Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(440,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.440");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.o (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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 440.3 | ||
Character | \(\chi\) | \(=\) | 1323.440 |
Dual form | 1323.2.o.e.881.3 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80506 | − | 1.04215i | −1.27637 | − | 0.736913i | −0.300191 | − | 0.953879i | \(-0.597050\pi\) |
−0.976179 | + | 0.216966i | \(0.930384\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.17216 | + | 2.03024i | 0.586081 | + | 1.01512i | ||||
\(5\) | −1.65233 | − | 2.86191i | −0.738942 | − | 1.27989i | −0.952972 | − | 0.303059i | \(-0.901992\pi\) |
0.214029 | − | 0.976827i | \(-0.431341\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 0.717672i | − | 0.253735i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.88790i | 2.17814i | ||||||||
\(11\) | −2.30482 | − | 1.33069i | −0.694929 | − | 0.401217i | 0.110527 | − | 0.993873i | \(-0.464746\pi\) |
−0.805456 | + | 0.592656i | \(0.798079\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.11249 | − | 1.21964i | 0.585899 | − | 0.338269i | −0.177576 | − | 0.984107i | \(-0.556825\pi\) |
0.763474 | + | 0.645839i | \(0.223492\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.59640 | − | 2.76504i | 0.399100 | − | 0.691261i | ||||
\(17\) | 7.18034 | 1.74149 | 0.870744 | − | 0.491736i | \(-0.163637\pi\) | ||||
0.870744 | + | 0.491736i | \(0.163637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.90454i | − | 1.12518i | −0.826736 | − | 0.562589i | \(-0.809805\pi\) | ||
0.826736 | − | 0.562589i | \(-0.190195\pi\) | |||||||
\(20\) | 3.87358 | − | 6.70924i | 0.866160 | − | 1.50023i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.77356 | + | 4.80394i | 0.591324 | + | 1.02420i | ||||
\(23\) | 4.32174 | − | 2.49516i | 0.901145 | − | 0.520276i | 0.0235732 | − | 0.999722i | \(-0.492496\pi\) |
0.877571 | + | 0.479446i | \(0.159162\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.96036 | + | 5.12749i | −0.592072 | + | 1.02550i | ||||
\(26\) | −5.08422 | −0.997098 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.50701 | − | 3.17947i | −1.02263 | − | 0.590413i | −0.107762 | − | 0.994177i | \(-0.534368\pi\) |
−0.914863 | + | 0.403764i | \(0.867702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.30833 | − | 1.33271i | 0.414588 | − | 0.239362i | −0.278171 | − | 0.960531i | \(-0.589728\pi\) |
0.692759 | + | 0.721169i | \(0.256395\pi\) | |||||||
\(32\) | −7.00624 | + | 4.04505i | −1.23854 | + | 0.715071i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.9609 | − | 7.48301i | −2.22278 | − | 1.28333i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.68957 | −0.277764 | −0.138882 | − | 0.990309i | \(-0.544351\pi\) | ||||
−0.138882 | + | 0.990309i | \(0.544351\pi\) | |||||||
\(38\) | −5.11128 | + | 8.85299i | −0.829159 | + | 1.43614i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.05391 | + | 1.18583i | −0.324752 | + | 0.187496i | ||||
\(41\) | −0.553137 | − | 0.958062i | −0.0863855 | − | 0.149624i | 0.819595 | − | 0.572943i | \(-0.194198\pi\) |
−0.905981 | + | 0.423319i | \(0.860865\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.93481 | − | 5.08323i | 0.447554 | − | 0.775186i | −0.550672 | − | 0.834721i | \(-0.685629\pi\) |
0.998226 | + | 0.0595356i | \(0.0189620\pi\) | |||||||
\(44\) | − | 6.23912i | − | 0.940582i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.4013 | −1.53359 | ||||||||
\(47\) | −2.44098 | + | 4.22790i | −0.356053 | + | 0.616703i | −0.987298 | − | 0.158881i | \(-0.949211\pi\) |
0.631244 | + | 0.775584i | \(0.282545\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 10.6873 | − | 6.17029i | 1.51141 | − | 0.872610i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.95235 | + | 2.85924i | 0.686767 | + | 0.396505i | ||||
\(53\) | − | 10.3232i | − | 1.41800i | −0.705210 | − | 0.708999i | \(-0.749147\pi\) | ||
0.705210 | − | 0.708999i | \(-0.250853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.79491i | 1.18591i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.62698 | + | 11.4783i | 0.870166 | + | 1.50717i | ||||
\(59\) | 2.56820 | + | 4.44826i | 0.334351 | + | 0.579114i | 0.983360 | − | 0.181667i | \(-0.0581494\pi\) |
−0.649009 | + | 0.760781i | \(0.724816\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.44613 | + | 2.56698i | 0.569269 | + | 0.328668i | 0.756857 | − | 0.653580i | \(-0.226734\pi\) |
−0.187588 | + | 0.982248i | \(0.560067\pi\) | |||||||
\(62\) | −5.55556 | −0.705556 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 10.4766 | 1.30958 | ||||||||
\(65\) | −6.98103 | − | 4.03050i | −0.865891 | − | 0.499922i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.16544 | − | 7.21476i | −0.508890 | − | 0.881423i | −0.999947 | − | 0.0102956i | \(-0.996723\pi\) |
0.491057 | − | 0.871127i | \(-0.336611\pi\) | |||||||
\(68\) | 8.41652 | + | 14.5778i | 1.02065 | + | 1.76782i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.07026i | 0.245695i | 0.992426 | + | 0.122848i | \(0.0392026\pi\) | ||||
−0.992426 | + | 0.122848i | \(0.960797\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.01491i | 0.938075i | 0.883178 | + | 0.469037i | \(0.155399\pi\) | ||||
−0.883178 | + | 0.469037i | \(0.844601\pi\) | |||||||
\(74\) | 3.04978 | + | 1.76079i | 0.354530 | + | 0.204688i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.95741 | − | 5.74891i | 1.14219 | − | 0.659445i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.50501 | + | 4.33881i | −0.281836 | + | 0.488155i | −0.971837 | − | 0.235654i | \(-0.924277\pi\) |
0.690001 | + | 0.723809i | \(0.257610\pi\) | |||||||
\(80\) | −10.5511 | −1.17965 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.30581i | 0.254634i | ||||||||
\(83\) | −1.04482 | + | 1.80968i | −0.114684 | + | 0.198638i | −0.917653 | − | 0.397382i | \(-0.869919\pi\) |
0.802970 | + | 0.596020i | \(0.203252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.8643 | − | 20.5495i | −1.28686 | − | 2.22891i | ||||
\(86\) | −10.5950 | + | 6.11703i | −1.14249 | + | 0.659616i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.954997 | + | 1.65410i | −0.101803 | + | 0.176328i | ||||
\(89\) | −1.08253 | −0.114748 | −0.0573741 | − | 0.998353i | \(-0.518273\pi\) | ||||
−0.0573741 | + | 0.998353i | \(0.518273\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.1315 | + | 5.84945i | 1.05629 | + | 0.609847i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.81223 | − | 5.08774i | 0.908912 | − | 0.524761i | ||||
\(95\) | −14.0364 | + | 8.10390i | −1.44010 | + | 0.831442i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.47203 | − | 5.46868i | −0.961739 | − | 0.555260i | −0.0650310 | − | 0.997883i | \(-0.520715\pi\) |
−0.896708 | + | 0.442623i | \(0.854048\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.8801 | −1.38801 | ||||||||
\(101\) | 0.263957 | − | 0.457188i | 0.0262647 | − | 0.0454919i | −0.852594 | − | 0.522573i | \(-0.824972\pi\) |
0.878859 | + | 0.477082i | \(0.158305\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.678733 | − | 0.391867i | 0.0668775 | − | 0.0386118i | −0.466188 | − | 0.884685i | \(-0.654373\pi\) |
0.533066 | + | 0.846074i | \(0.321040\pi\) | |||||||
\(104\) | −0.875305 | − | 1.51607i | −0.0858308 | − | 0.148663i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.7583 | + | 18.6340i | −1.04494 | + | 1.80989i | ||||
\(107\) | 5.35086i | 0.517288i | 0.965973 | + | 0.258644i | \(0.0832756\pi\) | ||||
−0.965973 | + | 0.258644i | \(0.916724\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.96522 | 0.571364 | 0.285682 | − | 0.958324i | \(-0.407780\pi\) | ||||
0.285682 | + | 0.958324i | \(0.407780\pi\) | |||||||
\(110\) | 9.16563 | − | 15.8753i | 0.873909 | − | 1.51365i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0024 | + | 5.77487i | −0.940944 | + | 0.543254i | −0.890256 | − | 0.455461i | \(-0.849475\pi\) |
