Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(68,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.i (of order \(6\), degree \(2\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 68.18 | ||
Character | \(\chi\) | \(=\) | 441.68 |
Dual form | 441.2.i.d.227.8 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.83202i | 1.29544i | 0.761880 | + | 0.647718i | \(0.224277\pi\) | ||||
−0.761880 | + | 0.647718i | \(0.775723\pi\) | |||||||
\(3\) | 1.55144 | + | 0.770089i | 0.895724 | + | 0.444611i | ||||
\(4\) | −1.35631 | −0.678156 | ||||||||
\(5\) | 0.322784 | + | 0.559079i | 0.144353 | + | 0.250028i | 0.929132 | − | 0.369749i | \(-0.120556\pi\) |
−0.784778 | + | 0.619777i | \(0.787223\pi\) | |||||||
\(6\) | −1.41082 | + | 2.84227i | −0.575966 | + | 1.16035i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.17925i | 0.416928i | ||||||||
\(9\) | 1.81393 | + | 2.38949i | 0.604642 | + | 0.796497i | ||||
\(10\) | −1.02425 | + | 0.591348i | −0.323895 | + | 0.187001i | ||||
\(11\) | −4.60375 | − | 2.65797i | −1.38808 | − | 0.801410i | −0.394983 | − | 0.918688i | \(-0.629250\pi\) |
−0.993099 | + | 0.117279i | \(0.962583\pi\) | |||||||
\(12\) | −2.10424 | − | 1.04448i | −0.607440 | − | 0.301516i | ||||
\(13\) | 4.44045 | + | 2.56370i | 1.23156 | + | 0.711041i | 0.967355 | − | 0.253425i | \(-0.0815572\pi\) |
0.264205 | + | 0.964467i | \(0.414890\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0702397 | + | 1.11595i | 0.0181358 | + | 0.288137i | ||||
\(16\) | −4.87304 | −1.21826 | ||||||||
\(17\) | −0.814931 | − | 1.41150i | −0.197650 | − | 0.342339i | 0.750116 | − | 0.661306i | \(-0.229998\pi\) |
−0.947766 | + | 0.318967i | \(0.896664\pi\) | |||||||
\(18\) | −4.37761 | + | 3.32316i | −1.03181 | + | 0.783275i | ||||
\(19\) | 2.09039 | + | 1.20689i | 0.479569 | + | 0.276879i | 0.720237 | − | 0.693728i | \(-0.244033\pi\) |
−0.240668 | + | 0.970608i | \(0.577366\pi\) | |||||||
\(20\) | −0.437796 | − | 0.758285i | −0.0978942 | − | 0.169558i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.86947 | − | 8.43418i | 1.03818 | − | 1.79817i | ||||
\(23\) | 1.27442 | − | 0.735784i | 0.265734 | − | 0.153422i | −0.361213 | − | 0.932483i | \(-0.617637\pi\) |
0.626947 | + | 0.779062i | \(0.284304\pi\) | |||||||
\(24\) | −0.908129 | + | 1.82954i | −0.185371 | + | 0.373453i | ||||
\(25\) | 2.29162 | − | 3.96920i | 0.458324 | − | 0.793841i | ||||
\(26\) | −4.69675 | + | 8.13502i | −0.921109 | + | 1.59541i | ||||
\(27\) | 0.974073 | + | 5.10404i | 0.187461 | + | 0.982272i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.43846 | + | 3.71724i | −1.19559 | + | 0.690275i | −0.959569 | − | 0.281473i | \(-0.909177\pi\) |
−0.236022 | + | 0.971748i | \(0.575844\pi\) | |||||||
\(30\) | −2.04445 | + | 0.128681i | −0.373263 | + | 0.0234938i | ||||
\(31\) | 5.66726i | 1.01787i | 0.860805 | + | 0.508935i | \(0.169961\pi\) | ||||
−0.860805 | + | 0.508935i | \(0.830039\pi\) | |||||||
\(32\) | − | 6.56903i | − | 1.16125i | ||||||
\(33\) | −5.09556 | − | 7.66898i | −0.887022 | − | 1.33500i | ||||
\(34\) | 2.58590 | − | 1.49297i | 0.443479 | − | 0.256043i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.46025 | − | 3.24090i | −0.410042 | − | 0.540150i | ||||
\(37\) | 3.99736 | − | 6.92362i | 0.657161 | − | 1.13824i | −0.324186 | − | 0.945993i | \(-0.605090\pi\) |
0.981347 | − | 0.192244i | \(-0.0615763\pi\) | |||||||
\(38\) | −2.21105 | + | 3.82965i | −0.358680 | + | 0.621251i | ||||
\(39\) | 4.91482 | + | 7.39696i | 0.787000 | + | 1.18446i | ||||
\(40\) | −0.659294 | + | 0.380644i | −0.104244 | + | 0.0601851i | ||||
\(41\) | 5.99052 | − | 10.3759i | 0.935562 | − | 1.62044i | 0.161934 | − | 0.986802i | \(-0.448227\pi\) |
0.773628 | − | 0.633640i | \(-0.218440\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.51281 | − | 2.62026i | −0.230701 | − | 0.399586i | 0.727314 | − | 0.686305i | \(-0.240769\pi\) |
−0.958015 | + | 0.286719i | \(0.907435\pi\) | |||||||
\(44\) | 6.24412 | + | 3.60504i | 0.941336 | + | 0.543481i | ||||
\(45\) | −0.750407 | + | 1.78542i | −0.111864 | + | 0.266154i | ||||
\(46\) | 1.34797 | + | 2.33476i | 0.198748 | + | 0.344241i | ||||
\(47\) | 3.08353 | 0.449779 | 0.224889 | − | 0.974384i | \(-0.427798\pi\) | ||||
0.224889 | + | 0.974384i | \(0.427798\pi\) | |||||||
\(48\) | −7.56023 | − | 3.75268i | −1.09122 | − | 0.541652i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.27168 | + | 4.19830i | 1.02837 | + | 0.593730i | ||||
\(51\) | −0.177334 | − | 2.81743i | −0.0248317 | − | 0.394519i | ||||
\(52\) | −6.02264 | − | 3.47717i | −0.835190 | − | 0.482197i | ||||
\(53\) | 2.04554 | − | 1.18100i | 0.280977 | − | 0.162222i | −0.352889 | − | 0.935665i | \(-0.614801\pi\) |
0.633866 | + | 0.773443i | \(0.281467\pi\) | |||||||
\(54\) | −9.35072 | + | 1.78453i | −1.27247 | + | 0.242843i | ||||
\(55\) | − | 3.43181i | − | 0.462745i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.31371 | + | 3.48220i | 0.306458 | + | 0.461229i | ||||
\(58\) | −6.81008 | − | 11.7954i | −0.894207 | − | 1.54881i | ||||
\(59\) | −2.95836 | −0.385146 | −0.192573 | − | 0.981283i | \(-0.561683\pi\) | ||||
−0.192573 | + | 0.981283i | \(0.561683\pi\) | |||||||
\(60\) | −0.0952669 | − | 1.51357i | −0.0122989 | − | 0.195402i | ||||
\(61\) | − | 10.6004i | − | 1.35724i | −0.734491 | − | 0.678618i | \(-0.762579\pi\) | ||
0.734491 | − | 0.678618i | \(-0.237421\pi\) | |||||||
\(62\) | −10.3825 | −1.31859 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.28853 | 0.286066 | ||||||||
\(65\) | 3.31008i | 0.410565i | ||||||||
\(66\) | 14.0498 | − | 9.33518i | 1.72941 | − | 1.14908i | ||||
\(67\) | −10.1549 | −1.24062 | −0.620312 | − | 0.784355i | \(-0.712994\pi\) | ||||
−0.620312 | + | 0.784355i | \(0.712994\pi\) | |||||||
\(68\) | 1.10530 | + | 1.91444i | 0.134037 | + | 0.232159i | ||||
\(69\) | 2.54380 | − | 0.160111i | 0.306237 | − | 0.0192751i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.76597i | 0.565617i | 0.959176 | + | 0.282808i | \(0.0912661\pi\) | ||||
−0.959176 | + | 0.282808i | \(0.908734\pi\) | |||||||
\(72\) | −2.81781 | + | 2.13908i | −0.332082 | + | 0.252092i | ||||
\(73\) | 10.2239 | − | 5.90277i | 1.19662 | − | 0.690867i | 0.236817 | − | 0.971554i | \(-0.423896\pi\) |
0.959799 | + | 0.280687i | \(0.0905624\pi\) | |||||||
\(74\) | 12.6842 | + | 7.32325i | 1.47451 | + | 0.851311i | ||||
\(75\) | 6.61195 | − | 4.39323i | 0.763482 | − | 0.507286i | ||||
\(76\) | −2.83523 | − | 1.63692i | −0.325223 | − | 0.187767i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.5514 | + | 9.00406i | −1.53440 | + | 1.01951i | ||||
\(79\) | 6.96209 | 0.783296 | 0.391648 | − | 0.920115i | \(-0.371905\pi\) | ||||
0.391648 | + | 0.920115i | \(0.371905\pi\) | |||||||
\(80\) | −1.57294 | − | 2.72441i | −0.175860 | − | 0.304599i | ||||
\(81\) | −2.41935 | + | 8.66872i | −0.268816 | + | 0.963191i | ||||
\(82\) | 19.0089 | + | 10.9748i | 2.09918 | + | 1.21196i | ||||
\(83\) | 3.51618 | + | 6.09021i | 0.385951 | + | 0.668487i | 0.991901 | − | 0.127016i | \(-0.0405399\pi\) |
−0.605949 | + | 0.795503i | \(0.707207\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.526093 | − | 0.911221i | 0.0570628 | − | 0.0988357i | ||||
\(86\) | 4.80038 | − | 2.77150i | 0.517638 | − | 0.298859i | ||||
\(87\) | −12.8515 | + | 0.808893i | −1.37782 | + | 0.0867225i | ||||
\(88\) | 3.13442 | − | 5.42898i | 0.334130 | − | 0.578731i | ||||
\(89\) | −2.16337 | + | 3.74706i | −0.229317 | + | 0.397188i | −0.957606 | − | 0.288082i | \(-0.906982\pi\) |
0.728289 | + | 0.685270i | \(0.240316\pi\) | |||||||
\(90\) | −3.27093 | − | 1.37476i | −0.344786 | − | 0.144913i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.72850 | + | 0.997953i | −0.180209 | + | 0.104044i | ||||
\(93\) | −4.36429 | + | 8.79240i | −0.452556 | + | 0.911730i | ||||
\(94\) | 5.64910i | 0.582660i | ||||||||
\(95\) | 1.55826i | 0.159874i | ||||||||
\(96\) | 5.05873 | − | 10.1914i | 0.516305 | − | 1.04016i | ||||
\(97\) | −14.3946 | + | 8.31075i | −1.46156 | + | 0.843829i | −0.999083 | − | 0.0428048i | \(-0.986371\pi\) |
−0.462472 | + | 0.886634i | \(0.653037\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.99965 | − | 15.8220i | −0.200972 | − | 1.59017i | ||||
\(100\) | −3.10815 | + | 5.38348i | −0.310815 | + | 0.538348i | ||||
\(101\) | 2.32577 | − | 4.02835i | 0.231423 | − | 0.400836i | −0.726804 | − | 0.686845i | \(-0.758995\pi\) |
0.958227 | + | 0.286009i | \(0.0923286\pi\) | |||||||
\(102\) | 5.16159 | − | 0.324879i | 0.511074 | − | 0.0321678i | ||||
\(103\) | 8.92382 | − | 5.15217i | 0.879290 | − | 0.507658i | 0.00886554 | − | 0.999961i | \(-0.497178\pi\) |
0.870424 | + | 0.492303i | \(0.163845\pi\) | |||||||
\(104\) | −3.02324 | + | 5.23641i | −0.296453 | + | 0.513472i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.16361 | + | 3.74749i | 0.210149 | + | 0.363988i | ||||
\(107\) | 0.267212 | + | 0.154275i | 0.0258324 | + | 0.0149143i | 0.512861 | − | 0.858472i | \(-0.328586\pi\) |
−0.487028 | + | 0.873386i | \(0.661919\pi\) | |||||||
\(108\) | −1.32115 | − | 6.92267i | −0.127127 | − | 0.666134i | ||||
\(109\) | 3.14423 | + | 5.44596i | 0.301162 | + | 0.521628i | 0.976399 | − | 0.215972i | \(-0.0692921\pi\) |
−0.675237 | + | 0.737601i | \(0.735959\pi\) | |||||||
\(110\) | 6.28716 | 0.599457 | ||||||||
\(111\) | 11.5335 | − | 7.66326i | 1.09471 | − | 0.727365i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.72869 | + | 4.46216i | 0.727054 | + | 0.419765i | 0.817343 | − | 0.576151i | \(-0.195446\pi\) |
−0.0902895 | + | 0.995916i | \(0.528779\pi\) | |||||||
\(114\) | −6.37948 | + | 4.23876i | −0.597493 | + | 0.396997i | ||||
