Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(227,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.227");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.bb (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 362.6 | ||
Character | \(\chi\) | \(=\) | 637.362 |
Dual form | 637.2.bb.a.227.6 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.14693 | + | 1.14693i | 0.811001 | + | 0.811001i | 0.984784 | − | 0.173783i | \(-0.0555992\pi\) |
−0.173783 | + | 0.984784i | \(0.555599\pi\) | |||||||
\(3\) | 0.445073 | + | 0.256963i | 0.256963 | + | 0.148358i | 0.622948 | − | 0.782263i | \(-0.285935\pi\) |
−0.365985 | + | 0.930621i | \(0.619268\pi\) | |||||||
\(4\) | 0.630890i | 0.315445i | ||||||||
\(5\) | −0.395109 | − | 1.47457i | −0.176698 | − | 0.659447i | −0.996256 | − | 0.0864504i | \(-0.972448\pi\) |
0.819558 | − | 0.572996i | \(-0.194219\pi\) | |||||||
\(6\) | 0.215749 | + | 0.805186i | 0.0880791 | + | 0.328716i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.57027 | − | 1.57027i | 0.555175 | − | 0.555175i | ||||
\(9\) | −1.36794 | − | 2.36934i | −0.455980 | − | 0.789780i | ||||
\(10\) | 1.23806 | − | 2.14439i | 0.391509 | − | 0.678114i | ||||
\(11\) | −0.745574 | − | 2.78252i | −0.224799 | − | 0.838961i | −0.982485 | − | 0.186342i | \(-0.940337\pi\) |
0.757686 | − | 0.652619i | \(-0.226330\pi\) | |||||||
\(12\) | −0.162115 | + | 0.280792i | −0.0467987 | + | 0.0810577i | ||||
\(13\) | 2.94467 | + | 2.08061i | 0.816704 | + | 0.577057i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.203057 | − | 0.757819i | 0.0524291 | − | 0.195668i | ||||
\(16\) | 4.86376 | 1.21594 | ||||||||
\(17\) | 6.21574 | 1.50754 | 0.753769 | − | 0.657139i | \(-0.228234\pi\) | ||||
0.753769 | + | 0.657139i | \(0.228234\pi\) | |||||||
\(18\) | 1.14854 | − | 4.28639i | 0.270712 | − | 1.01031i | ||||
\(19\) | −2.23387 | − | 0.598564i | −0.512485 | − | 0.137320i | −0.00669672 | − | 0.999978i | \(-0.502132\pi\) |
−0.505788 | + | 0.862658i | \(0.668798\pi\) | |||||||
\(20\) | 0.930289 | − | 0.249270i | 0.208019 | − | 0.0557385i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.33623 | − | 4.04647i | 0.498086 | − | 0.862710i | ||||
\(23\) | 5.62238i | 1.17235i | 0.810185 | + | 0.586174i | \(0.199367\pi\) | ||||
−0.810185 | + | 0.586174i | \(0.800633\pi\) | |||||||
\(24\) | 1.10239 | − | 0.295384i | 0.225024 | − | 0.0602950i | ||||
\(25\) | 2.31189 | − | 1.33477i | 0.462378 | − | 0.266954i | ||||
\(26\) | 0.991014 | + | 5.76363i | 0.194354 | + | 1.13034i | ||||
\(27\) | − | 2.94782i | − | 0.567308i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.379237 | + | 0.656858i | 0.0704225 | + | 0.121975i | 0.899087 | − | 0.437771i | \(-0.144232\pi\) |
−0.828664 | + | 0.559746i | \(0.810899\pi\) | |||||||
\(30\) | 1.10206 | − | 0.636273i | 0.201207 | − | 0.116167i | ||||
\(31\) | −8.36292 | − | 2.24084i | −1.50202 | − | 0.402466i | −0.588247 | − | 0.808682i | \(-0.700182\pi\) |
−0.913777 | + | 0.406215i | \(0.866848\pi\) | |||||||
\(32\) | 2.43784 | + | 2.43784i | 0.430953 | + | 0.430953i | ||||
\(33\) | 0.383170 | − | 1.43001i | 0.0667013 | − | 0.248933i | ||||
\(34\) | 7.12901 | + | 7.12901i | 1.22261 | + | 1.22261i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.49479 | − | 0.863019i | 0.249132 | − | 0.143837i | ||||
\(37\) | −4.26298 | + | 4.26298i | −0.700830 | + | 0.700830i | −0.964589 | − | 0.263759i | \(-0.915038\pi\) |
0.263759 | + | 0.964589i | \(0.415038\pi\) | |||||||
\(38\) | −1.87558 | − | 3.24860i | −0.304259 | − | 0.526992i | ||||
\(39\) | 0.775953 | + | 1.68269i | 0.124252 | + | 0.269447i | ||||
\(40\) | −2.93590 | − | 1.69504i | −0.464207 | − | 0.268010i | ||||
\(41\) | 1.94919 | + | 0.522283i | 0.304412 | + | 0.0815669i | 0.407792 | − | 0.913075i | \(-0.366299\pi\) |
−0.103380 | + | 0.994642i | \(0.532966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.24252 | − | 1.29472i | −0.341981 | − | 0.197443i | 0.319167 | − | 0.947699i | \(-0.396597\pi\) |
−0.661148 | + | 0.750256i | \(0.729930\pi\) | |||||||
\(44\) | 1.75546 | − | 0.470375i | 0.264646 | − | 0.0709116i | ||||
\(45\) | −2.95327 | + | 2.95327i | −0.440247 | + | 0.440247i | ||||
\(46\) | −6.44847 | + | 6.44847i | −0.950775 | + | 0.950775i | ||||
\(47\) | 2.13395 | − | 0.571791i | 0.311269 | − | 0.0834043i | −0.0998029 | − | 0.995007i | \(-0.531821\pi\) |
0.411072 | + | 0.911603i | \(0.365155\pi\) | |||||||
\(48\) | 2.16473 | + | 1.24981i | 0.312452 | + | 0.180394i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.18246 | + | 1.12069i | 0.591488 | + | 0.158489i | ||||
\(51\) | 2.76646 | + | 1.59722i | 0.387382 | + | 0.223655i | ||||
\(52\) | −1.31263 | + | 1.85776i | −0.182030 | + | 0.257625i | ||||
\(53\) | 2.47328 | + | 4.28385i | 0.339732 | + | 0.588433i | 0.984382 | − | 0.176045i | \(-0.0563304\pi\) |
−0.644650 | + | 0.764477i | \(0.722997\pi\) | |||||||
\(54\) | 3.38094 | − | 3.38094i | 0.460087 | − | 0.460087i | ||||
\(55\) | −3.80843 | + | 2.19880i | −0.513529 | + | 0.296486i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.840427 | − | 0.840427i | −0.111317 | − | 0.111317i | ||||
\(58\) | −0.318411 | + | 1.18833i | −0.0418094 | + | 0.156035i | ||||
\(59\) | 0.623268 | + | 0.623268i | 0.0811426 | + | 0.0811426i | 0.746513 | − | 0.665371i | \(-0.231726\pi\) |
−0.665371 | + | 0.746513i | \(0.731726\pi\) | |||||||
\(60\) | 0.478100 | + | 0.128107i | 0.0617225 | + | 0.0165385i | ||||
\(61\) | −4.48249 | + | 2.58797i | −0.573924 | + | 0.331355i | −0.758715 | − | 0.651423i | \(-0.774172\pi\) |
0.184791 | + | 0.982778i | \(0.440839\pi\) | |||||||
\(62\) | −7.02159 | − | 12.1617i | −0.891742 | − | 1.54454i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 4.13546i | − | 0.516933i | ||||||
\(65\) | 1.90453 | − | 5.16418i | 0.236228 | − | 0.640538i | ||||
\(66\) | 2.07959 | − | 1.20065i | 0.255980 | − | 0.147790i | ||||
\(67\) | 15.1664 | − | 4.06383i | 1.85287 | − | 0.496476i | 0.853189 | − | 0.521602i | \(-0.174665\pi\) |
0.999684 | + | 0.0251264i | \(0.00799882\pi\) | |||||||
\(68\) | 3.92145i | 0.475545i | ||||||||
\(69\) | −1.44475 | + | 2.50237i | −0.173927 | + | 0.301250i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.3040 | + | 2.76095i | −1.22286 | + | 0.327665i | −0.811796 | − | 0.583941i | \(-0.801510\pi\) |
−0.411066 | + | 0.911606i | \(0.634843\pi\) | |||||||
\(72\) | −5.86855 | − | 1.57247i | −0.691615 | − | 0.185318i | ||||
\(73\) | −1.80076 | + | 6.72052i | −0.210763 | + | 0.786578i | 0.776852 | + | 0.629683i | \(0.216815\pi\) |
−0.987615 | + | 0.156895i | \(0.949852\pi\) | |||||||
\(74\) | −9.77867 | −1.13675 | ||||||||
\(75\) | 1.37195 | 0.158419 | ||||||||
\(76\) | 0.377628 | − | 1.40933i | 0.0433169 | − | 0.161661i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.03997 | + | 2.81989i | −0.117753 | + | 0.319290i | ||||
\(79\) | −4.24764 | + | 7.35713i | −0.477897 | + | 0.827742i | −0.999679 | − | 0.0253371i | \(-0.991934\pi\) |
0.521782 | + | 0.853079i | \(0.325267\pi\) | |||||||
\(80\) | −1.92172 | − | 7.17194i | −0.214854 | − | 0.801847i | ||||
\(81\) | −3.34634 | + | 5.79603i | −0.371815 | + | 0.644003i | ||||
\(82\) | 1.63656 | + | 2.83460i | 0.180727 | + | 0.313029i | ||||
\(83\) | 1.51432 | − | 1.51432i | 0.166218 | − | 0.166218i | −0.619096 | − | 0.785315i | \(-0.712501\pi\) |
0.785315 | + | 0.619096i | \(0.212501\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.45590 | − | 9.16553i | −0.266379 | − | 0.994141i | ||||
\(86\) | −1.08706 | − | 4.05696i | −0.117221 | − | 0.437473i | ||||
\(87\) | 0.389800i | 0.0417909i | ||||||||
\(88\) | −5.54006 | − | 3.19856i | −0.590573 | − | 0.340967i | ||||
\(89\) | 5.91573 | + | 5.91573i | 0.627066 | + | 0.627066i | 0.947329 | − | 0.320263i | \(-0.103771\pi\) |
−0.320263 | + | 0.947329i | \(0.603771\pi\) | |||||||
\(90\) | −6.77438 | −0.714082 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.54710 | −0.369811 | ||||||||
\(93\) | −3.14630 | − | 3.14630i | −0.326256 | − | 0.326256i | ||||
\(94\) | 3.10329 | + | 1.79169i | 0.320080 | + | 0.184798i | ||||
\(95\) | 3.53049i | 0.362221i | ||||||||
\(96\) | 0.458582 | + | 1.71145i | 0.0468038 | + | 0.174674i | ||||
\(97\) | 0.933928 | + | 3.48547i | 0.0948260 | + | 0.353896i | 0.996993 | − | 0.0774914i | \(-0.0246910\pi\) |
−0.902167 | + | 0.431387i | \(0.858024\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.57284 | + | 5.57284i | −0.560091 | + | 0.560091i | ||||
\(100\) | 0.842092 | + | 1.45855i | 0.0842092 | + | 0.145855i | ||||
\(101\) | −9.84474 | + | 17.0516i | −0.979589 | + | 1.69670i | −0.315713 | + | 0.948855i | \(0.602244\pi\) |
−0.663876 | + | 0.747843i | \(0.731090\pi\) | |||||||
\(102\) | 1.34104 | + | 5.00482i | 0.132783 | + | 0.495551i | ||||
\(103\) | 4.70130 | − | 8.14290i | 0.463233 | − | 0.802344i | −0.535887 | − | 0.844290i | \(-0.680023\pi\) |
0.999120 | + | 0.0419464i | \(0.0133559\pi\) | |||||||
\(104\) | 7.89105 | − | 1.35681i | 0.773781 | − | 0.133046i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.07659 | + | 7.74995i | −0.201697 | + | 0.752742i | ||||
\(107\) | 0.0718412 | 0.00694515 | 0.00347258 | − | 0.999994i | \(-0.498895\pi\) | ||||
0.00347258 | + | 0.999994i | \(0.498895\pi\) | |||||||
\(108\) | 1.85975 | 0.178954 | ||||||||
\(109\) | 1.89580 | − | 7.07523i | 0.181585 | − | 0.677684i | −0.813751 | − | 0.581214i | \(-0.802578\pi\) |
0.995336 | − | 0.0964705i | \(-0.0307553\pi\) | |||||||
\(110\) | −6.88986 | − | 1.84613i | −0.656922 | − | 0.176022i | ||||
\(111\) | −2.99277 | + | 0.801910i | −0.284061 | + | 0.0761139i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.15754 | + | 14.1293i | −0.767396 | + | 1.32917i | 0.171574 | + | 0.985171i | \(0.445115\pi\) |
−0.938970 | + | 0.343998i | \(0.888219\pi\) | |||||||
\(114\) | − | 1.92782i | − | 0.180557i | ||||||
