LMFDB - Embedded newform 990.2.z.a.611.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(161,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.z (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			611.1
Character	$\chi$	$=$	990.611
Dual form			990.2.z.a.431.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-0.951057 - 0.309017i) q^{5} +(-1.27614 - 1.75646i) q^{7} +(-0.809017 - 0.587785i) q^{8} -1.00000i q^{10} +(-1.89530 + 2.72174i) q^{11} +(2.81073 - 0.913261i) q^{13} +(1.27614 - 1.75646i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.909547 - 2.79930i) q^{17} +(0.958278 - 1.31896i) q^{19} +(0.951057 - 0.309017i) q^{20} +(-3.17420 - 0.961471i) q^{22} -3.41555i q^{23} +(0.809017 + 0.587785i) q^{25} +(1.73712 + 2.39095i) q^{26} +(2.06484 + 0.670908i) q^{28} +(3.04327 - 2.21107i) q^{29} +(-3.14112 - 9.66737i) q^{31} +1.00000 q^{32} +2.94336 q^{34} +(0.670908 + 2.06484i) q^{35} +(9.51376 - 6.91215i) q^{37} +(1.55053 + 0.503797i) q^{38} +(0.587785 + 0.809017i) q^{40} +(3.73949 + 2.71690i) q^{41} -7.21249i q^{43} +(-0.0664698 - 3.31596i) q^{44} +(3.24838 - 1.05546i) q^{46} +(0.256076 - 0.352459i) q^{47} +(0.706510 - 2.17441i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-1.73712 + 2.39095i) q^{52} +(-9.58109 + 3.11308i) q^{53} +(2.64360 - 2.00285i) q^{55} +2.17110i q^{56} +(3.04327 + 2.21107i) q^{58} +(4.23873 + 5.83411i) q^{59} +(-12.6549 - 4.11183i) q^{61} +(8.22356 - 5.97476i) q^{62} +(0.309017 + 0.951057i) q^{64} -2.95537 q^{65} +5.20687 q^{67} +(0.909547 + 2.79930i) q^{68} +(-1.75646 + 1.27614i) q^{70} +(-8.20611 - 2.66633i) q^{71} +(4.04789 + 5.57145i) q^{73} +(9.51376 + 6.91215i) q^{74} +1.63032i q^{76} +(7.19929 - 0.144313i) q^{77} +(1.93416 - 0.628447i) q^{79} +(-0.587785 + 0.809017i) q^{80} +(-1.42836 + 4.39603i) q^{82} +(-3.19368 + 9.82914i) q^{83} +(-1.73006 + 2.38122i) q^{85} +(6.85948 - 2.22878i) q^{86} +(3.13312 - 1.08790i) q^{88} -7.02630i q^{89} +(-5.19099 - 3.77148i) q^{91} +(2.00761 + 2.76324i) q^{92} +(0.414340 + 0.134627i) q^{94} +(-1.31896 + 0.958278i) q^{95} +(1.99921 + 6.15293i) q^{97} +2.28631 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{2} - 8 q^{4} - 8 q^{8} - 8 q^{16} + 4 q^{17} + 8 q^{25} - 8 q^{29} + 32 q^{31} + 32 q^{32} + 24 q^{34} + 16 q^{37} + 32 q^{41} - 20 q^{46} - 20 q^{47} + 16 q^{49} + 8 q^{50} - 40 q^{53} + 8 q^{55}+ \cdots + 16 q^{98}+O(q^{100}) $ 32 * q - 8 * q^2 - 8 * q^4 - 8 * q^8 - 8 * q^16 + 4 * q^17 + 8 * q^25 - 8 * q^29 + 32 * q^31 + 32 * q^32 + 24 * q^34 + 16 * q^37 + 32 * q^41 - 20 * q^46 - 20 * q^47 + 16 * q^49 + 8 * q^50 - 40 * q^53 + 8 * q^55 - 8 * q^58 + 40 * q^59 - 28 * q^62 - 8 * q^64 + 8 * q^65 + 4 * q^68 - 40 * q^71 + 40 * q^73 + 16 * q^74 - 28 * q^77 + 20 * q^79 - 8 * q^82 - 24 * q^83 - 24 * q^91 + 20 * q^94 + 16 * q^95 + 48 * q^97 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.951057	−	0.309017i	−0.425325	−	0.138197i
$5$	−0.951057	−	0.309017i	−0.425325	−	0.138197i
$6$		0			0
$7$	−1.27614	−	1.75646i	−0.482336	−	0.663879i	0.496615	−	0.867971i	$-0.334576\pi$
$7$	−1.27614	−	1.75646i	−0.482336	−	0.663879i	−0.978952	+	0.204092i	$0.934576\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$		0			0
$10$		−	1.00000i		−	0.316228i
$11$	−1.89530	+	2.72174i	−0.571453	+	0.820635i
$11$	−1.89530	+	2.72174i	−0.571453	+	0.820635i
$12$		0			0
$13$	2.81073	−	0.913261i	0.779555	−	0.253293i	0.107905	−	0.994161i	$-0.465586\pi$
$13$	2.81073	−	0.913261i	0.779555	−	0.253293i	0.671650	+	0.740868i	$0.265586\pi$
$14$	1.27614	−	1.75646i	0.341063	−	0.469433i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.909547	−	2.79930i	0.220598	−	0.678929i	−0.778111	−	0.628127i	$-0.783822\pi$
$17$	0.909547	−	2.79930i	0.220598	−	0.678929i	0.998709	−	0.0508028i	$-0.0161780\pi$
$18$		0			0
$19$	0.958278	−	1.31896i	0.219844	−	0.302589i	−0.684822	−	0.728710i	$-0.740120\pi$
$19$	0.958278	−	1.31896i	0.219844	−	0.302589i	0.904666	+	0.426121i	$0.140120\pi$
$20$	0.951057	−	0.309017i	0.212663	−	0.0690983i
$21$		0			0
$22$	−3.17420	−	0.961471i	−0.676743	−	0.204986i
$23$		−	3.41555i		−	0.712192i	−0.934449	−	0.356096i	$-0.884108\pi$
$23$		−	3.41555i		−	0.712192i	0.934449	−	0.356096i	$-0.115892\pi$
$24$		0			0
$25$	0.809017	+	0.587785i	0.161803	+	0.117557i
$26$	1.73712	+	2.39095i	0.340678	+	0.468903i
$27$		0			0
$28$	2.06484	+	0.670908i	0.390218	+	0.126790i
$29$	3.04327	−	2.21107i	0.565121	−	0.410585i	−0.268209	−	0.963361i	$-0.586432\pi$
$29$	3.04327	−	2.21107i	0.565121	−	0.410585i	0.833330	+	0.552776i	$0.186432\pi$
$30$		0			0
$31$	−3.14112	−	9.66737i	−0.564162	−	1.73631i	−0.670430	−	0.741973i	$-0.733890\pi$
$31$	−3.14112	−	9.66737i	−0.564162	−	1.73631i	0.106268	−	0.994338i	$-0.466110\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	2.94336			0.504781
$35$	0.670908	+	2.06484i	0.113404	+	0.349022i
$36$		0			0
$37$	9.51376	−	6.91215i	1.56405	−	1.13635i	0.631467	−	0.775403i	$-0.282453\pi$
$37$	9.51376	−	6.91215i	1.56405	−	1.13635i	0.932586	−	0.360948i	$-0.117547\pi$
$38$	1.55053	+	0.503797i	0.251529	+	0.0817266i
$39$		0			0
$40$	0.587785	+	0.809017i	0.0929370	+	0.127917i
$41$	3.73949	+	2.71690i	0.584010	+	0.424308i	0.840168	−	0.542327i	$-0.182457\pi$
$41$	3.73949	+	2.71690i	0.584010	+	0.424308i	−0.256158	+	0.966635i	$0.582457\pi$
$42$		0			0
$43$		−	7.21249i		−	1.09989i	−0.835199	−	0.549947i	$-0.814648\pi$
$43$		−	7.21249i		−	1.09989i	0.835199	−	0.549947i	$-0.185352\pi$
$44$	−0.0664698	−	3.31596i	−0.0100207	−	0.499900i
$45$		0			0
$46$	3.24838	−	1.05546i	0.478948	−	0.155620i
$47$	0.256076	−	0.352459i	0.0373526	−	0.0514114i	−0.789932	−	0.613194i	$-0.789884\pi$
$47$	0.256076	−	0.352459i	0.0373526	−	0.0514114i	0.827285	+	0.561783i	$0.189884\pi$
$48$		0			0
$49$	0.706510	−	2.17441i	0.100930	−	0.310631i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$		0			0
$52$	−1.73712	+	2.39095i	−0.240896	+	0.331565i
$53$	−9.58109	+	3.11308i	−1.31606	+	0.427615i	−0.881141	−	0.472853i	$-0.843224\pi$
$53$	−9.58109	+	3.11308i	−1.31606	+	0.427615i	−0.434922	+	0.900468i	$0.643224\pi$
$54$		0			0
$55$	2.64360	−	2.00285i	0.356463	−	0.270064i
$56$			2.17110i			0.290126i
$57$		0			0
$58$	3.04327	+	2.21107i	0.399601	+	0.290327i
$59$	4.23873	+	5.83411i	0.551836	+	0.759537i	0.990260	−	0.139231i	$-0.0444631\pi$
$59$	4.23873	+	5.83411i	0.551836	+	0.759537i	−0.438424	+	0.898768i	$0.644463\pi$
$60$		0			0
$61$	−12.6549	−	4.11183i	−1.62029	−	0.526465i	−0.648282	−	0.761400i	$-0.724512\pi$
$61$	−12.6549	−	4.11183i	−1.62029	−	0.526465i	−0.972011	+	0.234935i	$0.924512\pi$
$62$	8.22356	−	5.97476i	1.04439	−	0.758796i
$63$		0			0
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−2.95537			−0.366569
$66$		0			0
$67$	5.20687			0.636121			0.318060	−	0.948070i	$-0.396968\pi$
$67$	5.20687			0.636121			0.318060	+	0.948070i	$0.396968\pi$
$68$	0.909547	+	2.79930i	0.110299	+	0.339465i
$69$		0			0
$70$	−1.75646	+	1.27614i	−0.209937	+	0.152528i
$71$	−8.20611	−	2.66633i	−0.973887	−	0.316435i	−0.221503	−	0.975160i	$-0.571096\pi$
$71$	−8.20611	−	2.66633i	−0.973887	−	0.316435i	−0.752384	+	0.658725i	$0.771096\pi$
$72$		0			0
$73$	4.04789	+	5.57145i	0.473770	+	0.652089i	0.977293	−	0.211893i	$-0.0679629\pi$
$73$	4.04789	+	5.57145i	0.473770	+	0.652089i	−0.503523	+	0.863982i	$0.667963\pi$
$74$	9.51376	+	6.91215i	1.10595	+	0.803521i
$75$		0			0
$76$			1.63032i			0.187011i
$77$	7.19929	−	0.144313i	0.820435	−	0.0164460i
$78$		0			0
