LMFDB - Embedded newform 820.2.bq.a.49.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(49,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 10, 19])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bq (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			49.18
Character	$\chi$	$=$	820.49
Dual form			820.2.bq.a.569.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.42551 - 1.42551i) q^{3} +(1.33373 + 1.79476i) q^{5} +(-0.459361 + 2.90029i) q^{7} -1.06416i q^{9} +(-1.43594 + 0.731647i) q^{11} +(3.86664 - 0.612416i) q^{13} +(4.45969 + 0.657199i) q^{15} +(-2.72415 + 1.38802i) q^{17} +(-0.538081 + 3.39731i) q^{19} +(3.47957 + 4.78922i) q^{21} +(5.36715 - 7.38725i) q^{23} +(-1.44232 + 4.78745i) q^{25} +(2.75957 + 2.75957i) q^{27} +(-1.89458 + 3.71832i) q^{29} +(-1.09553 + 3.37169i) q^{31} +(-1.00397 + 3.08991i) q^{33} +(-5.81799 + 3.04377i) q^{35} +(1.38324 - 0.449443i) q^{37} +(4.63893 - 6.38494i) q^{39} +(2.69801 - 5.80696i) q^{41} +(-3.53323 - 2.56704i) q^{43} +(1.90990 - 1.41930i) q^{45} +(-0.765037 - 4.83025i) q^{47} +(-1.54330 - 0.501447i) q^{49} +(-1.90466 + 5.86194i) q^{51} +(11.0070 + 5.60835i) q^{53} +(-3.22829 - 1.60134i) q^{55} +(4.07585 + 5.60993i) q^{57} +(-5.66244 - 4.11400i) q^{59} +(-8.92059 - 12.2781i) q^{61} +(3.08636 + 0.488832i) q^{63} +(6.25620 + 6.12289i) q^{65} +(3.44191 - 6.75512i) q^{67} +(-2.87967 - 18.1815i) q^{69} +(-3.40900 + 1.73697i) q^{71} +10.6516 q^{73} +(4.76852 + 8.88060i) q^{75} +(-1.46238 - 4.50073i) q^{77} +(-9.11926 - 9.11926i) q^{79} +11.0600 q^{81} -17.0333i q^{83} +(-6.12445 - 3.03794i) q^{85} +(2.59976 + 8.00125i) q^{87} +(14.7710 + 2.33950i) q^{89} +11.4957i q^{91} +(3.24469 + 6.36807i) q^{93} +(-6.81500 + 3.56537i) q^{95} +(-3.73080 + 7.32211i) q^{97} +(0.778586 + 1.52806i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) $ 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$-1$

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			0
$2$		0			0
$3$	1.42551	−	1.42551i	0.823018	−	0.823018i	−0.163521	−	0.986540i	$-0.552285\pi$
$3$	1.42551	−	1.42551i	0.823018	−	0.823018i	0.986540	+	0.163521i	$0.0522853\pi$
$4$		0			0
$5$	1.33373	+	1.79476i	0.596463	+	0.802641i
$5$	1.33373	+	1.79476i	0.596463	+	0.802641i
$6$		0			0
$7$	−0.459361	+	2.90029i	−0.173622	+	1.09621i	0.734840	+	0.678241i	$0.237257\pi$
$7$	−0.459361	+	2.90029i	−0.173622	+	1.09621i	−0.908462	+	0.417967i	$0.862743\pi$
$8$		0			0
$9$		−	1.06416i		−	0.354718i
$10$		0			0
$11$	−1.43594	+	0.731647i	−0.432952	+	0.220600i	−0.656863	−	0.754010i	$-0.728117\pi$
$11$	−1.43594	+	0.731647i	−0.432952	+	0.220600i	0.223912	+	0.974609i	$0.428117\pi$
$12$		0			0
$13$	3.86664	−	0.612416i	1.07241	−	0.169854i	0.404832	−	0.914391i	$-0.367330\pi$
$13$	3.86664	−	0.612416i	1.07241	−	0.169854i	0.667581	+	0.744537i	$0.267330\pi$
$14$		0			0
$15$	4.45969	+	0.657199i	1.15149	+	0.169688i
$16$		0			0
$17$	−2.72415	+	1.38802i	−0.660703	+	0.336645i	−0.751985	−	0.659180i	$-0.770903\pi$
$17$	−2.72415	+	1.38802i	−0.660703	+	0.336645i	0.0912823	+	0.995825i	$0.470903\pi$
$18$		0			0
$19$	−0.538081	+	3.39731i	−0.123444	+	0.779396i	0.845837	+	0.533441i	$0.179101\pi$
$19$	−0.538081	+	3.39731i	−0.123444	+	0.779396i	−0.969281	+	0.245955i	$0.920899\pi$
$20$		0			0
$21$	3.47957	+	4.78922i	0.759305	+	1.04509i
$22$		0			0
$23$	5.36715	−	7.38725i	1.11913	−	1.54035i	0.311895	−	0.950116i	$-0.399036\pi$
$23$	5.36715	−	7.38725i	1.11913	−	1.54035i	0.807233	−	0.590232i	$-0.200964\pi$
$24$		0			0
$25$	−1.44232	+	4.78745i	−0.288464	+	0.957491i
$26$		0			0
$27$	2.75957	+	2.75957i	0.531079	+	0.531079i
$28$		0			0
$29$	−1.89458	+	3.71832i	−0.351815	+	0.690475i	−0.997311	−	0.0732883i	$-0.976651\pi$
$29$	−1.89458	+	3.71832i	−0.351815	+	0.690475i	0.645496	+	0.763764i	$0.276651\pi$
$30$		0			0
$31$	−1.09553	+	3.37169i	−0.196763	+	0.605574i	0.803189	+	0.595725i	$0.203135\pi$
$31$	−1.09553	+	3.37169i	−0.196763	+	0.605574i	−0.999951	+	0.00984919i	$0.996865\pi$
$32$		0			0
$33$	−1.00397	+	3.08991i	−0.174769	+	0.537885i
$34$		0			0
$35$	−5.81799	+	3.04377i	−0.983420	+	0.514491i
$36$		0			0
$37$	1.38324	−	0.449443i	0.227404	−	0.0738879i	−0.193099	−	0.981179i	$-0.561854\pi$
$37$	1.38324	−	0.449443i	0.227404	−	0.0738879i	0.420503	+	0.907291i	$0.361854\pi$
$38$		0			0
$39$	4.63893	−	6.38494i	0.742823	−	1.02241i
$40$		0			0
$41$	2.69801	−	5.80696i	0.421358	−	0.906895i
$41$	2.69801	−	5.80696i	0.421358	−	0.906895i
$42$		0			0
$43$	−3.53323	−	2.56704i	−0.538812	−	0.391470i	0.284831	−	0.958578i	$-0.408062\pi$
$43$	−3.53323	−	2.56704i	−0.538812	−	0.391470i	−0.823644	+	0.567108i	$0.808062\pi$
$44$		0			0
$45$	1.90990	−	1.41930i	0.284711	−	0.211576i
$46$		0			0
$47$	−0.765037	−	4.83025i	−0.111592	−	0.704565i	−0.978523	−	0.206137i	$-0.933911\pi$
$47$	−0.765037	−	4.83025i	−0.111592	−	0.704565i	0.866931	−	0.498428i	$-0.166089\pi$
$48$		0			0
$49$	−1.54330	−	0.501447i	−0.220471	−	0.0716353i
$50$		0			0
$51$	−1.90466	+	5.86194i	−0.266706	+	0.820835i
$52$		0			0
$53$	11.0070	+	5.60835i	1.51193	+	0.770366i	0.996259	−	0.0864217i	$-0.0275432\pi$
$53$	11.0070	+	5.60835i	1.51193	+	0.770366i	0.515670	+	0.856788i	$0.327543\pi$
$54$		0			0
$55$	−3.22829	−	1.60134i	−0.435302	−	0.215925i
$56$		0			0
$57$	4.07585	+	5.60993i	0.539860	+	0.743054i
$58$		0			0
$59$	−5.66244	−	4.11400i	−0.737186	−	0.535597i	0.154642	−	0.987971i	$-0.450577\pi$
$59$	−5.66244	−	4.11400i	−0.737186	−	0.535597i	−0.891829	+	0.452373i	$0.850577\pi$
$60$		0			0
$61$	−8.92059	−	12.2781i	−1.14216	−	1.57205i	−0.762576	−	0.646899i	$-0.776065\pi$
$61$	−8.92059	−	12.2781i	−1.14216	−	1.57205i	−0.379589	−	0.925155i	$-0.623935\pi$
$62$		0			0
$63$	3.08636	+	0.488832i	0.388845	+	0.0615870i
$64$		0			0
$65$	6.25620	+	6.12289i	0.775986	+	0.759451i
$66$		0			0
$67$	3.44191	−	6.75512i	0.420496	−	0.825269i	−0.579452	−	0.815007i	$-0.696733\pi$
$67$	3.44191	−	6.75512i	0.420496	−	0.825269i	0.999947	−	0.0102628i	$-0.00326679\pi$
$68$		0			0
$69$	−2.87967	−	18.1815i	−0.346672	−	2.18880i
$70$		0			0
$71$	−3.40900	+	1.73697i	−0.404574	+	0.206141i	−0.644422	−	0.764670i	$-0.722902\pi$
$71$	−3.40900	+	1.73697i	−0.404574	+	0.206141i	0.239849	+	0.970810i	$0.422902\pi$
$72$		0			0
$73$	10.6516			1.24668			0.623339	−	0.781951i	$-0.285776\pi$
$73$	10.6516			1.24668			0.623339	+	0.781951i	$0.285776\pi$
$74$		0			0
$75$	4.76852	+	8.88060i	0.550621	+	1.02544i
$76$		0			0
$77$	−1.46238	−	4.50073i	−0.166653	−	0.512906i
$78$		0			0
$79$	−9.11926	−	9.11926i	−1.02600	−	1.02600i	−0.999653	−	0.0263445i	$-0.991613\pi$
$79$	−9.11926	−	9.11926i	−1.02600	−	1.02600i	−0.0263445	−	0.999653i	$-0.508387\pi$
$80$		0			0
$81$	11.0600			1.22889
$82$		0			0
$83$		−	17.0333i		−	1.86965i	−0.355108	−	0.934825i	$-0.615556\pi$
