Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,2,Mod(1,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, 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("648.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.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: | \(5.17430605098\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 72) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.37228 | 1.06092 | 0.530458 | − | 0.847711i | \(-0.322020\pi\) | ||||
0.530458 | + | 0.847711i | \(0.322020\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.37228 | 1.65257 | 0.826284 | − | 0.563254i | \(-0.190451\pi\) | ||||
0.826284 | + | 0.563254i | \(0.190451\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.372281 | −0.103252 | −0.0516261 | − | 0.998666i | \(-0.516440\pi\) | ||||
−0.0516261 | + | 0.998666i | \(0.516440\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.37228 | −1.30297 | −0.651485 | − | 0.758662i | \(-0.725854\pi\) | ||||
−0.651485 | + | 0.758662i | \(0.725854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.627719 | 0.144009 | 0.0720043 | − | 0.997404i | \(-0.477060\pi\) | ||||
0.0720043 | + | 0.997404i | \(0.477060\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.372281 | −0.0776260 | −0.0388130 | − | 0.999246i | \(-0.512358\pi\) | ||||
−0.0388130 | + | 0.999246i | \(0.512358\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.627719 | 0.125544 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.37228 | −0.811912 | −0.405956 | − | 0.913893i | \(-0.633061\pi\) | ||||
−0.405956 | + | 0.913893i | \(0.633061\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.37228 | 1.14450 | 0.572248 | − | 0.820081i | \(-0.306072\pi\) | ||||
0.572248 | + | 0.820081i | \(0.306072\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.3723 | 1.75324 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.74456 | 1.43760 | 0.718799 | − | 0.695218i | \(-0.244692\pi\) | ||||
0.718799 | + | 0.695218i | \(0.244692\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.7446 | −1.83419 | −0.917096 | − | 0.398666i | \(-0.869473\pi\) | ||||
−0.917096 | + | 0.398666i | \(0.869473\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.74456 | −0.266043 | −0.133022 | − | 0.991113i | \(-0.542468\pi\) | ||||
−0.133022 | + | 0.991113i | \(0.542468\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.37228 | 0.637763 | 0.318881 | − | 0.947795i | \(-0.396693\pi\) | ||||
0.318881 | + | 0.947795i | \(0.396693\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.1168 | 1.73098 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.744563 | 0.102274 | 0.0511368 | − | 0.998692i | \(-0.483716\pi\) | ||||
0.0511368 | + | 0.998692i | \(0.483716\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.37228 | 0.319878 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.00000 | 0.911322 | 0.455661 | − | 0.890153i | \(-0.349403\pi\) | ||||
0.455661 | + | 0.890153i | \(0.349403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.37228 | 0.303739 | 0.151870 | − | 0.988401i | \(-0.451471\pi\) | ||||
0.151870 | + | 0.988401i | \(0.451471\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.883156 | −0.109542 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.74456 | −0.457471 | −0.228736 | − | 0.973489i | \(-0.573459\pi\) | ||||
−0.228736 | + | 0.973489i | \(0.573459\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1168 | −1.41817 | −0.709085 | − | 0.705123i | \(-0.750892\pi\) | ||||
−0.709085 | + | 0.705123i | \(0.750892\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.37228 | 0.498268 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.37228 | −0.716938 | −0.358469 | − | 0.933542i | \(-0.616701\pi\) | ||||
−0.358469 | + | 0.933542i | \(0.616701\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.62772 | 1.05678 | 0.528390 | − | 0.849002i | \(-0.322796\pi\) | ||||
0.528390 | + | 0.849002i | \(0.322796\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.7446 | −1.38234 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.62772 | −0.170631 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.48913 | 0.152781 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.74456 | 0.177133 | 0.0885667 | − | 0.996070i | \(-0.471771\pi\) | ||||
0.0885667 | + | 0.996070i | \(0.471771\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.11684 | −0.708152 | −0.354076 | − | 0.935217i | \(-0.615205\pi\) | ||||
−0.354076 | + | 0.935217i | \(0.615205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.3723 | −1.21908 | −0.609539 | − | 0.792756i | \(-0.708645\pi\) | ||||
−0.609539 | + | 0.792756i | \(0.708645\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.8614 | −1.24336 | −0.621680 | − | 0.783272i | \(-0.713549\pi\) | ||||
−0.621680 | + | 0.783272i | \(0.713549\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.74456 | −0.454447 | −0.227223 | − | 0.973843i | \(-0.572965\pi\) | ||||
−0.227223 | + | 0.973843i | \(0.572965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.37228 | −0.411310 | −0.205655 | − | 0.978625i | \(-0.565932\pi\) | ||||