−0.0506876 | + | 0.998715i | \(0.516141\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.2818 | − | 8.24562i | −1.33179 | − | 0.768908i | ||||
\(116\) | − | 14.9074i | − | 1.38412i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 10.7058i | − | 0.985551i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.95854 | − | 3.39230i | −0.178049 | − | 0.308391i | ||||
\(122\) | −5.35036 | − | 9.26709i | −0.484399 | − | 0.839003i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.41146 | + | 3.12431i | 0.485963 | + | 0.280571i | ||||
\(125\) | 3.04265 | 0.272143 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0954 | −1.69444 | −0.847221 | − | 0.531241i | \(-0.821726\pi\) | ||||
−0.847221 | + | 0.531241i | \(0.821726\pi\) | |||||||
\(128\) | −4.89849 | − | 2.82815i | −0.432970 | − | 0.249975i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.40079 | + | 14.5506i | 0.736798 | + | 1.27617i | ||||
\(131\) | −2.07563 | − | 3.59509i | −0.181349 | − | 0.314105i | 0.760991 | − | 0.648762i | \(-0.224713\pi\) |
−0.942340 | + | 0.334657i | \(0.891380\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 17.3641i | 1.50003i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 5.15313i | − | 0.441877i | ||||||
\(137\) | 5.45092 | + | 3.14709i | 0.465704 | + | 0.268874i | 0.714440 | − | 0.699697i | \(-0.246682\pi\) |
−0.248736 | + | 0.968571i | \(0.580015\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.32575 | − | 0.765423i | 0.112449 | − | 0.0649223i | −0.442721 | − | 0.896660i | \(-0.645987\pi\) |
0.555170 | + | 0.831737i | \(0.312653\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.15753 | − | 3.73695i | 0.181056 | − | 0.313598i | ||||
\(143\) | −6.49186 | −0.542877 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.0141i | 1.74513i | ||||||||
\(146\) | 8.35276 | − | 14.4674i | 0.691279 | − | 1.19733i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.98045 | − | 3.43025i | −0.162792 | − | 0.281965i | ||||
\(149\) | 4.63163 | − | 2.67407i | 0.379438 | − | 0.219069i | −0.298136 | − | 0.954523i | \(-0.596365\pi\) |
0.677574 | + | 0.735455i | \(0.263031\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.74384 | + | 9.94862i | −0.467427 | + | 0.809607i | −0.999307 | − | 0.0372121i | \(-0.988152\pi\) |
0.531880 | + | 0.846820i | \(0.321486\pi\) | |||||||
\(152\) | −3.51985 | −0.285498 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.62821 | − | 4.40415i | −0.612713 | − | 0.353750i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.77243 | − | 3.33271i | 0.460690 | − | 0.265979i | −0.251644 | − | 0.967820i | \(-0.580971\pi\) |
0.712334 | + | 0.701840i | \(0.247638\pi\) | |||||||
\(158\) | 9.04340 | − | 5.22121i | 0.719454 | − | 0.415377i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 23.1532 | + | 13.3675i | 1.83042 | + | 1.05679i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.0921 | −1.80871 | −0.904356 | − | 0.426778i | \(-0.859649\pi\) | ||||
−0.904356 | + | 0.426778i | \(0.859649\pi\) | |||||||
\(164\) | 1.29673 | − | 2.24601i | 0.101258 | − | 0.175384i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.77192 | − | 2.17772i | 0.292757 | − | 0.169024i | ||||
\(167\) | 7.95418 | + | 13.7770i | 0.615513 | + | 1.06610i | 0.990294 | + | 0.138986i | \(0.0443844\pi\) |
−0.374782 | + | 0.927113i | \(0.622282\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.52493 | + | 6.10536i | −0.271149 | + | 0.469643i | ||||
\(170\) | 49.4575i | 3.79321i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.7603 | 1.04921 | ||||||||
\(173\) | 9.33097 | − | 16.1617i | 0.709421 | − | 1.22875i | −0.255651 | − | 0.966769i | \(-0.582290\pi\) |
0.965072 | − | 0.261984i | \(-0.0843767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.35882 | + | 4.24861i | −0.554692 | + | 0.320251i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.95404 | + | 1.12816i | 0.146461 | + | 0.0845595i | ||||
\(179\) | 22.0307i | 1.64665i | 0.567568 | + | 0.823326i | \(0.307884\pi\) | ||||
−0.567568 | + | 0.823326i | \(0.692116\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6986i | 1.31552i | 0.753226 | + | 0.657762i | \(0.228497\pi\) | ||||
−0.753226 | + | 0.657762i | \(0.771503\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.79070 | − | 3.10159i | −0.132012 | − | 0.228652i | ||||
\(185\) | 2.79173 | + | 4.83541i | 0.205252 | + | 0.355507i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.5494 | − | 9.55479i | −1.21021 | − | 0.698715i | ||||
\(188\) | −11.4449 | −0.834704 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 33.7820 | 2.45080 | ||||||||
\(191\) | −13.2711 | − | 7.66209i | −0.960265 | − | 0.554409i | −0.0640104 | − | 0.997949i | \(-0.520389\pi\) |
−0.896255 | + | 0.443540i | \(0.853722\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9333 | − | 22.4012i | −0.930962 | − | 1.61247i | −0.781681 | − | 0.623678i | \(-0.785638\pi\) |
−0.149280 | − | 0.988795i | \(-0.547696\pi\) | |||||||
\(194\) | 11.3984 | + | 19.7426i | 0.818356 | + | 1.41744i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.18301i | − | 0.298027i | −0.988835 | − | 0.149014i | \(-0.952390\pi\) | ||
0.988835 | − | 0.149014i | \(-0.0476098\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 22.0077i | − | 1.56008i | −0.625729 | − | 0.780041i | \(-0.715198\pi\) | ||
0.625729 | − | 0.780041i | \(-0.284802\pi\) | |||||||
\(200\) | 3.67986 | + | 2.12457i | 0.260205 | + | 0.150230i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.952918 | + | 0.550168i | −0.0670471 | + | 0.0387097i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.82793 | + | 3.16606i | −0.127668 | + | 0.221127i | ||||
\(206\) | −1.63354 | −0.113814 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 7.78816i | − | 0.540012i | ||||||
\(209\) | −6.52641 | + | 11.3041i | −0.451441 | + | 0.781919i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2926 | + | 21.2914i | 0.846257 | + | 1.46576i | 0.884525 | + | 0.466493i | \(0.154483\pi\) |
−0.0382677 | + | 0.999268i | \(0.512184\pi\) | |||||||
\(212\) | 20.9586 | − | 12.1004i | 1.43944 | − | 0.831061i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.57641 | − | 9.65863i | 0.381196 | − | 0.660250i | ||||
\(215\) | −19.3970 | −1.32287 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.7676 | − | 6.21666i | −0.729272 | − | 0.421045i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −17.8558 | + | 10.3091i | −1.20384 | + | 0.695036i | ||||
\(221\) | 15.1684 | − | 8.75747i | 1.02034 | − | 0.589091i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.31908 | − | 4.22567i | −0.490122 | − | 0.282972i | 0.234503 | − | 0.972115i | \(-0.424654\pi\) |
−0.724625 | + | 0.689143i | \(0.757987\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.0732 | 1.60132 | ||||||||
\(227\) | 2.91475 | − | 5.04849i | 0.193458 | − | 0.335080i | −0.752936 | − | 0.658094i | \(-0.771363\pi\) |
0.946394 | + | 0.323014i | \(0.104696\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.15541 | − | 2.39913i | 0.274597 | − | 0.158539i | −0.356378 | − | 0.934342i | \(-0.615988\pi\) |
0.630975 | + | 0.775803i | \(0.282655\pi\) | |||||||
\(230\) | 17.1864 | + | 29.7677i | 1.13324 | + | 1.96282i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.28182 | + | 3.95223i | −0.149809 | + | 0.259476i | ||||
\(233\) | − | 23.0463i | − | 1.50981i | −0.655831 | − | 0.754907i | \(-0.727682\pi\) | ||
0.655831 | − | 0.754907i | \(-0.272318\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.1332 | 1.05241 | ||||||||
\(236\) | −6.02069 | + | 10.4281i | −0.391914 | + | 0.678815i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.91972 | + | 3.41775i | −0.382915 | + | 0.221076i | −0.679086 | − | 0.734059i | \(-0.737624\pi\) |
