Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(1009,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.bb (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1009.4 | ||
Character | \(\chi\) | \(=\) | 1110.1009 |
Dual form | 1110.2.bb.e.1099.4 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.88087 | + | 1.20927i | −0.841151 | + | 0.540800i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.304101 | + | 0.175573i | −0.114939 | + | 0.0663602i | −0.556368 | − | 0.830936i | \(-0.687805\pi\) |
0.441428 | + | 0.897297i | \(0.354472\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 2.23352 | − | 0.106818i | 0.706299 | − | 0.0337789i | ||||
\(11\) | −1.03694 | −0.312649 | −0.156325 | − | 0.987706i | \(-0.549965\pi\) | ||||
−0.156325 | + | 0.987706i | \(0.549965\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | 1.89463 | − | 1.09386i | 0.525475 | − | 0.303383i | −0.213697 | − | 0.976900i | \(-0.568551\pi\) |
0.739172 | + | 0.673517i | \(0.235217\pi\) | |||||||
\(14\) | 0.351145 | 0.0938475 | ||||||||
\(15\) | −1.02425 | + | 1.98769i | −0.264460 | + | 0.513219i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −4.45383 | − | 2.57142i | −1.08021 | − | 0.623661i | −0.149259 | − | 0.988798i | \(-0.547689\pi\) |
−0.930954 | + | 0.365137i | \(0.881022\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | 4.10098 | + | 7.10310i | 0.940829 | + | 1.62956i | 0.763895 | + | 0.645341i | \(0.223285\pi\) |
0.176935 | + | 0.984223i | \(0.443382\pi\) | |||||||
\(20\) | −1.98769 | − | 1.02425i | −0.444461 | − | 0.229029i | ||||
\(21\) | −0.175573 | + | 0.304101i | −0.0383131 | + | 0.0663602i | ||||
\(22\) | 0.898016 | + | 0.518470i | 0.191458 | + | 0.110538i | ||||
\(23\) | 4.23909i | 0.883912i | 0.897037 | + | 0.441956i | \(0.145715\pi\) | ||||
−0.897037 | + | 0.441956i | \(0.854285\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 2.07536 | − | 4.54894i | 0.415071 | − | 0.909789i | ||||
\(26\) | −2.18772 | −0.429048 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −0.304101 | − | 0.175573i | −0.0574696 | − | 0.0331801i | ||||
\(29\) | 3.20052 | 0.594322 | 0.297161 | − | 0.954827i | \(-0.403960\pi\) | ||||
0.297161 | + | 0.954827i | \(0.403960\pi\) | |||||||
\(30\) | 1.88087 | − | 1.20927i | 0.343399 | − | 0.220781i | ||||
\(31\) | 0.148735 | 0.0267136 | 0.0133568 | − | 0.999911i | \(-0.495748\pi\) | ||||
0.0133568 | + | 0.999911i | \(0.495748\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −0.898016 | + | 0.518470i | −0.156325 | + | 0.0902540i | ||||
\(34\) | 2.57142 | + | 4.45383i | 0.440995 | + | 0.763826i | ||||
\(35\) | 0.359661 | − | 0.697968i | 0.0607937 | − | 0.117978i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.69935 | + | 2.12543i | −0.936967 | + | 0.349419i | ||||
\(38\) | − | 8.20196i | − | 1.33053i | ||||||
\(39\) | 1.09386 | − | 1.89463i | 0.175158 | − | 0.303383i | ||||
\(40\) | 1.20927 | + | 1.88087i | 0.191202 | + | 0.297392i | ||||
\(41\) | 5.56385 | + | 9.63687i | 0.868927 | + | 1.50503i | 0.863094 | + | 0.505043i | \(0.168523\pi\) |
0.00583262 | + | 0.999983i | \(0.498143\pi\) | |||||||
\(42\) | 0.304101 | − | 0.175573i | 0.0469238 | − | 0.0270915i | ||||
\(43\) | 6.34319i | 0.967328i | 0.875254 | + | 0.483664i | \(0.160694\pi\) | ||||
−0.875254 | + | 0.483664i | \(0.839306\pi\) | |||||||
\(44\) | −0.518470 | − | 0.898016i | −0.0781623 | − | 0.135381i | ||||
\(45\) | 0.106818 | + | 2.23352i | 0.0159235 | + | 0.332953i | ||||
\(46\) | 2.11955 | − | 3.67116i | 0.312510 | − | 0.541283i | ||||
\(47\) | 8.96463i | 1.30763i | 0.756656 | + | 0.653813i | \(0.226832\pi\) | ||||
−0.756656 | + | 0.653813i | \(0.773168\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −3.43835 | + | 5.95539i | −0.491193 | + | 0.850771i | ||||
\(50\) | −4.07178 | + | 2.90182i | −0.575837 | + | 0.410380i | ||||
\(51\) | −5.14284 | −0.720142 | ||||||||
\(52\) | 1.89463 | + | 1.09386i | 0.262737 | + | 0.151691i | ||||
\(53\) | −3.86558 | − | 2.23180i | −0.530979 | − | 0.306561i | 0.210436 | − | 0.977608i | \(-0.432512\pi\) |
−0.741415 | + | 0.671047i | \(0.765845\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 1.95035 | − | 1.25394i | 0.262985 | − | 0.169081i | ||||
\(56\) | 0.175573 | + | 0.304101i | 0.0234619 | + | 0.0406372i | ||||
\(57\) | 7.10310 | + | 4.10098i | 0.940829 | + | 0.543188i | ||||
\(58\) | −2.77173 | − | 1.60026i | −0.363946 | − | 0.210125i | ||||
\(59\) | −5.49650 | + | 9.52022i | −0.715584 | + | 1.23943i | 0.247150 | + | 0.968977i | \(0.420506\pi\) |
−0.962734 | + | 0.270450i | \(0.912828\pi\) | |||||||
\(60\) | −2.23352 | + | 0.106818i | −0.288346 | + | 0.0137902i | ||||
\(61\) | 1.15060 | + | 1.99289i | 0.147319 | + | 0.255164i | 0.930236 | − | 0.366963i | \(-0.119602\pi\) |
−0.782917 | + | 0.622126i | \(0.786269\pi\) | |||||||
\(62\) | −0.128809 | − | 0.0743676i | −0.0163587 | − | 0.00944470i | ||||
\(63\) | 0.351145i | 0.0442402i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.24078 | + | 4.34852i | −0.277934 | + | 0.539367i | ||||
\(66\) | 1.03694 | 0.127638 | ||||||||
\(67\) | 12.4250 | − | 7.17356i | 1.51795 | − | 0.876390i | 0.518175 | − | 0.855274i | \(-0.326611\pi\) |
0.999777 | − | 0.0211159i | \(-0.00672189\pi\) | |||||||
\(68\) | − | 5.14284i | − | 0.623661i | ||||||
\(69\) | 2.11955 | + | 3.67116i | 0.255163 | + | 0.441956i | ||||
\(70\) | −0.660459 | + | 0.424628i | −0.0789400 | + | 0.0507527i | ||||
\(71\) | −5.35314 | − | 9.27190i | −0.635300 | − | 1.10037i | −0.986451 | − | 0.164054i | \(-0.947543\pi\) |
0.351151 | − | 0.936319i | \(-0.385790\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 8.52271i | 0.997507i | 0.866744 | + | 0.498754i | \(0.166209\pi\) | ||||
−0.866744 | + | 0.498754i | \(0.833791\pi\) | |||||||
\(74\) | 5.99849 | + | 1.00900i | 0.697311 | + | 0.117293i | ||||
\(75\) | −0.477161 | − | 4.97718i | −0.0550978 | − | 0.574715i | ||||
\(76\) | −4.10098 | + | 7.10310i | −0.470415 | + | 0.814782i | ||||
\(77\) | 0.315334 | − | 0.182058i | 0.0359357 | − | 0.0207475i | ||||
\(78\) | −1.89463 | + | 1.09386i | −0.214524 | + | 0.123856i | ||||
\(79\) | 4.72489 | + | 8.18375i | 0.531592 | + | 0.920744i | 0.999320 | + | 0.0368718i | \(0.0117393\pi\) |
−0.467728 | + | 0.883872i | \(0.654927\pi\) | |||||||
\(80\) | −0.106818 | − | 2.23352i | −0.0119427 | − | 0.249715i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | − | 11.1277i | − | 1.22885i | ||||||
\(83\) | −3.80546 | − | 2.19708i | −0.417704 | − | 0.241161i | 0.276391 | − | 0.961045i | \(-0.410862\pi\) |
−0.694094 | + | 0.719884i | \(0.744195\pi\) | |||||||
\(84\) | −0.351145 | −0.0383131 | ||||||||
\(85\) | 11.4866 | − | 0.549350i | 1.24590 | − | 0.0595854i | ||||
\(86\) | 3.17160 | − | 5.49337i | 0.342002 | − | 0.592365i | ||||
\(87\) | 2.77173 | − | 1.60026i | 0.297161 | − | 0.171566i | ||||
\(88\) | 1.03694i | 0.110538i | ||||||||
\(89\) | 2.10936 | − | 3.65351i | 0.223591 | − | 0.387272i | −0.732305 | − | 0.680977i | \(-0.761555\pi\) |
0.955896 | + | 0.293706i | \(0.0948885\pi\) | |||||||
\(90\) | 1.02425 | − | 1.98769i | 0.107965 | − | 0.209521i | ||||
\(91\) | −0.384105 | + | 0.665289i | −0.0402651 | + | 0.0697412i | ||||
\(92\) | −3.67116 | + | 2.11955i | −0.382745 | + | 0.220978i | ||||
\(93\) | 0.128809 | − | 0.0743676i | 0.0133568 | − | 0.00771156i | ||||
\(94\) | 4.48232 | − | 7.76360i | 0.462316 | − | 0.800754i | ||||
\(95\) | −16.3029 | − | 8.40086i | −1.67265 | − | 0.861910i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 15.4855i | 1.57231i | 0.618027 | + | 0.786157i | \(0.287932\pi\) | ||||
−0.618027 | + | 0.786157i | \(0.712068\pi\) | |||||||
\(98\) | 5.95539 | − | 3.43835i | 0.601586 | − | 0.347326i | ||||
\(99\) | −0.518470 | + | 0.898016i | −0.0521082 | + | 0.0902540i | ||||
\(100\) | 4.97718 | − | 0.477161i | 0.497718 | − | 0.0477161i | ||||
\(101\) | −5.93705 | −0.590759 | −0.295379 | − | 0.955380i | \(-0.595446\pi\) | ||||
−0.295379 | + | 0.955380i | \(0.595446\pi\) | |||||||
\(102\) | 4.45383 | + | 2.57142i | 0.440995 | + | 0.254609i | ||||
\(103\) | − | 13.0217i | − | 1.28307i | −0.767095 | − | 0.641534i | \(-0.778298\pi\) | ||
0.767095 | − | 0.641534i | \(-0.221702\pi\) | |||||||
\(104\) | −1.09386 | − | 1.89463i | −0.107262 | − | 0.185783i | ||||
\(105\) | −0.0375088 | − | 0.784288i | −0.00366048 | − | 0.0765387i | ||||
\(106\) | 2.23180 | + | 3.86558i | 0.216771 | + | 0.375459i | ||||
\(107\) | 1.36568 | − | 0.788474i | 0.132025 | − | 0.0762247i | −0.432533 | − | 0.901618i | \(-0.642380\pi\) |
0.564558 | + | 0.825394i | \(0.309047\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 5.10648 | − | 8.84469i | 0.489112 | − | 0.847167i | −0.510809 | − | 0.859694i | \(-0.670654\pi\) |
0.999922 | + | 0.0125267i | \(0.00398747\pi\) | |||||||
\(110\) | −2.31602 | + | 0.110764i | −0.220824 | + | 0.0105610i | ||||
\(111\) | −3.87306 | + | 4.69035i | −0.367615 | + | 0.445188i | ||||
\(112\) | − | 0.351145i | − | 0.0331801i | ||||||
\(113\) | 2.52503 | + | 1.45783i | 0.237535 | + | 0.137141i | 0.614043 | − | 0.789272i | \(-0.289542\pi\) |
−0.376508 | + | 0.926413i | \(0.622875\pi\) | |||||||
\(114\) | −4.10098 | − | 7.10310i | −0.384092 | − | 0.665267i | ||||
\(115\) | −5.12618 | − | 7.97319i | −0.478019 | − | 0.743503i | ||||
\(116\) | 1.60026 | + | 2.77173i | 0.148580 | + | 0.257349i | ||||
\(117\) | − | 2.18772i | − | 0.202255i | ||||||
\(118\) | 9.52022 | − | 5.49650i | 0.876407 | − | 0.505994i | ||||
\(119\) | 1.80588 | 0.165545 | ||||||||
\(120\) | 1.98769 | + | 1.02425i | 0.181450 | + | 0.0935008i | ||||
\(121\) | −9.92476 | −0.902251 | ||||||||
\(122\) | − | 2.30120i | − | 0.208340i | ||||||
\(123\) | 9.63687 | + | 5.56385i | 0.868927 | + | 0.501675i | ||||
\(124\) | 0.0743676 | + | 0.128809i | 0.00667841 | + | 0.0115673i | ||||
