Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,2,Mod(35,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.v (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.17430605098\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 35.12 | ||
Character | \(\chi\) | \(=\) | 648.35 |
Dual form | 648.2.v.b.611.12 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{13}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.580483 | + | 1.28959i | −0.410464 | + | 0.911877i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.32608 | − | 1.49717i | −0.663039 | − | 0.748585i | ||||
\(5\) | −3.21529 | − | 1.17027i | −1.43792 | − | 0.523361i | −0.498731 | − | 0.866757i | \(-0.666200\pi\) |
−0.939191 | + | 0.343396i | \(0.888423\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.85909 | + | 0.504135i | 1.08064 | + | 0.190545i | 0.685496 | − | 0.728076i | \(-0.259585\pi\) |
0.395139 | + | 0.918621i | \(0.370696\pi\) | |||||||
\(8\) | 2.70050 | − | 0.841014i | 0.954771 | − | 0.297343i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.37559 | − | 3.46708i | 1.06745 | − | 1.09639i | ||||
\(11\) | 0.927560 | + | 2.54845i | 0.279670 | + | 0.768386i | 0.997400 | + | 0.0720650i | \(0.0229589\pi\) |
−0.717730 | + | 0.696321i | \(0.754819\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.60411 | − | 1.91170i | −0.444899 | − | 0.530210i | 0.496260 | − | 0.868174i | \(-0.334706\pi\) |
−0.941159 | + | 0.337964i | \(0.890262\pi\) | |||||||
\(14\) | −2.30978 | + | 3.39441i | −0.617315 | + | 0.907195i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.483033 | + | 3.97073i | −0.120758 | + | 0.992682i | ||||
\(17\) | −4.30856 | + | 2.48755i | −1.04498 | + | 0.603319i | −0.921240 | − | 0.388995i | \(-0.872822\pi\) |
−0.123740 | + | 0.992315i | \(0.539489\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.31569 | + | 2.27884i | −0.301839 | + | 0.522801i | −0.976553 | − | 0.215279i | \(-0.930934\pi\) |
0.674713 | + | 0.738080i | \(0.264267\pi\) | |||||||
\(20\) | 2.51163 | + | 6.36570i | 0.561618 | + | 1.42341i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.82488 | − | 0.283162i | −0.815468 | − | 0.0603703i | ||||
\(23\) | 0.157970 | + | 0.895893i | 0.0329391 | + | 0.186807i | 0.996838 | − | 0.0794621i | \(-0.0253203\pi\) |
−0.963899 | + | 0.266269i | \(0.914209\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.13833 | + | 4.31157i | 1.02767 | + | 0.862315i | ||||
\(26\) | 3.39646 | − | 0.958928i | 0.666101 | − | 0.188061i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.03660 | − | 4.94907i | −0.573864 | − | 0.935286i | ||||
\(29\) | −7.00248 | − | 5.87578i | −1.30033 | − | 1.09111i | −0.990088 | − | 0.140447i | \(-0.955146\pi\) |
−0.310241 | − | 0.950658i | \(-0.600410\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.90502 | + | 0.512234i | −0.521758 | + | 0.0920000i | −0.428324 | − | 0.903625i | \(-0.640896\pi\) |
−0.0934343 | + | 0.995625i | \(0.529785\pi\) | |||||||
\(32\) | −4.84021 | − | 2.92786i | −0.855637 | − | 0.517577i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.706867 | − | 7.00026i | −0.121227 | − | 1.20053i | ||||
\(35\) | −8.60284 | − | 4.96685i | −1.45414 | − | 0.839551i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.78021 | + | 5.64661i | −1.60786 | + | 0.928296i | −0.618008 | + | 0.786172i | \(0.712060\pi\) |
−0.989849 | + | 0.142124i | \(0.954607\pi\) | |||||||
\(38\) | −2.17503 | − | 3.01952i | −0.352836 | − | 0.489831i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.66710 | − | 0.456210i | −1.52850 | − | 0.0721332i | ||||
\(41\) | 3.04161 | + | 3.62485i | 0.475020 | + | 0.566106i | 0.949342 | − | 0.314245i | \(-0.101751\pi\) |
−0.474322 | + | 0.880351i | \(0.657307\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.12779 | + | 2.23033i | −0.934479 | + | 0.340123i | −0.763983 | − | 0.645236i | \(-0.776759\pi\) |
−0.170496 | + | 0.985358i | \(0.554537\pi\) | |||||||
\(44\) | 2.58544 | − | 4.76816i | 0.389770 | − | 0.718827i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.24703 | − | 0.316335i | −0.183865 | − | 0.0466410i | ||||
\(47\) | −0.225833 | + | 1.28076i | −0.0329411 | + | 0.186818i | −0.996838 | − | 0.0794561i | \(-0.974682\pi\) |
0.963897 | + | 0.266275i | \(0.0857928\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.34241 | + | 0.488598i | 0.191773 | + | 0.0697997i | ||||
\(50\) | −8.54287 | + | 4.12354i | −1.20814 | + | 0.583157i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.734968 | + | 4.93668i | −0.101922 | + | 0.684595i | ||||
\(53\) | 10.3399 | 1.42029 | 0.710146 | − | 0.704054i | \(-0.248629\pi\) | ||||
0.710146 | + | 0.704054i | \(0.248629\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9.27950i | − | 1.25125i | ||||||
\(56\) | 8.14496 | − | 1.04312i | 1.08842 | − | 0.139393i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.6422 | − | 5.61953i | 1.52869 | − | 0.737881i | ||||
\(59\) | −2.96267 | + | 8.13988i | −0.385707 | + | 1.05972i | 0.583207 | + | 0.812324i | \(0.301798\pi\) |
−0.968914 | + | 0.247398i | \(0.920425\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.720351 | − | 0.127017i | −0.0922315 | − | 0.0162629i | 0.127342 | − | 0.991859i | \(-0.459355\pi\) |
−0.219573 | + | 0.975596i | \(0.570467\pi\) | |||||||
\(62\) | 1.02575 | − | 4.04363i | 0.130270 | − | 0.513542i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.58539 | − | 4.54231i | 0.823174 | − | 0.567789i | ||||
\(65\) | 2.92046 | + | 8.02391i | 0.362239 | + | 0.995243i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.00144 | − | 4.19671i | 0.611023 | − | 0.512709i | −0.283944 | − | 0.958841i | \(-0.591643\pi\) |
0.894968 | + | 0.446131i | \(0.147199\pi\) | |||||||
\(68\) | 9.43778 | + | 3.15196i | 1.14450 | + | 0.382232i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.3990 | − | 8.21095i | 1.36244 | − | 0.981396i | ||||
\(71\) | −5.18176 | − | 8.97507i | −0.614961 | − | 1.06514i | −0.990391 | − | 0.138294i | \(-0.955838\pi\) |
0.375430 | − | 0.926851i | \(-0.377495\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.34034 | + | 12.7138i | −0.859122 | + | 1.48804i | 0.0136452 | + | 0.999907i | \(0.495656\pi\) |
−0.872767 | + | 0.488136i | \(0.837677\pi\) | |||||||
\(74\) | −1.60455 | − | 15.8902i | −0.186525 | − | 1.84720i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.15651 | − | 1.05211i | 0.591492 | − | 0.120685i | ||||
\(77\) | 1.36722 | + | 7.75387i | 0.155809 | + | 0.883635i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.64811 | + | 6.73115i | −0.635462 | + | 0.757314i | −0.983646 | − | 0.180112i | \(-0.942354\pi\) |
0.348184 | + | 0.937426i | \(0.386798\pi\) | |||||||
\(80\) | 6.19991 | − | 12.2018i | 0.693171 | − | 1.36420i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.44017 | + | 1.81826i | −0.711197 | + | 0.200793i | ||||
\(83\) | −3.15228 | + | 3.75674i | −0.346007 | + | 0.412356i | −0.910781 | − | 0.412891i | \(-0.864519\pi\) |
0.564773 | + | 0.825246i | \(0.308964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.7644 | − | 2.95601i | 1.81835 | − | 0.320625i | ||||
\(86\) | 0.680867 | − | 9.19700i | 0.0734198 | − | 0.991738i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.64815 | + | 6.10199i | 0.495495 | + | 0.650475i | ||||
\(89\) | 4.90094 | + | 2.82956i | 0.519499 | + | 0.299933i | 0.736730 | − | 0.676187i | \(-0.236369\pi\) |
−0.217231 | + | 0.976120i | \(0.569702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.62253 | − | 6.27441i | −0.379745 | − | 0.657737i | ||||
\(92\) | 1.13182 | − | 1.42453i | 0.118001 | − | 0.148518i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.52056 | − | 1.03469i | −0.156834 | − | 0.106720i | ||||
\(95\) | 6.89717 | − | 5.78741i | 0.707635 | − | 0.593776i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.126739 | + | 0.0461291i | −0.0128684 | + | 0.00468370i | −0.348446 | − | 0.937329i | \(-0.613291\pi\) |
0.335578 | + | 0.942012i | \(0.391068\pi\) | |||||||
\(98\) | −1.40934 | + | 1.44754i | −0.142365 | + | 0.146223i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.358675 | − | 13.4104i | −0.0358675 | − | 1.34104i | ||||
\(101\) | −2.26461 | + | 12.8432i | −0.225337 | + | 1.27795i | 0.636704 | + | 0.771109i | \(0.280298\pi\) |
−0.862040 | + | 0.506840i | \(0.830814\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.422665 | + | 1.16126i | −0.0416464 | + | 0.114423i | −0.958773 | − | 0.284174i | \(-0.908281\pi\) |
0.917126 | + | 0.398597i | \(0.130503\pi\) | |||||||
\(104\) | −5.93965 | − | 3.81347i | −0.582431 | − | 0.373941i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00213 | + | 13.3342i | −0.582979 | + | 1.29513i | ||||
\(107\) | − | 15.9792i | − | 1.54476i | −0.635159 | − | 0.772382i | \(-0.719065\pi\) | ||
0.635159 | − | 0.772382i | \(-0.280935\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.38211i | − | 0.228165i | −0.993471 | − | 0.114082i | \(-0.963607\pi\) | ||
0.993471 | − | 0.114082i | \(-0.0363927\pi\) | |||||||
\(110\) | 11.9667 | + | 5.38659i | 1.14098 | + | 0.513591i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.38282 | + | 11.1092i | −0.319646 | + | 1.04972i | ||||
