Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(43,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.dk (of order \(6\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(168\) |
Relative dimension: | \(84\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 43.40 | ||
Character | \(\chi\) | \(=\) | 819.43 |
Dual form | 819.2.dk.a.400.40 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0786329 | + | 0.0453987i | −0.0556019 | + | 0.0321018i | −0.527543 | − | 0.849528i | \(-0.676887\pi\) |
0.471941 | + | 0.881630i | \(0.343553\pi\) | |||||||
\(3\) | 1.72806 | − | 0.117510i | 0.997696 | − | 0.0678445i | ||||
\(4\) | −0.995878 | + | 1.72491i | −0.497939 | + | 0.862456i | ||||
\(5\) | 0.215002 | − | 0.124132i | 0.0961519 | − | 0.0555133i | −0.451153 | − | 0.892447i | \(-0.648987\pi\) |
0.547305 | + | 0.836933i | \(0.315654\pi\) | |||||||
\(6\) | −0.130548 | + | 0.0876919i | −0.0532958 | + | 0.0358001i | ||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | − | 0.362441i | − | 0.128142i | ||||||
\(9\) | 2.97238 | − | 0.406129i | 0.990794 | − | 0.135376i | ||||
\(10\) | −0.0112708 | + | 0.0195217i | −0.00356415 | + | 0.00617329i | ||||
\(11\) | 3.63017 | − | 2.09588i | 1.09454 | − | 0.631931i | 0.159757 | − | 0.987156i | \(-0.448929\pi\) |
0.934781 | + | 0.355225i | \(0.115596\pi\) | |||||||
\(12\) | −1.51824 | + | 3.09778i | −0.438279 | + | 0.894251i | ||||
\(13\) | −1.61458 | + | 3.22384i | −0.447803 | + | 0.894132i | ||||
\(14\) | 0.0453987 | + | 0.0786329i | 0.0121333 | + | 0.0210155i | ||||
\(15\) | 0.356950 | − | 0.239772i | 0.0921641 | − | 0.0619088i | ||||
\(16\) | −1.97530 | − | 3.42132i | −0.493825 | − | 0.855331i | ||||
\(17\) | 3.04852 | + | 5.28019i | 0.739374 | + | 1.28063i | 0.952778 | + | 0.303669i | \(0.0982117\pi\) |
−0.213404 | + | 0.976964i | \(0.568455\pi\) | |||||||
\(18\) | −0.215289 | + | 0.166878i | −0.0507442 | + | 0.0393334i | ||||
\(19\) | 4.13786 | − | 2.38900i | 0.949291 | − | 0.548074i | 0.0564306 | − | 0.998407i | \(-0.482028\pi\) |
0.892861 | + | 0.450333i | \(0.148695\pi\) | |||||||
\(20\) | 0.494480i | 0.110569i | ||||||||
\(21\) | −0.117510 | − | 1.72806i | −0.0256428 | − | 0.377094i | ||||
\(22\) | −0.190301 | + | 0.329610i | −0.0405722 | + | 0.0702732i | ||||
\(23\) | −1.30384 | −0.271869 | −0.135934 | − | 0.990718i | \(-0.543404\pi\) | ||||
−0.135934 | + | 0.990718i | \(0.543404\pi\) | |||||||
\(24\) | −0.0425905 | − | 0.626321i | −0.00869375 | − | 0.127847i | ||||
\(25\) | −2.46918 | + | 4.27675i | −0.493837 | + | 0.855350i | ||||
\(26\) | −0.0193993 | − | 0.326800i | −0.00380452 | − | 0.0640907i | ||||
\(27\) | 5.08873 | − | 1.05110i | 0.979327 | − | 0.202284i | ||||
\(28\) | 1.72491 | + | 0.995878i | 0.325978 | + | 0.188203i | ||||
\(29\) | −0.828897 | − | 1.43569i | −0.153922 | − | 0.266601i | 0.778744 | − | 0.627342i | \(-0.215857\pi\) |
−0.932666 | + | 0.360741i | \(0.882524\pi\) | |||||||
\(30\) | −0.0171827 | + | 0.0350590i | −0.00313712 | + | 0.00640088i | ||||
\(31\) | 5.08430 | − | 2.93542i | 0.913168 | − | 0.527218i | 0.0317186 | − | 0.999497i | \(-0.489902\pi\) |
0.881449 | + | 0.472279i | \(0.156569\pi\) | |||||||
\(32\) | 0.938415 | + | 0.541794i | 0.165890 | + | 0.0957765i | ||||
\(33\) | 6.02686 | − | 4.04839i | 1.04914 | − | 0.704734i | ||||
\(34\) | −0.479428 | − | 0.276798i | −0.0822212 | − | 0.0474704i | ||||
\(35\) | −0.124132 | − | 0.215002i | −0.0209821 | − | 0.0363420i | ||||
\(36\) | −2.25959 | + | 5.53155i | −0.376599 | + | 0.921925i | ||||
\(37\) | −4.52192 | − | 2.61073i | −0.743399 | − | 0.429201i | 0.0799050 | − | 0.996802i | \(-0.474538\pi\) |
−0.823304 | + | 0.567601i | \(0.807872\pi\) | |||||||
\(38\) | −0.216915 | + | 0.375708i | −0.0351883 | + | 0.0609478i | ||||
\(39\) | −2.41125 | + | 5.76072i | −0.386109 | + | 0.922453i | ||||
\(40\) | −0.0449904 | − | 0.0779257i | −0.00711361 | − | 0.0123211i | ||||
\(41\) | 9.35757i | 1.46141i | 0.682695 | + | 0.730704i | \(0.260808\pi\) | ||||
−0.682695 | + | 0.730704i | \(0.739192\pi\) | |||||||
\(42\) | 0.0876919 | + | 0.130548i | 0.0135312 | + | 0.0201439i | ||||
\(43\) | 7.41985 | 1.13152 | 0.565758 | − | 0.824571i | \(-0.308584\pi\) | ||||
0.565758 | + | 0.824571i | \(0.308584\pi\) | |||||||
\(44\) | 8.34896i | 1.25865i | ||||||||
\(45\) | 0.588655 | − | 0.456285i | 0.0877516 | − | 0.0680190i | ||||
\(46\) | 0.102524 | − | 0.0591925i | 0.0151164 | − | 0.00872746i | ||||
\(47\) | 5.25270 | + | 3.03265i | 0.766185 | + | 0.442357i | 0.831512 | − | 0.555507i | \(-0.187476\pi\) |
−0.0653270 | + | 0.997864i | \(0.520809\pi\) | |||||||
\(48\) | −3.81548 | − | 5.68013i | −0.550717 | − | 0.819857i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | − | 0.448391i | − | 0.0634121i | ||||||
\(51\) | 5.88849 | + | 8.76625i | 0.824554 | + | 1.22752i | ||||
\(52\) | −3.95291 | − | 5.99555i | −0.548171 | − | 0.831434i | ||||
\(53\) | −10.8656 | −1.49251 | −0.746255 | − | 0.665660i | \(-0.768150\pi\) | ||||
−0.746255 | + | 0.665660i | \(0.768150\pi\) | |||||||
\(54\) | −0.352423 | + | 0.313673i | −0.0479587 | + | 0.0426855i | ||||
\(55\) | 0.520330 | − | 0.901237i | 0.0701612 | − | 0.121523i | ||||
\(56\) | −0.362441 | −0.0484333 | ||||||||
\(57\) | 6.86975 | − | 4.61457i | 0.909920 | − | 0.611215i | ||||
\(58\) | 0.130357 | + | 0.0752618i | 0.0171167 | + | 0.00988236i | ||||
\(59\) | 3.38619 | + | 1.95502i | 0.440845 | + | 0.254522i | 0.703956 | − | 0.710244i | \(-0.251415\pi\) |
−0.263111 | + | 0.964766i | \(0.584749\pi\) | |||||||
\(60\) | 0.0581063 | + | 0.854490i | 0.00750150 | + | 0.110314i | ||||
\(61\) | −6.12360 | −0.784047 | −0.392023 | − | 0.919955i | \(-0.628225\pi\) | ||||
−0.392023 | + | 0.919955i | \(0.628225\pi\) | |||||||
\(62\) | −0.266529 | + | 0.461642i | −0.0338492 | + | 0.0586286i | ||||
\(63\) | −0.406129 | − | 2.97238i | −0.0511674 | − | 0.374485i | ||||
\(64\) | 7.80282 | 0.975352 | ||||||||
\(65\) | 0.0530427 | + | 0.893553i | 0.00657913 | + | 0.110832i | ||||
\(66\) | −0.290118 | + | 0.591949i | −0.0357111 | + | 0.0728638i | ||||
\(67\) | 6.50443i | 0.794643i | 0.917679 | + | 0.397321i | \(0.130060\pi\) | ||||
−0.917679 | + | 0.397321i | \(0.869940\pi\) | |||||||
\(68\) | −12.1438 | −1.47265 | ||||||||
\(69\) | −2.25311 | + | 0.153214i | −0.271242 | + | 0.0184448i | ||||
\(70\) | 0.0195217 | + | 0.0112708i | 0.00233328 | + | 0.00134712i | ||||
\(71\) | 0.413219 | − | 0.238572i | 0.0490401 | − | 0.0283133i | −0.475279 | − | 0.879835i | \(-0.657653\pi\) |
0.524320 | + | 0.851522i | \(0.324320\pi\) | |||||||
\(72\) | −0.147198 | − | 1.07731i | −0.0173474 | − | 0.126963i | ||||
\(73\) | − | 6.41037i | − | 0.750278i | −0.926969 | − | 0.375139i | \(-0.877595\pi\) | ||
0.926969 | − | 0.375139i | \(-0.122405\pi\) | |||||||
\(74\) | 0.474096 | 0.0551125 | ||||||||
\(75\) | −3.76433 | + | 7.68063i | −0.434668 | + | 0.886883i | ||||
\(76\) | 9.51660i | 1.09163i | ||||||||
\(77\) | −2.09588 | − | 3.63017i | −0.238848 | − | 0.413696i | ||||
\(78\) | −0.0719255 | − | 0.562450i | −0.00814396 | − | 0.0636849i | ||||
\(79\) | 3.66713 | − | 6.35166i | 0.412585 | − | 0.714618i | −0.582587 | − | 0.812768i | \(-0.697959\pi\) |
0.995172 | + | 0.0981508i | \(0.0312928\pi\) | |||||||
\(80\) | −0.849388 | − | 0.490395i | −0.0949645 | − | 0.0548278i | ||||
\(81\) | 8.67012 | − | 2.41434i | 0.963347 | − | 0.268260i | ||||
\(82\) | −0.424822 | − | 0.735813i | −0.0469137 | − | 0.0812570i | ||||
\(83\) | −13.9306 | − | 8.04285i | −1.52908 | − | 0.882818i | −0.999400 | − | 0.0346227i | \(-0.988977\pi\) |
−0.529684 | − | 0.848195i | \(-0.677690\pi\) | |||||||
\(84\) | 3.09778 | + | 1.51824i | 0.337995 | + | 0.165654i | ||||
\(85\) | 1.31088 | + | 0.756834i | 0.142184 | + | 0.0820902i | ||||
\(86\) | −0.583445 | + | 0.336852i | −0.0629145 | + | 0.0363237i | ||||
\(87\) | −1.60109 | − | 2.38356i | −0.171655 | − | 0.255544i | ||||
\(88\) | −0.759634 | − | 1.31572i | −0.0809772 | − | 0.140257i | ||||
\(89\) | −3.63694 | − | 2.09979i | −0.385515 | − | 0.222577i | 0.294700 | − | 0.955590i | \(-0.404780\pi\) |
−0.680215 | + | 0.733013i | \(0.738114\pi\) | |||||||
\(90\) | −0.0255729 | + | 0.0626033i | −0.00269562 | + | 0.00659896i | ||||
\(91\) | 3.22384 | + | 1.61458i | 0.337950 | + | 0.169254i | ||||
\(92\) | 1.29846 | − | 2.24900i | 0.135374 | − | 0.234475i | ||||
\(93\) | 8.44104 | − | 5.67004i | 0.875295 | − | 0.587956i | ||||
\(94\) | −0.550714 | −0.0568018 | ||||||||
\(95\) | 0.593100 | − | 1.02728i | 0.0608508 | − | 0.105397i | ||||
\(96\) | 1.68530 | + | 0.825979i | 0.172005 | + | 0.0843011i | ||||
\(97\) | − | 11.0898i | − | 1.12600i | −0.826457 | − | 0.563000i | \(-0.809647\pi\) | ||
0.826457 | − | 0.563000i | \(-0.190353\pi\) | |||||||
\(98\) | 0.0786329 | − | 0.0453987i | 0.00794313 | − | 0.00458597i | ||||
\(99\) | 9.93906 | − | 7.70407i | 0.998913 | − | 0.774289i | ||||
\(100\) | −4.91801 | − | 8.51824i | −0.491801 | − | 0.851824i | ||||
\(101\) | −0.573753 | − | 0.993770i | −0.0570906 | − | 0.0988838i | 0.836068 | − | 0.548626i | \(-0.184849\pi\) |
−0.893158 | + | 0.449743i | \(0.851516\pi\) | |||||||
\(102\) | −0.861006 | − | 0.421985i | −0.0852523 | − | 0.0417828i | ||||
\(103\) | −8.55696 | − | 14.8211i | −0.843143 | − | 1.46037i | −0.887225 | − | 0.461338i | \(-0.847370\pi\) |
0.0440819 | − | 0.999028i | \(-0.485964\pi\) | |||||||
\(104\) | 1.16845 | + | 0.585190i | 0.114576 | + | 0.0573826i | ||||
\(105\) | −0.239772 | − | 0.356950i | −0.0233993 | − | 0.0348348i | ||||
\(106\) | 0.854398 | − | 0.493287i | 0.0829864 | − | 0.0479122i | ||||
\(107\) | −3.39001 | + | 5.87167i | −0.327725 | + | 0.567636i | −0.982060 | − | 0.188569i | \(-0.939615\pi\) |
0.654335 | + | 0.756205i | \(0.272948\pi\) | |||||||
\(108\) | −3.25470 | + | 9.82438i | −0.313184 | + | 0.945351i | ||||
\(109\) | 4.64711i | 0.445112i | 0.974920 | + | 0.222556i | \(0.0714401\pi\) | ||||
−0.974920 | + | 0.222556i | \(0.928560\pi\) | |||||||
\(110\) | 0.0944893i | 0.00900920i | ||||||||
\(111\) | −8.12093 | − | 3.98013i | −0.770805 | − | 0.377777i | ||||
\(112\) | −3.42132 | + | 1.97530i | −0.323285 | + | 0.186648i | ||||
\(113\) | 4.92021 | − | 8.52206i | 0.462855 | − | 0.801688i | −0.536247 | − | 0.844061i | \(-0.680158\pi\) |
