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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.2 | ||
Root | \(2.73861 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.11 |
Dual form | 76.3.g.a.7.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(3\) | 4.23861 | + | 2.44716i | 1.41287 | + | 0.815721i | 0.995658 | − | 0.0930873i | \(-0.0296736\pi\) |
0.417213 | + | 0.908809i | \(0.363007\pi\) | |||||||
\(4\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(5\) | 1.73861 | − | 3.01137i | 0.347723 | − | 0.602273i | −0.638122 | − | 0.769935i | \(-0.720288\pi\) |
0.985845 | + | 0.167662i | \(0.0536218\pi\) | |||||||
\(6\) | − | 9.78866i | − | 1.63144i | ||||||
\(7\) | 10.0905i | 1.44150i | 0.693197 | + | 0.720749i | \(0.256202\pi\) | ||||
−0.693197 | + | 0.720749i | \(0.743798\pi\) | |||||||
\(8\) | 8.00000 | 1.00000 | ||||||||
\(9\) | 7.47723 | + | 12.9509i | 0.830803 | + | 1.43899i | ||||
\(10\) | −6.95445 | −0.695445 | ||||||||
\(11\) | − | 17.5434i | − | 1.59486i | −0.603413 | − | 0.797429i | \(-0.706193\pi\) | ||
0.603413 | − | 0.797429i | \(-0.293807\pi\) | |||||||
\(12\) | −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 | \(0.907458\pi\) | |||||||
\(14\) | 17.4772 | − | 10.0905i | 1.24837 | − | 0.720749i | ||||
\(15\) | 14.7386 | − | 8.50934i | 0.982574 | − | 0.567289i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(17\) | −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 | ||||
\(22\) | −30.3861 | + | 17.5434i | −1.38119 | + | 0.797429i | ||||
\(23\) | −27.6475 | + | 15.9623i | −1.20207 | + | 0.694013i | −0.961014 | − | 0.276499i | \(-0.910826\pi\) |
−0.241052 | + | 0.970512i | \(0.577492\pi\) | |||||||
\(24\) | 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 | ||||||||
\(28\) | −34.9545 | − | 20.1810i | −1.24837 | − | 0.720749i | ||||
\(29\) | −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 | \(0.0247475\pi\) | ||||
−0.996979 | + | 0.0776683i | \(0.975252\pi\) | |||||||
\(32\) | −16.0000 | + | 27.7128i | −0.500000 | + | 0.866025i | ||||
\(33\) | 42.9317 | − | 74.3598i | 1.30096 | − | 2.25333i | ||||
\(34\) | 10.0911 | 0.296797 | ||||||||
\(35\) | 30.3861 | + | 17.5434i | 0.868175 | + | 0.501241i | ||||
\(36\) | −59.8178 | −1.66161 | ||||||||
\(37\) | −51.3861 | −1.38881 | −0.694407 | − | 0.719582i | \(-0.744333\pi\) | ||||
−0.694407 | + | 0.719582i | \(0.744333\pi\) | |||||||
\(38\) | −30.3861 | + | 22.8185i | −0.799635 | + | 0.600486i | ||||
\(39\) | − | 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 | \(0.0266881\pi\) | |||||||
\(42\) | 98.7723 | 2.35172 | ||||||||
\(43\) | −9.38613 | − | 5.41908i | −0.218282 | − | 0.126025i | 0.386872 | − | 0.922133i | \(-0.373555\pi\) |
−0.605155 | + | 0.796108i | \(0.706889\pi\) | |||||||
\(44\) | 60.7723 | + | 35.0869i | 1.38119 | + | 0.797429i | ||||
\(45\) | 52.0000 | 1.15556 | ||||||||
\(46\) | 55.2950 | + | 31.9246i | 1.20207 | + | 0.694013i | ||||
\(47\) | 19.1703 | − | 11.0680i | 0.407879 | − | 0.235489i | −0.281999 | − | 0.959415i | \(-0.590998\pi\) |
0.689878 | + | 0.723926i | \(0.257664\pi\) | |||||||
\(48\) | − | 78.3093i | − | 1.63144i | ||||||
\(49\) | −52.8178 | −1.07791 | ||||||||
\(50\) | 12.9089 | − | 22.3589i | 0.258178 | − | 0.447177i | ||||
\(51\) | −21.3861 | + | 12.3473i | −0.419336 | + | 0.242104i | ||||
\(52\) | 24.0000 | 0.461538 | ||||||||
\(53\) | 20.0455 | + | 34.7199i | 0.378218 | + | 0.655093i | 0.990803 | − | 0.135312i | \(-0.0432037\pi\) |
−0.612585 | + | 0.790405i | \(0.709870\pi\) | |||||||
\(54\) | 50.4772 | − | 29.1430i | 0.934763 | − | 0.539686i | ||||
\(55\) | −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 | 0.635274 | − | 0.772287i | \(-0.280887\pi\) |
−0.351183 | + | 0.936307i | \(0.614220\pi\) | |||||||
\(60\) | 68.0747i | 1.13458i | ||||||||
\(61\) | −8.26139 | − | 14.3091i | −0.135433 | − | 0.234576i | 0.790330 | − | 0.612681i | \(-0.209909\pi\) |
−0.925763 | + | 0.378105i | \(0.876576\pi\) | |||||||
\(62\) | 8.34058 | − | 4.81544i | 0.134525 | − | 0.0776683i | ||||
\(63\) | −130.681 | + | 75.4488i | −2.07430 | + | 1.19760i | ||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | −20.8634 | −0.320975 | ||||||||
\(66\) | −171.727 | −2.60192 | ||||||||
\(67\) | 83.0109 | − | 47.9263i | 1.23897 | − | 0.715319i | 0.270085 | − | 0.962837i | \(-0.412948\pi\) |
0.968883 | + | 0.247518i | \(0.0796149\pi\) | |||||||
\(68\) | −10.0911 | − | 17.4783i | −0.148398 | − | 0.257034i | ||||
\(69\) | −156.249 | −2.26449 | ||||||||
\(70\) | − | 70.1738i | − | 1.00248i | ||||||
\(71\) | −12.6594 | − | 7.30892i | −0.178302 | − | 0.102943i | 0.408193 | − | 0.912896i | \(-0.366159\pi\) |
−0.586495 | + | 0.809953i | \(0.699492\pi\) | |||||||
\(72\) | 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 | \(0.243520\pi\) | |||||||
\(74\) | 51.3861 | + | 89.0034i | 0.694407 | + | 1.20275i | ||||
\(75\) | 63.1804i | 0.842405i | ||||||||
\(76\) | 69.9089 | + | 29.8118i | 0.919854 | + | 0.392261i | ||||
\(77\) | 177.022 | 2.29898 | ||||||||
\(78\) | −50.8634 | + | 29.3660i | −0.652094 | + | 0.376487i | ||||
\(79\) | 68.0911 | + | 39.3124i | 0.861913 | + | 0.497625i | 0.864652 | − | 0.502371i | \(-0.167539\pi\) |
−0.00273968 | + | 0.999996i | \(0.500872\pi\) | |||||||
\(80\) | −55.6356 | −0.695445 | ||||||||
\(81\) | −4.02277 | + | 6.96765i | −0.0496639 | + | 0.0860204i | ||||
\(82\) | −69.8178 | −0.851437 | ||||||||
\(83\) | − | 92.9922i | − | 1.12039i | −0.828361 | − | 0.560194i | \(-0.810726\pi\) | ||
0.828361 | − | 0.560194i | \(-0.189274\pi\) | |||||||
\(84\) | −98.7723 | − | 171.079i | −1.17586 | − | 2.03665i | ||||
\(85\) | 8.77226 | + | 15.1940i | 0.103203 | + | 0.178753i | ||||
\(86\) | 21.6763i | 0.252050i | ||||||||
\(87\) | − | 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 | \(0.615561\pi\) | |||||||
\(90\) | −52.0000 | − | 90.0666i | −0.577778 | − | 1.00074i | ||||
\(91\) | 52.4317 | − | 30.2714i | 0.576172 | − | 0.332653i | ||||
\(92\) | − | 127.698i | − | 1.38803i | ||||||
\(93\) | −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 | \(0.937410\pi\) | |||||||
\(98\) | 52.8178 | + | 91.4831i | 0.538957 | + | 0.933501i | ||||
\(99\) | 227.204 | − | 131.176i | 2.29499 | − | 1.32501i | ||||
\(100\) | −51.6356 | −0.516356 | ||||||||
\(101\) | −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 | \(0.300172\pi\) | ||||
−0.587349 | + | 0.809334i | \(0.699828\pi\) | |||||||
\(104\) | −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 | \(0.322633\pi\) | ||||
−0.528823 | + | 0.848732i | \(0.677367\pi\) | |||||||
\(108\) | −100.954 | − | 58.2861i | −0.934763 | − | 0.539686i | ||||
\(109\) | −40.8634 | + | 70.7774i | −0.374893 | + | 0.649334i | −0.990311 | − | 0.138867i | \(-0.955654\pi\) |
0.615418 | + | 0.788201i | \(0.288987\pi\) | |||||||
\(110\) | 122.005i | 1.10914i | ||||||||
\(111\) | −217.806 | − | 125.750i | −1.96222 | − | 1.13289i | ||||
\(112\) | 139.818 | − | 80.7238i | 1.24837 | − | 0.720749i | ||||
