Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(28,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(54))
chi = DirichletCharacter(H, H._module([44]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.g (of order \(27\), degree \(18\), 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: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{27})\) |
Twist minimal: | no (minimal twist has level 81) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{27}]$ |
Embedding invariants
Embedding label | 703.4 | ||
Character | \(\chi\) | \(=\) | 729.703 |
Dual form | 729.2.g.c.28.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{27}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.474230 | + | 0.311906i | 0.335331 | + | 0.220551i | 0.705996 | − | 0.708216i | \(-0.250500\pi\) |
−0.370665 | + | 0.928767i | \(0.620870\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.664551 | − | 1.54060i | −0.332275 | − | 0.770301i | ||||
\(5\) | −1.99266 | − | 2.11209i | −0.891144 | − | 0.944557i | 0.107623 | − | 0.994192i | \(-0.465676\pi\) |
−0.998767 | + | 0.0496342i | \(0.984194\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.10865 | + | 0.363349i | −1.17496 | + | 0.137333i | −0.681088 | − | 0.732201i | \(-0.738493\pi\) |
−0.493872 | + | 0.869535i | \(0.664419\pi\) | |||||||
\(8\) | 0.362501 | − | 2.05585i | 0.128164 | − | 0.726852i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.286203 | − | 1.62314i | −0.0905055 | − | 0.513282i | ||||
\(11\) | 0.984350 | + | 3.28796i | 0.296793 | + | 0.991357i | 0.968181 | + | 0.250251i | \(0.0805132\pi\) |
−0.671388 | + | 0.741106i | \(0.734302\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.231870 | + | 3.98106i | 0.0643092 | + | 1.10415i | 0.863920 | + | 0.503628i | \(0.168002\pi\) |
−0.799611 | + | 0.600518i | \(0.794961\pi\) | |||||||
\(14\) | −1.58755 | − | 0.797296i | −0.424290 | − | 0.213086i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.48964 | + | 1.57893i | −0.372410 | + | 0.394732i | ||||
\(17\) | 0.878443 | + | 0.319727i | 0.213054 | + | 0.0775452i | 0.446342 | − | 0.894862i | \(-0.352726\pi\) |
−0.233289 | + | 0.972408i | \(0.574949\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.55845 | + | 1.65914i | −1.04578 | + | 0.380633i | −0.807068 | − | 0.590458i | \(-0.798947\pi\) |
−0.238711 | + | 0.971091i | \(0.576725\pi\) | |||||||
\(20\) | −1.92967 | + | 4.47349i | −0.431488 | + | 1.00030i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.558725 | + | 1.86627i | −0.119121 | + | 0.397891i | ||||
\(23\) | 6.11065 | + | 0.714233i | 1.27416 | + | 0.148928i | 0.726145 | − | 0.687542i | \(-0.241310\pi\) |
0.548014 | + | 0.836469i | \(0.315384\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.199532 | + | 3.42583i | −0.0399063 | + | 0.685165i | ||||
\(26\) | −1.13175 | + | 1.96026i | −0.221955 | + | 0.384438i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.62564 | + | 4.54773i | 0.496198 | + | 0.859441i | ||||
\(29\) | 1.60828 | − | 0.807706i | 0.298649 | − | 0.149987i | −0.293165 | − | 0.956062i | \(-0.594708\pi\) |
0.591814 | + | 0.806075i | \(0.298412\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.403603 | − | 0.542133i | 0.0724892 | − | 0.0973699i | −0.764400 | − | 0.644743i | \(-0.776965\pi\) |
0.836889 | + | 0.547373i | \(0.184372\pi\) | |||||||
\(32\) | −5.26149 | + | 1.24700i | −0.930109 | + | 0.220440i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.316859 | + | 0.425615i | 0.0543409 | + | 0.0729924i | ||||
\(35\) | 6.96191 | + | 5.84174i | 1.17678 | + | 0.987434i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.73079 | + | 7.32600i | −1.43533 | + | 1.20439i | −0.492858 | + | 0.870110i | \(0.664048\pi\) |
−0.942475 | + | 0.334277i | \(0.891508\pi\) | |||||||
\(38\) | −2.67925 | − | 0.634993i | −0.434631 | − | 0.103009i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.06448 | + | 3.33096i | −0.800765 | + | 0.526672i | ||||
\(41\) | −5.55820 | + | 3.65568i | −0.868045 | + | 0.570922i | −0.903567 | − | 0.428447i | \(-0.859061\pi\) |
0.0355222 | + | 0.999369i | \(0.488691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.17613 | − | 0.515752i | −0.331857 | − | 0.0786515i | 0.0613098 | − | 0.998119i | \(-0.480472\pi\) |
−0.393166 | + | 0.919467i | \(0.628620\pi\) | |||||||
\(44\) | 4.41129 | − | 3.70151i | 0.665026 | − | 0.558023i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.67508 | + | 2.24466i | 0.394419 | + | 0.330957i | ||||
\(47\) | −1.89278 | − | 2.54245i | −0.276091 | − | 0.370854i | 0.642351 | − | 0.766411i | \(-0.277959\pi\) |
−0.918442 | + | 0.395556i | \(0.870552\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.72039 | − | 0.644744i | 0.388627 | − | 0.0921062i | ||||
\(50\) | −1.16316 | + | 1.56239i | −0.164496 | + | 0.220956i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.97913 | − | 3.00283i | 0.829157 | − | 0.416418i | ||||
\(53\) | −4.18963 | − | 7.25666i | −0.575490 | − | 0.996779i | −0.995988 | − | 0.0894851i | \(-0.971478\pi\) |
0.420498 | − | 0.907294i | \(-0.361855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.98301 | − | 8.63082i | 0.671909 | − | 1.16378i | ||||
\(56\) | −0.379900 | + | 6.52263i | −0.0507663 | + | 0.871623i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.01462 | + | 0.118592i | 0.133226 | + | 0.0155719i | ||||
\(59\) | 1.44287 | − | 4.81952i | 0.187846 | − | 0.627448i | −0.811241 | − | 0.584712i | \(-0.801207\pi\) |
0.999086 | − | 0.0427359i | \(-0.0136074\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.226018 | + | 0.523969i | −0.0289387 | + | 0.0670874i | −0.932073 | − | 0.362272i | \(-0.882001\pi\) |
0.903134 | + | 0.429359i | \(0.141261\pi\) | |||||||
\(62\) | 0.360495 | − | 0.131209i | 0.0457829 | − | 0.0166636i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.19553 | + | 0.435136i | 0.149441 | + | 0.0543920i | ||||
\(65\) | 7.94633 | − | 8.42262i | 0.985621 | − | 1.04470i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2150 | − | 6.13461i | −1.49230 | − | 0.749461i | −0.499173 | − | 0.866502i | \(-0.666363\pi\) |
−0.993127 | + | 0.117041i | \(0.962659\pi\) | |||||||
\(68\) | −0.0911978 | − | 1.56581i | −0.0110594 | − | 0.189882i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.47947 | + | 4.94179i | 0.176831 | + | 0.590657i | ||||
\(71\) | −2.31784 | − | 13.1452i | −0.275078 | − | 1.56004i | −0.738715 | − | 0.674017i | \(-0.764567\pi\) |
0.463638 | − | 0.886025i | \(-0.346544\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.17142 | + | 6.64347i | −0.137105 | + | 0.777560i | 0.836266 | + | 0.548324i | \(0.184734\pi\) |
−0.973371 | + | 0.229236i | \(0.926377\pi\) | |||||||
\(74\) | −6.42542 | + | 0.751024i | −0.746940 | + | 0.0873048i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.58539 | + | 5.92017i | 0.640688 | + | 0.679090i | ||||
\(77\) | −4.25468 | − | 9.86346i | −0.484866 | − | 1.12405i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.622719 | − | 0.409569i | −0.0700614 | − | 0.0460801i | 0.513995 | − | 0.857793i | \(-0.328165\pi\) |
−0.584056 | + | 0.811713i | \(0.698535\pi\) | |||||||
\(80\) | 6.30319 | 0.704718 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.77609 | −0.417000 | ||||||||
\(83\) | 3.04071 | + | 1.99991i | 0.333761 | + | 0.219518i | 0.705316 | − | 0.708893i | \(-0.250805\pi\) |
−0.371555 | + | 0.928411i | \(0.621175\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.07514 | − | 2.49246i | −0.116616 | − | 0.270345i | ||||
\(86\) | −0.871119 | − | 0.923332i | −0.0939352 | − | 0.0995655i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.11637 | − | 0.831784i | 0.758607 | − | 0.0886685i | ||||
\(89\) | −2.27781 | + | 12.9181i | −0.241447 | + | 1.36931i | 0.587154 | + | 0.809475i | \(0.300248\pi\) |
−0.828601 | + | 0.559839i | \(0.810863\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.16732 | − | 12.2915i | −0.227197 | − | 1.28850i | ||||
\(92\) | −2.96049 | − | 9.88873i | −0.308652 | − | 1.03097i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.104609 | − | 1.79607i | −0.0107896 | − | 0.185251i | ||||
\(95\) | 12.5877 | + | 6.32177i | 1.29147 | + | 0.648600i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.58165 | + | 9.09602i | −0.871335 | + | 0.923561i | −0.997656 | − | 0.0684283i | \(-0.978202\pi\) |
0.126321 | + | 0.991989i | \(0.459683\pi\) | |||||||
\(98\) | 1.49119 | + | 0.542748i | 0.150633 | + | 0.0548258i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.41044 | − | 1.96924i | 0.541044 | − | 0.196924i | ||||
\(101\) | −2.37006 | + | 5.49442i | −0.235830 | + | 0.546715i | −0.994497 | − | 0.104763i | \(-0.966592\pi\) |
0.758667 | + | 0.651478i | \(0.225851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.507240 | + | 1.69430i | −0.0499798 | + | 0.166944i | −0.979336 | − | 0.202240i | \(-0.935178\pi\) |
0.929356 | + | 0.369185i | \(0.120363\pi\) | |||||||
\(104\) | 8.26849 | + | 0.966448i | 0.810792 | + | 0.0947680i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.276545 | − | 4.74809i | 0.0268604 | − | 0.461176i | ||||
\(107\) | −3.57628 | + | 6.19429i | −0.345732 | + | 0.598825i | −0.985486 | − | 0.169754i | \(-0.945703\pi\) |
