Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(129,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.g (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.17668116698\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 641.1 | ||
Root | \(-0.991445 + 0.130526i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.641 |
Dual form | 1024.2.g.a.385.1 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.40211 | − | 0.580775i | −0.809511 | − | 0.335311i | −0.0607523 | − | 0.998153i | \(-0.519350\pi\) |
−0.748759 | + | 0.662842i | \(0.769350\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.36603 | − | 3.29788i | −0.610905 | − | 1.47486i | −0.862008 | − | 0.506895i | \(-0.830793\pi\) |
0.251103 | − | 0.967960i | \(-0.419207\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.02642 | − | 1.02642i | 0.387950 | − | 0.387950i | −0.486006 | − | 0.873956i | \(-0.661547\pi\) |
0.873956 | + | 0.486006i | \(0.161547\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.492694 | − | 0.492694i | −0.164231 | − | 0.164231i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.97171 | − | 2.05935i | 1.49903 | − | 0.620917i | 0.525768 | − | 0.850628i | \(-0.323778\pi\) |
0.973259 | + | 0.229710i | \(0.0737779\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.56583 | − | 3.78024i | 0.434282 | − | 1.04845i | −0.543610 | − | 0.839338i | \(-0.682943\pi\) |
0.977892 | − | 0.209112i | \(-0.0670572\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.41736i | 1.39876i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.35311i | 0.570714i | 0.958421 | + | 0.285357i | \(0.0921121\pi\) | ||||
−0.958421 | + | 0.285357i | \(0.907888\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.15885 | − | 2.79772i | 0.265859 | − | 0.641840i | −0.733421 | − | 0.679774i | \(-0.762078\pi\) |
0.999280 | + | 0.0379340i | \(0.0120777\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.03528 | + | 0.843039i | −0.444134 | + | 0.183966i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.06460 | − | 1.06460i | −0.221985 | − | 0.221985i | 0.587349 | − | 0.809334i | \(-0.300172\pi\) |
−0.809334 | + | 0.587349i | \(0.800172\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.47443 | + | 5.47443i | −1.09489 | + | 1.09489i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.14699 | + | 5.18330i | 0.413189 | + | 0.997527i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.86540 | − | 1.60110i | −0.717787 | − | 0.297317i | −0.00626466 | − | 0.999980i | \(-0.501994\pi\) |
−0.711523 | + | 0.702663i | \(0.751994\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.5829 | 1.90074 | 0.950370 | − | 0.311123i | \(-0.100705\pi\) | ||||
0.950370 | + | 0.311123i | \(0.100705\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.16693 | −1.42168 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.78712 | − | 1.98289i | −0.809171 | − | 0.335170i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.75201 | − | 4.22973i | −0.288029 | − | 0.695363i | 0.711948 | − | 0.702233i | \(-0.247813\pi\) |
−0.999976 | + | 0.00686951i | \(0.997813\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.39094 | + | 4.39094i | −0.703113 | + | 0.703113i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.27792 | − | 6.27792i | −0.980446 | − | 0.980446i | 0.0193666 | − | 0.999812i | \(-0.493835\pi\) |
−0.999812 | + | 0.0193666i | \(0.993835\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.60205 | + | 3.56308i | −1.31180 | + | 0.543365i | −0.925409 | − | 0.378970i | \(-0.876278\pi\) |
−0.386391 | + | 0.922335i | \(0.626278\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.951812 | + | 2.29788i | −0.141888 | + | 0.342547i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.06910i | − | 0.447674i | −0.974627 | − | 0.223837i | \(-0.928142\pi\) | ||
0.974627 | − | 0.223837i | \(-0.0718583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.89293i | 0.698990i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.36663 | − | 3.29934i | 0.191366 | − | 0.461999i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.384286 | − | 0.159176i | 0.0527857 | − | 0.0218646i | −0.356134 | − | 0.934435i | \(-0.615905\pi\) |
0.408920 | + | 0.912570i | \(0.365905\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.5830 | − | 13.5830i | −1.83153 | − | 1.83153i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.24969 | + | 3.24969i | −0.430432 | + | 0.430432i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.22287 | + | 7.78071i | 0.419583 | + | 1.01296i | 0.982469 | + | 0.186427i | \(0.0596909\pi\) |
−0.562886 | + | 0.826534i | \(0.690309\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.58044 | − | 1.06885i | −0.330391 | − | 0.136853i | 0.211321 | − | 0.977417i | \(-0.432224\pi\) |
−0.541712 | + | 0.840564i | \(0.682224\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.01142 | −0.127427 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.6057 | −1.81162 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.79363 | − | 1.98559i | −0.585635 | − | 0.242578i | 0.0701364 | − | 0.997537i | \(-0.477657\pi\) |
−0.655772 | + | 0.754959i | \(0.727657\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.874400 | + | 2.11099i | 0.105265 | + | 0.254133i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.84718 | − | 2.84718i | 0.337898 | − | 0.337898i | −0.517678 | − | 0.855576i | \(-0.673203\pi\) |
0.855576 | + | 0.517678i | \(0.173203\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.43123 | + | 8.43123i | 0.986801 | + | 0.986801i | 0.999914 | − | 0.0131133i | \(-0.00417420\pi\) |
−0.0131133 | + | 0.999914i | \(0.504174\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.8552 | − | 4.49637i | 1.25345 | − | 0.519196i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.98930 | − | 7.21682i | 0.340663 | − | 0.822433i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.59983i | 0.517521i | 0.965941 | + | 0.258761i | \(0.0833141\pi\) | ||||
−0.965941 | + | 0.258761i | \(0.916686\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 6.42418i | − | 0.713798i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.14911 | + | 7.60263i | −0.345660 | + | 0.834497i | 0.651462 | + | 0.758681i | \(0.274156\pi\) |
−0.997122 | + | 0.0758155i | \(0.975844\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.76028 | − | 3.21441i | 0.841720 | − | 0.348652i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.48986 | + | 4.48986i | 0.481363 | + | 0.481363i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.967128 | + | 0.967128i | −0.102515 | + | 0.102515i | −0.756504 | − | 0.653989i | \(-0.773094\pi\) |
0.653989 | + | 0.756504i | \(0.273094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.27292 | − | 5.48730i | −0.238266 | − | 0.575226i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.8384 | − | 6.14626i | −1.53867 | − | 0.637338i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.8096 | −1.10904 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.2672 | 1.14401 | 0.572006 | − | 0.820249i | \(-0.306165\pi\) | ||||
0.572006 | + | 0.820249i | \(0.306165\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.46416 | − | 1.43490i | −0.348161 | − | 0.144213i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.58649 | − | 8.65855i | −0.356869 | − | 0.861558i | −0.995737 | − | 0.0922416i | \(-0.970597\pi\) |
0.638868 | − | 0.769317i | \(-0.279403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.20450 | + | 1.20450i | −0.118683 | + | 0.118683i | −0.763954 | − | 0.645271i | \(-0.776744\pi\) |
0.645271 | + | 0.763954i | \(0.276744\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.56048 | + | 5.56048i | 0.542647 | + | 0.542647i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.68959 | + | 1.11406i | −0.260012 | + | 0.107701i | −0.508882 | − | 0.860836i | \(-0.669941\pi\) |
0.248870 | + | 0.968537i | \(0.419941\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.46240 | − | 3.53055i | 0.140073 | − | 0.338165i | −0.838239 | − | 0.545303i | \(-0.816415\pi\) |
