Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(47,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.c (of order \(2\), degree \(1\), 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: | \(2.20387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.3 | ||
Character | \(\chi\) | \(=\) | 276.47 |
Dual form | 276.2.c.a.47.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(139\) | \(185\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.37110 | − | 0.346521i | −0.969516 | − | 0.245028i | ||||
\(3\) | 1.70706 | − | 0.293173i | 0.985571 | − | 0.169264i | ||||
\(4\) | 1.75985 | + | 0.950233i | 0.879923 | + | 0.475116i | ||||
\(5\) | 2.20059i | 0.984132i | 0.870558 | + | 0.492066i | \(0.163758\pi\) | ||||
−0.870558 | + | 0.492066i | \(0.836242\pi\) | |||||||
\(6\) | −2.44214 | − | 0.189562i | −0.997001 | − | 0.0773883i | ||||
\(7\) | − | 3.71987i | − | 1.40598i | −0.711200 | − | 0.702990i | \(-0.751848\pi\) | ||
0.711200 | − | 0.702990i | \(-0.248152\pi\) | |||||||
\(8\) | −2.08365 | − | 1.91269i | −0.736683 | − | 0.676238i | ||||
\(9\) | 2.82810 | − | 1.00093i | 0.942700 | − | 0.333642i | ||||
\(10\) | 0.762550 | − | 3.01723i | 0.241140 | − | 0.954132i | ||||
\(11\) | 0.958233 | 0.288918 | 0.144459 | − | 0.989511i | \(-0.453856\pi\) | ||||
0.144459 | + | 0.989511i | \(0.453856\pi\) | |||||||
\(12\) | 3.28274 | + | 1.10616i | 0.947646 | + | 0.319322i | ||||
\(13\) | 2.52970 | 0.701612 | 0.350806 | − | 0.936448i | \(-0.385908\pi\) | ||||
0.350806 | + | 0.936448i | \(0.385908\pi\) | |||||||
\(14\) | −1.28901 | + | 5.10033i | −0.344504 | + | 1.36312i | ||||
\(15\) | 0.645153 | + | 3.75653i | 0.166578 | + | 0.969932i | ||||
\(16\) | 2.19412 | + | 3.34453i | 0.548529 | + | 0.836132i | ||||
\(17\) | 2.72185i | 0.660147i | 0.943955 | + | 0.330073i | \(0.107073\pi\) | ||||
−0.943955 | + | 0.330073i | \(0.892927\pi\) | |||||||
\(18\) | −4.22446 | + | 0.392378i | −0.995714 | + | 0.0924843i | ||||
\(19\) | 0.627384i | 0.143932i | 0.997407 | + | 0.0719659i | \(0.0229273\pi\) | ||||
−0.997407 | + | 0.0719659i | \(0.977073\pi\) | |||||||
\(20\) | −2.09107 | + | 3.87269i | −0.467577 | + | 0.865960i | ||||
\(21\) | −1.09057 | − | 6.35004i | −0.237981 | − | 1.38569i | ||||
\(22\) | −1.31384 | − | 0.332048i | −0.280111 | − | 0.0707929i | ||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −4.11767 | − | 2.65420i | −0.840516 | − | 0.541787i | ||||
\(25\) | 0.157420 | 0.0314841 | ||||||||
\(26\) | −3.46848 | − | 0.876595i | −0.680224 | − | 0.171914i | ||||
\(27\) | 4.53429 | − | 2.53776i | 0.872624 | − | 0.488393i | ||||
\(28\) | 3.53474 | − | 6.54640i | 0.668004 | − | 1.23715i | ||||
\(29\) | − | 6.59334i | − | 1.22435i | −0.790721 | − | 0.612177i | \(-0.790294\pi\) | ||
0.790721 | − | 0.612177i | \(-0.209706\pi\) | |||||||
\(30\) | 0.417147 | − | 5.37415i | 0.0761603 | − | 0.981181i | ||||
\(31\) | 9.19216i | 1.65096i | 0.564431 | + | 0.825480i | \(0.309096\pi\) | ||||
−0.564431 | + | 0.825480i | \(0.690904\pi\) | |||||||
\(32\) | −1.84941 | − | 5.34600i | −0.326932 | − | 0.945048i | ||||
\(33\) | 1.63576 | − | 0.280928i | 0.284749 | − | 0.0489033i | ||||
\(34\) | 0.943181 | − | 3.73194i | 0.161754 | − | 0.640023i | ||||
\(35\) | 8.18590 | 1.38367 | ||||||||
\(36\) | 5.92813 | + | 0.925875i | 0.988022 | + | 0.154312i | ||||
\(37\) | −8.67442 | −1.42607 | −0.713033 | − | 0.701130i | \(-0.752679\pi\) | ||||
−0.713033 | + | 0.701130i | \(0.752679\pi\) | |||||||
\(38\) | 0.217402 | − | 0.860208i | 0.0352673 | − | 0.139544i | ||||
\(39\) | 4.31834 | − | 0.741640i | 0.691489 | − | 0.118757i | ||||
\(40\) | 4.20904 | − | 4.58526i | 0.665508 | − | 0.724993i | ||||
\(41\) | 5.91840i | 0.924298i | 0.886802 | + | 0.462149i | \(0.152921\pi\) | ||||
−0.886802 | + | 0.462149i | \(0.847079\pi\) | |||||||
\(42\) | −0.705146 | + | 9.08446i | −0.108806 | + | 1.40176i | ||||
\(43\) | − | 7.53264i | − | 1.14872i | −0.818604 | − | 0.574358i | \(-0.805252\pi\) | ||
0.818604 | − | 0.574358i | \(-0.194748\pi\) | |||||||
\(44\) | 1.68634 | + | 0.910544i | 0.254226 | + | 0.137270i | ||||
\(45\) | 2.20263 | + | 6.22348i | 0.328348 | + | 0.927741i | ||||
\(46\) | −1.37110 | − | 0.346521i | −0.202158 | − | 0.0510918i | ||||
\(47\) | −4.76344 | −0.694820 | −0.347410 | − | 0.937713i | \(-0.612939\pi\) | ||||
−0.347410 | + | 0.937713i | \(0.612939\pi\) | |||||||
\(48\) | 4.72601 | + | 5.06605i | 0.682141 | + | 0.731221i | ||||
\(49\) | −6.83744 | −0.976777 | ||||||||
\(50\) | −0.215840 | − | 0.0545495i | −0.0305243 | − | 0.00771447i | ||||
\(51\) | 0.797975 | + | 4.64637i | 0.111739 | + | 0.650621i | ||||
\(52\) | 4.45188 | + | 2.40380i | 0.617365 | + | 0.333347i | ||||
\(53\) | − | 11.5826i | − | 1.59099i | −0.605963 | − | 0.795493i | \(-0.707212\pi\) | ||
0.605963 | − | 0.795493i | \(-0.292788\pi\) | |||||||
\(54\) | −7.09636 | + | 1.90831i | −0.965693 | + | 0.259688i | ||||
\(55\) | 2.10867i | 0.284334i | ||||||||
\(56\) | −7.11496 | + | 7.75092i | −0.950777 | + | 1.03576i | ||||
\(57\) | 0.183932 | + | 1.07098i | 0.0243624 | + | 0.141855i | ||||
\(58\) | −2.28473 | + | 9.04015i | −0.300000 | + | 1.18703i | ||||
\(59\) | 0.0894257 | 0.0116422 | 0.00582112 | − | 0.999983i | \(-0.498147\pi\) | ||||
0.00582112 | + | 0.999983i | \(0.498147\pi\) | |||||||
\(60\) | −2.43421 | + | 7.22396i | −0.314255 | + | 0.932609i | ||||
\(61\) | −14.4467 | −1.84971 | −0.924855 | − | 0.380320i | \(-0.875814\pi\) | ||||
−0.924855 | + | 0.380320i | \(0.875814\pi\) | |||||||
\(62\) | 3.18528 | − | 12.6034i | 0.404531 | − | 1.60063i | ||||
\(63\) | −3.72332 | − | 10.5202i | −0.469094 | − | 1.32542i | ||||
\(64\) | 0.683225 | + | 7.97077i | 0.0854031 | + | 0.996346i | ||||
\(65\) | 5.56682i | 0.690479i | ||||||||
\(66\) | −2.34014 | − | 0.181644i | −0.288052 | − | 0.0223589i | ||||
\(67\) | 13.6616i | 1.66902i | 0.550989 | + | 0.834512i | \(0.314251\pi\) | ||||
−0.550989 | + | 0.834512i | \(0.685749\pi\) | |||||||
\(68\) | −2.58640 | + | 4.79004i | −0.313647 | + | 0.580878i | ||||
\(69\) | 1.70706 | − | 0.293173i | 0.205506 | − | 0.0352939i | ||||
\(70\) | −11.2237 | − | 2.83659i | −1.34149 | − | 0.339037i | ||||
\(71\) | −12.6101 | −1.49654 | −0.748271 | − | 0.663394i | \(-0.769116\pi\) | ||||
−0.748271 | + | 0.663394i | \(0.769116\pi\) | |||||||
\(72\) | −7.80724 | − | 3.32369i | −0.920093 | − | 0.391701i | ||||
\(73\) | 4.66813 | 0.546363 | 0.273181 | − | 0.961963i | \(-0.411924\pi\) | ||||
0.273181 | + | 0.961963i | \(0.411924\pi\) | |||||||
\(74\) | 11.8935 | + | 3.00587i | 1.38259 | + | 0.349426i | ||||
\(75\) | 0.268726 | − | 0.0461514i | 0.0310298 | − | 0.00532911i | ||||
\(76\) | −0.596161 | + | 1.10410i | −0.0683843 | + | 0.126649i | ||||
\(77\) | − | 3.56450i | − | 0.406213i | ||||||
\(78\) | −6.17789 | − | 0.479534i | −0.699508 | − | 0.0542966i | ||||
\(79\) | 6.77610i | 0.762371i | 0.924499 | + | 0.381185i | \(0.124484\pi\) | ||||
−0.924499 | + | 0.381185i | \(0.875516\pi\) | |||||||
\(80\) | −7.35992 | + | 4.82834i | −0.822864 | + | 0.539825i | ||||
\(81\) | 6.99629 | − | 5.66144i | 0.777365 | − | 0.629049i | ||||
\(82\) | 2.05085 | − | 8.11473i | 0.226479 | − | 0.896122i | ||||
\(83\) | −12.4401 | −1.36548 | −0.682738 | − | 0.730664i | \(-0.739211\pi\) | ||||
−0.682738 | + | 0.730664i | \(0.739211\pi\) | |||||||
\(84\) | 4.11479 | − | 12.2114i | 0.448960 | − | 1.33237i | ||||
\(85\) | −5.98968 | −0.649672 | ||||||||
\(86\) | −2.61022 | + | 10.3280i | −0.281467 | + | 1.11370i | ||||
\(87\) | −1.93299 | − | 11.2552i | −0.207238 | − | 1.20669i | ||||
\(88\) | −1.99663 | − | 1.83280i | −0.212841 | − | 0.195378i | ||||
\(89\) | 0.323760i | 0.0343185i | 0.999853 | + | 0.0171592i | \(0.00546222\pi\) | ||||
−0.999853 | + | 0.0171592i | \(0.994538\pi\) | |||||||
\(90\) | −0.863461 | − | 9.29628i | −0.0910168 | − | 0.979914i | ||||
\(91\) | − | 9.41015i | − | 0.986452i | ||||||
\(92\) | 1.75985 | + | 0.950233i | 0.183477 | + | 0.0990686i | ||||
\(93\) | 2.69489 | + | 15.6916i | 0.279447 | + | 1.62714i | ||||
\(94\) | 6.53117 | + | 1.65064i | 0.673639 | + | 0.170250i | ||||
\(95\) | −1.38061 | −0.141648 | ||||||||
\(96\) | −4.72435 | − | 8.58374i | −0.482177 | − | 0.876074i | ||||
\(97\) | 7.00161 | 0.710906 | 0.355453 | − | 0.934694i | \(-0.384327\pi\) | ||||
0.355453 | + | 0.934694i | \(0.384327\pi\) | |||||||
\(98\) | 9.37483 | + | 2.36932i | 0.947001 | + | 0.239337i | ||||
\(99\) | 2.70998 | − | 0.959122i | 0.272363 | − | 0.0963953i | ||||
\(100\) | 0.277036 | + | 0.149586i | 0.0277036 | + | 0.0149586i | ||||
\(101\) | 9.88362i | 0.983457i | 0.870749 | + | 0.491728i | \(0.163635\pi\) | ||||
−0.870749 | + | 0.491728i | \(0.836365\pi\) | |||||||
\(102\) | 0.515960 | − | 6.64716i | 0.0510876 | − | 0.658167i | ||||
\(103\) | − | 2.08595i | − | 0.205535i | −0.994705 | − | 0.102768i | \(-0.967230\pi\) | ||
0.994705 | − | 0.102768i | \(-0.0327698\pi\) | |||||||
\(104\) | −5.27102 | − | 4.83853i | −0.516866 | − | 0.474457i | ||||
\(105\) | 13.9738 | − | 2.39988i | 1.36370 | − | 0.234205i | ||||
\(106\) | −4.01360 | + | 15.8809i | −0.389835 | + | 1.54249i | ||||
\(107\) | 1.05445 | 0.101937 | 0.0509687 | − | 0.998700i | \(-0.483769\pi\) | ||||
0.0509687 | + | 0.998700i | \(0.483769\pi\) | |||||||
\(108\) | 10.3911 | − | 0.157447i | 0.999885 | − | 0.0151503i | ||||
\(109\) | 4.32641 | 0.414395 | 0.207198 | − | 0.978299i | \(-0.433566\pi\) | ||||
0.207198 | + | 0.978299i | \(0.433566\pi\) | |||||||
\(110\) | 0.730701 | − | 2.89121i | 0.0696696 | − | 0.275666i | ||||
\(111\) | −14.8078 | + | 2.54311i | −1.40549 | + | 0.241381i | ||||
\(112\) | 12.4412 | − | 8.16182i | 1.17558 | − | 0.771220i | ||||
\(113\) | 4.35577i | 0.409756i | 0.978787 | + | 0.204878i | \(0.0656798\pi\) | ||||
