Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,2,Mod(1,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("810.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.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: | \(6.46788256372\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 810.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.37228 | 1.27460 | 0.637301 | − | 0.770615i | \(-0.280051\pi\) | ||||
0.637301 | + | 0.770615i | \(0.280051\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 4.37228 | 1.31829 | 0.659146 | − | 0.752015i | \(-0.270918\pi\) | ||||
0.659146 | + | 0.752015i | \(0.270918\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.74456 | −1.87061 | −0.935303 | − | 0.353849i | \(-0.884873\pi\) | ||||
−0.935303 | + | 0.353849i | \(0.884873\pi\) | |||||||
\(14\) | 3.37228 | 0.901280 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.62772 | 0.394780 | 0.197390 | − | 0.980325i | \(-0.436754\pi\) | ||||
0.197390 | + | 0.980325i | \(0.436754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.37228 | −0.544239 | −0.272119 | − | 0.962264i | \(-0.587725\pi\) | ||||
−0.272119 | + | 0.962264i | \(0.587725\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.37228 | 0.932174 | ||||||||
\(23\) | −1.37228 | −0.286140 | −0.143070 | − | 0.989713i | \(-0.545697\pi\) | ||||
−0.143070 | + | 0.989713i | \(0.545697\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.74456 | −1.32272 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.37228 | 0.637301 | ||||||||
\(29\) | −1.37228 | −0.254826 | −0.127413 | − | 0.991850i | \(-0.540667\pi\) | ||||
−0.127413 | + | 0.991850i | \(0.540667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.74456 | 0.852149 | 0.426074 | − | 0.904688i | \(-0.359896\pi\) | ||||
0.426074 | + | 0.904688i | \(0.359896\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.62772 | 0.279151 | ||||||||
\(35\) | 3.37228 | 0.570020 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | −2.37228 | −0.384835 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.62772 | −0.858219 | −0.429110 | − | 0.903252i | \(-0.641173\pi\) | ||||
−0.429110 | + | 0.903252i | \(0.641173\pi\) | |||||||
\(44\) | 4.37228 | 0.659146 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.37228 | −0.202332 | ||||||||
\(47\) | 7.37228 | 1.07536 | 0.537679 | − | 0.843150i | \(-0.319301\pi\) | ||||
0.537679 | + | 0.843150i | \(0.319301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.37228 | 0.624612 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.74456 | −0.935303 | ||||||||
\(53\) | 11.4891 | 1.57815 | 0.789076 | − | 0.614295i | \(-0.210560\pi\) | ||||
0.789076 | + | 0.614295i | \(0.210560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.37228 | 0.589558 | ||||||||
\(56\) | 3.37228 | 0.450640 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.37228 | −0.180189 | ||||||||
\(59\) | −4.37228 | −0.569223 | −0.284611 | − | 0.958643i | \(-0.591865\pi\) | ||||
−0.284611 | + | 0.958643i | \(0.591865\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.11684 | −1.03926 | −0.519628 | − | 0.854393i | \(-0.673929\pi\) | ||||
−0.519628 | + | 0.854393i | \(0.673929\pi\) | |||||||
\(62\) | 4.74456 | 0.602560 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.74456 | −0.836560 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | −0.855186 | −0.427593 | − | 0.903971i | \(-0.640638\pi\) | ||||
−0.427593 | + | 0.903971i | \(0.640638\pi\) | |||||||
\(68\) | 1.62772 | 0.197390 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.37228 | 0.403065 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.11684 | 0.364799 | 0.182399 | − | 0.983225i | \(-0.441614\pi\) | ||||
0.182399 | + | 0.983225i | \(0.441614\pi\) | |||||||
\(74\) | −4.00000 | −0.464991 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.37228 | −0.272119 | ||||||||
\(77\) | 14.7446 | 1.68030 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | 0.225018 | 0.112509 | − | 0.993651i | \(-0.464111\pi\) | ||||
0.112509 | + | 0.993651i | \(0.464111\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | 0.331295 | ||||||||
\(83\) | −7.37228 | −0.809213 | −0.404607 | − | 0.914491i | \(-0.632592\pi\) | ||||
−0.404607 | + | 0.914491i | \(0.632592\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.62772 | 0.176551 | ||||||||
\(86\) | −5.62772 | −0.606853 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.37228 | 0.466087 | ||||||||
\(89\) | −16.1168 | −1.70838 | −0.854191 | − | 0.519959i | \(-0.825947\pi\) | ||||
−0.854191 | + | 0.519959i | \(0.825947\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.7446 | −2.38428 | ||||||||
\(92\) | −1.37228 | −0.143070 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.37228 | 0.760393 | ||||||||
\(95\) | −2.37228 | −0.243391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.37228 | −0.850076 | −0.425038 | − | 0.905175i | \(-0.639739\pi\) | ||||
−0.425038 | + | 0.905175i | \(0.639739\pi\) | |||||||
\(98\) | 4.37228 | 0.441667 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.74456 | −0.273094 | −0.136547 | − | 0.990634i | \(-0.543601\pi\) | ||||
−0.136547 | + | 0.990634i | \(0.543601\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0000 | −1.57653 | −0.788263 | − | 0.615338i | \(-0.789020\pi\) | ||||
−0.788263 | + | 0.615338i | \(0.789020\pi\) | |||||||
\(104\) | −6.74456 | −0.661359 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.4891 | 1.11592 | ||||||||
\(107\) | −8.48913 | −0.820675 | −0.410337 | − | 0.911934i | \(-0.634589\pi\) | ||||
−0.410337 | + | 0.911934i | \(0.634589\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.3723 | 1.47240 | 0.736199 | − | 0.676765i | \(-0.236619\pi\) | ||||
0.736199 | + | 0.676765i | \(0.236619\pi\) | |||||||
\(110\) | 4.37228 | 0.416881 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.37228 | 0.318651 | ||||||||
\(113\) | −3.25544 | −0.306246 | −0.153123 | − | 0.988207i | \(-0.548933\pi\) | ||||
−0.153123 | + | 0.988207i | \(0.548933\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.37228 | −0.127966 | ||||||||
\(116\) | −1.37228 | −0.127413 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.37228 | −0.402501 | ||||||||
\(119\) | 5.48913 | 0.503187 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.11684 | 0.737895 | ||||||||
\(122\) | −8.11684 | −0.734865 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.74456 | 0.426074 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.11684 | −0.720253 | −0.360127 | − | 0.932903i | \(-0.617267\pi\) | ||||
−0.360127 | + | 0.932903i | \(0.617267\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.74456 | −0.591537 | ||||||||
\(131\) | 2.74456 | 0.239794 | 0.119897 | − | 0.992786i | \(-0.461744\pi\) | ||||
