Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(7,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.g (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: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 10x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-2.73861 - 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.11 |
Dual form | 76.3.g.b.7.1 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 1.00000 | ||||||||
\(3\) | −4.23861 | − | 2.44716i | −1.41287 | − | 0.815721i | −0.417213 | − | 0.908809i | \(-0.636993\pi\) |
−0.995658 | + | 0.0930873i | \(0.970326\pi\) | |||||||
\(4\) | 4.00000 | 1.00000 | ||||||||
\(5\) | 1.73861 | − | 3.01137i | 0.347723 | − | 0.602273i | −0.638122 | − | 0.769935i | \(-0.720288\pi\) |
0.985845 | + | 0.167662i | \(0.0536218\pi\) | |||||||
\(6\) | −8.47723 | − | 4.89433i | −1.41287 | − | 0.815721i | ||||
\(7\) | − | 10.0905i | − | 1.44150i | −0.693197 | − | 0.720749i | \(-0.743798\pi\) | ||
0.693197 | − | 0.720749i | \(-0.256202\pi\) | |||||||
\(8\) | 8.00000 | 1.00000 | ||||||||
\(9\) | 7.47723 | + | 12.9509i | 0.830803 | + | 1.43899i | ||||
\(10\) | 3.47723 | − | 6.02273i | 0.347723 | − | 0.602273i | ||||
\(11\) | 17.5434i | 1.59486i | 0.603413 | + | 0.797429i | \(0.293807\pi\) | ||||
−0.603413 | + | 0.797429i | \(0.706193\pi\) | |||||||
\(12\) | −16.9545 | − | 9.78866i | −1.41287 | − | 0.815721i | ||||
\(13\) | −3.00000 | − | 5.19615i | −0.230769 | − | 0.399704i | 0.727265 | − | 0.686356i | \(-0.240791\pi\) |
−0.958035 | + | 0.286652i | \(0.907458\pi\) | |||||||
\(14\) | − | 20.1810i | − | 1.44150i | ||||||
\(15\) | −14.7386 | + | 8.50934i | −0.982574 | + | 0.567289i | ||||
\(16\) | 16.0000 | 1.00000 | ||||||||
\(17\) | −2.52277 | + | 4.36957i | −0.148398 | + | 0.257034i | −0.930636 | − | 0.365947i | \(-0.880745\pi\) |
0.782237 | + | 0.622981i | \(0.214078\pi\) | |||||||
\(18\) | 14.9545 | + | 25.9019i | 0.830803 | + | 1.43899i | ||||
\(19\) | 2.28416 | + | 18.8622i | 0.120219 | + | 0.992747i | ||||
\(20\) | 6.95445 | − | 12.0455i | 0.347723 | − | 0.602273i | ||||
\(21\) | −24.6931 | + | 42.7696i | −1.17586 | + | 2.03665i | ||||
\(22\) | 35.0869i | 1.59486i | ||||||||
\(23\) | 27.6475 | − | 15.9623i | 1.20207 | − | 0.694013i | 0.241052 | − | 0.970512i | \(-0.422508\pi\) |
0.961014 | + | 0.276499i | \(0.0891743\pi\) | |||||||
\(24\) | −33.9089 | − | 19.5773i | −1.41287 | − | 0.815721i | ||||
\(25\) | 6.45445 | + | 11.1794i | 0.258178 | + | 0.447177i | ||||
\(26\) | −6.00000 | − | 10.3923i | −0.230769 | − | 0.399704i | ||||
\(27\) | − | 29.1430i | − | 1.07937i | ||||||
\(28\) | − | 40.3619i | − | 1.44150i | ||||||
\(29\) | −3.73861 | − | 6.47547i | −0.128918 | − | 0.223292i | 0.794340 | − | 0.607474i | \(-0.207817\pi\) |
−0.923258 | + | 0.384182i | \(0.874484\pi\) | |||||||
\(30\) | −29.4772 | + | 17.0187i | −0.982574 | + | 0.567289i | ||||
\(31\) | − | 4.81544i | − | 0.155337i | −0.996979 | − | 0.0776683i | \(-0.975252\pi\) | ||
0.996979 | − | 0.0776683i | \(-0.0247475\pi\) | |||||||
\(32\) | 32.0000 | 1.00000 | ||||||||
\(33\) | 42.9317 | − | 74.3598i | 1.30096 | − | 2.25333i | ||||
\(34\) | −5.04555 | + | 8.73915i | −0.148398 | + | 0.257034i | ||||
\(35\) | −30.3861 | − | 17.5434i | −0.868175 | − | 0.501241i | ||||
\(36\) | 29.9089 | + | 51.8037i | 0.830803 | + | 1.43899i | ||||
\(37\) | −51.3861 | −1.38881 | −0.694407 | − | 0.719582i | \(-0.744333\pi\) | ||||
−0.694407 | + | 0.719582i | \(0.744333\pi\) | |||||||
\(38\) | 4.56832 | + | 37.7244i | 0.120219 | + | 0.992747i | ||||
\(39\) | 29.3660i | 0.752974i | ||||||||
\(40\) | 13.9089 | − | 24.0909i | 0.347723 | − | 0.602273i | ||||
\(41\) | 17.4545 | − | 30.2320i | 0.425718 | − | 0.737366i | −0.570769 | − | 0.821111i | \(-0.693355\pi\) |
0.996487 | + | 0.0837450i | \(0.0266881\pi\) | |||||||
\(42\) | −49.3861 | + | 85.5393i | −1.17586 | + | 2.03665i | ||||
\(43\) | 9.38613 | + | 5.41908i | 0.218282 | + | 0.126025i | 0.605155 | − | 0.796108i | \(-0.293111\pi\) |
−0.386872 | + | 0.922133i | \(0.626445\pi\) | |||||||
\(44\) | 70.1738i | 1.59486i | ||||||||
\(45\) | 52.0000 | 1.15556 | ||||||||
\(46\) | 55.2950 | − | 31.9246i | 1.20207 | − | 0.694013i | ||||
\(47\) | −19.1703 | + | 11.0680i | −0.407879 | + | 0.235489i | −0.689878 | − | 0.723926i | \(-0.742336\pi\) |
0.281999 | + | 0.959415i | \(0.409002\pi\) | |||||||
\(48\) | −67.8178 | − | 39.1546i | −1.41287 | − | 0.815721i | ||||
\(49\) | −52.8178 | −1.07791 | ||||||||
\(50\) | 12.9089 | + | 22.3589i | 0.258178 | + | 0.447177i | ||||
\(51\) | 21.3861 | − | 12.3473i | 0.419336 | − | 0.242104i | ||||
\(52\) | −12.0000 | − | 20.7846i | −0.230769 | − | 0.399704i | ||||
\(53\) | 20.0455 | + | 34.7199i | 0.378218 | + | 0.655093i | 0.990803 | − | 0.135312i | \(-0.0432037\pi\) |
−0.612585 | + | 0.790405i | \(0.709870\pi\) | |||||||
\(54\) | − | 58.2861i | − | 1.07937i | ||||||
\(55\) | 52.8297 | + | 30.5012i | 0.960540 | + | 0.554568i | ||||
\(56\) | − | 80.7238i | − | 1.44150i | ||||||
\(57\) | 36.4772 | − | 85.5393i | 0.639951 | − | 1.50069i | ||||
\(58\) | −7.47723 | − | 12.9509i | −0.128918 | − | 0.223292i | ||||
\(59\) | −16.7614 | − | 9.67719i | −0.284091 | − | 0.164020i | 0.351183 | − | 0.936307i | \(-0.385780\pi\) |
−0.635274 | + | 0.772287i | \(0.719113\pi\) | |||||||
\(60\) | −58.9545 | + | 34.0374i | −0.982574 | + | 0.567289i | ||||
\(61\) | −8.26139 | − | 14.3091i | −0.135433 | − | 0.234576i | 0.790330 | − | 0.612681i | \(-0.209909\pi\) |
−0.925763 | + | 0.378105i | \(0.876576\pi\) | |||||||
\(62\) | − | 9.63087i | − | 0.155337i | ||||||
\(63\) | 130.681 | − | 75.4488i | 2.07430 | − | 1.19760i | ||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | −20.8634 | −0.320975 | ||||||||
\(66\) | 85.8634 | − | 148.720i | 1.30096 | − | 2.25333i | ||||
\(67\) | −83.0109 | + | 47.9263i | −1.23897 | + | 0.715319i | −0.968883 | − | 0.247518i | \(-0.920385\pi\) |
−0.270085 | + | 0.962837i | \(0.587052\pi\) | |||||||
\(68\) | −10.0911 | + | 17.4783i | −0.148398 | + | 0.257034i | ||||
\(69\) | −156.249 | −2.26449 | ||||||||
\(70\) | −60.7723 | − | 35.0869i | −0.868175 | − | 0.501241i | ||||
\(71\) | 12.6594 | + | 7.30892i | 0.178302 | + | 0.102943i | 0.586495 | − | 0.809953i | \(-0.300508\pi\) |
−0.408193 | + | 0.912896i | \(0.633841\pi\) | |||||||
\(72\) | 59.8178 | + | 103.607i | 0.830803 | + | 1.43899i | ||||
\(73\) | −17.4545 | + | 30.2320i | −0.239102 | + | 0.414137i | −0.960457 | − | 0.278429i | \(-0.910186\pi\) |
0.721355 | + | 0.692566i | \(0.243520\pi\) | |||||||
\(74\) | −102.772 | −1.38881 | ||||||||
\(75\) | − | 63.1804i | − | 0.842405i | ||||||
\(76\) | 9.13665 | + | 75.4488i | 0.120219 | + | 0.992747i | ||||
\(77\) | 177.022 | 2.29898 | ||||||||
\(78\) | 58.7319i | 0.752974i | ||||||||
\(79\) | −68.0911 | − | 39.3124i | −0.861913 | − | 0.497625i | 0.00273968 | − | 0.999996i | \(-0.499128\pi\) |
−0.864652 | + | 0.502371i | \(0.832461\pi\) | |||||||
\(80\) | 27.8178 | − | 48.1819i | 0.347723 | − | 0.602273i | ||||
\(81\) | −4.02277 | + | 6.96765i | −0.0496639 | + | 0.0860204i | ||||
\(82\) | 34.9089 | − | 60.4640i | 0.425718 | − | 0.737366i | ||||
\(83\) | 92.9922i | 1.12039i | 0.828361 | + | 0.560194i | \(0.189274\pi\) | ||||
−0.828361 | + | 0.560194i | \(0.810726\pi\) | |||||||
\(84\) | −98.7723 | + | 171.079i | −1.17586 | + | 2.03665i | ||||
\(85\) | 8.77226 | + | 15.1940i | 0.103203 | + | 0.178753i | ||||
\(86\) | 18.7723 | + | 10.8382i | 0.218282 | + | 0.126025i | ||||
\(87\) | 36.5960i | 0.420644i | ||||||||
\(88\) | 140.348i | 1.59486i | ||||||||
\(89\) | 56.2495 | + | 97.4270i | 0.632017 | + | 1.09468i | 0.987139 | + | 0.159865i | \(0.0511059\pi\) |
−0.355122 | + | 0.934820i | \(0.615561\pi\) | |||||||
\(90\) | 104.000 | 1.15556 | ||||||||
\(91\) | −52.4317 | + | 30.2714i | −0.576172 | + | 0.332653i | ||||
\(92\) | 110.590 | − | 63.8492i | 1.20207 | − | 0.694013i | ||||
\(93\) | −11.7842 | + | 20.4108i | −0.126711 | + | 0.219471i | ||||
\(94\) | −38.3406 | + | 22.1359i | −0.407879 | + | 0.235489i | ||||
\(95\) | 60.7723 | + | 25.9156i | 0.639708 | + | 0.272796i | ||||
\(96\) | −135.636 | − | 78.3093i | −1.41287 | − | 0.815721i | ||||
\(97\) | −63.9772 | + | 110.812i | −0.659559 | + | 1.14239i | 0.321171 | + | 0.947021i | \(0.395924\pi\) |
−0.980730 | + | 0.195368i | \(0.937410\pi\) | |||||||
\(98\) | −105.636 | −1.07791 | ||||||||
\(99\) | −227.204 | + | 131.176i | −2.29499 | + | 1.32501i | ||||
\(100\) | 25.8178 | + | 44.7177i | 0.258178 | + | 0.447177i | ||||
\(101\) | −80.9425 | − | 140.197i | −0.801411 | − | 1.38809i | −0.918687 | − | 0.394986i | \(-0.870750\pi\) |
0.117276 | − | 0.993099i | \(-0.462584\pi\) | |||||||
\(102\) | 42.7723 | − | 24.6946i | 0.419336 | − | 0.242104i | ||||
\(103\) | − | 166.723i | − | 1.61867i | −0.587349 | − | 0.809334i | \(-0.699828\pi\) | ||
0.587349 | − | 0.809334i | \(-0.300172\pi\) | |||||||
\(104\) | −24.0000 | − | 41.5692i | −0.230769 | − | 0.399704i | ||||
\(105\) | 85.8634 | + | 148.720i | 0.817746 | + | 1.41638i | ||||
\(106\) | 40.0911 | + | 69.4398i | 0.378218 | + | 0.655093i | ||||
\(107\) | − | 181.629i | − | 1.69746i | −0.528823 | − | 0.848732i | \(-0.677367\pi\) | ||
0.528823 | − | 0.848732i | \(-0.322633\pi\) | |||||||
\(108\) | − | 116.572i | − | 1.07937i | ||||||
\(109\) | −40.8634 | + | 70.7774i | −0.374893 | + | 0.649334i | −0.990311 | − | 0.138867i | \(-0.955654\pi\) |
0.615418 | + | 0.788201i | \(0.288987\pi\) | |||||||
\(110\) | 105.659 | + | 61.0025i | 0.960540 | + | 0.554568i | ||||
\(111\) | 217.806 | + | 125.750i | 1.96222 | + | 1.13289i | ||||
\(112\) | − | 161.448i | − | 1.44150i | ||||||