\(125\) | 1.59740 | + | 11.0656i | 0.142876 | + | 0.989741i | ||||
\(126\) | 0.175573 | − | 0.304101i | 0.0156413 | − | 0.0270915i | ||||
\(127\) | 12.4109 | + | 7.16541i | 1.10129 | + | 0.635828i | 0.936558 | − | 0.350511i | \(-0.113992\pi\) |
0.164727 | + | 0.986339i | \(0.447326\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 3.17160 | + | 5.49337i | 0.279244 | + | 0.483664i | ||||
\(130\) | 4.11483 | − | 2.64554i | 0.360894 | − | 0.232029i | ||||
\(131\) | −4.64477 | + | 8.04498i | −0.405816 | + | 0.702893i | −0.994416 | − | 0.105531i | \(-0.966346\pi\) |
0.588600 | + | 0.808424i | \(0.299679\pi\) | |||||||
\(132\) | −0.898016 | − | 0.518470i | −0.0781623 | − | 0.0451270i | ||||
\(133\) | −2.49422 | − | 1.44004i | −0.216276 | − | 0.124867i | ||||
\(134\) | −14.3471 | −1.23940 | ||||||||
\(135\) | 1.20927 | + | 1.88087i | 0.104077 | + | 0.161880i | ||||
\(136\) | −2.57142 | + | 4.45383i | −0.220498 | + | 0.381913i | ||||
\(137\) | − | 3.80455i | − | 0.325045i | −0.986705 | − | 0.162522i | \(-0.948037\pi\) | ||
0.986705 | − | 0.162522i | \(-0.0519630\pi\) | |||||||
\(138\) | − | 4.23909i | − | 0.360855i | ||||||
\(139\) | 7.47368 | − | 12.9448i | 0.633909 | − | 1.09796i | −0.352836 | − | 0.935685i | \(-0.614783\pi\) |
0.986745 | − | 0.162278i | \(-0.0518841\pi\) | |||||||
\(140\) | 0.784288 | − | 0.0375088i | 0.0662845 | − | 0.00317007i | ||||
\(141\) | 4.48232 | + | 7.76360i | 0.377479 | + | 0.653813i | ||||
\(142\) | 10.7063i | 0.898450i | ||||||||
\(143\) | −1.96461 | + | 1.13427i | −0.164289 | + | 0.0948524i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −6.01977 | + | 3.87028i | −0.499915 | + | 0.321409i | ||||
\(146\) | 4.26135 | − | 7.38088i | 0.352672 | − | 0.610846i | ||||
\(147\) | 6.87670i | 0.567180i | ||||||||
\(148\) | −4.69035 | − | 3.87306i | −0.385544 | − | 0.318364i | ||||
\(149\) | 21.2248 | 1.73880 | 0.869401 | − | 0.494107i | \(-0.164505\pi\) | ||||
0.869401 | + | 0.494107i | \(0.164505\pi\) | |||||||
\(150\) | −2.07536 | + | 4.54894i | −0.169452 | + | 0.371420i | ||||
\(151\) | −10.9668 | − | 18.9951i | −0.892469 | − | 1.54580i | −0.836906 | − | 0.547346i | \(-0.815638\pi\) |
−0.0555624 | − | 0.998455i | \(-0.517695\pi\) | |||||||
\(152\) | 7.10310 | − | 4.10098i | 0.576138 | − | 0.332633i | ||||
\(153\) | −4.45383 | + | 2.57142i | −0.360071 | + | 0.207887i | ||||
\(154\) | −0.364117 | −0.0293414 | ||||||||
\(155\) | −0.279752 | + | 0.179860i | −0.0224702 | + | 0.0144467i | ||||
\(156\) | 2.18772 | 0.175158 | ||||||||
\(157\) | 17.8306 | + | 10.2945i | 1.42304 | + | 0.821590i | 0.996557 | − | 0.0829079i | \(-0.0264207\pi\) |
0.426478 | + | 0.904498i | \(0.359754\pi\) | |||||||
\(158\) | − | 9.44979i | − | 0.751785i | ||||||
\(159\) | −4.46359 | −0.353986 | ||||||||
\(160\) | −1.02425 | + | 1.98769i | −0.0809741 | + | 0.157141i | ||||
\(161\) | −0.744269 | − | 1.28911i | −0.0586566 | − | 0.101596i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 4.52748 | + | 2.61394i | 0.354620 | + | 0.204740i | 0.666718 | − | 0.745310i | \(-0.267699\pi\) |
−0.312098 | + | 0.950050i | \(0.601032\pi\) | |||||||
\(164\) | −5.56385 | + | 9.63687i | −0.434463 | + | 0.752513i | ||||
\(165\) | 1.06209 | − | 2.06111i | 0.0826833 | − | 0.160458i | ||||
\(166\) | 2.19708 | + | 3.80546i | 0.170527 | + | 0.295361i | ||||
\(167\) | 6.62307 | − | 3.82383i | 0.512509 | − | 0.295897i | −0.221356 | − | 0.975193i | \(-0.571048\pi\) |
0.733864 | + | 0.679296i | \(0.237715\pi\) | |||||||
\(168\) | 0.304101 | + | 0.175573i | 0.0234619 | + | 0.0135457i | ||||
\(169\) | −4.10693 | + | 7.11341i | −0.315918 | + | 0.547185i | ||||
\(170\) | −10.2224 | − | 5.26756i | −0.784020 | − | 0.404003i | ||||
\(171\) | 8.20196 | 0.627219 | ||||||||
\(172\) | −5.49337 | + | 3.17160i | −0.418865 | + | 0.241832i | ||||
\(173\) | −8.50015 | − | 4.90756i | −0.646254 | − | 0.373115i | 0.140765 | − | 0.990043i | \(-0.455044\pi\) |
−0.787020 | + | 0.616928i | \(0.788377\pi\) | |||||||
\(174\) | −3.20052 | −0.242631 | ||||||||
\(175\) | 0.167553 | + | 1.74771i | 0.0126658 | + | 0.132115i | ||||
\(176\) | 0.518470 | − | 0.898016i | 0.0390811 | − | 0.0676905i | ||||
\(177\) | 10.9930i | 0.826285i | ||||||||
\(178\) | −3.65351 | + | 2.10936i | −0.273842 | + | 0.158103i | ||||
\(179\) | 5.67181 | 0.423931 | 0.211966 | − | 0.977277i | \(-0.432014\pi\) | ||||
0.211966 | + | 0.977277i | \(0.432014\pi\) | |||||||
\(180\) | −1.88087 | + | 1.20927i | −0.140192 | + | 0.0901333i | ||||
\(181\) | −8.40034 | − | 14.5498i | −0.624392 | − | 1.08148i | −0.988658 | − | 0.150184i | \(-0.952013\pi\) |
0.364266 | − | 0.931295i | \(-0.381320\pi\) | |||||||
\(182\) | 0.665289 | − | 0.384105i | 0.0493145 | − | 0.0284717i | ||||
\(183\) | 1.99289 | + | 1.15060i | 0.147319 | + | 0.0850546i | ||||
\(184\) | 4.23909 | 0.312510 | ||||||||
\(185\) | 8.14953 | − | 10.8897i | 0.599165 | − | 0.800625i | ||||
\(186\) | −0.148735 | −0.0109058 | ||||||||
\(187\) | 4.61835 | + | 2.66641i | 0.337728 | + | 0.194987i | ||||
\(188\) | −7.76360 | + | 4.48232i | −0.566219 | + | 0.326906i | ||||
\(189\) | 0.175573 | + | 0.304101i | 0.0127710 | + | 0.0221201i | ||||
\(190\) | 9.91834 | + | 15.4268i | 0.719552 | + | 1.11918i | ||||
\(191\) | −2.86947 | −0.207628 | −0.103814 | − | 0.994597i | \(-0.533105\pi\) | ||||
−0.103814 | + | 0.994597i | \(0.533105\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 13.0276i | 0.937746i | 0.883266 | + | 0.468873i | \(0.155340\pi\) | ||||
−0.883266 | + | 0.468873i | \(0.844660\pi\) | |||||||
\(194\) | 7.74275 | − | 13.4108i | 0.555897 | − | 0.962842i | ||||
\(195\) | 0.233689 | + | 4.88632i | 0.0167348 | + | 0.349916i | ||||
\(196\) | −6.87670 | −0.491193 | ||||||||
\(197\) | 1.19533 | + | 0.690124i | 0.0851637 | + | 0.0491693i | 0.541977 | − | 0.840393i | \(-0.317676\pi\) |
−0.456813 | + | 0.889563i | \(0.651009\pi\) | |||||||
\(198\) | 0.898016 | − | 0.518470i | 0.0638192 | − | 0.0368461i | ||||
\(199\) | −4.07318 | −0.288740 | −0.144370 | − | 0.989524i | \(-0.546116\pi\) | ||||
−0.144370 | + | 0.989524i | \(0.546116\pi\) | |||||||
\(200\) | −4.54894 | − | 2.07536i | −0.321659 | − | 0.146750i | ||||
\(201\) | 7.17356 | − | 12.4250i | 0.505984 | − | 0.876390i | ||||
\(202\) | 5.14164 | + | 2.96853i | 0.361764 | + | 0.208865i | ||||
\(203\) | −0.973281 | + | 0.561924i | −0.0683109 | + | 0.0394393i | ||||
\(204\) | −2.57142 | − | 4.45383i | −0.180035 | − | 0.311831i | ||||
\(205\) | −22.1184 | − | 11.3975i | −1.54482 | − | 0.796039i | ||||
\(206\) | −6.51086 | + | 11.2771i | −0.453633 | + | 0.785716i | ||||
\(207\) | 3.67116 | + | 2.11955i | 0.255163 | + | 0.147319i | ||||
\(208\) | 2.18772i | 0.151691i | ||||||||
\(209\) | −4.25247 | − | 7.36549i | −0.294149 | − | 0.509482i | ||||
\(210\) | −0.359661 | + | 0.697968i | −0.0248189 | + | 0.0481644i | ||||
\(211\) | −26.2931 | −1.81009 | −0.905046 | − | 0.425315i | \(-0.860163\pi\) | ||||
−0.905046 | + | 0.425315i | \(0.860163\pi\) | |||||||
\(212\) | − | 4.46359i | − | 0.306561i | ||||||
\(213\) | −9.27190 | − | 5.35314i | −0.635300 | − | 0.366791i | ||||
\(214\) | −1.57695 | −0.107798 | ||||||||
\(215\) | −7.67060 | − | 11.9307i | −0.523131 | − | 0.813669i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −0.0452305 | + | 0.0261138i | −0.00307045 | + | 0.00177272i | ||||
\(218\) | −8.84469 | + | 5.10648i | −0.599038 | + | 0.345855i | ||||
\(219\) | 4.26135 | + | 7.38088i | 0.287956 | + | 0.498754i | ||||
\(220\) | 2.06111 | + | 1.06209i | 0.138960 | + | 0.0716058i | ||||
\(221\) | −11.2511 | −0.756832 | ||||||||
\(222\) | 5.69935 | − | 2.12543i | 0.382515 | − | 0.142650i | ||||
\(223\) | 7.74058i | 0.518348i | 0.965831 | + | 0.259174i | \(0.0834503\pi\) | ||||
−0.965831 | + | 0.259174i | \(0.916550\pi\) | |||||||
\(224\) | −0.175573 | + | 0.304101i | −0.0117309 | + | 0.0203186i | ||||
\(225\) | −2.90182 | − | 4.07178i | −0.193455 | − | 0.271452i | ||||
\(226\) | −1.45783 | − | 2.52503i | −0.0969732 | − | 0.167962i | ||||
\(227\) | −7.11370 | + | 4.10709i | −0.472153 | + | 0.272597i | −0.717140 | − | 0.696929i | \(-0.754549\pi\) |
0.244988 | + | 0.969526i | \(0.421216\pi\) | |||||||
\(228\) | 8.20196i | 0.543188i | ||||||||
\(229\) | −7.53968 | − | 13.0591i | −0.498236 | − | 0.862970i | 0.501762 | − | 0.865006i | \(-0.332685\pi\) |
−0.999998 | + | 0.00203575i | \(0.999352\pi\) | |||||||
\(230\) | 0.452813 | + | 9.46807i | 0.0298576 | + | 0.624306i | ||||
\(231\) | 0.182058 | − | 0.315334i | 0.0119786 | − | 0.0207475i | ||||
\(232\) | − | 3.20052i | − | 0.210125i | ||||||
\(233\) | − | 5.64661i | − | 0.369922i | −0.982746 | − | 0.184961i | \(-0.940784\pi\) | ||
0.982746 | − | 0.184961i | \(-0.0592159\pi\) | |||||||
\(234\) | −1.09386 | + | 1.89463i | −0.0715080 | + | 0.123856i | ||||
\(235\) | −10.8406 | − | 16.8613i | −0.707164 | − | 1.09991i | ||||
\(236\) | −10.9930 | −0.715584 | ||||||||
\(237\) | 8.18375 | + | 4.72489i | 0.531592 | + | 0.306915i | ||||
\(238\) | −1.56394 | − | 0.902942i | −0.101375 | − | 0.0585291i | ||||
\(239\) | −5.72492 | + | 9.91584i | −0.370314 | + | 0.641403i | −0.989614 | − | 0.143752i | \(-0.954083\pi\) |
0.619300 | + | 0.785155i | \(0.287417\pi\) | |||||||
\(240\) | −1.20927 | − | 1.88087i | −0.0780577 | − | 0.121410i | ||||
\(241\) | −2.07844 | − | 3.59997i | −0.133884 | − | 0.231894i | 0.791286 | − | 0.611446i | \(-0.209412\pi\) |
−0.925171 | + | 0.379551i | \(0.876078\pi\) | |||||||
\(242\) | 8.59509 | + | 4.96238i | 0.552513 | + | 0.318994i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −1.15060 | + | 1.99289i | −0.0736595 | + | 0.127582i | ||||
\(245\) | −0.734558 | − | 15.3592i | −0.0469292 | − | 0.981264i | ||||
\(246\) | −5.56385 | − | 9.63687i | −0.354738 | − | 0.614424i | ||||