0.296171 | + | 0.955135i | \(0.404290\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.89112 | − | 2.24654i | −0.250649 | − | 0.144712i | 0.369412 | − | 0.929266i | \(-0.379559\pi\) |
−0.620061 | + | 0.784553i | \(0.712892\pi\) | |||||||
\(242\) | 8.16440i | 0.524828i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.0356i | 0.770503i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.98180 | − | 10.3608i | −0.380613 | − | 0.659241i | ||||
\(248\) | −0.956451 | − | 1.65662i | −0.0607347 | − | 0.105196i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.49217 | − | 3.17091i | −0.347355 | − | 0.200546i | ||||
\(251\) | 0.467438 | 0.0295044 | 0.0147522 | − | 0.999891i | \(-0.495304\pi\) | ||||
0.0147522 | + | 0.999891i | \(0.495304\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.2811 | −0.834975 | ||||||||
\(254\) | 34.4683 | + | 19.9003i | 2.16273 | + | 1.24866i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.58192 | − | 7.93613i | −0.286370 | − | 0.496008i | ||||
\(257\) | 10.7433 | + | 18.6079i | 0.670146 | + | 1.16073i | 0.977862 | + | 0.209249i | \(0.0671020\pi\) |
−0.307716 | + | 0.951478i | \(0.599565\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 18.8976i | − | 1.17198i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.65248i | 0.534552i | ||||||||
\(263\) | −9.60394 | − | 5.54484i | −0.592205 | − | 0.341909i | 0.173764 | − | 0.984787i | \(-0.444407\pi\) |
−0.765969 | + | 0.642878i | \(0.777740\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.5440 | + | 17.0572i | −1.81487 | + | 1.04782i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.76514 | − | 16.9137i | 0.596501 | − | 1.03317i | ||||
\(269\) | 22.0575 | 1.34487 | 0.672435 | − | 0.740156i | \(-0.265248\pi\) | ||||
0.672435 | + | 0.740156i | \(0.265248\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.74436i | − | 0.288199i | −0.989563 | − | 0.144100i | \(-0.953971\pi\) | ||
0.989563 | − | 0.144100i | \(-0.0460286\pi\) | |||||||
\(272\) | 11.4627 | − | 19.8540i | 0.695028 | − | 1.20382i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.55950 | − | 11.3614i | −0.396274 | − | 0.686366i | ||||
\(275\) | 13.6462 | − | 7.87862i | 0.822895 | − | 0.475099i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.21329 | − | 5.56558i | 0.193068 | − | 0.334404i | −0.753197 | − | 0.657794i | \(-0.771490\pi\) |
0.946265 | + | 0.323391i | \(0.104823\pi\) | |||||||
\(278\) | −3.19075 | −0.191368 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0883 | + | 9.86595i | 1.01940 | + | 0.588553i | 0.913931 | − | 0.405869i | \(-0.133031\pi\) |
0.105473 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.85087 | − | 2.80065i | 0.288354 | − | 0.166481i | −0.348845 | − | 0.937180i | \(-0.613426\pi\) |
0.637199 | + | 0.770699i | \(0.280093\pi\) | |||||||
\(284\) | −4.20314 | + | 2.42668i | −0.249410 | + | 0.143997i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.7182 | + | 6.76551i | 0.692912 | + | 0.400053i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.5573 | 2.03278 | ||||||||
\(290\) | 21.8999 | − | 37.9317i | 1.28600 | − | 2.22743i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −16.2722 | + | 9.39477i | −0.952260 | + | 0.549787i | ||||
\(293\) | −15.0393 | − | 26.0488i | −0.878603 | − | 1.52178i | −0.852875 | − | 0.522115i | \(-0.825143\pi\) |
−0.0257278 | − | 0.999669i | \(-0.508190\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.48701 | − | 14.6999i | 0.494133 | − | 0.855863i | ||||
\(296\) | 1.21256i | 0.0704787i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.1472 | −0.645738 | ||||||||
\(299\) | 6.08641 | − | 10.5420i | 0.351986 | − | 0.609658i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 20.7360 | − | 11.9719i | 1.19322 | − | 0.688906i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −13.5613 | − | 7.82960i | −0.777792 | − | 0.449059i | ||||
\(305\) | − | 16.9659i | − | 0.971466i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 23.4497i | − | 1.33835i | −0.743106 | − | 0.669173i | \(-0.766648\pi\) | ||
0.743106 | − | 0.669173i | \(-0.233352\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.17959 | + | 15.8995i | 0.521366 | + | 0.903032i | ||||
\(311\) | −8.35507 | − | 14.4714i | −0.473773 | − | 0.820599i | 0.525776 | − | 0.850623i | \(-0.323775\pi\) |
−0.999549 | + | 0.0300243i | \(0.990442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.8757 | + | 7.43377i | 0.727776 | + | 0.420182i | 0.817608 | − | 0.575775i | \(-0.195300\pi\) |
−0.0898319 | + | 0.995957i | \(0.528633\pi\) | |||||||
\(314\) | −13.8928 | −0.784014 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.7451 | −0.660715 | ||||||||
\(317\) | −1.96761 | − | 1.13600i | −0.110512 | − | 0.0638040i | 0.443725 | − | 0.896163i | \(-0.353657\pi\) |
−0.554237 | + | 0.832359i | \(0.686990\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.46176 | + | 14.6562i | 0.473768 | + | 0.820590i | ||||
\(320\) | −17.3108 | − | 29.9832i | −0.967704 | − | 1.67611i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 35.2163i | − | 1.95949i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.4423i | 0.801117i | ||||||||
\(326\) | 41.6826 | + | 24.0655i | 2.30859 | + | 1.33286i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.687575 | + | 0.396971i | −0.0379650 | + | 0.0219191i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.97440 | − | 10.3480i | 0.328383 | − | 0.568775i | −0.653808 | − | 0.756660i | \(-0.726830\pi\) |
0.982191 | + | 0.187885i | \(0.0601631\pi\) | |||||||
\(332\) | −4.89878 | −0.268855 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 33.1578i | − | 1.81432i | ||||||
\(335\) | −13.7653 | + | 23.8423i | −0.752080 | + | 1.30264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.34636 | + | 4.06402i | 0.127815 | + | 0.221381i | 0.922830 | − | 0.385208i | \(-0.125870\pi\) |
−0.795015 | + | 0.606590i | \(0.792537\pi\) | |||||||
\(338\) | 12.7254 | − | 7.34703i | 0.692172 | − | 0.399626i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 27.8137 | − | 48.1747i | 1.50841 | − | 2.61264i | ||||
\(341\) | −7.09369 | −0.384145 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.64810 | − | 2.10623i | −0.196692 | − | 0.113560i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −33.6859 | + | 19.4486i | −1.81097 | + | 1.04556i | ||||
\(347\) | −6.40529 | + | 3.69809i | −0.343854 | + | 0.198524i | −0.661975 | − | 0.749526i | \(-0.730281\pi\) |
0.318121 | + | 0.948050i | \(0.396948\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0496 | + | 10.4209i | 0.966171 | + | 0.557819i | 0.898067 | − | 0.439859i | \(-0.144972\pi\) |
0.0681042 | + | 0.997678i | \(0.478305\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21.5308 | 1.14760 | ||||||||
\(353\) | −3.54953 | + | 6.14797i | −0.188923 | + | 0.327224i | −0.944891 | − | 0.327384i | \(-0.893833\pi\) |
0.755969 | + | 0.654608i | \(0.227166\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.92491 | − | 3.42075i | 0.314462 | − | 0.181554i | ||||
\(356\) | −1.26890 | − | 2.19780i | −0.0672517 | − | 0.116483i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.9593 | − | 39.7668i | 1.21344 | − | 2.10174i | ||||
\(359\) | − | 9.89233i | − | 0.522097i | −0.965326 | − | 0.261049i | \(-0.915932\pi\) | ||
0.965326 | − | 0.261049i | \(-0.0840683\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.05452 | −0.266027 | ||||||||
\(362\) | 18.4446 | − | 31.9470i | 0.969426 | − | 1.67910i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.9380 | − | 13.2432i | 1.20063 | − | 0.693183i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.0321 | + | 15.6070i | 1.41107 | + | 0.814680i | 0.995489 | − | 0.0948779i | \(-0.0302461\pi\) |
0.415578 | + | 0.909558i | \(0.363579\pi\) | |||||||
\(368\) | − | 15.9331i | − | 0.830568i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 11.6376i | − | 0.605011i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5232 | − | 25.1549i | −0.751981 | − | 1.30247i | −0.946861 | − | 0.321642i | \(-0.895765\pi\) |
