Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,2,Mod(589,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, 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("1176.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.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: | \(9.39040727770\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 589.5 | ||
Root | \(-0.835949 + 1.14070i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.589 |
Dual form | 1176.2.c.c.589.6 |
$q$-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 \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).
\(n\) | \(295\) | \(589\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −0.602380 | − | 1.90713i | −0.301190 | − | 0.953564i | ||||
\(5\) | 0.467138i | 0.208910i | 0.994530 | + | 0.104455i | \(0.0333099\pi\) | ||||
−0.994530 | + | 0.104455i | \(0.966690\pi\) | |||||||
\(6\) | 1.14070 | + | 0.835949i | 0.465688 | + | 0.341275i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.67901 | − | 0.907128i | −0.947175 | − | 0.320718i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.532862 | + | 0.390503i | 0.168506 | + | 0.123488i | ||||
\(11\) | 4.87666i | 1.47037i | 0.677868 | + | 0.735184i | \(0.262904\pi\) | ||||
−0.677868 | + | 0.735184i | \(0.737096\pi\) | |||||||
\(12\) | 1.90713 | − | 0.602380i | 0.550541 | − | 0.173892i | ||||
\(13\) | 4.56279i | 1.26549i | 0.774360 | + | 0.632745i | \(0.218072\pi\) | ||||
−0.774360 | + | 0.632745i | \(0.781928\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.467138 | −0.120614 | ||||||||
\(16\) | −3.27428 | + | 2.29763i | −0.818569 | + | 0.574408i | ||||
\(17\) | −6.09565 | −1.47841 | −0.739206 | − | 0.673479i | \(-0.764799\pi\) | ||||
−0.739206 | + | 0.673479i | \(0.764799\pi\) | |||||||
\(18\) | −0.835949 | + | 1.14070i | −0.197035 | + | 0.268865i | ||||
\(19\) | − | 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 | \(-0.640430\pi\) | ||||
−0.427001 | + | 0.904251i | \(0.640430\pi\) | |||||||
\(24\) | 0.907128 | − | 2.67901i | 0.185167 | − | 0.546852i | ||||
\(25\) | 4.78178 | 0.956357 | ||||||||
\(26\) | 5.20476 | + | 3.81426i | 1.02074 | + | 0.748037i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.78178i | 1.44504i | 0.691350 | + | 0.722520i | \(0.257016\pi\) | ||||
−0.691350 | + | 0.722520i | \(0.742984\pi\) | |||||||
\(30\) | −0.390503 | + | 0.532862i | −0.0712958 | + | 0.0972869i | ||||
\(31\) | −4.40952 | −0.791973 | −0.395987 | − | 0.918256i | \(-0.629597\pi\) | ||||
−0.395987 | + | 0.918256i | \(0.629597\pi\) | |||||||
\(32\) | −0.116226 | + | 5.65566i | −0.0205460 | + | 0.999789i | ||||
\(33\) | −4.87666 | −0.848917 | ||||||||
\(34\) | −5.09565 | + | 6.95329i | −0.873897 | + | 1.19248i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.602380 | + | 1.90713i | 0.100397 | + | 0.317855i | ||||
\(37\) | − | 4.40952i | − | 0.724921i | −0.931999 | − | 0.362460i | \(-0.881937\pi\) | ||
0.931999 | − | 0.362460i | \(-0.118063\pi\) | |||||||
\(38\) | −1.53286 | − | 1.12334i | −0.248663 | − | 0.182230i | ||||
\(39\) | −4.56279 | −0.730631 | ||||||||
\(40\) | 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 | \(0.102569\pi\) | ||||
−0.948531 | + | 0.316684i | \(0.897431\pi\) | |||||||
\(44\) | 9.30041 | − | 2.93760i | 1.40209 | − | 0.442860i | ||||
\(45\) | − | 0.467138i | − | 0.0696368i | ||||||
\(46\) | −3.42375 | + | 4.67190i | −0.504805 | + | 0.688834i | ||||
\(47\) | 6.68759 | 0.975485 | 0.487743 | − | 0.872988i | \(-0.337820\pi\) | ||||
0.487743 | + | 0.872988i | \(0.337820\pi\) | |||||||
\(48\) | −2.29763 | − | 3.27428i | −0.331635 | − | 0.472601i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.99732 | − | 5.45457i | 0.565307 | − | 0.771392i | ||||
\(51\) | − | 6.09565i | − | 0.853562i | ||||||
\(52\) | 8.70182 | − | 2.74853i | 1.20673 | − | 0.381153i | ||||
\(53\) | − | 1.34379i | − | 0.184584i | −0.995732 | − | 0.0922922i | \(-0.970581\pi\) | ||
0.995732 | − | 0.0922922i | \(-0.0294194\pi\) | |||||||
\(54\) | −1.14070 | − | 0.835949i | −0.155229 | − | 0.113758i | ||||
\(55\) | −2.27807 | −0.307175 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.34379 | 0.177990 | ||||||||
\(58\) | 8.87666 | + | 6.50517i | 1.16556 | + | 0.854171i | ||||
\(59\) | − | 4.00000i | − | 0.520756i | −0.965507 | − | 0.260378i | \(-0.916153\pi\) | ||
0.965507 | − | 0.260378i | \(-0.0838471\pi\) | |||||||
\(60\) | 0.281394 | + | 0.890891i | 0.0363278 | + | 0.115014i | ||||
\(61\) | 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 | ||||||||
\(66\) | −4.07663 | + | 5.56279i | −0.501799 | + | 0.684732i | ||||
\(67\) | 5.90658i | 0.721604i | 0.932642 | + | 0.360802i | \(0.117497\pi\) | ||||
−0.932642 | + | 0.360802i | \(0.882503\pi\) | |||||||
\(68\) | 3.67190 | + | 11.6252i | 0.445283 | + | 1.40976i | ||||
\(69\) | − | 4.09565i | − | 0.493058i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.72339 | −0.560563 | −0.280281 | − | 0.959918i | \(-0.590428\pi\) | ||||
−0.280281 | + | 0.959918i | \(0.590428\pi\) | |||||||
\(72\) | 2.67901 | + | 0.907128i | 0.315725 | + | 0.106906i | ||||
\(73\) | 12.0599 | 1.41150 | 0.705749 | − | 0.708462i | \(-0.250610\pi\) | ||||
0.705749 | + | 0.708462i | \(0.250610\pi\) | |||||||
\(74\) | −5.02993 | − | 3.68613i | −0.584717 | − | 0.428504i | ||||
\(75\) | 4.78178i | 0.552153i | ||||||||
\(76\) | −2.56279 | + | 0.809475i | −0.293972 | + | 0.0928531i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.81426 | + | 5.20476i | −0.431880 | + | 0.589323i | ||||
\(79\) | −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 | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.09565 | − | 6.95329i | 0.562721 | − | 0.767863i | ||||
\(83\) | 13.7533i | 1.50962i | 0.655942 | + | 0.754811i | \(0.272272\pi\) | ||||
−0.655942 | + | 0.754811i | \(0.727728\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.84751i | − | 0.308856i | ||||||
\(86\) | 4.73762 | + | 3.47192i | 0.510871 | + | 0.374387i | ||||
\(87\) | −7.78178 | −0.834295 | ||||||||
\(88\) | 4.42375 | − | 13.0646i | 0.471574 | − | 1.39269i | ||||
\(89\) | −7.96420 | −0.844204 | −0.422102 | − | 0.906548i | \(-0.638708\pi\) | ||||
−0.422102 | + | 0.906548i | \(0.638708\pi\) | |||||||
\(90\) | −0.532862 | − | 0.390503i | −0.0561686 | − | 0.0411626i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.46714 | + | 7.81093i | 0.257217 | + | 0.814346i | ||||
\(93\) | − | 4.40952i | − | 0.457246i | ||||||
\(94\) | 5.59048 | − | 7.62851i | 0.576614 | − | 0.786821i | ||||
\(95\) | 0.627737 | 0.0644044 | ||||||||
\(96\) | −5.65566 | − | 0.116226i | −0.577228 | − | 0.0118623i | ||||
\(97\) | 12.8789 | 1.30765 | 0.653827 | − | 0.756644i | \(-0.273163\pi\) | ||||
0.653827 | + | 0.756644i | \(0.273163\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.87666i | − | 0.490122i | ||||||
\(100\) | −2.88045 | − | 9.11947i | −0.288045 | − | 0.911947i | ||||
\(101\) | − | 2.22045i | − | 0.220943i | −0.993879 | − | 0.110472i | \(-0.964764\pi\) | ||
0.993879 | − | 0.110472i | \(-0.0352361\pi\) | |||||||
\(102\) | −6.95329 | − | 5.09565i | −0.688478 | − | 0.504545i | ||||
\(103\) | −11.0971 | −1.09343 | −0.546715 | − | 0.837319i | \(-0.684122\pi\) | ||||
−0.546715 | + | 0.837319i | \(0.684122\pi\) | |||||||
\(104\) | 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 | \(0.951760\pi\) | |||||||
