Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(113,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.ba (of order \(10\), degree \(4\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 701.5 | ||
Character | \(\chi\) | \(=\) | 1148.701 |
Dual form | 1148.2.ba.a.113.16 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) |
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 | ||||||||
\(3\) | − | 2.20495i | − | 1.27303i | −0.771265 | − | 0.636515i | \(-0.780376\pi\) | ||
0.771265 | − | 0.636515i | \(-0.219624\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.330069 | − | 1.01585i | 0.147612 | − | 0.454302i | −0.849726 | − | 0.527224i | \(-0.823233\pi\) |
0.997338 | + | 0.0729229i | \(0.0232327\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.587785 | + | 0.809017i | −0.222162 | + | 0.305780i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.86181 | −0.620603 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.31657 | − | 1.72746i | 1.60301 | − | 0.520849i | 0.635159 | − | 0.772382i | \(-0.280935\pi\) |
0.967849 | + | 0.251533i | \(0.0809346\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00873 | − | 2.76478i | −0.557122 | − | 0.766813i | 0.433835 | − | 0.900992i | \(-0.357160\pi\) |
−0.990957 | + | 0.134180i | \(0.957160\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.23990 | − | 0.727787i | −0.578339 | − | 0.187914i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.76112 | − | 1.22206i | 0.912205 | − | 0.296393i | 0.184940 | − | 0.982750i | \(-0.440791\pi\) |
0.727265 | + | 0.686357i | \(0.240791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.02272 | − | 1.40766i | 0.234629 | − | 0.322939i | −0.675425 | − | 0.737429i | \(-0.736040\pi\) |
0.910054 | + | 0.414489i | \(0.136040\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.78384 | + | 1.29604i | 0.389266 | + | 0.282819i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.68573 | + | 2.67784i | −0.768527 | + | 0.558368i | −0.901514 | − | 0.432750i | \(-0.857543\pi\) |
0.132987 | + | 0.991118i | \(0.457543\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.12208 | + | 2.26832i | 0.624416 | + | 0.453665i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.50966i | − | 0.482984i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.36619 | − | 2.39342i | −1.36787 | − | 0.444447i | −0.469206 | − | 0.883089i | \(-0.655460\pi\) |
−0.898662 | + | 0.438642i | \(0.855460\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.928450 | − | 2.85747i | −0.166754 | − | 0.513218i | 0.832407 | − | 0.554165i | \(-0.186962\pi\) |
−0.999161 | + | 0.0409475i | \(0.986962\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.80896 | − | 11.7228i | −0.663056 | − | 2.04068i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.627829 | + | 0.864133i | 0.106123 | + | 0.146065i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.05950 | − | 3.26080i | 0.174181 | − | 0.536073i | −0.825415 | − | 0.564527i | \(-0.809059\pi\) |
0.999595 | + | 0.0284545i | \(0.00905856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.09621 | + | 4.42916i | −0.976175 | + | 0.709233i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.26380 | − | 3.64587i | −0.822068 | − | 0.569390i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.90364 | − | 3.56270i | 0.747798 | − | 0.543307i | −0.147346 | − | 0.989085i | \(-0.547073\pi\) |
0.895143 | + | 0.445778i | \(0.147073\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.614526 | + | 1.89132i | −0.0916081 | + | 0.281941i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.27597 | + | 8.63813i | 0.915444 | + | 1.26000i | 0.965273 | + | 0.261242i | \(0.0841322\pi\) |
−0.0498296 | + | 0.998758i | \(0.515868\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.309017 | − | 0.951057i | −0.0441453 | − | 0.135865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.69458 | − | 8.29308i | −0.377317 | − | 1.16126i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.9239 | + | 3.87430i | 1.63787 | + | 0.532176i | 0.976061 | − | 0.217497i | \(-0.0697893\pi\) |
0.661808 | + | 0.749673i | \(0.269789\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.97102i | − | 0.805132i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.10382 | − | 2.25506i | −0.411111 | − | 0.298690i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.16482 | + | 5.20554i | −0.932779 | + | 0.677704i | −0.946672 | − | 0.322200i | \(-0.895578\pi\) |
0.0138923 | + | 0.999903i | \(0.495578\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.86047 | − | 2.07825i | −0.366246 | − | 0.266093i | 0.389407 | − | 0.921066i | \(-0.372680\pi\) |
−0.755652 | + | 0.654973i | \(0.772680\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.09434 | − | 1.50623i | 0.137874 | − | 0.189768i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.47162 | + | 1.12800i | −0.430602 | + | 0.139911i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.6075 | − | 4.09644i | −1.54026 | − | 0.500460i | −0.588809 | − | 0.808272i | \(-0.700403\pi\) |
−0.951447 | + | 0.307812i | \(0.900403\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.90450 | + | 8.12684i | 0.710818 | + | 0.978357i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.7395 | + | 4.46425i | −1.63058 | + | 0.529809i | −0.974405 | − | 0.224798i | \(-0.927828\pi\) |
−0.656178 | + | 0.754606i | \(0.727828\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.9081 | −1.27670 | −0.638350 | − | 0.769746i | \(-0.720383\pi\) | ||||
−0.638350 | + | 0.769746i | \(0.720383\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.00155 | − | 6.88404i | 0.577529 | − | 0.794900i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.72746 | + | 5.31657i | −0.196862 | + | 0.605880i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.4283i | 1.39829i | 0.714979 | + | 0.699146i | \(0.246436\pi\) | ||||
−0.714979 | + | 0.699146i | \(0.753564\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1191 | −1.23545 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.53262 | −0.497520 | −0.248760 | − | 0.968565i | \(-0.580023\pi\) | ||||
−0.248760 | + | 0.968565i | \(0.580023\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 4.22409i | − | 0.458167i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.27738 | + | 16.2421i | −0.565794 | + | 1.74134i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.01885 | − | 12.4134i | 0.955997 | − | 1.31582i | 0.00718475 | − | 0.999974i | \(-0.497713\pi\) |
0.948812 | − | 0.315842i | \(-0.102287\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.41746 | 0.358247 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.30059 | + | 2.04719i | −0.653341 | + | 0.212283i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.09240 | − | 1.50356i | −0.112078 | − | 0.154262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.9484 | + | 5.18194i | 1.61931 | + | 0.526147i | 0.971780 | − | 0.235890i | \(-0.0758006\pi\) |
0.647533 | + | 0.762037i | \(0.275801\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.89844 | + | 3.21620i | −0.994831 | + | 0.323240i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.39981 | − | 11.5613i | 0.835812 | − | 1.15040i | −0.151001 | − | 0.988534i | \(-0.548250\pi\) |
0.986813 | − | 0.161863i | \(-0.0517502\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.14596 | − | 5.91839i | −0.802645 | − | 0.583156i | 0.109044 | − | 0.994037i | \(-0.465221\pi\) |
−0.911689 | + | 0.410881i | \(0.865221\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.90537 | − | 1.38433i | 0.185945 | − | 0.135097i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.7104 | + | 10.6878i | 1.42211 | + | 1.03322i | 0.991419 | + | 0.130725i | \(0.0417306\pi\) |
0.430692 | + | 0.902499i | \(0.358269\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.37498i | − | 0.514829i | −0.966301 | − | 0.257415i | \(-0.917129\pi\) | ||