$83$		−	17.0333i		−	1.86965i	0.355108	−	0.934825i	$-0.384444\pi$
$84$		0			0
$85$	−6.12445	−	3.03794i	−0.664290	−	0.329511i
$86$		0			0
$87$	2.59976	+	8.00125i	0.278724	+	0.857824i
$88$		0			0
$89$	14.7710	+	2.33950i	1.56572	+	0.247986i	0.878242	−	0.478217i	$-0.158717\pi$
$89$	14.7710	+	2.33950i	1.56572	+	0.247986i	0.687480	+	0.726203i	$0.258717\pi$
$90$		0			0
$91$			11.4957i			1.20508i
$92$		0			0
$93$	3.24469	+	6.36807i	0.336459	+	0.660338i
$94$		0			0
$95$	−6.81500	+	3.56537i	−0.699205	+	0.365799i
$96$		0			0
$97$	−3.73080	+	7.32211i	−0.378805	+	0.743447i	−0.999164	−	0.0408705i	$-0.986987\pi$
$97$	−3.73080	+	7.32211i	−0.378805	+	0.743447i	0.620359	+	0.784318i	$0.286987\pi$
$98$		0			0
$99$	0.778586	+	1.52806i	0.0782508	+	0.153576i
$100$		0			0
$101$	−1.74932	+	11.0448i	−0.174064	+	1.09900i	0.733686	+	0.679488i	$0.237798\pi$
$101$	−1.74932	+	11.0448i	−0.174064	+	1.09900i	−0.907751	+	0.419510i	$0.862202\pi$
$102$		0			0
$103$	−2.40984	+	1.75085i	−0.237448	+	0.172516i	−0.700146	−	0.714000i	$-0.746882\pi$
$103$	−2.40984	+	1.75085i	−0.237448	+	0.172516i	0.462697	+	0.886516i	$0.346882\pi$
$104$		0			0
$105$	−3.95468	+	12.6325i	−0.385937	+	1.23281i
$106$		0			0
$107$	−1.34733	−	1.85444i	−0.130251	−	0.179276i	0.738910	−	0.673804i	$-0.235341\pi$
$107$	−1.34733	−	1.85444i	−0.130251	−	0.179276i	−0.869161	+	0.494528i	$0.835341\pi$
$108$		0			0
$109$	2.65742	−	2.65742i	0.254534	−	0.254534i	−0.568292	−	0.822827i	$-0.692396\pi$
$109$	2.65742	−	2.65742i	0.254534	−	0.254534i	0.822827	+	0.568292i	$0.192396\pi$
$110$		0			0
$111$	1.33114	−	2.61251i	0.126346	−	0.247969i
$112$		0			0
$113$	−12.3944	−	4.02718i	−1.16597	−	0.378845i	−0.338830	−	0.940848i	$-0.610031\pi$
$113$	−12.3944	−	4.02718i	−1.16597	−	0.378845i	−0.827135	+	0.562003i	$0.810031\pi$
$114$		0			0
$115$	20.4167	−	0.219867i	1.90387	−	0.0205027i
$116$		0			0
$117$	−0.651705	−	4.11471i	−0.0602502	−	0.380405i
$118$		0			0
$119$	−2.77430	−	8.53843i	−0.254320	−	0.782717i
$120$		0			0
$121$	−4.93903	+	6.79799i	−0.449002	+	0.617999i
$122$		0			0
$123$	−4.43184	−	12.1239i	−0.399606	−	1.09318i
$124$		0			0
$125$	−10.5160	+	3.79656i	−0.940579	+	0.339575i
$126$		0			0
$127$	−7.59038	+	2.46626i	−0.673538	+	0.218846i	−0.625764	−	0.780013i	$-0.715213\pi$
$127$	−7.59038	+	2.46626i	−0.673538	+	0.218846i	−0.0477737	+	0.998858i	$0.515213\pi$
$128$		0			0
$129$	−8.69599	+	1.37731i	−0.765639	+	0.121265i
$130$		0			0
$131$	2.06842	+	0.672069i	0.180718	+	0.0587189i	0.397978	−	0.917395i	$-0.369712\pi$
$131$	2.06842	+	0.672069i	0.180718	+	0.0587189i	−0.217260	+	0.976114i	$0.569712\pi$
$132$		0			0
$133$	−9.60602	−	3.12118i	−0.832947	−	0.270641i
$134$		0			0
$135$	−1.27223	+	8.63327i	−0.109497	+	0.743034i
$136$		0			0
$137$	2.97005	+	2.97005i	0.253749	+	0.253749i	0.822506	−	0.568757i	$-0.192576\pi$
$137$	2.97005	+	2.97005i	0.253749	+	0.253749i	−0.568757	+	0.822506i	$0.692576\pi$
$138$		0			0
$139$	3.15115	−	2.28944i	0.267277	−	0.194188i	−0.446072	−	0.894997i	$-0.647177\pi$
$139$	3.15115	−	2.28944i	0.267277	−	0.194188i	0.713349	+	0.700809i	$0.247177\pi$
$140$		0			0
$141$	−7.97614	−	5.79500i	−0.671712	−	0.488027i
$142$		0			0
$143$	−5.10418	+	3.70841i	−0.426833	+	0.310113i
$144$		0			0
$145$	−9.20036	+	1.55893i	−0.764048	+	0.129462i
$146$		0			0
$147$	−2.91480	+	1.48516i	−0.240409	+	0.122494i
$148$		0			0
$149$	−15.0907	−	7.68907i	−1.23627	−	0.629913i	−0.291167	−	0.956672i	$-0.594044\pi$
$149$	−15.0907	−	7.68907i	−1.23627	−	0.629913i	−0.945108	+	0.326759i	$0.894044\pi$
$150$		0			0
$151$	−1.04904	−	6.62337i	−0.0853695	−	0.539002i	−0.992894	−	0.119003i	$-0.962030\pi$
$151$	−1.04904	−	6.62337i	−0.0853695	−	0.539002i	0.907524	−	0.419999i	$-0.137970\pi$
$152$		0			0
$153$	1.47707	+	2.89892i	0.119414	+	0.234363i
$154$		0			0
$155$	−7.51252	+	2.53072i	−0.603420	+	0.203273i
$156$		0			0
$157$	−0.879925	+	5.55563i	−0.0702257	+	0.443388i	0.927374	+	0.374137i	$0.122061\pi$
$157$	−0.879925	+	5.55563i	−0.0702257	+	0.443388i	−0.997599	+	0.0692509i	$0.977939\pi$
$158$		0			0
$159$	23.6853	−	7.69583i	1.87837	−	0.610319i
$160$		0			0
$161$	18.9597	+	18.9597i	1.49424	+	1.49424i
$162$		0			0
$163$			17.0756i			1.33747i	0.743503	+	0.668733i	$0.233163\pi$
$163$			17.0756i			1.33747i	−0.743503	+	0.668733i	$0.766837\pi$
$164$		0			0
$165$	−6.88468	+	2.31922i	−0.535972	+	0.180551i
$166$		0			0
$167$	14.5041	−	14.5041i	1.12236	−	1.12236i	0.130974	−	0.991386i	$-0.458189\pi$
$167$	14.5041	−	14.5041i	1.12236	−	1.12236i	0.991386	−	0.130974i	$-0.0418105\pi$
$168$		0			0
$169$	2.21212	−	0.718761i	0.170163	−	0.0552893i
$170$		0			0
$171$	3.61526	+	0.572601i	0.276466	+	0.0437879i
$172$		0			0
$173$	−10.5127			−0.799263			−0.399632	−	0.916676i	$-0.630862\pi$
$173$	−10.5127			−0.799263			−0.399632	+	0.916676i	$0.630862\pi$
$174$		0			0
$175$	−13.2225	−	6.38232i	−0.999525	−	0.482458i
$176$		0			0
$177$	−13.9364	+	2.20731i	−1.04752	+	0.165912i
$178$		0			0
$179$	1.94572	+	0.991396i	0.145430	+	0.0741004i	0.525191	−	0.850984i	$-0.323994\pi$
$179$	1.94572	+	0.991396i	0.145430	+	0.0741004i	−0.379761	+	0.925085i	$0.623994\pi$
$180$		0			0
$181$	2.62377	+	5.14943i	0.195023	+	0.382754i	0.967723	−	0.252018i	$-0.0810941\pi$
$181$	2.62377	+	5.14943i	0.195023	+	0.382754i	−0.772700	+	0.634772i	$0.781094\pi$
$182$		0			0
$183$	−30.2190	−	4.78622i	−2.23385	−	0.353807i
$184$		0			0
$185$	2.65152	+	1.88315i	0.194943	+	0.138452i
$186$		0			0
$187$	2.89616	−	3.98623i	0.211789	−	0.291502i
$188$		0			0
$189$	−9.27119	+	6.73591i	−0.674380	+	0.489966i
$190$		0			0
$191$	14.6350	−	14.6350i	1.05895	−	1.05895i	0.0608035	−	0.998150i	$-0.480634\pi$
$191$	14.6350	−	14.6350i	1.05895	−	1.05895i	0.998150	−	0.0608035i	$-0.0193663\pi$
$192$		0			0
$193$	6.54815	+	3.33645i	0.471346	+	0.240163i	0.673495	−	0.739192i	$-0.264792\pi$
$193$	6.54815	+	3.33645i	0.471346	+	0.240163i	−0.202149	+	0.979355i	$0.564792\pi$
$194$		0			0
$195$	17.6465	−	0.190035i	1.26369	−	0.0136087i
$196$		0			0
$197$	2.49272	−	7.67181i	0.177599	−	0.546594i	−0.822144	−	0.569280i	$-0.807222\pi$
$197$	2.49272	−	7.67181i	0.177599	−	0.546594i	0.999743	+	0.0226866i	$0.00722198\pi$
$198$		0			0
$199$	2.18777	−	0.346509i	0.155087	−	0.0245634i	−0.0784081	−	0.996921i	$-0.524984\pi$
$199$	2.18777	−	0.346509i	0.155087	−	0.0245634i	0.233495	+	0.972358i	$0.424984\pi$
$200$		0			0
$201$	−4.72302	−	14.5360i	−0.333136	−	1.02529i
$202$		0			0
$203$	−9.91393	−	7.20289i	−0.695822	−	0.505544i
$204$		0			0
$205$	14.0205	−	2.90265i	0.979235	−	0.202730i
$206$		0			0
$207$	−7.86118	−	5.71148i	−0.546390	−	0.396976i
$208$		0			0
$209$	−1.71298	−	5.27201i	−0.118489	−	0.364672i
$210$		0			0
$211$	−13.2139	+	2.09287i	−0.909681	+	0.144079i	−0.593700	−	0.804686i	$-0.702334\pi$