$79$	1.93416	−	0.628447i	0.217610	−	0.0707058i	−0.198183	−	0.980165i	$-0.563504\pi$
$79$	1.93416	−	0.628447i	0.217610	−	0.0707058i	0.415793	+	0.909459i	$0.363504\pi$
$80$	−0.587785	+	0.809017i	−0.0657164	+	0.0904508i
$81$		0			0
$82$	−1.42836	+	4.39603i	−0.157736	+	0.485461i
$83$	−3.19368	+	9.82914i	−0.350552	+	1.07889i	0.607992	+	0.793943i	$0.291975\pi$
$83$	−3.19368	+	9.82914i	−0.350552	+	1.07889i	−0.958544	+	0.284945i	$0.908025\pi$
$84$		0			0
$85$	−1.73006	+	2.38122i	−0.187651	+	0.258280i
$86$	6.85948	−	2.22878i	0.739677	−	0.240336i
$87$		0			0
$88$	3.13312	−	1.08790i	0.333992	−	0.115971i
$89$		−	7.02630i		−	0.744786i	−0.928075	−	0.372393i	$-0.878537\pi$
$89$		−	7.02630i		−	0.744786i	0.928075	−	0.372393i	$-0.121463\pi$
$90$		0			0
$91$	−5.19099	−	3.77148i	−0.544164	−	0.395358i
$92$	2.00761	+	2.76324i	0.209308	+	0.288088i
$93$		0			0
$94$	0.414340	+	0.134627i	0.0427359	+	0.0138858i
$95$	−1.31896	+	0.958278i	−0.135322	+	0.0983173i
$96$		0			0
$97$	1.99921	+	6.15293i	0.202989	+	0.624735i	0.999790	+	0.0204937i	$0.00652380\pi$
$97$	1.99921	+	6.15293i	0.202989	+	0.624735i	−0.796801	+	0.604242i	$0.793476\pi$
$98$	2.28631			0.230953
$99$		0			0
$100$	−1.00000			−0.100000
$101$	1.50262	+	4.62459i	0.149516	+	0.460164i	0.997564	−	0.0697559i	$-0.0222220\pi$
$101$	1.50262	+	4.62459i	0.149516	+	0.460164i	−0.848048	+	0.529920i	$0.822222\pi$
$102$		0			0
$103$	−3.34205	+	2.42814i	−0.329302	+	0.239252i	−0.740134	−	0.672459i	$-0.765238\pi$
$103$	−3.34205	+	2.42814i	−0.329302	+	0.239252i	0.410832	+	0.911711i	$0.365238\pi$
$104$	−2.81073	−	0.913261i	−0.275614	−	0.0895526i
$105$		0			0
$106$	−5.92144	−	8.15016i	−0.575141	−	0.791614i
$107$	5.50274	+	3.99797i	0.531970	+	0.386498i	0.821094	−	0.570793i	$-0.193364\pi$
$107$	5.50274	+	3.99797i	0.531970	+	0.386498i	−0.289124	+	0.957292i	$0.593364\pi$
$108$		0			0
$109$			5.34567i			0.512022i	0.966674	+	0.256011i	$0.0824083\pi$
$109$			5.34567i			0.512022i	−0.966674	+	0.256011i	$0.917592\pi$
$110$	2.72174	+	1.89530i	0.259507	+	0.180709i
$111$		0			0
$112$	−2.06484	+	0.670908i	−0.195109	+	0.0633948i
$113$	7.62808	−	10.4991i	0.717589	−	0.987677i	−0.282011	−	0.959411i	$-0.591002\pi$
$113$	7.62808	−	10.4991i	0.717589	−	0.987677i	0.999600	−	0.0282656i	$-0.00899842\pi$
$114$		0			0
$115$	−1.05546	+	3.24838i	−0.0984225	+	0.302913i
$116$	−1.16243	+	3.57758i	−0.107929	+	0.332170i
$117$		0			0
$118$	−4.23873	+	5.83411i	−0.390207	+	0.537074i
$119$	−6.07756	+	1.97472i	−0.557129	+	0.181022i
$120$		0			0
$121$	−3.81570	−	10.3170i	−0.346882	−	0.937909i
$122$		−	13.3061i		−	1.20468i
$123$		0			0
$124$	8.22356	+	5.97476i	0.738497	+	0.536550i
$125$	−0.587785	−	0.809017i	−0.0525731	−	0.0723607i
$126$		0			0
$127$	−3.18868	−	1.03607i	−0.282950	−	0.0919360i	0.164104	−	0.986443i	$-0.447527\pi$
$127$	−3.18868	−	1.03607i	−0.282950	−	0.0919360i	−0.447054	+	0.894507i	$0.647527\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$		0			0
$130$	−0.913261	−	2.81073i	−0.0800983	−	0.246517i
$131$	−14.9487			−1.30608			−0.653039	−	0.757324i	$-0.726506\pi$
$131$	−14.9487			−1.30608			−0.653039	+	0.757324i	$0.726506\pi$
$132$		0			0
$133$	−3.53959			−0.306922
$134$	1.60901	+	4.95203i	0.138998	+	0.427790i
$135$		0			0
$136$	−2.38122	+	1.73006i	−0.204188	+	0.148352i
$137$	−1.75553	−	0.570407i	−0.149985	−	0.0487332i	0.233062	−	0.972462i	$-0.425125\pi$
$137$	−1.75553	−	0.570407i	−0.149985	−	0.0487332i	−0.383047	+	0.923729i	$0.625125\pi$
$138$		0			0
$139$	−8.77734	−	12.0810i	−0.744485	−	1.02470i	−0.998348	−	0.0574552i	$-0.981701\pi$
$139$	−8.77734	−	12.0810i	−0.744485	−	1.02470i	0.253863	−	0.967240i	$-0.418299\pi$
$140$	−1.75646	−	1.27614i	−0.148448	−	0.107854i
$141$		0			0
$142$		−	8.62842i		−	0.724081i
$143$	−2.84151	+	9.38096i	−0.237619	+	0.784475i
$144$		0			0
$145$	−3.57758	+	1.16243i	−0.297102	+	0.0965342i
$146$	−4.04789	+	5.57145i	−0.335006	+	0.461096i
$147$		0			0
$148$	−3.63393	+	11.1841i	−0.298707	+	0.919327i
$149$	5.22853	−	16.0918i	0.428338	−	1.31829i	−0.471423	−	0.881907i	$-0.656260\pi$
$149$	5.22853	−	16.0918i	0.428338	−	1.31829i	0.899761	−	0.436382i	$-0.143740\pi$
$150$		0			0
$151$	−6.53099	+	8.98913i	−0.531484	+	0.731525i	−0.987356	−	0.158520i	$-0.949328\pi$
$151$	−6.53099	+	8.98913i	−0.531484	+	0.731525i	0.455872	+	0.890046i	$0.349328\pi$
$152$	−1.55053	+	0.503797i	−0.125764	+	0.0408633i
$153$		0			0
$154$	2.36195	+	6.80233i	0.190331	+	0.548148i
$155$			10.1649i			0.816462i
$156$		0			0
$157$	16.6676	+	12.1098i	1.33022	+	0.966464i	0.999743	+	0.0226504i	$0.00721045\pi$
$157$	16.6676	+	12.1098i	1.33022	+	0.966464i	0.330479	+	0.943813i	$0.392790\pi$
$158$	1.19538	+	1.64530i	0.0950991	+	0.130893i
$159$		0			0
$160$	−0.951057	−	0.309017i	−0.0751876	−	0.0244299i
$161$	−5.99928	+	4.35873i	−0.472809	+	0.343516i
$162$		0			0
$163$	5.06088	+	15.5758i	0.396399	+	1.21999i	0.927867	+	0.372912i	$0.121641\pi$
$163$	5.06088	+	15.5758i	0.396399	+	1.21999i	−0.531468	+	0.847079i	$0.678359\pi$
$164$	−4.62226			−0.360938
$165$		0			0
$166$	−10.3350			−0.802149
$167$	−7.23494	−	22.2669i	−0.559857	−	1.72306i	−0.682760	−	0.730643i	$-0.739221\pi$
$167$	−7.23494	−	22.2669i	−0.559857	−	1.72306i	0.122903	−	0.992419i	$-0.460779\pi$
$168$		0			0
$169$	−3.45108	+	2.50736i	−0.265468	+	0.192874i
$170$	−2.79930	−	0.909547i	−0.214696	−	0.0697591i
$171$		0			0
$172$	4.23939	+	5.83503i	0.323251	+	0.444917i
$173$	0.757949	+	0.550682i	0.0576258	+	0.0418676i	0.616225	−	0.787570i	$-0.288661\pi$
$173$	0.757949	+	0.550682i	0.0576258	+	0.0418676i	−0.558599	+	0.829438i	$0.688661\pi$
$174$		0			0
$175$		−	2.17110i		−	0.164120i
$176$	2.00285	+	2.64360i	0.150970	+	0.199269i
$177$		0			0
$178$	6.68241	−	2.17125i	0.500868	−	0.162742i
$179$	11.7077	−	16.1143i	0.875077	−	1.20444i	−0.102684	−	0.994714i	$-0.532743\pi$
$179$	11.7077	−	16.1143i	0.875077	−	1.20444i	0.977760	−	0.209725i	$-0.0672570\pi$
$180$		0			0
$181$	0.833100	−	2.56402i	0.0619238	−	0.190582i	−0.915309	−	0.402753i	$-0.868053\pi$
$181$	0.833100	−	2.56402i	0.0619238	−	0.190582i	0.977233	+	0.212171i	$0.0680534\pi$
$182$	1.98278	−	6.10238i	0.146974	−	0.452338i
$183$		0			0
$184$	−2.00761	+	2.76324i	−0.148003	+	0.203709i
$185$	−11.1841	+	3.63393i	−0.822271	+	0.267172i
$186$		0			0
$187$	5.89509	+	7.78105i	0.431092	+	0.569006i
$188$			0.435663i			0.0317740i
$189$		0			0
$190$	−1.31896	−	0.958278i	−0.0956872	−	0.0695208i
$191$	4.26512	+	5.87043i	0.308613	+	0.424769i	0.934948	−	0.354785i	$-0.115446\pi$
$191$	4.26512	+	5.87043i	0.308613	+	0.424769i	−0.626335	+	0.779554i	$0.715446\pi$
$192$		0			0
$193$	−12.6084	−	4.09673i	−0.907576	−	0.294889i	−0.182216	−	0.983259i	$-0.558327\pi$
$193$	−12.6084	−	4.09673i	−0.907576	−	0.294889i	−0.725360	+	0.688369i	$0.758327\pi$
$194$	−5.23399	+	3.80272i	−0.375779	+	0.273019i
$195$		0			0
$196$	0.706510	+	2.17441i	0.0504650	+	0.155315i
$197$	2.18020			0.155333			0.0776665	−	0.996979i	$-0.475253\pi$
$197$	2.18020			0.155333			0.0776665	+	0.996979i	$0.475253\pi$
$198$		0			0
$199$	2.48321			0.176030			0.0880152	−	0.996119i	$-0.471948\pi$
$199$	2.48321			0.176030			0.0880152	+	0.996119i	$0.471948\pi$
$200$	−0.309017	−	0.951057i	−0.0218508	−	0.0672499i
$201$		0			0
$202$	−3.93391	+	2.85815i	−0.276789	+	0.201099i
$203$	−7.76729	−	2.52375i	−0.545157	−	0.177132i
$204$		0			0
$205$	−2.71690	−	3.73949i	−0.189756	−	0.261177i
$206$	−3.34205	−	2.42814i	−0.232852	−	0.169177i
$207$		0			0
$208$		−	2.95537i		−	0.204918i