0.978312 | + | 0.207137i | \(0.0664147\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.94809i | 0.659483i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.13630i | − | 0.200966i | −0.994939 | − | 0.100483i | \(-0.967961\pi\) | ||
0.994939 | − | 0.100483i | \(-0.0320388\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.05665 | + | 4.96520i | −0.191784 | + | 0.463007i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.63397 | + | 1.09103i | −0.243511 | + | 0.100866i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.41528 | + | 2.41528i | 0.221408 | + | 0.221408i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.6988 | − | 12.6988i | 1.15444 | − | 1.15444i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.15630 | + | 12.4484i | 0.464928 | + | 1.12244i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.04284 | + | 3.74567i | 0.808816 | + | 0.335023i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.09821 | 0.0974502 | 0.0487251 | − | 0.998812i | \(-0.484484\pi\) | ||||
0.0487251 | + | 0.998812i | \(0.484484\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.1304 | 1.24411 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.655166 | + | 0.271379i | 0.0572421 | + | 0.0237105i | 0.411121 | − | 0.911581i | \(-0.365137\pi\) |
−0.353879 | + | 0.935291i | \(0.615137\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.68216 | − | 4.06110i | −0.145862 | − | 0.352142i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.1610 | − | 14.1610i | 1.21879 | − | 1.21879i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.4887 | − | 11.4887i | −0.981544 | − | 0.981544i | 0.0182885 | − | 0.999833i | \(-0.494178\pi\) |
−0.999833 | + | 0.0182885i | \(0.994178\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.781087 | + | 0.323537i | −0.0662510 | + | 0.0274421i | −0.415563 | − | 0.909564i | \(-0.636415\pi\) |
0.349312 | + | 0.937007i | \(0.386415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.78245 | + | 4.30323i | −0.150110 | + | 0.362397i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 22.0188i | − | 1.84131i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.9348i | 1.24027i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.84169 | − | 6.86045i | 0.234379 | − | 0.565840i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.52350 | + | 2.70212i | −0.534426 | + | 0.221367i | −0.633541 | − | 0.773710i | \(-0.718399\pi\) |
0.0991144 | + | 0.995076i | \(0.468399\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.87443 | + | 9.87443i | 0.803569 | + | 0.803569i | 0.983652 | − | 0.180082i | \(-0.0576364\pi\) |
−0.180082 | + | 0.983652i | \(0.557636\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.15937 | − | 1.15937i | 0.0937291 | − | 0.0937291i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.4565 | − | 34.9010i | −1.16117 | − | 2.80332i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.3677 | + | 9.26500i | 1.78514 | + | 0.739428i | 0.991352 | + | 0.131229i | \(0.0418924\pi\) |
0.793785 | + | 0.608199i | \(0.208108\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.631258 | −0.0500620 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.18546 | −0.172238 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.1774 | + | 6.70092i | 1.26712 | + | 0.524856i | 0.912086 | − | 0.409999i | \(-0.134471\pi\) |
0.355029 | + | 0.934855i | \(0.384471\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.1562 | + | 26.9335i | 0.868511 | + | 2.09677i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.9204 | + | 15.9204i | −1.23196 | + | 1.23196i | −0.268751 | + | 0.963210i | \(0.586611\pi\) |
−0.963210 | + | 0.268751i | \(0.913389\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.64601 | − | 2.64601i | −0.203539 | − | 0.203539i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.94938 | + | 0.807459i | −0.149073 | + | 0.0617479i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.46532 | + | 8.36603i | −0.263463 | + | 0.636057i | −0.999148 | − | 0.0412671i | \(-0.986861\pi\) |
0.735685 | + | 0.677324i | \(0.236861\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.2381i | 0.849523i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.7812i | − | 0.960695i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.0548557 | − | 0.132433i | 0.00410011 | − | 0.00989854i | −0.921816 | − | 0.387627i | \(-0.873295\pi\) |
0.925916 | + | 0.377729i | \(0.123295\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.37724 | + | 0.984684i | −0.176699 | + | 0.0731910i | −0.469279 | − | 0.883050i | \(-0.655486\pi\) |
0.292580 | + | 0.956241i | \(0.405486\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.99731 | + | 2.99731i | 0.221567 | + | 0.221567i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.5558 | + | 11.5558i | −0.849602 | + | 0.849602i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.84588 | + | 11.6990i | 0.354366 | + | 0.855516i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.52396 | + | 3.11653i | 0.547287 | + | 0.226694i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.4603 | 1.19103 | 0.595514 | − | 0.803345i | \(-0.296948\pi\) | ||||
0.595514 | + | 0.803345i | \(0.296948\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.84445 | 0.708619 | 0.354309 | − | 0.935128i | \(-0.384716\pi\) | ||||
0.354309 | + | 0.935128i | \(0.384716\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.4789 | + | 8.48264i | 1.46652 | + | 0.607454i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.91048 | + | 9.44074i | 0.278610 | + | 0.672625i | 0.999798 | − | 0.0201152i | \(-0.00640329\pi\) |
−0.721187 | + | 0.692740i | \(0.756403\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.41726 | + | 2.41726i | −0.171355 | + | 0.171355i | −0.787574 | − | 0.616220i | \(-0.788663\pi\) |
0.616220 | + | 0.787574i | \(0.288663\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.56804 | + | 5.56804i | 0.392739 | + | 0.392739i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.61093 | + | 2.32412i | −0.393810 | + | 0.163121i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.1280 | + | 29.2796i | −0.847057 | + | 2.04498i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.04905i | 0.0729137i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 16.2959i | − | 1.12721i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.06529 | − | 14.6429i | 0.417552 | − | 1.00806i | −0.565503 | − | 0.824746i | \(-0.691318\pi\) |
0.983055 | − | 0.183312i | \(-0.0586820\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.64564 | + | 2.33850i | −0.386833 | + | 0.160231i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.5012 | + | 23.5012i | 1.60277 | + | 1.60277i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.8625 | − | 10.8625i | 0.737392 | − | 0.737392i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.92490 | − | 16.7182i | −0.467942 | − | 1.12971i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.89533 | + | 3.68457i | 0.598365 | + | 0.247851i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.9031 | −1.39978 | −0.699888 | − | 0.714253i | \(-0.746767\pi\) | ||||
−0.699888 | + | 0.714253i | \(0.746767\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.39444 | 0.359629 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.5201 | + | 5.18600i | 0.830989 | + | 0.344207i | 0.757294 | − | 0.653074i | \(-0.226521\pi\) |
0.0736948 | + | 0.997281i | \(0.476521\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.21925 | + | 5.35773i | 0.146652 | + | 0.354049i | 0.980087 | − | 0.198568i | \(-0.0636292\pi\) |
−0.833435 | + | 0.552617i | \(0.813629\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.38269 | + | 8.38269i | −0.551541 | + | 0.551541i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.0268197 | − | 0.0268197i | −0.00175702 | − | 0.00175702i | 0.706228 | − | 0.707985i | \(-0.250395\pi\) |
−0.707985 | + | 0.706228i | \(0.750395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1215 | + | 4.19246i | −0.660254 | + | 0.273486i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.67147 | − | 6.44949i | 0.173530 | − | 0.418939i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.6128i | − | 1.65676i | −0.560169 | − | 0.828378i | \(-0.689264\pi\) | ||
