Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(35,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.35");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\), degree \(2\), not 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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 35.3 | ||
Character | \(\chi\) | \(=\) | 108.35 |
Dual form | 108.4.h.b.71.3 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.15223 | − | 1.83518i | −0.760929 | − | 0.648835i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.26420 | + | 7.89948i | 0.158025 | + | 0.987435i | ||||
\(5\) | −2.08666 | + | 1.20474i | −0.186637 | + | 0.107755i | −0.590407 | − | 0.807106i | \(-0.701033\pi\) |
0.403770 | + | 0.914860i | \(0.367699\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.30362 | − | 1.33000i | −0.124384 | − | 0.0718131i | 0.436517 | − | 0.899696i | \(-0.356212\pi\) |
−0.560901 | + | 0.827883i | \(0.689545\pi\) | |||||||
\(8\) | 11.7761 | − | 19.3216i | 0.520437 | − | 0.853900i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.70190 | + | 1.23654i | 0.211933 | + | 0.0391029i | ||||
\(11\) | 24.1428 | − | 41.8166i | 0.661758 | − | 1.14620i | −0.318395 | − | 0.947958i | \(-0.603144\pi\) |
0.980153 | − | 0.198241i | \(-0.0635229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.3570 | − | 35.2594i | −0.434309 | − | 0.752245i | 0.562930 | − | 0.826505i | \(-0.309674\pi\) |
−0.997239 | + | 0.0742593i | \(0.976341\pi\) | |||||||
\(14\) | 2.51714 | + | 7.09003i | 0.0480524 | + | 0.135349i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −60.8036 | + | 19.9731i | −0.950056 | + | 0.312079i | ||||
\(17\) | 36.3729i | 0.518925i | 0.965753 | + | 0.259463i | \(0.0835455\pi\) | ||||
−0.965753 | + | 0.259463i | \(0.916455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 125.173i | − | 1.51141i | −0.654914 | − | 0.755703i | \(-0.727295\pi\) | ||
0.654914 | − | 0.755703i | \(-0.272705\pi\) | |||||||
\(20\) | −12.1548 | − | 14.9605i | −0.135894 | − | 0.167264i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −128.702 | + | 45.6925i | −1.24725 | + | 0.442804i | ||||
\(23\) | −97.0560 | − | 168.106i | −0.879894 | − | 1.52402i | −0.851456 | − | 0.524426i | \(-0.824280\pi\) |
−0.0284384 | − | 0.999596i | \(-0.509053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −59.5972 | + | 103.225i | −0.476778 | + | 0.825803i | ||||
\(26\) | −20.8944 | + | 113.245i | −0.157605 | + | 0.854200i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.59405 | − | 19.8788i | 0.0512550 | − | 0.134169i | ||||
\(29\) | −153.593 | − | 88.6772i | −0.983503 | − | 0.567826i | −0.0801773 | − | 0.996781i | \(-0.525549\pi\) |
−0.903326 | + | 0.428955i | \(0.858882\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 152.058 | − | 87.7909i | 0.880983 | − | 0.508636i | 0.0100006 | − | 0.999950i | \(-0.496817\pi\) |
0.870982 | + | 0.491314i | \(0.163483\pi\) | |||||||
\(32\) | 167.518 | + | 68.5991i | 0.925413 | + | 0.378960i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 66.7510 | − | 78.2830i | 0.336697 | − | 0.394865i | ||||
\(35\) | 6.40918 | 0.0309529 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 199.364 | 0.885818 | 0.442909 | − | 0.896566i | \(-0.353946\pi\) | ||||
0.442909 | + | 0.896566i | \(0.353946\pi\) | |||||||
\(38\) | −229.716 | + | 269.402i | −0.980654 | + | 1.15007i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.29548 | + | 54.5047i | −0.00512084 | + | 0.215449i | ||||
\(41\) | 201.816 | − | 116.518i | 0.768740 | − | 0.443832i | −0.0636849 | − | 0.997970i | \(-0.520285\pi\) |
0.832425 | + | 0.554138i | \(0.186952\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 252.553 | + | 145.812i | 0.895674 | + | 0.517118i | 0.875794 | − | 0.482685i | \(-0.160338\pi\) |
0.0198798 | + | 0.999802i | \(0.493672\pi\) | |||||||
\(44\) | 360.851 | + | 137.851i | 1.23637 | + | 0.472315i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −99.6182 | + | 539.918i | −0.319302 | + | 1.73058i | ||||
\(47\) | −30.9476 | + | 53.6029i | −0.0960463 | + | 0.166357i | −0.910045 | − | 0.414510i | \(-0.863953\pi\) |
0.813998 | + | 0.580867i | \(0.197286\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −167.962 | − | 290.919i | −0.489686 | − | 0.848161i | ||||
\(50\) | 317.705 | − | 112.793i | 0.898604 | − | 0.319027i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 252.795 | − | 205.385i | 0.674162 | − | 0.547726i | ||||
\(53\) | 352.175i | 0.912735i | 0.889791 | + | 0.456367i | \(0.150850\pi\) | ||||
−0.889791 | + | 0.456367i | \(0.849150\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 116.343i | 0.285231i | ||||||||
\(56\) | −52.8254 | + | 28.8473i | −0.126055 | + | 0.0688373i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 167.830 | + | 472.726i | 0.379950 | + | 1.07021i | ||||
\(59\) | 70.7911 | + | 122.614i | 0.156207 | + | 0.270559i | 0.933498 | − | 0.358583i | \(-0.116740\pi\) |
−0.777291 | + | 0.629141i | \(0.783407\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.71518 | + | 13.3631i | −0.0161939 | + | 0.0280486i | −0.874009 | − | 0.485910i | \(-0.838488\pi\) |
0.857815 | + | 0.513959i | \(0.171822\pi\) | |||||||
\(62\) | −488.377 | − | 90.1086i | −1.00039 | − | 0.184577i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −234.645 | − | 455.067i | −0.458291 | − | 0.888802i | ||||
\(65\) | 84.9565 | + | 49.0496i | 0.162116 | + | 0.0935978i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −131.657 | + | 76.0120i | −0.240066 | + | 0.138602i | −0.615207 | − | 0.788366i | \(-0.710928\pi\) |
0.375141 | + | 0.926968i | \(0.377594\pi\) | |||||||
\(68\) | −287.327 | + | 45.9827i | −0.512405 | + | 0.0820033i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −13.7940 | − | 11.7620i | −0.0235529 | − | 0.0200833i | ||||
\(71\) | 28.0331 | 0.0468580 | 0.0234290 | − | 0.999726i | \(-0.492542\pi\) | ||||
0.0234290 | + | 0.999726i | \(0.492542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 124.499 | 0.199609 | 0.0998047 | − | 0.995007i | \(-0.468178\pi\) | ||||
0.0998047 | + | 0.995007i | \(0.468178\pi\) | |||||||
\(74\) | −429.078 | − | 365.870i | −0.674045 | − | 0.574750i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 988.804 | − | 158.244i | 1.49242 | − | 0.238840i | ||||
\(77\) | −111.232 | + | 64.2199i | −0.164624 | + | 0.0950459i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −648.411 | − | 374.360i | −0.923443 | − | 0.533150i | −0.0387108 | − | 0.999250i | \(-0.512325\pi\) |
−0.884732 | + | 0.466101i | \(0.845658\pi\) | |||||||
\(80\) | 102.814 | − | 114.929i | 0.143687 | − | 0.160619i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −648.187 | − | 119.595i | −0.872931 | − | 0.161061i | ||||
\(83\) | −174.444 | + | 302.146i | −0.230695 | + | 0.399576i | −0.958013 | − | 0.286725i | \(-0.907433\pi\) |
0.727318 | + | 0.686301i | \(0.240767\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −43.8198 | − | 75.8981i | −0.0559167 | − | 0.0968506i | ||||
\(86\) | −275.962 | − | 777.302i | −0.346020 | − | 0.974635i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −523.653 | − | 958.916i | −0.634336 | − | 1.16160i | ||||
\(89\) | − | 416.864i | − | 0.496488i | −0.968698 | − | 0.248244i | \(-0.920146\pi\) | ||
0.968698 | − | 0.248244i | \(-0.0798535\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 108.299i | 0.124756i | ||||||||
\(92\) | 1205.25 | − | 979.212i | 1.36583 | − | 1.10967i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 164.978 | − | 58.5712i | 0.181023 | − | 0.0642677i | ||||
\(95\) | 150.801 | + | 261.195i | 0.162861 | + | 0.282084i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −752.565 | + | 1303.48i | −0.787747 | + | 1.36442i | 0.139598 | + | 0.990208i | \(0.455419\pi\) |
−0.927344 | + | 0.374209i | \(0.877914\pi\) | |||||||
\(98\) | −172.396 | + | 934.367i | −0.177701 | + | 0.963115i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −890.770 | − | 340.289i | −0.890770 | − | 0.340289i | ||||
\(101\) | −377.088 | − | 217.712i | −0.371502 | − | 0.214487i | 0.302613 | − | 0.953114i | \(-0.402141\pi\) |
−0.674114 | + | 0.738627i | \(0.735474\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1511.52 | + | 872.679i | −1.44597 | + | 0.834831i | −0.998238 | − | 0.0593366i | \(-0.981101\pi\) |
−0.447732 | + | 0.894168i | \(0.647768\pi\) | |||||||
\(104\) | −920.993 | − | 21.8904i | −0.868373 | − | 0.0206397i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 646.306 | − | 757.962i | 0.592215 | − | 0.694526i | ||||
\(107\) | 783.805 | 0.708161 | 0.354081 | − | 0.935215i | \(-0.384794\pi\) | ||||
0.354081 | + | 0.935215i | \(0.384794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1581.89 | 1.39007 | 0.695035 | − | 0.718976i | \(-0.255389\pi\) | ||||
0.695035 | + | 0.718976i | \(0.255389\pi\) | |||||||
\(110\) | 213.511 | − | 250.397i | 0.185068 | − | 0.217040i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 166.633 | + | 34.8582i | 0.140583 | + | 0.0294088i | ||||
