Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(881,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.cc (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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 881.8 | ||
Character | \(\chi\) | \(=\) | 3024.881 |
Dual form | 3024.2.cc.d.2897.8 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.965651 | + | 1.67256i | −0.431852 | + | 0.747990i | −0.997033 | − | 0.0769771i | \(-0.975473\pi\) |
0.565181 | + | 0.824967i | \(0.308806\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.53170 | + | 0.768427i | −0.956894 | + | 0.290438i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.10681 | − | 0.639015i | 0.333715 | − | 0.192670i | −0.323774 | − | 0.946134i | \(-0.604952\pi\) |
0.657489 | + | 0.753464i | \(0.271619\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.52802 | + | 1.45955i | 0.701146 | + | 0.404807i | 0.807774 | − | 0.589492i | \(-0.200672\pi\) |
−0.106628 | + | 0.994299i | \(0.534005\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.475237 | 0.115262 | 0.0576310 | − | 0.998338i | \(-0.481645\pi\) | ||||
0.0576310 | + | 0.998338i | \(0.481645\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.10647i | 1.40092i | 0.713691 | + | 0.700460i | \(0.247022\pi\) | ||||
−0.713691 | + | 0.700460i | \(0.752978\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.51132 | − | 3.75931i | −1.35770 | − | 0.783871i | −0.368390 | − | 0.929671i | \(-0.620091\pi\) |
−0.989314 | + | 0.145801i | \(0.953424\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.635036 | + | 1.09991i | 0.127007 | + | 0.219983i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.76797 | + | 2.17544i | −0.699695 | + | 0.403969i | −0.807234 | − | 0.590232i | \(-0.799036\pi\) |
0.107539 | + | 0.994201i | \(0.465703\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.21872 | + | 2.43568i | 0.757705 | + | 0.437461i | 0.828471 | − | 0.560032i | \(-0.189211\pi\) |
−0.0707660 | + | 0.997493i | \(0.522544\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.15950 | − | 4.97645i | 0.195992 | − | 0.841173i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.76145 | 0.289580 | 0.144790 | − | 0.989462i | \(-0.453749\pi\) | ||||
0.144790 | + | 0.989462i | \(0.453749\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.16103 | − | 2.01097i | 0.181323 | − | 0.314060i | −0.761009 | − | 0.648742i | \(-0.775296\pi\) |
0.942331 | + | 0.334682i | \(0.108629\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.63638 | − | 8.03045i | −0.707042 | − | 1.22463i | −0.965950 | − | 0.258730i | \(-0.916696\pi\) |
0.258908 | − | 0.965902i | \(-0.416637\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00447 | − | 6.93595i | −0.584112 | − | 1.01171i | −0.994985 | − | 0.100020i | \(-0.968109\pi\) |
0.410873 | − | 0.911693i | \(-0.365224\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.81904 | − | 3.89086i | 0.831291 | − | 0.555837i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3345i | 1.41955i | 0.704428 | + | 0.709775i | \(0.251204\pi\) | ||||
−0.704428 | + | 0.709775i | \(0.748796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.46826i | 0.332820i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.74272 | + | 3.01848i | −0.226883 | + | 0.392973i | −0.956883 | − | 0.290475i | \(-0.906187\pi\) |
0.730000 | + | 0.683447i | \(0.239520\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.26195 | + | 2.46064i | −0.545686 | + | 0.315052i | −0.747380 | − | 0.664396i | \(-0.768689\pi\) |
0.201694 | + | 0.979449i | \(0.435355\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.88237 | + | 2.81883i | −0.605583 | + | 0.349633i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.602527 | + | 1.04361i | −0.0736104 | + | 0.127497i | −0.900481 | − | 0.434895i | \(-0.856785\pi\) |
0.826871 | + | 0.562392i | \(0.190119\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.2114i | 1.33055i | 0.746598 | + | 0.665275i | \(0.231686\pi\) | ||||
−0.746598 | + | 0.665275i | \(0.768314\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.84336i | − | 0.215749i | −0.994164 | − | 0.107875i | \(-0.965595\pi\) | ||
0.994164 | − | 0.107875i | \(-0.0344045\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.31107 | + | 2.46830i | −0.263371 | + | 0.281288i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.54654 | − | 14.8030i | −0.961561 | − | 1.66547i | −0.718584 | − | 0.695440i | \(-0.755209\pi\) |
−0.242977 | − | 0.970032i | \(-0.578124\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.225217 | − | 0.390088i | −0.0247208 | − | 0.0428177i | 0.853400 | − | 0.521256i | \(-0.174536\pi\) |
−0.878121 | + | 0.478438i | \(0.841203\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.458913 | + | 0.794861i | −0.0497761 | + | 0.0862148i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.2580 | 1.19335 | 0.596675 | − | 0.802483i | \(-0.296488\pi\) | ||||
0.596675 | + | 0.802483i | \(0.296488\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.52175 | − | 1.75255i | −0.788493 | − | 0.183718i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.2134 | − | 5.89672i | −1.04787 | − | 0.604991i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.22775 | + | 5.32764i | −0.936936 | + | 0.540940i | −0.888998 | − | 0.457910i | \(-0.848598\pi\) |
−0.0479373 | + | 0.998850i | \(0.515265\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.65330 | − | 11.5239i | −0.662028 | − | 1.14667i | −0.980082 | − | 0.198594i | \(-0.936363\pi\) |
0.318054 | − | 0.948073i | \(-0.396971\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.4947 | − | 9.52323i | −1.62527 | − | 0.938352i | −0.985478 | − | 0.169806i | \(-0.945686\pi\) |
−0.639795 | − | 0.768546i | \(-0.720981\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 16.1392i | − | 1.56024i | −0.625630 | − | 0.780120i | \(-0.715158\pi\) | ||
0.625630 | − | 0.780120i | \(-0.284842\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.40434 | 0.326077 | 0.163038 | − | 0.986620i | \(-0.447871\pi\) | ||||
