Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(267,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("380.267");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.k (of order \(4\), 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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 343.7 | ||
Character | \(\chi\) | \(=\) | 380.343 |
Dual form | 380.2.k.d.267.7 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.07073 | + | 0.923868i | −0.757122 | + | 0.653274i | ||||
\(3\) | −1.14885 | + | 1.14885i | −0.663287 | + | 0.663287i | −0.956153 | − | 0.292867i | \(-0.905391\pi\) |
0.292867 | + | 0.956153i | \(0.405391\pi\) | |||||||
\(4\) | 0.292934 | − | 1.97843i | 0.146467 | − | 0.989216i | ||||
\(5\) | 1.95382 | + | 1.08746i | 0.873776 | + | 0.486328i | ||||
\(6\) | 0.168724 | − | 2.29149i | 0.0688812 | − | 0.935496i | ||||
\(7\) | −2.70883 | − | 2.70883i | −1.02384 | − | 1.02384i | −0.999709 | − | 0.0241310i | \(-0.992318\pi\) |
−0.0241310 | − | 0.999709i | \(-0.507682\pi\) | |||||||
\(8\) | 1.51416 | + | 2.38900i | 0.535335 | + | 0.844640i | ||||
\(9\) | 0.360306i | 0.120102i | ||||||||
\(10\) | −3.09669 | + | 0.640694i | −0.979261 | + | 0.202605i | ||||
\(11\) | 4.11798i | 1.24162i | 0.783962 | + | 0.620809i | \(0.213196\pi\) | ||||
−0.783962 | + | 0.620809i | \(0.786804\pi\) | |||||||
\(12\) | 1.93638 | + | 2.60945i | 0.558984 | + | 0.753283i | ||||
\(13\) | −1.95079 | − | 1.95079i | −0.541053 | − | 0.541053i | 0.382785 | − | 0.923838i | \(-0.374965\pi\) |
−0.923838 | + | 0.382785i | \(0.874965\pi\) | |||||||
\(14\) | 5.40302 | + | 0.397828i | 1.44402 | + | 0.106324i | ||||
\(15\) | −3.49397 | + | 0.995314i | −0.902139 | + | 0.256989i | ||||
\(16\) | −3.82838 | − | 1.15910i | −0.957095 | − | 0.289775i | ||||
\(17\) | −4.15549 | + | 4.15549i | −1.00786 | + | 1.00786i | −0.00788621 | + | 0.999969i | \(0.502510\pi\) |
−0.999969 | + | 0.00788621i | \(0.997490\pi\) | |||||||
\(18\) | −0.332875 | − | 0.385791i | −0.0784594 | − | 0.0909318i | ||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 2.72381 | − | 3.54695i | 0.609063 | − | 0.793122i | ||||
\(21\) | 6.22405 | 1.35820 | ||||||||
\(22\) | −3.80447 | − | 4.40926i | −0.811117 | − | 0.940057i | ||||
\(23\) | −3.01995 | + | 3.01995i | −0.629703 | + | 0.629703i | −0.947993 | − | 0.318291i | \(-0.896891\pi\) |
0.318291 | + | 0.947993i | \(0.396891\pi\) | |||||||
\(24\) | −4.48413 | − | 1.00506i | −0.915319 | − | 0.205158i | ||||
\(25\) | 2.63485 | + | 4.24942i | 0.526970 | + | 0.849884i | ||||
\(26\) | 3.89106 | + | 0.286501i | 0.763099 | + | 0.0561875i | ||||
\(27\) | −3.86047 | − | 3.86047i | −0.742949 | − | 0.742949i | ||||
\(28\) | −6.15273 | + | 4.56572i | −1.16276 | + | 0.862839i | ||||
\(29\) | − | 2.35086i | − | 0.436544i | −0.975888 | − | 0.218272i | \(-0.929958\pi\) | ||
0.975888 | − | 0.218272i | \(-0.0700420\pi\) | |||||||
\(30\) | 2.82157 | − | 4.29368i | 0.515145 | − | 0.783916i | ||||
\(31\) | − | 5.48110i | − | 0.984434i | −0.870473 | − | 0.492217i | \(-0.836187\pi\) | ||
0.870473 | − | 0.492217i | \(-0.163813\pi\) | |||||||
\(32\) | 5.17002 | − | 2.29583i | 0.913940 | − | 0.405849i | ||||
\(33\) | −4.73093 | − | 4.73093i | −0.823549 | − | 0.823549i | ||||
\(34\) | 0.610291 | − | 8.28855i | 0.104664 | − | 1.42147i | ||||
\(35\) | −2.34682 | − | 8.23831i | −0.396685 | − | 1.39253i | ||||
\(36\) | 0.712840 | + | 0.105546i | 0.118807 | + | 0.0175910i | ||||
\(37\) | 3.69981 | − | 3.69981i | 0.608246 | − | 0.608246i | −0.334242 | − | 0.942487i | \(-0.608480\pi\) |
0.942487 | + | 0.334242i | \(0.108480\pi\) | |||||||
\(38\) | 1.07073 | − | 0.923868i | 0.173696 | − | 0.149871i | ||||
\(39\) | 4.48233 | 0.717746 | ||||||||
\(40\) | 0.360440 | + | 6.31428i | 0.0569905 | + | 0.998375i | ||||
\(41\) | −9.82744 | −1.53479 | −0.767394 | − | 0.641176i | \(-0.778447\pi\) | ||||
−0.767394 | + | 0.641176i | \(0.778447\pi\) | |||||||
\(42\) | −6.66429 | + | 5.75020i | −1.02832 | + | 0.887275i | ||||
\(43\) | −8.96408 | + | 8.96408i | −1.36701 | + | 1.36701i | −0.502339 | + | 0.864671i | \(0.667527\pi\) |
−0.864671 | + | 0.502339i | \(0.832473\pi\) | |||||||
\(44\) | 8.14714 | + | 1.20630i | 1.22823 | + | 0.181856i | ||||
\(45\) | −0.391819 | + | 0.703974i | −0.0584090 | + | 0.104942i | ||||
\(46\) | 0.443521 | − | 6.02359i | 0.0653936 | − | 0.888130i | ||||
\(47\) | −0.482563 | − | 0.482563i | −0.0703891 | − | 0.0703891i | 0.671036 | − | 0.741425i | \(-0.265850\pi\) |
−0.741425 | + | 0.671036i | \(0.765850\pi\) | |||||||
\(48\) | 5.72985 | − | 3.06659i | 0.827032 | − | 0.442624i | ||||
\(49\) | 7.67547i | 1.09650i | ||||||||
\(50\) | −6.74712 | − | 2.11574i | −0.954187 | − | 0.299211i | ||||
\(51\) | − | 9.54804i | − | 1.33699i | ||||||
\(52\) | −4.43097 | + | 3.28806i | −0.614465 | + | 0.455972i | ||||
\(53\) | −2.71437 | − | 2.71437i | −0.372848 | − | 0.372848i | 0.495666 | − | 0.868513i | \(-0.334924\pi\) |
−0.868513 | + | 0.495666i | \(0.834924\pi\) | |||||||
\(54\) | 7.70010 | + | 0.566964i | 1.04785 | + | 0.0771540i | ||||
\(55\) | −4.47815 | + | 8.04581i | −0.603834 | + | 1.08490i | ||||
\(56\) | 2.36981 | − | 10.5730i | 0.316679 | − | 1.41287i | ||||
\(57\) | 1.14885 | − | 1.14885i | 0.152168 | − | 0.152168i | ||||
\(58\) | 2.17189 | + | 2.51714i | 0.285183 | + | 0.330517i | ||||
\(59\) | 9.02322 | 1.17472 | 0.587361 | − | 0.809325i | \(-0.300167\pi\) | ||||
0.587361 | + | 0.809325i | \(0.300167\pi\) | |||||||
\(60\) | 0.945656 | + | 7.20414i | 0.122084 | + | 0.930050i | ||||
\(61\) | −4.23945 | −0.542806 | −0.271403 | − | 0.962466i | \(-0.587488\pi\) | ||||
−0.271403 | + | 0.962466i | \(0.587488\pi\) | |||||||
\(62\) | 5.06381 | + | 5.86878i | 0.643105 | + | 0.745336i | ||||
\(63\) | 0.976005 | − | 0.976005i | 0.122965 | − | 0.122965i | ||||
\(64\) | −3.41467 | + | 7.23464i | −0.426833 | + | 0.904330i | ||||
\(65\) | −1.69009 | − | 5.93292i | −0.209630 | − | 0.735889i | ||||
\(66\) | 9.43631 | + | 0.694802i | 1.16153 | + | 0.0855242i | ||||
\(67\) | 6.49679 | + | 6.49679i | 0.793710 | + | 0.793710i | 0.982095 | − | 0.188386i | \(-0.0603255\pi\) |
−0.188386 | + | 0.982095i | \(0.560325\pi\) | |||||||
\(68\) | 7.00407 | + | 9.43864i | 0.849368 | + | 1.14460i | ||||
\(69\) | − | 6.93891i | − | 0.835347i | ||||||
\(70\) | 10.1239 | + | 6.65288i | 1.21004 | + | 0.795171i | ||||
\(71\) | 14.9562i | 1.77497i | 0.460837 | + | 0.887485i | \(0.347549\pi\) | ||||
−0.460837 | + | 0.887485i | \(0.652451\pi\) | |||||||
\(72\) | −0.860771 | + | 0.545559i | −0.101443 | + | 0.0642947i | ||||
\(73\) | 7.29798 | + | 7.29798i | 0.854164 | + | 0.854164i | 0.990643 | − | 0.136479i | \(-0.0435785\pi\) |
−0.136479 | + | 0.990643i | \(0.543579\pi\) | |||||||
\(74\) | −0.543368 | + | 7.37965i | −0.0631653 | + | 0.857867i | ||||
\(75\) | −7.90896 | − | 1.85490i | −0.913249 | − | 0.214185i | ||||
\(76\) | −0.292934 | + | 1.97843i | −0.0336019 | + | 0.226942i | ||||
\(77\) | 11.1549 | − | 11.1549i | 1.27122 | − | 1.27122i | ||||
\(78\) | −4.79937 | + | 4.14108i | −0.543422 | + | 0.468885i | ||||
\(79\) | 3.64828 | 0.410464 | 0.205232 | − | 0.978713i | \(-0.434205\pi\) | ||||
0.205232 | + | 0.978713i | \(0.434205\pi\) | |||||||
\(80\) | −6.21949 | − | 6.42790i | −0.695361 | − | 0.718661i | ||||
\(81\) | 7.78926 | 0.865474 | ||||||||
\(82\) | 10.5226 | − | 9.07926i | 1.16202 | − | 1.00264i | ||||
\(83\) | 8.32940 | − | 8.32940i | 0.914270 | − | 0.914270i | −0.0823347 | − | 0.996605i | \(-0.526238\pi\) |
0.996605 | + | 0.0823347i | \(0.0262377\pi\) | |||||||
\(84\) | 1.82324 | − | 12.3138i | 0.198932 | − | 1.34355i | ||||
\(85\) | −12.6380 | + | 3.60015i | −1.37079 | + | 0.390491i | ||||
\(86\) | 1.31650 | − | 17.8798i | 0.141962 | − | 1.92802i | ||||
\(87\) | 2.70078 | + | 2.70078i | 0.289554 | + | 0.289554i | ||||
\(88\) | −9.83787 | + | 6.23527i | −1.04872 | + | 0.664682i | ||||
\(89\) | 9.76244i | 1.03482i | 0.855739 | + | 0.517408i | \(0.173103\pi\) | ||||
−0.855739 | + | 0.517408i | \(0.826897\pi\) | |||||||
\(90\) | −0.230846 | − | 1.11576i | −0.0243333 | − | 0.117611i | ||||
\(91\) | 10.5687i | 1.10790i | ||||||||
\(92\) | 5.09011 | + | 6.85941i | 0.530681 | + | 0.715142i | ||||
\(93\) | 6.29693 | + | 6.29693i | 0.652962 | + | 0.652962i | ||||
\(94\) | 0.962520 | + | 0.0708710i | 0.0992764 | + | 0.00730979i | ||||
\(95\) | −1.95382 | − | 1.08746i | −0.200458 | − | 0.111571i | ||||
\(96\) | −3.30201 | + | 8.57712i | −0.337010 | + | 0.875399i | ||||
\(97\) | 0.208633 | − | 0.208633i | 0.0211835 | − | 0.0211835i | −0.696436 | − | 0.717619i | \(-0.745232\pi\) |
0.717619 | + | 0.696436i | \(0.245232\pi\) | |||||||
\(98\) | −7.09112 | − | 8.21837i | −0.716312 | − | 0.830181i | ||||
\(99\) | −1.48373 | −0.149121 | ||||||||
\(100\) | 9.17902 | − | 3.96806i | 0.917902 | − | 0.396806i | ||||
\(101\) | −18.7952 | −1.87019 | −0.935096 | − | 0.354394i | \(-0.884687\pi\) | ||||
−0.935096 | + | 0.354394i | \(0.884687\pi\) | |||||||
\(102\) | 8.82114 | + | 10.2234i | 0.873423 | + | 1.01227i | ||||
\(103\) | −0.733254 | + | 0.733254i | −0.0722496 | + | 0.0722496i | −0.742308 | − | 0.670059i | \(-0.766269\pi\) |
0.670059 | + | 0.742308i | \(0.266269\pi\) | |||||||
\(104\) | 1.70665 | − | 7.61426i | 0.167350 | − | 0.746640i | ||||
\(105\) | 12.1607 | + | 6.76842i | 1.18676 | + | 0.660530i | ||||
\(106\) | 5.41409 | + | 0.398643i | 0.525863 | + | 0.0387196i | ||||
\(107\) | 4.19542 | + | 4.19542i | 0.405586 | + | 0.405586i | 0.880196 | − | 0.474610i | \(-0.157411\pi\) |
−0.474610 | + | 0.880196i | \(0.657411\pi\) | |||||||
\(108\) | −8.76855 | + | 6.50682i | −0.843754 | + | 0.626119i | ||||
\(109\) | − | 2.82743i | − | 0.270819i | −0.990790 | − | 0.135409i | \(-0.956765\pi\) | ||
0.990790 | − | 0.135409i | \(-0.0432350\pi\) | |||||||
\(110\) | −2.63836 | − | 12.7521i | −0.251558 | − | 1.21587i | ||||
\(111\) | 8.50103i | 0.806882i | ||||||||
\(112\) | 7.23061 | + | 13.5102i | 0.683228 | + | 1.27660i | ||||
\(113\) | 1.04439 | + | 1.04439i | 0.0982483 | + | 0.0982483i | 0.754522 | − | 0.656274i | \(-0.227869\pi\) |