0.999102 | + | 0.0423731i | \(0.0134918\pi\) | |||||||
\(114\) | −0.330693 | + | 0.674735i | −0.0309722 | + | 0.0631947i | ||||
\(115\) | −0.280328 | + | 0.161847i | −0.0261407 | + | 0.0150923i | ||||
\(116\) | 3.30192 | 0.306576 | ||||||||
\(117\) | −3.48985 | + | 10.2382i | −0.322636 | + | 0.946523i | ||||
\(118\) | −0.355022 | −0.0326824 | ||||||||
\(119\) | 5.28019 | − | 3.04852i | 0.484034 | − | 0.279457i | ||||
\(120\) | −0.0869032 | − | 0.129373i | −0.00793314 | − | 0.0118101i | ||||
\(121\) | 3.28542 | − | 5.69052i | 0.298675 | − | 0.517320i | ||||
\(122\) | 0.481517 | − | 0.278004i | 0.0435945 | − | 0.0251693i | ||||
\(123\) | 1.09961 | + | 16.1704i | 0.0991484 | + | 1.45804i | ||||
\(124\) | 11.6933i | 1.05009i | ||||||||
\(125\) | 2.46733i | 0.220685i | ||||||||
\(126\) | 0.166878 | + | 0.215289i | 0.0148666 | + | 0.0191795i | ||||
\(127\) | 3.18365 | − | 5.51424i | 0.282503 | − | 0.489310i | −0.689497 | − | 0.724288i | \(-0.742169\pi\) |
0.972001 | + | 0.234978i | \(0.0755019\pi\) | |||||||
\(128\) | −2.49039 | + | 1.43783i | −0.220121 | + | 0.127087i | ||||
\(129\) | 12.8219 | − | 0.871907i | 1.12891 | − | 0.0767672i | ||||
\(130\) | −0.0447371 | − | 0.0678546i | −0.00392370 | − | 0.00595124i | ||||
\(131\) | −0.408486 | − | 0.707518i | −0.0356896 | − | 0.0618162i | 0.847629 | − | 0.530590i | \(-0.178029\pi\) |
−0.883318 | + | 0.468773i | \(0.844696\pi\) | |||||||
\(132\) | 0.981087 | + | 14.4275i | 0.0853927 | + | 1.25575i | ||||
\(133\) | −2.38900 | − | 4.13786i | −0.207152 | − | 0.358798i | ||||
\(134\) | −0.295293 | − | 0.511463i | −0.0255094 | − | 0.0441836i | ||||
\(135\) | 0.963614 | − | 0.857661i | 0.0829347 | − | 0.0738157i | ||||
\(136\) | 1.91376 | − | 1.10491i | 0.164103 | − | 0.0947451i | ||||
\(137\) | 17.4176i | 1.48809i | 0.668131 | + | 0.744044i | \(0.267095\pi\) | ||||
−0.668131 | + | 0.744044i | \(0.732905\pi\) | |||||||
\(138\) | 0.170213 | − | 0.114336i | 0.0144895 | − | 0.00973291i | ||||
\(139\) | 5.11812 | − | 8.86485i | 0.434114 | − | 0.751907i | −0.563109 | − | 0.826382i | \(-0.690395\pi\) |
0.997223 | + | 0.0744757i | \(0.0237283\pi\) | |||||||
\(140\) | 0.494480 | 0.0417912 | ||||||||
\(141\) | 9.43335 | + | 4.62335i | 0.794431 | + | 0.389356i | ||||
\(142\) | −0.0216618 | + | 0.0375193i | −0.00181781 | + | 0.00314855i | ||||
\(143\) | 0.895590 | + | 15.0870i | 0.0748930 | + | 1.26164i | ||||
\(144\) | −7.26085 | − | 9.36725i | −0.605071 | − | 0.780604i | ||||
\(145\) | −0.356430 | − | 0.205785i | −0.0295999 | − | 0.0170895i | ||||
\(146\) | 0.291023 | + | 0.504067i | 0.0240852 | + | 0.0417168i | ||||
\(147\) | −1.72806 | + | 0.117510i | −0.142528 | + | 0.00969207i | ||||
\(148\) | 9.00656 | − | 5.19994i | 0.740334 | − | 0.427432i | ||||
\(149\) | 2.22584 | + | 1.28509i | 0.182348 | + | 0.105279i | 0.588395 | − | 0.808573i | \(-0.299760\pi\) |
−0.406047 | + | 0.913852i | \(0.633093\pi\) | |||||||
\(150\) | −0.0526905 | − | 0.774847i | −0.00430216 | − | 0.0632660i | ||||
\(151\) | −8.85960 | − | 5.11509i | −0.720984 | − | 0.416261i | 0.0941305 | − | 0.995560i | \(-0.469993\pi\) |
−0.815115 | + | 0.579299i | \(0.803326\pi\) | |||||||
\(152\) | −0.865872 | − | 1.49973i | −0.0702315 | − | 0.121644i | ||||
\(153\) | 11.2058 | + | 14.4566i | 0.905935 | + | 1.16875i | ||||
\(154\) | 0.329610 | + | 0.190301i | 0.0265608 | + | 0.0153349i | ||||
\(155\) | 0.728757 | − | 1.26224i | 0.0585352 | − | 0.101386i | ||||
\(156\) | −7.53541 | − | 9.89617i | −0.603316 | − | 0.792327i | ||||
\(157\) | −8.24495 | − | 14.2807i | −0.658018 | − | 1.13972i | −0.981128 | − | 0.193360i | \(-0.938062\pi\) |
0.323110 | − | 0.946362i | \(-0.395272\pi\) | |||||||
\(158\) | 0.665933i | 0.0529788i | ||||||||
\(159\) | −18.7765 | + | 1.27682i | −1.48907 | + | 0.101259i | ||||
\(160\) | 0.269015 | 0.0212675 | ||||||||
\(161\) | 1.30384i | 0.102757i | ||||||||
\(162\) | −0.572149 | + | 0.583459i | −0.0449523 | + | 0.0458409i | ||||
\(163\) | −5.81904 | + | 3.35963i | −0.455783 | + | 0.263146i | −0.710269 | − | 0.703930i | \(-0.751427\pi\) |
0.254487 | + | 0.967076i | \(0.418093\pi\) | |||||||
\(164\) | −16.1410 | − | 9.31900i | −1.26040 | − | 0.727691i | ||||
\(165\) | 0.793256 | − | 1.61854i | 0.0617549 | − | 0.126003i | ||||
\(166\) | 1.46054 | 0.113360 | ||||||||
\(167\) | − | 21.9842i | − | 1.70119i | −0.525822 | − | 0.850594i | \(-0.676242\pi\) | ||
0.525822 | − | 0.850594i | \(-0.323758\pi\) | |||||||
\(168\) | −0.626321 | + | 0.0425905i | −0.0483217 | + | 0.00328593i | ||||
\(169\) | −7.78628 | − | 10.4103i | −0.598945 | − | 0.800790i | ||||
\(170\) | −0.137437 | −0.0105410 | ||||||||
\(171\) | 11.3291 | − | 8.78152i | 0.866356 | − | 0.671540i | ||||
\(172\) | −7.38927 | + | 12.7986i | −0.563426 | + | 0.975883i | ||||
\(173\) | −25.4451 | −1.93455 | −0.967277 | − | 0.253723i | \(-0.918345\pi\) | ||||
−0.967277 | + | 0.253723i | \(0.918345\pi\) | |||||||
\(174\) | 0.234109 | + | 0.114739i | 0.0177478 | + | 0.00869831i | ||||
\(175\) | 4.27675 | + | 2.46918i | 0.323292 | + | 0.186653i | ||||
\(176\) | −14.3414 | − | 8.27999i | −1.08102 | − | 0.624128i | ||||
\(177\) | 6.08128 | + | 2.98048i | 0.457097 | + | 0.224027i | ||||
\(178\) | 0.381311 | 0.0285805 | ||||||||
\(179\) | −10.7336 | + | 18.5911i | −0.802265 | + | 1.38956i | 0.115858 | + | 0.993266i | \(0.463038\pi\) |
−0.918122 | + | 0.396297i | \(0.870295\pi\) | |||||||
\(180\) | 0.200822 | + | 1.46978i | 0.0149684 | + | 0.109551i | ||||
\(181\) | 14.5711 | 1.08306 | 0.541532 | − | 0.840680i | \(-0.317845\pi\) | ||||
0.541532 | + | 0.840680i | \(0.317845\pi\) | |||||||
\(182\) | −0.326800 | + | 0.0193993i | −0.0242240 | + | 0.00143797i | ||||
\(183\) | −10.5820 | + | 0.719585i | −0.782240 | + | 0.0531933i | ||||
\(184\) | 0.472564i | 0.0348379i | ||||||||
\(185\) | −1.29630 | −0.0953056 | ||||||||
\(186\) | −0.406331 | + | 0.829065i | −0.0297936 | + | 0.0607900i | ||||
\(187\) | 22.1333 | + | 12.7786i | 1.61854 | + | 0.934467i | ||||
\(188\) | −10.4621 | + | 6.04029i | −0.763027 | + | 0.440534i | ||||
\(189\) | −1.05110 | − | 5.08873i | −0.0764563 | − | 0.370151i | ||||
\(190\) | 0.107704i | 0.00781367i | ||||||||
\(191\) | −6.82420 | −0.493782 | −0.246891 | − | 0.969043i | \(-0.579409\pi\) | ||||
−0.246891 | + | 0.969043i | \(0.579409\pi\) | |||||||
\(192\) | 13.4837 | − | 0.916910i | 0.973105 | − | 0.0661723i | ||||
\(193\) | − | 8.37235i | − | 0.602655i | −0.953521 | − | 0.301327i | \(-0.902570\pi\) | ||
0.953521 | − | 0.301327i | \(-0.0974297\pi\) | |||||||
\(194\) | 0.503464 | + | 0.872025i | 0.0361466 | + | 0.0626077i | ||||
\(195\) | 0.196662 | + | 1.53788i | 0.0140833 | + | 0.110130i | ||||
\(196\) | 0.995878 | − | 1.72491i | 0.0711341 | − | 0.123208i | ||||
\(197\) | 4.82227 | + | 2.78414i | 0.343573 | + | 0.198362i | 0.661851 | − | 0.749636i | \(-0.269771\pi\) |
−0.318278 | + | 0.947997i | \(0.603105\pi\) | |||||||
\(198\) | −0.431782 | + | 1.05701i | −0.0306854 | + | 0.0751188i | ||||
\(199\) | −4.99237 | − | 8.64704i | −0.353900 | − | 0.612972i | 0.633029 | − | 0.774128i | \(-0.281811\pi\) |
−0.986929 | + | 0.161155i | \(0.948478\pi\) | |||||||
\(200\) | 1.55007 | + | 0.894934i | 0.109607 | + | 0.0632814i | ||||
\(201\) | 0.764336 | + | 11.2401i | 0.0539121 | + | 0.792812i | ||||
\(202\) | 0.0902318 | + | 0.0520954i | 0.00634869 | + | 0.00366542i | ||||
\(203\) | −1.43569 | + | 0.828897i | −0.100766 | + | 0.0581772i | ||||
\(204\) | −20.9852 | + | 1.42702i | −1.46926 | + | 0.0999113i | ||||
\(205\) | 1.16157 | + | 2.01190i | 0.0811276 | + | 0.140517i | ||||
\(206\) | 1.34572 | + | 0.776951i | 0.0937606 | + | 0.0541327i | ||||
\(207\) | −3.87550 | + | 0.529525i | −0.269366 | + | 0.0368046i | ||||
\(208\) | 14.2191 | − | 0.844066i | 0.985915 | − | 0.0585254i | ||||
\(209\) | 10.0141 | − | 17.3449i | 0.692690 | − | 1.19977i | ||||
\(210\) | 0.0350590 | + | 0.0171827i | 0.00241930 | + | 0.00118572i | ||||
\(211\) | −18.6837 | −1.28624 | −0.643118 | − | 0.765767i | \(-0.722359\pi\) | ||||
−0.643118 | + | 0.765767i | \(0.722359\pi\) | |||||||
\(212\) | 10.8209 | − | 18.7423i | 0.743179 | − | 1.28722i | ||||
\(213\) | 0.686033 | − | 0.460825i | 0.0470062 | − | 0.0315752i | ||||
\(214\) | − | 0.615609i | − | 0.0420822i | ||||||
\(215\) | 1.59528 | − | 0.921038i | 0.108797 | − | 0.0628143i | ||||
\(216\) | −0.380962 | − | 1.84437i | −0.0259212 | − | 0.125493i | ||||
\(217\) | −2.93542 | − | 5.08430i | −0.199269 | − | 0.345145i | ||||
\(218\) | −0.210973 | − | 0.365416i | −0.0142889 | − | 0.0247491i | ||||
\(219\) | −0.753284 | − | 11.0775i | −0.0509022 | − | 0.748549i | ||||
\(220\) | 1.03637 | + | 1.79505i | 0.0698720 | + | 0.121022i | ||||
\(221\) | −21.9445 | + | 1.30266i | −1.47615 | + | 0.0876265i | ||||
\(222\) | 0.819266 | − | 0.0557110i | 0.0549855 | − | 0.00373908i | ||||
\(223\) | −13.3816 | + | 7.72586i | −0.896097 | + | 0.517362i | −0.875932 | − | 0.482435i | \(-0.839753\pi\) |
−0.0201654 | + | 0.999797i | \(0.506419\pi\) | |||||||
\(224\) | 0.541794 | − | 0.938415i | 0.0362001 | − | 0.0627005i | ||||
\(225\) | −5.60244 | + | 13.7149i | −0.373496 | + | 0.914330i | ||||
\(226\) | 0.893486i | 0.0594338i | ||||||||
\(227\) | 13.3297i | 0.884726i | 0.896836 | + | 0.442363i | \(0.145860\pi\) | ||||
−0.896836 | + | 0.442363i | \(0.854140\pi\) | |||||||
\(228\) | 1.11830 | + | 16.4453i | 0.0740610 | + | 1.08911i | ||||
\(229\) | 20.4567 | − | 11.8107i | 1.35182 | − | 0.780472i | 0.363314 | − | 0.931667i | \(-0.381645\pi\) |
0.988504 | + | 0.151195i | \(0.0483121\pi\) | |||||||
\(230\) | 0.0146953 | − | 0.0254530i | 0.000968981 | − | 0.00167832i | ||||
\(231\) | −4.04839 | − | 6.02686i | −0.266364 | − | 0.396539i | ||||
\(232\) | −0.520354 | + | 0.300427i | −0.0341629 | + | 0.0197240i | ||||
\(233\) | −4.96236 | −0.325095 | −0.162548 | − | 0.986701i | \(-0.551971\pi\) | ||||
−0.162548 | + | 0.986701i | \(0.551971\pi\) | |||||||
\(234\) | −0.190385 | − | 0.963495i | −0.0124459 | − | 0.0629857i | ||||
\(235\) | 1.50579 | 0.0982269 | ||||||||
\(236\) | −6.74447 | + | 3.89392i | −0.439028 | + | 0.253473i | ||||
\(237\) | 5.59064 | − | 11.4070i | 0.363151 | − | 0.740963i | ||||
\(238\) | −0.276798 | + | 0.479428i | −0.0179421 | + | 0.0310767i | ||||