0.163038 | + | 0.986620i | \(0.447871\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.64150 | − | 2.10242i | −0.342563 | − | 0.197779i | 0.318842 | − | 0.947808i | \(-0.396706\pi\) |
−0.661405 | + | 0.750029i | \(0.730040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.5753 | − | 7.26037i | 1.17265 | − | 0.677033i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.20316 | + | 0.365185i | −0.110293 | + | 0.0334765i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.68332 | + | 8.11175i | −0.425756 | + | 0.737432i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1094 | −1.08310 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1828 | −1.52473 | −0.762363 | − | 0.647150i | \(-0.775961\pi\) | ||||
−0.762363 | + | 0.647150i | \(0.775961\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00420 | + | 6.93548i | −0.349848 | + | 0.605955i | −0.986222 | − | 0.165425i | \(-0.947100\pi\) |
0.636374 | + | 0.771381i | \(0.280434\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.69238 | − | 15.4598i | −0.406881 | − | 1.34053i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.44241 | + | 4.87423i | −0.721284 | + | 0.416433i | −0.815225 | − | 0.579144i | \(-0.803387\pi\) |
0.0939411 | + | 0.995578i | \(0.470053\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.76047 | − | 3.90316i | −0.573416 | − | 0.331062i | 0.185097 | − | 0.982720i | \(-0.440740\pi\) |
−0.758513 | + | 0.651658i | \(0.774074\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.73070 | 0.311977 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 8.40286i | − | 0.697820i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.62284 | − | 5.55575i | −0.788333 | − | 0.455145i | 0.0510420 | − | 0.998697i | \(-0.483746\pi\) |
−0.839376 | + | 0.543552i | \(0.817079\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.88730 | + | 3.26890i | 0.153586 | + | 0.266020i | 0.932543 | − | 0.361058i | \(-0.117584\pi\) |
−0.778957 | + | 0.627077i | \(0.784251\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.14763 | + | 4.70404i | −0.654433 | + | 0.377837i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.55162 | + | 2.05053i | 0.283450 | + | 0.163650i | 0.634984 | − | 0.772525i | \(-0.281007\pi\) |
−0.351534 | + | 0.936175i | \(0.614340\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.3735 | + | 4.51399i | 1.52684 | + | 0.355752i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.3871 | 1.12689 | 0.563443 | − | 0.826155i | \(-0.309477\pi\) | ||||
0.563443 | + | 0.826155i | \(0.309477\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.06975 | + | 13.9772i | −0.624456 | + | 1.08159i | 0.364190 | + | 0.931325i | \(0.381346\pi\) |
−0.988646 | + | 0.150265i | \(0.951987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.23942 | − | 3.87879i | −0.172263 | − | 0.298368i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.695376 | + | 1.20443i | 0.0528685 | + | 0.0915709i | 0.891248 | − | 0.453515i | \(-0.149830\pi\) |
−0.838380 | + | 0.545086i | \(0.816497\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.45293 | − | 2.29668i | −0.185424 | − | 0.173613i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.60605i | − | 0.344273i | −0.985073 | − | 0.172136i | \(-0.944933\pi\) | ||
0.985073 | − | 0.172136i | \(-0.0550669\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.3732i | − | 1.21701i | −0.793550 | − | 0.608505i | \(-0.791769\pi\) | ||
0.793550 | − | 0.608505i | \(-0.208231\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.70094 | + | 2.94612i | −0.125056 | + | 0.216603i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.525996 | − | 0.303684i | 0.0384646 | − | 0.0222075i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.7953 | + | 7.38735i | −0.925833 | + | 0.534530i | −0.885491 | − | 0.464656i | \(-0.846178\pi\) |
−0.0403419 | + | 0.999186i | \(0.512845\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.91923 | − | 15.4486i | 0.642020 | − | 1.11201i | −0.342961 | − | 0.939350i | \(-0.611430\pi\) |
0.984981 | − | 0.172662i | \(-0.0552369\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.00352i | − | 0.570227i | −0.958494 | − | 0.285113i | \(-0.907969\pi\) | ||
0.958494 | − | 0.285113i | \(-0.0920313\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.3034i | 1.15572i | 0.816137 | + | 0.577858i | \(0.196111\pi\) | ||||
−0.816137 | + | 0.577858i | \(0.803889\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.86772 | − | 8.40298i | 0.552205 | − | 0.589773i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.24230 | + | 3.88378i | 0.156609 | + | 0.271255i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.90213 | + | 6.75868i | 0.269916 | + | 0.467508i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1930 | − | 17.6548i | 0.701717 | − | 1.21541i | −0.266147 | − | 0.963933i | \(-0.585751\pi\) |
0.967863 | − | 0.251476i | \(-0.0809161\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.9085 | 1.22135 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5522 | − | 2.92464i | −0.852099 | − | 0.198537i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.20141 | + | 0.693633i | 0.0808154 | + | 0.0466588i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.95301 | − | 1.12757i | 0.130783 | − | 0.0755078i | −0.433181 | − | 0.901307i | \(-0.642609\pi\) |
0.563964 | + | 0.825799i | \(0.309276\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8916 | + | 18.8648i | 0.722899 | + | 1.25210i | 0.959833 | + | 0.280572i | \(0.0905243\pi\) |
−0.236934 | + | 0.971526i | \(0.576142\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.4832 | + | 6.05247i | 0.692748 | + | 0.399958i | 0.804641 | − | 0.593762i | \(-0.202358\pi\) |
−0.111893 | + | 0.993720i | \(0.535691\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 21.9876i | − | 1.44046i | −0.693736 | − | 0.720229i | \(-0.744037\pi\) | ||
0.693736 | − | 0.720229i | \(-0.255963\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.4677 | 1.00900 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.7861 | + | 10.8462i | 1.21517 | + | 0.701581i | 0.963882 | − | 0.266330i | \(-0.0858111\pi\) |
