Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(19,108)]
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, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.f (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: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.17 | ||
Character | \(\chi\) | \(=\) | 108.19 |
Dual form | 108.5.f.a.91.17 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.73046 | + | 2.92312i | 0.682614 | + | 0.730779i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.08921 | + | 15.9629i | −0.0680757 | + | 0.997680i | ||||
\(5\) | −19.5394 | − | 33.8433i | −0.781578 | − | 1.35373i | −0.931022 | − | 0.364962i | \(-0.881082\pi\) |
0.149444 | − | 0.988770i | \(-0.452251\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.5700 | − | 6.10260i | −0.215715 | − | 0.124543i | 0.388250 | − | 0.921554i | \(-0.373080\pi\) |
−0.603964 | + | 0.797011i | \(0.706413\pi\) | |||||||
\(8\) | −49.6354 | + | 40.4021i | −0.775553 | + | 0.631282i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 45.5763 | − | 149.524i | 0.455763 | − | 1.49524i | ||||
\(11\) | −96.1446 | − | 55.5091i | −0.794583 | − | 0.458753i | 0.0469902 | − | 0.998895i | \(-0.485037\pi\) |
−0.841574 | + | 0.540142i | \(0.818370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −104.491 | − | 180.984i | −0.618290 | − | 1.07091i | −0.989798 | − | 0.142480i | \(-0.954492\pi\) |
0.371507 | − | 0.928430i | \(-0.378841\pi\) | |||||||
\(14\) | −11.0224 | − | 47.5603i | −0.0562366 | − | 0.242654i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −253.627 | − | 34.7739i | −0.990731 | − | 0.135835i | ||||
\(17\) | −93.3790 | −0.323111 | −0.161555 | − | 0.986864i | \(-0.551651\pi\) | ||||
−0.161555 | + | 0.986864i | \(0.551651\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.8894i | 0.0744859i | 0.999306 | + | 0.0372429i | \(0.0118575\pi\) | ||||
−0.999306 | + | 0.0372429i | \(0.988142\pi\) | |||||||
\(20\) | 561.519 | − | 275.043i | 1.40380 | − | 0.687608i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −100.259 | − | 432.607i | −0.207147 | − | 0.893816i | ||||
\(23\) | 757.577 | − | 437.387i | 1.43209 | − | 0.826819i | 0.434812 | − | 0.900521i | \(-0.356815\pi\) |
0.997280 | + | 0.0737029i | \(0.0234816\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −451.080 | + | 781.293i | −0.721728 | + | 1.25007i | ||||
\(26\) | 243.728 | − | 799.608i | 0.360545 | − | 1.18285i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 108.928 | − | 162.081i | 0.138939 | − | 0.206736i | ||||
\(29\) | −650.809 | + | 1127.23i | −0.773851 | + | 1.34035i | 0.161587 | + | 0.986858i | \(0.448339\pi\) |
−0.935438 | + | 0.353491i | \(0.884995\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 593.492 | − | 342.653i | 0.617577 | − | 0.356558i | −0.158348 | − | 0.987383i | \(-0.550617\pi\) |
0.775925 | + | 0.630825i | \(0.217283\pi\) | |||||||
\(32\) | −590.870 | − | 836.330i | −0.577022 | − | 0.816729i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −254.967 | − | 272.958i | −0.220560 | − | 0.236122i | ||||
\(35\) | 476.966i | 0.389360i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1760.25 | −1.28579 | −0.642897 | − | 0.765953i | \(-0.722268\pi\) | ||||
−0.642897 | + | 0.765953i | \(0.722268\pi\) | |||||||
\(38\) | −78.6008 | + | 73.4203i | −0.0544327 | + | 0.0508451i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2337.19 | + | 890.392i | 1.46074 | + | 0.556495i | ||||
\(41\) | 39.0421 | + | 67.6229i | 0.0232255 | + | 0.0402278i | 0.877405 | − | 0.479751i | \(-0.159273\pi\) |
−0.854179 | + | 0.519979i | \(0.825940\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1405.46 | − | 811.442i | −0.760118 | − | 0.438855i | 0.0692198 | − | 0.997601i | \(-0.477949\pi\) |
−0.829338 | + | 0.558747i | \(0.811282\pi\) | |||||||
\(44\) | 990.807 | − | 1474.28i | 0.511780 | − | 0.761510i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3347.06 | + | 1020.22i | 1.58179 | + | 0.482144i | ||||
\(47\) | 1999.54 | + | 1154.43i | 0.905177 | + | 0.522604i | 0.878876 | − | 0.477050i | \(-0.158294\pi\) |
0.0263007 | + | 0.999654i | \(0.491627\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1126.02 | − | 1950.32i | −0.468978 | − | 0.812294i | ||||
\(50\) | −3515.46 | + | 814.729i | −1.40619 | + | 0.325892i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3002.84 | − | 1470.85i | 1.11052 | − | 0.543953i | ||||
\(53\) | 1313.48 | 0.467598 | 0.233799 | − | 0.972285i | \(-0.424884\pi\) | ||||
0.233799 | + | 0.972285i | \(0.424884\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4338.47i | 1.43420i | ||||||||
\(56\) | 771.205 | − | 124.146i | 0.245920 | − | 0.0395872i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5072.04 | + | 1175.47i | −1.50774 | + | 0.349427i | ||||
\(59\) | −4818.38 | + | 2781.89i | −1.38419 | + | 0.799164i | −0.992653 | − | 0.120997i | \(-0.961391\pi\) |
−0.391540 | + | 0.920161i | \(0.628058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1090.13 | + | 1888.16i | −0.292967 | + | 0.507433i | −0.974510 | − | 0.224345i | \(-0.927976\pi\) |
0.681543 | + | 0.731778i | \(0.261309\pi\) | |||||||
\(62\) | 2622.12 | + | 799.247i | 0.682132 | + | 0.207921i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 831.345 | − | 4010.75i | 0.202965 | − | 0.979186i | ||||
\(65\) | −4083.39 | + | 7072.65i | −0.966484 | + | 1.67400i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −213.077 | + | 123.020i | −0.0474665 | + | 0.0274048i | −0.523545 | − | 0.851998i | \(-0.675391\pi\) |
0.476079 | + | 0.879403i | \(0.342058\pi\) | |||||||
\(68\) | 101.709 | − | 1490.60i | 0.0219960 | − | 0.322361i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1394.23 | + | 1302.33i | −0.284536 | + | 0.265783i | ||||
\(71\) | − | 4608.15i | − | 0.914134i | −0.889432 | − | 0.457067i | \(-0.848900\pi\) | ||
0.889432 | − | 0.457067i | \(-0.151100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2564.79 | 0.481290 | 0.240645 | − | 0.970613i | \(-0.422641\pi\) | ||||
0.240645 | + | 0.970613i | \(0.422641\pi\) | |||||||
\(74\) | −4806.29 | − | 5145.42i | −0.877701 | − | 0.939631i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −429.232 | − | 29.2882i | −0.0743131 | − | 0.00507067i | ||||
\(77\) | 677.500 | + | 1173.46i | 0.114269 | + | 0.197919i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4486.29 | + | 2590.16i | 0.718842 | + | 0.415023i | 0.814326 | − | 0.580408i | \(-0.197107\pi\) |
−0.0954846 | + | 0.995431i | \(0.530440\pi\) | |||||||
\(80\) | 3778.87 | + | 9263.05i | 0.590449 | + | 1.44735i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −91.0669 | + | 298.766i | −0.0135436 | + | 0.0444328i | ||||
\(83\) | 1622.37 | + | 936.677i | 0.235502 | + | 0.135967i | 0.613108 | − | 0.789999i | \(-0.289919\pi\) |
−0.377606 | + | 0.925966i | \(0.623253\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1824.57 | + | 3160.25i | 0.252536 | + | 0.437405i | ||||
\(86\) | −1465.61 | − | 6323.93i | −0.198162 | − | 0.855047i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7014.86 | − | 1129.22i | 0.905844 | − | 0.145819i | ||||
\(89\) | 1167.17 | 0.147352 | 0.0736759 | − | 0.997282i | \(-0.476527\pi\) | ||||
0.0736759 | + | 0.997282i | \(0.476527\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2550.67i | 0.308015i | ||||||||
\(92\) | 6156.80 | + | 12569.5i | 0.727410 | + | 1.48506i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2085.11 | + | 8997.00i | 0.235979 | + | 1.01822i | ||||
\(95\) | 910.026 | − | 525.404i | 0.100834 | − | 0.0582165i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2869.58 | − | 4970.26i | 0.304983 | − | 0.528245i | −0.672275 | − | 0.740302i | \(-0.734683\pi\) |
0.977257 | + | 0.212056i | \(0.0680160\pi\) | |||||||
\(98\) | 2626.47 | − | 8616.73i | 0.273476 | − | 0.897203i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11980.4 | − | 8051.53i | −1.19804 | − | 0.805153i | ||||
\(101\) | 7793.37 | − | 13498.5i | 0.763981 | − | 1.32325i | −0.176802 | − | 0.984246i | \(-0.556575\pi\) |
0.940783 | − | 0.339008i | \(-0.110091\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9636.52 | − | 5563.65i | 0.908334 | − | 0.524427i | 0.0284395 | − | 0.999596i | \(-0.490946\pi\) |
0.879895 | + | 0.475168i | \(0.157613\pi\) | |||||||
\(104\) | 12498.6 | + | 4761.55i | 1.15556 | + | 0.440232i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3586.41 | + | 3839.46i | 0.319189 | + | 0.341711i | ||||
\(107\) | − | 4464.91i | − | 0.389983i | −0.980805 | − | 0.194991i | \(-0.937532\pi\) | ||
0.980805 | − | 0.194991i | \(-0.0624679\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4736.05 | −0.398624 | −0.199312 | − | 0.979936i | \(-0.563871\pi\) | ||||
−0.199312 | + | 0.979936i | \(0.563871\pi\) | |||||||
\(110\) | −12681.8 | + | 11846.0i | −1.04809 | + | 0.979008i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2468.63 | + | 1915.35i | 0.196798 | + | 0.152690i | ||||
