Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(191,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.191");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.f (of order \(2\), degree \(1\), 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: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.8 | ||
Root | \(0.323042 - 0.323042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.191 |
Dual form | 384.4.f.g.191.6 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.44949 | + | 4.58258i | 0.471405 | + | 0.881917i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.31464 | −0.207028 | −0.103514 | − | 0.994628i | \(-0.533009\pi\) | ||||
−0.103514 | + | 0.994628i | \(0.533009\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 29.6636i | − | 1.60168i | −0.598877 | − | 0.800841i | \(-0.704386\pi\) | ||
0.598877 | − | 0.800841i | \(-0.295614\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −15.0000 | + | 22.4499i | −0.555556 | + | 0.831479i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 22.8348i | 0.625906i | 0.949769 | + | 0.312953i | \(0.101318\pi\) | ||||
−0.949769 | + | 0.312953i | \(0.898682\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 8.66061i | − | 0.184771i | −0.995723 | − | 0.0923854i | \(-0.970551\pi\) | ||
0.995723 | − | 0.0923854i | \(-0.0294492\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.66970 | − | 10.6070i | −0.0975940 | − | 0.182582i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 93.3503i | − | 1.33181i | −0.746036 | − | 0.665905i | \(-0.768046\pi\) | ||
0.746036 | − | 0.665905i | \(-0.231954\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −85.4402 | −1.03165 | −0.515824 | − | 0.856694i | \(-0.672514\pi\) | ||||
−0.515824 | + | 0.856694i | \(0.672514\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 135.936 | − | 72.6606i | 1.41255 | − | 0.755040i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −116.661 | −1.05763 | −0.528813 | − | 0.848738i | \(-0.677363\pi\) | ||||
−0.528813 | + | 0.848738i | \(0.677363\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −119.642 | −0.957139 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −139.621 | − | 13.7477i | −0.995187 | − | 0.0979908i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −103.531 | −0.662936 | −0.331468 | − | 0.943467i | \(-0.607544\pi\) | ||||
−0.331468 | + | 0.943467i | \(0.607544\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.6070i | 0.0614542i | 0.999528 | + | 0.0307271i | \(0.00978227\pi\) | ||||
−0.999528 | + | 0.0307271i | \(0.990218\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −104.642 | + | 55.9337i | −0.551997 | + | 0.295055i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 68.6606i | 0.331593i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 380.624i | − | 1.69120i | −0.533820 | − | 0.845598i | \(-0.679244\pi\) | ||
0.533820 | − | 0.845598i | \(-0.320756\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.6879 | − | 21.2141i | 0.162952 | − | 0.0871018i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 257.983i | − | 0.982688i | −0.870966 | − | 0.491344i | \(-0.836506\pi\) | ||
0.870966 | − | 0.491344i | \(-0.163494\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 359.783 | 1.27596 | 0.637981 | − | 0.770052i | \(-0.279770\pi\) | ||||
0.637981 | + | 0.770052i | \(0.279770\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 34.7197 | − | 51.9636i | 0.115016 | − | 0.172140i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 293.285 | 0.910213 | 0.455106 | − | 0.890437i | \(-0.349601\pi\) | ||||
0.455106 | + | 0.890437i | \(0.349601\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −536.927 | −1.56539 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 427.785 | − | 228.661i | 1.17455 | − | 0.627821i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 679.678 | 1.76153 | 0.880763 | − | 0.473557i | \(-0.157030\pi\) | ||||
0.880763 | + | 0.473557i | \(0.157030\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 52.8545i | − | 0.129580i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −209.285 | − | 391.536i | −0.486324 | − | 0.909828i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 45.8258i | 0.101119i | 0.998721 | + | 0.0505594i | \(0.0161004\pi\) | ||||
−0.998721 | + | 0.0505594i | \(0.983900\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 595.230i | − | 1.24937i | −0.780878 | − | 0.624684i | \(-0.785228\pi\) | ||
0.780878 | − | 0.624684i | \(-0.214772\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 665.945 | + | 444.954i | 1.33177 | + | 0.889823i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.0462i | 0.0382527i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −206.341 | −0.376247 | −0.188124 | − | 0.982145i | \(-0.560241\pi\) | ||||
−0.188124 | + | 0.982145i | \(0.560241\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −285.759 | − | 534.606i | −0.498570 | − | 0.932739i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −996.515 | −1.66570 | −0.832849 | − | 0.553500i | \(-0.813292\pi\) | ||||
−0.832849 | + | 0.553500i | \(0.813292\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −593.927 | −0.952246 | −0.476123 | − | 0.879379i | \(-0.657958\pi\) | ||||
−0.476123 | + | 0.879379i | \(0.657958\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −293.063 | − | 548.270i | −0.451200 | − | 0.844118i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 677.363 | 1.00250 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 910.940i | 1.29733i | 0.761075 | + | 0.648663i | \(0.224672\pi\) | ||||
−0.761075 | + | 0.648663i | \(0.775328\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −279.000 | − | 673.498i | −0.382716 | − | 0.923866i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 332.889i | 0.440233i | 0.975474 | + | 0.220117i | \(0.0706438\pi\) | ||||
−0.975474 | + | 0.220117i | \(0.929356\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 216.073i | 0.275722i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −253.597 | − | 474.436i | −0.312511 | − | 0.584654i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 821.636i | 0.978575i | 0.872122 | + | 0.489288i | \(0.162743\pi\) | ||||
−0.872122 | + | 0.489288i | \(0.837257\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −256.904 | −0.295944 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −48.6075 | + | 25.9818i | −0.0541975 | + | 0.0289698i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 197.764 | 0.213580 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 420.715 | 0.440383 | 0.220192 | − | 0.975457i | \(-0.429332\pi\) | ||||
0.220192 | + | 0.975457i | \(0.429332\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −512.641 | − | 342.523i | −0.520428 | − | 0.347726i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −923.145 | −0.909469 | −0.454734 | − | 0.890627i | \(-0.650266\pi\) | ||||
−0.454734 | + | 0.890627i | \(0.650266\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1426.19i | − | 1.36434i | −0.731195 | − | 0.682168i | \(-0.761037\pi\) | ||
0.731195 | − | 0.682168i | \(-0.238963\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −314.642 | + | 168.183i | −0.292438 | + | 0.156315i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1581.83i | 1.42917i | 0.699550 | + | 0.714583i | \(0.253384\pi\) | ||||
−0.699550 | + | 0.714583i | \(0.746616\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 766.091i | − | 0.673195i | −0.941649 | − | 0.336597i | \(-0.890724\pi\) | ||