\(108\) | −1.90713 | + | 0.602380i | −0.183514 | + | 0.0579640i | ||||
\(109\) | − | 10.6876i | − | 1.02369i | −0.859079 | − | 0.511843i | \(-0.828963\pi\) | ||
0.859079 | − | 0.511843i | \(-0.171037\pi\) | |||||||
\(110\) | −1.90435 | + | 2.59859i | −0.181573 | + | 0.247766i | ||||
\(111\) | 4.40952 | 0.418533 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0599 | −1.13450 | −0.567248 | − | 0.823547i | \(-0.691992\pi\) | ||||
−0.567248 | + | 0.823547i | \(0.691992\pi\) | |||||||
\(114\) | 1.12334 | − | 1.53286i | 0.105211 | − | 0.143566i | ||||
\(115\) | − | 1.91323i | − | 0.178410i | ||||||
\(116\) | 14.8409 | − | 4.68759i | 1.37794 | − | 0.435232i | ||||
\(117\) | − | 4.56279i | − | 0.421830i | ||||||
\(118\) | −4.56279 | − | 3.34379i | −0.420039 | − | 0.307821i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.25147 | + | 0.423754i | 0.114243 | + | 0.0386832i | ||||
\(121\) | −12.7818 | −1.16198 | ||||||||
\(122\) | 6.27048 | + | 4.59526i | 0.567703 | + | 0.416036i | ||||
\(123\) | 6.09565i | 0.549626i | ||||||||
\(124\) | 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 | ||||
\(129\) | −4.15327 | −0.365675 | ||||||||
\(130\) | −1.78178 | + | 2.43134i | −0.156273 | + | 0.213243i | ||||
\(131\) | 4.93428i | 0.431110i | 0.976492 | + | 0.215555i | \(0.0691560\pi\) | ||||
−0.976492 | + | 0.215555i | \(0.930844\pi\) | |||||||
\(132\) | 2.93760 | + | 9.30041i | 0.255685 | + | 0.809497i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.73762 | + | 4.93760i | 0.582042 | + | 0.426544i | ||||
\(135\) | 0.467138 | 0.0402048 | ||||||||
\(136\) | 16.3303 | + | 5.52954i | 1.40031 | + | 0.474154i | ||||
\(137\) | 19.0103 | 1.62416 | 0.812082 | − | 0.583544i | \(-0.198334\pi\) | ||||
0.812082 | + | 0.583544i | \(0.198334\pi\) | |||||||
\(138\) | −4.67190 | − | 3.42375i | −0.397698 | − | 0.291449i | ||||
\(139\) | − | 10.4380i | − | 0.885339i | −0.896685 | − | 0.442669i | \(-0.854032\pi\) | ||
0.896685 | − | 0.442669i | \(-0.145968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.68759i | 0.563197i | ||||||||
\(142\) | −3.94851 | + | 5.38795i | −0.331352 | + | 0.452147i | ||||
\(143\) | −22.2512 | −1.86073 | ||||||||
\(144\) | 3.27428 | − | 2.29763i | 0.272856 | − | 0.191469i | ||||
\(145\) | −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 | \(0.912100\pi\) | |||||||
\(150\) | 5.45457 | + | 3.99732i | 0.445363 | + | 0.326380i | ||||
\(151\) | −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 | ||||
\(153\) | 6.09565 | 0.492804 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.05985i | − | 0.165451i | ||||||
\(156\) | 2.74853 | + | 8.70182i | 0.220059 | + | 0.696703i | ||||
\(157\) | − | 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 | ||||
\(159\) | 1.34379 | 0.106570 | ||||||||
\(160\) | −2.64197 | − | 0.0542935i | −0.208866 | − | 0.00429228i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.835949 | − | 1.14070i | 0.0656783 | − | 0.0896216i | ||||
\(163\) | − | 12.0380i | − | 0.942891i | −0.881895 | − | 0.471446i | \(-0.843732\pi\) | ||
0.881895 | − | 0.471446i | \(-0.156268\pi\) | |||||||
\(164\) | −3.67190 | − | 11.6252i | −0.286727 | − | 0.907775i | ||||
\(165\) | − | 2.27807i | − | 0.177347i | ||||||
\(166\) | 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 | ||||
\(171\) | 1.34379i | 0.102763i | ||||||||
\(172\) | 7.92082 | − | 2.50185i | 0.603957 | − | 0.190764i | ||||
\(173\) | − | 9.59271i | − | 0.729321i | −0.931141 | − | 0.364660i | \(-0.881185\pi\) | ||
0.931141 | − | 0.364660i | \(-0.118815\pi\) | |||||||
\(174\) | −6.50517 | + | 8.87666i | −0.493156 | + | 0.672938i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.2048 | − | 15.9675i | −0.844591 | − | 1.20360i | ||||
\(177\) | 4.00000 | 0.300658 | ||||||||
\(178\) | −6.65766 | + | 9.08474i | −0.499013 | + | 0.680930i | ||||
\(179\) | − | 7.69278i | − | 0.574985i | −0.957783 | − | 0.287493i | \(-0.907178\pi\) | ||
0.957783 | − | 0.287493i | \(-0.0928217\pi\) | |||||||
\(180\) | −0.890891 | + | 0.281394i | −0.0664031 | + | 0.0209739i | ||||
\(181\) | − | 15.2504i | − | 1.13355i | −0.823872 | − | 0.566776i | \(-0.808191\pi\) | ||
0.823872 | − | 0.566776i | \(-0.191809\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.49706 | −0.406355 | ||||||||
\(184\) | 10.9723 | + | 3.71528i | 0.808889 | + | 0.273894i | ||||
\(185\) | 2.05985 | 0.151443 | ||||||||
\(186\) | −5.02993 | − | 3.68613i | −0.368812 | − | 0.270280i | ||||
\(187\) | − | 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 | \(-0.554663\pi\) | ||||
−0.170886 | + | 0.985291i | \(0.554663\pi\) | |||||||
\(192\) | −4.86042 | + | 6.35424i | −0.350771 | + | 0.458578i | ||||
\(193\) | 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 | ||||
\(195\) | − | 2.13145i | − | 0.152636i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.53510i | 0.109371i | 0.998504 | + | 0.0546855i | \(0.0174156\pi\) | ||||
−0.998504 | + | 0.0546855i | \(0.982584\pi\) | |||||||
\(198\) | −5.56279 | − | 4.07663i | −0.395330 | − | 0.289714i | ||||
\(199\) | 14.6876 | 1.04118 | 0.520588 | − | 0.853808i | \(-0.325713\pi\) | ||||
0.520588 | + | 0.853808i | \(0.325713\pi\) | |||||||
\(200\) | −12.8105 | − | 4.33769i | −0.905837 | − | 0.306721i | ||||
\(201\) | −5.90658 | −0.416618 | ||||||||
\(202\) | −2.53286 | − | 1.85618i | −0.178212 | − | 0.130601i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −11.6252 | + | 3.67190i | −0.813926 | + | 0.257084i | ||||
\(205\) | 2.84751i | 0.198879i | ||||||||
\(206\) | −9.27661 | + | 12.6584i | −0.646332 | + | 0.881955i | ||||
\(207\) | 4.09565 | 0.284667 | ||||||||
\(208\) | −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 | \(-0.712038\pi\) | ||
0.617953 | − | 0.786215i | \(-0.287962\pi\) | |||||||
\(212\) | −2.56279 | + | 0.809475i | −0.176013 | + | 0.0555949i | ||||
\(213\) | − | 4.72339i | − | 0.323641i | ||||||
\(214\) | 3.56279 | + | 2.61095i | 0.243547 | + | 0.178481i | ||||
\(215\) | −1.94015 | −0.132317 | ||||||||
\(216\) | −0.907128 | + | 2.67901i | −0.0617223 | + | 0.182284i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −12.1913 | − | 8.93428i | −0.825699 | − | 0.605105i | ||||
\(219\) | 12.0599i | 0.814929i | ||||||||
\(220\) | 1.37226 | + | 4.34457i | 0.0925180 | + | 0.292911i | ||||
\(221\) | − | 27.8132i | − | 1.87092i | ||||||
\(222\) | 3.68613 | − | 5.02993i | 0.247397 | − | 0.337587i | ||||
\(223\) | −21.4321 | −1.43520 | −0.717600 | − | 0.696455i | \(-0.754760\pi\) | ||||
−0.717600 | + | 0.696455i | \(0.754760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.78178 | −0.318786 | ||||||||
\(226\) | −10.0814 | + | 13.7566i | −0.670606 | + | 0.915078i | ||||
\(227\) | 29.3169i | 1.94583i | 0.231164 | + | 0.972915i | \(0.425747\pi\) | ||||
−0.231164 | + | 0.972915i | \(0.574253\pi\) | |||||||
\(228\) | −0.809475 | − | 2.56279i | −0.0536088 | − | 0.169725i | ||||
\(229\) | 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 | \(-0.507170\pi\) | ||||
−0.0225227 | + | 0.999746i | \(0.507170\pi\) | |||||||
\(234\) | −5.20476 | − | 3.81426i | −0.340246 | − | 0.249346i | ||||
\(235\) | 3.12402i | 0.203789i | ||||||||
\(236\) | −7.62851 | + | 2.40952i | −0.496574 | + | 0.156846i | ||||
\(237\) | − | 16.1913i | − | 1.05174i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.59936 | −0.620931 | −0.310466 | − | 0.950585i | \(-0.600485\pi\) | ||||