−0.656274 | + | 0.754522i | \(0.727869\pi\) | |||||||
\(114\) | −0.168724 | + | 2.29149i | −0.0158024 | + | 0.214618i | ||||
\(115\) | −9.18453 | + | 2.61636i | −0.856461 | + | 0.243977i | ||||
\(116\) | −4.65102 | − | 0.688649i | −0.431836 | − | 0.0639394i | ||||
\(117\) | 0.702883 | − | 0.702883i | 0.0649815 | − | 0.0649815i | ||||
\(118\) | −9.66145 | + | 8.33627i | −0.889408 | + | 0.767415i | ||||
\(119\) | 22.5130 | 2.06376 | ||||||||
\(120\) | −7.66822 | − | 6.84004i | −0.700010 | − | 0.624407i | ||||
\(121\) | −5.95778 | −0.541616 | ||||||||
\(122\) | 4.53931 | − | 3.91669i | 0.410970 | − | 0.354601i | ||||
\(123\) | 11.2902 | − | 11.2902i | 1.01800 | − | 1.01800i | ||||
\(124\) | −10.8440 | − | 1.60560i | −0.973817 | − | 0.144187i | ||||
\(125\) | 0.526938 | + | 11.1679i | 0.0471308 | + | 0.998889i | ||||
\(126\) | −0.143340 | + | 1.94674i | −0.0127697 | + | 0.173429i | ||||
\(127\) | 2.30575 | + | 2.30575i | 0.204602 | + | 0.204602i | 0.801969 | − | 0.597366i | \(-0.203786\pi\) |
−0.597366 | + | 0.801969i | \(0.703786\pi\) | |||||||
\(128\) | −3.02767 | − | 10.9011i | −0.267610 | − | 0.963527i | ||||
\(129\) | − | 20.5967i | − | 1.81344i | ||||||
\(130\) | 7.29087 | + | 4.79115i | 0.639452 | + | 0.420212i | ||||
\(131\) | − | 1.87892i | − | 0.164162i | −0.996626 | − | 0.0820810i | \(-0.973843\pi\) | ||
0.996626 | − | 0.0820810i | \(-0.0261566\pi\) | |||||||
\(132\) | −10.7457 | + | 7.97396i | −0.935290 | + | 0.694044i | ||||
\(133\) | 2.70883 | + | 2.70883i | 0.234885 | + | 0.234885i | ||||
\(134\) | −12.9585 | − | 0.954143i | −1.11944 | − | 0.0824254i | ||||
\(135\) | −3.34456 | − | 11.7408i | −0.287854 | − | 1.01049i | ||||
\(136\) | −16.2195 | − | 3.63542i | −1.39081 | − | 0.311735i | ||||
\(137\) | 4.38444 | − | 4.38444i | 0.374588 | − | 0.374588i | −0.494557 | − | 0.869145i | \(-0.664670\pi\) |
0.869145 | + | 0.494557i | \(0.164670\pi\) | |||||||
\(138\) | 6.41064 | + | 7.42971i | 0.545710 | + | 0.632459i | ||||
\(139\) | 5.70518 | 0.483907 | 0.241953 | − | 0.970288i | \(-0.422212\pi\) | ||||
0.241953 | + | 0.970288i | \(0.422212\pi\) | |||||||
\(140\) | −16.9864 | + | 2.22973i | −1.43561 | + | 0.188447i | ||||
\(141\) | 1.10878 | 0.0933762 | ||||||||
\(142\) | −13.8175 | − | 16.0140i | −1.15954 | − | 1.34387i | ||||
\(143\) | 8.03334 | − | 8.03334i | 0.671781 | − | 0.671781i | ||||
\(144\) | 0.417631 | − | 1.37939i | 0.0348026 | − | 0.114949i | ||||
\(145\) | 2.55648 | − | 4.59317i | 0.212304 | − | 0.381442i | ||||
\(146\) | −14.5566 | − | 1.07181i | −1.20471 | − | 0.0887035i | ||||
\(147\) | −8.81793 | − | 8.81793i | −0.727291 | − | 0.727291i | ||||
\(148\) | −6.23602 | − | 8.40363i | −0.512598 | − | 0.690774i | ||||
\(149\) | 3.91665i | 0.320864i | 0.987047 | + | 0.160432i | \(0.0512888\pi\) | ||||
−0.987047 | + | 0.160432i | \(0.948711\pi\) | |||||||
\(150\) | 10.1821 | − | 5.32075i | 0.831362 | − | 0.434437i | ||||
\(151\) | − | 4.24151i | − | 0.345169i | −0.984995 | − | 0.172584i | \(-0.944788\pi\) | ||
0.984995 | − | 0.172584i | \(-0.0552118\pi\) | |||||||
\(152\) | −1.51416 | − | 2.38900i | −0.122814 | − | 0.193774i | ||||
\(153\) | −1.49725 | − | 1.49725i | −0.121045 | − | 0.121045i | ||||
\(154\) | −1.63825 | + | 22.2496i | −0.132014 | + | 1.79292i | ||||
\(155\) | 5.96049 | − | 10.7091i | 0.478758 | − | 0.860175i | ||||
\(156\) | 1.31303 | − | 8.86797i | 0.105126 | − | 0.710006i | ||||
\(157\) | −1.83855 | + | 1.83855i | −0.146733 | + | 0.146733i | −0.776657 | − | 0.629924i | \(-0.783086\pi\) |
0.629924 | + | 0.776657i | \(0.283086\pi\) | |||||||
\(158\) | −3.90633 | + | 3.37053i | −0.310771 | + | 0.268145i | ||||
\(159\) | 6.23679 | 0.494610 | ||||||||
\(160\) | 12.5979 | + | 1.13656i | 0.995955 | + | 0.0898532i | ||||
\(161\) | 16.3610 | 1.28943 | ||||||||
\(162\) | −8.34021 | + | 7.19625i | −0.655269 | + | 0.565391i | ||||
\(163\) | 1.72096 | − | 1.72096i | 0.134796 | − | 0.134796i | −0.636489 | − | 0.771285i | \(-0.719614\pi\) |
0.771285 | + | 0.636489i | \(0.219614\pi\) | |||||||
\(164\) | −2.87879 | + | 19.4429i | −0.224796 | + | 1.51824i | ||||
\(165\) | −4.09869 | − | 14.3881i | −0.319082 | − | 1.12011i | ||||
\(166\) | −1.22329 | + | 16.6138i | −0.0949454 | + | 1.28948i | ||||
\(167\) | 9.53008 | + | 9.53008i | 0.737460 | + | 0.737460i | 0.972086 | − | 0.234626i | \(-0.0753866\pi\) |
−0.234626 | + | 0.972086i | \(0.575387\pi\) | |||||||
\(168\) | 9.42417 | + | 14.8693i | 0.727091 | + | 1.14719i | ||||
\(169\) | − | 5.38880i | − | 0.414523i | ||||||
\(170\) | 10.2059 | − | 15.5307i | 0.782756 | − | 1.19115i | ||||
\(171\) | − | 0.360306i | − | 0.0275533i | ||||||
\(172\) | 15.1089 | + | 20.3607i | 1.15205 | + | 1.55249i | ||||
\(173\) | 1.38868 | + | 1.38868i | 0.105579 | + | 0.105579i | 0.757923 | − | 0.652344i | \(-0.226214\pi\) |
−0.652344 | + | 0.757923i | \(0.726214\pi\) | |||||||
\(174\) | −5.38697 | − | 0.396646i | −0.408386 | − | 0.0300697i | ||||
\(175\) | 4.37360 | − | 18.6483i | 0.330613 | − | 1.40968i | ||||
\(176\) | 4.77316 | − | 15.7652i | 0.359790 | − | 1.18835i | ||||
\(177\) | −10.3663 | + | 10.3663i | −0.779178 | + | 0.779178i | ||||
\(178\) | −9.01921 | − | 10.4530i | −0.676019 | − | 0.783483i | ||||
\(179\) | −20.9758 | −1.56780 | −0.783901 | − | 0.620886i | \(-0.786773\pi\) | ||||
−0.783901 | + | 0.620886i | \(0.786773\pi\) | |||||||
\(180\) | 1.27799 | + | 0.981405i | 0.0952555 | + | 0.0731496i | ||||
\(181\) | 15.9695 | 1.18701 | 0.593503 | − | 0.804832i | \(-0.297744\pi\) | ||||
0.593503 | + | 0.804832i | \(0.297744\pi\) | |||||||
\(182\) | −9.76411 | − | 11.3163i | −0.723764 | − | 0.838818i | ||||
\(183\) | 4.87047 | − | 4.87047i | 0.360036 | − | 0.360036i | ||||
\(184\) | −11.7873 | − | 2.64199i | −0.868974 | − | 0.194770i | ||||
\(185\) | 11.2522 | − | 3.20537i | 0.827277 | − | 0.235663i | ||||
\(186\) | −12.5599 | − | 0.924791i | −0.920934 | − | 0.0678090i | ||||
\(187\) | −17.1122 | − | 17.1122i | −1.25137 | − | 1.25137i | ||||
\(188\) | −1.09608 | + | 0.813358i | −0.0799396 | + | 0.0593203i | ||||
\(189\) | 20.9147i | 1.52132i | ||||||||
\(190\) | 3.09669 | − | 0.640694i | 0.224658 | − | 0.0464808i | ||||
\(191\) | − | 5.91787i | − | 0.428202i | −0.976811 | − | 0.214101i | \(-0.931318\pi\) | ||
0.976811 | − | 0.214101i | \(-0.0686822\pi\) | |||||||
\(192\) | −4.38857 | − | 12.2344i | −0.316717 | − | 0.882943i | ||||
\(193\) | 1.66414 | + | 1.66414i | 0.119788 | + | 0.119788i | 0.764460 | − | 0.644672i | \(-0.223006\pi\) |
−0.644672 | + | 0.764460i | \(0.723006\pi\) | |||||||
\(194\) | −0.0306406 | + | 0.416139i | −0.00219987 | + | 0.0298771i | ||||
\(195\) | 8.75767 | + | 4.87436i | 0.627150 | + | 0.349060i | ||||
\(196\) | 15.1854 | + | 2.24841i | 1.08467 | + | 0.160601i | ||||
\(197\) | −7.74801 | + | 7.74801i | −0.552023 | + | 0.552023i | −0.927024 | − | 0.375001i | \(-0.877642\pi\) |
0.375001 | + | 0.927024i | \(0.377642\pi\) | |||||||
\(198\) | 1.58868 | − | 1.37077i | 0.112903 | − | 0.0974167i | ||||
\(199\) | 18.3552 | 1.30117 | 0.650583 | − | 0.759435i | \(-0.274525\pi\) | ||||
0.650583 | + | 0.759435i | \(0.274525\pi\) | |||||||
\(200\) | −6.16231 | + | 12.7289i | −0.435741 | + | 0.900072i | ||||
\(201\) | −14.9276 | −1.05291 | ||||||||
\(202\) | 20.1246 | − | 17.3643i | 1.41596 | − | 1.22175i | ||||
\(203\) | −6.36808 | + | 6.36808i | −0.446951 | + | 0.446951i | ||||
\(204\) | −18.8901 | − | 2.79695i | −1.32257 | − | 0.195826i | ||||
\(205\) | −19.2011 | − | 10.6870i | −1.34106 | − | 0.746411i | ||||
\(206\) | 0.107688 | − | 1.46255i | 0.00750300 | − | 0.101901i | ||||
\(207\) | −1.08810 | − | 1.08810i | −0.0756285 | − | 0.0756285i | ||||
\(208\) | 5.20721 | + | 9.72955i | 0.361055 | + | 0.674623i | ||||
\(209\) | − | 4.11798i | − | 0.284847i | ||||||
\(210\) | −19.2740 | + | 3.98771i | −1.33003 | + | 0.275178i | ||||
\(211\) | 10.7675i | 0.741266i | 0.928779 | + | 0.370633i | \(0.120859\pi\) | ||||
−0.928779 | + | 0.370633i | \(0.879141\pi\) | |||||||
\(212\) | −6.16533 | + | 4.57507i | −0.423437 | + | 0.314217i | ||||
\(213\) | −17.1823 | − | 17.1823i | −1.17731 | − | 1.17731i | ||||
\(214\) | −8.36818 | − | 0.616155i | −0.572037 | − | 0.0421195i | ||||
\(215\) | −27.2623 | + | 7.76612i | −1.85928 | + | 0.529645i | ||||
\(216\) | 3.37732 | − | 15.0680i | 0.229798 | − | 1.02525i | ||||
\(217\) | −14.8473 | + | 14.8473i | −1.00790 | + | 1.00790i | ||||
\(218\) | 2.61217 | + | 3.02742i | 0.176919 | + | 0.205043i | ||||
\(219\) | −16.7685 | −1.13311 | ||||||||
\(220\) | 14.6063 | + | 11.2166i | 0.984755 | + | 0.756224i | ||||
\(221\) | 16.2130 | 1.09061 | ||||||||
\(222\) | −7.85383 | − | 9.10233i | −0.527115 | − | 0.610908i | ||||
\(223\) | −2.60632 | + | 2.60632i | −0.174532 | + | 0.174532i | −0.788967 | − | 0.614435i | \(-0.789384\pi\) |
0.614435 | + | 0.788967i | \(0.289384\pi\) | |||||||
\(224\) | −20.2237 | − | 7.78569i | −1.35125 | − | 0.520203i | ||||
\(225\) | −1.53109 | + | 0.949351i | −0.102073 | + | 0.0632901i | ||||
\(226\) | −2.08315 | − | 0.153384i | −0.138569 | − | 0.0102029i | ||||
\(227\) | 7.03256 | + | 7.03256i | 0.466767 | + | 0.466767i | 0.900866 | − | 0.434098i | \(-0.142933\pi\) |
−0.434098 | + | 0.900866i | \(0.642933\pi\) | |||||||
\(228\) | −1.93638 | − | 2.60945i | −0.128240 | − | 0.172815i | ||||
\(229\) | 3.08487i | 0.203854i | 0.994792 | + | 0.101927i | \(0.0325008\pi\) | ||||
−0.994792 | + | 0.101927i | \(0.967499\pi\) | |||||||
\(230\) | 7.41699 | − | 11.2867i | 0.489062 | − | 0.744224i | ||||
\(231\) | 25.6305i | 1.68636i | ||||||||
\(232\) | 5.61622 | − | 3.55957i | 0.368723 | − | 0.233697i | ||||
\(233\) | 16.5824 | + | 16.5824i | 1.08635 | + | 1.08635i | 0.995901 | + | 0.0904463i | \(0.0288294\pi\) |
0.0904463 | + | 0.995901i | \(0.471171\pi\) | |||||||
\(234\) | −0.103228 | + | 1.40197i | −0.00674822 | + | 0.0916496i | ||||
\(235\) | −0.418073 | − | 1.46761i | −0.0272721 | − | 0.0957365i | ||||
\(236\) | 2.64321 | − | 17.8518i | 0.172058 | − | 1.16205i | ||||
\(237\) | −4.19132 | + | 4.19132i | −0.272255 | + | 0.272255i | ||||
\(238\) | −24.1054 | + | 20.7991i | −1.56252 | + | 1.34820i | ||||