0.941649 | − | 0.336597i | \(-0.109276\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1744.24 | − | 932.335i | 1.49149 | − | 0.797237i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1047.66i | − | 0.872177i | −0.899904 | − | 0.436088i | \(-0.856364\pi\) | ||
0.899904 | − | 0.436088i | \(-0.143636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 270.028 | 0.218958 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 194.430 | + | 129.909i | 0.153633 | + | 0.102650i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2769.10 | −2.13314 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 809.570 | 0.608242 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1182.23 | − | 631.927i | 0.866649 | − | 0.463244i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 566.260 | 0.405183 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 553.181i | − | 0.386511i | −0.981148 | − | 0.193256i | \(-0.938095\pi\) | ||
0.981148 | − | 0.193256i | \(-0.0619046\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 881.285 | + | 1648.73i | 0.601495 | + | 1.12529i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2151.63i | 1.43503i | 0.696545 | + | 0.717513i | \(0.254720\pi\) | ||||
−0.696545 | + | 0.717513i | \(0.745280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2534.46i | 1.65237i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 323.173 | + | 31.8211i | 0.206032 | + | 0.0202868i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1476.62i | − | 0.920846i | −0.887700 | − | 0.460423i | \(-0.847698\pi\) | ||
0.887700 | − | 0.460423i | \(-0.152302\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1984.09 | −1.21071 | −0.605353 | − | 0.795957i | \(-0.706968\pi\) | ||||
−0.605353 | + | 0.795957i | \(0.706968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 718.398 | + | 1344.00i | 0.429078 | + | 0.802732i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 197.764 | 0.115649 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 239.636 | 0.137246 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1315.20 | − | 2460.51i | −0.737930 | − | 1.38054i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3026.56 | −1.66406 | −0.832031 | − | 0.554729i | \(-0.812822\pi\) | ||||
−0.832031 | + | 0.554729i | \(0.812822\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 350.032i | 0.188644i | 0.995542 | + | 0.0943219i | \(0.0300683\pi\) | ||||
−0.995542 | + | 0.0943219i | \(0.969932\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2095.71 | + | 1400.25i | 1.10737 | + | 0.739895i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 24.5515i | − | 0.0127227i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 372.406i | 0.189307i | 0.995510 | + | 0.0946536i | \(0.0301744\pi\) | ||||
−0.995510 | + | 0.0946536i | \(0.969826\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1664.86 | + | 3114.67i | 0.830392 | + | 1.55352i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3460.57i | 1.69398i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1353.69 | 0.650487 | 0.325243 | − | 0.945630i | \(-0.394554\pi\) | ||||
0.325243 | + | 0.945630i | \(0.394554\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 242.210 | − | 129.467i | 0.114279 | − | 0.0610846i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2592.48 | −1.20127 | −0.600635 | − | 0.799523i | \(-0.705085\pi\) | ||||
−0.600635 | + | 0.799523i | \(0.705085\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2121.99 | 0.965860 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1281.60 | − | 1918.13i | 0.573138 | − | 0.857794i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3643.74 | −1.60132 | −0.800660 | − | 0.599118i | \(-0.795518\pi\) | ||||
−0.800660 | + | 0.599118i | \(0.795518\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3549.02i | 1.53303i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −210.000 | + | 112.250i | −0.0891783 | + | 0.0476678i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 874.435i | − | 0.365130i | −0.983194 | − | 0.182565i | \(-0.941560\pi\) | ||
0.983194 | − | 0.182565i | \(-0.0584400\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2699.01i | 1.10838i | 0.832392 | + | 0.554188i | \(0.186971\pi\) | ||||
−0.832392 | + | 0.554188i | \(0.813029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2727.69 | − | 1458.01i | 1.10184 | − | 0.588958i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 881.010i | 0.350125i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2131.64 | 0.833588 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −407.807 | + | 4141.65i | −0.156950 | + | 1.59397i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 708.036 | 0.268229 | 0.134114 | − | 0.990966i | \(-0.457181\pi\) | ||||
0.134114 | + | 0.990966i | \(0.457181\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3531.07 | 1.31695 | 0.658476 | − | 0.752602i | \(-0.271201\pi\) | ||||
0.658476 | + | 0.752602i | \(0.271201\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −91.8633 | + | 49.1030i | −0.0337357 | + | 0.0180325i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4919.77 | 1.77928 | 0.889642 | − | 0.456658i | \(-0.150954\pi\) | ||||
0.889642 | + | 0.456658i | \(0.150954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 264.092i | − | 0.0940754i | −0.998893 | − | 0.0470377i | \(-0.985022\pi\) | ||
0.998893 | − | 0.0470377i | \(-0.0149781\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −505.430 | − | 945.574i | −0.177365 | − | 0.331819i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3071.08i | 1.06181i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 597.139i | 0.203444i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1749.91 | − | 2619.02i | 0.587570 | − | 0.879395i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1951.01i | − | 0.645715i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3422.86 | 1.11678 | 0.558388 | − | 0.829580i | \(-0.311420\pi\) | ||||
0.558388 | + | 0.829580i | \(0.311420\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2440.95 | − | 4566.61i | −0.785218 | − | 1.46901i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −832.770 | −0.264160 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 314.642 | 0.0984300 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1454.82 | − | 2721.72i | −0.448893 | − | 0.839802i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −808.470 | −0.246080 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4432.09i | − | 1.33092i | −0.746434 | − | 0.665460i | \(-0.768236\pi\) | ||
0.746434 | − | 0.665460i | \(-0.231764\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1794.64 | − | 2685.97i | 0.531744 | − | 0.795842i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4674.99i | 1.36692i | 0.729990 | + | 0.683458i | \(0.239525\pi\) | ||||
−0.729990 | + | 0.683458i | \(0.760475\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2317.95i | 0.668883i | 0.942417 | + | 0.334441i | \(0.108548\pi\) | ||||
−0.942417 | + | 0.334441i | \(0.891452\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1659.19 | + | 3104.07i | 0.472584 | + | 0.884124i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5342.54i | 1.50215i | 0.660215 | + | 0.751076i | \(0.270465\pi\) | ||||
