Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5184,2,Mod(1,5184)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5184, 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("5184.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5184 = 2^{6} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5184.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: | \(41.3944484078\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 648) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5184.1 |
$q$-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 | ||||||||
\(5\) | 3.73205 | 1.66902 | 0.834512 | − | 0.550990i | \(-0.185750\pi\) | ||||
0.834512 | + | 0.550990i | \(0.185750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.46410 | −1.30931 | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||||
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.46410 | 0.683419 | 0.341709 | − | 0.939806i | \(-0.388994\pi\) | ||||
0.341709 | + | 0.939806i | \(0.388994\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.26795 | −0.550058 | −0.275029 | − | 0.961436i | \(-0.588688\pi\) | ||||
−0.275029 | + | 0.961436i | \(0.588688\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.46410 | −1.71238 | −0.856191 | − | 0.516659i | \(-0.827175\pi\) | ||||
−0.856191 | + | 0.516659i | \(0.827175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.92820 | −1.02760 | −0.513801 | − | 0.857910i | \(-0.671763\pi\) | ||||
−0.513801 | + | 0.857910i | \(0.671763\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.92820 | 1.78564 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.26795 | 0.792538 | 0.396269 | − | 0.918134i | \(-0.370305\pi\) | ||||
0.396269 | + | 0.918134i | \(0.370305\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.9282 | 1.96276 | 0.981382 | − | 0.192068i | \(-0.0615194\pi\) | ||||
0.981382 | + | 0.192068i | \(0.0615194\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.9282 | −2.18527 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.464102 | 0.0762978 | 0.0381489 | − | 0.999272i | \(-0.487854\pi\) | ||||
0.0381489 | + | 0.999272i | \(0.487854\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.92820 | −1.08200 | −0.541002 | − | 0.841021i | \(-0.681955\pi\) | ||||
−0.541002 | + | 0.841021i | \(0.681955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.53590 | −0.691718 | −0.345859 | − | 0.938286i | \(-0.612412\pi\) | ||||
−0.345859 | + | 0.938286i | \(0.612412\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.92820 | 1.01058 | 0.505291 | − | 0.862949i | \(-0.331385\pi\) | ||||
0.505291 | + | 0.862949i | \(0.331385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.9282 | −1.50110 | −0.750552 | − | 0.660811i | \(-0.770212\pi\) | ||||
−0.750552 | + | 0.660811i | \(0.770212\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.46410 | −1.00646 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.4641 | −1.33979 | −0.669895 | − | 0.742455i | \(-0.733661\pi\) | ||||
−0.669895 | + | 0.742455i | \(0.733661\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.19615 | 1.14064 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.535898 | −0.0654704 | −0.0327352 | − | 0.999464i | \(-0.510422\pi\) | ||||
−0.0327352 | + | 0.999464i | \(0.510422\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | 0.117041 | 0.0585206 | − | 0.998286i | \(-0.481362\pi\) | ||||
0.0585206 | + | 0.998286i | \(0.481362\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.92820 | 0.789542 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.535898 | −0.0602933 | −0.0301466 | − | 0.999545i | \(-0.509597\pi\) | ||||
−0.0301466 | + | 0.999545i | \(0.509597\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.92820 | 0.321412 | 0.160706 | − | 0.987002i | \(-0.448623\pi\) | ||||
0.160706 | + | 0.987002i | \(0.448623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.46410 | −0.918061 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.19615 | 0.550791 | 0.275396 | − | 0.961331i | \(-0.411191\pi\) | ||||
0.275396 | + | 0.961331i | \(0.411191\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.53590 | −0.894805 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −27.8564 | −2.85801 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.8564 | −1.20384 | −0.601918 | − | 0.798558i | \(-0.705597\pi\) | ||||
−0.601918 | + | 0.798558i | \(0.705597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0000 | −1.19404 | −0.597022 | − | 0.802225i | \(-0.703650\pi\) | ||||
−0.597022 | + | 0.802225i | \(0.703650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9282 | −1.07679 | −0.538394 | − | 0.842693i | \(-0.680969\pi\) | ||||
−0.538394 | + | 0.842693i | \(0.680969\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.07180 | 0.490309 | 0.245155 | − | 0.969484i | \(-0.421161\pi\) | ||||
0.245155 | + | 0.969484i | \(0.421161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.46410 | −0.427583 | −0.213792 | − | 0.976879i | \(-0.568581\pi\) | ||||