\(239\) | 9.09479 | 0.588293 | 0.294146 | − | 0.955760i | \(-0.404965\pi\) | ||||
0.294146 | + | 0.955760i | \(0.404965\pi\) | |||||||
\(240\) | 14.5299 | + | 0.239425i | 0.937901 | + | 0.0154548i | ||||
\(241\) | 0.806689 | 0.0519634 | 0.0259817 | − | 0.999662i | \(-0.491729\pi\) | ||||
0.0259817 | + | 0.999662i | \(0.491729\pi\) | |||||||
\(242\) | 6.37919 | − | 5.50420i | 0.410070 | − | 0.353824i | ||||
\(243\) | 2.63276 | − | 2.63276i | 0.168892 | − | 0.168892i | ||||
\(244\) | −1.24188 | + | 8.38745i | −0.0795032 | + | 0.536952i | ||||
\(245\) | −8.34679 | + | 14.9965i | −0.533257 | + | 0.958092i | ||||
\(246\) | −1.65812 | + | 22.5195i | −0.105718 | + | 1.43579i | ||||
\(247\) | 1.95079 | + | 1.95079i | 0.124126 | + | 0.124126i | ||||
\(248\) | 13.0943 | − | 8.29923i | 0.831492 | − | 0.527002i | ||||
\(249\) | 19.1384i | 1.21285i | ||||||||
\(250\) | −10.8819 | − | 11.4710i | −0.688231 | − | 0.725491i | ||||
\(251\) | − | 2.39055i | − | 0.150890i | −0.997150 | − | 0.0754451i | \(-0.975962\pi\) | ||
0.997150 | − | 0.0754451i | \(-0.0240378\pi\) | |||||||
\(252\) | −1.64505 | − | 2.21687i | −0.103629 | − | 0.139649i | ||||
\(253\) | −12.4361 | − | 12.4361i | −0.781850 | − | 0.781850i | ||||
\(254\) | −4.59906 | − | 0.338631i | −0.288570 | − | 0.0212476i | ||||
\(255\) | 10.3831 | − | 18.6552i | 0.650218 | − | 1.16823i | ||||
\(256\) | 13.3130 | + | 8.87496i | 0.832061 | + | 0.554685i | ||||
\(257\) | 16.0798 | − | 16.0798i | 1.00303 | − | 1.00303i | 0.00303293 | − | 0.999995i | \(-0.499035\pi\) |
0.999995 | − | 0.00303293i | \(-0.000965412\pi\) | |||||||
\(258\) | 19.0286 | + | 22.0535i | 1.18467 | + | 1.37299i | ||||
\(259\) | −20.0443 | −1.24549 | ||||||||
\(260\) | −12.2330 | + | 1.60577i | −0.758656 | + | 0.0995856i | ||||
\(261\) | 0.847029 | 0.0524298 | ||||||||
\(262\) | 1.73587 | + | 2.01182i | 0.107243 | + | 0.124291i | ||||
\(263\) | −3.25350 | + | 3.25350i | −0.200619 | + | 0.200619i | −0.800265 | − | 0.599646i | \(-0.795308\pi\) |
0.599646 | + | 0.800265i | \(0.295308\pi\) | |||||||
\(264\) | 4.13884 | − | 18.4656i | 0.254728 | − | 1.13648i | ||||
\(265\) | −2.35162 | − | 8.25518i | −0.144459 | − | 0.507112i | ||||
\(266\) | −5.40302 | − | 0.397828i | −0.331281 | − | 0.0243924i | ||||
\(267\) | −11.2155 | − | 11.2155i | −0.686380 | − | 0.686380i | ||||
\(268\) | 14.7566 | − | 10.9503i | 0.901402 | − | 0.668897i | ||||
\(269\) | − | 19.3588i | − | 1.18033i | −0.807284 | − | 0.590163i | \(-0.799064\pi\) | ||
0.807284 | − | 0.590163i | \(-0.200936\pi\) | |||||||
\(270\) | 14.4281 | + | 9.48132i | 0.878065 | + | 0.577015i | ||||
\(271\) | − | 2.77454i | − | 0.168542i | −0.996443 | − | 0.0842708i | \(-0.973144\pi\) | ||
0.996443 | − | 0.0842708i | \(-0.0268561\pi\) | |||||||
\(272\) | 20.7254 | − | 11.0922i | 1.25666 | − | 0.672561i | ||||
\(273\) | −12.1418 | − | 12.1418i | −0.734857 | − | 0.734857i | ||||
\(274\) | −0.643915 | + | 8.74521i | −0.0389003 | + | 0.528317i | ||||
\(275\) | −17.4990 | + | 10.8503i | −1.05523 | + | 0.654295i | ||||
\(276\) | −13.7282 | − | 2.03265i | −0.826338 | − | 0.122351i | ||||
\(277\) | 3.48594 | − | 3.48594i | 0.209450 | − | 0.209450i | −0.594584 | − | 0.804034i | \(-0.702683\pi\) |
0.804034 | + | 0.594584i | \(0.202683\pi\) | |||||||
\(278\) | −6.10872 | + | 5.27083i | −0.366377 | + | 0.316124i | ||||
\(279\) | 1.97487 | 0.118232 | ||||||||
\(280\) | 16.1279 | − | 18.0806i | 0.963827 | − | 1.08052i | ||||
\(281\) | −27.6567 | −1.64986 | −0.824930 | − | 0.565235i | \(-0.808786\pi\) | ||||
−0.824930 | + | 0.565235i | \(0.808786\pi\) | |||||||
\(282\) | −1.18721 | + | 1.02437i | −0.0706972 | + | 0.0610002i | ||||
\(283\) | 6.97300 | − | 6.97300i | 0.414502 | − | 0.414502i | −0.468802 | − | 0.883304i | \(-0.655314\pi\) |
0.883304 | + | 0.468802i | \(0.155314\pi\) | |||||||
\(284\) | 29.5897 | + | 4.38117i | 1.75583 | + | 0.259975i | ||||
\(285\) | 3.49397 | − | 0.995314i | 0.206965 | − | 0.0589573i | ||||
\(286\) | −1.17981 | + | 16.0233i | −0.0697634 | + | 0.947478i | ||||
\(287\) | 26.6208 | + | 26.6208i | 1.57138 | + | 1.57138i | ||||
\(288\) | 0.827201 | + | 1.86279i | 0.0487433 | + | 0.109766i | ||||
\(289\) | − | 17.5362i | − | 1.03154i | ||||||
\(290\) | 1.50618 | + | 7.27990i | 0.0884461 | + | 0.427491i | ||||
\(291\) | 0.479374i | 0.0281014i | ||||||||
\(292\) | 16.5764 | − | 12.3007i | 0.970060 | − | 0.719846i | ||||
\(293\) | −4.11824 | − | 4.11824i | −0.240590 | − | 0.240590i | 0.576504 | − | 0.817094i | \(-0.304416\pi\) |
−0.817094 | + | 0.576504i | \(0.804416\pi\) | |||||||
\(294\) | 17.5883 | + | 1.29503i | 1.02577 | + | 0.0755279i | ||||
\(295\) | 17.6298 | + | 9.81242i | 1.02644 | + | 0.571301i | ||||
\(296\) | 14.4410 | + | 3.23677i | 0.839363 | + | 0.188133i | ||||
\(297\) | 15.8974 | − | 15.8974i | 0.922459 | − | 0.922459i | ||||
\(298\) | −3.61847 | − | 4.19368i | −0.209612 | − | 0.242933i | ||||
\(299\) | 11.7826 | 0.681405 | ||||||||
\(300\) | −5.98659 | + | 15.1040i | −0.345636 | + | 0.872029i | ||||
\(301\) | 48.5643 | 2.79920 | ||||||||
\(302\) | 3.91859 | + | 4.54152i | 0.225490 | + | 0.261335i | ||||
\(303\) | 21.5928 | − | 21.5928i | 1.24047 | − | 1.24047i | ||||
\(304\) | 3.82838 | + | 1.15910i | 0.219573 | + | 0.0664790i | ||||
\(305\) | −8.28313 | − | 4.61024i | −0.474291 | − | 0.263982i | ||||
\(306\) | 2.98641 | + | 0.219891i | 0.170722 | + | 0.0125704i | ||||
\(307\) | −23.2710 | − | 23.2710i | −1.32814 | − | 1.32814i | −0.906989 | − | 0.421155i | \(-0.861625\pi\) |
−0.421155 | − | 0.906989i | \(-0.638375\pi\) | |||||||
\(308\) | −18.8015 | − | 25.3368i | −1.07132 | − | 1.44370i | ||||
\(309\) | − | 1.68479i | − | 0.0958444i | ||||||
\(310\) | 3.51170 | + | 16.9733i | 0.199451 | + | 0.964017i | ||||
\(311\) | 31.9359i | 1.81092i | 0.424434 | + | 0.905459i | \(0.360473\pi\) | ||||
−0.424434 | + | 0.905459i | \(0.639527\pi\) | |||||||
\(312\) | 6.78694 | + | 10.7083i | 0.384235 | + | 0.606237i | ||||
\(313\) | 3.53818 | + | 3.53818i | 0.199990 | + | 0.199990i | 0.799996 | − | 0.600006i | \(-0.204835\pi\) |
−0.600006 | + | 0.799996i | \(0.704835\pi\) | |||||||
\(314\) | 0.270017 | − | 3.66718i | 0.0152379 | − | 0.206951i | ||||
\(315\) | 2.96831 | − | 0.845572i | 0.167245 | − | 0.0476426i | ||||
\(316\) | 1.06871 | − | 7.21788i | 0.0601195 | − | 0.406037i | ||||
\(317\) | −7.96927 | + | 7.96927i | −0.447599 | + | 0.447599i | −0.894556 | − | 0.446957i | \(-0.852508\pi\) |
0.446957 | + | 0.894556i | \(0.352508\pi\) | |||||||
\(318\) | −6.67793 | + | 5.76197i | −0.374480 | + | 0.323115i | ||||
\(319\) | 9.68081 | 0.542021 | ||||||||
\(320\) | −14.5391 | + | 10.4219i | −0.812758 | + | 0.582601i | ||||
\(321\) | −9.63978 | −0.538040 | ||||||||
\(322\) | −17.5183 | + | 15.1154i | −0.976255 | + | 0.842350i | ||||
\(323\) | 4.15549 | − | 4.15549i | 0.231218 | − | 0.231218i | ||||
\(324\) | 2.28174 | − | 15.4105i | 0.126764 | − | 0.856140i | ||||
\(325\) | 3.14970 | − | 13.4298i | 0.174714 | − | 0.744951i | ||||
\(326\) | −0.252747 | + | 3.43263i | −0.0139983 | + | 0.190116i | ||||
\(327\) | 3.24828 | + | 3.24828i | 0.179630 | + | 0.179630i | ||||
\(328\) | −14.8803 | − | 23.4778i | −0.821625 | − | 1.29634i | ||||
\(329\) | 2.61436i | 0.144134i | ||||||||
\(330\) | 17.6813 | + | 11.6192i | 0.973324 | + | 0.639614i | ||||
\(331\) | 0.243939i | 0.0134081i | 0.999978 | + | 0.00670406i | \(0.00213398\pi\) | ||||
−0.999978 | + | 0.00670406i | \(0.997866\pi\) | |||||||
\(332\) | −14.0392 | − | 18.9191i | −0.770500 | − | 1.03832i | ||||
\(333\) | 1.33306 | + | 1.33306i | 0.0730515 | + | 0.0730515i | ||||
\(334\) | −19.0087 | − | 1.39962i | −1.04011 | − | 0.0765840i | ||||
\(335\) | 5.62856 | + | 19.7586i | 0.307521 | + | 1.07953i | ||||
\(336\) | −23.8280 | − | 7.21430i | −1.29992 | − | 0.393572i | ||||
\(337\) | −21.6007 | + | 21.6007i | −1.17666 | + | 1.17666i | −0.196075 | + | 0.980589i | \(0.562820\pi\) |
−0.980589 | + | 0.196075i | \(0.937180\pi\) | |||||||
\(338\) | 4.97854 | + | 5.76996i | 0.270797 | + | 0.313845i | ||||
\(339\) | −2.39969 | −0.130334 | ||||||||
\(340\) | 3.42053 | + | 26.0581i | 0.185505 | + | 1.41320i | ||||
\(341\) | 22.5711 | 1.22229 | ||||||||
\(342\) | 0.332875 | + | 0.385791i | 0.0179998 | + | 0.0208612i | ||||
\(343\) | 1.82973 | − | 1.82973i | 0.0987963 | − | 0.0987963i | ||||
\(344\) | −34.9882 | − | 7.84220i | −1.88644 | − | 0.422823i | ||||
\(345\) | 7.54581 | − | 13.5574i | 0.406253 | − | 0.729906i | ||||
\(346\) | −2.76985 | − | 0.203946i | −0.148908 | − | 0.0109642i | ||||
\(347\) | −21.4891 | − | 21.4891i | −1.15360 | − | 1.15360i | −0.985826 | − | 0.167770i | \(-0.946343\pi\) |
−0.167770 | − | 0.985826i | \(-0.553657\pi\) | |||||||
\(348\) | 6.13446 | − | 4.55215i | 0.328841 | − | 0.244021i | ||||
\(349\) | 16.9878i | 0.909334i | 0.890661 | + | 0.454667i | \(0.150242\pi\) | ||||
−0.890661 | + | 0.454667i | \(0.849758\pi\) | |||||||
\(350\) | 12.5456 | + | 24.0079i | 0.670591 | + | 1.28328i | ||||
\(351\) | 15.0620i | 0.803949i | ||||||||
\(352\) | 9.45419 | + | 21.2901i | 0.503910 | + | 1.13476i | ||||
\(353\) | 21.9390 | + | 21.9390i | 1.16769 | + | 1.16769i | 0.982749 | + | 0.184946i | \(0.0592110\pi\) |
0.184946 | + | 0.982749i | \(0.440789\pi\) | |||||||
\(354\) | 1.52243 | − | 20.6766i | 0.0809163 | − | 1.09895i | ||||
\(355\) | −16.2643 | + | 29.2217i | −0.863218 | + | 1.55093i | ||||
\(356\) | 19.3143 | + | 2.85976i | 1.02366 | + | 0.151567i | ||||
\(357\) | −25.8640 | + | 25.8640i | −1.36887 | + | 1.36887i | ||||
\(358\) | 22.4594 | − | 19.3788i | 1.18702 | − | 1.02420i | ||||
\(359\) | −9.38281 | −0.495206 | −0.247603 | − | 0.968862i | \(-0.579643\pi\) | ||||
−0.247603 | + | 0.968862i | \(0.579643\pi\) | |||||||
\(360\) | −2.27507 | + | 0.129869i | −0.119907 | + | 0.00684467i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −17.0991 | + | 14.7538i | −0.898709 | + | 0.775440i | ||||
\(363\) | 6.84457 | − | 6.84457i | 0.359247 | − | 0.359247i | ||||
\(364\) | 20.9095 | + | 3.09594i | 1.09596 | + | 0.162272i | ||||
