Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(863,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.863");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 49x^{12} - 12x^{10} - 600x^{8} + 108x^{6} + 4057x^{4} + 18252x^{2} + 28561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 863.8 | ||
Root | \(2.13219 - 1.08896i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.863 |
Dual form | 2592.2.s.j.1727.8 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.47996 | + | 2.00916i | 1.55629 | + | 0.898523i | 0.997607 | + | 0.0691392i | \(0.0220253\pi\) |
0.558680 | + | 0.829383i | \(0.311308\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.66739 | − | 1.54002i | 1.00818 | − | 0.582072i | 0.0975199 | − | 0.995234i | \(-0.468909\pi\) |
0.910658 | + | 0.413162i | \(0.135576\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.97508 | − | 5.15300i | −0.897021 | − | 1.55369i | −0.831283 | − | 0.555850i | \(-0.812393\pi\) |
−0.0657387 | − | 0.997837i | \(-0.520940\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.673991 | − | 1.16739i | 0.186932 | − | 0.323775i | −0.757294 | − | 0.653074i | \(-0.773479\pi\) |
0.944226 | + | 0.329299i | \(0.106812\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.87346i | 1.18199i | 0.806676 | + | 0.590994i | \(0.201264\pi\) | ||||
−0.806676 | + | 0.590994i | \(0.798736\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.49484i | 1.71943i | 0.510771 | + | 0.859717i | \(0.329360\pi\) | ||||
−0.510771 | + | 0.859717i | \(0.670640\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.28929 | − | 2.23312i | 0.268836 | − | 0.465638i | −0.699725 | − | 0.714412i | \(-0.746694\pi\) |
0.968562 | + | 0.248774i | \(0.0800277\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.57343 | + | 9.65346i | 1.11469 | + | 1.93069i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.60128 | − | 3.23390i | 1.04013 | − | 0.600521i | 0.120261 | − | 0.992742i | \(-0.461627\pi\) |
0.919871 | + | 0.392222i | \(0.128293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.28744 | − | 0.743302i | −0.231230 | − | 0.133501i | 0.379909 | − | 0.925024i | \(-0.375955\pi\) |
−0.611140 | + | 0.791523i | \(0.709289\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.3765 | 2.09202 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.91997 | 0.315641 | 0.157820 | − | 0.987468i | \(-0.449553\pi\) | ||||
0.157820 | + | 0.987468i | \(0.449553\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.69513 | − | 0.978684i | −0.264735 | − | 0.152845i | 0.361758 | − | 0.932272i | \(-0.382177\pi\) |
−0.626493 | + | 0.779427i | \(0.715510\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.79671 | − | 3.92409i | 1.03649 | − | 0.598417i | 0.117652 | − | 0.993055i | \(-0.462463\pi\) |
0.918837 | + | 0.394637i | \(0.129130\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.14264 | + | 1.97910i | 0.166671 | + | 0.288682i | 0.937247 | − | 0.348665i | \(-0.113365\pi\) |
−0.770577 | + | 0.637347i | \(0.780032\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.24330 | − | 2.15346i | 0.177615 | − | 0.307637i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 0.871059i | − | 0.119649i | −0.998209 | − | 0.0598245i | \(-0.980946\pi\) | ||
0.998209 | − | 0.0598245i | \(-0.0190541\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 23.9096i | − | 3.22398i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.650515 | − | 1.12672i | 0.0846898 | − | 0.146687i | −0.820569 | − | 0.571547i | \(-0.806343\pi\) |
0.905259 | + | 0.424860i | \(0.139677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.29671 | + | 5.71008i | 0.422101 | + | 0.731101i | 0.996145 | − | 0.0877241i | \(-0.0279594\pi\) |
−0.574044 | + | 0.818825i | \(0.694626\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.69093 | − | 2.70831i | 0.581838 | − | 0.335924i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.44338 | + | 4.87479i | 1.03152 | + | 0.595550i | 0.917421 | − | 0.397919i | \(-0.130267\pi\) |
0.114103 | + | 0.993469i | \(0.463601\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.64914 | −0.551751 | −0.275876 | − | 0.961193i | \(-0.588968\pi\) | ||||
−0.275876 | + | 0.961193i | \(0.588968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.14686 | −0.251271 | −0.125635 | − | 0.992076i | \(-0.540097\pi\) | ||||
−0.125635 | + | 0.992076i | \(0.540097\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.8714 | − | 9.16336i | −1.80871 | − | 1.04426i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.08415 | − | 4.66739i | 0.909538 | − | 0.525122i | 0.0292556 | − | 0.999572i | \(-0.490686\pi\) |
0.880282 | + | 0.474450i | \(0.157353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.09779 | − | 8.82963i | −0.559555 | − | 0.969178i | −0.997533 | − | 0.0701921i | \(-0.977639\pi\) |
0.437979 | − | 0.898985i | \(-0.355695\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.79155 | + | 16.9595i | −1.06204 | + | 1.83951i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.947609i | 0.100446i | 0.998738 | + | 0.0502232i | \(0.0159933\pi\) | ||||
−0.998738 | + | 0.0502232i | \(0.984007\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4.15183i | − | 0.435230i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.0583 | + | 26.0818i | −1.54495 | + | 2.67593i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.15811 | − | 8.93411i | −0.523727 | − | 0.907121i | −0.999619 | − | 0.0276173i | \(-0.991208\pi\) |
0.475892 | − | 0.879504i | \(-0.342125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.85352 | − | 1.07013i | 0.184433 | − | 0.106482i | −0.404941 | − | 0.914343i | \(-0.632708\pi\) |
0.589374 | + | 0.807861i | \(0.299375\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.53590 | + | 4.92820i | 0.841067 | + | 0.485590i | 0.857627 | − | 0.514273i | \(-0.171938\pi\) |
−0.0165597 | + | 0.999863i | \(0.505271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.38765 | −0.424170 | −0.212085 | − | 0.977251i | \(-0.568025\pi\) | ||||