$211$	−13.2139	+	2.09287i	−0.909681	+	0.144079i	−0.315981	+	0.948766i	$0.602334\pi$
$212$		0			0
$213$	−2.38349	+	7.33563i	−0.163314	+	0.502629i
$214$		0			0
$215$	−0.105160	−	9.76504i	−0.00717183	−	0.665970i
$216$		0			0
$217$	−9.27566	−	4.72618i	−0.629673	−	0.320834i
$218$		0			0
$219$	15.1840	−	15.1840i	1.02604	−	1.02604i
$220$		0			0
$221$	−9.68325	+	7.03529i	−0.651366	+	0.473245i
$222$		0			0
$223$	−3.02714	+	4.16650i	−0.202712	+	0.279010i	−0.898254	−	0.439476i	$-0.855164\pi$
$223$	−3.02714	+	4.16650i	−0.202712	+	0.279010i	0.695542	+	0.718485i	$0.255164\pi$
$224$		0			0
$225$	5.09459	+	1.53485i	0.339640	+	0.102323i
$226$		0			0
$227$	2.00262	+	0.317184i	0.132919	+	0.0210523i	0.222539	−	0.974924i	$-0.428565\pi$
$227$	2.00262	+	0.317184i	0.132919	+	0.0210523i	−0.0896206	+	0.995976i	$0.528565\pi$
$228$		0			0
$229$	−9.51567	−	18.6755i	−0.628813	−	1.23411i	−0.957160	−	0.289558i	$-0.906492\pi$
$229$	−9.51567	−	18.6755i	−0.628813	−	1.23411i	0.328348	−	0.944557i	$-0.393508\pi$
$230$		0			0
$231$	−8.50047	−	4.33121i	−0.559290	−	0.284972i
$232$		0			0
$233$	12.0122	−	1.90255i	0.786948	−	0.124640i	0.249989	−	0.968249i	$-0.419573\pi$
$233$	12.0122	−	1.90255i	0.786948	−	0.124640i	0.536959	+	0.843608i	$0.319573\pi$
$234$		0			0
$235$	7.64879	−	7.81532i	0.498952	−	0.509815i
$236$		0			0
$237$	−25.9992			−1.68883
$238$		0			0
$239$	−18.8128	−	2.97966i	−1.21690	−	0.192738i	−0.485224	−	0.874390i	$-0.661262\pi$
$239$	−18.8128	−	2.97966i	−1.21690	−	0.192738i	−0.731677	+	0.681652i	$0.761262\pi$
$240$		0			0
$241$	−0.407914	+	0.132539i	−0.0262760	+	0.00853761i	−0.322126	−	0.946697i	$-0.604397\pi$
$241$	−0.407914	+	0.132539i	−0.0262760	+	0.00853761i	0.295849	+	0.955235i	$0.404397\pi$
$242$		0			0
$243$	7.48750	−	7.48750i	0.480323	−	0.480323i
$244$		0			0
$245$	−1.15837	−	3.43864i	−0.0740053	−	0.219687i
$246$		0			0
$247$			13.4657i			0.856802i
$248$		0			0
$249$	−24.2812	−	24.2812i	−1.53876	−	1.53876i
$250$		0			0
$251$	21.0114	−	6.82701i	1.32623	−	0.430917i	0.441597	−	0.897213i	$-0.354412\pi$
$251$	21.0114	−	6.82701i	1.32623	−	0.430917i	0.884628	+	0.466296i	$0.154412\pi$
$252$		0			0
$253$	−2.30204	+	14.5345i	−0.144728	+	0.913776i
$254$		0			0
$255$	−13.0611	+	4.39985i	−0.817916	+	0.275529i
$256$		0			0
$257$	−0.763264	−	1.49799i	−0.0476111	−	0.0934420i	0.865975	−	0.500087i	$-0.166699\pi$
$257$	−0.763264	−	1.49799i	−0.0476111	−	0.0934420i	−0.913586	+	0.406645i	$0.866699\pi$
$258$		0			0
$259$	0.668108	+	4.21827i	0.0415142	+	0.262110i
$260$		0			0
$261$	3.95687	+	2.01613i	0.244924	+	0.124795i
$262$		0			0
$263$	0.0801095	−	0.0408178i	0.00493976	−	0.00251694i	−0.451519	−	0.892262i	$-0.649118\pi$
$263$	0.0801095	−	0.0408178i	0.00493976	−	0.00251694i	0.456459	+	0.889745i	$0.349118\pi$
$264$		0			0
$265$	4.61476	+	27.2350i	0.283482	+	1.67303i
$266$		0			0
$267$	24.3912	−	17.7212i	1.49272	−	1.08452i
$268$		0			0
$269$	2.42076	+	1.75878i	0.147596	+	0.107235i	0.659133	−	0.752027i	$-0.270924\pi$
$269$	2.42076	+	1.75878i	0.147596	+	0.107235i	−0.511537	+	0.859262i	$0.670924\pi$
$270$		0			0
$271$	−21.6365	+	15.7198i	−1.31432	+	0.954911i	−0.314339	+	0.949311i	$0.601783\pi$
$271$	−21.6365	+	15.7198i	−1.31432	+	0.954911i	−0.999984	+	0.00560053i	$0.998217\pi$
$272$		0			0
$273$	16.3872	+	16.3872i	0.991801	+	0.991801i
$274$		0			0
$275$	−1.43165	−	7.92976i	−0.0863315	−	0.478182i
$276$		0			0
$277$	2.41986	+	0.786260i	0.145395	+	0.0472418i	0.380810	−	0.924653i	$-0.375645\pi$
$277$	2.41986	+	0.786260i	0.145395	+	0.0472418i	−0.235415	+	0.971895i	$0.575645\pi$
$278$		0			0
$279$	3.58801	+	1.16581i	0.214808	+	0.0697954i
$280$		0			0
$281$	15.0793	−	2.38832i	0.899554	−	0.142475i	0.310504	−	0.950572i	$-0.399502\pi$
$281$	15.0793	−	2.38832i	0.899554	−	0.142475i	0.589050	+	0.808097i	$0.299502\pi$
$282$		0			0
$283$	1.80123	−	0.585255i	0.107072	−	0.0347898i	−0.254991	−	0.966943i	$-0.582073\pi$
$283$	1.80123	−	0.585255i	0.107072	−	0.0347898i	0.362063	+	0.932154i	$0.382073\pi$
$284$		0			0
$285$	−4.63238	+	14.7973i	−0.274399	+	0.876518i
$286$		0			0
$287$	15.6025	+	10.4925i	0.920988	+	0.619353i
$288$		0			0
$289$	−4.49798	+	6.19094i	−0.264587	+	0.364173i
$290$		0			0
$291$	5.11944	+	15.7560i	0.300107	+	0.923635i
$292$		0			0
$293$	−1.78170	−	11.2492i	−0.104088	−	0.657186i	−0.983470	−	0.181070i	$-0.942044\pi$
$293$	−1.78170	−	11.2492i	−0.104088	−	0.657186i	0.879382	−	0.476117i	$-0.157956\pi$
$294$		0			0
$295$	−0.168531	−	15.6497i	−0.00981228	−	0.911160i
$296$		0			0
$297$	−5.98159	−	1.94354i	−0.347087	−	0.112775i
$298$		0			0
$299$	16.2288	−	31.8508i	0.938535	−	1.84198i
$300$		0			0
$301$	9.06820	−	9.06820i	0.522682	−	0.522682i
$302$		0			0
$303$	13.2508	+	18.2382i	0.761238	+	1.04775i
$304$		0			0
$305$	10.1386	−	32.3860i	0.580536	−	1.85442i
$306$		0			0
$307$	−12.3948	+	9.00532i	−0.707407	+	0.513961i	−0.882336	−	0.470620i	$-0.844030\pi$
$307$	−12.3948	+	9.00532i	−0.707407	+	0.513961i	0.174929	+	0.984581i	$0.444030\pi$
$308$		0			0
$309$	−0.939393	+	5.93110i	−0.0534402	+	0.337408i
$310$		0			0
$311$	−0.378685	−	0.743211i	−0.0214732	−	0.0421436i	0.880021	−	0.474935i	$-0.157529\pi$
$311$	−0.378685	−	0.743211i	−0.0214732	−	0.0421436i	−0.901494	+	0.432792i	$0.857529\pi$
$312$		0			0
$313$	−13.7057	+	26.8989i	−0.774690	+	1.52041i	0.0773892	+	0.997001i	$0.475342\pi$
$313$	−13.7057	+	26.8989i	−0.774690	+	1.52041i	−0.852079	+	0.523413i	$0.824658\pi$
$314$		0			0
$315$	3.23904	+	6.19125i	0.182499	+	0.348837i
$316$		0			0
$317$	−3.36448	−	6.60317i	−0.188968	−	0.370871i	0.777012	−	0.629485i	$-0.216734\pi$
$317$	−3.36448	−	6.60317i	−0.188968	−	0.370871i	−0.965981	+	0.258614i	$0.916734\pi$
$318$		0			0
$319$		−	6.72545i		−	0.376553i
$320$		0			0
$321$	−4.56416	−	0.722891i	−0.254746	−	0.0403478i
$322$		0			0
$323$	−3.24973	−	10.0016i	−0.180820	−	0.556506i
$324$		0			0
$325$	−2.64502	+	19.3947i	−0.146719	+	1.07582i
$326$		0			0
$327$		−	7.57634i		−	0.418973i
$328$		0			0
$329$	14.3606			0.791725
$330$		0			0
$331$	−23.1252	−	23.1252i	−1.27108	−	1.27108i	−0.945524	−	0.325551i	$-0.894450\pi$
$331$	−23.1252	−	23.1252i	−1.27108	−	1.27108i	−0.325551	−	0.945524i	$-0.605550\pi$
$332$		0			0
$333$	−0.478277	−	1.47198i	−0.0262094	−	0.0806643i
$334$		0			0
$335$	16.7144	−	2.83213i	0.913205	−	0.154736i
$336$		0			0
$337$	−22.4956			−1.22541			−0.612707	−	0.790310i	$-0.709920\pi$
$337$	−22.4956			−1.22541			−0.612707	+	0.790310i	$0.709920\pi$
$338$		0			0
$339$	−23.4091	+	11.9275i	−1.27141	+	0.647814i
$340$		0			0
$341$	−0.893777	−	5.64308i	−0.0484007	−	0.305590i
$342$		0			0
$343$	−7.16856	+	14.0691i	−0.387066	+	0.759659i
$344$		0			0
$345$	28.7908	−	29.4176i	1.55004	−	1.58379i
$346$		0			0
