Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(31,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bf (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.16 | ||
Character | \(\chi\) | \(=\) | 1008.31 |
Dual form | 1008.2.bf.i.943.16 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.72863 | + | 0.108820i | 0.998024 | + | 0.0628271i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.435427i | − | 0.194729i | −0.995249 | − | 0.0973643i | \(-0.968959\pi\) | ||
0.995249 | − | 0.0973643i | \(-0.0310412\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.49096 | − | 0.891704i | −0.941493 | − | 0.337032i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.97632 | + | 0.376218i | 0.992106 | + | 0.125406i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.82050i | − | 1.45344i | −0.686936 | − | 0.726718i | \(-0.741045\pi\) | ||
0.686936 | − | 0.726718i | \(-0.258955\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.31639 | − | 2.49207i | −1.19715 | − | 0.691176i | −0.237232 | − | 0.971453i | \(-0.576240\pi\) |
−0.959919 | + | 0.280277i | \(0.909574\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0473830 | − | 0.752691i | 0.0122342 | − | 0.194344i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.92142 | − | 2.84139i | −1.19362 | − | 0.689137i | −0.234495 | − | 0.972117i | \(-0.575344\pi\) |
−0.959126 | + | 0.282980i | \(0.908677\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.70969 | − | 6.42537i | −0.851061 | − | 1.47408i | −0.880252 | − | 0.474506i | \(-0.842627\pi\) |
0.0291916 | − | 0.999574i | \(-0.490707\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.20890 | − | 1.81249i | −0.918458 | − | 0.395518i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.16029i | 0.658966i | 0.944162 | + | 0.329483i | \(0.106874\pi\) | ||||
−0.944162 | + | 0.329483i | \(0.893126\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.81040 | 0.962081 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.10401 | + | 0.974224i | 0.982267 | + | 0.187489i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.49630 | + | 4.32372i | 0.463552 | + | 0.802895i | 0.999135 | − | 0.0415876i | \(-0.0132416\pi\) |
−0.535583 | + | 0.844482i | \(0.679908\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.32968 | + | 2.30307i | 0.238817 | + | 0.413644i | 0.960375 | − | 0.278710i | \(-0.0899069\pi\) |
−0.721558 | + | 0.692354i | \(0.756574\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.524566 | − | 8.33285i | 0.0913151 | − | 1.45056i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.388272 | + | 1.08463i | −0.0656299 | + | 0.183336i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.06500 | + | 1.84463i | 0.175085 | + | 0.303256i | 0.940191 | − | 0.340649i | \(-0.110647\pi\) |
−0.765106 | + | 0.643904i | \(0.777313\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.19025 | − | 4.77757i | −1.15136 | − | 0.765024i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.112731 | + | 0.0650855i | 0.0176057 | + | 0.0101646i | 0.508777 | − | 0.860898i | \(-0.330098\pi\) |
−0.491171 | + | 0.871063i | \(0.663431\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.53530 | − | 3.77315i | 0.996623 | − | 0.575401i | 0.0893758 | − | 0.995998i | \(-0.471513\pi\) |
0.907247 | + | 0.420597i | \(0.138179\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.163815 | − | 1.29597i | 0.0244201 | − | 0.193191i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.29337 | − | 7.43633i | 0.626252 | − | 1.08470i | −0.362045 | − | 0.932161i | \(-0.617921\pi\) |
0.988297 | − | 0.152540i | \(-0.0487453\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.40973 | + | 4.44239i | 0.772818 | + | 0.634627i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.19812 | − | 5.44725i | −1.14797 | − | 0.762768i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.61000 | + | 9.71680i | −0.770593 | + | 1.33471i | 0.166646 | + | 0.986017i | \(0.446706\pi\) |
−0.937239 | + | 0.348689i | \(0.886627\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.09897 | −0.283025 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.71347 | − | 11.5108i | −0.756767 | − | 1.52464i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.20064 | − | 10.7398i | −0.807255 | − | 1.39821i | −0.914758 | − | 0.404002i | \(-0.867619\pi\) |
0.107503 | − | 0.994205i | \(-0.465714\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.65803 | + | 4.42137i | 0.980510 | + | 0.566098i | 0.902424 | − | 0.430849i | \(-0.141786\pi\) |
0.0780862 | + | 0.996947i | \(0.475119\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.07840 | − | 3.59114i | −0.891795 | − | 0.452441i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.08511 | + | 1.87947i | −0.134592 | + | 0.233120i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.811298 | − | 0.468403i | 0.0991158 | − | 0.0572246i | −0.449623 | − | 0.893219i | \(-0.648442\pi\) |
0.548739 | + | 0.835994i | \(0.315108\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.343902 | + | 5.46297i | −0.0414009 | + | 0.657664i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.27328i | − | 0.744501i | −0.928132 | − | 0.372251i | \(-0.878586\pi\) | ||
0.928132 | − | 0.372251i | \(-0.121414\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.2357 | + | 6.48693i | 1.31504 | + | 0.759238i | 0.982926 | − | 0.184002i | \(-0.0589054\pi\) |
0.332112 | + | 0.943240i | \(0.392239\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.31540 | + | 0.523467i | 0.960180 | + | 0.0604448i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.29846 | + | 12.0077i | −0.489855 | + | 1.36840i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.98242 | − | 1.72190i | −0.335548 | − | 0.193729i | 0.322754 | − | 0.946483i | \(-0.395392\pi\) |
−0.658302 | + | 0.752754i | \(0.728725\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.71692 | + | 2.23949i | 0.968547 | + | 0.248832i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.68712 | + | 6.38628i | 0.404714 | + | 0.700985i | 0.994288 | − | 0.106729i | \(-0.0340377\pi\) |
−0.589574 | + | 0.807714i | \(0.700704\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.23721 | + | 2.14292i | −0.134195 | + | 0.232432i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.84467 | + | 7.74576i | 0.412192 | + | 0.830432i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.2599 | + | 7.65563i | −1.40555 | + | 0.811495i | −0.994955 | − | 0.100322i | \(-0.968013\pi\) |
−0.410596 | + | 0.911817i | \(0.634679\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.52975 | + | 10.0566i | 0.894161 | + | 1.05422i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.04790 | + | 4.12585i | 0.212358 | + | 0.427831i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.79778 | + | 1.61530i | −0.287046 | + | 0.165726i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.83887 | + | 1.63902i | −0.288244 | + | 0.166418i | −0.637150 | − | 0.770740i | \(-0.719887\pi\) |
0.348906 | + | 0.937158i | \(0.386553\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.81356 | − | 14.3473i | 0.182269 | − | 1.44196i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 16.8555i | − | 1.67719i | −0.544759 | − | 0.838593i | \(-0.683379\pi\) | ||
0.544759 | − | 0.838593i | \(-0.316621\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.29089 | −0.324261 | −0.162130 | − | 0.986769i | \(-0.551837\pi\) | ||||
−0.162130 | + | 0.986769i | \(0.551837\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.789206 | + | 1.83267i | −0.0770187 | + | 0.178850i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.1078 | + | 5.83572i | −0.977154 | + | 0.564160i | −0.901410 | − | 0.432967i | \(-0.857467\pi\) |
−0.0757442 | + | 0.997127i | \(0.524133\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.15538 | − | 15.8576i | 0.876926 | − | 1.51888i | 0.0222293 | − | 0.999753i | \(-0.492924\pi\) |
0.854697 | − | 0.519128i | \(-0.173743\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.64025 | + | 3.30458i | 0.155686 | + | 0.313657i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.20802 | + | 3.82441i | −0.207713 | + | 0.359770i | −0.950994 | − | 0.309210i | \(-0.899935\pi\) |