\(113\) | −27.0911 | −0.239744 | −0.119872 | − | 0.992789i | \(-0.538248\pi\) | ||||
−0.119872 | + | 0.992789i | \(0.538248\pi\) | |||||||
\(114\) | 72.9545 | − | 171.079i | 0.639951 | − | 1.50069i | ||||
\(115\) | − | 111.009i | − | 0.965296i | ||||||
\(116\) | −14.9545 | − | 25.9019i | −0.128918 | − | 0.223292i | ||||
\(117\) | 44.8634 | − | 77.7056i | 0.383447 | − | 0.664150i | ||||
\(118\) | −33.5228 | − | 19.3544i | −0.284091 | − | 0.164020i | ||||
\(119\) | 44.0911 | + | 25.4560i | 0.370513 | + | 0.213916i | ||||
\(120\) | −117.909 | + | 68.0747i | −0.982574 | + | 0.567289i | ||||
\(121\) | −186.772 | −1.54357 | ||||||||
\(122\) | −16.5228 | − | 28.6183i | −0.135433 | − | 0.234576i | ||||
\(123\) | −147.965 | + | 85.4278i | −1.20297 | + | 0.694535i | ||||
\(124\) | − | 19.2617i | − | 0.155337i | ||||||
\(125\) | 131.818 | 1.05454 | ||||||||
\(126\) | 261.362 | − | 150.898i | 2.07430 | − | 1.19760i | ||||
\(127\) | −122.204 | + | 70.5545i | −0.962236 | + | 0.555547i | −0.896860 | − | 0.442314i | \(-0.854158\pi\) |
−0.0653753 | + | 0.997861i | \(0.520824\pi\) | |||||||
\(128\) | 128.000 | 1.00000 | ||||||||
\(129\) | −26.5228 | − | 45.9388i | −0.205603 | − | 0.356115i | ||||
\(130\) | −41.7267 | −0.320975 | ||||||||
\(131\) | 117.056 | + | 67.5826i | 0.893560 | + | 0.515897i | 0.875105 | − | 0.483932i | \(-0.160792\pi\) |
0.0184550 | + | 0.999830i | \(0.494125\pi\) | |||||||
\(132\) | 171.727 | − | 297.439i | 1.30096 | − | 2.25333i | ||||
\(133\) | 190.329 | − | 23.0483i | 1.43104 | − | 0.173295i | ||||
\(134\) | −166.022 | + | 95.8527i | −1.23897 | + | 0.715319i | ||||
\(135\) | −87.7603 | − | 50.6685i | −0.650077 | − | 0.375322i | ||||
\(136\) | −20.1822 | + | 34.9566i | −0.148398 | + | 0.257034i | ||||
\(137\) | 55.5911 | + | 96.2866i | 0.405774 | + | 0.702822i | 0.994411 | − | 0.105576i | \(-0.0336685\pi\) |
−0.588637 | + | 0.808398i | \(0.700335\pi\) | |||||||
\(138\) | −312.499 | −2.26449 | ||||||||
\(139\) | −13.7376 | + | 7.93139i | −0.0988315 | + | 0.0570604i | −0.548601 | − | 0.836084i | \(-0.684839\pi\) |
0.449770 | + | 0.893145i | \(0.351506\pi\) | |||||||
\(140\) | −121.545 | − | 70.1738i | −0.868175 | − | 0.501241i | ||||
\(141\) | 108.341 | 0.768373 | ||||||||
\(142\) | 25.3188 | + | 14.6178i | 0.178302 | + | 0.102943i | ||||
\(143\) | 91.1584 | − | 52.6303i | 0.637471 | − | 0.368044i | ||||
\(144\) | 119.636 | + | 207.215i | 0.830803 | + | 1.43899i | ||||
\(145\) | −26.0000 | −0.179310 | ||||||||
\(146\) | −34.9089 | + | 60.4640i | −0.239102 | + | 0.414137i | ||||
\(147\) | 223.874 | + | 129.254i | 1.52295 | + | 0.879278i | ||||
\(148\) | −205.545 | −1.38881 | ||||||||
\(149\) | 19.7842 | − | 34.2672i | 0.132780 | − | 0.229981i | −0.791967 | − | 0.610563i | \(-0.790943\pi\) |
0.924747 | + | 0.380582i | \(0.124276\pi\) | |||||||
\(150\) | − | 126.361i | − | 0.842405i | ||||||
\(151\) | − | 4.81544i | − | 0.0318903i | −0.999873 | − | 0.0159452i | \(-0.994924\pi\) | ||
0.999873 | − | 0.0159452i | \(-0.00507571\pi\) | |||||||
\(152\) | 18.2733 | + | 150.898i | 0.120219 | + | 0.992747i | ||||
\(153\) | −75.4534 | −0.493160 | ||||||||
\(154\) | 354.043 | 2.29898 | ||||||||
\(155\) | −14.5010 | − | 8.37218i | −0.0935551 | − | 0.0540141i | ||||
\(156\) | 117.464i | 0.752974i | ||||||||
\(157\) | −29.0455 | + | 50.3084i | −0.185003 | + | 0.320435i | −0.943578 | − | 0.331151i | \(-0.892563\pi\) |
0.758574 | + | 0.651587i | \(0.225896\pi\) | |||||||
\(158\) | −136.182 | − | 78.6248i | −0.861913 | − | 0.497625i | ||||
\(159\) | − | 196.219i | − | 1.23408i | ||||||
\(160\) | 55.6356 | − | 96.3637i | 0.347723 | − | 0.602273i | ||||
\(161\) | −161.067 | − | 278.977i | −1.00042 | − | 1.73277i | ||||
\(162\) | −8.04555 | + | 13.9353i | −0.0496639 | + | 0.0860204i | ||||
\(163\) | − | 207.884i | − | 1.27536i | −0.770301 | − | 0.637680i | \(-0.779894\pi\) | ||
0.770301 | − | 0.637680i | \(-0.220106\pi\) | |||||||
\(164\) | 69.8178 | − | 120.928i | 0.425718 | − | 0.737366i | ||||
\(165\) | −149.283 | − | 258.566i | −0.904746 | − | 1.56707i | ||||
\(166\) | 185.984i | 1.12039i | ||||||||
\(167\) | −103.319 | + | 59.6512i | −0.618676 | + | 0.357193i | −0.776353 | − | 0.630298i | \(-0.782933\pi\) |
0.157678 | + | 0.987491i | \(0.449599\pi\) | |||||||
\(168\) | −197.545 | + | 342.157i | −1.17586 | + | 2.03665i | ||||
\(169\) | 66.5000 | − | 115.181i | 0.393491 | − | 0.681547i | ||||
\(170\) | 17.5445 | + | 30.3880i | 0.103203 | + | 0.178753i | ||||
\(171\) | −227.204 | + | 170.619i | −1.32868 | + | 0.997772i | ||||
\(172\) | 37.5445 | + | 21.6763i | 0.218282 | + | 0.126025i | ||||
\(173\) | 48.1366 | − | 83.3751i | 0.278247 | − | 0.481937i | −0.692703 | − | 0.721223i | \(-0.743580\pi\) |
0.970949 | + | 0.239286i | \(0.0769135\pi\) | |||||||
\(174\) | 73.1920i | 0.420644i | ||||||||
\(175\) | 112.806 | − | 65.1285i | 0.644605 | − | 0.372163i | ||||
\(176\) | 280.695i | 1.59486i | ||||||||
\(177\) | 47.3634 | + | 82.0357i | 0.267590 | + | 0.463479i | ||||
\(178\) | 112.499 | + | 194.854i | 0.632017 | + | 1.09468i | ||||
\(179\) | − | 205.366i | − | 1.14730i | −0.819101 | − | 0.573649i | \(-0.805527\pi\) | ||
0.819101 | − | 0.573649i | \(-0.194473\pi\) | |||||||
\(180\) | 208.000 | 1.15556 | ||||||||
\(181\) | 107.943 | + | 186.962i | 0.596368 | + | 1.03294i | 0.993352 | + | 0.115114i | \(0.0367233\pi\) |
−0.396985 | + | 0.917825i | \(0.629943\pi\) | |||||||
\(182\) | −104.863 | + | 60.5429i | −0.576172 | + | 0.332653i | ||||
\(183\) | 80.8679i | 0.441901i | ||||||||
\(184\) | 221.180 | − | 127.698i | 1.20207 | − | 0.694013i | ||||
\(185\) | −89.3406 | + | 154.742i | −0.482922 | + | 0.836446i | ||||
\(186\) | −23.5683 | + | 40.8215i | −0.126711 | + | 0.219471i | ||||
\(187\) | −76.6573 | − | 44.2581i | −0.409932 | − | 0.236675i | ||||
\(188\) | −76.6812 | + | 44.2719i | −0.407879 | + | 0.235489i | ||||
\(189\) | −294.067 | −1.55591 | ||||||||
\(190\) | 121.545 | + | 51.8312i | 0.639708 | + | 0.272796i | ||||
\(191\) | 182.548i | 0.955748i | 0.878428 | + | 0.477874i | \(0.158592\pi\) | ||||
−0.878428 | + | 0.477874i | \(0.841408\pi\) | |||||||
\(192\) | −271.271 | − | 156.619i | −1.41287 | − | 0.815721i | ||||
\(193\) | 50.5228 | − | 87.5080i | 0.261776 | − | 0.453409i | −0.704938 | − | 0.709269i | \(-0.749025\pi\) |
0.966714 | + | 0.255860i | \(0.0823585\pi\) | |||||||
\(194\) | −127.954 | + | 221.624i | −0.659559 | + | 1.14239i | ||||
\(195\) | 88.4317 | + | 51.0561i | 0.453496 | + | 0.261826i | ||||
\(196\) | −211.271 | −1.07791 | ||||||||
\(197\) | 10.1584 | 0.0515654 | 0.0257827 | − | 0.999668i | \(-0.491792\pi\) | ||||
0.0257827 | + | 0.999668i | \(0.491792\pi\) | |||||||
\(198\) | −454.408 | + | 262.353i | −2.29499 | + | 1.32501i | ||||
\(199\) | 158.976 | − | 91.7849i | 0.798875 | − | 0.461231i | −0.0442024 | − | 0.999023i | \(-0.514075\pi\) |
0.843078 | + | 0.537792i | \(0.180741\pi\) | |||||||
\(200\) | 51.6356 | + | 89.4355i | 0.258178 | + | 0.447177i | ||||
\(201\) | 469.135 | 2.33400 | ||||||||
\(202\) | −161.885 | − | 280.393i | −0.801411 | − | 1.38809i | ||||
\(203\) | −65.3406 | + | 37.7244i | −0.321875 | + | 0.185834i | ||||
\(204\) | 85.5445 | − | 49.3891i | 0.419336 | − | 0.242104i | ||||
\(205\) | −60.6931 | − | 105.123i | −0.296064 | − | 0.512797i | ||||
\(206\) | − | 333.445i | − | 1.61867i | ||||||
\(207\) | 413.453 | + | 238.707i | 1.99736 | + | 1.15318i | ||||
\(208\) | −48.0000 | − | 83.1384i | −0.230769 | − | 0.399704i | ||||
\(209\) | −330.908 | + | 40.0721i | −1.58329 | + | 0.191732i | ||||
\(210\) | 171.727 | + | 297.439i | 0.817746 | + | 1.41638i | ||||
\(211\) | 255.226 | + | 147.355i | 1.20960 | + | 0.698363i | 0.962672 | − | 0.270671i | \(-0.0872454\pi\) |
0.246928 | + | 0.969034i | \(0.420579\pi\) | |||||||
\(212\) | 80.1822 | + | 138.880i | 0.378218 | + | 0.655093i | ||||
\(213\) | −35.7723 | − | 61.9594i | −0.167945 | − | 0.290889i | ||||
\(214\) | − | 363.257i | − | 1.69746i | ||||||
\(215\) | 32.6377 | − | 18.8434i | 0.151803 | − | 0.0876436i | ||||
\(216\) | − | 233.144i | − | 1.07937i | ||||||
\(217\) | −48.5901 | −0.223917 | ||||||||
\(218\) | −81.7267 | + | 141.555i | −0.374893 | + | 0.649334i | ||||
\(219\) | 147.965 | − | 85.4278i | 0.675641 | − | 0.390081i | ||||
\(220\) | 211.319 | + | 122.005i | 0.960540 | + | 0.554568i | ||||
\(221\) | 30.2733 | 0.136983 | ||||||||
\(222\) | 435.612 | + | 251.501i | 1.96222 | + | 1.13289i | ||||
\(223\) | 28.9425 | + | 16.7100i | 0.129787 | + | 0.0749327i | 0.563488 | − | 0.826124i | \(-0.309459\pi\) |
−0.433701 | + | 0.901057i | \(0.642792\pi\) | |||||||
\(224\) | − | 322.895i | − | 1.44150i | ||||||
\(225\) | −96.5228 | + | 167.182i | −0.428990 | + | 0.743033i | ||||
\(226\) | −54.1822 | −0.239744 | ||||||||
\(227\) | − | 27.1743i | − | 0.119711i | −0.998207 | − | 0.0598553i | \(-0.980936\pi\) | ||
0.998207 | − | 0.0598553i | \(-0.0190639\pi\) | |||||||
\(228\) | 145.909 | − | 342.157i | 0.639951 | − | 1.50069i | ||||
\(229\) | −251.818 | −1.09964 | −0.549821 | − | 0.835283i | \(-0.685304\pi\) | ||||
−0.549821 | + | 0.835283i | \(0.685304\pi\) | |||||||
\(230\) | − | 222.018i | − | 0.965296i | ||||||
\(231\) | −750.327 | − | 433.201i | −3.24817 | − | 1.87533i | ||||
\(232\) | −29.9089 | − | 51.8037i | −0.128918 | − | 0.223292i | ||||
\(233\) | 82.2723 | − | 142.500i | 0.353100 | − | 0.611587i | −0.633691 | − | 0.773586i | \(-0.718461\pi\) |
0.986791 | + | 0.161999i | \(0.0517943\pi\) | |||||||
\(234\) | 89.7267 | − | 155.411i | 0.383447 | − | 0.664150i | ||||
\(235\) | 76.9717i | 0.327539i | ||||||||
\(236\) | −67.0455 | − | 38.7088i | −0.284091 | − | 0.164020i | ||||
\(237\) | 192.408 | + | 333.260i | 0.811848 | + | 1.40616i | ||||