\(113\) | −27.0911 | −0.239744 | −0.119872 | − | 0.992789i | \(-0.538248\pi\) | ||||
−0.119872 | + | 0.992789i | \(0.538248\pi\) | |||||||
\(114\) | −184.636 | + | 22.3589i | −1.61961 | + | 0.196130i | ||||
\(115\) | 111.009i | 0.965296i | ||||||||
\(116\) | 29.9089 | 0.257835 | ||||||||
\(117\) | 44.8634 | − | 77.7056i | 0.383447 | − | 0.664150i | ||||
\(118\) | − | 38.7088i | − | 0.328040i | ||||||
\(119\) | −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 | ||||
\(124\) | −16.6812 | − | 9.63087i | −0.134525 | − | 0.0776683i | ||||
\(125\) | 131.818 | 1.05454 | ||||||||
\(126\) | 261.362 | + | 150.898i | 2.07430 | + | 1.19760i | ||||
\(127\) | 122.204 | − | 70.5545i | 0.962236 | − | 0.555547i | 0.0653753 | − | 0.997861i | \(-0.479176\pi\) |
0.896860 | + | 0.442314i | \(0.145842\pi\) | |||||||
\(128\) | −64.0000 | − | 110.851i | −0.500000 | − | 0.866025i | ||||
\(129\) | −26.5228 | − | 45.9388i | −0.205603 | − | 0.356115i | ||||
\(130\) | 20.8634 | + | 36.1364i | 0.160487 | + | 0.277972i | ||||
\(131\) | −117.056 | − | 67.5826i | −0.893560 | − | 0.515897i | −0.0184550 | − | 0.999830i | \(-0.505875\pi\) |
−0.875105 | + | 0.483932i | \(0.839208\pi\) | |||||||
\(132\) | 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 | \(0.700335\pi\) | |||||||
\(138\) | 156.249 | + | 270.632i | 1.13224 | + | 1.96110i | ||||
\(139\) | 13.7376 | − | 7.93139i | 0.0988315 | − | 0.0570604i | −0.449770 | − | 0.893145i | \(-0.648494\pi\) |
0.548601 | + | 0.836084i | \(0.315161\pi\) | |||||||
\(140\) | −121.545 | + | 70.1738i | −0.868175 | + | 0.501241i | ||||
\(141\) | 108.341 | 0.768373 | ||||||||
\(142\) | 29.2357i | 0.205885i | ||||||||
\(143\) | −91.1584 | + | 52.6303i | −0.637471 | + | 0.368044i | ||||
\(144\) | 119.636 | − | 207.215i | 0.830803 | − | 1.43899i | ||||
\(145\) | −26.0000 | −0.179310 | ||||||||
\(146\) | 69.8178 | 0.478204 | ||||||||
\(147\) | −223.874 | − | 129.254i | −1.52295 | − | 0.879278i | ||||
\(148\) | 102.772 | − | 178.007i | 0.694407 | − | 1.20275i | ||||
\(149\) | 19.7842 | − | 34.2672i | 0.132780 | − | 0.229981i | −0.791967 | − | 0.610563i | \(-0.790943\pi\) |
0.924747 | + | 0.380582i | \(0.124276\pi\) | |||||||
\(150\) | 109.432 | − | 63.1804i | 0.729545 | − | 0.421203i | ||||
\(151\) | 4.81544i | 0.0318903i | 0.999873 | + | 0.0159452i | \(0.00507571\pi\) | ||||
−0.999873 | + | 0.0159452i | \(0.994924\pi\) | |||||||
\(152\) | −18.2733 | − | 150.898i | −0.120219 | − | 0.992747i | ||||
\(153\) | −75.4534 | −0.493160 | ||||||||
\(154\) | −177.022 | − | 306.611i | −1.14949 | − | 1.99098i | ||||
\(155\) | 14.5010 | + | 8.37218i | 0.0935551 | + | 0.0540141i | ||||
\(156\) | 101.727 | + | 58.7319i | 0.652094 | + | 0.376487i | ||||
\(157\) | −29.0455 | + | 50.3084i | −0.185003 | + | 0.320435i | −0.943578 | − | 0.331151i | \(-0.892563\pi\) |
0.758574 | + | 0.651587i | \(0.225896\pi\) | |||||||
\(158\) | − | 157.250i | − | 0.995251i | ||||||
\(159\) | 196.219i | 1.23408i | ||||||||
\(160\) | 55.6356 | + | 96.3637i | 0.347723 | + | 0.602273i | ||||
\(161\) | −161.067 | − | 278.977i | −1.00042 | − | 1.73277i | ||||
\(162\) | 16.0911 | 0.0993278 | ||||||||
\(163\) | 207.884i | 1.27536i | 0.770301 | + | 0.637680i | \(0.220106\pi\) | ||||
−0.770301 | + | 0.637680i | \(0.779894\pi\) | |||||||
\(164\) | 69.8178 | + | 120.928i | 0.425718 | + | 0.737366i | ||||
\(165\) | −149.283 | − | 258.566i | −0.904746 | − | 1.56707i | ||||
\(166\) | −161.067 | + | 92.9922i | −0.970285 | + | 0.560194i | ||||
\(167\) | 103.319 | − | 59.6512i | 0.618676 | − | 0.357193i | −0.157678 | − | 0.987491i | \(-0.550401\pi\) |
0.776353 | + | 0.630298i | \(0.217067\pi\) | |||||||
\(168\) | −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 | \(0.0769135\pi\) | |||||||
\(174\) | −63.3861 | + | 36.5960i | −0.364288 | + | 0.210322i | ||||
\(175\) | −112.806 | + | 65.1285i | −0.644605 | + | 0.372163i | ||||
\(176\) | −243.089 | + | 140.348i | −1.38119 | + | 0.797429i | ||||
\(177\) | 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 | \(0.194473\pi\) | ||||
−0.819101 | + | 0.573649i | \(0.805527\pi\) | |||||||
\(180\) | −104.000 | + | 180.133i | −0.577778 | + | 1.00074i | ||||
\(181\) | 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 | ||||
\(186\) | 47.1366 | 0.253423 | ||||||||
\(187\) | 76.6573 | + | 44.2581i | 0.409932 | + | 0.236675i | ||||
\(188\) | 88.5438i | 0.470978i | ||||||||
\(189\) | −294.067 | −1.55591 | ||||||||
\(190\) | 15.8851 | + | 131.176i | 0.0836057 | + | 0.690401i | ||||
\(191\) | − | 182.548i | − | 0.955748i | −0.878428 | − | 0.477874i | \(-0.841408\pi\) | ||
0.878428 | − | 0.477874i | \(-0.158592\pi\) | |||||||
\(192\) | 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 | \(0.0823585\pi\) | |||||||
\(194\) | 255.909 | 1.31912 | ||||||||
\(195\) | −88.4317 | − | 51.0561i | −0.453496 | − | 0.261826i | ||||
\(196\) | 105.636 | − | 182.966i | 0.538957 | − | 0.933501i | ||||
\(197\) | 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 | −0.843078 | − | 0.537792i | \(-0.819259\pi\) |
0.0442024 | + | 0.999023i | \(0.485925\pi\) | |||||||
\(200\) | 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 | ||||
\(204\) | − | 98.7783i | − | 0.484207i | ||||||
\(205\) | −60.6931 | − | 105.123i | −0.296064 | − | 0.512797i | ||||
\(206\) | 288.772 | − | 166.723i | 1.40181 | − | 0.809334i | ||||
\(207\) | −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 | −0.246928 | − | 0.969034i | \(-0.579421\pi\) |
−0.962672 | + | 0.270671i | \(0.912755\pi\) | |||||||
\(212\) | −160.364 | −0.756436 | ||||||||
\(213\) | −35.7723 | − | 61.9594i | −0.167945 | − | 0.290889i | ||||
\(214\) | 314.590 | − | 181.629i | 1.47005 | − | 0.848732i | ||||
\(215\) | −32.6377 | + | 18.8434i | −0.151803 | + | 0.0876436i | ||||
\(216\) | 233.144i | 1.07937i | ||||||||
\(217\) | −48.5901 | −0.223917 | ||||||||
\(218\) | 163.453 | 0.749786 | ||||||||
\(219\) | −147.965 | + | 85.4278i | −0.675641 | + | 0.390081i | ||||
\(220\) | 211.319 | − | 122.005i | 0.960540 | − | 0.554568i | ||||
\(221\) | 30.2733 | 0.136983 | ||||||||
\(222\) | 503.001i | 2.26577i | ||||||||
\(223\) | −28.9425 | − | 16.7100i | −0.129787 | − | 0.0749327i | 0.433701 | − | 0.901057i | \(-0.357208\pi\) |
−0.563488 | + | 0.826124i | \(0.690541\pi\) | |||||||
\(224\) | −279.636 | − | 161.448i | −1.24837 | − | 0.720749i | ||||
\(225\) | −96.5228 | + | 167.182i | −0.428990 | + | 0.743033i | ||||
\(226\) | 27.0911 | + | 46.9232i | 0.119872 | + | 0.207625i | ||||
\(227\) | 27.1743i | 0.119711i | 0.998207 | + | 0.0598553i | \(0.0190639\pi\) | ||||
−0.998207 | + | 0.0598553i | \(0.980936\pi\) | |||||||
\(228\) | 223.362 | + | 297.439i | 0.979659 | + | 1.30456i | ||||
\(229\) | −251.818 | −1.09964 | −0.549821 | − | 0.835283i | \(-0.685304\pi\) | ||||
−0.549821 | + | 0.835283i | \(0.685304\pi\) | |||||||
\(230\) | 192.273 | − | 111.009i | 0.835971 | − | 0.482648i | ||||
\(231\) | 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 | \(0.0517943\pi\) | |||||||