−0.660215 | + | 0.751076i | \(0.729535\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −678.850 | −0.188440 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4174.45 | + | 2231.34i | −1.14413 | + | 0.611566i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5306.42 | −1.43617 | −0.718084 | − | 0.695957i | \(-0.754981\pi\) | ||||
−0.718084 | + | 0.695957i | \(0.754981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1220.35 | −0.326182 | −0.163091 | − | 0.986611i | \(-0.552146\pi\) | ||||
−0.163091 | + | 0.986611i | \(0.552146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2402.95 | − | 2928.27i | 0.634359 | − | 0.773038i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1242.80 | 0.324079 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 739.964i | 0.190618i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1525.49 | + | 815.409i | −0.388249 | + | 0.207528i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 385.695i | 0.0969916i | 0.998823 | + | 0.0484958i | \(0.0154427\pi\) | ||||
−0.998823 | + | 0.0484958i | \(0.984557\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2663.93i | − | 0.661975i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −990.170 | + | 529.268i | −0.243164 | + | 0.129977i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1158.77i | 0.281253i | 0.990063 | + | 0.140626i | \(0.0449116\pi\) | ||||
−0.990063 | + | 0.140626i | \(0.955088\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11290.7 | −2.70876 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1552.96 | − | 2324.25i | 0.368298 | − | 0.551217i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1677.25 | 0.393247 | 0.196623 | − | 0.980479i | \(-0.437002\pi\) | ||||
0.196623 | + | 0.980479i | \(0.437002\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1573.21 | −0.364685 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3765.21 | + | 2012.59i | −0.863022 | + | 0.461305i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4080.38 | 0.924852 | 0.462426 | − | 0.886658i | \(-0.346979\pi\) | ||||
0.462426 | + | 0.886658i | \(0.346979\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 550.301i | − | 0.123352i | −0.998096 | − | 0.0616761i | \(-0.980355\pi\) | ||
0.998096 | − | 0.0616761i | \(-0.0196446\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −629.285 | − | 1177.28i | −0.139509 | − | 0.260998i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2732.02i | − | 0.599079i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 468.115i | − | 0.101539i | −0.998710 | − | 0.0507695i | \(-0.983833\pi\) | ||
0.998710 | − | 0.0507695i | \(-0.0161674\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −238.127 | − | 159.105i | −0.0510979 | − | 0.0341412i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5322.22i | − | 1.12988i | −0.825131 | − | 0.564942i | \(-0.808899\pi\) | ||
0.825131 | − | 0.564942i | \(-0.191101\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −109.886 | −0.0230814 | −0.0115407 | − | 0.999933i | \(-0.503674\pi\) | ||||
−0.0115407 | + | 0.999933i | \(0.503674\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 484.420 | + | 906.267i | 0.100683 | + | 0.188360i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7652.70 | −1.57395 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3801.28 | −0.773718 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1030.54 | + | 1927.96i | 0.207599 | + | 0.388381i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2671.59 | −0.532683 | −0.266341 | − | 0.963879i | \(-0.585815\pi\) | ||||
−0.266341 | + | 0.963879i | \(0.585815\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 106.070i | − | 0.0209344i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 313.927 | − | 3188.22i | 0.0613330 | − | 0.622894i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1010.35i | 0.195419i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 10672.4i | − | 2.04369i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2261.23 | − | 4230.38i | −0.428728 | − | 0.802076i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1377.75i | 0.258654i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2441.80 | 0.453944 | 0.226972 | − | 0.973901i | \(-0.427117\pi\) | ||||
0.226972 | + | 0.973901i | \(0.427117\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6535.62 | − | 3493.44i | 1.20323 | − | 0.643154i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6897.58 | 1.25764 | 0.628820 | − | 0.777551i | \(-0.283538\pi\) | ||||
0.628820 | + | 0.777551i | \(0.283538\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5278.92 | −0.953298 | −0.476649 | − | 0.879094i | \(-0.658149\pi\) | ||||
−0.476649 | + | 0.879094i | \(0.658149\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1541.43 | − | 1029.91i | −0.275713 | − | 0.184218i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1537.58 | 0.272427 | 0.136213 | − | 0.990680i | \(-0.456507\pi\) | ||||
0.136213 | + | 0.990680i | \(0.456507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2364.10i | − | 0.414935i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7248.84 | + | 3874.67i | −1.26041 | + | 0.673716i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7975.87i | 1.37396i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1036.18i | 0.176851i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3510.67 | − | 1876.53i | 0.593702 | − | 0.317347i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 8699.87i | − | 1.45787i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8894.54 | 1.47700 | 0.738502 | − | 0.674252i | \(-0.235534\pi\) | ||||
0.738502 | + | 0.674252i | \(0.235534\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8544.99 | + | 5709.36i | 1.40619 | + | 0.939553i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 477.606 | 0.0778938 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6422.48 | −1.03815 | −0.519073 | − | 0.854730i | \(-0.673723\pi\) | ||||
−0.519073 | + | 0.854730i | \(0.673723\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4801.00 | − | 2566.24i | 0.769187 | − | 0.411148i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −242.210 | −0.0384645 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5752.57i | 0.905568i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 661.430 | + | 1237.42i | 0.103218 | + | 0.193103i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3357.43i | − | 0.519413i | −0.965688 | − | 0.259707i | \(-0.916374\pi\) | ||
0.965688 | − | 0.259707i | \(-0.0836259\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 11693.7i | − | 1.79354i | −0.442493 | − | 0.896772i | \(-0.645906\pi\) | ||
0.442493 | − | 0.896772i | \(-0.354094\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −119.064 | + | 1209.20i | −0.0181058 | + | 0.183882i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9945.93i | − | 1.49963i | −0.661649 | − | 0.749813i | \(-0.730143\pi\) | ||
0.661649 | − | 0.749813i | \(-0.269857\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2306.58 | 0.344846 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6782.89 | − | 12689.6i | −1.00557 | − | 1.88125i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8527.75 | 1.25370 | 0.626849 | − | 0.779141i | \(-0.284344\pi\) | ||||
0.626849 | + | 0.779141i | \(0.284344\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 441.024 | 0.0642986 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1983.03 | + | 3709.91i | 0.286728 | + | 0.536419i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1374.73 | 0.197142 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 891.162i | − | 0.126753i | −0.997990 | − | 0.0633764i | \(-0.979813\pi\) | ||