$347$	30.0804	+	4.76427i	1.61480	+	0.255759i	0.897503	−	0.441008i	$-0.145379\pi$
$347$	30.0804	+	4.76427i	1.61480	+	0.255759i	0.717297	+	0.696767i	$0.245379\pi$
$348$		0			0
$349$	7.19785	+	9.90700i	0.385292	+	0.530309i	0.956977	−	0.290164i	$-0.0937099\pi$
$349$	7.19785	+	9.90700i	0.385292	+	0.530309i	−0.571685	+	0.820473i	$0.693710\pi$
$350$		0			0
$351$	12.3602	+	8.98025i	0.659741	+	0.479330i
$352$		0			0
$353$	−5.01301	−	6.89982i	−0.266816	−	0.367240i	0.654496	−	0.756066i	$-0.272881\pi$
$353$	−5.01301	−	6.89982i	−0.266816	−	0.367240i	−0.921312	+	0.388825i	$0.872881\pi$
$354$		0			0
$355$	−7.66413	−	3.80168i	−0.406770	−	0.201772i
$356$		0			0
$357$	−16.1264	−	8.21682i	−0.853500	−	0.434880i
$358$		0			0
$359$	6.49416	−	19.9870i	0.342749	−	1.05487i	−0.620029	−	0.784579i	$-0.712879\pi$
$359$	6.49416	−	19.9870i	0.342749	−	1.05487i	0.962778	−	0.270294i	$-0.0871208\pi$
$360$		0			0
$361$	6.81791	+	2.21527i	0.358837	+	0.116593i
$362$		0			0
$363$	2.64997	+	16.7312i	0.139087	+	0.878162i
$364$		0			0
$365$	14.2064	+	19.1171i	0.743598	+	1.00063i
$366$		0			0
$367$	5.02334	+	3.64967i	0.262216	+	0.190511i	0.711123	−	0.703067i	$-0.248187\pi$
$367$	5.02334	+	3.64967i	0.262216	+	0.190511i	−0.448907	+	0.893578i	$0.648187\pi$
$368$		0			0
$369$	−6.17950	−	2.87110i	−0.321692	−	0.149463i
$370$		0			0
$371$	−21.3221	+	29.3473i	−1.10699	+	1.52364i
$372$		0			0
$373$	4.63621	−	1.50639i	0.240054	−	0.0779982i	−0.186519	−	0.982451i	$-0.559721\pi$
$373$	4.63621	−	1.50639i	0.240054	−	0.0779982i	0.426573	+	0.904453i	$0.359721\pi$
$374$		0			0
$375$	−9.57861	+	20.4027i	−0.494637	+	1.05359i
$376$		0			0
$377$	−5.04850	+	15.5377i	−0.260011	+	0.800232i
$378$		0			0
$379$	−1.59675	+	4.91428i	−0.0820194	+	0.252430i	−0.983654	−	0.180069i	$-0.942368\pi$
$379$	−1.59675	+	4.91428i	−0.0820194	+	0.252430i	0.901635	+	0.432499i	$0.142368\pi$
$380$		0			0
$381$	−7.30448	+	14.3358i	−0.374220	+	0.734448i
$382$		0			0
$383$	−11.0222	−	11.0222i	−0.563206	−	0.563206i	0.367011	−	0.930217i	$-0.380381\pi$
$383$	−11.0222	−	11.0222i	−0.563206	−	0.563206i	−0.930217	+	0.367011i	$0.880381\pi$
$384$		0			0
$385$	6.12731	−	8.62738i	0.312277	−	0.439692i
$386$		0			0
$387$	−2.73173	+	3.75990i	−0.138862	+	0.191127i
$388$		0			0
$389$	13.8130	+	19.0119i	0.700344	+	0.963941i	0.999951	+	0.00987864i	$0.00314452\pi$
$389$	13.8130	+	19.0119i	0.700344	+	0.963941i	−0.299607	+	0.954063i	$0.596855\pi$
$390$		0			0
$391$	−4.36724	+	27.5737i	−0.220861	+	1.39446i
$392$		0			0
$393$	3.90659	−	1.99051i	0.197061	−	0.100408i
$394$		0			0
$395$	4.20423	−	28.5295i	0.211538	−	1.43548i
$396$		0			0
$397$	38.5244	−	6.10167i	1.93349	−	0.306234i	0.934697	−	0.355446i	$-0.115671\pi$
$397$	38.5244	−	6.10167i	1.93349	−	0.306234i	0.998788	+	0.0492123i	$0.0156711\pi$
$398$		0			0
$399$	−18.1427	+	9.24419i	−0.908273	+	0.462788i
$400$		0			0
$401$			15.8856i			0.793291i	0.917972	+	0.396645i	$0.129826\pi$
$401$			15.8856i			0.793291i	−0.917972	+	0.396645i	$0.870174\pi$
$402$		0			0
$403$	−2.17114	+	13.7080i	−0.108152	+	0.682846i
$404$		0			0
$405$	14.7511	+	19.8501i	0.732989	+	0.986360i
$406$		0			0
$407$	−1.65742	+	1.65742i	−0.0821551	+	0.0821551i
$408$		0			0
$409$	17.4722			0.863944			0.431972	−	0.901887i	$-0.357818\pi$
$409$	17.4722			0.863944			0.431972	+	0.901887i	$0.357818\pi$
$410$		0			0
$411$	8.46767			0.417679
$412$		0			0
$413$	14.5329	−	14.5329i	0.715118	−	0.715118i
$414$		0			0
$415$	30.5707	−	22.7179i	1.50066	−	1.11518i
$416$		0			0
$417$	1.22837	−	7.75562i	0.0601535	−	0.379794i
$418$		0			0
$419$			33.5338i			1.63823i	0.573627	+	0.819117i	$0.305536\pi$
$419$			33.5338i			1.63823i	−0.573627	+	0.819117i	$0.694464\pi$
$420$		0			0
$421$	27.4293	−	13.9759i	1.33682	−	0.681145i	0.368215	−	0.929741i	$-0.379969\pi$
$421$	27.4293	−	13.9759i	1.33682	−	0.681145i	0.968607	+	0.248596i	$0.0799691\pi$
$422$		0			0
$423$	−5.14014	+	0.814118i	−0.249922	+	0.0395838i
$424$		0			0
$425$	−2.71600	−	15.0437i	−0.131745	−	0.729727i
$426$		0			0
$427$	39.7080	−	20.2322i	1.92160	−	0.979106i
$428$		0			0
$429$	−1.98969	+	12.5624i	−0.0960633	+	0.606520i
$430$		0			0
$431$	−13.0104	−	17.9073i	−0.626691	−	0.862567i	0.371127	−	0.928582i	$-0.378971\pi$
$431$	−13.0104	−	17.9073i	−0.626691	−	0.862567i	−0.997819	+	0.0660155i	$0.978971\pi$
$432$		0			0
$433$	−9.90552	+	13.6338i	−0.476029	+	0.655198i	−0.977736	−	0.209840i	$-0.932706\pi$
$433$	−9.90552	+	13.6338i	−0.476029	+	0.655198i	0.501707	+	0.865038i	$0.332706\pi$
$434$		0			0
$435$	−10.8929	+	15.3375i	−0.522276	+	0.735375i
$436$		0			0
$437$	22.2088	+	22.2088i	1.06239	+	1.06239i
$438$		0			0
$439$	8.25521	−	16.2018i	0.394000	−	0.773268i	−0.605750	−	0.795655i	$-0.707127\pi$
$439$	8.25521	−	16.2018i	0.394000	−	0.773268i	0.999749	+	0.0223874i	$0.00712674\pi$
$440$		0			0
$441$	−0.533618	+	1.64231i	−0.0254104	+	0.0782050i
$442$		0			0
$443$	0.672101	−	2.06851i	0.0319325	−	0.0982781i	−0.933820	−	0.357743i	$-0.883546\pi$
$443$	0.672101	−	2.06851i	0.0319325	−	0.0982781i	0.965752	+	0.259465i	$0.0835463\pi$
$444$		0			0
$445$	15.5017	+	29.6306i	0.734852	+	1.40463i
$446$		0			0
$447$	−32.4727	+	10.5510i	−1.53591	+	0.499046i
$448$		0			0
$449$	0.782337	−	1.07679i	0.0369207	−	0.0508171i	−0.790158	−	0.612904i	$-0.790001\pi$
$449$	0.782337	−	1.07679i	0.0369207	−	0.0508171i	0.827078	+	0.562087i	$0.190001\pi$
$450$		0			0
$451$	0.374474	+	10.3124i	0.0176333	+	0.485593i
$452$		0			0
$453$	−10.9371	−	7.94626i	−0.513869	−	0.373348i
$454$		0			0
$455$	−20.6320	+	15.3322i	−0.967245	+	0.718785i
$456$		0			0
$457$	3.44136	+	21.7279i	0.160980	+	1.01639i	0.927406	+	0.374055i	$0.122033\pi$
$457$	3.44136	+	21.7279i	0.160980	+	1.01639i	−0.766427	+	0.642332i	$0.777967\pi$
$458$		0			0
$459$	−11.3478	−	3.68712i	−0.529670	−	0.172100i
$460$		0			0
$461$	0.571669	−	1.75942i	0.0266253	−	0.0819441i	−0.936861	−	0.349702i	$-0.886283\pi$
$461$	0.571669	−	1.75942i	0.0266253	−	0.0819441i	0.963486	+	0.267758i	$0.0862828\pi$
$462$		0			0
$463$	19.8356	+	10.1068i	0.921840	+	0.469701i	0.849446	−	0.527675i	$-0.176936\pi$
$463$	19.8356	+	10.1068i	0.921840	+	0.469701i	0.0723938	+	0.997376i	$0.476936\pi$
$464$		0			0
$465$	−7.10160	+	14.3167i	−0.329329	+	0.663923i
$466$		0			0
$467$	−3.43803	−	4.73204i	−0.159093	−	0.218973i	0.722028	−	0.691864i	$-0.243210\pi$
$467$	−3.43803	−	4.73204i	−0.159093	−	0.218973i	−0.881121	+	0.472891i	$0.843210\pi$
$468$		0			0
$469$	18.0108	+	13.0856i	0.831660	+	0.604236i
$470$		0			0
$471$	6.66526	+	9.17395i	0.307119	+	0.422713i
$472$		0			0
$473$	6.95166	+	1.10104i	0.319638	+	0.0506257i
$474$		0			0
$475$	−15.4884	−	7.47604i	−0.710655	−	0.343024i
$476$		0			0
$477$	5.96815	−	11.7132i	0.273263	−	0.536309i
$478$		0			0