0.743281 | + | 0.668980i | \(0.233269\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.37607 | 0.128320 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.9094 | − | 9.04109i | −1.10102 | − | 0.835849i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.72538 | + | 11.4662i | 0.891524 | + | 1.05111i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.2372 | −1.11247 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.187788 | + | 0.124776i | 0.0169323 | + | 0.0112507i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 4.27171i | − | 0.382073i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.65009i | − | 0.235158i | −0.993064 | − | 0.117579i | \(-0.962487\pi\) | ||
0.993064 | − | 0.117579i | \(-0.0375133\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.7077 | − | 5.81122i | 1.03081 | − | 0.511649i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.863493 | 0.0754437 | 0.0377219 | − | 0.999288i | \(-0.487990\pi\) | ||||
0.0377219 | + | 0.999288i | \(0.487990\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.51115 | + | 19.3132i | 0.304455 | + | 1.67467i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.424203 | − | 2.22242i | 0.0365096 | − | 0.191275i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.86336 | 0.586377 | 0.293188 | − | 0.956055i | \(-0.405284\pi\) | ||||
0.293188 | + | 0.956055i | \(0.405284\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.26364 | − | 7.38484i | 0.361637 | − | 0.626374i | −0.626593 | − | 0.779346i | \(-0.715551\pi\) |
0.988230 | + | 0.152972i | \(0.0488846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.23086 | − | 12.3875i | 0.693164 | − | 1.04321i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.0130 | + | 20.8072i | −1.00458 | + | 1.73998i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.88266 | − | 1.08696i | 0.156347 | − | 0.0902668i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.86799 | + | 8.26793i | 0.731420 | + | 0.681927i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5895 | −0.867527 | −0.433764 | − | 0.901027i | \(-0.642815\pi\) | ||||
−0.433764 | + | 0.901027i | \(0.642815\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.37187i | − | 0.681293i | −0.940191 | − | 0.340647i | \(-0.889354\pi\) | ||
0.940191 | − | 0.340647i | \(-0.110646\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.5787 | − | 10.3084i | −1.09778 | − | 0.833384i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00282 | − | 0.578978i | 0.0805483 | − | 0.0465046i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.9034 | − | 8.02712i | 1.10961 | − | 0.640634i | 0.170882 | − | 0.985292i | \(-0.445338\pi\) |
0.938728 | + | 0.344658i | \(0.112005\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.7550 | + | 16.1863i | −0.852926 | + | 1.28365i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.81804 | − | 7.87214i | 0.222093 | − | 0.620412i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.55417 | − | 3.78405i | 0.513362 | − | 0.296390i | −0.220852 | − | 0.975307i | \(-0.570884\pi\) |
0.734215 | + | 0.678917i | \(0.237551\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.62835 | − | 0.228410i | −0.282466 | − | 0.0177817i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.74172 | − | 3.01674i | 0.134778 | − | 0.233443i | −0.790735 | − | 0.612159i | \(-0.790301\pi\) |
0.925513 | + | 0.378717i | \(0.123635\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.92082 | + | 10.2552i | 0.455447 | + | 0.788858i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.62386 | − | 20.5196i | −0.659483 | − | 1.56917i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.69039 | + | 3.86270i | 0.508661 | + | 0.293676i | 0.732283 | − | 0.681000i | \(-0.238455\pi\) |
−0.223622 | + | 0.974676i | \(0.571788\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.9825 | − | 4.28946i | −0.905792 | − | 0.324252i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.54991 | − | 19.2399i | −0.717815 | − | 1.44616i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.3972 | + | 10.6216i | 1.37507 | + | 0.793899i | 0.991561 | − | 0.129637i | \(-0.0413813\pi\) |
0.383511 | + | 0.923536i | \(0.374715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.62129i | − | 0.417827i | −0.977934 | − | 0.208914i | \(-0.933007\pi\) | ||
0.977934 | − | 0.208914i | \(-0.0669927\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.7568 | + | 8.47625i | 0.943007 | + | 0.626582i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.803202 | − | 0.463729i | 0.0590525 | − | 0.0340940i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.6969 | + | 23.7237i | −1.00162 | + | 1.73485i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.8451 | − | 6.97801i | −0.861607 | − | 0.507576i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.8827 | − | 6.28314i | −0.787446 | − | 0.454632i | 0.0516165 | − | 0.998667i | \(-0.483563\pi\) |
−0.839063 | + | 0.544035i | \(0.816896\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.5334 | + | 18.2443i | 0.758209 | + | 1.31326i | 0.943763 | + | 0.330622i | \(0.107259\pi\) |
−0.185554 | + | 0.982634i | \(0.559408\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.08028 | + | 3.13083i | −0.148972 | + | 0.224203i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.1720 | −1.50844 | −0.754222 | − | 0.656619i | \(-0.771986\pi\) | ||||
−0.754222 | + | 0.656619i | \(0.771986\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.87039 | + | 10.1678i | −0.416141 | + | 0.720778i | −0.995548 | − | 0.0942612i | \(-0.969951\pi\) |
0.579406 | + | 0.815039i | \(0.303284\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.45341 | − | 0.721410i | 0.102515 | − | 0.0508843i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.36270 | − | 12.9962i | −0.165829 | − | 0.912152i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0283399 | − | 0.0490862i | 0.00197935 | − | 0.00342833i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.18896 | + | 9.40602i | −0.0826383 | + | 0.653764i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −30.9735 | + | 17.8825i | −2.14248 | + | 1.23696i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.83611 | + | 4.52418i | 0.539460 | + | 0.311457i | 0.744860 | − | 0.667221i | \(-0.232516\pi\) |
−0.205400 | + | 0.978678i | \(0.565850\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.682657 | − | 10.8442i | 0.0467749 | − | 0.743031i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.64293 | − | 2.84564i | −0.112047 | − | 0.194071i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.25852 | − | 6.92253i | −0.0854336 | − | 0.469932i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.7164 | + | 12.4362i | 1.26474 | + | 0.840358i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.1619 | + | 24.5291i | 0.952630 | + | 1.65000i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.74216 | + | 11.6778i | 0.451488 | + | 0.782001i | 0.998479 | − | 0.0551381i | \(-0.0175599\pi\) |
−0.546990 | + | 0.837139i | \(0.684227\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.3173 | + | 1.80976i | 0.954486 | + | 0.120651i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.0716 | 1.59769 | 0.798845 | − | 0.601537i | \(-0.205445\pi\) | ||||
0.798845 | + | 0.601537i | \(0.205445\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.0833i | − | 0.930651i | −0.885140 | − | 0.465326i | \(-0.845937\pi\) | ||
0.885140 | − | 0.465326i | \(-0.154063\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.73711 | + | 20.2890i | −0.574859 | + | 1.33492i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.10903 | + | 1.92090i | 0.0726551 | + | 0.125842i | 0.900064 | − | 0.435757i | \(-0.143519\pi\) |
−0.827409 | + | 0.561600i | \(0.810186\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.23798 | − | 1.86945i | −0.211222 | − | 0.121949i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.96811 | − | 3.30107i | −0.322714 | − | 0.214428i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.5001 | − | 6.06225i | −0.679197 | − | 0.392134i | 0.120356 | − | 0.992731i | \(-0.461597\pi\) |
