Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(253,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.c (of order \(2\), degree \(1\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.386672896.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 253.3 | ||
Root | \(-0.835949 + 1.14070i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.253 |
Dual form | 504.2.c.f.253.4 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.835949 | − | 1.14070i | −0.591105 | − | 0.806595i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.602380 | + | 1.90713i | −0.301190 | + | 0.953564i | ||||
\(5\) | − | 0.467138i | − | 0.208910i | −0.994530 | − | 0.104455i | \(-0.966690\pi\) | ||
0.994530 | − | 0.104455i | \(-0.0333099\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.67901 | − | 0.907128i | 0.947175 | − | 0.320718i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.532862 | + | 0.390503i | −0.168506 | + | 0.123488i | ||||
\(11\) | 4.87666i | 1.47037i | 0.677868 | + | 0.735184i | \(0.262904\pi\) | ||||
−0.677868 | + | 0.735184i | \(0.737096\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.56279i | 1.26549i | 0.774360 | + | 0.632745i | \(0.218072\pi\) | ||||
−0.774360 | + | 0.632745i | \(0.781928\pi\) | |||||||
\(14\) | −0.835949 | − | 1.14070i | −0.223417 | − | 0.304864i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.27428 | − | 2.29763i | −0.818569 | − | 0.574408i | ||||
\(17\) | −6.09565 | −1.47841 | −0.739206 | − | 0.673479i | \(-0.764799\pi\) | ||||
−0.739206 | + | 0.673479i | \(0.764799\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.34379i | − | 0.308288i | −0.988048 | − | 0.154144i | \(-0.950738\pi\) | ||
0.988048 | − | 0.154144i | \(-0.0492619\pi\) | |||||||
\(20\) | 0.890891 | + | 0.281394i | 0.199209 | + | 0.0629217i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.56279 | − | 4.07663i | 1.18599 | − | 0.869141i | ||||
\(23\) | 4.09565 | 0.854002 | 0.427001 | − | 0.904251i | \(-0.359570\pi\) | ||||
0.427001 | + | 0.904251i | \(0.359570\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.78178 | 0.956357 | ||||||||
\(26\) | 5.20476 | − | 3.81426i | 1.02074 | − | 0.748037i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.602380 | + | 1.90713i | −0.113839 | + | 0.360413i | ||||
\(29\) | 7.78178i | 1.44504i | 0.691350 | + | 0.722520i | \(0.257016\pi\) | ||||
−0.691350 | + | 0.722520i | \(0.742984\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.40952 | 0.791973 | 0.395987 | − | 0.918256i | \(-0.370403\pi\) | ||||
0.395987 | + | 0.918256i | \(0.370403\pi\) | |||||||
\(32\) | 0.116226 | + | 5.65566i | 0.0205460 | + | 0.999789i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.09565 | + | 6.95329i | 0.873897 | + | 1.19248i | ||||
\(35\) | − | 0.467138i | − | 0.0789607i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.40952i | 0.724921i | 0.931999 | + | 0.362460i | \(0.118063\pi\) | ||||
−0.931999 | + | 0.362460i | \(0.881937\pi\) | |||||||
\(38\) | −1.53286 | + | 1.12334i | −0.248663 | + | 0.182230i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.423754 | − | 1.25147i | −0.0670013 | − | 0.197874i | ||||
\(41\) | 6.09565 | 0.951981 | 0.475990 | − | 0.879450i | \(-0.342090\pi\) | ||||
0.475990 | + | 0.879450i | \(0.342090\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.15327i | − | 0.633368i | −0.948531 | − | 0.316684i | \(-0.897431\pi\) | ||
0.948531 | − | 0.316684i | \(-0.102569\pi\) | |||||||
\(44\) | −9.30041 | − | 2.93760i | −1.40209 | − | 0.442860i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.42375 | − | 4.67190i | −0.504805 | − | 0.688834i | ||||
\(47\) | 6.68759 | 0.975485 | 0.487743 | − | 0.872988i | \(-0.337820\pi\) | ||||
0.487743 | + | 0.872988i | \(0.337820\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.99732 | − | 5.45457i | −0.565307 | − | 0.771392i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.70182 | − | 2.74853i | −1.20673 | − | 0.381153i | ||||
\(53\) | − | 1.34379i | − | 0.184584i | −0.995732 | − | 0.0922922i | \(-0.970581\pi\) | ||
0.995732 | − | 0.0922922i | \(-0.0294194\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.27807 | 0.307175 | ||||||||
\(56\) | 2.67901 | − | 0.907128i | 0.357998 | − | 0.121220i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.87666 | − | 6.50517i | 1.16556 | − | 0.854171i | ||||
\(59\) | 4.00000i | 0.520756i | 0.965507 | + | 0.260378i | \(0.0838471\pi\) | ||||
−0.965507 | + | 0.260378i | \(0.916153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.49706i | 0.703827i | 0.936033 | + | 0.351913i | \(0.114469\pi\) | ||||
−0.936033 | + | 0.351913i | \(0.885531\pi\) | |||||||
\(62\) | −3.68613 | − | 5.02993i | −0.468139 | − | 0.638801i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.35424 | − | 4.86042i | 0.794280 | − | 0.607552i | ||||
\(65\) | 2.13145 | 0.264374 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.90658i | − | 0.721604i | −0.932642 | − | 0.360802i | \(-0.882503\pi\) | ||
0.932642 | − | 0.360802i | \(-0.117497\pi\) | |||||||
\(68\) | 3.67190 | − | 11.6252i | 0.445283 | − | 1.40976i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.532862 | + | 0.390503i | −0.0636892 | + | 0.0466740i | ||||
\(71\) | 4.72339 | 0.560563 | 0.280281 | − | 0.959918i | \(-0.409572\pi\) | ||||
0.280281 | + | 0.959918i | \(0.409572\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0599 | −1.41150 | −0.705749 | − | 0.708462i | \(-0.749390\pi\) | ||||
−0.705749 | + | 0.708462i | \(0.749390\pi\) | |||||||
\(74\) | 5.02993 | − | 3.68613i | 0.584717 | − | 0.428504i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.56279 | + | 0.809475i | 0.293972 | + | 0.0928531i | ||||
\(77\) | 4.87666i | 0.555747i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.1913 | −1.82166 | −0.910832 | − | 0.412778i | \(-0.864559\pi\) | ||||
−0.910832 | + | 0.412778i | \(0.864559\pi\) | |||||||
\(80\) | −1.07331 | + | 1.52954i | −0.120000 | + | 0.171008i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.09565 | − | 6.95329i | −0.562721 | − | 0.767863i | ||||
\(83\) | − | 13.7533i | − | 1.50962i | −0.655942 | − | 0.754811i | \(-0.727728\pi\) | ||
0.655942 | − | 0.754811i | \(-0.272272\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.84751i | 0.308856i | ||||||||
\(86\) | −4.73762 | + | 3.47192i | −0.510871 | + | 0.374387i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.42375 | + | 13.0646i | 0.471574 | + | 1.39269i | ||||
\(89\) | −7.96420 | −0.844204 | −0.422102 | − | 0.906548i | \(-0.638708\pi\) | ||||
−0.422102 | + | 0.906548i | \(0.638708\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.56279i | 0.478310i | ||||||||
\(92\) | −2.46714 | + | 7.81093i | −0.257217 | + | 0.814346i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.59048 | − | 7.62851i | −0.576614 | − | 0.786821i | ||||
\(95\) | −0.627737 | −0.0644044 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.8789 | −1.30765 | −0.653827 | − | 0.756644i | \(-0.726837\pi\) | ||||
−0.653827 | + | 0.756644i | \(0.726837\pi\) | |||||||
\(98\) | −0.835949 | − | 1.14070i | −0.0844436 | − | 0.115228i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.88045 | + | 9.11947i | −0.288045 | + | 0.911947i | ||||
\(101\) | 2.22045i | 0.220943i | 0.993879 | + | 0.110472i | \(0.0352361\pi\) | ||||
−0.993879 | + | 0.110472i | \(0.964764\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0971 | 1.09343 | 0.546715 | − | 0.837319i | \(-0.315878\pi\) | ||||
0.546715 | + | 0.837319i | \(0.315878\pi\) | |||||||
\(104\) | 4.13903 | + | 12.2238i | 0.405866 | + | 1.19864i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.53286 | + | 1.12334i | −0.148885 | + | 0.109109i | ||||
\(107\) | 3.12334i | 0.301945i | 0.988538 | + | 0.150972i | \(0.0482405\pi\) | ||||
−0.988538 | + | 0.150972i | \(0.951760\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.6876i | 1.02369i | 0.859079 | + | 0.511843i | \(0.171037\pi\) | ||||
−0.859079 | + | 0.511843i | \(0.828963\pi\) | |||||||
\(110\) | −1.90435 | − | 2.59859i | −0.181573 | − | 0.247766i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.27428 | − | 2.29763i | −0.309390 | − | 0.217106i | ||||
