Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,2,Mod(364,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.69570878012\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 727.8 | ||
Character | \(\chi\) | \(=\) | 1089.727 |
Dual form | 1089.2.e.p.364.8 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.288906 | + | 0.500400i | −0.204287 | + | 0.353836i | −0.949905 | − | 0.312537i | \(-0.898821\pi\) |
0.745618 | + | 0.666374i | \(0.232154\pi\) | |||||||
\(3\) | −1.33220 | − | 1.10691i | −0.769147 | − | 0.639072i | ||||
\(4\) | 0.833067 | + | 1.44291i | 0.416533 | + | 0.721457i | ||||
\(5\) | −1.50221 | − | 2.60191i | −0.671810 | − | 1.16361i | −0.977390 | − | 0.211443i | \(-0.932184\pi\) |
0.305580 | − | 0.952166i | \(-0.401150\pi\) | |||||||
\(6\) | 0.938776 | − | 0.346842i | 0.383254 | − | 0.141598i | ||||
\(7\) | 0.582160 | − | 1.00833i | 0.220036 | − | 0.381113i | −0.734783 | − | 0.678303i | \(-0.762716\pi\) |
0.954819 | + | 0.297189i | \(0.0960492\pi\) | |||||||
\(8\) | −2.11834 | −0.748945 | ||||||||
\(9\) | 0.549521 | + | 2.94924i | 0.183174 | + | 0.983081i | ||||
\(10\) | 1.73599 | 0.548970 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.487356 | − | 2.84438i | 0.140688 | − | 0.821101i | ||||
\(13\) | 1.97309 | + | 3.41748i | 0.547236 | + | 0.947840i | 0.998463 | + | 0.0554305i | \(0.0176531\pi\) |
−0.451227 | + | 0.892409i | \(0.649014\pi\) | |||||||
\(14\) | 0.336379 | + | 0.582626i | 0.0899011 | + | 0.155713i | ||||
\(15\) | −0.878818 | + | 5.12908i | −0.226910 | + | 1.32432i | ||||
\(16\) | −1.05413 | + | 1.82581i | −0.263533 | + | 0.456453i | ||||
\(17\) | −0.314191 | −0.0762024 | −0.0381012 | − | 0.999274i | \(-0.512131\pi\) | ||||
−0.0381012 | + | 0.999274i | \(0.512131\pi\) | |||||||
\(18\) | −1.63456 | − | 0.577073i | −0.385270 | − | 0.136018i | ||||
\(19\) | 6.36839 | 1.46101 | 0.730504 | − | 0.682908i | \(-0.239285\pi\) | ||||
0.730504 | + | 0.682908i | \(0.239285\pi\) | |||||||
\(20\) | 2.50289 | − | 4.33513i | 0.559663 | − | 0.969365i | ||||
\(21\) | −1.89168 | + | 0.698904i | −0.412799 | + | 0.152513i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0427501 | + | 0.0740453i | 0.00891401 | + | 0.0154395i | 0.870448 | − | 0.492260i | \(-0.163829\pi\) |
−0.861534 | + | 0.507700i | \(0.830496\pi\) | |||||||
\(24\) | 2.82205 | + | 2.34480i | 0.576049 | + | 0.478630i | ||||
\(25\) | −2.01329 | + | 3.48713i | −0.402659 | + | 0.697425i | ||||
\(26\) | −2.28015 | −0.447173 | ||||||||
\(27\) | 2.53246 | − | 4.53725i | 0.487372 | − | 0.873195i | ||||
\(28\) | 1.93991 | 0.366609 | ||||||||
\(29\) | 3.84991 | − | 6.66824i | 0.714910 | − | 1.23826i | −0.248084 | − | 0.968739i | \(-0.579801\pi\) |
0.962994 | − | 0.269522i | \(-0.0868658\pi\) | |||||||
\(30\) | −2.31269 | − | 1.92158i | −0.422238 | − | 0.350831i | ||||
\(31\) | −3.26442 | − | 5.65414i | −0.586307 | − | 1.01551i | −0.994711 | − | 0.102712i | \(-0.967248\pi\) |
0.408404 | − | 0.912801i | \(-0.366085\pi\) | |||||||
\(32\) | −2.72743 | − | 4.72404i | −0.482146 | − | 0.835101i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0907715 | − | 0.157221i | 0.0155672 | − | 0.0269632i | ||||
\(35\) | −3.49812 | −0.591290 | ||||||||
\(36\) | −3.79771 | + | 3.24983i | −0.632952 | + | 0.541638i | ||||
\(37\) | −6.24309 | −1.02636 | −0.513179 | − | 0.858282i | \(-0.671532\pi\) | ||||
−0.513179 | + | 0.858282i | \(0.671532\pi\) | |||||||
\(38\) | −1.83987 | + | 3.18674i | −0.298466 | + | 0.516958i | ||||
\(39\) | 1.15428 | − | 6.73680i | 0.184833 | − | 1.07875i | ||||
\(40\) | 3.18219 | + | 5.51172i | 0.503149 | + | 0.871480i | ||||
\(41\) | −2.90454 | − | 5.03080i | −0.453612 | − | 0.785679i | 0.544995 | − | 0.838439i | \(-0.316532\pi\) |
−0.998607 | + | 0.0527599i | \(0.983198\pi\) | |||||||
\(42\) | 0.196787 | − | 1.14851i | 0.0303649 | − | 0.177220i | ||||
\(43\) | 3.39229 | − | 5.87562i | 0.517320 | − | 0.896024i | −0.482478 | − | 0.875908i | \(-0.660263\pi\) |
0.999798 | − | 0.0201157i | \(-0.00640347\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.84817 | − | 5.86020i | 1.02086 | − | 0.873587i | ||||
\(46\) | −0.0494030 | −0.00728408 | ||||||||
\(47\) | 0.163868 | − | 0.283827i | 0.0239026 | − | 0.0414005i | −0.853827 | − | 0.520557i | \(-0.825724\pi\) |
0.877729 | + | 0.479157i | \(0.159058\pi\) | |||||||
\(48\) | 3.42532 | − | 1.26552i | 0.494402 | − | 0.182663i | ||||
\(49\) | 2.82218 | + | 4.88816i | 0.403168 | + | 0.698308i | ||||
\(50\) | −1.16331 | − | 2.01490i | −0.164516 | − | 0.284950i | ||||
\(51\) | 0.418565 | + | 0.347779i | 0.0586108 | + | 0.0486988i | ||||
\(52\) | −3.28742 | + | 5.69398i | −0.455884 | + | 0.789614i | ||||
\(53\) | −2.42269 | −0.332782 | −0.166391 | − | 0.986060i | \(-0.553211\pi\) | ||||
−0.166391 | + | 0.986060i | \(0.553211\pi\) | |||||||
\(54\) | 1.53880 | + | 2.57808i | 0.209404 | + | 0.350832i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.23321 | + | 2.13598i | −0.164795 | + | 0.285433i | ||||
\(57\) | −8.48398 | − | 7.04920i | −1.12373 | − | 0.933690i | ||||
\(58\) | 2.22452 | + | 3.85299i | 0.292094 | + | 0.505922i | ||||
\(59\) | 1.14802 | + | 1.98842i | 0.149459 | + | 0.258870i | 0.931028 | − | 0.364949i | \(-0.118913\pi\) |
−0.781569 | + | 0.623819i | \(0.785580\pi\) | |||||||
\(60\) | −8.13293 | + | 3.00481i | −1.04996 | + | 0.387919i | ||||
\(61\) | 6.84360 | − | 11.8535i | 0.876233 | − | 1.51768i | 0.0207900 | − | 0.999784i | \(-0.493382\pi\) |
0.855443 | − | 0.517897i | \(-0.173285\pi\) | |||||||
\(62\) | 3.77244 | 0.479100 | ||||||||
\(63\) | 3.29372 | + | 1.16283i | 0.414970 | + | 0.146503i | ||||
\(64\) | −1.06465 | −0.133081 | ||||||||
\(65\) | 5.92799 | − | 10.2676i | 0.735277 | − | 1.27354i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.83989 | − | 10.1150i | −0.713456 | − | 1.23574i | −0.963552 | − | 0.267521i | \(-0.913795\pi\) |
0.250096 | − | 0.968221i | \(-0.419538\pi\) | |||||||
\(68\) | −0.261742 | − | 0.453350i | −0.0317408 | − | 0.0549767i | ||||
\(69\) | 0.0250094 | − | 0.145964i | 0.00301078 | − | 0.0175719i | ||||
\(70\) | 1.01063 | − | 1.75046i | 0.120793 | − | 0.209220i | ||||
\(71\) | 8.71765 | 1.03459 | 0.517297 | − | 0.855806i | \(-0.326938\pi\) | ||||
0.517297 | + | 0.855806i | \(0.326938\pi\) | |||||||
\(72\) | −1.16407 | − | 6.24749i | −0.137187 | − | 0.736273i | ||||
\(73\) | 2.94656 | 0.344869 | 0.172434 | − | 0.985021i | \(-0.444837\pi\) | ||||
0.172434 | + | 0.985021i | \(0.444837\pi\) | |||||||
\(74\) | 1.80367 | − | 3.12404i | 0.209672 | − | 0.363162i | ||||
\(75\) | 6.54203 | − | 2.41703i | 0.755409 | − | 0.279095i | ||||
\(76\) | 5.30529 | + | 9.18904i | 0.608559 | + | 1.05405i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.03761 | + | 2.52391i | 0.343942 | + | 0.285776i | ||||
\(79\) | 4.44360 | − | 7.69654i | 0.499944 | − | 0.865928i | −0.500056 | − | 0.865993i | \(-0.666687\pi\) |
1.00000 | 6.50093e-5i | \(2.06931e-5\pi\) | ||||||||
\(80\) | 6.33413 | 0.708178 | ||||||||
\(81\) | −8.39605 | + | 3.24134i | −0.932895 | + | 0.360149i | ||||
\(82\) | 3.35655 | 0.370669 | ||||||||
\(83\) | −2.47889 | + | 4.29357i | −0.272094 | + | 0.471280i | −0.969398 | − | 0.245495i | \(-0.921049\pi\) |
0.697304 | + | 0.716775i | \(0.254383\pi\) | |||||||
\(84\) | −2.58435 | − | 2.14730i | −0.281976 | − | 0.234290i | ||||
\(85\) | 0.471981 | + | 0.817496i | 0.0511936 | + | 0.0886699i | ||||
\(86\) | 1.96011 | + | 3.39500i | 0.211364 | + | 0.366093i | ||||
\(87\) | −12.5100 | + | 4.62195i | −1.34121 | + | 0.495525i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.12862 | 0.225634 | 0.112817 | − | 0.993616i | \(-0.464013\pi\) | ||||
0.112817 | + | 0.993616i | \(0.464013\pi\) | |||||||
\(90\) | 0.953966 | + | 5.11987i | 0.100557 | + | 0.539681i | ||||
\(91\) | 4.59461 | 0.481646 | ||||||||
\(92\) | −0.0712273 | + | 0.123369i | −0.00742596 | + | 0.0128621i | ||||
\(93\) | −1.90973 | + | 11.1459i | −0.198030 | + | 1.15577i | ||||
\(94\) | 0.0946848 | + | 0.163999i | 0.00976599 | + | 0.0169152i | ||||
\(95\) | −9.56668 | − | 16.5700i | −0.981521 | − | 1.70004i | ||||
\(96\) | −1.59559 | + | 9.31238i | −0.162849 | + | 0.950441i | ||||
\(97\) | 0.0444196 | − | 0.0769370i | 0.00451013 | − | 0.00781177i | −0.863762 | − | 0.503901i | \(-0.831898\pi\) |
0.868272 | + | 0.496089i | \(0.165231\pi\) | |||||||
\(98\) | −3.26138 | −0.329449 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.70883 | −0.670883 | ||||||||
\(101\) | 1.02824 | − | 1.78097i | 0.102314 | − | 0.177213i | −0.810324 | − | 0.585983i | \(-0.800709\pi\) |
0.912638 | + | 0.408770i | \(0.134042\pi\) | |||||||
\(102\) | −0.294955 | + | 0.108974i | −0.0292049 | + | 0.0107901i | ||||
\(103\) | 1.50836 | + | 2.61255i | 0.148623 | + | 0.257422i | 0.930719 | − | 0.365736i | \(-0.119183\pi\) |
−0.782096 | + | 0.623158i | \(0.785849\pi\) | |||||||
\(104\) | −4.17966 | − | 7.23938i | −0.409849 | − | 0.709880i | ||||
\(105\) | 4.66020 | + | 3.87208i | 0.454788 | + | 0.377877i | ||||
\(106\) | 0.699931 | − | 1.21232i | 0.0679833 | − | 0.117750i | ||||
\(107\) | 11.9929 | 1.15939 | 0.579697 | − | 0.814832i | \(-0.303171\pi\) | ||||
0.579697 | + | 0.814832i | \(0.303171\pi\) | |||||||
\(108\) | 8.65657 | − | 0.125714i | 0.832979 | − | 0.0120968i | ||||
\(109\) | 5.20013 | 0.498082 | 0.249041 | − | 0.968493i | \(-0.419885\pi\) | ||||
0.249041 | + | 0.968493i | \(0.419885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.31705 | + | 6.91051i | 0.789420 | + | 0.655916i | ||||
\(112\) | 1.22735 | + | 2.12583i | 0.115974 | + | 0.200872i | ||||
\(113\) | −9.61378 | − | 16.6515i | −0.904388 | − | 1.56645i | −0.821737 | − | 0.569867i | \(-0.806995\pi\) |
−0.0826514 | − | 0.996579i | \(-0.526339\pi\) | |||||||
\(114\) | 5.97849 | − | 2.20882i | 0.559937 | − | 0.206875i | ||||
\(115\) | 0.128440 | − | 0.222464i | 0.0119770 | − | 0.0207449i | ||||