\(113\) | 384.367 | − | 221.914i | 0.319984 | − | 0.184743i | −0.331401 | − | 0.943490i | \(-0.607521\pi\) |
0.651386 | + | 0.758747i | \(0.274188\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 405.046 | + | 233.854i | 0.328442 | + | 0.189626i | ||||
\(116\) | 506.331 | − | 1325.41i | 0.405273 | − | 1.06088i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 72.6600 | − | 393.808i | 0.0566855 | − | 0.307228i | ||||
\(119\) | 48.3759 | − | 83.7895i | 0.0372657 | − | 0.0645460i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −500.254 | − | 866.466i | −0.375848 | − | 0.650989i | ||||
\(122\) | 41.1286 | − | 14.6017i | 0.0305214 | − | 0.0108359i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 885.735 | + | 1090.20i | 0.641462 | + | 0.789536i | ||||
\(125\) | − | 588.380i | − | 0.421010i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 425.829i | 0.297529i | 0.988873 | + | 0.148765i | \(0.0475297\pi\) | ||||
−0.988873 | + | 0.148765i | \(0.952470\pi\) | |||||||
\(128\) | −330.121 | + | 1410.03i | −0.227960 | + | 0.973671i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −92.8309 | − | 261.477i | −0.0626293 | − | 0.176408i | ||||
\(131\) | 871.836 | + | 1510.06i | 0.581471 | + | 1.00714i | 0.995305 | + | 0.0967846i | \(0.0308558\pi\) |
−0.413835 | + | 0.910352i | \(0.635811\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −166.480 | + | 288.352i | −0.108539 | + | 0.187995i | ||||
\(134\) | 422.851 | + | 78.0187i | 0.272603 | + | 0.0502969i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 702.782 | + | 428.333i | 0.443110 | + | 0.270068i | ||||
\(137\) | 1274.32 | + | 735.731i | 0.794692 | + | 0.458816i | 0.841612 | − | 0.540083i | \(-0.181607\pi\) |
−0.0469195 | + | 0.998899i | \(0.514940\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1107.04 | − | 639.151i | 0.675526 | − | 0.390015i | −0.122641 | − | 0.992451i | \(-0.539136\pi\) |
0.798167 | + | 0.602436i | \(0.205803\pi\) | |||||||
\(140\) | 8.10250 | + | 50.6292i | 0.00489133 | + | 0.0305639i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −60.3338 | − | 51.4459i | −0.0356556 | − | 0.0304031i | ||||
\(143\) | −1965.90 | −1.14963 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 427.331 | 0.244744 | ||||||||
\(146\) | −267.950 | − | 228.478i | −0.151889 | − | 0.129514i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 252.037 | + | 1574.87i | 0.139982 | + | 0.874688i | ||||
\(149\) | −1861.15 | + | 1074.53i | −1.02330 | + | 0.590800i | −0.915057 | − | 0.403325i | \(-0.867854\pi\) |
−0.108239 | + | 0.994125i | \(0.534521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 828.626 | + | 478.407i | 0.446574 | + | 0.257829i | 0.706382 | − | 0.707831i | \(-0.250326\pi\) |
−0.259808 | + | 0.965660i | \(0.583659\pi\) | |||||||
\(152\) | −2418.54 | − | 1474.06i | −1.29059 | − | 0.786592i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 357.252 | + | 65.9152i | 0.186936 | + | 0.0344909i | ||||
\(155\) | −211.530 | + | 366.380i | −0.109616 | + | 0.189860i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1046.60 | − | 1812.77i | −0.532024 | − | 0.921493i | −0.999301 | − | 0.0373822i | \(-0.988098\pi\) |
0.467277 | − | 0.884111i | \(-0.345235\pi\) | |||||||
\(158\) | 708.511 | + | 1995.66i | 0.356748 | + | 1.00485i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −432.197 | + | 58.6713i | −0.213551 | + | 0.0289899i | ||||
\(161\) | 516.337i | 0.252752i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1468.60i | − | 0.705703i | −0.935679 | − | 0.352851i | \(-0.885212\pi\) | ||
0.935679 | − | 0.352851i | \(-0.114788\pi\) | |||||||
\(164\) | 1175.57 | + | 1446.94i | 0.559736 | + | 0.688944i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 929.936 | − | 330.151i | 0.434801 | − | 0.154365i | ||||
\(167\) | −1524.19 | − | 2639.98i | −0.706261 | − | 1.22328i | −0.966235 | − | 0.257664i | \(-0.917047\pi\) |
0.259974 | − | 0.965616i | \(-0.416286\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 269.685 | − | 467.108i | 0.122751 | − | 0.212612i | ||||
\(170\) | −44.9766 | + | 243.768i | −0.0202915 | + | 0.109977i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −832.558 | + | 2179.37i | −0.369081 | + | 0.966137i | ||||
\(173\) | 2403.71 | + | 1387.79i | 1.05636 | + | 0.609892i | 0.924424 | − | 0.381365i | \(-0.124546\pi\) |
0.131940 | + | 0.991258i | \(0.457879\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 274.579 | − | 158.528i | 0.118607 | − | 0.0684778i | ||||
\(176\) | −632.765 | + | 3024.81i | −0.271003 | + | 1.29547i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −765.021 | + | 897.187i | −0.322139 | + | 0.377792i | ||||
\(179\) | 477.618 | 0.199435 | 0.0997174 | − | 0.995016i | \(-0.468206\pi\) | ||||
0.0997174 | + | 0.995016i | \(0.468206\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −732.350 | −0.300747 | −0.150373 | − | 0.988629i | \(-0.548048\pi\) | ||||
−0.150373 | + | 0.988629i | \(0.548048\pi\) | |||||||
\(182\) | 198.749 | − | 233.085i | 0.0809463 | − | 0.0949307i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4391.01 | − | 104.367i | −1.75929 | − | 0.0418153i | ||||
\(185\) | −416.006 | + | 240.181i | −0.165326 | + | 0.0954512i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1520.99 | + | 878.146i | 0.594792 | + | 0.343403i | ||||
\(188\) | −462.559 | − | 176.705i | −0.179445 | − | 0.0685509i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 154.782 | − | 838.898i | 0.0591003 | − | 0.320316i | ||||
\(191\) | 1543.00 | − | 2672.55i | 0.584542 | − | 1.01246i | −0.410391 | − | 0.911910i | \(-0.634608\pi\) |
0.994932 | − | 0.100546i | \(-0.0320590\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 817.160 | + | 1415.36i | 0.304769 | + | 0.527876i | 0.977210 | − | 0.212275i | \(-0.0680873\pi\) |
−0.672441 | + | 0.740151i | \(0.734754\pi\) | |||||||
\(194\) | 4011.82 | − | 1424.30i | 1.48470 | − | 0.527106i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2085.77 | − | 1694.59i | 0.760121 | − | 0.617564i | ||||
\(197\) | − | 3350.67i | − | 1.21181i | −0.795539 | − | 0.605903i | \(-0.792812\pi\) | ||
0.795539 | − | 0.605903i | \(-0.207188\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1046.61i | − | 0.372826i | −0.982471 | − | 0.186413i | \(-0.940314\pi\) | ||
0.982471 | − | 0.186413i | \(-0.0596863\pi\) | |||||||
\(200\) | 1292.65 | + | 2367.11i | 0.457021 | + | 0.836899i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 412.040 | + | 1160.59i | 0.143520 | + | 0.404252i | ||||
\(203\) | 235.881 | + | 408.558i | 0.0815547 | + | 0.141257i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −280.748 | + | 486.270i | −0.0956502 | + | 0.165671i | ||||
\(206\) | 4854.68 | + | 895.718i | 1.64195 | + | 0.302950i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1942.02 | + | 1737.30i | 0.647378 | + | 0.579136i | ||||
\(209\) | −5234.33 | − | 3022.04i | −1.73237 | − | 1.00019i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4570.77 | − | 2638.94i | 1.49130 | − | 0.861004i | 0.491352 | − | 0.870961i | \(-0.336503\pi\) |
0.999950 | + | 0.00995667i | \(0.00316936\pi\) | |||||||
\(212\) | −2782.00 | + | 445.220i | −0.901266 | + | 0.144235i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1686.93 | − | 1438.43i | −0.538860 | − | 0.459480i | ||||
\(215\) | −702.658 | −0.222888 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −467.047 | −0.146107 | ||||||||
\(218\) | −3404.60 | − | 2903.06i | −1.05774 | − | 0.901927i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −919.050 | + | 147.081i | −0.281647 | + | 0.0450737i | ||||
\(221\) | 1282.49 | − | 740.444i | 0.390359 | − | 0.225374i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4122.02 | − | 2379.85i | −1.23781 | − | 0.714648i | −0.269161 | − | 0.963095i | \(-0.586746\pi\) |
−0.968645 | + | 0.248447i | \(0.920080\pi\) | |||||||
\(224\) | −294.661 | − | 380.824i | −0.0878923 | − | 0.113593i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1234.50 | − | 227.773i | −0.363353 | − | 0.0670409i | ||||
\(227\) | 1115.23 | − | 1931.63i | 0.326080 | − | 0.564788i | −0.655650 | − | 0.755065i | \(-0.727605\pi\) |
0.981730 | + | 0.190277i | \(0.0609387\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2917.29 | + | 5052.89i | 0.841833 | + | 1.45810i | 0.888343 | + | 0.459181i | \(0.151857\pi\) |
−0.0465095 | + | 0.998918i | \(0.514810\pi\) | |||||||
\(230\) | −442.589 | − | 1246.64i | −0.126885 | − | 0.357396i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3522.12 | + | 1923.39i | −0.996718 | + | 0.544296i | ||||
\(233\) | 3080.09i | 0.866022i | 0.901389 | + | 0.433011i | \(0.142549\pi\) | ||||
−0.901389 | + | 0.433011i | \(0.857451\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 149.135i | − | 0.0413978i | ||||||
\(236\) | −879.091 | + | 714.221i | −0.242474 | + | 0.196999i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −257.885 | + | 91.5558i | −0.0702362 | + | 0.0249356i | ||||
