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 | 19.2 | ||
Character | \(\chi\) | \(=\) | 108.19 |
Dual form | 108.5.f.a.91.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.89672 | − | 0.903087i | −0.974180 | − | 0.225772i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 14.3689 | + | 7.03816i | 0.898054 | + | 0.439885i | ||||
\(5\) | −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 | 0.603964 | − | 0.797011i | \(-0.293587\pi\) |
−0.388250 | + | 0.921554i | \(0.626920\pi\) | |||||||
\(8\) | −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 | 0.841574 | − | 0.540142i | \(-0.181630\pi\) |
−0.0469902 | + | 0.998895i | \(0.514963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −104.491 | − | 180.984i | −0.618290 | − | 1.07091i | −0.989798 | − | 0.142480i | \(-0.954492\pi\) |
0.371507 | − | 0.928430i | \(-0.378841\pi\) | |||||||
\(14\) | −35.6772 | − | 33.3258i | −0.182027 | − | 0.170030i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 156.929 | + | 202.261i | 0.613003 | + | 0.790081i | ||||
\(17\) | −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 | \(-0.988142\pi\) | ||
0.999306 | − | 0.0372429i | \(-0.0118575\pi\) | |||||||
\(20\) | −42.5651 | − | 623.812i | −0.106413 | − | 1.55953i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −324.519 | − | 303.130i | −0.670494 | − | 0.626303i | ||||
\(23\) | −757.577 | + | 437.387i | −1.43209 | + | 0.826819i | −0.997280 | − | 0.0737029i | \(-0.976518\pi\) |
−0.434812 | + | 0.900521i | \(0.643185\pi\) | |||||||
\(24\) | 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 | −0.775925 | − | 0.630825i | \(-0.782717\pi\) |
0.158348 | + | 0.987383i | \(0.449383\pi\) | |||||||
\(32\) | −428.848 | − | 929.874i | −0.418797 | − | 0.908080i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 363.872 | + | 84.3293i | 0.314768 | + | 0.0729493i | ||||
\(35\) | − | 476.966i | − | 0.389360i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1760.25 | −1.28579 | −0.642897 | − | 0.765953i | \(-0.722268\pi\) | ||||
−0.642897 | + | 0.765953i | \(0.722268\pi\) | |||||||
\(38\) | −24.2835 | + | 104.780i | −0.0168168 | + | 0.0725626i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −397.492 | + | 2469.26i | −0.248432 | + | 1.54329i | ||||
\(41\) | 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 | 0.829338 | − | 0.558747i | \(-0.188718\pi\) |
−0.0692198 | + | 0.997601i | \(0.522051\pi\) | |||||||
\(44\) | 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 | −0.0263007 | − | 0.999654i | \(-0.508373\pi\) |
−0.878876 | + | 0.477050i | \(0.841706\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1126.02 | − | 1950.32i | −0.468978 | − | 0.812294i | ||||
\(50\) | 2463.31 | − | 2637.12i | 0.985323 | − | 1.05485i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −227.626 | − | 3335.96i | −0.0841811 | − | 1.23371i | ||||
\(53\) | 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 | ||||||
\(56\) | −278.089 | − | 729.956i | −0.0886764 | − | 0.232767i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3554.01 | − | 3804.78i | 1.05648 | − | 1.13103i | ||||
\(59\) | 4818.38 | − | 2781.89i | 1.38419 | − | 0.799164i | 0.391540 | − | 0.920161i | \(-0.371942\pi\) |
0.992653 | + | 0.120997i | \(0.0386091\pi\) | |||||||
\(60\) | 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 | −0.476079 | − | 0.879403i | \(-0.657942\pi\) |
0.523545 | + | 0.851998i | \(0.324609\pi\) | |||||||
\(68\) | −1341.75 | − | 657.216i | −0.290171 | − | 0.142131i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −430.742 | + | 1858.60i | −0.0879065 | + | 0.379307i | ||||
\(71\) | 4608.15i | 0.914134i | 0.889432 | + | 0.457067i | \(0.151100\pi\) | ||||
−0.889432 | + | 0.457067i | \(0.848900\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2564.79 | 0.481290 | 0.240645 | − | 0.970613i | \(-0.422641\pi\) | ||||
0.240645 | + | 0.970613i | \(0.422641\pi\) | |||||||
\(74\) | 6859.21 | + | 1589.66i | 1.25259 | + | 0.290296i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 189.252 | − | 386.370i | 0.0327652 | − | 0.0668923i | ||||
\(77\) | 677.500 | + | 1173.46i | 0.114269 | + | 0.197919i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4486.29 | − | 2590.16i | −0.718842 | − | 0.415023i | 0.0954846 | − | 0.995431i | \(-0.469560\pi\) |
−0.814326 | + | 0.580408i | \(0.802893\pi\) | |||||||
\(80\) | 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 | 0.377606 | − | 0.925966i | \(-0.376747\pi\) |
−0.613108 | + | 0.789999i | \(0.710081\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1824.57 | + | 3160.25i | 0.252536 | + | 0.437405i | ||||
\(86\) | −4743.88 | − | 4431.22i | −0.641411 | − | 0.599137i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2529.49 | − | 6639.66i | −0.326639 | − | 0.857394i | ||||
\(89\) | 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 | ||||||
\(92\) | −13963.9 | + | 952.813i | −1.64980 | + | 0.112572i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6749.08 | + | 6304.26i | 0.763816 | + | 0.713474i | ||||
\(95\) | −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 | −0.879895 | − | 0.475168i | \(-0.842387\pi\) |
−0.0284395 | + | 0.999596i | \(0.509054\pi\) | |||||||
\(104\) | −2125.67 | + | 13204.9i | −0.196530 | + | 1.22086i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5118.28 | − | 1186.19i | −0.455525 | − | 0.105570i | ||||
\(107\) | 4464.91i | 0.389983i | 0.980805 | + | 0.194991i | \(0.0624679\pi\) | ||||