\(234\) | −179.453 | −0.766895 | ||||||||
\(235\) | − | 76.9717i | − | 0.327539i | ||||||
\(236\) | −67.0455 | + | 38.7088i | −0.284091 | + | 0.164020i | ||||
\(237\) | 192.408 | + | 333.260i | 0.811848 | + | 1.40616i | ||||
\(238\) | 101.824i | 0.427832i | ||||||||
\(239\) | − | 119.247i | − | 0.498943i | −0.968382 | − | 0.249471i | \(-0.919743\pi\) | ||
0.968382 | − | 0.249471i | \(-0.0802569\pi\) | |||||||
\(240\) | −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 | \(0.789458\pi\) | |||||||
\(242\) | 186.772 | + | 323.499i | 0.771786 | + | 1.33677i | ||||
\(243\) | 193.046 | − | 111.455i | 0.794426 | − | 0.458662i | ||||
\(244\) | 66.0911 | 0.270865 | ||||||||
\(245\) | −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 | ||||
\(250\) | −131.818 | − | 228.315i | −0.527271 | − | 0.913261i | ||||
\(251\) | 161.124 | − | 93.0248i | 0.641927 | − | 0.370617i | −0.143429 | − | 0.989661i | \(-0.545813\pi\) |
0.785356 | + | 0.619044i | \(0.212480\pi\) | |||||||
\(252\) | − | 603.590i | − | 2.39520i | ||||||
\(253\) | 280.034 | + | 485.032i | 1.10685 | + | 1.91712i | ||||
\(254\) | −244.408 | − | 141.109i | −0.962236 | − | 0.555547i | ||||
\(255\) | 85.8686i | 0.336740i | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.500000 | + | 0.866025i | ||||
\(257\) | −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 | ||||||
\(260\) | 41.7267 | − | 72.2728i | 0.160487 | − | 0.277972i | ||||
\(261\) | 55.9089 | − | 96.8371i | 0.214210 | − | 0.371023i | ||||
\(262\) | 270.330i | 1.03179i | ||||||||
\(263\) | −75.2376 | − | 43.4384i | −0.286074 | − | 0.165165i | 0.350096 | − | 0.936714i | \(-0.386149\pi\) |
−0.636170 | + | 0.771549i | \(0.719482\pi\) | |||||||
\(264\) | 343.453 | − | 594.879i | 1.30096 | − | 2.25333i | ||||
\(265\) | 139.406 | 0.526060 | ||||||||
\(266\) | −230.249 | − | 306.611i | −0.865600 | − | 1.15267i | ||||
\(267\) | 550.607i | 2.06220i | ||||||||
\(268\) | 383.411i | 1.43064i | ||||||||
\(269\) | −97.6356 | + | 169.110i | −0.362958 | + | 0.628661i | −0.988446 | − | 0.151572i | \(-0.951566\pi\) |
0.625489 | + | 0.780233i | \(0.284900\pi\) | |||||||
\(270\) | − | 202.674i | − | 0.750644i | ||||||
\(271\) | 304.010 | + | 175.520i | 1.12181 | + | 0.647676i | 0.941862 | − | 0.336001i | \(-0.109074\pi\) |
0.179946 | + | 0.983677i | \(0.442408\pi\) | |||||||
\(272\) | 80.7288 | 0.296797 | ||||||||
\(273\) | 296.317 | 1.08541 | ||||||||
\(274\) | 111.182 | − | 192.573i | 0.405774 | − | 0.702822i | ||||
\(275\) | 196.126 | − | 113.233i | 0.713185 | − | 0.411757i | ||||
\(276\) | 312.499 | − | 541.264i | 1.13224 | − | 1.96110i | ||||
\(277\) | −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 | \(0.819737\pi\) | |||||||
\(282\) | −108.341 | − | 187.651i | −0.384186 | − | 0.665430i | ||||
\(283\) | 125.237 | + | 72.3053i | 0.442532 | + | 0.255496i | 0.704671 | − | 0.709534i | \(-0.251095\pi\) |
−0.262139 | + | 0.965030i | \(0.584428\pi\) | |||||||
\(284\) | 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 | ||||
\(288\) | −478.542 | −1.66161 | ||||||||
\(289\) | 131.771 | + | 228.234i | 0.455956 | + | 0.789739i | ||||
\(290\) | 26.0000 | + | 45.0333i | 0.0896552 | + | 0.155287i | ||||
\(291\) | −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 | \(0.379957\pi\) | |||||||
\(294\) | 517.015i | 1.75856i | ||||||||
\(295\) | 58.2831 | − | 33.6498i | 0.197570 | − | 0.114067i | ||||
\(296\) | −411.089 | −1.38881 | ||||||||
\(297\) | 511.269 | 1.72144 | ||||||||
\(298\) | −79.1366 | −0.265559 | ||||||||
\(299\) | 165.885 | + | 95.7738i | 0.554800 | + | 0.320314i | ||||
\(300\) | −218.863 | − | 126.361i | −0.729545 | − | 0.421203i | ||||
\(301\) | 54.6812 | − | 94.7105i | 0.181665 | − | 0.314653i | ||||
\(302\) | 8.34058 | − | 4.81544i | 0.0276178 | − | 0.0159452i | ||||
\(303\) | − | 792.319i | − | 2.61491i | ||||||
\(304\) | −243.089 | + | 182.548i | −0.799635 | + | 0.600486i | ||||
\(305\) | −57.4534 | −0.188372 | ||||||||
\(306\) | 75.4534 | + | 130.689i | 0.246580 | + | 0.427089i | ||||
\(307\) | −77.7831 | − | 44.9081i | −0.253365 | − | 0.146280i | 0.367939 | − | 0.929850i | \(-0.380064\pi\) |
−0.621304 | + | 0.783569i | \(0.713397\pi\) | |||||||
\(308\) | −354.043 | + | 613.221i | −1.14949 | + | 1.99098i | ||||
\(309\) | −407.998 | + | 706.673i | −1.32038 | + | 2.28697i | ||||
\(310\) | − | 33.4887i | − | 0.108028i | ||||||
\(311\) | − | 345.134i | − | 1.10976i | −0.831932 | − | 0.554878i | \(-0.812765\pi\) | ||
0.831932 | − | 0.554878i | \(-0.187235\pi\) | |||||||
\(312\) | − | 234.928i | − | 0.752974i | ||||||
\(313\) | −261.361 | − | 452.691i | −0.835020 | − | 1.44630i | −0.894014 | − | 0.448039i | \(-0.852123\pi\) |
0.0589940 | − | 0.998258i | \(-0.481211\pi\) | |||||||
\(314\) | 116.182 | 0.370007 | ||||||||
\(315\) | 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 | \(0.834886\pi\) | |||||||
\(318\) | 339.861 | − | 196.219i | 1.06875 | − | 0.617041i | ||||
\(319\) | −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 | ||||
\(326\) | 360.065 | − | 207.884i | 1.10449 | − | 0.637680i | ||||
\(327\) | −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 | \(0.0499916\pi\) | ||||
−0.987692 | + | 0.156408i | \(0.950008\pi\) | |||||||
\(332\) | 322.135 | + | 185.984i | 0.970285 | + | 0.560194i | ||||
\(333\) | −384.226 | − | 665.498i | −1.15383 | − | 1.99849i | ||||
\(334\) | −206.638 | − | 119.302i | −0.618676 | − | 0.357193i | ||||
\(335\) | − | 333.301i | − | 0.994930i | ||||||
\(336\) | 790.178 | 2.35172 | ||||||||
\(337\) | 248.203 | − | 429.900i | 0.736507 | − | 1.27567i | −0.217552 | − | 0.976049i | \(-0.569807\pi\) |
0.954059 | − | 0.299619i | \(-0.0968595\pi\) | |||||||
\(338\) | −266.000 | −0.786982 | ||||||||
\(339\) | −114.829 | − | 66.2964i | −0.338728 | − | 0.195564i | ||||
\(340\) | −70.1780 | −0.206406 | ||||||||
\(341\) | 84.4793 | 0.247740 | ||||||||
\(342\) | −522.725 | − | 222.910i | −1.52843 | − | 0.651783i | ||||
\(343\) | − | 38.5235i | − | 0.112313i | ||||||
\(344\) | −75.0890 | − | 43.3527i | −0.218282 | − | 0.126025i | ||||
\(345\) | −271.657 | + | 470.524i | −0.787413 | + | 1.36384i | ||||
\(346\) | −192.547 | −0.556493 | ||||||||
\(347\) | −484.351 | − | 279.640i | −1.39583 | − | 0.805880i | −0.401873 | − | 0.915695i | \(-0.631641\pi\) |
−0.993952 | + | 0.109815i | \(0.964974\pi\) | |||||||
\(348\) | 126.772 | + | 73.1920i | 0.364288 | + | 0.210322i | ||||
\(349\) | −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 | ||||
\(352\) | 486.178 | + | 280.695i | 1.38119 | + | 0.797429i | ||||
\(353\) | −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 | ||||
\(356\) | −449.996 | −1.26403 | ||||||||
\(357\) | −124.590 | − | 215.796i | −0.348992 | − | 0.604471i | ||||
\(358\) | 355.705 | − | 205.366i | 0.993589 | − | 0.573649i | ||||
\(359\) | 185.715 | + | 107.222i | 0.517311 | + | 0.298670i | 0.735834 | − | 0.677162i | \(-0.236790\pi\) |