0.251292 | + | 0.967911i | \(0.419144\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.1674 | + | 13.3757i | −1.49234 | + | 0.861604i | −0.999961 | − | 0.00877651i | \(-0.997206\pi\) |
−0.492380 | + | 0.870380i | \(0.663873\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.888520 | + | 13.4899i | 0.0567655 | + | 0.861837i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.91271 | + | 15.4373i | −0.567102 | + | 0.982250i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.75601 | −0.110839 | −0.0554193 | − | 0.998463i | \(-0.517650\pi\) | ||||
−0.0554193 | + | 0.998463i | \(0.517650\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.60903 | −0.604114 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.9860 | + | 25.9565i | −0.934800 | + | 1.61912i | −0.159809 | + | 0.987148i | \(0.551088\pi\) |
−0.774991 | + | 0.631972i | \(0.782246\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.45946 | + | 1.35354i | −0.277097 | + | 0.0841050i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.4273 | + | 7.75223i | −0.827960 | + | 0.478023i | −0.853154 | − | 0.521659i | \(-0.825313\pi\) |
0.0251934 | + | 0.999683i | \(0.491980\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.2850 | − | 9.97951i | −1.06181 | − | 0.613036i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.412404 | −0.0251447 | −0.0125724 | − | 0.999921i | \(-0.504002\pi\) | ||||
−0.0125724 | + | 0.999921i | \(0.504002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.360056i | 0.0218718i | 0.999940 | + | 0.0109359i | \(0.00348108\pi\) | ||||
−0.999940 | + | 0.0109359i | \(0.996519\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.40572 | + | 0.811595i | 0.0847683 | + | 0.0489410i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.03617 | − | 5.25881i | −0.182426 | − | 0.315971i | 0.760280 | − | 0.649595i | \(-0.225062\pi\) |
−0.942706 | + | 0.333624i | \(0.891728\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.22494 | − | 4.74867i | 0.490659 | − | 0.283282i | −0.234189 | − | 0.972191i | \(-0.575243\pi\) |
0.724848 | + | 0.688909i | \(0.241910\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.81761 | + | 5.66820i | 0.583596 | + | 0.336939i | 0.762561 | − | 0.646916i | \(-0.223942\pi\) |
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.39411 | + | 5.98333i | −0.0822915 | + | 0.353185i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7741 | −0.986715 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.22450 | + | 15.9773i | −0.538901 | + | 0.933404i | 0.460062 | + | 0.887887i | \(0.347827\pi\) |
−0.998964 | + | 0.0455177i | \(0.985506\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.36572 | − | 5.82960i | −0.195960 | − | 0.339412i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.9738 | − | 19.0072i | −0.634632 | − | 1.09922i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.9088 | + | 16.7680i | 1.03224 | + | 0.966491i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 9.50447i | − | 0.544224i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 11.0961i | − | 0.633285i | −0.948545 | − | 0.316643i | \(-0.897444\pi\) | ||
0.948545 | − | 0.316643i | \(-0.102556\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.06866 | − | 1.85097i | 0.0605979 | − | 0.104959i | −0.834135 | − | 0.551560i | \(-0.814033\pi\) |
0.894733 | + | 0.446602i | \(0.147366\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.3161 | − | 12.8842i | 1.26138 | − | 0.728259i | 0.288039 | − | 0.957619i | \(-0.406997\pi\) |
0.973342 | + | 0.229360i | \(0.0736634\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.82524 | − | 3.36320i | 0.327178 | − | 0.188896i | −0.327409 | − | 0.944883i | \(-0.606176\pi\) |
0.654588 | + | 0.755986i | \(0.272842\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.78028 | + | 4.81558i | −0.155666 | + | 0.269621i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.90202i | 0.161473i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.70747i | 0.205653i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.4679 | + | 14.4826i | 0.852773 | + | 0.798453i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0006 | + | 20.7857i | 0.659615 | + | 1.14249i | 0.980715 | + | 0.195441i | \(0.0626139\pi\) |
−0.321101 | + | 0.947045i | \(0.604053\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.16366 | − | 2.01552i | −0.0635777 | − | 0.110120i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.07839 | + | 1.86783i | −0.0587438 | + | 0.101747i | −0.893902 | − | 0.448263i | \(-0.852043\pi\) |
0.835158 | + | 0.550010i | \(0.185376\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.22575 | 0.337143 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.7422 | + | 14.3220i | −0.634021 | + | 0.773316i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.31897 | + | 4.22561i | 0.392903 | + | 0.226843i | 0.683417 | − | 0.730028i | \(-0.260493\pi\) |
−0.290514 | + | 0.956871i | \(0.593826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.6656 | + | 6.73516i | −0.624447 | + | 0.360525i | −0.778598 | − | 0.627523i | \(-0.784069\pi\) |
0.154151 | + | 0.988047i | \(0.450736\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.8956 | − | 25.7999i | −0.792813 | − | 1.37319i | −0.924219 | − | 0.381863i | \(-0.875282\pi\) |
0.131406 | − | 0.991329i | \(-0.458051\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.7517 | − | 10.8263i | −0.995239 | − | 0.574601i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.88758i | 0.469068i | 0.972108 | + | 0.234534i | \(0.0753565\pi\) | ||||
−0.972108 | + | 0.234534i | \(0.924644\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2890 | −0.962579 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.08313 | + | 1.78005i | 0.161378 | + | 0.0931719i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.0068 | − | 18.4792i | 1.67074 | − | 0.964604i | 0.703520 | − | 0.710675i | \(-0.251610\pi\) |