0.194881 | − | 0.980827i | \(-0.437568\pi\) | |||||||
\(374\) | 19.9151 | + | 34.4939i | 1.02978 | + | 1.78364i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.03425 | + | 1.75182i | 0.156479 | + | 0.0903434i | ||||
\(377\) | −15.5113 | −0.798873 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.518354 | −0.0266261 | −0.0133130 | − | 0.999911i | \(-0.504238\pi\) | ||||
−0.0133130 | + | 0.999911i | \(0.504238\pi\) | |||||||
\(380\) | −32.9058 | − | 18.9981i | −1.68803 | − | 0.974584i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.9701 | + | 27.6611i | 0.817102 | + | 1.41526i | ||||
\(383\) | −6.60511 | − | 11.4404i | −0.337505 | − | 0.584576i | 0.646458 | − | 0.762950i | \(-0.276250\pi\) |
−0.983963 | + | 0.178374i | \(0.942916\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 53.9140i | 2.74415i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 25.6407i | − | 1.30171i | ||||||
\(389\) | 29.2921 | + | 16.9118i | 1.48517 | + | 0.857461i | 0.999857 | − | 0.0168815i | \(-0.00537382\pi\) |
0.485309 | + | 0.874343i | \(0.338707\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.0316 | − | 17.9161i | 1.56933 | − | 0.906055i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.35933 | + | 7.55059i | −0.219620 | + | 0.380393i | ||||
\(395\) | 16.5564 | 0.833043 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.57345i | 0.430289i | 0.976582 | + | 0.215145i | \(0.0690223\pi\) | ||||
−0.976582 | + | 0.215145i | \(0.930978\pi\) | |||||||
\(398\) | −22.9353 | + | 39.7251i | −1.14964 | + | 1.99124i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.45183 | + | 16.3710i | 0.472591 | + | 0.818552i | ||||
\(401\) | −13.9743 | + | 8.06808i | −0.697844 | + | 0.402900i | −0.806544 | − | 0.591174i | \(-0.798665\pi\) |
0.108700 | + | 0.994075i | \(0.465331\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.25087 | − | 5.63068i | 0.161938 | − | 0.280484i | ||||
\(404\) | 1.23760 | 0.0615730 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.89416 | + | 2.24830i | 0.193026 | + | 0.111444i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.1364 | − | 8.16165i | 0.699000 | − | 0.403568i | −0.107975 | − | 0.994154i | \(-0.534437\pi\) |
0.806975 | + | 0.590586i | \(0.201103\pi\) | |||||||
\(410\) | 6.59903 | − | 3.80995i | 0.325903 | − | 0.188160i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.59117 | + | 0.918662i | 0.0783913 | + | 0.0452592i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.90551 | 0.338978 | ||||||||
\(416\) | −9.86706 | + | 17.0902i | −0.483772 | + | 0.837918i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 23.5611 | − | 13.6030i | 1.15241 | − | 0.665345i | ||||
\(419\) | 0.589031 | + | 1.02023i | 0.0287760 | + | 0.0498415i | 0.880055 | − | 0.474872i | \(-0.157506\pi\) |
−0.851279 | + | 0.524714i | \(0.824172\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.43544 | − | 5.95035i | 0.167433 | − | 0.290002i | −0.770084 | − | 0.637943i | \(-0.779786\pi\) |
0.937517 | + | 0.347941i | \(0.113119\pi\) | |||||||
\(422\) | − | 51.2430i | − | 2.49447i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.40866 | −0.359796 | ||||||||
\(425\) | −21.2564 | + | 36.8172i | −1.03109 | + | 1.78589i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10.8636 | + | 6.27208i | −0.525110 | + | 0.303172i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 35.0128 | + | 20.2146i | 1.68847 | + | 0.974837i | ||||
\(431\) | 0.811164i | 0.0390724i | 0.999809 | + | 0.0195362i | \(0.00621896\pi\) | ||||
−0.999809 | + | 0.0195362i | \(0.993781\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.59662i | − | 0.413127i | −0.978433 | − | 0.206564i | \(-0.933772\pi\) | ||
0.978433 | − | 0.206564i | \(-0.0662280\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.99219 | + | 12.1108i | 0.334865 | + | 0.580004i | ||||
\(437\) | −12.2376 | − | 21.1961i | −0.585404 | − | 1.01395i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.8968 | − | 13.7968i | −1.14053 | − | 0.658486i | −0.193969 | − | 0.981008i | \(-0.562136\pi\) |
−0.946562 | + | 0.322522i | \(0.895470\pi\) | |||||||
\(440\) | 6.31186 | 0.300906 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −36.5065 | −1.73643 | ||||||||
\(443\) | 10.6051 | + | 6.12286i | 0.503864 | + | 0.290906i | 0.730308 | − | 0.683118i | \(-0.239377\pi\) |
−0.226444 | + | 0.974024i | \(0.572710\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.78870 | + | 3.09811i | 0.0847924 | + | 0.146865i | ||||
\(446\) | 8.80759 | + | 15.2552i | 0.417051 | + | 0.722354i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.0163i | − | 1.03901i | −0.854466 | − | 0.519507i | \(-0.826116\pi\) | ||
0.854466 | − | 0.519507i | \(-0.173884\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.94421i | 0.138637i | ||||||||
\(452\) | −23.4488 | − | 13.5382i | −1.10294 | − | 0.636781i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.5226 | + | 6.07522i | −0.493849 | + | 0.285124i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.0780 | + | 20.9196i | −0.564983 | + | 0.978579i | 0.432069 | + | 0.901841i | \(0.357784\pi\) |
−0.997051 | + | 0.0767380i | \(0.975550\pi\) | |||||||
\(458\) | −10.0010 | −0.467317 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 38.6608i | − | 1.80257i | ||||||
\(461\) | 16.3899 | − | 28.3881i | 0.763352 | − | 1.32216i | −0.177762 | − | 0.984074i | \(-0.556886\pi\) |
0.941114 | − | 0.338091i | \(-0.109781\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.7659 | + | 27.3074i | 0.732704 | + | 1.26908i | 0.955723 | + | 0.294266i | \(0.0950753\pi\) |
−0.223020 | + | 0.974814i | \(0.571591\pi\) | |||||||
\(464\) | −17.5828 | + | 10.1514i | −0.816259 | + | 0.471267i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.0178 | + | 41.6000i | −1.11260 | + | 1.92708i | ||||
\(467\) | −33.1531 | −1.53414 | −0.767070 | − | 0.641563i | \(-0.778286\pi\) | ||||
−0.767070 | + | 0.641563i | \(0.778286\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −29.1213 | − | 16.8132i | −1.34327 | − | 0.775536i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.19239 | − | 1.84313i | 0.146942 | − | 0.0848368i | ||||
\(473\) | −13.5284 | + | 7.81062i | −0.622036 | + | 0.359133i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.1480 | + | 14.5192i | 1.15387 | + | 0.666187i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.2473 | 0.651655 | ||||||||
\(479\) | −11.3972 | + | 19.7406i | −0.520754 | + | 0.901972i | 0.478955 | + | 0.877839i | \(0.341016\pi\) |
−0.999709 | + | 0.0241323i | \(0.992318\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.56921 | + | 2.06068i | −0.162742 | + | 0.0939590i | ||||
\(482\) | 4.68247 | + | 8.11027i | 0.213281 | + | 0.369413i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.59146 | − | 7.95264i | 0.208703 | − | 0.361484i | ||||
\(485\) | 36.1441i | 1.64122i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.73119 | −0.123762 | −0.0618811 | − | 0.998084i | \(-0.519710\pi\) | ||||
−0.0618811 | + | 0.998084i | \(0.519710\pi\) | |||||||
\(488\) | 1.84225 | − | 3.19087i | 0.0833946 | − | 0.144444i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.6775 | + | 12.5155i | −0.978291 | + | 0.564817i | −0.901754 | − | 0.432250i | \(-0.857720\pi\) |
−0.0765375 | + | 0.997067i | \(0.524387\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −39.5422 | − | 22.8297i | −1.78089 | − | 1.02820i | ||||
\(494\) | 24.9358i | 1.12191i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.51016i | − | 0.382118i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.29981 | − | 7.44749i | −0.192486 | − | 0.333395i | 0.753588 | − | 0.657348i | \(-0.228322\pi\) |
−0.946073 | + | 0.323952i | \(0.894988\pi\) | |||||||
\(500\) | 3.56648 | + | 6.17732i | 0.159498 | + | 0.276258i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.843754 | − | 0.487141i | −0.0376586 | − | 0.0217422i | ||||
