Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,2,Mod(95,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.s (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(2.29969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 95.11 | ||
Character | \(\chi\) | \(=\) | 288.95 |
Dual form | 288.2.s.a.191.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 1.55381 | − | 0.765299i | 0.897091 | − | 0.441846i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.81740 | + | 1.04928i | 0.812767 | + | 0.469251i | 0.847916 | − | 0.530131i | \(-0.177857\pi\) |
−0.0351491 | + | 0.999382i | \(0.511191\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.143714 | − | 0.0829731i | 0.0543187 | − | 0.0313609i | −0.472595 | − | 0.881280i | \(-0.656683\pi\) |
0.526913 | + | 0.849919i | \(0.323349\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.82863 | − | 2.37826i | 0.609544 | − | 0.792752i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.784910 | − | 1.35950i | −0.236659 | − | 0.409906i | 0.723094 | − | 0.690749i | \(-0.242719\pi\) |
−0.959754 | + | 0.280843i | \(0.909386\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.93212 | + | 3.34652i | −0.535872 | + | 0.928158i | 0.463248 | + | 0.886229i | \(0.346684\pi\) |
−0.999121 | + | 0.0419297i | \(0.986649\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.62690 | + | 0.239518i | 0.936462 | + | 0.0618433i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.27221i | 1.27870i | 0.768917 | + | 0.639349i | \(0.220796\pi\) | ||||
−0.768917 | + | 0.639349i | \(0.779204\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 8.05210i | − | 1.84728i | −0.383264 | − | 0.923639i | \(-0.625200\pi\) | ||
0.383264 | − | 0.923639i | \(-0.374800\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.159804 | − | 0.238908i | 0.0348721 | − | 0.0521340i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.67564 | + | 4.63435i | −0.557910 | + | 0.966328i | 0.439761 | + | 0.898115i | \(0.355063\pi\) |
−0.997671 | + | 0.0682135i | \(0.978270\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.298034 | − | 0.516211i | −0.0596069 | − | 0.103242i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.02127 | − | 5.09480i | 0.196543 | − | 0.980495i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.75334 | − | 3.89904i | 1.25406 | − | 0.724034i | 0.282150 | − | 0.959370i | \(-0.408952\pi\) |
0.971914 | + | 0.235336i | \(0.0756191\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.10800 | − | 1.21705i | −0.378608 | − | 0.218589i | 0.298604 | − | 0.954377i | \(-0.403479\pi\) |
−0.677212 | + | 0.735788i | \(0.736812\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.26003 | − | 1.51172i | −0.393420 | − | 0.263156i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.348247 | 0.0588645 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.53566 | −1.40325 | −0.701627 | − | 0.712544i | \(-0.747543\pi\) | ||||
−0.701627 | + | 0.712544i | \(0.747543\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.441043 | + | 6.67850i | −0.0706234 | + | 1.06942i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.47895 | + | 1.43122i | 0.387146 | + | 0.223519i | 0.680923 | − | 0.732355i | \(-0.261579\pi\) |
−0.293777 | + | 0.955874i | \(0.594912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.42127 | + | 1.97527i | −0.521739 | + | 0.301226i | −0.737646 | − | 0.675188i | \(-0.764063\pi\) |
0.215907 | + | 0.976414i | \(0.430729\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.81881 | − | 2.40350i | 0.867417 | − | 0.358293i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.68689 | + | 6.38588i | 0.537788 | + | 0.931477i | 0.999023 | + | 0.0441985i | \(0.0140734\pi\) |
−0.461234 | + | 0.887278i | \(0.652593\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.48623 | + | 6.03833i | −0.498033 | + | 0.862618i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.03482 | + | 8.19199i | 0.564988 | + | 1.14711i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.40174i | − | 0.329904i | −0.986302 | − | 0.164952i | \(-0.947253\pi\) | ||
0.986302 | − | 0.164952i | \(-0.0527469\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.29435i | − | 0.444211i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.16227 | − | 12.5114i | −0.816212 | − | 1.65718i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.49855 | + | 9.52376i | −0.715850 | + | 1.23989i | 0.246781 | + | 0.969071i | \(0.420627\pi\) |
−0.962631 | + | 0.270817i | \(0.912706\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.11998 | − | 12.3322i | −0.911620 | − | 1.57897i | −0.811776 | − | 0.583969i | \(-0.801499\pi\) |
−0.0998446 | − | 0.995003i | \(-0.531835\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0654683 | − | 0.493515i | 0.00824823 | − | 0.0621771i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.02286 | + | 4.05465i | −0.871079 | + | 0.502917i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.45698 | + | 0.841190i | 0.177999 | + | 0.102768i | 0.586352 | − | 0.810056i | \(-0.300564\pi\) |
−0.408353 | + | 0.912824i | \(0.633897\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.610768 | + | 9.24855i | −0.0735278 | + | 1.11339i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.5669 | −1.49142 | −0.745709 | − | 0.666272i | \(-0.767889\pi\) | ||||
−0.745709 | + | 0.666272i | \(0.767889\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4679 | 1.22518 | 0.612590 | − | 0.790401i | \(-0.290128\pi\) | ||||
0.612590 | + | 0.790401i | \(0.290128\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.858144 | − | 0.574006i | −0.0990899 | − | 0.0662805i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.225605 | − | 0.130253i | −0.0257100 | − | 0.0148437i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.31710 | + | 3.64718i | −0.710729 | + | 0.410339i | −0.811331 | − | 0.584587i | \(-0.801256\pi\) |
0.100602 | + | 0.994927i | \(0.467923\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.31220 | − | 8.69792i | −0.256911 | − | 0.966435i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.35365 | − | 2.34460i | −0.148583 | − | 0.257353i | 0.782121 | − | 0.623126i | \(-0.214138\pi\) |
−0.930704 | + | 0.365774i | \(0.880804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.53201 | + | 9.58172i | −0.600031 | + | 1.03928i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.50945 | − | 11.2267i | 0.805098 | − | 1.20363i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.40174i | 0.254584i | 0.991865 | + | 0.127292i | \(0.0406285\pi\) | ||||
−0.991865 | + | 0.127292i | \(0.959372\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.641255i | 0.0672217i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.20684 | − | 0.277816i | −0.436229 | − | 0.0288082i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.44888 | − | 14.6339i | 0.866837 | − | 1.50141i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.903600 | + | 1.56508i | 0.0917467 | + | 0.158910i | 0.908246 | − | 0.418436i | \(-0.137422\pi\) |
−0.816499 | + | 0.577346i | \(0.804088\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.66856 | − | 0.619318i | −0.469208 | − | 0.0622438i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.08158 | + | 1.77915i | −0.306628 | + | 0.177032i | −0.645417 | − | 0.763831i | \(-0.723316\pi\) |
0.338788 | + | 0.940863i | \(0.389983\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.28138 | + | 4.78126i | 0.815989 | + | 0.471111i | 0.849031 | − | 0.528343i | \(-0.177186\pi\) |
−0.0330425 | + | 0.999454i | \(0.510520\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.541109 | − | 0.266513i | 0.0528068 | − | 0.0260090i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.60313 | 0.541675 | 0.270838 | − | 0.962625i | \(-0.412699\pi\) | ||||
0.270838 | + | 0.962625i | \(0.412699\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.56853 | 0.724934 | 0.362467 | − | 0.931997i | \(-0.381935\pi\) | ||||
0.362467 | + | 0.931997i | \(0.381935\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.2628 | + | 6.53234i | −1.25885 | + | 0.620022i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.495124 | + | 0.285860i | 0.0465773 | + | 0.0268914i | 0.523108 | − | 0.852266i | \(-0.324772\pi\) |
