Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,2,Mod(49,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.n (of order \(8\), degree \(4\), 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: | \(3.06625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 337.3 | ||
Character | \(\chi\) | \(=\) | 384.337 |
Dual form | 384.2.n.a.49.3 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.923880 | − | 0.382683i | −0.533402 | − | 0.220942i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.00259461 | − | 0.00626394i | −0.00116034 | − | 0.00280132i | 0.923298 | − | 0.384084i | \(-0.125483\pi\) |
−0.924459 | + | 0.381282i | \(0.875483\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.41880 | − | 2.41880i | 0.914220 | − | 0.914220i | −0.0823812 | − | 0.996601i | \(-0.526253\pi\) |
0.996601 | + | 0.0823812i | \(0.0262525\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.707107 | + | 0.707107i | 0.235702 | + | 0.235702i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.29952 | + | 0.538278i | −0.391819 | + | 0.162297i | −0.569890 | − | 0.821721i | \(-0.693014\pi\) |
0.178071 | + | 0.984018i | \(0.443014\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.559497 | + | 1.35074i | −0.155176 | + | 0.374629i | −0.982280 | − | 0.187421i | \(-0.939987\pi\) |
0.827103 | + | 0.562050i | \(0.189987\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.00678004i | 0.00175060i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.82199i | − | 1.41204i | −0.708192 | − | 0.706020i | \(-0.750489\pi\) | ||
0.708192 | − | 0.706020i | \(-0.249511\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.67819 | − | 6.46573i | 0.614420 | − | 1.48334i | −0.243679 | − | 0.969856i | \(-0.578354\pi\) |
0.858099 | − | 0.513484i | \(-0.171646\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.16031 | + | 1.30904i | −0.689637 | + | 0.285657i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.178878 | − | 0.178878i | −0.0372987 | − | 0.0372987i | 0.688211 | − | 0.725510i | \(-0.258396\pi\) |
−0.725510 | + | 0.688211i | \(0.758396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.53550 | − | 3.53550i | 0.707100 | − | 0.707100i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.382683 | − | 0.923880i | −0.0736475 | − | 0.177801i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.72901 | + | 2.37303i | 1.06385 | + | 0.440661i | 0.844817 | − | 0.535056i | \(-0.179710\pi\) |
0.219034 | + | 0.975717i | \(0.429710\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.19719 | 1.11305 | 0.556524 | − | 0.830832i | \(-0.312135\pi\) | ||||
0.556524 | + | 0.830832i | \(0.312135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.40659 | 0.244855 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0214270 | − | 0.00887537i | −0.00362183 | − | 0.00150021i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.02932 | − | 4.89922i | −0.333619 | − | 0.805427i | −0.998299 | − | 0.0582992i | \(-0.981432\pi\) |
0.664680 | − | 0.747128i | \(-0.268568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.03381 | − | 1.03381i | 0.165543 | − | 0.165543i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.36712 | − | 3.36712i | −0.525856 | − | 0.525856i | 0.393478 | − | 0.919334i | \(-0.371272\pi\) |
−0.919334 | + | 0.393478i | \(0.871272\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.37558 | + | 3.88349i | −1.42976 | + | 0.592227i | −0.957293 | − | 0.289120i | \(-0.906637\pi\) |
−0.472470 | + | 0.881347i | \(0.656637\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.00259461 | − | 0.00626394i | 0.000386782 | − | 0.000933773i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.5050i | 1.82405i | 0.410137 | + | 0.912024i | \(0.365481\pi\) | ||||
−0.410137 | + | 0.912024i | \(0.634519\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 4.70117i | − | 0.671595i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.22798 | + | 5.37882i | −0.311979 | + | 0.753185i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.36811 | + | 3.46618i | −1.14945 | + | 0.476117i | −0.874348 | − | 0.485299i | \(-0.838711\pi\) |
−0.275100 | + | 0.961416i | \(0.588711\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.00674348 | + | 0.00674348i | 0.000909291 | + | 0.000909291i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.94866 | + | 4.94866i | −0.655465 | + | 0.655465i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.59507 | − | 3.85084i | −0.207661 | − | 0.501337i | 0.785393 | − | 0.618997i | \(-0.212461\pi\) |
−0.993054 | + | 0.117660i | \(0.962461\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.27395 | + | 3.01297i | 0.931333 | + | 0.385771i | 0.796184 | − | 0.605054i | \(-0.206849\pi\) |
0.135149 | + | 0.990825i | \(0.456849\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.42070 | 0.430967 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.00991266 | 0.00122951 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.38775 | + | 1.81747i | 0.536049 | + | 0.222039i | 0.634250 | − | 0.773128i | \(-0.281309\pi\) |
−0.0982011 | + | 0.995167i | \(0.531309\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0968082 | + | 0.233716i | 0.0116543 | + | 0.0281361i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.95188 | + | 5.95188i | −0.706358 | + | 0.706358i | −0.965768 | − | 0.259409i | \(-0.916472\pi\) |
0.259409 | + | 0.965768i | \(0.416472\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.85539 | + | 7.85539i | 0.919404 | + | 0.919404i | 0.996986 | − | 0.0775823i | \(-0.0247201\pi\) |
−0.0775823 | + | 0.996986i | \(0.524720\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.61936 | + | 1.91340i | −0.533397 | + | 0.220940i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.84128 | + | 4.44525i | −0.209834 | + | 0.506584i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.42456i | − | 0.160276i | −0.996784 | − | 0.0801378i | \(-0.974464\pi\) | ||
0.996784 | − | 0.0801378i | \(-0.0255360\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000i | 0.111111i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.03596 | − | 7.32946i | 0.333240 | − | 0.804513i | −0.665091 | − | 0.746763i | \(-0.731607\pi\) |
0.998331 | − | 0.0577507i | \(-0.0183929\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0364686 | + | 0.0151058i | −0.00395557 | + | 0.00163845i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.38479 | − | 4.38479i | −0.470099 | − | 0.470099i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.96127 | + | 9.96127i | −1.05589 | + | 1.05589i | −0.0575498 | + | 0.998343i | \(0.518329\pi\) |
−0.998343 | + | 0.0575498i | \(0.981671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.91387 | + | 4.62049i | 0.200628 | + | 0.484359i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.72545 | − | 2.37156i | −0.593702 | − | 0.245919i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0474498 | −0.00486825 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.24058 | −0.125961 | −0.0629807 | − | 0.998015i | \(-0.520061\pi\) | ||||
−0.0629807 | + | 0.998015i | \(0.520061\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.29952 | − | 0.538278i | −0.130606 | − | 0.0540989i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.15953 | + | 14.8704i | 0.612896 | + | 1.47966i | 0.859804 | + | 0.510624i | \(0.170585\pi\) |
−0.246908 | + | 0.969039i | \(0.579415\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.60558 | − | 5.60558i | 0.552334 | − | 0.552334i | −0.374779 | − | 0.927114i | \(-0.622282\pi\) |
0.927114 | + | 0.374779i | \(0.122282\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0163995 | + | 0.0163995i | 0.00160043 | + | 0.00160043i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.46375 | − | 2.26316i | 0.528201 | − | 0.218788i | −0.102614 | − | 0.994721i | \(-0.532721\pi\) |
0.630815 | + | 0.775933i | \(0.282721\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.982918 | + | 2.37297i | −0.0941464 | + | 0.227290i | −0.963936 | − | 0.266132i | \(-0.914254\pi\) |