\(365\) | 6.32268 | + | 22.1953i | 0.330944 | + | 1.16175i | ||||
\(366\) | −0.715296 | + | 9.71465i | −0.0373891 | + | 0.507793i | ||||
\(367\) | −8.72035 | − | 8.72035i | −0.455199 | − | 0.455199i | 0.441877 | − | 0.897076i | \(-0.354313\pi\) |
−0.897076 | + | 0.441877i | \(0.854313\pi\) | |||||||
\(368\) | 15.0619 | − | 8.06108i | 0.785157 | − | 0.420213i | ||||
\(369\) | − | 3.54088i | − | 0.184331i | ||||||
\(370\) | −9.08674 | + | 13.8276i | −0.472397 | + | 0.718864i | ||||
\(371\) | 14.7055i | 0.763473i | ||||||||
\(372\) | 14.3026 | − | 10.6135i | 0.741557 | − | 0.550282i | ||||
\(373\) | 16.4931 | + | 16.4931i | 0.853979 | + | 0.853979i | 0.990621 | − | 0.136641i | \(-0.0436308\pi\) |
−0.136641 | + | 0.990621i | \(0.543631\pi\) | |||||||
\(374\) | 34.1321 | + | 2.51317i | 1.76493 | + | 0.129953i | ||||
\(375\) | −13.4356 | − | 12.2248i | −0.693811 | − | 0.631288i | ||||
\(376\) | 0.422169 | − | 1.88352i | 0.0217717 | − | 0.0971351i | ||||
\(377\) | −4.58605 | + | 4.58605i | −0.236194 | + | 0.236194i | ||||
\(378\) | −19.3224 | − | 22.3940i | −0.993839 | − | 1.15183i | ||||
\(379\) | −29.7168 | −1.52645 | −0.763224 | − | 0.646133i | \(-0.776385\pi\) | ||||
−0.763224 | + | 0.646133i | \(0.776385\pi\) | |||||||
\(380\) | −2.72381 | + | 3.54695i | −0.139729 | + | 0.181955i | ||||
\(381\) | −5.29791 | −0.271420 | ||||||||
\(382\) | 5.46734 | + | 6.33646i | 0.279733 | + | 0.324201i | ||||
\(383\) | −8.57457 | + | 8.57457i | −0.438140 | + | 0.438140i | −0.891386 | − | 0.453246i | \(-0.850266\pi\) |
0.453246 | + | 0.891386i | \(0.350266\pi\) | |||||||
\(384\) | 16.0020 | + | 9.04532i | 0.816597 | + | 0.461592i | ||||
\(385\) | 33.9252 | − | 9.66415i | 1.72899 | − | 0.492531i | ||||
\(386\) | −3.31930 | − | 0.244402i | −0.168948 | − | 0.0124398i | ||||
\(387\) | −3.22981 | − | 3.22981i | −0.164180 | − | 0.164180i | ||||
\(388\) | −0.351650 | − | 0.473881i | −0.0178523 | − | 0.0240577i | ||||
\(389\) | − | 9.66869i | − | 0.490222i | −0.969495 | − | 0.245111i | \(-0.921176\pi\) | ||
0.969495 | − | 0.245111i | \(-0.0788244\pi\) | |||||||
\(390\) | −13.8804 | + | 2.87180i | −0.702861 | + | 0.145419i | ||||
\(391\) | − | 25.0987i | − | 1.26930i | ||||||
\(392\) | −18.3367 | + | 11.6219i | −0.926144 | + | 0.586992i | ||||
\(393\) | 2.15859 | + | 2.15859i | 0.108886 | + | 0.108886i | ||||
\(394\) | 1.13790 | − | 15.4542i | 0.0573266 | − | 0.778570i | ||||
\(395\) | 7.12810 | + | 3.96737i | 0.358654 | + | 0.199620i | ||||
\(396\) | −0.434636 | + | 2.93546i | −0.0218413 | + | 0.147513i | ||||
\(397\) | 19.0447 | − | 19.0447i | 0.955827 | − | 0.955827i | −0.0432378 | − | 0.999065i | \(-0.513767\pi\) |
0.999065 | + | 0.0432378i | \(0.0137673\pi\) | |||||||
\(398\) | −19.6535 | + | 16.9578i | −0.985141 | + | 0.850017i | ||||
\(399\) | −6.22405 | −0.311592 | ||||||||
\(400\) | −5.16169 | − | 19.3224i | −0.258084 | − | 0.966122i | ||||
\(401\) | −0.178250 | −0.00890139 | −0.00445069 | − | 0.999990i | \(-0.501417\pi\) | ||||
−0.00445069 | + | 0.999990i | \(0.501417\pi\) | |||||||
\(402\) | 15.9835 | − | 13.7912i | 0.797184 | − | 0.687841i | ||||
\(403\) | −10.6925 | + | 10.6925i | −0.532631 | + | 0.532631i | ||||
\(404\) | −5.50576 | + | 37.1850i | −0.273922 | + | 1.85002i | ||||
\(405\) | 15.2188 | + | 8.47054i | 0.756230 | + | 0.420904i | ||||
\(406\) | 0.935239 | − | 12.7018i | 0.0464151 | − | 0.630378i | ||||
\(407\) | 15.2358 | + | 15.2358i | 0.755209 | + | 0.755209i | ||||
\(408\) | 22.8103 | − | 14.4572i | 1.12928 | − | 0.715739i | ||||
\(409\) | − | 2.01061i | − | 0.0994184i | −0.998764 | − | 0.0497092i | \(-0.984171\pi\) | ||
0.998764 | − | 0.0497092i | \(-0.0158295\pi\) | |||||||
\(410\) | 30.4326 | − | 6.29637i | 1.50296 | − | 0.310956i | ||||
\(411\) | 10.0741i | 0.496918i | ||||||||
\(412\) | 1.23590 | + | 1.66549i | 0.0608882 | + | 0.0820526i | ||||
\(413\) | −24.4423 | − | 24.4423i | −1.20273 | − | 1.20273i | ||||
\(414\) | 2.17033 | + | 0.159803i | 0.106666 | + | 0.00785389i | ||||
\(415\) | 25.3321 | − | 7.21625i | 1.24350 | − | 0.354232i | ||||
\(416\) | −14.5644 | − | 5.60696i | −0.714076 | − | 0.274904i | ||||
\(417\) | −6.55437 | + | 6.55437i | −0.320969 | + | 0.320969i | ||||
\(418\) | 3.80447 | + | 4.40926i | 0.186083 | + | 0.215664i | ||||
\(419\) | −13.6641 | −0.667536 | −0.333768 | − | 0.942655i | \(-0.608320\pi\) | ||||
−0.333768 | + | 0.942655i | \(0.608320\pi\) | |||||||
\(420\) | 16.9531 | − | 22.0764i | 0.827228 | − | 1.07722i | ||||
\(421\) | −13.8989 | −0.677390 | −0.338695 | − | 0.940896i | \(-0.609985\pi\) | ||||
−0.338695 | + | 0.940896i | \(0.609985\pi\) | |||||||
\(422\) | −9.94776 | − | 11.5291i | −0.484249 | − | 0.561229i | ||||
\(423\) | 0.173870 | − | 0.173870i | 0.00845386 | − | 0.00845386i | ||||
\(424\) | 2.37466 | − | 10.5946i | 0.115324 | − | 0.514520i | ||||
\(425\) | −28.6075 | − | 6.70935i | −1.38767 | − | 0.325451i | ||||
\(426\) | 34.2719 | + | 2.52346i | 1.66048 | + | 0.122262i | ||||
\(427\) | 11.4839 | + | 11.4839i | 0.555746 | + | 0.555746i | ||||
\(428\) | 9.52933 | − | 7.07136i | 0.460618 | − | 0.341807i | ||||
\(429\) | 18.4581i | 0.891167i | ||||||||
\(430\) | 22.0158 | − | 33.5022i | 1.06170 | − | 1.61562i | ||||
\(431\) | − | 20.3636i | − | 0.980879i | −0.871475 | − | 0.490440i | \(-0.836836\pi\) | ||
0.871475 | − | 0.490440i | \(-0.163164\pi\) | |||||||
\(432\) | 10.3047 | + | 19.2540i | 0.495784 | + | 0.926360i | ||||
\(433\) | 5.89872 | + | 5.89872i | 0.283475 | + | 0.283475i | 0.834493 | − | 0.551018i | \(-0.185761\pi\) |
−0.551018 | + | 0.834493i | \(0.685761\pi\) | |||||||
\(434\) | 2.18053 | − | 29.6145i | 0.104669 | − | 1.42154i | ||||
\(435\) | 2.33985 | + | 8.21384i | 0.112187 | + | 0.393824i | ||||
\(436\) | −5.59388 | − | 0.828252i | −0.267898 | − | 0.0396661i | ||||
\(437\) | 3.01995 | − | 3.01995i | 0.144464 | − | 0.144464i | ||||
\(438\) | 17.9546 | − | 15.4919i | 0.857903 | − | 0.740232i | ||||
\(439\) | −27.2435 | −1.30026 | −0.650131 | − | 0.759822i | \(-0.725286\pi\) | ||||
−0.650131 | + | 0.759822i | \(0.725286\pi\) | |||||||
\(440\) | −26.0021 | + | 1.48428i | −1.23960 | + | 0.0707605i | ||||
\(441\) | −2.76552 | −0.131691 | ||||||||
\(442\) | −17.3598 | + | 14.9787i | −0.825722 | + | 0.712464i | ||||
\(443\) | 20.1874 | − | 20.1874i | 0.959131 | − | 0.959131i | −0.0400656 | − | 0.999197i | \(-0.512757\pi\) |
0.999197 | + | 0.0400656i | \(0.0127567\pi\) | |||||||
\(444\) | 16.8187 | + | 2.49024i | 0.798180 | + | 0.118182i | ||||
\(445\) | −10.6163 | + | 19.0741i | −0.503261 | + | 0.904198i | ||||
\(446\) | 0.382774 | − | 5.19857i | 0.0181249 | − | 0.246159i | ||||
\(447\) | −4.49963 | − | 4.49963i | −0.212825 | − | 0.212825i | ||||
\(448\) | 28.8471 | − | 10.3477i | 1.36290 | − | 0.488881i | ||||
\(449\) | 4.84516i | 0.228657i | 0.993443 | + | 0.114329i | \(0.0364717\pi\) | ||||
−0.993443 | + | 0.114329i | \(0.963528\pi\) | |||||||
\(450\) | 0.762313 | − | 2.43103i | 0.0359358 | − | 0.114600i | ||||
\(451\) | − | 40.4692i | − | 1.90562i | ||||||
\(452\) | 2.37220 | − | 1.76032i | 0.111579 | − | 0.0827986i | ||||
\(453\) | 4.87284 | + | 4.87284i | 0.228946 | + | 0.228946i | ||||
\(454\) | −14.0271 | − | 1.03283i | −0.658326 | − | 0.0484730i | ||||
\(455\) | −11.4931 | + | 20.6494i | −0.538805 | + | 0.968060i | ||||
\(456\) | 4.48413 | + | 1.00506i | 0.209989 | + | 0.0470664i | ||||
\(457\) | −14.6913 | + | 14.6913i | −0.687230 | + | 0.687230i | −0.961619 | − | 0.274389i | \(-0.911524\pi\) |
0.274389 | + | 0.961619i | \(0.411524\pi\) | |||||||
\(458\) | −2.85002 | − | 3.30307i | −0.133172 | − | 0.154342i | ||||
\(459\) | 32.0843 | 1.49757 | ||||||||
\(460\) | 2.48583 | + | 18.9374i | 0.115902 | + | 0.882960i | ||||
\(461\) | 24.5016 | 1.14115 | 0.570577 | − | 0.821244i | \(-0.306720\pi\) | ||||
0.570577 | + | 0.821244i | \(0.306720\pi\) | |||||||
\(462\) | −23.6792 | − | 27.4434i | −1.10166 | − | 1.27678i | ||||
\(463\) | −25.8168 | + | 25.8168i | −1.19981 | + | 1.19981i | −0.225586 | + | 0.974223i | \(0.572430\pi\) |
−0.974223 | + | 0.225586i | \(0.927570\pi\) | |||||||
\(464\) | −2.72489 | + | 8.99999i | −0.126500 | + | 0.417814i | ||||
\(465\) | 5.45541 | + | 19.1508i | 0.252989 | + | 0.888096i | ||||
\(466\) | −33.0752 | − | 2.43535i | −1.53218 | − | 0.112815i | ||||
\(467\) | −6.04830 | − | 6.04830i | −0.279882 | − | 0.279882i | 0.553180 | − | 0.833062i | \(-0.313414\pi\) |
−0.833062 | + | 0.553180i | \(0.813414\pi\) | |||||||
\(468\) | −1.18471 | − | 1.59650i | −0.0547631 | − | 0.0737984i | ||||
\(469\) | − | 35.1974i | − | 1.62526i | ||||||
\(470\) | 1.80352 | + | 1.18517i | 0.0831904 | + | 0.0546680i | ||||
\(471\) | − | 4.22443i | − | 0.194651i | ||||||
\(472\) | 13.6626 | + | 21.5565i | 0.628870 | + | 0.992218i | ||||
\(473\) | −36.9139 | − | 36.9139i | −1.69730 | − | 1.69730i | ||||
\(474\) | 0.615552 | − | 8.36000i | 0.0282733 | − | 0.383988i | ||||
\(475\) | −2.63485 | − | 4.24942i | −0.120895 | − | 0.194977i | ||||
\(476\) | 6.59484 | − | 44.5404i | 0.302274 | − | 2.04151i | ||||
\(477\) | 0.978004 | − | 0.978004i | 0.0447797 | − | 0.0447797i | ||||
\(478\) | −9.73808 | + | 8.40239i | −0.445409 | + | 0.384316i | ||||
\(479\) | −22.0969 | −1.00963 | −0.504816 | − | 0.863227i | \(-0.668440\pi\) | ||||
−0.504816 | + | 0.863227i | \(0.668440\pi\) | |||||||
\(480\) | −15.7788 | + | 13.1674i | −0.720202 | + | 0.601005i | ||||
\(481\) | −14.4352 | −0.658186 | ||||||||
\(482\) | −0.863748 | + | 0.745275i | −0.0393427 | + | 0.0339463i | ||||
\(483\) | −18.7963 | + | 18.7963i | −0.855261 | + | 0.855261i | ||||
\(484\) | −1.74524 | + | 11.7871i | −0.0793290 | + | 0.535775i | ||||
\(485\) | 0.634512 | − | 0.180751i | 0.0288117 | − | 0.00820748i | ||||
\(486\) | −0.386657 | + | 5.25130i | −0.0175391 | + | 0.238204i | ||||
\(487\) | −21.8223 | − | 21.8223i | −0.988864 | − | 0.988864i | 0.0110744 | − | 0.999939i | \(-0.496475\pi\) |
−0.999939 | + | 0.0110744i | \(0.996475\pi\) | |||||||
\(488\) | −6.41918 | − | 10.1280i | −0.290583 | − | 0.458475i | ||||
\(489\) | 3.95424i | 0.178817i | ||||||||
\(490\) | −4.91762 | − | 23.7686i | −0.222156 | − | 1.07376i | ||||