−0.213792 | + | 0.976879i | \(0.568581\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.73205 | 0.162938 | 0.0814688 | − | 0.996676i | \(-0.474039\pi\) | ||||
0.0814688 | + | 0.996676i | \(0.474039\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.3923 | −1.71509 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.85641 | 0.720196 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 14.6603 | 1.31125 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.535898 | −0.0475533 | −0.0237766 | − | 0.999717i | \(-0.507569\pi\) | ||||
−0.0237766 | + | 0.999717i | \(0.507569\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.07180 | 0.617866 | 0.308933 | − | 0.951084i | \(-0.400028\pi\) | ||||
0.308933 | + | 0.951084i | \(0.400028\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.8564 | 2.24203 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.6603 | −1.76512 | −0.882562 | − | 0.470195i | \(-0.844183\pi\) | ||||
−0.882562 | + | 0.470195i | \(0.844183\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.07180 | −0.430184 | −0.215092 | − | 0.976594i | \(-0.569005\pi\) | ||||
−0.215092 | + | 0.976594i | \(0.569005\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.92820 | −0.412117 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.9282 | 1.32277 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.7321 | −1.28882 | −0.644410 | − | 0.764680i | \(-0.722897\pi\) | ||||
−0.644410 | + | 0.764680i | \(0.722897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.07180 | −0.0872216 | −0.0436108 | − | 0.999049i | \(-0.513886\pi\) | ||||
−0.0436108 | + | 0.999049i | \(0.513886\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 40.7846 | 3.27590 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.39230 | −0.430353 | −0.215176 | − | 0.976575i | \(-0.569033\pi\) | ||||
−0.215176 | + | 0.976575i | \(0.569033\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.0718 | 1.34545 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.0000 | 1.39288 | 0.696441 | − | 0.717614i | \(-0.254766\pi\) | ||||
0.696441 | + | 0.717614i | \(0.254766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.92820 | −0.532939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.73205 | −0.587857 | −0.293928 | − | 0.955827i | \(-0.594963\pi\) | ||||
−0.293928 | + | 0.955827i | \(0.594963\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −30.9282 | −2.33795 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.92820 | 0.517838 | 0.258919 | − | 0.965899i | \(-0.416634\pi\) | ||||
0.258919 | + | 0.965899i | \(0.416634\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.85641 | −0.583962 | −0.291981 | − | 0.956424i | \(-0.594314\pi\) | ||||
−0.291981 | + | 0.956424i | \(0.594314\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.73205 | 0.127343 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.53590 | 0.331698 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.8564 | 1.43676 | 0.718380 | − | 0.695651i | \(-0.244884\pi\) | ||||
0.718380 | + | 0.695651i | \(0.244884\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.9282 | 1.29050 | 0.645250 | − | 0.763971i | \(-0.276753\pi\) | ||||
0.645250 | + | 0.763971i | \(0.276753\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.66025 | −0.189535 | −0.0947676 | − | 0.995499i | \(-0.530211\pi\) | ||||
−0.0947676 | + | 0.995499i | \(0.530211\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.7846 | −1.03768 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25.8564 | −1.80589 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.9282 | 1.03261 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.3205 | −1.74314 | −0.871568 | − | 0.490275i | \(-0.836896\pi\) | ||||
−0.871568 | + | 0.490275i | \(0.836896\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.9282 | −1.15449 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −37.8564 | −2.56986 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.58846 | −0.375920 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.535898 | −0.0358864 | −0.0179432 | − | 0.999839i | \(-0.505712\pi\) | ||||
−0.0179432 | + | 0.999839i | \(0.505712\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.7846 | 0.981289 | 0.490645 | − | 0.871360i | \(-0.336761\pi\) | ||||
0.490645 | + | 0.871360i | \(0.336761\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.53590 | 0.497986 | 0.248993 | − | 0.968505i | \(-0.419900\pi\) | ||||
0.248993 | + | 0.968505i | \(0.419900\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.73205 | −0.637568 | −0.318784 | − | 0.947827i | \(-0.603274\pi\) | ||||
−0.318784 | + | 0.947827i | \(0.603274\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.8564 | 1.68669 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.9282 | 0.706887 | 0.353443 | − | 0.935456i | \(-0.385011\pi\) | ||||