−0.218523 | + | 0.975832i | \(0.570124\pi\) | |||||||
\(360\) | 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 | ||||
\(364\) | 242.172i | 0.665306i | ||||||||
\(365\) | 60.6931 | + | 105.123i | 0.166282 | + | 0.288010i | ||||
\(366\) | −140.067 | + | 80.8679i | −0.382698 | + | 0.220951i | ||||
\(367\) | 332.602 | − | 192.028i | 0.906272 | − | 0.523237i | 0.0270425 | − | 0.999634i | \(-0.491391\pi\) |
0.879230 | + | 0.476398i | \(0.158058\pi\) | |||||||
\(368\) | 442.360 | + | 255.397i | 1.20207 | + | 0.694013i | ||||
\(369\) | 522.043 | 1.41475 | ||||||||
\(370\) | 357.362 | 0.965844 | ||||||||
\(371\) | −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 | \(0.387551\pi\) | |||||||
\(374\) | − | 177.033i | − | 0.473349i | ||||||
\(375\) | 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 | ||||
\(378\) | 294.067 | + | 509.339i | 0.777956 | + | 1.34746i | ||||
\(379\) | − | 118.568i | − | 0.312845i | −0.987690 | − | 0.156423i | \(-0.950004\pi\) | ||
0.987690 | − | 0.156423i | \(-0.0499962\pi\) | |||||||
\(380\) | 211.319 | − | 158.690i | 0.556102 | − | 0.417605i | ||||
\(381\) | 690.634 | 1.81269 | ||||||||
\(382\) | −316.182 | + | 182.548i | −0.827702 | + | 0.477874i | ||||
\(383\) | −534.077 | − | 308.350i | −1.39446 | − | 0.805090i | −0.400652 | − | 0.916230i | \(-0.631217\pi\) |
−0.993805 | + | 0.111140i | \(0.964550\pi\) | |||||||
\(384\) | − | 626.474i | − | 1.63144i | ||||||
\(385\) | 307.772 | − | 533.077i | 0.799408 | − | 1.38462i | ||||
\(386\) | −202.091 | −0.523552 | ||||||||
\(387\) | − | 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 | \(-0.349113\pi\) | |||||||
\(390\) | 204.224i | 0.523652i | ||||||||
\(391\) | − | 161.077i | − | 0.411962i | ||||||
\(392\) | −422.542 | −1.07791 | ||||||||
\(393\) | −330.771 | − | 572.913i | −0.841657 | − | 1.45779i | ||||
\(394\) | −10.1584 | − | 17.5948i | −0.0257827 | − | 0.0446569i | ||||
\(395\) | 236.768 | − | 136.698i | 0.599413 | − | 0.346071i | ||||
\(396\) | 1049.41i | 2.65003i | ||||||||
\(397\) | 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 | \(0.167425\pi\) | |||||||
\(402\) | −469.135 | − | 812.565i | −1.16700 | − | 2.02131i | ||||
\(403\) | 25.0217 | − | 14.4463i | 0.0620887 | − | 0.0358469i | ||||
\(404\) | 647.540 | 1.60282 | ||||||||
\(405\) | 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 | ||||||||
\(412\) | −577.545 | − | 333.445i | −1.40181 | − | 0.809334i | ||||
\(413\) | −97.6475 | + | 169.130i | −0.236435 | + | 0.409517i | ||||
\(414\) | 954.830i | 2.30635i | ||||||||
\(415\) | −280.034 | − | 161.677i | −0.674780 | − | 0.389584i | ||||
\(416\) | 192.000 | 0.461538 | ||||||||
\(417\) | 77.6377 | 0.186181 | ||||||||
\(418\) | 400.315 | + | 533.077i | 0.957691 | + | 1.27530i | ||||
\(419\) | 833.373i | 1.98896i | 0.104936 | + | 0.994479i | \(0.466536\pi\) | ||||
−0.104936 | + | 0.994479i | \(0.533464\pi\) | |||||||
\(420\) | −686.907 | −1.63549 | ||||||||
\(421\) | 404.964 | − | 701.419i | 0.961910 | − | 1.66608i | 0.244214 | − | 0.969721i | \(-0.421470\pi\) |
0.717696 | − | 0.696356i | \(-0.245197\pi\) | |||||||
\(422\) | 589.418i | 1.39673i | ||||||||
\(423\) | 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 | ||||
\(428\) | −629.180 | − | 363.257i | −1.47005 | − | 0.848732i | ||||
\(429\) | −515.180 | −1.20089 | ||||||||
\(430\) | 65.2754 | + | 37.6868i | 0.151803 | + | 0.0876436i | ||||
\(431\) | −222.564 | + | 128.497i | −0.516390 | + | 0.298138i | −0.735456 | − | 0.677572i | \(-0.763032\pi\) |
0.219066 | + | 0.975710i | \(0.429699\pi\) | |||||||
\(432\) | 403.818 | − | 233.144i | 0.934763 | − | 0.539686i | ||||
\(433\) | 121.137 | + | 209.815i | 0.279761 | + | 0.484561i | 0.971325 | − | 0.237754i | \(-0.0764113\pi\) |
−0.691564 | + | 0.722315i | \(0.743078\pi\) | |||||||
\(434\) | 48.5901 | + | 84.1605i | 0.111959 | + | 0.193918i | ||||
\(435\) | −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 | 0.758046 | − | 0.652201i | \(-0.226154\pi\) |
−0.185800 | + | 0.982588i | \(0.559488\pi\) | |||||||
\(440\) | −422.638 | − | 244.010i | −0.960540 | − | 0.554568i | ||||
\(441\) | −394.931 | − | 684.040i | −0.895534 | − | 1.55111i | ||||
\(442\) | −30.2733 | − | 52.4349i | −0.0684916 | − | 0.118631i | ||||
\(443\) | −187.649 | + | 108.339i | −0.423586 | + | 0.244557i | −0.696610 | − | 0.717450i | \(-0.745309\pi\) |
0.273024 | + | 0.962007i | \(0.411976\pi\) | |||||||
\(444\) | 871.224 | − | 503.001i | 1.96222 | − | 1.13289i | ||||
\(445\) | 391.184 | 0.879066 | ||||||||
\(446\) | 66.8399i | 0.149865i | ||||||||
\(447\) | 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 | \(0.614394\pi\) | |||||||
\(450\) | 386.091 | 0.857980 | ||||||||
\(451\) | −530.373 | − | 306.211i | −1.17599 | − | 0.678960i | ||||
\(452\) | 54.1822 | − | 93.8463i | 0.119872 | − | 0.207625i | ||||
\(453\) | −11.7842 | + | 20.4108i | −0.0260136 | + | 0.0450569i | ||||
\(454\) | 47.0673 | − | 27.1743i | 0.103672 | − | 0.0598553i | ||||
\(455\) | − | 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 | \(0.748379\pi\) | |||||||
\(458\) | 251.818 | + | 436.161i | 0.549821 | + | 0.952317i | ||||
\(459\) | −127.343 | − | 73.5213i | −0.277435 | − | 0.160177i | ||||
\(460\) | −384.547 | − | 222.018i | −0.835971 | − | 0.482648i | ||||
\(461\) | 109.907 | − | 190.364i | 0.238410 | − | 0.412938i | −0.721848 | − | 0.692051i | \(-0.756707\pi\) |
0.960258 | + | 0.279114i | \(0.0900406\pi\) | |||||||
\(462\) | − | 1732.81i | − | 3.75066i | ||||||
\(463\) | − | 66.7372i | − | 0.144141i | −0.997400 | − | 0.0720704i | \(-0.977039\pi\) | ||
0.997400 | − | 0.0720704i | \(-0.0229606\pi\) | |||||||
\(464\) | −59.8178 | + | 103.607i | −0.128918 | + | 0.223292i | ||||
\(465\) | 40.9762 | + | 70.9728i | 0.0881208 | + | 0.152630i | ||||
\(466\) | −329.089 | −0.706200 | ||||||||
\(467\) | − | 171.878i | − | 0.368046i | −0.982922 | − | 0.184023i | \(-0.941088\pi\) | ||
0.982922 | − | 0.184023i | \(-0.0589121\pi\) | |||||||
\(468\) | 179.453 | + | 310.822i | 0.383447 | + | 0.664150i | ||||
\(469\) | 483.600 | + | 837.620i | 1.03113 | + | 1.78597i | ||||
\(470\) | −133.319 | + | 76.9717i | −0.283657 | + | 0.163770i | ||||
\(471\) | −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 | ||||
\(478\) | −206.542 | + | 119.247i | −0.432097 | + | 0.249471i | ||||
\(479\) | 19.8178 | − | 11.4418i | 0.0413733 | − | 0.0238869i | −0.479171 | − | 0.877722i | \(-0.659063\pi\) |
0.520544 | + | 0.853835i | \(0.325729\pi\) | |||||||
\(480\) | 544.598i | 1.13458i | ||||||||
\(481\) | 154.158 | + | 267.010i | 0.320496 | + | 0.555115i | ||||
\(482\) | 66.2277 | − | 114.710i | 0.137402 | − | 0.237987i | ||||
\(483\) | − | 1576.63i | − | 3.26425i | ||||||
\(484\) | 373.545 | − | 646.998i | 0.771786 | − | 1.33677i | ||||
\(485\) | 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 | \(0.0479215\pi\) | ||||
−0.988689 | + | 0.149982i | \(0.952079\pi\) | |||||||
\(488\) | −66.0911 | − | 114.473i | −0.135433 | − | 0.234576i | ||||
