\(912\) | −6.54983 | −0.216887 | ||||||||
\(913\) | 47.2990 | 1.56537 | ||||||||
\(914\) | −17.0000 | −0.562310 | ||||||||
\(915\) | 38.4743 | 1.27192 | ||||||||
\(916\) | −12.7251 | −0.420449 | ||||||||
\(917\) | 2.72508 | 0.0899902 | ||||||||
\(918\) | −3.00000 | −0.0990148 | ||||||||
\(919\) | 39.6495 | 1.30792 | 0.653958 | − | 0.756531i | \(-0.273107\pi\) | ||||
0.653958 | + | 0.756531i | \(0.273107\pi\) | |||||||
\(920\) | −22.5498 | −0.743446 | ||||||||
\(921\) | 1.45017 | 0.0477846 | ||||||||
\(922\) | −19.3746 | −0.638068 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −4.00000 | −0.131590 | ||||||||
\(925\) | −3.64950 | −0.119995 | ||||||||
\(926\) | −10.5498 | −0.346689 | ||||||||
\(927\) | 5.27492 | 0.173251 | ||||||||
\(928\) | −8.27492 | −0.271637 | ||||||||
\(929\) | −53.5498 | −1.75691 | −0.878457 | − | 0.477822i | \(-0.841426\pi\) | ||||
−0.878457 | + | 0.477822i | \(0.841426\pi\) | |||||||
\(930\) | 5.45017 | 0.178718 | ||||||||
\(931\) | −6.54983 | −0.214662 | ||||||||
\(932\) | 7.45017 | 0.244038 | ||||||||
\(933\) | −2.54983 | −0.0834778 | ||||||||
\(934\) | 8.17525 | 0.267502 | ||||||||
\(935\) | −51.2990 | −1.67766 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.1752 | 0.626428 | 0.313214 | − | 0.949683i | \(-0.398594\pi\) | ||||
0.313214 | + | 0.949683i | \(0.398594\pi\) | |||||||
\(938\) | 2.72508 | 0.0889771 | ||||||||
\(939\) | 17.6495 | 0.575970 | ||||||||
\(940\) | −28.0000 | −0.913259 | ||||||||
\(941\) | −37.6495 | −1.22734 | −0.613669 | − | 0.789563i | \(-0.710307\pi\) | ||||
−0.613669 | + | 0.789563i | \(0.710307\pi\) | |||||||
\(942\) | 3.72508 | 0.121370 | ||||||||
\(943\) | 43.6495 | 1.42142 | ||||||||
\(944\) | 11.8248 | 0.384863 | ||||||||
\(945\) | 4.27492 | 0.139063 | ||||||||
\(946\) | 47.2990 | 1.53782 | ||||||||
\(947\) | 9.09967 | 0.295700 | 0.147850 | − | 0.989010i | \(-0.452765\pi\) | ||||
0.147850 | + | 0.989010i | \(0.452765\pi\) | |||||||
\(948\) | −8.00000 | −0.259828 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 86.9485 | 2.82098 | ||||||||
\(951\) | 7.54983 | 0.244820 | ||||||||
\(952\) | 3.00000 | 0.0972306 | ||||||||
\(953\) | −11.0997 | −0.359554 | −0.179777 | − | 0.983707i | \(-0.557538\pi\) | ||||
−0.179777 | + | 0.983707i | \(0.557538\pi\) | |||||||
\(954\) | 3.54983 | 0.114930 | ||||||||
\(955\) | −28.7492 | −0.930301 | ||||||||
\(956\) | 5.27492 | 0.170603 | ||||||||
\(957\) | 33.0997 | 1.06996 | ||||||||
\(958\) | 20.0000 | 0.646171 | ||||||||
\(959\) | 22.8248 | 0.737050 | ||||||||
\(960\) | −4.27492 | −0.137972 | ||||||||
\(961\) | −29.3746 | −0.947567 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.54983 | 0.0821673 | ||||||||