0.967223 | − | 0.253929i | \(-0.0817230\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.94130 | − | 26.1638i | −0.412292 | − | 1.35836i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.8546 | − | 29.1931i | 0.872700 | − | 1.51156i | 0.0135064 | − | 0.999909i | \(-0.495701\pi\) |
0.859193 | − | 0.511651i | \(-0.170966\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.7007 | −0.654117 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.7512 | 1.52821 | 0.764107 | − | 0.645089i | \(-0.223180\pi\) | ||||
0.764107 | + | 0.645089i | \(0.223180\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.62871 | + | 13.2133i | −0.389809 | + | 0.675169i | −0.992424 | − | 0.122863i | \(-0.960792\pi\) |
0.602615 | + | 0.798032i | \(0.294126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.89668 | − | 6.24891i | −0.0966637 | − | 0.318474i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.947612 | − | 0.547104i | 0.0480458 | − | 0.0277393i | −0.475785 | − | 0.879562i | \(-0.657836\pi\) |
0.523831 | + | 0.851823i | \(0.324503\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.09442 | − | 1.78656i | −0.156492 | − | 0.0903504i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.0119 | 1.66101 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2381i | 0.915345i | 0.889121 | + | 0.457672i | \(0.151317\pi\) | ||||
−0.889121 | + | 0.457672i | \(0.848683\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.3050 | − | 8.25900i | −0.714358 | − | 0.412435i | 0.0983146 | − | 0.995155i | \(-0.468655\pi\) |
−0.812673 | + | 0.582721i | \(0.801988\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.11001 | + | 12.3149i | 0.354175 | + | 0.613448i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.94958 | − | 1.12559i | 0.0966371 | − | 0.0557934i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.3657 | − | 7.13935i | −0.611445 | − | 0.353018i | 0.162086 | − | 0.986777i | \(-0.448178\pi\) |
−0.773531 | + | 0.633759i | \(0.781511\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.09257 | − | 8.98105i | 0.102969 | − | 0.441928i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.869925 | 0.0427029 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.2168 | + | 33.2845i | −0.938804 | + | 1.62606i | −0.171098 | + | 0.985254i | \(0.554732\pi\) |
−0.767706 | + | 0.640802i | \(0.778602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.90196 | − | 10.2225i | −0.287644 | − | 0.498214i | 0.685603 | − | 0.727976i | \(-0.259539\pi\) |
−0.973247 | + | 0.229762i | \(0.926205\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.301793 | + | 0.522720i | 0.0146391 | + | 0.0253557i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.89917 | − | 9.50460i | 0.430661 | − | 0.459960i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.9984i | 1.63765i | 0.574047 | + | 0.818823i | \(0.305373\pi\) | ||||
−0.574047 | + | 0.818823i | \(0.694627\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.24413i | − | 0.0597893i | −0.999553 | − | 0.0298946i | \(-0.990483\pi\) | ||
0.999553 | − | 0.0298946i | \(-0.00951718\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.9561 | − | 39.7612i | 1.09814 | − | 1.90204i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.3661 | + | 5.98485i | −0.494745 | + | 0.285641i | −0.726541 | − | 0.687123i | \(-0.758873\pi\) |
0.231796 | + | 0.972765i | \(0.425540\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.07711 | − | 2.93127i | 0.241221 | − | 0.139269i | −0.374517 | − | 0.927220i | \(-0.622191\pi\) |
0.615738 | + | 0.787951i | \(0.288858\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.8713 | + | 18.8297i | −0.515351 | + | 0.892614i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.7990i | 0.651215i | 0.945505 | + | 0.325607i | \(0.105569\pi\) | ||||
−0.945505 | + | 0.325607i | \(0.894431\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.96767i | − | 0.139742i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.1946 | − | 10.8882i | 0.477932 | − | 0.510446i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.6082 | + | 30.4983i | 0.823676 | + | 1.42665i | 0.902927 | + | 0.429794i | \(0.141414\pi\) |
−0.0792505 | + | 0.996855i | \(0.525253\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.6988 | − | 20.2629i | −0.544867 | − | 0.943736i | −0.998615 | − | 0.0526068i | \(-0.983247\pi\) |
0.453749 | − | 0.891130i | \(-0.350086\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.67980 | + | 4.64155i | −0.124541 | + | 0.215711i | −0.921553 | − | 0.388252i | \(-0.873079\pi\) |
0.797013 | + | 0.603963i | \(0.206412\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.3997 | −1.45300 | −0.726502 | − | 0.687164i | \(-0.758855\pi\) | ||||
−0.726502 | + | 0.687164i | \(0.758855\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.723484 | − | 3.10510i | 0.0334074 | − | 0.143380i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.2632 | − | 5.92544i | −0.471901 | − | 0.272452i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.71660 | + | 3.87783i | −0.308179 | + | 0.177927i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.7485 | + | 18.6169i | 0.491109 | + | 0.850626i | 0.999948 | − | 0.0102359i | \(-0.00325824\pi\) |
−0.508838 | + | 0.860862i | \(0.669925\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.45296 | + | 2.57092i | 0.203038 | + | 0.117224i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 20.5786i | − | 0.934425i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.61173 | −0.118349 | −0.0591744 | − | 0.998248i | \(-0.518847\pi\) | ||||
−0.0591744 | + | 0.998248i | \(0.518847\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.1818 | − | 6.45580i | −0.504626 | − | 0.291346i | 0.225996 | − | 0.974128i | \(-0.427437\pi\) |
−0.730622 | + | 0.682782i | \(0.760770\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.79068 | + | 1.03385i | −0.0806482 | + | 0.0465622i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.61516 | − | 28.3840i | −0.386443 | − | 1.27320i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.117182 | + | 0.202964i | −0.00524577 | + | 0.00908593i | −0.868636 | − | 0.495450i | \(-0.835003\pi\) |