−0.310466 | + | 0.950585i | \(0.600485\pi\) | |||||||
\(240\) | 1.52954 | − | 1.07331i | 0.0987312 | − | 0.0692819i | ||||
\(241\) | −0.496287 | −0.0319687 | −0.0159843 | − | 0.999872i | \(-0.505088\pi\) | ||||
−0.0159843 | + | 0.999872i | \(0.505088\pi\) | |||||||
\(242\) | −10.6849 | + | 14.5801i | −0.686852 | + | 0.937247i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 10.4836 | − | 3.31132i | 0.671144 | − | 0.211986i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.95329 | + | 5.09565i | 0.443326 | + | 0.324887i | ||||
\(247\) | 6.13145 | 0.390135 | ||||||||
\(248\) | 11.8132 | + | 4.00000i | 0.750137 | + | 0.254000i | ||||
\(249\) | −13.7533 | −0.871581 | ||||||||
\(250\) | 5.21234 | + | 3.81982i | 0.329658 | + | 0.241586i | ||||
\(251\) | 22.1359i | 1.39721i | 0.715509 | + | 0.698603i | \(0.246195\pi\) | ||||
−0.715509 | + | 0.698603i | \(0.753805\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 19.9731i | − | 1.25570i | ||||||
\(254\) | 15.7818 | − | 21.5351i | 0.990237 | − | 1.35123i | ||||
\(255\) | 2.84751 | 0.178318 | ||||||||
\(256\) | 5.44178 | − | 15.0462i | 0.340111 | − | 0.940385i | ||||
\(257\) | −2.28695 | −0.142656 | −0.0713281 | − | 0.997453i | \(-0.522724\pi\) | ||||
−0.0713281 | + | 0.997453i | \(0.522724\pi\) | |||||||
\(258\) | −3.47192 | + | 4.73762i | −0.216152 | + | 0.294951i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.28394 | + | 4.06495i | 0.0796267 | + | 0.252097i | ||||
\(261\) | − | 7.78178i | − | 0.481680i | ||||||
\(262\) | 5.62851 | + | 4.12480i | 0.347731 | + | 0.254831i | ||||
\(263\) | −30.1555 | −1.85947 | −0.929734 | − | 0.368232i | \(-0.879963\pi\) | ||||
−0.929734 | + | 0.368232i | \(0.879963\pi\) | |||||||
\(264\) | 13.0646 | + | 4.42375i | 0.804073 | + | 0.272263i | ||||
\(265\) | 0.627737 | 0.0385616 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 7.96420i | − | 0.487401i | ||||||
\(268\) | 11.2646 | − | 3.55801i | 0.688096 | − | 0.217340i | ||||
\(269\) | 9.47748i | 0.577852i | 0.957351 | + | 0.288926i | \(0.0932982\pi\) | ||||
−0.957351 | + | 0.288926i | \(0.906702\pi\) | |||||||
\(270\) | 0.390503 | − | 0.532862i | 0.0237653 | − | 0.0324290i | ||||
\(271\) | 13.2855 | 0.807036 | 0.403518 | − | 0.914972i | \(-0.367787\pi\) | ||||
0.403518 | + | 0.914972i | \(0.367787\pi\) | |||||||
\(272\) | 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 | ||||||||
\(276\) | −7.81093 | + | 2.46714i | −0.470163 | + | 0.148504i | ||||
\(277\) | 26.8475i | 1.61311i | 0.591159 | + | 0.806555i | \(0.298671\pi\) | ||||
−0.591159 | + | 0.806555i | \(0.701329\pi\) | |||||||
\(278\) | −11.9066 | − | 8.72562i | −0.714109 | − | 0.523328i | ||||
\(279\) | 4.40952 | 0.263991 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.8686 | 0.708018 | 0.354009 | − | 0.935242i | \(-0.384818\pi\) | ||||
0.354009 | + | 0.935242i | \(0.384818\pi\) | |||||||
\(282\) | 7.62851 | + | 5.59048i | 0.454271 | + | 0.332908i | ||||
\(283\) | 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 | ||||
\(285\) | 0.627737i | 0.0371839i | ||||||||
\(286\) | −18.6008 | + | 25.3818i | −1.09989 | + | 1.50086i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.116226 | − | 5.65566i | 0.00684868 | − | 0.333263i | ||||
\(289\) | 20.1570 | 1.18570 | ||||||||
\(290\) | −3.03881 | + | 4.14662i | −0.178445 | + | 0.243498i | ||||
\(291\) | 12.8789i | 0.754974i | ||||||||
\(292\) | −7.26461 | − | 22.9997i | −0.425129 | − | 1.34595i | ||||
\(293\) | 22.7899i | 1.33140i | 0.746220 | + | 0.665700i | \(0.231867\pi\) | ||||
−0.746220 | + | 0.665700i | \(0.768133\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.86855 | 0.108791 | ||||||||
\(296\) | −4.00000 | + | 11.8132i | −0.232495 | + | 0.686626i | ||||
\(297\) | 4.87666 | 0.282972 | ||||||||
\(298\) | 7.59271 | + | 5.56425i | 0.439834 | + | 0.322328i | ||||
\(299\) | − | 18.6876i | − | 1.08073i | ||||||
\(300\) | 9.11947 | − | 2.88045i | 0.526513 | − | 0.166303i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.24669 | + | 3.06572i | −0.129282 | + | 0.176413i | ||||
\(303\) | 2.22045 | 0.127562 | ||||||||
\(304\) | 3.08754 | + | 4.39996i | 0.177083 | + | 0.252355i | ||||
\(305\) | −2.56788 | −0.147037 | ||||||||
\(306\) | 5.09565 | − | 6.95329i | 0.291299 | − | 0.397493i | ||||
\(307\) | 9.34379i | 0.533279i | 0.963796 | + | 0.266639i | \(0.0859132\pi\) | ||||
−0.963796 | + | 0.266639i | \(0.914087\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 11.0971i | − | 0.631292i | ||||||
\(310\) | −2.34967 | − | 1.72193i | −0.133452 | − | 0.0977991i | ||||
\(311\) | −6.68759 | −0.379218 | −0.189609 | − | 0.981860i | \(-0.560722\pi\) | ||||
−0.189609 | + | 0.981860i | \(0.560722\pi\) | |||||||
\(312\) | 12.2238 | + | 4.13903i | 0.692035 | + | 0.234327i | ||||
\(313\) | 15.6381 | 0.883916 | 0.441958 | − | 0.897036i | \(-0.354284\pi\) | ||||
0.441958 | + | 0.897036i | \(0.354284\pi\) | |||||||
\(314\) | −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 | \(-0.0845139\pi\) | |||||||
\(318\) | 1.12334 | − | 1.53286i | 0.0629940 | − | 0.0859587i | ||||
\(319\) | −37.9491 | −2.12474 | ||||||||
\(320\) | −2.27048 | + | 2.96830i | −0.126924 | + | 0.165933i | ||||
\(321\) | −3.12334 | −0.174328 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.19130i | 0.455776i | ||||||||
\(324\) | −0.602380 | − | 1.90713i | −0.0334655 | − | 0.105952i | ||||
\(325\) | 21.8183i | 1.21026i | ||||||||
\(326\) | −13.7317 | − | 10.0632i | −0.760531 | − | 0.557348i | ||||
\(327\) | 10.6876 | 0.591025 | ||||||||
\(328\) | −16.3303 | − | 5.52954i | −0.901692 | − | 0.305318i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.59859 | − | 1.90435i | −0.143048 | − | 0.104831i | ||||
\(331\) | 5.40874i | 0.297291i | 0.988891 | + | 0.148646i | \(0.0474914\pi\) | ||||
−0.988891 | + | 0.148646i | \(0.952509\pi\) | |||||||
\(332\) | 26.2293 | − | 8.28472i | 1.43952 | − | 0.454683i | ||||
\(333\) | 4.40952i | 0.241640i | ||||||||
\(334\) | −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 | ||||
\(339\) | − | 12.0599i | − | 0.655001i | ||||||
\(340\) | −5.43056 | + | 1.71528i | −0.294514 | + | 0.0930242i | ||||
\(341\) | − | 21.5037i | − | 1.16449i | ||||||
\(342\) | 1.53286 | + | 1.12334i | 0.0828877 | + | 0.0607434i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.76755 | − | 11.1267i | 0.203133 | − | 0.599910i | ||||
\(345\) | 1.91323 | 0.103005 | ||||||||
\(346\) | −10.9424 | − | 8.01902i | −0.588266 | − | 0.431105i | ||||
\(347\) | 24.9964i | 1.34187i | 0.741514 | + | 0.670937i | \(0.234108\pi\) | ||||
−0.741514 | + | 0.670937i | \(0.765892\pi\) | |||||||
\(348\) | 4.68759 | + | 14.8409i | 0.251281 | + | 0.795553i | ||||
\(349\) | − | 27.1921i | − | 1.45556i | −0.685811 | − | 0.727779i | \(-0.740553\pi\) | ||
0.685811 | − | 0.727779i | \(-0.259447\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.56279 | 0.243544 | ||||||||
\(352\) | −27.5807 | − | 0.566794i | −1.47006 | − | 0.0302102i | ||||
\(353\) | 30.2870 | 1.61201 | 0.806006 | − | 0.591907i | \(-0.201625\pi\) | ||||
0.806006 | + | 0.591907i | \(0.201625\pi\) | |||||||
\(354\) | 3.34379 | − | 4.56279i | 0.177721 | − | 0.242509i | ||||
\(355\) | − | 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 | \(-0.444345\pi\) | ||||
0.173955 | + | 0.984754i | \(0.444345\pi\) | |||||||
\(360\) | −0.423754 | + | 1.25147i | −0.0223338 | + | 0.0659582i | ||||
