Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(287,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, 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("864.287");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.s (of order \(6\), degree \(2\), not 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 575.4 | ||
Character | \(\chi\) | \(=\) | 864.575 |
Dual form | 864.2.s.a.287.4 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.81740 | + | 1.04928i | −0.812767 | + | 0.469251i | −0.847916 | − | 0.530131i | \(-0.822143\pi\) |
0.0351491 | + | 0.999382i | \(0.488809\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.143714 | + | 0.0829731i | 0.0543187 | + | 0.0313609i | 0.526913 | − | 0.849919i | \(-0.323349\pi\) |
−0.472595 | + | 0.881280i | \(0.656683\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.784910 | − | 1.35950i | 0.236659 | − | 0.409906i | −0.723094 | − | 0.690749i | \(-0.757281\pi\) |
0.959754 | + | 0.280843i | \(0.0906141\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.93212 | − | 3.34652i | −0.535872 | − | 0.928158i | −0.999121 | − | 0.0419297i | \(-0.986649\pi\) |
0.463248 | − | 0.886229i | \(-0.346684\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 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 | \(0.374800\pi\) | ||||
−0.383264 | + | 0.923639i | \(0.625200\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.67564 | + | 4.63435i | 0.557910 | + | 0.966328i | 0.997671 | + | 0.0682135i | \(0.0217299\pi\) |
−0.439761 | + | 0.898115i | \(0.644937\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.298034 | + | 0.516211i | −0.0596069 | + | 0.103242i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.75334 | − | 3.89904i | −1.25406 | − | 0.724034i | −0.282150 | − | 0.959370i | \(-0.591048\pi\) |
−0.971914 | + | 0.235336i | \(0.924381\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.10800 | + | 1.21705i | −0.378608 | + | 0.218589i | −0.677212 | − | 0.735788i | \(-0.736812\pi\) |
0.298604 | + | 0.954377i | \(0.403479\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.47895 | + | 1.43122i | −0.387146 | + | 0.223519i | −0.680923 | − | 0.732355i | \(-0.738421\pi\) |
0.293777 | + | 0.955874i | \(0.405088\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.42127 | − | 1.97527i | −0.521739 | − | 0.301226i | 0.215907 | − | 0.976414i | \(-0.430729\pi\) |
−0.737646 | + | 0.675188i | \(0.764063\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.68689 | + | 6.38588i | −0.537788 | + | 0.931477i | 0.461234 | + | 0.887278i | \(0.347407\pi\) |
−0.999023 | + | 0.0441985i | \(0.985927\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.48623 | − | 6.03833i | −0.498033 | − | 0.862618i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.49855 | + | 9.52376i | 0.715850 | + | 1.23989i | 0.962631 | + | 0.270817i | \(0.0872939\pi\) |
−0.246781 | + | 0.969071i | \(0.579373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.11998 | + | 12.3322i | −0.911620 | + | 1.57897i | −0.0998446 | + | 0.995003i | \(0.531835\pi\) |
−0.811776 | + | 0.583969i | \(0.801499\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.02286 | + | 4.05465i | 0.871079 | + | 0.502917i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.45698 | − | 0.841190i | 0.177999 | − | 0.102768i | −0.408353 | − | 0.912824i | \(-0.633897\pi\) |
0.586352 | + | 0.810056i | \(0.300564\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.5669 | 1.49142 | 0.745709 | − | 0.666272i | \(-0.232111\pi\) | ||||
0.745709 | + | 0.666272i | \(0.232111\pi\) | |||||||
\(72\) | 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 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.225605 | − | 0.130253i | 0.0257100 | − | 0.0148437i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.31710 | − | 3.64718i | −0.710729 | − | 0.410339i | 0.100602 | − | 0.994927i | \(-0.467923\pi\) |
−0.811331 | + | 0.584587i | \(0.801256\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.35365 | − | 2.34460i | 0.148583 | − | 0.257353i | −0.782121 | − | 0.623126i | \(-0.785862\pi\) |
0.930704 | + | 0.365774i | \(0.119196\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.53201 | − | 9.58172i | −0.600031 | − | 1.03928i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 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 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.44888 | − | 14.6339i | −0.866837 | − | 1.50141i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.903600 | − | 1.56508i | 0.0917467 | − | 0.158910i | −0.816499 | − | 0.577346i | \(-0.804088\pi\) |
0.908246 | + | 0.418436i | \(0.137422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.08158 | + | 1.77915i | 0.306628 | + | 0.177032i | 0.645417 | − | 0.763831i | \(-0.276684\pi\) |
−0.338788 | + | 0.940863i | \(0.610017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.28138 | − | 4.78126i | 0.815989 | − | 0.471111i | −0.0330425 | − | 0.999454i | \(-0.510520\pi\) |
0.849031 | + | 0.528343i | \(0.177186\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.60313 | −0.541675 | −0.270838 | − | 0.962625i | \(-0.587301\pi\) | ||||