\(115\) | 8.29059 | − | 2.22146i | 0.773101 | − | 0.207152i | ||||
\(116\) | −0.414405 | + | 0.239257i | −0.0384765 | + | 0.0222144i | ||||
\(117\) | 0.901544 | − | 9.82307i | 0.0833478 | − | 0.908143i | ||||
\(118\) | 1.42969i | 0.131613i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.871127 | − | 1.50884i | −0.0795227 | − | 0.137737i | ||||
\(121\) | 2.33975 | − | 1.35085i | 0.212704 | − | 0.122805i | ||||
\(122\) | −8.10931 | − | 2.17288i | −0.734182 | − | 0.196724i | ||||
\(123\) | 0.733324 | + | 0.733324i | 0.0661216 | + | 0.0661216i | ||||
\(124\) | 1.41372 | − | 5.27608i | 0.126956 | − | 0.473806i | ||||
\(125\) | −8.27895 | − | 8.27895i | −0.740492 | − | 0.740492i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9037 | − | 8.60464i | 1.32249 | − | 0.763538i | 0.338362 | − | 0.941016i | \(-0.390127\pi\) |
0.984125 | + | 0.177478i | \(0.0567937\pi\) | |||||||
\(128\) | 9.61876 | − | 9.61876i | 0.850186 | − | 0.850186i | ||||
\(129\) | −0.665390 | − | 1.15249i | −0.0585843 | − | 0.101471i | ||||
\(130\) | 8.10731 | − | 3.73858i | 0.711058 | − | 0.327895i | ||||
\(131\) | −4.73734 | − | 2.73511i | −0.413904 | − | 0.238967i | 0.278562 | − | 0.960418i | \(-0.410142\pi\) |
−0.692466 | + | 0.721451i | \(0.743476\pi\) | |||||||
\(132\) | 0.902178 | + | 0.241738i | 0.0785245 | + | 0.0210406i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 22.0557 | + | 12.7339i | 1.90532 | + | 1.10004i | ||||
\(135\) | −4.34676 | + | 1.16471i | −0.374110 | + | 0.100242i | ||||
\(136\) | 9.76040 | − | 9.76040i | 0.836947 | − | 0.836947i | ||||
\(137\) | −1.24060 | + | 1.24060i | −0.105991 | + | 0.105991i | −0.758114 | − | 0.652122i | \(-0.773879\pi\) |
0.652122 | + | 0.758114i | \(0.273879\pi\) | |||||||
\(138\) | −4.52706 | + | 1.21302i | −0.385369 | + | 0.103259i | ||||
\(139\) | −7.13953 | − | 4.12201i | −0.605567 | − | 0.349624i | 0.165662 | − | 0.986183i | \(-0.447024\pi\) |
−0.771228 | + | 0.636559i | \(0.780357\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.09669 | + | 0.293858i | 0.0923583 | + | 0.0247473i | ||||
\(142\) | −14.9846 | − | 8.65135i | −1.25748 | − | 0.726005i | ||||
\(143\) | 3.59387 | − | 9.74484i | 0.300534 | − | 0.814904i | ||||
\(144\) | −6.65333 | − | 11.5239i | −0.554444 | − | 0.960325i | ||||
\(145\) | 0.818741 | − | 0.818741i | 0.0679927 | − | 0.0679927i | ||||
\(146\) | −9.77330 | + | 5.64262i | −0.808844 | + | 0.466986i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.68947 | − | 2.68947i | −0.221073 | − | 0.221073i | ||||
\(149\) | 1.15185 | − | 4.29875i | 0.0943628 | − | 0.352167i | −0.902559 | − | 0.430566i | \(-0.858314\pi\) |
0.996922 | + | 0.0783988i | \(0.0249807\pi\) | |||||||
\(150\) | 1.57352 | + | 1.57352i | 0.128478 | + | 0.128478i | ||||
\(151\) | −8.69443 | − | 2.32966i | −0.707542 | − | 0.189585i | −0.112936 | − | 0.993602i | \(-0.536025\pi\) |
−0.594606 | + | 0.804017i | \(0.702692\pi\) | |||||||
\(152\) | −4.44769 | + | 2.56788i | −0.360755 | + | 0.208282i | ||||
\(153\) | −8.50276 | − | 14.7272i | −0.687407 | − | 1.19062i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.2171i | 1.06162i | ||||||||
\(156\) | −1.06159 | + | 0.489541i | −0.0849956 | + | 0.0391946i | ||||
\(157\) | 4.21105 | − | 2.43125i | 0.336078 | − | 0.194035i | −0.322458 | − | 0.946584i | \(-0.604509\pi\) |
0.658537 | + | 0.752549i | \(0.271176\pi\) | |||||||
\(158\) | −13.3098 | + | 3.56636i | −1.05887 | + | 0.283724i | ||||
\(159\) | 2.54217i | 0.201607i | ||||||||
\(160\) | 2.63155 | − | 4.55797i | 0.208042 | − | 0.360339i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −10.4856 | + | 2.80962i | −0.823830 | + | 0.220744i | ||||
\(163\) | 6.17099 | + | 1.65351i | 0.483349 | + | 0.129513i | 0.492262 | − | 0.870447i | \(-0.336170\pi\) |
−0.00891239 | + | 0.999960i | \(0.502837\pi\) | |||||||
\(164\) | −0.329503 | + | 1.22972i | −0.0257299 | + | 0.0960252i | ||||
\(165\) | −2.26004 | −0.175944 | ||||||||
\(166\) | 3.47364 | 0.269607 | ||||||||
\(167\) | −2.62064 | + | 9.78037i | −0.202791 | + | 0.756828i | 0.787320 | + | 0.616544i | \(0.211468\pi\) |
−0.990111 | + | 0.140283i | \(0.955199\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.34213 | + | 12.2534i | 0.334010 | + | 0.942569i | ||||
\(170\) | 7.69547 | − | 13.3289i | 0.590215 | − | 1.02228i | ||||
\(171\) | 1.63760 | + | 6.11160i | 0.125230 | + | 0.467366i | ||||
\(172\) | 0.816825 | − | 1.41478i | 0.0622823 | − | 0.107876i | ||||
\(173\) | 8.82380 | + | 15.2833i | 0.670861 | + | 1.16197i | 0.977660 | + | 0.210192i | \(0.0674088\pi\) |
−0.306799 | + | 0.951774i | \(0.599258\pi\) | |||||||
\(174\) | −0.447072 | + | 0.447072i | −0.0338925 | + | 0.0338925i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.62629 | − | 13.5335i | −0.273342 | − | 1.02013i | ||||
\(177\) | 0.117243 | + | 0.437557i | 0.00881253 | + | 0.0328888i | ||||
\(178\) | 13.5698i | 1.01710i | ||||||||
\(179\) | −17.5138 | − | 10.1116i | −1.30904 | − | 0.755775i | −0.327105 | − | 0.944988i | \(-0.606073\pi\) |
−0.981936 | + | 0.189213i | \(0.939406\pi\) | |||||||
\(180\) | −1.86319 | − | 1.86319i | −0.138874 | − | 0.138874i | ||||
\(181\) | 17.4649 | 1.29815 | 0.649077 | − | 0.760722i | \(-0.275155\pi\) | ||||
0.649077 | + | 0.760722i | \(0.275155\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.66005 | −0.196636 | ||||||||
\(184\) | 8.82867 | + | 8.82867i | 0.650858 | + | 0.650858i | ||||
\(185\) | 7.97040 | + | 4.60171i | 0.585995 | + | 0.338324i | ||||
\(186\) | − | 7.21716i | − | 0.529188i | ||||||
\(187\) | −4.63429 | − | 17.2954i | −0.338893 | − | 1.26477i | ||||
\(188\) | 0.360737 | + | 1.34629i | 0.0263094 | + | 0.0981882i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.04922 | + | 4.04922i | −0.293761 | + | 0.293761i | ||||
\(191\) | −0.0207944 | − | 0.0360170i | −0.00150463 | − | 0.00260610i | 0.865272 | − | 0.501302i | \(-0.167146\pi\) |
−0.866777 | + | 0.498696i | \(0.833812\pi\) | |||||||
\(192\) | 1.06266 | − | 1.84058i | 0.0766910 | − | 0.132833i | ||||
\(193\) | 3.23272 | + | 12.0647i | 0.232696 | + | 0.868434i | 0.979174 | + | 0.203024i | \(0.0650769\pi\) |
−0.746478 | + | 0.665411i | \(0.768256\pi\) | |||||||
\(194\) | −2.92643 | + | 5.06873i | −0.210106 | + | 0.363914i | ||||
\(195\) | 2.17466 | − | 1.80904i | 0.155731 | − | 0.129548i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.962573 | − | 3.59237i | 0.0685805 | − | 0.255946i | −0.923121 | − | 0.384510i | \(-0.874370\pi\) |
0.991701 | + | 0.128565i | \(0.0410369\pi\) | |||||||
\(198\) | −12.7833 | −0.908469 | ||||||||
\(199\) | 8.77707 | 0.622190 | 0.311095 | − | 0.950379i | \(-0.399304\pi\) | ||||
0.311095 | + | 0.950379i | \(0.399304\pi\) | |||||||
\(200\) | 1.53434 | − | 5.72624i | 0.108494 | − | 0.404907i | ||||
\(201\) | 7.79442 | + | 2.08851i | 0.549776 | + | 0.147312i | ||||
\(202\) | −30.8482 | + | 8.26575i | −2.17047 | + | 0.581576i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.00767 | + | 1.74533i | −0.0705508 | + | 0.122198i | ||||
\(205\) | − | 3.08057i | − | 0.215156i | ||||||
\(206\) | 14.7314 | − | 3.94726i | 1.02638 | − | 0.275019i | ||||
\(207\) | 13.3213 | − | 7.69108i | 0.925898 | − | 0.534567i | ||||
\(208\) | 14.3221 | + | 10.1196i | 0.993062 | + | 0.701666i | ||||
\(209\) | 6.66206i | 0.460824i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.33665 | − | 5.77924i | −0.229704 | − | 0.397859i | 0.728016 | − | 0.685560i | \(-0.240443\pi\) |
−0.957720 | + | 0.287701i | \(0.907109\pi\) | |||||||
\(212\) | −2.70264 | + | 1.56037i | −0.185618 | + | 0.107167i | ||||
\(213\) | −5.29551 | − | 1.41893i | −0.362842 | − | 0.0972232i | ||||
\(214\) | 0.0823968 | + | 0.0823968i | 0.00563253 | + | 0.00563253i | ||||
\(215\) | −1.02311 | + | 3.81830i | −0.0697756 | + | 0.260406i | ||||
\(216\) | −4.62888 | − | 4.62888i | −0.314955 | − | 0.314955i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.2891 | − | 5.94043i | 0.696868 | − | 0.402337i | ||||
\(219\) | −2.52840 | + | 2.52840i | −0.170853 | + | 0.170853i | ||||
\(220\) | −1.38720 | − | 2.40270i | −0.0935249 | − | 0.161990i | ||||
\(221\) | 18.3033 | + | 12.9325i | 1.23121 | + | 0.869936i | ||||
\(222\) | −4.35222 | − | 2.51276i | −0.292102 | − | 0.168645i | ||||
\(223\) | 6.10027 | + | 1.63456i | 0.408505 | + | 0.109458i | 0.457219 | − | 0.889354i | \(-0.348846\pi\) |
−0.0487142 | + | 0.998813i | \(0.515512\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.32505 | − | 3.65177i | −0.421670 | − | 0.243451i | ||||
\(226\) | −25.5614 | + | 6.84915i | −1.70032 | + | 0.455599i | ||||
\(227\) | −16.6512 | + | 16.6512i | −1.10518 | + | 1.10518i | −0.111402 | + | 0.993775i | \(0.535534\pi\) |
−0.993775 | + | 0.111402i | \(0.964466\pi\) | |||||||
\(228\) | 0.530217 | − | 0.530217i | 0.0351145 | − | 0.0351145i | ||||
\(229\) | −18.2790 | + | 4.89785i | −1.20791 | + | 0.323659i | −0.805942 | − | 0.591995i | \(-0.798341\pi\) |
−0.401969 | + | 0.915653i | \(0.631674\pi\) | |||||||
\(230\) | 12.0566 | + | 6.96086i | 0.794986 | + | 0.458985i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.62695 | + | 0.435940i | 0.106814 | + | 0.0286209i | ||||
\(233\) | 6.36747 | + | 3.67626i | 0.417147 | + | 0.240840i | 0.693856 | − | 0.720114i | \(-0.255910\pi\) |
−0.276709 | + | 0.960954i | \(0.589244\pi\) | |||||||
\(234\) | 12.3004 | − | 10.2324i | 0.804100 | − | 0.668910i | ||||
\(235\) | −1.68629 | − | 2.92074i | −0.110001 | − | 0.190528i | ||||
\(236\) | −0.393214 | + | 0.393214i | −0.0255960 | + | 0.0255960i | ||||
\(237\) | −3.78102 | + | 2.18297i | −0.245604 | + | 0.141799i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.08646 | − | 4.08646i | −0.264331 | − | 0.264331i | 0.562480 | − | 0.826811i | \(-0.309847\pi\) |
−0.826811 | + | 0.562480i | \(0.809847\pi\) | |||||||