\(503\) | 39.0362 | 1.74054 | 0.870269 | − | 0.492577i | \(-0.163945\pi\) | ||||
0.870269 | + | 0.492577i | \(0.163945\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.74457 | −0.0776325 | ||||||||
\(506\) | 23.9732 | + | 13.8409i | 1.06574 | + | 0.615304i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22.3829 | − | 38.7683i | −0.993079 | − | 1.72006i | ||||
\(509\) | −16.2909 | − | 28.2167i | −0.722083 | − | 1.25068i | −0.960163 | − | 0.279439i | \(-0.909851\pi\) |
0.238080 | − | 0.971245i | \(-0.423482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 30.4128i | 1.34407i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 44.7844i | − | 1.97536i | ||||||
\(515\) | −2.24298 | − | 1.29498i | −0.0988373 | − | 0.0570638i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.2520 | − | 6.49636i | 0.494864 | − | 0.285710i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.89258 | + | 5.01009i | −0.126848 | + | 0.219707i | ||||
\(521\) | −7.36912 | −0.322847 | −0.161424 | − | 0.986885i | \(-0.551609\pi\) | ||||
−0.161424 | + | 0.986885i | \(0.551609\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.4157i | 1.89843i | 0.314622 | + | 0.949217i | \(0.398122\pi\) | ||||
−0.314622 | + | 0.949217i | \(0.601878\pi\) | |||||||
\(524\) | 4.86594 | − | 8.42806i | 0.212570 | − | 0.368181i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.5571 | + | 20.0175i | 0.503915 | + | 0.872806i | ||||
\(527\) | 16.5746 | − | 9.56933i | 0.722000 | − | 0.416847i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.951610 | − | 1.64824i | 0.0413744 | − | 0.0716625i | ||||
\(530\) | 71.1050 | 3.08860 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.33699 | − | 1.34926i | −0.101226 | − | 0.0584430i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.3137 | − | 8.84137i | 0.662069 | − | 0.382246i | ||||
\(536\) | −5.17783 | + | 2.98942i | −0.223648 | + | 0.129123i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −39.8151 | − | 22.9873i | −1.71655 | − | 0.991052i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.6442 | −0.930555 | −0.465278 | − | 0.885165i | \(-0.654045\pi\) | ||||
−0.465278 | + | 0.885165i | \(0.654045\pi\) | |||||||
\(542\) | −4.94434 | + | 8.56385i | −0.212378 | + | 0.367849i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −50.3072 | + | 29.0449i | −2.15690 | + | 1.24529i | ||||
\(545\) | −9.85648 | − | 17.0719i | −0.422205 | − | 0.731281i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.9092 | + | 20.6273i | −0.509200 | + | 0.881960i | 0.490743 | + | 0.871304i | \(0.336725\pi\) |
−0.999943 | + | 0.0106561i | \(0.996608\pi\) | |||||||
\(548\) | 14.7556i | 0.630328i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −32.8429 | −1.40043 | ||||||||
\(551\) | −15.5938 | + | 27.0093i | −0.664320 | + | 1.15064i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −11.6004 | + | 6.69748i | −0.492852 | + | 0.284548i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.10799 | + | 1.79440i | 0.131808 | + | 0.0760994i | ||||
\(557\) | 10.8777i | 0.460905i | 0.973084 | + | 0.230452i | \(0.0740206\pi\) | ||||
−0.973084 | + | 0.230452i | \(0.925979\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 14.3177i | − | 0.605574i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.5636 | − | 35.6173i | −0.867425 | − | 1.50242i | ||||
\(563\) | −6.67759 | − | 11.5659i | −0.281427 | − | 0.487445i | 0.690310 | − | 0.723514i | \(-0.257474\pi\) |
−0.971736 | + | 0.236069i | \(0.924141\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.0543 | + | 19.0839i | 1.39061 | + | 0.802867i | ||||
\(566\) | −11.6748 | −0.490729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.48577 | 0.0623415 | ||||||||
\(569\) | −8.34729 | − | 4.81931i | −0.349937 | − | 0.202036i | 0.314721 | − | 0.949184i | \(-0.398089\pi\) |
−0.664657 | + | 0.747148i | \(0.731422\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.2031 | + | 29.7966i | 0.719926 | + | 1.24695i | 0.961028 | + | 0.276449i | \(0.0891578\pi\) |
−0.241102 | + | 0.970500i | \(0.577509\pi\) | |||||||
\(572\) | −7.60951 | − | 13.1801i | −0.318170 | − | 0.551086i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.5462i | 1.23216i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.1352i | 1.00476i | 0.864647 | + | 0.502381i | \(0.167542\pi\) | ||||
−0.864647 | + | 0.502381i | \(0.832458\pi\) | |||||||
\(578\) | −62.3780 | − | 36.0140i | −2.59458 | − | 1.49798i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −42.6637 | + | 24.6319i | −1.77151 | + | 1.02278i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.7369 | + | 23.7930i | −0.568925 | + | 0.985407i | ||||
\(584\) | 5.75208 | 0.238023 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 62.6928i | 2.58981i | ||||||||
\(587\) | 3.96848 | − | 6.87362i | 0.163797 | − | 0.283704i | −0.772431 | − | 0.635099i | \(-0.780959\pi\) |
0.936227 | + | 0.351395i | \(0.114293\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.53634 | − | 11.3213i | −0.269325 | − | 0.466485i | ||||
\(590\) | −30.6391 | + | 17.6895i | −1.26139 | + | 0.728266i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.69724 | + | 4.67175i | −0.110856 | + | 0.192008i | ||||
\(593\) | 41.8293 | 1.71772 | 0.858862 | − | 0.512207i | \(-0.171172\pi\) | ||||
0.858862 | + | 0.512207i | \(0.171172\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.8580 | + | 6.26889i | 0.444763 | + | 0.256784i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −21.9727 | + | 12.6859i | −0.898529 | + | 0.518766i | ||||
\(599\) | 7.57344 | − | 4.37253i | 0.309442 | − | 0.178657i | −0.337235 | − | 0.941421i | \(-0.609492\pi\) |
0.646677 | + | 0.762764i | \(0.276158\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.6427 | + | 7.29924i | 0.515705 | + | 0.297742i | 0.735176 | − | 0.677877i | \(-0.237100\pi\) |
−0.219471 | + | 0.975619i | \(0.570433\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −26.9308 | −1.09580 | ||||||||
\(605\) | −6.47230 | + | 11.2104i | −0.263137 | + | 0.455766i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.51436 | + | 5.49312i | −0.386176 | + | 0.222959i | −0.680502 | − | 0.732746i | \(-0.738238\pi\) |
0.294326 | + | 0.955705i | \(0.404905\pi\) | |||||||
\(608\) | 19.8391 | + | 34.3624i | 0.804583 | + | 1.39358i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.6811 | + | 30.6245i | −0.715885 | + | 1.23995i | ||||
\(611\) | 11.9085i | 0.481767i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.8135 | 0.961818 | 0.480909 | − | 0.876770i | \(-0.340307\pi\) | ||||
0.480909 | + | 0.876770i | \(0.340307\pi\) | |||||||
\(614\) | −24.4382 | + | 42.3282i | −0.986244 | + | 1.70823i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.5255 | − | 21.0880i | 1.47046 | − | 0.848971i | 0.471011 | − | 0.882127i | \(-0.343889\pi\) |
0.999450 | + | 0.0331557i | \(0.0105557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.6532 | + | 13.0789i | 0.910511 | + | 0.525683i | 0.880595 | − | 0.473869i | \(-0.157143\pi\) |
0.0299151 | + | 0.999552i | \(0.490476\pi\) | |||||||
\(620\) | − | 20.6495i | − | 0.829304i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 34.8290i | 1.39652i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.77434 | + | 16.9297i | 0.390974 | + | 0.677186i | ||||
\(626\) | −15.4942 | − | 26.8368i | −0.619274 | − | 1.07261i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.5324 | + | 7.81295i | 0.540003 | + | 0.311771i | ||||
\(629\) | −12.1317 | −0.483724 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.2419 | −0.766009 | −0.383004 | − | 0.923746i | \(-0.625111\pi\) | ||||
−0.383004 | + | 0.923746i | \(0.625111\pi\) | |||||||
\(632\) | 3.11385 | + | 1.79778i | 0.123862 | + | 0.0715118i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.36776 | + | 4.10109i | 0.0940359 | + | 0.162875i | ||||