−0.978787 | + | 0.204878i | \(0.934320\pi\) | |||||||
\(114\) | 0.118928 | − | 1.53216i | 0.0111386 | − | 0.143500i | ||||
\(115\) | 2.20059i | 0.205206i | ||||||||
\(116\) | 6.26521 | − | 11.6033i | 0.581710 | − | 1.07734i | ||||
\(117\) | 7.15424 | − | 2.53205i | 0.661410 | − | 0.234088i | ||||
\(118\) | −0.122612 | − | 0.0309879i | −0.0112873 | − | 0.00285267i | ||||
\(119\) | 10.1249 | 0.928153 | ||||||||
\(120\) | 5.84081 | − | 9.06129i | 0.533190 | − | 0.827178i | ||||
\(121\) | −10.0818 | −0.916526 | ||||||||
\(122\) | 19.8079 | + | 5.00609i | 1.79332 | + | 0.453230i | ||||
\(123\) | 1.73511 | + | 10.1030i | 0.156450 | + | 0.910961i | ||||
\(124\) | −8.73469 | + | 16.1768i | −0.784398 | + | 1.45272i | ||||
\(125\) | 11.3493i | 1.01512i | ||||||||
\(126\) | 1.45959 | + | 15.7144i | 0.130031 | + | 1.39995i | ||||
\(127\) | − | 7.13737i | − | 0.633339i | −0.948536 | − | 0.316670i | \(-0.897435\pi\) | ||
0.948536 | − | 0.316670i | \(-0.102565\pi\) | |||||||
\(128\) | 1.82527 | − | 11.1655i | 0.161333 | − | 0.986900i | ||||
\(129\) | −2.20837 | − | 12.8587i | −0.194436 | − | 1.13214i | ||||
\(130\) | 1.92902 | − | 7.63268i | 0.169186 | − | 0.669431i | ||||
\(131\) | 1.02516 | 0.0895682 | 0.0447841 | − | 0.998997i | \(-0.485740\pi\) | ||||
0.0447841 | + | 0.998997i | \(0.485740\pi\) | |||||||
\(132\) | 3.14563 | + | 1.05996i | 0.273792 | + | 0.0922579i | ||||
\(133\) | 2.33379 | 0.202365 | ||||||||
\(134\) | 4.73402 | − | 18.7314i | 0.408957 | − | 1.61815i | ||||
\(135\) | 5.58457 | + | 9.97809i | 0.480643 | + | 0.858777i | ||||
\(136\) | 5.20607 | − | 5.67140i | 0.446417 | − | 0.486319i | ||||
\(137\) | − | 1.11266i | − | 0.0950611i | −0.998870 | − | 0.0475306i | \(-0.984865\pi\) | ||
0.998870 | − | 0.0475306i | \(-0.0151352\pi\) | |||||||
\(138\) | −2.44214 | − | 0.189562i | −0.207889 | − | 0.0161366i | ||||
\(139\) | 1.76757i | 0.149923i | 0.997186 | + | 0.0749616i | \(0.0238834\pi\) | ||||
−0.997186 | + | 0.0749616i | \(0.976117\pi\) | |||||||
\(140\) | 14.4059 | + | 7.77851i | 1.21752 | + | 0.657404i | ||||
\(141\) | −8.13148 | + | 1.39651i | −0.684794 | + | 0.117608i | ||||
\(142\) | 17.2897 | + | 4.36966i | 1.45092 | + | 0.366694i | ||||
\(143\) | 2.42404 | 0.202708 | ||||||||
\(144\) | 9.55280 | + | 7.26250i | 0.796067 | + | 0.605209i | ||||
\(145\) | 14.5092 | 1.20493 | ||||||||
\(146\) | −6.40048 | − | 1.61761i | −0.529708 | − | 0.133874i | ||||
\(147\) | −11.6719 | + | 2.00455i | −0.962683 | + | 0.165333i | ||||
\(148\) | −15.2657 | − | 8.24272i | −1.25483 | − | 0.677548i | ||||
\(149\) | − | 16.1678i | − | 1.32452i | −0.749274 | − | 0.662260i | \(-0.769598\pi\) | ||
0.749274 | − | 0.662260i | \(-0.230402\pi\) | |||||||
\(150\) | −0.384443 | − | 0.0298409i | −0.0313897 | − | 0.00243650i | ||||
\(151\) | − | 18.1394i | − | 1.47616i | −0.674712 | − | 0.738082i | \(-0.735732\pi\) | ||
0.674712 | − | 0.738082i | \(-0.264268\pi\) | |||||||
\(152\) | 1.19999 | − | 1.30725i | 0.0973322 | − | 0.106032i | ||||
\(153\) | 2.72438 | + | 7.69767i | 0.220253 | + | 0.622320i | ||||
\(154\) | −1.23518 | + | 4.88730i | −0.0995333 | + | 0.393830i | ||||
\(155\) | −20.2281 | −1.62476 | ||||||||
\(156\) | 8.30435 | + | 2.79826i | 0.664880 | + | 0.224040i | ||||
\(157\) | −12.6703 | −1.01120 | −0.505600 | − | 0.862768i | \(-0.668729\pi\) | ||||
−0.505600 | + | 0.862768i | \(0.668729\pi\) | |||||||
\(158\) | 2.34806 | − | 9.29073i | 0.186802 | − | 0.739131i | ||||
\(159\) | −3.39569 | − | 19.7721i | −0.269296 | − | 1.56803i | ||||
\(160\) | 11.7643 | − | 4.06978i | 0.930052 | − | 0.321744i | ||||
\(161\) | − | 3.71987i | − | 0.293167i | ||||||
\(162\) | −11.5544 | + | 5.33806i | −0.907803 | + | 0.419397i | ||||
\(163\) | − | 8.15381i | − | 0.638656i | −0.947644 | − | 0.319328i | \(-0.896543\pi\) | ||
0.947644 | − | 0.319328i | \(-0.103457\pi\) | |||||||
\(164\) | −5.62385 | + | 10.4155i | −0.439149 | + | 0.813311i | ||||
\(165\) | 0.618207 | + | 3.59963i | 0.0481273 | + | 0.280231i | ||||
\(166\) | 17.0566 | + | 4.31075i | 1.32385 | + | 0.334579i | ||||
\(167\) | 15.7788 | 1.22100 | 0.610501 | − | 0.792016i | \(-0.290968\pi\) | ||||
0.610501 | + | 0.792016i | \(0.290968\pi\) | |||||||
\(168\) | −9.87330 | + | 15.3172i | −0.761742 | + | 1.18175i | ||||
\(169\) | −6.60062 | −0.507740 | ||||||||
\(170\) | 8.21246 | + | 2.07555i | 0.629867 | + | 0.159187i | ||||
\(171\) | 0.627966 | + | 1.77430i | 0.0480217 | + | 0.135684i | ||||
\(172\) | 7.15776 | − | 13.2563i | 0.545774 | − | 1.01078i | ||||
\(173\) | − | 6.82180i | − | 0.518652i | −0.965790 | − | 0.259326i | \(-0.916500\pi\) | ||
0.965790 | − | 0.259326i | \(-0.0835004\pi\) | |||||||
\(174\) | −1.24985 | + | 16.1019i | −0.0947506 | + | 1.22068i | ||||
\(175\) | − | 0.585584i | − | 0.0442660i | ||||||
\(176\) | 2.10247 | + | 3.20484i | 0.158480 | + | 0.241574i | ||||
\(177\) | 0.152655 | − | 0.0262172i | 0.0114742 | − | 0.00197061i | ||||
\(178\) | 0.112190 | − | 0.443908i | 0.00840897 | − | 0.0332723i | ||||
\(179\) | 23.6302 | 1.76620 | 0.883102 | − | 0.469182i | \(-0.155451\pi\) | ||||
0.883102 | + | 0.469182i | \(0.155451\pi\) | |||||||
\(180\) | −2.03747 | + | 13.0454i | −0.151864 | + | 0.972344i | ||||
\(181\) | 4.79466 | 0.356385 | 0.178192 | − | 0.983996i | \(-0.442975\pi\) | ||||
0.178192 | + | 0.983996i | \(0.442975\pi\) | |||||||
\(182\) | −3.26082 | + | 12.9023i | −0.241708 | + | 0.956381i | ||||
\(183\) | −24.6614 | + | 4.23538i | −1.82302 | + | 0.313089i | ||||
\(184\) | −2.08365 | − | 1.91269i | −0.153609 | − | 0.141005i | ||||
\(185\) | − | 19.0888i | − | 1.40344i | ||||||
\(186\) | 1.74248 | − | 22.4486i | 0.127765 | − | 1.64601i | ||||
\(187\) | 2.60817i | 0.190728i | ||||||||
\(188\) | −8.38293 | − | 4.52638i | −0.611388 | − | 0.330120i | ||||
\(189\) | −9.44016 | − | 16.8670i | −0.686670 | − | 1.22689i | ||||
\(190\) | 1.89296 | + | 0.478412i | 0.137330 | + | 0.0347076i | ||||
\(191\) | −9.33989 | −0.675810 | −0.337905 | − | 0.941180i | \(-0.609718\pi\) | ||||
−0.337905 | + | 0.941180i | \(0.609718\pi\) | |||||||
\(192\) | 3.50312 | + | 13.4063i | 0.252816 | + | 0.967514i | ||||
\(193\) | 6.46649 | 0.465468 | 0.232734 | − | 0.972540i | \(-0.425233\pi\) | ||||
0.232734 | + | 0.972540i | \(0.425233\pi\) | |||||||
\(194\) | −9.59993 | − | 2.42621i | −0.689235 | − | 0.174192i | ||||
\(195\) | 1.63204 | + | 9.50289i | 0.116873 | + | 0.680516i | ||||
\(196\) | −12.0328 | − | 6.49716i | −0.859489 | − | 0.464083i | ||||
\(197\) | 24.9756i | 1.77944i | 0.456510 | + | 0.889718i | \(0.349099\pi\) | ||||
−0.456510 | + | 0.889718i | \(0.650901\pi\) | |||||||
\(198\) | −4.04801 | + | 0.375989i | −0.287680 | + | 0.0267204i | ||||
\(199\) | 11.2235i | 0.795615i | 0.917469 | + | 0.397807i | \(0.130229\pi\) | ||||
−0.917469 | + | 0.397807i | \(0.869771\pi\) | |||||||
\(200\) | −0.328010 | − | 0.301097i | −0.0231938 | − | 0.0212907i | ||||
\(201\) | 4.00520 | + | 23.3211i | 0.282505 | + | 1.64494i | ||||
\(202\) | 3.42488 | − | 13.5515i | 0.240974 | − | 0.953477i | ||||
\(203\) | −24.5264 | −1.72141 | ||||||||
\(204\) | −3.01082 | + | 8.93515i | −0.210799 | + | 0.625586i | ||||
\(205\) | −13.0239 | −0.909631 | ||||||||
\(206\) | −0.722828 | + | 2.86006i | −0.0503618 | + | 0.199270i | ||||
\(207\) | 2.82810 | − | 1.00093i | 0.196566 | − | 0.0695693i | ||||
\(208\) | 5.55045 | + | 8.46065i | 0.384854 | + | 0.586640i | ||||
\(209\) | 0.601180i | 0.0415845i | ||||||||
\(210\) | −19.9911 | − | 1.55173i | −1.37952 | − | 0.107080i | ||||
\(211\) | 1.44381i | 0.0993960i | 0.998764 | + | 0.0496980i | \(0.0158259\pi\) | ||||
−0.998764 | + | 0.0496980i | \(0.984174\pi\) | |||||||
\(212\) | 11.0061 | − | 20.3835i | 0.755903 | − | 1.39994i | ||||
\(213\) | −21.5262 | + | 3.69694i | −1.47495 | + | 0.253310i | ||||
\(214\) | −1.44576 | − | 0.365389i | −0.0988300 | − | 0.0249775i | ||||
\(215\) | 16.5762 | 1.13049 | ||||||||
\(216\) | −14.3018 | − | 3.38487i | −0.973117 | − | 0.230311i | ||||
\(217\) | 34.1936 | 2.32122 | ||||||||
\(218\) | −5.93196 | − | 1.49919i | −0.401763 | − | 0.101538i | ||||
\(219\) | 7.96877 | − | 1.36857i | 0.538479 | − | 0.0924794i | ||||
\(220\) | −2.00373 | + | 3.71094i | −0.135092 | + | 0.250192i | ||||
\(221\) | 6.88547i | 0.463167i | ||||||||
\(222\) | 21.1842 | + | 1.64434i | 1.42179 | + | 0.110361i | ||||
\(223\) | 11.4471i | 0.766556i | 0.923633 | + | 0.383278i | \(0.125205\pi\) | ||||
−0.923633 | + | 0.383278i | \(0.874795\pi\) | |||||||
\(224\) | −19.8864 | + | 6.87956i | −1.32872 | + | 0.459660i | ||||
\(225\) | 0.445201 | − | 0.157566i | 0.0296800 | − | 0.0105044i | ||||
\(226\) | 1.50937 | − | 5.97221i | 0.100402 | − | 0.397265i | ||||
\(227\) | 11.5592 | 0.767210 | 0.383605 | − | 0.923497i | \(-0.374682\pi\) | ||||
0.383605 | + | 0.923497i | \(0.374682\pi\) | |||||||
\(228\) | −0.693989 | + | 2.05954i | −0.0459606 | + | 0.136396i | ||||
\(229\) | −11.4270 | −0.755115 | −0.377558 | − | 0.925986i | \(-0.623236\pi\) | ||||
−0.377558 | + | 0.925986i | \(0.623236\pi\) | |||||||
\(230\) | 0.762550 | − | 3.01723i | 0.0502811 | − | 0.198950i | ||||
\(231\) | −1.04502 | − | 6.08482i | −0.0687570 | − | 0.400351i | ||||
\(232\) | −12.6110 | + | 13.7382i | −0.827955 | + | 0.901960i | ||||
\(233\) | 14.6817i | 0.961832i | 0.876767 | + | 0.480916i | \(0.159696\pi\) | ||||
−0.876767 | + | 0.480916i | \(0.840304\pi\) | |||||||
\(234\) | −10.6866 | + | 0.992597i | −0.698605 | + | 0.0648881i | ||||
\(235\) | − | 10.4824i | − | 0.683794i | ||||||
\(236\) | 0.157375 | + | 0.0849752i | 0.0102443 | + | 0.00553142i | ||||
\(237\) | 1.98657 | + | 11.5672i | 0.129042 | + | 0.751370i | ||||