−0.270838 | + | 0.962625i | \(0.587301\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.56853 | 0.724934 | 0.362467 | − | 0.931997i | \(-0.381935\pi\) | ||||
0.362467 | + | 0.931997i | \(0.381935\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.495124 | + | 0.285860i | −0.0465773 | + | 0.0268914i | −0.523108 | − | 0.852266i | \(-0.675228\pi\) |
0.476531 | + | 0.879158i | \(0.341894\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.72543 | − | 5.61498i | −0.906901 | − | 0.523600i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.7437i | − | 1.05038i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0438i | 1.24619i | 0.782146 | + | 0.623095i | \(0.214125\pi\) | ||||
−0.782146 | + | 0.623095i | \(0.785875\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.699837 | − | 1.21215i | −0.0611450 | − | 0.105906i | 0.833832 | − | 0.552018i | \(-0.186142\pi\) |
−0.894977 | + | 0.446111i | \(0.852809\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.668108 | + | 1.15720i | −0.0579323 | + | 0.100342i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.21477 | + | 0.701347i | 0.103785 | + | 0.0599201i | 0.550994 | − | 0.834509i | \(-0.314249\pi\) |
−0.447209 | + | 0.894429i | \(0.647582\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.6630 | − | 10.7751i | 1.58298 | − | 0.913933i | 0.588557 | − | 0.808456i | \(-0.299696\pi\) |
0.994422 | − | 0.105477i | \(-0.0336369\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.06615 | −0.507277 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.3647 | 1.35902 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.10263 | + | 2.94601i | −0.418024 | + | 0.241346i | −0.694232 | − | 0.719752i | \(-0.744256\pi\) |
0.276208 | + | 0.961098i | \(0.410922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.86723 | + | 3.96480i | 0.558847 | + | 0.322651i | 0.752683 | − | 0.658383i | \(-0.228759\pi\) |
−0.193835 | + | 0.981034i | \(0.562093\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.55405 | − | 4.42375i | 0.205147 | − | 0.355324i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.00382 | + | 1.73867i | 0.0801138 | + | 0.138761i | 0.903299 | − | 0.429012i | \(-0.141138\pi\) |
−0.823185 | + | 0.567773i | \(0.807805\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.888025i | 0.0699862i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.06036i | − | 0.161379i | −0.996739 | − | 0.0806897i | \(-0.974288\pi\) | ||
0.996739 | − | 0.0806897i | \(-0.0257123\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.45382 | − | 16.3745i | −0.731559 | − | 1.26710i | −0.956217 | − | 0.292659i | \(-0.905460\pi\) |
0.224658 | − | 0.974438i | \(-0.427873\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.966142 | + | 1.67341i | −0.0743186 | + | 0.128724i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.29843 | − | 5.36845i | −0.706946 | − | 0.408156i | 0.102983 | − | 0.994683i | \(-0.467161\pi\) |
−0.809929 | + | 0.586528i | \(0.800495\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0856632 | + | 0.0494577i | −0.00647553 | + | 0.00373865i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.7748 | −1.70227 | −0.851133 | − | 0.524950i | \(-0.824084\pi\) | ||||
−0.851133 | + | 0.524950i | \(0.824084\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.72780 | 0.723062 | 0.361531 | − | 0.932360i | \(-0.382254\pi\) | ||||
0.361531 | + | 0.932360i | \(0.382254\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.27410 | − | 2.20681i | 0.0921908 | − | 0.159679i | −0.816242 | − | 0.577710i | \(-0.803946\pi\) |
0.908433 | + | 0.418031i | \(0.137280\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.49967 | − | 4.32955i | −0.179930 | − | 0.311648i | 0.761926 | − | 0.647664i | \(-0.224254\pi\) |
−0.941856 | + | 0.336016i | \(0.890921\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 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 | \(-0.828564\pi\) | ||
0.858436 | − | 0.512921i | \(-0.171436\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 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 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.9469 | + | 6.32017i | 0.757210 | + | 0.437176i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7320 | + | 7.35080i | −0.876505 | + | 0.506050i | −0.869504 | − | 0.493925i | \(-0.835562\pi\) |
−0.00700041 | + | 0.999975i | \(0.502228\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.29043 | 0.565403 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.403931 | −0.0274206 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.6436 | − | 10.1865i | 1.18683 | − | 0.685219i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.6729 | − | 9.04876i | −1.04954 | − | 0.605950i | −0.127016 | − | 0.991901i | \(-0.540540\pi\) |
−0.922519 | + | 0.385951i | \(0.873873\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.29529 | − | 10.9038i | 0.417833 | − | 0.723708i | −0.577888 | − | 0.816116i | \(-0.696123\pi\) |
0.995721 | + | 0.0924078i | \(0.0294564\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.19995 | + | 10.7386i | 0.409704 | + | 0.709628i | 0.994856 | − | 0.101295i | \(-0.0322986\pi\) |