\(113\) | −9173.06 | − | 15888.2i | −0.718385 | − | 1.24428i | −0.961639 | − | 0.274317i | \(-0.911548\pi\) |
0.243254 | − | 0.969963i | \(-0.421785\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −29605.3 | − | 17092.6i | −2.23858 | − | 1.29245i | ||||
\(116\) | −17285.0 | − | 11616.6i | −1.28456 | − | 0.863301i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −21288.2 | − | 6488.84i | −1.52888 | − | 0.466018i | ||||
\(119\) | 987.017 | + | 569.855i | 0.0696997 | + | 0.0402411i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1157.98 | − | 2005.68i | −0.0790915 | − | 0.136990i | ||||
\(122\) | −8495.85 | + | 1968.96i | −0.570804 | + | 0.132287i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4823.29 | + | 9847.06i | 0.313689 | + | 0.640417i | ||||
\(125\) | 10831.1 | 0.693190 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8169.42i | − | 0.506505i | −0.967400 | − | 0.253252i | \(-0.918500\pi\) | ||
0.967400 | − | 0.253252i | \(-0.0815003\pi\) | |||||||
\(128\) | 13993.8 | − | 8521.05i | 0.854115 | − | 0.520084i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −31823.7 | + | 7375.32i | −1.88306 | + | 0.436410i | ||||
\(131\) | 9131.01 | − | 5271.79i | 0.532079 | − | 0.307196i | −0.209784 | − | 0.977748i | \(-0.567276\pi\) |
0.741863 | + | 0.670552i | \(0.233943\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 164.095 | − | 284.221i | 0.00927669 | − | 0.0160677i | ||||
\(134\) | −941.399 | − | 286.948i | −0.0524281 | − | 0.0159806i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4634.90 | − | 3772.70i | 0.250589 | − | 0.203974i | ||||
\(137\) | 1612.85 | − | 2793.54i | 0.0859318 | − | 0.148838i | −0.819856 | − | 0.572570i | \(-0.805947\pi\) |
0.905788 | + | 0.423731i | \(0.139280\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16276.4 | − | 9397.17i | 0.842419 | − | 0.486371i | −0.0156666 | − | 0.999877i | \(-0.504987\pi\) |
0.858086 | + | 0.513506i | \(0.171654\pi\) | |||||||
\(140\) | −7613.75 | − | 519.516i | −0.388457 | − | 0.0265059i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13470.2 | − | 12582.4i | 0.668030 | − | 0.624001i | ||||
\(143\) | 23200.8i | 1.13457i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 50865.8 | 2.41930 | ||||||||
\(146\) | 7003.05 | + | 7497.18i | 0.328535 | + | 0.351716i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1917.28 | − | 28098.7i | 0.0875313 | − | 1.28281i | ||||
\(149\) | −3825.13 | − | 6625.31i | −0.172295 | − | 0.298424i | 0.766927 | − | 0.641735i | \(-0.221785\pi\) |
−0.939222 | + | 0.343311i | \(0.888452\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −974.974 | − | 562.901i | −0.0427601 | − | 0.0246876i | 0.478468 | − | 0.878105i | \(-0.341192\pi\) |
−0.521228 | + | 0.853418i | \(0.674526\pi\) | |||||||
\(152\) | −1086.39 | − | 1334.67i | −0.0470216 | − | 0.0577677i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1580.29 | + | 5184.51i | −0.0666338 | + | 0.218608i | ||||
\(155\) | −23193.0 | − | 13390.5i | −0.965369 | − | 0.557356i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1755.81 | + | 3041.15i | 0.0712326 | + | 0.123378i | 0.899442 | − | 0.437041i | \(-0.143973\pi\) |
−0.828209 | + | 0.560419i | \(0.810640\pi\) | |||||||
\(158\) | 4678.28 | + | 20186.3i | 0.187401 | + | 0.808615i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16758.9 | + | 36338.4i | −0.654645 | + | 1.41947i | ||||
\(161\) | −10676.8 | −0.411898 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 41947.9i | 1.57883i | 0.613861 | + | 0.789414i | \(0.289615\pi\) | ||||
−0.613861 | + | 0.789414i | \(0.710385\pi\) | |||||||
\(164\) | −1121.98 | + | 549.569i | −0.0417156 | + | 0.0204331i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1691.80 | + | 7299.94i | 0.0613951 | + | 0.264913i | ||||
\(167\) | −5900.58 | + | 3406.70i | −0.211574 | + | 0.122152i | −0.602043 | − | 0.798464i | \(-0.705646\pi\) |
0.390469 | + | 0.920616i | \(0.372313\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7556.26 | + | 13087.8i | −0.264566 | + | 0.458241i | ||||
\(170\) | −4255.87 | + | 13962.4i | −0.147262 | + | 0.483127i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14483.8 | − | 21551.3i | 0.489582 | − | 0.728480i | ||||
\(173\) | 7874.16 | − | 13638.4i | 0.263095 | − | 0.455693i | −0.703968 | − | 0.710232i | \(-0.748590\pi\) |
0.967063 | + | 0.254539i | \(0.0819236\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9535.85 | − | 5505.52i | 0.311375 | − | 0.179772i | ||||
\(176\) | 22454.6 | + | 17421.9i | 0.724904 | + | 0.562434i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3186.92 | + | 3411.79i | 0.100584 | + | 0.107682i | ||||
\(179\) | − | 22497.6i | − | 0.702151i | −0.936347 | − | 0.351075i | \(-0.885816\pi\) | ||
0.936347 | − | 0.351075i | \(-0.114184\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21847.2 | −0.666867 | −0.333434 | − | 0.942774i | \(-0.608207\pi\) | ||||
−0.333434 | + | 0.942774i | \(0.608207\pi\) | |||||||
\(182\) | −7455.90 | + | 6964.49i | −0.225091 | + | 0.210255i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19931.3 | + | 52317.5i | −0.588707 | + | 1.54530i | ||||
\(185\) | 34394.3 | + | 59572.7i | 1.00495 | + | 1.74062i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8977.88 | + | 5183.38i | 0.256738 | + | 0.148228i | ||||
\(188\) | −20606.0 | + | 30660.9i | −0.583012 | + | 0.867500i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4020.60 | + | 1225.52i | 0.111374 | + | 0.0339479i | ||||
\(191\) | −16182.1 | − | 9342.76i | −0.443577 | − | 0.256099i | 0.261537 | − | 0.965194i | \(-0.415771\pi\) |
−0.705114 | + | 0.709094i | \(0.749104\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23049.7 | − | 39923.2i | −0.618800 | − | 1.07179i | −0.989705 | − | 0.143123i | \(-0.954286\pi\) |
0.370905 | − | 0.928671i | \(-0.379048\pi\) | |||||||
\(194\) | 22363.9 | − | 5182.96i | 0.594216 | − | 0.137713i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 32359.2 | − | 15850.2i | 0.842336 | − | 0.412593i | ||||
\(197\) | −15934.7 | −0.410592 | −0.205296 | − | 0.978700i | \(-0.565816\pi\) | ||||
−0.205296 | + | 0.978700i | \(0.565816\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 73733.8i | 1.86192i | 0.365124 | + | 0.930959i | \(0.381026\pi\) | ||||
−0.365124 | + | 0.930959i | \(0.618974\pi\) | |||||||
\(200\) | −9176.34 | − | 57004.4i | −0.229408 | − | 1.42511i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 60737.2 | − | 14076.2i | 1.48851 | − | 0.344971i | ||||
\(203\) | 13758.1 | − | 7943.25i | 0.333862 | − | 0.192755i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1525.72 | − | 2642.63i | 0.0363051 | − | 0.0628823i | ||||
\(206\) | 42575.3 | + | 12977.4i | 1.00328 | + | 0.305810i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20208.3 | + | 49536.0i | 0.467092 | + | 1.14497i | ||||
\(209\) | 1492.61 | − | 2585.27i | 0.0341706 | − | 0.0591852i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15431.2 | − | 8909.20i | 0.346605 | − | 0.200112i | −0.316584 | − | 0.948564i | \(-0.602536\pi\) |
0.663189 | + | 0.748452i | \(0.269203\pi\) | |||||||
\(212\) | −1430.66 | + | 20967.0i | −0.0318321 | + | 0.466513i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13051.4 | − | 12191.2i | 0.284991 | − | 0.266208i | ||||
\(215\) | 63420.5i | 1.37200i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8364.29 | −0.177627 | ||||||||
\(218\) | −12931.6 | − | 13844.0i | −0.272106 | − | 0.291306i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −69254.5 | − | 4725.51i | −1.43088 | − | 0.0976344i | ||||
\(221\) | 9757.27 | + | 16900.1i | 0.199776 | + | 0.346022i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −58353.8 | − | 33690.6i | −1.17344 | − | 0.677483i | −0.218949 | − | 0.975736i | \(-0.570263\pi\) |
−0.954487 | + | 0.298253i | \(0.903596\pi\) | |||||||
\(224\) | 1141.72 | + | 12445.9i | 0.0227542 | + | 0.248044i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21396.4 | − | 70196.0i | 0.418914 | − | 1.37434i | ||||
\(227\) | 54381.5 | + | 31397.2i | 1.05536 | + | 0.609310i | 0.924144 | − | 0.382044i | \(-0.124780\pi\) |
0.131212 | + | 0.991354i | \(0.458113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20463.2 | + | 35443.2i | 0.390213 | + | 0.675868i | 0.992477 | − | 0.122428i | \(-0.0390681\pi\) |
−0.602265 | + | 0.798297i | \(0.705735\pi\) | |||||||
\(230\) | −30872.2 | − | 133210.i | −0.583596 | − | 2.51815i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13239.4 | − | 82244.7i | −0.245976 | − | 1.52803i | ||||
\(233\) | −79254.5 | −1.45986 | −0.729932 | − | 0.683520i | \(-0.760448\pi\) | ||||
−0.729932 | + | 0.683520i | \(0.760448\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 90227.9i | − | 1.63382i | ||||||
\(236\) | −39158.8 | − | 79945.2i | −0.703080 | − | 1.43539i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1029.26 | + | 4441.13i | 0.0181706 | + | 0.0784042i | ||||
\(239\) | −39084.7 | + | 22565.5i | −0.684243 | + | 0.395048i | −0.801452 | − | 0.598059i | \(-0.795939\pi\) |