$209$	1.77363	+	5.10799i	0.122685	+	0.353327i
$210$		0			0
$211$	18.2803	−	5.93962i	1.25846	−	0.408900i	0.397518	−	0.917594i	$-0.369872\pi$
$211$	18.2803	−	5.93962i	1.25846	−	0.408900i	0.860947	+	0.508694i	$0.169872\pi$
$212$	5.92144	−	8.15016i	0.406686	−	0.559755i
$213$		0			0
$214$	−2.10186	+	6.46885i	−0.143680	+	0.442202i
$215$	−2.22878	+	6.85948i	−0.152002	+	0.467813i
$216$		0			0
$217$	−12.9718	+	17.8542i	−0.880585	+	1.21202i
$218$	−5.08403	+	1.65190i	−0.344334	+	0.111881i
$219$		0			0
$220$	−0.961471	+	3.17420i	−0.0648224	+	0.214005i
$221$		−	8.69871i		−	0.585139i
$222$		0			0
$223$	12.5868	+	9.14488i	0.842878	+	0.612387i	0.923173	−	0.384385i	$-0.125586\pi$
$223$	12.5868	+	9.14488i	0.842878	+	0.612387i	−0.0802953	+	0.996771i	$0.525586\pi$
$224$	−1.27614	−	1.75646i	−0.0852658	−	0.117358i
$225$		0			0
$226$	12.3425	+	4.01032i	0.821010	+	0.266762i
$227$	−12.1804	+	8.84958i	−0.808442	+	0.587368i	−0.913379	−	0.407111i	$-0.866536\pi$
$227$	−12.1804	+	8.84958i	−0.808442	+	0.587368i	0.104936	+	0.994479i	$0.466536\pi$
$228$		0			0
$229$	3.59361	+	11.0600i	0.237472	+	0.730864i	0.996784	+	0.0801372i	$0.0255359\pi$
$229$	3.59361	+	11.0600i	0.237472	+	0.730864i	−0.759312	+	0.650727i	$0.774464\pi$
$230$	−3.41555			−0.225215
$231$		0			0
$232$	−3.76169			−0.246967
$233$	−2.59400	−	7.98352i	−0.169939	−	0.523018i	0.829427	−	0.558614i	$-0.188667\pi$
$233$	−2.59400	−	7.98352i	−0.169939	−	0.523018i	−0.999366	+	0.0355966i	$0.988667\pi$
$234$		0			0
$235$	−0.352459	+	0.256076i	−0.0229919	+	0.0167046i
$236$	−6.85841	−	2.22843i	−0.446445	−	0.145059i
$237$		0			0
$238$	−3.75614	−	5.16988i	−0.243474	−	0.335114i
$239$	−11.1708	−	8.11608i	−0.722580	−	0.524985i	0.164627	−	0.986356i	$-0.447358\pi$
$239$	−11.1708	−	8.11608i	−0.722580	−	0.524985i	−0.887208	+	0.461370i	$0.847358\pi$
$240$		0			0
$241$		−	0.850746i		−	0.0548013i	−0.999625	−	0.0274007i	$-0.991277\pi$
$241$		−	0.850746i		−	0.0548013i	0.999625	−	0.0274007i	$-0.00872300\pi$
$242$	8.63293	−	6.81708i	0.554946	−	0.438218i
$243$		0			0
$244$	12.6549	−	4.11183i	0.810147	−	0.263233i
$245$	−1.34386	+	1.84967i	−0.0858562	+	0.118171i
$246$		0			0
$247$	1.48891	−	4.58238i	0.0947369	−	0.291570i
$248$	−3.14112	+	9.66737i	−0.199461	+	0.613879i
$249$		0			0
$250$	0.587785	−	0.809017i	0.0371748	−	0.0511667i
$251$	−17.6122	+	5.72256i	−1.11167	+	0.361205i	−0.806584	−	0.591119i	$-0.798686\pi$
$251$	−17.6122	+	5.72256i	−1.11167	+	0.361205i	−0.305090	+	0.952324i	$0.598686\pi$
$252$		0			0
$253$	9.29624	+	6.47348i	0.584449	+	0.406985i
$254$		−	3.35278i		−	0.210372i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	5.83354	+	8.02917i	0.363886	+	0.500846i	0.951226	−	0.308494i	$-0.0998250\pi$
$257$	5.83354	+	8.02917i	0.363886	+	0.500846i	−0.587340	+	0.809340i	$0.699825\pi$
$258$		0			0
$259$	−24.2818	−	7.88964i	−1.50880	−	0.490238i
$260$	2.39095	−	1.73712i	0.148280	−	0.107732i
$261$		0			0
$262$	−4.61942	−	14.2171i	−0.285389	−	0.878336i
$263$	−8.60914			−0.530862			−0.265431	−	0.964130i	$-0.585514\pi$
$263$	−8.60914			−0.530862			−0.265431	+	0.964130i	$0.585514\pi$
$264$		0			0
$265$	10.0742			0.618850
$266$	−1.09379	−	3.36635i	−0.0670648	−	0.206404i
$267$		0			0
$268$	−4.21245	+	3.06052i	−0.257316	+	0.186951i
$269$	−18.5881	−	6.03964i	−1.13334	−	0.368243i	−0.318493	−	0.947925i	$-0.603177\pi$
$269$	−18.5881	−	6.03964i	−1.13334	−	0.368243i	−0.814843	+	0.579682i	$0.803177\pi$
$270$		0			0
$271$	−12.6600	−	17.4250i	−0.769041	−	1.05849i	−0.996408	−	0.0846846i	$-0.973012\pi$
$271$	−12.6600	−	17.4250i	−0.769041	−	1.05849i	0.227367	−	0.973809i	$-0.426988\pi$
$272$	−2.38122	−	1.73006i	−0.144383	−	0.104900i
$273$		0			0
$274$		−	1.84588i		−	0.111513i
$275$	−3.13312	+	1.08790i	−0.188934	+	0.0656031i
$276$		0			0
$277$	16.8009	−	5.45894i	1.00947	−	0.327996i	0.242825	−	0.970070i	$-0.421926\pi$
$277$	16.8009	−	5.45894i	1.00947	−	0.327996i	0.766643	+	0.642074i	$0.221926\pi$
$278$	8.77734	−	12.0810i	0.526430	−	0.724569i
$279$		0			0
$280$	0.670908	−	2.06484i	0.0400944	−	0.123398i
$281$	−7.26948	+	22.3732i	−0.433661	+	1.33467i	0.460792	+	0.887508i	$0.347565\pi$
$281$	−7.26948	+	22.3732i	−0.433661	+	1.33467i	−0.894453	+	0.447162i	$0.852435\pi$
$282$		0			0
$283$	−2.45806	+	3.38323i	−0.146116	+	0.201112i	−0.875802	−	0.482671i	$-0.839667\pi$
$283$	−2.45806	+	3.38323i	−0.146116	+	0.201112i	0.729685	+	0.683783i	$0.239667\pi$
$284$	8.20611	−	2.66633i	0.486943	−	0.158217i
$285$		0			0
$286$	−9.79990	+	0.196443i	−0.579480	+	0.0116159i
$287$		−	10.0354i		−	0.592371i
$288$		0			0
$289$	6.74450	+	4.90016i	0.396735	+	0.288245i
$290$	−2.21107	−	3.04327i	−0.129838	−	0.178707i
$291$		0			0
$292$	−6.54963	−	2.12810i	−0.383288	−	0.124538i
$293$	26.4329	−	19.2046i	1.54422	−	1.12194i	0.596609	−	0.802532i	$-0.296514\pi$
$293$	26.4329	−	19.2046i	1.54422	−	1.12194i	0.947616	−	0.319413i	$-0.103486\pi$
$294$		0			0
$295$	−2.22843	−	6.85841i	−0.129744	−	0.399312i
$296$	−11.7597			−0.683516
$297$		0			0
$298$	16.9199			0.980143
$299$	−3.11929	−	9.60019i	−0.180393	−	0.555193i
$300$		0			0
$301$	−12.6684	+	9.20416i	−0.730197	+	0.530519i
$302$	−10.5674	−	3.43354i	−0.608083	−	0.197578i
$303$		0			0
$304$	−0.958278	−	1.31896i	−0.0549610	−	0.0756473i
$305$	10.7649	+	7.82116i	0.616396	+	0.447838i
$306$		0			0
$307$			4.82788i			0.275542i	0.990464	+	0.137771i	$0.0439938\pi$
$307$			4.82788i			0.275542i	−0.990464	+	0.137771i	$0.956006\pi$
$308$	−5.73952	+	4.34839i	−0.327039	+	0.247772i
$309$		0			0
$310$	−9.66737	+	3.14112i	−0.549070	+	0.178404i
$311$	−11.8471	+	16.3061i	−0.671787	+	0.924636i	−0.999799	−	0.0200380i	$-0.993621\pi$
$311$	−11.8471	+	16.3061i	−0.671787	+	0.924636i	0.328012	+	0.944673i	$0.393621\pi$
$312$		0			0
$313$	−1.77491	+	5.46260i	−0.100324	+	0.308765i	−0.988605	−	0.150536i	$-0.951900\pi$
$313$	−1.77491	+	5.46260i	−0.100324	+	0.308765i	0.888281	+	0.459301i	$0.151900\pi$
$314$	−6.36647	+	19.5940i	−0.359281	+	1.10575i
$315$		0			0
$316$	−1.19538	+	1.64530i	−0.0672452	+	0.0925551i
$317$	26.1314	−	8.49061i	1.46769	−	0.476880i	0.537278	−	0.843405i	$-0.319452\pi$
$317$	26.1314	−	8.49061i	1.46769	−	0.476880i	0.930408	+	0.366525i	$0.119452\pi$
$318$		0			0
$319$	0.250039	+	12.4736i	0.0139995	+	0.698388i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	−5.99928	−	4.35873i	−0.334327	−	0.242903i
$323$	−2.82055	−	3.88216i	−0.156940	−	0.216009i
$324$		0			0
$325$	2.81073	+	0.913261i	0.155911	+	0.0506586i
$326$	−13.2496	+	9.62637i	−0.733826	+	0.533156i
$327$		0			0
$328$	−1.42836	−	4.39603i	−0.0788679	−	0.242730i
$329$	−0.945869			−0.0521475
$330$		0			0
$331$	−30.3697			−1.66927			−0.834636	−	0.550802i	$-0.814322\pi$
$331$	−30.3697			−1.66927			−0.834636	+	0.550802i	$0.814322\pi$
$332$	−3.19368	−	9.82914i	−0.175276	−	0.539444i
$333$		0			0
$334$	18.9413	−	13.7617i	1.03642	−	0.753005i
$335$	−4.95203	−	1.60901i	−0.270558	−	0.0879098i
$336$		0			0
$337$	14.1360	+	19.4566i	0.770038	+	1.05987i	0.996312	+	0.0858033i	$0.0273457\pi$
$337$	14.1360	+	19.4566i	0.770038	+	1.05987i	−0.226274	+	0.974064i	$0.572654\pi$
$338$	−3.45108	−	2.50736i	−0.187714	−	0.136382i
$339$		0			0
$340$		−	2.94336i		−	0.159626i
$341$	32.2654	+	9.77323i	1.74727	+	0.529250i
$342$		0			0
$343$	−19.1748	+	6.23026i	−1.03534	+	0.336402i
$344$	−4.23939	+	5.83503i	−0.228573	+	0.314604i
$345$		0			0
$346$	−0.289511	+	0.891022i	−0.0155642	+	0.0479016i
$347$	5.25524	−	16.1740i	0.282116	−	0.868263i	−0.705132	−	0.709076i	$-0.749112\pi$