\(115\) | 0.822722 | + | 0.474999i | 0.0767192 | + | 0.0442939i | ||||
\(116\) | 8.73256 | − | 5.04174i | 0.810797 | − | 0.468114i | ||||
\(117\) | 1.92872 | + | 15.2608i | 0.178310 | + | 1.41086i | ||||
\(118\) | − | 5.41979i | − | 0.498932i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.31598 | + | 0.0828302i | −0.120132 | + | 0.00756133i | ||||
\(121\) | 8.62966 | + | 14.9470i | 0.784515 | + | 1.35882i | ||||
\(122\) | 19.4201 | 1.75821 | ||||||||
\(123\) | 17.2843 | − | 11.4843i | 1.55847 | − | 1.03551i | ||||
\(124\) | − | 7.68657i | − | 0.690274i | ||||||
\(125\) | 6.18664 | 0.553350 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.49989 | −0.221829 | −0.110915 | − | 0.993830i | \(-0.535378\pi\) | ||||
−0.110915 | + | 0.993830i | \(0.535378\pi\) | |||||||
\(128\) | − | 8.94541i | − | 0.790670i | ||||||
\(129\) | −0.329196 | − | 5.23017i | −0.0289840 | − | 0.460491i | ||||
\(130\) | −6.06415 | −0.531861 | ||||||||
\(131\) | 1.26725 | + | 2.19494i | 0.110720 | + | 0.191773i | 0.916061 | − | 0.401039i | \(-0.131351\pi\) |
−0.805341 | + | 0.592812i | \(0.798018\pi\) | |||||||
\(132\) | 6.91116 | + | 10.4015i | 0.601540 | + | 0.905337i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 18.6041i | − | 1.60715i | ||||||
\(135\) | −2.53914 | + | 2.19209i | −0.218535 | + | 0.188665i | ||||
\(136\) | 1.66452 | − | 0.961008i | 0.142731 | − | 0.0824058i | ||||
\(137\) | −1.05041 | − | 0.606456i | −0.0897429 | − | 0.0518131i | 0.454457 | − | 0.890769i | \(-0.349833\pi\) |
−0.544200 | + | 0.838956i | \(0.683167\pi\) | |||||||
\(138\) | 0.293327 | + | 4.66030i | 0.0249696 | + | 0.396711i | ||||
\(139\) | −6.11754 | − | 3.53196i | −0.518883 | − | 0.299577i | 0.217594 | − | 0.976039i | \(-0.430179\pi\) |
−0.736478 | + | 0.676462i | \(0.763512\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.78390 | + | 2.37459i | 0.402877 | + | 0.199977i | ||||
\(142\) | −8.73137 | −0.732721 | ||||||||
\(143\) | −13.6285 | − | 23.6052i | −1.13967 | − | 1.97397i | ||||
\(144\) | −8.83934 | − | 11.6441i | −0.736611 | − | 0.970341i | ||||
\(145\) | −4.15646 | − | 2.39974i | −0.345175 | − | 0.199287i | ||||
\(146\) | 10.8140 | + | 18.7304i | 0.894974 | + | 1.55014i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.42166 | + | 9.39060i | −0.445658 | + | 0.771902i | ||||
\(149\) | −6.00270 | + | 3.46566i | −0.491760 | + | 0.283918i | −0.725304 | − | 0.688428i | \(-0.758301\pi\) |
0.233544 | + | 0.972346i | \(0.424968\pi\) | |||||||
\(150\) | 8.04849 | + | 12.1133i | 0.657157 | + | 0.989043i | ||||
\(151\) | −3.15939 | + | 5.47223i | −0.257108 | + | 0.445323i | −0.965466 | − | 0.260530i | \(-0.916103\pi\) |
0.708358 | + | 0.705853i | \(0.249436\pi\) | |||||||
\(152\) | −1.42323 | + | 2.46510i | −0.115439 | + | 0.199946i | ||||
\(153\) | 1.89455 | − | 4.50763i | 0.153165 | − | 0.364420i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.16844 | + | 1.82930i | −0.254495 | + | 0.146933i | ||||
\(156\) | −6.66602 | − | 10.0326i | −0.533709 | − | 0.803250i | ||||
\(157\) | − | 1.99028i | − | 0.158842i | −0.996841 | − | 0.0794208i | \(-0.974693\pi\) | ||
0.996841 | − | 0.0794208i | \(-0.0253071\pi\) | |||||||
\(158\) | 12.7547i | 1.01471i | ||||||||
\(159\) | 4.08301 | − | 0.256991i | 0.323804 | − | 0.0203807i | ||||
\(160\) | 3.67260 | − | 2.12038i | 0.290345 | − | 0.167631i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −15.8813 | − | 4.43230i | −1.24775 | − | 0.348234i | ||||
\(163\) | 2.99365 | − | 5.18515i | 0.234480 | − | 0.406132i | −0.724641 | − | 0.689126i | \(-0.757994\pi\) |
0.959122 | + | 0.282994i | \(0.0913278\pi\) | |||||||
\(164\) | −8.12502 | + | 14.0729i | −0.634457 | + | 1.09891i | ||||
\(165\) | 2.64280 | − | 5.32424i | 0.205742 | − | 0.414492i | ||||
\(166\) | −11.1574 | + | 6.44173i | −0.865983 | + | 0.499976i | ||||
\(167\) | −0.697990 | + | 1.20895i | −0.0540121 | + | 0.0935516i | −0.891767 | − | 0.452494i | \(-0.850534\pi\) |
0.837755 | + | 0.546046i | \(0.183868\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.64508 | + | 11.5096i | 0.511160 | + | 0.885355i | ||||
\(170\) | 1.66938 | + | 0.963816i | 0.128035 | + | 0.0739213i | ||||
\(171\) | 0.907966 | + | 7.18419i | 0.0694339 | + | 0.549388i | ||||
\(172\) | 2.05184 | + | 3.55389i | 0.156451 | + | 0.270982i | ||||
\(173\) | −7.61012 | −0.578586 | −0.289293 | − | 0.957241i | \(-0.593420\pi\) | ||||
−0.289293 | + | 0.957241i | \(0.593420\pi\) | |||||||
\(174\) | −1.48191 | − | 23.5442i | −0.112343 | − | 1.78488i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 22.4343 | + | 12.9524i | 1.69105 | + | 0.976326i | ||||
\(177\) | −4.58972 | − | 2.27820i | −0.344984 | − | 0.171240i | ||||
\(178\) | −6.86471 | − | 3.96334i | −0.514532 | − | 0.297065i | ||||
\(179\) | −8.00888 | + | 4.62393i | −0.598612 | + | 0.345609i | −0.768495 | − | 0.639855i | \(-0.778994\pi\) |
0.169883 | + | 0.985464i | \(0.445661\pi\) | |||||||
\(180\) | 1.01779 | − | 2.42158i | 0.0758613 | − | 0.180494i | ||||
\(181\) | − | 11.9634i | − | 0.889234i | −0.895721 | − | 0.444617i | \(-0.853340\pi\) | ||
0.895721 | − | 0.444617i | \(-0.146660\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.16322 | − | 16.4458i | 0.603443 | − | 1.21571i | ||||
\(184\) | 0.867674 | + | 1.50286i | 0.0639658 | + | 0.110792i | ||||
\(185\) | 5.16113 | 0.379454 | ||||||||
\(186\) | −16.1079 | − | 7.99549i | −1.18109 | − | 0.586258i | ||||
\(187\) | 8.66426i | 0.633593i | ||||||||
\(188\) | −4.18223 | −0.305020 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.85477 | −0.207107 | ||||||||
\(191\) | − | 20.2749i | − | 1.46704i | −0.679666 | − | 0.733521i | \(-0.737875\pi\) | ||
0.679666 | − | 0.733521i | \(-0.262125\pi\) | |||||||
\(192\) | 3.55052 | + | 1.76237i | 0.256236 | + | 0.127188i | ||||
\(193\) | −16.8917 | −1.21589 | −0.607944 | − | 0.793980i | \(-0.708006\pi\) | ||||
−0.607944 | + | 0.793980i | \(0.708006\pi\) | |||||||
\(194\) | −15.2255 | − | 26.3713i | −1.09313 | − | 1.89335i | ||||
\(195\) | −2.54906 | + | 5.13539i | −0.182542 | + | 0.367753i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.7102i | − | 1.33305i | −0.745484 | − | 0.666524i | \(-0.767781\pi\) | ||
0.745484 | − | 0.666524i | \(-0.232219\pi\) | |||||||
\(198\) | 28.9863 | − | 3.66340i | 2.05996 | − | 0.260346i | ||||
\(199\) | −15.6271 | + | 9.02231i | −1.10778 | + | 0.639574i | −0.938252 | − | 0.345952i | \(-0.887556\pi\) |
−0.169523 | + | 0.985526i | \(0.554223\pi\) | |||||||
\(200\) | 4.68069 | + | 2.70240i | 0.330975 | + | 0.191088i | ||||
\(201\) | −15.7548 | − | 7.82021i | −1.11126 | − | 0.551595i | ||||
\(202\) | 7.38004 | + | 4.26087i | 0.519258 | + | 0.299794i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.240520 | + | 3.82131i | 0.0168397 | + | 0.267545i | ||||
\(205\) | 7.73458 | 0.540207 | ||||||||
\(206\) | 9.43889 | + | 16.3486i | 0.657639 | + | 1.13906i | ||||
\(207\) | 4.06984 | + | 1.71055i | 0.282874 | + | 0.118891i | ||||
\(208\) | −21.6385 | − | 12.4930i | −1.50036 | − | 0.866234i | ||||
\(209\) | −6.41576 | − | 11.1124i | −0.443788 | − | 0.768663i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.03491 | + | 6.98868i | −0.277775 | + | 0.481120i | −0.970831 | − | 0.239763i | \(-0.922930\pi\) |
0.693057 | + | 0.720883i | \(0.256264\pi\) | |||||||
\(212\) | −2.77440 | + | 1.60180i | −0.190546 | + | 0.110012i | ||||
\(213\) | −3.67022 | + | 7.39411i | −0.251479 | + | 0.506636i | ||||
\(214\) | −0.282636 | + | 0.489540i | −0.0193206 | + | 0.0334642i | ||||
\(215\) | 0.976621 | − | 1.69156i | 0.0666050 | − | 0.115363i | ||||
\(216\) | −6.01894 | + | 1.14868i | −0.409537 | + | 0.0781576i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.97713 | + | 5.76030i | −0.675736 | + | 0.390137i | ||||
\(219\) | 20.4074 | − | 1.28448i | 1.37900 | − | 0.0867968i | ||||
\(220\) | 4.65460i | 0.313813i | ||||||||
\(221\) | − | 8.35694i | − | 0.562148i | ||||||
\(222\) | 14.0393 | + | 21.1296i | 0.942255 | + | 1.41812i | ||||
\(223\) | −20.2450 | + | 11.6884i | −1.35570 | + | 0.782716i | −0.989041 | − | 0.147638i | \(-0.952833\pi\) |
−0.366662 | + | 0.930354i | \(0.619500\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.6412 | − | 1.72403i | 0.909414 | − | 0.114935i | ||||
\(226\) | −8.17479 | + | 14.1591i | −0.543779 | + | 0.941852i | ||||
\(227\) | −7.22154 | + | 12.5081i | −0.479310 | + | 0.830190i | −0.999718 | − | 0.0237280i | \(-0.992446\pi\) |
0.520408 | + | 0.853918i | \(0.325780\pi\) | |||||||
\(228\) | −3.13811 | − | 4.72296i | −0.207826 | − | 0.312785i | ||||
\(229\) | −11.3568 | + | 6.55685i | −0.750479 | + | 0.433289i | −0.825867 | − | 0.563865i | \(-0.809314\pi\) |
0.0753881 | + | 0.997154i | \(0.475980\pi\) | |||||||
\(230\) | −0.870209 | + | 1.50725i | −0.0573799 | + | 0.0993849i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.38357 | − | 7.59256i | −0.287795 | − | 0.498476i | ||||
\(233\) | −7.31966 | − | 4.22601i | −0.479527 | − | 0.276855i | 0.240692 | − | 0.970601i | \(-0.422626\pi\) |
−0.720219 | + | 0.693746i | \(0.755959\pi\) | |||||||
\(234\) | −27.9581 | + | 3.53346i | −1.82768 | + | 0.230989i | ||||
\(235\) | 0.995314 | + | 1.72393i | 0.0649271 | + | 0.112457i | ||||
\(236\) | 4.01246 | 0.261189 | ||||||||
\(237\) | 10.8013 | + | 5.36143i | 0.701617 | + | 0.348262i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.2111 | − | 13.9783i | −1.56608 | − | 0.904179i | −0.996619 | − | 0.0821642i | \(-0.973817\pi\) |
−0.569466 | − | 0.822015i | \(-0.692850\pi\) | |||||||
\(240\) | −0.342281 | − | 5.43807i | −0.0220941 | − | 0.351026i | ||||
\(241\) | 19.4058 | + | 11.2039i | 1.25004 | + | 0.721710i | 0.971117 | − | 0.238605i | \(-0.0766900\pi\) |
0.278921 | + | 0.960314i | \(0.410023\pi\) | |||||||