−0.585152 | + | 0.810923i | \(0.698965\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 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 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.273904 | + | 0.474416i | 0.0177174 | + | 0.0306874i | 0.874748 | − | 0.484578i | \(-0.161027\pi\) |
−0.857031 | + | 0.515265i | \(0.827693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.28792 | + | 16.0872i | −0.598288 | + | 1.03626i | 0.394786 | + | 0.918773i | \(0.370819\pi\) |
−0.993074 | + | 0.117491i | \(0.962515\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 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 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.2012 | 1.21197 | 0.605985 | − | 0.795476i | \(-0.292779\pi\) | ||||
0.605985 | + | 0.795476i | \(0.292779\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.40056 | 0.528138 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.90205 | + | 2.25285i | −0.243403 | + | 0.140529i | −0.616740 | − | 0.787167i | \(-0.711547\pi\) |
0.373337 | + | 0.927696i | \(0.378214\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.22669 | − | 0.708231i | −0.0762229 | − | 0.0440073i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.92767 | + | 17.1952i | −0.612166 | + | 1.06030i | 0.378708 | + | 0.925516i | \(0.376368\pi\) |
−0.990875 | + | 0.134787i | \(0.956965\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.52009 | + | 4.36492i | 0.154808 | + | 0.268135i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 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 | \(0.00839488\pi\) | ||||
−0.999652 | + | 0.0263702i | \(0.991605\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.467861 | + | 0.810358i | 0.0282131 | + | 0.0488664i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.25608 | − | 3.90765i | 0.135555 | − | 0.234788i | −0.790254 | − | 0.612779i | \(-0.790052\pi\) |
0.925809 | + | 0.377991i | \(0.123385\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.6156 | − | 14.2118i | −1.46844 | − | 0.847805i | −0.469066 | − | 0.883163i | \(-0.655409\pi\) |
−0.999375 | + | 0.0353583i | \(0.988743\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.92629 | − | 2.26684i | 0.233394 | − | 0.134750i | −0.378743 | − | 0.925502i | \(-0.623644\pi\) |
0.612137 | + | 0.790752i | \(0.290310\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.475011 | −0.0280390 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.7962 | −0.635069 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.2072 | − | 7.62516i | 0.771570 | − | 0.445466i | −0.0618642 | − | 0.998085i | \(-0.519705\pi\) |
0.833435 | + | 0.552618i | \(0.186371\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.9861 | − | 11.5390i | −1.16364 | − | 0.671827i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 29.8833i | − | 1.71111i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.85996i | 0.391519i | 0.980652 | + | 0.195759i | \(0.0627171\pi\) | ||||
−0.980652 | + | 0.195759i | \(0.937283\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.1876 | + | 21.1096i | 0.691097 | + | 1.19702i | 0.971479 | + | 0.237127i | \(0.0762058\pi\) |
−0.280381 | + | 0.959889i | \(0.590461\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.96030 | − | 6.85944i | 0.223849 | − | 0.387719i | −0.732124 | − | 0.681171i | \(-0.761471\pi\) |
0.955974 | + | 0.293453i | \(0.0948043\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.4030 | + | 10.0476i | 0.977447 | + | 0.564329i | 0.901498 | − | 0.432782i | \(-0.142468\pi\) |
0.0759487 | + | 0.997112i | \(0.475801\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.6015 | + | 6.12080i | −0.593572 | + | 0.342699i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −42.4523 | −2.36211 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.30335 | 0.127767 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.05971 | + | 0.611826i | −0.0584239 | + | 0.0337310i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.2223 | + | 6.47921i | 0.616835 | + | 0.356130i | 0.775636 | − | 0.631181i | \(-0.217429\pi\) |
−0.158801 | + | 0.987311i | \(0.550763\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.76528 | + | 3.05756i | −0.0964477 | + | 0.167052i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.96429 | − | 12.0625i | −0.379369 | − | 0.657086i | 0.611602 | − | 0.791166i | \(-0.290526\pi\) |
−0.990971 | + | 0.134080i | \(0.957192\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.82111i | 0.206925i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.31868i | − | 0.125197i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.0232 | + | 29.4851i | 0.913854 | + | 1.58284i | 0.808570 | + | 0.588399i | \(0.200242\pi\) |
0.105284 | + | 0.994442i | \(0.466425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.599892 | + | 1.03904i | −0.0321115 | + | 0.0556188i | −0.881635 | − | 0.471933i | \(-0.843557\pi\) |
0.849523 | + | 0.527552i | \(0.176890\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.6933 | − | 11.3699i | −1.04817 | − | 0.605159i | −0.126031 | − | 0.992026i | \(-0.540224\pi\) |
−0.922135 | + | 0.386867i | \(0.873557\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.8391 | + | 13.1862i | −1.21218 | + | 0.699850i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.5652 | 1.13817 | 0.569083 | − | 0.822280i | \(-0.307298\pi\) | ||||