$347$	5.25524	−	16.1740i	0.282116	−	0.868263i	0.987248	−	0.159188i	$-0.0508875\pi$
$348$		0			0
$349$	−7.90156	+	10.8756i	−0.422961	+	0.582156i	−0.966320	−	0.257345i	$-0.917152\pi$
$349$	−7.90156	+	10.8756i	−0.422961	+	0.582156i	0.543359	+	0.839501i	$0.317152\pi$
$350$	2.06484	−	0.670908i	0.110370	−	0.0358615i
$351$		0			0
$352$	−1.89530	+	2.72174i	−0.101020	+	0.145069i
$353$		−	5.31870i		−	0.283086i	−0.989932	−	0.141543i	$-0.954794\pi$
$353$		−	5.31870i		−	0.283086i	0.989932	−	0.141543i	$-0.0452063\pi$
$354$		0			0
$355$	6.98054	+	5.07166i	0.370488	+	0.269176i
$356$	4.12995	+	5.68440i	0.218887	+	0.301272i
$357$		0			0
$358$	18.9435	+	6.15512i	1.00120	+	0.325308i
$359$	12.3354	−	8.96218i	0.651036	−	0.473006i	−0.212588	−	0.977142i	$-0.568189\pi$
$359$	12.3354	−	8.96218i	0.651036	−	0.473006i	0.863624	+	0.504136i	$0.168189\pi$
$360$		0			0
$361$	5.04997	+	15.5422i	0.265788	+	0.818012i
$362$	2.69597			0.141697
$363$		0			0
$364$	6.41642			0.336312
$365$	−2.12810	−	6.54963i	−0.111390	−	0.342823i
$366$		0			0
$367$	9.93552	−	7.21858i	0.518630	−	0.376807i	−0.297458	−	0.954735i	$-0.596139\pi$
$367$	9.93552	−	7.21858i	0.518630	−	0.376807i	0.816087	+	0.577928i	$0.196139\pi$
$368$	−3.24838	−	1.05546i	−0.169334	−	0.0550199i
$369$		0			0
$370$	−6.91215	−	9.51376i	−0.359346	−	0.494597i
$371$	17.6948	+	12.8560i	0.918670	+	0.667453i
$372$		0			0
$373$		−	32.9413i		−	1.70564i	−0.522209	−	0.852818i	$-0.674892\pi$
$373$		−	32.9413i		−	1.70564i	0.522209	−	0.852818i	$-0.325108\pi$
$374$	−5.57853	+	8.01104i	−0.288459	+	0.414241i
$375$		0			0
$376$	−0.414340	+	0.134627i	−0.0213680	+	0.00694288i
$377$	6.53452	−	8.99400i	0.336545	−	0.463215i
$378$		0			0
$379$	8.12100	−	24.9939i	0.417148	−	1.28385i	−0.493168	−	0.869934i	$-0.664161\pi$
$379$	8.12100	−	24.9939i	0.417148	−	1.28385i	0.910316	−	0.413914i	$-0.135839\pi$
$380$	0.503797	−	1.55053i	0.0258442	−	0.0795403i
$381$		0			0
$382$	−4.26512	+	5.87043i	−0.218222	+	0.300357i
$383$	8.84153	−	2.87279i	0.451781	−	0.146793i	−0.0742836	−	0.997237i	$-0.523667\pi$
$383$	8.84153	−	2.87279i	0.451781	−	0.146793i	0.526065	+	0.850445i	$0.323667\pi$
$384$		0			0
$385$	−6.89152	−	2.08745i	−0.351225	−	0.106386i
$386$		−	13.2573i		−	0.674779i
$387$		0			0
$388$	−5.23399	−	3.80272i	−0.265716	−	0.193054i
$389$	12.9712	+	17.8534i	0.657668	+	0.905202i	0.999401	−	0.0345945i	$-0.0110140\pi$
$389$	12.9712	+	17.8534i	0.657668	+	0.905202i	−0.341733	+	0.939797i	$0.611014\pi$
$390$		0			0
$391$	−9.56115	−	3.10661i	−0.483528	−	0.157108i
$392$	−1.84967	+	1.34386i	−0.0934223	+	0.0678753i
$393$		0			0
$394$	0.673720	+	2.07350i	0.0339415	+	0.104461i
$395$	−2.03370			−0.102326
$396$		0			0
$397$	12.0800			0.606277			0.303139	−	0.952947i	$-0.401966\pi$
$397$	12.0800			0.606277			0.303139	+	0.952947i	$0.401966\pi$
$398$	0.767356	+	2.36168i	0.0384641	+	0.118380i
$399$		0			0
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	−11.5659	−	3.75800i	−0.577575	−	0.187665i	0.00563912	−	0.999984i	$-0.498205\pi$
$401$	−11.5659	−	3.75800i	−0.577575	−	0.187665i	−0.583214	+	0.812319i	$0.698205\pi$
$402$		0			0
$403$	−17.6577	−	24.3037i	−0.879590	−	1.21065i
$404$	−3.93391	−	2.85815i	−0.195719	−	0.142198i
$405$		0			0
$406$		−	8.16701i		−	0.405322i
$407$	0.781662	+	38.9945i	0.0387456	+	1.93289i
$408$		0			0
$409$	−7.00134	+	2.27487i	−0.346194	+	0.112485i	−0.476953	−	0.878929i	$-0.658259\pi$
$409$	−7.00134	+	2.27487i	−0.346194	+	0.112485i	0.130759	+	0.991414i	$0.458259\pi$
$410$	2.71690	−	3.73949i	0.134178	−	0.184680i
$411$		0			0
$412$	1.27655	−	3.92882i	0.0628911	−	0.193559i
$413$	4.83816	−	14.8903i	0.238070	−	0.732705i
$414$		0			0
$415$	6.07474	−	8.36116i	0.298197	−	0.410433i
$416$	2.81073	−	0.913261i	0.137807	−	0.0447763i
$417$		0			0
$418$	−4.30991	+	3.26528i	−0.210805	+	0.159710i
$419$			20.1621i			0.984981i	0.870318	+	0.492490i	$0.163913\pi$
$419$			20.1621i			0.984981i	−0.870318	+	0.492490i	$0.836087\pi$
$420$		0			0
$421$	28.3503	+	20.5977i	1.38171	+	1.00387i	0.996718	+	0.0809522i	$0.0257961\pi$
$421$	28.3503	+	20.5977i	1.38171	+	1.00387i	0.384993	+	0.922920i	$0.374204\pi$
$422$	11.2978	+	15.5501i	0.549969	+	0.756968i
$423$		0			0
$424$	9.58109	+	3.11308i	0.465299	+	0.151185i
$425$	2.38122	−	1.73006i	0.115506	−	0.0839203i
$426$		0			0
$427$	8.92719	+	27.4751i	0.432017	+	1.32961i
$428$	−6.80176			−0.328775
$429$		0			0
$430$	−7.21249			−0.347817
$431$	−5.01283	−	15.4279i	−0.241459	−	0.743136i	−0.996199	−	0.0871108i	$-0.972237\pi$
$431$	−5.01283	−	15.4279i	−0.241459	−	0.743136i	0.754739	−	0.656025i	$-0.227763\pi$
$432$		0			0
$433$	−11.1385	+	8.09262i	−0.535284	+	0.388906i	−0.822330	−	0.569010i	$-0.807326\pi$
$433$	−11.1385	+	8.09262i	−0.535284	+	0.388906i	0.287047	+	0.957917i	$0.407326\pi$
$434$	−20.9888	−	6.81969i	−1.00750	−	0.327356i
$435$		0			0
$436$	−3.14210	−	4.32473i	−0.150479	−	0.207117i
$437$	−4.50497	−	3.27305i	−0.215502	−	0.156571i
$438$		0			0
$439$			12.2140i			0.582942i	0.956580	+	0.291471i	$0.0941447\pi$
$439$			12.2140i			0.582942i	−0.956580	+	0.291471i	$0.905855\pi$
$440$	−3.31596	+	0.0664698i	−0.158082	+	0.00316883i
$441$		0			0
$442$	8.27297	−	2.68805i	0.393505	−	0.127858i
$443$	11.6068	−	15.9754i	0.551456	−	0.759015i	−0.438752	−	0.898608i	$-0.644580\pi$
$443$	11.6068	−	15.9754i	0.551456	−	0.759015i	0.990209	+	0.139593i	$0.0445795\pi$
$444$		0			0
$445$	−2.17125	+	6.68241i	−0.102927	+	0.316776i
$446$	−4.80775	+	14.7967i	−0.227653	+	0.700645i
$447$		0			0
$448$	1.27614	−	1.75646i	0.0602920	−	0.0829849i
$449$	22.1132	−	7.18500i	1.04358	−	0.339081i	0.263437	−	0.964677i	$-0.415144\pi$
$449$	22.1132	−	7.18500i	1.04358	−	0.339081i	0.780148	+	0.625595i	$0.215144\pi$
$450$		0			0
$451$	−14.4821	+	5.02858i	−0.681936	+	0.236787i
$452$			12.9777i			0.610418i
$453$		0			0
$454$	−12.1804	−	8.84958i	−0.571655	−	0.415332i
$455$	3.77148	+	5.19099i	0.176810	+	0.243357i
$456$		0			0
$457$	5.13103	+	1.66717i	0.240019	+	0.0779870i	0.426557	−	0.904461i	$-0.359726\pi$
$457$	5.13103	+	1.66717i	0.240019	+	0.0779870i	−0.186537	+	0.982448i	$0.559726\pi$
$458$	−9.40819	+	6.83545i	−0.439616	+	0.319399i
$459$		0			0
$460$	−1.05546	−	3.24838i	−0.0492113	−	0.151457i
$461$	−1.35065			−0.0629062			−0.0314531	−	0.999505i	$-0.510013\pi$
$461$	−1.35065			−0.0629062			−0.0314531	+	0.999505i	$0.510013\pi$
$462$		0			0
$463$	19.7560			0.918138			0.459069	−	0.888401i	$-0.348183\pi$
$463$	19.7560			0.918138			0.459069	+	0.888401i	$0.348183\pi$
$464$	−1.16243	−	3.57758i	−0.0539643	−	0.166085i
$465$		0			0
$466$	6.79119	−	4.93409i	0.314596	−	0.228567i
$467$	15.7837	+	5.12844i	0.730384	+	0.237316i	0.650519	−	0.759490i	$-0.274551\pi$
$467$	15.7837	+	5.12844i	0.730384	+	0.237316i	0.0798643	+	0.996806i	$0.474551\pi$
$468$		0			0
$469$	−6.64471	−	9.14566i	−0.306824	−	0.422307i
$470$	−0.352459	−	0.256076i	−0.0162577	−	0.0118119i
$471$		0			0
$472$		−	7.21136i		−	0.331930i
$473$	19.6305	+	13.6698i	0.902611	+	0.628538i
$474$		0			0
$475$	1.55053	−	0.503797i	0.0711430	−	0.0231158i
$476$	3.75614	−	5.16988i	0.172162	−	0.236961i
$477$		0			0
$478$	4.26687	−	13.1321i	0.195162	−	0.600648i
$479$	−1.54696	+	4.76107i	−0.0706826	+	0.217539i	−0.980158	−	0.198220i	$-0.936484\pi$
$479$	−1.54696	+	4.76107i	−0.0706826	+	0.217539i	0.909475	+	0.415759i	$0.136484\pi$
$480$		0			0
$481$	20.4280	−	28.1167i	0.931436	−	1.28201i
$482$	0.809107	−	0.262895i	0.0368538	−	0.0119745i