−0.212085 | + | 0.977251i | \(0.568025\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.4588 | 1.57646 | 0.788231 | − | 0.615379i | \(-0.210997\pi\) | ||||
0.788231 | + | 0.615379i | \(0.210997\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.5032 | − | 7.21875i | −1.17621 | − | 0.679082i | −0.221072 | − | 0.975258i | \(-0.570955\pi\) |
−0.955134 | + | 0.296175i | \(0.904289\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.97338 | − | 5.18078i | 0.836772 | − | 0.483111i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.50521 | + | 12.9994i | 0.688002 | + | 1.19165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.2022 | + | 21.1349i | −1.10929 | + | 1.92136i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24.7000i | 2.20924i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.17862i | − | 0.104586i | −0.998632 | − | 0.0522929i | \(-0.983347\pi\) | ||
0.998632 | − | 0.0522929i | \(-0.0166530\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0552077 | + | 0.0956225i | −0.00482352 | + | 0.00835458i | −0.868427 | − | 0.495817i | \(-0.834869\pi\) |
0.863604 | + | 0.504171i | \(0.168202\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.5422 | + | 19.9916i | 1.00083 | + | 1.73349i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.05915 | + | 5.23030i | −0.773975 | + | 0.446855i | −0.834291 | − | 0.551325i | \(-0.814123\pi\) |
0.0603156 | + | 0.998179i | \(0.480789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.7042 | − | 7.33477i | −1.07756 | − | 0.622127i | −0.147320 | − | 0.989089i | \(-0.547065\pi\) |
−0.930236 | + | 0.366961i | \(0.880398\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.02072 | −0.670726 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.9897 | 2.15833 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.95575 | − | 1.70651i | −0.242145 | − | 0.139802i | 0.374017 | − | 0.927422i | \(-0.377980\pi\) |
−0.616162 | + | 0.787619i | \(0.711313\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.64667 | + | 4.41481i | −0.622277 | + | 0.359272i | −0.777755 | − | 0.628567i | \(-0.783642\pi\) |
0.155478 | + | 0.987839i | \(0.450308\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.98682 | − | 5.17333i | −0.239907 | − | 0.415531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1981 | − | 17.6637i | 0.813899 | − | 1.40971i | −0.0962168 | − | 0.995360i | \(-0.530674\pi\) |
0.910116 | − | 0.414354i | \(-0.135992\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.94213i | − | 0.625927i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 11.3880i | − | 0.891978i | −0.895038 | − | 0.445989i | \(-0.852852\pi\) | ||
0.895038 | − | 0.445989i | \(-0.147148\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.6463 | + | 20.1720i | −0.901219 | + | 1.56096i | −0.0753056 | + | 0.997161i | \(0.523993\pi\) |
−0.825914 | + | 0.563797i | \(0.809340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.59147 | + | 9.68471i | 0.430113 | + | 0.744978i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.6270 | + | 6.71284i | −0.883984 | + | 0.510368i | −0.871970 | − | 0.489560i | \(-0.837158\pi\) |
−0.0120137 | + | 0.999928i | \(0.503824\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 29.7330 | + | 17.1663i | 2.24760 | + | 1.29765i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.7141 | 1.54824 | 0.774120 | − | 0.633038i | \(-0.218192\pi\) | ||||
0.774120 | + | 0.633038i | \(0.218192\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.06148 | −0.599205 | −0.299602 | − | 0.954064i | \(-0.596854\pi\) | ||||
−0.299602 | + | 0.954064i | \(0.596854\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.68141 | + | 3.85752i | 0.491227 | + | 0.283610i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.1129 | − | 14.4990i | 1.83644 | − | 1.06027i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3965 | − | 19.7393i | −0.824620 | − | 1.42828i | −0.902209 | − | 0.431298i | \(-0.858056\pi\) |
0.0775893 | − | 0.996985i | \(-0.475278\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.22670 | − | 14.2491i | 0.592171 | − | 1.02567i | −0.401768 | − | 0.915741i | \(-0.631604\pi\) |
0.993939 | − | 0.109929i | \(-0.0350623\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 21.9544i | − | 1.56419i | −0.623160 | − | 0.782095i | \(-0.714151\pi\) | ||
0.623160 | − | 0.782095i | \(-0.285849\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2933i | 0.800564i | 0.916392 | + | 0.400282i | \(0.131088\pi\) | ||||
−0.916392 | + | 0.400282i | \(0.868912\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.96053 | − | 17.2521i | 0.699092 | − | 1.21086i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.93266 | − | 6.81157i | −0.274669 | − | 0.475741i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 38.6209 | − | 22.2978i | 2.67146 | − | 1.54237i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.2667 | − | 7.08219i | −0.844476 | − | 0.487558i | 0.0143073 | − | 0.999898i | \(-0.495446\pi\) |
−0.858783 | + | 0.512339i | \(0.828779\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.5364 | 2.15077 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.57879 | −0.310828 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.68922 | + | 3.28467i | 0.382698 | + | 0.220951i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.9548 | + | 9.21152i | −1.06841 | + | 0.616849i | −0.927748 | − | 0.373208i | \(-0.878258\pi\) |
−0.140666 | + | 0.990057i | \(0.544924\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.53415 | − | 6.12133i | −0.234570 | − | 0.406287i | 0.724578 | − | 0.689193i | \(-0.242035\pi\) |
−0.959148 | + | 0.282906i | \(0.908701\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.13614 | + | 8.89605i | −0.339405 | + | 0.587867i | −0.984321 | − | 0.176386i | \(-0.943559\pi\) |
0.644916 | + | 0.764254i | \(0.276892\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.49420i | 0.490961i | 0.969401 | + | 0.245481i | \(0.0789458\pi\) | ||||