\(361\) | 17.1942 | 0.904959 | ||||||||
\(362\) | −17.3961 | − | 12.7485i | −0.914317 | − | 0.670048i | ||||
\(363\) | − | 12.7818i | − | 0.670870i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.63361i | 0.294877i | ||||||||
\(366\) | −4.59526 | + | 6.27048i | −0.240198 | + | 0.327763i | ||||
\(367\) | 6.68759 | 0.349089 | 0.174545 | − | 0.984649i | \(-0.444155\pi\) | ||||
0.174545 | + | 0.984649i | \(0.444155\pi\) | |||||||
\(368\) | 13.4103 | − | 9.41030i | 0.699060 | − | 0.490546i | ||||
\(369\) | −6.09565 | −0.317327 | ||||||||
\(370\) | 1.72193 | − | 2.34967i | 0.0895189 | − | 0.122153i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.40952 | + | 2.65621i | −0.436013 | + | 0.137718i | ||||
\(373\) | 17.1256i | 0.886729i | 0.896341 | + | 0.443364i | \(0.146215\pi\) | ||||
−0.896341 | + | 0.443364i | \(0.853785\pi\) | |||||||
\(374\) | −33.9088 | − | 24.8497i | −1.75338 | − | 1.28495i | ||||
\(375\) | −4.56944 | −0.235965 | ||||||||
\(376\) | −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 | \(0.141188\pi\) | ||||
−0.903232 | + | 0.429152i | \(0.858812\pi\) | |||||||
\(380\) | −0.378136 | − | 1.19717i | −0.0193980 | − | 0.0614138i | ||||
\(381\) | 18.8789i | 0.967195i | ||||||||
\(382\) | −3.94851 | + | 5.38795i | −0.202023 | + | 0.275672i | ||||
\(383\) | 9.94015 | 0.507918 | 0.253959 | − | 0.967215i | \(-0.418267\pi\) | ||||
0.253959 | + | 0.967215i | \(0.418267\pi\) | |||||||
\(384\) | 3.18520 | + | 10.8561i | 0.162544 | + | 0.553997i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.6734 | − | 25.4808i | 0.950449 | − | 1.29694i | ||||
\(387\) | − | 4.15327i | − | 0.211123i | ||||||
\(388\) | −7.75798 | − | 24.5617i | −0.393852 | − | 1.24693i | ||||
\(389\) | − | 19.2884i | − | 0.977961i | −0.872295 | − | 0.488981i | \(-0.837369\pi\) | ||
0.872295 | − | 0.488981i | \(-0.162631\pi\) | |||||||
\(390\) | −2.43134 | − | 1.78178i | −0.123116 | − | 0.0902241i | ||||
\(391\) | 24.9657 | 1.26257 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.93428 | −0.248901 | ||||||||
\(394\) | 1.75108 | + | 1.28326i | 0.0882181 | + | 0.0646498i | ||||
\(395\) | − | 7.56357i | − | 0.380564i | ||||||
\(396\) | −9.30041 | + | 2.93760i | −0.467363 | + | 0.147620i | ||||
\(397\) | 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 | \(-0.630842\pi\) | ||||
−0.399574 | + | 0.916701i | \(0.630842\pi\) | |||||||
\(402\) | −4.93760 | + | 6.73762i | −0.246265 | + | 0.336042i | ||||
\(403\) | − | 20.1197i | − | 1.00223i | ||||||
\(404\) | −4.23469 | + | 1.33756i | −0.210683 | + | 0.0665459i | ||||
\(405\) | 0.467138i | 0.0232123i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.5037 | 1.06590 | ||||||||
\(408\) | −5.52954 | + | 16.3303i | −0.273753 | + | 0.808472i | ||||
\(409\) | −15.5665 | −0.769713 | −0.384856 | − | 0.922976i | \(-0.625749\pi\) | ||||
−0.384856 | + | 0.922976i | \(0.625749\pi\) | |||||||
\(410\) | 3.24814 | + | 2.38037i | 0.160414 | + | 0.117558i | ||||
\(411\) | 19.0103i | 0.937711i | ||||||||
\(412\) | 6.68467 | + | 21.1636i | 0.329330 | + | 1.04266i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.42375 | − | 4.67190i | 0.168268 | − | 0.229611i | ||||
\(415\) | −6.42469 | −0.315376 | ||||||||
\(416\) | −25.8056 | − | 0.530314i | −1.26522 | − | 0.0260008i | ||||
\(417\) | 10.4380 | 0.511150 | ||||||||
\(418\) | 5.47816 | − | 7.47524i | 0.267946 | − | 0.365626i | ||||
\(419\) | 1.31241i | 0.0641155i | 0.999486 | + | 0.0320577i | \(0.0102060\pi\) | ||||
−0.999486 | + | 0.0320577i | \(0.989794\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.66655i | 0.178697i | 0.996000 | + | 0.0893483i | \(0.0284784\pi\) | ||||
−0.996000 | + | 0.0893483i | \(0.971522\pi\) | |||||||
\(422\) | −26.0545 | − | 19.0938i | −1.26831 | − | 0.929471i | ||||
\(423\) | −6.68759 | −0.325162 | ||||||||
\(424\) | −1.21899 | + | 3.60004i | −0.0591996 | + | 0.174834i | ||||
\(425\) | −29.1481 | −1.41389 | ||||||||
\(426\) | −5.38795 | − | 3.94851i | −0.261047 | − | 0.191306i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.95662 | − | 1.88144i | 0.287924 | − | 0.0909428i | ||||
\(429\) | − | 22.2512i | − | 1.07430i | ||||||
\(430\) | −1.62186 | + | 2.21312i | −0.0782132 | + | 0.106726i | ||||
\(431\) | 20.0957 | 0.967973 | 0.483987 | − | 0.875075i | \(-0.339188\pi\) | ||||
0.483987 | + | 0.875075i | \(0.339188\pi\) | |||||||
\(432\) | 2.29763 | + | 3.27428i | 0.110545 | + | 0.157534i | ||||
\(433\) | −8.68759 | −0.417499 | −0.208749 | − | 0.977969i | \(-0.566939\pi\) | ||||
−0.208749 | + | 0.977969i | \(0.566939\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 3.63516i | − | 0.174293i | ||||||
\(436\) | −20.3826 | + | 6.43799i | −0.976150 | + | 0.308324i | ||||
\(437\) | 5.50371i | 0.263278i | ||||||||
\(438\) | 13.7566 | + | 10.0814i | 0.657318 | + | 0.481709i | ||||
\(439\) | 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 | \(0.965374\pi\) | |||||||
\(444\) | −2.65621 | − | 8.40952i | −0.126058 | − | 0.399098i | ||||
\(445\) | − | 3.72038i | − | 0.176363i | ||||||
\(446\) | −17.9161 | + | 24.4476i | −0.848354 | + | 1.15763i | ||||
\(447\) | −6.65621 | −0.314828 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.94015 | −0.185947 | −0.0929735 | − | 0.995669i | \(-0.529637\pi\) | ||||
−0.0929735 | + | 0.995669i | \(0.529637\pi\) | |||||||
\(450\) | −3.99732 | + | 5.45457i | −0.188436 | + | 0.257131i | ||||
\(451\) | 29.7264i | 1.39976i | ||||||||
\(452\) | 7.26461 | + | 22.9997i | 0.341699 | + | 1.08181i | ||||
\(453\) | − | 2.68759i | − | 0.126274i | ||||||
\(454\) | 33.4417 | + | 24.5074i | 1.56950 | + | 1.15019i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.60004 | − | 1.21899i | −0.168588 | − | 0.0570846i | ||||
\(457\) | 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 | ||||
\(459\) | 6.09565i | 0.284521i | ||||||||
\(460\) | −3.64878 | + | 1.15249i | −0.170125 | + | 0.0537352i | ||||
\(461\) | − | 34.6031i | − | 1.61162i | −0.592171 | − | 0.805812i | \(-0.701729\pi\) | ||
0.592171 | − | 0.805812i | \(-0.298271\pi\) | |||||||
\(462\) | 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 | ||||
\(465\) | 2.05985 | 0.0955234 | ||||||||
\(466\) | −0.574789 | + | 0.784331i | −0.0266266 | + | 0.0363334i | ||||
\(467\) | 4.49784i | 0.208135i | 0.994570 | + | 0.104068i | \(0.0331858\pi\) | ||||
−0.994570 | + | 0.104068i | \(0.966814\pi\) | |||||||
\(468\) | −8.70182 | + | 2.74853i | −0.402242 | + | 0.127051i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.56357 | + | 2.61152i | 0.164375 | + | 0.120461i | ||||
\(471\) | 23.1351 | 1.06601 | ||||||||
\(472\) | −3.62851 | + | 10.7161i | −0.167016 | + | 0.493247i | ||||
\(473\) | −20.2541 | −0.931283 | ||||||||
\(474\) | −18.4694 | − | 13.5351i | −0.848326 | − | 0.621688i | ||||
\(475\) | − | 6.42573i | − | 0.294833i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.34379i | 0.0615281i | ||||||||
\(478\) | −8.02457 | + | 10.9500i | −0.367036 | + | 0.500840i | ||||
\(479\) | 22.2512 | 1.01668 | 0.508341 | − | 0.861156i | \(-0.330259\pi\) | ||||
0.508341 | + | 0.861156i | \(0.330259\pi\) | |||||||
\(480\) | 0.0542935 | − | 2.64197i | 0.00247815 | − | 0.120589i | ||||
\(481\) | 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 | ||||||||
\(486\) | 1.14070 | + | 0.835949i | 0.0517431 | + | 0.0379194i | ||||