−0.205655 | + | 0.978625i | \(0.565932\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.883156 | −0.0823547 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −23.4891 | −2.15324 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.3723 | −0.927725 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.74456 | 0.598483 | 0.299242 | − | 0.954177i | \(-0.403266\pi\) | ||||
0.299242 | + | 0.954177i | \(0.403266\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.3723 | 1.60519 | 0.802597 | − | 0.596522i | \(-0.203451\pi\) | ||||
0.802597 | + | 0.596522i | \(0.203451\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.74456 | 0.237984 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.7446 | 1.51602 | 0.758010 | − | 0.652243i | \(-0.226172\pi\) | ||||
0.758010 | + | 0.652243i | \(0.226172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.74456 | 0.487247 | 0.243624 | − | 0.969870i | \(-0.421664\pi\) | ||||
0.243624 | + | 0.969870i | \(0.421664\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.372281 | −0.0311317 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.3723 | −0.861371 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.37228 | −0.685884 | −0.342942 | − | 0.939357i | \(-0.611423\pi\) | ||||
−0.342942 | + | 0.939357i | \(0.611423\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.372281 | 0.0302958 | 0.0151479 | − | 0.999885i | \(-0.495178\pi\) | ||||
0.0151479 | + | 0.999885i | \(0.495178\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.1168 | 1.21421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.11684 | −0.248751 | −0.124376 | − | 0.992235i | \(-0.539693\pi\) | ||||
−0.124376 | + | 0.992235i | \(0.539693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.62772 | −0.128282 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.1168 | −1.47931 | −0.739653 | − | 0.672989i | \(-0.765010\pi\) | ||||
−0.739653 | + | 0.672989i | \(0.765010\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8614 | −0.989339 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.3723 | −1.24476 | −0.622381 | − | 0.782715i | \(-0.713834\pi\) | ||||
−0.622381 | + | 0.782715i | \(0.713834\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.74456 | 0.207469 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9783 | 1.71748 | 0.858738 | − | 0.512416i | \(-0.171249\pi\) | ||||
0.858738 | + | 0.512416i | \(0.171249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.510875 | −0.0379730 | −0.0189865 | − | 0.999820i | \(-0.506044\pi\) | ||||
−0.0189865 | + | 0.999820i | \(0.506044\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.7446 | 1.52517 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.37228 | −0.392860 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.86141 | 0.713546 | 0.356773 | − | 0.934191i | \(-0.383877\pi\) | ||||
0.356773 | + | 0.934191i | \(0.383877\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.74456 | 0.125576 | 0.0627882 | − | 0.998027i | \(-0.480001\pi\) | ||||
0.0627882 | + | 0.998027i | \(0.480001\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.2554 | 1.08690 | 0.543452 | − | 0.839440i | \(-0.317117\pi\) | ||||
0.543452 | + | 0.839440i | \(0.317117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.2337 | −1.15078 | −0.575388 | − | 0.817881i | \(-0.695149\pi\) | ||||
−0.575388 | + | 0.817881i | \(0.695149\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.1168 | −1.34174 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −27.8614 | −1.94593 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.627719 | 0.0434202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.62772 | −0.662799 | −0.331400 | − | 0.943490i | \(-0.607521\pi\) | ||||
−0.331400 | + | 0.943490i | \(0.607521\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.13859 | −0.282250 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.8614 | 1.89136 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | 0.134535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.6060 | −0.978088 | −0.489044 | − | 0.872259i | \(-0.662654\pi\) | ||||
−0.489044 | + | 0.872259i | \(0.662654\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.0000 | −0.995585 | −0.497792 | − | 0.867296i | \(-0.665856\pi\) | ||||
−0.497792 | + | 0.867296i | \(0.665856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.6060 | 1.49384 | 0.746922 | − | 0.664911i | \(-0.231531\pi\) | ||||
0.746922 | + | 0.664911i | \(0.231531\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.37228 | 0.351950 | 0.175975 | − | 0.984395i | \(-0.443692\pi\) | ||||
0.175975 | + | 0.984395i | \(0.443692\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.3723 | 0.676613 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.8614 | −0.896620 | −0.448310 | − | 0.893878i | \(-0.647974\pi\) | ||||
−0.448310 | + | 0.893878i | \(0.647974\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.74456 | 0.370040 | 0.185020 | − | 0.982735i | \(-0.440765\pi\) | ||||