0.869790 | + | 0.493422i | \(0.164254\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.30288i | 0.503327i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.42809i | − | 0.416560i | −0.978069 | − | 0.208280i | \(-0.933213\pi\) | ||
0.978069 | − | 0.208280i | \(-0.0667865\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.000656364 | 0.00158460i | −6.12062e−5 | 0.000147765i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.35074 | + | 0.559497i | −0.124876 | + | 0.0517255i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.0822 | − | 14.0822i | −1.29091 | − | 1.29091i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.37917 | + | 6.37917i | −0.579925 | + | 0.579925i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.82227 | + | 4.39936i | 0.164309 | + | 0.396677i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.0626391 | − | 0.0259460i | −0.00560261 | − | 0.00232068i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.5930 | −1.29492 | −0.647458 | − | 0.762101i | \(-0.724168\pi\) | ||||
−0.647458 | + | 0.762101i | \(0.724168\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.1481 | 0.893487 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.62727 | + | 3.57353i | 0.753768 | + | 0.312221i | 0.726278 | − | 0.687401i | \(-0.241248\pi\) |
0.0274902 | + | 0.999622i | \(0.491248\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.16129 | − | 22.1173i | −0.794384 | − | 1.91781i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.00479421 | + | 0.00479421i | −0.000412620 | + | 0.000412620i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.109126 | − | 0.109126i | −0.00932323 | − | 0.00932323i | 0.702430 | − | 0.711753i | \(-0.252098\pi\) |
−0.711753 | + | 0.702430i | \(0.752098\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.80724 | + | 2.40544i | −0.492564 | + | 0.204027i | −0.615118 | − | 0.788435i | \(-0.710892\pi\) |
0.122554 | + | 0.992462i | \(0.460892\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.78547 | − | 11.5532i | 0.403009 | − | 0.972951i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.05648i | − | 0.171971i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.0420433i | − | 0.00349150i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.79906 | + | 4.34331i | −0.148384 | + | 0.358230i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.4722 | − | 6.40879i | 1.26753 | − | 0.525028i | 0.355318 | − | 0.934745i | \(-0.384373\pi\) |
0.912213 | + | 0.409717i | \(0.134373\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.38822 | + | 9.38822i | 0.764003 | + | 0.764003i | 0.977043 | − | 0.213041i | \(-0.0683367\pi\) |
−0.213041 | + | 0.977043i | \(0.568337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.11677 | − | 4.11677i | 0.332821 | − | 0.332821i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.0160793 | − | 0.0388188i | −0.00129152 | − | 0.00311800i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.959615 | − | 0.397486i | −0.0765856 | − | 0.0317228i | 0.344062 | − | 0.938947i | \(-0.388197\pi\) |
−0.420647 | + | 0.907224i | \(0.638197\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.05757 | 0.718312 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.865341 | −0.0681984 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.39543 | + | 3.06329i | 0.579255 | + | 0.239935i | 0.653020 | − | 0.757340i | \(-0.273502\pi\) |
−0.0737655 | + | 0.997276i | \(0.523502\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.00364954 | − | 0.00881078i | −0.000284117 | − | 0.000685918i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.697073 | + | 0.697073i | −0.0539412 | + | 0.0539412i | −0.733563 | − | 0.679622i | \(-0.762144\pi\) |
0.679622 | + | 0.733563i | \(0.262144\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.68091 | + | 7.68091i | 0.590840 | + | 0.590840i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.46573 | − | 2.67819i | 0.494447 | − | 0.204807i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.61178 | − | 15.9623i | 0.502685 | − | 1.21359i | −0.445331 | − | 0.895366i | \(-0.646914\pi\) |
0.948016 | − | 0.318222i | \(-0.103086\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 17.1033i | − | 1.29289i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.16812i | 0.313295i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.14101 | + | 2.75465i | −0.0852832 | + | 0.205892i | −0.960768 | − | 0.277354i | \(-0.910542\pi\) |
0.875484 | + | 0.483246i | \(0.160542\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.23325 | + | 2.58190i | −0.463314 | + | 0.191911i | −0.602115 | − | 0.798409i | \(-0.705675\pi\) |
0.138801 | + | 0.990320i | \(0.455675\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.56724 | − | 5.56724i | −0.411542 | − | 0.411542i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0254231 | + | 0.0254231i | −0.00186915 | + | 0.00186915i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.13385 | + | 7.56577i | 0.229170 | + | 0.553264i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.16031 | − | 1.30904i | −0.229879 | − | 0.0952189i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.12197 | 0.370613 | 0.185306 | − | 0.982681i | \(-0.440672\pi\) | ||||
0.185306 | + | 0.982681i | \(0.440672\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.7951 | −1.49686 | −0.748431 | − | 0.663213i | \(-0.769192\pi\) | ||||
−0.748431 | + | 0.663213i | \(0.769192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.00915810 | − | 0.00379341i | −0.000655825 | − | 0.000271652i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.47339 | − | 8.38550i | −0.247469 | − | 0.597442i | 0.750519 | − | 0.660849i | \(-0.229804\pi\) |
−0.997988 | + | 0.0634065i | \(0.979804\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.79652 | + | 9.79652i | −0.694457 | + | 0.694457i | −0.963209 | − | 0.268753i | \(-0.913389\pi\) |
0.268753 | + | 0.963209i | \(0.413389\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.35824 | − | 3.35824i | −0.236872 | − | 0.236872i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.5972 | − | 8.11743i | 1.37545 | − | 0.569732i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0123551 | + | 0.0298278i | −0.000862917 | + | 0.00208326i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.252972i | − | 0.0175828i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.84394i | 0.680919i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.59646 | − | 6.26841i | 0.178748 | − | 0.431535i | −0.808957 | − | 0.587868i | \(-0.799967\pi\) |
0.987704 | + | 0.156333i | \(0.0499673\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.77651 | − | 3.22114i | 0.532838 | − | 0.220709i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.0486519 | + | 0.0486519i | 0.00331804 | + | 0.00331804i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.9897 | − | 14.9897i | 1.01757 | − | 1.01757i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.25131 | − | 10.2636i | −0.287277 | − | 0.693547i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.86402 | + | 3.25738i | 0.528991 | + | 0.219115i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.6051 | −0.978032 | −0.489016 | − | 0.872275i | \(-0.662644\pi\) | ||||
−0.489016 | + | 0.872275i | \(0.662644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.99995 | 0.333330 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.75119 | + | 1.55379i | 0.248975 | + | 0.103129i | 0.503681 | − | 0.863890i | \(-0.331979\pi\) |
−0.254706 | + | 0.967019i | \(0.581979\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.06540 | + | 4.98631i | 0.136485 | + | 0.329505i | 0.977314 | − | 0.211797i | \(-0.0679316\pi\) |
−0.840828 | + | 0.541302i | \(0.817932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.40225 | − | 3.40225i | 0.223852 | − | 0.223852i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.5003 | − | 20.5003i | −1.34302 | − | 1.34302i | −0.893035 | − | 0.449987i | \(-0.851428\pi\) |
−0.449987 | − | 0.893035i | \(-0.648572\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0783308 | − | 0.0324457i | 0.00510974 | − | 0.00211652i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.545156 | + | 1.31612i | −0.0354117 | + | 0.0854913i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.23671i | − | 0.144680i | −0.997380 | − | 0.0723402i | \(-0.976953\pi\) | ||