\(635\) | 31.5518 | + | 54.6493i | 1.25209 | + | 2.16869i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 35.2738i | − | 1.39650i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.6921i | 0.738869i | ||||||||
\(641\) | −15.2483 | − | 8.80362i | −0.602272 | − | 0.347722i | 0.167663 | − | 0.985844i | \(-0.446378\pi\) |
−0.769935 | + | 0.638122i | \(0.779711\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.1158 | + | 24.8929i | −1.70032 | + | 0.981680i | −0.754893 | + | 0.655848i | \(0.772311\pi\) |
−0.945428 | + | 0.325832i | \(0.894355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −36.7007 | + | 63.5675i | −1.44397 | + | 2.50103i | ||||
\(647\) | 11.5407 | 0.453712 | 0.226856 | − | 0.973928i | \(-0.427155\pi\) | ||||
0.226856 | + | 0.973928i | \(0.427155\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 13.6699i | − | 0.536590i | ||||||
\(650\) | 15.0511 | − | 26.0693i | 0.590354 | − | 1.02252i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −27.0677 | − | 46.8826i | −1.06005 | − | 1.83606i | ||||
\(653\) | −18.2249 | + | 10.5222i | −0.713197 | + | 0.411765i | −0.812244 | − | 0.583318i | \(-0.801754\pi\) |
0.0990464 | + | 0.995083i | \(0.468421\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.85923 | + | 11.8805i | −0.268012 | + | 0.464211i | ||||
\(656\) | −3.53211 | −0.137906 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.8016 | + | 18.3607i | 1.23881 | + | 0.715230i | 0.968852 | − | 0.247641i | \(-0.0796555\pi\) |
0.269962 | + | 0.962871i | \(0.412989\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.9819 | − | 11.5365i | 0.777205 | − | 0.448719i | −0.0582339 | − | 0.998303i | \(-0.518547\pi\) |
0.835439 | + | 0.549583i | \(0.185214\pi\) | |||||||
\(662\) | −21.5683 | + | 12.4525i | −0.838276 | + | 0.483979i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.29875 | + | 0.749836i | 0.0504015 | + | 0.0290993i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.7331 | −1.22871 | ||||||||
\(668\) | −18.6472 | + | 32.2978i | −0.721480 | + | 1.24964i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 49.6945 | − | 28.6911i | 1.91987 | − | 1.10844i | ||||
\(671\) | −6.83168 | − | 11.8328i | −0.263734 | − | 0.456801i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.7594 | − | 42.8846i | 0.954406 | − | 1.65308i | 0.218684 | − | 0.975796i | \(-0.429824\pi\) |
0.735722 | − | 0.677284i | \(-0.236843\pi\) | |||||||
\(674\) | − | 9.78107i | − | 0.376753i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.5272 | −0.635660 | ||||||||
\(677\) | 14.9077 | − | 25.8208i | 0.572948 | − | 0.992374i | −0.423314 | − | 0.905983i | \(-0.639133\pi\) |
0.996261 | − | 0.0863911i | \(-0.0275335\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −14.7478 | + | 8.51465i | −0.565553 | + | 0.326522i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.8045 | + | 7.39271i | 0.490311 | + | 0.283081i | ||||
\(683\) | − | 30.2348i | − | 1.15690i | −0.815717 | − | 0.578451i | \(-0.803658\pi\) | ||
0.815717 | − | 0.578451i | \(-0.196342\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 20.8001i | − | 0.794731i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.37024 | − | 16.2297i | −0.357237 | − | 0.618753i | ||||
\(689\) | −12.5906 | − | 21.8076i | −0.479664 | − | 0.830802i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.7555 | − | 15.4473i | −1.01783 | − | 0.587642i | −0.104352 | − | 0.994540i | \(-0.533277\pi\) |
−0.913473 | + | 0.406899i | \(0.866610\pi\) | |||||||
\(692\) | 43.7496 | 1.66311 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.4159 | 0.585180 | ||||||||
\(695\) | −4.38115 | − | 2.52946i | −0.166186 | − | 0.0959478i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.97172 | − | 6.87921i | −0.150439 | − | 0.260569i | ||||
\(698\) | −21.7204 | − | 37.6208i | −0.822128 | − | 1.42397i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.757329i | 0.0286039i | 0.999898 | + | 0.0143020i | \(0.00455261\pi\) | ||||
−0.999898 | + | 0.0143020i | \(0.995447\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.28659i | 0.312535i | ||||||||
\(704\) | −24.1467 | − | 13.9411i | −0.910065 | − | 0.525426i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.8142 | − | 7.39831i | 0.482270 | − | 0.278439i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.7544 | − | 18.6271i | 0.403889 | − | 0.699556i | −0.590303 | − | 0.807182i | \(-0.700992\pi\) |
0.994191 | + | 0.107626i | \(0.0343249\pi\) | |||||||
\(710\) | −14.2598 | −0.535159 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.776904i | 0.0291157i | ||||||||
\(713\) | 6.65065 | − | 11.5193i | 0.249069 | − | 0.431400i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7267 | + | 18.5791i | 0.401155 | + | 0.694820i | ||||
\(716\) | −44.7277 | + | 25.8235i | −1.67155 | + | 0.965071i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.3093 | + | 17.8562i | −0.384740 | + | 0.666389i | ||||
\(719\) | 44.2509 | 1.65028 | 0.825140 | − | 0.564929i | \(-0.191096\pi\) | ||||
0.825140 | + | 0.564929i | \(0.191096\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.12371 | + | 5.26758i | 0.339549 | + | 0.196039i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −35.9324 | + | 20.7456i | −1.33542 | + | 0.771003i | ||||
\(725\) | 32.6054 | − | 18.8248i | 1.21094 | − | 0.699134i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.95166 | + | 1.70414i | 0.109471 | + | 0.0632031i | 0.553736 | − | 0.832692i | \(-0.313202\pi\) |
−0.444265 | + | 0.895895i | \(0.646535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −55.2059 | −2.04326 | ||||||||
\(731\) | 21.0729 | − | 36.4994i | 0.779410 | − | 1.34998i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.46407 | − | 3.15468i | 0.201820 | − | 0.116521i | −0.395684 | − | 0.918387i | \(-0.629492\pi\) |
0.597504 | + | 0.801866i | \(0.296159\pi\) | |||||||
\(734\) | −32.5298 | − | 56.3432i | −1.20070 | − | 2.07967i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.1861 | + | 34.9633i | −0.744069 | + | 1.28876i | ||||
\(737\) | 22.1716i | 0.816701i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.90776 | −0.180535 | −0.0902674 | − | 0.995918i | \(-0.528772\pi\) | ||||
−0.0902674 | + | 0.995918i | \(0.528772\pi\) | |||||||
\(740\) | −6.54471 | + | 11.3358i | −0.240588 | + | 0.416711i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.1921 | + | 15.1220i | −0.960895 | + | 0.554773i | −0.896448 | − | 0.443148i | \(-0.853862\pi\) |
−0.0644465 | + | 0.997921i | \(0.520528\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.3059 | − | 8.83688i | −0.560766 | − | 0.323758i | ||||
\(746\) | 60.5414i | 2.21658i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 44.7990i | − | 1.63801i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0321 | + | 43.3569i | 0.913435 | + | 1.58212i | 0.809177 | + | 0.587565i | \(0.199913\pi\) |
0.104257 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(752\) | 7.79355 | + | 13.4988i | 0.284202 | + | 0.492252i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 27.9988 | + | 16.1651i | 1.01966 | + | 0.588700i | ||||
\(755\) | 37.9628 | 1.38161 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.2695 | 1.35458 | 0.677291 | − | 0.735716i | \(-0.263154\pi\) | ||||
0.677291 | + | 0.735716i | \(0.263154\pi\) | |||||||
\(758\) | 0.935660 | + | 0.540204i | 0.0339847 | + | 0.0196211i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.81594 | + | 10.0735i | 0.210966 | + | 0.365405i | ||||
\(761\) | 5.27174 | + | 9.13092i | 0.191100 | + | 0.330996i | 0.945615 | − | 0.325287i | \(-0.105461\pi\) |
−0.754515 | + | 0.656283i | \(0.772128\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 35.9248i | − | 1.29971i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.5341i | 0.994848i | ||||||||
\(767\) | 10.8506 | + | 6.26459i | 0.391792 | + | 0.226201i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.4720 | + | 7.20070i | −0.449751 | + | 0.259664i | −0.707725 | − | 0.706488i | \(-0.750278\pi\) |