\(247\) | 15.5396 | + | 8.97181i | 0.988763 | + | 0.570863i | ||||
\(248\) | − | 0.148735i | − | 0.00944470i | ||||||
\(249\) | −4.39417 | −0.278469 | ||||||||
\(250\) | 4.14943 | − | 10.3818i | 0.262433 | − | 0.656604i | ||||
\(251\) | 24.8423 | 1.56803 | 0.784016 | − | 0.620740i | \(-0.213168\pi\) | ||||
0.784016 | + | 0.620740i | \(0.213168\pi\) | |||||||
\(252\) | −0.304101 | + | 0.175573i | −0.0191565 | + | 0.0110600i | ||||
\(253\) | − | 4.39568i | − | 0.276354i | ||||||
\(254\) | −7.16541 | − | 12.4109i | −0.449598 | − | 0.778727i | ||||
\(255\) | 9.67302 | − | 6.21906i | 0.605748 | − | 0.389453i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3.62690 | − | 2.09399i | −0.226240 | − | 0.130620i | 0.382596 | − | 0.923916i | \(-0.375030\pi\) |
−0.608836 | + | 0.793296i | \(0.708363\pi\) | |||||||
\(258\) | − | 6.34319i | − | 0.394910i | ||||||
\(259\) | 1.36001 | − | 1.64699i | 0.0845068 | − | 0.102339i | ||||
\(260\) | −4.88632 | + | 0.233689i | −0.303036 | + | 0.0144928i | ||||
\(261\) | 1.60026 | − | 2.77173i | 0.0990536 | − | 0.171566i | ||||
\(262\) | 8.04498 | − | 4.64477i | 0.497021 | − | 0.286955i | ||||
\(263\) | −5.44423 | + | 3.14323i | −0.335706 | + | 0.193820i | −0.658371 | − | 0.752693i | \(-0.728754\pi\) |
0.322666 | + | 0.946513i | \(0.395421\pi\) | |||||||
\(264\) | 0.518470 | + | 0.898016i | 0.0319096 | + | 0.0552691i | ||||
\(265\) | 9.96950 | − | 0.476794i | 0.612421 | − | 0.0292892i | ||||
\(266\) | 1.44004 | + | 2.49422i | 0.0882945 | + | 0.152931i | ||||
\(267\) | − | 4.21871i | − | 0.258181i | ||||||
\(268\) | 12.4250 | + | 7.17356i | 0.758976 | + | 0.438195i | ||||
\(269\) | −25.1995 | −1.53644 | −0.768220 | − | 0.640186i | \(-0.778857\pi\) | ||||
−0.768220 | + | 0.640186i | \(0.778857\pi\) | |||||||
\(270\) | −0.106818 | − | 2.23352i | −0.00650076 | − | 0.135927i | ||||
\(271\) | 9.81317 | − | 16.9969i | 0.596108 | − | 1.03249i | −0.397282 | − | 0.917697i | \(-0.630047\pi\) |
0.993390 | − | 0.114792i | \(-0.0366201\pi\) | |||||||
\(272\) | 4.45383 | − | 2.57142i | 0.270053 | − | 0.155915i | ||||
\(273\) | 0.768209i | 0.0464941i | ||||||||
\(274\) | −1.90228 | + | 3.29484i | −0.114921 | + | 0.199049i | ||||
\(275\) | −2.15202 | + | 4.71698i | −0.129772 | + | 0.284445i | ||||
\(276\) | −2.11955 | + | 3.67116i | −0.127582 | + | 0.220978i | ||||
\(277\) | −8.48886 | + | 4.90105i | −0.510046 | + | 0.294475i | −0.732853 | − | 0.680387i | \(-0.761812\pi\) |
0.222807 | + | 0.974863i | \(0.428478\pi\) | |||||||
\(278\) | −12.9448 | + | 7.47368i | −0.776377 | + | 0.448242i | ||||
\(279\) | 0.0743676 | − | 0.128809i | 0.00445227 | − | 0.00771156i | ||||
\(280\) | −0.697968 | − | 0.359661i | −0.0417116 | − | 0.0214938i | ||||
\(281\) | 6.23548 | − | 10.8002i | 0.371978 | − | 0.644285i | −0.617892 | − | 0.786263i | \(-0.712013\pi\) |
0.989870 | + | 0.141979i | \(0.0453464\pi\) | |||||||
\(282\) | − | 8.96463i | − | 0.533836i | ||||||
\(283\) | −5.25871 | + | 3.03612i | −0.312598 | + | 0.180479i | −0.648088 | − | 0.761565i | \(-0.724431\pi\) |
0.335490 | + | 0.942044i | \(0.391098\pi\) | |||||||
\(284\) | 5.35314 | − | 9.27190i | 0.317650 | − | 0.550186i | ||||
\(285\) | −18.3192 | + | 0.876120i | −1.08514 | + | 0.0518969i | ||||
\(286\) | 2.26854 | 0.134142 | ||||||||
\(287\) | −3.38394 | − | 1.95372i | −0.199748 | − | 0.115324i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 4.72441 | + | 8.18292i | 0.277906 | + | 0.481348i | ||||
\(290\) | 7.14841 | − | 0.341875i | 0.419769 | − | 0.0200756i | ||||
\(291\) | 7.74275 | + | 13.4108i | 0.453888 | + | 0.786157i | ||||
\(292\) | −7.38088 | + | 4.26135i | −0.431933 | + | 0.249377i | ||||
\(293\) | −11.4814 | + | 6.62880i | −0.670751 | + | 0.387258i | −0.796361 | − | 0.604821i | \(-0.793245\pi\) |
0.125610 | + | 0.992080i | \(0.459911\pi\) | |||||||
\(294\) | 3.43835 | − | 5.95539i | 0.200529 | − | 0.347326i | ||||
\(295\) | −1.17426 | − | 24.5530i | −0.0683678 | − | 1.42953i | ||||
\(296\) | 2.12543 | + | 5.69935i | 0.123538 | + | 0.331268i | ||||
\(297\) | 1.03694i | 0.0601694i | ||||||||
\(298\) | −18.3812 | − | 10.6124i | −1.06479 | − | 0.614759i | ||||
\(299\) | 4.63698 | + | 8.03149i | 0.268164 | + | 0.464473i | ||||
\(300\) | 4.07178 | − | 2.90182i | 0.235085 | − | 0.167537i | ||||
\(301\) | −1.11369 | − | 1.92897i | −0.0641921 | − | 0.111184i | ||||
\(302\) | 21.9337i | 1.26214i | ||||||||
\(303\) | −5.14164 | + | 2.96853i | −0.295379 | + | 0.170537i | ||||
\(304\) | −8.20196 | −0.470415 | ||||||||
\(305\) | −4.57406 | − | 2.35700i | −0.261910 | − | 0.134961i | ||||
\(306\) | 5.14284 | 0.293997 | ||||||||
\(307\) | − | 24.4956i | − | 1.39804i | −0.715104 | − | 0.699018i | \(-0.753621\pi\) | ||
0.715104 | − | 0.699018i | \(-0.246379\pi\) | |||||||
\(308\) | 0.315334 | + | 0.182058i | 0.0179678 | + | 0.0103737i | ||||
\(309\) | −6.51086 | − | 11.2771i | −0.370390 | − | 0.641534i | ||||
\(310\) | 0.332202 | − | 0.0158877i | 0.0188678 | − | 0.000902359i | ||||
\(311\) | 12.5340 | − | 21.7096i | 0.710740 | − | 1.23104i | −0.253840 | − | 0.967246i | \(-0.581694\pi\) |
0.964580 | − | 0.263791i | \(-0.0849730\pi\) | |||||||
\(312\) | −1.89463 | − | 1.09386i | −0.107262 | − | 0.0619278i | ||||
\(313\) | −27.0113 | − | 15.5950i | −1.52677 | − | 0.881482i | −0.999495 | − | 0.0317875i | \(-0.989880\pi\) |
−0.527276 | − | 0.849694i | \(-0.676787\pi\) | |||||||
\(314\) | −10.2945 | − | 17.8306i | −0.580952 | − | 1.00624i | ||||
\(315\) | −0.424628 | − | 0.660459i | −0.0239251 | − | 0.0372127i | ||||
\(316\) | −4.72489 | + | 8.18375i | −0.265796 | + | 0.460372i | ||||
\(317\) | −3.95290 | − | 2.28221i | −0.222017 | − | 0.128182i | 0.384867 | − | 0.922972i | \(-0.374247\pi\) |
−0.606884 | + | 0.794790i | \(0.707581\pi\) | |||||||
\(318\) | 3.86558 | + | 2.23180i | 0.216771 | + | 0.125153i | ||||
\(319\) | −3.31875 | −0.185814 | ||||||||
\(320\) | 1.88087 | − | 1.20927i | 0.105144 | − | 0.0676000i | ||||
\(321\) | 0.788474 | − | 1.36568i | 0.0440083 | − | 0.0762247i | ||||
\(322\) | 1.48854i | 0.0829529i | ||||||||
\(323\) | − | 42.1814i | − | 2.34703i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −1.04390 | − | 10.8887i | −0.0579050 | − | 0.603996i | ||||
\(326\) | −2.61394 | − | 4.52748i | −0.144773 | − | 0.250754i | ||||
\(327\) | − | 10.2130i | − | 0.564778i | ||||||
\(328\) | 9.63687 | − | 5.56385i | 0.532107 | − | 0.307212i | ||||
\(329\) | −1.57394 | − | 2.72615i | −0.0867743 | − | 0.150298i | ||||
\(330\) | −1.95035 | + | 1.25394i | −0.107363 | + | 0.0690269i | ||||
\(331\) | −6.08628 | + | 10.5418i | −0.334532 | + | 0.579427i | −0.983395 | − | 0.181479i | \(-0.941912\pi\) |
0.648863 | + | 0.760906i | \(0.275245\pi\) | |||||||
\(332\) | − | 4.39417i | − | 0.241161i | ||||||
\(333\) | −1.00900 | + | 5.99849i | −0.0552926 | + | 0.328715i | ||||
\(334\) | −7.64767 | −0.418462 | ||||||||
\(335\) | −14.6950 | + | 28.5176i | −0.802876 | + | 1.55809i | ||||
\(336\) | −0.175573 | − | 0.304101i | −0.00957827 | − | 0.0165901i | ||||
\(337\) | 25.8863 | − | 14.9455i | 1.41012 | − | 0.814131i | 0.414718 | − | 0.909950i | \(-0.363880\pi\) |
0.995399 | + | 0.0958189i | \(0.0305470\pi\) | |||||||
\(338\) | 7.11341 | − | 4.10693i | 0.386919 | − | 0.223388i | ||||
\(339\) | 2.91565 | 0.158356 | ||||||||
\(340\) | 6.21906 | + | 9.67302i | 0.337276 | + | 0.524593i | ||||
\(341\) | −0.154229 | −0.00835200 | ||||||||
\(342\) | −7.10310 | − | 4.10098i | −0.384092 | − | 0.221756i | ||||
\(343\) | − | 4.87274i | − | 0.263103i | ||||||
\(344\) | 6.34319 | 0.342002 | ||||||||
\(345\) | −8.42600 | − | 4.34189i | −0.453641 | − | 0.233759i | ||||
\(346\) | 4.90756 | + | 8.50015i | 0.263832 | + | 0.456971i | ||||
\(347\) | − | 9.15356i | − | 0.491389i | −0.969347 | − | 0.245695i | \(-0.920984\pi\) | ||
0.969347 | − | 0.245695i | \(-0.0790160\pi\) | |||||||
\(348\) | 2.77173 | + | 1.60026i | 0.148580 | + | 0.0857830i | ||||
\(349\) | 7.08124 | − | 12.2651i | 0.379050 | − | 0.656534i | −0.611874 | − | 0.790955i | \(-0.709584\pi\) |
0.990924 | + | 0.134421i | \(0.0429175\pi\) | |||||||
\(350\) | 0.728752 | − | 1.59734i | 0.0389534 | − | 0.0853815i | ||||
\(351\) | −1.09386 | − | 1.89463i | −0.0583861 | − | 0.101128i | ||||
\(352\) | −0.898016 | + | 0.518470i | −0.0478644 | + | 0.0276345i | ||||
\(353\) | 22.9078 | + | 13.2258i | 1.21926 | + | 0.703939i | 0.964759 | − | 0.263134i | \(-0.0847562\pi\) |
0.254499 | + | 0.967073i | \(0.418090\pi\) | |||||||
\(354\) | 5.49650 | − | 9.52022i | 0.292136 | − | 0.505994i | ||||
\(355\) | 21.2807 | + | 10.9659i | 1.12946 | + | 0.582010i | ||||
\(356\) | 4.21871 | 0.223591 | ||||||||
\(357\) | 1.56394 | − | 0.902942i | 0.0827726 | − | 0.0477888i | ||||
\(358\) | −4.91193 | − | 2.83591i | −0.259604 | − | 0.149882i | ||||
\(359\) | −5.09170 | −0.268729 | −0.134365 | − | 0.990932i | \(-0.542899\pi\) | ||||
−0.134365 | + | 0.990932i | \(0.542899\pi\) | |||||||
\(360\) | 2.23352 | − | 0.106818i | 0.117717 | − | 0.00562982i | ||||
\(361\) | −24.1361 | + | 41.8049i | −1.27032 | + | 2.20026i | ||||
\(362\) | 16.8007i | 0.883024i | ||||||||
\(363\) | −8.59509 | + | 4.96238i | −0.451125 | + | 0.260457i | ||||
\(364\) | −0.768209 | −0.0402651 | ||||||||
\(365\) | −10.3062 | − | 16.0301i | −0.539452 | − | 0.839055i | ||||
\(366\) | −1.15060 | − | 1.99289i | −0.0601427 | − | 0.104170i | ||||
\(367\) | −8.68282 | + | 5.01303i | −0.453239 | + | 0.261678i | −0.709197 | − | 0.705010i | \(-0.750942\pi\) |
0.255958 | + | 0.966688i | \(0.417609\pi\) | |||||||
\(368\) | −3.67116 | − | 2.11955i | −0.191372 | − | 0.110489i | ||||
\(369\) | 11.1277 | 0.579285 | ||||||||
\(370\) | −12.5025 | + | 5.35598i | −0.649976 | + | 0.278444i | ||||
\(371\) | 1.56737 | 0.0813738 | ||||||||
\(372\) | 0.128809 | + | 0.0743676i | 0.00667841 | + | 0.00385578i | ||||