0.117209 | + | 0.993107i | \(0.462605\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −37826.8 | + | 65517.9i | −0.651276 | + | 1.12804i | 0.331537 | + | 0.943442i | \(0.392433\pi\) |
−0.982814 | + | 0.184601i | \(0.940901\pi\) | |||||||
\(242\) | 2701.02 | − | 8861.32i | 0.0461208 | − | 0.151310i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −28953.1 | − | 19458.2i | −0.486312 | − | 0.326831i | ||||
\(245\) | −44003.5 | + | 76216.3i | −0.733086 | + | 1.26974i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4866.55 | − | 2809.70i | 0.0797677 | − | 0.0460539i | ||||
\(248\) | −15614.3 | + | 40986.0i | −0.253875 | + | 0.666395i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 29573.8 | + | 31660.6i | 0.473182 | + | 0.506569i | ||||
\(251\) | − | 78270.9i | − | 1.24238i | −0.783662 | − | 0.621188i | \(-0.786650\pi\) | ||
0.783662 | − | 0.621188i | \(-0.213350\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −97115.9 | −1.51722 | ||||||||
\(254\) | 23880.2 | − | 22306.2i | 0.370143 | − | 0.345747i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 63117.6 | + | 17639.2i | 0.963097 | + | 0.269153i | ||||
\(257\) | −11506.3 | − | 19929.5i | −0.174209 | − | 0.301739i | 0.765678 | − | 0.643224i | \(-0.222403\pi\) |
−0.939887 | + | 0.341485i | \(0.889070\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18605.9 | + | 10742.1i | 0.277365 | + | 0.160136i | ||||
\(260\) | −108452. | − | 72886.4i | −1.60432 | − | 1.07820i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 40341.9 | + | 12296.6i | 0.587697 | + | 0.179136i | ||||
\(263\) | 75237.8 | + | 43438.5i | 1.08774 | + | 0.628006i | 0.932973 | − | 0.359945i | \(-0.117205\pi\) |
0.154765 | + | 0.987951i | \(0.450538\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25664.7 | − | 44452.6i | −0.365464 | − | 0.633003i | ||||
\(266\) | 1278.87 | − | 296.385i | 0.0180743 | − | 0.00418883i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1731.67 | − | 3535.32i | −0.0241099 | − | 0.0492220i | ||||
\(269\) | 54083.3 | 0.747409 | 0.373705 | − | 0.927548i | \(-0.378087\pi\) | ||||
0.373705 | + | 0.927548i | \(0.378087\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 47957.3i | − | 0.653004i | −0.945197 | − | 0.326502i | \(-0.894130\pi\) | ||
0.945197 | − | 0.326502i | \(-0.105870\pi\) | |||||||
\(272\) | 23683.5 | + | 3247.15i | 0.320116 | + | 0.0438899i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12569.7 | − | 2913.09i | 0.167426 | − | 0.0388019i | ||||
\(275\) | 86737.8 | − | 50078.1i | 1.14695 | − | 0.662190i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 36861.8 | − | 63846.5i | 0.480415 | − | 0.832103i | −0.519332 | − | 0.854572i | \(-0.673819\pi\) |
0.999748 | + | 0.0224689i | \(0.00715269\pi\) | |||||||
\(278\) | 71911.0 | + | 21919.2i | 0.930477 | + | 0.283618i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19270.4 | − | 23674.4i | −0.245796 | − | 0.301969i | ||||
\(281\) | 28062.0 | − | 48604.7i | 0.355390 | − | 0.615554i | −0.631795 | − | 0.775136i | \(-0.717681\pi\) |
0.987185 | + | 0.159582i | \(0.0510147\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −132300. | + | 76383.2i | −1.65191 | + | 0.953730i | −0.675621 | + | 0.737249i | \(0.736124\pi\) |
−0.976287 | + | 0.216481i | \(0.930542\pi\) | |||||||
\(284\) | 73559.3 | + | 5019.25i | 0.912013 | + | 0.0622303i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −67818.7 | + | 63348.8i | −0.829120 | + | 0.774474i | ||||
\(287\) | − | 953.034i | − | 0.0115703i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −74801.4 | −0.895600 | ||||||||
\(290\) | 138887. | + | 148687.i | 1.65145 | + | 1.76797i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2793.60 | + | 40941.5i | −0.0327641 | + | 0.480173i | ||||
\(293\) | −19420.1 | − | 33636.7i | −0.226213 | − | 0.391812i | 0.730470 | − | 0.682945i | \(-0.239301\pi\) |
−0.956683 | + | 0.291133i | \(0.905968\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 188297. | + | 108713.i | 2.16371 | + | 1.24922i | ||||
\(296\) | 87370.8 | − | 71117.8i | 0.997201 | − | 0.811699i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8922.21 | − | 29271.4i | 0.100471 | − | 0.329618i | ||||
\(299\) | −158320. | − | 91406.1i | −1.77090 | − | 1.02243i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9903.82 | + | 17153.9i | 0.109312 | + | 0.189335i | ||||
\(302\) | −1016.70 | − | 4386.94i | −0.0111475 | − | 0.0481003i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 935.049 | − | 6819.88i | 0.0101178 | − | 0.0737955i | ||||
\(305\) | 85202.0 | 0.915905 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 457.528i | − | 0.00485446i | −0.999997 | − | 0.00242723i | \(-0.999227\pi\) | ||
0.999997 | − | 0.00242723i | \(-0.000772612\pi\) | |||||||
\(308\) | −19469.8 | + | 9536.70i | −0.205239 | + | 0.100530i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24185.5 | − | 104358.i | −0.251671 | − | 1.08593i | ||||
\(311\) | 9285.82 | − | 5361.17i | 0.0960062 | − | 0.0554292i | −0.451228 | − | 0.892409i | \(-0.649014\pi\) |
0.547234 | + | 0.836979i | \(0.315681\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8976.10 | + | 15547.1i | −0.0916218 | + | 0.158694i | −0.908194 | − | 0.418550i | \(-0.862538\pi\) |
0.816572 | + | 0.577244i | \(0.195872\pi\) | |||||||
\(314\) | −4095.48 | + | 13436.2i | −0.0415380 | + | 0.136275i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −46232.9 | + | 68792.9i | −0.462996 | + | 0.688921i | ||||
\(317\) | −30685.9 | + | 53149.6i | −0.305366 | + | 0.528909i | −0.977343 | − | 0.211663i | \(-0.932112\pi\) |
0.671977 | + | 0.740572i | \(0.265445\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 125143. | − | 72251.6i | 1.22978 | − | 0.710013i | ||||
\(320\) | −151981. | + | 50232.3i | −1.48419 | + | 0.490550i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −29152.5 | − | 31209.5i | −0.281167 | − | 0.301006i | ||||
\(323\) | − | 2510.90i | − | 0.0240672i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 188535. | 1.78495 | ||||||||
\(326\) | −122619. | + | 114537.i | −1.15377 | + | 1.07773i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4669.98 | − | 1779.11i | −0.0434077 | − | 0.0165369i | ||||
\(329\) | −14090.1 | − | 24404.7i | −0.130173 | − | 0.225467i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −160993. | − | 92949.3i | −1.46944 | − | 0.848379i | −0.470023 | − | 0.882654i | \(-0.655755\pi\) |
−0.999412 | + | 0.0342747i | \(0.989088\pi\) | |||||||
\(332\) | −16719.2 | + | 24877.5i | −0.151684 | + | 0.225700i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −26069.4 | − | 7946.22i | −0.233689 | − | 0.0712308i | ||||
\(335\) | 8326.81 | + | 4807.49i | 0.0741975 | + | 0.0428379i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 73998.8 | + | 128170.i | 0.651576 | + | 1.12856i | 0.982741 | + | 0.184989i | \(0.0592251\pi\) |
−0.331165 | + | 0.943573i | \(0.607442\pi\) | |||||||
\(338\) | −58889.3 | + | 13647.9i | −0.515469 | + | 0.119463i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −52434.1 | + | 25683.3i | −0.453582 | + | 0.222174i | ||||
\(341\) | −76081.3 | −0.654289 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 56791.2i | 0.482717i | ||||||||
\(344\) | 102544. | − | 16507.2i | 0.866553 | − | 0.139494i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 61366.8 | − | 14222.1i | 0.512603 | − | 0.118799i | ||||
\(347\) | −125556. | + | 72490.0i | −1.04275 | + | 0.602031i | −0.920611 | − | 0.390482i | \(-0.872308\pi\) |
−0.122138 | + | 0.992513i | \(0.538975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 89475.8 | − | 154977.i | 0.734606 | − | 1.27238i | −0.220290 | − | 0.975435i | \(-0.570700\pi\) |
0.954896 | − | 0.296941i | \(-0.0959664\pi\) | |||||||
\(350\) | 42130.5 | + | 12841.8i | 0.343922 | + | 0.104831i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10385.0 | + | 113207.i | 0.0838150 | + | 0.913670i | ||||
\(353\) | 13197.7 | − | 22859.1i | 0.105913 | − | 0.183446i | −0.808198 | − | 0.588911i | \(-0.799557\pi\) |
0.914111 | + | 0.405465i | \(0.132890\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −155955. | + | 90040.7i | −1.23749 | + | 0.714467i | ||||
\(356\) | −1271.30 | + | 18631.5i | −0.0100311 | + | 0.147010i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 65763.1 | − | 61428.8i | 0.513117 | − | 0.479298i | ||||
\(359\) | 181364.i | 1.40722i | 0.710587 | + | 0.703609i | \(0.248429\pi\) | ||||
−0.710587 | + | 0.703609i | \(0.751571\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 129598. | 0.994452 | ||||||||
\(362\) | −59652.9 | − | 63862.0i | −0.455213 | − | 0.487333i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −40716.0 | − | 2778.22i | −0.307300 | − | 0.0209683i | ||||
\(365\) | −50114.6 | − | 86801.1i | −0.376165 | − | 0.651537i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 181000. | + | 104500.i | 1.34383 | + | 0.775863i | 0.987368 | − | 0.158445i | \(-0.0506481\pi\) |