0.997990 | − | 0.0633764i | \(-0.0201869\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5791.71 | + | 3869.75i | 0.817085 | + | 0.545938i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 20161.7i | − | 2.82141i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9107.23i | 1.26422i | 0.774878 | + | 0.632111i | \(0.217811\pi\) | ||||
−0.774878 | + | 0.632111i | \(0.782189\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1387.05 | + | 2594.93i | 0.191005 | + | 0.357338i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 896.637i | 0.122491i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1451.32 | −0.196699 | −0.0983497 | − | 0.995152i | \(-0.531356\pi\) | ||||
−0.0983497 | + | 0.995152i | \(0.531356\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2535.00 | − | 1355.01i | 0.340871 | − | 0.182203i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3320.30 | −0.442975 | −0.221488 | − | 0.975163i | \(-0.571091\pi\) | ||||
−0.221488 | + | 0.975163i | \(0.571091\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1567.85 | −0.207546 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5396.75 | + | 8077.11i | −0.708868 | + | 1.06094i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5726.58 | −0.746399 | −0.373200 | − | 0.927751i | \(-0.621739\pi\) | ||||
−0.373200 | + | 0.927751i | \(0.621739\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10890.3i | 1.40856i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9859.99 | + | 5270.39i | −1.26557 | + | 0.676478i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 2108.50i | − | 0.268583i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 5389.36i | − | 0.681321i | −0.940186 | − | 0.340660i | \(-0.889349\pi\) | ||
0.940186 | − | 0.340660i | \(-0.110651\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11614.4 | + | 6208.14i | −1.45726 | + | 0.778936i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 573.267i | − | 0.0713905i | −0.999363 | − | 0.0356953i | \(-0.988635\pi\) | ||
0.999363 | − | 0.0356953i | \(-0.0113646\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 91.8633 | 0.0113549 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 645.786 | + | 1558.91i | 0.0792330 | + | 0.191266i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8691.50 | 1.05853 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6576.42 | −0.795069 | −0.397535 | − | 0.917587i | \(-0.630134\pi\) | ||||
−0.397535 | + | 0.917587i | \(0.630134\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6766.71 | − | 3616.96i | 0.812110 | − | 0.434091i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1359.36 | 0.161960 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 770.521i | − | 0.0911406i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4860.00 | − | 9092.23i | −0.570732 | − | 1.06774i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8544.87i | 0.996286i | 0.867095 | + | 0.498143i | \(0.165985\pi\) | ||||
−0.867095 | + | 0.498143i | \(0.834015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1822.38i | 0.210968i | 0.994421 | + | 0.105484i | \(0.0336392\pi\) | ||||
−0.994421 | + | 0.105484i | \(0.966361\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4399.27 | + | 6584.23i | −0.505674 | + | 0.756823i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11168.7i | 1.27473i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17656.7 | −2.00109 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 484.420 | + | 906.267i | 0.0545175 | + | 0.101993i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2373.58 | 0.265269 | 0.132635 | − | 0.991165i | \(-0.457656\pi\) | ||||
0.132635 | + | 0.991165i | \(0.457656\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12307.8 | 1.36600 | 0.682999 | − | 0.730419i | \(-0.260675\pi\) | ||||
0.682999 | + | 0.730419i | \(0.260675\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 586.987 | + | 1098.15i | 0.0646985 | + | 0.121040i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9967.50 | 1.09110 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 5371.26i | − | 0.583955i | −0.956425 | − | 0.291978i | \(-0.905687\pi\) | ||
0.956425 | − | 0.291978i | \(-0.0943133\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8053.91 | − | 12054.0i | 0.869659 | − | 1.30159i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 9066.41i | − | 0.972366i | −0.873857 | − | 0.486183i | \(-0.838389\pi\) | ||
0.873857 | − | 0.486183i | \(-0.161611\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 1901.79i | − | 0.202593i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7413.52 | − | 13869.4i | −0.784447 | − | 1.46757i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6049.97i | − | 0.635892i | −0.948109 | − | 0.317946i | \(-0.897007\pi\) | ||
0.948109 | − | 0.317946i | \(-0.102993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5891.01 | 0.615070 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1604.05 | + | 857.400i | −0.166368 | + | 0.0889275i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 594.642 | 0.0612687 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6664.98 | 0.682220 | 0.341110 | − | 0.940023i | \(-0.389197\pi\) | ||||
0.341110 | + | 0.940023i | \(0.389197\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1283.35 | + | 13033.7i | −0.130505 | + | 1.32540i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2588.66 | 0.261531 | 0.130766 | − | 0.991413i | \(-0.458256\pi\) | ||||
0.130766 | + | 0.991413i | \(0.458256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12241.7i | − | 1.22877i | −0.789006 | − | 0.614385i | \(-0.789404\pi\) | ||
0.789006 | − | 0.614385i | \(-0.210596\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 112.509 | − | 60.1387i | 0.0112204 | − | 0.00599756i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 6144.26i | − | 0.608828i | −0.952540 | − | 0.304414i | \(-0.901539\pi\) | ||
0.952540 | − | 0.304414i | \(-0.0984606\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6120.81i | 0.602629i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1706.58 | + | 912.205i | −0.166953 | + | 0.0892403i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8215.59i | 0.798633i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10222.3 | 0.987431 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10195.2 | + | 15258.7i | −0.978626 | + | 1.46467i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12210.4 | 1.16473 | 0.582365 | − | 0.812928i | \(-0.302128\pi\) | ||||
0.582365 | + | 0.812928i | \(0.302128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3296.44 | −0.312483 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15858.3 | + | 8476.63i | −1.49395 | + | 0.798551i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −973.806 | −0.0911716 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14354.5i | − | 1.33565i | −0.744317 | − | 0.667827i | \(-0.767225\pi\) | ||
0.744317 | − | 0.667827i | \(-0.232775\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3315.85 | + | 6203.40i | 0.306642 | + | 0.573675i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3894.57i | 0.357962i | 0.983853 | + | 0.178981i | \(0.0572800\pi\) | ||||