0.966301 | − | 0.257415i | \(-0.0828706\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.18991 | − | 2.33614i | −0.682436 | − | 0.221737i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.76907 | − | 8.52231i | −0.260492 | − | 0.801712i | −0.992698 | − | 0.120628i | \(-0.961509\pi\) |
0.732206 | − | 0.681083i | \(-0.238491\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50373 | + | 4.62801i | 0.140224 | + | 0.431564i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.73988 | + | 5.14750i | 0.345752 | + | 0.475886i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.22206 | + | 3.76112i | −0.112026 | + | 0.344781i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.3827 | − | 11.9027i | 1.48933 | − | 1.08206i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.03897 | + | 11.6064i | −0.724850 | + | 1.04652i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.65544 | − | 5.56201i | 0.684724 | − | 0.497481i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.21449 | + | 12.9709i | −0.373976 | + | 1.15098i | 0.570191 | + | 0.821512i | \(0.306869\pi\) |
−0.944167 | + | 0.329467i | \(0.893131\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.85558 | − | 10.8123i | −0.691645 | − | 0.951968i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.26107 | − | 13.1142i | −0.372291 | − | 1.14579i | −0.945288 | − | 0.326237i | \(-0.894219\pi\) |
0.572997 | − | 0.819558i | \(-0.305781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.537678 | + | 1.65480i | 0.0466226 | + | 0.143490i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.54943 | − | 0.828361i | −0.219420 | − | 0.0712939i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.4026i | 1.82855i | 0.405096 | + | 0.914274i | \(0.367238\pi\) | ||||
−0.405096 | + | 0.914274i | \(0.632762\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.8585 | + | 10.7953i | 1.26028 | + | 0.915646i | 0.998771 | − | 0.0495552i | \(-0.0157804\pi\) |
0.261507 | + | 0.965201i | \(0.415780\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.0466 | − | 13.8382i | 1.60402 | − | 1.16539i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.4556 | − | 11.2292i | −1.29246 | − | 0.939030i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.86271 | + | 6.69295i | −0.403826 | + | 0.555819i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.09703 | + | 0.681367i | −0.172960 | + | 0.0561982i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.57343 | − | 1.48600i | −0.374670 | − | 0.121738i | 0.115628 | − | 0.993293i | \(-0.463112\pi\) |
−0.490298 | + | 0.871555i | \(0.663112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.53809 | + | 8.99891i | 0.532062 | + | 0.732321i | 0.987443 | − | 0.157976i | \(-0.0504969\pi\) |
−0.455381 | + | 0.890297i | \(0.650497\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.00248 | + | 2.27524i | −0.566117 | + | 0.183943i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.20922 | −0.257770 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.84359 | − | 5.29024i | 0.306752 | − | 0.422207i | −0.627613 | − | 0.778525i | \(-0.715968\pi\) |
0.934365 | + | 0.356318i | \(0.115968\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.54264 | − | 26.2915i | 0.677475 | − | 2.08505i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.55581i | − | 0.359048i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.6077 | 1.92743 | 0.963713 | − | 0.266940i | \(-0.0860124\pi\) | ||||
0.963713 | + | 0.266940i | \(0.0860124\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.1658 | −1.02496 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.59827i | − | 0.665354i | −0.943041 | − | 0.332677i | \(-0.892048\pi\) | ||
0.943041 | − | 0.332677i | \(-0.107952\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.408202 | − | 1.25632i | 0.0314001 | − | 0.0966396i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.90412 | + | 2.62079i | −0.145611 | + | 0.200417i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.08318 | 0.690581 | 0.345291 | − | 0.938496i | \(-0.387780\pi\) | ||||
0.345291 | + | 0.938496i | \(0.387780\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.67023 | + | 1.19253i | −0.277443 | + | 0.0901467i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.4780 | + | 15.7981i | 0.862737 | + | 1.18746i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.4649 | − | 4.37502i | −1.00642 | − | 0.327004i | −0.240989 | − | 0.970528i | \(-0.577472\pi\) |
−0.765426 | + | 0.643523i | \(0.777472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.33116 | − | 0.432519i | 0.0989440 | − | 0.0321488i | −0.259127 | − | 0.965843i | \(-0.583435\pi\) |
0.358071 | + | 0.933695i | \(0.383435\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.58244 | + | 6.30719i | −0.338744 | + | 0.466241i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.96278 | − | 2.15258i | −0.217828 | − | 0.158261i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.8852 | − | 12.9944i | 1.30789 | − | 0.950241i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.03035 | + | 1.47514i | 0.147687 | + | 0.107301i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 9.92297i | − | 0.718001i | −0.933337 | − | 0.359000i | \(-0.883118\pi\) | ||
0.933337 | − | 0.359000i | \(-0.116882\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.2100 | + | 7.86629i | 1.74267 | + | 0.566228i | 0.995182 | − | 0.0980465i | \(-0.0312594\pi\) |
0.747489 | + | 0.664274i | \(0.231259\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.48718 | + | 7.65476i | 0.178111 | + | 0.548169i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.95627 | − | 15.2538i | −0.353119 | − | 1.08679i | −0.957092 | − | 0.289784i | \(-0.906416\pi\) |
0.603973 | − | 0.797005i | \(-0.293584\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.1025 | + | 15.2812i | 0.787032 | + | 1.08326i | 0.994471 | + | 0.105009i | \(0.0334870\pi\) |
−0.207439 | + | 0.978248i | \(0.566513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.03245 | + | 27.7990i | −0.637100 | + | 1.96079i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.26606 | − | 4.55256i | 0.439791 | − | 0.319527i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.44108 | + | 4.14384i | −0.380021 | + | 0.289418i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.86212 | − | 4.98562i | 0.476950 | − | 0.346524i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.00572 | − | 9.25064i | 0.207910 | − | 0.639880i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.55354 | + | 6.26741i | 0.313478 | + | 0.431466i | 0.936462 | − | 0.350769i | \(-0.114080\pi\) |
−0.622984 | + | 0.782235i | \(0.714080\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.84345 | + | 30.2950i | 0.674462 | + | 2.07578i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.00063 | − | 6.15729i | −0.136442 | − | 0.419924i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.85747 | + | 0.928450i | 0.193978 | + | 0.0630273i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.0519i | 1.62528i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.9338 | − | 7.94388i | −0.735488 | − | 0.534363i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.503414 | + | 0.365751i | −0.0337111 | + | 0.0244925i | −0.604513 | − | 0.796595i | \(-0.706632\pi\) |
0.570802 | + | 0.821088i | \(0.306632\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.81272 | − | 4.22319i | −0.387515 | − | 0.281546i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.914233 | − | 1.25833i | 0.0606798 | − | 0.0835185i | −0.777599 | − | 0.628761i | \(-0.783562\pi\) |
0.838278 | + | 0.545242i | \(0.183562\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.43963 | + | 1.76744i | −0.359461 | + | 0.116796i | −0.483179 | − | 0.875521i | \(-0.660518\pi\) |
0.123718 | + | 0.992317i | \(0.460518\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.7228 | + | 3.80896i | 0.771303 | + | 0.250611i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.87218 | + | 2.57683i | 0.122650 | + | 0.168814i | 0.865927 | − | 0.500171i | \(-0.166729\pi\) |