−0.799552 | + | 0.600596i | \(0.794930\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.67094i | − | 0.300881i | −0.988619 | − | 0.150441i | \(-0.951931\pi\) | ||
0.988619 | − | 0.150441i | \(-0.0480693\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8246 | + | 4.81982i | 0.951000 | + | 0.309191i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.93433 | − | 2.35554i | 0.123580 | − | 0.150490i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.9792i | 2.35293i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.67871 | + | 11.4407i | 0.359874 | + | 0.725028i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.4901 | 0.662132 | 0.331066 | − | 0.943608i | \(-0.392592\pi\) | ||||
0.331066 | + | 0.943608i | \(0.392592\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.2342 | 0.957764 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.37188 | + | 3.56968i | −0.148533 | + | 0.223542i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 5.12259i | − | 0.319538i | −0.987154 | − | 0.159769i | \(-0.948925\pi\) | ||
0.987154 | − | 0.159769i | \(-0.0510750\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00800 | − | 5.54456i | −0.0626341 | − | 0.344522i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.80312 | + | 13.8079i | 0.359204 | + | 0.854688i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.0949i | 1.17744i | 0.808336 | + | 0.588722i | \(0.200369\pi\) | ||||
−0.808336 | + | 0.588722i | \(0.799631\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.23095 | + | 2.44274i | 0.259905 | + | 0.150056i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.7546 | + | 11.7908i | −1.45376 | + | 0.721585i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.02481 | + | 3.47842i | 0.367339 | + | 0.212083i | 0.672295 | − | 0.740283i | \(-0.265309\pi\) |
−0.304956 | + | 0.952366i | \(0.598642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.40013 | + | 2.42510i | 0.0850521 | + | 0.147315i | 0.905413 | − | 0.424531i | \(-0.139561\pi\) |
−0.820361 | + | 0.571846i | \(0.806228\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.6504 | + | 18.3123i | 0.826161 | + | 1.10831i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 23.1885i | − | 1.39832i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3011 | 0.859270 | 0.429635 | − | 0.903003i | \(-0.358642\pi\) | ||||
0.429635 | + | 0.903003i | \(0.358642\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.09109 | + | 7.35492i | 0.185059 | + | 0.440328i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.38363 | − | 16.2529i | −0.559780 | − | 0.969568i | −0.997514 | − | 0.0704634i | \(-0.977552\pi\) |
0.437734 | − | 0.899104i | \(-0.355781\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.73617 | − | 16.8635i | −0.578755 | − | 1.00243i | −0.995622 | − | 0.0934662i | \(-0.970205\pi\) |
0.416867 | − | 0.908967i | \(-0.363128\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.01209 | + | 2.48779i | −0.296891 | + | 0.147364i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.222772 | − | 0.262648i | −0.0131498 | − | 0.0155036i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.64694 | + | 13.2449i | 0.449820 | + | 0.779111i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.08571 | + | 2.52434i | −0.298130 | + | 0.147979i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.77997 | + | 5.06912i | 0.512932 | + | 0.296141i | 0.734038 | − | 0.679109i | \(-0.237633\pi\) |
−0.221106 | + | 0.975250i | \(0.570967\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.67641 | + | 2.69992i | −0.272271 | + | 0.157196i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.69624 | − | 24.6039i | 0.272504 | − | 1.42766i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.87566 | − | 13.6410i | 0.455461 | − | 0.788882i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.6437 | + | 3.57122i | −1.13224 | + | 0.205841i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.83421 | − | 29.1369i | 0.105373 | − | 1.67387i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.92518 | − | 3.33451i | 0.110236 | − | 0.190933i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.48057 | 0.541085 | 0.270542 | − | 0.962708i | \(-0.412797\pi\) | ||||
0.270542 | + | 0.962708i | \(0.412797\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.68872 | − | 0.358114i | −0.323620 | − | 0.0203724i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.470145 | + | 0.814314i | 0.0266595 | + | 0.0461755i | 0.879047 | − | 0.476735i | \(-0.158180\pi\) |
−0.852388 | + | 0.522910i | \(0.824846\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6547 | − | 6.72885i | −0.658763 | − | 0.380337i | 0.133042 | − | 0.991110i | \(-0.457525\pi\) |
−0.791806 | + | 0.610773i | \(0.790859\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.56368 | + | 3.08212i | −0.0881031 | + | 0.173658i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.19415 | − | 3.80037i | 0.123236 | − | 0.213450i | −0.797806 | − | 0.602914i | \(-0.794006\pi\) |
0.921042 | + | 0.389464i | \(0.127340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.8425 | − | 12.0334i | 1.16696 | − | 0.673742i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.1076 | + | 8.98787i | −1.01067 | + | 0.501654i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.1626i | 2.34599i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.7636 | − | 11.9879i | −1.15176 | − | 0.664967i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.5519 | − | 26.4156i | 0.970621 | − | 1.46079i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.3256 | + | 14.6952i | −0.955191 | + | 0.810171i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.65849 | + | 2.11223i | 0.201089 | + | 0.116099i | 0.597163 | − | 0.802120i | \(-0.296294\pi\) |
−0.396075 | + | 0.918218i | \(0.629628\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.47579 | + | 5.89088i | 0.135672 | + | 0.322818i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.203955 | − | 0.353261i | −0.0111433 | − | 0.0193007i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.959055 | + | 1.66113i | −0.0522431 | + | 0.0904876i | −0.890964 | − | 0.454073i | \(-0.849970\pi\) |
0.838721 | + | 0.544561i | \(0.183304\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.23302 | + | 6.37070i | −0.229906 | + | 0.346009i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.1020 | − | 6.40972i | 0.601205 | − | 0.347106i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.51410 | − | 15.8897i | −0.513713 | − | 0.857962i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.37872 | + | 0.149744i | 0.128066 | + | 0.00806195i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.3138 | + | 13.4602i | −1.25155 | + | 0.722583i | −0.971417 | − | 0.237378i | \(-0.923712\pi\) |
−0.280133 | + | 0.959961i | \(0.590379\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.15394 | + | 4.70768i | −0.436470 | + | 0.251996i | −0.702099 | − | 0.712079i | \(-0.747754\pi\) |
0.265629 | + | 0.964075i | \(0.414420\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.6031 | − | 16.9247i | −1.04633 | − | 0.903372i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.76281i | 0.413173i | 0.978428 | + | 0.206586i | \(0.0662354\pi\) | ||||
−0.978428 | + | 0.206586i | \(0.933765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.73155 | −0.144976 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.5638 | + | 20.8792i | 0.823725 | + | 1.10504i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.8936 | + | 10.3309i | −0.944387 | + | 0.545242i | −0.891333 | − | 0.453350i | \(-0.850229\pi\) |
−0.0530541 | + | 0.998592i | \(0.516896\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0236 | + | 31.2177i | −0.948608 | + | 1.64304i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.1536 | − | 1.33165i | −1.11028 | − | 0.0698935i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.82458 | − | 4.89232i | 0.147845 | − | 0.256076i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.1596 | 0.895725 | 0.447862 | − | 0.894102i | \(-0.352185\pi\) | ||||