\(113\) | 3.24570 | − | 8.91748i | 0.305330 | − | 0.838886i | −0.688221 | − | 0.725501i | \(-0.741608\pi\) |
0.993551 | − | 0.113386i | \(-0.0361695\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.540517 | − | 3.06542i | 0.0504035 | − | 0.285852i | ||||
\(116\) | 0.488800 | + | 18.2757i | 0.0453840 | + | 1.69685i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.77731 | − | 8.54569i | −0.808017 | − | 0.786695i | ||||
\(119\) | −13.5726 | + | 4.94004i | −1.24420 | + | 0.452853i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.79226 | − | 2.34299i | 0.253842 | − | 0.212999i | ||||
\(122\) | 0.581952 | − | 0.855225i | 0.0526874 | − | 0.0774284i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.61919 | + | 3.67005i | 0.414816 | + | 0.329580i | ||||
\(125\) | −2.92143 | − | 5.06006i | −0.261300 | − | 0.452586i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.94090 | + | 2.27528i | 0.349698 | + | 0.201898i | 0.664552 | − | 0.747242i | \(-0.268622\pi\) |
−0.314854 | + | 0.949140i | \(0.601956\pi\) | |||||||
\(128\) | 2.03501 | + | 11.1292i | 0.179871 | + | 0.983690i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.0428 | − | 0.891548i | −1.05623 | − | 0.0781939i | ||||
\(131\) | −1.53208 | + | 0.270147i | −0.133858 | + | 0.0236028i | −0.240176 | − | 0.970729i | \(-0.577205\pi\) |
0.106318 | + | 0.994332i | \(0.466094\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.91051 | + | 5.85212i | −0.425796 | + | 0.507443i | ||||
\(134\) | 2.50877 | + | 8.88592i | 0.216725 | + | 0.767627i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.54321 | + | 10.3412i | −0.818323 | + | 0.886749i | ||||
\(137\) | 0.557261 | − | 0.664118i | 0.0476101 | − | 0.0567394i | −0.741714 | − | 0.670716i | \(-0.765987\pi\) |
0.789324 | + | 0.613977i | \(0.210431\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.63752 | − | 14.9581i | −0.223711 | − | 1.26873i | −0.865133 | − | 0.501542i | \(-0.832766\pi\) |
0.641422 | − | 0.767188i | \(-0.278345\pi\) | |||||||
\(140\) | 3.97182 | + | 19.4663i | 0.335680 | + | 1.64521i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.5821 | − | 1.47246i | 1.22370 | − | 0.123566i | ||||
\(143\) | 3.38397 | − | 5.86120i | 0.282981 | − | 0.490138i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.6388 | + | 27.0871i | 1.29873 | + | 2.24946i | ||||
\(146\) | −12.1347 | − | 16.8462i | −1.00427 | − | 1.39420i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 21.4232 | + | 7.15479i | 1.76098 | + | 0.588120i | ||||
\(149\) | −6.54605 | + | 5.49279i | −0.536273 | + | 0.449987i | −0.870261 | − | 0.492591i | \(-0.836050\pi\) |
0.333988 | + | 0.942577i | \(0.391606\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.59322 | − | 9.87229i | −0.292412 | − | 0.803396i | −0.995712 | − | 0.0925028i | \(-0.970513\pi\) |
0.703300 | − | 0.710893i | \(-0.251709\pi\) | |||||||
\(152\) | −1.63648 | + | 7.26051i | −0.132736 | + | 0.588905i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.7929 | − | 2.73784i | −0.869720 | − | 0.220622i | ||||
\(155\) | 9.93995 | + | 1.75268i | 0.798396 | + | 0.140779i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.29479 | + | 9.05237i | −0.262953 | + | 0.722458i | 0.736012 | + | 0.676969i | \(0.236707\pi\) |
−0.998965 | + | 0.0454891i | \(0.985515\pi\) | |||||||
\(158\) | −5.40179 | − | 11.1911i | −0.429743 | − | 0.890313i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.1363 | + | 15.0783i | 0.959459 | + | 1.19204i | ||||
\(161\) | 2.64108i | 0.208146i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.6202 | 1.53678 | 0.768388 | − | 0.639984i | \(-0.221059\pi\) | ||||
0.768388 | + | 0.639984i | \(0.221059\pi\) | |||||||
\(164\) | 1.39360 | − | 9.36064i | 0.108822 | − | 0.730943i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.01480 | − | 6.24587i | −0.233994 | − | 0.484773i | ||||
\(167\) | −10.7043 | − | 3.89606i | −0.828327 | − | 0.301486i | −0.107155 | − | 0.994242i | \(-0.534174\pi\) |
−0.721172 | + | 0.692756i | \(0.756396\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.17599 | − | 6.66936i | 0.0904606 | − | 0.513028i | ||||
\(170\) | −5.91940 | + | 23.3351i | −0.453998 | + | 1.78972i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.4651 | + | 6.21674i | 0.874207 | + | 0.474022i | ||||
\(173\) | 14.8832 | − | 5.41704i | 1.13155 | − | 0.411850i | 0.292694 | − | 0.956206i | \(-0.405448\pi\) |
0.838854 | + | 0.544356i | \(0.183226\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.5174 | + | 14.9176i | 0.946223 | + | 1.12767i | ||||
\(176\) | −10.5672 | + | 2.45210i | −0.796536 | + | 0.184834i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.49389 | + | 4.67769i | −0.486737 | + | 0.350608i | ||||
\(179\) | −13.6572 | + | 7.88498i | −1.02079 | + | 0.589351i | −0.914331 | − | 0.404967i | \(-0.867283\pi\) |
−0.106454 | + | 0.994318i | \(0.533950\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.39147 | − | 2.53542i | −0.326416 | − | 0.188456i | 0.327833 | − | 0.944736i | \(-0.393682\pi\) |
−0.654249 | + | 0.756280i | \(0.727015\pi\) | |||||||
\(182\) | 10.1942 | − | 1.02939i | 0.755647 | − | 0.0763033i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.18006 | + | 2.28650i | 0.0869949 | + | 0.168563i | ||||
\(185\) | 38.0543 | − | 6.70999i | 2.79780 | − | 0.493328i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.3358 | − | 8.67280i | −0.755832 | − | 0.634218i | ||||
\(188\) | 2.21699 | − | 1.36028i | 0.161691 | − | 0.0992087i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.45969 | + | 12.2540i | 0.250992 | + | 0.888999i | ||||
\(191\) | 19.1259 | + | 16.0486i | 1.38390 | + | 1.16123i | 0.967742 | + | 0.251944i | \(0.0810697\pi\) |
0.416163 | + | 0.909290i | \(0.363375\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.63585 | − | 9.27734i | −0.117751 | − | 0.667798i | −0.985351 | − | 0.170536i | \(-0.945450\pi\) |
0.867601 | − | 0.497262i | \(-0.165661\pi\) | |||||||
\(194\) | 0.0140821 | − | 0.190218i | 0.00101104 | − | 0.0136569i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.04863 | − | 2.65774i | −0.0749021 | − | 0.189838i | ||||
\(197\) | 0.195281 | − | 0.338236i | 0.0139132 | − | 0.0240983i | −0.858985 | − | 0.512001i | \(-0.828904\pi\) |
0.872898 | + | 0.487902i | \(0.162238\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.27422 | + | 3.62242i | −0.444768 | + | 0.256787i | −0.705618 | − | 0.708592i | \(-0.749330\pi\) |
0.260850 | + | 0.965379i | \(0.415997\pi\) | |||||||
\(200\) | 17.5022 | + | 7.32199i | 1.23759 | + | 0.517743i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.2479 | − | 10.3757i | −1.07284 | − | 0.730031i | ||||
\(203\) | −17.0586 | − | 20.3296i | −1.19728 | − | 1.42686i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.53760 | − | 15.2144i | −0.386763 | − | 1.06262i | ||||
\(206\) | −1.25220 | − | 1.21916i | −0.0872450 | − | 0.0849427i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.36568 | − | 5.44606i | 0.580055 | − | 0.377616i | ||||
\(209\) | −7.02788 | − | 1.23920i | −0.486128 | − | 0.0857176i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.9809 | + | 7.63642i | 1.44438 | + | 0.525713i | 0.941017 | − | 0.338359i | \(-0.109872\pi\) |
0.503368 | + | 0.864072i | \(0.332094\pi\) | |||||||
\(212\) | −13.7115 | − | 15.4806i | −0.941710 | − | 1.06321i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.6065 | + | 9.27563i | 1.40863 | + | 0.634069i | ||||
\(215\) | 22.3127 | 1.52171 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.56397 | −0.581360 | ||||||||
\(218\) | 3.07194 | + | 1.38277i | 0.208058 | + | 0.0936532i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13.8930 | + | 12.3053i | −0.936664 | + | 0.829626i | ||||
\(221\) | 11.6668 | + | 4.24638i | 0.784797 | + | 0.285643i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.83765 | + | 1.38199i | 0.524848 | + | 0.0925448i | 0.429793 | − | 0.902927i | \(-0.358586\pi\) |
0.0950544 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(224\) | −12.3626 | − | 10.8111i | −0.826010 | − | 0.722349i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.61581 | + | 9.36207i | 0.639634 | + | 0.622755i | ||||
\(227\) | 2.95471 | + | 8.11801i | 0.196111 | + | 0.538811i | 0.998302 | − | 0.0582571i | \(-0.0185543\pi\) |
−0.802190 | + | 0.597068i | \(0.796332\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.90565 | + | 5.84633i | 0.324175 | + | 0.386336i | 0.903377 | − | 0.428848i | \(-0.141080\pi\) |
−0.579202 | + | 0.815184i | \(0.696636\pi\) | |||||||
\(230\) | 3.63938 | + | 2.47647i | 0.239973 | + | 0.163294i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −23.8518 | − | 9.97836i | −1.56595 | − | 0.655111i | ||||
\(233\) | 6.15633 | − | 3.55436i | 0.403315 | − | 0.232854i | −0.284599 | − | 0.958647i | \(-0.591860\pi\) |
0.687913 | + | 0.725793i | \(0.258527\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.22496 | − | 3.85374i | 0.145140 | − | 0.251390i | ||||
\(236\) | 16.1155 | − | 6.35849i | 1.04903 | − | 0.413902i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.50808 | − | 20.3707i | 0.0977540 | − | 1.32044i | ||||