\(239\) | −2645.73 | − | 4582.53i | −0.716058 | − | 1.24025i | −0.962550 | − | 0.271104i | \(-0.912611\pi\) |
0.246492 | − | 0.969145i | \(-0.420722\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2501.61 | − | 4332.91i | 0.668642 | − | 1.15812i | −0.309642 | − | 0.950853i | \(-0.600209\pi\) |
0.978284 | − | 0.207268i | \(-0.0664573\pi\) | |||||||
\(242\) | −513.461 | + | 2782.89i | −0.136391 | + | 0.739220i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −115.315 | − | 44.0523i | −0.0302553 | − | 0.0115580i | ||||
\(245\) | 700.961 | + | 404.700i | 0.182787 | + | 0.105532i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4413.53 | + | 2548.15i | −1.13695 | + | 0.656417i | ||||
\(248\) | 94.4037 | − | 3971.84i | 0.0241719 | − | 1.01698i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1079.78 | + | 1266.33i | −0.273166 | + | 0.320359i | ||||
\(251\) | 2577.68 | 0.648215 | 0.324107 | − | 0.946020i | \(-0.394936\pi\) | ||||
0.324107 | + | 0.946020i | \(0.394936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9372.83 | −2.32911 | ||||||||
\(254\) | 781.475 | − | 916.483i | 0.193048 | − | 0.226399i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3298.15 | − | 2428.87i | 0.805213 | − | 0.592986i | ||||
\(257\) | 753.933 | − | 435.283i | 0.182992 | − | 0.105651i | −0.405705 | − | 0.914004i | \(-0.632974\pi\) |
0.588698 | + | 0.808353i | \(0.299641\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −459.260 | − | 265.154i | −0.110182 | − | 0.0636134i | ||||
\(260\) | −280.065 | + | 733.121i | −0.0668033 | + | 0.174870i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 894.852 | − | 4849.99i | 0.211008 | − | 1.14364i | ||||
\(263\) | −2155.19 | + | 3732.90i | −0.505304 | + | 0.875212i | 0.494677 | + | 0.869077i | \(0.335286\pi\) |
−0.999981 | + | 0.00613515i | \(0.998047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −424.278 | − | 734.871i | −0.0983516 | − | 0.170350i | ||||
\(266\) | 887.483 | − | 315.079i | 0.204568 | − | 0.0726268i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −766.896 | − | 943.924i | −0.174797 | − | 0.215147i | ||||
\(269\) | 5603.52i | 1.27008i | 0.772478 | + | 0.635042i | \(0.219017\pi\) | ||||
−0.772478 | + | 0.635042i | \(0.780983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2149.22i | 0.481756i | 0.970555 | + | 0.240878i | \(0.0774353\pi\) | ||||
−0.970555 | + | 0.240878i | \(0.922565\pi\) | |||||||
\(272\) | −726.479 | − | 2211.60i | −0.161946 | − | 0.493008i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1392.44 | − | 3922.08i | −0.307008 | − | 0.864751i | ||||
\(275\) | 2877.69 | + | 4984.31i | 0.631023 | + | 1.09296i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1604.99 | − | 2779.93i | 0.348140 | − | 0.602995i | −0.637779 | − | 0.770219i | \(-0.720147\pi\) |
0.985919 | + | 0.167224i | \(0.0534802\pi\) | |||||||
\(278\) | −3555.57 | − | 656.025i | −0.767083 | − | 0.141531i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 75.4755 | − | 123.835i | 0.0161090 | − | 0.0264306i | ||||
\(281\) | 814.389 | + | 470.188i | 0.172891 | + | 0.0998187i | 0.583948 | − | 0.811791i | \(-0.301507\pi\) |
−0.411057 | + | 0.911610i | \(0.634840\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1775.44 | − | 1025.05i | 0.372929 | − | 0.215310i | −0.301809 | − | 0.953369i | \(-0.597590\pi\) |
0.674737 | + | 0.738058i | \(0.264257\pi\) | |||||||
\(284\) | 35.4395 | + | 221.447i | 0.00740475 | + | 0.0462693i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4231.08 | + | 3607.80i | 0.874787 | + | 0.745921i | ||||
\(287\) | −619.877 | −0.127492 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3590.01 | 0.730716 | ||||||||
\(290\) | −919.715 | − | 784.230i | −0.186233 | − | 0.158799i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 157.392 | + | 983.476i | 0.0315433 | + | 0.197101i | ||||
\(293\) | 3842.30 | − | 2218.35i | 0.766108 | − | 0.442312i | −0.0653767 | − | 0.997861i | \(-0.520825\pi\) |
0.831484 | + | 0.555548i | \(0.187492\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −295.434 | − | 170.569i | −0.0583080 | − | 0.0336641i | ||||
\(296\) | 2347.74 | − | 3852.03i | 0.461013 | − | 0.756400i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5977.58 | + | 1102.90i | 1.16199 | + | 0.214394i | ||||
\(299\) | −3951.54 | + | 6844.26i | −0.764292 | + | 1.32379i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −387.858 | − | 671.790i | −0.0742716 | − | 0.128642i | ||||
\(302\) | −905.429 | − | 2550.32i | −0.172522 | − | 0.485943i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2500.09 | + | 7610.98i | 0.471678 | + | 1.43592i | ||||
\(305\) | − | 37.1790i | − | 0.00697988i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7392.80i | 1.37436i | 0.726486 | + | 0.687181i | \(0.241152\pi\) | ||||
−0.726486 | + | 0.687181i | \(0.758848\pi\) | |||||||
\(308\) | −647.923 | − | 797.489i | −0.119866 | − | 0.147536i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1127.64 | − | 400.339i | 0.206598 | − | 0.0733475i | ||||
\(311\) | 2448.25 | + | 4240.50i | 0.446391 | + | 0.773172i | 0.998148 | − | 0.0608332i | \(-0.0193758\pi\) |
−0.551757 | + | 0.834005i | \(0.686042\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −340.861 | + | 590.388i | −0.0615546 | + | 0.106616i | −0.895160 | − | 0.445744i | \(-0.852939\pi\) |
0.833606 | + | 0.552360i | \(0.186273\pi\) | |||||||
\(314\) | −1074.23 | + | 5822.20i | −0.193065 | + | 1.04639i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2137.53 | − | 5595.38i | 0.380524 | − | 0.996091i | ||||
\(317\) | −1344.13 | − | 776.034i | −0.238151 | − | 0.137497i | 0.376176 | − | 0.926548i | \(-0.377239\pi\) |
−0.614327 | + | 0.789052i | \(0.710572\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7416.37 | + | 4281.84i | −1.30168 | + | 0.751527i | ||||
\(320\) | 1037.86 | + | 666.886i | 0.181307 | + | 0.116500i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 947.573 | − | 1111.28i | 0.163994 | − | 0.192326i | ||||
\(323\) | 4552.92 | 0.784307 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4852.88 | 0.828276 | ||||||||
\(326\) | −2695.15 | + | 3160.76i | −0.457885 | + | 0.536990i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 125.295 | − | 5271.53i | 0.0210923 | − | 0.887414i | ||||
\(329\) | 142.583 | − | 82.3206i | 0.0238932 | − | 0.0137948i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6410.22 | + | 3700.94i | 1.06446 | + | 0.614569i | 0.926664 | − | 0.375891i | \(-0.122663\pi\) |
0.137801 | + | 0.990460i | \(0.455997\pi\) | |||||||
\(332\) | −2607.33 | − | 996.043i | −0.431011 | − | 0.164653i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1564.43 | + | 8479.02i | −0.256293 | + | 1.38908i | ||||
\(335\) | 183.149 | − | 317.223i | 0.0298701 | − | 0.0517365i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4871.58 | + | 8437.83i | 0.787454 | + | 1.36391i | 0.927522 | + | 0.373769i | \(0.121935\pi\) |
−0.140068 | + | 0.990142i | \(0.544732\pi\) | |||||||
\(338\) | −1437.65 | + | 510.403i | −0.231355 | + | 0.0821368i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 544.158 | − | 442.104i | 0.0867975 | − | 0.0705190i | ||||
\(341\) | − | 8478.09i | − | 1.34638i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1805.94i | 0.284290i | ||||||||
\(344\) | 5791.41 | − | 3162.62i | 0.907709 | − | 0.495689i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2626.51 | − | 7398.09i | −0.408098 | − | 1.14949i | ||||
\(347\) | 3523.75 | + | 6103.31i | 0.545143 | + | 0.944216i | 0.998598 | + | 0.0529363i | \(0.0168580\pi\) |
−0.453455 | + | 0.891279i | \(0.649809\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 603.773 | − | 1045.77i | 0.0926052 | − | 0.160397i | −0.816001 | − | 0.578050i | \(-0.803814\pi\) |
0.908607 | + | 0.417653i | \(0.137147\pi\) | |||||||
\(350\) | −881.886 | − | 162.713i | −0.134682 | − | 0.0248497i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6912.94 | − | 5348.85i | 1.04676 | − | 0.809928i | ||||
\(353\) | −1316.47 | − | 760.063i | −0.198494 | − | 0.114601i | 0.397459 | − | 0.917620i | \(-0.369892\pi\) |
−0.595953 | + | 0.803019i | \(0.703226\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −58.4957 | + | 33.7725i | −0.00874544 | + | 0.00504918i | ||||
\(356\) | 3293.01 | − | 527.000i | 0.490250 | − | 0.0784576i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1027.94 | − | 876.517i | −0.151756 | − | 0.129400i | ||||
\(359\) | −6515.20 | −0.957825 | −0.478912 | − | 0.877863i | \(-0.658969\pi\) | ||||
−0.478912 | + | 0.877863i | \(0.658969\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8809.35 | −1.28435 | ||||||||
\(362\) | 1576.19 | + | 1344.00i | 0.228847 | + | 0.195135i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −855.506 | + | 136.912i | −0.123189 | + | 0.0197146i | ||||
\(365\) | −259.787 | + | 149.988i | −0.0372545 | + | 0.0215089i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3492.35 | − | 2016.31i | −0.496729 | − | 0.286786i | 0.230633 | − | 0.973041i | \(-0.425920\pi\) |