0.639755 | + | 0.768579i | \(0.279036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.68613 | − | 9.84867i | −0.544633 | − | 0.943332i | −0.998630 | − | 0.0523287i | \(-0.983336\pi\) |
0.453997 | − | 0.891003i | \(-0.349998\pi\) | |||||||
\(110\) | 5.05509 | − | 2.53876i | 0.481984 | − | 0.242062i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.05708 | − | 5.44960i | 0.383358 | − | 0.514939i | ||||
\(113\) | −5.66711 | + | 1.34313i | −0.533116 | + | 0.126351i | −0.488352 | − | 0.872647i | \(-0.662402\pi\) |
−0.0447643 | + | 0.998998i | \(0.514254\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.6679 | − | 14.3295i | −0.994788 | − | 1.33623i | ||||
\(116\) | −2.31313 | − | 1.94095i | −0.214769 | − | 0.180213i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.18749 | − | 1.83552i | 0.201375 | − | 0.168973i | ||||
\(119\) | −2.84695 | − | 0.674739i | −0.260979 | − | 0.0618532i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.651365 | + | 0.428410i | −0.0592150 | + | 0.0389463i | ||||
\(122\) | −0.270614 | + | 0.177985i | −0.0245002 | + | 0.0161140i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.10343 | − | 0.261517i | −0.0990906 | − | 0.0234849i | ||||
\(125\) | −3.48865 | + | 2.92733i | −0.312034 | + | 0.261828i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.22802 | + | 6.90413i | 0.730119 | + | 0.612643i | 0.930164 | − | 0.367144i | \(-0.119664\pi\) |
−0.200045 | + | 0.979787i | \(0.564109\pi\) | |||||||
\(128\) | 6.88920 | + | 9.25380i | 0.608925 | + | 0.817928i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.39545 | − | 1.51575i | 0.560918 | − | 0.132940i | ||||
\(131\) | −4.27722 | + | 5.74530i | −0.373702 | + | 0.501969i | −0.948697 | − | 0.316188i | \(-0.897597\pi\) |
0.574994 | + | 0.818158i | \(0.305004\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.5678 | − | 6.81400i | 1.17648 | − | 0.590848i | ||||
\(134\) | −3.87930 | − | 6.71914i | −0.335120 | − | 0.580446i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.975746 | − | 1.69004i | 0.0836695 | − | 0.144920i | ||||
\(137\) | 0.501738 | − | 8.61452i | 0.0428664 | − | 0.735988i | −0.906575 | − | 0.422044i | \(-0.861313\pi\) |
0.949442 | − | 0.313944i | \(-0.101650\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.85926 | + | 0.684849i | 0.496976 | + | 0.0580882i | 0.360889 | − | 0.932609i | \(-0.382473\pi\) |
0.136087 | + | 0.990697i | \(0.456547\pi\) | |||||||
\(140\) | 4.37325 | − | 14.6077i | 0.369607 | − | 1.23457i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.00086 | − | 6.95677i | 0.251826 | − | 0.583799i | ||||
\(143\) | −12.8613 | + | 4.68113i | −1.07552 | + | 0.391456i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.91069 | − | 1.78735i | −0.407811 | − | 0.148431i | ||||
\(146\) | −2.62766 | + | 2.78516i | −0.217467 | + | 0.230501i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.0885 | + | 8.58217i | 1.40467 | + | 0.705450i | ||||
\(149\) | 0.802085 | + | 13.7713i | 0.0657094 | + | 1.12819i | 0.856516 | + | 0.516121i | \(0.172624\pi\) |
−0.790807 | + | 0.612066i | \(0.790339\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.80026 | − | 6.01330i | −0.146503 | − | 0.489356i | 0.852965 | − | 0.521969i | \(-0.174802\pi\) |
−0.999468 | + | 0.0326132i | \(0.989617\pi\) | |||||||
\(152\) | 1.75849 | + | 9.97291i | 0.142633 | + | 0.808910i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.05877 | − | 6.00461i | 0.0853185 | − | 0.483865i | ||||
\(155\) | −1.94928 | + | 0.227838i | −0.156570 | + | 0.0183004i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.113981 | + | 0.120812i | 0.00909664 | + | 0.00964187i | 0.731906 | − | 0.681406i | \(-0.238631\pi\) |
−0.722809 | + | 0.691048i | \(0.757150\pi\) | |||||||
\(158\) | −0.167565 | − | 0.388460i | −0.0133308 | − | 0.0309042i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.1181 | + | 8.62793i | 1.03708 | + | 0.682098i | ||||
\(161\) | −19.2554 | −1.51754 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.2014 | 1.26899 | 0.634495 | − | 0.772927i | \(-0.281208\pi\) | ||||
0.634495 | + | 0.772927i | \(0.281208\pi\) | |||||||
\(164\) | 9.32566 | + | 6.13358i | 0.728212 | + | 0.478952i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.818213 | + | 1.89683i | 0.0635056 | + | 0.147223i | ||||
\(167\) | 12.5418 | + | 13.2935i | 0.970513 | + | 1.02868i | 0.999576 | + | 0.0291056i | \(0.00926592\pi\) |
−0.0290638 | + | 0.999578i | \(0.509253\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.88294 | + | 0.336968i | −0.221765 | + | 0.0259206i | ||||
\(170\) | 0.267548 | − | 1.51734i | 0.0205200 | − | 0.116375i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.651580 | + | 3.69529i | 0.0496825 | + | 0.281763i | ||||
\(173\) | −5.40734 | − | 18.0618i | −0.411112 | − | 1.37321i | −0.873626 | − | 0.486598i | \(-0.838238\pi\) |
0.462514 | − | 0.886612i | \(-0.346948\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.624497 | − | 10.7222i | −0.0472076 | − | 0.810523i | ||||
\(176\) | −6.65778 | − | 3.34366i | −0.501849 | − | 0.252038i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.10943 | + | 5.41568i | −0.382968 | + | 0.405922i | ||||
\(179\) | 9.67521 | + | 3.52149i | 0.723159 | + | 0.263209i | 0.677266 | − | 0.735738i | \(-0.263164\pi\) |
0.0458930 | + | 0.998946i | \(0.485387\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.770198 | − | 0.280329i | 0.0572484 | − | 0.0208367i | −0.313237 | − | 0.949675i | \(-0.601414\pi\) |
0.370486 | + | 0.928838i | \(0.379191\pi\) | |||||||
\(182\) | 2.80597 | − | 6.50498i | 0.207993 | − | 0.482181i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.68347 | − | 12.3037i | 0.271549 | − | 0.907037i | ||||
\(185\) | 32.8707 | + | 3.84203i | 2.41670 | + | 0.282472i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.186554 | + | 3.20301i | −0.0136422 | + | 0.234227i | ||||
\(188\) | −2.65905 | + | 4.60561i | −0.193931 | + | 0.335899i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.99766 | + | 6.92415i | 0.290021 | + | 0.502330i | ||||
\(191\) | −0.683675 | + | 0.343354i | −0.0494690 | + | 0.0248442i | −0.473362 | − | 0.880868i | \(-0.656960\pi\) |
0.423893 | + | 0.905712i | \(0.360663\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.58623 | − | 7.50362i | 0.402106 | − | 0.540122i | −0.554241 | − | 0.832356i | \(-0.686991\pi\) |
0.956347 | + | 0.292234i | \(0.0943987\pi\) | |||||||
\(194\) | −6.90678 | + | 1.63694i | −0.495878 | + | 0.117525i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.80113 | − | 3.76257i | −0.200081 | − | 0.268755i | ||||
\(197\) | 0.857832 | + | 0.719807i | 0.0611180 | + | 0.0512841i | 0.672835 | − | 0.739793i | \(-0.265076\pi\) |
−0.611717 | + | 0.791077i | \(0.709521\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.88368 | − | 4.93699i | 0.417083 | − | 0.349974i | −0.409969 | − | 0.912099i | \(-0.634461\pi\) |
0.827052 | + | 0.562125i | \(0.190016\pi\) | |||||||
\(200\) | 6.97064 | + | 1.65207i | 0.492899 | + | 0.116819i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.83769 | + | 1.86638i | −0.199660 | + | 0.131318i | ||||
\(203\) | −4.70609 | + | 3.09524i | −0.330303 | + | 0.217244i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.7967 | + | 4.45491i | 1.31282 | + | 0.311144i | ||||
\(206\) | −0.769010 | + | 0.645276i | −0.0535794 | + | 0.0449585i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.63120 | − | 5.56424i | −0.459791 | − | 0.385811i | ||||
\(209\) | −9.94229 | − | 13.3548i | −0.687723 | − | 0.923772i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.96134 | + | 2.36088i | −0.685767 | + | 0.162530i | −0.558707 | − | 0.829365i | \(-0.688702\pi\) |
−0.127060 | + | 0.991895i | \(0.540554\pi\) | |||||||
\(212\) | −8.39540 | + | 11.2770i | −0.576598 | + | 0.774506i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.62801 | + | 1.82206i | −0.248006 | + | 0.124553i | ||||
\(215\) | 3.24697 | + | 5.62391i | 0.221441 | + | 0.383547i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.05768 | + | 1.83195i | −0.0717999 | + | 0.124361i | ||||
\(218\) | 0.375325 | − | 6.44407i | 0.0254202 | − | 0.436448i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −16.6081 | − | 1.94121i | −1.11972 | − | 0.130876i | ||||
\(221\) | −1.06917 | + | 3.57126i | −0.0719199 | + | 0.240229i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.84243 | + | 4.27124i | −0.123379 | + | 0.286024i | −0.968700 | − | 0.248234i | \(-0.920150\pi\) |
0.845321 | + | 0.534258i | \(0.179409\pi\) | |||||||
\(224\) | 15.9031 | − | 5.78824i | 1.06257 | − | 0.386743i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.10644 | − | 1.13065i | −0.206637 | − | 0.0752098i | ||||
\(227\) | −9.68944 | + | 10.2702i | −0.643111 | + | 0.681658i | −0.964135 | − | 0.265414i | \(-0.914492\pi\) |
0.321024 | + | 0.947071i | \(0.395973\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.63378 | − | 2.32717i | −0.306208 | − | 0.153784i | 0.289059 | − | 0.957311i | \(-0.406658\pi\) |
−0.595268 | + | 0.803528i | \(0.702954\pi\) | |||||||
\(230\) | −0.589589 | − | 10.1229i | −0.0388764 | − | 0.667481i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.07752 | − | 3.59916i | −0.0707425 | − | 0.236297i | ||||
\(233\) | 0.773336 | + | 4.38581i | 0.0506629 | + | 0.287324i | 0.999604 | − | 0.0281287i | \(-0.00895483\pi\) |