\(116\) | 12.8289 | 1.19114 | ||||||||
\(117\) | −8.99474 | + | 7.69709i | −0.831564 | + | 0.711596i | ||||
\(118\) | −1.32667 | −0.122130 | ||||||||
\(119\) | −0.182909 | + | 0.316808i | −0.0167673 | + | 0.0290417i | ||||
\(120\) | 1.86163 | − | 10.8651i | 0.169943 | − | 0.991844i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.95432 | + | 6.84907i | 0.358007 | + | 0.620086i | ||||
\(123\) | −1.69920 | + | 9.91709i | −0.153211 | + | 0.894194i | ||||
\(124\) | 5.43896 | − | 9.42055i | 0.488433 | − | 0.845990i | ||||
\(125\) | −2.92455 | −0.261580 | ||||||||
\(126\) | −1.53346 | + | 1.31223i | −0.136611 | + | 0.116903i | ||||
\(127\) | −13.1829 | −1.16980 | −0.584898 | − | 0.811107i | \(-0.698865\pi\) | ||||
−0.584898 | + | 0.811107i | \(0.698865\pi\) | |||||||
\(128\) | 5.76244 | − | 9.98084i | 0.509332 | − | 0.882190i | ||||
\(129\) | −11.0230 | + | 4.07256i | −0.970518 | + | 0.358569i | ||||
\(130\) | 3.42527 | + | 5.93274i | 0.300416 | + | 0.520335i | ||||
\(131\) | 8.98588 | + | 15.5640i | 0.785100 | + | 1.35983i | 0.928939 | + | 0.370233i | \(0.120722\pi\) |
−0.143839 | + | 0.989601i | \(0.545945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.70742 | − | 6.42144i | 0.321474 | − | 0.556810i | ||||
\(134\) | 6.74872 | 0.583001 | ||||||||
\(135\) | −15.6098 | + | 0.226691i | −1.34348 | + | 0.0195105i | ||||
\(136\) | 0.665561 | 0.0570714 | ||||||||
\(137\) | 8.20087 | − | 14.2043i | 0.700648 | − | 1.21356i | −0.267592 | − | 0.963532i | \(-0.586228\pi\) |
0.968239 | − | 0.250025i | \(-0.0804388\pi\) | |||||||
\(138\) | 0.0658148 | + | 0.0546845i | 0.00560253 | + | 0.00465505i | ||||
\(139\) | 5.95080 | + | 10.3071i | 0.504740 | + | 0.874236i | 0.999985 | + | 0.00548243i | \(0.00174512\pi\) |
−0.495245 | + | 0.868754i | \(0.664922\pi\) | |||||||
\(140\) | −2.91416 | − | 5.04748i | −0.246292 | − | 0.426590i | ||||
\(141\) | −0.532475 | + | 0.196729i | −0.0448425 | + | 0.0165676i | ||||
\(142\) | −2.51858 | + | 4.36231i | −0.211355 | + | 0.366077i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.96403 | − | 2.10557i | −0.497002 | − | 0.175464i | ||||
\(145\) | −23.1336 | −1.92114 | ||||||||
\(146\) | −0.851279 | + | 1.47446i | −0.0704524 | + | 0.122027i | ||||
\(147\) | 1.65102 | − | 9.63590i | 0.136174 | − | 0.794755i | ||||
\(148\) | −5.20091 | − | 9.00824i | −0.427512 | − | 0.740473i | ||||
\(149\) | 2.26586 | + | 3.92458i | 0.185626 | + | 0.321514i | 0.943787 | − | 0.330553i | \(-0.107235\pi\) |
−0.758161 | + | 0.652067i | \(0.773902\pi\) | |||||||
\(150\) | −0.680551 | + | 3.97193i | −0.0555667 | + | 0.324306i | ||||
\(151\) | 1.46543 | − | 2.53820i | 0.119255 | − | 0.206556i | −0.800218 | − | 0.599710i | \(-0.795283\pi\) |
0.919473 | + | 0.393154i | \(0.128616\pi\) | |||||||
\(152\) | −13.4904 | −1.09422 | ||||||||
\(153\) | −0.172654 | − | 0.926624i | −0.0139583 | − | 0.0749131i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.80771 | + | 16.9874i | −0.787774 | + | 1.36446i | ||||
\(156\) | 10.6822 | − | 3.94667i | 0.855261 | − | 0.315986i | ||||
\(157\) | 9.02682 | + | 15.6349i | 0.720419 | + | 1.24780i | 0.960832 | + | 0.277131i | \(0.0893837\pi\) |
−0.240413 | + | 0.970671i | \(0.577283\pi\) | |||||||
\(158\) | 2.56756 | + | 4.44715i | 0.204264 | + | 0.353796i | ||||
\(159\) | 3.22752 | + | 2.68169i | 0.255959 | + | 0.212672i | ||||
\(160\) | −8.19436 | + | 14.1930i | −0.647821 | + | 1.12206i | ||||
\(161\) | 0.0995496 | 0.00784561 | ||||||||
\(162\) | 0.803704 | − | 5.13783i | 0.0631449 | − | 0.403666i | ||||
\(163\) | −5.82347 | −0.456130 | −0.228065 | − | 0.973646i | \(-0.573240\pi\) | ||||
−0.228065 | + | 0.973646i | \(0.573240\pi\) | |||||||
\(164\) | 4.83934 | − | 8.38199i | 0.377889 | − | 0.654523i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.43233 | − | 2.48087i | −0.111171 | − | 0.192553i | ||||
\(167\) | 2.51086 | + | 4.34894i | 0.194296 | + | 0.336531i | 0.946670 | − | 0.322206i | \(-0.104424\pi\) |
−0.752373 | + | 0.658737i | \(0.771091\pi\) | |||||||
\(168\) | 4.00722 | − | 1.48051i | 0.309163 | − | 0.114224i | ||||
\(169\) | −1.28613 | + | 2.22765i | −0.0989334 | + | 0.171358i | ||||
\(170\) | −0.545433 | −0.0418328 | ||||||||
\(171\) | 3.49956 | + | 18.7819i | 0.267618 | + | 1.43629i | ||||
\(172\) | 11.3040 | 0.861923 | ||||||||
\(173\) | 7.79493 | − | 13.5012i | 0.592638 | − | 1.02648i | −0.401238 | − | 0.915974i | \(-0.631420\pi\) |
0.993876 | − | 0.110505i | \(-0.0352467\pi\) | |||||||
\(174\) | 1.30138 | − | 7.59530i | 0.0986574 | − | 0.575798i | ||||
\(175\) | 2.34412 | + | 4.06013i | 0.177199 | + | 0.306917i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.671606 | − | 3.91972i | 0.0504810 | − | 0.294624i | ||||
\(178\) | −0.614972 | + | 1.06516i | −0.0460941 | + | 0.0798373i | ||||
\(179\) | 7.04887 | 0.526857 | 0.263428 | − | 0.964679i | \(-0.415147\pi\) | ||||
0.263428 | + | 0.964679i | \(0.415147\pi\) | |||||||
\(180\) | 14.1607 | + | 4.99938i | 1.05548 | + | 0.372632i | ||||
\(181\) | 2.49770 | 0.185652 | 0.0928262 | − | 0.995682i | \(-0.470410\pi\) | ||||
0.0928262 | + | 0.995682i | \(0.470410\pi\) | |||||||
\(182\) | −1.32741 | + | 2.29914i | −0.0983942 | + | 0.170424i | ||||
\(183\) | −22.2377 | + | 8.21598i | −1.64386 | + | 0.607343i | ||||
\(184\) | −0.0905590 | − | 0.156853i | −0.00667610 | − | 0.0115633i | ||||
\(185\) | 9.37845 | + | 16.2440i | 0.689518 | + | 1.19428i | ||||
\(186\) | −5.02565 | − | 4.17573i | −0.368499 | − | 0.306180i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.546051 | 0.0398249 | ||||||||
\(189\) | −3.10075 | − | 5.19496i | −0.225547 | − | 0.377878i | ||||
\(190\) | 11.0555 | 0.802050 | ||||||||
\(191\) | 5.91149 | − | 10.2390i | 0.427740 | − | 0.740868i | −0.568932 | − | 0.822385i | \(-0.692643\pi\) |
0.996672 | + | 0.0815168i | \(0.0259764\pi\) | |||||||
\(192\) | 1.41833 | + | 1.17847i | 0.102359 | + | 0.0850486i | ||||
\(193\) | −3.37333 | − | 5.84278i | −0.242817 | − | 0.420572i | 0.718698 | − | 0.695322i | \(-0.244738\pi\) |
−0.961516 | + | 0.274750i | \(0.911405\pi\) | |||||||
\(194\) | 0.0256662 | + | 0.0444551i | 0.00184272 | + | 0.00319169i | ||||
\(195\) | −19.2625 | + | 7.11676i | −1.37942 | + | 0.509642i | ||||
\(196\) | −4.70213 | + | 8.14432i | −0.335866 | + | 0.581737i | ||||
\(197\) | −20.6474 | −1.47107 | −0.735534 | − | 0.677488i | \(-0.763069\pi\) | ||||
−0.735534 | + | 0.677488i | \(0.763069\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2862 | −0.941832 | −0.470916 | − | 0.882178i | \(-0.656077\pi\) | ||||
−0.470916 | + | 0.882178i | \(0.656077\pi\) | |||||||
\(200\) | 4.26483 | − | 7.38691i | 0.301569 | − | 0.522333i | ||||
\(201\) | −3.41642 | + | 19.9394i | −0.240976 | + | 1.40642i | ||||
\(202\) | 0.594131 | + | 1.02906i | 0.0418029 | + | 0.0724047i | ||||
\(203\) | −4.48253 | − | 7.76397i | −0.314612 | − | 0.544924i | ||||
\(204\) | −0.153123 | + | 0.893676i | −0.0107207 | + | 0.0625699i | ||||
\(205\) | −8.72647 | + | 15.1147i | −0.609483 | + | 1.05566i | ||||
\(206\) | −1.74309 | −0.121447 | ||||||||
\(207\) | −0.194885 | + | 0.166770i | −0.0135455 | + | 0.0115913i | ||||
\(208\) | −8.31958 | −0.576859 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.28395 | + | 1.21329i | −0.226614 | + | 0.0837252i | ||||
\(211\) | 4.17251 | + | 7.22700i | 0.287247 | + | 0.497527i | 0.973152 | − | 0.230165i | \(-0.0739265\pi\) |
−0.685904 | + | 0.727692i | \(0.740593\pi\) | |||||||
\(212\) | −2.01826 | − | 3.49574i | −0.138615 | − | 0.240088i | ||||
\(213\) | −11.6137 | − | 9.64961i | −0.795755 | − | 0.661180i | ||||
\(214\) | −3.46481 | + | 6.00123i | −0.236850 | + | 0.410235i | ||||
\(215\) | −20.3838 | −1.39016 | ||||||||
\(216\) | −5.36460 | + | 9.61142i | −0.365015 | + | 0.653975i | ||||
\(217\) | −7.60166 | −0.516034 | ||||||||
\(218\) | −1.50235 | + | 2.60214i | −0.101752 | + | 0.176239i | ||||
\(219\) | −3.92541 | − | 3.26156i | −0.265255 | − | 0.220396i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.619925 | − | 1.07374i | −0.0417007 | − | 0.0722277i | ||||
\(222\) | −5.86086 | + | 2.16536i | −0.393355 | + | 0.145330i | ||||
\(223\) | 0.191828 | − | 0.332255i | 0.0128457 | − | 0.0222495i | −0.859531 | − | 0.511083i | \(-0.829244\pi\) |
0.872377 | + | 0.488834i | \(0.162578\pi\) | |||||||
\(224\) | −6.35120 | −0.424357 | ||||||||
\(225\) | −11.3907 | − | 4.02144i | −0.759382 | − | 0.268096i | ||||
\(226\) | 11.1099 | 0.739020 | ||||||||
\(227\) | −9.00701 | + | 15.6006i | −0.597817 | + | 1.03545i | 0.395326 | + | 0.918541i | \(0.370632\pi\) |
−0.993143 | + | 0.116908i | \(0.962702\pi\) | |||||||
\(228\) | 3.10368 | − | 18.1141i | 0.205546 | − | 1.19964i | ||||
\(229\) | −6.71393 | − | 11.6289i | −0.443669 | − | 0.768458i | 0.554289 | − | 0.832324i | \(-0.312990\pi\) |
−0.997958 | + | 0.0638664i | \(0.979657\pi\) | |||||||
\(230\) | 0.0742139 | + | 0.128542i | 0.00489352 | + | 0.00847583i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.15540 | + | 14.1256i | −0.535428 | + | 0.927389i | ||||
\(233\) | −3.36965 | −0.220753 | −0.110377 | − | 0.993890i | \(-0.535206\pi\) | ||||
−0.110377 | + | 0.993890i | \(0.535206\pi\) | |||||||
\(234\) | −1.25299 | − | 6.72470i | −0.0819104 | − | 0.439607i | ||||
\(235\) | −0.984658 | −0.0642320 | ||||||||
\(236\) | −1.91275 | + | 3.31298i | −0.124509 | + | 0.215656i | ||||
\(237\) | −14.4391 | + | 5.33469i | −0.937920 | + | 0.346526i | ||||
\(238\) | −0.105687 | − | 0.183056i | −0.00685068 | − | 0.0118657i | ||||
\(239\) | 11.5984 | + | 20.0890i | 0.750238 | + | 1.29945i | 0.947707 | + | 0.319141i | \(0.103394\pi\) |
−0.197469 | + | 0.980309i | \(0.563272\pi\) | |||||||
\(240\) | −8.43834 | − | 7.01129i | −0.544693 | − | 0.452577i | ||||
\(241\) | −7.58206 | + | 13.1325i | −0.488404 | + | 0.845940i | −0.999911 | − | 0.0133389i | \(-0.995754\pi\) |