0.185020 | + | 0.982735i | \(0.440765\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 28.7446 | 1.83642 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.233688 | −0.0148692 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.88316 | 0.623819 | 0.311910 | − | 0.950112i | \(-0.399031\pi\) | ||||
0.311910 | + | 0.950112i | \(0.399031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.372281 | −0.0234051 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.48913 | 0.280024 | 0.140012 | − | 0.990150i | \(-0.455286\pi\) | ||||
0.140012 | + | 0.990150i | \(0.455286\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.2337 | 2.37573 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.1168 | −1.30212 | −0.651060 | − | 0.759026i | \(-0.725675\pi\) | ||||
−0.651060 | + | 0.759026i | \(0.725675\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.76631 | 0.108504 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.7446 | −0.777050 | −0.388525 | − | 0.921438i | \(-0.627015\pi\) | ||||
−0.388525 | + | 0.921438i | \(0.627015\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.4891 | −1.30537 | −0.652686 | − | 0.757629i | \(-0.726358\pi\) | ||||
−0.652686 | + | 0.757629i | \(0.726358\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.627719 | 0.0378529 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.1168 | 1.74946 | 0.874731 | − | 0.484609i | \(-0.161038\pi\) | ||||
0.874731 | + | 0.484609i | \(0.161038\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.8614 | −0.826902 | −0.413451 | − | 0.910526i | \(-0.635677\pi\) | ||||
−0.413451 | + | 0.910526i | \(0.635677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.8614 | 1.41841 | 0.709207 | − | 0.705001i | \(-0.249053\pi\) | ||||
0.709207 | + | 0.705001i | \(0.249053\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −51.3505 | −3.03113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.8614 | 0.697730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.6277 | 1.14666 | 0.573332 | − | 0.819323i | \(-0.305651\pi\) | ||||
0.573332 | + | 0.819323i | \(0.305651\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.6060 | 0.966837 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.138593 | 0.00801506 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.62772 | −0.439654 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.62772 | 0.322242 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.3723 | 1.79051 | 0.895255 | − | 0.445553i | \(-0.146993\pi\) | ||||
0.895255 | + | 0.445553i | \(0.146993\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.8832 | −0.617127 | −0.308564 | − | 0.951204i | \(-0.599848\pi\) | ||||
−0.308564 | + | 0.951204i | \(0.599848\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.2337 | 0.634966 | 0.317483 | − | 0.948264i | \(-0.397162\pi\) | ||||
0.317483 | + | 0.948264i | \(0.397162\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.6060 | 1.71900 | 0.859501 | − | 0.511134i | \(-0.170774\pi\) | ||||
0.859501 | + | 0.511134i | \(0.170774\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.37228 | −0.244801 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.37228 | −0.187639 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.233688 | −0.0129627 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.1168 | 1.05395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.8614 | −1.75126 | −0.875631 | − | 0.482981i | \(-0.839554\pi\) | ||||
−0.875631 | + | 0.482981i | \(0.839554\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.88316 | −0.485339 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.9783 | −1.08828 | −0.544142 | − | 0.838993i | \(-0.683145\pi\) | ||||
−0.544142 | + | 0.838993i | \(0.683145\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.37228 | 0.345078 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 22.3723 | 1.20799 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.7228 | 1.54192 | 0.770961 | − | 0.636883i | \(-0.219776\pi\) | ||||
0.770961 | + | 0.636883i | \(0.219776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.8832 | 0.903735 | 0.451867 | − | 0.892085i | \(-0.350758\pi\) | ||||
0.451867 | + | 0.892085i | \(0.350758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.9783 | −1.27623 | −0.638117 | − | 0.769940i | \(-0.720286\pi\) | ||||
−0.638117 | + | 0.769940i | \(0.720286\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.48913 | −0.503630 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.2337 | 1.06789 | 0.533947 | − | 0.845518i | \(-0.320708\pi\) | ||||
0.533947 | + | 0.845518i | \(0.320708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6060 | −0.979262 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.7446 | −1.50456 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.6277 | 0.920159 | 0.460080 | − | 0.887878i | \(-0.347821\pi\) | ||||
0.460080 | + | 0.887878i | \(0.347821\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.25544 | 0.169014 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.1168 | 1.09339 | 0.546694 | − | 0.837332i | \(-0.315886\pi\) | ||||