−0.948941 | + | 0.315452i | \(0.897844\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.59822 | + | 9.06397i | −0.104257 | + | 0.591268i | ||||
\(236\) | −8.38382 | + | 0.979929i | −0.545740 | + | 0.0637879i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.13965 | − | 1.20796i | −0.0738726 | − | 0.0783004i | ||||
\(239\) | −11.5106 | − | 26.6846i | −0.744561 | − | 1.72609i | −0.685773 | − | 0.727815i | \(-0.740536\pi\) |
−0.0587876 | − | 0.998271i | \(-0.518723\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.8739 | − | 13.7290i | −1.34460 | − | 0.884360i | −0.346055 | − | 0.938214i | \(-0.612479\pi\) |
−0.998549 | + | 0.0538543i | \(0.982849\pi\) | |||||||
\(242\) | −0.442520 | −0.0284463 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.957429 | 0.0612931 | ||||||||
\(245\) | −6.78256 | − | 4.46096i | −0.433322 | − | 0.285000i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.66209 | − | 17.7627i | −0.487527 | − | 1.13022i | ||||
\(248\) | −0.968235 | − | 1.02627i | −0.0614830 | − | 0.0651682i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.56747 | + | 0.300094i | −0.162381 | + | 0.0189796i | ||||
\(251\) | 2.46091 | − | 13.9565i | 0.155331 | − | 0.880926i | −0.803152 | − | 0.595775i | \(-0.796845\pi\) |
0.958483 | − | 0.285151i | \(-0.0920438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.66665 | + | 20.7946i | 0.230521 | + | 1.30735i | ||||
\(254\) | 1.74853 | + | 5.84051i | 0.109713 | + | 0.366466i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.232799 | + | 3.99701i | 0.0145499 | + | 0.249813i | ||||
\(257\) | 13.1355 | + | 6.59688i | 0.819367 | + | 0.411502i | 0.808541 | − | 0.588440i | \(-0.200258\pi\) |
0.0108263 | + | 0.999941i | \(0.496554\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.4791 | − | 25.9463i | 1.52106 | − | 1.61223i | ||||
\(260\) | −18.2566 | − | 6.64487i | −1.13223 | − | 0.412098i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.82038 | + | 1.39050i | −0.236024 | + | 0.0859056i | ||||
\(263\) | 6.49135 | − | 15.0486i | 0.400274 | − | 0.927939i | −0.592235 | − | 0.805765i | \(-0.701754\pi\) |
0.992509 | − | 0.122174i | \(-0.0389865\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.97824 | + | 23.3089i | −0.428670 | + | 1.43186i | ||||
\(266\) | 8.55957 | + | 1.00047i | 0.524821 | + | 0.0613428i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.33349 | + | 22.8952i | −0.0814561 | + | 1.39855i | ||||
\(269\) | 5.68131 | − | 9.84032i | 0.346396 | − | 0.599975i | −0.639211 | − | 0.769032i | \(-0.720739\pi\) |
0.985606 | + | 0.169057i | \(0.0540721\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.38266 | − | 2.39483i | −0.0839903 | − | 0.145476i | 0.820970 | − | 0.570971i | \(-0.193433\pi\) |
−0.904961 | + | 0.425496i | \(0.860100\pi\) | |||||||
\(272\) | −1.81339 | + | 0.910719i | −0.109953 | + | 0.0552204i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.92486 | − | 3.92877i | 0.176697 | − | 0.237345i | ||||
\(275\) | −11.4604 | + | 2.71616i | −0.691087 | + | 0.163791i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.9854 | + | 14.7559i | 0.660048 | + | 0.886598i | 0.998520 | − | 0.0543783i | \(-0.0173177\pi\) |
−0.338473 | + | 0.940976i | \(0.609910\pi\) | |||||||
\(278\) | 2.56503 | + | 2.15231i | 0.153840 | + | 0.129087i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 14.5334 | − | 12.1950i | 0.868538 | − | 0.728790i | ||||
\(281\) | 10.4439 | + | 2.47524i | 0.623028 | + | 0.147660i | 0.529992 | − | 0.848002i | \(-0.322195\pi\) |
0.0930358 | + | 0.995663i | \(0.470343\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.9407 | − | 7.85355i | 0.709804 | − | 0.466845i | −0.142566 | − | 0.989785i | \(-0.545535\pi\) |
0.852369 | + | 0.522940i | \(0.175165\pi\) | |||||||
\(284\) | −18.7111 | + | 12.3065i | −1.11030 | + | 0.730256i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.55929 | − | 1.79158i | −0.446990 | − | 0.105939i | ||||
\(287\) | 15.9502 | − | 13.3838i | 0.941512 | − | 0.790022i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3533 | − | 10.3657i | −0.726666 | − | 0.609745i | ||||
\(290\) | −1.77131 | − | 2.37929i | −0.104015 | − | 0.139717i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.0134 | − | 2.61023i | 0.644512 | − | 0.152752i | ||||
\(293\) | −13.0455 | + | 17.5231i | −0.762125 | + | 1.02371i | 0.236518 | + | 0.971627i | \(0.423994\pi\) |
−0.998643 | + | 0.0520843i | \(0.983414\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.0544 | + | 6.55618i | −0.760058 | + | 0.381716i | ||||
\(296\) | 11.8962 | + | 20.6048i | 0.691453 | + | 1.19763i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.91497 | + | 6.78092i | −0.226788 | + | 0.392808i | ||||
\(299\) | −1.42652 | + | 24.4925i | −0.0824979 | + | 1.41643i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.95223 | + | 0.812599i | 0.400720 | + | 0.0468374i | ||||
\(302\) | 1.02184 | − | 3.41320i | 0.0588006 | − | 0.196408i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.17079 | − | 9.66898i | 0.239211 | − | 0.554554i | ||||
\(305\) | 1.55705 | − | 0.566720i | 0.0891564 | − | 0.0324503i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.6368 | − | 10.4229i | −1.63439 | − | 0.594869i | −0.648344 | − | 0.761347i | \(-0.724538\pi\) |
−0.986045 | + | 0.166478i | \(0.946760\pi\) | |||||||
\(308\) | −12.3682 | + | 13.1095i | −0.704745 | + | 0.746986i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.995470 | − | 0.499944i | −0.0565389 | − | 0.0283949i | ||||
\(311\) | −1.57644 | − | 27.0664i | −0.0893915 | − | 1.53479i | −0.683227 | − | 0.730206i | \(-0.739424\pi\) |
0.593835 | − | 0.804587i | \(-0.297613\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.32494 | + | 7.76583i | 0.131413 | + | 0.438950i | 0.998216 | − | 0.0596999i | \(-0.0190144\pi\) |
−0.866803 | + | 0.498650i | \(0.833829\pi\) | |||||||
\(314\) | 0.0163709 | + | 0.0928440i | 0.000923863 | + | 0.00523949i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.217154 | + | 1.23154i | −0.0122159 | + | 0.0692797i | ||||
\(317\) | 19.2878 | − | 2.25442i | 1.08331 | − | 0.126621i | 0.444345 | − | 0.895856i | \(-0.353437\pi\) |
0.638966 | + | 0.769235i | \(0.279363\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.23881 | + | 4.49288i | 0.237328 | + | 0.251553i | ||||
\(320\) | −1.46323 | − | 3.39214i | −0.0817969 | − | 0.189627i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.13149 | − | 6.00587i | −0.508878 | − | 0.334694i | ||||
\(323\) | −4.53480 | −0.252323 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.6847 | −0.759089 | ||||||||
\(326\) | 7.68317 | + | 5.05330i | 0.425531 | + | 0.279876i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.50067 | + | 12.7520i | 0.303724 | + | 0.704111i | ||||
\(329\) | 6.80780 | + | 7.21585i | 0.375326 | + | 0.397823i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.97328 | + | 0.230643i | −0.108461 | + | 0.0126773i | −0.170150 | − | 0.985418i | \(-0.554425\pi\) |
0.0616891 | + | 0.998095i | \(0.480351\pi\) | |||||||
\(332\) | 1.06035 | − | 6.01357i | 0.0581945 | − | 0.330037i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.80136 | + | 10.2160i | 0.0985662 | + | 0.558997i | ||||
\(335\) | 11.3835 | + | 38.0234i | 0.621945 | + | 2.07744i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.06728 | + | 18.3245i | 0.0581385 | + | 0.998199i | 0.893661 | + | 0.448743i | \(0.148128\pi\) |
−0.835522 | + | 0.549456i | \(0.814835\pi\) | |||||||
\(338\) | −1.47228 | − | 0.739406i | −0.0800814 | − | 0.0402184i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.12540 | + | 3.31273i | −0.169499 | + | 0.179658i | ||||
\(341\) | 2.17980 | + | 0.793381i | 0.118043 | + | 0.0429640i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.3650 | − | 4.50048i | 0.667646 | − | 0.243003i | ||||
\(344\) | −1.84916 | + | 4.28683i | −0.0996999 | + | 0.231130i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.06925 | − | 10.2520i | 0.165004 | − | 0.551151i | ||||
\(347\) | −26.6029 | − | 3.10943i | −1.42812 | − | 0.166923i | −0.633364 | − | 0.773854i | \(-0.718326\pi\) |
−0.794754 | + | 0.606931i | \(0.792400\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.762246 | − | 13.0873i | 0.0408021 | − | 0.700545i | −0.914440 | − | 0.404721i | \(-0.867369\pi\) |
0.955242 | − | 0.295824i | \(-0.0955943\pi\) | |||||||
\(350\) | 3.04816 | − | 5.27957i | 0.162931 | − | 0.282205i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.27922 | − | 16.0721i | −0.494584 | − | 0.856645i | ||||
\(353\) | −17.3676 | + | 8.72232i | −0.924383 | + | 0.464242i | −0.846301 | − | 0.532705i | \(-0.821176\pi\) |
−0.0780814 | + | 0.996947i | \(0.524879\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.1451 | + | 31.0893i | −1.22842 | + | 1.65005i | ||||
\(356\) | 21.4153 | − | 5.07553i | 1.13501 | − | 0.269003i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.48990 | + | 4.68775i | 0.184447 | + | 0.247755i | ||||
\(359\) | −11.2428 | − | 9.43384i | −0.593373 | − | 0.497899i | 0.295935 | − | 0.955208i | \(-0.404369\pi\) |
−0.889308 | + | 0.457309i | \(0.848813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.47185 | − | 2.91323i | 0.182729 | − | 0.153328i | ||||