\(491\) | 29.1044i | 1.31346i | 0.754124 | + | 0.656732i | \(0.228062\pi\) | ||||
−0.754124 | + | 0.656732i | \(0.771938\pi\) | |||||||
\(492\) | −19.0296 | − | 25.6442i | −0.857921 | − | 1.15613i | ||||
\(493\) | 9.76899 | + | 9.76899i | 0.439973 | + | 0.439973i | ||||
\(494\) | −3.89106 | − | 0.286501i | −0.175067 | − | 0.0128903i | ||||
\(495\) | −2.89895 | − | 1.61350i | −0.130298 | − | 0.0725216i | ||||
\(496\) | −6.35314 | + | 20.9837i | −0.285265 | + | 0.942196i | ||||
\(497\) | 40.5136 | − | 40.5136i | 1.81728 | − | 1.81728i | ||||
\(498\) | −17.6814 | − | 20.4921i | −0.792320 | − | 0.918272i | ||||
\(499\) | 25.5652 | 1.14446 | 0.572228 | − | 0.820094i | \(-0.306079\pi\) | ||||
0.572228 | + | 0.820094i | \(0.306079\pi\) | |||||||
\(500\) | 22.2493 | + | 2.22896i | 0.995019 | + | 0.0996820i | ||||
\(501\) | −21.8972 | −0.978294 | ||||||||
\(502\) | 2.20855 | + | 2.55964i | 0.0985726 | + | 0.114242i | ||||
\(503\) | −23.8295 | + | 23.8295i | −1.06250 | + | 1.06250i | −0.0645931 | + | 0.997912i | \(0.520575\pi\) |
−0.997912 | + | 0.0645931i | \(0.979425\pi\) | |||||||
\(504\) | 3.80950 | + | 0.853855i | 0.169689 | + | 0.0380337i | ||||
\(505\) | −36.7225 | − | 20.4391i | −1.63413 | − | 0.909527i | ||||
\(506\) | 24.8050 | + | 1.82641i | 1.10272 | + | 0.0811939i | ||||
\(507\) | 6.19090 | + | 6.19090i | 0.274948 | + | 0.274948i | ||||
\(508\) | 5.23721 | − | 3.88634i | 0.232363 | − | 0.172428i | ||||
\(509\) | − | 0.373579i | − | 0.0165586i | −0.999966 | − | 0.00827931i | \(-0.997365\pi\) | ||
0.999966 | − | 0.00827931i | \(-0.00263542\pi\) | |||||||
\(510\) | 6.11737 | + | 29.5674i | 0.270882 | + | 1.30926i | ||||
\(511\) | − | 39.5379i | − | 1.74905i | ||||||
\(512\) | −22.4539 | + | 2.79673i | −0.992332 | + | 0.123599i | ||||
\(513\) | 3.86047 | + | 3.86047i | 0.170444 | + | 0.170444i | ||||
\(514\) | −2.36153 | + | 32.0727i | −0.104163 | + | 1.41467i | ||||
\(515\) | −2.23003 | + | 0.635261i | −0.0982670 | + | 0.0279930i | ||||
\(516\) | −40.7491 | − | 6.03348i | −1.79388 | − | 0.265609i | ||||
\(517\) | 1.98719 | − | 1.98719i | 0.0873963 | − | 0.0873963i | ||||
\(518\) | 21.4621 | − | 18.5183i | 0.942989 | − | 0.813647i | ||||
\(519\) | −3.19075 | −0.140058 | ||||||||
\(520\) | 11.6147 | − | 13.0210i | 0.509339 | − | 0.571009i | ||||
\(521\) | −21.9839 | −0.963131 | −0.481566 | − | 0.876410i | \(-0.659932\pi\) | ||||
−0.481566 | + | 0.876410i | \(0.659932\pi\) | |||||||
\(522\) | −0.906942 | + | 0.782544i | −0.0396958 | + | 0.0342510i | ||||
\(523\) | 25.4734 | − | 25.4734i | 1.11388 | − | 1.11388i | 0.121255 | − | 0.992621i | \(-0.461308\pi\) |
0.992621 | − | 0.121255i | \(-0.0386918\pi\) | |||||||
\(524\) | −3.71731 | − | 0.550400i | −0.162392 | − | 0.0240443i | ||||
\(525\) | 16.3994 | + | 26.4486i | 0.715729 | + | 1.15431i | ||||
\(526\) | 0.477821 | − | 6.48943i | 0.0208340 | − | 0.282953i | ||||
\(527\) | 22.7767 | + | 22.7767i | 0.992167 | + | 0.992167i | ||||
\(528\) | 12.6282 | + | 23.5954i | 0.549570 | + | 1.02686i | ||||
\(529\) | 4.75983i | 0.206949i | ||||||||
\(530\) | 10.1447 | + | 6.66650i | 0.440656 | + | 0.289574i | ||||
\(531\) | 3.25112i | 0.141086i | ||||||||
\(532\) | 6.15273 | − | 4.56572i | 0.266755 | − | 0.197949i | ||||
\(533\) | 19.1713 | + | 19.1713i | 0.830402 | + | 0.830402i | ||||
\(534\) | 22.3705 | + | 1.64716i | 0.968067 | + | 0.0712794i | ||||
\(535\) | 3.63474 | + | 12.7595i | 0.157144 | + | 0.551640i | ||||
\(536\) | −5.68370 | + | 25.3580i | −0.245498 | + | 1.09530i | ||||
\(537\) | 24.0979 | − | 24.0979i | 1.03990 | − | 1.03990i | ||||
\(538\) | 17.8850 | + | 20.7281i | 0.771075 | + | 0.893650i | ||||
\(539\) | −31.6075 | −1.36143 | ||||||||
\(540\) | −24.2081 | + | 3.17769i | −1.04175 | + | 0.136746i | ||||
\(541\) | −11.3955 | −0.489932 | −0.244966 | − | 0.969532i | \(-0.578777\pi\) | ||||
−0.244966 | + | 0.969532i | \(0.578777\pi\) | |||||||
\(542\) | 2.56331 | + | 2.97079i | 0.110104 | + | 0.127606i | ||||
\(543\) | −18.3465 | + | 18.3465i | −0.787326 | + | 0.787326i | ||||
\(544\) | −11.9437 | + | 31.0243i | −0.512082 | + | 1.33016i | ||||
\(545\) | 3.07473 | − | 5.52430i | 0.131707 | − | 0.236635i | ||||
\(546\) | 24.2181 | + | 1.78320i | 1.03644 | + | 0.0763137i | ||||
\(547\) | −20.7225 | − | 20.7225i | −0.886032 | − | 0.886032i | 0.108107 | − | 0.994139i | \(-0.465521\pi\) |
−0.994139 | + | 0.108107i | \(0.965521\pi\) | |||||||
\(548\) | −7.38996 | − | 9.95867i | −0.315683 | − | 0.425413i | ||||
\(549\) | − | 1.52750i | − | 0.0651920i | ||||||
\(550\) | 8.71257 | − | 27.7845i | 0.371505 | − | 1.18474i | ||||
\(551\) | 2.35086i | 0.100150i | ||||||||
\(552\) | 16.5771 | − | 10.5066i | 0.705567 | − | 0.447190i | ||||
\(553\) | −9.88257 | − | 9.88257i | −0.420249 | − | 0.420249i | ||||
\(554\) | −0.511958 | + | 6.95306i | −0.0217510 | + | 0.295407i | ||||
\(555\) | −9.24456 | + | 16.6095i | −0.392410 | + | 0.705034i | ||||
\(556\) | 1.67124 | − | 11.2873i | 0.0708765 | − | 0.478688i | ||||
\(557\) | 12.2789 | − | 12.2789i | 0.520272 | − | 0.520272i | −0.397382 | − | 0.917653i | \(-0.630081\pi\) |
0.917653 | + | 0.397382i | \(0.130081\pi\) | |||||||
\(558\) | −2.11456 | + | 1.82452i | −0.0895163 | + | 0.0772381i | ||||
\(559\) | 34.9742 | 1.47925 | ||||||||
\(560\) | −0.564532 | + | 34.2596i | −0.0238558 | + | 1.44773i | ||||
\(561\) | 39.3187 | 1.66004 | ||||||||
\(562\) | 29.6129 | − | 25.5512i | 1.24915 | − | 1.07781i | ||||
\(563\) | 13.3587 | − | 13.3587i | 0.563001 | − | 0.563001i | −0.367158 | − | 0.930159i | \(-0.619669\pi\) |
0.930159 | + | 0.367158i | \(0.119669\pi\) | |||||||
\(564\) | 0.324800 | − | 2.19365i | 0.0136766 | − | 0.0923692i | ||||
\(565\) | 0.904821 | + | 3.17630i | 0.0380661 | + | 0.133628i | ||||
\(566\) | −1.02408 | + | 13.9084i | −0.0430453 | + | 0.584612i | ||||
\(567\) | −21.0998 | − | 21.0998i | −0.886106 | − | 0.886106i | ||||
\(568\) | −35.7303 | + | 22.6459i | −1.49921 | + | 0.950203i | ||||
\(569\) | − | 17.3531i | − | 0.727478i | −0.931501 | − | 0.363739i | \(-0.881500\pi\) | ||
0.931501 | − | 0.363739i | \(-0.118500\pi\) | |||||||
\(570\) | −2.82157 | + | 4.29368i | −0.118182 | + | 0.179843i | ||||
\(571\) | 19.3548i | 0.809972i | 0.914323 | + | 0.404986i | \(0.132724\pi\) | ||||
−0.914323 | + | 0.404986i | \(0.867276\pi\) | |||||||
\(572\) | −13.5402 | − | 18.2466i | −0.566143 | − | 0.762931i | ||||
\(573\) | 6.79873 | + | 6.79873i | 0.284021 | + | 0.284021i | ||||
\(574\) | −53.0979 | − | 3.90963i | −2.21626 | − | 0.163185i | ||||
\(575\) | −20.7901 | − | 4.87593i | −0.867008 | − | 0.203340i | ||||
\(576\) | −2.60668 | − | 1.23032i | −0.108612 | − | 0.0512635i | ||||
\(577\) | 3.22845 | − | 3.22845i | 0.134402 | − | 0.134402i | −0.636705 | − | 0.771107i | \(-0.719703\pi\) |
0.771107 | + | 0.636705i | \(0.219703\pi\) | |||||||
\(578\) | 16.2012 | + | 18.7766i | 0.673880 | + | 0.781004i | ||||
\(579\) | −3.82369 | −0.158907 | ||||||||
\(580\) | −8.33839 | − | 6.40331i | −0.346233 | − | 0.265883i | ||||
\(581\) | −45.1258 | −1.87213 | ||||||||
\(582\) | −0.442878 | − | 0.513281i | −0.0183579 | − | 0.0212762i | ||||
\(583\) | 11.1777 | − | 11.1777i | 0.462935 | − | 0.462935i | ||||
\(584\) | −6.38462 | + | 28.4852i | −0.264197 | + | 1.17873i | ||||
\(585\) | 2.13767 | − | 0.608949i | 0.0883817 | − | 0.0251770i | ||||
\(586\) | 8.21425 | + | 0.604820i | 0.339327 | + | 0.0249849i | ||||
\(587\) | −19.7717 | − | 19.7717i | −0.816064 | − | 0.816064i | 0.169471 | − | 0.985535i | \(-0.445794\pi\) |
−0.985535 | + | 0.169471i | \(0.945794\pi\) | |||||||
\(588\) | −20.0288 | + | 14.8626i | −0.825972 | + | 0.612923i | ||||
\(589\) | 5.48110i | 0.225845i | ||||||||
\(590\) | −27.9421 | + | 5.78112i | −1.15036 | + | 0.238005i | ||||
\(591\) | − | 17.8025i | − | 0.732298i | ||||||
\(592\) | −18.4527 | + | 9.87583i | −0.758403 | + | 0.405894i | ||||
\(593\) | 0.671001 | + | 0.671001i | 0.0275547 | + | 0.0275547i | 0.720750 | − | 0.693195i | \(-0.243798\pi\) |
−0.693195 | + | 0.720750i | \(0.743798\pi\) | |||||||
\(594\) | −2.33475 | + | 31.7089i | −0.0957958 | + | 1.30103i | ||||
\(595\) | 43.9864 | + | 24.4821i | 1.80327 | + | 1.00367i | ||||
\(596\) | 7.74882 | + | 1.14732i | 0.317404 | + | 0.0469961i | ||||
\(597\) | −21.0873 | + | 21.0873i | −0.863046 | + | 0.863046i | ||||
\(598\) | −12.6160 | + | 10.8856i | −0.515907 | + | 0.445144i | ||||
\(599\) | 6.84669 | 0.279748 | 0.139874 | − | 0.990169i | \(-0.455330\pi\) | ||||
0.139874 | + | 0.990169i | \(0.455330\pi\) | |||||||
\(600\) | −7.54405 | − | 21.7031i | −0.307985 | − | 0.886027i | ||||
\(601\) | −28.9163 | −1.17952 | −0.589761 | − | 0.807578i | \(-0.700778\pi\) | ||||
−0.589761 | + | 0.807578i | \(0.700778\pi\) | |||||||
\(602\) | −51.9993 | + | 44.8670i | −2.11933 | + | 1.82864i | ||||
\(603\) | −2.34083 | + | 2.34083i | −0.0953261 | + | 0.0953261i | ||||
\(604\) | −8.39153 | − | 1.24248i | −0.341446 | − | 0.0505559i | ||||
\(605\) | −11.6404 | − | 6.47887i | −0.473251 | − | 0.263403i | ||||
\(606\) | −3.17120 | + | 43.0690i | −0.128821 | + | 1.74956i | ||||
\(607\) | 5.48920 | + | 5.48920i | 0.222800 | + | 0.222800i | 0.809676 | − | 0.586877i | \(-0.199643\pi\) |
−0.586877 | + | 0.809676i | \(0.699643\pi\) | |||||||
\(608\) | −5.17002 | + | 2.29583i | −0.209672 | + | 0.0931083i | ||||
\(609\) | − | 14.6319i | − | 0.592914i | ||||||
\(610\) | 13.1283 | − | 2.71619i | 0.531548 | − | 0.109975i | ||||
\(611\) | 1.88276i | 0.0761684i | ||||||||
\(612\) | −3.40080 | + | 2.52361i | −0.137469 | + | 0.102011i | ||||
\(613\) | 8.13079 | + | 8.13079i | 0.328399 | + | 0.328399i | 0.851978 | − | 0.523578i | \(-0.175403\pi\) |
−0.523578 | + | 0.851978i | \(0.675403\pi\) | |||||||
\(614\) | 46.4163 | + | 3.41766i | 1.87321 | + | 0.137925i | ||||
\(615\) | 34.3368 | − | 9.78138i | 1.38459 | − | 0.394423i | ||||
\(616\) | 43.5393 | + | 9.75883i | 1.75425 | + | 0.393194i | ||||
\(617\) | −10.8891 | + | 10.8891i | −0.438379 | + | 0.438379i | −0.891466 | − | 0.453087i | \(-0.850323\pi\) |
0.453087 | + | 0.891466i | \(0.350323\pi\) | |||||||