\(239\) | 9.88126 | − | 5.70495i | 0.639165 | − | 0.369022i | −0.145128 | − | 0.989413i | \(-0.546359\pi\) |
0.784293 | + | 0.620391i | \(0.213026\pi\) | |||||||
\(240\) | −1.52542 | − | 0.747620i | −0.0984655 | − | 0.0482586i | ||||
\(241\) | 1.76217i | 0.113511i | 0.998388 | + | 0.0567557i | \(0.0180756\pi\) | ||||
−0.998388 | + | 0.0567557i | \(0.981924\pi\) | |||||||
\(242\) | 0.596616i | 0.0383520i | ||||||||
\(243\) | 14.6988 | − | 5.19095i | 0.942927 | − | 0.333000i | ||||
\(244\) | 6.09836 | − | 10.5627i | 0.390408 | − | 0.676206i | ||||
\(245\) | −0.215002 | + | 0.124132i | −0.0137360 | + | 0.00793048i | ||||
\(246\) | −0.820583 | − | 1.22161i | −0.0523185 | − | 0.0778869i | ||||
\(247\) | 1.02084 | + | 17.1970i | 0.0649546 | + | 1.09422i | ||||
\(248\) | −1.06392 | − | 1.84276i | −0.0675589 | − | 0.117015i | ||||
\(249\) | −25.0181 | − | 12.2615i | −1.58546 | − | 0.777043i | ||||
\(250\) | −0.112014 | − | 0.194013i | −0.00708437 | − | 0.0122705i | ||||
\(251\) | −3.29409 | − | 5.70554i | −0.207921 | − | 0.360130i | 0.743138 | − | 0.669138i | \(-0.233336\pi\) |
−0.951060 | + | 0.309008i | \(0.900003\pi\) | |||||||
\(252\) | 5.53155 | + | 2.25959i | 0.348455 | + | 0.142341i | ||||
\(253\) | −4.73314 | + | 2.73268i | −0.297570 | + | 0.171802i | ||||
\(254\) | 0.578135i | 0.0362754i | ||||||||
\(255\) | 2.35421 | + | 1.15381i | 0.147426 | + | 0.0722546i | ||||
\(256\) | −7.67227 | + | 13.2888i | −0.479517 | + | 0.830547i | ||||
\(257\) | 12.3642 | 0.771255 | 0.385627 | − | 0.922655i | \(-0.373985\pi\) | ||||
0.385627 | + | 0.922655i | \(0.373985\pi\) | |||||||
\(258\) | −0.968644 | + | 0.650661i | −0.0603051 | + | 0.0405084i | ||||
\(259\) | −2.61073 | + | 4.52192i | −0.162223 | + | 0.280978i | ||||
\(260\) | −1.59412 | − | 0.798375i | −0.0988633 | − | 0.0495131i | ||||
\(261\) | −3.04688 | − | 3.93079i | −0.188597 | − | 0.243310i | ||||
\(262\) | 0.0642409 | + | 0.0370895i | 0.00396882 | + | 0.00229140i | ||||
\(263\) | 8.72654 | + | 15.1148i | 0.538102 | + | 0.932019i | 0.999006 | + | 0.0445698i | \(0.0141917\pi\) |
−0.460905 | + | 0.887450i | \(0.652475\pi\) | |||||||
\(264\) | −1.46730 | − | 2.18439i | −0.0903063 | − | 0.134440i | ||||
\(265\) | −2.33614 | + | 1.34877i | −0.143508 | + | 0.0828543i | ||||
\(266\) | 0.375708 | + | 0.216915i | 0.0230361 | + | 0.0132999i | ||||
\(267\) | −6.53160 | − | 3.20118i | −0.399727 | − | 0.195909i | ||||
\(268\) | −11.2196 | − | 6.47762i | −0.685344 | − | 0.395684i | ||||
\(269\) | 2.23646 | + | 3.87367i | 0.136360 | + | 0.236182i | 0.926116 | − | 0.377239i | \(-0.123126\pi\) |
−0.789756 | + | 0.613421i | \(0.789793\pi\) | |||||||
\(270\) | −0.0368350 | + | 0.111187i | −0.00224171 | + | 0.00676664i | ||||
\(271\) | −15.7347 | − | 9.08442i | −0.955814 | − | 0.551839i | −0.0609315 | − | 0.998142i | \(-0.519407\pi\) |
−0.894882 | + | 0.446303i | \(0.852740\pi\) | |||||||
\(272\) | 12.0435 | − | 20.8599i | 0.730243 | − | 1.26482i | ||||
\(273\) | 5.76072 | + | 2.41125i | 0.348654 | + | 0.145936i | ||||
\(274\) | −0.790738 | − | 1.36960i | −0.0477702 | − | 0.0827404i | ||||
\(275\) | 20.7004i | 1.24828i | ||||||||
\(276\) | 1.97954 | − | 4.03899i | 0.119154 | − | 0.243119i | ||||
\(277\) | 0.0700777 | 0.00421056 | 0.00210528 | − | 0.999998i | \(-0.499330\pi\) | ||||
0.00210528 | + | 0.999998i | \(0.499330\pi\) | |||||||
\(278\) | 0.929426i | 0.0557432i | ||||||||
\(279\) | 13.9203 | − | 10.7901i | 0.833388 | − | 0.645985i | ||||
\(280\) | −0.0779257 | + | 0.0449904i | −0.00465695 | + | 0.00268869i | ||||
\(281\) | −14.9845 | − | 8.65133i | −0.893903 | − | 0.516095i | −0.0186857 | − | 0.999825i | \(-0.505948\pi\) |
−0.875217 | + | 0.483730i | \(0.839282\pi\) | |||||||
\(282\) | −0.951666 | + | 0.0647144i | −0.0566709 | + | 0.00385369i | ||||
\(283\) | −33.6033 | −1.99751 | −0.998756 | − | 0.0498695i | \(-0.984119\pi\) | ||||
−0.998756 | + | 0.0498695i | \(0.984119\pi\) | |||||||
\(284\) | 0.950355i | 0.0563932i | ||||||||
\(285\) | 0.904197 | − | 1.84490i | 0.0535600 | − | 0.109282i | ||||
\(286\) | −0.755356 | − | 1.14568i | −0.0446651 | − | 0.0677455i | ||||
\(287\) | 9.35757 | 0.552360 | ||||||||
\(288\) | 3.00937 | + | 1.22930i | 0.177329 | + | 0.0724373i | ||||
\(289\) | −10.0869 | + | 17.4710i | −0.593348 | + | 1.02771i | ||||
\(290\) | 0.0373695 | 0.00219441 | ||||||||
\(291\) | −1.30316 | − | 19.1639i | −0.0763929 | − | 1.12341i | ||||
\(292\) | 11.0573 | + | 6.38395i | 0.647081 | + | 0.373592i | ||||
\(293\) | 20.6110 | + | 11.8998i | 1.20411 | + | 0.695192i | 0.961466 | − | 0.274924i | \(-0.0886527\pi\) |
0.242642 | + | 0.970116i | \(0.421986\pi\) | |||||||
\(294\) | 0.130548 | − | 0.0876919i | 0.00761369 | − | 0.00511430i | ||||
\(295\) | 0.970719 | 0.0565175 | ||||||||
\(296\) | −0.946237 | + | 1.63893i | −0.0549989 | + | 0.0952609i | ||||
\(297\) | 16.2700 | − | 14.4810i | 0.944080 | − | 0.840275i | ||||
\(298\) | −0.233366 | −0.0135185 | ||||||||
\(299\) | 2.10514 | − | 4.20336i | 0.121744 | − | 0.243086i | ||||
\(300\) | −9.49959 | − | 14.1421i | −0.548459 | − | 0.816495i | ||||
\(301\) | − | 7.41985i | − | 0.427673i | ||||||
\(302\) | 0.928876 | 0.0534508 | ||||||||
\(303\) | −1.10826 | − | 1.64987i | −0.0636678 | − | 0.0947827i | ||||
\(304\) | −16.3471 | − | 9.43798i | −0.937568 | − | 0.541305i | ||||
\(305\) | −1.31659 | + | 0.760132i | −0.0753876 | + | 0.0435251i | ||||
\(306\) | −1.53746 | − | 0.628039i | −0.0878906 | − | 0.0359026i | ||||
\(307\) | − | 0.710917i | − | 0.0405742i | −0.999794 | − | 0.0202871i | \(-0.993542\pi\) | ||
0.999794 | − | 0.0202871i | \(-0.00645802\pi\) | |||||||
\(308\) | 8.34896 | 0.475726 | ||||||||
\(309\) | −16.5286 | − | 24.6062i | −0.940278 | − | 1.39980i | ||||
\(310\) | 0.132339i | 0.00751633i | ||||||||
\(311\) | −3.55087 | − | 6.15029i | −0.201351 | − | 0.348751i | 0.747613 | − | 0.664135i | \(-0.231200\pi\) |
−0.948964 | + | 0.315384i | \(0.897867\pi\) | |||||||
\(312\) | 2.08792 | + | 0.873938i | 0.118205 | + | 0.0494770i | ||||
\(313\) | −4.76973 | + | 8.26141i | −0.269601 | + | 0.466962i | −0.968759 | − | 0.248005i | \(-0.920225\pi\) |
0.699158 | + | 0.714967i | \(0.253558\pi\) | |||||||
\(314\) | 1.29665 | + | 0.748621i | 0.0731741 | + | 0.0422471i | ||||
\(315\) | −0.456285 | − | 0.588655i | −0.0257088 | − | 0.0331670i | ||||
\(316\) | 7.30403 | + | 12.6510i | 0.410884 | + | 0.711672i | ||||
\(317\) | 14.6877 | + | 8.47996i | 0.824945 | + | 0.476282i | 0.852119 | − | 0.523348i | \(-0.175317\pi\) |
−0.0271737 | + | 0.999631i | \(0.508651\pi\) | |||||||
\(318\) | 1.41848 | − | 0.952829i | 0.0795446 | − | 0.0534320i | ||||
\(319\) | −6.01808 | − | 3.47454i | −0.336948 | − | 0.194537i | ||||
\(320\) | 1.67762 | − | 0.968576i | 0.0937820 | − | 0.0541451i | ||||
\(321\) | −5.16816 | + | 10.5450i | −0.288459 | + | 0.588562i | ||||
\(322\) | −0.0591925 | − | 0.102524i | −0.00329867 | − | 0.00571346i | ||||
\(323\) | 25.2287 | + | 14.5658i | 1.40376 | + | 0.810463i | ||||
\(324\) | −4.46986 | + | 17.3596i | −0.248325 | + | 0.964421i | ||||
\(325\) | −9.80087 | − | 14.8654i | −0.543654 | − | 0.824584i | ||||
\(326\) | 0.305046 | − | 0.528355i | 0.0168949 | − | 0.0292629i | ||||
\(327\) | 0.546082 | + | 8.03048i | 0.0301984 | + | 0.444087i | ||||
\(328\) | 3.39157 | 0.187268 | ||||||||
\(329\) | 3.03265 | − | 5.25270i | 0.167195 | − | 0.289591i | ||||
\(330\) | 0.0111034 | + | 0.163283i | 0.000611224 | + | 0.00898844i | ||||
\(331\) | 0.459834i | 0.0252748i | 0.999920 | + | 0.0126374i | \(0.00402271\pi\) | ||||
−0.999920 | + | 0.0126374i | \(0.995977\pi\) | |||||||
\(332\) | 27.7464 | − | 16.0194i | 1.52278 | − | 0.879178i | ||||
\(333\) | −14.5012 | − | 5.92361i | −0.794659 | − | 0.324612i | ||||
\(334\) | 0.998055 | + | 1.72868i | 0.0546112 | + | 0.0945893i | ||||
\(335\) | 0.807406 | + | 1.39847i | 0.0441133 | + | 0.0764064i | ||||
\(336\) | −5.68013 | + | 3.81548i | −0.309877 | + | 0.208151i | ||||
\(337\) | 14.9959 | + | 25.9736i | 0.816877 | + | 1.41487i | 0.907972 | + | 0.419030i | \(0.137630\pi\) |
−0.0910958 | + | 0.995842i | \(0.529037\pi\) | |||||||
\(338\) | 1.08487 | + | 0.465103i | 0.0590092 | + | 0.0252983i | ||||
\(339\) | 7.50100 | − | 15.3048i | 0.407398 | − | 0.831243i | ||||
\(340\) | −2.61094 | + | 1.50743i | −0.141598 | + | 0.0817518i | ||||
\(341\) | 12.3046 | − | 21.3122i | 0.666331 | − | 1.15412i | ||||
\(342\) | −0.492169 | + | 1.20484i | −0.0266134 | + | 0.0651504i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | − | 2.68926i | − | 0.144995i | ||||||
\(345\) | −0.465404 | + | 0.312623i | −0.0250565 | + | 0.0168311i | ||||
\(346\) | 2.00082 | − | 1.15518i | 0.107565 | − | 0.0621026i | ||||
\(347\) | 17.9348 | − | 31.0639i | 0.962788 | − | 1.66760i | 0.247344 | − | 0.968928i | \(-0.420442\pi\) |
0.715444 | − | 0.698670i | \(-0.246224\pi\) | |||||||
\(348\) | 5.70592 | − | 0.388009i | 0.305869 | − | 0.0207995i | ||||
\(349\) | 26.3197 | − | 15.1957i | 1.40886 | − | 0.813406i | 0.413582 | − | 0.910467i | \(-0.364277\pi\) |
0.995278 | + | 0.0970608i | \(0.0309441\pi\) | |||||||
\(350\) | −0.448391 | −0.0239675 | ||||||||
\(351\) | −4.82757 | + | 18.1023i | −0.257677 | + | 0.966231i | ||||
\(352\) | 4.54214 | 0.242097 | ||||||||
\(353\) | −29.0215 | + | 16.7555i | −1.54466 | + | 0.891808i | −0.546121 | + | 0.837707i | \(0.683896\pi\) |
−0.998535 | + | 0.0541011i | \(0.982771\pi\) | |||||||
\(354\) | −0.613499 | + | 0.0417187i | −0.0326071 | + | 0.00221732i | ||||
\(355\) | 0.0592287 | − | 0.102587i | 0.00314353 | − | 0.00544476i | ||||
\(356\) | 7.24390 | − | 4.18227i | 0.383926 | − | 0.221660i | ||||
\(357\) | 8.76625 | − | 5.88849i | 0.463959 | − | 0.311652i | ||||
\(358\) | − | 1.94916i | − | 0.103016i | ||||||
\(359\) | 21.8569i | 1.15356i | 0.816898 | + | 0.576782i | \(0.195692\pi\) | ||||
−0.816898 | + | 0.576782i | \(0.804308\pi\) | |||||||
\(360\) | −0.165377 | − | 0.213353i | −0.00871612 | − | 0.0112447i | ||||
\(361\) | 1.91462 | − | 3.31621i | 0.100769 | − | 0.174537i | ||||
\(362\) | −1.14577 | + | 0.661511i | −0.0602203 | + | 0.0347682i | ||||
\(363\) | 5.00871 | − | 10.2196i | 0.262889 | − | 0.536391i | ||||
\(364\) | −5.99555 | + | 3.95291i | −0.314252 | + | 0.207189i | ||||