\(362\) | 0.452687 | + | 0.107289i | 0.0237927 | + | 0.00563898i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.4960 | + | 11.5073i | −0.917038 | + | 0.603146i | ||||
\(365\) | 16.3659 | − | 10.7640i | 0.856630 | − | 0.563414i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.6977 | − | 2.53540i | −0.558415 | − | 0.132347i | −0.0582894 | − | 0.998300i | \(-0.518565\pi\) |
−0.500125 | + | 0.865953i | \(0.666713\pi\) | |||||||
\(368\) | −10.2304 | + | 8.58433i | −0.533297 | + | 0.447489i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 14.3899 | + | 12.0746i | 0.748096 | + | 0.627727i | ||||
\(371\) | 15.6608 | + | 21.0361i | 0.813069 | + | 1.09214i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.8678 | + | 4.70876i | −1.02872 | + | 0.243810i | −0.710121 | − | 0.704080i | \(-0.751360\pi\) |
−0.318596 | + | 0.947890i | \(0.603211\pi\) | |||||||
\(374\) | −1.08751 | + | 1.46077i | −0.0562336 | + | 0.0755348i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.91302 | + | 2.96963i | −0.304941 | + | 0.153147i | ||||
\(377\) | 3.58843 | + | 6.21535i | 0.184814 | + | 0.320107i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.0154 | + | 22.5433i | −0.668556 | + | 1.15797i | 0.309753 | + | 0.950817i | \(0.399754\pi\) |
−0.978308 | + | 0.207155i | \(0.933580\pi\) | |||||||
\(380\) | 1.37418 | − | 23.5938i | 0.0704939 | − | 1.21033i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.431313 | − | 0.0504133i | −0.0220679 | − | 0.00257937i | ||||
\(383\) | 6.74866 | − | 22.5421i | 0.344840 | − | 1.15185i | −0.593123 | − | 0.805112i | \(-0.702105\pi\) |
0.937963 | − | 0.346735i | \(-0.112710\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.3544 | + | 28.6408i | −0.629640 | + | 1.45967i | ||||
\(386\) | 4.98958 | − | 1.81606i | 0.253963 | − | 0.0924349i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.7163 | + | 7.17615i | 1.00094 | + | 0.364314i | ||||
\(389\) | 22.6942 | − | 24.0545i | 1.15064 | − | 1.21961i | 0.178825 | − | 0.983881i | \(-0.442770\pi\) |
0.971819 | − | 0.235730i | \(-0.0757481\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.13950 | + | 2.58115i | 0.259916 | + | 0.130534i | ||||
\(392\) | −0.339350 | − | 5.82642i | −0.0171398 | − | 0.294279i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.182298 | + | 0.608917i | 0.00918403 | + | 0.0306768i | ||||
\(395\) | 0.375819 | + | 2.13137i | 0.0189095 | + | 0.107241i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.00960087 | + | 0.0544493i | −0.000481854 | + | 0.00273273i | −0.985048 | − | 0.172282i | \(-0.944886\pi\) |
0.984566 | + | 0.175014i | \(0.0559972\pi\) | |||||||
\(398\) | 4.33009 | − | 0.506115i | 0.217048 | − | 0.0253693i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.11190 | − | 5.41830i | −0.255595 | − | 0.270915i | ||||
\(401\) | −11.3452 | − | 26.3011i | −0.566551 | − | 1.31341i | −0.925037 | − | 0.379878i | \(-0.875966\pi\) |
0.358486 | − | 0.933535i | \(-0.383293\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.25184 | + | 1.48106i | 0.112172 | + | 0.0737769i | ||||
\(404\) | 10.0397 | 0.499496 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.19719 | −0.158674 | ||||||||
\(407\) | −32.6817 | − | 21.4951i | −1.61997 | − | 1.06547i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.4515 | + | 28.8659i | 0.615688 | + | 1.42732i | 0.885604 | + | 0.464441i | \(0.153745\pi\) |
−0.269916 | + | 0.962884i | \(0.586996\pi\) | |||||||
\(410\) | 7.52446 | + | 7.97546i | 0.371607 | + | 0.393880i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.94733 | − | 0.344493i | 0.145204 | − | 0.0169720i | ||||
\(413\) | −2.73421 | + | 15.5065i | −0.134542 | + | 0.763024i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.83511 | − | 10.4074i | −0.0900818 | − | 0.510879i | ||||
\(416\) | −6.18434 | − | 20.6571i | −0.303212 | − | 1.01280i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.549486 | − | 9.43431i | −0.0268762 | − | 0.461447i | ||||
\(419\) | −3.01535 | − | 1.51436i | −0.147309 | − | 0.0739816i | 0.373617 | − | 0.927583i | \(-0.378117\pi\) |
−0.520927 | + | 0.853601i | \(0.674414\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.3369 | + | 18.3761i | −0.844950 | + | 0.895594i | −0.995668 | − | 0.0929825i | \(-0.970360\pi\) |
0.150718 | + | 0.988577i | \(0.451841\pi\) | |||||||
\(422\) | −5.46033 | − | 1.98740i | −0.265805 | − | 0.0967451i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16.4373 | + | 5.98270i | −0.798267 | + | 0.290545i | ||||
\(425\) | −1.27061 | + | 2.94560i | −0.0616335 | + | 0.142882i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.512228 | − | 1.71096i | 0.0247885 | − | 0.0827992i | ||||
\(428\) | 11.9196 | + | 1.39320i | 0.576154 | + | 0.0673427i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.214322 | + | 3.67977i | −0.0103355 | + | 0.177454i | ||||
\(431\) | 16.4068 | − | 28.4174i | 0.790288 | − | 1.36882i | −0.135501 | − | 0.990777i | \(-0.543264\pi\) |
0.925789 | − | 0.378041i | \(-0.123402\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.46122 | + | 11.1912i | 0.310507 | + | 0.537813i | 0.978472 | − | 0.206379i | \(-0.0661680\pi\) |
−0.667966 | + | 0.744192i | \(0.732835\pi\) | |||||||
\(434\) | −1.07298 | + | 0.538870i | −0.0515046 | + | 0.0258666i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.3942 | + | 15.3050i | −0.545681 | + | 0.732977i | ||||
\(437\) | −29.0401 | + | 6.88263i | −1.38918 | + | 0.329241i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.0216 | + | 29.5802i | 1.05103 | + | 1.41178i | 0.906460 | + | 0.422291i | \(0.138774\pi\) |
0.144574 | + | 0.989494i | \(0.453819\pi\) | |||||||
\(440\) | −15.9373 | − | 13.3730i | −0.759781 | − | 0.637532i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.62093 | + | 1.36012i | −0.0770997 | + | 0.0646943i | ||||
\(443\) | −33.4372 | − | 7.92477i | −1.58865 | − | 0.376517i | −0.661125 | − | 0.750276i | \(-0.729921\pi\) |
−0.927526 | + | 0.373759i | \(0.878069\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.8231 | − | 20.9304i | 1.50856 | − | 0.992196i | ||||
\(446\) | −2.20596 | + | 1.45088i | −0.104455 | + | 0.0687014i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.87459 | − | 0.918294i | −0.183057 | − | 0.0433853i | ||||
\(449\) | −13.4520 | + | 11.2876i | −0.634838 | + | 0.532693i | −0.902428 | − | 0.430840i | \(-0.858217\pi\) |
0.267590 | + | 0.963533i | \(0.413773\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.4910 | − | 14.6767i | −0.823617 | − | 0.691097i | ||||
\(452\) | 5.83531 | + | 7.83818i | 0.274470 | + | 0.368677i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.79836 | + | 1.84824i | −0.365995 | + | 0.0867424i | ||||
\(455\) | −21.6420 | + | 29.0703i | −1.01459 | + | 1.36284i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.46084 | + | 3.74697i | −0.349003 | + | 0.175276i | −0.614661 | − | 0.788791i | \(-0.710707\pi\) |
0.265658 | + | 0.964067i | \(0.414411\pi\) | |||||||
\(458\) | −1.47162 | − | 2.54891i | −0.0687641 | − | 0.119103i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.9867 | + | 25.9577i | −0.698758 | + | 1.21028i | ||||
\(461\) | −1.18266 | + | 20.3054i | −0.0550818 | + | 0.945718i | 0.851677 | + | 0.524067i | \(0.175586\pi\) |
−0.906759 | + | 0.421650i | \(0.861451\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.57184 | + | 0.300605i | 0.119524 | + | 0.0139703i | 0.175644 | − | 0.984454i | \(-0.443799\pi\) |
−0.0561208 | + | 0.998424i | \(0.517873\pi\) | |||||||
\(464\) | −1.12044 | + | 3.74254i | −0.0520153 | + | 0.173743i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.00122 | + | 2.32109i | −0.0463806 | + | 0.107522i | ||||
\(467\) | 11.5019 | − | 4.18635i | 0.532244 | − | 0.193721i | −0.0618958 | − | 0.998083i | \(-0.519715\pi\) |
0.594140 | + | 0.804361i | \(0.297492\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.2012 | + | 14.6320i | 1.85632 | + | 0.675645i | ||||
\(470\) | −3.58503 | + | 3.79991i | −0.165365 | + | 0.175277i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.38515 | − | 4.71340i | −0.431987 | − | 0.216952i | ||||
\(473\) | −0.446302 | − | 7.66271i | −0.0205210 | − | 0.352332i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.77437 | − | 15.9475i | −0.219063 | − | 0.731721i | ||||
\(476\) | 0.852437 | + | 4.83441i | 0.0390714 | + | 0.221585i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.86441 | − | 16.2449i | 0.131015 | − | 0.743024i | ||||
\(479\) | 27.2416 | − | 3.18408i | 1.24470 | − | 0.145485i | 0.531873 | − | 0.846824i | \(-0.321488\pi\) |
0.712827 | + | 0.701340i | \(0.247414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.1896 | − | 33.0591i | −1.42212 | − | 1.50736i | ||||
\(482\) | −5.61687 | − | 13.0214i | −0.255841 | − | 0.593107i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.09287 | + | 0.718795i | 0.0496761 | + | 0.0326725i | ||||
\(485\) | 36.3120 | 1.64884 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.02417 | −0.272981 | −0.136491 | − | 0.990641i | \(-0.543582\pi\) | ||||
−0.136491 | + | 0.990641i | \(0.543582\pi\) | |||||||
\(488\) | 0.995268 | + | 0.654598i | 0.0450537 | + | 0.0296323i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.82509 | − | 4.23104i | −0.0824493 | − | 0.191139i | ||||
\(491\) | 0.334399 | + | 0.354442i | 0.0150912 | + | 0.0159958i | 0.734875 | − | 0.678202i | \(-0.237241\pi\) |