\(113\) | 12.0599 | 1.13450 | 0.567248 | − | 0.823547i | \(-0.308008\pi\) | ||||
0.567248 | + | 0.823547i | \(0.308008\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.91323i | − | 0.178410i | ||||||
\(116\) | −14.8409 | − | 4.68759i | −1.37794 | − | 0.435232i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.56279 | − | 3.34379i | 0.420039 | − | 0.307821i | ||||
\(119\) | −6.09565 | −0.558787 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.7818 | −1.16198 | ||||||||
\(122\) | 6.27048 | − | 4.59526i | 0.567703 | − | 0.416036i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.65621 | + | 8.40952i | −0.238534 | + | 0.755197i | ||||
\(125\) | − | 4.56944i | − | 0.408703i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.8789 | 1.67523 | 0.837615 | − | 0.546261i | \(-0.183949\pi\) | ||||
0.837615 | + | 0.546261i | \(0.183949\pi\) | |||||||
\(128\) | −10.8561 | − | 3.18520i | −0.959551 | − | 0.281534i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.78178 | − | 2.43134i | −0.156273 | − | 0.213243i | ||||
\(131\) | − | 4.93428i | − | 0.431110i | −0.976492 | − | 0.215555i | \(-0.930844\pi\) | ||
0.976492 | − | 0.215555i | \(-0.0691560\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.34379i | − | 0.116522i | ||||||
\(134\) | −6.73762 | + | 4.93760i | −0.582042 | + | 0.426544i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.3303 | + | 5.52954i | −1.40031 | + | 0.474154i | ||||
\(137\) | −19.0103 | −1.62416 | −0.812082 | − | 0.583544i | \(-0.801666\pi\) | ||||
−0.812082 | + | 0.583544i | \(0.801666\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.4380i | − | 0.885339i | −0.896685 | − | 0.442669i | \(-0.854032\pi\) | ||
0.896685 | − | 0.442669i | \(-0.145968\pi\) | |||||||
\(140\) | 0.890891 | + | 0.281394i | 0.0752941 | + | 0.0237822i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.94851 | − | 5.38795i | −0.331352 | − | 0.452147i | ||||
\(143\) | −22.2512 | −1.86073 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.63516 | 0.301884 | ||||||||
\(146\) | 10.0814 | + | 13.7566i | 0.834344 | + | 1.13851i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.40952 | − | 2.65621i | −0.691258 | − | 0.218339i | ||||
\(149\) | 6.65621i | 0.545298i | 0.962114 | + | 0.272649i | \(0.0878997\pi\) | ||||
−0.962114 | + | 0.272649i | \(0.912100\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.68759 | −0.218713 | −0.109356 | − | 0.994003i | \(-0.534879\pi\) | ||||
−0.109356 | + | 0.994003i | \(0.534879\pi\) | |||||||
\(152\) | −1.21899 | − | 3.60004i | −0.0988735 | − | 0.292002i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.56279 | − | 4.07663i | 0.448262 | − | 0.328505i | ||||
\(155\) | − | 2.05985i | − | 0.165451i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 23.1351i | − | 1.84639i | −0.384338 | − | 0.923193i | \(-0.625570\pi\) | ||
0.384338 | − | 0.923193i | \(-0.374430\pi\) | |||||||
\(158\) | 13.5351 | + | 18.4694i | 1.07679 | + | 1.46934i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.64197 | − | 0.0542935i | 0.208866 | − | 0.00429228i | ||||
\(161\) | 4.09565 | 0.322783 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0380i | 0.942891i | 0.881895 | + | 0.471446i | \(0.156268\pi\) | ||||
−0.881895 | + | 0.471446i | \(0.843732\pi\) | |||||||
\(164\) | −3.67190 | + | 11.6252i | −0.286727 | + | 0.907775i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.6884 | + | 11.4971i | −1.21765 | + | 0.892345i | ||||
\(167\) | −9.01034 | −0.697241 | −0.348621 | − | 0.937264i | \(-0.613350\pi\) | ||||
−0.348621 | + | 0.937264i | \(0.613350\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.81904 | −0.601465 | ||||||||
\(170\) | 3.24814 | − | 2.38037i | 0.249121 | − | 0.182566i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.92082 | + | 2.50185i | 0.603957 | + | 0.190764i | ||||
\(173\) | 9.59271i | 0.729321i | 0.931141 | + | 0.364660i | \(0.118815\pi\) | ||||
−0.931141 | + | 0.364660i | \(0.881185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.78178 | 0.361469 | ||||||||
\(176\) | 11.2048 | − | 15.9675i | 0.844591 | − | 1.20360i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.65766 | + | 9.08474i | 0.499013 | + | 0.680930i | ||||
\(179\) | − | 7.69278i | − | 0.574985i | −0.957783 | − | 0.287493i | \(-0.907178\pi\) | ||
0.957783 | − | 0.287493i | \(-0.0928217\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.2504i | − | 1.13355i | −0.823872 | − | 0.566776i | \(-0.808191\pi\) | ||
0.823872 | − | 0.566776i | \(-0.191809\pi\) | |||||||
\(182\) | 5.20476 | − | 3.81426i | 0.385802 | − | 0.282732i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.9723 | − | 3.71528i | 0.808889 | − | 0.273894i | ||||
\(185\) | 2.05985 | 0.151443 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 29.7264i | − | 2.17381i | ||||||
\(188\) | −4.02847 | + | 12.7541i | −0.293806 | + | 0.930188i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.524756 | + | 0.716058i | 0.0380698 | + | 0.0519483i | ||||
\(191\) | 4.72339 | 0.341772 | 0.170886 | − | 0.985291i | \(-0.445337\pi\) | ||||
0.170886 | + | 0.985291i | \(0.445337\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.3379 | 1.60792 | 0.803959 | − | 0.594684i | \(-0.202723\pi\) | ||||
0.803959 | + | 0.594684i | \(0.202723\pi\) | |||||||
\(194\) | 10.7661 | + | 14.6909i | 0.772960 | + | 1.05475i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.602380 | + | 1.90713i | −0.0430271 | + | 0.136223i | ||||
\(197\) | 1.53510i | 0.109371i | 0.998504 | + | 0.0546855i | \(0.0174156\pi\) | ||||
−0.998504 | + | 0.0546855i | \(0.982584\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.6876 | −1.04118 | −0.520588 | − | 0.853808i | \(-0.674287\pi\) | ||||
−0.520588 | + | 0.853808i | \(0.674287\pi\) | |||||||
\(200\) | 12.8105 | − | 4.33769i | 0.905837 | − | 0.306721i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.53286 | − | 1.85618i | 0.178212 | − | 0.130601i | ||||
\(203\) | 7.78178i | 0.546174i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 2.84751i | − | 0.198879i | ||||||
\(206\) | −9.27661 | − | 12.6584i | −0.646332 | − | 0.881955i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.4836 | − | 14.9398i | 0.726907 | − | 1.03589i | ||||
\(209\) | 6.55322 | 0.453296 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.8409i | 1.57243i | 0.617953 | + | 0.786215i | \(0.287962\pi\) | ||||
−0.617953 | + | 0.786215i | \(0.712038\pi\) | |||||||
\(212\) | 2.56279 | + | 0.809475i | 0.176013 | + | 0.0555949i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.56279 | − | 2.61095i | 0.243547 | − | 0.178481i | ||||
\(215\) | −1.94015 | −0.132317 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.40952 | 0.299338 | ||||||||
\(218\) | 12.1913 | − | 8.93428i | 0.825699 | − | 0.605105i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.37226 | + | 4.34457i | −0.0925180 | + | 0.292911i | ||||
\(221\) | − | 27.8132i | − | 1.87092i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.4321 | 1.43520 | 0.717600 | − | 0.696455i | \(-0.245240\pi\) | ||||
0.717600 | + | 0.696455i | \(0.245240\pi\) | |||||||
\(224\) | 0.116226 | + | 5.65566i | 0.00776567 | + | 0.377885i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.0814 | − | 13.7566i | −0.670606 | − | 0.915078i | ||||
\(227\) | − | 29.3169i | − | 1.94583i | −0.231164 | − | 0.972915i | \(-0.574253\pi\) | ||
0.231164 | − | 0.972915i | \(-0.425747\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.5074i | 1.48733i | 0.668552 | + | 0.743666i | \(0.266914\pi\) | ||||
−0.668552 | + | 0.743666i | \(0.733086\pi\) | |||||||
\(230\) | −2.18242 | + | 1.59936i | −0.143904 | + | 0.105459i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.05908 | + | 20.8475i | 0.463451 | + | 1.36871i | ||||
\(233\) | 0.687589 | 0.0450454 | 0.0225227 | − | 0.999746i | \(-0.492830\pi\) | ||||
0.0225227 | + | 0.999746i | \(0.492830\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.12402i | − | 0.203789i | ||||||
\(236\) | −7.62851 | − | 2.40952i | −0.496574 | − | 0.156846i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.09565 | + | 6.95329i | 0.330302 | + | 0.450715i | ||||