0.546694 | + | 0.837332i | \(0.315886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.62772 | 0.0838318 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.88316 | −0.302197 | −0.151099 | − | 0.988519i | \(-0.548281\pi\) | ||||
−0.151099 | + | 0.988519i | \(0.548281\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.3505 | 1.09096 | 0.545481 | − | 0.838123i | \(-0.316347\pi\) | ||||
0.545481 | + | 0.838123i | \(0.316347\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.3723 | 0.528620 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.6060 | 0.537744 | 0.268872 | − | 0.963176i | \(-0.413349\pi\) | ||||
0.268872 | + | 0.963176i | \(0.413349\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.1168 | −0.760611 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.2337 | −0.915123 | −0.457561 | − | 0.889178i | \(-0.651277\pi\) | ||||
−0.457561 | + | 0.889178i | \(0.651277\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.2337 | −0.860609 | −0.430305 | − | 0.902684i | \(-0.641594\pi\) | ||||
−0.430305 | + | 0.902684i | \(0.641594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.37228 | −0.118172 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.74456 | 0.433452 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.74456 | 0.284050 | 0.142025 | − | 0.989863i | \(-0.454639\pi\) | ||||
0.142025 | + | 0.989863i | \(0.454639\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.6060 | 1.50602 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.8397 | 1.12115 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.6060 | −0.615842 | −0.307921 | − | 0.951412i | \(-0.599633\pi\) | ||||
−0.307921 | + | 0.951412i | \(0.599633\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.1168 | −1.71149 | −0.855745 | − | 0.517398i | \(-0.826901\pi\) | ||||
−0.855745 | + | 0.517398i | \(0.826901\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.37228 | −0.163580 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.3723 | 0.501950 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.25544 | −0.0604723 | −0.0302361 | − | 0.999543i | \(-0.509626\pi\) | ||||
−0.0302361 | + | 0.999543i | \(0.509626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.1168 | 1.54344 | 0.771719 | − | 0.635964i | \(-0.219397\pi\) | ||||
0.771719 | + | 0.635964i | \(0.219397\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.233688 | −0.0111788 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.11684 | 0.339668 | 0.169834 | − | 0.985473i | \(-0.445677\pi\) | ||||
0.169834 | + | 0.985473i | \(0.445677\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.7228 | 1.45968 | 0.729842 | − | 0.683615i | \(-0.239593\pi\) | ||||
0.729842 | + | 0.683615i | \(0.239593\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.2337 | 0.674742 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.8832 | −0.749572 | −0.374786 | − | 0.927111i | \(-0.622284\pi\) | ||||
−0.374786 | + | 0.927111i | \(0.622284\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.7446 | −0.553030 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.86141 | −0.181026 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.74456 | −0.175163 | −0.0875816 | − | 0.996157i | \(-0.527914\pi\) | ||||
−0.0875816 | + | 0.996157i | \(0.527914\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.88316 | −0.320581 | −0.160290 | − | 0.987070i | \(-0.551243\pi\) | ||||
−0.160290 | + | 0.987070i | \(0.551243\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 41.3505 | 1.92172 | 0.960861 | − | 0.277031i | \(-0.0893503\pi\) | ||||
0.960861 | + | 0.277031i | \(0.0893503\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.37228 | 0.341148 | 0.170574 | − | 0.985345i | \(-0.445438\pi\) | ||||
0.170574 | + | 0.985345i | \(0.445438\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.3723 | −0.756002 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.74456 | −0.0802151 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.394031 | 0.0180794 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.6060 | −0.484599 | −0.242300 | − | 0.970201i | \(-0.577902\pi\) | ||||
−0.242300 | + | 0.970201i | \(0.577902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.25544 | −0.148435 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.13859 | 0.187924 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.74456 | 0.305625 | 0.152813 | − | 0.988255i | \(-0.451167\pi\) | ||||
0.152813 | + | 0.988255i | \(0.451167\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.255437 | 0.0115277 | 0.00576386 | − | 0.999983i | \(-0.498165\pi\) | ||||
0.00576386 | + | 0.999983i | \(0.498165\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.4891 | 1.05790 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.4891 | −0.784494 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.9783 | −0.894349 | −0.447175 | − | 0.894447i | \(-0.647570\pi\) | ||||