\(489\) | −508.726 | + | 881.139i | −1.04034 | + | 1.80192i | ||||
\(490\) | 367.319 | 0.749630 | ||||||||
\(491\) | 412.931 | + | 238.406i | 0.840999 | + | 0.485551i | 0.857604 | − | 0.514311i | \(-0.171952\pi\) |
−0.0166045 | + | 0.999862i | \(0.505286\pi\) | |||||||
\(492\) | 683.423i | 1.38907i | ||||||||
\(493\) | 37.7267 | 0.0765248 | ||||||||
\(494\) | 209.727 | + | 89.4355i | 0.424548 | + | 0.181044i | ||||
\(495\) | − | 912.259i | − | 1.84295i | ||||||
\(496\) | 66.7246 | − | 38.5235i | 0.134525 | − | 0.0776683i | ||||
\(497\) | 73.7505 | − | 127.740i | 0.148391 | − | 0.257021i | ||||
\(498\) | −910.269 | −1.82785 | ||||||||
\(499\) | −501.621 | − | 289.611i | −1.00525 | − | 0.580382i | −0.0954538 | − | 0.995434i | \(-0.530430\pi\) |
−0.909798 | + | 0.415052i | \(0.863764\pi\) | |||||||
\(500\) | −263.636 | + | 456.630i | −0.527271 | + | 0.913261i | ||||
\(501\) | 583.905 | 1.16548 | ||||||||
\(502\) | −322.247 | − | 186.050i | −0.641927 | − | 0.370617i | ||||
\(503\) | 181.830 | − | 104.979i | 0.361490 | − | 0.208707i | −0.308244 | − | 0.951307i | \(-0.599741\pi\) |
0.669734 | + | 0.742601i | \(0.266408\pi\) | |||||||
\(504\) | −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 | ||||
\(508\) | 564.436i | 1.11109i | ||||||||
\(509\) | 70.9545 | + | 122.897i | 0.139400 | + | 0.241447i | 0.927270 | − | 0.374394i | \(-0.122149\pi\) |
−0.787870 | + | 0.615842i | \(0.788816\pi\) | |||||||
\(510\) | 148.729 | − | 85.8686i | 0.291625 | − | 0.168370i | ||||
\(511\) | −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 | ||||
\(516\) | 212.182 | 0.411206 | ||||||||
\(517\) | −194.170 | − | 336.313i | −0.375571 | − | 0.650508i | ||||
\(518\) | −898.087 | + | 518.511i | −1.73376 | + | 1.00099i | ||||
\(519\) | 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 | \(0.549901\pi\) | |||||||
\(522\) | −223.636 | −0.428421 | ||||||||
\(523\) | −531.564 | + | 306.899i | −1.01638 | + | 0.586804i | −0.913052 | − | 0.407843i | \(-0.866281\pi\) |
−0.103323 | + | 0.994648i | \(0.532948\pi\) | |||||||
\(524\) | 468.226 | − | 270.330i | 0.893560 | − | 0.515897i | ||||
\(525\) | −637.521 | −1.21433 | ||||||||
\(526\) | 173.754i | 0.330330i | ||||||||
\(527\) | −21.0414 | − | 12.1483i | −0.0399268 | − | 0.0230517i | ||||
\(528\) | −1373.81 | −2.60192 | ||||||||
\(529\) | 245.090 | − | 424.508i | 0.463308 | − | 0.802473i | ||||
\(530\) | −139.406 | − | 241.458i | −0.263030 | − | 0.455581i | ||||
\(531\) | 289.434i | 0.545074i | ||||||||
\(532\) | −300.816 | + | 705.414i | −0.565443 | + | 1.32597i | ||||
\(533\) | −209.453 | −0.392971 | ||||||||
\(534\) | 953.679 | − | 550.607i | 1.78592 | − | 1.03110i | ||||
\(535\) | 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 | ||||
\(538\) | 390.542 | 0.725915 | ||||||||
\(539\) | 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 | \(0.908045\pi\) | |||||||
\(542\) | − | 702.081i | − | 1.29535i | ||||||
\(543\) | 1056.61i | 1.94588i | ||||||||
\(544\) | −80.7288 | − | 139.826i | −0.148398 | − | 0.257034i | ||||
\(545\) | 142.091 | + | 246.109i | 0.260718 | + | 0.451576i | ||||
\(546\) | −296.317 | − | 513.236i | −0.542705 | − | 0.939992i | ||||
\(547\) | −289.521 | + | 167.155i | −0.529288 | + | 0.305585i | −0.740727 | − | 0.671807i | \(-0.765519\pi\) |
0.211438 | + | 0.977391i | \(0.432185\pi\) | |||||||
\(548\) | −444.729 | −0.811549 | ||||||||
\(549\) | 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 | ||||
\(554\) | 115.430 | + | 199.930i | 0.208357 | + | 0.360884i | ||||
\(555\) | −757.360 | + | 437.262i | −1.36461 | + | 0.787860i | ||||
\(556\) | 63.4511i | 0.114121i | ||||||||
\(557\) | −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 | ||||||||
\(560\) | − | 561.390i | − | 1.00248i | ||||||
\(561\) | 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 | \(-0.961428\pi\) | ||
0.992667 | − | 0.120881i | \(-0.0385719\pi\) | |||||||
\(564\) | −216.681 | + | 375.303i | −0.384186 | + | 0.665430i | ||||
\(565\) | −47.1009 | + | 81.5812i | −0.0833645 | + | 0.144392i | ||||
\(566\) | − | 289.221i | − | 0.510992i | ||||||
\(567\) | −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 | \(0.154211\pi\) | |||||||
\(570\) | −253.679 | + | 594.879i | −0.445051 | + | 1.04365i | ||||
\(571\) | − | 433.551i | − | 0.759284i | −0.925133 | − | 0.379642i | \(-0.876047\pi\) | ||
0.925133 | − | 0.379642i | \(-0.123953\pi\) | |||||||
\(572\) | − | 421.043i | − | 0.736088i | ||||||
\(573\) | 446.725 | − | 773.750i | 0.779624 | − | 1.35035i | ||||
\(574\) | − | 704.495i | − | 1.22734i | ||||||
\(575\) | −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 | ||||
\(580\) | 52.0000 | − | 90.0666i | 0.0896552 | − | 0.155287i | ||||
\(581\) | 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 | ||||
\(586\) | −215.794 | − | 373.766i | −0.368249 | − | 0.637826i | ||||
\(587\) | 805.568 | + | 465.095i | 1.37235 | + | 0.792326i | 0.991223 | − | 0.132198i | \(-0.0422035\pi\) |
0.381125 | + | 0.924524i | \(0.375537\pi\) | |||||||
\(588\) | 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 | ||||
\(592\) | 411.089 | + | 712.027i | 0.694407 | + | 1.20275i | ||||
\(593\) | 218.181 | + | 377.901i | 0.367928 | + | 0.637270i | 0.989241 | − | 0.146292i | \(-0.0467340\pi\) |
−0.621314 | + | 0.783562i | \(0.713401\pi\) | |||||||
\(594\) | −511.269 | − | 885.544i | −0.860722 | − | 1.49082i | ||||
\(595\) | −153.315 | + | 88.5163i | −0.257672 | + | 0.148767i | ||||
\(596\) | 79.1366 | + | 137.069i | 0.132780 | + | 0.229981i | ||||
\(597\) | −898.451 | −1.50494 | ||||||||
\(598\) | − | 383.095i | − | 0.640627i | ||||||
\(599\) | 618.142 | − | 356.885i | 1.03196 | − | 0.595801i | 0.114412 | − | 0.993433i | \(-0.463501\pi\) |
0.917545 | + | 0.397633i | \(0.130168\pi\) | |||||||
\(600\) | 505.443i | 0.842405i | ||||||||
\(601\) | 21.9586 | 0.0365368 | 0.0182684 | − | 0.999833i | \(-0.494185\pi\) | ||||
0.0182684 | + | 0.999833i | \(0.494185\pi\) | |||||||
\(602\) | −218.725 | −0.363330 | ||||||||
\(603\) | 1241.38 | + | 716.712i | 2.05868 | + | 1.18858i | ||||
\(604\) | −16.6812 | − | 9.63087i | −0.0276178 | − | 0.0159452i | ||||
\(605\) | −324.725 | + | 562.440i | −0.536735 | + | 0.929652i | ||||
\(606\) | −1372.34 | + | 792.319i | −2.26458 | + | 1.30746i | ||||
\(607\) | − | 305.012i | − | 0.502492i | −0.967923 | − | 0.251246i | \(-0.919160\pi\) | ||
0.967923 | − | 0.251246i | \(-0.0808403\pi\) | |||||||
\(608\) | 559.271 | + | 238.495i | 0.919854 | + | 0.392261i | ||||
\(609\) | 369.271 | 0.606357 | ||||||||
\(610\) | 57.4534 | + | 99.5122i | 0.0941859 | + | 0.163135i | ||||
\(611\) | −115.022 | − | 66.4078i | −0.188252 | − | 0.108687i | ||||
\(612\) | 150.907 | − | 261.378i | 0.246580 | − | 0.427089i | ||||
\(613\) | 499.043 | − | 864.369i | 0.814100 | − | 1.41006i | −0.0958719 | − | 0.995394i | \(-0.530564\pi\) |
0.909972 | − | 0.414669i | \(-0.136103\pi\) | |||||||
\(614\) | 179.632i | 0.292561i | ||||||||