0.356467 | + | 0.934308i | \(0.383981\pi\) | |||||||
\(368\) | −207352. | + | 84589.4i | −1.53113 | + | 0.624626i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −80225.8 | + | 263199.i | −0.586017 | + | 1.92257i | ||||
\(371\) | −13883.5 | − | 8015.67i | −0.100868 | − | 0.0582360i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 38298.0 | + | 66334.0i | 0.275269 | + | 0.476781i | 0.970203 | − | 0.242293i | \(-0.0778996\pi\) |
−0.694934 | + | 0.719074i | \(0.744566\pi\) | |||||||
\(374\) | 9362.09 | + | 40396.4i | 0.0669314 | + | 0.288801i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −145889. | + | 23484.7i | −1.03192 | + | 0.166115i | ||||
\(377\) | 272015. | 1.91386 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 232118.i | − | 1.61596i | −0.589211 | − | 0.807979i | \(-0.700561\pi\) | ||
0.589211 | − | 0.807979i | \(-0.299439\pi\) | |||||||
\(380\) | 7395.75 | + | 15098.9i | 0.0512171 | + | 0.104563i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16874.7 | − | 72812.3i | −0.115640 | − | 0.498974i | ||||
\(383\) | −74119.1 | + | 42792.7i | −0.505280 | + | 0.291724i | −0.730891 | − | 0.682494i | \(-0.760895\pi\) |
0.225611 | + | 0.974217i | \(0.427562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26476.0 | − | 45857.7i | 0.178620 | − | 0.309379i | ||||
\(386\) | 53764.1 | − | 176386.i | 0.360842 | − | 1.18383i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 76214.1 | + | 51220.4i | 0.506258 | + | 0.340236i | ||||
\(389\) | 60869.2 | − | 105429.i | 0.402252 | − | 0.696721i | −0.591745 | − | 0.806125i | \(-0.701561\pi\) |
0.993997 | + | 0.109404i | \(0.0348942\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −70741.7 | + | 40842.8i | −0.462724 | + | 0.267154i | ||||
\(392\) | 134687. | + | 51311.4i | 0.876504 | + | 0.333919i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −43508.9 | − | 46578.9i | −0.280276 | − | 0.300052i | ||||
\(395\) | − | 202441.i | − | 1.29749i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −71690.8 | −0.454865 | −0.227432 | − | 0.973794i | \(-0.573033\pi\) | ||||
−0.227432 | + | 0.973794i | \(0.573033\pi\) | |||||||
\(398\) | −215532. | + | 201327.i | −1.36065 | + | 1.27097i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 141575. | − | 182471.i | 0.884842 | − | 1.14045i | ||||
\(401\) | −43140.3 | − | 74721.1i | −0.268283 | − | 0.464681i | 0.700135 | − | 0.714010i | \(-0.253123\pi\) |
−0.968419 | + | 0.249330i | \(0.919790\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −124029. | − | 71608.3i | −0.763684 | − | 0.440913i | ||||
\(404\) | 206987. | + | 139107.i | 1.26818 | + | 0.852291i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 60785.0 | + | 18527.9i | 0.368761 | + | 0.112402i | ||||
\(407\) | 169239. | + | 97710.0i | 1.02167 | + | 0.589862i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −115231. | − | 199585.i | −0.688844 | − | 1.19311i | −0.972212 | − | 0.234102i | \(-0.924785\pi\) |
0.283368 | − | 0.959011i | \(-0.408548\pi\) | |||||||
\(410\) | 11890.6 | − | 2755.72i | 0.0707355 | − | 0.0163933i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 78315.6 | + | 159887.i | 0.461375 | + | 0.941928i | ||||
\(413\) | 67907.1 | 0.398121 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 73208.6i | − | 0.425075i | ||||||
\(416\) | −89621.6 | + | 194327.i | −0.517876 | + | 1.12291i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11632.5 | − | 2695.91i | 0.0665767 | − | 0.0154295i | ||||
\(419\) | −48172.3 | + | 27812.3i | −0.274391 | + | 0.158420i | −0.630881 | − | 0.775879i | \(-0.717307\pi\) |
0.356491 | + | 0.934299i | \(0.383973\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −70485.7 | + | 122085.i | −0.397683 | + | 0.688807i | −0.993440 | − | 0.114358i | \(-0.963519\pi\) |
0.595757 | + | 0.803165i | \(0.296852\pi\) | |||||||
\(422\) | 68176.8 | + | 20781.0i | 0.382835 | + | 0.116692i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −65195.3 | + | 53067.4i | −0.362647 | + | 0.295186i | ||||
\(425\) | 42121.4 | − | 72956.4i | 0.233198 | − | 0.403911i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23045.4 | − | 13305.2i | 0.126394 | − | 0.0729738i | ||||
\(428\) | 71272.8 | + | 4863.23i | 0.389078 | + | 0.0265483i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −185386. | + | 173167.i | −1.00263 | + | 0.936544i | ||||
\(431\) | − | 191015.i | − | 1.02828i | −0.857705 | − | 0.514142i | \(-0.828111\pi\) | ||
0.857705 | − | 0.514142i | \(-0.171889\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 48243.4 | 0.257313 | 0.128657 | − | 0.991689i | \(-0.458933\pi\) | ||||
0.128657 | + | 0.991689i | \(0.458933\pi\) | |||||||
\(434\) | −22838.3 | − | 24449.8i | −0.121251 | − | 0.129806i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5158.56 | − | 75601.0i | 0.0271366 | − | 0.397699i | ||||
\(437\) | 11761.1 | + | 20370.8i | 0.0615863 | + | 0.106671i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 227081. | + | 131105.i | 1.17829 | + | 0.680285i | 0.955618 | − | 0.294609i | \(-0.0951893\pi\) |
0.222670 | + | 0.974894i | \(0.428523\pi\) | |||||||
\(440\) | −175283. | − | 215342.i | −0.905388 | − | 1.11230i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22759.1 | + | 74666.6i | −0.116496 | + | 0.382192i | ||||
\(443\) | 78793.6 | + | 45491.5i | 0.401498 | + | 0.231805i | 0.687130 | − | 0.726534i | \(-0.258870\pi\) |
−0.285632 | + | 0.958339i | \(0.592204\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22805.9 | − | 39501.0i | −0.115167 | − | 0.199475i | ||||
\(446\) | −60851.0 | − | 262566.i | −0.305913 | − | 1.31998i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −33263.3 | + | 37320.3i | −0.165733 | + | 0.185947i | ||||
\(449\) | −283350. | −1.40550 | −0.702748 | − | 0.711438i | \(-0.748044\pi\) | ||||
−0.702748 | + | 0.711438i | \(0.748044\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 8668.77i | − | 0.0426191i | ||||||
\(452\) | 263613. | − | 129123.i | 1.29030 | − | 0.632014i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 56708.7 | + | 244692.i | 0.275130 | + | 1.18716i | ||||
\(455\) | 86323.1 | − | 49838.7i | 0.416970 | − | 0.240737i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −99226.7 | + | 171866.i | −0.475112 | + | 0.822918i | −0.999594 | − | 0.0285035i | \(-0.990926\pi\) |
0.524482 | + | 0.851422i | \(0.324259\pi\) | |||||||
\(458\) | −47730.9 | + | 156592.i | −0.227546 | + | 0.746517i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 305094. | − | 453968.i | 1.44184 | − | 2.14541i | ||||
\(461\) | −104347. | + | 180735.i | −0.490998 | + | 0.850433i | −0.999946 | − | 0.0103639i | \(-0.996701\pi\) |
0.508949 | + | 0.860797i | \(0.330034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22687.9 | + | 13098.9i | −0.105836 | + | 0.0611044i | −0.551984 | − | 0.833855i | \(-0.686129\pi\) |
0.446148 | + | 0.894959i | \(0.352796\pi\) | |||||||
\(464\) | 204261. | − | 263266.i | 0.948746 | − | 1.22281i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −216401. | − | 231670.i | −0.996524 | − | 1.06684i | ||||
\(467\) | − | 96607.8i | − | 0.442974i | −0.975163 | − | 0.221487i | \(-0.928909\pi\) | ||
0.975163 | − | 0.221487i | \(-0.0710911\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3002.97 | 0.0136523 | ||||||||
\(470\) | 263747. | − | 246363.i | 1.19396 | − | 1.11527i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 126768. | − | 332753.i | 0.569017 | − | 1.49361i | ||||
\(473\) | 90084.9 | + | 156032.i | 0.402652 | + | 0.697413i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21008.5 | − | 12129.3i | −0.0931125 | − | 0.0537585i | ||||
\(476\) | −10171.6 | + | 15135.0i | −0.0448926 | + | 0.0667986i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −172681. | − | 52634.7i | −0.755767 | − | 0.230365i | ||||
\(479\) | 29664.3 | + | 17126.7i | 0.129289 | + | 0.0746453i | 0.563250 | − | 0.826287i | \(-0.309551\pi\) |
−0.433960 | + | 0.900932i | \(0.642884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 183931. | + | 318577.i | 0.794994 | + | 1.37697i | ||||
\(482\) | −294801. | + | 68321.7i | −1.26892 | + | 0.294080i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 33277.7 | − | 16300.1i | 0.142057 | − | 0.0695823i | ||||
\(485\) | −224280. | −0.953470 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 69521.4i | − | 0.293130i | −0.989201 | − | 0.146565i | \(-0.953178\pi\) | ||
0.989201 | − | 0.146565i | \(-0.0468218\pi\) | |||||||
\(488\) | −22176.5 | − | 137763.i | −0.0931224 | − | 0.578486i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −342939. | + | 79477.9i | −1.42832 | + | 0.331020i | ||||
\(491\) | 174305. | − | 100635.i | 0.723016 | − | 0.417433i | −0.0928458 | − | 0.995681i | \(-0.529596\pi\) |
0.815862 | + | 0.578247i | \(0.196263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 60771.9 | − | 105260.i | 0.250040 | − | 0.433081i | ||||