\(238\) | −13.8823 | − | 3.50851i | −0.899859 | − | 0.227423i | ||||
\(239\) | 14.7775 | 0.955876 | 0.477938 | − | 0.878393i | \(-0.341384\pi\) | ||||
0.477938 | + | 0.878393i | \(0.341384\pi\) | |||||||
\(240\) | −11.1483 | + | 10.4000i | −0.719618 | + | 0.671316i | ||||
\(241\) | −17.3937 | −1.12043 | −0.560213 | − | 0.828349i | \(-0.689281\pi\) | ||||
−0.560213 | + | 0.828349i | \(0.689281\pi\) | |||||||
\(242\) | 13.8232 | + | 3.49356i | 0.888587 | + | 0.224574i | ||||
\(243\) | 10.2833 | − | 11.7155i | 0.659673 | − | 0.751552i | ||||
\(244\) | −25.4240 | − | 13.7277i | −1.62760 | − | 0.878828i | ||||
\(245\) | − | 15.0464i | − | 0.961278i | ||||||
\(246\) | 1.12190 | − | 14.4536i | 0.0715299 | − | 0.921526i | ||||
\(247\) | 1.58709i | 0.100984i | ||||||||
\(248\) | 17.5818 | − | 19.1533i | 1.11644 | − | 1.21623i | ||||
\(249\) | −21.2359 | + | 3.64709i | −1.34577 | + | 0.231125i | ||||
\(250\) | 3.93279 | − | 15.5611i | 0.248732 | − | 0.984172i | ||||
\(251\) | −12.7892 | −0.807250 | −0.403625 | − | 0.914925i | \(-0.632250\pi\) | ||||
−0.403625 | + | 0.914925i | \(0.632250\pi\) | |||||||
\(252\) | 3.44413 | − | 22.0519i | 0.216960 | − | 1.38914i | ||||
\(253\) | 0.958233 | 0.0602436 | ||||||||
\(254\) | −2.47325 | + | 9.78607i | −0.155186 | + | 0.614033i | ||||
\(255\) | −10.2247 | + | 1.75601i | −0.640297 | + | 0.109966i | ||||
\(256\) | −6.37172 | + | 14.6766i | −0.398232 | + | 0.917285i | ||||
\(257\) | − | 15.5053i | − | 0.967196i | −0.875290 | − | 0.483598i | \(-0.839330\pi\) | ||
0.875290 | − | 0.483598i | \(-0.160670\pi\) | |||||||
\(258\) | −1.42790 | + | 18.3958i | −0.0888972 | + | 1.14527i | ||||
\(259\) | 32.2677i | 2.00502i | ||||||||
\(260\) | −5.28978 | + | 9.79675i | −0.328058 | + | 0.607568i | ||||
\(261\) | −6.59946 | − | 18.6466i | −0.408496 | − | 1.15420i | ||||
\(262\) | −1.40559 | − | 0.355238i | −0.0868378 | − | 0.0219467i | ||||
\(263\) | 15.8314 | 0.976204 | 0.488102 | − | 0.872787i | \(-0.337689\pi\) | ||||
0.488102 | + | 0.872787i | \(0.337689\pi\) | |||||||
\(264\) | −3.94569 | − | 2.54335i | −0.242840 | − | 0.156532i | ||||
\(265\) | 25.4884 | 1.56574 | ||||||||
\(266\) | −3.19986 | − | 0.808707i | −0.196196 | − | 0.0495850i | ||||
\(267\) | 0.0949176 | + | 0.552677i | 0.00580886 | + | 0.0338233i | ||||
\(268\) | −12.9817 | + | 24.0422i | −0.792981 | + | 1.46861i | ||||
\(269\) | 3.60658i | 0.219897i | 0.993937 | + | 0.109949i | \(0.0350686\pi\) | ||||
−0.993937 | + | 0.109949i | \(0.964931\pi\) | |||||||
\(270\) | −4.19940 | − | 15.6162i | −0.255567 | − | 0.950369i | ||||
\(271\) | 21.4184i | 1.30107i | 0.759474 | + | 0.650537i | \(0.225456\pi\) | ||||
−0.759474 | + | 0.650537i | \(0.774544\pi\) | |||||||
\(272\) | −9.10332 | + | 5.97206i | −0.551970 | + | 0.362109i | ||||
\(273\) | −2.75880 | − | 16.0637i | −0.166970 | − | 0.972218i | ||||
\(274\) | −0.385561 | + | 1.52557i | −0.0232926 | + | 0.0921633i | ||||
\(275\) | 0.150845 | 0.00909632 | ||||||||
\(276\) | 3.28274 | + | 1.10616i | 0.197598 | + | 0.0665832i | ||||
\(277\) | 30.3603 | 1.82418 | 0.912088 | − | 0.409994i | \(-0.134469\pi\) | ||||
0.912088 | + | 0.409994i | \(0.134469\pi\) | |||||||
\(278\) | 0.612500 | − | 2.42352i | 0.0367353 | − | 0.145353i | ||||
\(279\) | 9.20068 | + | 25.9963i | 0.550831 | + | 1.55636i | ||||
\(280\) | −17.0566 | − | 15.6571i | −1.01933 | − | 0.935690i | ||||
\(281\) | 6.32399i | 0.377257i | 0.982048 | + | 0.188629i | \(0.0604043\pi\) | ||||
−0.982048 | + | 0.188629i | \(0.939596\pi\) | |||||||
\(282\) | 11.6330 | + | 0.902967i | 0.692736 | + | 0.0537709i | ||||
\(283\) | − | 12.0709i | − | 0.717540i | −0.933426 | − | 0.358770i | \(-0.883196\pi\) | ||
0.933426 | − | 0.358770i | \(-0.116804\pi\) | |||||||
\(284\) | −22.1918 | − | 11.9825i | −1.31684 | − | 0.711031i | ||||
\(285\) | −2.35679 | + | 0.404758i | −0.139604 | + | 0.0239758i | ||||
\(286\) | −3.32361 | − | 0.839982i | −0.196529 | − | 0.0496692i | ||||
\(287\) | 22.0157 | 1.29954 | ||||||||
\(288\) | −10.5813 | − | 13.2679i | −0.623507 | − | 0.781818i | ||||
\(289\) | 9.59151 | 0.564206 | ||||||||
\(290\) | −19.8936 | − | 5.02776i | −1.16819 | − | 0.295240i | ||||
\(291\) | 11.9522 | − | 2.05269i | 0.700648 | − | 0.120331i | ||||
\(292\) | 8.21518 | + | 4.43581i | 0.480757 | + | 0.259586i | ||||
\(293\) | − | 5.89202i | − | 0.344216i | −0.985078 | − | 0.172108i | \(-0.944942\pi\) | ||
0.985078 | − | 0.172108i | \(-0.0550577\pi\) | |||||||
\(294\) | 16.6980 | + | 1.29612i | 0.973848 | + | 0.0755911i | ||||
\(295\) | 0.196789i | 0.0114575i | ||||||||
\(296\) | 18.0745 | + | 16.5915i | 1.05056 | + | 0.964361i | ||||
\(297\) | 4.34490 | − | 2.43177i | 0.252117 | − | 0.141106i | ||||
\(298\) | −5.60249 | + | 22.1677i | −0.324544 | + | 1.28414i | ||||
\(299\) | 2.52970 | 0.146296 | ||||||||
\(300\) | 0.516771 | + | 0.174133i | 0.0298358 | + | 0.0100536i | ||||
\(301\) | −28.0204 | −1.61507 | ||||||||
\(302\) | −6.28569 | + | 24.8710i | −0.361701 | + | 1.43116i | ||||
\(303\) | 2.89761 | + | 16.8719i | 0.166463 | + | 0.969266i | ||||
\(304\) | −2.09830 | + | 1.37655i | −0.120346 | + | 0.0789507i | ||||
\(305\) | − | 31.7912i | − | 1.82036i | ||||||
\(306\) | −1.06800 | − | 11.4984i | −0.0610532 | − | 0.657317i | ||||
\(307\) | − | 29.0210i | − | 1.65632i | −0.560494 | − | 0.828158i | \(-0.689389\pi\) | ||
0.560494 | − | 0.828158i | \(-0.310611\pi\) | |||||||
\(308\) | 3.38711 | − | 6.27298i | 0.192998 | − | 0.357436i | ||||
\(309\) | −0.611546 | − | 3.56085i | −0.0347896 | − | 0.202570i | ||||
\(310\) | 27.7349 | + | 7.00948i | 1.57523 | + | 0.398112i | ||||
\(311\) | 31.8428 | 1.80564 | 0.902820 | − | 0.430019i | \(-0.141493\pi\) | ||||
0.902820 | + | 0.430019i | \(0.141493\pi\) | |||||||
\(312\) | −10.4165 | − | 6.71434i | −0.589716 | − | 0.380125i | ||||
\(313\) | 32.8768 | 1.85831 | 0.929153 | − | 0.369694i | \(-0.120538\pi\) | ||||
0.929153 | + | 0.369694i | \(0.120538\pi\) | |||||||
\(314\) | 17.3723 | + | 4.39053i | 0.980374 | + | 0.247772i | ||||
\(315\) | 23.1505 | − | 8.19349i | 1.30438 | − | 0.461651i | ||||
\(316\) | −6.43887 | + | 11.9249i | −0.362215 | + | 0.670828i | ||||
\(317\) | − | 28.6626i | − | 1.60985i | −0.593375 | − | 0.804926i | \(-0.702205\pi\) | ||
0.593375 | − | 0.804926i | \(-0.297795\pi\) | |||||||
\(318\) | −2.19561 | + | 28.2863i | −0.123124 | + | 1.58621i | ||||
\(319\) | − | 6.31796i | − | 0.353738i | ||||||
\(320\) | −17.5404 | + | 1.50350i | −0.980537 | + | 0.0840480i | ||||
\(321\) | 1.80001 | − | 0.309136i | 0.100467 | − | 0.0172543i | ||||
\(322\) | −1.28901 | + | 5.10033i | −0.0718340 | + | 0.284230i | ||||
\(323\) | −1.70765 | −0.0950161 | ||||||||
\(324\) | 17.6921 | − | 3.31517i | 0.982893 | − | 0.184176i | ||||
\(325\) | 0.398226 | 0.0220896 | ||||||||
\(326\) | −2.82547 | + | 11.1797i | −0.156488 | + | 0.619187i | ||||
\(327\) | 7.38544 | − | 1.26839i | 0.408416 | − | 0.0701420i | ||||
\(328\) | 11.3201 | − | 12.3319i | 0.625046 | − | 0.680914i | ||||
\(329\) | 17.7194i | 0.976902i | ||||||||
\(330\) | 0.399724 | − | 5.14968i | 0.0220041 | − | 0.283481i | ||||
\(331\) | − | 23.2121i | − | 1.27585i | −0.770098 | − | 0.637926i | \(-0.779793\pi\) | ||
0.770098 | − | 0.637926i | \(-0.220207\pi\) | |||||||
\(332\) | −21.8926 | − | 11.8210i | −1.20151 | − | 0.648760i | ||||
\(333\) | −24.5321 | + | 8.68247i | −1.34435 | + | 0.475796i | ||||
\(334\) | −21.6344 | − | 5.46770i | −1.18378 | − | 0.299179i | ||||
\(335\) | −30.0634 | −1.64254 | ||||||||
\(336\) | 18.8450 | − | 17.5801i | 1.02808 | − | 0.959075i | ||||
\(337\) | −24.9496 | −1.35909 | −0.679546 | − | 0.733632i | \(-0.737823\pi\) | ||||
−0.679546 | + | 0.733632i | \(0.737823\pi\) | |||||||
\(338\) | 9.05013 | + | 2.28726i | 0.492262 | + | 0.124410i | ||||
\(339\) | 1.27699 | + | 7.43556i | 0.0693568 | + | 0.403844i | ||||
\(340\) | −10.5409 | − | 5.69159i | −0.571661 | − | 0.308670i | ||||
\(341\) | 8.80823i | 0.476992i | ||||||||
\(342\) | −0.246171 | − | 2.65036i | −0.0133114 | − | 0.143315i | ||||
\(343\) | − | 0.604700i | − | 0.0326507i | ||||||
\(344\) | −14.4076 | + | 15.6954i | −0.776806 | + | 0.846239i | ||||
\(345\) | 0.645153 | + | 3.75653i | 0.0347339 | + | 0.202245i | ||||
\(346\) | −2.36390 | + | 9.35340i | −0.127084 | + | 0.502842i | ||||
\(347\) | 2.44357 | 0.131177 | 0.0655887 | − | 0.997847i | \(-0.479107\pi\) | ||||
0.0655887 | + | 0.997847i | \(0.479107\pi\) | |||||||
\(348\) | 7.29332 | − | 21.6443i | 0.390963 | − | 1.16025i | ||||
\(349\) | −16.8631 | −0.902663 | −0.451331 | − | 0.892356i | \(-0.649051\pi\) | ||||
−0.451331 | + | 0.892356i | \(0.649051\pi\) | |||||||
\(350\) | −0.202917 | + | 0.802895i | −0.0108464 | + | 0.0429166i | ||||
\(351\) | 11.4704 | − | 6.41978i | 0.612243 | − | 0.342663i | ||||
\(352\) | −1.77216 | − | 5.12271i | −0.0944566 | − | 0.273041i | ||||
\(353\) | 35.2238i | 1.87477i | 0.348290 | + | 0.937387i | \(0.386762\pi\) | ||||
−0.348290 | + | 0.937387i | \(0.613238\pi\) | |||||||
\(354\) | −0.218390 | − | 0.0169517i | −0.0116073 | − | 0.000900973i | ||||
\(355\) | − | 27.7496i | − | 1.47279i | ||||||
\(356\) | −0.307647 | + | 0.569767i | −0.0163053 | + | 0.0301976i | ||||
\(357\) | 17.2839 | − | 2.96836i | 0.914760 | − | 0.157102i | ||||
\(358\) | −32.3994 | − | 8.18837i | −1.71236 | − | 0.432769i | ||||
\(359\) | −9.90967 | −0.523012 | −0.261506 | − | 0.965202i | \(-0.584219\pi\) | ||||
−0.261506 | + | 0.965202i | \(0.584219\pi\) | |||||||
\(360\) | 7.31407 | − | 17.1805i | 0.385486 | − | 0.905493i | ||||
\(361\) | 18.6064 | 0.979284 | ||||||||
\(362\) | −6.57398 | − | 1.66145i | −0.345521 | − | 0.0873241i | ||||
\(363\) | −17.2102 | + | 2.95571i | −0.903302 | + | 0.155135i | ||||