\(615\) | − | 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 | \(0.799183\pi\) | |||||||
\(618\) | 1631.99 | 2.64076 | ||||||||
\(619\) | 432.512i | 0.698727i | 0.936987 | + | 0.349363i | \(0.113602\pi\) | ||||
−0.936987 | + | 0.349363i | \(0.886398\pi\) | |||||||
\(620\) | −58.0041 | + | 33.4887i | −0.0935551 | + | 0.0540141i | ||||
\(621\) | −465.190 | − | 805.733i | −0.749098 | − | 1.29748i | ||||
\(622\) | −597.790 | + | 345.134i | −0.961077 | + | 0.554878i | ||||
\(623\) | −983.085 | + | 567.584i | −1.57799 | + | 0.911050i | ||||
\(624\) | −406.907 | + | 234.928i | −0.652094 | + | 0.376487i | ||||
\(625\) | 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 | ||||
\(630\) | 908.816 | − | 524.705i | 1.44256 | − | 0.832865i | ||||
\(631\) | −592.283 | + | 341.955i | −0.938642 | + | 0.541925i | −0.889534 | − | 0.456868i | \(-0.848971\pi\) |
−0.0491077 | + | 0.998793i | \(0.515638\pi\) | |||||||
\(632\) | 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 | ||||||
\(636\) | −679.723 | − | 392.438i | −1.06875 | − | 0.617041i | ||||
\(637\) | 158.453 | + | 274.449i | 0.248749 | + | 0.430847i | ||||
\(638\) | 227.204 | + | 131.176i | 0.356119 | + | 0.205605i | ||||
\(639\) | − | 218.602i | − | 0.342100i | ||||||
\(640\) | −445.085 | −0.695445 | ||||||||
\(641\) | 197.363 | − | 341.843i | 0.307899 | − | 0.533297i | −0.670003 | − | 0.742358i | \(-0.733707\pi\) |
0.977903 | + | 0.209061i | \(0.0670407\pi\) | |||||||
\(642\) | 1777.90 | 2.76932 | ||||||||
\(643\) | 854.326 | + | 493.245i | 1.32866 | + | 0.767100i | 0.985092 | − | 0.172030i | \(-0.0550325\pi\) |
0.343564 | + | 0.939129i | \(0.388366\pi\) | |||||||
\(644\) | 1288.54 | 2.00084 | ||||||||
\(645\) | −184.451 | −0.285971 | ||||||||
\(646\) | −23.0497 | − | 190.340i | −0.0356806 | − | 0.294644i | ||||
\(647\) | − | 1173.93i | − | 1.81442i | −0.420674 | − | 0.907212i | \(-0.638206\pi\) | ||
0.420674 | − | 0.907212i | \(-0.361794\pi\) | |||||||
\(648\) | −32.1822 | + | 55.7412i | −0.0496639 | + | 0.0860204i | ||||
\(649\) | 169.771 | − | 294.052i | 0.261589 | − | 0.453085i | ||||
\(650\) | −154.907 | −0.238318 | ||||||||
\(651\) | −205.954 | − | 118.908i | −0.316366 | − | 0.182654i | ||||
\(652\) | −720.130 | − | 415.767i | −1.10449 | − | 0.637680i | ||||
\(653\) | −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 | ||||
\(656\) | −558.542 | −0.851437 | ||||||||
\(657\) | −522.043 | −0.794587 | ||||||||
\(658\) | 223.362 | − | 386.875i | 0.339456 | − | 0.587956i | ||||
\(659\) | −566.364 | + | 326.991i | −0.859430 | + | 0.496192i | −0.863821 | − | 0.503798i | \(-0.831936\pi\) |
0.00439135 | + | 0.999990i | \(0.498602\pi\) | |||||||
\(660\) | 1194.26 | 1.80949 | ||||||||
\(661\) | 154.170 | + | 267.031i | 0.233238 | + | 0.403980i | 0.958759 | − | 0.284220i | \(-0.0917346\pi\) |
−0.725521 | + | 0.688200i | \(0.758401\pi\) | |||||||
\(662\) | 179.341 | − | 103.542i | 0.270907 | − | 0.156408i | ||||
\(663\) | 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 | ||||
\(668\) | 477.209i | 0.714385i | ||||||||
\(669\) | −81.7842 | − | 141.654i | −0.122248 | − | 0.211740i | ||||
\(670\) | −577.295 | + | 333.301i | −0.861634 | + | 0.497465i | ||||
\(671\) | −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 | \(0.473893\pi\) | |||||||
\(674\) | −992.812 | −1.47301 | ||||||||
\(675\) | −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 | \(0.734713\pi\) | |||||||
\(678\) | 265.185i | 0.391129i | ||||||||
\(679\) | −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 | ||||
\(682\) | −84.4793 | − | 146.322i | −0.123870 | − | 0.214549i | ||||
\(683\) | − | 289.407i | − | 0.423729i | −0.977299 | − | 0.211864i | \(-0.932047\pi\) | ||
0.977299 | − | 0.211864i | \(-0.0679535\pi\) | |||||||
\(684\) | 136.634 | + | 1128.30i | 0.199757 | + | 1.64955i | ||||
\(685\) | 386.606 | 0.564388 | ||||||||
\(686\) | −66.7246 | + | 38.5235i | −0.0972662 | + | 0.0561567i | ||||
\(687\) | −1067.36 | − | 616.240i | −1.55365 | − | 0.897001i | ||||
\(688\) | 173.411i | 0.252050i | ||||||||
\(689\) | 120.273 | − | 208.319i | 0.174562 | − | 0.302350i | ||||
\(690\) | 1086.63 | 1.57483 | ||||||||
\(691\) | 308.668i | 0.446698i | 0.974739 | + | 0.223349i | \(0.0716990\pi\) | ||||
−0.974739 | + | 0.223349i | \(0.928301\pi\) | |||||||
\(692\) | 192.547 | + | 333.500i | 0.278247 | + | 0.481937i | ||||
\(693\) | 1323.63 | + | 2292.60i | 1.91000 | + | 3.30822i | ||||
\(694\) | 1118.56i | 1.61176i | ||||||||
\(695\) | − | 55.1585i | − | 0.0793647i | ||||||
\(696\) | − | 292.768i | − | 0.420644i | ||||||
\(697\) | 88.0673 | + | 152.537i | 0.126352 | + | 0.218848i | ||||
\(698\) | 507.271 | + | 878.620i | 0.726750 | + | 1.25877i | ||||
\(699\) | 697.440 | − | 402.667i | 0.997769 | − | 0.576062i | ||||
\(700\) | − | 521.028i | − | 0.744326i | ||||||
\(701\) | −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 | ||||
\(706\) | 95.7723 | + | 165.882i | 0.135655 | + | 0.234961i | ||||
\(707\) | 1414.65 | − | 816.749i | 2.00092 | − | 1.15523i | ||||
\(708\) | −378.907 | −0.535179 | ||||||||
\(709\) | −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 | ||||||||
\(716\) | −711.410 | − | 410.733i | −0.993589 | − | 0.573649i | ||||
\(717\) | 291.818 | − | 505.443i | 0.406998 | − | 0.704942i | ||||
\(718\) | − | 428.890i | − | 0.597340i | ||||||
\(719\) | −391.610 | − | 226.096i | −0.544659 | − | 0.314459i | 0.202306 | − | 0.979322i | \(-0.435156\pi\) |
−0.746965 | + | 0.664863i | \(0.768490\pi\) | |||||||
\(720\) | −416.000 | − | 720.533i | −0.577778 | − | 1.00074i | ||||
\(721\) | −1682.31 | −2.33330 | ||||||||
\(722\) | 499.814 | + | 521.028i | 0.692263 | + | 0.721646i | ||||
\(723\) | 324.140i | 0.448327i | ||||||||
\(724\) | −863.540 | −1.19274 | ||||||||
\(725\) | 48.2614 | − | 83.5912i | 0.0665674 | − | 0.115298i | ||||
\(726\) | 1828.25i | 2.51825i | ||||||||
\(727\) | 1194.95 | + | 689.905i | 1.64367 | + | 0.948975i | 0.979512 | + | 0.201385i | \(0.0645444\pi\) |
0.664161 | + | 0.747590i | \(0.268789\pi\) | |||||||
\(728\) | 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 | ||||
\(732\) | 280.135 | + | 161.736i | 0.382698 | + | 0.220951i | ||||
\(733\) | 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 | ||||
\(736\) | − | 1021.59i | − | 1.38803i | ||||||
\(737\) | −840.793 | − | 1456.30i | −1.14083 | − | 1.97598i | ||||
\(738\) | −522.043 | − | 904.206i | −0.707376 | − | 1.22521i | ||||
\(739\) | −699.757 | − | 404.005i | −0.946897 | − | 0.546692i | −0.0547817 | − | 0.998498i | \(-0.517446\pi\) |
−0.892116 | + | 0.451807i | \(0.850780\pi\) | |||||||
\(740\) | −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 | 0.246434 | − | 0.969160i | \(-0.420741\pi\) |
−0.716100 | + | 0.697998i | \(0.754075\pi\) | |||||||
\(744\) | −94.2733 | + | 163.286i | −0.126711 | + | 0.219471i | ||||
\(745\) | −68.7940 | − | 119.155i | −0.0923409 | − | 0.159939i | ||||
\(746\) | −258.091 | − | 447.027i | −0.345967 | − | 0.599232i | ||||