\(365\) | −0.795730 | − | 1.37824i | −0.0416504 | − | 0.0721406i | ||||
\(366\) | 0.799422 | − | 0.536990i | 0.0417864 | − | 0.0280689i | ||||
\(367\) | −1.77629 | − | 3.07663i | −0.0927217 | − | 0.160599i | 0.815934 | − | 0.578145i | \(-0.196223\pi\) |
−0.908655 | + | 0.417547i | \(0.862890\pi\) | |||||||
\(368\) | 2.57547 | + | 4.46084i | 0.134256 | + | 0.232537i | ||||
\(369\) | 3.80038 | + | 27.8143i | 0.197840 | + | 1.44795i | ||||
\(370\) | 0.101932 | − | 0.0588502i | 0.00529917 | − | 0.00305948i | ||||
\(371\) | 10.8656i | 0.564116i | ||||||||
\(372\) | 1.37408 | + | 20.2067i | 0.0712427 | + | 1.04767i | ||||
\(373\) | −17.9062 | + | 31.0144i | −0.927146 | + | 1.60586i | −0.139073 | + | 0.990282i | \(0.544412\pi\) |
−0.788073 | + | 0.615582i | \(0.788921\pi\) | |||||||
\(374\) | −2.32054 | −0.119992 | ||||||||
\(375\) | 0.289936 | + | 4.26369i | 0.0149722 | + | 0.220176i | ||||
\(376\) | 1.09916 | − | 1.90380i | 0.0566847 | − | 0.0981808i | ||||
\(377\) | 5.96676 | − | 0.354196i | 0.307304 | − | 0.0182420i | ||||
\(378\) | 0.313673 | + | 0.352423i | 0.0161336 | + | 0.0181267i | ||||
\(379\) | −16.8619 | − | 9.73521i | −0.866136 | − | 0.500064i | −7.38628e−5 | − | 1.00000i | \(-0.500024\pi\) |
−0.866062 | + | 0.499936i | \(0.833357\pi\) | |||||||
\(380\) | 1.18131 | + | 2.04609i | 0.0605999 | + | 0.104962i | ||||
\(381\) | 4.85356 | − | 9.90305i | 0.248655 | − | 0.507349i | ||||
\(382\) | 0.536607 | − | 0.309810i | 0.0274552 | − | 0.0158513i | ||||
\(383\) | 0.809753 | + | 0.467511i | 0.0413764 | + | 0.0238887i | 0.520546 | − | 0.853834i | \(-0.325729\pi\) |
−0.479169 | + | 0.877723i | \(0.659062\pi\) | |||||||
\(384\) | −4.13458 | + | 2.77730i | −0.210992 | + | 0.141728i | ||||
\(385\) | −0.901237 | − | 0.520330i | −0.0459313 | − | 0.0265185i | ||||
\(386\) | 0.380094 | + | 0.658342i | 0.0193463 | + | 0.0335087i | ||||
\(387\) | 22.0546 | − | 3.01342i | 1.12110 | − | 0.153181i | ||||
\(388\) | 19.1289 | + | 11.0441i | 0.971125 | + | 0.560679i | ||||
\(389\) | −6.81773 | + | 11.8087i | −0.345673 | + | 0.598723i | −0.985476 | − | 0.169816i | \(-0.945683\pi\) |
0.639803 | + | 0.768539i | \(0.279016\pi\) | |||||||
\(390\) | −0.0852819 | − | 0.112000i | −0.00431842 | − | 0.00567133i | ||||
\(391\) | −3.97476 | − | 6.88449i | −0.201012 | − | 0.348164i | ||||
\(392\) | 0.362441i | 0.0183061i | ||||||||
\(393\) | −0.789029 | − | 1.17463i | −0.0398012 | − | 0.0592524i | ||||
\(394\) | −0.505586 | −0.0254710 | ||||||||
\(395\) | − | 1.82083i | − | 0.0916158i | ||||||
\(396\) | 3.39075 | + | 24.8163i | 0.170392 | + | 1.24707i | ||||
\(397\) | −18.5471 | + | 10.7082i | −0.930851 | + | 0.537427i | −0.887081 | − | 0.461615i | \(-0.847270\pi\) |
−0.0437704 | + | 0.999042i | \(0.513937\pi\) | |||||||
\(398\) | 0.785130 | + | 0.453295i | 0.0393550 | + | 0.0227216i | ||||
\(399\) | −4.61457 | − | 6.86975i | −0.231018 | − | 0.343918i | ||||
\(400\) | 19.5095 | 0.975476 | ||||||||
\(401\) | 9.97613i | 0.498184i | 0.968480 | + | 0.249092i | \(0.0801322\pi\) | ||||
−0.968480 | + | 0.249092i | \(0.919868\pi\) | |||||||
\(402\) | −0.570386 | − | 0.849138i | −0.0284483 | − | 0.0423512i | ||||
\(403\) | 1.25434 | + | 21.1304i | 0.0624829 | + | 1.05258i | ||||
\(404\) | 2.28555 | 0.113711 | ||||||||
\(405\) | 1.56440 | − | 1.59532i | 0.0777356 | − | 0.0792723i | ||||
\(406\) | 0.0752618 | − | 0.130357i | 0.00373518 | − | 0.00646952i | ||||
\(407\) | −21.8871 | −1.08490 | ||||||||
\(408\) | 3.17725 | − | 2.13423i | 0.157297 | − | 0.105660i | ||||
\(409\) | 21.8042 | + | 12.5887i | 1.07815 | + | 0.622469i | 0.930396 | − | 0.366556i | \(-0.119463\pi\) |
0.147752 | + | 0.989025i | \(0.452796\pi\) | |||||||
\(410\) | −0.182675 | − | 0.105468i | −0.00902169 | − | 0.00520868i | ||||
\(411\) | 2.04675 | + | 30.0987i | 0.100958 | + | 1.48466i | ||||
\(412\) | 34.0868 | 1.67933 | ||||||||
\(413\) | 1.95502 | − | 3.38619i | 0.0962003 | − | 0.166624i | ||||
\(414\) | 0.280702 | − | 0.217581i | 0.0137958 | − | 0.0106935i | ||||
\(415\) | −3.99349 | −0.196033 | ||||||||
\(416\) | −3.26180 | + | 2.15053i | −0.159923 | + | 0.105438i | ||||
\(417\) | 7.80271 | − | 15.9204i | 0.382101 | − | 0.779626i | ||||
\(418\) | 1.81851i | 0.0889463i | ||||||||
\(419\) | 3.51627 | 0.171781 | 0.0858905 | − | 0.996305i | \(-0.472626\pi\) | ||||
0.0858905 | + | 0.996305i | \(0.472626\pi\) | |||||||
\(420\) | 0.854490 | − | 0.0581063i | 0.0416949 | − | 0.00283530i | ||||
\(421\) | 10.2082 | + | 5.89371i | 0.497518 | + | 0.287242i | 0.727688 | − | 0.685908i | \(-0.240595\pi\) |
−0.230170 | + | 0.973150i | \(0.573928\pi\) | |||||||
\(422\) | 1.46915 | − | 0.848214i | 0.0715171 | − | 0.0412904i | ||||
\(423\) | 16.8447 | + | 6.88092i | 0.819016 | + | 0.334562i | ||||
\(424\) | 3.93816i | 0.191254i | ||||||||
\(425\) | −30.1094 | −1.46052 | ||||||||
\(426\) | −0.0330239 | + | 0.0673810i | −0.00160001 | + | 0.00326462i | ||||
\(427\) | 6.12360i | 0.296342i | ||||||||
\(428\) | −6.75207 | − | 11.6949i | −0.326374 | − | 0.565296i | ||||
\(429\) | 3.32051 | + | 25.9661i | 0.160316 | + | 1.25365i | ||||
\(430\) | −0.0836279 | + | 0.144848i | −0.00403290 | + | 0.00698518i | ||||
\(431\) | 29.9512 | + | 17.2923i | 1.44270 | + | 0.832942i | 0.998029 | − | 0.0627527i | \(-0.0199880\pi\) |
0.444669 | + | 0.895695i | \(0.353321\pi\) | |||||||
\(432\) | −13.6479 | − | 15.3340i | −0.656636 | − | 0.737755i | ||||
\(433\) | 7.61126 | + | 13.1831i | 0.365774 | + | 0.633539i | 0.988900 | − | 0.148582i | \(-0.0474710\pi\) |
−0.623126 | + | 0.782121i | \(0.714138\pi\) | |||||||
\(434\) | 0.461642 | + | 0.266529i | 0.0221595 | + | 0.0127938i | ||||
\(435\) | −0.640113 | − | 0.313724i | −0.0306911 | − | 0.0150419i | ||||
\(436\) | −8.01585 | − | 4.62795i | −0.383890 | − | 0.221639i | ||||
\(437\) | −5.39509 | + | 3.11486i | −0.258082 | + | 0.149004i | ||||
\(438\) | 0.562138 | + | 0.836859i | 0.0268600 | + | 0.0399867i | ||||
\(439\) | 13.9594 | + | 24.1783i | 0.666244 | + | 1.15397i | 0.978946 | + | 0.204117i | \(0.0654324\pi\) |
−0.312702 | + | 0.949851i | \(0.601234\pi\) | |||||||
\(440\) | −0.326646 | − | 0.188589i | −0.0155722 | − | 0.00899063i | ||||
\(441\) | −2.97238 | + | 0.406129i | −0.141542 | + | 0.0193395i | ||||
\(442\) | 1.66642 | − | 1.09869i | 0.0792637 | − | 0.0522592i | ||||
\(443\) | 10.1816 | − | 17.6351i | 0.483745 | − | 0.837870i | −0.516081 | − | 0.856540i | \(-0.672610\pi\) |
0.999826 | + | 0.0186696i | \(0.00594305\pi\) | |||||||
\(444\) | 14.9528 | − | 10.0442i | 0.709630 | − | 0.476675i | ||||
\(445\) | −1.04260 | −0.0494240 | ||||||||
\(446\) | 0.701489 | − | 1.21501i | 0.0332165 | − | 0.0575326i | ||||
\(447\) | 3.99740 | + | 1.95915i | 0.189070 | + | 0.0926648i | ||||
\(448\) | − | 7.80282i | − | 0.368649i | ||||||
\(449\) | 20.5983 | − | 11.8924i | 0.972094 | − | 0.561239i | 0.0722199 | − | 0.997389i | \(-0.476992\pi\) |
0.899874 | + | 0.436150i | \(0.143658\pi\) | |||||||
\(450\) | −0.182105 | − | 1.33279i | −0.00858450 | − | 0.0628283i | ||||
\(451\) | 19.6123 | + | 33.9696i | 0.923509 | + | 1.59956i | ||||
\(452\) | 9.79986 | + | 16.9739i | 0.460947 | + | 0.798383i | ||||
\(453\) | −15.9110 | − | 7.79810i | −0.747564 | − | 0.366387i | ||||
\(454\) | −0.605153 | − | 1.04816i | −0.0284013 | − | 0.0491924i | ||||
\(455\) | 0.893553 | − | 0.0530427i | 0.0418904 | − | 0.00248668i | ||||
\(456\) | −1.67251 | − | 2.48988i | −0.0783225 | − | 0.116599i | ||||
\(457\) | 12.5668 | − | 7.25547i | 0.587852 | − | 0.339397i | −0.176396 | − | 0.984319i | \(-0.556444\pi\) |
0.764248 | + | 0.644923i | \(0.223110\pi\) | |||||||
\(458\) | −1.07238 | + | 1.85742i | −0.0501091 | + | 0.0867915i | ||||
\(459\) | 21.0631 | + | 23.6652i | 0.983141 | + | 1.10459i | ||||
\(460\) | − | 0.644720i | − | 0.0300602i | ||||||
\(461\) | − | 15.5111i | − | 0.722423i | −0.932484 | − | 0.361211i | \(-0.882363\pi\) | ||
0.932484 | − | 0.361211i | \(-0.117637\pi\) | |||||||
\(462\) | 0.591949 | + | 0.290118i | 0.0275399 | + | 0.0134975i | ||||
\(463\) | 8.86168 | − | 5.11629i | 0.411837 | − | 0.237774i | −0.279742 | − | 0.960075i | \(-0.590249\pi\) |
0.691579 | + | 0.722301i | \(0.256916\pi\) | |||||||
\(464\) | −3.27464 | + | 5.67185i | −0.152022 | + | 0.263309i | ||||
\(465\) | 1.11101 | − | 2.26687i | 0.0515219 | − | 0.105124i | ||||
\(466\) | 0.390205 | − | 0.225285i | 0.0180759 | − | 0.0104361i | ||||
\(467\) | −10.9633 | −0.507319 | −0.253660 | − | 0.967294i | \(-0.581634\pi\) | ||||
−0.253660 | + | 0.967294i | \(0.581634\pi\) | |||||||
\(468\) | −14.1845 | − | 16.2157i | −0.655681 | − | 0.749570i | ||||
\(469\) | 6.50443 | 0.300347 | ||||||||
\(470\) | −0.118405 | + | 0.0683610i | −0.00546160 | + | 0.00315326i | ||||
\(471\) | −15.9259 | − | 23.7090i | −0.733826 | − | 1.09245i | ||||
\(472\) | 0.708580 | − | 1.22730i | 0.0326151 | − | 0.0564909i | ||||
\(473\) | 26.9353 | − | 15.5511i | 1.23849 | − | 0.715041i | ||||
\(474\) | 0.0782538 | + | 1.15077i | 0.00359432 | + | 0.0528567i | ||||
\(475\) | 23.5955i | 1.08264i | ||||||||
\(476\) | 12.1438i | 0.556610i | ||||||||
\(477\) | −32.2969 | + | 4.41285i | −1.47877 | + | 0.202051i | ||||
\(478\) | −0.517995 | + | 0.897193i | −0.0236925 | + | 0.0410367i | ||||
\(479\) | 13.9452 | − | 8.05126i | 0.637172 | − | 0.367871i | −0.146352 | − | 0.989233i | \(-0.546753\pi\) |
0.783524 | + | 0.621361i | \(0.213420\pi\) | |||||||
\(480\) | 0.464874 | − | 0.0316120i | 0.0212185 | − | 0.00144288i | ||||
\(481\) | 15.7176 | − | 10.3627i | 0.716659 | − | 0.472499i | ||||
\(482\) | −0.0800004 | − | 0.138565i | −0.00364392 | − | 0.00631145i | ||||
\(483\) | 0.153214 | + | 2.25311i | 0.00697147 | + | 0.102520i | ||||
\(484\) | 6.54376 | + | 11.3341i | 0.297444 | + | 0.515187i | ||||
\(485\) | −1.37660 | − | 2.38433i | −0.0625080 | − | 0.108267i | ||||
\(486\) | −0.920145 | + | 1.07549i | −0.0417386 | + | 0.0487850i | ||||
\(487\) | −12.4030 | + | 7.16087i | −0.562033 | + | 0.324490i | −0.753961 | − | 0.656919i | \(-0.771859\pi\) |
0.191928 | + | 0.981409i | \(0.438526\pi\) | |||||||
\(488\) | 2.21945i | 0.100470i | ||||||||
\(489\) | −9.66087 | + | 6.48943i | −0.436879 | + | 0.293462i | ||||
\(490\) | 0.0112708 | − | 0.0195217i | 0.000509165 | − | 0.000881899i | ||||