0.511507 | + | 0.859279i | \(0.329087\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.7731 | + | 4.97552i | 0.947694 | + | 0.319180i | ||||
\(244\) | 22.8047 | 1.45992 | ||||||||
\(245\) | 8.47903 | − | 14.6861i | 0.541706 | − | 0.938262i | ||||
\(246\) | −4.47160 | − | 3.71538i | −0.285099 | − | 0.236884i | ||||
\(247\) | 12.5654 | + | 21.7639i | 0.799516 | + | 1.38480i | ||||
\(248\) | 6.91513 | + | 11.9774i | 0.439111 | + | 0.760563i | ||||
\(249\) | 8.05495 | − | 2.97600i | 0.510462 | − | 0.188596i | ||||
\(250\) | 0.844920 | − | 1.46344i | 0.0534375 | − | 0.0925564i | ||||
\(251\) | −0.582306 | −0.0367548 | −0.0183774 | − | 0.999831i | \(-0.505850\pi\) | ||||
−0.0183774 | + | 0.999831i | \(0.505850\pi\) | |||||||
\(252\) | 1.06602 | + | 5.72127i | 0.0671531 | + | 0.360406i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.80863 | − | 6.59673i | 0.238974 | − | 0.413916i | ||||
\(255\) | 0.276116 | − | 1.61151i | 0.0172911 | − | 0.100917i | ||||
\(256\) | 2.26495 | + | 3.92302i | 0.141560 | + | 0.245189i | ||||
\(257\) | 5.48571 | + | 9.50153i | 0.342189 | + | 0.592689i | 0.984839 | − | 0.173471i | \(-0.0554983\pi\) |
−0.642650 | + | 0.766160i | \(0.722165\pi\) | |||||||
\(258\) | 1.14669 | − | 6.69248i | 0.0713899 | − | 0.416656i | ||||
\(259\) | −3.63448 | + | 6.29510i | −0.225835 | + | 0.391158i | ||||
\(260\) | 19.7537 | 1.22507 | ||||||||
\(261\) | 21.7819 | + | 7.68998i | 1.34826 | + | 0.475998i | ||||
\(262\) | −10.3843 | −0.641544 | ||||||||
\(263\) | 7.19768 | − | 12.4668i | 0.443828 | − | 0.768733i | −0.554142 | − | 0.832422i | \(-0.686953\pi\) |
0.997970 | + | 0.0636896i | \(0.0202868\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.63940 | + | 6.30363i | 0.223567 | + | 0.387229i | ||||
\(266\) | 2.14219 | + | 3.71039i | 0.131346 | + | 0.227498i | ||||
\(267\) | −2.83575 | − | 2.35618i | −0.173545 | − | 0.144196i | ||||
\(268\) | 9.73004 | − | 16.8529i | 0.594357 | − | 1.02946i | ||||
\(269\) | 0.488976 | 0.0298134 | 0.0149067 | − | 0.999889i | \(-0.495255\pi\) | ||||
0.0149067 | + | 0.999889i | \(0.495255\pi\) | |||||||
\(270\) | 4.39633 | − | 7.87665i | 0.267552 | − | 0.479357i | ||||
\(271\) | 21.9389 | 1.33270 | 0.666348 | − | 0.745641i | \(-0.267857\pi\) | ||||
0.666348 | + | 0.745641i | \(0.267857\pi\) | |||||||
\(272\) | 0.331199 | − | 0.573653i | 0.0200819 | − | 0.0347828i | ||||
\(273\) | −6.12094 | − | 5.08580i | −0.370456 | − | 0.307806i | ||||
\(274\) | 4.73856 | + | 8.20743i | 0.286267 | + | 0.495829i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.231447 | − | 0.0855109i | 0.0139315 | − | 0.00514715i | ||||
\(277\) | −1.43476 | + | 2.48508i | −0.0862065 | + | 0.149314i | −0.905905 | − | 0.423482i | \(-0.860808\pi\) |
0.819698 | + | 0.572796i | \(0.194141\pi\) | |||||||
\(278\) | −6.87689 | −0.412448 | ||||||||
\(279\) | 14.8816 | − | 12.7346i | 0.890935 | − | 0.762402i | ||||
\(280\) | 7.41019 | 0.442843 | ||||||||
\(281\) | −9.08903 | + | 15.7427i | −0.542206 | + | 0.939129i | 0.456571 | + | 0.889687i | \(0.349078\pi\) |
−0.998777 | + | 0.0494416i | \(0.984256\pi\) | |||||||
\(282\) | 0.0553920 | − | 0.323287i | 0.00329855 | − | 0.0192514i | ||||
\(283\) | 10.2686 | + | 17.7857i | 0.610402 | + | 1.05725i | 0.991173 | + | 0.132578i | \(0.0423255\pi\) |
−0.380770 | + | 0.924670i | \(0.624341\pi\) | |||||||
\(284\) | 7.26238 | + | 12.5788i | 0.430943 | + | 0.746415i | ||||
\(285\) | −5.59665 | + | 32.6640i | −0.331517 | + | 1.93485i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.76362 | −0.399244 | ||||||||
\(288\) | 12.4336 | − | 10.6398i | 0.732655 | − | 0.626956i | ||||
\(289\) | −16.9013 | −0.994193 | ||||||||
\(290\) | 6.68342 | − | 11.5760i | 0.392464 | − | 0.679768i | ||||
\(291\) | −0.144338 | + | 0.0533273i | −0.00846124 | + | 0.00312610i | ||||
\(292\) | 2.45468 | + | 4.25163i | 0.143649 | + | 0.248808i | ||||
\(293\) | −0.430033 | − | 0.744840i | −0.0251228 | − | 0.0435140i | 0.853191 | − | 0.521599i | \(-0.174664\pi\) |
−0.878313 | + | 0.478085i | \(0.841331\pi\) | |||||||
\(294\) | 4.34481 | + | 3.61004i | 0.253395 | + | 0.210542i | ||||
\(295\) | 3.44913 | − | 5.97407i | 0.200816 | − | 0.347824i | ||||
\(296\) | 13.2250 | 0.768685 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.61848 | −0.151684 | ||||||||
\(299\) | −0.168699 | + | 0.292196i | −0.00975612 | + | 0.0168981i | ||||
\(300\) | 8.93751 | + | 7.42604i | 0.516007 | + | 0.428743i | ||||
\(301\) | −3.94971 | − | 6.84110i | −0.227658 | − | 0.394315i | ||||
\(302\) | 0.846744 | + | 1.46660i | 0.0487247 | + | 0.0843936i | ||||
\(303\) | −3.34119 | + | 1.23444i | −0.191946 | + | 0.0709167i | ||||
\(304\) | −6.71313 | + | 11.6275i | −0.385024 | + | 0.666882i | ||||
\(305\) | −41.1222 | −2.35465 | ||||||||
\(306\) | 0.513563 | + | 0.181311i | 0.0293585 | + | 0.0103649i | ||||
\(307\) | 3.48920 | 0.199139 | 0.0995696 | − | 0.995031i | \(-0.468253\pi\) | ||||
0.0995696 | + | 0.995031i | \(0.468253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.882412 | − | 5.15005i | 0.0501986 | − | 0.292976i | ||||
\(310\) | −5.66701 | − | 9.81555i | −0.321865 | − | 0.557486i | ||||
\(311\) | −5.42265 | − | 9.39231i | −0.307490 | − | 0.532589i | 0.670322 | − | 0.742070i | \(-0.266156\pi\) |
−0.977813 | + | 0.209481i | \(0.932822\pi\) | |||||||
\(312\) | −2.44516 | + | 14.2708i | −0.138430 | + | 0.807925i | ||||
\(313\) | 14.1405 | − | 24.4921i | 0.799270 | − | 1.38438i | −0.120822 | − | 0.992674i | \(-0.538553\pi\) |
0.920092 | − | 0.391702i | \(-0.128114\pi\) | |||||||
\(314\) | −10.4316 | −0.588690 | ||||||||
\(315\) | −1.92229 | − | 10.3168i | −0.108309 | − | 0.581285i | ||||
\(316\) | 14.8072 | 0.832973 | ||||||||
\(317\) | 0.556263 | − | 0.963477i | 0.0312429 | − | 0.0541142i | −0.849981 | − | 0.526813i | \(-0.823387\pi\) |
0.881224 | + | 0.472699i | \(0.156720\pi\) | |||||||
\(318\) | −2.27437 | + | 0.840291i | −0.127540 | + | 0.0471212i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.59933 | + | 2.77013i | 0.0894055 | + | 0.154855i | ||||
\(321\) | −15.9769 | − | 13.2750i | −0.891744 | − | 0.740936i | ||||
\(322\) | −0.0287605 | + | 0.0498146i | −0.00160276 | + | 0.00277606i | ||||
\(323\) | −2.00089 | −0.111332 | ||||||||
\(324\) | −11.6714 | − | 9.41453i | −0.648414 | − | 0.523029i | ||||
\(325\) | −15.8896 | −0.881396 | ||||||||
\(326\) | 1.68244 | − | 2.91407i | 0.0931816 | − | 0.161395i | ||||
\(327\) | −6.92762 | − | 5.75605i | −0.383098 | − | 0.318310i | ||||
\(328\) | 6.15278 | + | 10.6569i | 0.339731 | + | 0.588431i | ||||
\(329\) | −0.190795 | − | 0.330466i | −0.0105188 | − | 0.0182192i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.18915 | − | 10.7199i | 0.340187 | − | 0.589221i | −0.644281 | − | 0.764789i | \(-0.722843\pi\) |
0.984467 | + | 0.175569i | \(0.0561764\pi\) | |||||||
\(332\) | −8.26033 | −0.453344 | ||||||||
\(333\) | −3.43071 | − | 18.4124i | −0.188002 | − | 1.00899i | ||||
\(334\) | −2.90161 | −0.158769 | ||||||||
\(335\) | −17.5455 | + | 30.3897i | −0.958615 | + | 1.66037i | ||||
\(336\) | 0.718017 | − | 4.19059i | 0.0391710 | − | 0.228616i | ||||
\(337\) | −6.73681 | − | 11.6685i | −0.366977 | − | 0.635623i | 0.622114 | − | 0.782927i | \(-0.286274\pi\) |
−0.989091 | + | 0.147303i | \(0.952941\pi\) | |||||||
\(338\) | −0.743144 | − | 1.28716i | −0.0404217 | − | 0.0700124i | ||||
\(339\) | −5.62420 | + | 32.8248i | −0.305465 | + | 1.78280i | ||||
\(340\) | −0.786384 | + | 1.36206i | −0.0426477 | + | 0.0738679i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −10.4095 | − | 3.67503i | −0.562882 | − | 0.198723i | ||||
\(343\) | 14.7221 | 0.794918 | ||||||||
\(344\) | −7.18601 | + | 12.4465i | −0.387444 | + | 0.671072i | ||||
\(345\) | −0.417354 | + | 0.154196i | −0.0224696 | + | 0.00830164i | ||||
\(346\) | 4.50400 | + | 7.80117i | 0.242137 | + | 0.419393i | ||||
\(347\) | −4.86958 | − | 8.43437i | −0.261413 | − | 0.452781i | 0.705205 | − | 0.709004i | \(-0.250855\pi\) |
−0.966618 | + | 0.256223i | \(0.917522\pi\) | |||||||
\(348\) | −17.0907 | − | 14.2004i | −0.916158 | − | 0.761222i | ||||
\(349\) | 2.22010 | − | 3.84532i | 0.118839 | − | 0.205835i | −0.800469 | − | 0.599374i | \(-0.795416\pi\) |
0.919308 | + | 0.393539i | \(0.128749\pi\) | |||||||
\(350\) | −2.70892 | −0.144798 | ||||||||
\(351\) | 20.5027 | − | 0.297748i | 1.09436 | − | 0.0158926i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.2618 | + | 28.1662i | −0.865527 | + | 1.49914i | 0.000996749 | 1.00000i | \(0.499683\pi\) | |
−0.866523 | + | 0.499137i | \(0.833651\pi\) | |||||||
\(354\) | 1.76740 | + | 1.46850i | 0.0939361 | + | 0.0780501i | ||||
\(355\) | −13.0958 | − | 22.6825i | −0.695051 | − | 1.20386i | ||||
\(356\) | 1.77328 | + | 3.07142i | 0.0939839 | + | 0.162785i | ||||
\(357\) | 0.594348 | − | 0.219589i | 0.0314563 | − | 0.0116219i | ||||
\(358\) | −2.03646 | + | 3.52725i | −0.107630 | + | 0.186421i | ||||
\(359\) | −27.7701 | −1.46565 | −0.732825 | − | 0.680417i | \(-0.761799\pi\) | ||||
−0.732825 | + | 0.680417i | \(0.761799\pi\) | |||||||
\(360\) | −14.5067 | + | 12.4139i | −0.764571 | + | 0.654268i | ||||
\(361\) | 21.5564 | 1.13455 | ||||||||
\(362\) | −0.721600 | + | 1.24985i | −0.0379264 | + | 0.0656905i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.82761 | + | 6.62962i | 0.200621 | + | 0.347487i | ||||
\(365\) | −4.42637 | − | 7.66669i | −0.231687 | − | 0.401293i | ||||
\(366\) | 2.31333 | − | 13.5014i | 0.120920 | − | 0.705729i | ||||
\(367\) | −0.586098 | + | 1.01515i | −0.0305941 | + | 0.0529905i | −0.880917 | − | 0.473271i | \(-0.843073\pi\) |
0.850323 | + | 0.526261i | \(0.176407\pi\) | |||||||
\(368\) | −0.180257 | −0.00939655 | ||||||||
\(369\) | 13.2409 | − | 11.3307i | 0.689296 | − | 0.589853i | ||||
\(370\) | −10.8380 | −0.563439 | ||||||||