\(240\) | 0.987620 | − | 3.68585i | 0.0637506 | − | 0.237921i | ||||
\(241\) | −20.3223 | − | 20.3223i | −1.30907 | − | 1.30907i | −0.922085 | − | 0.386988i | \(-0.873515\pi\) |
−0.386988 | − | 0.922085i | \(-0.626485\pi\) | |||||||
\(242\) | 4.23286 | + | 1.13419i | 0.272098 | + | 0.0729086i | ||||
\(243\) | −10.6374 | + | 6.14150i | −0.682389 | + | 0.393977i | ||||
\(244\) | −1.63272 | − | 2.82796i | −0.104524 | − | 0.181041i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.68214i | 0.107249i | ||||||||
\(247\) | −5.33263 | − | 6.41038i | −0.339307 | − | 0.407883i | ||||
\(248\) | −16.6508 | + | 9.61333i | −1.05732 | + | 0.610447i | ||||
\(249\) | 1.06311 | − | 0.284859i | 0.0673718 | − | 0.0180522i | ||||
\(250\) | − | 18.9907i | − | 1.20108i | ||||||
\(251\) | 9.72695 | − | 16.8476i | 0.613960 | − | 1.06341i | −0.376606 | − | 0.926373i | \(-0.622909\pi\) |
0.990566 | − | 0.137036i | \(-0.0437576\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.6444 | − | 4.19190i | 0.983554 | − | 0.263543i | ||||
\(254\) | 26.9624 | + | 7.22454i | 1.69177 | + | 0.453308i | ||||
\(255\) | 1.26215 | − | 4.71041i | 0.0790389 | − | 0.294977i | ||||
\(256\) | 13.7931 | 0.862070 | ||||||||
\(257\) | 25.2048 | 1.57223 | 0.786116 | − | 0.618080i | \(-0.212089\pi\) | ||||
0.786116 | + | 0.618080i | \(0.212089\pi\) | |||||||
\(258\) | 0.558668 | − | 2.08498i | 0.0347812 | − | 0.129805i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.25803 | + | 1.20155i | 0.202054 | + | 0.0745170i | ||||
\(261\) | 1.03755 | − | 1.79708i | 0.0642225 | − | 0.111237i | ||||
\(262\) | −2.29642 | − | 8.57036i | −0.141873 | − | 0.529479i | ||||
\(263\) | −15.6393 | + | 27.0881i | −0.964362 | + | 1.67032i | −0.253041 | + | 0.967455i | \(0.581431\pi\) |
−0.711320 | + | 0.702868i | \(0.751902\pi\) | |||||||
\(264\) | −1.64382 | − | 2.84718i | −0.101170 | − | 0.175232i | ||||
\(265\) | 5.33961 | − | 5.33961i | 0.328010 | − | 0.328010i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.11281 | + | 4.15306i | 0.0681027 | + | 0.254163i | ||||
\(268\) | 2.56383 | + | 9.56834i | 0.156611 | + | 0.584479i | ||||
\(269\) | 9.01798i | 0.549836i | 0.961468 | + | 0.274918i | \(0.0886507\pi\) | ||||
−0.961468 | + | 0.274918i | \(0.911349\pi\) | |||||||
\(270\) | −6.32126 | − | 3.64958i | −0.384700 | − | 0.222107i | ||||
\(271\) | −2.40845 | − | 2.40845i | −0.146303 | − | 0.146303i | 0.630161 | − | 0.776464i | \(-0.282989\pi\) |
−0.776464 | + | 0.630161i | \(0.782989\pi\) | |||||||
\(272\) | 30.2318 | 1.83308 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.84575 | −0.171918 | ||||||||
\(275\) | −5.43770 | − | 5.43770i | −0.327906 | − | 0.327906i | ||||
\(276\) | −1.57872 | − | 0.911475i | −0.0950279 | − | 0.0548644i | ||||
\(277\) | 4.02905i | 0.242082i | 0.992648 | + | 0.121041i | \(0.0386232\pi\) | ||||
−0.992648 | + | 0.121041i | \(0.961377\pi\) | |||||||
\(278\) | −3.46088 | − | 12.9162i | −0.207570 | − | 0.774661i | ||||
\(279\) | 6.13066 | + | 22.8799i | 0.367033 | + | 1.36979i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.28511 | + | 3.28511i | −0.195973 | + | 0.195973i | −0.798271 | − | 0.602298i | \(-0.794252\pi\) |
0.602298 | + | 0.798271i | \(0.294252\pi\) | |||||||
\(282\) | 0.920795 | + | 1.59486i | 0.0548326 | + | 0.0949728i | ||||
\(283\) | −0.514830 | + | 0.891711i | −0.0306035 | + | 0.0530067i | −0.880921 | − | 0.473262i | \(-0.843076\pi\) |
0.850318 | + | 0.526269i | \(0.176410\pi\) | |||||||
\(284\) | −1.74186 | − | 6.50070i | −0.103360 | − | 0.385745i | ||||
\(285\) | −0.907206 | + | 1.57133i | −0.0537383 | + | 0.0930774i | ||||
\(286\) | 15.2985 | − | 7.05473i | 0.904622 | − | 0.417155i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.44126 | − | 9.11089i | 0.143852 | − | 0.536864i | ||||
\(289\) | 21.6354 | 1.27267 | ||||||||
\(290\) | 1.87807 | 0.110284 | ||||||||
\(291\) | −0.479970 | + | 1.79127i | −0.0281364 | + | 0.105006i | ||||
\(292\) | −4.23991 | − | 1.13608i | −0.248122 | − | 0.0664840i | ||||
\(293\) | −24.6989 | + | 6.61806i | −1.44293 | + | 0.386631i | −0.893558 | − | 0.448948i | \(-0.851799\pi\) |
−0.549369 | + | 0.835580i | \(0.685132\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.672792 | − | 1.16531i | 0.0391715 | − | 0.0678470i | ||||
\(296\) | 13.3881i | 0.778166i | ||||||||
\(297\) | −8.20236 | + | 2.19782i | −0.475949 | + | 0.127530i | ||||
\(298\) | 6.25144 | − | 3.60927i | 0.362136 | − | 0.209079i | ||||
\(299\) | −11.6980 | + | 16.5561i | −0.676512 | + | 0.957461i | ||||
\(300\) | 0.865547i | 0.0499724i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.29993 | − | 12.6438i | −0.420064 | − | 0.727571i | ||||
\(303\) | −8.76327 | + | 5.05947i | −0.503436 | + | 0.290659i | ||||
\(304\) | −10.8650 | − | 2.91127i | −0.623151 | − | 0.166973i | ||||
\(305\) | 5.58721 | + | 5.58721i | 0.319922 | + | 0.319922i | ||||
\(306\) | 7.13900 | − | 26.6431i | 0.408109 | − | 1.52309i | ||||
\(307\) | 14.0195 | + | 14.0195i | 0.800136 | + | 0.800136i | 0.983117 | − | 0.182981i | \(-0.0585745\pi\) |
−0.182981 | + | 0.983117i | \(0.558575\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.18485 | − | 2.41612i | 0.238068 | − | 0.137449i | ||||
\(310\) | −15.1590 | + | 15.1590i | −0.860975 | + | 0.860975i | ||||
\(311\) | −3.20853 | − | 5.55733i | −0.181939 | − | 0.315127i | 0.760602 | − | 0.649219i | \(-0.224904\pi\) |
−0.942541 | + | 0.334091i | \(0.891571\pi\) | |||||||
\(312\) | 3.86074 | + | 1.42383i | 0.218572 | + | 0.0806085i | ||||
\(313\) | 21.8008 | + | 12.5867i | 1.23225 | + | 0.711441i | 0.967499 | − | 0.252875i | \(-0.0813762\pi\) |
0.264753 | + | 0.964316i | \(0.414709\pi\) | |||||||
\(314\) | 7.61824 | + | 2.04130i | 0.429922 | + | 0.115197i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.64154 | − | 2.67979i | −0.261107 | − | 0.150750i | ||||
\(317\) | 23.2745 | − | 6.23639i | 1.30723 | − | 0.350271i | 0.463049 | − | 0.886333i | \(-0.346755\pi\) |
0.844178 | + | 0.536062i | \(0.180089\pi\) | |||||||
\(318\) | −2.91569 | + | 2.91569i | −0.163504 | + | 0.163504i | ||||
\(319\) | 1.54497 | − | 1.54497i | 0.0865017 | − | 0.0865017i | ||||
\(320\) | −6.09802 | + | 1.63396i | −0.340890 | + | 0.0913411i | ||||
\(321\) | 0.0319746 | + | 0.0184606i | 0.00178465 | + | 0.00103037i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.8852 | − | 3.72052i | −0.772591 | − | 0.207015i | ||||
\(324\) | −3.65665 | − | 2.11117i | −0.203147 | − | 0.117287i | ||||
\(325\) | 9.58488 | + | 0.879683i | 0.531673 | + | 0.0487960i | ||||
\(326\) | 5.18123 | + | 8.97415i | 0.286962 | + | 0.497032i | ||||
\(327\) | 2.66185 | − | 2.66185i | 0.147200 | − | 0.147200i | ||||
\(328\) | 3.88088 | − | 2.24063i | 0.214286 | − | 0.123718i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.59210 | − | 2.59210i | −0.142691 | − | 0.142691i | ||||
\(331\) | −1.52989 | + | 5.70964i | −0.0840905 | + | 0.313830i | −0.995140 | − | 0.0984660i | \(-0.968606\pi\) |
0.911050 | + | 0.412296i | \(0.135273\pi\) | |||||||
\(332\) | 0.955370 | + | 0.955370i | 0.0524328 | + | 0.0524328i | ||||
\(333\) | 15.9320 | + | 4.26895i | 0.873066 | + | 0.233937i | ||||
\(334\) | −14.2231 | + | 8.21169i | −0.778252 | + | 0.449324i | ||||
\(335\) | −11.9848 | − | 20.7583i | −0.654799 | − | 1.13414i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 11.5318i | − | 0.628179i | −0.949393 | − | 0.314089i | \(-0.898301\pi\) | ||
0.949393 | − | 0.314089i | \(-0.101699\pi\) | |||||||
\(338\) | −9.07366 | + | 19.0339i | −0.493542 | + | 1.03531i | ||||
\(339\) | −7.26140 | + | 4.19237i | −0.394385 | + | 0.227698i | ||||
\(340\) | 5.78244 | − | 1.54940i | 0.313597 | − | 0.0840280i | ||||
\(341\) | 24.9407i | 1.35061i | ||||||||
\(342\) | −5.13136 | + | 8.88778i | −0.277472 | + | 0.480596i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.55442 | + | 1.48830i | −0.299474 | + | 0.0802439i | ||||
\(345\) | 4.26075 | + | 1.14166i | 0.229391 | + | 0.0614652i | ||||
\(346\) | −7.40855 | + | 27.6491i | −0.398286 | + | 1.48642i | ||||
\(347\) | 9.07305 | 0.487067 | 0.243533 | − | 0.969893i | \(-0.421693\pi\) | ||||
0.243533 | + | 0.969893i | \(0.421693\pi\) | |||||||
\(348\) | −0.245921 | −0.0131827 | ||||||||
\(349\) | 7.77792 | − | 29.0276i | 0.416342 | − | 1.55381i | −0.365789 | − | 0.930698i | \(-0.619201\pi\) |
0.782132 | − | 0.623113i | \(-0.214132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.13326 | − | 8.68035i | 0.327369 | − | 0.463323i | ||||
\(352\) | 4.96574 | − | 8.60092i | 0.264675 | − | 0.458431i | ||||
\(353\) | −7.50007 | − | 27.9907i | −0.399189 | − | 1.48979i | −0.814527 | − | 0.580125i | \(-0.803004\pi\) |
0.415338 | − | 0.909667i | \(-0.363663\pi\) | |||||||
\(354\) | −0.367377 | + | 0.636316i | −0.0195259 | + | 0.0338198i | ||||
\(355\) | 8.14242 | + | 14.1031i | 0.432155 | + | 0.748514i | ||||
\(356\) | −3.73217 | + | 3.73217i | −0.197805 | + | 0.197805i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.48978 | − | 31.6843i | −0.448699 | − | 1.67457i | ||||
\(359\) | 2.28482 | + | 8.52708i | 0.120588 | + | 0.450042i | 0.999644 | − | 0.0266770i | \(-0.00849258\pi\) |
−0.879056 | + | 0.476719i | \(0.841826\pi\) | |||||||
\(360\) | 9.27487i | 0.488828i | ||||||||
\(361\) | −11.8226 | − | 6.82577i | −0.622241 | − | 0.359251i | ||||
\(362\) | 20.0310 | + | 20.0310i | 1.05280 | + | 1.05280i | ||||
\(363\) | 1.38848 | 0.0728763 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.6214 | 0.555947 | ||||||||
\(366\) | −3.05089 | − | 3.05089i | −0.159472 | − | 0.159472i | ||||
\(367\) | 11.5082 | + | 6.64427i | 0.600724 | + | 0.346828i | 0.769326 | − | 0.638856i | \(-0.220592\pi\) |
−0.168602 | + | 0.985684i | \(0.553925\pi\) | |||||||
\(368\) | 27.3459i | 1.42550i | ||||||||
\(369\) | −1.42890 | − | 5.33274i | −0.0743858 | − | 0.277611i | ||||