0.863391 | + | 0.504536i | \(0.168336\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.6460 | 0.608445 | 0.304223 | − | 0.952601i | \(-0.401603\pi\) | ||||
0.304223 | + | 0.952601i | \(0.401603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.6991 | 1.14359 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.71269 | − | 2.96647i | 0.0759136 | − | 0.131486i | −0.825570 | − | 0.564300i | \(-0.809146\pi\) |
0.901483 | + | 0.432814i | \(0.142479\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.41649 | + | 4.66685i | 0.0626619 | + | 0.206449i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.8563 | − | 18.3922i | 1.40376 | − | 0.810459i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.86435 | − | 5.11784i | −0.389854 | − | 0.225082i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.3500 | 1.63633 | 0.818167 | − | 0.574981i | \(-0.194991\pi\) | ||||
0.818167 | + | 0.574981i | \(0.194991\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.99132i | 0.393163i | 0.980487 | + | 0.196581i | \(0.0629840\pi\) | ||||
−0.980487 | + | 0.196581i | \(0.937016\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.00489 | + | 1.15753i | 0.0873346 | + | 0.0504226i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.7648 | + | 29.0376i | 0.728906 | + | 1.26250i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.87021 | − | 3.38917i | 0.254267 | − | 0.146801i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.9938 | + | 15.5849i | 1.16704 | + | 0.673793i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.95423 | − | 8.02488i | 0.170321 | − | 0.345656i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.90934 | 0.340049 | 0.170025 | − | 0.985440i | \(-0.445615\pi\) | ||||
0.170025 | + | 0.985440i | \(0.445615\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.28741 | + | 5.69396i | −0.140817 | + | 0.243902i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.2958 | + | 29.9573i | 0.739516 | + | 1.28088i | 0.952713 | + | 0.303871i | \(0.0982790\pi\) |
−0.213197 | + | 0.977009i | \(0.568388\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.2843 | − | 23.0090i | −0.565928 | − | 0.980217i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.0124 | + | 30.9095i | 1.40383 | + | 1.31441i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.42861i | 0.102903i | 0.998675 | + | 0.0514517i | \(0.0163848\pi\) | ||||
−0.998675 | + | 0.0514517i | \(0.983615\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 27.0682i | − | 1.14486i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.53869 | − | 14.7894i | 0.359863 | − | 0.623301i | −0.628075 | − | 0.778153i | \(-0.716157\pi\) |
0.987938 | + | 0.154852i | \(0.0494901\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.03283 | − | 4.06041i | 0.295873 | − | 0.170823i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.9471 | + | 11.5165i | −0.836228 | + | 0.482796i | −0.855980 | − | 0.517008i | \(-0.827046\pi\) |
0.0197523 | + | 0.999805i | \(0.493712\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.11356 | + | 7.12490i | −0.172147 | + | 0.298168i | −0.939170 | − | 0.343452i | \(-0.888404\pi\) |
0.767023 | + | 0.641619i | \(0.221737\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 9.54919i | − | 0.398229i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.3064i | 0.470691i | 0.971912 | + | 0.235346i | \(0.0756222\pi\) | ||||
−0.971912 | + | 0.235346i | \(0.924378\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.869937 | + | 0.814523i | 0.0360911 | + | 0.0337921i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.60389 | + | 11.4383i | 0.273505 | + | 0.473725i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.2862 | − | 29.9407i | −0.713480 | − | 1.23578i | −0.963543 | − | 0.267553i | \(-0.913785\pi\) |
0.250063 | − | 0.968229i | \(-0.419549\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.8734 | + | 25.7615i | −0.612849 | + | 1.06149i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.64649 | −0.396134 | −0.198067 | − | 0.980188i | \(-0.563466\pi\) | ||||
−0.198067 | + | 0.980188i | \(0.563466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.551039 | − | 2.36499i | 0.0225904 | − | 0.0969553i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.22049 | + | 3.01405i | 0.213303 | + | 0.123151i | 0.602846 | − | 0.797858i | \(-0.294033\pi\) |
−0.389542 | + | 0.921009i | \(0.627367\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.4624 | + | 13.5460i | −0.957052 | + | 0.552555i | −0.895265 | − | 0.445535i | \(-0.853014\pi\) |
−0.0617879 | + | 0.998089i | \(0.519680\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.04491 | − | 15.6662i | −0.367728 | − | 0.636923i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.1410 | + | 9.31904i | 0.655145 | + | 0.378248i | 0.790425 | − | 0.612559i | \(-0.209860\pi\) |
−0.135280 | + | 0.990807i | \(0.543193\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 23.3789i | − | 0.945811i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.7398 | 0.999232 | 0.499616 | − | 0.866247i | \(-0.333474\pi\) | ||||
0.499616 | + | 0.866247i | \(0.333474\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.5759 | + | 24.5812i | 1.71404 | + | 0.989603i | 0.928934 | + | 0.370245i | \(0.120726\pi\) |
0.785109 | + | 0.619358i | \(0.212607\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.334357 | + | 0.193041i | −0.0134389 | + | 0.00775898i | −0.506704 | − | 0.862120i | \(-0.669136\pi\) |
0.493265 | + | 0.869879i | \(0.335803\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −28.5020 | + | 8.65098i | −1.14191 | + | 0.346594i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.51828 | − | 14.7541i | 0.340731 | − | 0.590164i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.837104 | 0.0333775 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.6531 | −1.81742 | −0.908710 | − | 0.417429i | \(-0.862931\pi\) | ||||