\(487\) | −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 | ||||
\(489\) | 12.0380 | 0.544379 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.6374i | 0.795965i | 0.917393 | + | 0.397982i | \(0.130289\pi\) | ||||
−0.917393 | + | 0.397982i | \(0.869711\pi\) | |||||||
\(492\) | 11.6252 | − | 3.67190i | 0.524104 | − | 0.165542i | ||||
\(493\) | − | 47.4350i | − | 2.13637i | ||||||
\(494\) | 5.12558 | − | 6.99413i | 0.230611 | − | 0.314681i | ||||
\(495\) | 2.27807 | 0.102392 | ||||||||
\(496\) | 14.4380 | − | 10.1314i | 0.648285 | − | 0.454916i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −11.4971 | + | 15.6884i | −0.515196 | + | 0.703012i | ||||
\(499\) | − | 21.5854i | − | 0.966295i | −0.875539 | − | 0.483147i | \(-0.839494\pi\) | ||
0.875539 | − | 0.483147i | \(-0.160506\pi\) | |||||||
\(500\) | 8.71450 | − | 2.75254i | 0.389724 | − | 0.123097i | ||||
\(501\) | − | 9.01034i | − | 0.402552i | ||||||
\(502\) | 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 | ||||
\(507\) | − | 7.81904i | − | 0.347256i | ||||||
\(508\) | −11.3723 | − | 36.0045i | −0.504563 | − | 1.59744i | ||||
\(509\) | 18.3357i | 0.812715i | 0.913714 | + | 0.406358i | \(0.133201\pi\) | ||||
−0.913714 | + | 0.406358i | \(0.866799\pi\) | |||||||
\(510\) | 2.38037 | − | 3.24814i | 0.105405 | − | 0.143830i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −12.6141 | − | 18.7852i | −0.557468 | − | 0.830198i | ||||
\(513\) | −1.34379 | −0.0593300 | ||||||||
\(514\) | −1.91178 | + | 2.60872i | −0.0843248 | + | 0.115066i | ||||
\(515\) | − | 5.18388i | − | 0.228429i | ||||||
\(516\) | 2.50185 | + | 7.92082i | 0.110138 | + | 0.348695i | ||||
\(517\) | 32.6131i | 1.43432i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.59271 | 0.421073 | ||||||||
\(520\) | 5.71018 | + | 1.93350i | 0.250408 | + | 0.0847895i | ||||
\(521\) | −6.78033 | −0.297051 | −0.148526 | − | 0.988909i | \(-0.547453\pi\) | ||||
−0.148526 | + | 0.988909i | \(0.547453\pi\) | |||||||
\(522\) | −8.87666 | − | 6.50517i | −0.388521 | − | 0.284724i | ||||
\(523\) | 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 | ||||||||
\(528\) | 15.9675 | − | 11.2048i | 0.694897 | − | 0.487625i | ||||
\(529\) | −6.22564 | −0.270680 | ||||||||
\(530\) | 0.524756 | − | 0.716058i | 0.0227939 | − | 0.0311036i | ||||
\(531\) | 4.00000i | 0.173585i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.8132i | 1.20472i | ||||||||
\(534\) | −9.08474 | − | 6.65766i | −0.393135 | − | 0.288105i | ||||
\(535\) | −1.45903 | −0.0630794 | ||||||||
\(536\) | 5.35803 | − | 15.8238i | 0.231432 | − | 0.683485i | ||||
\(537\) | 7.69278 | 0.331968 | ||||||||
\(538\) | 10.8109 | + | 7.92268i | 0.466092 | + | 0.341571i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.281394 | − | 0.890891i | −0.0121093 | − | 0.0383379i | ||||
\(541\) | 5.21526i | 0.224222i | 0.993696 | + | 0.112111i | \(0.0357611\pi\) | ||||
−0.993696 | + | 0.112111i | \(0.964239\pi\) | |||||||
\(542\) | 11.1060 | − | 15.1547i | 0.477043 | − | 0.650951i | ||||
\(543\) | 15.2504 | 0.654456 | ||||||||
\(544\) | 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 | \(0.198327\pi\) | ||||
−0.812094 | + | 0.583526i | \(0.801673\pi\) | |||||||
\(548\) | −11.4514 | − | 36.2552i | −0.489182 | − | 1.54874i | ||||
\(549\) | − | 5.49706i | − | 0.234609i | ||||||
\(550\) | 26.6000 | + | 19.4936i | 1.13423 | + | 0.831209i | ||||
\(551\) | 10.4571 | 0.445488 | ||||||||
\(552\) | −3.71528 | + | 10.9723i | −0.158133 | + | 0.467012i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 30.6249 | + | 22.4431i | 1.30113 | + | 0.953518i | ||||
\(555\) | 2.05985i | 0.0874359i | ||||||||
\(556\) | −19.9066 | + | 6.28763i | −0.844227 | + | 0.266655i | ||||
\(557\) | − | 4.78766i | − | 0.202859i | −0.994843 | − | 0.101430i | \(-0.967658\pi\) | ||
0.994843 | − | 0.101430i | \(-0.0323417\pi\) | |||||||
\(558\) | 3.68613 | − | 5.02993i | 0.156046 | − | 0.212934i | ||||
\(559\) | −18.9505 | −0.801520 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 29.7264 | 1.25505 | ||||||||
\(562\) | 9.92150 | − | 13.5384i | 0.418513 | − | 0.571084i | ||||
\(563\) | − | 18.7445i | − | 0.789988i | −0.918684 | − | 0.394994i | \(-0.870747\pi\) | ||
0.918684 | − | 0.394994i | \(-0.129253\pi\) | |||||||
\(564\) | 12.7541 | − | 4.02847i | 0.537044 | − | 0.169629i | ||||
\(565\) | − | 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 | \(-0.302850\pi\) | ||||
0.580518 | + | 0.814248i | \(0.302850\pi\) | |||||||
\(570\) | 0.716058 | + | 0.524756i | 0.0299924 | + | 0.0219796i | ||||
\(571\) | − | 17.4132i | − | 0.728720i | −0.931258 | − | 0.364360i | \(-0.881288\pi\) | ||
0.931258 | − | 0.364360i | \(-0.118712\pi\) | |||||||
\(572\) | 13.4036 | + | 42.4358i | 0.560435 | + | 1.77433i | ||||
\(573\) | − | 4.72339i | − | 0.197322i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.5845 | −0.816731 | ||||||||
\(576\) | −6.35424 | − | 4.86042i | −0.264760 | − | 0.202517i | ||||
\(577\) | 6.81904 | 0.283880 | 0.141940 | − | 0.989875i | \(-0.454666\pi\) | ||||
0.141940 | + | 0.989875i | \(0.454666\pi\) | |||||||
\(578\) | 16.8502 | − | 22.9930i | 0.700875 | − | 0.956382i | ||||
\(579\) | 22.3379i | 0.928332i | ||||||||
\(580\) | 2.18975 | + | 6.93272i | 0.0909244 | + | 0.287866i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14.6909 | + | 10.7661i | 0.608958 | + | 0.446269i | ||||
\(583\) | 6.55322 | 0.271407 | ||||||||
\(584\) | −32.3085 | − | 10.9398i | −1.33694 | − | 0.452694i | ||||
\(585\) | 2.13145 | 0.0881246 | ||||||||
\(586\) | 25.9964 | + | 19.0512i | 1.07390 | + | 0.786997i | ||||
\(587\) | 9.81025i | 0.404912i | 0.979291 | + | 0.202456i | \(0.0648924\pi\) | ||||
−0.979291 | + | 0.202456i | \(0.935108\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.92549i | 0.244155i | ||||||||
\(590\) | 1.56201 | − | 2.13145i | 0.0643070 | − | 0.0877504i | ||||
\(591\) | −1.53510 | −0.0631454 | ||||||||
\(592\) | 10.1314 | + | 14.4380i | 0.416400 | + | 0.593398i | ||||
\(593\) | 39.0913 | 1.60529 | 0.802644 | − | 0.596458i | \(-0.203426\pi\) | ||||
0.802644 | + | 0.596458i | \(0.203426\pi\) | |||||||
\(594\) | 4.07663 | − | 5.56279i | 0.167266 | − | 0.228244i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.6942 | − | 4.00956i | 0.519976 | − | 0.164238i | ||||
\(597\) | 14.6876i | 0.601123i | ||||||||
\(598\) | −21.3169 | − | 15.6219i | −0.871712 | − | 0.638826i | ||||
\(599\) | 22.0270 | 0.899998 | 0.449999 | − | 0.893029i | \(-0.351424\pi\) | ||||
0.449999 | + | 0.893029i | \(0.351424\pi\) | |||||||
\(600\) | 4.33769 | − | 12.8105i | 0.177085 | − | 0.522985i | ||||
\(601\) | 20.2512 | 0.826062 | 0.413031 | − | 0.910717i | \(-0.364470\pi\) | ||||
0.413031 | + | 0.910717i | \(0.364470\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 5.90658i | − | 0.240535i | ||||||
\(604\) | 1.61895 | + | 5.12558i | 0.0658741 | + | 0.208557i | ||||
\(605\) | − | 5.97085i | − | 0.242750i | ||||||
\(606\) | 1.85618 | − | 2.53286i | 0.0754023 | − | 0.102891i | ||||
\(607\) | −44.4454 | −1.80398 | −0.901991 | − | 0.431755i | \(-0.857895\pi\) | ||||
−0.901991 | + | 0.431755i | \(0.857895\pi\) | |||||||
\(608\) | 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 | ||||||||
\(612\) | −3.67190 | − | 11.6252i | −0.148428 | − | 0.469920i | ||||
\(613\) | 47.6263i | 1.92361i | 0.273737 | + | 0.961805i | \(0.411740\pi\) | ||||