$483$		0			0
$484$	9.15115	+	6.10381i	0.415961	+	0.277446i
$485$		−	6.46957i		−	0.293768i
$486$		0			0
$487$	12.3948	+	9.00534i	0.561662	+	0.408071i	0.832067	−	0.554676i	$-0.187158\pi$
$487$	12.3948	+	9.00534i	0.561662	+	0.408071i	−0.270405	+	0.962747i	$0.587158\pi$
$488$	7.82116	+	10.7649i	0.354047	+	0.487304i
$489$		0			0
$490$	−2.17441	−	0.706510i	−0.0982300	−	0.0319169i
$491$	−7.10090	+	5.15910i	−0.320459	+	0.232827i	−0.736371	−	0.676578i	$-0.763462\pi$
$491$	−7.10090	+	5.15910i	−0.320459	+	0.232827i	0.415912	+	0.909405i	$0.363462\pi$
$492$		0			0
$493$	−3.42143	−	10.5301i	−0.154094	−	0.474251i
$494$	4.81820			0.216781
$495$		0			0
$496$	−10.1649			−0.456416
$497$	5.78887	+	17.8163i	0.259666	+	0.799171i
$498$		0			0
$499$	−2.34627	+	1.70466i	−0.105033	+	0.0763113i	−0.639062	−	0.769155i	$-0.720677\pi$
$499$	−2.34627	+	1.70466i	−0.105033	+	0.0763113i	0.534029	+	0.845466i	$0.320677\pi$
$500$	0.951057	+	0.309017i	0.0425325	+	0.0138197i
$501$		0			0
$502$	−10.8850	−	14.9819i	−0.485819	−	0.668673i
$503$	24.9214	+	18.1065i	1.11119	+	0.807327i	0.982851	−	0.184403i	$-0.0590352\pi$
$503$	24.9214	+	18.1065i	1.11119	+	0.807327i	0.128340	+	0.991730i	$0.459035\pi$
$504$		0			0
$505$		−	4.86258i		−	0.216382i
$506$	−3.28395	+	10.8417i	−0.145990	+	0.481971i
$507$		0			0
$508$	3.18868	−	1.03607i	0.141475	−	0.0459680i
$509$	25.1023	−	34.5504i	1.11264	−	1.53142i	0.295176	−	0.955443i	$-0.404622\pi$
$509$	25.1023	−	34.5504i	1.11264	−	1.53142i	0.817466	−	0.575978i	$-0.195378\pi$
$510$		0			0
$511$	4.62033	−	14.2199i	0.204391	−	0.629052i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$		0			0
$514$	−5.83354	+	8.02917i	−0.257306	+	0.354152i
$515$	3.92882	−	1.27655i	0.173124	−	0.0562515i
$516$		0			0
$517$	0.473960	+	1.36499i	0.0208447	+	0.0600321i
$518$		−	25.5314i		−	1.12179i
$519$		0			0
$520$	2.39095	+	1.73712i	0.104850	+	0.0761780i
$521$	5.10032	+	7.01999i	0.223449	+	0.307551i	0.905992	−	0.423294i	$-0.139126\pi$
$521$	5.10032	+	7.01999i	0.223449	+	0.307551i	−0.682543	+	0.730845i	$0.739126\pi$
$522$		0			0
$523$	−11.7306	−	3.81151i	−0.512944	−	0.166666i	0.0410965	−	0.999155i	$-0.486915\pi$
$523$	−11.7306	−	3.81151i	−0.512944	−	0.166666i	−0.554041	+	0.832489i	$0.686915\pi$
$524$	12.0938	−	8.78665i	0.528320	−	0.383847i
$525$		0			0
$526$	−2.66037	−	8.18778i	−0.115998	−	0.357004i
$527$	−29.9188			−1.30328
$528$		0			0
$529$	11.3340			0.492783
$530$	3.11308	+	9.58109i	0.135224	+	0.416176i
$531$		0			0
$532$	2.86359	−	2.08052i	0.124152	−	0.0902020i
$533$	12.9919	+	4.22133i	0.562742	+	0.182846i
$534$		0			0
$535$	−3.99797	−	5.50274i	−0.172847	−	0.237904i
$536$	−4.21245	−	3.06052i	−0.181950	−	0.132195i
$537$		0			0
$538$		−	19.5447i		−	0.842631i
$539$	4.57914	+	6.04409i	0.197237	+	0.260338i
$540$		0			0
$541$	23.4000	−	7.60312i	1.00604	−	0.326884i	0.240766	−	0.970583i	$-0.422601\pi$
$541$	23.4000	−	7.60312i	1.00604	−	0.326884i	0.765278	+	0.643700i	$0.222601\pi$
$542$	12.6600	−	17.4250i	0.543794	−	0.748468i
$543$		0			0
$544$	0.909547	−	2.79930i	0.0389965	−	0.120019i
$545$	1.65190	−	5.08403i	0.0707597	−	0.217776i
$546$		0			0
$547$	1.62116	−	2.23134i	0.0693158	−	0.0954050i	−0.772952	−	0.634465i	$-0.781220\pi$
$547$	1.62116	−	2.23134i	0.0693158	−	0.0954050i	0.842267	+	0.539060i	$0.181220\pi$
$548$	1.75553	−	0.570407i	0.0749926	−	0.0243666i
$549$		0			0
$550$	−2.00285	−	2.64360i	−0.0854017	−	0.112723i
$551$		−	6.13276i		−	0.261264i
$552$		0			0
$553$	−3.57210	−	2.59529i	−0.151901	−	0.110363i
$554$	10.3835	+	14.2917i	0.441154	+	0.607196i
$555$		0			0
$556$	14.2020	+	4.61452i	0.602301	+	0.195699i
$557$	−10.4713	+	7.60784i	−0.443683	+	0.322355i	−0.787097	−	0.616830i	$-0.788417\pi$
$557$	−10.4713	+	7.60784i	−0.443683	+	0.322355i	0.343414	+	0.939184i	$0.388417\pi$
$558$		0			0
$559$	−6.58688	−	20.2723i	−0.278595	−	0.857429i
$560$	2.17110			0.0917458
$561$		0			0
$562$	−23.5245			−0.992322
$563$	10.8605	+	33.4251i	0.457715	+	1.40870i	0.867918	+	0.496708i	$0.165458\pi$
$563$	10.8605	+	33.4251i	0.457715	+	1.40870i	−0.410203	+	0.911994i	$0.634542\pi$
$564$		0			0
$565$	−10.4991	+	7.62808i	−0.441702	+	0.320916i
$566$	−3.97722	−	1.29228i	−0.167175	−	0.0543185i
$567$		0			0
$568$	5.07166	+	6.98054i	0.212802	+	0.292897i
$569$	30.2344	+	21.9666i	1.26749	+	0.920886i	0.999100	−	0.0424239i	$-0.0135080\pi$
$569$	30.2344	+	21.9666i	1.26749	+	0.920886i	0.268391	+	0.963310i	$0.413508\pi$
$570$		0			0
$571$			37.1195i			1.55340i	0.629870	+	0.776700i	$0.283108\pi$
$571$			37.1195i			1.55340i	−0.629870	+	0.776700i	$0.716892\pi$
$572$	−3.21516	−	9.25955i	−0.134433	−	0.387161i
$573$		0			0
$574$	9.54424	−	3.10111i	0.398369	−	0.129438i
$575$	2.00761	−	2.76324i	0.0837232	−	0.115235i
$576$		0			0
$577$	9.94256	−	30.6001i	0.413914	−	1.27390i	−0.499304	−	0.866427i	$-0.666411\pi$
$577$	9.94256	−	30.6001i	0.413914	−	1.27390i	0.913218	−	0.407470i	$-0.133589\pi$
$578$	−2.57617	+	7.92863i	−0.107154	+	0.329788i
$579$		0			0
$580$	2.21107	−	3.04327i	0.0918095	−	0.126365i
$581$	21.3401	−	6.93381i	0.885335	−	0.287663i
$582$		0			0
$583$	9.68601	−	31.9774i	0.401153	−	1.32437i
$584$		−	6.88669i		−	0.284973i
$585$		0			0
$586$	26.4329	+	19.2046i	1.09193	+	0.793335i
$587$	10.9681	+	15.0963i	0.452702	+	0.623091i	0.972975	−	0.230909i	$-0.0741699\pi$
$587$	10.9681	+	15.0963i	0.452702	+	0.623091i	−0.520273	+	0.854000i	$0.674170\pi$
$588$		0			0
$589$	−15.7609	−	5.12103i	−0.649417	−	0.211008i
$590$	5.83411	−	4.23873i	0.240187	−	0.174506i
$591$		0			0
$592$	−3.63393	−	11.1841i	−0.149354	−	0.459664i
$593$	−2.69018			−0.110472			−0.0552362	−	0.998473i	$-0.517591\pi$
$593$	−2.69018			−0.110472			−0.0552362	+	0.998473i	$0.517591\pi$
$594$		0			0
$595$	6.39033			0.261978
$596$	5.22853	+	16.0918i	0.214169	+	0.659145i
$597$		0			0
$598$	8.16641	−	5.93324i	0.333949	−	0.242628i
$599$	34.7907	+	11.3042i	1.42151	+	0.461876i	0.916081	−	0.400993i	$-0.131335\pi$
$599$	34.7907	+	11.3042i	1.42151	+	0.461876i	0.505428	+	0.862869i	$0.331335\pi$
$600$		0			0
$601$	−8.40074	−	11.5626i	−0.342673	−	0.471649i	0.602547	−	0.798084i	$-0.294153\pi$
$601$	−8.40074	−	11.5626i	−0.342673	−	0.471649i	−0.945220	+	0.326434i	$0.894153\pi$
$602$	−12.6684	−	9.20416i	−0.516327	−	0.375134i
$603$		0			0
$604$		−	11.1112i		−	0.452107i
$605$	0.440822	+	10.9912i	0.0179220	+	0.446854i
$606$		0			0
$607$	3.85294	−	1.25190i	0.156386	−	0.0508129i	−0.229778	−	0.973243i	$-0.573800\pi$
$607$	3.85294	−	1.25190i	0.156386	−	0.0508129i	0.386164	+	0.922430i	$0.373800\pi$
$608$	0.958278	−	1.31896i	0.0388633	−	0.0534908i
$609$		0			0
$610$	−4.11183	+	12.6549i	−0.166483	+	0.512382i
$611$	0.397874	−	1.22453i	0.0160963	−	0.0495392i
$612$		0			0
$613$	−20.5695	+	28.3114i	−0.830793	+	1.14349i	0.156982	+	0.987601i	$0.449824\pi$
$613$	−20.5695	+	28.3114i	−0.830793	+	1.14349i	−0.987775	+	0.155887i	$0.950176\pi$
$614$	−4.59159	+	1.49190i	−0.185302	+	0.0602081i
$615$		0			0
$616$	−5.90917	−	4.11488i	−0.238087	−	0.165793i
$617$			11.8147i			0.475642i	0.971309	+	0.237821i	$0.0764332\pi$
$617$			11.8147i			0.475642i	−0.971309	+	0.237821i	$0.923567\pi$
$618$		0			0
$619$	13.2833	+	9.65088i	0.533901	+	0.387902i	0.821815	−	0.569755i	$-0.192962\pi$
$619$	13.2833	+	9.65088i	0.533901	+	0.387902i	−0.287914	+	0.957656i	$0.592962\pi$
$620$	−5.97476	−	8.22356i	−0.239952	−	0.330266i
$621$		0			0
$622$	−19.1690	−	6.22839i	−0.768607	−	0.249736i