$479$	1.43090	+	9.03432i	0.0653793	+	0.412788i	0.998572	+	0.0534134i	$0.0170101\pi$
$479$	1.43090	+	9.03432i	0.0653793	+	0.412788i	−0.933193	+	0.359375i	$0.882990\pi$
$480$		0			0
$481$	5.07326	−	2.58495i	0.231321	−	0.117864i
$482$		0			0
$483$	54.0546			2.45957
$484$		0			0
$485$	−18.1173	+	3.06984i	−0.822664	+	0.139394i
$486$		0			0
$487$	0.233617	+	0.719000i	0.0105862	+	0.0325810i	0.956210	−	0.292681i	$-0.0945475\pi$
$487$	0.233617	+	0.719000i	0.0105862	+	0.0325810i	−0.945624	+	0.325262i	$0.894547\pi$
$488$		0			0
$489$	24.3414	+	24.3414i	1.10076	+	1.10076i
$490$		0			0
$491$	−11.2803			−0.509072			−0.254536	−	0.967063i	$-0.581923\pi$
$491$	−11.2803			−0.509072			−0.254536	+	0.967063i	$0.581923\pi$
$492$		0			0
$493$		−	12.7590i		−	0.574636i
$494$		0			0
$495$	−1.70408	+	3.43540i	−0.0765925	+	0.154410i
$496$		0			0
$497$	−3.47177	−	10.6850i	−0.155730	−	0.479288i
$498$		0			0
$499$	33.8462	+	5.36071i	1.51516	+	0.239978i	0.857953	−	0.513728i	$-0.171736\pi$
$499$	33.8462	+	5.36071i	1.51516	+	0.239978i	0.657211	+	0.753707i	$0.271736\pi$
$500$		0			0
$501$		−	41.3514i		−	1.84745i
$502$		0			0
$503$	−2.88721	−	5.66648i	−0.128735	−	0.252656i	0.817638	−	0.575732i	$-0.195283\pi$
$503$	−2.88721	−	5.66648i	−0.128735	−	0.252656i	−0.946373	+	0.323076i	$0.895283\pi$
$504$		0			0
$505$	−22.1559	+	11.5912i	−0.985924	+	0.515801i
$506$		0			0
$507$	2.12880	−	4.17800i	0.0945432	−	0.185551i
$508$		0			0
$509$	−6.64563	−	13.0428i	−0.294562	−	0.578111i	0.695535	−	0.718492i	$-0.255167\pi$
$509$	−6.64563	−	13.0428i	−0.294562	−	0.578111i	−0.990098	+	0.140381i	$0.955167\pi$
$510$		0			0
$511$	−4.89295	+	30.8928i	−0.216451	+	1.36662i
$512$		0			0
$513$	−10.8600	+	7.89022i	−0.479479	+	0.348362i
$514$		0			0
$515$	−6.35643	−	1.98991i	−0.280098	−	0.0876860i
$516$		0			0
$517$	4.63259	+	6.37621i	0.203741	+	0.280425i
$518$		0			0
$519$	−14.9859	+	14.9859i	−0.657808	+	0.657808i
$520$		0			0
$521$	18.0866	−	35.4969i	0.792388	−	1.55515i	−0.0388582	−	0.999245i	$-0.512372\pi$
$521$	18.0866	−	35.4969i	0.792388	−	1.55515i	0.831246	−	0.555904i	$-0.187628\pi$
$522$		0			0
$523$	17.6494	+	5.73463i	0.771753	+	0.250758i	0.668315	−	0.743878i	$-0.267016\pi$
$523$	17.6494	+	5.73463i	0.771753	+	0.250758i	0.103438	+	0.994636i	$0.467016\pi$
$524$		0			0
$525$	−27.9468	+	9.75071i	−1.21970	+	0.425556i
$526$		0			0
$527$	−1.69560	−	10.7056i	−0.0738616	−	0.466344i
$528$		0			0
$529$	−18.6578	−	57.4227i	−0.811208	−	2.49664i
$530$		0			0
$531$	−4.37793	+	6.02571i	−0.189986	+	0.261494i
$532$		0			0
$533$	6.87595	−	24.1057i	0.297830	−	1.04413i
$534$		0			0
$535$	1.53130	−	4.89146i	0.0662038	−	0.211476i
$536$		0			0
$537$	4.18689	−	1.36040i	0.180678	−	0.0587057i
$538$		0			0
$539$	2.58296	−	0.409101i	0.111256	−	0.0176212i
$540$		0			0
$541$	−8.11836	−	2.63782i	−0.349036	−	0.113409i	0.129252	−	0.991612i	$-0.458742\pi$
$541$	−8.11836	−	2.63782i	−0.349036	−	0.113409i	−0.478288	+	0.878203i	$0.658742\pi$
$542$		0			0
$543$	11.0808	+	3.60036i	0.475521	+	0.154506i
$544$		0			0
$545$	8.31370	+	1.22514i	0.356120	+	0.0524793i
$546$		0			0
$547$	6.74210	+	6.74210i	0.288271	+	0.288271i	0.836396	−	0.548125i	$-0.184658\pi$
$547$	6.74210	+	6.74210i	0.288271	+	0.288271i	−0.548125	+	0.836396i	$0.684658\pi$
$548$		0			0
$549$	−13.0658	+	9.49289i	−0.557637	+	0.405147i
$550$		0			0
$551$	−11.6129	−	8.43723i	−0.494724	−	0.359438i
$552$		0			0
$553$	30.6376	−	22.2595i	1.30284	−	0.946571i
$554$		0			0
$555$	6.46421	−	1.09531i	0.274391	−	0.0464934i
$556$		0			0
$557$	22.7462	−	11.5898i	0.963789	−	0.491075i	0.100033	−	0.994984i	$-0.468105\pi$
$557$	22.7462	−	11.5898i	0.963789	−	0.491075i	0.863757	+	0.503909i	$0.168105\pi$
$558$		0			0
$559$	−15.2338	−	7.76202i	−0.644322	−	0.328298i
$560$		0			0
$561$	−1.55390	−	9.81092i	−0.0656056	−	0.414217i
$562$		0			0
$563$	−12.1762	−	23.8972i	−0.513167	−	1.00715i	−0.991639	−	0.129044i	$-0.958809\pi$
$563$	−12.1762	−	23.8972i	−0.513167	−	1.00715i	0.478472	−	0.878103i	$-0.341191\pi$
$564$		0			0
$565$	−9.30296	−	27.6161i	−0.391379	−	1.16182i
$566$		0			0
$567$	−5.08056	+	32.0774i	−0.213363	+	1.34712i
$568$		0			0
$569$	−29.3553	+	9.53811i	−1.23064	+	0.399858i	−0.850945	−	0.525255i	$-0.823970\pi$
$569$	−29.3553	+	9.53811i	−1.23064	+	0.399858i	−0.379692	+	0.925113i	$0.623970\pi$
$570$		0			0
$571$	−15.9440	−	15.9440i	−0.667237	−	0.667237i	0.289839	−	0.957076i	$-0.406398\pi$
$571$	−15.9440	−	15.9440i	−0.667237	−	0.667237i	−0.957076	+	0.289839i	$0.906398\pi$
$572$		0			0
$573$		−	41.7247i		−	1.74308i
$574$		0			0
$575$	27.6250	+	36.3498i	1.15204	+	1.51589i
$576$		0			0
$577$	31.8623	−	31.8623i	1.32644	−	1.32644i	0.417996	−	0.908449i	$-0.362733\pi$
$577$	31.8623	−	31.8623i	1.32644	−	1.32644i	0.908449	−	0.417996i	$-0.137267\pi$
$578$		0			0
$579$	14.0906	−	4.57831i	0.585585	−	0.190268i
$580$		0			0
$581$	49.4017	+	7.82445i	2.04953	+	0.324613i
$582$		0			0
$583$	−19.9087			−0.824534
$584$		0			0
$585$	6.51570	−	6.65757i	0.269391	−	0.275257i
$586$		0			0
$587$	10.4284	−	1.65170i	0.430426	−	0.0681728i	0.0625373	−	0.998043i	$-0.480081\pi$
$587$	10.4284	−	1.65170i	0.430426	−	0.0681728i	0.367889	+	0.929870i	$0.380081\pi$
$588$		0			0
$589$	−10.8652	−	5.53609i	−0.447693	−	0.228111i
$590$		0			0
$591$	−7.38284	−	14.4896i	−0.303689	−	0.596024i
$592$		0			0
$593$	−15.5431	−	2.46179i	−0.638280	−	0.101094i	−0.171097	−	0.985254i	$-0.554731\pi$
$593$	−15.5431	−	2.46179i	−0.638280	−	0.101094i	−0.467183	+	0.884160i	$0.654731\pi$
$594$		0			0
$595$	11.6242	−	16.3672i	0.476548	−	0.670989i
$596$		0			0
$597$	2.62474	−	3.61264i	0.107423	−	0.147856i
$598$		0			0
$599$	−31.5874	+	22.9496i	−1.29063	+	0.937695i	−0.999818	−	0.0190856i	$-0.993925\pi$
$599$	−31.5874	+	22.9496i	−1.29063	+	0.937695i	−0.290809	+	0.956781i	$0.593925\pi$
$600$		0			0
$601$	−5.28846	+	5.28846i	−0.215721	+	0.215721i	−0.806692	−	0.590972i	$-0.798745\pi$
$601$	−5.28846	+	5.28846i	−0.215721	+	0.215721i	0.590972	+	0.806692i	$0.298745\pi$
$602$		0			0
$603$	−7.18850	−	3.66272i	−0.292738	−	0.149158i
$604$		0			0
$605$	−18.7881	+	0.202329i	−0.763844	+	0.00822584i
$606$		0			0
$607$	−9.80616	+	30.1802i	−0.398020	+	1.22498i	0.528565	+	0.848893i	$0.322730\pi$
$607$	−9.80616	+	30.1802i	−0.398020	+	1.22498i	−0.926585	+	0.376086i	$0.877270\pi$
$608$		0			0
$609$	−24.4002	+	3.86461i	−0.988746	+	0.156602i
$610$		0			0
$611$	−5.91625	−	18.2083i	−0.239346	−	0.736630i
$612$		0			0
$613$	−29.7737	−	21.6319i	−1.20255	−	0.873703i	−0.208016	−	0.978125i	$-0.566701\pi$
$613$	−29.7737	−	21.6319i	−1.20255	−	0.873703i	−0.994533	+	0.104422i	$0.966701\pi$
$614$		0			0
$615$	15.8486	−	24.1241i	0.639077	−	0.972779i
$616$		0			0
$617$	−18.0071	−	13.0830i	−0.724940	−	0.526700i	0.163018	−	0.986623i	$-0.447877\pi$