−0.719784 | + | 0.694198i | \(0.755759\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.67102 | − | 0.195315i | 0.0752591 | − | 0.00879652i | ||||
\(494\) | 1.90671 | − | 10.8135i | 0.0857867 | − | 0.486521i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.254765 | + | 1.44484i | 0.0114393 | + | 0.0648754i | ||||
\(497\) | 11.9817 | + | 40.0215i | 0.537451 | + | 1.79521i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.318908 | − | 5.47545i | −0.0142763 | − | 0.245115i | −0.997895 | − | 0.0648523i | \(-0.979342\pi\) |
0.983619 | − | 0.180262i | \(-0.0576947\pi\) | |||||||
\(500\) | 6.82823 | + | 3.42927i | 0.305368 | + | 0.153361i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.52014 | − | 5.85101i | 0.246376 | − | 0.261143i | ||||
\(503\) | 9.93090 | + | 3.61455i | 0.442797 | + | 0.161165i | 0.553790 | − | 0.832656i | \(-0.313181\pi\) |
−0.110993 | + | 0.993821i | \(0.535403\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.3275 | − | 5.94271i | 0.726562 | − | 0.264447i | ||||
\(506\) | −4.74713 | + | 11.0051i | −0.211036 | + | 0.489236i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.16858 | − | 17.2643i | 0.229319 | − | 0.765977i | ||||
\(509\) | 12.3227 | + | 1.44032i | 0.546196 | + | 0.0638412i | 0.384716 | − | 0.923035i | \(-0.374299\pi\) |
0.161480 | + | 0.986876i | \(0.448373\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.22765 | − | 21.0779i | 0.0543079 | − | 0.932431i | ||||
\(512\) | 10.4003 | − | 18.0139i | 0.459634 | − | 0.796110i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.17162 | + | 7.22546i | 0.184002 | + | 0.318701i | ||||
\(515\) | 4.58927 | − | 2.30482i | 0.202228 | − | 0.101562i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.49630 | − | 8.72605i | 0.285707 | − | 0.383771i | ||||
\(518\) | 19.7015 | − | 4.66935i | 0.865635 | − | 0.205159i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14.4351 | − | 19.3896i | −0.633019 | − | 0.850292i | ||||
\(521\) | −13.6270 | − | 11.4344i | −0.597011 | − | 0.500952i | 0.293472 | − | 0.955968i | \(-0.405189\pi\) |
−0.890483 | + | 0.455016i | \(0.849634\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.4002 | + | 8.72680i | −0.454769 | + | 0.381596i | −0.841202 | − | 0.540721i | \(-0.818151\pi\) |
0.386433 | + | 0.922317i | \(0.373707\pi\) | |||||||
\(524\) | 11.6937 | + | 2.77145i | 0.510840 | + | 0.121071i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.77215 | − | 5.11182i | 0.338882 | − | 0.222886i | ||||
\(527\) | 0.527877 | − | 0.347190i | 0.0229947 | − | 0.0151238i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.4499 | + | 3.42469i | 0.628256 | + | 0.148899i | ||||
\(530\) | −10.5795 | + | 8.87724i | −0.459543 | + | 0.385603i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −19.5141 | − | 16.3743i | −0.846045 | − | 0.709916i | ||||
\(533\) | −15.8423 | − | 21.2799i | −0.686205 | − | 0.921733i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.2092 | − | 4.78968i | 0.873722 | − | 0.207076i | ||||
\(536\) | −17.0398 | + | 22.8884i | −0.736006 | + | 0.988627i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.76350 | − | 2.89454i | 0.248482 | − | 0.124792i | ||||
\(539\) | 4.79771 | + | 8.30987i | 0.206652 | + | 0.357931i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.6538 | − | 23.6492i | 0.587025 | − | 1.01676i | −0.407595 | − | 0.913163i | \(-0.633632\pi\) |
0.994620 | − | 0.103594i | \(-0.0330342\pi\) | |||||||
\(542\) | 0.0912649 | − | 1.56696i | 0.00392016 | − | 0.0673066i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.02062 | − | 0.586826i | −0.215257 | − | 0.0251600i | ||||
\(545\) | −9.47081 | + | 31.6347i | −0.405685 | + | 1.35508i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.02926 | − | 11.6591i | 0.215036 | − | 0.498509i | −0.776220 | − | 0.630462i | \(-0.782865\pi\) |
0.991256 | + | 0.131953i | \(0.0421247\pi\) | |||||||
\(548\) | −13.6050 | + | 4.95181i | −0.581176 | + | 0.211531i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.28204 | − | 2.28648i | −0.267867 | − | 0.0974957i | ||||
\(551\) | −5.99114 | + | 6.35024i | −0.255231 | + | 0.270529i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.08464 | + | 1.04694i | 0.0886477 | + | 0.0445206i | ||||
\(554\) | 0.607135 | + | 10.4241i | 0.0257947 | + | 0.442878i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.83870 | − | 9.48191i | −0.120388 | − | 0.402122i | ||||
\(557\) | 2.62356 | + | 14.8789i | 0.111164 | + | 0.630441i | 0.988578 | + | 0.150708i | \(0.0481553\pi\) |
−0.877415 | + | 0.479733i | \(0.840734\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.54866 | − | 8.78288i | 0.0655013 | − | 0.371476i | ||||
\(560\) | −19.5944 | + | 2.29026i | −0.828016 | + | 0.0967812i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.18075 | + | 4.43133i | 0.176354 | + | 0.186924i | ||||
\(563\) | 2.42888 | + | 5.63077i | 0.102365 | + | 0.237309i | 0.961700 | − | 0.274104i | \(-0.0883814\pi\) |
−0.859335 | + | 0.511413i | \(0.829122\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.1294 | + | 9.29307i | 0.594429 | + | 0.390962i | ||||
\(566\) | 8.11223 | 0.340982 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.8646 | −1.16917 | ||||||||
\(569\) | −1.23600 | − | 0.812928i | −0.0518157 | − | 0.0340797i | 0.523337 | − | 0.852126i | \(-0.324687\pi\) |
−0.575153 | + | 0.818046i | \(0.695057\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.49187 | + | 8.09506i | 0.146130 | + | 0.338768i | 0.975523 | − | 0.219898i | \(-0.0705726\pi\) |
−0.829393 | + | 0.558666i | \(0.811313\pi\) | |||||||
\(572\) | 15.7588 | + | 16.7033i | 0.658907 | + | 0.698400i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.7386 | − | 1.37204i | 0.489958 | − | 0.0572679i | ||||
\(575\) | −3.66611 | + | 20.7915i | −0.152887 | + | 0.867066i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.48608 | + | 14.0993i | 0.103497 | + | 0.586960i | 0.991810 | + | 0.127722i | \(0.0407665\pi\) |
−0.888313 | + | 0.459238i | \(0.848122\pi\) | |||||||
\(578\) | −2.62520 | − | 8.76878i | −0.109194 | − | 0.364733i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.509816 | + | 8.75321i | 0.0211690 | + | 0.363457i | ||||
\(581\) | −10.1792 | − | 5.11218i | −0.422304 | − | 0.212089i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.7355 | − | 20.9184i | 0.817362 | − | 0.866353i | ||||
\(584\) | 13.2333 | + | 4.81654i | 0.547599 | + | 0.199310i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.6521 | + | 4.24102i | −0.481344 | + | 0.175195i | ||||
\(587\) | −3.38197 | + | 7.84028i | −0.139589 | + | 0.323603i | −0.973642 | − | 0.228080i | \(-0.926755\pi\) |
0.834054 | + | 0.551683i | \(0.186014\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.940329 | + | 3.14092i | −0.0387456 | + | 0.129419i | ||||
\(590\) | −8.23571 | − | 0.962617i | −0.339059 | − | 0.0396303i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.43852 | − | 24.6984i | 0.0591227 | − | 1.01510i | ||||
\(593\) | −19.8740 | + | 34.4227i | −0.816125 | + | 1.41357i | 0.0923915 | + | 0.995723i | \(0.470549\pi\) |
−0.908517 | + | 0.417848i | \(0.862784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.24788 | + | 7.35754i | 0.174146 | + | 0.301630i | ||||
\(596\) | 20.6830 | − | 10.3874i | 0.847210 | − | 0.425485i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.31584 | + | 11.1701i | −0.340060 | + | 0.456780i | ||||
\(599\) | −19.8283 | + | 4.69940i | −0.810164 | + | 0.192012i | −0.614764 | − | 0.788711i | \(-0.710749\pi\) |
−0.195400 | + | 0.980724i | \(0.562601\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.17441 | − | 10.9801i | −0.333441 | − | 0.447889i | 0.603507 | − | 0.797358i | \(-0.293770\pi\) |
−0.936948 | + | 0.349469i | \(0.886362\pi\) | |||||||
\(602\) | 3.04350 | + | 2.55380i | 0.124044 | + | 0.104085i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.06774 | + | 6.76964i | −0.328272 | + | 0.275453i | ||||
\(605\) | 2.20279 | + | 0.522071i | 0.0895562 | + | 0.0212252i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.75977 | − | 2.47284i | 0.152604 | − | 0.100369i | −0.470910 | − | 0.882181i | \(-0.656075\pi\) |
0.623515 | + | 0.781812i | \(0.285704\pi\) | |||||||
\(608\) | 21.9153 | − | 14.4139i | 0.888782 | − | 0.584561i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.915162 | + | 0.216897i | 0.0370538 | + | 0.00878192i | ||||
\(611\) | 9.68275 | − | 8.12479i | 0.391722 | − | 0.328694i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.4040 | + | 22.9947i | 1.10684 | + | 0.928746i | 0.997866 | − | 0.0652986i | \(-0.0208000\pi\) |
0.108971 | + | 0.994045i | \(0.465244\pi\) | |||||||
\(614\) | −10.3295 | − | 13.8749i | −0.416863 | − | 0.559944i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −21.8201 | + | 5.17146i | −0.879157 | + | 0.208364i | ||||
\(617\) | 16.4713 | − | 22.1249i | 0.663112 | − | 0.890713i | −0.335572 | − | 0.942015i | \(-0.608929\pi\) |
0.998683 | + | 0.0513013i | \(0.0163369\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.8724 | + | 15.0025i | −1.20067 | + | 0.603001i | −0.932780 | − | 0.360447i | \(-0.882624\pi\) |
−0.267894 | + | 0.963448i | \(0.586328\pi\) | |||||||