\(964\) | 15.7251 | 0.506471 | ||||||||
\(965\) | −106.124 | −3.41624 | ||||||||
\(966\) | −5.27492 | −0.169718 | ||||||||
\(967\) | 18.5498 | 0.596522 | 0.298261 | − | 0.954484i | \(-0.403593\pi\) | ||||
0.298261 | + | 0.954484i | \(0.403593\pi\) | |||||||
\(968\) | −5.00000 | −0.160706 | ||||||||
\(969\) | −19.6495 | −0.631233 | ||||||||
\(970\) | 2.35050 | 0.0754699 | ||||||||
\(971\) | 48.5739 | 1.55881 | 0.779406 | − | 0.626520i | \(-0.215521\pi\) | ||||
0.779406 | + | 0.626520i | \(0.215521\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 9.09967 | 0.291722 | ||||||||
\(974\) | −1.09967 | −0.0352357 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.00000 | −0.288083 | ||||||||
\(977\) | −24.6254 | −0.787837 | −0.393918 | − | 0.919145i | \(-0.628881\pi\) | ||||
−0.393918 | + | 0.919145i | \(0.628881\pi\) | |||||||
\(978\) | −13.2749 | −0.424485 | ||||||||
\(979\) | −2.90033 | −0.0926950 | ||||||||
\(980\) | −4.27492 | −0.136557 | ||||||||
\(981\) | 4.54983 | 0.145265 | ||||||||
\(982\) | −25.0997 | −0.800963 | ||||||||
\(983\) | −53.8488 | −1.71751 | −0.858756 | − | 0.512385i | \(-0.828762\pi\) | ||||
−0.858756 | + | 0.512385i | \(0.828762\pi\) | |||||||
\(984\) | 8.27492 | 0.263795 | ||||||||
\(985\) | −93.2990 | −2.97275 | ||||||||
\(986\) | −24.8248 | −0.790581 | ||||||||
\(987\) | −6.54983 | −0.208484 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 62.3746 | 1.98340 | ||||||||
\(990\) | 17.0997 | 0.543463 | ||||||||
\(991\) | −36.7492 | −1.16738 | −0.583688 | − | 0.811978i | \(-0.698391\pi\) | ||||
−0.583688 | + | 0.811978i | \(0.698391\pi\) | |||||||
\(992\) | −1.27492 | −0.0404787 | ||||||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | −5.27492 | −0.167310 | ||||||||
\(995\) | −50.5498 | −1.60254 | ||||||||
\(996\) | 11.8248 | 0.374682 | ||||||||
\(997\) | −3.90033 | −0.123525 | −0.0617624 | − | 0.998091i | \(-0.519672\pi\) | ||||
−0.0617624 | + | 0.998091i | \(0.519672\pi\) | |||||||
\(998\) | −31.8248 | −1.00739 | ||||||||
\(999\) | −0.274917 | −0.00869800 |
(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 | 7098.2.a.bm.1.1 | 2 | ||
13.4 | even | 6 | 546.2.l.j.211.2 | ✓ | 4 | ||
13.10 | even | 6 | 546.2.l.j.295.2 | yes | 4 | ||
13.12 | even | 2 | 7098.2.a.ca.1.2 | 2 | |||
39.17 | odd | 6 | 1638.2.r.x.757.1 | 4 | |||
39.23 | odd | 6 | 1638.2.r.x.1387.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.j.211.2 | ✓ | 4 | 13.4 | even | 6 | ||
546.2.l.j.295.2 | yes | 4 | 13.10 | even | 6 | ||
1638.2.r.x.757.1 | 4 | 39.17 | odd | 6 | |||
1638.2.r.x.1387.1 | 4 | 39.23 | odd | 6 | |||
7098.2.a.bm.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7098.2.a.ca.1.2 | 2 | 13.12 | even | 2 |