$623$	−12.3414	+	8.96655i	−0.494448	+	0.359237i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−5.74372			−0.229565
$627$		0			0
$628$	−20.6023			−0.822123
$629$	−10.6960	−	32.9188i	−0.426476	−	1.31256i
$630$		0			0
$631$	−34.4072	+	24.9983i	−1.36973	+	0.995165i	−0.371969	+	0.928245i	$0.621317\pi$
$631$	−34.4072	+	24.9983i	−1.36973	+	0.995165i	−0.997758	+	0.0669202i	$0.978683\pi$
$632$	−1.93416	−	0.628447i	−0.0769368	−	0.0249983i
$633$		0			0
$634$	16.1501	+	22.2287i	0.641403	+	0.882815i
$635$	2.71246	+	1.97071i	0.107641	+	0.0782054i
$636$		0			0
$637$		−	6.75691i		−	0.267719i
$638$	−11.7858	+	4.09236i	−0.466606	+	0.162018i
$639$		0			0
$640$	0.951057	−	0.309017i	0.0375938	−	0.0122150i
$641$	−12.2000	+	16.7919i	−0.481872	+	0.663240i	−0.978863	−	0.204515i	$-0.934438\pi$
$641$	−12.2000	+	16.7919i	−0.481872	+	0.663240i	0.496991	+	0.867756i	$0.334438\pi$
$642$		0			0
$643$	15.3243	−	47.1634i	0.604332	−	1.85994i	0.103014	−	0.994680i	$-0.467151\pi$
$643$	15.3243	−	47.1634i	0.604332	−	1.85994i	0.501318	−	0.865263i	$-0.332849\pi$
$644$	2.29152	−	7.05257i	0.0902985	−	0.277910i
$645$		0			0
$646$	2.82055	−	3.88216i	0.110973	−	0.152741i
$647$	−37.7755	+	12.2740i	−1.48511	+	0.482541i	−0.935634	−	0.352971i	$-0.885171\pi$
$647$	−37.7755	+	12.2740i	−1.48511	+	0.482541i	−0.549473	+	0.835512i	$0.685171\pi$
$648$		0			0
$649$	−23.9126	+	0.479338i	−0.938651	+	0.0188157i
$650$			2.95537i			0.115919i
$651$		0			0
$652$	−13.2496	−	9.62637i	−0.518893	−	0.376998i
$653$	−21.3597	−	29.3991i	−0.835869	−	1.15047i	−0.986802	−	0.161931i	$-0.948228\pi$
$653$	−21.3597	−	29.3991i	−0.835869	−	1.15047i	0.150933	−	0.988544i	$-0.451772\pi$
$654$		0			0
$655$	14.2171	+	4.61942i	0.555508	+	0.180496i
$656$	3.73949	−	2.71690i	0.146003	−	0.106077i
$657$		0			0
$658$	−0.292290	−	0.899575i	−0.0113946	−	0.0350691i
$659$	−46.1554			−1.79796			−0.898979	−	0.437992i	$-0.855690\pi$
$659$	−46.1554			−1.79796			−0.898979	+	0.437992i	$0.855690\pi$
$660$		0			0
$661$	49.9012			1.94093			0.970466	−	0.241239i	$-0.0775539\pi$
$661$	49.9012			1.94093			0.970466	+	0.241239i	$0.0775539\pi$
$662$	−9.38476	−	28.8833i	−0.364749	−	1.12258i
$663$		0			0
$664$	8.36116	−	6.07474i	0.324476	−	0.235746i
$665$	3.36635	+	1.09379i	0.130542	+	0.0424155i
$666$		0			0
$667$	−7.55201	−	10.3945i	−0.292415	−	0.402475i
$668$	18.9413	+	13.7617i	0.732862	+	0.532455i
$669$		0			0
$670$		−	5.20687i		−	0.201159i
$671$	35.1761	−	26.6502i	1.35796	−	1.02882i
$672$		0			0
$673$	−31.2825	+	10.1643i	−1.20585	+	0.391805i	−0.841911	−	0.539616i	$-0.818569\pi$
$673$	−31.2825	+	10.1643i	−1.20585	+	0.391805i	−0.363942	+	0.931422i	$0.618569\pi$
$674$	−14.1360	+	19.4566i	−0.544499	+	0.749439i
$675$		0			0
$676$	1.31819	−	4.05699i	0.0506998	−	0.156038i
$677$	6.45255	−	19.8589i	0.247992	−	0.763240i	−0.747138	−	0.664669i	$-0.768573\pi$
$677$	6.45255	−	19.8589i	0.247992	−	0.763240i	0.995130	−	0.0985715i	$-0.0314273\pi$
$678$		0			0
$679$	8.25609	−	11.3635i	0.316840	−	0.436092i
$680$	2.79930	−	0.909547i	0.107348	−	0.0348795i
$681$		0			0
$682$	0.675657	+	33.7063i	0.0258723	+	1.29068i
$683$		−	25.8461i		−	0.988972i	−0.869186	−	0.494486i	$-0.835356\pi$
$683$		−	25.8461i		−	0.988972i	0.869186	−	0.494486i	$-0.164644\pi$
$684$		0			0
$685$	1.49334	+	1.08498i	0.0570578	+	0.0414549i
$686$	−11.8507	−	16.3110i	−0.452460	−	0.622758i
$687$		0			0
$688$	−6.85948	−	2.22878i	−0.261515	−	0.0849715i
$689$	−24.0868	+	17.5001i	−0.917633	+	0.666699i
$690$		0			0
$691$	−0.451065	−	1.38824i	−0.0171593	−	0.0528110i	0.942110	−	0.335303i	$-0.108839\pi$
$691$	−0.451065	−	1.38824i	−0.0171593	−	0.0528110i	−0.959270	+	0.282492i	$0.908839\pi$
$692$	−0.936876			−0.0356147
$693$		0			0
$694$	17.0063			0.645550
$695$	4.61452	+	14.2020i	0.175039	+	0.538714i
$696$		0			0
$697$	11.0066	−	7.99680i	0.416906	−	0.302900i
$698$	−12.7850	−	4.15410i	−0.483919	−	0.157235i
$699$		0			0
$700$	1.27614	+	1.75646i	0.0482336	+	0.0663879i
$701$	−17.2156	−	12.5078i	−0.650223	−	0.472415i	0.213124	−	0.977025i	$-0.431636\pi$
$701$	−17.2156	−	12.5078i	−0.650223	−	0.472415i	−0.863347	+	0.504610i	$0.831636\pi$
$702$		0			0
$703$		−	19.1720i		−	0.723086i
$704$	−3.17420	−	0.961471i	−0.119632	−	0.0362368i
$705$		0			0
$706$	5.05838	−	1.64357i	0.190375	−	0.0618565i
$707$	6.20534	−	8.54092i	0.233376	−	0.321214i
$708$		0			0
$709$	−5.80501	+	17.8660i	−0.218012	+	0.670971i	0.780914	+	0.624638i	$0.214754\pi$
$709$	−5.80501	+	17.8660i	−0.218012	+	0.670971i	−0.998926	+	0.0463332i	$0.985246\pi$
$710$	−2.66633	+	8.20611i	−0.100066	+	0.307970i
$711$		0			0
$712$	−4.12995	+	5.68440i	−0.154777	+	0.213032i
$713$	−33.0194	+	10.7287i	−1.23659	+	0.401791i
$714$		0			0
$715$	5.60131	−	8.04375i	0.209477	−	0.300819i
$716$			19.9184i			0.744385i
$717$		0			0
$718$	12.3354	+	8.96218i	0.460352	+	0.334466i
$719$	−12.8075	−	17.6280i	−0.477639	−	0.657413i	0.500410	−	0.865788i	$-0.333183\pi$
$719$	−12.8075	−	17.6280i	−0.477639	−	0.657413i	−0.978049	+	0.208375i	$0.933183\pi$
$720$		0			0
$721$	8.52986	+	2.77152i	0.317669	+	0.103217i
$722$	−13.2210	+	9.60562i	−0.492035	+	0.357484i
$723$		0			0
$724$	0.833100	+	2.56402i	0.0309619	+	0.0952910i
$725$	3.76169			0.139706
$726$		0			0
$727$	−4.33889			−0.160921			−0.0804603	−	0.996758i	$-0.525639\pi$
$727$	−4.33889			−0.160921			−0.0804603	+	0.996758i	$0.525639\pi$
$728$	1.98278	+	6.10238i	0.0734868	+	0.226169i
$729$		0			0
$730$	5.57145	−	4.04789i	0.206209	−	0.149819i
$731$	−20.1899	−	6.56010i	−0.746751	−	0.242634i
$732$		0			0
$733$	24.4947	+	33.7141i	0.904734	+	1.24526i	0.968933	+	0.247322i	$0.0795506\pi$
$733$	24.4947	+	33.7141i	0.904734	+	1.24526i	−0.0641994	+	0.997937i	$0.520449\pi$
$734$	9.93552	+	7.21858i	0.366727	+	0.266443i
$735$		0			0
$736$		−	3.41555i		−	0.125899i
$737$	−9.86857	+	14.1717i	−0.363513	+	0.522023i
$738$		0			0
$739$	−22.8157	+	7.41327i	−0.839289	+	0.272702i	−0.696953	−	0.717117i	$-0.745461\pi$
$739$	−22.8157	+	7.41327i	−0.839289	+	0.272702i	−0.142336	+	0.989818i	$0.545461\pi$
$740$	6.91215	−	9.51376i	0.254096	−	0.349733i
$741$		0			0
$742$	−6.75883	+	20.8015i	−0.248124	+	0.763648i
$743$	−7.50279	+	23.0912i	−0.275251	+	0.847134i	0.713902	+	0.700245i	$0.246926\pi$
$743$	−7.50279	+	23.0912i	−0.275251	+	0.847134i	−0.989153	+	0.146889i	$0.953074\pi$
$744$		0			0
$745$	−9.94526	+	13.6885i	−0.364366	+	0.501507i
$746$	31.3290	−	10.1794i	1.14704	−	0.372695i
$747$		0			0
$748$	−9.34281	−	2.82995i	−0.341607	−	0.103473i
$749$		−	14.7673i		−	0.539586i
$750$		0			0
$751$	16.1133	+	11.7070i	0.587984	+	0.427195i	0.841594	−	0.540111i	$-0.181618\pi$
$751$	16.1133	+	11.7070i	0.587984	+	0.427195i	−0.253610	+	0.967307i	$0.581618\pi$
$752$	−0.256076	−	0.352459i	−0.00933815	−	0.0128529i
$753$		0			0
$754$	10.5731	+	3.43540i	0.385049	+	0.125110i
$755$	8.98913	−	6.53099i	0.327148	−	0.237687i
$756$		0			0
$757$	10.4833	+	32.2643i	0.381023	+	1.17267i	0.939325	+	0.343029i	$0.111453\pi$
$757$	10.4833	+	32.2643i	0.381023	+	1.17267i	−0.558302	+	0.829638i	$0.688547\pi$
$758$	26.2801			0.954536
$759$		0			0
$760$	1.63032			0.0591379
$761$	−10.9848	−	33.8078i	−0.398200	−	1.22553i	−0.926442	−	0.376439i	$-0.877149\pi$
$761$	−10.9848	−	33.8078i	−0.398200	−	1.22553i	0.528242	−	0.849094i	$-0.322851\pi$
$762$		0			0
$763$	9.38944	−	6.82183i	0.339921	−	0.246967i
$764$	−6.90110	−	2.24230i	−0.249673	−	0.0811237i
$765$		0			0
$766$	5.46436	+	7.52105i	0.197435	+	0.271747i
$767$	17.2420	+	12.5270i	0.622572	+	0.452325i
$768$		0			0