\(620\) | 1.64640 | + | 2.85165i | 0.0661211 | + | 0.114525i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.69456 | − | 13.3274i | 0.308524 | − | 0.534379i | ||||
\(623\) | 2.38713 | − | 40.9855i | 0.0956384 | − | 1.64205i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30.1766 | + | 3.52714i | 1.20707 | + | 0.141086i | ||||
\(626\) | −1.31965 | + | 4.40795i | −0.0527439 | + | 0.176177i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.110378 | − | 0.255885i | 0.00440455 | − | 0.0102109i | ||||
\(629\) | −10.0118 | + | 3.64400i | −0.399197 | + | 0.145296i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.2732 | + | 3.73914i | 0.408970 | + | 0.148853i | 0.538309 | − | 0.842748i | \(-0.319063\pi\) |
−0.129339 | + | 0.991600i | \(0.541286\pi\) | |||||||
\(632\) | −1.06775 | + | 1.13175i | −0.0424727 | + | 0.0450185i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.85001 | + | 4.94686i | 0.391194 | + | 0.196465i | ||||
\(635\) | −1.81346 | − | 31.1359i | −0.0719650 | − | 1.23559i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.19754 | + | 10.6805i | 0.126691 | + | 0.423177i | ||||
\(638\) | 0.608816 | + | 3.45277i | 0.0241032 | + | 0.136696i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.81708 | − | 32.9903i | 0.229940 | − | 1.30406i | ||||
\(641\) | 9.25236 | − | 1.08145i | 0.365446 | − | 0.0427145i | 0.0686116 | − | 0.997643i | \(-0.478143\pi\) |
0.296835 | + | 0.954929i | \(0.404069\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.883538 | − | 0.936495i | −0.0348433 | − | 0.0369318i | 0.709718 | − | 0.704486i | \(-0.248823\pi\) |
−0.744561 | + | 0.667555i | \(0.767341\pi\) | |||||||
\(644\) | 12.7962 | + | 29.6649i | 0.504241 | + | 1.16896i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.15054 | − | 1.41443i | −0.0846118 | − | 0.0556501i | ||||
\(647\) | −25.7409 | −1.01198 | −0.505989 | − | 0.862540i | \(-0.668872\pi\) | ||||
−0.505989 | + | 0.862540i | \(0.668872\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.2667 | 0.677776 | ||||||||
\(650\) | −6.48968 | − | 4.26833i | −0.254546 | − | 0.167418i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.7666 | − | 24.9599i | −0.421654 | − | 0.977504i | ||||
\(653\) | 26.7355 | + | 28.3380i | 1.04624 | + | 1.10895i | 0.993896 | + | 0.110323i | \(0.0351885\pi\) |
0.0523464 | + | 0.998629i | \(0.483330\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.6577 | − | 2.41453i | 0.807162 | − | 0.0943437i | ||||
\(656\) | 2.50766 | − | 14.2217i | 0.0979077 | − | 0.555262i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.977797 | + | 5.54536i | 0.0381185 | + | 0.216181i | ||||
\(659\) | 9.63166 | + | 32.1720i | 0.375196 | + | 1.25324i | 0.912229 | + | 0.409681i | \(0.134360\pi\) |
−0.537033 | + | 0.843561i | \(0.680455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.06029 | − | 35.3739i | −0.0801361 | − | 1.37588i | −0.763501 | − | 0.645807i | \(-0.776521\pi\) |
0.683365 | − | 0.730077i | \(-0.260516\pi\) | |||||||
\(662\) | −1.00773 | − | 0.506100i | −0.0391664 | − | 0.0196701i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.21376 | − | 5.52627i | 0.202333 | − | 0.214461i | ||||
\(665\) | −41.4278 | − | 15.0785i | −1.60650 | − | 0.584718i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.4045 | − | 3.78693i | 0.402864 | − | 0.146630i | ||||
\(668\) | 12.1454 | − | 28.1561i | 0.469918 | − | 1.08939i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.46135 | + | 21.5824i | −0.249624 | + | 0.833801i | ||||
\(671\) | −1.94527 | − | 0.227369i | −0.0750963 | − | 0.00877750i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.59738 | + | 27.4260i | −0.0615746 | + | 1.05720i | 0.816091 | + | 0.577923i | \(0.196137\pi\) |
−0.877666 | + | 0.479273i | \(0.840900\pi\) | |||||||
\(674\) | −5.20938 | + | 9.02292i | −0.200658 | + | 0.347550i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.43499 | + | 4.21753i | 0.0936536 | + | 0.162213i | ||||
\(677\) | −8.53705 | + | 4.28747i | −0.328106 | + | 0.164781i | −0.605225 | − | 0.796055i | \(-0.706917\pi\) |
0.277119 | + | 0.960836i | \(0.410620\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.3724 | − | 31.3945i | 0.896948 | − | 1.20481i | ||||
\(680\) | −5.51386 | + | 1.30681i | −0.211447 | + | 0.0501138i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.786265 | + | 1.05614i | 0.0301076 | + | 0.0404416i | ||||
\(683\) | 25.4573 | + | 21.3612i | 0.974095 | + | 0.817363i | 0.983188 | − | 0.182596i | \(-0.0584500\pi\) |
−0.00909301 | + | 0.999959i | \(0.502894\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.1945 | + | 16.1061i | −0.733383 | + | 0.615381i | ||||
\(686\) | 7.26757 | + | 1.72245i | 0.277477 | + | 0.0657633i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.05599 | − | 2.66767i | 0.154633 | − | 0.101704i | ||||
\(689\) | 27.9177 | − | 18.3618i | 1.06358 | − | 0.699528i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.28329 | − | 1.25216i | −0.200986 | − | 0.0476345i | 0.128890 | − | 0.991659i | \(-0.458859\pi\) |
−0.329876 | + | 0.944024i | \(0.607007\pi\) | |||||||
\(692\) | −24.2325 | + | 20.3335i | −0.921183 | + | 0.772964i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.6460 | − | 9.77218i | −0.442077 | − | 0.370947i | ||||
\(695\) | −10.2290 | − | 13.7400i | −0.388010 | − | 0.521187i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.05138 | + | 1.43420i | −0.229212 | + | 0.0543243i | ||||
\(698\) | 4.44347 | − | 5.96862i | 0.168188 | − | 0.225916i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −16.1036 | + | 8.08755i | −0.608661 | + | 0.305681i | ||||
\(701\) | −16.8694 | − | 29.2187i | −0.637150 | − | 1.10358i | −0.986055 | − | 0.166418i | \(-0.946780\pi\) |
0.348906 | − | 0.937158i | \(-0.386553\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.6440 | − | 47.8808i | 1.04261 | − | 1.80586i | ||||
\(704\) | −0.253893 | + | 4.35917i | −0.00956894 | + | 0.164292i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.9568 | − | 1.28066i | −0.412363 | − | 0.0481983i | ||||
\(707\) | 5.37130 | − | 17.9414i | 0.202009 | − | 0.674756i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.67820 | + | 17.8001i | −0.288361 | + | 0.668495i | −0.999399 | − | 0.0346578i | \(-0.988966\pi\) |
0.711039 | + | 0.703153i | \(0.248225\pi\) | |||||||
\(710\) | −20.6730 | + | 7.52437i | −0.775846 | + | 0.282385i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 25.7319 | + | 9.36564i | 0.964343 | + | 0.350992i | ||||
\(713\) | 2.85349 | − | 3.02452i | 0.106864 | − | 0.113269i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.5152 | + | 17.8364i | 1.32819 | + | 0.667044i | ||||
\(716\) | −1.00446 | − | 17.2459i | −0.0375383 | − | 0.644508i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.38921 | − | 7.98051i | −0.0891644 | − | 0.297830i | ||||
\(719\) | −0.831346 | − | 4.71480i | −0.0310040 | − | 0.175832i | 0.965374 | − | 0.260871i | \(-0.0840097\pi\) |
−0.996378 | + | 0.0850387i | \(0.972899\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.961210 | − | 5.45129i | 0.0357973 | − | 0.203017i | ||||
\(722\) | 2.55511 | − | 0.298649i | 0.0950912 | − | 0.0111146i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.943712 | − | 1.00028i | −0.0350728 | − | 0.0371750i | ||||
\(725\) | 2.44616 | + | 5.67083i | 0.0908481 | + | 0.210610i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.31649 | + | 4.15442i | 0.234266 | + | 0.154079i | 0.661215 | − | 0.750197i | \(-0.270041\pi\) |
−0.426949 | + | 0.904276i | \(0.640412\pi\) | |||||||
\(728\) | −26.0550 | −0.965664 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.1186 | 0.411516 | ||||||||
\(731\) | −1.74670 | − | 1.14883i | −0.0646042 | − | 0.0424909i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.3050 | + | 35.4810i | 0.565303 | + | 1.31052i | 0.925890 | + | 0.377794i | \(0.123317\pi\) |
−0.360587 | + | 0.932726i | \(0.617423\pi\) | |||||||
\(734\) | −4.28236 | − | 4.53903i | −0.158065 | − | 0.167539i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33.0418 | + | 3.86203i | −1.21794 | + | 0.142356i | ||||
\(737\) | 8.14649 | − | 46.2010i | 0.300080 | − | 1.70184i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.79173 | − | 49.8604i | −0.323409 | − | 1.83414i | −0.520627 | − | 0.853784i | \(-0.674302\pi\) |
0.197218 | − | 0.980360i | \(-0.436809\pi\) | |||||||
\(740\) | −15.9252 | − | 53.1939i | −0.585422 | − | 1.95545i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.865535 | + | 14.8607i | 0.0317748 | + | 0.545552i | ||||
\(743\) | 13.7207 | + | 6.89082i | 0.503365 | + | 0.252800i | 0.682315 | − | 0.731059i | \(-0.260973\pi\) |
−0.178949 | + | 0.983858i | \(0.557270\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.4880 | − | 29.1355i | 1.00708 | − | 1.06744i | ||||
\(746\) | −10.8906 | − | 3.96386i | −0.398733 | − | 0.145127i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.05853 | − | 1.84116i | 0.184958 | − | 0.0673193i | ||||
\(749\) | 8.86671 | − | 20.5554i | 0.323983 | − | 0.751076i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.3810 | − | 44.6956i | 0.488279 | − | 1.63097i | −0.258585 | − | 0.965989i | \(-0.583256\pi\) |
0.746864 | − | 0.664977i | \(-0.231559\pi\) | |||||||
\(752\) | 6.83391 | + | 0.798770i | 0.249207 | + | 0.0291281i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.236862 | + | 4.06676i | −0.00862599 | + | 0.148103i | ||||