−0.743277 | + | 0.668984i | \(0.766729\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.8465 | − | 3.52425i | 0.707550 | − | 0.229897i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.4038 | 1.78007 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.74546 | + | 6.53157i | −0.306959 | + | 0.422492i | −0.934430 | − | 0.356148i | \(-0.884090\pi\) |
0.627471 | + | 0.778640i | \(0.284090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.916839 | + | 2.82174i | −0.0590588 | + | 0.181764i | −0.976234 | − | 0.216721i | \(-0.930464\pi\) |
0.917175 | + | 0.398485i | \(0.130464\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.9881i | 1.08979i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.06813 | −0.0682401 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.94625 | −0.378351 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.99420i | 0.633357i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.791662 | + | 2.43649i | −0.0499693 | + | 0.153790i | −0.972928 | − | 0.231111i | \(-0.925764\pi\) |
0.922958 | + | 0.384900i | \(0.125764\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.9696 | + | 20.6039i | −0.941130 | + | 1.29535i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.31391 | −0.583260 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.4365 | − | 5.99037i | 1.15004 | − | 0.373669i | 0.328879 | − | 0.944372i | \(-0.393329\pi\) |
0.821156 | + | 0.570703i | \(0.193329\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.01529 | + | 2.77380i | 0.125224 | + | 0.172356i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.7144 | + | 4.45609i | 0.848903 | + | 0.275825i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.91625 | − | 2.24722i | 0.426474 | − | 0.138570i | −0.0879126 | − | 0.996128i | \(-0.528020\pi\) |
0.514387 | + | 0.857558i | \(0.328020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.87141 | − | 10.8341i | 0.483537 | − | 0.665531i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.3709 | − | 19.8861i | −1.67507 | − | 1.21701i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.56637 | + | 4.77074i | −0.400358 | + | 0.290877i | −0.769687 | − | 0.638421i | \(-0.779588\pi\) |
0.369329 | + | 0.929299i | \(0.379588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.4038 | + | 7.55881i | 0.631986 | + | 0.459165i | 0.857088 | − | 0.515170i | \(-0.172271\pi\) |
−0.225101 | + | 0.974335i | \(0.572271\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 7.53533i | − | 0.456059i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.5172 | + | 6.66645i | 1.23723 | + | 0.402002i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.11028 | + | 6.49478i | 0.126795 | + | 0.390234i | 0.994224 | − | 0.107327i | \(-0.0342292\pi\) |
−0.867429 | + | 0.497561i | \(0.834229\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.72860 | + | 5.32007i | 0.103488 | + | 0.318504i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.04328 | − | 12.4470i | −0.539477 | − | 0.742526i | 0.449061 | − | 0.893501i | \(-0.351759\pi\) |
−0.988538 | + | 0.150975i | \(0.951759\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.44165 | + | 13.6700i | −0.264029 | + | 0.812598i | 0.727887 | + | 0.685698i | \(0.240503\pi\) |
−0.991916 | + | 0.126900i | \(0.959497\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.31527 | + | 2.40869i | −0.196380 | + | 0.142678i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.04356 | − | 2.11552i | 0.356740 | − | 0.124875i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.10073 | + | 0.799726i | −0.0647487 | + | 0.0470427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.4259 | − | 35.1654i | 0.669800 | − | 2.06143i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1292 | + | 16.6944i | 0.708593 | + | 0.975295i | 0.999826 | + | 0.0186429i | \(0.00593457\pi\) |
−0.291233 | + | 0.956652i | \(0.594065\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.92316 | + | 8.99656i | 0.170193 | + | 0.523800i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.33533 | − | 13.3428i | −0.251561 | − | 0.774226i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.8073 | + | 4.81117i | 0.856327 | + | 0.278237i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.06123i | 0.349363i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.4922 | − | 18.5212i | −1.46449 | − | 1.06401i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.05534 | + | 2.21984i | −0.174948 | + | 0.127108i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.82298 | + | 2.77756i | 0.218189 | + | 0.158524i | 0.691511 | − | 0.722366i | \(-0.256945\pi\) |
−0.473322 | + | 0.880889i | \(0.656945\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.0498 | + | 17.9614i | −0.742374 | + | 1.02179i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.54491 | − | 0.501971i | 0.0876037 | − | 0.0284642i | −0.264887 | − | 0.964279i | \(-0.585335\pi\) |
0.352491 | + | 0.935815i | \(0.385335\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0227 | − | 3.90641i | −0.679562 | − | 0.220803i | −0.0511584 | − | 0.998691i | \(-0.516291\pi\) |
−0.628404 | + | 0.777887i | \(0.716291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.16890 | − | 1.60885i | −0.0658599 | − | 0.0906484i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.83338 | − | 0.920620i | 0.159138 | − | 0.0517072i | −0.228364 | − | 0.973576i | \(-0.573338\pi\) |
0.387503 | + | 0.921869i | \(0.373338\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −43.2975 | −2.42419 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.5660 | − | 32.4358i | 1.31532 | − | 1.81039i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.12634 | − | 6.54420i | 0.118313 | − | 0.364129i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 13.1883i | − | 0.731557i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.8516 | −0.655393 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.6773 | −0.588659 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.86236i | 0.487119i | 0.969886 | + | 0.243560i | \(0.0783152\pi\) | ||||
−0.969886 | + | 0.243560i | \(0.921685\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.97258 | + | 6.07099i | −0.108097 | + | 0.332688i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.32273 | + | 11.4553i | −0.454719 | + | 0.625867i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.39537 | 0.457325 | 0.228662 | − | 0.973506i | \(-0.426565\pi\) | ||||
0.228662 | + | 0.973506i | \(0.426565\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.7913 | + | 6.10566i | −1.02060 | + | 0.331614i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.87234 | − | 13.5881i | −0.534617 | − | 0.735838i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.951057 | + | 0.309017i | 0.0513522 | + | 0.0166853i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.2045 | − | 3.31566i | 0.549394 | − | 0.178509i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.5449 | + | 17.2665i | −0.673443 | + | 0.926915i | −0.999832 | − | 0.0183206i | \(-0.994168\pi\) |
0.326389 | + | 0.945236i | \(0.394168\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.08784 | + | 6.60270i | 0.486461 | + | 0.353434i | 0.803822 | − | 0.594870i | \(-0.202797\pi\) |
−0.317361 | + | 0.948305i | \(0.602797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.93865 | + | 5.04123i | −0.370358 | + | 0.269081i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7785 | + | 9.28410i | 0.680129 | + | 0.494143i | 0.873401 | − | 0.487003i | \(-0.161910\pi\) |
−0.193271 | + | 0.981145i | \(0.561910\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.4308i | 0.818982i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.29308 | + | 2.69458i | 0.438916 | + | 0.142612i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.15607 | − | 18.9464i | −0.324905 | − | 0.999954i | −0.971484 | − | 0.237107i | \(-0.923801\pi\) |