0.447862 | + | 0.894102i | \(0.352185\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.311038 | + | 0.236127i | 0.0161920 | + | 0.0122923i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.6388 | − | 19.2017i | 1.17535 | − | 0.996901i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.68029 | −0.0870022 | −0.0435011 | − | 0.999053i | \(-0.513851\pi\) | ||||
−0.0435011 | + | 0.999053i | \(0.513851\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.464847 | − | 7.38420i | 0.0240046 | − | 0.381319i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 24.8838i | − | 1.28158i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.3442i | 0.839543i | 0.907630 | + | 0.419771i | \(0.137890\pi\) | ||||
−0.907630 | + | 0.419771i | \(0.862110\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.288382 | − | 4.58103i | 0.0147743 | − | 0.234693i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.9832 | −0.867802 | −0.433901 | − | 0.900961i | \(-0.642863\pi\) | ||||
−0.433901 | + | 0.900961i | \(0.642863\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.22845 | + | 1.87166i | 0.266467 | + | 0.0953887i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.8706 | − | 8.77141i | 1.06091 | − | 0.445876i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 38.9596 | 1.97533 | 0.987666 | − | 0.156575i | \(-0.0500452\pi\) | ||||
0.987666 | + | 0.156575i | \(0.0500452\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.97960 | − | 15.5531i | 0.454118 | − | 0.786555i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.49266 | + | 0.0939651i | 0.0752947 | + | 0.00473991i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.749760 | + | 1.29862i | −0.0377245 | + | 0.0653408i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.84820 | − | 5.10851i | 0.444078 | − | 0.256389i | −0.261248 | − | 0.965272i | \(-0.584134\pi\) |
0.705326 | + | 0.708883i | \(0.250801\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.96780 | + | 33.7675i | 0.198639 | + | 1.69049i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.73966 | −0.186750 | −0.0933750 | − | 0.995631i | \(-0.529766\pi\) | ||||
−0.0933750 | + | 0.995631i | \(0.529766\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 13.2546i | − | 0.660259i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.975133 | − | 3.79558i | 0.0484547 | − | 0.188604i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.89204 | − | 5.13382i | 0.440762 | − | 0.254474i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.47660 | − | 0.852515i | 0.0730131 | − | 0.0421541i | −0.463049 | − | 0.886333i | \(-0.653245\pi\) |
0.536062 | + | 0.844179i | \(0.319911\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.8642 | + | 0.746870i | 0.585218 | + | 0.0368404i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.86879 | + | 32.2816i | 0.288784 | + | 1.58847i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.78076 | − | 1.60547i | 0.136502 | − | 0.0788094i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.17387 | − | 12.3017i | 0.400276 | − | 0.602416i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.00198 | + | 13.8598i | −0.390922 | + | 0.677097i | −0.992571 | − | 0.121663i | \(-0.961177\pi\) |
0.601649 | + | 0.798761i | \(0.294511\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7342 | − | 27.2524i | −0.766837 | − | 1.32820i | −0.939270 | − | 0.343179i | \(-0.888496\pi\) |
0.172433 | − | 0.985021i | \(-0.444837\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.5761 | − | 20.5176i | 0.757336 | − | 0.997602i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −23.6740 | − | 13.6682i | −1.14836 | − | 0.663006i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.1333 | − | 17.8421i | −0.732350 | − | 0.863441i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −23.0303 | + | 34.6606i | −1.11191 | + | 1.67343i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.78381 | + | 2.76193i | 0.230428 | + | 0.133038i | 0.610769 | − | 0.791809i | \(-0.290860\pi\) |
−0.380342 | + | 0.924846i | \(0.624194\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.56302i | 0.363456i | 0.983349 | + | 0.181728i | \(0.0581690\pi\) | ||||
−0.983349 | + | 0.181728i | \(0.941831\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.37271 | − | 1.67407i | 0.161709 | − | 0.0802656i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.3060 | − | 11.7237i | 0.971369 | − | 0.560820i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.50453 | + | 16.4623i | −0.453627 | + | 0.785704i | −0.998608 | − | 0.0527438i | \(-0.983203\pi\) |
0.544981 | + | 0.838448i | \(0.316537\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.4298 | + | 15.2572i | 0.687131 | + | 0.726533i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.50830 | − | 1.44817i | −0.119173 | − | 0.0688046i | 0.439229 | − | 0.898375i | \(-0.355252\pi\) |
−0.558402 | + | 0.829571i | \(0.688585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.33346 | + | 5.77373i | 0.158021 | + | 0.273701i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.3053 | − | 1.15235i | −0.865813 | − | 0.0545042i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.1794 | 1.47145 | 0.735724 | − | 0.677281i | \(-0.236842\pi\) | ||||
0.735724 | + | 0.677281i | \(0.236842\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.313744 | − | 0.543421i | 0.0147736 | − | 0.0255887i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.911025 | − | 14.4719i | 0.0428037 | − | 0.679947i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.37890 | − | 3.71408i | 0.205286 | − | 0.174119i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.51412 | − | 7.81868i | 0.211162 | − | 0.365743i | −0.740917 | − | 0.671597i | \(-0.765609\pi\) |
0.952078 | + | 0.305854i | \(0.0989420\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.3508 | − | 19.2970i | −1.04325 | − | 0.900708i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.19412 | − | 0.689428i | 0.0556159 | − | 0.0321099i | −0.471934 | − | 0.881634i | \(-0.656444\pi\) |
0.527550 | + | 0.849524i | \(0.323111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.94275 | − | 1.69900i | −0.136761 | − | 0.0789592i | 0.430058 | − | 0.902801i | \(-0.358493\pi\) |
−0.566820 | + | 0.823842i | \(0.691826\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.79651 | − | 0.891711i | 0.0833110 | − | 0.0413521i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.37470 | − | 14.5054i | −0.387535 | − | 0.671230i | 0.604582 | − | 0.796543i | \(-0.293340\pi\) |
−0.992117 | + | 0.125312i | \(0.960007\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.43859 | + | 0.443334i | −0.112603 | + | 0.0204713i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.9073 | − | 12.3629i | 1.14767 | − | 0.569655i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.1885 | − | 31.5034i | −0.836308 | − | 1.44853i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.8451 | − | 30.9086i | −0.818789 | − | 1.41818i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.3528 | + | 26.8097i | −0.931889 | + | 1.22753i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.68011 | 0.213840 | 0.106920 | − | 0.994268i | \(-0.465901\pi\) | ||||
0.106920 | + | 0.994268i | \(0.465901\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 10.6162i | − | 0.484057i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.72799 | − | 13.3014i | 0.260633 | − | 0.605233i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.713674 | + | 1.23612i | 0.0324063 | + | 0.0561293i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.9661 | + | 8.64071i | 0.678181 | + | 0.391548i | 0.799169 | − | 0.601106i | \(-0.205273\pi\) |
−0.120988 | + | 0.992654i | \(0.538606\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.7415 | − | 5.82800i | 0.530969 | − | 0.263551i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.7916 | − | 9.11730i | −0.712666 | − | 0.411458i | 0.0993812 | − | 0.995049i | \(-0.468314\pi\) |
−0.812047 | + | 0.583591i | \(0.801647\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 28.3718i | − | 1.27780i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.24721 | − | 0.789672i | −0.280791 | − | 0.0354931i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.59391 | + | 15.6265i | −0.250921 | + | 0.700943i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.6591i | 1.41725i | 0.705583 | + | 0.708627i | \(0.250685\pi\) | ||||