0.560169 | − | 0.828378i | \(-0.310736\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.28132i | − | 0.0825369i | −0.999148 | − | 0.0412684i | \(-0.986860\pi\) | ||
0.999148 | − | 0.0412684i | \(-0.0131399\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.70998 | − | 6.54247i | 0.173845 | − | 0.419699i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.1363 | − | 6.68386i | 1.03091 | − | 0.427016i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.76148 | − | 8.76148i | −0.557480 | − | 0.557480i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.83083 | − | 8.83083i | 0.559631 | − | 0.559631i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.01245 | − | 9.68691i | −0.253263 | − | 0.611432i | 0.745200 | − | 0.666841i | \(-0.232354\pi\) |
−0.998464 | + | 0.0554086i | \(0.982354\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.48528 | − | 3.10051i | −0.470596 | − | 0.194927i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.7477 | −0.798289 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.01513 | 0.499970 | 0.249985 | − | 0.968250i | \(-0.419574\pi\) | ||||
0.249985 | + | 0.968250i | \(0.419574\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.13977 | − | 2.54318i | −0.381507 | − | 0.158025i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.11561 | + | 2.69331i | 0.0690544 | + | 0.166712i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.8663 | − | 13.8663i | 0.855030 | − | 0.855030i | −0.135718 | − | 0.990748i | \(-0.543334\pi\) |
0.990748 | + | 0.135718i | \(0.0433340\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.04989 | − | 1.04989i | −0.0644941 | − | 0.0644941i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.91771 | − | 0.794341i | 0.117362 | − | 0.0486129i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.54616 | − | 15.8038i | 0.399126 | − | 0.963576i | −0.588748 | − | 0.808317i | \(-0.700379\pi\) |
0.987874 | − | 0.155259i | \(-0.0496212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 15.6152i | − | 0.948557i | −0.880375 | − | 0.474279i | \(-0.842709\pi\) | ||
0.880375 | − | 0.474279i | \(-0.157291\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.01388i | 0.545545i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.9435 | + | 38.4911i | −0.961431 | + | 2.32110i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.8489 | + | 5.32219i | −0.772016 | + | 0.319779i | −0.733689 | − | 0.679486i | \(-0.762203\pi\) |
−0.0383271 | + | 0.999265i | \(0.512203\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.21412 | − | 5.21412i | −0.312161 | − | 0.312161i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.7289 | − | 18.7289i | 1.11727 | − | 1.11727i | 0.125134 | − | 0.992140i | \(-0.460064\pi\) |
0.992140 | − | 0.125134i | \(-0.0399360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.410064 | + | 0.989981i | 0.0243758 | + | 0.0588483i | 0.935599 | − | 0.353065i | \(-0.114861\pi\) |
−0.911223 | + | 0.411913i | \(0.864861\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.1562 | + | 6.27792i | 0.897778 | + | 0.371872i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.8875 | −0.760728 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.4629 | 0.674286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.7979 | − | 6.54372i | −0.926091 | − | 0.383600i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.81087 | − | 16.4429i | −0.397895 | − | 0.960604i | −0.988165 | − | 0.153398i | \(-0.950978\pi\) |
0.590269 | − | 0.807206i | \(-0.299022\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.2573 | − | 21.2573i | 1.23765 | − | 1.23765i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.3485 | + | 21.3485i | 1.23876 | + | 1.23876i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.69143 | + | 2.35747i | −0.329144 | + | 0.136336i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.17209 | + | 12.4865i | −0.298114 | + | 0.719711i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.2232i | 0.817103i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.97005i | 0.570883i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.89068 | + | 19.0498i | −0.450345 | + | 1.08723i | 0.521846 | + | 0.853040i | \(0.325243\pi\) |
−0.972191 | + | 0.234189i | \(0.924757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.38839 | − | 0.989303i | 0.135871 | − | 0.0562795i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.42704 | + | 1.42704i | 0.0809203 | + | 0.0809203i | 0.746408 | − | 0.665488i | \(-0.231777\pi\) |
−0.665488 | + | 0.746408i | \(0.731777\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.27186 | + | 1.27186i | −0.0718900 | + | 0.0718900i | −0.742138 | − | 0.670248i | \(-0.766188\pi\) |
0.670248 | + | 0.742138i | \(0.266188\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.38163 | + | 3.33554i | 0.0778459 | + | 0.187937i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.9106 | − | 9.48990i | −1.28679 | − | 0.533006i | −0.368763 | − | 0.929523i | \(-0.620219\pi\) |
−0.918027 | + | 0.396518i | \(0.870219\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.5149 | −1.26059 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.41813 | 0.246596 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.58335 | + | 2.72691i | 0.366307 | + | 0.151729i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.1227 | + | 29.2667i | 0.672444 | + | 1.62342i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.10091 | + | 4.10091i | −0.226781 | + | 0.226781i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.15018 | − | 3.15018i | −0.173675 | − | 0.173675i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.1789 | − | 8.77257i | 1.16410 | − | 0.482184i | 0.284859 | − | 0.958570i | \(-0.408053\pi\) |
0.879236 | + | 0.476386i | \(0.158053\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.22076 | + | 2.94717i | −0.0668971 | + | 0.161504i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.5212i | 1.01192i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 27.4961i | − | 1.49781i | −0.662677 | − | 0.748905i | \(-0.730580\pi\) | ||
0.662677 | − | 0.748905i | \(-0.269420\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.24071 | + | 2.99533i | −0.0673860 | + | 0.162684i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 52.6150 | − | 21.7938i | 2.84926 | − | 1.18020i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.2071 | + | 12.2071i | 0.659123 | + | 0.659123i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.76733 | − | 5.76733i | 0.310502 | − | 0.310502i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.87785 | + | 4.53353i | 0.100808 | + | 0.243373i | 0.966235 | − | 0.257663i | \(-0.0829525\pi\) |
−0.865427 | + | 0.501036i | \(0.832952\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.9976 | − | 8.28327i | −1.07045 | − | 0.443393i | −0.223298 | − | 0.974750i | \(-0.571682\pi\) |
−0.847148 | + | 0.531357i | \(0.821682\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.9559 | 1.22530 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.5498 | −0.614733 | −0.307366 | − | 0.951591i | \(-0.599448\pi\) | ||||
−0.307366 | + | 0.951591i | \(0.599448\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.2790 | − | 5.50033i | −0.704774 | − | 0.291927i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.98377 | − | 4.78924i | −0.104992 | − | 0.253473i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.0741 | + | 19.0741i | −1.00669 | + | 1.00669i | −0.00671431 | + | 0.999977i | \(0.502137\pi\) |
−0.999977 | + | 0.00671431i | \(0.997863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.95074 | + | 6.95074i | 0.365829 | + | 0.365829i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.1803 | + | 10.4300i | −1.32163 | + | 0.547435i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.2879 | − | 39.3224i | 0.852547 | − | 2.05823i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 12.4379i | − | 0.649251i | −0.945843 | − | 0.324626i | \(-0.894762\pi\) | ||