−0.969401 | + | 0.245481i | \(0.921054\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.18294i | 0.599029i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.309224 | − | 0.535592i | 0.0200020 | − | 0.0346445i | −0.855851 | − | 0.517222i | \(-0.826966\pi\) |
0.875853 | + | 0.482578i | \(0.160299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.4521 | + | 21.5678i | 0.802113 | + | 1.38930i | 0.918223 | + | 0.396065i | \(0.129624\pi\) |
−0.116109 | + | 0.993236i | \(0.537042\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.65329 | − | 4.99598i | 0.552838 | − | 0.319181i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.74938 | + | 5.05146i | 0.556710 | + | 0.321416i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.54676 | 0.160750 | 0.0803751 | − | 0.996765i | \(-0.474388\pi\) | ||||
0.0803751 | + | 0.996765i | \(0.474388\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.3430 | −0.964607 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.74647 | + | 4.47243i | 0.483212 | + | 0.278982i | 0.721754 | − | 0.692150i | \(-0.243336\pi\) |
−0.238542 | + | 0.971132i | \(0.576670\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.12129 | − | 2.95678i | 0.318222 | − | 0.183725i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.43595 | − | 2.48714i | −0.0885444 | − | 0.153363i | 0.818352 | − | 0.574718i | \(-0.194888\pi\) |
−0.906896 | + | 0.421354i | \(0.861555\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.75009 | − | 3.03125i | 0.107507 | − | 0.186208i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.51044i | 0.275006i | 0.990501 | + | 0.137503i | \(0.0439077\pi\) | ||||
−0.990501 | + | 0.137503i | \(0.956092\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.72670i | 0.165635i | 0.996565 | + | 0.0828177i | \(0.0263919\pi\) | ||||
−0.996565 | + | 0.0828177i | \(0.973608\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 33.1628 | − | 57.4397i | 1.99979 | − | 3.46374i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.76814 | − | 4.79455i | −0.166321 | − | 0.288077i | 0.770802 | − | 0.637074i | \(-0.219856\pi\) |
−0.937124 | + | 0.348997i | \(0.886522\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.0968 | + | 9.87083i | −1.01991 | + | 0.588844i | −0.914077 | − | 0.405540i | \(-0.867083\pi\) |
−0.105831 | + | 0.994384i | \(0.533750\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.3348 | − | 6.54413i | −0.673782 | − | 0.389008i | 0.123726 | − | 0.992316i | \(-0.460516\pi\) |
−0.797508 | + | 0.603308i | \(0.793849\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.02876 | −0.355866 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.75064 | −0.397096 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.5916 | + | 11.3112i | 1.14455 | + | 0.660808i | 0.947554 | − | 0.319595i | \(-0.103547\pi\) |
0.196999 | + | 0.980404i | \(0.436880\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.52754 | − | 2.61397i | 0.263603 | − | 0.152191i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.73794 | − | 3.01021i | −0.100508 | − | 0.174085i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0863 | − | 20.9341i | 0.696643 | − | 1.20662i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.4945i | 1.51707i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.64667i | − | 0.436418i | −0.975902 | − | 0.218209i | \(-0.929978\pi\) | ||
0.975902 | − | 0.218209i | \(-0.0700215\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.6632 | + | 18.4692i | −0.604654 | + | 1.04729i | 0.387452 | + | 0.921890i | \(0.373355\pi\) |
−0.992106 | + | 0.125402i | \(0.959978\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.86747 | + | 15.3589i | 0.501219 | + | 0.868137i | 0.999999 | + | 0.00140816i | \(0.000448232\pi\) |
−0.498780 | + | 0.866729i | \(0.666218\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.80699 | − | 1.62061i | 0.157656 | − | 0.0910228i | −0.419096 | − | 0.907942i | \(-0.637653\pi\) |
0.576752 | + | 0.816919i | \(0.304320\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −33.3286 | − | 19.2423i | −1.86604 | − | 1.07736i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −36.5258 | −2.03235 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.0258 | 0.833480 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.09570 | + | 3.51936i | 0.336067 | + | 0.194028i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.08415 | − | 4.66739i | 0.444345 | − | 0.256543i | −0.261094 | − | 0.965313i | \(-0.584083\pi\) |
0.705439 | + | 0.708771i | \(0.250750\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.5884 | + | 33.9282i | 1.07023 | + | 1.85369i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.03270 | + | 12.1810i | −0.383095 | + | 0.663541i | −0.991503 | − | 0.130084i | \(-0.958475\pi\) |
0.608408 | + | 0.793625i | \(0.291809\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.84554i | 0.479013i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.9014i | 0.750606i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.28431 | + | 5.68859i | −0.176311 | + | 0.305379i | −0.940614 | − | 0.339478i | \(-0.889750\pi\) |
0.764303 | + | 0.644857i | \(0.223083\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.12737 | − | 10.6129i | −0.327991 | − | 0.568096i | 0.654122 | − | 0.756389i | \(-0.273038\pi\) |
−0.982113 | + | 0.188292i | \(0.939705\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.37831 | + | 2.52782i | −0.233034 | + | 0.134542i | −0.611971 | − | 0.790880i | \(-0.709623\pi\) |
0.378937 | + | 0.925422i | \(0.376290\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.1788 | − | 9.34085i | −0.858683 | − | 0.495761i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.8214 | −1.67947 | −0.839734 | − | 0.542998i | \(-0.817289\pi\) | ||||
−0.839734 | + | 0.542998i | \(0.817289\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −37.1726 | −1.95645 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.47099 | − | 4.31338i | −0.391049 | − | 0.225772i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.17667 | + | 1.25670i | −0.113621 | + | 0.0655991i | −0.555734 | − | 0.831360i | \(-0.687563\pi\) |
