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 | 897.1 | ||
Root | \(-0.991445 - 0.130526i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.897 |
Dual form | 1024.2.g.g.129.1 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.580775 | − | 1.40211i | −0.335311 | − | 0.809511i | −0.998153 | − | 0.0607523i | \(-0.980650\pi\) |
0.662842 | − | 0.748759i | \(-0.269350\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.29788 | + | 1.36603i | 1.47486 | + | 0.610905i | 0.967960 | − | 0.251103i | \(-0.0807932\pi\) |
0.506895 | + | 0.862008i | \(0.330793\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.02642 | − | 1.02642i | −0.387950 | − | 0.387950i | 0.486006 | − | 0.873956i | \(-0.338453\pi\) |
−0.873956 | + | 0.486006i | \(0.838453\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.492694 | − | 0.492694i | 0.164231 | − | 0.164231i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.05935 | − | 4.97171i | 0.620917 | − | 1.49903i | −0.229710 | − | 0.973259i | \(-0.573778\pi\) |
0.850628 | − | 0.525768i | \(-0.176222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.78024 | + | 1.56583i | −1.04845 | + | 0.434282i | −0.839338 | − | 0.543610i | \(-0.817057\pi\) |
−0.209112 | + | 0.977892i | \(0.567057\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 5.41736i | − | 1.39876i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.35311i | − | 0.570714i | −0.958421 | − | 0.285357i | \(-0.907888\pi\) | ||
0.958421 | − | 0.285357i | \(-0.0921121\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.79772 | + | 1.15885i | −0.641840 | + | 0.265859i | −0.679774 | − | 0.733421i | \(-0.737922\pi\) |
0.0379340 | + | 0.999280i | \(0.487922\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.843039 | + | 2.03528i | −0.183966 | + | 0.444134i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.06460 | − | 1.06460i | 0.221985 | − | 0.221985i | −0.587349 | − | 0.809334i | \(-0.699828\pi\) |
0.809334 | + | 0.587349i | \(0.199828\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47443 | + | 5.47443i | 1.09489 | + | 1.09489i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.18330 | − | 2.14699i | −0.997527 | − | 0.413189i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.60110 | − | 3.86540i | −0.297317 | − | 0.717787i | −0.999980 | − | 0.00626466i | \(-0.998006\pi\) |
0.702663 | − | 0.711523i | \(-0.251994\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −1.98289 | − | 4.78712i | −0.335170 | − | 0.809171i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.22973 | + | 1.75201i | 0.695363 | + | 0.288029i | 0.702233 | − | 0.711948i | \(-0.252187\pi\) |
−0.00686951 | + | 0.999976i | \(0.502187\pi\) | |||||||
\(38\) | 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 | \(-0.506165\pi\) |
0.999812 | + | 0.0193666i | \(0.00616495\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.56308 | + | 8.60205i | −0.543365 | + | 1.31180i | 0.378970 | + | 0.925409i | \(0.376278\pi\) |
−0.922335 | + | 0.386391i | \(0.873722\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.29788 | − | 0.951812i | 0.342547 | − | 0.141888i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.06910i | 0.447674i | 0.974627 | + | 0.223837i | \(0.0718583\pi\) | ||||
−0.974627 | + | 0.223837i | \(0.928142\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 4.89293i | − | 0.698990i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.29934 | + | 1.36663i | −0.461999 | + | 0.191366i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.159176 | − | 0.384286i | 0.0218646 | − | 0.0527857i | −0.912570 | − | 0.408920i | \(-0.865905\pi\) |
0.934435 | + | 0.356134i | \(0.115905\pi\) | |||||||
\(54\) | 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 | ||||||||
\(59\) | −7.78071 | − | 3.22287i | −1.01296 | − | 0.419583i | −0.186427 | − | 0.982469i | \(-0.559691\pi\) |
−0.826534 | + | 0.562886i | \(0.809691\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.06885 | − | 2.58044i | −0.136853 | − | 0.330391i | 0.840564 | − | 0.541712i | \(-0.182224\pi\) |
−0.977417 | + | 0.211321i | \(0.932224\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.01142 | −0.127427 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.6057 | −1.81162 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.98559 | − | 4.79363i | −0.242578 | − | 0.585635i | 0.754959 | − | 0.655772i | \(-0.227657\pi\) |
−0.997537 | + | 0.0701364i | \(0.977657\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.11099 | − | 0.874400i | −0.254133 | − | 0.105265i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.84718 | − | 2.84718i | −0.337898 | − | 0.337898i | 0.517678 | − | 0.855576i | \(-0.326797\pi\) |
−0.855576 | + | 0.517678i | \(0.826797\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.43123 | + | 8.43123i | −0.986801 | + | 0.986801i | −0.999914 | − | 0.0131133i | \(-0.995826\pi\) |
0.0131133 | + | 0.999914i | \(0.495826\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.49637 | − | 10.8552i | 0.519196 | − | 1.25345i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.21682 | + | 2.98930i | −0.822433 | + | 0.340663i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.59983i | − | 0.517521i | −0.965941 | − | 0.258761i | \(-0.916686\pi\) | ||
0.965941 | − | 0.258761i | \(-0.0833141\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.42418i | 0.713798i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.60263 | − | 3.14911i | 0.834497 | − | 0.345660i | 0.0758155 | − | 0.997122i | \(-0.475844\pi\) |
0.758681 | + | 0.651462i | \(0.225844\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.21441 | − | 7.76028i | 0.348652 | − | 0.841720i | ||||
\(86\) | 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 | \(-0.226906\pi\) |
−0.653989 | + | 0.756504i | \(0.726906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.48730 | + | 2.27292i | 0.575226 | + | 0.238266i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.14626 | − | 14.8384i | −0.637338 | − | 1.53867i | ||||
\(94\) | 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 | ||||||||
\(99\) | −1.43490 | − | 3.46416i | −0.144213 | − | 0.348161i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.65855 | + | 3.58649i | 0.861558 | + | 0.356869i | 0.769317 | − | 0.638868i | \(-0.220597\pi\) |
0.0922416 | + | 0.995737i | \(0.470597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.20450 | + | 1.20450i | 0.118683 | + | 0.118683i | 0.763954 | − | 0.645271i | \(-0.223256\pi\) |
−0.645271 | + | 0.763954i | \(0.723256\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.56048 | + | 5.56048i | −0.542647 | + | 0.542647i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.11406 | + | 2.68959i | −0.107701 | + | 0.260012i | −0.968537 | − | 0.248870i | \(-0.919941\pi\) |
0.860836 | + | 0.508882i | \(0.169941\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.53055 | + | 1.46240i | −0.338165 | + | 0.140073i | −0.545303 | − | 0.838239i | \(-0.683585\pi\) |