−0.983853 | + | 0.178981i | \(0.942720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9664.61i | 0.882905i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1186.58 | + | 792.818i | 0.107743 | + | 0.0719889i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29560.2i | 2.66792i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13373.6 | 1.19977 | 0.599886 | − | 0.800086i | \(-0.295213\pi\) | ||||
0.599886 | + | 0.800086i | \(0.295213\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6350.25 | − | 11880.2i | −0.566284 | − | 1.05942i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3757.55 | −0.333083 | −0.166541 | − | 0.986034i | \(-0.553260\pi\) | ||||
−0.166541 | + | 0.986034i | \(0.553260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2136.75 | 0.188286 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5197.80 | + | 9724.20i | 0.455311 | + | 0.851808i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5968.10 | −0.519708 | −0.259854 | − | 0.965648i | \(-0.583674\pi\) | ||||
−0.259854 | + | 0.965648i | \(0.583674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17618.0i | 1.52519i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11929.2 | + | 1174.61i | 1.02668 | + | 0.101092i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3301.12i | 0.282456i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6697.12i | 0.569708i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8925.31 | − | 16697.7i | −0.754870 | − | 1.41223i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 10169.5i | − | 0.855151i | −0.903980 | − | 0.427575i | \(-0.859368\pi\) | ||
0.903980 | − | 0.427575i | \(-0.140632\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13759.2 | −1.15038 | −0.575188 | − | 0.818021i | \(-0.695071\pi\) | ||||
−0.575188 | + | 0.818021i | \(0.695071\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16263.7 | + | 8693.29i | −1.35201 | + | 0.722679i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 990.170 | 0.0818453 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1442.70 | 0.118575 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1028.79 | − | 687.386i | −0.0840781 | − | 0.0561771i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2234.29 | −0.181572 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3661.36i | − | 0.295878i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4007.16 | − | 2141.92i | 0.322015 | − | 0.172124i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 12260.7i | − | 0.979784i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10310.6i | 0.819386i | 0.912223 | + | 0.409693i | \(0.134364\pi\) | ||||
−0.912223 | + | 0.409693i | \(0.865636\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12368.4 | + | 6611.20i | −0.977495 | + | 0.522493i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1773.23i | 0.139370i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19226.5 | −1.50287 | −0.751433 | − | 0.659810i | \(-0.770637\pi\) | ||||
−0.751433 | + | 0.659810i | \(0.770637\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13362.9 | + | 8928.45i | 1.03882 | + | 0.694093i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8845.67 | 0.683917 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27021.7 | 2.07791 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4037.29 | + | 2158.02i | −0.308781 | + | 0.165050i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14675.8 | −1.11640 | −0.558199 | − | 0.829707i | \(-0.688508\pi\) | ||||
−0.558199 | + | 0.829707i | \(0.688508\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3115.94i | − | 0.235761i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5221.43 | + | 9768.40i | 0.392957 | + | 0.735156i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 21002.2i | − | 1.57218i | −0.618110 | − | 0.786092i | \(-0.712101\pi\) | ||
0.618110 | − | 0.786092i | \(-0.287899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2424.97i | 0.180565i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19978.4 | + | 8276.14i | −1.47974 | + | 0.612989i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 4389.21i | − | 0.323384i | −0.986841 | − | 0.161692i | \(-0.948305\pi\) | ||
0.986841 | − | 0.161692i | \(-0.0516951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3964.70 | −0.290574 | −0.145287 | − | 0.989390i | \(-0.546410\pi\) | ||||
−0.145287 | + | 0.989390i | \(0.546410\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1734.33 | + | 3244.63i | 0.126444 | + | 0.236556i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13957.6 | 1.01230 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5848.93 | 0.422000 | 0.211000 | − | 0.977486i | \(-0.432328\pi\) | ||||
0.211000 | + | 0.977486i | \(0.432328\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8649.31 | + | 16181.4i | 0.620817 | + | 1.16144i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9874.69 | 0.705114 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15520.3i | 1.10255i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −450.037 | − | 300.693i | −0.0318064 | − | 0.0212515i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 7642.83i | − | 0.537399i | −0.963224 | − | 0.268700i | \(-0.913406\pi\) | ||
0.963224 | − | 0.268700i | \(-0.0865939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 906.267i | − | 0.0633991i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12050.9 | + | 22545.2i | 0.838763 | + | 1.56918i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 16852.3i | − | 1.16702i | −0.812107 | − | 0.583509i | \(-0.801679\pi\) | ||
0.812107 | − | 0.583509i | \(-0.198321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6409.49 | 0.441619 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1210.22 | − | 646.891i | 0.0829667 | − | 0.0443475i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7456.85 | −0.508646 | −0.254323 | − | 0.967119i | \(-0.581853\pi\) | ||||
−0.254323 | + | 0.967119i | \(0.581853\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8982.48 | −0.609656 | −0.304828 | − | 0.952407i | \(-0.598599\pi\) | ||||
−0.304828 | + | 0.952407i | \(0.598599\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3095.12 | − | 4632.35i | 0.209026 | − | 0.312842i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1873.87 | −0.125923 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6289.93i | 0.420594i | 0.977638 | + | 0.210297i | \(0.0674431\pi\) | ||||
−0.977638 | + | 0.210297i | \(0.932557\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14073.5 | + | 7522.59i | −0.936430 | + | 0.500543i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2540.02i | − | 0.168181i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11497.6i | 0.757556i | 0.925488 | + | 0.378778i | \(0.123656\pi\) | ||||
−0.925488 | + | 0.378778i | \(0.876344\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2736.44 | + | 1462.69i | −0.179421 | + | 0.0959044i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13336.4i | 0.870181i | 0.900387 | + | 0.435090i | \(0.143284\pi\) | ||||
−0.900387 | + | 0.435090i | \(0.856716\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27960.9 | 1.81558 | 0.907788 | − | 0.419429i | \(-0.137770\pi\) | ||||
0.907788 | + | 0.419429i | \(0.137770\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16288.3 | + | 1603.82i | 1.05254 | + | 0.103638i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24372.6 | 1.56737 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13644.6 | 0.873255 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8940.67 | − | 4778.99i | 0.569467 | − | 0.304393i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35531.4 | −2.25235 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2435.82i | − | 0.153675i | −0.997044 | − | 0.0768373i | \(-0.975518\pi\) | ||