−0.727362 | + | 0.686254i | \(0.759254\pi\) | |||||||
\(368\) | 9258.94 | + | 8282.93i | 1.31156 | + | 1.17331i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1336.12 | + | 246.522i | 0.187734 | + | 0.0346380i | ||||
\(371\) | 468.392 | − | 811.278i | 0.0655463 | − | 0.113530i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1227.68 | − | 2126.40i | −0.170420 | − | 0.295176i | 0.768147 | − | 0.640274i | \(-0.221179\pi\) |
−0.938567 | + | 0.345098i | \(0.887846\pi\) | |||||||
\(374\) | −1661.97 | − | 4681.28i | −0.229782 | − | 0.647228i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 671.247 | + | 1229.19i | 0.0920663 | + | 0.168592i | ||||
\(377\) | 7220.81i | 0.986448i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9518.27i | − | 1.29003i | −0.764171 | − | 0.645014i | \(-0.776851\pi\) | ||
0.764171 | − | 0.645014i | \(-0.223149\pi\) | |||||||
\(380\) | −1872.66 | + | 1521.45i | −0.252804 | + | 0.205391i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8225.52 | + | 2920.27i | −1.10171 | + | 0.391136i | ||||
\(383\) | −4727.72 | − | 8188.65i | −0.630744 | − | 1.09248i | −0.987400 | − | 0.158245i | \(-0.949416\pi\) |
0.356655 | − | 0.934236i | \(-0.383917\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 154.736 | − | 268.011i | 0.0204833 | − | 0.0354781i | ||||
\(386\) | 838.733 | − | 4545.83i | 0.110597 | − | 0.599421i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11248.2 | − | 4297.01i | −1.47176 | − | 0.562236i | ||||
\(389\) | 2568.69 | + | 1483.04i | 0.334802 | + | 0.193298i | 0.657971 | − | 0.753043i | \(-0.271415\pi\) |
−0.323169 | + | 0.946341i | \(0.604748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6114.50 | − | 3530.21i | 0.790854 | − | 0.456600i | ||||
\(392\) | −7598.96 | − | 180.614i | −0.979095 | − | 0.0232714i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6149.10 | + | 7211.43i | −0.786262 | + | 0.922097i | ||||
\(395\) | 1804.02 | 0.229798 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1296.85 | 0.163947 | 0.0819733 | − | 0.996635i | \(-0.473878\pi\) | ||||
0.0819733 | + | 0.996635i | \(0.473878\pi\) | |||||||
\(398\) | −1920.73 | + | 2252.55i | −0.241903 | + | 0.283694i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1562.00 | − | 7466.82i | 0.195250 | − | 0.933352i | ||||
\(401\) | 1782.15 | − | 1028.93i | 0.221936 | − | 0.128135i | −0.384910 | − | 0.922954i | \(-0.625768\pi\) |
0.606847 | + | 0.794819i | \(0.292434\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6190.90 | − | 3574.32i | −0.765238 | − | 0.441810i | ||||
\(404\) | 1243.10 | − | 3254.03i | 0.153085 | − | 0.400728i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 242.108 | − | 1312.20i | 0.0295951 | − | 0.160402i | ||||
\(407\) | 4813.22 | − | 8336.74i | 0.586198 | − | 1.01532i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2897.54 | − | 5018.69i | −0.350304 | − | 0.606744i | 0.635999 | − | 0.771690i | \(-0.280588\pi\) |
−0.986303 | + | 0.164946i | \(0.947255\pi\) | |||||||
\(410\) | 1496.63 | − | 531.341i | 0.180276 | − | 0.0640026i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8804.58 | − | 10837.0i | −1.05284 | − | 1.29588i | ||||
\(413\) | − | 376.608i | − | 0.0448709i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 840.635i | − | 0.0994341i | ||||||
\(416\) | −991.398 | − | 7303.04i | −0.116844 | − | 0.860723i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5719.48 | + | 16110.1i | 0.669256 | + | 1.88509i | ||||
\(419\) | −7052.61 | − | 12215.5i | −0.822298 | − | 1.42426i | −0.903967 | − | 0.427602i | \(-0.859359\pi\) |
0.0816695 | − | 0.996659i | \(-0.473975\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3210.43 | + | 5560.63i | −0.371655 | + | 0.643726i | −0.989820 | − | 0.142323i | \(-0.954543\pi\) |
0.618165 | + | 0.786048i | \(0.287876\pi\) | |||||||
\(422\) | −14680.3 | − | 2708.60i | −1.69343 | − | 0.312447i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6804.57 | + | 4147.26i | 0.779384 | + | 0.475021i | ||||
\(425\) | −3754.61 | − | 2167.73i | −0.428530 | − | 0.247412i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.5457 | − | 20.5223i | 0.00402852 | − | 0.00232587i | ||||
\(428\) | 990.887 | + | 6191.65i | 0.111907 | + | 0.699263i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1512.28 | + | 1289.51i | 0.169602 | + | 0.144617i | ||||
\(431\) | 1119.73 | 0.125140 | 0.0625700 | − | 0.998041i | \(-0.480070\pi\) | ||||
0.0625700 | + | 0.998041i | \(0.480070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −299.833 | −0.0332773 | −0.0166387 | − | 0.999862i | \(-0.505296\pi\) | ||||
−0.0166387 | + | 0.999862i | \(0.505296\pi\) | |||||||
\(434\) | 1005.19 | + | 857.116i | 0.111177 | + | 0.0947993i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1999.83 | + | 12496.1i | 0.219666 | + | 1.37260i | ||||
\(437\) | −21042.4 | + | 12148.8i | −2.30342 | + | 1.32988i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2090.02 | − | 1206.67i | −0.227224 | − | 0.131188i | 0.382067 | − | 0.924135i | \(-0.375212\pi\) |
−0.609291 | + | 0.792947i | \(0.708546\pi\) | |||||||
\(440\) | 2247.93 | + | 1370.07i | 0.243559 | + | 0.148445i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4119.06 | − | 759.992i | −0.443266 | − | 0.0817853i | ||||
\(443\) | 2409.36 | − | 4173.14i | 0.258402 | − | 0.447566i | −0.707412 | − | 0.706802i | \(-0.750137\pi\) |
0.965814 | + | 0.259236i | \(0.0834706\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 502.211 | + | 869.854i | 0.0534990 | + | 0.0926630i | ||||
\(446\) | 4504.08 | + | 12686.7i | 0.478194 | + | 1.34693i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −64.7043 | + | 1360.38i | −0.00682364 | + | 0.143464i | ||||
\(449\) | − | 8677.13i | − | 0.912024i | −0.889974 | − | 0.456012i | \(-0.849277\pi\) | ||
0.889974 | − | 0.456012i | \(-0.150723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 11252.3i | − | 1.17484i | ||||||
\(452\) | 2238.93 | + | 2755.76i | 0.232987 | + | 0.286770i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5945.12 | + | 2110.67i | −0.614578 | + | 0.218191i | ||||
\(455\) | −130.472 | − | 225.984i | −0.0134431 | − | 0.0232841i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3460.04 | − | 5992.97i | 0.354166 | − | 0.613434i | −0.632809 | − | 0.774308i | \(-0.718098\pi\) |
0.986975 | + | 0.160874i | \(0.0514313\pi\) | |||||||
\(458\) | 2994.30 | − | 16228.8i | 0.305491 | − | 1.65572i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1335.26 | + | 3495.29i | −0.135341 | + | 0.354280i | ||||
\(461\) | 13470.8 | + | 7777.39i | 1.36095 | + | 0.785747i | 0.989751 | − | 0.142805i | \(-0.0456121\pi\) |
0.371203 | + | 0.928552i | \(0.378945\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9994.39 | − | 5770.27i | 1.00319 | − | 0.579194i | 0.0940023 | − | 0.995572i | \(-0.470034\pi\) |
0.909192 | + | 0.416378i | \(0.136701\pi\) | |||||||
\(464\) | 11110.2 | + | 2324.16i | 1.11159 | + | 0.232535i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5652.53 | − | 6629.06i | 0.561906 | − | 0.658981i | ||||
\(467\) | 7.01271 | 0.000694881 | 0.000347441 | − | 1.00000i | \(-0.499889\pi\) | ||||
0.000347441 | 1.00000i | \(0.499889\pi\) | ||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 404.383 | 0.0398138 | ||||||||
\(470\) | −273.690 | + | 320.973i | −0.0268604 | + | 0.0315008i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3202.73 | + | 76.1234i | 0.312326 | + | 0.00742344i | ||||
\(473\) | 12194.7 | − | 7040.61i | 1.18544 | − | 0.684414i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12921.1 | + | 7459.98i | 1.24812 | + | 0.720605i | ||||
\(476\) | 723.051 | + | 276.218i | 0.0696239 | + | 0.0265975i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2715.57 | + | 14718.1i | −0.259848 | + | 1.40834i | ||||
\(479\) | 2830.70 | − | 4902.92i | 0.270017 | − | 0.467683i | −0.698849 | − | 0.715269i | \(-0.746304\pi\) |
0.968866 | + | 0.247586i | \(0.0796373\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4058.46 | − | 7029.46i | −0.384719 | − | 0.666353i | ||||
\(482\) | −13335.7 | + | 4734.52i | −1.26022 | + | 0.447409i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6212.21 | − | 5047.14i | 0.583415 | − | 0.473999i | ||||
\(485\) | − | 3626.57i | − | 0.339534i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9082.26i | 0.845085i | 0.906343 | + | 0.422542i | \(0.138862\pi\) | ||||
−0.906343 | + | 0.422542i | \(0.861138\pi\) | |||||||
\(488\) | 167.340 | + | 306.435i | 0.0155228 | + | 0.0284255i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −765.932 | − | 2157.40i | −0.0706149 | − | 0.198901i | ||||
\(491\) | 5098.79 | + | 8831.36i | 0.468646 | + | 0.811718i | 0.999358 | − | 0.0358342i | \(-0.0114088\pi\) |
−0.530712 | + | 0.847552i | \(0.678075\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3225.45 | − | 5586.65i | 0.294659 | − | 0.510365i | ||||