0.119897 | + | 0.992786i | \(0.461744\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | −7.00000 | −0.604708 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.62772 | 0.139576 | ||||||||
\(137\) | 19.1168 | 1.63326 | 0.816631 | − | 0.577160i | \(-0.195839\pi\) | ||||
0.816631 | + | 0.577160i | \(0.195839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.883156 | 0.0749083 | 0.0374542 | − | 0.999298i | \(-0.488075\pi\) | ||||
0.0374542 | + | 0.999298i | \(0.488075\pi\) | |||||||
\(140\) | 3.37228 | 0.285010 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | −29.4891 | −2.46600 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.37228 | −0.113962 | ||||||||
\(146\) | 3.11684 | 0.257952 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | −1.88316 | −0.154274 | −0.0771371 | − | 0.997020i | \(-0.524578\pi\) | ||||
−0.0771371 | + | 0.997020i | \(0.524578\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | −0.813788 | −0.406894 | − | 0.913475i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(152\) | −2.37228 | −0.192417 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.7446 | 1.18815 | ||||||||
\(155\) | 4.74456 | 0.381092 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.74456 | −0.538275 | −0.269137 | − | 0.963102i | \(-0.586739\pi\) | ||||
−0.269137 | + | 0.963102i | \(0.586739\pi\) | |||||||
\(158\) | 2.00000 | 0.159111 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −4.62772 | −0.364715 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.4891 | −1.68316 | −0.841579 | − | 0.540134i | \(-0.818374\pi\) | ||||
−0.841579 | + | 0.540134i | \(0.818374\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.37228 | −0.572200 | ||||||||
\(167\) | −13.3723 | −1.03478 | −0.517389 | − | 0.855750i | \(-0.673096\pi\) | ||||
−0.517389 | + | 0.855750i | \(0.673096\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.4891 | 2.49916 | ||||||||
\(170\) | 1.62772 | 0.124840 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.62772 | −0.429110 | ||||||||
\(173\) | −20.7446 | −1.57718 | −0.788590 | − | 0.614919i | \(-0.789189\pi\) | ||||
−0.788590 | + | 0.614919i | \(0.789189\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.37228 | 0.254921 | ||||||||
\(176\) | 4.37228 | 0.329573 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.1168 | −1.20801 | ||||||||
\(179\) | 14.7446 | 1.10206 | 0.551030 | − | 0.834485i | \(-0.314235\pi\) | ||||
0.551030 | + | 0.834485i | \(0.314235\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.8614 | 1.55062 | 0.775308 | − | 0.631583i | \(-0.217595\pi\) | ||||
0.775308 | + | 0.631583i | \(0.217595\pi\) | |||||||
\(182\) | −22.7446 | −1.68594 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.37228 | −0.101166 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.11684 | 0.520435 | ||||||||
\(188\) | 7.37228 | 0.537679 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.37228 | −0.172103 | ||||||||
\(191\) | −17.4891 | −1.26547 | −0.632734 | − | 0.774369i | \(-0.718067\pi\) | ||||
−0.632734 | + | 0.774369i | \(0.718067\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.1168 | 1.52002 | 0.760012 | − | 0.649909i | \(-0.225193\pi\) | ||||
0.760012 | + | 0.649909i | \(0.225193\pi\) | |||||||
\(194\) | −8.37228 | −0.601095 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.37228 | 0.312306 | ||||||||
\(197\) | 5.48913 | 0.391084 | 0.195542 | − | 0.980695i | \(-0.437353\pi\) | ||||
0.195542 | + | 0.980695i | \(0.437353\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.4891 | 0.956219 | 0.478109 | − | 0.878300i | \(-0.341322\pi\) | ||||
0.478109 | + | 0.878300i | \(0.341322\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.74456 | −0.193107 | ||||||||
\(203\) | −4.62772 | −0.324802 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | 0.209529 | ||||||||
\(206\) | −16.0000 | −1.11477 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.74456 | −0.467651 | ||||||||
\(209\) | −10.3723 | −0.717466 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.7446 | −1.29043 | −0.645214 | − | 0.764002i | \(-0.723232\pi\) | ||||
−0.645214 | + | 0.764002i | \(0.723232\pi\) | |||||||
\(212\) | 11.4891 | 0.789076 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.48913 | −0.580305 | ||||||||
\(215\) | −5.62772 | −0.383807 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000 | 1.08615 | ||||||||
\(218\) | 15.3723 | 1.04114 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.37228 | 0.294779 | ||||||||
\(221\) | −10.9783 | −0.738477 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.62772 | 0.443825 | 0.221912 | − | 0.975067i | \(-0.428770\pi\) | ||||
0.221912 | + | 0.975067i | \(0.428770\pi\) | |||||||
\(224\) | 3.37228 | 0.225320 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.25544 | −0.216548 | ||||||||
\(227\) | −19.1168 | −1.26883 | −0.634415 | − | 0.772993i | \(-0.718759\pi\) | ||||
−0.634415 | + | 0.772993i | \(0.718759\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6277 | 0.834463 | 0.417232 | − | 0.908800i | \(-0.363000\pi\) | ||||
0.417232 | + | 0.908800i | \(0.363000\pi\) | |||||||
\(230\) | −1.37228 | −0.0904856 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.37228 | −0.0900947 | ||||||||
\(233\) | −7.11684 | −0.466240 | −0.233120 | − | 0.972448i | \(-0.574893\pi\) | ||||
−0.233120 | + | 0.972448i | \(0.574893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.37228 | 0.480915 | ||||||||
\(236\) | −4.37228 | −0.284611 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.48913 | 0.355807 | ||||||||
\(239\) | 3.25544 | 0.210577 | 0.105288 | − | 0.994442i | \(-0.466423\pi\) | ||||
0.105288 | + | 0.994442i | \(0.466423\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.4891 | −0.804495 | −0.402248 | − | 0.915531i | \(-0.631771\pi\) | ||||
−0.402248 | + | 0.915531i | \(0.631771\pi\) | |||||||
\(242\) | 8.11684 | 0.521770 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.11684 | −0.519628 | ||||||||
\(245\) | 4.37228 | 0.279335 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.0000 | 1.01806 | ||||||||
\(248\) | 4.74456 | 0.301280 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 24.6060 | 1.55312 | 0.776558 | − | 0.630046i | \(-0.216964\pi\) | ||||
0.776558 | + | 0.630046i | \(0.216964\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | −8.11684 | −0.509296 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.37228 | −0.272735 | −0.136368 | − | 0.990658i | \(-0.543543\pi\) | ||||
−0.136368 | + | 0.990658i | \(0.543543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.4891 | −0.838173 | ||||||||
\(260\) | −6.74456 | −0.418280 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.74456 | 0.169560 | ||||||||