−0.447175 | + | 0.894447i | \(0.647570\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.51087 | 0.290306 | 0.145153 | − | 0.989409i | \(-0.453633\pi\) | ||||
0.145153 | + | 0.989409i | \(0.453633\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.8832 | −0.751291 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.1168 | −1.37923 | −0.689615 | − | 0.724176i | \(-0.742220\pi\) | ||||
−0.689615 | + | 0.724176i | \(0.742220\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −52.9783 | −2.34362 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29.3505 | −1.29334 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.37228 | 0.192293 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.1168 | 0.530849 | 0.265424 | − | 0.964132i | \(-0.414488\pi\) | ||||
0.265424 | + | 0.964132i | \(0.414488\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.4891 | −0.589838 | −0.294919 | − | 0.955522i | \(-0.595293\pi\) | ||||
−0.294919 | + | 0.955522i | \(0.595293\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.2337 | −1.49124 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8614 | −0.993974 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.37228 | 0.189385 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.5109 | −1.31910 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.1168 | 0.521909 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.23369 | 0.0960337 | 0.0480169 | − | 0.998847i | \(-0.484710\pi\) | ||||
0.0480169 | + | 0.998847i | \(0.484710\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.2554 | −0.482130 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.2554 | −0.695032 | −0.347516 | − | 0.937674i | \(-0.612975\pi\) | ||||
−0.347516 | + | 0.937674i | \(0.612975\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.74456 | −0.116922 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.8614 | −1.18479 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.649468 | 0.0274696 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.74456 | 0.410684 | 0.205342 | − | 0.978690i | \(-0.434169\pi\) | ||||
0.205342 | + | 0.978690i | \(0.434169\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.3723 | −0.436365 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.2337 | 1.14170 | 0.570848 | − | 0.821056i | \(-0.306615\pi\) | ||||
0.570848 | + | 0.821056i | \(0.306615\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.4891 | −1.10854 | −0.554268 | − | 0.832338i | \(-0.687002\pi\) | ||||
−0.554268 | + | 0.832338i | \(0.687002\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.233688 | −0.00974546 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.8614 | 0.618688 | 0.309344 | − | 0.950950i | \(-0.399890\pi\) | ||||
0.309344 | + | 0.950950i | \(0.399890\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 42.0951 | 1.74640 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.744563 | 0.0308366 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.23369 | 0.381115 | 0.190558 | − | 0.981676i | \(-0.438970\pi\) | ||||
0.190558 | + | 0.981676i | \(0.438970\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.0000 | −1.06769 | −0.533846 | − | 0.845582i | \(-0.679254\pi\) | ||||
−0.533846 | + | 0.845582i | \(0.679254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −55.7228 | −2.28441 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.8614 | 1.62869 | 0.814346 | − | 0.580379i | \(-0.197096\pi\) | ||||
0.814346 | + | 0.580379i | \(0.197096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.97825 | 0.243858 | 0.121929 | − | 0.992539i | \(-0.461092\pi\) | ||||
0.121929 | + | 0.992539i | \(0.461092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.7228 | −0.964470 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.1168 | −0.451219 | −0.225609 | − | 0.974218i | \(-0.572437\pi\) | ||||
−0.225609 | + | 0.974218i | \(0.572437\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.62772 | −0.0658504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.7446 | −0.514748 | −0.257374 | − | 0.966312i | \(-0.582857\pi\) | ||||
−0.257374 | + | 0.966312i | \(0.582857\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.9783 | 1.52895 | 0.764473 | − | 0.644655i | \(-0.222999\pi\) | ||||
0.764473 | + | 0.644655i | \(0.222999\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.2337 | 0.853454 | 0.426727 | − | 0.904380i | \(-0.359667\pi\) | ||||
0.426727 | + | 0.904380i | \(0.359667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.2337 | 1.05103 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.7446 | −1.10978 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −46.9783 | −1.87315 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.0000 | −1.27390 | −0.636950 | − | 0.770905i | \(-0.719804\pi\) | ||||
−0.636950 | + | 0.770905i | \(0.719804\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.0000 | 0.634941 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.51087 | −0.178727 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.23369 | 0.127723 | 0.0638615 | − | 0.997959i | \(-0.479658\pi\) | ||||