\(494\) | 14175.3 | + | 2615.42i | 1.29104 | + | 0.238205i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7492.24 | + | 8375.07i | −0.678249 | + | 0.758169i | ||||
\(497\) | −64.5778 | − | 37.2840i | −0.00582839 | − | 0.00336502i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2353.15 | − | 1358.59i | 0.211105 | − | 0.121881i | −0.390720 | − | 0.920510i | \(-0.627774\pi\) |
0.601825 | + | 0.798628i | \(0.294441\pi\) | |||||||
\(500\) | 4647.89 | − | 743.831i | 0.415720 | − | 0.0665302i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5547.77 | − | 4730.52i | −0.493245 | − | 0.420585i | ||||
\(503\) | −8294.45 | −0.735251 | −0.367626 | − | 0.929974i | \(-0.619829\pi\) | ||||
−0.367626 | + | 0.929974i | \(0.619829\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1049.14 | 0.0924479 | ||||||||
\(506\) | 20172.5 | + | 17200.9i | 1.77229 | + | 1.51121i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3363.83 | + | 538.334i | −0.293791 | + | 0.0470171i | ||||
\(509\) | −2866.64 | + | 1655.05i | −0.249629 | + | 0.144124i | −0.619595 | − | 0.784922i | \(-0.712703\pi\) |
0.369965 | + | 0.929046i | \(0.379370\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −286.798 | − | 165.583i | −0.0248282 | − | 0.0143346i | ||||
\(512\) | −11555.8 | − | 825.228i | −0.997460 | − | 0.0712310i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2421.46 | − | 446.775i | −0.207794 | − | 0.0383393i | ||||
\(515\) | 2102.70 | − | 3641.98i | 0.179914 | − | 0.311621i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1494.33 | + | 2588.25i | 0.127119 | + | 0.220176i | ||||
\(518\) | 501.828 | + | 1413.50i | 0.0425657 | + | 0.119895i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1948.17 | − | 1063.88i | 0.164294 | − | 0.0897193i | ||||
\(521\) | 5030.71i | 0.423031i | 0.977375 | + | 0.211516i | \(0.0678400\pi\) | ||||
−0.977375 | + | 0.211516i | \(0.932160\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9680.16i | 0.809338i | 0.914463 | + | 0.404669i | \(0.132613\pi\) | ||||
−0.914463 | + | 0.404669i | \(0.867387\pi\) | |||||||
\(524\) | −10826.5 | + | 8796.08i | −0.902595 | + | 0.733317i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11489.0 | − | 4078.90i | 0.952369 | − | 0.338115i | ||||
\(527\) | 3193.21 | + | 5530.81i | 0.263944 | + | 0.457164i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12756.2 | + | 22094.4i | −1.04843 | + | 1.81593i | ||||
\(530\) | −435.479 | + | 2360.24i | −0.0356905 | + | 0.193438i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2488.30 | − | 950.571i | −0.202784 | − | 0.0774671i | ||||
\(533\) | −8216.73 | − | 4743.93i | −0.667742 | − | 0.385521i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1635.54 | + | 944.278i | −0.132169 | + | 0.0763078i | ||||
\(536\) | −81.7376 | + | 3438.94i | −0.00658680 | + | 0.277126i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10283.5 | − | 12060.1i | 0.824076 | − | 0.966443i | ||||
\(539\) | −16220.3 | −1.29621 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18659.8 | 1.48290 | 0.741449 | − | 0.671009i | \(-0.234139\pi\) | ||||
0.741449 | + | 0.671009i | \(0.234139\pi\) | |||||||
\(542\) | 3944.21 | − | 4625.62i | 0.312580 | − | 0.366582i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2495.15 | + | 6093.11i | −0.196652 | + | 0.480220i | ||||
\(545\) | −3300.88 | + | 1905.76i | −0.259438 | + | 0.149787i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3928.78 | − | 2268.28i | −0.307098 | − | 0.177303i | 0.338529 | − | 0.940956i | \(-0.390071\pi\) |
−0.645627 | + | 0.763653i | \(0.723404\pi\) | |||||||
\(548\) | −4200.89 | + | 10996.6i | −0.327469 | + | 0.857212i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2953.66 | − | 16008.5i | 0.228990 | − | 1.24110i | ||||
\(551\) | −11100.0 | + | 19225.8i | −0.858216 | + | 1.48647i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 995.797 | + | 1724.77i | 0.0765743 | + | 0.132631i | ||||
\(554\) | −8556.00 | + | 3037.59i | −0.656154 | + | 0.232951i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6448.49 | + | 7937.04i | 0.491865 | + | 0.605406i | ||||
\(557\) | − | 17657.1i | − | 1.34319i | −0.740918 | − | 0.671596i | \(-0.765609\pi\) | ||
0.740918 | − | 0.671596i | \(-0.234391\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 11873.1i | − | 0.898355i | ||||||
\(560\) | −389.701 | + | 128.011i | −0.0294069 | + | 0.00965974i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −889.873 | − | 2506.51i | −0.0667919 | − | 0.188133i | ||||
\(563\) | −4972.47 | − | 8612.57i | −0.372229 | − | 0.644719i | 0.617679 | − | 0.786430i | \(-0.288073\pi\) |
−0.989908 | + | 0.141711i | \(0.954740\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −534.697 | + | 926.122i | −0.0398139 | + | 0.0689597i | ||||
\(566\) | −5702.30 | − | 1052.11i | −0.423473 | − | 0.0781334i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 330.122 | − | 541.643i | 0.0243866 | − | 0.0400121i | ||||
\(569\) | 4084.02 | + | 2357.91i | 0.300898 | + | 0.173724i | 0.642846 | − | 0.765995i | \(-0.277753\pi\) |
−0.341948 | + | 0.939719i | \(0.611087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7993.20 | + | 4614.88i | −0.585823 | + | 0.338225i | −0.763444 | − | 0.645874i | \(-0.776493\pi\) |
0.177621 | + | 0.984099i | \(0.443160\pi\) | |||||||
\(572\) | −2485.30 | − | 15529.6i | −0.181671 | − | 1.13519i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1334.12 | + | 1137.59i | 0.0970123 | + | 0.0827213i | ||||
\(575\) | 23137.1 | 1.67806 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4076.34 | 0.294108 | 0.147054 | − | 0.989128i | \(-0.453021\pi\) | ||||
0.147054 | + | 0.989128i | \(0.453021\pi\) | |||||||
\(578\) | −7726.53 | − | 6588.33i | −0.556023 | − | 0.474115i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 540.232 | + | 3375.69i | 0.0386757 | + | 0.241669i | ||||
\(581\) | 803.706 | − | 464.020i | 0.0573896 | − | 0.0331339i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14726.8 | + | 8502.51i | 1.04618 | + | 0.604010i | ||||
\(584\) | 1466.12 | − | 2405.51i | 0.103884 | − | 0.170447i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12340.6 | − | 2276.92i | −0.869941 | − | 0.160509i | ||||
\(587\) | −4317.74 | + | 7478.55i | −0.303599 | + | 0.525848i | −0.976948 | − | 0.213476i | \(-0.931522\pi\) |
0.673350 | + | 0.739324i | \(0.264855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10989.1 | − | 19033.6i | −0.768755 | − | 1.33152i | ||||
\(590\) | 322.818 | + | 909.281i | 0.0225258 | + | 0.0634483i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12122.1 | + | 3981.92i | −0.841577 | + | 0.276446i | ||||
\(593\) | 24260.9i | 1.68006i | 0.542537 | + | 0.840032i | \(0.317464\pi\) | ||||
−0.542537 | + | 0.840032i | \(0.682536\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 233.121i | 0.0160622i | ||||||||
\(596\) | −10841.1 | − | 13343.7i | −0.745083 | − | 0.917076i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21065.1 | − | 7478.64i | 1.44050 | − | 0.511412i | ||||
\(599\) | 7549.02 | + | 13075.3i | 0.514932 | + | 0.891889i | 0.999850 | + | 0.0173291i | \(0.00551631\pi\) |
−0.484917 | + | 0.874560i | \(0.661150\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2964.13 | + | 5134.03i | −0.201180 | + | 0.348455i | −0.948909 | − | 0.315550i | \(-0.897811\pi\) |
0.747729 | + | 0.664004i | \(0.231144\pi\) | |||||||
\(602\) | −398.097 | + | 2157.64i | −0.0269522 | + | 0.146078i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2731.62 | + | 7150.52i | −0.184020 | + | 0.481706i | ||||
\(605\) | 2087.73 | + | 1205.35i | 0.140294 | + | 0.0809990i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16115.3 | + | 9304.20i | −1.07760 | + | 0.622151i | −0.930247 | − | 0.366933i | \(-0.880408\pi\) |
−0.147350 | + | 0.989084i | \(0.547074\pi\) | |||||||
\(608\) | 8586.77 | − | 20968.7i | 0.572762 | − | 1.39867i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −68.2303 | + | 80.0179i | −0.00452880 | + | 0.00531119i | ||||
\(611\) | 2520.01 | 0.166855 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7939.25 | 0.523105 | 0.261552 | − | 0.965189i | \(-0.415766\pi\) | ||||
0.261552 | + | 0.965189i | \(0.415766\pi\) | |||||||
\(614\) | 13567.1 | − | 15911.0i | 0.891735 | − | 1.04579i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −69.0572 | + | 2905.44i | −0.00451687 | + | 0.190038i | ||||
\(617\) | 25269.7 | − | 14589.5i | 1.64882 | − | 0.951946i | 0.671277 | − | 0.741206i | \(-0.265746\pi\) |
0.977542 | − | 0.210740i | \(-0.0675873\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14117.6 | − | 8150.83i | −0.916698 | − | 0.529256i | −0.0341179 | − | 0.999418i | \(-0.510862\pi\) |
−0.882580 | + | 0.470162i | \(0.844196\pi\) | |||||||
\(620\) | −3161.63 | − | 1207.80i | −0.204797 | − | 0.0782359i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2512.88 | − | 13619.5i | 0.161990 | − | 0.877963i | ||||