0.997380 | − | 0.0723402i | \(-0.0230467\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.6755i | 1.26741i | 0.773575 | + | 0.633704i | \(0.218466\pi\) | ||||
−0.773575 | + | 0.633704i | \(0.781534\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.382683 | − | 0.923880i | 0.0245492 | − | 0.0592669i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.0294478 | + | 0.0121977i | −0.00188135 | + | 0.000779282i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.23511 | + | 7.23511i | 0.460359 | + | 0.460359i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.60973 | + | 5.60973i | −0.355502 | + | 0.355502i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.41942 | − | 5.84100i | −0.152712 | − | 0.368680i | 0.828946 | − | 0.559329i | \(-0.188941\pi\) |
−0.981658 | + | 0.190648i | \(0.938941\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.328742 | + | 0.136169i | 0.0206678 | + | 0.00856088i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.0394733 | 0.00247191 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.46013 | 0.590106 | 0.295053 | − | 0.955481i | \(-0.404663\pi\) | ||||
0.295053 | + | 0.955481i | \(0.404663\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.7588 | − | 6.94170i | −1.04134 | − | 0.431336i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.37303 | + | 5.72901i | 0.146887 | + | 0.354617i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.01762 | − | 7.01762i | 0.432725 | − | 0.432725i | −0.456829 | − | 0.889554i | \(-0.651015\pi\) |
0.889554 | + | 0.456829i | \(0.151015\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0434239 | + | 0.0434239i | 0.00266751 | + | 0.00266751i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.0150 | − | 5.39100i | 0.796507 | − | 0.329924i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.579856 | − | 1.39990i | 0.0353545 | − | 0.0853532i | −0.905216 | − | 0.424952i | \(-0.860291\pi\) |
0.940571 | + | 0.339598i | \(0.110291\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.19594i | − | 0.133394i | −0.997773 | − | 0.0666969i | \(-0.978754\pi\) | ||
0.997773 | − | 0.0666969i | \(-0.0212460\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 5.00118i | − | 0.302685i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.69136 | + | 6.49753i | −0.162295 | + | 0.391816i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.0612 | − | 9.96649i | 1.44570 | − | 0.598829i | 0.484527 | − | 0.874776i | \(-0.338992\pi\) |
0.961173 | + | 0.275948i | \(0.0889916\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.38207 | + | 4.38207i | 0.262348 | + | 0.262348i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0180 | − | 18.0180i | 1.07487 | − | 1.07487i | 0.0779048 | − | 0.996961i | \(-0.475177\pi\) |
0.996961 | − | 0.0779048i | \(-0.0248230\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.15856 | + | 2.79702i | 0.0688695 | + | 0.166266i | 0.954566 | − | 0.297998i | \(-0.0963189\pi\) |
−0.885697 | + | 0.464264i | \(0.846319\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0438379 | + | 0.0181583i | 0.00259673 | + | 0.00107560i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.2888 | −0.961496 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8955 | −0.993855 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.14614 | + | 0.474748i | 0.0671881 | + | 0.0278302i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.52001 | + | 8.49805i | 0.205641 | + | 0.496461i | 0.992728 | − | 0.120381i | \(-0.0384116\pi\) |
−0.787087 | + | 0.616842i | \(0.788412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0199829 | + | 0.0199829i | −0.00116345 | + | 0.00116345i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.994607 | + | 0.994607i | 0.0577130 | + | 0.0577130i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.341700 | − | 0.141537i | 0.0197610 | − | 0.00818529i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.2843 | + | 32.0710i | −0.765692 | + | 1.84854i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 16.0956i | − | 0.924670i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 0.0533810i | − | 0.00305659i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.41754 | − | 3.42224i | 0.0809032 | − | 0.195318i | −0.878252 | − | 0.478198i | \(-0.841290\pi\) |
0.959155 | + | 0.282881i | \(0.0912900\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.32405 | + | 3.03372i | −0.416650 | + | 0.172582i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.4396 | + | 22.4396i | 1.27243 | + | 1.27243i | 0.944809 | + | 0.327622i | \(0.106247\pi\) |
0.327622 | + | 0.944809i | \(0.393753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.24961 | + | 2.24961i | −0.127155 | + | 0.127155i | −0.767821 | − | 0.640665i | \(-0.778659\pi\) |
0.640665 | + | 0.767821i | \(0.278659\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.00887537 | − | 0.0214270i | −0.000500071 | − | 0.00120728i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.4340 | − | 13.0204i | −1.76551 | − | 0.731298i | −0.995659 | − | 0.0930756i | \(-0.970330\pi\) |
−0.769852 | − | 0.638223i | \(-0.779670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.72230 | −0.488355 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.91392 | −0.330083 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −37.6434 | − | 15.5924i | −2.09453 | − | 0.867585i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.79746 | + | 6.75366i | 0.155175 | + | 0.374626i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.81620 | − | 1.81620i | 0.100436 | − | 0.100436i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.2472 | + | 30.2472i | 1.66758 | + | 1.66758i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6043 | + | 10.1914i | −1.35237 | + | 0.560172i | −0.936952 | − | 0.349457i | \(-0.886366\pi\) |
−0.415422 | + | 0.909629i | \(0.636366\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.02932 | − | 4.89922i | 0.111206 | − | 0.268476i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 0.0322002i | − | 0.00175929i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.1009i | 1.09497i | 0.836817 | + | 0.547483i | \(0.184414\pi\) | ||||
−0.836817 | + | 0.547483i | \(0.815586\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.69456 | + | 4.09103i | −0.0920358 | + | 0.222194i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.05335 | + | 3.33581i | −0.436113 | + | 0.180644i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.56041 | + | 5.56041i | 0.300234 | + | 0.300234i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.00121280 | − | 0.00121280i | 6.52950e−5 | − | 6.52950e-5i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.23707 | + | 12.6434i | 0.281141 | + | 0.678734i | 0.999863 | − | 0.0165638i | \(-0.00527266\pi\) |
−0.718722 | + | 0.695297i | \(0.755273\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.5877 | − | 6.87085i | −0.887920 | − | 0.367788i | −0.108357 | − | 0.994112i | \(-0.534559\pi\) |
−0.779563 | + | 0.626324i | \(0.784559\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.46203 | 0.0780377 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.8817 | 0.579174 | 0.289587 | − | 0.957152i | \(-0.406482\pi\) | ||||
0.289587 | + | 0.957152i | \(0.406482\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0527250 | + | 0.0218394i | 0.00279835 | + | 0.00115912i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.62124 | + | 18.3993i | 0.403359 | + | 0.973794i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.54201 | + | 5.54201i | −0.292496 | + | 0.292496i | −0.838066 | − | 0.545570i | \(-0.816313\pi\) |
0.545570 | + | 0.838066i | \(0.316313\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −21.1979 | − | 21.1979i | −1.11568 | − | 1.11568i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.33479 | − | 3.45238i | 0.437463 | − | 0.181203i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.0288240 | − | 0.0695874i | 0.00150872 | − | 0.00364237i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.99994i | 0.156596i | 0.996930 | + | 0.0782979i | \(0.0249485\pi\) | ||||