$769$		−	27.6948i		−	0.998701i	−0.866400	−	0.499351i	$-0.833572\pi$
$769$		−	27.6948i		−	0.998701i	0.866400	−	0.499351i	$-0.166428\pi$
$770$	−0.144313	−	7.19929i	−0.00520067	−	0.259444i
$771$		0			0
$772$	12.6084	−	4.09673i	0.453788	−	0.147445i
$773$	27.9789	−	38.5097i	1.00633	−	1.38510i	0.0849748	−	0.996383i	$-0.472919\pi$
$773$	27.9789	−	38.5097i	1.00633	−	1.38510i	0.921358	−	0.388715i	$-0.127081\pi$
$774$		0			0
$775$	3.14112	−	9.66737i	0.112832	−	0.347262i
$776$	1.99921	−	6.15293i	0.0717674	−	0.220877i
$777$		0			0
$778$	−12.9712	+	17.8534i	−0.465042	+	0.640075i
$779$	7.16694	−	2.32868i	0.256782	−	0.0834336i
$780$		0			0
$781$	22.8101	−	17.2814i	0.816208	−	0.618377i
$782$		−	10.0532i		−	0.359501i
$783$		0			0
$784$	−1.84967	−	1.34386i	−0.0660596	−	0.0479951i
$785$	−12.1098	−	16.6676i	−0.432216	−	0.594894i
$786$		0			0
$787$	−20.5218	−	6.66795i	−0.731524	−	0.237687i	−0.0805117	−	0.996754i	$-0.525655\pi$
$787$	−20.5218	−	6.66795i	−0.731524	−	0.237687i	−0.651012	+	0.759067i	$0.725655\pi$
$788$	−1.76382	+	1.28149i	−0.0628335	+	0.0456512i
$789$		0			0
$790$	−0.628447	−	1.93416i	−0.0223591	−	0.0688143i
$791$	−28.1758			−1.00182
$792$		0			0
$793$	−39.3246			−1.39646
$794$	3.73292	+	11.4887i	0.132476	+	0.407720i
$795$		0			0
$796$	−2.00896	+	1.45960i	−0.0712058	+	0.0517340i
$797$	−30.2700	−	9.83531i	−1.07222	−	0.348384i	−0.280866	−	0.959747i	$-0.590622\pi$
$797$	−30.2700	−	9.83531i	−1.07222	−	0.348384i	−0.791351	+	0.611362i	$0.790622\pi$
$798$		0			0
$799$	−0.753724	−	1.03741i	−0.0266648	−	0.0367010i
$800$	0.809017	+	0.587785i	0.0286031	+	0.0207813i
$801$		0			0
$802$		−	12.1611i		−	0.429424i
$803$	−22.8360	+	0.457757i	−0.805864	+	0.0161539i
$804$		0			0
$805$	7.05257	−	2.29152i	0.248571	−	0.0807655i
$806$	17.6577	−	24.3037i	0.621964	−	0.856060i
$807$		0			0
$808$	1.50262	−	4.62459i	0.0528620	−	0.162692i
$809$	−3.46369	+	10.6602i	−0.121777	+	0.374791i	−0.993300	−	0.115563i	$-0.963133\pi$
$809$	−3.46369	+	10.6602i	−0.121777	+	0.374791i	0.871523	+	0.490354i	$0.163133\pi$
$810$		0			0
$811$	−13.4404	+	18.4992i	−0.471957	+	0.649594i	−0.976935	−	0.213539i	$-0.931501\pi$
$811$	−13.4404	+	18.4992i	−0.471957	+	0.649594i	0.504977	+	0.863133i	$0.331501\pi$
$812$	7.76729	−	2.52375i	0.272578	−	0.0885661i
$813$		0			0
$814$	−36.8445	+	12.7934i	−1.29140	+	0.448408i
$815$		−	16.3774i		−	0.573674i
$816$		0			0
$817$	−9.51296	−	6.91157i	−0.332816	−	0.241805i
$818$	−4.32707	−	5.95570i	−0.151292	−	0.208236i
$819$		0			0
$820$	4.39603	+	1.42836i	0.153516	+	0.0498804i
$821$	17.5440	−	12.7465i	0.612290	−	0.444854i	−0.237930	−	0.971282i	$-0.576469\pi$
$821$	17.5440	−	12.7465i	0.612290	−	0.444854i	0.850220	+	0.526428i	$0.176469\pi$
$822$		0			0
$823$	7.10488	+	21.8666i	0.247661	+	0.762221i	0.995187	+	0.0979893i	$0.0312411\pi$
$823$	7.10488	+	21.8666i	0.247661	+	0.762221i	−0.747527	+	0.664231i	$0.768759\pi$
$824$	4.13100			0.143910
$825$		0			0
$826$	15.6566			0.544763
$827$	5.31978	+	16.3726i	0.184987	+	0.569331i	0.999948	−	0.0101845i	$-0.00324188\pi$
$827$	5.31978	+	16.3726i	0.184987	+	0.569331i	−0.814961	+	0.579515i	$0.803242\pi$
$828$		0			0
$829$	18.8438	−	13.6908i	0.654473	−	0.475503i	−0.210319	−	0.977633i	$-0.567450\pi$
$829$	18.8438	−	13.6908i	0.654473	−	0.475503i	0.864792	+	0.502130i	$0.167450\pi$
$830$	9.82914	+	3.19368i	0.341174	+	0.110854i
$831$		0			0
$832$	1.73712	+	2.39095i	0.0602240	+	0.0828912i
$833$	−5.44423	−	3.95546i	−0.188631	−	0.137049i
$834$		0			0
$835$			23.4128i			0.810232i
$836$	−4.43730	−	3.08994i	−0.153467	−	0.106868i
$837$		0			0
$838$	−19.1752	+	6.23042i	−0.662398	+	0.215226i
$839$	1.15121	−	1.58450i	0.0397441	−	0.0547031i	−0.788682	−	0.614801i	$-0.789236\pi$
$839$	1.15121	−	1.58450i	0.0397441	−	0.0547031i	0.828427	+	0.560098i	$0.189236\pi$
$840$		0			0
$841$	−4.58881	+	14.1229i	−0.158235	+	0.486996i
$842$	−10.8289	+	33.3278i	−0.373187	+	1.14855i
$843$		0			0
$844$	−11.2978	+	15.5501i	−0.388887	+	0.535257i
$845$	4.05699	−	1.31819i	0.139565	−	0.0453473i
$846$		0			0
$847$	−13.2520	+	19.8681i	−0.455344	+	0.682675i
$848$			10.0742i			0.345948i
$849$		0			0
$850$	2.38122	+	1.73006i	0.0816753	+	0.0593406i
$851$	−23.6088	−	32.4948i	−0.809300	−	1.11391i
$852$		0			0
$853$	−18.6695	−	6.06608i	−0.639231	−	0.207699i	−0.0285710	−	0.999592i	$-0.509096\pi$
$853$	−18.6695	−	6.06608i	−0.639231	−	0.207699i	−0.610660	+	0.791893i	$0.709096\pi$
$854$	−23.3717	+	16.9805i	−0.799763	+	0.581062i
$855$		0			0
$856$	−2.10186	−	6.46885i	−0.0718400	−	0.221101i
$857$	−13.9010			−0.474850			−0.237425	−	0.971406i	$-0.576303\pi$
$857$	−13.9010			−0.474850			−0.237425	+	0.971406i	$0.576303\pi$
$858$		0			0
$859$	−1.33380			−0.0455088			−0.0227544	−	0.999741i	$-0.507244\pi$
$859$	−1.33380			−0.0455088			−0.0227544	+	0.999741i	$0.507244\pi$
$860$	−2.22878	−	6.85948i	−0.0760008	−	0.233906i
$861$		0			0
$862$	13.1238	−	9.53497i	0.446997	−	0.324762i
$863$	14.5348	+	4.72265i	0.494771	+	0.160761i	0.545765	−	0.837938i	$-0.316239\pi$
$863$	14.5348	+	4.72265i	0.494771	+	0.160761i	−0.0509943	+	0.998699i	$0.516239\pi$
$864$		0			0
$865$	−0.550682	−	0.757949i	−0.0187237	−	0.0257710i
$866$	−11.1385	−	8.09262i	−0.378503	−	0.274998i
$867$		0			0
$868$		−	22.0690i		−	0.749070i
$869$	−1.95534	+	6.45537i	−0.0663304	+	0.218983i
$870$		0			0
$871$	14.6351	−	4.75523i	0.495892	−	0.161125i
$872$	3.14210	−	4.32473i	0.106405	−	0.146454i
$873$		0			0
$874$	1.72074	−	5.29591i	0.0582050	−	0.179137i
$875$	−0.670908	+	2.06484i	−0.0226808	+	0.0698044i
$876$		0			0
$877$	18.4436	−	25.3854i	0.622794	−	0.857203i	−0.374758	−	0.927123i	$-0.622274\pi$
$877$	18.4436	−	25.3854i	0.622794	−	0.857203i	0.997553	+	0.0699195i	$0.0222743\pi$
$878$	−11.6162	+	3.77433i	−0.392028	+	0.127377i
$879$		0			0
$880$	−1.08790	−	3.13312i	−0.0366732	−	0.105618i
$881$			14.8675i			0.500900i	0.968130	+	0.250450i	$0.0805785\pi$
$881$			14.8675i			0.500900i	−0.968130	+	0.250450i	$0.919421\pi$
$882$		0			0
$883$	21.5919	+	15.6874i	0.726624	+	0.527924i	0.888494	−	0.458889i	$-0.151752\pi$
$883$	21.5919	+	15.6874i	0.726624	+	0.527924i	−0.161869	+	0.986812i	$0.551752\pi$
$884$	5.11298	+	7.03741i	0.171968	+	0.236694i
$885$		0			0
$886$	18.7802	+	6.10206i	0.630934	+	0.205003i
$887$	−24.8033	+	18.0207i	−0.832814	+	0.605075i	−0.920354	−	0.391086i	$-0.872099\pi$
$887$	−24.8033	+	18.0207i	−0.832814	+	0.605075i	0.0875402	+	0.996161i	$0.472099\pi$
$888$		0			0
$889$	2.24941	+	6.92296i	0.0754426	+	0.232189i
$890$	−7.02630			−0.235522
$891$		0			0
$892$	−15.5582			−0.520927
$893$	−0.219486	−	0.675507i	−0.00734481	−	0.0226050i
$894$		0			0
$895$	−16.1143	+	11.7077i	−0.538642	+	0.391346i
$896$	2.06484	+	0.670908i	0.0689815	+	0.0224134i
$897$		0			0
$898$	13.6667	+	18.8106i	0.456063	+	0.627717i
$899$	−30.9345	−	22.4752i	−1.03172	−	0.749590i
$900$		0			0
$901$			29.6518i			0.987845i
$902$	−9.25768	−	12.2194i	−0.308247	−	0.406861i
$903$		0			0
$904$	−12.3425	+	4.01032i	−0.410505	+	0.133381i
$905$	−1.58465	+	2.18108i	−0.0526755	+	0.0725017i
$906$		0			0
$907$	8.77726	−	27.0136i	0.291444	−	0.896972i	−0.692949	−	0.720987i	$-0.743689\pi$
$907$	8.77726	−	27.0136i	0.291444	−	0.896972i	0.984393	−	0.175986i	$-0.0563112\pi$
$908$	4.65250	−	14.3189i	0.154399	−	0.475190i
$909$		0			0
$910$	−3.77148	+	5.19099i	−0.125023	+	0.172080i
$911$	34.9293	−	11.3492i	1.15726	−	0.376016i	0.333385	−	0.942791i	$-0.391809\pi$
$911$	34.9293	−	11.3492i	1.15726	−	0.376016i	0.823873	+	0.566775i	$0.191809\pi$