0.569083 | + | 0.822280i | \(0.307298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −45.8363 | −2.41244 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.0245 | + | 10.9838i | −0.995786 | + | 0.574917i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0399 | + | 16.1889i | 1.46367 | + | 0.845051i | 0.999179 | − | 0.0405253i | \(-0.0129031\pi\) |
0.464493 | + | 0.885577i | \(0.346236\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.199280 | − | 0.345163i | 0.0103461 | − | 0.0179199i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.19629 | + | 9.00024i | 0.269054 | + | 0.466015i | 0.968618 | − | 0.248555i | \(-0.0799557\pi\) |
−0.699564 | + | 0.714570i | \(0.746622\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.1336i | 1.55196i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.1762i | 1.03638i | 0.855265 | + | 0.518190i | \(0.173394\pi\) | ||||
−0.855265 | + | 0.518190i | \(0.826606\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.8556 | − | 20.5344i | −0.605791 | − | 1.04926i | −0.991926 | − | 0.126818i | \(-0.959524\pi\) |
0.386135 | − | 0.922442i | \(-0.373810\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.273343 | + | 0.473444i | −0.0139308 | + | 0.0241289i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.76371 | − | 1.01828i | −0.0894236 | − | 0.0516288i | 0.454621 | − | 0.890685i | \(-0.349775\pi\) |
−0.544045 | + | 0.839056i | \(0.683108\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.4332 | + | 14.1065i | −1.23564 | + | 0.713399i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.4143 | + | 11.7862i | −1.01944 | + | 0.588574i | −0.913942 | − | 0.405846i | \(-0.866977\pi\) |
−0.105498 | + | 0.994419i | \(0.533644\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.14580 | + | 4.70298i | 0.405771 | + | 0.234272i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.69973 | + | 11.6043i | −0.332093 | + | 0.575202i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.8999 | − | 18.8792i | −0.538965 | − | 0.933515i | −0.998960 | − | 0.0455934i | \(-0.985482\pi\) |
0.459995 | − | 0.887922i | \(-0.347851\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.82493i | 0.0897988i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.68143i | 0.278891i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5076 | − | 18.1997i | −0.513329 | − | 0.889112i | −0.999880 | − | 0.0154599i | \(-0.995079\pi\) |
0.486552 | − | 0.873652i | \(-0.338255\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.86839 | − | 11.8964i | 0.334745 | − | 0.579795i | −0.648691 | − | 0.761052i | \(-0.724683\pi\) |
0.983436 | + | 0.181257i | \(0.0580166\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 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 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.476344 | −0.0229447 | −0.0114723 | − | 0.999934i | \(-0.503652\pi\) | ||||
−0.0114723 | + | 0.999934i | \(0.503652\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.6601 | −0.560348 | −0.280174 | − | 0.959949i | \(-0.590392\pi\) | ||||
−0.280174 | + | 0.959949i | \(0.590392\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −37.3162 | + | 21.5445i | −1.78508 | + | 1.03061i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.8138 | + | 17.2130i | 1.42294 | + | 0.821533i | 0.996549 | − | 0.0830082i | \(-0.0264528\pi\) |
0.426387 | + | 0.904541i | \(0.359786\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.84473 | + | 8.39132i | −0.230180 | + | 0.398684i | −0.957861 | − | 0.287232i | \(-0.907265\pi\) |
0.727681 | + | 0.685916i | \(0.240598\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.52009 | − | 4.36492i | −0.119464 | − | 0.206917i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 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 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.672854 | + | 1.16542i | 0.0315439 | + | 0.0546356i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.95237 | − | 12.0419i | 0.325218 | − | 0.563295i | −0.656338 | − | 0.754467i | \(-0.727896\pi\) |
0.981557 | + | 0.191172i | \(0.0612289\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.80521 | + | 1.04224i | 0.0840772 | + | 0.0485420i | 0.541449 | − | 0.840733i | \(-0.317876\pi\) |
−0.457372 | + | 0.889275i | \(0.651209\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.0337 | + | 17.9173i | −1.44226 | + | 0.832688i | −0.998000 | − | 0.0632104i | \(-0.979866\pi\) |
−0.444258 | + | 0.895899i | \(0.646533\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.4185 | 1.17623 | 0.588114 | − | 0.808778i | \(-0.299871\pi\) | ||||
0.588114 | + | 0.808778i | \(0.299871\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.279185 | 0.0128915 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 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 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.4545 | + | 19.8398i | −0.523370 | + | 0.906503i | 0.476260 | + | 0.879304i | \(0.341992\pi\) |