\(373\) | −26.2347 | + | 15.1466i | −1.35838 | + | 0.784262i | −0.989406 | − | 0.145176i | \(-0.953625\pi\) |
−0.368976 | + | 0.929439i | \(0.620292\pi\) | |||||||
\(374\) | −2.66641 | − | 4.61835i | −0.137877 | − | 0.238809i | ||||
\(375\) | 6.91621 | + | 8.78442i | 0.357151 | + | 0.453626i | ||||
\(376\) | 8.96463 | 0.462316 | ||||||||
\(377\) | 6.06379 | − | 3.50093i | 0.312301 | − | 0.180307i | ||||
\(378\) | − | 0.351145i | − | 0.0180610i | ||||||
\(379\) | 0.592452 | − | 1.02616i | 0.0304322 | − | 0.0527101i | −0.850408 | − | 0.526123i | \(-0.823645\pi\) |
0.880840 | + | 0.473413i | \(0.156978\pi\) | |||||||
\(380\) | −0.876120 | − | 18.3192i | −0.0449440 | − | 0.939755i | ||||
\(381\) | 14.3308 | 0.734191 | ||||||||
\(382\) | 2.48504 | + | 1.43474i | 0.127146 | + | 0.0734075i | ||||
\(383\) | 27.4338 | − | 15.8389i | 1.40180 | − | 0.809332i | 0.407226 | − | 0.913327i | \(-0.366496\pi\) |
0.994578 | + | 0.103996i | \(0.0331628\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.372946 | + | 0.723751i | −0.0190071 | + | 0.0368858i | ||||
\(386\) | 6.51379 | − | 11.2822i | 0.331543 | − | 0.574250i | ||||
\(387\) | 5.49337 | + | 3.17160i | 0.279244 | + | 0.161221i | ||||
\(388\) | −13.4108 | + | 7.74275i | −0.680832 | + | 0.393078i | ||||
\(389\) | 8.19649 | + | 14.1967i | 0.415578 | + | 0.719803i | 0.995489 | − | 0.0948773i | \(-0.0302459\pi\) |
−0.579911 | + | 0.814680i | \(0.696913\pi\) | |||||||
\(390\) | 2.24078 | − | 4.34852i | 0.113466 | − | 0.220196i | ||||
\(391\) | 10.9005 | − | 18.8802i | 0.551261 | − | 0.954813i | ||||
\(392\) | 5.95539 | + | 3.43835i | 0.300793 | + | 0.173663i | ||||
\(393\) | 9.28954i | 0.468595i | ||||||||
\(394\) | −0.690124 | − | 1.19533i | −0.0347679 | − | 0.0602198i | ||||
\(395\) | −18.7832 | − | 9.67894i | −0.945088 | − | 0.487001i | ||||
\(396\) | −1.03694 | −0.0521082 | ||||||||
\(397\) | 4.91832i | 0.246843i | 0.992354 | + | 0.123422i | \(0.0393868\pi\) | ||||
−0.992354 | + | 0.123422i | \(0.960613\pi\) | |||||||
\(398\) | 3.52748 | + | 2.03659i | 0.176816 | + | 0.102085i | ||||
\(399\) | −2.88008 | −0.144184 | ||||||||
\(400\) | 2.90182 | + | 4.07178i | 0.145091 | + | 0.203589i | ||||
\(401\) | 30.0213 | 1.49919 | 0.749596 | − | 0.661896i | \(-0.230248\pi\) | ||||
0.749596 | + | 0.661896i | \(0.230248\pi\) | |||||||
\(402\) | −12.4250 | + | 7.17356i | −0.619701 | + | 0.357785i | ||||
\(403\) | 0.281798 | − | 0.162696i | 0.0140373 | − | 0.00810446i | ||||
\(404\) | −2.96853 | − | 5.14164i | −0.147690 | − | 0.255806i | ||||
\(405\) | 1.98769 | + | 1.02425i | 0.0987691 | + | 0.0508954i | ||||
\(406\) | 1.12385 | 0.0557756 | ||||||||
\(407\) | 5.90988 | − | 2.20394i | 0.292942 | − | 0.109245i | ||||
\(408\) | 5.14284i | 0.254609i | ||||||||
\(409\) | −14.8741 | + | 25.7626i | −0.735475 | + | 1.27388i | 0.219040 | + | 0.975716i | \(0.429707\pi\) |
−0.954515 | + | 0.298164i | \(0.903626\pi\) | |||||||
\(410\) | 13.4563 | + | 20.9298i | 0.664561 | + | 1.03365i | ||||
\(411\) | −1.90228 | − | 3.29484i | −0.0938324 | − | 0.162522i | ||||
\(412\) | 11.2771 | − | 6.51086i | 0.555585 | − | 0.320767i | ||||
\(413\) | − | 3.86014i | − | 0.189945i | ||||||
\(414\) | −2.11955 | − | 3.67116i | −0.104170 | − | 0.180428i | ||||
\(415\) | 9.81444 | − | 0.469378i | 0.481772 | − | 0.0230409i | ||||
\(416\) | 1.09386 | − | 1.89463i | 0.0536310 | − | 0.0928916i | ||||
\(417\) | − | 14.9474i | − | 0.731976i | ||||||
\(418\) | 8.50494i | 0.415990i | ||||||||
\(419\) | 12.3182 | − | 21.3357i | 0.601782 | − | 1.04232i | −0.390769 | − | 0.920489i | \(-0.627791\pi\) |
0.992551 | − | 0.121829i | \(-0.0388758\pi\) | |||||||
\(420\) | 0.660459 | − | 0.424628i | 0.0322271 | − | 0.0207197i | ||||
\(421\) | −39.3615 | −1.91836 | −0.959182 | − | 0.282790i | \(-0.908740\pi\) | ||||
−0.959182 | + | 0.282790i | \(0.908740\pi\) | |||||||
\(422\) | 22.7705 | + | 13.1465i | 1.10845 | + | 0.639964i | ||||
\(423\) | 7.76360 | + | 4.48232i | 0.377479 | + | 0.217938i | ||||
\(424\) | −2.23180 | + | 3.86558i | −0.108386 | + | 0.187729i | ||||
\(425\) | −20.9405 | + | 14.9236i | −1.01577 | + | 0.723902i | ||||
\(426\) | 5.35314 | + | 9.27190i | 0.259360 | + | 0.449225i | ||||
\(427\) | −0.699795 | − | 0.404027i | −0.0338655 | − | 0.0195522i | ||||
\(428\) | 1.36568 | + | 0.788474i | 0.0660125 | + | 0.0381123i | ||||
\(429\) | −1.13427 | + | 1.96461i | −0.0547630 | + | 0.0948524i | ||||
\(430\) | 0.677570 | + | 14.1676i | 0.0326753 | + | 0.683223i | ||||
\(431\) | 5.50220 | + | 9.53008i | 0.265032 | + | 0.459048i | 0.967572 | − | 0.252596i | \(-0.0812843\pi\) |
−0.702540 | + | 0.711644i | \(0.747951\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 16.8494i | 0.809731i | 0.914376 | + | 0.404865i | \(0.132682\pi\) | ||||
−0.914376 | + | 0.404865i | \(0.867318\pi\) | |||||||
\(434\) | 0.0522277 | 0.00250701 | ||||||||
\(435\) | −3.27813 | + | 6.36164i | −0.157175 | + | 0.305017i | ||||
\(436\) | 10.2130 | 0.489112 | ||||||||
\(437\) | −30.1107 | + | 17.3844i | −1.44039 | + | 0.831610i | ||||
\(438\) | − | 8.52271i | − | 0.407231i | ||||||
\(439\) | 1.92873 | + | 3.34066i | 0.0920534 | + | 0.159441i | 0.908375 | − | 0.418156i | \(-0.137324\pi\) |
−0.816322 | + | 0.577598i | \(0.803990\pi\) | |||||||
\(440\) | −1.25394 | − | 1.95035i | −0.0597790 | − | 0.0929793i | ||||
\(441\) | 3.43835 | + | 5.95539i | 0.163731 | + | 0.283590i | ||||
\(442\) | 9.74376 | + | 5.62556i | 0.463463 | + | 0.267581i | ||||
\(443\) | − | 18.7295i | − | 0.889866i | −0.895564 | − | 0.444933i | \(-0.853228\pi\) | ||
0.895564 | − | 0.444933i | \(-0.146772\pi\) | |||||||
\(444\) | −5.99849 | − | 1.00900i | −0.284676 | − | 0.0478848i | ||||
\(445\) | 0.450636 | + | 9.42256i | 0.0213622 | + | 0.446672i | ||||
\(446\) | 3.87029 | − | 6.70354i | 0.183264 | − | 0.317422i | ||||
\(447\) | 18.3812 | − | 10.6124i | 0.869401 | − | 0.501949i | ||||
\(448\) | 0.304101 | − | 0.175573i | 0.0143674 | − | 0.00829503i | ||||
\(449\) | 13.7190 | + | 23.7620i | 0.647439 | + | 1.12140i | 0.983732 | + | 0.179640i | \(0.0574933\pi\) |
−0.336293 | + | 0.941757i | \(0.609173\pi\) | |||||||
\(450\) | 0.477161 | + | 4.97718i | 0.0224936 | + | 0.234626i | ||||
\(451\) | −5.76937 | − | 9.99285i | −0.271669 | − | 0.470545i | ||||
\(452\) | 2.91565i | 0.137141i | ||||||||
\(453\) | −18.9951 | − | 10.9668i | −0.892469 | − | 0.515267i | ||||
\(454\) | 8.21419 | 0.385511 | ||||||||
\(455\) | −0.0820589 | − | 1.71581i | −0.00384698 | − | 0.0804383i | ||||
\(456\) | 4.10098 | − | 7.10310i | 0.192046 | − | 0.332633i | ||||
\(457\) | 8.23909 | − | 4.75684i | 0.385408 | − | 0.222516i | −0.294760 | − | 0.955571i | \(-0.595240\pi\) |
0.680169 | + | 0.733056i | \(0.261906\pi\) | |||||||
\(458\) | 15.0794i | 0.704612i | ||||||||
\(459\) | −2.57142 | + | 4.45383i | −0.120024 | + | 0.207887i | ||||
\(460\) | 4.34189 | − | 8.42600i | 0.202442 | − | 0.392864i | ||||
\(461\) | −12.8493 | + | 22.2556i | −0.598451 | + | 1.03655i | 0.394599 | + | 0.918854i | \(0.370884\pi\) |
−0.993050 | + | 0.117694i | \(0.962450\pi\) | |||||||
\(462\) | −0.315334 | + | 0.182058i | −0.0146707 | + | 0.00847012i | ||||
\(463\) | 22.2273 | − | 12.8330i | 1.03299 | − | 0.596398i | 0.115151 | − | 0.993348i | \(-0.463265\pi\) |
0.917840 | + | 0.396950i | \(0.129931\pi\) | |||||||
\(464\) | −1.60026 | + | 2.77173i | −0.0742902 | + | 0.128674i | ||||
\(465\) | −0.152342 | + | 0.295640i | −0.00706470 | + | 0.0137100i | ||||
\(466\) | −2.82331 | + | 4.89011i | −0.130787 | + | 0.226530i | ||||
\(467\) | 38.2172i | 1.76848i | 0.467031 | + | 0.884241i | \(0.345324\pi\) | ||||
−0.467031 | + | 0.884241i | \(0.654676\pi\) | |||||||
\(468\) | 1.89463 | − | 1.09386i | 0.0875791 | − | 0.0505638i | ||||
\(469\) | −2.51896 | + | 4.36297i | −0.116315 | + | 0.201463i | ||||
\(470\) | 0.957588 | + | 20.0226i | 0.0441702 | + | 0.923575i | ||||
\(471\) | 20.5890 | 0.948690 | ||||||||
\(472\) | 9.52022 | + | 5.49650i | 0.438204 | + | 0.252997i | ||||
\(473\) | − | 6.57751i | − | 0.302434i | ||||||
\(474\) | −4.72489 | − | 8.18375i | −0.217022 | − | 0.375892i | ||||
\(475\) | 40.8226 | − | 3.91365i | 1.87307 | − | 0.179571i | ||||
\(476\) | 0.902942 | + | 1.56394i | 0.0413863 | + | 0.0716832i | ||||
\(477\) | −3.86558 | + | 2.23180i | −0.176993 | + | 0.102187i | ||||
\(478\) | 9.91584 | − | 5.72492i | 0.453540 | − | 0.261852i | ||||
\(479\) | −6.20726 | + | 10.7513i | −0.283617 | + | 0.491239i | −0.972273 | − | 0.233850i | \(-0.924868\pi\) |
0.688656 | + | 0.725088i | \(0.258201\pi\) | |||||||
\(480\) | 0.106818 | + | 2.23352i | 0.00487557 | + | 0.101946i | ||||
\(481\) | −8.47319 | + | 10.2612i | −0.386344 | + | 0.467870i | ||||
\(482\) | 4.15689i | 0.189341i | ||||||||
\(483\) | −1.28911 | − | 0.744269i | −0.0586566 | − | 0.0338654i | ||||
\(484\) | −4.96238 | − | 8.59509i | −0.225563 | − | 0.390686i | ||||
\(485\) | −18.7261 | − | 29.1262i | −0.850307 | − | 1.32255i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | − | 12.0323i | − | 0.545236i | −0.962122 | − | 0.272618i | \(-0.912110\pi\) | ||
0.962122 | − | 0.272618i | \(-0.0878895\pi\) | |||||||
\(488\) | 1.99289 | − | 1.15060i | 0.0902141 | − | 0.0520851i | ||||
\(489\) | 5.22788 | 0.236413 | ||||||||
\(490\) | −7.04346 | + | 13.6687i | −0.318191 | + | 0.617491i | ||||
\(491\) | 5.77157 | 0.260467 | 0.130234 | − | 0.991483i | \(-0.458427\pi\) | ||||
0.130234 | + | 0.991483i | \(0.458427\pi\) | |||||||
\(492\) | 11.1277i | 0.501675i | ||||||||
\(493\) | −14.2546 | − | 8.22989i | −0.641994 | − | 0.370655i | ||||
\(494\) | −8.97181 | − | 15.5396i | −0.403661 | − | 0.699161i | ||||
\(495\) | −0.110764 | − | 2.31602i | −0.00497848 | − | 0.104097i | ||||
\(496\) | −0.0743676 | + | 0.128809i | −0.00333920 | + | 0.00578367i | ||||