−0.908710 | + | 0.417429i | \(0.862931\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.5926 | − | 28.7392i | 0.658456 | − | 1.14048i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.3895 | − | 1.34297i | 0.807863 | − | 0.0532104i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.2119 | − | 19.7523i | 1.35129 | − | 0.780167i | 0.362859 | − | 0.931844i | \(-0.381801\pi\) |
0.988430 | + | 0.151677i | \(0.0484674\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.1404 | − | 13.3601i | −0.912570 | − | 0.526873i | −0.0313129 | − | 0.999510i | \(-0.509969\pi\) |
−0.881257 | + | 0.472637i | \(0.843302\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.2634 | 1.58292 | 0.791459 | − | 0.611222i | \(-0.209322\pi\) | ||||
0.791459 | + | 0.611222i | \(0.209322\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.45450i | 0.174854i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.6920 | + | 21.1841i | 1.43587 | + | 0.828998i | 0.997559 | − | 0.0698266i | \(-0.0222446\pi\) |
0.438308 | + | 0.898825i | \(0.355578\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.73332 | − | 13.3945i | −0.302166 | − | 0.523366i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.3031 | − | 19.2276i | 1.29731 | − | 0.749000i | 0.317368 | − | 0.948302i | \(-0.397201\pi\) |
0.979938 | + | 0.199302i | \(0.0638676\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.2400 | − | 8.22149i | −0.553874 | − | 0.319779i | 0.196809 | − | 0.980442i | \(-0.436942\pi\) |
−0.750683 | + | 0.660663i | \(0.770275\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.3885 | + | 7.08048i | 1.17842 | + | 0.274569i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.7126 | 1.26664 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.14477 | + | 5.44690i | −0.121402 | + | 0.210275i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.8254 | − | 29.1424i | −0.648570 | − | 1.12336i | −0.983465 | − | 0.181100i | \(-0.942034\pi\) |
0.334895 | − | 0.942255i | \(-0.391299\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.0119 | + | 36.3938i | 0.807555 | + | 1.39873i | 0.914553 | + | 0.404466i | \(0.132543\pi\) |
−0.106998 | + | 0.994259i | \(0.534124\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.2680 | − | 20.5789i | 0.739438 | − | 0.789744i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 28.0238i | − | 1.07230i | −0.844122 | − | 0.536151i | \(-0.819878\pi\) | ||
0.844122 | − | 0.536151i | \(-0.180122\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 18.8272i | − | 0.719351i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.0837 | + | 26.1258i | −0.574644 | + | 0.995312i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.58578 | − | 2.64760i | 0.174451 | − | 0.100720i | −0.410232 | − | 0.911981i | \(-0.634552\pi\) |
0.584683 | + | 0.811262i | \(0.301219\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.0565 | − | 7.53818i | 0.495262 | − | 0.285940i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.551765 | − | 0.955685i | 0.0208996 | − | 0.0361992i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.6055i | 1.45811i | 0.684455 | + | 0.729055i | \(0.260040\pi\) | ||||
−0.684455 | + | 0.729055i | \(0.739960\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.7562i | 0.405678i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.6994 | + | 24.0624i | 0.966526 | + | 0.904960i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.9037 | + | 37.9383i | 0.822610 | + | 1.42480i | 0.903732 | + | 0.428098i | \(0.140816\pi\) |
−0.0811228 | + | 0.996704i | \(0.525851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.3130 | − | 31.7190i | −0.685826 | − | 1.18789i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.60256 | + | 6.23981i | −0.134728 | + | 0.233356i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.2855 | −0.793813 | −0.396907 | − | 0.917859i | \(-0.629916\pi\) | ||||
−0.396907 | + | 0.917859i | \(0.629916\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.0776 | + | 11.4350i | 1.82775 | + | 0.425862i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.78559 | − | 2.76296i | −0.177733 | − | 0.102614i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.2267 | + | 20.9155i | −1.34358 | + | 0.775713i | −0.987330 | − | 0.158679i | \(-0.949276\pi\) |
−0.356245 | + | 0.934393i | \(0.615943\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.20338 | − | 3.81637i | −0.0814950 | − | 0.141154i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.6457 | − | 21.1574i | −1.35354 | − | 0.781466i | −0.364795 | − | 0.931088i | \(-0.618861\pi\) |
−0.988743 | + | 0.149622i | \(0.952194\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.54010i | 0.0567302i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.4280 | −0.751456 | −0.375728 | − | 0.926730i | \(-0.622607\pi\) | ||||
−0.375728 | + | 0.926730i | \(0.622607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.44740 | − | 4.29976i | −0.273219 | − | 0.157743i | 0.357131 | − | 0.934054i | \(-0.383755\pi\) |
−0.630349 | + | 0.776312i | \(0.717088\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.5846 | − | 10.7298i | 0.680887 | − | 0.393110i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.4018 | + | 40.8598i | 0.453153 | + | 1.49298i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.0359 | + | 34.7032i | −0.731120 | + | 1.26634i | 0.225285 | + | 0.974293i | \(0.427669\pi\) |
−0.956405 | + | 0.292043i | \(0.905665\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.28990 | −0.265307 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.6186 | 0.385941 | 0.192970 | − | 0.981205i | \(-0.438188\pi\) | ||||
0.192970 | + | 0.981205i | \(0.438188\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.36550 | − | 2.36512i | 0.0494993 | − | 0.0857354i | −0.840214 | − | 0.542255i | \(-0.817571\pi\) |
0.889713 | + | 0.456519i | \(0.150904\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.61878 | + | 2.61599i | −0.312021 | + | 0.0947052i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.81125 | + | 5.08718i | −0.318156 | + | 0.183687i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.44566 | − | 3.14405i | −0.196376 | − | 0.113377i | 0.398588 | − | 0.917130i | \(-0.369500\pi\) |