\(239\) | 9.59936 | 0.620931 | 0.310466 | − | 0.950585i | \(-0.399515\pi\) | ||||
0.310466 | + | 0.950585i | \(0.399515\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.496287 | 0.0319687 | 0.0159843 | − | 0.999872i | \(-0.494912\pi\) | ||||
0.0159843 | + | 0.999872i | \(0.494912\pi\) | |||||||
\(242\) | 10.6849 | + | 14.5801i | 0.686852 | + | 0.937247i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.4836 | − | 3.31132i | −0.671144 | − | 0.211986i | ||||
\(245\) | − | 0.467138i | − | 0.0298443i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.13145 | 0.390135 | ||||||||
\(248\) | 11.8132 | − | 4.00000i | 0.750137 | − | 0.254000i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.21234 | + | 3.81982i | −0.329658 | + | 0.241586i | ||||
\(251\) | − | 22.1359i | − | 1.39721i | −0.715509 | − | 0.698603i | \(-0.753805\pi\) | ||
0.715509 | − | 0.698603i | \(-0.246195\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.9731i | 1.25570i | ||||||||
\(254\) | −15.7818 | − | 21.5351i | −0.990237 | − | 1.35123i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.44178 | + | 15.0462i | 0.340111 | + | 0.940385i | ||||
\(257\) | −2.28695 | −0.142656 | −0.0713281 | − | 0.997453i | \(-0.522724\pi\) | ||||
−0.0713281 | + | 0.997453i | \(0.522724\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.40952i | 0.273994i | ||||||||
\(260\) | −1.28394 | + | 4.06495i | −0.0796267 | + | 0.252097i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.62851 | + | 4.12480i | −0.347731 | + | 0.254831i | ||||
\(263\) | 30.1555 | 1.85947 | 0.929734 | − | 0.368232i | \(-0.120037\pi\) | ||||
0.929734 | + | 0.368232i | \(0.120037\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.627737 | −0.0385616 | ||||||||
\(266\) | −1.53286 | + | 1.12334i | −0.0939858 | + | 0.0688766i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.2646 | + | 3.55801i | 0.688096 | + | 0.217340i | ||||
\(269\) | − | 9.47748i | − | 0.577852i | −0.957351 | − | 0.288926i | \(-0.906702\pi\) | ||
0.957351 | − | 0.288926i | \(-0.0932982\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.2855 | −0.807036 | −0.403518 | − | 0.914972i | \(-0.632213\pi\) | ||||
−0.403518 | + | 0.914972i | \(0.632213\pi\) | |||||||
\(272\) | 19.9589 | + | 14.0056i | 1.21018 | + | 0.849212i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.8917 | + | 21.6850i | 0.960051 | + | 1.31004i | ||||
\(275\) | 23.3191i | 1.40620i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 26.8475i | − | 1.61311i | −0.591159 | − | 0.806555i | \(-0.701329\pi\) | ||
0.591159 | − | 0.806555i | \(-0.298671\pi\) | |||||||
\(278\) | −11.9066 | + | 8.72562i | −0.714109 | + | 0.523328i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.423754 | − | 1.25147i | −0.0253241 | − | 0.0747895i | ||||
\(281\) | −11.8686 | −0.708018 | −0.354009 | − | 0.935242i | \(-0.615182\pi\) | ||||
−0.354009 | + | 0.935242i | \(0.615182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.46937i | 0.146789i | 0.997303 | + | 0.0733944i | \(0.0233832\pi\) | ||||
−0.997303 | + | 0.0733944i | \(0.976617\pi\) | |||||||
\(284\) | −2.84527 | + | 9.00811i | −0.168836 | + | 0.534533i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.6008 | + | 25.3818i | 1.09989 | + | 1.50086i | ||||
\(287\) | 6.09565 | 0.359815 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.1570 | 1.18570 | ||||||||
\(290\) | −3.03881 | − | 4.14662i | −0.178445 | − | 0.243498i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.26461 | − | 22.9997i | 0.425129 | − | 1.34595i | ||||
\(293\) | − | 22.7899i | − | 1.33140i | −0.746220 | − | 0.665700i | \(-0.768133\pi\) | ||
0.746220 | − | 0.665700i | \(-0.231867\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.86855 | 0.108791 | ||||||||
\(296\) | 4.00000 | + | 11.8132i | 0.232495 | + | 0.686626i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.59271 | − | 5.56425i | 0.439834 | − | 0.322328i | ||||
\(299\) | 18.6876i | 1.08073i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 4.15327i | − | 0.239390i | ||||||
\(302\) | 2.24669 | + | 3.06572i | 0.129282 | + | 0.176413i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.08754 | + | 4.39996i | −0.177083 | + | 0.252355i | ||||
\(305\) | 2.56788 | 0.147037 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.34379i | 0.533279i | 0.963796 | + | 0.266639i | \(0.0859132\pi\) | ||||
−0.963796 | + | 0.266639i | \(0.914087\pi\) | |||||||
\(308\) | −9.30041 | − | 2.93760i | −0.529940 | − | 0.167385i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.34967 | + | 1.72193i | −0.133452 | + | 0.0977991i | ||||
\(311\) | −6.68759 | −0.379218 | −0.189609 | − | 0.981860i | \(-0.560722\pi\) | ||||
−0.189609 | + | 0.981860i | \(0.560722\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.6381 | −0.883916 | −0.441958 | − | 0.897036i | \(-0.645716\pi\) | ||||
−0.441958 | + | 0.897036i | \(0.645716\pi\) | |||||||
\(314\) | −26.3902 | + | 19.3398i | −1.48928 | + | 1.09141i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.75331 | − | 30.8789i | 0.548667 | − | 1.73707i | ||||
\(317\) | − | 9.34379i | − | 0.524800i | −0.964959 | − | 0.262400i | \(-0.915486\pi\) | ||
0.964959 | − | 0.262400i | \(-0.0845139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.9491 | −2.12474 | ||||||||
\(320\) | −2.27048 | − | 2.96830i | −0.126924 | − | 0.165933i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.42375 | − | 4.67190i | −0.190798 | − | 0.260355i | ||||
\(323\) | 8.19130i | 0.455776i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.8183i | 1.21026i | ||||||||
\(326\) | 13.7317 | − | 10.0632i | 0.760531 | − | 0.557348i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16.3303 | − | 5.52954i | 0.901692 | − | 0.305318i | ||||
\(329\) | 6.68759 | 0.368699 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 5.40874i | − | 0.297291i | −0.988891 | − | 0.148646i | \(-0.952509\pi\) | ||
0.988891 | − | 0.148646i | \(-0.0474914\pi\) | |||||||
\(332\) | 26.2293 | + | 8.28472i | 1.43952 | + | 0.454683i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.53218 | + | 10.2781i | 0.412143 | + | 0.562391i | ||||
\(335\) | −2.75919 | −0.150750 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.55614 | −0.357136 | −0.178568 | − | 0.983928i | \(-0.557146\pi\) | ||||
−0.178568 | + | 0.983928i | \(0.557146\pi\) | |||||||
\(338\) | 6.53631 | + | 8.91915i | 0.355529 | + | 0.485138i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.43056 | − | 1.71528i | −0.294514 | − | 0.0930242i | ||||
\(341\) | 21.5037i | 1.16449i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −3.76755 | − | 11.1267i | −0.203133 | − | 0.599910i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.9424 | − | 8.01902i | 0.588266 | − | 0.431105i | ||||
\(347\) | 24.9964i | 1.34187i | 0.741514 | + | 0.670937i | \(0.234108\pi\) | ||||
−0.741514 | + | 0.670937i | \(0.765892\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 27.1921i | − | 1.45556i | −0.685811 | − | 0.727779i | \(-0.740553\pi\) | ||
0.685811 | − | 0.727779i | \(-0.259447\pi\) | |||||||
\(350\) | −3.99732 | − | 5.45457i | −0.213666 | − | 0.291559i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −27.5807 | + | 0.566794i | −1.47006 | + | 0.0302102i | ||||
\(353\) | 30.2870 | 1.61201 | 0.806006 | − | 0.591907i | \(-0.201625\pi\) | ||||
0.806006 | + | 0.591907i | \(0.201625\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2.20647i | − | 0.117107i | ||||||
\(356\) | 4.79747 | − | 15.1888i | 0.254266 | − | 0.805002i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.77513 | + | 6.43077i | −0.463780 | + | 0.339877i | ||||
\(359\) | −6.59194 | −0.347909 | −0.173955 | − | 0.984754i | \(-0.555655\pi\) | ||||
−0.173955 | + | 0.984754i | \(0.555655\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.1942 | 0.904959 | ||||||||
\(362\) | −17.3961 | + | 12.7485i | −0.914317 | + | 0.670048i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.70182 | − | 2.74853i | −0.456099 | − | 0.144062i | ||||
\(365\) | 5.63361i | 0.294877i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.68759 | −0.349089 | −0.174545 | − | 0.984649i | \(-0.555845\pi\) | ||||