0.997044 | − | 0.0768373i | \(-0.0244822\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8384.27 | + | 15685.5i | 0.526453 | + | 0.984903i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1280.42i | 0.0800186i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4650.12i | 0.289237i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14947.7 | − | 22371.7i | 0.925388 | − | 1.38499i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 882.215i | 0.0543610i | 0.999631 | + | 0.0271805i | \(0.00865288\pi\) | ||||
−0.999631 | + | 0.0271805i | \(0.991347\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3761.20 | −0.230680 | −0.115340 | − | 0.993326i | \(-0.536796\pi\) | ||||
−0.115340 | + | 0.993326i | \(0.536796\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2039.86 | − | 3816.23i | −0.124526 | − | 0.232967i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6601.59 | −0.401137 | −0.200568 | − | 0.979680i | \(-0.564279\pi\) | ||||
−0.200568 | + | 0.979680i | \(0.564279\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1046.42 | −0.0632908 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 770.713 | + | 1441.87i | 0.0464004 | + | 0.0868071i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13790.5 | −0.826436 | −0.413218 | − | 0.910632i | \(-0.635595\pi\) | ||||
−0.413218 | + | 0.910632i | \(0.635595\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4980.25i | − | 0.297091i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8908.91 | − | 13333.6i | 0.529025 | − | 0.791773i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 12482.7i | − | 0.737868i | −0.929456 | − | 0.368934i | \(-0.879723\pi\) | ||
0.929456 | − | 0.368934i | \(-0.120277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6286.85i | − | 0.369940i | −0.982744 | − | 0.184970i | \(-0.940781\pi\) | ||
0.982744 | − | 0.184970i | \(-0.0592188\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1980.34 | − | 3704.88i | −0.116003 | − | 0.217022i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 5866.37i | − | 0.342088i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12077.9 | 0.701139 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20310.4 | − | 10856.4i | 1.17376 | − | 0.627401i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13592.0 | 0.781987 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13687.8 | 0.783992 | 0.391996 | − | 0.919967i | \(-0.371785\pi\) | ||||
0.391996 | + | 0.919967i | \(0.371785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16704.6 | + | 1644.81i | 0.952533 | + | 0.0937908i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20519.0 | 1.16486 | 0.582428 | − | 0.812882i | \(-0.302103\pi\) | ||||
0.582428 | + | 0.812882i | \(0.302103\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 12479.9i | − | 0.705354i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21423.5 | + | 11451.3i | −1.20551 | + | 0.644370i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11851.0i | 0.663933i | 0.943291 | + | 0.331967i | \(0.107712\pi\) | ||||
−0.943291 | + | 0.331967i | \(0.892288\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3417.84i | 0.190641i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10622.2 | + | 5677.78i | −0.589899 | + | 0.315314i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 5886.42i | − | 0.325479i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −720.586 | −0.0396706 | −0.0198353 | − | 0.999803i | \(-0.506314\pi\) | ||||
−0.0198353 | + | 0.999803i | \(0.506314\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10160.4 | + | 15206.8i | −0.556946 | + | 0.833560i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4592.45 | 0.250650 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24082.8 | −1.30875 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24482.6 | + | 13086.5i | −1.32477 | + | 0.708122i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3475.26 | 0.187245 | 0.0936226 | − | 0.995608i | \(-0.470155\pi\) | ||||
0.0936226 | + | 0.995608i | \(0.470155\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32520.6i | 1.74472i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1662.84 | − | 3110.88i | −0.0888313 | − | 0.166188i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27383.8i | 1.45668i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3963.46i | − | 0.209945i | −0.994475 | − | 0.104972i | \(-0.966525\pi\) | ||
0.994475 | − | 0.104972i | \(-0.0334754\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20450.6 | − | 13664.1i | −1.07870 | − | 0.720737i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1237.42i | − | 0.0649956i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −457.752 | −0.0239426 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12998.0 | − | 24317.1i | −0.677016 | − | 1.26658i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3328.38 | 0.172639 | 0.0863195 | − | 0.996268i | \(-0.472489\pi\) | ||||
0.0863195 | + | 0.996268i | \(0.472489\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42305.9 | −2.18523 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2989.24 | − | 5592.35i | −0.153763 | − | 0.287665i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12386.6 | 0.634522 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19880.2i | − | 1.01419i | −0.861891 | − | 0.507094i | \(-0.830720\pi\) | ||
0.861891 | − | 0.507094i | \(-0.169280\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19305.0 | + | 3838.94i | 0.980796 | + | 0.195038i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 33585.9i | − | 1.69934i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 11000.8i | − | 0.554330i | −0.960822 | − | 0.277165i | \(-0.910605\pi\) | ||
0.960822 | − | 0.277165i | \(-0.0893949\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3044.22 | + | 5695.20i | 0.152772 | + | 0.285811i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4711.77i | − | 0.235495i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24841.3 | −1.23654 | −0.618269 | − | 0.785966i | \(-0.712166\pi\) | ||||
−0.618269 | + | 0.785966i | \(0.712166\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3390.94 | + | 1812.53i | −0.168110 | + | 0.0898584i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40146.8 | −1.98229 | −0.991147 | − | 0.132769i | \(-0.957613\pi\) | ||||
−0.991147 | + | 0.132769i | \(0.957613\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7005.41 | 0.344508 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7473.35 | − | 4993.34i | −0.366045 | − | 0.244574i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46922.6 | 2.28907 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14430.3i | 0.701159i | 0.936533 | + | 0.350580i | \(0.114015\pi\) | ||||
−0.936533 | + | 0.350580i | \(0.885985\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1767.48 | + | 944.757i | −0.0855385 | + | 0.0457223i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 810.200i | − | 0.0390546i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 36743.8i | − | 1.76417i | −0.471091 | − | 0.882085i | \(-0.656140\pi\) | ||