\(371\) | −1.41040 | + | 2.44288i | −0.0732241 | + | 0.126828i | ||||
\(372\) | −17.6734 | + | 6.52966i | −0.916325 | + | 0.338547i | ||||
\(373\) | −10.8834 | − | 18.8506i | −0.563520 | − | 0.976046i | −0.997186 | − | 0.0749719i | \(-0.976113\pi\) |
0.433665 | − | 0.901074i | \(-0.357220\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.89609 | + | 3.23720i | 0.201193 | + | 0.167168i | ||||
\(376\) | −0.347127 | + | 0.601242i | −0.0179017 | + | 0.0310067i | ||||
\(377\) | 30.3848 | 1.56490 | ||||||||
\(378\) | 3.49539 | − | 0.0507612i | 0.179783 | − | 0.00261087i | ||||
\(379\) | −16.2469 | −0.834545 | −0.417273 | − | 0.908781i | \(-0.637014\pi\) | ||||
−0.417273 | + | 0.908781i | \(0.637014\pi\) | |||||||
\(380\) | 15.9394 | − | 27.6078i | 0.817672 | − | 1.41625i | ||||
\(381\) | 17.5623 | + | 14.5922i | 0.899744 | + | 0.747584i | ||||
\(382\) | 3.41573 | + | 5.91622i | 0.174764 | + | 0.302700i | ||||
\(383\) | −3.09667 | − | 5.36360i | −0.158233 | − | 0.274067i | 0.775999 | − | 0.630734i | \(-0.217246\pi\) |
−0.934231 | + | 0.356667i | \(0.883913\pi\) | |||||||
\(384\) | −18.7246 | + | 6.91801i | −0.955534 | + | 0.353033i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.89830 | 0.198418 | ||||||||
\(387\) | 19.1928 | + | 6.77591i | 0.975623 | + | 0.344439i | ||||
\(388\) | 0.148018 | 0.00751447 | ||||||||
\(389\) | 0.361607 | − | 0.626321i | 0.0183342 | − | 0.0317557i | −0.856713 | − | 0.515794i | \(-0.827497\pi\) |
0.875047 | + | 0.484038i | \(0.160830\pi\) | |||||||
\(390\) | 2.00383 | − | 11.6950i | 0.101468 | − | 0.592202i | ||||
\(391\) | −0.0134317 | − | 0.0232643i | −0.000679269 | − | 0.00117653i | ||||
\(392\) | −5.97832 | − | 10.3548i | −0.301951 | − | 0.522994i | ||||
\(393\) | 5.25688 | − | 30.6809i | 0.265174 | − | 1.54765i | ||||
\(394\) | 5.96517 | − | 10.3320i | 0.300521 | − | 0.520517i | ||||
\(395\) | −26.7009 | −1.34347 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.08994 | 0.205268 | 0.102634 | − | 0.994719i | \(-0.467273\pi\) | ||||
0.102634 | + | 0.994719i | \(0.467273\pi\) | |||||||
\(398\) | 3.83846 | − | 6.64840i | 0.192404 | − | 0.333254i | ||||
\(399\) | −12.0470 | + | 4.45089i | −0.603103 | + | 0.222823i | ||||
\(400\) | −4.24456 | − | 7.35179i | −0.212228 | − | 0.367590i | ||||
\(401\) | 2.82313 | + | 4.88981i | 0.140981 | + | 0.244185i | 0.927866 | − | 0.372913i | \(-0.121641\pi\) |
−0.786886 | + | 0.617099i | \(0.788308\pi\) | |||||||
\(402\) | −8.99065 | − | 7.47019i | −0.448413 | − | 0.372579i | ||||
\(403\) | 12.8820 | − | 22.3122i | 0.641696 | − | 1.11145i | ||||
\(404\) | 3.42638 | 0.170469 | ||||||||
\(405\) | 21.0463 | + | 16.9766i | 1.04580 | + | 0.843574i | ||||
\(406\) | 5.18012 | 0.257085 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.886662 | − | 0.736713i | −0.0438963 | − | 0.0364727i | ||||
\(409\) | −4.72439 | − | 8.18288i | −0.233606 | − | 0.404617i | 0.725261 | − | 0.688474i | \(-0.241719\pi\) |
−0.958867 | + | 0.283857i | \(0.908386\pi\) | |||||||
\(410\) | −5.04226 | − | 8.73345i | −0.249019 | − | 0.431314i | ||||
\(411\) | −26.6481 | + | 9.84543i | −1.31445 | + | 0.485639i | ||||
\(412\) | −2.51312 | + | 4.35286i | −0.123813 | + | 0.214450i | ||||
\(413\) | 2.67332 | 0.131545 | ||||||||
\(414\) | −0.0271480 | − | 0.145701i | −0.00133425 | − | 0.00716084i | ||||
\(415\) | 14.8953 | 0.731182 | ||||||||
\(416\) | 10.7629 | − | 18.6419i | 0.527694 | − | 0.913993i | ||||
\(417\) | 3.48131 | − | 20.3181i | 0.170480 | − | 0.994981i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.0757820 | − | 0.131258i | −0.00370219 | − | 0.00641238i | 0.864168 | − | 0.503203i | \(-0.167845\pi\) |
−0.867871 | + | 0.496790i | \(0.834512\pi\) | |||||||
\(420\) | −1.70483 | + | 9.94996i | −0.0831871 | + | 0.485508i | ||||
\(421\) | −8.48828 | + | 14.7021i | −0.413693 | + | 0.716538i | −0.995290 | − | 0.0969391i | \(-0.969095\pi\) |
0.581597 | + | 0.813477i | \(0.302428\pi\) | |||||||
\(422\) | −4.82185 | −0.234724 | ||||||||
\(423\) | 0.927124 | + | 0.327317i | 0.0450783 | + | 0.0159147i | ||||
\(424\) | 5.13208 | 0.249236 | ||||||||
\(425\) | 0.632558 | − | 1.09562i | 0.0306836 | − | 0.0531455i | ||||
\(426\) | 8.18392 | − | 3.02364i | 0.396512 | − | 0.146496i | ||||
\(427\) | −7.96814 | − | 13.8012i | −0.385605 | − | 0.667888i | ||||
\(428\) | 9.99085 | + | 17.3047i | 0.482926 | + | 0.836453i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.88900 | − | 10.2000i | 0.283993 | − | 0.491890i | ||||
\(431\) | −25.3694 | −1.22200 | −0.610999 | − | 0.791631i | \(-0.709232\pi\) | ||||
−0.610999 | + | 0.791631i | \(0.709232\pi\) | |||||||
\(432\) | 5.61462 | + | 9.40666i | 0.270134 | + | 0.452578i | ||||
\(433\) | 16.5347 | 0.794607 | 0.397303 | − | 0.917687i | \(-0.369946\pi\) | ||||
0.397303 | + | 0.917687i | \(0.369946\pi\) | |||||||
\(434\) | 2.19616 | − | 3.80387i | 0.105419 | − | 0.182592i | ||||
\(435\) | 30.8185 | + | 25.6067i | 1.47764 | + | 1.22774i | ||||
\(436\) | 4.33205 | + | 7.50333i | 0.207468 | + | 0.359344i | ||||
\(437\) | 0.272249 | + | 0.471549i | 0.0130234 | + | 0.0225573i | ||||
\(438\) | 2.76616 | − | 1.02199i | 0.132172 | − | 0.0488326i | ||||
\(439\) | 19.6207 | − | 33.9840i | 0.936443 | − | 1.62197i | 0.164403 | − | 0.986393i | \(-0.447430\pi\) |
0.772040 | − | 0.635574i | \(-0.219237\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.8655 | + | 11.0094i | −0.612643 | + | 0.524259i | ||||
\(442\) | 0.716400 | 0.0340757 | ||||||||
\(443\) | −16.0947 | + | 27.8768i | −0.764681 | + | 1.32447i | 0.175734 | + | 0.984438i | \(0.443770\pi\) |
−0.940415 | + | 0.340029i | \(0.889563\pi\) | |||||||
\(444\) | −3.04261 | + | 17.7577i | −0.144396 | + | 0.842743i | ||||
\(445\) | −3.19765 | − | 5.53849i | −0.151583 | − | 0.262549i | ||||
\(446\) | 0.110840 | + | 0.191981i | 0.00524845 | + | 0.00909057i | ||||
\(447\) | 1.32556 | − | 7.73642i | 0.0626969 | − | 0.365920i | ||||
\(448\) | −0.619798 | + | 1.07352i | −0.0292827 | + | 0.0507191i | ||||
\(449\) | −25.8443 | −1.21967 | −0.609833 | − | 0.792530i | \(-0.708764\pi\) | ||||
−0.609833 | + | 0.792530i | \(0.708764\pi\) | |||||||
\(450\) | 5.30318 | − | 4.53810i | 0.249994 | − | 0.213928i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 16.0178 | − | 27.7437i | 0.753415 | − | 1.30495i | ||||
\(453\) | −4.76180 | + | 1.75930i | −0.223729 | + | 0.0826592i | ||||
\(454\) | −5.20436 | − | 9.01422i | −0.244253 | − | 0.423058i | ||||
\(455\) | −6.90208 | − | 11.9548i | −0.323575 | − | 0.560448i | ||||
\(456\) | 17.9719 | + | 14.9326i | 0.841612 | + | 0.699282i | ||||
\(457\) | 6.35814 | − | 11.0126i | 0.297421 | − | 0.515149i | −0.678124 | − | 0.734947i | \(-0.737207\pi\) |
0.975545 | + | 0.219799i | \(0.0705401\pi\) | |||||||
\(458\) | 7.75879 | 0.362544 | ||||||||
\(459\) | −0.795675 | + | 1.42556i | −0.0371389 | + | 0.0665395i | ||||
\(460\) | 0.427995 | 0.0199554 | ||||||||
\(461\) | 9.51087 | − | 16.4733i | 0.442965 | − | 0.767238i | −0.554943 | − | 0.831889i | \(-0.687260\pi\) |
0.997908 | + | 0.0646502i | \(0.0205932\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4334 | + | 19.8032i | 0.531353 | + | 0.920331i | 0.999330 | + | 0.0365903i | \(0.0116497\pi\) |
−0.467977 | + | 0.883741i | \(0.655017\pi\) | |||||||
\(464\) | 8.11663 | + | 14.0584i | 0.376805 | + | 0.652646i | ||||
\(465\) | 31.8693 | − | 11.7745i | 1.47791 | − | 0.546029i | ||||
\(466\) | 0.973513 | − | 1.68617i | 0.0450971 | − | 0.0781105i | ||||
\(467\) | 15.9228 | 0.736821 | 0.368411 | − | 0.929663i | \(-0.379902\pi\) | ||||
0.368411 | + | 0.929663i | \(0.379902\pi\) | |||||||
\(468\) | −18.5994 | − | 6.56644i | −0.859760 | − | 0.303534i | ||||
\(469\) | −13.5990 | −0.627944 | ||||||||
\(470\) | 0.284474 | − | 0.492723i | 0.0131218 | − | 0.0227276i | ||||
\(471\) | 5.28082 | − | 30.8207i | 0.243328 | − | 1.42014i | ||||
\(472\) | −2.43188 | − | 4.21215i | −0.111936 | − | 0.193880i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.50206 | − | 8.76655i | 0.0689920 | − | 0.402661i | ||||
\(475\) | −12.8214 | + | 22.2074i | −0.588288 | + | 1.01894i | ||||
\(476\) | −0.609502 | −0.0279365 | ||||||||
\(477\) | −1.33132 | − | 7.14511i | −0.0609570 | − | 0.327152i | ||||
\(478\) | −13.4034 | −0.613057 | ||||||||
\(479\) | 8.19498 | − | 14.1941i | 0.374438 | − | 0.648546i | −0.615805 | − | 0.787899i | \(-0.711169\pi\) |
0.990243 | + | 0.139353i | \(0.0445022\pi\) | |||||||
\(480\) | 26.6269 | − | 9.83761i | 1.21535 | − | 0.449024i | ||||
\(481\) | −12.3181 | − | 21.3357i | −0.561659 | − | 0.972822i | ||||
\(482\) | −4.38101 | − | 7.58813i | −0.199549 | − | 0.345630i | ||||
\(483\) | −0.132620 | − | 0.110192i | −0.00603442 | − | 0.00501391i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.266911 | −0.0121198 | ||||||||
\(486\) | −6.75778 | + | 5.95500i | −0.306539 | + | 0.270124i | ||||
\(487\) | 22.7865 | 1.03256 | 0.516278 | − | 0.856421i | \(-0.327317\pi\) | ||||
0.516278 | + | 0.856421i | \(0.327317\pi\) | |||||||
\(488\) | −14.4970 | + | 25.1096i | −0.656250 | + | 1.13666i | ||||
\(489\) | 7.75804 | + | 6.44603i | 0.350831 | + | 0.291500i | ||||
\(490\) | 4.89929 | + | 8.48582i | 0.221327 | + | 0.383350i | ||||
\(491\) | 21.8215 | + | 37.7960i | 0.984791 | + | 1.70571i | 0.642863 | + | 0.765981i | \(0.277747\pi\) |
0.341928 | + | 0.939726i | \(0.388920\pi\) | |||||||
\(492\) | −15.7250 | + | 5.80980i | −0.708940 | + | 0.261926i | ||||
\(493\) | −1.20961 | + | 2.09510i | −0.0544779 | + | 0.0943585i | ||||
\(494\) | −14.5209 | −0.653324 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.7645 | 0.618045 | ||||||||
\(497\) | 5.07507 | − | 8.79027i | 0.227648 | − | 0.394298i | ||||
\(498\) | −0.837937 | + | 4.89048i | −0.0375488 | + | 0.219148i | ||||
\(499\) | 10.0518 | + | 17.4102i | 0.449978 | + | 0.779385i | 0.998384 | − | 0.0568270i | \(-0.0180983\pi\) |