\(497\) | 3.25579 | + | 1.87973i | 0.146042 | + | 0.0843174i | ||||
\(498\) | 3.80546 | + | 2.19708i | 0.170527 | + | 0.0984537i | ||||
\(499\) | 2.36226 | + | 4.09155i | 0.105749 | + | 0.183163i | 0.914044 | − | 0.405615i | \(-0.132943\pi\) |
−0.808295 | + | 0.588778i | \(0.799609\pi\) | |||||||
\(500\) | −8.78442 | + | 6.91621i | −0.392851 | + | 0.309302i | ||||
\(501\) | 3.82383 | − | 6.62307i | 0.170836 | − | 0.295897i | ||||
\(502\) | −21.5141 | − | 12.4212i | −0.960220 | − | 0.554383i | ||||
\(503\) | 34.0945 | + | 19.6845i | 1.52020 | + | 0.877686i | 0.999716 | + | 0.0238131i | \(0.00758066\pi\) |
0.520481 | + | 0.853873i | \(0.325753\pi\) | |||||||
\(504\) | 0.351145 | 0.0156413 | ||||||||
\(505\) | 11.1668 | − | 7.17947i | 0.496918 | − | 0.319482i | ||||
\(506\) | −2.19784 | + | 3.80677i | −0.0977060 | + | 0.169232i | ||||
\(507\) | 8.21386i | 0.364790i | ||||||||
\(508\) | 14.3308i | 0.635828i | ||||||||
\(509\) | −3.14558 | + | 5.44830i | −0.139425 | + | 0.241492i | −0.927279 | − | 0.374370i | \(-0.877859\pi\) |
0.787854 | + | 0.615862i | \(0.211192\pi\) | |||||||
\(510\) | −11.4866 | + | 0.549350i | −0.508636 | + | 0.0243256i | ||||
\(511\) | −1.49635 | − | 2.59176i | −0.0661948 | − | 0.114653i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 7.10310 | − | 4.10098i | 0.313610 | − | 0.181063i | ||||
\(514\) | 2.09399 | + | 3.62690i | 0.0923621 | + | 0.159976i | ||||
\(515\) | 15.7467 | + | 24.4922i | 0.693883 | + | 1.07925i | ||||
\(516\) | −3.17160 | + | 5.49337i | −0.139622 | + | 0.241832i | ||||
\(517\) | − | 9.29578i | − | 0.408828i | ||||||
\(518\) | −2.00130 | + | 0.746335i | −0.0879320 | + | 0.0327921i | ||||
\(519\) | −9.81513 | −0.430836 | ||||||||
\(520\) | 4.34852 | + | 2.24078i | 0.190695 | + | 0.0982646i | ||||
\(521\) | 5.15531 | + | 8.92926i | 0.225858 | + | 0.391198i | 0.956577 | − | 0.291481i | \(-0.0941480\pi\) |
−0.730718 | + | 0.682679i | \(0.760815\pi\) | |||||||
\(522\) | −2.77173 | + | 1.60026i | −0.121315 | + | 0.0700415i | ||||
\(523\) | 11.9515 | − | 6.90023i | 0.522605 | − | 0.301726i | −0.215395 | − | 0.976527i | \(-0.569104\pi\) |
0.738000 | + | 0.674801i | \(0.235771\pi\) | |||||||
\(524\) | −9.28954 | −0.405816 | ||||||||
\(525\) | 1.01896 | + | 1.42979i | 0.0444711 | + | 0.0624011i | ||||
\(526\) | 6.28646 | 0.274103 | ||||||||
\(527\) | −0.662442 | − | 0.382461i | −0.0288564 | − | 0.0166603i | ||||
\(528\) | − | 1.03694i | − | 0.0451270i | ||||||
\(529\) | 5.03010 | 0.218700 | ||||||||
\(530\) | −8.87223 | − | 4.57183i | −0.385385 | − | 0.198588i | ||||
\(531\) | 5.49650 | + | 9.52022i | 0.238528 | + | 0.413142i | ||||
\(532\) | − | 2.88008i | − | 0.124867i | ||||||
\(533\) | 21.0828 | + | 12.1722i | 0.913198 | + | 0.527235i | ||||
\(534\) | −2.10936 | + | 3.65351i | −0.0912808 | + | 0.158103i | ||||
\(535\) | −1.61519 | + | 3.13448i | −0.0698307 | + | 0.135516i | ||||
\(536\) | −7.17356 | − | 12.4250i | −0.309851 | − | 0.536677i | ||||
\(537\) | 4.91193 | − | 2.83591i | 0.211966 | − | 0.122378i | ||||
\(538\) | 21.8234 | + | 12.5997i | 0.940873 | + | 0.543214i | ||||
\(539\) | 3.56536 | − | 6.17539i | 0.153571 | − | 0.265993i | ||||
\(540\) | −1.02425 | + | 1.98769i | −0.0440767 | + | 0.0855366i | ||||
\(541\) | −31.7423 | −1.36471 | −0.682354 | − | 0.731022i | \(-0.739044\pi\) | ||||
−0.682354 | + | 0.731022i | \(0.739044\pi\) | |||||||
\(542\) | −16.9969 | + | 9.81317i | −0.730080 | + | 0.421512i | ||||
\(543\) | −14.5498 | − | 8.40034i | −0.624392 | − | 0.360493i | ||||
\(544\) | −5.14284 | −0.220498 | ||||||||
\(545\) | 1.09093 | + | 22.8108i | 0.0467304 | + | 0.977108i | ||||
\(546\) | 0.384105 | − | 0.665289i | 0.0164382 | − | 0.0284717i | ||||
\(547\) | 35.1291i | 1.50201i | 0.660295 | + | 0.751007i | \(0.270431\pi\) | ||||
−0.660295 | + | 0.751007i | \(0.729569\pi\) | |||||||
\(548\) | 3.29484 | − | 1.90228i | 0.140749 | − | 0.0812612i | ||||
\(549\) | 2.30120 | 0.0982126 | ||||||||
\(550\) | 4.22219 | − | 3.00902i | 0.180035 | − | 0.128305i | ||||
\(551\) | 13.1253 | + | 22.7336i | 0.559155 | + | 0.968485i | ||||
\(552\) | 3.67116 | − | 2.11955i | 0.156255 | − | 0.0902139i | ||||
\(553\) | −2.87369 | − | 1.65912i | −0.122202 | − | 0.0705531i | ||||
\(554\) | 9.80209 | 0.416451 | ||||||||
\(555\) | 1.61286 | − | 13.5055i | 0.0684619 | − | 0.573277i | ||||
\(556\) | 14.9474 | 0.633909 | ||||||||
\(557\) | −19.8368 | − | 11.4528i | −0.840514 | − | 0.485271i | 0.0169250 | − | 0.999857i | \(-0.494612\pi\) |
−0.857439 | + | 0.514586i | \(0.827946\pi\) | |||||||
\(558\) | −0.128809 | + | 0.0743676i | −0.00545290 | + | 0.00314823i | ||||
\(559\) | 6.93858 | + | 12.0180i | 0.293471 | + | 0.508306i | ||||
\(560\) | 0.424628 | + | 0.660459i | 0.0179438 | + | 0.0279095i | ||||
\(561\) | 5.33282 | 0.225152 | ||||||||
\(562\) | −10.8002 | + | 6.23548i | −0.455578 | + | 0.263028i | ||||
\(563\) | 4.77144i | 0.201092i | 0.994932 | + | 0.100546i | \(0.0320590\pi\) | ||||
−0.994932 | + | 0.100546i | \(0.967941\pi\) | |||||||
\(564\) | −4.48232 | + | 7.76360i | −0.188740 | + | 0.326906i | ||||
\(565\) | −6.51215 | + | 0.311445i | −0.273968 | + | 0.0131026i | ||||
\(566\) | 6.07224 | 0.255235 | ||||||||
\(567\) | 0.304101 | + | 0.175573i | 0.0127710 | + | 0.00737336i | ||||
\(568\) | −9.27190 | + | 5.35314i | −0.389040 | + | 0.224613i | ||||
\(569\) | −8.99096 | −0.376920 | −0.188460 | − | 0.982081i | \(-0.560350\pi\) | ||||
−0.188460 | + | 0.982081i | \(0.560350\pi\) | |||||||
\(570\) | 16.3029 | + | 8.40086i | 0.682855 | + | 0.351873i | ||||
\(571\) | 5.84667 | − | 10.1267i | 0.244676 | − | 0.423791i | −0.717365 | − | 0.696698i | \(-0.754652\pi\) |
0.962040 | + | 0.272907i | \(0.0879852\pi\) | |||||||
\(572\) | −1.96461 | − | 1.13427i | −0.0821446 | − | 0.0474262i | ||||
\(573\) | −2.48504 | + | 1.43474i | −0.103814 | + | 0.0599370i | ||||
\(574\) | 1.95372 | + | 3.38394i | 0.0815467 | + | 0.141243i | ||||
\(575\) | 19.2834 | + | 8.79762i | 0.804173 | + | 0.366886i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 20.6234 | + | 11.9069i | 0.858564 | + | 0.495692i | 0.863531 | − | 0.504296i | \(-0.168248\pi\) |
−0.00496739 | + | 0.999988i | \(0.501581\pi\) | |||||||
\(578\) | − | 9.44882i | − | 0.393019i | ||||||
\(579\) | 6.51379 | + | 11.2822i | 0.270704 | + | 0.468873i | ||||
\(580\) | −6.36164 | − | 3.27813i | −0.264153 | − | 0.136117i | ||||
\(581\) | 1.54299 | 0.0640141 | ||||||||
\(582\) | − | 15.4855i | − | 0.641895i | ||||||
\(583\) | 4.00838 | + | 2.31424i | 0.166010 | + | 0.0958459i | ||||
\(584\) | 8.52271 | 0.352672 | ||||||||
\(585\) | 2.64554 | + | 4.11483i | 0.109380 | + | 0.170127i | ||||
\(586\) | 13.2576 | 0.547666 | ||||||||
\(587\) | 35.3186 | − | 20.3912i | 1.45776 | − | 0.841636i | 0.458856 | − | 0.888511i | \(-0.348259\pi\) |
0.998901 | + | 0.0468745i | \(0.0149261\pi\) | |||||||
\(588\) | −5.95539 | + | 3.43835i | −0.245596 | + | 0.141795i | ||||
\(589\) | 0.609960 | + | 1.05648i | 0.0251330 | + | 0.0435316i | ||||
\(590\) | −11.2596 | + | 21.8507i | −0.463550 | + | 0.899578i | ||||
\(591\) | 1.38025 | 0.0567758 | ||||||||
\(592\) | 1.00900 | − | 5.99849i | 0.0414694 | − | 0.246537i | ||||
\(593\) | 19.9212i | 0.818066i | 0.912519 | + | 0.409033i | \(0.134134\pi\) | ||||
−0.912519 | + | 0.409033i | \(0.865866\pi\) | |||||||
\(594\) | 0.518470 | − | 0.898016i | 0.0212731 | − | 0.0368461i | ||||
\(595\) | −3.39664 | + | 2.18379i | −0.139249 | + | 0.0895268i | ||||
\(596\) | 10.6124 | + | 18.3812i | 0.434701 | + | 0.752923i | ||||
\(597\) | −3.52748 | + | 2.03659i | −0.144370 | + | 0.0833521i | ||||
\(598\) | − | 9.27397i | − | 0.379241i | ||||||
\(599\) | 2.95130 | + | 5.11181i | 0.120587 | + | 0.208863i | 0.919999 | − | 0.391920i | \(-0.128189\pi\) |
−0.799412 | + | 0.600783i | \(0.794856\pi\) | |||||||
\(600\) | −4.97718 | + | 0.477161i | −0.203193 | + | 0.0194800i | ||||
\(601\) | 8.64560 | − | 14.9746i | 0.352661 | − | 0.610827i | −0.634054 | − | 0.773289i | \(-0.718610\pi\) |
0.986715 | + | 0.162462i | \(0.0519435\pi\) | |||||||
\(602\) | 2.22738i | 0.0907813i | ||||||||
\(603\) | − | 14.3471i | − | 0.584260i | ||||||
\(604\) | 10.9668 | − | 18.9951i | 0.446234 | − | 0.772901i | ||||
\(605\) | 18.6672 | − | 12.0017i | 0.758929 | − | 0.487937i | ||||
\(606\) | 5.93705 | 0.241176 | ||||||||
\(607\) | −35.1499 | − | 20.2938i | −1.42669 | − | 0.823700i | −0.429832 | − | 0.902909i | \(-0.641427\pi\) |
−0.996858 | + | 0.0792093i | \(0.974760\pi\) | |||||||
\(608\) | 7.10310 | + | 4.10098i | 0.288069 | + | 0.166317i | ||||
\(609\) | −0.561924 | + | 0.973281i | −0.0227703 | + | 0.0394393i | ||||
\(610\) | 2.78275 | + | 4.32825i | 0.112670 | + | 0.175246i | ||||
\(611\) | 9.80607 | + | 16.9846i | 0.396711 | + | 0.687124i | ||||
\(612\) | −4.45383 | − | 2.57142i | −0.180035 | − | 0.103944i | ||||
\(613\) | −31.0066 | − | 17.9017i | −1.25235 | − | 0.723042i | −0.280771 | − | 0.959775i | \(-0.590590\pi\) |
−0.971575 | + | 0.236733i | \(0.923923\pi\) | |||||||
\(614\) | −12.2478 | + | 21.2138i | −0.494280 | + | 0.856118i | ||||
\(615\) | −24.8539 | + | 1.18864i | −1.00220 | + | 0.0479307i | ||||
\(616\) | −0.182058 | − | 0.315334i | −0.00733534 | − | 0.0127052i | ||||
\(617\) | 29.3879 | + | 16.9671i | 1.18311 | + | 0.683070i | 0.956732 | − | 0.290970i | \(-0.0939779\pi\) |
0.226379 | + | 0.974039i | \(0.427311\pi\) | |||||||
\(618\) | 13.0217i | 0.523810i | ||||||||
\(619\) | 16.2711 | 0.653992 | 0.326996 | − | 0.945026i | \(-0.393964\pi\) | ||||
0.326996 | + | 0.945026i | \(0.393964\pi\) | |||||||
\(620\) | −0.295640 | − | 0.152342i | −0.0118732 | − | 0.00611821i | ||||
\(621\) | 4.23909 | 0.170109 | ||||||||
\(622\) | −21.7096 | + | 12.5340i | −0.870475 | + | 0.502569i | ||||
\(623\) | 1.48138i | 0.0593503i | ||||||||