−0.999630 | + | 0.0271987i | \(0.991341\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.4919 | + | 28.5648i | 0.751965 | + | 1.30244i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.79251i | 0.172209i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.6846i | − | 0.710738i | −0.934726 | − | 0.355369i | \(-0.884355\pi\) | ||
0.934726 | − | 0.355369i | \(-0.115645\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.2976 | + | 21.3001i | 0.554982 | + | 0.961258i | 0.997905 | + | 0.0646979i | \(0.0206084\pi\) |
−0.442922 | + | 0.896560i | \(0.646058\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.5566 | − | 35.6050i | 0.925821 | − | 1.60357i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.80604 | + | 1.04272i | 0.0810118 | + | 0.0467722i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.96333 | − | 3.44293i | 0.266955 | − | 0.154127i | −0.360548 | − | 0.932741i | \(-0.617410\pi\) |
0.627503 | + | 0.778614i | \(0.284077\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.6347 | 0.786294 | 0.393147 | − | 0.919476i | \(-0.371386\pi\) | ||||
0.393147 | + | 0.919476i | \(0.371386\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.46729 | −0.332290 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.1218 | − | 8.15320i | 0.625936 | − | 0.361384i | −0.153240 | − | 0.988189i | \(-0.548971\pi\) |
0.779177 | + | 0.626805i | \(0.215638\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.50439 | + | 0.868558i | 0.0665502 | + | 0.0384228i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 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 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 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 | \(-0.835742\pi\) | ||
0.869784 | − | 0.493433i | \(-0.164258\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 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 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.7551 | + | 7.94149i | −0.589202 | + | 0.340176i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.6339 | − | 8.44889i | −0.625701 | − | 0.361249i | 0.153384 | − | 0.988167i | \(-0.450983\pi\) |
−0.779085 | + | 0.626918i | \(0.784316\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 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 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 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 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.58426 | + | 13.1363i | 0.319639 | + | 0.553630i | 0.980413 | − | 0.196955i | \(-0.0631052\pi\) |
−0.660774 | + | 0.750585i | \(0.729772\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.599892 | − | 1.03904i | 0.0252377 | − | 0.0437129i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.18052 | + | 2.41363i | 0.175257 | + | 0.101184i | 0.585062 | − | 0.810988i | \(-0.301070\pi\) |
−0.409806 | + | 0.912173i | \(0.634403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.07311 | + | 2.35161i | −0.170454 | + | 0.0984118i | −0.582800 | − | 0.812616i | \(-0.698043\pi\) |
0.412346 | + | 0.911027i | \(0.364710\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | 0 | ||||||||
\(580\) | 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 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.83368 | + | 15.3004i | −0.364605 | + | 0.631515i | −0.988713 | − | 0.149824i | \(-0.952129\pi\) |
0.624108 | + | 0.781338i | \(0.285463\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.79984 | − | 16.9738i | −0.403795 | − | 0.699394i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 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 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.3209 | + | 23.0726i | 0.544279 | + | 0.942719i | 0.998652 | + | 0.0519076i | \(0.0165301\pi\) |
−0.454373 | + | 0.890812i | \(0.650137\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.2321 | + | 21.1866i | −0.498959 | + | 0.864221i | −0.999999 | − | 0.00120220i | \(-0.999617\pi\) |
0.501041 | + | 0.865424i | \(0.332951\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.5127 | − | 8.95628i | −0.630682 | − | 0.364124i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.5942 | + | 14.1995i | −0.998247 | + | 0.576338i | −0.907729 | − | 0.419556i | \(-0.862186\pi\) |
−0.0905181 | + | 0.995895i | \(0.528852\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.6817 | − | 18.8688i | 1.31571 | − | 0.759628i | 0.332678 | − | 0.943040i | \(-0.392048\pi\) |
0.983036 | + | 0.183412i | \(0.0587143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.89600 | + | 4.55876i | 0.317367 | + | 0.183232i | 0.650218 | − | 0.759747i | \(-0.274677\pi\) |
−0.332851 | + | 0.942979i | \(0.608011\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 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 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 45.0018i | − | 1.79434i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.05133i | 0.360328i | 0.983637 | + | 0.180164i | \(0.0576628\pi\) | ||||
−0.983637 | + | 0.180164i | \(0.942337\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 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 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.1865 | + | 15.6961i | 1.07380 | + | 0.619959i | 0.929217 | − | 0.369533i | \(-0.120482\pi\) |