−0.980805 | + | 0.194991i | \(0.937532\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4736.05 | −0.398624 | −0.199312 | − | 0.979936i | \(-0.563871\pi\) | ||||
−0.199312 | + | 0.979936i | \(0.563871\pi\) | |||||||
\(110\) | −3918.02 | + | 16905.8i | −0.323803 | + | 1.39717i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 424.422 | + | 3095.57i | 0.0338347 | + | 0.246777i | ||||
\(113\) | −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 | ||||
\(122\) | 5953.10 | − | 6373.14i | 0.399966 | − | 0.428188i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10939.4 | + | 746.442i | −0.711462 | + | 0.0485459i | ||||
\(125\) | 10831.1 | 0.693190 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8169.42i | 0.506505i | 0.967400 | + | 0.253252i | \(0.0815003\pi\) | ||||
−0.967400 | + | 0.253252i | \(0.918500\pi\) | |||||||
\(128\) | 382.534 | − | 16379.5i | 0.0233480 | − | 0.999727i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 22299.1 | − | 23872.5i | 1.31947 | − | 1.41257i | ||||
\(131\) | −9131.01 | + | 5271.79i | −0.532079 | + | 0.307196i | −0.741863 | − | 0.670552i | \(-0.766057\pi\) |
0.209784 | + | 0.977748i | \(0.432724\pi\) | |||||||
\(132\) | 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 | −0.858086 | − | 0.513506i | \(-0.828346\pi\) |
0.0156666 | + | 0.999877i | \(0.495013\pi\) | |||||||
\(140\) | 3356.96 | − | 6853.46i | 0.171274 | − | 0.349666i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4161.56 | − | 17956.7i | 0.206386 | − | 0.890531i | ||||
\(143\) | − | 23200.8i | − | 1.13457i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 50865.8 | 2.41930 | ||||||||
\(146\) | −9994.28 | − | 2316.23i | −0.468863 | − | 0.108662i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −25292.8 | − | 12388.9i | −1.15471 | − | 0.565601i | ||||
\(149\) | −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 | 0.521228 | − | 0.853418i | \(-0.325474\pi\) |
−0.478468 | + | 0.878105i | \(0.658808\pi\) | |||||||
\(152\) | −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 | \(0.810640\pi\) | |||||||
\(158\) | 15142.7 | + | 14144.6i | 0.606581 | + | 0.566602i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −23090.6 | + | 32682.9i | −0.901975 | + | 1.27667i | ||||
\(161\) | −10676.8 | −0.411898 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 41947.9i | − | 1.57883i | −0.613861 | − | 0.789414i | \(-0.710385\pi\) | ||
0.613861 | − | 0.789414i | \(-0.289615\pi\) | |||||||
\(164\) | 85.0502 | + | 1246.45i | 0.00316219 | + | 0.0463433i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5476.03 | + | 5115.11i | 0.198724 | + | 0.185626i | ||||
\(167\) | 5900.58 | − | 3406.70i | 0.211574 | − | 0.122152i | −0.390469 | − | 0.920616i | \(-0.627687\pi\) |
0.602043 | + | 0.798464i | \(0.294354\pi\) | |||||||
\(168\) | 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 | ||||
\(176\) | 3860.53 | + | 28157.2i | 0.124630 | + | 0.909002i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4548.15 | − | 1054.06i | −0.143547 | − | 0.0332679i | ||||
\(179\) | 22497.6i | 0.702151i | 0.936347 | + | 0.351075i | \(0.114184\pi\) | ||||
−0.936347 | + | 0.351075i | \(0.885816\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21847.2 | −0.666867 | −0.333434 | − | 0.942774i | \(-0.608207\pi\) | ||||
−0.333434 | + | 0.942774i | \(0.608207\pi\) | |||||||
\(182\) | −2303.48 | + | 9939.25i | −0.0695410 | + | 0.300062i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 55274.0 | + | 8897.79i | 1.63262 | + | 0.262813i | ||||
\(185\) | 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 | 0.705114 | − | 0.709094i | \(-0.250896\pi\) |
−0.261537 | + | 0.965194i | \(0.584229\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23049.7 | − | 39923.2i | −0.618800 | − | 1.07179i | −0.989705 | − | 0.143123i | \(-0.954286\pi\) |
0.370905 | − | 0.928671i | \(-0.379048\pi\) | |||||||
\(194\) | −15670.5 | + | 16776.2i | −0.416371 | + | 0.445750i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2452.94 | − | 35948.9i | −0.0638520 | − | 0.935780i | ||||
\(197\) | −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 | \(-0.618974\pi\) | ||
0.365124 | − | 0.930959i | \(-0.381026\pi\) | |||||||
\(200\) | 53955.4 | − | 20555.2i | 1.34888 | − | 0.513881i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −42558.9 | + | 45561.9i | −1.04301 | + | 1.11660i | ||||
\(203\) | −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 | −0.663189 | − | 0.748452i | \(-0.730797\pi\) |
0.316584 | + | 0.948564i | \(0.397464\pi\) | |||||||
\(212\) | 18873.3 | + | 9244.50i | 0.419929 | + | 0.205689i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4032.20 | − | 17398.5i | 0.0880471 | − | 0.379913i | ||||
\(215\) | − | 63420.5i | − | 1.37200i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8364.29 | −0.177627 | ||||||||
\(218\) | 18455.1 | + | 4277.07i | 0.388332 | + | 0.0899980i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 30534.8 | − | 62338.9i | 0.630885 | − | 1.28799i | ||||
\(221\) | 9757.27 | + | 16900.1i | 0.199776 | + | 0.346022i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 58353.8 | + | 33690.6i | 1.17344 | + | 0.677483i | 0.954487 | − | 0.298253i | \(-0.0964039\pi\) |
0.218949 | + | 0.975736i | \(0.429737\pi\) | |||||||
\(224\) | 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 | −0.131212 | − | 0.991354i | \(-0.541887\pi\) |
−0.924144 | + | 0.382044i | \(0.875220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20463.2 | + | 35443.2i | 0.390213 | + | 0.675868i | 0.992477 | − | 0.122428i | \(-0.0390681\pi\) |