\(623\) | −554.427 | + | 960.297i | −0.0356544 | + | 0.0617552i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6740.81 | − | 11675.4i | −0.431412 | − | 0.747227i | ||||
\(626\) | 1817.08 | − | 645.110i | 0.116015 | − | 0.0411882i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12996.8 | − | 10559.3i | 0.825842 | − | 0.670959i | ||||
\(629\) | 7251.46i | 0.459674i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2517.83i | − | 0.158848i | −0.996841 | − | 0.0794242i | \(-0.974692\pi\) | ||
0.996841 | − | 0.0794242i | \(-0.0253082\pi\) | |||||||
\(632\) | −14869.0 | + | 8119.79i | −0.935850 | + | 0.511057i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1468.72 | + | 4136.93i | 0.0920034 | + | 0.259146i | ||||
\(635\) | −513.012 | − | 888.562i | −0.0320602 | − | 0.0555300i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6838.42 | + | 11844.5i | −0.425350 | + | 0.736728i | ||||
\(638\) | 23819.7 | + | 4394.88i | 1.47811 | + | 0.272720i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1009.86 | − | 3339.96i | −0.0623720 | − | 0.206287i | ||||
\(641\) | −14572.0 | − | 8413.13i | −0.897907 | − | 0.518407i | −0.0213863 | − | 0.999771i | \(-0.506808\pi\) |
−0.876520 | + | 0.481365i | \(0.840141\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17687.6 | + | 10211.9i | −1.08481 | + | 0.626313i | −0.932189 | − | 0.361973i | \(-0.882103\pi\) |
−0.152617 | + | 0.988285i | \(0.548770\pi\) | |||||||
\(644\) | −4078.79 | + | 652.754i | −0.249576 | + | 0.0399412i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9798.94 | − | 8355.44i | −0.596802 | − | 0.508886i | ||||
\(647\) | 21477.2 | 1.30503 | 0.652515 | − | 0.757776i | \(-0.273714\pi\) | ||||
0.652515 | + | 0.757776i | \(0.273714\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6836.40 | 0.413485 | ||||||||
\(650\) | −10444.5 | − | 8905.93i | −0.630259 | − | 0.537415i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11601.2 | − | 1856.61i | 0.696836 | − | 0.111519i | ||||
\(653\) | −21836.5 | + | 12607.3i | −1.30862 | + | 0.755533i | −0.981866 | − | 0.189576i | \(-0.939289\pi\) |
−0.326756 | + | 0.945109i | \(0.605955\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3638.46 | − | 2100.66i | −0.217048 | − | 0.125313i | ||||
\(656\) | −9943.90 | + | 11115.6i | −0.591835 | + | 0.661573i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −457.946 | − | 84.4938i | −0.0271316 | − | 0.00500595i | ||||
\(659\) | 6865.03 | − | 11890.6i | 0.405802 | − | 0.702870i | −0.588612 | − | 0.808416i | \(-0.700325\pi\) |
0.994415 | + | 0.105545i | \(0.0336588\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −772.039 | − | 1337.21i | −0.0454294 | − | 0.0786860i | 0.842417 | − | 0.538827i | \(-0.181132\pi\) |
−0.887846 | + | 0.460141i | \(0.847799\pi\) | |||||||
\(662\) | −7004.37 | − | 19729.2i | −0.411228 | − | 1.15831i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3783.65 | + | 6928.64i | 0.221135 | + | 0.404945i | ||||
\(665\) | − | 802.258i | − | 0.0467823i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34426.6i | 1.99851i | ||||||||
\(668\) | 18927.6 | − | 15377.8i | 1.09630 | − | 0.890696i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −976.341 | + | 346.626i | −0.0562975 | + | 0.0199870i | ||||
\(671\) | 372.533 | + | 645.246i | 0.0214329 | + | 0.0371229i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2684.11 | − | 4649.02i | 0.153737 | − | 0.266280i | −0.778861 | − | 0.627196i | \(-0.784202\pi\) |
0.932598 | + | 0.360916i | \(0.117536\pi\) | |||||||
\(674\) | 5000.19 | − | 27100.4i | 0.285757 | − | 1.54877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4030.84 | + | 1539.85i | 0.229338 | + | 0.0876110i | ||||
\(677\) | 16713.8 | + | 9649.71i | 0.948838 | + | 0.547812i | 0.892720 | − | 0.450612i | \(-0.148794\pi\) |
0.0561181 | + | 0.998424i | \(0.482128\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3467.25 | − | 2001.82i | 0.195966 | − | 0.113141i | ||||
\(680\) | −1982.50 | − | 47.1205i | −0.111802 | − | 0.00265734i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15558.9 | + | 18246.8i | −0.873576 | + | 1.02450i | ||||
\(683\) | −7466.11 | −0.418276 | −0.209138 | − | 0.977886i | \(-0.567066\pi\) | ||||
−0.209138 | + | 0.977886i | \(0.567066\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3545.45 | −0.197759 | ||||||||
\(686\) | 3314.22 | − | 3886.79i | 0.184457 | − | 0.216324i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18268.4 | − | 3821.61i | −1.01232 | − | 0.211769i | ||||
\(689\) | 12417.5 | − | 7169.23i | 0.686600 | − | 0.396409i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20587.2 | − | 11886.0i | −1.13339 | − | 0.654364i | −0.188606 | − | 0.982053i | \(-0.560397\pi\) |
−0.944786 | + | 0.327689i | \(0.893730\pi\) | |||||||
\(692\) | −7924.00 | + | 20742.5i | −0.435297 | + | 1.13947i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3616.77 | − | 19602.5i | 0.197825 | − | 1.07219i | ||||
\(695\) | −1540.02 | + | 2667.39i | −0.0840520 | + | 0.145582i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4238.12 | + | 7340.64i | 0.230316 | + | 0.398919i | ||||
\(698\) | −3218.63 | + | 1142.70i | −0.174537 | + | 0.0619651i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1599.41 | + | 1968.62i | 0.0863603 | + | 0.106296i | ||||
\(701\) | − | 3501.89i | − | 0.188680i | −0.995540 | − | 0.0943399i | \(-0.969926\pi\) | ||
0.995540 | − | 0.0943399i | \(-0.0300740\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 24955.1i | − | 1.33883i | ||||||
\(704\) | −24694.4 | − | 1174.55i | −1.32202 | − | 0.0628799i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1438.49 | + | 4051.79i | 0.0766830 | + | 0.215993i | ||||
\(707\) | 579.113 | + | 1003.05i | 0.0308059 | + | 0.0533574i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2079.38 | + | 3601.59i | −0.110145 | + | 0.190777i | −0.915829 | − | 0.401569i | \(-0.868465\pi\) |
0.805684 | + | 0.592346i | \(0.201798\pi\) | |||||||
\(710\) | 187.875 | + | 34.6641i | 0.00993074 | + | 0.00183228i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8054.45 | − | 4909.04i | −0.423951 | − | 0.258391i | ||||
\(713\) | −29516.3 | − | 17041.3i | −1.55034 | − | 0.895091i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4102.18 | − | 2368.40i | 0.214564 | − | 0.123878i | ||||
\(716\) | 603.805 | + | 3772.93i | 0.0315157 | + | 0.196929i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14022.2 | + | 11956.6i | 0.728836 | + | 0.621470i | ||||
\(719\) | −20077.1 | −1.04137 | −0.520687 | − | 0.853748i | \(-0.674324\pi\) | ||||
−0.520687 | + | 0.853748i | \(0.674324\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4642.64 | 0.239807 | ||||||||
\(722\) | 18959.8 | + | 16166.8i | 0.977298 | + | 0.833331i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −925.838 | − | 5785.19i | −0.0475256 | − | 0.296968i | ||||
\(725\) | 18307.5 | − | 10569.8i | 0.937825 | − | 0.541454i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31220.9 | + | 18025.4i | 1.59274 | + | 0.919566i | 0.992835 | + | 0.119491i | \(0.0381263\pi\) |
0.599900 | + | 0.800075i | \(0.295207\pi\) | |||||||
\(728\) | 2092.51 | + | 1275.35i | 0.106529 | + | 0.0649278i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 834.378 | + | 153.948i | 0.0423037 | + | 0.00780530i | ||||
\(731\) | −5303.59 | + | 9186.10i | −0.268345 | + | 0.464788i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10850.9 | + | 18794.4i | 0.546779 | + | 0.947049i | 0.998493 | + | 0.0548859i | \(0.0174795\pi\) |
−0.451714 | + | 0.892163i | \(0.649187\pi\) | |||||||
\(734\) | 3816.05 | + | 10748.7i | 0.191898 | + | 0.540519i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4726.68 | − | 34818.7i | −0.236723 | − | 1.74379i | ||||
\(737\) | 7340.58i | 0.366884i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 26112.0i | − | 1.29979i | −0.760024 | − | 0.649895i | \(-0.774813\pi\) | ||
0.760024 | − | 0.649895i | \(-0.225187\pi\) | |||||||
\(740\) | −2423.22 | − | 2982.60i | −0.120378 | − | 0.148165i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2496.93 | + | 886.474i | −0.123538 | + | 0.0438591i | ||||
\(743\) | 2806.43 | + | 4860.88i | 0.138570 | + | 0.240011i | 0.926956 | − | 0.375171i | \(-0.122416\pi\) |
−0.788385 | + | 0.615182i | \(0.789083\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2589.06 | − | 4484.38i | 0.127323 | − | 0.220530i | ||||
\(746\) | −1260.09 | + | 6829.51i | −0.0618432 | + | 0.335182i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5014.06 | + | 13125.2i | −0.245096 | + | 0.641585i | ||||
\(749\) | −1805.59 | − | 1042.46i | −0.0880839 | − | 0.0508553i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24027.9 | − | 13872.5i | 1.16750 | − | 0.674056i | 0.214409 | − | 0.976744i | \(-0.431217\pi\) |
0.953090 | + | 0.302688i | \(0.0978841\pi\) | |||||||
\(752\) | 811.113 | − | 3877.37i | 0.0393328 | − | 0.188023i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13251.5 | − | 15540.9i | 0.640042 | − | 0.750616i | ||||