−0.548406 | + | 0.836212i | \(0.684765\pi\) | |||||||
\(500\) | −2.43635 | − | 4.21987i | −0.108957 | − | 0.188718i | ||||
\(501\) | 1.46889 | − | 8.57296i | 0.0656253 | − | 0.383011i | ||||
\(502\) | 0.168232 | − | 0.291386i | 0.00750854 | − | 0.0130052i | ||||
\(503\) | −10.6083 | −0.473001 | −0.236500 | − | 0.971631i | \(-0.576000\pi\) | ||||
−0.236500 | + | 0.971631i | \(0.576000\pi\) | |||||||
\(504\) | −6.97721 | − | 2.46327i | −0.310790 | − | 0.109723i | ||||
\(505\) | −6.17856 | −0.274942 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.17919 | − | 1.54405i | 0.185604 | − | 0.0685736i | ||||
\(508\) | −10.9823 | − | 19.0218i | −0.487259 | − | 0.843957i | ||||
\(509\) | 22.2342 | + | 38.5107i | 0.985513 | + | 1.70696i | 0.639635 | + | 0.768679i | \(0.279086\pi\) |
0.345878 | + | 0.938280i | \(0.387581\pi\) | |||||||
\(510\) | 0.726627 | + | 0.603743i | 0.0321756 | + | 0.0267342i | ||||
\(511\) | 1.71537 | − | 2.97111i | 0.0758835 | − | 0.131434i | ||||
\(512\) | 20.4323 | 0.902989 | ||||||||
\(513\) | 16.1277 | − | 28.8950i | 0.712055 | − | 1.27574i | ||||
\(514\) | −6.33942 | −0.279620 | ||||||||
\(515\) | 4.53175 | − | 7.84922i | 0.199693 | − | 0.345878i | ||||
\(516\) | −15.0592 | − | 12.5125i | −0.662946 | − | 0.550831i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.10004 | − | 3.63738i | −0.0922707 | − | 0.159817i | ||||
\(519\) | −25.3290 | + | 9.35809i | −1.11182 | + | 0.410774i | ||||
\(520\) | −12.5575 | + | 21.7502i | −0.550682 | + | 0.953809i | ||||
\(521\) | 16.9511 | 0.742643 | 0.371322 | − | 0.928504i | \(-0.378905\pi\) | ||||
0.371322 | + | 0.928504i | \(0.378905\pi\) | |||||||
\(522\) | −10.1410 | + | 8.67796i | −0.443858 | + | 0.379824i | ||||
\(523\) | 30.2142 | 1.32117 | 0.660587 | − | 0.750749i | \(-0.270307\pi\) | ||||
0.660587 | + | 0.750749i | \(0.270307\pi\) | |||||||
\(524\) | −14.9717 | + | 25.9317i | −0.654041 | + | 1.13283i | ||||
\(525\) | 1.37134 | − | 8.00363i | 0.0598504 | − | 0.349307i | ||||
\(526\) | 4.15891 | + | 7.20344i | 0.181337 | + | 0.314085i | ||||
\(527\) | 1.02565 | + | 1.77648i | 0.0446780 | + | 0.0773845i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4963 | − | 19.9123i | 0.499841 | − | 0.865750i | ||||
\(530\) | −4.20578 | −0.182688 | ||||||||
\(531\) | −5.23348 | + | 4.47846i | −0.227114 | + | 0.194348i | ||||
\(532\) | 12.3541 | 0.535619 | ||||||||
\(533\) | 11.4618 | − | 19.8524i | 0.496465 | − | 0.859903i | ||||
\(534\) | 1.99830 | − | 0.738296i | 0.0864750 | − | 0.0319492i | ||||
\(535\) | −18.0158 | − | 31.2044i | −0.778893 | − | 1.34908i | ||||
\(536\) | 12.3709 | + | 21.4269i | 0.534339 | + | 0.925503i | ||||
\(537\) | −9.39051 | − | 7.80243i | −0.405230 | − | 0.336700i | ||||
\(538\) | −0.141268 | + | 0.244683i | −0.00609050 | + | 0.0105491i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −13.3311 | − | 22.3348i | −0.573680 | − | 0.961136i | ||||
\(541\) | 11.8312 | 0.508663 | 0.254332 | − | 0.967117i | \(-0.418145\pi\) | ||||
0.254332 | + | 0.967117i | \(0.418145\pi\) | |||||||
\(542\) | −6.33829 | + | 10.9782i | −0.272253 | + | 0.471556i | ||||
\(543\) | −3.32744 | − | 2.76471i | −0.142794 | − | 0.118645i | ||||
\(544\) | 0.856932 | + | 1.48425i | 0.0367406 | + | 0.0636367i | ||||
\(545\) | −7.81170 | − | 13.5303i | −0.334617 | − | 0.579573i | ||||
\(546\) | 4.31331 | − | 1.59360i | 0.184593 | − | 0.0681999i | ||||
\(547\) | −1.27290 | + | 2.20474i | −0.0544255 | + | 0.0942677i | −0.891955 | − | 0.452125i | \(-0.850666\pi\) |
0.837529 | + | 0.546393i | \(0.183999\pi\) | |||||||
\(548\) | 27.3275 | 1.16737 | ||||||||
\(549\) | 38.7194 | + | 13.6697i | 1.65251 | + | 0.583409i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.5177 | − | 42.4659i | 1.04449 | − | 1.80911i | ||||
\(552\) | −0.0529784 | + | 0.309200i | −0.00225491 | + | 0.0131604i | ||||
\(553\) | −5.17377 | − | 8.96123i | −0.220011 | − | 0.381070i | ||||
\(554\) | −0.829023 | − | 1.43591i | −0.0352218 | − | 0.0610060i | ||||
\(555\) | 5.48654 | − | 32.0213i | 0.232890 | − | 1.35923i | ||||
\(556\) | −9.91483 | + | 17.1730i | −0.420482 | + | 0.728297i | ||||
\(557\) | 9.67543 | 0.409961 | 0.204981 | − | 0.978766i | \(-0.434287\pi\) | ||||
0.204981 | + | 0.978766i | \(0.434287\pi\) | |||||||
\(558\) | 2.07304 | + | 11.1258i | 0.0877586 | + | 0.470994i | ||||
\(559\) | 26.7731 | 1.13238 | ||||||||
\(560\) | 3.68748 | − | 6.38690i | 0.155824 | − | 0.269896i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.25175 | − | 9.09630i | −0.221532 | − | 0.383704i | ||||
\(563\) | 11.9936 | + | 20.7735i | 0.505470 | + | 0.875501i | 0.999980 | + | 0.00632830i | \(0.00201437\pi\) |
−0.494510 | + | 0.869172i | \(0.664652\pi\) | |||||||
\(564\) | −0.727450 | − | 0.604427i | −0.0306312 | − | 0.0254510i | ||||
\(565\) | −28.8839 | + | 50.0284i | −1.21515 | + | 2.10471i | ||||
\(566\) | −11.8666 | −0.498790 | ||||||||
\(567\) | −1.61950 | + | 10.3530i | −0.0680127 | + | 0.434784i | ||||
\(568\) | −18.4669 | −0.774854 | ||||||||
\(569\) | 18.8096 | − | 32.5791i | 0.788538 | − | 1.36579i | −0.138325 | − | 0.990387i | \(-0.544172\pi\) |
0.926863 | − | 0.375401i | \(-0.122495\pi\) | |||||||
\(570\) | −14.7281 | − | 12.2374i | −0.616894 | − | 0.512568i | ||||
\(571\) | 7.37740 | + | 12.7780i | 0.308735 | + | 0.534744i | 0.978086 | − | 0.208202i | \(-0.0667612\pi\) |
−0.669351 | + | 0.742946i | \(0.733428\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.2089 | + | 7.09695i | −0.802463 | + | 0.296479i | ||||
\(574\) | 1.95405 | − | 3.38451i | 0.0815605 | − | 0.141267i | ||||
\(575\) | −0.344274 | −0.0143572 | ||||||||
\(576\) | −0.585049 | − | 3.13992i | −0.0243770 | − | 0.130830i | ||||
\(577\) | −22.3068 | −0.928644 | −0.464322 | − | 0.885667i | \(-0.653702\pi\) | ||||
−0.464322 | + | 0.885667i | \(0.653702\pi\) | |||||||
\(578\) | 4.88288 | − | 8.45740i | 0.203101 | − | 0.351782i | ||||
\(579\) | −1.97345 | + | 11.5177i | −0.0820137 | + | 0.478660i | ||||
\(580\) | −19.2718 | − | 33.3797i | −0.800217 | − | 1.38602i | ||||
\(581\) | 2.88622 | + | 4.99909i | 0.119741 | + | 0.207397i | ||||
\(582\) | 0.0150151 | − | 0.0876332i | 0.000622396 | − | 0.00363251i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −6.24181 | −0.258288 | ||||||||
\(585\) | 33.5391 | + | 11.8408i | 1.38667 | + | 0.489558i | ||||
\(586\) | 0.496957 | 0.0205291 | ||||||||
\(587\) | 1.25008 | − | 2.16521i | 0.0515965 | − | 0.0893677i | −0.839074 | − | 0.544018i | \(-0.816902\pi\) |
0.890670 | + | 0.454650i | \(0.150236\pi\) | |||||||
\(588\) | 15.2792 | − | 5.64507i | 0.630102 | − | 0.232799i | ||||
\(589\) | −20.7891 | − | 36.0078i | −0.856599 | − | 1.48367i | ||||
\(590\) | 1.99295 | + | 3.45189i | 0.0820484 | + | 0.142112i | ||||
\(591\) | 27.5065 | + | 22.8547i | 1.13147 | + | 0.940119i | ||||
\(592\) | 6.58105 | − | 11.3987i | 0.270479 | − | 0.468484i | ||||
\(593\) | −10.8953 | −0.447417 | −0.223708 | − | 0.974656i | \(-0.571816\pi\) | ||||
−0.223708 | + | 0.974656i | \(0.571816\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.09907 | 0.0450577 | ||||||||
\(596\) | −3.77522 | + | 6.53887i | −0.154639 | + | 0.267843i | ||||
\(597\) | 17.6999 | + | 14.7065i | 0.724407 | + | 0.601899i | ||||
\(598\) | −0.0974764 | − | 0.168834i | −0.00398611 | − | 0.00690414i | ||||
\(599\) | 18.4190 | + | 31.9027i | 0.752582 | + | 1.30351i | 0.946568 | + | 0.322506i | \(0.104525\pi\) |
−0.193986 | + | 0.981004i | \(0.562142\pi\) | |||||||
\(600\) | −13.8582 | + | 5.12008i | −0.565759 | + | 0.209026i | ||||
\(601\) | 7.72714 | − | 13.3838i | 0.315197 | − | 0.545937i | −0.664283 | − | 0.747482i | \(-0.731263\pi\) |
0.979479 | + | 0.201545i | \(0.0645962\pi\) | |||||||
\(602\) | 4.56438 | 0.186030 | ||||||||
\(603\) | 26.6224 | − | 22.7816i | 1.08415 | − | 0.927740i | ||||
\(604\) | 4.88321 | 0.198695 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.347575 | − | 2.02857i | 0.0141193 | − | 0.0824049i | ||||
\(607\) | 12.7385 | + | 22.0636i | 0.517038 | + | 0.895536i | 0.999804 | + | 0.0197865i | \(0.00629866\pi\) |
−0.482766 | + | 0.875749i | \(0.660368\pi\) | |||||||
\(608\) | −17.3693 | − | 30.0845i | −0.704419 | − | 1.22009i | ||||
\(609\) | −2.62235 | + | 15.3049i | −0.106263 | + | 0.620186i | ||||
\(610\) | 11.8805 | − | 20.5776i | 0.481026 | − | 0.833161i | ||||
\(611\) | 1.29330 | 0.0523214 | ||||||||
\(612\) | 1.19321 | − | 1.02106i | 0.0482325 | − | 0.0412741i | ||||
\(613\) | −37.7740 | −1.52568 | −0.762839 | − | 0.646588i | \(-0.776195\pi\) | ||||
−0.762839 | + | 0.646588i | \(0.776195\pi\) | |||||||
\(614\) | −1.00805 | + | 1.74600i | −0.0406816 | + | 0.0704626i | ||||
\(615\) | 28.3559 | − | 10.4764i | 1.14342 | − | 0.422450i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.9464 | − | 36.2802i | −0.843271 | − | 1.46059i | −0.887115 | − | 0.461549i | \(-0.847294\pi\) |
0.0438437 | − | 0.999038i | \(-0.486040\pi\) | |||||||
\(618\) | 2.32215 | + | 1.92944i | 0.0934107 | + | 0.0776135i | ||||
\(619\) | 2.99480 | − | 5.18715i | 0.120371 | − | 0.208489i | −0.799543 | − | 0.600609i | \(-0.794925\pi\) |
0.919914 | + | 0.392120i | \(0.128258\pi\) | |||||||
\(620\) | −32.6819 | −1.31254 | ||||||||
\(621\) | 0.444225 | − | 0.00645119i | 0.0178261 | − | 0.000258877i | ||||
\(622\) | 6.26655 | 0.251266 | ||||||||
\(623\) | 1.23920 | − | 2.14636i | 0.0496475 | − | 0.0859920i | ||||
\(624\) | 11.0834 | + | 9.20899i | 0.443689 | + | 0.368655i | ||||
\(625\) | 14.4598 | + | 25.0451i | 0.578391 | + | 1.00180i | ||||
\(626\) | 8.17057 | + | 14.1518i | 0.326562 | + | 0.565621i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.0399 | + | 26.0498i | −0.600157 | + | 1.03950i | ||||
\(629\) | 1.96152 | 0.0782109 | ||||||||
\(630\) | 5.71788 | + | 2.01867i | 0.227806 | + | 0.0804257i | ||||
\(631\) | −21.4994 | −0.855878 | −0.427939 | − | 0.903808i | \(-0.640760\pi\) | ||||