\(263\) | 17.4891 | 1.07843 | 0.539213 | − | 0.842170i | \(-0.318722\pi\) | ||||
0.539213 | + | 0.842170i | \(0.318722\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.4891 | 0.705771 | ||||||||
\(266\) | −8.00000 | −0.490511 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.00000 | −0.427593 | ||||||||
\(269\) | 1.37228 | 0.0836695 | 0.0418347 | − | 0.999125i | \(-0.486680\pi\) | ||||
0.0418347 | + | 0.999125i | \(0.486680\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 1.62772 | 0.0986949 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.1168 | 1.15489 | ||||||||
\(275\) | 4.37228 | 0.263658 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.7446 | 1.00608 | 0.503042 | − | 0.864262i | \(-0.332214\pi\) | ||||
0.503042 | + | 0.864262i | \(0.332214\pi\) | |||||||
\(278\) | 0.883156 | 0.0529682 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.37228 | 0.201532 | ||||||||
\(281\) | 1.37228 | 0.0818634 | 0.0409317 | − | 0.999162i | \(-0.486967\pi\) | ||||
0.0409317 | + | 0.999162i | \(0.486967\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.13859 | −0.186570 | −0.0932850 | − | 0.995639i | \(-0.529737\pi\) | ||||
−0.0932850 | + | 0.995639i | \(0.529737\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.4891 | −1.74373 | ||||||||
\(287\) | 10.1168 | 0.597178 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3505 | −0.844149 | ||||||||
\(290\) | −1.37228 | −0.0805831 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.11684 | 0.182399 | ||||||||
\(293\) | −26.2337 | −1.53259 | −0.766294 | − | 0.642490i | \(-0.777901\pi\) | ||||
−0.766294 | + | 0.642490i | \(0.777901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.37228 | −0.254564 | ||||||||
\(296\) | −4.00000 | −0.232495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.88316 | −0.109088 | ||||||||
\(299\) | 9.25544 | 0.535256 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.9783 | −1.09389 | ||||||||
\(302\) | −10.0000 | −0.575435 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.37228 | −0.136060 | ||||||||
\(305\) | −8.11684 | −0.464769 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.23369 | 0.0704103 | 0.0352051 | − | 0.999380i | \(-0.488792\pi\) | ||||
0.0352051 | + | 0.999380i | \(0.488792\pi\) | |||||||
\(308\) | 14.7446 | 0.840149 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.74456 | 0.269473 | ||||||||
\(311\) | 20.7446 | 1.17632 | 0.588158 | − | 0.808746i | \(-0.299853\pi\) | ||||
0.588158 | + | 0.808746i | \(0.299853\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.62772 | 0.205051 | 0.102525 | − | 0.994730i | \(-0.467308\pi\) | ||||
0.102525 | + | 0.994730i | \(0.467308\pi\) | |||||||
\(314\) | −6.74456 | −0.380618 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | −2.74456 | −0.154150 | −0.0770750 | − | 0.997025i | \(-0.524558\pi\) | ||||
−0.0770750 | + | 0.997025i | \(0.524558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | −0.335936 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.62772 | −0.257893 | ||||||||
\(323\) | −3.86141 | −0.214854 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.74456 | −0.374121 | ||||||||
\(326\) | −21.4891 | −1.19017 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000 | 0.165647 | ||||||||
\(329\) | 24.8614 | 1.37065 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.2337 | 0.892284 | 0.446142 | − | 0.894962i | \(-0.352798\pi\) | ||||
0.446142 | + | 0.894962i | \(0.352798\pi\) | |||||||
\(332\) | −7.37228 | −0.404607 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.3723 | −0.731699 | ||||||||
\(335\) | −7.00000 | −0.382451 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.37228 | −0.129226 | −0.0646132 | − | 0.997910i | \(-0.520581\pi\) | ||||
−0.0646132 | + | 0.997910i | \(0.520581\pi\) | |||||||
\(338\) | 32.4891 | 1.76718 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.62772 | 0.0882754 | ||||||||
\(341\) | 20.7446 | 1.12338 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.86141 | −0.478471 | ||||||||
\(344\) | −5.62772 | −0.303426 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.7446 | −1.11523 | ||||||||
\(347\) | 4.88316 | 0.262142 | 0.131071 | − | 0.991373i | \(-0.458158\pi\) | ||||
0.131071 | + | 0.991373i | \(0.458158\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.1168 | 0.969772 | 0.484886 | − | 0.874577i | \(-0.338861\pi\) | ||||
0.484886 | + | 0.874577i | \(0.338861\pi\) | |||||||
\(350\) | 3.37228 | 0.180256 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.37228 | 0.233043 | ||||||||
\(353\) | 21.3505 | 1.13637 | 0.568187 | − | 0.822899i | \(-0.307645\pi\) | ||||
0.568187 | + | 0.822899i | \(0.307645\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | 0.318447 | ||||||||
\(356\) | −16.1168 | −0.854191 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.7446 | 0.779274 | ||||||||
\(359\) | 17.4891 | 0.923041 | 0.461520 | − | 0.887130i | \(-0.347304\pi\) | ||||
0.461520 | + | 0.887130i | \(0.347304\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.3723 | −0.703804 | ||||||||
\(362\) | 20.8614 | 1.09645 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −22.7446 | −1.19214 | ||||||||
\(365\) | 3.11684 | 0.163143 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | −0.835193 | −0.417597 | − | 0.908633i | \(-0.637127\pi\) | ||||
−0.417597 | + | 0.908633i | \(0.637127\pi\) | |||||||
\(368\) | −1.37228 | −0.0715351 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | 38.7446 | 2.01152 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.4891 | −0.801997 | −0.400998 | − | 0.916079i | \(-0.631337\pi\) | ||||
−0.400998 | + | 0.916079i | \(0.631337\pi\) | |||||||
\(374\) | 7.11684 | 0.368003 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.37228 | 0.380196 | ||||||||
\(377\) | 9.25544 | 0.476679 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.8614 | 0.917479 | 0.458739 | − | 0.888571i | \(-0.348301\pi\) | ||||
0.458739 | + | 0.888571i | \(0.348301\pi\) | |||||||
\(380\) | −2.37228 | −0.121695 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.4891 | −0.894821 | ||||||||
\(383\) | 22.9783 | 1.17413 | 0.587067 | − | 0.809538i | \(-0.300283\pi\) | ||||
0.587067 | + | 0.809538i | \(0.300283\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.7446 | 0.751452 | ||||||||
\(386\) | 21.1168 | 1.07482 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.37228 | −0.425038 | ||||||||
\(389\) | 4.62772 | 0.234635 | 0.117317 | − | 0.993094i | \(-0.462571\pi\) | ||||
0.117317 | + | 0.993094i | \(0.462571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.23369 | −0.112962 | ||||||||
\(392\) | 4.37228 | 0.220834 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.48913 | 0.276538 | ||||||||