−0.174545 | + | 0.984649i | \(0.555845\pi\) | |||||||
\(368\) | −13.4103 | − | 9.41030i | −0.699060 | − | 0.490546i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.72193 | − | 2.34967i | −0.0895189 | − | 0.122153i | ||||
\(371\) | − | 1.34379i | − | 0.0697663i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 17.1256i | − | 0.886729i | −0.896341 | − | 0.443364i | \(-0.853785\pi\) | ||
0.896341 | − | 0.443364i | \(-0.146215\pi\) | |||||||
\(374\) | −33.9088 | + | 24.8497i | −1.75338 | + | 1.28495i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.9161 | − | 6.06650i | 0.923955 | − | 0.312856i | ||||
\(377\) | −35.5066 | −1.82868 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.7094i | − | 0.858305i | −0.903232 | − | 0.429152i | \(-0.858812\pi\) | ||
0.903232 | − | 0.429152i | \(-0.141188\pi\) | |||||||
\(380\) | 0.378136 | − | 1.19717i | 0.0193980 | − | 0.0614138i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.94851 | − | 5.38795i | −0.202023 | − | 0.275672i | ||||
\(383\) | 9.94015 | 0.507918 | 0.253959 | − | 0.967215i | \(-0.418267\pi\) | ||||
0.253959 | + | 0.967215i | \(0.418267\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.27807 | 0.116101 | ||||||||
\(386\) | −18.6734 | − | 25.4808i | −0.950449 | − | 1.29694i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.75798 | − | 24.5617i | 0.393852 | − | 1.24693i | ||||
\(389\) | − | 19.2884i | − | 0.977961i | −0.872295 | − | 0.488981i | \(-0.837369\pi\) | ||
0.872295 | − | 0.488981i | \(-0.162631\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.9657 | −1.26257 | ||||||||
\(392\) | 2.67901 | − | 0.907128i | 0.135311 | − | 0.0458169i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.75108 | − | 1.28326i | 0.0882181 | − | 0.0646498i | ||||
\(395\) | 7.56357i | 0.380564i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.4417i | 1.17650i | 0.808678 | + | 0.588252i | \(0.200184\pi\) | ||||
−0.808678 | + | 0.588252i | \(0.799816\pi\) | |||||||
\(398\) | 12.2781 | + | 16.7541i | 0.615444 | + | 0.839807i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −15.6569 | − | 10.9868i | −0.782844 | − | 0.549339i | ||||
\(401\) | 16.0029 | 0.799147 | 0.399574 | − | 0.916701i | \(-0.369158\pi\) | ||||
0.399574 | + | 0.916701i | \(0.369158\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.1197i | 1.00223i | ||||||||
\(404\) | −4.23469 | − | 1.33756i | −0.210683 | − | 0.0665459i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.87666 | − | 6.50517i | 0.440541 | − | 0.322846i | ||||
\(407\) | −21.5037 | −1.06590 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.5665 | 0.769713 | 0.384856 | − | 0.922976i | \(-0.374251\pi\) | ||||
0.384856 | + | 0.922976i | \(0.374251\pi\) | |||||||
\(410\) | −3.24814 | + | 2.38037i | −0.160414 | + | 0.117558i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.68467 | + | 21.1636i | −0.329330 | + | 1.04266i | ||||
\(413\) | 4.00000i | 0.196827i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.42469 | −0.315376 | ||||||||
\(416\) | −25.8056 | + | 0.530314i | −1.26522 | + | 0.0260008i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.47816 | − | 7.47524i | −0.267946 | − | 0.365626i | ||||
\(419\) | − | 1.31241i | − | 0.0641155i | −0.999486 | − | 0.0320577i | \(-0.989794\pi\) | ||
0.999486 | − | 0.0320577i | \(-0.0102060\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3.66655i | − | 0.178697i | −0.996000 | − | 0.0893483i | \(-0.971522\pi\) | ||
0.996000 | − | 0.0893483i | \(-0.0284784\pi\) | |||||||
\(422\) | 26.0545 | − | 19.0938i | 1.26831 | − | 0.929471i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.21899 | − | 3.60004i | −0.0591996 | − | 0.174834i | ||||
\(425\) | −29.1481 | −1.41389 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.49706i | 0.266022i | ||||||||
\(428\) | −5.95662 | − | 1.88144i | −0.287924 | − | 0.0909428i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.62186 | + | 2.21312i | 0.0782132 | + | 0.106726i | ||||
\(431\) | −20.0957 | −0.967973 | −0.483987 | − | 0.875075i | \(-0.660812\pi\) | ||||
−0.483987 | + | 0.875075i | \(0.660812\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.68759 | 0.417499 | 0.208749 | − | 0.977969i | \(-0.433061\pi\) | ||||
0.208749 | + | 0.977969i | \(0.433061\pi\) | |||||||
\(434\) | −3.68613 | − | 5.02993i | −0.176940 | − | 0.241444i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.3826 | − | 6.43799i | −0.976150 | − | 0.308324i | ||||
\(437\) | − | 5.50371i | − | 0.263278i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 6.10298 | − | 2.06650i | 0.290948 | − | 0.0985166i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −31.7264 | + | 23.2504i | −1.50907 | + | 1.10591i | ||||
\(443\) | 4.57012i | 0.217133i | 0.994089 | + | 0.108566i | \(0.0346260\pi\) | ||||
−0.994089 | + | 0.108566i | \(0.965374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.72038i | 0.176363i | ||||||||
\(446\) | −17.9161 | − | 24.4476i | −0.848354 | − | 1.15763i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.35424 | − | 4.86042i | 0.300209 | − | 0.229633i | ||||
\(449\) | 3.94015 | 0.185947 | 0.0929735 | − | 0.995669i | \(-0.470363\pi\) | ||||
0.0929735 | + | 0.995669i | \(0.470363\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.7264i | 1.39976i | ||||||||
\(452\) | −7.26461 | + | 22.9997i | −0.341699 | + | 1.08181i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −33.4417 | + | 24.5074i | −1.56950 | + | 1.15019i | ||||
\(455\) | 2.13145 | 0.0999239 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 40.0207 | 1.87209 | 0.936044 | − | 0.351882i | \(-0.114458\pi\) | ||||
0.936044 | + | 0.351882i | \(0.114458\pi\) | |||||||
\(458\) | 25.6741 | − | 18.8150i | 1.19967 | − | 0.879169i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.64878 | + | 1.15249i | 0.170125 | + | 0.0537352i | ||||
\(461\) | 34.6031i | 1.61162i | 0.592171 | + | 0.805812i | \(0.298271\pi\) | ||||
−0.592171 | + | 0.805812i | \(0.701729\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.191302 | 0.00889055 | 0.00444528 | − | 0.999990i | \(-0.498585\pi\) | ||||
0.00444528 | + | 0.999990i | \(0.498585\pi\) | |||||||
\(464\) | 17.8797 | − | 25.4797i | 0.830043 | − | 1.18287i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.574789 | − | 0.784331i | −0.0266266 | − | 0.0363334i | ||||
\(467\) | − | 4.49784i | − | 0.208135i | −0.994570 | − | 0.104068i | \(-0.966814\pi\) | ||
0.994570 | − | 0.104068i | \(-0.0331858\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.90658i | − | 0.272741i | ||||||
\(470\) | −3.56357 | + | 2.61152i | −0.164375 | + | 0.120461i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.62851 | + | 10.7161i | 0.167016 | + | 0.493247i | ||||
\(473\) | 20.2541 | 0.931283 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.42573i | − | 0.294833i | ||||||
\(476\) | 3.67190 | − | 11.6252i | 0.168301 | − | 0.532840i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.02457 | − | 10.9500i | −0.367036 | − | 0.500840i | ||||
\(479\) | 22.2512 | 1.01668 | 0.508341 | − | 0.861156i | \(-0.330259\pi\) | ||||
0.508341 | + | 0.861156i | \(0.330259\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.1197 | −0.917380 | ||||||||
\(482\) | −0.414870 | − | 0.566113i | −0.0188968 | − | 0.0257857i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.69949 | − | 24.3765i | 0.349977 | − | 1.10802i | ||||
\(485\) | 6.01621i | 0.273182i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.86855 | −0.0846721 | −0.0423360 | − | 0.999103i | \(-0.513480\pi\) | ||||
−0.0423360 | + | 0.999103i | \(0.513480\pi\) | |||||||
\(488\) | 4.98654 | + | 14.7267i | 0.225730 | + | 0.666647i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.532862 | + | 0.390503i | −0.0240723 | + | 0.0176411i | ||||
\(491\) | 17.6374i | 0.795965i | 0.917393 | + | 0.397982i | \(0.130289\pi\) | ||||
−0.917393 | + | 0.397982i | \(0.869711\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 47.4350i | − | 2.13637i | ||||||
\(494\) | −5.12558 | − | 6.99413i | −0.230611 | − | 0.314681i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.4380 | − | 10.1314i | −0.648285 | − | 0.454916i | ||||