0.207137 | + | 0.978312i | \(0.433585\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 6.94809i | − | 0.659483i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.13630i | 0.200966i | 0.994939 | + | 0.100483i | \(0.0320388\pi\) | ||||
−0.994939 | + | 0.100483i | \(0.967961\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.96520 | − | 2.05665i | 0.463007 | − | 0.191784i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.09103 | + | 2.63397i | −0.100866 | + | 0.243511i | ||||
\(118\) | 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 | ||||||||
\(123\) | −12.4484 | − | 5.15630i | −1.12244 | − | 0.464928i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.74567 | + | 9.04284i | 0.335023 | + | 0.808816i | ||||
\(126\) | 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 | ||||||||
\(131\) | 0.271379 | + | 0.655166i | 0.0237105 | + | 0.0572421i | 0.935291 | − | 0.353879i | \(-0.115137\pi\) |
−0.911581 | + | 0.411121i | \(0.865137\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.06110 | + | 1.68216i | 0.352142 | + | 0.145862i | ||||
\(134\) | 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 | \(-0.505822\pi\) |
0.999833 | + | 0.0182885i | \(0.00582173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.323537 | + | 0.781087i | −0.0274421 | + | 0.0662510i | −0.937007 | − | 0.349312i | \(-0.886415\pi\) |
0.909564 | + | 0.415563i | \(0.136415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.30323 | − | 1.78245i | 0.362397 | − | 0.150110i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.0188i | 1.84131i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 14.9348i | − | 1.24027i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.86045 | + | 2.84169i | −0.565840 | + | 0.234379i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.70212 | + | 6.52350i | −0.221367 | + | 0.534426i | −0.995076 | − | 0.0991144i | \(-0.968399\pi\) |
0.773710 | + | 0.633541i | \(0.218399\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.87443 | + | 9.87443i | −0.803569 | + | 0.803569i | −0.983652 | − | 0.180082i | \(-0.942364\pi\) |
0.180082 | + | 0.983652i | \(0.442364\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.15937 | − | 1.15937i | −0.0937291 | − | 0.0937291i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 34.9010 | + | 14.4565i | 2.80332 | + | 1.16117i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.26500 | + | 22.3677i | 0.739428 | + | 1.78514i | 0.608199 | + | 0.793785i | \(0.291892\pi\) |
0.131229 | + | 0.991352i | \(0.458108\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.631258 | −0.0500620 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.18546 | −0.172238 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.70092 | + | 16.1774i | 0.524856 | + | 1.26712i | 0.934855 | + | 0.355029i | \(0.115529\pi\) |
−0.409999 | + | 0.912086i | \(0.634471\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −26.9335 | − | 11.1562i | −2.09677 | − | 0.868511i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.9204 | + | 15.9204i | 1.23196 | + | 1.23196i | 0.963210 | + | 0.268751i | \(0.0866108\pi\) |
0.268751 | + | 0.963210i | \(0.413389\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.64601 | − | 2.64601i | 0.203539 | − | 0.203539i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.807459 | + | 1.94938i | −0.0617479 | + | 0.149073i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.36603 | − | 3.46532i | 0.636057 | − | 0.263463i | −0.0412671 | − | 0.999148i | \(-0.513139\pi\) |
0.677324 | + | 0.735685i | \(0.263139\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 11.2381i | − | 0.849523i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.7812i | 0.960695i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.132433 | + | 0.0548557i | −0.00989854 | + | 0.00410011i | −0.387627 | − | 0.921816i | \(-0.626705\pi\) |
0.377729 | + | 0.925916i | \(0.376705\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.984684 | + | 2.37724i | −0.0731910 | + | 0.176699i | −0.956241 | − | 0.292580i | \(-0.905486\pi\) |
0.883050 | + | 0.469279i | \(0.155486\pi\) | |||||||
\(182\) | 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 | ||||||||
\(187\) | −11.6990 | − | 4.84588i | −0.855516 | − | 0.354366i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.11653 | + | 7.52396i | 0.226694 | + | 0.547287i | ||||
\(190\) | 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 | ||||||||
\(195\) | 8.48264 | + | 20.4789i | 0.607454 | + | 1.46652i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.44074 | − | 3.91048i | −0.672625 | − | 0.278610i | 0.0201152 | − | 0.999798i | \(-0.493597\pi\) |
−0.692740 | + | 0.721187i | \(0.743597\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.41726 | + | 2.41726i | 0.171355 | + | 0.171355i | 0.787574 | − | 0.616220i | \(-0.211337\pi\) |
−0.616220 | + | 0.787574i | \(0.711337\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.56804 | + | 5.56804i | −0.392739 | + | 0.392739i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.32412 | + | 5.61093i | −0.163121 | + | 0.393810i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.2796 | − | 12.1280i | 2.04498 | − | 0.847057i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.04905i | − | 0.0729137i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.2959i | 1.12721i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.6429 | + | 6.06529i | −1.00806 | + | 0.417552i | −0.824746 | − | 0.565503i | \(-0.808682\pi\) |
−0.183312 | + | 0.983055i | \(0.558682\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.33850 | + | 5.64564i | −0.160231 | + | 0.386833i | ||||
\(214\) | 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 | ||||||||
\(219\) | 16.7182 | + | 6.92490i | 1.12971 | + | 0.467942i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.68457 | + | 8.89533i | 0.247851 | + | 0.598365i | ||||
\(222\) | 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 | ||||||||
\(227\) | 5.18600 | + | 12.5201i | 0.344207 | + | 0.830989i | 0.997281 | + | 0.0736948i | \(0.0234791\pi\) |
−0.653074 | + | 0.757294i | \(0.726521\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.35773 | − | 2.21925i | −0.354049 | − | 0.146652i | 0.198568 | − | 0.980087i | \(-0.436371\pi\) |
−0.552617 | + | 0.833435i | \(0.686371\pi\) | |||||||
\(230\) | 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 | \(-0.749605\pi\) |
0.707985 | + | 0.706228i | \(0.249605\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.19246 | + | 10.1215i | −0.273486 | + | 0.660254i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.44949 | + | 2.67147i | −0.418939 | + | 0.173530i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.6128i | 1.65676i | 0.560169 | + | 0.828378i | \(0.310736\pi\) | ||||
−0.560169 | + | 0.828378i | \(0.689264\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.28132i | 0.0825369i | 0.999148 | + | 0.0412684i | \(0.0131399\pi\) | ||||