\(238\) | 88.1822 | + | 50.9120i | 0.370513 | + | 0.213916i | ||||
\(239\) | 119.247i | 0.498943i | 0.968382 | + | 0.249471i | \(0.0802569\pi\) | ||||
−0.968382 | + | 0.249471i | \(0.919743\pi\) | |||||||
\(240\) | −235.818 | + | 136.149i | −0.982574 | + | 0.567289i | ||||
\(241\) | 33.1139 | + | 57.3549i | 0.137402 | + | 0.237987i | 0.926512 | − | 0.376264i | \(-0.122791\pi\) |
−0.789110 | + | 0.614251i | \(0.789458\pi\) | |||||||
\(242\) | −373.545 | −1.54357 | ||||||||
\(243\) | −193.046 | + | 111.455i | −0.794426 | + | 0.458662i | ||||
\(244\) | −33.0455 | − | 57.2366i | −0.135433 | − | 0.234576i | ||||
\(245\) | −91.8297 | + | 159.054i | −0.374815 | + | 0.649199i | ||||
\(246\) | −295.931 | + | 170.856i | −1.20297 | + | 0.694535i | ||||
\(247\) | 91.1584 | − | 68.4555i | 0.369062 | − | 0.277148i | ||||
\(248\) | − | 38.5235i | − | 0.155337i | ||||||
\(249\) | 227.567 | − | 394.158i | 0.913925 | − | 1.58296i | ||||
\(250\) | 263.636 | 1.05454 | ||||||||
\(251\) | −161.124 | + | 93.0248i | −0.641927 | + | 0.370617i | −0.785356 | − | 0.619044i | \(-0.787520\pi\) |
0.143429 | + | 0.989661i | \(0.454187\pi\) | |||||||
\(252\) | 522.725 | − | 301.795i | 2.07430 | − | 1.19760i | ||||
\(253\) | 280.034 | + | 485.032i | 1.10685 | + | 1.91712i | ||||
\(254\) | −244.408 | + | 141.109i | −0.962236 | + | 0.555547i | ||||
\(255\) | − | 85.8686i | − | 0.336740i | ||||||
\(256\) | 256.000 | 1.00000 | ||||||||
\(257\) | −151.862 | − | 263.033i | −0.590904 | − | 1.02348i | −0.994111 | − | 0.108367i | \(-0.965438\pi\) |
0.403207 | − | 0.915109i | \(-0.367895\pi\) | |||||||
\(258\) | −53.0455 | − | 91.8776i | −0.205603 | − | 0.356115i | ||||
\(259\) | 518.511i | 2.00197i | ||||||||
\(260\) | −83.4534 | −0.320975 | ||||||||
\(261\) | 55.9089 | − | 96.8371i | 0.214210 | − | 0.371023i | ||||
\(262\) | 234.113 | + | 135.165i | 0.893560 | + | 0.515897i | ||||
\(263\) | 75.2376 | + | 43.4384i | 0.286074 | + | 0.165165i | 0.636170 | − | 0.771549i | \(-0.280518\pi\) |
−0.350096 | + | 0.936714i | \(0.613851\pi\) | |||||||
\(264\) | 343.453 | − | 594.879i | 1.30096 | − | 2.25333i | ||||
\(265\) | 139.406 | 0.526060 | ||||||||
\(266\) | 380.657 | − | 46.0966i | 1.43104 | − | 0.173295i | ||||
\(267\) | − | 550.607i | − | 2.06220i | ||||||
\(268\) | −332.043 | + | 191.705i | −1.23897 | + | 0.715319i | ||||
\(269\) | −97.6356 | + | 169.110i | −0.362958 | + | 0.628661i | −0.988446 | − | 0.151572i | \(-0.951566\pi\) |
0.625489 | + | 0.780233i | \(0.284900\pi\) | |||||||
\(270\) | −175.521 | − | 101.337i | −0.650077 | − | 0.375322i | ||||
\(271\) | −304.010 | − | 175.520i | −1.12181 | − | 0.647676i | −0.179946 | − | 0.983677i | \(-0.557592\pi\) |
−0.941862 | + | 0.336001i | \(0.890926\pi\) | |||||||
\(272\) | −40.3644 | + | 69.9132i | −0.148398 | + | 0.257034i | ||||
\(273\) | 296.317 | 1.08541 | ||||||||
\(274\) | 111.182 | + | 192.573i | 0.405774 | + | 0.702822i | ||||
\(275\) | −196.126 | + | 113.233i | −0.713185 | + | 0.411757i | ||||
\(276\) | −624.998 | −2.26449 | ||||||||
\(277\) | −115.430 | −0.416713 | −0.208357 | − | 0.978053i | \(-0.566811\pi\) | ||||
−0.208357 | + | 0.978053i | \(0.566811\pi\) | |||||||
\(278\) | −27.4752 | + | 15.8628i | −0.0988315 | + | 0.0570604i | ||||
\(279\) | 62.3644 | − | 36.0061i | 0.223528 | − | 0.129054i | ||||
\(280\) | −243.089 | − | 140.348i | −0.868175 | − | 0.501241i | ||||
\(281\) | 11.9990 | + | 20.7828i | 0.0427009 | + | 0.0739602i | 0.886586 | − | 0.462564i | \(-0.153070\pi\) |
−0.843885 | + | 0.536524i | \(0.819737\pi\) | |||||||
\(282\) | 216.681 | 0.768373 | ||||||||
\(283\) | −125.237 | − | 72.3053i | −0.442532 | − | 0.255496i | 0.262139 | − | 0.965030i | \(-0.415572\pi\) |
−0.704671 | + | 0.709534i | \(0.748905\pi\) | |||||||
\(284\) | 50.6377 | + | 29.2357i | 0.178302 | + | 0.102943i | ||||
\(285\) | −194.170 | − | 258.566i | −0.681299 | − | 0.907249i | ||||
\(286\) | 182.317 | − | 105.261i | 0.637471 | − | 0.368044i | ||||
\(287\) | −305.055 | − | 176.124i | −1.06291 | − | 0.613672i | ||||
\(288\) | 239.271 | + | 414.430i | 0.830803 | + | 1.43899i | ||||
\(289\) | 131.771 | + | 228.234i | 0.455956 | + | 0.789739i | ||||
\(290\) | −52.0000 | −0.179310 | ||||||||
\(291\) | 542.349 | − | 313.126i | 1.86374 | − | 1.07603i | ||||
\(292\) | −69.8178 | + | 120.928i | −0.239102 | + | 0.414137i | ||||
\(293\) | 215.794 | 0.736498 | 0.368249 | − | 0.929727i | \(-0.379957\pi\) | ||||
0.368249 | + | 0.929727i | \(0.379957\pi\) | |||||||
\(294\) | 447.748 | + | 258.508i | 1.52295 | + | 0.879278i | ||||
\(295\) | −58.2831 | + | 33.6498i | −0.197570 | + | 0.114067i | ||||
\(296\) | −411.089 | −1.38881 | ||||||||
\(297\) | 511.269 | 1.72144 | ||||||||
\(298\) | 39.5683 | − | 68.5343i | 0.132780 | − | 0.229981i | ||||
\(299\) | −165.885 | − | 95.7738i | −0.554800 | − | 0.320314i | ||||
\(300\) | − | 252.722i | − | 0.842405i | ||||||
\(301\) | 54.6812 | − | 94.7105i | 0.181665 | − | 0.314653i | ||||
\(302\) | − | 9.63087i | − | 0.0318903i | ||||||
\(303\) | 792.319i | 2.61491i | ||||||||
\(304\) | 36.5466 | + | 301.795i | 0.120219 | + | 0.992747i | ||||
\(305\) | −57.4534 | −0.188372 | ||||||||
\(306\) | −150.907 | −0.493160 | ||||||||
\(307\) | 77.7831 | + | 44.9081i | 0.253365 | + | 0.146280i | 0.621304 | − | 0.783569i | \(-0.286603\pi\) |
−0.367939 | + | 0.929850i | \(0.619936\pi\) | |||||||
\(308\) | 708.087 | 2.29898 | ||||||||
\(309\) | −407.998 | + | 706.673i | −1.32038 | + | 2.28697i | ||||
\(310\) | −29.0021 | − | 16.7444i | −0.0935551 | − | 0.0540141i | ||||
\(311\) | 345.134i | 1.10976i | 0.831932 | + | 0.554878i | \(0.187235\pi\) | ||||
−0.831932 | + | 0.554878i | \(0.812765\pi\) | |||||||
\(312\) | 234.928i | 0.752974i | ||||||||
\(313\) | −261.361 | − | 452.691i | −0.835020 | − | 1.44630i | −0.894014 | − | 0.448039i | \(-0.852123\pi\) |
0.0589940 | − | 0.998258i | \(-0.481211\pi\) | |||||||
\(314\) | −58.0911 | + | 100.617i | −0.185003 | + | 0.320435i | ||||
\(315\) | − | 524.705i | − | 1.66573i | ||||||
\(316\) | −272.364 | − | 157.250i | −0.861913 | − | 0.497625i | ||||
\(317\) | −1.54659 | − | 2.67877i | −0.00487882 | − | 0.00845037i | 0.863576 | − | 0.504219i | \(-0.168220\pi\) |
−0.868455 | + | 0.495769i | \(0.834886\pi\) | |||||||
\(318\) | − | 392.438i | − | 1.23408i | ||||||
\(319\) | 113.602 | − | 65.5881i | 0.356119 | − | 0.205605i | ||||
\(320\) | 111.271 | − | 192.727i | 0.347723 | − | 0.602273i | ||||
\(321\) | −444.475 | + | 769.854i | −1.38466 | + | 2.39830i | ||||
\(322\) | −322.135 | − | 557.953i | −1.00042 | − | 1.73277i | ||||
\(323\) | −88.1822 | − | 37.6043i | −0.273010 | − | 0.116422i | ||||
\(324\) | −16.0911 | + | 27.8706i | −0.0496639 | + | 0.0860204i | ||||
\(325\) | 38.7267 | − | 67.0766i | 0.119159 | − | 0.206390i | ||||
\(326\) | − | 415.767i | − | 1.27536i | ||||||
\(327\) | 346.408 | − | 199.999i | 1.05935 | − | 0.611617i | ||||
\(328\) | 139.636 | − | 241.856i | 0.425718 | − | 0.737366i | ||||
\(329\) | 111.681 | + | 193.437i | 0.339456 | + | 0.587956i | ||||
\(330\) | −298.566 | − | 517.132i | −0.904746 | − | 1.56707i | ||||
\(331\) | − | 103.542i | − | 0.312817i | −0.987692 | − | 0.156408i | \(-0.950008\pi\) | ||
0.987692 | − | 0.156408i | \(-0.0499916\pi\) | |||||||
\(332\) | 371.969i | 1.12039i | ||||||||
\(333\) | −384.226 | − | 665.498i | −1.15383 | − | 1.99849i | ||||
\(334\) | −206.638 | + | 119.302i | −0.618676 | + | 0.357193i | ||||
\(335\) | 333.301i | 0.994930i | ||||||||
\(336\) | −395.089 | + | 684.314i | −1.17586 | + | 2.03665i | ||||
\(337\) | 248.203 | − | 429.900i | 0.736507 | − | 1.27567i | −0.217552 | − | 0.976049i | \(-0.569807\pi\) |
0.954059 | − | 0.299619i | \(-0.0968595\pi\) | |||||||
\(338\) | 133.000 | − | 230.363i | 0.393491 | − | 0.681547i | ||||
\(339\) | 114.829 | + | 66.2964i | 0.338728 | + | 0.195564i | ||||
\(340\) | 35.0890 | + | 60.7760i | 0.103203 | + | 0.178753i | ||||
\(341\) | 84.4793 | 0.247740 | ||||||||
\(342\) | −454.408 | + | 341.238i | −1.32868 | + | 0.997772i | ||||
\(343\) | 38.5235i | 0.112313i | ||||||||
\(344\) | 75.0890 | + | 43.3527i | 0.218282 | + | 0.126025i | ||||
\(345\) | −271.657 | + | 470.524i | −0.787413 | + | 1.36384i | ||||
\(346\) | 96.2733 | − | 166.750i | 0.278247 | − | 0.481937i | ||||
\(347\) | 484.351 | + | 279.640i | 1.39583 | + | 0.805880i | 0.993952 | − | 0.109815i | \(-0.0350258\pi\) |
0.401873 | + | 0.915695i | \(0.368359\pi\) | |||||||
\(348\) | 146.384i | 0.420644i | ||||||||
\(349\) | −507.271 | −1.45350 | −0.726750 | − | 0.686902i | \(-0.758970\pi\) | ||||
−0.726750 | + | 0.686902i | \(0.758970\pi\) | |||||||
\(350\) | 225.612 | − | 130.257i | 0.644605 | − | 0.372163i | ||||
\(351\) | −151.432 | + | 87.4291i | −0.431429 | + | 0.249086i | ||||
\(352\) | 561.390i | 1.59486i | ||||||||
\(353\) | −95.7723 | −0.271310 | −0.135655 | − | 0.990756i | \(-0.543314\pi\) | ||||
−0.135655 | + | 0.990756i | \(0.543314\pi\) | |||||||
\(354\) | 94.7267 | + | 164.071i | 0.267590 | + | 0.463479i | ||||
\(355\) | 44.0197 | − | 25.4148i | 0.123999 | − | 0.0715909i | ||||
\(356\) | 224.998 | + | 389.708i | 0.632017 | + | 1.09468i | ||||
\(357\) | −124.590 | − | 215.796i | −0.348992 | − | 0.604471i | ||||
\(358\) | − | 410.733i | − | 1.14730i | ||||||
\(359\) | −185.715 | − | 107.222i | −0.517311 | − | 0.298670i | 0.218523 | − | 0.975832i | \(-0.429876\pi\) |
−0.735834 | + | 0.677162i | \(0.763210\pi\) | |||||||
\(360\) | 416.000 | 1.15556 | ||||||||
\(361\) | −350.565 | + | 86.1686i | −0.971095 | + | 0.238694i | ||||
\(362\) | 215.885 | + | 373.924i | 0.596368 | + | 1.03294i | ||||
\(363\) | 791.655 | + | 457.062i | 2.18087 | + | 1.25913i | ||||