\(491\) | 32.0463 | 1.44623 | 0.723115 | − | 0.690728i | \(-0.242710\pi\) | ||||
0.723115 | + | 0.690728i | \(0.242710\pi\) | |||||||
\(492\) | −28.9877 | − | 14.2071i | −1.30686 | − | 0.640504i | ||||
\(493\) | 5.05381 | − | 8.75346i | 0.227612 | − | 0.394236i | ||||
\(494\) | −0.860996 | − | 1.30591i | −0.0387380 | − | 0.0587556i | ||||
\(495\) | 1.18060 | − | 2.89014i | 0.0530640 | − | 0.129902i | ||||
\(496\) | −20.0861 | − | 11.5967i | −0.901891 | − | 0.520707i | ||||
\(497\) | −0.238572 | − | 0.413219i | −0.0107014 | − | 0.0185354i | ||||
\(498\) | 2.52390 | − | 0.171628i | 0.113099 | − | 0.00769085i | ||||
\(499\) | 4.74072 | − | 2.73706i | 0.212224 | − | 0.122528i | −0.390121 | − | 0.920764i | \(-0.627567\pi\) |
0.602345 | + | 0.798236i | \(0.294233\pi\) | |||||||
\(500\) | −4.25593 | − | 2.45716i | −0.190331 | − | 0.109888i | ||||
\(501\) | −2.58337 | − | 37.9900i | −0.115416 | − | 1.69727i | ||||
\(502\) | 0.518049 | + | 0.299095i | 0.0231216 | + | 0.0133493i | ||||
\(503\) | 3.70097 | + | 6.41027i | 0.165018 | + | 0.285820i | 0.936662 | − | 0.350235i | \(-0.113898\pi\) |
−0.771644 | + | 0.636055i | \(0.780565\pi\) | |||||||
\(504\) | −1.07731 | + | 0.147198i | −0.0479874 | + | 0.00655672i | ||||
\(505\) | −0.246717 | − | 0.142442i | −0.0109787 | − | 0.00633858i | ||||
\(506\) | 0.248121 | − | 0.429758i | 0.0110303 | − | 0.0191051i | ||||
\(507\) | −14.6785 | − | 17.0746i | −0.651894 | − | 0.758310i | ||||
\(508\) | 6.34105 | + | 10.9830i | 0.281339 | + | 0.487293i | ||||
\(509\) | 5.35400i | 0.237312i | 0.992935 | + | 0.118656i | \(0.0378585\pi\) | ||||
−0.992935 | + | 0.118656i | \(0.962141\pi\) | |||||||
\(510\) | −0.237500 | + | 0.0161503i | −0.0105167 | + | 0.000715146i | ||||
\(511\) | −6.41037 | −0.283578 | ||||||||
\(512\) | − | 7.14455i | − | 0.315747i | ||||||
\(513\) | 18.5454 | − | 16.5063i | 0.818800 | − | 0.728770i | ||||
\(514\) | −0.972230 | + | 0.561317i | −0.0428832 | + | 0.0247586i | ||||
\(515\) | −3.67953 | − | 2.12438i | −0.162140 | − | 0.0936113i | ||||
\(516\) | −11.2651 | + | 22.9850i | −0.495920 | + | 1.01186i | ||||
\(517\) | 25.4243 | 1.11816 | ||||||||
\(518\) | − | 0.474096i | − | 0.0208306i | ||||||
\(519\) | −43.9706 | + | 2.99005i | −1.93010 | + | 0.131249i | ||||
\(520\) | 0.323860 | − | 0.0192249i | 0.0142022 | − | 0.000843066i | ||||
\(521\) | 29.4381 | 1.28971 | 0.644854 | − | 0.764305i | \(-0.276918\pi\) | ||||
0.644854 | + | 0.764305i | \(0.276918\pi\) | |||||||
\(522\) | 0.418038 | + | 0.170765i | 0.0182970 | + | 0.00747418i | ||||
\(523\) | −1.31103 | + | 2.27078i | −0.0573275 | + | 0.0992942i | −0.893265 | − | 0.449531i | \(-0.851591\pi\) |
0.835937 | + | 0.548825i | \(0.184925\pi\) | |||||||
\(524\) | 1.62721 | 0.0710849 | ||||||||
\(525\) | 7.68063 | + | 3.76433i | 0.335210 | + | 0.164289i | ||||
\(526\) | −1.37239 | − | 0.792348i | −0.0598389 | − | 0.0345480i | ||||
\(527\) | 30.9992 | + | 17.8974i | 1.35034 | + | 0.779622i | ||||
\(528\) | −25.7557 | − | 12.6231i | −1.12087 | − | 0.549348i | ||||
\(529\) | −21.3000 | −0.926088 | ||||||||
\(530\) | 0.122465 | − | 0.212115i | 0.00531954 | − | 0.00921371i | ||||
\(531\) | 10.8591 | + | 4.43584i | 0.471243 | + | 0.192499i | ||||
\(532\) | 9.51660 | 0.412597 | ||||||||
\(533\) | −30.1673 | − | 15.1085i | −1.30669 | − | 0.654423i | ||||
\(534\) | 0.658929 | − | 0.0448079i | 0.0285146 | − | 0.00193903i | ||||
\(535\) | 1.68323i | 0.0727723i | ||||||||
\(536\) | 2.35748 | 0.101827 | ||||||||
\(537\) | −16.3636 | + | 33.3878i | −0.706142 | + | 1.44079i | ||||
\(538\) | −0.351720 | − | 0.203065i | −0.0151637 | − | 0.00875477i | ||||
\(539\) | −3.63017 | + | 2.09588i | −0.156362 | + | 0.0902759i | ||||
\(540\) | 0.519748 | + | 2.51627i | 0.0223664 | + | 0.108283i | ||||
\(541\) | − | 4.91202i | − | 0.211184i | −0.994410 | − | 0.105592i | \(-0.966326\pi\) | ||
0.994410 | − | 0.105592i | \(-0.0336738\pi\) | |||||||
\(542\) | 1.64969 | 0.0708600 | ||||||||
\(543\) | 25.1798 | − | 1.71225i | 1.08057 | − | 0.0734798i | ||||
\(544\) | 6.60667i | 0.283259i | ||||||||
\(545\) | 0.576853 | + | 0.999139i | 0.0247097 | + | 0.0427984i | ||||
\(546\) | −0.562450 | + | 0.0719255i | −0.0240706 | + | 0.00307813i | ||||
\(547\) | 4.36380 | − | 7.55832i | 0.186583 | − | 0.323170i | −0.757526 | − | 0.652805i | \(-0.773592\pi\) |
0.944109 | + | 0.329634i | \(0.106925\pi\) | |||||||
\(548\) | −30.0438 | − | 17.3458i | −1.28341 | − | 0.740977i | ||||
\(549\) | −18.2017 | + | 2.48697i | −0.776829 | + | 0.106141i | ||||
\(550\) | −0.939774 | − | 1.62774i | −0.0400721 | − | 0.0694069i | ||||
\(551\) | −6.85973 | − | 3.96047i | −0.292234 | − | 0.168722i | ||||
\(552\) | 0.0555310 | + | 0.816619i | 0.00236356 | + | 0.0347576i | ||||
\(553\) | −6.35166 | − | 3.66713i | −0.270100 | − | 0.155942i | ||||
\(554\) | −0.00551042 | + | 0.00318144i | −0.000234115 | + | 0.000135167i | ||||
\(555\) | −2.24008 | + | 0.152328i | −0.0950860 | + | 0.00646596i | ||||
\(556\) | 10.1941 | + | 17.6566i | 0.432324 | + | 0.748807i | ||||
\(557\) | 22.7689 | + | 13.1457i | 0.964751 | + | 0.556999i | 0.897632 | − | 0.440745i | \(-0.145286\pi\) |
0.0671193 | + | 0.997745i | \(0.478619\pi\) | |||||||
\(558\) | −0.604740 | + | 1.48042i | −0.0256007 | + | 0.0626712i | ||||
\(559\) | −11.9799 | + | 23.9204i | −0.506697 | + | 1.01173i | ||||
\(560\) | −0.490395 | + | 0.849388i | −0.0207230 | + | 0.0358932i | ||||
\(561\) | 39.7492 | + | 19.4814i | 1.67821 | + | 0.822505i | ||||
\(562\) | 1.57104 | 0.0662702 | ||||||||
\(563\) | 5.57059 | − | 9.64854i | 0.234772 | − | 0.406638i | −0.724434 | − | 0.689344i | \(-0.757899\pi\) |
0.959206 | + | 0.282706i | \(0.0912322\pi\) | |||||||
\(564\) | −17.3693 | + | 11.6674i | −0.731381 | + | 0.491286i | ||||
\(565\) | − | 2.44302i | − | 0.102778i | ||||||
\(566\) | 2.64233 | − | 1.52555i | 0.111065 | − | 0.0641236i | ||||
\(567\) | −2.41434 | − | 8.67012i | −0.101393 | − | 0.364111i | ||||
\(568\) | −0.0864685 | − | 0.149768i | −0.00362814 | − | 0.00628412i | ||||
\(569\) | 1.97632 | + | 3.42309i | 0.0828518 | + | 0.143503i | 0.904474 | − | 0.426529i | \(-0.140264\pi\) |
−0.821622 | + | 0.570033i | \(0.806931\pi\) | |||||||
\(570\) | 0.0126563 | + | 0.186119i | 0.000530114 | + | 0.00779567i | ||||
\(571\) | −16.9637 | − | 29.3819i | −0.709907 | − | 1.22959i | −0.964891 | − | 0.262649i | \(-0.915404\pi\) |
0.254985 | − | 0.966945i | \(-0.417930\pi\) | |||||||
\(572\) | −26.9157 | − | 13.4800i | −1.12540 | − | 0.563629i | ||||
\(573\) | −11.7926 | + | 0.801913i | −0.492644 | + | 0.0335004i | ||||
\(574\) | −0.735813 | + | 0.424822i | −0.0307123 | + | 0.0177317i | ||||
\(575\) | 3.21941 | − | 5.57618i | 0.134259 | − | 0.232543i | ||||
\(576\) | 23.1930 | − | 3.16895i | 0.966373 | − | 0.132040i | ||||
\(577\) | 3.83353i | 0.159592i | 0.996811 | + | 0.0797959i | \(0.0254269\pi\) | ||||
−0.996811 | + | 0.0797959i | \(0.974573\pi\) | |||||||
\(578\) | − | 1.83173i | − | 0.0761900i | ||||||
\(579\) | −0.983835 | − | 14.4679i | −0.0408868 | − | 0.601266i | ||||
\(580\) | 0.709921 | − | 0.409873i | 0.0294778 | − | 0.0170190i | ||||
\(581\) | −8.04285 | + | 13.9306i | −0.333674 | + | 0.577940i | ||||
\(582\) | 0.972487 | + | 1.44775i | 0.0403109 | + | 0.0600111i | ||||
\(583\) | −39.4441 | + | 22.7731i | −1.63361 | + | 0.943165i | ||||
\(584\) | −2.32339 | −0.0961424 | ||||||||
\(585\) | 0.520561 | + | 2.63444i | 0.0215225 | + | 0.108921i | ||||
\(586\) | −2.16094 | −0.0892676 | ||||||||
\(587\) | −28.0108 | + | 16.1721i | −1.15613 | + | 0.667492i | −0.950374 | − | 0.311111i | \(-0.899299\pi\) |
−0.205757 | + | 0.978603i | \(0.565966\pi\) | |||||||
\(588\) | 1.51824 | − | 3.09778i | 0.0626113 | − | 0.127750i | ||||
\(589\) | 14.0254 | − | 24.2928i | 0.577908 | − | 1.00097i | ||||
\(590\) | −0.0763305 | + | 0.0440694i | −0.00314248 | + | 0.00181431i | ||||
\(591\) | 8.66034 | + | 4.24449i | 0.356239 | + | 0.174595i | ||||
\(592\) | 20.6279i | 0.847802i | ||||||||
\(593\) | − | 31.4950i | − | 1.29335i | −0.762768 | − | 0.646673i | \(-0.776160\pi\) | ||
0.762768 | − | 0.646673i | \(-0.223840\pi\) | |||||||
\(594\) | −0.621935 | + | 1.87732i | −0.0255183 | + | 0.0770275i | ||||
\(595\) | 0.756834 | − | 1.31088i | 0.0310272 | − | 0.0537407i | ||||
\(596\) | −4.43333 | + | 2.55959i | −0.181596 | + | 0.104845i | ||||
\(597\) | −9.64323 | − | 14.3560i | −0.394671 | − | 0.587550i | ||||
\(598\) | 0.0252935 | + | 0.426093i | 0.00103433 | + | 0.0174242i | ||||
\(599\) | −6.76799 | − | 11.7225i | −0.276533 | − | 0.478968i | 0.693988 | − | 0.719987i | \(-0.255852\pi\) |
−0.970521 | + | 0.241018i | \(0.922519\pi\) | |||||||
\(600\) | 2.78378 | + | 1.36435i | 0.113647 | + | 0.0556994i | ||||
\(601\) | −19.0294 | − | 32.9599i | −0.776225 | − | 1.34446i | −0.934103 | − | 0.357003i | \(-0.883799\pi\) |
0.157878 | − | 0.987459i | \(-0.449535\pi\) | |||||||
\(602\) | 0.336852 | + | 0.583445i | 0.0137291 | + | 0.0237794i | ||||
\(603\) | 2.64164 | + | 19.3337i | 0.107576 | + | 0.787328i | ||||
\(604\) | 17.6462 | − | 10.1880i | 0.718012 | − | 0.414545i | ||||
\(605\) | − | 1.63130i | − | 0.0663217i | ||||||
\(606\) | 0.162048 | + | 0.0794208i | 0.00658274 | + | 0.00322625i | ||||
\(607\) | −0.210095 | + | 0.363895i | −0.00852748 | + | 0.0147700i | −0.870258 | − | 0.492597i | \(-0.836048\pi\) |
0.861730 | + | 0.507367i | \(0.169381\pi\) | |||||||
\(608\) | 5.17738 | 0.209970 | ||||||||
\(609\) | −2.38356 | + | 1.60109i | −0.0965867 | + | 0.0648795i | ||||
\(610\) | 0.0690181 | − | 0.119543i | 0.00279446 | − | 0.00484015i | ||||
\(611\) | −18.2577 | + | 12.0374i | −0.738626 | + | 0.486982i | ||||
\(612\) | −36.0960 | + | 4.93195i | −1.45910 | + | 0.199362i | ||||
\(613\) | −37.4075 | − | 21.5972i | −1.51087 | − | 0.872303i | −0.999919 | − | 0.0126955i | \(-0.995959\pi\) |
−0.510954 | − | 0.859608i | \(-0.670708\pi\) | |||||||
\(614\) | 0.0322747 | + | 0.0559015i | 0.00130250 | + | 0.00225600i | ||||
\(615\) | 2.24368 | + | 3.34018i | 0.0904740 | + | 0.134689i | ||||
\(616\) | −1.31572 | + | 0.759634i | −0.0530120 | + | 0.0306065i | ||||
\(617\) | −2.26975 | − | 1.31044i | −0.0913769 | − | 0.0527565i | 0.453615 | − | 0.891198i | \(-0.350134\pi\) |
−0.544992 | + | 0.838441i | \(0.683467\pi\) | |||||||