−0.999148 | + | 0.0412684i | \(0.986860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.54247 | + | 2.70998i | −0.419699 | + | 0.173845i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.68386 | − | 16.1363i | 0.427016 | − | 1.03091i | ||||
\(246\) | 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 | ||||||||
\(251\) | 9.68691 | + | 4.01245i | 0.611432 | + | 0.253263i | 0.666841 | − | 0.745200i | \(-0.267646\pi\) |
−0.0554086 | + | 0.998464i | \(0.517646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.10051 | − | 7.48528i | −0.194927 | − | 0.470596i | ||||
\(254\) | 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 | ||||||||
\(259\) | −2.54318 | − | 6.13977i | −0.158025 | − | 0.381507i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.69331 | − | 1.11561i | −0.166712 | − | 0.0690544i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.8663 | − | 13.8663i | −0.855030 | − | 0.855030i | 0.135718 | − | 0.990748i | \(-0.456666\pi\) |
−0.990748 | + | 0.135718i | \(0.956666\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.04989 | − | 1.04989i | 0.0644941 | − | 0.0644941i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.794341 | − | 1.91771i | 0.0486129 | − | 0.117362i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.8038 | + | 6.54616i | −0.963576 | + | 0.399126i | −0.808317 | − | 0.588748i | \(-0.799621\pi\) |
−0.155259 | + | 0.987874i | \(0.549621\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.6152i | 0.948557i | 0.880375 | + | 0.474279i | \(0.157291\pi\) | ||||
−0.880375 | + | 0.474279i | \(0.842709\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 9.01388i | − | 0.545545i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 38.4911 | − | 15.9435i | 2.32110 | − | 0.961431i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.32219 | + | 12.8489i | −0.319779 | + | 0.772016i | 0.679486 | + | 0.733689i | \(0.262203\pi\) |
−0.999265 | + | 0.0383271i | \(0.987797\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.21412 | − | 5.21412i | 0.312161 | − | 0.312161i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.7289 | − | 18.7289i | −1.11727 | − | 1.11727i | −0.992140 | − | 0.125134i | \(-0.960064\pi\) |
−0.125134 | − | 0.992140i | \(-0.539936\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.989981 | − | 0.410064i | −0.0588483 | − | 0.0243758i | 0.353065 | − | 0.935599i | \(-0.385139\pi\) |
−0.411913 | + | 0.911223i | \(0.635139\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.27792 | + | 15.1562i | 0.371872 | + | 0.897778i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.8875 | −0.760728 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.4629 | 0.674286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.54372 | − | 15.7979i | −0.383600 | − | 0.926091i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.4429 | + | 6.81087i | 0.960604 | + | 0.397895i | 0.807206 | − | 0.590269i | \(-0.200978\pi\) |
0.153398 | + | 0.988165i | \(0.450978\pi\) | |||||||
\(294\) | 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 | ||||||||
\(299\) | −2.35747 | + | 5.69143i | −0.136336 | + | 0.329144i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.4865 | − | 5.17209i | 0.719711 | − | 0.298114i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 14.2232i | − | 0.817103i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 9.97005i | − | 0.570883i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.0498 | − | 7.89068i | 1.08723 | − | 0.450345i | 0.234189 | − | 0.972191i | \(-0.424757\pi\) |
0.853040 | + | 0.521846i | \(0.174757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.989303 | − | 2.38839i | 0.0562795 | − | 0.135871i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.42704 | + | 1.42704i | −0.0809203 | + | 0.0809203i | −0.746408 | − | 0.665488i | \(-0.768223\pi\) |
0.665488 | + | 0.746408i | \(0.268223\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.27186 | + | 1.27186i | 0.0718900 | + | 0.0718900i | 0.742138 | − | 0.670248i | \(-0.233812\pi\) |
−0.670248 | + | 0.742138i | \(0.733812\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.33554 | − | 1.38163i | −0.187937 | − | 0.0778459i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.48990 | − | 22.9106i | −0.533006 | − | 1.28679i | −0.929523 | − | 0.368763i | \(-0.879781\pi\) |
0.396518 | − | 0.918027i | \(-0.370219\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.5149 | −1.26059 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.41813 | 0.246596 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.72691 | + | 6.58335i | 0.151729 | + | 0.366307i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −29.2667 | − | 12.1227i | −1.62342 | − | 0.672444i | ||||
\(326\) | 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 | ||||||||
\(331\) | 8.77257 | − | 21.1789i | 0.482184 | − | 1.16410i | −0.476386 | − | 0.879236i | \(-0.658053\pi\) |
0.958570 | − | 0.284859i | \(-0.0919466\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.94717 | − | 1.22076i | 0.161504 | − | 0.0668971i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 18.5212i | − | 1.01192i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.4961i | 1.49781i | 0.662677 | + | 0.748905i | \(0.269420\pi\) | ||||
−0.662677 | + | 0.748905i | \(0.730580\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.99533 | − | 1.24071i | 0.162684 | − | 0.0673860i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.7938 | − | 52.6150i | 1.18020 | − | 2.84926i | ||||
\(342\) | 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 | ||||||||
\(347\) | −4.53353 | − | 1.87785i | −0.243373 | − | 0.100808i | 0.257663 | − | 0.966235i | \(-0.417048\pi\) |
−0.501036 | + | 0.865427i | \(0.667048\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.28327 | − | 19.9976i | −0.443393 | − | 1.07045i | −0.974750 | − | 0.223298i | \(-0.928318\pi\) |
0.531357 | − | 0.847148i | \(-0.321682\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | −5.50033 | − | 13.2790i | −0.291927 | − | 0.704774i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.78924 | + | 1.98377i | 0.253473 | + | 0.104992i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.0741 | + | 19.0741i | 1.00669 | + | 1.00669i | 0.999977 | + | 0.00671431i | \(0.00213725\pi\) |
0.00671431 | + | 0.999977i | \(0.497863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.95074 | + | 6.95074i | −0.365829 | + | 0.365829i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.4300 | + | 25.1803i | −0.547435 | + | 1.32163i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −39.3224 | + | 16.2879i | −2.05823 | + | 0.852547i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.4379i | 0.649251i | 0.945843 | + | 0.324626i | \(0.105238\pi\) | ||||