\(494\) | 21501.0 | + | 6553.71i | 0.0881057 | + | 0.0268555i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −162441. | + | 66268.0i | −0.660286 | + | 0.269365i | ||||
\(497\) | −28121.7 | + | 48708.2i | −0.113849 | + | 0.197192i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 46850.8 | − | 27049.3i | 0.188155 | − | 0.108631i | −0.402964 | − | 0.915216i | \(-0.632020\pi\) |
0.591119 | + | 0.806585i | \(0.298687\pi\) | |||||||
\(500\) | −11797.3 | + | 172896.i | −0.0471894 | + | 0.691582i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 228795. | − | 213715.i | 0.907902 | − | 0.848064i | ||||
\(503\) | 239548.i | 0.946795i | 0.880849 | + | 0.473397i | \(0.156973\pi\) | ||||
−0.880849 | + | 0.473397i | \(0.843027\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −609113. | −2.38844 | ||||||||
\(506\) | −265171. | − | 283881.i | −1.03568 | − | 1.10875i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 130407. | + | 8898.22i | 0.505330 | + | 0.0344807i | ||||
\(509\) | 57738.0 | + | 100005.i | 0.222857 | + | 0.386000i | 0.955674 | − | 0.294426i | \(-0.0951284\pi\) |
−0.732817 | + | 0.680425i | \(0.761795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27109.9 | − | 15651.9i | −0.103821 | − | 0.0599412i | ||||
\(512\) | 120778. | + | 232663.i | 0.460733 | + | 0.887539i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26838.8 | − | 88051.1i | 0.101587 | − | 0.333279i | ||||
\(515\) | −376584. | − | 217421.i | −1.41987 | − | 0.819761i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −128163. | − | 221985.i | −0.479492 | − | 0.830505i | ||||
\(518\) | 19402.1 | + | 83718.1i | 0.0723086 | + | 0.312004i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −83068.7 | − | 516031.i | −0.307207 | − | 1.90840i | ||||
\(521\) | −217267. | −0.800420 | −0.400210 | − | 0.916424i | \(-0.631063\pi\) | ||||
−0.400210 | + | 0.916424i | \(0.631063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39683.4i | 0.145079i | 0.997366 | + | 0.0725397i | \(0.0231104\pi\) | ||||
−0.997366 | + | 0.0725397i | \(0.976890\pi\) | |||||||
\(524\) | 74207.4 | + | 151499.i | 0.270262 | + | 0.551757i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 78457.6 | + | 338536.i | 0.283572 | + | 1.22358i | ||||
\(527\) | −55419.6 | + | 31996.5i | −0.199546 | + | 0.115208i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 242694. | − | 420359.i | 0.867258 | − | 1.50213i | ||||
\(530\) | 59863.7 | − | 196397.i | 0.213114 | − | 0.699170i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4358.26 | + | 2929.01i | 0.0153989 | + | 0.0103490i | ||||
\(533\) | 8159.11 | − | 14132.0i | 0.0287202 | − | 0.0497449i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −151107. | + | 87241.9i | −0.527932 | + | 0.304802i | ||||
\(536\) | 5605.90 | − | 14714.9i | 0.0195126 | − | 0.0512186i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 147672. | + | 158092.i | 0.510192 | + | 0.546191i | ||||
\(539\) | 250017.i | 0.860580i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −194992. | −0.666228 | −0.333114 | − | 0.942887i | \(-0.608099\pi\) | ||||
−0.333114 | + | 0.942887i | \(0.608099\pi\) | |||||||
\(542\) | 140185. | − | 130945.i | 0.477201 | − | 0.445750i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 55174.8 | + | 78095.7i | 0.186442 | + | 0.263894i | ||||
\(545\) | 92539.8 | + | 160284.i | 0.311556 | + | 0.539630i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 81637.9 | + | 47133.6i | 0.272846 | + | 0.157527i | 0.630180 | − | 0.776449i | \(-0.282981\pi\) |
−0.357335 | + | 0.933976i | \(0.616314\pi\) | |||||||
\(548\) | 42836.3 | + | 28788.5i | 0.142643 | + | 0.0958647i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 383218. | + | 116809.i | 1.26684 | + | 0.386144i | ||||
\(551\) | −30310.6 | − | 17499.9i | −0.0998371 | − | 0.0576410i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31613.4 | − | 54756.1i | −0.103376 | − | 0.179053i | ||||
\(554\) | 287280. | − | 66578.8i | 0.936022 | − | 0.216928i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 132278. | + | 270053.i | 0.427894 | + | 0.873575i | ||||
\(557\) | 563587. | 1.81656 | 0.908282 | − | 0.418358i | \(-0.137394\pi\) | ||||
0.908282 | + | 0.418358i | \(0.137394\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 339154.i | 1.08536i | ||||||||
\(560\) | 16586.0 | − | 120972.i | 0.0528889 | − | 0.385751i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 218699. | − | 50684.8i | 0.692428 | − | 0.160474i | ||||
\(563\) | 543509. | − | 313795.i | 1.71471 | − | 0.989986i | 0.786771 | − | 0.617245i | \(-0.211751\pi\) |
0.927935 | − | 0.372741i | \(-0.121582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −358473. | + | 620894.i | −1.12295 | + | 1.94500i | ||||
\(566\) | −584516. | − | 178166.i | −1.82458 | − | 0.556150i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 186179. | + | 228727.i | 0.577077 | + | 0.708959i | ||||
\(569\) | −38859.9 | + | 67307.3i | −0.120026 | + | 0.207892i | −0.919778 | − | 0.392439i | \(-0.871631\pi\) |
0.799751 | + | 0.600331i | \(0.204965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −276094. | + | 159403.i | −0.846809 | + | 0.488905i | −0.859573 | − | 0.511013i | \(-0.829270\pi\) |
0.0127640 | + | 0.999919i | \(0.495937\pi\) | |||||||
\(572\) | −370352. | − | 25270.6i | −1.13194 | − | 0.0772366i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2785.83 | − | 2602.22i | 0.00845533 | − | 0.00789805i | ||||
\(575\) | 789186.i | 2.38695i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40053.7 | 0.120307 | 0.0601534 | − | 0.998189i | \(-0.480841\pi\) | ||||
0.0601534 | + | 0.998189i | \(0.480841\pi\) | |||||||
\(578\) | −204242. | − | 218653.i | −0.611349 | − | 0.654485i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −55403.5 | + | 811964.i | −0.164695 | + | 2.41369i | ||||
\(581\) | −11432.3 | − | 19801.4i | −0.0338675 | − | 0.0586602i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −126284. | − | 72910.3i | −0.371546 | − | 0.214512i | ||||
\(584\) | −127304. | + | 103623.i | −0.373266 | + | 0.303830i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 45298.0 | − | 148611.i | 0.131912 | − | 0.432768i | ||||
\(587\) | 11894.5 | + | 6867.28i | 0.0345199 | + | 0.0199301i | 0.517161 | − | 0.855888i | \(-0.326989\pi\) |
−0.482641 | + | 0.875818i | \(0.660322\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9213.72 | + | 15958.6i | 0.0265586 | + | 0.0460008i | ||||
\(590\) | 196355. | + | 847250.i | 0.564076 | + | 2.43393i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 446448. | + | 61210.8i | 1.27388 | + | 0.174656i | ||||
\(593\) | −537582. | −1.52875 | −0.764373 | − | 0.644775i | \(-0.776951\pi\) | ||||
−0.764373 | + | 0.644775i | \(0.776951\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 44538.6i | − | 0.125806i | ||||||
\(596\) | 109925. | − | 53843.7i | 0.309461 | − | 0.151580i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −165095. | − | 712368.i | −0.461671 | − | 1.99206i | ||||
\(599\) | −394401. | + | 227708.i | −1.09922 | + | 0.634635i | −0.936016 | − | 0.351958i | \(-0.885516\pi\) |
−0.163204 | + | 0.986592i | \(0.552183\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 118996. | − | 206108.i | 0.329446 | − | 0.570618i | −0.652956 | − | 0.757396i | \(-0.726471\pi\) |
0.982402 | + | 0.186778i | \(0.0598046\pi\) | |||||||
\(602\) | −23100.9 | + | 75788.0i | −0.0637436 | + | 0.209126i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10047.5 | − | 14950.3i | 0.0275412 | − | 0.0409803i | ||||
\(605\) | −45252.5 | + | 78379.7i | −0.123632 | + | 0.214137i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 516142. | − | 297995.i | 1.40085 | − | 0.808781i | 0.406371 | − | 0.913708i | \(-0.366794\pi\) |
0.994480 | + | 0.104927i | \(0.0334608\pi\) | |||||||
\(608\) | 22488.4 | − | 15888.1i | 0.0608347 | − | 0.0429799i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 232640. | + | 249055.i | 0.625209 | + | 0.669324i | ||||
\(611\) | − | 482511.i | − | 1.29248i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 547275. | 1.45641 | 0.728206 | − | 0.685358i | \(-0.240354\pi\) | ||||
0.728206 | + | 0.685358i | \(0.240354\pi\) | |||||||
\(614\) | 1337.41 | − | 1249.26i | 0.00354754 | − | 0.00331372i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −81038.4 | − | 30873.0i | −0.213565 | − | 0.0813611i | ||||
\(617\) | 259077. | + | 448735.i | 0.680549 | + | 1.17874i | 0.974814 | + | 0.223021i | \(0.0715919\pi\) |
−0.294265 | + | 0.955724i | \(0.595075\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 176869. | + | 102115.i | 0.461605 | + | 0.266508i | 0.712719 | − | 0.701450i | \(-0.247463\pi\) |
−0.251114 | + | 0.967958i | \(0.580797\pi\) | |||||||
\(620\) | 239013. | − | 355642.i | 0.621781 | − | 0.925187i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 41025.8 | + | 12505.1i | 0.106042 | + | 0.0323226i | ||||