−0.602265 | + | 0.798297i | \(0.705735\pi\) | |||||||
\(230\) | −99927.3 | − | 93341.2i | −1.88898 | − | 1.76448i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 77845.7 | − | 29656.7i | 1.44630 | − | 0.550993i | ||||
\(233\) | −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 | ||||||||
\(236\) | 88814.0 | − | 6060.13i | 1.59462 | − | 0.108807i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3331.50 | + | 3111.93i | 0.0588148 | + | 0.0549383i | ||||
\(239\) | 39084.7 | − | 22565.5i | 0.684243 | − | 0.395048i | −0.117209 | − | 0.993107i | \(-0.537395\pi\) |
0.801452 | + | 0.598059i | \(0.204061\pi\) | |||||||
\(240\) | 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 | ||||
\(248\) | 43302.1 | + | 6970.60i | 0.704053 | + | 0.113336i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −42205.8 | − | 9781.43i | −0.675292 | − | 0.156503i | ||||
\(251\) | 78270.9i | 1.24238i | 0.783662 | + | 0.621188i | \(0.213350\pi\) | ||||
−0.783662 | + | 0.621188i | \(0.786650\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −97115.9 | −1.51722 | ||||||||
\(254\) | 7377.70 | − | 31833.9i | 0.114355 | − | 0.493427i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16282.8 | + | 63481.0i | −0.248455 | + | 0.968643i | ||||
\(257\) | −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 | −0.154765 | − | 0.987951i | \(-0.549462\pi\) |
−0.932973 | + | 0.359945i | \(0.882795\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25664.7 | − | 44452.6i | −0.365464 | − | 0.633003i | ||||
\(266\) | −896.110 | + | 959.339i | −0.0126648 | + | 0.0135584i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3927.51 | − | 267.990i | 0.0546824 | − | 0.00373120i | ||||
\(269\) | 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 | \(0.105870\pi\) | ||||
−0.945197 | + | 0.326502i | \(0.894130\pi\) | |||||||
\(272\) | −14653.8 | − | 18886.9i | −0.198068 | − | 0.255284i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8807.65 | + | 9429.11i | −0.117316 | + | 0.125594i | ||||
\(275\) | −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 | \(-0.263876\pi\) |
0.976287 | − | 0.216481i | \(-0.0694578\pi\) | |||||||
\(284\) | −32432.9 | + | 66213.9i | −0.402114 | + | 0.820942i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20952.4 | + | 90407.1i | −0.256154 | + | 1.10528i | ||||
\(287\) | 953.034i | 0.0115703i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −74801.4 | −0.895600 | ||||||||
\(290\) | −198210. | − | 45936.2i | −2.35683 | − | 0.546210i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 36853.2 | + | 18051.4i | 0.432224 | + | 0.211712i | ||||
\(293\) | −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 | ||||
\(302\) | −3290.85 | − | 3073.96i | −0.0360823 | − | 0.0337042i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5438.67 | − | 4219.72i | 0.0588498 | − | 0.0456600i | ||||
\(305\) | 85202.0 | 0.915905 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 457.528i | 0.00485446i | 0.999997 | + | 0.00242723i | \(0.000772612\pi\) | ||||
−0.999997 | + | 0.00242723i | \(0.999227\pi\) | |||||||
\(308\) | 1475.88 | + | 21629.7i | 0.0155579 | + | 0.228008i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −78283.9 | − | 73124.3i | −0.814608 | − | 0.760919i | ||||
\(311\) | −9285.82 | + | 5361.17i | −0.0960062 | + | 0.0554292i | −0.547234 | − | 0.836979i | \(-0.684319\pi\) |
0.451228 | + | 0.892409i | \(0.350986\pi\) | |||||||
\(312\) | 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 | ||||
\(320\) | 119493. | − | 106503.i | 1.16692 | − | 1.04007i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 41604.5 | + | 9642.08i | 0.401262 | + | 0.0929949i | ||||
\(323\) | 2510.90i | 0.0240672i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 188535. | 1.78495 | ||||||||
\(326\) | −37882.6 | + | 163459.i | −0.356455 | + | 1.53806i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 794.236 | − | 4933.87i | 0.00738247 | − | 0.0458607i | ||||
\(329\) | −14090.1 | − | 24404.7i | −0.130173 | − | 0.225467i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 160993. | + | 92949.3i | 1.46944 | + | 0.848379i | 0.999412 | − | 0.0342747i | \(-0.0109121\pi\) |
0.470023 | + | 0.882654i | \(0.344245\pi\) | |||||||
\(332\) | −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 | \(0.607442\pi\) | |||||||
\(338\) | 41264.1 | − | 44175.7i | 0.361193 | − | 0.386678i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3974.69 | + | 58250.9i | 0.0343831 | + | 0.503901i | ||||
\(341\) | −76081.3 | −0.654289 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 56791.2i | − | 0.482717i | ||||||
\(344\) | −36976.6 | − | 97059.7i | −0.312471 | − | 0.820204i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −43000.1 | + | 46034.1i | −0.359184 | + | 0.384528i | ||||
\(347\) | 125556. | − | 72490.0i | 1.04275 | − | 0.602031i | 0.122138 | − | 0.992513i | \(-0.461025\pi\) |
0.920611 | + | 0.390482i | \(0.127692\pi\) | |||||||
\(348\) | 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 | ||||
\(356\) | 16771.0 | + | 8214.76i | 0.132330 | + | 0.0648179i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20317.3 | − | 87666.9i | 0.158526 | − | 0.684022i | ||||
\(359\) | − | 181364.i | − | 1.40722i | −0.710587 | − | 0.703609i | \(-0.751571\pi\) | ||
0.710587 | − | 0.703609i | \(-0.248429\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 129598. | 0.994452 | ||||||||
\(362\) | 85132.6 | + | 19730.0i | 0.649649 | + | 0.150560i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 17952.0 | − | 36650.2i | 0.135491 | − | 0.276614i | ||||