−0.945843 | + | 0.324626i | \(0.894762\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.18618i | − | 0.322040i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.557820 | + | 0.231057i | −0.0289606 | + | 0.0119959i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.8919 | + | 31.1238i | −0.667518 | + | 1.61153i | 0.118232 | + | 0.992986i | \(0.462277\pi\) |
−0.785750 | + | 0.618544i | \(0.787723\pi\) | |||||||
\(374\) | 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 | ||||||||
\(379\) | −13.0991 | − | 5.42584i | −0.672858 | − | 0.278707i | 0.0199800 | − | 0.999800i | \(-0.493640\pi\) |
−0.692838 | + | 0.721094i | \(0.743640\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.637812 | − | 1.53981i | −0.0326761 | − | 0.0788870i | ||||
\(382\) | 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 | ||||||||
\(387\) | 2.48267 | + | 5.99369i | 0.126201 | + | 0.304676i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.2131 | + | 10.8578i | 1.32906 | + | 0.550514i | 0.930387 | − | 0.366579i | \(-0.119471\pi\) |
0.398672 | + | 0.917093i | \(0.369471\pi\) | |||||||
\(390\) | 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 | ||||||||
\(395\) | 6.28348 | − | 15.1697i | 0.316156 | − | 0.763269i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.57919 | − | 3.55362i | 0.430577 | − | 0.178351i | −0.156860 | − | 0.987621i | \(-0.550137\pi\) |
0.587437 | + | 0.809270i | \(0.300137\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 6.67109i | − | 0.333972i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.43274i | 0.471049i | 0.971868 | + | 0.235524i | \(0.0756807\pi\) | ||||
−0.971868 | + | 0.235524i | \(0.924319\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −40.0058 | + | 16.5709i | −1.99283 | + | 0.825457i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.77559 | + | 21.1862i | −0.436063 | + | 1.05275i | ||||
\(406\) | 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 | \(-0.0683566\pi\) |
−0.213102 | + | 0.977030i | \(0.568357\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.7808 | − | 9.43611i | −1.12369 | − | 0.465449i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.67825 | + | 11.2943i | 0.230202 | + | 0.555756i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.3743 | 1.44193 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.28308 | 0.0628325 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.18452 | + | 19.7592i | 0.399840 | + | 0.965299i | 0.987703 | + | 0.156339i | \(0.0499692\pi\) |
−0.587864 | + | 0.808960i | \(0.700031\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.5052 | − | 10.1504i | −1.19431 | − | 0.494700i | −0.305155 | − | 0.952303i | \(-0.598708\pi\) |
−0.889157 | + | 0.457602i | \(0.848708\pi\) | |||||||
\(422\) | 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 | ||||||||
\(427\) | −1.55152 | + | 3.74570i | −0.0750833 | + | 0.181267i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 30.8729 | − | 12.7880i | 1.49056 | − | 0.617410i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.7162i | 1.19054i | 0.803528 | + | 0.595268i | \(0.202954\pi\) | ||||
−0.803528 | + | 0.595268i | \(0.797046\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.69501i | − | 0.465913i | −0.972487 | − | 0.232956i | \(-0.925160\pi\) | ||
0.972487 | − | 0.232956i | \(-0.0748399\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.9403 | + | 8.67374i | −1.00401 | + | 0.415874i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.74474 | + | 4.21217i | −0.0834622 | + | 0.201496i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.45429 | − | 8.45429i | 0.403501 | − | 0.403501i | −0.475964 | − | 0.879465i | \(-0.657901\pi\) |
0.879465 | + | 0.475964i | \(0.157901\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.41072 | − | 2.41072i | −0.114796 | − | 0.114796i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.0500 | + | 14.5182i | 1.66528 | + | 0.689780i | 0.998462 | − | 0.0554440i | \(-0.0176574\pi\) |
0.666814 | + | 0.745224i | \(0.267657\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.86835 | + | 4.51059i | 0.0885682 | + | 0.213822i | ||||
\(446\) | 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 | ||||||||
\(451\) | −18.2836 | − | 44.1404i | −0.860939 | − | 2.07849i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.5799 | + | 8.11026i | 0.919944 | + | 0.381053i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.9916 | + | 14.9916i | 0.702817 | + | 0.702817i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.4049 | − | 22.4049i | 1.04806 | − | 1.04806i | 0.0492728 | − | 0.998785i | \(-0.484310\pi\) |
0.998785 | − | 0.0492728i | \(-0.0156904\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.05212 | + | 12.1969i | −0.235813 | + | 0.569302i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.92070 | − | 1.20979i | 0.136031 | − | 0.0563457i | −0.313630 | − | 0.949545i | \(-0.601545\pi\) |
0.449660 | + | 0.893200i | \(0.351545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26.3825i | − | 1.22610i | −0.790045 | − | 0.613048i | \(-0.789943\pi\) | ||
0.790045 | − | 0.613048i | \(-0.210057\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 57.3312i | − | 2.65867i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.48183 | − | 3.92750i | 0.438767 | − | 0.181743i | −0.152354 | − | 0.988326i | \(-0.548686\pi\) |
0.591121 | + | 0.806583i | \(0.298686\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.88223 | + | 6.95832i | −0.133089 | + | 0.321305i | ||||
\(470\) | 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 | ||||||||
\(475\) | −21.6600 | − | 8.97186i | −0.993828 | − | 0.411657i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.110910 | − | 0.267761i | −0.00507822 | − | 0.0122599i | ||||
\(478\) | 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 | ||||||||
\(483\) | 1.26926 | + | 3.06426i | 0.0577532 | + | 0.139429i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 37.1579 | + | 15.3913i | 1.68725 | + | 0.698883i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.38394 | − | 5.38394i | −0.243970 | − | 0.243970i | 0.574521 | − | 0.818490i | \(-0.305189\pi\) |
−0.818490 | + | 0.574521i | \(0.805189\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.7909 | − | 18.7909i | 0.849754 | − | 0.849754i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.62284 | − | 15.9889i | 0.298884 | − | 0.721571i | −0.701080 | − | 0.713083i | \(-0.747298\pi\) |
0.999964 | − | 0.00848784i | \(-0.00270180\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.09573 | + | 3.76758i | −0.409651 | + | 0.169683i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 13.3845i | − | 0.601588i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.84480i | 0.262175i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.07217 | + | 1.68675i | −0.182295 | + | 0.0755091i | −0.471964 | − | 0.881618i | \(-0.656455\pi\) |
0.289669 | + | 0.957127i | \(0.406455\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.0761 | − | 31.5685i | 0.584197 | − | 1.41038i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.1132 | + | 22.1132i | −0.985978 | + | 0.985978i | −0.999903 | − | 0.0139248i | \(-0.995567\pi\) |