\(370\) | 3.86364 | + | 14.4193i | 0.200861 | + | 0.749624i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.98497 | − | 1.98497i | 0.102916 | − | 0.102916i | ||||
\(373\) | 4.12496 | + | 7.14464i | 0.213582 | + | 0.369935i | 0.952833 | − | 0.303495i | \(-0.0981535\pi\) |
−0.739251 | + | 0.673430i | \(0.764820\pi\) | |||||||
\(374\) | 14.5214 | − | 25.1518i | 0.750884 | − | 1.30057i | ||||
\(375\) | −1.55735 | − | 5.81212i | −0.0804214 | − | 0.300137i | ||||
\(376\) | 2.45302 | − | 4.24875i | 0.126505 | − | 0.219113i | ||||
\(377\) | −0.249937 | + | 2.72327i | −0.0128724 | + | 0.140256i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.896568 | − | 3.34604i | 0.0460536 | − | 0.171874i | −0.939069 | − | 0.343730i | \(-0.888310\pi\) |
0.985122 | + | 0.171855i | \(0.0549762\pi\) | |||||||
\(380\) | −2.22735 | −0.114261 | ||||||||
\(381\) | 8.84430 | 0.453107 | ||||||||
\(382\) | 0.0174592 | − | 0.0651586i | 0.000893291 | − | 0.00333381i | ||||
\(383\) | −33.2559 | − | 8.91088i | −1.69930 | − | 0.455325i | −0.726534 | − | 0.687131i | \(-0.758870\pi\) |
−0.972762 | + | 0.231806i | \(0.925537\pi\) | |||||||
\(384\) | 6.75272 | − | 1.80939i | 0.344598 | − | 0.0923348i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.1296 | + | 17.5450i | −0.515584 | + | 0.893018i | ||||
\(387\) | 7.08439i | 0.360120i | ||||||||
\(388\) | −2.19894 | + | 0.589205i | −0.111635 | + | 0.0299124i | ||||
\(389\) | −8.07601 | + | 4.66269i | −0.409470 | + | 0.236408i | −0.690562 | − | 0.723273i | \(-0.742637\pi\) |
0.281092 | + | 0.959681i | \(0.409303\pi\) | |||||||
\(390\) | 4.56902 | + | 0.419337i | 0.231362 | + | 0.0212340i | ||||
\(391\) | 34.9473i | 1.76736i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.40564 | − | 2.43465i | −0.0709053 | − | 0.122812i | ||||
\(394\) | 5.22420 | − | 3.01619i | 0.263191 | − | 0.151954i | ||||
\(395\) | 12.5269 | + | 3.35656i | 0.630295 | + | 0.168887i | ||||
\(396\) | −3.51584 | − | 3.51584i | −0.176678 | − | 0.176678i | ||||
\(397\) | 5.12022 | − | 19.1089i | 0.256977 | − | 0.959049i | −0.710004 | − | 0.704198i | \(-0.751307\pi\) |
0.966980 | − | 0.254852i | \(-0.0820266\pi\) | |||||||
\(398\) | 10.0667 | + | 10.0667i | 0.504596 | + | 0.504596i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.2445 | − | 6.49199i | 0.562223 | − | 0.324600i | ||||
\(401\) | 8.51496 | − | 8.51496i | 0.425217 | − | 0.425217i | −0.461778 | − | 0.886995i | \(-0.652788\pi\) |
0.886995 | + | 0.461778i | \(0.152788\pi\) | |||||||
\(402\) | 6.54427 | + | 11.3350i | 0.326399 | + | 0.565339i | ||||
\(403\) | −19.9637 | − | 23.9985i | −0.994463 | − | 1.19545i | ||||
\(404\) | −10.7577 | − | 6.21095i | −0.535214 | − | 0.309006i | ||||
\(405\) | 9.86881 | + | 2.64434i | 0.490385 | + | 0.131398i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.0402 | + | 8.68346i | 0.745514 | + | 0.430423i | ||||
\(408\) | 6.85216 | − | 1.83603i | 0.339232 | − | 0.0908970i | ||||
\(409\) | 13.7865 | − | 13.7865i | 0.681696 | − | 0.681696i | −0.278686 | − | 0.960382i | \(-0.589899\pi\) |
0.960382 | + | 0.278686i | \(0.0898988\pi\) | |||||||
\(410\) | 3.53319 | − | 3.53319i | 0.174492 | − | 0.174492i | ||||
\(411\) | −0.870943 | + | 0.233368i | −0.0429605 | + | 0.0115112i | ||||
\(412\) | 5.13727 | + | 2.96600i | 0.253095 | + | 0.146125i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 24.0998 | + | 6.45751i | 1.18444 | + | 0.317369i | ||||
\(415\) | −2.83129 | − | 1.63465i | −0.138983 | − | 0.0802417i | ||||
\(416\) | 2.10644 | + | 12.2508i | 0.103277 | + | 0.600645i | ||||
\(417\) | −2.11841 | − | 3.66919i | −0.103739 | − | 0.179681i | ||||
\(418\) | −7.64091 | + | 7.64091i | −0.373729 | + | 0.373729i | ||||
\(419\) | 3.34749 | − | 1.93268i | 0.163536 | − | 0.0944174i | −0.415999 | − | 0.909365i | \(-0.636568\pi\) |
0.579534 | + | 0.814948i | \(0.303235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.65782 | + | 3.65782i | 0.178271 | + | 0.178271i | 0.790602 | − | 0.612331i | \(-0.209768\pi\) |
−0.612331 | + | 0.790602i | \(0.709768\pi\) | |||||||
\(422\) | 2.80148 | − | 10.4553i | 0.136374 | − | 0.508955i | ||||
\(423\) | −4.27389 | − | 4.27389i | −0.207803 | − | 0.207803i | ||||
\(424\) | 10.6105 | + | 2.84309i | 0.515293 | + | 0.138072i | ||||
\(425\) | 14.3701 | − | 8.29658i | 0.697052 | − | 0.402443i | ||||
\(426\) | −4.44616 | − | 7.70097i | −0.215417 | − | 0.373113i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.0453239i | 0.00219081i | ||||||||
\(429\) | 4.10360 | − | 3.41368i | 0.198124 | − | 0.164814i | ||||
\(430\) | −5.55275 | + | 3.20588i | −0.267778 | + | 0.154601i | ||||
\(431\) | 9.71910 | − | 2.60423i | 0.468153 | − | 0.125441i | −0.0170280 | − | 0.999855i | \(-0.505420\pi\) |
0.485181 | + | 0.874414i | \(0.338754\pi\) | |||||||
\(432\) | − | 14.3375i | − | 0.689812i | ||||||
\(433\) | 3.80951 | − | 6.59826i | 0.183073 | − | 0.317092i | −0.759852 | − | 0.650096i | \(-0.774729\pi\) |
0.942926 | + | 0.333004i | \(0.108062\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.574786 | − | 0.154013i | 0.0275589 | − | 0.00738438i | ||||
\(436\) | 4.46369 | + | 1.19604i | 0.213772 | + | 0.0572800i | ||||
\(437\) | 3.36536 | − | 12.5597i | 0.160987 | − | 0.600811i | ||||
\(438\) | −5.79978 | −0.277124 | ||||||||
\(439\) | −22.3628 | −1.06732 | −0.533658 | − | 0.845700i | \(-0.679183\pi\) | ||||
−0.533658 | + | 0.845700i | \(0.679183\pi\) | |||||||
\(440\) | −2.52756 | + | 9.43298i | −0.120497 | + | 0.449700i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.15988 | + | 35.8252i | 0.292996 | + | 1.70403i | ||||
\(443\) | −12.8459 | + | 22.2497i | −0.610326 | + | 1.05712i | 0.380859 | + | 0.924633i | \(0.375628\pi\) |
−0.991185 | + | 0.132483i | \(0.957705\pi\) | |||||||
\(444\) | −0.505917 | − | 1.88811i | −0.0240097 | − | 0.0896056i | ||||
\(445\) | 6.38578 | − | 11.0605i | 0.302715 | − | 0.524318i | ||||
\(446\) | 5.12185 | + | 8.87130i | 0.242527 | + | 0.420068i | ||||
\(447\) | 1.61727 | − | 1.61727i | 0.0764945 | − | 0.0764945i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.821652 | − | 3.06645i | −0.0387761 | − | 0.144715i | 0.943824 | − | 0.330449i | \(-0.107200\pi\) |
−0.982600 | + | 0.185735i | \(0.940534\pi\) | |||||||
\(450\) | −3.06606 | − | 11.4427i | −0.144535 | − | 0.539414i | ||||
\(451\) | − | 5.81305i | − | 0.273726i | ||||||
\(452\) | −8.91401 | − | 5.14650i | −0.419280 | − | 0.242071i | ||||
\(453\) | −3.27102 | − | 3.27102i | −0.153686 | − | 0.153686i | ||||
\(454\) | −38.1954 | −1.79260 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.63940 | −0.123601 | ||||||||
\(457\) | −23.2165 | − | 23.2165i | −1.08602 | − | 1.08602i | −0.995934 | − | 0.0900871i | \(-0.971285\pi\) |
−0.0900871 | − | 0.995934i | \(-0.528715\pi\) | |||||||
\(458\) | −26.5822 | − | 15.3472i | −1.24210 | − | 0.717129i | ||||
\(459\) | − | 18.3229i | − | 0.855239i | ||||||
\(460\) | 1.40149 | + | 5.23045i | 0.0653450 | + | 0.243871i | ||||
\(461\) | 1.38662 | + | 5.17492i | 0.0645811 | + | 0.241020i | 0.990669 | − | 0.136287i | \(-0.0435169\pi\) |
−0.926088 | + | 0.377307i | \(0.876850\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.0182 | + | 17.0182i | −0.790903 | + | 0.790903i | −0.981641 | − | 0.190738i | \(-0.938912\pi\) |
0.190738 | + | 0.981641i | \(0.438912\pi\) | |||||||
\(464\) | 1.84452 | + | 3.19480i | 0.0856295 | + | 0.148315i | ||||
\(465\) | −3.39630 | + | 5.88256i | −0.157500 | + | 0.272797i | ||||
\(466\) | 3.08663 | + | 11.5194i | 0.142985 | + | 0.533628i | ||||
\(467\) | 3.73447 | − | 6.46829i | 0.172811 | − | 0.299317i | −0.766591 | − | 0.642136i | \(-0.778049\pi\) |
0.939401 | + | 0.342819i | \(0.111382\pi\) | |||||||
\(468\) | 6.19727 | + | 0.568775i | 0.286469 | + | 0.0262916i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.41582 | − | 5.28393i | 0.0653071 | − | 0.243729i | ||||
\(471\) | 2.49897 | 0.115146 | ||||||||
\(472\) | 1.95740 | 0.0900967 | ||||||||
\(473\) | −1.93062 | + | 7.20516i | −0.0887698 | + | 0.331294i | ||||
\(474\) | −6.84028 | − | 1.83285i | −0.314184 | − | 0.0841854i | ||||
\(475\) | −5.96340 | + | 1.59789i | −0.273620 | + | 0.0733162i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.76661 | − | 11.7201i | 0.309822 | − | 0.536627i | ||||
\(478\) | − | 9.37376i | − | 0.428746i | ||||||
\(479\) | 20.1369 | − | 5.39566i | 0.920078 | − | 0.246534i | 0.232459 | − | 0.972606i | \(-0.425323\pi\) |
0.687619 | + | 0.726072i | \(0.258656\pi\) | |||||||
\(480\) | 2.34246 | − | 1.35242i | 0.106918 | − | 0.0617293i | ||||
\(481\) | −21.4227 | + | 3.68347i | −0.976789 | + | 0.167952i | ||||
\(482\) | − | 46.6164i | − | 2.12332i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.852240 | + | 1.47612i | 0.0387382 | + | 0.0670965i | ||||
\(485\) | 4.77055 | − | 2.75428i | 0.216620 | − | 0.125065i | ||||
\(486\) | −19.2442 | − | 5.15647i | −0.872934 | − | 0.233902i | ||||
\(487\) | −13.2023 | − | 13.2023i | −0.598255 | − | 0.598255i | 0.341593 | − | 0.939848i | \(-0.389034\pi\) |
−0.939848 | + | 0.341593i | \(0.889034\pi\) | |||||||
\(488\) | −2.97492 | + | 11.1025i | −0.134668 | + | 0.502588i | ||||
\(489\) | 2.32165 | + | 2.32165i | 0.104989 | + | 0.104989i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.9636 | − | 15.5675i | 1.21685 | − | 0.702550i | 0.252609 | − | 0.967569i | \(-0.418711\pi\) |
0.964243 | + | 0.265019i | \(0.0853781\pi\) | |||||||
\(492\) | −0.462646 | + | 0.462646i | −0.0208577 | + | 0.0208577i | ||||
\(493\) | 2.35724 | + | 4.08286i | 0.106165 | + | 0.183883i | ||||
\(494\) | 1.23611 | − | 13.4684i | 0.0556150 | − | 0.605972i | ||||
\(495\) | 10.4194 | + | 6.01565i | 0.468317 | + | 0.270383i | ||||
\(496\) | −40.6752 | − | 10.8989i | −1.82637 | − | 0.489374i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.54602 | + | 0.892597i | 0.0692790 | + | 0.0399982i | ||||