\(623\) | −12337.1 | − | 7122.80i | −0.0317860 | − | 0.0183516i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 70291.3 | + | 121748.i | 0.179946 | + | 0.311675i | ||||
\(626\) | −69954.7 | + | 16212.4i | −0.178512 | + | 0.0413712i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −50458.0 | + | 24715.4i | −0.127941 | + | 0.0626683i | ||||
\(629\) | 164370. | 0.415454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 177036.i | − | 0.444633i | −0.974975 | − | 0.222317i | \(-0.928638\pi\) | ||
0.974975 | − | 0.222317i | \(-0.0713618\pi\) | |||||||
\(632\) | −327327. | + | 52691.8i | −0.819497 | + | 0.131919i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −239149. | + | 55424.1i | −0.594963 | + | 0.137886i | ||||
\(635\) | −276480. | + | 159626.i | −0.685672 | + | 0.395873i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −235317. | + | 407582.i | −0.579929 | + | 1.00447i | ||||
\(638\) | 552899. | + | 168529.i | 1.35833 | + | 0.414031i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −561812. | − | 307101.i | −1.37161 | − | 0.749758i | ||||
\(641\) | 109444. | − | 189562.i | 0.266364 | − | 0.461356i | −0.701556 | − | 0.712614i | \(-0.747511\pi\) |
0.967920 | + | 0.251258i | \(0.0808444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 298938. | − | 172592.i | 0.723035 | − | 0.417445i | −0.0928336 | − | 0.995682i | \(-0.529592\pi\) |
0.815869 | + | 0.578237i | \(0.196259\pi\) | |||||||
\(644\) | 11629.3 | − | 170432.i | 0.0280402 | − | 0.410942i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7339.66 | − | 6855.91i | 0.0175878 | − | 0.0164286i | ||||
\(647\) | − | 398251.i | − | 0.951366i | −0.879617 | − | 0.475683i | \(-0.842201\pi\) | ||
0.879617 | − | 0.475683i | \(-0.157799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 617681. | 1.46648 | ||||||||
\(650\) | 514787. | + | 551110.i | 1.21843 | + | 1.30440i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −669609. | − | 45690.1i | −1.57517 | − | 0.107480i | ||||
\(653\) | −171144. | − | 296430.i | −0.401361 | − | 0.695178i | 0.592529 | − | 0.805549i | \(-0.298129\pi\) |
−0.993890 | + | 0.110371i | \(0.964796\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −356830. | − | 206016.i | −0.831722 | − | 0.480195i | ||||
\(656\) | −7550.63 | − | 18508.7i | −0.0175459 | − | 0.0430098i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 32865.5 | − | 107823.i | 0.0759082 | − | 0.249035i | ||||
\(659\) | 452868. | + | 261464.i | 1.04280 | + | 0.602061i | 0.920625 | − | 0.390447i | \(-0.127680\pi\) |
0.122175 | + | 0.992509i | \(0.461013\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −154294. | − | 267245.i | −0.353140 | − | 0.611656i | 0.633658 | − | 0.773613i | \(-0.281553\pi\) |
−0.986798 | + | 0.161957i | \(0.948219\pi\) | |||||||
\(662\) | −167883. | − | 724395.i | −0.383080 | − | 1.65295i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −118371. | + | 19054.9i | −0.268478 | + | 0.0432185i | ||||
\(665\) | −12825.3 | −0.0290018 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.13862e6i | 2.55934i | ||||||||
\(668\) | −47953.8 | − | 97900.8i | −0.107466 | − | 0.219398i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8683.16 | + | 37466.9i | 0.0193432 | + | 0.0834637i | ||||
\(671\) | 209620. | − | 121024.i | 0.465573 | − | 0.268798i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 124260. | − | 215225.i | 0.274348 | − | 0.475184i | −0.695623 | − | 0.718407i | \(-0.744871\pi\) |
0.969970 | + | 0.243223i | \(0.0782047\pi\) | |||||||
\(674\) | −172604. | + | 566269.i | −0.379955 | + | 1.24653i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −200689. | − | 134875.i | −0.439168 | − | 0.295147i | ||||
\(677\) | 134761. | − | 233413.i | 0.294027 | − | 0.509270i | −0.680731 | − | 0.732533i | \(-0.738338\pi\) |
0.974758 | + | 0.223264i | \(0.0716711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −60663.0 | + | 35023.8i | −0.131578 | + | 0.0759668i | ||||
\(680\) | −218244. | − | 83143.9i | −0.471981 | − | 0.179809i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −207737. | − | 222395.i | −0.446627 | − | 0.478140i | ||||
\(683\) | − | 124482.i | − | 0.266848i | −0.991059 | − | 0.133424i | \(-0.957403\pi\) | ||
0.991059 | − | 0.133424i | \(-0.0425972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −126057. | −0.268649 | ||||||||
\(686\) | −166007. | + | 155066.i | −0.352760 | + | 0.329510i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 328246. | + | 254677.i | 0.693461 | + | 0.538038i | ||||
\(689\) | −137247. | − | 237719.i | −0.289111 | − | 0.500756i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −771402. | − | 445369.i | −1.61557 | − | 0.932747i | −0.988048 | − | 0.154145i | \(-0.950738\pi\) |
−0.627518 | − | 0.778602i | \(-0.715929\pi\) | |||||||
\(692\) | 209132. | + | 140549.i | 0.436726 | + | 0.293506i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −554723. | − | 169085.i | −1.15175 | − | 0.351064i | ||||
\(695\) | −636063. | − | 367231.i | −1.31683 | − | 0.760274i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3645.71 | − | 6314.56i | −0.00750442 | − | 0.0129980i | ||||
\(698\) | 697324. | − | 161609.i | 1.43128 | − | 0.331707i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 77497.5 | + | 158216.i | 0.158158 | + | 0.322890i | ||||
\(701\) | 170934. | 0.347851 | 0.173925 | − | 0.984759i | \(-0.444355\pi\) | ||||
0.173925 | + | 0.984759i | \(0.444355\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 47332.1i | − | 0.0957734i | ||||||
\(704\) | −302562. | + | 339464.i | −0.610477 | + | 0.684934i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 102855. | − | 23837.3i | 0.206356 | − | 0.0478242i | ||||
\(707\) | −164752. | + | 95119.7i | −0.329604 | + | 0.190297i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 350963. | − | 607886.i | 0.698183 | − | 1.20929i | −0.270913 | − | 0.962604i | \(-0.587326\pi\) |
0.969096 | − | 0.246684i | \(-0.0793410\pi\) | |||||||
\(710\) | −689028. | − | 210022.i | −1.36685 | − | 0.416628i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −57933.2 | + | 47156.3i | −0.114279 | + | 0.0930206i | ||||
\(713\) | 299744. | − | 519171.i | 0.589618 | − | 1.02125i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 785193. | − | 453331.i | 1.53590 | − | 0.886755i | ||||
\(716\) | 359127. | + | 24504.6i | 0.700522 | + | 0.0477994i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −530147. | + | 495206.i | −1.02837 | + | 0.960587i | ||||
\(719\) | − | 768366.i | − | 1.48631i | −0.669117 | − | 0.743157i | \(-0.733328\pi\) | ||
0.669117 | − | 0.743157i | \(-0.266672\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −135811. | −0.261255 | ||||||||
\(722\) | 353862. | + | 378830.i | 0.678827 | + | 0.726724i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23796.2 | − | 348745.i | 0.0453974 | − | 0.665320i | ||||
\(725\) | −587133. | − | 1.01695e6i | −1.11702 | − | 1.93473i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −221493. | − | 127879.i | −0.419074 | − | 0.241952i | 0.275607 | − | 0.961270i | \(-0.411121\pi\) |
−0.694681 | + | 0.719318i | \(0.744454\pi\) | |||||||
\(728\) | −103052. | − | 126604.i | −0.194444 | − | 0.238882i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 116894. | − | 383497.i | 0.219354 | − | 0.719642i | ||||
\(731\) | 131240. | + | 75771.6i | 0.245602 | + | 0.141799i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −184829. | − | 320133.i | −0.344003 | − | 0.595831i | 0.641169 | − | 0.767400i | \(-0.278450\pi\) |
−0.985172 | + | 0.171569i | \(0.945116\pi\) | |||||||
\(734\) | 188746. | + | 814416.i | 0.350336 | + | 1.51166i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −813429. | − | 375145.i | −1.50163 | − | 0.692539i | ||||
\(737\) | 27314.9 | 0.0502881 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.03557e6i | − | 1.89623i | −0.317932 | − | 0.948114i | \(-0.602988\pi\) | ||
0.317932 | − | 0.948114i | \(-0.397012\pi\) | |||||||
\(740\) | −988415. | + | 484146.i | −1.80500 | + | 0.884123i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14477.7 | − | 62469.6i | −0.0262961 | − | 0.113465i | ||||
\(743\) | −486002. | + | 280593.i | −0.880360 | + | 0.508276i | −0.870777 | − | 0.491678i | \(-0.836384\pi\) |
−0.00958322 | + | 0.999954i | \(0.503050\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −149482. | + | 258910.i | −0.269324 | + | 0.466483i | ||||
\(746\) | −89331.1 | + | 293072.i | −0.160518 | + | 0.526618i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −92520.5 | + | 137667.i | −0.165362 | + | 0.246052i | ||||
\(749\) | −27247.6 | + | 47194.2i | −0.0485696 | + | 0.0841250i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −164898. | + | 95204.1i | −0.292372 | + | 0.168801i | −0.639011 | − | 0.769197i | \(-0.720656\pi\) |
0.346639 | + | 0.937999i | \(0.387323\pi\) | |||||||
\(752\) | −466993. | − | 362327.i | −0.825799 | − | 0.640715i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 742725. | + | 795131.i | 1.30643 | + | 1.39861i | ||||