\(747\) | 1204.34 | − | 695.324i | 1.61223 | − | 0.930822i | ||||
\(748\) | −306.629 | + | 177.033i | −0.409932 | + | 0.236675i | ||||
\(749\) | −1832.72 | −2.44689 | ||||||||
\(750\) | − | 1290.32i | − | 1.72043i | ||||||
\(751\) | 1181.79 | − | 682.308i | 1.57362 | − | 0.908532i | 0.577905 | − | 0.816104i | \(-0.303870\pi\) |
0.995719 | − | 0.0924285i | \(-0.0294629\pi\) | |||||||
\(752\) | −306.725 | − | 177.088i | −0.407879 | − | 0.235489i | ||||
\(753\) | 910.588 | 1.20928 | ||||||||
\(754\) | 89.7267 | 0.119001 | ||||||||
\(755\) | 14.5010 | + | 8.37218i | 0.0192067 | + | 0.0110890i | ||||
\(756\) | 588.135 | − | 1018.68i | 0.777956 | − | 1.34746i | ||||
\(757\) | −555.043 | + | 961.363i | −0.733215 | + | 1.26996i | 0.222288 | + | 0.974981i | \(0.428648\pi\) |
−0.955502 | + | 0.294984i | \(0.904686\pi\) | |||||||
\(758\) | −205.366 | + | 118.568i | −0.270932 | + | 0.156423i | ||||
\(759\) | 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 | \(0.186369\pi\) | |||||||
\(762\) | −690.634 | − | 1196.21i | −0.906343 | − | 1.56983i | ||||
\(763\) | −714.178 | − | 412.331i | −0.936013 | − | 0.540407i | ||||
\(764\) | 632.364 | + | 365.096i | 0.827702 | + | 0.477874i | ||||
\(765\) | −131.184 | + | 227.218i | −0.171483 | + | 0.297017i | ||||
\(766\) | 1233.40i | 1.61018i | ||||||||
\(767\) | − | 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 | \(0.583889\pi\) | |||||||
\(770\) | −1231.09 | −1.59882 | ||||||||
\(771\) | − | 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 | \(0.614966\pi\) | |||||||
\(774\) | −280.729 | + | 162.079i | −0.362699 | + | 0.209404i | ||||
\(775\) | −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 | ||||
\(782\) | −278.994 | + | 161.077i | −0.356770 | + | 0.205981i | ||||
\(783\) | 188.715 | − | 108.955i | 0.241015 | − | 0.139150i | ||||
\(784\) | 422.542 | + | 731.865i | 0.538957 | + | 0.933501i | ||||
\(785\) | 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 | \(-0.981232\pi\) | ||
0.998262 | − | 0.0589276i | \(-0.0187681\pi\) | |||||||
\(788\) | −20.3168 | + | 35.1897i | −0.0257827 | + | 0.0446569i | ||||
\(789\) | −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 | ||||
\(794\) | −1058.13 | −1.33266 | ||||||||
\(795\) | 590.887 | + | 341.149i | 0.743254 | + | 0.429118i | ||||
\(796\) | − | 734.280i | − | 0.922462i | ||||||
\(797\) | 1276.61 | 1.60176 | 0.800882 | − | 0.598822i | \(-0.204365\pi\) | ||||
0.800882 | + | 0.598822i | \(0.204365\pi\) | |||||||
\(798\) | −225.612 | − | 1863.06i | −0.282722 | − | 2.33466i | ||||
\(799\) | 111.688i | 0.139785i | ||||||||
\(800\) | −413.085 | −0.516356 | ||||||||
\(801\) | −841.180 | + | 1456.97i | −1.05016 | + | 1.81893i | ||||
\(802\) | 3.82195 | 0.00476553 | ||||||||
\(803\) | 530.373 | + | 306.211i | 0.660490 | + | 0.381334i | ||||
\(804\) | −938.269 | + | 1625.13i | −1.16700 | + | 2.02131i | ||||
\(805\) | −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 | 0.178738 | − | 0.983897i | \(-0.442799\pi\) |
0.941448 | + | 0.337157i | \(0.109465\pi\) | |||||||
\(812\) | 301.795i | 0.371669i | ||||||||
\(813\) | 859.053 | + | 1487.92i | 1.05665 | + | 1.83016i | ||||
\(814\) | 1561.43 | − | 901.489i | 1.91821 | − | 1.10748i | ||||
\(815\) | 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 | ||||
\(820\) | 485.545 | 0.592127 | ||||||||
\(821\) | −200.770 | − | 347.744i | −0.244543 | − | 0.423562i | 0.717460 | − | 0.696600i | \(-0.245305\pi\) |
−0.962003 | + | 0.273038i | \(0.911971\pi\) | |||||||
\(822\) | 942.517 | − | 544.162i | 1.14661 | − | 0.661998i | ||||
\(823\) | −243.748 | + | 140.728i | −0.296171 | + | 0.170994i | −0.640721 | − | 0.767774i | \(-0.721365\pi\) |
0.344551 | + | 0.938768i | \(0.388031\pi\) | |||||||
\(824\) | 1333.78i | 1.61867i | ||||||||
\(825\) | 1108.40 | 1.34352 | ||||||||
\(826\) | 390.590 | 0.472869 | ||||||||
\(827\) | −551.534 | + | 318.428i | −0.666909 | + | 0.385040i | −0.794904 | − | 0.606735i | \(-0.792479\pi\) |
0.127995 | + | 0.991775i | \(0.459146\pi\) | |||||||
\(828\) | 1653.81 | − | 954.830i | 1.99736 | − | 1.15318i | ||||
\(829\) | −52.2774 | −0.0630608 | −0.0315304 | − | 0.999503i | \(-0.510038\pi\) | ||||
−0.0315304 | + | 0.999503i | \(0.510038\pi\) | |||||||
\(830\) | 646.710i | 0.779169i | ||||||||
\(831\) | −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 | ||||
\(834\) | −77.6377 | − | 134.472i | −0.0930907 | − | 0.161238i | ||||
\(835\) | − | 414.841i | − | 0.496816i | ||||||
\(836\) | 523.002 | − | 1226.44i | 0.625601 | − | 1.46704i | ||||
\(837\) | −140.336 | −0.167666 | ||||||||
\(838\) | 1443.45 | − | 833.373i | 1.72249 | − | 0.994479i | ||||
\(839\) | −934.461 | − | 539.511i | −1.11378 | − | 0.643041i | −0.173974 | − | 0.984750i | \(-0.555661\pi\) |
−0.939806 | + | 0.341709i | \(0.888994\pi\) | |||||||
\(840\) | 686.907 | + | 1189.76i | 0.817746 | + | 1.41638i | ||||
\(841\) | 392.546 | − | 679.909i | 0.466760 | − | 0.808453i | ||||
\(842\) | −1619.86 | −1.92382 | ||||||||
\(843\) | 117.454i | 0.139328i | ||||||||
\(844\) | 1020.90 | − | 589.418i | 1.20960 | − | 0.698363i | ||||
\(845\) | −231.236 | − | 400.512i | −0.273651 | − | 0.473978i | ||||
\(846\) | − | 662.062i | − | 0.782579i | ||||||
\(847\) | − | 1884.62i | − | 2.22506i | ||||||
\(848\) | 320.729 | − | 555.519i | 0.378218 | − | 0.655093i | ||||
\(849\) | 353.886 | + | 612.949i | 0.416827 | + | 0.721966i | ||||
\(850\) | 65.1325 | + | 112.813i | 0.0766265 | + | 0.132721i | ||||
\(851\) | 1420.70 | − | 820.241i | 1.66945 | − | 0.963855i | ||||
\(852\) | 286.178 | 0.335890 | ||||||||
\(853\) | 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 | \(0.273414\pi\) | |||||||
\(858\) | 515.180 | + | 892.318i | 0.600443 | + | 1.04000i | ||||
\(859\) | −794.551 | + | 458.734i | −0.924972 | + | 0.534033i | −0.885218 | − | 0.465176i | \(-0.845991\pi\) |
−0.0397544 | + | 0.999209i | \(0.512658\pi\) | |||||||
\(860\) | − | 150.747i | − | 0.175287i | ||||||
\(861\) | 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 | \(-0.912670\pi\) | ||
0.962600 | − | 0.270927i | \(-0.0873301\pi\) | |||||||
\(864\) | −807.636 | − | 466.289i | −0.934763 | − | 0.539686i | ||||
\(865\) | −167.382 | − | 289.914i | −0.193505 | − | 0.335161i | ||||
\(866\) | 242.273 | − | 419.630i | 0.279761 | − | 0.484561i | ||||
\(867\) | 1289.86i | 1.48773i | ||||||||
\(868\) | 97.1801 | − | 168.321i | 0.111959 | − | 0.193918i | ||||
\(869\) | 689.675 | − | 1194.55i | 0.793642 | − | 1.37463i | ||||
\(870\) | 254.505i | 0.292535i | ||||||||
\(871\) | −498.065 | − | 287.558i | −0.571831 | − | 0.330147i | ||||
\(872\) | −326.907 | + | 566.219i | −0.374893 | + | 0.649334i | ||||
\(873\) | −1913.49 | −2.19185 | ||||||||
\(874\) | 475.865 | − | 1115.91i | 0.544468 | − | 1.27678i | ||||
\(875\) | 1330.11i | 1.52012i | ||||||||
\(876\) | − | 683.423i | − | 0.780163i | ||||||
\(877\) | −753.758 | + | 1305.55i | −0.859474 | + | 1.48865i | 0.0129583 | + | 0.999916i | \(0.495875\pi\) |