0.945843 | − | 0.324626i | \(-0.105238\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.18618i | 0.322040i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.231057 | − | 0.557820i | 0.0119959 | − | 0.0289606i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.1238 | + | 12.8919i | −1.61153 | + | 0.667518i | −0.992986 | − | 0.118232i | \(-0.962277\pi\) |
−0.618544 | + | 0.785750i | \(0.712277\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5037 | − | 10.5037i | −0.542409 | − | 0.542409i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.1051 | + | 12.1051i | −0.623444 | + | 0.623444i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.42584 | + | 13.0991i | 0.278707 | + | 0.672858i | 0.999800 | − | 0.0199800i | \(-0.00636025\pi\) |
−0.721094 | + | 0.692838i | \(0.756360\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.53981 | − | 0.637812i | −0.0788870 | − | 0.0326761i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.14287 | −0.364984 | −0.182492 | − | 0.983207i | \(-0.558416\pi\) | ||||
−0.182492 | + | 0.983207i | \(0.558416\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −27.8836 | −1.42108 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.99369 | + | 2.48267i | 0.304676 | + | 0.126201i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.8578 | − | 26.2131i | −0.550514 | − | 1.32906i | −0.917093 | − | 0.398672i | \(-0.869471\pi\) |
0.366579 | − | 0.930387i | \(-0.380529\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.50513 | − | 2.50513i | 0.126690 | − | 0.126690i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.761008 | − | 0.761008i | −0.0383878 | − | 0.0383878i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.1697 | − | 6.28348i | 0.763269 | − | 0.316156i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.55362 | + | 8.57919i | −0.178351 | + | 0.430577i | −0.987621 | − | 0.156860i | \(-0.949863\pi\) |
0.809270 | + | 0.587437i | \(0.199863\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.67109i | 0.333972i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 9.43274i | − | 0.471049i | −0.971868 | − | 0.235524i | \(-0.924319\pi\) | ||
0.971868 | − | 0.235524i | \(-0.0756807\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.5709 | − | 40.0058i | 0.825457 | − | 1.99283i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.1862 | + | 8.77559i | −1.05275 | + | 0.436063i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.4210 | − | 17.4210i | −0.863526 | − | 0.863526i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.4495 | + | 15.4495i | −0.763928 | + | 0.763928i | −0.977030 | − | 0.213102i | \(-0.931643\pi\) |
0.213102 | + | 0.977030i | \(0.431643\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.43611 | + | 22.7808i | 0.465449 | + | 1.12369i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.2943 | + | 4.67825i | 0.555756 | + | 0.230202i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.3743 | 1.44193 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.28308 | 0.0628325 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.7592 | + | 8.18452i | 0.965299 | + | 0.399840i | 0.808960 | − | 0.587864i | \(-0.200031\pi\) |
0.156339 | + | 0.987703i | \(0.450031\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.1504 | + | 24.5052i | 0.494700 | + | 1.19431i | 0.952303 | + | 0.305155i | \(0.0987084\pi\) |
−0.457602 | + | 0.889157i | \(0.651292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.51213 | + | 1.51213i | −0.0735221 | + | 0.0735221i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.8820 | − | 12.8820i | −0.624867 | − | 0.624867i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.74570 | + | 1.55152i | −0.181267 | + | 0.0750833i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.7880 | + | 30.8729i | −0.617410 | + | 1.49056i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 24.7162i | − | 1.19054i | −0.803528 | − | 0.595268i | \(-0.797046\pi\) | ||
0.803528 | − | 0.595268i | \(-0.202954\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.69501i | 0.465913i | 0.972487 | + | 0.232956i | \(0.0748399\pi\) | ||||
−0.972487 | + | 0.232956i | \(0.925160\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.67374 | − | 20.9403i | 0.415874 | − | 1.00401i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.21217 | + | 1.74474i | −0.201496 | + | 0.0834622i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.45429 | − | 8.45429i | −0.403501 | − | 0.403501i | 0.475964 | − | 0.879465i | \(-0.342099\pi\) |
−0.879465 | + | 0.475964i | \(0.842099\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.41072 | − | 2.41072i | 0.114796 | − | 0.114796i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.5182 | − | 35.0500i | −0.689780 | − | 1.66528i | −0.745224 | − | 0.666814i | \(-0.767657\pi\) |
0.0554440 | − | 0.998462i | \(-0.482343\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.51059 | + | 1.86835i | 0.213822 | + | 0.0885682i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.7160 | 0.506851 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.3365 | −1.05413 | −0.527063 | − | 0.849826i | \(-0.676707\pi\) | ||||
−0.527063 | + | 0.849826i | \(0.676707\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.1404 | − | 18.2836i | −2.07849 | − | 0.860939i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.11026 | − | 19.5799i | −0.381053 | − | 0.919944i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.9916 | + | 14.9916i | −0.702817 | + | 0.702817i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.4049 | − | 22.4049i | −1.04806 | − | 1.04806i | −0.998785 | − | 0.0492728i | \(-0.984310\pi\) |
−0.0492728 | − | 0.998785i | \(-0.515690\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.1969 | + | 5.05212i | −0.569302 | + | 0.235813i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.20979 | + | 2.92070i | −0.0563457 | + | 0.136031i | −0.949545 | − | 0.313630i | \(-0.898455\pi\) |
0.893200 | + | 0.449660i | \(0.148455\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.3825i | 1.22610i | 0.790045 | + | 0.613048i | \(0.210057\pi\) | ||||
−0.790045 | + | 0.613048i | \(0.789943\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 57.3312i | 2.65867i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.92750 | + | 9.48183i | −0.181743 | + | 0.438767i | −0.988326 | − | 0.152354i | \(-0.951314\pi\) |
0.806583 | + | 0.591121i | \(0.201314\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.95832 | + | 2.88223i | −0.321305 | + | 0.133089i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.9812 | − | 25.9812i | −1.19715 | − | 1.19715i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35.4293 | + | 35.4293i | −1.62904 | + | 1.62904i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.97186 | + | 21.6600i | 0.411657 | + | 0.993828i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.267761 | − | 0.110910i | −0.0122599 | − | 0.00507822i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.4855 | 1.21015 | 0.605077 | − | 0.796167i | \(-0.293142\pi\) | ||||
0.605077 | + | 0.796167i | \(0.293142\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.7327 | −0.854139 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.06426 | + | 1.26926i | 0.139429 | + | 0.0577532i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.3913 | − | 37.1579i | −0.698883 | − | 1.68725i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.38394 | − | 5.38394i | 0.243970 | − | 0.243970i | −0.574521 | − | 0.818490i | \(-0.694811\pi\) |
0.818490 | + | 0.574521i | \(0.194811\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.7909 | − | 18.7909i | −0.849754 | − | 0.849754i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.9889 | − | 6.62284i | 0.721571 | − | 0.298884i | 0.00848784 | − | 0.999964i | \(-0.497298\pi\) |
0.713083 | + | 0.701080i | \(0.247298\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.76758 | − | 9.09573i | 0.169683 | − | 0.409651i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.3845i | 0.601588i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5.84480i | − | 0.262175i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.68675 | − | 4.07217i | 0.0755091 | − | 0.182295i | −0.881618 | − | 0.471964i | \(-0.843545\pi\) |