0.353443 | + | 0.935456i | \(0.385011\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.07180 | −0.519950 | −0.259975 | − | 0.965615i | \(-0.583714\pi\) | ||||
−0.259975 | + | 0.965615i | \(0.583714\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.6603 | 1.19216 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.3923 | −1.17027 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.0000 | −0.631194 | −0.315597 | − | 0.948893i | \(-0.602205\pi\) | ||||
−0.315597 | + | 0.948893i | \(0.602205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.85641 | 0.619667 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.0526 | 1.68749 | 0.843746 | − | 0.536742i | \(-0.180345\pi\) | ||||
0.843746 | + | 0.536742i | \(0.180345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.60770 | −0.0998973 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.7846 | 1.77494 | 0.887468 | − | 0.460870i | \(-0.152463\pi\) | ||||
0.887468 | + | 0.460870i | \(0.152463\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −40.7846 | −2.50538 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.5167 | 1.25092 | 0.625461 | − | 0.780255i | \(-0.284911\pi\) | ||||
0.625461 | + | 0.780255i | \(0.284911\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.5359 | −1.00448 | −0.502242 | − | 0.864727i | \(-0.667491\pi\) | ||||
−0.502242 | + | 0.864727i | \(0.667491\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.8564 | −1.07678 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0000 | 0.841178 | 0.420589 | − | 0.907251i | \(-0.361823\pi\) | ||||
0.420589 | + | 0.907251i | \(0.361823\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.12436 | −0.246038 | −0.123019 | − | 0.992404i | \(-0.539258\pi\) | ||||
−0.123019 | + | 0.992404i | \(0.539258\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.8564 | −1.06145 | −0.530727 | − | 0.847543i | \(-0.678081\pi\) | ||||
−0.530727 | + | 0.847543i | \(0.678081\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.0000 | 1.41668 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.8564 | −0.697436 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.12436 | −0.357789 | −0.178894 | − | 0.983868i | \(-0.557252\pi\) | ||||
−0.178894 | + | 0.983868i | \(0.557252\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.8564 | −1.73831 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.1436 | −0.702282 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.7128 | 0.905671 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −39.0526 | −2.23614 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.9282 | −1.08029 | −0.540145 | − | 0.841572i | \(-0.681631\pi\) | ||||
−0.540145 | + | 0.841572i | \(0.681631\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.7846 | 1.34439 | 0.672193 | − | 0.740376i | \(-0.265353\pi\) | ||||
0.672193 | + | 0.740376i | \(0.265353\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.73205 | 0.434275 | 0.217138 | − | 0.976141i | \(-0.430328\pi\) | ||||
0.217138 | + | 0.976141i | \(0.430328\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.53590 | −0.477919 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.9282 | 0.941910 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.0000 | 1.22034 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.0000 | −1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.2487 | 1.11297 | 0.556485 | − | 0.830858i | \(-0.312150\pi\) | ||||
0.556485 | + | 0.830858i | \(0.312150\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00000 | −0.109272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.85641 | 0.427966 | 0.213983 | − | 0.976837i | \(-0.431356\pi\) | ||||
0.213983 | + | 0.976837i | \(0.431356\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.8564 | −1.18359 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.92820 | 0.374088 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.9282 | −1.33822 | −0.669108 | − | 0.743165i | \(-0.733324\pi\) | ||||
−0.669108 | + | 0.743165i | \(0.733324\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.14359 | −0.114092 | −0.0570460 | − | 0.998372i | \(-0.518168\pi\) | ||||
−0.0570460 | + | 0.998372i | \(0.518168\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.46410 | −0.396153 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.7846 | −0.780302 | −0.390151 | − | 0.920751i | \(-0.627577\pi\) | ||||
−0.390151 | + | 0.920751i | \(0.627577\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.7128 | 1.93225 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.73205 | 0.195344 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.9282 | −1.19684 | −0.598421 | − | 0.801182i | \(-0.704205\pi\) | ||||
−0.598421 | + | 0.801182i | \(0.704205\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.8564 | 1.96541 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.5167 | 0.541636 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.7846 | −1.27310 | −0.636550 | − | 0.771235i | \(-0.719639\pi\) | ||||