\(499\) | 17.9002 | − | 4.79636i | 0.801325 | − | 0.214714i | 0.165159 | − | 0.986267i | \(-0.447186\pi\) |
0.636166 | + | 0.771553i | \(0.280519\pi\) | |||||||
\(500\) | 5.22310 | − | 5.22310i | 0.233584 | − | 0.233584i | ||||
\(501\) | −3.67957 | + | 3.67957i | −0.164391 | + | 0.164391i | ||||
\(502\) | 30.4791 | − | 8.16684i | 1.36035 | − | 0.364504i | ||||
\(503\) | 22.0368 | + | 12.7230i | 0.982573 | + | 0.567289i | 0.903046 | − | 0.429544i | \(-0.141326\pi\) |
0.0795268 | + | 0.996833i | \(0.474659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.0335 | + | 7.77950i | 1.29197 | + | 0.346183i | ||||
\(506\) | 22.7508 | + | 13.1352i | 1.01140 | + | 0.583930i | ||||
\(507\) | −1.21611 | + | 6.56943i | −0.0540091 | + | 0.291759i | ||||
\(508\) | 5.42858 | + | 9.40257i | 0.240854 | + | 0.417172i | ||||
\(509\) | 17.5363 | − | 17.5363i | 0.777285 | − | 0.777285i | −0.202084 | − | 0.979368i | \(-0.564771\pi\) |
0.979368 | + | 0.202084i | \(0.0647713\pi\) | |||||||
\(510\) | 6.85009 | − | 3.95490i | 0.303327 | − | 0.175126i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.41779 | − | 3.41779i | −0.151046 | − | 0.151046i | ||||
\(513\) | −1.76446 | + | 6.58505i | −0.0779027 | + | 0.290737i | ||||
\(514\) | 28.9081 | + | 28.9081i | 1.27508 | + | 1.27508i | ||||
\(515\) | −13.8648 | − | 3.71506i | −0.610955 | − | 0.163705i | ||||
\(516\) | 0.727094 | − | 0.419788i | 0.0320085 | − | 0.0184801i | ||||
\(517\) | −3.18204 | − | 5.51145i | −0.139946 | − | 0.242393i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.06957i | 0.398110i | ||||||||
\(520\) | −5.11853 | − | 11.0998i | −0.224462 | − | 0.486758i | ||||
\(521\) | 3.53287 | − | 2.03970i | 0.154778 | − | 0.0893610i | −0.420611 | − | 0.907241i | \(-0.638184\pi\) |
0.575389 | + | 0.817880i | \(0.304851\pi\) | |||||||
\(522\) | 3.25112 | − | 0.871134i | 0.142298 | − | 0.0381285i | ||||
\(523\) | − | 29.4455i | − | 1.28756i | −0.765209 | − | 0.643781i | \(-0.777365\pi\) | ||
0.765209 | − | 0.643781i | \(-0.222635\pi\) | |||||||
\(524\) | 1.72555 | − | 2.98874i | 0.0753810 | − | 0.130564i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −49.0053 | + | 13.1309i | −2.13673 | + | 0.572536i | ||||
\(527\) | −51.9817 | − | 13.9285i | −2.26436 | − | 0.606733i | ||||
\(528\) | 1.86365 | − | 6.95522i | 0.0811048 | − | 0.302687i | ||||
\(529\) | −8.61121 | −0.374400 | ||||||||
\(530\) | 12.2483 | 0.532033 | ||||||||
\(531\) | 0.624142 | − | 2.32933i | 0.0270854 | − | 0.101084i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.65304 | + | 5.59345i | 0.201546 | + | 0.242279i | ||||
\(534\) | −3.48695 | + | 6.03957i | −0.150895 | + | 0.261358i | ||||
\(535\) | −0.0283851 | − | 0.105935i | −0.00122720 | − | 0.00457996i | ||||
\(536\) | 17.4341 | − | 30.1967i | 0.753038 | − | 1.30430i | ||||
\(537\) | −5.19661 | − | 9.00079i | −0.224250 | − | 0.388413i | ||||
\(538\) | −10.3430 | + | 10.3430i | −0.445917 | + | 0.445917i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.734804 | − | 2.74233i | −0.0316209 | − | 0.118011i | ||||
\(541\) | −9.74099 | − | 36.3539i | −0.418798 | − | 1.56298i | −0.777105 | − | 0.629371i | \(-0.783312\pi\) |
0.358307 | − | 0.933604i | \(-0.383354\pi\) | |||||||
\(542\) | − | 5.52463i | − | 0.237303i | ||||||
\(543\) | 7.77315 | + | 4.48783i | 0.333578 | + | 0.192591i | ||||
\(544\) | 15.1530 | + | 15.1530i | 0.649678 | + | 0.649678i | ||||
\(545\) | −11.1820 | −0.478982 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.7251 | −1.57025 | −0.785125 | − | 0.619337i | \(-0.787401\pi\) | ||||
−0.785125 | + | 0.619337i | \(0.787401\pi\) | |||||||
\(548\) | −0.782679 | − | 0.782679i | −0.0334344 | − | 0.0334344i | ||||
\(549\) | 12.2636 | + | 7.08037i | 0.523396 | + | 0.302183i | ||||
\(550\) | − | 12.4733i | − | 0.531864i | ||||||
\(551\) | −0.453995 | − | 1.69433i | −0.0193408 | − | 0.0721810i | ||||
\(552\) | 1.66076 | + | 6.19805i | 0.0706867 | + | 0.263806i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.62103 | + | 4.62103i | −0.196329 | + | 0.196329i | ||||
\(555\) | 2.36494 | + | 4.09620i | 0.100386 | + | 0.173874i | ||||
\(556\) | 2.60053 | − | 4.50425i | 0.110287 | − | 0.191023i | ||||
\(557\) | −5.17843 | − | 19.3262i | −0.219417 | − | 0.818876i | −0.984565 | − | 0.175021i | \(-0.944001\pi\) |
0.765148 | − | 0.643855i | \(-0.222666\pi\) | |||||||
\(558\) | −19.2102 | + | 33.2731i | −0.813233 | + | 1.40856i | ||||
\(559\) | −3.90967 | − | 8.47832i | −0.165361 | − | 0.358595i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.38168 | − | 8.88857i | 0.100555 | − | 0.375276i | ||||
\(562\) | −7.53556 | −0.317869 | ||||||||
\(563\) | −15.6920 | −0.661340 | −0.330670 | − | 0.943746i | \(-0.607275\pi\) | ||||
−0.330670 | + | 0.943746i | \(0.607275\pi\) | |||||||
\(564\) | −0.185392 | + | 0.691893i | −0.00780642 | + | 0.0291340i | ||||
\(565\) | 24.0577 | + | 6.44624i | 1.01211 | + | 0.271195i | ||||
\(566\) | −1.61320 | + | 0.432256i | −0.0678079 | + | 0.0181691i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.8447 | + | 20.5155i | −0.496991 | + | 0.860813i | ||||
\(569\) | − | 5.07533i | − | 0.212769i | −0.994325 | − | 0.106385i | \(-0.966073\pi\) | ||
0.994325 | − | 0.106385i | \(-0.0339275\pi\) | |||||||
\(570\) | −2.84270 | + | 0.761699i | −0.119068 | + | 0.0319041i | ||||
\(571\) | −17.5642 | + | 10.1407i | −0.735038 | + | 0.424374i | −0.820262 | − | 0.571988i | \(-0.806173\pi\) |
0.0852246 | + | 0.996362i | \(0.472839\pi\) | |||||||
\(572\) | 6.14792 | + | 2.26733i | 0.257057 | + | 0.0948020i | ||||
\(573\) | − | 0.0213736i | − | 0.000892895i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.50459 | + | 12.9983i | 0.312963 | + | 0.542068i | ||||
\(576\) | −9.79832 | + | 5.65706i | −0.408263 | + | 0.235711i | ||||
\(577\) | 25.2962 | + | 6.77811i | 1.05310 | + | 0.282176i | 0.743531 | − | 0.668702i | \(-0.233150\pi\) |
0.309566 | + | 0.950878i | \(0.399816\pi\) | |||||||
\(578\) | 24.8143 | + | 24.8143i | 1.03214 | + | 1.03214i | ||||
\(579\) | −1.66138 | + | 6.20036i | −0.0690446 | + | 0.257678i | ||||
\(580\) | 0.516535 | + | 0.516535i | 0.0214480 | + | 0.0214480i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.60495 | + | 1.50397i | −0.107979 | + | 0.0623416i | ||||
\(583\) | 10.0759 | − | 10.0759i | 0.417301 | − | 0.417301i | ||||
\(584\) | 7.72537 | + | 13.3807i | 0.319678 | + | 0.553698i | ||||
\(585\) | −14.8410 | + | 2.55180i | −0.613599 | + | 0.105504i | ||||
\(586\) | −35.9183 | − | 20.7375i | −1.48377 | − | 0.856657i | ||||
\(587\) | −1.75410 | − | 0.470009i | −0.0723994 | − | 0.0193994i | 0.222438 | − | 0.974947i | \(-0.428599\pi\) |
−0.294837 | + | 0.955548i | \(0.595265\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.3404 | + | 10.0115i | 0.714498 | + | 0.412516i | ||||
\(590\) | 2.10817 | − | 0.564883i | 0.0867921 | − | 0.0232559i | ||||
\(591\) | 1.35152 | − | 1.35152i | 0.0555942 | − | 0.0555942i | ||||
\(592\) | −20.7341 | + | 20.7341i | −0.852166 | + | 0.852166i | ||||
\(593\) | −30.9506 | + | 8.29320i | −1.27099 | + | 0.340561i | −0.830410 | − | 0.557153i | \(-0.811894\pi\) |
−0.440580 | + | 0.897713i | \(0.645227\pi\) | |||||||
\(594\) | −11.9283 | − | 6.88679i | −0.489423 | − | 0.282568i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.71203 | + | 0.726687i | 0.111089 | + | 0.0297663i | ||||
\(597\) | 3.90644 | + | 2.25538i | 0.159880 | + | 0.0923067i | ||||
\(598\) | −32.4054 | + | 5.57186i | −1.32515 | + | 0.227850i | ||||
\(599\) | 1.81349 | + | 3.14105i | 0.0740970 | + | 0.128340i | 0.900693 | − | 0.434456i | \(-0.143059\pi\) |
−0.826596 | + | 0.562795i | \(0.809726\pi\) | |||||||
\(600\) | 2.15433 | − | 2.15433i | 0.0879501 | − | 0.0879501i | ||||
\(601\) | −22.0032 | + | 12.7035i | −0.897529 | + | 0.518189i | −0.876398 | − | 0.481588i | \(-0.840060\pi\) |
−0.0211313 | + | 0.999777i | \(0.506727\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.3753 | − | 30.3753i | −1.23698 | − | 1.23698i | ||||
\(604\) | 1.46976 | − | 5.48522i | 0.0598037 | − | 0.223191i | ||||
\(605\) | −2.91638 | − | 2.91638i | −0.118568 | − | 0.118568i | ||||
\(606\) | −15.8537 | − | 4.24798i | −0.644012 | − | 0.172563i | ||||
\(607\) | −3.52942 | + | 2.03771i | −0.143255 | + | 0.0827081i | −0.569914 | − | 0.821704i | \(-0.693024\pi\) |
0.426660 | + | 0.904412i | \(0.359690\pi\) | |||||||
\(608\) | −3.98661 | − | 6.90502i | −0.161679 | − | 0.280035i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.8162i | 0.518915i | ||||||||
\(611\) | 7.47345 | + | 2.75619i | 0.302344 | + | 0.111503i | ||||
\(612\) | 9.29124 | − | 5.36430i | 0.375576 | − | 0.216839i | ||||
\(613\) | −22.4119 | + | 6.00524i | −0.905207 | + | 0.242550i | −0.681251 | − | 0.732050i | \(-0.738564\pi\) |
−0.223956 | + | 0.974599i | \(0.571897\pi\) | |||||||
\(614\) | 32.1588i | 1.29782i | ||||||||
\(615\) | 0.791593 | − | 1.37108i | 0.0319201 | − | 0.0552872i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.685439 | − | 0.183663i | 0.0275948 | − | 0.00739399i | −0.244995 | − | 0.969524i | \(-0.578786\pi\) |
0.272590 | + | 0.962130i | \(0.412120\pi\) | |||||||
\(618\) | 7.57085 | + | 2.02860i | 0.304544 | + | 0.0816023i | ||||
\(619\) | 3.54491 | − | 13.2298i | 0.142482 | − | 0.531751i | −0.857372 | − | 0.514697i | \(-0.827905\pi\) |
0.999855 | − | 0.0170541i | \(-0.00542874\pi\) | |||||||
\(620\) | −8.33851 | −0.334882 | ||||||||
\(621\) | 16.5738 | 0.665083 | ||||||||
\(622\) | 2.69391 | − | 10.0538i | 0.108016 | − | 0.403121i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.77405 | + | 8.18422i | 0.151083 | + | 0.327631i | ||||
\(625\) | −2.26294 | + | 3.91952i | −0.0905174 | + | 0.156781i | ||||
\(626\) | 10.5679 | + | 39.4399i | 0.422378 | + | 1.57634i | ||||