0.646579 | − | 0.762847i | \(-0.276199\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.93578 | + | 15.1908i | 0.259778 | + | 0.799515i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −26.2449 | − | 36.1230i | −1.37750 | − | 1.89596i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.60044 | + | 11.0810i | −0.188456 | + | 0.580007i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0800 | − | 10.9562i | 0.787167 | − | 0.571911i | −0.119954 | − | 0.992779i | \(-0.538275\pi\) |
0.907121 | + | 0.420869i | \(0.138275\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.80019 | + | 6.78792i | 0.510178 | + | 0.353365i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.1430 | + | 7.36935i | −0.526601 | + | 0.382598i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.79228 | − | 17.8268i | 0.299913 | − | 0.923038i | −0.681614 | − | 0.731712i | \(-0.738721\pi\) |
0.981527 | − | 0.191325i | \(-0.0612786\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.2639 | − | 16.8799i | −0.633308 | − | 0.871673i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.17942 | + | 25.1737i | 0.421262 | + | 1.29651i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.80057 | + | 8.61927i | 0.143856 | + | 0.442742i | 0.996862 | − | 0.0791582i | \(-0.0252232\pi\) |
−0.853006 | + | 0.521901i | \(0.825223\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.6001 | + | 9.29275i | 1.46523 | + | 0.476082i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.82414i | 0.501990i | 0.967988 | + | 0.250995i | \(0.0807578\pi\) | ||||
−0.967988 | + | 0.250995i | \(0.919242\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.83066 | + | 3.50968i | 0.246193 | + | 0.178870i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.12964 | + | 6.63307i | −0.464085 | + | 0.337178i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.1740 | + | 17.5634i | 1.22567 | + | 0.890500i | 0.996558 | − | 0.0829006i | \(-0.0264184\pi\) |
0.229110 | + | 0.973401i | \(0.426418\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.5900 | + | 14.5758i | −0.535557 | + | 0.737132i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.9162 | + | 9.39545i | −1.45863 | + | 0.473938i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.6253 | + | 4.10220i | 0.635247 | + | 0.206404i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.1494 | + | 29.1097i | 1.06146 | + | 1.46097i | 0.878433 | + | 0.477865i | \(0.158589\pi\) |
0.183026 | + | 0.983108i | \(0.441411\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.64876 | − | 1.18555i | 0.182666 | − | 0.0593519i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.2722 | −0.562906 | −0.281453 | − | 0.959575i | \(-0.590816\pi\) | ||||
−0.281453 | + | 0.959575i | \(0.590816\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.03529 | + | 8.30686i | −0.300639 | + | 0.413794i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.67007 | + | 11.2953i | −0.182367 | + | 0.561269i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 19.1665i | − | 0.950050i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.62406 | 0.179198 | 0.0895991 | − | 0.995978i | \(-0.471441\pi\) | ||||
0.0895991 | + | 0.995978i | \(0.471441\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 47.1917 | 2.32779 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 8.85620i | − | 0.435785i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.49608 | + | 4.60446i | −0.0734396 | + | 0.226024i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.8031 | − | 32.7622i | 1.16564 | − | 1.60437i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.7161 | −1.84255 | −0.921277 | − | 0.388907i | \(-0.872853\pi\) | ||||
−0.921277 | + | 0.388907i | \(0.872853\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.6788 | + | 8.66846i | −1.30024 | + | 0.422475i | −0.875666 | − | 0.482917i | \(-0.839577\pi\) |
−0.424577 | + | 0.905392i | \(0.639577\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.6846 | − | 16.0825i | −0.568127 | − | 0.781960i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.5145 | + | 4.71606i | 0.704059 | + | 0.228763i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.36268 | − | 1.09260i | 0.162732 | − | 0.0528747i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.7598 | + | 34.0789i | −1.19541 | + | 1.64534i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.39678 | + | 1.01482i | 0.0672803 | + | 0.0488820i | 0.620917 | − | 0.783876i | \(-0.286760\pi\) |
−0.553637 | + | 0.832758i | \(0.686760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.41555 | + | 5.38771i | −0.356368 | + | 0.258917i | −0.751536 | − | 0.659692i | \(-0.770687\pi\) |
0.395167 | + | 0.918609i | \(0.370687\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.7576 | + | 10.7220i | 0.707574 | + | 0.514082i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.92694i | 0.379197i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.29845 | + | 2.37141i | 0.348336 | + | 0.113181i | 0.477959 | − | 0.878382i | \(-0.341377\pi\) |
−0.129623 | + | 0.991563i | \(0.541377\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.575331 | + | 1.77069i | 0.0273967 | + | 0.0843183i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.33269 | − | 10.2570i | −0.158341 | − | 0.487323i | 0.840143 | − | 0.542365i | \(-0.182471\pi\) |
−0.998484 | + | 0.0550417i | \(0.982471\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.63328 | − | 13.2591i | −0.456661 | − | 0.628540i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.27655 | + | 10.0842i | −0.154976 | + | 0.476966i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.16655 | + | 5.20680i | −0.338210 | + | 0.245724i | −0.743906 | − | 0.668284i | \(-0.767029\pi\) |
0.405696 | + | 0.914008i | \(0.367029\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −34.2835 | − | 10.2905i | −1.61435 | − | 0.484563i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.8421 | − | 14.4162i | 0.932266 | − | 0.677331i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.12800 | − | 3.47162i | 0.0528814 | − | 0.162752i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5036 | − | 17.2097i | −0.584894 | − | 0.805037i | 0.409328 | − | 0.912387i | \(-0.365763\pi\) |
−0.994221 | + | 0.107350i | \(0.965763\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.06695 | − | 9.43911i | −0.143153 | − | 0.440580i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.17138 | − | 15.9159i | −0.240855 | − | 0.741277i | −0.996291 | − | 0.0860532i | \(-0.972574\pi\) |
0.755435 | − | 0.655223i | \(-0.227426\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.22163 | + | 0.721852i | 0.103248 | + | 0.0335473i | 0.360185 | − | 0.932881i | \(-0.382713\pi\) |
−0.256937 | + | 0.966428i | \(0.582713\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.07616i | 0.328149i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.4367 | + | 9.03582i | 0.575504 | + | 0.418128i | 0.837100 | − | 0.547049i | \(-0.184249\pi\) |
−0.261596 | + | 0.965177i | \(0.584249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.7246 | − | 7.79189i | 0.495217 | − | 0.359796i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.6647 | − | 8.47492i | −0.537482 | − | 0.390504i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.9161 | − | 27.4122i | 0.915745 | − | 1.26041i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.38606 | − | 2.07496i | 0.293012 | − | 0.0952055i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.2000 | − | 7.21320i | −1.01647 | − | 0.330270i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.79468 | − | 6.59932i | −0.219075 | − | 0.301530i | 0.685307 | − | 0.728254i | \(-0.259668\pi\) |
−0.904382 | + | 0.426723i | \(0.859668\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.1437 | + | 3.62080i | −0.508107 | + | 0.165094i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.0453 | −0.457078 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.5281 | − | 14.4908i | 0.478058 | − | 0.657991i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.24971 | − | 28.4677i | 0.419144 | − | 1.28999i | −0.489347 | − | 0.872089i | \(-0.662765\pi\) |