\(755\) | −9.11335 | + | 15.7848i | −0.331669 | + | 0.574467i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.85224 | + | 10.1364i | 0.212703 | + | 0.368413i | 0.952560 | − | 0.304352i | \(-0.0984399\pi\) |
−0.739856 | + | 0.672765i | \(0.765107\pi\) | |||||||
\(758\) | −13.2037 | + | 6.63113i | −0.479579 | + | 0.240854i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17.5596 | − | 23.5867i | 0.636955 | − | 0.855580i | ||||
\(761\) | 25.4732 | − | 6.03726i | 0.923403 | − | 0.218851i | 0.258700 | − | 0.965958i | \(-0.416706\pi\) |
0.664704 | + | 0.747107i | \(0.268558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.2547 | + | 28.5501i | 0.769473 | + | 1.03358i | ||||
\(764\) | 0.983309 | + | 0.825094i | 0.0355749 | + | 0.0298509i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.2314 | − | 8.58519i | 0.369676 | − | 0.310195i | ||||
\(767\) | 19.5213 | + | 4.62664i | 0.704875 | + | 0.167058i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.0508 | + | 25.0264i | −1.37215 | + | 0.902476i | −0.999673 | − | 0.0255660i | \(-0.991861\pi\) |
−0.372475 | + | 0.928042i | \(0.621491\pi\) | |||||||
\(770\) | −14.7921 | + | 9.72890i | −0.533069 | + | 0.350605i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.2724 | − | 3.61963i | −0.549667 | − | 0.130273i | ||||
\(773\) | 10.7154 | − | 8.99131i | 0.385407 | − | 0.323395i | −0.429414 | − | 0.903108i | \(-0.641280\pi\) |
0.814821 | + | 0.579713i | \(0.196835\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.77672 | + | 1.49085i | 0.0638217 | + | 0.0535528i | ||||
\(776\) | 15.5892 | + | 20.9399i | 0.559618 | + | 0.751698i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.2650 | − | 4.32889i | 0.654833 | − | 0.155198i | ||||
\(779\) | 19.2715 | − | 25.8861i | 0.690472 | − | 0.927465i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.9391 | − | 20.5604i | 1.46492 | − | 0.735709i | ||||
\(782\) | 1.63223 | + | 2.82710i | 0.0583683 | + | 0.101097i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.03440 | + | 5.25573i | −0.108371 | + | 0.187705i | ||||
\(785\) | 0.0280427 | − | 0.481475i | 0.00100089 | − | 0.0171846i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.1067 | − | 1.64884i | −0.502850 | − | 0.0587748i | −0.139113 | − | 0.990276i | \(-0.544425\pi\) |
−0.363737 | + | 0.931502i | \(0.618499\pi\) | |||||||
\(788\) | 0.538863 | − | 1.79993i | 0.0191962 | − | 0.0641197i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.486563 | + | 1.12798i | −0.0173112 | + | 0.0401318i | ||||
\(791\) | 17.1290 | − | 6.23446i | 0.609039 | − | 0.221672i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.13836 | − | 0.778298i | −0.0759353 | − | 0.0276382i | ||||
\(794\) | −0.0215361 | + | 0.0228269i | −0.000764286 | + | 0.000810096i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.5159 | − | 5.78353i | −0.408172 | − | 0.204992i | ||||
\(797\) | 2.40151 | + | 41.2323i | 0.0850658 | + | 1.46052i | 0.723222 | + | 0.690616i | \(0.242661\pi\) |
−0.638156 | + | 0.769907i | \(0.720302\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.849812 | − | 2.83857i | −0.0300642 | − | 0.100421i | ||||
\(800\) | −3.22216 | − | 18.2738i | −0.113921 | − | 0.646075i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.82324 | − | 16.0114i | 0.0996920 | − | 0.565381i | ||||
\(803\) | −22.9966 | + | 2.68791i | −0.811531 | + | 0.0948544i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.3695 | + | 40.6693i | 1.35235 | + | 1.43340i | ||||
\(806\) | 0.605940 | + | 1.40473i | 0.0213433 | + | 0.0494794i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.4365 | + | 6.86422i | 0.367156 | + | 0.241482i | ||||
\(809\) | 23.8379 | 0.838097 | 0.419048 | − | 0.907964i | \(-0.362364\pi\) | ||||
0.419048 | + | 0.907964i | \(0.362364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.33188 | −0.116998 | −0.0584991 | − | 0.998287i | \(-0.518631\pi\) | ||||
−0.0584991 | + | 0.998287i | \(0.518631\pi\) | |||||||
\(812\) | 7.89598 | + | 5.19326i | 0.277094 | + | 0.182248i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.79420 | − | 20.3873i | −0.308237 | − | 0.714573i | ||||
\(815\) | −32.2838 | − | 34.2188i | −1.13085 | − | 1.19863i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.7755 | − | 1.25947i | 0.376986 | − | 0.0440634i | ||||
\(818\) | −3.09855 | + | 17.5727i | −0.108338 | + | 0.614417i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.62815 | − | 31.9188i | −0.196543 | − | 1.11465i | ||||
\(821\) | −2.57453 | − | 8.59953i | −0.0898518 | − | 0.300126i | 0.901237 | − | 0.433326i | \(-0.142660\pi\) |
−0.991089 | + | 0.133200i | \(0.957475\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0754800 | + | 1.29594i | 0.00263107 | + | 0.0451737i | 0.999368 | − | 0.0355431i | \(-0.0113161\pi\) |
−0.996737 | + | 0.0807168i | \(0.974279\pi\) | |||||||
\(824\) | 3.29934 | + | 1.65699i | 0.114938 | + | 0.0577241i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.13321 | + | 6.50082i | −0.213402 | + | 0.226192i | ||||
\(827\) | 29.6308 | + | 10.7847i | 1.03036 | + | 0.375022i | 0.801219 | − | 0.598371i | \(-0.204185\pi\) |
0.229144 | + | 0.973392i | \(0.426407\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.1437 | + | 9.15156i | −0.873277 | + | 0.317847i | −0.739493 | − | 0.673164i | \(-0.764935\pi\) |
−0.133783 | + | 0.991011i | \(0.542713\pi\) | |||||||
\(830\) | 2.37587 | − | 5.50788i | 0.0824676 | − | 0.191181i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.45509 | + | 4.86035i | −0.0504463 | + | 0.168502i | ||||
\(833\) | 2.59585 | + | 0.303411i | 0.0899407 | + | 0.0105126i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.08567 | − | 52.9789i | 0.106784 | − | 1.83341i | ||||
\(836\) | −13.9673 | + | 24.1921i | −0.483069 | + | 0.836700i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.957629 | − | 1.65866i | −0.0330807 | − | 0.0572975i | ||||
\(839\) | 3.46674 | − | 1.74106i | 0.119685 | − | 0.0601082i | −0.387949 | − | 0.921681i | \(-0.626816\pi\) |
0.507634 | + | 0.861573i | \(0.330520\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.3834 | + | 20.6635i | −0.530463 | + | 0.712536i | ||||
\(842\) | −13.9533 | + | 3.30699i | −0.480862 | + | 0.113966i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.2570 | + | 13.7775i | 0.353060 | + | 0.474242i | ||||
\(845\) | 6.45643 | + | 5.41758i | 0.222108 | + | 0.186371i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.86921 | − | 1.56845i | 0.0642267 | − | 0.0538926i | ||||
\(848\) | 17.6988 | + | 4.19469i | 0.607779 | + | 0.144046i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.52131 | + | 1.00058i | −0.0521804 | + | 0.0343196i | ||||
\(851\) | −58.5833 | + | 38.5308i | −2.00821 | + | 1.32082i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.34652 | − | 0.793140i | −0.114583 | − | 0.0271566i | 0.172924 | − | 0.984935i | \(-0.444678\pi\) |
−0.287507 | + | 0.957778i | \(0.592827\pi\) | |||||||
\(854\) | 0.776573 | − | 0.651622i | 0.0265738 | − | 0.0222980i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.4381 | + | 9.59772i | 0.390947 | + | 0.328043i | ||||
\(857\) | 8.75386 | + | 11.7585i | 0.299026 | + | 0.401662i | 0.926088 | − | 0.377308i | \(-0.123150\pi\) |
−0.627062 | + | 0.778969i | \(0.715743\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.27804 | − | 2.19894i | 0.316563 | − | 0.0750268i | −0.0692629 | − | 0.997598i | \(-0.522065\pi\) |
0.385826 | + | 0.922572i | \(0.373917\pi\) | |||||||
\(860\) | 6.50643 | − | 8.73966i | 0.221868 | − | 0.298020i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.6441 | − | 8.35900i | 0.566902 | − | 0.284709i | ||||
\(863\) | −8.00876 | − | 13.8716i | −0.272621 | − | 0.472194i | 0.696911 | − | 0.717158i | \(-0.254557\pi\) |
−0.969532 | + | 0.244964i | \(0.921224\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.3732 | + | 47.4117i | −0.930716 | + | 1.61205i | ||||
\(866\) | −0.426486 | + | 7.32248i | −0.0144926 | + | 0.248828i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.52519 | + | 0.412036i | 0.119653 | + | 0.0139854i | ||||
\(869\) | 0.733672 | − | 2.45064i | 0.0248881 | − | 0.0831321i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.5899 | − | 50.0510i | 0.731546 | − | 1.69591i | ||||
\(872\) | −22.3086 | + | 8.11966i | −0.755464 | + | 0.274967i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.9184 | − | 5.79383i | −0.538448 | − | 0.195979i | ||||
\(875\) | 9.78136 | − | 10.3676i | 0.330670 | − | 0.350490i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.5974 | − | 14.8644i | −0.999432 | − | 0.501934i | −0.127646 | − | 0.991820i | \(-0.540742\pi\) |
−0.871786 | + | 0.489886i | \(0.837038\pi\) | |||||||
\(878\) | 1.21708 | + | 20.8965i | 0.0410745 | + | 0.705222i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.20455 | + | 20.7246i | 0.209155 | + | 0.698628i | ||||
\(881\) | 2.00755 | + | 11.3854i | 0.0676360 | + | 0.383583i | 0.999770 | + | 0.0214681i | \(0.00683402\pi\) |
−0.932134 | + | 0.362115i | \(0.882055\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.24692 | + | 41.0993i | −0.243878 | + | 1.38310i | 0.579206 | + | 0.815182i | \(0.303363\pi\) |
−0.823084 | + | 0.567920i | \(0.807748\pi\) | |||||||