\(618\) | 2.41678 | + | 1.18448i | 0.0972172 | + | 0.0476469i | ||||
\(619\) | 7.21384 | + | 4.16492i | 0.289949 | + | 0.167402i | 0.637919 | − | 0.770104i | \(-0.279796\pi\) |
−0.347970 | + | 0.937506i | \(0.613129\pi\) | |||||||
\(620\) | 1.45151 | + | 2.51408i | 0.0582939 | + | 0.100968i | ||||
\(621\) | −6.63487 | + | 1.37046i | −0.266248 | + | 0.0549947i | ||||
\(622\) | 0.558431 | + | 0.322410i | 0.0223910 | + | 0.0129275i | ||||
\(623\) | −2.09979 | + | 3.63694i | −0.0841263 | + | 0.145711i | ||||
\(624\) | 24.4722 | − | 3.12948i | 0.979673 | − | 0.125279i | ||||
\(625\) | −12.0396 | − | 20.8533i | −0.481586 | − | 0.834131i | ||||
\(626\) | − | 0.866158i | − | 0.0346186i | ||||||
\(627\) | 15.2668 | − | 31.1498i | 0.609696 | − | 1.24400i | ||||
\(628\) | 32.8438 | 1.31061 | ||||||||
\(629\) | − | 31.8354i | − | 1.26936i | ||||||
\(630\) | 0.0626033 | + | 0.0255729i | 0.00249417 | + | 0.00101885i | ||||
\(631\) | 23.9372 | − | 13.8201i | 0.952925 | − | 0.550171i | 0.0589364 | − | 0.998262i | \(-0.481229\pi\) |
0.893988 | + | 0.448090i | \(0.147896\pi\) | |||||||
\(632\) | −2.30210 | − | 1.32912i | −0.0915728 | − | 0.0528696i | ||||
\(633\) | −32.2865 | + | 2.19552i | −1.28327 | + | 0.0872640i | ||||
\(634\) | −1.53992 | −0.0611580 | ||||||||
\(635\) | − | 1.58077i | − | 0.0627308i | ||||||
\(636\) | 16.4967 | − | 33.6593i | 0.654136 | − | 1.33468i | ||||
\(637\) | 1.61458 | − | 3.22384i | 0.0639719 | − | 0.127733i | ||||
\(638\) | 0.630959 | 0.0249799 | ||||||||
\(639\) | 1.13135 | − | 0.876948i | 0.0447557 | − | 0.0346915i | ||||
\(640\) | −0.356959 | + | 0.618272i | −0.0141101 | + | 0.0244393i | ||||
\(641\) | −36.5161 | −1.44230 | −0.721149 | − | 0.692780i | \(-0.756386\pi\) | ||||
−0.721149 | + | 0.692780i | \(0.756386\pi\) | |||||||
\(642\) | −0.0723403 | − | 1.06381i | −0.00285504 | − | 0.0419852i | ||||
\(643\) | 4.25878 | + | 2.45881i | 0.167950 | + | 0.0969659i | 0.581619 | − | 0.813461i | \(-0.302420\pi\) |
−0.413669 | + | 0.910427i | \(0.635753\pi\) | |||||||
\(644\) | −2.24900 | − | 1.29846i | −0.0886230 | − | 0.0511665i | ||||
\(645\) | 2.64852 | − | 1.77907i | 0.104285 | − | 0.0700508i | ||||
\(646\) | −2.64508 | −0.104069 | ||||||||
\(647\) | 11.9059 | − | 20.6216i | 0.468068 | − | 0.810717i | −0.531266 | − | 0.847205i | \(-0.678284\pi\) |
0.999334 | + | 0.0364875i | \(0.0116169\pi\) | |||||||
\(648\) | −0.875057 | − | 3.14241i | −0.0343755 | − | 0.123446i | ||||
\(649\) | 16.3900 | 0.643362 | ||||||||
\(650\) | 1.44554 | + | 0.723962i | 0.0566988 | + | 0.0283961i | ||||
\(651\) | −5.67004 | − | 8.44104i | −0.222227 | − | 0.330830i | ||||
\(652\) | − | 13.3831i | − | 0.524123i | ||||||
\(653\) | 22.2338 | 0.870077 | 0.435038 | − | 0.900412i | \(-0.356735\pi\) | ||||
0.435038 | + | 0.900412i | \(0.356735\pi\) | |||||||
\(654\) | −0.407514 | − | 0.606669i | −0.0159351 | − | 0.0237226i | ||||
\(655\) | −0.175651 | − | 0.101412i | −0.00686324 | − | 0.00396249i | ||||
\(656\) | 32.0153 | − | 18.4840i | 1.24999 | − | 0.721680i | ||||
\(657\) | −2.60344 | − | 19.0541i | −0.101570 | − | 0.743371i | ||||
\(658\) | 0.550714i | 0.0214691i | ||||||||
\(659\) | −22.5087 | −0.876813 | −0.438406 | − | 0.898777i | \(-0.644457\pi\) | ||||
−0.438406 | + | 0.898777i | \(0.644457\pi\) | |||||||
\(660\) | 2.00184 | + | 2.98016i | 0.0779217 | + | 0.116003i | ||||
\(661\) | − | 10.7965i | − | 0.419934i | −0.977709 | − | 0.209967i | \(-0.932664\pi\) | ||
0.977709 | − | 0.209967i | \(-0.0673356\pi\) | |||||||
\(662\) | −0.0208759 | − | 0.0361581i | −0.000811365 | − | 0.00140532i | ||||
\(663\) | −37.7684 | + | 4.82978i | −1.46680 | + | 0.187573i | ||||
\(664\) | −2.91506 | + | 5.04904i | −0.113126 | + | 0.195941i | ||||
\(665\) | −1.02728 | − | 0.593100i | −0.0398362 | − | 0.0229994i | ||||
\(666\) | 1.40919 | − | 0.192544i | 0.0546051 | − | 0.00746093i | ||||
\(667\) | 1.08075 | + | 1.87191i | 0.0418466 | + | 0.0724805i | ||||
\(668\) | 37.9208 | + | 21.8936i | 1.46720 | + | 0.847088i | ||||
\(669\) | −22.2163 | + | 14.9232i | −0.858933 | + | 0.576965i | ||||
\(670\) | −0.126977 | − | 0.0733104i | −0.00490556 | − | 0.00283223i | ||||
\(671\) | −22.2297 | + | 12.8343i | −0.858169 | + | 0.495464i | ||||
\(672\) | 0.825979 | − | 1.68530i | 0.0318628 | − | 0.0650120i | ||||
\(673\) | 8.03730 | + | 13.9210i | 0.309815 | + | 0.536615i | 0.978322 | − | 0.207091i | \(-0.0663995\pi\) |
−0.668507 | + | 0.743706i | \(0.733066\pi\) | |||||||
\(674\) | −2.35834 | − | 1.36159i | −0.0908398 | − | 0.0524464i | ||||
\(675\) | −8.06972 | + | 24.3586i | −0.310603 | + | 0.937563i | ||||
\(676\) | 25.7110 | − | 3.06328i | 0.988884 | − | 0.117819i | ||||
\(677\) | 14.4424 | − | 25.0150i | 0.555067 | − | 0.961405i | −0.442831 | − | 0.896605i | \(-0.646026\pi\) |
0.997898 | − | 0.0647999i | \(-0.0206409\pi\) | |||||||
\(678\) | 0.104994 | + | 1.54400i | 0.00403226 | + | 0.0592969i | ||||
\(679\) | −11.0898 | −0.425588 | ||||||||
\(680\) | 0.274308 | − | 0.475116i | 0.0105192 | − | 0.0182199i | ||||
\(681\) | 1.56638 | + | 23.0346i | 0.0600238 | + | 0.882687i | ||||
\(682\) | 2.23445i | 0.0855616i | ||||||||
\(683\) | −28.8556 | + | 16.6598i | −1.10413 | + | 0.637468i | −0.937302 | − | 0.348518i | \(-0.886685\pi\) |
−0.166826 | + | 0.985986i | \(0.553352\pi\) | |||||||
\(684\) | 3.86497 | + | 28.2870i | 0.147781 | + | 1.08158i | ||||
\(685\) | 2.16208 | + | 3.74483i | 0.0826087 | + | 0.143082i | ||||
\(686\) | −0.0453987 | − | 0.0786329i | −0.00173333 | − | 0.00300222i | ||||
\(687\) | 33.9625 | − | 22.8134i | 1.29575 | − | 0.870387i | ||||
\(688\) | −14.6564 | − | 25.3857i | −0.558772 | − | 0.967821i | ||||
\(689\) | 17.5434 | − | 35.0291i | 0.668351 | − | 1.33450i | ||||
\(690\) | 0.0224034 | − | 0.0457112i | 0.000852883 | − | 0.00174020i | ||||
\(691\) | −7.89841 | + | 4.56015i | −0.300470 | + | 0.173476i | −0.642654 | − | 0.766157i | \(-0.722167\pi\) |
0.342184 | + | 0.939633i | \(0.388833\pi\) | |||||||
\(692\) | 25.3402 | − | 43.8905i | 0.963290 | − | 1.66847i | ||||
\(693\) | −7.70407 | − | 9.93906i | −0.292654 | − | 0.377554i | ||||
\(694\) | 3.25686i | 0.123629i | ||||||||
\(695\) | − | 2.54128i | − | 0.0963964i | ||||||
\(696\) | −0.863900 | + | 0.580302i | −0.0327461 | + | 0.0219963i | ||||
\(697\) | −49.4097 | + | 28.5267i | −1.87153 | + | 1.08053i | ||||
\(698\) | −1.37973 | + | 2.38976i | −0.0522235 | + | 0.0904538i | ||||
\(699\) | −8.57526 | + | 0.583128i | −0.324346 | + | 0.0220559i | ||||
\(700\) | −8.51824 | + | 4.91801i | −0.321959 | + | 0.185883i | ||||
\(701\) | −40.1282 | −1.51562 | −0.757811 | − | 0.652474i | \(-0.773731\pi\) | ||||
−0.757811 | + | 0.652474i | \(0.773731\pi\) | |||||||
\(702\) | −0.442217 | − | 1.64261i | −0.0166904 | − | 0.0619962i | ||||
\(703\) | −24.9481 | −0.940936 | ||||||||
\(704\) | 28.3256 | − | 16.3538i | 1.06756 | − | 0.616356i | ||||
\(705\) | 2.60209 | − | 0.176945i | 0.0980005 | − | 0.00666415i | ||||
\(706\) | 1.52136 | − | 2.63508i | 0.0572572 | − | 0.0991724i | ||||
\(707\) | −0.993770 | + | 0.573753i | −0.0373746 | + | 0.0215782i | ||||
\(708\) | −11.1973 | + | 7.52148i | −0.420820 | + | 0.282674i | ||||
\(709\) | 11.4936i | 0.431652i | 0.976432 | + | 0.215826i | \(0.0692444\pi\) | ||||
−0.976432 | + | 0.215826i | \(0.930756\pi\) | |||||||
\(710\) | 0.0107556i | 0.000403652i | ||||||||
\(711\) | 8.32053 | − | 20.3689i | 0.312044 | − | 0.763893i | ||||
\(712\) | −0.761051 | + | 1.31818i | −0.0285216 | + | 0.0494008i | ||||
\(713\) | −6.62909 | + | 3.82731i | −0.248261 | + | 0.143334i | ||||
\(714\) | −0.421985 | + | 0.861006i | −0.0157924 | + | 0.0322224i | ||||
\(715\) | 2.06533 | + | 3.13258i | 0.0772391 | + | 0.117152i | ||||
\(716\) | −21.3786 | − | 37.0289i | −0.798958 | − | 1.38384i | ||||
\(717\) | 16.4050 | − | 11.0196i | 0.612657 | − | 0.411536i | ||||
\(718\) | −0.992277 | − | 1.71867i | −0.0370315 | − | 0.0641404i | ||||
\(719\) | −17.3069 | − | 29.9764i | −0.645438 | − | 1.11793i | −0.984200 | − | 0.177060i | \(-0.943341\pi\) |
0.338762 | − | 0.940872i | \(-0.389992\pi\) | |||||||
\(720\) | −2.72387 | − | 1.11268i | −0.101513 | − | 0.0414671i | ||||
\(721\) | −14.8211 | + | 8.55696i | −0.551966 | + | 0.318678i | ||||
\(722\) | 0.347685i | 0.0129395i | ||||||||
\(723\) | 0.207073 | + | 3.04514i | 0.00770112 | + | 0.113250i | ||||
\(724\) | −14.5111 | + | 25.1339i | −0.539299 | + | 0.934094i | ||||
\(725\) | 8.18680 | 0.304050 | ||||||||
\(726\) | 0.0701084 | + | 1.03099i | 0.00260197 | + | 0.0382636i | ||||
\(727\) | −6.38601 | + | 11.0609i | −0.236844 | + | 0.410226i | −0.959807 | − | 0.280661i | \(-0.909446\pi\) |
0.722963 | + | 0.690887i | \(0.242780\pi\) | |||||||
\(728\) | 0.585190 | − | 1.16845i | 0.0216886 | − | 0.0433058i | ||||
\(729\) | 24.7904 | − | 10.6975i | 0.918162 | − | 0.396205i | ||||
\(730\) | 0.125141 | + | 0.0722503i | 0.00463168 | + | 0.00267410i | ||||
\(731\) | 22.6195 | + | 39.1782i | 0.836614 | + | 1.44906i | ||||
\(732\) | 9.29711 | − | 18.9695i | 0.343631 | − | 0.701135i | ||||
\(733\) | 44.6212 | − | 25.7621i | 1.64812 | − | 0.951544i | 0.670304 | − | 0.742086i | \(-0.266164\pi\) |
0.977818 | − | 0.209457i | \(-0.0671697\pi\) | |||||||
\(734\) | 0.279350 | + | 0.161283i | 0.0103110 | + | 0.00595306i | ||||
\(735\) | −0.356950 | + | 0.239772i | −0.0131663 | + | 0.00884411i | ||||
\(736\) | −1.22354 | − | 0.706410i | −0.0451002 | − | 0.0260386i | ||||
\(737\) | 13.6325 | + | 23.6122i | 0.502160 | + | 0.869766i | ||||
\(738\) | −1.56157 | − | 2.01459i | −0.0574821 | − | 0.0741579i | ||||
\(739\) | 35.7221 | + | 20.6242i | 1.31406 | + | 0.758673i | 0.982766 | − | 0.184855i | \(-0.0591814\pi\) |
0.331294 | + | 0.943528i | \(0.392515\pi\) | |||||||
\(740\) | 1.29095 | − | 2.23600i | 0.0474564 | − | 0.0821969i | ||||
\(741\) | 3.78490 | + | 29.5975i | 0.139042 | + | 1.08729i | ||||
\(742\) | −0.493287 | − | 0.854398i | −0.0181091 | − | 0.0313659i | ||||
\(743\) | 16.6004i | 0.609011i | 0.952511 | + | 0.304505i | \(0.0984912\pi\) | ||||
−0.952511 | + | 0.304505i | \(0.901509\pi\) | |||||||
\(744\) | −2.05506 | − | 3.05938i | −0.0753421 | − | 0.112162i | ||||
\(745\) | 0.638081 | 0.0233775 | ||||||||
\(746\) | − | 3.25167i | − | 0.119052i | ||||||