0.257974 | + | 0.966152i | \(0.416945\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 30.3199 | − | 52.5156i | 1.09124 | − | 1.89008i | ||||
\(773\) | −21.8771 | −0.786866 | −0.393433 | − | 0.919353i | \(-0.628713\pi\) | ||||
−0.393433 | + | 0.919353i | \(0.628713\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.7812i | 0.566879i | ||||||||
\(776\) | −3.92472 | + | 6.79781i | −0.140889 | + | 0.244027i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.2493 | − | 61.0536i | −1.26375 | − | 2.18888i | ||||
\(779\) | −4.69885 | + | 2.71288i | −0.168354 | + | 0.0971992i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.75487 | − | 4.77158i | 0.0985771 | − | 0.170740i | ||||
\(782\) | −74.6851 | −2.67073 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.0759 | − | 11.0135i | −0.680847 | − | 0.393087i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.9804 | + | 13.8451i | −0.854807 | + | 0.493523i | −0.862270 | − | 0.506449i | \(-0.830958\pi\) |
0.00746275 | + | 0.999972i | \(0.497625\pi\) | |||||||
\(788\) | 8.49253 | − | 4.90316i | 0.302534 | − | 0.174668i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −29.8853 | − | 17.2543i | −1.06327 | − | 0.613880i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.5232 | 0.444712 | ||||||||
\(794\) | 8.93484 | − | 15.4756i | 0.317086 | − | 0.549208i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 44.6809 | − | 25.7965i | 1.58367 | − | 0.914334i | ||||
\(797\) | −21.3285 | − | 36.9420i | −0.755493 | − | 1.30855i | −0.945129 | − | 0.326697i | \(-0.894064\pi\) |
0.189636 | − | 0.981854i | \(-0.439269\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.5271 | + | 30.3578i | −0.620063 | + | 1.07398i | ||||
\(800\) | − | 47.8992i | − | 1.69349i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 33.6326 | 1.18761 | ||||||||
\(803\) | 10.6653 | − | 18.4729i | 0.376372 | − | 0.651895i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.7360 | + | 6.77581i | −0.413384 | + | 0.238668i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.328111 | − | 0.189435i | −0.0115429 | − | 0.00666430i | ||||
\(809\) | − | 35.7254i | − | 1.25604i | −0.778198 | − | 0.628019i | \(-0.783866\pi\) | ||
0.778198 | − | 0.628019i | \(-0.216134\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.85377i | − | 0.205554i | −0.994704 | − | 0.102777i | \(-0.967227\pi\) | ||
0.994704 | − | 0.102777i | \(-0.0327728\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.68613 | − | 8.11662i | −0.164249 | − | 0.284487i | ||||
\(815\) | 38.1557 | + | 66.0875i | 1.33653 | + | 2.31495i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.9309 | − | 14.3939i | −0.872223 | − | 0.503578i | ||||
\(818\) | −34.0227 | −1.18958 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.57050 | −0.299295 | ||||||||
\(821\) | −15.2220 | − | 8.78841i | −0.531251 | − | 0.306718i | 0.210275 | − | 0.977642i | \(-0.432564\pi\) |
−0.741526 | + | 0.670925i | \(0.765897\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.1893 | − | 26.3086i | −0.529465 | − | 0.917060i | −0.999409 | − | 0.0343640i | \(-0.989059\pi\) |
0.469945 | − | 0.882696i | \(-0.344274\pi\) | |||||||
\(824\) | −0.281232 | − | 0.487108i | −0.00979717 | − | 0.0169692i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.4454i | 0.537089i | 0.963267 | + | 0.268545i | \(0.0865426\pi\) | ||||
−0.963267 | + | 0.268545i | \(0.913457\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 40.8946i | − | 1.42033i | −0.704036 | − | 0.710164i | \(-0.748621\pi\) | ||
0.704036 | − | 0.710164i | \(-0.251379\pi\) | |||||||
\(830\) | −12.4649 | − | 7.19659i | −0.432662 | − | 0.249797i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 22.1318 | − | 12.7778i | 0.767281 | − | 0.442990i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.2858 | − | 45.5283i | 0.909657 | − | 1.57557i | ||||
\(836\) | −30.6000 | −1.05832 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 2.45544i | − | 0.0848217i | ||||||
\(839\) | −16.8620 | + | 29.2058i | −0.582140 | + | 1.00830i | 0.413086 | + | 0.910692i | \(0.364451\pi\) |
−0.995225 | + | 0.0976035i | \(0.968882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.71808 | + | 9.90401i | 0.197175 | + | 0.341517i | ||||
\(842\) | −12.4023 | + | 7.16049i | −0.427413 | + | 0.246767i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.8178 | + | 49.9139i | −0.991950 | + | 1.71811i | ||||
\(845\) | 23.2973 | 0.801453 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −28.5440 | − | 16.4799i | −0.980206 | − | 0.565922i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 76.7381 | − | 44.3048i | 2.63210 | − | 1.51964i | ||||
\(851\) | −7.30190 | + | 4.21575i | −0.250306 | + | 0.144514i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.6715 | − | 21.7497i | −1.28985 | − | 0.744694i | −0.311221 | − | 0.950337i | \(-0.600738\pi\) |
−0.978627 | + | 0.205643i | \(0.934071\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.84017 | 0.131254 | ||||||||
\(857\) | −4.21534 | + | 7.30118i | −0.143993 | + | 0.249404i | −0.928997 | − | 0.370088i | \(-0.879328\pi\) |
0.785004 | + | 0.619491i | \(0.212661\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.07929 | + | 1.20048i | −0.0709445 | + | 0.0409598i | −0.535053 | − | 0.844819i | \(-0.679708\pi\) |
0.464108 | + | 0.885779i | \(0.346375\pi\) | |||||||
\(860\) | −22.7364 | − | 39.3807i | −0.775306 | − | 1.34287i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.845356 | − | 1.46420i | 0.0287929 | − | 0.0498708i | ||||
\(863\) | − | 9.37637i | − | 0.319175i | −0.987184 | − | 0.159588i | \(-0.948984\pi\) | ||
0.987184 | − | 0.159588i | \(-0.0510165\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −61.6712 | −2.09688 | ||||||||
\(866\) | −8.95898 | + | 15.5174i | −0.304439 | + | 0.527303i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.5472 | − | 6.66678i | 0.391712 | − | 0.226155i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.5989 | − | 10.1607i | −0.596316 | − | 0.344283i | ||||
\(872\) | − | 4.28107i | − | 0.144975i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 51.0137i | 1.72557i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.71542 | − | 2.97119i | −0.0579256 | − | 0.100330i | 0.835608 | − | 0.549326i | \(-0.185115\pi\) |
−0.893534 | + | 0.448995i | \(0.851782\pi\) | |||||||
\(878\) | 28.7568 | + | 49.8082i | 0.970493 | + | 1.68094i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 24.3183 | + | 14.0402i | 0.819770 | + | 0.473295i | ||||
\(881\) | 43.4962 | 1.46542 | 0.732712 | − | 0.680539i | \(-0.238254\pi\) | ||||
0.732712 | + | 0.680539i | \(0.238254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.6074 | 1.66942 | 0.834711 | − | 0.550688i | \(-0.185635\pi\) | ||||
0.834711 | + | 0.550688i | \(0.185635\pi\) | |||||||
\(884\) | 35.5596 | + | 20.5303i | 1.19600 | + | 0.690510i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.7619 | − | 22.1043i | −0.428745 | − | 0.742607i | ||||
\(887\) | −17.5766 | − | 30.4436i | −0.590164 | − | 1.02219i | −0.994210 | − | 0.107456i | \(-0.965730\pi\) |
0.404045 | − | 0.914739i | \(-0.367604\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 7.45638i | − | 0.249938i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 19.8127i | − | 0.663378i | ||||||
\(893\) | 20.7359 | + | 11.9719i | 0.693901 | + | 0.400624i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 63.0500 | − | 36.4019i | 2.10753 | − | 1.21678i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.9443 | + | 39.7407i | −0.765662 | + | 1.32617i | ||||
\(899\) | −16.9493 | −0.565290 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 74.1239i | − | 2.46943i | ||||||
\(902\) | 3.06832 | − | 5.31448i | 0.102164 | − | 0.176953i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.14446 | + | 7.17842i | 0.137843 | + | 0.238751i | ||||