\(365\) | −50114.6 | − | 86801.1i | −0.376165 | − | 0.651537i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −181000. | − | 104500.i | −1.34383 | − | 0.775863i | −0.356467 | − | 0.934308i | \(-0.616019\pi\) |
−0.987368 | + | 0.158445i | \(0.949352\pi\) | |||||||
\(368\) | −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 | \(0.744566\pi\) | |||||||
\(374\) | 30303.3 | + | 28306.0i | 0.216644 | + | 0.202365i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 52606.3 | + | 138086.i | 0.372102 | + | 0.976729i | ||||
\(377\) | 272015. | 1.91386 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 232118.i | 1.61596i | 0.589211 | + | 0.807979i | \(0.299439\pi\) | ||||
−0.589211 | + | 0.807979i | \(0.700561\pi\) | |||||||
\(380\) | −16773.9 | + | 1144.55i | −0.116163 | + | 0.00792625i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −54620.0 | − | 51020.0i | −0.374304 | − | 0.349634i | ||||
\(383\) | 74119.1 | − | 42792.7i | 0.505280 | − | 0.291724i | −0.225611 | − | 0.974217i | \(-0.572438\pi\) |
0.730891 | + | 0.682494i | \(0.239105\pi\) | |||||||
\(384\) | 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 | ||||
\(392\) | −22906.6 | + | 142298.i | −0.149069 | + | 0.926035i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 62092.9 | + | 14390.4i | 0.399990 | + | 0.0927001i | ||||
\(395\) | 202441.i | 1.29749i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −71690.8 | −0.454865 | −0.227432 | − | 0.973794i | \(-0.573033\pi\) | ||||
−0.227432 | + | 0.973794i | \(0.573033\pi\) | |||||||
\(398\) | −66588.0 | + | 287320.i | −0.420368 | + | 1.81384i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −228812. | + | 31371.6i | −1.43008 | + | 0.196073i | ||||
\(401\) | −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 | \(-0.408548\pi\) | |||||||
\(410\) | −8331.84 | + | 8919.73i | −0.0495648 | + | 0.0530620i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −177624. | + | 12120.0i | −1.04642 | + | 0.0714015i | ||||
\(413\) | 67907.1 | 0.398121 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 73208.6i | 0.425075i | ||||||||
\(416\) | −123481. | + | 174778.i | −0.713534 | + | 1.00995i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8150.99 | + | 8726.12i | −0.0466507 | + | 0.0499423i | ||||
\(419\) | 48172.3 | − | 27812.3i | 0.274391 | − | 0.158420i | −0.356491 | − | 0.934299i | \(-0.616027\pi\) |
0.630881 | + | 0.775879i | \(0.282693\pi\) | |||||||
\(420\) | 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 | ||||
\(428\) | −31424.7 | + | 64155.7i | −0.171547 | + | 0.350225i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −57274.3 | + | 247132.i | −0.309758 | + | 1.33657i | ||||
\(431\) | 191015.i | 1.02828i | 0.857705 | + | 0.514142i | \(0.171889\pi\) | ||||
−0.857705 | + | 0.514142i | \(0.828111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 48243.4 | 0.257313 | 0.128657 | − | 0.991689i | \(-0.458933\pi\) | ||||
0.128657 | + | 0.991689i | \(0.458933\pi\) | |||||||
\(434\) | 32593.3 | + | 7553.68i | 0.173041 | + | 0.0401032i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −68051.7 | − | 33333.1i | −0.357986 | − | 0.175349i | ||||
\(437\) | 11761.1 | + | 20370.8i | 0.0615863 | + | 0.106671i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −227081. | − | 131105.i | −1.17829 | − | 0.680285i | −0.222670 | − | 0.974894i | \(-0.571477\pi\) |
−0.955618 | + | 0.294609i | \(0.904811\pi\) | |||||||
\(440\) | −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 | 0.285632 | − | 0.958339i | \(-0.407796\pi\) |
−0.687130 | + | 0.726534i | \(0.741130\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22805.9 | − | 39501.0i | −0.115167 | − | 0.199475i | ||||
\(446\) | −196963. | − | 183981.i | −0.990181 | − | 0.924920i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −15688.7 | + | 47467.0i | −0.0781681 | + | 0.236503i | ||||
\(449\) | −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 | ||||||||
\(452\) | −19982.8 | − | 292857.i | −0.0978091 | − | 1.43344i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 183555. | + | 171457.i | 0.890542 | + | 0.831848i | ||||
\(455\) | −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 | −0.446148 | − | 0.894959i | \(-0.647204\pi\) |
0.551984 | + | 0.833855i | \(0.313871\pi\) | |||||||
\(464\) | −330126. | + | 45262.3i | −1.53336 | + | 0.210233i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 308833. | + | 71573.7i | 1.42217 | + | 0.329596i | ||||
\(467\) | 96607.8i | 0.442974i | 0.975163 | + | 0.221487i | \(0.0710911\pi\) | ||||
−0.975163 | + | 0.221487i | \(0.928909\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3002.97 | 0.0136523 | ||||||||
\(470\) | 81483.6 | − | 351593.i | 0.368871 | − | 1.59164i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −351556. | − | 56592.1i | −1.57801 | − | 0.254022i | ||||
\(473\) | 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 | 0.433960 | − | 0.900932i | \(-0.357116\pi\) |
−0.563250 | + | 0.826287i | \(0.690449\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 183931. | + | 318577.i | 0.794994 | + | 1.37697i | ||||
\(482\) | 206569. | − | 221144.i | 0.889141 | − | 0.951878i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2522.57 | − | 36969.4i | −0.0107684 | − | 0.157816i | ||||
\(485\) | −224280. | −0.953470 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 69521.4i | 0.293130i | 0.989201 | + | 0.146565i | \(0.0468218\pi\) | ||||
−0.989201 | + | 0.146565i | \(0.953178\pi\) | |||||||