−0.476531 | + | 0.879158i | \(0.658106\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.72543 | + | 5.61498i | −0.906901 | + | 0.523600i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.42575 | + | 10.7146i | 0.409161 | + | 0.990568i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.437452 | + | 0.757688i | 0.0401011 | + | 0.0694572i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.26783 | − | 7.39210i | 0.387985 | − | 0.672009i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.94712 | + | 0.326704i | 0.446066 | + | 0.0294579i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.7437i | − | 1.05038i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.0438i | − | 1.24619i | −0.782146 | − | 0.623095i | \(-0.785875\pi\) | ||
0.782146 | − | 0.623095i | \(-0.214125\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.80432 | + | 5.68749i | −0.334952 | + | 0.500755i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.699837 | − | 1.21215i | 0.0611450 | − | 0.105906i | −0.833832 | − | 0.552018i | \(-0.813858\pi\) |
0.894977 | + | 0.446111i | \(0.147191\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.668108 | − | 1.15720i | −0.0579323 | − | 0.100342i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.20191 | − | 8.18771i | 0.619842 | − | 0.704686i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.21477 | + | 0.701347i | −0.103785 | + | 0.0599201i | −0.550994 | − | 0.834509i | \(-0.685751\pi\) |
0.447209 | + | 0.894429i | \(0.352418\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.6630 | + | 10.7751i | 1.58298 | + | 0.913933i | 0.994422 | + | 0.105477i | \(0.0336369\pi\) |
0.588557 | + | 0.808456i | \(0.299696\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.6158 | + | 7.10086i | 0.894014 | + | 0.598000i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.06615 | 0.507277 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.3647 | 1.35902 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.795800 | + | 12.0504i | −0.0656365 | + | 0.993901i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.10263 | + | 2.94601i | 0.418024 | + | 0.241346i | 0.694232 | − | 0.719752i | \(-0.255744\pi\) |
−0.276208 | + | 0.961098i | \(0.589078\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.86723 | − | 3.96480i | 0.558847 | − | 0.322651i | −0.193835 | − | 0.981034i | \(-0.562093\pi\) |
0.752683 | + | 0.658383i | \(0.228759\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.5387 | + | 9.64094i | 1.01369 | + | 0.779423i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.55405 | − | 4.42375i | −0.205147 | − | 0.355324i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.00382 | − | 1.73867i | 0.0801138 | − | 0.138761i | −0.823185 | − | 0.567773i | \(-0.807805\pi\) |
0.903299 | + | 0.429012i | \(0.141138\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.83805 | − | 3.73184i | −0.145767 | − | 0.295954i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.888025i | 0.0699862i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.06036i | 0.161379i | 0.996739 | + | 0.0806897i | \(0.0257123\pi\) | ||||
−0.996739 | + | 0.0806897i | \(0.974288\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.52117 | − | 5.11879i | −0.196273 | − | 0.398497i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.45382 | − | 16.3745i | 0.731559 | − | 1.26710i | −0.224658 | − | 0.974438i | \(-0.572127\pi\) |
0.956217 | − | 0.292659i | \(-0.0945401\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.966142 | − | 1.67341i | −0.0743186 | − | 0.128724i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.1499 | − | 14.7243i | −1.46443 | − | 1.12600i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.29843 | − | 5.36845i | 0.706946 | − | 0.408156i | −0.102983 | − | 0.994683i | \(-0.532839\pi\) |
0.809929 | + | 0.586528i | \(0.199505\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0856632 | − | 0.0494577i | −0.00647553 | − | 0.00373865i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.25515 | + | 19.0061i | −0.0943429 | + | 1.42859i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.7748 | 1.70227 | 0.851133 | − | 0.524950i | \(-0.175916\pi\) | ||||
0.851133 | + | 0.524950i | \(0.175916\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.72780 | 0.723062 | 0.361531 | − | 0.932360i | \(-0.382254\pi\) | ||||
0.361531 | + | 0.932360i | \(0.382254\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.5009 | − | 13.7129i | −1.51547 | − | 1.01369i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.5127 | − | 8.95628i | −1.14052 | − | 0.658479i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.16759 | − | 4.13821i | 0.524146 | − | 0.302616i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.275962 | − | 0.816930i | −0.0200733 | − | 0.0594229i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.27410 | − | 2.20681i | −0.0921908 | − | 0.159679i | 0.816242 | − | 0.577710i | \(-0.196054\pi\) |
−0.908433 | + | 0.418031i | \(0.862720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.49967 | + | 4.32955i | −0.179930 | + | 0.311648i | −0.941856 | − | 0.336016i | \(-0.890921\pi\) |
0.761926 | + | 0.647664i | \(0.224254\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.80915 | + | 11.6747i | −0.559225 | + | 0.836045i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.65685i | − | 0.403034i | −0.979485 | − | 0.201517i | \(-0.935413\pi\) | ||
0.979485 | − | 0.201517i | \(-0.0645872\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.4713i | 1.02584i | 0.858436 | + | 0.512921i | \(0.171436\pi\) | ||||
−0.858436 | + | 0.512921i | \(0.828564\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.90763 | + | 0.192018i | 0.205089 | + | 0.0135439i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.647031 | − | 1.12069i | 0.0454127 | − | 0.0786571i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00349 | + | 5.20220i | 0.209773 | + | 0.363338i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.12890 | + | 14.8379i | 0.425988 | + | 1.03130i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.9469 | + | 6.32017i | −0.757210 | + | 0.437176i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7320 | − | 7.35080i | −0.876505 | − | 0.506050i | −0.00700041 | − | 0.999975i | \(-0.502228\pi\) |
−0.869504 | + | 0.493925i | \(0.835562\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19.5266 | + | 9.61745i | −1.33794 | + | 0.658977i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.29043 | −0.565403 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.403931 | −0.0274206 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.2652 | − | 8.01111i | 1.09910 | − | 0.541341i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.6436 | − | 10.1865i | −1.18683 | − | 0.685219i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.6729 | + | 9.04876i | −1.04954 | + | 0.605950i | −0.922519 | − | 0.385951i | \(-0.873873\pi\) |
−0.127016 | + | 0.991901i | \(0.540540\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.77268 | − | 0.235158i | −0.118178 | − | 0.0156772i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.29529 | − | 10.9038i | −0.417833 | − | 0.723708i | 0.577888 | − | 0.816116i | \(-0.303877\pi\) |
−0.995721 | + | 0.0924078i | \(0.970544\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.19995 | − | 10.7386i | 0.409704 | − | 0.709628i | −0.585152 | − | 0.810923i | \(-0.698965\pi\) |
0.994856 | + | 0.101295i | \(0.0322986\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.450229 | − | 0.0297328i | −0.0296229 | − | 0.00195627i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 7.13560i | − | 0.467469i | −0.972300 | − | 0.233734i | \(-0.924905\pi\) | ||
0.972300 | − | 0.233734i | \(-0.0750947\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.4743i | 1.00943i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.02437 | + | 10.5015i | −0.456282 | + | 0.682144i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.273904 | + | 0.474416i | −0.0177174 | + | 0.0306874i | −0.874748 | − | 0.484578i | \(-0.838973\pi\) |
0.857031 | + | 0.515265i | \(0.172307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.28792 | − | 16.0872i | −0.598288 | − | 1.03626i | −0.993074 | − | 0.117491i | \(-0.962515\pi\) |