0.471091 | − | 0.882085i | \(-0.343860\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12207.6 | − | 6525.26i | 0.583807 | − | 0.312058i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 12211.3i | − | 0.581681i | −0.956772 | − | 0.290841i | \(-0.906065\pi\) | ||
0.956772 | − | 0.290841i | \(-0.0939350\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22725.0 | −1.07824 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4850.82 | − | 3241.09i | −0.229257 | − | 0.153179i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 396.879 | 0.0186838 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 547.115 | 0.0256560 | 0.0128280 | − | 0.999918i | \(-0.495917\pi\) | ||||
0.0128280 | + | 0.999918i | \(0.495917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5310.14 | + | 2838.39i | −0.248041 | + | 0.132584i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25467.3 | −1.18499 | −0.592494 | − | 0.805575i | \(-0.701857\pi\) | ||||
−0.592494 | + | 0.805575i | \(0.701857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1269.05i | − | 0.0588202i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −27656.4 | − | 51740.4i | −1.27692 | − | 2.38890i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22042.1i | 1.01379i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 22755.3i | − | 1.04257i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14455.0 | + | 1423.31i | 0.659745 | + | 0.0649616i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 861.987i | − | 0.0391919i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7196.98 | −0.325978 | −0.162989 | − | 0.986628i | \(-0.552113\pi\) | ||||
−0.162989 | + | 0.986628i | \(0.552113\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4108.42 | + | 7686.15i | 0.185378 | + | 0.346811i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31077.5 | −1.39695 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5155.05 | −0.230847 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3853.57 | − | 7209.36i | −0.171914 | − | 0.321622i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30718.6 | 1.36526 | 0.682628 | − | 0.730766i | \(-0.260837\pi\) | ||||
0.682628 | + | 0.730766i | \(0.260837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 27378.2i | − | 1.21223i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18445.7 | − | 12324.5i | −0.813665 | − | 0.543653i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 13562.2i | − | 0.596016i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 8009.99i | − | 0.350702i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9994.85 | + | 18698.7i | 0.435979 | + | 0.815643i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 10427.2i | − | 0.453153i | −0.973993 | − | 0.226577i | \(-0.927247\pi\) | ||
0.973993 | − | 0.226577i | \(-0.0727534\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6840.19 | −0.296167 | −0.148084 | − | 0.988975i | \(-0.547310\pi\) | ||||
−0.148084 | + | 0.988975i | \(0.547310\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2521.80 | − | 1347.96i | 0.108786 | − | 0.0581488i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3133.32 | −0.134669 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30739.9 | −1.31635 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3853.57 | − | 5767.49i | 0.164413 | − | 0.246071i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19729.3 | 0.838683 | 0.419341 | − | 0.907829i | \(-0.362261\pi\) | ||||
0.419341 | + | 0.907829i | \(0.362261\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 13924.4i | − | 0.589763i | −0.955534 | − | 0.294882i | \(-0.904720\pi\) | ||
0.955534 | − | 0.294882i | \(-0.0952803\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12519.7 | − | 6692.05i | 0.528338 | − | 0.282409i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40307.7i | 1.69484i | 0.530921 | + | 0.847421i | \(0.321846\pi\) | ||||
−0.530921 | + | 0.847421i | \(0.678154\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 9091.40i | − | 0.380889i | −0.981698 | − | 0.190445i | \(-0.939007\pi\) | ||
0.981698 | − | 0.190445i | \(-0.0609930\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2145.17 | − | 1146.64i | 0.0895490 | − | 0.0478660i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 50122.3i | 2.08480i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6000.67 | 0.248697 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 145.823 | − | 1480.96i | 0.00602194 | − | 0.0611584i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22517.0 | 0.926549 | 0.463274 | − | 0.886215i | \(-0.346674\pi\) | ||||
0.463274 | + | 0.886215i | \(0.346674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13670.4 | −0.560516 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24389.5 | − | 13036.7i | 0.996464 | − | 0.532632i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4911.66 | −0.199960 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 24014.7i | − | 0.974210i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −269.164 | − | 503.559i | −0.0108807 | − | 0.0203558i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44403.9i | 1.78865i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8230.04i | 0.330353i | 0.986264 | + | 0.165177i | \(0.0528194\pi\) | ||||
−0.986264 | + | 0.165177i | \(0.947181\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2966.45 | + | 4439.78i | −0.118656 | + | 0.177588i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12042.6i | 0.480009i | 0.970772 | + | 0.240005i | \(0.0771490\pi\) | ||||
−0.970772 | + | 0.240005i | \(0.922851\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26661.8 | 1.05901 | 0.529505 | − | 0.848307i | \(-0.322378\pi\) | ||||
0.529505 | + | 0.848307i | \(0.322378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18745.2 | − | 35069.1i | −0.741969 | − | 1.38810i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18444.3 | −0.727521 | −0.363760 | − | 0.931493i | \(-0.618507\pi\) | ||||
−0.363760 | + | 0.931493i | \(0.618507\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8433.96 | 0.331518 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9311.19 | − | 17419.6i | −0.364734 | − | 0.682356i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20801.2 | −0.812005 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1787.04i | 0.0695195i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6310.73 | + | 9445.03i | −0.244657 | + | 0.366169i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 16797.3i | − | 0.648974i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17206.7i | 0.662520i | 0.943539 | + | 0.331260i | \(0.107474\pi\) | ||||
−0.943539 | + | 0.331260i | \(0.892526\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6544.03 | − | 12242.8i | −0.251109 | − | 0.469782i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 34837.3i | − | 1.33223i | −0.745847 | − | 0.666117i | \(-0.767955\pi\) | ||
0.745847 | − | 0.666117i | \(-0.232045\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27943.9 | 1.06499 | 0.532496 | − | 0.846432i | \(-0.321254\pi\) | ||||
0.532496 | + | 0.846432i | \(0.321254\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 486.075 | − | 259.818i | 0.0184624 | − | 0.00986858i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3273.25 | −0.123907 | −0.0619533 | − | 0.998079i | \(-0.519733\pi\) | ||||