\(364\) | −209.727 | + | 121.086i | −0.576172 | + | 0.332653i | ||||
\(365\) | 60.6931 | + | 105.123i | 0.166282 | + | 0.288010i | ||||
\(366\) | 161.736i | 0.441901i | ||||||||
\(367\) | −332.602 | + | 192.028i | −0.906272 | + | 0.523237i | −0.879230 | − | 0.476398i | \(-0.841942\pi\) |
−0.0270425 | + | 0.999634i | \(0.508609\pi\) | |||||||
\(368\) | 442.360 | − | 255.397i | 1.20207 | − | 0.694013i | ||||
\(369\) | 522.043 | 1.41475 | ||||||||
\(370\) | −178.681 | + | 309.485i | −0.482922 | + | 0.836446i | ||||
\(371\) | 350.341 | − | 202.269i | 0.944314 | − | 0.545200i | ||||
\(372\) | −47.1366 | + | 81.6431i | −0.126711 | + | 0.219471i | ||||
\(373\) | 258.091 | 0.691933 | 0.345967 | − | 0.938247i | \(-0.387551\pi\) | ||||
0.345967 | + | 0.938247i | \(0.387551\pi\) | |||||||
\(374\) | −153.315 | − | 88.5163i | −0.409932 | − | 0.236675i | ||||
\(375\) | −558.725 | − | 322.580i | −1.48993 | − | 0.860213i | ||||
\(376\) | −153.362 | + | 88.5438i | −0.407879 | + | 0.235489i | ||||
\(377\) | −22.4317 | + | 38.8528i | −0.0595005 | + | 0.103058i | ||||
\(378\) | −588.135 | −1.55591 | ||||||||
\(379\) | 118.568i | 0.312845i | 0.987690 | + | 0.156423i | \(0.0499962\pi\) | ||||
−0.987690 | + | 0.156423i | \(0.950004\pi\) | |||||||
\(380\) | 243.089 | + | 103.662i | 0.639708 | + | 0.272796i | ||||
\(381\) | 690.634 | 1.81269 | ||||||||
\(382\) | 365.096i | 0.955748i | ||||||||
\(383\) | 534.077 | + | 308.350i | 1.39446 | + | 0.805090i | 0.993805 | − | 0.111140i | \(-0.0354502\pi\) |
0.400652 | + | 0.916230i | \(0.368783\pi\) | |||||||
\(384\) | −542.542 | − | 313.237i | −1.41287 | − | 0.815721i | ||||
\(385\) | 307.772 | − | 533.077i | 0.799408 | − | 1.38462i | ||||
\(386\) | 101.046 | − | 175.016i | 0.261776 | − | 0.453409i | ||||
\(387\) | 162.079i | 0.418808i | ||||||||
\(388\) | −255.909 | + | 443.247i | −0.659559 | + | 1.14239i | ||||
\(389\) | −210.954 | − | 365.384i | −0.542299 | − | 0.939290i | −0.998772 | − | 0.0495524i | \(-0.984221\pi\) |
0.456472 | − | 0.889738i | \(-0.349113\pi\) | |||||||
\(390\) | 176.863 | + | 102.112i | 0.453496 | + | 0.261826i | ||||
\(391\) | 161.077i | 0.411962i | ||||||||
\(392\) | −422.542 | −1.07791 | ||||||||
\(393\) | −330.771 | − | 572.913i | −0.841657 | − | 1.45779i | ||||
\(394\) | 20.3168 | 0.0515654 | ||||||||
\(395\) | −236.768 | + | 136.698i | −0.599413 | + | 0.346071i | ||||
\(396\) | −908.816 | + | 524.705i | −2.29499 | + | 1.32501i | ||||
\(397\) | 264.533 | − | 458.184i | 0.666329 | − | 1.15412i | −0.312594 | − | 0.949887i | \(-0.601198\pi\) |
0.978923 | − | 0.204229i | \(-0.0654687\pi\) | |||||||
\(398\) | 317.952 | − | 183.570i | 0.798875 | − | 0.461231i | ||||
\(399\) | −863.132 | − | 368.073i | −2.16324 | − | 0.922488i | ||||
\(400\) | 103.271 | + | 178.871i | 0.258178 | + | 0.447177i | ||||
\(401\) | −0.955488 | + | 1.65495i | −0.00238276 | + | 0.00412707i | −0.867214 | − | 0.497935i | \(-0.834092\pi\) |
0.864832 | + | 0.502062i | \(0.167425\pi\) | |||||||
\(402\) | 938.269 | 2.33400 | ||||||||
\(403\) | −25.0217 | + | 14.4463i | −0.0620887 | + | 0.0358469i | ||||
\(404\) | −323.770 | − | 560.786i | −0.801411 | − | 1.38809i | ||||
\(405\) | 13.9881 | + | 24.2281i | 0.0345385 | + | 0.0598224i | ||||
\(406\) | −130.681 | + | 75.4488i | −0.321875 | + | 0.185834i | ||||
\(407\) | − | 901.489i | − | 2.21496i | ||||||
\(408\) | 171.089 | − | 98.7783i | 0.419336 | − | 0.242104i | ||||
\(409\) | 142.932 | + | 247.565i | 0.349466 | + | 0.605293i | 0.986155 | − | 0.165828i | \(-0.0530296\pi\) |
−0.636689 | + | 0.771121i | \(0.719696\pi\) | |||||||
\(410\) | −121.386 | − | 210.247i | −0.296064 | − | 0.512797i | ||||
\(411\) | − | 544.162i | − | 1.32400i | ||||||
\(412\) | − | 666.891i | − | 1.61867i | ||||||
\(413\) | −97.6475 | + | 169.130i | −0.236435 | + | 0.409517i | ||||
\(414\) | 826.907 | + | 477.415i | 1.99736 | + | 1.15318i | ||||
\(415\) | 280.034 | + | 161.677i | 0.674780 | + | 0.389584i | ||||
\(416\) | −96.0000 | − | 166.277i | −0.230769 | − | 0.399704i | ||||
\(417\) | 77.6377 | 0.186181 | ||||||||
\(418\) | −661.816 | + | 80.1441i | −1.58329 | + | 0.191732i | ||||
\(419\) | − | 833.373i | − | 1.98896i | −0.104936 | − | 0.994479i | \(-0.533464\pi\) | ||
0.104936 | − | 0.994479i | \(-0.466536\pi\) | |||||||
\(420\) | 343.453 | + | 594.879i | 0.817746 | + | 1.41638i | ||||
\(421\) | 404.964 | − | 701.419i | 0.961910 | − | 1.66608i | 0.244214 | − | 0.969721i | \(-0.421470\pi\) |
0.717696 | − | 0.696356i | \(-0.245197\pi\) | |||||||
\(422\) | 510.451 | + | 294.709i | 1.20960 | + | 0.698363i | ||||
\(423\) | −286.681 | − | 165.515i | −0.677733 | − | 0.391289i | ||||
\(424\) | 160.364 | + | 277.759i | 0.378218 | + | 0.655093i | ||||
\(425\) | −65.1325 | −0.153253 | ||||||||
\(426\) | −71.5445 | − | 123.919i | −0.167945 | − | 0.290889i | ||||
\(427\) | −144.386 | + | 83.3614i | −0.338141 | + | 0.195226i | ||||
\(428\) | − | 726.515i | − | 1.69746i | ||||||
\(429\) | −515.180 | −1.20089 | ||||||||
\(430\) | 65.2754 | − | 37.6868i | 0.151803 | − | 0.0876436i | ||||
\(431\) | 222.564 | − | 128.497i | 0.516390 | − | 0.298138i | −0.219066 | − | 0.975710i | \(-0.570301\pi\) |
0.735456 | + | 0.677572i | \(0.236968\pi\) | |||||||
\(432\) | − | 466.289i | − | 1.07937i | ||||||
\(433\) | 121.137 | + | 209.815i | 0.279761 | + | 0.484561i | 0.971325 | − | 0.237754i | \(-0.0764113\pi\) |
−0.691564 | + | 0.722315i | \(0.743078\pi\) | |||||||
\(434\) | −97.1801 | −0.223917 | ||||||||
\(435\) | 110.204 | + | 63.6263i | 0.253342 | + | 0.146267i | ||||
\(436\) | −163.453 | + | 283.110i | −0.374893 | + | 0.649334i | ||||
\(437\) | 364.236 | + | 485.032i | 0.833491 | + | 1.10991i | ||||
\(438\) | 295.931 | − | 170.856i | 0.675641 | − | 0.390081i | ||||
\(439\) | −251.216 | − | 145.040i | −0.572246 | − | 0.330386i | 0.185800 | − | 0.982588i | \(-0.440512\pi\) |
−0.758046 | + | 0.652201i | \(0.773846\pi\) | |||||||
\(440\) | 422.638 | + | 244.010i | 0.960540 | + | 0.554568i | ||||
\(441\) | −394.931 | − | 684.040i | −0.895534 | − | 1.55111i | ||||
\(442\) | 60.5466 | 0.136983 | ||||||||
\(443\) | 187.649 | − | 108.339i | 0.423586 | − | 0.244557i | −0.273024 | − | 0.962007i | \(-0.588024\pi\) |
0.696610 | + | 0.717450i | \(0.254691\pi\) | |||||||
\(444\) | 871.224 | + | 503.001i | 1.96222 | + | 1.13289i | ||||
\(445\) | 391.184 | 0.879066 | ||||||||
\(446\) | 57.8851 | + | 33.4200i | 0.129787 | + | 0.0749327i | ||||
\(447\) | −167.715 | + | 96.8302i | −0.375201 | + | 0.216622i | ||||
\(448\) | − | 645.791i | − | 1.44150i | ||||||
\(449\) | −315.820 | −0.703385 | −0.351693 | − | 0.936116i | \(-0.614394\pi\) | ||||
−0.351693 | + | 0.936116i | \(0.614394\pi\) | |||||||
\(450\) | −193.046 | + | 334.365i | −0.428990 | + | 0.743033i | ||||
\(451\) | 530.373 | + | 306.211i | 1.17599 | + | 0.678960i | ||||
\(452\) | −108.364 | −0.239744 | ||||||||
\(453\) | −11.7842 | + | 20.4108i | −0.0260136 | + | 0.0450569i | ||||
\(454\) | − | 54.3486i | − | 0.119711i | ||||||
\(455\) | 210.521i | 0.462684i | ||||||||
\(456\) | 291.818 | − | 684.314i | 0.639951 | − | 1.50069i | ||||
\(457\) | −642.996 | −1.40699 | −0.703497 | − | 0.710699i | \(-0.748379\pi\) | ||||
−0.703497 | + | 0.710699i | \(0.748379\pi\) | |||||||
\(458\) | −503.636 | −1.09964 | ||||||||
\(459\) | 127.343 | + | 73.5213i | 0.277435 | + | 0.160177i | ||||
\(460\) | − | 444.036i | − | 0.965296i | ||||||
\(461\) | 109.907 | − | 190.364i | 0.238410 | − | 0.412938i | −0.721848 | − | 0.692051i | \(-0.756707\pi\) |
0.960258 | + | 0.279114i | \(0.0900406\pi\) | |||||||
\(462\) | −1500.65 | − | 866.403i | −3.24817 | − | 1.87533i | ||||
\(463\) | 66.7372i | 0.144141i | 0.997400 | + | 0.0720704i | \(0.0229606\pi\) | ||||
−0.997400 | + | 0.0720704i | \(0.977039\pi\) | |||||||
\(464\) | −59.8178 | − | 103.607i | −0.128918 | − | 0.223292i | ||||
\(465\) | 40.9762 | + | 70.9728i | 0.0881208 | + | 0.152630i | ||||
\(466\) | 164.545 | − | 284.999i | 0.353100 | − | 0.611587i | ||||
\(467\) | 171.878i | 0.368046i | 0.982922 | + | 0.184023i | \(0.0589121\pi\) | ||||
−0.982922 | + | 0.184023i | \(0.941088\pi\) | |||||||
\(468\) | 179.453 | − | 310.822i | 0.383447 | − | 0.664150i | ||||
\(469\) | 483.600 | + | 837.620i | 1.03113 | + | 1.78597i | ||||
\(470\) | 153.943i | 0.327539i | ||||||||
\(471\) | 246.226 | − | 142.158i | 0.522772 | − | 0.301823i | ||||
\(472\) | −134.091 | − | 77.4175i | −0.284091 | − | 0.164020i | ||||
\(473\) | −95.0694 | + | 164.665i | −0.200992 | + | 0.348129i | ||||
\(474\) | 384.816 | + | 666.520i | 0.811848 | + | 1.40616i | ||||
\(475\) | −196.126 | + | 147.281i | −0.412896 | + | 0.310065i | ||||
\(476\) | 176.364 | + | 101.824i | 0.370513 | + | 0.213916i | ||||
\(477\) | −299.770 | + | 519.217i | −0.628449 | + | 1.08851i | ||||
\(478\) | 238.495i | 0.498943i | ||||||||
\(479\) | −19.8178 | + | 11.4418i | −0.0413733 | + | 0.0238869i | −0.520544 | − | 0.853835i | \(-0.674271\pi\) |
0.479171 | + | 0.877722i | \(0.340937\pi\) | |||||||
\(480\) | −471.636 | + | 272.299i | −0.982574 | + | 0.567289i | ||||
\(481\) | 154.158 | + | 267.010i | 0.320496 | + | 0.555115i | ||||
\(482\) | 66.2277 | + | 114.710i | 0.137402 | + | 0.237987i | ||||
\(483\) | 1576.63i | 3.26425i | ||||||||
\(484\) | −747.089 | −1.54357 | ||||||||
\(485\) | 222.463 | + | 385.318i | 0.458687 | + | 0.794469i | ||||
\(486\) | −386.091 | + | 222.910i | −0.794426 | + | 0.458662i | ||||
\(487\) | − | 146.082i | − | 0.299963i | −0.988689 | − | 0.149982i | \(-0.952079\pi\) | ||
0.988689 | − | 0.149982i | \(-0.0479215\pi\) | |||||||
\(488\) | −66.0911 | − | 114.473i | −0.135433 | − | 0.234576i | ||||