0.0139248 | + | 0.999903i | \(0.495567\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.6556 | + | 23.6556i | 1.05266 | + | 1.05266i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.24674 | − | 2.17327i | −0.233016 | − | 0.0965183i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.24094 | + | 12.6528i | 0.232301 | + | 0.560823i | 0.996447 | − | 0.0842193i | \(-0.0268396\pi\) |
−0.764147 | + | 0.645043i | \(0.776840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.3080 | 0.765659 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.9895 | 0.750103 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.32691 | + | 5.61767i | 0.102536 | + | 0.247544i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.2587 | + | 6.32034i | 0.671075 | + | 0.277968i | ||||
\(518\) | 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 | \(-0.828676\pi\) |
0.512618 | + | 0.858617i | \(0.328676\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.66429 | − | 11.2606i | 0.203955 | − | 0.492391i | −0.788495 | − | 0.615041i | \(-0.789139\pi\) |
0.992450 | + | 0.122650i | \(0.0391393\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15.7571 | + | 6.52682i | −0.687698 | + | 0.284854i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 24.9027i | − | 1.08478i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.7332i | 0.901445i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.42140 | + | 2.24562i | −0.235269 | + | 0.0974515i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.9019 | + | 33.5622i | −0.602158 | + | 1.45374i | ||||
\(534\) | 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 | ||||||||
\(539\) | −24.3262 | − | 10.0763i | −1.04780 | − | 0.434015i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.88194 | − | 11.7860i | −0.209891 | − | 0.506722i | 0.783515 | − | 0.621373i | \(-0.213425\pi\) |
−0.993406 | + | 0.114652i | \(0.963425\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.90504 | 0.167581 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.6410 | −0.584316 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.8254 | − | 26.1348i | −0.462861 | − | 1.11745i | −0.967217 | − | 0.253950i | \(-0.918270\pi\) |
0.504356 | − | 0.863496i | \(-0.331730\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.79798 | − | 0.744749i | −0.0767361 | − | 0.0317851i | ||||
\(550\) | 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 | ||||||||
\(555\) | 9.49127 | − | 22.9139i | 0.402882 | − | 0.972643i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.8089 | + | 13.5899i | −1.39016 | + | 0.575822i | −0.947178 | − | 0.320709i | \(-0.896079\pi\) |
−0.442980 | + | 0.896532i | \(0.646079\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 38.0970i | − | 1.61133i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.2177i | 0.811372i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.8336 | + | 4.48742i | −0.456582 | + | 0.189122i | −0.599107 | − | 0.800669i | \(-0.704478\pi\) |
0.142526 | + | 0.989791i | \(0.454478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.91824 | + | 7.04524i | −0.122771 | + | 0.296396i | ||||
\(566\) | 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 | \(-0.437790\pi\) |
−0.980963 | + | 0.194196i | \(0.937790\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.1516 | − | 5.03334i | −0.508527 | − | 0.210639i | 0.113642 | − | 0.993522i | \(-0.463748\pi\) |
−0.622169 | + | 0.782883i | \(0.713748\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.55975 | − | 23.0793i | −0.399364 | − | 0.964151i | ||||
\(574\) | 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 | ||||||||
\(579\) | −5.71741 | − | 13.8030i | −0.237607 | − | 0.573635i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.0358 | − | 4.57117i | −0.457842 | − | 0.189644i | ||||
\(582\) | 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 | ||||||||
\(587\) | 6.83331 | − | 16.4971i | 0.282041 | − | 0.680907i | −0.717842 | − | 0.696206i | \(-0.754870\pi\) |
0.999883 | + | 0.0152989i | \(0.00487000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.6079 | + | 12.2640i | −1.21997 | + | 0.505329i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.5081i | 0.637919i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 41.3009i | − | 1.69602i | −0.529976 | − | 0.848012i | \(-0.677799\pi\) | ||
0.529976 | − | 0.848012i | \(-0.322201\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.2646 | + | 4.66596i | −0.461805 | + | 0.191286i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.98539 | − | 4.79315i | 0.0812565 | − | 0.196171i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.73920 | − | 6.73920i | 0.275356 | − | 0.275356i | −0.555896 | − | 0.831252i | \(-0.687625\pi\) |
0.831252 | + | 0.555896i | \(0.187625\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.2456 | − | 23.2456i | −0.948206 | − | 0.948206i | 0.0505170 | − | 0.998723i | \(-0.483913\pi\) |
−0.998723 | + | 0.0505170i | \(0.983913\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.34008 | − | 1.38351i | −0.136019 | − | 0.0563407i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.5322 | − | 59.2260i | −0.997377 | − | 2.40788i | ||||
\(606\) | 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 | ||||||||
\(611\) | −4.80567 | − | 11.6019i | −0.194417 | − | 0.469363i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.4288 | + | 14.2609i | 1.39057 | + | 0.575991i | 0.947285 | − | 0.320391i | \(-0.103814\pi\) |
0.443281 | + | 0.896383i | \(0.353814\pi\) | |||||||
\(614\) | 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 | \(-0.643386\pi\) |
0.900246 | + | 0.435381i | \(0.143386\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.5076 | − | 39.8529i | 0.663498 | − | 1.60182i | −0.128786 | − | 0.991672i | \(-0.541108\pi\) |
0.792284 | − | 0.610153i | \(-0.208892\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.80385 | + | 3.23246i | −0.313158 | + | 0.129714i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1.98536i | − | 0.0795417i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 3.77124i | − | 0.150850i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22.8488 | − | 9.46427i | 0.912492 | − | 0.377966i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.12268 | − | 9.95303i | 0.164382 | − | 0.396853i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.48591 | − | 4.48591i | 0.178581 | − | 0.178581i | −0.612156 | − | 0.790737i | \(-0.709698\pi\) |
0.790737 | + | 0.612156i | \(0.209698\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.0085 | + | 17.0085i | 0.676025 | + | 0.676025i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.62175 | + | 1.50018i | 0.143725 | + | 0.0595328i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.66147 | + | 18.4964i | 0.303559 | + | 0.732855i | ||||