0.908491 | − | 0.417904i | \(-0.137235\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 54.2588i | − | 2.45367i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.63713 | −0.434918 | −0.217459 | − | 0.976069i | \(-0.569777\pi\) | ||||
−0.217459 | + | 0.976069i | \(0.569777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.6300 | −1.37951 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.1169i | 0.499667i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.46425 | − | 13.7395i | 0.200249 | − | 0.616303i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.80684 | − | 6.61605i | 0.215184 | − | 0.296175i | −0.687756 | − | 0.725942i | \(-0.741404\pi\) |
0.902940 | + | 0.429767i | \(0.141404\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.9588 | −0.847015 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.2337 | − | 3.97496i | 0.545472 | − | 0.177235i | −0.0233018 | − | 0.999728i | \(-0.507418\pi\) |
0.568774 | + | 0.822494i | \(0.307418\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.97206 | − | 12.3490i | −0.399251 | − | 0.549522i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.77011 | − | 0.900064i | −0.123025 | − | 0.0399733i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.9104 | + | 3.54501i | −0.483596 | + | 0.157130i | −0.540661 | − | 0.841241i | \(-0.681826\pi\) |
0.0570651 | + | 0.998370i | \(0.481826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.41164 | − | 8.82486i | 0.283634 | − | 0.390389i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.53274 | − | 2.56669i | −0.155974 | − | 0.113322i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.70092 | + | 6.32159i | −0.383408 | + | 0.278562i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 48.2887 | + | 35.0838i | 2.12373 | + | 1.54298i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 20.0280i | − | 0.879130i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.4065 | − | 6.30554i | −0.850213 | − | 0.276251i | −0.148678 | − | 0.988886i | \(-0.547502\pi\) |
−0.701535 | + | 0.712635i | \(0.747502\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.71513 | + | 23.7447i | 0.337359 | + | 1.03828i | 0.965548 | + | 0.260224i | \(0.0837964\pi\) |
−0.628189 | + | 0.778061i | \(0.716204\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.62947 | + | 8.09267i | 0.114759 | + | 0.353193i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.98401 | − | 9.61267i | −0.304228 | − | 0.418734i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.693625 | + | 2.13476i | −0.0301576 | + | 0.0928156i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.3395 | − | 9.69172i | 0.578886 | − | 0.420585i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.493523 | + | 21.8769i | 0.0213768 | + | 0.947592i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.7126 | − | 11.4159i | 0.679315 | − | 0.493551i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.64670 | + | 29.6895i | −0.416286 | + | 1.28120i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.28582 | − | 4.52255i | −0.141530 | − | 0.194800i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.41570 | + | 16.6678i | 0.232839 | + | 0.716606i | 0.997401 | + | 0.0720548i | \(0.0229556\pi\) |
−0.764561 | + | 0.644551i | \(0.777044\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.953682 | − | 2.93513i | −0.0409264 | − | 0.125959i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.46017 | − | 1.77412i | −0.233888 | − | 0.0759947i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.75156i | − | 0.331433i | −0.986173 | − | 0.165716i | \(-0.947006\pi\) | ||
0.986173 | − | 0.165716i | \(-0.0529936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.32565 | + | 3.86931i | 0.227293 | + | 0.165138i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.9027 | + | 7.92128i | −0.464471 | + | 0.337458i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0547 | − | 7.30517i | −0.427570 | − | 0.310647i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.74634 | + | 6.53277i | −0.201471 | + | 0.277301i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.305159 | + | 0.0991523i | −0.0129300 | + | 0.00420122i | −0.315475 | − | 0.948934i | \(-0.602164\pi\) |
0.302545 | + | 0.953135i | \(0.402164\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.7002 | − | 6.40098i | −0.833229 | − | 0.270733i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.6519 | − | 39.4360i | −1.20968 | − | 1.66499i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.5981 | + | 10.5918i | −1.37385 | + | 0.446389i | −0.900641 | − | 0.434564i | \(-0.856903\pi\) |
−0.473204 | + | 0.880953i | \(0.656903\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.57137 | −0.402671 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.53564 | − | 8.99554i | 0.274471 | − | 0.377777i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.39260 | − | 22.7521i | 0.309914 | − | 0.953817i | −0.667884 | − | 0.744266i | \(-0.732800\pi\) |
0.977798 | − | 0.209551i | \(-0.0672004\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 27.2312i | − | 1.13959i | −0.821787 | − | 0.569795i | \(-0.807023\pi\) | ||
0.821787 | − | 0.569795i | \(-0.192977\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.8797 | −0.914036 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.5813 | −0.733193 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.6446i | 0.734556i | 0.930111 | + | 0.367278i | \(0.119710\pi\) | ||||
−0.930111 | + | 0.367278i | \(0.880290\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.3448 | − | 53.3818i | 0.720825 | − | 2.21847i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.66421 | − | 3.66697i | 0.110530 | − | 0.152131i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 70.0868 | 2.90270 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.46350 | − | 2.10012i | 0.267233 | − | 0.0868292i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.1829 | + | 23.6502i | 0.709214 | + | 0.976150i | 0.999814 | + | 0.0193049i | \(0.00614531\pi\) |
−0.290599 | + | 0.956845i | \(0.593855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.97190 | − | 1.61547i | −0.204864 | − | 0.0665642i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −33.6339 | + | 10.9283i | −1.38351 | + | 0.449531i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.6676 | − | 36.7048i | 1.09511 | − | 1.50728i | 0.253390 | − | 0.967364i | \(-0.418454\pi\) |
0.841716 | − | 0.539920i | \(-0.181546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.41736 | + | 2.48286i | 0.140098 | + | 0.101787i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33.6943 | − | 24.4804i | 1.37902 | − | 1.00191i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.6826 | + | 18.6595i | 1.04936 | + | 0.762408i | 0.972091 | − | 0.234602i | \(-0.0753788\pi\) |
0.0772727 | + | 0.997010i | \(0.475379\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.02470i | 0.0417982i | 0.999782 | + | 0.0208991i | \(0.00665288\pi\) | ||||
−0.999782 | + | 0.0208991i | \(0.993347\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.4728 | + | 7.62679i | 0.955888 | + | 0.310587i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.68393 | − | 20.5710i | −0.271741 | − | 0.836331i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.30145 | − | 10.1608i | −0.134002 | − | 0.412415i | 0.861432 | − | 0.507874i | \(-0.169568\pi\) |
−0.995433 | + | 0.0954583i | \(0.969568\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.0382 | − | 13.8164i | −0.406767 | − | 0.559867i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.2758 | − | 34.7034i | 0.456170 | − | 1.40395i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.4795 | + | 24.3243i | −1.35223 | + | 0.982450i | −0.353329 | + | 0.935499i | \(0.614950\pi\) |