\(395\) | 2.00000 | 0.100631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.7446 | 1.14152 | 0.570758 | − | 0.821118i | \(-0.306649\pi\) | ||||
0.570758 | + | 0.821118i | \(0.306649\pi\) | |||||||
\(398\) | 13.4891 | 0.676149 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.11684 | 0.0557725 | 0.0278863 | − | 0.999611i | \(-0.491122\pi\) | ||||
0.0278863 | + | 0.999611i | \(0.491122\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.0000 | −1.59403 | ||||||||
\(404\) | −2.74456 | −0.136547 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.62772 | −0.229670 | ||||||||
\(407\) | −17.4891 | −0.866904 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.8614 | 0.883190 | 0.441595 | − | 0.897215i | \(-0.354413\pi\) | ||||
0.441595 | + | 0.897215i | \(0.354413\pi\) | |||||||
\(410\) | 3.00000 | 0.148159 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.0000 | −0.788263 | ||||||||
\(413\) | −14.7446 | −0.725532 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.37228 | −0.361891 | ||||||||
\(416\) | −6.74456 | −0.330679 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.3723 | −0.507325 | ||||||||
\(419\) | −25.7228 | −1.25664 | −0.628321 | − | 0.777954i | \(-0.716257\pi\) | ||||
−0.628321 | + | 0.777954i | \(0.716257\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.4674 | 1.48489 | 0.742445 | − | 0.669908i | \(-0.233666\pi\) | ||||
0.742445 | + | 0.669908i | \(0.233666\pi\) | |||||||
\(422\) | −18.7446 | −0.912471 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.4891 | 0.557961 | ||||||||
\(425\) | 1.62772 | 0.0789560 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.3723 | −1.32464 | ||||||||
\(428\) | −8.48913 | −0.410337 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.62772 | −0.271393 | ||||||||
\(431\) | −8.23369 | −0.396603 | −0.198301 | − | 0.980141i | \(-0.563542\pi\) | ||||
−0.198301 | + | 0.980141i | \(0.563542\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.37228 | 0.306232 | 0.153116 | − | 0.988208i | \(-0.451069\pi\) | ||||
0.153116 | + | 0.988208i | \(0.451069\pi\) | |||||||
\(434\) | 16.0000 | 0.768025 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.3723 | 0.736199 | ||||||||
\(437\) | 3.25544 | 0.155729 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.2337 | −0.870246 | −0.435123 | − | 0.900371i | \(-0.643295\pi\) | ||||
−0.435123 | + | 0.900371i | \(0.643295\pi\) | |||||||
\(440\) | 4.37228 | 0.208440 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.9783 | −0.522182 | ||||||||
\(443\) | 3.51087 | 0.166807 | 0.0834033 | − | 0.996516i | \(-0.473421\pi\) | ||||
0.0834033 | + | 0.996516i | \(0.473421\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.1168 | −0.764012 | ||||||||
\(446\) | 6.62772 | 0.313832 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.37228 | 0.159325 | ||||||||
\(449\) | −9.86141 | −0.465389 | −0.232694 | − | 0.972550i | \(-0.574754\pi\) | ||||
−0.232694 | + | 0.972550i | \(0.574754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.1168 | 0.617648 | ||||||||
\(452\) | −3.25544 | −0.153123 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.1168 | −0.897198 | ||||||||
\(455\) | −22.7446 | −1.06628 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.8832 | 0.602649 | 0.301324 | − | 0.953522i | \(-0.402571\pi\) | ||||
0.301324 | + | 0.953522i | \(0.402571\pi\) | |||||||
\(458\) | 12.6277 | 0.590055 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.37228 | −0.0639829 | ||||||||
\(461\) | −1.88316 | −0.0877073 | −0.0438537 | − | 0.999038i | \(-0.513964\pi\) | ||||
−0.0438537 | + | 0.999038i | \(0.513964\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.0000 | 0.929479 | 0.464739 | − | 0.885448i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | −1.37228 | −0.0637066 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.11684 | −0.329681 | ||||||||
\(467\) | −43.1168 | −1.99521 | −0.997605 | − | 0.0691713i | \(-0.977964\pi\) | ||||
−0.997605 | + | 0.0691713i | \(0.977964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.6060 | −1.09002 | ||||||||
\(470\) | 7.37228 | 0.340058 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.37228 | −0.201251 | ||||||||
\(473\) | −24.6060 | −1.13138 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.37228 | −0.108848 | ||||||||
\(476\) | 5.48913 | 0.251594 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.25544 | 0.148900 | ||||||||
\(479\) | 0.510875 | 0.0233425 | 0.0116712 | − | 0.999932i | \(-0.496285\pi\) | ||||
0.0116712 | + | 0.999932i | \(0.496285\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.9783 | 1.23010 | ||||||||
\(482\) | −12.4891 | −0.568864 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.11684 | 0.368947 | ||||||||
\(485\) | −8.37228 | −0.380166 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.7446 | −0.577511 | −0.288756 | − | 0.957403i | \(-0.593242\pi\) | ||||
−0.288756 | + | 0.957403i | \(0.593242\pi\) | |||||||
\(488\) | −8.11684 | −0.367432 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.37228 | 0.197520 | ||||||||
\(491\) | 36.6060 | 1.65200 | 0.826002 | − | 0.563667i | \(-0.190610\pi\) | ||||
0.826002 | + | 0.563667i | \(0.190610\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.23369 | −0.100600 | ||||||||
\(494\) | 16.0000 | 0.719874 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.74456 | 0.213037 | ||||||||
\(497\) | 20.2337 | 0.907605 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.1168 | 0.676723 | 0.338361 | − | 0.941016i | \(-0.390127\pi\) | ||||
0.338361 | + | 0.941016i | \(0.390127\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.6060 | 1.09822 | ||||||||
\(503\) | 6.86141 | 0.305935 | 0.152967 | − | 0.988231i | \(-0.451117\pi\) | ||||
0.152967 | + | 0.988231i | \(0.451117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.74456 | −0.122131 | ||||||||
\(506\) | −6.00000 | −0.266733 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.11684 | −0.360127 | ||||||||
\(509\) | 42.3505 | 1.87715 | 0.938577 | − | 0.345069i | \(-0.112145\pi\) | ||||
0.938577 | + | 0.345069i | \(0.112145\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.5109 | 0.464974 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.37228 | −0.192853 | ||||||||
\(515\) | −16.0000 | −0.705044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.2337 | 1.41764 | ||||||||
\(518\) | −13.4891 | −0.592678 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.74456 | −0.295769 | ||||||||
\(521\) | 6.76631 | 0.296438 | 0.148219 | − | 0.988955i | \(-0.452646\pi\) | ||||
0.148219 | + | 0.988955i | \(0.452646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.11684 | 0.267471 | 0.133735 | − | 0.991017i | \(-0.457303\pi\) | ||||