−0.636550 | + | 0.771235i | \(0.719639\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.0000 | 0.919757 | 0.459879 | − | 0.887982i | \(-0.347893\pi\) | ||||
0.459879 | + | 0.887982i | \(0.347893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.8564 | 1.31776 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.9282 | 1.36531 | 0.682657 | − | 0.730739i | \(-0.260824\pi\) | ||||
0.682657 | + | 0.730739i | \(0.260824\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.1769 | 0.565241 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.00000 | −0.100631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.607695 | −0.0304993 | −0.0152497 | − | 0.999884i | \(-0.504854\pi\) | ||||
−0.0152497 | + | 0.999884i | \(0.504854\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1962 | 0.858735 | 0.429367 | − | 0.903130i | \(-0.358737\pi\) | ||||
0.429367 | + | 0.903130i | \(0.358737\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.9282 | 1.34139 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.928203 | −0.0460093 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.9282 | 0.787599 | 0.393799 | − | 0.919196i | \(-0.371160\pi\) | ||||
0.393799 | + | 0.919196i | \(0.371160\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.7128 | 1.36366 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.9282 | 0.536444 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.8564 | −1.26317 | −0.631584 | − | 0.775307i | \(-0.717595\pi\) | ||||
−0.631584 | + | 0.775307i | \(0.717595\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.39230 | −0.165331 | −0.0826654 | − | 0.996577i | \(-0.526343\pi\) | ||||
−0.0826654 | + | 0.996577i | \(0.526343\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.2487 | −0.982207 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.2487 | 1.75420 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.9282 | −1.29709 | −0.648543 | − | 0.761178i | \(-0.724621\pi\) | ||||
−0.648543 | + | 0.761178i | \(0.724621\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.7846 | 1.33524 | 0.667622 | − | 0.744501i | \(-0.267312\pi\) | ||||
0.667622 | + | 0.744501i | \(0.267312\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.7846 | 1.75965 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0000 | 0.572729 | 0.286364 | − | 0.958121i | \(-0.407553\pi\) | ||||
0.286364 | + | 0.958121i | \(0.407553\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.07180 | 0.0509226 | 0.0254613 | − | 0.999676i | \(-0.491895\pi\) | ||||
0.0254613 | + | 0.999676i | \(0.491895\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.3923 | 0.919283 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.7846 | −1.35843 | −0.679215 | − | 0.733939i | \(-0.737680\pi\) | ||||
−0.679215 | + | 0.733939i | \(0.737680\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.8564 | 0.652473 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −31.8564 | −1.49345 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.9282 | −1.77421 | −0.887103 | − | 0.461571i | \(-0.847286\pi\) | ||||
−0.887103 | + | 0.461571i | \(0.847286\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.7846 | −1.15433 | −0.577167 | − | 0.816626i | \(-0.695842\pi\) | ||||
−0.577167 | + | 0.816626i | \(0.695842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.0000 | 1.85896 | 0.929479 | − | 0.368875i | \(-0.120257\pi\) | ||||
0.929479 | + | 0.368875i | \(0.120257\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.7128 | −1.83769 | −0.918845 | − | 0.394619i | \(-0.870877\pi\) | ||||
−0.918845 | + | 0.394619i | \(0.870877\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.85641 | 0.0857209 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.07180 | 0.417122 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −66.6410 | −3.05770 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.8564 | 0.541733 | 0.270867 | − | 0.962617i | \(-0.412690\pi\) | ||||
0.270867 | + | 0.962617i | \(0.412690\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.14359 | 0.0521434 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −44.2487 | −2.00923 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.9282 | −1.58275 | −0.791374 | − | 0.611332i | \(-0.790634\pi\) | ||||
−0.791374 | + | 0.611332i | \(0.790634\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.8564 | 1.97921 | 0.989606 | − | 0.143806i | \(-0.0459340\pi\) | ||||
0.989606 | + | 0.143806i | \(0.0459340\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.67949 | −0.435942 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.92820 | 0.310772 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.2487 | 1.08552 | 0.542761 | − | 0.839887i | \(-0.317379\pi\) | ||||
0.542761 | + | 0.839887i | \(0.317379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.8564 | 1.15288 | 0.576440 | − | 0.817139i | \(-0.304441\pi\) | ||||