0.394786 | − | 0.918773i | \(-0.370819\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.2492 | − | 11.7454i | −0.657488 | − | 0.753465i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.6718 | + | 7.31605i | −0.809569 | + | 0.467405i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.9465 | + | 15.5576i | 1.71457 | + | 0.989905i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.89764 | − | 2.60710i | −0.247003 | − | 0.165218i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.2012 | −1.21197 | −0.605985 | − | 0.795476i | \(-0.707221\pi\) | ||||
−0.605985 | + | 0.795476i | \(0.707221\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.40056 | 0.528138 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.26279 | + | 19.1218i | −0.0790789 | + | 1.19745i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.90205 | + | 2.25285i | 0.243403 | + | 0.140529i | 0.616740 | − | 0.787167i | \(-0.288453\pi\) |
−0.373337 | + | 0.927696i | \(0.621786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.22669 | + | 0.708231i | −0.0762229 | + | 0.0440073i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.07646 | − | 23.1911i | 0.190428 | − | 1.43549i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.92767 | + | 17.1952i | 0.612166 | + | 1.06030i | 0.990875 | + | 0.134787i | \(0.0430351\pi\) |
−0.378708 | + | 0.925516i | \(0.623632\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.52009 | − | 4.36492i | 0.154808 | − | 0.268135i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.83805 | + | 3.73184i | 0.112487 | + | 0.228385i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.3938i | 1.91411i | 0.289901 | + | 0.957057i | \(0.406378\pi\) | ||||
−0.289901 | + | 0.957057i | \(0.593622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 0.868217i | − | 0.0527405i | −0.999652 | − | 0.0263702i | \(-0.991605\pi\) | ||
0.999652 | − | 0.0263702i | \(-0.00839488\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.490752 | + | 0.996386i | 0.0297017 | + | 0.0603040i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.467861 | + | 0.810358i | −0.0282131 | + | 0.0488664i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.25608 | + | 3.90765i | 0.135555 | + | 0.234788i | 0.925809 | − | 0.377991i | \(-0.123385\pi\) |
−0.790254 | + | 0.612779i | \(0.790052\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.74923 | + | 2.78782i | −0.404066 | + | 0.166902i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.6156 | − | 14.2118i | 1.46844 | − | 0.847805i | 0.469066 | − | 0.883163i | \(-0.344591\pi\) |
0.999375 | + | 0.0353583i | \(0.0112572\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.92629 | + | 2.26684i | 0.233394 | + | 0.134750i | 0.612137 | − | 0.790752i | \(-0.290310\pi\) |
−0.378743 | + | 0.925502i | \(0.623644\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.92862 | − | 29.2042i | 0.114242 | − | 1.72991i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.475011 | 0.0280390 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.7962 | −0.635069 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.60178 | + | 1.74031i | 0.152519 | + | 0.102019i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.2072 | − | 7.62516i | −0.771570 | − | 0.445466i | 0.0618642 | − | 0.998085i | \(-0.480295\pi\) |
−0.833435 | + | 0.552618i | \(0.813629\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.9861 | + | 11.5390i | −1.16364 | + | 0.671827i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.72801 | + | 2.61055i | −0.448425 | + | 0.151479i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.3393 | − | 17.9082i | −0.597937 | − | 1.03566i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.327789 | + | 0.567747i | −0.0188934 | + | 0.0327244i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.42660 | + | 5.12279i | −0.196853 | + | 0.294296i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 29.8833i | − | 1.71111i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.85996i | − | 0.391519i | −0.980652 | − | 0.195759i | \(-0.937283\pi\) | ||
0.980652 | − | 0.195759i | \(-0.0627171\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.5268 | + | 1.09142i | 0.940175 | + | 0.0620885i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.1876 | + | 21.1096i | −0.691097 | + | 1.19702i | 0.280381 | + | 0.959889i | \(0.409539\pi\) |
−0.971479 | + | 0.237127i | \(0.923794\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.96030 | + | 6.85944i | 0.223849 | + | 0.387719i | 0.955974 | − | 0.293453i | \(-0.0948043\pi\) |
−0.732124 | + | 0.681171i | \(0.761471\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.636816 | − | 0.828221i | 0.0358805 | − | 0.0466650i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.4030 | + | 10.0476i | −0.977447 | + | 0.564329i | −0.901498 | − | 0.432782i | \(-0.857532\pi\) |
−0.0759487 | + | 0.997112i | \(0.524199\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.6015 | − | 6.12080i | −0.593572 | − | 0.342699i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.70619 | − | 4.28807i | 0.485932 | − | 0.239337i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.4523 | 2.36211 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.30335 | 0.127767 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.7600 | − | 5.79219i | 0.650332 | − | 0.320309i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.05971 | + | 0.611826i | 0.0584239 | + | 0.0337310i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.2223 | − | 6.47921i | 0.616835 | − | 0.356130i | −0.158801 | − | 0.987311i | \(-0.550763\pi\) |
0.775636 | + | 0.631181i | \(0.217429\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.6086 | + | 20.3000i | −0.855346 | + | 1.11243i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.76528 | + | 3.05756i | 0.0964477 | + | 0.167052i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.96429 | + | 12.0625i | −0.379369 | + | 0.657086i | −0.990971 | − | 0.134080i | \(-0.957192\pi\) |
0.611602 | + | 0.791166i | \(0.290526\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.988095 | + | 0.0652531i | 0.0536660 | + | 0.00354406i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.82111i | 0.206925i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.31868i | 0.125197i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.8143 | + | 16.1675i | −0.582223 | + | 0.870427i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.0232 | + | 29.4851i | −0.913854 | + | 1.58284i | −0.105284 | + | 0.994442i | \(0.533575\pi\) |
−0.808570 | + | 0.588399i | \(0.799758\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.599892 | − | 1.03904i | −0.0321115 | − | 0.0556188i | 0.849523 | − | 0.527552i | \(-0.176890\pi\) |
−0.881635 | + | 0.471933i | \(0.843557\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.0767 | + | 13.2614i | 0.804733 | + | 0.707843i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.6933 | − | 11.3699i | 1.04817 | − | 0.605159i | 0.126031 | − | 0.992026i | \(-0.459776\pi\) |
0.922135 | + | 0.386867i | \(0.126443\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.8391 | − | 13.1862i | −1.21218 | − | 0.699850i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.25957 | + | 0.842520i | 0.0666637 | + | 0.0445909i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.5652 | −1.13817 | −0.569083 | − | 0.822280i | \(-0.692702\pi\) | ||||
−0.569083 | + | 0.822280i | \(0.692702\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −45.8363 | −2.41244 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.974216 | − | 14.7521i | 0.0511331 | − | 0.774283i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.0245 | + | 10.9838i | 0.995786 | + | 0.574917i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0399 | − | 16.1889i | 1.46367 | − | 0.845051i | 0.464493 | − | 0.885577i | \(-0.346236\pi\) |
0.999179 | + | 0.0405253i | \(0.0129031\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.93689 | − | 3.27839i | 0.413178 | − | 0.170666i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.199280 | − | 0.345163i | −0.0103461 | − | 0.0179199i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.19629 | − | 9.00024i | 0.269054 | − | 0.466015i | −0.699564 | − | 0.714570i | \(-0.746622\pi\) |