\(618\) | 1.55652 | + | 1.80396i | 0.0626126 | + | 0.0725659i | ||||
\(619\) | −1.24466 | −0.0500273 | −0.0250136 | − | 0.999687i | \(-0.507963\pi\) | ||||
−0.0250136 | + | 0.999687i | \(0.507963\pi\) | |||||||
\(620\) | −19.4412 | − | 14.9295i | −0.780776 | − | 0.599582i | ||||
\(621\) | 23.3169 | 0.935673 | ||||||||
\(622\) | −29.5046 | − | 34.1948i | −1.18302 | − | 1.37109i | ||||
\(623\) | 26.4448 | − | 26.4448i | 1.05949 | − | 1.05949i | ||||
\(624\) | −17.1600 | − | 5.19547i | −0.686951 | − | 0.207985i | ||||
\(625\) | −11.1152 | + | 22.3932i | −0.444606 | + | 0.895726i | ||||
\(626\) | −7.05725 | − | 0.519630i | −0.282064 | − | 0.0207686i | ||||
\(627\) | 4.73093 | + | 4.73093i | 0.188935 | + | 0.188935i | ||||
\(628\) | 3.09888 | + | 4.17603i | 0.123659 | + | 0.166642i | ||||
\(629\) | 30.7491i | 1.22605i | ||||||||
\(630\) | −2.39707 | + | 3.64771i | −0.0955015 | + | 0.145328i | ||||
\(631\) | 5.70526i | 0.227123i | 0.993531 | + | 0.113561i | \(0.0362259\pi\) | ||||
−0.993531 | + | 0.113561i | \(0.963774\pi\) | |||||||
\(632\) | 5.52407 | + | 8.71576i | 0.219736 | + | 0.346694i | ||||
\(633\) | −12.3702 | − | 12.3702i | −0.491672 | − | 0.491672i | ||||
\(634\) | 1.17040 | − | 15.8955i | 0.0464824 | − | 0.631291i | ||||
\(635\) | 1.99761 | + | 7.01245i | 0.0792728 | + | 0.278281i | ||||
\(636\) | 1.82697 | − | 12.3391i | 0.0724441 | − | 0.489276i | ||||
\(637\) | 14.9733 | − | 14.9733i | 0.593262 | − | 0.593262i | ||||
\(638\) | −10.3656 | + | 8.94379i | −0.410376 | + | 0.354088i | ||||
\(639\) | −5.38879 | −0.213177 | ||||||||
\(640\) | 5.93898 | − | 24.5912i | 0.234759 | − | 0.972054i | ||||
\(641\) | −0.458904 | −0.0181256 | −0.00906280 | − | 0.999959i | \(-0.502885\pi\) | ||||
−0.00906280 | + | 0.999959i | \(0.502885\pi\) | |||||||
\(642\) | 10.3216 | − | 8.90589i | 0.407362 | − | 0.351487i | ||||
\(643\) | 2.89559 | − | 2.89559i | 0.114191 | − | 0.114191i | −0.647702 | − | 0.761893i | \(-0.724270\pi\) |
0.761893 | + | 0.647702i | \(0.224270\pi\) | |||||||
\(644\) | 4.79271 | − | 32.3692i | 0.188859 | − | 1.27552i | ||||
\(645\) | 22.3981 | − | 40.2423i | 0.881926 | − | 1.58454i | ||||
\(646\) | −0.610291 | + | 8.28855i | −0.0240116 | + | 0.326109i | ||||
\(647\) | 26.0239 | + | 26.0239i | 1.02311 | + | 1.02311i | 0.999727 | + | 0.0233789i | \(0.00744243\pi\) |
0.0233789 | + | 0.999727i | \(0.492558\pi\) | |||||||
\(648\) | 11.7942 | + | 18.6086i | 0.463318 | + | 0.731014i | ||||
\(649\) | 37.1575i | 1.45856i | ||||||||
\(650\) | 9.03488 | + | 17.2896i | 0.354377 | + | 0.678155i | ||||
\(651\) | − | 34.1146i | − | 1.33706i | ||||||
\(652\) | −2.90067 | − | 3.90893i | −0.113599 | − | 0.153086i | ||||
\(653\) | −19.7494 | − | 19.7494i | −0.772852 | − | 0.772852i | 0.205752 | − | 0.978604i | \(-0.434036\pi\) |
−0.978604 | + | 0.205752i | \(0.934036\pi\) | |||||||
\(654\) | −6.47903 | − | 0.477055i | −0.253350 | − | 0.0186543i | ||||
\(655\) | 2.04326 | − | 3.67108i | 0.0798366 | − | 0.143441i | ||||
\(656\) | 37.6231 | + | 11.3910i | 1.46894 | + | 0.444744i | ||||
\(657\) | −2.62951 | + | 2.62951i | −0.102587 | + | 0.102587i | ||||
\(658\) | −2.41532 | − | 2.79928i | −0.0941591 | − | 0.109127i | ||||
\(659\) | −7.33213 | −0.285619 | −0.142810 | − | 0.989750i | \(-0.545614\pi\) | ||||
−0.142810 | + | 0.989750i | \(0.545614\pi\) | |||||||
\(660\) | −29.6665 | + | 3.89420i | −1.15477 | + | 0.151581i | ||||
\(661\) | −32.0891 | −1.24812 | −0.624061 | − | 0.781376i | \(-0.714518\pi\) | ||||
−0.624061 | + | 0.781376i | \(0.714518\pi\) | |||||||
\(662\) | −0.225368 | − | 0.261194i | −0.00875917 | − | 0.0101516i | ||||
\(663\) | −18.6263 | + | 18.6263i | −0.723384 | + | 0.723384i | ||||
\(664\) | 32.5110 | + | 7.28695i | 1.26167 | + | 0.282788i | ||||
\(665\) | 2.34682 | + | 8.23831i | 0.0910057 | + | 0.319468i | ||||
\(666\) | −2.65893 | − | 0.195779i | −0.103031 | − | 0.00758627i | ||||
\(667\) | 7.09948 | + | 7.09948i | 0.274893 | + | 0.274893i | ||||
\(668\) | 21.6463 | − | 16.0629i | 0.837520 | − | 0.621493i | ||||
\(669\) | − | 5.98852i | − | 0.231530i | ||||||
\(670\) | −24.2810 | − | 15.9561i | −0.938058 | − | 0.616439i | ||||
\(671\) | − | 17.4580i | − | 0.673957i | ||||||
\(672\) | 32.1785 | − | 14.2894i | 1.24131 | − | 0.551224i | ||||
\(673\) | 24.8279 | + | 24.8279i | 0.957047 | + | 0.957047i | 0.999115 | − | 0.0420678i | \(-0.0133945\pi\) |
−0.0420678 | + | 0.999115i | \(0.513395\pi\) | |||||||
\(674\) | 3.17236 | − | 43.0847i | 0.122195 | − | 1.65956i | ||||
\(675\) | 6.23302 | − | 26.5765i | 0.239909 | − | 1.02293i | ||||
\(676\) | −10.6614 | − | 1.57857i | −0.410053 | − | 0.0607140i | ||||
\(677\) | −28.6500 | + | 28.6500i | −1.10111 | + | 1.10111i | −0.106832 | + | 0.994277i | \(0.534071\pi\) |
−0.994277 | + | 0.106832i | \(0.965929\pi\) | |||||||
\(678\) | 2.56943 | − | 2.21700i | 0.0986784 | − | 0.0851434i | ||||
\(679\) | −1.13030 | −0.0433769 | ||||||||
\(680\) | −27.7367 | − | 24.7411i | −1.06366 | − | 0.948779i | ||||
\(681\) | −16.1587 | −0.619201 | ||||||||
\(682\) | −24.1676 | + | 20.8527i | −0.925423 | + | 0.798490i | ||||
\(683\) | 10.3844 | − | 10.3844i | 0.397349 | − | 0.397349i | −0.479948 | − | 0.877297i | \(-0.659345\pi\) |
0.877297 | + | 0.479948i | \(0.159345\pi\) | |||||||
\(684\) | −0.712840 | − | 0.105546i | −0.0272561 | − | 0.00403565i | ||||
\(685\) | 13.3343 | − | 3.79850i | 0.509479 | − | 0.145133i | ||||
\(686\) | −0.268721 | + | 3.64959i | −0.0102598 | + | 0.139342i | ||||
\(687\) | −3.54404 | − | 3.54404i | −0.135214 | − | 0.135214i | ||||
\(688\) | 44.7082 | − | 23.9276i | 1.70448 | − | 0.912232i | ||||
\(689\) | 10.5904i | 0.403461i | ||||||||
\(690\) | 4.44571 | + | 21.4877i | 0.169245 | + | 0.818022i | ||||
\(691\) | − | 4.95589i | − | 0.188531i | −0.995547 | − | 0.0942654i | \(-0.969950\pi\) | ||
0.995547 | − | 0.0942654i | \(-0.0300502\pi\) | |||||||
\(692\) | 3.15419 | − | 2.34061i | 0.119904 | − | 0.0889766i | ||||
\(693\) | 4.01917 | + | 4.01917i | 0.152676 | + | 0.152676i | ||||
\(694\) | 42.8622 | + | 3.15597i | 1.62703 | + | 0.119799i | ||||
\(695\) | 11.1469 | + | 6.20417i | 0.422826 | + | 0.235338i | ||||
\(696\) | −2.36277 | + | 10.5416i | −0.0895605 | + | 0.399577i | ||||
\(697\) | 40.8378 | − | 40.8378i | 1.54684 | − | 1.54684i | ||||
\(698\) | −15.6945 | − | 18.1893i | −0.594044 | − | 0.688477i | ||||
\(699\) | −38.1012 | −1.44112 | ||||||||
\(700\) | −35.6132 | − | 14.1156i | −1.34605 | − | 0.533519i | ||||
\(701\) | 50.5194 | 1.90809 | 0.954045 | − | 0.299662i | \(-0.0968739\pi\) | ||||
0.954045 | + | 0.299662i | \(0.0968739\pi\) | |||||||
\(702\) | −13.9153 | − | 16.1273i | −0.525199 | − | 0.608688i | ||||
\(703\) | −3.69981 | + | 3.69981i | −0.139541 | + | 0.139541i | ||||
\(704\) | −29.7921 | − | 14.0615i | −1.12283 | − | 0.529964i | ||||
\(705\) | 2.16636 | + | 1.20576i | 0.0815899 | + | 0.0454115i | ||||
\(706\) | −43.7595 | − | 3.22204i | −1.64691 | − | 0.121263i | ||||
\(707\) | 50.9129 | + | 50.9129i | 1.91478 | + | 1.91478i | ||||
\(708\) | 17.4723 | + | 23.5456i | 0.656651 | + | 0.884899i | ||||
\(709\) | 28.2010i | 1.05911i | 0.848276 | + | 0.529555i | \(0.177641\pi\) | ||||
−0.848276 | + | 0.529555i | \(0.822359\pi\) | |||||||
\(710\) | −9.58231 | − | 46.3146i | −0.359618 | − | 1.73816i | ||||
\(711\) | 1.31450i | 0.0492975i | ||||||||
\(712\) | −23.3225 | + | 14.7819i | −0.874048 | + | 0.553974i | ||||
\(713\) | 16.5526 | + | 16.5526i | 0.619901 | + | 0.619901i | ||||
\(714\) | 3.79848 | − | 51.5883i | 0.142155 | − | 1.93064i | ||||
\(715\) | 24.4317 | − | 6.95976i | 0.913693 | − | 0.260280i | ||||
\(716\) | −6.14452 | + | 41.4991i | −0.229632 | + | 1.55089i | ||||
\(717\) | −10.4485 | + | 10.4485i | −0.390207 | + | 0.390207i | ||||
\(718\) | 10.0465 | − | 8.66848i | 0.374931 | − | 0.323505i | ||||
\(719\) | 7.39857 | 0.275920 | 0.137960 | − | 0.990438i | \(-0.455945\pi\) | ||||
0.137960 | + | 0.990438i | \(0.455945\pi\) | |||||||
\(720\) | 2.31601 | − | 2.24092i | 0.0863126 | − | 0.0835142i | ||||
\(721\) | 3.97251 | 0.147944 | ||||||||
\(722\) | −1.07073 | + | 0.923868i | −0.0398485 | + | 0.0343828i | ||||
\(723\) | −0.926762 | + | 0.926762i | −0.0344666 | + | 0.0344666i | ||||
\(724\) | 4.67803 | − | 31.5946i | 0.173858 | − | 1.17421i | ||||
\(725\) | 9.98980 | − | 6.19417i | 0.371012 | − | 0.230046i | ||||
\(726\) | −1.00522 | + | 13.6522i | −0.0373072 | + | 0.506680i | ||||
\(727\) | −4.97602 | − | 4.97602i | −0.184550 | − | 0.184550i | 0.608785 | − | 0.793335i | \(-0.291657\pi\) |
−0.793335 | + | 0.608785i | \(0.791657\pi\) | |||||||
\(728\) | −25.2487 | + | 16.0027i | −0.935779 | + | 0.593099i | ||||
\(729\) | 29.4171i | 1.08952i | ||||||||
\(730\) | −27.2754 | − | 17.9238i | −1.00951 | − | 0.663391i | ||||
\(731\) | − | 74.5004i | − | 2.75550i | ||||||
\(732\) | −8.20916 | − | 11.0626i | −0.303419 | − | 0.408886i | ||||
\(733\) | −34.5680 | − | 34.5680i | −1.27680 | − | 1.27680i | −0.942450 | − | 0.334348i | \(-0.891484\pi\) |
−0.334348 | − | 0.942450i | \(-0.608516\pi\) | |||||||
\(734\) | 17.3936 | + | 1.28070i | 0.642010 | + | 0.0472716i | ||||
\(735\) | −7.63950 | − | 26.8179i | −0.281787 | − | 0.989192i | ||||
\(736\) | −8.67991 | + | 22.5465i | −0.319946 | + | 0.831075i | ||||
\(737\) | −26.7537 | + | 26.7537i | −0.985484 | + | 0.985484i | ||||
\(738\) | 3.27131 | + | 3.79134i | 0.120419 | + | 0.139561i | ||||
\(739\) | 32.5879 | 1.19877 | 0.599383 | − | 0.800462i | \(-0.295413\pi\) | ||||
0.599383 | + | 0.800462i | \(0.295413\pi\) | |||||||
\(740\) | −3.04545 | − | 23.2006i | −0.111953 | − | 0.852873i | ||||
\(741\) | −4.48233 | −0.164662 | ||||||||
\(742\) | −13.5860 | − | 15.7457i | −0.498756 | − | 0.578042i | ||||
\(743\) | −2.79042 | + | 2.79042i | −0.102371 | + | 0.102371i | −0.756437 | − | 0.654066i | \(-0.773062\pi\) |
0.654066 | + | 0.756437i | \(0.273062\pi\) | |||||||
\(744\) | −5.50885 | + | 24.5779i | −0.201964 | + | 0.901071i | ||||
\(745\) | −4.25921 | + | 7.65244i | −0.156045 | + | 0.280364i | ||||
\(746\) | −32.8971 | − | 2.42224i | −1.20445 | − | 0.0886843i | ||||