0.144583 | + | 0.989493i | \(0.453816\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.03917 | + | 3.48672i | −0.238162 | + | 0.137503i | −0.614332 | − | 0.789048i | \(-0.710574\pi\) |
0.376170 | + | 0.926551i | \(0.377241\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.4189 | −1.43178 | −0.715888 | − | 0.698215i | \(-0.753978\pi\) | ||||
−0.715888 | + | 0.698215i | \(0.753978\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.2635 | 0.677650 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.9837 | − | 16.1564i | 1.09509 | − | 0.632248i | 0.160159 | − | 0.987091i | \(-0.448799\pi\) |
0.934926 | + | 0.354843i | \(0.115466\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.54377 | + | 1.46865i | 0.0993933 | + | 0.0573847i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.52870 | + | 4.37984i | −0.0985042 | + | 0.170614i | −0.911066 | − | 0.412261i | \(-0.864739\pi\) |
0.812562 | + | 0.582875i | \(0.198072\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.31245 | + | 10.9335i | 0.245526 | + | 0.425263i | 0.962279 | − | 0.272063i | \(-0.0877060\pi\) |
−0.716753 | + | 0.697327i | \(0.754373\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.80412i | − | 0.108739i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 41.7298i | − | 1.61578i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.1771 | + | 19.3593i | 0.431487 | + | 0.747357i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.5547 | − | 40.7980i | 0.907967 | − | 1.57265i | 0.0910837 | − | 0.995843i | \(-0.470967\pi\) |
0.816884 | − | 0.576802i | \(-0.195700\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.1335 | − | 9.31465i | −0.620059 | − | 0.357991i | 0.156833 | − | 0.987625i | \(-0.449872\pi\) |
−0.776892 | + | 0.629634i | \(0.783205\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.259719 | − | 0.149949i | 0.00996712 | − | 0.00575452i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.4857 | −0.592544 | −0.296272 | − | 0.955104i | \(-0.595743\pi\) | ||||
−0.296272 | + | 0.955104i | \(0.595743\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.94363 | −0.112470 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.03747 | + | 4.64044i | −0.306203 | + | 0.176787i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.34942 | + | 5.39789i | 0.355669 | + | 0.205345i | 0.667179 | − | 0.744897i | \(-0.267502\pi\) |
−0.311510 | + | 0.950243i | \(0.600835\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 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 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.295243 | + | 0.511376i | 0.0111038 | + | 0.0192323i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5763 | + | 20.0508i | −0.434759 | + | 0.753024i | −0.997276 | − | 0.0737615i | \(-0.976500\pi\) |
0.562517 | + | 0.826786i | \(0.309833\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 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 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.49075 | −0.279358 | −0.139679 | − | 0.990197i | \(-0.544607\pi\) | ||||
−0.139679 | + | 0.990197i | \(0.544607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.58686 | 0.0590979 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.02546 | − | 2.32410i | 0.149502 | − | 0.0863148i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.2968 | + | 16.3372i | 1.04947 | + | 0.605911i | 0.922501 | − | 0.385995i | \(-0.126142\pi\) |
0.126969 | + | 0.991907i | \(0.459475\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.4140 | − | 18.0376i | 0.385177 | − | 0.667146i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.2248 | + | 41.9586i | 0.894765 | + | 1.54978i | 0.834095 | + | 0.551620i | \(0.185990\pi\) |
0.0606693 | + | 0.998158i | \(0.480676\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.64103i | − | 0.0972838i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.58382i | 0.168619i | 0.996440 | + | 0.0843094i | \(0.0268684\pi\) | ||||
−0.996440 | + | 0.0843094i | \(0.973132\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.5816 | − | 32.1842i | −0.681691 | − | 1.18072i | −0.974464 | − | 0.224542i | \(-0.927911\pi\) |
0.292773 | − | 0.956182i | \(-0.405422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.18235 | − | 10.7082i | 0.226504 | − | 0.392316i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.805247 | − | 0.464909i | −0.0294231 | − | 0.0169874i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.1292 | − | 17.9724i | 1.13592 | − | 0.655824i | 0.190503 | − | 0.981687i | \(-0.438988\pi\) |
0.945417 | + | 0.325863i | \(0.105655\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0903 | − | 5.82561i | 0.365771 | − | 0.211178i | −0.305838 | − | 0.952084i | \(-0.598937\pi\) |
0.671609 | + | 0.740905i | \(0.265603\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.08770 | + | 0.627985i | 0.0393774 | + | 0.0227346i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.2477 | − | 36.8020i | 0.767208 | − | 1.32884i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.86238 | + | 17.0821i | 0.355646 | + | 0.615998i | 0.987228 | − | 0.159312i | \(-0.0509274\pi\) |