\(884\) | 6.21241 | − | 0.726127i | 0.208946 | − | 0.0244223i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.3851 | − | 14.1874i | −0.449683 | − | 0.476636i | ||||
\(887\) | 9.54630 | + | 22.1308i | 0.320533 | + | 0.743080i | 0.999956 | + | 0.00933326i | \(0.00297091\pi\) |
−0.679423 | + | 0.733747i | \(0.737770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.0867 | − | 18.4729i | −0.941997 | − | 0.619561i | ||||
\(890\) | 21.6198 | 0.724697 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.80468 | 0.261320 | ||||||||
\(893\) | 12.8464 | + | 8.44922i | 0.429889 | + | 0.282743i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.8417 | − | 27.4521i | −0.395824 | − | 0.917622i | ||||
\(896\) | −24.7785 | − | 26.2637i | −0.827791 | − | 0.877407i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.89998 | + | 1.15714i | −0.330367 | + | 0.0386143i | ||||
\(899\) | 0.211221 | − | 1.19789i | 0.00704460 | − | 0.0399519i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.36020 | − | 7.71410i | −0.0453149 | − | 0.256994i | ||||
\(902\) | −3.71700 | − | 12.4156i | −0.123762 | − | 0.413396i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.706934 | + | 12.1376i | 0.0235123 | + | 0.403690i | ||||
\(905\) | −2.12682 | − | 1.06813i | −0.0706980 | − | 0.0355059i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.8463 | + | 16.7961i | −0.526169 | + | 0.557707i | −0.934883 | − | 0.354956i | \(-0.884496\pi\) |
0.408714 | + | 0.912663i | \(0.365977\pi\) | |||||||
\(908\) | 22.2614 | + | 8.10250i | 0.738771 | + | 0.268891i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −19.3305 | + | 7.03572i | −0.640799 | + | 0.233232i | ||||
\(911\) | −9.06991 | + | 21.0264i | −0.300500 | + | 0.696637i | −0.999835 | − | 0.0181571i | \(-0.994220\pi\) |
0.699335 | + | 0.714794i | \(0.253479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.58249 | + | 11.9663i | −0.118563 | + | 0.396028i | ||||
\(914\) | −4.70685 | − | 0.550152i | −0.155689 | − | 0.0181974i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.505863 | + | 8.68533i | −0.0167142 | + | 0.286971i | ||||
\(917\) | 11.2088 | − | 19.4143i | 0.370148 | − | 0.641116i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.84136 | − | 17.0457i | −0.324636 | − | 0.562287i | 0.656802 | − | 0.754063i | \(-0.271909\pi\) |
−0.981439 | + | 0.191776i | \(0.938575\pi\) | |||||||
\(920\) | −33.3264 | + | 16.7371i | −1.09874 | + | 0.551807i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.89423 | + | 9.26056i | −0.227049 | + | 0.304980i | ||||
\(923\) | 51.7941 | − | 12.2754i | 1.70482 | − | 0.404051i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.3555 | − | 31.3719i | −0.767926 | − | 1.03150i | ||||
\(926\) | 1.12588 | + | 0.944728i | 0.0369988 | + | 0.0310457i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.45472 | + | 6.25525i | −0.244713 | + | 0.205339i | ||||
\(929\) | −28.1380 | − | 6.66884i | −0.923179 | − | 0.218797i | −0.258573 | − | 0.965992i | \(-0.583252\pi\) |
−0.664606 | + | 0.747194i | \(0.731401\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.3310 | + | 7.45253i | −0.371359 | + | 0.244247i | ||||
\(932\) | 6.24286 | − | 4.10599i | 0.204492 | − | 0.134496i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.76029 | + | 1.60222i | 0.221203 | + | 0.0524262i | ||||
\(935\) | 7.13679 | − | 5.98848i | 0.233398 | − | 0.195844i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.9990 | + | 12.5856i | 0.489995 | + | 0.411155i | 0.854025 | − | 0.520233i | \(-0.174155\pi\) |
−0.364029 | + | 0.931388i | \(0.618599\pi\) | |||||||
\(938\) | 14.5008 | + | 19.4779i | 0.473468 | + | 0.635977i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.0261 | − | 3.56124i | 0.490096 | − | 0.116155i | ||||
\(941\) | −6.02898 | + | 8.09833i | −0.196539 | + | 0.263998i | −0.889457 | − | 0.457018i | \(-0.848917\pi\) |
0.692918 | + | 0.721016i | \(0.256325\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.5752 | + | 18.3688i | −1.19105 | + | 0.598169i | ||||
\(944\) | 5.46032 | + | 9.45755i | 0.177718 | + | 0.307817i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.17839 | − | 3.77309i | 0.0708257 | − | 0.122674i | ||||
\(947\) | −1.22145 | + | 20.9715i | −0.0396918 | + | 0.681483i | 0.918511 | + | 0.395394i | \(0.129392\pi\) |
−0.958203 | + | 0.286088i | \(0.907645\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.7197 | − | 3.12308i | −0.867357 | − | 0.101379i | ||||
\(950\) | 2.70997 | − | 9.05193i | 0.0879231 | − | 0.293683i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.41918 | + | 5.60829i | −0.0784061 | + | 0.181766i | ||||
\(953\) | 6.34571 | − | 2.30965i | 0.205558 | − | 0.0748169i | −0.237189 | − | 0.971463i | \(-0.576226\pi\) |
0.442747 | + | 0.896647i | \(0.354004\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.08753 | + | 0.759798i | 0.0675508 | + | 0.0245865i | ||||
\(956\) | −33.4610 | + | 35.4666i | −1.08221 | + | 1.14707i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.9119 | + | 6.98682i | 0.449473 | + | 0.225734i | ||||
\(959\) | 1.57035 | + | 26.9619i | 0.0507092 | + | 0.870644i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.75989 | + | 29.2601i | 0.282577 | + | 0.943873i | ||||
\(962\) | −4.47973 | − | 25.4058i | −0.144432 | − | 0.819117i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.27912 | + | 41.2819i | −0.234445 | + | 1.32960i | ||||
\(965\) | −26.9798 | + | 3.15349i | −0.868511 | + | 0.101514i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.09307 | − | 8.57815i | −0.260256 | − | 0.275855i | 0.584049 | − | 0.811718i | \(-0.301468\pi\) |
−0.844305 | + | 0.535864i | \(0.819986\pi\) | |||||||
\(968\) | 0.644624 | + | 1.49441i | 0.0207190 | + | 0.0480320i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.2202 | + | 11.3259i | 0.552908 | + | 0.363653i | ||||
\(971\) | 24.4687 | 0.785239 | 0.392620 | − | 0.919701i | \(-0.371569\pi\) | ||||
0.392620 | + | 0.919701i | \(0.371569\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.4632 | −0.591905 | ||||||||
\(974\) | −2.85684 | − | 1.87897i | −0.0915391 | − | 0.0602062i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.490623 | − | 1.13739i | −0.0157045 | − | 0.0364071i | ||||
\(977\) | −26.7064 | − | 28.3071i | −0.854413 | − | 0.905625i | 0.142032 | − | 0.989862i | \(-0.454636\pi\) |
−0.996446 | + | 0.0842367i | \(0.973155\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44.7163 | + | 5.22659i | −1.42914 | + | 0.167042i | ||||
\(980\) | −2.36521 | + | 13.4138i | −0.0755538 | + | 0.428487i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.0480294 | + | 0.272388i | 0.00153268 | + | 0.00869226i | ||||
\(983\) | −5.36807 | − | 17.9306i | −0.171215 | − | 0.571897i | −0.999925 | − | 0.0122197i | \(-0.996110\pi\) |
0.828711 | − | 0.559677i | \(-0.189075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.189067 | − | 3.24615i | −0.00602417 | − | 0.103431i | ||||
\(986\) | 0.853368 | + | 0.428578i | 0.0271768 | + | 0.0136487i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.2734 | + | 23.6085i | −0.708613 | + | 0.751085i | ||||
\(989\) | −12.9292 | − | 4.70584i | −0.411125 | − | 0.149637i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.15353 | + | 0.783819i | −0.0684090 | + | 0.0248988i | −0.375998 | − | 0.926620i | \(-0.622700\pi\) |
0.307589 | + | 0.951519i | \(0.400478\pi\) | |||||||
\(992\) | −1.44752 | + | 3.35572i | −0.0459587 | + | 0.106544i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.80089 | + | 22.7165i | −0.215711 | + | 0.720525i | ||||
\(995\) | −22.1516 | − | 2.58915i | −0.702252 | − | 0.0820815i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.81875 | + | 31.2268i | −0.0576005 | + | 0.988963i | 0.838441 | + | 0.544992i | \(0.183467\pi\) |
−0.896042 | + | 0.443970i | \(0.853570\pi\) | |||||||
\(998\) | 1.55659 | − | 2.69609i | 0.0492729 | − | 0.0853432i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 729.2.g.c.703.4 | 144 | ||
3.2 | odd | 2 | 729.2.g.b.703.5 | 144 | |||
9.2 | odd | 6 | 729.2.g.a.217.5 | 144 | |||
9.4 | even | 3 | 81.2.g.a.25.5 | yes | 144 | ||
9.5 | odd | 6 | 243.2.g.a.73.4 | 144 | |||
9.7 | even | 3 | 729.2.g.d.217.4 | 144 | |||
81.13 | even | 27 | 729.2.g.d.514.4 | 144 | |||
81.14 | odd | 54 | 729.2.g.b.28.5 | 144 | |||
81.38 | odd | 54 | 6561.2.a.d.1.41 | 72 | |||
81.40 | even | 27 | 81.2.g.a.13.5 | ✓ | 144 | ||
81.41 | odd | 54 | 243.2.g.a.10.4 | 144 | |||
81.43 | even | 27 | 6561.2.a.c.1.32 | 72 | |||
81.67 | even | 27 | inner | 729.2.g.c.28.4 | 144 | ||
81.68 | odd | 54 | 729.2.g.a.514.5 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.2.g.a.13.5 | ✓ | 144 | 81.40 | even | 27 | ||
81.2.g.a.25.5 | yes | 144 | 9.4 | even | 3 | ||
243.2.g.a.10.4 | 144 | 81.41 | odd | 54 | |||
243.2.g.a.73.4 | 144 | 9.5 | odd | 6 | |||
729.2.g.a.217.5 | 144 | 9.2 | odd | 6 | |||
729.2.g.a.514.5 | 144 | 81.68 | odd | 54 | |||
729.2.g.b.28.5 | 144 | 81.14 | odd | 54 | |||
729.2.g.b.703.5 | 144 | 3.2 | odd | 2 | |||
729.2.g.c.28.4 | 144 | 81.67 | even | 27 | inner | ||
729.2.g.c.703.4 | 144 | 1.1 | even | 1 | trivial | ||
729.2.g.d.217.4 | 144 | 9.7 | even | 3 | |||
729.2.g.d.514.4 | 144 | 81.13 | even | 27 | |||
6561.2.a.c.1.32 | 72 | 81.43 | even | 27 | |||
6561.2.a.d.1.41 | 72 | 81.38 | odd | 54 |