\(624\) | 1.09386 | + | 1.89463i | 0.0437895 | + | 0.0758457i | ||||
\(625\) | −16.3858 | − | 18.8814i | −0.655432 | − | 0.755254i | ||||
\(626\) | 15.5950 | + | 27.0113i | 0.623302 | + | 1.07959i | ||||
\(627\) | −7.36549 | − | 4.25247i | −0.294149 | − | 0.169827i | ||||
\(628\) | 20.5890i | 0.821590i | ||||||||
\(629\) | 30.8493 | + | 5.18910i | 1.23004 | + | 0.206903i | ||||
\(630\) | 0.0375088 | + | 0.784288i | 0.00149439 | + | 0.0312468i | ||||
\(631\) | 21.2168 | − | 36.7486i | 0.844628 | − | 1.46294i | −0.0413166 | − | 0.999146i | \(-0.513155\pi\) |
0.885944 | − | 0.463792i | \(-0.153511\pi\) | |||||||
\(632\) | 8.18375 | − | 4.72489i | 0.325532 | − | 0.187946i | ||||
\(633\) | −22.7705 | + | 13.1465i | −0.905046 | + | 0.522528i | ||||
\(634\) | 2.28221 | + | 3.95290i | 0.0906381 | + | 0.156990i | ||||
\(635\) | −32.0081 | + | 1.53080i | −1.27020 | + | 0.0607478i | ||||
\(636\) | −2.23180 | − | 3.86558i | −0.0884964 | − | 0.153280i | ||||
\(637\) | 15.0443i | 0.596078i | ||||||||
\(638\) | 2.87412 | + | 1.65937i | 0.113787 | + | 0.0656952i | ||||
\(639\) | −10.7063 | −0.423534 | ||||||||
\(640\) | −2.23352 | + | 0.106818i | −0.0882874 | + | 0.00422237i | ||||
\(641\) | −6.92226 | + | 11.9897i | −0.273413 | + | 0.473565i | −0.969733 | − | 0.244166i | \(-0.921486\pi\) |
0.696321 | + | 0.717731i | \(0.254819\pi\) | |||||||
\(642\) | −1.36568 | + | 0.788474i | −0.0538990 | + | 0.0311186i | ||||
\(643\) | − | 10.3728i | − | 0.409062i | −0.978860 | − | 0.204531i | \(-0.934433\pi\) | ||
0.978860 | − | 0.204531i | \(-0.0655669\pi\) | |||||||
\(644\) | 0.744269 | − | 1.28911i | 0.0293283 | − | 0.0507981i | ||||
\(645\) | −12.6083 | − | 6.49702i | −0.496451 | − | 0.255820i | ||||
\(646\) | −21.0907 | + | 36.5301i | −0.829802 | + | 1.43726i | ||||
\(647\) | 1.70856 | − | 0.986437i | 0.0671704 | − | 0.0387808i | −0.466039 | − | 0.884764i | \(-0.654319\pi\) |
0.533209 | + | 0.845984i | \(0.320986\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 5.69954 | − | 9.87190i | 0.223727 | − | 0.387506i | ||||
\(650\) | −4.54031 | + | 9.95184i | −0.178086 | + | 0.390343i | ||||
\(651\) | −0.0261138 | + | 0.0452305i | −0.00102348 | + | 0.00177272i | ||||
\(652\) | 5.22788i | 0.204740i | ||||||||
\(653\) | 20.5764 | − | 11.8798i | 0.805218 | − | 0.464893i | −0.0400743 | − | 0.999197i | \(-0.512759\pi\) |
0.845293 | + | 0.534304i | \(0.179426\pi\) | |||||||
\(654\) | −5.10648 | + | 8.84469i | −0.199679 | + | 0.345855i | ||||
\(655\) | −0.992294 | − | 20.7483i | −0.0387721 | − | 0.810705i | ||||
\(656\) | −11.1277 | −0.434463 | ||||||||
\(657\) | 7.38088 | + | 4.26135i | 0.287956 | + | 0.166251i | ||||
\(658\) | 3.14789i | 0.122717i | ||||||||
\(659\) | 0.0838988 | + | 0.145317i | 0.00326824 | + | 0.00566075i | 0.867655 | − | 0.497167i | \(-0.165626\pi\) |
−0.864387 | + | 0.502828i | \(0.832293\pi\) | |||||||
\(660\) | 2.31602 | − | 0.110764i | 0.0901510 | − | 0.00431149i | ||||
\(661\) | 11.8069 | + | 20.4502i | 0.459237 | + | 0.795421i | 0.998921 | − | 0.0464464i | \(-0.0147897\pi\) |
−0.539684 | + | 0.841868i | \(0.681456\pi\) | |||||||
\(662\) | 10.5418 | − | 6.08628i | 0.409717 | − | 0.236550i | ||||
\(663\) | −9.74376 | + | 5.62556i | −0.378416 | + | 0.218479i | ||||
\(664\) | −2.19708 | + | 3.80546i | −0.0852634 | + | 0.147681i | ||||
\(665\) | 6.43270 | − | 0.307645i | 0.249449 | − | 0.0119300i | ||||
\(666\) | 3.87306 | − | 4.69035i | 0.150078 | − | 0.181747i | ||||
\(667\) | 13.5673i | 0.525328i | ||||||||
\(668\) | 6.62307 | + | 3.82383i | 0.256254 | + | 0.147949i | ||||
\(669\) | 3.87029 | + | 6.70354i | 0.149634 | + | 0.259174i | ||||
\(670\) | 26.9851 | − | 17.3495i | 1.04253 | − | 0.670269i | ||||
\(671\) | −1.19310 | − | 2.06651i | −0.0460591 | − | 0.0797768i | ||||
\(672\) | 0.351145i | 0.0135457i | ||||||||
\(673\) | −0.949348 | + | 0.548106i | −0.0365947 | + | 0.0211279i | −0.518186 | − | 0.855268i | \(-0.673392\pi\) |
0.481591 | + | 0.876396i | \(0.340059\pi\) | |||||||
\(674\) | −29.8909 | −1.15136 | ||||||||
\(675\) | −4.54894 | − | 2.07536i | −0.175089 | − | 0.0798805i | ||||
\(676\) | −8.21386 | −0.315918 | ||||||||
\(677\) | − | 36.6324i | − | 1.40790i | −0.710251 | − | 0.703948i | \(-0.751419\pi\) | ||
0.710251 | − | 0.703948i | \(-0.248581\pi\) | |||||||
\(678\) | −2.52503 | − | 1.45783i | −0.0969732 | − | 0.0559875i | ||||
\(679\) | −2.71883 | − | 4.70915i | −0.104339 | − | 0.180721i | ||||
\(680\) | −0.549350 | − | 11.4866i | −0.0210666 | − | 0.440492i | ||||
\(681\) | −4.10709 | + | 7.11370i | −0.157384 | + | 0.272597i | ||||
\(682\) | 0.133567 | + | 0.0771147i | 0.00511453 | + | 0.00295288i | ||||
\(683\) | 0.469910 | + | 0.271303i | 0.0179806 | + | 0.0103811i | 0.508963 | − | 0.860788i | \(-0.330029\pi\) |
−0.490983 | + | 0.871169i | \(0.663362\pi\) | |||||||
\(684\) | 4.10098 | + | 7.10310i | 0.156805 | + | 0.271594i | ||||
\(685\) | 4.60071 | + | 7.15588i | 0.175784 | + | 0.273412i | ||||
\(686\) | −2.43637 | + | 4.21991i | −0.0930210 | + | 0.161117i | ||||
\(687\) | −13.0591 | − | 7.53968i | −0.498236 | − | 0.287657i | ||||
\(688\) | −5.49337 | − | 3.17160i | −0.209433 | − | 0.120916i | ||||
\(689\) | −9.76511 | −0.372021 | ||||||||
\(690\) | 5.12618 | + | 7.97319i | 0.195151 | + | 0.303534i | ||||
\(691\) | −14.8083 | + | 25.6487i | −0.563334 | + | 0.975723i | 0.433869 | + | 0.900976i | \(0.357148\pi\) |
−0.997203 | + | 0.0747469i | \(0.976185\pi\) | |||||||
\(692\) | − | 9.81513i | − | 0.373115i | ||||||
\(693\) | − | 0.364117i | − | 0.0138316i | ||||||
\(694\) | −4.57678 | + | 7.92722i | −0.173732 | + | 0.300913i | ||||
\(695\) | 1.59665 | + | 33.3852i | 0.0605645 | + | 1.26637i | ||||
\(696\) | −1.60026 | − | 2.77173i | −0.0606577 | − | 0.105062i | ||||
\(697\) | − | 57.2280i | − | 2.16766i | ||||||
\(698\) | −12.2651 | + | 7.08124i | −0.464240 | + | 0.268029i | ||||
\(699\) | −2.82331 | − | 4.89011i | −0.106787 | − | 0.184961i | ||||
\(700\) | −1.42979 | + | 1.01896i | −0.0540409 | + | 0.0385131i | ||||
\(701\) | 21.2332 | − | 36.7770i | 0.801968 | − | 1.38905i | −0.116351 | − | 0.993208i | \(-0.537120\pi\) |
0.918319 | − | 0.395841i | \(-0.129547\pi\) | |||||||
\(702\) | 2.18772i | 0.0825704i | ||||||||
\(703\) | −38.4701 | − | 31.7667i | −1.45093 | − | 1.19810i | ||||
\(704\) | 1.03694 | 0.0390811 | ||||||||
\(705\) | −17.8189 | − | 9.18202i | −0.671099 | − | 0.345815i | ||||
\(706\) | −13.2258 | − | 22.9078i | −0.497760 | − | 0.862145i | ||||
\(707\) | 1.80546 | − | 1.04238i | 0.0679014 | − | 0.0392029i | ||||
\(708\) | −9.52022 | + | 5.49650i | −0.357792 | + | 0.206571i | ||||
\(709\) | −3.69702 | −0.138844 | −0.0694222 | − | 0.997587i | \(-0.522116\pi\) | ||||
−0.0694222 | + | 0.997587i | \(0.522116\pi\) | |||||||
\(710\) | −12.9467 | − | 20.1371i | −0.485882 | − | 0.755733i | ||||
\(711\) | 9.44979 | 0.354395 | ||||||||
\(712\) | −3.65351 | − | 2.10936i | −0.136921 | − | 0.0790515i | ||||
\(713\) | 0.630502i | 0.0236125i | ||||||||
\(714\) | −1.80588 | −0.0675835 | ||||||||
\(715\) | 2.32355 | − | 4.50915i | 0.0868959 | − | 0.168633i | ||||
\(716\) | 2.83591 | + | 4.91193i | 0.105983 | + | 0.183568i | ||||
\(717\) | 11.4498i | 0.427602i | ||||||||
\(718\) | 4.40954 | + | 2.54585i | 0.164562 | + | 0.0950102i | ||||
\(719\) | 2.14283 | − | 3.71149i | 0.0799140 | − | 0.138415i | −0.823299 | − | 0.567608i | \(-0.807869\pi\) |
0.903213 | + | 0.429193i | \(0.141202\pi\) | |||||||
\(720\) | −1.98769 | − | 1.02425i | −0.0740768 | − | 0.0381715i | ||||
\(721\) | 2.28626 | + | 3.95992i | 0.0851447 | + | 0.147475i | ||||
\(722\) | 41.8049 | − | 24.1361i | 1.55582 | − | 0.898251i | ||||
\(723\) | −3.59997 | − | 2.07844i | −0.133884 | − | 0.0772981i | ||||
\(724\) | 8.40034 | − | 14.5498i | 0.312196 | − | 0.540740i | ||||
\(725\) | 6.64222 | − | 14.5590i | 0.246686 | − | 0.540707i | ||||
\(726\) | 9.92476 | 0.368342 | ||||||||
\(727\) | −15.0030 | + | 8.66199i | −0.556431 | + | 0.321255i | −0.751712 | − | 0.659492i | \(-0.770771\pi\) |
0.195281 | + | 0.980747i | \(0.437438\pi\) | |||||||
\(728\) | 0.665289 | + | 0.384105i | 0.0246572 | + | 0.0142359i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0.910382 | + | 19.0356i | 0.0336948 | + | 0.704539i | ||||
\(731\) | 16.3110 | − | 28.2515i | 0.603285 | − | 1.04492i | ||||
\(732\) | 2.30120i | 0.0850546i | ||||||||
\(733\) | 26.4474 | − | 15.2694i | 0.976856 | − | 0.563988i | 0.0755367 | − | 0.997143i | \(-0.475933\pi\) |
0.901320 | + | 0.433155i | \(0.142600\pi\) | |||||||
\(734\) | 10.0261 | 0.370068 | ||||||||
\(735\) | −8.31575 | − | 12.9342i | −0.306731 | − | 0.477085i | ||||
\(736\) | 2.11955 | + | 3.67116i | 0.0781275 | + | 0.135321i | ||||
\(737\) | −12.8840 | + | 7.43855i | −0.474586 | + | 0.274003i | ||||
\(738\) | −9.63687 | − | 5.56385i | −0.354738 | − | 0.204808i | ||||
\(739\) | −3.59115 | −0.132103 | −0.0660513 | − | 0.997816i | \(-0.521040\pi\) | ||||
−0.0660513 | + | 0.997816i | \(0.521040\pi\) | |||||||
\(740\) | 13.5055 | + | 1.61286i | 0.496472 | + | 0.0592898i | ||||
\(741\) | 17.9436 | 0.659176 | ||||||||
\(742\) | −1.35738 | − | 0.783685i | −0.0498310 | − | 0.0287700i | ||||
\(743\) | 16.3085 | − | 9.41573i | 0.598301 | − | 0.345429i | −0.170072 | − | 0.985432i | \(-0.554400\pi\) |
0.768373 | + | 0.640002i | \(0.221067\pi\) | |||||||
\(744\) | −0.0743676 | − | 0.128809i | −0.00272645 | − | 0.00472235i | ||||
\(745\) | −39.9211 | + | 25.6664i | −1.46260 | + | 0.940344i | ||||
\(746\) | 30.2932 | 1.10911 | ||||||||
\(747\) | −3.80546 | + | 2.19708i | −0.139235 | + | 0.0803871i | ||||
\(748\) | 5.33282i | 0.194987i | ||||||||
\(749\) | −0.276869 | + | 0.479551i | −0.0101166 | + | 0.0175224i | ||||
\(750\) | −1.59740 | − | 11.0656i | −0.0583288 | − | 0.404060i | ||||
\(751\) | 13.4876 | 0.492171 | 0.246086 | − | 0.969248i | \(-0.420856\pi\) | ||||