\(747\) | 3.00113 | + | 3.00113i | 0.109806 | + | 0.109806i | ||||
\(748\) | −38.8682 | + | 28.8426i | −1.42116 | + | 1.05459i | ||||
\(749\) | − | 22.7293i | − | 0.830511i | ||||||
\(750\) | 25.6801 | + | 0.676820i | 0.937703 | + | 0.0247140i | ||||
\(751\) | 10.9120i | 0.398186i | 0.979981 | + | 0.199093i | \(0.0637996\pi\) | ||||
−0.979981 | + | 0.199093i | \(0.936200\pi\) | |||||||
\(752\) | 1.28809 | + | 2.40677i | 0.0469720 | + | 0.0877660i | ||||
\(753\) | 2.74637 | + | 2.74637i | 0.100083 | + | 0.100083i | ||||
\(754\) | 0.673524 | − | 9.14734i | 0.0245283 | − | 0.333126i | ||||
\(755\) | 4.61248 | − | 8.28715i | 0.167865 | − | 0.301600i | ||||
\(756\) | 41.3783 | + | 6.12664i | 1.50491 | + | 0.222824i | ||||
\(757\) | 27.9482 | − | 27.9482i | 1.01579 | − | 1.01579i | 0.0159213 | − | 0.999873i | \(-0.494932\pi\) |
0.999873 | − | 0.0159213i | \(-0.00506814\pi\) | |||||||
\(758\) | 31.8187 | − | 27.4544i | 1.15571 | − | 0.997189i | ||||
\(759\) | 28.5743 | 1.03718 | ||||||||
\(760\) | −0.360440 | − | 6.31428i | −0.0130745 | − | 0.229043i | ||||
\(761\) | 32.7705 | 1.18793 | 0.593964 | − | 0.804491i | \(-0.297562\pi\) | ||||
0.593964 | + | 0.804491i | \(0.297562\pi\) | |||||||
\(762\) | 5.67264 | − | 4.89457i | 0.205498 | − | 0.177312i | ||||
\(763\) | −7.65902 | + | 7.65902i | −0.277275 | + | 0.277275i | ||||
\(764\) | −11.7081 | − | 1.73355i | −0.423584 | − | 0.0627176i | ||||
\(765\) | −1.29716 | − | 4.55356i | −0.0468988 | − | 0.164634i | ||||
\(766\) | 1.25929 | − | 17.1028i | 0.0455001 | − | 0.617951i | ||||
\(767\) | −17.6024 | − | 17.6024i | −0.635587 | − | 0.635587i | ||||
\(768\) | −25.4905 | + | 5.09859i | −0.919810 | + | 0.183980i | ||||
\(769\) | − | 48.5580i | − | 1.75104i | −0.483178 | − | 0.875522i | \(-0.660518\pi\) | ||
0.483178 | − | 0.875522i | \(-0.339482\pi\) | |||||||
\(770\) | −27.3964 | + | 41.6902i | −0.987299 | + | 1.50241i | ||||
\(771\) | 36.9464i | 1.33059i | ||||||||
\(772\) | 3.77988 | − | 2.80491i | 0.136041 | − | 0.100951i | ||||
\(773\) | 12.6933 | + | 12.6933i | 0.456545 | + | 0.456545i | 0.897519 | − | 0.440975i | \(-0.145367\pi\) |
−0.440975 | + | 0.897519i | \(0.645367\pi\) | |||||||
\(774\) | 6.44218 | + | 0.474342i | 0.231559 | + | 0.0170499i | ||||
\(775\) | 23.2915 | − | 14.4419i | 0.836655 | − | 0.518767i | ||||
\(776\) | 0.814327 | + | 0.182522i | 0.0292326 | + | 0.00655215i | ||||
\(777\) | 23.0278 | − | 23.0278i | 0.826118 | − | 0.826118i | ||||
\(778\) | 8.93260 | + | 10.3526i | 0.320249 | + | 0.371158i | ||||
\(779\) | 9.82744 | 0.352104 | ||||||||
\(780\) | 12.2090 | − | 15.8986i | 0.437153 | − | 0.569260i | ||||
\(781\) | −61.5892 | −2.20383 | ||||||||
\(782\) | 23.1879 | + | 26.8740i | 0.829199 | + | 0.961013i | ||||
\(783\) | −9.07544 | + | 9.07544i | −0.324330 | + | 0.324330i | ||||
\(784\) | 8.89665 | − | 29.3846i | 0.317737 | − | 1.04945i | ||||
\(785\) | −5.59157 | + | 1.59285i | −0.199572 | + | 0.0568512i | ||||
\(786\) | −4.30552 | − | 0.317018i | −0.153573 | − | 0.0113077i | ||||
\(787\) | −5.38808 | − | 5.38808i | −0.192064 | − | 0.192064i | 0.604523 | − | 0.796587i | \(-0.293364\pi\) |
−0.796587 | + | 0.604523i | \(0.793364\pi\) | |||||||
\(788\) | 13.0592 | + | 17.5986i | 0.465216 | + | 0.626923i | ||||
\(789\) | − | 7.47554i | − | 0.266136i | ||||||
\(790\) | −11.2976 | + | 2.33743i | −0.401951 | + | 0.0831621i | ||||
\(791\) | − | 5.65816i | − | 0.201181i | ||||||
\(792\) | −2.24660 | − | 3.54464i | −0.0798295 | − | 0.125953i | ||||
\(793\) | 8.27029 | + | 8.27029i | 0.293687 | + | 0.293687i | ||||
\(794\) | −2.79698 | + | 37.9866i | −0.0992610 | + | 1.34809i | ||||
\(795\) | 12.1856 | + | 6.78228i | 0.432178 | + | 0.240543i | ||||
\(796\) | 5.37687 | − | 36.3145i | 0.190578 | − | 1.28713i | ||||
\(797\) | −3.86906 | + | 3.86906i | −0.137049 | + | 0.137049i | −0.772303 | − | 0.635254i | \(-0.780895\pi\) |
0.635254 | + | 0.772303i | \(0.280895\pi\) | |||||||
\(798\) | 6.66429 | − | 5.75020i | 0.235913 | − | 0.203555i | ||||
\(799\) | 4.01057 | 0.141884 | ||||||||
\(800\) | 23.3782 | + | 15.9204i | 0.826544 | + | 0.562873i | ||||
\(801\) | −3.51746 | −0.124284 | ||||||||
\(802\) | 0.190858 | − | 0.164680i | 0.00673944 | − | 0.00581504i | ||||
\(803\) | −30.0530 | + | 30.0530i | −1.06055 | + | 1.06055i | ||||
\(804\) | −4.37282 | + | 29.5333i | −0.154217 | + | 1.04156i | ||||
\(805\) | 31.9665 | + | 17.7920i | 1.12667 | + | 0.627086i | ||||
\(806\) | 1.57034 | − | 21.3272i | 0.0553128 | − | 0.751220i | ||||
\(807\) | 22.2402 | + | 22.2402i | 0.782894 | + | 0.782894i | ||||
\(808\) | −28.4589 | − | 44.9018i | −1.00118 | − | 1.57964i | ||||
\(809\) | 22.3427i | 0.785529i | 0.919639 | + | 0.392764i | \(0.128481\pi\) | ||||
−0.919639 | + | 0.392764i | \(0.871519\pi\) | |||||||
\(810\) | −24.1210 | + | 4.99053i | −0.847524 | + | 0.175349i | ||||
\(811\) | − | 2.96304i | − | 0.104046i | −0.998646 | − | 0.0520232i | \(-0.983433\pi\) | ||
0.998646 | − | 0.0520232i | \(-0.0165670\pi\) | |||||||
\(812\) | 10.7334 | + | 14.4642i | 0.376667 | + | 0.507595i | ||||
\(813\) | 3.18752 | + | 3.18752i | 0.111791 | + | 0.111791i | ||||
\(814\) | −30.3893 | − | 2.23758i | −1.06514 | − | 0.0784272i | ||||
\(815\) | 5.23393 | − | 1.49097i | 0.183337 | − | 0.0522264i | ||||
\(816\) | −11.0671 | + | 36.5535i | −0.387428 | + | 1.27963i | ||||
\(817\) | 8.96408 | − | 8.96408i | 0.313614 | − | 0.313614i | ||||
\(818\) | 1.85754 | + | 2.15283i | 0.0649474 | + | 0.0752719i | ||||
\(819\) | −3.80797 | −0.133061 | ||||||||
\(820\) | −26.7681 | + | 34.8574i | −0.934782 | + | 1.21727i | ||||
\(821\) | 37.0186 | 1.29196 | 0.645979 | − | 0.763355i | \(-0.276449\pi\) | ||||
0.645979 | + | 0.763355i | \(0.276449\pi\) | |||||||
\(822\) | −9.30714 | − | 10.7867i | −0.324624 | − | 0.376228i | ||||
\(823\) | −26.4232 | + | 26.4232i | −0.921055 | + | 0.921055i | −0.997104 | − | 0.0760490i | \(-0.975769\pi\) |
0.0760490 | + | 0.997104i | \(0.475769\pi\) | |||||||
\(824\) | −2.86200 | − | 0.641485i | −0.0997026 | − | 0.0223472i | ||||
\(825\) | 7.63843 | − | 32.5690i | 0.265936 | − | 1.13391i | ||||
\(826\) | 48.7527 | + | 3.58969i | 1.69632 | + | 0.124901i | ||||
\(827\) | −17.2236 | − | 17.2236i | −0.598925 | − | 0.598925i | 0.341101 | − | 0.940026i | \(-0.389200\pi\) |
−0.940026 | + | 0.341101i | \(0.889200\pi\) | |||||||
\(828\) | −2.47148 | + | 1.83400i | −0.0858900 | + | 0.0637358i | ||||
\(829\) | − | 20.0047i | − | 0.694792i | −0.937718 | − | 0.347396i | \(-0.887066\pi\) | ||
0.937718 | − | 0.347396i | \(-0.112934\pi\) | |||||||
\(830\) | −20.4570 | + | 31.1302i | −0.710073 | + | 1.08054i | ||||
\(831\) | 8.00962i | 0.277851i | ||||||||
\(832\) | 20.7746 | − | 7.45199i | 0.720230 | − | 0.258351i | ||||
\(833\) | −31.8954 | − | 31.8954i | −1.10511 | − | 1.10511i | ||||
\(834\) | 0.962599 | − | 13.0734i | 0.0333321 | − | 0.452693i | ||||
\(835\) | 8.25648 | + | 28.9837i | 0.285727 | + | 1.00302i | ||||
\(836\) | −8.14714 | − | 1.20630i | −0.281775 | − | 0.0417207i | ||||
\(837\) | −21.1596 | + | 21.1596i | −0.731384 | + | 0.731384i | ||||
\(838\) | 14.6306 | − | 12.6239i | 0.505406 | − | 0.436084i | ||||
\(839\) | −25.6540 | −0.885675 | −0.442838 | − | 0.896602i | \(-0.646028\pi\) | ||||
−0.442838 | + | 0.896602i | \(0.646028\pi\) | |||||||
\(840\) | 2.24339 | + | 39.3003i | 0.0774045 | + | 1.35599i | ||||
\(841\) | 23.4734 | 0.809429 | ||||||||
\(842\) | 14.8820 | − | 12.8407i | 0.512867 | − | 0.442521i | ||||
\(843\) | 31.7733 | − | 31.7733i | 1.09433 | − | 1.09433i | ||||
\(844\) | 21.3028 | + | 3.15417i | 0.733272 | + | 0.108571i | ||||
\(845\) | 5.86012 | − | 10.5288i | 0.201594 | − | 0.362200i | ||||
\(846\) | −0.0255352 | + | 0.346802i | −0.000877919 | + | 0.0119233i | ||||
\(847\) | 16.1386 | + | 16.1386i | 0.554528 | + | 0.554528i | ||||
\(848\) | 7.24541 | + | 13.5379i | 0.248809 | + | 0.464893i | ||||
\(849\) | 16.0218i | 0.549867i | ||||||||
\(850\) | 36.8296 | − | 19.2457i | 1.26324 | − | 0.660121i | ||||
\(851\) | 22.3465i | 0.766028i | ||||||||
\(852\) | −39.0273 | + | 28.9607i | −1.33705 | + | 0.992179i | ||||
\(853\) | −23.8080 | − | 23.8080i | −0.815170 | − | 0.815170i | 0.170234 | − | 0.985404i | \(-0.445548\pi\) |
−0.985404 | + | 0.170234i | \(0.945548\pi\) | |||||||
\(854\) | −22.9058 | − | 1.68657i | −0.783822 | − | 0.0577133i | ||||
\(855\) | 0.391819 | − | 0.703974i | 0.0133999 | − | 0.0240754i | ||||
\(856\) | −3.67035 | + | 16.3754i | −0.125450 | + | 0.559699i | ||||
\(857\) | 38.1592 | − | 38.1592i | 1.30349 | − | 1.30349i | 0.377471 | − | 0.926021i | \(-0.376794\pi\) |
0.926021 | − | 0.377471i | \(-0.123206\pi\) | |||||||
\(858\) | −17.0529 | − | 19.7637i | −0.582176 | − | 0.674722i | ||||
\(859\) | 44.6170 | 1.52231 | 0.761157 | − | 0.648568i | \(-0.224632\pi\) | ||||
0.761157 | + | 0.648568i | \(0.224632\pi\) | |||||||
\(860\) | 7.37866 | + | 56.2116i | 0.251610 | + | 1.91680i | ||||
\(861\) | −61.1664 | −2.08455 | ||||||||
\(862\) | 18.8133 | + | 21.8039i | 0.640783 | + | 0.742645i | ||||
\(863\) | 9.40276 | − | 9.40276i | 0.320074 | − | 0.320074i | −0.528722 | − | 0.848795i | \(-0.677328\pi\) |
0.848795 | + | 0.528722i | \(0.177328\pi\) | |||||||
\(864\) | −28.8217 | − | 11.0957i | −0.980536 | − | 0.377485i | ||||
\(865\) | 1.20309 | + | 4.22336i | 0.0409064 | + | 0.143599i | ||||
\(866\) | −11.7656 | − | 0.866308i | −0.399811 | − | 0.0294384i | ||||
\(867\) | 20.1464 | + | 20.1464i | 0.684209 | + | 0.684209i | ||||
\(868\) | 25.0251 | + | 33.7237i | 0.849408 | + | 1.14466i | ||||
\(869\) | 15.0236i | 0.509640i | ||||||||
\(870\) | −10.0939 | − | 6.63311i | −0.342214 | − | 0.224884i | ||||
\(871\) | − | 25.3478i | − | 0.858878i | ||||||
\(872\) | 6.75474 | − | 4.28117i | 0.228744 | − | 0.144979i | ||||
\(873\) | 0.0751716 | + | 0.0751716i | 0.00254417 | + | 0.00254417i | ||||
\(874\) | −0.443521 | + | 6.02359i | −0.0150023 | + | 0.203751i | ||||
\(875\) | 28.8246 | − | 31.6793i | 0.974448 | − | 1.07096i | ||||
\(876\) | −4.91208 | + | 33.1754i | −0.165964 | + | 1.12089i | ||||