\(747\) | −44.6736 | − | 18.2488i | −1.63452 | − | 0.667689i | ||||
\(748\) | −44.0841 | + | 25.4519i | −1.61187 | + | 0.930615i | ||||
\(749\) | 5.87167 | + | 3.39001i | 0.214546 | + | 0.123868i | ||||
\(750\) | −0.216365 | − | 0.322104i | −0.00790053 | − | 0.0117616i | ||||
\(751\) | −21.5659 | −0.786951 | −0.393476 | − | 0.919335i | \(-0.628727\pi\) | ||||
−0.393476 | + | 0.919335i | \(0.628727\pi\) | |||||||
\(752\) | − | 23.9616i | − | 0.873789i | ||||||
\(753\) | −6.36285 | − | 9.47242i | −0.231875 | − | 0.345194i | ||||
\(754\) | −0.453104 | + | 0.298735i | −0.0165011 | + | 0.0108793i | ||||
\(755\) | −2.53978 | −0.0924320 | ||||||||
\(756\) | 9.82438 | + | 3.25470i | 0.357309 | + | 0.118372i | ||||
\(757\) | −24.5354 | + | 42.4966i | −0.891756 | + | 1.54457i | −0.0539865 | + | 0.998542i | \(0.517193\pi\) |
−0.837769 | + | 0.546025i | \(0.816141\pi\) | |||||||
\(758\) | 1.76786 | 0.0642117 | ||||||||
\(759\) | −7.85804 | + | 5.27843i | −0.285229 | + | 0.191595i | ||||
\(760\) | −0.372329 | − | 0.214964i | −0.0135058 | − | 0.00779756i | ||||
\(761\) | 16.7628 | + | 9.67803i | 0.607652 | + | 0.350828i | 0.772046 | − | 0.635567i | \(-0.219233\pi\) |
−0.164394 | + | 0.986395i | \(0.552567\pi\) | |||||||
\(762\) | 0.0679367 | + | 0.999052i | 0.00246109 | + | 0.0361918i | ||||
\(763\) | 4.64711 | 0.168237 | ||||||||
\(764\) | 6.79607 | − | 11.7711i | 0.245873 | − | 0.425865i | ||||
\(765\) | 4.20380 | + | 1.71722i | 0.151989 | + | 0.0620861i | ||||
\(766\) | −0.0848977 | −0.00306748 | ||||||||
\(767\) | −11.7699 | + | 7.76002i | −0.424988 | + | 0.280198i | ||||
\(768\) | −11.6966 | + | 23.8653i | −0.422064 | + | 0.861166i | ||||
\(769\) | − | 24.7761i | − | 0.893447i | −0.894672 | − | 0.446724i | \(-0.852591\pi\) | ||
0.894672 | − | 0.446724i | \(-0.147409\pi\) | |||||||
\(770\) | 0.0944893 | 0.00340516 | ||||||||
\(771\) | 21.3660 | − | 1.45291i | 0.769478 | − | 0.0523254i | ||||
\(772\) | 14.4416 | + | 8.33783i | 0.519763 | + | 0.300085i | ||||
\(773\) | −43.4295 | + | 25.0740i | −1.56205 | + | 0.901849i | −0.564999 | + | 0.825092i | \(0.691123\pi\) |
−0.997050 | + | 0.0767577i | \(0.975543\pi\) | |||||||
\(774\) | −1.59742 | + | 1.23821i | −0.0574179 | + | 0.0445064i | ||||
\(775\) | 28.9924i | 1.04144i | ||||||||
\(776\) | −4.01941 | −0.144288 | ||||||||
\(777\) | −3.98013 | + | 8.12093i | −0.142786 | + | 0.291337i | ||||
\(778\) | − | 1.23807i | − | 0.0443868i | ||||||
\(779\) | 22.3552 | + | 38.7204i | 0.800959 | + | 1.38730i | ||||
\(780\) | −2.84856 | − | 1.19232i | −0.101995 | − | 0.0426917i | ||||
\(781\) | 1.00004 | − | 1.73212i | 0.0357841 | − | 0.0619800i | ||||
\(782\) | 0.625095 | + | 0.360899i | 0.0223533 | + | 0.0129057i | ||||
\(783\) | −5.72709 | − | 6.43460i | −0.204670 | − | 0.229954i | ||||
\(784\) | 1.97530 | + | 3.42132i | 0.0705465 | + | 0.122190i | ||||
\(785\) | −3.54536 | − | 2.04692i | −0.126539 | − | 0.0730576i | ||||
\(786\) | 0.115371 | + | 0.0565439i | 0.00411513 | + | 0.00201685i | ||||
\(787\) | 14.1104 | + | 8.14664i | 0.502981 | + | 0.290396i | 0.729944 | − | 0.683507i | \(-0.239546\pi\) |
−0.226963 | + | 0.973903i | \(0.572880\pi\) | |||||||
\(788\) | −9.60479 | + | 5.54533i | −0.342156 | + | 0.197544i | ||||
\(789\) | 16.8561 | + | 25.0939i | 0.600094 | + | 0.893365i | ||||
\(790\) | 0.0826633 | + | 0.143177i | 0.00294103 | + | 0.00509401i | ||||
\(791\) | −8.52206 | − | 4.92021i | −0.303010 | − | 0.174943i | ||||
\(792\) | −2.79228 | − | 3.60233i | −0.0992192 | − | 0.128003i | ||||
\(793\) | 9.88703 | − | 19.7415i | 0.351099 | − | 0.701042i | ||||
\(794\) | 0.972274 | − | 1.68403i | 0.0345047 | − | 0.0597639i | ||||
\(795\) | −3.87849 | + | 2.60527i | −0.137556 | + | 0.0923996i | ||||
\(796\) | 19.8872 | 0.704882 | ||||||||
\(797\) | −22.9236 | + | 39.7049i | −0.811997 | + | 1.40642i | 0.0994681 | + | 0.995041i | \(0.468286\pi\) |
−0.911465 | + | 0.411378i | \(0.865047\pi\) | |||||||
\(798\) | 0.674735 | + | 0.330693i | 0.0238854 | + | 0.0117064i | ||||
\(799\) | 36.9803i | 1.30827i | ||||||||
\(800\) | −4.63423 | + | 2.67558i | −0.163845 | + | 0.0945959i | ||||
\(801\) | −11.6632 | − | 4.76431i | −0.412098 | − | 0.168339i | ||||
\(802\) | −0.452904 | − | 0.784452i | −0.0159926 | − | 0.0277000i | ||||
\(803\) | −13.4354 | − | 23.2707i | −0.474124 | − | 0.821207i | ||||
\(804\) | −20.1493 | − | 9.87531i | −0.710610 | − | 0.348275i | ||||
\(805\) | 0.161847 | + | 0.280328i | 0.00570436 | + | 0.00988025i | ||||
\(806\) | −1.05793 | − | 1.60460i | −0.0372639 | − | 0.0565197i | ||||
\(807\) | 4.31994 | + | 6.43113i | 0.152069 | + | 0.226386i | ||||
\(808\) | −0.360183 | + | 0.207952i | −0.0126712 | + | 0.00731573i | ||||
\(809\) | −3.31177 | + | 5.73616i | −0.116436 | + | 0.201673i | −0.918353 | − | 0.395763i | \(-0.870480\pi\) |
0.801917 | + | 0.597435i | \(0.203814\pi\) | |||||||
\(810\) | −0.0505875 | + | 0.196467i | −0.00177746 | + | 0.00690314i | ||||
\(811\) | − | 49.7150i | − | 1.74573i | −0.487962 | − | 0.872865i | \(-0.662259\pi\) | ||
0.487962 | − | 0.872865i | \(-0.337741\pi\) | |||||||
\(812\) | − | 3.30192i | − | 0.115875i | ||||||
\(813\) | −28.2580 | − | 13.8494i | −0.991050 | − | 0.485721i | ||||
\(814\) | 1.72105 | − | 0.993647i | 0.0603227 | − | 0.0348273i | ||||
\(815\) | −0.834071 | + | 1.44465i | −0.0292162 | + | 0.0506040i | ||||
\(816\) | 18.3606 | − | 37.4624i | 0.642750 | − | 1.31145i | ||||
\(817\) | 30.7023 | − | 17.7260i | 1.07414 | − | 0.620154i | ||||
\(818\) | −2.28604 | −0.0799294 | ||||||||
\(819\) | 10.2382 | + | 3.48985i | 0.357752 | + | 0.121945i | ||||
\(820\) | −4.62713 | −0.161586 | ||||||||
\(821\) | 31.9374 | − | 18.4391i | 1.11462 | − | 0.643527i | 0.174599 | − | 0.984640i | \(-0.444137\pi\) |
0.940023 | + | 0.341112i | \(0.110804\pi\) | |||||||
\(822\) | −1.52738 | − | 2.27383i | −0.0532736 | − | 0.0793089i | ||||
\(823\) | −0.505428 | + | 0.875428i | −0.0176181 | + | 0.0305155i | −0.874700 | − | 0.484665i | \(-0.838942\pi\) |
0.857082 | + | 0.515180i | \(0.172275\pi\) | |||||||
\(824\) | −5.37178 | + | 3.10140i | −0.187135 | + | 0.108042i | ||||
\(825\) | 2.43251 | + | 35.7716i | 0.0846891 | + | 1.24541i | ||||
\(826\) | 0.355022i | 0.0123528i | ||||||||
\(827\) | 34.6870i | 1.20619i | 0.797671 | + | 0.603093i | \(0.206065\pi\) | ||||
−0.797671 | + | 0.603093i | \(0.793935\pi\) | |||||||
\(828\) | 2.94614 | − | 7.21223i | 0.102385 | − | 0.250642i | ||||
\(829\) | 0.528334 | − | 0.915101i | 0.0183498 | − | 0.0317828i | −0.856705 | − | 0.515807i | \(-0.827492\pi\) |
0.875054 | + | 0.484024i | \(0.160825\pi\) | |||||||
\(830\) | 0.314020 | − | 0.181299i | 0.0108998 | − | 0.00629299i | ||||
\(831\) | 0.121099 | − | 0.00823484i | 0.00420086 | − | 0.000285664i | ||||
\(832\) | −12.5983 | + | 25.1550i | −0.436766 | + | 0.872094i | ||||
\(833\) | −3.04852 | − | 5.28019i | −0.105625 | − | 0.182948i | ||||
\(834\) | 0.109217 | + | 1.60610i | 0.00378187 | + | 0.0556148i | ||||
\(835\) | −2.72893 | − | 4.72665i | −0.0944387 | − | 0.163573i | ||||
\(836\) | 19.9456 | + | 34.5469i | 0.689835 | + | 1.19483i | ||||
\(837\) | 22.7872 | − | 20.2817i | 0.787642 | − | 0.701038i | ||||
\(838\) | −0.276495 | + | 0.159634i | −0.00955135 | + | 0.00551447i | ||||
\(839\) | 19.9048i | 0.687189i | 0.939118 | + | 0.343594i | \(0.111645\pi\) | ||||
−0.939118 | + | 0.343594i | \(0.888355\pi\) | |||||||
\(840\) | −0.129373 | + | 0.0869032i | −0.00446381 | + | 0.00299845i | ||||
\(841\) | 13.1259 | − | 22.7347i | 0.452616 | − | 0.783954i | ||||
\(842\) | −1.07027 | −0.0368839 | ||||||||
\(843\) | −26.9108 | − | 13.1892i | −0.926857 | − | 0.454260i | ||||
\(844\) | 18.6066 | − | 32.2276i | 0.640467 | − | 1.10932i | ||||
\(845\) | −2.96631 | − | 1.27171i | −0.102044 | − | 0.0437481i | ||||
\(846\) | −1.63693 | + | 0.223661i | −0.0562789 | + | 0.00768962i | ||||
\(847\) | −5.69052 | − | 3.28542i | −0.195529 | − | 0.112888i | ||||
\(848\) | 21.4629 | + | 37.1749i | 0.737040 | + | 1.27659i | ||||
\(849\) | −58.0686 | + | 3.94873i | −1.99291 | + | 0.135520i | ||||
\(850\) | 2.36759 | − | 1.36693i | 0.0812076 | − | 0.0468852i | ||||
\(851\) | 5.89584 | + | 3.40396i | 0.202107 | + | 0.116686i | ||||
\(852\) | 0.111676 | + | 1.64227i | 0.00382597 | + | 0.0562633i | ||||
\(853\) | 2.74547 | + | 1.58510i | 0.0940032 | + | 0.0542728i | 0.546265 | − | 0.837613i | \(-0.316049\pi\) |
−0.452261 | + | 0.891885i | \(0.649383\pi\) | |||||||
\(854\) | −0.278004 | − | 0.481517i | −0.00951310 | − | 0.0164772i | ||||
\(855\) | 1.34571 | − | 3.29434i | 0.0460224 | − | 0.112664i | ||||
\(856\) | 2.12814 | + | 1.22868i | 0.0727382 | + | 0.0419954i | ||||
\(857\) | 21.8402 | − | 37.8284i | 0.746048 | − | 1.29219i | −0.203655 | − | 0.979043i | \(-0.565282\pi\) |
0.949703 | − | 0.313151i | \(-0.101385\pi\) | |||||||
\(858\) | −1.43993 | − | 1.89104i | −0.0491584 | − | 0.0645591i | ||||
\(859\) | 17.6050 | + | 30.4928i | 0.600675 | + | 1.04040i | 0.992719 | + | 0.120453i | \(0.0384347\pi\) |
−0.392044 | + | 0.919946i | \(0.628232\pi\) | |||||||
\(860\) | 3.66896i | 0.125111i | ||||||||
\(861\) | 16.1704 | − | 1.09961i | 0.551087 | − | 0.0374746i | ||||
\(862\) | −3.14020 | −0.106956 | ||||||||
\(863\) | 35.5346i | 1.20961i | 0.796372 | + | 0.604807i | \(0.206750\pi\) | ||||
−0.796372 | + | 0.604807i | \(0.793250\pi\) | |||||||
\(864\) | 5.34482 | + | 1.77068i | 0.181834 | + | 0.0602396i | ||||
\(865\) | −5.47075 | + | 3.15854i | −0.186011 | + | 0.107394i | ||||
\(866\) | −1.19699 | − | 0.691084i | −0.0406755 | − | 0.0234840i | ||||
\(867\) | −15.3778 | + | 31.3763i | −0.522256 | + | 1.06560i | ||||
\(868\) | 11.6933 | 0.396896 | ||||||||
\(869\) | − | 30.7435i | − | 1.04290i | ||||||
\(870\) | 0.0645767 | − | 0.00439129i | 0.00218935 | − | 0.000148879i | ||||
\(871\) | −20.9692 | − | 10.5019i | −0.710516 | − | 0.355844i | ||||
\(872\) | 1.68430 | 0.0570378 | ||||||||
\(873\) | −4.50389 | − | 32.9632i | −0.152434 | − | 1.11563i | ||||
\(874\) | 0.282821 | − | 0.489861i | 0.00956658 | − | 0.0165698i | ||||
\(875\) | 2.46733 | 0.0834110 | ||||||||
\(876\) | 19.8579 | + | 9.73250i | 0.670936 | + | 0.328831i | ||||
\(877\) | −10.5404 | − | 6.08550i | −0.355924 | − | 0.205493i | 0.311367 | − | 0.950290i | \(-0.399213\pi\) |