−0.631582 | + | 0.775309i | \(0.717594\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 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 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.64870 | − | 2.10658i | −0.130228 | − | 0.0751870i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.6360 | + | 11.3369i | −0.699949 | + | 0.404116i | −0.807329 | − | 0.590102i | \(-0.799087\pi\) |
0.107379 | + | 0.994218i | \(0.465754\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.0948747 | −0.00337336 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.0265 | 1.95405 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.38454 | − | 0.799367i | 0.0490431 | − | 0.0283150i | −0.475278 | − | 0.879836i | \(-0.657653\pi\) |
0.524321 | + | 0.851521i | \(0.324319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.6677 | − | 19.4381i | −1.19108 | − | 0.687669i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 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 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 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 | \(0.222060\pi\) | ||||
−0.766372 | + | 0.642397i | \(0.777940\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.1310 | + | 19.1282i | 1.15628 | + | 0.667579i | 0.950410 | − | 0.311000i | \(-0.100664\pi\) |
0.205871 | + | 0.978579i | \(0.433997\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.874309 | + | 0.504783i | −0.0304765 | + | 0.0175956i | −0.515161 | − | 0.857094i | \(-0.672268\pi\) |
0.484684 | + | 0.874689i | \(0.338934\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.17121 | −0.214594 | −0.107297 | − | 0.994227i | \(-0.534220\pi\) | ||||
−0.107297 | + | 0.994227i | \(0.534220\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.6949 | −0.371450 | −0.185725 | − | 0.982602i | \(-0.559463\pi\) | ||||
−0.185725 | + | 0.982602i | \(0.559463\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 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 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.6888 | − | 46.2263i | 0.921399 | − | 1.59591i | 0.124147 | − | 0.992264i | \(-0.460381\pi\) |
0.797252 | − | 0.603646i | \(-0.206286\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.9051 | + | 27.5484i | 0.548451 | + | 0.949945i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 4.05500i | − | 0.139496i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.41646i | 0.0486702i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.8384 | − | 39.5572i | −0.782890 | − | 1.35600i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.32038 | − | 12.6793i | 0.250645 | − | 0.434130i | −0.713059 | − | 0.701104i | \(-0.752691\pi\) |
0.963704 | + | 0.266975i | \(0.0860240\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.8376 | + | 12.6080i | 0.745959 | + | 0.430680i | 0.824232 | − | 0.566252i | \(-0.191607\pi\) |
−0.0782730 | + | 0.996932i | \(0.524941\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.77869 | − | 2.18163i | 0.128927 | − | 0.0744361i | −0.434149 | − | 0.900841i | \(-0.642951\pi\) |
0.563076 | + | 0.826405i | \(0.309618\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.7626 | −1.25141 | −0.625706 | − | 0.780059i | \(-0.715189\pi\) | ||||
−0.625706 | + | 0.780059i | \(0.715189\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.5320 | 0.766110 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 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 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.974408 | − | 1.68772i | 0.0329410 | − | 0.0570555i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.02843 | + | 3.51334i | 0.0684951 | + | 0.118637i | 0.898239 | − | 0.439507i | \(-0.144847\pi\) |
−0.829744 | + | 0.558144i | \(0.811514\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 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 | \(-0.748743\pi\) | ||
0.704309 | − | 0.709894i | \(-0.251257\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.1442 | + | 26.2305i | 0.508491 | + | 0.880733i | 0.999952 | + | 0.00983292i | \(0.00312997\pi\) |
−0.491460 | + | 0.870900i | \(0.663537\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.16526 | + | 2.01829i | −0.0390816 | + | 0.0676913i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 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 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.9814 | 0.633065 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.6625 | 0.421848 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.6793 | + | 10.2072i | −0.587681 | + | 0.339298i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.8861 | − | 12.0586i | −0.693510 | − | 0.400398i | 0.111416 | − | 0.993774i | \(-0.464462\pi\) |
−0.804926 | + | 0.593376i | \(0.797795\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.0067 | + | 17.3322i | −0.331538 | + | 0.574241i | −0.982814 | − | 0.184600i | \(-0.940901\pi\) |
0.651276 | + | 0.758841i | \(0.274234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.12499 | − | 3.68060i | −0.0703270 | − | 0.121810i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 0.232271i | − | 0.00767025i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 7.25070i | − | 0.239178i | −0.992823 | − | 0.119589i | \(-0.961842\pi\) | ||