\(239\) | 0.386367 | + | 2.19120i | 0.0249920 | + | 0.141737i | 0.994751 | − | 0.102330i | \(-0.0326297\pi\) |
−0.969759 | + | 0.244066i | \(0.921519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.156407 | + | 0.131241i | 0.0100750 | + | 0.00845397i | 0.647811 | − | 0.761801i | \(-0.275685\pi\) |
−0.637736 | + | 0.770255i | \(0.720129\pi\) | |||||||
\(242\) | 1.40063 | + | 4.96094i | 0.0900358 | + | 0.318901i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.765075 | + | 1.24692i | 0.0489789 | + | 0.0798260i | ||||
\(245\) | −3.74445 | − | 3.14197i | −0.239224 | − | 0.200733i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.46696 | − | 1.14030i | 0.411483 | − | 0.0725555i | ||||
\(248\) | −7.41422 | + | 3.82645i | −0.470804 | + | 0.242980i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.22124 | − | 0.830159i | 0.519957 | − | 0.0525039i | ||||
\(251\) | −11.4836 | − | 6.63004i | −0.724837 | − | 0.418485i | 0.0916936 | − | 0.995787i | \(-0.470772\pi\) |
−0.816530 | + | 0.577303i | \(0.804105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.13661 | + | 1.23357i | −0.134328 | + | 0.0775541i | ||||
\(254\) | −5.22180 | + | 3.76138i | −0.327645 | + | 0.236010i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.5334 | − | 3.83599i | −0.970835 | − | 0.239749i | ||||
\(257\) | −14.5879 | − | 17.3851i | −0.909966 | − | 1.08446i | −0.996105 | − | 0.0881721i | \(-0.971897\pi\) |
0.0861393 | − | 0.996283i | \(-0.472547\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −30.8092 | + | 11.2136i | −1.91439 | + | 0.696781i | ||||
\(260\) | 8.14039 | − | 15.0128i | 0.504845 | − | 0.931052i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.540968 | − | 2.13257i | 0.0334211 | − | 0.131750i | ||||
\(263\) | 3.05022 | − | 17.2987i | 0.188085 | − | 1.06668i | −0.733843 | − | 0.679319i | \(-0.762275\pi\) |
0.921927 | − | 0.387363i | \(-0.126614\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −33.2457 | − | 12.1005i | −2.04227 | − | 0.743325i | ||||
\(266\) | −4.69636 | − | 9.72960i | −0.287952 | − | 0.596560i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.9155 | − | 1.92284i | −0.788939 | − | 0.117456i | ||||
\(269\) | −25.2404 | −1.53894 | −0.769468 | − | 0.638686i | \(-0.779478\pi\) | ||||
−0.769468 | + | 0.638686i | \(0.779478\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.2779i | 1.71776i | 0.512175 | + | 0.858881i | \(0.328840\pi\) | ||||
−0.512175 | + | 0.858881i | \(0.671160\pi\) | |||||||
\(272\) | −7.79621 | − | 18.3097i | −0.472714 | − | 1.11019i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.532958 | + | 1.10415i | 0.0321972 | + | 0.0667040i | ||||
\(275\) | −6.22172 | + | 17.0940i | −0.375184 | + | 1.03081i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.7115 | + | 1.88873i | 0.643592 | + | 0.113483i | 0.485912 | − | 0.874008i | \(-0.338488\pi\) |
0.157680 | + | 0.987490i | \(0.449599\pi\) | |||||||
\(278\) | 20.8208 | + | 5.28162i | 1.24875 | + | 0.316770i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −27.4091 | − | 6.17787i | −1.63801 | − | 0.369199i | ||||
\(281\) | −1.98862 | − | 5.46370i | −0.118631 | − | 0.325937i | 0.866137 | − | 0.499806i | \(-0.166595\pi\) |
−0.984769 | + | 0.173869i | \(0.944373\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.97262 | − | 5.85072i | 0.414479 | − | 0.347789i | −0.411579 | − | 0.911374i | \(-0.635023\pi\) |
0.826058 | + | 0.563585i | \(0.190578\pi\) | |||||||
\(284\) | −6.56578 | + | 19.6596i | −0.389607 | + | 1.16658i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.59420 | + | 7.76625i | 0.330792 | + | 0.459228i | ||||
\(287\) | 6.86883 | + | 11.8972i | 0.405454 | + | 0.702267i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.87581 | − | 6.71310i | 0.227989 | − | 0.394888i | ||||
\(290\) | −44.0093 | + | 4.44394i | −2.58432 | + | 0.260957i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 28.7687 | − | 5.86982i | 1.68356 | − | 0.343505i | ||||
\(293\) | 0.704403 | + | 3.99487i | 0.0411517 | + | 0.233383i | 0.998446 | − | 0.0557335i | \(-0.0177497\pi\) |
−0.957294 | + | 0.289116i | \(0.906639\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.0517 | − | 22.7049i | 1.10923 | − | 1.32193i | ||||
\(296\) | −21.6626 | + | 23.4739i | −1.25911 | + | 1.36440i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.28357 | − | 11.6302i | −0.190212 | − | 0.673719i | ||||
\(299\) | 1.45928 | − | 1.73910i | 0.0843922 | − | 0.100575i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.6443 | + | 3.28749i | −1.07464 | + | 0.189488i | ||||
\(302\) | 14.8170 | + | 1.09692i | 0.852623 | + | 0.0631209i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.41312 | − | 6.32499i | −0.482526 | − | 0.362763i | ||||
\(305\) | 2.16749 | + | 1.25140i | 0.124110 | + | 0.0716551i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.8379 | − | 29.1641i | −0.960989 | − | 1.66448i | −0.720025 | − | 0.693948i | \(-0.755870\pi\) |
−0.240964 | − | 0.970534i | \(-0.577464\pi\) | |||||||
\(308\) | 9.79582 | − | 12.3292i | 0.558169 | − | 0.702521i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.03021 | + | 11.8010i | −0.456085 | + | 0.670254i | ||||
\(311\) | −9.39589 | + | 7.88409i | −0.532792 | + | 0.447066i | −0.869064 | − | 0.494699i | \(-0.835278\pi\) |
0.336272 | + | 0.941765i | \(0.390834\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.01611 | + | 1.82572i | −0.283528 | + | 0.103196i | −0.479869 | − | 0.877340i | \(-0.659316\pi\) |
0.196342 | + | 0.980535i | \(0.437094\pi\) | |||||||
\(314\) | −9.76126 | − | 9.50368i | −0.550860 | − | 0.536324i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.5675 | − | 0.469860i | 0.988250 | − | 0.0264317i | ||||
\(317\) | 0.00253246 | − | 0.0143623i | 0.000142237 | − | 0.000806666i | −0.984737 | − | 0.174051i | \(-0.944314\pi\) |
0.984879 | + | 0.173245i | \(0.0554252\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.47891 | − | 23.2956i | 0.474728 | − | 1.30430i | ||||
\(320\) | −26.4897 | + | 6.89817i | −1.48082 | + | 0.385619i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.40591 | − | 1.53310i | −0.189804 | − | 0.0854365i | ||||
\(323\) | − | 13.0914i | − | 0.728422i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 16.7392i | − | 0.928523i | ||||||
\(326\) | −11.3892 | + | 25.3021i | −0.630791 | + | 1.40135i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.2624 | + | 7.23087i | 0.621863 | + | 0.399258i | ||||
\(329\) | −1.29136 | + | 3.54797i | −0.0711947 | + | 0.195606i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.663118 | − | 3.76073i | 0.0364482 | − | 0.206708i | −0.961145 | − | 0.276043i | \(-0.910977\pi\) |
0.997593 | + | 0.0693351i | \(0.0220878\pi\) | |||||||
\(332\) | 9.80464 | − | 0.262235i | 0.538100 | − | 0.0143920i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.2380 | − | 11.5426i | 0.614917 | − | 0.631583i | ||||
\(335\) | −20.9924 | + | 7.64060i | −1.14694 | + | 0.417450i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.62429 | − | 5.55844i | 0.360848 | − | 0.302787i | −0.444281 | − | 0.895888i | \(-0.646541\pi\) |
0.805129 | + | 0.593100i | \(0.202096\pi\) | |||||||
\(338\) | 7.91809 | + | 5.38799i | 0.430687 | + | 0.293068i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −26.6565 | − | 21.1792i | −1.44565 | − | 1.14860i | ||||
\(341\) | −3.99999 | − | 6.92818i | −0.216611 | − | 0.375182i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.0079 | − | 8.08749i | −0.756358 | − | 0.436684i | ||||
\(344\) | −14.6723 | + | 11.1766i | −0.791080 | + | 0.602600i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.65369 | + | 22.3377i | −0.0889031 | + | 1.20088i | ||||
\(347\) | 24.1858 | − | 4.26461i | 1.29836 | − | 0.228936i | 0.518602 | − | 0.855016i | \(-0.326453\pi\) |
0.779759 | + | 0.626079i | \(0.215341\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.36508 | − | 5.20210i | 0.233658 | − | 0.278462i | −0.636457 | − | 0.771313i | \(-0.719601\pi\) |
0.870114 | + | 0.492850i | \(0.164045\pi\) | |||||||
\(350\) | −26.5037 | + | 7.48282i | −1.41668 | + | 0.399974i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.97190 | − | 15.0508i | 0.158403 | − | 0.802210i | ||||
\(353\) | −9.32471 | + | 11.1128i | −0.496304 | + | 0.591472i | −0.954809 | − | 0.297220i | \(-0.903941\pi\) |
0.458505 | + | 0.888692i | \(0.348385\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.15760 | + | 34.9215i | 0.326812 | + | 1.85344i | ||||
\(356\) | −2.26270 | − | 11.0898i | −0.119923 | − | 0.587756i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.24061 | − | 22.1893i | −0.118420 | − | 1.17274i | ||||
\(359\) | −1.61294 | + | 2.79370i | −0.0851279 | + | 0.147446i | −0.905446 | − | 0.424462i | \(-0.860463\pi\) |
0.820318 | + | 0.571908i | \(0.193797\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.03793 | + | 10.4580i | 0.317786 | + | 0.550422i | ||||
\(362\) | 5.81882 | − | 4.19142i | 0.305830 | − | 0.220296i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.59010 | + | 13.7439i | −0.240586 | + | 0.720377i | ||||
\(365\) | 38.4800 | − | 32.2885i | 2.01413 | − | 1.69006i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.2734 | − | 28.2260i | −0.536268 | − | 1.47338i | −0.851492 | − | 0.524367i | \(-0.824302\pi\) |