\(242\) | −27.3833 | + | 15.8097i | −1.76026 | + | 1.01629i | ||||
\(243\) | −10.4292 | + | 11.5859i | −0.669031 | + | 0.743235i | ||||
\(244\) | 14.3774i | 0.920418i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 21.0396 | + | 31.6652i | 1.34143 | + | 2.01890i | ||||
\(247\) | 6.18819 | + | 10.7183i | 0.393745 | + | 0.681987i | ||||
\(248\) | −6.68312 | −0.424379 | ||||||||
\(249\) | 0.765142 | + | 12.1564i | 0.0484889 | + | 0.770378i | ||||
\(250\) | 11.3341i | 0.716829i | ||||||||
\(251\) | −6.39587 | −0.403704 | −0.201852 | − | 0.979416i | \(-0.564696\pi\) | ||||
−0.201852 | + | 0.979416i | \(0.564696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.82278 | −0.491814 | ||||||||
\(254\) | − | 4.57985i | − | 0.287366i | ||||||
\(255\) | 1.51792 | − | 1.00856i | 0.0950560 | − | 0.0631587i | ||||
\(256\) | 20.9653 | 1.31033 | ||||||||
\(257\) | −1.65705 | − | 2.87009i | −0.103364 | − | 0.179031i | 0.809705 | − | 0.586837i | \(-0.199627\pi\) |
−0.913069 | + | 0.407806i | \(0.866294\pi\) | |||||||
\(258\) | 9.58180 | − | 0.603094i | 0.596537 | − | 0.0375470i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 4.48950i | − | 0.278427i | ||||||
\(261\) | −20.5612 | − | 8.64184i | −1.27271 | − | 0.534916i | ||||
\(262\) | −4.02118 | + | 2.32163i | −0.248429 | + | 0.143431i | ||||
\(263\) | −19.6502 | − | 11.3451i | −1.21169 | − | 0.699567i | −0.248559 | − | 0.968617i | \(-0.579957\pi\) |
−0.963126 | + | 0.269050i | \(0.913290\pi\) | |||||||
\(264\) | 9.04366 | − | 6.00894i | 0.556599 | − | 0.369825i | ||||
\(265\) | 1.32054 | + | 0.762413i | 0.0811200 | + | 0.0468347i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.24191 | + | 4.14736i | −0.381999 | + | 0.253814i | ||||
\(268\) | 13.7733 | 0.841336 | ||||||||
\(269\) | 1.38050 | + | 2.39110i | 0.0841707 | + | 0.145788i | 0.905038 | − | 0.425332i | \(-0.139843\pi\) |
−0.820867 | + | 0.571120i | \(0.806509\pi\) | |||||||
\(270\) | −4.01595 | − | 4.65177i | −0.244403 | − | 0.283098i | ||||
\(271\) | −5.27342 | − | 3.04461i | −0.320337 | − | 0.184947i | 0.331206 | − | 0.943559i | \(-0.392545\pi\) |
−0.651543 | + | 0.758612i | \(0.725878\pi\) | |||||||
\(272\) | 3.97119 | + | 6.87830i | 0.240789 | + | 0.417058i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.11104 | − | 1.92438i | 0.0671205 | − | 0.116256i | ||||
\(275\) | −21.1001 | + | 12.1821i | −1.27238 | + | 0.734611i | ||||
\(276\) | −3.45018 | + | 0.217160i | −0.207677 | + | 0.0130715i | ||||
\(277\) | 4.71684 | − | 8.16980i | 0.283407 | − | 0.490876i | −0.688814 | − | 0.724938i | \(-0.741869\pi\) |
0.972222 | + | 0.234062i | \(0.0752019\pi\) | |||||||
\(278\) | 6.47064 | − | 11.2075i | 0.388083 | − | 0.672180i | ||||
\(279\) | −13.5419 | + | 10.2800i | −0.810730 | + | 0.615446i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.57153 | − | 2.63938i | 0.272715 | − | 0.157452i | −0.357406 | − | 0.933949i | \(-0.616339\pi\) |
0.630121 | + | 0.776497i | \(0.283005\pi\) | |||||||
\(282\) | −4.35031 | + | 8.76423i | −0.259057 | + | 0.521902i | ||||
\(283\) | − | 19.6699i | − | 1.16926i | −0.811302 | − | 0.584628i | \(-0.801241\pi\) | ||
0.811302 | − | 0.584628i | \(-0.198759\pi\) | |||||||
\(284\) | − | 6.46414i | − | 0.383576i | ||||||
\(285\) | −1.20000 | + | 2.41754i | −0.0710818 | + | 0.143203i | ||||
\(286\) | 43.2453 | − | 24.9677i | 2.55715 | − | 1.47637i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 15.6966 | − | 11.9157i | 0.924933 | − | 0.702141i | ||||
\(289\) | 7.17178 | − | 12.4219i | 0.421869 | − | 0.730699i | ||||
\(290\) | 4.39637 | − | 7.61474i | 0.258164 | − | 0.447153i | ||||
\(291\) | −28.7324 | + | 1.80847i | −1.68433 | + | 0.106014i | ||||
\(292\) | −13.8668 | + | 8.00600i | −0.811493 | + | 0.468516i | ||||
\(293\) | 9.11647 | − | 15.7902i | 0.532590 | − | 0.922473i | −0.466686 | − | 0.884423i | \(-0.654552\pi\) |
0.999276 | − | 0.0380495i | \(-0.0121145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.954912 | − | 1.65396i | −0.0555971 | − | 0.0962970i | ||||
\(296\) | 8.16470 | + | 4.71389i | 0.474563 | + | 0.273989i | ||||
\(297\) | 9.08201 | − | 26.0868i | 0.526992 | − | 1.51371i | ||||
\(298\) | −6.34917 | − | 10.9971i | −0.367797 | − | 0.637044i | ||||
\(299\) | 7.54531 | 0.436356 | ||||||||
\(300\) | −8.96787 | + | 5.95858i | −0.517760 | + | 0.344019i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.0253 | − | 5.78808i | −0.576888 | − | 0.333067i | ||||
\(303\) | 6.71048 | − | 4.45869i | 0.385507 | − | 0.256145i | ||||
\(304\) | −10.1866 | − | 5.88122i | −0.584240 | − | 0.337311i | ||||
\(305\) | 5.92643 | − | 3.42163i | 0.339347 | − | 0.195922i | ||||
\(306\) | 8.25808 | + | 3.47086i | 0.472083 | + | 0.198416i | ||||
\(307\) | 26.0447i | 1.48645i | 0.669042 | + | 0.743224i | \(0.266704\pi\) | ||||
−0.669042 | + | 0.743224i | \(0.733296\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.8124 | − | 1.12114i | 1.01331 | − | 0.0637795i | ||||
\(310\) | −3.35132 | − | 5.80466i | −0.190342 | − | 0.329683i | ||||
\(311\) | 28.2866 | 1.60398 | 0.801992 | − | 0.597334i | \(-0.203773\pi\) | ||||
0.801992 | + | 0.597334i | \(0.203773\pi\) | |||||||
\(312\) | −8.72288 | + | 5.79581i | −0.493836 | + | 0.328123i | ||||
\(313\) | 5.57595i | 0.315171i | 0.987505 | + | 0.157586i | \(0.0503710\pi\) | ||||
−0.987505 | + | 0.157586i | \(0.949629\pi\) | |||||||
\(314\) | 3.64624 | 0.205769 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.44276 | −0.531197 | ||||||||
\(317\) | 33.5681i | 1.88537i | 0.333680 | + | 0.942686i | \(0.391709\pi\) | ||||
−0.333680 | + | 0.942686i | \(0.608291\pi\) | |||||||
\(318\) | 0.470814 | + | 7.48017i | 0.0264019 | + | 0.419467i | ||||
\(319\) | 39.5214 | 2.21277 | ||||||||
\(320\) | 0.738701 | + | 1.27947i | 0.0412947 | + | 0.0715244i | ||||
\(321\) | 0.295758 | + | 0.445126i | 0.0165076 | + | 0.0248445i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.93412i | − | 0.218901i | ||||||
\(324\) | 3.28139 | − | 11.7575i | 0.182299 | − | 0.653194i | ||||
\(325\) | 20.3517 | − | 11.7500i | 1.12891 | − | 0.651775i | ||||
\(326\) | 9.49931 | + | 5.48443i | 0.526118 | + | 0.303755i | ||||
\(327\) | 0.684201 | + | 10.8704i | 0.0378364 | + | 0.601135i | ||||
\(328\) | 12.2358 | + | 7.06433i | 0.675608 | + | 0.390063i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 9.75414 | + | 4.84167i | 0.536948 | + | 0.266525i | ||||
\(331\) | −30.3735 | −1.66948 | −0.834739 | − | 0.550646i | \(-0.814381\pi\) | ||||
−0.834739 | + | 0.550646i | \(0.814381\pi\) | |||||||
\(332\) | −4.76904 | − | 8.26023i | −0.261735 | − | 0.453339i | ||||
\(333\) | 23.7949 | − | 3.00729i | 1.30395 | − | 0.164798i | ||||
\(334\) | −2.21483 | − | 1.27873i | −0.121190 | − | 0.0699692i | ||||
\(335\) | −3.27785 | − | 5.67741i | −0.179088 | − | 0.310190i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.86121 | − | 3.22371i | 0.101387 | − | 0.175607i | −0.810870 | − | 0.585227i | \(-0.801005\pi\) |
0.912256 | + | 0.409620i | \(0.134339\pi\) | |||||||
\(338\) | −21.0859 | + | 12.1739i | −1.14692 | + | 0.662175i | ||||
\(339\) | 8.55433 | + | 12.8745i | 0.464607 | + | 0.699249i | ||||
\(340\) | −0.713547 | + | 1.23590i | −0.0386975 | + | 0.0670261i | ||||
\(341\) | 15.0634 | − | 26.0906i | 0.815730 | − | 1.41289i | ||||
\(342\) | −13.1616 | + | 1.66342i | −0.711698 | + | 0.0899472i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.08995 | − | 1.78398i | 0.166599 | − | 0.0961858i | ||||
\(345\) | 0.910612 | + | 1.37050i | 0.0490257 | + | 0.0737853i | ||||
\(346\) | − | 13.9419i | − | 0.749522i | ||||||
\(347\) | − | 7.13637i | − | 0.383100i | −0.981483 | − | 0.191550i | \(-0.938649\pi\) | ||
0.981483 | − | 0.191550i | \(-0.0613515\pi\) | |||||||
\(348\) | 17.4306 | − | 1.09711i | 0.934379 | − | 0.0588114i | ||||
\(349\) | 13.2087 | − | 7.62607i | 0.707047 | − | 0.408214i | −0.102920 | − | 0.994690i | \(-0.532818\pi\) |
0.809967 | + | 0.586476i | \(0.199485\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.75987 | + | 25.1615i | −0.467567 | + | 1.34302i | ||||
\(352\) | −17.4603 | + | 30.2421i | −0.930637 | + | 1.61191i | ||||
\(353\) | −17.2359 | + | 29.8534i | −0.917373 | + | 1.58894i | −0.113985 | + | 0.993482i | \(0.536362\pi\) |
−0.803389 | + | 0.595455i | \(0.796972\pi\) | |||||||
\(354\) | 4.17372 | − | 8.40847i | 0.221831 | − | 0.446905i | ||||
\(355\) | −2.66455 | + | 1.53838i | −0.141420 | + | 0.0816487i | ||||
\(356\) | 2.93420 | − | 5.08219i | 0.155512 | − | 0.269355i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.47115 | − | 14.6725i | −0.447714 | − | 0.775464i | ||||
\(359\) | −5.73791 | − | 3.31278i | −0.302835 | − | 0.174842i | 0.340881 | − | 0.940107i | \(-0.389275\pi\) |
−0.643716 | + | 0.765265i | \(0.722608\pi\) | |||||||
\(360\) | −2.10546 | − | 0.884919i | −0.110967 | − | 0.0466393i | ||||
\(361\) | −6.58684 | − | 11.4087i | −0.346676 | − | 0.600460i | ||||
\(362\) | 21.9173 | 1.15195 | ||||||||
\(363\) | 1.87786 | + | 29.8350i | 0.0985622 | + | 1.56593i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.60022 | + | 3.81064i | 0.345472 | + | 0.199458i | ||||
\(366\) | 30.1291 | + | 14.9552i | 1.57487 | + | 0.781722i | ||||
\(367\) | 2.68222 | + | 1.54858i | 0.140011 | + | 0.0808352i | 0.568369 | − | 0.822774i | \(-0.307575\pi\) |
−0.428358 | + | 0.903609i | \(0.640908\pi\) | |||||||
\(368\) | −6.21028 | + | 3.58551i | −0.323733 | + | 0.186907i | ||||
\(369\) | 35.6595 | − | 4.50679i | 1.85636 | − | 0.234614i | ||||
\(370\) | 9.45532i | 0.491559i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.91934 | − | 11.9252i | 0.306904 | − | 0.618295i | ||||