\(489\) | −508.726 | + | 881.139i | −1.04034 | + | 1.80192i | ||||
\(490\) | −183.659 | + | 318.107i | −0.374815 | + | 0.649199i | ||||
\(491\) | −412.931 | − | 238.406i | −0.840999 | − | 0.485551i | 0.0166045 | − | 0.999862i | \(-0.494714\pi\) |
−0.857604 | + | 0.514311i | \(0.828048\pi\) | |||||||
\(492\) | −591.861 | + | 341.711i | −1.20297 | + | 0.694535i | ||||
\(493\) | 37.7267 | 0.0765248 | ||||||||
\(494\) | 182.317 | − | 136.911i | 0.369062 | − | 0.277148i | ||||
\(495\) | 912.259i | 1.84295i | ||||||||
\(496\) | − | 77.0470i | − | 0.155337i | ||||||
\(497\) | 73.7505 | − | 127.740i | 0.148391 | − | 0.257021i | ||||
\(498\) | 455.135 | − | 788.316i | 0.913925 | − | 1.58296i | ||||
\(499\) | 501.621 | + | 289.611i | 1.00525 | + | 0.580382i | 0.909798 | − | 0.415052i | \(-0.136236\pi\) |
0.0954538 | + | 0.995434i | \(0.469570\pi\) | |||||||
\(500\) | 527.271 | 1.05454 | ||||||||
\(501\) | 583.905 | 1.16548 | ||||||||
\(502\) | −322.247 | + | 186.050i | −0.641927 | + | 0.370617i | ||||
\(503\) | −181.830 | + | 104.979i | −0.361490 | + | 0.208707i | −0.669734 | − | 0.742601i | \(-0.733592\pi\) |
0.308244 | + | 0.951307i | \(0.400259\pi\) | |||||||
\(504\) | 1045.45 | − | 603.590i | 2.07430 | − | 1.19760i | ||||
\(505\) | −562.911 | −1.11468 | ||||||||
\(506\) | 560.067 | + | 970.065i | 1.10685 | + | 1.91712i | ||||
\(507\) | −563.736 | + | 325.473i | −1.11190 | + | 0.641958i | ||||
\(508\) | −488.816 | + | 282.218i | −0.962236 | + | 0.555547i | ||||
\(509\) | 70.9545 | + | 122.897i | 0.139400 | + | 0.241447i | 0.927270 | − | 0.374394i | \(-0.122149\pi\) |
−0.787870 | + | 0.615842i | \(0.788816\pi\) | |||||||
\(510\) | − | 171.737i | − | 0.336740i | ||||||
\(511\) | 305.055 | + | 176.124i | 0.596977 | + | 0.344665i | ||||
\(512\) | 512.000 | 1.00000 | ||||||||
\(513\) | 549.702 | − | 66.5674i | 1.07154 | − | 0.129761i | ||||
\(514\) | −303.725 | − | 526.066i | −0.590904 | − | 1.02348i | ||||
\(515\) | −502.063 | − | 289.866i | −0.974880 | − | 0.562847i | ||||
\(516\) | −106.091 | − | 183.755i | −0.205603 | − | 0.356115i | ||||
\(517\) | −194.170 | − | 336.313i | −0.375571 | − | 0.650508i | ||||
\(518\) | 1037.02i | 2.00197i | ||||||||
\(519\) | −408.065 | + | 235.597i | −0.786253 | + | 0.453943i | ||||
\(520\) | −166.907 | −0.320975 | ||||||||
\(521\) | −162.683 | −0.312252 | −0.156126 | − | 0.987737i | \(-0.549901\pi\) | ||||
−0.156126 | + | 0.987737i | \(0.549901\pi\) | |||||||
\(522\) | 111.818 | − | 193.674i | 0.214210 | − | 0.371023i | ||||
\(523\) | 531.564 | − | 306.899i | 1.01638 | − | 0.586804i | 0.103323 | − | 0.994648i | \(-0.467052\pi\) |
0.913052 | + | 0.407843i | \(0.133719\pi\) | |||||||
\(524\) | 468.226 | + | 270.330i | 0.893560 | + | 0.515897i | ||||
\(525\) | −637.521 | −1.21433 | ||||||||
\(526\) | 150.475 | + | 86.8769i | 0.286074 | + | 0.165165i | ||||
\(527\) | 21.0414 | + | 12.1483i | 0.0399268 | + | 0.0230517i | ||||
\(528\) | 686.907 | − | 1189.76i | 1.30096 | − | 2.25333i | ||||
\(529\) | 245.090 | − | 424.508i | 0.463308 | − | 0.802473i | ||||
\(530\) | 278.812 | 0.526060 | ||||||||
\(531\) | − | 289.434i | − | 0.545074i | ||||||
\(532\) | 761.315 | − | 92.1932i | 1.43104 | − | 0.173295i | ||||
\(533\) | −209.453 | −0.392971 | ||||||||
\(534\) | − | 1101.21i | − | 2.06220i | ||||||
\(535\) | −546.950 | − | 315.782i | −1.02234 | − | 0.590247i | ||||
\(536\) | −664.087 | + | 383.411i | −1.23897 | + | 0.715319i | ||||
\(537\) | −502.565 | + | 870.468i | −0.935876 | + | 1.62098i | ||||
\(538\) | −195.271 | + | 338.220i | −0.362958 | + | 0.628661i | ||||
\(539\) | − | 926.606i | − | 1.71912i | ||||||
\(540\) | −351.041 | − | 202.674i | −0.650077 | − | 0.375322i | ||||
\(541\) | −125.818 | − | 217.923i | −0.232565 | − | 0.402815i | 0.725997 | − | 0.687698i | \(-0.241379\pi\) |
−0.958562 | + | 0.284883i | \(0.908045\pi\) | |||||||
\(542\) | −608.020 | − | 351.040i | −1.12181 | − | 0.647676i | ||||
\(543\) | − | 1056.61i | − | 1.94588i | ||||||
\(544\) | −80.7288 | + | 139.826i | −0.148398 | + | 0.257034i | ||||
\(545\) | 142.091 | + | 246.109i | 0.260718 | + | 0.451576i | ||||
\(546\) | 592.634 | 1.08541 | ||||||||
\(547\) | 289.521 | − | 167.155i | 0.529288 | − | 0.305585i | −0.211438 | − | 0.977391i | \(-0.567815\pi\) |
0.740727 | + | 0.671807i | \(0.234481\pi\) | |||||||
\(548\) | 222.364 | + | 385.146i | 0.405774 | + | 0.702822i | ||||
\(549\) | 123.545 | − | 213.985i | 0.225036 | − | 0.389773i | ||||
\(550\) | −392.252 | + | 226.467i | −0.713185 | + | 0.411757i | ||||
\(551\) | 113.602 | − | 85.3095i | 0.206174 | − | 0.154827i | ||||
\(552\) | −1250.00 | −2.26449 | ||||||||
\(553\) | −396.681 | + | 687.072i | −0.717326 | + | 1.24244i | ||||
\(554\) | −230.859 | −0.416713 | ||||||||
\(555\) | 757.360 | − | 437.262i | 1.36461 | − | 0.787860i | ||||
\(556\) | −54.9503 | + | 31.7256i | −0.0988315 | + | 0.0570604i | ||||
\(557\) | −303.180 | − | 525.123i | −0.544309 | − | 0.942771i | −0.998650 | − | 0.0519430i | \(-0.983459\pi\) |
0.454341 | − | 0.890828i | \(-0.349875\pi\) | |||||||
\(558\) | 124.729 | − | 72.0122i | 0.223528 | − | 0.129054i | ||||
\(559\) | − | 65.0290i | − | 0.116331i | ||||||
\(560\) | −486.178 | − | 280.695i | −0.868175 | − | 0.501241i | ||||
\(561\) | 216.614 | + | 375.186i | 0.386121 | + | 0.668781i | ||||
\(562\) | 23.9979 | + | 41.5656i | 0.0427009 | + | 0.0739602i | ||||
\(563\) | 136.112i | 0.241762i | 0.992667 | + | 0.120881i | \(0.0385719\pi\) | ||||
−0.992667 | + | 0.120881i | \(0.961428\pi\) | |||||||
\(564\) | 433.362 | 0.768373 | ||||||||
\(565\) | −47.1009 | + | 81.5812i | −0.0833645 | + | 0.144392i | ||||
\(566\) | −250.473 | − | 144.611i | −0.442532 | − | 0.255496i | ||||
\(567\) | 70.3069 | + | 40.5917i | 0.123998 | + | 0.0715904i | ||||
\(568\) | 101.275 | + | 58.4714i | 0.178302 | + | 0.102943i | ||||
\(569\) | 1007.04 | 1.76984 | 0.884922 | − | 0.465739i | \(-0.154211\pi\) | ||||
0.884922 | + | 0.465739i | \(0.154211\pi\) | |||||||
\(570\) | −388.341 | − | 517.132i | −0.681299 | − | 0.907249i | ||||
\(571\) | 433.551i | 0.759284i | 0.925133 | + | 0.379642i | \(0.123953\pi\) | ||||
−0.925133 | + | 0.379642i | \(0.876047\pi\) | |||||||
\(572\) | 364.634 | − | 210.521i | 0.637471 | − | 0.368044i | ||||
\(573\) | 446.725 | − | 773.750i | 0.779624 | − | 1.35035i | ||||
\(574\) | −610.111 | − | 352.248i | −1.06291 | − | 0.613672i | ||||
\(575\) | 356.899 | + | 206.056i | 0.620694 | + | 0.358358i | ||||
\(576\) | 478.542 | + | 828.860i | 0.830803 | + | 1.43899i | ||||
\(577\) | 459.998 | 0.797223 | 0.398612 | − | 0.917120i | \(-0.369492\pi\) | ||||
0.398612 | + | 0.917120i | \(0.369492\pi\) | |||||||
\(578\) | 263.542 | + | 456.469i | 0.455956 | + | 0.789739i | ||||
\(579\) | −428.293 | + | 247.275i | −0.739711 | + | 0.427073i | ||||
\(580\) | −104.000 | −0.179310 | ||||||||
\(581\) | 938.336 | 1.61504 | ||||||||
\(582\) | 1084.70 | − | 626.251i | 1.86374 | − | 1.07603i | ||||
\(583\) | −609.107 | + | 351.668i | −1.04478 | + | 0.603204i | ||||
\(584\) | −139.636 | + | 241.856i | −0.239102 | + | 0.414137i | ||||
\(585\) | −156.000 | − | 270.200i | −0.266667 | − | 0.461880i | ||||
\(586\) | 431.588 | 0.736498 | ||||||||
\(587\) | −805.568 | − | 465.095i | −1.37235 | − | 0.792326i | −0.381125 | − | 0.924524i | \(-0.624463\pi\) |
−0.991223 | + | 0.132198i | \(0.957797\pi\) | |||||||
\(588\) | 895.497 | + | 517.015i | 1.52295 | + | 0.879278i | ||||
\(589\) | 90.8297 | − | 10.9992i | 0.154210 | − | 0.0186744i | ||||
\(590\) | −116.566 | + | 67.2996i | −0.197570 | + | 0.114067i | ||||
\(591\) | −43.0575 | − | 24.8592i | −0.0728553 | − | 0.0420630i | ||||
\(592\) | −822.178 | −1.38881 | ||||||||
\(593\) | 218.181 | + | 377.901i | 0.367928 | + | 0.637270i | 0.989241 | − | 0.146292i | \(-0.0467340\pi\) |
−0.621314 | + | 0.783562i | \(0.713401\pi\) | |||||||
\(594\) | 1022.54 | 1.72144 | ||||||||
\(595\) | 153.315 | − | 88.5163i | 0.257672 | − | 0.148767i | ||||
\(596\) | 79.1366 | − | 137.069i | 0.132780 | − | 0.229981i | ||||
\(597\) | −898.451 | −1.50494 | ||||||||
\(598\) | −331.770 | − | 191.548i | −0.554800 | − | 0.320314i | ||||
\(599\) | −618.142 | + | 356.885i | −1.03196 | + | 0.595801i | −0.917545 | − | 0.397633i | \(-0.869832\pi\) |
−0.114412 | + | 0.993433i | \(0.536499\pi\) | |||||||
\(600\) | − | 505.443i | − | 0.842405i | ||||||
\(601\) | 21.9586 | 0.0365368 | 0.0182684 | − | 0.999833i | \(-0.494185\pi\) | ||||
0.0182684 | + | 0.999833i | \(0.494185\pi\) | |||||||
\(602\) | 109.362 | − | 189.421i | 0.181665 | − | 0.314653i | ||||
\(603\) | −1241.38 | − | 716.712i | −2.05868 | − | 1.18858i | ||||
\(604\) | − | 19.2617i | − | 0.0318903i | ||||||
\(605\) | −324.725 | + | 562.440i | −0.536735 | + | 0.929652i | ||||
\(606\) | 1584.64i | 2.61491i | ||||||||
\(607\) | 305.012i | 0.502492i | 0.967923 | + | 0.251246i | \(0.0808403\pi\) | ||||
−0.967923 | + | 0.251246i | \(0.919160\pi\) | |||||||
\(608\) | 73.0932 | + | 603.590i | 0.120219 | + | 0.992747i | ||||
\(609\) | 369.271 | 0.606357 | ||||||||
\(610\) | −114.907 | −0.188372 | ||||||||
\(611\) | 115.022 | + | 66.4078i | 0.188252 | + | 0.108687i | ||||
\(612\) | −301.814 | −0.493160 | ||||||||
\(613\) | 499.043 | − | 864.369i | 0.814100 | − | 1.41006i | −0.0958719 | − | 0.995394i | \(-0.530564\pi\) |
0.909972 | − | 0.414669i | \(-0.136103\pi\) | |||||||
\(614\) | 155.566 | + | 89.8162i | 0.253365 | + | 0.146280i | ||||
\(615\) | 594.104i | 0.966022i | ||||||||
\(616\) | 1416.17 | 2.29898 | ||||||||
\(617\) | 66.0683 | + | 114.434i | 0.107080 | + | 0.185468i | 0.914586 | − | 0.404391i | \(-0.132517\pi\) |
−0.807506 | + | 0.589859i | \(0.799183\pi\) | |||||||