0.315224 | − | 0.949017i | \(-0.397920\pi\) | |||||||
\(368\) | −3.63365 | + | 0.194510i | −0.189417 | + | 0.0101396i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −13.4367 | + | 52.9694i | −0.698542 | + | 2.75375i | ||||
\(371\) | 29.5627 | + | 5.21270i | 1.53482 | + | 0.270630i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.31103 | − | 14.5919i | 0.274995 | − | 0.755542i | −0.722916 | − | 0.690936i | \(-0.757199\pi\) |
0.997911 | − | 0.0646062i | \(-0.0205791\pi\) | |||||||
\(374\) | 17.1841 | − | 8.29457i | 0.888570 | − | 0.428902i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.467277 | + | 3.64863i | 0.0240980 | + | 0.188164i | ||||
\(377\) | 22.8120i | 1.17488i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.68763 | −0.343521 | −0.171760 | − | 0.985139i | \(-0.554945\pi\) | ||||
−0.171760 | + | 0.985139i | \(0.554945\pi\) | |||||||
\(380\) | −17.8109 | − | 2.65167i | −0.913681 | − | 0.136028i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −31.7983 | + | 15.3487i | −1.62694 | + | 0.785306i | ||||
\(383\) | 6.52420 | + | 2.37461i | 0.333371 | + | 0.121337i | 0.503282 | − | 0.864122i | \(-0.332126\pi\) |
−0.169911 | + | 0.985459i | \(0.554348\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.67812 | − | 26.5309i | 0.238419 | − | 1.35214i | ||||
\(386\) | 12.9135 | + | 3.27577i | 0.657282 | + | 0.166732i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.237129 | + | 0.128579i | 0.0120384 | + | 0.00652759i | ||||
\(389\) | −1.33770 | + | 0.486883i | −0.0678241 | + | 0.0246860i | −0.375709 | − | 0.926738i | \(-0.622601\pi\) |
0.307885 | + | 0.951423i | \(0.400379\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.90920 | − | 3.46705i | −0.147125 | − | 0.175336i | ||||
\(392\) | 4.03610 | + | 0.190472i | 0.203854 | + | 0.00962028i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.322828 | + | 0.448172i | 0.0162639 | + | 0.0225786i | ||||
\(395\) | 26.0376 | − | 15.0328i | 1.31009 | − | 0.756382i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.5544 | + | 9.55769i | 0.830842 | + | 0.479687i | 0.854141 | − | 0.520042i | \(-0.174084\pi\) |
−0.0232990 | + | 0.999729i | \(0.507417\pi\) | |||||||
\(398\) | −1.02936 | − | 10.1939i | −0.0515969 | − | 0.510975i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.6021 | + | 18.3203i | −0.980104 | + | 0.916015i | ||||
\(401\) | 18.4212 | − | 3.24815i | 0.919909 | − | 0.162205i | 0.306409 | − | 0.951900i | \(-0.400872\pi\) |
0.613500 | + | 0.789695i | \(0.289761\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.63921 | + | 4.73186i | 0.280909 | + | 0.235711i | ||||
\(404\) | 22.2315 | − | 13.6406i | 1.10606 | − | 0.678646i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 36.1190 | − | 10.1975i | 1.79256 | − | 0.506095i | ||||
\(407\) | −23.4618 | − | 19.6868i | −1.16296 | − | 0.975838i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.21877 | − | 18.2546i | −0.159158 | − | 0.902630i | −0.954885 | − | 0.296975i | \(-0.904022\pi\) |
0.795727 | − | 0.605655i | \(-0.207089\pi\) | |||||||
\(410\) | 22.8349 | + | 1.69050i | 1.12773 | + | 0.0834877i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.29909 | − | 0.907124i | 0.113268 | − | 0.0446908i | ||||
\(413\) | −12.5742 | + | 21.7791i | −0.618734 | + | 1.07168i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.5319 | − | 8.38999i | 0.713342 | − | 0.411848i | ||||
\(416\) | 2.16704 | + | 13.9496i | 0.106248 | + | 0.683937i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.67763 | − | 8.34373i | 0.277702 | − | 0.408105i | ||||
\(419\) | 14.4375 | + | 17.2059i | 0.705317 | + | 0.840564i | 0.993117 | − | 0.117126i | \(-0.0373682\pi\) |
−0.287800 | + | 0.957691i | \(0.592924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.98056 | + | 16.4314i | 0.291475 | + | 0.800820i | 0.995851 | + | 0.0909935i | \(0.0290043\pi\) |
−0.704377 | + | 0.709826i | \(0.748774\pi\) | |||||||
\(422\) | −22.0269 | + | 22.6239i | −1.07225 | + | 1.10131i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 27.9229 | − | 8.69599i | 1.35605 | − | 0.422314i | ||||
\(425\) | −32.8641 | − | 5.79483i | −1.59414 | − | 0.281090i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.99552 | − | 0.726309i | −0.0965698 | − | 0.0351485i | ||||
\(428\) | −23.9235 | + | 21.1896i | −1.15639 | + | 1.02424i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.9522 | + | 28.7742i | −0.624608 | + | 1.38762i | ||||
\(431\) | −13.1374 | −0.632807 | −0.316403 | − | 0.948625i | \(-0.602475\pi\) | ||||
−0.316403 | + | 0.948625i | \(0.602475\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.6607 | −1.08900 | −0.544502 | − | 0.838759i | \(-0.683281\pi\) | ||||
−0.544502 | + | 0.838759i | \(0.683281\pi\) | |||||||
\(434\) | 4.97124 | − | 11.0440i | 0.238627 | − | 0.530129i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.56642 | + | 3.15886i | −0.170800 | + | 0.151282i | ||||
\(437\) | −2.24943 | − | 0.818727i | −0.107605 | − | 0.0391650i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.8982 | − | 2.62696i | −0.711053 | − | 0.125378i | −0.193589 | − | 0.981083i | \(-0.562013\pi\) |
−0.517464 | + | 0.855705i | \(0.673124\pi\) | |||||||
\(440\) | −7.80418 | − | 25.0593i | −0.372050 | − | 1.19465i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.2485 | + | 12.5805i | −0.582602 | + | 0.598392i | ||||
\(443\) | −1.36146 | − | 3.74057i | −0.0646848 | − | 0.177720i | 0.903139 | − | 0.429347i | \(-0.141256\pi\) |
−0.967824 | + | 0.251628i | \(0.919034\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.4466 | − | 14.8333i | −0.590026 | − | 0.703165i | ||||
\(446\) | −6.33182 | + | 9.30512i | −0.299821 | + | 0.440610i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 21.1182 | − | 9.66697i | 0.997741 | − | 0.456721i | ||||
\(449\) | −22.3682 | + | 12.9143i | −1.05562 | + | 0.609464i | −0.924218 | − | 0.381865i | \(-0.875282\pi\) |
−0.131404 | + | 0.991329i | \(0.541948\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.41647 | + | 11.1136i | −0.302140 | + | 0.523321i | ||||
\(452\) | −17.6550 | + | 6.96592i | −0.830423 | + | 0.327649i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.1841 | − | 0.902004i | −0.571826 | − | 0.0423331i | ||||
\(455\) | 4.30474 | + | 24.4134i | 0.201809 | + | 1.14452i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.14884 | + | 1.80309i | 0.100518 | + | 0.0843449i | 0.691662 | − | 0.722221i | \(-0.256879\pi\) |
−0.591143 | + | 0.806566i | \(0.701323\pi\) | |||||||
\(458\) | −10.3870 | + | 2.93258i | −0.485353 | + | 0.137030i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.30623 | + | 3.25575i | −0.247404 | + | 0.151800i | ||||
\(461\) | −11.5119 | − | 9.65964i | −0.536163 | − | 0.449894i | 0.334060 | − | 0.942552i | \(-0.391581\pi\) |
−0.870223 | + | 0.492657i | \(0.836026\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.5380 | + | 3.79772i | −1.00095 | + | 0.176495i | −0.650030 | − | 0.759909i | \(-0.725244\pi\) |
−0.350924 | + | 0.936404i | \(0.614132\pi\) | |||||||
\(464\) | 26.7136 | − | 24.9668i | 1.24015 | − | 1.15905i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.01001 | + | 10.0024i | 0.0467880 | + | 0.463351i | ||||
\(467\) | 16.2109 | + | 9.35938i | 0.750152 | + | 0.433100i | 0.825749 | − | 0.564038i | \(-0.190753\pi\) |
−0.0755968 | + | 0.997138i | \(0.524086\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.4153 | − | 9.47738i | 0.757988 | − | 0.437625i | ||||
\(470\) | 3.67819 | + | 5.10631i | 0.169662 | + | 0.235536i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.15495 | + | 24.4734i | −0.0531608 | + | 1.12648i | ||||
\(473\) | −11.3678 | − | 13.5476i | −0.522691 | − | 0.622919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.5858 | + | 6.03674i | −0.761009 | + | 0.276985i | ||||
\(476\) | 25.3945 | + | 13.7697i | 1.16395 | + | 0.631132i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.05002 | − | 0.773698i | −0.139505 | − | 0.0353881i | ||||
\(479\) | 3.48398 | − | 19.7587i | 0.159187 | − | 0.902796i | −0.795670 | − | 0.605731i | \(-0.792881\pi\) |
0.954857 | − | 0.297065i | \(-0.0960080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.4831 | + | 9.63907i | 1.20753 | + | 0.439504i | ||||
\(482\) | −0.260038 | + | 0.125517i | −0.0118444 | + | 0.00571716i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.21061 | − | 1.07351i | −0.327755 | − | 0.0487958i | ||||
\(485\) | 0.461485 | 0.0209550 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.0996i | 0.638916i | 0.947600 | + | 0.319458i | \(0.103501\pi\) | ||||
−0.947600 | + | 0.319458i | \(0.896499\pi\) | |||||||
\(488\) | −2.05213 | + | 0.262815i | −0.0928956 | + | 0.0118971i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.22544 | − | 3.00494i | 0.281237 | − | 0.135749i | ||||
\(491\) | −0.766879 | + | 2.10698i | −0.0346088 | + | 0.0950868i | −0.955794 | − | 0.294039i | \(-0.905001\pi\) |
0.921185 | + | 0.389125i | \(0.127223\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 44.7869 | + | 7.89715i | 2.01710 | + | 0.355670i | ||||