\(373\) | −4.84999 | − | 8.40043i | −0.251123 | − | 0.434958i | 0.712712 | − | 0.701457i | \(-0.247467\pi\) |
−0.963835 | + | 0.266499i | \(0.914133\pi\) | |||||||
\(374\) | −15.8731 | −0.820780 | ||||||||
\(375\) | 9.59819 | + | 4.76426i | 0.495648 | + | 0.246025i | ||||
\(376\) | 3.63625i | 0.187526i | ||||||||
\(377\) | −38.1195 | −1.96326 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.76103 | 0.398657 | 0.199329 | − | 0.979933i | \(-0.436124\pi\) | ||||
0.199329 | + | 0.979933i | \(0.436124\pi\) | |||||||
\(380\) | − | 2.11349i | − | 0.108420i | ||||||
\(381\) | −3.87842 | − | 1.92514i | −0.198698 | − | 0.0986277i | ||||
\(382\) | 37.1442 | 1.90046 | ||||||||
\(383\) | 12.3063 | + | 21.3152i | 0.628825 | + | 1.08916i | 0.987788 | + | 0.155804i | \(0.0497970\pi\) |
−0.358963 | + | 0.933352i | \(0.616870\pi\) | |||||||
\(384\) | 6.88876 | − | 13.8783i | 0.351541 | − | 0.708222i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 30.9459i | − | 1.57511i | ||||||
\(387\) | 3.51697 | − | 8.36780i | 0.178778 | − | 0.425359i | ||||
\(388\) | 19.5236 | − | 11.2720i | 0.991162 | − | 0.572248i | ||||
\(389\) | −5.56578 | − | 3.21340i | −0.282196 | − | 0.162926i | 0.352221 | − | 0.935917i | \(-0.385427\pi\) |
−0.634417 | + | 0.772991i | \(0.718760\pi\) | |||||||
\(390\) | −9.40816 | − | 4.66994i | −0.476401 | − | 0.236471i | ||||
\(391\) | −2.07712 | − | 1.19923i | −0.105044 | − | 0.0606474i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.275761 | + | 4.38121i | 0.0139103 | + | 0.221003i | ||||
\(394\) | 34.2776 | 1.72688 | ||||||||
\(395\) | 2.24725 | + | 3.89235i | 0.113071 | + | 0.195846i | ||||
\(396\) | 2.71214 | + | 21.4596i | 0.136290 | + | 1.07838i | ||||
\(397\) | −11.4835 | − | 6.62998i | −0.576338 | − | 0.332749i | 0.183339 | − | 0.983050i | \(-0.441310\pi\) |
−0.759677 | + | 0.650301i | \(0.774643\pi\) | |||||||
\(398\) | −16.5291 | − | 28.6292i | −0.828528 | − | 1.43505i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.1672 | + | 19.3421i | −0.558358 | + | 0.967105i | ||||
\(401\) | 13.6877 | − | 7.90259i | 0.683530 | − | 0.394636i | −0.117653 | − | 0.993055i | \(-0.537537\pi\) |
0.801184 | + | 0.598418i | \(0.204204\pi\) | |||||||
\(402\) | 14.3268 | − | 28.8631i | 0.714556 | − | 1.43956i | ||||
\(403\) | −14.5291 | + | 25.1652i | −0.723747 | + | 1.25357i | ||||
\(404\) | −3.15447 | + | 5.46370i | −0.156941 | + | 0.271829i | ||||
\(405\) | −5.62742 | + | 1.44552i | −0.279629 | + | 0.0718286i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −36.8056 | + | 21.2497i | −1.82439 | + | 1.05331i | ||||
\(408\) | 3.32246 | − | 0.209121i | 0.164486 | − | 0.0103530i | ||||
\(409\) | − | 5.41851i | − | 0.267928i | −0.990986 | − | 0.133964i | \(-0.957229\pi\) | ||
0.990986 | − | 0.133964i | \(-0.0427707\pi\) | |||||||
\(410\) | 14.1699i | 0.699803i | ||||||||
\(411\) | −1.16263 | − | 1.74979i | −0.0573481 | − | 0.0863109i | ||||
\(412\) | −12.1035 | + | 6.98795i | −0.596296 | + | 0.344271i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.13376 | + | 7.45605i | −0.154016 | + | 0.366445i | ||||
\(415\) | −2.26994 | + | 3.93165i | −0.111427 | + | 0.192997i | ||||
\(416\) | 16.8410 | − | 29.1694i | 0.825697 | − | 1.43015i | ||||
\(417\) | −6.77107 | − | 10.1907i | −0.331581 | − | 0.499040i | ||||
\(418\) | 20.3582 | − | 11.7538i | 0.995754 | − | 0.574899i | ||||
\(419\) | 12.2469 | − | 21.2123i | 0.598302 | − | 1.03629i | −0.394770 | − | 0.918780i | \(-0.629176\pi\) |
0.993072 | − | 0.117509i | \(-0.0374909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.99347 | + | 10.3810i | 0.292104 | + | 0.505939i | 0.974307 | − | 0.225224i | \(-0.0723113\pi\) |
−0.682203 | + | 0.731163i | \(0.738978\pi\) | |||||||
\(422\) | −12.8034 | − | 7.39206i | −0.623261 | − | 0.359840i | ||||
\(423\) | 5.59329 | + | 7.36806i | 0.271955 | + | 0.358248i | ||||
\(424\) | 1.39269 | + | 2.41221i | 0.0676350 | + | 0.117147i | ||||
\(425\) | −7.47005 | −0.362351 | ||||||||
\(426\) | −13.5462 | − | 6.72394i | −0.656315 | − | 0.325776i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.362424 | − | 0.209245i | −0.0175184 | − | 0.0101143i | ||||
\(429\) | −2.96563 | − | 47.1172i | −0.143182 | − | 2.27484i | ||||
\(430\) | 3.09897 | + | 1.78919i | 0.149446 | + | 0.0862825i | ||||
\(431\) | 26.6926 | − | 15.4110i | 1.28574 | − | 0.742320i | 0.307845 | − | 0.951437i | \(-0.400392\pi\) |
0.977891 | + | 0.209117i | \(0.0670590\pi\) | |||||||
\(432\) | −4.74670 | − | 24.8722i | −0.228376 | − | 1.19666i | ||||
\(433\) | − | 6.06173i | − | 0.291308i | −0.989336 | − | 0.145654i | \(-0.953471\pi\) | ||
0.989336 | − | 0.145654i | \(-0.0465287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.60049 | − | 6.92389i | −0.220577 | − | 0.331975i | ||||
\(436\) | −4.26455 | − | 7.38642i | −0.204235 | − | 0.353745i | ||||
\(437\) | 3.55204 | 0.169917 | ||||||||
\(438\) | 2.35319 | + | 37.3869i | 0.112440 | + | 1.78641i | ||||
\(439\) | 27.1448i | 1.29555i | 0.761831 | + | 0.647776i | \(0.224301\pi\) | ||||
−0.761831 | + | 0.647776i | \(0.775699\pi\) | |||||||
\(440\) | 4.04697 | 0.192932 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.3101 | 0.728228 | ||||||||
\(443\) | − | 5.35163i | − | 0.254264i | −0.991886 | − | 0.127132i | \(-0.959423\pi\) | ||
0.991886 | − | 0.127132i | \(-0.0405771\pi\) | |||||||
\(444\) | −15.6430 | + | 10.3938i | −0.742383 | + | 0.493267i | ||||
\(445\) | −2.79320 | −0.132411 | ||||||||
\(446\) | −21.4135 | − | 37.0893i | −1.01396 | − | 1.75623i | ||||
\(447\) | −11.9817 | + | 0.754147i | −0.566714 | + | 0.0356699i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.2418i | 1.61597i | 0.589204 | + | 0.807985i | \(0.299442\pi\) | ||||
−0.589204 | + | 0.807985i | \(0.700558\pi\) | |||||||
\(450\) | 3.15847 | + | 24.9910i | 0.148891 | + | 1.17809i | ||||
\(451\) | −55.1577 | + | 31.8453i | −2.59727 | + | 1.49954i | ||||
\(452\) | −10.4825 | − | 6.05208i | −0.493056 | − | 0.284666i | ||||
\(453\) | −9.11571 | + | 6.05681i | −0.428293 | + | 0.284574i | ||||
\(454\) | −22.9151 | − | 13.2300i | −1.07546 | − | 0.620916i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.10640 | + | 2.72844i | −0.192300 | + | 0.127771i | ||||
\(457\) | −15.8604 | −0.741917 | −0.370958 | − | 0.928649i | \(-0.620971\pi\) | ||||
−0.370958 | + | 0.928649i | \(0.620971\pi\) | |||||||
\(458\) | −12.0123 | − | 20.8059i | −0.561299 | − | 0.972198i | ||||
\(459\) | 6.41055 | − | 5.53434i | 0.299219 | − | 0.258321i | ||||
\(460\) | −1.11587 | − | 0.644247i | −0.0520276 | − | 0.0300382i | ||||
\(461\) | 6.50676 | + | 11.2700i | 0.303050 | + | 0.524898i | 0.976825 | − | 0.214038i | \(-0.0686618\pi\) |
−0.673775 | + | 0.738936i | \(0.735328\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.01941 | + | 10.4259i | −0.279746 | + | 0.484534i | −0.971321 | − | 0.237770i | \(-0.923583\pi\) |
0.691576 | + | 0.722304i | \(0.256917\pi\) | |||||||
\(464\) | 31.3749 | − | 18.1143i | 1.45654 | − | 0.840935i | ||||
\(465\) | −6.32437 | + | 0.398066i | −0.293286 | + | 0.0184599i | ||||
\(466\) | 7.74215 | − | 13.4098i | 0.358648 | − | 0.621197i | ||||
\(467\) | −10.1728 | + | 17.6199i | −0.470743 | + | 0.815351i | −0.999440 | − | 0.0334596i | \(-0.989347\pi\) |
0.528697 | + | 0.848811i | \(0.322681\pi\) | |||||||
\(468\) | −2.61594 | − | 20.6984i | −0.120922 | − | 0.956783i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.15829 | + | 1.82344i | −0.145681 | + | 0.0841090i | ||||
\(471\) | 1.53269 | − | 3.08780i | 0.0706227 | − | 0.142278i | ||||
\(472\) | − | 3.48865i | − | 0.160578i | ||||||
\(473\) | 16.0840i | 0.739544i | ||||||||
\(474\) | −9.82226 | + | 19.7882i | −0.451151 | + | 0.908900i | ||||
\(475\) | 9.58078 | − | 5.53146i | 0.439596 | − | 0.253801i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.53244 | + | 2.74557i | 0.299100 | + | 0.125711i | ||||
\(478\) | 25.6085 | − | 44.3553i | 1.17131 | − | 2.02876i | ||||
\(479\) | 12.1492 | − | 21.0430i | 0.555109 | − | 0.961477i | −0.442786 | − | 0.896627i | \(-0.646010\pi\) |
0.997895 | − | 0.0648499i | \(-0.0206569\pi\) | |||||||
\(480\) | 7.33070 | − | 0.461406i | 0.334599 | − | 0.0210602i | ||||
\(481\) | 35.5001 | − | 20.4960i | 1.61867 | − | 0.934538i | ||||
\(482\) | −20.5259 | + | 35.5519i | −0.934929 | + | 1.61934i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.7045 | − | 20.2728i | −0.532023 | − | 0.921491i | ||||
\(485\) | −9.29273 | − | 5.36516i | −0.421961 | − | 0.243619i | ||||
\(486\) | −21.2256 | − | 19.1065i | −0.962813 | − | 0.866687i | ||||
\(487\) | 13.6546 | + | 23.6504i | 0.618747 | + | 1.07170i | 0.989715 | + | 0.143055i | \(0.0456927\pi\) |
−0.370968 | + | 0.928646i | \(0.620974\pi\) | |||||||
\(488\) | 12.5005 | 0.565871 | ||||||||
\(489\) | 8.63748 | − | 5.73907i | 0.390601 | − | 0.259530i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.2899 | − | 7.67290i | −0.599763 | − | 0.346273i | 0.169185 | − | 0.985584i | \(-0.445886\pi\) |
−0.768948 | + | 0.639311i | \(0.779220\pi\) | |||||||
\(492\) | −23.4429 | + | 15.5763i | −1.05689 | + | 0.702235i | ||||
\(493\) | 10.4938 | + | 6.05859i | 0.472616 | + | 0.272865i | ||||
\(494\) | −19.6361 | + | 11.3369i | −0.883471 | + | 0.510072i | ||||
\(495\) | 8.20028 | − | 6.22505i | 0.368575 | − | 0.279795i | ||||
\(496\) | − | 27.6168i | − | 1.24003i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −22.2708 | + | 1.40176i | −0.997976 | + | 0.0628143i | ||||
\(499\) | 5.15504 | + | 8.92879i | 0.230771 | + | 0.399707i | 0.958035 | − | 0.286650i | \(-0.0925418\pi\) |
−0.727264 | + | 0.686358i | \(0.759208\pi\) | |||||||
\(500\) | −8.39101 | −0.375257 | ||||||||
\(501\) | −2.01389 | + | 1.33810i | −0.0899740 | + | 0.0597820i | ||||