\(488\) | 130394. | − | 49676.0i | 0.547545 | − | 0.208597i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 240299. | − | 257255.i | 1.00083 | − | 1.07145i | ||||
\(491\) | −174305. | + | 100635.i | −0.723016 | + | 0.417433i | −0.815862 | − | 0.578247i | \(-0.803737\pi\) |
0.0928458 | + | 0.995681i | \(0.470404\pi\) | |||||||
\(492\) | 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 | −0.591119 | − | 0.806585i | \(-0.701313\pi\) |
0.402964 | + | 0.915216i | \(0.367980\pi\) | |||||||
\(500\) | 155631. | + | 76231.0i | 0.622522 | + | 0.304924i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 70685.5 | − | 305000.i | 0.280493 | − | 1.21030i | ||||
\(503\) | − | 239548.i | − | 0.946795i | −0.880849 | − | 0.473397i | \(-0.843027\pi\) | ||
0.880849 | − | 0.473397i | \(-0.156973\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −609113. | −2.38844 | ||||||||
\(506\) | 378433. | + | 87704.1i | 1.47805 | + | 0.342546i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −57497.6 | + | 117385.i | −0.222804 | + | 0.454869i | ||||
\(509\) | 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 | ||||
\(518\) | 62800.9 | + | 58661.8i | 0.234049 | + | 0.218623i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 488431. | − | 186076.i | 1.80633 | − | 0.688151i | ||||
\(521\) | −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 | \(-0.976890\pi\) | ||
0.997366 | − | 0.0725397i | \(-0.0231104\pi\) | |||||||
\(524\) | −168306. | + | 11484.2i | −0.612967 | + | 0.0418251i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 253952. | + | 237214.i | 0.917867 | + | 0.857372i | ||||
\(527\) | 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 | ||||
\(536\) | −15546.4 | − | 2502.60i | −0.0541129 | − | 0.00871089i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −210747. | − | 48841.9i | −0.728111 | − | 0.168744i | ||||
\(539\) | − | 250017.i | − | 0.860580i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −194992. | −0.666228 | −0.333114 | − | 0.942887i | \(-0.608099\pi\) | ||||
−0.333114 | + | 0.942887i | \(0.608099\pi\) | |||||||
\(542\) | 43309.6 | − | 186876.i | 0.147430 | − | 0.636143i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 40045.4 | + | 86830.7i | 0.135318 | + | 0.293410i | ||||
\(545\) | 92539.8 | + | 160284.i | 0.311556 | + | 0.539630i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −81637.9 | − | 47133.6i | −0.272846 | − | 0.157527i | 0.357335 | − | 0.933976i | \(-0.383686\pi\) |
−0.630180 | + | 0.776449i | \(0.717019\pi\) | |||||||
\(548\) | 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 | ||||
\(554\) | −201299. | + | 215502.i | −0.655876 | + | 0.702154i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −300012. | + | 20471.0i | −0.970485 | + | 0.0662201i | ||||
\(557\) | 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 | ||||||
\(560\) | 96471.5 | − | 74849.6i | 0.307626 | − | 0.238679i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −153244. | + | 164057.i | −0.485189 | + | 0.519423i | ||||
\(563\) | −543509. | + | 313795.i | −1.71471 | + | 0.989986i | −0.786771 | + | 0.617245i | \(0.788249\pi\) |
−0.927935 | + | 0.372741i | \(0.878418\pi\) | |||||||
\(564\) | 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 | −0.0127640 | − | 0.999919i | \(-0.504063\pi\) |
0.859573 | + | 0.511013i | \(0.170730\pi\) | |||||||
\(572\) | 163291. | − | 333370.i | 0.499080 | − | 1.01891i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 860.673 | − | 3713.71i | 0.00261225 | − | 0.0112716i | ||||
\(575\) | − | 789186.i | − | 2.38695i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40053.7 | 0.120307 | 0.0601534 | − | 0.998189i | \(-0.480841\pi\) | ||||
0.0601534 | + | 0.998189i | \(0.480841\pi\) | |||||||
\(578\) | 291480. | + | 67552.2i | 0.872475 | + | 0.202201i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 730883. | + | 358001.i | 2.17266 | + | 1.06421i | ||||
\(581\) | −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 | 0.482641 | − | 0.875818i | \(-0.339678\pi\) |
−0.517161 | + | 0.855888i | \(0.673011\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9213.72 | + | 15958.6i | 0.0265586 | + | 0.0460008i | ||||
\(590\) | 635563. | + | 593673.i | 1.82580 | + | 1.70547i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −276234. | − | 356030.i | −0.788195 | − | 1.01588i | ||||
\(593\) | −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 | ||||||||
\(596\) | −8332.74 | − | 122120.i | −0.0234582 | − | 0.343791i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −534381. | − | 499161.i | −1.49434 | − | 1.39585i | ||||
\(599\) | 394401. | − | 227708.i | 1.09922 | − | 0.634635i | 0.163204 | − | 0.986592i | \(-0.447817\pi\) |
0.936016 | + | 0.351958i | \(0.114484\pi\) | |||||||
\(600\) | 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 | −0.994480 | − | 0.104927i | \(-0.966539\pi\) |
−0.406371 | + | 0.913708i | \(0.633206\pi\) | |||||||
\(608\) | −25003.7 | + | 11531.5i | −0.0676391 | + | 0.0311945i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −332008. | − | 76944.8i | −0.892256 | − | 0.206785i | ||||
\(611\) | 482511.i | 1.29248i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 547275. | 1.45641 | 0.728206 | − | 0.685358i | \(-0.240354\pi\) | ||||
0.728206 | + | 0.685358i | \(0.240354\pi\) | |||||||
\(614\) | 413.188 | − | 1782.86i | 0.00109600 | − | 0.00472912i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13782.4 | − | 85617.8i | 0.0363215 | − | 0.225633i | ||||