0.968618 | + | 0.248555i | \(0.0799557\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.98741 | − | 18.2474i | −0.464108 | − | 0.942290i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.1336i | 1.55196i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 20.1762i | − | 1.03638i | −0.855265 | − | 0.518190i | \(-0.826606\pi\) | ||
0.855265 | − | 0.518190i | \(-0.173394\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.7477 | − | 21.8214i | −0.550624 | − | 1.11795i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.8556 | − | 20.5344i | 0.605791 | − | 1.04926i | −0.386135 | − | 0.922442i | \(-0.626190\pi\) |
0.991926 | − | 0.126818i | \(-0.0404765\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.273343 | − | 0.473444i | −0.0139308 | − | 0.0241289i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.55855 | + | 11.7487i | −0.0792255 | + | 0.597220i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.76371 | − | 1.01828i | 0.0894236 | − | 0.0516288i | −0.454621 | − | 0.890685i | \(-0.650225\pi\) |
0.544045 | + | 0.839056i | \(0.316892\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.4332 | − | 14.1065i | −1.23564 | − | 0.713399i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.159751 | − | 2.41904i | 0.00805840 | − | 0.122024i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.3076 | −0.770209 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.74252 | 0.0874547 | 0.0437274 | − | 0.999044i | \(-0.486077\pi\) | ||||
0.0437274 | + | 0.999044i | \(0.486077\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.92371 | − | 1.28676i | −0.0963061 | − | 0.0644184i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.4143 | + | 11.7862i | 1.01944 | + | 0.588574i | 0.913942 | − | 0.405846i | \(-0.133023\pi\) |
0.105498 | + | 0.994419i | \(0.466356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.14580 | − | 4.70298i | 0.405771 | − | 0.234272i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.92433 | − | 18.2337i | 0.244692 | − | 0.906042i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.69973 | + | 11.6043i | 0.332093 | + | 0.575202i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.8999 | + | 18.8792i | −0.538965 | + | 0.933515i | 0.459995 | + | 0.887922i | \(0.347851\pi\) |
−0.998960 | + | 0.0455934i | \(0.985482\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.35078 | + | 2.01942i | −0.0666289 | + | 0.0996107i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.82493i | 0.0897988i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 5.68143i | − | 0.278891i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.2450 | + | 2.45963i | 1.82389 | + | 0.120449i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.5076 | − | 18.1997i | 0.513329 | − | 0.889112i | −0.486552 | − | 0.873652i | \(-0.661745\pi\) |
0.999880 | − | 0.0154599i | \(-0.00492125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.86839 | + | 11.8964i | 0.334745 | + | 0.579795i | 0.983436 | − | 0.181257i | \(-0.0580166\pi\) |
−0.648691 | + | 0.761052i | \(0.724683\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.9292 | + | 2.90907i | 1.06624 | + | 0.141444i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.72157 | − | 1.57130i | 0.132016 | − | 0.0762192i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.04648 | − | 1.18153i | −0.0990360 | − | 0.0571784i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.42563 | − | 4.64242i | 0.455074 | − | 0.224138i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.476344 | 0.0229447 | 0.0114723 | − | 0.999934i | \(-0.496348\pi\) | ||||
0.0114723 | + | 0.999934i | \(0.496348\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.6601 | −0.560348 | −0.280174 | − | 0.959949i | \(-0.590392\pi\) | ||||
−0.280174 | + | 0.959949i | \(0.590392\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 25.4276 | − | 12.5239i | 1.21916 | − | 0.600475i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 37.3162 | + | 21.5445i | 1.78508 | + | 1.03061i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.8138 | − | 17.2130i | 1.42294 | − | 0.821533i | 0.426387 | − | 0.904541i | \(-0.359786\pi\) |
0.996549 | + | 0.0830082i | \(0.0264528\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.98565 | + | 19.3330i | 0.380269 | + | 0.920621i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.84473 | + | 8.39132i | 0.230180 | + | 0.398684i | 0.957861 | − | 0.287232i | \(-0.0927351\pi\) |
−0.727681 | + | 0.685916i | \(0.759402\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.52009 | + | 4.36492i | −0.119464 | + | 0.206917i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.1831 | + | 0.672484i | 0.481643 | + | 0.0318074i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.9789i | − | 0.848477i | −0.905550 | − | 0.424239i | \(-0.860542\pi\) | ||
0.905550 | − | 0.424239i | \(-0.139458\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.49352i | − | 0.211591i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.63609 | − | 11.4160i | 0.358775 | − | 0.536371i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.672854 | + | 1.16542i | −0.0315439 | + | 0.0546356i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.95237 | + | 12.0419i | 0.325218 | + | 0.563295i | 0.981557 | − | 0.191172i | \(-0.0612289\pi\) |
−0.656338 | + | 0.754467i | \(0.727896\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.8609 | + | 5.38433i | 1.25376 | + | 0.251319i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.80521 | + | 1.04224i | −0.0840772 | + | 0.0485420i | −0.541449 | − | 0.840733i | \(-0.682124\pi\) |
0.457372 | + | 0.889275i | \(0.348791\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.0337 | − | 17.9173i | −1.44226 | − | 0.832688i | −0.444258 | − | 0.895899i | \(-0.646533\pi\) |
−0.998000 | + | 0.0632104i | \(0.979866\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.35400 | − | 4.91904i | −0.341034 | − | 0.228115i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.4185 | −1.17623 | −0.588114 | − | 0.808778i | \(-0.700129\pi\) | ||||
−0.588114 | + | 0.808778i | \(0.700129\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.279185 | 0.0128915 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.229142 | − | 3.46979i | 0.0105583 | − | 0.159879i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.37078 | + | 3.10082i | 0.246949 | + | 0.142576i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.15658 | + | 2.39980i | −0.190717 | + | 0.110110i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.71195 | − | 4.39190i | −0.261532 | − | 0.201091i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.4545 | + | 19.8398i | 0.523370 | + | 0.906503i | 0.999630 | + | 0.0271987i | \(0.00865867\pi\) |
−0.476260 | + | 0.879304i | \(0.658008\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.4919 | − | 28.5648i | 0.751965 | − | 1.30244i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.679605 | + | 1.37982i | 0.0309231 | + | 0.0627840i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.79251i | 0.172209i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.6846i | 0.710738i | 0.934726 | + | 0.355369i | \(0.115645\pi\) | ||||
−0.934726 | + | 0.355369i | \(0.884355\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.57679 | + | 3.20139i | 0.0713049 | + | 0.144772i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.2976 | + | 21.3001i | −0.554982 | + | 0.961258i | 0.442922 | + | 0.896560i | \(0.353942\pi\) |
−0.997905 | + | 0.0646979i | \(0.979392\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.5566 | + | 35.6050i | 0.925821 | + | 1.60357i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.83482 | − | 6.02417i | −0.352149 | − | 0.270766i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.80604 | + | 1.04272i | −0.0810118 | + | 0.0467722i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.96333 | + | 3.44293i | 0.266955 | + | 0.154127i | 0.627503 | − | 0.778614i | \(-0.284077\pi\) |
−0.360548 | + | 0.932741i | \(0.617410\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.15802 | − | 32.6778i | 0.0964132 | − | 1.45994i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.6347 | −0.786294 | −0.393147 | − | 0.919476i | \(-0.628614\pi\) | ||||