0.992823 | − | 0.119589i | \(-0.0381578\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.6167 | + | 9.01628i | 0.512366 | + | 0.295815i | 0.733806 | − | 0.679360i | \(-0.237742\pi\) |
−0.221440 | + | 0.975174i | \(0.571076\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 48.6212 | − | 28.0715i | 1.59350 | − | 0.920005i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.6987 | − | 17.7239i | 1.00075 | − | 0.577782i | 0.0922782 | − | 0.995733i | \(-0.470585\pi\) |
0.908469 | + | 0.417951i | \(0.137252\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.2655 | − | 7.65886i | −0.431986 | − | 0.249407i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.1432 | − | 17.5686i | 0.329610 | − | 0.570901i | −0.652824 | − | 0.757509i | \(-0.726416\pi\) |
0.982434 | + | 0.186608i | \(0.0597494\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.2253 | − | 35.0312i | −0.656541 | − | 1.13716i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 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 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 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 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.08581 | + | 5.24569i | 0.292482 | + | 0.168865i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.4921 | + | 10.6764i | −0.594665 | + | 0.343330i | −0.766940 | − | 0.641719i | \(-0.778222\pi\) |
0.172275 | + | 0.985049i | \(0.444888\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.9224 | 0.382608 | 0.191304 | − | 0.981531i | \(-0.438728\pi\) | ||||
0.191304 | + | 0.981531i | \(0.438728\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.57618 | 0.114647 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.3300 | − | 9.42812i | 0.522442 | − | 0.301632i | −0.215491 | − | 0.976506i | \(-0.569135\pi\) |
0.737933 | + | 0.674874i | \(0.235802\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.26517 | + | 1.88515i | 0.104355 | + | 0.0602496i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.3810 | + | 42.2290i | −0.777632 | + | 1.34690i | 0.155672 | + | 0.987809i | \(0.450246\pi\) |
−0.933303 | + | 0.359089i | \(0.883088\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.93561 | + | 10.2808i | 0.189124 | + | 0.327573i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 21.1405i | − | 0.672228i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.4703i | 0.872622i | 0.899796 | + | 0.436311i | \(0.143715\pi\) | ||||
−0.899796 | + | 0.436311i | \(0.856285\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.1844 | + | 26.3001i | 0.481377 | + | 0.833770i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.0675 | + | 38.2220i | −0.698885 | + | 1.21050i | 0.269969 | + | 0.962869i | \(0.412987\pi\) |
−0.968853 | + | 0.247635i | \(0.920347\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 864.2.s.a.575.4 | 24 | ||
3.2 | odd | 2 | 288.2.s.a.191.11 | yes | 24 | ||
4.3 | odd | 2 | inner | 864.2.s.a.575.3 | 24 | ||
8.3 | odd | 2 | 1728.2.s.g.575.9 | 24 | |||
8.5 | even | 2 | 1728.2.s.g.575.10 | 24 | |||
9.2 | odd | 6 | 2592.2.c.c.2591.19 | 24 | |||
9.4 | even | 3 | 288.2.s.a.95.2 | ✓ | 24 | ||
9.5 | odd | 6 | inner | 864.2.s.a.287.3 | 24 | ||
9.7 | even | 3 | 2592.2.c.c.2591.5 | 24 | |||
12.11 | even | 2 | 288.2.s.a.191.2 | yes | 24 | ||
24.5 | odd | 2 | 576.2.s.g.191.2 | 24 | |||
24.11 | even | 2 | 576.2.s.g.191.11 | 24 | |||
36.7 | odd | 6 | 2592.2.c.c.2591.6 | 24 | |||
36.11 | even | 6 | 2592.2.c.c.2591.20 | 24 | |||
36.23 | even | 6 | inner | 864.2.s.a.287.4 | 24 | ||
36.31 | odd | 6 | 288.2.s.a.95.11 | yes | 24 | ||
72.5 | odd | 6 | 1728.2.s.g.1151.9 | 24 | |||
72.11 | even | 6 | 5184.2.c.m.5183.6 | 24 | |||
72.13 | even | 6 | 576.2.s.g.383.11 | 24 | |||
72.29 | odd | 6 | 5184.2.c.m.5183.5 | 24 | |||
72.43 | odd | 6 | 5184.2.c.m.5183.20 | 24 | |||
72.59 | even | 6 | 1728.2.s.g.1151.10 | 24 | |||
72.61 | even | 6 | 5184.2.c.m.5183.19 | 24 | |||
72.67 | odd | 6 | 576.2.s.g.383.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.s.a.95.2 | ✓ | 24 | 9.4 | even | 3 | ||
288.2.s.a.95.11 | yes | 24 | 36.31 | odd | 6 | ||
288.2.s.a.191.2 | yes | 24 | 12.11 | even | 2 | ||
288.2.s.a.191.11 | yes | 24 | 3.2 | odd | 2 | ||
576.2.s.g.191.2 | 24 | 24.5 | odd | 2 | |||
576.2.s.g.191.11 | 24 | 24.11 | even | 2 | |||
576.2.s.g.383.2 | 24 | 72.67 | odd | 6 | |||
576.2.s.g.383.11 | 24 | 72.13 | even | 6 | |||
864.2.s.a.287.3 | 24 | 9.5 | odd | 6 | inner | ||
864.2.s.a.287.4 | 24 | 36.23 | even | 6 | inner | ||
864.2.s.a.575.3 | 24 | 4.3 | odd | 2 | inner | ||
864.2.s.a.575.4 | 24 | 1.1 | even | 1 | trivial | ||
1728.2.s.g.575.9 | 24 | 8.3 | odd | 2 | |||
1728.2.s.g.575.10 | 24 | 8.5 | even | 2 | |||
1728.2.s.g.1151.9 | 24 | 72.5 | odd | 6 | |||
1728.2.s.g.1151.10 | 24 | 72.59 | even | 6 | |||
2592.2.c.c.2591.5 | 24 | 9.7 | even | 3 | |||
2592.2.c.c.2591.6 | 24 | 36.7 | odd | 6 | |||
2592.2.c.c.2591.19 | 24 | 9.2 | odd | 6 | |||
2592.2.c.c.2591.20 | 24 | 36.11 | even | 6 | |||
5184.2.c.m.5183.5 | 24 | 72.29 | odd | 6 | |||
5184.2.c.m.5183.6 | 24 | 72.11 | even | 6 | |||
5184.2.c.m.5183.19 | 24 | 72.61 | even | 6 | |||
5184.2.c.m.5183.20 | 24 | 72.43 | odd | 6 |