\(627\) | −1.71190 | + | 2.96510i | −0.0683669 | + | 0.118415i | ||||
\(628\) | 1.53385 | + | 2.65671i | 0.0612073 | + | 0.106014i | ||||
\(629\) | −26.4976 | + | 26.4976i | −1.05653 | + | 1.05653i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.371814 | − | 1.38763i | −0.0148017 | − | 0.0552407i | 0.958130 | − | 0.286334i | \(-0.0924365\pi\) |
−0.972932 | + | 0.231093i | \(0.925770\pi\) | |||||||
\(632\) | 4.88274 | + | 18.2226i | 0.194225 | + | 0.724858i | ||||
\(633\) | − | 3.42958i | − | 0.136314i | ||||||
\(634\) | 33.8469 | + | 19.5415i | 1.34423 | + | 0.776093i | ||||
\(635\) | −18.5767 | − | 18.5767i | −0.737194 | − | 0.737194i | ||||
\(636\) | −1.60383 | −0.0635960 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.54394 | 0.140306 | ||||||||
\(639\) | 20.6369 | + | 20.6369i | 0.816384 | + | 0.816384i | ||||
\(640\) | −17.9840 | − | 10.3830i | −0.710879 | − | 0.410426i | ||||
\(641\) | 11.0407i | 0.436083i | 0.975939 | + | 0.218042i | \(0.0699669\pi\) | ||||
−0.975939 | + | 0.218042i | \(0.930033\pi\) | |||||||
\(642\) | 0.0154997 | + | 0.0578455i | 0.000611723 | + | 0.00228298i | ||||
\(643\) | −11.5604 | − | 43.1441i | −0.455899 | − | 1.70144i | −0.685431 | − | 0.728138i | \(-0.740386\pi\) |
0.229532 | − | 0.973301i | \(-0.426281\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.43652 | + | 1.43652i | −0.0565630 | + | 0.0565630i | ||||
\(646\) | −11.6581 | − | 20.1924i | −0.458682 | − | 0.794461i | ||||
\(647\) | 5.20304 | − | 9.01192i | 0.204552 | − | 0.354295i | −0.745438 | − | 0.666575i | \(-0.767759\pi\) |
0.949990 | + | 0.312280i | \(0.101093\pi\) | |||||||
\(648\) | 3.84668 | + | 14.3560i | 0.151112 | + | 0.563957i | ||||
\(649\) | 1.26956 | − | 2.19895i | 0.0498347 | − | 0.0863163i | ||||
\(650\) | 9.98423 | + | 12.0021i | 0.391614 | + | 0.470761i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.04318 | + | 3.89321i | −0.0408542 | + | 0.152470i | ||||
\(653\) | −10.4386 | −0.408493 | −0.204246 | − | 0.978920i | \(-0.565474\pi\) | ||||
−0.204246 | + | 0.978920i | \(0.565474\pi\) | |||||||
\(654\) | 6.10589 | 0.238759 | ||||||||
\(655\) | −2.16133 | + | 8.06620i | −0.0844502 | + | 0.315172i | ||||
\(656\) | 9.48038 | + | 2.54026i | 0.370146 | + | 0.0991804i | ||||
\(657\) | 18.3865 | − | 4.92666i | 0.717327 | − | 0.192207i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.86557 | + | 6.69537i | −0.150581 | + | 0.260815i | −0.931441 | − | 0.363892i | \(-0.881448\pi\) |
0.780860 | + | 0.624706i | \(0.214781\pi\) | |||||||
\(660\) | − | 1.42584i | − | 0.0555006i | ||||||
\(661\) | −43.2687 | + | 11.5938i | −1.68296 | + | 0.450947i | −0.968558 | − | 0.248790i | \(-0.919967\pi\) |
−0.714401 | + | 0.699737i | \(0.753301\pi\) | |||||||
\(662\) | −8.30322 | + | 4.79387i | −0.322714 | + | 0.186319i | ||||
\(663\) | 4.82312 | + | 10.4592i | 0.187315 | + | 0.406201i | ||||
\(664\) | − | 4.75580i | − | 0.184561i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.3766 | + | 23.1690i | 0.518334 | + | 0.897780i | ||||
\(667\) | −3.69311 | + | 2.13222i | −0.142998 | + | 0.0825597i | ||||
\(668\) | −6.17033 | − | 1.65334i | −0.238737 | − | 0.0639695i | ||||
\(669\) | 2.29505 | + | 2.29505i | 0.0887316 | + | 0.0887316i | ||||
\(670\) | 10.0625 | − | 37.5539i | 0.388750 | − | 1.45083i | ||||
\(671\) | 10.5431 | + | 10.5431i | 0.407012 | + | 0.407012i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.6804 | + | 11.3625i | −0.758625 | + | 0.437992i | −0.828802 | − | 0.559542i | \(-0.810977\pi\) |
0.0701768 | + | 0.997535i | \(0.477644\pi\) | |||||||
\(674\) | 13.2262 | − | 13.2262i | 0.509454 | − | 0.509454i | ||||
\(675\) | −3.93466 | − | 6.81503i | −0.151445 | − | 0.262311i | ||||
\(676\) | −7.73054 | + | 2.73941i | −0.297329 | + | 0.105362i | ||||
\(677\) | 7.56955 | + | 4.37028i | 0.290921 | + | 0.167964i | 0.638357 | − | 0.769740i | \(-0.279614\pi\) |
−0.347436 | + | 0.937704i | \(0.612948\pi\) | |||||||
\(678\) | −13.1367 | − | 3.51996i | −0.504510 | − | 0.135183i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −18.2488 | − | 10.5359i | −0.699809 | − | 0.404035i | ||||
\(681\) | −11.6897 | + | 3.13226i | −0.447952 | + | 0.120028i | ||||
\(682\) | −28.6052 | + | 28.6052i | −1.09535 | + | 1.09535i | ||||
\(683\) | 1.57793 | − | 1.57793i | 0.0603777 | − | 0.0603777i | −0.676273 | − | 0.736651i | \(-0.736406\pi\) |
0.736651 | + | 0.676273i | \(0.236406\pi\) | |||||||
\(684\) | −3.85575 | + | 1.03314i | −0.147428 | + | 0.0395032i | ||||
\(685\) | 2.31951 | + | 1.33917i | 0.0886240 | + | 0.0511671i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.39407 | − | 2.51713i | −0.358406 | − | 0.0960346i | ||||
\(688\) | −10.9071 | − | 6.29720i | −0.415828 | − | 0.240078i | ||||
\(689\) | −1.63002 | + | 17.7605i | −0.0620990 | + | 0.676620i | ||||
\(690\) | 3.57737 | + | 6.19618i | 0.136188 | + | 0.235885i | ||||
\(691\) | 3.25857 | − | 3.25857i | 0.123962 | − | 0.123962i | −0.642404 | − | 0.766366i | \(-0.722063\pi\) |
0.766366 | + | 0.642404i | \(0.222063\pi\) | |||||||
\(692\) | −9.64206 | + | 5.56685i | −0.366536 | + | 0.211620i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.4061 | + | 10.4061i | 0.395012 | + | 0.395012i | ||||
\(695\) | −3.25729 | + | 12.1564i | −0.123556 | + | 0.461117i | ||||
\(696\) | 0.612091 | + | 0.612091i | 0.0232013 | + | 0.0232013i | ||||
\(697\) | 12.1156 | + | 3.24638i | 0.458913 | + | 0.122965i | ||||
\(698\) | 42.2133 | − | 24.3718i | 1.59780 | − | 0.922488i | ||||
\(699\) | 1.88933 | + | 3.27241i | 0.0714609 | + | 0.123774i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.7910i | 0.407569i | 0.979016 | + | 0.203784i | \(0.0653242\pi\) | ||||
−0.979016 | + | 0.203784i | \(0.934676\pi\) | |||||||
\(702\) | 16.9901 | − | 2.92133i | 0.641252 | − | 0.110258i | ||||
\(703\) | 12.0746 | − | 6.97128i | 0.455403 | − | 0.262927i | ||||
\(704\) | −11.5070 | + | 3.08329i | −0.433686 | + | 0.116206i | ||||
\(705\) | − | 1.73326i | − | 0.0652782i | ||||||
\(706\) | 23.5012 | − | 40.7053i | 0.884481 | − | 1.53197i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.276050 | + | 0.0739674i | −0.0103746 | + | 0.00277987i | ||||
\(709\) | −22.3737 | − | 5.99502i | −0.840262 | − | 0.225148i | −0.187076 | − | 0.982345i | \(-0.559901\pi\) |
−0.653186 | + | 0.757198i | \(0.726568\pi\) | |||||||
\(710\) | −6.83646 | + | 25.5140i | −0.256568 | + | 0.957524i | ||||
\(711\) | 23.2421 | 0.871646 | ||||||||
\(712\) | 18.5786 | 0.696262 | ||||||||
\(713\) | 12.5988 | − | 47.0195i | 0.471830 | − | 1.76090i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.7894 | − | 1.44912i | −0.590490 | − | 0.0541941i | ||||
\(716\) | 6.37929 | − | 11.0493i | 0.238405 | − | 0.412930i | ||||
\(717\) | −0.768705 | − | 2.86885i | −0.0287078 | − | 0.107139i | ||||
\(718\) | −7.15942 | + | 12.4005i | −0.267187 | + | 0.462782i | ||||
\(719\) | −17.9493 | − | 31.0890i | −0.669394 | − | 1.15942i | −0.978074 | − | 0.208259i | \(-0.933220\pi\) |
0.308679 | − | 0.951166i | \(-0.400113\pi\) | |||||||
\(720\) | −14.3640 | + | 14.3640i | −0.535314 | + | 0.535314i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.73099 | − | 21.3883i | −0.213285 | − | 0.795991i | ||||
\(723\) | −3.82283 | − | 14.2670i | −0.142172 | − | 0.530595i | ||||
\(724\) | 11.0184i | 0.409496i | ||||||||
\(725\) | 1.75351 | + | 1.01239i | 0.0651236 | + | 0.0375991i | ||||
\(726\) | 1.59249 | + | 1.59249i | 0.0591027 | + | 0.0591027i | ||||
\(727\) | −40.7770 | −1.51234 | −0.756168 | − | 0.654377i | \(-0.772931\pi\) | ||||
−0.756168 | + | 0.654377i | \(0.772931\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.7655 | 0.509832 | ||||||||
\(730\) | 12.1819 | + | 12.1819i | 0.450874 | + | 0.450874i | ||||
\(731\) | −13.9389 | − | 8.04764i | −0.515549 | − | 0.297653i | ||||
\(732\) | − | 1.67820i | − | 0.0620279i | ||||||
\(733\) | 6.43098 | + | 24.0007i | 0.237533 | + | 0.886487i | 0.976990 | + | 0.213283i | \(0.0684157\pi\) |
−0.739457 | + | 0.673204i | \(0.764918\pi\) | |||||||
\(734\) | 5.57860 | + | 20.8196i | 0.205910 | + | 0.768466i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.7065 | + | 13.7065i | −0.505227 | + | 0.505227i | ||||
\(737\) | −22.6154 | − | 39.1710i | −0.833048 | − | 1.44288i | ||||
\(738\) | 4.47742 | − | 7.75512i | 0.164816 | − | 0.285470i | ||||
\(739\) | −10.9878 | − | 41.0071i | −0.404194 | − | 1.50847i | −0.805538 | − | 0.592544i | \(-0.798124\pi\) |
0.401344 | − | 0.915927i | \(-0.368543\pi\) | |||||||
\(740\) | −2.90317 | + | 5.02844i | −0.106723 | + | 0.184849i | ||||
\(741\) | −0.726179 | − | 4.22338i | −0.0266768 | − | 0.155150i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.30753 | + | 23.5400i | −0.231401 | + | 0.863600i | 0.748337 | + | 0.663318i | \(0.230852\pi\) |
−0.979738 | + | 0.200282i | \(0.935814\pi\) | |||||||
\(744\) | −9.88108 | −0.362258 | ||||||||
\(745\) | −6.79390 | −0.248909 | ||||||||
\(746\) | −3.46336 | + | 12.9254i | −0.126802 | + | 0.473233i | ||||
\(747\) | −5.65945 | − | 1.51644i | −0.207068 | − | 0.0554838i | ||||
\(748\) | 10.9115 | − | 2.92373i | 0.398964 | − | 0.106902i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.87992 | − | 8.45226i | 0.178189 | − | 0.308633i | ||||
\(751\) | 28.4458i | 1.03800i | 0.854774 | + | 0.519001i | \(0.173696\pi\) | ||||
−0.854774 | + | 0.519001i | \(0.826304\pi\) | |||||||
\(752\) | 10.3790 | − | 2.78105i | 0.378484 | − | 0.101415i | ||||
\(753\) | 8.65841 | − | 4.99894i | 0.315530 | − | 0.182171i | ||||
\(754\) | −3.41006 | + | 2.83674i | −0.124187 | + | 0.103308i | ||||
\(755\) | 13.7410i | 0.500086i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.0081 | − | 45.0474i | −0.945282 | − | 1.63728i | −0.755187 | − | 0.655510i | \(-0.772454\pi\) |
−0.190095 | − | 0.981766i | \(-0.560880\pi\) | |||||||
\(758\) | 4.86597 | − | 2.80937i | 0.176740 | − | 0.102041i | ||||