0.957127 | + | 0.289669i | \(0.0935452\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.5685 | − | 13.0761i | 1.41038 | − | 0.584197i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.1132 | + | 22.1132i | 0.985978 | + | 0.985978i | 0.999903 | − | 0.0139248i | \(-0.00443254\pi\) |
−0.0139248 | + | 0.999903i | \(0.504433\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.6556 | + | 23.6556i | −1.05266 | + | 1.05266i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.17327 | + | 5.24674i | 0.0965183 | + | 0.233016i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.6528 | + | 5.24094i | 0.560823 | + | 0.232301i | 0.645043 | − | 0.764147i | \(-0.276840\pi\) |
−0.0842193 | + | 0.996447i | \(0.526840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.3080 | 0.765659 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.9895 | 0.750103 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.61767 | + | 2.32691i | 0.247544 | + | 0.102536i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.32034 | − | 15.2587i | −0.277968 | − | 0.671075i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.71756 | − | 9.71756i | 0.426553 | − | 0.426553i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.89757 | + | 7.89757i | 0.345999 | + | 0.345999i | 0.858617 | − | 0.512618i | \(-0.171324\pi\) |
−0.512618 | + | 0.858617i | \(0.671324\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.2606 | − | 4.66429i | 0.492391 | − | 0.203955i | −0.122650 | − | 0.992450i | \(-0.539139\pi\) |
0.615041 | + | 0.788495i | \(0.289139\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.52682 | − | 15.7571i | 0.284854 | − | 0.687698i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.9027i | 1.08478i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 20.7332i | − | 0.901445i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.24562 | − | 5.42140i | 0.0974515 | − | 0.235269i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.5622 | + | 13.9019i | −1.45374 | + | 0.602158i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.34809 | + | 7.34809i | 0.317685 | + | 0.317685i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.153828 | + | 0.153828i | −0.00663817 | + | 0.00663817i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.0763 | + | 24.3262i | 0.434015 | + | 1.04780i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.7860 | − | 4.88194i | −0.506722 | − | 0.209891i | 0.114652 | − | 0.993406i | \(-0.463425\pi\) |
−0.621373 | + | 0.783515i | \(0.713425\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.90504 | 0.167581 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.6410 | −0.584316 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.1348 | − | 10.8254i | −1.11745 | − | 0.462861i | −0.253950 | − | 0.967217i | \(-0.581730\pi\) |
−0.863496 | + | 0.504356i | \(0.831730\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.744749 | + | 1.79798i | 0.0317851 | + | 0.0767361i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.95887 | + | 8.95887i | −0.381661 | + | 0.381661i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.72135 | + | 4.72135i | 0.200772 | + | 0.200772i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.9139 | − | 9.49127i | 0.972643 | − | 0.402882i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.5899 | − | 32.8089i | 0.575822 | − | 1.39016i | −0.320709 | − | 0.947178i | \(-0.603921\pi\) |
0.896532 | − | 0.442980i | \(-0.146079\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.0970i | 1.61133i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 19.2177i | − | 0.811372i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.48742 | − | 10.8336i | 0.189122 | − | 0.456582i | −0.800669 | − | 0.599107i | \(-0.795522\pi\) |
0.989791 | + | 0.142526i | \(0.0455223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.04524 | + | 2.91824i | −0.296396 | + | 0.122771i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.59390 | − | 6.59390i | −0.276918 | − | 0.276918i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.7673 | − | 18.7673i | 0.786767 | − | 0.786767i | −0.194196 | − | 0.980963i | \(-0.562210\pi\) |
0.980963 | + | 0.194196i | \(0.0622096\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.03334 | + | 12.1516i | 0.210639 | + | 0.508527i | 0.993522 | − | 0.113642i | \(-0.0362517\pi\) |
−0.782883 | + | 0.622169i | \(0.786252\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.0793 | − | 9.55975i | −0.964151 | − | 0.399364i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.6562 | 0.486097 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.2275 | 1.05024 | 0.525118 | − | 0.851029i | \(-0.324021\pi\) | ||||
0.525118 | + | 0.851029i | \(0.324021\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.8030 | − | 5.71741i | −0.573635 | − | 0.237607i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.57117 | + | 11.0358i | 0.189644 | + | 0.457842i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.58276 | − | 1.58276i | 0.0655511 | − | 0.0655511i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.19615 | + | 7.19615i | 0.297524 | + | 0.297524i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.4971 | − | 6.83331i | 0.680907 | − | 0.282041i | −0.0152989 | − | 0.999883i | \(-0.504870\pi\) |
0.696206 | + | 0.717842i | \(0.254870\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.2640 | − | 29.6079i | 0.505329 | − | 1.21997i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 15.5081i | − | 0.637919i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.3009i | 1.69602i | 0.529976 | + | 0.848012i | \(0.322201\pi\) | ||||
−0.529976 | + | 0.848012i | \(0.677799\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.66596 | − | 11.2646i | 0.191286 | − | 0.461805i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.79315 | − | 1.98539i | 0.196171 | − | 0.0812565i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.73920 | − | 6.73920i | −0.275356 | − | 0.275356i | 0.555896 | − | 0.831252i | \(-0.312375\pi\) |
−0.831252 | + | 0.555896i | \(0.812375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.2456 | − | 23.2456i | 0.948206 | − | 0.948206i | −0.0505170 | − | 0.998723i | \(-0.516087\pi\) |
0.998723 | + | 0.0505170i | \(0.0160869\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.38351 | + | 3.34008i | 0.0563407 | + | 0.136019i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −59.2260 | − | 24.5322i | −2.40788 | − | 0.997377i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.7402 | −0.760642 | −0.380321 | − | 0.924855i | \(-0.624187\pi\) | ||||
−0.380321 | + | 0.924855i | \(0.624187\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.21695 | 0.373490 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.6019 | − | 4.80567i | −0.469363 | − | 0.194417i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.2609 | − | 34.4288i | −0.575991 | − | 1.39057i | −0.896383 | − | 0.443281i | \(-0.853814\pi\) |
0.320391 | − | 0.947285i | \(-0.396186\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 34.0097 | − | 34.0097i | 1.37140 | − | 1.37140i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.5470 | − | 11.5470i | −0.464866 | − | 0.464866i | 0.435381 | − | 0.900246i | \(-0.356614\pi\) |
−0.900246 | + | 0.435381i | \(0.856614\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.8529 | − | 16.5076i | 1.60182 | − | 0.663498i | 0.610153 | − | 0.792284i | \(-0.291108\pi\) |
0.991672 | + | 0.128786i | \(0.0411081\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.23246 | − | 7.80385i | 0.129714 | − | 0.313158i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.98536i | 0.0795417i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.77124i | 0.150850i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.46427 | + | 22.8488i | −0.377966 | + | 0.912492i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.95303 | − | 4.12268i | 0.396853 | − | 0.164382i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.48591 | − | 4.48591i | −0.178581 | − | 0.178581i | 0.612156 | − | 0.790737i | \(-0.290302\pi\) |