$617$	−18.0071	−	13.0830i	−0.724940	−	0.526700i	−0.887959	+	0.459923i	$0.847877\pi$
$618$		0			0
$619$	9.41436	+	28.9744i	0.378395	+	1.16458i	0.941159	+	0.337963i	$0.109738\pi$
$619$	9.41436	+	28.9744i	0.378395	+	1.16458i	−0.562764	+	0.826617i	$0.690262\pi$
$620$		0			0
$621$	35.1966	−	5.57460i	1.41239	−	0.223701i
$622$		0			0
$623$	−13.5704	+	41.7655i	−0.543689	+	1.67330i
$624$		0			0
$625$	−20.8394	−	13.8101i	−0.833577	−	0.552403i
$626$		0			0
$627$	−9.95717	−	5.07343i	−0.397651	−	0.202613i
$628$		0			0
$629$	−3.14432	+	3.14432i	−0.125372	+	0.125372i
$630$		0			0
$631$	−13.8801	+	10.0845i	−0.552558	+	0.401457i	−0.828728	−	0.559652i	$-0.810935\pi$
$631$	−13.8801	+	10.0845i	−0.552558	+	0.401457i	0.276170	+	0.961109i	$0.410935\pi$
$632$		0			0
$633$	−15.8531	+	21.8199i	−0.630104	+	0.867264i
$634$		0			0
$635$	−14.5499	−	10.3336i	−0.577395	−	0.410075i
$636$		0			0
$637$	−6.27446	−	0.993777i	−0.248603	−	0.0393749i
$638$		0			0
$639$	1.84841	+	3.62770i	0.0731219	+	0.143510i
$640$		0			0
$641$	−34.0495	−	17.3491i	−1.34488	−	0.685249i	−0.374586	−	0.927192i	$-0.622215\pi$
$641$	−34.0495	−	17.3491i	−1.34488	−	0.685249i	−0.970290	+	0.241943i	$0.922215\pi$
$642$		0			0
$643$	25.4171	−	4.02567i	1.00235	−	0.158757i	0.366377	−	0.930467i	$-0.380598\pi$
$643$	25.4171	−	4.02567i	1.00235	−	0.158757i	0.635975	+	0.771710i	$0.280598\pi$
$644$		0			0
$645$	−14.0701	−	13.7702i	−0.554008	−	0.542203i
$646$		0			0
$647$	−19.1353			−0.752287			−0.376143	−	0.926561i	$-0.622750\pi$
$647$	−19.1353			−0.752287			−0.376143	+	0.926561i	$0.622750\pi$
$648$		0			0
$649$	11.1409	+	1.76455i	0.437319	+	0.0692645i
$650$		0			0
$651$	−19.9598	+	6.48532i	−0.782285	+	0.254180i
$652$		0			0
$653$	12.6193	−	12.6193i	0.493830	−	0.493830i	−0.415681	−	0.909511i	$-0.636457\pi$
$653$	12.6193	−	12.6193i	0.493830	−	0.493830i	0.909511	+	0.415681i	$0.136457\pi$
$654$		0			0
$655$	1.55251	+	4.60867i	0.0606616	+	0.180076i
$656$		0			0
$657$		−	11.3350i		−	0.442220i
$658$		0			0
$659$	21.7718	+	21.7718i	0.848108	+	0.848108i	0.989897	−	0.141789i	$-0.0452855\pi$
$659$	21.7718	+	21.7718i	0.848108	+	0.848108i	−0.141789	+	0.989897i	$0.545286\pi$
$660$		0			0
$661$	−13.4999	+	4.38638i	−0.525085	+	0.170611i	−0.559552	−	0.828795i	$-0.689027\pi$
$661$	−13.4999	+	4.38638i	−0.525085	+	0.170611i	0.0344666	+	0.999406i	$0.489027\pi$
$662$		0			0
$663$	−3.77469	+	23.8324i	−0.146597	+	0.925575i
$664$		0			0
$665$	−7.21008	−	21.4033i	−0.279595	−	0.829985i
$666$		0			0
$667$	17.2997	+	33.9526i	0.669847	+	1.31465i
$668$		0			0
$669$	1.62417	+	10.2546i	0.0627941	+	0.396466i
$670$		0			0
$671$	21.7927	+	11.1039i	0.841297	+	0.428662i
$672$		0			0
$673$	−19.2324	+	9.79937i	−0.741353	+	0.377738i	−0.783515	−	0.621373i	$-0.786575\pi$
$673$	−19.2324	+	9.79937i	−0.741353	+	0.377738i	0.0421624	+	0.999111i	$0.486575\pi$
$674$		0			0
$675$	−17.1915	+	9.23112i	−0.661700	+	0.355306i
$676$		0			0
$677$	27.7124	−	20.1342i	1.06507	−	0.773822i	0.0900537	−	0.995937i	$-0.471296\pi$
$677$	27.7124	−	20.1342i	1.06507	−	0.773822i	0.975020	+	0.222115i	$0.0712961\pi$
$678$		0			0
$679$	−19.5225	−	14.1839i	−0.749204	−	0.544329i
$680$		0			0
$681$	3.30691	−	2.40261i	0.126721	−	0.0920681i
$682$		0			0
$683$	13.0556	+	13.0556i	0.499558	+	0.499558i	0.911300	−	0.411742i	$-0.135080\pi$
$683$	13.0556	+	13.0556i	0.499558	+	0.499558i	−0.411742	+	0.911300i	$0.635080\pi$
$684$		0			0
$685$	−1.36927	+	9.29177i	−0.0523173	+	0.355020i
$686$		0			0
$687$	−40.1868	−	13.0575i	−1.53322	−	0.498175i
$688$		0			0
$689$	45.9948	+	14.9446i	1.75226	+	0.569344i
$690$		0			0
$691$	−34.3754	+	5.44453i	−1.30770	+	0.207120i	−0.771099	−	0.636715i	$-0.780293\pi$
$691$	−34.3754	+	5.44453i	−1.30770	+	0.207120i	−0.536603	+	0.843835i	$0.680293\pi$
$692$		0			0
$693$	−4.78948	+	1.55620i	−0.181937	+	0.0591150i
$694$		0			0
$695$	8.31179	+	2.60205i	0.315284	+	0.0987014i
$696$		0			0
$697$	0.710422	+	19.5639i	0.0269092	+	0.741036i
$698$		0			0
$699$	14.4115	−	19.8357i	0.545091	−	0.750254i
$700$		0			0
$701$	−2.15558	−	6.63418i	−0.0814150	−	0.250570i	0.902061	−	0.431609i	$-0.142054\pi$
$701$	−2.15558	−	6.63418i	−0.0814150	−	0.250570i	−0.983476	+	0.181039i	$0.942054\pi$
$702$		0			0
$703$	0.782599	+	4.94114i	0.0295163	+	0.186359i
$704$		0			0
$705$	−0.237394	−	22.0442i	−0.00894079	−	0.830234i
$706$		0			0
$707$	−31.2296	−	10.1471i	−1.17451	−	0.381621i
$708$		0			0
$709$	−2.12361	+	4.16782i	−0.0797539	+	0.156526i	−0.927440	−	0.373973i	$-0.877995\pi$
$709$	−2.12361	+	4.16782i	−0.0797539	+	0.156526i	0.847686	+	0.530499i	$0.177995\pi$
$710$		0			0
$711$	−9.70431	+	9.70431i	−0.363940	+	0.363940i
$712$		0			0
$713$	19.0277	+	26.1894i	0.712592	+	0.980799i
$714$		0			0
$715$	−13.4633	−	4.21476i	−0.503499	−	0.157623i
$716$		0			0
$717$	−31.0654	+	22.5703i	−1.16016	+	0.842904i
$718$		0			0
$719$	0.0282146	−	0.178140i	0.00105223	−	0.00664350i	−0.987157	−	0.159755i	$-0.948929\pi$
$719$	0.0282146	−	0.178140i	0.00105223	−	0.00664350i	0.988209	+	0.153112i	$0.0489295\pi$
$720$		0			0
$721$	−3.97099	−	7.79350i	−0.147887	−	0.290245i
$722$		0			0
$723$	−0.392549	+	0.770421i	−0.0145991	+	0.0286523i
$724$		0			0
$725$	−15.0687	−	14.4332i	−0.559638	−	0.536037i
$726$		0			0
$727$	−12.3923	−	24.3212i	−0.459603	−	0.902022i	−0.998230	−	0.0594774i	$-0.981057\pi$
$727$	−12.3923	−	24.3212i	−0.459603	−	0.902022i	0.538626	−	0.842545i	$-0.318943\pi$
$728$		0			0
$729$			11.8331i			0.438264i
$730$		0			0
$731$	13.1881	+	2.08880i	0.487781	+	0.0772569i
$732$		0			0
$733$	−14.2438	−	43.8380i	−0.526107	−	1.61919i	−0.762116	−	0.647441i	$-0.775839\pi$
$733$	−14.2438	−	43.8380i	−0.526107	−	1.61919i	0.236008	−	0.971751i	$-0.424161\pi$
$734$		0			0
$735$	−6.55307	−	3.25055i	−0.241714	−	0.119898i
$736$		0			0
$737$			12.2182i			0.450063i
$738$		0			0
$739$	32.2177			1.18515			0.592575	−	0.805516i	$-0.298112\pi$
$739$	32.2177			1.18515			0.592575	+	0.805516i	$0.298112\pi$
$740$		0			0
$741$	19.1955	+	19.1955i	0.705163	+	0.705163i
$742$		0			0
$743$	−7.58733	−	23.3514i	−0.278352	−	0.856679i	−0.988313	−	0.152438i	$-0.951287\pi$
$743$	−7.58733	−	23.3514i	−0.278352	−	0.856679i	0.709961	−	0.704241i	$-0.248713\pi$
$744$		0			0
$745$	−6.32685	−	37.3392i	−0.231798	−	1.36800i
$746$		0			0
$747$	−18.1261			−0.663200
$748$		0			0
$749$	5.99733	−	3.05579i	0.219138	−	0.111656i
$750$		0			0
$751$	−0.259551	−	1.63874i	−0.00947116	−	0.0597986i	0.982500	−	0.186262i	$-0.0596373\pi$
$751$	−0.259551	−	1.63874i	−0.00947116	−	0.0597986i	−0.991971	+	0.126463i	$0.959637\pi$
$752$		0			0
$753$	20.2199	−	39.6839i	0.736856	−	1.44616i
$754$		0			0
$755$	10.4882	−	10.7166i	0.381705	−	0.390016i
$756$		0			0
$757$	−25.0917	−	3.97413i	−0.911973	−	0.144442i	−0.317221	−	0.948352i	$-0.602750\pi$