−0.996930 | + | 0.0782979i | \(0.975051\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 4.76183i | − | 0.247891i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.8568 | + | 28.6248i | −0.615572 | + | 1.48612i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.3503 | + | 6.35832i | −0.794811 | + | 0.329221i | −0.742876 | − | 0.669429i | \(-0.766539\pi\) |
−0.0519347 | + | 0.998650i | \(0.516539\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.0479419 | + | 0.0479419i | 0.00247571 | + | 0.00247571i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.41072 | + | 6.41072i | −0.330169 | + | 0.330169i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.50517 | + | 6.04801i | 0.128682 | + | 0.310665i | 0.975069 | − | 0.221903i | \(-0.0712269\pi\) |
−0.846387 | + | 0.532568i | \(0.821227\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.4821 | + | 5.58448i | 0.690711 | + | 0.286102i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.1450 | 1.64253 | 0.821266 | − | 0.570545i | \(-0.193268\pi\) | ||||
0.821266 | + | 0.570545i | \(0.193268\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0326222 | 0.00166258 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.37558 | − | 3.88349i | −0.476588 | − | 0.197409i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.48310 | + | 5.99473i | 0.125898 | + | 0.303945i | 0.974244 | − | 0.225498i | \(-0.0724010\pi\) |
−0.848346 | + | 0.529443i | \(0.822401\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.04143 | + | 1.04143i | −0.0526672 | + | 0.0526672i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.60303 | − | 6.60303i | −0.333079 | − | 0.333079i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.00892336 | + | 0.00369618i | −0.000448983 | + | 0.000185975i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.62118 | + | 23.2276i | −0.482873 | + | 1.16576i | 0.475365 | + | 0.879788i | \(0.342316\pi\) |
−0.958238 | + | 0.285970i | \(0.907684\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.9396i | 1.19848i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4.48158i | − | 0.223800i | −0.993719 | − | 0.111900i | \(-0.964306\pi\) | ||
0.993719 | − | 0.111900i | \(-0.0356936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.46730 | + | 8.37081i | −0.172719 | + | 0.416980i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.00626394 | − | 0.00259461i | 0.000311258 | − | 0.000128927i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.27428 | + | 5.27428i | 0.261437 | + | 0.261437i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.1171 | − | 22.1171i | 1.09362 | − | 1.09362i | 0.0984792 | − | 0.995139i | \(-0.468602\pi\) |
0.995139 | − | 0.0984792i | \(-0.0313978\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.0590584 | + | 0.142579i | 0.00291313 | + | 0.00703293i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.1726 | − | 5.45626i | −0.648180 | − | 0.268485i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0537885 | −0.00264037 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.28571 | 0.307813 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.59414 | + | 3.55981i | 0.419851 | + | 0.173908i | 0.582599 | − | 0.812760i | \(-0.302036\pi\) |
−0.162748 | + | 0.986668i | \(0.552036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.82429 | + | 18.8895i | 0.381333 | + | 0.920619i | 0.991709 | + | 0.128507i | \(0.0410184\pi\) |
−0.610376 | + | 0.792112i | \(0.708982\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.84240 | + | 8.84240i | −0.429932 | + | 0.429932i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.5836 | − | 20.5836i | −0.998453 | − | 0.998453i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.8820 | − | 10.3064i | 1.20412 | − | 0.498764i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.786981 | + | 1.89994i | −0.0379958 | + | 0.0917300i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17.2386i | − | 0.830353i | −0.909741 | − | 0.415177i | \(-0.863720\pi\) | ||
0.909741 | − | 0.415177i | \(-0.136280\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 20.8456i | − | 1.00177i | −0.865513 | − | 0.500887i | \(-0.833007\pi\) | ||
0.865513 | − | 0.500887i | \(-0.166993\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0160893 | + | 0.0388429i | −0.000771421 | + | 0.00186238i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.63565 | + | 0.677508i | −0.0782437 | + | 0.0324096i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.5583 | + | 11.5583i | 0.551648 | + | 0.551648i | 0.926916 | − | 0.375269i | \(-0.122450\pi\) |
−0.375269 | + | 0.926916i | \(0.622450\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.32423 | − | 3.32423i | 0.158297 | − | 0.158297i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.86432 | − | 18.9861i | −0.373645 | − | 0.902059i | −0.993126 | − | 0.117047i | \(-0.962657\pi\) |
0.619481 | − | 0.785011i | \(-0.287343\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.0882424 | + | 0.0365512i | 0.00418309 | + | 0.00173269i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.7470 | −0.792105 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.11825 | −0.0999665 | −0.0499832 | − | 0.998750i | \(-0.515917\pi\) | ||||
−0.0499832 | + | 0.998750i | \(0.515917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.18808 | + | 2.56319i | 0.291385 | + | 0.120696i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.08087 | − | 12.2663i | −0.238720 | − | 0.576321i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0239767 | − | 0.0239767i | 0.00112405 | − | 0.00112405i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.54089 | + | 7.54089i | 0.352748 | + | 0.352748i | 0.861131 | − | 0.508383i | \(-0.169757\pi\) |
−0.508383 | + | 0.861131i | \(0.669757\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.37882 | + | 2.22798i | −0.251062 | + | 0.103993i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.56851 | + | 3.78672i | −0.0730529 | + | 0.176365i | −0.956188 | − | 0.292754i | \(-0.905428\pi\) |
0.883135 | + | 0.469119i | \(0.155428\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.35374i | 0.388231i | 0.980979 | + | 0.194116i | \(0.0621837\pi\) | ||||
−0.980979 | + | 0.194116i | \(0.937816\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.0420172i | 0.00194850i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.8505 | + | 28.6097i | −0.548377 | + | 1.32390i | 0.370308 | + | 0.928909i | \(0.379252\pi\) |
−0.918685 | + | 0.394990i | \(0.870748\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.0092 | − | 6.21700i | 0.693059 | − | 0.287075i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.734458 | + | 0.734458i | 0.0338420 | + | 0.0338420i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.0933 | − | 10.0933i | 0.464092 | − | 0.464092i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.3908 | − | 32.3283i | −0.614414 | − | 1.48333i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.36811 | − | 3.46618i | −0.383149 | − | 0.158706i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.36086 | 0.199253 | 0.0996264 | − | 0.995025i | \(-0.468235\pi\) | ||||
0.0996264 | + | 0.995025i | \(0.468235\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.75299 | 0.353506 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.799470 | + | 0.331151i | 0.0363772 | + | 0.0150679i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.00321881 | + | 0.00777090i | 0.000146159 | + | 0.000352858i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.91861 | + | 7.91861i | −0.358827 | + | 0.358827i | −0.863380 | − | 0.504554i | \(-0.831657\pi\) |
0.504554 | + | 0.863380i | \(0.331657\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.66022 | − | 5.66022i | −0.255964 | − | 0.255964i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.8921 | + | 15.6954i | −1.71005 | + | 0.708324i | −0.710054 | + | 0.704147i | \(0.751329\pi\) |