\(617\) | 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 | 0.251114 | − | 0.967958i | \(-0.419203\pi\) |
−0.712719 | + | 0.701450i | \(0.752537\pi\) | |||||||
\(620\) | 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 | ||||
\(626\) | 49017.7 | − | 52476.4i | 0.125085 | − | 0.133911i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3824.90 | + | 56055.6i | 0.00969841 | + | 0.142135i | ||||
\(629\) | 164370. | 0.415454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 177036.i | 0.444633i | 0.974975 | + | 0.222317i | \(0.0713618\pi\) | ||||
−0.974975 | + | 0.222317i | \(0.928638\pi\) | |||||||
\(632\) | 118031. | + | 309819.i | 0.295503 | + | 0.775665i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 167573. | − | 179397.i | 0.416894 | − | 0.446310i | ||||
\(635\) | 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 | −0.815869 | − | 0.578237i | \(-0.803741\pi\) |
0.0928336 | + | 0.995682i | \(0.470408\pi\) | |||||||
\(644\) | −153413. | − | 75145.0i | −0.369906 | − | 0.181187i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2267.56 | − | 9784.29i | 0.00543369 | − | 0.0234458i | ||||
\(647\) | 398251.i | 0.951366i | 0.879617 | + | 0.475683i | \(0.157799\pi\) | ||||
−0.879617 | + | 0.475683i | \(0.842201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 617681. | 1.46648 | ||||||||
\(650\) | −734669. | − | 170264.i | −1.73886 | − | 0.402991i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 295236. | − | 602744.i | 0.694502 | − | 1.41787i | ||||
\(653\) | −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 | −0.122175 | − | 0.992509i | \(-0.538987\pi\) |
−0.920625 | + | 0.390447i | \(0.872320\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −154294. | − | 267245.i | −0.353140 | − | 0.611656i | 0.633658 | − | 0.773613i | \(-0.281553\pi\) |
−0.986798 | + | 0.161957i | \(0.948219\pi\) | |||||||
\(662\) | −543403. | − | 507588.i | −1.23996 | − | 1.15823i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 42683.4 | + | 112040.i | 0.0968106 | + | 0.254118i | ||||
\(665\) | −12825.3 | −0.0290018 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.13862e6i | − | 2.55934i | ||||||
\(668\) | 108761. | − | 7421.23i | 0.243737 | − | 0.0166312i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 28105.7 | + | 26253.3i | 0.0626101 | + | 0.0584836i | ||||
\(671\) | −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 | ||||
\(680\) | 37117.4 | − | 230577.i | 0.0802712 | − | 0.498653i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 296468. | + | 68708.1i | 0.637395 | + | 0.147720i | ||||
\(683\) | 124482.i | 0.266848i | 0.991059 | + | 0.133424i | \(0.0425972\pi\) | ||||
−0.991059 | + | 0.133424i | \(0.957403\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −126057. | −0.268649 | ||||||||
\(686\) | −51287.4 | + | 221300.i | −0.108984 | + | 0.470254i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 56434.0 | + | 411608.i | 0.119224 | + | 0.869574i | ||||
\(689\) | −137247. | − | 237719.i | −0.289111 | − | 0.500756i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 771402. | + | 445369.i | 1.61557 | + | 0.932747i | 0.988048 | + | 0.154145i | \(0.0492623\pi\) |
0.627518 | + | 0.778602i | \(0.284071\pi\) | |||||||
\(692\) | 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 | ||||
\(698\) | −488619. | + | 523096.i | −1.00291 | + | 1.07367i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −175768. | + | 11993.3i | −0.358710 | + | 0.0244762i | ||||
\(701\) | 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 | ||||||||
\(704\) | −142704. | + | 431759.i | −0.287932 | + | 0.871156i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −72071.4 | + | 77156.7i | −0.144595 | + | 0.154798i | ||||
\(707\) | 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 | ||||
\(716\) | −158342. | + | 323265.i | −0.308866 | + | 0.630570i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −163787. | + | 706724.i | −0.317710 | + | 1.37088i | ||||
\(719\) | 768366.i | 1.48631i | 0.669117 | + | 0.743157i | \(0.266672\pi\) | ||||
−0.669117 | + | 0.743157i | \(0.733328\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −135811. | −0.261255 | ||||||||
\(722\) | −505007. | − | 117038.i | −0.968775 | − | 0.224519i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −313920. | − | 153764.i | −0.598883 | − | 0.293345i | ||||
\(725\) | −587133. | − | 1.01695e6i | −1.11702 | − | 1.93473i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 221493. | + | 127879.i | 0.419074 | + | 0.241952i | 0.694681 | − | 0.719318i | \(-0.255546\pi\) |
−0.275607 | + | 0.961270i | \(0.588879\pi\) | |||||||
\(728\) | −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 | \(0.945116\pi\) | |||||||
\(734\) | 610932. | + | 570667.i | 1.13397 | + | 1.05923i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 731600. | + | 516878.i | 1.35057 | + | 0.954184i | ||||
\(737\) | 27314.9 | 0.0502881 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.03557e6i | 1.89623i | 0.317932 | + | 0.948114i | \(0.397012\pi\) | ||||
−0.317932 | + | 0.948114i | \(0.602988\pi\) | |||||||
\(740\) | 74925.4 | + | 1.09807e6i | 0.136825 | + | 2.00523i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −46861.4 | − | 43772.9i | −0.0851153 | − | 0.0795055i | ||||
\(743\) | 486002. | − | 280593.i | 0.880360 | − | 0.508276i | 0.00958322 | − | 0.999954i | \(-0.496950\pi\) |
0.870777 | + | 0.491678i | \(0.163616\pi\) | |||||||
\(744\) | 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 | −0.346639 | − | 0.937999i | \(-0.612677\pi\) |