\(618\) | −815.996 | + | 1413.35i | −1.32038 | + | 2.28697i | ||||
\(619\) | − | 432.512i | − | 0.698727i | −0.936987 | − | 0.349363i | \(-0.886398\pi\) | ||
0.936987 | − | 0.349363i | \(-0.113602\pi\) | |||||||
\(620\) | −58.0041 | − | 33.4887i | −0.0935551 | − | 0.0540141i | ||||
\(621\) | −465.190 | − | 805.733i | −0.749098 | − | 1.29748i | ||||
\(622\) | 690.268i | 1.10976i | ||||||||
\(623\) | 983.085 | − | 567.584i | 1.57799 | − | 0.911050i | ||||
\(624\) | 469.856i | 0.752974i | ||||||||
\(625\) | 67.8188 | − | 117.466i | 0.108510 | − | 0.187945i | ||||
\(626\) | −522.723 | − | 905.382i | −0.835020 | − | 1.44630i | ||||
\(627\) | 1500.65 | + | 639.936i | 2.39339 | + | 1.02063i | ||||
\(628\) | −116.182 | + | 201.233i | −0.185003 | + | 0.320435i | ||||
\(629\) | 129.636 | − | 224.535i | 0.206098 | − | 0.356972i | ||||
\(630\) | − | 1049.41i | − | 1.66573i | ||||||
\(631\) | 592.283 | − | 341.955i | 0.938642 | − | 0.541925i | 0.0491077 | − | 0.998793i | \(-0.484362\pi\) |
0.889534 | + | 0.456868i | \(0.151029\pi\) | |||||||
\(632\) | −544.729 | − | 314.499i | −0.861913 | − | 0.497625i | ||||
\(633\) | −721.202 | − | 1249.16i | −1.13934 | − | 1.97339i | ||||
\(634\) | −3.09317 | − | 5.35753i | −0.00487882 | − | 0.00845037i | ||||
\(635\) | 490.668i | 0.772705i | ||||||||
\(636\) | − | 784.876i | − | 1.23408i | ||||||
\(637\) | 158.453 | + | 274.449i | 0.248749 | + | 0.430847i | ||||
\(638\) | 227.204 | − | 131.176i | 0.356119 | − | 0.205605i | ||||
\(639\) | 218.602i | 0.342100i | ||||||||
\(640\) | 222.542 | − | 385.455i | 0.347723 | − | 0.602273i | ||||
\(641\) | 197.363 | − | 341.843i | 0.307899 | − | 0.533297i | −0.670003 | − | 0.742358i | \(-0.733707\pi\) |
0.977903 | + | 0.209061i | \(0.0670407\pi\) | |||||||
\(642\) | −888.950 | + | 1539.71i | −1.38466 | + | 2.39830i | ||||
\(643\) | −854.326 | − | 493.245i | −1.32866 | − | 0.767100i | −0.343564 | − | 0.939129i | \(-0.611634\pi\) |
−0.985092 | + | 0.172030i | \(0.944968\pi\) | |||||||
\(644\) | −644.269 | − | 1115.91i | −1.00042 | − | 1.73277i | ||||
\(645\) | −184.451 | −0.285971 | ||||||||
\(646\) | −176.364 | − | 75.2085i | −0.273010 | − | 0.116422i | ||||
\(647\) | 1173.93i | 1.81442i | 0.420674 | + | 0.907212i | \(0.361794\pi\) | ||||
−0.420674 | + | 0.907212i | \(0.638206\pi\) | |||||||
\(648\) | −32.1822 | + | 55.7412i | −0.0496639 | + | 0.0860204i | ||||
\(649\) | 169.771 | − | 294.052i | 0.261589 | − | 0.453085i | ||||
\(650\) | 77.4534 | − | 134.153i | 0.119159 | − | 0.206390i | ||||
\(651\) | 205.954 | + | 118.908i | 0.316366 | + | 0.182654i | ||||
\(652\) | − | 831.535i | − | 1.27536i | ||||||
\(653\) | −847.540 | −1.29792 | −0.648959 | − | 0.760823i | \(-0.724795\pi\) | ||||
−0.648959 | + | 0.760823i | \(0.724795\pi\) | |||||||
\(654\) | 692.816 | − | 399.997i | 1.05935 | − | 0.611617i | ||||
\(655\) | 407.032 | − | 235.000i | 0.621422 | − | 0.358778i | ||||
\(656\) | 279.271 | − | 483.712i | 0.425718 | − | 0.737366i | ||||
\(657\) | −522.043 | −0.794587 | ||||||||
\(658\) | 223.362 | + | 386.875i | 0.339456 | + | 0.587956i | ||||
\(659\) | 566.364 | − | 326.991i | 0.859430 | − | 0.496192i | −0.00439135 | − | 0.999990i | \(-0.501398\pi\) |
0.863821 | + | 0.503798i | \(0.168064\pi\) | |||||||
\(660\) | −597.132 | − | 1034.26i | −0.904746 | − | 1.56707i | ||||
\(661\) | 154.170 | + | 267.031i | 0.233238 | + | 0.403980i | 0.958759 | − | 0.284220i | \(-0.0917346\pi\) |
−0.725521 | + | 0.688200i | \(0.758401\pi\) | |||||||
\(662\) | − | 207.085i | − | 0.312817i | ||||||
\(663\) | −128.317 | − | 74.0837i | −0.193540 | − | 0.111740i | ||||
\(664\) | 743.938i | 1.12039i | ||||||||
\(665\) | 261.501 | − | 613.221i | 0.393235 | − | 0.922137i | ||||
\(666\) | −768.451 | − | 1331.00i | −1.15383 | − | 1.99849i | ||||
\(667\) | −206.727 | − | 119.354i | −0.309935 | − | 0.178941i | ||||
\(668\) | −413.275 | + | 238.605i | −0.618676 | + | 0.357193i | ||||
\(669\) | −81.7842 | − | 141.654i | −0.122248 | − | 0.211740i | ||||
\(670\) | 666.603i | 0.994930i | ||||||||
\(671\) | 251.032 | − | 144.933i | 0.374116 | − | 0.215996i | ||||
\(672\) | −790.178 | + | 1368.63i | −1.17586 | + | 2.03665i | ||||
\(673\) | 110.273 | 0.163853 | 0.0819267 | − | 0.996638i | \(-0.473893\pi\) | ||||
0.0819267 | + | 0.996638i | \(0.473893\pi\) | |||||||
\(674\) | 496.406 | − | 859.800i | 0.736507 | − | 1.27567i | ||||
\(675\) | 325.803 | − | 188.102i | 0.482671 | − | 0.278670i | ||||
\(676\) | 266.000 | − | 460.726i | 0.393491 | − | 0.681547i | ||||
\(677\) | −910.356 | −1.34469 | −0.672346 | − | 0.740237i | \(-0.734713\pi\) | ||||
−0.672346 | + | 0.740237i | \(0.734713\pi\) | |||||||
\(678\) | 229.657 | + | 132.593i | 0.338728 | + | 0.195564i | ||||
\(679\) | 1118.14 | + | 645.561i | 1.64675 | + | 0.950753i | ||||
\(680\) | 70.1780 | + | 121.552i | 0.103203 | + | 0.178753i | ||||
\(681\) | −66.5000 | + | 115.181i | −0.0976505 | + | 0.169136i | ||||
\(682\) | 168.959 | 0.247740 | ||||||||
\(683\) | 289.407i | 0.423729i | 0.977299 | + | 0.211864i | \(0.0679535\pi\) | ||||
−0.977299 | + | 0.211864i | \(0.932047\pi\) | |||||||
\(684\) | −908.816 | + | 682.476i | −1.32868 | + | 0.997772i | ||||
\(685\) | 386.606 | 0.564388 | ||||||||
\(686\) | 77.0470i | 0.112313i | ||||||||
\(687\) | 1067.36 | + | 616.240i | 1.55365 | + | 0.897001i | ||||
\(688\) | 150.178 | + | 86.7053i | 0.218282 | + | 0.126025i | ||||
\(689\) | 120.273 | − | 208.319i | 0.174562 | − | 0.302350i | ||||
\(690\) | −543.315 | + | 941.049i | −0.787413 | + | 1.36384i | ||||
\(691\) | − | 308.668i | − | 0.446698i | −0.974739 | − | 0.223349i | \(-0.928301\pi\) | ||
0.974739 | − | 0.223349i | \(-0.0716990\pi\) | |||||||
\(692\) | 192.547 | − | 333.500i | 0.278247 | − | 0.481937i | ||||
\(693\) | 1323.63 | + | 2292.60i | 1.91000 | + | 3.30822i | ||||
\(694\) | 968.703 | + | 559.281i | 1.39583 | + | 0.805880i | ||||
\(695\) | 55.1585i | 0.0793647i | ||||||||
\(696\) | 292.768i | 0.420644i | ||||||||
\(697\) | 88.0673 | + | 152.537i | 0.126352 | + | 0.218848i | ||||
\(698\) | −1014.54 | −1.45350 | ||||||||
\(699\) | −697.440 | + | 402.667i | −0.997769 | + | 0.576062i | ||||
\(700\) | 451.224 | − | 260.514i | 0.644605 | − | 0.372163i | ||||
\(701\) | −606.075 | + | 1049.75i | −0.864586 | + | 1.49751i | 0.00287094 | + | 0.999996i | \(0.499086\pi\) |
−0.867457 | + | 0.497512i | \(0.834247\pi\) | |||||||
\(702\) | −302.863 | + | 174.858i | −0.431429 | + | 0.249086i | ||||
\(703\) | −117.374 | − | 969.255i | −0.166962 | − | 1.37874i | ||||
\(704\) | 1122.78i | 1.59486i | ||||||||
\(705\) | 188.362 | − | 326.253i | 0.267181 | − | 0.462770i | ||||
\(706\) | −191.545 | −0.271310 | ||||||||
\(707\) | −1414.65 | + | 816.749i | −2.00092 | + | 1.15523i | ||||
\(708\) | 189.453 | + | 328.143i | 0.267590 | + | 0.463479i | ||||
\(709\) | −457.689 | − | 792.740i | −0.645541 | − | 1.11811i | −0.984176 | − | 0.177193i | \(-0.943298\pi\) |
0.338635 | − | 0.940918i | \(-0.390035\pi\) | |||||||
\(710\) | 88.0393 | − | 50.8295i | 0.123999 | − | 0.0715909i | ||||
\(711\) | − | 1175.79i | − | 1.65371i | ||||||
\(712\) | 449.996 | + | 779.416i | 0.632017 | + | 1.09468i | ||||
\(713\) | −76.8654 | − | 133.135i | −0.107806 | − | 0.186725i | ||||
\(714\) | −249.180 | − | 431.593i | −0.348992 | − | 0.604471i | ||||
\(715\) | − | 366.015i | − | 0.511909i | ||||||
\(716\) | − | 821.465i | − | 1.14730i | ||||||
\(717\) | 291.818 | − | 505.443i | 0.406998 | − | 0.704942i | ||||
\(718\) | −371.430 | − | 214.445i | −0.517311 | − | 0.298670i | ||||
\(719\) | 391.610 | + | 226.096i | 0.544659 | + | 0.314459i | 0.746965 | − | 0.664863i | \(-0.231510\pi\) |
−0.202306 | + | 0.979322i | \(0.564844\pi\) | |||||||
\(720\) | 832.000 | 1.15556 | ||||||||
\(721\) | −1682.31 | −2.33330 | ||||||||
\(722\) | −701.130 | + | 172.337i | −0.971095 | + | 0.238694i | ||||
\(723\) | − | 324.140i | − | 0.448327i | ||||||
\(724\) | 431.770 | + | 747.848i | 0.596368 | + | 1.03294i | ||||
\(725\) | 48.2614 | − | 83.5912i | 0.0665674 | − | 0.115298i | ||||
\(726\) | 1583.31 | + | 914.125i | 2.18087 | + | 1.25913i | ||||
\(727\) | −1194.95 | − | 689.905i | −1.64367 | − | 0.948975i | −0.979512 | − | 0.201385i | \(-0.935456\pi\) |
−0.664161 | − | 0.747590i | \(-0.731211\pi\) | |||||||
\(728\) | −419.453 | + | 242.172i | −0.576172 | + | 0.332653i | ||||
\(729\) | 1163.40 | 1.59589 | ||||||||
\(730\) | 121.386 | + | 210.247i | 0.166282 | + | 0.288010i | ||||
\(731\) | −47.3582 | + | 27.3423i | −0.0647855 | + | 0.0374039i | ||||
\(732\) | 323.472i | 0.441901i | ||||||||
\(733\) | 694.475 | 0.947442 | 0.473721 | − | 0.880675i | \(-0.342910\pi\) | ||||
0.473721 | + | 0.880675i | \(0.342910\pi\) | |||||||
\(734\) | −665.204 | + | 384.056i | −0.906272 | + | 0.523237i | ||||
\(735\) | 778.461 | − | 449.445i | 1.05913 | − | 0.611489i | ||||
\(736\) | 884.720 | − | 510.794i | 1.20207 | − | 0.694013i | ||||
\(737\) | −840.793 | − | 1456.30i | −1.14083 | − | 1.97598i | ||||
\(738\) | 1044.09 | 1.41475 | ||||||||
\(739\) | 699.757 | + | 404.005i | 0.946897 | + | 0.546692i | 0.892116 | − | 0.451807i | \(-0.149220\pi\) |
0.0547817 | + | 0.998498i | \(0.482554\pi\) | |||||||
\(740\) | −357.362 | + | 618.970i | −0.482922 | + | 0.836446i | ||||
\(741\) | −553.907 | + | 67.0766i | −0.747513 | + | 0.0905218i | ||||
\(742\) | 700.681 | − | 404.538i | 0.944314 | − | 0.545200i | ||||
\(743\) | 348.962 | + | 201.473i | 0.469666 | + | 0.271162i | 0.716100 | − | 0.697998i | \(-0.245925\pi\) |
−0.246434 | + | 0.969160i | \(0.579259\pi\) | |||||||
\(744\) | −94.2733 | + | 163.286i | −0.126711 | + | 0.219471i | ||||
\(745\) | −68.7940 | − | 119.155i | −0.0923409 | − | 0.159939i | ||||