−0.705583 | + | 0.708627i | \(0.749315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.33906 | − | 5.02529i | 0.149178 | − | 0.224514i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.7607 | −1.23779 | −0.618894 | − | 0.785474i | \(-0.712419\pi\) | ||||
−0.618894 | + | 0.785474i | \(0.712419\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.33933 | −0.326596 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.11893 | + | 18.3717i | 0.404986 | + | 0.815914i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 24.5474i | − | 1.08805i | −0.839070 | − | 0.544023i | \(-0.816900\pi\) | ||
0.839070 | − | 0.544023i | \(-0.183100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.2032 | − | 26.1776i | −0.982211 | − | 1.15803i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.6745 | − | 36.4092i | −0.559594 | − | 1.60750i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.43294i | 0.0631429i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −35.8468 | − | 20.6962i | −1.57654 | − | 0.910217i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.1449 | + | 7.40522i | 0.489205 | + | 0.325053i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.9064 | + | 6.29680i | 0.477817 | + | 0.275868i | 0.719506 | − | 0.694486i | \(-0.244368\pi\) |
−0.241689 | + | 0.970354i | \(0.577701\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.2363 | − | 19.4619i | −0.491330 | − | 0.851009i | 0.508620 | − | 0.860991i | \(-0.330156\pi\) |
−0.999950 | + | 0.00998216i | \(0.996823\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −20.2465 | − | 8.71881i | −0.883631 | − | 0.380520i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 15.1125i | − | 0.658312i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0126 | 0.565764 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.4146 | − | 34.2979i | −0.625539 | − | 1.48840i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.324395 | − | 0.561869i | −0.0140511 | − | 0.0243372i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.54103 | + | 4.40119i | 0.109858 | + | 0.190280i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.6461 | + | 20.3629i | 1.32248 | + | 0.878722i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.4145 | − | 26.0776i | 0.922389 | − | 1.12324i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.43945 | − | 12.8855i | −0.319847 | − | 0.553991i | 0.660609 | − | 0.750730i | \(-0.270298\pi\) |
−0.980456 | + | 0.196739i | \(0.936965\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.611708 | − | 9.71712i | 0.0262509 | − | 0.417002i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.90481 | − | 3.98649i | −0.295770 | − | 0.170763i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.5042 | − | 21.6531i | 1.60356 | − | 0.925818i | 0.612797 | − | 0.790240i | \(-0.290044\pi\) |
0.990767 | − | 0.135578i | \(-0.0432891\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21.1293 | + | 16.0405i | 0.901778 | + | 0.684591i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.5210 | − | 32.0793i | 0.789021 | − | 1.36662i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.89365 | + | 6.94861i | 0.250623 | + | 0.295485i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.43890 | − | 0.714211i | 0.0610779 | − | 0.0303165i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.44755 | − | 16.3636i | 0.400305 | − | 0.693349i | −0.593457 | − | 0.804866i | \(-0.702237\pi\) |
0.993763 | + | 0.111516i | \(0.0355707\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.6118 | −1.59081 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26.2585 | + | 39.5190i | −1.10863 | + | 1.66849i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.61497 | − | 16.6536i | −0.405223 | − | 0.701866i | 0.589125 | − | 0.808042i | \(-0.299473\pi\) |
−0.994347 | + | 0.106176i | \(0.966139\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.66525 | + | 0.961432i | 0.0700575 | + | 0.0404477i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.7165 | − | 13.3514i | −0.828016 | − | 0.560705i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.33650 | − | 5.77899i | 0.139874 | − | 0.242268i | −0.787575 | − | 0.616219i | \(-0.788664\pi\) |
0.927449 | + | 0.373951i | \(0.121997\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.3391 | − | 6.54665i | 0.474528 | − | 0.273969i | −0.243605 | − | 0.969874i | \(-0.578330\pi\) |
0.718133 | + | 0.695906i | \(0.244997\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.1285 | − | 12.0455i | −0.757327 | − | 0.503207i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.2023i | 0.633978i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.59957 | − | 4.38761i | −0.316374 | − | 0.182659i | 0.333401 | − | 0.942785i | \(-0.391804\pi\) |
−0.649775 | + | 0.760126i | \(0.725137\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.2230 | + | 32.6839i | 0.674203 | + | 1.35830i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.48979 | − | 19.1958i | −0.144781 | − | 0.796375i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 46.8398 | + | 27.0430i | 1.93991 | + | 1.12001i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.93673 | + | 5.18566i | −0.162764 | + | 0.214401i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.22575 | + | 2.12306i | 0.0505920 | + | 0.0876279i | 0.890212 | − | 0.455546i | \(-0.150556\pi\) |
−0.839620 | + | 0.543174i | \(0.817223\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.86539 | − | 17.0874i | 0.406496 | − | 0.704072i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −36.5986 | − | 2.30394i | −1.50546 | − | 0.0947712i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.67653 | + | 4.43205i | −0.315237 | + | 0.182002i | −0.649268 | − | 0.760560i | \(-0.724925\pi\) |
0.334030 | + | 0.942562i | \(0.391591\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.99270 | − | 4.23469i | 0.204681 | − | 0.173605i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.2542 | + | 16.9376i | −0.460603 | + | 0.693209i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.8781 | − | 24.1783i | 1.71109 | − | 0.987899i | 0.777998 | − | 0.628267i | \(-0.216236\pi\) |
0.933094 | − | 0.359632i | \(-0.117098\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.4198 | + | 18.1402i | −1.28164 | + | 0.739955i | −0.977148 | − | 0.212560i | \(-0.931820\pi\) |
−0.304492 | + | 0.952515i | \(0.598487\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.59090 | − | 1.08889i | 0.105510 | − | 0.0443431i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.32840i | 0.216630i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.9894 | −1.33900 | −0.669499 | − | 0.742813i | \(-0.733491\pi\) | ||||
−0.669499 | + | 0.742813i | \(0.733491\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.66999 | − | 22.7227i | −0.108194 | − | 0.920768i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.0637 | + | 21.3987i | −1.49944 | + | 0.865701i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.91100 | + | 8.50611i | −0.198354 | + | 0.343558i | −0.947995 | − | 0.318286i | \(-0.896893\pi\) |
0.749641 | + | 0.661844i | \(0.230226\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.0543308 | − | 0.0817679i | 0.00219083 | − | 0.00329720i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.68396 | − | 6.38080i | 0.148311 | − | 0.256881i | −0.782293 | − | 0.622911i | \(-0.785950\pi\) |
0.930603 | + | 0.366030i | \(0.119283\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.1718 | 0.609805 | 0.304902 | − | 0.952384i | \(-0.401376\pi\) | ||||
0.304902 | + | 0.952384i | \(0.401376\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.07883 | + | 16.1301i | −0.123549 | + | 0.647280i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.8565 | − | 7.24590i | 1.59682 | − | 0.290301i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.1920 | 0.887680 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −55.4876 | + | 27.5418i | −2.21596 | + | 1.09991i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 12.1043i | − | 0.482629i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.33987i | − | 0.252386i | −0.992006 | − | 0.126193i | \(-0.959724\pi\) | ||