\(502\) | − | 11.7174i | − | 0.522972i | ||||||
\(503\) | 24.6770 | 1.10029 | 0.550146 | − | 0.835068i | \(-0.314572\pi\) | ||||
0.550146 | + | 0.835068i | \(0.314572\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.00289 | 0.133627 | ||||||||
\(506\) | − | 14.3315i | − | 0.637114i | ||||||
\(507\) | 1.44601 | + | 22.9738i | 0.0642194 | + | 1.02030i | ||||
\(508\) | 3.39063 | 0.150435 | ||||||||
\(509\) | 2.58601 | + | 4.47911i | 0.114623 | + | 0.198533i | 0.917629 | − | 0.397438i | \(-0.130101\pi\) |
−0.803006 | + | 0.595971i | \(0.796767\pi\) | |||||||
\(510\) | 1.84771 | + | 2.78087i | 0.0818181 | + | 0.123139i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.5181i | 0.906778i | ||||||||
\(513\) | −4.12381 | + | 11.8450i | −0.182071 | + | 0.522971i | ||||
\(514\) | 5.25807 | − | 3.03575i | 0.231924 | − | 0.133901i | ||||
\(515\) | 5.76093 | + | 3.32608i | 0.253857 | + | 0.146564i | ||||
\(516\) | 0.446492 | + | 7.09374i | 0.0196557 | + | 0.312285i | ||||
\(517\) | −14.1958 | − | 8.19594i | −0.624330 | − | 0.360457i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.8066 | − | 5.86047i | −0.518254 | − | 0.257246i | ||||
\(520\) | −3.90342 | −0.171176 | ||||||||
\(521\) | 19.1664 | + | 33.1972i | 0.839696 | + | 1.45440i | 0.890149 | + | 0.455669i | \(0.150600\pi\) |
−0.0504538 | + | 0.998726i | \(0.516067\pi\) | |||||||
\(522\) | 15.8320 | − | 37.6686i | 0.692950 | − | 1.64871i | ||||
\(523\) | −23.6468 | − | 13.6525i | −1.03400 | − | 0.596982i | −0.115874 | − | 0.993264i | \(-0.536967\pi\) |
−0.918129 | + | 0.396282i | \(0.870300\pi\) | |||||||
\(524\) | −1.71878 | − | 2.97702i | −0.0750855 | − | 0.130052i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.7844 | − | 35.9997i | 0.906245 | − | 1.56966i | ||||
\(527\) | 7.99934 | − | 4.61842i | 0.348457 | − | 0.201182i | ||||
\(528\) | 24.8309 | + | 37.3713i | 1.08062 | + | 1.62638i | ||||
\(529\) | −10.4172 | + | 18.0432i | −0.452924 | + | 0.784487i | ||||
\(530\) | −1.39676 | + | 2.41926i | −0.0606714 | + | 0.105086i | ||||
\(531\) | −5.36625 | − | 7.06898i | −0.232875 | − | 0.306768i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 53.2012 | − | 30.7158i | 2.30440 | − | 1.33045i | ||||
\(534\) | −7.59805 | − | 11.4353i | −0.328800 | − | 0.494855i | ||||
\(535\) | 0.199190i | 0.00861175i | ||||||||
\(536\) | − | 11.9752i | − | 0.517251i | ||||||
\(537\) | −15.9861 | + | 1.00619i | −0.689853 | + | 0.0434205i | ||||
\(538\) | −4.38055 | + | 2.52911i | −0.188859 | + | 0.109038i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.44387 | − | 2.97315i | 0.148201 | − | 0.127944i | ||||
\(541\) | −9.78052 | + | 16.9404i | −0.420498 | + | 0.728323i | −0.995988 | − | 0.0894853i | \(-0.971478\pi\) |
0.575491 | + | 0.817808i | \(0.304811\pi\) | |||||||
\(542\) | 5.57779 | − | 9.66102i | 0.239587 | − | 0.414977i | ||||
\(543\) | 9.21290 | − | 18.5605i | 0.395363 | − | 0.796508i | ||||
\(544\) | −9.27219 | + | 5.35330i | −0.397542 | + | 0.229521i | ||||
\(545\) | −2.02981 | + | 3.51574i | −0.0869476 | + | 0.150598i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.6246 | + | 21.8665i | 0.539790 | + | 0.934944i | 0.998915 | + | 0.0465723i | \(0.0148298\pi\) |
−0.459125 | + | 0.888372i | \(0.651837\pi\) | |||||||
\(548\) | 1.42469 | + | 0.822544i | 0.0608597 | + | 0.0351373i | ||||
\(549\) | 25.3295 | − | 19.2283i | 1.08104 | − | 0.820642i | ||||
\(550\) | −22.3180 | − | 38.6559i | −0.951642 | − | 1.64829i | ||||
\(551\) | −17.9452 | −0.764492 | ||||||||
\(552\) | 0.188811 | + | 2.99978i | 0.00803632 | + | 0.127679i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14.9673 | + | 8.64136i | 0.635898 | + | 0.367136i | ||||
\(555\) | 8.00718 | + | 3.97453i | 0.339886 | + | 0.168710i | ||||
\(556\) | 8.29730 | + | 4.79045i | 0.351884 | + | 0.203160i | ||||
\(557\) | 28.8204 | − | 16.6395i | 1.22116 | − | 0.705036i | 0.255994 | − | 0.966678i | \(-0.417597\pi\) |
0.965165 | + | 0.261642i | \(0.0842640\pi\) | |||||||
\(558\) | −18.8332 | − | 24.8090i | −0.797272 | − | 1.05025i | ||||
\(559\) | − | 15.5135i | − | 0.656152i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.67225 | + | 13.4421i | −0.281703 | + | 0.567525i | ||||
\(562\) | 4.83540 | + | 8.37516i | 0.203969 | + | 0.353285i | ||||
\(563\) | −30.5175 | −1.28616 | −0.643079 | − | 0.765800i | \(-0.722343\pi\) | ||||
−0.643079 | + | 0.765800i | \(0.722343\pi\) | |||||||
\(564\) | −6.48847 | − | 3.22069i | −0.273214 | − | 0.135615i | ||||
\(565\) | 5.76126i | 0.242378i | ||||||||
\(566\) | 36.0358 | 1.51470 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.62028 | −0.235822 | ||||||||
\(569\) | 15.4781i | 0.648876i | 0.945907 | + | 0.324438i | \(0.105175\pi\) | ||||
−0.945907 | + | 0.324438i | \(0.894825\pi\) | |||||||
\(570\) | −4.42900 | − | 2.19843i | −0.185510 | − | 0.0920819i | ||||
\(571\) | −24.4085 | −1.02146 | −0.510731 | − | 0.859740i | \(-0.670625\pi\) | ||||
−0.510731 | + | 0.859740i | \(0.670625\pi\) | |||||||
\(572\) | 18.4845 | + | 32.0160i | 0.772875 | + | 1.33866i | ||||
\(573\) | 15.6135 | − | 31.4553i | 0.652264 | − | 1.31407i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.74455i | − | 0.281267i | ||||||
\(576\) | 4.15122 | + | 5.46843i | 0.172968 | + | 0.227851i | ||||
\(577\) | −12.6901 | + | 7.32664i | −0.528296 | + | 0.305012i | −0.740322 | − | 0.672252i | \(-0.765327\pi\) |
0.212026 | + | 0.977264i | \(0.431994\pi\) | |||||||
\(578\) | 22.7572 | + | 13.1389i | 0.946574 | + | 0.546505i | ||||
\(579\) | −26.2064 | − | 13.0081i | −1.08910 | − | 0.540598i | ||||
\(580\) | 5.63746 | + | 3.25479i | 0.234083 | + | 0.135148i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.31316 | − | 52.6385i | −0.137335 | − | 2.18194i | ||||
\(583\) | −12.5562 | −0.520026 | ||||||||
\(584\) | 6.96085 | + | 12.0565i | 0.288042 | + | 0.498904i | ||||
\(585\) | −7.90942 | + | 6.00424i | −0.327014 | + | 0.248245i | ||||
\(586\) | 28.9280 | + | 16.7016i | 1.19500 | + | 0.689936i | ||||
\(587\) | 11.6129 | + | 20.1141i | 0.479314 | + | 0.830197i | 0.999719 | − | 0.0237232i | \(-0.00755204\pi\) |
−0.520404 | + | 0.853920i | \(0.674219\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.83975 | + | 11.8468i | −0.281827 | + | 0.488139i | ||||
\(590\) | 3.03009 | − | 1.74942i | 0.124747 | − | 0.0720225i | ||||
\(591\) | 14.4085 | − | 29.0278i | 0.592688 | − | 1.19404i | ||||
\(592\) | −19.4793 | + | 33.7391i | −0.800594 | + | 1.38667i | ||||
\(593\) | −5.55605 | + | 9.62337i | −0.228160 | + | 0.395184i | −0.957263 | − | 0.289220i | \(-0.906604\pi\) |
0.729103 | + | 0.684404i | \(0.239938\pi\) | |||||||
\(594\) | 47.7916 | + | 16.6385i | 1.96091 | + | 0.682684i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.14153 | − | 4.70051i | 0.333490 | − | 0.192541i | ||||
\(597\) | −31.1925 | + | 1.96330i | −1.27662 | + | 0.0803527i | ||||
\(598\) | 13.8232i | 0.565272i | ||||||||
\(599\) | 15.6555i | 0.639667i | 0.947474 | + | 0.319833i | \(0.103627\pi\) | ||||
−0.947474 | + | 0.319833i | \(0.896373\pi\) | |||||||
\(600\) | 5.18072 | + | 7.79715i | 0.211502 | + | 0.318317i | ||||
\(601\) | −30.5665 | + | 17.6476i | −1.24684 | + | 0.719861i | −0.970477 | − | 0.241194i | \(-0.922461\pi\) |
−0.276358 | + | 0.961055i | \(0.589128\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.4203 | − | 24.2652i | −0.750133 | − | 0.988154i | ||||
\(604\) | 4.28512 | − | 7.42205i | 0.174359 | − | 0.301999i | ||||
\(605\) | −5.57104 | + | 9.64932i | −0.226495 | + | 0.392301i | ||||
\(606\) | 8.16843 | + | 12.2938i | 0.331820 | + | 0.499400i | ||||
\(607\) | 33.6062 | − | 19.4025i | 1.36403 | − | 0.787524i | 0.373874 | − | 0.927479i | \(-0.378029\pi\) |
0.990158 | + | 0.139955i | \(0.0446959\pi\) | |||||||
\(608\) | 7.92809 | − | 13.7318i | 0.321526 | − | 0.556900i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.26850 | + | 10.8574i | 0.253804 | + | 0.439602i | ||||
\(611\) | 13.6923 | + | 7.90523i | 0.553929 | + | 0.319811i | ||||
\(612\) | −2.56960 | + | 6.11375i | −0.103870 | + | 0.247134i | ||||
\(613\) | −15.8786 | − | 27.5025i | −0.641330 | − | 1.11082i | −0.985136 | − | 0.171776i | \(-0.945049\pi\) |
0.343806 | − | 0.939041i | \(-0.388284\pi\) | |||||||
\(614\) | −47.7145 | −1.92560 | ||||||||
\(615\) | 11.9997 | + | 5.95632i | 0.483876 | + | 0.240182i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.25518 | + | 0.724680i | 0.0505317 | + | 0.0291745i | 0.525053 | − | 0.851070i | \(-0.324045\pi\) |
−0.474521 | + | 0.880244i | \(0.657379\pi\) | |||||||
\(618\) | 2.05396 | + | 32.6327i | 0.0826223 | + | 1.31268i | ||||
\(619\) | −25.2590 | − | 14.5833i | −1.01524 | − | 0.586152i | −0.102522 | − | 0.994731i | \(-0.532691\pi\) |
−0.912723 | + | 0.408579i | \(0.866024\pi\) | |||||||
\(620\) | 4.29740 | − | 2.48110i | 0.172588 | − | 0.0996435i | ||||
\(621\) | 4.99684 | + | 5.78795i | 0.200516 | + | 0.232263i | ||||
\(622\) | 51.8217i | 2.07786i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −23.9501 | − | 36.0457i | −0.958771 | − | 1.44298i | ||||
\(625\) | −9.46116 | − | 16.3872i | −0.378446 | − | 0.655488i | ||||
\(626\) | −10.2153 | −0.408284 | ||||||||
\(627\) | −1.39611 | − | 22.1810i | −0.0557551 | − | 0.885822i | ||||
\(628\) | 2.69944i | 0.107719i | ||||||||
\(629\) | −13.0303 | −0.519551 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.7428 | 0.467473 | 0.233736 | − | 0.972300i | \(-0.424905\pi\) | ||||
0.233736 | + | 0.972300i | \(0.424905\pi\) | |||||||
\(632\) | 8.21005i | 0.326578i | ||||||||
\(633\) | −11.6418 | + | 7.73526i | −0.462721 | + | 0.307449i | ||||
\(634\) | −61.4976 | −2.44238 | ||||||||
\(635\) | −0.806924 | − | 1.39763i | −0.0320218 | − | 0.0554634i | ||||