\(364\) | 8.94184 | − | 16.5604i | 0.468680 | − | 0.868002i | ||||
\(365\) | 10.2726i | 0.537693i | ||||||||
\(366\) | 35.2809 | + | 2.73854i | 1.84416 | + | 0.143146i | ||||
\(367\) | 2.74401i | 0.143236i | 0.997432 | + | 0.0716180i | \(0.0228162\pi\) | ||||
−0.997432 | + | 0.0716180i | \(0.977184\pi\) | |||||||
\(368\) | 2.19412 | + | 3.34453i | 0.114376 | + | 0.174346i | ||||
\(369\) | 5.92388 | + | 16.7378i | 0.308385 | + | 0.871335i | ||||
\(370\) | −6.61468 | + | 26.1727i | −0.343881 | + | 1.36066i | ||||
\(371\) | −43.0856 | −2.23689 | ||||||||
\(372\) | −10.1680 | + | 30.1755i | −0.527188 | + | 1.56453i | ||||
\(373\) | −4.92429 | −0.254970 | −0.127485 | − | 0.991840i | \(-0.540691\pi\) | ||||
−0.127485 | + | 0.991840i | \(0.540691\pi\) | |||||||
\(374\) | 0.903787 | − | 3.57607i | 0.0467337 | − | 0.184914i | ||||
\(375\) | 3.32732 | + | 19.3740i | 0.171822 | + | 1.00047i | ||||
\(376\) | 9.92537 | + | 9.11100i | 0.511862 | + | 0.469864i | ||||
\(377\) | − | 16.6792i | − | 0.859021i | ||||||
\(378\) | 7.09866 | + | 26.3976i | 0.365116 | + | 1.35774i | ||||
\(379\) | 5.86840i | 0.301440i | 0.988577 | + | 0.150720i | \(0.0481591\pi\) | ||||
−0.988577 | + | 0.150720i | \(0.951841\pi\) | |||||||
\(380\) | −2.42967 | − | 1.31190i | −0.124639 | − | 0.0672992i | ||||
\(381\) | −2.09249 | − | 12.1839i | −0.107201 | − | 0.624201i | ||||
\(382\) | 12.8059 | + | 3.23647i | 0.655209 | + | 0.165592i | ||||
\(383\) | 12.2927 | 0.628126 | 0.314063 | − | 0.949402i | \(-0.398310\pi\) | ||||
0.314063 | + | 0.949402i | \(0.398310\pi\) | |||||||
\(384\) | −0.157579 | − | 19.5953i | −0.00804144 | − | 0.999968i | ||||
\(385\) | 7.84400 | 0.399767 | ||||||||
\(386\) | −8.86622 | − | 2.24078i | −0.451279 | − | 0.114053i | ||||
\(387\) | −7.53962 | − | 21.3030i | −0.383261 | − | 1.08289i | ||||
\(388\) | 12.3218 | + | 6.65316i | 0.625543 | + | 0.337763i | ||||
\(389\) | 17.7283i | 0.898858i | 0.893316 | + | 0.449429i | \(0.148373\pi\) | ||||
−0.893316 | + | 0.449429i | \(0.851627\pi\) | |||||||
\(390\) | 1.05526 | − | 13.5950i | 0.0534350 | − | 0.688408i | ||||
\(391\) | 2.72185i | 0.137650i | ||||||||
\(392\) | 14.2469 | + | 13.0779i | 0.719575 | + | 0.660534i | ||||
\(393\) | 1.75000 | − | 0.300548i | 0.0882758 | − | 0.0151606i | ||||
\(394\) | 8.65457 | − | 34.2441i | 0.436011 | − | 1.72519i | ||||
\(395\) | −14.9114 | −0.750274 | ||||||||
\(396\) | 5.68053 | + | 0.887203i | 0.285457 | + | 0.0445836i | ||||
\(397\) | −10.6156 | −0.532781 | −0.266391 | − | 0.963865i | \(-0.585831\pi\) | ||||
−0.266391 | + | 0.963865i | \(0.585831\pi\) | |||||||
\(398\) | 3.88919 | − | 15.3886i | 0.194948 | − | 0.771361i | ||||
\(399\) | 3.98391 | − | 0.684204i | 0.199445 | − | 0.0342530i | ||||
\(400\) | 0.345398 | + | 0.526497i | 0.0172699 | + | 0.0263248i | ||||
\(401\) | − | 19.1200i | − | 0.954807i | −0.878684 | − | 0.477404i | \(-0.841578\pi\) | ||
0.878684 | − | 0.477404i | \(-0.158422\pi\) | |||||||
\(402\) | 2.58971 | − | 33.3635i | 0.129163 | − | 1.66402i | ||||
\(403\) | 23.2534i | 1.15833i | ||||||||
\(404\) | −9.39174 | + | 17.3936i | −0.467256 | + | 0.865366i | ||||
\(405\) | 12.4585 | + | 15.3959i | 0.619068 | + | 0.765030i | ||||
\(406\) | 33.6282 | + | 8.49892i | 1.66894 | + | 0.421794i | ||||
\(407\) | −8.31212 | −0.412016 | ||||||||
\(408\) | 7.22436 | − | 11.2077i | 0.357659 | − | 0.554864i | ||||
\(409\) | −22.4004 | −1.10763 | −0.553814 | − | 0.832641i | \(-0.686828\pi\) | ||||
−0.553814 | + | 0.832641i | \(0.686828\pi\) | |||||||
\(410\) | 17.8572 | + | 4.51307i | 0.881902 | + | 0.222885i | ||||
\(411\) | −0.326203 | − | 1.89938i | −0.0160904 | − | 0.0936895i | ||||
\(412\) | 1.98214 | − | 3.67096i | 0.0976532 | − | 0.180855i | ||||
\(413\) | − | 0.332652i | − | 0.0163687i | ||||||
\(414\) | −4.22446 | + | 0.392378i | −0.207621 | + | 0.0192843i | ||||
\(415\) | − | 27.3754i | − | 1.34381i | ||||||
\(416\) | −4.67844 | − | 13.5238i | −0.229380 | − | 0.663057i | ||||
\(417\) | 0.518204 | + | 3.01734i | 0.0253765 | + | 0.147760i | ||||
\(418\) | 0.208322 | − | 0.824279i | 0.0101893 | − | 0.0403168i | ||||
\(419\) | 9.56749 | 0.467402 | 0.233701 | − | 0.972308i | \(-0.424916\pi\) | ||||
0.233701 | + | 0.972308i | \(0.424916\pi\) | |||||||
\(420\) | 26.8722 | + | 9.05494i | 1.31123 | + | 0.441836i | ||||
\(421\) | 33.4727 | 1.63136 | 0.815681 | − | 0.578502i | \(-0.196363\pi\) | ||||
0.815681 | + | 0.578502i | \(0.196363\pi\) | |||||||
\(422\) | 0.500311 | − | 1.97961i | 0.0243548 | − | 0.0963660i | ||||
\(423\) | −13.4715 | + | 4.76786i | −0.655006 | + | 0.231821i | ||||
\(424\) | −22.1538 | + | 24.1340i | −1.07589 | + | 1.17205i | ||||
\(425\) | 0.428475i | 0.0207841i | ||||||||
\(426\) | 30.7956 | + | 2.39039i | 1.49205 | + | 0.115815i | ||||
\(427\) | 53.7399i | 2.60065i | ||||||||
\(428\) | 1.85567 | + | 1.00197i | 0.0896971 | + | 0.0484321i | ||||
\(429\) | 4.13798 | − | 0.710663i | 0.199784 | − | 0.0343112i | ||||
\(430\) | −22.7277 | − | 5.74401i | −1.09603 | − | 0.277001i | ||||
\(431\) | −15.5475 | −0.748897 | −0.374449 | − | 0.927248i | \(-0.622168\pi\) | ||||
−0.374449 | + | 0.927248i | \(0.622168\pi\) | |||||||
\(432\) | 18.4364 | + | 9.59689i | 0.887020 | + | 0.461731i | ||||
\(433\) | 0.627720 | 0.0301663 | 0.0150832 | − | 0.999886i | \(-0.495199\pi\) | ||||
0.0150832 | + | 0.999886i | \(0.495199\pi\) | |||||||
\(434\) | −46.8830 | − | 11.8488i | −2.25046 | − | 0.568762i | ||||
\(435\) | 24.7681 | − | 4.25371i | 1.18754 | − | 0.203950i | ||||
\(436\) | 7.61382 | + | 4.11110i | 0.364636 | + | 0.196886i | ||||
\(437\) | 0.627384i | 0.0300118i | ||||||||
\(438\) | −11.4002 | − | 0.884899i | −0.544724 | − | 0.0422821i | ||||
\(439\) | 5.07380i | 0.242159i | 0.992643 | + | 0.121080i | \(0.0386356\pi\) | ||||
−0.992643 | + | 0.121080i | \(0.961364\pi\) | |||||||
\(440\) | 4.03324 | − | 4.39375i | 0.192277 | − | 0.209464i | ||||
\(441\) | −19.3370 | + | 6.84378i | −0.920808 | + | 0.325894i | ||||
\(442\) | 2.38596 | − | 9.44069i | 0.113489 | − | 0.449048i | ||||
\(443\) | −8.83365 | −0.419700 | −0.209850 | − | 0.977734i | \(-0.567297\pi\) | ||||
−0.209850 | + | 0.977734i | \(0.567297\pi\) | |||||||
\(444\) | −28.4759 | − | 9.59533i | −1.35141 | − | 0.455374i | ||||
\(445\) | −0.712461 | −0.0337739 | ||||||||
\(446\) | 3.96667 | − | 15.6952i | 0.187827 | − | 0.743189i | ||||
\(447\) | −4.73997 | − | 27.5994i | −0.224193 | − | 1.30541i | ||||
\(448\) | 29.6502 | − | 2.54151i | 1.40084 | − | 0.120075i | ||||
\(449\) | 16.0724i | 0.758502i | 0.925294 | + | 0.379251i | \(0.123818\pi\) | ||||
−0.925294 | + | 0.379251i | \(0.876182\pi\) | |||||||
\(450\) | −0.665016 | + | 0.0617683i | −0.0313491 | + | 0.00291178i | ||||
\(451\) | 5.67120i | 0.267046i | ||||||||
\(452\) | −4.13900 | + | 7.66549i | −0.194682 | + | 0.360554i | ||||
\(453\) | −5.31798 | − | 30.9650i | −0.249861 | − | 1.45486i | ||||
\(454\) | −15.8488 | − | 4.00551i | −0.743823 | − | 0.187988i | ||||
\(455\) | 20.7079 | 0.970799 | ||||||||
\(456\) | 1.66521 | − | 2.58336i | 0.0779804 | − | 0.120977i | ||||
\(457\) | 16.3723 | 0.765864 | 0.382932 | − | 0.923776i | \(-0.374914\pi\) | ||||
0.382932 | + | 0.923776i | \(0.374914\pi\) | |||||||
\(458\) | 15.6676 | + | 3.95969i | 0.732097 | + | 0.185024i | ||||
\(459\) | 6.90743 | + | 12.3417i | 0.322411 | + | 0.576060i | ||||
\(460\) | −2.09107 | + | 3.87269i | −0.0974966 | + | 0.180565i | ||||
\(461\) | 9.35232i | 0.435581i | 0.975996 | + | 0.217790i | \(0.0698849\pi\) | ||||
−0.975996 | + | 0.217790i | \(0.930115\pi\) | |||||||
\(462\) | −0.675694 | + | 8.70503i | −0.0314361 | + | 0.404995i | ||||
\(463\) | − | 10.2286i | − | 0.475365i | −0.971343 | − | 0.237682i | \(-0.923612\pi\) | ||
0.971343 | − | 0.237682i | \(-0.0763877\pi\) | |||||||
\(464\) | 22.0516 | − | 14.4666i | 1.02372 | − | 0.671593i | ||||
\(465\) | −34.5306 | + | 5.93035i | −1.60132 | + | 0.275013i | ||||
\(466\) | 5.08753 | − | 20.1302i | 0.235675 | − | 0.932511i | ||||
\(467\) | −8.62755 | −0.399236 | −0.199618 | − | 0.979874i | \(-0.563970\pi\) | ||||
−0.199618 | + | 0.979874i | \(0.563970\pi\) | |||||||
\(468\) | 14.9964 | + | 2.34218i | 0.693208 | + | 0.108267i | ||||
\(469\) | 50.8192 | 2.34661 | ||||||||
\(470\) | −3.63237 | + | 14.3724i | −0.167549 | + | 0.662950i | ||||
\(471\) | −21.6289 | + | 3.71459i | −0.996609 | + | 0.171159i | ||||
\(472\) | −0.186332 | − | 0.171044i | −0.00857663 | − | 0.00787293i | ||||
\(473\) | − | 7.21802i | − | 0.331885i | ||||||
\(474\) | 1.28449 | − | 16.5482i | 0.0589986 | − | 0.760084i | ||||
\(475\) | 0.0987630i | 0.00453156i | ||||||||
\(476\) | 17.8183 | + | 9.62106i | 0.816703 | + | 0.440981i | ||||
\(477\) | −11.5933 | − | 32.7566i | −0.530820 | − | 1.49982i | ||||
\(478\) | −20.2615 | − | 5.12072i | −0.926737 | − | 0.234216i | ||||
\(479\) | 6.82356 | 0.311776 | 0.155888 | − | 0.987775i | \(-0.450176\pi\) | ||||
0.155888 | + | 0.987775i | \(0.450176\pi\) | |||||||
\(480\) | 18.8893 | − | 10.3963i | 0.862172 | − | 0.474526i | ||||
\(481\) | −21.9437 | −1.00055 | ||||||||
\(482\) | 23.8485 | + | 6.02728i | 1.08627 | + | 0.274535i | ||||
\(483\) | −1.09057 | − | 6.35004i | −0.0496225 | − | 0.288937i | ||||
\(484\) | −17.7424 | − | 9.58005i | −0.806473 | − | 0.435457i | ||||
\(485\) | 15.4077i | 0.699626i | ||||||||
\(486\) | −18.1591 | + | 12.4998i | −0.823715 | + | 0.567004i | ||||
\(487\) | 6.28290i | 0.284705i | 0.989816 | + | 0.142353i | \(0.0454667\pi\) | ||||
−0.989816 | + | 0.142353i | \(0.954533\pi\) | |||||||
\(488\) | 30.1019 | + | 27.6321i | 1.36265 | + | 1.25085i | ||||
\(489\) | −2.39048 | − | 13.9190i | −0.108101 | − | 0.629441i | ||||