\(746\) | 516.182 | 0.691933 | ||||||||
\(747\) | −1204.34 | + | 695.324i | −1.61223 | + | 0.930822i | ||||
\(748\) | −306.629 | − | 177.033i | −0.409932 | − | 0.236675i | ||||
\(749\) | −1832.72 | −2.44689 | ||||||||
\(750\) | −1117.45 | − | 645.160i | −1.48993 | − | 0.860213i | ||||
\(751\) | −1181.79 | + | 682.308i | −1.57362 | + | 0.908532i | −0.577905 | + | 0.816104i | \(0.696130\pi\) |
−0.995719 | + | 0.0924285i | \(0.970537\pi\) | |||||||
\(752\) | −306.725 | + | 177.088i | −0.407879 | + | 0.235489i | ||||
\(753\) | 910.588 | 1.20928 | ||||||||
\(754\) | −44.8634 | + | 77.7056i | −0.0595005 | + | 0.103058i | ||||
\(755\) | −14.5010 | − | 8.37218i | −0.0192067 | − | 0.0110890i | ||||
\(756\) | −1176.27 | −1.55591 | ||||||||
\(757\) | −555.043 | + | 961.363i | −0.733215 | + | 1.26996i | 0.222288 | + | 0.974981i | \(0.428648\pi\) |
−0.955502 | + | 0.294984i | \(0.904686\pi\) | |||||||
\(758\) | 237.137i | 0.312845i | ||||||||
\(759\) | − | 2741.15i | − | 3.61153i | ||||||
\(760\) | 486.178 | + | 207.325i | 0.639708 | + | 0.272796i | ||||
\(761\) | 1268.49 | 1.66688 | 0.833438 | − | 0.552613i | \(-0.186369\pi\) | ||||
0.833438 | + | 0.552613i | \(0.186369\pi\) | |||||||
\(762\) | 1381.27 | 1.81269 | ||||||||
\(763\) | 714.178 | + | 412.331i | 0.936013 | + | 0.540407i | ||||
\(764\) | 730.192i | 0.955748i | ||||||||
\(765\) | −131.184 | + | 227.218i | −0.171483 | + | 0.297017i | ||||
\(766\) | 1068.15 | + | 616.699i | 1.39446 | + | 0.805090i | ||||
\(767\) | 116.126i | 0.151403i | ||||||||
\(768\) | −1085.08 | − | 626.474i | −1.41287 | − | 0.815721i | ||||
\(769\) | 542.816 | + | 940.184i | 0.705872 | + | 1.22261i | 0.966376 | + | 0.257134i | \(0.0827781\pi\) |
−0.260504 | + | 0.965473i | \(0.583889\pi\) | |||||||
\(770\) | 615.545 | − | 1066.15i | 0.799408 | − | 1.38462i | ||||
\(771\) | 1486.53i | 1.92805i | ||||||||
\(772\) | 202.091 | − | 350.032i | 0.261776 | − | 0.453409i | ||||
\(773\) | 489.667 | + | 848.128i | 0.633463 | + | 1.09719i | 0.986838 | + | 0.161709i | \(0.0517006\pi\) |
−0.353375 | + | 0.935482i | \(0.614966\pi\) | |||||||
\(774\) | 324.158i | 0.418808i | ||||||||
\(775\) | 53.8339 | − | 31.0810i | 0.0694630 | − | 0.0401045i | ||||
\(776\) | −511.818 | + | 886.494i | −0.659559 | + | 1.14239i | ||||
\(777\) | 1268.88 | − | 2197.77i | 1.63305 | − | 2.82853i | ||||
\(778\) | −421.909 | − | 730.768i | −0.542299 | − | 0.939290i | ||||
\(779\) | 610.111 | + | 260.175i | 0.783197 | + | 0.333985i | ||||
\(780\) | 353.727 | + | 204.224i | 0.453496 | + | 0.261826i | ||||
\(781\) | −128.224 | + | 222.090i | −0.164179 | + | 0.284366i | ||||
\(782\) | 322.154i | 0.411962i | ||||||||
\(783\) | −188.715 | + | 108.955i | −0.241015 | + | 0.139150i | ||||
\(784\) | −845.085 | −1.07791 | ||||||||
\(785\) | 100.998 | + | 174.934i | 0.128660 | + | 0.222845i | ||||
\(786\) | −661.542 | − | 1145.83i | −0.841657 | − | 1.45779i | ||||
\(787\) | 92.7520i | 0.117855i | 0.998262 | + | 0.0589276i | \(0.0187681\pi\) | ||||
−0.998262 | + | 0.0589276i | \(0.981232\pi\) | |||||||
\(788\) | 40.6335 | 0.0515654 | ||||||||
\(789\) | −212.602 | − | 368.237i | −0.269457 | − | 0.466714i | ||||
\(790\) | −473.536 | + | 273.396i | −0.599413 | + | 0.346071i | ||||
\(791\) | 273.362i | 0.345591i | ||||||||
\(792\) | −1817.63 | + | 1049.41i | −2.29499 | + | 1.32501i | ||||
\(793\) | −49.5683 | + | 85.8549i | −0.0625073 | + | 0.108266i | ||||
\(794\) | 529.065 | − | 916.368i | 0.666329 | − | 1.15412i | ||||
\(795\) | −590.887 | − | 341.149i | −0.743254 | − | 0.429118i | ||||
\(796\) | 635.905 | − | 367.140i | 0.798875 | − | 0.461231i | ||||
\(797\) | 1276.61 | 1.60176 | 0.800882 | − | 0.598822i | \(-0.204365\pi\) | ||||
0.800882 | + | 0.598822i | \(0.204365\pi\) | |||||||
\(798\) | −1726.26 | − | 736.145i | −2.16324 | − | 0.922488i | ||||
\(799\) | − | 111.688i | − | 0.139785i | ||||||
\(800\) | 206.542 | + | 357.742i | 0.258178 | + | 0.447177i | ||||
\(801\) | −841.180 | + | 1456.97i | −1.05016 | + | 1.81893i | ||||
\(802\) | −1.91098 | + | 3.30991i | −0.00238276 | + | 0.00412707i | ||||
\(803\) | −530.373 | − | 306.211i | −0.660490 | − | 0.381334i | ||||
\(804\) | 1876.54 | 2.33400 | ||||||||
\(805\) | −1120.13 | −1.39147 | ||||||||
\(806\) | −50.0435 | + | 28.8926i | −0.0620887 | + | 0.0358469i | ||||
\(807\) | 827.679 | − | 477.861i | 1.02562 | − | 0.592145i | ||||
\(808\) | −647.540 | − | 1121.57i | −0.801411 | − | 1.38809i | ||||
\(809\) | −1144.13 | −1.41425 | −0.707125 | − | 0.707089i | \(-0.750008\pi\) | ||||
−0.707125 | + | 0.707089i | \(0.750008\pi\) | |||||||
\(810\) | 27.9762 | + | 48.4562i | 0.0345385 | + | 0.0598224i | ||||
\(811\) | −908.471 | + | 524.506i | −1.12019 | + | 0.646740i | −0.941448 | − | 0.337157i | \(-0.890535\pi\) |
−0.178738 | + | 0.983897i | \(0.557201\pi\) | |||||||
\(812\) | −261.362 | + | 150.898i | −0.321875 | + | 0.185834i | ||||
\(813\) | 859.053 | + | 1487.92i | 1.05665 | + | 1.83016i | ||||
\(814\) | − | 1802.98i | − | 2.21496i | ||||||
\(815\) | −626.014 | − | 361.429i | −0.768115 | − | 0.443472i | ||||
\(816\) | 342.178 | − | 197.557i | 0.419336 | − | 0.242104i | ||||
\(817\) | −80.7764 | + | 189.421i | −0.0988695 | + | 0.231850i | ||||
\(818\) | 285.863 | + | 495.130i | 0.349466 | + | 0.605293i | ||||
\(819\) | −784.087 | − | 452.693i | −0.957371 | − | 0.552738i | ||||
\(820\) | −242.772 | − | 420.494i | −0.296064 | − | 0.512797i | ||||
\(821\) | −200.770 | − | 347.744i | −0.244543 | − | 0.423562i | 0.717460 | − | 0.696600i | \(-0.245305\pi\) |
−0.962003 | + | 0.273038i | \(0.911971\pi\) | |||||||
\(822\) | − | 1088.32i | − | 1.32400i | ||||||
\(823\) | 243.748 | − | 140.728i | 0.296171 | − | 0.170994i | −0.344551 | − | 0.938768i | \(-0.611969\pi\) |
0.640721 | + | 0.767774i | \(0.278635\pi\) | |||||||
\(824\) | − | 1333.78i | − | 1.61867i | ||||||
\(825\) | 1108.40 | 1.34352 | ||||||||
\(826\) | −195.295 | + | 338.261i | −0.236435 | + | 0.409517i | ||||
\(827\) | 551.534 | − | 318.428i | 0.666909 | − | 0.385040i | −0.127995 | − | 0.991775i | \(-0.540854\pi\) |
0.794904 | + | 0.606735i | \(0.207521\pi\) | |||||||
\(828\) | 1653.81 | + | 954.830i | 1.99736 | + | 1.15318i | ||||
\(829\) | −52.2774 | −0.0630608 | −0.0315304 | − | 0.999503i | \(-0.510038\pi\) | ||||
−0.0315304 | + | 0.999503i | \(0.510038\pi\) | |||||||
\(830\) | 560.067 | + | 323.355i | 0.674780 | + | 0.389584i | ||||
\(831\) | 489.261 | + | 282.475i | 0.588762 | + | 0.339922i | ||||
\(832\) | −192.000 | − | 332.554i | −0.230769 | − | 0.399704i | ||||
\(833\) | 133.247 | − | 230.791i | 0.159961 | − | 0.277060i | ||||
\(834\) | 155.275 | 0.186181 | ||||||||
\(835\) | 414.841i | 0.496816i | ||||||||
\(836\) | −1323.63 | + | 160.288i | −1.58329 | + | 0.191732i | ||||
\(837\) | −140.336 | −0.167666 | ||||||||
\(838\) | − | 1666.75i | − | 1.98896i | ||||||
\(839\) | 934.461 | + | 539.511i | 1.11378 | + | 0.643041i | 0.939806 | − | 0.341709i | \(-0.111006\pi\) |
0.173974 | + | 0.984750i | \(0.444339\pi\) | |||||||
\(840\) | 686.907 | + | 1189.76i | 0.817746 | + | 1.41638i | ||||
\(841\) | 392.546 | − | 679.909i | 0.466760 | − | 0.808453i | ||||
\(842\) | 809.929 | − | 1402.84i | 0.961910 | − | 1.66608i | ||||
\(843\) | − | 117.454i | − | 0.139328i | ||||||
\(844\) | 1020.90 | + | 589.418i | 1.20960 | + | 0.698363i | ||||
\(845\) | −231.236 | − | 400.512i | −0.273651 | − | 0.473978i | ||||
\(846\) | −573.362 | − | 331.031i | −0.677733 | − | 0.391289i | ||||
\(847\) | 1884.62i | 2.22506i | ||||||||
\(848\) | 320.729 | + | 555.519i | 0.378218 | + | 0.655093i | ||||
\(849\) | 353.886 | + | 612.949i | 0.416827 | + | 0.721966i | ||||
\(850\) | −130.265 | −0.153253 | ||||||||
\(851\) | −1420.70 | + | 820.241i | −1.66945 | + | 0.963855i | ||||
\(852\) | −143.089 | − | 247.837i | −0.167945 | − | 0.290889i | ||||
\(853\) | 120.683 | − | 209.029i | 0.141481 | − | 0.245052i | −0.786574 | − | 0.617497i | \(-0.788147\pi\) |
0.928055 | + | 0.372444i | \(0.121480\pi\) | |||||||
\(854\) | −288.772 | + | 166.723i | −0.338141 | + | 0.195226i | ||||
\(855\) | 118.776 | + | 980.834i | 0.138920 | + | 1.14717i | ||||
\(856\) | − | 1453.03i | − | 1.69746i | ||||||
\(857\) | −282.045 | + | 488.515i | −0.329107 | + | 0.570030i | −0.982335 | − | 0.187132i | \(-0.940081\pi\) |
0.653228 | + | 0.757161i | \(0.273414\pi\) | |||||||
\(858\) | −1030.36 | −1.20089 | ||||||||
\(859\) | 794.551 | − | 458.734i | 0.924972 | − | 0.534033i | 0.0397544 | − | 0.999209i | \(-0.487342\pi\) |
0.885218 | + | 0.465176i | \(0.154009\pi\) | |||||||
\(860\) | 130.551 | − | 75.3735i | 0.151803 | − | 0.0876436i | ||||
\(861\) | 862.008 | + | 1493.04i | 1.00117 | + | 1.73408i | ||||
\(862\) | 445.128 | − | 256.995i | 0.516390 | − | 0.298138i | ||||
\(863\) | 467.620i | 0.541854i | 0.962600 | + | 0.270927i | \(0.0873301\pi\) | ||||
−0.962600 | + | 0.270927i | \(0.912670\pi\) | |||||||
\(864\) | − | 932.577i | − | 1.07937i | ||||||
\(865\) | −167.382 | − | 289.914i | −0.193505 | − | 0.335161i | ||||
\(866\) | 242.273 | + | 419.630i | 0.279761 | + | 0.484561i | ||||
\(867\) | − | 1289.86i | − | 1.48773i | ||||||
\(868\) | −194.360 | −0.223917 | ||||||||
\(869\) | 689.675 | − | 1194.55i | 0.793642 | − | 1.37463i | ||||
\(870\) | 220.408 | + | 127.253i | 0.253342 | + | 0.146267i | ||||
\(871\) | 498.065 | + | 287.558i | 0.571831 | + | 0.330147i | ||||
\(872\) | −326.907 | + | 566.219i | −0.374893 | + | 0.649334i | ||||
\(873\) | −1913.49 | −2.19185 | ||||||||
\(874\) | 728.471 | + | 970.065i | 0.833491 | + | 1.10991i | ||||
\(875\) | − | 1330.11i | − | 1.52012i | ||||||
\(876\) | 591.861 | − | 341.711i | 0.675641 | − | 0.390081i | ||||