\(877\) | −2.40711 | + | 2.40711i | −0.0812823 | + | 0.0812823i | −0.746579 | − | 0.665297i | \(-0.768305\pi\) |
0.665297 | + | 0.746579i | \(0.268305\pi\) | |||||||
\(878\) | 29.1705 | − | 25.1694i | 0.984458 | − | 0.849427i | ||||
\(879\) | 9.46245 | 0.319160 | ||||||||
\(880\) | 26.4700 | − | 25.6118i | 0.892303 | − | 0.863373i | ||||
\(881\) | −39.5208 | −1.33149 | −0.665744 | − | 0.746180i | \(-0.731886\pi\) | ||||
−0.665744 | + | 0.746180i | \(0.731886\pi\) | |||||||
\(882\) | 2.96113 | − | 2.55497i | 0.0997063 | − | 0.0860304i | ||||
\(883\) | −19.8634 | + | 19.8634i | −0.668457 | + | 0.668457i | −0.957359 | − | 0.288901i | \(-0.906710\pi\) |
0.288901 | + | 0.957359i | \(0.406710\pi\) | |||||||
\(884\) | 4.74935 | − | 32.0764i | 0.159738 | − | 1.07884i | ||||
\(885\) | −31.5268 | + | 8.98093i | −1.05976 | + | 0.301891i | ||||
\(886\) | −2.96479 | + | 40.2658i | −0.0996042 | + | 1.35275i | ||||
\(887\) | 12.1860 | + | 12.1860i | 0.409164 | + | 0.409164i | 0.881447 | − | 0.472283i | \(-0.156570\pi\) |
−0.472283 | + | 0.881447i | \(0.656570\pi\) | |||||||
\(888\) | −20.3090 | + | 12.8719i | −0.681525 | + | 0.431952i | ||||
\(889\) | − | 12.4918i | − | 0.418960i | ||||||
\(890\) | −6.25473 | − | 30.2313i | −0.209659 | − | 1.01336i | ||||
\(891\) | 32.0760i | 1.07459i | ||||||||
\(892\) | 4.39294 | + | 5.91991i | 0.147087 | + | 0.198213i | ||||
\(893\) | 0.482563 | + | 0.482563i | 0.0161484 | + | 0.0161484i | ||||
\(894\) | 8.97495 | + | 0.660832i | 0.300167 | + | 0.0221015i | ||||
\(895\) | −40.9829 | − | 22.8104i | −1.36991 | − | 0.762466i | ||||
\(896\) | −21.3277 | + | 37.7305i | −0.712507 | + | 1.26049i | ||||
\(897\) | −13.5364 | + | 13.5364i | −0.451967 | + | 0.451967i | ||||
\(898\) | −4.47629 | − | 5.18787i | −0.149376 | − | 0.173122i | ||||
\(899\) | −12.8853 | −0.429749 | ||||||||
\(900\) | 1.42972 | + | 3.30726i | 0.0476572 | + | 0.110242i | ||||
\(901\) | 22.5591 | 0.751553 | ||||||||
\(902\) | 37.3882 | + | 43.3317i | 1.24489 | + | 1.44279i | ||||
\(903\) | −55.7929 | + | 55.7929i | −1.85667 | + | 1.85667i | ||||
\(904\) | −0.913684 | + | 4.07643i | −0.0303887 | + | 0.135580i | ||||
\(905\) | 31.2017 | + | 17.3663i | 1.03718 | + | 0.577275i | ||||
\(906\) | −9.71936 | − | 0.715643i | −0.322904 | − | 0.0237756i | ||||
\(907\) | 25.8877 | + | 25.8877i | 0.859586 | + | 0.859586i | 0.991289 | − | 0.131704i | \(-0.0420447\pi\) |
−0.131704 | + | 0.991289i | \(0.542045\pi\) | |||||||
\(908\) | 15.9735 | − | 11.8534i | 0.530099 | − | 0.393367i | ||||
\(909\) | − | 6.77202i | − | 0.224614i | ||||||
\(910\) | −6.77131 | − | 32.7281i | −0.224467 | − | 1.08493i | ||||
\(911\) | − | 18.5615i | − | 0.614971i | −0.951553 | − | 0.307485i | \(-0.900513\pi\) | ||
0.951553 | − | 0.307485i | \(-0.0994875\pi\) | |||||||
\(912\) | −5.72985 | + | 3.06659i | −0.189734 | + | 0.101545i | ||||
\(913\) | 34.3003 | + | 34.3003i | 1.13517 | + | 1.13517i | ||||
\(914\) | 2.15762 | − | 29.3033i | 0.0713677 | − | 0.969266i | ||||
\(915\) | 14.8125 | − | 4.21958i | 0.489686 | − | 0.139495i | ||||
\(916\) | 6.10321 | + | 0.903665i | 0.201656 | + | 0.0298579i | ||||
\(917\) | −5.08966 | + | 5.08966i | −0.168076 | + | 0.168076i | ||||
\(918\) | −34.3537 | + | 29.6417i | −1.13384 | + | 0.978322i | ||||
\(919\) | 21.3400 | 0.703943 | 0.351971 | − | 0.936011i | \(-0.385511\pi\) | ||||
0.351971 | + | 0.936011i | \(0.385511\pi\) | |||||||
\(920\) | −20.1573 | − | 17.9803i | −0.664566 | − | 0.592792i | ||||
\(921\) | 53.4695 | 1.76188 | ||||||||
\(922\) | −26.2347 | + | 22.6363i | −0.863993 | + | 0.745486i | ||||
\(923\) | 29.1764 | − | 29.1764i | 0.960352 | − | 0.960352i | ||||
\(924\) | 50.7082 | + | 7.50806i | 1.66818 | + | 0.246997i | ||||
\(925\) | 25.4705 | + | 5.97362i | 0.837465 | + | 0.196411i | ||||
\(926\) | 3.79155 | − | 51.4942i | 0.124598 | − | 1.69221i | ||||
\(927\) | −0.264195 | − | 0.264195i | −0.00867732 | − | 0.00867732i | ||||
\(928\) | −5.39718 | − | 12.1540i | −0.177171 | − | 0.398975i | ||||
\(929\) | 23.7510i | 0.779244i | 0.920975 | + | 0.389622i | \(0.127394\pi\) | ||||
−0.920975 | + | 0.389622i | \(0.872606\pi\) | |||||||
\(930\) | −23.5341 | − | 15.4653i | −0.771713 | − | 0.507126i | ||||
\(931\) | − | 7.67547i | − | 0.251553i | ||||||
\(932\) | 37.6646 | − | 27.9495i | 1.23375 | − | 0.915518i | ||||
\(933\) | −36.6894 | − | 36.6894i | −1.20116 | − | 1.20116i | ||||
\(934\) | 12.0639 | + | 0.888276i | 0.394744 | + | 0.0290653i | ||||
\(935\) | −14.8254 | − | 52.0432i | −0.484841 | − | 1.70200i | ||||
\(936\) | 2.74346 | + | 0.614915i | 0.0896729 | + | 0.0200991i | ||||
\(937\) | −20.1997 | + | 20.1997i | −0.659895 | + | 0.659895i | −0.955355 | − | 0.295460i | \(-0.904527\pi\) |
0.295460 | + | 0.955355i | \(0.404527\pi\) | |||||||
\(938\) | 32.5177 | + | 37.6869i | 1.06174 | + | 1.23052i | ||||
\(939\) | −8.12964 | −0.265301 | ||||||||
\(940\) | −3.02604 | + | 0.397215i | −0.0986985 | + | 0.0129557i | ||||
\(941\) | 56.6392 | 1.84639 | 0.923193 | − | 0.384337i | \(-0.125570\pi\) | ||||
0.923193 | + | 0.384337i | \(0.125570\pi\) | |||||||
\(942\) | 3.90282 | + | 4.52323i | 0.127161 | + | 0.147375i | ||||
\(943\) | 29.6783 | − | 29.6783i | 0.966460 | − | 0.966460i | ||||
\(944\) | −34.5443 | − | 10.4588i | −1.12432 | − | 0.340406i | ||||
\(945\) | −22.7440 | + | 40.8636i | −0.739861 | + | 1.32929i | ||||
\(946\) | 73.6285 | + | 5.42132i | 2.39387 | + | 0.176262i | ||||
\(947\) | 40.2926 | + | 40.2926i | 1.30933 | + | 1.30933i | 0.921896 | + | 0.387437i | \(0.126639\pi\) |
0.387437 | + | 0.921896i | \(0.373361\pi\) | |||||||
\(948\) | 7.06445 | + | 9.52001i | 0.229443 | + | 0.309196i | ||||
\(949\) | − | 28.4737i | − | 0.924296i | ||||||
\(950\) | 6.74712 | + | 2.11574i | 0.218906 | + | 0.0686436i | ||||
\(951\) | − | 18.3109i | − | 0.593773i | ||||||
\(952\) | 34.0882 | + | 53.7836i | 1.10480 | + | 1.74314i | ||||
\(953\) | 4.11215 | + | 4.11215i | 0.133206 | + | 0.133206i | 0.770566 | − | 0.637360i | \(-0.219974\pi\) |
−0.637360 | + | 0.770566i | \(0.719974\pi\) | |||||||
\(954\) | −0.143633 | + | 1.95073i | −0.00465030 | + | 0.0631571i | ||||
\(955\) | 6.43547 | − | 11.5625i | 0.208247 | − | 0.374153i | ||||
\(956\) | 2.66418 | − | 17.9934i | 0.0861656 | − | 0.581948i | ||||
\(957\) | −11.1218 | + | 11.1218i | −0.359515 | + | 0.359515i | ||||
\(958\) | 23.6598 | − | 20.4146i | 0.764414 | − | 0.659565i | ||||
\(959\) | −23.7534 | −0.767036 | ||||||||
\(960\) | 4.73000 | − | 28.6763i | 0.152660 | − | 0.925523i | ||||
\(961\) | 0.957597 | 0.0308902 | ||||||||
\(962\) | 15.4562 | − | 13.3362i | 0.498327 | − | 0.429976i | ||||
\(963\) | −1.51163 | + | 1.51163i | −0.0487117 | + | 0.0487117i | ||||
\(964\) | 0.236307 | − | 1.59598i | 0.00761094 | − | 0.0514030i | ||||
\(965\) | 1.44175 | + | 5.06114i | 0.0464115 | + | 0.162924i | ||||
\(966\) | 2.76049 | − | 37.4911i | 0.0888174 | − | 1.20626i | ||||
\(967\) | 37.1217 | + | 37.1217i | 1.19375 | + | 1.19375i | 0.976005 | + | 0.217747i | \(0.0698707\pi\) |
0.217747 | + | 0.976005i | \(0.430129\pi\) | |||||||
\(968\) | −9.02100 | − | 14.2331i | −0.289946 | − | 0.457471i | ||||
\(969\) | 9.54804i | 0.306727i | ||||||||
\(970\) | −0.512402 | + | 0.779742i | −0.0164522 | + | 0.0250360i | ||||
\(971\) | − | 5.78287i | − | 0.185581i | −0.995686 | − | 0.0927905i | \(-0.970421\pi\) | ||
0.995686 | − | 0.0927905i | \(-0.0295787\pi\) | |||||||
\(972\) | −4.43751 | − | 5.97996i | −0.142333 | − | 0.191807i | ||||
\(973\) | −15.4543 | − | 15.4543i | −0.495443 | − | 0.495443i | ||||
\(974\) | 43.5268 | + | 3.20491i | 1.39469 | + | 0.102692i | ||||
\(975\) | 11.8102 | + | 19.0473i | 0.378231 | + | 0.610001i | ||||
\(976\) | 16.2302 | + | 4.91395i | 0.519516 | + | 0.157292i | ||||
\(977\) | −42.5957 | + | 42.5957i | −1.36276 | + | 1.36276i | −0.492373 | + | 0.870384i | \(0.663870\pi\) |
−0.870384 | + | 0.492373i | \(0.836130\pi\) | |||||||
\(978\) | −3.65319 | − | 4.23393i | −0.116816 | − | 0.135386i | ||||
\(979\) | −40.2016 | −1.28485 | ||||||||
\(980\) | 27.2245 | + | 20.9065i | 0.869655 | + | 0.667835i | ||||
\(981\) | 1.01874 | 0.0325259 | ||||||||
\(982\) | −26.8886 | − | 31.1630i | −0.858051 | − | 0.994452i | ||||
\(983\) | −19.1593 | + | 19.1593i | −0.611085 | + | 0.611085i | −0.943229 | − | 0.332143i | \(-0.892228\pi\) |
0.332143 | + | 0.943229i | \(0.392228\pi\) | |||||||
\(984\) | 44.0675 | + | 9.87720i | 1.40482 | + | 0.314874i | ||||
\(985\) | −23.5639 | + | 6.71256i | −0.750809 | + | 0.213880i | ||||
\(986\) | −19.4852 | − | 1.43471i | −0.620536 | − | 0.0456905i | ||||
\(987\) | −3.00349 | − | 3.00349i | −0.0956023 | − | 0.0956023i | ||||
\(988\) | 4.43097 | − | 3.28806i | 0.140968 | − | 0.104607i | ||||
\(989\) | − | 54.1421i | − | 1.72162i | ||||||
\(990\) | 4.59467 | − | 0.950618i | 0.146028 | − | 0.0302126i | ||||
\(991\) | − | 29.9003i | − | 0.949815i | −0.880036 | − | 0.474908i | \(-0.842481\pi\) | ||
0.880036 | − | 0.474908i | \(-0.157519\pi\) | |||||||
\(992\) | −12.5837 | − | 28.3374i | −0.399532 | − | 0.899713i | ||||
\(993\) | −0.280249 | − | 0.280249i | −0.00889342 | − | 0.00889342i | ||||
\(994\) | −5.94998 | + | 80.8085i | −0.188722 | + | 2.56309i | ||||
\(995\) | 35.8628 | + | 19.9606i | 1.13693 | + | 0.632794i | ||||
\(996\) | 37.8640 | + | 5.60629i | 1.19977 | + | 0.177642i | ||||
\(997\) | −26.0472 | + | 26.0472i | −0.824923 | + | 0.824923i | −0.986809 | − | 0.161886i | \(-0.948242\pi\) |
0.161886 | + | 0.986809i | \(0.448242\pi\) | |||||||
\(998\) | −27.3735 | + | 23.6189i | −0.866493 | + | 0.747643i | ||||
\(999\) | −28.5661 | −0.903790 |
(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 | 380.2.k.d.343.7 | yes | 52 | |
4.3 | odd | 2 | 380.2.k.c.343.7 | yes | 52 | ||
5.2 | odd | 4 | 380.2.k.c.267.7 | ✓ | 52 | ||
20.7 | even | 4 | inner | 380.2.k.d.267.7 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.k.c.267.7 | ✓ | 52 | 5.2 | odd | 4 | ||
380.2.k.c.343.7 | yes | 52 | 4.3 | odd | 2 | ||
380.2.k.d.267.7 | yes | 52 | 20.7 | even | 4 | inner | |
380.2.k.d.343.7 | yes | 52 | 1.1 | even | 1 | trivial |