−0.427939 | + | 0.903808i | \(0.640760\pi\) | |||||||
\(632\) | −9.41303 | + | 16.3038i | −0.374430 | + | 0.648532i | ||||
\(633\) | 2.44098 | − | 14.2464i | 0.0970202 | − | 0.566243i | ||||
\(634\) | 0.321416 | + | 0.556708i | 0.0127651 | + | 0.0221097i | ||||
\(635\) | 19.8036 | + | 34.3008i | 0.785881 | + | 1.36119i | ||||
\(636\) | −1.18071 | + | 6.89105i | −0.0468184 | + | 0.273248i | ||||
\(637\) | −11.1368 | + | 19.2895i | −0.441256 | + | 0.764278i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.79053 | + | 25.7104i | 0.189510 | + | 1.01709i | ||||
\(640\) | −34.6257 | −1.36870 | ||||||||
\(641\) | −6.41850 | + | 11.1172i | −0.253516 | + | 0.439102i | −0.964491 | − | 0.264115i | \(-0.914920\pi\) |
0.710976 | + | 0.703217i | \(0.248254\pi\) | |||||||
\(642\) | 11.2586 | − | 4.15963i | 0.444342 | − | 0.164167i | ||||
\(643\) | −14.1778 | − | 24.5566i | −0.559117 | − | 0.968419i | −0.997570 | − | 0.0696654i | \(-0.977807\pi\) |
0.438453 | − | 0.898754i | \(-0.355527\pi\) | |||||||
\(644\) | 0.0829314 | + | 0.143641i | 0.00326796 | + | 0.00566027i | ||||
\(645\) | 27.1553 | + | 22.5629i | 1.06924 | + | 0.888414i | ||||
\(646\) | 0.578069 | − | 1.00124i | 0.0227438 | − | 0.0393934i | ||||
\(647\) | −17.4948 | −0.687792 | −0.343896 | − | 0.939008i | \(-0.611747\pi\) | ||||
−0.343896 | + | 0.939008i | \(0.611747\pi\) | |||||||
\(648\) | 17.7857 | − | 6.86625i | 0.698687 | − | 0.269732i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.59060 | − | 7.95116i | 0.180058 | − | 0.311870i | ||||
\(651\) | 10.1269 | + | 8.41431i | 0.396906 | + | 0.329783i | ||||
\(652\) | −4.85134 | − | 8.40277i | −0.189993 | − | 0.329078i | ||||
\(653\) | 14.6511 | + | 25.3765i | 0.573342 | + | 0.993058i | 0.996220 | + | 0.0868708i | \(0.0276867\pi\) |
−0.422877 | + | 0.906187i | \(0.638980\pi\) | |||||||
\(654\) | 4.88176 | − | 1.80362i | 0.190892 | − | 0.0705272i | ||||
\(655\) | 26.9974 | − | 46.7609i | 1.05488 | − | 1.82710i | ||||
\(656\) | 12.2471 | 0.478168 | ||||||||
\(657\) | 1.61920 | + | 8.69012i | 0.0631709 | + | 0.339034i | ||||
\(658\) | 0.220487 | 0.00859547 | ||||||||
\(659\) | −13.7935 | + | 23.8911i | −0.537319 | + | 0.930664i | 0.461728 | + | 0.887021i | \(0.347229\pi\) |
−0.999047 | + | 0.0436422i | \(0.986104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.8776 | − | 25.7688i | −0.578672 | − | 1.00229i | −0.995632 | − | 0.0933649i | \(-0.970238\pi\) |
0.416960 | − | 0.908925i | \(-0.363096\pi\) | |||||||
\(662\) | 3.57617 | + | 6.19410i | 0.138992 | + | 0.240741i | ||||
\(663\) | −0.362665 | + | 2.11664i | −0.0140848 | + | 0.0822034i | ||||
\(664\) | 5.25113 | − | 9.09522i | 0.203783 | − | 0.352963i | ||||
\(665\) | −22.2774 | −0.863879 | ||||||||
\(666\) | 10.2047 | + | 3.60272i | 0.395424 | + | 0.139603i | ||||
\(667\) | 0.658336 | 0.0254909 | ||||||||
\(668\) | −4.18343 | + | 7.24592i | −0.161862 | + | 0.280353i | ||||
\(669\) | −0.623329 | + | 0.230296i | −0.0240993 | + | 0.00890376i | ||||
\(670\) | −10.1380 | − | 17.5596i | −0.391666 | − | 0.678385i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 8.46107 | + | 7.03017i | 0.326393 | + | 0.271195i | ||||
\(673\) | −4.82684 | + | 8.36033i | −0.186061 | + | 0.322267i | −0.943934 | − | 0.330136i | \(-0.892906\pi\) |
0.757873 | + | 0.652403i | \(0.226239\pi\) | |||||||
\(674\) | 7.78522 | 0.299875 | ||||||||
\(675\) | 10.7234 | + | 17.9658i | 0.412743 | + | 0.691505i | ||||
\(676\) | −4.28574 | −0.164836 | ||||||||
\(677\) | 0.0490576 | − | 0.0849702i | 0.00188544 | − | 0.00326567i | −0.865081 | − | 0.501632i | \(-0.832733\pi\) |
0.866967 | + | 0.498366i | \(0.166067\pi\) | |||||||
\(678\) | −14.8006 | − | 12.2976i | −0.568415 | − | 0.472287i | ||||
\(679\) | −0.0517187 | − | 0.0895793i | −0.00198478 | − | 0.00343774i | ||||
\(680\) | −0.999815 | − | 1.73173i | −0.0383412 | − | 0.0664088i | ||||
\(681\) | 29.2676 | − | 10.8132i | 1.12153 | − | 0.414364i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.5246 | 1.16799 | 0.583996 | − | 0.811756i | \(-0.301488\pi\) | ||||
0.583996 | + | 0.811756i | \(0.301488\pi\) | |||||||
\(684\) | −24.1853 | + | 20.6962i | −0.924749 | + | 0.791337i | ||||
\(685\) | −49.2778 | −1.88281 | ||||||||
\(686\) | −4.25330 | + | 7.36693i | −0.162392 | + | 0.281271i | ||||
\(687\) | −3.92775 | + | 22.9237i | −0.149853 | + | 0.874593i | ||||
\(688\) | 7.15185 | + | 12.3874i | 0.272662 | + | 0.472264i | ||||
\(689\) | −4.78018 | − | 8.27952i | −0.182110 | − | 0.315424i | ||||
\(690\) | 0.0434163 | − | 0.253392i | 0.00165283 | − | 0.00964647i | ||||
\(691\) | −16.4008 | + | 28.4071i | −0.623918 | + | 1.08066i | 0.364832 | + | 0.931074i | \(0.381127\pi\) |
−0.988749 | + | 0.149583i | \(0.952207\pi\) | |||||||
\(692\) | 25.9748 | 0.987413 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.62741 | 0.213614 | ||||||||
\(695\) | 17.8788 | − | 30.9669i | 0.678180 | − | 1.17464i | ||||
\(696\) | 26.5003 | − | 9.79085i | 1.00449 | − | 0.371121i | ||||
\(697\) | 0.912577 | + | 1.58063i | 0.0345663 | + | 0.0598707i | ||||
\(698\) | 1.28280 | + | 2.22187i | 0.0485547 | + | 0.0840991i | ||||
\(699\) | 4.48906 | + | 3.72989i | 0.169792 | + | 0.141077i | ||||
\(700\) | −3.90561 | + | 6.76472i | −0.147618 | + | 0.255682i | ||||
\(701\) | −8.74920 | −0.330453 | −0.165226 | − | 0.986256i | \(-0.552835\pi\) | ||||
−0.165226 | + | 0.986256i | \(0.552835\pi\) | |||||||
\(702\) | −5.77437 | + | 10.3456i | −0.217940 | + | 0.390469i | ||||
\(703\) | −39.7584 | −1.49952 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.31176 | + | 1.08992i | 0.0494039 | + | 0.0410489i | ||||
\(706\) | −9.39625 | − | 16.2748i | −0.353632 | − | 0.612509i | ||||
\(707\) | −1.19720 | − | 2.07362i | −0.0450254 | − | 0.0779863i | ||||
\(708\) | 6.21531 | − | 2.29632i | 0.233586 | − | 0.0863010i | ||||
\(709\) | −13.3879 | + | 23.1886i | −0.502795 | + | 0.870866i | 0.497200 | + | 0.867636i | \(0.334361\pi\) |
−0.999995 | + | 0.00322996i | \(0.998972\pi\) | |||||||
\(710\) | 15.1338 | 0.567961 | ||||||||
\(711\) | 25.1408 | + | 8.87583i | 0.942853 | + | 0.332870i | ||||
\(712\) | −4.50914 | −0.168987 | ||||||||
\(713\) | 0.279108 | − | 0.483430i | 0.0104527 | − | 0.0181046i | ||||
\(714\) | −0.0618286 | + | 0.360852i | −0.00231388 | + | 0.0135046i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.87217 | + | 10.1709i | 0.219453 | + | 0.380105i | ||||
\(717\) | 6.78524 | − | 39.6009i | 0.253399 | − | 1.47892i | ||||
\(718\) | 8.02295 | − | 13.8962i | 0.299414 | − | 0.518600i | ||||
\(719\) | −15.0047 | −0.559582 | −0.279791 | − | 0.960061i | \(-0.590265\pi\) | ||||
−0.279791 | + | 0.960061i | \(0.590265\pi\) | |||||||
\(720\) | 3.48074 | + | 18.6809i | 0.129720 | + | 0.696196i | ||||
\(721\) | 3.51242 | 0.130809 | ||||||||
\(722\) | −6.22777 | + | 10.7868i | −0.231774 | + | 0.401444i | ||||
\(723\) | 24.6373 | − | 9.10253i | 0.916271 | − | 0.338527i | ||||
\(724\) | 2.08075 | + | 3.60396i | 0.0773304 | + | 0.133940i | ||||
\(725\) | 15.5020 | + | 26.8502i | 0.575730 | + | 0.997193i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.7663 | + | 23.8438i | −0.510562 | + | 0.884319i | 0.489363 | + | 0.872080i | \(0.337229\pi\) |
−0.999925 | + | 0.0122391i | \(0.996104\pi\) | |||||||
\(728\) | −9.73292 | −0.360726 | ||||||||
\(729\) | −14.1733 | − | 22.9808i | −0.524937 | − | 0.851141i | ||||
\(730\) | 5.11522 | 0.189323 | ||||||||
\(731\) | −1.06583 | + | 1.84606i | −0.0394210 | + | 0.0682792i | ||||
\(732\) | −30.3805 | − | 25.2426i | −1.12289 | − | 0.932995i | ||||
\(733\) | −23.8698 | − | 41.3438i | −0.881653 | − | 1.52707i | −0.849503 | − | 0.527584i | \(-0.823098\pi\) |
−0.0321496 | − | 0.999483i | \(-0.510235\pi\) | |||||||
\(734\) | −0.338655 | − | 0.586567i | −0.0125000 | − | 0.0216506i | ||||
\(735\) | −27.5519 | + | 10.1794i | −1.01627 | + | 0.375472i | ||||
\(736\) | 0.233195 | − | 0.403906i | 0.00859570 | − | 0.0148882i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.84450 | + | 9.89928i | 0.0678968 | + | 0.364398i | ||||
\(739\) | 1.48849 | 0.0547549 | 0.0273774 | − | 0.999625i | \(-0.491284\pi\) | ||||
0.0273774 | + | 0.999625i | \(0.491284\pi\) | |||||||
\(740\) | −15.6258 | + | 27.0646i | −0.574414 | + | 0.994914i | ||||
\(741\) | 7.35093 | − | 42.9025i | 0.270043 | − | 1.57606i | ||||
\(742\) | −0.814943 | − | 1.41152i | −0.0299175 | − | 0.0518187i | ||||
\(743\) | 9.08009 | + | 15.7272i | 0.333116 | + | 0.576974i | 0.983121 | − | 0.182956i | \(-0.0585666\pi\) |
−0.650005 | + | 0.759930i | \(0.725233\pi\) | |||||||
\(744\) | 4.04546 | − | 23.6107i | 0.148314 | − | 0.865609i | ||||
\(745\) | 6.80761 | − | 11.7911i | 0.249411 | − | 0.431993i | ||||
\(746\) | 12.5771 | 0.460481 | ||||||||
\(747\) | −14.0250 | − | 4.95145i | −0.513147 | − | 0.181164i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.98177 | − | 12.0928i | 0.255108 | − | 0.441860i | ||||
\(750\) | −2.74550 | + | 1.01436i | −0.100251 | + | 0.0370391i | ||||
\(751\) | 2.19733 | + | 3.80588i | 0.0801816 | + | 0.138879i | 0.903328 | − | 0.428951i | \(-0.141117\pi\) |
−0.823146 | + | 0.567829i | \(0.807783\pi\) | |||||||
\(752\) | 0.345477 | + | 0.598384i | 0.0125983 | + | 0.0218208i | ||||
\(753\) | 0.775748 | + | 0.644557i | 0.0282698 | + | 0.0234890i | ||||
\(754\) | −8.77835 | + | 15.2046i | −0.319689 | + | 0.553717i | ||||
\(755\) | −8.80557 | −0.320467 | ||||||||
\(756\) | 4.91275 | − | 8.80187i | 0.178675 | − | 0.320121i | ||||
\(757\) | −13.7659 | −0.500331 | −0.250165 | − | 0.968203i | \(-0.580485\pi\) | ||||
−0.250165 | + | 0.968203i | \(0.580485\pi\) | |||||||
\(758\) | 4.69382 | − | 8.12993i | 0.170487 | − | 0.295292i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20.2655 | + | 35.1008i | 0.735105 | + | 1.27324i | ||||
\(761\) | 15.5531 | + | 26.9387i | 0.563798 | + | 0.976526i | 0.997160 | + | 0.0753068i | \(0.0239936\pi\) |