0.992006 | − | 0.126193i | \(-0.0402759\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.0534 | + | 8.67335i | 0.518826 | + | 0.344735i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.15392 | −0.0457919 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.2798 | − | 32.6565i | −0.486542 | − | 1.29390i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.36012 | − | 18.6713i | 0.0933650 | − | 0.738624i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.91338 | 0.312560 | 0.156280 | − | 0.987713i | \(-0.450050\pi\) | ||||
0.156280 | + | 0.987713i | \(0.450050\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.71529 | + | 15.0953i | −0.343697 | + | 0.595301i | −0.985116 | − | 0.171890i | \(-0.945013\pi\) |
0.641419 | + | 0.767191i | \(0.278346\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.53036 | − | 5.09784i | −0.0996327 | − | 0.200727i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.396991 | − | 0.687609i | 0.0156073 | − | 0.0270327i | −0.858116 | − | 0.513455i | \(-0.828365\pi\) |
0.873724 | + | 0.486423i | \(0.161698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −51.7713 | + | 29.8902i | −2.03220 | + | 1.17329i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.42220 | − | 12.1034i | −0.0557403 | − | 0.474371i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.3455 | 0.483117 | 0.241559 | − | 0.970386i | \(-0.422341\pi\) | ||||
0.241559 | + | 0.970386i | \(0.422341\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 0.375988i | − | 0.0146911i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.0005 | + | 23.5342i | 1.20944 | + | 0.918157i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.112430 | + | 0.0649117i | −0.00437966 | + | 0.00252860i | −0.502188 | − | 0.864758i | \(-0.667472\pi\) |
0.497809 | + | 0.867287i | \(0.334138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.63535 | + | 2.67622i | −0.180294 | + | 0.104093i | −0.587431 | − | 0.809274i | \(-0.699861\pi\) |
0.407137 | + | 0.913367i | \(0.366527\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.8114 | + | 43.9427i | 0.847083 | + | 1.70659i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.40950 | − | 1.52885i | 0.326106 | − | 0.0592861i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.6642 | + | 7.88904i | −0.529080 | + | 0.305465i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.3839 | + | 20.9202i | 0.401466 | + | 0.808822i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.3132 | − | 36.9155i | 0.822787 | − | 1.42511i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.1452 | − | 17.5720i | −0.391069 | − | 0.677351i | 0.601522 | − | 0.798856i | \(-0.294561\pi\) |
−0.992591 | + | 0.121505i | \(0.961228\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.5523 | + | 4.68641i | 0.945020 | + | 0.180380i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.5452 | + | 18.2126i | 1.21238 | + | 0.699967i | 0.963277 | − | 0.268510i | \(-0.0865312\pi\) |
0.249102 | + | 0.968477i | \(0.419865\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.53303 | − | 1.55130i | 0.327468 | − | 0.0595335i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41.6109 | + | 2.61947i | 1.59453 | + | 0.100378i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.6439 | + | 8.45468i | 0.560334 | + | 0.323509i | 0.753280 | − | 0.657700i | \(-0.228471\pi\) |
−0.192945 | + | 0.981210i | \(0.561804\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.98849i | − | 0.114184i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.53254 | − | 24.3448i | 0.0584701 | − | 0.928813i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 48.4299 | − | 27.9610i | 1.84503 | − | 1.06523i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.43736 | + | 14.6139i | −0.320972 | + | 0.555940i | −0.980689 | − | 0.195574i | \(-0.937343\pi\) |
0.659717 | + | 0.751514i | \(0.270676\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17.3111 | + | 34.1214i | −0.657593 | + | 1.29617i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.21556 | − | 1.85650i | −0.121973 | − | 0.0704211i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.369866 | − | 0.640626i | −0.0140097 | − | 0.0242655i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.70807 | + | 3.44121i | 0.0646053 | + | 0.130159i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.8133 | 1.54150 | 0.770748 | − | 0.637140i | \(-0.219883\pi\) | ||||
0.770748 | + | 0.637140i | \(0.219883\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.90162 | − | 13.6860i | 0.298015 | − | 0.516178i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.39383 | − | 3.58394i | −0.203143 | − | 0.134979i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.0301 | + | 41.9863i | −0.565266 | + | 1.57906i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.3529 | + | 36.9843i | −0.801925 | + | 1.38898i | 0.116422 | + | 0.993200i | \(0.462858\pi\) |
−0.918347 | + | 0.395776i | \(0.870476\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.22881 | − | 6.24695i | −0.308604 | − | 0.234279i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.27838 | + | 4.20217i | −0.272577 | + | 0.157373i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.05999 | + | 5.23079i | 0.338824 | + | 0.195620i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.4911 | − | 11.6220i | −0.653218 | − | 0.434032i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.82946 | − | 17.0251i | −0.366577 | − | 0.634930i | 0.622451 | − | 0.782659i | \(-0.286137\pi\) |
−0.989028 | + | 0.147729i | \(0.952804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.19746 | + | 2.93450i | 0.305289 | + | 0.109286i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.508290 | − | 8.07432i | 0.0189035 | − | 0.300287i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.0082 | + | 20.7988i | 0.445974 | + | 0.772450i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.8591 | − | 30.9329i | −0.662358 | − | 1.14724i | −0.979994 | − | 0.199026i | \(-0.936222\pi\) |
0.317636 | − | 0.948213i | \(-0.397111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.1018 | + | 9.94489i | 0.929695 | + | 0.368329i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.8840 | −1.58612 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.4533i | 1.30950i | 0.755847 | + | 0.654749i | \(0.227225\pi\) | ||||
−0.755847 | + | 0.654749i | \(0.772775\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.60008 | − | 3.86136i | 0.132791 | − | 0.142428i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.25794 | − | 3.91086i | −0.0831722 | − | 0.144058i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.6506 | − | 10.7679i | −0.686072 | − | 0.396104i | 0.116067 | − | 0.993241i | \(-0.462971\pi\) |
−0.802139 | + | 0.597137i | \(0.796305\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.02407 | + | 63.9233i | −0.147828 | + | 2.34828i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.1882 | − | 9.92361i | −0.630574 | − | 0.364062i | 0.150400 | − | 0.988625i | \(-0.451944\pi\) |
−0.780974 | + | 0.624563i | \(0.785277\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.61096i | 0.168932i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.57140 | + | 20.3948i | 0.313611 | + | 0.746205i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.3817 | − | 5.52339i | 1.11012 | − | 0.201820i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 34.1548i | − | 1.24633i | −0.782092 | − | 0.623163i | \(-0.785847\pi\) | ||
0.782092 | − | 0.623163i | \(-0.214153\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.1336 | + | 1.14153i | 0.660824 | + | 0.0415998i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.64534 | −0.132667 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.3294 | −0.738885 | −0.369442 | − | 0.929254i | \(-0.620451\pi\) | ||||
−0.369442 | + | 0.929254i | \(0.620451\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26.3342 | + | 1.65778i | 0.955872 | + | 0.0601736i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 36.7989i | − | 1.33396i | −0.745075 | − | 0.666980i | \(-0.767587\pi\) | ||