−0.273737 | + | 0.961805i | \(0.588260\pi\) | |||||||
\(614\) | 10.6584 | + | 7.81093i | 0.430140 | + | 0.315224i | ||||
\(615\) | −2.84751 | −0.114823 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.01034 | −0.121192 | −0.0605959 | − | 0.998162i | \(-0.519300\pi\) | ||||
−0.0605959 | + | 0.998162i | \(0.519300\pi\) | |||||||
\(618\) | −12.6584 | − | 9.27661i | −0.509197 | − | 0.373160i | ||||
\(619\) | 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 | ||||
\(621\) | 4.09565i | 0.164353i | ||||||||
\(622\) | −5.59048 | + | 7.62851i | −0.224158 | + | 0.305876i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 14.9398 | − | 10.4836i | 0.598072 | − | 0.419680i | ||||
\(625\) | 21.7744 | 0.870974 | ||||||||
\(626\) | 13.0726 | − | 17.8383i | 0.522487 | − | 0.712962i | ||||
\(627\) | 6.55322i | 0.261711i | ||||||||
\(628\) | −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 | ||||
\(633\) | 22.8409 | 0.907843 | ||||||||
\(634\) | −10.6584 | − | 7.81093i | −0.423301 | − | 0.310212i | ||||
\(635\) | 8.81904i | 0.349973i | ||||||||
\(636\) | −0.809475 | − | 2.56279i | −0.0320978 | − | 0.101621i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −31.7235 | + | 43.2884i | −1.25594 | + | 1.71380i | ||||
\(639\) | 4.72339 | 0.186854 | ||||||||
\(640\) | 1.48793 | + | 5.07128i | 0.0588154 | + | 0.200460i | ||||
\(641\) | −16.9358 | −0.668925 | −0.334462 | − | 0.942409i | \(-0.608555\pi\) | ||||
−0.334462 | + | 0.942409i | \(0.608555\pi\) | |||||||
\(642\) | −2.61095 | + | 3.56279i | −0.103046 | + | 0.140612i | ||||
\(643\) | − | 19.5189i | − | 0.769750i | −0.922969 | − | 0.384875i | \(-0.874245\pi\) | ||
0.922969 | − | 0.384875i | \(-0.125755\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.94015i | − | 0.0763933i | ||||||
\(646\) | 9.34379 | + | 6.84751i | 0.367627 | + | 0.269412i | ||||
\(647\) | 23.3723 | 0.918858 | 0.459429 | − | 0.888214i | \(-0.348054\pi\) | ||||
0.459429 | + | 0.888214i | \(0.348054\pi\) | |||||||
\(648\) | −2.67901 | − | 0.907128i | −0.105242 | − | 0.0356354i | ||||
\(649\) | 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 | \(-0.00908839\pi\) | |||||||
\(654\) | 8.93428 | − | 12.1913i | 0.349358 | − | 0.476718i | ||||
\(655\) | −2.30499 | −0.0900632 | ||||||||
\(656\) | −19.9589 | + | 14.0056i | −0.779262 | + | 0.546825i | ||||
\(657\) | −12.0599 | −0.470500 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 10.8929i | − | 0.424326i | −0.977234 | − | 0.212163i | \(-0.931949\pi\) | ||
0.977234 | − | 0.212163i | \(-0.0680508\pi\) | |||||||
\(660\) | −4.34457 | + | 1.37226i | −0.169112 | + | 0.0534153i | ||||
\(661\) | 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 | ||||
\(663\) | 27.8132 | 1.08017 | ||||||||
\(664\) | 12.4760 | − | 36.8453i | 0.484164 | − | 1.42988i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.02993 | + | 3.68613i | 0.194906 | + | 0.142835i | ||||
\(667\) | − | 31.8715i | − | 1.23407i | ||||||
\(668\) | 5.42765 | + | 17.1839i | 0.210002 | + | 0.664864i | ||||
\(669\) | − | 21.4321i | − | 0.828613i | ||||||
\(670\) | −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 | ||||
\(675\) | − | 4.78178i | − | 0.184051i | ||||||
\(676\) | 4.71003 | + | 14.9119i | 0.181155 | + | 0.573535i | ||||
\(677\) | − | 28.7781i | − | 1.10603i | −0.833170 | − | 0.553017i | \(-0.813476\pi\) | ||
0.833170 | − | 0.553017i | \(-0.186524\pi\) | |||||||
\(678\) | −13.7566 | − | 10.0814i | −0.528321 | − | 0.387174i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.58305 | + | 7.62851i | −0.0990556 | + | 0.292540i | ||||
\(681\) | −29.3169 | −1.12343 | ||||||||
\(682\) | −24.5292 | − | 17.9760i | −0.939273 | − | 0.688337i | ||||
\(683\) | − | 34.4431i | − | 1.31793i | −0.752174 | − | 0.658965i | \(-0.770995\pi\) | ||
0.752174 | − | 0.658965i | \(-0.229005\pi\) | |||||||
\(684\) | 2.56279 | − | 0.809475i | 0.0979907 | − | 0.0309510i | ||||
\(685\) | 8.88044i | 0.339304i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.5074 | −0.858711 | ||||||||
\(688\) | −9.54268 | − | 13.5990i | −0.363811 | − | 0.518455i | ||||
\(689\) | 6.13145 | 0.233590 | ||||||||
\(690\) | 1.59936 | − | 2.18242i | 0.0608867 | − | 0.0830833i | ||||
\(691\) | − | 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 | ||||||||
\(696\) | 20.8475 | + | 7.05908i | 0.790223 | + | 0.267574i | ||||
\(697\) | −37.1570 | −1.40742 | ||||||||
\(698\) | −31.0179 | − | 22.7312i | −1.17405 | − | 0.860388i | ||||
\(699\) | − | 0.687589i | − | 0.0260070i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.7804i | 1.76687i | 0.468553 | + | 0.883435i | \(0.344775\pi\) | ||||
−0.468553 | + | 0.883435i | \(0.655225\pi\) | |||||||
\(702\) | 3.81426 | − | 5.20476i | 0.143960 | − | 0.196441i | ||||
\(703\) | −5.92549 | −0.223484 | ||||||||
\(704\) | −23.7026 | + | 30.9874i | −0.893325 | + | 1.16788i | ||||
\(705\) | −3.12402 | −0.117658 | ||||||||
\(706\) | 25.3183 | − | 34.5482i | 0.952868 | − | 1.30024i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.40952 | − | 7.62851i | −0.0905553 | − | 0.286697i | ||||
\(709\) | − | 8.43643i | − | 0.316837i | −0.987372 | − | 0.158418i | \(-0.949360\pi\) | ||
0.987372 | − | 0.158418i | \(-0.0506395\pi\) | |||||||
\(710\) | −2.51692 | − | 1.84450i | −0.0944582 | − | 0.0692227i | ||||
\(711\) | 16.1913 | 0.607221 | ||||||||
\(712\) | 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 | ||||
\(717\) | − | 9.59936i | − | 0.358495i | ||||||
\(718\) | 5.51052 | − | 7.51940i | 0.205651 | − | 0.280622i | ||||
\(719\) | 38.4425 | 1.43366 | 0.716831 | − | 0.697247i | \(-0.245592\pi\) | ||||
0.716831 | + | 0.697247i | \(0.245592\pi\) | |||||||
\(720\) | 1.07331 | + | 1.52954i | 0.0399999 | + | 0.0570025i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14.3735 | − | 19.6134i | 0.534926 | − | 0.729935i | ||||
\(723\) | − | 0.496287i | − | 0.0184571i | ||||||
\(724\) | −29.0844 | + | 9.18652i | −1.08091 | + | 0.341414i | ||||
\(725\) | 37.2108i | 1.38197i | ||||||||
\(726\) | −14.5801 | − | 10.6849i | −0.541120 | − | 0.396554i | ||||
\(727\) | 17.5484 | 0.650834 | 0.325417 | − | 0.945571i | \(-0.394495\pi\) | ||||
0.325417 | + | 0.945571i | \(0.394495\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 6.42624 | + | 4.70941i | 0.237846 | + | 0.174303i | ||||
\(731\) | − | 25.3169i | − | 0.936379i | ||||||
\(732\) | 3.31132 | + | 10.4836i | 0.122390 | + | 0.387485i | ||||
\(733\) | 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 | ||||||||
\(738\) | −5.09565 | + | 6.95329i | −0.187574 | + | 0.255954i | ||||
\(739\) | − | 13.9066i | − | 0.511562i | −0.966735 | − | 0.255781i | \(-0.917667\pi\) | ||
0.966735 | − | 0.255781i | \(-0.0823326\pi\) | |||||||
\(740\) | −1.24081 | − | 3.92840i | −0.0456132 | − | 0.144411i | ||||
\(741\) | 6.13145i | 0.225244i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.2300 | 1.47590 | 0.737948 | − | 0.674858i | \(-0.235795\pi\) | ||||
0.737948 | + | 0.674858i | \(0.235795\pi\) | |||||||
\(744\) | −4.00000 | + | 11.8132i | −0.146647 | + | 0.433092i | ||||
\(745\) | −3.10936 | −0.113918 | ||||||||
\(746\) | 19.5351 | + | 14.3161i | 0.715231 | + | 0.524150i | ||||
\(747\) | − | 13.7533i | − | 0.503207i | ||||||
\(748\) | −56.6921 | + | 17.9066i | −2.07287 | + | 0.654730i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.81982 | + | 5.21234i | −0.139480 | + | 0.190328i | ||||