−0.998897 | + | 0.0469507i | \(0.985050\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.13696 | + | 11.9973i | 0.368438 | + | 0.483778i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.49118 | + | 2.53649i | −0.140550 | + | 0.102115i | −0.655838 | − | 0.754901i | \(-0.727685\pi\) |
0.515289 | + | 0.857017i | \(0.327685\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.5968 | − | 35.6912i | 0.466114 | − | 1.43455i | −0.391462 | − | 0.920194i | \(-0.628031\pi\) |
0.857576 | − | 0.514357i | \(-0.171969\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.72045 | + | 9.24990i | 0.269682 | + | 0.371186i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.74149 | + | 14.5928i | 0.189964 | + | 0.584649i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.83931 | + | 8.73851i | 0.113573 | + | 0.349540i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.3972 | − | 6.62746i | −0.814586 | − | 0.264675i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 13.5590i | − | 0.540634i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.0099 | + | 16.7177i | 0.916011 | + | 0.665521i | 0.942528 | − | 0.334128i | \(-0.108442\pi\) |
−0.0265172 | + | 0.999648i | \(0.508442\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.8193 | − | 10.0403i | 0.549269 | − | 0.399067i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.7854 | + | 8.56258i | 0.467688 | + | 0.339796i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.00873 | + | 2.76478i | −0.0795889 | + | 0.109545i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.5804 | − | 8.31157i | 1.01194 | − | 0.328801i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.20271 | − | 0.715703i | −0.0870017 | − | 0.0282686i | 0.265193 | − | 0.964195i | \(-0.414564\pi\) |
−0.352194 | + | 0.935927i | \(0.614564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.6102 | + | 31.1203i | 0.891659 | + | 1.22726i | 0.973053 | + | 0.230581i | \(0.0740628\pi\) |
−0.0813941 | + | 0.996682i | \(0.525937\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.5765 | + | 4.41128i | −0.534575 | + | 0.173694i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.2154 | −1.46309 | −0.731545 | − | 0.681793i | \(-0.761200\pi\) | ||||
−0.731545 | + | 0.681793i | \(0.761200\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.0999 | + | 40.0526i | −1.14227 | + | 1.57220i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.04719 | − | 6.30059i | 0.0802355 | − | 0.246940i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 3.29204i | − | 0.128828i | −0.997923 | − | 0.0644138i | \(-0.979482\pi\) | ||
0.997923 | − | 0.0644138i | \(-0.0205178\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.7285 | −0.575491 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.3088 | 0.792324 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.7347i | 1.39203i | 0.718029 | + | 0.696013i | \(0.245044\pi\) | ||||
−0.718029 | + | 0.696013i | \(0.754956\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.6180 | − | 35.7566i | 0.451888 | − | 1.39077i | −0.422862 | − | 0.906194i | \(-0.638974\pi\) |
0.874750 | − | 0.484575i | \(-0.161026\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.5159 | + | 24.1085i | −0.680260 | + | 0.936297i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.85850 | 0.0720696 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.5590 | − | 10.9040i | 1.29941 | − | 0.422203i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.806464 | + | 1.11000i | 0.0311797 | + | 0.0429152i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.7980 | − | 6.10784i | −0.725689 | − | 0.235790i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.8961 | − | 3.86528i | 0.458562 | − | 0.148996i | −0.0706218 | − | 0.997503i | \(-0.522498\pi\) |
0.529183 | + | 0.848507i | \(0.322498\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.69272 | − | 7.83535i | 0.219113 | − | 0.301583i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.1060 | − | 20.4202i | −1.08020 | − | 0.784811i | −0.102482 | − | 0.994735i | \(-0.532678\pi\) |
−0.977718 | + | 0.209924i | \(0.932678\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.5665 | + | 9.85664i | −0.520635 | + | 0.378263i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.77456 | − | 2.01584i | −0.106322 | − | 0.0772471i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 22.9328i | − | 0.877498i | −0.898610 | − | 0.438749i | \(-0.855422\pi\) | ||
0.898610 | − | 0.438749i | \(-0.144578\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.7418 | + | 7.06435i | 0.830712 | + | 0.269915i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.89712 | + | 11.9941i | 0.148685 | + | 0.457604i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.2403 | − | 40.7493i | −0.504414 | − | 1.55243i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.68166 | − | 7.82013i | −0.216140 | − | 0.297492i | 0.687155 | − | 0.726511i | \(-0.258859\pi\) |
−0.903295 | + | 0.429019i | \(0.858859\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.21620 | − | 9.89844i | 0.122173 | − | 0.376011i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.8707 | − | 11.5308i | 0.602011 | − | 0.437387i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.2532 | − | 7.27986i | −0.918657 | − | 0.275745i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.68178 | − | 4.12806i | 0.214905 | − | 0.156137i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.2314 | + | 43.7998i | −0.537513 | + | 1.65429i | 0.200643 | + | 0.979664i | \(0.435697\pi\) |
−0.738156 | + | 0.674630i | \(0.764303\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.50652 | − | 4.82632i | −0.132251 | − | 0.182028i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.77081 | − | 23.9161i | −0.292665 | − | 0.900732i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.41604 | + | 13.5912i | 0.166082 | + | 0.511149i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.7980 | − | 11.6315i | −1.34442 | − | 0.436830i | −0.453611 | − | 0.891200i | \(-0.649864\pi\) |
−0.890813 | + | 0.454370i | \(0.849864\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 23.1391i | − | 0.867785i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.0739 | + | 8.04563i | 0.414719 | + | 0.301311i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.5086 | + | 11.9942i | −0.617386 | + | 0.448557i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.4018 | + | 10.4635i | 0.537845 | + | 0.390767i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.4842 | + | 29.5704i | −0.801225 | + | 1.10279i | 0.191394 | + | 0.981513i | \(0.438699\pi\) |
−0.992619 | + | 0.121278i | \(0.961301\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.57615 | − | 3.11148i | 0.356634 | − | 0.115878i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.22180 | + | 2.02159i | 0.231391 | + | 0.0751836i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.5688 | − | 24.1814i | −0.652489 | − | 0.898074i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.8788 | + | 6.78394i | −0.774352 | + | 0.251602i | −0.669427 | − | 0.742878i | \(-0.733460\pi\) |
−0.104925 | + | 0.994480i | \(0.533460\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.10062 | 0.151875 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.0893 | − | 19.3923i | 0.521112 | − | 0.717249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.79225 | + | 5.51599i | −0.0661984 | + | 0.203738i | −0.978684 | − | 0.205370i | \(-0.934160\pi\) |
0.912486 | + | 0.409108i | \(0.134160\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.35517i | 0.0868717i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −74.1054 | −2.72971 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.3353 | 1.59412 | 0.797058 | − | 0.603902i | \(-0.206388\pi\) | ||||
0.797058 | + | 0.603902i | \(0.206388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.1112i | 0.481652i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.3917 | − | 47.3708i | 0.564667 | − | 1.73787i | −0.104270 | − | 0.994549i | \(-0.533251\pi\) |