\(494\) | −2.28344 | + | 9.00164i | −0.102737 | + | 0.405003i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.630720 | − | 11.7825i | −0.0283201 | − | 0.529049i | ||||
\(497\) | −10.2905 | − | 28.2729i | −0.461591 | − | 1.26821i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.09602 | + | 5.95427i | −0.317661 | + | 0.266550i | −0.787650 | − | 0.616123i | \(-0.788702\pi\) |
0.469989 | + | 0.882672i | \(0.344258\pi\) | |||||||
\(500\) | −3.70173 | + | 11.0839i | −0.165546 | + | 0.495688i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.2161 | − | 10.9605i | 0.679126 | − | 0.489189i | ||||
\(503\) | 7.08381 | + | 12.2695i | 0.315852 | + | 0.547071i | 0.979618 | − | 0.200869i | \(-0.0643765\pi\) |
−0.663767 | + | 0.747940i | \(0.731043\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.3114 | − | 38.6445i | 0.992844 | − | 1.71966i | ||||
\(506\) | −0.350535 | − | 3.47142i | −0.0155832 | − | 0.154323i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.81946 | − | 8.91739i | −0.0807255 | − | 0.395645i | ||||
\(509\) | 7.28735 | + | 41.3286i | 0.323006 | + | 1.83186i | 0.523333 | + | 0.852129i | \(0.324689\pi\) |
−0.200327 | + | 0.979729i | \(0.564200\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.3962 | + | 32.6495i | −1.21194 | + | 1.44433i | ||||
\(512\) | 13.9637 | − | 17.8049i | 0.617114 | − | 0.786874i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.8877 | − | 8.72056i | 1.36240 | − | 0.384647i | ||||
\(515\) | 2.71798 | − | 3.23916i | 0.119769 | − | 0.142735i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.47343 | + | 0.612460i | −0.152761 | + | 0.0269359i | ||||
\(518\) | 3.42325 | − | 46.2405i | 0.150409 | − | 2.03169i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 14.6349 | + | 19.2124i | 0.641784 | + | 0.842520i | ||||
\(521\) | −4.99532 | − | 2.88405i | −0.218849 | − | 0.126353i | 0.386568 | − | 0.922261i | \(-0.373660\pi\) |
−0.605417 | + | 0.795908i | \(0.706994\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.83688 | − | 6.64566i | −0.167775 | − | 0.290595i | 0.769862 | − | 0.638210i | \(-0.220325\pi\) |
−0.937637 | + | 0.347615i | \(0.886991\pi\) | |||||||
\(524\) | 2.43611 | + | 1.93555i | 0.106422 | + | 0.0845547i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.5376 | + | 13.9751i | 0.895481 | + | 0.609344i | ||||
\(527\) | 11.2423 | − | 9.43339i | 0.489721 | − | 0.410925i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.8353 | − | 7.58341i | 0.905881 | − | 0.329714i | ||||
\(530\) | 34.9032 | − | 35.8492i | 1.51610 | − | 1.55719i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.2733 | − | 0.408501i | 0.662183 | − | 0.0177107i | ||||
\(533\) | 2.05056 | − | 11.6293i | 0.0888195 | − | 0.503720i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.6999 | + | 51.3776i | −0.808468 | + | 2.22125i | ||||
\(536\) | 9.97690 | − | 15.5395i | 0.430937 | − | 0.671204i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.6516 | − | 32.5498i | 0.631677 | − | 1.40332i | ||||
\(539\) | 3.87427i | 0.166877i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.8844i | 1.49980i | 0.661552 | + | 0.749899i | \(0.269898\pi\) | ||||
−0.661552 | + | 0.749899i | \(0.730102\pi\) | |||||||
\(542\) | −36.4669 | − | 16.4149i | −1.56639 | − | 0.705079i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 28.1375 | + | 0.574577i | 1.20639 | + | 0.0246348i | ||||
\(545\) | −2.78771 | + | 7.65917i | −0.119412 | + | 0.328083i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.15974 | + | 29.2623i | −0.220614 | + | 1.25117i | 0.650279 | + | 0.759695i | \(0.274652\pi\) |
−0.870894 | + | 0.491471i | \(0.836459\pi\) | |||||||
\(548\) | −1.73327 | + | 0.0463580i | −0.0740416 | + | 0.00198032i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −18.4327 | − | 17.9463i | −0.785971 | − | 0.765231i | ||||
\(551\) | 22.6030 | − | 8.22683i | 0.962921 | − | 0.350475i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.5419 | + | 16.3976i | −0.831005 | + | 0.697296i | ||||
\(554\) | −8.65353 | + | 12.7171i | −0.367653 | + | 0.540296i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.8973 | + | 23.7844i | −0.801422 | + | 1.00868i | ||||
\(557\) | 8.65814 | + | 14.9963i | 0.366857 | + | 0.635415i | 0.989072 | − | 0.147431i | \(-0.0471004\pi\) |
−0.622215 | + | 0.782846i | \(0.713767\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.0934 | + | 8.13680i | 0.596085 | + | 0.344150i | ||||
\(560\) | 23.8775 | − | 31.7604i | 1.00901 | − | 1.34212i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.20029 | + | 0.607080i | 0.345908 | + | 0.0256081i | ||||
\(563\) | −19.0265 | + | 3.35488i | −0.801870 | + | 0.141391i | −0.559541 | − | 0.828803i | \(-0.689022\pi\) |
−0.242329 | + | 0.970194i | \(0.577911\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.8717 | + | 24.8739i | −0.878080 | + | 1.04645i | ||||
\(566\) | 3.49753 | + | 12.3881i | 0.147012 | + | 0.520709i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.5415 | − | 19.8792i | −0.903861 | − | 0.834114i | ||||
\(569\) | −14.3568 | + | 17.1097i | −0.601867 | + | 0.717277i | −0.977840 | − | 0.209353i | \(-0.932864\pi\) |
0.375973 | + | 0.926631i | \(0.377309\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.51955 | + | 36.9742i | 0.272835 | + | 1.54732i | 0.745757 | + | 0.666218i | \(0.232088\pi\) |
−0.472922 | + | 0.881104i | \(0.656801\pi\) | |||||||
\(572\) | −13.2626 | + | 2.70604i | −0.554538 | + | 0.113145i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.3297 | + | 1.95186i | −0.806805 | + | 0.0814691i | ||||
\(575\) | −3.05101 | + | 5.28450i | −0.127236 | + | 0.220379i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.0922 | + | 19.2123i | 0.461775 | + | 0.799817i | 0.999050 | − | 0.0435901i | \(-0.0138796\pi\) |
−0.537275 | + | 0.843407i | \(0.680546\pi\) | |||||||
\(578\) | 6.40729 | + | 8.89504i | 0.266508 | + | 0.369985i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19.8158 | − | 59.3335i | 0.822807 | − | 2.46369i | ||||
\(581\) | −10.9066 | + | 9.15169i | −0.452480 | + | 0.379676i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.59086 | + | 26.3507i | 0.397213 | + | 1.09133i | ||||
\(584\) | −9.13007 | + | 40.5071i | −0.377805 | + | 1.67619i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.56063 | − | 1.41056i | −0.229708 | − | 0.0582699i | ||||
\(587\) | 8.52654 | + | 1.50346i | 0.351928 | + | 0.0620544i | 0.346818 | − | 0.937933i | \(-0.387262\pi\) |
0.00511024 | + | 0.999987i | \(0.498373\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.65481 | − | 7.29402i | 0.109389 | − | 0.300545i | ||||
\(590\) | 18.2208 | + | 37.7487i | 0.750140 | + | 1.55409i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.6970 | − | 41.5620i | −0.727341 | − | 1.70819i | ||||
\(593\) | 19.4361i | 0.798144i | 0.916920 | + | 0.399072i | \(0.130668\pi\) | ||||
−0.916920 | + | 0.399072i | \(0.869332\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 49.4212 | 2.02607 | ||||||||
\(596\) | 16.9042 | + | 2.51668i | 0.692424 | + | 0.103087i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.39564 | + | 2.89139i | 0.0570719 | + | 0.118238i | ||||
\(599\) | −6.17877 | − | 2.24889i | −0.252458 | − | 0.0918871i | 0.212691 | − | 0.977119i | \(-0.431777\pi\) |
−0.465149 | + | 0.885232i | \(0.653999\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.821185 | + | 4.65717i | −0.0334968 | + | 0.189970i | −0.996965 | − | 0.0778536i | \(-0.975193\pi\) |
0.963468 | + | 0.267824i | \(0.0863044\pi\) | |||||||
\(602\) | 6.58319 | − | 25.9518i | 0.268311 | − | 1.05772i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.0156 | + | 18.4711i | −0.407529 | + | 0.751578i | ||||
\(605\) | −11.7199 | + | 4.26568i | −0.476480 | + | 0.173425i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.8132 | − | 27.1877i | −0.925960 | − | 1.10352i | −0.994381 | − | 0.105859i | \(-0.966241\pi\) |
0.0684212 | − | 0.997657i | \(-0.478204\pi\) | |||||||
\(608\) | 13.0403 | − | 7.17791i | 0.528854 | − | 0.291103i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.87199 | + | 2.06876i | −0.116283 | + | 0.0837615i | ||||
\(611\) | 2.81069 | − | 1.62275i | 0.113709 | − | 0.0656496i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.0635 | − | 20.2439i | −1.41620 | − | 0.817644i | −0.420238 | − | 0.907414i | \(-0.638053\pi\) |
−0.995963 | + | 0.0897701i | \(0.971387\pi\) | |||||||
\(614\) | 47.3838 | − | 4.78469i | 1.91225 | − | 0.193094i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.2133 | + | 19.7895i | 0.411505 | + | 0.797340i | ||||
\(617\) | −10.1725 | + | 1.79368i | −0.409528 | + | 0.0722109i | −0.374617 | − | 0.927179i | \(-0.622226\pi\) |
−0.0349111 | + | 0.999390i | \(0.511115\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0980 | + | 8.47326i | 0.405874 | + | 0.340569i | 0.822759 | − | 0.568390i | \(-0.192434\pi\) |
−0.416885 | + | 0.908959i | \(0.636878\pi\) | |||||||
\(620\) | −10.5571 | − | 17.2060i | −0.423983 | − | 0.691009i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.71307 | − | 16.6934i | −0.188977 | − | 0.669345i | ||||