\(751\) | 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 | ||||
\(753\) | −22.1359 | −0.806678 | ||||||||
\(754\) | −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 | \(-0.945168\pi\) | ||
0.985200 | − | 0.171408i | \(-0.0548316\pi\) | |||||||
\(758\) | 19.0604 | + | 13.9682i | 0.692304 | + | 0.507348i | ||||
\(759\) | 19.9731 | 0.724977 | ||||||||
\(760\) | −1.68172 | − | 0.569438i | −0.0610023 | − | 0.0206557i | ||||
\(761\) | 9.41098 | 0.341148 | 0.170574 | − | 0.985345i | \(-0.445438\pi\) | ||||
0.170574 | + | 0.985345i | \(0.445438\pi\) | |||||||
\(762\) | 21.5351 | + | 15.7818i | 0.780134 | + | 0.571714i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.84527 | + | 9.00811i | 0.102938 | + | 0.325902i | ||||
\(765\) | 2.84751i | 0.102952i | ||||||||
\(766\) | 8.30945 | − | 11.3387i | 0.300233 | − | 0.409684i | ||||
\(767\) | 18.2512 | 0.659011 | ||||||||
\(768\) | 15.0462 | + | 5.44178i | 0.542932 | + | 0.196363i | ||||
\(769\) | −27.6950 | −0.998708 | −0.499354 | − | 0.866398i | \(-0.666429\pi\) | ||||
−0.499354 | + | 0.866398i | \(0.666429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 2.28695i | − | 0.0823626i | ||||||
\(772\) | −13.4559 | − | 42.6013i | −0.484289 | − | 1.53325i | ||||
\(773\) | 33.8993i | 1.21927i | 0.792682 | + | 0.609636i | \(0.208684\pi\) | ||||
−0.792682 | + | 0.609636i | \(0.791316\pi\) | |||||||
\(774\) | −4.73762 | − | 3.47192i | −0.170290 | − | 0.124796i | ||||
\(775\) | −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 | ||||||
\(780\) | −4.06495 | + | 1.28394i | −0.145548 | + | 0.0459725i | ||||
\(781\) | − | 23.0343i | − | 0.824234i | ||||||
\(782\) | 20.8700 | − | 28.4783i | 0.746310 | − | 1.01838i | ||||
\(783\) | 7.78178 | 0.278098 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.8073 | 0.385729 | ||||||||
\(786\) | −4.12480 | + | 5.62851i | −0.147127 | + | 0.200762i | ||||
\(787\) | − | 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 | ||||
\(789\) | − | 30.1555i | − | 1.07356i | ||||||
\(790\) | −8.62774 | − | 6.32275i | −0.306961 | − | 0.224953i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.42375 | + | 13.0646i | −0.157191 | + | 0.464232i | ||||
\(793\) | −25.0819 | −0.890686 | ||||||||
\(794\) | 26.7399 | + | 19.5960i | 0.948962 | + | 0.695437i | ||||
\(795\) | 0.627737i | 0.0222635i | ||||||||
\(796\) | −8.84751 | − | 28.0111i | −0.313592 | − | 0.992828i | ||||
\(797\) | 32.2848i | 1.14359i | 0.820398 | + | 0.571793i | \(0.193752\pi\) | ||||
−0.820398 | + | 0.571793i | \(0.806248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.7652 | −1.44217 | ||||||||
\(800\) | −0.555767 | + | 27.0441i | −0.0196493 | + | 0.956155i | ||||
\(801\) | 7.96420 | 0.281401 | ||||||||
\(802\) | −13.3776 | + | 18.2545i | −0.472380 | + | 0.644588i | ||||
\(803\) | 58.8118i | 2.07542i | ||||||||
\(804\) | 3.55801 | + | 11.2646i | 0.125481 | + | 0.397272i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −22.9505 | − | 16.8190i | −0.808396 | − | 0.592425i | ||||
\(807\) | −9.47748 | −0.333623 | ||||||||
\(808\) | −2.01423 | + | 5.94862i | −0.0708605 | + | 0.209272i | ||||
\(809\) | 8.49629 | 0.298714 | 0.149357 | − | 0.988783i | \(-0.452280\pi\) | ||||
0.149357 | + | 0.988783i | \(0.452280\pi\) | |||||||
\(810\) | 0.532862 | + | 0.390503i | 0.0187229 | + | 0.0137209i | ||||
\(811\) | − | 12.3826i | − | 0.434812i | −0.976081 | − | 0.217406i | \(-0.930240\pi\) | ||
0.976081 | − | 0.217406i | \(-0.0697596\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.2855i | 0.465943i | ||||||||
\(814\) | 17.9760 | − | 24.5292i | 0.630058 | − | 0.859749i | ||||
\(815\) | 5.62342 | 0.196980 | ||||||||
\(816\) | 14.0056 | + | 19.9589i | 0.490293 | + | 0.698700i | ||||
\(817\) | 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 | \(0.875182\pi\) | |||||||
\(822\) | 21.6850 | + | 15.8917i | 0.756353 | + | 0.554286i | ||||
\(823\) | −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 | ||||
\(825\) | −23.3191 | −0.811867 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 32.8051i | − | 1.14074i | −0.821387 | − | 0.570372i | \(-0.806799\pi\) | ||
0.821387 | − | 0.570372i | \(-0.193201\pi\) | |||||||
\(828\) | −2.46714 | − | 7.81093i | −0.0857390 | − | 0.271449i | ||||
\(829\) | 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 | ||||
\(831\) | −26.8475 | −0.931330 | ||||||||
\(832\) | −22.1771 | + | 28.9930i | −0.768851 | + | 1.00515i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.72562 | − | 11.9066i | 0.302144 | − | 0.412291i | ||||
\(835\) | − | 4.20907i | − | 0.145661i | ||||||
\(836\) | −3.94753 | − | 12.4978i | −0.136528 | − | 0.432247i | ||||
\(837\) | 4.40952i | 0.152415i | ||||||||
\(838\) | 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 | ||||
\(843\) | 11.8686i | 0.408775i | ||||||||
\(844\) | −43.5604 | + | 13.7589i | −1.49941 | + | 0.473600i | ||||
\(845\) | − | 3.65257i | − | 0.125652i | ||||||
\(846\) | −5.59048 | + | 7.62851i | −0.192205 | + | 0.262274i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.08754 | + | 4.39996i | 0.106027 | + | 0.151095i | ||||
\(849\) | −2.46937 | −0.0847486 | ||||||||
\(850\) | −24.3663 | + | 33.2491i | −0.835757 | + | 1.14044i | ||||
\(851\) | 18.0599i | 0.619084i | ||||||||
\(852\) | −9.00811 | + | 2.84527i | −0.308613 | + | 0.0974775i | ||||
\(853\) | 1.44013i | 0.0493090i | 0.999696 | + | 0.0246545i | \(0.00784856\pi\) | ||||
−0.999696 | + | 0.0246545i | \(0.992151\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.627737 | −0.0214681 | ||||||||
\(856\) | 2.83327 | − | 8.36748i | 0.0968393 | − | 0.285995i | ||||
\(857\) | −34.9775 | −1.19481 | −0.597404 | − | 0.801941i | \(-0.703801\pi\) | ||||
−0.597404 | + | 0.801941i | \(0.703801\pi\) | |||||||
\(858\) | −25.3818 | − | 18.6008i | −0.866521 | − | 0.635022i | ||||
\(859\) | 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 | \(-0.699125\pi\) | ||||
−0.585559 | + | 0.810630i | \(0.699125\pi\) | |||||||
\(864\) | 5.65566 | + | 0.116226i | 0.192409 | + | 0.00395409i | ||||
\(865\) | 4.48112 | 0.152363 | ||||||||
\(866\) | −7.26238 | + | 9.90991i | −0.246786 | + | 0.336752i | ||||
\(867\) | 20.1570i | 0.684566i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 78.9594i | − | 2.67852i | ||||||
\(870\) | −4.14662 | − | 3.03881i | −0.140584 | − | 0.103025i | ||||
\(871\) | −26.9505 | −0.913182 | ||||||||
\(872\) | −9.69501 | + | 28.6322i | −0.328315 | + | 0.969609i | ||||
\(873\) | −12.8789 | −0.435884 | ||||||||
\(874\) | 6.27807 | + | 4.60082i | 0.212359 | + | 0.155625i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 22.9997 | − | 7.26461i | 0.777087 | − | 0.245448i | ||||
\(877\) | 40.3826i | 1.36362i | 0.731528 | + | 0.681812i | \(0.238808\pi\) | ||||
−0.731528 | + | 0.681812i | \(0.761192\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.7899 | −0.768684 | ||||||||
\(880\) | 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 | \(0.140041\pi\) | ||||
−0.904772 | + | 0.425896i | \(0.859959\pi\) | |||||||
\(884\) | −53.0433 | + | 16.7541i | −1.78404 | + | 0.563501i | ||||
\(885\) | 1.86855i | 0.0628106i | ||||||||
\(886\) | 5.21312 | + | 3.82038i | 0.175138 | + | 0.128348i | ||||
\(887\) | −19.6352 | −0.659284 | −0.329642 | − | 0.944106i | \(-0.606928\pi\) | ||||