0.442113 | + | 0.896960i | \(0.354229\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.34144 | − | 2.32345i | −0.0696443 | − | 0.120628i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.9589 | + | 27.6417i | −0.826323 | + | 1.43123i | 0.0745816 | + | 0.997215i | \(0.476238\pi\) |
−0.900904 | + | 0.434018i | \(0.857095\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.71849i | − | 0.449025i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.9053i | 1.22793i | 0.789332 | + | 0.613967i | \(0.210427\pi\) | ||||
−0.789332 | + | 0.613967i | \(0.789573\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.63058 | − | 2.82425i | 0.0833189 | − | 0.144313i | −0.821355 | − | 0.570418i | \(-0.806781\pi\) |
0.904674 | + | 0.426105i | \(0.140115\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −36.8213 | − | 63.7763i | −1.87658 | − | 3.25034i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.1379 | − | 7.58519i | 0.666120 | − | 0.384584i | −0.128485 | − | 0.991711i | \(-0.541011\pi\) |
0.794605 | + | 0.607127i | \(0.207678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.8830 | + | 6.28332i | 0.550378 | + | 0.317761i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 37.5101 | 1.88734 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.1683 | −1.26316 | −0.631580 | − | 0.775310i | \(-0.717593\pi\) | ||||
−0.631580 | + | 0.775310i | \(0.717593\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.58225 | − | 3.22291i | −0.278764 | − | 0.160945i | 0.354100 | − | 0.935208i | \(-0.384787\pi\) |
−0.632864 | + | 0.774263i | \(0.718121\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.73544 | + | 1.00196i | −0.0864485 | + | 0.0499111i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.71206 | − | 9.89358i | −0.283136 | − | 0.490407i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.2583 | − | 22.9641i | 0.655582 | − | 1.13550i | −0.326165 | − | 0.945313i | \(-0.605757\pi\) |
0.981747 | − | 0.190189i | \(-0.0609101\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 4.00721i | − | 0.197182i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 40.9690i | − | 2.01109i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.3635 | + | 28.3424i | −0.799410 | + | 1.38462i | 0.120591 | + | 0.992702i | \(0.461521\pi\) |
−0.920001 | + | 0.391917i | \(0.871812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.8096 | − | 20.4548i | −0.575565 | − | 0.996907i | −0.995980 | − | 0.0895754i | \(-0.971449\pi\) |
0.420415 | − | 0.907332i | \(-0.361884\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −47.0458 | + | 27.1619i | −2.28206 | + | 1.31755i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.5872 | + | 10.1540i | 0.851106 | + | 0.491386i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.7052 | −1.38268 | −0.691340 | − | 0.722530i | \(-0.742979\pi\) | ||||
−0.691340 | + | 0.722530i | \(0.742979\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.2444 | 0.492315 | 0.246158 | − | 0.969230i | \(-0.420832\pi\) | ||||
0.246158 | + | 0.969230i | \(0.420832\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.7369 | + | 9.66304i | 0.800633 | + | 0.462246i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.0720 | + | 19.6715i | −1.62617 | + | 0.938870i | −0.640949 | + | 0.767584i | \(0.721459\pi\) |
−0.985221 | + | 0.171286i | \(0.945208\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.18611 | − | 2.05440i | −0.0563536 | − | 0.0976073i | 0.836472 | − | 0.548009i | \(-0.184614\pi\) |
−0.892826 | + | 0.450402i | \(0.851281\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.90390 | + | 3.29765i | −0.0902533 | + | 0.156323i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 33.6097i | − | 1.58614i | −0.609129 | − | 0.793071i | \(-0.708481\pi\) | ||
0.609129 | − | 0.793071i | \(-0.291519\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.6467i | 0.548420i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.34168 | − | 14.4482i | 0.391064 | − | 0.677343i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.9768 | − | 24.2085i | −0.653807 | − | 1.13243i | −0.982191 | − | 0.187883i | \(-0.939838\pi\) |
0.328384 | − | 0.944544i | \(-0.393496\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.63590 | + | 1.52184i | −0.122766 | + | 0.0708791i | −0.560126 | − | 0.828408i | \(-0.689247\pi\) |
0.437359 | + | 0.899287i | \(0.355914\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.2385 | + | 9.95266i | 0.801142 | + | 0.462539i | 0.843870 | − | 0.536547i | \(-0.180272\pi\) |
−0.0427284 | + | 0.999087i | \(0.513605\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.82289 | 0.130628 | 0.0653139 | − | 0.997865i | \(-0.479195\pi\) | ||||
0.0653139 | + | 0.997865i | \(0.479195\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.0290 | 1.38661 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −40.4416 | − | 23.3490i | −1.85951 | − | 1.07359i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −72.3511 | + | 41.7720i | −3.31970 | + | 1.91663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.1687 | + | 26.2730i | 0.693077 | + | 1.20044i | 0.970825 | + | 0.239790i | \(0.0770787\pi\) |
−0.277748 | + | 0.960654i | \(0.589588\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.29404 | − | 2.24134i | 0.0590032 | − | 0.102196i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 41.4538i | − | 1.88232i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 11.9668i | − | 0.542268i | −0.962542 | − | 0.271134i | \(-0.912601\pi\) | ||
0.962542 | − | 0.271134i | \(-0.0873986\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.10953 | − | 8.84996i | 0.230590 | − | 0.399393i | −0.727392 | − | 0.686222i | \(-0.759268\pi\) |