\(636\) | −5.53783 | + | 0.348560i | −0.219589 | + | 0.0138213i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 72.4041i | 2.86651i | ||||||||
\(639\) | −11.3883 | + | 8.64512i | −0.450512 | + | 0.341996i | ||||
\(640\) | 5.00119 | − | 2.88744i | 0.197689 | − | 0.114136i | ||||
\(641\) | 10.0267 | + | 5.78891i | 0.396030 | + | 0.228648i | 0.684770 | − | 0.728760i | \(-0.259903\pi\) |
−0.288740 | + | 0.957408i | \(0.593236\pi\) | |||||||
\(642\) | −0.815481 | + | 0.541836i | −0.0321845 | + | 0.0213846i | ||||
\(643\) | 13.1240 | + | 7.57712i | 0.517558 | + | 0.298812i | 0.735935 | − | 0.677052i | \(-0.236743\pi\) |
−0.218377 | + | 0.975865i | \(0.570076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.81782 | − | 1.87226i | 0.110951 | − | 0.0737203i | ||||
\(646\) | 7.20741 | 0.283572 | ||||||||
\(647\) | −6.22057 | − | 10.7743i | −0.244556 | − | 0.423583i | 0.717451 | − | 0.696609i | \(-0.245309\pi\) |
−0.962007 | + | 0.273026i | \(0.911975\pi\) | |||||||
\(648\) | −10.2226 | − | 2.85302i | −0.401582 | − | 0.112077i | ||||
\(649\) | 13.6195 | + | 7.86325i | 0.534614 | + | 0.308659i | ||||
\(650\) | 21.5264 | + | 37.2847i | 0.844333 | + | 1.46243i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.06032 | + | 7.03268i | −0.159014 | + | 0.275421i | ||||
\(653\) | 3.97013 | − | 2.29216i | 0.155363 | − | 0.0896990i | −0.420303 | − | 0.907384i | \(-0.638076\pi\) |
0.575666 | + | 0.817685i | \(0.304743\pi\) | |||||||
\(654\) | −19.9148 | + | 1.25347i | −0.778732 | + | 0.0490147i | ||||
\(655\) | −0.818096 | + | 1.41698i | −0.0319656 | + | 0.0553661i | ||||
\(656\) | −29.1921 | + | 50.5621i | −1.13976 | + | 1.97412i | ||||
\(657\) | 32.6500 | + | 13.7227i | 1.27380 | + | 0.535375i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.6110 | − | 9.01301i | 0.608118 | − | 0.351097i | −0.164111 | − | 0.986442i | \(-0.552475\pi\) |
0.772228 | + | 0.635345i | \(0.219142\pi\) | |||||||
\(660\) | −3.58446 | + | 7.22133i | −0.139525 | + | 0.281090i | ||||
\(661\) | 0.640781i | 0.0249235i | 0.999922 | + | 0.0124617i | \(0.00396680\pi\) | ||||
−0.999922 | + | 0.0124617i | \(0.996033\pi\) | |||||||
\(662\) | − | 55.6449i | − | 2.16270i | ||||||
\(663\) | 6.43559 | − | 12.9653i | 0.249937 | − | 0.503530i | ||||
\(664\) | −7.18189 | + | 4.14647i | −0.278711 | + | 0.160914i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.50943 | + | 43.5927i | 0.213486 | + | 1.68918i | ||||
\(667\) | −5.47018 | + | 9.47462i | −0.211806 | + | 0.366859i | ||||
\(668\) | 0.946692 | − | 1.63972i | 0.0366286 | − | 0.0634426i | ||||
\(669\) | −40.4100 | + | 2.54347i | −1.56234 | + | 0.0983363i | ||||
\(670\) | 10.4012 | − | 6.00511i | 0.401832 | − | 0.231998i | ||||
\(671\) | −28.1755 | + | 48.8014i | −1.08770 | + | 1.88396i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0695 | − | 19.1729i | −0.426697 | − | 0.739061i | 0.569880 | − | 0.821728i | \(-0.306990\pi\) |
−0.996577 | + | 0.0826667i | \(0.973656\pi\) | |||||||
\(674\) | 5.90591 | + | 3.40978i | 0.227487 | + | 0.131340i | ||||
\(675\) | 22.4912 | + | 7.83022i | 0.865685 | + | 0.301385i | ||||
\(676\) | −9.01280 | − | 15.6106i | −0.346646 | − | 0.600409i | ||||
\(677\) | 20.0320 | 0.769893 | 0.384947 | − | 0.922939i | \(-0.374220\pi\) | ||||
0.384947 | + | 0.922939i | \(0.374220\pi\) | |||||||
\(678\) | −23.5865 | + | 15.6717i | −0.905833 | + | 0.601869i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.07456 | + | 0.620397i | 0.0412074 | + | 0.0237911i | ||||
\(681\) | −20.8361 | + | 13.8443i | −0.798441 | + | 0.530514i | ||||
\(682\) | 47.7986 | + | 27.5966i | 1.83030 | + | 1.05673i | ||||
\(683\) | −18.1316 | + | 10.4683i | −0.693786 | + | 0.400558i | −0.805029 | − | 0.593235i | \(-0.797850\pi\) |
0.111243 | + | 0.993793i | \(0.464517\pi\) | |||||||
\(684\) | −1.23149 | − | 9.74400i | −0.0470870 | − | 0.372571i | ||||
\(685\) | − | 0.783018i | − | 0.0299176i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.6688 | + | 1.42681i | −0.864867 | + | 0.0544361i | ||||
\(688\) | 7.37198 | + | 12.7686i | 0.281054 | + | 0.486800i | ||||
\(689\) | 12.1109 | 0.461387 | ||||||||
\(690\) | −2.51079 | + | 1.66826i | −0.0955842 | + | 0.0635097i | ||||
\(691\) | 1.54072i | 0.0586116i | 0.999570 | + | 0.0293058i | \(0.00932966\pi\) | ||||
−0.999570 | + | 0.0293058i | \(0.990670\pi\) | |||||||
\(692\) | 10.3217 | 0.392372 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.0740 | 0.496282 | ||||||||
\(695\) | − | 4.56025i | − | 0.172980i | ||||||
\(696\) | −0.953889 | − | 15.1551i | −0.0361571 | − | 0.574454i | ||||
\(697\) | −19.5274 | −0.739654 | ||||||||
\(698\) | 13.9711 | + | 24.1987i | 0.528815 | + | 0.915935i | ||||
\(699\) | −8.10161 | − | 12.1932i | −0.306431 | − | 0.461189i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.6641i | − | 1.19593i | −0.801520 | − | 0.597967i | \(-0.795975\pi\) | ||
0.801520 | − | 0.597967i | \(-0.204025\pi\) | |||||||
\(702\) | −46.0964 | − | 16.0483i | −1.73980 | − | 0.605704i | ||||
\(703\) | 16.7121 | − | 9.64873i | 0.630309 | − | 0.363909i | ||||
\(704\) | −10.5358 | − | 6.08286i | −0.397083 | − | 0.229256i | ||||
\(705\) | 0.216586 | + | 3.44106i | 0.00815710 | + | 0.129598i | ||||
\(706\) | −54.6922 | − | 31.5766i | −2.05837 | − | 1.18840i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.22509 | + | 3.08995i | 0.233953 | + | 0.116127i | ||||
\(709\) | 22.3524 | 0.839463 | 0.419732 | − | 0.907648i | \(-0.362124\pi\) | ||||
0.419732 | + | 0.907648i | \(0.362124\pi\) | |||||||
\(710\) | −2.81835 | − | 4.88152i | −0.105771 | − | 0.183200i | ||||
\(711\) | 12.6287 | + | 16.6358i | 0.473613 | + | 0.623893i | ||||
\(712\) | −4.41873 | − | 2.55116i | −0.165599 | − | 0.0956086i | ||||
\(713\) | 4.16988 | + | 7.22244i | 0.156163 | + | 0.270482i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.79812 | − | 15.2388i | 0.329031 | − | 0.569898i | ||||
\(716\) | 10.8625 | − | 6.27149i | 0.405952 | − | 0.234377i | ||||
\(717\) | −26.7975 | − | 40.3311i | −1.00077 | − | 1.50619i | ||||
\(718\) | 6.06910 | − | 10.5120i | 0.226497 | − | 0.392304i | ||||
\(719\) | 19.4544 | − | 33.6959i | 0.725525 | − | 1.25665i | −0.233232 | − | 0.972421i | \(-0.574930\pi\) |
0.958757 | − | 0.284226i | \(-0.0917365\pi\) | |||||||
\(720\) | 3.65677 | − | 8.70041i | 0.136280 | − | 0.324245i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 20.9011 | − | 12.0672i | 0.777858 | − | 0.449096i | ||||
\(723\) | 21.4789 | + | 32.3264i | 0.798808 | + | 1.20223i | ||||
\(724\) | 16.2261i | 0.603039i | ||||||||
\(725\) | 34.0741i | 1.26548i | ||||||||
\(726\) | −54.6584 | + | 3.44029i | −2.02856 | + | 0.127681i | ||||
\(727\) | 11.4647 | − | 6.61915i | 0.425202 | − | 0.245491i | −0.272098 | − | 0.962269i | \(-0.587718\pi\) |
0.697301 | + | 0.716779i | \(0.254384\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.1024 | + | 9.94341i | −0.929717 | + | 0.368274i | ||||
\(730\) | −6.98119 | + | 12.0918i | −0.258385 | + | 0.447536i | ||||
\(731\) | −2.46567 | + | 4.27066i | −0.0911960 | + | 0.157956i | ||||
\(732\) | −11.0719 | + | 22.3056i | −0.409228 | + | 0.824440i | ||||
\(733\) | −28.1222 | + | 16.2364i | −1.03872 | + | 0.599704i | −0.919470 | − | 0.393161i | \(-0.871382\pi\) |
−0.119248 | + | 0.992865i | \(0.538048\pi\) | |||||||
\(734\) | −2.83703 | + | 4.91389i | −0.104717 | + | 0.181375i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.83338 | − | 8.37167i | −0.178161 | − | 0.308584i | ||||
\(737\) | 46.7508 | + | 26.9916i | 1.72209 | + | 0.994248i | ||||
\(738\) | 8.25654 | + | 65.3290i | 0.303927 | + | 2.40479i | ||||
\(739\) | 6.91965 | + | 11.9852i | 0.254543 | + | 0.440882i | 0.964771 | − | 0.263090i | \(-0.0847415\pi\) |
−0.710228 | + | 0.703972i | \(0.751408\pi\) | |||||||
\(740\) | −7.00011 | −0.257329 | ||||||||
\(741\) | 1.34659 | + | 21.3942i | 0.0494681 | + | 0.785936i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.8593 | + | 18.3940i | 1.16880 | + | 0.674810i | 0.953398 | − | 0.301715i | \(-0.0975591\pi\) |
0.215406 | + | 0.976525i | \(0.430892\pi\) | |||||||
\(744\) | −10.3685 | − | 5.14660i | −0.380126 | − | 0.188683i | ||||
\(745\) | −3.87515 | − | 2.23732i | −0.141975 | − | 0.0819690i | ||||
\(746\) | 15.3898 | − | 8.88530i | 0.563461 | − | 0.325314i | ||||
\(747\) | −8.17441 | + | 19.4491i | −0.299086 | + | 0.711605i | ||||
\(748\) | − | 11.7514i | − | 0.429675i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.72824 | + | 17.5841i | −0.318710 | + | 0.642081i | ||||
\(751\) | 1.82952 | + | 3.16883i | 0.0667602 | + | 0.115632i | 0.897473 | − | 0.441068i | \(-0.145400\pi\) |
−0.830713 | + | 0.556701i | \(0.812067\pi\) | |||||||
\(752\) | −15.0262 | −0.547948 | ||||||||
\(753\) | −9.92280 | − | 4.92539i | −0.361607 | − | 0.179491i | ||||
\(754\) | − | 69.8359i | − | 2.54327i | ||||||
\(755\) | −4.07921 | −0.148458 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.8901 | 0.504842 | 0.252421 | − | 0.967617i | \(-0.418773\pi\) | ||||
0.252421 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(758\) | 14.2184i | 0.516435i | ||||||||
\(759\) | −12.1366 | − | 6.02424i | −0.440529 | − | 0.218666i | ||||
\(760\) | −1.83758 | −0.0666560 | ||||||||
\(761\) | 6.82083 | + | 11.8140i | 0.247255 | + | 0.428258i | 0.962763 | − | 0.270346i | \(-0.0871381\pi\) |
−0.715508 | + | 0.698604i | \(0.753805\pi\) | |||||||
\(762\) | 3.52689 | − | 7.10536i | 0.127766 | − | 0.257400i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 27.4991i | 0.994884i | ||||||||
\(765\) | 3.13165 | − | 0.395790i | 0.113225 | − | 0.0143098i | ||||
\(766\) | −39.0500 | + | 22.5455i | −1.41093 | + | 0.814602i | ||||