\(490\) | −5.21389 | + | 20.6301i | −0.235540 | + | 0.931974i | ||||
\(491\) | −22.1458 | −0.999425 | −0.499713 | − | 0.866191i | \(-0.666561\pi\) | ||||
−0.499713 | + | 0.866191i | \(0.666561\pi\) | |||||||
\(492\) | −6.54671 | + | 19.4286i | −0.295149 | + | 0.875908i | ||||
\(493\) | 17.9461 | 0.808253 | ||||||||
\(494\) | 0.549961 | − | 2.17607i | 0.0247439 | − | 0.0979059i | ||||
\(495\) | 2.11063 | + | 5.96354i | 0.0948657 | + | 0.268041i | ||||
\(496\) | −30.7434 | + | 20.1687i | −1.38042 | + | 0.905599i | ||||
\(497\) | 46.9079i | 2.10411i | ||||||||
\(498\) | 30.3804 | + | 2.35816i | 1.36138 | + | 0.105672i | ||||
\(499\) | − | 29.0340i | − | 1.29974i | −0.760045 | − | 0.649871i | \(-0.774823\pi\) | ||
0.760045 | − | 0.649871i | \(-0.225177\pi\) | |||||||
\(500\) | −10.7845 | + | 19.9731i | −0.482299 | + | 0.893224i | ||||
\(501\) | 26.9354 | − | 4.62592i | 1.20338 | − | 0.206671i | ||||
\(502\) | 17.5354 | + | 4.43175i | 0.782642 | + | 0.197799i | ||||
\(503\) | −7.77873 | −0.346836 | −0.173418 | − | 0.984848i | \(-0.555481\pi\) | ||||
−0.173418 | + | 0.984848i | \(0.555481\pi\) | |||||||
\(504\) | −12.3637 | + | 29.0419i | −0.550724 | + | 1.29363i | ||||
\(505\) | −21.7498 | −0.967851 | ||||||||
\(506\) | −1.31384 | − | 0.332048i | −0.0584071 | − | 0.0147613i | ||||
\(507\) | −11.2677 | + | 1.93513i | −0.500414 | + | 0.0859419i | ||||
\(508\) | 6.78217 | − | 12.5607i | 0.300910 | − | 0.557290i | ||||
\(509\) | − | 10.9884i | − | 0.487052i | −0.969894 | − | 0.243526i | \(-0.921696\pi\) | ||
0.969894 | − | 0.243526i | \(-0.0783040\pi\) | |||||||
\(510\) | 14.6277 | + | 1.13541i | 0.647723 | + | 0.0502770i | ||||
\(511\) | − | 17.3648i | − | 0.768175i | ||||||
\(512\) | 13.8220 | − | 17.9151i | 0.610853 | − | 0.791744i | ||||
\(513\) | 1.59215 | + | 2.84474i | 0.0702953 | + | 0.125598i | ||||
\(514\) | −5.37293 | + | 21.2594i | −0.236990 | + | 0.937712i | ||||
\(515\) | 4.59032 | 0.202274 | ||||||||
\(516\) | 8.33233 | − | 24.7277i | 0.366810 | − | 1.08858i | ||||
\(517\) | −4.56449 | −0.200746 | ||||||||
\(518\) | 11.1815 | − | 44.2424i | 0.491285 | − | 1.94390i | ||||
\(519\) | −1.99997 | − | 11.6452i | −0.0877889 | − | 0.511168i | ||||
\(520\) | 10.6476 | − | 11.5993i | 0.466928 | − | 0.508664i | ||||
\(521\) | − | 39.5660i | − | 1.73342i | −0.498816 | − | 0.866708i | \(-0.666232\pi\) | ||
0.498816 | − | 0.866708i | \(-0.333768\pi\) | |||||||
\(522\) | 2.58708 | + | 27.8533i | 0.113233 | + | 1.21911i | ||||
\(523\) | 2.37731i | 0.103952i | 0.998648 | + | 0.0519762i | \(0.0165520\pi\) | ||||
−0.998648 | + | 0.0519762i | \(0.983448\pi\) | |||||||
\(524\) | 1.80412 | + | 0.974136i | 0.0788131 | + | 0.0425553i | ||||
\(525\) | −0.171677 | − | 0.999626i | −0.00749262 | − | 0.0436272i | ||||
\(526\) | −21.7064 | − | 5.48591i | −0.946446 | − | 0.239197i | ||||
\(527\) | −25.0197 | −1.08988 | ||||||||
\(528\) | 4.52862 | + | 4.85445i | 0.197083 | + | 0.211263i | ||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −34.9472 | − | 8.83228i | −1.51801 | − | 0.383650i | ||||
\(531\) | 0.252905 | − | 0.0895086i | 0.0109751 | − | 0.00388434i | ||||
\(532\) | 4.10711 | + | 2.21764i | 0.178066 | + | 0.0961469i | ||||
\(533\) | 14.9718i | 0.648499i | ||||||||
\(534\) | 0.0613725 | − | 0.790668i | 0.00265585 | − | 0.0342155i | ||||
\(535\) | 2.32041i | 0.100320i | ||||||||
\(536\) | 26.1303 | − | 28.4660i | 1.12866 | − | 1.22954i | ||||
\(537\) | 40.3381 | − | 6.92774i | 1.74072 | − | 0.298954i | ||||
\(538\) | 1.24976 | − | 4.94500i | 0.0538809 | − | 0.213194i | ||||
\(539\) | −6.55186 | −0.282209 | ||||||||
\(540\) | 0.346475 | + | 22.8665i | 0.0149099 | + | 0.984019i | ||||
\(541\) | 29.0791 | 1.25021 | 0.625103 | − | 0.780542i | \(-0.285057\pi\) | ||||
0.625103 | + | 0.780542i | \(0.285057\pi\) | |||||||
\(542\) | 7.42193 | − | 29.3668i | 0.318799 | − | 1.26141i | ||||
\(543\) | 8.18477 | − | 1.40567i | 0.351242 | − | 0.0603229i | ||||
\(544\) | 14.5510 | − | 5.03382i | 0.623870 | − | 0.215823i | ||||
\(545\) | 9.52065i | 0.407820i | ||||||||
\(546\) | −1.78381 | + | 22.9809i | −0.0763398 | + | 0.983494i | ||||
\(547\) | 10.0489i | 0.429658i | 0.976652 | + | 0.214829i | \(0.0689194\pi\) | ||||
−0.976652 | + | 0.214829i | \(0.931081\pi\) | |||||||
\(548\) | 1.05729 | − | 1.95811i | 0.0451651 | − | 0.0836465i | ||||
\(549\) | −40.8567 | + | 14.4601i | −1.74372 | + | 0.617142i | ||||
\(550\) | −0.206825 | − | 0.0522712i | −0.00881903 | − | 0.00222885i | ||||
\(551\) | 4.13656 | 0.176223 | ||||||||
\(552\) | −4.11767 | − | 2.65420i | −0.175260 | − | 0.112970i | ||||
\(553\) | 25.2062 | 1.07188 | ||||||||
\(554\) | −41.6272 | − | 10.5205i | −1.76857 | − | 0.446974i | ||||
\(555\) | −5.59633 | − | 32.5857i | −0.237551 | − | 1.38319i | ||||
\(556\) | −1.67960 | + | 3.11065i | −0.0712310 | + | 0.131921i | ||||
\(557\) | − | 29.2920i | − | 1.24114i | −0.784150 | − | 0.620571i | \(-0.786901\pi\) | ||
0.784150 | − | 0.620571i | \(-0.213099\pi\) | |||||||
\(558\) | −3.60680 | − | 38.8319i | −0.152688 | − | 1.64388i | ||||
\(559\) | − | 19.0553i | − | 0.805953i | ||||||
\(560\) | 17.9608 | + | 27.3780i | 0.758982 | + | 1.15693i | ||||
\(561\) | 0.764646 | + | 4.45230i | 0.0322834 | + | 0.187976i | ||||
\(562\) | 2.19140 | − | 8.67084i | 0.0924385 | − | 0.365757i | ||||
\(563\) | −12.2397 | −0.515844 | −0.257922 | − | 0.966166i | \(-0.583038\pi\) | ||||
−0.257922 | + | 0.966166i | \(0.583038\pi\) | |||||||
\(564\) | −15.6372 | − | 5.26915i | −0.658443 | − | 0.221871i | ||||
\(565\) | −9.58525 | −0.403254 | ||||||||
\(566\) | −4.18282 | + | 16.5504i | −0.175817 | + | 0.695666i | ||||
\(567\) | −21.0598 | − | 26.0253i | −0.884430 | − | 1.09296i | ||||
\(568\) | 26.2750 | + | 24.1192i | 1.10248 | + | 1.01202i | ||||
\(569\) | 28.6863i | 1.20259i | 0.799027 | + | 0.601295i | \(0.205348\pi\) | ||||
−0.799027 | + | 0.601295i | \(0.794652\pi\) | |||||||
\(570\) | 3.37165 | + | 0.261711i | 0.141223 | + | 0.0109619i | ||||
\(571\) | 8.12001i | 0.339812i | 0.985460 | + | 0.169906i | \(0.0543464\pi\) | ||||
−0.985460 | + | 0.169906i | \(0.945654\pi\) | |||||||
\(572\) | 4.26594 | + | 2.30340i | 0.178368 | + | 0.0963101i | ||||
\(573\) | −15.9437 | + | 2.73820i | −0.666059 | + | 0.114390i | ||||
\(574\) | −30.1857 | − | 7.62890i | −1.25993 | − | 0.318424i | ||||
\(575\) | 0.157420 | 0.00656488 | ||||||||
\(576\) | 9.91039 | + | 21.8583i | 0.412933 | + | 0.910761i | ||||
\(577\) | −34.8648 | −1.45144 | −0.725719 | − | 0.687991i | \(-0.758493\pi\) | ||||
−0.725719 | + | 0.687991i | \(0.758493\pi\) | |||||||
\(578\) | −13.1509 | − | 3.32366i | −0.547007 | − | 0.138246i | ||||
\(579\) | 11.0387 | − | 1.89580i | 0.458752 | − | 0.0787868i | ||||
\(580\) | 25.5340 | + | 13.7871i | 1.06024 | + | 0.572480i | ||||
\(581\) | 46.2755i | 1.91983i | ||||||||
\(582\) | −17.0989 | − | 1.32724i | −0.708774 | − | 0.0550158i | ||||
\(583\) | − | 11.0988i | − | 0.459665i | ||||||
\(584\) | −9.72676 | − | 8.92869i | −0.402496 | − | 0.369472i | ||||
\(585\) | 5.57198 | + | 15.7435i | 0.230373 | + | 0.650914i | ||||
\(586\) | −2.04171 | + | 8.07857i | −0.0843423 | + | 0.333723i | ||||
\(587\) | −16.2131 | −0.669187 | −0.334594 | − | 0.942362i | \(-0.608599\pi\) | ||||
−0.334594 | + | 0.942362i | \(0.608599\pi\) | |||||||
\(588\) | −22.4456 | − | 7.56333i | −0.925639 | − | 0.311906i | ||||
\(589\) | −5.76701 | −0.237626 | ||||||||
\(590\) | 0.0681916 | − | 0.269818i | 0.00280740 | − | 0.0111082i | ||||
\(591\) | 7.32217 | + | 42.6348i | 0.301194 | + | 1.75376i | ||||
\(592\) | −19.0327 | − | 29.0118i | −0.782239 | − | 1.19238i | ||||
\(593\) | − | 8.79493i | − | 0.361165i | −0.983560 | − | 0.180582i | \(-0.942202\pi\) | ||
0.983560 | − | 0.180582i | \(-0.0577982\pi\) | |||||||
\(594\) | −6.79997 | + | 1.82860i | −0.279006 | + | 0.0750286i | ||||
\(595\) | 22.2808i | 0.913425i | ||||||||
\(596\) | 15.3632 | − | 28.4529i | 0.629301 | − | 1.16547i | ||||
\(597\) | 3.29044 | + | 19.1592i | 0.134669 | + | 0.784135i | ||||
\(598\) | −3.46848 | − | 0.876595i | −0.141837 | − | 0.0358466i | ||||
\(599\) | 11.7207 | 0.478896 | 0.239448 | − | 0.970909i | \(-0.423034\pi\) | ||||
0.239448 | + | 0.970909i | \(0.423034\pi\) | |||||||
\(600\) | −0.648205 | − | 0.417826i | −0.0264629 | − | 0.0170577i | ||||
\(601\) | 4.64820 | 0.189604 | 0.0948021 | − | 0.995496i | \(-0.469778\pi\) | ||||
0.0948021 | + | 0.995496i | \(0.469778\pi\) | |||||||
\(602\) | 38.4189 | + | 9.70968i | 1.56584 | + | 0.395737i | ||||
\(603\) | 13.6742 | + | 38.6362i | 0.556858 | + | 1.57339i | ||||
\(604\) | 17.2366 | − | 31.9225i | 0.701349 | − | 1.29891i | ||||
\(605\) | − | 22.1858i | − | 0.901983i | ||||||
\(606\) | 1.87356 | − | 24.1372i | 0.0761080 | − | 0.980507i | ||||
\(607\) | − | 19.8336i | − | 0.805020i | −0.915416 | − | 0.402510i | \(-0.868138\pi\) | ||
0.915416 | − | 0.402510i | \(-0.131862\pi\) | |||||||
\(608\) | 3.35399 | − | 1.16029i | 0.136022 | − | 0.0470559i | ||||
\(609\) | −41.8680 | + | 7.19048i | −1.69658 | + | 0.291373i | ||||
\(610\) | −11.0163 | + | 43.5890i | −0.446038 | + | 1.76487i | ||||
\(611\) | −12.0501 | −0.487494 | ||||||||
\(612\) | −2.52010 | + | 16.1355i | −0.101869 | + | 0.652240i | ||||
\(613\) | −19.6394 | −0.793229 | −0.396615 | − | 0.917985i | \(-0.629815\pi\) | ||||
−0.396615 | + | 0.917985i | \(0.629815\pi\) | |||||||
\(614\) | −10.0564 | + | 39.7908i | −0.405843 | + | 1.60583i | ||||
\(615\) | −22.2326 | + | 3.81827i | −0.896506 | + | 0.153967i | ||||
\(616\) | −6.81779 | + | 7.42719i | −0.274697 | + | 0.299250i | ||||
\(617\) | − | 18.8290i | − | 0.758028i | −0.925391 | − | 0.379014i | \(-0.876263\pi\) | ||
0.925391 | − | 0.379014i | \(-0.123737\pi\) | |||||||