−0.790737 | + | 0.612156i | \(0.790302\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.0085 | + | 17.0085i | −0.676025 | + | 0.676025i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.50018 | − | 3.62175i | −0.0595328 | − | 0.143725i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.4964 | + | 7.66147i | 0.732855 | + | 0.303559i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.80558 | −0.110987 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.5996 | −1.56409 | −0.782045 | − | 0.623221i | \(-0.785824\pi\) | ||||
−0.782045 | + | 0.623221i | \(0.785824\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.6057 | + | 9.36360i | 0.891483 | + | 0.369264i | 0.780939 | − | 0.624607i | \(-0.214741\pi\) |
0.110544 | + | 0.993871i | \(0.464741\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.3025 | − | 46.6003i | −0.760035 | − | 1.83489i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.4317 | + | 25.4317i | −0.999823 | + | 0.999823i | −1.00000 | 0.000176614i | \(-0.999944\pi\) | |
0.000176614 | 1.00000i | \(0.499944\pi\) | ||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.0464 | + | 32.0464i | 1.25793 | + | 1.25793i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.5391 | + | 8.92177i | −0.844182 | + | 0.349672i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.37458 | − | 22.6322i | 0.366856 | − | 0.885668i | −0.627406 | − | 0.778692i | \(-0.715883\pi\) |
0.994262 | − | 0.106976i | \(-0.0341168\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.53137i | − | 0.0989087i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 8.30803i | − | 0.324127i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3595 | + | 25.0100i | −0.403547 | + | 0.974250i | 0.583250 | + | 0.812292i | \(0.301781\pi\) |
−0.986798 | + | 0.161957i | \(0.948219\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.6719 | − | 4.83467i | 0.453985 | − | 0.188047i | −0.143961 | − | 0.989583i | \(-0.545984\pi\) |
0.597946 | + | 0.801537i | \(0.295984\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.3324 | − | 10.3324i | −0.401276 | − | 0.401276i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.0951 | + | 11.0951i | −0.430251 | + | 0.430251i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.41058 | + | 5.81965i | 0.0933380 | + | 0.225338i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.3085 | + | 12.1400i | 1.13313 | + | 0.469359i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0303 | −0.580240 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.29926 | 0.358460 | 0.179230 | − | 0.983807i | \(-0.442639\pi\) | ||||
0.179230 | + | 0.983807i | \(0.442639\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −40.1292 | − | 16.6221i | −1.54457 | − | 0.639784i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.59697 | + | 20.7549i | 0.330409 | + | 0.797677i | 0.998560 | + | 0.0536513i | \(0.0170859\pi\) |
−0.668151 | + | 0.744026i | \(0.732914\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.5649 | − | 11.5649i | 0.443820 | − | 0.443820i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.5427 | − | 14.5427i | −0.557279 | − | 0.557279i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.15512 | + | 2.13532i | −0.197255 | + | 0.0817058i | −0.479124 | − | 0.877747i | \(-0.659046\pi\) |
0.281869 | + | 0.959453i | \(0.409046\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.1944 | + | 53.5821i | −0.848005 | + | 2.04727i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 8.80104i | − | 0.335781i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.70193i | − | 0.0648385i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.50357 | + | 22.9436i | −0.361533 | + | 0.872817i | 0.633544 | + | 0.773707i | \(0.281600\pi\) |
−0.995076 | + | 0.0991103i | \(0.968400\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.02849 | + | 2.08287i | −0.191017 | + | 0.0791217i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.13397 | + | 2.13397i | 0.0809461 | + | 0.0809461i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.7727 | − | 14.7727i | 0.559554 | − | 0.559554i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.0220281 | + | 0.0531806i | 0.000833180 | + | 0.00201147i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.3625 | + | 7.60601i | 0.693544 | + | 0.287275i | 0.701476 | − | 0.712693i | \(-0.252525\pi\) |
−0.00793210 | + | 0.999969i | \(0.502525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.8639 | −0.522887 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.6264 | 0.626186 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.5685 | − | 5.20606i | −0.472689 | − | 0.195794i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0866 | + | 24.3512i | 0.378810 | + | 0.914529i | 0.992189 | + | 0.124740i | \(0.0398097\pi\) |
−0.613379 | + | 0.789788i | \(0.710190\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.26631 | − | 2.26631i | 0.0849932 | − | 0.0849932i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.2665 | − | 11.2665i | −0.421935 | − | 0.421935i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −72.6154 | + | 30.0783i | −2.71566 | + | 1.12486i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.8753 | + | 35.9121i | −0.555528 | + | 1.34116i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 34.6091i | − | 1.29070i | −0.763887 | − | 0.645350i | \(-0.776711\pi\) | ||
0.763887 | − | 0.645350i | \(-0.223289\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.47264i | 0.0920860i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.744157 | + | 1.79655i | −0.0276755 | + | 0.0668145i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.9260 | − | 12.3958i | 1.11142 | − | 0.460367i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.7749 | − | 30.7749i | −1.14138 | − | 1.14138i | −0.988198 | − | 0.153181i | \(-0.951048\pi\) |
−0.153181 | − | 0.988198i | \(-0.548952\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.2271 | + | 21.2271i | −0.786191 | + | 0.786191i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.38434 | − | 20.2416i | −0.310106 | − | 0.748662i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.0588 | − | 17.4213i | −1.55348 | − | 0.643472i | −0.569537 | − | 0.821965i | \(-0.692878\pi\) |
−0.983941 | + | 0.178494i | \(0.942878\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26.5067 | −0.977715 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.9216 | −1.02850 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.8560 | + | 10.7099i | 0.951128 | + | 0.393970i | 0.803655 | − | 0.595096i | \(-0.202886\pi\) |
0.147474 | + | 0.989066i | \(0.452886\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.19615 | + | 17.3730i | 0.264357 | + | 0.638215i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.2978 | − | 26.2978i | 0.964774 | − | 0.964774i | −0.0346265 | − | 0.999400i | \(-0.511024\pi\) |
0.999400 | + | 0.0346265i | \(0.0110242\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.8225 | + | 17.8225i | 0.652967 | + | 0.652967i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.29732 | − | 2.19422i | 0.193819 | − | 0.0802823i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.61715 | + | 3.90414i | −0.0590893 | + | 0.142654i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.4098i | 1.36510i | 0.730837 | + | 0.682552i | \(0.239130\pi\) | ||||
−0.730837 | + | 0.682552i | \(0.760870\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.9125i | 0.579883i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.0759 | − | 46.0534i | 0.694244 | − | 1.67605i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.53295 | − | 3.12025i | 0.273790 | − | 0.113407i | −0.241564 | − | 0.970385i | \(-0.577660\pi\) |
0.515354 | + | 0.856977i | \(0.327660\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.69453 | + | 8.69453i | 0.315591 | + | 0.315591i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.08516 | − | 8.08516i | 0.293087 | − | 0.293087i | −0.545212 | − | 0.838299i | \(-0.683551\pi\) |
0.838299 | + | 0.545212i | \(0.183551\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.12279 | − | 5.12486i | −0.0768501 | − | 0.185532i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.40717 | − | 2.23972i | −0.195496 | − | 0.0809773i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.4594 | 1.24426 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.6572 | −1.10553 | −0.552764 | − | 0.833338i | \(-0.686427\pi\) | ||||