0.957982 | + | 0.286829i | \(0.0926012\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.7603 | + | 27.2976i | 0.709808 | + | 1.22942i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.4010 | + | 7.15975i | −0.556263 | + | 0.321159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.72060 | − | 5.61219i | −0.435154 | − | 0.251236i | 0.266386 | − | 0.963866i | \(-0.414170\pi\) |
−0.701540 | + | 0.712630i | \(0.747504\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.4842 | −0.913346 | −0.456673 | − | 0.889635i | \(-0.650959\pi\) | ||||
−0.456673 | + | 0.889635i | \(0.650959\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.60026 | 0.382707 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.9102 | − | 16.1139i | −1.23710 | − | 0.714238i | −0.268597 | − | 0.963253i | \(-0.586560\pi\) |
−0.968500 | + | 0.249015i | \(0.919893\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.72650 | + | 3.30620i | −0.253325 | + | 0.146258i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.8031 | + | 34.2999i | 0.872628 | + | 1.51144i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.79888 | − | 11.7760i | 0.299014 | − | 0.517908i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 27.2971i | − | 1.19591i | −0.801531 | − | 0.597953i | \(-0.795981\pi\) | ||
0.801531 | − | 0.597953i | \(-0.204019\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.4845i | 1.15809i | 0.815297 | + | 0.579044i | \(0.196574\pi\) | ||||
−0.815297 | + | 0.579044i | \(0.803426\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.62245 | − | 6.27427i | 0.157797 | − | 0.273312i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.17545 | + | 14.1603i | 0.355454 | + | 0.615665i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.28501 | + | 1.31925i | −0.0989746 | + | 0.0571430i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.2688 | − | 8.81547i | −0.660130 | − | 0.381126i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.7957 | −0.637296 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.15472 | 0.307605 | 0.153803 | − | 0.988102i | \(-0.450848\pi\) | ||||
0.153803 | + | 0.988102i | \(0.450848\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 57.2759 | + | 33.0682i | 2.45343 | + | 1.41649i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.89513 | + | 5.13561i | −0.380328 | + | 0.219583i | −0.677961 | − | 0.735098i | \(-0.737136\pi\) |
0.297633 | + | 0.954680i | \(0.403803\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.2376 | + | 41.9807i | 1.03256 | + | 1.78844i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.3757 | − | 24.8995i | 0.611317 | − | 1.05883i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 9.44585i | − | 0.400234i | −0.979772 | − | 0.200117i | \(-0.935868\pi\) | ||
0.979772 | − | 0.200117i | \(-0.0641322\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 10.5792i | − | 0.447452i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.0784 | + | 26.1166i | −0.635479 | + | 1.10068i | 0.350935 | + | 0.936400i | \(0.385864\pi\) |
−0.986413 | + | 0.164282i | \(0.947469\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.0072 | − | 50.2419i | −1.22034 | − | 2.11369i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.8243 | − | 12.6002i | 0.914920 | − | 0.528230i | 0.0329094 | − | 0.999458i | \(-0.489523\pi\) |
0.882011 | + | 0.471229i | \(0.156189\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.3079 | + | 18.6529i | 1.35204 | + | 0.780602i | 0.988535 | − | 0.150990i | \(-0.0482462\pi\) |
0.363506 | + | 0.931592i | \(0.381580\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.7431 | 1.19867 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.7799 | −0.740189 | −0.370094 | − | 0.928994i | \(-0.620675\pi\) | ||||
−0.370094 | + | 0.928994i | \(0.620675\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.1955 | − | 15.7014i | −1.12826 | − | 0.651402i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.48856 | + | 2.59147i | −0.185897 | + | 0.107328i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.2653 | − | 24.7083i | −0.588793 | − | 1.01982i | −0.994391 | − | 0.105767i | \(-0.966270\pi\) |
0.405598 | − | 0.914051i | \(-0.367063\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.57093 | − | 9.64913i | 0.229546 | − | 0.397585i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 31.3024i | − | 1.28544i | −0.766102 | − | 0.642718i | \(-0.777807\pi\) | ||
0.766102 | − | 0.642718i | \(-0.222193\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 60.3166i | 2.47274i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.72926 | + | 2.99517i | −0.0706557 | + | 0.122379i | −0.899189 | − | 0.437561i | \(-0.855842\pi\) |
0.828533 | + | 0.559940i | \(0.189176\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.78744 | + | 11.7562i | 0.276865 | + | 0.479545i | 0.970604 | − | 0.240682i | \(-0.0773711\pi\) |
−0.693739 | + | 0.720227i | \(0.744038\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −84.9267 | + | 49.0325i | −3.45276 | + | 1.99345i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.8069 | − | 17.7864i | −1.25042 | − | 0.721927i | −0.279223 | − | 0.960226i | \(-0.590077\pi\) |
−0.971192 | + | 0.238299i | \(0.923410\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.08051 | 0.124624 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.5978 | −0.953104 | −0.476552 | − | 0.879146i | \(-0.658114\pi\) | ||||
−0.476552 | + | 0.879146i | \(0.658114\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.5804 | + | 6.68594i | 0.466209 | + | 0.269166i | 0.714651 | − | 0.699481i | \(-0.246585\pi\) |
−0.248442 | + | 0.968647i | \(0.579919\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.2014 | + | 18.5915i | −1.29428 | + | 0.747254i | −0.979410 | − | 0.201880i | \(-0.935295\pi\) |
−0.314872 | + | 0.949134i | \(0.601962\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.45933 | + | 2.52764i | 0.0584670 | + | 0.101268i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.7591 | + | 37.6878i | −0.870363 | + | 1.50751i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.35689i | 0.373084i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.8564i | 1.50704i | 0.657425 | + | 0.753520i | \(0.271646\pi\) | ||||