\(618\) | −0.395417 | + | 5.09420i | −0.0159060 | + | 0.204919i | ||||
\(619\) | 1.87158i | 0.0752251i | 0.999292 | + | 0.0376125i | \(0.0119753\pi\) | ||||
−0.999292 | + | 0.0376125i | \(0.988025\pi\) | |||||||
\(620\) | −35.5984 | − | 19.2214i | −1.42967 | − | 0.771952i | ||||
\(621\) | 4.53429 | − | 2.53776i | 0.181955 | − | 0.101837i | ||||
\(622\) | −43.6598 | − | 11.0342i | −1.75060 | − | 0.442432i | ||||
\(623\) | 1.20434 | 0.0482510 | ||||||||
\(624\) | 11.9554 | + | 12.8156i | 0.478598 | + | 0.513034i | ||||
\(625\) | −24.1881 | −0.967525 | ||||||||
\(626\) | −45.0775 | − | 11.3925i | −1.80166 | − | 0.455336i | ||||
\(627\) | 0.176250 | + | 1.02625i | 0.00703874 | + | 0.0409845i | ||||
\(628\) | −22.2978 | − | 12.0397i | −0.889778 | − | 0.480438i | ||||
\(629\) | − | 23.6105i | − | 0.941413i | ||||||
\(630\) | −34.5810 | + | 3.21196i | −1.37774 | + | 0.127968i | ||||
\(631\) | 36.3862i | 1.44851i | 0.689532 | + | 0.724255i | \(0.257816\pi\) | ||||
−0.689532 | + | 0.724255i | \(0.742184\pi\) | |||||||
\(632\) | 12.9606 | − | 14.1190i | 0.515544 | − | 0.561625i | ||||
\(633\) | 0.423286 | + | 2.46467i | 0.0168241 | + | 0.0979618i | ||||
\(634\) | −9.93221 | + | 39.2994i | −0.394458 | + | 1.56078i | ||||
\(635\) | 15.7064 | 0.623290 | ||||||||
\(636\) | 12.8122 | − | 38.0225i | 0.508037 | − | 1.50769i | ||||
\(637\) | −17.2967 | −0.685319 | ||||||||
\(638\) | −2.18931 | + | 8.66257i | −0.0866755 | + | 0.342954i | ||||
\(639\) | −35.6626 | + | 12.6218i | −1.41079 | + | 0.499310i | ||||
\(640\) | 24.5706 | + | 4.01667i | 0.971240 | + | 0.158773i | ||||
\(641\) | − | 16.3458i | − | 0.645620i | −0.946464 | − | 0.322810i | \(-0.895372\pi\) | ||
0.946464 | − | 0.322810i | \(-0.104628\pi\) | |||||||
\(642\) | −2.57512 | − | 0.199883i | −0.101632 | − | 0.00788876i | ||||
\(643\) | 11.5323i | 0.454791i | 0.973803 | + | 0.227395i | \(0.0730210\pi\) | ||||
−0.973803 | + | 0.227395i | \(0.926979\pi\) | |||||||
\(644\) | 3.53474 | − | 6.54640i | 0.139288 | − | 0.257964i | ||||
\(645\) | 28.2966 | − | 4.85970i | 1.11418 | − | 0.191351i | ||||
\(646\) | 2.34136 | + | 0.591737i | 0.0921196 | + | 0.0232816i | ||||
\(647\) | −2.56200 | −0.100723 | −0.0503614 | − | 0.998731i | \(-0.516037\pi\) | ||||
−0.0503614 | + | 0.998731i | \(0.516037\pi\) | |||||||
\(648\) | −25.4064 | − | 1.58525i | −0.998059 | − | 0.0622745i | ||||
\(649\) | 0.0856906 | 0.00336365 | ||||||||
\(650\) | −0.546009 | − | 0.137994i | −0.0214162 | − | 0.00541257i | ||||
\(651\) | 58.3706 | − | 10.0247i | 2.28772 | − | 0.392897i | ||||
\(652\) | 7.74802 | − | 14.3495i | 0.303436 | − | 0.561968i | ||||
\(653\) | 7.49322i | 0.293232i | 0.989193 | + | 0.146616i | \(0.0468382\pi\) | ||||
−0.989193 | + | 0.146616i | \(0.953162\pi\) | |||||||
\(654\) | −10.5657 | − | 0.820123i | −0.413153 | − | 0.0320693i | ||||
\(655\) | 2.25594i | 0.0881470i | ||||||||
\(656\) | −19.7942 | + | 12.9856i | −0.772835 | + | 0.507004i | ||||
\(657\) | 13.2019 | − | 4.67246i | 0.515056 | − | 0.182290i | ||||
\(658\) | 6.14015 | − | 24.2951i | 0.239368 | − | 0.947122i | ||||
\(659\) | 10.5898 | 0.412518 | 0.206259 | − | 0.978497i | \(-0.433871\pi\) | ||||
0.206259 | + | 0.978497i | \(0.433871\pi\) | |||||||
\(660\) | −2.33254 | + | 6.92223i | −0.0907939 | + | 0.269448i | ||||
\(661\) | −11.5819 | −0.450482 | −0.225241 | − | 0.974303i | \(-0.572317\pi\) | ||||
−0.225241 | + | 0.974303i | \(0.572317\pi\) | |||||||
\(662\) | −8.04348 | + | 31.8262i | −0.312619 | + | 1.23696i | ||||
\(663\) | 2.01864 | + | 11.7539i | 0.0783973 | + | 0.456484i | ||||
\(664\) | 25.9208 | + | 23.7940i | 1.00592 | + | 0.923387i | ||||
\(665\) | 5.13570i | 0.199154i | ||||||||
\(666\) | 36.6447 | − | 3.40365i | 1.41995 | − | 0.131889i | ||||
\(667\) | − | 6.59334i | − | 0.255295i | ||||||
\(668\) | 27.7683 | + | 14.9935i | 1.07439 | + | 0.580118i | ||||
\(669\) | 3.35599 | + | 19.5409i | 0.129750 | + | 0.755495i | ||||
\(670\) | 41.2201 | + | 10.4176i | 1.59247 | + | 0.402468i | ||||
\(671\) | −13.8433 | −0.534415 | ||||||||
\(672\) | −31.9304 | + | 17.5740i | −1.23174 | + | 0.677931i | ||||
\(673\) | −28.1359 | −1.08456 | −0.542279 | − | 0.840199i | \(-0.682438\pi\) | ||||
−0.542279 | + | 0.840199i | \(0.682438\pi\) | |||||||
\(674\) | 34.2085 | + | 8.64558i | 1.31766 | + | 0.333015i | ||||
\(675\) | 0.713789 | − | 0.399496i | 0.0274738 | − | 0.0153766i | ||||
\(676\) | −11.6161 | − | 6.27213i | −0.446772 | − | 0.241236i | ||||
\(677\) | 13.6085i | 0.523018i | 0.965201 | + | 0.261509i | \(0.0842200\pi\) | ||||
−0.965201 | + | 0.261509i | \(0.915780\pi\) | |||||||
\(678\) | 0.825688 | − | 10.6374i | 0.0317104 | − | 0.408528i | ||||
\(679\) | − | 26.0451i | − | 0.999519i | ||||||
\(680\) | 12.4804 | + | 11.4564i | 0.478602 | + | 0.439333i | ||||
\(681\) | 19.7322 | − | 3.38884i | 0.756140 | − | 0.129861i | ||||
\(682\) | 3.05224 | − | 12.0770i | 0.116876 | − | 0.462452i | ||||
\(683\) | −24.2770 | −0.928932 | −0.464466 | − | 0.885591i | \(-0.653754\pi\) | ||||
−0.464466 | + | 0.885591i | \(0.653754\pi\) | |||||||
\(684\) | −0.580879 | + | 3.71922i | −0.0222105 | + | 0.142208i | ||||
\(685\) | 2.44851 | 0.0935527 | ||||||||
\(686\) | −0.209541 | + | 0.829106i | −0.00800033 | + | 0.0316554i | ||||
\(687\) | −19.5065 | + | 3.35008i | −0.744220 | + | 0.127814i | ||||
\(688\) | 25.1931 | − | 16.5275i | 0.960478 | − | 0.630104i | ||||
\(689\) | − | 29.3004i | − | 1.11626i | ||||||
\(690\) | 0.417147 | − | 5.37415i | 0.0158805 | − | 0.204590i | ||||
\(691\) | − | 3.51437i | − | 0.133693i | −0.997763 | − | 0.0668466i | \(-0.978706\pi\) | ||
0.997763 | − | 0.0668466i | \(-0.0212938\pi\) | |||||||
\(692\) | 6.48230 | − | 12.0053i | 0.246420 | − | 0.456374i | ||||
\(693\) | −3.56781 | − | 10.0808i | −0.135530 | − | 0.382937i | ||||
\(694\) | −3.35038 | − | 0.846748i | −0.127179 | − | 0.0321421i | ||||
\(695\) | −3.88969 | −0.147544 | ||||||||
\(696\) | −17.5001 | + | 27.1492i | −0.663339 | + | 1.02909i | ||||
\(697\) | −16.1090 | −0.610172 | ||||||||
\(698\) | 23.1211 | + | 5.84344i | 0.875146 | + | 0.221177i | ||||
\(699\) | 4.30429 | + | 25.0626i | 0.162803 | + | 0.947953i | ||||
\(700\) | 0.556441 | − | 1.03054i | 0.0210315 | − | 0.0389506i | ||||
\(701\) | 5.32303i | 0.201048i | 0.994935 | + | 0.100524i | \(0.0320520\pi\) | ||||
−0.994935 | + | 0.100524i | \(0.967948\pi\) | |||||||
\(702\) | −17.9517 | + | 4.82745i | −0.677542 | + | 0.182200i | ||||
\(703\) | − | 5.44219i | − | 0.205256i | ||||||
\(704\) | 0.654689 | + | 7.63786i | 0.0246745 | + | 0.287862i | ||||
\(705\) | −3.07315 | − | 17.8940i | −0.115741 | − | 0.673928i | ||||
\(706\) | 12.2058 | − | 48.2955i | 0.459371 | − | 1.81762i | ||||
\(707\) | 36.7658 | 1.38272 | ||||||||
\(708\) | 0.293562 | + | 0.0989195i | 0.0110327 | + | 0.00371762i | ||||
\(709\) | 48.1004 | 1.80645 | 0.903225 | − | 0.429167i | \(-0.141193\pi\) | ||||
0.903225 | + | 0.429167i | \(0.141193\pi\) | |||||||
\(710\) | −9.61582 | + | 38.0475i | −0.360875 | + | 1.42790i | ||||
\(711\) | 6.78238 | + | 19.1635i | 0.254359 | + | 0.718687i | ||||
\(712\) | 0.619252 | − | 0.674603i | 0.0232075 | − | 0.0252818i | ||||
\(713\) | 9.19216i | 0.344249i | ||||||||
\(714\) | −24.7266 | − | 1.91930i | −0.925369 | − | 0.0718281i | ||||
\(715\) | 5.33431i | 0.199492i | ||||||||
\(716\) | 41.5855 | + | 22.4542i | 1.55412 | + | 0.839152i | ||||
\(717\) | 25.2260 | − | 4.33236i | 0.942084 | − | 0.161795i | ||||
\(718\) | 13.5872 | + | 3.43391i | 0.507069 | + | 0.128152i | ||||
\(719\) | 39.4347 | 1.47067 | 0.735333 | − | 0.677706i | \(-0.237026\pi\) | ||||
0.735333 | + | 0.677706i | \(0.237026\pi\) | |||||||
\(720\) | −15.9818 | + | 21.0218i | −0.595605 | + | 0.783435i | ||||
\(721\) | −7.75948 | −0.288978 | ||||||||
\(722\) | −25.5113 | − | 6.44751i | −0.949431 | − | 0.239952i | ||||
\(723\) | −29.6920 | + | 5.09936i | −1.10426 | + | 0.189647i | ||||
\(724\) | 8.43787 | + | 4.55605i | 0.313591 | + | 0.169324i | ||||
\(725\) | − | 1.03793i | − | 0.0385476i | ||||||
\(726\) | 24.6212 | + | 1.91112i | 0.913778 | + | 0.0709284i | ||||
\(727\) | − | 30.8119i | − | 1.14275i | −0.820689 | − | 0.571374i | \(-0.806410\pi\) | ||
0.820689 | − | 0.571374i | \(-0.193590\pi\) | |||||||
\(728\) | −17.9987 | + | 19.6075i | −0.667077 | + | 0.726702i | ||||
\(729\) | 14.1195 | − | 23.0139i | 0.522944 | − | 0.852367i | ||||
\(730\) | 3.55968 | − | 14.0848i | 0.131750 | − | 0.521302i | ||||
\(731\) | 20.5027 | 0.758321 | ||||||||
\(732\) | −47.4248 | − | 15.9804i | −1.75287 | − | 0.590653i | ||||
\(733\) | −25.7605 | −0.951486 | −0.475743 | − | 0.879584i | \(-0.657821\pi\) | ||||
−0.475743 | + | 0.879584i | \(0.657821\pi\) | |||||||
\(734\) | 0.950857 | − | 3.76231i | 0.0350968 | − | 0.138870i | ||||
\(735\) | −4.41119 | − | 25.6850i | −0.162709 | − | 0.947407i | ||||
\(736\) | −1.84941 | − | 5.34600i | −0.0681701 | − | 0.197056i | ||||
\(737\) | 13.0910i | 0.482211i | ||||||||
\(738\) | −2.32225 | − | 25.0020i | −0.0854831 | − | 0.920337i | ||||
\(739\) | 4.15414i | 0.152813i | 0.997077 | + | 0.0764063i | \(0.0243446\pi\) | ||||
−0.997077 | + | 0.0764063i | \(0.975655\pi\) | |||||||
\(740\) | 18.1388 | − | 33.5934i | 0.666796 | − | 1.23492i | ||||
\(741\) | 0.465293 | + | 2.70926i | 0.0170930 | + | 0.0995271i | ||||
\(742\) | 59.0748 | + | 14.9301i | 2.16870 | + | 0.548100i | ||||
\(743\) | 1.36108 | 0.0499332 | 0.0249666 | − | 0.999688i | \(-0.492052\pi\) | ||||
0.0249666 | + | 0.999688i | \(0.492052\pi\) | |||||||
\(744\) | 24.3979 | − | 37.8503i | 0.894469 | − | 1.38766i | ||||
\(745\) | 35.5787 | 1.30350 | ||||||||
\(746\) | 6.75171 | + | 1.70637i | 0.247198 | + | 0.0624748i | ||||