\(638\) | 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 | ||||||||
\(643\) | 9.36360 | + | 22.6057i | 0.369264 | + | 0.891483i | 0.993871 | + | 0.110544i | \(0.0352592\pi\) |
−0.624607 | + | 0.780939i | \(0.714741\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 46.6003 | + | 19.3025i | 1.83489 | + | 0.760035i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.4317 | + | 25.4317i | 0.999823 | + | 0.999823i | 1.00000 | 0.000176614i | \(-5.62181e-5\pi\) | |
−0.000176614 | 1.00000i | \(0.500056\pi\) | ||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.0464 | + | 32.0464i | −1.25793 | + | 1.25793i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.92177 | + | 21.5391i | −0.349672 | + | 0.844182i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.6322 | + | 9.37458i | −0.885668 | + | 0.366856i | −0.778692 | − | 0.627406i | \(-0.784117\pi\) |
−0.106976 | + | 0.994262i | \(0.534117\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.53137i | 0.0989087i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.30803i | 0.324127i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.0100 | − | 10.3595i | 0.974250 | − | 0.403547i | 0.161957 | − | 0.986798i | \(-0.448219\pi\) |
0.812292 | + | 0.583250i | \(0.198219\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.83467 | − | 11.6719i | 0.188047 | − | 0.453985i | −0.801537 | − | 0.597946i | \(-0.795984\pi\) |
0.989583 | + | 0.143961i | \(0.0459838\pi\) | |||||||
\(662\) | 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 | ||||||||
\(667\) | −5.81965 | − | 2.41058i | −0.225338 | − | 0.0933380i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.1400 | + | 29.3085i | 0.469359 | + | 1.13313i | ||||
\(670\) | 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 | ||||||||
\(675\) | −16.6221 | − | 40.1292i | −0.639784 | − | 1.54457i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.7549 | − | 8.59697i | −0.797677 | − | 0.330409i | −0.0536513 | − | 0.998560i | \(-0.517086\pi\) |
−0.744026 | + | 0.668151i | \(0.767086\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | −2.13532 | + | 5.15512i | −0.0817058 | + | 0.197255i | −0.959453 | − | 0.281869i | \(-0.909046\pi\) |
0.877747 | + | 0.479124i | \(0.159046\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 53.5821 | − | 22.1944i | 2.04727 | − | 0.848005i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.80104i | 0.335781i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.70193i | 0.0648385i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.9436 | − | 9.50357i | 0.872817 | − | 0.361533i | 0.0991103 | − | 0.995076i | \(-0.468400\pi\) |
0.773707 | + | 0.633544i | \(0.218400\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.08287 | + | 5.02849i | −0.0791217 | + | 0.191017i | ||||
\(694\) | 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 | ||||||||
\(699\) | −0.0531806 | − | 0.0220281i | −0.00201147 | − | 0.000833180i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.60601 | + | 18.3625i | 0.287275 | + | 0.693544i | 0.999969 | − | 0.00793210i | \(-0.00252489\pi\) |
−0.712693 | + | 0.701476i | \(0.752525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.8639 | −0.522887 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.6264 | 0.626186 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.20606 | − | 12.5685i | −0.195794 | − | 0.472689i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.3512 | − | 10.0866i | −0.914529 | − | 0.378810i | −0.124740 | − | 0.992189i | \(-0.539810\pi\) |
−0.789788 | + | 0.613379i | \(0.789810\pi\) | |||||||
\(710\) | 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 | ||||||||
\(715\) | −30.0783 | + | 72.6154i | −1.12486 | + | 2.71566i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 35.9121 | − | 14.8753i | 1.34116 | − | 0.555528i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.6091i | 1.29070i | 0.763887 | + | 0.645350i | \(0.223289\pi\) | ||||
−0.763887 | + | 0.645350i | \(0.776711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 2.47264i | − | 0.0920860i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.79655 | − | 0.744157i | 0.0668145 | − | 0.0276755i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.3958 | − | 29.9260i | 0.460367 | − | 1.11142i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.7749 | − | 30.7749i | 1.14138 | − | 1.14138i | 0.153181 | − | 0.988198i | \(-0.451048\pi\) |
0.988198 | − | 0.153181i | \(-0.0489516\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.2271 | + | 21.2271i | 0.786191 | + | 0.786191i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.2416 | + | 8.38434i | 0.748662 | + | 0.310106i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.4213 | − | 42.0588i | −0.643472 | − | 1.55348i | −0.821965 | − | 0.569537i | \(-0.807122\pi\) |
0.178494 | − | 0.983941i | \(-0.442878\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26.5067 | −0.977715 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.9216 | −1.02850 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.7099 | + | 25.8560i | 0.393970 | + | 0.951128i | 0.989066 | + | 0.147474i | \(0.0471141\pi\) |
−0.595096 | + | 0.803655i | \(0.702886\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.3730 | − | 7.19615i | −0.638215 | − | 0.264357i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.2978 | − | 26.2978i | −0.964774 | − | 0.964774i | 0.0346265 | − | 0.999400i | \(-0.488976\pi\) |
−0.999400 | + | 0.0346265i | \(0.988976\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.8225 | + | 17.8225i | −0.652967 | + | 0.652967i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.19422 | − | 5.29732i | 0.0802823 | − | 0.193819i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.90414 | − | 1.61715i | 0.142654 | − | 0.0590893i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 37.4098i | − | 1.36510i | −0.730837 | − | 0.682552i | \(-0.760870\pi\) | ||
0.730837 | − | 0.682552i | \(-0.239130\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 15.9125i | − | 0.579883i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −46.0534 | + | 19.0759i | −1.67605 | + | 0.694244i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.12025 | − | 7.53295i | 0.113407 | − | 0.273790i | −0.856977 | − | 0.515354i | \(-0.827660\pi\) |
0.970385 | + | 0.241564i | \(0.0776604\pi\) | |||||||
\(758\) | 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 | \(-0.316449\pi\) |
−0.838299 | + | 0.545212i | \(0.816449\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.12486 | + | 2.12279i | 0.185532 | + | 0.0768501i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.23972 | − | 5.40717i | −0.0809773 | − | 0.195496i | ||||
\(766\) | 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 | ||||||||
\(771\) | −4.65499 | − | 11.2381i | −0.167645 | − | 0.404731i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.4394 | − | 12.1942i | −1.05886 | − | 0.438595i | −0.215815 | − | 0.976434i | \(-0.569241\pi\) |