\(497\) | 4.72339 | 0.211873 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.5854i | 0.966295i | 0.875539 | + | 0.483147i | \(0.160506\pi\) | ||||
−0.875539 | + | 0.483147i | \(0.839494\pi\) | |||||||
\(500\) | 8.71450 | + | 2.75254i | 0.389724 | + | 0.123097i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.2504 | + | 18.5045i | −1.12698 | + | 0.825896i | ||||
\(503\) | −5.24081 | −0.233676 | −0.116838 | − | 0.993151i | \(-0.537276\pi\) | ||||
−0.116838 | + | 0.993151i | \(0.537276\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.03726 | 0.0461573 | ||||||||
\(506\) | 22.7832 | − | 16.6965i | 1.01284 | − | 0.742249i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.3723 | + | 36.0045i | −0.504563 | + | 1.59744i | ||||
\(509\) | − | 18.3357i | − | 0.812715i | −0.913714 | − | 0.406358i | \(-0.866799\pi\) | ||
0.913714 | − | 0.406358i | \(-0.133201\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0599 | −0.533496 | ||||||||
\(512\) | 12.6141 | − | 18.7852i | 0.557468 | − | 0.830198i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.91178 | + | 2.60872i | 0.0843248 | + | 0.115066i | ||||
\(515\) | − | 5.18388i | − | 0.228429i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.6131i | 1.43432i | ||||||||
\(518\) | 5.02993 | − | 3.68613i | 0.221002 | − | 0.161959i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.71018 | − | 1.93350i | 0.250408 | − | 0.0847895i | ||||
\(521\) | −6.78033 | −0.297051 | −0.148526 | − | 0.988909i | \(-0.547453\pi\) | ||||
−0.148526 | + | 0.988909i | \(0.547453\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.5066i | 1.02787i | 0.857828 | + | 0.513937i | \(0.171813\pi\) | ||||
−0.857828 | + | 0.513937i | \(0.828187\pi\) | |||||||
\(524\) | 9.41030 | + | 2.97231i | 0.411091 | + | 0.129846i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25.2085 | − | 34.3983i | −1.09914 | − | 1.49984i | ||||
\(527\) | −26.8789 | −1.17086 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.22564 | −0.270680 | ||||||||
\(530\) | 0.524756 | + | 0.716058i | 0.0227939 | + | 0.0311036i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.56279 | + | 0.809475i | 0.111111 | + | 0.0350952i | ||||
\(533\) | 27.8132i | 1.20472i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.45903 | 0.0630794 | ||||||||
\(536\) | −5.35803 | − | 15.8238i | −0.231432 | − | 0.683485i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.8109 | + | 7.92268i | −0.466092 | + | 0.341571i | ||||
\(539\) | 4.87666i | 0.210052i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 5.21526i | − | 0.224222i | −0.993696 | − | 0.112111i | \(-0.964239\pi\) | ||
0.993696 | − | 0.112111i | \(-0.0357611\pi\) | |||||||
\(542\) | 11.1060 | + | 15.1547i | 0.477043 | + | 0.650951i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.708473 | − | 34.4749i | −0.0303755 | − | 1.47810i | ||||
\(545\) | 4.99257 | 0.213858 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 27.2951i | − | 1.16705i | −0.812094 | − | 0.583526i | \(-0.801673\pi\) | ||
0.812094 | − | 0.583526i | \(-0.198327\pi\) | |||||||
\(548\) | 11.4514 | − | 36.2552i | 0.489182 | − | 1.54874i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 26.6000 | − | 19.4936i | 1.13423 | − | 0.831209i | ||||
\(551\) | 10.4571 | 0.445488 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.1913 | −0.688524 | ||||||||
\(554\) | −30.6249 | + | 22.4431i | −1.30113 | + | 0.953518i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.9066 | + | 6.28763i | 0.844227 | + | 0.266655i | ||||
\(557\) | − | 4.78766i | − | 0.202859i | −0.994843 | − | 0.101430i | \(-0.967658\pi\) | ||
0.994843 | − | 0.101430i | \(-0.0323417\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.9505 | 0.801520 | ||||||||
\(560\) | −1.07331 | + | 1.52954i | −0.0453556 | + | 0.0646348i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.92150 | + | 13.5384i | 0.418513 | + | 0.571084i | ||||
\(563\) | 18.7445i | 0.789988i | 0.918684 | + | 0.394994i | \(0.129253\pi\) | ||||
−0.918684 | + | 0.394994i | \(0.870747\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 5.63361i | − | 0.237008i | ||||||
\(566\) | 2.81680 | − | 2.06427i | 0.118399 | − | 0.0867676i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.6540 | − | 4.28472i | 0.530951 | − | 0.179783i | ||||
\(569\) | −27.6950 | −1.16104 | −0.580518 | − | 0.814248i | \(-0.697150\pi\) | ||||
−0.580518 | + | 0.814248i | \(0.697150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.4132i | 0.728720i | 0.931258 | + | 0.364360i | \(0.118712\pi\) | ||||
−0.931258 | + | 0.364360i | \(0.881288\pi\) | |||||||
\(572\) | 13.4036 | − | 42.4358i | 0.560435 | − | 1.77433i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.09565 | − | 6.95329i | −0.212688 | − | 0.290225i | ||||
\(575\) | 19.5845 | 0.816731 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.81904 | −0.283880 | −0.141940 | − | 0.989875i | \(-0.545334\pi\) | ||||
−0.141940 | + | 0.989875i | \(0.545334\pi\) | |||||||
\(578\) | −16.8502 | − | 22.9930i | −0.700875 | − | 0.956382i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.18975 | + | 6.93272i | −0.0909244 | + | 0.287866i | ||||
\(581\) | − | 13.7533i | − | 0.570584i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.55322 | 0.271407 | ||||||||
\(584\) | −32.3085 | + | 10.9398i | −1.33694 | + | 0.452694i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.9964 | + | 19.0512i | −1.07390 | + | 0.786997i | ||||
\(587\) | − | 9.81025i | − | 0.404912i | −0.979291 | − | 0.202456i | \(-0.935108\pi\) | ||
0.979291 | − | 0.202456i | \(-0.0648924\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.92549i | − | 0.244155i | ||||||
\(590\) | −1.56201 | − | 2.13145i | −0.0643070 | − | 0.0877504i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.1314 | − | 14.4380i | 0.416400 | − | 0.593398i | ||||
\(593\) | 39.0913 | 1.60529 | 0.802644 | − | 0.596458i | \(-0.203426\pi\) | ||||
0.802644 | + | 0.596458i | \(0.203426\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.84751i | 0.116736i | ||||||||
\(596\) | −12.6942 | − | 4.00956i | −0.519976 | − | 0.164238i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21.3169 | − | 15.6219i | 0.871712 | − | 0.638826i | ||||
\(599\) | −22.0270 | −0.899998 | −0.449999 | − | 0.893029i | \(-0.648576\pi\) | ||||
−0.449999 | + | 0.893029i | \(0.648576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2512 | −0.826062 | −0.413031 | − | 0.910717i | \(-0.635530\pi\) | ||||
−0.413031 | + | 0.910717i | \(0.635530\pi\) | |||||||
\(602\) | −4.73762 | + | 3.47192i | −0.193091 | + | 0.141505i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.61895 | − | 5.12558i | 0.0658741 | − | 0.208557i | ||||
\(605\) | 5.97085i | 0.242750i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.4454 | 1.80398 | 0.901991 | − | 0.431755i | \(-0.142105\pi\) | ||||
0.901991 | + | 0.431755i | \(0.142105\pi\) | |||||||
\(608\) | 7.60004 | − | 0.156184i | 0.308223 | − | 0.00633409i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.14662 | − | 2.92918i | −0.0869141 | − | 0.118599i | ||||
\(611\) | 30.5141i | 1.23447i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 47.6263i | − | 1.92361i | −0.273737 | − | 0.961805i | \(-0.588260\pi\) | ||
0.273737 | − | 0.961805i | \(-0.411740\pi\) | |||||||
\(614\) | 10.6584 | − | 7.81093i | 0.430140 | − | 0.315224i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.42375 | + | 13.0646i | 0.178238 | + | 0.526389i | ||||
\(617\) | 3.01034 | 0.121192 | 0.0605959 | − | 0.998162i | \(-0.480700\pi\) | ||||
0.0605959 | + | 0.998162i | \(0.480700\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.5141i | 0.744143i | 0.928204 | + | 0.372071i | \(0.121352\pi\) | ||||
−0.928204 | + | 0.372071i | \(0.878648\pi\) | |||||||
\(620\) | 3.92840 | + | 1.24081i | 0.157768 | + | 0.0498323i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.59048 | + | 7.62851i | 0.224158 | + | 0.305876i | ||||
\(623\) | −7.96420 | −0.319079 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7744 | 0.870974 | ||||||||
\(626\) | 13.0726 | + | 17.8383i | 0.522487 | + | 0.712962i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 44.1217 | + | 13.9361i | 1.76065 | + | 0.556113i | ||||