−0.393147 | + | 0.919476i | \(0.628614\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.46729 | −0.332290 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.78186 | − | 1.86076i | −0.123547 | − | 0.0826394i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.1218 | − | 8.15320i | −0.625936 | − | 0.361384i | 0.153240 | − | 0.988189i | \(-0.451029\pi\) |
−0.779177 | + | 0.626805i | \(0.784362\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.50439 | − | 0.868558i | 0.0665502 | − | 0.0384228i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −41.0238 | − | 8.22333i | −1.81125 | − | 0.363069i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.0337 | + | 17.3789i | 0.442139 | + | 0.765807i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.78776 | − | 10.0247i | 0.254545 | − | 0.440885i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.3395 | − | 15.4576i | 0.453853 | − | 0.678514i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.44397i | 0.413748i | 0.978368 | + | 0.206874i | \(0.0663290\pi\) | ||||
−0.978368 | + | 0.206874i | \(0.933671\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.5688i | 0.986865i | 0.869784 | + | 0.493433i | \(0.164258\pi\) | ||||
−0.869784 | + | 0.493433i | \(0.835742\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.170954 | − | 0.0112897i | −0.00746105 | − | 0.000492722i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.41656 | − | 11.1138i | 0.279510 | − | 0.484125i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.81812 | − | 4.88113i | −0.122527 | − | 0.212223i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.5951 | + | 30.4924i | 0.546582 | + | 1.32326i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.57922 | + | 5.53056i | −0.414922 | + | 0.239555i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.1831 | + | 5.87924i | 0.440256 | + | 0.254182i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 35.3876 | − | 17.4295i | 1.52709 | − | 0.752139i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.9455 | 0.471457 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.0491 | −1.37790 | −0.688950 | − | 0.724809i | \(-0.741928\pi\) | ||||
−0.688950 | + | 0.724809i | \(0.741928\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.1151 | − | 7.44468i | 0.648652 | − | 0.319482i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.7551 | + | 7.94149i | 0.589202 | + | 0.340176i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.6339 | + | 8.44889i | −0.625701 | + | 0.361249i | −0.779085 | − | 0.626918i | \(-0.784316\pi\) |
0.153384 | + | 0.988167i | \(0.450983\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −42.3489 | − | 5.61788i | −1.80741 | − | 0.239765i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.3955 | − | 54.3786i | −1.33749 | − | 2.31660i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.605235 | + | 1.04830i | −0.0257372 | + | 0.0445782i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −30.9580 | − | 2.04445i | −1.31409 | − | 0.0867819i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.6034i | 1.38145i | 0.723118 | + | 0.690725i | \(0.242708\pi\) | ||||
−0.723118 | + | 0.690725i | \(0.757292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.2658i | − | 0.645675i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.97008 | − | 11.9153i | 0.336497 | − | 0.503066i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.58426 | + | 13.1363i | −0.319639 | + | 0.553630i | −0.980413 | − | 0.196955i | \(-0.936895\pi\) |
0.660774 | + | 0.750585i | \(0.270228\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.599892 | + | 1.03904i | 0.0252377 | + | 0.0437129i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.05399 | − | 1.05816i | −0.0442633 | − | 0.0444385i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.18052 | + | 2.41363i | −0.175257 | + | 0.101184i | −0.585062 | − | 0.810988i | \(-0.698930\pi\) |
0.409806 | + | 0.912173i | \(0.365597\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.07311 | − | 2.35161i | −0.170454 | − | 0.0984118i | 0.412346 | − | 0.911027i | \(-0.364710\pi\) |
−0.582800 | + | 0.812616i | \(0.698043\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.66858 | − | 2.45389i | −0.153257 | − | 0.102513i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.18973 | 0.133021 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.5812 | −0.815175 | −0.407587 | − | 0.913166i | \(-0.633630\pi\) | ||||
−0.407587 | + | 0.913166i | \(0.633630\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.570598 | + | 8.64029i | −0.0237133 | + | 0.359078i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.389077 | − | 0.224634i | −0.0161416 | − | 0.00931938i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.26517 | + | 1.88515i | −0.135230 | + | 0.0780749i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.19924 | + | 24.1166i | −0.132272 | + | 0.997100i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.83368 | + | 15.3004i | 0.364605 | + | 0.631515i | 0.988713 | − | 0.149824i | \(-0.0478707\pi\) |
−0.624108 | + | 0.781338i | \(0.714537\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.79984 | + | 16.9738i | −0.403795 | + | 0.699394i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.32919 | − | 8.78966i | −0.178079 | − | 0.361558i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14.1557i | − | 0.581307i | −0.956828 | − | 0.290653i | \(-0.906127\pi\) | ||
0.956828 | − | 0.290653i | \(-0.0938727\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.83603i | 0.0752700i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.0749 | + | 22.4856i | 0.453264 | + | 0.920273i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.3209 | + | 23.0726i | −0.544279 | + | 0.942719i | 0.454373 | + | 0.890812i | \(0.349863\pi\) |
−0.998652 | + | 0.0519076i | \(0.983470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.2321 | − | 21.1866i | −0.498959 | − | 0.864221i | 0.501041 | − | 0.865424i | \(-0.332951\pi\) |
−0.999999 | + | 0.00120220i | \(0.999617\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.66485 | − | 1.92685i | 0.189968 | − | 0.0784675i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.5127 | − | 8.95628i | 0.630682 | − | 0.364124i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.5942 | − | 14.1995i | −0.998247 | − | 0.576338i | −0.0905181 | − | 0.995895i | \(-0.528852\pi\) |
−0.907729 | + | 0.419556i | \(0.862186\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.147698 | − | 2.23651i | 0.00598501 | − | 0.0906280i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.4940 | −1.15274 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.79923 | −0.274618 | −0.137309 | − | 0.990528i | \(-0.543845\pi\) | ||||
−0.137309 | + | 0.990528i | \(0.543845\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.64809 | + | 5.78465i | 0.348725 | + | 0.233260i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.6817 | − | 18.8688i | −1.31571 | − | 0.759628i | −0.332678 | − | 0.943040i | \(-0.607952\pi\) |
−0.983036 | + | 0.183412i | \(0.941286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.89600 | − | 4.55876i | 0.317367 | − | 0.183232i | −0.332851 | − | 0.942979i | \(-0.608011\pi\) |
0.650218 | + | 0.759747i | \(0.274677\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.8785 | + | 18.3648i | 0.837827 | + | 0.736953i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.199280 | + | 0.345163i | 0.00798397 | + | 0.0138286i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.8322 | − | 18.7619i | 0.433287 | − | 0.750475i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.1725 | + | 18.1980i | −0.486122 | + | 0.726756i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 45.0018i | − | 1.79434i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.05133i | − | 0.360328i | −0.983637 | − | 0.180164i | \(-0.942337\pi\) | ||