\(755\) | −2305.42 | −0.111129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22792.6 | −1.09433 | −0.547167 | − | 0.837023i | \(-0.684294\pi\) | ||||
−0.547167 | + | 0.837023i | \(0.684294\pi\) | |||||||
\(758\) | −17467.8 | + | 20485.5i | −0.837016 | + | 0.981620i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6822.54 | + | 162.160i | 0.325631 | + | 0.00773968i | ||||
\(761\) | −27979.1 | + | 16153.7i | −1.33277 | + | 0.769477i | −0.985724 | − | 0.168370i | \(-0.946150\pi\) |
−0.347049 | + | 0.937847i | \(0.612816\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3644.08 | − | 2103.91i | −0.172902 | − | 0.0998253i | ||||
\(764\) | 23062.4 | + | 8810.24i | 1.09211 | + | 0.417203i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4852.53 | + | 26300.1i | −0.228889 | + | 1.24055i | ||||
\(767\) | 2882.19 | − | 4992.10i | 0.135684 | − | 0.235012i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1200.97 | + | 2080.14i | 0.0563174 | + | 0.0975446i | 0.892810 | − | 0.450434i | \(-0.148731\pi\) |
−0.836492 | + | 0.547979i | \(0.815397\pi\) | |||||||
\(770\) | −824.876 | + | 292.852i | −0.0386058 | + | 0.0137060i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10147.6 | + | 8244.44i | −0.473082 | + | 0.384358i | ||||
\(773\) | − | 21135.4i | − | 0.983424i | −0.870758 | − | 0.491712i | \(-0.836371\pi\) | ||
0.870758 | − | 0.491712i | \(-0.163629\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20928.4i | 0.970025i | ||||||||
\(776\) | 16323.0 | + | 29890.7i | 0.755103 | + | 1.38275i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2806.78 | − | 7905.87i | −0.129342 | − | 0.364318i | ||||
\(779\) | −14585.0 | − | 25262.0i | −0.670811 | − | 1.16188i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 676.799 | − | 1172.25i | 0.0310087 | − | 0.0537086i | ||||
\(782\) | −19638.4 | − | 3623.41i | −0.898041 | − | 0.165694i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16023.3 | + | 14334.2i | 0.729922 | + | 0.652979i | ||||
\(785\) | 4367.81 | + | 2521.76i | 0.198591 | + | 0.114656i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3776.51 | + | 2180.37i | −0.171052 | + | 0.0987570i | −0.583082 | − | 0.812413i | \(-0.698153\pi\) |
0.412030 | + | 0.911170i | \(0.364820\pi\) | |||||||
\(788\) | 26468.6 | − | 4235.93i | 1.19658 | − | 0.191496i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3882.67 | − | 3310.71i | −0.174860 | − | 0.149101i | ||||
\(791\) | −1180.58 | −0.0530679 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 628.232 | 0.0281326 | ||||||||
\(794\) | −2791.11 | − | 2379.95i | −0.124752 | − | 0.106374i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8267.70 | − | 1323.13i | 0.368142 | − | 0.0589159i | ||||
\(797\) | 17755.1 | − | 10250.9i | 0.789106 | − | 0.455590i | −0.0505420 | − | 0.998722i | \(-0.516095\pi\) |
0.839648 | + | 0.543132i | \(0.182762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1949.69 | − | 1125.66i | −0.0863270 | − | 0.0498409i | ||||
\(800\) | −17064.8 | + | 13203.8i | −0.754163 | + | 0.583530i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5723.88 | − | 1056.09i | −0.252016 | − | 0.0464985i | ||||
\(803\) | 3005.76 | − | 5206.12i | 0.132093 | − | 0.228792i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −622.050 | − | 1077.42i | −0.0272352 | − | 0.0471728i | ||||
\(806\) | 6764.72 | + | 19054.2i | 0.295629 | + | 0.832699i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8647.18 | + | 4722.12i | −0.376493 | + | 0.205599i | ||||
\(809\) | 34550.7i | 1.50153i | 0.660568 | + | 0.750766i | \(0.270315\pi\) | ||||
−0.660568 | + | 0.750766i | \(0.729685\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19709.5i | 0.853384i | 0.904397 | + | 0.426692i | \(0.140321\pi\) | ||||
−0.904397 | + | 0.426692i | \(0.859679\pi\) | |||||||
\(812\) | −2929.19 | + | 2379.84i | −0.126594 | + | 0.102852i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25658.6 | + | 9109.46i | −1.10483 | + | 0.392244i | ||||
\(815\) | 1769.27 | + | 3064.47i | 0.0760429 | + | 0.131710i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18251.7 | − | 31612.9i | 0.781575 | − | 1.35373i | ||||
\(818\) | −2974.03 | + | 16118.9i | −0.127121 | + | 0.688978i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4196.20 | − | 1603.02i | −0.178704 | − | 0.0682682i | ||||
\(821\) | 28891.8 | + | 16680.7i | 1.22817 | + | 0.709086i | 0.966648 | − | 0.256110i | \(-0.0824409\pi\) |
0.261526 | + | 0.965196i | \(0.415774\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36540.4 | − | 21096.6i | 1.54765 | − | 0.893537i | 0.549330 | − | 0.835605i | \(-0.314883\pi\) |
0.998321 | − | 0.0579313i | \(-0.0184504\pi\) | |||||||
\(824\) | −938.413 | + | 39481.8i | −0.0396738 | + | 1.66919i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −691.145 | + | 810.548i | −0.0291138 | + | 0.0341435i | ||||
\(827\) | 13992.0 | 0.588329 | 0.294165 | − | 0.955755i | \(-0.404959\pi\) | ||||
0.294165 | + | 0.955755i | \(0.404959\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23454.8 | −0.982653 | −0.491327 | − | 0.870975i | \(-0.663488\pi\) | ||||
−0.491327 | + | 0.870975i | \(0.663488\pi\) | |||||||
\(830\) | −1542.72 | + | 1809.24i | −0.0645164 | + | 0.0756623i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11268.7 | + | 17537.2i | −0.469558 | + | 0.730762i | ||||
\(833\) | 10581.6 | − | 6109.28i | 0.440132 | − | 0.254110i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6360.95 | + | 3672.50i | 0.263629 | + | 0.152206i | ||||
\(836\) | 17255.3 | − | 45168.9i | 0.713860 | − | 1.86866i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7238.80 | + | 39233.4i | −0.298401 | + | 1.61730i | ||||
\(839\) | −4579.55 | + | 7932.02i | −0.188443 | + | 0.326393i | −0.944731 | − | 0.327846i | \(-0.893677\pi\) |
0.756288 | + | 0.654238i | \(0.227011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3532.81 | + | 6119.00i | 0.144852 | + | 0.250892i | ||||
\(842\) | 17114.4 | − | 6076.03i | 0.700475 | − | 0.248686i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 26624.6 | + | 32770.6i | 1.08585 | + | 1.33650i | ||||
\(845\) | 1299.60i | 0.0529082i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2661.35i | 0.107963i | ||||||||
\(848\) | −7034.01 | − | 21413.5i | −0.284846 | − | 0.867149i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4102.62 | + | 11555.8i | 0.165551 | + | 0.466309i | ||||
\(851\) | −19349.5 | − | 33514.3i | −0.779427 | − | 1.35001i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16740.3 | − | 28995.1i | 0.671955 | − | 1.16386i | −0.305394 | − | 0.952226i | \(-0.598788\pi\) |
0.977349 | − | 0.211634i | \(-0.0678784\pi\) | |||||||
\(854\) | −114.165 | − | 21.0641i | −0.00457452 | − | 0.000844028i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9230.20 | − | 15144.3i | 0.368553 | − | 0.604699i | ||||
\(857\) | −26803.0 | − | 15474.7i | −1.06835 | − | 0.616811i | −0.140618 | − | 0.990064i | \(-0.544909\pi\) |
−0.927730 | + | 0.373253i | \(0.878242\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5321.93 | − | 3072.62i | 0.211388 | − | 0.122045i | −0.390568 | − | 0.920574i | \(-0.627722\pi\) |
0.601956 | + | 0.798529i | \(0.294388\pi\) | |||||||
\(860\) | −888.301 | − | 5550.63i | −0.0352219 | − | 0.220087i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2409.91 | − | 2054.91i | −0.0952227 | − | 0.0811953i | ||||
\(863\) | 13685.9 | 0.539830 | 0.269915 | − | 0.962884i | \(-0.413004\pi\) | ||||
0.269915 | + | 0.962884i | \(0.413004\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6687.66 | −0.262875 | ||||||||
\(866\) | 645.311 | + | 550.249i | 0.0253217 | + | 0.0215915i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −590.441 | − | 3689.43i | −0.0230886 | − | 0.144271i | ||||
\(869\) | −31309.0 | + | 18076.3i | −1.22219 | + | 0.705633i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5360.27 | + | 3094.75i | 0.208526 | + | 0.120392i | ||||
\(872\) | 18628.6 | − | 30564.6i | 0.723444 | − | 1.18698i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 67583.3 | + | 12469.5i | 2.61561 | + | 0.482595i | ||||
\(875\) | −782.544 | + | 1355.41i | −0.0302341 | + | 0.0523669i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2574.73 | + | 4459.56i | 0.0991361 | + | 0.171709i | 0.911327 | − | 0.411683i | \(-0.135059\pi\) |
−0.812191 | + | 0.583391i | \(0.801725\pi\) | |||||||
\(878\) | 2283.74 | + | 6432.61i | 0.0877819 | + | 0.247255i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2323.73 | − | 7074.07i | −0.0890146 | − | 0.270985i | ||||
\(881\) | − | 26936.4i | − | 1.03009i | −0.857162 | − | 0.515046i | \(-0.827775\pi\) | ||
0.857162 | − | 0.515046i | \(-0.172225\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 37301.8i | − | 1.42164i | −0.703376 | − | 0.710818i | \(-0.748325\pi\) | ||
0.703376 | − | 0.710818i | \(-0.251675\pi\) | |||||||