\(629\) | − | 26.8789i | − | 1.07173i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.2658 | 0.408676 | 0.204338 | − | 0.978900i | \(-0.434496\pi\) | ||||
0.204338 | + | 0.978900i | \(0.434496\pi\) | |||||||
\(632\) | −43.3767 | + | 14.6876i | −1.72543 | + | 0.584241i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.6584 | + | 7.81093i | −0.423301 | + | 0.310212i | ||||
\(635\) | − | 8.81904i | − | 0.349973i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.56279i | 0.180784i | ||||||||
\(638\) | 31.7235 | + | 43.2884i | 1.25594 | + | 1.71380i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.48793 | + | 5.07128i | −0.0588154 | + | 0.200460i | ||||
\(641\) | 16.9358 | 0.668925 | 0.334462 | − | 0.942409i | \(-0.391445\pi\) | ||||
0.334462 | + | 0.942409i | \(0.391445\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 19.5189i | − | 0.769750i | −0.922969 | − | 0.384875i | \(-0.874245\pi\) | ||
0.922969 | − | 0.384875i | \(-0.125755\pi\) | |||||||
\(644\) | −2.46714 | + | 7.81093i | −0.0972188 | + | 0.307794i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.34379 | − | 6.84751i | 0.367627 | − | 0.269412i | ||||
\(647\) | 23.3723 | 0.918858 | 0.459429 | − | 0.888214i | \(-0.348054\pi\) | ||||
0.459429 | + | 0.888214i | \(0.348054\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.5066 | −0.765702 | ||||||||
\(650\) | 24.8880 | − | 18.2389i | 0.976189 | − | 0.715390i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −22.9581 | − | 7.25147i | −0.899108 | − | 0.283989i | ||||
\(653\) | − | 1.45903i | − | 0.0570963i | −0.999592 | − | 0.0285481i | \(-0.990912\pi\) | ||
0.999592 | − | 0.0285481i | \(-0.00908839\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.30499 | −0.0900632 | ||||||||
\(656\) | −19.9589 | − | 14.0056i | −0.779262 | − | 0.546825i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.59048 | − | 7.62851i | −0.217940 | − | 0.297390i | ||||
\(659\) | − | 10.8929i | − | 0.424326i | −0.977234 | − | 0.212163i | \(-0.931949\pi\) | ||
0.977234 | − | 0.212163i | \(-0.0680508\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.69715i | 0.338280i | 0.985592 | + | 0.169140i | \(0.0540990\pi\) | ||||
−0.985592 | + | 0.169140i | \(0.945901\pi\) | |||||||
\(662\) | −6.16974 | + | 4.52143i | −0.239794 | + | 0.175730i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.4760 | − | 36.8453i | −0.484164 | − | 1.42988i | ||||
\(665\) | −0.627737 | −0.0243426 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.8715i | 1.23407i | ||||||||
\(668\) | 5.42765 | − | 17.1839i | 0.210002 | − | 0.664864i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.30654 | + | 3.14740i | 0.0891093 | + | 0.121595i | ||||
\(671\) | −26.8073 | −1.03488 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0447 | 0.695571 | 0.347786 | − | 0.937574i | \(-0.386934\pi\) | ||||
0.347786 | + | 0.937574i | \(0.386934\pi\) | |||||||
\(674\) | 5.48060 | + | 7.47857i | 0.211105 | + | 0.288064i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.71003 | − | 14.9119i | 0.181155 | − | 0.573535i | ||||
\(677\) | 28.7781i | 1.10603i | 0.833170 | + | 0.553017i | \(0.186524\pi\) | ||||
−0.833170 | + | 0.553017i | \(0.813476\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.8789 | −0.494246 | ||||||||
\(680\) | 2.58305 | + | 7.62851i | 0.0990556 | + | 0.292540i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 24.5292 | − | 17.9760i | 0.939273 | − | 0.688337i | ||||
\(683\) | − | 34.4431i | − | 1.31793i | −0.752174 | − | 0.658965i | \(-0.770995\pi\) | ||
0.752174 | − | 0.658965i | \(-0.229005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.88044i | 0.339304i | ||||||||
\(686\) | −0.835949 | − | 1.14070i | −0.0319167 | − | 0.0435520i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.54268 | + | 13.5990i | −0.363811 | + | 0.518455i | ||||
\(689\) | 6.13145 | 0.233590 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 41.5651i | − | 1.58121i | −0.612325 | − | 0.790606i | \(-0.709766\pi\) | ||
0.612325 | − | 0.790606i | \(-0.290234\pi\) | |||||||
\(692\) | −18.2945 | − | 5.77846i | −0.695454 | − | 0.219664i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.5133 | − | 20.8957i | 1.08235 | − | 0.793189i | ||||
\(695\) | −4.87598 | −0.184956 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.1570 | −1.40742 | ||||||||
\(698\) | −31.0179 | + | 22.7312i | −1.17405 | + | 0.860388i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.88045 | + | 9.11947i | −0.108871 | + | 0.344684i | ||||
\(701\) | 46.7804i | 1.76687i | 0.468553 | + | 0.883435i | \(0.344775\pi\) | ||||
−0.468553 | + | 0.883435i | \(0.655225\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.92549 | 0.223484 | ||||||||
\(704\) | 23.7026 | + | 30.9874i | 0.893325 | + | 1.16788i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −25.3183 | − | 34.5482i | −0.952868 | − | 1.30024i | ||||
\(707\) | 2.22045i | 0.0835087i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.43643i | 0.316837i | 0.987372 | + | 0.158418i | \(0.0506395\pi\) | ||||
−0.987372 | + | 0.158418i | \(0.949360\pi\) | |||||||
\(710\) | −2.51692 | + | 1.84450i | −0.0944582 | + | 0.0692227i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21.3362 | + | 7.22455i | −0.799608 | + | 0.270752i | ||||
\(713\) | 18.0599 | 0.676347 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.3943i | 0.388727i | ||||||||
\(716\) | 14.6711 | + | 4.63398i | 0.548286 | + | 0.173180i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.51052 | + | 7.51940i | 0.205651 | + | 0.280622i | ||||
\(719\) | 38.4425 | 1.43366 | 0.716831 | − | 0.697247i | \(-0.245592\pi\) | ||||
0.716831 | + | 0.697247i | \(0.245592\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.0971 | 0.413278 | ||||||||
\(722\) | −14.3735 | − | 19.6134i | −0.534926 | − | 0.729935i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 29.0844 | + | 9.18652i | 1.08091 | + | 0.341414i | ||||
\(725\) | 37.2108i | 1.38197i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.5484 | −0.650834 | −0.325417 | − | 0.945571i | \(-0.605505\pi\) | ||||
−0.325417 | + | 0.945571i | \(0.605505\pi\) | |||||||
\(728\) | 4.13903 | + | 12.2238i | 0.153403 | + | 0.453043i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.42624 | − | 4.70941i | 0.237846 | − | 0.174303i | ||||
\(731\) | 25.3169i | 0.936379i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.8272i | 1.43412i | 0.697013 | + | 0.717058i | \(0.254512\pi\) | ||||
−0.697013 | + | 0.717058i | \(0.745488\pi\) | |||||||
\(734\) | 5.59048 | + | 7.62851i | 0.206348 | + | 0.281574i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.476021 | + | 23.1636i | 0.0175464 | + | 0.853822i | ||||
\(737\) | 28.8044 | 1.06102 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.9066i | 0.511562i | 0.966735 | + | 0.255781i | \(0.0823326\pi\) | ||||
−0.966735 | + | 0.255781i | \(0.917667\pi\) | |||||||
\(740\) | −1.24081 | + | 3.92840i | −0.0456132 | + | 0.144411i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.53286 | + | 1.12334i | −0.0562732 | + | 0.0412392i | ||||
\(743\) | −40.2300 | −1.47590 | −0.737948 | − | 0.674858i | \(-0.764205\pi\) | ||||
−0.737948 | + | 0.674858i | \(0.764205\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.10936 | 0.113918 | ||||||||
\(746\) | −19.5351 | + | 14.3161i | −0.715231 | + | 0.524150i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 56.6921 | + | 17.9066i | 2.07287 | + | 0.654730i | ||||
\(749\) | 3.12334i | 0.114124i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.9957 | 0.620181 | 0.310091 | − | 0.950707i | \(-0.399641\pi\) | ||||
0.310091 | + | 0.950707i | \(0.399641\pi\) | |||||||
\(752\) | −21.8970 | − | 15.3656i | −0.798502 | − | 0.560326i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 29.6817 | + | 40.5023i | 1.08094 | + | 1.47501i | ||||
\(755\) | 1.25547i | 0.0456914i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.43212i | 0.342816i | 0.985200 | + | 0.171408i | \(0.0548316\pi\) | ||||
−0.985200 | + | 0.171408i | \(0.945168\pi\) | |||||||