−0.872432 | + | 0.488736i | \(0.837458\pi\) | |||||||
\(878\) | − | 580.158i | − | 0.660772i | ||||||
\(879\) | 914.667 | + | 528.083i | 1.04058 | + | 0.600777i | ||||
\(880\) | 976.040i | 1.10914i | ||||||||
\(881\) | −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 | −0.317217 | − | 0.948353i | \(-0.602748\pi\) |
0.662689 | + | 0.748894i | \(0.269415\pi\) | |||||||
\(884\) | −60.5466 | + | 104.870i | −0.0684916 | + | 0.118631i | ||||
\(885\) | 329.386 | 0.372188 | ||||||||
\(886\) | 375.297 | + | 216.678i | 0.423586 | + | 0.244557i | ||||
\(887\) | −79.7702 | + | 46.0553i | −0.0899326 | + | 0.0519226i | −0.544292 | − | 0.838896i | \(-0.683202\pi\) |
0.454359 | + | 0.890819i | \(0.349868\pi\) | |||||||
\(888\) | −1742.45 | − | 1006.00i | −1.96222 | − | 1.13289i | ||||
\(889\) | 711.929 | + | 1233.10i | 0.800820 | + | 1.38706i | ||||
\(890\) | −391.184 | − | 677.551i | −0.439533 | − | 0.761293i | ||||
\(891\) | 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 | ||||
\(896\) | 1118.54 | − | 645.791i | 1.24837 | − | 0.720749i | ||||
\(897\) | 468.748 | + | 811.896i | 0.522574 | + | 0.905124i | ||||
\(898\) | 315.820 | + | 547.016i | 0.351693 | + | 0.609149i | ||||
\(899\) | 31.1822 | − | 18.0030i | 0.0346854 | − | 0.0200256i | ||||
\(900\) | −386.091 | − | 668.729i | −0.428990 | − | 0.743033i | ||||
\(901\) | −202.282 | −0.224508 | ||||||||
\(902\) | 1224.84i | 1.35792i | ||||||||
\(903\) | 463.545 | − | 267.628i | 0.513338 | − | 0.296376i | ||||
\(904\) | −216.729 | −0.239744 | ||||||||
\(905\) | 750.681 | 0.829482 | ||||||||
\(906\) | 47.1366 | 0.0520272 | ||||||||
\(907\) | 1071.41 | + | 618.580i | 1.18127 | + | 0.682007i | 0.956308 | − | 0.292360i | \(-0.0944407\pi\) |
0.224962 | + | 0.974367i | \(0.427774\pi\) | |||||||
\(908\) | −94.1346 | − | 54.3486i | −0.103672 | − | 0.0598553i | ||||
\(909\) | 1210.45 | − | 2096.56i | 1.33163 | − | 2.30645i | ||||
\(910\) | −364.634 | + | 210.521i | −0.400696 | + | 0.231342i | ||||
\(911\) | − | 391.450i | − | 0.429693i | −0.976648 | − | 0.214846i | \(-0.931075\pi\) | ||
0.976648 | − | 0.214846i | \(-0.0689251\pi\) | |||||||
\(912\) | −1477.08 | + | 178.871i | −1.61961 | + | 0.196130i | ||||
\(913\) | −1631.40 | −1.78686 | ||||||||
\(914\) | 642.996 | + | 1113.70i | 0.703497 | + | 1.21849i | ||||
\(915\) | −243.523 | − | 140.598i | −0.266145 | − | 0.153659i | ||||
\(916\) | 503.636 | − | 872.322i | 0.549821 | − | 0.952317i | ||||
\(917\) | 681.940 | − | 1181.16i | 0.743665 | − | 1.28806i | ||||
\(918\) | 294.085i | 0.320354i | ||||||||
\(919\) | 166.723i | 0.181418i | 0.995877 | + | 0.0907088i | \(0.0289132\pi\) | ||||
−0.995877 | + | 0.0907088i | \(0.971087\pi\) | |||||||
\(920\) | 888.072i | 0.965296i | ||||||||
\(921\) | −219.795 | − | 380.696i | −0.238648 | − | 0.413351i | ||||
\(922\) | −439.627 | −0.476819 | ||||||||
\(923\) | 87.7070i | 0.0950239i | ||||||||
\(924\) | −3001.31 | + | 1732.81i | −3.24817 | + | 1.87533i | ||||
\(925\) | −331.669 | − | 574.468i | −0.358561 | − | 0.621046i | ||||
\(926\) | −115.592 | + | 66.7372i | −0.124830 | + | 0.0720704i | ||||
\(927\) | −2159.22 | + | 1246.62i | −2.32925 | + | 1.34479i | ||||
\(928\) | 239.271 | 0.257835 | ||||||||
\(929\) | −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 | ||||
\(934\) | −297.701 | + | 171.878i | −0.318737 | + | 0.184023i | ||||
\(935\) | 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 | ||||||
\(940\) | 266.638 | + | 153.943i | 0.283657 | + | 0.163770i | ||||
\(941\) | 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 | ||||||||
\(944\) | − | 309.670i | − | 0.328040i | ||||||
\(945\) | −511.269 | + | 885.544i | −0.541026 | + | 0.937084i | ||||
\(946\) | 380.277 | 0.401985 | ||||||||
\(947\) | 66.9503 | + | 38.6538i | 0.0706973 | + | 0.0408171i | 0.534932 | − | 0.844895i | \(-0.320337\pi\) |
−0.464235 | + | 0.885712i | \(0.653671\pi\) | |||||||
\(948\) | −1539.26 | −1.62370 | ||||||||
\(949\) | 209.453 | 0.220710 | ||||||||
\(950\) | −451.224 | − | 192.419i | −0.474972 | − | 0.202546i | ||||
\(951\) | − | 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 | \(0.966037\pi\) | |||||||
\(954\) | 1199.08 | 1.25690 | ||||||||
\(955\) | −549.718 | − | 317.380i | −0.575621 | − | 0.332335i | ||||
\(956\) | 413.085 | + | 238.495i | 0.432097 | + | 0.249471i | ||||
\(957\) | −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 | ||||
\(964\) | −264.911 | −0.274804 | ||||||||
\(965\) | −175.679 | − | 304.285i | −0.182051 | − | 0.315321i | ||||
\(966\) | −2730.81 | + | 1576.63i | −2.82692 | + | 1.63212i | ||||
\(967\) | 1025.02 | + | 591.795i | 1.06000 | + | 0.611991i | 0.925432 | − | 0.378913i | \(-0.123702\pi\) |
0.134567 | + | 0.990904i | \(0.457035\pi\) | |||||||
\(968\) | −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 | 0.141911 | − | 0.989879i | \(-0.454675\pi\) |
−0.786306 | + | 0.617838i | \(0.788009\pi\) | |||||||
\(972\) | 891.639i | 0.917324i | ||||||||
\(973\) | 80.0316 | + | 138.619i | 0.0822524 | + | 0.142465i | ||||
\(974\) | 253.022 | − | 146.082i | 0.259776 | − | 0.149982i | ||||
\(975\) | 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 | \(0.732858\pi\) | |||||||
\(978\) | 2034.90 | 2.08068 | ||||||||
\(979\) | 1709.20 | − | 986.809i | 1.74587 | − | 1.00798i | ||||
\(980\) | −367.319 | − | 636.215i | −0.374815 | − | 0.649199i | ||||
\(981\) | −1222.18 | −1.24585 | ||||||||
\(982\) | − | 953.622i | − | 0.971102i | ||||||
\(983\) | −857.727 | − | 495.209i | −0.872560 | − | 0.503773i | −0.00436204 | − | 0.999990i | \(-0.501388\pi\) |
−0.868198 | + | 0.496218i | \(0.834722\pi\) | |||||||
\(984\) | 1183.72 | − | 683.423i | 1.20297 | − | 0.694535i | ||||
\(985\) | 17.6615 | − | 30.5906i | 0.0179305 | − | 0.0310565i | ||||
\(986\) | −37.7267 | − | 65.3446i | −0.0382624 | − | 0.0662724i | ||||
\(987\) | 1093.21i | 1.10761i | ||||||||
\(988\) | −54.8199 | − | 452.693i | −0.0554857 | − | 0.458191i | ||||
\(989\) | 346.004 | 0.349853 | ||||||||
\(990\) | −1580.08 | + | 912.259i | −1.59604 | + | 0.921474i | ||||
\(991\) | 974.899 | + | 562.858i | 0.983752 | + | 0.567970i | 0.903401 | − | 0.428797i | \(-0.141062\pi\) |
0.0803514 | + | 0.996767i | \(0.474396\pi\) | |||||||
\(992\) | −133.449 | − | 77.0470i | −0.134525 | − | 0.0776683i | ||||
\(993\) | −253.385 | + | 438.876i | −0.255171 | + | 0.441970i | ||||
\(994\) | −295.002 | −0.296783 | ||||||||
\(995\) | 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 | \(-0.388420\pi\) | |||||||
\(998\) | 1158.44i | 1.16076i | ||||||||
\(999\) | − | 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.a.11.2 | yes | 4 | |
4.3 | odd | 2 | 76.3.g.b.11.1 | yes | 4 | ||
19.7 | even | 3 | 76.3.g.b.7.1 | yes | 4 | ||
76.7 | odd | 6 | inner | 76.3.g.a.7.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.g.a.7.2 | ✓ | 4 | 76.7 | odd | 6 | inner | |
76.3.g.a.11.2 | yes | 4 | 1.1 | even | 1 | trivial | |
76.3.g.b.7.1 | yes | 4 | 19.7 | even | 3 | ||
76.3.g.b.11.1 | yes | 4 | 4.3 | odd | 2 |