0.0638615 | + | 0.997959i | \(0.479658\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.00000 | 0.118308 | 0.0591542 | − | 0.998249i | \(-0.481160\pi\) | ||||
0.0591542 | + | 0.998249i | \(0.481160\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.7228 | 1.32578 | 0.662890 | − | 0.748717i | \(-0.269330\pi\) | ||||
0.662890 | + | 0.748717i | \(0.269330\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.00000 | 0.274774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.8832 | −0.895487 | −0.447744 | − | 0.894162i | \(-0.647772\pi\) | ||||
−0.447744 | + | 0.894162i | \(0.647772\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.5842 | 1.70298 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.1168 | 0.744687 | 0.372343 | − | 0.928095i | \(-0.378554\pi\) | ||||
0.372343 | + | 0.928095i | \(0.378554\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.0951 | −1.79289 | −0.896446 | − | 0.443154i | \(-0.853860\pi\) | ||||
−0.896446 | + | 0.443154i | \(0.853860\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.51087 | 0.252481 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.62772 | 0.0630255 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.37228 | 0.0915809 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.372281 | −0.0143504 | −0.00717520 | − | 0.999974i | \(-0.502284\pi\) | ||||
−0.00717520 | + | 0.999974i | \(0.502284\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.6060 | −0.791952 | −0.395976 | − | 0.918261i | \(-0.629594\pi\) | ||||
−0.395976 | + | 0.918261i | \(0.629594\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.62772 | 0.292725 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.3723 | −0.588204 | −0.294102 | − | 0.955774i | \(-0.595021\pi\) | ||||
−0.294102 | + | 0.955774i | \(0.595021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42.0951 | 1.60837 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.277187 | −0.0105600 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.1168 | 0.575072 | 0.287536 | − | 0.957770i | \(-0.407164\pi\) | ||||
0.287536 | + | 0.957770i | \(0.407164\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.6277 | 0.516929 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 63.0951 | 2.38990 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.4891 | −1.34041 | −0.670203 | − | 0.742178i | \(-0.733793\pi\) | ||||
−0.670203 | + | 0.742178i | \(0.733793\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.48913 | 0.207026 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.1168 | −1.17027 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.6060 | −1.07432 | −0.537160 | − | 0.843480i | \(-0.680503\pi\) | ||||
−0.537160 | + | 0.843480i | \(0.680503\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.37228 | −0.0888426 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.883156 | −0.0330282 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.4891 | 1.69646 | 0.848229 | − | 0.529630i | \(-0.177669\pi\) | ||||
0.848229 | + | 0.529630i | \(0.177669\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −54.0951 | −2.01461 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.74456 | −0.101930 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.8832 | 0.403634 | 0.201817 | − | 0.979423i | \(-0.435315\pi\) | ||||
0.201817 | + | 0.979423i | \(0.435315\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.37228 | 0.346646 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.8614 | −1.39844 | −0.699221 | − | 0.714905i | \(-0.746470\pi\) | ||||
−0.699221 | + | 0.714905i | \(0.746470\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.74456 | −0.137933 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.1168 | 1.54929 | 0.774647 | − | 0.632394i | \(-0.217928\pi\) | ||||
0.774647 | + | 0.632394i | \(0.217928\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.6277 | 1.30705 | 0.653527 | − | 0.756903i | \(-0.273289\pi\) | ||||
0.653527 | + | 0.756903i | \(0.273289\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.8614 | −0.727666 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −56.2337 | −2.05473 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.6277 | −1.37305 | −0.686527 | − | 0.727104i | \(-0.740866\pi\) | ||||
−0.686527 | + | 0.727104i | \(0.740866\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.883156 | 0.0321413 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.51087 | 0.309333 | 0.154667 | − | 0.987967i | \(-0.450570\pi\) | ||||
0.154667 | + | 0.987967i | \(0.450570\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.3505 | −0.701456 | −0.350728 | − | 0.936477i | \(-0.614066\pi\) | ||||
−0.350728 | + | 0.936477i | \(0.614066\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.7446 | −0.751004 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.60597 | −0.0940961 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.1168 | 1.19422 | 0.597112 | − | 0.802158i | \(-0.296315\pi\) | ||||
0.597112 | + | 0.802158i | \(0.296315\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.9783 | 1.04228 | 0.521138 | − | 0.853473i | \(-0.325508\pi\) | ||||