−0.999991 | + | 0.00417652i | \(0.998671\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.8158 | − | 33.3542i | 0.622231 | − | 1.50220i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.00953672i | 0.000428644i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.7928i | 1.29153i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.18191 | − | 22.1671i | 0.411039 | − | 0.992336i | −0.573821 | − | 0.818981i | \(-0.694539\pi\) |
0.984859 | − | 0.173355i | \(-0.0554607\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.910770 | − | 0.377253i | 0.0406902 | − | 0.0168544i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.5963 | − | 16.5963i | −0.739995 | − | 0.739995i | 0.232582 | − | 0.972577i | \(-0.425283\pi\) |
−0.972577 | + | 0.232582i | \(0.925283\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.0771659 | − | 0.0771659i | 0.00343384 | − | 0.00343384i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.15688 | − | 10.0356i | −0.184614 | − | 0.445697i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.26058 | + | 2.17900i | 0.233171 | + | 0.0965826i | 0.496210 | − | 0.868203i | \(-0.334725\pi\) |
−0.263039 | + | 0.964785i | \(0.584725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.0012 | 1.68107 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.99846 | −0.308989 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.0496573 | − | 0.0205687i | −0.00218816 | − | 0.000906367i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.73118 | − | 16.2505i | −0.296037 | − | 0.714697i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.2170 | + | 12.2170i | −0.536266 | + | 0.536266i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.8290 | + | 13.8290i | 0.605861 | + | 0.605861i | 0.941862 | − | 0.336001i | \(-0.109074\pi\) |
−0.336001 | + | 0.941862i | \(0.609074\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.8657 | − | 8.64286i | 0.912393 | − | 0.377926i | 0.123421 | − | 0.992354i | \(-0.460613\pi\) |
0.788972 | + | 0.614429i | \(0.210613\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.54516 | + | 15.8014i | −0.285654 | + | 0.689630i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 36.0799i | − | 1.57167i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 22.9360i | − | 0.997218i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.59507 | − | 3.85084i | 0.0692202 | − | 0.167112i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.43201 | − | 2.66423i | 0.278601 | − | 0.115400i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.0283526 | − | 0.0283526i | −0.00122579 | − | 0.00122579i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.10832 | − | 2.10832i | 0.0909805 | − | 0.0909805i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.53053 | + | 6.10925i | 0.108998 | + | 0.263144i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.5863 | + | 10.1840i | 1.05705 | + | 0.437843i | 0.842402 | − | 0.538849i | \(-0.181141\pi\) |
0.214645 | + | 0.976692i | \(0.431141\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.74682 | 0.289534 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0174145 | 0.000745953 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.15022 | − | 3.79015i | −0.391235 | − | 0.162055i | 0.178389 | − | 0.983960i | \(-0.442911\pi\) |
−0.569625 | + | 0.821905i | \(0.692911\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.01297 | + | 7.27395i | 0.128590 | + | 0.310444i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.6868 | − | 30.6868i | 1.30730 | − | 1.30730i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.44572 | − | 3.44572i | −0.146527 | − | 0.146527i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.0332169 | − | 0.0137589i | 0.00140998 | − | 0.000584033i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.57099 | + | 6.20693i | −0.108936 | + | 0.262996i | −0.968942 | − | 0.247289i | \(-0.920460\pi\) |
0.860005 | + | 0.510285i | \(0.170460\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 14.8368i | − | 0.627530i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 8.18913i | − | 0.345746i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.2626 | − | 39.2615i | 0.685388 | − | 1.65467i | −0.0684842 | − | 0.997652i | \(-0.521816\pi\) |
0.753872 | − | 0.657021i | \(-0.228184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.0277373 | + | 0.0114892i | −0.00116692 | + | 0.000483353i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.41880 | + | 2.41880i | 0.101580 | + | 0.101580i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.1230 | + | 23.1230i | −0.969368 | + | 0.969368i | −0.999545 | − | 0.0301764i | \(-0.990393\pi\) |
0.0301764 | + | 0.999545i | \(0.490393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.47053 | + | 8.37861i | 0.145237 | + | 0.350634i | 0.979711 | − | 0.200413i | \(-0.0642285\pi\) |
−0.834474 | + | 0.551047i | \(0.814228\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.73208 | − | 1.96009i | −0.197686 | − | 0.0818841i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.26485 | −0.0527478 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.7910 | 0.782278 | 0.391139 | − | 0.920332i | \(-0.372081\pi\) | ||||
0.391139 | + | 0.920332i | \(0.372081\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.2121 | + | 7.95793i | 0.798429 | + | 0.330720i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.3851 | − | 25.0719i | −0.430847 | − | 1.04016i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00873 | − | 9.00873i | 0.373104 | − | 0.373104i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.00700931 | + | 0.00700931i | 0.000289799 | + | 0.000289799i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.1601 | − | 11.6643i | 1.16229 | − | 0.481436i | 0.283653 | − | 0.958927i | \(-0.408453\pi\) |
0.878637 | + | 0.477490i | \(0.158453\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.5973 | − | 40.0693i | 0.683878 | − | 1.65103i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.07640i | 0.373353i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.2535i | 0.503189i | 0.967833 | + | 0.251594i | \(0.0809549\pi\) | ||||
−0.967833 | + | 0.251594i | \(0.919045\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0516723 | + | 0.124748i | −0.00211836 | + | 0.00511417i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.7998 | − | 5.30184i | 0.523859 | − | 0.216990i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.63937 | − | 8.63937i | −0.352995 | − | 0.352995i | 0.508228 | − | 0.861223i | \(-0.330301\pi\) |
−0.861223 | + | 0.508228i | \(0.830301\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.3695 | + | 14.3695i | −0.586143 | + | 0.586143i | −0.936585 | − | 0.350441i | \(-0.886032\pi\) |
0.350441 | + | 0.936585i | \(0.386032\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.81747 | + | 4.38775i | 0.0740130 | + | 0.178683i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.0565102 | + | 0.0234073i | 0.00229747 | + | 0.000951642i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.4916 | −0.872319 | −0.436159 | − | 0.899869i | \(-0.643662\pi\) | ||||
−0.436159 | + | 0.899869i | \(0.643662\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.2119 | −0.859548 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.8911 | − | 6.99653i | −0.683341 | − | 0.283049i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.3921 | + | 29.9172i | 0.500513 | + | 1.20834i | 0.949205 | + | 0.314658i | \(0.101890\pi\) |
−0.448693 | + | 0.893686i | \(0.648110\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.0228292 | − | 0.0228292i | 0.000920563 | − | 0.000920563i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.5651 | + | 17.5651i | 0.707143 | + | 0.707143i | 0.965933 | − | 0.258790i | \(-0.0833239\pi\) |
−0.258790 | + | 0.965933i | \(0.583324\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.3569 | − | 6.77526i | 0.657440 | − | 0.272321i | −0.0289208 | − | 0.999582i | \(-0.509207\pi\) |