0.983637 | − | 0.180164i | \(-0.0576628\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.4086 | − | 1.67797i | −1.00990 | − | 0.0666931i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.7359 | − | 25.5233i | 0.584776 | − | 1.01286i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.4716 | − | 23.3335i | −0.533764 | − | 0.924507i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.9803 | + | 29.8873i | −0.909086 | + | 1.18232i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.1865 | + | 15.6961i | −1.07380 | + | 0.619959i | −0.929217 | − | 0.369533i | \(-0.879518\pi\) |
−0.144583 | + | 0.989493i | \(0.546184\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.03917 | − | 3.48672i | −0.238162 | − | 0.137503i | 0.376170 | − | 0.926551i | \(-0.377241\pi\) |
−0.614332 | + | 0.789048i | \(0.710574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.8817 | + | 6.34466i | −0.507218 | + | 0.249821i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.4189 | 1.43178 | 0.715888 | − | 0.698215i | \(-0.246022\pi\) | ||||
0.715888 | + | 0.698215i | \(0.246022\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.2635 | 0.677650 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.627631 | + | 0.309128i | −0.0245988 | + | 0.0121157i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.9837 | − | 16.1564i | −1.09509 | − | 0.632248i | −0.160159 | − | 0.987091i | \(-0.551201\pi\) |
−0.934926 | + | 0.354843i | \(0.884534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.54377 | − | 1.46865i | 0.0993933 | − | 0.0573847i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.1420 | − | 24.8955i | 0.746802 | − | 0.971264i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.52870 | + | 4.37984i | 0.0985042 | + | 0.170614i | 0.911066 | − | 0.412261i | \(-0.135261\pi\) |
−0.812562 | + | 0.582875i | \(0.801928\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.31245 | − | 10.9335i | 0.245526 | − | 0.425263i | −0.716753 | − | 0.697327i | \(-0.754373\pi\) |
0.962279 | + | 0.272063i | \(0.0877060\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −35.2104 | − | 2.32527i | −1.36746 | − | 0.0903061i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.80412i | − | 0.108739i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 41.7298i | 1.61578i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.4277 | + | 26.0545i | −0.673793 | + | 1.00733i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.1771 | + | 19.3593i | −0.431487 | + | 0.747357i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.5547 | + | 40.7980i | 0.907967 | + | 1.57265i | 0.816884 | + | 0.576802i | \(0.195700\pi\) |
0.0910837 | + | 0.995843i | \(0.470967\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.93436 | + | 0.991238i | −0.112944 | + | 0.0381528i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.1335 | − | 9.31465i | 0.620059 | − | 0.357991i | −0.156833 | − | 0.987625i | \(-0.550128\pi\) |
0.776892 | + | 0.629634i | \(0.216795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.259719 | + | 0.149949i | 0.00996712 | + | 0.00575452i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.1263 | − | 12.1246i | −0.694602 | − | 0.464614i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.4857 | 0.592544 | 0.296272 | − | 0.955104i | \(-0.404257\pi\) | ||||
0.296272 | + | 0.955104i | \(0.404257\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.94363 | −0.112470 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.41526 | − | 21.4306i | 0.0539955 | − | 0.817627i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.03747 | + | 4.64044i | 0.306203 | + | 0.176787i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.34942 | − | 5.39789i | 0.355669 | − | 0.205345i | −0.311510 | − | 0.950243i | \(-0.600835\pi\) |
0.667179 | + | 0.744897i | \(0.267502\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.722323 | + | 0.298361i | −0.0274388 | + | 0.0113338i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.6122 | + | 39.1654i | 0.857728 | + | 1.48563i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.54569 | + | 13.0695i | −0.285813 | + | 0.495043i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.46087 | − | 11.0874i | −0.206549 | − | 0.419362i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.59493i | 0.286857i | 0.989661 | + | 0.143428i | \(0.0458127\pi\) | ||||
−0.989661 | + | 0.143428i | \(0.954187\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 68.7300i | 2.59220i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.8425 | + | 24.0441i | 0.446013 | + | 0.905552i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.295243 | + | 0.511376i | −0.0111038 | + | 0.0192323i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5763 | − | 20.0508i | −0.434759 | − | 0.753024i | 0.562517 | − | 0.826786i | \(-0.309833\pi\) |
−0.997276 | + | 0.0737615i | \(0.976500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.87773 | + | 21.6930i | −0.107923 | + | 0.813552i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.2805 | − | 6.51280i | 0.422458 | − | 0.243906i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.0246 | + | 6.36507i | 0.412298 | + | 0.238040i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.0625240 | + | 0.946771i | −0.00233500 | + | 0.0353578i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.49075 | 0.279358 | 0.139679 | − | 0.990197i | \(-0.455393\pi\) | ||||
0.139679 | + | 0.990197i | \(0.455393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.58686 | 0.0590979 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.7431 | − | 17.8883i | −0.994588 | − | 0.665273i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.02546 | − | 2.32410i | −0.149502 | − | 0.0863148i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.2968 | − | 16.3372i | 1.04947 | − | 0.605911i | 0.126969 | − | 0.991907i | \(-0.459475\pi\) |
0.922501 | + | 0.385995i | \(0.126142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.9140 | − | 10.4063i | −0.922742 | − | 0.385418i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.4140 | − | 18.0376i | −0.385177 | − | 0.667146i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.2248 | − | 41.9586i | 0.894765 | − | 1.54978i | 0.0606693 | − | 0.998158i | \(-0.480676\pi\) |
0.834095 | − | 0.551620i | \(-0.185990\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.0905 | + | 21.0654i | −0.519736 | + | 0.777010i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.64103i | − | 0.0972838i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4.58382i | − | 0.168619i | −0.996440 | − | 0.0843094i | \(-0.973132\pi\) | ||
0.996440 | − | 0.0843094i | \(-0.0268684\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 53.7759 | + | 3.55132i | 1.97551 | + | 0.130461i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.5816 | − | 32.1842i | 0.681691 | − | 1.18072i | −0.292773 | − | 0.956182i | \(-0.594578\pi\) |
0.974464 | − | 0.224542i | \(-0.0720886\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.18235 | + | 10.7082i | 0.226504 | + | 0.392316i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.05139 | − | 1.06807i | −0.294585 | − | 0.0390788i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.805247 | − | 0.464909i | 0.0294231 | − | 0.0169874i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.1292 | + | 17.9724i | 1.13592 | + | 0.655824i | 0.945417 | − | 0.325863i | \(-0.105655\pi\) |
0.190503 | + | 0.981687i | \(0.438988\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.8350 | + | 14.6947i | −1.08725 | + | 0.535504i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.6407 | 0.605617 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.99097 | −0.181400 | −0.0907000 | − | 0.995878i | \(-0.528910\pi\) | ||||
−0.0907000 | + | 0.995878i | \(0.528910\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.0528 | − | 6.42894i | 0.473788 | − | 0.233356i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.0903 | − | 5.82561i | −0.365771 | − | 0.211178i | 0.305838 | − | 0.952084i | \(-0.401063\pi\) |
−0.671609 | + | 0.740905i | \(0.734397\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.08770 | − | 0.627985i | 0.0393774 | − | 0.0227346i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.6718 | + | 30.6780i | 0.458149 | + | 1.10916i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.2477 | − | 36.8020i | −0.767208 | − | 1.32884i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.86238 | − | 17.0821i | 0.355646 | − | 0.615998i | −0.631582 | − | 0.775309i | \(-0.717594\pi\) |