\(623\) | 12.5858 | + | 10.5607i | 0.504238 | + | 0.423106i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.35223 | − | 13.3402i | −0.0940891 | − | 0.533606i | ||||
\(626\) | 0.557347 | − | 7.52852i | 0.0222761 | − | 0.300900i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.9221 | − | 7.07129i | 0.715169 | − | 0.282175i | ||||
\(629\) | 28.0924 | − | 48.6575i | 1.12012 | − | 1.94010i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.9490 | − | 17.8684i | 1.23206 | − | 0.711329i | 0.264600 | − | 0.964358i | \(-0.414760\pi\) |
0.967459 | + | 0.253029i | \(0.0814267\pi\) | |||||||
\(632\) | −9.59172 | + | 22.9276i | −0.381538 | + | 0.912012i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.0170514 | + | 0.0116029i | 0.000677197 | + | 0.000460810i | ||||
\(635\) | −10.0084 | − | 11.9276i | −0.397173 | − | 0.473332i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.21932 | − | 3.35005i | −0.0483112 | − | 0.132734i | ||||
\(638\) | 25.1199 | + | 24.4570i | 0.994506 | + | 0.968263i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.48102 | − | 38.1651i | 0.256185 | − | 1.50861i | ||||
\(641\) | −23.8743 | − | 4.20968i | −0.942977 | − | 0.166272i | −0.319035 | − | 0.947743i | \(-0.603359\pi\) |
−0.623942 | + | 0.781471i | \(0.714470\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.2825 | + | 8.83811i | 0.957609 | + | 0.348541i | 0.773096 | − | 0.634289i | \(-0.218707\pi\) |
0.184513 | + | 0.982830i | \(0.440929\pi\) | |||||||
\(644\) | 3.95415 | − | 3.50228i | 0.155815 | − | 0.138009i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.8825 | + | 7.59931i | 0.664231 | + | 0.298991i | ||||
\(647\) | −19.0593 | −0.749298 | −0.374649 | − | 0.927167i | \(-0.622237\pi\) | ||||
−0.374649 | + | 0.927167i | \(0.622237\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.4921 | −0.922146 | ||||||||
\(650\) | 21.5867 | + | 9.71681i | 0.846698 | + | 0.381125i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −26.0180 | − | 29.3748i | −1.01894 | − | 1.15041i | ||||
\(653\) | −37.3455 | − | 13.5927i | −1.46144 | − | 0.531922i | −0.515680 | − | 0.856781i | \(-0.672461\pi\) |
−0.945762 | + | 0.324860i | \(0.894683\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.24222 | + | 0.924345i | 0.204831 | + | 0.0361172i | ||||
\(656\) | −15.8625 | + | 10.3265i | −0.619326 | + | 0.403181i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.82581 | − | 3.72485i | −0.149146 | − | 0.145210i | ||||
\(659\) | 8.73494 | + | 23.9990i | 0.340265 | + | 0.934870i | 0.985318 | + | 0.170732i | \(0.0546132\pi\) |
−0.645053 | + | 0.764138i | \(0.723165\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.94246 | + | 5.89019i | 0.192239 | + | 0.229102i | 0.853551 | − | 0.521009i | \(-0.174444\pi\) |
−0.661312 | + | 0.750111i | \(0.730000\pi\) | |||||||
\(662\) | 4.46486 | + | 3.03819i | 0.173532 | + | 0.118083i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.35326 | + | 12.7962i | −0.207747 | + | 0.496588i | ||||
\(665\) | 22.6373 | − | 13.0696i | 0.877836 | − | 0.506819i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.15789 | − | 7.20168i | 0.160994 | − | 0.278850i | ||||
\(668\) | 8.36173 | + | 21.1927i | 0.323525 | + | 0.819970i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.33249 | − | 31.5068i | 0.0901120 | − | 1.21721i | ||||
\(671\) | −0.344471 | − | 1.95359i | −0.0132982 | − | 0.0754176i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.06476 | + | 6.76714i | 0.310874 | + | 0.260854i | 0.784853 | − | 0.619682i | \(-0.212738\pi\) |
−0.473979 | + | 0.880536i | \(0.657183\pi\) | |||||||
\(674\) | 3.32281 | + | 11.7692i | 0.127990 | + | 0.453332i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5446 | + | 7.08344i | −0.444024 | + | 0.272440i | ||||
\(677\) | 27.3660 | + | 22.9628i | 1.05176 | + | 0.882533i | 0.993278 | − | 0.115756i | \(-0.0369290\pi\) |
0.0584838 | + | 0.998288i | \(0.481373\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.385613 | + | 0.0679940i | −0.0147985 | + | 0.00260937i | ||||
\(680\) | 42.7862 | − | 22.0818i | 1.64077 | − | 0.846798i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.2564 | − | 1.13664i | 0.431031 | − | 0.0435244i | ||||
\(683\) | −11.6024 | − | 6.69864i | −0.443953 | − | 0.256316i | 0.261320 | − | 0.965252i | \(-0.415842\pi\) |
−0.705273 | + | 0.708936i | \(0.749176\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.56895 | + | 1.48319i | −0.0981547 | + | 0.0566696i | ||||
\(686\) | 18.5609 | − | 13.3698i | 0.708659 | − | 0.510463i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.89612 | − | 25.4091i | −0.224787 | − | 0.968713i | ||||
\(689\) | −16.5863 | − | 19.7668i | −0.631887 | − | 0.753054i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.2794 | − | 11.7487i | 1.22797 | − | 0.446943i | 0.355066 | − | 0.934841i | \(-0.384458\pi\) |
0.872901 | + | 0.487898i | \(0.162236\pi\) | |||||||
\(692\) | −27.8465 | − | 15.0992i | −1.05857 | − | 0.573987i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.53986 | + | 33.6653i | −0.324169 | + | 1.27792i | ||||
\(695\) | −9.02463 | + | 51.1812i | −0.342324 | + | 1.94142i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.1220 | − | 8.05173i | −0.837929 | − | 0.304981i | ||||
\(698\) | 4.17472 | + | 8.64890i | 0.158015 | + | 0.327366i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.73519 | − | 38.5225i | 0.216770 | − | 1.45601i | ||||
\(701\) | 5.81942 | 0.219796 | 0.109898 | − | 0.993943i | \(-0.464948\pi\) | ||||
0.109898 | + | 0.993943i | \(0.464948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 29.7167i | − | 1.12079i | ||||||
\(704\) | 17.6842 | + | 12.5693i | 0.666498 | + | 0.473722i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.91804 | − | 18.4758i | −0.335635 | − | 0.695346i | ||||
\(707\) | −12.9494 | + | 35.5783i | −0.487014 | + | 1.33806i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.2874 | − | 7.63273i | −1.62569 | − | 0.286653i | −0.714809 | − | 0.699320i | \(-0.753486\pi\) |
−0.910882 | + | 0.412666i | \(0.864598\pi\) | |||||||
\(710\) | −48.6087 | − | 12.3306i | −1.82425 | − | 0.462758i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.6147 | + | 3.51947i | 0.585185 | + | 0.131898i | ||||
\(713\) | −0.917815 | − | 2.52167i | −0.0343724 | − | 0.0944375i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.7396 | + | 14.8853i | −0.663424 | + | 0.556679i | ||||
\(716\) | 29.9156 | + | 9.99102i | 1.11800 | + | 0.373382i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.66644 | − | 3.70173i | −0.0995106 | − | 0.138147i | ||||
\(719\) | −13.4590 | − | 23.3117i | −0.501938 | − | 0.869381i | −0.999997 | − | 0.00223877i | \(-0.999287\pi\) |
0.498060 | − | 0.867143i | \(-0.334046\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.79387 | + | 3.10708i | −0.0668073 | + | 0.115714i | ||||
\(722\) | −16.9915 | + | 1.71575i | −0.632356 | + | 0.0638537i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.02749 | + | 9.93694i | 0.0753509 | + | 0.369303i | ||||
\(725\) | −10.6472 | − | 60.3835i | −0.395428 | − | 2.24259i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.10391 | − | 8.46611i | 0.263470 | − | 0.313991i | −0.618050 | − | 0.786139i | \(-0.712077\pi\) |
0.881519 | + | 0.472148i | \(0.156521\pi\) | |||||||
\(728\) | −15.0595 | − | 13.8975i | −0.558143 | − | 0.515074i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 19.3019 | + | 68.3663i | 0.714397 | + | 2.53035i | ||||
\(731\) | 20.8539 | − | 24.8527i | 0.771309 | − | 0.919211i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.25607 | + | 0.926787i | −0.194137 | + | 0.0342316i | −0.269871 | − | 0.962896i | \(-0.586981\pi\) |
0.0757339 | + | 0.997128i | \(0.475870\pi\) | |||||||
\(734\) | 42.3635 | + | 3.13623i | 1.56366 | + | 0.115760i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.85844 | − | 4.79883i | 0.0685029 | − | 0.176887i | ||||
\(737\) | 15.3342 | + | 8.85322i | 0.564844 | + | 0.326113i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.72474 | + | 13.3796i | 0.284159 | + | 0.492178i | 0.972405 | − | 0.233299i | \(-0.0749522\pi\) |
−0.688246 | + | 0.725478i | \(0.741619\pi\) | |||||||
\(740\) | −60.5089 | − | 48.0757i | −2.22435 | − | 1.76730i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23.8829 | + | 35.0978i | −0.876769 | + | 1.28848i | ||||
\(743\) | 21.9616 | − | 18.4280i | 0.805692 | − | 0.676056i | −0.143883 | − | 0.989595i | \(-0.545959\pi\) |
0.949575 | + | 0.313539i | \(0.101515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.4755 | − | 10.0003i | 1.00662 | − | 0.366381i | ||||
\(746\) | 15.7346 | + | 15.3194i | 0.576086 | + | 0.560884i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.721481 | + | 26.9753i | 0.0263800 | + | 0.986315i | ||||
\(749\) | 8.05566 | − | 45.6859i | 0.294347 | − | 1.66933i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.91474 | + | 24.4930i | −0.325303 | + | 0.893764i | 0.663979 | + | 0.747751i | \(0.268866\pi\) |
−0.989283 | + | 0.146013i | \(0.953356\pi\) | |||||||
\(752\) | −4.97647 | − | 1.51537i | −0.181473 | − | 0.0552599i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −29.4181 | − | 13.2420i | −1.07135 | − | 0.482245i | ||||