$757$	−25.0917	−	3.97413i	−0.911973	−	0.144442i	−0.594752	+	0.803909i	$0.702750\pi$
$758$		0			0
$759$	17.4375	+	24.0006i	0.632941	+	0.871168i
$760$		0			0
$761$	25.1012	+	18.2371i	0.909916	+	0.661093i	0.940994	−	0.338424i	$-0.109894\pi$
$761$	25.1012	+	18.2371i	0.909916	+	0.661093i	−0.0310775	+	0.999517i	$0.509894\pi$
$762$		0			0
$763$	6.48657	+	8.92800i	0.234830	+	0.323215i
$764$		0			0
$765$	−3.23284	+	6.51736i	−0.116883	+	0.235636i
$766$		0			0
$767$	−24.4141	−	12.4396i	−0.881541	−	0.449168i
$768$		0			0
$769$	−14.2917	+	43.9855i	−0.515373	+	1.58616i	0.267228	+	0.963633i	$0.413892\pi$
$769$	−14.2917	+	43.9855i	−0.515373	+	1.58616i	−0.782602	+	0.622523i	$0.786108\pi$
$770$		0			0
$771$	−3.22344	−	1.04736i	−0.116089	−	0.0377197i
$772$		0			0
$773$	0.233667	+	1.47532i	0.00840443	+	0.0530635i	0.991534	−	0.129846i	$-0.0414484\pi$
$773$	0.233667	+	1.47532i	0.00840443	+	0.0530635i	−0.983130	+	0.182910i	$0.941448\pi$
$774$		0			0
$775$	−14.5617	−	10.1079i	−0.523073	−	0.363085i
$776$		0			0
$777$	6.96557	+	5.06079i	0.249889	+	0.181555i
$778$		0			0
$779$	18.2763	+	12.2906i	0.654816	+	0.440355i
$780$		0			0
$781$	3.62426	−	4.98837i	0.129686	−	0.178498i
$782$		0			0
$783$	−15.4892	+	5.03274i	−0.553538	+	0.179855i
$784$		0			0
$785$	−11.1446	+	5.83047i	−0.397768	+	0.208098i
$786$		0			0
$787$	−9.06249	+	27.8915i	−0.323043	+	0.994224i	0.649273	+	0.760555i	$0.275073\pi$
$787$	−9.06249	+	27.8915i	−0.323043	+	0.994224i	−0.972316	+	0.233669i	$0.924927\pi$
$788$		0			0
$789$	0.0560107	−	0.172383i	0.00199403	−	0.00613700i
$790$		0			0
$791$	17.3735	−	34.0974i	0.617731	−	1.21236i
$792$		0			0
$793$	−42.0120	−	42.0120i	−1.49189	−	1.49189i
$794$		0			0
$795$	45.4021	+	32.2453i	1.61025	+	1.14362i
$796$		0			0
$797$	−22.5762	+	31.0734i	−0.799688	+	1.10068i	0.193145	+	0.981170i	$0.438131\pi$
$797$	−22.5762	+	31.0734i	−0.799688	+	1.10068i	−0.992833	+	0.119506i	$0.961869\pi$
$798$		0			0
$799$	8.78857	+	12.0964i	0.310917	+	0.427941i
$800$		0			0
$801$	2.48959	−	15.7186i	0.0879652	−	0.555390i
$802$		0			0
$803$	−15.2951	+	7.79323i	−0.539752	+	0.275017i
$804$		0			0
$805$	−8.74096	+	59.3154i	−0.308078	+	2.09059i
$806$		0			0
$807$	5.95798	−	0.943651i	0.209731	−	0.0332181i
$808$		0			0
$809$	−19.5386	+	9.95541i	−0.686940	+	0.350014i	−0.762373	−	0.647137i	$-0.775966\pi$
$809$	−19.5386	+	9.95541i	−0.686940	+	0.350014i	0.0754332	+	0.997151i	$0.475966\pi$
$810$		0			0
$811$		−	55.3132i		−	1.94231i	−0.238450	−	0.971155i	$-0.576639\pi$
$811$		−	55.3132i		−	1.94231i	0.238450	−	0.971155i	$-0.423361\pi$
$812$		0			0
$813$	−8.43425	+	53.2518i	−0.295802	+	1.86762i
$814$		0			0
$815$	−30.6466	+	22.7743i	−1.07350	+	0.797748i
$816$		0			0
$817$	10.6222	−	10.6222i	0.371623	−	0.371623i
$818$		0			0
$819$	12.2332			0.427463
$820$		0			0
$821$	13.7770			0.480820			0.240410	−	0.970671i	$-0.422718\pi$
$821$	13.7770			0.480820			0.240410	+	0.970671i	$0.422718\pi$
$822$		0			0
$823$	28.5816	−	28.5816i	0.996293	−	0.996293i	−0.00370042	−	0.999993i	$-0.501178\pi$
$823$	28.5816	−	28.5816i	0.996293	−	0.996293i	0.999993	+	0.00370042i	$0.00117788\pi$
$824$		0			0
$825$	−13.3448	−	9.26312i	−0.464605	−	0.322500i
$826$		0			0
$827$	1.75733	−	11.0953i	0.0611082	−	0.385822i	−0.938112	−	0.346333i	$-0.887427\pi$
$827$	1.75733	−	11.0953i	0.0611082	−	0.385822i	0.999220	−	0.0394894i	$-0.0125731\pi$
$828$		0			0
$829$			13.0050i			0.451682i	0.974164	+	0.225841i	$0.0725129\pi$
$829$			13.0050i			0.451682i	−0.974164	+	0.225841i	$0.927487\pi$
$830$		0			0
$831$	4.57035	−	2.32871i	0.158544	−	0.0807821i
$832$		0			0
$833$	4.90018	−	0.776113i	0.169781	−	0.0268907i
$834$		0			0
$835$	45.3759	+	6.68678i	1.57030	+	0.231406i
$836$		0			0
$837$	−12.3276	+	6.28122i	−0.426104	+	0.217111i
$838$		0			0
$839$	6.27800	−	39.6377i	0.216741	−	1.36845i	−0.603927	−	0.797040i	$-0.706398\pi$
$839$	6.27800	−	39.6377i	0.216741	−	1.36845i	0.820667	−	0.571406i	$-0.193602\pi$
$840$		0			0
$841$	6.80928	+	9.37217i	0.234803	+	0.323178i
$842$		0			0
$843$	18.0911	−	24.9002i	0.623089	−	0.857609i
$844$		0			0
$845$	4.24038	+	3.01159i	0.145873	+	0.103602i
$846$		0			0
$847$	−17.4474	−	17.4474i	−0.599498	−	0.599498i
$848$		0			0
$849$	1.73338	−	3.40196i	0.0594896	−	0.116755i
$850$		0			0
$851$	4.10393	−	12.6306i	0.140681	−	0.432971i
$852$		0			0
$853$	16.6847	−	51.3503i	0.571274	−	1.75820i	−0.0772566	−	0.997011i	$-0.524616\pi$
$853$	16.6847	−	51.3503i	0.571274	−	1.75820i	0.648530	−	0.761189i	$-0.275384\pi$
$854$		0			0
$855$	3.79411	+	7.25222i	0.129756	+	0.248021i
$856$		0			0
$857$	−0.489814	+	0.159150i	−0.0167317	+	0.00543647i	−0.317371	−	0.948301i	$-0.602800\pi$
$857$	−0.489814	+	0.159150i	−0.0167317	+	0.00543647i	0.300639	+	0.953738i	$0.402800\pi$
$858$		0			0
$859$	−23.0502	+	31.7259i	−0.786462	+	1.08247i	0.208077	+	0.978112i	$0.433280\pi$
$859$	−23.0502	+	31.7259i	−0.786462	+	1.08247i	−0.994540	+	0.104360i	$0.966720\pi$
$860$		0			0
$861$	37.1987	−	7.28439i	1.26773	−	0.248251i
$862$		0			0
$863$	20.5370	+	14.9210i	0.699087	+	0.507916i	0.879635	−	0.475650i	$-0.157787\pi$
$863$	20.5370	+	14.9210i	0.699087	+	0.507916i	−0.180548	+	0.983566i	$0.557787\pi$
$864$		0			0
$865$	−14.0211	−	18.8677i	−0.476731	−	0.641521i
$866$		0			0
$867$	2.41333	+	15.2371i	0.0819609	+	0.517481i
$868$		0			0
$869$	19.7668	+	6.42262i	0.670542	+	0.217872i
$870$		0			0
$871$	9.17167	−	28.2275i	0.310770	−	0.956452i
$872$		0			0
$873$	7.79186	+	3.97015i	0.263714	+	0.134369i
$874$		0			0
$875$	−6.18051	−	32.2435i	−0.208939	−	1.09003i
$876$		0			0
$877$	15.3719	+	21.1576i	0.519071	+	0.714440i	0.985416	−	0.170163i	$-0.0544295\pi$
$877$	15.3719	+	21.1576i	0.519071	+	0.714440i	−0.466345	+	0.884603i	$0.654429\pi$
$878$		0			0
$879$	−18.5757	−	13.4960i	−0.626543	−	0.455210i
$880$		0			0
$881$	−7.08670	−	9.75401i	−0.238757	−	0.328621i	0.672777	−	0.739845i	$-0.265101\pi$
$881$	−7.08670	−	9.75401i	−0.238757	−	0.328621i	−0.911534	+	0.411224i	$0.865101\pi$
$882$		0			0
$883$	−22.8049	−	3.61195i	−0.767448	−	0.121552i	−0.239578	−	0.970877i	$-0.577009\pi$
$883$	−22.8049	−	3.61195i	−0.767448	−	0.121552i	−0.527870	+	0.849325i	$0.677009\pi$
$884$		0			0
$885$	−22.5490	−	22.0685i	−0.757977	−	0.741825i
$886$		0			0
$887$	−25.4357	+	49.9203i	−0.854046	+	1.67616i	−0.124509	+	0.992218i	$0.539736\pi$
$887$	−25.4357	+	49.9203i	−0.854046	+	1.67616i	−0.729537	+	0.683941i	$0.760264\pi$
$888$		0			0
$889$	−3.66616	−	23.1472i	−0.122959	−	0.776334i
$890$		0			0
$891$	−15.8815	+	8.09204i	−0.532051	+	0.271094i
$892$		0			0
$893$	16.8215			0.562910
$894$		0			0
$895$	0.815757	+	4.81436i	0.0272677	+	0.160926i
$896$		0			0
$897$	−22.2693	−	68.5379i	−0.743550	−	2.28841i
$898$		0			0