\(884\) | 7470.44 | + | 9194.91i | 0.284229 | + | 0.349840i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12844.0 | + | 4559.94i | −0.487023 | + | 0.172905i | ||||
\(887\) | 17421.8 | + | 30175.4i | 0.659488 | + | 1.14227i | 0.980748 | + | 0.195276i | \(0.0625601\pi\) |
−0.321261 | + | 0.946991i | \(0.604107\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 566.352 | − | 980.950i | 0.0213665 | − | 0.0370079i | ||||
\(890\) | 515.469 | − | 2793.78i | 0.0194141 | − | 0.105222i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13588.5 | − | 35570.4i | 0.510064 | − | 1.33519i | ||||
\(893\) | 6709.65 | + | 3873.82i | 0.251433 | + | 0.145165i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −996.628 | + | 575.404i | −0.0372219 | + | 0.0214901i | ||||
\(896\) | 2635.80 | − | 2809.11i | 0.0982769 | − | 0.104739i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15924.1 | + | 18675.2i | −0.591754 | + | 0.693985i | ||||
\(899\) | −31140.2 | −1.15527 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12809.6 | −0.473641 | ||||||||
\(902\) | −20650.1 | + | 24217.7i | −0.762277 | + | 0.893969i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 238.630 | − | 10039.9i | 0.00877956 | − | 0.369382i | ||||
\(905\) | 1528.17 | − | 882.289i | 0.0561304 | − | 0.0324069i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7693.07 | + | 4441.59i | 0.281636 | + | 0.162603i | 0.634164 | − | 0.773199i | \(-0.281344\pi\) |
−0.352528 | + | 0.935801i | \(0.614678\pi\) | |||||||
\(908\) | 16668.8 | + | 6367.75i | 0.609220 | + | 0.232732i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −133.916 | + | 725.809i | −0.00487833 | + | 0.0264399i | ||||
\(911\) | 22256.0 | − | 38548.6i | 0.809413 | − | 1.40194i | −0.103858 | − | 0.994592i | \(-0.533119\pi\) |
0.913271 | − | 0.407352i | \(-0.133548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8423.14 | + | 14589.3i | 0.305329 | + | 0.528845i | ||||
\(914\) | −18445.0 | + | 6548.45i | −0.667513 | + | 0.236984i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −36227.2 | + | 29432.9i | −1.30675 | + | 1.06167i | ||||
\(917\) | − | 4638.16i | − | 0.167029i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 7223.63i | − | 0.259288i | −0.991561 | − | 0.129644i | \(-0.958617\pi\) | ||
0.991561 | − | 0.129644i | \(-0.0413834\pi\) | |||||||
\(920\) | 9288.30 | − | 5072.23i | 0.332855 | − | 0.181768i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14719.4 | − | 41460.2i | −0.525768 | − | 1.48093i | ||||
\(923\) | −570.670 | − | 988.430i | −0.0203509 | − | 0.0352487i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11881.6 | + | 20579.5i | −0.422339 | + | 0.731512i | ||||
\(926\) | −32099.7 | − | 5922.60i | −1.13916 | − | 0.210182i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −19646.4 | − | 25391.4i | −0.694964 | − | 0.898182i | ||||
\(929\) | 30912.2 | + | 17847.2i | 1.09171 | + | 0.630298i | 0.934031 | − | 0.357193i | \(-0.116266\pi\) |
0.157677 | + | 0.987491i | \(0.449599\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36415.3 | + | 21024.4i | −1.28192 | + | 0.740114i | ||||
\(932\) | −24331.1 | + | 3893.85i | −0.855141 | + | 0.136853i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.0930 | − | 12.8696i | −0.000528755 | − | 0.000450864i | ||||
\(935\) | −4231.74 | −0.148014 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4657.90 | −0.162398 | −0.0811991 | − | 0.996698i | \(-0.525875\pi\) | ||||
−0.0811991 | + | 0.996698i | \(0.525875\pi\) | |||||||
\(938\) | −870.326 | − | 742.117i | −0.0302955 | − | 0.0258326i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1178.09 | − | 188.537i | 0.0408777 | − | 0.00654190i | ||||
\(941\) | −22129.9 | + | 12776.7i | −0.766645 | + | 0.442623i | −0.831676 | − | 0.555260i | \(-0.812619\pi\) |
0.0650314 | + | 0.997883i | \(0.479285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39174.9 | − | 22617.6i | −1.35282 | − | 0.781051i | ||||
\(944\) | −6753.33 | − | 6041.44i | −0.232841 | − | 0.208297i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39166.6 | − | 7226.48i | −1.34611 | − | 0.248365i | ||||
\(947\) | 26469.6 | − | 45846.6i | 0.908285 | − | 1.57319i | 0.0918380 | − | 0.995774i | \(-0.470726\pi\) |
0.816447 | − | 0.577421i | \(-0.195941\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2534.42 | − | 4389.75i | −0.0866922 | − | 0.150155i | ||||
\(950\) | −14118.7 | − | 39768.1i | −0.482180 | − | 1.35816i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1049.26 | − | 1921.42i | −0.0357214 | − | 0.0654133i | ||||
\(953\) | − | 744.138i | − | 0.0252938i | −0.999920 | − | 0.0126469i | \(-0.995974\pi\) | ||
0.999920 | − | 0.0126469i | \(-0.00402574\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7435.63i | 0.251949i | ||||||||
\(956\) | 32854.9 | − | 26693.1i | 1.11151 | − | 0.903051i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15090.1 | + | 5357.36i | −0.508913 | + | 0.180677i | ||||
\(959\) | −1957.04 | − | 3389.70i | −0.0658980 | − | 0.114139i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 518.981 | − | 898.901i | 0.0174207 | − | 0.0301736i | ||||
\(962\) | −4165.60 | + | 22577.0i | −0.139610 | + | 0.756666i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 37390.3 | + | 14283.7i | 1.24923 | + | 0.477228i | ||||
\(965\) | −3410.28 | − | 1968.92i | −0.113762 | − | 0.0656807i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14044.5 | − | 8108.61i | 0.467054 | − | 0.269654i | −0.247952 | − | 0.968772i | \(-0.579757\pi\) |
0.715006 | + | 0.699119i | \(0.246424\pi\) | |||||||
\(968\) | −22632.5 | − | 537.936i | −0.751485 | − | 0.0178615i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6655.42 | + | 7805.22i | −0.220302 | + | 0.258361i | ||||
\(971\) | −33620.7 | −1.11116 | −0.555582 | − | 0.831462i | \(-0.687504\pi\) | ||||
−0.555582 | + | 0.831462i | \(0.687504\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3400.28 | −0.112033 | ||||||||
\(974\) | 16667.6 | − | 19547.1i | 0.548321 | − | 0.643049i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 202.209 | − | 966.619i | 0.00663171 | − | 0.0317016i | ||||
\(977\) | −18376.3 | + | 10609.6i | −0.601751 | + | 0.347421i | −0.769730 | − | 0.638369i | \(-0.779609\pi\) |
0.167979 | + | 0.985791i | \(0.446276\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17431.8 | − | 10064.3i | −0.569074 | − | 0.328555i | ||||
\(980\) | −2310.77 | + | 6048.85i | −0.0753211 | + | 0.197167i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5233.39 | − | 28364.3i | 0.170065 | − | 0.921733i | ||||
\(983\) | −19149.3 | + | 33167.6i | −0.621331 | + | 1.07618i | 0.367907 | + | 0.929862i | \(0.380074\pi\) |
−0.989238 | + | 0.146314i | \(0.953259\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4036.68 | + | 6991.73i | 0.130578 | + | 0.226168i | ||||
\(986\) | −17194.4 | + | 6104.46i | −0.555358 | + | 0.197166i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25708.7 | − | 31643.2i | −0.827836 | − | 1.01893i | ||||
\(989\) | − | 56607.5i | − | 1.82004i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 17803.2i | − | 0.570674i | −0.958427 | − | 0.285337i | \(-0.907894\pi\) | ||
0.958427 | − | 0.285337i | \(-0.0921055\pi\) | |||||||
\(992\) | 31494.8 | − | 4275.47i | 1.00803 | − | 0.136841i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 70.5633 | + | 198.756i | 0.00225164 | + | 0.00634220i | ||||
\(995\) | 1260.89 | + | 2183.93i | 0.0401738 | + | 0.0695831i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4517.89 | + | 7825.21i | −0.143513 | + | 0.248573i | −0.928817 | − | 0.370538i | \(-0.879173\pi\) |
0.785304 | + | 0.619110i | \(0.212507\pi\) | |||||||
\(998\) | −7557.78 | − | 1394.46i | −0.239717 | − | 0.0442292i | ||||
\(999\) | 0 | 0 |
(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 | 108.4.h.b.35.3 | 24 | ||
3.2 | odd | 2 | 36.4.h.b.11.10 | ✓ | 24 | ||
4.3 | odd | 2 | inner | 108.4.h.b.35.2 | 24 | ||
9.2 | odd | 6 | 324.4.b.c.323.13 | 24 | |||
9.4 | even | 3 | 36.4.h.b.23.11 | yes | 24 | ||
9.5 | odd | 6 | inner | 108.4.h.b.71.2 | 24 | ||
9.7 | even | 3 | 324.4.b.c.323.12 | 24 | |||
12.11 | even | 2 | 36.4.h.b.11.11 | yes | 24 | ||
36.7 | odd | 6 | 324.4.b.c.323.14 | 24 | |||
36.11 | even | 6 | 324.4.b.c.323.11 | 24 | |||
36.23 | even | 6 | inner | 108.4.h.b.71.3 | 24 | ||
36.31 | odd | 6 | 36.4.h.b.23.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.4.h.b.11.10 | ✓ | 24 | 3.2 | odd | 2 | ||
36.4.h.b.11.11 | yes | 24 | 12.11 | even | 2 | ||
36.4.h.b.23.10 | yes | 24 | 36.31 | odd | 6 | ||
36.4.h.b.23.11 | yes | 24 | 9.4 | even | 3 | ||
108.4.h.b.35.2 | 24 | 4.3 | odd | 2 | inner | ||
108.4.h.b.35.3 | 24 | 1.1 | even | 1 | trivial | ||
108.4.h.b.71.2 | 24 | 9.5 | odd | 6 | inner | ||
108.4.h.b.71.3 | 24 | 36.23 | even | 6 | inner | ||
324.4.b.c.323.11 | 24 | 36.11 | even | 6 | |||
324.4.b.c.323.12 | 24 | 9.7 | even | 3 | |||
324.4.b.c.323.13 | 24 | 9.2 | odd | 6 | |||
324.4.b.c.323.14 | 24 | 36.7 | odd | 6 |