0.133735 | + | 0.991017i | \(0.457303\pi\) | |||||||
\(524\) | 2.74456 | 0.119897 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.4891 | 0.762562 | ||||||||
\(527\) | 7.72281 | 0.336411 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.1168 | −0.918124 | ||||||||
\(530\) | 11.4891 | 0.499056 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.00000 | −0.346844 | ||||||||
\(533\) | −20.2337 | −0.876418 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.48913 | −0.367017 | ||||||||
\(536\) | −7.00000 | −0.302354 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.37228 | 0.0591632 | ||||||||
\(539\) | 19.1168 | 0.823421 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.3723 | 1.17683 | 0.588413 | − | 0.808560i | \(-0.299753\pi\) | ||||
0.588413 | + | 0.808560i | \(0.299753\pi\) | |||||||
\(542\) | 8.00000 | 0.343629 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.62772 | 0.0697879 | ||||||||
\(545\) | 15.3723 | 0.658476 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.4674 | −1.25993 | −0.629967 | − | 0.776622i | \(-0.716932\pi\) | ||||
−0.629967 | + | 0.776622i | \(0.716932\pi\) | |||||||
\(548\) | 19.1168 | 0.816631 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.37228 | 0.186435 | ||||||||
\(551\) | 3.25544 | 0.138686 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.74456 | 0.286808 | ||||||||
\(554\) | 16.7446 | 0.711408 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.883156 | 0.0374542 | ||||||||
\(557\) | 44.2337 | 1.87424 | 0.937121 | − | 0.349005i | \(-0.113480\pi\) | ||||
0.937121 | + | 0.349005i | \(0.113480\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.9565 | 1.60539 | ||||||||
\(560\) | 3.37228 | 0.142505 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.37228 | 0.0578862 | ||||||||
\(563\) | 40.7228 | 1.71626 | 0.858131 | − | 0.513431i | \(-0.171626\pi\) | ||||
0.858131 | + | 0.513431i | \(0.171626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.25544 | −0.136957 | ||||||||
\(566\) | −3.13859 | −0.131925 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | 30.6060 | 1.28307 | 0.641534 | − | 0.767094i | \(-0.278298\pi\) | ||||
0.641534 | + | 0.767094i | \(0.278298\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.60597 | 0.360149 | 0.180074 | − | 0.983653i | \(-0.442366\pi\) | ||||
0.180074 | + | 0.983653i | \(0.442366\pi\) | |||||||
\(572\) | −29.4891 | −1.23300 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.1168 | 0.422269 | ||||||||
\(575\) | −1.37228 | −0.0572281 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.1168 | −1.71172 | −0.855858 | − | 0.517210i | \(-0.826970\pi\) | ||||
−0.855858 | + | 0.517210i | \(0.826970\pi\) | |||||||
\(578\) | −14.3505 | −0.596903 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.37228 | −0.0569809 | ||||||||
\(581\) | −24.8614 | −1.03142 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.2337 | 2.08047 | ||||||||
\(584\) | 3.11684 | 0.128976 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.2337 | −1.08370 | ||||||||
\(587\) | −27.0000 | −1.11441 | −0.557205 | − | 0.830375i | \(-0.688126\pi\) | ||||
−0.557205 | + | 0.830375i | \(0.688126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.2554 | −0.463772 | ||||||||
\(590\) | −4.37228 | −0.180004 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.00000 | −0.164399 | ||||||||
\(593\) | 19.7228 | 0.809919 | 0.404959 | − | 0.914335i | \(-0.367286\pi\) | ||||
0.404959 | + | 0.914335i | \(0.367286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.48913 | 0.225032 | ||||||||
\(596\) | −1.88316 | −0.0771371 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.25544 | 0.378483 | ||||||||
\(599\) | 3.76631 | 0.153887 | 0.0769437 | − | 0.997035i | \(-0.475484\pi\) | ||||
0.0769437 | + | 0.997035i | \(0.475484\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.86141 | −0.0759284 | −0.0379642 | − | 0.999279i | \(-0.512087\pi\) | ||||
−0.0379642 | + | 0.999279i | \(0.512087\pi\) | |||||||
\(602\) | −18.9783 | −0.773496 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.0000 | −0.406894 | ||||||||
\(605\) | 8.11684 | 0.329997 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.1168 | 0.735340 | 0.367670 | − | 0.929956i | \(-0.380156\pi\) | ||||
0.367670 | + | 0.929956i | \(0.380156\pi\) | |||||||
\(608\) | −2.37228 | −0.0962087 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.11684 | −0.328641 | ||||||||
\(611\) | −49.7228 | −2.01157 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.2337 | 1.38269 | 0.691343 | − | 0.722527i | \(-0.257019\pi\) | ||||
0.691343 | + | 0.722527i | \(0.257019\pi\) | |||||||
\(614\) | 1.23369 | 0.0497876 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.7446 | 0.594075 | ||||||||
\(617\) | 4.88316 | 0.196588 | 0.0982942 | − | 0.995157i | \(-0.468661\pi\) | ||||
0.0982942 | + | 0.995157i | \(0.468661\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.8832 | −0.839365 | −0.419682 | − | 0.907671i | \(-0.637859\pi\) | ||||
−0.419682 | + | 0.907671i | \(0.637859\pi\) | |||||||
\(620\) | 4.74456 | 0.190546 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.7446 | 0.831781 | ||||||||
\(623\) | −54.3505 | −2.17751 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.62772 | 0.144993 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.74456 | −0.269137 | ||||||||
\(629\) | −6.51087 | −0.259606 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.7228 | −0.944390 | −0.472195 | − | 0.881494i | \(-0.656538\pi\) | ||||
−0.472195 | + | 0.881494i | \(0.656538\pi\) | |||||||
\(632\) | 2.00000 | 0.0795557 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.74456 | −0.109001 | ||||||||
\(635\) | −8.11684 | −0.322107 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.4891 | −1.16840 | ||||||||
\(638\) | −6.00000 | −0.237542 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 39.0000 | 1.54041 | 0.770204 | − | 0.637798i | \(-0.220155\pi\) | ||||
0.770204 | + | 0.637798i | \(0.220155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.0000 | 0.433798 | 0.216899 | − | 0.976194i | \(-0.430406\pi\) | ||||
0.216899 | + | 0.976194i | \(0.430406\pi\) | |||||||
\(644\) | −4.62772 | −0.182358 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.86141 | −0.151925 | ||||||||
\(647\) | 39.0951 | 1.53699 | 0.768493 | − | 0.639858i | \(-0.221007\pi\) | ||||
0.768493 | + | 0.639858i | \(0.221007\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.1168 | −0.750402 | ||||||||
\(650\) | −6.74456 | −0.264544 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21.4891 | −0.841579 | ||||||||
\(653\) | −19.7228 | −0.771813 | −0.385907 | − | 0.922538i | \(-0.626111\pi\) | ||||