−0.657425 | + | 0.753520i | \(0.728354\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.36804 | − | 4.10156i | 0.0939728 | − | 0.162766i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.67595 | − | 2.90283i | −0.0664035 | − | 0.115014i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.54689 | − | 4.35720i | 0.298084 | − | 0.172099i | −0.343498 | − | 0.939154i | \(-0.611612\pi\) |
0.641582 | + | 0.767054i | \(0.278278\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.2487 | + | 14.0000i | 0.956276 | + | 0.552106i | 0.895025 | − | 0.446016i | \(-0.147158\pi\) |
0.0612510 | + | 0.998122i | \(0.480491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.9855 | −0.864339 | −0.432169 | − | 0.901792i | \(-0.642252\pi\) | ||||
−0.432169 | + | 0.901792i | \(0.642252\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.74134 | −0.303874 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 41.0423 | + | 23.6958i | 1.60611 | + | 0.927289i | 0.990229 | + | 0.139450i | \(0.0445336\pi\) |
0.615882 | + | 0.787838i | \(0.288800\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.384241 | + | 0.221842i | −0.0150136 | + | 0.00866808i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.4752 | − | 21.6077i | −0.485966 | − | 0.841717i | 0.513904 | − | 0.857848i | \(-0.328199\pi\) |
−0.999870 | + | 0.0161304i | \(0.994865\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.0029 | − | 36.3781i | 0.816918 | − | 1.41494i | −0.0910240 | − | 0.995849i | \(-0.529014\pi\) |
0.907942 | − | 0.419095i | \(-0.137653\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 92.7602i | 3.59709i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 16.6778i | − | 0.645766i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.6160 | − | 33.9759i | 0.757267 | − | 1.31163i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.5926 | − | 39.1315i | −0.870880 | − | 1.50841i | −0.861087 | − | 0.508457i | \(-0.830216\pi\) |
−0.00979297 | − | 0.999952i | \(-0.503117\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.7614 | − | 14.2960i | 0.951658 | − | 0.549440i | 0.0580623 | − | 0.998313i | \(-0.481508\pi\) |
0.893596 | + | 0.448873i | \(0.148174\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.5173 | − | 15.8871i | −1.05602 | − | 0.609693i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.4357 | −0.973269 | −0.486634 | − | 0.873606i | \(-0.661776\pi\) | ||||
−0.486634 | + | 0.873606i | \(0.661776\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.0340 | −1.60604 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.01686 | − | 0.587086i | −0.0387394 | − | 0.0223662i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.1105 | − | 16.8069i | 1.10741 | − | 0.639366i | 0.169256 | − | 0.985572i | \(-0.445864\pi\) |
0.938159 | + | 0.346206i | \(0.112530\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.4734 | − | 51.0495i | −1.11799 | − | 1.93642i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.76958 | − | 8.26116i | 0.180661 | − | 0.312914i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.1433i | 0.458648i | 0.973350 | + | 0.229324i | \(0.0736515\pi\) | ||||
−0.973350 | + | 0.229324i | \(0.926349\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.3898i | 0.542723i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.29604 | − | 5.70892i | 0.123961 | − | 0.214706i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.1361 | − | 29.6807i | −0.643561 | − | 1.11468i | −0.984632 | − | 0.174643i | \(-0.944123\pi\) |
0.341071 | − | 0.940038i | \(-0.389210\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.31976 | + | 1.91667i | −0.124326 | + | 0.0717797i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27.9118 | − | 16.1149i | −1.04384 | − | 0.602663i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.4119 | 1.05958 | 0.529792 | − | 0.848128i | \(-0.322270\pi\) | ||||
0.529792 | + | 0.848128i | \(0.322270\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.3581 | 1.13059 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 62.4367 | + | 36.0479i | 2.31884 | + | 1.33878i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.9650 | − | 13.2589i | 0.851725 | − | 0.491744i | −0.00950728 | − | 0.999955i | \(-0.503026\pi\) |
0.861233 | + | 0.508211i | \(0.169693\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.1239 | + | 33.1235i | 0.707322 | + | 1.22512i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.0307 | + | 20.8378i | −0.444365 | + | 0.769664i | −0.998008 | − | 0.0630910i | \(-0.979904\pi\) |
0.553642 | + | 0.832755i | \(0.313237\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 58.0116i | − | 2.13689i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20.9740i | − | 0.771540i | −0.922595 | − | 0.385770i | \(-0.873936\pi\) | ||
0.922595 | − | 0.385770i | \(-0.126064\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.3620 | − | 33.5359i | 0.710322 | − | 1.23031i | −0.254414 | − | 0.967095i | \(-0.581882\pi\) |
0.964736 | − | 0.263219i | \(-0.0847842\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.85728 | − | 11.8771i | −0.251231 | − | 0.435145i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.7036 | + | 6.75705i | −0.427638 | + | 0.246897i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.3784 | − | 8.87871i | −0.561165 | − | 0.323989i | 0.192448 | − | 0.981307i | \(-0.438357\pi\) |
−0.753613 | + | 0.657319i | \(0.771691\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −35.4802 | −1.29126 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.7760 | −0.973191 | −0.486596 | − | 0.873627i | \(-0.661761\pi\) | ||||
−0.486596 | + | 0.873627i | \(0.661761\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.81297 | + | 2.77877i | 0.174470 | + | 0.100730i | 0.584692 | − | 0.811255i | \(-0.301215\pi\) |