0.576440 | + | 0.817139i | \(0.304441\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −44.7846 | −1.99289 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.7846 | −1.45315 | −0.726576 | − | 0.687086i | \(-0.758890\pi\) | ||||
−0.726576 | + | 0.687086i | \(0.758890\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.46410 | −0.153243 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −40.7846 | −1.79718 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.8564 | −0.609404 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.7846 | 1.26108 | 0.630538 | − | 0.776158i | \(-0.282834\pi\) | ||||
0.630538 | + | 0.776158i | \(0.282834\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.4641 | −1.55074 | −0.775368 | − | 0.631509i | \(-0.782436\pi\) | ||||
−0.775368 | + | 0.631509i | \(0.782436\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.7846 | −1.07963 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.28719 | 0.0559647 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.0718 | −0.739462 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.9282 | 0.818338 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.0000 | −0.430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.39230 | −0.317820 | −0.158910 | − | 0.987293i | \(-0.550798\pi\) | ||||
−0.158910 | + | 0.987293i | \(0.550798\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.6603 | −0.713647 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.8564 | −0.763485 | −0.381742 | − | 0.924269i | \(-0.624676\pi\) | ||||
−0.381742 | + | 0.924269i | \(0.624676\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.8564 | −1.35713 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.85641 | 0.0789424 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.5885 | −0.575761 | −0.287881 | − | 0.957666i | \(-0.592951\pi\) | ||||
−0.287881 | + | 0.957666i | \(0.592951\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.1769 | −0.472733 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.07180 | −0.0451708 | −0.0225854 | − | 0.999745i | \(-0.507190\pi\) | ||||
−0.0225854 | + | 0.999745i | \(0.507190\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.46410 | 0.271947 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 43.5885 | 1.82732 | 0.913662 | − | 0.406476i | \(-0.133242\pi\) | ||||
0.913662 | + | 0.406476i | \(0.133242\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.8564 | −0.579873 | −0.289936 | − | 0.957046i | \(-0.593634\pi\) | ||||
−0.289936 | + | 0.957046i | \(0.593634\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −44.0000 | −1.83493 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.85641 | −0.118914 | −0.0594569 | − | 0.998231i | \(-0.518937\pi\) | ||||
−0.0594569 | + | 0.998231i | \(0.518937\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.1436 | −0.420827 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.8564 | 0.905200 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.0000 | −1.07313 | −0.536567 | − | 0.843857i | \(-0.680279\pi\) | ||||
−0.536567 | + | 0.843857i | \(0.680279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −81.5692 | −3.36100 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.411543 | 0.0169000 | 0.00845002 | − | 0.999964i | \(-0.497310\pi\) | ||||
0.00845002 | + | 0.999964i | \(0.497310\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29.3205 | 1.20202 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.9282 | −0.773385 | −0.386693 | − | 0.922209i | \(-0.626383\pi\) | ||||
−0.386693 | + | 0.922209i | \(0.626383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.85641 | −0.279679 | −0.139839 | − | 0.990174i | \(-0.544659\pi\) | ||||
−0.139839 | + | 0.990174i | \(0.544659\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.1244 | −1.06211 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.1769 | −1.59014 | −0.795071 | − | 0.606516i | \(-0.792566\pi\) | ||||
−0.795071 | + | 0.606516i | \(0.792566\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.0718 | 0.690651 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.85641 | −0.155759 | −0.0778794 | − | 0.996963i | \(-0.524815\pi\) | ||||
−0.0778794 | + | 0.996963i | \(0.524815\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.4449 | −1.18541 | −0.592703 | − | 0.805421i | \(-0.701939\pi\) | ||||
−0.592703 | + | 0.805421i | \(0.701939\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.78461 | −0.192310 | −0.0961549 | − | 0.995366i | \(-0.530654\pi\) | ||||
−0.0961549 | + | 0.995366i | \(0.530654\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.0000 | −0.721155 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.05256 | −0.0419683 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.7846 | −0.508947 | −0.254474 | − | 0.967080i | \(-0.581902\pi\) | ||||
−0.254474 | + | 0.967080i | \(0.581902\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.00000 | −0.0793676 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.3205 | 0.488156 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.9808 | 1.18417 | 0.592084 | − | 0.805876i | \(-0.298305\pi\) | ||||