0.686361 | + | 0.727261i | \(0.259207\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0968082 | + | 0.233716i | −0.00388478 | + | 0.00937869i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 48.1886i | 1.93064i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 24.9993i | − | 0.999972i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.76711 | − | 9.09461i | 0.150444 | − | 0.363204i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28.5232 | + | 11.8147i | −1.13729 | + | 0.471083i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.6874 | − | 23.6874i | −0.942982 | − | 0.942982i | 0.0554784 | − | 0.998460i | \(-0.482332\pi\) |
−0.998460 | + | 0.0554784i | \(0.982332\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.79763 | + | 4.79763i | −0.190689 | + | 0.190689i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.0378630 | + | 0.0914094i | 0.00150255 | + | 0.00362747i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.35007 | + | 2.63029i | 0.251599 | + | 0.104216i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.41723 | −0.332981 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.79529 | 0.268398 | 0.134199 | − | 0.990954i | \(-0.457154\pi\) | ||||
0.134199 | + | 0.990954i | \(0.457154\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.4729 | + | 7.65173i | 0.728500 | + | 0.301755i | 0.715935 | − | 0.698166i | \(-0.246000\pi\) |
0.0125646 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0263302 | − | 0.0635668i | −0.00103675 | − | 0.00250294i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.34732 | − | 5.34732i | 0.210225 | − | 0.210225i | −0.594138 | − | 0.804363i | \(-0.702507\pi\) |
0.804363 | + | 0.594138i | \(0.202507\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.14565 | + | 4.14565i | 0.162731 | + | 0.162731i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.5850 | + | 8.11239i | −0.767598 | + | 0.317950i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.51225 | + | 3.65091i | −0.0591791 | + | 0.142871i | −0.950703 | − | 0.310102i | \(-0.899637\pi\) |
0.891524 | + | 0.452973i | \(0.149637\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 0.0633126i | − | 0.00247383i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.1092i | 0.433411i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.07771 | − | 17.0871i | 0.275708 | − | 0.665619i | −0.723999 | − | 0.689801i | \(-0.757698\pi\) |
0.999708 | + | 0.0241818i | \(0.00769807\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.2261 | − | 6.30685i | 0.592226 | − | 0.245308i | −0.0663821 | − | 0.997794i | \(-0.521146\pi\) |
0.658608 | + | 0.752486i | \(0.271146\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.01886 | − | 6.01886i | −0.233753 | − | 0.233753i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.114772 | + | 0.114772i | −0.00445065 | + | 0.00445065i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.600311 | − | 1.44928i | −0.0232441 | − | 0.0561163i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.4934 | + | 5.58914i | 0.521684 | + | 0.216089i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.0744 | −0.427524 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.46222 | 0.210553 | 0.105276 | − | 0.994443i | \(-0.466427\pi\) | ||||
0.105276 | + | 0.994443i | \(0.466427\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.61936 | − | 1.91340i | −0.177799 | − | 0.0736468i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.02477 | − | 9.71665i | −0.154684 | − | 0.373441i | 0.827472 | − | 0.561507i | \(-0.189778\pi\) |
−0.982156 | + | 0.188066i | \(0.939778\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.00070 | + | 3.00070i | −0.115156 | + | 0.115156i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.87104 | − | 2.87104i | −0.110018 | − | 0.110018i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.7212 | + | 16.4530i | −1.51989 | + | 0.629558i | −0.977569 | − | 0.210615i | \(-0.932453\pi\) |
−0.542319 | + | 0.840173i | \(0.682453\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.000400418 | 0 | 0.000966695i | −1.52992e−5 | 0 | 3.69355e-5i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 5.39714i | − | 0.205914i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 13.2425i | − | 0.504499i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.36888 | + | 17.7900i | −0.280325 | + | 0.676765i | −0.999843 | − | 0.0177088i | \(-0.994363\pi\) |
0.719518 | + | 0.694474i | \(0.244363\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.44525 | + | 1.84128i | −0.168861 | + | 0.0699446i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0301350 | + | 0.0301350i | 0.00114309 | + | 0.00114309i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.6033 | + | 19.6033i | −0.742529 | + | 0.742529i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.0947 | + | 26.7850i | 0.419640 | + | 1.01310i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.759834 | + | 0.314734i | 0.0286985 | + | 0.0118873i | 0.396987 | − | 0.917824i | \(-0.370056\pi\) |
−0.368288 | + | 0.929712i | \(0.620056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.1120 | −1.39970 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0847847 | −0.00319318 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 50.8672 | + | 21.0699i | 1.91306 | + | 0.792415i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.3991 | − | 44.4194i | −0.690994 | − | 1.66821i | −0.742768 | − | 0.669548i | \(-0.766488\pi\) |
0.0517745 | − | 0.998659i | \(-0.483512\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.00732 | − | 1.00732i | 0.0377773 | − | 0.0377773i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.10854 | − | 1.10854i | −0.0415152 | − | 0.0415152i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0128817 | + | 0.00533576i | −0.000481747 | + | 0.000199546i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.855950 | + | 2.06645i | −0.0319660 | + | 0.0771729i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.494401i | 0.0184380i | 0.999958 | + | 0.00921901i | \(0.00293455\pi\) | ||||
−0.999958 | + | 0.00921901i | \(0.997065\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 27.1175i | − | 1.00991i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.52948 | − | 18.1778i | 0.280024 | − | 0.676039i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.6448 | − | 11.8651i | 1.06384 | − | 0.440657i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.9621 | − | 13.9621i | −0.517826 | − | 0.517826i | 0.399087 | − | 0.916913i | \(-0.369327\pi\) |
−0.916913 | + | 0.399087i | \(0.869327\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.707107 | + | 0.707107i | −0.0261891 | + | 0.0261891i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.6097 | + | 54.5845i | 0.836248 | + | 2.01888i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.0117 | + | 8.70335i | 0.776087 | + | 0.321466i | 0.735335 | − | 0.677704i | \(-0.237025\pi\) |
0.0407515 | + | 0.999169i | \(0.487025\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0318741 | 0.00117569 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.68026 | −0.246071 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.9176 | + | 9.90698i | 0.879822 | + | 0.364434i | 0.776428 | − | 0.630206i | \(-0.217030\pi\) |
0.103394 | + | 0.994640i | \(0.467030\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.91561 | − | 9.45312i | −0.143844 | − | 0.347269i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.7644 | + | 22.7644i | −0.835144 | + | 0.835144i | −0.988215 | − | 0.153071i | \(-0.951084\pi\) |
0.153071 | + | 0.988215i | \(0.451084\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.0802886 | − | 0.0802886i | −0.00294155 | − | 0.00294155i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.32946 | − | 3.03596i | 0.268171 | − | 0.111080i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.74158 | − | 18.6898i | 0.282871 | − | 0.682912i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.4436i | 1.14739i | 0.819068 | + | 0.573697i | \(0.194491\pi\) | ||||