\(905\) | 50.6517 | − | 29.2438i | 1.68372 | − | 0.972097i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.0816 | + | 33.0504i | −0.633596 | + | 1.09742i | 0.353215 | + | 0.935542i | \(0.385088\pi\) |
−0.986811 | + | 0.161878i | \(0.948245\pi\) | |||||||
\(908\) | 13.6662 | 0.453529 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.9027 | + | 23.0378i | 1.32203 | + | 0.763277i | 0.984053 | − | 0.177876i | \(-0.0569226\pi\) |
0.337981 | + | 0.941153i | \(0.390256\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.81623 | − | 2.78065i | 0.159394 | − | 0.0920261i | ||||
\(914\) | 43.6028 | − | 25.1741i | 1.44225 | − | 0.832686i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.74163 | + | 5.62433i | 0.321872 | + | 0.185833i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.5515 | 0.348061 | 0.174031 | − | 0.984740i | \(-0.444321\pi\) | ||||
0.174031 | + | 0.984740i | \(0.444321\pi\) | |||||||
\(920\) | −5.91765 | + | 10.2497i | −0.195099 | + | 0.337922i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −59.1694 | + | 34.1615i | −1.94864 | + | 1.12505i | ||||
\(923\) | 2.52499 | + | 4.37340i | 0.0831109 | + | 0.143952i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.00175 | − | 8.66328i | 0.164456 | − | 0.284847i | ||||
\(926\) | − | 65.7219i | − | 2.15975i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 51.4445 | 1.68875 | ||||||||
\(929\) | −26.4514 | + | 45.8152i | −0.867843 | + | 1.50315i | −0.00364718 | + | 0.999993i | \(0.501161\pi\) |
−0.864196 | + | 0.503155i | \(0.832172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 46.7896 | − | 27.0140i | 1.53265 | − | 0.884873i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 59.8433 | + | 34.5505i | 1.95813 | + | 1.13053i | ||||
\(935\) | 63.1505i | 2.06524i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.3265i | 0.337353i | 0.985671 | + | 0.168676i | \(0.0539493\pi\) | ||||
−0.985671 | + | 0.168676i | \(0.946051\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18.9107 | + | 32.7543i | 0.616798 | + | 1.06833i | ||||
\(941\) | 0.505336 | + | 0.875268i | 0.0164735 | + | 0.0285329i | 0.874145 | − | 0.485666i | \(-0.161423\pi\) |
−0.857671 | + | 0.514199i | \(0.828089\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.78103 | − | 2.76033i | −0.155692 | − | 0.0898887i | ||||
\(944\) | 16.3995 | 0.533758 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.5594 | 1.05860 | ||||||||
\(947\) | −9.36454 | − | 5.40662i | −0.304307 | − | 0.175692i | 0.340069 | − | 0.940400i | \(-0.389549\pi\) |
−0.644376 | + | 0.764709i | \(0.722883\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.77535 | + | 16.9314i | 0.317321 | + | 0.549616i | ||||
\(950\) | −30.2624 | − | 52.4161i | −0.981843 | − | 1.70060i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 26.7466i | − | 0.866408i | −0.901296 | − | 0.433204i | \(-0.857383\pi\) | ||
0.901296 | − | 0.433204i | \(-0.142617\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.6411i | 1.63871i | ||||||||
\(956\) | −13.8777 | − | 8.01232i | −0.448838 | − | 0.259137i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 41.1454 | − | 23.7553i | 1.32935 | − | 0.767500i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.9478 | + | 20.6941i | −0.385411 | + | 0.667552i | ||||
\(962\) | 8.59017 | 0.276958 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 10.5332i | − | 0.339252i | ||||||
\(965\) | −42.7402 | + | 74.0281i | −1.37585 | + | 2.38305i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.62313 | + | 2.81134i | 0.0521962 | + | 0.0904065i | 0.890943 | − | 0.454115i | \(-0.150045\pi\) |
−0.838747 | + | 0.544522i | \(0.816711\pi\) | |||||||
\(968\) | −2.43456 | + | 1.40559i | −0.0782497 | + | 0.0451775i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 37.6677 | − | 65.2424i | 1.20944 | − | 2.09481i | ||||
\(971\) | −8.82846 | −0.283319 | −0.141659 | − | 0.989915i | \(-0.545244\pi\) | ||||
−0.141659 | + | 0.989915i | \(0.545244\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.92997 | + | 2.84632i | 0.157966 | + | 0.0912019i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.1956 | − | 8.19584i | 0.454390 | − | 0.262342i | ||||
\(977\) | −36.2748 | + | 20.9433i | −1.16053 | + | 0.670035i | −0.951432 | − | 0.307859i | \(-0.900388\pi\) |
−0.209102 | + | 0.977894i | \(0.567054\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.49504 | + | 1.44051i | 0.0797419 | + | 0.0460390i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 52.1722 | 1.66488 | ||||||||
\(983\) | −2.35194 | + | 4.07368i | −0.0750153 | + | 0.129930i | −0.901093 | − | 0.433626i | \(-0.857234\pi\) |
0.826078 | + | 0.563556i | \(0.190567\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.9714 | + | 6.91170i | −0.381441 | + | 0.220225i | ||||
\(986\) | 47.5840 | + | 82.4179i | 1.51538 | + | 2.62472i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.0233 | − | 24.2890i | 0.446139 | − | 0.772736i | ||||
\(989\) | − | 29.2912i | − | 0.931406i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.8654 | 1.20284 | 0.601418 | − | 0.798935i | \(-0.294603\pi\) | ||||
0.601418 | + | 0.798935i | \(0.294603\pi\) | |||||||
\(992\) | −10.7818 | + | 18.6746i | −0.342322 | + | 0.592919i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −62.9840 | + | 36.3638i | −1.99673 | + | 1.15281i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.18336 | − | 1.83791i | −0.100818 | − | 0.0582073i | 0.448743 | − | 0.893661i | \(-0.351872\pi\) |
−0.549561 | + | 0.835453i | \(0.685205\pi\) | |||||||
\(998\) | 17.9242i | 0.567381i | ||||||||
\(999\) | 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 | 1323.2.o.e.440.3 | 48 | ||
3.2 | odd | 2 | 441.2.o.e.146.21 | ✓ | 48 | ||
7.2 | even | 3 | 1323.2.i.d.521.23 | 48 | |||
7.3 | odd | 6 | 1323.2.s.d.656.21 | 48 | |||
7.4 | even | 3 | 1323.2.s.d.656.22 | 48 | |||
7.5 | odd | 6 | 1323.2.i.d.521.16 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.o.e.440.4 | 48 | ||
9.4 | even | 3 | 441.2.o.e.293.22 | yes | 48 | ||
9.5 | odd | 6 | inner | 1323.2.o.e.881.4 | 48 | ||
21.2 | odd | 6 | 441.2.i.d.227.3 | 48 | |||
21.5 | even | 6 | 441.2.i.d.227.4 | 48 | |||
21.11 | odd | 6 | 441.2.s.d.362.4 | 48 | |||
21.17 | even | 6 | 441.2.s.d.362.3 | 48 | |||
21.20 | even | 2 | 441.2.o.e.146.22 | yes | 48 | ||
63.4 | even | 3 | 441.2.i.d.68.22 | 48 | |||
63.5 | even | 6 | 1323.2.s.d.962.22 | 48 | |||
63.13 | odd | 6 | 441.2.o.e.293.21 | yes | 48 | ||
63.23 | odd | 6 | 1323.2.s.d.962.21 | 48 | |||
63.31 | odd | 6 | 441.2.i.d.68.21 | 48 | |||
63.32 | odd | 6 | 1323.2.i.d.1097.16 | 48 | |||
63.40 | odd | 6 | 441.2.s.d.374.4 | 48 | |||
63.41 | even | 6 | inner | 1323.2.o.e.881.3 | 48 | ||
63.58 | even | 3 | 441.2.s.d.374.3 | 48 | |||
63.59 | even | 6 | 1323.2.i.d.1097.23 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.21 | 48 | 63.31 | odd | 6 | |||
441.2.i.d.68.22 | 48 | 63.4 | even | 3 | |||
441.2.i.d.227.3 | 48 | 21.2 | odd | 6 | |||
441.2.i.d.227.4 | 48 | 21.5 | even | 6 | |||
441.2.o.e.146.21 | ✓ | 48 | 3.2 | odd | 2 | ||
441.2.o.e.146.22 | yes | 48 | 21.20 | even | 2 | ||
441.2.o.e.293.21 | yes | 48 | 63.13 | odd | 6 | ||
441.2.o.e.293.22 | yes | 48 | 9.4 | even | 3 | ||
441.2.s.d.362.3 | 48 | 21.17 | even | 6 | |||
441.2.s.d.362.4 | 48 | 21.11 | odd | 6 | |||
441.2.s.d.374.3 | 48 | 63.58 | even | 3 | |||
441.2.s.d.374.4 | 48 | 63.40 | odd | 6 | |||
1323.2.i.d.521.16 | 48 | 7.5 | odd | 6 | |||
1323.2.i.d.521.23 | 48 | 7.2 | even | 3 | |||
1323.2.i.d.1097.16 | 48 | 63.32 | odd | 6 | |||
1323.2.i.d.1097.23 | 48 | 63.59 | even | 6 | |||
1323.2.o.e.440.3 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.o.e.440.4 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.o.e.881.3 | 48 | 63.41 | even | 6 | inner | ||
1323.2.o.e.881.4 | 48 | 9.5 | odd | 6 | inner | ||
1323.2.s.d.656.21 | 48 | 7.3 | odd | 6 | |||
1323.2.s.d.656.22 | 48 | 7.4 | even | 3 | |||
1323.2.s.d.962.21 | 48 | 63.23 | odd | 6 | |||
1323.2.s.d.962.22 | 48 | 63.5 | even | 6 |