0.592084 | + | 0.805876i | \(0.298305\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.7846 | 1.29290 | 0.646449 | − | 0.762957i | \(-0.276253\pi\) | ||||
0.646449 | + | 0.762957i | \(0.276253\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.7128 | 1.48264 | 0.741322 | − | 0.671150i | \(-0.234199\pi\) | ||||
0.741322 | + | 0.671150i | \(0.234199\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0000 | 0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.78461 | 0.343768 | 0.171884 | − | 0.985117i | \(-0.445015\pi\) | ||||
0.171884 | + | 0.985117i | \(0.445015\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.3923 | 1.03123 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.78461 | −0.108473 | −0.0542365 | − | 0.998528i | \(-0.517272\pi\) | ||||
−0.0542365 | + | 0.998528i | \(0.517272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.3205 | 1.17933 | 0.589666 | − | 0.807648i | \(-0.299260\pi\) | ||||
0.589666 | + | 0.807648i | \(0.299260\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 96.4974 | 3.74201 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.0333 | −0.814413 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.9282 | 0.807924 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.9282 | 0.999459 | 0.499729 | − | 0.866182i | \(-0.333433\pi\) | ||||
0.499729 | + | 0.866182i | \(0.333433\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.6410 | 1.17763 | 0.588815 | − | 0.808268i | \(-0.299595\pi\) | ||||
0.588815 | + | 0.808268i | \(0.299595\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.0718 | 1.57619 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.07180 | −0.0410112 | −0.0205056 | − | 0.999790i | \(-0.506528\pi\) | ||||
−0.0205056 | + | 0.999790i | \(0.506528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −77.1051 | −2.94604 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.9282 | −1.02588 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.6077 | −0.669828 | −0.334914 | − | 0.942249i | \(-0.608707\pi\) | ||||
−0.334914 | + | 0.942249i | \(0.608707\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.9282 | −0.717988 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7128 | 0.595165 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.4449 | 1.33873 | 0.669367 | − | 0.742932i | \(-0.266565\pi\) | ||||
0.669367 | + | 0.742932i | \(0.266565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.46410 | −0.130651 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 41.5692 | 1.56337 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.3205 | −0.838264 | −0.419132 | − | 0.907925i | \(-0.637666\pi\) | ||||
−0.419132 | + | 0.907925i | \(0.637666\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −53.8564 | −2.01694 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.3923 | −0.687833 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.92820 | 0.332966 | 0.166483 | − | 0.986044i | \(-0.446759\pi\) | ||||
0.166483 | + | 0.986044i | \(0.446759\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.8564 | 1.40985 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.1051 | 1.41519 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1769 | 1.15629 | 0.578144 | − | 0.815935i | \(-0.303777\pi\) | ||||
0.578144 | + | 0.815935i | \(0.303777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.2872 | 0.380485 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.8564 | −1.47213 | −0.736065 | − | 0.676911i | \(-0.763318\pi\) | ||||
−0.736065 | + | 0.676911i | \(0.763318\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.07180 | 0.0394801 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.0000 | −1.03000 | −0.514998 | − | 0.857191i | \(-0.672207\pi\) | ||||
−0.514998 | + | 0.857191i | \(0.672207\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.9282 | −0.841154 | −0.420577 | − | 0.907257i | \(-0.638172\pi\) | ||||
−0.420577 | + | 0.907257i | \(0.638172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −58.7128 | −2.15107 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.5692 | −0.641965 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.3205 | 0.632034 | 0.316017 | − | 0.948753i | \(-0.397654\pi\) | ||||
0.316017 | + | 0.948753i | \(0.397654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.00000 | −0.145575 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.8564 | 1.30322 | 0.651612 | − | 0.758553i | \(-0.274093\pi\) | ||||
0.651612 | + | 0.758553i | \(0.274093\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.1962 | 1.78336 | 0.891680 | − | 0.452667i | \(-0.149527\pi\) | ||||
0.891680 | + | 0.452667i | \(0.149527\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.4641 | 0.559838 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.7128 | −0.711788 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.78461 | −0.352842 | −0.176421 | − | 0.984315i | \(-0.556452\pi\) | ||||