\(767\) | −13.1365 | − | 7.58434i | −0.474330 | − | 0.273855i | ||||
\(768\) | 32.5263 | + | 16.1451i | 1.17369 | + | 0.582587i | ||||
\(769\) | 22.9328 | + | 13.2402i | 0.826976 | + | 0.477455i | 0.852816 | − | 0.522211i | \(-0.174893\pi\) |
−0.0258399 | + | 0.999666i | \(0.508226\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.360583 | − | 5.72884i | −0.0129861 | − | 0.206319i | ||||
\(772\) | 22.9104 | 0.824562 | ||||||||
\(773\) | 13.1109 | + | 22.7087i | 0.471566 | + | 0.816776i | 0.999471 | − | 0.0325274i | \(-0.0103556\pi\) |
−0.527905 | + | 0.849303i | \(0.677022\pi\) | |||||||
\(774\) | 15.3300 | + | 6.44317i | 0.551026 | + | 0.231595i | ||||
\(775\) | 22.4945 | + | 12.9872i | 0.808026 | + | 0.466514i | ||||
\(776\) | −9.80047 | − | 16.9749i | −0.351816 | − | 0.609364i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.88703 | − | 10.1966i | 0.211060 | − | 0.365567i | ||||
\(779\) | 25.0451 | − | 14.4598i | 0.897334 | − | 0.518076i | ||||
\(780\) | 3.45732 | − | 6.96519i | 0.123792 | − | 0.249394i | ||||
\(781\) | 12.6678 | − | 21.9413i | 0.453291 | − | 0.785123i | ||||
\(782\) | 2.19701 | − | 3.80533i | 0.0785649 | − | 0.136078i | ||||
\(783\) | −25.2445 | − | 29.2412i | −0.902164 | − | 1.04500i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.11272 | − | 0.642430i | 0.0397148 | − | 0.0229293i | ||||
\(786\) | −8.02648 | + | 0.505200i | −0.286295 | + | 0.0180199i | ||||
\(787\) | 29.0470i | 1.03541i | 0.855558 | + | 0.517706i | \(0.173214\pi\) | ||||
−0.855558 | + | 0.517706i | \(0.826786\pi\) | |||||||
\(788\) | 25.3769i | 0.904014i | ||||||||
\(789\) | −21.7494 | − | 32.7336i | −0.774300 | − | 1.16535i | ||||
\(790\) | −7.13088 | + | 4.11702i | −0.253705 | + | 0.146477i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 18.6581 | − | 2.35809i | 0.662987 | − | 0.0837909i | ||||
\(793\) | 27.1761 | − | 47.0704i | 0.965052 | − | 1.67152i | ||||
\(794\) | 12.1463 | − | 21.0380i | 0.431055 | − | 0.746610i | ||||
\(795\) | 1.46161 | + | 2.19977i | 0.0518379 | + | 0.0780178i | ||||
\(796\) | 21.1952 | − | 12.2371i | 0.751245 | − | 0.433731i | ||||
\(797\) | 15.8184 | − | 27.3983i | 0.560317 | − | 0.970498i | −0.437151 | − | 0.899388i | \(-0.644013\pi\) |
0.997469 | − | 0.0711097i | \(-0.0226540\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.51286 | − | 4.35240i | −0.0888986 | − | 0.153977i | ||||
\(800\) | −26.0738 | − | 15.0537i | −0.921848 | − | 0.532229i | ||||
\(801\) | −12.8778 | + | 1.62754i | −0.455014 | + | 0.0575064i | ||||
\(802\) | 14.4777 | + | 25.0762i | 0.511227 | + | 0.885470i | ||||
\(803\) | −62.7577 | −2.21467 | ||||||||
\(804\) | 21.3684 | + | 10.6066i | 0.753605 | + | 0.374068i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −46.1032 | − | 26.6177i | −1.62392 | − | 0.937569i | ||||
\(807\) | 0.300405 | + | 4.77276i | 0.0105748 | + | 0.168009i | ||||
\(808\) | 4.75044 | + | 2.74267i | 0.167120 | + | 0.0964868i | ||||
\(809\) | 34.5466 | − | 19.9455i | 1.21459 | − | 0.701245i | 0.250836 | − | 0.968029i | \(-0.419294\pi\) |
0.963756 | + | 0.266784i | \(0.0859610\pi\) | |||||||
\(810\) | −2.64823 | − | 10.3096i | −0.0930493 | − | 0.362242i | ||||
\(811\) | − | 28.9516i | − | 1.01663i | −0.861172 | − | 0.508314i | \(-0.830269\pi\) | ||
0.861172 | − | 0.508314i | \(-0.169731\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.83676 | − | 8.78452i | −0.204704 | − | 0.308087i | ||||
\(814\) | −38.9300 | − | 67.4288i | −1.36450 | − | 2.36338i | ||||
\(815\) | 3.86521 | 0.135392 | ||||||||
\(816\) | 0.864154 | + | 13.7294i | 0.0302514 | + | 0.480627i | ||||
\(817\) | − | 7.30317i | − | 0.255505i | ||||||
\(818\) | 9.92684 | 0.347084 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.4905 | −0.366344 | ||||||||
\(821\) | 0.414973i | 0.0144826i | 0.999974 | + | 0.00724132i | \(0.00230500\pi\) | ||||
−0.999974 | + | 0.00724132i | \(0.997695\pi\) | |||||||
\(822\) | 3.20566 | − | 2.12996i | 0.111810 | − | 0.0742909i | ||||
\(823\) | −13.0963 | −0.456508 | −0.228254 | − | 0.973602i | \(-0.573302\pi\) | ||||
−0.228254 | + | 0.973602i | \(0.573302\pi\) | |||||||
\(824\) | 6.07570 | + | 10.5234i | 0.211657 | + | 0.366601i | ||||
\(825\) | −42.1168 | + | 2.65090i | −1.46632 | + | 0.0922926i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.2637i | 1.22624i | 0.789990 | + | 0.613120i | \(0.210086\pi\) | ||||
−0.789990 | + | 0.613120i | \(0.789914\pi\) | |||||||
\(828\) | −5.51998 | − | 2.32004i | −0.191833 | − | 0.0806268i | ||||
\(829\) | 29.0164 | − | 16.7526i | 1.00778 | − | 0.581842i | 0.0972388 | − | 0.995261i | \(-0.468999\pi\) |
0.910541 | + | 0.413419i | \(0.135666\pi\) | |||||||
\(830\) | −7.20287 | − | 4.15858i | −0.250015 | − | 0.144346i | ||||
\(831\) | 13.6094 | − | 9.04256i | 0.472103 | − | 0.313683i | ||||
\(832\) | 10.1621 | + | 5.86710i | 0.352308 | + | 0.203405i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 18.6696 | − | 12.4048i | 0.646474 | − | 0.429542i | ||||
\(835\) | −0.901200 | −0.0311873 | ||||||||
\(836\) | 8.70178 | + | 15.0719i | 0.300957 | + | 0.521273i | ||||
\(837\) | −28.9259 | + | 5.52032i | −0.999825 | + | 0.190810i | ||||
\(838\) | 38.8615 | + | 22.4367i | 1.34245 | + | 0.775062i | ||||
\(839\) | −22.4984 | − | 38.9684i | −0.776731 | − | 1.34534i | −0.933816 | − | 0.357753i | \(-0.883543\pi\) |
0.157085 | − | 0.987585i | \(-0.449790\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.1358 | − | 22.7519i | 0.452959 | − | 0.784548i | ||||
\(842\) | −19.0182 | + | 10.9802i | −0.655412 | + | 0.378402i | ||||
\(843\) | 9.12501 | − | 0.574343i | 0.314282 | − | 0.0197814i | ||||
\(844\) | 5.47260 | − | 9.47882i | 0.188375 | − | 0.326275i | ||||
\(845\) | −4.28985 | + | 7.43024i | −0.147575 | + | 0.255608i | ||||
\(846\) | −13.4985 | + | 10.2470i | −0.464087 | + | 0.352301i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.96802 | + | 5.75504i | −0.342303 | + | 0.197629i | ||||
\(849\) | 15.1476 | − | 30.5167i | 0.519864 | − | 1.04733i | ||||
\(850\) | − | 13.6853i | − | 0.469402i | ||||||
\(851\) | − | 11.7648i | − | 0.403291i | ||||||
\(852\) | 4.97797 | − | 10.0287i | 0.170542 | − | 0.343578i | ||||
\(853\) | 15.8457 | − | 9.14854i | 0.542548 | − | 0.313240i | −0.203563 | − | 0.979062i | \(-0.565252\pi\) |
0.746111 | + | 0.665822i | \(0.231919\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.72345 | + | 2.82657i | −0.127339 | + | 0.0966665i | ||||
\(856\) | −0.181929 | + | 0.315111i | −0.00621822 | + | 0.0107703i | ||||
\(857\) | 5.28926 | − | 9.16126i | 0.180678 | − | 0.312943i | −0.761434 | − | 0.648243i | \(-0.775504\pi\) |
0.942111 | + | 0.335300i | \(0.108838\pi\) | |||||||
\(858\) | 86.3198 | − | 5.43311i | 2.94691 | − | 0.185483i | ||||
\(859\) | −28.2972 | + | 16.3374i | −0.965488 | + | 0.557425i | −0.897858 | − | 0.440286i | \(-0.854877\pi\) |
−0.0676303 | + | 0.997710i | \(0.521544\pi\) | |||||||
\(860\) | −1.32460 | + | 2.29428i | −0.0451686 | + | 0.0782343i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.2332 | + | 48.9014i | 0.961628 | + | 1.66559i | ||||
\(863\) | −8.09878 | − | 4.67583i | −0.275686 | − | 0.159167i | 0.355783 | − | 0.934569i | \(-0.384214\pi\) |
−0.631469 | + | 0.775401i | \(0.717548\pi\) | |||||||
\(864\) | 33.5285 | − | 6.39871i | 1.14066 | − | 0.217689i | ||||
\(865\) | −2.45643 | − | 4.25465i | −0.0835210 | − | 0.144663i | ||||
\(866\) | 11.1052 | 0.377372 | ||||||||
\(867\) | 20.6925 | − | 13.7489i | 0.702755 | − | 0.466937i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.0517 | − | 18.5050i | −1.08728 | − | 0.627741i | ||||
\(870\) | 12.6847 | − | 8.42821i | 0.430053 | − | 0.285743i | ||||
\(871\) | −45.0925 | − | 26.0342i | −1.52790 | − | 0.882135i | ||||
\(872\) | −6.42216 | + | 3.70783i | −0.217482 | + | 0.125563i | ||||
\(873\) | −45.9693 | − | 19.3208i | −1.55583 | − | 0.653910i | ||||
\(874\) | 6.50742i | 0.220117i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −27.6788 | + | 1.74215i | −0.935181 | + | 0.0588618i | ||||
\(877\) | −0.619077 | − | 1.07227i | −0.0209048 | − | 0.0362081i | 0.855384 | − | 0.517995i | \(-0.173321\pi\) |
−0.876289 | + | 0.481787i | \(0.839988\pi\) | |||||||
\(878\) | −49.7300 | −1.67831 | ||||||||
\(879\) | 26.3035 | − | 17.4770i | 0.887195 | − | 0.589485i | ||||
\(880\) | 16.7233i | 0.563744i | ||||||||
\(881\) | 37.3480 | 1.25828 | 0.629142 | − | 0.777290i | \(-0.283406\pi\) | ||||
0.629142 | + | 0.777290i | \(0.283406\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.90708 | 0.131484 | 0.0657419 | − | 0.997837i | \(-0.479059\pi\) | ||||
0.0657419 | + | 0.997837i | \(0.479059\pi\) | |||||||
\(884\) | 11.3346i | 0.381224i | ||||||||
\(885\) | −0.207794 | − | 3.30138i | −0.00698493 | − | 0.110975i | ||||
\(886\) | 9.80432 | 0.329383 | ||||||||
\(887\) | 7.25578 | + | 12.5674i | 0.243625 | + | 0.421972i | 0.961744 | − | 0.273949i | \(-0.0883299\pi\) |
−0.718119 | + | 0.695920i | \(0.754997\pi\) | |||||||
\(888\) | 9.03691 | + | 13.6009i | 0.303259 | + | 0.456415i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 5.11722i | − | 0.171530i | ||||||
\(891\) | 34.1793 | − | 33.4781i | 1.14505 | − | 1.12156i | ||||
\(892\) | 27.4585 | − | 15.8532i | 0.919379 | − | 0.530804i | ||||
\(893\) | 6.44579 | + | 3.72148i | 0.215700 | + | 0.124534i | ||||
\(894\) | −1.38162 | − | 21.9507i | −0.0462081 | − | 0.734142i | ||||
\(895\) | −5.17028 | − | 2.98506i | −0.172823 | − | 0.0997797i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.7061 | + | 5.81056i | 0.390855 | + | 0.194009i | ||||
\(898\) | −62.7317 | −2.09339 | ||||||||
\(899\) | −21.0666 | − | 36.4884i | −0.702610 | − | 1.21696i | ||||
\(900\) | −18.5017 | + | 2.33832i | −0.616725 | + | 0.0779441i | ||||