−0.843047 | + | 0.537839i | \(0.819241\pi\) | |||||||
\(774\) | 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 | ||||||||
\(779\) | −10.2887 | + | 24.8390i | −0.368629 | + | 0.889950i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.0187 | + | 8.29201i | −0.716325 | + | 0.296712i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.4731i | 0.838861i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 86.4222i | 3.08454i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.505757 | + | 0.209491i | −0.0180283 | + | 0.00746756i | −0.391679 | − | 0.920102i | \(-0.628106\pi\) |
0.373651 | + | 0.927569i | \(0.378106\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.3889 | + | 27.4952i | −0.405456 | + | 0.978857i | ||||
\(790\) | 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 | ||||||||
\(795\) | −2.08181 | − | 0.862315i | −0.0738343 | − | 0.0305832i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.9978 | + | 28.9652i | 0.424983 | + | 1.02600i | 0.980856 | + | 0.194733i | \(0.0623841\pi\) |
−0.555873 | + | 0.831267i | \(0.687616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.22193 | 0.255494 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.952996 | 0.0336725 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.5548 | + | 59.2805i | 0.866519 | + | 2.09196i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.20736 | − | 2.98539i | −0.254026 | − | 0.105221i | ||||
\(806\) | 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 | \(-0.794525\pi\) |
0.601613 | + | 0.798787i | \(0.294525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.7458 | − | 38.0138i | 0.552910 | − | 1.33484i | −0.362373 | − | 0.932033i | \(-0.618033\pi\) |
0.915283 | − | 0.402811i | \(-0.131967\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.8943 | − | 9.06893i | 0.767868 | − | 0.318061i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 62.5049i | 2.18945i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 28.1952i | − | 0.986425i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.82341 | − | 1.58371i | 0.133601 | − | 0.0553393i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.2032 | + | 24.6328i | −0.356095 | + | 0.859689i | 0.639746 | + | 0.768586i | \(0.279039\pi\) |
−0.995841 | + | 0.0911034i | \(0.970961\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.4269 | + | 26.4269i | −0.921185 | + | 0.921185i | −0.997113 | − | 0.0759281i | \(-0.975808\pi\) |
0.0759281 | + | 0.997113i | \(0.475808\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −44.7093 | − | 44.7093i | −1.55658 | − | 1.55658i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.59197 | − | 1.90206i | −0.159678 | − | 0.0661410i | 0.301413 | − | 0.953494i | \(-0.402542\pi\) |
−0.461091 | + | 0.887353i | \(0.652542\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.0153511 | − | 0.0370609i | −0.000533166 | − | 0.00128718i | 0.923613 | − | 0.383327i | \(-0.125222\pi\) |
−0.924146 | + | 0.382040i | \(0.875222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.1066 | 0.732181 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.5136 | −0.398923 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.7559 | + | 74.2514i | 1.06435 | + | 2.56957i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −54.8542 | − | 22.7214i | −1.89604 | − | 0.785365i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.78014 | − | 3.78014i | −0.130505 | − | 0.130505i | 0.638837 | − | 0.769342i | \(-0.279416\pi\) |
−0.769342 | + | 0.638837i | \(0.779416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.12828 | − | 8.12828i | 0.280286 | − | 0.280286i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.3828 | + | 37.1374i | −0.529812 | + | 1.27908i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.3407 | − | 5.11169i | 0.424534 | − | 0.175848i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.0686i | 0.895728i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.62622i | 0.0558118i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.36817 | − | 2.63778i | 0.218298 | − | 0.0904220i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.7231 | − | 42.7872i | 0.606826 | − | 1.46501i | −0.259607 | − | 0.965714i | \(-0.583593\pi\) |
0.866433 | − | 0.499293i | \(-0.166407\pi\) | |||||||
\(854\) | 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 | \(-0.240312\pi\) |
−0.685261 | + | 0.728298i | \(0.740312\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.2626 | − | 4.66511i | −0.384274 | − | 0.159171i | 0.182179 | − | 0.983265i | \(-0.441685\pi\) |
−0.566453 | + | 0.824094i | \(0.691685\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.48477 | + | 18.0698i | 0.255080 | + | 0.615818i | ||||
\(862\) | 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 | ||||||||
\(867\) | −6.65734 | − | 16.0722i | −0.226095 | − | 0.545842i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.8690 | − | 9.47266i | −0.775779 | − | 0.321338i | ||||
\(870\) | 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 | ||||||||
\(875\) | 5.43712 | − | 13.1264i | 0.183808 | − | 0.443752i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.3225 | + | 4.27570i | −0.348565 | + | 0.144380i | −0.550095 | − | 0.835102i | \(-0.685409\pi\) |
0.201530 | + | 0.979482i | \(0.435409\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 27.0104i | − | 0.911039i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.1185i | 0.441972i | 0.975277 | + | 0.220986i | \(0.0709276\pi\) | ||||
−0.975277 | + | 0.220986i | \(0.929072\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.5395 | − | 4.36561i | 0.354683 | − | 0.146915i | −0.198226 | − | 0.980156i | \(-0.563518\pi\) |
0.552909 | + | 0.833242i | \(0.313518\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.4595 | + | 42.1509i | −0.586893 | + | 1.41689i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.1505 | + | 32.1505i | −1.07951 | + | 1.07951i | −0.0829550 | + | 0.996553i | \(0.526436\pi\) |
−0.996553 | + | 0.0829550i | \(0.973564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.12722 | − | 1.12722i | −0.0378058 | − | 0.0378058i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.9392 | + | 13.2296i | 1.07000 | + | 0.443210i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.55663 | − | 8.58647i | −0.119018 | − | 0.287335i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.511683 | −0.0171037 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.34920 | 0.312161 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.9443 | − | 40.9070i | −0.565123 | − | 1.36433i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.904268 | − | 0.374560i | −0.0301255 | − | 0.0124784i | ||||
\(902\) | 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 | ||||||||
\(907\) | −12.1129 | + | 29.2431i | −0.402202 | + | 0.971000i | 0.584929 | + | 0.811084i | \(0.301122\pi\) |