\(759\) | 8.04006 | + | 2.15433i | 0.291836 | + | 0.0781972i | ||||
\(760\) | 5.54383 | + | 5.54383i | 0.201096 | + | 0.201096i | ||||
\(761\) | −1.53417 | + | 5.72561i | −0.0556137 | + | 0.207553i | −0.988142 | − | 0.153544i | \(-0.950931\pi\) |
0.932528 | + | 0.361098i | \(0.117598\pi\) | |||||||
\(762\) | 10.1438 | + | 10.1438i | 0.367470 | + | 0.367470i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.0227228 | − | 0.0131190i | 0.000822080 | − | 0.000474628i | ||||
\(765\) | −18.3567 | + | 18.3567i | −0.663690 | + | 0.663690i | ||||
\(766\) | −27.9220 | − | 48.3623i | −1.00886 | − | 1.74740i | ||||
\(767\) | 0.538541 | + | 3.13210i | 0.0194456 | + | 0.113093i | ||||
\(768\) | 6.13895 | + | 3.54433i | 0.221520 | + | 0.127895i | ||||
\(769\) | −0.310861 | − | 0.0832949i | −0.0112099 | − | 0.00300369i | 0.253210 | − | 0.967411i | \(-0.418514\pi\) |
−0.264420 | + | 0.964408i | \(0.585180\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.2180 | + | 6.47670i | 0.404005 | + | 0.233253i | ||||
\(772\) | −7.61148 | + | 2.03949i | −0.273943 | + | 0.0734028i | ||||
\(773\) | −22.4820 | + | 22.4820i | −0.808623 | + | 0.808623i | −0.984425 | − | 0.175802i | \(-0.943748\pi\) |
0.175802 | + | 0.984425i | \(0.443748\pi\) | |||||||
\(774\) | −8.12529 | + | 8.12529i | −0.292057 | + | 0.292057i | ||||
\(775\) | −22.3251 | + | 5.98200i | −0.801942 | + | 0.214880i | ||||
\(776\) | 6.93965 | + | 4.00661i | 0.249119 | + | 0.143829i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.6104 | − | 3.91484i | −0.523807 | − | 0.140354i | ||||
\(779\) | −4.04161 | − | 2.33343i | −0.144806 | − | 0.0836037i | ||||
\(780\) | 1.14131 | + | 1.37197i | 0.0408653 | + | 0.0491244i | ||||
\(781\) | 15.3648 | + | 26.6126i | 0.549796 | + | 0.952274i | ||||
\(782\) | −40.0820 | + | 40.0820i | −1.43333 | + | 1.43333i | ||||
\(783\) | 1.93630 | − | 1.11792i | 0.0691976 | − | 0.0399513i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.24887 | − | 5.24887i | −0.187340 | − | 0.187340i | ||||
\(786\) | 1.18019 | − | 4.40454i | 0.0420960 | − | 0.157105i | ||||
\(787\) | −23.7400 | − | 23.7400i | −0.846239 | − | 0.846239i | 0.143423 | − | 0.989662i | \(-0.454189\pi\) |
−0.989662 | + | 0.143423i | \(0.954189\pi\) | |||||||
\(788\) | 2.26639 | + | 0.607277i | 0.0807368 | + | 0.0216334i | ||||
\(789\) | −13.9213 | + | 8.03746i | −0.495611 | + | 0.286141i | ||||
\(790\) | 10.5177 | + | 18.2172i | 0.374202 | + | 0.648137i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 17.5017i | 0.621897i | ||||||||
\(793\) | −18.5840 | − | 1.70561i | −0.659937 | − | 0.0605678i | ||||
\(794\) | 27.7891 | − | 16.0440i | 0.986198 | − | 0.569382i | ||||
\(795\) | 3.74860 | − | 1.00444i | 0.132949 | − | 0.0356237i | ||||
\(796\) | 5.53736i | 0.196267i | ||||||||
\(797\) | −6.34434 | + | 10.9887i | −0.224728 | + | 0.389240i | −0.956238 | − | 0.292591i | \(-0.905483\pi\) |
0.731510 | + | 0.681831i | \(0.238816\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.2641 | − | 3.55410i | 0.469250 | − | 0.125735i | ||||
\(800\) | 8.88996 | + | 2.38206i | 0.314308 | + | 0.0842185i | ||||
\(801\) | 5.92402 | − | 22.1087i | 0.209315 | − | 0.781174i | ||||
\(802\) | 19.5321 | 0.689703 | ||||||||
\(803\) | 20.0426 | 0.707287 | ||||||||
\(804\) | −1.31762 | + | 4.91742i | −0.0464688 | + | 0.173424i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.62759 | − | 50.4215i | 0.163000 | − | 1.77602i | ||||
\(807\) | −2.31729 | + | 4.01366i | −0.0815724 | + | 0.141288i | ||||
\(808\) | 11.3167 | + | 42.2346i | 0.398121 | + | 1.48581i | ||||
\(809\) | 21.4022 | − | 37.0698i | 0.752463 | − | 1.30330i | −0.194163 | − | 0.980969i | \(-0.562199\pi\) |
0.946626 | − | 0.322334i | \(-0.104467\pi\) | |||||||
\(810\) | 8.28595 | + | 14.3517i | 0.291138 | + | 0.504267i | ||||
\(811\) | −1.51360 | + | 1.51360i | −0.0531496 | + | 0.0531496i | −0.733182 | − | 0.680032i | \(-0.761966\pi\) |
0.680032 | + | 0.733182i | \(0.261966\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.453053 | − | 1.69082i | −0.0158893 | − | 0.0592995i | ||||
\(814\) | 7.29072 | + | 27.2093i | 0.255539 | + | 0.953686i | ||||
\(815\) | − | 9.75286i | − | 0.341628i | ||||||
\(816\) | 13.4554 | + | 7.76847i | 0.471033 | + | 0.271951i | ||||
\(817\) | 4.23453 | + | 4.23453i | 0.148147 | + | 0.148147i | ||||
\(818\) | 31.6242 | 1.10571 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.94350 | 0.0678699 | ||||||||
\(821\) | 26.6039 | + | 26.6039i | 0.928481 | + | 0.928481i | 0.997608 | − | 0.0691268i | \(-0.0220213\pi\) |
−0.0691268 | + | 0.997608i | \(0.522021\pi\) | |||||||
\(822\) | −1.26657 | − | 0.731252i | −0.0441766 | − | 0.0255054i | ||||
\(823\) | − | 44.4969i | − | 1.55107i | −0.631308 | − | 0.775533i | \(-0.717481\pi\) | ||
0.631308 | − | 0.775533i | \(-0.282519\pi\) | |||||||
\(824\) | −5.40424 | − | 20.1689i | −0.188266 | − | 0.702616i | ||||
\(825\) | −1.02289 | − | 3.81747i | −0.0356124 | − | 0.132907i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.3898 | − | 12.3898i | 0.430835 | − | 0.430835i | −0.458077 | − | 0.888912i | \(-0.651462\pi\) |
0.888912 | + | 0.458077i | \(0.151462\pi\) | |||||||
\(828\) | 4.85222 | + | 8.40430i | 0.168626 | + | 0.292070i | ||||
\(829\) | 21.1381 | − | 36.6122i | 0.734155 | − | 1.27159i | −0.220938 | − | 0.975288i | \(-0.570912\pi\) |
0.955093 | − | 0.296306i | \(-0.0957548\pi\) | |||||||
\(830\) | −1.37247 | − | 5.12212i | −0.0476390 | − | 0.177791i | ||||
\(831\) | −1.03532 | + | 1.79322i | −0.0359147 | + | 0.0622061i | ||||
\(832\) | 8.60428 | − | 12.1776i | 0.298300 | − | 0.422181i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.77864 | − | 6.63796i | 0.0615891 | − | 0.229854i | ||||
\(835\) | 15.4573 | 0.534920 | ||||||||
\(836\) | −4.20302 | −0.145365 | ||||||||
\(837\) | −6.60558 | + | 24.6524i | −0.228322 | + | 0.852110i | ||||
\(838\) | 6.05597 | + | 1.62269i | 0.209200 | + | 0.0560550i | ||||
\(839\) | −25.6907 | + | 6.88379i | −0.886940 | + | 0.237655i | −0.673399 | − | 0.739279i | \(-0.735166\pi\) |
−0.213541 | + | 0.976934i | \(0.568500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.2124 | − | 24.6165i | 0.490081 | − | 0.848846i | ||||
\(842\) | 8.39052i | 0.289156i | ||||||||
\(843\) | −2.30626 | + | 0.617962i | −0.0794320 | + | 0.0212837i | ||||
\(844\) | 3.64606 | − | 2.10506i | 0.125503 | − | 0.0724590i | ||||
\(845\) | 16.3529 | − | 11.2442i | 0.562555 | − | 0.386812i | ||||
\(846\) | − | 9.80368i | − | 0.337058i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.0295 | + | 20.8356i | 0.413093 | + | 0.715498i | ||||
\(849\) | −0.458274 | + | 0.264585i | −0.0157279 | + | 0.00908052i | ||||
\(850\) | 25.9971 | + | 6.96589i | 0.891691 | + | 0.238928i | ||||
\(851\) | −23.9681 | − | 23.9681i | −0.821616 | − | 0.821616i | ||||
\(852\) | 0.895186 | − | 3.34088i | 0.0306686 | − | 0.114457i | ||||
\(853\) | 0.950856 | + | 0.950856i | 0.0325567 | + | 0.0325567i | 0.723198 | − | 0.690641i | \(-0.242672\pi\) |
−0.690641 | + | 0.723198i | \(0.742672\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.36494 | − | 4.82950i | 0.286075 | − | 0.165165i | ||||
\(856\) | 0.112810 | − | 0.112810i | 0.00385578 | − | 0.00385578i | ||||
\(857\) | 21.1903 | + | 36.7026i | 0.723845 | + | 1.25374i | 0.959447 | + | 0.281887i | \(0.0909605\pi\) |
−0.235602 | + | 0.971850i | \(0.575706\pi\) | |||||||
\(858\) | 8.62178 | + | 0.791292i | 0.294343 | + | 0.0270142i | ||||
\(859\) | 5.83030 | + | 3.36613i | 0.198927 | + | 0.114851i | 0.596155 | − | 0.802869i | \(-0.296694\pi\) |
−0.397228 | + | 0.917720i | \(0.630028\pi\) | |||||||
\(860\) | −2.40893 | − | 0.645470i | −0.0821437 | − | 0.0220103i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.1340 | + | 8.16026i | 0.481405 | + | 0.277939i | ||||
\(863\) | 17.8200 | − | 4.77484i | 0.606598 | − | 0.162537i | 0.0575702 | − | 0.998341i | \(-0.481665\pi\) |
0.549028 | + | 0.835804i | \(0.314998\pi\) | |||||||
\(864\) | 7.18631 | − | 7.18631i | 0.244483 | − | 0.244483i | ||||
\(865\) | 19.0499 | − | 19.0499i | 0.647715 | − | 0.647715i | ||||
\(866\) | 11.9370 | − | 3.19850i | 0.405634 | − | 0.108689i | ||||
\(867\) | 9.62934 | + | 5.55950i | 0.327030 | + | 0.188811i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.6383 | + | 6.33386i | 0.801874 | + | 0.214861i | ||||
\(870\) | 0.835881 | + | 0.482596i | 0.0283390 | + | 0.0163615i | ||||
\(871\) | 53.1153 | + | 19.5888i | 1.79974 | + | 0.663740i | ||||
\(872\) | −8.13311 | − | 14.0870i | −0.275422 | − | 0.477045i | ||||
\(873\) | 6.98070 | − | 6.98070i | 0.236261 | − | 0.236261i | ||||
\(874\) | 18.2649 | − | 10.5452i | 0.617819 | − | 0.356698i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.59514 | − | 1.59514i | −0.0538948 | − | 0.0538948i | ||||
\(877\) | 3.89991 | − | 14.5547i | 0.131691 | − | 0.491476i | −0.868299 | − | 0.496041i | \(-0.834787\pi\) |
0.999990 | + | 0.00456529i | \(0.00145318\pi\) | |||||||
\(878\) | −25.6485 | − | 25.6485i | −0.865595 | − | 0.865595i | ||||
\(879\) | −12.6934 | − | 3.40120i | −0.428139 | − | 0.114719i | ||||
\(880\) | −18.5233 | + | 10.6944i | −0.624420 | + | 0.360509i | ||||
\(881\) | 22.3633 | + | 38.7344i | 0.753439 | + | 1.30500i | 0.946146 | + | 0.323739i | \(0.104940\pi\) |
−0.192707 | + | 0.981256i | \(0.561727\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 46.5076i | − | 1.56510i | −0.622585 | − | 0.782552i | \(-0.713917\pi\) | ||
0.622585 | − | 0.782552i | \(-0.286083\pi\) | |||||||
\(884\) | −8.15899 | + | 11.5474i | −0.274417 | + | 0.388380i | ||||
\(885\) | 0.598884 | − | 0.345766i | 0.0201313 | − | 0.0116228i | ||||
\(886\) | −40.2522 | + | 10.7855i | −1.35230 | + | 0.362347i | ||||
\(887\) | − | 46.0518i | − | 1.54627i | −0.634244 | − | 0.773133i | \(-0.718688\pi\) | ||