−0.0619533 | + | 0.998079i | \(0.519733\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16409.3 | −0.619068 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15379.2 | − | 6370.92i | 0.578253 | − | 0.239544i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25058.3 | −0.939019 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2024.01i | 0.0755922i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4630.01 | + | 2474.85i | −0.172343 | + | 0.0921212i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1098.15i | − | 0.0407402i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 63448.1i | − | 2.34602i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 48907.3 | − | 26142.1i | 1.80236 | − | 0.963403i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 6247.25i | − | 0.229465i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21401.7 | −0.783499 | −0.391749 | − | 0.920072i | \(-0.628130\pi\) | ||||
−0.391749 | + | 0.920072i | \(0.628130\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13847.2 | − | 20724.5i | 0.505260 | − | 0.756204i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3638.18 | 0.132314 | 0.0661572 | − | 0.997809i | \(-0.478926\pi\) | ||||
0.0661572 | + | 0.997809i | \(0.478926\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7601.48 | −0.275545 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6313.63 | + | 3374.78i | −0.228112 | + | 0.121931i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 63824.9 | 2.29846 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53008.1i | 1.90269i | 0.308124 | + | 0.951346i | \(0.400299\pi\) | ||||
−0.308124 | + | 0.951346i | \(0.599701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5981.16 | + | 11189.7i | 0.213991 | + | 0.400341i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8630.42i | 0.307772i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45538.8i | 1.61871i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32017.9 | + | 21392.8i | 1.13442 | + | 0.757964i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 24985.8i | − | 0.882409i | −0.897407 | − | 0.441205i | \(-0.854551\pi\) | ||
0.897407 | − | 0.441205i | \(-0.145449\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45875.2 | 1.61493 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16895.6 | + | 31608.7i | 0.592857 | + | 1.10913i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4933.99 | −0.172576 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14614.3 | 0.509528 | 0.254764 | − | 0.967003i | \(-0.418002\pi\) | ||||
0.254764 | + | 0.967003i | \(0.418002\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12930.7 | − | 24191.1i | −0.449389 | − | 0.840730i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1389.68 | −0.0481425 | −0.0240713 | − | 0.999710i | \(-0.507663\pi\) | ||||
−0.0240713 | + | 0.999710i | \(0.507663\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30096.5i | 1.03932i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 943.927 | − | 9586.46i | 0.0324931 | − | 0.329997i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 28674.0i | − | 0.983928i | −0.870616 | − | 0.491964i | \(-0.836279\pi\) | ||
0.870616 | − | 0.491964i | \(-0.163721\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5143.77i | 0.175947i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3766.29 | + | 7046.09i | 0.128423 | + | 0.240258i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13984.4i | 0.475339i | 0.971346 | + | 0.237669i | \(0.0763835\pi\) | ||||
−0.971346 | + | 0.237669i | \(0.923616\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1638.85 | −0.0555309 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10833.7 | − | 5790.85i | 0.365939 | − | 0.195602i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43801.7 | −1.47490 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29678.5 | 0.996223 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −35511.9 | − | 23727.4i | −1.18832 | − | 0.793982i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8173.16 | −0.272646 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27834.7i | 0.925649i | 0.886450 | + | 0.462825i | \(0.153164\pi\) | ||||
−0.886450 | + | 0.462825i | \(0.846836\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36550.0 | + | 19536.8i | −1.21172 | + | 0.647691i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12546.9i | 0.414676i | 0.978269 | + | 0.207338i | \(0.0664800\pi\) | ||||
−0.978269 | + | 0.207338i | \(0.933520\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 58855.1i | 1.93917i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4748.35 | + | 2538.10i | −0.155968 | + | 0.0833685i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 47934.6i | − | 1.56967i | −0.619708 | − | 0.784833i | \(-0.712749\pi\) | ||
0.619708 | − | 0.784833i | \(-0.287251\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18761.9 | −0.612496 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17198.7 | + | 11491.4i | 0.559747 | + | 0.373997i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44432.7 | 1.44169 | 0.720846 | − | 0.693095i | \(-0.243753\pi\) | ||||
0.720846 | + | 0.693095i | \(0.243753\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11387.5 | −0.368362 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 39867.8 | − | 21310.3i | 1.28572 | − | 0.687247i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −41972.5 | −1.34949 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24714.1i | − | 0.792199i | −0.918208 | − | 0.396100i | \(-0.870363\pi\) | ||
0.918208 | − | 0.396100i | \(-0.129637\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21787.1 | + | 40759.9i | 0.696266 | + | 1.30259i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 611.279i | 0.0194762i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 49387.0i | − | 1.56881i | −0.620250 | − | 0.784405i | \(-0.712969\pi\) | ||
0.620250 | − | 0.784405i | \(-0.287031\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5232.72 | + | 53143.1i | −0.165722 | + | 1.68306i |
(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 | 384.4.f.g.191.8 | yes | 8 | |
3.2 | odd | 2 | 384.4.f.h.191.5 | yes | 8 | ||
4.3 | odd | 2 | 384.4.f.h.191.2 | yes | 8 | ||
8.3 | odd | 2 | 384.4.f.h.191.7 | yes | 8 | ||
8.5 | even | 2 | inner | 384.4.f.g.191.1 | ✓ | 8 | |
12.11 | even | 2 | inner | 384.4.f.g.191.3 | yes | 8 | |
16.3 | odd | 4 | 768.4.c.m.767.3 | 4 | |||
16.5 | even | 4 | 768.4.c.n.767.3 | 4 | |||
16.11 | odd | 4 | 768.4.c.p.767.2 | 4 | |||
16.13 | even | 4 | 768.4.c.o.767.2 | 4 | |||
24.5 | odd | 2 | 384.4.f.h.191.4 | yes | 8 | ||
24.11 | even | 2 | inner | 384.4.f.g.191.6 | yes | 8 | |
48.5 | odd | 4 | 768.4.c.p.767.1 | 4 | |||
48.11 | even | 4 | 768.4.c.n.767.4 | 4 | |||
48.29 | odd | 4 | 768.4.c.m.767.4 | 4 | |||
48.35 | even | 4 | 768.4.c.o.767.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.f.g.191.1 | ✓ | 8 | 8.5 | even | 2 | inner | |
384.4.f.g.191.3 | yes | 8 | 12.11 | even | 2 | inner | |
384.4.f.g.191.6 | yes | 8 | 24.11 | even | 2 | inner | |
384.4.f.g.191.8 | yes | 8 | 1.1 | even | 1 | trivial | |
384.4.f.h.191.2 | yes | 8 | 4.3 | odd | 2 | ||
384.4.f.h.191.4 | yes | 8 | 24.5 | odd | 2 | ||
384.4.f.h.191.5 | yes | 8 | 3.2 | odd | 2 | ||
384.4.f.h.191.7 | yes | 8 | 8.3 | odd | 2 | ||
768.4.c.m.767.3 | 4 | 16.3 | odd | 4 | |||
768.4.c.m.767.4 | 4 | 48.29 | odd | 4 | |||
768.4.c.n.767.3 | 4 | 16.5 | even | 4 | |||
768.4.c.n.767.4 | 4 | 48.11 | even | 4 | |||
768.4.c.o.767.1 | 4 | 48.35 | even | 4 | |||
768.4.c.o.767.2 | 4 | 16.13 | even | 4 | |||
768.4.c.p.767.1 | 4 | 48.5 | odd | 4 | |||
768.4.c.p.767.2 | 4 | 16.11 | odd | 4 |