−0.819068 | + | 0.573697i | \(0.805509\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.32225i | 0.230396i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.0344485 | − | 0.0831660i | 0.00125371 | − | 0.00302672i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.6692 | + | 9.80412i | −0.860273 | + | 0.356337i | −0.768814 | − | 0.639472i | \(-0.779153\pi\) |
−0.0914586 | + | 0.995809i | \(0.529153\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.251608 | − | 0.251608i | −0.00913279 | − | 0.00913279i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.35154 | + | 5.35154i | −0.193993 | + | 0.193993i | −0.797419 | − | 0.603426i | \(-0.793802\pi\) |
0.603426 | + | 0.797419i | \(0.293802\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.36226 | + | 8.11722i | 0.121722 | + | 0.293863i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0364686 | − | 0.0151058i | −0.00131852 | − | 0.000546151i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.09394 | 0.220040 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.9993 | 0.613011 | 0.306505 | − | 0.951869i | \(-0.400840\pi\) | ||||
0.306505 | + | 0.951869i | \(0.400840\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.74002 | − | 3.62023i | −0.314764 | − | 0.130380i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.2444 | − | 39.2174i | −0.584269 | − | 1.41055i | −0.888910 | − | 0.458083i | \(-0.848536\pi\) |
0.304640 | − | 0.952467i | \(-0.401464\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.9102 | − | 21.9102i | 0.787036 | − | 0.787036i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.8266 | + | 12.8266i | 0.460151 | + | 0.460151i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.7887 | + | 12.7531i | −1.10312 | + | 0.456927i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.53081 | − | 10.9383i | 0.162125 | − | 0.391405i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 6.20104i | − | 0.221607i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.00704229i | 0.000251350i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.91880 | + | 4.63239i | −0.0683978 | + | 0.165127i | −0.954382 | − | 0.298589i | \(-0.903484\pi\) |
0.885984 | + | 0.463716i | \(0.153484\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.16896 | + | 3.79791i | −0.326424 | + | 0.135209i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.7107 | − | 10.7107i | −0.380827 | − | 0.380827i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.13949 | + | 8.13949i | −0.289042 | + | 0.289042i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0235009 | − | 0.0567361i | −0.000833490 | − | 0.00201222i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.85578 | − | 3.66818i | −0.313688 | − | 0.129934i | 0.220285 | − | 0.975436i | \(-0.429301\pi\) |
−0.533972 | + | 0.845502i | \(0.679301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 72.8042 | 2.57563 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.0874 | −0.497752 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.4366 | − | 5.97983i | −0.509456 | − | 0.211024i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.00224522 | + | 0.00542044i | 7.91336e−5 | + | 0.000191045i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.07143 | + | 1.07143i | −0.0377163 | + | 0.0377163i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.2208 | + | 13.2208i | 0.464819 | + | 0.464819i | 0.900231 | − | 0.435412i | \(-0.143397\pi\) |
−0.435412 | + | 0.900231i | \(0.643397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.46797 | − | 3.92176i | 0.332465 | − | 0.137712i | −0.210205 | − | 0.977657i | \(-0.567413\pi\) |
0.542671 | + | 0.839946i | \(0.317413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.840349 | + | 2.02878i | −0.0294723 | + | 0.0711525i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 0.0542726i | − | 0.00190109i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 71.0207i | 2.48470i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.91387 | + | 4.62049i | −0.0668760 | + | 0.161453i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.1649 | + | 19.5363i | −1.64607 | + | 0.681823i | −0.996889 | − | 0.0788144i | \(-0.974887\pi\) |
−0.649177 | + | 0.760637i | \(0.724887\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.1355 | − | 17.1355i | −0.597306 | − | 0.597306i | 0.342289 | − | 0.939595i | \(-0.388798\pi\) |
−0.939595 | + | 0.342289i | \(0.888798\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.97299 | − | 4.97299i | 0.173137 | − | 0.173137i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.74891 | − | 18.7075i | −0.269456 | − | 0.650524i | 0.730002 | − | 0.683445i | \(-0.239519\pi\) |
−0.999458 | + | 0.0329210i | \(0.989519\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.18250 | + | 0.904020i | 0.0758013 | + | 0.0313979i | 0.420262 | − | 0.907403i | \(-0.361938\pi\) |
−0.344461 | + | 0.938801i | \(0.611938\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.0437 | −0.903446 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.3701 | −0.948319 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.00617506 | + | 0.00255779i | 0.000213697 | + | 8.85161e-5i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.37156 | − | 5.72545i | −0.0819731 | − | 0.197901i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.2057 | + | 19.2057i | −0.663056 | + | 0.663056i | −0.956099 | − | 0.293043i | \(-0.905332\pi\) |
0.293043 | + | 0.956099i | \(0.405332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.68416 | + | 6.68416i | 0.230488 | + | 0.230488i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.5417 | + | 9.75129i | −0.810819 | + | 0.335852i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.0281838 | − | 0.0680418i | 0.000969553 | − | 0.00234071i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.8599i | 1.06036i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 3.02747i | − | 0.103903i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.513362 | + | 1.23937i | −0.0175978 | + | 0.0424849i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.6393 | + | 14.7623i | −1.22026 | + | 0.505450i | −0.897494 | − | 0.441027i | \(-0.854614\pi\) |
−0.322771 | + | 0.946477i | \(0.604614\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0335521 | − | 0.0335521i | −0.00114746 | − | 0.00114746i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.16918 | − | 8.16918i | 0.279054 | − | 0.279054i | −0.553677 | − | 0.832731i | \(-0.686776\pi\) |
0.832731 | + | 0.553677i | \(0.186776\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.26963 | − | 5.47938i | −0.0774389 | − | 0.186954i | 0.880419 | − | 0.474197i | \(-0.157261\pi\) |
−0.957858 | + | 0.287243i | \(0.907261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.0489 | + | 6.23344i | 0.512864 | + | 0.212435i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.5672 | −1.38092 | −0.690462 | − | 0.723369i | \(-0.742593\pi\) | ||||
−0.690462 | + | 0.723369i | \(0.742593\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.117142 | −0.00398294 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.6094 | + | 6.46564i | 0.530125 | + | 0.219585i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.766809 | + | 1.85124i | 0.0260122 | + | 0.0627991i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.90987 | + | 4.90987i | −0.166364 | + | 0.166364i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.877220 | − | 0.877220i | −0.0296894 | − | 0.0296894i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.214269 | + | 0.0887533i | −0.00724363 | + | 0.00300041i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.389401 | − | 0.940098i | 0.0131491 | − | 0.0317449i | −0.917169 | − | 0.398499i | \(-0.869531\pi\) |
0.930318 | + | 0.366755i | \(0.119531\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 9.19822i | − | 0.310248i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 19.7730i | − | 0.666169i | −0.942897 | − | 0.333085i | \(-0.891910\pi\) | ||
0.942897 | − | 0.333085i | \(-0.108090\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.09620 | + | 2.64647i | −0.0368902 | + | 0.0890608i | −0.941251 | − | 0.337708i | \(-0.890348\pi\) |