0.634244 | − | 0.773133i | \(-0.281312\pi\) | |||||||
\(888\) | −3.44024 | + | 5.95867i | −0.115447 | + | 0.199960i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 20.0096 | − | 5.36156i | 0.670724 | − | 0.179720i | ||||
\(891\) | 18.6225 | + | 4.98988i | 0.623877 | + | 0.167167i | ||||
\(892\) | −1.03123 | + | 3.84860i | −0.0345281 | + | 0.128861i | ||||
\(893\) | −5.10923 | −0.170974 | ||||||||
\(894\) | 3.70980 | 0.124074 | ||||||||
\(895\) | −7.99036 | + | 29.8204i | −0.267088 | + | 0.996787i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.46076 | + | 4.36271i | −0.315885 | + | 0.145667i | ||||
\(898\) | 2.57462 | − | 4.45937i | 0.0859161 | − | 0.148811i | ||||
\(899\) | −1.69962 | − | 6.34305i | −0.0566854 | − | 0.211553i | ||||
\(900\) | 2.30386 | − | 3.99041i | 0.0767954 | − | 0.133014i | ||||
\(901\) | 15.3733 | + | 26.6273i | 0.512158 | + | 0.887085i | ||||
\(902\) | 6.66715 | − | 6.66715i | 0.221992 | − | 0.221992i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.37724 | + | 34.9963i | 0.311882 | + | 1.16396i | ||||
\(905\) | −6.90054 | − | 25.7532i | −0.229382 | − | 0.856064i | ||||
\(906\) | − | 7.50325i | − | 0.249279i | ||||||
\(907\) | 27.6067 | + | 15.9387i | 0.916666 | + | 0.529237i | 0.882570 | − | 0.470181i | \(-0.155811\pi\) |
0.0340961 | + | 0.999419i | \(0.489145\pi\) | |||||||
\(908\) | −10.5051 | − | 10.5051i | −0.348623 | − | 0.348623i | ||||
\(909\) | 53.8681 | 1.78669 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.8516 | 1.15469 | 0.577343 | − | 0.816502i | \(-0.304090\pi\) | ||||
0.577343 | + | 0.816502i | \(0.304090\pi\) | |||||||
\(912\) | −4.08763 | − | 4.08763i | −0.135355 | − | 0.135355i | ||||
\(913\) | −5.34267 | − | 3.08459i | −0.176817 | − | 0.102085i | ||||
\(914\) | − | 53.2553i | − | 1.76153i | ||||||
\(915\) | 1.05101 | + | 3.92242i | 0.0347453 | + | 0.129671i | ||||
\(916\) | −3.09000 | − | 11.5320i | −0.102096 | − | 0.381029i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 21.0150 | − | 21.0150i | 0.693599 | − | 0.693599i | ||||
\(919\) | 1.90511 | + | 3.29975i | 0.0628439 | + | 0.108849i | 0.895736 | − | 0.444587i | \(-0.146650\pi\) |
−0.832892 | + | 0.553436i | \(0.813316\pi\) | |||||||
\(920\) | 9.53018 | − | 16.5068i | 0.314201 | − | 0.544212i | ||||
\(921\) | 2.63721 | + | 9.84221i | 0.0868991 | + | 0.324312i | ||||
\(922\) | −4.34491 | + | 7.52561i | −0.143092 | + | 0.247843i | ||||
\(923\) | −36.0864 | − | 13.3085i | −1.18780 | − | 0.438056i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.16544 | + | 15.5456i | −0.136959 | + | 0.511137i | ||||
\(926\) | −39.0373 | −1.28285 | ||||||||
\(927\) | −25.7244 | −0.844900 | ||||||||
\(928\) | −0.676794 | + | 2.52583i | −0.0222169 | + | 0.0829145i | ||||
\(929\) | −36.3444 | − | 9.73846i | −1.19242 | − | 0.319509i | −0.392579 | − | 0.919718i | \(-0.628417\pi\) |
−0.799843 | + | 0.600210i | \(0.795084\pi\) | |||||||
\(930\) | −10.6422 | + | 2.85157i | −0.348971 | + | 0.0935065i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.31931 | + | 4.01717i | −0.0759717 | + | 0.131587i | ||||
\(933\) | − | 3.29789i | − | 0.107968i | ||||||
\(934\) | 11.7018 | − | 3.13550i | 0.382895 | − | 0.102597i | ||||
\(935\) | −23.6722 | + | 13.6672i | −0.774164 | + | 0.446964i | ||||
\(936\) | −14.0092 | − | 16.8406i | −0.457906 | − | 0.550451i | ||||
\(937\) | 38.0350i | 1.24255i | 0.783593 | + | 0.621275i | \(0.213385\pi\) | ||||
−0.783593 | + | 0.621275i | \(0.786615\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.46863 | + | 11.2040i | 0.211096 | + | 0.365628i | ||||
\(940\) | 1.84266 | − | 1.06386i | 0.0601010 | − | 0.0346993i | ||||
\(941\) | 25.3679 | + | 6.79732i | 0.826971 | + | 0.221586i | 0.647392 | − | 0.762157i | \(-0.275860\pi\) |
0.179579 | + | 0.983744i | \(0.442526\pi\) | |||||||
\(942\) | 2.86614 | + | 2.86614i | 0.0933838 | + | 0.0933838i | ||||
\(943\) | −2.93648 | + | 10.9591i | −0.0956248 | + | 0.356877i | ||||
\(944\) | 3.03143 | + | 3.03143i | 0.0986645 | + | 0.0986645i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.4781 | + | 6.04952i | −0.340672 | + | 0.196687i | ||||
\(947\) | −5.51091 | + | 5.51091i | −0.179081 | + | 0.179081i | −0.790955 | − | 0.611874i | \(-0.790416\pi\) |
0.611874 | + | 0.790955i | \(0.290416\pi\) | |||||||
\(948\) | −1.37722 | − | 2.38541i | −0.0447299 | − | 0.0774745i | ||||
\(949\) | −19.2854 | + | 16.0430i | −0.626031 | + | 0.520779i | ||||
\(950\) | −8.67226 | − | 5.00693i | −0.281365 | − | 0.162446i | ||||
\(951\) | 11.9614 | + | 3.20505i | 0.387875 | + | 0.103931i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.95143 | − | 4.59076i | −0.257572 | − | 0.148709i | 0.365654 | − | 0.930751i | \(-0.380845\pi\) |
−0.623227 | + | 0.782041i | \(0.714179\pi\) | |||||||
\(954\) | 21.2029 | − | 5.68131i | 0.686470 | − | 0.183939i | ||||
\(955\) | −0.0448934 | + | 0.0448934i | −0.00145272 | + | 0.00145272i | ||||
\(956\) | 2.57811 | − | 2.57811i | 0.0833820 | − | 0.0833820i | ||||
\(957\) | 1.08462 | − | 0.290624i | 0.0350609 | − | 0.00939455i | ||||
\(958\) | 29.2840 | + | 16.9071i | 0.946124 | + | 0.546245i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.13393 | − | 0.839735i | −0.101147 | − | 0.0271023i | ||||
\(961\) | 38.0702 | + | 21.9798i | 1.22807 | + | 0.709027i | ||||
\(962\) | −28.7949 | − | 20.3456i | −0.928386 | − | 0.655968i | ||||
\(963\) | −0.0982745 | − | 0.170216i | −0.00316685 | − | 0.00548515i | ||||
\(964\) | 12.8211 | − | 12.8211i | 0.412940 | − | 0.412940i | ||||
\(965\) | 16.5129 | − | 9.53373i | 0.531569 | − | 0.306902i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.3315 | + | 29.3315i | 0.943237 | + | 0.943237i | 0.998473 | − | 0.0552359i | \(-0.0175911\pi\) |
−0.0552359 | + | 0.998473i | \(0.517591\pi\) | |||||||
\(968\) | 1.55283 | − | 5.79525i | 0.0499099 | − | 0.186266i | ||||
\(969\) | −5.22388 | − | 5.22388i | −0.167815 | − | 0.167815i | ||||
\(970\) | 8.63045 | + | 2.31252i | 0.277107 | + | 0.0742506i | ||||
\(971\) | −32.5158 | + | 18.7730i | −1.04348 | + | 0.602455i | −0.920818 | − | 0.389993i | \(-0.872478\pi\) |
−0.122665 | + | 0.992448i | \(0.539144\pi\) | |||||||
\(972\) | −3.87461 | − | 6.71102i | −0.124278 | − | 0.215256i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 30.2843i | − | 0.970371i | ||||||
\(975\) | 4.03993 | + | 2.85448i | 0.129381 | + | 0.0914166i | ||||
\(976\) | −21.8017 | + | 12.5872i | −0.697857 | + | 0.402908i | ||||
\(977\) | 27.8219 | − | 7.45485i | 0.890101 | − | 0.238502i | 0.215341 | − | 0.976539i | \(-0.430914\pi\) |
0.674760 | + | 0.738037i | \(0.264247\pi\) | |||||||
\(978\) | 5.32554i | 0.170292i | ||||||||
\(979\) | 12.0500 | − | 20.8712i | 0.385120 | − | 0.667047i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.3570 | + | 5.18669i | −0.618021 | + | 0.165598i | ||||
\(982\) | 48.7801 | + | 13.0706i | 1.55664 | + | 0.417099i | ||||
\(983\) | −5.09738 | + | 19.0237i | −0.162581 | + | 0.606762i | 0.835755 | + | 0.549102i | \(0.185030\pi\) |
−0.998336 | + | 0.0576591i | \(0.981636\pi\) | |||||||
\(984\) | 2.30303 | 0.0734181 | ||||||||
\(985\) | −5.67752 | −0.180901 | ||||||||
\(986\) | −1.97916 | + | 7.38633i | −0.0630293 | + | 0.235229i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.04424 | − | 3.36430i | 0.128665 | − | 0.107033i | ||||
\(989\) | 7.27941 | − | 12.6083i | 0.231472 | − | 0.400921i | ||||
\(990\) | 5.05080 | + | 18.8498i | 0.160525 | + | 0.599087i | ||||
\(991\) | −17.6102 | + | 30.5018i | −0.559407 | + | 0.968921i | 0.438139 | + | 0.898907i | \(0.355638\pi\) |
−0.997546 | + | 0.0700140i | \(0.977696\pi\) | |||||||
\(992\) | −14.9246 | − | 25.8502i | −0.473858 | − | 0.820746i | ||||
\(993\) | −2.14808 | + | 2.14808i | −0.0681673 | + | 0.0681673i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.46790 | − | 12.9424i | −0.109940 | − | 0.410301i | ||||
\(996\) | 0.179715 | + | 0.670705i | 0.00569448 | + | 0.0212521i | ||||
\(997\) | − | 36.6156i | − | 1.15963i | −0.814749 | − | 0.579814i | \(-0.803125\pi\) | ||
0.814749 | − | 0.579814i | \(-0.196875\pi\) | |||||||
\(998\) | 26.0314 | + | 15.0292i | 0.824009 | + | 0.475742i | ||||
\(999\) | 12.5665 | + | 12.5665i | 0.397586 | + | 0.397586i |
(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 | 637.2.bb.a.362.6 | 28 | ||
7.2 | even | 3 | 637.2.bd.a.440.6 | 28 | |||
7.3 | odd | 6 | 637.2.x.a.570.2 | 28 | |||
7.4 | even | 3 | 91.2.w.a.24.2 | yes | 28 | ||
7.5 | odd | 6 | 637.2.bd.b.440.6 | 28 | |||
7.6 | odd | 2 | 91.2.ba.a.89.6 | yes | 28 | ||
13.6 | odd | 12 | 637.2.x.a.19.2 | 28 | |||
21.11 | odd | 6 | 819.2.gh.b.388.6 | 28 | |||
21.20 | even | 2 | 819.2.et.b.271.2 | 28 | |||
91.6 | even | 12 | 91.2.w.a.19.2 | ✓ | 28 | ||
91.19 | even | 12 | 637.2.bd.a.97.6 | 28 | |||
91.32 | odd | 12 | 91.2.ba.a.45.6 | yes | 28 | ||
91.45 | even | 12 | inner | 637.2.bb.a.227.6 | 28 | ||
91.58 | odd | 12 | 637.2.bd.b.97.6 | 28 | |||
273.32 | even | 12 | 819.2.et.b.136.2 | 28 | |||
273.188 | odd | 12 | 819.2.gh.b.19.6 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.w.a.19.2 | ✓ | 28 | 91.6 | even | 12 | ||
91.2.w.a.24.2 | yes | 28 | 7.4 | even | 3 | ||
91.2.ba.a.45.6 | yes | 28 | 91.32 | odd | 12 | ||
91.2.ba.a.89.6 | yes | 28 | 7.6 | odd | 2 | ||
637.2.x.a.19.2 | 28 | 13.6 | odd | 12 | |||
637.2.x.a.570.2 | 28 | 7.3 | odd | 6 | |||
637.2.bb.a.227.6 | 28 | 91.45 | even | 12 | inner | ||
637.2.bb.a.362.6 | 28 | 1.1 | even | 1 | trivial | ||
637.2.bd.a.97.6 | 28 | 91.19 | even | 12 | |||
637.2.bd.a.440.6 | 28 | 7.2 | even | 3 | |||
637.2.bd.b.97.6 | 28 | 91.58 | odd | 12 | |||
637.2.bd.b.440.6 | 28 | 7.5 | odd | 6 | |||
819.2.et.b.136.2 | 28 | 273.32 | even | 12 | |||
819.2.et.b.271.2 | 28 | 21.20 | even | 2 | |||
819.2.gh.b.19.6 | 28 | 273.188 | odd | 12 | |||
819.2.gh.b.388.6 | 28 | 21.11 | odd | 6 |