$899$	−10.4615	−	10.4615i	−0.348910	−	0.348910i
$900$		0			0
$901$	−37.7692			−1.25827
$902$		0			0
$903$		−	25.8536i		−	0.860354i
$904$		0			0
$905$	−5.74259	+	11.5770i	−0.190890	+	0.384832i
$906$		0			0
$907$	11.7201	+	36.0707i	0.389159	+	1.19771i	0.933418	+	0.358791i	$0.116811\pi$
$907$	11.7201	+	36.0707i	0.389159	+	1.19771i	−0.544259	+	0.838917i	$0.683189\pi$
$908$		0			0
$909$	11.7534	+	1.86155i	0.389835	+	0.0617438i
$910$		0			0
$911$			36.9855i			1.22538i	0.790322	+	0.612692i	$0.209913\pi$
$911$			36.9855i			1.22538i	−0.790322	+	0.612692i	$0.790087\pi$
$912$		0			0
$913$	12.4624	+	24.4588i	0.412445	+	0.809468i
$914$		0			0
$915$	−31.7139	−	60.6193i	−1.04843	−	2.00401i
$916$		0			0
$917$	−2.89935	+	5.69029i	−0.0957449	+	0.187910i
$918$		0			0
$919$	9.35438	+	18.3590i	0.308573	+	0.605608i	0.992261	−	0.124166i	$-0.0396255\pi$
$919$	9.35438	+	18.3590i	0.308573	+	0.605608i	−0.683689	+	0.729774i	$0.739625\pi$
$920$		0			0
$921$	−4.83168	+	30.5060i	−0.159209	+	1.00521i
$922$		0			0
$923$	−12.1176	+	8.80397i	−0.398856	+	0.289786i
$924$		0			0
$925$	0.156609	+	7.27045i	0.00514928	+	0.239051i
$926$		0			0
$927$	1.86317	+	2.56444i	0.0611947	+	0.0842272i
$928$		0			0
$929$	−9.29173	+	9.29173i	−0.304852	+	0.304852i	−0.842909	−	0.538057i	$-0.819159\pi$
$929$	−9.29173	+	9.29173i	−0.304852	+	0.304852i	0.538057	+	0.842909i	$0.319159\pi$
$930$		0			0
$931$	2.53399	−	4.97323i	0.0830481	−	0.162991i
$932$		0			0
$933$	−1.59927	−	0.519635i	−0.0523578	−	0.0170121i
$934$		0			0
$935$	11.0170	−	0.118642i	0.360295	−	0.00388002i
$936$		0			0
$937$	2.95732	+	18.6718i	0.0966114	+	0.609980i	0.987725	+	0.156201i	$0.0499247\pi$
$937$	2.95732	+	18.6718i	0.0966114	+	0.609980i	−0.891114	+	0.453780i	$0.850075\pi$
$938$		0			0
$939$	18.8071	+	57.8822i	0.613745	+	1.88891i
$940$		0			0
$941$	6.36826	−	8.76516i	0.207600	−	0.285736i	−0.692502	−	0.721416i	$-0.743492\pi$
$941$	6.36826	−	8.76516i	0.207600	−	0.285736i	0.900102	+	0.435679i	$0.143492\pi$
$942$		0			0
$943$	−28.4169	−	51.0977i	−0.925380	−	1.66397i
$944$		0			0
$945$	−24.4546	−	7.65565i	−0.795509	−	0.249038i
$946$		0			0
$947$	−2.76554	+	0.898579i	−0.0898680	+	0.0291999i	−0.353606	−	0.935394i	$-0.615045\pi$
$947$	−2.76554	+	0.898579i	−0.0898680	+	0.0291999i	0.263738	+	0.964594i	$0.415045\pi$
$948$		0			0
$949$	41.1860	−	6.52322i	1.33695	−	0.211753i
$950$		0			0
$951$	−14.2090	−	4.61678i	−0.460758	−	0.149709i
$952$		0			0
$953$	41.8716	+	13.6049i	1.35635	+	0.440706i	0.894825	−	0.446418i	$-0.147301\pi$
$953$	41.8716	+	13.6049i	1.35635	+	0.440706i	0.461530	+	0.887124i	$0.347301\pi$
$954$		0			0
$955$	45.7855	+	6.74714i	1.48159	+	0.218332i
$956$		0			0
$957$	−9.58719	−	9.58719i	−0.309910	−	0.309910i
$958$		0			0
$959$	−9.97834	+	7.24969i	−0.322218	+	0.234105i
$960$		0			0
$961$	14.9114	+	10.8338i	0.481013	+	0.349476i
$962$		0			0
$963$	−1.97341	+	1.43377i	−0.0635923	+	0.0462025i
$964$		0			0
$965$	2.74535	+	16.2023i	0.0883760	+	0.521570i
$966$		0			0
$967$	42.7007	−	21.7571i	1.37316	−	0.699661i	0.397226	−	0.917721i	$-0.369973\pi$
$967$	42.7007	−	21.7571i	1.37316	−	0.699661i	0.975935	+	0.218060i	$0.0699730\pi$
$968$		0			0
$969$	−18.8899	−	9.62491i	−0.606832	−	0.309197i
$970$		0			0
$971$	3.82825	+	24.1706i	0.122854	+	0.775671i	0.969784	+	0.243966i	$0.0784486\pi$
$971$	3.82825	+	24.1706i	0.122854	+	0.775671i	−0.846929	+	0.531705i	$0.821551\pi$
$972$		0			0
$973$	5.19254	+	10.1909i	0.166465	+	0.326707i
$974$		0			0
$975$	23.8768	+	31.4178i	0.764669	+	1.00617i
$976$		0			0
$977$	6.14350	−	38.7885i	0.196548	−	1.24095i	−0.670190	−	0.742190i	$-0.733787\pi$
$977$	6.14350	−	38.7885i	0.196548	−	1.24095i	0.866737	−	0.498765i	$-0.166213\pi$
$978$		0			0
$979$	−22.9219	+	7.44778i	−0.732588	+	0.238032i
$980$		0			0
$981$	−2.82790	−	2.82790i	−0.0902880	−	0.0902880i
$982$		0			0
$983$			30.8494i			0.983943i	0.870611	+	0.491971i	$0.163724\pi$
$983$			30.8494i			0.983943i	−0.870611	+	0.491971i	$0.836276\pi$
$984$		0			0
$985$	17.0937	−	5.75830i	0.544649	−	0.183475i
$986$		0			0
$987$	20.4711	−	20.4711i	0.651604	−	0.651604i
$988$		0			0
$989$	−37.9268	+	12.3231i	−1.20600	+	0.391853i
$990$		0			0
$991$	−48.9516	−	7.75316i	−1.55500	−	0.246287i	−0.681024	−	0.732261i	$-0.738465\pi$
$991$	−48.9516	−	7.75316i	−1.55500	−	0.246287i	−0.873973	+	0.485974i	$0.838465\pi$
$992$		0			0
$993$	−65.9304			−2.09224
$994$		0			0
$995$	3.53980	+	3.46437i	0.112219	+	0.109828i
$996$		0			0
$997$	−39.8679	+	6.31445i	−1.26263	+	0.199981i	−0.751621	−	0.659595i	$-0.770728\pi$
$997$	−39.8679	+	6.31445i	−1.26263	+	0.199981i	−0.511008	+	0.859576i	$0.670728\pi$
$998$		0			0
$999$	5.05742	+	2.57688i	0.160010	+	0.0815289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bq.a.49.18	yes	176
5.4	even	2	inner	820.2.bq.a.49.5	✓	176
41.36	even	20	inner	820.2.bq.a.569.5	yes	176
205.159	even	20	inner	820.2.bq.a.569.18	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bq.a.49.5	✓	176	5.4	even	2	inner
820.2.bq.a.49.18	yes	176	1.1	even	1	trivial
820.2.bq.a.569.5	yes	176	41.36	even	20	inner
820.2.bq.a.569.18	yes	176	205.159	even	20	inner

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42551 - 1.42551i) q^{3} +(1.33373 + 1.79476i) q^{5} +(-0.459361 + 2.90029i) q^{7} -1.06416i q^{9} +(-1.43594 + 0.731647i) q^{11} +(3.86664 - 0.612416i) q^{13} +(4.45969 + 0.657199i) q^{15} +(-2.72415 + 1.38802i) q^{17} +(-0.538081 + 3.39731i) q^{19} +(3.47957 + 4.78922i) q^{21} +(5.36715 - 7.38725i) q^{23} +(-1.44232 + 4.78745i) q^{25} +(2.75957 + 2.75957i) q^{27} +(-1.89458 + 3.71832i) q^{29} +(-1.09553 + 3.37169i) q^{31} +(-1.00397 + 3.08991i) q^{33} +(-5.81799 + 3.04377i) q^{35} +(1.38324 - 0.449443i) q^{37} +(4.63893 - 6.38494i) q^{39} +(2.69801 - 5.80696i) q^{41} +(-3.53323 - 2.56704i) q^{43} +(1.90990 - 1.41930i) q^{45} +(-0.765037 - 4.83025i) q^{47} +(-1.54330 - 0.501447i) q^{49} +(-1.90466 + 5.86194i) q^{51} +(11.0070 + 5.60835i) q^{53} +(-3.22829 - 1.60134i) q^{55} +(4.07585 + 5.60993i) q^{57} +(-5.66244 - 4.11400i) q^{59} +(-8.92059 - 12.2781i) q^{61} +(3.08636 + 0.488832i) q^{63} +(6.25620 + 6.12289i) q^{65} +(3.44191 - 6.75512i) q^{67} +(-2.87967 - 18.1815i) q^{69} +(-3.40900 + 1.73697i) q^{71} +10.6516 q^{73} +(4.76852 + 8.88060i) q^{75} +(-1.46238 - 4.50073i) q^{77} +(-9.11926 - 9.11926i) q^{79} +11.0600 q^{81} -17.0333i q^{83} +(-6.12445 - 3.03794i) q^{85} +(2.59976 + 8.00125i) q^{87} +(14.7710 + 2.33950i) q^{89} +11.4957i q^{91} +(3.24469 + 6.36807i) q^{93} +(-6.81500 + 3.56537i) q^{95} +(-3.73080 + 7.32211i) q^{97} +(0.778586 + 1.52806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) \) 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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