−0.433363 | + | 0.901220i | \(0.642673\pi\) | |||||||
\(762\) | −12.3758 | + | 4.57239i | −0.448329 | + | 0.165640i | ||||
\(763\) | 3.02731 | − | 5.24345i | 0.109596 | − | 0.189826i | ||||
\(764\) | 19.6987 | 0.712672 | ||||||||
\(765\) | −2.15163 | + | 1.84122i | −0.0777923 | + | 0.0665694i | ||||
\(766\) | 3.57859 | 0.129300 | ||||||||
\(767\) | −4.53027 | + | 7.84665i | −0.163578 | + | 0.283326i | ||||
\(768\) | 1.32503 | − | 7.73334i | 0.0478130 | − | 0.279053i | ||||
\(769\) | −10.9677 | − | 18.9966i | −0.395504 | − | 0.685034i | 0.597661 | − | 0.801749i | \(-0.296097\pi\) |
−0.993165 | + | 0.116715i | \(0.962764\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.20922 | − | 18.7301i | 0.115577 | − | 0.674549i | ||||
\(772\) | 5.62041 | − | 9.73484i | 0.202283 | − | 0.350365i | ||||
\(773\) | −12.7166 | −0.457385 | −0.228693 | − | 0.973499i | \(-0.573445\pi\) | ||||
−0.228693 | + | 0.973499i | \(0.573445\pi\) | |||||||
\(774\) | −8.93557 | + | 7.64646i | −0.321182 | + | 0.274846i | ||||
\(775\) | 26.2889 | 0.944326 | ||||||||
\(776\) | −0.0940957 | + | 0.162978i | −0.00337784 | + | 0.00585059i | ||||
\(777\) | 11.8099 | − | 4.36332i | 0.423679 | − | 0.156533i | ||||
\(778\) | 0.208941 | + | 0.361896i | 0.00749089 | + | 0.0129746i | ||||
\(779\) | −18.4972 | − | 32.0381i | −0.662731 | − | 1.14788i | ||||
\(780\) | −26.3158 | − | 21.8654i | −0.942258 | − | 0.782908i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.0155220 | 0.000555064 | ||||||||
\(783\) | −20.5057 | − | 34.3550i | −0.732815 | − | 1.22775i | ||||
\(784\) | −11.8998 | −0.424993 | ||||||||
\(785\) | 27.1204 | − | 46.9740i | 0.967970 | − | 1.67657i | ||||
\(786\) | 13.8340 | + | 11.4944i | 0.493442 | + | 0.409993i | ||||
\(787\) | 8.63083 | + | 14.9490i | 0.307656 | + | 0.532875i | 0.977849 | − | 0.209311i | \(-0.0671222\pi\) |
−0.670193 | + | 0.742187i | \(0.733789\pi\) | |||||||
\(788\) | −17.2007 | − | 29.7924i | −0.612749 | − | 1.06131i | ||||
\(789\) | −23.3883 | + | 8.64107i | −0.832645 | + | 0.307630i | ||||
\(790\) | 7.71406 | − | 13.3611i | 0.274454 | − | 0.475368i | ||||
\(791\) | −22.3870 | −0.795991 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.0120 | 1.91802 | ||||||||
\(794\) | −1.18161 | + | 2.04660i | −0.0419337 | + | 0.0726312i | ||||
\(795\) | 2.12911 | − | 12.4262i | 0.0755116 | − | 0.440711i | ||||
\(796\) | −11.0683 | − | 19.1708i | −0.392304 | − | 0.679491i | ||||
\(797\) | −17.6008 | − | 30.4854i | −0.623451 | − | 1.07985i | −0.988838 | − | 0.148993i | \(-0.952397\pi\) |
0.365388 | − | 0.930855i | \(-0.380936\pi\) | |||||||
\(798\) | 1.25322 | − | 7.31419i | 0.0443633 | − | 0.258920i | ||||
\(799\) | −0.0514857 | + | 0.0891759i | −0.00182143 | + | 0.00315482i | ||||
\(800\) | 21.9644 | 0.776560 | ||||||||
\(801\) | 1.16972 | + | 6.27782i | 0.0413301 | + | 0.221816i | ||||
\(802\) | −3.26248 | −0.115202 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −31.6170 | + | 11.6812i | −1.11504 | + | 0.411966i | ||||
\(805\) | −0.149545 | − | 0.259019i | −0.00527076 | − | 0.00912922i | ||||
\(806\) | 7.44335 | + | 12.8923i | 0.262181 | + | 0.454110i | ||||
\(807\) | −0.651414 | − | 0.541250i | −0.0229309 | − | 0.0190529i | ||||
\(808\) | −2.17816 | + | 3.77269i | −0.0766275 | + | 0.132723i | ||||
\(809\) | −19.0808 | −0.670845 | −0.335423 | − | 0.942068i | \(-0.608879\pi\) | ||||
−0.335423 | + | 0.942068i | \(0.608879\pi\) | |||||||
\(810\) | −14.5755 | + | 5.62695i | −0.512131 | + | 0.197711i | ||||
\(811\) | −31.0588 | −1.09062 | −0.545311 | − | 0.838234i | \(-0.683588\pi\) | ||||
−0.545311 | + | 0.838234i | \(0.683588\pi\) | |||||||
\(812\) | 7.46849 | − | 12.9358i | 0.262093 | − | 0.453958i | ||||
\(813\) | −29.2271 | − | 24.2843i | −1.02504 | − | 0.851688i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.74810 | + | 15.1522i | 0.306433 | + | 0.530757i | ||||
\(816\) | −1.07620 | + | 0.397616i | −0.0376746 | + | 0.0139193i | ||||
\(817\) | 21.6034 | − | 37.4182i | 0.755808 | − | 1.30910i | ||||
\(818\) | 5.45961 | 0.190891 | ||||||||
\(819\) | 2.52483 | + | 13.5506i | 0.0882248 | + | 0.473497i | ||||
\(820\) | −29.0789 | −1.01548 | ||||||||
\(821\) | −17.0043 | + | 29.4522i | −0.593453 | + | 1.02789i | 0.400311 | + | 0.916380i | \(0.368902\pi\) |
−0.993763 | + | 0.111511i | \(0.964431\pi\) | |||||||
\(822\) | 2.77213 | − | 16.1791i | 0.0966891 | − | 0.564311i | ||||
\(823\) | −7.77800 | − | 13.4719i | −0.271124 | − | 0.469601i | 0.698026 | − | 0.716073i | \(-0.254062\pi\) |
−0.969150 | + | 0.246472i | \(0.920729\pi\) | |||||||
\(824\) | −3.19521 | − | 5.53426i | −0.111310 | − | 0.192795i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.772337 | + | 1.33773i | −0.0268730 | + | 0.0465455i | ||||
\(827\) | 16.0277 | 0.557337 | 0.278669 | − | 0.960387i | \(-0.410107\pi\) | ||||
0.278669 | + | 0.960387i | \(0.410107\pi\) | |||||||
\(828\) | −0.402987 | − | 0.142273i | −0.0140048 | − | 0.00494431i | ||||
\(829\) | 19.0994 | 0.663351 | 0.331675 | − | 0.943394i | \(-0.392386\pi\) | ||||
0.331675 | + | 0.943394i | \(0.392386\pi\) | |||||||
\(830\) | −4.30334 | + | 7.45361i | −0.149371 | + | 0.258719i | ||||
\(831\) | 4.66214 | − | 1.72248i | 0.161728 | − | 0.0597523i | ||||
\(832\) | −2.10065 | − | 3.63843i | −0.0728269 | − | 0.126140i | ||||
\(833\) | −0.886702 | − | 1.53581i | −0.0307224 | − | 0.0532128i | ||||
\(834\) | 9.16140 | + | 7.61207i | 0.317233 | + | 0.263584i | ||||
\(835\) | 7.54371 | − | 13.0661i | 0.261061 | − | 0.452171i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −33.9213 | + | 0.492616i | −1.17249 | + | 0.0170273i | ||||
\(838\) | 0.0875755 | 0.00302524 | ||||||||
\(839\) | −0.743960 | + | 1.28858i | −0.0256844 | + | 0.0444866i | −0.878582 | − | 0.477592i | \(-0.841510\pi\) |
0.852898 | + | 0.522078i | \(0.174843\pi\) | |||||||
\(840\) | −9.87186 | − | 8.20237i | −0.340612 | − | 0.283009i | ||||
\(841\) | −15.1436 | − | 26.2295i | −0.522193 | − | 0.904465i | ||||
\(842\) | −4.90463 | − | 8.49507i | −0.169025 | − | 0.292759i | ||||
\(843\) | 29.5341 | − | 10.9117i | 1.01721 | − | 0.375819i | ||||
\(844\) | −6.95196 | + | 12.0411i | −0.239296 | + | 0.414473i | ||||
\(845\) | 7.72819 | 0.265858 | ||||||||
\(846\) | −0.431641 | + | 0.369369i | −0.0148401 | + | 0.0126992i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.55384 | − | 4.42338i | 0.0876993 | − | 0.151900i | ||||
\(849\) | 6.00726 | − | 35.0604i | 0.206169 | − | 1.20327i | ||||
\(850\) | 0.365500 | + | 0.633064i | 0.0125365 | + | 0.0217139i | ||||
\(851\) | −0.266893 | − | 0.462271i | −0.00914896 | − | 0.0158465i | ||||
\(852\) | 4.24860 | − | 24.7963i | 0.145555 | − | 0.849506i | ||||
\(853\) | −18.9010 | + | 32.7376i | −0.647159 | + | 1.12091i | 0.336639 | + | 0.941634i | \(0.390710\pi\) |
−0.983798 | + | 0.179279i | \(0.942624\pi\) | |||||||
\(854\) | 9.20818 | 0.315097 | ||||||||
\(855\) | 43.6118 | − | 37.3200i | 1.49149 | − | 1.27632i | ||||
\(856\) | −25.4049 | −0.868322 | ||||||||
\(857\) | −9.91348 | + | 17.1706i | −0.338638 | + | 0.586538i | −0.984177 | − | 0.177189i | \(-0.943300\pi\) |
0.645539 | + | 0.763727i | \(0.276633\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.85764 | + | 13.6098i | 0.268099 | + | 0.464362i | 0.968371 | − | 0.249515i | \(-0.0802711\pi\) |
−0.700272 | + | 0.713876i | \(0.746938\pi\) | |||||||
\(860\) | −16.9811 | − | 29.4120i | −0.579049 | − | 1.00294i | ||||
\(861\) | 9.01050 | + | 7.48668i | 0.307077 | + | 0.255146i | ||||
\(862\) | 7.32936 | − | 12.6948i | 0.249639 | − | 0.432387i | ||||
\(863\) | 8.12774 | 0.276671 | 0.138336 | − | 0.990385i | \(-0.455825\pi\) | ||||
0.138336 | + | 0.990385i | \(0.455825\pi\) | |||||||
\(864\) | −28.3413 | + | 0.411581i | −0.964189 | + | 0.0140023i | ||||
\(865\) | −46.8386 | −1.59256 | ||||||||
\(866\) | −4.77697 | + | 8.27396i | −0.162328 | + | 0.281161i | ||||
\(867\) | 22.5159 | + | 18.7081i | 0.764681 | + | 0.635361i | ||||
\(868\) | −6.33269 | − | 10.9685i | −0.214945 | − | 0.372296i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −21.7172 | + | 8.02368i | −0.736283 | + | 0.272028i | ||||
\(871\) | 23.0452 | − | 39.9155i | 0.780857 | − | 1.35248i | ||||
\(872\) | −11.0156 | −0.373036 | ||||||||
\(873\) | 0.251315 | + | 0.0887257i | 0.00850574 | + | 0.00300291i | ||||
\(874\) | −0.314618 | −0.0106421 | ||||||||
\(875\) | −1.70256 | + | 2.94891i | −0.0575569 | + | 0.0996915i | ||||
\(876\) | 1.43603 | − | 8.38113i | 0.0485188 | − | 0.283172i | ||||
\(877\) | 1.26676 | + | 2.19410i | 0.0427756 | + | 0.0740895i | 0.886621 | − | 0.462498i | \(-0.153047\pi\) |
−0.843845 | + | 0.536587i | \(0.819713\pi\) | |||||||
\(878\) | 11.3371 | + | 19.6364i | 0.382607 | + | 0.662695i | ||||
\(879\) | −0.251576 | + | 1.46828i | −0.00848544 | + | 0.0495239i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.4109 | −1.59731 | −0.798657 | − | 0.601786i | \(-0.794456\pi\) | ||||
−0.798657 | + | 0.601786i | \(0.794456\pi\) | |||||||
\(882\) | −1.79220 | − | 9.61859i | −0.0603464 | − | 0.323875i | ||||
\(883\) | 26.5129 | 0.892231 | 0.446116 | − | 0.894975i | \(-0.352807\pi\) | ||||
0.446116 | + | 0.894975i | \(0.352807\pi\) | |||||||
\(884\) | 1.03288 | − | 1.78900i | 0.0347394 | − | 0.0601705i | ||||
\(885\) | −11.2077 | + | 4.14080i | −0.376742 | + | 0.139192i | ||||
\(886\) | −9.29970 | − | 16.1076i | −0.312430 | − | 0.541144i | ||||
\(887\) | 23.9147 | + | 41.4214i | 0.802976 | + | 1.39080i | 0.917649 | + | 0.397392i | \(0.130085\pi\) |
−0.114673 | + | 0.993403i | \(0.536582\pi\) | |||||||
\(888\) | −17.6183 | − | 14.6388i | −0.591232 | − | 0.491245i | ||||
\(889\) | −7.67457 | + | 13.2927i | −0.257397 | + | 0.445825i | ||||
\(890\) | 3.69528 | 0.123866 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.639221 | 0.0214027 | ||||||||