0.639011 | + | 0.769197i | \(0.279344\pi\) | |||||||
\(752\) | −80288.2 | − | 585591.i | −0.141976 | − | 1.03552i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.05997e6 | − | 245653.i | −1.86444 | − | 0.432095i | ||||
\(755\) | − | 43995.1i | − | 0.0771810i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 523077. | 0.912797 | 0.456398 | − | 0.889776i | \(-0.349139\pi\) | ||||
0.456398 | + | 0.889776i | \(0.349139\pi\) | |||||||
\(758\) | 209623. | − | 904499.i | 0.364838 | − | 1.57424i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 66396.9 | + | 10688.3i | 0.114953 | + | 0.0185047i | ||||
\(761\) | −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 | \(0.665345\pi\) | |||||||
\(770\) | −144583. | + | 154785.i | −0.243857 | + | 0.261063i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −50212.0 | − | 735879.i | −0.0842505 | − | 1.23473i | ||||
\(773\) | 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 | ||||||
\(776\) | −343242. | + | 130764.i | −0.570002 | + | 0.217152i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −332401. | + | 355855.i | −0.549166 | + | 0.587915i | ||||
\(779\) | 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 | −0.616954 | − | 0.786999i | \(-0.711634\pi\) |
0.373084 | + | 0.927798i | \(0.378300\pi\) | |||||||
\(788\) | −228963. | − | 112151.i | −0.368734 | − | 0.180613i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 182822. | − | 788857.i | 0.292937 | − | 1.26399i | ||||
\(791\) | − | 223918.i | − | 0.357879i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 455635. | 0.724553 | ||||||||
\(794\) | 279359. | + | 64743.0i | 0.443120 | + | 0.102696i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 518950. | − | 1.05947e6i | 0.819029 | − | 1.67210i | ||||
\(797\) | 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 | ||||
\(806\) | −418638. | − | 391047.i | −0.644420 | − | 0.601947i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −932195. | + | 355136.i | −1.42786 | + | 0.543966i | ||||
\(809\) | −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 | \(-0.908490\pi\) | ||
0.958960 | − | 0.283543i | \(-0.0915097\pi\) | |||||||
\(812\) | −253594. | + | 17303.8i | −0.384616 | + | 0.0262439i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 571235. | + | 533586.i | 0.862117 | + | 0.805296i | ||||
\(815\) | −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 | −0.889748 | − | 0.456452i | \(-0.849120\pi\) |
−0.0495745 | + | 0.998770i | \(0.515787\pi\) | |||||||
\(824\) | 703095. | + | 113182.i | 1.03552 | + | 0.166694i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −264615. | − | 61326.0i | −0.387842 | − | 0.0898845i | ||||
\(827\) | − | 1.27112e6i | − | 1.85856i | −0.369375 | − | 0.929281i | \(-0.620428\pi\) | ||
0.369375 | − | 0.929281i | \(-0.379572\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −427267. | −0.621714 | −0.310857 | − | 0.950457i | \(-0.600616\pi\) | ||||
−0.310857 | + | 0.950457i | \(0.600616\pi\) | |||||||
\(830\) | 66113.8 | − | 285274.i | 0.0959700 | − | 0.414100i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 639012. | − | 569547.i | 0.923129 | − | 0.822779i | ||||
\(833\) | 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 | 0.862317 | − | 0.506369i | \(-0.169013\pi\) |
−0.00737025 | + | 0.999973i | \(0.502346\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −493464. | − | 854704.i | −0.697691 | − | 1.20844i | ||||
\(842\) | 384917. | − | 412076.i | 0.542928 | − | 0.581237i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −284433. | + | 19408.0i | −0.399296 | + | 0.0272456i | ||||
\(845\) | 590581. | 0.827115 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 28266.7i | − | 0.0394011i | ||||||
\(848\) | 206123. | + | 265666.i | 0.286639 | + | 0.369440i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −230021. | + | 246251.i | −0.318368 | + | 0.340832i | ||||
\(851\) | 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 | \(-0.299062\pi\) |
0.994209 | − | 0.107460i | \(-0.0342718\pi\) | |||||||
\(860\) | 446364. | − | 911281.i | 0.603520 | − | 1.23213i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 172503. | − | 744332.i | 0.232157 | − | 1.00173i | ||||
\(863\) | 916363.i | 1.23040i | 0.788372 | + | 0.615199i | \(0.210924\pi\) | ||||
−0.788372 | + | 0.615199i | \(0.789076\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −615427. | −0.822515 | ||||||||
\(866\) | −187991. | − | 43568.0i | −0.250670 | − | 0.0580941i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −120185. | − | 58869.2i | −0.159519 | − | 0.0781355i | ||||
\(869\) | −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 | \(0.717776\pi\) | |||||||
\(878\) | 766471. | + | 715954.i | 0.994276 | + | 0.928744i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 877502. | − | 680830.i | 1.13314 | − | 0.879171i | ||||
\(881\) | −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 | \(0.0287056\pi\) | ||||
−0.995936 | + | 0.0900593i | \(0.971294\pi\) | |||||||
\(884\) | 21255.4 | + | 311508.i | 0.0271998 | + | 0.398625i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 265954. | + | 248425.i | 0.338796 | + | 0.316467i | ||||
\(887\) | −307169. | + | 177344.i | −0.390418 | + | 0.225408i | −0.682341 | − | 0.731034i | \(-0.739038\pi\) |
0.291923 | + | 0.956442i | \(0.405705\pi\) | |||||||
\(888\) | 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 | ||||
\(896\) | 104001. | − | 170798.i | 0.129545 | − | 0.212748i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.10413e6 | + | 255889.i | 1.36921 | + | 0.317322i | ||||