−0.329642 | + | 0.944106i | \(0.606928\pi\) | |||||||
\(888\) | −11.8132 | − | 4.00000i | −0.396424 | − | 0.134231i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.24382 | − | 3.11004i | −0.142253 | − | 0.104249i | ||||
\(891\) | 4.87666i | 0.163374i | ||||||||
\(892\) | 12.9103 | + | 40.8738i | 0.432268 | + | 1.36856i | ||||
\(893\) | − | 8.98674i | − | 0.300730i | ||||||
\(894\) | −5.56425 | + | 7.59271i | −0.186096 | + | 0.253938i | ||||
\(895\) | 3.59359 | 0.120120 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.6876 | 0.623960 | ||||||||
\(898\) | −3.29376 | + | 4.49452i | −0.109914 | + | 0.149984i | ||||
\(899\) | − | 34.3139i | − | 1.14443i | ||||||
\(900\) | 2.88045 | + | 9.11947i | 0.0960150 | + | 0.303982i | ||||
\(901\) | 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 | ||||||||
\(906\) | −3.06572 | − | 2.24669i | −0.101852 | − | 0.0746411i | ||||
\(907\) | 4.84241i | 0.160790i | 0.996763 | + | 0.0803948i | \(0.0256181\pi\) | ||||
−0.996763 | + | 0.0803948i | \(0.974382\pi\) | |||||||
\(908\) | 55.9111 | − | 17.6599i | 1.85547 | − | 0.586064i | ||||
\(909\) | 2.22045i | 0.0736477i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.9176 | −0.626768 | −0.313384 | − | 0.949626i | \(-0.601463\pi\) | ||||
−0.313384 | + | 0.949626i | \(0.601463\pi\) | |||||||
\(912\) | −4.39996 | + | 3.08754i | −0.145697 | + | 0.102239i | ||||
\(913\) | −67.0702 | −2.21970 | ||||||||
\(914\) | 33.4552 | − | 45.6515i | 1.10660 | − | 1.51002i | ||||
\(915\) | − | 2.56788i | − | 0.0848917i | ||||||
\(916\) | 42.9245 | − | 13.5580i | 1.41827 | − | 0.447969i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.95329 | + | 5.09565i | 0.229493 | + | 0.168182i | ||||
\(919\) | −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 | ||||
\(921\) | −9.34379 | −0.307888 | ||||||||
\(922\) | −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 | ||||
\(927\) | 11.0971 | 0.364477 | ||||||||
\(928\) | −44.0111 | − | 0.904445i | −1.44474 | − | 0.0296899i | ||||
\(929\) | −32.7294 | −1.07382 | −0.536909 | − | 0.843640i | \(-0.680408\pi\) | ||||
−0.536909 | + | 0.843640i | \(0.680408\pi\) | |||||||
\(930\) | 1.72193 | − | 2.34967i | 0.0564643 | − | 0.0770486i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.414190 | + | 1.31132i | 0.0135672 | + | 0.0429537i | ||||
\(933\) | − | 6.68759i | − | 0.218942i | ||||||
\(934\) | 5.13067 | + | 3.75996i | 0.167881 | + | 0.123030i | ||||
\(935\) | 13.8863 | 0.454131 | ||||||||
\(936\) | −4.13903 | + | 12.2238i | −0.135289 | + | 0.399547i | ||||
\(937\) | 21.5066 | 0.702591 | 0.351295 | − | 0.936265i | \(-0.385741\pi\) | ||||
0.351295 | + | 0.936265i | \(0.385741\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.6381i | 0.510329i | ||||||||
\(940\) | 5.95791 | − | 1.88185i | 0.194326 | − | 0.0613791i | ||||
\(941\) | − | 1.85115i | − | 0.0603456i | −0.999545 | − | 0.0301728i | \(-0.990394\pi\) | ||
0.999545 | − | 0.0301728i | \(-0.00960577\pi\) | |||||||
\(942\) | 19.3398 | − | 26.3902i | 0.630124 | − | 0.859839i | ||||
\(943\) | −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 | \(-0.263570\pi\) | |||||||
\(948\) | −30.8789 | + | 9.75331i | −1.00290 | + | 0.316773i | ||||
\(949\) | 55.0266i | 1.78624i | ||||||||
\(950\) | −7.32981 | − | 5.37158i | −0.237811 | − | 0.174277i | ||||
\(951\) | 9.34379 | 0.302993 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.5768 | 1.31441 | 0.657206 | − | 0.753711i | \(-0.271738\pi\) | ||||
0.657206 | + | 0.753711i | \(0.271738\pi\) | |||||||
\(954\) | 1.53286 | + | 1.12334i | 0.0496283 | + | 0.0363696i | ||||
\(955\) | − | 2.20647i | − | 0.0713997i | ||||||
\(956\) | 5.78246 | + | 18.3072i | 0.187018 | + | 0.592098i | ||||
\(957\) | − | 37.9491i | − | 1.22672i | ||||||
\(958\) | 18.6008 | − | 25.3818i | 0.600965 | − | 0.820050i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.96830 | − | 2.27048i | −0.0958015 | − | 0.0732796i | ||||
\(961\) | −11.5561 | −0.372779 | ||||||||
\(962\) | 16.8190 | − | 22.9505i | 0.542268 | − | 0.739953i | ||||
\(963\) | − | 3.12334i | − | 0.100648i | ||||||
\(964\) | 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 | ||||
\(969\) | −8.19130 | −0.263143 | ||||||||
\(970\) | 6.86268 | + | 5.02925i | 0.220347 | + | 0.161479i | ||||
\(971\) | 14.6876i | 0.471347i | 0.971832 | + | 0.235674i | \(0.0757296\pi\) | ||||
−0.971832 | + | 0.235674i | \(0.924270\pi\) | |||||||
\(972\) | 1.90713 | − | 0.602380i | 0.0611712 | − | 0.0193213i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.56201 | + | 2.13145i | −0.0500501 | + | 0.0682961i | ||||
\(975\) | −21.8183 | −0.698744 | ||||||||
\(976\) | −12.6302 | − | 17.9989i | −0.404284 | − | 0.576131i | ||||
\(977\) | −21.2437 | −0.679647 | −0.339824 | − | 0.940489i | \(-0.610367\pi\) | ||||
−0.339824 | + | 0.940489i | \(0.610367\pi\) | |||||||
\(978\) | 10.0632 | − | 13.7317i | 0.321785 | − | 0.439093i | ||||
\(979\) | − | 38.8387i | − | 1.24129i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.6876i | 0.341228i | ||||||||
\(982\) | 20.1189 | + | 14.7440i | 0.642021 | + | 0.470499i | ||||
\(983\) | −11.8265 | −0.377206 | −0.188603 | − | 0.982053i | \(-0.560396\pi\) | ||||
−0.188603 | + | 0.982053i | \(0.560396\pi\) | |||||||
\(984\) | 5.52954 | − | 16.3303i | 0.176275 | − | 0.520592i | ||||
\(985\) | −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 | ||||||
\(990\) | 1.90435 | − | 2.59859i | 0.0605242 | − | 0.0825885i | ||||
\(991\) | 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 | ||||
\(993\) | −5.40874 | −0.171641 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.86112i | 0.217512i | ||||||||
\(996\) | 8.28472 | + | 26.2293i | 0.262511 | + | 0.831108i | ||||
\(997\) | 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 | ||||
\(999\) | −4.40952 | −0.139511 |
(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 | 1176.2.c.c.589.5 | 8 | ||
4.3 | odd | 2 | 4704.2.c.c.2353.2 | 8 | |||
7.6 | odd | 2 | 168.2.c.b.85.5 | ✓ | 8 | ||
8.3 | odd | 2 | 4704.2.c.c.2353.7 | 8 | |||
8.5 | even | 2 | inner | 1176.2.c.c.589.6 | 8 | ||
21.20 | even | 2 | 504.2.c.f.253.4 | 8 | |||
28.27 | even | 2 | 672.2.c.b.337.7 | 8 | |||
56.13 | odd | 2 | 168.2.c.b.85.6 | yes | 8 | ||
56.27 | even | 2 | 672.2.c.b.337.2 | 8 | |||
84.83 | odd | 2 | 2016.2.c.e.1009.5 | 8 | |||
112.13 | odd | 4 | 5376.2.a.bp.1.3 | 4 | |||
112.27 | even | 4 | 5376.2.a.bq.1.2 | 4 | |||
112.69 | odd | 4 | 5376.2.a.bm.1.2 | 4 | |||
112.83 | even | 4 | 5376.2.a.bl.1.3 | 4 | |||
168.83 | odd | 2 | 2016.2.c.e.1009.4 | 8 | |||
168.125 | even | 2 | 504.2.c.f.253.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.c.b.85.5 | ✓ | 8 | 7.6 | odd | 2 | ||
168.2.c.b.85.6 | yes | 8 | 56.13 | odd | 2 | ||
504.2.c.f.253.3 | 8 | 168.125 | even | 2 | |||
504.2.c.f.253.4 | 8 | 21.20 | even | 2 | |||
672.2.c.b.337.2 | 8 | 56.27 | even | 2 | |||
672.2.c.b.337.7 | 8 | 28.27 | even | 2 | |||
1176.2.c.c.589.5 | 8 | 1.1 | even | 1 | trivial | ||
1176.2.c.c.589.6 | 8 | 8.5 | even | 2 | inner | ||
2016.2.c.e.1009.4 | 8 | 168.83 | odd | 2 | |||
2016.2.c.e.1009.5 | 8 | 84.83 | odd | 2 | |||
4704.2.c.c.2353.2 | 8 | 4.3 | odd | 2 | |||
4704.2.c.c.2353.7 | 8 | 8.3 | odd | 2 | |||
5376.2.a.bl.1.3 | 4 | 112.83 | even | 4 | |||
5376.2.a.bm.1.2 | 4 | 112.69 | odd | 4 | |||
5376.2.a.bp.1.3 | 4 | 112.13 | odd | 4 | |||
5376.2.a.bq.1.2 | 4 | 112.27 | even | 4 |