\(758\) | −19.0604 | + | 13.9682i | −0.692304 | + | 0.507348i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.68172 | + | 0.569438i | −0.0610023 | + | 0.0206557i | ||||
\(761\) | 9.41098 | 0.341148 | 0.170574 | − | 0.985345i | \(-0.445438\pi\) | ||||
0.170574 | + | 0.985345i | \(0.445438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.6876i | 0.386917i | ||||||||
\(764\) | −2.84527 | + | 9.00811i | −0.102938 | + | 0.325902i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.30945 | − | 11.3387i | −0.300233 | − | 0.409684i | ||||
\(767\) | −18.2512 | −0.659011 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.6950 | 0.998708 | 0.499354 | − | 0.866398i | \(-0.333571\pi\) | ||||
0.499354 | + | 0.866398i | \(0.333571\pi\) | |||||||
\(770\) | −1.90435 | − | 2.59859i | −0.0686280 | − | 0.0936466i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.4559 | + | 42.6013i | −0.484289 | + | 1.53325i | ||||
\(773\) | − | 33.8993i | − | 1.21927i | −0.792682 | − | 0.609636i | \(-0.791316\pi\) | ||
0.792682 | − | 0.609636i | \(-0.208684\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.0854 | 0.757409 | ||||||||
\(776\) | −34.5027 | + | 11.6828i | −1.23858 | + | 0.419388i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.0022 | + | 16.1241i | −0.788818 | + | 0.578078i | ||||
\(779\) | − | 8.19130i | − | 0.293484i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.0343i | 0.824234i | ||||||||
\(782\) | 20.8700 | + | 28.4783i | 0.746310 | + | 1.01838i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.27428 | − | 2.29763i | −0.116938 | − | 0.0820583i | ||||
\(785\) | −10.8073 | −0.385729 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 31.2001i | − | 1.11216i | −0.831128 | − | 0.556082i | \(-0.812304\pi\) | ||
0.831128 | − | 0.556082i | \(-0.187696\pi\) | |||||||
\(788\) | −2.92763 | − | 0.924711i | −0.104292 | − | 0.0329415i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.62774 | − | 6.32275i | 0.306961 | − | 0.224953i | ||||
\(791\) | 12.0599 | 0.428799 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.0819 | −0.890686 | ||||||||
\(794\) | 26.7399 | − | 19.5960i | 0.948962 | − | 0.695437i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.84751 | − | 28.0111i | 0.313592 | − | 0.992828i | ||||
\(797\) | − | 32.2848i | − | 1.14359i | −0.820398 | − | 0.571793i | \(-0.806248\pi\) | ||
0.820398 | − | 0.571793i | \(-0.193752\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.7652 | −1.44217 | ||||||||
\(800\) | 0.555767 | + | 27.0441i | 0.0196493 | + | 0.956155i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13.3776 | − | 18.2545i | −0.472380 | − | 0.644588i | ||||
\(803\) | − | 58.8118i | − | 2.07542i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.91323i | − | 0.0674326i | ||||||
\(806\) | 22.9505 | − | 16.8190i | 0.808396 | − | 0.592425i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.01423 | + | 5.94862i | 0.0708605 | + | 0.209272i | ||||
\(809\) | −8.49629 | −0.298714 | −0.149357 | − | 0.988783i | \(-0.547720\pi\) | ||||
−0.149357 | + | 0.988783i | \(0.547720\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12.3826i | − | 0.434812i | −0.976081 | − | 0.217406i | \(-0.930240\pi\) | ||
0.976081 | − | 0.217406i | \(-0.0697596\pi\) | |||||||
\(812\) | −14.8409 | − | 4.68759i | −0.520812 | − | 0.164502i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 17.9760 | + | 24.5292i | 0.630058 | + | 0.859749i | ||||
\(815\) | 5.62342 | 0.196980 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.58114 | −0.195259 | ||||||||
\(818\) | −13.0128 | − | 17.7566i | −0.454981 | − | 0.620846i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.43056 | + | 1.71528i | 0.189643 | + | 0.0599002i | ||||
\(821\) | 21.8999i | 0.764313i | 0.924098 | + | 0.382156i | \(0.124818\pi\) | ||||
−0.924098 | + | 0.382156i | \(0.875182\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.88321 | −0.0656446 | −0.0328223 | − | 0.999461i | \(-0.510450\pi\) | ||||
−0.0328223 | + | 0.999461i | \(0.510450\pi\) | |||||||
\(824\) | 29.7293 | − | 10.0665i | 1.03567 | − | 0.350683i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.56279 | − | 3.34379i | 0.158760 | − | 0.116345i | ||||
\(827\) | − | 32.8051i | − | 1.14074i | −0.821387 | − | 0.570372i | \(-0.806799\pi\) | ||
0.821387 | − | 0.570372i | \(-0.193201\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.63143i | 0.334513i | 0.985913 | + | 0.167257i | \(0.0534909\pi\) | ||||
−0.985913 | + | 0.167257i | \(0.946509\pi\) | |||||||
\(830\) | 5.37071 | + | 7.32862i | 0.186420 | + | 0.254380i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 22.1771 | + | 28.9930i | 0.768851 | + | 1.00515i | ||||
\(833\) | −6.09565 | −0.211202 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.20907i | 0.145661i | ||||||||
\(836\) | −3.94753 | + | 12.4978i | −0.136528 | + | 0.432247i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.49706 | + | 1.09711i | −0.0517152 | + | 0.0378990i | ||||
\(839\) | 48.0481 | 1.65880 | 0.829402 | − | 0.558652i | \(-0.188681\pi\) | ||||
0.829402 | + | 0.558652i | \(0.188681\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31.5561 | −1.08814 | ||||||||
\(842\) | −4.18242 | + | 3.06504i | −0.144136 | + | 0.105628i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −43.5604 | − | 13.7589i | −1.49941 | − | 0.473600i | ||||
\(845\) | 3.65257i | 0.125652i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.7818 | −0.439187 | ||||||||
\(848\) | −3.08754 | + | 4.39996i | −0.106027 | + | 0.151095i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.3663 | + | 33.2491i | 0.835757 | + | 1.14044i | ||||
\(851\) | 18.0599i | 0.619084i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.44013i | 0.0493090i | 0.999696 | + | 0.0246545i | \(0.00784856\pi\) | ||||
−0.999696 | + | 0.0246545i | \(0.992151\pi\) | |||||||
\(854\) | 6.27048 | − | 4.59526i | 0.214572 | − | 0.157247i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.83327 | + | 8.36748i | 0.0968393 | + | 0.285995i | ||||
\(857\) | −34.9775 | −1.19481 | −0.597404 | − | 0.801941i | \(-0.703801\pi\) | ||||
−0.597404 | + | 0.801941i | \(0.703801\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.45024i | 0.220079i | 0.993927 | + | 0.110040i | \(0.0350978\pi\) | ||||
−0.993927 | + | 0.110040i | \(0.964902\pi\) | |||||||
\(860\) | 1.16871 | − | 3.70011i | 0.0398525 | − | 0.126173i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.7989 | + | 22.9231i | 0.572174 | + | 0.780762i | ||||
\(863\) | 34.4037 | 1.17112 | 0.585559 | − | 0.810630i | \(-0.300875\pi\) | ||||
0.585559 | + | 0.810630i | \(0.300875\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.48112 | 0.152363 | ||||||||
\(866\) | −7.26238 | − | 9.90991i | −0.246786 | − | 0.336752i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.65621 | + | 8.40952i | −0.0901575 | + | 0.285438i | ||||
\(869\) | − | 78.9594i | − | 2.67852i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.9505 | 0.913182 | ||||||||
\(872\) | 9.69501 | + | 28.6322i | 0.328315 | + | 0.969609i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.27807 | + | 4.60082i | −0.212359 | + | 0.155625i | ||||
\(875\) | − | 4.56944i | − | 0.154475i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 40.3826i | − | 1.36362i | −0.731528 | − | 0.681812i | \(-0.761192\pi\) | ||
0.731528 | − | 0.681812i | \(-0.238808\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.45903 | − | 5.23416i | −0.251444 | − | 0.176444i | ||||
\(881\) | −15.8926 | −0.535435 | −0.267718 | − | 0.963497i | \(-0.586269\pi\) | ||||
−0.267718 | + | 0.963497i | \(0.586269\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 25.3113i | − | 0.851792i | −0.904772 | − | 0.425896i | \(-0.859959\pi\) | ||
0.904772 | − | 0.425896i | \(-0.140041\pi\) | |||||||
\(884\) | 53.0433 | + | 16.7541i | 1.78404 | + | 0.563501i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.21312 | − | 3.82038i | 0.175138 | − | 0.128348i | ||||
\(887\) | −19.6352 | −0.659284 | −0.329642 | − | 0.944106i | \(-0.606928\pi\) | ||||
−0.329642 | + | 0.944106i | \(0.606928\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.8789 | 0.633178 | ||||||||