0.904361 | + | 0.426769i | \(0.140348\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0261089 | − | 0.0108147i | 0.000877641 | − | 0.000363531i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.5575 | + | 24.5575i | 0.824561 | + | 0.824561i | 0.986758 | − | 0.162198i | \(-0.0518582\pi\) |
−0.162198 | + | 0.986758i | \(0.551858\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.2974 | + | 35.2974i | −1.18384 | + | 1.18384i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.538278 | − | 1.29952i | −0.0180330 | − | 0.0435355i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 80.8542 | + | 33.4909i | 2.70568 | + | 1.12073i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0202154 | 0.000675727 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.369854 | −0.0123491 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.5037 | + | 14.7061i | 1.18412 | + | 0.490477i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.1801 | + | 48.7190i | 0.672296 | + | 1.62307i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.5461 | − | 24.5461i | 0.816843 | − | 0.816843i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.0323457 | + | 0.0323457i | 0.00107521 | + | 0.00107521i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.3745 | + | 8.43938i | −0.676523 | + | 0.280225i | −0.694373 | − | 0.719616i | \(-0.744318\pi\) |
0.0178494 | + | 0.999841i | \(0.494318\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.15953 | + | 14.8704i | −0.204299 | + | 0.493221i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 15.6069i | − | 0.517081i | −0.966000 | − | 0.258540i | \(-0.916758\pi\) | ||
0.966000 | − | 0.258540i | \(-0.0832415\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.1590i | 0.369308i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0204280 | + | 0.0493176i | −0.000675330 | + | 0.00163039i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.5113 | − | 12.2240i | 0.974548 | − | 0.403671i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.7928 | − | 37.7928i | −1.24667 | − | 1.24667i | −0.957181 | − | 0.289489i | \(-0.906515\pi\) |
−0.289489 | − | 0.957181i | \(-0.593485\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.61927 | + | 2.61927i | −0.0863078 | + | 0.0863078i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.70941 | − | 11.3695i | −0.155012 | − | 0.374233i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.4959 | − | 10.1465i | −0.805420 | − | 0.333616i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.92749 | 0.260373 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.36281 | 0.274375 | 0.137187 | − | 0.990545i | \(-0.456194\pi\) | ||||
0.137187 | + | 0.990545i | \(0.456194\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.3965 | − | 12.5906i | −0.996204 | − | 0.412641i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.1442 | − | 29.3187i | −0.397583 | − | 0.959851i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0392605 | − | 0.0392605i | 0.00128395 | − | 0.00128395i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.8809 | − | 37.8809i | −1.23752 | − | 1.23752i | −0.961013 | − | 0.276502i | \(-0.910825\pi\) |
−0.276502 | − | 0.961013i | \(-0.589175\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.93926 | − | 1.21748i | 0.0959190 | − | 0.0397310i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.7558 | + | 47.6947i | −0.644020 | + | 1.55480i | 0.177191 | + | 0.984176i | \(0.443299\pi\) |
−0.821211 | + | 0.570625i | \(0.806701\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.20461i | 0.0392275i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0231925i | 0.000754451i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.05678 | + | 4.96550i | −0.0668363 | + | 0.161357i | −0.953768 | − | 0.300543i | \(-0.902832\pi\) |
0.886932 | + | 0.461900i | \(0.152832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0057 | + | 6.21556i | −0.487105 | + | 0.201766i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.0586 | + | 24.0586i | 0.780152 | + | 0.780152i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.72605 | + | 4.72605i | −0.153092 | + | 0.153092i | −0.779497 | − | 0.626406i | \(-0.784525\pi\) |
0.626406 | + | 0.779497i | \(0.284525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0132895 | − | 0.0320837i | −0.000430038 | − | 0.00103820i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.05835 | + | 3.33788i | 0.260490 | + | 0.107898i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.527906 | −0.0170470 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.40512 | 0.238875 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.46375 | + | 2.26316i | 0.176067 | + | 0.0729293i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0539551 | + | 0.130259i | 0.00173688 | + | 0.00419319i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.3805 | + | 29.3805i | −0.944812 | + | 0.944812i | −0.998555 | − | 0.0537426i | \(-0.982885\pi\) |
0.0537426 | + | 0.998555i | \(0.482885\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.8110 | + | 28.8110i | 0.925543 | + | 0.925543i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.4822 | − | 9.31244i | 0.721489 | − | 0.298850i | 0.00843940 | − | 0.999964i | \(-0.497314\pi\) |
0.713049 | + | 0.701114i | \(0.247314\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.22827 | + | 19.8648i | −0.263786 | + | 0.636836i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 7.31011i | − | 0.234111i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 30.9704i | − | 0.990831i | −0.868656 | − | 0.495415i | \(-0.835016\pi\) | ||
0.868656 | − | 0.495415i | \(-0.164984\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.58291 | − | 18.3068i | 0.242351 | − | 0.585087i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.37297 | + | 0.982918i | −0.0757632 | + | 0.0313821i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.78738 | − | 8.78738i | −0.280274 | − | 0.280274i | 0.552944 | − | 0.833218i | \(-0.313504\pi\) |
−0.833218 | + | 0.552944i | \(0.813504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.0435142 | + | 0.0435142i | −0.00138648 | + | 0.00138648i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.3696 | − | 39.5198i | −0.521052 | − | 1.25793i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.37176 | + | 0.982415i | 0.0754176 | + | 0.0312390i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.3371 | 1.37665 | 0.688324 | − | 0.725403i | \(-0.258347\pi\) | ||||
0.688324 | + | 0.725403i | \(0.258347\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.6315 | 0.845125 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.0867829 | + | 0.0359467i | 0.00275120 | + | 0.00113959i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.40977 | + | 10.6461i | 0.139659 | + | 0.337166i | 0.978198 | − | 0.207675i | \(-0.0665897\pi\) |
−0.838539 | + | 0.544842i | \(0.816590\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.74970 | + | 3.74970i | −0.118635 | + | 0.118635i |
(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 | 384.2.n.a.337.3 | 32 | ||
3.2 | odd | 2 | 1152.2.v.c.721.5 | 32 | |||
4.3 | odd | 2 | 96.2.n.a.61.7 | ✓ | 32 | ||
8.3 | odd | 2 | 768.2.n.a.673.2 | 32 | |||
8.5 | even | 2 | 768.2.n.b.673.6 | 32 | |||
12.11 | even | 2 | 288.2.v.d.253.2 | 32 | |||
32.5 | even | 8 | 768.2.n.b.97.6 | 32 | |||
32.11 | odd | 8 | 96.2.n.a.85.7 | yes | 32 | ||
32.21 | even | 8 | inner | 384.2.n.a.49.3 | 32 | ||
32.27 | odd | 8 | 768.2.n.a.97.2 | 32 | |||
96.11 | even | 8 | 288.2.v.d.181.2 | 32 | |||
96.53 | odd | 8 | 1152.2.v.c.433.5 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.n.a.61.7 | ✓ | 32 | 4.3 | odd | 2 | ||
96.2.n.a.85.7 | yes | 32 | 32.11 | odd | 8 | ||
288.2.v.d.181.2 | 32 | 96.11 | even | 8 | |||
288.2.v.d.253.2 | 32 | 12.11 | even | 2 | |||
384.2.n.a.49.3 | 32 | 32.21 | even | 8 | inner | ||
384.2.n.a.337.3 | 32 | 1.1 | even | 1 | trivial | ||
768.2.n.a.97.2 | 32 | 32.27 | odd | 8 | |||
768.2.n.a.673.2 | 32 | 8.3 | odd | 2 | |||
768.2.n.b.97.6 | 32 | 32.5 | even | 8 | |||
768.2.n.b.673.6 | 32 | 8.5 | even | 2 | |||
1152.2.v.c.433.5 | 32 | 96.53 | odd | 8 | |||
1152.2.v.c.721.5 | 32 | 3.2 | odd | 2 |