−0.987131 | + | 0.159916i | \(0.948878\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.03306 | − | 2.49898i | 0.200104 | − | 0.0828858i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 41.1501i | − | 1.36336i | −0.731649 | − | 0.681681i | \(-0.761249\pi\) | ||
0.731649 | − | 0.681681i | \(-0.238751\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 44.2832i | − | 1.46556i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.9792 | + | 5.79035i | −0.462136 | + | 0.191423i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.393927 | − | 0.951023i | 0.0130086 | − | 0.0314055i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.00540 | − | 1.00540i | 0.0331651 | − | 0.0331651i | −0.690330 | − | 0.723495i | \(-0.742535\pi\) |
0.723495 | + | 0.690330i | \(0.242535\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.1273 | − | 22.1273i | −0.729119 | − | 0.729119i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.2212 | + | 6.30483i | 0.501012 | + | 0.207526i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.5641 | + | 32.7466i | 0.445985 | + | 1.07670i | ||||
\(926\) | 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 | ||||||||
\(931\) | 5.67018 | + | 13.6890i | 0.185833 | + | 0.448640i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.82967 | + | 1.17209i | 0.0926393 | + | 0.0383724i | ||||
\(934\) | 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 | \(-0.778361\pi\) |
0.641382 | + | 0.767222i | \(0.278361\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.04463 | − | 2.52197i | 0.0340903 | − | 0.0823013i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.2107 | − | 16.2416i | 1.27823 | − | 0.529462i | 0.362776 | − | 0.931876i | \(-0.381829\pi\) |
0.915458 | + | 0.402415i | \(0.131829\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 13.3670i | − | 0.435288i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 29.0703i | 0.945658i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.3640 | − | 13.4056i | 1.05169 | − | 0.435624i | 0.211194 | − | 0.977444i | \(-0.432265\pi\) |
0.840494 | + | 0.541820i | \(0.182265\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.6702 | − | 45.0739i | 0.606061 | − | 1.46316i | ||||
\(950\) | 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 | \(-0.146878\pi\) |
−0.445230 | + | 0.895416i | \(0.646878\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.2842 | + | 22.4852i | 1.75659 | + | 0.727605i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.0761 | + | 31.5685i | 0.422690 | + | 1.02046i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.5844 | −0.761580 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 80.9971 | 2.61281 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.776251 | + | 1.87404i | 0.0250143 | + | 0.0603900i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.4658 | + | 13.4478i | 1.04511 | + | 0.432899i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.8527 | − | 36.8527i | −1.18510 | − | 1.18510i | −0.978404 | − | 0.206700i | \(-0.933728\pi\) |
−0.206700 | − | 0.978404i | \(-0.566272\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.64689 | − | 7.64689i | 0.245653 | − | 0.245653i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.5625 | − | 37.5712i | 0.499425 | − | 1.20572i | −0.450370 | − | 0.892842i | \(-0.648708\pi\) |
0.949794 | − | 0.312875i | \(-0.101292\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.13381 | − | 0.469639i | 0.0363482 | − | 0.0150559i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 48.0758i | 1.53966i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.89004i | − | 0.0924607i | −0.998931 | − | 0.0462303i | \(-0.985279\pi\) | ||
0.998931 | − | 0.0462303i | \(-0.0147208\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.79994 | − | 2.81663i | 0.217327 | − | 0.0900197i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.01896 | + | 2.46000i | −0.0325330 | + | 0.0785417i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.1625 | + | 10.1625i | −0.324135 | + | 0.324135i | −0.850351 | − | 0.526216i | \(-0.823610\pi\) |
0.526216 | + | 0.850351i | \(0.323610\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.7926 | − | 25.7926i | −0.821820 | − | 0.821820i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.24646 | − | 2.58737i | −0.198827 | − | 0.0823568i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.36449 | + | 12.9510i | 0.170581 | + | 0.411819i | ||||
\(990\) | 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 | ||||||||
\(995\) | 4.66978 | + | 11.2738i | 0.148042 | + | 0.357405i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.0280 | + | 7.46746i | 0.570954 | + | 0.236497i | 0.649433 | − | 0.760419i | \(-0.275006\pi\) |
−0.0784791 | + | 0.996916i | \(0.525006\pi\) | |||||||
\(998\) | 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.g.897.1 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.g.897.4 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.d.897.1 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.d.897.4 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.f.385.1 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.a.385.1 | ✓ | 16 | ||
16.11 | odd | 4 | 1024.2.g.a.385.4 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.f.385.4 | yes | 16 | ||
32.3 | odd | 8 | 1024.2.g.d.129.1 | yes | 16 | ||
32.5 | even | 8 | 1024.2.g.f.641.4 | yes | 16 | ||
32.11 | odd | 8 | 1024.2.g.a.641.4 | yes | 16 | ||
32.13 | even | 8 | inner | 1024.2.g.g.129.1 | yes | 16 | |
32.19 | odd | 8 | inner | 1024.2.g.g.129.4 | yes | 16 | |
32.21 | even | 8 | 1024.2.g.a.641.1 | yes | 16 | ||
32.27 | odd | 8 | 1024.2.g.f.641.1 | yes | 16 | ||
32.29 | even | 8 | 1024.2.g.d.129.4 | yes | 16 | ||
64.13 | even | 16 | 4096.2.a.i.1.4 | 8 | |||
64.19 | odd | 16 | 4096.2.a.i.1.3 | 8 | |||
64.45 | even | 16 | 4096.2.a.s.1.5 | 8 | |||
64.51 | odd | 16 | 4096.2.a.s.1.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.a.385.1 | ✓ | 16 | 16.5 | even | 4 | ||
1024.2.g.a.385.4 | yes | 16 | 16.11 | odd | 4 | ||
1024.2.g.a.641.1 | yes | 16 | 32.21 | even | 8 | ||
1024.2.g.a.641.4 | yes | 16 | 32.11 | odd | 8 | ||
1024.2.g.d.129.1 | yes | 16 | 32.3 | odd | 8 | ||
1024.2.g.d.129.4 | yes | 16 | 32.29 | even | 8 | ||
1024.2.g.d.897.1 | yes | 16 | 8.3 | odd | 2 | ||
1024.2.g.d.897.4 | yes | 16 | 8.5 | even | 2 | ||
1024.2.g.f.385.1 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.f.385.4 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.f.641.1 | yes | 16 | 32.27 | odd | 8 | ||
1024.2.g.f.641.4 | yes | 16 | 32.5 | even | 8 | ||
1024.2.g.g.129.1 | yes | 16 | 32.13 | even | 8 | inner | |
1024.2.g.g.129.4 | yes | 16 | 32.19 | odd | 8 | inner | |
1024.2.g.g.897.1 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.g.897.4 | yes | 16 | 4.3 | odd | 2 | inner | |
4096.2.a.i.1.3 | 8 | 64.19 | odd | 16 | |||
4096.2.a.i.1.4 | 8 | 64.13 | even | 16 | |||
4096.2.a.s.1.5 | 8 | 64.45 | even | 16 | |||
4096.2.a.s.1.6 | 8 | 64.51 | odd | 16 |