−0.176421 | + | 0.984315i | \(0.556452\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.2679 | 1.01673 | 0.508364 | − | 0.861142i | \(-0.330251\pi\) | ||||
0.508364 | + | 0.861142i | \(0.330251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 97.5692 | 3.50479 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 51.7128 | 1.85280 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.1244 | −0.718269 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.4641 | 0.693820 | 0.346910 | − | 0.937898i | \(-0.387231\pi\) | ||||
0.346910 | + | 0.937898i | \(0.387231\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.7846 | −0.915638 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.48334 | 0.123386 | 0.0616931 | − | 0.998095i | \(-0.480350\pi\) | ||||
0.0616931 | + | 0.998095i | \(0.480350\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.7128 | −0.555879 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.00000 | −0.0705785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 63.7128 | 2.24558 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.7321 | −1.04532 | −0.522662 | − | 0.852540i | \(-0.675061\pi\) | ||||
−0.522662 | + | 0.852540i | \(0.675061\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.5692 | 1.17877 | 0.589387 | − | 0.807851i | \(-0.299369\pi\) | ||||
0.589387 | + | 0.807851i | \(0.299369\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.8564 | 1.18449 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.33975 | −0.325959 | −0.162980 | − | 0.986629i | \(-0.552111\pi\) | ||||
−0.162980 | + | 0.986629i | \(0.552111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0000 | −0.697156 | −0.348578 | − | 0.937280i | \(-0.613335\pi\) | ||||
−0.348578 | + | 0.937280i | \(0.613335\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.8564 | −0.412288 | −0.206144 | − | 0.978522i | \(-0.566091\pi\) | ||||
−0.206144 | + | 0.978522i | \(0.566091\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.8564 | −0.828567 | −0.414284 | − | 0.910148i | \(-0.635968\pi\) | ||||
−0.414284 | + | 0.910148i | \(0.635968\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.3397 | −0.392899 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 67.1769 | 2.32475 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.0718 | 0.796527 | 0.398263 | − | 0.917271i | \(-0.369613\pi\) | ||||
0.398263 | + | 0.917271i | \(0.369613\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.7846 | −0.371883 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.8564 | −0.889487 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.2487 | 0.833196 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.28719 | −0.0784038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.0000 | −0.479351 | −0.239675 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239675 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.5885 | −0.942404 | −0.471202 | − | 0.882025i | \(-0.656180\pi\) | ||||
−0.471202 | + | 0.882025i | \(0.656180\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.8564 | −0.882209 | −0.441105 | − | 0.897456i | \(-0.645413\pi\) | ||||
−0.441105 | + | 0.897456i | \(0.645413\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.9282 | 1.12089 | 0.560445 | − | 0.828192i | \(-0.310630\pi\) | ||||
0.560445 | + | 0.828192i | \(0.310630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.8564 | −0.981147 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.07180 | 0.0363582 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.32051 | −0.0447437 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −50.7846 | −1.71683 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.3205 | −0.686175 | −0.343087 | − | 0.939303i | \(-0.611473\pi\) | ||||
−0.343087 | + | 0.939303i | \(0.611473\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.6410 | −1.70614 | −0.853070 | − | 0.521797i | \(-0.825262\pi\) | ||||
−0.853070 | + | 0.521797i | \(0.825262\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.0718 | 1.24757 | 0.623783 | − | 0.781598i | \(-0.285595\pi\) | ||||
0.623783 | + | 0.781598i | \(0.285595\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.6410 | 1.49890 | 0.749449 | − | 0.662062i | \(-0.230318\pi\) | ||||
0.749449 | + | 0.662062i | \(0.230318\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.85641 | 0.0622619 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −51.7128 | −1.73050 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.8564 | 0.864284 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 46.6410 | 1.55556 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.7846 | 0.825695 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.3205 | −0.974647 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.7846 | 1.22141 | 0.610706 | − | 0.791857i | \(-0.290886\pi\) | ||||