\(890\) | 4.24382 | − | 3.11004i | 0.142253 | − | 0.104249i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.9103 | + | 40.8738i | −0.432268 | + | 1.36856i | ||||
\(893\) | − | 8.98674i | − | 0.300730i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.59359 | −0.120120 | ||||||||
\(896\) | −10.8561 | − | 3.18520i | −0.362676 | − | 0.106410i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.29376 | − | 4.49452i | −0.109914 | − | 0.149984i | ||||
\(899\) | 34.3139i | 1.14443i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.19130i | 0.272892i | ||||||||
\(902\) | 33.9088 | − | 24.8497i | 1.12904 | − | 0.827406i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.3085 | − | 10.9398i | 1.07457 | − | 0.363853i | ||||
\(905\) | −7.12402 | −0.236811 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 4.84241i | − | 0.160790i | −0.996763 | − | 0.0803948i | \(-0.974382\pi\) | ||
0.996763 | − | 0.0803948i | \(-0.0256181\pi\) | |||||||
\(908\) | 55.9111 | + | 17.6599i | 1.85547 | + | 0.586064i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.78178 | − | 2.43134i | −0.0590655 | − | 0.0805981i | ||||
\(911\) | 18.9176 | 0.626768 | 0.313384 | − | 0.949626i | \(-0.398537\pi\) | ||||
0.313384 | + | 0.949626i | \(0.398537\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 67.0702 | 2.21970 | ||||||||
\(914\) | −33.4552 | − | 45.6515i | −1.10660 | − | 1.51002i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −42.9245 | − | 13.5580i | −1.41827 | − | 0.447969i | ||||
\(917\) | − | 4.93428i | − | 0.162944i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.11228 | −0.300586 | −0.150293 | − | 0.988641i | \(-0.548022\pi\) | ||||
−0.150293 | + | 0.988641i | \(0.548022\pi\) | |||||||
\(920\) | −1.73555 | − | 5.12558i | −0.0572193 | − | 0.168985i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 39.4716 | − | 28.9264i | 1.29993 | − | 0.952639i | ||||
\(923\) | 21.5518i | 0.709387i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.0854i | 0.693282i | ||||||||
\(926\) | −0.159919 | − | 0.218217i | −0.00525525 | − | 0.00717107i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −44.0111 | + | 0.904445i | −1.44474 | + | 0.0296899i | ||||
\(929\) | −32.7294 | −1.07382 | −0.536909 | − | 0.843640i | \(-0.680408\pi\) | ||||
−0.536909 | + | 0.843640i | \(0.680408\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.34379i | − | 0.0440411i | ||||||
\(932\) | −0.414190 | + | 1.31132i | −0.0135672 | + | 0.0429537i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.13067 | + | 3.75996i | −0.167881 | + | 0.123030i | ||||
\(935\) | −13.8863 | −0.454131 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.5066 | −0.702591 | −0.351295 | − | 0.936265i | \(-0.614259\pi\) | ||||
−0.351295 | + | 0.936265i | \(0.614259\pi\) | |||||||
\(938\) | −6.73762 | + | 4.93760i | −0.219991 | + | 0.161218i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.95791 | + | 1.88185i | 0.194326 | + | 0.0613791i | ||||
\(941\) | 1.85115i | 0.0603456i | 0.999545 | + | 0.0301728i | \(0.00960577\pi\) | ||||
−0.999545 | + | 0.0301728i | \(0.990394\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.9657 | 0.812994 | ||||||||
\(944\) | 9.19053 | − | 13.0971i | 0.299126 | − | 0.426275i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.9314 | − | 23.1038i | −0.550486 | − | 0.751168i | ||||
\(947\) | − | 45.3353i | − | 1.47320i | −0.676329 | − | 0.736600i | \(-0.736430\pi\) | ||
0.676329 | − | 0.736600i | \(-0.263570\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 55.0266i | − | 1.78624i | ||||||
\(950\) | −7.32981 | + | 5.37158i | −0.237811 | + | 0.174277i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16.3303 | + | 5.52954i | −0.529269 | + | 0.179213i | ||||
\(953\) | −40.5768 | −1.31441 | −0.657206 | − | 0.753711i | \(-0.728262\pi\) | ||||
−0.657206 | + | 0.753711i | \(0.728262\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2.20647i | − | 0.0713997i | ||||||
\(956\) | −5.78246 | + | 18.3072i | −0.187018 | + | 0.592098i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.6008 | − | 25.3818i | −0.600965 | − | 0.820050i | ||||
\(959\) | −19.0103 | −0.613876 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.5561 | −0.372779 | ||||||||
\(962\) | 16.8190 | + | 22.9505i | 0.542268 | + | 0.739953i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.298953 | + | 0.946483i | −0.00962864 | + | 0.0304842i | ||||
\(965\) | − | 10.4349i | − | 0.335911i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.8715 | 0.510392 | 0.255196 | − | 0.966889i | \(-0.417860\pi\) | ||||
0.255196 | + | 0.966889i | \(0.417860\pi\) | |||||||
\(968\) | −34.2426 | + | 11.5947i | −1.10060 | + | 0.372668i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.86268 | − | 5.02925i | 0.220347 | − | 0.161479i | ||||
\(971\) | − | 14.6876i | − | 0.471347i | −0.971832 | − | 0.235674i | \(-0.924270\pi\) | ||
0.971832 | − | 0.235674i | \(-0.0757296\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 10.4380i | − | 0.334627i | ||||||
\(974\) | 1.56201 | + | 2.13145i | 0.0500501 | + | 0.0682961i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.6302 | − | 17.9989i | 0.404284 | − | 0.576131i | ||||
\(977\) | 21.2437 | 0.679647 | 0.339824 | − | 0.940489i | \(-0.389633\pi\) | ||||
0.339824 | + | 0.940489i | \(0.389633\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 38.8387i | − | 1.24129i | ||||||
\(980\) | 0.890891 | + | 0.281394i | 0.0284585 | + | 0.00898881i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 20.1189 | − | 14.7440i | 0.642021 | − | 0.470499i | ||||
\(983\) | −11.8265 | −0.377206 | −0.188603 | − | 0.982053i | \(-0.560396\pi\) | ||||
−0.188603 | + | 0.982053i | \(0.560396\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.717101 | 0.0228487 | ||||||||
\(986\) | −54.1090 | + | 39.6532i | −1.72318 | + | 1.26282i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.69346 | + | 11.6935i | −0.117505 | + | 0.372019i | ||||
\(989\) | − | 17.0103i | − | 0.540897i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.9387 | 0.919269 | 0.459635 | − | 0.888108i | \(-0.347980\pi\) | ||||
0.459635 | + | 0.888108i | \(0.347980\pi\) | |||||||
\(992\) | 0.512500 | + | 24.9387i | 0.0162719 | + | 0.791806i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.94851 | − | 5.38795i | −0.125239 | − | 0.170896i | ||||
\(995\) | 6.86112i | 0.217512i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.0548i | 1.77527i | 0.460546 | + | 0.887636i | \(0.347654\pi\) | ||||
−0.460546 | + | 0.887636i | \(0.652346\pi\) | |||||||
\(998\) | 24.6224 | − | 18.0443i | 0.779408 | − | 0.571181i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.c.f.253.3 | 8 | ||
3.2 | odd | 2 | 168.2.c.b.85.6 | yes | 8 | ||
4.3 | odd | 2 | 2016.2.c.e.1009.4 | 8 | |||
8.3 | odd | 2 | 2016.2.c.e.1009.5 | 8 | |||
8.5 | even | 2 | inner | 504.2.c.f.253.4 | 8 | ||
12.11 | even | 2 | 672.2.c.b.337.2 | 8 | |||
21.20 | even | 2 | 1176.2.c.c.589.6 | 8 | |||
24.5 | odd | 2 | 168.2.c.b.85.5 | ✓ | 8 | ||
24.11 | even | 2 | 672.2.c.b.337.7 | 8 | |||
48.5 | odd | 4 | 5376.2.a.bp.1.3 | 4 | |||
48.11 | even | 4 | 5376.2.a.bl.1.3 | 4 | |||
48.29 | odd | 4 | 5376.2.a.bm.1.2 | 4 | |||
48.35 | even | 4 | 5376.2.a.bq.1.2 | 4 | |||
84.83 | odd | 2 | 4704.2.c.c.2353.7 | 8 | |||
168.83 | odd | 2 | 4704.2.c.c.2353.2 | 8 | |||
168.125 | even | 2 | 1176.2.c.c.589.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.c.b.85.5 | ✓ | 8 | 24.5 | odd | 2 | ||
168.2.c.b.85.6 | yes | 8 | 3.2 | odd | 2 | ||
504.2.c.f.253.3 | 8 | 1.1 | even | 1 | trivial | ||
504.2.c.f.253.4 | 8 | 8.5 | even | 2 | inner | ||
672.2.c.b.337.2 | 8 | 12.11 | even | 2 | |||
672.2.c.b.337.7 | 8 | 24.11 | even | 2 | |||
1176.2.c.c.589.5 | 8 | 168.125 | even | 2 | |||
1176.2.c.c.589.6 | 8 | 21.20 | even | 2 | |||
2016.2.c.e.1009.4 | 8 | 4.3 | odd | 2 | |||
2016.2.c.e.1009.5 | 8 | 8.3 | odd | 2 | |||
4704.2.c.c.2353.2 | 8 | 168.83 | odd | 2 | |||
4704.2.c.c.2353.7 | 8 | 84.83 | odd | 2 | |||
5376.2.a.bl.1.3 | 4 | 48.11 | even | 4 | |||
5376.2.a.bm.1.2 | 4 | 48.29 | odd | 4 | |||
5376.2.a.bp.1.3 | 4 | 48.5 | odd | 4 | |||
5376.2.a.bq.1.2 | 4 | 48.35 | even | 4 |