\(755\) | 35.9473i | 1.30826i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 6.07158i | − | 0.220675i | −0.993894 | − | 0.110338i | \(-0.964807\pi\) | ||
0.993894 | − | 0.110338i | \(-0.0351932\pi\) | |||||||
\(758\) | 3.88206 | − | 8.62430i | 0.141003 | − | 0.313249i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.7585 | − | 21.4295i | 0.499074 | − | 0.777330i | ||||
\(761\) | −7.74422 | + | 21.2771i | −0.280728 | + | 0.771293i | 0.716549 | + | 0.697537i | \(0.245721\pi\) |
−0.997276 | + | 0.0737560i | \(0.976501\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.20090 | − | 6.81067i | 0.0434757 | − | 0.246563i | ||||
\(764\) | −1.33506 | − | 49.9164i | −0.0483009 | − | 1.80591i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.84946 | + | 7.03511i | −0.247481 | + | 0.254189i | ||||
\(767\) | 20.3134 | − | 7.39349i | 0.733476 | − | 0.266963i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.2565 | + | 9.44536i | −0.405921 | + | 0.340608i | −0.822777 | − | 0.568364i | \(-0.807576\pi\) |
0.416856 | + | 0.908973i | \(0.363132\pi\) | |||||||
\(770\) | 31.4984 | + | 21.4336i | 1.13512 | + | 0.772414i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.7205 | + | 14.7516i | −0.421830 | + | 0.530922i | ||||
\(773\) | 9.84699 | + | 17.0555i | 0.354172 | + | 0.613443i | 0.986976 | − | 0.160869i | \(-0.0514296\pi\) |
−0.632804 | + | 0.774312i | \(0.718096\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.1355 | − | 9.89320i | −0.615526 | − | 0.355374i | ||||
\(776\) | −0.303463 | + | 0.231161i | −0.0108937 | + | 0.00829818i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.148634 | − | 2.00771i | 0.00532878 | − | 0.0719799i | ||||
\(779\) | −12.2622 | + | 2.16216i | −0.439341 | + | 0.0774676i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0661 | − | 21.5304i | 0.646456 | − | 0.770417i | ||||
\(782\) | 6.15982 | − | 1.73911i | 0.220275 | − | 0.0621904i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.58852 | + | 5.09434i | −0.0924471 | + | 0.181941i | ||||
\(785\) | 21.1874 | − | 25.2502i | 0.756212 | − | 0.901218i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.49296 | − | 14.1383i | −0.0888646 | − | 0.503976i | −0.996456 | − | 0.0841207i | \(-0.973192\pi\) |
0.907591 | − | 0.419855i | \(-0.137919\pi\) | |||||||
\(788\) | −0.765354 | + | 0.156159i | −0.0272646 | + | 0.00556294i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.27175 | + | 42.3041i | 0.151982 | + | 1.50511i | ||||
\(791\) | 13.7754 | − | 23.8596i | 0.489796 | − | 0.848351i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.912701 | + | 1.58084i | 0.0324110 | + | 0.0561374i | ||||
\(794\) | −21.9350 | + | 15.8003i | −0.778446 | + | 0.560732i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.7435 | + | 4.58996i | 0.487125 | + | 0.162687i | ||||
\(797\) | −16.5677 | + | 13.9019i | −0.586857 | + | 0.492431i | −0.887191 | − | 0.461403i | \(-0.847346\pi\) |
0.300334 | + | 0.953834i | \(0.402902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.21295 | − | 6.08002i | −0.0782884 | − | 0.215096i | ||||
\(800\) | −12.2470 | − | 35.9132i | −0.432996 | − | 1.26972i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.50440 | + | 25.6412i | −0.229678 | + | 0.905423i | ||||
\(803\) | −39.2092 | − | 6.91364i | −1.38366 | − | 0.243977i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.09078 | − | 8.49184i | 0.108936 | − | 0.299298i | ||||
\(806\) | −9.37562 | + | 4.52550i | −0.330242 | + | 0.159404i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.68576 | + | 36.5877i | 0.164844 | + | 1.28715i | ||||
\(809\) | − | 27.7706i | − | 0.976363i | −0.872742 | − | 0.488182i | \(-0.837660\pi\) | ||
0.872742 | − | 0.488182i | \(-0.162340\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.91746 | −0.242905 | −0.121452 | − | 0.992597i | \(-0.538755\pi\) | ||||
−0.121452 | + | 0.992597i | \(0.538755\pi\) | |||||||
\(812\) | −7.81587 | + | 52.4982i | −0.274283 | + | 1.84233i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 39.0071 | − | 18.8282i | 1.36720 | − | 0.659929i | ||||
\(815\) | −63.0848 | − | 22.9610i | −2.20976 | − | 0.804288i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.97969 | − | 16.8987i | 0.104246 | − | 0.591209i | ||||
\(818\) | 25.4093 | + | 6.44558i | 0.888416 | + | 0.225364i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.4353 | + | 28.4663i | −0.539024 | + | 0.994085i | ||||
\(821\) | 6.71754 | − | 2.44498i | 0.234444 | − | 0.0853305i | −0.222127 | − | 0.975018i | \(-0.571300\pi\) |
0.456570 | + | 0.889687i | \(0.349078\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.29022 | − | 1.53762i | −0.0449742 | − | 0.0535981i | 0.743088 | − | 0.669193i | \(-0.233360\pi\) |
−0.788063 | + | 0.615595i | \(0.788916\pi\) | |||||||
\(824\) | −0.164769 | + | 3.49146i | −0.00574000 | + | 0.121631i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.7870 | − | 28.8579i | −0.723271 | − | 1.00409i | ||||
\(827\) | 22.7464 | − | 13.1326i | 0.790969 | − | 0.456666i | −0.0493347 | − | 0.998782i | \(-0.515710\pi\) |
0.840303 | + | 0.542116i | \(0.182377\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.0689 | + | 20.8244i | 1.25272 | + | 0.723260i | 0.971649 | − | 0.236426i | \(-0.0759761\pi\) |
0.281074 | + | 0.959686i | \(0.409309\pi\) | |||||||
\(830\) | 2.38412 | + | 23.6104i | 0.0827539 | + | 0.819529i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −19.2472 | − | 5.30294i | −0.667277 | − | 0.183846i | ||||
\(833\) | −6.99928 | + | 1.23416i | −0.242511 | + | 0.0427611i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.8581 | + | 25.0539i | 1.03328 | + | 0.867027i | ||||
\(836\) | 7.46422 | + | 12.1652i | 0.258155 | + | 0.420742i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −30.5693 | + | 8.63066i | −1.05600 | + | 0.298141i | ||||
\(839\) | 17.8040 | + | 14.9393i | 0.614662 | + | 0.515762i | 0.896120 | − | 0.443811i | \(-0.146374\pi\) |
−0.281459 | + | 0.959573i | \(0.590818\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.47417 | + | 53.7307i | 0.326696 | + | 1.85278i | ||||
\(842\) | −24.6614 | − | 1.82572i | −0.849889 | − | 0.0629185i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.3893 | − | 41.5385i | −0.564143 | − | 1.42981i | ||||
\(845\) | −11.5861 | + | 20.0677i | −0.398574 | + | 0.690350i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.16452 | − | 5.29114i | 0.314897 | − | 0.181806i | ||||
\(848\) | −4.99451 | + | 41.0569i | −0.171512 | + | 1.40990i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26.5500 | − | 39.0174i | 0.910658 | − | 1.33828i | ||||
\(851\) | −6.60374 | − | 7.87003i | −0.226373 | − | 0.269781i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.546744 | − | 1.50217i | −0.0187202 | − | 0.0514332i | 0.929981 | − | 0.367609i | \(-0.119823\pi\) |
−0.948701 | + | 0.316175i | \(0.897601\pi\) | |||||||
\(854\) | 2.09500 | − | 2.15179i | 0.0716895 | − | 0.0736326i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.4387 | − | 43.1517i | −0.459325 | − | 1.47489i | ||||
\(857\) | 21.3303 | + | 3.76110i | 0.728629 | + | 0.128477i | 0.525644 | − | 0.850705i | \(-0.323825\pi\) |
0.202985 | + | 0.979182i | \(0.434936\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.9293 | − | 5.06987i | −0.475263 | − | 0.172982i | 0.0932719 | − | 0.995641i | \(-0.470267\pi\) |
−0.568535 | + | 0.822659i | \(0.692490\pi\) | |||||||
\(860\) | −29.5884 | − | 33.4059i | −1.00896 | − | 1.13913i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.62605 | − | 16.9419i | 0.259744 | − | 0.577042i | ||||
\(863\) | −37.5749 | −1.27907 | −0.639533 | − | 0.768764i | \(-0.720872\pi\) | ||||
−0.639533 | + | 0.768764i | \(0.720872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −54.1932 | −1.84262 | ||||||||
\(866\) | 13.1542 | − | 29.2230i | 0.446997 | − | 0.993038i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.3565 | + | 12.8217i | 0.385465 | + | 0.435197i | ||||
\(869\) | −22.3930 | − | 8.15037i | −0.759629 | − | 0.276482i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.0457 | − | 2.82929i | −0.543688 | − | 0.0958668i | ||||
\(872\) | −2.00338 | − | 6.43288i | −0.0678432 | − | 0.217845i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.36158 | − | 2.42559i | 0.0798816 | − | 0.0820467i | ||||
\(875\) | −5.80168 | − | 15.9400i | −0.196133 | − | 0.538870i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.3049 | + | 30.1572i | 0.854484 | + | 1.01833i | 0.999582 | + | 0.0289176i | \(0.00920603\pi\) |
−0.145097 | + | 0.989417i | \(0.546350\pi\) | |||||||
\(878\) | 12.0359 | − | 17.6877i | 0.406191 | − | 0.596930i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 36.8464 | + | 4.48230i | 1.24209 | + | 0.151098i | ||||
\(881\) | −22.6325 | + | 13.0669i | −0.762509 | + | 0.440235i | −0.830196 | − | 0.557472i | \(-0.811772\pi\) |
0.0676867 | + | 0.997707i | \(0.478438\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.4508 | + | 42.3501i | −0.822837 | + | 1.42519i | 0.0807251 | + | 0.996736i | \(0.474276\pi\) |
−0.903562 | + | 0.428458i | \(0.859057\pi\) | |||||||