0.745075 | − | 0.666980i | \(-0.232413\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.9459 | + | 31.3367i | −1.33753 | + | 1.13446i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.48855 | + | 5.91254i | −0.162284 | + | 0.213768i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 61.8097i | 2.23182i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.6942 | + | 20.0307i | 1.25111 | + | 0.722326i | 0.971329 | − | 0.237739i | \(-0.0764063\pi\) |
0.279777 | + | 0.960065i | \(0.409740\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.557439 | − | 8.85505i | 0.0200757 | − | 0.318907i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.0859 | − | 15.6381i | −0.974213 | − | 0.562462i | −0.0736952 | − | 0.997281i | \(-0.523479\pi\) |
−0.900518 | + | 0.434818i | \(0.856813\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.39629 | + | 11.0787i | 0.229762 | + | 0.397959i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.13910 | − | 9.69418i | −0.0408650 | − | 0.347777i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 0.965787i | − | 0.0346029i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.2403 | −1.08208 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.52887 | + | 24.5003i | 0.304797 | + | 0.875568i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.49522 | − | 6.05390i | −0.124750 | − | 0.216073i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.3830 | + | 35.3043i | 0.726574 | + | 1.25846i | 0.958323 | + | 0.285687i | \(0.0922218\pi\) |
−0.231749 | + | 0.972776i | \(0.574445\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.07791 | + | 33.0080i | −0.0739754 | + | 1.17512i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.91033 | − | 7.55753i | 0.316815 | − | 0.268715i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.0367 | − | 38.1687i | −0.782546 | − | 1.35541i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.04793 | + | 4.68301i | 0.249964 | + | 0.166089i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.6301 | + | 6.13732i | 0.376539 | + | 0.217395i | 0.676311 | − | 0.736616i | \(-0.263577\pi\) |
−0.299772 | + | 0.954011i | \(0.596911\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42.2590 | + | 24.3982i | −1.49502 | + | 0.863148i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −42.3460 | + | 17.7969i | −1.49622 | + | 0.628824i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.2702 | − | 54.1616i | 1.10350 | − | 1.91132i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.42774 | − | 1.22705i | −0.120812 | − | 0.0432478i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.0361 | + | 6.66852i | 0.353289 | + | 0.234743i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.5729 | + | 25.2410i | −0.512356 | + | 0.887427i | 0.487541 | + | 0.873100i | \(0.337894\pi\) |
−0.999897 | + | 0.0143273i | \(0.995439\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.9170 | 0.699379 | 0.349690 | − | 0.936866i | \(-0.386287\pi\) | ||||
0.349690 | + | 0.936866i | \(0.386287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.15641 | + | 4.34447i | 0.0756287 | + | 0.152367i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.64768 | − | 2.85386i | −0.0577156 | − | 0.0999664i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −48.4878 | − | 27.9944i | −1.69637 | − | 0.979402i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.6038 | + | 33.1406i | 0.754897 | + | 1.15803i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.3309 | + | 23.0897i | −0.465250 | + | 0.805837i | −0.999213 | − | 0.0396708i | \(-0.987369\pi\) |
0.533962 | + | 0.845508i | \(0.320702\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.5281 | − | 15.8934i | 0.959570 | − | 0.554008i | 0.0635296 | − | 0.997980i | \(-0.479764\pi\) |
0.896041 | + | 0.443972i | \(0.146431\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.52337 | − | 40.0844i | 0.0878525 | − | 1.39556i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.7367i | 1.52087i | 0.649413 | + | 0.760436i | \(0.275015\pi\) | ||||
−0.649413 | + | 0.760436i | \(0.724985\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.03642 | − | 3.48513i | −0.209653 | − | 0.121043i | 0.391497 | − | 0.920179i | \(-0.371957\pi\) |
−0.601150 | + | 0.799136i | \(0.705291\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.7213 | + | 1.55624i | 0.857572 | + | 0.0539855i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.0010 | − | 37.2340i | −0.485107 | − | 1.29008i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.31357 | − | 0.758390i | −0.0454580 | − | 0.0262452i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.54299 | + | 13.0503i | 0.157029 | + | 0.451084i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.6379 | + | 46.1382i | 0.919643 | + | 1.59287i | 0.799958 | + | 0.600056i | \(0.204855\pi\) |
0.119685 | + | 0.992812i | \(0.461811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.03696 | − | 3.52812i | 0.0702400 | − | 0.121659i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.4522 | − | 29.1164i | −0.497759 | − | 1.00282i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.46537 | − | 2.57808i | 0.153613 | − | 0.0886887i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.4823 | + | 10.9120i | 1.04739 | + | 0.374940i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.9951 | − | 30.2103i | −0.514632 | − | 1.03681i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.82957 | + | 3.36570i | −0.199835 | + | 0.115375i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.1872 | − | 27.2435i | 1.61566 | − | 0.932801i | 0.627632 | − | 0.778510i | \(-0.284024\pi\) |
0.988025 | − | 0.154291i | \(-0.0493093\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.93477 | + | 3.75506i | −0.305563 | + | 0.128420i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.7099i | 0.912394i | 0.889879 | + | 0.456197i | \(0.150789\pi\) | ||||
−0.889879 | + | 0.456197i | \(0.849211\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.4926 | −1.68867 | −0.844333 | − | 0.535819i | \(-0.820003\pi\) | ||||
−0.844333 | + | 0.535819i | \(0.820003\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.356509 | − | 0.478263i | −0.0121498 | − | 0.0162992i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.7843 | + | 11.9998i | −0.707506 | + | 0.408479i | −0.810137 | − | 0.586241i | \(-0.800607\pi\) |
0.102631 | + | 0.994719i | \(0.467274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.68192 | − | 2.91317i | 0.0571870 | − | 0.0990509i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.7774 | + | 23.7276i | 0.399982 | + | 0.805833i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.30041 | + | 14.3767i | −0.281572 | + | 0.487697i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.66917 | −0.158209 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.06601 | + | 3.81022i | −0.306838 | + | 0.128956i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.80910 | + | 10.6406i | −0.128771 | + | 0.359719i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.48573 | 0.219008 | 0.109504 | − | 0.993986i | \(-0.465074\pi\) | ||||
0.109504 | + | 0.993986i | \(0.465074\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.6257 | + | 9.71806i | 0.493313 | + | 0.327782i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.29737i | 0.144782i | 0.997376 | + | 0.0723910i | \(0.0230630\pi\) | ||||
−0.997376 | + | 0.0723910i | \(0.976937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.8931i | 0.602150i | 0.953600 | + | 0.301075i | \(0.0973455\pi\) | ||||
−0.953600 | + | 0.301075i | \(0.902654\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.37758 | + | 4.15828i | −0.281609 | + | 0.139779i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.42110 | 0.215599 | 0.107800 | − | 0.994173i | \(-0.465619\pi\) | ||||