−0.385907 | + | 0.922538i | \(0.626111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.74456 | 0.107239 | ||||||||
\(656\) | 3.00000 | 0.117130 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.8614 | 0.969199 | ||||||||
\(659\) | −17.4891 | −0.681280 | −0.340640 | − | 0.940194i | \(-0.610644\pi\) | ||||
−0.340640 | + | 0.940194i | \(0.610644\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.2337 | −0.475835 | −0.237918 | − | 0.971285i | \(-0.576465\pi\) | ||||
−0.237918 | + | 0.971285i | \(0.576465\pi\) | |||||||
\(662\) | 16.2337 | 0.630940 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.37228 | −0.286100 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.88316 | 0.0729161 | ||||||||
\(668\) | −13.3723 | −0.517389 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.00000 | −0.270434 | ||||||||
\(671\) | −35.4891 | −1.37004 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0000 | −0.385472 | −0.192736 | − | 0.981251i | \(-0.561736\pi\) | ||||
−0.192736 | + | 0.981251i | \(0.561736\pi\) | |||||||
\(674\) | −2.37228 | −0.0913769 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 32.4891 | 1.24958 | ||||||||
\(677\) | −13.7228 | −0.527411 | −0.263705 | − | 0.964603i | \(-0.584945\pi\) | ||||
−0.263705 | + | 0.964603i | \(0.584945\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.2337 | −1.08351 | ||||||||
\(680\) | 1.62772 | 0.0624202 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 20.7446 | 0.794350 | ||||||||
\(683\) | 30.0951 | 1.15156 | 0.575778 | − | 0.817606i | \(-0.304699\pi\) | ||||
0.575778 | + | 0.817606i | \(0.304699\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.1168 | 0.730417 | ||||||||
\(686\) | −8.86141 | −0.338330 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.62772 | −0.214555 | ||||||||
\(689\) | −77.4891 | −2.95210 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.2337 | −1.37839 | −0.689197 | − | 0.724574i | \(-0.742037\pi\) | ||||
−0.689197 | + | 0.724574i | \(0.742037\pi\) | |||||||
\(692\) | −20.7446 | −0.788590 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.88316 | 0.185362 | ||||||||
\(695\) | 0.883156 | 0.0335000 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.88316 | 0.184963 | ||||||||
\(698\) | 18.1168 | 0.685733 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.37228 | 0.127460 | ||||||||
\(701\) | −42.8614 | −1.61885 | −0.809426 | − | 0.587221i | \(-0.800222\pi\) | ||||
−0.809426 | + | 0.587221i | \(0.800222\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.48913 | 0.357889 | ||||||||
\(704\) | 4.37228 | 0.164787 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.3505 | 0.803538 | ||||||||
\(707\) | −9.25544 | −0.348087 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.86141 | 0.107462 | 0.0537312 | − | 0.998555i | \(-0.482889\pi\) | ||||
0.0537312 | + | 0.998555i | \(0.482889\pi\) | |||||||
\(710\) | 6.00000 | 0.225176 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.1168 | −0.604004 | ||||||||
\(713\) | −6.51087 | −0.243834 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29.4891 | −1.10283 | ||||||||
\(716\) | 14.7446 | 0.551030 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.4891 | 0.652688 | ||||||||
\(719\) | 3.76631 | 0.140460 | 0.0702299 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702299 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −53.9565 | −2.00945 | ||||||||
\(722\) | −13.3723 | −0.497665 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.8614 | 0.775308 | ||||||||
\(725\) | −1.37228 | −0.0509652 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.1168 | 0.671917 | 0.335958 | − | 0.941877i | \(-0.390940\pi\) | ||||
0.335958 | + | 0.941877i | \(0.390940\pi\) | |||||||
\(728\) | −22.7446 | −0.842970 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.11684 | 0.115360 | ||||||||
\(731\) | −9.16034 | −0.338808 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.233688 | −0.00863146 | −0.00431573 | − | 0.999991i | \(-0.501374\pi\) | ||||
−0.00431573 | + | 0.999991i | \(0.501374\pi\) | |||||||
\(734\) | −16.0000 | −0.590571 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.37228 | −0.0505830 | ||||||||
\(737\) | −30.6060 | −1.12739 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.1168 | −1.51251 | −0.756254 | − | 0.654278i | \(-0.772972\pi\) | ||||
−0.756254 | + | 0.654278i | \(0.772972\pi\) | |||||||
\(740\) | −4.00000 | −0.147043 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 38.7446 | 1.42236 | ||||||||
\(743\) | −7.88316 | −0.289205 | −0.144602 | − | 0.989490i | \(-0.546190\pi\) | ||||
−0.144602 | + | 0.989490i | \(0.546190\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.88316 | −0.0689935 | ||||||||
\(746\) | −15.4891 | −0.567097 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.11684 | 0.260218 | ||||||||
\(749\) | −28.6277 | −1.04603 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.2337 | 0.592376 | 0.296188 | − | 0.955130i | \(-0.404285\pi\) | ||||
0.296188 | + | 0.955130i | \(0.404285\pi\) | |||||||
\(752\) | 7.37228 | 0.268839 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.25544 | 0.337063 | ||||||||
\(755\) | −10.0000 | −0.363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 17.8614 | 0.648756 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.37228 | −0.0860517 | ||||||||
\(761\) | 51.0951 | 1.85220 | 0.926098 | − | 0.377283i | \(-0.123142\pi\) | ||||
0.926098 | + | 0.377283i | \(0.123142\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51.8397 | 1.87672 | ||||||||
\(764\) | −17.4891 | −0.632734 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.9783 | 0.830238 | ||||||||
\(767\) | 29.4891 | 1.06479 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.8614 | −1.68987 | −0.844933 | − | 0.534873i | \(-0.820360\pi\) | ||||
−0.844933 | + | 0.534873i | \(0.820360\pi\) | |||||||
\(770\) | 14.7446 | 0.531357 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.1168 | 0.760012 | ||||||||
\(773\) | −3.25544 | −0.117090 | −0.0585450 | − | 0.998285i | \(-0.518646\pi\) | ||||
−0.0585450 | + | 0.998285i | \(0.518646\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.74456 | 0.170430 | ||||||||
\(776\) | −8.37228 | −0.300547 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.62772 | 0.165912 | ||||||||
\(779\) | −7.11684 | −0.254987 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.2337 | 0.938715 | ||||||||
\(782\) | −2.23369 | −0.0798765 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.37228 | 0.156153 | ||||||||
\(785\) | −6.74456 | −0.240724 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.0000 | −0.998092 | −0.499046 | − | 0.866575i | \(-0.666316\pi\) | ||||
−0.499046 | + | 0.866575i | \(0.666316\pi\) | |||||||