\(899\) | − | 892005.i | − | 1.10369i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −122652. | −0.151086 | ||||||||
\(902\) | 7828.66 | − | 33779.8i | 0.00962220 | − | 0.0415187i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −186608. | + | 1.15923e6i | −0.228346 | + | 1.41851i | ||||
\(905\) | 426883. | + | 739383.i | 0.521209 | + | 0.902760i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.27955e6 | − | 738746.i | −1.55540 | − | 0.898008i | −0.997687 | − | 0.0679717i | \(-0.978347\pi\) |
−0.557709 | − | 0.830037i | \(-0.688319\pi\) | |||||||
\(908\) | −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 | 0.524913 | − | 0.851156i | \(-0.324098\pi\) |
−0.474666 | + | 0.880166i | \(0.657431\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −103988. | − | 180113.i | −0.124751 | − | 0.216074i | ||||
\(914\) | 541868. | − | 580102.i | 0.648637 | − | 0.694404i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 44577.4 | + | 653302.i | 0.0531280 | + | 0.778615i | ||||
\(917\) | −128687. | −0.153036 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 346372.i | − | 0.410120i | −0.978749 | − | 0.205060i | \(-0.934261\pi\) | ||
0.978749 | − | 0.205060i | \(-0.0657390\pi\) | |||||||
\(920\) | −778892. | − | 2.04451e6i | −0.920241 | − | 2.41554i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 569832. | − | 610039.i | 0.670324 | − | 0.717622i | ||||
\(923\) | 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 | ||||
\(932\) | −1.13880e6 | − | 557806.i | −1.31104 | − | 0.642172i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 87245.3 | − | 376454.i | 0.100011 | − | 0.431537i | ||||
\(935\) | 405122.i | 0.463407i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.00280e6 | −1.14219 | −0.571094 | − | 0.820885i | \(-0.693481\pi\) | ||||
−0.571094 | + | 0.820885i | \(0.693481\pi\) | |||||||
\(938\) | −11701.7 | − | 2711.94i | −0.0132998 | − | 0.00308230i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −635038. | + | 1.29647e6i | −0.718694 | + | 1.46726i | ||||
\(941\) | −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 | 0.406910 | − | 0.913468i | \(-0.366606\pi\) |
−0.587631 | + | 0.809129i | \(0.699939\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −267998. | − | 464186.i | −0.297577 | − | 0.515418i | ||||
\(950\) | −70910.5 | − | 66236.9i | −0.0785712 | − | 0.0733927i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 25967.7 | + | 68162.5i | 0.0286523 | + | 0.0752093i | ||||
\(953\) | −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 | ||||||
\(956\) | 720422. | − | 49157.2i | 0.788263 | − | 0.0537863i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 100127. | + | 93527.4i | 0.109098 | + | 0.101908i | ||||
\(959\) | 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 | −0.686625 | − | 0.727011i | \(-0.740909\pi\) |
0.286298 | + | 0.958141i | \(0.407575\pi\) | |||||||
\(968\) | −23556.8 | + | 146337.i | −0.0251400 | + | 0.156172i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 873957. | + | 202544.i | 0.928852 | + | 0.215267i | ||||
\(971\) | 756598.i | 0.802467i | 0.915976 | + | 0.401233i | \(0.131418\pi\) | ||||
−0.915976 | + | 0.401233i | \(0.868582\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −229389. | −0.242296 | ||||||||
\(974\) | 62783.9 | − | 270906.i | 0.0661806 | − | 0.285562i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −552973. | + | 75816.0i | −0.580502 | + | 0.0795905i | ||||
\(977\) | 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 | 0.591138 | − | 0.806570i | \(-0.298679\pi\) |
−0.402942 | + | 0.915226i | \(0.632012\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 311354. | + | 539282.i | 0.320910 | + | 0.555832i | ||||
\(986\) | −331870. | + | 355286.i | −0.341361 | + | 0.365447i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −89701.9 | + | 6120.71i | −0.0918941 | + | 0.00627030i | ||||
\(989\) | −1.41966e6 | −1.45141 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.66713e6i | 1.69755i | 0.528754 | + | 0.848775i | \(0.322659\pi\) | ||||
−0.528754 | + | 0.848775i | \(0.677341\pi\) | |||||||
\(992\) | 573141. | + | 404926.i | 0.582423 | + | 0.411484i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 153570. | − | 164406.i | 0.155430 | − | 0.166397i | ||||
\(995\) | −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.19.2 | 44 | ||
3.2 | odd | 2 | 36.5.f.a.7.21 | yes | 44 | ||
4.3 | odd | 2 | inner | 108.5.f.a.19.17 | 44 | ||
9.2 | odd | 6 | 324.5.d.f.163.9 | 22 | |||
9.4 | even | 3 | inner | 108.5.f.a.91.17 | 44 | ||
9.5 | odd | 6 | 36.5.f.a.31.6 | yes | 44 | ||
9.7 | even | 3 | 324.5.d.e.163.14 | 22 | |||
12.11 | even | 2 | 36.5.f.a.7.6 | ✓ | 44 | ||
36.7 | odd | 6 | 324.5.d.e.163.13 | 22 | |||
36.11 | even | 6 | 324.5.d.f.163.10 | 22 | |||
36.23 | even | 6 | 36.5.f.a.31.21 | yes | 44 | ||
36.31 | odd | 6 | inner | 108.5.f.a.91.2 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.6 | ✓ | 44 | 12.11 | even | 2 | ||
36.5.f.a.7.21 | yes | 44 | 3.2 | odd | 2 | ||
36.5.f.a.31.6 | yes | 44 | 9.5 | odd | 6 | ||
36.5.f.a.31.21 | yes | 44 | 36.23 | even | 6 | ||
108.5.f.a.19.2 | 44 | 1.1 | even | 1 | trivial | ||
108.5.f.a.19.17 | 44 | 4.3 | odd | 2 | inner | ||
108.5.f.a.91.2 | 44 | 36.31 | odd | 6 | inner | ||
108.5.f.a.91.17 | 44 | 9.4 | even | 3 | inner | ||
324.5.d.e.163.13 | 22 | 36.7 | odd | 6 | |||
324.5.d.e.163.14 | 22 | 9.7 | even | 3 | |||
324.5.d.f.163.9 | 22 | 9.2 | odd | 6 | |||
324.5.d.f.163.10 | 22 | 36.11 | even | 6 |