−0.594964 | + | 0.803753i | \(0.702834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.6236 | −0.561942 | −0.280971 | − | 0.959716i | \(-0.590656\pi\) | ||||
−0.280971 | + | 0.959716i | \(0.590656\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.18698i | 0.222243i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.2799 | + | 7.08981i | 0.439973 | + | 0.254019i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.16426 | + | 12.4089i | 0.256358 | + | 0.444024i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.85925 | + | 3.96019i | −0.244817 | + | 0.141345i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.7379 | + | 22.9427i | 1.41650 | + | 0.817819i | 0.995990 | − | 0.0894671i | \(-0.0285164\pi\) |
0.420514 | + | 0.907286i | \(0.361850\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.8347 | + | 2.52448i | 0.385239 | + | 0.0897600i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.3657 | −0.510141 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.8057 | + | 25.6442i | −0.524444 | + | 0.908364i | 0.475151 | + | 0.879904i | \(0.342394\pi\) |
−0.999595 | + | 0.0284597i | \(0.990940\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.90307 | − | 3.29622i | −0.0673259 | − | 0.116612i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.17794 | − | 2.04025i | −0.0415685 | − | 0.0719987i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.2579 | + | 28.0443i | −0.925470 | + | 0.988432i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.7761i | 0.976556i | 0.872688 | + | 0.488278i | \(0.162375\pi\) | ||||
−0.872688 | + | 0.488278i | \(0.837625\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.8221i | 0.625820i | 0.949783 | + | 0.312910i | \(0.101304\pi\) | ||||
−0.949783 | + | 0.312910i | \(0.898696\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.8929 | + | 24.0633i | −0.486648 | + | 0.842899i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.0377 | − | 28.3119i | 1.71561 | − | 0.990510i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.242236 | + | 0.139855i | −0.00845409 | + | 0.00488097i | −0.504221 | − | 0.863575i | \(-0.668220\pi\) |
0.495767 | + | 0.868456i | \(0.334887\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.56224 | − | 9.63408i | 0.193887 | − | 0.335823i | −0.752648 | − | 0.658423i | \(-0.771224\pi\) |
0.946535 | + | 0.322600i | \(0.104557\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22.9832i | − | 0.799205i | −0.916688 | − | 0.399603i | \(-0.869148\pi\) | ||
0.916688 | − | 0.399603i | \(-0.130852\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.30082i | 0.218837i | 0.993996 | + | 0.109418i | \(0.0348988\pi\) | ||||
−0.993996 | + | 0.109418i | \(0.965101\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.76542 | − | 1.84908i | 0.0958163 | − | 0.0640668i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.5851 | − | 26.9942i | −0.539345 | − | 0.934174i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.7701 | + | 20.3864i | 0.406349 | + | 0.703816i | 0.994477 | − | 0.104951i | \(-0.0334685\pi\) |
−0.588129 | + | 0.808767i | \(0.700135\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.03493 | + | 8.72075i | −0.173618 | + | 0.300716i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.64999 | 0.297569 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.62349 | − | 24.1353i | 0.193225 | − | 0.829300i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.4693 | − | 6.62182i | −0.393164 | − | 0.226993i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.56621 | + | 0.904252i | −0.0536260 | + | 0.0309610i | −0.526573 | − | 0.850130i | \(-0.676523\pi\) |
0.472947 | + | 0.881091i | \(0.343190\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.704571 | − | 1.22035i | −0.0240677 | − | 0.0416865i | 0.853741 | − | 0.520698i | \(-0.174328\pi\) |
−0.877808 | + | 0.479012i | \(0.840995\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.4862 | − | 20.4879i | −1.21077 | − | 0.699040i | −0.247845 | − | 0.968800i | \(-0.579722\pi\) |
−0.962928 | + | 0.269760i | \(0.913056\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 7.34316i | − | 0.249964i | −0.992159 | − | 0.124982i | \(-0.960113\pi\) | ||
0.992159 | − | 0.124982i | \(-0.0398873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.68596 | −0.0913255 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.9187 | − | 10.9227i | −0.641774 | − | 0.370528i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.04640 | + | 1.75884i | −0.103223 | + | 0.0595960i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.6574 | − | 9.30519i | 1.03641 | − | 0.314573i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.80443 | − | 3.12536i | 0.0609312 | − | 0.105536i | −0.833951 | − | 0.551839i | \(-0.813926\pi\) |
0.894882 | + | 0.446303i | \(0.147260\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.6937 | −0.427660 | −0.213830 | − | 0.976871i | \(-0.568594\pi\) | ||||
−0.213830 | + | 0.976871i | \(0.568594\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.55621 | 0.287939 | 0.143970 | − | 0.989582i | \(-0.454013\pi\) | ||||
0.143970 | + | 0.989582i | \(0.454013\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.45990 | + | 12.9209i | −0.250479 | + | 0.433842i | −0.963658 | − | 0.267140i | \(-0.913921\pi\) |
0.713179 | + | 0.700982i | \(0.247255\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43.5017 | − | 13.2037i | 1.45900 | − | 0.442839i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.3542 | − | 24.4532i | 1.41733 | − | 0.818295i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.70388 | + | 4.44784i | 0.257512 | + | 0.148675i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.1947 | −0.706883 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.91133i | 0.163620i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.3851 | + | 15.8108i | 0.910312 | + | 0.525569i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.1506 | − | 27.9737i | −0.536273 | − | 0.928852i | −0.999101 | − | 0.0424034i | \(-0.986499\pi\) |