−0.552764 | + | 0.833338i | \(0.686427\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.2381 | − | 4.65499i | −0.404731 | − | 0.167645i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.1942 | + | 29.4394i | 0.438595 | + | 1.05886i | 0.976434 | + | 0.215815i | \(0.0692407\pi\) |
−0.537839 | + | 0.843047i | \(0.680759\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −57.9352 | + | 57.9352i | −2.08109 | + | 2.08109i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.13165 | + | 7.13165i | 0.255847 | + | 0.255847i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.8390 | + | 10.2887i | −0.889950 | + | 0.368629i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.29201 | − | 20.0187i | 0.296712 | − | 0.716325i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 23.4731i | − | 0.838861i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 86.4222i | − | 3.08454i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.209491 | − | 0.505757i | 0.00746756 | − | 0.0180283i | −0.920102 | − | 0.391679i | \(-0.871894\pi\) |
0.927569 | + | 0.373651i | \(0.121894\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.4952 | + | 11.3889i | −0.978857 | + | 0.405456i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.19274 | − | 2.19274i | −0.0779647 | − | 0.0779647i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.08104 | + | 8.08104i | −0.286966 | + | 0.286966i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.862315 | + | 2.08181i | 0.0305832 | + | 0.0738343i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.9652 | + | 11.9978i | 1.02600 | + | 0.424983i | 0.831267 | − | 0.555873i | \(-0.187616\pi\) |
0.194733 | + | 0.980856i | \(0.437616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.22193 | 0.255494 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.952996 | 0.0336725 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 59.2805 | + | 24.5548i | 2.09196 | + | 0.866519i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.98539 | + | 7.20736i | 0.105221 | + | 0.254026i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.3569 | + | 18.3569i | −0.646194 | + | 0.646194i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.60821 | + | 5.60821i | 0.197174 | + | 0.197174i | 0.798787 | − | 0.601613i | \(-0.205475\pi\) |
−0.601613 | + | 0.798787i | \(0.705475\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.0138 | − | 15.7458i | 1.33484 | − | 0.552910i | 0.402811 | − | 0.915283i | \(-0.368033\pi\) |
0.932033 | + | 0.362373i | \(0.118033\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.06893 | + | 21.8943i | −0.318061 | + | 0.767868i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 62.5049i | − | 2.18945i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.1952i | 0.986425i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.58371 | + | 3.82341i | −0.0553393 | + | 0.133601i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.6328 | + | 10.2032i | −0.859689 | + | 0.356095i | −0.768586 | − | 0.639746i | \(-0.779039\pi\) |
−0.0911034 | + | 0.995841i | \(0.529039\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.4269 | + | 26.4269i | 0.921185 | + | 0.921185i | 0.997113 | − | 0.0759281i | \(-0.0241919\pi\) |
−0.0759281 | + | 0.997113i | \(0.524192\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 44.7093 | − | 44.7093i | 1.55658 | − | 1.55658i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.90206 | + | 4.59197i | 0.0661410 | + | 0.159678i | 0.953494 | − | 0.301413i | \(-0.0974581\pi\) |
−0.887353 | + | 0.461091i | \(0.847458\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.0370609 | − | 0.0153511i | −0.00128718 | − | 0.000533166i | 0.382040 | − | 0.924146i | \(-0.375222\pi\) |
−0.383327 | + | 0.923613i | \(0.625222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.1066 | 0.732181 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.5136 | −0.398923 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 74.2514 | + | 30.7559i | 2.56957 | + | 1.06435i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.7214 | + | 54.8542i | 0.785365 | + | 1.89604i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.78014 | − | 3.78014i | 0.130505 | − | 0.130505i | −0.638837 | − | 0.769342i | \(-0.720584\pi\) |
0.769342 | + | 0.638837i | \(0.220584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.12828 | − | 8.12828i | −0.280286 | − | 0.280286i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −37.1374 | + | 15.3828i | −1.27908 | + | 0.529812i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.11169 | + | 12.3407i | −0.175848 | + | 0.424534i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 26.0686i | − | 0.895728i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1.62622i | − | 0.0558118i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.63778 | + | 6.36817i | −0.0904220 | + | 0.218298i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.7872 | − | 17.7231i | 1.46501 | − | 0.606826i | 0.499293 | − | 0.866433i | \(-0.333593\pi\) |
0.965714 | + | 0.259607i | \(0.0835932\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.32580 | + | 5.32580i | 0.182139 | + | 0.182139i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.25991 | + | 1.25991i | −0.0430375 | + | 0.0430375i | −0.728298 | − | 0.685261i | \(-0.759688\pi\) |
0.685261 | + | 0.728298i | \(0.259688\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.66511 | + | 11.2626i | 0.159171 | + | 0.384274i | 0.983265 | − | 0.182179i | \(-0.0583152\pi\) |
−0.824094 | + | 0.566453i | \(0.808315\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.0698 | + | 7.48477i | 0.615818 | + | 0.255080i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −55.7303 | −1.89708 | −0.948541 | − | 0.316653i | \(-0.897441\pi\) | ||||
−0.948541 | + | 0.316653i | \(0.897441\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.3238 | 1.09904 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.0722 | − | 6.65734i | −0.545842 | − | 0.226095i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.47266 | + | 22.8690i | 0.321338 | + | 0.775779i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.0120 | + | 15.0120i | −0.508662 | + | 0.508662i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.55129 | − | 5.55129i | −0.187883 | − | 0.187883i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.1264 | − | 5.43712i | 0.443752 | − | 0.183808i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.27570 | − | 10.3225i | 0.144380 | − | 0.348565i | −0.835102 | − | 0.550095i | \(-0.814591\pi\) |
0.979482 | + | 0.201530i | \(0.0645915\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.0104i | 0.911039i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.1185i | − | 0.441972i | −0.975277 | − | 0.220986i | \(-0.929072\pi\) | ||
0.975277 | − | 0.220986i | \(-0.0709276\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.36561 | + | 10.5395i | −0.146915 | + | 0.354683i | −0.980156 | − | 0.198226i | \(-0.936482\pi\) |
0.833242 | + | 0.552909i | \(0.186482\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −42.1509 | + | 17.4595i | −1.41689 | + | 0.586893i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.1505 | + | 32.1505i | 1.07951 | + | 1.07951i | 0.996553 | + | 0.0829550i | \(0.0264358\pi\) |
0.0829550 | + | 0.996553i | \(0.473564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.12722 | − | 1.12722i | 0.0378058 | − | 0.0378058i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.2296 | − | 31.9392i | −0.443210 | − | 1.07000i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.58647 | − | 3.55663i | −0.287335 | − | 0.119018i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.511683 | −0.0171037 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.34920 | 0.312161 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −40.9070 | − | 16.9443i | −1.36433 | − | 0.565123i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.374560 | + | 0.904268i | 0.0124784 | + | 0.0301255i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.5037 | − | 14.5037i | 0.482654 | − | 0.482654i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.49473 | + | 6.49473i | 0.215892 | + | 0.215892i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.2431 | + | 12.1129i | −0.971000 | + | 0.402202i | −0.811084 | − | 0.584929i | \(-0.801122\pi\) |