0.668937 | − | 0.743319i | \(-0.266749\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.01910 | + | 4.15543i | −0.110611 | + | 0.152243i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.43887 | 0.308762 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.2931 | + | 5.61888i | −0.631878 | + | 0.205310i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.55063 | − | 2.13427i | −0.0565835 | − | 0.0778804i | 0.779788 | − | 0.626044i | \(-0.215327\pi\) |
−0.836371 | + | 0.548164i | \(0.815327\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.37233 | + | 1.74558i | 0.195779 | + | 0.0636123i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.2996 | − | 3.67145i | 0.411233 | − | 0.133618i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.00879 | + | 8.27039i | −0.218393 | + | 0.300592i | −0.904130 | − | 0.427257i | \(-0.859480\pi\) |
0.685737 | + | 0.727849i | \(0.259480\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 45.4305 | + | 33.0072i | 1.64902 | + | 1.19809i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.18656 | − | 2.31517i | 0.115513 | − | 0.0839250i | −0.528529 | − | 0.848915i | \(-0.677256\pi\) |
0.644042 | + | 0.764990i | \(0.277256\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.34845 | + | 3.15933i | 0.157424 | + | 0.114376i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.86445i | 0.284340i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.7844 | + | 9.35262i | 1.03934 | + | 0.337703i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.27027 | − | 28.5309i | −0.334294 | − | 1.02885i | −0.967069 | − | 0.254516i | \(-0.918084\pi\) |
0.632774 | − | 0.774336i | \(-0.281916\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.2085 | − | 40.6515i | −0.475692 | − | 1.46403i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.2232 | − | 26.4584i | −0.691409 | − | 0.951643i | −1.00000 | 0.000448177i | \(-0.999857\pi\) | |
0.308591 | − | 0.951195i | \(-0.400143\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.58298 | − | 11.0273i | 0.128705 | − | 0.396112i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.11610 | − | 4.44361i | 0.219414 | − | 0.159414i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.5156 | + | 3.68092i | −0.376759 | + | 0.131883i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −65.3355 | + | 47.4690i | −2.33789 | + | 1.69857i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.00666 | + | 18.4866i | −0.214661 | + | 0.660658i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.10544 | − | 5.65065i | −0.146529 | − | 0.201680i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.66403 | − | 14.3544i | −0.166255 | − | 0.511679i | 0.832872 | − | 0.553466i | \(-0.186695\pi\) |
−0.999127 | + | 0.0417865i | \(0.986695\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.95502 | − | 15.2500i | −0.176403 | − | 0.542914i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.52231 | + | 2.76907i | 0.303019 | + | 0.0984567i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0832i | 0.429088i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23.8886 | − | 17.3561i | −0.847240 | − | 0.615556i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.6868 | + | 27.3811i | −1.33494 | + | 0.969888i | −0.335322 | + | 0.942103i | \(0.608845\pi\) |
−0.999614 | + | 0.0277847i | \(0.991155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.1609 | + | 24.8194i | 1.20853 | + | 0.878047i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.7914 | + | 23.1113i | −0.593294 | + | 0.816599i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −57.9939 | + | 18.8434i | −2.04656 | + | 0.664967i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.62801 | − | 1.50373i | −0.163116 | − | 0.0529996i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.5193 | + | 14.4785i | 0.370295 | + | 0.509668i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.99276 | + | 2.59701i | −0.281011 | + | 0.0913059i | −0.446131 | − | 0.894967i | \(-0.647199\pi\) |
0.165121 | + | 0.986273i | \(0.447199\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.8233 | −0.380057 | −0.190028 | − | 0.981779i | \(-0.560858\pi\) | ||||
−0.190028 | + | 0.981779i | \(0.560858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.6668 | − | 22.9399i | 0.584530 | − | 0.804537i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.12226 | − | 24.9977i | 0.284510 | − | 0.875633i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 10.5463i | − | 0.368969i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.36266 | −0.222329 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.1495 | −0.424020 | −0.212010 | − | 0.977267i | \(-0.568001\pi\) | ||||
−0.212010 | + | 0.977267i | \(0.568001\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.0413i | 1.43061i | 0.698813 | + | 0.715305i | \(0.253712\pi\) | ||||
−0.698813 | + | 0.715305i | \(0.746288\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.6992 | − | 45.2395i | 0.511760 | − | 1.57504i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.33570 | − | 3.21482i | 0.0812204 | − | 0.111790i | −0.766474 | − | 0.642276i | \(-0.777990\pi\) |
0.847694 | + | 0.530486i | \(0.177990\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.2545 | 0.772929 | 0.386465 | − | 0.922304i | \(-0.373696\pi\) | ||||
0.386465 | + | 0.922304i | \(0.373696\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.3207 | − | 4.65307i | 0.496779 | − | 0.161413i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.32450 | − | 3.19940i | −0.0805391 | − | 0.110853i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.73454 | − | 2.83802i | −0.302271 | − | 0.0982139i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.17128 | + | 2.33009i | −0.247876 | + | 0.0805397i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.7056 | + | 22.9933i | −0.576742 | + | 0.793817i | −0.993333 | − | 0.115277i | \(-0.963225\pi\) |
0.416592 | + | 0.909094i | \(0.363225\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0709 | + | 18.2150i | 0.864512 | + | 0.628105i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −27.4450 | + | 19.9400i | −0.945257 | + | 0.686770i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.14149 | − | 0.829342i | −0.0392685 | − | 0.0285302i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.2501i | 0.695801i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.1417 | + | 9.79363i | 1.03446 | + | 0.336117i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.82687 | + | 14.8556i | 0.165463 | + | 0.509243i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.8474 | − | 39.5403i | −0.439888 | − | 1.35384i | −0.887994 | − | 0.459855i | \(-0.847901\pi\) |
0.448106 | − | 0.893980i | \(-0.352099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.03384 | + | 2.79934i | 0.0695558 | + | 0.0957354i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.7925 | + | 36.2936i | −0.402824 | + | 1.23977i | 0.519874 | + | 0.854243i | \(0.325979\pi\) |
−0.922698 | + | 0.385522i | \(0.874021\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.1355 | + | 30.6132i | −1.43764 | + | 1.04451i | −0.449116 | + | 0.893473i | \(0.648261\pi\) |
−0.988528 | + | 0.151036i | \(0.951739\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.66461 | − | 13.3257i | −0.158969 | − | 0.454140i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.37606 | + | 3.17940i | −0.148963 | + | 0.108228i | −0.659770 | − | 0.751467i | \(-0.729346\pi\) |
0.510808 | + | 0.859695i | \(0.329346\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.99808 | − | 9.22714i | 0.101938 | − | 0.313732i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.76336 | + | 2.42705i | 0.0598867 | + | 0.0824270i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.4694 | + | 66.0760i | 0.728299 | + | 2.24147i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.9994 | + | 43.0858i | 0.474352 | + | 1.45991i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.6928 | − | 9.64779i | −1.00495 | − | 0.326528i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.46265i | 0.319896i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.4037 | + | 11.1914i | 0.520145 | + | 0.377907i | 0.816658 | − | 0.577121i | \(-0.195824\pi\) |