\(877\) | −753.758 | + | 1305.55i | −0.859474 | + | 1.48865i | 0.0129583 | + | 0.999916i | \(0.495875\pi\) |
−0.872432 | + | 0.488736i | \(0.837458\pi\) | |||||||
\(878\) | −502.432 | − | 290.079i | −0.572246 | − | 0.330386i | ||||
\(879\) | −914.667 | − | 528.083i | −1.04058 | − | 0.600777i | ||||
\(880\) | 845.275 | + | 488.020i | 0.960540 | + | 0.554568i | ||||
\(881\) | −279.998 | −0.317818 | −0.158909 | − | 0.987293i | \(-0.550798\pi\) | ||||
−0.158909 | + | 0.987293i | \(0.550798\pi\) | |||||||
\(882\) | −789.861 | − | 1368.08i | −0.895534 | − | 1.55111i | ||||
\(883\) | −305.052 | + | 176.122i | −0.345473 | + | 0.199459i | −0.662689 | − | 0.748894i | \(-0.730585\pi\) |
0.317217 | + | 0.948353i | \(0.397252\pi\) | |||||||
\(884\) | 121.093 | 0.136983 | ||||||||
\(885\) | 329.386 | 0.372188 | ||||||||
\(886\) | 375.297 | − | 216.678i | 0.423586 | − | 0.244557i | ||||
\(887\) | 79.7702 | − | 46.0553i | 0.0899326 | − | 0.0519226i | −0.454359 | − | 0.890819i | \(-0.650132\pi\) |
0.544292 | + | 0.838896i | \(0.316798\pi\) | |||||||
\(888\) | 1742.45 | + | 1006.00i | 1.96222 | + | 1.13289i | ||||
\(889\) | 711.929 | + | 1233.10i | 0.800820 | + | 1.38706i | ||||
\(890\) | 782.369 | 0.879066 | ||||||||
\(891\) | −122.237 | − | 70.5733i | −0.137190 | − | 0.0792068i | ||||
\(892\) | 115.770 | + | 66.8399i | 0.129787 | + | 0.0749327i | ||||
\(893\) | −252.554 | − | 336.313i | −0.282816 | − | 0.376610i | ||||
\(894\) | −335.430 | + | 193.660i | −0.375201 | + | 0.216622i | ||||
\(895\) | −618.433 | − | 357.053i | −0.690987 | − | 0.398941i | ||||
\(896\) | − | 1291.58i | − | 1.44150i | ||||||
\(897\) | 468.748 | + | 811.896i | 0.522574 | + | 0.905124i | ||||
\(898\) | −631.640 | −0.703385 | ||||||||
\(899\) | −31.1822 | + | 18.0030i | −0.0346854 | + | 0.0200256i | ||||
\(900\) | −386.091 | + | 668.729i | −0.428990 | + | 0.743033i | ||||
\(901\) | −202.282 | −0.224508 | ||||||||
\(902\) | 1060.75 | + | 612.422i | 1.17599 | + | 0.678960i | ||||
\(903\) | −463.545 | + | 267.628i | −0.513338 | + | 0.296376i | ||||
\(904\) | −216.729 | −0.239744 | ||||||||
\(905\) | 750.681 | 0.829482 | ||||||||
\(906\) | −23.5683 | + | 40.8215i | −0.0260136 | + | 0.0450569i | ||||
\(907\) | −1071.41 | − | 618.580i | −1.18127 | − | 0.682007i | −0.224962 | − | 0.974367i | \(-0.572226\pi\) |
−0.956308 | + | 0.292360i | \(0.905559\pi\) | |||||||
\(908\) | − | 108.697i | − | 0.119711i | ||||||
\(909\) | 1210.45 | − | 2096.56i | 1.33163 | − | 2.30645i | ||||
\(910\) | 421.043i | 0.462684i | ||||||||
\(911\) | 391.450i | 0.429693i | 0.976648 | + | 0.214846i | \(0.0689251\pi\) | ||||
−0.976648 | + | 0.214846i | \(0.931075\pi\) | |||||||
\(912\) | 583.636 | − | 1368.63i | 0.639951 | − | 1.50069i | ||||
\(913\) | −1631.40 | −1.78686 | ||||||||
\(914\) | −1285.99 | −1.40699 | ||||||||
\(915\) | 243.523 | + | 140.598i | 0.266145 | + | 0.153659i | ||||
\(916\) | −1007.27 | −1.09964 | ||||||||
\(917\) | 681.940 | − | 1181.16i | 0.743665 | − | 1.28806i | ||||
\(918\) | 254.685 | + | 147.043i | 0.277435 | + | 0.160177i | ||||
\(919\) | − | 166.723i | − | 0.181418i | −0.995877 | − | 0.0907088i | \(-0.971087\pi\) | ||
0.995877 | − | 0.0907088i | \(-0.0289132\pi\) | |||||||
\(920\) | − | 888.072i | − | 0.965296i | ||||||
\(921\) | −219.795 | − | 380.696i | −0.238648 | − | 0.413351i | ||||
\(922\) | 219.814 | − | 380.728i | 0.238410 | − | 0.412938i | ||||
\(923\) | − | 87.7070i | − | 0.0950239i | ||||||
\(924\) | −3001.31 | − | 1732.81i | −3.24817 | − | 1.87533i | ||||
\(925\) | −331.669 | − | 574.468i | −0.358561 | − | 0.621046i | ||||
\(926\) | 133.474i | 0.144141i | ||||||||
\(927\) | 2159.22 | − | 1246.62i | 2.32925 | − | 1.34479i | ||||
\(928\) | −119.636 | − | 207.215i | −0.128918 | − | 0.223292i | ||||
\(929\) | −99.9969 | + | 173.200i | −0.107639 | + | 0.186437i | −0.914813 | − | 0.403877i | \(-0.867662\pi\) |
0.807174 | + | 0.590313i | \(0.200996\pi\) | |||||||
\(930\) | 81.9524 | + | 141.946i | 0.0881208 | + | 0.152630i | ||||
\(931\) | −120.644 | − | 996.260i | −0.129586 | − | 1.07010i | ||||
\(932\) | 329.089 | − | 569.999i | 0.353100 | − | 0.611587i | ||||
\(933\) | 844.600 | − | 1462.89i | 0.905252 | − | 1.56794i | ||||
\(934\) | 343.755i | 0.368046i | ||||||||
\(935\) | −266.555 | + | 153.896i | −0.285085 | + | 0.164594i | ||||
\(936\) | 358.907 | − | 621.645i | 0.383447 | − | 0.664150i | ||||
\(937\) | 526.676 | + | 912.230i | 0.562087 | + | 0.973564i | 0.997314 | + | 0.0732431i | \(0.0233349\pi\) |
−0.435227 | + | 0.900321i | \(0.643332\pi\) | |||||||
\(938\) | 967.200 | + | 1675.24i | 1.03113 | + | 1.78597i | ||||
\(939\) | 2558.38i | 2.72457i | ||||||||
\(940\) | 307.887i | 0.327539i | ||||||||
\(941\) | 18.6356 | + | 32.2778i | 0.0198040 | + | 0.0343016i | 0.875758 | − | 0.482751i | \(-0.160362\pi\) |
−0.855954 | + | 0.517053i | \(0.827029\pi\) | |||||||
\(942\) | 492.451 | − | 284.317i | 0.522772 | − | 0.301823i | ||||
\(943\) | − | 1114.45i | − | 1.18182i | ||||||
\(944\) | −268.182 | − | 154.835i | −0.284091 | − | 0.164020i | ||||
\(945\) | −511.269 | + | 885.544i | −0.541026 | + | 0.937084i | ||||
\(946\) | −190.139 | + | 329.330i | −0.200992 | + | 0.348129i | ||||
\(947\) | −66.9503 | − | 38.6538i | −0.0706973 | − | 0.0408171i | 0.464235 | − | 0.885712i | \(-0.346329\pi\) |
−0.534932 | + | 0.844895i | \(0.679663\pi\) | |||||||
\(948\) | 769.631 | + | 1333.04i | 0.811848 | + | 1.40616i | ||||
\(949\) | 209.453 | 0.220710 | ||||||||
\(950\) | −392.252 | + | 294.562i | −0.412896 | + | 0.310065i | ||||
\(951\) | 15.1390i | 0.0159190i | ||||||||
\(952\) | 352.729 | + | 203.648i | 0.370513 | + | 0.213916i | ||||
\(953\) | −561.682 | + | 972.862i | −0.589383 | + | 1.02084i | 0.404930 | + | 0.914348i | \(0.367296\pi\) |
−0.994313 | + | 0.106494i | \(0.966037\pi\) | |||||||
\(954\) | −599.540 | + | 1038.43i | −0.628449 | + | 1.08851i | ||||
\(955\) | 549.718 | + | 317.380i | 0.575621 | + | 0.332335i | ||||
\(956\) | 476.989i | 0.498943i | ||||||||
\(957\) | −642.020 | −0.670867 | ||||||||
\(958\) | −39.6356 | + | 22.8836i | −0.0413733 | + | 0.0238869i | ||||
\(959\) | 971.578 | − | 560.941i | 1.01312 | − | 0.584923i | ||||
\(960\) | −943.271 | + | 544.598i | −0.982574 | + | 0.567289i | ||||
\(961\) | 937.812 | 0.975871 | ||||||||
\(962\) | 308.317 | + | 534.020i | 0.320496 | + | 0.555115i | ||||
\(963\) | 2352.26 | − | 1358.08i | 2.44264 | − | 1.41026i | ||||
\(964\) | 132.455 | + | 229.420i | 0.137402 | + | 0.237987i | ||||
\(965\) | −175.679 | − | 304.285i | −0.182051 | − | 0.315321i | ||||
\(966\) | 3153.26i | 3.26425i | ||||||||
\(967\) | −1025.02 | − | 591.795i | −1.06000 | − | 0.611991i | −0.134567 | − | 0.990904i | \(-0.542965\pi\) |
−0.925432 | + | 0.378913i | \(0.876298\pi\) | |||||||
\(968\) | −1494.18 | −1.54357 | ||||||||
\(969\) | 281.746 | + | 375.186i | 0.290760 | + | 0.387189i | ||||
\(970\) | 444.926 | + | 770.635i | 0.458687 | + | 0.794469i | ||||
\(971\) | 625.708 | + | 361.252i | 0.644395 | + | 0.372042i | 0.786306 | − | 0.617838i | \(-0.211991\pi\) |
−0.141911 | + | 0.989879i | \(0.545325\pi\) | |||||||
\(972\) | −772.182 | + | 445.820i | −0.794426 | + | 0.458662i | ||||
\(973\) | 80.0316 | + | 138.619i | 0.0822524 | + | 0.142465i | ||||
\(974\) | − | 292.164i | − | 0.299963i | ||||||
\(975\) | −328.295 | + | 189.541i | −0.336713 | + | 0.194401i | ||||
\(976\) | −132.182 | − | 228.946i | −0.135433 | − | 0.234576i | ||||
\(977\) | −1305.31 | −1.33604 | −0.668021 | − | 0.744143i | \(-0.732858\pi\) | ||||
−0.668021 | + | 0.744143i | \(0.732858\pi\) | |||||||
\(978\) | −1017.45 | + | 1762.28i | −1.04034 | + | 1.80192i | ||||
\(979\) | −1709.20 | + | 986.809i | −1.74587 | + | 1.00798i | ||||
\(980\) | −367.319 | + | 636.215i | −0.374815 | + | 0.649199i | ||||
\(981\) | −1222.18 | −1.24585 | ||||||||
\(982\) | −825.861 | − | 476.811i | −0.840999 | − | 0.485551i | ||||
\(983\) | 857.727 | + | 495.209i | 0.872560 | + | 0.503773i | 0.868198 | − | 0.496218i | \(-0.165278\pi\) |
0.00436204 | + | 0.999990i | \(0.498612\pi\) | |||||||
\(984\) | −1183.72 | + | 683.423i | −1.20297 | + | 0.694535i | ||||
\(985\) | 17.6615 | − | 30.5906i | 0.0179305 | − | 0.0310565i | ||||
\(986\) | 75.4534 | 0.0765248 | ||||||||
\(987\) | − | 1093.21i | − | 1.10761i | ||||||
\(988\) | 364.634 | − | 273.822i | 0.369062 | − | 0.277148i | ||||
\(989\) | 346.004 | 0.349853 | ||||||||
\(990\) | 1824.52i | 1.84295i | ||||||||
\(991\) | −974.899 | − | 562.858i | −0.983752 | − | 0.567970i | −0.0803514 | − | 0.996767i | \(-0.525604\pi\) |
−0.903401 | + | 0.428797i | \(0.858938\pi\) | |||||||
\(992\) | − | 154.094i | − | 0.155337i | ||||||
\(993\) | −253.385 | + | 438.876i | −0.255171 | + | 0.441970i | ||||
\(994\) | 147.501 | − | 255.479i | 0.148391 | − | 0.257021i | ||||
\(995\) | − | 638.314i | − | 0.641522i | ||||||
\(996\) | 910.269 | − | 1576.63i | 0.913925 | − | 1.58296i | ||||
\(997\) | −639.734 | − | 1108.05i | −0.641659 | − | 1.11139i | −0.985062 | − | 0.172199i | \(-0.944913\pi\) |
0.343403 | − | 0.939188i | \(-0.388420\pi\) | |||||||
\(998\) | 1003.24 | + | 579.222i | 1.00525 | + | 0.580382i | ||||
\(999\) | 1497.55i | 1.49905i |
(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 | 76.3.g.b.11.1 | yes | 4 | |
4.3 | odd | 2 | 76.3.g.a.11.2 | yes | 4 | ||
19.7 | even | 3 | 76.3.g.a.7.2 | ✓ | 4 | ||
76.7 | odd | 6 | inner | 76.3.g.b.7.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.g.a.7.2 | ✓ | 4 | 19.7 | even | 3 | ||
76.3.g.a.11.2 | yes | 4 | 4.3 | odd | 2 | ||
76.3.g.b.7.1 | yes | 4 | 76.7 | odd | 6 | inner | |
76.3.g.b.11.1 | yes | 4 | 1.1 | even | 1 | trivial |