0.107800 | + | 0.994173i | \(0.465619\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.36310 | + | 6.60127i | −0.0792558 | + | 0.221399i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.7954 | − | 42.0199i | 0.361661 | − | 1.40772i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −63.7082 | −2.13191 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.62494 | − | 8.01064i | 0.154595 | − | 0.267766i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.0985 | − | 22.7233i | 0.504125 | − | 0.758708i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.63856 | + | 11.4983i | −0.221408 | + | 0.383491i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.2184 | − | 31.8803i | 1.83959 | − | 1.06209i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −34.3452 | + | 4.03569i | −1.14294 | + | 0.134299i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.44766 | −0.0813629 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 11.9139i | − | 0.395593i | −0.980243 | − | 0.197797i | \(-0.936621\pi\) | ||
0.980243 | − | 0.197797i | \(-0.0633786\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.34135 | − | 50.1673i | 0.210329 | − | 1.66394i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.6598 | + | 22.3203i | −1.28086 | + | 0.739504i | −0.977005 | − | 0.213215i | \(-0.931606\pi\) |
−0.303853 | + | 0.952719i | \(0.598273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.7851 | − | 17.7738i | 1.01884 | − | 0.588226i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.69078 | − | 5.55463i | 0.122014 | − | 0.183631i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.15092 | − | 0.769980i | −0.0710297 | − | 0.0254270i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.4378 | − | 16.4185i | 0.938075 | − | 0.541598i | 0.0487187 | − | 0.998813i | \(-0.484486\pi\) |
0.889356 | + | 0.457215i | \(0.151153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.3884 | + | 1.03167i | 0.540016 | + | 0.0339948i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.6334 | + | 27.0779i | −0.514581 | + | 0.891281i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.12307 | + | 8.87342i | 0.168446 | + | 0.291756i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.79472 | − | 1.23809i | −0.321701 | − | 0.0406643i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.0150 | + | 7.51419i | 0.427007 | + | 0.246533i | 0.698071 | − | 0.716029i | \(-0.254042\pi\) |
−0.271064 | + | 0.962561i | \(0.587375\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.47559 | − | 51.2394i | 0.277776 | − | 1.67930i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.724092 | + | 1.45881i | 0.0237057 | + | 0.0477593i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.3299 | + | 5.96399i | 0.337825 | + | 0.195043i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.0428i | 0.458758i | 0.973337 | + | 0.229379i | \(0.0736695\pi\) | ||||
−0.973337 | + | 0.229379i | \(0.926330\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.4144 | − | 12.9000i | −0.633566 | − | 0.420974i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.8936 | + | 17.2591i | −0.974505 | + | 0.562631i | −0.900607 | − | 0.434635i | \(-0.856877\pi\) |
−0.0738984 | + | 0.997266i | \(0.523544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.205689 | + | 0.356264i | −0.00669815 | + | 0.0116015i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.03841 | + | 5.15769i | −0.0988395 | + | 0.167780i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.51834 | − | 3.76336i | −0.211817 | − | 0.122293i | 0.390338 | − | 0.920672i | \(-0.372358\pi\) |
−0.602156 | + | 0.798379i | \(0.705691\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.3317 | − | 56.0002i | −1.04953 | − | 1.81784i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.20642 | − | 6.33067i | 0.136403 | − | 0.205286i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.3406 | 1.43633 | 0.718166 | − | 0.695871i | \(-0.244982\pi\) | ||||
0.718166 | + | 0.695871i | \(0.244982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.73585 | + | 4.73863i | −0.0885299 | + | 0.153338i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37.3384 | − | 18.5332i | 1.20698 | − | 0.599095i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.0963 | − | 6.12009i | −0.552070 | − | 0.197628i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.9639 | − | 20.7221i | 0.385932 | − | 0.668455i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −32.2794 | + | 13.5662i | −1.04019 | + | 0.437165i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.94407 | − | 4.58651i | 0.255729 | − | 0.147645i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.3694 | + | 24.4620i | 1.36251 | + | 0.786644i | 0.989957 | − | 0.141367i | \(-0.0451499\pi\) |
0.372551 | + | 0.928012i | \(0.378483\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.58813 | + | 72.8835i | −0.147392 | + | 2.34136i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.57411 | + | 4.45849i | 0.0826072 | + | 0.143080i | 0.904369 | − | 0.426751i | \(-0.140342\pi\) |
−0.821762 | + | 0.569831i | \(0.807009\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.2056 | + | 14.5934i | −0.551587 | + | 0.467843i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −34.5880 | − | 22.9820i | −1.10770 | − | 0.736015i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.6343 | − | 32.2756i | −0.596165 | − | 1.03259i | −0.993381 | − | 0.114863i | \(-0.963357\pi\) |
0.397217 | − | 0.917725i | \(-0.369976\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.9040 | + | 63.9195i | 1.17946 | + | 2.04288i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.2152 | − | 43.7528i | 1.06048 | − | 1.39692i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.58746 | −0.305793 | −0.152896 | − | 0.988242i | \(-0.548860\pi\) | ||||
−0.152896 | + | 0.988242i | \(0.548860\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.21886i | 0.293737i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −31.5487 | + | 23.5171i | −1.00421 | + | 0.748559i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.9243 | + | 20.6534i | 0.379169 | + | 0.656741i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.50543 | + | 5.48797i | 0.301950 | + | 0.174331i | 0.643319 | − | 0.765599i | \(-0.277557\pi\) |
−0.341369 | + | 0.939930i | \(0.610890\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.09431 | + | 4.04937i | 0.193397 | + | 0.128503i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.42734 | + | 2.55613i | 0.140356 | + | 0.0810346i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.0337i | 0.697814i | 0.937157 | + | 0.348907i | \(0.113447\pi\) | ||||
−0.937157 | + | 0.348907i | \(0.886553\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.63868 | + | 10.4526i | 0.115123 | + | 0.330704i |
(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 | 1008.2.bf.i.31.16 | yes | 32 | |
3.2 | odd | 2 | 3024.2.bf.i.1711.10 | 32 | |||
4.3 | odd | 2 | inner | 1008.2.bf.i.31.1 | ✓ | 32 | |
7.5 | odd | 6 | 1008.2.cz.i.607.12 | yes | 32 | ||
9.2 | odd | 6 | 3024.2.cz.i.2719.7 | 32 | |||
9.7 | even | 3 | 1008.2.cz.i.367.5 | yes | 32 | ||
12.11 | even | 2 | 3024.2.bf.i.1711.9 | 32 | |||
21.5 | even | 6 | 3024.2.cz.i.1279.8 | 32 | |||
28.19 | even | 6 | 1008.2.cz.i.607.5 | yes | 32 | ||
36.7 | odd | 6 | 1008.2.cz.i.367.12 | yes | 32 | ||
36.11 | even | 6 | 3024.2.cz.i.2719.8 | 32 | |||
63.47 | even | 6 | 3024.2.bf.i.2287.8 | 32 | |||
63.61 | odd | 6 | inner | 1008.2.bf.i.943.1 | yes | 32 | |
84.47 | odd | 6 | 3024.2.cz.i.1279.7 | 32 | |||
252.47 | odd | 6 | 3024.2.bf.i.2287.7 | 32 | |||
252.187 | even | 6 | inner | 1008.2.bf.i.943.16 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.bf.i.31.1 | ✓ | 32 | 4.3 | odd | 2 | inner | |
1008.2.bf.i.31.16 | yes | 32 | 1.1 | even | 1 | trivial | |
1008.2.bf.i.943.1 | yes | 32 | 63.61 | odd | 6 | inner | |
1008.2.bf.i.943.16 | yes | 32 | 252.187 | even | 6 | inner | |
1008.2.cz.i.367.5 | yes | 32 | 9.7 | even | 3 | ||
1008.2.cz.i.367.12 | yes | 32 | 36.7 | odd | 6 | ||
1008.2.cz.i.607.5 | yes | 32 | 28.19 | even | 6 | ||
1008.2.cz.i.607.12 | yes | 32 | 7.5 | odd | 6 | ||
3024.2.bf.i.1711.9 | 32 | 12.11 | even | 2 | |||
3024.2.bf.i.1711.10 | 32 | 3.2 | odd | 2 | |||
3024.2.bf.i.2287.7 | 32 | 252.47 | odd | 6 | |||
3024.2.bf.i.2287.8 | 32 | 63.47 | even | 6 | |||
3024.2.cz.i.1279.7 | 32 | 84.47 | odd | 6 | |||
3024.2.cz.i.1279.8 | 32 | 21.5 | even | 6 | |||
3024.2.cz.i.2719.7 | 32 | 9.2 | odd | 6 | |||
3024.2.cz.i.2719.8 | 32 | 36.11 | even | 6 |