−0.296514 | + | 0.955029i | \(0.595824\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 36.8103 | − | 26.7442i | 1.24158 | − | 0.902060i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.02210 | + | 2.92223i | 0.135508 | + | 0.0984523i | 0.653474 | − | 0.756949i | \(-0.273311\pi\) |
−0.517966 | + | 0.855401i | \(0.673311\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.9656 | + | 16.4693i | −0.402676 | + | 0.554236i | −0.961413 | − | 0.275109i | \(-0.911286\pi\) |
0.558737 | + | 0.829345i | \(0.311286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.8370 | − | 6.44542i | 0.666813 | − | 0.216661i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.7372 | + | 3.81364i | 0.394096 | + | 0.128050i | 0.499360 | − | 0.866395i | \(-0.333569\pi\) |
−0.105264 | + | 0.994444i | \(0.533569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.01644 | − | 11.0337i | −0.268863 | − | 0.370058i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −59.1155 | + | 19.2078i | −1.98044 | + | 0.643485i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.5781 | 0.621693 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.88872 | + | 12.2343i | −0.297117 | + | 0.408947i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.6084 | − | 32.6493i | 0.354204 | − | 1.09013i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.2709i | 0.776127i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.5817 | 1.65181 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.3647 | 0.444750 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.49501i | − | 0.0496959i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.07583 | − | 3.31107i | 0.0357224 | − | 0.109942i | −0.931605 | − | 0.363471i | \(-0.881591\pi\) |
0.967328 | + | 0.253529i | \(0.0815914\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.6388 | + | 21.5250i | −0.518707 | + | 0.713939i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.7898 | 0.788190 | 0.394095 | − | 0.919070i | \(-0.371058\pi\) | ||||
0.394095 | + | 0.919070i | \(0.371058\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0980 | + | 7.82992i | −0.797528 | + | 0.259132i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.89463 | + | 6.73688i | 0.161812 | + | 0.222714i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.1142 | + | 4.26107i | 0.433070 | + | 0.140713i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.9393 | − | 6.47868i | 0.657738 | − | 0.213712i | 0.0389150 | − | 0.999243i | \(-0.487610\pi\) |
0.618823 | + | 0.785531i | \(0.287610\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.12438 | − | 8.42948i | 0.201805 | − | 0.277761i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.9417 | + | 29.0194i | 1.31470 | + | 0.955184i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.7044 | − | 7.77720i | 0.351959 | − | 0.255713i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.1662 | + | 11.0189i | 0.498124 | + | 0.361908i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.0637i | 0.527032i | 0.964655 | + | 0.263516i | \(0.0848822\pi\) | ||||
−0.964655 | + | 0.263516i | \(0.915118\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.65480 | − | 0.537678i | −0.0542340 | − | 0.0176217i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.10682 | − | 3.40644i | −0.0362357 | − | 0.111522i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.29695 | − | 22.4577i | −0.238636 | − | 0.734445i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.6239 | + | 33.8919i | 0.804428 | + | 1.10720i | 0.992159 | + | 0.124980i | \(0.0398866\pi\) |
−0.187731 | + | 0.982220i | \(0.560113\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.61343 | + | 26.5094i | −0.281089 | + | 0.865102i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.1271 | − | 18.9825i | 0.851720 | − | 0.618811i | −0.0738996 | − | 0.997266i | \(-0.523544\pi\) |
0.925620 | + | 0.378455i | \(0.123544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.1640 | − | 0.657914i | 0.949710 | − | 0.0214246i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.16868 | − | 1.57564i | 0.0705470 | − | 0.0512554i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.4552 | + | 38.3332i | −0.404740 | + | 1.24566i | 0.516373 | + | 0.856364i | \(0.327282\pi\) |
−0.921112 | + | 0.389297i | \(0.872718\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.9115 | + | 30.1586i | 0.711278 | + | 0.978990i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.02992 | − | 6.24746i | −0.0658247 | − | 0.202588i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.0337 | − | 46.2691i | −0.486991 | − | 1.49880i | −0.829077 | − | 0.559135i | \(-0.811134\pi\) |
0.342086 | − | 0.939669i | \(-0.388866\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0802 | − | 3.27527i | −0.326189 | − | 0.105985i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 95.4688i | 3.08607i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.3151 | − | 12.5801i | −0.559133 | − | 0.406234i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.7764 | − | 12.9153i | 0.573432 | − | 0.416623i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −27.3880 | − | 19.8986i | −0.882566 | − | 0.641222i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.9819 | − | 21.9972i | 0.514476 | − | 0.708116i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.5449 | + | 8.94988i | −0.885785 | + | 0.287809i | −0.716357 | − | 0.697734i | \(-0.754192\pi\) |
−0.169428 | + | 0.985543i | \(0.554192\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.4296 | − | 4.68848i | −0.463547 | − | 0.150616i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.663030 | + | 0.912583i | 0.0212776 | + | 0.0292862i | 0.819523 | − | 0.573046i | \(-0.194238\pi\) |
−0.798246 | + | 0.602332i | \(0.794238\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.4672 | + | 5.67543i | −0.559972 | + | 0.181946i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −29.0796 | −0.931294 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.88505 | + | 9.47646i | −0.220272 | + | 0.303179i | −0.904824 | − | 0.425785i | \(-0.859998\pi\) |
0.684552 | + | 0.728964i | \(0.259998\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.5058 | − | 81.5764i | 0.847128 | − | 2.60719i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0072i | 0.319505i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.3359 | 0.584826 | 0.292413 | − | 0.956292i | \(-0.405542\pi\) | ||||
0.292413 | + | 0.956292i | \(0.405542\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.1315 | −0.545855 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 23.5429i | 0.749380i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.53313 | + | 26.2623i | −0.271338 | + | 0.835092i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.1554 | − | 18.1069i | 0.417895 | − | 0.575184i | −0.547227 | − | 0.836985i | \(-0.684316\pi\) |
0.965122 | + | 0.261801i | \(0.0843164\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.5411 | 0.620117 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.1880 | − | 6.23455i | 0.608300 | − | 0.197649i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.4486 | − | 22.6395i | −0.520932 | − | 0.717001i | 0.464783 | − | 0.885425i | \(-0.346132\pi\) |
−0.985715 | + | 0.168424i | \(0.946132\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.18349 | − | 2.65898i | −0.258914 | − | 0.0841263i |
(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 | 1148.2.ba.a.701.5 | yes | 80 | |
41.31 | even | 10 | inner | 1148.2.ba.a.113.16 | ✓ | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.ba.a.113.16 | ✓ | 80 | 41.31 | even | 10 | inner | |
1148.2.ba.a.701.5 | yes | 80 | 1.1 | even | 1 | trivial |