0.987228 | + | 0.159312i | \(0.0509274\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.78714 | + | 0.514257i | 0.280447 | + | 0.0185205i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 39.5946i | − | 1.42412i | −0.702120 | − | 0.712059i | \(-0.747763\pi\) | ||
0.702120 | − | 0.712059i | \(-0.252237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.45090i | 0.0521177i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.36403 | + | 2.03924i | −0.0489344 | + | 0.0731573i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.5243 | − | 19.9607i | 0.412902 | − | 0.715167i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.86390 | + | 17.0848i | 0.352958 | + | 0.611341i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.9679 | − | 38.3889i | −0.463435 | − | 1.37191i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.64870 | − | 2.10658i | 0.130228 | − | 0.0751870i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.6360 | − | 11.3369i | −0.699949 | − | 0.404116i | 0.107379 | − | 0.994218i | \(-0.465754\pi\) |
−0.807329 | + | 0.590102i | \(0.799087\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.5852 | + | 19.1204i | 1.01766 | + | 0.680705i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.0948747 | 0.00337336 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.0265 | 1.95405 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.575260 | − | 8.71087i | 0.0204024 | − | 0.308943i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.38454 | − | 0.799367i | −0.0490431 | − | 0.0283150i | 0.475278 | − | 0.879836i | \(-0.342347\pi\) |
−0.524321 | + | 0.851521i | \(0.675681\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.6677 | + | 19.4381i | −1.19108 | + | 0.687669i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.71195 | + | 4.39190i | 0.201822 | + | 0.155180i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.21640 | − | 14.2312i | −0.289950 | − | 0.502209i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.931785 | + | 1.61390i | −0.0328411 | + | 0.0568825i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.0257 | + | 48.7799i | 0.845743 | + | 1.71713i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.2740i | 1.76754i | 0.467922 | + | 0.883770i | \(0.345003\pi\) | ||||
−0.467922 | + | 0.883770i | \(0.654997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.5884i | − | 1.28479i | −0.766372 | − | 0.642397i | \(-0.777940\pi\) | ||
0.766372 | − | 0.642397i | \(-0.222060\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.664446 | − | 1.34904i | −0.0233032 | − | 0.0473130i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.16188 | + | 3.74449i | −0.0757275 | + | 0.131164i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.9051 | + | 27.5484i | 0.556448 | + | 0.963796i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.52507 | + | 1.17262i | 0.0532902 | + | 0.0409746i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.1310 | + | 19.1282i | −1.15628 | + | 0.667579i | −0.950410 | − | 0.311000i | \(-0.899336\pi\) |
−0.205871 | + | 0.978579i | \(0.566003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.874309 | − | 0.504783i | −0.0304765 | − | 0.0175956i | 0.484684 | − | 0.874689i | \(-0.338934\pi\) |
−0.515161 | + | 0.857094i | \(0.672268\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.106798 | + | 1.61719i | −0.00371824 | + | 0.0563035i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.17121 | 0.214594 | 0.107297 | − | 0.994227i | \(-0.465780\pi\) | ||||
0.107297 | + | 0.994227i | \(0.465780\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.6949 | −0.371450 | −0.185725 | − | 0.982602i | \(-0.559463\pi\) | ||||
−0.185725 | + | 0.982602i | \(0.559463\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.49603 | + | 4.34515i | 0.225345 | + | 0.150732i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.8353 | − | 18.3801i | −1.10303 | − | 0.636834i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.3628 | − | 19.8394i | 1.18917 | − | 0.686569i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.35348 | + | 9.49691i | −0.288739 | + | 0.328261i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.6888 | − | 46.2263i | −0.921399 | − | 1.59591i | −0.797252 | − | 0.603646i | \(-0.793714\pi\) |
−0.124147 | − | 0.992264i | \(-0.539619\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.9051 | − | 27.5484i | 0.548451 | − | 0.949945i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.3715 | − | 40.9207i | 0.942726 | − | 1.40938i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 4.05500i | − | 0.139496i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.41646i | − | 0.0486702i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.83551 | + | 0.517451i | 0.268914 | + | 0.0177589i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.8384 | − | 39.5572i | 0.782890 | − | 1.35600i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.32038 | + | 12.6793i | 0.250645 | + | 0.434130i | 0.963704 | − | 0.266975i | \(-0.0860240\pi\) |
−0.713059 | + | 0.701104i | \(0.752691\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.3532 | − | 46.8536i | −0.661867 | − | 1.60236i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.8376 | + | 12.6080i | −0.745959 | + | 0.430680i | −0.824232 | − | 0.566252i | \(-0.808393\pi\) |
0.0782730 | + | 0.996932i | \(0.475059\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.77869 | + | 2.18163i | 0.128927 | + | 0.0744361i | 0.563076 | − | 0.826405i | \(-0.309618\pi\) |
−0.434149 | + | 0.900841i | \(0.642951\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.738076 | − | 0.363526i | 0.0251535 | − | 0.0123889i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.7626 | 1.25141 | 0.625706 | − | 0.780059i | \(-0.284811\pi\) | ||||
0.625706 | + | 0.780059i | \(0.284811\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.5320 | 0.766110 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.7752 | + | 8.26231i | −0.569715 | + | 0.280603i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.91671 | + | 5.72541i | 0.336401 | + | 0.194221i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.63012 | + | 3.25055i | −0.190769 | + | 0.110141i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.37452 | + | 0.712968i | 0.181900 | + | 0.0241303i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.974408 | − | 1.68772i | −0.0329410 | − | 0.0570555i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.02843 | − | 3.51334i | 0.0684951 | − | 0.118637i | −0.829744 | − | 0.558144i | \(-0.811514\pi\) |
0.898239 | + | 0.439507i | \(0.144847\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.3569 | − | 1.74059i | −0.888996 | − | 0.0587087i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.5979i | 0.997179i | 0.866838 | + | 0.498589i | \(0.166148\pi\) | ||||
−0.866838 | + | 0.498589i | \(0.833852\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.1894i | 1.41979i | 0.704309 | + | 0.709894i | \(0.251257\pi\) | ||||
−0.704309 | + | 0.709894i | \(0.748743\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22.2238 | + | 33.2248i | −0.747045 | + | 1.11684i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.1442 | + | 26.2305i | −0.508491 | + | 0.880733i | 0.491460 | + | 0.870900i | \(0.336463\pi\) |
−0.999952 | + | 0.00983292i | \(0.996870\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.16526 | − | 2.01829i | −0.0390816 | − | 0.0676913i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.0100 | + | 9.97053i | −0.335347 | + | 0.334025i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51.4198 | − | 29.6872i | 1.72070 | − | 0.993445i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41.3909 | + | 23.8970i | 1.38355 | + | 0.798790i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.7704 | − | 19.9132i | −0.994005 | − | 0.664883i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.9814 | −0.633065 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.6625 | 0.421848 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.0748242 | + | 1.13303i | −0.00248999 | + | 0.0377047i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.6793 | + | 10.2072i | 0.587681 | + | 0.339298i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.8861 | + | 12.0586i | −0.693510 | + | 0.400398i | −0.804926 | − | 0.593376i | \(-0.797795\pi\) |