\(893\) | 1.04357 | − | 1.80752i | 0.0349219 | − | 0.0604865i | ||||
\(894\) | 3.48834 | + | 2.89841i | 0.116668 | + | 0.0969373i | ||||
\(895\) | −10.5889 | − | 18.3405i | −0.353948 | − | 0.613056i | ||||
\(896\) | −6.70932 | − | 11.6209i | −0.224143 | − | 0.388227i | ||||
\(897\) | 0.548174 | − | 0.202529i | 0.0183030 | − | 0.00676226i | ||||
\(898\) | 7.46657 | − | 12.9325i | 0.249163 | − | 0.431562i | ||||
\(899\) | −50.2709 | −1.67663 | ||||||||
\(900\) | −3.68664 | − | 19.7860i | −0.122888 | − | 0.659532i | ||||
\(901\) | 0.761187 | 0.0253588 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.31064 | + | 13.4857i | −0.0768933 | + | 0.448776i | ||||
\(904\) | 20.3652 | + | 35.2736i | 0.677337 | + | 1.17318i | ||||
\(905\) | −3.75208 | − | 6.49879i | −0.124723 | − | 0.216027i | ||||
\(906\) | 0.495358 | − | 2.89108i | 0.0164572 | − | 0.0960496i | ||||
\(907\) | −23.7292 | + | 41.1001i | −0.787914 | + | 1.36471i | 0.139328 | + | 0.990246i | \(0.455506\pi\) |
−0.927243 | + | 0.374461i | \(0.877828\pi\) | |||||||
\(908\) | −30.0138 | −0.996042 | ||||||||
\(909\) | 5.81754 | + | 2.05385i | 0.192956 | + | 0.0681221i | ||||
\(910\) | 7.97621 | 0.264409 | ||||||||
\(911\) | 14.2161 | − | 24.6230i | 0.471001 | − | 0.815797i | −0.528449 | − | 0.848965i | \(-0.677226\pi\) |
0.999450 | + | 0.0331677i | \(0.0105595\pi\) | |||||||
\(912\) | 21.8138 | − | 8.05935i | 0.722326 | − | 0.266872i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 3.67381 | + | 6.36322i | 0.121519 | + | 0.210477i | ||||
\(915\) | 54.7831 | + | 45.5184i | 1.81107 | + | 1.50479i | ||||
\(916\) | 11.1863 | − | 19.3753i | 0.369606 | − | 0.640176i | ||||
\(917\) | 20.9249 | 0.691001 | ||||||||
\(918\) | −0.483476 | − | 0.810009i | −0.0159571 | − | 0.0267343i | ||||
\(919\) | 38.3728 | 1.26580 | 0.632901 | − | 0.774233i | \(-0.281864\pi\) | ||||
0.632901 | + | 0.774233i | \(0.281864\pi\) | |||||||
\(920\) | −0.272078 | + | 0.471253i | −0.00897015 | + | 0.0155368i | ||||
\(921\) | −4.64832 | − | 3.86221i | −0.153167 | − | 0.127264i | ||||
\(922\) | 5.49549 | + | 9.51848i | 0.180984 | + | 0.313474i | ||||
\(923\) | 17.2007 | + | 29.7924i | 0.566167 | + | 0.980629i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.5692 | − | 21.7704i | 0.413272 | − | 0.715808i | ||||
\(926\) | −13.2127 | −0.434195 | ||||||||
\(927\) | −6.87617 | + | 5.88416i | −0.225843 | + | 0.193261i | ||||
\(928\) | −42.0014 | −1.37876 | ||||||||
\(929\) | −6.69383 | + | 11.5941i | −0.219618 | + | 0.380389i | −0.954691 | − | 0.297599i | \(-0.903814\pi\) |
0.735073 | + | 0.677987i | \(0.237148\pi\) | |||||||
\(930\) | −3.31529 | + | 19.3491i | −0.108713 | + | 0.634483i | ||||
\(931\) | 17.9727 | + | 31.1297i | 0.589033 | + | 1.02023i | ||||
\(932\) | −2.80715 | − | 4.86212i | −0.0919511 | − | 0.159264i | ||||
\(933\) | −3.17233 | + | 18.5148i | −0.103857 | + | 0.606147i | ||||
\(934\) | −4.60021 | + | 7.96779i | −0.150523 | + | 0.260714i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 19.0539 | − | 16.3050i | 0.622795 | − | 0.532946i | ||||
\(937\) | −24.6705 | −0.805950 | −0.402975 | − | 0.915211i | \(-0.632024\pi\) | ||||
−0.402975 | + | 0.915211i | \(0.632024\pi\) | |||||||
\(938\) | 3.92884 | − | 6.80494i | 0.128281 | − | 0.222189i | ||||
\(939\) | −45.9485 | + | 16.9762i | −1.49947 | + | 0.553998i | ||||
\(940\) | −0.820286 | − | 1.42078i | −0.0267548 | − | 0.0463406i | ||||
\(941\) | −4.15115 | − | 7.19000i | −0.135324 | − | 0.234387i | 0.790397 | − | 0.612594i | \(-0.209874\pi\) |
−0.925721 | + | 0.378207i | \(0.876541\pi\) | |||||||
\(942\) | 13.8970 | + | 11.5468i | 0.452789 | + | 0.376215i | ||||
\(943\) | 0.248338 | − | 0.430134i | 0.00808701 | − | 0.0140071i | ||||
\(944\) | −4.84065 | −0.157550 | ||||||||
\(945\) | −8.85883 | + | 15.8718i | −0.288178 | + | 0.516311i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.9748 | + | 32.8653i | −0.616598 | + | 1.06798i | 0.373503 | + | 0.927629i | \(0.378156\pi\) |
−0.990102 | + | 0.140351i | \(0.955177\pi\) | |||||||
\(948\) | −19.7262 | − | 16.3902i | −0.640678 | − | 0.532330i | ||||
\(949\) | 5.81382 | + | 10.0698i | 0.188725 | + | 0.326880i | ||||
\(950\) | −7.40838 | − | 12.8317i | −0.240360 | − | 0.416315i | ||||
\(951\) | −1.80753 | + | 0.667814i | −0.0586133 | + | 0.0216553i | ||||
\(952\) | 0.387463 | − | 0.671106i | 0.0125578 | − | 0.0217507i | ||||
\(953\) | −48.6705 | −1.57659 | −0.788297 | − | 0.615295i | \(-0.789037\pi\) | ||||
−0.788297 | + | 0.615295i | \(0.789037\pi\) | |||||||
\(954\) | 3.96004 | + | 1.39807i | 0.128211 | + | 0.0452642i | ||||
\(955\) | −35.5213 | −1.14944 | ||||||||
\(956\) | −19.3245 | + | 33.4710i | −0.624998 | + | 1.08253i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.73516 | + | 8.20154i | 0.152986 | + | 0.264980i | ||||
\(959\) | −9.54844 | − | 16.5384i | −0.308335 | − | 0.534052i | ||||
\(960\) | 0.935635 | − | 5.46068i | 0.0301975 | − | 0.176243i | ||||
\(961\) | −5.81285 | + | 10.0682i | −0.187511 | + | 0.324779i | ||||
\(962\) | 14.2352 | 0.458960 | ||||||||
\(963\) | 6.59033 | + | 35.3698i | 0.212370 | + | 1.13978i | ||||
\(964\) | −25.2655 | −0.813746 | ||||||||
\(965\) | −10.1349 | + | 17.5542i | −0.326255 | + | 0.565090i | ||||
\(966\) | 0.0934548 | − | 0.0345280i | 0.00300686 | − | 0.00111092i | ||||
\(967\) | −5.48901 | − | 9.50724i | −0.176515 | − | 0.305732i | 0.764170 | − | 0.645015i | \(-0.223149\pi\) |
−0.940684 | + | 0.339283i | \(0.889816\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.66559 | + | 2.21479i | 0.0856309 | + | 0.0711494i | ||||
\(970\) | 0.0771122 | − | 0.133562i | 0.00247592 | − | 0.00428843i | ||||
\(971\) | 13.0636 | 0.419231 | 0.209615 | − | 0.977784i | \(-0.432779\pi\) | ||||
0.209615 | + | 0.977784i | \(0.432779\pi\) | |||||||
\(972\) | 5.12773 | + | 25.4612i | 0.164472 | + | 0.816669i | ||||
\(973\) | 13.8573 | 0.444244 | ||||||||
\(974\) | −6.58316 | + | 11.4024i | −0.210938 | + | 0.365355i | ||||
\(975\) | 21.1681 | + | 17.5883i | 0.677923 | + | 0.563276i | ||||
\(976\) | 14.4281 | + | 24.9903i | 0.461833 | + | 0.799919i | ||||
\(977\) | 5.53815 | + | 9.59236i | 0.177181 | + | 0.306887i | 0.940914 | − | 0.338646i | \(-0.109969\pi\) |
−0.763733 | + | 0.645533i | \(0.776635\pi\) | |||||||
\(978\) | −5.46694 | + | 2.01982i | −0.174813 | + | 0.0645869i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 28.2544 | 0.902554 | ||||||||
\(981\) | 2.85758 | + | 15.3364i | 0.0912355 | + | 0.489655i | ||||
\(982\) | −25.2175 | −0.804721 | ||||||||
\(983\) | 13.2157 | − | 22.8903i | 0.421517 | − | 0.730088i | −0.574571 | − | 0.818455i | \(-0.694831\pi\) |
0.996088 | + | 0.0883661i | \(0.0281645\pi\) | |||||||
\(984\) | 3.59947 | − | 21.0077i | 0.114747 | − | 0.669702i | ||||
\(985\) | 31.0168 | + | 53.7228i | 0.988279 | + | 1.71175i | ||||
\(986\) | −0.698925 | − | 1.21057i | −0.0222583 | − | 0.0385525i | ||||
\(987\) | −0.111618 | + | 0.651439i | −0.00355283 | + | 0.0207355i | ||||
\(988\) | −20.9356 | + | 36.2615i | −0.666050 | + | 1.15363i | ||||
\(989\) | 0.580083 | 0.0184456 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.9911 | −0.603272 | −0.301636 | − | 0.953423i | \(-0.597533\pi\) | ||||
−0.301636 | + | 0.953423i | \(0.597533\pi\) | |||||||
\(992\) | −17.8069 | + | 30.8425i | −0.565370 | + | 0.979250i | ||||
\(993\) | −20.1111 | + | 7.43030i | −0.638208 | + | 0.235793i | ||||
\(994\) | 2.93243 | + | 5.07913i | 0.0930112 | + | 0.161100i | ||||
\(995\) | 19.9587 | + | 34.5694i | 0.632733 | + | 1.09593i | ||||
\(996\) | 11.0044 | + | 9.14340i | 0.348688 | + | 0.289720i | ||||
\(997\) | −11.0566 | + | 19.1506i | −0.350165 | + | 0.606504i | −0.986278 | − | 0.165092i | \(-0.947208\pi\) |
0.636113 | + | 0.771596i | \(0.280541\pi\) | |||||||
\(998\) | −11.6161 | −0.367700 | ||||||||
\(999\) | −15.8104 | + | 28.3265i | −0.500218 | + | 0.896210i |
(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 | 1089.2.e.p.727.8 | 36 | ||
9.2 | odd | 6 | 9801.2.a.cp.1.8 | 18 | |||
9.4 | even | 3 | inner | 1089.2.e.p.364.8 | 36 | ||
9.7 | even | 3 | 9801.2.a.cm.1.11 | 18 | |||
11.5 | even | 5 | 99.2.m.b.25.4 | yes | 72 | ||
11.9 | even | 5 | 99.2.m.b.70.6 | yes | 72 | ||
11.10 | odd | 2 | 1089.2.e.o.727.11 | 36 | |||
33.5 | odd | 10 | 297.2.n.b.289.6 | 72 | |||
33.20 | odd | 10 | 297.2.n.b.235.4 | 72 | |||
99.5 | odd | 30 | 297.2.n.b.91.4 | 72 | |||
99.16 | even | 15 | 891.2.f.f.487.4 | 36 | |||
99.20 | odd | 30 | 891.2.f.e.730.6 | 36 | |||
99.31 | even | 15 | 99.2.m.b.4.4 | ✓ | 72 | ||
99.38 | odd | 30 | 891.2.f.e.487.6 | 36 | |||
99.43 | odd | 6 | 9801.2.a.co.1.8 | 18 | |||
99.49 | even | 15 | 99.2.m.b.58.6 | yes | 72 | ||
99.65 | even | 6 | 9801.2.a.cn.1.11 | 18 | |||
99.76 | odd | 6 | 1089.2.e.o.364.11 | 36 | |||
99.86 | odd | 30 | 297.2.n.b.37.6 | 72 | |||
99.97 | even | 15 | 891.2.f.f.730.4 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.4.4 | ✓ | 72 | 99.31 | even | 15 | ||
99.2.m.b.25.4 | yes | 72 | 11.5 | even | 5 | ||
99.2.m.b.58.6 | yes | 72 | 99.49 | even | 15 | ||
99.2.m.b.70.6 | yes | 72 | 11.9 | even | 5 | ||
297.2.n.b.37.6 | 72 | 99.86 | odd | 30 | |||
297.2.n.b.91.4 | 72 | 99.5 | odd | 30 | |||
297.2.n.b.235.4 | 72 | 33.20 | odd | 10 | |||
297.2.n.b.289.6 | 72 | 33.5 | odd | 10 | |||
891.2.f.e.487.6 | 36 | 99.38 | odd | 30 | |||
891.2.f.e.730.6 | 36 | 99.20 | odd | 30 | |||
891.2.f.f.487.4 | 36 | 99.16 | even | 15 | |||
891.2.f.f.730.4 | 36 | 99.97 | even | 15 | |||
1089.2.e.o.364.11 | 36 | 99.76 | odd | 6 | |||
1089.2.e.o.727.11 | 36 | 11.10 | odd | 2 | |||
1089.2.e.p.364.8 | 36 | 9.4 | even | 3 | inner | ||
1089.2.e.p.727.8 | 36 | 1.1 | even | 1 | trivial | ||
9801.2.a.cm.1.11 | 18 | 9.7 | even | 3 | |||
9801.2.a.cn.1.11 | 18 | 99.65 | even | 6 | |||
9801.2.a.co.1.8 | 18 | 99.43 | odd | 6 | |||
9801.2.a.cp.1.8 | 18 | 9.2 | odd | 6 |