\(747\) | −35.1818 | + | 12.4516i | −1.28723 | + | 0.455581i | ||||
\(748\) | −2.47837 | + | 4.58998i | −0.0906182 | + | 0.167826i | ||||
\(749\) | − | 3.92241i | − | 0.143322i | ||||||
\(750\) | 2.15140 | − | 27.7167i | 0.0785581 | − | 1.01207i | ||||
\(751\) | 15.2763i | 0.557439i | 0.960373 | + | 0.278720i | \(0.0899100\pi\) | ||||
−0.960373 | + | 0.278720i | \(0.910090\pi\) | |||||||
\(752\) | −10.4515 | − | 15.9315i | −0.381129 | − | 0.580961i | ||||
\(753\) | −21.8320 | + | 3.74946i | −0.795602 | + | 0.136638i | ||||
\(754\) | −5.77969 | + | 22.8689i | −0.210484 | + | 0.832835i | ||||
\(755\) | 39.9173 | 1.45274 | ||||||||
\(756\) | −0.585682 | − | 38.6536i | −0.0213011 | − | 1.40582i | ||||
\(757\) | −33.9871 | −1.23528 | −0.617641 | − | 0.786460i | \(-0.711911\pi\) | ||||
−0.617641 | + | 0.786460i | \(0.711911\pi\) | |||||||
\(758\) | 2.03353 | − | 8.04619i | 0.0738610 | − | 0.292251i | ||||
\(759\) | 1.63576 | − | 0.280928i | 0.0593743 | − | 0.0101970i | ||||
\(760\) | 2.87672 | + | 2.64069i | 0.104350 | + | 0.0957877i | ||||
\(761\) | − | 7.51143i | − | 0.272289i | −0.990689 | − | 0.136145i | \(-0.956529\pi\) | ||
0.990689 | − | 0.136145i | \(-0.0434712\pi\) | |||||||
\(762\) | −1.35297 | + | 17.4305i | −0.0490131 | + | 0.631440i | ||||
\(763\) | − | 16.0937i | − | 0.582631i | ||||||
\(764\) | −16.4368 | − | 8.87507i | −0.594661 | − | 0.321089i | ||||
\(765\) | −16.9394 | + | 5.99523i | −0.612445 | + | 0.216758i | ||||
\(766\) | −16.8545 | − | 4.25967i | −0.608978 | − | 0.153908i | ||||
\(767\) | 0.226220 | 0.00816833 | ||||||||
\(768\) | −6.57413 | + | 26.9218i | −0.237223 | + | 0.971455i | ||||
\(769\) | 19.6743 | 0.709474 | 0.354737 | − | 0.934966i | \(-0.384570\pi\) | ||||
0.354737 | + | 0.934966i | \(0.384570\pi\) | |||||||
\(770\) | −10.7549 | − | 2.71811i | −0.387581 | − | 0.0979540i | ||||
\(771\) | −4.54575 | − | 26.4685i | −0.163711 | − | 0.953240i | ||||
\(772\) | 11.3800 | + | 6.14467i | 0.409576 | + | 0.221152i | ||||
\(773\) | − | 39.9906i | − | 1.43836i | −0.694822 | − | 0.719182i | \(-0.744517\pi\) | ||
0.694822 | − | 0.719182i | \(-0.255483\pi\) | |||||||
\(774\) | 2.95564 | + | 31.8213i | 0.106238 | + | 1.14379i | ||||
\(775\) | 1.44703i | 0.0519790i | ||||||||
\(776\) | −14.5889 | − | 13.3919i | −0.523712 | − | 0.480742i | ||||
\(777\) | 9.46003 | + | 55.0829i | 0.339377 | + | 1.97609i | ||||
\(778\) | 6.14322 | − | 24.3073i | 0.220245 | − | 0.871458i | ||||
\(779\) | −3.71311 | −0.133036 | ||||||||
\(780\) | −6.15782 | + | 18.2744i | −0.220485 | + | 0.654330i | ||||
\(781\) | −12.0834 | −0.432378 | ||||||||
\(782\) | 0.943181 | − | 3.73194i | 0.0337281 | − | 0.133454i | ||||
\(783\) | −16.7324 | − | 29.8961i | −0.597966 | − | 1.06840i | ||||
\(784\) | −15.0021 | − | 22.8680i | −0.535790 | − | 0.816714i | ||||
\(785\) | − | 27.8821i | − | 0.995154i | ||||||
\(786\) | −2.50358 | − | 0.194330i | −0.0892996 | − | 0.00693153i | ||||
\(787\) | 41.2555i | 1.47060i | 0.677742 | + | 0.735300i | \(0.262959\pi\) | ||||
−0.677742 | + | 0.735300i | \(0.737041\pi\) | |||||||
\(788\) | −23.7326 | + | 43.9532i | −0.845439 | + | 1.56577i | ||||
\(789\) | 27.0251 | − | 4.64133i | 0.962118 | − | 0.165236i | ||||
\(790\) | 20.4451 | + | 5.16712i | 0.727402 | + | 0.183838i | ||||
\(791\) | 16.2029 | 0.576109 | ||||||||
\(792\) | −7.48116 | − | 3.18487i | −0.265831 | − | 0.113170i | ||||
\(793\) | −36.5458 | −1.29778 | ||||||||
\(794\) | 14.5551 | + | 3.67853i | 0.516540 | + | 0.130546i | ||||
\(795\) | 43.5102 | − | 7.47251i | 1.54315 | − | 0.265023i | ||||
\(796\) | −10.6650 | + | 19.7517i | −0.378010 | + | 0.700080i | ||||
\(797\) | 37.2029i | 1.31780i | 0.752233 | + | 0.658898i | \(0.228977\pi\) | ||||
−0.752233 | + | 0.658898i | \(0.771023\pi\) | |||||||
\(798\) | −5.69944 | − | 0.442397i | −0.201758 | − | 0.0156607i | ||||
\(799\) | − | 12.9654i | − | 0.458683i | ||||||
\(800\) | −0.291134 | − | 0.841569i | −0.0102932 | − | 0.0297540i | ||||
\(801\) | 0.324060 | + | 0.915624i | 0.0114501 | + | 0.0323520i | ||||
\(802\) | −6.62549 | + | 26.2155i | −0.233954 | + | 0.925701i | ||||
\(803\) | 4.47315 | 0.157854 | ||||||||
\(804\) | −15.1119 | + | 44.8474i | −0.532956 | + | 1.58165i | ||||
\(805\) | 8.18590 | 0.288515 | ||||||||
\(806\) | 8.05780 | − | 31.8828i | 0.283824 | − | 1.12302i | ||||
\(807\) | 1.05735 | + | 6.15665i | 0.0372206 | + | 0.216724i | ||||
\(808\) | 18.9043 | − | 20.5940i | 0.665051 | − | 0.724496i | ||||
\(809\) | − | 39.0244i | − | 1.37202i | −0.727590 | − | 0.686012i | \(-0.759360\pi\) | ||
0.727590 | − | 0.686012i | \(-0.240640\pi\) | |||||||
\(810\) | −11.7469 | − | 25.4265i | −0.412743 | − | 0.893398i | ||||
\(811\) | − | 46.5108i | − | 1.63321i | −0.577194 | − | 0.816607i | \(-0.695853\pi\) | ||
0.577194 | − | 0.816607i | \(-0.304147\pi\) | |||||||
\(812\) | −43.1627 | − | 23.3058i | −1.51471 | − | 0.817873i | ||||
\(813\) | 6.27930 | + | 36.5624i | 0.220224 | + | 1.28230i | ||||
\(814\) | 11.3968 | + | 2.88033i | 0.399457 | + | 0.100955i | ||||
\(815\) | 17.9432 | 0.628522 | ||||||||
\(816\) | −13.7890 | + | 12.8635i | −0.482713 | + | 0.450313i | ||||
\(817\) | 4.72585 | 0.165337 | ||||||||
\(818\) | 30.7132 | + | 7.76221i | 1.07386 | + | 0.271399i | ||||
\(819\) | −9.41888 | − | 26.6128i | −0.329122 | − | 0.929928i | ||||
\(820\) | −22.9201 | − | 12.3758i | −0.800405 | − | 0.432181i | ||||
\(821\) | − | 13.1005i | − | 0.457209i | −0.973519 | − | 0.228605i | \(-0.926584\pi\) | ||
0.973519 | − | 0.228605i | \(-0.0734163\pi\) | |||||||
\(822\) | −0.210918 | + | 2.71728i | −0.00735662 | + | 0.0947760i | ||||
\(823\) | − | 38.5602i | − | 1.34412i | −0.740495 | − | 0.672062i | \(-0.765409\pi\) | ||
0.740495 | − | 0.672062i | \(-0.234591\pi\) | |||||||
\(824\) | −3.98979 | + | 4.34641i | −0.138991 | + | 0.151414i | ||||
\(825\) | 0.257502 | − | 0.0442238i | 0.00896507 | − | 0.00153968i | ||||
\(826\) | −0.115271 | + | 0.456100i | −0.00401079 | + | 0.0158698i | ||||
\(827\) | 21.1614 | 0.735853 | 0.367927 | − | 0.929855i | \(-0.380068\pi\) | ||||
0.367927 | + | 0.929855i | \(0.380068\pi\) | |||||||
\(828\) | 5.92813 | + | 0.925875i | 0.206017 | + | 0.0321764i | ||||
\(829\) | 10.5121 | 0.365099 | 0.182550 | − | 0.983197i | \(-0.441565\pi\) | ||||
0.182550 | + | 0.983197i | \(0.441565\pi\) | |||||||
\(830\) | −9.48618 | + | 37.5346i | −0.329270 | + | 1.30284i | ||||
\(831\) | 51.8269 | − | 8.90084i | 1.79786 | − | 0.308767i | ||||
\(832\) | 1.72835 | + | 20.1637i | 0.0599199 | + | 0.699049i | ||||
\(833\) | − | 18.6105i | − | 0.644816i | ||||||
\(834\) | 0.335064 | − | 4.31666i | 0.0116023 | − | 0.149474i | ||||
\(835\) | 34.7226i | 1.20163i | ||||||||
\(836\) | −0.571261 | + | 1.05798i | −0.0197575 | + | 0.0365911i | ||||
\(837\) | 23.3275 | + | 41.6799i | 0.806318 | + | 1.44067i | ||||
\(838\) | −13.1180 | − | 3.31534i | −0.453154 | − | 0.114526i | ||||
\(839\) | 16.7666 | 0.578847 | 0.289424 | − | 0.957201i | \(-0.406536\pi\) | ||||
0.289424 | + | 0.957201i | \(0.406536\pi\) | |||||||
\(840\) | −33.7068 | − | 21.7270i | −1.16300 | − | 0.749654i | ||||
\(841\) | −14.4722 | −0.499041 | ||||||||
\(842\) | −45.8946 | − | 11.5990i | −1.58163 | − | 0.399729i | ||||
\(843\) | 1.85402 | + | 10.7954i | 0.0638559 | + | 0.371814i | ||||
\(844\) | −1.37196 | + | 2.54088i | −0.0472247 | + | 0.0874608i | ||||
\(845\) | − | 14.5252i | − | 0.499684i | ||||||
\(846\) | 20.1230 | − | 1.86907i | 0.691842 | − | 0.0642599i | ||||
\(847\) | 37.5030i | 1.28862i | ||||||||
\(848\) | 38.7382 | − | 25.4134i | 1.33027 | − | 0.872701i | ||||
\(849\) | −3.53886 | − | 20.6057i | −0.121453 | − | 0.707186i | ||||
\(850\) | 0.148476 | − | 0.587484i | 0.00509268 | − | 0.0201505i | ||||
\(851\) | −8.67442 | −0.297355 | ||||||||
\(852\) | −41.3957 | − | 13.9488i | −1.41819 | − | 0.477879i | ||||
\(853\) | 16.3383 | 0.559414 | 0.279707 | − | 0.960085i | \(-0.409763\pi\) | ||||
0.279707 | + | 0.960085i | \(0.409763\pi\) | |||||||
\(854\) | 18.6220 | − | 73.6829i | 0.637232 | − | 2.52138i | ||||
\(855\) | −3.90451 | + | 1.38189i | −0.133531 | + | 0.0472597i | ||||
\(856\) | −2.19711 | − | 2.01684i | −0.0750955 | − | 0.0689340i | ||||
\(857\) | − | 9.30340i | − | 0.317798i | −0.987295 | − | 0.158899i | \(-0.949206\pi\) | ||
0.987295 | − | 0.158899i | \(-0.0507945\pi\) | |||||||
\(858\) | −5.91986 | − | 0.459506i | −0.202101 | − | 0.0156873i | ||||
\(859\) | 51.5860i | 1.76009i | 0.474889 | + | 0.880046i | \(0.342488\pi\) | ||||
−0.474889 | + | 0.880046i | \(0.657512\pi\) | |||||||
\(860\) | 29.1716 | + | 15.7513i | 0.994743 | + | 0.537114i | ||||
\(861\) | 37.5820 | − | 6.45440i | 1.28079 | − | 0.219965i | ||||
\(862\) | 21.3172 | + | 5.38754i | 0.726068 | + | 0.183501i | ||||
\(863\) | −25.6415 | −0.872847 | −0.436423 | − | 0.899741i | \(-0.643755\pi\) | ||||
−0.436423 | + | 0.899741i | \(0.643755\pi\) | |||||||
\(864\) | −21.9526 | − | 19.5469i | −0.746843 | − | 0.665000i | ||||
\(865\) | 15.0120 | 0.510422 | ||||||||
\(866\) | −0.860669 | − | 0.217518i | −0.0292467 | − | 0.00739158i | ||||
\(867\) | 16.3733 | − | 2.81197i | 0.556065 | − | 0.0954996i | ||||
\(868\) | 60.1755 | + | 32.4919i | 2.04249 | + | 1.10285i | ||||
\(869\) | 6.49308i | 0.220263i | ||||||||
\(870\) | −35.4336 | − | 2.75039i | −1.20131 | − | 0.0932471i | ||||
\(871\) | 34.5596i | 1.17101i | ||||||||
\(872\) | −9.01475 | − | 8.27509i | −0.305278 | − | 0.280230i | ||||
\(873\) | 19.8013 | − | 7.00811i | 0.670171 | − | 0.237189i | ||||
\(874\) | 0.217402 | − | 0.860208i | 0.00735373 | − | 0.0290970i | ||||
\(875\) | 42.2181 | 1.42723 | ||||||||
\(876\) | 15.3243 | + | 5.16371i | 0.517759 | + | 0.174466i | ||||