0.521138 | + | 0.853473i | \(0.325508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.37228 | −0.264139 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.39403 | −0.263904 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.8397 | 1.52707 | 0.763534 | − | 0.645767i | \(-0.223462\pi\) | ||||
0.763534 | + | 0.645767i | \(0.223462\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.1168 | −0.679717 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.883156 | −0.0313618 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.39403 | 0.120223 | 0.0601114 | − | 0.998192i | \(-0.480854\pi\) | ||||
0.0601114 | + | 0.998192i | \(0.480854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.4891 | −0.830986 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.1168 | −0.427594 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.86141 | −0.136097 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.1386 | 0.461928 | 0.230964 | − | 0.972962i | \(-0.425812\pi\) | ||||
0.230964 | + | 0.972962i | \(0.425812\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.3505 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.4674 | −0.997169 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.09509 | −0.0383125 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.6277 | 0.685012 | 0.342506 | − | 0.939516i | \(-0.388724\pi\) | ||||
0.342506 | + | 0.939516i | \(0.388724\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.8832 | 0.867372 | 0.433686 | − | 0.901064i | \(-0.357213\pi\) | ||||
0.433686 | + | 0.901064i | \(0.357213\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.9783 | 1.07722 | 0.538610 | − | 0.842555i | \(-0.318950\pi\) | ||||
0.538610 | + | 0.842555i | \(0.318950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.4891 | 0.537960 | 0.268980 | − | 0.963146i | \(-0.413314\pi\) | ||||
0.268980 | + | 0.963146i | \(0.413314\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −65.0951 | −2.25541 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −45.3505 | −1.56942 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.0951 | 1.03900 | 0.519499 | − | 0.854471i | \(-0.326119\pi\) | ||||
0.519499 | + | 0.854471i | \(0.326119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.88316 | −0.340798 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30.5109 | −1.04961 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.7228 | −1.50233 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.25544 | −0.111595 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.1168 | 1.13390 | 0.566950 | − | 0.823753i | \(-0.308123\pi\) | ||||
0.566950 | + | 0.823753i | \(0.308123\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.1168 | 1.26789 | 0.633944 | − | 0.773379i | \(-0.281435\pi\) | ||||
0.633944 | + | 0.773379i | \(0.281435\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.48913 | −0.0849279 | −0.0424639 | − | 0.999098i | \(-0.513521\pi\) | ||||
−0.0424639 | + | 0.999098i | \(0.513521\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.9783 | −0.646027 | −0.323014 | − | 0.946394i | \(-0.604696\pi\) | ||||
−0.323014 | + | 0.946394i | \(0.604696\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.8397 | −1.32059 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.37228 | −0.216165 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.39403 | 0.0472349 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −45.3505 | −1.53313 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.8614 | 0.940813 | 0.470406 | − | 0.882450i | \(-0.344107\pi\) | ||||
0.470406 | + | 0.882450i | \(0.344107\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.9783 | 0.841539 | 0.420769 | − | 0.907168i | \(-0.361760\pi\) | ||||
0.420769 | + | 0.907168i | \(0.361760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.8397 | 1.07149 | 0.535745 | − | 0.844380i | \(-0.320031\pi\) | ||||
0.535745 | + | 0.844380i | \(0.320031\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.8614 | 0.398267 | 0.199134 | − | 0.979972i | \(-0.436187\pi\) | ||||
0.199134 | + | 0.979972i | \(0.436187\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.4891 | 0.989034 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.74456 | 0.0918433 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 54.5109 | 1.82210 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.8614 | −0.929230 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | −0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.21194 | −0.0402862 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.0000 | 1.22856 | 0.614282 | − | 0.789086i | \(-0.289446\pi\) | ||||
0.614282 | + | 0.789086i | \(0.289446\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.883156 | −0.0292603 | −0.0146301 | − | 0.999893i | \(-0.504657\pi\) | ||||
−0.0146301 | + | 0.999893i | \(0.504657\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.62772 | 0.318631 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 80.3288 | 2.65269 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.2337 | 1.19524 | 0.597620 | − | 0.801780i | \(-0.296113\pi\) | ||||