\(788\) | 5.48913 | 0.195542 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.00000 | 0.0711568 | ||||||||
\(791\) | −10.9783 | −0.390342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.7446 | 1.94404 | ||||||||
\(794\) | 22.7446 | 0.807174 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.4891 | 0.478109 | ||||||||
\(797\) | −14.7446 | −0.522279 | −0.261140 | − | 0.965301i | \(-0.584098\pi\) | ||||
−0.261140 | + | 0.965301i | \(0.584098\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.11684 | 0.0394371 | ||||||||
\(803\) | 13.6277 | 0.480912 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.62772 | −0.163106 | ||||||||
\(806\) | −32.0000 | −1.12715 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.74456 | −0.0965534 | ||||||||
\(809\) | −39.3505 | −1.38349 | −0.691746 | − | 0.722141i | \(-0.743158\pi\) | ||||
−0.691746 | + | 0.722141i | \(0.743158\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.62772 | 0.127386 | 0.0636932 | − | 0.997970i | \(-0.479712\pi\) | ||||
0.0636932 | + | 0.997970i | \(0.479712\pi\) | |||||||
\(812\) | −4.62772 | −0.162401 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.4891 | −0.612994 | ||||||||
\(815\) | −21.4891 | −0.752731 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.3505 | 0.467076 | ||||||||
\(818\) | 17.8614 | 0.624509 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.00000 | 0.104765 | ||||||||
\(821\) | 23.8397 | 0.832010 | 0.416005 | − | 0.909362i | \(-0.363430\pi\) | ||||
0.416005 | + | 0.909362i | \(0.363430\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.0951 | −0.874760 | −0.437380 | − | 0.899277i | \(-0.644094\pi\) | ||||
−0.437380 | + | 0.899277i | \(0.644094\pi\) | |||||||
\(824\) | −16.0000 | −0.557386 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.7446 | −0.513029 | ||||||||
\(827\) | −36.8614 | −1.28180 | −0.640898 | − | 0.767626i | \(-0.721438\pi\) | ||||
−0.640898 | + | 0.767626i | \(0.721438\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.1168 | −1.74063 | −0.870315 | − | 0.492496i | \(-0.836085\pi\) | ||||
−0.870315 | + | 0.492496i | \(0.836085\pi\) | |||||||
\(830\) | −7.37228 | −0.255896 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.74456 | −0.233826 | ||||||||
\(833\) | 7.11684 | 0.246584 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.3723 | −0.462767 | ||||||||
\(836\) | −10.3723 | −0.358733 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.7228 | −0.888580 | ||||||||
\(839\) | −9.76631 | −0.337171 | −0.168585 | − | 0.985687i | \(-0.553920\pi\) | ||||
−0.168585 | + | 0.985687i | \(0.553920\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1168 | −0.935064 | ||||||||
\(842\) | 30.4674 | 1.04998 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18.7446 | −0.645214 | ||||||||
\(845\) | 32.4891 | 1.11766 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.3723 | 0.940523 | ||||||||
\(848\) | 11.4891 | 0.394538 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.62772 | 0.0558303 | ||||||||
\(851\) | 5.48913 | 0.188165 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.2337 | −1.24062 | −0.620309 | − | 0.784358i | \(-0.712993\pi\) | ||||
−0.620309 | + | 0.784358i | \(0.712993\pi\) | |||||||
\(854\) | −27.3723 | −0.936660 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.48913 | −0.290152 | ||||||||
\(857\) | −0.510875 | −0.0174511 | −0.00872557 | − | 0.999962i | \(-0.502777\pi\) | ||||
−0.00872557 | + | 0.999962i | \(0.502777\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.1168 | −0.584019 | −0.292010 | − | 0.956415i | \(-0.594324\pi\) | ||||
−0.292010 | + | 0.956415i | \(0.594324\pi\) | |||||||
\(860\) | −5.62772 | −0.191904 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.23369 | −0.280441 | ||||||||
\(863\) | 2.39403 | 0.0814938 | 0.0407469 | − | 0.999170i | \(-0.487026\pi\) | ||||
0.0407469 | + | 0.999170i | \(0.487026\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.7446 | −0.705336 | ||||||||
\(866\) | 6.37228 | 0.216539 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.0000 | 0.543075 | ||||||||
\(869\) | 8.74456 | 0.296639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 47.2119 | 1.59972 | ||||||||
\(872\) | 15.3723 | 0.520571 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.25544 | 0.110117 | ||||||||
\(875\) | 3.37228 | 0.114004 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.9565 | 1.21416 | 0.607082 | − | 0.794639i | \(-0.292340\pi\) | ||||
0.607082 | + | 0.794639i | \(0.292340\pi\) | |||||||
\(878\) | −18.2337 | −0.615357 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.37228 | 0.147390 | ||||||||
\(881\) | 24.3505 | 0.820390 | 0.410195 | − | 0.911998i | \(-0.365461\pi\) | ||||
0.410195 | + | 0.911998i | \(0.365461\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.7228 | −1.50504 | −0.752521 | − | 0.658568i | \(-0.771163\pi\) | ||||
−0.752521 | + | 0.658568i | \(0.771163\pi\) | |||||||
\(884\) | −10.9783 | −0.369239 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.51087 | 0.117950 | ||||||||
\(887\) | −19.7228 | −0.662227 | −0.331114 | − | 0.943591i | \(-0.607424\pi\) | ||||
−0.331114 | + | 0.943591i | \(0.607424\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.3723 | −0.918037 | ||||||||
\(890\) | −16.1168 | −0.540238 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.62772 | 0.221912 | ||||||||
\(893\) | −17.4891 | −0.585251 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.7446 | 0.492856 | ||||||||
\(896\) | 3.37228 | 0.112660 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.86141 | −0.329079 | ||||||||
\(899\) | −6.51087 | −0.217150 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.7011 | 0.623023 | ||||||||
\(902\) | 13.1168 | 0.436743 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.25544 | −0.108274 | ||||||||
\(905\) | 20.8614 | 0.693457 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.00000 | −0.232431 | −0.116216 | − | 0.993224i | \(-0.537076\pi\) | ||||
−0.116216 | + | 0.993224i | \(0.537076\pi\) | |||||||
\(908\) | −19.1168 | −0.634415 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.7446 | −0.753975 | ||||||||
\(911\) | 42.0000 | 1.39152 | 0.695761 | − | 0.718273i | \(-0.255067\pi\) | ||||
0.695761 | + | 0.718273i | \(0.255067\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.2337 | −1.06678 | ||||||||
\(914\) | 12.8832 | 0.426137 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.6277 | 0.417232 | ||||||||
\(917\) | 9.25544 | 0.305641 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.4674 | −0.873078 | −0.436539 | − | 0.899685i | \(-0.643796\pi\) | ||||
−0.436539 | + | 0.899685i | \(0.643796\pi\) | |||||||