$912$		0			0
$913$	−20.6994	−	27.3215i	−0.685049	−	0.904209i
$914$			5.39508i			0.178453i
$915$		0			0
$916$	−9.40819	−	6.83545i	−0.310855	−	0.225850i
$917$	19.0767	+	26.2569i	0.629969	+	0.867078i
$918$		0			0
$919$	−37.1303	−	12.0644i	−1.22482	−	0.397967i	−0.375983	−	0.926627i	$-0.622695\pi$
$919$	−37.1303	−	12.0644i	−1.22482	−	0.397967i	−0.848834	+	0.528660i	$0.822695\pi$
$920$	2.76324	−	2.00761i	0.0911013	−	0.0661890i
$921$		0			0
$922$	−0.417375	−	1.28455i	−0.0137455	−	0.0423043i
$923$	−25.5002			−0.839349
$924$		0			0
$925$	11.7597			0.386655
$926$	6.10493	+	18.7890i	0.200621	+	0.617446i
$927$		0			0
$928$	3.04327	−	2.21107i	0.0999002	−	0.0725818i
$929$	−14.9921	−	4.87123i	−0.491875	−	0.159820i	0.0525688	−	0.998617i	$-0.483259\pi$
$929$	−14.9921	−	4.87123i	−0.491875	−	0.159820i	−0.544443	+	0.838798i	$0.683259\pi$
$930$		0			0
$931$	−2.19093	−	3.01555i	−0.0718047	−	0.0988307i
$932$	6.79119	+	4.93409i	0.222453	+	0.161621i
$933$		0			0
$934$			16.5960i			0.543037i
$935$	−3.20209	−	9.22190i	−0.104720	−	0.301588i
$936$		0			0
$937$	−50.8834	+	16.5330i	−1.66229	+	0.540111i	−0.981350	−	0.192229i	$-0.938428\pi$
$937$	−50.8834	+	16.5330i	−1.66229	+	0.540111i	−0.680940	+	0.732340i	$0.738428\pi$
$938$	6.64471	−	9.14566i	0.216958	−	0.298616i
$939$		0			0
$940$	0.134627	−	0.414340i	0.00439106	−	0.0135143i
$941$	−5.26886	+	16.2159i	−0.171760	+	0.528622i	−0.999471	−	0.0325325i	$-0.989643\pi$
$941$	−5.26886	+	16.2159i	−0.171760	+	0.528622i	0.827711	+	0.561155i	$0.189643\pi$
$942$		0			0
$943$	9.27971	−	12.7724i	0.302189	−	0.415927i
$944$	6.85841	−	2.22843i	0.223222	−	0.0725293i
$945$		0			0
$946$	−6.93460	+	22.8939i	−0.225463	+	0.744345i
$947$		−	6.85596i		−	0.222789i	−0.993776	−	0.111394i	$-0.964468\pi$
$947$		−	6.85596i		−	0.222789i	0.993776	−	0.111394i	$-0.0355317\pi$
$948$		0			0
$949$	16.4657	+	11.9630i	0.534500	+	0.388337i
$950$	0.958278	+	1.31896i	0.0310906	+	0.0427926i
$951$		0			0
$952$	6.07756	+	1.97472i	0.196975	+	0.0640010i
$953$	−34.9516	+	25.3938i	−1.13219	+	0.822586i	−0.986012	−	0.166672i	$-0.946698\pi$
$953$	−34.9516	+	25.3938i	−1.13219	+	0.822586i	−0.146180	+	0.989258i	$0.546698\pi$
$954$		0			0
$955$	−2.24230	−	6.90110i	−0.0725593	−	0.223314i
$956$	13.8079			0.446579
$957$		0			0
$958$	−5.00608			−0.161739
$959$	1.23841	+	3.81144i	0.0399904	+	0.123078i
$960$		0			0
$961$	−58.5119	+	42.5114i	−1.88748	+	1.37133i
$962$	33.0532	+	10.7396i	1.06568	+	0.346260i
$963$		0			0
$964$	0.500056	+	0.688268i	0.0161057	+	0.0221676i
$965$	10.7254	+	7.79245i	0.345262	+	0.250848i
$966$		0			0
$967$			0.923105i			0.0296850i	0.999890	+	0.0148425i	$0.00472469\pi$
$967$			0.923105i			0.0296850i	−0.999890	+	0.0148425i	$0.995275\pi$
$968$	−2.97721	+	10.5894i	−0.0956911	+	0.340357i
$969$		0			0
$970$	6.15293	−	1.99921i	0.197559	−	0.0641907i
$971$	23.2942	−	32.0617i	0.747545	−	1.02891i	−0.250604	−	0.968090i	$-0.580629\pi$
$971$	23.2942	−	32.0617i	0.747545	−	1.02891i	0.998149	−	0.0608176i	$-0.0193708\pi$
$972$		0			0
$973$	−10.0186	+	30.8341i	−0.321182	+	0.988495i
$974$	−4.73439	+	14.5710i	−0.151700	+	0.466883i
$975$		0			0
$976$	−7.82116	+	10.7649i	−0.250349	+	0.344576i
$977$	−43.3945	+	14.0997i	−1.38831	+	0.451091i	−0.905393	−	0.424574i	$-0.860424\pi$
$977$	−43.3945	+	14.0997i	−1.38831	+	0.451091i	−0.482920	+	0.875664i	$0.660424\pi$
$978$		0			0
$979$	19.1237	+	13.3169i	0.611197	+	0.425611i
$980$		−	2.28631i		−	0.0730336i
$981$		0			0
$982$	−7.10090	−	5.15910i	−0.226599	−	0.164634i
$983$	−4.75580	−	6.54580i	−0.151687	−	0.208779i	0.726411	−	0.687261i	$-0.241187\pi$
$983$	−4.75580	−	6.54580i	−0.151687	−	0.208779i	−0.878097	+	0.478482i	$0.841187\pi$
$984$		0			0
$985$	−2.07350	−	0.673720i	−0.0660671	−	0.0214665i
$986$	8.95743	−	6.50795i	0.285263	−	0.207255i
$987$		0			0
$988$	1.48891	+	4.58238i	0.0473684	+	0.145785i
$989$	−24.6346			−0.783336
$990$		0			0
$991$	−25.1632			−0.799336			−0.399668	−	0.916660i	$-0.630875\pi$
$991$	−25.1632			−0.799336			−0.399668	+	0.916660i	$0.630875\pi$
$992$	−3.14112	−	9.66737i	−0.0997306	−	0.306939i
$993$		0			0
$994$	−15.1555	+	11.0111i	−0.480702	+	0.349250i
$995$	−2.36168	−	0.767356i	−0.0748702	−	0.0243268i
$996$		0			0
$997$	7.41024	+	10.1993i	0.234685	+	0.323016i	0.910074	−	0.414446i	$-0.136024\pi$
$997$	7.41024	+	10.1993i	0.234685	+	0.323016i	−0.675390	+	0.737461i	$0.736024\pi$
$998$	−2.34627	−	1.70466i	−0.0742698	−	0.0539602i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.z.a.611.1	yes	32
3.2	odd	2		990.2.z.b.611.5	yes	32
11.2	odd	10		990.2.z.b.431.5	yes	32
33.2	even	10	inner	990.2.z.a.431.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.z.a.431.1	✓	32	33.2	even	10	inner
990.2.z.a.611.1	yes	32	1.1	even	1	trivial
990.2.z.b.431.5	yes	32	11.2	odd	10
990.2.z.b.611.5	yes	32	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-0.951057 - 0.309017i) q^{5} +(-1.27614 - 1.75646i) q^{7} +(-0.809017 - 0.587785i) q^{8} -1.00000i q^{10} +(-1.89530 + 2.72174i) q^{11} +(2.81073 - 0.913261i) q^{13} +(1.27614 - 1.75646i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.909547 - 2.79930i) q^{17} +(0.958278 - 1.31896i) q^{19} +(0.951057 - 0.309017i) q^{20} +(-3.17420 - 0.961471i) q^{22} -3.41555i q^{23} +(0.809017 + 0.587785i) q^{25} +(1.73712 + 2.39095i) q^{26} +(2.06484 + 0.670908i) q^{28} +(3.04327 - 2.21107i) q^{29} +(-3.14112 - 9.66737i) q^{31} +1.00000 q^{32} +2.94336 q^{34} +(0.670908 + 2.06484i) q^{35} +(9.51376 - 6.91215i) q^{37} +(1.55053 + 0.503797i) q^{38} +(0.587785 + 0.809017i) q^{40} +(3.73949 + 2.71690i) q^{41} -7.21249i q^{43} +(-0.0664698 - 3.31596i) q^{44} +(3.24838 - 1.05546i) q^{46} +(0.256076 - 0.352459i) q^{47} +(0.706510 - 2.17441i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-1.73712 + 2.39095i) q^{52} +(-9.58109 + 3.11308i) q^{53} +(2.64360 - 2.00285i) q^{55} +2.17110i q^{56} +(3.04327 + 2.21107i) q^{58} +(4.23873 + 5.83411i) q^{59} +(-12.6549 - 4.11183i) q^{61} +(8.22356 - 5.97476i) q^{62} +(0.309017 + 0.951057i) q^{64} -2.95537 q^{65} +5.20687 q^{67} +(0.909547 + 2.79930i) q^{68} +(-1.75646 + 1.27614i) q^{70} +(-8.20611 - 2.66633i) q^{71} +(4.04789 + 5.57145i) q^{73} +(9.51376 + 6.91215i) q^{74} +1.63032i q^{76} +(7.19929 - 0.144313i) q^{77} +(1.93416 - 0.628447i) q^{79} +(-0.587785 + 0.809017i) q^{80} +(-1.42836 + 4.39603i) q^{82} +(-3.19368 + 9.82914i) q^{83} +(-1.73006 + 2.38122i) q^{85} +(6.85948 - 2.22878i) q^{86} +(3.13312 - 1.08790i) q^{88} -7.02630i q^{89} +(-5.19099 - 3.77148i) q^{91} +(2.00761 + 2.76324i) q^{92} +(0.414340 + 0.134627i) q^{94} +(-1.31896 + 0.958278i) q^{95} +(1.99921 + 6.15293i) q^{97} +2.28631 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{2} - 8 q^{4} - 8 q^{8} - 8 q^{16} + 4 q^{17} + 8 q^{25} - 8 q^{29} + 32 q^{31} + 32 q^{32} + 24 q^{34} + 16 q^{37} + 32 q^{41} - 20 q^{46} - 20 q^{47} + 16 q^{49} + 8 q^{50} - 40 q^{53} + 8 q^{55}+ \cdots + 16 q^{98}+O(q^{100}) \) 32 * q - 8 * q^2 - 8 * q^4 - 8 * q^8 - 8 * q^16 + 4 * q^17 + 8 * q^25 - 8 * q^29 + 32 * q^31 + 32 * q^32 + 24 * q^34 + 16 * q^37 + 32 * q^41 - 20 * q^46 - 20 * q^47 + 16 * q^49 + 8 * q^50 - 40 * q^53 + 8 * q^55 - 8 * q^58 + 40 * q^59 - 28 * q^62 - 8 * q^64 + 8 * q^65 + 4 * q^68 - 40 * q^71 + 40 * q^73 + 16 * q^74 - 28 * q^77 + 20 * q^79 - 8 * q^82 - 24 * q^83 - 24 * q^91 + 20 * q^94 + 16 * q^95 + 48 * q^97 + 16 * q^98

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