0.597620 | + | 0.801780i | \(0.296113\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.48913 | 0.0490152 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.48913 | 0.180481 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.5842 | 1.23310 | 0.616549 | − | 0.787316i | \(-0.288530\pi\) | ||||
0.616549 | + | 0.787316i | \(0.288530\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.60597 | 0.249276 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.7446 | −0.416792 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.8397 | 0.874948 | 0.437474 | − | 0.899231i | \(-0.355873\pi\) | ||||
0.437474 | + | 0.899231i | \(0.355873\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.37228 | 0.142381 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.7446 | −1.74646 | −0.873232 | − | 0.487305i | \(-0.837980\pi\) | ||||
−0.873232 | + | 0.487305i | \(0.837980\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.51087 | 0.146429 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.88316 | −0.255360 | −0.127680 | − | 0.991815i | \(-0.540753\pi\) | ||||
−0.127680 | + | 0.991815i | \(0.540753\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.3940 | 0.757013 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 77.5842 | 2.50533 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.60597 | 0.309870 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.13859 | 0.133226 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.37228 | −0.269234 | −0.134617 | − | 0.990898i | \(-0.542980\pi\) | ||||
−0.134617 | + | 0.990898i | \(0.542980\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.48913 | −0.176154 | −0.0880772 | − | 0.996114i | \(-0.528072\pi\) | ||||
−0.0880772 | + | 0.996114i | \(0.528072\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.1168 | 0.805209 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.255437 | 0.00817216 | 0.00408608 | − | 0.999992i | \(-0.498699\pi\) | ||||
0.00408608 | + | 0.999992i | \(0.498699\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 55.1168 | 1.75795 | 0.878977 | − | 0.476864i | \(-0.158227\pi\) | ||||
0.878977 | + | 0.476864i | \(0.158227\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.1902 | 1.15312 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.649468 | 0.0206519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.9783 | 1.61938 | 0.809689 | − | 0.586860i | \(-0.199636\pi\) | ||||
0.809689 | + | 0.586860i | \(0.199636\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.5109 | −1.22088 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.3505 | 1.56295 | 0.781474 | − | 0.623938i | \(-0.214468\pi\) | ||||
0.781474 | + | 0.623938i | \(0.214468\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 648.2.a.f.1.2 | 2 | ||
3.2 | odd | 2 | 648.2.a.g.1.1 | 2 | |||
4.3 | odd | 2 | 1296.2.a.n.1.2 | 2 | |||
8.3 | odd | 2 | 5184.2.a.bs.1.1 | 2 | |||
8.5 | even | 2 | 5184.2.a.bt.1.1 | 2 | |||
9.2 | odd | 6 | 216.2.i.b.145.2 | 4 | |||
9.4 | even | 3 | 72.2.i.b.25.2 | ✓ | 4 | ||
9.5 | odd | 6 | 216.2.i.b.73.2 | 4 | |||
9.7 | even | 3 | 72.2.i.b.49.2 | yes | 4 | ||
12.11 | even | 2 | 1296.2.a.p.1.1 | 2 | |||
24.5 | odd | 2 | 5184.2.a.bp.1.2 | 2 | |||
24.11 | even | 2 | 5184.2.a.bo.1.2 | 2 | |||
36.7 | odd | 6 | 144.2.i.d.49.1 | 4 | |||
36.11 | even | 6 | 432.2.i.d.145.2 | 4 | |||
36.23 | even | 6 | 432.2.i.d.289.2 | 4 | |||
36.31 | odd | 6 | 144.2.i.d.97.1 | 4 | |||
72.5 | odd | 6 | 1728.2.i.i.1153.1 | 4 | |||
72.11 | even | 6 | 1728.2.i.j.577.1 | 4 | |||
72.13 | even | 6 | 576.2.i.j.385.1 | 4 | |||
72.29 | odd | 6 | 1728.2.i.i.577.1 | 4 | |||
72.43 | odd | 6 | 576.2.i.l.193.2 | 4 | |||
72.59 | even | 6 | 1728.2.i.j.1153.1 | 4 | |||
72.61 | even | 6 | 576.2.i.j.193.1 | 4 | |||
72.67 | odd | 6 | 576.2.i.l.385.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.i.b.25.2 | ✓ | 4 | 9.4 | even | 3 | ||
72.2.i.b.49.2 | yes | 4 | 9.7 | even | 3 | ||
144.2.i.d.49.1 | 4 | 36.7 | odd | 6 | |||
144.2.i.d.97.1 | 4 | 36.31 | odd | 6 | |||
216.2.i.b.73.2 | 4 | 9.5 | odd | 6 | |||
216.2.i.b.145.2 | 4 | 9.2 | odd | 6 | |||
432.2.i.d.145.2 | 4 | 36.11 | even | 6 | |||
432.2.i.d.289.2 | 4 | 36.23 | even | 6 | |||
576.2.i.j.193.1 | 4 | 72.61 | even | 6 | |||
576.2.i.j.385.1 | 4 | 72.13 | even | 6 | |||
576.2.i.l.193.2 | 4 | 72.43 | odd | 6 | |||
576.2.i.l.385.2 | 4 | 72.67 | odd | 6 | |||
648.2.a.f.1.2 | 2 | 1.1 | even | 1 | trivial | ||
648.2.a.g.1.1 | 2 | 3.2 | odd | 2 | |||
1296.2.a.n.1.2 | 2 | 4.3 | odd | 2 | |||
1296.2.a.p.1.1 | 2 | 12.11 | even | 2 | |||
1728.2.i.i.577.1 | 4 | 72.29 | odd | 6 | |||
1728.2.i.i.1153.1 | 4 | 72.5 | odd | 6 | |||
1728.2.i.j.577.1 | 4 | 72.11 | even | 6 | |||
1728.2.i.j.1153.1 | 4 | 72.59 | even | 6 | |||
5184.2.a.bo.1.2 | 2 | 24.11 | even | 2 | |||
5184.2.a.bp.1.2 | 2 | 24.5 | odd | 2 | |||
5184.2.a.bs.1.1 | 2 | 8.3 | odd | 2 | |||
5184.2.a.bt.1.1 | 2 | 8.5 | even | 2 |