−0.667291 | + | 0.744797i | \(0.732546\pi\) | |||||||
\(878\) | −2.19533 | − | 1.26748i | −0.0740888 | − | 0.0427752i | ||||
\(879\) | 37.0154 | + | 18.1415i | 1.24850 | + | 0.611898i | ||||
\(880\) | −4.11123 | −0.138590 | ||||||||
\(881\) | −22.5114 | + | 38.9910i | −0.758430 | + | 1.31364i | 0.185221 | + | 0.982697i | \(0.440700\pi\) |
−0.943651 | + | 0.330942i | \(0.892633\pi\) | |||||||
\(882\) | 0.215289 | − | 0.166878i | 0.00724917 | − | 0.00561906i | ||||
\(883\) | −47.9950 | −1.61516 | −0.807580 | − | 0.589759i | \(-0.799223\pi\) | ||||
−0.807580 | + | 0.589759i | \(0.799223\pi\) | |||||||
\(884\) | 19.6071 | − | 39.1497i | 0.659458 | − | 1.31675i | ||||
\(885\) | 1.67746 | − | 0.114069i | 0.0563872 | − | 0.00383440i | ||||
\(886\) | 1.84894i | 0.0621162i | ||||||||
\(887\) | −1.82237 | −0.0611891 | −0.0305946 | − | 0.999532i | \(-0.509740\pi\) | ||||
−0.0305946 | + | 0.999532i | \(0.509740\pi\) | |||||||
\(888\) | −1.44256 | + | 2.94336i | −0.0484093 | + | 0.0987728i | ||||
\(889\) | −5.51424 | − | 3.18365i | −0.184942 | − | 0.106776i | ||||
\(890\) | 0.0819828 | − | 0.0473328i | 0.00274807 | − | 0.00158660i | ||||
\(891\) | 26.4138 | − | 26.9360i | 0.884897 | − | 0.902390i | ||||
\(892\) | − | 30.7761i | − | 1.03046i | ||||||
\(893\) | 28.9799 | 0.969777 | ||||||||
\(894\) | −0.403270 | + | 0.0274229i | −0.0134874 | + | 0.000917158i | ||||
\(895\) | 5.32950i | 0.178146i | ||||||||
\(896\) | 1.43783 | + | 2.49039i | 0.0480344 | + | 0.0831980i | ||||
\(897\) | 3.14388 | − | 7.51103i | 0.104971 | − | 0.250786i | ||||
\(898\) | −1.07980 | + | 1.87027i | −0.0360335 | + | 0.0624119i | ||||
\(899\) | −8.42873 | − | 4.86633i | −0.281114 | − | 0.162301i | ||||
\(900\) | −18.0777 | − | 23.3221i | −0.602590 | − | 0.777404i | ||||
\(901\) | −33.1241 | − | 57.3726i | −1.10352 | − | 1.91136i | ||||
\(902\) | −3.08435 | − | 1.78075i | −0.102698 | − | 0.0592925i | ||||
\(903\) | −0.871907 | − | 12.8219i | −0.0290153 | − | 0.426688i | ||||
\(904\) | −3.08875 | − | 1.78329i | −0.102730 | − | 0.0593113i | ||||
\(905\) | 3.13282 | − | 1.80874i | 0.104139 | − | 0.0601244i | ||||
\(906\) | 1.60515 | − | 0.109152i | 0.0533276 | − | 0.00362634i | ||||
\(907\) | −19.9257 | − | 34.5124i | −0.661623 | − | 1.14597i | −0.980189 | − | 0.198064i | \(-0.936534\pi\) |
0.318566 | − | 0.947901i | \(-0.396799\pi\) | |||||||
\(908\) | −22.9926 | − | 13.2748i | −0.763037 | − | 0.440539i | ||||
\(909\) | −2.10901 | − | 2.72085i | −0.0699516 | − | 0.0902448i | ||||
\(910\) | −0.0678546 | + | 0.0447371i | −0.00224936 | + | 0.00148302i | ||||
\(911\) | −13.8869 | + | 24.0528i | −0.460093 | + | 0.796905i | −0.998965 | − | 0.0454827i | \(-0.985517\pi\) |
0.538872 | + | 0.842388i | \(0.318851\pi\) | |||||||
\(912\) | −29.3578 | − | 14.3885i | −0.972133 | − | 0.476449i | ||||
\(913\) | −67.4274 | −2.23152 | ||||||||
\(914\) | −0.658779 | + | 1.14104i | −0.0217905 | + | 0.0377422i | ||||
\(915\) | −2.18582 | + | 1.46827i | −0.0722610 | + | 0.0485394i | ||||
\(916\) | 47.0480i | 1.55451i | ||||||||
\(917\) | −0.707518 | + | 0.408486i | −0.0233643 | + | 0.0134894i | ||||
\(918\) | −2.73062 | − | 0.904623i | −0.0901239 | − | 0.0298570i | ||||
\(919\) | 20.0412 | + | 34.7124i | 0.661098 | + | 1.14506i | 0.980327 | + | 0.197378i | \(0.0632426\pi\) |
−0.319229 | + | 0.947677i | \(0.603424\pi\) | |||||||
\(920\) | 0.0586601 | + | 0.101602i | 0.00193397 | + | 0.00334973i | ||||
\(921\) | −0.0835399 | − | 1.22851i | −0.00275273 | − | 0.0404807i | ||||
\(922\) | 0.704183 | + | 1.21968i | 0.0231910 | + | 0.0401681i | ||||
\(923\) | 0.101944 | + | 1.71735i | 0.00335554 | + | 0.0565271i | ||||
\(924\) | 14.4275 | − | 0.981087i | 0.474630 | − | 0.0322754i | ||||
\(925\) | 22.3309 | − | 12.8927i | 0.734235 | − | 0.423911i | ||||
\(926\) | −0.464546 | + | 0.804618i | −0.0152659 | + | 0.0264414i | ||||
\(927\) | −31.4538 | − | 40.5787i | −1.03308 | − | 1.33278i | ||||
\(928\) | − | 1.79637i | − | 0.0589686i | ||||||
\(929\) | − | 51.0241i | − | 1.67405i | −0.547168 | − | 0.837023i | \(-0.684294\pi\) | ||
0.547168 | − | 0.837023i | \(-0.315706\pi\) | |||||||
\(930\) | 0.0155511 | + | 0.228689i | 0.000509942 | + | 0.00749901i | ||||
\(931\) | −4.13786 | + | 2.38900i | −0.135613 | + | 0.0782962i | ||||
\(932\) | 4.94191 | − | 8.55964i | 0.161878 | − | 0.280380i | ||||
\(933\) | −6.85884 | − | 10.2108i | −0.224548 | − | 0.334287i | ||||
\(934\) | 0.862073 | − | 0.497718i | 0.0282079 | − | 0.0162858i | ||||
\(935\) | 6.34494 | 0.207502 | ||||||||
\(936\) | 3.71075 | + | 1.26486i | 0.121290 | + | 0.0413434i | ||||
\(937\) | 46.1191 | 1.50664 | 0.753322 | − | 0.657651i | \(-0.228450\pi\) | ||||
0.753322 | + | 0.657651i | \(0.228450\pi\) | |||||||
\(938\) | −0.511463 | + | 0.295293i | −0.0166998 | + | 0.00964166i | ||||
\(939\) | −7.27157 | + | 14.8367i | −0.237299 | + | 0.484177i | ||||
\(940\) | −1.49958 | + | 2.59735i | −0.0489110 | + | 0.0847163i | ||||
\(941\) | −30.1514 | + | 17.4079i | −0.982908 | + | 0.567482i | −0.903147 | − | 0.429332i | \(-0.858749\pi\) |
−0.0797612 | + | 0.996814i | \(0.525416\pi\) | |||||||
\(942\) | 2.32866 | + | 1.14129i | 0.0758718 | + | 0.0371853i | ||||
\(943\) | − | 12.2007i | − | 0.397311i | ||||||
\(944\) | − | 15.4470i | − | 0.502758i | ||||||
\(945\) | −0.857661 | − | 0.963614i | −0.0278997 | − | 0.0313464i | ||||
\(946\) | −1.41200 | + | 2.44566i | −0.0459082 | + | 0.0795153i | ||||
\(947\) | 28.2929 | − | 16.3349i | 0.919397 | − | 0.530814i | 0.0359545 | − | 0.999353i | \(-0.488553\pi\) |
0.883443 | + | 0.468539i | \(0.155220\pi\) | |||||||
\(948\) | 14.1084 | + | 21.0033i | 0.458220 | + | 0.682156i | ||||
\(949\) | 20.6660 | + | 10.3500i | 0.670847 | + | 0.335977i | ||||
\(950\) | −1.07121 | − | 1.85538i | −0.0347545 | − | 0.0601965i | ||||
\(951\) | 26.3778 | + | 12.9279i | 0.855357 | + | 0.419217i | ||||
\(952\) | −1.10491 | − | 1.91376i | −0.0358103 | − | 0.0620253i | ||||
\(953\) | 4.77841 | + | 8.27645i | 0.154788 | + | 0.268101i | 0.932982 | − | 0.359924i | \(-0.117197\pi\) |
−0.778194 | + | 0.628024i | \(0.783864\pi\) | |||||||
\(954\) | 2.33926 | − | 1.81323i | 0.0757363 | − | 0.0587056i | ||||
\(955\) | −1.46722 | + | 0.847099i | −0.0474781 | + | 0.0274115i | ||||
\(956\) | 22.7257i | 0.735002i | ||||||||
\(957\) | −10.8079 | − | 5.29703i | −0.349369 | − | 0.171229i | ||||
\(958\) | −0.731034 | + | 1.26619i | −0.0236186 | + | 0.0409087i | ||||
\(959\) | 17.4176 | 0.562444 | ||||||||
\(960\) | 2.78522 | − | 1.87090i | 0.0898925 | − | 0.0603829i | ||||
\(961\) | 1.73342 | − | 3.00236i | 0.0559166 | − | 0.0968505i | ||||
\(962\) | −0.765464 | + | 1.52841i | −0.0246795 | + | 0.0492779i | ||||
\(963\) | −7.69175 | + | 18.8296i | −0.247863 | + | 0.606776i | ||||
\(964\) | −3.03959 | − | 1.75491i | −0.0978986 | − | 0.0565218i | ||||
\(965\) | −1.03927 | − | 1.80007i | −0.0334554 | − | 0.0579464i | ||||
\(966\) | −0.114336 | − | 0.170213i | −0.00367870 | − | 0.00547650i | ||||
\(967\) | −15.0263 | + | 8.67545i | −0.483214 | + | 0.278984i | −0.721755 | − | 0.692149i | \(-0.756664\pi\) |
0.238541 | + | 0.971132i | \(0.423331\pi\) | |||||||
\(968\) | −2.06248 | − | 1.19077i | −0.0662906 | − | 0.0382729i | ||||
\(969\) | 45.3083 | + | 22.2059i | 1.45551 | + | 0.713358i | ||||
\(970\) | 0.216492 | + | 0.124991i | 0.00695113 | + | 0.00401323i | ||||
\(971\) | 6.58186 | + | 11.4001i | 0.211222 | + | 0.365847i | 0.952097 | − | 0.305795i | \(-0.0989224\pi\) |
−0.740875 | + | 0.671643i | \(0.765589\pi\) | |||||||
\(972\) | −5.68425 | + | 30.5236i | −0.182322 | + | 0.979046i | ||||
\(973\) | −8.86485 | − | 5.11812i | −0.284194 | − | 0.164080i | ||||
\(974\) | 0.650189 | − | 1.12616i | 0.0208334 | − | 0.0360845i | ||||
\(975\) | −18.6833 | − | 24.5366i | −0.598345 | − | 0.785800i | ||||
\(976\) | 12.0960 | + | 20.9508i | 0.387182 | + | 0.670619i | ||||
\(977\) | 56.2363i | 1.79916i | 0.436759 | + | 0.899579i | \(0.356126\pi\) | ||||
−0.436759 | + | 0.899579i | \(0.643874\pi\) | |||||||
\(978\) | 0.465050 | − | 0.948874i | 0.0148707 | − | 0.0303417i | ||||
\(979\) | −17.6036 | −0.562614 | ||||||||
\(980\) | − | 0.494480i | − | 0.0157956i | ||||||
\(981\) | 1.88733 | + | 13.8130i | 0.0602577 | + | 0.441015i | ||||
\(982\) | −2.51990 | + | 1.45486i | −0.0804131 | + | 0.0464265i | ||||
\(983\) | 47.7301 | + | 27.5570i | 1.52235 | + | 0.878932i | 0.999651 | + | 0.0264178i | \(0.00841003\pi\) |
0.522704 | + | 0.852514i | \(0.324923\pi\) | |||||||
\(984\) | 5.86084 | − | 0.398544i | 0.186837 | − | 0.0127051i | ||||
\(985\) | 1.38240 | 0.0440469 | ||||||||
\(986\) | 0.917747i | 0.0292270i | ||||||||
\(987\) | 4.62335 | − | 9.43335i | 0.147163 | − | 0.300267i | ||||
\(988\) | −30.6800 | − | 15.3653i | −0.976060 | − | 0.488835i | ||||
\(989\) | −9.67427 | −0.307624 | ||||||||
\(990\) | 0.0383748 | + | 0.280858i | 0.00121963 | + | 0.00892626i | ||||
\(991\) | 7.86399 | − | 13.6208i | 0.249808 | − | 0.432680i | −0.713664 | − | 0.700488i | \(-0.752966\pi\) |
0.963472 | + | 0.267808i | \(0.0862992\pi\) | |||||||
\(992\) | 6.36158 | 0.201980 | ||||||||
\(993\) | 0.0540351 | + | 0.794621i | 0.00171475 | + | 0.0252165i | ||||
\(994\) | 0.0375193 | + | 0.0216618i | 0.00119004 | + | 0.000687069i | ||||
\(995\) | −2.14674 | − | 1.23942i | −0.0680563 | − | 0.0392923i | ||||
\(996\) | 46.0650 | − | 30.9430i | 1.45963 | − | 0.980465i | ||||
\(997\) | 0.612224 | 0.0193893 | 0.00969466 | − | 0.999953i | \(-0.496914\pi\) | ||||
0.00969466 | + | 0.999953i | \(0.496914\pi\) | |||||||
\(998\) | −0.248518 | + | 0.430446i | −0.00786670 | + | 0.0136255i | ||||
\(999\) | −25.7550 | − | 8.53232i | −0.814851 | − | 0.269951i |
(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 | 819.2.dk.a.43.40 | yes | 168 | |
9.4 | even | 3 | 819.2.bh.a.589.40 | ✓ | 168 | ||
13.10 | even | 6 | 819.2.bh.a.673.45 | yes | 168 | ||
117.49 | even | 6 | inner | 819.2.dk.a.400.40 | yes | 168 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
819.2.bh.a.589.40 | ✓ | 168 | 9.4 | even | 3 | ||
819.2.bh.a.673.45 | yes | 168 | 13.10 | even | 6 | ||
819.2.dk.a.43.40 | yes | 168 | 1.1 | even | 1 | trivial | |
819.2.dk.a.400.40 | yes | 168 | 117.49 | even | 6 | inner |