−0.410222 | + | 0.911986i | \(0.634549\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.9019 | − | 25.3468i | 1.58935 | − | 0.917614i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.876882 | − | 1.51881i | −0.0316624 | − | 0.0548409i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.58003 | − | 2.73670i | 0.0569774 | − | 0.0986878i | −0.836130 | − | 0.548532i | \(-0.815187\pi\) |
0.893107 | + | 0.449844i | \(0.148520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 8.55146i | − | 0.307575i | −0.988104 | − | 0.153787i | \(-0.950853\pi\) | ||
0.988104 | − | 0.153787i | \(-0.0491471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 16.5710i | − | 0.595246i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.33508 | − | 12.7047i | 0.262807 | − | 0.455194i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8316 | + | 23.9570i | 0.494933 | + | 0.857248i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 70.9782 | − | 40.9793i | 2.53332 | − | 1.46261i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.2138 | − | 23.2174i | −1.43347 | − | 0.827612i | −0.436082 | − | 0.899907i | \(-0.643634\pi\) |
−0.997383 | + | 0.0722950i | \(0.976968\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −44.4679 | −1.58110 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.88783 | 0.315616 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.84163 | + | 4.52737i | 0.277765 | + | 0.160368i | 0.632411 | − | 0.774633i | \(-0.282065\pi\) |
−0.354646 | + | 0.935001i | \(0.615399\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.64509 | + | 5.56859i | −0.341219 | + | 0.197003i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.38708 | + | 11.0627i | 0.225395 | + | 0.390396i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.9570 | − | 27.6383i | 0.562410 | − | 0.974122i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.0623i | 1.16241i | 0.813758 | + | 0.581204i | \(0.197418\pi\) | ||||
−0.813758 | + | 0.581204i | \(0.802582\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 20.5874i | − | 0.722922i | −0.932387 | − | 0.361461i | \(-0.882278\pi\) | ||
0.932387 | − | 0.361461i | \(-0.117722\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.8803 | − | 39.6299i | 0.801462 | − | 1.38817i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.4104 | + | 50.9403i | 1.02894 | + | 1.78218i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.6299 | − | 24.6124i | 1.48779 | − | 0.858978i | 0.487890 | − | 0.872905i | \(-0.337767\pi\) |
0.999903 | + | 0.0139273i | \(0.00443334\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.4802 | − | 13.5563i | −0.818469 | − | 0.472543i | 0.0314190 | − | 0.999506i | \(-0.489997\pi\) |
−0.849888 | + | 0.526963i | \(0.823331\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.5040 | 1.30414 | 0.652070 | − | 0.758159i | \(-0.273901\pi\) | ||||
0.652070 | + | 0.758159i | \(0.273901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.78386 | −0.235613 | −0.117807 | − | 0.993037i | \(-0.537586\pi\) | ||||
−0.117807 | + | 0.993037i | \(0.537586\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.4948 | + | 6.05918i | 0.363624 | + | 0.209938i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −81.0575 | + | 46.7986i | −2.80511 | + | 1.61953i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.0402 | − | 34.7106i | −0.691863 | − | 1.19834i | −0.971227 | − | 0.238156i | \(-0.923457\pi\) |
0.279364 | − | 0.960185i | \(-0.409876\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.41625 | − | 11.1133i | 0.221250 | − | 0.383216i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 44.9366i | 1.54587i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 75.1666i | 2.58276i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.47540 | − | 4.28752i | 0.0848556 | − | 0.146974i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.71847 | + | 13.3688i | 0.264275 | + | 0.457738i | 0.967373 | − | 0.253355i | \(-0.0815339\pi\) |
−0.703098 | + | 0.711093i | \(0.748201\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.6520 | + | 7.30464i | −0.432184 | + | 0.249522i | −0.700277 | − | 0.713872i | \(-0.746940\pi\) |
0.268093 | + | 0.963393i | \(0.413607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.02878 | − | 2.90337i | −0.171580 | − | 0.0990616i | 0.411751 | − | 0.911297i | \(-0.364917\pi\) |
−0.583331 | + | 0.812235i | \(0.698251\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.5724 | 0.666254 | 0.333127 | − | 0.942882i | \(-0.391896\pi\) | ||||
0.333127 | + | 0.942882i | \(0.391896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −53.9487 | −1.83431 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.1020 | − | 27.7717i | −1.63175 | − | 0.942091i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.3815 | − | 6.57113i | 0.385649 | − | 0.222654i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 38.0384 | + | 65.8845i | 1.28593 | + | 2.22730i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.64809 | − | 4.58662i | 0.0894196 | − | 0.154879i | −0.817846 | − | 0.575437i | \(-0.804832\pi\) |
0.907266 | + | 0.420557i | \(0.138165\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16.5467i | − | 0.557473i | −0.960368 | − | 0.278736i | \(-0.910084\pi\) | ||
0.960368 | − | 0.278736i | \(-0.0899155\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 24.9361i | − | 0.839166i | −0.907717 | − | 0.419583i | \(-0.862176\pi\) | ||
0.907717 | − | 0.419583i | \(-0.137824\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.50506 | − | 11.2671i | 0.218419 | − | 0.378312i | −0.735906 | − | 0.677084i | \(-0.763244\pi\) |
0.954325 | + | 0.298772i | \(0.0965769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.81510 | − | 3.14384i | −0.0608765 | − | 0.105441i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.8331 | + | 8.56387i | −0.496370 | + | 0.286579i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 72.0841 | + | 41.6178i | 2.40951 | + | 1.39113i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.61506 | −0.320680 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.24507 | 0.141424 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.0536 | − | 16.1968i | −0.932535 | − | 0.538399i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.7534 | − | 17.7555i | 1.02115 | − | 0.589561i | 0.106713 | − | 0.994290i | \(-0.465967\pi\) |