0.462828 | − | 0.886448i | \(-0.346835\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.3778 | − | 7.72366i | 0.443225 | − | 0.255896i | −0.261740 | − | 0.965139i | \(-0.584296\pi\) |
0.704965 | + | 0.709242i | \(0.250963\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.498544 | − | 0.287834i | −0.0164994 | − | 0.00952593i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.80803 | − | 20.6355i | 0.158775 | − | 0.681444i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.01879 | 0.0336069 | 0.0168034 | − | 0.999859i | \(-0.494651\pi\) | ||||
0.0168034 | + | 0.999859i | \(0.494651\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.3636 | + | 28.3427i | −0.538616 | + | 0.932910i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.11858 | + | 1.93744i | 0.0367787 | + | 0.0637026i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.5872 | − | 30.4619i | −0.577016 | − | 0.999421i | −0.995819 | − | 0.0913443i | \(-0.970884\pi\) |
0.418803 | − | 0.908077i | \(-0.362450\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.7594 | + | 35.5338i | 0.778684 | + | 1.16457i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.17301i | 0.0383615i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.5780i | − | 0.639586i | −0.947487 | − | 0.319793i | \(-0.896387\pi\) | ||
0.947487 | − | 0.319793i | \(-0.103613\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.2160 | − | 40.2113i | 0.756820 | − | 1.31085i | −0.187645 | − | 0.982237i | \(-0.560085\pi\) |
0.944464 | − | 0.328614i | \(-0.106581\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.1197 | + | 8.72936i | −0.492365 | + | 0.284267i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.1063 | + | 18.5366i | −1.04331 | + | 0.602358i | −0.920770 | − | 0.390105i | \(-0.872439\pi\) |
−0.122544 | + | 0.992463i | \(0.539105\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.69048 | − | 4.66006i | 0.0873368 | − | 0.151272i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.73116i | 0.0884709i | 0.999021 | + | 0.0442354i | \(0.0140852\pi\) | ||||
−0.999021 | + | 0.0442354i | \(0.985915\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 28.5344i | − | 0.923352i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.6282 | − | 18.8275i | 0.569244 | − | 0.607971i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.63491 | − | 6.29585i | −0.117255 | − | 0.203092i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.2257 | + | 29.8358i | 0.554516 | + | 0.960450i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.6811 | + | 25.4285i | −0.472113 | + | 0.817724i | −0.999491 | − | 0.0319070i | \(-0.989842\pi\) |
0.527378 | + | 0.849631i | \(0.323175\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.1103 | 0.549094 | 0.274547 | − | 0.961574i | \(-0.411472\pi\) | ||||
0.274547 | + | 0.961574i | \(0.411472\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.1148 | + | 4.68671i | 0.644851 | + | 0.150249i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.4251 | − | 21.0301i | −1.16534 | − | 0.672812i | −0.212765 | − | 0.977103i | \(-0.568247\pi\) |
−0.952579 | + | 0.304292i | \(0.901580\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.4605 | − | 7.19406i | 0.398238 | − | 0.229923i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.87731 | − | 6.71569i | −0.123667 | − | 0.214197i | 0.797544 | − | 0.603261i | \(-0.206132\pi\) |
−0.921211 | + | 0.389063i | \(0.872799\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.3863 | + | 7.72860i | 0.426524 | + | 0.246254i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 69.7184i | 2.21692i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.5135 | 0.365738 | 0.182869 | − | 0.983137i | \(-0.441462\pi\) | ||||
0.182869 | + | 0.983137i | \(0.441462\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.2683 | − | 15.7434i | −0.864464 | − | 0.499099i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.0836 | − | 8.70850i | 0.477701 | − | 0.275801i | −0.241757 | − | 0.970337i | \(-0.577724\pi\) |
0.719458 | + | 0.694536i | \(0.244390\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3024.2.cc.d.881.8 | 48 | ||
3.2 | odd | 2 | 1008.2.cc.d.545.20 | 48 | |||
4.3 | odd | 2 | 1512.2.bu.a.881.8 | 48 | |||
7.6 | odd | 2 | inner | 3024.2.cc.d.881.17 | 48 | ||
9.2 | odd | 6 | inner | 3024.2.cc.d.2897.17 | 48 | ||
9.7 | even | 3 | 1008.2.cc.d.209.5 | 48 | |||
12.11 | even | 2 | 504.2.bu.a.41.5 | ✓ | 48 | ||
21.20 | even | 2 | 1008.2.cc.d.545.5 | 48 | |||
28.27 | even | 2 | 1512.2.bu.a.881.17 | 48 | |||
36.7 | odd | 6 | 504.2.bu.a.209.20 | yes | 48 | ||
36.11 | even | 6 | 1512.2.bu.a.1385.17 | 48 | |||
36.23 | even | 6 | 4536.2.k.a.3401.16 | 48 | |||
36.31 | odd | 6 | 4536.2.k.a.3401.33 | 48 | |||
63.20 | even | 6 | inner | 3024.2.cc.d.2897.8 | 48 | ||
63.34 | odd | 6 | 1008.2.cc.d.209.20 | 48 | |||
84.83 | odd | 2 | 504.2.bu.a.41.20 | yes | 48 | ||
252.83 | odd | 6 | 1512.2.bu.a.1385.8 | 48 | |||
252.139 | even | 6 | 4536.2.k.a.3401.15 | 48 | |||
252.167 | odd | 6 | 4536.2.k.a.3401.34 | 48 | |||
252.223 | even | 6 | 504.2.bu.a.209.5 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bu.a.41.5 | ✓ | 48 | 12.11 | even | 2 | ||
504.2.bu.a.41.20 | yes | 48 | 84.83 | odd | 2 | ||
504.2.bu.a.209.5 | yes | 48 | 252.223 | even | 6 | ||
504.2.bu.a.209.20 | yes | 48 | 36.7 | odd | 6 | ||
1008.2.cc.d.209.5 | 48 | 9.7 | even | 3 | |||
1008.2.cc.d.209.20 | 48 | 63.34 | odd | 6 | |||
1008.2.cc.d.545.5 | 48 | 21.20 | even | 2 | |||
1008.2.cc.d.545.20 | 48 | 3.2 | odd | 2 | |||
1512.2.bu.a.881.8 | 48 | 4.3 | odd | 2 | |||
1512.2.bu.a.881.17 | 48 | 28.27 | even | 2 | |||
1512.2.bu.a.1385.8 | 48 | 252.83 | odd | 6 | |||
1512.2.bu.a.1385.17 | 48 | 36.11 | even | 6 | |||
3024.2.cc.d.881.8 | 48 | 1.1 | even | 1 | trivial | ||
3024.2.cc.d.881.17 | 48 | 7.6 | odd | 2 | inner | ||
3024.2.cc.d.2897.8 | 48 | 63.20 | even | 6 | inner | ||
3024.2.cc.d.2897.17 | 48 | 9.2 | odd | 6 | inner | ||
4536.2.k.a.3401.15 | 48 | 252.139 | even | 6 | |||
4536.2.k.a.3401.16 | 48 | 36.23 | even | 6 | |||
4536.2.k.a.3401.33 | 48 | 36.31 | odd | 6 | |||
4536.2.k.a.3401.34 | 48 | 252.167 | odd | 6 |