0.610706 | + | 0.791857i | \(0.290886\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.21539 | 0.172794 | 0.0863968 | − | 0.996261i | \(-0.472465\pi\) | ||||
0.0863968 | + | 0.996261i | \(0.472465\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.85641 | −0.193819 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.4974 | −0.808976 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.1769 | 0.896484 | 0.448242 | − | 0.893912i | \(-0.352050\pi\) | ||||
0.448242 | + | 0.893912i | \(0.352050\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.92820 | −0.162214 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.14359 | 0.136241 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.5885 | 1.16762 | 0.583810 | − | 0.811891i | \(-0.301561\pi\) | ||||
0.583810 | + | 0.811891i | \(0.301561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.3205 | −1.22313 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.9282 | 0.553611 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.5692 | 1.06399 | 0.531995 | − | 0.846747i | \(-0.321443\pi\) | ||||
0.531995 | + | 0.846747i | \(0.321443\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.12436 | 0.199648 | 0.0998241 | − | 0.995005i | \(-0.468172\pi\) | ||||
0.0998241 | + | 0.995005i | \(0.468172\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.1436 | 1.11187 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.928203 | −0.0301626 | −0.0150813 | − | 0.999886i | \(-0.504801\pi\) | ||||
−0.0150813 | + | 0.999886i | \(0.504801\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.46410 | 0.0799881 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.9808 | 1.23032 | 0.615159 | − | 0.788403i | \(-0.289092\pi\) | ||||
0.615159 | + | 0.788403i | \(0.289092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 74.1051 | 2.39799 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 71.5692 | 2.31109 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 88.4256 | 2.85244 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 66.9090 | 2.15388 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.3205 | −0.814253 | −0.407126 | − | 0.913372i | \(-0.633469\pi\) | ||||
−0.407126 | + | 0.913372i | \(0.633469\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.9282 | 0.414886 | 0.207443 | − | 0.978247i | \(-0.433486\pi\) | ||||
0.207443 | + | 0.978247i | \(0.433486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.5692 | 0.563243 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.9282 | −0.989481 | −0.494740 | − | 0.869041i | \(-0.664737\pi\) | ||||
−0.494740 | + | 0.869041i | \(0.664737\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.3923 | −0.332140 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.0000 | 1.14822 | 0.574111 | − | 0.818778i | \(-0.305348\pi\) | ||||
0.574111 | + | 0.818778i | \(0.305348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.92820 | −0.316339 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.3538 | 0.710810 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.1051 | −0.956321 | −0.478160 | − | 0.878273i | \(-0.658696\pi\) | ||||
−0.478160 | + | 0.878273i | \(0.658696\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.9282 | −0.473256 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.1769 | −0.448987 | −0.224494 | − | 0.974476i | \(-0.572073\pi\) | ||||
−0.224494 | + | 0.974476i | \(0.572073\pi\) | |||||||
\(998\) | 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 | 5184.2.a.bz.1.2 | 2 | ||
3.2 | odd | 2 | 5184.2.a.bi.1.1 | 2 | |||
4.3 | odd | 2 | 5184.2.a.cb.1.2 | 2 | |||
8.3 | odd | 2 | 648.2.a.e.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 1296.2.a.m.1.1 | 2 | |||
12.11 | even | 2 | 5184.2.a.bg.1.1 | 2 | |||
24.5 | odd | 2 | 1296.2.a.q.1.2 | 2 | |||
24.11 | even | 2 | 648.2.a.h.1.2 | yes | 2 | ||
72.5 | odd | 6 | 1296.2.i.r.865.1 | 4 | |||
72.11 | even | 6 | 648.2.i.i.433.1 | 4 | |||
72.13 | even | 6 | 1296.2.i.t.865.2 | 4 | |||
72.29 | odd | 6 | 1296.2.i.r.433.1 | 4 | |||
72.43 | odd | 6 | 648.2.i.j.433.2 | 4 | |||
72.59 | even | 6 | 648.2.i.i.217.1 | 4 | |||
72.61 | even | 6 | 1296.2.i.t.433.2 | 4 | |||
72.67 | odd | 6 | 648.2.i.j.217.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.2.a.e.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
648.2.a.h.1.2 | yes | 2 | 24.11 | even | 2 | ||
648.2.i.i.217.1 | 4 | 72.59 | even | 6 | |||
648.2.i.i.433.1 | 4 | 72.11 | even | 6 | |||
648.2.i.j.217.2 | 4 | 72.67 | odd | 6 | |||
648.2.i.j.433.2 | 4 | 72.43 | odd | 6 | |||
1296.2.a.m.1.1 | 2 | 8.5 | even | 2 | |||
1296.2.a.q.1.2 | 2 | 24.5 | odd | 2 | |||
1296.2.i.r.433.1 | 4 | 72.29 | odd | 6 | |||
1296.2.i.r.865.1 | 4 | 72.5 | odd | 6 | |||
1296.2.i.t.433.2 | 4 | 72.61 | even | 6 | |||
1296.2.i.t.865.2 | 4 | 72.13 | even | 6 | |||
5184.2.a.bg.1.1 | 2 | 12.11 | even | 2 | |||
5184.2.a.bi.1.1 | 2 | 3.2 | odd | 2 | |||
5184.2.a.bz.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5184.2.a.cb.1.2 | 2 | 4.3 | odd | 2 |