0.246086 | + | 0.969248i | \(0.420856\pi\) | |||||||
\(752\) | −7.76360 | − | 4.48232i | −0.283109 | − | 0.163453i | ||||
\(753\) | 21.5141 | − | 12.4212i | 0.784016 | − | 0.452652i | ||||
\(754\) | −7.00186 | −0.254993 | ||||||||
\(755\) | 43.5974 | + | 22.4656i | 1.58667 | + | 0.817606i | ||||
\(756\) | −0.175573 | + | 0.304101i | −0.00638552 | + | 0.0110600i | ||||
\(757\) | −3.81556 | − | 2.20291i | −0.138679 | − | 0.0800663i | 0.429055 | − | 0.903278i | \(-0.358847\pi\) |
−0.567734 | + | 0.823212i | \(0.692180\pi\) | |||||||
\(758\) | −1.02616 | + | 0.592452i | −0.0372717 | + | 0.0215188i | ||||
\(759\) | −2.19784 | − | 3.80677i | −0.0797766 | − | 0.138177i | ||||
\(760\) | −8.40086 | + | 16.3029i | −0.304731 | + | 0.591370i | ||||
\(761\) | 13.2151 | − | 22.8892i | 0.479046 | − | 0.829732i | −0.520665 | − | 0.853761i | \(-0.674316\pi\) |
0.999711 | + | 0.0240287i | \(0.00764929\pi\) | |||||||
\(762\) | −12.4109 | − | 7.16541i | −0.449598 | − | 0.259576i | ||||
\(763\) | 3.58624i | 0.129830i | ||||||||
\(764\) | −1.43474 | − | 2.48504i | −0.0519070 | − | 0.0899055i | ||||
\(765\) | 5.26756 | − | 10.2224i | 0.190449 | − | 0.369591i | ||||
\(766\) | −31.6779 | −1.14457 | ||||||||
\(767\) | 24.0497i | 0.868383i | ||||||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | 53.8224 | 1.94089 | 0.970443 | − | 0.241331i | \(-0.0775841\pi\) | ||||
0.970443 | + | 0.241331i | \(0.0775841\pi\) | |||||||
\(770\) | 0.684857 | − | 0.440313i | 0.0246805 | − | 0.0158678i | ||||
\(771\) | −4.18799 | −0.150827 | ||||||||
\(772\) | −11.2822 | + | 6.51379i | −0.406056 | + | 0.234437i | ||||
\(773\) | 5.01032 | − | 2.89271i | 0.180209 | − | 0.104043i | −0.407182 | − | 0.913347i | \(-0.633489\pi\) |
0.587391 | + | 0.809304i | \(0.300155\pi\) | |||||||
\(774\) | −3.17160 | − | 5.49337i | −0.114001 | − | 0.197455i | ||||
\(775\) | 0.308679 | − | 0.676588i | 0.0110881 | − | 0.0243038i | ||||
\(776\) | 15.4855 | 0.555897 | ||||||||
\(777\) | 0.354304 | − | 2.10634i | 0.0127106 | − | 0.0755646i | ||||
\(778\) | − | 16.3930i | − | 0.587717i | ||||||
\(779\) | −45.6344 | + | 79.0412i | −1.63502 | + | 2.83194i | ||||
\(780\) | −4.11483 | + | 2.64554i | −0.147335 | + | 0.0947255i | ||||
\(781\) | 5.55088 | + | 9.61441i | 0.198626 | + | 0.344030i | ||||
\(782\) | −18.8802 | + | 10.9005i | −0.675154 | + | 0.389801i | ||||
\(783\) | − | 3.20052i | − | 0.114377i | ||||||
\(784\) | −3.43835 | − | 5.95539i | −0.122798 | − | 0.212693i | ||||
\(785\) | −45.9858 | + | 2.19928i | −1.64130 | + | 0.0784958i | ||||
\(786\) | 4.64477 | − | 8.04498i | 0.165674 | − | 0.286955i | ||||
\(787\) | − | 38.5550i | − | 1.37434i | −0.726499 | − | 0.687168i | \(-0.758854\pi\) | ||
0.726499 | − | 0.687168i | \(-0.241146\pi\) | |||||||
\(788\) | 1.38025i | 0.0491693i | ||||||||
\(789\) | −3.14323 | + | 5.44423i | −0.111902 | + | 0.193820i | ||||
\(790\) | 11.4273 | + | 17.7738i | 0.406565 | + | 0.632365i | ||||
\(791\) | −1.02382 | −0.0364028 | ||||||||
\(792\) | 0.898016 | + | 0.518470i | 0.0319096 | + | 0.0184230i | ||||
\(793\) | 4.35990 | + | 2.51719i | 0.154825 | + | 0.0893881i | ||||
\(794\) | 2.45916 | − | 4.25939i | 0.0872723 | − | 0.151160i | ||||
\(795\) | 8.39544 | − | 5.39766i | 0.297756 | − | 0.191435i | ||||
\(796\) | −2.03659 | − | 3.52748i | −0.0721850 | − | 0.125028i | ||||
\(797\) | −27.0678 | − | 15.6276i | −0.958790 | − | 0.553558i | −0.0629896 | − | 0.998014i | \(-0.520064\pi\) |
−0.895800 | + | 0.444456i | \(0.853397\pi\) | |||||||
\(798\) | 2.49422 | + | 1.44004i | 0.0882945 | + | 0.0509769i | ||||
\(799\) | 23.0518 | − | 39.9270i | 0.815515 | − | 1.41251i | ||||
\(800\) | −0.477161 | − | 4.97718i | −0.0168702 | − | 0.175970i | ||||
\(801\) | −2.10936 | − | 3.65351i | −0.0745305 | − | 0.129091i | ||||
\(802\) | −25.9992 | − | 15.0106i | −0.918063 | − | 0.530044i | ||||
\(803\) | − | 8.83753i | − | 0.311870i | ||||||
\(804\) | 14.3471 | 0.505984 | ||||||||
\(805\) | 2.95875 | + | 1.52463i | 0.104282 | + | 0.0537363i | ||||
\(806\) | −0.325392 | −0.0114614 | ||||||||
\(807\) | −21.8234 | + | 12.5997i | −0.768220 | + | 0.443532i | ||||
\(808\) | 5.93705i | 0.208865i | ||||||||
\(809\) | 5.31272 | + | 9.20190i | 0.186785 | + | 0.323522i | 0.944177 | − | 0.329440i | \(-0.106860\pi\) |
−0.757391 | + | 0.652961i | \(0.773526\pi\) | |||||||
\(810\) | −1.20927 | − | 1.88087i | −0.0424892 | − | 0.0660871i | ||||
\(811\) | 10.1316 | + | 17.5484i | 0.355767 | + | 0.616207i | 0.987249 | − | 0.159184i | \(-0.0508862\pi\) |
−0.631482 | + | 0.775391i | \(0.717553\pi\) | |||||||
\(812\) | −0.973281 | − | 0.561924i | −0.0341555 | − | 0.0197197i | ||||
\(813\) | − | 19.6263i | − | 0.688326i | ||||||
\(814\) | −6.22008 | − | 1.04627i | −0.218014 | − | 0.0366716i | ||||
\(815\) | −11.6766 | + | 0.558434i | −0.409012 | + | 0.0195611i | ||||
\(816\) | 2.57142 | − | 4.45383i | 0.0900177 | − | 0.155915i | ||||
\(817\) | −45.0564 | + | 26.0133i | −1.57632 | + | 0.910090i | ||||
\(818\) | 25.7626 | − | 14.8741i | 0.900769 | − | 0.520059i | ||||
\(819\) | 0.384105 | + | 0.665289i | 0.0134217 | + | 0.0232471i | ||||
\(820\) | −1.18864 | − | 24.8539i | −0.0415092 | − | 0.867935i | ||||
\(821\) | 5.37951 | + | 9.31759i | 0.187746 | + | 0.325186i | 0.944498 | − | 0.328516i | \(-0.106548\pi\) |
−0.756752 | + | 0.653702i | \(0.773215\pi\) | |||||||
\(822\) | 3.80455i | 0.132699i | ||||||||
\(823\) | 34.7362 | + | 20.0550i | 1.21083 | + | 0.699072i | 0.962940 | − | 0.269717i | \(-0.0869301\pi\) |
0.247888 | + | 0.968789i | \(0.420263\pi\) | |||||||
\(824\) | −13.0217 | −0.453633 | ||||||||
\(825\) | 0.494787 | + | 5.16104i | 0.0172263 | + | 0.179684i | ||||
\(826\) | −1.93007 | + | 3.34298i | −0.0671558 | + | 0.116317i | ||||
\(827\) | −27.9009 | + | 16.1086i | −0.970208 | + | 0.560150i | −0.899300 | − | 0.437333i | \(-0.855923\pi\) |
−0.0709082 | + | 0.997483i | \(0.522590\pi\) | |||||||
\(828\) | 4.23909i | 0.147319i | ||||||||
\(829\) | −1.91397 | + | 3.31510i | −0.0664750 | + | 0.115138i | −0.897347 | − | 0.441325i | \(-0.854509\pi\) |
0.830872 | + | 0.556463i | \(0.187842\pi\) | |||||||
\(830\) | −8.73424 | − | 4.50073i | −0.303170 | − | 0.156223i | ||||
\(831\) | −4.90105 | + | 8.48886i | −0.170015 | + | 0.294475i | ||||
\(832\) | −1.89463 | + | 1.09386i | −0.0656843 | + | 0.0379229i | ||||
\(833\) | 30.6276 | − | 17.6829i | 1.06119 | − | 0.612676i | ||||
\(834\) | −7.47368 | + | 12.9448i | −0.258792 | + | 0.448242i | ||||
\(835\) | −7.83312 | + | 15.2012i | −0.271076 | + | 0.526059i | ||||
\(836\) | 4.25247 | − | 7.36549i | 0.147075 | − | 0.254741i | ||||
\(837\) | − | 0.148735i | − | 0.00514104i | ||||||
\(838\) | −21.3357 | + | 12.3182i | −0.737030 | + | 0.425524i | ||||
\(839\) | 6.96994 | − | 12.0723i | 0.240629 | − | 0.416782i | −0.720265 | − | 0.693699i | \(-0.755980\pi\) |
0.960894 | + | 0.276918i | \(0.0893130\pi\) | |||||||
\(840\) | −0.784288 | + | 0.0375088i | −0.0270605 | + | 0.00129418i | ||||
\(841\) | −18.7567 | −0.646782 | ||||||||
\(842\) | 34.0881 | + | 19.6808i | 1.17475 | + | 0.678244i | ||||
\(843\) | − | 12.4710i | − | 0.429523i | ||||||
\(844\) | −13.1465 | − | 22.7705i | −0.452523 | − | 0.783792i | ||||
\(845\) | −0.877391 | − | 18.3458i | −0.0301832 | − | 0.631114i | ||||
\(846\) | −4.48232 | − | 7.76360i | −0.154105 | − | 0.266918i | ||||
\(847\) | 3.01813 | − | 1.74252i | 0.103704 | − | 0.0598736i | ||||
\(848\) | 3.86558 | − | 2.23180i | 0.132745 | − | 0.0766402i | ||||
\(849\) | −3.03612 | + | 5.25871i | −0.104199 | + | 0.180479i | ||||
\(850\) | 25.5968 | − | 2.45396i | 0.877965 | − | 0.0841703i | ||||
\(851\) | −9.00990 | − | 24.1600i | −0.308855 | − | 0.828196i | ||||
\(852\) | − | 10.7063i | − | 0.366791i | ||||||
\(853\) | 11.4111 | + | 6.58817i | 0.390707 | + | 0.225575i | 0.682466 | − | 0.730917i | \(-0.260907\pi\) |
−0.291759 | + | 0.956492i | \(0.594241\pi\) | |||||||
\(854\) | 0.404027 | + | 0.699795i | 0.0138255 | + | 0.0239465i | ||||
\(855\) | −15.4268 | + | 9.91834i | −0.527586 | + | 0.339200i | ||||
\(856\) | −0.788474 | − | 1.36568i | −0.0269495 | − | 0.0466779i | ||||
\(857\) | 27.9617i | 0.955154i | 0.878590 | + | 0.477577i | \(0.158485\pi\) | ||||
−0.878590 | + | 0.477577i | \(0.841515\pi\) | |||||||
\(858\) | 1.96461 | − | 1.13427i | 0.0670708 | − | 0.0387233i | ||||
\(859\) | 43.7281 | 1.49199 | 0.745993 | − | 0.665954i | \(-0.231975\pi\) | ||||
0.745993 | + | 0.665954i | \(0.231975\pi\) | |||||||
\(860\) | 6.49702 | − | 12.6083i | 0.221546 | − | 0.429940i | ||||
\(861\) | −3.90744 | −0.133165 | ||||||||
\(862\) | − | 11.0044i | − | 0.374811i | ||||||
\(863\) | 20.9209 | + | 12.0787i | 0.712156 | + | 0.411163i | 0.811859 | − | 0.583854i | \(-0.198456\pi\) |
−0.0997031 | + | 0.995017i | \(0.531789\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 21.9222 | − | 1.04844i | 0.745378 | − | 0.0356479i | ||||
\(866\) | 8.42470 | − | 14.5920i | 0.286283 | − | 0.495857i | ||||
\(867\) | 8.18292 | + | 4.72441i | 0.277906 | + | 0.160449i | ||||
\(868\) | −0.0452305 | − | 0.0261138i | −0.00153522 | − | 0.000886362i | ||||
\(869\) | −4.89943 | − | 8.48606i | −0.166202 | − | 0.287870i | ||||
\(870\) | 6.01977 | − | 3.87028i | 0.204089 | − | 0.131215i | ||||
\(871\) | 15.6938 | − | 27.1824i | 0.531764 | − | 0.921041i | ||||
\(872\) | −8.84469 | − | 5.10648i | −0.299519 | − | 0.172927i | ||||
\(873\) | 13.4108 | + | 7.74275i | 0.453888 | + | 0.262052i | ||||
\(874\) | 34.7688 | 1.17607 | ||||||||
\(875\) | −2.42859 | − | 3.08461i | −0.0821015 | − | 0.104279i | ||||
\(876\) | −4.26135 | + | 7.38088i | −0.143978 | + | 0.249377i | ||||
\(877\) | − | 21.9678i | − | 0.741799i | −0.928673 | − | 0.370899i | \(-0.879049\pi\) | ||
0.928673 | − | 0.370899i | \(-0.120951\pi\) | |||||||