0.111416 | + | 0.993774i | \(0.464462\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.40380 | + | 10.5822i | −0.0465612 | + | 0.350989i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.0067 | + | 17.3322i | 0.331538 | + | 0.574241i | 0.982814 | − | 0.184600i | \(-0.0590991\pi\) |
−0.651276 | + | 0.758841i | \(0.725766\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.12499 | + | 3.68060i | −0.0703270 | + | 0.121810i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −22.8697 | − | 46.4329i | −0.756049 | − | 1.53503i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 0.232271i | − | 0.00767025i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.25070i | 0.239178i | 0.992823 | + | 0.119589i | \(0.0381578\pi\) | ||||
−0.992823 | + | 0.119589i | \(0.961842\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.24992 | − | 10.6591i | −0.172991 | − | 0.351228i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.2807 | − | 42.0555i | 0.799210 | − | 1.38427i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.54392 | + | 4.40620i | 0.0836436 | + | 0.144875i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.5147 | − | 10.9521i | 0.870856 | − | 0.359713i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.6167 | + | 9.01628i | −0.512366 | + | 0.295815i | −0.733806 | − | 0.679360i | \(-0.762258\pi\) |
0.221440 | + | 0.975174i | \(0.428924\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 48.6212 | + | 28.0715i | 1.59350 | + | 0.920005i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.78207 | + | 42.1275i | −0.0910808 | + | 1.37919i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.3685 | 0.568011 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.2806 | 0.858551 | 0.429276 | − | 0.903174i | \(-0.358769\pi\) | ||||
0.429276 | + | 0.903174i | \(0.358769\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.4031 | + | 7.62743i | 0.372125 | + | 0.248912i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.6987 | − | 17.7239i | −1.00075 | − | 0.577782i | −0.0922782 | − | 0.995733i | \(-0.529415\pi\) |
−0.908469 | + | 0.417951i | \(0.862748\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.2655 | + | 7.65886i | −0.431986 | + | 0.249407i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.355653 | − | 1.77425i | 0.0115694 | − | 0.0577164i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.1432 | − | 17.5686i | −0.329610 | − | 0.570901i | 0.652824 | − | 0.757509i | \(-0.273584\pi\) |
−0.982434 | + | 0.186608i | \(0.940251\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.2253 | + | 35.0312i | −0.656541 | + | 1.13716i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.3514 | + | 28.9305i | −0.627512 | + | 0.938136i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 27.1172i | − | 0.878411i | −0.898387 | − | 0.439205i | \(-0.855260\pi\) | ||
0.898387 | − | 0.439205i | \(-0.144740\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 5.34755i | − | 0.173043i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.1570 | − | 1.39719i | −0.683908 | − | 0.0451648i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.116386 | + | 0.201586i | −0.00375830 | + | 0.00650956i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.5376 | − | 21.7157i | −0.404437 | − | 0.700506i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.2461 | − | 13.3257i | 0.330175 | − | 0.429414i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.08581 | + | 5.24569i | −0.292482 | + | 0.168865i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.4921 | − | 10.6764i | −0.594665 | − | 0.343330i | 0.172275 | − | 0.985049i | \(-0.444888\pi\) |
−0.766940 | + | 0.641719i | \(0.778222\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 65.9627 | − | 32.4887i | 2.11903 | − | 1.04369i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.9224 | −0.382608 | −0.191304 | − | 0.981531i | \(-0.561272\pi\) | ||||
−0.191304 | + | 0.981531i | \(0.561272\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.57618 | 0.114647 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.57896 | − | 1.76275i | 0.114618 | − | 0.0564532i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.3300 | − | 9.42812i | −0.522442 | − | 0.301632i | 0.215491 | − | 0.976506i | \(-0.430865\pi\) |
−0.737933 | + | 0.674874i | \(0.764198\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.26517 | − | 1.88515i | 0.104355 | − | 0.0602496i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.8401 | − | 17.9999i | 0.441879 | − | 0.574693i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.3810 | + | 42.2290i | 0.777632 | + | 1.34690i | 0.933303 | + | 0.359089i | \(0.116912\pi\) |
−0.155672 | + | 0.987809i | \(0.549754\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.93561 | − | 10.2808i | 0.189124 | − | 0.327573i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.11482 | + | 0.139661i | 0.0673155 | + | 0.00444547i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 21.1405i | − | 0.672228i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 27.4703i | − | 0.872622i | −0.899796 | − | 0.436311i | \(-0.856285\pi\) | ||
0.899796 | − | 0.436311i | \(-0.143715\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.4788 | − | 18.6559i | 0.396002 | − | 0.592027i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.1844 | + | 26.3001i | −0.481377 | + | 0.833770i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.0675 | − | 38.2220i | −0.698885 | − | 1.21050i | −0.968853 | − | 0.247635i | \(-0.920347\pi\) |
0.269969 | − | 0.962869i | \(-0.412987\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.71718 | + | 43.4875i | −0.275799 | + | 1.37588i |
(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 | 288.2.s.a.95.11 | yes | 24 | |
3.2 | odd | 2 | 864.2.s.a.287.4 | 24 | |||
4.3 | odd | 2 | inner | 288.2.s.a.95.2 | ✓ | 24 | |
8.3 | odd | 2 | 576.2.s.g.383.11 | 24 | |||
8.5 | even | 2 | 576.2.s.g.383.2 | 24 | |||
9.2 | odd | 6 | inner | 288.2.s.a.191.2 | yes | 24 | |
9.4 | even | 3 | 2592.2.c.c.2591.6 | 24 | |||
9.5 | odd | 6 | 2592.2.c.c.2591.20 | 24 | |||
9.7 | even | 3 | 864.2.s.a.575.3 | 24 | |||
12.11 | even | 2 | 864.2.s.a.287.3 | 24 | |||
24.5 | odd | 2 | 1728.2.s.g.1151.10 | 24 | |||
24.11 | even | 2 | 1728.2.s.g.1151.9 | 24 | |||
36.7 | odd | 6 | 864.2.s.a.575.4 | 24 | |||
36.11 | even | 6 | inner | 288.2.s.a.191.11 | yes | 24 | |
36.23 | even | 6 | 2592.2.c.c.2591.19 | 24 | |||
36.31 | odd | 6 | 2592.2.c.c.2591.5 | 24 | |||
72.5 | odd | 6 | 5184.2.c.m.5183.6 | 24 | |||
72.11 | even | 6 | 576.2.s.g.191.2 | 24 | |||
72.13 | even | 6 | 5184.2.c.m.5183.20 | 24 | |||
72.29 | odd | 6 | 576.2.s.g.191.11 | 24 | |||
72.43 | odd | 6 | 1728.2.s.g.575.10 | 24 | |||
72.59 | even | 6 | 5184.2.c.m.5183.5 | 24 | |||
72.61 | even | 6 | 1728.2.s.g.575.9 | 24 | |||
72.67 | odd | 6 | 5184.2.c.m.5183.19 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.s.a.95.2 | ✓ | 24 | 4.3 | odd | 2 | inner | |
288.2.s.a.95.11 | yes | 24 | 1.1 | even | 1 | trivial | |
288.2.s.a.191.2 | yes | 24 | 9.2 | odd | 6 | inner | |
288.2.s.a.191.11 | yes | 24 | 36.11 | even | 6 | inner | |
576.2.s.g.191.2 | 24 | 72.11 | even | 6 | |||
576.2.s.g.191.11 | 24 | 72.29 | odd | 6 | |||
576.2.s.g.383.2 | 24 | 8.5 | even | 2 | |||
576.2.s.g.383.11 | 24 | 8.3 | odd | 2 | |||
864.2.s.a.287.3 | 24 | 12.11 | even | 2 | |||
864.2.s.a.287.4 | 24 | 3.2 | odd | 2 | |||
864.2.s.a.575.3 | 24 | 9.7 | even | 3 | |||
864.2.s.a.575.4 | 24 | 36.7 | odd | 6 | |||
1728.2.s.g.575.9 | 24 | 72.61 | even | 6 | |||
1728.2.s.g.575.10 | 24 | 72.43 | odd | 6 | |||
1728.2.s.g.1151.9 | 24 | 24.11 | even | 2 | |||
1728.2.s.g.1151.10 | 24 | 24.5 | odd | 2 | |||
2592.2.c.c.2591.5 | 24 | 36.31 | odd | 6 | |||
2592.2.c.c.2591.6 | 24 | 9.4 | even | 3 | |||
2592.2.c.c.2591.19 | 24 | 36.23 | even | 6 | |||
2592.2.c.c.2591.20 | 24 | 9.5 | odd | 6 | |||
5184.2.c.m.5183.5 | 24 | 72.59 | even | 6 | |||
5184.2.c.m.5183.6 | 24 | 72.5 | odd | 6 | |||
5184.2.c.m.5183.19 | 24 | 72.67 | odd | 6 | |||
5184.2.c.m.5183.20 | 24 | 72.13 | even | 6 |