−0.159916 | + | 0.987131i | \(0.551122\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.49898 | + | 6.03306i | −0.0828858 | + | 0.200104i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.1501i | 1.36336i | 0.731649 | + | 0.681681i | \(0.238751\pi\) | ||||
−0.731649 | + | 0.681681i | \(0.761249\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.2832i | 1.46556i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.79035 | − | 13.9792i | 0.191423 | − | 0.462136i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.951023 | − | 0.393927i | 0.0314055 | − | 0.0130086i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.00540 | − | 1.00540i | −0.0331651 | − | 0.0331651i | 0.690330 | − | 0.723495i | \(-0.257465\pi\) |
−0.723495 | + | 0.690330i | \(0.757465\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.1273 | − | 22.1273i | 0.729119 | − | 0.729119i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.30483 | − | 15.2212i | −0.207526 | − | 0.501012i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.7466 | + | 13.5641i | 1.07670 | + | 0.445985i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.18690 | 0.0389829 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.8710 | 1.73464 | 0.867320 | − | 0.497751i | \(-0.165841\pi\) | ||||
0.867320 | + | 0.497751i | \(0.165841\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.6890 | + | 5.67018i | 0.448640 | + | 0.185833i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.17209 | − | 2.82967i | −0.0383724 | − | 0.0926393i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.9623 | − | 31.9623i | 1.04528 | − | 1.04528i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.85201 | + | 3.85201i | 0.125840 | + | 0.125840i | 0.767222 | − | 0.641382i | \(-0.221639\pi\) |
−0.641382 | + | 0.767222i | \(0.721639\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.52197 | − | 1.04463i | 0.0823013 | − | 0.0340903i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.2416 | + | 39.2107i | −0.529462 | + | 1.27823i | 0.402415 | + | 0.915458i | \(0.368171\pi\) |
−0.931876 | + | 0.362776i | \(0.881829\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3670i | 0.435288i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 29.0703i | − | 0.945658i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.4056 | + | 32.3640i | −0.435624 | + | 1.05169i | 0.541820 | + | 0.840494i | \(0.317735\pi\) |
−0.977444 | + | 0.211194i | \(0.932265\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.0739 | − | 18.6702i | 1.46316 | − | 0.606061i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.6119 | + | 26.6119i | 0.862949 | + | 0.862949i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.8976 | + | 13.8976i | −0.450186 | + | 0.450186i | −0.895416 | − | 0.445230i | \(-0.853122\pi\) |
0.445230 | + | 0.895416i | \(0.353122\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.4852 | − | 54.2842i | −0.727605 | − | 1.75659i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 31.5685 | + | 13.0761i | 1.02046 | + | 0.422690i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.5844 | −0.761580 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 80.9971 | 2.61281 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.87404 | + | 0.776251i | 0.0603900 | + | 0.0250143i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.4478 | − | 32.4658i | −0.432899 | − | 1.04511i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.8527 | − | 36.8527i | 1.18510 | − | 1.18510i | 0.206700 | − | 0.978404i | \(-0.433728\pi\) |
0.978404 | − | 0.206700i | \(-0.0662724\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.64689 | − | 7.64689i | −0.245653 | − | 0.245653i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.5712 | − | 15.5625i | 1.20572 | − | 0.499425i | 0.312875 | − | 0.949794i | \(-0.398708\pi\) |
0.892842 | + | 0.450370i | \(0.148708\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.469639 | + | 1.13381i | −0.0150559 | + | 0.0363482i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 48.0758i | − | 1.53966i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.89004i | 0.0924607i | 0.998931 | + | 0.0462303i | \(0.0147208\pi\) | ||||
−0.998931 | + | 0.0462303i | \(0.985279\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.81663 | + | 6.79994i | −0.0900197 | + | 0.217327i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.46000 | + | 1.01896i | −0.0785417 | + | 0.0325330i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.1625 | + | 10.1625i | 0.324135 | + | 0.324135i | 0.850351 | − | 0.526216i | \(-0.176390\pi\) |
−0.526216 | + | 0.850351i | \(0.676390\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.7926 | − | 25.7926i | 0.821820 | − | 0.821820i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.58737 | + | 6.24646i | 0.0823568 | + | 0.198827i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.9510 | + | 5.36449i | 0.411819 | + | 0.170581i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.7294 | 1.64324 | 0.821619 | − | 0.570038i | \(-0.193071\pi\) | ||||
0.821619 | + | 0.570038i | \(0.193071\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.7901 | −1.10403 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.2738 | + | 4.66978i | 0.357405 | + | 0.148042i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.46746 | − | 18.0280i | −0.236497 | − | 0.570954i | 0.760419 | − | 0.649433i | \(-0.224994\pi\) |
−0.996916 | + | 0.0784791i | \(0.974994\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.1624 | − | 18.1624i | 0.574633 | − | 0.574633i |
(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 | 1024.2.g.a.641.1 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.a.641.4 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.f.641.1 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.f.641.4 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.d.129.1 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.g.129.1 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.g.129.4 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.d.129.4 | yes | 16 | ||
32.3 | odd | 8 | 1024.2.g.g.897.4 | yes | 16 | ||
32.5 | even | 8 | 1024.2.g.f.385.4 | yes | 16 | ||
32.11 | odd | 8 | inner | 1024.2.g.a.385.4 | yes | 16 | |
32.13 | even | 8 | 1024.2.g.d.897.4 | yes | 16 | ||
32.19 | odd | 8 | 1024.2.g.d.897.1 | yes | 16 | ||
32.21 | even | 8 | inner | 1024.2.g.a.385.1 | ✓ | 16 | |
32.27 | odd | 8 | 1024.2.g.f.385.1 | yes | 16 | ||
32.29 | even | 8 | 1024.2.g.g.897.1 | yes | 16 | ||
64.11 | odd | 16 | 4096.2.a.s.1.6 | 8 | |||
64.21 | even | 16 | 4096.2.a.s.1.5 | 8 | |||
64.43 | odd | 16 | 4096.2.a.i.1.3 | 8 | |||
64.53 | even | 16 | 4096.2.a.i.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.a.385.1 | ✓ | 16 | 32.21 | even | 8 | inner | |
1024.2.g.a.385.4 | yes | 16 | 32.11 | odd | 8 | inner | |
1024.2.g.a.641.1 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.a.641.4 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.d.129.1 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.d.129.4 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.d.897.1 | yes | 16 | 32.19 | odd | 8 | ||
1024.2.g.d.897.4 | yes | 16 | 32.13 | even | 8 | ||
1024.2.g.f.385.1 | yes | 16 | 32.27 | odd | 8 | ||
1024.2.g.f.385.4 | yes | 16 | 32.5 | even | 8 | ||
1024.2.g.f.641.1 | yes | 16 | 8.3 | odd | 2 | ||
1024.2.g.f.641.4 | yes | 16 | 8.5 | even | 2 | ||
1024.2.g.g.129.1 | yes | 16 | 16.5 | even | 4 | ||
1024.2.g.g.129.4 | yes | 16 | 16.11 | odd | 4 | ||
1024.2.g.g.897.1 | yes | 16 | 32.29 | even | 8 | ||
1024.2.g.g.897.4 | yes | 16 | 32.3 | odd | 8 | ||
4096.2.a.i.1.3 | 8 | 64.43 | odd | 16 | |||
4096.2.a.i.1.4 | 8 | 64.53 | even | 16 | |||
4096.2.a.s.1.5 | 8 | 64.21 | even | 16 | |||
4096.2.a.s.1.6 | 8 | 64.11 | odd | 16 |