\(878\) | − | 3.85747i | − | 0.130183i | ||||||
\(879\) | −6.62880 | + | 11.4814i | −0.223584 | + | 0.387258i | ||||
\(880\) | 0.110764 | + | 2.31602i | 0.00373386 | + | 0.0780730i | ||||
\(881\) | 13.9118 | + | 24.0960i | 0.468702 | + | 0.811816i | 0.999360 | − | 0.0357702i | \(-0.0113884\pi\) |
−0.530658 | + | 0.847586i | \(0.678055\pi\) | |||||||
\(882\) | − | 6.87670i | − | 0.231550i | ||||||
\(883\) | 8.08341 | − | 4.66696i | 0.272028 | − | 0.157056i | −0.357781 | − | 0.933806i | \(-0.616466\pi\) |
0.629809 | + | 0.776750i | \(0.283133\pi\) | |||||||
\(884\) | −5.62556 | − | 9.74376i | −0.189208 | − | 0.327718i | ||||
\(885\) | −13.2935 | − | 20.6764i | −0.446855 | − | 0.695031i | ||||
\(886\) | −9.36475 | + | 16.2202i | −0.314615 | + | 0.544929i | ||||
\(887\) | − | 5.13029i | − | 0.172258i | −0.996284 | − | 0.0861291i | \(-0.972550\pi\) | ||
0.996284 | − | 0.0861291i | \(-0.0274498\pi\) | |||||||
\(888\) | 4.69035 | + | 3.87306i | 0.157398 | + | 0.129971i | ||||
\(889\) | −5.03220 | −0.168775 | ||||||||
\(890\) | 4.32102 | − | 8.38550i | 0.144841 | − | 0.281082i | ||||
\(891\) | 0.518470 | + | 0.898016i | 0.0173694 | + | 0.0300847i | ||||
\(892\) | −6.70354 | + | 3.87029i | −0.224451 | + | 0.129587i | ||||
\(893\) | −63.6767 | + | 36.7638i | −2.13086 | + | 1.23025i | ||||
\(894\) | −21.2248 | −0.709863 | ||||||||
\(895\) | −10.6680 | + | 6.85872i | −0.356590 | + | 0.229262i | ||||
\(896\) | −0.351145 | −0.0117309 | ||||||||
\(897\) | 8.03149 | + | 4.63698i | 0.268164 | + | 0.154824i | ||||
\(898\) | − | 27.4380i | − | 0.915617i | ||||||
\(899\) | 0.476030 | 0.0158765 | ||||||||
\(900\) | 2.07536 | − | 4.54894i | 0.0691785 | − | 0.151631i | ||||
\(901\) | 11.4778 | + | 19.8801i | 0.382380 | + | 0.662301i | ||||
\(902\) | 11.5387i | 0.384198i | ||||||||
\(903\) | −1.92897 | − | 1.11369i | −0.0641921 | − | 0.0370613i | ||||
\(904\) | 1.45783 | − | 2.52503i | 0.0484866 | − | 0.0839812i | ||||
\(905\) | 33.3945 | + | 17.2081i | 1.11007 | + | 0.572017i | ||||
\(906\) | 10.9668 | + | 18.9951i | 0.364349 | + | 0.631071i | ||||
\(907\) | −2.25302 | + | 1.30078i | −0.0748103 | + | 0.0431918i | −0.536939 | − | 0.843621i | \(-0.680419\pi\) |
0.462128 | + | 0.886813i | \(0.347086\pi\) | |||||||
\(908\) | −7.11370 | − | 4.10709i | −0.236076 | − | 0.136299i | ||||
\(909\) | −2.96853 | + | 5.14164i | −0.0984598 | + | 0.170537i | ||||
\(910\) | −0.786839 | + | 1.52696i | −0.0260834 | + | 0.0506183i | ||||
\(911\) | −53.5330 | −1.77363 | −0.886814 | − | 0.462126i | \(-0.847087\pi\) | ||||
−0.886814 | + | 0.462126i | \(0.847087\pi\) | |||||||
\(912\) | −7.10310 | + | 4.10098i | −0.235207 | + | 0.135797i | ||||
\(913\) | 3.94603 | + | 2.27824i | 0.130595 | + | 0.0753989i | ||||
\(914\) | −9.51368 | −0.314685 | ||||||||
\(915\) | −5.13975 | + | 0.245810i | −0.169915 | + | 0.00812623i | ||||
\(916\) | 7.53968 | − | 13.0591i | 0.249118 | − | 0.431485i | ||||
\(917\) | − | 3.26198i | − | 0.107720i | ||||||
\(918\) | 4.45383 | − | 2.57142i | 0.146998 | − | 0.0848695i | ||||
\(919\) | −19.2472 | −0.634905 | −0.317453 | − | 0.948274i | \(-0.602827\pi\) | ||||
−0.317453 | + | 0.948274i | \(0.602827\pi\) | |||||||
\(920\) | −7.97319 | + | 5.12618i | −0.262868 | + | 0.169005i | ||||
\(921\) | −12.2478 | − | 21.2138i | −0.403578 | − | 0.699018i | ||||
\(922\) | 22.2556 | − | 12.8493i | 0.732950 | − | 0.423169i | ||||
\(923\) | −20.2844 | − | 11.7112i | −0.667668 | − | 0.385478i | ||||
\(924\) | 0.364117 | 0.0119786 | ||||||||
\(925\) | −2.15970 | + | 30.3370i | −0.0710106 | + | 0.997476i | ||||
\(926\) | −25.6659 | −0.843434 | ||||||||
\(927\) | −11.2771 | − | 6.51086i | −0.370390 | − | 0.213845i | ||||
\(928\) | 2.77173 | − | 1.60026i | 0.0909866 | − | 0.0525311i | ||||
\(929\) | −11.7772 | − | 20.3986i | −0.386396 | − | 0.669257i | 0.605566 | − | 0.795795i | \(-0.292947\pi\) |
−0.991962 | + | 0.126538i | \(0.959613\pi\) | |||||||
\(930\) | 0.279752 | − | 0.179860i | 0.00917343 | − | 0.00589785i | ||||
\(931\) | −56.4024 | −1.84851 | ||||||||
\(932\) | 4.89011 | − | 2.82331i | 0.160181 | − | 0.0924805i | ||||
\(933\) | − | 25.0681i | − | 0.820692i | ||||||
\(934\) | 19.1086 | − | 33.0971i | 0.625253 | − | 1.08297i | ||||
\(935\) | −11.9109 | + | 0.569643i | −0.389529 | + | 0.0186293i | ||||
\(936\) | −2.18772 | −0.0715080 | ||||||||
\(937\) | 38.5661 | + | 22.2662i | 1.25990 | + | 0.727404i | 0.973055 | − | 0.230574i | \(-0.0740602\pi\) |
0.286845 | + | 0.957977i | \(0.407394\pi\) | |||||||
\(938\) | 4.36297 | − | 2.51896i | 0.142456 | − | 0.0822471i | ||||
\(939\) | −31.1900 | −1.01785 | ||||||||
\(940\) | 9.18202 | − | 17.8189i | 0.299485 | − | 0.581189i | ||||
\(941\) | 2.75666 | − | 4.77467i | 0.0898645 | − | 0.155650i | −0.817589 | − | 0.575802i | \(-0.804690\pi\) |
0.907454 | + | 0.420152i | \(0.138023\pi\) | |||||||
\(942\) | −17.8306 | − | 10.2945i | −0.580952 | − | 0.335413i | ||||
\(943\) | −40.8516 | + | 23.5857i | −1.33031 | + | 0.768055i | ||||
\(944\) | −5.49650 | − | 9.52022i | −0.178896 | − | 0.309857i | ||||
\(945\) | −0.697968 | − | 0.359661i | −0.0227049 | − | 0.0116998i | ||||
\(946\) | −3.28875 | + | 5.69629i | −0.106927 | + | 0.185202i | ||||
\(947\) | −15.2638 | − | 8.81253i | −0.496005 | − | 0.286369i | 0.231057 | − | 0.972940i | \(-0.425782\pi\) |
−0.727062 | + | 0.686571i | \(0.759115\pi\) | |||||||
\(948\) | 9.44979i | 0.306915i | ||||||||
\(949\) | 9.32267 | + | 16.1473i | 0.302627 | + | 0.524165i | ||||
\(950\) | −37.3103 | − | 17.0220i | −1.21050 | − | 0.552266i | ||||
\(951\) | −4.56442 | −0.148011 | ||||||||
\(952\) | − | 1.80588i | − | 0.0585291i | ||||||
\(953\) | 13.3304 | + | 7.69631i | 0.431814 | + | 0.249308i | 0.700119 | − | 0.714026i | \(-0.253130\pi\) |
−0.268305 | + | 0.963334i | \(0.586464\pi\) | |||||||
\(954\) | 4.46359 | 0.144514 | ||||||||
\(955\) | 5.39711 | − | 3.46996i | 0.174646 | − | 0.112285i | ||||
\(956\) | −11.4498 | −0.370314 | ||||||||
\(957\) | −2.87412 | + | 1.65937i | −0.0929071 | + | 0.0536399i | ||||
\(958\) | 10.7513 | − | 6.20726i | 0.347358 | − | 0.200547i | ||||
\(959\) | 0.667976 | + | 1.15697i | 0.0215701 | + | 0.0373604i | ||||
\(960\) | 1.02425 | − | 1.98769i | 0.0330575 | − | 0.0641524i | ||||
\(961\) | −30.9779 | −0.999286 | ||||||||
\(962\) | 12.4686 | − | 4.64986i | 0.402004 | − | 0.149917i | ||||
\(963\) | − | 1.57695i | − | 0.0508164i | ||||||
\(964\) | 2.07844 | − | 3.59997i | 0.0669421 | − | 0.115947i | ||||
\(965\) | −15.7538 | − | 24.5032i | −0.507133 | − | 0.788786i | ||||
\(966\) | 0.744269 | + | 1.28911i | 0.0239465 | + | 0.0414765i | ||||
\(967\) | −22.4827 | + | 12.9804i | −0.722994 | + | 0.417421i | −0.815854 | − | 0.578259i | \(-0.803732\pi\) |
0.0928599 | + | 0.995679i | \(0.470399\pi\) | |||||||
\(968\) | 9.92476i | 0.318994i | ||||||||
\(969\) | −21.0907 | − | 36.5301i | −0.677530 | − | 1.17352i | ||||
\(970\) | 1.65414 | + | 34.5871i | 0.0531111 | + | 1.11052i | ||||
\(971\) | 21.5442 | − | 37.3157i | 0.691387 | − | 1.19752i | −0.279996 | − | 0.960001i | \(-0.590333\pi\) |
0.971383 | − | 0.237517i | \(-0.0763334\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 5.24870i | 0.168266i | ||||||||
\(974\) | −6.01615 | + | 10.4203i | −0.192770 | + | 0.333888i | ||||
\(975\) | −6.34839 | − | 8.90794i | −0.203311 | − | 0.285282i | ||||
\(976\) | −2.30120 | −0.0736595 | ||||||||
\(977\) | −8.98984 | − | 5.19028i | −0.287610 | − | 0.166052i | 0.349253 | − | 0.937028i | \(-0.386435\pi\) |
−0.636864 | + | 0.770976i | \(0.719769\pi\) | |||||||
\(978\) | −4.52748 | − | 2.61394i | −0.144773 | − | 0.0835846i | ||||
\(979\) | −2.18728 | + | 3.78847i | −0.0699057 | + | 0.121080i | ||||
\(980\) | 12.9342 | − | 8.31575i | 0.413167 | − | 0.265637i | ||||
\(981\) | −5.10648 | − | 8.84469i | −0.163037 | − | 0.282389i | ||||
\(982\) | −4.99833 | − | 2.88579i | −0.159503 | − | 0.0920891i | ||||
\(983\) | 9.34020 | + | 5.39257i | 0.297906 | + | 0.171996i | 0.641502 | − | 0.767121i | \(-0.278312\pi\) |
−0.343596 | + | 0.939118i | \(0.611645\pi\) | |||||||
\(984\) | 5.56385 | − | 9.63687i | 0.177369 | − | 0.307212i | ||||
\(985\) | −3.08280 | + | 0.147436i | −0.0982263 | + | 0.00469770i | ||||
\(986\) | 8.22989 | + | 14.2546i | 0.262093 | + | 0.453958i | ||||
\(987\) | −2.72615 | − | 1.57394i | −0.0867743 | − | 0.0500992i | ||||
\(988\) | 17.9436i | 0.570863i | ||||||||
\(989\) | −26.8894 | −0.855032 | ||||||||
\(990\) | −1.06209 | + | 2.06111i | −0.0337553 | + | 0.0655065i | ||||
\(991\) | 1.91476 | 0.0608243 | 0.0304122 | − | 0.999537i | \(-0.490318\pi\) | ||||
0.0304122 | + | 0.999537i | \(0.490318\pi\) | |||||||
\(992\) | 0.128809 | − | 0.0743676i | 0.00408967 | − | 0.00236117i | ||||
\(993\) | 12.1726i | 0.386285i | ||||||||
\(994\) | −1.87973 | − | 3.25579i | −0.0596214 | − | 0.103267i | ||||
\(995\) | 7.66113 | − | 4.92555i | 0.242874 | − | 0.156151i | ||||
\(996\) | −2.19708 | − | 3.80546i | −0.0696173 | − | 0.120581i | ||||
\(997\) | −42.4017 | − | 24.4806i | −1.34287 | − | 0.775309i | −0.355647 | − | 0.934621i | \(-0.615739\pi\) |
−0.987228 | + | 0.159311i | \(0.949073\pi\) | |||||||
\(998\) | − | 4.72452i | − | 0.149552i | ||||||
\(999\) | 2.12543 | + | 5.69935i | 0.0672457 | + | 0.180319i |
(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 | 1110.2.bb.e.1009.4 | ✓ | 40 | |
5.4 | even | 2 | inner | 1110.2.bb.e.1009.17 | yes | 40 | |
37.26 | even | 3 | inner | 1110.2.bb.e.1099.17 | yes | 40 | |
185.174 | even | 6 | inner | 1110.2.bb.e.1099.4 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.bb.e.1009.4 | ✓ | 40 | 1.1 | even | 1 | trivial | |
1110.2.bb.e.1009.17 | yes | 40 | 5.4 | even | 2 | inner | |
1110.2.bb.e.1099.4 | yes | 40 | 185.174 | even | 6 | inner | |
1110.2.bb.e.1099.17 | yes | 40 | 37.26 | even | 3 | inner |