\(877\) | −5.45955 | −0.184356 | −0.0921779 | − | 0.995743i | \(-0.529383\pi\) | ||||
−0.0921779 | + | 0.995743i | \(0.529383\pi\) | |||||||
\(878\) | 1.75818 | − | 6.95670i | 0.0593357 | − | 0.234777i | ||||
\(879\) | −1.72738 | − | 10.0580i | −0.0582632 | − | 0.339249i | ||||
\(880\) | −7.05252 | + | 4.62667i | −0.237740 | + | 0.155965i | ||||
\(881\) | 56.3574i | 1.89873i | 0.314178 | + | 0.949364i | \(0.398271\pi\) | ||||
−0.314178 | + | 0.949364i | \(0.601729\pi\) | |||||||
\(882\) | 28.8845 | − | 2.68286i | 0.972591 | − | 0.0903366i | ||||
\(883\) | − | 21.4218i | − | 0.720902i | −0.932778 | − | 0.360451i | \(-0.882623\pi\) | ||
0.932778 | − | 0.360451i | \(-0.117377\pi\) | |||||||
\(884\) | −6.54280 | + | 12.1174i | −0.220058 | + | 0.407551i | ||||
\(885\) | 0.0576932 | + | 0.335930i | 0.00193934 | + | 0.0112922i | ||||
\(886\) | 12.1118 | + | 3.06105i | 0.406905 | + | 0.102838i | ||||
\(887\) | 13.6688 | 0.458954 | 0.229477 | − | 0.973314i | \(-0.426298\pi\) | ||||
0.229477 | + | 0.973314i | \(0.426298\pi\) | |||||||
\(888\) | 35.7184 | + | 23.0237i | 1.19863 | + | 0.772625i | ||||
\(889\) | −26.5501 | −0.890462 | ||||||||
\(890\) | 0.976857 | + | 0.246883i | 0.0327443 | + | 0.00827554i | ||||
\(891\) | 6.70407 | − | 5.42498i | 0.224595 | − | 0.181744i | ||||
\(892\) | −10.8774 | + | 20.1452i | −0.364203 | + | 0.674510i | ||||
\(893\) | − | 2.98851i | − | 0.100007i | ||||||
\(894\) | −3.06480 | + | 39.4841i | −0.102502 | + | 1.32055i | ||||
\(895\) | 52.0003i | 1.73818i | ||||||||
\(896\) | −41.5342 | − | 6.78977i | −1.38756 | − | 0.226830i | ||||
\(897\) | 4.31834 | − | 0.741640i | 0.144185 | − | 0.0247626i | ||||
\(898\) | 5.56942 | − | 22.0369i | 0.185854 | − | 0.735380i | ||||
\(899\) | 60.6071 | 2.02136 | ||||||||
\(900\) | 0.933209 | + | 0.145752i | 0.0311070 | + | 0.00485839i | ||||
\(901\) | 31.5260 | 1.05028 | ||||||||
\(902\) | 1.96519 | − | 7.77580i | 0.0654337 | − | 0.258906i | ||||
\(903\) | −47.8325 | + | 8.21484i | −1.59177 | + | 0.273373i | ||||
\(904\) | 8.33124 | − | 9.07592i | 0.277093 | − | 0.301861i | ||||
\(905\) | 10.5511i | 0.350730i | ||||||||
\(906\) | −3.43854 | + | 44.2990i | −0.114238 | + | 1.47174i | ||||
\(907\) | − | 43.0069i | − | 1.42802i | −0.700135 | − | 0.714010i | \(-0.746877\pi\) | ||
0.700135 | − | 0.714010i | \(-0.253123\pi\) | |||||||
\(908\) | 20.3424 | + | 10.9839i | 0.675086 | + | 0.364514i | ||||
\(909\) | 9.89278 | + | 27.9518i | 0.328123 | + | 0.927104i | ||||
\(910\) | −28.3926 | − | 7.17571i | −0.941205 | − | 0.237873i | ||||
\(911\) | 32.0270 | 1.06110 | 0.530551 | − | 0.847653i | \(-0.321985\pi\) | ||||
0.530551 | + | 0.847653i | \(0.321985\pi\) | |||||||
\(912\) | −3.17836 | + | 2.96502i | −0.105246 | + | 0.0981817i | ||||
\(913\) | −11.9205 | −0.394510 | ||||||||
\(914\) | −22.4481 | − | 5.67336i | −0.742518 | − | 0.187658i | ||||
\(915\) | −9.32033 | − | 54.2694i | −0.308120 | − | 1.79409i | ||||
\(916\) | −20.1097 | − | 10.8583i | −0.664443 | − | 0.358768i | ||||
\(917\) | − | 3.81345i | − | 0.125931i | ||||||
\(918\) | −5.19414 | − | 19.3153i | −0.171432 | − | 0.637499i | ||||
\(919\) | 2.94437i | 0.0971259i | 0.998820 | + | 0.0485629i | \(0.0154641\pi\) | ||||
−0.998820 | + | 0.0485629i | \(0.984536\pi\) | |||||||
\(920\) | 4.20904 | − | 4.58526i | 0.138768 | − | 0.151172i | ||||
\(921\) | −8.50818 | − | 49.5406i | −0.280354 | − | 1.63242i | ||||
\(922\) | 3.24078 | − | 12.8230i | 0.106729 | − | 0.422303i | ||||
\(923\) | −31.8997 | −1.04999 | ||||||||
\(924\) | 3.94292 | − | 11.7013i | 0.129713 | − | 0.384946i | ||||
\(925\) | −1.36553 | −0.0448984 | ||||||||
\(926\) | −3.54444 | + | 14.0245i | −0.116477 | + | 0.460874i | ||||
\(927\) | −2.08789 | − | 5.89929i | −0.0685753 | − | 0.193758i | ||||
\(928\) | −35.2480 | + | 12.1938i | −1.15707 | + | 0.400280i | ||||
\(929\) | − | 14.7359i | − | 0.483468i | −0.970343 | − | 0.241734i | \(-0.922284\pi\) | ||
0.970343 | − | 0.241734i | \(-0.0777161\pi\) | |||||||
\(930\) | 49.4000 | + | 3.83448i | 1.61989 | + | 0.125738i | ||||
\(931\) | − | 4.28970i | − | 0.140589i | ||||||
\(932\) | −13.9511 | + | 25.8376i | −0.456982 | + | 0.846338i | ||||
\(933\) | 54.3575 | − | 9.33545i | 1.77959 | − | 0.305629i | ||||
\(934\) | 11.8293 | + | 2.98963i | 0.387065 | + | 0.0978237i | ||||
\(935\) | −5.73950 | −0.187702 | ||||||||
\(936\) | −19.7500 | − | 8.40794i | −0.645548 | − | 0.274822i | ||||
\(937\) | 33.9922 | 1.11048 | 0.555238 | − | 0.831692i | \(-0.312627\pi\) | ||||
0.555238 | + | 0.831692i | \(0.312627\pi\) | |||||||
\(938\) | −69.6784 | − | 17.6099i | −2.27508 | − | 0.574985i | ||||
\(939\) | 56.1226 | − | 9.63859i | 1.83149 | − | 0.314544i | ||||
\(940\) | 9.96069 | − | 18.4474i | 0.324882 | − | 0.601686i | ||||
\(941\) | − | 42.1318i | − | 1.37346i | −0.726913 | − | 0.686729i | \(-0.759046\pi\) | ||
0.726913 | − | 0.686729i | \(-0.240954\pi\) | |||||||
\(942\) | 30.9427 | + | 2.40180i | 1.00817 | + | 0.0782550i | ||||
\(943\) | 5.91840i | 0.192729i | ||||||||
\(944\) | 0.196210 | + | 0.299087i | 0.00638610 | + | 0.00973444i | ||||
\(945\) | 37.1172 | − | 20.7739i | 1.20742 | − | 0.675774i | ||||
\(946\) | −2.50120 | + | 9.89665i | −0.0813209 | + | 0.321768i | ||||
\(947\) | −47.9731 | −1.55892 | −0.779458 | − | 0.626454i | \(-0.784506\pi\) | ||||
−0.779458 | + | 0.626454i | \(0.784506\pi\) | |||||||
\(948\) | −7.49548 | + | 22.2442i | −0.243442 | + | 0.722458i | ||||
\(949\) | 11.8090 | 0.383335 | ||||||||
\(950\) | 0.0342235 | − | 0.135414i | 0.00111036 | − | 0.00439342i | ||||
\(951\) | −8.40311 | − | 48.9288i | −0.272489 | − | 1.58662i | ||||
\(952\) | −21.0969 | − | 19.3659i | −0.683754 | − | 0.627652i | ||||
\(953\) | 40.9003i | 1.32489i | 0.749111 | + | 0.662445i | \(0.230481\pi\) | ||||
−0.749111 | + | 0.662445i | \(0.769519\pi\) | |||||||
\(954\) | 4.54473 | + | 48.9300i | 0.147141 | + | 1.58417i | ||||
\(955\) | − | 20.5532i | − | 0.665087i | ||||||
\(956\) | 26.0061 | + | 14.0421i | 0.841097 | + | 0.454153i | ||||
\(957\) | −1.85226 | − | 10.7851i | −0.0598749 | − | 0.348634i | ||||
\(958\) | −9.35580 | − | 2.36451i | −0.302272 | − | 0.0763938i | ||||
\(959\) | −4.13896 | −0.133654 | ||||||||
\(960\) | −29.5017 | + | 7.70892i | −0.952162 | + | 0.248804i | ||||
\(961\) | −53.4958 | −1.72567 | ||||||||
\(962\) | 30.0870 | + | 7.60395i | 0.970045 | + | 0.245161i | ||||
\(963\) | 2.98209 | − | 1.05543i | 0.0960964 | − | 0.0340107i | ||||
\(964\) | −30.6102 | − | 16.5280i | −0.985888 | − | 0.532332i | ||||
\(965\) | 14.2301i | 0.458082i | ||||||||
\(966\) | −0.705146 | + | 9.08446i | −0.0226877 | + | 0.292288i | ||||
\(967\) | 51.7116i | 1.66293i | 0.555574 | + | 0.831467i | \(0.312498\pi\) | ||||
−0.555574 | + | 0.831467i | \(0.687502\pi\) | |||||||
\(968\) | 21.0070 | + | 19.2834i | 0.675189 | + | 0.619790i | ||||
\(969\) | −2.91506 | + | 0.500636i | −0.0936451 | + | 0.0160828i | ||||
\(970\) | 5.33908 | − | 21.1255i | 0.171428 | − | 0.678298i | ||||
\(971\) | −3.77813 | −0.121246 | −0.0606229 | − | 0.998161i | \(-0.519309\pi\) | ||||
−0.0606229 | + | 0.998161i | \(0.519309\pi\) | |||||||
\(972\) | 29.2295 | − | 10.8460i | 0.937537 | − | 0.347886i | ||||
\(973\) | 6.57513 | 0.210789 | ||||||||
\(974\) | 2.17716 | − | 8.61450i | 0.0697607 | − | 0.276027i | ||||
\(975\) | 0.679796 | − | 0.116749i | 0.0217709 | − | 0.00373897i | ||||
\(976\) | −31.6977 | − | 48.3174i | −1.01462 | − | 1.54660i | ||||
\(977\) | 36.6311i | 1.17193i | 0.810335 | + | 0.585967i | \(0.199285\pi\) | ||||
−0.810335 | + | 0.585967i | \(0.800715\pi\) | |||||||
\(978\) | −1.54565 | + | 19.9128i | −0.0494245 | + | 0.636741i | ||||
\(979\) | 0.310237i | 0.00991522i | ||||||||
\(980\) | 14.2976 | − | 26.4793i | 0.456719 | − | 0.845850i | ||||
\(981\) | 12.2355 | − | 4.33043i | 0.390650 | − | 0.138260i | ||||
\(982\) | 30.3641 | + | 7.67399i | 0.968959 | + | 0.244887i | ||||
\(983\) | 36.6169 | 1.16790 | 0.583949 | − | 0.811791i | \(-0.301507\pi\) | ||||
0.583949 | + | 0.811791i | \(0.301507\pi\) | |||||||
\(984\) | 15.7086 | − | 24.3700i | 0.500773 | − | 0.776887i | ||||
\(985\) | −54.9609 | −1.75120 | ||||||||
\(986\) | −24.6060 | − | 6.21872i | −0.783614 | − | 0.198044i | ||||
\(987\) | 5.19485 | + | 30.2481i | 0.165354 | + | 0.962806i | ||||
\(988\) | −1.50811 | + | 2.79304i | −0.0479793 | + | 0.0888584i | ||||
\(989\) | − | 7.53264i | − | 0.239524i | ||||||
\(990\) | −0.827397 | − | 8.90800i | −0.0262964 | − | 0.283115i | ||||
\(991\) | 46.5569i | 1.47893i | 0.673196 | + | 0.739464i | \(0.264921\pi\) | ||||
−0.673196 | + | 0.739464i | \(0.735079\pi\) | |||||||
\(992\) | 49.1413 | − | 17.0000i | 1.56024 | − | 0.539752i | ||||
\(993\) | −6.80516 | − | 39.6244i | −0.215955 | − | 1.25744i | ||||
\(994\) | 16.2546 | − | 64.3155i | 0.515564 | − | 2.03996i | ||||
\(995\) | −24.6983 | −0.782990 | ||||||||
\(996\) | −40.8376 | − | 13.7608i | −1.29399 | − | 0.436026i | ||||
\(997\) | −8.99973 | −0.285024 | −0.142512 | − | 0.989793i | \(-0.545518\pi\) | ||||
−0.142512 | + | 0.989793i | \(0.545518\pi\) | |||||||
\(998\) | −10.0609 | + | 39.8086i | −0.318473 | + | 1.26012i | ||||
\(999\) | −39.3323 | + | 22.0136i | −1.24442 | + | 0.696481i |
(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 | 276.2.c.a.47.3 | ✓ | 22 | |
3.2 | odd | 2 | 276.2.c.b.47.20 | yes | 22 | ||
4.3 | odd | 2 | 276.2.c.b.47.19 | yes | 22 | ||
12.11 | even | 2 | inner | 276.2.c.a.47.4 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.c.a.47.3 | ✓ | 22 | 1.1 | even | 1 | trivial | |
276.2.c.a.47.4 | yes | 22 | 12.11 | even | 2 | inner | |
276.2.c.b.47.19 | yes | 22 | 4.3 | odd | 2 | ||
276.2.c.b.47.20 | yes | 22 | 3.2 | odd | 2 |