0.914437 | + | 0.404729i | \(0.132634\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.2073 | − | 36.7321i | −0.702629 | − | 1.21699i | −0.967540 | − | 0.252716i | \(-0.918676\pi\) |
0.264912 | − | 0.964273i | \(-0.414657\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.3327 | + | 52.5378i | −1.00387 | + | 1.73875i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.340083i | 0.0112305i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.12106i | − | 0.102954i | −0.998674 | − | 0.0514772i | \(-0.983607\pi\) | ||
0.998674 | − | 0.0514772i | \(-0.0163929\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.13348 | + | 5.42734i | −0.103140 | + | 0.178643i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.7008 | + | 18.5343i | 0.351840 | + | 0.609405i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51.7148 | + | 29.8576i | −1.69671 | + | 0.979595i | −0.747863 | + | 0.663853i | \(0.768920\pi\) |
−0.948845 | + | 0.315742i | \(0.897747\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.1399 | + | 9.31835i | 0.528962 | + | 0.305397i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 116.523 | 3.81070 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.8793 | −0.649428 | −0.324714 | − | 0.945812i | \(-0.605268\pi\) | ||||
−0.324714 | + | 0.945812i | \(0.605268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.37354 | − | 5.41181i | −0.305569 | − | 0.176420i | 0.339373 | − | 0.940652i | \(-0.389785\pi\) |
−0.644942 | + | 0.764232i | \(0.723118\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.37104 | + | 2.52362i | −0.142341 | + | 0.0821804i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.5953 | − | 20.0836i | −0.376796 | − | 0.652630i | 0.613798 | − | 0.789463i | \(-0.289641\pi\) |
−0.990594 | + | 0.136833i | \(0.956308\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.44696 | + | 2.50621i | −0.0469704 | + | 0.0813551i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 17.7414i | − | 0.574700i | −0.957826 | − | 0.287350i | \(-0.907226\pi\) | ||
0.957826 | − | 0.287350i | \(-0.0927743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 91.5893i | − | 2.96376i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.1095 | + | 27.9025i | −0.520203 | + | 0.901018i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.3950 | − | 24.9329i | −0.464355 | − | 0.804286i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 57.2572 | − | 33.0575i | 1.84318 | − | 1.06416i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.6547 | + | 6.72886i | 0.374791 | + | 0.216386i | 0.675549 | − | 0.737315i | \(-0.263906\pi\) |
−0.300759 | + | 0.953700i | \(0.597240\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.8995 | −0.574423 | −0.287211 | − | 0.957867i | \(-0.592728\pi\) | ||||
−0.287211 | + | 0.957867i | \(0.592728\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45.1827 | −1.44849 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.0208 | + | 9.82699i | 0.544545 | + | 0.314393i | 0.746919 | − | 0.664915i | \(-0.231532\pi\) |
−0.202374 | + | 0.979308i | \(0.564866\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.88303 | − | 2.81922i | 0.156062 | − | 0.0901026i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.8264 | + | 51.6608i | 0.951314 | + | 1.64772i | 0.742587 | + | 0.669749i | \(0.233598\pi\) |
0.208726 | + | 0.977974i | \(0.433068\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.1099 | − | 76.4006i | 1.40546 | − | 2.43433i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 20.2372i | − | 0.643505i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.0373i | 1.52595i | 0.646426 | + | 0.762977i | \(0.276263\pi\) | ||||
−0.646426 | + | 0.762977i | \(0.723737\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.6901 | + | 39.3004i | −0.719324 | + | 1.24591i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.19614 | + | 5.53587i | 0.101223 | + | 0.175323i | 0.912189 | − | 0.409770i | \(-0.134391\pi\) |
−0.810966 | + | 0.585093i | \(0.801058\pi\) | |||||||
\(998\) | 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 | 2592.2.s.j.863.8 | 16 | ||
3.2 | odd | 2 | inner | 2592.2.s.j.863.1 | 16 | ||
4.3 | odd | 2 | 2592.2.s.i.863.8 | 16 | |||
9.2 | odd | 6 | 2592.2.s.i.1727.8 | 16 | |||
9.4 | even | 3 | 2592.2.c.b.2591.2 | yes | 16 | ||
9.5 | odd | 6 | 2592.2.c.b.2591.16 | yes | 16 | ||
9.7 | even | 3 | 2592.2.s.i.1727.1 | 16 | |||
12.11 | even | 2 | 2592.2.s.i.863.1 | 16 | |||
36.7 | odd | 6 | inner | 2592.2.s.j.1727.1 | 16 | ||
36.11 | even | 6 | inner | 2592.2.s.j.1727.8 | 16 | ||
36.23 | even | 6 | 2592.2.c.b.2591.15 | yes | 16 | ||
36.31 | odd | 6 | 2592.2.c.b.2591.1 | ✓ | 16 | ||
72.5 | odd | 6 | 5184.2.c.l.5183.2 | 16 | |||
72.13 | even | 6 | 5184.2.c.l.5183.16 | 16 | |||
72.59 | even | 6 | 5184.2.c.l.5183.1 | 16 | |||
72.67 | odd | 6 | 5184.2.c.l.5183.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2592.2.c.b.2591.1 | ✓ | 16 | 36.31 | odd | 6 | ||
2592.2.c.b.2591.2 | yes | 16 | 9.4 | even | 3 | ||
2592.2.c.b.2591.15 | yes | 16 | 36.23 | even | 6 | ||
2592.2.c.b.2591.16 | yes | 16 | 9.5 | odd | 6 | ||
2592.2.s.i.863.1 | 16 | 12.11 | even | 2 | |||
2592.2.s.i.863.8 | 16 | 4.3 | odd | 2 | |||
2592.2.s.i.1727.1 | 16 | 9.7 | even | 3 | |||
2592.2.s.i.1727.8 | 16 | 9.2 | odd | 6 | |||
2592.2.s.j.863.1 | 16 | 3.2 | odd | 2 | inner | ||
2592.2.s.j.863.8 | 16 | 1.1 | even | 1 | trivial | ||
2592.2.s.j.1727.1 | 16 | 36.7 | odd | 6 | inner | ||
2592.2.s.j.1727.8 | 16 | 36.11 | even | 6 | inner | ||
5184.2.c.l.5183.1 | 16 | 72.59 | even | 6 | |||
5184.2.c.l.5183.2 | 16 | 72.5 | odd | 6 | |||
5184.2.c.l.5183.15 | 16 | 72.67 | odd | 6 | |||
5184.2.c.l.5183.16 | 16 | 72.13 | even | 6 |