\(920\) | −1.37228 | −0.0452428 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.88316 | −0.0620184 | ||||||||
\(923\) | −40.4674 | −1.33200 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 20.0000 | 0.657241 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.37228 | −0.0450473 | ||||||||
\(929\) | −51.9565 | −1.70464 | −0.852319 | − | 0.523023i | \(-0.824804\pi\) | ||||
−0.852319 | + | 0.523023i | \(0.824804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.3723 | −0.339938 | ||||||||
\(932\) | −7.11684 | −0.233120 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −43.1168 | −1.41083 | ||||||||
\(935\) | 7.11684 | 0.232746 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.7228 | 1.29769 | 0.648844 | − | 0.760922i | \(-0.275253\pi\) | ||||
0.648844 | + | 0.760922i | \(0.275253\pi\) | |||||||
\(938\) | −23.6060 | −0.770762 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.37228 | 0.240457 | ||||||||
\(941\) | −43.3723 | −1.41390 | −0.706948 | − | 0.707266i | \(-0.749929\pi\) | ||||
−0.706948 | + | 0.707266i | \(0.749929\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.11684 | −0.134063 | ||||||||
\(944\) | −4.37228 | −0.142306 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.6060 | −0.800009 | ||||||||
\(947\) | 34.7228 | 1.12834 | 0.564170 | − | 0.825659i | \(-0.309196\pi\) | ||||
0.564170 | + | 0.825659i | \(0.309196\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.0217 | −0.682395 | ||||||||
\(950\) | −2.37228 | −0.0769670 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.48913 | 0.177904 | ||||||||
\(953\) | −2.13859 | −0.0692758 | −0.0346379 | − | 0.999400i | \(-0.511028\pi\) | ||||
−0.0346379 | + | 0.999400i | \(0.511028\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.4891 | −0.565935 | ||||||||
\(956\) | 3.25544 | 0.105288 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.510875 | 0.0165056 | ||||||||
\(959\) | 64.4674 | 2.08176 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.48913 | −0.273843 | ||||||||
\(962\) | 26.9783 | 0.869814 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.4891 | −0.402248 | ||||||||
\(965\) | 21.1168 | 0.679775 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.1168 | 1.16144 | 0.580720 | − | 0.814104i | \(-0.302771\pi\) | ||||
0.580720 | + | 0.814104i | \(0.302771\pi\) | |||||||
\(968\) | 8.11684 | 0.260885 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.37228 | −0.268818 | ||||||||
\(971\) | 22.9783 | 0.737407 | 0.368704 | − | 0.929547i | \(-0.379802\pi\) | ||||
0.368704 | + | 0.929547i | \(0.379802\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.97825 | 0.0954783 | ||||||||
\(974\) | −12.7446 | −0.408362 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.11684 | −0.259814 | ||||||||
\(977\) | 22.8832 | 0.732097 | 0.366049 | − | 0.930596i | \(-0.380710\pi\) | ||||
0.366049 | + | 0.930596i | \(0.380710\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −70.4674 | −2.25215 | ||||||||
\(980\) | 4.37228 | 0.139667 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.6060 | 1.16814 | ||||||||
\(983\) | 12.8614 | 0.410215 | 0.205108 | − | 0.978739i | \(-0.434246\pi\) | ||||
0.205108 | + | 0.978739i | \(0.434246\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.48913 | 0.174898 | ||||||||
\(986\) | −2.23369 | −0.0711351 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.0000 | 0.509028 | ||||||||
\(989\) | 7.72281 | 0.245571 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.2337 | 0.515680 | 0.257840 | − | 0.966188i | \(-0.416989\pi\) | ||||
0.257840 | + | 0.966188i | \(0.416989\pi\) | |||||||
\(992\) | 4.74456 | 0.150640 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20.2337 | 0.641774 | ||||||||
\(995\) | 13.4891 | 0.427634 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.0000 | 0.443384 | 0.221692 | − | 0.975117i | \(-0.428842\pi\) | ||||
0.221692 | + | 0.975117i | \(0.428842\pi\) | |||||||
\(998\) | 15.1168 | 0.478515 | ||||||||
\(999\) | 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 | 810.2.a.k.1.2 | 2 | ||
3.2 | odd | 2 | 810.2.a.i.1.2 | 2 | |||
4.3 | odd | 2 | 6480.2.a.bn.1.1 | 2 | |||
5.2 | odd | 4 | 4050.2.c.ba.649.4 | 4 | |||
5.3 | odd | 4 | 4050.2.c.ba.649.1 | 4 | |||
5.4 | even | 2 | 4050.2.a.bo.1.1 | 2 | |||
9.2 | odd | 6 | 90.2.e.c.31.2 | ✓ | 4 | ||
9.4 | even | 3 | 270.2.e.c.181.1 | 4 | |||
9.5 | odd | 6 | 90.2.e.c.61.1 | yes | 4 | ||
9.7 | even | 3 | 270.2.e.c.91.1 | 4 | |||
12.11 | even | 2 | 6480.2.a.be.1.1 | 2 | |||
15.2 | even | 4 | 4050.2.c.v.649.2 | 4 | |||
15.8 | even | 4 | 4050.2.c.v.649.3 | 4 | |||
15.14 | odd | 2 | 4050.2.a.bw.1.1 | 2 | |||
36.7 | odd | 6 | 2160.2.q.f.1441.2 | 4 | |||
36.11 | even | 6 | 720.2.q.f.481.1 | 4 | |||
36.23 | even | 6 | 720.2.q.f.241.2 | 4 | |||
36.31 | odd | 6 | 2160.2.q.f.721.2 | 4 | |||
45.2 | even | 12 | 450.2.j.g.49.2 | 8 | |||
45.4 | even | 6 | 1350.2.e.l.451.2 | 4 | |||
45.7 | odd | 12 | 1350.2.j.f.199.4 | 8 | |||
45.13 | odd | 12 | 1350.2.j.f.1099.4 | 8 | |||
45.14 | odd | 6 | 450.2.e.j.151.2 | 4 | |||
45.22 | odd | 12 | 1350.2.j.f.1099.1 | 8 | |||
45.23 | even | 12 | 450.2.j.g.349.2 | 8 | |||
45.29 | odd | 6 | 450.2.e.j.301.1 | 4 | |||
45.32 | even | 12 | 450.2.j.g.349.3 | 8 | |||
45.34 | even | 6 | 1350.2.e.l.901.2 | 4 | |||
45.38 | even | 12 | 450.2.j.g.49.3 | 8 | |||
45.43 | odd | 12 | 1350.2.j.f.199.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.2.e.c.31.2 | ✓ | 4 | 9.2 | odd | 6 | ||
90.2.e.c.61.1 | yes | 4 | 9.5 | odd | 6 | ||
270.2.e.c.91.1 | 4 | 9.7 | even | 3 | |||
270.2.e.c.181.1 | 4 | 9.4 | even | 3 | |||
450.2.e.j.151.2 | 4 | 45.14 | odd | 6 | |||
450.2.e.j.301.1 | 4 | 45.29 | odd | 6 | |||
450.2.j.g.49.2 | 8 | 45.2 | even | 12 | |||
450.2.j.g.49.3 | 8 | 45.38 | even | 12 | |||
450.2.j.g.349.2 | 8 | 45.23 | even | 12 | |||
450.2.j.g.349.3 | 8 | 45.32 | even | 12 | |||
720.2.q.f.241.2 | 4 | 36.23 | even | 6 | |||
720.2.q.f.481.1 | 4 | 36.11 | even | 6 | |||
810.2.a.i.1.2 | 2 | 3.2 | odd | 2 | |||
810.2.a.k.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1350.2.e.l.451.2 | 4 | 45.4 | even | 6 | |||
1350.2.e.l.901.2 | 4 | 45.34 | even | 6 | |||
1350.2.j.f.199.1 | 8 | 45.43 | odd | 12 | |||
1350.2.j.f.199.4 | 8 | 45.7 | odd | 12 | |||
1350.2.j.f.1099.1 | 8 | 45.22 | odd | 12 | |||
1350.2.j.f.1099.4 | 8 | 45.13 | odd | 12 | |||
2160.2.q.f.721.2 | 4 | 36.31 | odd | 6 | |||
2160.2.q.f.1441.2 | 4 | 36.7 | odd | 6 | |||
4050.2.a.bo.1.1 | 2 | 5.4 | even | 2 | |||
4050.2.a.bw.1.1 | 2 | 15.14 | odd | 2 | |||
4050.2.c.v.649.2 | 4 | 15.2 | even | 4 | |||
4050.2.c.v.649.3 | 4 | 15.8 | even | 4 | |||
4050.2.c.ba.649.1 | 4 | 5.3 | odd | 4 | |||
4050.2.c.ba.649.4 | 4 | 5.2 | odd | 4 | |||
6480.2.a.be.1.1 | 2 | 12.11 | even | 2 | |||
6480.2.a.bn.1.1 | 2 | 4.3 | odd | 2 |