\(901\) | −3.33395 | − | 1.92486i | −0.111070 | − | 0.0641263i | ||||
\(902\) | −58.3414 | − | 101.050i | −1.94256 | − | 3.36460i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.26201 | + | 9.11407i | −0.175012 | + | 0.303129i | ||||
\(905\) | 6.68849 | − | 3.86160i | 0.222333 | − | 0.128364i | ||||
\(906\) | −11.0962 | − | 16.7002i | −0.368647 | − | 0.554827i | ||||
\(907\) | 9.60695 | − | 16.6397i | 0.318993 | − | 0.552513i | −0.661285 | − | 0.750135i | \(-0.729989\pi\) |
0.980278 | + | 0.197622i | \(0.0633219\pi\) | |||||||
\(908\) | 9.79466 | − | 16.9648i | 0.325047 | − | 0.562998i | ||||
\(909\) | 13.8445 | − | 1.74972i | 0.459193 | − | 0.0580346i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.1252 | − | 5.84579i | 0.335463 | − | 0.193680i | −0.322801 | − | 0.946467i | \(-0.604624\pi\) |
0.658264 | + | 0.752787i | \(0.271291\pi\) | |||||||
\(912\) | −11.2748 | − | 16.9689i | −0.373345 | − | 0.561897i | ||||
\(913\) | − | 37.3837i | − | 1.23722i | ||||||
\(914\) | − | 29.0566i | − | 0.961106i | ||||||
\(915\) | 11.8295 | − | 0.744565i | 0.391070 | − | 0.0246146i | ||||
\(916\) | 15.4034 | − | 8.89314i | 0.508942 | − | 0.293838i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.1390 | + | 11.7443i | 0.334638 | + | 0.387619i | ||||
\(919\) | −19.9930 | + | 34.6289i | −0.659508 | + | 1.14230i | 0.321236 | + | 0.946999i | \(0.395902\pi\) |
−0.980743 | + | 0.195301i | \(0.937432\pi\) | |||||||
\(920\) | −0.560143 | + | 0.970196i | −0.0184674 | + | 0.0319864i | ||||
\(921\) | −20.0567 | + | 40.4067i | −0.660892 | + | 1.33145i | ||||
\(922\) | −20.6470 | + | 11.9205i | −0.679972 | + | 0.392582i | ||||
\(923\) | −12.2185 | + | 21.1631i | −0.402177 | + | 0.696591i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.3209 | − | 31.7326i | −0.602386 | − | 1.04336i | ||||
\(926\) | −19.1005 | − | 11.0277i | −0.627683 | − | 0.362393i | ||||
\(927\) | 28.4982 | + | 11.9777i | 0.936004 | + | 0.393401i | ||||
\(928\) | 24.4187 | + | 42.2944i | 0.801582 | + | 1.38838i | ||||
\(929\) | 12.7672 | 0.418877 | 0.209439 | − | 0.977822i | \(-0.432836\pi\) | ||||
0.209439 | + | 0.977822i | \(0.432836\pi\) | |||||||
\(930\) | −0.729267 | − | 11.5864i | −0.0239136 | − | 0.379933i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.92775 | + | 5.73179i | 0.325194 | + | 0.187751i | ||||
\(933\) | 43.8849 | + | 21.7832i | 1.43673 | + | 0.713149i | ||||
\(934\) | −32.2801 | − | 18.6369i | −1.05624 | − | 0.609818i | ||||
\(935\) | −4.84400 | + | 2.79669i | −0.158416 | + | 0.0914614i | ||||
\(936\) | −17.9963 | + | 2.27444i | −0.588228 | + | 0.0743425i | ||||
\(937\) | − | 11.9436i | − | 0.390179i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||
0.980785 | − | 0.195090i | \(-0.0624997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.29398 | + | 8.65074i | −0.140129 | + | 0.282306i | ||||
\(940\) | −1.34996 | − | 2.33819i | −0.0440307 | − | 0.0762634i | ||||
\(941\) | −25.0317 | −0.816011 | −0.408006 | − | 0.912979i | \(-0.633776\pi\) | ||||
−0.408006 | + | 0.912979i | \(0.633776\pi\) | |||||||
\(942\) | 5.65692 | + | 2.80793i | 0.184312 | + | 0.0914872i | ||||
\(943\) | − | 17.6309i | − | 0.574142i | ||||||
\(944\) | 14.4162 | 0.469208 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.4663 | −0.958032 | ||||||||
\(947\) | − | 32.7555i | − | 1.06441i | −0.846615 | − | 0.532205i | \(-0.821363\pi\) | ||
0.846615 | − | 0.532205i | \(-0.178637\pi\) | |||||||
\(948\) | −14.6499 | − | 7.27177i | −0.475806 | − | 0.236176i | ||||
\(949\) | 60.5316 | 1.96494 | ||||||||
\(950\) | 10.1338 | + | 17.5522i | 0.328783 | + | 0.569469i | ||||
\(951\) | −25.8504 | + | 52.0789i | −0.838258 | + | 1.68877i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.77705i | 0.219530i | 0.993958 | + | 0.109765i | \(0.0350099\pi\) | ||||
−0.993958 | + | 0.109765i | \(0.964990\pi\) | |||||||
\(954\) | −5.02996 | + | 11.9676i | −0.162851 | + | 0.387465i | ||||
\(955\) | 11.3353 | − | 6.54443i | 0.366801 | − | 0.211773i | ||||
\(956\) | 32.8378 | + | 18.9589i | 1.06205 | + | 0.613175i | ||||
\(957\) | 61.3150 | + | 30.4350i | 1.98203 | + | 0.983823i | ||||
\(958\) | 38.5512 | + | 22.2575i | 1.24553 | + | 0.719109i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.160746 | + | 2.55388i | 0.00518804 | + | 0.0824262i | ||||
\(961\) | −1.11779 | −0.0360578 | ||||||||
\(962\) | 37.5492 | + | 65.0371i | 1.21063 | + | 2.09688i | ||||
\(963\) | 0.116064 | + | 0.918346i | 0.00374012 | + | 0.0295933i | ||||
\(964\) | −26.3203 | − | 15.1960i | −0.847721 | − | 0.489432i | ||||
\(965\) | −5.45236 | − | 9.44377i | −0.175518 | − | 0.304006i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.7901 | − | 36.0096i | 0.668566 | − | 1.15799i | −0.309739 | − | 0.950822i | \(-0.600242\pi\) |
0.978305 | − | 0.207169i | \(-0.0664249\pi\) | |||||||
\(968\) | −17.6263 | + | 10.1765i | −0.566530 | + | 0.327086i | ||||
\(969\) | 3.02963 | − | 6.10355i | 0.0973256 | − | 0.196074i | ||||
\(970\) | 9.82910 | − | 17.0245i | 0.315593 | − | 0.546624i | ||||
\(971\) | 20.6257 | − | 35.7248i | 0.661910 | − | 1.14646i | −0.318203 | − | 0.948023i | \(-0.603079\pi\) |
0.980113 | − | 0.198439i | \(-0.0635873\pi\) | |||||||
\(972\) | 14.1452 | − | 15.7141i | 0.453707 | − | 0.504029i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −43.3281 | + | 25.0155i | −1.38832 | + | 0.801547i | ||||
\(975\) | 40.6229 | − | 2.55687i | 1.30098 | − | 0.0818855i | ||||
\(976\) | 51.6560i | 1.65347i | ||||||||
\(977\) | − | 4.57847i | − | 0.146478i | −0.997314 | − | 0.0732391i | \(-0.976666\pi\) | ||
0.997314 | − | 0.0732391i | \(-0.0233336\pi\) | |||||||
\(978\) | 10.5141 | + | 15.8241i | 0.336204 | + | 0.505998i | ||||
\(979\) | 19.9192 | − | 11.5004i | 0.636621 | − | 0.367553i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.30968 | + | 17.3917i | −0.233380 | + | 0.555273i | ||||
\(982\) | 14.0569 | − | 24.3473i | 0.448575 | − | 0.776955i | ||||
\(983\) | 12.2401 | − | 21.2004i | 0.390397 | − | 0.676188i | −0.602105 | − | 0.798417i | \(-0.705671\pi\) |
0.992502 | + | 0.122229i | \(0.0390044\pi\) | |||||||
\(984\) | 13.5429 | + | 20.3825i | 0.431732 | + | 0.649771i | ||||
\(985\) | 10.4605 | − | 6.03936i | 0.333299 | − | 0.192430i | ||||
\(986\) | −11.0995 | + | 19.2249i | −0.353480 | + | 0.612245i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.39312 | − | 14.5373i | −0.267021 | − | 0.462494i | ||||
\(989\) | −3.85589 | − | 2.22620i | −0.122610 | − | 0.0707890i | ||||
\(990\) | 11.4044 | + | 15.0231i | 0.362457 | + | 0.477466i | ||||
\(991\) | 21.0927 | + | 36.5337i | 0.670032 | + | 1.16053i | 0.977894 | + | 0.209099i | \(0.0670531\pi\) |
−0.307862 | + | 0.951431i | \(0.599614\pi\) | |||||||
\(992\) | 37.2284 | 1.18200 | ||||||||
\(993\) | −47.1226 | − | 23.3903i | −1.49539 | − | 0.742268i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.0884 | − | 5.82452i | −0.319822 | − | 0.184650i | ||||
\(996\) | −1.03777 | − | 16.4878i | −0.0328830 | − | 0.522437i | ||||
\(997\) | −8.38168 | − | 4.83917i | −0.265451 | − | 0.153258i | 0.361368 | − | 0.932423i | \(-0.382310\pi\) |
−0.626818 | + | 0.779165i | \(0.715643\pi\) | |||||||
\(998\) | −16.3578 | + | 9.44415i | −0.517796 | + | 0.298949i | ||||
\(999\) | 39.2321 | + | 13.6585i | 1.24125 | + | 0.432137i |
(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 | 441.2.i.d.68.18 | 48 | ||
3.2 | odd | 2 | 1323.2.i.d.1097.17 | 48 | |||
7.2 | even | 3 | 441.2.o.e.293.17 | yes | 48 | ||
7.3 | odd | 6 | 441.2.s.d.374.8 | 48 | |||
7.4 | even | 3 | 441.2.s.d.374.7 | 48 | |||
7.5 | odd | 6 | 441.2.o.e.293.18 | yes | 48 | ||
7.6 | odd | 2 | inner | 441.2.i.d.68.17 | 48 | ||
9.2 | odd | 6 | 441.2.s.d.362.8 | 48 | |||
9.7 | even | 3 | 1323.2.s.d.656.17 | 48 | |||
21.2 | odd | 6 | 1323.2.o.e.881.8 | 48 | |||
21.5 | even | 6 | 1323.2.o.e.881.7 | 48 | |||
21.11 | odd | 6 | 1323.2.s.d.962.18 | 48 | |||
21.17 | even | 6 | 1323.2.s.d.962.17 | 48 | |||
21.20 | even | 2 | 1323.2.i.d.1097.15 | 48 | |||
63.2 | odd | 6 | 441.2.o.e.146.18 | yes | 48 | ||
63.11 | odd | 6 | inner | 441.2.i.d.227.7 | 48 | ||
63.16 | even | 3 | 1323.2.o.e.440.7 | 48 | |||
63.20 | even | 6 | 441.2.s.d.362.7 | 48 | |||
63.25 | even | 3 | 1323.2.i.d.521.15 | 48 | |||
63.34 | odd | 6 | 1323.2.s.d.656.18 | 48 | |||
63.38 | even | 6 | inner | 441.2.i.d.227.8 | 48 | ||
63.47 | even | 6 | 441.2.o.e.146.17 | ✓ | 48 | ||
63.52 | odd | 6 | 1323.2.i.d.521.17 | 48 | |||
63.61 | odd | 6 | 1323.2.o.e.440.8 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.17 | 48 | 7.6 | odd | 2 | inner | ||
441.2.i.d.68.18 | 48 | 1.1 | even | 1 | trivial | ||
441.2.i.d.227.7 | 48 | 63.11 | odd | 6 | inner | ||
441.2.i.d.227.8 | 48 | 63.38 | even | 6 | inner | ||
441.2.o.e.146.17 | ✓ | 48 | 63.47 | even | 6 | ||
441.2.o.e.146.18 | yes | 48 | 63.2 | odd | 6 | ||
441.2.o.e.293.17 | yes | 48 | 7.2 | even | 3 | ||
441.2.o.e.293.18 | yes | 48 | 7.5 | odd | 6 | ||
441.2.s.d.362.7 | 48 | 63.20 | even | 6 | |||
441.2.s.d.362.8 | 48 | 9.2 | odd | 6 | |||
441.2.s.d.374.7 | 48 | 7.4 | even | 3 | |||
441.2.s.d.374.8 | 48 | 7.3 | odd | 6 | |||
1323.2.i.d.521.15 | 48 | 63.25 | even | 3 | |||
1323.2.i.d.521.17 | 48 | 63.52 | odd | 6 | |||
1323.2.i.d.1097.15 | 48 | 21.20 | even | 2 | |||
1323.2.i.d.1097.17 | 48 | 3.2 | odd | 2 | |||
1323.2.o.e.440.7 | 48 | 63.16 | even | 3 | |||
1323.2.o.e.440.8 | 48 | 63.61 | odd | 6 | |||
1323.2.o.e.881.7 | 48 | 21.5 | even | 6 | |||
1323.2.o.e.881.8 | 48 | 21.2 | odd | 6 | |||
1323.2.s.d.656.17 | 48 | 9.7 | even | 3 | |||
1323.2.s.d.656.18 | 48 | 63.34 | odd | 6 | |||
1323.2.s.d.962.17 | 48 | 21.17 | even | 6 | |||
1323.2.s.d.962.18 | 48 | 21.11 | odd | 6 |