\(884\) | −9.11359 | − | 23.0983i | −0.306523 | − | 0.776879i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.61410 | + | 0.415620i | 0.188609 | + | 0.0139630i | ||||
\(887\) | −2.89846 | − | 16.4380i | −0.0973207 | − | 0.551933i | −0.994011 | − | 0.109276i | \(-0.965147\pi\) |
0.896691 | − | 0.442658i | \(-0.145964\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.1203 | + | 8.49198i | 0.339425 | + | 0.284812i | ||||
\(890\) | 26.3539 | − | 7.44052i | 0.883384 | − | 0.249407i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.32427 | − | 13.5669i | −0.278717 | − | 0.454254i | ||||
\(893\) | −2.62152 | − | 2.19972i | −0.0877259 | − | 0.0736108i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 53.1394 | − | 9.36990i | 1.77625 | − | 0.313201i | ||||
\(896\) | 0.207655 | + | 32.8453i | 0.00693728 | + | 1.09728i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.66976 | − | 36.3423i | −0.122461 | − | 1.21276i | ||||
\(899\) | 23.3522 | + | 13.4824i | 0.778838 | + | 0.449663i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44.5501 | + | 25.7210i | −1.48418 | + | 0.856890i | ||||
\(902\) | −10.6074 | − | 14.7259i | −0.353187 | − | 0.490319i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.26528 | − | 26.8113i | 0.0420826 | − | 0.891732i | ||||
\(905\) | 11.1527 | + | 13.2913i | 0.370729 | + | 0.441818i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.94085 | − | 3.61817i | 0.330081 | − | 0.120140i | −0.171663 | − | 0.985156i | \(-0.554914\pi\) |
0.501744 | + | 0.865016i | \(0.332692\pi\) | |||||||
\(908\) | 8.23586 | − | 15.1888i | 0.273316 | − | 0.504059i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −33.9821 | − | 8.62023i | −1.12649 | − | 0.285758i | ||||
\(911\) | −10.2298 | + | 58.0158i | −0.338927 | + | 1.92215i | 0.0454332 | + | 0.998967i | \(0.485533\pi\) |
−0.384360 | + | 0.923183i | \(0.625578\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.4978 | − | 4.54882i | −0.413616 | − | 0.150544i | ||||
\(914\) | −3.57261 | + | 1.72445i | −0.118171 | + | 0.0570399i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.24767 | − | 15.0973i | 0.0742650 | − | 0.498828i | ||||
\(917\) | −4.51655 | −0.149150 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.4259i | 0.838724i | 0.907819 | + | 0.419362i | \(0.137746\pi\) | ||||
−0.907819 | + | 0.419362i | \(0.862254\pi\) | |||||||
\(920\) | −1.11840 | − | 8.73276i | −0.0368725 | − | 0.287911i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19.1394 | − | 9.23837i | 0.630324 | − | 0.304250i | ||||
\(923\) | −8.84554 | + | 24.3029i | −0.291155 | + | 0.799941i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −74.5997 | − | 13.1539i | −2.45282 | − | 0.432499i | ||||
\(926\) | 7.60492 | − | 29.9796i | 0.249913 | − | 0.985191i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.6901 | + | 48.9423i | 0.547879 | + | 1.60661i | ||||
\(929\) | 1.65289 | + | 4.54128i | 0.0542296 | + | 0.148995i | 0.963850 | − | 0.266446i | \(-0.0858495\pi\) |
−0.909620 | + | 0.415441i | \(0.863627\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.87963 | + | 2.41630i | −0.0943760 | + | 0.0791909i | ||||
\(932\) | −13.4853 | − | 4.50371i | −0.441724 | − | 0.147524i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.4799 | + | 15.4725i | −0.702845 | + | 0.506274i | ||||
\(935\) | 23.0832 | + | 39.9813i | 0.754902 | + | 1.30753i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.7048 | − | 44.5220i | 0.839738 | − | 1.45447i | −0.0503753 | − | 0.998730i | \(-0.516042\pi\) |
0.890114 | − | 0.455739i | \(-0.150625\pi\) | |||||||
\(938\) | 2.69311 | + | 26.6704i | 0.0879332 | + | 0.870821i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.72016 | + | 1.77922i | −0.284420 | + | 0.0580318i | ||||
\(941\) | 6.83831 | + | 38.7820i | 0.222922 | + | 1.26426i | 0.866617 | + | 0.498973i | \(0.166289\pi\) |
−0.643695 | + | 0.765282i | \(0.722599\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.76699 | + | 3.29758i | −0.0901057 | + | 0.107384i | ||||
\(944\) | −30.8902 | − | 15.6958i | −1.00539 | − | 0.510855i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.0696 | − | 6.79561i | 0.782571 | − | 0.220944i | ||||
\(947\) | −18.2848 | + | 21.7910i | −0.594178 | + | 0.708113i | −0.976403 | − | 0.215956i | \(-0.930713\pi\) |
0.382226 | + | 0.924069i | \(0.375158\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.0798 | − | 6.36183i | 1.17120 | − | 0.206514i | ||||
\(950\) | 1.84287 | − | 24.8931i | 0.0597907 | − | 0.807639i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −32.4983 | + | 24.7553i | −1.05328 | + | 0.802325i | ||||
\(953\) | 24.5811 | + | 14.1919i | 0.796261 | + | 0.459722i | 0.842162 | − | 0.539224i | \(-0.181282\pi\) |
−0.0459008 | + | 0.998946i | \(0.514616\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.7143 | − | 73.9833i | −1.38220 | − | 2.39404i | ||||
\(956\) | 2.76824 | − | 3.48415i | 0.0895312 | − | 0.112686i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.4581 | + | 15.9625i | 0.757898 | + | 0.515724i | ||||
\(959\) | 1.92807 | − | 1.61784i | 0.0622605 | − | 0.0522428i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.9537 | + | 7.62652i | −0.675925 | + | 0.246017i | ||||
\(962\) | −27.8034 | + | 28.5570i | −0.896419 | + | 0.920715i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.0109178 | − | 0.408203i | −0.000351638 | − | 0.0131473i | ||||
\(965\) | −5.59727 | + | 31.7437i | −0.180183 | + | 1.02187i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.1101 | − | 38.7671i | 0.453749 | − | 1.24667i | −0.476317 | − | 0.879274i | \(-0.658028\pi\) |
0.930066 | − | 0.367392i | \(-0.119749\pi\) | |||||||
\(968\) | 5.57002 | − | 8.67557i | 0.179027 | − | 0.278843i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.267884 | + | 0.595126i | −0.00860125 | + | 0.0191083i | ||||
\(971\) | − | 5.59715i | − | 0.179621i | −0.995959 | − | 0.0898105i | \(-0.971374\pi\) | ||
0.995959 | − | 0.0898105i | \(-0.0286261\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 44.0963i | − | 1.41366i | ||||||
\(974\) | −18.1827 | − | 8.18461i | −0.582613 | − | 0.262252i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.852305 | − | 2.79896i | 0.0272816 | − | 0.0895927i | ||||
\(977\) | −7.61083 | + | 20.9106i | −0.243492 | + | 0.668989i | 0.756397 | + | 0.654112i | \(0.226958\pi\) |
−0.999889 | + | 0.0148763i | \(0.995265\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.66507 | + | 15.1144i | −0.0851762 | + | 0.483058i | ||||
\(980\) | 0.261377 | + | 9.77257i | 0.00834938 | + | 0.312173i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.27198 | − | 2.21203i | −0.0725018 | − | 0.0705886i | ||||
\(983\) | 43.7402 | − | 15.9201i | 1.39510 | − | 0.507774i | 0.468378 | − | 0.883528i | \(-0.344839\pi\) |
0.926719 | + | 0.375755i | \(0.122617\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.02371 | + | 0.858996i | −0.0326182 | + | 0.0273699i | ||||
\(986\) | −36.1821 | + | 53.1726i | −1.15227 | + | 1.69336i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.2829 | − | 8.17000i | −0.327143 | − | 0.259922i | ||||
\(989\) | −2.96615 | − | 5.13752i | −0.0943180 | − | 0.163364i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.1847 | − | 22.0460i | −1.21298 | − | 0.700313i | −0.249571 | − | 0.968357i | \(-0.580289\pi\) |
−0.963407 | + | 0.268044i | \(0.913623\pi\) | |||||||
\(992\) | 15.5607 | + | 6.02617i | 0.494052 | + | 0.191331i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 42.4338 | + | 3.14144i | 1.34592 | + | 0.0996403i | ||||
\(995\) | 24.4127 | − | 4.30461i | 0.773933 | − | 0.136465i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.4946 | − | 16.0822i | 0.427378 | − | 0.509330i | −0.508786 | − | 0.860893i | \(-0.669905\pi\) |
0.936164 | + | 0.351563i | \(0.114350\pi\) | |||||||
\(998\) | −3.55943 | − | 12.6073i | −0.112672 | − | 0.399077i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 648.2.v.b.35.12 | 192 | ||
3.2 | odd | 2 | 216.2.v.b.11.21 | ✓ | 192 | ||
8.3 | odd | 2 | inner | 648.2.v.b.35.6 | 192 | ||
12.11 | even | 2 | 864.2.bh.b.335.28 | 192 | |||
24.5 | odd | 2 | 864.2.bh.b.335.27 | 192 | |||
24.11 | even | 2 | 216.2.v.b.11.27 | yes | 192 | ||
27.5 | odd | 18 | inner | 648.2.v.b.611.6 | 192 | ||
27.22 | even | 9 | 216.2.v.b.59.27 | yes | 192 | ||
108.103 | odd | 18 | 864.2.bh.b.815.27 | 192 | |||
216.59 | even | 18 | inner | 648.2.v.b.611.12 | 192 | ||
216.157 | even | 18 | 864.2.bh.b.815.28 | 192 | |||
216.211 | odd | 18 | 216.2.v.b.59.21 | yes | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.v.b.11.21 | ✓ | 192 | 3.2 | odd | 2 | ||
216.2.v.b.11.27 | yes | 192 | 24.11 | even | 2 | ||
216.2.v.b.59.21 | yes | 192 | 216.211 | odd | 18 | ||
216.2.v.b.59.27 | yes | 192 | 27.22 | even | 9 | ||
648.2.v.b.35.6 | 192 | 8.3 | odd | 2 | inner | ||
648.2.v.b.35.12 | 192 | 1.1 | even | 1 | trivial | ||
648.2.v.b.611.6 | 192 | 27.5 | odd | 18 | inner | ||
648.2.v.b.611.12 | 192 | 216.59 | even | 18 | inner | ||
864.2.bh.b.335.27 | 192 | 24.5 | odd | 2 | |||
864.2.bh.b.335.28 | 192 | 12.11 | even | 2 | |||
864.2.bh.b.815.27 | 192 | 108.103 | odd | 18 | |||
864.2.bh.b.815.28 | 192 | 216.157 | even | 18 |