\(755\) | 43995.1i | 0.0771810i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 523077. | 0.912797 | 0.456398 | − | 0.889776i | \(-0.349139\pi\) | ||||
0.456398 | + | 0.889776i | \(0.349139\pi\) | |||||||
\(758\) | 678508. | − | 633788.i | 1.18091 | − | 1.10308i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −23942.1 | + | 62845.6i | −0.0414510 | + | 0.108805i | ||||
\(761\) | −80448.7 | − | 139341.i | −0.138915 | − | 0.240608i | 0.788171 | − | 0.615456i | \(-0.211028\pi\) |
−0.927086 | + | 0.374848i | \(0.877695\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 50060.1 | + | 28902.2i | 0.0859890 | + | 0.0496458i | ||||
\(764\) | 166763. | − | 248137.i | 0.285702 | − | 0.425114i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −327467. | − | 99815.1i | −0.558097 | − | 0.170113i | ||||
\(767\) | 1.00695e6 | + | 581365.i | 1.71167 | + | 0.988231i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 297804. | + | 515812.i | 0.503591 | + | 0.872246i | 0.999991 | + | 0.00415186i | \(0.00132158\pi\) |
−0.496400 | + | 0.868094i | \(0.665345\pi\) | |||||||
\(770\) | 206339. | − | 47820.2i | 0.348016 | − | 0.0806547i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 662396. | − | 324455.i | 1.11143 | − | 0.544402i | ||||
\(773\) | 583394. | 0.976345 | 0.488172 | − | 0.872747i | \(-0.337664\pi\) | ||||
0.488172 | + | 0.872747i | \(0.337664\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 618255.i | 1.02935i | ||||||||
\(776\) | 58376.0 | + | 362638.i | 0.0969418 | + | 0.602212i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 474381. | − | 109940.i | 0.783732 | − | 0.181634i | ||||
\(779\) | −1818.34 | + | 1049.82i | −0.00299640 | + | 0.00172997i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −255794. | + | 443049.i | −0.419362 | + | 0.726356i | ||||
\(782\) | −312545. | − | 95266.9i | −0.511092 | − | 0.155786i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 217768. | + | 533810.i | 0.354293 | + | 0.868469i | ||||
\(785\) | 68615.2 | − | 118845.i | 0.111348 | − | 0.192860i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 151046. | − | 87206.2i | 0.243870 | − | 0.140798i | −0.373084 | − | 0.927798i | \(-0.621700\pi\) |
0.616954 | + | 0.786999i | \(0.288366\pi\) | |||||||
\(788\) | 17356.2 | − | 254363.i | 0.0279513 | − | 0.409639i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 591759. | − | 552757.i | 0.948180 | − | 0.885687i | ||||
\(791\) | 223918.i | 0.357879i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 455635. | 0.724553 | ||||||||
\(794\) | −195749. | − | 209560.i | −0.310497 | − | 0.332406i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.17700e6 | − | 80311.6i | −1.85760 | − | 0.126751i | ||||
\(797\) | 423576. | + | 733655.i | 0.666829 | + | 1.15498i | 0.978786 | + | 0.204886i | \(0.0656823\pi\) |
−0.311957 | + | 0.950096i | \(0.600984\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −186715. | − | 107800.i | −0.292472 | − | 0.168859i | ||||
\(800\) | 919949. | − | 84391.1i | 1.43742 | − | 0.131861i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 100626. | − | 330127.i | 0.156445 | − | 0.513254i | ||||
\(803\) | −246591. | − | 142369.i | −0.382425 | − | 0.220793i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 208619. | + | 361338.i | 0.321930 | + | 0.557599i | ||||
\(806\) | −129337. | − | 558075.i | −0.199091 | − | 0.859058i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 158541. | + | 984873.i | 0.242839 | + | 1.50854i | ||||
\(809\) | −43118.8 | −0.0658824 | −0.0329412 | − | 0.999457i | \(-0.510487\pi\) | ||||
−0.0329412 | + | 0.999457i | \(0.510487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 372984.i | 0.567085i | 0.958960 | + | 0.283543i | \(0.0915097\pi\) | ||||
−0.958960 | + | 0.283543i | \(0.908490\pi\) | |||||||
\(812\) | 111812. | + | 228271.i | 0.169580 | + | 0.346209i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 176481. | + | 761497.i | 0.266348 | + | 1.14926i | ||||
\(815\) | 1.41966e6 | − | 819638.i | 2.13731 | − | 1.23398i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21819.2 | − | 37791.9i | 0.0326885 | − | 0.0566181i | ||||
\(818\) | 268778. | − | 881791.i | 0.401687 | − | 1.31783i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 40522.2 | + | 27233.3i | 0.0602650 | + | 0.0405017i | ||||
\(821\) | −665022. | + | 1.15185e6i | −0.986620 | + | 1.70888i | −0.352116 | + | 0.935956i | \(0.614538\pi\) |
−0.634504 | + | 0.772920i | \(0.718796\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 636230. | − | 367328.i | 0.939322 | − | 0.542318i | 0.0495745 | − | 0.998770i | \(-0.484213\pi\) |
0.889748 | + | 0.456452i | \(0.150880\pi\) | |||||||
\(824\) | −253530. | + | 665489.i | −0.373400 | + | 0.980136i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 185417. | + | 198500.i | 0.271763 | + | 0.290938i | ||||
\(827\) | 1.27112e6i | 1.85856i | 0.369375 | + | 0.929281i | \(0.379572\pi\) | ||||
−0.369375 | + | 0.929281i | \(0.620428\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −427267. | −0.621714 | −0.310857 | − | 0.950457i | \(-0.600616\pi\) | ||||
−0.310857 | + | 0.950457i | \(0.600616\pi\) | |||||||
\(830\) | 213997. | − | 199893.i | 0.310636 | − | 0.290163i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −812748. | + | 268627.i | −1.17411 | + | 0.388064i | ||||
\(833\) | 105146. | + | 182119.i | 0.151532 | + | 0.262461i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 230588. | + | 133130.i | 0.330723 | + | 0.190943i | ||||
\(836\) | 39642.6 | + | 26642.2i | 0.0567217 | + | 0.0381204i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −212831. | − | 64873.0i | −0.303073 | − | 0.0923796i | ||||
\(839\) | −601815. | − | 347458.i | −0.854947 | − | 0.493604i | 0.00737025 | − | 0.999973i | \(-0.497654\pi\) |
−0.862317 | + | 0.506369i | \(0.830987\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −493464. | − | 854704.i | −0.697691 | − | 1.20844i | ||||
\(842\) | −549327. | + | 127310.i | −0.774830 | + | 0.179571i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 125409. | + | 256030.i | 0.176053 | + | 0.359423i | ||||
\(845\) | 590581. | 0.827115 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28266.7i | 0.0394011i | ||||||||
\(848\) | −333135. | − | 45674.9i | −0.463264 | − | 0.0635164i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 328270. | − | 76078.5i | 0.454354 | − | 0.105299i | ||||
\(851\) | −1.33353e6 | + | 769911.i | −1.84137 | + | 1.06312i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −72314.7 | + | 125253.i | −0.0993867 | + | 0.172143i | −0.911431 | − | 0.411453i | \(-0.865021\pi\) |
0.812044 | + | 0.583596i | \(0.198355\pi\) | |||||||
\(854\) | 101817. | + | 31034.8i | 0.139606 | + | 0.0425534i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 180392. | + | 221618.i | 0.246189 | + | 0.302452i | ||||
\(857\) | −318005. | + | 550800.i | −0.432984 | + | 0.749951i | −0.997129 | − | 0.0757255i | \(-0.975873\pi\) |
0.564145 | + | 0.825676i | \(0.309206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.16908e6 | + | 674970.i | −1.58438 | + | 0.914741i | −0.590168 | + | 0.807281i | \(0.700938\pi\) |
−0.994209 | + | 0.107460i | \(0.965728\pi\) | |||||||
\(860\) | −1.01237e6 | − | 69078.3i | −1.36881 | − | 0.0933996i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 558359. | − | 521558.i | 0.751448 | − | 0.701921i | ||||
\(863\) | − | 916363.i | − | 1.23040i | −0.788372 | − | 0.615199i | \(-0.789076\pi\) | ||
0.788372 | − | 0.615199i | \(-0.210924\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −615427. | −0.822515 | ||||||||
\(866\) | 131727. | + | 141021.i | 0.175646 | + | 0.188039i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9110.47 | − | 133518.i | 0.0120921 | − | 0.177215i | ||||
\(869\) | −287555. | − | 498060.i | −0.380786 | − | 0.659541i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44529.3 | + | 25709.0i | 0.0586961 | + | 0.0338882i | ||||
\(872\) | 235076. | − | 191346.i | 0.309154 | − | 0.251644i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −27433.0 | + | 90000.5i | −0.0359129 | + | 0.117821i | ||||
\(875\) | −114485. | − | 66097.9i | −0.149531 | − | 0.0863319i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 273128. | + | 473071.i | 0.355113 | + | 0.615074i | 0.987137 | − | 0.159875i | \(-0.0511090\pi\) |
−0.632024 | + | 0.774949i | \(0.717776\pi\) | |||||||
\(878\) | 236799. | + | 1.02176e6i | 0.307178 | + | 1.32544i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 150865. | − | 1.10035e6i | 0.194816 | − | 1.42091i | ||||
\(881\) | −446863. | −0.575735 | −0.287867 | − | 0.957670i | \(-0.592946\pi\) | ||||
−0.287867 | + | 0.957670i | \(0.592946\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 140436.i | − | 0.180119i | −0.995936 | − | 0.0900593i | \(-0.971294\pi\) | ||
0.995936 | − | 0.0900593i | \(-0.0287056\pi\) | |||||||
\(884\) | −280402. | + | 137346.i | −0.358820 | + | 0.175757i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 82165.5 | + | 354535.i | 0.104670 | + | 0.451639i | ||||
\(887\) | 307169. | − | 177344.i | 0.390418 | − | 0.225408i | −0.291923 | − | 0.956442i | \(-0.594295\pi\) |
0.682341 | + | 0.731034i | \(0.260962\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −49854.7 | + | 86350.9i | −0.0630816 | + | 0.109261i | ||||
\(890\) | 53195.5 | − | 174520.i | 0.0671575 | − | 0.220326i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 601358. | − | 894798.i | 0.755794 | − | 1.12459i | ||||
\(893\) | −31042.0 | + | 53766.3i | −0.0389266 | + | 0.0674229i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −761394. | + | 439591.i | −0.950525 | + | 0.548786i | ||||
\(896\) | −199916. | + | 4668.90i | −0.249018 | + | 0.00581565i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −773674. | − | 828264.i | −0.959412 | − | 1.02711i | ||||
\(899\) | 892005.i | 1.10369i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −122652. | −0.151086 | ||||||||
\(902\) | 25339.8 | − | 23669.7i | 0.0311452 | − | 0.0290924i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.09723e6 | + | 418007.i | 1.34264 | + | 0.511501i | ||||
\(905\) | 426883. | + | 739383.i | 0.521209 | + | 0.902760i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.27955e6 | + | 738746.i | 1.55540 | + | 0.898008i | 0.997687 | + | 0.0679717i | \(0.0216528\pi\) |
0.557709 | + | 0.830037i | \(0.311681\pi\) | |||||||
\(908\) | −560422. | + | 833887.i | −0.679741 | + | 1.01143i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 381386. | + | 116250.i | 0.460555 | + | 0.140382i | ||||
\(911\) | −41701.0 | − | 24076.1i | −0.0502470 | − | 0.0290101i | 0.474666 | − | 0.880166i | \(-0.342569\pi\) |
−0.524913 | + | 0.851156i | \(0.675902\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −103988. | − | 180113.i | −0.124751 | − | 0.216074i | ||||
\(914\) | −773317. | + | 179221.i | −0.925690 | + | 0.214534i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −588065. | + | 288046.i | −0.700865 | + | 0.343297i | ||||
\(917\) | −128687. | −0.153036 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 346372.i | 0.410120i | 0.978749 | + | 0.205060i | \(0.0657390\pi\) | ||||
−0.978749 | + | 0.205060i | \(0.934261\pi\) | |||||||
\(920\) | 2.16004e6 | − | 347716.i | 2.55204 | − | 0.410817i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −813225. | + | 188469.i | −0.956641 | + | 0.221707i | ||||
\(923\) | −834000. | + | 481510.i | −0.978955 | + | 0.565200i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 794014. | − | 1.37527e6i | 0.927993 | − | 1.60733i | ||||
\(926\) | −100238. | − | 30553.5i | −0.116899 | − | 0.0356319i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.32728e6 | − | 121758.i | 1.54123 | − | 0.141384i | ||||
\(929\) | 435392. | − | 754120.i | 0.504485 | − | 0.873794i | −0.495501 | − | 0.868607i | \(-0.665016\pi\) |
0.999987 | − | 0.00518706i | \(-0.00165110\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 52442.9 | − | 30277.9i | 0.0605044 | − | 0.0349322i | ||||
\(932\) | 86324.9 | − | 1.26513e6i | 0.0993812 | − | 1.45648i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 282396. | − | 263783.i | 0.323716 | − | 0.302380i | ||||
\(935\) | − | 405122.i | − | 0.463407i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.00280e6 | −1.14219 | −0.571094 | − | 0.820885i | \(-0.693481\pi\) | ||||
−0.571094 | + | 0.820885i | \(0.693481\pi\) | |||||||
\(938\) | 8199.48 | + | 8778.03i | 0.00931924 | + | 0.00997680i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.44030e6 | + | 98277.2i | 1.63003 | + | 0.111224i | ||||
\(941\) | −630949. | − | 1.09284e6i | −0.712550 | − | 1.23417i | −0.963897 | − | 0.266275i | \(-0.914207\pi\) |
0.251348 | − | 0.967897i | \(-0.419126\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 59154.8 | + | 34153.0i | 0.0665222 | + | 0.0384066i | ||||
\(944\) | 1.31881e6 | − | 538010.i | 1.47992 | − | 0.603735i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −210125. | + | 689366.i | −0.234799 | + | 0.770314i | ||||
\(947\) | 162072. | + | 93572.3i | 0.180721 | + | 0.104339i | 0.587631 | − | 0.809129i | \(-0.300061\pi\) |
−0.406910 | + | 0.913468i | \(0.633394\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −267998. | − | 464186.i | −0.297577 | − | 0.515418i | ||||
\(950\) | −21907.6 | − | 94528.7i | −0.0242743 | − | 0.104741i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −72014.3 | + | 11592.6i | −0.0794593 | + | 0.0127911i | ||||
\(953\) | −194925. | −0.214626 | −0.107313 | − | 0.994225i | \(-0.534225\pi\) | ||||
−0.107313 | + | 0.994225i | \(0.534225\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 730210.i | 0.800647i | ||||||||
\(956\) | −317640. | − | 648482.i | −0.347551 | − | 0.709549i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30933.8 | + | 133476.i | 0.0337056 | + | 0.145436i | ||||
\(959\) | −34095.8 | + | 19685.2i | −0.0370735 | + | 0.0214044i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −226939. | + | 393070.i | −0.245732 | + | 0.425621i | ||||
\(962\) | −429023. | + | 1.40751e6i | −0.463586 | + | 1.52090i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.00465e6 | − | 675187.i | −1.08109 | − | 0.726557i | ||||
\(965\) | −900757. | + | 1.56016e6i | −0.967281 | + | 1.67538i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 374342. | − | 216127.i | 0.400328 | − | 0.231129i | −0.286298 | − | 0.958141i | \(-0.592425\pi\) |
0.686625 | + | 0.727011i | \(0.259091\pi\) | |||||||
\(968\) | 138510. | + | 52767.9i | 0.147819 | + | 0.0563143i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −612387. | − | 655597.i | −0.650852 | − | 0.696776i | ||||
\(971\) | − | 756598.i | − | 0.802467i | −0.915976 | − | 0.401233i | \(-0.868582\pi\) | ||
0.915976 | − | 0.401233i | \(-0.131418\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −229389. | −0.242296 | ||||||||
\(974\) | 203219. | − | 189825.i | 0.214213 | − | 0.200095i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 342145. | − | 440980.i | 0.359179 | − | 0.462934i | ||||
\(977\) | 903593. | + | 1.56507e6i | 0.946638 | + | 1.63962i | 0.752438 | + | 0.658663i | \(0.228878\pi\) |
0.194200 | + | 0.980962i | \(0.437789\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −112217. | − | 64788.8i | −0.117083 | − | 0.0675981i | ||||
\(980\) | −1.16870e6 | − | 785438.i | −1.21689 | − | 0.817824i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 770102. | + | 234735.i | 0.798593 | + | 0.243419i | ||||
\(983\) | −181852. | − | 104992.i | −0.188196 | − | 0.108655i | 0.402942 | − | 0.915226i | \(-0.367988\pi\) |
−0.591138 | + | 0.806570i | \(0.701321\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 311354. | + | 539282.i | 0.320910 | + | 0.555832i | ||||
\(986\) | 473622. | − | 109765.i | 0.487167 | − | 0.112904i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 39550.2 | + | 80744.4i | 0.0405168 | + | 0.0827178i | ||||
\(989\) | −1.41966e6 | −1.45141 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.66713e6i | − | 1.69755i | −0.528754 | − | 0.848775i | \(-0.677341\pi\) | ||
0.528754 | − | 0.848775i | \(-0.322659\pi\) | |||||||
\(992\) | −637247. | − | 293892.i | −0.647567 | − | 0.298651i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −219165. | + | 50792.7i | −0.221819 | + | 0.0514077i | ||||
\(995\) | 2.49540e6 | − | 1.44072e6i | 2.52054 | − | 1.45523i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −671417. | + | 1.16293e6i | −0.675464 | + | 1.16994i | 0.300869 | + | 0.953666i | \(0.402723\pi\) |
−0.976333 | + | 0.216273i | \(0.930610\pi\) | |||||||
\(998\) | 206992. | + | 63093.3i | 0.207823 | + | 0.0633464i | ||||
\(999\) | 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 | 108.5.f.a.19.17 | 44 | ||
3.2 | odd | 2 | 36.5.f.a.7.6 | ✓ | 44 | ||
4.3 | odd | 2 | inner | 108.5.f.a.19.2 | 44 | ||
9.2 | odd | 6 | 324.5.d.f.163.10 | 22 | |||
9.4 | even | 3 | inner | 108.5.f.a.91.2 | 44 | ||
9.5 | odd | 6 | 36.5.f.a.31.21 | yes | 44 | ||
9.7 | even | 3 | 324.5.d.e.163.13 | 22 | |||
12.11 | even | 2 | 36.5.f.a.7.21 | yes | 44 | ||
36.7 | odd | 6 | 324.5.d.e.163.14 | 22 | |||
36.11 | even | 6 | 324.5.d.f.163.9 | 22 | |||
36.23 | even | 6 | 36.5.f.a.31.6 | yes | 44 | ||
36.31 | odd | 6 | inner | 108.5.f.a.91.17 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.6 | ✓ | 44 | 3.2 | odd | 2 | ||
36.5.f.a.7.21 | yes | 44 | 12.11 | even | 2 | ||
36.5.f.a.31.6 | yes | 44 | 36.23 | even | 6 | ||
36.5.f.a.31.21 | yes | 44 | 9.5 | odd | 6 | ||
108.5.f.a.19.2 | 44 | 4.3 | odd | 2 | inner | ||
108.5.f.a.19.17 | 44 | 1.1 | even | 1 | trivial | ||
108.5.f.a.91.2 | 44 | 9.4 | even | 3 | inner | ||
108.5.f.a.91.17 | 44 | 36.31 | odd | 6 | inner | ||
324.5.d.e.163.13 | 22 | 9.7 | even | 3 | |||
324.5.d.e.163.14 | 22 | 36.7 | odd | 6 | |||
324.5.d.f.163.9 | 22 | 36.11 | even | 6 | |||
324.5.d.f.163.10 | 22 | 9.2 | odd | 6 |